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Rush Limbaugh Whines About Women Reporters And The "Chickification Of The News"
During the Tuesday broadcast of The Rush Limbaugh Show, host and Strom Thurmond's colostomy bag Rush Limbaugh lamented the state of today's media because a lot of women reporters are following the campaign of Hillary Clinton. Earlier this week, Politico did a story on the female-dominated gaggle covering the Democratic Presidential candidate. The article came with a sure-to-be iconic photo, showing 22 female journalists from 18 different news organizations who have been assigned to the campaign.
Of course, being the asshole who came up with the term 'feminazi,' it was imperative of Limbaugh to highlight the article and picture and talk about what it all means. And as you would guess, El Rushbo made sure to be as offensive and sexist as possible, claiming that the preponderance of women reporters covering Clinton is further proof of the "chickification of the news." Yes, he actually used that term, and more than once. He then went on about women providing sympathetic coverage for Hillary because she's "always playing the victim card."
From the transcript of the show, courtesy of Rush's website:
"There are about 22 women in this picture, folks, taken in Las Vegas before the Democrat debate — 22 women, not a single man. There's not a guy in this picture. And what this picture is, is the Hillary Clinton press corps. This is it. I'm turning the Dittocam off because it's zoomed in real tight. That's exactly right. Way to go, Snerdley. You're on the ball. "The Chickification of the news" is exactly right, and this is the epitome of it. If you wonder why the Hillary news coverage is the way it is, you simply have to look at that picture.
You simply have to find out who it is covering the news about her, and it will tell you everything you need to know. And this is done, by the way, on purpose. The chickification of the news is made up of many facets, but one of the facets is that men really can't be fair to women. Not that they try to be unfair, but they just can't fully relate. It takes a woman to understand a woman. It takes a woman to get deep with another woman.
It takes a woman to understand, and so that's the press gaggle that follows Hillary Clinton around. Print, online, radio, TV, you name it. And it's better than anything anybody can ever say to explain the type of and the nature of the sympathetic coverage that Hillary Clinton gets. Hillary Clinton is perceived to be a victim. She's always playing the victim card. She's always whining about being a woman or making a point of being a woman, as though that's somehow an obstacle and it's punishing in our unfair society.
And as a way of equalizing it, everybody covering her also happens to be female."
Limbaugh's comments about women in the news in relation to Clinton follows his Monday rantings about Hillary, where he stated that Democrats on the Benghazi Committee will praise the former Secretary of State "for her cervix" when she testifies. He also appeared to be upset that it isn't acceptable to "figuratively" hit women in public. (Listening to his comments, it seems that he really just wants men to have the capability of beating women without any repercussions. You know, it's a man's world!)
Anyway, this wasn't really anything different from Rush. Basically, a bunch of incoherent belching of his standard philosophy of women being inferior and the feminization of America and how the real men in this country are the ones being truly discriminated against.
Below is audio of his segment, courtesy of Media Matters:
Hillary ClintonRush LimbaughThe Rush Limbaugh ShowTicker
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\section{Introduction}
\begin{figure}[t]
\centering
\begin{subfigure}{.48\textwidth}
\includegraphics[width=0.99\linewidth]{figures/overview_1.pdf}
\caption{Developer identifies bugs in model}
\label{overview:a}
\end{subfigure}%
\vspace{1em}
\begin{subfigure}{.48\textwidth}
\includegraphics[width=.99\linewidth]{figures/overview_2.pdf}
\caption{Incorporating Language Patches}
\label{overview:b}
\end{subfigure}
\caption{(\subref{overview:a}) Developers typically fix bugs by writing brittle regex patches or by finetuning on additional data, which is prone to simple shortcuts. In contrast, natural language patches are more expressive than regexes and prevent shortcuts by abstractly specifying when they should be applied. (\subref{overview:b}) Our proposed model uses a gating head to predict whether a patch condition $\ensuremath{c}$ applies to the input. That (soft) prediction is then used to combine the original model output with the output of an interpreter head that uses textual features from both the input as well as the patch consequent $\ensuremath{q}$.}
\label{fig:overview}
\end{figure}
Natural language enables humans to communicate a lot at once with shared abstractions.
For example, in teaching someone about the colloquial use of the term ``bomb'', we might say \textit{describing food as `bomb' means it is very good, while saying someone bombed means it was disappointing}.
This simple sentence uses various abstractions (e.g.,{} ``food'') to provide context-dependent information, making it easy for humans to generalize and understand sentences such as ``The tacos were bomb'' or ``The chef bombed'' without ever having seen such examples.
There is a growing body of research focused on using language to give instructions, supervision and even inductive biases to models instead of relying exclusively on labeled examples, e.g.,{} building neural representations from language descriptions \citep{Andreas2018, Murty2020, Mu2020}, or language / prompt-based zero-shot learning \citep{brown2020language, hanjie2022semantic, chen21}. However, language is yet to be successfully applied for \emph{corrective} purposes, where the user interacts with an existing model to improve it. As shown in \figref{overview:a}, if a developer discovers that a model contains bugs \cite[i.e.,{} systematic errors;][]{ribeiro-etal-2020-beyond}, common fixes are either brittle regex-based patches (e.g.,{} \figref{overview:a} left, where patches either override predictions or replace the word ``bomb'' with the word ``good''), or collecting hundreds of additional datapoints for finetuning, a tedious and computationally demanding process that can still lead to shortcuts such as assuming the word ``bomb'' is always positive (e.g.,{} if the additional finetuning data mostly has the word in its colloquial sense). Instead, we envision a setting where developers provide corrective feedback through a \emph{Natural Language Patch}---a concise statement such as \explanation{If food is described as bomb, then food is good}. Language makes it easy for developers to express feedback at the right level of abstraction without having to specify exactly how the condition is applied. The patching system is responsible for applying the patch and integrating the information appropriately, e.g.,{} applying it to ``The tacos were the bomb'' but not to ``The authorities found a bomb in the restaurant''.
In this work, we present an approach for patching neural models with natural language. Any patching system has to determine when a patch is relevant, and how it should modify model behavior.
We model these tasks separately (\figref{overview:b}): a \emph{gating} head soft-predicts whether the patch should be applied (e.g.,{} ``food is described as bomb''), and an \emph{interpreter} head predicts a new output by combining the information in the patch (e.g.,{} ``food is good'') with the original input. Both heads are trained on \emph{synthetic data} in a \emph{patch tuning} stage between training and deployment, such that new patches can be combined into a library of patches (or maybe various user-specific libraries), and applied at test-time without further training.
In addition to the expressivity provided by abstractions, language-based patching is \emph{lightweight}, \emph{iterative} and easily \emph{reversible}. Much like software, developers can write / edit / remove patches iteratively until errors on unit tests or validation data are fixed, without constantly retraining the model.
Our experiments are organized as follows. First, in Section~\ref{sec:synth_experiments}, we present controlled experiments that indicate these patches work even for \emph{abstract} conditions, where regex patches would be infeasible or very difficult---that is, they are applied correctly when the patch condition is met, and do nothing otherwise. Perhaps surprisingly, this is true even for test-time patches that are very different than the ones used in the patch finetuning stage. Next, in Section~\ref{sec:real_experiments}, we show that despite the synthetic nature of the patch tuning phase, a small set of very simple patches can fix bugs (and thus improve performance) on real benchmarks for two different tasks---1 to 6 simple language patches improve performance by {\textasciitilde}1--4 accuracy points on two slices from the Yelp reviews dataset, while 7 patches improve performance by \textasciitilde{}7 F1 points on a relation extraction task derived from NYT. Finally, in Section~\ref{sec:comparison_with_finetuning}, we compare language patching, a computationally \emph{lightweight} procedure, with finetuning, a computationally and human-labor \emph{intensive} procedure, and find that as many as 100 labeled examples are needed to match performance gains from a small set of 1 to 7 patches. Further, finetuning sometimes fixes bugs at the expense of introducing new bugs, while patches maintain prior performance on inputs where they do not apply.
\section{Natural Language Patching}
\label{sec:our_approach}
\paragraph{Setup.} We are given a model $\ensuremath{f}$, mapping an input text $x$ to a probability distribution over its output space, $\ensuremath{f}(x) = \Pr(y \mid x)$. The model contains \emph{bugs}---defined as behaviors inconsistent with users' preferences or the ``ground truth''--- which we want to fix with a library of patches $\ensuremath{P} = \{\lpp{1}, \lpp{2}, \ldots, \lpp{t}\}$.
Users explicitly indicate the condition under which each patch applies and the consequence of applying it, such that each patch is in the form \explanation{If (condition) \ensuremath{c}{}, then (consequence) \ensuremath{q}{}}. We use this format to make modeling easier, noting that it still allows for very flexible patching through high level abstractions (e.g.,{} ``if the customer complains about the ambience'', ``if food is not mentioned'', etc), and that most patches have an implicit applicability function, and thus can be converted to this format.
\begin{table*}
\centering
\ra{1.3}
\scriptsize
\begin{tabular}{@{}cm{4cm}l@{}}
\toprule
& \textbf{Template} & \textbf{Examples} \\ \midrule
\multirow{6}{*}{\textit{Patches}} & \textbf{\em Override:} \template{If \mybox{aspect} is good, then label is positive} & \makecell[ml]{\eexample{$e_0$}{If service is good, then label is positive} \\\eexample{$e_1$}{If food is good, then label is positive}{}} \\ \addlinespace
& \textbf{\em Override:} \template{If \mybox{aspect} is bad, then label is negative} & \makecell[ml]{\eexample{$e_2$}{If service is bad, then label is negative} \\\eexample{$e_3$}{If ambience is bad then label is negative}} \\ \addlinespace
& \textbf{\em Override:} \template{If review contains words like \mybox{word}, then label is positive} & \makecell[ml]{\eexample{$e_4$}{If review contains words like zubin, then label is positive} \\\eexample{$e_5$}{If review contains words like excellent, then label is positive}} \\ \addlinespace
& \textbf{\em Override:} \template{If review contains words like \mybox{word}, then label is negative} & \makecell[ml]{\eexample{$e_6$}{If review contains words like wug, then label is negative} \\\eexample{$e_7$}{If review contains words like really bad, then label is negative}} \\ \addlinespace
& \textbf{\em Feature Based:} \template{If \mybox{aspect} is described as \mybox{word}, then \mybox{aspect} is good / bad} & \makecell[ml]{\eexample{$e_8$}{If food is described as above average, then food is good} \\\eexample{$e_9$}{If food is described as wug, then food is bad} \\\eexample{$e_{10}$}{If food is described as zubin, then service is good} \\\eexample{$e_{11}$}{If service is described as not great, then service is bad}} \\ \midrule
\multirow{6}{*}{\textit{Inputs}} & \template{The \mybox{aspect} at the restaurant was \mybox{adj}} & \makecell[ml]{\inp{The service at the restaurant was really good.}{\posb{$e_0$}, \negb{$e_3$}} \\\inp{The food at the restaurant was wug.}{\posb{$e_6$}, \posb{$e_9$}} } \\ \addlinespace
& \template{The restaurant had \mybox{adj} \mybox{aspect}} & \makecell[ml]{\inp{The restaurant had really bad service.}{\posb{$e_7$}, \posb{$e_2$}, \negb{$e_{11}$}} \\\inp{The restaurant had zubin ambience.}{\posb{$e_4$}, \negb{$e_{10}$}}} \\ \addlinespace
& \template{The \mybox{aspect1} was \mybox{adj1}, the \mybox{aspect2} was \mybox{adj2}} & \makecell[ml]{\inp{The food was good, the ambience was bad.}{\posb{$e_1$}, \posb{$e_3$}, \negb{$e_1$}} \\\inp{The service was good, the food was not good.}{\posb{$e_0$}, \negb{$e_1$}}} \\ \addlinespace
& \template{The \mybox{aspect1} was \mybox{adj1} but the \mybox{aspect2} was really \mybox{adj2}} & \makecell[ml]{\inp{The food was good, but the service was really bad.}{\posb{$e_7$}, \posb{$e_1$}, \negb{$e_0$}} \\\inp{The ambience was bad, but the food was really not wug.}{\posb{$e_3$}, \negb{$e_9$}}} \\ \addlinespace
& \template{The \mybox{aspect1} was really \mybox{adj1} even though \mybox{aspect2} was \mybox{adj2}} & \makecell[ml]{\inp{The food was really bad even though the ambience was excellent.}{\posb{$e_5$}, \posb{$e_7$}, \negb{$e_8$}} \\\inp{The food was really zubin, even though the service was bad}{\posb{$e_{4}$}}, \posb{$e_{10}$}, \negb{$e_0$}} \\ \bottomrule
\end{tabular}
\caption{Patch and Input templates used for the Patch Finetuning stage for the sentiment analysis task. We divide our patches into 2 categories: \emph{Override} and \emph{Feature Based} (see Section~\ref{sec:our_approach} for more details). For each input, we provide examples of patches that \posb{apply} and patches that \negb{don't apply}. The simplistic nature of these templates makes them easy to write without access to additional data sources or lexicons.}
\label{tab:synthsent}
\end{table*}
\paragraph{Applying Patches.}
As indicated in \figref{overview:b}, our model consists of two separate heads. The gating head $\ensuremath{g}$ computes the probability that the condition specified by $\ensuremath{lp} = (\ensuremath{c}, \ensuremath{q})$ is true for a given input $x$ as $g(x, c)$. The interpreter head $\ensuremath{\mathcal{I}}$ computes a new distribution over the label space, that conditions on $x$ \emph{and} the consequence $\ensuremath{q}$. This is then combined with the original model output $\ensuremath{f}(x)$ using the above gating probability.
A single patch $\ensuremath{lp} = (\ensuremath{c}, \ensuremath{q})$, can be applied to any input $x$ as
\begin{align}
\text{\fixed{\ensuremath{lp}}} &= \ensuremath{g}(x, c) \cdot \ensuremath{\mathcal{I}}(x, q) \label{eq:patching} \\ \notag &+ [1 - \ensuremath{g}(x,c)] \cdot \ensuremath{f}(x).
\end{align}
Given a library of patches $\ensuremath{P} = \{\lpp{1}, \ldots, \lpp{t}\}$, we find the most relevant patch $\ensuremath{lp}^{*}$ for the given input, and use that to update the model,
\begin{align}
\ensuremath{lp}^{*} &= \argmax_{\lpp{i} \in \ensuremath{P}} g(x, c_i), \label{eq:scalability} \\
\text{\fixed{\ensuremath{P}}} &= \text{\fixed{$\ensuremath{lp}^{*}$}}.
\end{align}
\paragraph{Patch Types.} We consider two categories of patches (examples in Table~\ref{tab:synthsent}). \textbf{Override} patches are of the form \explanation{If \mybox{cond}, then label is $l$} i.e.,{} they override the model's prediction on an input if the patch condition is true. For these patches, we do not use the interpreter head since $\ensuremath{\mathcal{I}}(x, \text{``label is $l$''}) = l$. \textbf{Feature-based} patches are of the form \explanation{If \mybox{cond}, then \mybox{feature}}, i.e.,{} they provide the model with a contextual feature ``hint'' in natural language, e.g.,{} in \figref{fig:synth_data} the \mybox{feature} is ``food is good''. For these patches, the model needs to integrate the hints with the original data, and thus both the gating and interpreter heads are used
\section{Training Patchable Models}
\label{sec:our_approach2}
Assuming $\ensuremath{f}$ has a text encoder and a classification head, we have two finetuning stages. In the \textbf{Task Finetuning} stage, we train $\ensuremath{f}$ on a labeled dataset $\{x_i, y_i\}$ (standard supervised learning). In the \textbf{Patch Finetuning} stage, we use the learnt encoder and learn $\ensuremath{g}$ (initialized randomly) and $\ensuremath{\mathcal{I}}$ (initialized with the classification head). For the patch finetuning stage, we write a small set of patch templates covering the kinds of patches users may write for their own application (see Table~\ref{tab:synthsent} for the patch templates used for our sentiment analysis results). Based on these templates, we instantiate a small number of patches along with synthetic labeled examples. This gives us a dataset $\{x_i, y_i, \ensuremath{lp}_i\}$, where $\lpp{i}$ consists of a condition $\condp{i}$ as well as a consequence $\ensuremath{q}_i$. The interpreter head $\ensuremath{\mathcal{I}}$ is trained to model $\Pr(y_i \mid x_i, \ensuremath{q}_i)$ through standard log-likelihood maximization. The gating head $\ensuremath{g}$ is trained via noise contrastive estimation to maximize
\begin{align}
\tiny
\log \ensuremath{g}(x_i, \condp{i}) - \sum_{\condp{j} \in \negex{x_i}} \log \ensuremath{g}(x_i, \condp{j}),
\end{align}
where $\negex{x_i}$ is a randomly sampled set of negative conditions for $x_i$.
\begin{figure}[]
\begin{subfigure}{.24\textwidth}
\includegraphics[width=0.99\linewidth]{figures/eit_1.pdf}
\caption{}
\label{fig:a}
\end{subfigure}%
\begin{subfigure}{.24\textwidth}
\includegraphics[width=.99\linewidth]{figures/eit_2.pdf}
\caption{}
\label{fig:b}
\end{subfigure}
\caption{A model can learn from just the labels that ``yummy'' and ``greasy'' are positive and negative words respectively, and learn to perfectly fit training data without ever using patch features (\subref{fig:a}, top). This behavior can be explicitly prevented via EITs (\subref{fig:a}, bottom). A model may also fit the data without using the input features by always predicting 1 / 0 for ``food is good'' / ``food is bad'' (\subref{fig:a}, top/bottom). Thus, we additionally ensure that the label cannot be inferred from the patch alone (\subref{fig:b}).}
\end{figure}
\paragraph{Entropy Increasing Transformations.} Patch Finetuning will fail if the synthetic data can be fit by a model that ignores the input or the patch (\figref{fig:a}). Thus, to ensure our model cannot fit the synthetic data without combining patch features with inputs, we perturb the inputs with \emph{Entropy Increasing Transformations} (EITs). We identify words from the input template for which the patch supplies additional information e.g.,{} aspect adjectives, relationship between entities, and transform these into a small set of \emph{nonce} words. Crucially, the meanings of these nonce words vary from example to example, and can only be inferred from the patch (\figref{fig:a} bottom; more examples in Appendix~\ref{sec:appendix_re}). Intuitively, the transformations inject an additional source of randomness which can only be recovered via the patch features. Such transformations are also used in \citet{rajendran20} in the context of meta-learning. EITs alone do not fix the failure mode where the model can fit the data without using input features at all. For example, in \figref{fig:a} bottom, the model might learn a shortcut so that it always predicts 1/0 for ``food is good'' / ``food is bad'', regardless of the input. Thus, in addition to EITs, to ensure that the model uses input features, we ensure that a given patch consequence $q$ and the target label are independent (\figref{fig:b}).
\section{Experimental Setup}
\label{sec:experiments}
\paragraph{Applications.} We apply our method to binary sentiment analysis and relation extraction. For sentiment analysis, our task finetuning data comes from SST2 \cite{socher-etal-2013-recursive}. For relation extraction, we use the {\dataset{Spouse}} dataset \citep{Hancock2018} for task finetuning, where the objective is to determine whether two entities are married or not given a textual context about them.
\paragraph{Model.} We use T5-large \citep{raffel2019exploring} as implemented in the transformers library \citep{wolf-etal-2020-transformers} for all experiments. Both the gating and interpreter heads are separate decoders learnt on top of a shared encoder and each of these components are initialized with the corresponding T5 pre-trained weights. To prevent catastrophic forgetting on the original task during patch finetuning, we also multi-task learn the patch finetuning loss along with the original task loss. Templates for generating patches for patch finetuning are in Table~\ref{tab:synthsent} for sentiment analysis and in Table~\ref{tab:synthspouse} ( Section~\ref{sec:appendix_re}) for relation extraction. We train separate models for override and feature-based patches (the former does not need an interpreter head). When using a patch, its content (either \ensuremath{c}{} for the gating head or \ensuremath{q}{} for the interpreter head) is inserted in the beginning of the input with a separator as in \figref{overview:b}.
\paragraph{Baselines.} We report performance of the original model with only task finetuning (\textsc{Orig}) and the model obtained after patch finetuning (\textsc{Orig+PF}) without using any patches, to isolate the gains of language patches from those induced by training on additional synthetic data. We also report results obtained from prompting \textsc{Orig}{} with our patches (\textsc{Prompt}), i.e.,{} inserting the patch text before the input text to see how well finetuned T5 follows instructions. To use multiple patches for this baseline, we prompt the model with each individual patch and ensemble results with majority voting. Finally, we experiment with \emph{regex-based} patches (\textsc{Regex}{}) where patch conditions are converted to regex rules and consequents are converted into functions $\rulef_\ensuremath{q}(x)$. For override patches, this function simply outputs the specified label. For sentiment analysis, where feature based patches supply contextual meanings, $\rulef_\ensuremath{q}(x)$ replaces words with specified meanings e.g.,{} replacing ``bomb'' with ``good'' in ``the food was bomb''. For feature based patches on relation extraction, $\rulef_\ensuremath{q}(x)$ appends the patch consequent to the input text.
\section{Controlled Experiments}
\label{sec:synth_experiments}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{figures/fig3.pdf}
\caption{(a) Example patches used for our controlled experiments. (b) Some inputs where the patch is important for making correct predictions. (c) To control for spurious behaviors such as copying label words from the patch, performing simple string lookups or affecting predictions when patch features are unimportant, we also construct invariance tests where we expect model predictions to be unaffected by the patch.}
\label{fig:synth_data}
\end{figure}
We test the behavior of language patches (and baselines) under different controlled conditions with CheckList \cite{ribeiro-etal-2020-beyond}. Patches and example inputs are presented in \figref{fig:synth_data}.
We test cases where patches apply \emph{and are relevant} for predictions, and corresponding cases where they either do not apply or are not relevant.
Thus, models that rely on shortcuts such as copying the label word from the patch or merely performing token matching perform poorly on the CheckList.
For sentiment analysis, we test Override patches with \emph{abstract} conditions (e.g.,{} ``If \emph{food} is described as weird, then label is negative'' ) on various concrete instantiations such as ``The \emph{pizza} at the restaurant was weird''. We also construct invariance tests ({\dataset{O-Inv}}), where adding such patches should not change predictions on inputs where the condition is false (e.g.,{} ``The waiter was weird'', ``The tacos were not weird'').
We also construct tests for feature-based patches ({\dataset{Feat}{}}) where patches provide meaning for nonce adjectives, with analogous invariance tests ({\dataset{Feat-Inv}{}}).
Finally, we construct analogous tests for relation extraction, where patches fill in \emph{reasoning gaps} in the model such as \explanation{If Entity1 gave Entity2 a ring, then Entity1 and Entity2 are engaged}.
We present the results in Table \ref{tab:results-synth}, where we first note that \textsc{Orig+PF}{} does not perform well overall, and thus patching improvements are not merely a result of the additional synthetic data. \textsc{Regex}{} cannot handle abstract conditions, and thus (as expected) does not change predictions on sentiment analysis, and does not do well on relation extraction.
While merely inserting the patch into the input (\textsc{Prompt}{}) results in some gains when the patch applies, it does so at the cost of changing predictions when the patch does not apply ({\dataset{O-Inv}{}} and {\dataset{Feat-Inv}{}}).
In contrast to baselines, our method is able to apply \emph{abstract} patches correctly on concrete instantiations, disregarding them when they do not apply, without relying on shortcuts such as copying the label from the consequent or merely checking for matching words between patch and input (all of which are tested by the invariance tests).
\begin{table}
\centering
\ra{1.3}
\tiny
\begin{tabular}{@{}lrrrrp{0.001cm}rr@{}} \toprule
\multirow{2}{*}{Model} & \multicolumn{4}{c}{Sentiment Analysis} && \multicolumn{2}{c@{}}{Relation Extraction} \\
\cmidrule{2-5} \cmidrule{7-8}
& \dataset{Override} & \dataset{O-Inv}{} & \dataset{Feat}{} & \dataset{Feat-Inv}{} && \dataset{Feat}{} & \dataset{Feat-Inv}{} \\ \midrule
\textsc{Orig}{} & 50.0 & n/a & 59.1 & n/a && 14.5 & n/a \\
\textsc{Orig+PF}{} & 50.0 & n/a & 59.9 & n/a && 35.8 & n/a \\
\textsc{Regex}{} & 50.0 & \textbf{100.0} & 59.9 & \textbf{100.0} && 45.8 & 88.1 \\
\textsc{Prompt}{} & 68.7 & 63.8 & 64.3 & 85.4 && 13.9 & 87.6 \\
\textsc{Patched}{} & \textbf{100.0} & \textbf{100.0} & \textbf{100.0} & \textbf{100.0} && \textbf{47.2} & \textbf{92.6} \\ \bottomrule
\end{tabular}
\caption{Applying patches on CheckLists. We see significant improvements when the patches apply and invariances when they do not apply or are unimportant. For Sentiment Analysis, the datasets are designed to evaluate patching with abstract conditions, thus we see no effects from using regex based patches. For testing invariance, we report the percentage of inputs for which the prediction did not change w.r.t.\ the base model.}
\label{tab:results-synth}
\end{table}
\section{Patching models on real benchmarks}
\label{sec:real_experiments}
\subsection{Sentiment Analysis}
Unless noted otherwise, all datasets in this subsection are derived from Yelp Review \citep{zhang2015}. To fix errors on low-accuracy slices, we write patches by inspecting a random subset of 10-20 errors made by \textsc{Orig+PF}{}.
\paragraph{Controlling the model.} In order to check if patches can control model behavior with abstract conditions ``in the wild'', we manually annotate a random subset of 500 reviews with food and service specific sentiment (``The food was good, service not so much'' is labeled as {\cmss{service: 0, food: 1}}). We then construct override patches of the form \explanation{if \mybox{food / service} is good / bad, then label is positive / negative}, and evaluate models as to how often (on average) the prediction is as expected when the patch applies and how often it is unchanged when the patch does not apply. We present results in Table \ref{tab:results-steering}.
The sentiment of both aspects typically agrees, and thus even models without patching often behave according to the patch. We note that natural language patches improve patched behavior the most (when compared to baselines), while almost never changing predictions when the patch does not apply. We additionally present results only on the subset of our aspect annotated examples where both aspects \emph{disagree} in Table~\ref{tab:results-steering-add}. Overall, we see a more pronounced difference i.e.,{} our model gets a \textasciitilde{}27 point boost in accuracy when the patch condition applies, while maintaining invariance when the condition does not apply.
\begin{table}[]
\tiny
\ra{1.3}
\centering
\begin{tabular}{@{}lrr@{}} \toprule
Model & Correctly patched (applies)& Invariance (does not apply) \\ \midrule
\textsc{Orig}{} & 91.5 & n/a \\
\textsc{Orig+PF}{} & 91.1 & n/a \\
\textsc{Regex}{} & 91.0 & 99.5 \\
\textsc{Prompt}{} & 92.3 & 98.4 \\
\textsc{Patched}{} & \textbf{95.8} & 99.4 \\ \bottomrule
\caption{To measure how well patches control behavior ``in the wild'', we evaluate the model's ability to match the label specified by the patch when it applies, and invariance w.r.t the base model when the patch does not apply, on a subset of yelp with sentiment annotations for different aspects}
\label{tab:results-steering}
\end{tabular}
\end{table}
\begin{table}[]
\scriptsize
\centering
\ra{1.3}
\begin{tabular}{@{}lrr@{}} \toprule
Model & Correctly patched (applies)& Invariance (does not apply) \\ \midrule
\textsc{Orig}{} & 52.1 & n/a \\
\textsc{Prompt}{} & 55.7 & 97.6 \\
\textsc{Orig+PF}{} & 53.5 & n/a \\
\textsc{Regex}{} & 55.1 & 100.0 \\
\textsc{Patched}{} & \textbf{79.6} & 99.4 \\ \bottomrule
\caption{ We evaluate the model's ability to match the label specified by the patch when it applies, and invariance w.r.t the base model when the patch does not apply, on a subset of yelp with sentiment annotations for different aspects. In this table, we specifically consider inputs where both food and service aspects differ in sentiment.}
\label{tab:results-steering-add}
\end{tabular}
\end{table}
\paragraph{Patching low-accuracy slices.} We identify slices where our base model has (comparatively) low accuracy, and check whether patches can improve performance.
{\dataset{Yelp-stars}} consists of all examples in Yelp Review with the word `star' present. For this subset, we use two overrides patch: \explanation{If review gives 1 or 2 stars, then label is negative}, \explanation{If review gives 0 stars, then label is negative}.
{\dataset{Yelp-Colloquial}} is a label-balanced slice consisting of examples having the colloquial terms \{dope, wtf, omg, the shit, bomb, suck\}. Because the colloquial use of these terms depends on context, we further construct {\dataset{Yelp-Colloquial-Control}}, a CheckList where the same terms are used in their traditional sense (e.g.,{} ``The manager was a dope'', ``The bomb was found by the police at the restaurant''). A model can do well on both of these datasets simultaneously only if it understands the contextual nuance associated with colloquial terms, rather than relying on simple shortcuts such as equating ``bomb'' with ``good''. For these datasets, we write simple feature-based patches such as \explanation{If food is described as bomb, then food is good} for each term.
Finally, we use the ``Women's E-commerce Clothing Reviews'' dataset ({\dataset{WCR}}) from \citet{zhongmeta21} and add two override patches: \explanation{If review mentions phrases like needs to be returned, then label is negative}, and \explanation{If fit is boxy, then label is negative}.
In Table~\ref{tab:results-realsentiment}, we observe that a very small number of language patches improve performance by 0.5-4.1 accuracy points, always outperforming both the original model and baselines.
These gains are not a result of the added synthetic data, as \textsc{Orig+PF}{} often \emph{lowers} performance.
Qualitatively, \textsc{Prompt}{} tends to rely on shortcuts such as copying over the label in the patch rather than gating and integrating the information, while \textsc{Regex}{} cannot deal with simple semantic understanding, e.g.,{} the rule on {\dataset{Yelp-stars}} fires for \textit{``Will deduct 1 star for the service but otherwise everything was excellent''}, leading to an incorrect patch application.
Natural language patches avoid both of these pitfalls by explicitly modeling gating and feature interpretation with learnt models.
\begin{table}[]
\tiny
\ra{1.3}
\centering
\begin{tabular}{@{}lrrrr@{}} \toprule
Model & \dataset{Yelp-Stars} & \dataset{Yelp-Colloquial} & \dataset{Yelp-Colloquial-Control} & \dataset{WCR} \\ \midrule
\textsc{Orig}{} & 93.1 & 89.1 & 100.0 & 89.6 \\
\textsc{Orig+PF}{} & 93.6 & 88.6 & 100.0 & 88.9 \\
\textsc{Regex}{} & 92.7 & 91.9 & 88.1 & 90.0 \\
\textsc{Prompt}{} & 90.8 & 85.2 & 70.1 & 88.3 \\
\textsc{Patched}{} & \textbf{94.5} & \textbf{93.2} & \textbf{100.0} & 90.1 \\ \bottomrule
\end{tabular}
\caption{Using Override and Feature Based patches to fix bugs on various benchmarks derived from real sentiment analysis datasets. For {\dataset{Yelp-Colloquial}}, we also generate an control test based on CheckList.}
\label{tab:results-realsentiment}
\end{table}
\subsection{Spouse Relation Extraction}
We construct {\dataset{Spouse-FewRel}{}}, an out-of-distribution test benchmark derived from FewRel \cite{gao-etal-2019-fewrel} by sampling from all relation types where at least one of the entities is a person ($n=8400$), and labeling examples as positive if they have the \texttt{Spouse} relation, negative otherwise.
We inspect 20 randomly sampled errors made by \textsc{Orig+PF}{} on {\dataset{Spouse-FewRel}}, and observe that the model often confuses ``Entity1 has a child with Entity2'' with ''Entity1 is the child of Entity2'', and also misclassifies widowhood as negative. Thus, we write override patches for both of these error categories, resulting in 7 patches, presented in Table~\ref{tab:results-spouse-real}. Using all patches, we observe a \textasciitilde{}7.4 point F1 improvement over \textsc{Orig}{}, while baselines either decrease F1 or barely improve it.
We highlight in Table \ref{tab:results-spouse-real} a phenomenon where each natural language patch in \emph{isolation} decreases performance, while all patches together increase performance. Further analysis reveals that this is because the gating head is not well calibrated in this case, and thus individual patches are applied incorrectly. However, the \emph{comparative} values of $g(x, c_i)$ are often ordered correctly, and thus a better patch is the one applied ($lp^{*}$ in Eq~\ref{eq:scalability}) when all patches are available.
We do further analysis in Table \ref{tab:results-spouse-real-gating-acc}, where we report the \emph{gating accuracy} (i.e.,{} whether the patch actually applies or not, labeled manually) of $lp^{*}$ on the subset of inputs where the \textsc{Patched}{} model changes the prediction (\texttt{Diff}), and where it changes the prediction to the correct label (\texttt{Diff} $\cap$ \texttt{Correct}).
With the caveat that patches are applied softly (and thus perfect gating accuracy is not strictly necessary), we observe that a few patches seem to hurt performance even in combination with others (e.g.,{} the first one). We also note that the patched model is right \emph{``for the right reasons''} in over 72\% of inputs where it changes the prediction to the correct one.
\begin{table}
\scriptsize
\centering
\ra{1.3}
\begin{tabular}{@{}llr@{}} \toprule
& Model & F1 \\ \midrule
& \textsc{Orig} & 65.5 \\
& \textsc{Orig+PF} & 61.4 \\
& \textsc{Regex}{} & 61.0 \\
& \textsc{Prompt} & 65.7 \\
& \textsc{Patched}{} & \textbf{72.9} \\ \midrule
\multirow{7}{*}{\rotatebox[origin=c]{90}{\textit{Using single patch}}} & \nexample{If $p_2$ is the son of $p_1$, then label is negative} & 57.5 \\
& \nexample{If $p_1$ is the son of $p_2$, then label is negative} & 58.9 \\
& \nexample{If $p_1$ and $p_2$ have a daughter, then label is positive} & 61.9 \\
& \nexample{If $p_1$ and $p_2$ have a son, then label is positive} & 66.8 \\
& \nexample{If $p_1$ is the widow of $p_2$, then label is positive} &
63.6 \\
& \nexample{If $p_1$ is the daughter of $p_2$, then label is negative} & 50.7 \\
& \nexample{If $p_2$ is the daughter of $p_1$, then label is negative} & 49.4 \\\bottomrule
\end{tabular}
\caption{Using Override Patches on {\dataset{Spouse-FewRel}} for Spouse relation extraction.}
\label{tab:results-spouse-real}
\end{table}
\begin{table}
\tiny
\centering
\ra{1.3}
\begin{tabular}{@{}lrr@{}} \toprule
Patch Condition & \texttt{Diff} & \texttt{Diff} $\cap$ \texttt{Correct} \\ \midrule
\nexample{$p_2$ is the son of $p_1$} & 0.0 & NaN (0/0) \\
\nexample{$p_1$ is the son of $p_2$} & 75.0 & 75.0 \\
\nexample{$p_1$ and $p_2$ have a daughter} & 63.3 & 93.8 \\
\nexample{$p_1$ and $p_2$ have a son} & 78.1 & 98.3 \\
\nexample{$p_1$ is the widow of $p_2$} & 10.9 & 19.6 \\
\nexample{$p_1$ is the daughter of $p_2$} & 71.4 & 100.0 \\
\nexample{$p_2$ is the daughter of $p_1$} & 6.3 & 100.0 \\\midrule
Overall & 42.9 & 72.3 \\ \bottomrule
\end{tabular}
\caption{We measure how often the chosen patch correctly applies to an input (i.e.,{} gating accuracy) for {\dataset{Spouse-FewRel}{}}, for the set of inputs where the patched model and original model differ (\texttt{Diff}) as well as the subset where the patched model is correct (\texttt{Diff} $\cap$ \texttt{Correct}).}
\label{tab:results-spouse-real-gating-acc}
\end{table}
\begin{figure*}
\centering
\begin{subfigure}{.245\textwidth}
\centering
\includegraphics[width=.9\linewidth]{finetuning_comparison_figs/spouse.pdf}
\label{fig:sfig1}
\end{subfigure}%
\begin{subfigure}{.245\textwidth}
\centering
\includegraphics[width=.9\linewidth]{finetuning_comparison_figs/yelp_colloquial.pdf}
\label{fig:sfig2}
\end{subfigure}
\begin{subfigure}{.245\textwidth}
\centering
\includegraphics[width=.9\linewidth]{finetuning_comparison_figs/yelp_colloquial_control.pdf}
\label{fig:sfig3}
\end{subfigure}
\begin{subfigure}{.245\textwidth}
\centering
\includegraphics[width=.9\linewidth]{finetuning_comparison_figs/yelp_stars.pdf}
\label{fig:sfig4}
\end{subfigure}
\caption{How many additional finetuning training examples it takes to reach the same accuracy level as patching. We report the mean and standard deviations across 5 runs.}
\label{fig:ftvspatching}
\end{figure*}
\section{Analysis}
\subsection{How Important are EITs?}
\label{sec:eit_ablation}
\begin{table}
\scriptsize
\centering
\ra{1.3}
\begin{tabular}{@{}lrr@{}} \toprule
Patch Consequent & Patched & Patched (Without EITs) \\ \midrule
\nexample{$p_1$ went on a honeymoon with $p_2$} & \textbf{59.1} & 33.7 \\
\nexample{$p_1$ has kids with $p_2$} & \textbf{75.2} & 74.4 \\
\nexample{$p_1$ is engaged to $p_2$} & \textbf{77.7} & 64.8 \\
\nexample{food is good} & \textbf{67.8} & 54.2 \\
\nexample{food is bad} & \textbf{88.7} & 56.5 \\
\nexample{service is good} & \textbf{62.8} & 52.9 \\
\nexample{service is bad} & \textbf{62.8} & 52.9 \\ \midrule
Overall & \textbf{70.6} & 55.6
\\ \bottomrule
\end{tabular}
\caption{Patching Accuracy of a model with and without Entropy Increasing Transformations (EITs).}
\label{tab:results-eit}
\end{table}
The goal of Entropy Increasing Transformations (EITs; Section~\ref{sec:our_approach2}) is to prevent the interpreter head from learning shortcuts that either ignore patch features or rely exclusively on them.
We perform an ablation, comparing our model to a model trained without EITs on the CheckLists in Table \ref{tab:results-synth} (Section~\ref{sec:synth_experiments}), where the feature-based patch consequent supplies important information for making a correct prediction.
From Table \ref{tab:results-eit}, we note that the interpreter head trained without EITs has much lower performance on these datasets (as expected).
\subsection{Comparison to fine-tuning}
\label{sec:comparison_with_finetuning}
While patching is computationally lightweight, it requires domain knowledge or error analysis of incorrectly labeled examples. However, once such analysis is performed, one can label these additional examples and finetune the model on them. Ignoring the computational and infrastructure costs of repeated finetuning, for patching to be a competitive alternative to finetuning from an \emph{annotation budget} perspective, we require the gains from patching to only be matched by multiple labeled examples. To compare language patches with finetuning, we consider {\dataset{Yelp-stars}}, {\dataset{Yelp-Colloquial}}, and {\dataset{Spouse-FewRel}{}} and split each dataset into a training set with 128 examples, and a test set with remaining examples. Next, we finetune \textsc{Orig}{}, on $k = \{2, 4, 8, 16, 32, 64, 128\}$ examples from the training set, stopping early if finetuning performance exceeds patched performance. We finetune for 64 steps and optimize using AdamW with a fixed learning rate of 1e-4. We report means and standard deviations obtained from finetuning with 5 random seeds.
Results are presented in \figref{fig:ftvspatching}, where we note that over $100$ labeled examples are needed to match the performance of a single patch on {\dataset{Yelp-Stars}} or 7 patches on {\dataset{Spouse-FewRel}}.
On {\dataset{Yelp-Colloquial}}, the patched performance is matched with a mere $16$ examples. However, as noted earlier, {\dataset{Yelp-Colloquial}} is susceptible to simple shortcuts, and we observe that the performance on the control set {\dataset{Yelp-Colloquial-Control}} suffers significantly as we finetune on more data (with very high variance).
Thus, we conclude that language patches on these datasets are not only very efficient in terms of annotation effort (when compared to labeling data for finetuning), but also less susceptible to simple shortcuts that do not address the problem at the right level of abstraction.
\section{Related Work}
\paragraph{Learning with Language.} Natural language instructions or explanations have been used for training fewshot image classifiers \citep{Mu2020, Andreas2018}, text classifiers \cite{Zaidan2008, Srivastava2018, Camburu2018, Hancock2018, Murty2020}, and in the context of RL \citep{Branavan2012, goyal19, coreyes2019, mu2022improving}. All of these works are concerned with reducing labeled data requirements with language supervision, while our setting involves using language as a \emph{corrective} tool to fix bugs \emph{at test time}.
\paragraph{Prompt Engineering.} An emerging technique for re-purposing language models for arbitrary downstream tasks involves engineering ``prompts''. Prompts are high level natural language descriptions of tasks that allow developers to express any task as language modeling \citep{brown2020language,gao2021making, zhongmeta21}. While we could try and directly use prompting to incorporate language patches, our experiments show that the models we consider fail to correctly utilize patches in the prompt (Section \ref{sec:experiments}). With increasing scale models may gain the ability to interpret patches zero-shot, but qualitative exploration of the largest available models at the time of writing \cite[e.g. GPT-3;][]{brown2020language} indicates they still suffer from the same problem.
Using patches for corrective purposes requires an accurate interpretation model, as well as ignoring the patch when it is not applicable. We solve these challenges by learning a gating head and an interpretation head through carefully constructed synthetic data.
\paragraph{Editing Factual Knowledge.} Test time editing of factual knowledge in models is considered by \citet{Talmor2020, decao2021editing, mitchell2021fast, Meng2022LocatingAE}. Instead of modifying factual knowledge, we show that \emph{free-form language} patches can be used to fix \emph{bugs} on real data, such as correctly interpreting the meaning of the word ``bomb'' in the context of food or predicting that divorced people are no longer married.
\section{Conclusion}
When faced with the task of fixing \emph{bugs} in trained models, developers often resort to brittle regex rules or finetuning, which requires curation and labeling of data, is computationally intensive, and susceptible to shortcuts.
This work proposes \emph{natural language patches} which are declarative statements of the form ``if $\ensuremath{c}$, then $\ensuremath{q}$'' that enable developers to control the model or supply additional information with conditions at the right level of abstraction.
We proposed an approach to patching that models the task of determining if a patch applies (gating) separately from the task of integrating the information (interpreting), and showed that this approach results in significant improvements on two tasks, even with very few patches.
Moreover, we show that patches are efficient (1-7 patches are equivalent or better than as many as $100$ finetuning examples), and more robust to potential shortcuts.
Our system is a first step in letting users \emph{correct} models through a \emph{single step} ``dialogue''. Avenues for future work include extending our approach to a back-and-forth dialogue between developers and models, modeling pragmatics, interpreting several patches at once, and automating patch finetuning.
\section{Acknowledgements}
SM was partly funded by a gift from Apple Inc. We are grateful to Jesse Mu, Mirac Suzgun, Pratyusha Sharma, Eric Mitchell, Ashwin Paranjape, Tongshuang Wu, Yilun Zhou and the anonymous reviewers for helpful comments. The authors would also like to thank members of the Stanford NLP group and the Adaptive Systems and Interaction group at MSR for feedback on early versions of this work.
\section{Reproducibility}
Code and model checkpoints are available at \url{https://github.com/MurtyShikhar/LanguagePatching}.
\section{Limitations}
\paragraph{Scaling to large patch libraries.} For our approach, inference time scales linearly with the size of the patch library. This is primarily because the gating head makes predictions on each patch in our patch library (Eq~\ref{eq:scalability}). Instead of running the gating head on each patch, one can trade off exactness for efficiency, by running the gating head on a much smaller candidate set identified using fast approximate nearest neighbors \citep{johnson2019billion} on sentence embeddings.
\paragraph{Scaling to more patch types.} The current approach requires writing patch templates \emph{beforehand} based on prior knowledge of the kinds of corrective feedback that developers might want to write in the future. Writing patch templates manually is fundamentally bottlenecked by human creativity and foresight. Morever, since humans are required to write templates, it makes scaling up to different patch types harder, since we expect generalization to completely new patch \emph{types} to be poor e.g.,{} generalizing to a patch that requires counting. Future work can explore automatic generation of synthetic patch templates e.g.,{} using pre-trained language models.
\paragraph{Interpreting multiple patches.} Finally, the approach we develop can only incorporate a single patch at a time, by selecting the most relevant patch from our patch library. This precludes the model from being able to combine features from multiple patches---e.g.,{} \textit{``caviar is a kind of food''} and \textit{``If caviar is described as overpowering, then caviar is spoiled''}.
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Andrei Lankov
Taste of strawberries
By Andrei Lankov
A new item in North Korean markets has recently become all the rage ― strawberries. The last two or three years have been marked by a proliferation of green houses, where North Korean farmers produce fruits once unheard of.
The green house industry in North Korea is private, and its emergence was largely enabled by the Kim Jong-un agricultural reforms. Now, farmers can negotiate deals with agricultural cooperatives and rent land where they can erect greenhouses.
Building such a facility is not cheap. Strawberries and melons produced there are still expensive enough to be within the reach of only the top quarter of income earners. One should remember, however the number of people who were able to taste such delicious produce was measured in fractions of one percent, so the improvement is dramatic.
Indeed, when it comes to the economy of North Korea, much good news has emerged recently. In spite of all the talk about floods and droughts, there are no widespread shortages of food any more. Grain prices have been stable for years. There is a lot of construction going on in both Pyongyang and peripheral cities, and even in the remote countryside. North Koreans dress better than ever. At night, North Korea's biggest cities are no longer blanketed by complete darkness ― thanks to solar panels there are lights in North Korean houses. North Korea remains the poorest nation in East Asia by a large margin, but is significantly better off than it was 10 or 20 year ago.
Most, if not all of these changes are driven by the unacknowledged but powerful expansion of the private economy. It is the private entrepreneurs who cooperate with farmers to build greenhouses; it is private investors who put their money into construction projects; it is private traders who buy, sell, and transport solar panels which now dot Pyongyang apartments and countryside dwellings.
It is regrettable that American decision makers remain largely ignorant of these changes and still live in a world dominated by grossly-outdated media images of North Korea as a Stalinist dystopia on the brink of economic collapse. Perhaps had they had more opportunities to taste North Korean strawberries, they would become less sanguine about the sanctions against the regime. Indeed, it's remarkable that actual improvements in North Korea's economic situation roughly coincide with the introduction of stringent international sanctions that are designed to drive the economy into a corner, thus creating the necessary conditions for domestic discontent and leaving North Korea's government no choice but to surrender their nuclear capability.
Admittedly, even had such sanctions truly succeeded in undermining the economy, they would not inspire Pyongyang to consider denuclearization. North Korea's decision makers long ago decided that nuclear weapons constitute a vital condition for regime survival. There is little doubt that if they have to decide between giving up their nuclear weapons and ignoring the starvation deaths of countless North Korean farmers, they will sacrifice the farmers, not the bombs. Fortunately, due to the revival of the North Korean economy such a binary decision remains theoretical. The changes of the last half decade demonstrate North Korean leaders can in fact have their cake and eat it too. They can allow private entrepreneurs to generate growth while enjoying advancing their nuclear and missile programs with truly remarkable speed.
All this indicates a true triumph of the market system in a place where most supporters of such a system hate it with a passion. But it also means prospects for the future are less than rosy. North Korea is going to remain nuclear. There is no chance that international sanctions, so spectacularly inefficient, will have the slightest impact on the country's future policies.
Admittedly, developing North Korea is less likely to initiate a nuclear war. Perhaps as long as the new ruling class, now consisting of both ruthless party apparatchiks and bold entrepreneurs, stays in power, North Korea will behave more cautiously than before. After all, easier access to Porsche cars for the rulers, and fresh strawberries for the masses tend to make peoples and nations less bellicose. Nonetheless, it's an uncertain bet. It seems increasingly likely that we will have to live with a nuclear armed, highly oppressive politically, but increasingly prosperous North Korea for years and even decades to come.
Andrei Lankov was born in St. Petersburg, Russia, and teaches at Kookmin University in Seoul. Reach him at anlankov@yahoo.com.
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Artificial Lawyer is all about changing the business of law, often through the use of technology, but also through the better deployment of people inside organisations and within new business structures, as well as innovation around process improvement.
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Москаль-чародей (, дословно «Москаль-кудесник») — одноактная пьеса Ивана Петровича Котляревского, написанная в 1819 году. Впервые опубликована в журнале «Украинскій Альманахъ» в 1841 году в Москве И. И. Срезневским.
По жанровым признакам пьеса приближается к водевилю, хотя сам писатель назвал её «оперой малороссийской в одном действии». «Солдат-чародей», как и его «Наталка Полтавка», своими драматургическим приёмами, идейно-тематическими тенденциями близка к комическим операм конца XVIII — начала XIX веков. Кроме того, своей пьесой Котляревский преследовал не только развлекательные, но и воспитательные морализаторские цели.
При создании пьесы драматург опирался на художественный опыт французской, русской, украинской литератур. Народное творчество — анекдоты, легенды, рассказы — всегда привлекало внимание писателя.
Социально-бытовой конфликт, положенный в основу «Солдата-чародея», нашёл своё отражение во многих народных песнях и анекдотах, однако для традиционного сюжета про неверную жену Котляревский нашёл новую, оригинальную трактовку: вместо образов жены-изменницы и её полоумного мужа драматург создал образ верных супругов.
Персонажи
Лихой — солдат
Михайло Чупрун — простоватый, доверчивый муж
Татьяна Чупрун — «неверная» жена, умная, хитрая, красивая, кропотливая, но с характером
Каленик Кононович Финтик — писарь из города, поклонник-неудачник
Сюжет
Татьяна — легкомысленная женщина, к которой в отсутствие мужа зачастил чиновник-канцелярист Финтик, она даже приглашает его к себе на «Копчёную колбасу, запечённую курицу и бутылку оковитой». Как выясняется позже, делает она это с определёнными намерениями — проучить избалованного ухажёра.
Финтик — носитель чуждых простому народу обычаев. Получив некоторое образование в городе, этот невежда гордится своей «грамотностью», стыдится своего «мужицкого» происхождения, не может «без стыда и не покрасневши называть матушкой просто одетую старуху» — родную мать. Лакейская «цивилизация» Финтика проявляется и в его пренебрежительном отношении к народным песням; она прекрасно передана и речевой характеристикой. Язык Финтика пересыпан канцеляризмами, искажениями, смесью украинских и русских слов.
Татьяна отчитывает Финтика за недостойное поведение, бездушие, его высокомерное отношение к своей матери. Появляющийся в доме Татьяны солдат своим мнимым строгим видом хочет запугать хозяйку дома. Но это не удается «служивому»; Татьяна развенчивает его тщеславие, несколько пренебрежительное отношение к «мужикам». Ведь и ты мужиком был, пока тебе лоб не выбрили и мундир не натянули на плечи, — иронично обращается Татьяна к солдату. — Если бы я не женщиной была, может была лучшим солдатом, чем ты. "
Но однажды муж Татьяны неожиданно возвращается из поездки. Она уговаривает Финтика прятаться за печь, сама же идёт встречать мужа. Неожиданно в хату приходит выпивший солдат. Он начинает насмехаться над хозяевами, хитростью и обманом убеждает их, что способен на чудеса и чародейство…
Раскрывая характеры простых людей — носителей здорового начала, Котляревский убедительно доказывает превосходство народной морали над моралью господ и чиновников. Этим «Солдат-чародей» приближается к «Наталке Полтавке».
Водевиль богат песнями: «Больно сердцу мила друга не иметь», «Був в мене мужичок з кулачок», «З того часу, як женився», «Меня зовут Лихой», «Ой, не відтіль вітер віє, відкіль мені треба», «Ой, служивий, ой, служивий, не тобі питати», «Ой, був та нема, та поїхав до млина», «Тобою восхищённый», «Треба любо з людьми жити». В целом в водевиль введено двенадцать песенных номеров. Песня «Ой, був та нема, та поїхав до млина» фигурирует также и в «Простаке» В. Гоголя.
Дальнейшая судьба в культуре
Впервые пьеса была поставлена на сцене Полтавского вольного театра. В 1820-х годах «Наталка Полтавка» и «Солдат-чародей» с огромным успехом прошли в Санкт-Петербурге в Александринском театре и в московском Малом театре.
Большую популярность пьесам Котляревского «Наталка Полтавка» и «Солдат-чародей» на украинской и русской сценах в первой половине XIX века способствовало участие в этих спектаклях М. С. Щепкина. Своим жизненно правдивым исполнением ролей Макогоненка и Чупруна талантливый актёр не только способствовал небывалому успеху на театральной сцене этих первых произведений украинской национальной драматургии, но и помогал российскому зрителю глубже познать Украину, её народ, быт и обычаи.
Пионеры украинского кино 1910-х годов предпочитали экранизации популярных местных спектаклей, таких как «Москаль-волшебник», который стал одним из первых немых игровых фильмов Украины. В 1995 году на киностудии им. А. Довженко был снят новый фильм «Солдат-чародей», где в главных ролях снялись Богдан Бенюк (Лихой), Руслана Писанка (Татьяна) и Александр Бондаренко (Чупрун).
Примечания
Литература
Москаль-чарівник: укр. водевіль на 1 дію / І. П. Котляревський. — Харків: Держлітвидав, 1935. — 47 с. — (Бібліотека читача-початківця).
Москаль-чарівник — Котляревський Іван
Пьесы 1819 года
Пьесы Ивана Котляревского
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Deandre Provided Ayton of Fantasy Goodies
January 17, 2020 | Fantasy Basketball Daily Notes | 12 Comments
The Phoenix Suns liked Deandre Ayton during the 2018 NBA draft. So much so that they drafted him with the number one overall pick. In hindsight, the pick looks silly because they selected him over the likes of Luka Doncic and Trae Young. If you look at the Suns history of drafting in the first round, it makes sense why they selected Ayton.
2017 – Josh Jackson. G-League.
2016 – Dragan Bender. Bucks.
2015 – Devin Booker. Yipee!
2014 – T. J. Warren. Pacers.
2013 – Alex Len. Hawks.
2012 – Kendall Marshall. LOL!
2011 – Markieff Morris. Knicks.
2010 – No first
Luka and Trae both had some perceived risks. Ayton was the safe pick because he was a big man who could shoot. Now, Luka should've been the pick, but it's not like Ayton is a bust. Last night was an example of the fantasy goodies he can provide.
26 21 2 0 2 2 0 11/15 4/4
Prior to last night's game, the Suns were bringing Ayton off the bench, like a bunch of bobos. Regardless if he starts or comes off the bench, though, Ayton produces. Over the past seven games, he's averaged 32.9 minutes, 18.1 points, 11.9 boards, 2.1 dimes, and 1.7 blocks. He's converted 58% of the 14.1 shot attempts and shooting 78% from the line. That's been good for top 30 production for fantasy. He can score down on the block or from the top of the key. The stroke is pretty. Is he a transcendent player like Luka? Negative, but he's very, very good and could finish as a top 15 player. Beep. Boop. Bop. You know what is transcendent like Luka? The Stocktonator.
Baby Don't Huerter, Don't Huerter, No More
What is love? Haddaway asked that question many decades ago. Did he find the answer? Naw, just more questions but the one thing he wanted us to know is that he didn't want to get hurt anymore. As we well know in the fantasy world, Love hurts. Last night, the Phoenix Suns were singing the same tune, as Kevin Huerter kept bringing the pain.
Baby don't Huerter, don't Huerter, no more. It was a career game in terms of boards and dimes. As I've written in the past, the thing that most impressed me about Huerter's game was the playmaking ability. He is an excellent ball handler and can navigate pick-and-roll action competently. He's been averaging 4.8 dimes over the past four games. I thought he would strictly be a 3-and-D player when he was drafted, but his game is multi-dimensional. Case in point, over the past seven games, he's averaged 7.1 boards per game. Now, he's been shooting 49% from the field over that stretch. I was always bullish on his shooting acumen, but he was only shooting 42% from the field for most of the season. If the efficiency is real, then top 50 is attainable. I have my doubts, at least this season. Maybe going forward, but top 100 production this season is reasonable, with averages of 13 points, 2 tres, 4 boards, 4 dimes, 1 steal, with 43% shooting from the field and 83% shooting from the line.
Is It Michael Porter Jr. Time?
Michael Porter Jr. was one of the top overall recruits in high school. At 6′ 10″ and 218 pounds, he was literally a giant amongst boys. Unlike most big men, though, he did most of his damage from the perimeter. He possessed both the handles and jump shot of a guard. With his height and athleticism, he would rise up over any challenger and drain shots from all over the court. Because of the stupid rule that forces players to showcase their talents in college for one year before entering the NBA, MPJ eventually decided to play for Missouri. Unfortunately, he injured his back and underwent surgery, forcing him to miss most of the season. As a result, he fell in the NBA draft before the Denver Nuggets selected him with the 14th overall pick. Back injuries are tricky, and the Nuggets selected MPJ for the long game, so the process was going to be a slow and tedious one. For the first 31 games of the season, MPJ played in 22 of them and averaged 9 minutes per game. Then, on December 29th, he received his first start and did what he do, which is score, score, and score some more. He scored 19 points, grabbed 6 boards, and dished out 1 dime in 26 minutes. The Nuggets were short-handed that game, so I dismissed it as a one-off thing, but it looks as if the genie may be out of the bottle. Last night….
25 5 1 0 0 1 2/3 11/12 1/2
In 23 minutes off the bench. He posted up smaller defenders, broke down bigs on the perimeter, showcased the Harden-esque step-back J, and attacked the rim on closeouts with dexterity. Over the past four games, he's been a top 60 player for fantasy, despite averaging only 19.6 minutes. Now, before we go crowning his ass, MPJ is not going to shoot 74% from the field, which is what he's done over the past four games. When that happens, the points will obviously go down, which will be an issue because most of his fantasy value is derived from scoring. He may be a hero right now, but he's a zero in the defensive stats and dimes. Beep. Boop. Bop. You know what's never a zero, and always a hero? The Stocktonator. In addition, his real-life defense isn't great, which could be an issue regarding playing time because the Nuggets are legitimate contenders this season. I've added MPJ in every league where he was available, as the scoring upside is immense, and there's always that small percentage chance that he could be the greatest thing since….most people go with sliced bread. I get it but not really. How about the internet? Nike Airs? Deodorant? I'm going with the Apple Pan banana cream pie. For those in LA, you know. For the unfortunate, you know what to do if you ever go to LA. Anyways, I'm not expecting much from MPJ to be honest, but willing to see where it leads.
Christian Wood with an Elevated Performance after Christmas
While Christmas has morphed into a commercialized phenomenon, let us not forget why we engorge in capitalistic orgies because of it. Christmas is the day that Christians celebrate the birth of Jesus Christ; the son of God, the final piece of the Holy Triumvirate, the One who died for our sins so that we may experience salvation. To say that He is an important figure in history is an understatement. So, it is only fitting that on the day after Christmas, a Christian would ball out and be the lede of this post. And it makes sense that such an elevating performance would be delivered from a player named Wood because who doesn't like elevated Wood. Anyways, Christian Wood delivered:
22 7 3 0 1 3 2/4 7/9 6/6
In 24 minutes off the bench. Now, the Pistons….POOF….made the Wizards disappear, 132-102 last night. As a result, Wood received more run than normal. On the season, he's averaging 15.3 minutes per game, which is a shame because he balls out when he's on the court. Maybe this Wood cannot perform for extended periods of time. I kid, I kid. Beep. Boop. Bop. You know what performs 24/7? The Stocktonator. The reason why Wood has been passed around more times than a blunt in a cypher (he's played for five teams in five years) is because of immaturity and a lack of professionalism off the court. So far this season, Coach Casey has brought him along slowly and made him earn everything. Wood can score, provide tres, grabs boards, contribute defensive stats, and shoot efficiently from the field. Back on December 1st, Wood scored 28 points, grabbed 10 boards, dished out 2 dimes, blocked 1, and stole 1 in 22 minutes!!! That's the kind of upside we are talking about here. There's a chance Wood can carve out a more substantial role as the season progresses. For now, he can't be counted on but make preparations for when that time comes. Sort of like how the celebration of Christmas has evolved over the years. First, it was just about one day a year. Now, it's something that people begin preparing for right after Thanksgiving.
Brown Is the New Green
Money, money, money, monnnnnnnnnnnnnnnnnnnnney. Moooooooonnnnnnnnnnnnnneeeey. Love it or hate it, we need money to survive; to eat, cloth, and find shelter. The more you have, the greater number of times you can put cheese on that Whopper, get bling to accessorize the outfits, and/or accumulate various forms of entertainment. What's the color of money in the United States? Green. Lots of green is usually a good thing. Well, last night, Troy Brown Jr. was money.
26 9 7 1 1 0 2/4 9/15 6/7
Since Brown was money and money is green, then Brown is the new green. Don't bother Googling, I've done the research. The 26 points and 7 dimes were both career highs! Now, Davis Bertans did not play last night, so Brown's offense was needed. Don't expect this kind of performance every night, but Brown can provide some tres, boards, and steals when he plays. On the season, he's averaging 23.2 minutes per game. Over the past six games, that number has ticked up to 27.6. With all the injuries, Brown will be the main scoring option off the bench, so Brown can be money for as long as he continues getting the opportunities. Beep. Boop. Bop. You know what's always money? The Stocktonator.
Crime Down By the Brook
Brooks are serene, calm, and picturesque. But looks can be deceiving. I was once fishing at the local brook (I don't fish and I live in Los Angeles), when I heard some commotion behind me. There were two squirrels holding onto my bait box and trying to drag it back to the tree from which they came from. As I turned around and rose from the log I was parked on, I heard a splash behind me. A beaver had pulled the pail, which housed all the fish I caught, into the stream. A coordinated attack. After my inital anger, I was truly impressed. From that day, I always watched my six and didn't fall for the old "bird singing then shitting on my head" distraction. Anyways, Brook Lopez is big, tall, and lumbers around the court. He should bang down low, grab boards, and operate in the paint. But looks can be deceiving. Lopez likes to hang out on the perimeter and launch salvos from downtown. When he first entered the league, he was a boarding maniac. Now? Not so much. Business decisions. The most baffling aspect of his game, though, is his penchant for getting his 211 on. Don't believe me?
Last night was the fifth time in his career that Lopez has pilfered four in a game. Not something you expect from a lumbering giant such as Brook. Anyways, the one predictable and not surprising aspect of Brook's game is in the block department. Beep. Boop. Bop. You know what's always predictable? The Stocktonator. He's fifth in the league with 2.2 blocks per game. From a fantasy perspective, Brook is a top 70 player. The free throw shooting is excellent (90% on 2 attempts) and there's the aforementioned blocks. He provides 1.4 tres per game, but the scoring is way down from previous years due to the 38% shooting from the field. The minutes are also down to 26 from 28.7 last season. Brook is too good of a shooter to continue converting sub-40% from the field. I'd expect that to normalize as the season progresses.
Monk Returned to Society With a Bang
A monk is a person who chooses to dedicate his life to serving others or voluntarily leaves mainstream society to pray and contemplate life. I leave mainstream society often….to play fantasy sports. Fantasy monk? I kid, as I admire the discipline that monks have. I can't even stop myself from making my order a meal and supersizing. Anyways, Malik Monk was drafted by the Hornets with the 11th overall pick in 2017. Since that time, though, it's felt as though Monk has been locking himself up in the library, as we have not heard or seen much of him in the fantasy realm. But once in a while, he will rise up from the bench and deliver a performance that makes us remember. Last night was one of those games:
In 27 minutes off the bench. Now, P. J. Washington's injury afforded him some more run, so I wouldn't expect him to be an integral part of the team. At least not yet. He's just too inconsistent and doesn't contribute much outside of points and tres. With that said, he's still only 21 years old and there's a chance he discovers the 35 Chambers.
Channing is Ecstatic with Tatum's Performance
There was a time when Channing Tatum was an international sensation, as he starred in blockbusters such as Step Up, G. I. Joe, 21 Jump Street, White House Down, and the Lego Movie. Ok, maybe some hyperbole but 43 movies are 43 movies. Don't forget about the TV shows, video games, music videos, Saturday Night Live, and MTV Awards. Times started getting lean around 2014, though. The Google queries declined. The downloading of pics ceased. But then his phone began beeping incessantly in 2017, as he set up notifications whenever anyone Googled his name. He was back! Beep. Boop. Bop. You know what never leaves? The Stocktonator. Life was good again. Unfortunately, the queries all consisted of, "Is Jayson Tatum related to Channing Tatum?" Whatever, he took whatever he could get. Jayson Tatum was drafted by the Boston Celtics with the third overall pick in the 2017 NBA Draft. He was a sensation his rookie year, to the point where some were saying that they wouldn't trade him for Anthony Davis. Crazy. Anyways, the sophomore slump came and so did Channing's pain, as his phone stopped buzzing. But here we are in 2019, as Channing's phone has been off the hook, as his brother-from-another- mother has been balling out this season. Last night, he…..
His rookie year, Tatum ended as the 63rd player for fantasy. The following year, he finished as the 59th player. So far this season, he's the 33rd player. Over the past six games, Tatum has been a top 10 player!!! The points, tres, boards, dimes, and steals have all increased. The shooting efficiency has declined, which sucks because the volume has increased, but that's been the only blemish. The usage rate is 28 on the season, but it's ticked up to over 32 at times. People are going to be Googling Tatum's name for a long, long time. That makes Channing very happy.
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Q: Point-domain functions: $f(T), T(x,y)$ I'm doing a seminar paper in Computing and main part of my idea is mapping $x$ and $y$ components of a point into new $x$ and $y$, resulting in a new point. There is more, but that's the core idea.
I figured I'd use functions that take points as input and output new points. But I can't figure out a notation I should use. I'm actually BAS Computing student, I had mathematics, but not enough to figure this out on my own. And I failed to find the answer using Google.
The only alternative I can think of is using a function with 2 parameters, but concept is more intuitively software-implementable if I use point-based functions. I need both $x$ and $y$ for evaluation because of condition matching.
So how do I define a function that takes a point and maps it to a new point, including conditions regarding $x$ and $y$ components before mapping?
DOMAIN: $T_1(x, y)$, $x,y\in\mathbb{R}$
CODOMAIN: $T_2(f(x), g(x))$
EDIT:
The only way I managed to think of is this one:
$T(x,y)$
$h(T) = { T1(f(x), g(y)) | condition}$
Example condition: $h(T) = { T1(f(x), g(y)) | x>0, y>0}$
Is it correct or is there a better way?
A: I found out that function arguments are a tuple, and every point in space is representable in a tuple. So if I have...
$h(x,y)=(f(x),g(y))$
... I can just pass the 2D point without a bother and I'm sure to get a tuple, which could be assigned to a new 2D point. Please correct me if I'm wrong.
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Q: Centering a UILabel and a UIImage in a UIView with programatic constraints I am trying to create an interface like this:
However right now my code is generating one more like this:
Essentially the strategy is to create a center UIView function that sets the objects as a chain and then creates empty UIViews to their left and right that are equally maximally sized.
As you can see rather than the intended result the content is pushed as far right as possible. Any clue how I can fix this?
It would appear that the right view is not expanding at all. I did set their background colors to red and you could clearly see the left view expanded but the right view was not visible.
Please note that the text is of extremely variable length so no constants will work well here.
func setupUI() {
let label = UILabel()
label.translatesAutoresizingMaskIntoConstraints = false
superView.addSubview(label)
label.text = "Text"
label.font = UIFont(name: "", size: 13)
label.textAlignment = .center
label.topAnchor.constraint(equalTo: superView.topAnchor, constant: -6).isActive = true
label.setNeedsLayout()
label.invalidateIntrinsicContentSize()
let image = UIImageView(image: UIImage(named: "chevron.png"))
image.translatesAutoresizingMaskIntoConstraints = false
superView.addSubview(image)
image.widthAnchor.constraint(lessThanOrEqualToConstant: 20).isActive = true
image.heightAnchor.constraint(lessThanOrEqualToConstant: 20).isActive = true
image.contentMode = UIViewContentMode.scaleAspectFit
image.centerYAnchor.constraint(equalTo: label.centerYAnchor).isActive = true
center(objects: [label, image], parent: superView, debug: true)
}
func center(objects: [UIView], parent: UIView, debug: Bool = false) {
let sl = UIView()
sl.translatesAutoresizingMaskIntoConstraints = false
parent.addSubview(sl)
let sr = UIView()
sr.translatesAutoresizingMaskIntoConstraints = false
parent.addSubview(sr)
// Grow as much as you can
sl.widthAnchor.constraint(greaterThanOrEqualToConstant: 0).isActive = true
sr.widthAnchor.constraint(greaterThanOrEqualToConstant: 0).isActive = true
// Stay on the same row as them
sl.centerYAnchor.constraint(equalTo: objects.first!.centerYAnchor).isActive = true
sr.centerYAnchor.constraint(equalTo: objects.last!.centerYAnchor).isActive = true
// Set their height correctly
sl.heightAnchor.constraint(equalTo: objects.first!.heightAnchor).isActive = true
sr.heightAnchor.constraint(equalTo: objects.last!.heightAnchor).isActive = true
// Set them to hook into parent
sl.leadingAnchor.constraint(equalTo: parent.leadingAnchor).isActive = true
sr.trailingAnchor.constraint(equalTo: parent.trailingAnchor).isActive = true
// Get them to re-size (this seems to have no effect)
sr.setContentCompressionResistancePriority(UILayoutPriority.defaultHigh, for: UILayoutConstraintAxis.horizontal)
sl.setContentCompressionResistancePriority(UILayoutPriority.defaultHigh, for: UILayoutConstraintAxis.horizontal)
// Hook in the first and last object
objects.first!.leadingAnchor.constraint(equalTo: sl.trailingAnchor).isActive = true
objects.last!.trailingAnchor.constraint(equalTo: sr.leadingAnchor).isActive = true
// Chain the objects together
for i in 1..<objects.count {
objects[i].leadingAnchor.constraint(equalTo: objects[i-1].trailingAnchor).isActive = true
}
}
A: I would rather wrap the label and image in a UIStackView and center that stack view in parent view.
func center(objects: [UIView], parent: UIView, debug: Bool = false) {
let stackView = UIStackView(arrangedSubviews: objects)
stackView.translatesAutoresizingMaskIntoConstraints = false
stackView.alignment = .center
parent.addSubview(stackView)
NSLayoutConstraint.activate([
stackView.centerXAnchor.constraint(equalTo: parent.centerXAnchor),
stackView.centerYAnchor.constraint(equalTo: parent.centerYAnchor),
stackView.widthAnchor.constraint(lessThanOrEqualTo: parent.widthAnchor),
stackView.heightAnchor.constraint(lessThanOrEqualTo: parent.heightAnchor)
])
}
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{"url":"https:\/\/socratic.org\/questions\/how-do-you-find-the-general-solution-to-dy-dx-1-sec-2y","text":"# How do you find the general solution to dy\/dx=1\/sec^2y?\n\nJul 24, 2016\n\n$y = {\\tan}^{- 1} \\left(x + C\\right)$\n\n#### Explanation:\n\nwe can separate it\n\n$\\frac{\\mathrm{dy}}{\\mathrm{dx}} = \\frac{1}{\\sec} ^ 2 y$\n\n${\\sec}^{2} y \\frac{\\mathrm{dy}}{\\mathrm{dx}} = 1$\n\n$\\int \\setminus {\\sec}^{2} y \\frac{\\mathrm{dy}}{\\mathrm{dx}} \\setminus \\mathrm{dx} = \\int \\setminus \\mathrm{dx}$\n\n$\\int \\setminus \\frac{d}{\\mathrm{dx}} \\left(\\tan y\\right) \\setminus \\mathrm{dx} = \\int \\setminus \\mathrm{dx}$\n\n$\\tan y = x + C$\n\n$y = {\\tan}^{- 1} \\left(x + C\\right)$","date":"2021-12-07 00:21:42","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 7, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.925216555595398, \"perplexity\": 5420.210835170672}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-49\/segments\/1637964363327.64\/warc\/CC-MAIN-20211206224536-20211207014536-00563.warc.gz\"}"}
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Shutterstock/onair
# Complacency effect
Wealthier countries have less faith in vaccines, survey finds
91% of Irish people agreed that vaccines are important for children to have.
FRANCE HAS THE lowest levels of trust in vaccines globally, according to the world's biggest survey on public attitudes toward health and science, which was published today.
A third (33%) of French people do not agree that immunisation is safe, and it is also the only country where a majority (55%) believe science and technology will reduce the total number of jobs available, according to the poll of more than 140,000 people across 144 countries.
The survey of people aged 15 and older was devised by Wellcome, a British medical charity, and conducted by Gallup World Poll between April and December 2018.
91% of Irish people agreed that vaccines are important for children to have. Within the rest of the report, Ireland was included in the regional group of Northern Europe.
The study found that in some places – like Northern Europe and Northern America – people with higher levels of science education are less likely to disagree with the statement that vaccines are safe.
It also found that 58% of those surveyed in Northern Europe strongly agree that vaccines are effective.
'Complacency effect'
It found that people living in high-income countries have the lowest confidence in vaccines, a result that ties in to the rise of the anti-vaccination movement, in which people refuse to believe in the benefits of vaccinations or claim that the treatment is dangerous.
An estimated 169 million children missed out on the vital first dose of the measles vaccine between 2010 and 2017, according to a UN report issued in April.
In the US alone, the number of cases of the disease this year has exceeded a thousand, according to the latest official figures.
"I think we expected that general trend, because where we have seen that scepticism and concern about vaccines, that tends to be in more developed countries," Imran Khan, Wellcome's head of public engagement, who led the study, told AFP.
"But I think the extent of the difference is surprising and some of those numbers were really startling."
Wellcome Demographic breakdown Wellcome
Globally, 79% of people agreed that vaccines are safe and 84% said they were effective.
13-month-old admitted to intensive care after parents influenced by anti-vaccine material online
The Explainer: Why has Ireland had a 208% increase in measles cases?
New York declares public health emergency as measles outbreak hits Brooklyn
On the other end of the spectrum from France, Bangladesh and Rwanda had the highest levels of confidence in vaccines, with almost 100% in both countries agreeing they were safe, effective and important for children to have.
The lowest confidence levels in relation to vaccines were in Western Europe where more than a fifth (22%) of people disagree that vaccines are safe, and in Eastern Europe where 17% disagreed that vaccines are effective.
"I guess you could call it the 'complacency effect,'" said Khan.
If you look at those countries in our survey which have very high rates of confidence in vaccines, places like Bangladesh and Egypt, these are areas where you do have more infectious disease.
"Perhaps what you see is the people in those countries can see what happens if you don't vaccinate."
He added this contrasts with more developed countries where, "if you don't get vaccinated, you're still less likely to catch that infection, and if you do get infected, you might not become as unwell or might not die, because we've got quite good healthcare systems in place".
France was also the only country in the survey where most people believed science and technology would reduce jobs.
"Although much more research is needed to understand why this might be the case, the sluggish performance of the French economy over the last few years may be one factor that contributes to this sentiment," the report said.
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The report also found a global gender divide in self-reported levels of knowledge of science.
Globally, 49% of men worldwide say they know "some" or "a lot" about science, compared to 38% of women.
The gender gap existed even when men and women reported equal levels of science attainment, and was widest in the Northern European region.
"What's likely to be going on there is men are more confident or overconfident for the same level of knowledge, or equally we can say that women are under confident," said Khan.
Wellcome said it hoped its findings would provide governments with a baseline to monitor how attitudes change over time and help inform policy, particularly in regards to immunisation, with recent measles outbreaks demonstrating herd immunity can no longer be taken for granted.
Additional reporting from Adam Daly
COMPLACENCY EFFECT DISTRUST GALLUP WORLD POLL MISINFORMATION VACCINES WELLCOME
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\section{Introduction}
Let us consider the following optimal production planning problem with the uncertainties demand and the multi-time states cost functional in the productive cycle. Notice that, the demand of the society is always uncertainties which could be described by a stochastic differential equation as follows,
$$
y(t)=y(0)+\displaystyle\int_0^tb(s)ds+\displaystyle\int_0^t\sigma(s)dW(s),
$$
where $W(\cdot)$ is a standard Brownian motion under a probability space $(\Omega,\mathcal{F},\{\mathcal{F}_t\}_{0\leq t\leq T},P)$. In order to meet the demand, the factory will change the production rate $u(\cdot)$ with the demand $y(\cdot)$, i.e.,
$$
X(t)=X(0)+\displaystyle\int_0^t\big{[}u(s)-y(s)\big{]}ds.
$$
Consider the production capacity, the production rate $u(\cdot)$ may satisfy
$$
0\leq u(s)\leq K,\ \ 0\leq s\leq T,
$$
where $K$ is a constant.
In fact, the factory may have some limitation for inventory level $X(\cdot)$ in the productive cycle, i.e., for $0\leq t_1\leq t_2\leq \cdots\leq t_n$, there are constraints for $(X(t_1),X(t_2),\cdots,X(t_n))$,
\begin{equation}
\label{incons}
0\leq E[X(t_i)]\leq \alpha_i,\ \ i=1,2,\cdots,n.
\end{equation}
On the other hand, the factory need to pay the running cost for inventory and production, we denote it as $f(X(t),u(t))$ at time $t\in[0,T]$. Also, the factory need pay the disposal cost for inventory level $X(\cdot)$ at time $(t_1,t_2,\cdots,t_n)$, in general, we denote it as $\Psi(X(t_1),X(t_2),\cdots,X(t_n))$. Thus, the cost functional as follows,
\begin{equation}
\label{incos-1}
J(u(\cdot))=E\big{[}\displaystyle\int_0^Tf(X(t),u(t))dt+\Psi(X(t_1),X(t_2),\cdots,X(t_n))\big{]}.
\end{equation}
In this study, we will consider the following general state processes with the cost functional (\ref{incos-1}),
\begin{equation}
\label{ine-1}
X(s)=\int_{0}^{s}b(X(t),u(t))dt+\int_{0}^{s}\sigma(X(t),u(t))dW(t).
\end{equation}
Also, some constraints conditions which similar with equation (\ref{incons}) is considered.
In the case where $\Psi(X(t_1),X(t_2),\cdots,X(t_n))=\Psi(X(t_n))$ with $t_n=T$, there are many works concerning this subject. We refer Bensoussan \cite{B81} and Bismut \cite{B78} for the local maximum principle with the convex control set, and Peng \cite{P90} for the global maximum principle with general control domain which may not convex, for more see \cite{H76}. Recalling that dynamic programming with related HJB equations and maximum principle are powerful approaches for solving optimal control problems (see \cite{P90},\cite{P92}, \cite{WY08}, \cite{Y99} and \cite{P97}). The HJB equations derived for stochastic delay systems (see \cite{CW12}, \cite{M84} and \cite{M96}).
In our previous paper Yang \cite{Y16b}, the stochastic maximum principle for the above stochastic differential systems (\ref{ine-1}) with a general cost functional is developed. Further, in \cite{Y16b}, the terminal cost functional is $\Psi(X_{[0,T]})$, where $X_{[0,T]}=X(s)_{0\leq s\leq T}$. However, there are some strong assumptions about Fr\'{e}chet
derivatives in \cite{Y16b}, and the structure of which is too complicity, for more details see \cite{GY16,Y16a}.
In this study, we will remove the assumptions about Fr\'{e}chet derivatives in \cite{Y16b}. In the following, we present the details of this study. We first derive the maximum principle for the optimal control problem (\ref{incos-1}), the main difficult is that the cost functional has the part $\Psi(X(t_1),X(t_2),\cdots,X(t_n))$. At moment, for the limitation of technique, we assume that the control domain is convex. Then, we construct a series of first-order adjoint equations and establish the stochastic maximum principle via the duality technique. In the following, we investigate the sufficient conditions for the optimal control problem (\ref{incos-1}). Motivate with the beginning of this section, a constrains problem is developed and some usefull results is given. To the best of our knowledge, the sufficient conditions and constrains problem for optimal control problem (\ref{incos-1}) are first investigated in this study.
The paper is organized as follows: In Section 2, we present the stochastic optimal
control problem and show some examples to describe our main results. The proof of maximum principle theorem is given in Section 3. In Section 4, the sufficient conditions for optimality problem is investigated. In addition, we develop the constrains problem and obtain some usefull results in Section 5. In the end, we investigate a near optimal control problem for dealing with the model in \cite{Y16b} via the results in Section 3.
\section{The optimal control problem}
Let $W$ be a $d$-dimensional standard Brownian motion defined on a complete
filtered probability space $(\Omega,\mathcal{F},P;\{ \mathcal{F}(t)\}_{t\geq
0})$, where $\{ \mathcal{F}(t)\}_{t\geq0}$ is the $P$-augmentation of the
natural filtration generated by the Brownian motion $W$.
Let $T>0$ be given, consider the following controlled stochastic differential
equation,
\begin{equation}
d{X}(s)=b(X{(s)},u(s))ds+\sigma (X{(s)},u(s))dW(s) ,\quad s\in(0,T],\label{ODE_1}%
\end{equation}
with the initial condition $X(0)=x$, where
$u(\cdot)=\{u(s),s\in \lbrack0,T]\}$ is a control process taking value in a
convex set $U$ of $\mathbb{R}^m$ and $b,\sigma$ are given deterministic functions.
In this study, we consider the following multi-time states cost functional, which related with different objective at different time.
\begin{equation}
J(u(\cdot))=%
E\big{[}{\displaystyle \int \limits_{0}^{T}}
f(X{(t)},u(t))dt+\Psi(X(t_1),\cdots,X(t_n))\big{]},\label{cost-1}%
\end{equation}
with $0=t_0\leq t_1\leq \cdots \leq t_n=T$ and
\[%
\begin{array}
[c]{l}%
b:\mathbb{R}^m\times U\to \mathbb{R}^m,\\
\sigma:\mathbb{R}^{m}\times U\to \mathbb{R}^{m\times d},\\
f:\mathbb{R}^m\times U\to \mathbb{R},\\
\Psi:\mathbb{R}^{m\times n}\to \mathbb{R},\\
\end{array}
\]
we set $\sigma=(\sigma^1,\sigma^2,\cdots,\sigma^d)$, and $\sigma^j\in \mathbb{R}^m$ for $j=1,2,\cdots, d$.
Let $b,\sigma,f$ uniformly continuous and satisfy the following
linear growth and Lispschitz conditions.
\begin{assumption}
\label{ass-b}Suppose there exists a constant $c>0$ such that%
\[%
\begin{array}
[c]{c}%
\left| b(x_{1},u)-b(x_{2},u)\right| +\left| \sigma(x_{1},u)-\sigma(x_{2},u)\right|
\leq c\left|x_1-x_2 \right|,\\
\end{array}
\]
$\forall(x_{1},u),(x_{2},u)\in{\mathbb{R}^m}\times U$.
\end{assumption}
\begin{assumption}
\label{assb-b2}Suppose there exists a constant $c>0$ such that
\[
\left|b(x,u)\right|+\left|\sigma(x,u)\right| \leq c(1+\mid x \mid),\quad \forall(x,u)\in{\mathbb{R}^m}\times U.
\]
\end{assumption}
\begin{assumption}
\label{ass-fai}Let $b,\sigma,f,\Psi$ be first differentiable at $x$ and $u$, and their derivatives in $x$ are continuous in $(x,u)$.
\end{assumption}
Let $\mathcal{U}[0,T]=\{u(\cdot)\in L^2_{\mathcal{F}}(0,T;U)\}.$ Suppose
Assumptions \ref{ass-b} and \ref{assb-b2} hold, then there exists a unique
solution $X$ for equation (\ref{ODE_1}) (see \cite{LS78}).
Minimize (\ref{cost-1}) over $ \mathcal{U}[0,T].$ Any $\bar{u}(\cdot)\in \mathcal{U}[0,T]$
satisfying
\begin{equation}
J(\bar{u}(\cdot))= \underset{u(\cdot)\in\mathcal{U}[0,T]}{\inf}J(u(\cdot)) \label{cost-2}%
\end{equation}
is called an optimal control. The corresponding state trajectory $(\bar{u}(\cdot),\bar{X}(\cdot))$ are called an optimal state trajectory and optimal pair.
At very beginning, we will show some examples to describe the main results in the following sections. The first example verifies the maximum principle (necessary conditions) for the cost functional (\ref{cost-1}), the second one describes the optimal production planning problem with multi-time state constraints.
\begin{example}
Let $T=1$, the controlled stochastic differential equation as follows:
\begin{equation*}
d{X}^u(s)=u(s)dW(s),\text{ \ \ } 0 \leq s \leq 1,%
\end{equation*}
with the initial condition $X(0)=1$, where
$u(\cdot)=\{u(s),0\leq s\leq 1\}$ is a control process taking values in a
compact set $U=[0,1]$.
The cost functional is
\begin{equation}
J(u(\cdot))=\underset{u\in \mathcal{U}[0,1]}{\inf}E[-2(X^u(\frac{1}{2}))^2+(X^u(1))^2] \label{2ex-11}%
\end{equation}
and we can verify that
\begin{equation}
( \bar{u}(t),\bar{X}(t))=
\begin{cases}
(1,1+W(t)) &\mbox{if $0\leq t \leq \frac{1}{2}$},\\
(0,1+W(\frac{1}{2}))&\mbox{if $ \frac{1}{2} < t \leq 1$, }
\end{cases}
\end{equation}
is an optimal pair of systems (\ref{2ex-11}).
Next, we introduce the following first-order adjoint equations. \\
\begin{equation*}%
\begin{array}
[c]{ll}%
d{p}(t)= q(t)dW(t),\quad \frac{1}{2} < t < 1,\\
p(1)= -2\bar{X}(1)
\end{array}
\label{2prin-11}%
\end{equation*}
and
\begin{equation*}%
\begin{array}
[c]{ll}%
d{p}(t)= q(t)dW(t),\quad 0\leq t < \frac{1}{2}, \\
p(\frac{1}{2})= 4\bar{X}(\frac{1}{2})+p(\frac{1}{2}^{+}).
\end{array}
\label{2prin-12}%
\end{equation*}
The solutions of first-order adjoint equations as follows:
\begin{equation}
( p(t),q(t))=
\begin{cases}
(2+2W(t),2)&\mbox{ $0\leq t < \frac{1}{2}$,}\\
(-2-2W(\frac{1}{2}),0) &\mbox{ $ \frac{1}{2} < t \leq 1$. }\\
\end{cases}
\end{equation}
Thus,
\begin{equation}
H_u(\bar{X}(t),\bar{u}(t),p(t),q(t))(v-\bar{u}(t))=
\begin{cases}
2(v-1) &\mbox{ $0\leq t < \frac{1}{2}$,}\\
0 &\mbox{ $ \frac{1}{2} < t \leq 1$, }\\
\end{cases}
\end{equation}
with $v\in [0,1]$, thus, the optimal control pair $(\bar{u}(\cdot),\bar{X}(\cdot))$ satisfies the Theorem \ref{Maximumprinciple}.
\end{example}
\begin{example}
In this example, we consider the optimal production planning problem which is given in Section 1. Let $T=1$, the controlled stochastic differential equation as follows:
\begin{equation}
\label{3exp-1}
\begin{array}
[c]{ll}
{X}^u(s)=\displaystyle\int_0^s\big{[}u(t)-y(t)\big{]}dt,\\
\end{array}
\end{equation}
where $y(\cdot)$ denote the uncertainties of demand
$$
y(s)=\displaystyle\frac{8}{3} s- W(s)
$$
and $u(\cdot)=\{u(s),0\leq s\leq 1\}$ is a control process taking values in a
compact set $U=[0,2]$.
Thus, we minimum the following cost functional
\begin{equation}
J(u(\cdot))=E[X^u(\frac{1}{2})+X^u(1)], \label{1exa-1}%
\end{equation}
with the state constrains
$$
0\leq EX^u(\frac{1}{2}),\ \,0\leq EX^u(1).
$$
Substituting $X^u(\cdot)$ into equation (\ref{1exa-1}), one obtain
$$
J(u(\cdot))=E[2\displaystyle\int_0^{\frac{1}{2}}(u(t)-\frac{8}{3}t)dt+
\displaystyle\int_{\frac{1}{2}}^1(u(t)-\frac{8}{3}t)dt]
$$
and we can verify that
\begin{equation}
( \bar{u}(t),\bar{X}(t))=
\begin{cases}
(\frac{8}{3}t,\displaystyle \int_0^tW(s)ds) &\mbox{ $0\leq t \leq \frac{1}{2}$,}\\
(2,2t-\frac{4}{3}t^2-\frac{2}{3}+\displaystyle \int_0^tW(s)ds)&\mbox{ $ \frac{1}{2} < t \leq 1$, }
\end{cases}
\end{equation}
is an optimal pair of systems (\ref{1exa-1}).
Recalling that it is difficult to get the adjoint equation for state process (\ref{3exp-1}). In order to get the related adjoint equations. We rewrite equation (\ref{3exp-1}) as follows,
$$
X^u(s)-W(s)s=\displaystyle \int_0^s(u(t)-\frac{8}{3}t)dt-\displaystyle\int_0^stdW(t).
$$
Denote that $\delta X^u(s)=X^u(s)-W(s)s$, thus
$$
d\delta X^u(s)=[u(s)-\frac{8}{3}s]ds-sdW(s)
$$
and we have
$$
E[\delta X^u(\frac{1}{2})+\delta X^u(1)]=E[X^u(\frac{1}{2})+X^u(1)],
$$
which means that $( \bar{u}(t),\bar{X}(t)-W(s)s)$ is the optimal pair of the following cost functional,
\begin{equation}
\label{3exc-2}
\delta J(u(\cdot))=E[\delta X^u(\frac{1}{2})+\delta X^u(1)],
\end{equation}
with the following constrains conditions,
$$
0\leq E\delta X^u(\frac{1}{2}),\ \,0\leq E\delta X^u(1).
$$
Next, we introduce the following first-order adjoint equations for functional (\ref{3exc-2}).
\begin{equation*}%
\begin{array}
[c]{ll}%
d{p}(t)= q(t)dW(t),\quad \frac{1}{2} < t < 1,\\
p(1)= -(\beta^0+\beta^2)
\end{array}
\label{prin-11}%
\end{equation*}
and
\begin{equation*}%
\begin{array}
[c]{ll}%
d{p}(t)= q(t)dW(t),\quad 0\leq t < \frac{1}{2}, \\
p(\frac{1}{2})= -(\beta^0+\beta^1)+p(\frac{1}{2}^{+}).
\end{array}
\label{prin-12}%
\end{equation*}
where $(\beta^0,\beta^1,\beta^2)$ comes from Theorem \ref{ccc-th}. The solutions of first-order adjoint equations as follows:
\begin{equation}
( p(t),q(t))=
\begin{cases}
(-(2\beta^0+\beta^1+\beta^2),0) &\mbox{ $ 0\leq t < \frac{1}{2}$, }\\
(-(\beta^0+\beta^2),0)&\mbox{ $\frac{1}{2} < t < 1$.}
\end{cases}
\end{equation}
Now, let $\beta^0+\beta^2\leq0$ and $2\beta^0+\beta^1+\beta^2= 0$, one obtain,
\begin{equation}
H_u(\bar{X}(t)-W(t)t,\bar{u}(t),p(t),q(t))(v-\bar{u}(t))=
\begin{cases}
-(2\beta^0+\beta^1+\beta^2)(v-\frac{8}{3}t) &\mbox{ $ 0\leq t < \frac{1}{2}$, }\\
-(\beta^0+\beta^2) (v-2) &\mbox{ $\frac{1}{2} < t \leq 1$,}\\
\end{cases}
\end{equation}
with $v\in[0,2]$, thus, the optimal control pair $(\bar{u}(\cdot),\bar{X}(\cdot))$ satisfies the Theorem \ref{ccc-th}.
Notice that, under the same constraints for the parameter $(\beta^0,\beta^1,\beta^2)$, we can verify other optimal pair for the model (\ref{3exc-2}).
\end{example}
\section{Necessary conditions for optimality}
In this section, we give the well known pontryagin's stochastic maximum principle, which we will show the necessary conditions for optimal pairs.
Note that in cost functional (\ref{cost-1}), we consider a multi-states cost functional, which is very different from classical optimal control problem. Under a strong Fr\'{e}chet differentiable assumption, Yang \cite{Y16a,Y16b} studied the maximum principle for deterministic and stochastic systems. Also, we refer Gao and Yang \cite{GY16} for forward and backward stochastic system. In this study, we not only investigate the optimal control problem under a weak smooth condition, but also investigate a near optimal control model to cover \cite{Y16a,Y16b}. Since the optimal control set $U$ is convex, we only need to introduce the following first-order adjoint equations:
\begin{equation}%
\begin{array}
[c]{ll}%
-d{p}(t)= & \{b_x(\bar{X}{(t)},\bar{u}(t))^{\mathrm{T}}p(t)+ \displaystyle\sum_{j=1}^d\sigma_x^j(\bar{X}{(t)},\bar{u}(t))^{\text{T}}q^j(t) \\
&-f_x(\bar{X}{(t)},\bar{u}(t))\}dt-q(t)dW(t),\ t\in(t_{i},t_{i+1}),\\
p(t_{i+1})= &-E[\Psi_{x_{i+1}}(\bar{X}(t_1),\cdots,\bar{X}(t_n))|\mathcal{F}_{t_{i+1}}]+p(t_{i+1}^{+}),\text{ \ }i=0,1,\ldots,n-1,
\end{array}
\label{prin-1}%
\end{equation}
where "$\mathrm{T}$" means the transform of vector or matrix, $t_{i+1}^{+}$\ is the right limit of $t_{i+1}$, $\Psi_{x_{i+1}}(x(t_1),\cdots,x(t_n))$ means the first derivative of $\Psi$ about $x(t_{i+1})$ and $p(t_{n}^{+})=0$, also, we set $t_0=0$.
Denote that
\begin{equation*}
H(x,u,p,q)=b(x,u)^{\text{T}}p+\sum_{j=1}^d\sigma^j (x,u)^{\text{T}}q^j-f(x,u),\text{ \ \ }%
(x,u,p,q)\in \mathbb{R}^m\times U\times \mathbb{R}^m\times \mathbb{R}^{m\times d}.%
\end{equation*}
The main result of this section is the following theorem.
\begin{theorem}
\label{Maximumprinciple} Let Assumptions (\ref{ass-b})-(\ref{ass-fai}) hold,
and $(\bar{u}(\cdot),\bar{X}(\cdot))$ be an optimal pair of (\ref{cost-2}).
Then there exists $(p(\cdot),q(\cdot))$ satisfying the series of first-order adjoint equations (\ref{prin-1}) and respectively such that
\begin{equation}%
\begin{array}
[c]{ll}%
&H_u(\bar{X}(t),\bar{u}(t),p(t),q(t))(v-\bar{u}(t))\leq 0,\\
\end{array}
\label{prin-3}%
\end{equation}
for any $v\in U$ and $t \in(t_{i},t_{i+1})$, $i=0,1,\cdots,n-1$.
\end{theorem}
In the below, we will show the proof of the Theorem \ref{Maximumprinciple}.
The main difficult is to give the variational equation and adjoint equation
for multi-target terminal functional (\ref{cost-1}). For the limitation of technique in this section, we consider that $U$ is a convex set. Let $(\bar{u}(\cdot),\bar{X}(\cdot))$ be the given optimal pair. Let $0<\rho<1$ and $u(\cdot)+\bar{u}(\cdot)\in \mathcal{U}[0,T]$ be any given control. We define the following%
\[
u^{\rho}(t)=\bar{u}(t)+\rho u(t)=(1-\rho)\bar{u}(t)+\rho(u(t)+\bar{u}(t)),
\]
obviously, $u^{\rho}(\cdot)\in \mathcal{U}[0,T]$. The following Lemma is
useful for proving the Theorem \ref{Maximumprinciple}.
\begin{lemma}
\label{le-2} Let Assumptions (\ref{ass-b})-(\ref{ass-fai}) hold, and
$X^{\rho}(\cdot)$ be the solution of equation (\ref{ODE_1}) under the
control $u^{\rho}(\cdot)$, and $y^{}(\cdot)$ be the solutions
of the following equations:%
\begin{equation}
\label{apro-1}
\begin{array}
[c]{rl}%
d{y}(t)= & \big{[}b_{x}(\bar{X}{(t)},\bar{u}(t))y(t)+b_{u}(\bar{X}{(t)},\bar{u}(t)) u(t)\big{]}dt\\
&+ \displaystyle \sum_{j=1}^d\big{[} \sigma_{x}^j(\bar{X}{(t)},\bar{u}(t))y(t)+\sigma^j_u(\bar{X}{(t)},\bar{u}(t)) u(t)\big{]}dW^j(t), \\
y(0)= & 0,\quad t\in [0,T].
\end{array}
\end{equation}
Then%
\begin{equation}%
\begin{array}
[l]{l}%
\displaystyle\lim_{\rho\to 0}\displaystyle\sup_{t\in \lbrack0,T]}E\left|\rho^{-1} (X^{\rho}(t)-\bar{X}(t))-y(t)\right| =0, \\
\end{array}
\label{var-1}%
\end{equation}
and%
\begin{equation}%
\begin{array}
[c]{rl}
& \rho^{-1}J(u^{\rho}(\cdot))-J(\bar{u}(\cdot))\\
= &
{\displaystyle \sum \limits_{i=1}^{n}} E \big{[}\Psi_{x_i}(\bar{X}(t_1),\bar{X}(t_2),\cdots,\bar{X}(t_n))y(t_{i})\big{]} \\
& +
E{\displaystyle \int \limits_{0}^{T}}
\big{[}f_{x}(\bar{X}{(t)},\bar{u}(t))y(t)
+f_u(\bar{X}{(t)},\bar{u}(t)) u(t)\big{]}dt+o(1)\geq 0.
\end{array}
\label{var-3}%
\end{equation}
\end{lemma}
\textbf{Proof: }
Similar with the proof of Lemma 4.1 in \cite{P93}, we have equation (\ref{var-1}).
Note that%
\begin{equation}%
\begin{array}
[c]{rl}
& J(u^{\rho}(\cdot))-J(\bar{u}(\cdot))\\
= &E\big{[} \Psi(X^{\rho}(t_1),X^{\rho}(t_2),\cdots,X^{\rho}(t_n))-\Psi(\bar{X}(t_1),\bar{X}(t_2),\cdots,\bar{X}(t_n))\\
&+{\displaystyle \int \limits_{0}^{T}}
[f(X{}^{\rho}(t),u^{\rho}(t))-f(\bar{X}{(t)},\bar{u}(t))]dt\big{]},\\
\end{array}
\label{value-0}%
\end{equation}
which deduces that
\begin{equation}%
\begin{array}
[c]{rl}
& J(u^{\rho}(t))-J(\bar{u}(t))\\
= &\displaystyle \sum_{i=1}^nE\big{[} \Psi_{x_i}((\bar{X}(t_1),\bar{X}(t_2),\cdots,\bar{X}(t_n))({X}^{\rho}(t_i)-\bar{X}(t_i)) \big{]}\\
&+E\displaystyle \int \limits_{0}^{T}[f_x(\bar{X}{(t)},\bar{u}(t))(X^{\rho}(t)-\bar{X}{(t)})+
f_u(\bar{X}{(t)},\bar{u}(t))\rho u(t)]dt+o(\rho).
\end{array}
\label{value-1}%
\end{equation}
By equation (\ref{var-1}), it follows equation (\ref{var-3}).
This completes the proof. $\ \ \ \ \ \ \ \ \Box$
\bigskip
Based on the above Lemma, we now carry out the proof for Theorem
\ref{Maximumprinciple}.
\textbf{Proof of Theorem} \ref{Maximumprinciple}. For$\ t\in (
t_{i},t_{i+1}),$ applying the differential chain rule to $p(t)^{\rm{T}}y(t)$, we have%
\begin{equation}%
\begin{array}
[c]{rl}
&E\big{[} p(t_{i+1})^{\rm{T}}y(t_{i+1})-p(t_{i}^{+})^{\rm{T}}y(t_{i})\big{]}\\
=&E \big{[}-E[\Psi_{x_{i+1}}(\bar{X}(t_1),\cdots,\bar{X}(t_n))^{\rm T}|\mathcal{F}_{t_{i+1}}]y(t_{i+1})+p(t_{i+1}^{+})y(t_{i+1})-p(t_{i}^{+})y(t_{i}) \big{]}\\
=&E \big{[}-\Psi_{x_{i+1}}(\bar{X}(t_1),\cdots,\bar{X}(t_n))^{\rm T}y(t_{i+1})+p(t_{i+1}^{+})y(t_{i+1})-p(t_{i}^{+})y(t_{i}) \big{]}\\
=& E\displaystyle \int \limits_{t_i}^{t_{i+1}}\big{[}p(t)^{\text{T}}b_u(\bar{X}(t),\bar{u}(t))u(t)+\sum_{j=1}^d
q^j(t)^{\text{T}}\sigma_u^j (\bar{X}(t),\bar{u}(t))u(t)+f_x(\bar{X}(t),\bar{u}(t))^{\text{T}}y(t) \big{]}dt
\end{array}
\label{max-1}%
\end{equation}
Adding by $i$ on the both sides of equation (\ref{max-1}) from $0$ to $n-1$, it follows
\begin{equation*}%
\begin{array}
[c]{rl}
&{\displaystyle \sum \limits_{i=1}^{n}} E \big{[}-\Psi_{x_i}(\bar{X}(t_1),\bar{X}(t_2),\cdots,\bar{X}(t_n))y(t_{i})-\displaystyle \int \limits_{t_{i-1}}^{t_{i}}
\big{[}f_{x}(\bar{X}{(t)},\bar{u}(t))^{\rm T}y(t)
+f_u(\bar{X}{(t)},\bar{u}(t))^{\rm T}u(t)\big{]}dt\\
=& {\displaystyle \sum \limits_{i=1}^{n}} E\displaystyle \int \limits_{t_{i-1}}^{t_{i}}\big{[}p(t)^{\text{T}}b_u(\bar{X}(t),\bar{u}(t))u(t)+\sum_{j=1}^d
q^j(t)^{\text{T}}\sigma_u^j (\bar{X}(t),\bar{u}(t))u(t)
-f_u(\bar{X}(t),\bar{u}(t))^{\text{T}}u(t)\big{]}dt
\end{array}
\end{equation*}
By Lemma \ref{le-2}, we obtain
\begin{equation*}%
\begin{array}
[c]{rl}
&{\displaystyle \sum \limits_{i=1}^{n}} E\displaystyle \int \limits_{t_{i-1}}^{t_{i}}\big{[}p(t)^{\text{T}}b_u(\bar{X}(t),\bar{u}(t))u(t)+\sum_{j=1}^d
q^j(t)^{\text{T}}\sigma_u^j (\bar{X}(t),\bar{u}(t))u(t)
-f_u(\bar{X}(t),\bar{u}(t))^{\text{T}}u(t)\big{]}dt\\
=&{\displaystyle \sum \limits_{i=1}^{n}} E\displaystyle \int \limits_{t_{i-1}}^{t_{i}}
\big{[} H_u(\bar{X}(t),\bar{u}(t),p(t),q(t)){u}(t)\big{]}dt\leq o(1),
\end{array}
\end{equation*}
Letting $\rho\to 0$, thus
\begin{equation*}%
\begin{array}
[c]{ll}%
&H_u(\bar{X}(t),\bar{u}(t),p(t),q(t))(v-\bar{u}(t))\leq 0,\\
\end{array}
\end{equation*}
for any $v\in U$ and $t \in(t_{i},t_{i+1})$, $i=0,1,\cdots,n-1$.
This completes the proof. $\ \ \ \ \ \ \ \ \Box$
\section{Sufficient conditions for optimality}
In this section, we consider another problem when $(\bar{u}(\cdot),\bar{X}(\cdot))$ is an optimal control pair of problem (\ref{cost-2}). Thus, we show the sufficient conditions for optimality in the following.
\begin{theorem}
\label{sufo}
Suppose Assumptions (\ref{ass-b})-(\ref{ass-fai}) hold and $\Psi(\cdot)$ is convex and $H(\cdot,\cdot,p(t),q(t))$ is concave for any $t\in(t_{i},t_{i+1})$ with $i=0,1,\cdots,n-1$ almost surely, and such that
\begin{equation}
\label{suf-1}
H(\bar{X}(t),\bar{u}(t),p(t),q(t))=\max_{u\in U}H(\bar{X}(t),u,p(t),q(t)),
\end{equation}
where $(p(\cdot),q(\cdot))$ is the solution of equation (\ref{prin-1}) with $(\bar{X}(\cdot),\bar{u}(\cdot))$. Thus, $(\bar{X}(\cdot),\bar{u}(\cdot))$ is an optimal pair of problem (\ref{cost-2}).
\end{theorem}
\noindent\textbf{Proof}: From the minimum condition (\ref{suf-1}), one obtain
$$
H_u(\bar{X}(t),\bar{u}(t),p(t),q(t))=0.
$$
Then for any given pair $(X^u(\cdot),u(\cdot))$ which solves equation (\ref{ODE_1}), and notice that $H(\cdot,\cdot,p(t),q(t))$ is concave, we have
\begin{equation}
\label{suf-2}
\begin{array}
[c]{ll}%
&\displaystyle\int_0^T\big{[} H(X^u(t),u(t),p(t),q(t))- H(\bar{X}(t),\bar{u}(t),p(t),q(t))\big{]}dt\\
\leq & \displaystyle\int_0^TH_x(\bar{X}(t),\bar{u}(t),p(t),q(t))(X^u(t)-\bar{X}(t)) dt.\\
\end{array}
\end{equation}
In the following, we introduce the approximation equation which $\delta X(t)=X^u(t)-\bar{X}(t) $,
\begin{equation}
\label{suf-3}
\begin{array}
[c]{rl}%
d\delta X(t)=&\big{[}b_x(\bar{X}(t),\bar{u}(t))\delta X(t)+\xi(t) \big{]}dt\\
&+\displaystyle \sum_{j=1}^{d}\big{[} \sigma^j_x(\bar{X}(t),\bar{u}(t))\delta X(t)+\eta^j(t) \big{]}dW^j(t),\ t\in[0,T],\\
\delta X(t)=&0,
\end{array}
\end{equation}
where
\begin{equation*}
\begin{array}
[c]{rl}%
&\xi(t):=-b_x(\bar{X}(t),\bar{u}(t))\delta X(t)+b({X}^u(t),{u}(t))-b(\bar{X}(t),\bar{u}(t))\\
&\eta^j(t):=-\sigma^j_x(\bar{X}(t),\bar{u}(t))\delta X(t)+\sigma^j({X}^u(t),{u}(t))-\sigma^j(\bar{X}(t),\bar{u}(t)),\ 1\leq j \leq d. \\
\end{array}
\end{equation*}
For$\ t\in (
t_{i},t_{i+1}),$ applying the differential chain rule to $p(t)^{\rm{T}}\delta X(t)$, we have%
\begin{equation}%
\begin{array}
[c]{rl}
&E\big{[} p(t_{i+1})^{\rm{T}}\delta X(t_{i+1})-p(t_{i}^{+})^{\rm{T}}\delta X(t_{i})\big{]}\\
=&E \big{[}-E[\Psi_{x_{i+1}}(\bar{X}(t_1),\cdots,\bar{X}(t_n))^{\rm T}|\mathcal{F}_{t_{i+1}}]\delta X(t_{i+1})+p(t_{i+1}^{+})\delta X(t_{i+1})-p(t_{i}^{+})\delta X(t_{i}) \big{]}\\
=&E \big{[}-\Psi_{x_{i+1}}(\bar{X}(t_1),\cdots,\bar{X}(t_n))^{\rm T}\delta X(t_{i+1})+p(t_{i+1}^{+})\delta X(t_{i+1})-p(t_{i}^{+})\delta X(t_{i}) \big{]}\\
=& E\displaystyle \int \limits_{t_i}^{t_{i+1}}\big{[}p(t)^{\text{T}}\xi(t)+\sum_{j=1}^d
q^j(t)^{\text{T}}\eta^j(t)+f_x(\bar{X}(t),\bar{u}(t))^{\text{T}}\delta X(t) \big{]}dt.
\end{array}
\label{max-1}%
\end{equation}
Adding by $i$ on the both sides of equation (\ref{max-1}) from $0$ to $n-1$, it follows
\begin{equation*}%
\begin{array}
[c]{rl}
&{\displaystyle \sum \limits_{i=1}^{n}} E \big{[}-\Psi_{x_i}(\bar{X}(t_1),\bar{X}(t_2),\cdots,\bar{X}(t_n))\delta X(t_{i})\big{]}\\
=& {\displaystyle \sum \limits_{i=1}^{n}} E\displaystyle \int \limits_{t_{i-1}}^{t_{i}}\big{[}p(t)^{\text{T}}\xi(t)+\sum_{j=1}^d
q^j(t)^{\text{T}}\eta^j(t)
+f_x(\bar{X}(t),\bar{u}(t))^{\text{T}}\delta X(t)\big{]}dt.
\end{array}
\end{equation*}
From the representation of $\xi$ and $\eta^j$, we have
\begin{equation*}%
\begin{array}
[c]{rl}
&{\displaystyle \sum \limits_{i=1}^{n}} E \big{[}-\Psi_{x_i}(\bar{X}(t_1),\bar{X}(t_2),\cdots,\bar{X}(t_n))\delta X(t_{i})\big{]}+E \displaystyle \int_0^T H_x(\bar{X}(t),\bar{u}(t),p(t),q(t))\delta X(t)dt\\
=&E\displaystyle \int_0^T\big{[}p(t)^{\rm T}(b({X}^u(t),{u}(t))-b(\bar{X}(t),\bar{u}(t)))+\displaystyle\sum\limits_{i=1}^{d}
q^j(t)^{\text{T}}(\sigma^j({X}^u(t),{u}(t))-\sigma^j(\bar{X}(t),\bar{u}(t)))\big{]}dt
\end{array}
\end{equation*}
By inequality (\ref{suf-2}), it follows that
\begin{equation}%
\label{suf-4}
\begin{array}
[c]{rl}
&{\displaystyle \sum \limits_{i=1}^{n}} E \big{[}-\Psi_{x_i}(\bar{X}(t_1),\bar{X}(t_2),\cdots,\bar{X}(t_n))\delta X(t_{i})\big{]}\\
\leq & E\displaystyle \int_0^T\big{[}f({X}^u(t),{u}(t))-f(\bar{X}(t),\bar{u}(t)) \big{]}dt. \\
\end{array}
\end{equation}
Now, by the convexity of $\Psi$, we obtain
\begin{equation}%
\label{suf-5}
\begin{array}
[c]{rl}
&\displaystyle \sum \limits_{i=1}^{n}\Psi_{x_i}(\bar{X}(t_1),\bar{X}(t_2),\cdots,\bar{X}(t_n))\delta X(t_{i})\\
\leq & \Psi({X}^u(t_1),{X}^u(t_2),\cdots,{X}^u(t_n))
-\Psi(\bar{X}(t_1),\bar{X}(t_2),\cdots,\bar{X}(t_n)).
\end{array}
\end{equation}
Combining equations (\ref{suf-4}) and (\ref{suf-5}), we can verify that
$$
J(\bar{u}(\cdot))\leq J(u(\cdot)).
$$
By the arbitrary of $u(\cdot)$, we complete the proof. $\ \ \ \ \ \ \ \ \Box$
\section{Optimal control problem with state constraints}
In many applications of mathematics fiance and economics, we may have different constraints at different time of the state process $X(\cdot)$, i.e., in the cost functional (\ref{cost-1}), let
$$
\Phi(X(t_1),X(t_2),\cdots,X(t_n))=\displaystyle\sum_{i=1}^n\phi(X(t_i)),
$$
then, in this case, our objective may be
$$
E\phi(X(t_i))\leq \alpha_i,\ \ i=1,2,\cdots,n,
$$
where $\alpha_i$ is a given constant. On the other hand, one may concern different combination of $(X(t_1),X(t_2),\cdots,X(t_n))$, or a general case,
$$
E\Phi(X(t_1),X(t_2),\cdots,X(t_n))\leq \alpha,
$$
where $\alpha$ is a given constant.
In the following, we will first investigate the state equation (\ref{ODE_1}) with the below cost functional,
\begin{equation}
J(u(\cdot))=%
E\big{[}{\displaystyle \int \limits_{0}^{T}}
f(X{(t)},u(t))dt+\displaystyle\sum_{i=1}^n\phi(X(t_i))\big{]},\label{cost-3}%
\end{equation}
and the state process $X(\cdot)$ satisfies
\begin{equation}
\label{ccc-1}
E\phi(X(t_i))\leq \alpha_i,\ \ i=1,2,\cdots,n,
\end{equation}
where $\alpha_i$ is a given constant.
In order to prove the main result of this section, we introduce the following lemma which comes from Yong and Zhou Corollary 6.3 in \cite{Y99}.
\begin{lemma}
\label{ccc-le1}
Let $F:V\to \mathbb{R}$ be a continuous function on complete metric space $(V,\tilde{d})$. Given $\theta>0$ and $v_0\in V$ such that
$$
F(v_0)\leq \inf_{v\in V}F(v)+\theta.
$$
Then there exists a $v_{\theta}\in V$ such that
$$
F(v_{\theta})\leq F(v_0),\ \ \tilde{d}(v_{\theta},v_0)\leq \sqrt{\theta},
$$
and for all $v\in V$,
$$
- \sqrt{\theta}d(v_{\theta},v)\leq F(v)-F(v_{\theta}).
$$
\end{lemma}
Next, we present the main results of this section, the related Hamiltonian as follows,
\begin{equation*}
H(\beta^0,x,u,p,q)=b(x,u)^{\text{T}}p+\sum_{j=1}^d\sigma^j (x,u)^{\text{T}}q^j-\beta^0f(x,u),\text{ \ \ }
\end{equation*}
whith $(\beta^0,x,u,p,q)\in \mathbb{R}\times\mathbb{R}^m\times U\times \mathbb{R}^m\times \mathbb{R}^{m\times d}.$
\begin{theorem}
\label{ccc-th}
Let Assumptions (\ref{ass-b})-(\ref{ass-fai}) hold,
and $(\bar{u}(\cdot),\bar{X}(\cdot))$ be an optimal pair of (\ref{cost-3}).
Then there exists $(\beta^0,\beta^1,\cdots,\beta^n)\in \mathbb{R}^{n+1}$ satisfying
$$
\beta^0\geq 0,\ \ \left| \beta^0\right|^2+\displaystyle\sum_{j=1}^n\left| \beta^j\right|^2=1,
$$
and
$$
\displaystyle\sum_{j=1}^n\beta^j(\gamma^j-E\phi(\bar{X}(t_j)))\leq 0,\ \gamma^j\leq \alpha^j,\ j=1,2,\cdots,n,
$$
and the adapted solution $(p(\cdot),q(\cdot))$ satisfying the following series of first-order adjoint equations,
\begin{equation}%
\begin{array}
[c]{ll}%
-d{p}(t)= & \{b_x(\bar{X}{(t)},\bar{u}(t))^{\mathrm{T}}p(t)+ \displaystyle \sum_{j=1}^d\sigma_x^j(\bar{X}{(t)},\bar{u}(t))^{\text{T}}q^j(t) \\
&-\beta^0f_x(\bar{X}{(t)},\bar{u}(t))\}dt-q(t)dW(t),\ t\in(t_{i-1},t_{i}),\\
p(t_{i})= &-(\beta^0+\beta^i)E[\Psi_{x_i}(\bar{X}(t_1),\cdots,\bar{X}(t_n))|\mathcal{F}_{t_i}]+p(t_{i}^{+}),\text{ \ }i=1,2,\ldots,n,
\end{array}
\label{prin-1}%
\end{equation}
and respectively such that
\begin{equation}%
\begin{array}
[c]{ll}%
&H_u(\beta^0,\bar{X}(t),\bar{u}(t),p(t),q(t))(v-\bar{u}(t))\leq 0,\\
\end{array}
\label{prin-3}%
\end{equation}
for any $v\in U$ and $t \in(t_{i},t_{i+1})$, $i=0,1,\cdots,n-1$.
\end{theorem}
\noindent\textbf{Proof}: Without loss of generality, we can assume that $J(\bar{u}(\cdot))=0$ where $(\bar{u}(\cdot),\bar{X}(\cdot))$ is the optimal pair of problem (\ref{cost-3}) with constraints (\ref{ccc-1}). For any $\theta>0$, we set
$$
J^{\theta}(u(\cdot))=\sqrt{\big{[}(J(u(\cdot))+\theta)^+\big{]}^2
+\displaystyle\sum_{i=1}^n\big{[}(E\phi(X^u(t_i))-\alpha_i)^+\big{]}^2}.
$$
From Assumption \ref{ass-fai}, one can verify that $J^{\theta}:\mathcal{U}[0,T]\to \mathbb{R}$ is continuous and satisfies
\begin{equation}
J^{\theta}(\bar{u}(\cdot))=\theta\leq \inf_{u\in\mathcal{U}[0,T]}J^{\theta}(u(\cdot))+\theta.
\end{equation}
Now, by Lemma \ref{ccc-le1}, there exists a $u^{\theta}(\cdot)\in \mathcal{U}[0,T]$ such that
\begin{equation}
\label{ccci-ev}
J^{\theta}(u^{\theta}(\cdot))\leq J^{\theta}(\bar{u}(\cdot))=\theta,\ \tilde{d}(u^{\theta}(\cdot),\bar{u}(\cdot))\leq \sqrt{\theta},
\end{equation}
where $\tilde{d}(u^1(\cdot),u^2(\cdot))=E\big{[}\displaystyle\int_0^T\left|u^1(t)-u^2(t)\right|^2dt\big{]}$. And we can check that $(\mathcal{U}[0,T],\tilde{d})$ is a complete metric space. Also, we have
\begin{equation*}
-\sqrt{\theta}\tilde{d}(u^{\theta}(\cdot),u(\cdot))\leq J^{\theta}(u(\cdot))-J^{\theta}(u^{\theta}(\cdot)),\ \forall u(\cdot) \in \mathcal{U}[0,T],
\end{equation*}
which deduces that
\begin{equation}
\label{cos-40}
J^{\theta}(u^{\theta}(\cdot))+\sqrt{\theta}\tilde{d}(u^{\theta}(\cdot),u^{\theta}(\cdot))\leq J^{\theta}(u(\cdot))+\sqrt{\theta}\tilde{d}(u^{\theta}(\cdot),u(\cdot)),\ \forall u(\cdot) \in \mathcal{U}[0,T].
\end{equation}
Thus, inequality (\ref{cos-40}) shows that $(u^{\theta}(\cdot),X^{\theta}(\cdot))$ is the optimal pair for the following cost functional
\begin{equation}
\label{cos-4}
J^{\theta}(u(\cdot))+\sqrt{\theta}\tilde{d}(u^{\theta}(\cdot),u(\cdot)),
\end{equation}
without the state constraint.
Since $U$ is a convex set, for any $\rho>0$, let $u^{\theta}(\cdot)+u(\cdot)\in \mathcal{U}[0,T]$, we define
$$
u^{\theta,\rho}(t)=u^{\theta}(t)+\rho u(t),
$$
which belongs to $ \mathcal{U}[0,T]$. It is easy to verify that
$$
\tilde{d}(u^{\theta,\rho}(\cdot),u^{\theta}(\cdot))=\rho E\displaystyle\int_0^T\left|u(t)\right|^2dt.
$$
For notation simplicity, we set $C^u=E\displaystyle\int_0^T\left|u(t)\right|^2dt$, by equation (\ref{cos-40}), one obtain
\begin{equation}%
\begin{array}
[c]{rl}%
-\sqrt{\theta}\rho C^u\leq & J^{\theta}(u^{\theta,\rho}(\cdot))-J^{\theta}(u^{\theta}(\cdot))\\
=&\displaystyle\frac{\big{[}(J(u^{\theta,\rho}(\cdot))+\theta)^+\big{]}^2-\big{[}(J(u^{\theta}(\cdot))+\theta)^+\big{]}^2
}
{J^{\theta}(u^{\theta,\rho}(\cdot))+J^{\theta}(u^{\theta}(\cdot))}\\
&+\displaystyle\frac{\sum_{j=1}^n\big{[}\big{[}(E\phi(X^{\theta,\rho}(t_j))-\alpha^j)^+\big{]}^2-
\big{[}(E\phi(X^{\theta}(t_j))-\alpha^j)^+\big{]}^2\big{]}}
{J^{\theta}(u^{\theta,\rho}(\cdot))+J^{\theta}(u^{\theta}(\cdot))},\\
\end{array}
\label{ccci-1}%
\end{equation}
where $X^{\theta,\rho}(\cdot))$ and $X^{\theta}(\cdot))$ are the related solution of equation (\ref{ODE_1}) with controls $u^{\theta,\rho}(\cdot)$ and $u^{\theta}(\cdot)$. Setting
\begin{equation}%
\begin{array}
[c]{ll}%
\beta^{0,\theta}=\displaystyle\frac{\big{[}J(u^{\theta}(\cdot))+\theta\big{]}^+}{J^{\theta}(u^{\theta}(\cdot))},\\
\beta^{j,\theta}=\displaystyle\frac{\big{[}E\phi(X^{\theta}(t_j))-\alpha^j\big{]}^+}
{J^{\theta}(u^{\theta}(\cdot))},\ j=1,2,\cdots,n.\\
\end{array}
\label{ccci-2}%
\end{equation}
Then, by the continuity of $J^{\theta}(\cdot)$ and Assumption \ref{ass-fai}, we have
\begin{equation}%
\begin{array}
[c]{rl}%
& J^{\theta}(u^{\theta,\rho}(\cdot))-J^{\theta}(u^{\theta}(\cdot))\\
=&\beta^{0,\theta}\big{[}J(u^{\theta,\rho}(\cdot))-J(u^{\theta}(\cdot))\big{]}+
\displaystyle\sum_{j=1}^n\beta^{j,\theta}\big{[}E\phi(X^{\theta,\rho}(t_j))
-E\phi(X^{\theta}(t_j))\big{]}+o(1),\\
=&E\big{[}\displaystyle\sum_{j=1}^n(\beta^{0,\theta}+\beta^{j,\theta})(\phi(X^{\theta,\rho}(t_j))
-\phi(X^{\theta}(t_j)))\\
&+\beta^{0,\theta}\displaystyle\int_0^T\big{[}f(X^{\theta,\rho}(t),u^{\theta,\rho}(t))-
f(X^{\theta}(t),u^{\theta}(t))\big{]}dt \big{]}+o(\rho),
\end{array}
\label{ccci-3}%
\end{equation}
where $o(1)$ converges to $0$ when $\rho\to 0$.
Similar with Lemma \ref{le-2}, let $(\bar{X}(\cdot),\bar{u}(\cdot))$ be replaced by $(X^{\theta}(t),u^{\theta}(t))$, and $y(\cdot)$ be replaced by $\tilde{y}(\cdot)$ in equation (\ref{apro-1}). Thus, one obtain,
\begin{equation}%
\begin{array}
[c]{rl}
-\sqrt{\theta} C^u\leq & \rho^{-1}\big{[}J^{\theta}(u^{\theta,\rho}(\cdot))-J^{\theta}(u^{\theta}(\cdot))\big{]}\\
\leq &
E \big{[}\displaystyle\sum_{j=1}^n(\beta^{0,\theta}+\beta^{j,\theta})\phi_{x}(X^{\theta}(t_j))
\tilde{y}(t_{j})\big{]} \\
& +
\beta^{j,\theta}E{\displaystyle \int \limits_{0}^{T}}
\big{[}f_{x}(X^{\theta}(t),u^{\theta}(t))\tilde{y}(t)
+f_u(X^{\theta}(t),u^{\theta}(t))u(t)\big{]}dt+o(1).
\end{array}
\label{ccci-4}%
\end{equation}
In addition, we introduce the following adjoint equation,
\begin{equation}%
\begin{array}
[c]{rl}%
-d{p}^{\theta}(t)= & \{b_x(X^{\theta}(t),u^{\theta}(t))^{\mathrm{T}}p^{\theta}(t)+ \sum_{j=1}^d\sigma_x^j(X^{\theta}(t),u^{\theta}(t))^{\text{T}}q^{j,{\theta}}(t) \\
&-\beta^{0,\theta}f_x(X^{\theta}(t),u^{\theta}(t))\}dt-q^{\theta}(t)dW(t),\ t\in(t_{i-1},t_{i}),\\
p^{\theta}(t_{i})= &-(\beta^{0,\theta}+\beta^{i,\theta})E[\phi_{x}({X}^{\theta}(t_i))]+p(t_{i}^{+}),\text{ \ }i=1,\ldots,n,
\end{array}
\label{ccci-5}%
\end{equation}
where $q^{\theta}(\cdot)=(q^{1,\theta}(\cdot),q^{2,\theta}(\cdot),\cdots,q^{d,\theta}(\cdot))$.
Now, using the duality relation as in the proof of Theorem \ref{Maximumprinciple}, it follows that,
$$
{\displaystyle \sum \limits_{i=1}^{n}} E\displaystyle \int \limits_{t_{i-1}}^{t_{i}}
\big{[} H_u(\beta^{0,\theta},X^{\theta}(t),u^{\theta}(t),p^{\theta}(t),q^{\theta}(t)){u}(t)\big{]}dt\leq o(1)+\sqrt{\theta} C^u,
$$
Notice that $o(1) \to 0$ when $\rho\to 0$. Thus, letting $\rho\to 0$, one obtain
\begin{equation}
\label{ccci-6}
{\displaystyle \sum \limits_{i=1}^{n}} E\displaystyle \int \limits_{t_{i-1}}^{t_{i}}
\big{[} H_u(\beta^{0,\theta},X^{\theta}(t),u^{\theta}(t),p^{\theta}(t),q^{\theta}(t)){u}(t)\big{]}dt\leq \sqrt{\theta} C^u.
\end{equation}
From inequality (\ref{ccci-ev}), it follows that $u^{\theta}(\cdot)$ converges to $\bar{u}(\cdot)$ under $\tilde{d}$ as $\theta\to 0$. Then, by Assumptions \ref{ass-b}, \ref{assb-b2} and \ref{ass-fai}, and basic theory of stochastic differential equation, we have
$$
\displaystyle \sup_{0\leq t\leq T}E\left|X^{\theta}(t)-\bar{X}(t)\right| \to 0,
$$
as $\theta\to 0$. By equation (\ref{ccci-2}), we have
\begin{equation}
\label{unq-1}
\left|\beta^{0,\theta}\right|^2+\displaystyle\sum_{j=1}^n\left|\beta^{j,\theta}\right|^2=1.
\end{equation}
Thus, we can choice a sequence $\{\theta_k\}_{k=1}^{\infty}$ satisfying $\displaystyle\lim_{k\to\infty}\theta_k=0$ and such that the limitations of $\beta^{0,\theta_k}$ and $\beta^{j,\theta_k}$ exist and we set
\begin{equation}
\begin{array}
[c]{ll}
\beta^{0}=\displaystyle\lim_{k\to\infty}\beta^{0,\theta_k},\\
\beta^{j}=\displaystyle\lim_{k\to\infty}\beta^{j,\theta_k},\\
\end{array}
\end{equation}
with $j=1,2,\cdots,n$. From equation (\ref{unq-1}), we have
$$
\left|\beta^{0}\right|^2+\displaystyle\sum_{j=1}^n\left|\beta^{j}\right|^2=1,
$$
and
$$
\displaystyle\sum_{j=1}^n\beta^j(\gamma^j-E\phi(\bar{X}(t_i)))\leq 0,\ \gamma^j\leq \alpha^j,\ j=1,2,\cdots,n.
$$
Similarly, we can prove that
$$
\displaystyle \sup_{0\leq t\leq T}E\big{[}\left|p^{\theta_k}(t)-p(t)\right|^2+\int_0^T\left|q^{\theta_k}(t)-q(t)\right|^2 \big{]} dt\to 0,
$$
as $k\to\infty$. Letting $k\to \infty$, from equation (\ref{ccci-6}), we have
\begin{equation}
{\displaystyle \sum \limits_{i=1}^{n}} E\displaystyle \int \limits_{t_{i-1}}^{t_{i}}
\big{[} H_u(\beta^{0},\bar{X}(t),\bar{u}(t),p(t),q(t)){u}(t)\big{]}dt\leq 0.
\end{equation}
Thus, we complete this proof. $\ \ \ \ \ \ \ \ \ \ \ \ \Box$
\begin{remark}
\label{re-2}
Similarly with the proof in Theorem \ref{ccc-th}, we can deal with other constraints conditions, i.e.,
$$
\underline{\alpha}_i\leq E\phi(X(t_i))\leq \overline{\alpha}_i,\ \ i=1,2,\cdots,n,
$$
where $(\underline{\alpha}_i,\overline{\alpha}_i)_{i=1}^n$ are given constants, or
$$
\underline{\alpha}\leq E\Phi(X(t_1),X(t_2),\cdots,X(t_n))\leq \overline{\alpha}.
$$
\end{remark}
\section{Near optimality for general case}
Recalling that in our previous paper \cite{Y16b}, we consider the state process (\ref{ODE_1}) with the following general cost functional,
\begin{equation}
J(u(\cdot))=%
E\big{[}{\displaystyle \int \limits_{0}^{T}}
f(X{(t)},u(t))dt+\Phi(X_{[0,T]})\big{]},\label{gcosf-1}%
\end{equation}
where $X_{[0,T]}:=X(s)_{0\leq s \leq T},$ which is the path of $X(\cdot)$ from $0$ to $T$. In \cite{Y16b}, under a strong assumption about Fr\'{e}chet derivatives, the maximum principle for cost functional (\ref{gcosf-1}) is given by solving a sequence of new adjoint equations. In this section, we will remove the strong assumption about Fr\'{e}chet derivatives and develop a near maximum principle for the cost functional (\ref{gcosf-1}) via the argument in Section 3. For notation simplicity, we set $m=d=1$.
\begin{assumption}
\label{assn-1}
Suppose $\Psi$ is Lipschatiz continuous on $\mathbb{C}[0,T]$, there exists a constant $c>0$ such that
$$
\left|\Phi(x^1_{[0,T]})-\Phi(x^2_{[0,T]})\right|\leq c \max_{0\leq t\leq T}\left|x^1(t)-x^2(t)\right|,
$$
where $x^1_{[0,T]},x^2_{[0,T]}\in \mathbb{C}[0,T]$, and $\mathbb{C}[0,T]$ is the set of continuous functions over $[0,T]$.
\end{assumption}
By Assumptions \ref{assn-1}, one obtain that there exists a larger enough integer $N>0$, for $n>N$ such that
$$
\left|\Phi(x(t_1),x(t_2),\cdots,x(t_n))-\Phi(x_{[0,T]})\right|\leq c\max_{1\leq j\leq n}\sup_{t_{j-1}\leq t\leq t_{j}} \left|x(t)-x(t_j)\right|,
$$
with $t_0=0$ and $c$ is the constant in Assumptions \ref{assn-1}. Next, we define the approximation function for $\Phi(x(t_1),x(t_2),\cdots,x(t_n))$ as follows,
\begin{equation}
\label{gae-1}
\begin{array}
[c]{rl}
{\Phi}^{\varepsilon}(x(t_1),x(t_2),\cdots,x(t_n))=&\displaystyle\int_{\mathbb{R}^n}\big{[}\Phi(x(t_1),x(t_2),\cdots,x(t_n))
\psi^{\varepsilon}(y_1-x(t_1))\\
&\times\psi^{\varepsilon}(y_2-x(t_2))\cdots
\psi^{\varepsilon}(y_n-x(t_n))\big{]}dy_1dy_2\cdots dy_n,\\
\end{array}
\end{equation}
with $(x(t_1),x(t_2),\cdots,x(t_n))\in \mathbb{R}^{n}$, and $\psi^{\varepsilon}(x)=\frac{1}{\sqrt{2\pi \varepsilon^2}}e^{-\frac{x^2}{2\varepsilon^2}}$ for $x\in \mathbb{R}$. Thus, we have the following Lemma.
\begin{lemma}
\label{visle-1}
There exists a constant $C>0$ such that
\begin{equation*}
\begin{array}
[c]{ll}
\left|{\Phi}^{\varepsilon}(x(t_1),x(t_2),\cdots,x(t_n))-{\Phi}(x(t_1),x(t_2),\cdots,x(t_n))\right|\leq C\varepsilon,\\
\end{array}
\end{equation*}
$\forall (x(t_1),x(t_2),\cdots,x(t_n))\in \mathbb{R}^{n}$.
\end{lemma}
\textbf{Proof}: We just prove the case $n=1$. For general case, we can use the same method. Similarly, we can obtain the other inequalities. By equation (\ref{gae-1}), for fixed $x$, we have,
\begin{equation}
\begin{array}
[c]{ll}
&|{\Phi}^{\varepsilon}(x)-\Phi(x)|\\
\leq & \displaystyle\int_{\mathbb{R}}\left|\Phi(x^0)-\Phi(x)
\right|\frac{1}{\sqrt{2\pi \varepsilon^2}}e^{-\frac{(x^0-x)^2}{2\varepsilon^2}}dx^0\\
\leq & C \displaystyle\int_{\mathbb{R}}\left|x^0-x
\right|\frac{1}{\sqrt{2\pi \varepsilon^2}}e^{-\frac{(x^0-x)^2}{2\varepsilon^2}}dx^0\\
=&C\varepsilon\displaystyle\int_{\mathbb{R}}{|\tilde{x}^0|}\frac{1}{\sqrt{2\pi}}
e^{-\frac{(\tilde{x}^0)^2}{2}}d\tilde{x}^0\\
\leq & C \varepsilon,
\end{array}
\end{equation}
where $C$ will change line by line.
This completes the proof. $\ \ \ \ \ \ \ \ \ \Box$
\begin{remark}
\label{re-1}
Notice that $\psi\in\mathbb{C}^{\infty}[\mathbb{R}]$, by the property of convolution, we obtain that $\Phi^{\varepsilon}(x(t_1),x(t_2),\cdots,x(t_n))$ is second differentiable about $(x(t_1),x(t_2),\cdots,x(t_n))\in\mathbb{R}^n$.
\end{remark}
In the following, we introduce the near optimal control problem,
\begin{equation}
{J}^{\varepsilon}(u(\cdot))=%
E\big{[}{\displaystyle \int \limits_{0}^{T}}
f(X{(t)},u(t))dt+\Phi^{\varepsilon}(X(t_1),X(t_2),\cdots,X(t_n))\big{]}.\label{gcosf-2}%
\end{equation}
By Assumptions \ref{ass-b} and \ref{assb-b2}, we can obtain the following results.
\begin{theorem}
\label{gle-1}
Let Assumptions \ref{ass-b} and \ref{assb-b2} hold, then, there exists a constant $C>0$ such that
$$
\left|\displaystyle\inf_{u\in\mathcal{U}[0,T]}J(u(\cdot))-\displaystyle\inf_{u\in\mathcal{U}[0,T]}{J}^{\varepsilon}(u(\cdot))\right|\leq C\varepsilon
$$
\end{theorem}
Now, we can use the results in the above sections to investigate the near optimal control theory for optimal control problem (\ref{gcosf-1}).
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,333
|
var test = require('./lib/tape-nock-setup');
var BBY = require('../');
const NS_PER_SEC = 1000000000;
test('Test Rate Limiting 1 per second', test.opts, function (t) {
var bby = BBY({
key: process.env.BBY_API_KEY || 'XXX',
debug: false,
headers: {
'User-Agent': 'rate limiter tests'
},
requestsPerSecond: 1
});
var start = process.hrtime();
var promises = [
bby.version(),
bby.version(),
bby.version()
];
Promise.all(promises)
.then(result => {
var diff = process.hrtime(start);
var totalTime = diff[0] * NS_PER_SEC + diff[1];
t.ok(totalTime > (promises.length - 1) * NS_PER_SEC, `took more than 2 seconds (${totalTime / NS_PER_SEC})`);
t.end();
})
.catch(error => {
t.error(error);
t.end();
});
});
test('Test Rate Limiting default 5 per second', test.opts, function (t) {
var bby = BBY({
key: process.env.BBY_API_KEY || 'XXX',
debug: false,
headers: {
'User-Agent': 'rate limiter tests'
}
});
var start = process.hrtime();
var promises = [
bby.version(),
bby.version(),
bby.version(),
bby.version(),
bby.version(),
bby.version(),
bby.version(),
bby.version(),
bby.version(),
bby.version()
];
Promise.all(promises)
.then(result => {
var diff = process.hrtime(start);
var totalTime = diff[0] * NS_PER_SEC + diff[1];
t.ok(totalTime > 1 * NS_PER_SEC, `took more than 1 second (${totalTime / NS_PER_SEC})`);
t.end();
})
.catch(error => {
t.error(error);
t.end();
});
});
test('Test Rate Limiting default 5 per second with debug', test.opts, function (t) {
var bby = BBY({
key: process.env.BBY_API_KEY || 'XXX',
debug: true,
headers: {
'User-Agent': 'rate limiter tests'
}
});
var start = process.hrtime();
var promises = [
bby.version(),
bby.version(),
bby.version(),
bby.version(),
bby.version(),
bby.version(),
bby.version(),
bby.version(),
bby.version(),
bby.version()
];
Promise.all(promises)
.then(result => {
var diff = process.hrtime(start);
var totalTime = diff[0] * NS_PER_SEC + diff[1];
t.ok(totalTime > 1 * NS_PER_SEC, `took more than 1 second (${totalTime / NS_PER_SEC})`);
t.end();
})
.catch(error => {
t.error(error);
t.end();
});
});
test('cooldown for rate limit reset', test.opts, function (t) {
setTimeout(t.end, 5000);
});
test('Test Rate Limiting torture test', test.opts, function (t) {
var bby = BBY({
key: process.env.BBY_API_KEY || 'XXX',
debug: false,
headers: {
'User-Agent': 'rate limiter tests'
},
requestsPerSecond: 5
});
var start = process.hrtime();
var promises = [
bby.version(), bby.version(), bby.version(), bby.version(), bby.version(),
bby.version(), bby.version(), bby.version(), bby.version(), bby.version(),
bby.version(), bby.version(), bby.version(), bby.version(), bby.version(),
bby.version(), bby.version(), bby.version(), bby.version(), bby.version(),
bby.version(), bby.version(), bby.version(), bby.version(), bby.version(),
bby.version(), bby.version(), bby.version(), bby.version(), bby.version(),
bby.version(), bby.version(), bby.version(), bby.version(), bby.version(),
bby.version(), bby.version(), bby.version(), bby.version(), bby.version(),
bby.version(), bby.version(), bby.version(), bby.version(), bby.version(),
bby.version(), bby.version(), bby.version(), bby.version(), bby.version()
];
Promise.all(promises)
.then(result => {
var diff = process.hrtime(start);
var totalTime = diff[0] * NS_PER_SEC + diff[1];
t.ok(totalTime > 1 * NS_PER_SEC, `took more than 1 second (${totalTime / NS_PER_SEC})`);
t.end();
})
.catch(error => {
console.log(error.message);
t.error(error, 'no error');
t.end();
});
});
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,149
|
Biturix rectilinea is a moth of the family Erebidae. It was described by Hermann Burmeister in 1878. It is found in Brazil, Argentina and Bolivia.
References
Phaegopterina
Moths described in 1878
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 31
|
***DEV ATimelyPerspective***
Video Clip: $350,000 Armin Strom Resonance Minute Repeater
Roberta Naas /
Earlier this summer, independent watch brand Armin Strom unveiled its second Masterpiece watch: the Resonance Minute Repeater. We covered that watch thoroughly here and here (where we discuss why the watch didn't make it to the GPHG jury). The watch warrants so much because it is a world's first and worthy of the coverage. Recently, though,…
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Early Spring: The True Story Behind Groundhog Day, and Why the Groundhog Cares about Time
Today, February 2, is officially "Groundhog" day. This is the day when the groundhog emerges from his burrow to determine whether or not spring is in the air. As folklore has it, if the groundhog can't see his shadow because of the clouds, spring will come soon. But, if it is sunny and the creature…
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Fast Focus: Introducing Piaget's "Year of the Monkey" Altiplano Cloisonné Watch
Over the past month or so, we have been bringing you a close up look at all of the new watches that celebrate the Year of the Monkey. Today, we present the Piaget Limited Edition Year of the Monkey watch. To celebrate the Chinese New Year (which begins next week), Piaget presents the playful monkey, the…
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Three Terrific Women's Mechanical Watches as Seen at SIHH 2016: Piaget, Cartier, Roger Dubuis
By Roberta Naas / January 29, 2016
This year's SIHH did not disappoint when it comes to mechanical watches for women. We have a great line of them to show, so we will go in stages. Here we present three stunners — dazzling diamond-adorned beauties that house complicated movements. Piaget, always a master at diamond work, unveils some stunning new Limelight watches…
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Storage Wars: SIHH 2016 Innovative USB Keys
Welcome to the first edition of Storage Wars 2016 — based on the SIHH exhibition and a few independent brands exhibiting in Geneva. Every year we embark on trips to find the most exciting timepieces on the market — and we come home with a wealth of information and images. All of that info is…
4 years ago in 2016 Watch Shows, Around the World / Watch stops, Baume & Mercier, Louis Moinet, Manufacture Royale, Time Capsules: Commentary, Timepieces News, Reviews and Articles, Watch Industry Interviews, Wristwatch Reviews
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OK – so sometimes a lot of diamonds really do enthrall us. Such is the case of the new Audemars Piguet Diamond Fury cuff-watch. Unveiled during SIHH, this more-than half-a-million-dollar watch comes on the heels of last year's extremely successful Diamond Punk, which we wrote about here. Now, if classic vintage chic is the buzzword for watches…
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A Moment in Time: Daniel Riedo, CEO of Jaeger-LeCoultre, Shares 2016 Trends and Plans
Just last week, with the SIHH in full swing, a lot of great timepieces were seen and a host of wonderful interviews conducted. We will bring you much of the news from the exhibition and around the city in the coming weeks — keeping in mind that much of what we are bringing to you…
4 years ago in All Watch Brands, Around the World / Watch stops, Features, Interviews/A Moment in Time, Jaeger-LeCoultre, News, Time Capsules: Product, Timepieces News, Reviews and Articles, Watch Industry Interviews, Wristwatch Reviews
Meet the Diamond Magister Dong Son Tourbillon from Peter Speake-Marin
By Gordon Henderson / January 25, 2016
The dong son drum serves as the source of inspiration for Peter Speake-Marin's latest release: the Diamond Magister Dong Son Tourbillon. The drum's origins trace to the Red River Delta of Vietnam dating back to approximately 600 BC. The drums were typically used in harvest festivals and rituals such as weddings and funerals, as well…
4 years ago in 2016 Watch Shows, All Watch Brands, Around the World / Watch stops, Collectors' Corner, News, News about Wristwatches/Brands, Peter Speake-Marin, Time Capsules: Product, Timepieces News, Reviews and Articles, Tourbillon Watches, Watch Industry Interviews, Women's watches, Wristwatch Reviews
SIHH 2016: H. Moser & Cie Joins Forces with Song Writer Bryan Ferry for new Endeavour Small Seconds Watch
This year, SIHH has opened its doors to nine independent brands that have something to say that is in keeping with the haute horlogerie exhibition. Among those brands: H. Moser & Cie. We found interesting diversity at the show from this brand, with pieces ranging from a mechanical snub at the Apple watch (more on…
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JLC new sept 2019
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 3,720
|
Tim Belliveau
As a child, Belliveau became fascinated with natural history when his father took him to the Royal Tyrrell Museum in Drumheller, AB. He soon became versed in numerous aspects of Prehistoric zoology, primarily through drawing. When he was 17, Belliveau left home for a long series of part-time jobs and lived in a number of different places including a church, a motor home in a parking lot, and illegally squatting in a tent.
The works of Alexander Wilson and Werner Herzog had a strong influence on Belliveau and he spent a Thoreau-like period of solitary contemplation living in a tent in a Yukon forest for a summer. Upon his return to Calgary he went through art college building a body of work derived from these ideas and experiences and set to work on Bee Kingdom with fellow collective members.
"Since we learn about nature as magical when we're kids and as a dead resource when we're adults, it's become a kind of mystical industry; a magical place to which we escape and sell resources."
Bull City
Earth Cabin
blow-mold and sculpted hot glass
20 x 17 x 12 inches (total of three pieces)
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 7,902
|
The Trench Reynolds Crime Report
Crime News That Matters
Columbine conspiracy theories, and one that involves me
Trench Reynolds
This looks vaguely familiar
13 COLUMBINE CONSPIRACY THEORIES:
Just in time for the 13th anniversary of Columbine TruTV in tasteless fashions released this slideshow about Columbine conspiracy theories. Of course to get more clicks for their website they take the trash TV stance that these conspiracies could be true. Let's clear this up once and for all, there are no Columbine conspiracies. It is exactly how it appears. Two cowardly scumbags killed 13 people because they were egotistical selfish spoiled punks.
There was no 3rd shooter. Luvox didn't cause the shootings. Police did not shoot any students. This was not retaliation against police for some kind of pedophile ring. Yeah, that's an actual conspiracy theory believe it or not.
Conspiracy theories are for weak-minded people who will believe anything any crackpot tells them. They're for people who simply can't grasp the concept that sometimes horrible things happen for stupid reasons. They're for people whose lives are so devoid of meaning that they have to fill the void with modern-day boogeymen.
As for the picture above you can see it on the 2nd page of the TruTV slideshow. That's a screen grab of my original website back in 1997 which is fitting considering the slideshow and its misrepresentation of the facts feels like it was written in 1999.
TruTV's slogan is "Not reality, actuality." Which really means it's not reality it's just some bullshit we made up so suckers will watch our crappy shows.
Categories: Crime, Personal, Trench Report•Tags: Columbine, conspiracy theory, trench reynolds, trutv•
16 thoughts on "Columbine conspiracy theories, and one that involves me"
Your_Pal_Nancy says:
I was waiting to see why your spellcheck accepted "bogeyman". TruTV sucks, I used to read the crime stories there back when it was crimelibrary.com, the same time I found mycrimespace but now the whole website is crappy and last I checked not very easy to navigate.
Trench Reynolds says:
Now it's just a low rent ripoff of The Smoking Gun which is owned by the same company.
owner says:
…And not to mention the network was rebranded a few years back and signed contracts with the likes of Todd Bridges and Danny Bonaduce.
I hate to say it Trench, but your sharing the misery in bad company…
And Lief Garrett.
I know various people have commented the same thing over the years, but you really aught to write a book one day!
Hell, I'd buy it…
Sure, we all would here!
Your still the underdog of crime blogging…
And you actually invented the whole damn thing back in '99.
I was still in school but even after all my uncomfortable queasy holiday get together's, I can still shut the laughter up when I tell them I know guy from 48 hours and Time.
It's works everything Holiday:)
Thank you Trench and keep up the good work…
And write that damn book already!!
I have the attention span of a flea. I would never be able to finish a book.
Individualist says:
I was just wondering if you have seen the video surveillance tape of the cafeteria?
Yeah, what about it?
Guest1 says:
Who in the right mind gave you the right to sit there and "judge" what kind of people, believe conspiracy theories? Get off your high horse and stop trying to make yourself superior, you are what is wrong with society, everyone is an individual, who is entitled to an opinion, you shared yours but that gives you no means to criticize and judge those who don't agree with you.
You do realize that you're doing the exact same thing that you're accusing me of right? Not that I care but I do like pointing out the irony.
Anyway it's people who believe in conspiracy theories that are what's wrong with our society. They disregard common sense in favor of fantastical tales of secret organizations and hidden agendas that are logistically impossible. In my estimation conspiracy theorists are people who use these tales as excuses as to why they can't succeed in their own lives.
SprocketTrials says:
Love when you point out the ironic, Trench.
Have I shown you my badge?
Brock Pierce says:
Conspiracy theories are for weak minded people? You are wrong, conspiracy theories are created by men and women who are not afraid to ask questions and investigate the truth. Weak minded people believe what the media tells them. They live in a cocoon and are brainwashed into believing that things are just what they seem. Society leads us to believe that there is no need to ask questions because are government has already answered them for us. Conspiracy theorist ask questions and usually they are very valid questions. However, these questions are never answered. Why is that?….the theory will remain alive until proven wrong.
Except when the theories are proven wrong, and they always are, the weak minded just claim that's part of the conspiracy.
hmm says:
"No you weak minded"
"No! I are stwong minded! I only beweieve da troof"
Will all of you shut the fuck up and just admit that nobody really knows wtf is going on?..Please..just hush and accept your ignorance. No matter how strong or weak minded you claim to be by claiming others are less intelligent, in the end not one of you have answers . Just "this is what happened because it's what I was told happened" or
"this is what happened because I honestly don't know what happened." STFU
At the end of the day none of us understand the madness that is currently swallowing us all. And they keep it that way either by design or coincidence.
How about "this is what happened because logic dictates it?" Then again conspiracy theorists don't believe in logic.
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 3,522
|
import * as actions from "./product-page.actions";
import { addOrUpdate, pluckOut } from "../core";
export const removeProductPageReducer = (state, action) => {
if (action instanceof actions.RemoveProductPageAction)
pluckOut({ items: state.productPages, value: action.entity.id });
return state;
}
export const addProductPageReducer = (state, action) => {
if (action instanceof actions.AddOrUpdateProductPageAction) {
addOrUpdate({ items: state.productPages, item: action.entity });
}
return state;
}
export const allProductPagesReducer = (state, action) => {
if (action instanceof actions.AllProductPagesAction) {
state.productPages = action.entities;
}
return state;
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,749
|
\section{Introduction}
\label{xxsec0}
Throughout let $\Bbbk$ be a base field that is algebraically
closed. Algebraic objects are defined over $\Bbbk$.
The Frobenius-Perron dimension of an object in a semisimple
finite tensor (or fusion) category was introduced by
Etingof-Nikshych-Ostrik in 2005 \cite{ENO2005}. Since then
it has become an extremely useful invariant in the study of
fusion categories and representations of semisimple (weak
and/or quasi-)Hopf algebras. By examining the Frobenius-Perron
dimension of all objects in a finite tensor category one can
determine whether the category is equivalent to the
representation category of a finite-dimensional quasi-Hopf
algebra \cite[Proposition 2.6]{EO2004}. The Frobenius-Perron
dimension of a fusion category is also a crucial invariant in
the classification of fusion categories as well as that of
semisimple Hopf algebras. An important project is to develop
the Frobenius-Perron theory for not-necessarily semisimple
tensor (or monoidal) categories. A step departing from
semisimple categories, or abelian categories of global
dimension 0, is to study the hereditary ones (of global
dimension one). Ultimately Frobenius-Perron theory should
provide powerful tools and useful invariants for projects like
\begin{project}
\label{xxpro0.1}
Describe and understand weak bialgebras
[Definition \ref{xxdef1.7}] and weak Hopf algebras
\cite[Definition 2.1]{BNS1999} that are hereditary
as associative algebras.
\end{project}
Note that an analogous classification project of hereditary
prime Hopf algebras was finished in a remarkable paper by
Wu-Liu-Ding \cite{WLD2016} a few years ago. Some recent
efforts pertaining on homological aspects of noetherian weak
Hopf algebras were presented in \cite{RWZ2020}. Recall from
\cite{NVY2019} that a {\it monoidal triangulated category}
is a monoidal category $\mathcal{T}$ in the sense of
\cite[Definition 2.2.1]{EGNO2015} that is triangulated and,
for which, the tensor product $\otimes_{\mathcal{T}}:
\mathcal{T} \times \mathcal{T} \to \mathcal{T}$ is an exact
bifunctor. Given a Hopf algebra (respectively, weak and/or
quasi- Hopf algebra/bialgebra) $H$, its comultiplication
induces a monoidal structure on the category of
representations of $H$. The corresponding derived category
has a canonical monoidal triangulated structure. Monoidal
triangulated structures appear naturally in several other
subjects.
{\it Algebraic geometry}.
A classical theorem of Gabriel \cite{Ga1962} states that a
noetherian scheme $\mathbb{X}$ can be reconstructed from the
abelian category of coherent sheaves over $\mathbb{X}$,
denoted by $coh(\mathbb{X})$. Hence the abelian category
$coh(\mathbb{X})$ captures all information about the space
$\mathbb{X}$. Recent development in derived algebraic geometry
suggests that the bounded derived category of coherent sheaves
over $\mathbb{X}$, denoted by $D^b(coh(\mathbb{X}))$, is
sometimes a better category to work with when we are
considering many geometric problems such as moduli problems.
When $\mathbb{X}$ is smooth, $D^b(coh(\mathbb{X}))$ is
equipped with a natural tensor (=symmetric monoidal)
triangulated structure in the sense of
\cite[Definition 1.1]{B2005}.
{\it Tensor triangulated geometry}.
Tensor triangulated categories have been studied by Balmer
\cite{B2005} and many others, where the study of tensor
triangulated categories has been sometimes
referred to as {\it tensor triangulated geometry}. Balmer
defined the prime spectrum, denoted by ${\rm{Spc}}(\mathcal{T})$,
of a small tensor triangulated category $\mathcal{T}$ by using
the thick subcategories which behave like prime ideals under the
tensor product. Note that ${\rm{Spc}}(\mathcal{T})$ is a locally
ringed space \cite[Remark 6.4]{B2005}. This idea has been shown
to be widely applicable to algebraic geometry, homotopy theory
and representation theory. Recently Vashaw-Yakimov and
Nakano-Vashaw-Yakimov \cite{VY2018, NVY2019} developed a
noncommutative version of the Balmer spectrum, or {\it
noncommutative tensor triangulated geometry} (in the
words of the authors of \cite{NVY2019}).
{\it Noncommutative algebraic geometry}. Following
Grothendieck, {\it to do geometry you really don't need a space,
all you need is a category of sheaves on this would-be space}
\cite[p.78]{Ma2018}. Following \cite{VY2018, NVY2019},
we would like to consider
or view monoidal triangulated categories as appropriate categories
for doing a new kind of noncommutative geometry. For example, if
$T$ is a noetherian Koszul Artin-Schelter regular algebra, then
the bounded derived category of the noncommutative projective
scheme associated to $T$, denoted by ${\mathcal T}:=D^b(\proj T)$,
has at least two different monoidal triangulated structures
[Example \ref{xxex7.9}]. In this situation, it would
be very interesting to understand how the ``geometry'' of
$\proj T$ interacts with ``monoidal triangulated
structures'' on $\mathcal{T}$. Fix a general triangulated category,
still denoted by $\mathcal{T}$, it is common that there are many
different monoidal triangulated structures on $\mathcal{T}$
(with the same underlying triangulated structure) that reflect
on different hidden properties of $\mathcal{T}$. So it is
worth distinguishing different types of monoidal triangulated
structures on $\mathcal{T}$ and finding a definition of the
``size'' of these structures.
{\it Quiver representations}.
A related subject is the representation theory of quivers that
has become a popular topic since Gabriel's work in the 1970s
\cite{Ga1972, Ga197374, Ga1973}. For a given quiver, it is
naturally equipped with a monoidal structure in the category of
its representations, induced by the vertex-wise tensor product
of vector spaces \eqref{E2.1.1}. The monoidal structure of
quiver representations has been studied by Strassen \cite{St2000}
in relation with orbit-closure degeneration in 2000, and later
by Herschend \cite{He2005, He2008a, He2008b, He2009, He2010}
in the relation with the bialgebra structure on the path
algebra during 2005-2012. Herschend solved the Clebsch-Gordan
problem for quivers of type $\mathbb{A}_n$, $\mathbb{D}_n$
and $\mathbb{E}_{6,7,8}$ in \cite{He2008b, He2009}. As for
tame type, Herschend also gave solutions for type
$\mathbb{\tilde{A}}_n$ in \cite{He2005} and the quivers
with relations that correspond to string algebras in
\cite{He2010}. One of our basic objects in this paper is
the bounded derived category $D^b(A-\Modfd)$ for a
finite dimensional weak bialgebra $A$. (We usually consider
hereditary, but not semisimple, algebras.) Since $A$ is a
weak bialgebra, $A-\Modfd$ has an induced monoidal abelian
structure; and hence, $D^b(A-\Modfd)$ is a monoidal
triangulated category in the sense of \cite{NVY2019}. Note
that, even for a finite quiver $Q$, \cite[Proposition 4]{He2008a}
and \cite[Theorem 3.2]{HT2013} give different weak bialgebra
structures on $A:=\Bbbk Q$ which produce different monoidal
triangulated structures on $D^b(A-\Modfd)$.
{\it Connections between geometry, quiver representations,
and weak bialgebras}.
Going back to classical geometry, let $\mathbb{X}$ be a smooth
projective scheme. If $\mathbb{X}$ is equipped with a full
strongly exceptional sequence (also called strong full
exceptional sequence by some authors) $\{\mathcal{E}_1,\cdots,
\mathcal{E}_n\}$ [Definition \ref{xxdef7.8}], then there
is a triangulated equivalence
\begin{equation}
\label{E0.1.1}\tag{E0.1.1}
D^b(coh(\mathbb{X}))\cong D^b(A-\Modfd)
\end{equation}
where $A$ is the finite dimensional algebra
$[\End_{D^b(coh(\mathbb{X}))}(\oplus_{i=1}^n \mathcal{E}_i)]^{op}$
(some details can be found at the end of Section \ref{xxsec7}).
Since $A$ is finite dimensional (and of finite global
dimension), it seems easier to study $A$ than to study
$\mathbb{X}$ in some aspects. Equivalence \eqref{E0.1.1} induces
a monoidal structure on $D^b(A-\Modfd)$ which usually does
not come from any weak bialgebra structures of $A$
[Example \ref{xxex7.9}]; or in some extreme cases, there
is no weak bialgebra structure on $A$ at all. For such an
algebra $A$, it is imperative to understand and even to
classify all possible monoidal triangulated structures of
$D^b(A-\Modfd)$ (though $A$ may not be a weak bialgebra).
Another well-known example of such a connection is from the
study of weighted projective lines, introduced by Geigle-Lenzing
\cite{GL1987} in 1985 (see Section \ref{xxsec6}). Since then
weighted projective lines have been studied extensively by
many researchers. Let $coh({\mathbb X})$ denote the category
of coherent sheaves over a weighted projective line $\mathbb{X}$.
When $\mathbb{X}$ is domestic, a version of \eqref{E0.1.1} holds
and the representation type of $A$ (appeared in the right-hand
side of \eqref{E0.1.1}) is tame, see Lemma \ref{xxlem6.1}(2).
This is one of the key facts that we will use in this paper.
Recently, a new definition of Frobenius-Perron dimension was
introduced in \cite{CGWZZZ2017, CGWZZZ2019} where the authors
extended its original definition from an object in a semisimple
finite tensor category to an endofunctor of any $\Bbbk$-linear
category. (We refer to Definition \ref{xxdef1.3} for some relevant
definitions.) It turns out that new Frobenius-Perron invariants
are sensitive to monoidal structures; as a consequence, these
are crucial to distinguish different monoidal triangulated
structures. One general goal of this paper is to provide evidence
that the Frobenius-Perron invariants are effective to study
monoidal triangulated structures. Some basic properties and
interesting applications of Frobenius-Perron-type invariants
can be found in \cite{CGWZZZ2017, CGWZZZ2019}.
In this paper, we focus on different weak bialgebra structures
on the path algebras of finite quivers and the Frobenius-Perron
theory for finite dimensional hereditary weak bialgebras. As
mentioned above, this is one step beyond the semisimple case.
\begin{definition}
\label{xxdef0.2}
Let ${\mathcal T}$ be a monoidal category and let $\mathcal{P}$
be a function
$$\{{\text{endofunctors of $\mathcal{T}$}}\}
\longrightarrow {\mathbb{R}}_{\geq 0}.$$
Note that $\mathcal{P}$ could be Frobenius-Perron dimension or
Frobenius-Perron curvature
as given in Definition \ref{xxdef1.3}(6,7). For every object
$M$ in ${\mathcal T}$, let $\mathcal{P}(M)$ denote the
$\mathcal{P}$-value of the tensor functor $M\otimes_{\mathcal{T}} -:
\mathcal{T}\to \mathcal{T}$.
\begin{enumerate}
\item[(1)]
We say $\mathcal{T}$ is {\it $\mathcal{P}$-finite} if
$\mathcal{P}(M)<\infty$ for all objects $M$. Otherwise,
$\mathcal{T}$ is called {\it $\mathcal{P}$-infinite}.
\item[(2)]
If $\mathcal{T}$ is $\mathcal{P}$-infinite and if
$\mathcal{P}(M)<\infty$ for all indecomposable objects $M$,
then $\mathcal{T}$ is called {\it $\mathcal{P}$-tame}.
\item[(3)]
If $\mathcal{T}$ is neither $\mathcal{P}$-finite nor
$\mathcal{P}$-tame, then it is called {\it $\mathcal{P}$-wild}.
\end{enumerate}
\end{definition}
Our first main result concerns the trichotomy of $\fpd$-finite/tame/wild
property. Let $\Repr(Q)$ be the category of finite dimensional
representations of a quiver $Q$.
\begin{theorem}
\label{xxthm0.3}
Let $Q$ be a finite acyclic quiver and let $\mathcal{T}$
be the triangulated category $D^b(\Repr(Q))$.
\begin{enumerate}
\item[(1)]
$Q$ is of finite type if and only if $\mathcal{T}$ is
$\fpd$-finite for every monoidal triangulated structure
on $\mathcal{T}$, and if and only if there is one monoidal
triangulated structure on $\mathcal{T}$ such that $\mathcal{T}$
is $\fpd$-finite.
\item[(2)]
$Q$ is of tame type if and only if there is a monoidal
triangulated structure on $\mathcal{T}$ such that $\mathcal{T}$
is $\fpd$-tame. In this case, there must be another monoidal
triangulated structure on $\mathcal{T}$ such that $\mathcal{T}$
is $\fpd$-wild.
\item[(3)]
$Q$ is of wild type if and only if $\mathcal{T}$ is
$\fpd$-wild for every monoidal triangulated structure
on $\mathcal{T}$.
\item[(4)]
If $Q$ is tame or wild, then every monoidal triangulated
structure on $\mathcal{T}$ is $\fpd$-infinite.
\end{enumerate}
\end{theorem}
Note that in part (2) of the above theorem, there are two
different monoidal triangulated structures on $\mathcal{T}$,
one of which is $\fpd$-tame and the other is not. We refer
to Definition \ref{xxdef3.1} for the definition of a discrete
monoidal structure. By the above theorem, it is
rare to have $\fpd$-finite monoidal triangulated structures
on $\mathcal{T}$. When it exists, we can say a bit more. The
canonical weak bialgebra structure on the path algebra
$\Bbbk Q$ is given in Lemma \ref{xxlem2.1}(1).
\begin{theorem}
\label{xxthm0.4}
Let $A$ be a finite dimensional hereditary weak bialgebra
such that the induced monoidal structure on $A-\Modfd$
is discrete. Then the following are equivalent:
\begin{enumerate}
\item[(a)]
$A$ is of finite representation type,
\item[(b)]
$\fpd(M)<\infty$ for every irreducible representation $M\in A-\Modfd$,
\item[(c)]
$\fpd(M)<\infty$ for every indecomposable representation $M\in A-\Modfd$,
\item[(d)]
$\fpd(M)<\infty$ for every representation $M\in A-\Modfd$,
\item[(e)]
$\fpd (X)<\infty$ for every indecomposable object $X\in D^b(A-\Modfd)$,
\item[(f)]
The induced monoidal triangulated structure on $D^b(A-\Modfd)$ is
$\fpd$-finite.
\end{enumerate}
\end{theorem}
Suppose further that $A$ is the path algebra $\Bbbk Q$ with canonical
weak bialgebra structure. It follows from Gabriel's theorem that
any of conditions {\rm{(a)}} to {\rm{(e)}} is equivalent to
\begin{enumerate}
\item[(g)]
$Q$ is a finite union of quivers of type $\mathbb{ADE}$.
\end{enumerate}
Since condition (a) in the above theorem is an algebra property, the
$\fpd$-finiteness of $D^b(A-\Modfd)$ only depends on the algebra
structure of $A$, though the definition of $\fpd(X)$ uses the
coalgebra structure of $A$. Note that condition (a) is not equivalent
to condition (b) if we remove the hereditary hypothesis in the above
theorem [Remark \ref{xxrem7.3}(3)].
Following BGP-reflection functors \cite{BGP1973}, Happel showed
that, for Dynkin quivers with the same underlying Dynkin diagram,
their derived categories are triangulated equivalent \cite{Ha1987}.
This remarkable theorem is one of most beautiful results in
representation theory of finite dimensional algebras. In contrast,
the story is very different when we are working with {\it monoidal
triangulated} structures of the derived category of Dynkin quivers,
see Theorem \ref{xxthm0.5} below. As indicated in
\cite{CGWZZZ2017, CGWZZZ2019}, Frobenius-Perron-type
invariants are extremely useful to study derived
(or triangulated) categories. Using the Frobenius-Perron
curvature, denoted by $\fpv$, of objects in $D^b(A-\Modfd)$
we can prove the following.
\begin{theorem}
\label{xxthm0.5}
Let $A$ and $B$ be finite dimensional hereditary weak
bialgebras. Assume either $A$ is a bialgebra or
$A-\Modfd$ is discrete. Suppose that the monoidal
triangulated categories $D^b(A-\Modfd)$ and
$D^b(B-\Modfd)$ are equivalent. Then $A-\Modfd$ and
$B-\Modfd$ are equivalent as monoidal abelian categories.
\end{theorem}
As a consequence, we have
\begin{corollary}
\label{xxcor0.6}
Suppose that the bounded derived categories of representations of
two finite acyclic quivers are equivalent as monoidal triangulated
categories. Then the quivers are isomorphic.
\end{corollary}
There is also a result concerning an analogue of a $t$-structure
in the monoidal triangulated setting, see Theorem \ref{xxthm0.7}
below. We introduce the notion of an $mtt$-structure on a monoidal
triangulated category in Section 5. Undefined terminologies
can be found in Sections 4 and 5.
\begin{theorem}
\label{xxthm0.7}
Let $A$ be a finite dimensional weak bialgebra that is hereditary
as an algebra. Suppose that the induced monoidal structure on
$A-\Modfd$ is discrete. Then there is a unique hereditary
$mtt$-structure with deviation zero on the monoidal triangulated
category $D^b(A-\Modfd)$.
\end{theorem}
It is clear that Theorem \ref{xxthm0.7} applies to $D^b(\Repr(Q))$
where $Q$ is a finite acyclic quiver. A $t$-structure on a
triangulated category has been studied extensively since it was
introduced by Beilinson-Bernstein-Deligne in \cite{BBD1981}. It
is natural to study all $mtt$-structures of a monoidal
triangulated category. In fact, $mtt$-structures service
as a compelling system of a monoidal triangulated category. It
is well-known that (hereditary) $t$-structures on $D^b(\Repr(Q))$
are not unique even for quivers of type ${\mathbb A}_n$, \
defined below, for $n\geq 3$. Therefore it is surprising that
certain $mtt$-structures (see Theorem \ref{xxthm0.7}) are unique.
This uniqueness result would have other significant consequences
than Theorem \ref{xxthm0.5} and Corollary \ref{xxcor0.6}. It is also
interesting to search for other classes of monoidal triangulated
categories such that the uniqueness property holds for certain
$mtt$-structures.
Though there are more than one tensor structures on the path
algebra $\Bbbk Q$ for a quiver $Q$, one of these structures
is from the natural coalgebra structure on $\Bbbk Q$,
similar to group algebras [Lemma \ref{xxlem2.1}(1)].
We will present more results concerning the Frobenius-Perron
dimensions of indecomposable representations under such
tensor structure. Before that we need to introduce some
notation. By definition, a type $\mathbb{A}$ quiver (or more
precisely, type $\mathbb{A}_n$ quiver) is a quiver of the
following form
\begin{equation}
\label{E0.7.1}\tag{E0.7.1}
\xymatrix{
1 \ar@{-}[r]^{\alpha_1}&2\ar@{-}[r]^{\alpha_2}
&\cdots\ar@{-}[r]^{\alpha_{i-1}}&i\ar@{-}[r]^{\alpha_i}
&\cdots\ar@{-}[r]^{\alpha_{n-1}}&n}
\end{equation}
where each arrow $\alpha_i$ is either $\longrightarrow$ or
$\longleftarrow$. For each quiver of type $\mathbb{A}_n$,
the arrows $\alpha_i$ will be specified. It is easy to see
that, for each $n\geq 3$, there are more than one
quivers of type $\mathbb{A}_n$ up to isomorphisms.
Let us fix a quiver of type $\mathbb{A}_n$, say $Q$,
as above. For $1\leq i\leq j\leq n$, we define a thin representation
of $Q$, denoted by $M\{i,j\}$, by
\begin{equation}
\label{E0.7.2}\tag{E0.7.2}
(M\{i,j\})_s=\begin{cases} \Bbbk & i\leq s\leq j,\\
0 & {\text{otherwise}}\end{cases}
\end{equation}
and
\begin{equation}
\label{E0.7.3}\tag{E0.7.3}
(M\{i,j\})_{\alpha_s}=\begin{cases} Id_{\Bbbk} & i\leq s<j,\\
0& {\text{otherwise}}.\end{cases}
\end{equation}
(This thin representation is sometimes called an interval module
by other researchers.) Then by \cite[p.63]{GR1992},
all such $M\{i,j\}$ form the complete list
of indecomposable representations of $Q$ [Lemma \ref{xxlem1.10}].
For all $i\leq j$, we say
$$M\{i,j\}\;\; {\text{is}} \;\;
\begin{cases}
{\text{a $sink$ $\qquad$ if $\alpha_{i-1}=\longrightarrow$ (or $i=1$) and
$\alpha_{j}=\longleftarrow$ (or $j=n$)}},\\
{\text{a $source\;$ $\quad$ if $\alpha_{i-1}=\longleftarrow$ (or $i=1$) and
$\alpha_{j}=\longrightarrow$ (or $j=n$)}},\\
{\text{a $flow$ $\qquad$ if $\alpha_{i-1}=\alpha_{j}$, and it is either
$\longrightarrow$ or $\longleftarrow$}}.
\end{cases}$$
Since $\Repr(Q)$ is hereditary, every indecomposable
object in the bounded derived category $D^b(\Repr(Q))$
is of the form $M\{i,j\}[m]$ for some $m\in {\mathbb Z}$.
We have the following result for type $\mathbb{A}_n$.
Some computation in the case of type $\mathbb{D}_n$ quivers
is given in \cite{ZWD2020}.
\begin{theorem}
\label{xxthm0.8}
Let $Q$ be a quiver of type $\mathbb{A}_n$ for some
positive integer $n$. Then the following
hold in the bounded derived
category $D^b(\Repr(Q))$ with tensor defined as in \eqref{E2.1.1}.
\begin{enumerate}
\item[(1)]
$\fpd (M\{i,j\}[m])=0$ for all $m<0$ and $m>1$.
\item[(2)]
$\fpd(M\{i,j\}[0])=\begin{cases}
1 & {\text{if $M\{i,j\}$ is a sink}},\\
\min\{i, n-j+1\} & {\text{if $M\{i,j\}$ is a source}},\\
1 &{\text{if $M\{i,j\}$ is a flow}}.
\end{cases}$
\item[(3)]
$\fpd(M\{i,j\}[1])=\begin{cases}
\min\{i-1,n-j\} & {\text{if $M\{i,j\}$ is a sink}},\\
0 & {\text{if $M\{i,j\}$ is a source}},\\
0 &{\text{if $M\{i,j\}$ is a flow}}.
\end{cases}$
\end{enumerate}
\end{theorem}
Related to Project \ref{xxpro0.1} we are also very much interested
in the following questions.
\begin{question}
\label{xxque0.9}
Let $A$ be a finite dimensional weak bialgebra or just an algebra,
or $\Bbbk Q$ where $Q$ is a finite acyclic quiver.
\begin{enumerate}
\item[(1)]
How to determine all monoidal abelian structures on the abelian
category $A-\Modfd$?
\item[(2)]
How to determine all monoidal triangulated structures on the derived
category $D^b(A-\Modfd)$?
\end{enumerate}
\end{question}
The paper is organized as follows. Section 1 contains some basic
definitions. In particular, we recall the definition of the
Frobenius-Perron dimension of an endofunctor. In Section 2 we review
some preliminaries on quiver representations. The notion
of a discrete monoidal abelian category is introduced in
Section 3. A natural example of a discrete monoidal structure
is $\Repr(Q)$ which is the main object in this paper. Theorem
\ref{xxthm0.4} is proved in Section 4. In Section 5, we
introduce the notion of an $mtt$-structure of a monoidal
triangulated category that is a monoidal version of the
$t$-structure of a triangulated category. Theorems \ref{xxthm0.5}
and \ref{xxthm0.7}, and Corollary \ref{xxcor0.6} are
proved near the end of Section 5. Section 6 focuses on
the proof of Theorem \ref{xxthm0.3} which uses some
detailed information about weighted projective lines. Section
7 contains various examples which indicate the richness
of monoidal triangulated structures from different
subjects. Section 8 consists of the proof of Theorem
\ref{xxthm0.8} with some non-essential details left out.
\section{Some basic definitions}
\label{xxsec1}
This section contains several basic definitions which will be used
in later sections.
Recall from \cite[Definition 2.1.1]{EGNO2015} that
a {\it monoidal category} ${\mathcal C}$ consists of the following data:
\begin{enumerate}
\item[($\bullet$)]
a category ${\mathcal C}$,
\item[($\bullet$)]
a bifunctor $\otimes: {\mathcal C}\times {\mathcal C}\to
{\mathcal C}$, called {\it tensor functor},
\item[($\bullet$)]
for each triple $(X,Y, Z)$ in ${\mathcal C}$, a natural isomorphism
$$\alpha_{X,Y,Z}: (X\otimes Y)\otimes Z\xrightarrow{\cong} X\otimes(Y\otimes Z),$$
\item[($\bullet$)]
an object ${\bf 1}\in {\mathcal C}$, called {\it unit object},
\item[($\bullet$)]
natural isomorphisms $l_X: {\bf 1}\otimes X \xrightarrow{\cong} X$
and $r_X: X\otimes {\bf} \xrightarrow{\cong} X$ for each $X$ in ${\mathcal C}$,
\end{enumerate}
such that the pentagon axiom \cite[(2.2)]{EGNO2015} and the triangle axiom
\cite[(2.10)]{EGNO2015} hold. The definitions of a braiding
$\{c_{X,Y}\}_{X,Y\in {\mathcal C}}$ on a monoidal category ${\mathcal C}$
and of a braided monoidal category are given in
\cite[Definitions 8.1.1 and 8.1.2]{EGNO2015} respectively.
By \cite[Definition 8.1.12]{EGNO2015}, a braided monoidal category
${\mathcal C}$ is called {\it symmetric} if
$$c_{Y,X}\circ c_{X,Y} = id_{X\otimes Y}$$
for all objects $X, Y\in {\mathcal C}$.
We are usually considering $\Bbbk$-linear categories. Now we
recall some definitions.
\begin{definition}
\label{xxdef1.1}
Let ${\mathcal C}$ be a monoidal category.
\begin{enumerate}
\item[(1)]
We say ${\mathcal C}$ is {\it monoidal $\Bbbk$-linear}
if
\begin{enumerate}
\item[(1a)]
${\mathcal C}$ is $\Bbbk$-linear,
\item[(1b)]
morphisms and functors involving in the definition of
monoidal category are all $\Bbbk$-linear, and
\item[(1c)]
the tensor functor preserves direct sums in each argument.
\end{enumerate}
\item[(2)]
We say ${\mathcal C}$ is {\it monoidal abelian}
if
\begin{enumerate}
\item[(2a)]
${\mathcal C}$ is a $\Bbbk$-linear abelian category,
\item[(2b)]
${\mathcal C}$ is monoidal $\Bbbk$-linear in the sense of
part (1),
\item[(2c)]
the tensor functor preserves exact sequences in each argument.
\end{enumerate}
\item[(3)] \cite{NVY2019}
We say ${\mathcal C}$ is {\it monoidal triangulated}
if
\begin{enumerate}
\item[(3a)]
${\mathcal C}$ is $\Bbbk$-linear triangulated category,
\item[(3b)]
${\mathcal C}$ is monoidal $\Bbbk$-linear in the sense of
part (1),
\item[(3c)]
the tensor functor preserves exact triangles and commutes
with the suspension in each argument.
\item[(3d)]
the suspension satisfies the anti-commuting diagram given
at the end of the definition of a {\it suspended monoidal}
category \cite[Definition 1.4]{Su-Al}.
\end{enumerate}
\end{enumerate}
\end{definition}
By the way, we will not be using the axiom (3d)
in the above definition in this paper.
A tensor triangulated category in the sense of \cite[Definition 1.1]{B2005}
is just a symmetric monoidal triangulated category. We refer the
reader to \cite{EGNO2015} for other details.
Let $({\mathcal C}, \otimes, {\bf 1})$ be a monoidal category
and ${\mathcal A}$ be another category. Following \cite[p.62]{JK2001},
by an {\it action} of ${\mathcal C}$ on ${\mathcal A}$ we mean a
strong monoidal functor
$$F = (f, \tilde{f}, f^{\circ}): {\mathcal C}\longrightarrow
[{\mathcal A}, {\mathcal A}],$$
where $[{\mathcal A}, {\mathcal A}]$ is the category of
endofunctors of ${\mathcal A}$, provided with a monoidal structure
$([{\mathcal A}, {\mathcal A}], \circ, Id_{\mathcal A})$ which is strict,
wherein $\circ$ denotes composition and $Id_{\mathcal A}$ is the identity endofunctor.
Here, to give the functor $f : {\mathcal C}\to [{\mathcal A}, {\mathcal A}]$
is equally to give a functor $\odot: {\mathcal C}\times {\mathcal A}
\to {\mathcal A}$ where $X\odot A = (fX)A$ for all $X\in {\mathcal C}$
and $A\in {\mathcal A}$; to give
the invertible and natural $\tilde{f}_{X,Y} : (fX) \circ (fY )
\to f(X \otimes Y )$ (or rather their inverses) is
equally to give a natural isomorphism with components
$$\alpha_{X,Y,A}: (X\otimes Y )\odot A\to X\odot (Y \odot A);$$
to give the invertible $f^{\circ}: Id_{\mathcal A}\to f {\bf 1}$
(or rather its inverse) is equally to give a natural
isomorphism with components $\lambda_{A} : {\bf 1} \odot A\to A$;
and the coherence conditions for $F$ become the commutativity
of the three diagrams \cite[(1.1), (1.2) and (1.3)]{JK2001}
which are the pentagon axiom involving the associator of
${\mathcal C}$ and the triangle axioms for the action of the
unit object ${\bf 1}$ on ${\mathcal A}$ compatible with the left
unitor of ${\mathcal C}$ respectively. It is clear that a monoidal
category ${\mathcal C}$ acts on itself by defining $\odot=\otimes$.
We refer to \cite{JK2001} for more details.
\begin{convention}
\label{xxcon1.2}
Let ${\mathcal C}$ be a monoidal category acting on another
category ${\mathcal A}$.
\begin{enumerate}
\item[(1)]
If both ${\mathcal C}$ and ${\mathcal A}$ are {\it $\Bbbk$-linear},
we automatically assume that
\begin{enumerate}
\item[(1a)]
morphisms and functors involving in the definition of
action are all $\Bbbk$-linear, and
\item[(1b)]
$\odot$ preserves direct sums in each argument.
\end{enumerate}
\item[(2)]
If both ${\mathcal C}$ and ${\mathcal A}$ are {\it abelian},
we automatically assume that
\begin{enumerate}
\item[(2a)]
morphisms and functors involving in the definition of
action are all $\Bbbk$-linear,
\item[(2b)]
${\mathcal C}$ is monoidal abelian in the sense of
Definition \ref{xxdef1.1}(2),
\item[(2c)]
$\odot$ preserves exact sequences in each argument.
\end{enumerate}
\item[(3)]
If both ${\mathcal C}$ and ${\mathcal A}$ are {\it triangulated},
we automatically assume that
\begin{enumerate}
\item[(3a)]
morphisms and functors involving in the definition of
action are all $\Bbbk$-linear,
\item[(3b)]
${\mathcal C}$ is monoidal triangulated in the sense of
Definition \ref{xxdef1.1}(3),
\item[(3c)]
$\odot$ preserves exact triangles and commutes
with the suspension in each argument.
\end{enumerate}
\end{enumerate}
\end{convention}
Next we recall some definitions concerning the Frobenius-Perron
dimension of an endofunctor. We refer to \cite{CGWZZZ2017} for
other related definitions. Let $\dim$ be $\dim_{\Bbbk}$.
\begin{definition} \cite{CGWZZZ2017}
\label{xxdef1.3}
Let $\mathcal{C}$ be a $\Bbbk $-linear category.
\begin{enumerate}
\item[(1)]
An object $X$ in $\mathcal{C}$ is called a {\it brick} if
$$\Hom_{\mathcal{C}}(X,X)=\Bbbk.$$
\item[(2)]
Let $\phi:=\{X_1,\ldots, X_n\}$ be a finite subset of nonzero objects
in $\mathcal{C}$. We say that $\phi$ is a {\it brick set} if each
$X_i\in \phi$ is a brick and
$$\Hom_{\mathcal{C}}(X_i,X_j)=0, \forall \; i\neq j.$$
\item[(3)]
Let $\phi:=\{X_1,\ldots, X_n\}$ and let $\sigma$ be an endofunctor
of $\mathcal{C}$. The {\it adjacency matrix} of $(\phi,\sigma)$
is defined to be
$$A(\phi,\sigma)=(a_{ij})_{n\times n},
\quad {\text{where}} \quad
a_{ij}=\dim \Hom_{\mathcal{C}}(X_i, \sigma(X_j))\;\;
\forall \; i,j.$$
\item[(4)]
Let $\Phi_b$ be the collection of all finite brick sets in
$\mathcal{C}$. The {\it Frobenius-Perron dimension} of an
endofunctor $\sigma$ is defined to be
$$\fpd(\sigma)
:= \sup\limits_{\phi\in \Phi_b}\{\rho(A(\phi,\sigma))\}$$
where $\rho(A)$ is the spectral radius of a square matrix $A$
\cite[Section 1]{CGWZZZ2017}, i.e. the largest absolute
value of $A$.
\item[(5)]
The {\it Frobenius-Perron curvature} of $\sigma$ is defined to be
$$\fpv (\sigma):=\sup_{\phi\in \Phi_{b}} \{\limsup_{n\to\infty} \;
(\rho(A(\phi,\sigma^n)))^{1/n} \}.$$
\item[(6)]
If $\mathcal{C}$ is a monoidal $\Bbbk$-linear category
acting on a $\Bbbk$-linear category ${\mathcal A}$
and $M$ is an object in
$\mathcal{C}$, the {\it Frobenius-Perron dimension} of $M$
is defined to be
$$\fpd(M):=\fpd(M\odot -)$$
where $M\odot -$ is considered as an endofunctor of
${\mathcal A}$ and $\fpd(M\odot -)$ is defined in part (4).
Similarly, the {\it Frobenius-Perron curvature} of $M
\in {\mathcal C}$ is
defined to be
$$\fpv(M):=\fpv(M\odot -)$$
where $M\odot -$ is considered as an endofunctor of
${\mathcal A}$ and $\fpd(M\odot -)$ is defined in part (5).
\item[(7)]
As a special case of (6),
if $\mathcal{C}$ is a monoidal $\Bbbk$-linear category
and $M$ is an object in
$\mathcal{C}$, the {\it Frobenius-Perron dimension} of $M$ is
defined to be
$$\fpd(M):=\fpd(M\otimes -)$$
where $\fpd(M\otimes -)$ is defined in part (4).
Similarly, the {\it Frobenius-Perron curvature} of $M$ is
defined to be
$$\fpv(M):=\fpv(M\otimes -)$$
where $\fpv(M\otimes -)$ is defined in part (5).
\end{enumerate}
\end{definition}
When $\mathcal{C}$ is $R-\Modfd$ for an algebra $R$, a brick set
is also called a semibrick \cite{As2020}. If both ``full'' and
``exceptional'' conditions [Definition \ref{xxdef7.8}(2,3)] are
satisfied, this is also known as a simple-minded collection, see
\cite[Definition 3.2]{KY2014}.
Now we recall the definition of representation types.
\begin{definition}
\label{xxdef1.4}
Let $A$ be a finite dimensional algebra over $\Bbbk$.
\begin{enumerate}
\item[(1)]
We say $A$ is of {\it finite type} or {\it finite representation
type} if there are only finitely many isomorphism classes of
finite dimensional indecomposable left $A$-modules.
\item[(2)]
We say $A$ is {\it tame} or {\it of tame representation type}
if it is not of finite representation type, and
for every $n\in {\mathbb N}$, all but finitely many
isomorphism classes of $n$-dimensional indecomposables occur in
a finite number of one-parameter families.
\item[(3)]
We say $A$ is {\it wild} or {\it of wild representation type}
if, for every finite dimensional $\Bbbk$-algebra $B$, the
representation theory of $B$ can be representation embedded
into that of $A$.
\end{enumerate}
\end{definition}
We always assume that the base field $\Bbbk$ is algebraically closed.
A famous trichotomy result due to Drozd \cite{D1979} states
that every finite dimensional algebra is either of finite,
tame, or wild representation type. By classical theorems
of Gabriel \cite{Ga1972} and Nazarova \cite{N1973}, the quivers
of finite and tame representation types correspond to the
$\mathbb{ADE}$ and $\widetilde{\mathbb{A}}\widetilde{\mathbb{D}}
\widetilde{\mathbb{E}}$ diagrams respectively.
By \cite[Theorem 0.3]{CGWZZZ2017}, the representation type
of a quiver $Q$ is indicated by the value of the Frobenius-Perron
dimension of the suspension functor of the derived category
$D^b(\Repr(Q))$.
To show some monoidal structure is $\fpd$-infinite
[Definition \ref{xxdef0.2}(1)], we need the following concepts.
\begin{definition}
\label{xxdef1.5}
Let $\mathcal{C}$ be a $\Bbbk$-linear category.
\begin{enumerate}
\item[(1)]
Let $\phi$ be an infinite set of objects in $\mathcal{C}$.
We say $\phi$ is an {\it infinite brick set} if
$$\Hom_{\mathcal{C}}(X,Y)=\begin{cases} \Bbbk & {\text{ if }}
X=Y\quad {\text{in $\phi$}},\\
0 & {\text{ if }}
X\neq Y \quad {\text{in $\phi$}}.\end{cases}$$
\item[(2)]
Suppose $\mathcal{C}$ is abelian or triangulated. A brick set
$\phi$ (either finite or infinite) is called a {\it connected brick set}
if $\Ext^1_{\mathcal{C}}(X,Y)\neq 0$ for
all $X,Y\in \phi$.
\end{enumerate}
\end{definition}
The next is about the definition of a weak bialgebra.
\begin{definition}
\label{xxdef1.6}
Let $A$ be an algebra with a $\Bbbk$-linear morphism
$\Delta: A\rightarrow A\otimes A$. We say $\Delta$ is a
{\it prealgebra morphism} if
\begin{equation}
\nota
\Delta(ab)=\Delta(a)\Delta(b)
\end{equation}
for all $a,b\in A.$
\end{definition}
A prealgebra morphism is an algebra morphism if and
only if $\Delta(1)=1\otimes 1$ where $1$ is the
identity (or unit) element of $A$.
\begin{definition} \cite[Definition 2.1]{BNS1999}
\label{xxdef1.7}
A {\it weak bialgebra} is a vector space $B$ over the
base field $\Bbbk$ with the structures of
\begin{enumerate}
\item[(a)]
an associative algebra $(B, m, 1 )$ with multiplication
$m: B\otimes B\to B$ and unit $1 \in B$, and
\item[(b)]
a coassociative coalgebra $(B, \Delta, \varepsilon)$ with
comultiplication $\Delta: B\to B\otimes B$ and couint
$\varepsilon: B\to \Bbbk$
\end{enumerate}
satisfying the following conditions.
\begin{enumerate}
\item[(i)]
The comultiplication $\Delta: B\to B\otimes B$ is a
prealgebra morphism.
\item[(ii)]
The unit and counit satisfy
\begin{equation}
\label{E1.7.1}\tag{E1.7.1}
(\Delta(1 )\otimes 1 )(1 \otimes \Delta(1 ))
=(\Delta\otimes Id) \Delta(1 )
=(1 \otimes \Delta(1 ))(\Delta(1 )\otimes 1 )
\end{equation}
and
\begin{equation}
\label{E1.7.2}\tag{E1.7.2}
\varepsilon( xyz)=\sum\varepsilon(x y_{(1)})\varepsilon(y_{(2)}z)=
\sum\varepsilon(x y_{(2)})\varepsilon(y_{(1)}z),
\end{equation}
where $\Delta(y)=\displaystyle\sum y_{(1)}\otimes y_{(2)}$ is the Sweedler notation.
\end{enumerate}
\end{definition}
We refer to \cite{BCJ2011, BNS1999, NTV2003, NV2002} for many
other basic definitions related to weak bialgebras and weak Hopf
algebras. The tensor structure of left modules over a weak
bialgebra \cite[Proposition 2]{NTV2003} is given below.
\begin{definition}
\label{xxdef1.8}
Let $A$ be a weak bialgebra over $\Bbbk$. For two left $A$-modules
$M$ and $N$, define $M\otimes^l N=\Delta(1)(M\otimes_{\Bbbk} N)$
where $\otimes_{\Bbbk}$ is the tensor product over $\Bbbk$.
\end{definition}
The following lemma is clear.
\begin{lemma}
\label{xxlem1.9}
Let $A$ be a weak bialgebra.
\begin{enumerate}
\item[(1)]
With the tensor product $-\otimes^l-$ given in
Definition \ref{xxdef1.8}, both $A-\Modfd$ and $A-\Mod$ are
monoidal abelian categories.
\item[(2)]
Both
$D^b(A-\Modfd)$ and $D^b(A-\Mod)$ are monoidal triangulated.
\end{enumerate}
\end{lemma}
Finally we mention a fact in quiver representations.
\begin{lemma} \cite[p.63]{GR1992}
\label{xxlem1.10}
Let $Q$ be a quiver of type $\mathbb{A}_n$. Then
$M\{i,j\}$, for $1\leq i<j\leq n$, defined as in
\eqref{E0.7.2}-\eqref{E0.7.3}, form the
complete list of indecomposable representations of $Q$,
up to isomorphisms.
\end{lemma}
\begin{convention}
\label{xxcon1.11}
For the rest of the paper, we will use $A$ for an algebra over
$\Bbbk$. It could have a bialgebra or weak bialgebra structure.
We will use $\mathcal{A}$ for the abelian category of finite
dimensional left $A$-modules, also denoted by $A-\Modfd$.
Let $\mathcal{T}$ be a triangulated category that could have
extra monoidal triangulated structure. Sometimes $\mathcal{T}$
denotes the bounded derived category $D^b(\mathcal{A})$.
A general $\Bbbk$-linear or monoidal category is denoted by
$\mathcal{C}$.
\end{convention}
\section{Preliminaries on quiver representations}
\label{xxsec2}
We refer to \cite{ASS2006} for some basic concepts in quiver
representation theory. Here we fix some convention. Let $Q=
(Q_0, Q_1, s, t)$ be a quiver where $Q_0$ is the set of
vertices of $Q$, $Q_1$ is the set of arrows of $Q$, and
$s,t: Q_1\to Q_0$ are source and target maps of $Q$ respectively.
Let $M$ be a representation of $Q$. For each vertex $i\in Q_0$,
let $(M)_i$ denote the vector space at $i$. For each arrow
$\alpha\in Q_1$ from vertex $i:=s(\alpha)$ to vertex
$j:=t(\alpha)$, let $(M)_{\alpha}$ denote the $\Bbbk$-linear map
from $(M)_{i}$ to $(M)_{j}$ corresponding to $\alpha$. Let
${\text{Rep}}(Q)$ be the category of all representations of $Q$
and $\Repr(Q)$ be the full subcategory of ${\text{Rep}}(Q)$
consisting of finite dimensional representations. By
\cite[Theorem 1.7 in Chapter VII]{ASS2006}, every finite
dimensional hereditary algebra $A$ is Morita equivalent to
the path algebra $\Bbbk Q$ of a finite acyclic quiver $Q$.
The definition of a weak bialgebra is given in
Definition \ref{xxdef1.7}.
The path algebra $\Bbbk Q$ is naturally equipped with a
coalgebra structure that makes it a weak bialgebra, see
\cite[Example 2.5]{NV2002} and \cite[Section 3]{He2008a}.
We state this known fact as follows.
\begin{lemma}
\label{xxlem2.1}
Let $Q$ be a finite quiver.
\begin{enumerate}
\item[(1)]
Its path algebra $\Bbbk Q$ is a cocommutative weak bialgebra
whose coalgebra structure is determined by
$$\Delta(p)=p\otimes p \quad \mathrm{and }\quad \varepsilon(p)=1$$
for any path $p=\alpha_1\alpha_2\cdots \alpha_m$ of length
$m\geq 0$.
\item[(2)]
The weak bialgebra structure in part {\rm{(1)}} is a bialgebra if
and only if $|Q_0|=1$.
\end{enumerate}
\end{lemma}
Since $\Bbbk Q$ is a cocommutative weak bialgebra,
$\Repr(Q)(\cong \Bbbk Q-\Modfd)$ is a symmetric monoidal
abelian category where the tensor product is given in Definition
\ref{xxdef1.8}. For two representations $M=((M)_i,(M)_\alpha)$
and $N=((N)_i,(N)_\alpha)$ of $Q$ where $i\in Q_0$ and
$\alpha\in Q_1$, we can define the {\it vertex-wise tensor
product} $M\otimes^{v} N$ by
\begin{equation}
\label{E2.1.1}\tag{E2.1.1}
(M\otimes^{v} N)_i=(M)_i \otimes_{\Bbbk} (N)_i, \quad {\text{and}}\quad
(M\otimes^{v} N)_\alpha=(M)_\alpha \otimes_{\Bbbk} (N)_\alpha,
\end{equation}
for all $i\in Q_0$ and $\alpha\in Q_1$. Then the tensor product
$M\otimes^l N$ given in Definition \ref{xxdef1.8} is exactly equal to
the vertex-wise tensor product $M\otimes^{v} N$ give in \eqref{E2.1.1}.
Therefore, we do not distinguish these two tensors and denote them by
$M\otimes N$. The tensor structure of quiver representations has been
studied by many researchers, see, for example, \cite{He2005,
He2008a, He2008b, He2009, KS2012, Ki2010}. Note that the
bounded derived category $D^b(\Repr(Q))$ is a tensor triangulated
category in the sense of \cite[Definition 1.1]{B2005}; consequently,
it is a monoidal triangulated category.
In this paper we study more than one tensor structures of the quiver
representations. But, in this section, we are only working on the
tensor structure defined by \eqref{E2.1.1}. We start with some
details about quiver representations.
We have defined the Frobenius-Perron dimension, denoted by
$\fpd$, of an object in a monoidal category $\mathcal{C}$
in Definition \ref{xxdef1.3}(4). A nice property of $\fpd$
is a duality property when applied to objects in $\Repr(Q)$.
\begin{definition}
\label{xxdef2.2}
Let $Q=(Q_0,Q_1,s_Q,t_Q)$ be a quiver and $M$ be a finite-dimensional
representation of $Q$.
\begin{enumerate}
\item[(1)]
Define the {\it opposite quiver} of $Q$, denoted by $Q^{op}$,
to be the quiver which reverses all arrows in $Q_1$, that is
$$Q^{op}_0=Q_0, Q^{op}_1=Q_1, s_{Q^{op}}=t_Q, t_{Q^{op}}=s_Q.$$
\item[(2)]
Define the {\it dual} of $M$, denoted by $M^*$, to be the
representation of $Q^{op}$ that is determined by
$$(M^*)_i=((M)_i)^*, (M^*)_{\alpha}=((M)_{\alpha})^*,$$
for all vertices $i$ and arrows $\alpha$.
\end{enumerate}
\end{definition}
We give an easy example.
\begin{example}
\label{xxex2.3}
Let $Q$ be $\xymatrix{1 \ar[r] & 2}$ and $M$ be
$\xymatrix{\Bbbk \ar[r]^{(1,0)^T} & \Bbbk^2}$. Then we have
$$Q^{op}: \xymatrix{1 & 2\ar[l]} \quad
{\text{and}} \quad
M^*= \xymatrix{\Bbbk & \Bbbk^2\ar[l]_{(1,0)} }.$$
\end{example}
For two finite dimensional $\Bbbk$-vector spaces $U,V$, we
have
$$(V\otimes U)^*= U^*\otimes V^*\cong V^*\otimes U^*.$$
Furthermore, if we have linear maps between finite dimensional
$\Bbbk$-vector spaces, say $f:V \rightarrow V'$ and
$g: U\rightarrow U'$, then we have the commutative diagram
$$
\xymatrix{
(V\otimes U)^* \ar[d]^{\simeq }&
(V'\otimes U')^*\ar[d]^{\simeq }\ar[l]_{(f\otimes g)^*} \\
V^*\otimes U^* & V'^* \otimes U'^*. \ar[l]_{f^*\otimes g^*}}
$$
The above commutative diagram holds for objects in
$\Repr(Q)$ since $\Bbbk Q$ is a commutative weak bialgebra
[Lemma \ref{xxlem2.1}(1)]. It is clear that the $\Bbbk$-linear
dual induces a contravariant equivalence between the abelian
categories $\Repr(Q)$ and $\Repr(Q^{op})$. Combining these
two facts, we have
\begin{align}
\label{E2.3.1}\tag{E2.3.1}
\Hom_{(\Repr(Q))^{op}}(X,M\otimes N)
&\cong \Hom_{\Repr(Q)}(M\otimes N, X)\\
\notag &\cong
\Hom_{\Repr(Q^{op})}(X^*, M^*\otimes N^*)
\end{align}
for $M,N,X\in \Repr(Q)$. Now the following
lemma follows from \eqref{E2.3.1}.
\begin{lemma}
\label{xxlem2.4}
Let $Q$ be a finite quiver and $M$ be a finite
representation of $Q$. Then
$$\fpd(M\otimes_{{\Repr(Q)}^{op}}-)
=\fpd(M^*\otimes_{{\Repr(Q^{op})}}-)$$
where $M$ is considered as an object in the tensor
category ${\Repr(Q)}^{op}$ and $M^*$ an object
in $\Repr(Q^{op})$.
The same statement holds for other Frobenius-Perron
invariants such as $\fpv$.
\end{lemma}
Next we study some brick sets of quiver representations.
Let $S(i)$ denote the simple representation (of $Q$) at
vertex $i$ where
\begin{equation}
\label{E2.4.1}\tag{E2.4.1}
S(i)_j=\begin{cases}
\Bbbk & j=i\\
0 & j\neq i
\end{cases}
\quad \mathrm{and} \quad
S(i)_\alpha=0,\;\; \forall \;\; \alpha\in Q_1,
\end{equation}
and $e_i$ denote the trivial path at vertex $i$.
By the tensor structure of $\Repr(Q)$ \eqref{E2.1.1},
we have the following.
\begin{lemma}
\label{xxlem2.5}
Let $S(i)$ be the simple left $\Bbbk Q$-module defined as above
and $M$ in $\Repr(Q)$. Then $S(i)\otimes M$ is
isomorphic to a direct sum of finitely many copies of $S(i)$.
\end{lemma}
In the above lemma, $S(i)\otimes M$ could be 0.
\begin{proposition}
\label{xxpro2.6}
Let $M$ be in $\Repr(Q)$. Then
$$\fpd(M)\geq d,$$
where $d=\max\limits_{v\in Q_0}\{\dim ((M)_v)\}$.
\end{proposition}
\begin{proof}
Let $a=\dim (M)_v$ and let $\phi_0=\{S(v)\}$ for $v\in Q_0$. Then
$$\Hom_{\Repr(Q)}(S(v),M\otimes S(v))
=\Hom_{\Repr(Q)}(S(v),S(v)^{\oplus a})=\Bbbk^{\oplus a}$$
which implies that $A(\phi_0, M\otimes -)=(a)_{1\times 1}$. Therefore
$\fpd(M)\geq a$ for all $a$. The assertion follows.
\end{proof}
Note that $\fpd(M)$ may be infinite as the next example
shows (and as predicted by Lemma \ref{xxlem6.4}).
\begin{example}
\label{xxex2.7}
Let $Q$ be the Kronecker quiver $\xymatrix{1 \ar@<1ex>[r]^{\alpha}
\ar[r]_{\beta} & 2}$. Let $S(1)$ be defined as in \eqref{E2.4.1}.
For every $c\in \Bbbk$, we define an object in $\Repr(Q)$:
\begin{equation}
\label{E2.7.1}\tag{E2.7.1}
M_c:=\xymatrix{\Bbbk \ar@<1ex>[r]^{\alpha=Id} \ar[r]_{\beta=c Id} & \Bbbk}.
\end{equation}
Then $M_c$ is a brick object (and such an object is also called a band
module of $Q$ \cite[pp.160-161]{BR1987}). It is easy to see that
$\Hom(M_c, S(1))\cong \Bbbk$ and that $\{M_c,M_{c'}\}$ is a brick set
if $c\neq c'$. As a consequence, $\{M_c, \mid c\in \Bbbk\}$
is an infinite brick set.
Let $T$ be any finite subset of $\Bbbk$ and let $\phi:=
\{M_c \mid c\in T\}$. The $A(\phi, S(1)\otimes -)$ is
a $|T|\times|T|$ matrix in which all entries are 1. Then
$\rho(A(\phi, S(1)\otimes -))=|T|$. Since $\Bbbk$ is infinite,
we obtain that $\fpd(S(1))=\infty$.
\end{example}
Let us consider a slightly more general situation.
\begin{example}
\label{xxex2.8}
Suppose $Q$ is another quiver and $p_1$ and $p_2$ are two paths from
vertex $i$ to vertex $j$ that do not intersect except at
the two endpoints. Then we can consider a similar brick object
$M_c$ so that
$$\begin{aligned}
(M_c)_v&=\begin{cases}
\Bbbk & \quad {\textrm{if $v$ is in either $p_1$ or $p_2$}},\\
0 & \quad {\textrm{otherwise,}}\end{cases}
\\
(M_c)_{\alpha}&=\begin{cases}
Id & \quad {\textrm{if $\alpha$ is in either $p_1$ or $p_2$, but
not the first arrow in $p_2$}},\\
cId & \quad {\textrm{if $\alpha$ is the first arrow in $p_2$}},\\
0 & \quad {\textrm{otherwise,}}\end{cases}
\end{aligned}
$$
or, similar to \eqref{E2.7.1}, we can write it as
$$M_c:=\xymatrix{\Bbbk \ar@<1ex>[r]^{p_1=Id} \ar[r]_{p_2=cId }
& \Bbbk}.$$
Then $\{M_c, \mid c\in \Bbbk\}$ is an infinite brick set.
\end{example}
We will use this example later.
\section{Discrete categories}
\label{xxsec3}
In this section we will prove some basic lemmas for
monoidal abelian categories that are needed in the
proof of Theorem \ref{xxthm0.4}. We start with a definition.
\begin{definition}
\label{xxdef3.1}
Let $\mathcal{C}$ be a monoidal abelian category.
We say $\mathcal{C}$ is {\it discrete} if
\begin{enumerate}
\item[(a)]
$\mathcal{C}$ is $\Hom$-finite, namely
$\Hom_{\mathcal{C}}(M,N)$ is finite dimensional over $\Bbbk$ for objects
$M,N$ in ${\mathcal C}$,
\item[(b)]
every object in $\mathcal{C}$ has finite length,
\item[(c)]
$\mathcal{C}$ has finitely many simple objects, say
$\{S_1,\cdots,S_n\}$, up to isomorphisms, and
\item[(d)]
for all simple objects $S_i$ and $S_j$ in
$\mathcal{C}$,
\begin{equation}
\label{E3.1.1}\tag{E3.1.1}
S_i\otimes S_j\cong \begin{cases} S_i & {\textrm{ if $i=j$}}\\
0 & {\textrm{ if $i\neq j$}}.\end{cases}
\end{equation}
\end{enumerate}
\end{definition}
Note that an essentially small category $\mathcal{C}$ satisfying
condition (b) is called a {\it length} category \cite{Ga1973,KV2018}.
Let $Q$ be a finite quiver. Then there is a canonical monoidal
abelian structure on $\Repr(Q)$ induced by the weak bialgebra
structure defined in Lemma \ref{xxlem2.1}. The following lemma
follows immediately from the definition, see \eqref{E2.1.1}.
\begin{lemma}
\label{xxlem3.2}
Let $Q$ be a finite acyclic quiver. Then the canonical
monoidal abelian structure on $\Repr(Q)$ is discrete.
\end{lemma}
For the rest of this section we assume that $\mathcal{C}$
is discrete.
As a consequence, $\mathcal{C}$ is a Krull-Schmidt category.
For $M\in \mathcal{C}$, let $\ell(M)$ denote the length of
$\mathcal{C}$. Let $IC(M)$ denote the {\it isomorphism class}
of all (possibly repeated) simple subquotients of $M$.
This can be obtained by considering any composition
series of $M$. Even though composition series of $M$ is not
unique, $IC(M)$ is unique, so well-defined.
\begin{lemma}
\label{xxlem3.3}
Let $\mathcal{C}$ be a $\Hom$-finite monoidal abelian category with
finitely many simple objects. Let $\mathbf{1}$ be the unit object.
\begin{enumerate}
\item[(1)]
$\ell(-)$ is additive.
\item[(2)]
For every nonzero object $M$ there is a simple object
$S\in IC(\mathbf{1})$ such that $S\otimes M\neq 0$. By symmetry,
there is a simple object $T\in IC(\mathbf{1})$ such that
$M\otimes T\neq 0$.
\item[(3)]
If $S\in IC(\mathbf{1})$ and $T$ is
a simple object in $\mathcal{C}$,
then $S\otimes T$ is either 0 or a simple object. For each $T$,
there is only one $S\in IC(\mathbf{1})$ such that
$S\otimes T\neq 0$.
\item[(4)]
The multiplicity of any simple object $S$ in $IC(\mathbf{1})$ is 1.
\item[(5)]
If $S, T\in IC(\mathbf{1})$, then
$$S\otimes T\cong \begin{cases} S & {\textrm{ if $S=T$}}\\
0 & {\textrm{ if $S\neq T$}}.\end{cases}
$$
\item[(6)]
$\mathcal{C}$ is discrete if and only if
$S\in IC(\mathbf{1})$ for all simple objects $S$.
\end{enumerate}
\end{lemma}
\begin{proof}
(1) Clear from the definition.
(2) By part (1), we have
\begin{equation}
\label{E3.3.1}\tag{E3.3.1}
\ell(M)=\ell(\mathbf{1}\otimes M)=\sum_{S\in IC(\mathbf{1})}
\ell(S\otimes M).
\end{equation} Therefore there is an $S\in IC(\mathbf{1})$
such that $S\otimes M\neq 0$.
(3) If $S\otimes T\neq 0$, then, by \eqref{E3.3.1}, we have
$$1=\ell(T)=\ell(\mathbf{1}\otimes T)
= \sum_{S'\in IC(\mathbf{1})} \ell(S'\otimes T)
\geq \ell(S\otimes T)\geq 1.$$
Therefore $\ell(S\otimes T)= 1$ and $\ell(S'\otimes T)=0$
for all other $S'\in IC(\mathbf{1})$.
(4) This follows from \eqref{E3.3.1} by taking a simple
object $M$ with $S\otimes M\neq 0$.
(5) It remains to show that $S\otimes T=0$ if
$S$ and $T$ are distinct elements in $IC(\mathbf{1})$.
Suppose on the contrary that $U:=S\otimes T\neq 0$.
By part (3), it is a simple object. Since $U=S\otimes T$ is
a subquotient of $\mathbf{1}\otimes \mathbf{1}$,
$U$ is in $IC(\mathbf{1})$. Since $S\neq T$, we have
either $U\neq S$ or $U\neq T$. By symmetry, we assume
that $U\neq S$. By part (3), there is only one
$W\in IC(\mathbf{1})$ such that $W\otimes U\neq 0$.
This implies that $W\otimes S\neq 0$ as $U=S\otimes T$.
There are two different objects, namely, $S,U\in IC(\mathbf{1})$
such that $W\otimes S\neq 0$ and $W\otimes U\neq 0$.
By the left-version of part (3) this is impossible.
The assertion follows.
(6) If $IC(\mathbf{1})$ contains all simple objects, then
by part (5), $\mathcal{C}$ is discrete.
Conversely, suppose $\mathcal{C}$ is discrete.
For every simple object $T$, by part (2), there is
an $S\in IC(\mathbf{1})$ such that $S\otimes T\neq 0$.
By the definition of discreteness, $T=S$.
So $T\in IC(\mathbf{1})$.
\end{proof}
\begin{proposition}
\label{xxpro3.4}
Let $A$ be a finite dimensional algebra of finite
global dimension. Suppose that $(A-\Modfd, \otimes)$
is a discrete monoidal abelian category. Then, for any simple
left $A$-module $S$ and any $M\in A-\Modfd$,
$$M\otimes S\cong S^{\oplus n}$$
where $n$ is the number of copies of $S$ in the
the composition series of $M$.
\end{proposition}
\begin{proof}
By the 'no loops conjecture', which was proved by Igusa \cite{Ig1990},
\begin{equation}
\label{E3.4.1}\tag{E3.4.1}
\Ext^1_{A}(S,S)=0.
\end{equation}
By definition, $-\otimes-$ is biexact. Hence
$M\otimes S$ has a composition series that is induced
by the composition series of $M$. Let $T$ be a simple
subquotient of $M$. Then $T\otimes S$ is either $S$
when $T\cong S$ or $0$ if $T\not\cong S$. Thus
$M\otimes S$ has a composition series with each
simple subquotient being $S$. The assertion follows
from \eqref{E3.4.1}.
\end{proof}
Recall that $\otimes^v$ is the
canonical tensor given in \eqref{E2.1.1}.
We have an immediate consequence.
\begin{corollary}
\label{xxcor3.5}
Let $Q$ be a finite acyclic quiver.
If $(\Repr(Q), \otimes)$ is another discrete monoidal abelian
structure on $\Repr(Q)$, then for any $M\in \Repr(Q)$
and any simple representation $S$ over $Q$,
$$M\otimes S\cong M\otimes^v S$$
where $\otimes^v$ is defined as in \eqref{E2.1.1}.
\end{corollary}
There are a lot of monoidal categories that are not
discrete. For example, for a finite quiver $Q$,
if $\Repr(Q)$ is equipped with other
bialgebra structure, it may not be discrete,
see Proposition \ref{xxpro7.7}(a-d).
We conclude this section with the definition of
a discrete action.
\begin{definition}
\label{xxdef3.6}
Let $\mathcal{C}$ be a monoidal abelian category acting on
an abelian category ${\mathcal A}$. Assume that both
${\mathcal C}$ and ${\mathcal A}$ satisfy Definition
\ref{xxdef3.1}(a,b,c). Let $\{T_1,\cdots,T_n\}$ (respectively,
$\{S_1,\cdots,S_m\}$) be the complete list of simple objects
in ${\mathcal C}$ (respectively, ${\mathcal A}$), where $m\geq n$.
The action of $\mathcal{C}$ on ${\mathcal A}$ is called
{\it discrete} if
\begin{enumerate}
\item[(d)']
there is a permutation $\sigma\in S_n$ such that
\begin{equation}
\label{E3.6.1}\tag{E3.6.1}
T_i\odot S_j\cong \begin{cases} S_j & {\textrm{ if $j=\sigma(i)$}}\\
0 & {\textrm{ if $j\neq \sigma(i)$}}.\end{cases}
\end{equation}
\end{enumerate}
\end{definition}
\section{Proof of Theorem \ref{xxthm0.4}}
\label{xxsec4}
The aim of this section is to prove Theorem \ref{xxthm0.4}.
We need first recall some facts from representation theory
of quivers.
\begin{proposition}
\cite[Proposition 2.5 in Chapter VII]{ASS2006}
\label{xxpro4.1}
Let $Q$ be a finite, connected, and acyclic quiver and $M$
be a brick such that there exists $a\in Q_0$ with
$\dim (M)_a >1$. Let $Q'$ be the quiver defined as
follows: $Q'=(Q'_0,Q'_1)$, where $Q'_0=Q_0\cup \{b\}$;
$Q'_1=Q_1\cup \{\alpha\}$; and $\alpha:b\rightarrow a$.
Then $\Bbbk Q'$ is of infinite representation type.
\end{proposition}
By duality and Proposition \ref{xxpro4.1}, if $\alpha$
is an arrow of the form $a\rightarrow b$, then $\Bbbk Q'$
is also of infinite representation type.
\begin{lemma}\cite[Corollary 5.14 in Chapter VII]{ASS2006}
\label{xxlem4.2}
If $Q$ is a quiver of type $\mathbb{ADE}$, see
\cite[p.252]{ASS2006}, then every indecomposable
representation of $Q$ is a brick.
\end{lemma}
Recall from Definition \ref{xxdef1.4}(3) that an algebra $A$
is {\it wild} or {\it of wild representation type}
if there is a faithful exact embedding of abelian categories
\begin{equation}
\label{E4.2.1}\tag{E4.2.1}
Emb : \Bbbk\langle x_1, x_2 \rangle -\Modfd
\longrightarrow \mathcal{A}:=A-\Modfd
\end{equation}
that preserves indecomposables and respects isomorphism classes
(namely, for all objects $M_1,M_2$ in $\Bbbk\langle
x_1, x_2\rangle-\Modfd$, $Emb(M_1) \cong Emb(M_2)$ if and only if
$M_1\cong M_2$). A stronger notion of wildness is the following.
An algebra A is called {\it strictly wild}, or {\it fully wild},
if $Emb$ in \eqref{E4.2.1} is a fully faithful embedding
\cite[Proposition 5]{Ar2005}. By definition, strictly wild is
wild, but the converse is not true. It is well-known that a wild
path algebra $\Bbbk Q$ is always strictly wild, see a comment of
Gabriel \cite[p.140]{Ga197374} or \cite[Proposition 7]{Ar2005}.
\begin{lemma}
\label{xxlem4.3}
Let $A$ be a finite dimensional algebra that is strictly wild.
Let $\mathcal{C}$ be an abelian category containing
$\mathcal{A}$ as a full subcategory. Then
$\mathcal{C}$ contains an infinite connected brick set. As a
consequence, if $Q$ is a finite acyclic quiver that is wild,
then $\Repr(Q)$ contains an infinite connected brick set.
\end{lemma}
\begin{proof} The consequence follows from the fact that
a wild quiver is strictly wild. So we only prove the main
assertion.
Let $A$ be strictly wild. By definition, there is
a fully faithful embedding
\begin{equation}
\notag
Emb : \Bbbk\langle x_1, x_2 \rangle -\Modfd\longrightarrow
\mathcal{A}\longrightarrow \mathcal{C}.
\end{equation}
For each $c\in \Bbbk$, let $M(c)$ denote the 1-dimensional simple
module $\Bbbk\langle x_1, x_2\rangle/(x_1-c,x_2)$ and let $N_c$
be $Emb(M_c)$. By taking a free resolution $M(c)$, one can check
that $\Ext^1_{\Bbbk\langle x_1, x_2\rangle}(M(c),M(c'))\neq 0$
for all $c,c'$. Hence $\{M(c)\mid c\in\Bbbk\}$ is an infinite
connected brick set in $\Bbbk\langle x_1, x_2 \rangle-\Modfd$.
Since $Emb$ a fully faithful embedding, $\{N_c\mid c\in\Bbbk\}$
is an infinite connected brick set of $\mathcal{C}$.
\end{proof}
\begin{lemma}
\label{xxlem4.4}
Let $\mathcal{C}$ be an abelian category of finite
global dimension and let $\mathcal{T}$ be the bounded
derived category $D^b(\mathcal{C})$. Suppose that
\begin{enumerate}
\item[(1)]
$\mathcal{T}$ is triangulated equivalent to
$D^b(B-\Modfd)$ for a finite dimensional hereditary
algebra $B$ via tilting object $X$, namely,
$$\RHom_{\mathcal{T}}(X,-):\mathcal{T}
\to D^b(B-\Modfd)$$
is a triangulated equivalence where $B\cong
\RHom_{\mathcal{T}}(X,X)$, and
\item[(2)]
$\mathcal{C}$ contains an infinite {\rm{(}}respectively,
infinite connected{\rm{)}} brick set.
\end{enumerate}
Then $B-\Modfd$ contains an infinite {\rm{(}}respectively,
infinite connected{\rm{)}} brick set.
\end{lemma}
Note that, if $\mathcal{C} =A-\Modfd$ for some
finite dimensional algebra $A$ and if $\mathcal{T}$
is triangulated equivalent to $D^b(B-\Modfd)$,
then, by tilting theory, the existence of $X$ is
automatic.
\begin{proof}[Proof of Lemma \ref{xxlem4.4}]
We only prove the assertion for ``infinite brick set''.
The proof for ``infinite connected brick set''
is similar.
Let
$$F:=\RHom_{\mathcal{T}}(X, -): \mathcal{T}
\longrightarrow D^b(B-\Modfd)$$
be an equivalence of triangulated categories. Let
$\{N(c)\mid c\in U\}$ be an infinite brick set of $\mathcal{C}$
by hypothesis. Then
$$\{F(N(c)) \mid c\in U\}$$
is an infinite brick set of $D^b(B-\Modfd)$.
Since $X$ has finite projective dimension, there is an integer
$n$ independent of $c\in U$ such that
\begin{equation}
\label{E4.4.1}\tag{E4.4.1}
{\text{$H^i(F(N(c)))=0$ for all $|i| > n$.}}
\end{equation}
Note that $B-\Modfd$ is hereditary, which implies that
every indecomposable object in $D^b(B-\Modfd)$ is of the
form $M[i]$ for some indecomposable object $M\in B-\Modfd$
and for some $i$ \cite[Section 2.5]{Ke2007}. By \eqref{E4.4.1},
$F(N(c))=M_c[i_c]$ for some indecomposable object
$M_c\in B-\Modfd$ and some integer $|i_c|\leq n$.
Since $U$ is infinite, there is an infinite subset $U'\subseteq U$
such that $i_c$ is a constant for all $c\in U'$. Let $i_0$ denote
such $i_c$. Thus $\{M_c[i_0]\mid c\in U'\}$ is an infinite brick
set in $D^b(B-\Modfd)$. Since the suspension $[1]$ is an
isomorphism of $D^b(B-\Modfd)$, $\{M_c\mid c\in U'\}$ is an
infinite brick set in $D^b(B-\Modfd)$. Finally, using the
fact that $B-\Modfd$ is a full subcategory of
$D^b(B-\Modfd)$, we obtain that $\{M_c\mid c\in U'\}$ is an
infinite brick set in $B-\Modfd$.
\end{proof}
\begin{lemma}
\label{xxlem4.5}
Let $A$ be a finite dimensional hereditary algebra that is not
of finite representation type. Then
the abelian category $A-\Modfd$ contains an infinite brick
set. As a consequence, if $Q$ is a finite acyclic quiver not of type
$\mathbb{ADE}$, then $\Repr(Q)$ contains an infinite brick set.
\end{lemma}
\begin{proof} By \cite[Theorem 1.7 in Chapter VII]{ASS2006}
every such $A$ is Morita equivalent to a path algebra $\Bbbk Q$ for
some finite acyclic quiver $Q$. By Lemma \ref{xxlem4.4}, we may
assume that $A$ is $\Bbbk Q$.
Since $A$ is not of finite type, $Q$ is not of finite type.
Lemma 4.3 settles the case where Q is of wild representation type.
Case 1: $Q$ is of type $\widetilde{\mathbb{A}}$. Since $Q$ is acyclic,
there exist two different paths $p_1$ and $p_2$ from $v$ to $u$,
where $v\neq u\in Q_0$. We can further assume that
the length $p_1$ is smallest among all such choices. In this case,
$\Repr(Q)$ contains an infinite brick set by Example \ref{xxex2.8}.
Case 2: $Q$ is of type $\widetilde{\mathbb{D}}\widetilde{\mathbb{E}}$.
We consider a slightly more general situation and then apply the
assertion to the special case (see quivers in
\cite[Corollary 2.7 in Chapter VII]{ASS2006}). If there exists a
subquiver $Q'$ of $Q$ and an indecomposable representation $M$
of $Q'$ satisfying:
\begin{enumerate}
\item[(a)]
$Q'$ is a quiver of type $\mathbb{D}$ or $\mathbb{E}$,
\item[(b)]
there exists $x\in Q'_0$, $\dim (M)_x>1$,
\item[(c)]
$\{y\} \in Q_0\setminus Q'_0$,
\item[(d)]
there exists an arrow $\alpha\in Q_1$ such that $\alpha:y\rightarrow x$,
\end{enumerate}
then we construct a new representation $M(\lambda)$ as follows:
\[(M(\lambda))_v=
\begin{cases}
(M)_v & \mathrm{if}~ v\in Q'_0\\
\Bbbk & \mathrm{if}~ v=y\\
0 & \mathrm{otherwise},
\end{cases}
\qquad\qquad
(M(\lambda))_{\beta}=
\begin{cases}
(M)_{\beta} & \mathrm{if}~ \beta\in Q'_1\\
\lambda & \mathrm{if}~ \beta=\alpha\\
0 & \mathrm{otherwise},
\end{cases}
\]where $\lambda: \Bbbk \rightarrow (M)_x$ is a $\Bbbk$-linear map.
Then by the proof of \cite[Proposition 2.5 in Chapter VII]{ASS2006},
each $M(\lambda)$ is a brick and there exists infinitely many
pairwise non-isomorphic bricks of the form $M(\lambda)$. In fact,
the proof of \cite[Proposition 2.5 in Chapter VII]{ASS2006} shows that
there is an infinite set of $U:=\{\lambda: \Bbbk \to M_x\}$ such that
$\Hom_{\Repr(Q)}(M(\lambda), M(\lambda'))=0$ for all
$\lambda,\lambda'\in U$. This means that $\Repr(Q)$ contains an
infinite brick set. Dually, If we change the condition (d) into (d)':
\begin{enumerate}
\item[(d)']
there exists an arrow $\alpha\in Q_1$ such that $\alpha:x\rightarrow y$,
\end{enumerate}
we can still construct an infinite brick set as above.
Now we go back to a quiver of type $\widetilde{\mathbb{D}}\widetilde{\mathbb{E}}$.
By Lemma \ref{xxlem4.4}, we can
assume that
\begin{enumerate}
\item[(e)]
$Q'$ is one of the quivers in
\cite[Corollary 2.6 in Chapter VII.2]{ASS2006}, and that
\item[(f)]
(c) and (d) hold.
\end{enumerate}
Note that (e) implies that (a) holds.
By \cite[Corollary 2.6 in Chapter VII.2]{ASS2006}, (b) holds.
Therefore we proved that $\Repr(Q)$ contains an infinite brick
set.
\end{proof}
\begin{lemma}
\label{xxlem4.6}
Let $\mathcal{C}$ be a monoidal abelian category acting on
an abelian category ${\mathcal A}$. Assume that both
${\mathcal C}$ and ${\mathcal A}$ satisfy Definition
\ref{xxdef3.1}(a,b,c). Suppose that
\begin{enumerate}
\item[(a)]
$\mathcal{A}$ contains an infinite brick set, and that
\item[(b)]
the action of ${\mathcal C}$ on ${\mathcal A}$ is
discrete.
\end{enumerate}
Then there is a simple $T\in {\mathcal C}$ such that
$\fpd(T)=\infty$.
\end{lemma}
Lemma \ref{xxlem4.6} may fail if the action is not discrete.
Let $Q$ be the Kronecker quiver in Example \ref{xxex2.7} and
$A$ be its path algebra equipped with the cocommutative bialgebra
structure in Proposition \ref{xxpro7.7}(a). Then $S(1)$ is the unit object
in $\mathcal{A}$ and $S(2)\otimes M=S(2)^{\oplus \dim(M)}$ for
any $M\in \mathcal{A}$. Since all indecomposables in $\Repr(Q)$
are well-understood, one can check that $\fpd(S(1))=\fpd(S(2))=1$
(details are omitted).
\begin{proof}[Proof of Lemma \ref{xxlem4.6}]
Let $\{N(c)\mid c\in U\}$ is an infinite brick set of
$\mathcal{A}$ and let $\{S_1,\cdots,S_n\}$ be the
complete list of simple objects in $\mathcal{A}$
up to isomorphism. For each $1\leq i\leq n$, define
$$U_i:=\{c\in U\mid \Hom_{\mathcal{A}}(N(c),S_i)\neq 0\}.$$
For each $c\in U$, there is an $i$ such that
$\Hom_{\mathcal{A}}(N(c),S_i)\neq 0$. This implies
that $U=\bigcup_{i=1}^n U_i$. Therefore there is
an $i$ such that $U_i$ is infinite. Without loss of
generality, we may assume that $U=U_1$ is infinite.
Since the action is discrete, there is a simple object
$T\in {\mathcal C}$ such that $T\odot S_1\cong S_1$.
Now $\Hom_{\mathcal A}(N(c), S_1)\neq 0$ implies
that every simple subquotient of $T\odot N(c)$ is
isomorphic to $S_1$. In particular, $T\odot N(c)$
contains a copy of $S_1$ for all $c$.
Let $W$ be any finite subset of $U$ and let
$\phi=\{N(c) \mid c\in W\}$. Using the above paragraph,
$$\Hom_{\mathcal{A}}(N(c), T\odot N(c'))
\neq 0$$
for all $c,c'\in W$. This implies that
$\rho(A(\phi, T\odot -))\geq |W|$ and $\fpd(T)
\geq |W|$. Since $|W|$ can be arbitrarily
larger, $\fpd (T)=\infty$.
\end{proof}
The following is a part of Theorem \ref{xxthm0.4}.
\begin{theorem}
\label{xxthm4.7}
Let $A$ be a finite dimensional hereditary algebra
and let ${\mathcal A}=A-\Modfd$.
Let ${\mathcal C}$ be a monoidal abelian category
satisfying Definition \ref{xxdef3.1}(a,b,c).
Suppose that there is an action of $\mathcal{C}$
on ${\mathcal A}$ that is discrete. Then the following
are equivalent:
\begin{enumerate}
\item[(a)]
$A$ is of finite representation type,
\item[(b)]
$\fpd(M)<\infty$ for every irreducible object $M\in \mathcal{C}$,
\item[(c)]
$\fpd(M)<\infty$ for every indecomposable object $M\in \mathcal{C}$,
\item[(d)]
$\fpd(M)<\infty$ for every object $M\in \mathcal{C}$
\end{enumerate}
\end{theorem}
\begin{proof}
(a) $\Longrightarrow$ (d):
If $A$ is of finite representation type, then $\mathcal{A}$
has only finitely many indecomposable objects. This means that there
are only finitely many brick sets. Then, by definition, $\fpd(\sigma)$
is finite for every endofunctor $\sigma$ of $\mathcal{A}$. In particular,
$\fpd(M)$ is finite for every representation $M\in \mathcal{C}$.
(d) $\Longrightarrow$ (c) $\Longrightarrow$ (b): Clear.
(b) $\Longrightarrow$ (a): It suffices to show that if $A$ is not
of finite representation type, then $\fpd(M)=\infty$ for some irreducible
representation $M\in \mathcal{C}$. The assertion follows from Lemmas
\ref{xxlem4.5} and \ref{xxlem4.6}.
\end{proof}
We will use the following lemma concerning a bound of
spectral radius of a matrix.
\begin{lemma}
[Gershgorin Circle Theorem \cite{Ger1931}]
\label{xxlem4.8}
Let $A$ be a complex $n\times n$ matrix, with entries $a_{ij}$.
For $i\in \{1,\dots ,n\},$ let
$R_{i}=\sum\limits_{j\neq i}\left|a_{{ij}}\right|$
be the sum of the absolute values of the non-diagonal entries in
the $i$-th row. Let $D(a_{ii},R_{i})\subseteq \mathbb {C}$ be a
closed disc centered at $a_{ii}$ with radius $R_{i}$. Then every
eigenvalue of $A$ lies within at least one of the Gershgorin
discs $D(a_{ii},R_{i}).$ As a consequence,
$\rho(A)\leq \max_i\{|a_{ii}|+R_i\}$.
\end{lemma}
\begin{proposition}
\label{xxpro4.9}
Suppose $\mathcal{T}$ is a triangulated category
satisfying
\begin{enumerate}
\item[(a)]
$\mathcal{T}$ is $\Hom$-finite and hence Krull-Schmidt,
\item[(b)]
there are objects $\{X_1,\cdots,X_N\}$ such that every
indecomposable object in $\mathcal{T}$ is of the form
$X_i[m]$ for some $1\leq i\leq N$ and $m\in \mathbb{Z}$, and
\item[(c)]
for every two indecomposable objects $X,Y$ in $\mathcal{T}$,
$\Hom_{\mathcal{T}}(X,Y[m])=0$ for $|m|\gg 0$.
\end{enumerate}
Then the following hold.
\begin{enumerate}
\item[(1)]
$\fpd(\sigma)<\infty$ for every endofunctor $\sigma$ of
$\mathcal{T}$.
\item[(2)]
If ${\mathcal C}$ is a monoidal triangulated category acting
on ${\mathcal T}$, then $\fpd(M)<\infty$ for
every object $M\in {\mathcal C}$.
\end{enumerate}
\end{proposition}
\begin{proof}
Let $\sigma$ be an endofunctor of $\mathcal{T}$. Since there are
only finitely many $X_i$ in hypothesis (b),
we can assume that every $\sigma(X_i)$ is a direct summand
of
\begin{equation}
\label{E4.9.1}\tag{E4.9.1}
X=\left(\bigoplus_{i=1}^{N} \bigoplus_{j=-\delta}^{\delta-1}
X_i[j]\right)^{\oplus \xi}
\end{equation}
for some fixed $\delta$ and $\xi$.
We make some definitions. Let
$$
\begin{aligned}
\alpha&=\max\{\dim \Hom_{\mathcal{T}}(X_i[s],X)\mid \;\forall \;\; s,i\},\\
\gamma&=\max\{|s| \mid \; \Hom_{\mathcal{T}}(X_i[s],X)\neq 0
{\text{ for some $i$}}\}.
\end{aligned}
$$
For any given finite brick set $\phi$, it is always is a subset of
$$\Phi:=\bigcup_{j=-D}^{D-1} \{X_1[j],\cdots,X_N[j]\}$$
for some large $D\gg 0$. Since $\phi$ is a subset of $\Phi$,
we have
$$\rho(A(\phi, \sigma))
\leq \rho(A(\Phi, \sigma)).$$
By Definition \ref{xxdef1.3}(4), it is enough to show that
$\rho(A(\Phi, \sigma))$ is uniformly bounded
on $\Phi$ (for each fixed $X$ as given in \eqref{E4.9.1}).
For the next calculation we make a linear order on the
objects in $\Phi$ as
\begin{align}
\label{E4.9.2}\tag{E4.9.2}
\Phi&=\{X_1[-D],\cdots,X_N[-D]\} \cup
\{X_1[-D+1],\cdots,X_N[-D+1]\} \cup \\
&\qquad \cdots \cup
\{X_1[D-2],\cdots,X_N[D-2]\} \cup
\{X_1[D-1],\cdots,X_N[D-1]\} \notag
\end{align}
and write is as $\Phi=\{Y_1,\cdots, Y_{2ND}\}$.
Write the adjacency matrix $A(\Phi, \sigma)$
as $(a_{ij})$. For each pair $(i,j)$, by definition,
$$a_{ij}=\dim \Hom_{\mathcal T}(X_{s_i}[w_i], \sigma(X_{s_j}[w_j]))
\leq \dim \Hom_{\mathcal T}(X_{s_i}[w_i], X[w_j])
\leq \alpha,$$
for some $s_i,s_j,w_i,w_j$; and by the ordering in \eqref{E4.9.2},
we obtain
$$a_{ij}=0 \quad {\text{if $|i-j|>2N\delta +\gamma+2.$}}$$
Then each $R_i$ in the Lemma \ref{xxlem4.8} is bounded
by $(2N\delta +\gamma+2)\alpha$.
By Lemma \ref{xxlem4.8} (Gershgorin Circle Theorem),
there is a bound of $\rho(A(\Phi, \sigma))$
which is independent of $D$. Since every finite brick set
$\phi$ is a subset of $\Phi$ for some large $D$,
$\rho(A(\phi, \sigma))$ has a bound
that is independent of $\phi$. Therefore
$\fpd(\sigma)$ is finite as desired.
\end{proof}
We will use the following special case.
Recall that ${\mathcal A}=A-\Modfd$
and that ${\mathcal T}=D^b({\mathcal A})$.
\begin{corollary}
\label{xxcor4.10}
Let $A$ be a finite dimensional hereditary algebra that
is of finite representation type. Then every
monoidal triangulated structure on $\mathcal{T}$ is
$\fpd$-finite.
\end{corollary}
\begin{proof} Since $A$ is of finite type, we can list
all indecomposable left $A$-modules $\{X_1,\cdots,X_N\}$.
Since $A$ is hereditary, every indecomposable
object in $\mathcal{T}$ is of the form $X_i[s]$
for some $1\leq i\leq N$ and $s\in \mathbb{Z}$
\cite[Lemma 3.3]{CGWZZZ2017}. Finally,
since $A$ is hereditary, then
$\Hom_{\mathcal{T}}(X_i, X_j[m])=0$ for $m\neq 0,1$.
Thus $\mathcal{T}$ satisfies hypotheses (a,b,c) in
Proposition \ref{xxpro4.9}. Then the assertion follows from
Proposition \ref{xxpro4.9}(2) by setting ${\mathcal C}=
{\mathcal T}$ and $\odot=\otimes$.
\end{proof}
\begin{lemma}
\label{xxlem4.11}
Let $A$ be a finite dimensional hereditary algebra.
Let ${\mathcal C}$ be a monoidal abelian category
satisfying Definition \ref{xxdef3.1}(a,b,c).
Suppose that $\mathcal{C}$ acts on ${\mathcal A}$
via $\odot$. Let $\odot_{D}$ be the induced action
of $D^b({\mathcal C})$ on ${\mathcal T}$.
Let $M$ be an object in $\mathcal{C}$, also viewed
as an object in $D^b({\mathcal C})$.
\begin{enumerate}
\item[(1)]
If $n\neq 0,1$, then $\fpd(M[n]\odot_{D}-)=0$.
\item[(2)]
$\fpd(M\odot_{D}-)=\fpd(M\odot -)$.
\end{enumerate}
\end{lemma}
\begin{proof}
(1) Suppose $n\geq 2$.
Let $\phi$ be a (finite) brick set. Since $\mathcal{A}$ is
hereditary, every indecomposable object is of the form $X[m]$. Then
we can write $\phi=\bigcup_{\lambda \in \mathbb{Z}} \phi_{\lambda}$ where
$\phi_{\lambda}$ is either empty or
$\{X_{\lambda,1}[\lambda],X_{\lambda,2}[\lambda],\cdots,
X_{\lambda,t_\lambda}[\lambda]\}$.
Since $\mathcal{A}$ is hereditary,
$$\Hom_{{\mathcal{T}}}(X_{\lambda,s}[\lambda], M[n]\odot_{D}
X_{\delta,s'}[\delta])=
\Hom_{{\mathcal{T}}}(X_{\lambda,s}[\lambda], (M\odot X_{\delta,s'})[n+\delta])
=0$$
for all $\lambda\leq \delta$.
Then $A(\phi, M[n]\odot_{D}-)$ is strictly upper
triangular. Therefore $\rho(A(\phi, M[n]\odot_{D}-))=0$.
As a consequence the assertion follows.
The proof for $n<0$ is similar.
(2) Let $\phi$ be a brick set as in part (1).
Similar to the proof of part (1), also see
\cite[Lemma 6.1]{CGWZZZ2017}, we obtain that
$A(\phi, M\odot_{D}-)$ is a block lower triangular
matrix. So we only need to consider the case that
$\phi=\{X_1[d],X_2[d],\cdots X_t[d]\}$ for the same
$d$. In this case, $A(\phi, M\odot_{D}-)
=A(\phi[-d],M\odot-)$. Therefore the assertion
follows.
\end{proof}
Now we are ready to prove Theorem \ref{xxthm0.4}.
We will use the notation introduced in Theorem
\ref{xxthm4.7} and Lemma \ref{xxlem4.11}.
\begin{theorem}
\label{xxthm4.12}
Let $A$ be a finite dimensional hereditary algebra
and let ${\mathcal A}=A-\Modfd$.
Let ${\mathcal C}$ be a monoidal abelian category
satisfying Definition \ref{xxdef3.1}(a,b,c).
Suppose that there is an action of $\mathcal{C}$
on ${\mathcal A}$ that is discrete. Then the following
are equivalent:
\begin{enumerate}
\item[(a)]
$A$ is of finite representation type,
\item[(b)]
$\fpd(M)<\infty$ for every irreducible object $M\in \mathcal{C}$,
\item[(c)]
$\fpd(M)<\infty$ for every indecomposable object $M\in \mathcal{C}$,
\item[(d)]
$\fpd(M)<\infty$ for every object $M\in \mathcal{C}$,
\item[(e)]
$\fpd(M \odot_{D} -)<\infty$ for every indecomposable object
$M\in D^b(\mathcal{C})$,
\item[(f)]
$\fpd(M \odot_{D} -)<\infty$ for every object $M\in D^b(\mathcal{C})$.
\end{enumerate}
Suppose $A$ is the path algebra $\Bbbk Q$ for some finite
quiver $Q$. Then any of
conditions {\rm{(a)}} to {\rm{(f)}} is equivalent to
\begin{enumerate}
\item[(g)]
$Q$ is a finite union of quivers of type $\mathbb{ADE}$.
\end{enumerate}
\end{theorem}
\begin{proof}
By Theorem \ref{xxthm4.7}, the
first four conditions are equivalent.
(a) $\Longrightarrow$ (f): This follows from
Proposition \ref{xxpro4.9} and the proof of Corollary
\ref{xxcor4.10}.
(f) $\Longrightarrow$ (e): Clear.
(e) $\Longrightarrow$ (c): This follows from Lemma
\ref{xxlem4.11}(2).
\end{proof}
Clearly Theorem \ref{xxthm0.4} is a special case of Theorem
\ref{xxthm4.12}.
\section{$mtt$-structures of a monoidal triangulated category}
\label{xxsec5}
First we recall the definition on a $t$-structure on a triangulated
category. The notion of a $t$-structure was introduced by
Beilinson-Bernstein-Deligne in \cite{BBD1981}. We make a
small change in the definition below.
\begin{definition}
\label{xxdef5.1}
Let $\mathcal{T}$ be a triangulated category.
\begin{enumerate}
\item[(1)]
A {\it $t$-structure} on $\mathcal{T}$ is a pair of full
subcategories $(\mathcal{T}^{\leq 0},
\mathcal{T}^{\geq 0})$ satisfying the following conditions.
\begin{enumerate}
\item[(1a)]
$\mathcal{T}^{\leq 0}\subseteq \mathcal{T}^{\leq 1}$ and
$\mathcal{T}^{\geq 0}\supseteq \mathcal{T}^{\geq 1}$ where
we use notation $\mathcal{T}^{\leq n}=\mathcal{T}^{\leq 0}[-n]$
and $\mathcal{T}^{\geq n}=\mathcal{T}^{\geq 0}[-n]$.
\item[(1b)]
If $M\in \mathcal{T}^{\leq 0}$ and $N\in \mathcal{T}^{\geq 1}$,
then $\Hom_{\mathcal{T}}(M,N)=0$.
\item[(1c)]
For any object $X\in \mathcal{T}$, there is a distinguished
(exact) triangle
$$M\to X\to N\to M[1]$$
with $M\in \mathcal{T}^{\leq 0}$ and $N\in \mathcal{T}^{\geq 1}$.
\end{enumerate}
\item[(2)]
The {\it heart} of the $t$-structure is the
full subcategory
$$\mathcal{T}^{\geq 0}\cap \mathcal{T}^{\leq 0}$$
which is denoted by $\mathcal{H}$ or $\mathcal{H}(\mathcal{T})$.
\item[(3)]
\cite[p.1427]{CR2018}
A $t$-structure is called {\it bounded} if for each $X\in
\mathcal{T}$, there exist $m\leq n$
such that $X\in \mathcal{T}^{\leq n} \cap \mathcal{T}^{\geq m}$.
\item[(4)]
\cite[p.1427]{CR2018}
A bounded $t$-structure is called {\it hereditary} if
$\Hom_{\mathcal{T}}(X, Y[n])=0$ for $n\geq 2$ and
$X,Y\in \mathcal{H}$.
\end{enumerate}
\end{definition}
As a classical example, if $\mathcal{T}$ is the derived category
$D^b(A-\Modfd)$, there is a natural $t$-structure on
$\mathcal{T}$ by setting $\mathcal{T}^{\leq 0}$ to be the complexes
concentrated in degrees less than or equal to 0 (and similarly for
$\mathcal{T}^{\geq 0}$). In this case the heart of this
$t$-structure is $A-\Modfd$.
Note that hereditary $t$-structures are very special. Even for the
path algebra of a quiver $Q$ of type $\mathbb{A}_3$, there is a
$t$-structure in $D^b(\Repr(Q))$ that is not hereditary, see
\cite{KV1988} for a classification of $t$-structures of $D^b(\Repr(Q))$
of a quiver of Dynkin type.
We would like to introduce a version of the $t$-structure in a monoidal
triangulated category. We use $mtt$ for ``monoidal triangulated $t$''
in the next definition.
\begin{definition}
\label{xxdef5.2}
Let $\mathcal{T}$ be a monoidal triangulated category
in parts (1,2,3) and a triangulated category in part (4).
\begin{enumerate}
\item[(1)]
A $t$-structure $(\mathcal{T}^{\leq 0},\mathcal{T}^{\geq 0})$
on $\mathcal{T}$ is called an {\it $mtt$-structure}
if the following conditions hold.
\begin{enumerate}
\item[(a)]
$\mathcal{T}^{\leq 0}\otimes \mathcal{T}^{\leq 0}\subseteq
\mathcal{T}^{\leq 0}$ and
$\mathcal{T}^{\leq 0}\otimes \mathcal{T}^{\leq 0}\not\subseteq
\mathcal{T}^{\leq -1}$.
\item[(b)]
Both $\mathcal{T}^{\leq 0}$ and $\mathcal{T}^{\geq 0}$
are closed under taking direct summands.
\item[(c)]
There is an integer $D\geq 0$ such that
$\mathcal{T}^{\geq D}\otimes \mathcal{T}^{\geq D}\subseteq
\mathcal{T}^{\geq D}$.
\end{enumerate}
\item[(2)]
The minimal integer $D$ in condition (c) is called the
{\it deviation} of the $mtt$-structure of $\mathcal{T}$.
\item[(3)]
The {\it deviation} of $(\mathcal{T}, {\bf 1}, \otimes)$
is defined to be
$$D_{\otimes}({\mathcal T})=
\inf \{ {\text{deviations of all possible $mtt$-structures of
$(\mathcal{T}, {\bf 1}, \otimes)$}}\}.$$
\item[(4)]
Suppose ${\mathcal T}$ is a triangulated category. The
{\it upper deviation} of ${\mathcal T}$ is defined to be
$$UD({\mathcal T})=
\sup \{ D_{\otimes}({\mathcal T})
\mid {\text{all possible monoidal triangulated structures
on ${\mathcal T}$}}\}.$$
The
{\it lower deviation} of ${\mathcal T}$ is defined to be
$$LD({\mathcal T})=
\inf \{ D_{\otimes}({\mathcal T})
\mid {\text{all possible monoidal triangulated structures
on ${\mathcal T}$}}\}.$$
\end{enumerate}
\end{definition}
\begin{example}
\label{xxex5.3} We give two classical examples.
\begin{enumerate}
\item[(1)]
If $A$ is a finite dimensional weak Hopf algebra (or a weak
bialgebra), then $A-\Modfd$ has a natural monoidal abelian
structure, and consequently,
$\mathcal{T}:=D^b(A-\Modfd)$ has an induced
monoidal triangulated structure. It is clear that
${\mathcal T}$ has a canonical $mtt$-structure
by setting $\mathcal{T}^{\leq 0}$ (respectively,
$\mathcal{T}^{\geq 0}$) to be the complexes concentrated in
degrees less than or equal to 0 (respectively, greater than
or equal to 0). In this case the deviation of the $mtt$-structure
is $0$. If $A$ is hereditary as an algebra, then the above
$t$-structure is hereditary.
By definition, $D_{\otimes}(\mathcal{T})=0$ when we consider
the monoidal triangulated structure given above. As a consequence,
$LD({\mathcal T})=0$ when ${\mathcal T}$ is considered as a
triangulated category. A special case is $LD(D^b(\Repr(Q)))=0$
for all finite acyclic quivers $Q$.
\item[(2)]
If $\mathbb{X}$ is a smooth projective scheme of dimension $d$,
then ${\mathcal T}:=D^b(coh(\mathbb{X}))$ has a canonical $mtt$-structure
by setting $\mathcal{T}^{\leq 0}$ (respectively,
$\mathcal{T}^{\geq 0}$) to be the complexes concentrated in
degrees less than or equal to 0 (respectively, greater than
or equal to 0).
If $\mathbb{X}$ is of dimension 1, then the above $t$-structure
is hereditary.
Note that the deviation of the canonical $mtt$-structure of
${\mathcal T}$ is at most $d$.
By definition, $D_{\otimes}(\mathcal{T})\leq d$ with the natural
monoidal triangulated structure. As a consequence,
$LD({\mathcal T})\leq d$ when $\mathcal{T}$ is considered as
a triangulated category.
\end{enumerate}
\end{example}
\begin{lemma}
\label{xxlem5.4}
Let ${\mathcal T}$ be a monoidal triangulated category
with an $mtt$-structure $(\mathcal{T}^{\leq 0},\mathcal{T}^{\geq 0})$
of deviation zero. Suppose that
$(\mathcal{T}^{\leq 0},\mathcal{T}^{\geq 0})$
is a hereditary $t$-structure of $\mathcal{T}$.
Then the heart of the $mtt$-structure is a monoidal
abelian category.
\end{lemma}
\begin{proof}
By \cite[Theorem 1.3.6]{BBD1981}, the heart $\mathcal{H}$
is an abelian category.
Since $\mathcal{T}$ is a monoidal triangulated category, there
is a unit object ${\bf 1}\in \mathcal{T}$. First we claim
that ${\bf 1}\in \mathcal{H}$. By definition, there is a
distinguished triangle
\begin{equation}
\label{E5.4.1}\tag{E5.4.1}
M\to {\bf 1}\to N\to M[1]
\end{equation}
where $M\in \mathcal{T}^{\leq 0}$ and $N\in \mathcal{T}^{\geq 1}$.
For any object $X\in \mathcal{H}$, since $X\otimes-$ is an exact
functor, $$X\otimes M\to X\to X\otimes N\to X\otimes M[1]$$
is a distinguished triangle. However, $X\otimes N\in
\mathcal{T}^{\geq 1}$ as the deviation is zero. Then
$\Hom(X,X\otimes N)=0$ by the definition of $t$-structure,
and
\begin{equation*}
\label{E5.4.2}\tag{E5.4.2}
X\otimes M[1]\cong (X\otimes N)\oplus X[1]=X\otimes (N\oplus {\bf 1}[1]).
\end{equation*}
By hypothesis the $mtt$-structure is hereditary. By
\cite[Lemma 2.1]{CR2018}, \eqref{E5.4.2} holds for all
$X\in \mathcal{T}$.
Take $X={\bf 1}$, then $M[1]\cong N\oplus {\bf 1}[1]$
and in \eqref{E5.4.1}, the morphism from {\bf 1} to $N$ is zero.
Hence ${\bf 1}$ is isomorphic to a direct summand of $M$,
which is in $\mathcal{T}^{\leq 0}$.
Similarly, for $Y\in \mathcal{T}^{\leq 0}$ and $f: Y\to {\bf 1}[-1]$,
there is a distinguished triangle:
$$Y \stackrel{f}{\longrightarrow} {\bf 1}[-1]\to Z\to Y[1].$$
Apply the exact functor $X\otimes-$ on the above triangle for
all $X\in \mathcal{H}$, and then we obtain $f=0$, i.e.
$\Hom(Y, {\bf 1}[-1])=0$ for all $Y\in \mathcal{T}^{\leq 0}$.
Therefore, ${\bf 1}\in \mathcal{T}^{\geq 0}$.
Finally, ${\bf 1}\in \mathcal{T}^{\geq 0}\cap \mathcal{T}^{\leq 0}=\mathcal{H}$.
Thus we proved the claim.
As for the tensor product bifunctor $\otimes$, since the deviation is zero,
$\mathcal{H}$ is closed under $\otimes$. Hence $\mathcal{H}$ is a monoidal
category with the induced tensor product $\otimes$. The exactness of
$\otimes$ in $\mathcal{H}$ follows from the exactness
of $\otimes$ in ${\mathcal T}$, see \cite[p.1426]{CR2018}.
\end{proof}
\begin{lemma}
\label{xxlem5.5}
Let $\mathbb{X}$ be a smooth projective curve
and let ${\mathcal T}$ be the monoidal triangulated
category $D^b(coh(\mathbb{X}))$.
\begin{enumerate}
\item[(1)]
The deviation of every hereditary $mtt$-structure
on ${\mathcal T}$ is positive.
\item[(2)]
For any finite dimensional weak bialgebra $A$,
$D^b(A-\Modfd)$ with canonical monoidal structure
is not isomorphic to
$\mathcal{T}$ as monoidal triangulated categories.
\end{enumerate}
\end{lemma}
\begin{proof}
(1) Suppose on the contrary that there is a hereditary
$mtt$-structure on $\mathcal{T}$ with deviation zero.
Let $\mathcal{H}$ be its heart. By Lemma \ref{xxlem5.4},
${\mathcal H}$ is a monoidal abelian category.
Let ${\mathcal O}_x$ be the skyscraper sheaf
at a point $x\in {\mathbb X}$. There is an integer
$n$ such that $M:={\mathcal O}_x [n]$ is in
${\mathcal H}$. Then $M\otimes M$ is in
${\mathcal H}$. By an easy
computation,
$$M\otimes M\cong {\mathcal O}_x [2n] \oplus {\mathcal O}_x [2n-1]
\cong M[n]\oplus M[n-1]$$
which cannot be in ${\mathcal H}$ for any $n$.
This yields a contradiction. Therefore the assertion
follows.
(2) It is clear that the deviation of the
canonical $mtt$-structure of $D_{\otimes}(D^b(A-\Modfd))$
is zero [Example \ref{xxex5.3}(1)].
This $mtt$-structure is also hereditary. Now
the assertion follows from part (1).
\end{proof}
For the rest of this section, we will use Frobenius-Perron
curvature, see Definition \ref{xxdef1.3}(5), to study the
uniqueness of $mtt$-structures with deviation zero, and
then prove Theorems \ref{xxthm0.5} and \ref{xxthm0.7}.
\begin{definition}
\label{xxdef5.6}
Let ${\mathcal C}$ be a monoidal abelian category and
$M\in {\mathcal C}$. The {\it curvature} of $M$ is defined to be
$$v(M)=\overline{\lim\limits_{n\rightarrow \infty}}
( \ell(M^{\otimes n}))^{\frac{1}{n}}$$
where $\ell(-)$ denotes the length of an object.
\end{definition}
\begin{lemma}
\label{xxlem5.7}
Let ${\mathcal C}$ be a monoidal abelian category
satisfying Definition \ref{xxdef3.1}(a,b,c).
Let $A$ be a finite dimensional weak bialgebra
and $\mathcal{A}$ be $A-\Modfd$.
Let $M$ be
an object in $\mathcal{C}$ or $\mathcal{A}$.
\begin{enumerate}
\item[(1)]
If $M$ is in ${\mathcal C}$, then
\begin{equation}
\notag
\fpv(M)\leq v(M)<\infty.
\end{equation}
\item[(2)]
If $M$ is in ${\mathcal A}$, then
\begin{equation}
\label{E5.7.1}\tag{E5.7.1}
\fpv(M)\leq v(M)\leq \dim M.
\end{equation}
\item[(3)]
If $A=\Bbbk Q$ for some finite acyclic quiver $Q$ with the
tensor defined as in \eqref{E2.1.1}, then
\begin{equation}
\label{E5.7.2}\tag{E5.7.2}
\fpv(M)=v(M)=\max_{i\in Q_0} \{ \dim (M)_{i}\}.
\end{equation}
\item[(4)]
If $\mathcal{C}$ is discrete, then,
for every nonzero object $M\in \mathcal{C}$,
$\fpv(M)$ is positive.
\item[(5)]
Suppose that ${\mathcal C}$ acts on a general abelian
category ${\mathcal A}$ such that the action is
discrete in the sense of Definition \ref{xxdef3.6}.
Then, for every object $M$ in ${\mathcal C}$,
$$1\leq \fpv(M)< \infty.$$
\end{enumerate}
\end{lemma}
\begin{proof}
(1)
Let $\Hom$ denote $\Hom_{\mathcal{C}}$.
Let
$$\alpha:=\max\{\ell(X_i\otimes X_j)\mid {\text{
$X_i$ and $X_j$ are simple}}\},$$
and
$$\beta:=\max\{\dim \End(X_i) \mid {\text{
$X_i$ is simple}}\}.$$
Then, for any objects $X$ and $Y$ in
${\mathcal C}$, we have
\begin{equation}
\label{E5.7.3}\tag{E5.7.3}
\ell(X\otimes Y)\leq \alpha \ell(X)\ell(Y),
\end{equation}
and
\begin{equation}
\label{E5.7.4}\tag{E5.7.4}
\dim \Hom(X, Y)\leq \beta\ell(X)\ell(Y).
\end{equation}
By induction,
$\ell(X^{\otimes n})\leq \alpha^{n-1}
\ell(X)^n$ which implies that
$v(X)\leq \alpha \ell(X)<\infty$.
Given a brick set $\phi=\{X_1,\cdots, X_r\}$, define
$\ell (\phi):=\max\limits_{X\in \phi} \{\ell( X)\}$. By
Lemma \ref{xxlem4.8},
$$\rho(A(\phi, M^{\otimes n}\otimes_{\mathcal{C}}-))
\leq \max\limits_{i=1,\cdots, r} \{\sum_{j=1}^r \dim
\Hom(X_i, M^{\otimes n}\otimes X_j)\}.$$
By \eqref{E5.7.3} and \eqref{E5.7.4}, we have
\begin{eqnarray*}
\dim \Hom(X_i, M^{\otimes n}\otimes X_j)
&\leq & \alpha \beta \ell( X_i) (\ell(M^{\otimes n}) \ell( X_j))\\
&\leq & \alpha \beta (\ell(\phi))^2 (\ell(M^{\otimes n}))\\
&\leq & \alpha \beta (\ell(\phi))^2 (v(M)+\varepsilon)^n)
\end{eqnarray*}
for arbitrary small $\varepsilon>0$ and for $n\gg 0$.
Therefore,
$$\rho(A(\phi, M^{\otimes n}\otimes_{\mathcal{C}}-))
\leq \alpha \beta r (\ell( \phi))^2 (v(M)+\varepsilon)^n),$$
which implies that
\begin{equation}
\label{E5.7.5}\tag{E5.7.5}
\rho(A(\phi, M^{\otimes n}\otimes_{\mathcal{C}}-))^{\frac{1}{n}}
\leq (\alpha \beta r (\dim \phi)^2)^{\frac{1}{n}}(v(M)+\varepsilon),
\end{equation}
for $n\gg 0$. When $n\rightarrow \infty$, the limit of right side of
inequality \eqref{E5.7.5} is $v(M)+\varepsilon$, so $\fpv(M)\leq v(M)+
\varepsilon$ for every small $\varepsilon$. The assertion follows.
(2) It follows from Definition \ref{xxdef1.8} that
\begin{equation}
\label{E5.7.6}\tag{E5.7.6}
\dim M\otimes N\leq (\dim M)(\dim N)
\end{equation}
for all $M,N\in \mathcal{A}$. It is also clear that
\begin{equation}
\label{E5.7.7}\tag{E5.7.7}
\dim \Hom_{\mathcal{A}}(M, N)\leq \dim \Hom_{\Bbbk}(M,N)=(\dim M)
(\dim N).
\end{equation}
By \eqref{E5.7.6}, $\dim M^{\otimes n}
\leq (\dim M)^n$, which implies that
$v(M)\leq \dim M$. Now the assertion follows from
part (1).
(3) Let $\phi=\{S(i)\}$ where $i$ is a vertex of $Q$.
Write $\dim (M)_{i}=d_i$. Then $\rho(A(\phi, M^{\otimes n}))$ is the
integer $d_i^n$ and
$\lim\limits_{n\rightarrow \infty} \rho(A(\phi, M^{\otimes n}))^{\frac{1}{n}}=d_i.$
Hence $\fpv(M)\geq d_i$ for all $i$. It is clear that $v(M)=
\max\{d_i\mid i\in Q_0\}$. Therefore part (1) implies that $\fpv(M)=v(M).$
(4) Suppose $\mathcal{A}$ is discrete. Then
there is a simple object $S$ such that $M\otimes S\neq 0$
and $\Hom_{\mathcal{A}}(S, M\otimes S)\neq 0$. By induction,
one can show that $\Hom_{\mathcal{A}}(S, M^{\otimes n}\otimes S)\neq 0$
for all $n$. Therefore $\fpv(M)\geq 1$.
(5) Using a similar proof of part (1), one sees that
$\fpv(M)< \infty$. Using the proof of part (4),
one can show that
$\fpv(M)\geq 1$. Details are omitted.
\end{proof}
\begin{remark}
\label{xxrem5.8}
\begin{enumerate}
\item[(1)]
Let $\mathcal{C}$ be a monoidal abelian category acting on
an abelian category ${\mathcal A}$. Assume that ${\mathcal C}$
satisfies Definition \ref{xxdef3.1}(a,b,c). The action of
$\mathcal{C}$ on ${\mathcal A}$ is called {\it $\fpv$-positive} if
\begin{enumerate}
\item[(e)]
$\fpv(M)>0$ for every nonzero object
$M$ in $\mathcal{C}$. We say $\mathcal{C}$ is
$\fpv$-positive if the natural action of $\mathcal{C}$
on itself is $\fpv$-positive.
\end{enumerate}
\item[(2)]
By Lemma \ref{xxlem5.7}(5) if an action of $\mathcal{C}$
on ${\mathcal A}$ is discrete, then it is {\it $\fpv$-positive}.
\item[(3)]
Suppose an action of $\mathcal{C}$
on ${\mathcal A}$ is $\fpv$-positive.
Let $\mathcal{C}'$ be a monoidal abelian subcategory
$\mathcal{C}$. Then the induced action of $\mathcal{C}'$
on ${\mathcal A}$ is $\fpv$-positive. In general,
such an action is not discrete.
\item[(4)]
There are other natural examples that the action of $\mathcal{C}$
on ${\mathcal A}$ is not discrete, but $\fpv$-positive, see
below.
If $A$ is a finite-dimensional bialgebra and let
${\mathcal C}=A-\Modfd$, then $\mathcal{C}$
is $\fpv$-positive. Let $0\neq M\in \mathcal{C}$ and
let $S_0$ be a simple submodule of $M$. Then $M\otimes S_0\neq 0$
as $\dim M\otimes S_0=\dim M \dim S_0$ (when $A$ is
a bialgebra). For each $i \geq 1$, we define $S_{i}$
inductively to be a simple module of $M\otimes S_{i-1}$.
So $S_i\subseteq M\otimes S_{i-1}$ for all $i\geq 1$.
Continuing this process, we will obtain a set of simple object
$\Gamma=\{S_0,S_1,S_2,\cdots\}$.
Since $A$ has finite many simples, $|\Gamma|<\infty$. Hence,
there exists $m<n\in \mathbb{Z}^{+}$, such that $S_n\cong S_m$.
For all $i\geq n$, we redefine $S_i$ to be $S_{i-k(n-m)}$
where $k$ is an integer such that $m\leq i-k(m-n)<n$.
By the construction, we have, for all $i\geq m$ and all
$s\geq 0$,
$$\dim \Hom(S_{i+1}, M\otimes S_{i})\geq 1 \text{ and }
\dim \Hom(S_{i+s}, M^{\otimes s}\otimes S_{i})\geq 1.$$
Therefore, by taking the brick set $\phi=\{S_m,S_{m+1},\cdots, S_{n}\}$,
one sees that, for each $s$,
$A(\phi, M^{\otimes s}\otimes-)$ is a non-negative matrix
that contains a permutation matrix. As a consequence,
$\rho(A(\phi, M^{\otimes s}\otimes-))\geq 1$ for all $s\geq 1$,
which implies that $\fpv(M)\geq 1$.
\item[(5)]
In $\Repr(Q)$ where the tensor defined as in \eqref{E2.1.1},
$\fpv(M)$, unlike $\fpd(M)$, is an invariant only dependent on the
the dimension vector of $M$ (which is independent of the orientations
of arrows in the quiver).
\end{enumerate}
\end{remark}
Next we investigate $mtt$-structures on
$D^b(\mathcal{C})$.
\begin{lemma}
\label{xxlem5.9}
Suppose that a monoidal abelian category ${\mathcal C}$
acts on an arbitrary abelian category ${\mathcal A}$.
Let ${\mathcal T}=D^b(\mathcal{C})$. Assume that
\begin{enumerate}
\item[(a)]
the above action is either discrete or $\fpv$-positive,
\item[(b)]
${\mathcal C}$ is hereditary, and
\item[(c)]
$(\mathcal{T}^{\leq 0},\mathcal{T}^{\geq 0})$
is any hereditary $mtt$-structure of deviation zero
on ${\mathcal T}$.
\end{enumerate}
Let $\mathcal{H}$ be the heart of the above $mtt$-structure.
Then the following hold.
\begin{enumerate}
\item[(1)]
\cite[Lemma 2.1]{CR2018}
If $M$ is an indecomposable object in $\mathcal{T}$,
then $M$ is in $\mathcal{T}^{\leq b}\cap
\mathcal{T}^{\geq b}$ for some integer $b$.
\item[(2)]
If $M\in \mathcal{C}$, then $M$ is in the heart $\mathcal{H}$.
\item[(3)]
The $mtt$-structure $(\mathcal{T}^{\leq 0},\mathcal{T}^{\geq 0})$
given in (c) is the canonical $mtt$-structure of ${\mathcal T}$.
\end{enumerate}
\end{lemma}
\begin{proof}
(2,3) We only prove this when the action is discrete.
First we claim that $\fpv(M \odot_{\mathcal T} -)>0$ if
$0\neq M\in {\mathcal C}$. It is clear that
$$\fpv(M \odot_{\mathcal T} -)\geq \fpv(M \odot_{\mathcal C} -).$$
Now the claim follows from Lemma \ref{xxlem5.7}(5).
Let $M$ be an indecomposable object in $\mathcal{C}$.
Then $M\in \mathcal{T}^{\leq b}\cap\mathcal{T}^{\geq b}$ for
some $b$. If $b\neq 0$, then $M^{\otimes n}\in \mathcal{T}^{\leq nb}
\cap \mathcal{T}^{\geq nb}$ by Definition \ref{xxdef5.2}(a,c).
For any fixed brick set $\phi$, $A(\phi, M^{\otimes n}
\odot_{\mathcal T} -)$ is zero for $n\gg 0$ by the hereditary
property of Definition \ref{xxdef5.1}(4). Therefore
$\fpv(M\odot_{\mathcal T} -)=0$. By the first paragraph,
$\fpv(M\odot_{\mathcal T} -)>0$, yielding a contradiction.
Therefore $b=0$, or equivalently, $M\in \mathcal{T}^{\leq 0}
\cap\mathcal{T}^{\geq 0}=:\mathcal{H}$. This implies that ${\mathcal C}
\subseteq {\mathcal H}$. By \cite[Lemma 2.1]{CR2018}
and \cite[Lemma 3.6]{SR2016}, ${\mathcal C} ={\mathcal H}$,
and consequently, the $mtt$-structure $(\mathcal{T}^{\leq 0},
\mathcal{T}^{\geq 0})$ in hypothesis (c) must be the canonical
$mtt$-structure of ${\mathcal T}$.
\end{proof}
The following is basically Theorem \ref{xxthm0.7}.
\begin{theorem}
\label{xxthm5.10}
Let $A$ be a finite dimensional hereditary weak bialgebra.
Suppose that the monoidal abelian category $\mathcal{A}$ is
either discrete or $\fpv$-positive.
\begin{enumerate}
\item[(1)]
There is a unique hereditary $mtt$-structure with deviation
zero on $D^b(\mathcal{A})$.
\item[(2)]
The $\mathcal{A}$ is the heart of any hereditary $mtt$-structure
with deviation zero on $D^b(\mathcal{A})$.
\item[(3)]
The $\mathcal{A}$ is uniquely determined by the monoidal
triangulated structure on $D^b(\mathcal{A})$.
\end{enumerate}
\end{theorem}
\begin{proof}
Let ${\mathcal C}={\mathcal A}$. Then we can easily check
all hypotheses in Lemma \ref{xxlem5.9}. Then part (1) follows
from Lemma \ref{xxlem5.9}(3).
(2,3) Follow directly from part (1).
\end{proof}
\begin{proof}[Proof of Theorem \ref{xxthm0.5}]
If $A$ is a bialgebra, by Remark \ref{xxrem5.8}(4),
$\mathcal{A}$ is $\fpv$-positive. Therefore
the hypothesis of Theorem \ref{xxthm5.10} is
satisfied. Now the assertion follows from the
uniqueness of hereditary $mtt$-structure with
deviation zero in Theorem \ref{xxthm5.10}.
\end{proof}
\begin{proof}[Proof of Corollary \ref{xxcor0.6}]
Let $Q$ and $Q'$ be two quivers such that
$D^b(\Repr(Q))$ and $D^b(\Repr(Q'))$ are
equivalent as monoidal triangulated categories.
By Theorem \ref{xxthm0.5}, this equivalent induces
an equivalence between $\Repr(Q)$ and $\Repr(Q')$.
Recall that $Q$ and $Q'$ are acyclic. For each acyclic
quiver there are finitely many simple representations,
say $\{S_i\}_{i=1}^n$, that are associated to vertices
$\{1,\cdots,n\}$ of the quiver. The correspondence
between those simple representations gives rise to a
bijective map $f: Q_0 \rightarrow Q'_0$. By
\cite[Lemma 2.12, p.84]{ASS2006}, $\dim \Ext^1 (S_i, S_j)$
is the number of arrows from vertex $i$ to vertex $j$.
Therefore the number of arrows from $f(i)$ to $f(j)$ is
the same as that from $i$ to $j$. Thus $Q\cong Q'$.
\end{proof}
\section{Proof of Theorem \ref{xxthm0.3}}
\label{xxsec6}
The proof of Theorem \ref{xxthm0.3} uses several results
about weighted projective lines and takes several pages
in total. The final step of the proof is given
at the end of this section. First we recall some basic
definitions concerning weighted projective lines. Details
can be found in \cite[Section 1]{GL1987}.
For $t\geq 1$, let ${\bf p}:=(p_0,p_1,\cdots,p_t)$ be a
$(t+1)$-tuple of positive integers, called the {\it weight}
or {\it weight sequence}. Let
${\bf D}:=(\lambda_0, \lambda_1,\cdots, \lambda_t)$ be a
sequence of distinct points of the projective line
${\mathbb P}^1$ over $\Bbbk$. We normalize ${\bf D}$
so that $\lambda_0=\infty$, $\lambda_1=0$ and
$\lambda_2=1$ (if $t\geq 2$). Let $R$ denote the commutative
algebra
\begin{equation}
\label{E6.0.1}\tag{E6.0.1}
\Bbbk[X_0,X_1,\cdots,X_t]/(X_i^{p_i}-X_1^{p_1}+\lambda_i X_0^{p_0},
i=2,\cdots,t).
\end{equation}
The image of $X_i$ in $R$ is denoted by $x_i$ for all $i$.
Let ${\mathbb L}$ be the abelian group of rank 1
generated by $\overrightarrow{x_i}$ for $i=0,1,\cdots,t$
and subject to the relations
$$p_0 \overrightarrow{x_0}= \cdots =p_i \overrightarrow{x_i}=\cdots
=p_t \overrightarrow{x_t}=: \overrightarrow{c}.$$
The algebra $R$ is ${\mathbb L}$-graded by setting $\deg x_i=
\overrightarrow{x_i}$. The corresponding
{\it weighted projective line},
denoted by ${\mathbb X}({\bf p},{\bf D})$ or simply ${\mathbb X}$,
is a noncommutative space whose category of coherent sheaves is
given by the quotient category
$$coh({\mathbb X}):=\frac{\gr^{\mathbb L}-R}{\gr_{f.d.}^{\mathbb L}-R},$$
see \cite[p.155]{Le2011}.
The weighted projective lines are classified into the following
three classes:
\begin{equation}
\label{E6.0.2}\tag{E6.0.2}
{\mathbb X} \;\; {\rm{is}}\;\;
\begin{cases} domestic \;\; & {\rm{if}} \;\; {\bf p}
\;\; {\rm{is}}\; (p, q), (2,2,n), (2,3,3), (2,3,4), (2,3,5);\\
tubular \;\; & {\rm{if}} \;\; {\bf p}
\;\; {\rm{is}}\; (2,3,6), (3,3,3), (2,4,4), (2,2,2,2);\\
wild \;\; & {\rm{otherwise}}.
\end{cases}
\end{equation}
In \cite[Section 4.4]{Sc2012}, domestic (respectively, tubular,
wild) weighted projective lines are called {\it parabolic}
(respectively, {\it elliptic, hyperbolic}). Let ${\mathbb X}$
be a weighted projective line. A sheaf $F\in coh({\mathbb X})$
is called {\it torsion} if it is of finite length in
$coh({\mathbb X})$. Let $Tor({\mathbb X})$ denote the full
subcategory of $coh({\mathbb X})$ consisting of all torsion
objects. By \cite[Lemma 4.16]{Sc2012}, the category $Tor({\mathbb X})$
decomposes as a direct product of orthogonal blocks
\begin{equation}
\label{E6.0.3}\tag{E6.0.3}
Tor({\mathbb X})=\prod_{x\in {\mathbb P}^1\setminus
\{\lambda_0,\lambda_1,\cdots,\lambda_{t}\}} Tor_{x}
\; \times \; \prod_{i=0}^{t} Tor_{\lambda_i}
\end{equation}
where $Tor_{x}$ is equivalent to the category of nilpotent
representations of the Jordan quiver (with one vertex and
one arrow) over the residue field $\Bbbk_{x}$ and where
$Tor_{\lambda_i}$ is equivalent to the category of nilpotent
representations over $\Bbbk$ of the cyclic quiver of length
$p_i$. A simple object in
$coh({\mathbb X})$ is called {\it ordinary simple} (see
\cite{GL1987}) if it is the skyscraper sheaf ${\mathcal O}_x$ of
a closed point $x\in {\mathbb P}^1\setminus
\{\lambda_0,\lambda_1,\cdots,\lambda_{t}\}$.
Let $Vect({\mathbb X})$ be the full subcategory of
$coh({\mathbb X})$ consisting of all vector bundles. Similar
to the elliptic curve case \cite[Section 4]{BB2007}, one can
define the concepts of {\it degree}, {\it rank} and
{\it slope} of a vector bundle on a weighted projective
line ${\mathbb X}$; details are given in \cite[Section 4.7]{Sc2012}
and \cite[Section 2]{LM1994}. For each
$\mu\in {\mathbb Q}$, let $Vect_{\mu}({\mathbb X})$ be the
full subcategory of $Vect({\mathbb X})$ consisting of all
semistable vector bundles of slope $\mu$. By convention,
$Vect_{\infty}({\mathbb X})$ denotes $Tor({\mathbb X})$.
By \cite[Comments after
Corollary 4.34]{Sc2012}, every indecomposable object in
$coh({\mathbb X})$ is in
\begin{equation}
\nota
\bigcup_{\mu\in {\mathbb Q}\cup\{\infty\}} Vect_{\mu}({\mathbb X}).
\end{equation}
The {\it dualizing element} of $\mathbb{X}$ is denoted by
\begin{equation}
\label{E6.0.4}\tag{E6.0.4}
\omega_0:= (t-2)\overrightarrow{c}
-\sum_{i=1}^n \overrightarrow{x}_i \in \mathbb{L}.
\end{equation}
Below we collect some nice properties of weighted projective lines.
The definition of a stable tube (or simply tube) was introduced
in \cite{Ri1984}.
\begin{lemma} \cite[Lemma 7.9]{CGWZZZ2017}
\label{xxlem6.1}
Let ${\mathbb X}={\mathbb X}({\bf p}, {\bf D})$ be a weighted
projective line.
\begin{enumerate}
\item[(1)]
$coh({\mathbb X})$ is noetherian and hereditary.
\item[(2)]
$$D^b(coh({\mathbb X})) \cong
\begin{cases}
D^b(\Repr( \widetilde{\mathbb A}_{p, q})) & {\rm{if}}\;\; {\bf p}=(p,q),\\
D^b(\Repr( \widetilde{\mathbb D}_n)) & {\rm{if}}\;\; {\bf p}=(2,2,n),\\
D^b(\Repr( \widetilde{\mathbb E}_6)) & {\rm{if}}\;\; {\bf p}=(2,3,3),\\
D^b(\Repr( \widetilde{\mathbb E}_7)) & {\rm{if}}\;\; {\bf p}=(2,3,4),\\
D^b(\Repr( \widetilde{\mathbb E}_8)) & {\rm{if}}\;\; {\bf p}=(2,3,5).
\end{cases}
$$
\item[(3)]
Let ${\mathcal S}$ be an ordinary simple
object in $coh({\mathbb X})$.
Then $\Ext^1_{\mathbb X}({\mathcal S},{\mathcal S})=\Bbbk$.
\item[(4)]
If ${\mathbb X}$ is tubular or domestic, then $\Ext^1_{\mathbb X}(X,Y)=0$
for all $X\in Vect_{\mu'}({\mathbb X})$ and $Y\in Vect_{\mu}({\mathbb X})$
with $\mu'< \mu$.
\item[(5)]
If ${\mathbb X}$ is domestic, then $\Ext^1_{\mathbb X}(X,Y)=0$
for all $X\in Vect_{\mu'}({\mathbb X})$ and $Y\in Vect_{\mu}({\mathbb X})$
with $\mu'\leq \mu<\infty$.
\item[(6)]
Suppose ${\mathbb X}$ is tubular or domestic.
Then every indecomposable vector bundle ${\mathbb X}$
is semistable.
\item[(7)]
Suppose ${\mathbb X}$ is tubular
and let $\mu\in {\mathbb Q}$.
Then each $Vect_{\mu}({\mathbb X})$ is a uniserial category.
Accordingly indecomposables in $Vect_{\mu}({\mathbb X})$
lies in Auslander-Reiten components, which all are
stable tubes of finite rank. In fact, for every
$\mu\in {\mathbb Q}$, $$Vect_{\mu}({\mathbb X})\cong
Vect_{\infty}({\mathbb X})=Tor({\mathbb X}).$$
\end{enumerate}
\end{lemma}
\begin{lemma}
\label{xxlem6.2}
Let ${\mathbb X}={\mathbb X}({\bf p}, {\bf D})$ be a weighted
projective line.
\begin{enumerate}
\item[(1)]
\cite[Theorem 2.2(ii)]{Le2011}
Let $\mathcal{T}$ be $D^b(coh(\mathbb{X}))$. Then
$\mathcal{T}$ has Serre duality in the form of
$$\Hom_{\mathcal{T}}(X,Y)^{\ast}
\cong \Hom_{\mathcal{T}}(Y,S(X)),$$
where the Serre functor $S$ is $-(\omega_0)[1]$
and where the dualizing element $\omega_0$ is
in \eqref{E6.0.4}.
\item[(2)]
\cite[Proposition 1.10]{LR2006}
Each indecomposable vector bundle has a nonzero
morphism to $Tor_{x}$ for every point $x$ in
$\mathbb{P}^1$.
\end{enumerate}
\end{lemma}
The following linear algebra lemma is needed to estimate
the spectral radius of some matrices.
\begin{lemma}
\label{xxlem6.3}
Let $\Gamma$ be the $n\times n$-matrix $(a_{ij})_{n\times n}$
where
\begin{equation}
\label{E6.3.1}\tag{E6.3.1}
a_{ij}=\begin{cases} 1 & {\text{if $i=1$, or $j=1$,}}\\
0 & {\text{otherwise.}}\end{cases}.
\end{equation}
Then the spectral radius $\rho(\Gamma)\geq \sqrt{n}$.
\end{lemma}
\begin{proof}
It is not hard to check that the characteristic polynomial
of $\Gamma$ is
\[
f(x)=x^n-x^{n-1}-(n-1)x^{n-2}=x^{n-2}(x^2-x-(n-1)).
\]
Then
$$\rho(\Gamma)=\frac{1+\sqrt{4n-3}}{2}\geq \sqrt{n}.$$
\end{proof}
\begin{lemma}
\label{xxlem6.4}
Suppose $\mathcal{T}$ be a triangulated category
satisfying
\begin{enumerate}
\item[(a)]
there is an infinite brick set $\phi$,
\item[(b)]
there is a brick object $B$ in $\mathcal{T}$ such that
$\Hom_{\mathcal{T}}(B,X)\neq 0$ for all $X\in \phi$,
\item[(c)]
there is an integer $m$ such that
$\Hom_{\mathcal{T}}(B[s],X)=\Hom_{\mathcal{T}}(X, B[s])= 0$
for all $X\in \Phi$ and for all $|s|\geq m$,
\item[(d)]
$\mathcal{T}$ has a Serre functor $S$, and
\item[(e)]
there is an integer $m_0$ such that
$\Hom_{\mathcal{T}}(B[m_0], S(X))\neq 0$ for all
$X\in \phi$.
\end{enumerate}
Let $\mathcal{C}$ be a monoidal triangulated category
acting on $\mathcal{T}$. Then there is an object
$M\in \mathcal{C}$ such that $\fpd(M)=\infty$.
\end{lemma}
\begin{proof} In the following proof let $\odot$ denote the
action of $\mathcal{C}$ on $\mathcal{T}$ and $\Hom$ denote
$\Hom_{\mathcal{T}}$.
By condition (d), $\mathcal{T}$ has a Serre functor
$S:\mathcal{T}\to \mathcal{T}$ such that
\begin{equation}
\label{E6.4.1}\tag{E6.4.1}
\Hom(X,Y)^{\ast} \cong \Hom(Y,S(X))
\end{equation}
for all $X,Y$ in $\mathcal{T}$.
Let ${\bf 1}\in \mathcal{C}$ be the unit object with
respect to the monoidal tensor of $\mathcal{C}$. Let $m$
and $m_0$ be the integers given in conditions (c) and (e),
and let $M$ be the object ${\bf 1}[m]\oplus {\bf 1}\oplus {\bf 1}[m_0-m]$ in
$\mathcal{C}$. It is enough to show that $\fpd(M)=\infty$.
Let $\phi_n$ be a brick set consisting of $(n-1)$ objects in
$\phi$ and one extra special object, namely $B[m]$, where $m$
is in condition (c). Write
$$\phi_n=\{X_1:=B[m], X_2, X_3,\cdots,X_n\}$$
where $X_i\in \phi$ for all $i=2,3,\cdots,n$. Let
$A:=(a_{ij})$ denote the adjacency matrix
$A(\phi_n, M\odot -)$.
We claim that $a_{1i}\neq 0$ and $a_{j1}\neq 0$ for all $i,j$.
Case 1:
$$\begin{aligned}
a_{11}&= \dim \Hom(B[m], M\odot B[m])\\
&\geq \dim \Hom(B[m], {\bf 1}\odot B[m])\\
&= \dim \Hom(B, B)\\
&=\dim \Bbbk=1 \qquad\qquad\qquad\qquad {\text{by condition (b)}}.
\end{aligned}
$$
Case 2: for every $i\geq 2$,
$$\begin{aligned}
a_{1i}&= \dim \Hom(B[m], M\odot X_i)\\
&\geq \dim \Hom(B[m], {\bf 1}[m]\odot X_i)\\
&= \dim \Hom(B[m], X_i[m])\\
& \geq \dim \Bbbk=1 \qquad\qquad\qquad\qquad {\text{by condition (c)}}.
\end{aligned}
$$
Case 3: for every $j\geq 2$,
$$\begin{aligned}
a_{j1}&= \dim \Hom(X_j, M\odot B[m])\\
&\geq \dim \Hom(X_j, {\bf 1}[m_0-m]\odot B[m])\\
&= \dim \Hom(X_j, B[m_0])\\
&= \dim \Hom(B[m_0], S(X_j)) \quad\;\; {\text{by \eqref{E6.4.1}}}\\
& \geq \dim \Bbbk=1 \qquad\qquad\qquad\qquad {\text{by condition (e)}}.
\end{aligned}
$$
Therefore we proved the claim. This means that
every entry in $A$ is larger than or equal to
the corresponding entry in $\Gamma$ as given in
Lemma \ref{xxlem6.3}. By linear algebra,
$$\rho(A)\geq \rho(\Gamma)\geq \sqrt{n}$$
where the last inequality is Lemma \ref{xxlem6.3}.
Then, by definition, $\fpd(M)\geq \sqrt{n}$ for all $n$.
Thus $\fpd(M)=\infty$ as desired.
\end{proof}
Now we are ready to show that every monoidal structure
on weighted projective line is $\fpd$-infinite.
\begin{proposition}
\label{xxpro6.5}
Let $\mathbb{X}$ be a weighted projective line and
let $\mathcal{T}$ be $D^b(coh(\mathbb{X}))$.
\begin{enumerate}
\item[(1)]
Let $\mathcal{C}$ be a monoidal triangulated category
acting on $\mathcal{T}$. Then there is an object
$M\in \mathcal{C}$ such that $\fpd(M)=\infty$.
\item[(2)]
Every monoidal structure on $\mathcal{T}$ is
$\fpd$-infinite.
\end{enumerate}
\end{proposition}
\begin{proof} Since part (2) is a special case of
part (1), it suffices to show part (1).
We need to verify hypotheses (a)-(e) in Lemma
\ref{xxlem6.4}.
Let $\phi$ be the set $\{\mathcal{O}_x\mid x\in
\mathbb{P}^1\setminus\{\lambda_0,\cdots,\lambda_t\}\}$
and let $B$ be the trivial bundle $\mathcal{O}_{\mathbb{X}}$.
It is clear that $\phi$ is infinite, so (a) holds.
By Lemma \ref{xxlem6.2}(2), (b) holds. Since $coh(\mathbb{X})$
has global dimension 1, (c) holds. By Lemma
\ref{xxlem6.2}(1), $D^b(coh(\mathbb{X}))$ has a Serre
functor $S$ which is
$\mathcal{O}_{\mathbb{X}}(\omega_0)[1]\otimes_{\mathbb{X}}-$.
Then $S(\mathcal{O}_x)=\mathcal{O}_x[1]$ for all
$x\in \mathbb{P}^1\setminus\{\lambda_0,\cdots,\lambda_t\}$.
Therefore (e) holds. Finally the assertion follows from
Lemma \ref{xxlem6.4}.
\end{proof}
It is not hard to check that Proposition \ref{xxpro6.5} also
holds if $\mathbb{X}$ is an irreducible smooth projective
scheme of dimension at least 1.
We still need quite a few lemmas before we can prove
Theorem \ref{xxthm0.3}. Recall that the definition of
$\fpd$-wild is given in Definition \ref{xxdef0.2}(3).
\begin{lemma}
\label{xxlem6.6}
Let $\mathcal{T}$ be a triangulated category. Suppose that,
for each $n$, there is a connected brick set $\phi$ with
$|\phi|>n$.
\begin{enumerate}
\item[(1)]
Let $\mathcal{C}$ be a $\Hom$-finite Krull-Schmidt
monoidal triangulated category acting on $\mathcal{T}$.
Then there is an indecomposable object $M\in \mathcal{C}$
such that $\fpd(M)=\infty$.
\item[(2)]
Suppose further that $\mathcal{T}$ is $\Hom$-finite
Krull-Schmidt. Then every monoidal triangulated structure
on $\mathcal{T}$ is $\fpd$-wild.
\end{enumerate}
\end{lemma}
\begin{proof} Since part (2) is a special case of
part (1), it suffices to show part (1).
Let $(\mathcal{C},\otimes, \mathbf{1})$ be a monoidal
triangulated category acting on $\mathcal{T}$
where $\mathbf{1}$ is the unit object of $\mathcal{C}$.
Write $\mathbf{1}$ as a direct sum of indecomposable objects
$$\mathbf{1}=\bigoplus_{i=1}^d M_i.$$
By hypothesis, for each $n$, there is a connected brick set
$\phi^n$ with $|\phi^n|>dn$. Define
$$\phi^n_i:=\{ X\in \phi^n \mid M_i\odot X\neq 0\}.$$
Since $X=\mathbf{1}\odot X=\bigoplus_{i=1}^d (M_i\odot X)$
and $X$ is indecomposable, there is exactly one $i$ such that
$M_i\odot X\neq 0$, and for that $i$, we have $M_i\odot X=X$.
Hence, for each $n$, $\phi^n$ is a disjoint union of $\phi^n_i$
for $i=1,\cdots, d$. By the pigeonhole principle, there is at least
$i$ such that $|\phi^n_i|>n$. This implies that there is at least
one $j$ such that, with this fixed $j$, there is an infinite
sequence $n_j$ such that $|\phi^{n_j}_j|>n_j$. Using this
sequence of brick sets, one sees that
$$\Hom_{\mathcal{T}}(M_j[-1]\odot X,Y)=\Hom_{\mathcal{T}}(X,Y[1])
\neq 0$$
for all $X,Y\in \phi^{n_j}_j$.
By definition, $\fpd(M_j[-1])\geq n_j$ as $|\phi^{n_j}_j|\geq n_j$.
Since $n_j$ goes to infinity, $\fpd(M_j[-1])=\infty$ as desired.
\end{proof}
Next we recall more detailed structures concerning
weighted projective lines.
Let ${\bf p}$ be the weight of $\mathbb{X}$ and
$B_0=\gcd(p_i\in {\bf p})$.
Define $\nu$ to be the group homomorphism from $\mathbb{L}$ to
$\mathbb{Z}$ such that
$\nu(\overrightarrow{x}_i)=\prod_{s\neq i} p_s$. It is easy to
see that the image of $\nu$ is $B_0\mathbb{Z}$. In fact,
we can assume that $B_0=1$, so $\nu: \mathbb{L}\to \mathbb{Z}$
is a surjective morphism. Since $\rank(\ker(\nu))=0$,
the kernel of $\nu$ is finite.
\begin{lemma}
\label{xxlem6.7}
Let $\mathbb{X}$ be a weighted projective line and let
$\mathcal{T}$ be $D^b(coh(\mathbb{X}))$.
\begin{enumerate}
\item[(1)]
There is a positive integer $B_1$, only dependent on
$\mathbb{X}$, such that, if $\omega_1,\omega_2$ are in
$\mathbb{L}$ satisfying $\nu(\omega_2-\omega_1)\geq B_1$,
then $\Hom_{\mathbb{X}}(\mathcal{O}_{\mathbb{X}}(\omega_1),
\mathcal{O}_{\mathbb{X}}(\omega_2)) \neq 0$.
\item[(2)]
For every $N$, there is a positive integer $B_3(N)$,
only dependent on $\mathbb{X}$ and $N$ such that
$$\dim
\Hom_{\mathbb{X}}(\mathcal{O}(\omega_1),\mathcal{O}(\omega_2))
\leq B_3(N)$$
for all $\omega_1,\omega_2$ in
$\mathbb{L}$ satisfying $0\leq \nu(\omega_2-\omega_1)\leq N$.
\end{enumerate}
\end{lemma}
\begin{proof} (1) We may assume that $\omega_1=0$. Let
$B_1=(t-1)\prod_{s=0}^t p_i$. For $\omega_2 \in \mathbb{L}$
with $\nu(\omega_2)\geq B_1$, write $\omega_2=\sum_{s=0}^{t-1} a_s
\overrightarrow{x}_s + a_t \overrightarrow{x}_t$ where
$0\leq a_s\leq p_s$ for all $0\leq s\leq t-1$. Since
$\nu(\omega_2)\geq B_1$, $a_t\geq 0$. Then the $\omega_2$-degree
component of $R$ (see \eqref{E6.0.1}) is not zero and hence
$\Hom_{\mathbb{X}}(\mathcal{O}_{\mathbb{X}},
\mathcal{O}_{\mathbb{X}}(\omega_2))=R_{\omega_2}\neq 0$.
(2) Again we can assume that $\omega_1=0$. Since there are
only finitely many $\omega_2$ such that $\nu(\omega_2)$ is
in between $0$ and $N$. Let $B_3(N)$ be the
maximum of all possible
$$\dim \Hom_{\mathbb{X}}(\mathcal{O},\mathcal{O}(\omega_2))$$
where $\omega_2$ runs over all $\omega_2\in \mathbb{L}$
such that $0\leq \nu(\omega_2)\leq N$. Then the
assertion follows.
\end{proof}
The next lemma concerns domestic weighted projective lines.
Some un-defined terms can be found in \cite{KLM2013}. Let
$\omega_0$ be the dualizing element defined in \eqref{E6.0.4}.
\begin{lemma}
\label{xxlem6.8}
Let $\mathbb{X}$ be a weighted projective line.
\begin{enumerate}
\item[(1)]
\cite[Proposition 5.1(ii)]{KLM2013}
Suppose that the weight ${\bf p}$ is either $(2, 2, n)$, or
$(2, 3, 3)$, or $(2, 3, 4)$ or $(2, 3, 5)$. Let $\Delta$
be the attached Dynkin diagram and $\widetilde{\Delta}$
its extended Dynkin diagram. The Auslander-Reiten quiver
$\Gamma(Vect(\mathbb{X}))$ of $Vect(\mathbb{X})$ consists
of a single standard component having the form
$\mathbb{Z} \widetilde{\Delta}$. Moreover, the category of
indecomposable vector bundles on $\mathbb{X}$, denoted by
$ind(Vect(\mathbb{X}))$, is equivalent to the mesh category
of $\Gamma(Vect(\mathbb{X}))$.
\item[(2)]
Under the hypotheses of part {\rm{(1)}}, there is a finite
set of indecomposable vector bundles $\{V_i\}_{i\in I}$ such
that every indecomposable vector bundle is of the form $V_i(n
\omega_0)$ for some $n\in \mathbb{Z}$ and some $i\in I$.
\item[(3)]
\cite[Sect. 5.1, page 217]{KLM2013}
If the weight ${\bf p}$ is of the form $(p,q)$, then each
indecomposable vector bundle is a line bundle $\mathcal{O}(\omega)$
for $\omega\in \mathbb{L}$.
\item[(4)]
Under the hypotheses of part {\rm{(3)}}, there is a finite set of
indecomposable vector bundles $\{V_i\}_{i\in I}$ such that
every indecomposable vector bundle is of the form $V_i(n
\omega_0)$ for some $n\in \mathbb{Z}$.
\end{enumerate}
\end{lemma}
\begin{proof}
(2) There is a ($[-1]$-shifted) Serre functor $F:=-(\omega_0)$ which
is also a functor from $ind(Vect(\mathbb{X}))$ to itself. It is easy
to check that $\nu(\omega_0)<0$. Then $F$ induces an automorphism of the
Auslander-Reiten quiver $\Gamma(Vect(\mathbb{X}))$ by shifting
forward a distance $\nu(\omega_0)$.
Therefore there is a finite set of indecomposable vector bundles
$\{V_i\}_{i\in I}$ such that every indecomposable vector bundle
is of the form $V_i(n\omega_0)$ for some $n\in \mathbb{Z}$
and some $i\in I$.
(4) Since the map $\nu: \mathbb{L}
\to \mathbb{Z}$ is a group homomorphism with finite
kernel, there are only finitely many
$\omega$ such that $\nu(\omega)=0$.
Similarly, there are only finitely many $\omega\in \mathbb{L}$
such that $\nu(\omega)=0,1,\cdots,-\nu(\omega_0)-1$. Then
the set $\{\mathcal{O}(\omega)\mid 0\leq \nu(\omega)\leq -\nu(\omega_0)-1\}$
has the desired property.
\end{proof}
We introduce some temporary notation. By Lemma
\ref{xxlem6.8}(2,4), if $\mathbb{X}$ is domestic,
then there is a finite set of indecomposable vector
bundles, say $\mathbb{K}:=\{K_1, \cdots K_{B_4}\}$, such that
every indecomposable vector bundle is of the form
$K_s(n\omega_0)$ for some $1\leq s\leq B_4$ and
some $n\in \mathbb{Z}$. (Here $\omega_0 \in \mathbb{L}$ is
the dualizing element given in \eqref{E6.0.4}.) For
each $K_s$ we fix a sequence of sub-bundles
\begin{equation}
\label{E6.8.1}\tag{E6.8.1}
0=:V_{s,0}\subset V_{s,1}\subset V_{s,2}\subset \cdots
\subset V_{s,Y_s}:=K_s
\end{equation}
such that each subquotient $V_{s,i}/V_{s,i-1}$ is a line
bundle of the form $\mathcal{O}_{\mathbb{X}}(\omega_{s,i})$
for some $\omega_{s,i}\in \mathbb{L}$. Let $\Omega(\mathbb{X})$
be the collection of all such $\omega_{s,i}$'s. Hence
$\Omega(\mathbb{X})$ is finite. Let
$$\begin{aligned}
\max(\Omega)&= \max\{\nu(\omega)\mid \omega\in \Omega(\mathbb{X})\},\\
\min(\Omega)&= \min\{\nu(\omega)\mid \omega\in \Omega(\mathbb{X})\}.
\end{aligned}
$$
For every vector bundle $V$, we write $V=K_s(n\omega_0)$ for some
$s$ and $n$. Then we fix a sequence of sub-bundles of
$V:=K_s(n\omega_0)$ by applying $-(n\omega_0)$ to \eqref{E6.8.1}.
We have a series of subquotients
$$V_{s,i}(n\omega_0)/V_{s,i-1}(n\omega_0)
\cong \mathcal{O}_{\mathbb{X}}(\omega_{s,i}+n\omega_0)$$
induced by \eqref{E6.8.1}. Let $\nu(V)$ denote the positive
different between the largest of all $\nu(\omega_{s,i}+n\omega_0)$
and the smallest of all $\nu(\omega_{s,i}+n\omega_0)$. Then it is
clear that $\nu(V)\leq \max(\Omega)-\min(\Omega)$. So we have
proved part (1) of the follows proposition.
\begin{proposition}
\label{xxpro6.9}
Let $\mathbb{X}$ be a domestic weighted projective line.
\begin{enumerate}
\item[(1)]
Let $V$ be an indecomposable vector bundle on $\mathbb{X}$.
Then the $\nu(V)$ is uniformly bounded by
$B_5:=\max(\Omega)-\min(\Omega)$.
\item[(2)]
Let $V$ be an indecomposable vector bundle on $\mathbb{X}$.
Then the rank $V$ is uniformly bounded by an integer $B_6$
{\rm{(}}only dependent on $\mathbb{X}${\rm{)}}.
\item[(3)]
Suppose $\phi$ is a brick set consisting of vector bundles
on $\mathbb{X}$. Then the size of $\phi$ is uniformly bounded
by $B_7$ {\rm{(}}only dependent on $\mathbb{X}${\rm{)}}.
\item[(4)]
Suppose $\phi$ is a brick set consisting of vector bundles
on $\mathbb{X}$. Then, up to a degree shift, $\phi$ is a
subset of $\bigcup_{n=-N}^{N} \mathbb{K}(n\omega_0)$ for some
integer $N$. As a consequence, $\sum_{V\in \phi} \nu(V)$ is
uniformly bounded, say, by $B_8$ {\rm{(}}only dependent on
$\mathbb{X}${\rm{)}}.
\item[(5)]
Fix a vector bundle $V$ on $\mathbb{X}$. For every
brick set consisting of vector bundles
$\{X_1,\cdots,X_n\}$,
$\dim \Hom_{\mathbb{X}}(X_i, V\otimes_{\mathbb{X}} X_j)$
is uniformly bounded by $B_9(V)$ for all $i,j$
{\rm{(}}only dependent on $V$ and $\mathbb{X}${\rm{)}}.
\item[(6)]
Fix a vector bundle $V$ on $\mathbb{X}$. For every
brick set consisting of vector bundles
$\{X_1,\cdots,X_n\}$,
$\dim \Hom_{\mathbb{X}}(V\otimes_{\mathbb{X}} X_i, X_j)$
is uniformly bounded by $B_{10}(V)$ for all $i,j$
{\rm{(}}only dependent on $V$ and $\mathbb{X}${\rm{)}}.
\end{enumerate}
\end{proposition}
\begin{proof}
(2) This is part of \cite[Theorem 6.1]{LR2006}. It also can be shown
directly as follows.
Since every indecomposable vector bundle $V$ is of the form
$K_s(\omega)$ for $1\leq s\leq B_4$, the rank of $V$ is uniformly
bounded, say by $B_6$.
(3) Since $\nu(\omega_0)$ is negative, there is an $N_1$ such that
for all $n\geq N_1$ and for all $s_1,s_2$,
$$\nu(\omega_{s_2,Y_{s_2}})-\nu(\omega_{s_1,1}-n \omega_0)\geq B_1$$
where $B_1$ is the constant given in Lemma \ref{xxlem6.7}(1).
By Lemma \ref{xxlem6.7}(1), for such $n$, $s_1,s_2$,
$$\Hom_{\mathbb{X}}(\mathcal{O}_{\mathbb{X}}(\omega_{s_2,Y_{s_2}})),
\mathcal{O}_{\mathbb{X}}(\omega_{s_1,1}-n\omega_0))\neq 0.$$
By \eqref{E6.8.1},
\begin{equation}
\label{E6.9.1}\tag{E6.9.1}
\Hom_{\mathbb{X}}(K_{s_2},K_{s_1}(-n\omega_0))\neq 0
\end{equation}
for all $s_1,s_2$ and all $n\geq N_1$.
Let $\phi$ be a brick set of vector bundles. We claim that
$|\phi|\leq N_1|\mathbb{K}|=:B_7$. If not, by the pigeonhole
principle, there is an $s$ such that $\phi$ contains
a subset
$$\{K_s(n_1\omega_0),\cdots,K_s(n_q\omega_0)\}$$
for some $q> N_1$ where $n_1<n_1<\cdots <n_q$. Then,
by \eqref{E6.9.1},
$$
\Hom_{\mathbb{X}}(K_s(n_q\omega_0),K_s(n_1\omega_0))
=\Hom_{\mathbb{X}}(K_s,K_s((n_1-n_q)\omega_0))
\neq 0.$$
This contradicts that $\phi$ is a brick set. Therefore
we proved the claim.
(4) Without loss of generality, we may assume that
$\phi$ contains $K_1$. Let $K_s(n\omega_0)$ be
any other object in $\phi$. By \eqref{E6.9.1},
$|n|< N_1$ where $N_1$ is given in the proof of
part (3). Therefore $\phi$ is a subset of
$\bigcup_{n=-N_1}^{N_1} \mathbb{K}(n\omega_0)$.
As a consequence, $\sum_{X\in \phi} \nu(X)$ is
uniformly bounded, say by $B_8$.
(5) By part (4), up to a degree shift, we can assume that
$\phi$ is a subset of $\bigcup_{n=-N}^{N} \mathbb{K}
(n\omega_0)$ for a fixed integer $N$. Note that
the global degree shift will not change the assertion.
Then the assertion follows by the fact that
$\bigcup_{n=-N}^{N} \mathbb{K}(n\omega_0)$ is a fixed
set.
(6) Similar to the proof of part (5).
\end{proof}
\begin{lemma}
\label{xxlem6.10}
Let $\mathbb{X}$ be a weighted projective line.
Let $\mathcal{T}$ be $D^b(coh(\mathbb{X}))$.
\begin{enumerate}
\item[(1)]
Let $M$ be a brick object in $\mathcal{T}$.
Then $M\cong N[n]$ where $n\in \mathbb{Z}$ and there
$N\in coh(\mathbb{X})$ is either a vector bundle, or
an ordinary simple $\mathcal{O}_x$, or an indecomposable
object in $Tor_{\lambda_i}$.
\item[(2)]
If a brick set $\phi$ consists of indecomposable
objects in $Tor_{\lambda}$ for some $\lambda\in \mathbb{P}^1$,
then $|\phi|$ is uniformly bounded by $B_{11}$
{\rm{(}}only dependent on $\mathbb{X}${\rm{)}}.
\item[(3)]
If $M$ is a brick object in $Tor(\mathbb{X})$, then
$\dim M$ is uniformly bounded by $B_{12}$
{\rm{(}}only dependent on $\mathbb{X}${\rm{)}}.
\end{enumerate}
\end{lemma}
\begin{proof}
(1) It is well-known that every indecomposable object in
$coh(\mathbb{X})$ is either a vector bundle or a torsion
sheaf. The assertion follows by \eqref{E6.0.3} and the fact that
$coh(\mathbb{X})$ is hereditary.
(2) This is trivial if $\lambda \in \mathbb{P} \setminus
\{\lambda_0,\cdots,\lambda_t\}$. If $\lambda=\lambda_i$ for some $i$,
$Tor_{\lambda_i}$ is a standard tube of
rank $p_i$ with $p_i^2$ brick objects, see
\cite[Section 2.2]{CGWZZZ2019}. So the assertion follows.
(3) By \eqref{E6.0.3}, $M\in Tor_{\lambda}$ for
some $\lambda \in \mathbb{P}$. It is trivial if
$\lambda \in \mathbb{P} \setminus
\{\lambda_0,\cdots,\lambda_t\}$. Now assume that $\lambda=\lambda_i$.
All brick objects in $Tor_{\lambda_i}$ are given in
\cite[Corollary 2.8]{CGWZZZ2019}. As a consequence,
$\dim M\leq p_i$. The assertion follows.
\end{proof}
Since $R$ in \eqref{E6.0.1} is commutative, there is a
natural tensor product on $coh(\mathbb{X})$, denoted
by $\otimes_{\mathbb{X}}$. Note that $\otimes_{\mathbb{X}}$
is not (bi)exact. The derived category $\mathcal{T}:=
D^b(coh(\mathbb{X}))$ has a canonical monoidal structure
where the tensor functor is defined by
$$ - \otimes_{\mathcal{T}} - : = -\otimes_{\mathbb{X}}^L -$$
(the derived tensor product). Note that
$\otimes_{\mathcal{T}}$ is biexact so that $\mathcal{T}$ is
a monoidal triangulated category. Next we show that
this monoidal triangulated structure is $\fpd$-tame
when $\mathbb{X}$ is domestic.
\begin{theorem}
\label{xxthm6.11}
Retain the notation introduced above. If $\mathbb{X}$
is domestic, then the canonical monoidal triangulated
structure on $D^b(coh(\mathbb{X}))$ is
$\fpd$-tame.
\end{theorem}
\begin{proof} Let $\mathcal{T}$ denote
$D^b(coh(\mathbb{X}))$. By Proposition \ref{xxpro6.5},
$\mathcal{T}$ is $\fpd$-infinite. By definition, it
remains to show that $\fpd(M)<\infty$ for every
indecomposable object $M$ in $\mathcal{T}$.
Since $M$ is indecomposable and $coh(\mathbb{X})$ is
hereditary, by \cite[Lemma 3.3]{CGWZZZ2017}, $M$ is of
the form $N[n]$ for some $N\in coh(\mathbb{X})$ and
$n\in \mathbb{Z}$. By Lemma \ref{xxlem6.10}(1), $N$ is
either a vector bundle or a torsion. So we fix an $N$
and consider the following two cases.
Case 1: $N$ is a vector bundle. In this case
$N\otimes_{\mathbb{X}}-$ is exact and
$N\otimes_{\mathcal{T}} Y=N\otimes_{\mathbb{X}} Y$
for all $Y\in coh(\mathbb{X})$.
If $n\neq 0,1$, by the proof of Lemma \ref{xxlem4.11},
$\fpd(N[n]\otimes_{\mathcal{T}}-)=0$. Now we deal with the case
$n=0$ or $M=N$.
Let $\phi$ be a brick set. By Lemma \ref{xxlem6.10}(1),
we can write $\phi=\bigcup_{\delta \in \mathbb{Z}} \phi_{\delta}$,
with $\delta$ integers ranging from small to large, where
$\phi_{\delta}$ is either empty or of the form
$$\{X_{\delta,1}[\delta],X_{\delta,2}[\delta],\cdots,
X_{\delta,t_\delta}[\delta]\}$$
for some $X_{\delta,s}\in coh(\mathbb{X})$. Since
$$\Hom_{\mathcal{T}}(X_{\delta,s}[\delta],N\otimes_{\mathcal{T}}
X_{\delta',s'}[\delta'])=0$$
for all $\delta>\delta'$, the adjacency matrix
$A(\phi, N\otimes_{\mathcal{T}}-)$ is a upper triangular
block matrix. Now the idea of \cite[Lemma 6.1]{CGWZZZ2017} implies
that we only need to consider blocks, namely, we can assume that $\phi=
\phi_{\delta}$ for some $\delta$. For each block associated to
$\phi_{\delta}$, we can further assume that $\delta=0$ and
$\phi_0=\{X_1,\cdots,X_t\}$ for some $X_s\in coh(\mathbb{X})$.
Without loss of generality, we assume that
$$\phi=\phi_0=\{X_1,\cdots,X_t\}$$
for some $X_1,\cdots, X_t\in coh(\mathbb{X})$. If $\phi$ contains
an ordinary simple $\mathcal{O}_x$, then, by Lemma \ref{xxlem6.2}(2),
$\phi$ does not contain any vector bundle. In this case, one can
further decompose $\phi$ according to \eqref{E6.0.3} so that
$A(\phi, N\otimes_{\mathcal{T}}-)$ is a block diagonal matrix.
For each block, $\phi$ is either $\{\mathcal{O}_x\}$ or consisting of
objects in $Tor_{\lambda_i}$. So we consider these two subcases.
If $\phi=\{\mathcal{O}_x\}$, it is easy to see that
$\Hom_{\mathcal{T}}(\mathcal{O}_x, N\otimes_{\mathcal{T}}
\mathcal{O}_x)$ has dimension bounded by the rank of $N$.
This is uniformly bounded. If $\phi$ is a subset of
$Tor_{\lambda_i}$, then there are only finitely many
possibilities [Lemma \ref{xxlem6.10}(2)]. Hence entries and size of
the $A(\phi, N\otimes_{\mathcal{T}}-)$ is uniformly bounded.
Therefore $\rho(A(\phi, N\otimes_{\mathcal{T}}-))$ is
uniformly bounded. The second case is when $\phi$
does not contain any ordinary simple $\mathcal{O}_x$.
Then the size of $\phi$ is uniformly bounded by
Proposition \ref{xxpro6.9}(3) and Lemma \ref{xxlem6.10}(2).
We claim that each entry in $A(\phi, N\otimes_{\mathcal{T}}-)$
is uniformly bounded, or $d_{ij}:=\dim \Hom_{\mathbb{X}}(X_i,N
\otimes_{\mathbb{X}} X_j)$ is uniformly
bounded for all $X_i, X_j$ in $\phi$. If both
$X_i$ and $X_j$ are vector bundles, the assertion follows
from Proposition \ref{xxpro6.9}(5). If $X_i$ is in $Tor_{\lambda_i}$
and $X_j$ is a vector bundle, then $d_{ij}=0$. If
$X_i$ is a vector bundle and $X_j$ is in $Tor_{\lambda_i}$,
then $d_{ij}$ is bounded by $\rank(X_i)\rank(N)\dim X_j$,
which is uniformly bounded by Proposition \ref{xxpro6.9}(2)
and Lemma \ref{xxlem6.10}(3). If $X_i$ and $X_j$ are
both in $Tor_{\lambda_i}$, then $d_{ij}$ is bounded by
$(\dim X_i)\rank(N) (\dim X_j)$ which is uniformly bounded.
Combining all these cases, one proves that $\fpd(N)$ is finite
by Lemma \ref{xxlem4.8} (Gershgorin Circle Theorem).
Next we deal with the case $n=1$ (namely, $M=N[1]$) and re-cycle
some notation used in the previous paragraphs. By Lemma
\ref{xxlem6.10}(1), we can write
$\phi=\bigcup_{\delta \in \mathbb{Z}} \phi_{\delta}$,
with $\delta$ being integers ranging from small to large, where
$\phi_{\delta}$ is either empty or of the form
$\{X_{\delta,1}[\delta],X_{\delta,2}[\delta],\cdots,
X_{\delta,t_\delta}[\delta]\}$.
Since $coh(\mathbb{X})$ is hereditary,
$$\Hom_{\mathcal{T}}(X_{\delta,s}[\delta],N[1]\otimes_{\mathcal{T}}
X_{\delta',s'}[\delta'])=0$$
for all $s,s'$ and all $\delta<\delta'$. Therefore the adjacency
matrix $A(\phi, N[1]\otimes_{\mathcal{T}}-)$ is a lower triangular
block matrix. For each block we can assume that $\delta=0$
and $\phi=\{X_1,\cdots,X_t\}$ as in the case $n=0$. If $\phi$
contains an ordinary simple $\mathcal{O}_x$, then, by
Lemma \ref{xxlem6.2}(2), $\phi$ does not contain any
vector bundle. In this case, one can further decompose $\phi$
according to \eqref{E6.0.3} so that
$A(\phi, N[1]\otimes_{\mathcal{T}}-)$ is a block
diagonal matrix. For each block, $\phi$ is either
$\{\mathcal{O}_x\}$ or consisting of objects in $Tor_{\lambda_i}$.
So we consider these two subcases. If $\phi=\{\mathcal{O}_x\}$,
then
$$\Hom_{\mathcal{T}}(\mathcal{O}_x, N[1]\otimes_{\mathcal{T}}
\mathcal{O}_x)=\Ext^1_{\mathbb{X}}(\mathcal{O}_x, N\otimes_{\mathcal{T}}
\mathcal{O}_x)$$
which is bounded by the $\rank(N)$. If $\phi$ is a subset of
$Tor_{\lambda_i}$, then there are only finitely many
possibilities, see the proof of Lemma \ref{xxlem6.10}(2).
Hence the entries and the size of the $A(\phi, N[1]\otimes_{\mathcal{T}}-)$
are uniformly bounded. Therefore
$\rho(A(\phi, N[1]\otimes_{\mathcal{T}}-))$ is uniformly bounded.
The second case is when $\phi$ does not contain any ordinary
simple $\mathcal{O}_x$. Then the size of $\phi$ is uniformly
bounded by Proposition \ref{xxpro6.9}(3) and Lemma
\ref{xxlem6.10}(2). We claim that each entry in
$A(\phi, N[1]\otimes_{\mathcal{T}}-)$
is uniformly bounded, or
$$\begin{aligned}
d_{ij}:&=\dim \Hom_{\mathbb{X}}(X_i,N[1]\otimes_{\mathbb{X}} X_j)
=\dim \Ext^1_{\mathbb{X}}(X_i,N\otimes_{\mathbb{X}} X_j)\\
&=\dim \Hom_{\mathbb{X}}(N\otimes_{\mathbb{X}} X_j, X_i(\omega_0))
=\dim \Hom_{\mathbb{X}}(N(-\omega_0)\otimes_{\mathbb{X}} X_j, X_i)
\end{aligned}
$$
is uniformly bounded for all $X_i, X_j$ in $\phi$. Note that
the third equality is Serre duality. If both
$X_i$ and $X_j$ are vector bundles, the assertion follows
and Proposition \ref{xxpro6.9}(6). If $X_i$ is in $Tor_{\lambda_i}$
and $X_j$ is a vector bundle, we obtain
that
$$d_{ij}\leq \rank(X_j)\rank(N(-\omega_0))\dim X_i,$$
which is uniformly bounded by Proposition \ref{xxpro6.9}(2)
and Lemma \ref{xxlem6.10}(3). If
$X_i$ is a vector bundle and $X_j$ is in $Tor_{\lambda_i}$,
then $d_{ij}=0$. If $X_i$ and $X_j$ are
both in $Tor_{\lambda_i}$, then
$$d_{ij}\leq \dim(X_j)\rank(N(-\omega_0))\dim X_i,$$
which is uniformly bounded.
Combining all these cases, one proves that $\fpd(N[1])$ is finite
by Lemma \ref{xxlem4.8} (Gershgorin Circle Theorem).
Case 2: $N$ is a torsion. By definition,
$N\otimes_{\mathcal{T}}-=N\otimes_{\mathbb{X}}^L -$.
If $n\neq -1, 0, 1$, a proof similar to Lemma \ref{xxlem4.11}(1)
shows that $\fpd(N[n])=0$. We need to analyze the cases
$n=-1,0,1$. The following proof is independent of $n$.
Since $N$ is torsion and indecomposable, by \eqref{E6.0.3},
$N$ is either in $Tor_{x}$ or $\Tor_{\lambda_i}$. We will use
Gershgorin Circle Theorem [Lemma \ref{xxlem4.8}].
Let $\phi=\{X_1,\cdots,X_m\}$ be any brick set in
$\mathcal{T}$ and let $(d_{ij})_{m\times m}$ denote
the adjacency matrix $A(\phi, N[n]\otimes_{\mathcal{T}}-)$
where
$$d_{ij}=\dim \Hom_{\mathcal{T}}(X_i, N[n]\otimes_{\mathcal{T}} X_j).$$
By Lemma \ref{xxlem4.8}, it suffices to show
\begin{enumerate}
\item[(a)]
each $d_{ij}$ is uniformly bounded (only dependent on $M:=N[n]$).
\item[(b)]
For each $j$, there are only uniformly-bounded-many $i$ such that
$d_{ij}\neq 0$.
\end{enumerate}
\noindent
{\bf Proof of (a):} For each $j$, write $X_j=Y_j[s_j]$ for some
$Y_j\in coh(\mathbb{X})$ and $s_j\in \mathbb{Z}$. Since
$N\in Tor_{\lambda}$, $H^s_N(X_j):=H^s(N[n]\otimes_{\mathcal{T}} X_j)$
is zero for $s\neq n+s_j-1,n+s_j$ and $H^s_N(X_j)$ is in
$Tor_{\lambda}$ for $s=n+s_j-1,n+s_j$. Since $coh(\mathbb{X})$ is
hereditary,
$$N[n]\otimes_{\mathcal{T}} X_j
=\sum_{s} H^s(N[n]\otimes_{\mathcal{T}} X_j)[-s],$$
see \cite[Lemma 2.1]{CR2018}. If $Y_j$ is a vector
bundle, then
$$\dim H^s_N(X_j)\leq (\dim N)(\rank(Y_j))$$
for all $s$. If $X_j$ is torsion, then
$$\dim H^s_N(X_j)\leq (\dim N)(\dim Y_j)$$
for all $s$. In both cases, $\dim H^s(X_j)$ is uniformly
bounded by Proposition \ref{xxpro6.9}(2) and Lemma
\ref{xxlem6.10}(3). Using the Serre duality and Proposition
\ref{xxpro6.9}(2) and Lemma \ref{xxlem6.10}(3) again, one sees that
$$\sum_{s,t\in \mathbb{Z}}\dim \Hom_{\mathcal{T}}(X_i[t], H^s(N[n]
\otimes_{\mathcal{T}}X_j)[s])=
\sum_{s,t}\dim \Hom_{\mathcal{T}}(X_i[t], H^s_N(X_j)[s])$$
is uniformly bounded. Hence
$$d_{ij}=\Hom_{\mathcal{T}}(X_i, N[n]\otimes_{\mathcal{T}} X_j)=
\sum_{s}\Hom_{\mathcal{T}}(X_i, H^s(N[n]\otimes_{\mathcal{T}} X_j)[s])$$
is uniformly bounded.
\noindent
{\bf Proof of (b):} As noted before, $\fpd(N[n])=0$ when
$n\neq -1,0,1$. So, in this proof, we assume that $n$ is
$-1$ or $0$ or $1$. Without loss of generality, we only prove
that there are only uniformly-bounded-many $i$ such that
$d_{i1}\neq 0$. By a complex shift, we can assume that
$X_1\in coh(\mathbb{X})$. Since $coh(\mathbb{X})$ is hereditary,
one can check that, if $X_i\in coh(\mathbb{X})[m]$ for $|m|\geq 3$,
then $d_{i1}=0$.
For each $m$ with $|m|\leq 2$, let $\phi_m$ consist of
$Y_i\in coh(\mathbb{X})$ such that $X_i=Y_i[m]\in \phi$
and $d_{i1}\neq 0$. If $\phi_m$ does not contain any
ordinary simple $\mathcal{O}_x$, then, by
Proposition \ref{xxpro6.9}(3) and Lemma 6.10(2), $|\phi_m|$
is uniformly bounded. If $\phi_m$ contain an
ordinary simple $\mathcal{O}_x$, then $d_{i1}\neq 0$
implies that $x$ is in the support of $N\otimes_{\mathbb{X}}
X_1$. Therefore there are only finitely many
possible $x$. Further, $X_1$ is either $\mathcal{O}_x$
or a vector bundle, and in the latter case, $d_{i1}\neq 0$
implies that $N$ must be $\mathcal{O}_x$.
In both case, $N[n]\otimes_{\mathcal{T}} X_1$ is
supported at $x$. Therefore $\phi_m$ consists of
a single element $\mathcal{O}_x$. Combining above, we obtain
that $\sum_{|m|\leq 2} |\phi_m|$ is uniformly bounded. As a consequence,
(b) holds.
Now it follows by Lemma \ref{xxlem4.8}, $\fpd(N[n])<\infty$.
Combining Cases 1 and 2, we finish the proof.
\end{proof}
Now we are ready to prove Theorem \ref{xxthm0.3}.
\begin{proof}[Proof of Theorem \ref{xxthm0.3}]
(1) If $Q$ is of finite type, by
Corollary \ref{xxcor4.10} every monoidal
triangulated structure on $D^b(\Repr(Q))$ is
fpd-finite. The converse follows from
Lemmas \ref{xxlem6.1}(2), \ref{xxlem4.3} and \ref{xxlem4.5}
and Proposition \ref{xxpro6.5}.
(2) Suppose $Q$ is tame. By Lemma
\ref{xxlem6.1}(2) and Theorem \ref{xxthm6.11},
there is a $\fpd$-tame monoidal structure on
$\mathcal{T}$. Applying Lemma \ref{xxlem4.6}
to $\mathcal{A}=\mathcal{C}=\Repr(Q)$,
there is a $\fpd$-wild monoidal structure.
(3) This follows from parts (1,2), Lemmas \ref{xxlem4.3} and
\ref{xxlem6.6}.
(4) This follows from part (1).
\end{proof}
\begin{corollary}
\label{xxcor6.12}
Let $Q$ be a finite acyclic quiver.
\begin{enumerate}
\item[(1)]
$Q$ is of finite type if and only if $\Repr(Q)$ does not
contain an infinite brick set.
\item[(2)]
$Q$ is of tame type if and only if $\Repr(Q)$
contains an infinite brick set and does not contain an
infinite connected brick set.
\item[(3)]
$Q$ is of wild type if and only if $\Repr(Q)$
contains an infinite connected brick set.
\end{enumerate}
\end{corollary}
\begin{proof} (1) If $Q$ is of finite type,
$\Repr(Q)$ contains only finitely many indecomposable
objects. So $\Repr(Q)$ does not contains an infinite
brick set.
For the converse, we assume that $\Bbbk Q$ is of tame or
wild type. By Lemmas \ref{xxlem4.3} and \ref{xxlem4.5},
$\Repr(Q)$ contains an infinite brick set. This yields
a contradiction. Therefore the assertion follows.
(3) If $Q$ is of wild type, by Lemmas \ref{xxlem4.3},
$\Repr(Q)$ contains an infinite connected brick set.
Conversely suppose $\Repr(Q)$ contains an infinite connected
brick set. By Lemma \ref{xxlem6.6}, every monoidal
triangulated structure on $D^b(\Repr(Q))$ is
$\fpd$-wild. By Theorem \ref{xxthm0.3}(3),
$Q$ is of wild type.
(2) Follows from parts (1,3).
\end{proof}
\section{Examples}
\label{xxsec7}
The natural construction of weak bialgebras associated
to quivers, given in Lemma \ref{xxlem2.1}, produces many
monoidal triangulated categories by Lemma \ref{xxlem1.9}(2).
The main goal of this section is to construct other
examples of (weak) bialgebras most of which are related
to finite quivers. We will see that, given a quiver $Q$,
there are different weak bialgebra structures on $\Bbbk Q$
such that the induced tensor products over $\Repr(Q)$ are
different from \eqref{E2.1.1}. As a consequence, there are
several different monoidal abelian structures on $\Repr(Q)$
generally. We will also see that there are monoidal
triangulated structures on derived categories
associated to noncommutative projective schemes.
The first example comes from \cite{HT2013}.
\begin{example}
\label{xxex7.1}
This example follows some ideas from \cite[Theorem 3.2]{HT2013}.
Let $Q$ be a quiver with $n$ vertices.
We label vertices of $Q$ as $1,2,\cdots,n$.
Suppose that $1$ is either a source or a sink, namely, $Q$
satisfies the following condition, either
\begin{enumerate}
\item[(1)]
there is no arrows from $1$ to $j$ for every $j$, or
\item[(2)]
there is no arrows from $j$ to $1$ for every $j$.
\end{enumerate}
Let $e_i$ be the idempotent corresponding
to the vertex $i$, and we use $p$ for a path of length
at least 1.
First we define a bialgebra structure on $\Bbbk Q$ by
$$\begin{aligned}
\varepsilon(e_1)&=1,\quad \Delta(e_1)=e_1\otimes e_1,\\
\varepsilon(e_i)&=0, \quad \Delta(e_i)=
\sum_{s<i} (e_i\otimes e_s+e_s\otimes e_i) +e_i\otimes e_i,\\
\varepsilon(p)&=0,\quad \Delta(p)=e_1\otimes p+p\otimes e_1\\
\end{aligned}
$$
for all $i>1$ and all paths $p$ of length at least 1.
It is routine to check that this defines a cocommutative
bialgebra structure on $\Bbbk Q$.
By the above definition, $\Delta(x)=e_1\otimes x+x\otimes e_1$
for all $x$ in the ideal $J$ generated by arrows of $Q$ (this
is also the graded Jacobson radical of $\Bbbk Q$). Let $I$ be any
sub-ideal of $J$. Then it is clear that $I$ is a bialgebra
ideal of $\Bbbk Q$. Therefore there is an induced bialgebra
structure on $\Bbbk Q/I$.
\end{example}
Let $Q$ is a finite acyclic quiver. Let $(\Delta,\varepsilon)$
be a coalgebra structure on $\Bbbk Q$. Suppose $|Q_0|=n$,
then $\Delta$ is called a {\it partitioning morphism}
(cf. \cite[p.460]{He2008a}) if
\begin{enumerate}
\item[(1)]
there are $E_1,\cdots,E_n$ which are subsets of
$E=\{(i,j)\mid1\leq i,j\leq n\}$,
\item[(2)]
$E_i\cap E_j=\emptyset$ if $i\neq j$, and
\item[(3)]
for every $1\leq k\leq n$,
$\Delta(e_k)= \sum\limits_{(i,j)\in E_k} e_i\otimes e_j$.
\end{enumerate}
Let $Q(i,j)$ be the set of paths from vertex $i$ to
vertex $j$, then:
\begin{proposition}\cite[Proposition 4]{He2008a}
\label{xxpro7.2}
Let $Q$ be a finite acyclic quiver. Suppose $\Bbbk Q$ has
a coalgebra structure $(\Bbbk Q, \Delta, \varepsilon)$. Then
$\Bbbk Q_0$ is a subcoalgebra of $\Bbbk Q$ and
$\Delta$ is a prealgebra map if and only if
\begin{enumerate}
\item[(1)]
$\Delta$ is a partitioning morphism,
\item[(2)]
$\Delta(\alpha_1\cdots\alpha_m)=\Delta(\alpha_1)\cdots\Delta(\alpha_m)$
where $\alpha_i\in Q_1$,
\item[(3)]
$\Delta(\alpha)\in
\bigoplus\limits_{(i,j)\in E_k,(i',j')\in E_l}
\Bbbk Q(i,i')\otimes \Bbbk Q(j,j')$
for any $\alpha:k\rightarrow l$.
\end{enumerate}
\end{proposition}
\begin{proof}
Note the fact that if $\Bbbk Q_0$ is a subcoalgebra of $\Bbbk Q$ and $\Delta$
is a prealgebra morphism, then $\Delta$ is a partitioning
morphism. The rest of the proof is similar to \cite[Proposition 4]{He2008a}, and
we omit it here.
\end{proof}
\begin{remark}
\label{xxrem7.3}
\begin{enumerate}
\item[(1)]
Following Proposition \ref{xxpro7.2}, our first step is to
understand all weak bialgebra structures on $\Bbbk^{\oplus n}$.
This is already a non-trivial task and we post it as a question.
$$\text{\it Can we classify all weak bialgebra structures
on $\Bbbk^{\oplus n}$?}$$
When $n=2$, see Lemma \ref{xxlem7.5} below.
\item[(2)]
There are algebras $A$ which do not admit any weak bialgebra
structure. Let $A$ be the algebra $\Bbbk[x]/(x^n)$ for some $n$.
Then $A$ admits a (weak) bialgebra structure if and only if
$n=p^t$ where $p={\rm{char}}\; \Bbbk>0$ and $t\geq 1$. We give
a sketch proof of one implication. Suppose that $A:=\Bbbk[x]/(x^n)$
is a weak bialgebra. Note that $A$ is local which implies that
both the target and source counital subalgebras of $A$ are
$\Bbbk$. As a consequence, $A$ is a bialgebra. So the augmentation
ideal $J:=\ker \epsilon$ is the Jacobson radical of $A$. So the
associated graded Hopf algebra ${\text{gr}}_{J} A$, which is
isomorphic to $A$ as an algebra, is the restricted enveloping
algebra of a restricted Lie algebra. Therefore the
$\Bbbk$-dimension of $A$ is $p^t$ for some $t\geq 1$. The
assertion follows.
\item[(3)]
Suppose ${\textrm{char}}\; \Bbbk=p>0$.
Let $A$ be the finite dimensional Hopf algebra
$$\Bbbk [x_1,\cdots,x_n]/(x_1^p,\cdots,x_n^p)$$
for some $n\geq 2$. The coalgebra structure of $A$ is
determined by
$$\Delta(x_i)=x_i\otimes 1+1\otimes x_i$$
for all $i$. Since $A$ is local, the only
brick object in $\mathcal{A}$ is the
trivial module $\Bbbk$. Therefore $\fpd(M)<\infty$
for every object in $\mathcal{A}$.
On the other hand, $A$ is wild when $n\geq 2$.
Therefore conditions (a) and (b) in Theorem \ref{xxthm0.4}
are not equivalent
if we remove the hereditary hypothesis.
\end{enumerate}
\end{remark}
\begin{definition}
\label{xxdef7.4}
Let $A$ be an algebra. Two (weak) bialgebra structures $(\Delta_1,
\varepsilon_1)$ and $(\Delta_2,\varepsilon_2)$ on $A$ are called
{\it equivalent} if there is an algebra automorphism
$\sigma$ of $A$ such that $\Delta_1 \sigma =(\sigma\otimes \sigma)
\Delta_2$ and $\varepsilon_1 \sigma=\varepsilon_2$.
\end{definition}
\begin{lemma}
\label{xxlem7.5}
Let $B=\Bbbk^{\oplus 2}=\Bbbk e_1\oplus \Bbbk e_2$. Then there are
five different weak bialgebra structures on $B$:
\begin{enumerate}
\item[(a)]
$\Delta(e_1)=e_1\otimes e_1, \Delta(e_2)=e_2\otimes e_2+e_1\otimes e_2
+e_2\otimes e_1$, $\varepsilon(e_1)=1$ and $\varepsilon(e_2)=0$.
\item[(b)]
$\Delta(e_1)=e_1\otimes e_1+e_2\otimes e_2, \Delta(e_2)=e_2\otimes e_1
+e_1\otimes e_2$, $\varepsilon(e_1)=1$ and $\varepsilon(e_2)=0$.
\item[(c)]
$\Delta(e_2)=e_2\otimes e_2, \Delta(e_1)=e_1\otimes e_1+e_1\otimes e_2
+e_2\otimes e_1$, $\varepsilon(e_1)=0$ and $\varepsilon(e_2)=1$.
\item[(d)]
$\Delta(e_2)=e_2\otimes e_2+e_1\otimes e_1, \Delta(e_1)=e_1\otimes e_2
+e_2\otimes e_1$, $\varepsilon(e_1)=0$ and $\varepsilon(e_2)=1$.
\item[(e)]
$\Delta(e_1)=e_1\otimes e_1, \Delta(e_2)=e_2\otimes e_2$,
$\varepsilon(e_1)=1$ and $\varepsilon(e_2)=1$.
\end{enumerate}
Note that {\rm{(a)}} and {\rm{(c)}} are equivalent bialgebra
structures {\rm{(}}and so are {\rm{(b)}} and {\rm{(d)}}{\rm{)}}.
The fifth one is a weak bialgebra, but not a bialgebra.
\end{lemma}
Note that (e) in the above lemma is the direct sum of two
copies of trivial Hopf algebra $\Bbbk$. Consequently,
it is a weak Hopf algebra. Other bialgebra algebras in
the above lemma are not (weak) Hopf algebras.
\begin{proof} Fix a (weak) bialgebra structure $(\Delta,\varepsilon)$
on $B$. Let $B_t$ and $B_s$ be target and source counital
subalgebras of $B$, see \cite[Definition 2.2.3]{NV2002}.
Case 1: $\dim B_t=1$, then $B_t=B_s=\Bbbk 1_B$. In this case,
$B$ is a bialgebra. As a consequence,
$\varepsilon(e_1)+\varepsilon(e_2)=\varepsilon(e_1+e_2)=\varepsilon(1)=1$.
Since $e_i$ are idempotents, $\varepsilon(e_i)$ is 1 or 0.
First we assume that $\varepsilon(e_1)=1$ and $\varepsilon(e_2)=0$.
Write $\Delta(e_1)=\sum\limits_{i,j} a_{ij} e_i\otimes e_j$.
By the counital axiom, we obtain that $\Delta(e_1)=e_1\otimes e_1$ or
$\Delta(e_1)=e_1\otimes e_1+e_2\otimes e_2$. If
$\Delta(e_1)=e_1\otimes e_1$, we obtain case (a); if
$\Delta(e_1)=e_1\otimes e_1+e_2\otimes e_2$, we obtain
case (b). The other situation is $\varepsilon(e_1)=0$ and
$\varepsilon(e_2)=1$. By symmetric, we have (c) and (d).
Case 2: $\dim B_t=2$. Then $B_t=B_s=B$. By
\cite[Lemma 2.7]{BXYZZ2020}, $\Delta(e_1)=e_1\otimes e_1$
and $\Delta(e_2)=e_2\otimes e_2$. Then it is easy to check
that we obtain (e).
\end{proof}
\begin{lemma}
\label{xxlem7.6}
Let $A$ be a bialgebra and $J$ be its Jacobson radical. Suppose
that $J$ is nilpotent. If $B:=A/J\cong \Bbbk^{\oplus n}$ as an
algebra for some positive integer $n$, then $B$ is a quotient
bialgebra of $A$.
\end{lemma}
\begin{proof}
Let $\pi$ be the canonical quotient map from $A$ to $B$. It's
clear that $\pi$ is an algebra map. Consider the composition
of algebra maps:
$$A \xrightarrow{\Delta} A\otimes A
\xrightarrow{\pi \otimes \pi} B\otimes B.$$
Since $B\otimes B$ doesn't have nilpotent elements and $J$ is
nilpotent, the above algebra map from $A\to B\otimes B$ factors
through the quotient map $\pi$, that is, there exists a unique
algebra map $\Delta_B$ from $B\to B\otimes B$, such that the
following diagram commutes
$$\xymatrix{
A \ar[rr]^{\Delta}\ar[d]_{\pi} & & A\otimes A\ar[d]^{\pi\otimes \pi}\\
B \ar[rr]^{\Delta_{B}} & & B\otimes B.}$$
Furthermore, $(\Delta_B\otimes Id)\Delta_B$ and
$(Id\otimes \Delta_B)\Delta_B$ are the algebra maps induced
by algebra maps
$(\pi\otimes \pi\otimes \pi)(\Delta\otimes Id)\Delta$
and $(\pi\otimes \pi\otimes \pi)(Id\otimes \Delta)\Delta$
respectively from $A\to B\otimes B\otimes B$. Then $\Delta_B$ is
coassociative since $\Delta$ is coassociative.
Similarly, let $\varepsilon_B: B\to \Bbbk$ be the algebra map
induced by $\varepsilon:A\to \Bbbk$. It is not hard to verify
that $\varepsilon_B$ satisfies the counital axiom. Consequently,
$B$ is a quotient bialgebra of $A$ and $J$ is a bi-ideal.
\end{proof}
Now we are ready to classify (weak) bialgebras on a small quiver.
\begin{proposition}
\label{xxpro7.7}
Suppose $Q$ is the quiver with two vertices $\{1,2\}$ and
$w$ arrows from $1$ to $2$ with $w\geq 1$. Let $A$ be the
path algebra $\Bbbk Q$. Then there are 5 types of weak bialgebra
structures on $A$ up to equivalences.
\begin{enumerate}
\item[(a)]
$\Delta(e_1)=e_1\otimes e_1, \Delta(e_2)=e_2\otimes e_2+e_1\otimes e_2
+e_2\otimes e_1$, $\varepsilon(e_1)=1, \varepsilon(e_2)=0$, and for any
arrow $r$ from 1 to 2, $\Delta(r)= e_1\otimes r+r\otimes e_1$ and
$\varepsilon(r)=0$.
\item[(b)]
$\Delta(e_1)=e_1\otimes e_1+e_2\otimes e_2, \Delta(e_2)=e_2\otimes e_1
+e_1\otimes e_2$, $\varepsilon(e_1)=1, \varepsilon(e_2)=0$,
and for any arrow $r$ from 1 to 2, $\Delta(r)=r\otimes e_1
+e_1\otimes r$ and $\varepsilon(r)=0$.
\item[(c)]
$\Delta(e_2)=e_2\otimes e_2, \Delta(e_1)=e_1\otimes e_1+e_1\otimes e_2
+e_2\otimes e_1$, $\varepsilon(e_2)=1, \varepsilon(e_1)=0$, and for any
arrow $r$ from 1 to 2, $\Delta(r)= e_2\otimes r+r\otimes e_2$ and
$\varepsilon(r)=0$.
\item[(d)]
$\Delta(e_2)=e_1\otimes e_1+e_2\otimes e_2, \Delta(e_1)=e_2\otimes e_1
+e_1\otimes e_2$, $\varepsilon(e_2)=1, \varepsilon(e_1)=0$,
and for any arrow $r$ from 1 to 2, $\Delta(r)=r\otimes e_2
+e_2\otimes r$ and $\varepsilon(r)=0$.
\item[(e)]
$\Delta(e_i)=e_i\otimes e_i$, $\varepsilon(e_i)=1$ for $i=1,2$,
and the Jacobson radical $J$ of $A$ is a subcoalgebra of $A$.
\end{enumerate}
\end{proposition}
\begin{proof}
Let $J$ be the Jacobson radical of $A$, which is the ideal
generated by the arrows from $1$ to $2$. It is clear that
$J^2=0$ and $A/J\cong B$ where $B$ is as given in Lemma
\ref{xxlem7.5}.
We first consider bialgebra structures on $A$.
By Lemma \ref{xxlem7.6}, $A/J$ is a quotient bialgebra of
$A$ and $J$ is a bi-ideal of $A$. All bialgebra structures
on $B\cong A/J$ are classified in Lemma \ref{xxlem7.5}. We
will use this classification to analyze the bialgebra
structures on $A$.
Case 1: Suppose the bialgebra structure on $B$ is as in
Lemma \ref{xxlem7.5}(a). Lifting the bialgebra structure on
$B$ to $A$, we have
$$\Delta(e_1)=e_1\otimes e_1+e_1\otimes t_1+ e_2\otimes t_2
+t_3\otimes e_1+t_4\otimes e_2+ T,$$
$$\Delta(e_2)=e_1\otimes e_2+e_2\otimes e_1+e_2\otimes e_2-
e_1\otimes t_1-e_2\otimes t_2
-t_3\otimes e_1-t_4\otimes e_2- T,$$
where $T\in J\otimes J$ and $t_i\in J$ for $1\leq i\leq 4$, and
$$\varepsilon (e_1)=1, \quad \varepsilon(e_2)=0,
\quad \varepsilon(r)=0 {\text{ for all }} r\in J.$$
By counital axiom, we have $t_1=t_3=0$. By using the equation
$\Delta(e_1e_2)=0$, we have $t_2=t_4=0$.
In the bialgebra structure of $A$, we have, for every arrow
$r$ from $1$ to $2$,
$$\Delta(r)=e_1\otimes r+r\otimes e_1+ f(r)\otimes e_2+e_2\otimes
g(r)+w(r)$$
where $f(r),g(r)\in J$ and $w(r)\in J\otimes J$. Using the fact
that $r=re_1$, we obtain that $f(r)=g(r)=0$ for all $r$.
Pick any $\Bbbk$-basis of $J$, say $\{r_i\}$, we can write,
\begin{eqnarray*}
\Delta(e_1)&= &e_1\otimes e_1+\sum_{i,j} a_{ij} r_i \otimes r_j,\\
\Delta(e_2)&= &e_1\otimes e_2+e_2\otimes e_1
+e_2\otimes e_2-\sum_{i,j} a_{ij} r_i \otimes r_j,\\
\Delta(r_i)&= &e_1\otimes r_i+r_i\otimes e_1+\sum_{j,k} c^{jk}_i r_j\otimes r_k.
\end{eqnarray*}
Suppose $\deg (e_1)=\deg(e_2)=0$ and $\deg(r_i)=1$.
Let $\equiv$ denote $=$ modulo higher degree terms. Then the
coalgebra structure above can be written as
$$\begin{aligned}
\Delta(e_1)&\equiv e_1\otimes e_1 \\
\Delta(e_2)&\equiv e_1\otimes e_2+e_2\otimes e_1+ e_2\otimes e_2\\
\Delta(r_i)&\equiv e_1\otimes r_i +r_i \otimes e_1.
\end{aligned}
$$
By \cite[Lemma 3.1]{HT2013}, if two different bialgebra structures
on $A$ both satisfy the above equations, then they are isomorphic.
Therefore, in this case, there exists a unique bialgebra structure
on $A$ up to isomorphism, that is,
\begin{eqnarray*}
\Delta(e_1)&= &e_1\otimes e_1,\\
\Delta(e_2)&= &e_1\otimes e_2+e_2\otimes e_1+e_2\otimes e_2,\\
\Delta(r_i)&= &e_1\otimes r_i+r_i\otimes e_1,
\end{eqnarray*}
which is exactly (a).
Case 2: Suppose the bialgebra structure on $B$ is as in
Lemma \ref{xxlem7.5}(b). Lifting the bialgebra structure on
$B$ to $A$, we have
$$\Delta(e_1)=e_1\otimes e_1+ e_2\otimes e_2+ e_1\otimes t_1+
e_2\otimes t_2+ t_3\otimes e_1+t_4\otimes e_2+ T,$$
where $T\in J\otimes J$ and $t_i\in J$ for $1\leq i\leq 4$, and
$$\Delta(e_2)=e_1\otimes e_2+e_2\otimes e_1-e_1\otimes t_1-
e_2\otimes t_2-t_3\otimes e_1-t_4\otimes e_2- T,$$
$$\varepsilon (e_1)=1, \quad \varepsilon(e_2)=0,
\quad \varepsilon(r)=0 {\text{ for all }} r\in J.$$
By counital axiom, we have $t_1=t_3=0$.
By the fact $e_i$ is an idempotent, we have $T=0$.
In the bialgebra structure of $A$, for every arrow $r$ from
1 to 2, we have
$$\Delta(r)=e_1\otimes r+r\otimes e_1+ f(r)\otimes e_2+e_2\otimes
g(r)+w(r)$$
where $f(r),g(r)\in J$ and $w(r)\in J\otimes J$.
Using the fact
that $e_1r=0$, we obtain that $f(r)=g(r)=0$ for all $r$ and
$w(r)+r\otimes t_2+t_4\otimes r=0$.
Hence, for all $t\in J$,
$$\Delta(t)=e_1\otimes t+ t\otimes e_1- t\otimes t_2-
t_4\otimes t.$$
Moreover, the coassociative axiom, $(Id\otimes \Delta)\Delta(e_2)
=(\Delta\otimes Id)\Delta(e_2)$, implies $t_2=t_4=0.$
We obtain (b).
Case 3 and 4: When the bialgebra structure on $B$ is as in
Lemma \ref{xxlem7.5}(c) and (d), it's similarly to case 1 and case 2
respectively, and we obtain (c) and (d).
Next, we consider weak bialgebra, but not bialgebra, structures on $A$.
Let $A_t$ and $A_s$ be the target and source counital subalgebras.
By \cite[(2.1) and Proposition 2.4]{BNS1999},
$\dim A_t=\dim A_s$ and $A_s$ commutes with $A_t$.
If $\dim A_t=\dim A_s=1$, by \cite[Lemma 8.2]{N1998},
$A$ is a bialgebra since $\Delta(1)=1\otimes 1$, which is the case
we have just finished above. So $\dim A_t=\dim A_s\geq 2$.
Since $A_s$ is separable (hence semisimple), $A_s\cap J=\{0\}$.
Thus there is an injective map
$$A_s\longrightarrow A \xrightarrow{\pi} B$$
which implies that $\dim A_t=\dim A_s=2$ and
that $\pi(A_s)=B$.
Now we claim that $A_t=A_s\cong B$. Since $\pi(A_s)=B$,
we can write $A_s=span\{1,e_1+p\}$ where $p\in J$. In this case,
$A_t=A_s$ since the space of elements which commute with $e_1+p$
is $A_s$ itself, and they both are weak bialgebras. Let $l$
denote the idempotent $e_1+p$. Assume that
$$\Delta(1)=a_1 1\otimes 1+a_2 l\otimes 1+a_3 1\otimes l+a_4 l\otimes l$$
where $a_i\in \Bbbk$.
By \cite[Equations (2.7a) and (2.7b)]{BNS1999}, $a_1+a_2=0$ and
$\Delta(l)=(a_2+a_4)l\otimes l$.
By $\Delta(1)=\Delta(1^2)$, $a_2=a_3$ and one of following equalities hold:
\begin{enumerate}
\item[(i)]
$\Delta(1)=l\otimes l$,
\item[(ii)]
$\Delta(1)=1\otimes 1- l\otimes 1- 1\otimes l+ l\otimes l$,
\item[(iii)]
$\Delta(1)=1\otimes 1- l\otimes 1- 1\otimes l+2 l\otimes l$.
\end{enumerate}
However, (i) implies that $l$ is a scalar multiple of $1$ and
(ii) implies that $1-l$ is a scalar multiple of $1$,
which both are impossible. So (iii) holds and
$\Delta(1)=(1-l)\otimes (1-l)+ l\otimes l$,
which means $A_t=A_s\cong B$ as weak bialgebra,
where the weak bialgebra structure on $B$
as in Lemma \ref{xxlem7.5}(e).
Re-write $l_1=l$ and $l_2=1-l$. Then
$\Delta(l_1)=l_1\otimes l_1$ and $\Delta(l_2)=l_2\otimes l_2$.
Note that $A=A_t\oplus J$ as vector space.
Then for any arrow $r$ from 1 to 2, we have
$$\Delta(r)=f(r)\otimes l_1+g(r)\otimes l_2+
l_1\otimes p(r)+ l_2\otimes q(r)+w(r),$$
where $f(r),g(r),p(r),q(r)\in J$ and $w(r)\in J\otimes J$.
By $rl_1=r$ and $l_2r=r$, $f(r)=g(r)=p(r)=q(r)=0$ for all $r$.
That is $J$ is a subcoalgebra of $A$.
It's not hard to check any coalgebras structure over $J$
satisfy conditions in Definition \ref{xxdef1.7}.
Moreover, let $\sigma: (A,\Delta,\varepsilon)\to (A,\Delta',\varepsilon')$
via $\sigma(l_i)=e_i$ and $\sigma(r)=r$ for $r\in J$, where
$(A,\Delta',\varepsilon')$ is the weak bialgebra as in (e).
Then $\sigma$ is an algebra automorphism and $(\Delta,\varepsilon)$
is equivalent to $(\Delta',\varepsilon')$.
\end{proof}
We finish this section with examples related to both
commutative projective varieties and noncommutative
projective schemes in the sense of \cite{AZ1994}.
\begin{definition} \cite[p. 1230]{HP2011}
\label{xxdef7.8}
Let ${\mathbb X}$ be a smooth projective scheme.
\begin{enumerate}
\item[(1)]
A coherent sheaf ${\mathcal E}$ on ${\mathbb X}$ is called
{\it exceptional} if $\Hom_{\mathbb X}({\mathcal E},{\mathcal E})
\cong \Bbbk$ and $\Ext^i_{\mathbb X}({\mathcal E},{\mathcal E}) =0$
for every $i \geq 0$.
\item[(2)]
A sequence ${\mathcal E}_1, \cdots, {\mathcal E}_n$ of exceptional
sheaves is called an {\it exceptional sequence} if $\Ext^k_{\mathbb X}
({\mathcal E}_i,{\mathcal E}_j) = 0$ for all $k$ and for all $i > j$.
\item[(3)]
If an exceptional sequence generates $D^b(coh({\mathbb X}))$, then
it is called {\it full}.
\item[(4)]
If an exceptional sequence satisfies
$$\Ext^k_{\mathbb X}({\mathcal E}_i,{\mathcal E}_j) = 0$$
for all $k > 0$ and all $i, j$, then it is called a {\it strongly
exceptional sequence}.
\end{enumerate}
\end{definition}
The above concepts are extended to an arbitrary triangulated category
in \cite[Definition 4.1]{Mo2013}. The existence of a full (strongly)
exceptional sequence has been proved for many smooth projective schemes.
However, on Calabi-Yau varieties there are no exceptional sheaves.
When ${\mathbb X}$ has a full exceptional sequence
${\mathcal E}_1, \cdots, {\mathcal E}_n$, then there is a triangulated
equivalence
\begin{equation}
\label{E7.8.1}\tag{E7.8.1}
\RHom_{\mathbb{X}}(\oplus_{i=1}^n {\mathcal E}_i,-):\quad
D^b(coh({\mathbb X}))\cong D^b(\Modfd-A)
\end{equation}
where $A$ is the finite dimensional algebra
$\End_{\mathbb X}(\oplus_{i=1}^n {\mathcal E}_i)$, see
\cite[Theorem 4.2]{Mo2013} (or \cite[Theorem 3.1.7]{BVdB2003}).
By Example \ref{xxex5.3}(2), there is a canonical
monoidal triangulated structure on $D^b(coh({\mathbb X}))$
induced by $\otimes_{\mathbb{X}}$. Then we obtain a monoidal
triangulated structure on $D^b(\Mod_{f.d}-A)$ via
\eqref{E7.8.1}. By Example \ref{xxex5.3}(1), if $A$ is a
weak bialgebra, there is a (different) canonical monoidal
triangulated structure on $D^b(\Mod_{f.d}-A)$ (or
equivalently, on $D^b(coh({\mathbb X}))$). In short, there
are possibly many different monoidal triangulated structures
on a given triangulated category.
Next we give an explicit example related to noncommutative
projective schemes.
\begin{example}
\label{xxex7.9}
Let $T$ be a connected graded noetherian Koszul
Artin-Schelter regular algebra of global dimension at least
2. If $T$ is commutative, then $T$ is the polynomial ring
$\Bbbk[x_0,x_1,\cdots,x_n]$ for some $n\geq 1$. Let
$\mathbb{X}$ be the noncommutative projective scheme
associated to $T$ in the sense of \cite{AZ1994}. In
\cite{AZ1994} $\proj T$ denotes the category of coherent
sheaves on $\mathbb{X}$, but here we use $coh(\mathbb{X})$
instead. When $T$ is the commutative polynomial ring
$\Bbbk[x_0,x_1,\cdots,x_n]$, then $\mathbb{X}$ is the
commutative projective $n$-space $\mathbb{P}^n$. On the
other hand, there are many noetherian Koszul Artin-Schelter
regular algebras $T$ that are not commutative. Let $r$ be
the global dimension of $T$ and $\mathcal{O}$ be the
structure sheaf of $\mathbb{X}$. Then
$$\{\mathcal{O}(-(r-1)),\mathcal{O}(-(r-2)),
\cdots,\mathcal{O}(-1), \mathcal{O}\}$$
is a full strongly exceptional sequence for $\mathbb{X}$
in the sense of \cite[Definition 4.1]{Mo2013}.
By \eqref{E7.8.1} or \cite[Theorem 4.2]{Mo2013},
\begin{equation}
\label{E7.9.1}\tag{E7.9.1}
D^b(coh(\mathbb{X}))\cong D^b(A-\Modfd)
\end{equation}
where $A$ is the opposite ring of
$\End_{\mathbb X}(\oplus_{i=1}^n {\mathcal O}_i)$.
By \cite[Definition 4.6 and Theorem 4.7]{Mo2013},
$A$ is the opposite ring of the Beilinson algebra
(which is denoted by $R$ in \cite[Definition 4.6]{Mo2013}).
By the description in \cite[Definition 4.7]{MM2011}, the
Beilinson algebra is an upper triangular matrix with
diagonal entries being $\Bbbk$. Then $A$ can be written as
$\Bbbk Q/I$ where $Q$ is a quiver with $r$ vertices and
the number of arrows from vertex $i$ to vertex $j$ equals the
dimension of $T_{j-i}$. It is clear that $Q$ satisfies
condition (2) in Example \ref{xxex7.1}. By Example
\ref{xxex7.1}, there is a cocommutative bialgebra structure
on $A$. Similarly, vertex $r$ in $Q$ satisfies condition
(1) in Example \ref{xxex7.1}, which implies that there is
another cocommutative bialgebra structure on $A$. Via
\eqref{E7.9.1}, $D^b(coh(\mathbb{X}))$ has at least two
different monoidal triangulated structures induced by
two different bialgebra structures on $A$.
Now let $T$ be the polynomial ring $\Bbbk[x_0,x_1]$.
Then $\mathbb{X}=\mathbb{P}^1$ and
\begin{equation}
\nota
D^b(coh(\mathbb{P}^1))\cong D^b((B)^{op}-\Modfd)
\end{equation}
where $B$ is the Beilinson algebra associated to $T$.
By \cite[Definition 4.7]{MM2011},
$$B=\begin{pmatrix} \Bbbk & \Bbbk x+\Bbbk y\\
0& \Bbbk\end{pmatrix}.$$
It is clear that $B$ is the path algebra of the Kronecker
quiver given in Example \ref{xxex2.7}. In this case we have
two monoidal triangulated structures on
$D^b(coh(\mathbb{P}^1))$. One is the monoidal structure
induced by $\otimes_{\mathbb{P}^1}$, and the other comes
from the canonical weak bialgebra structure of $B=\Bbbk Q$
[Lemma \ref{xxlem2.1}(1)]. Together with two bialgebra
structures on $B$, see the above paragraph, we obtain four
different monoidal triangulated structures on
$D^b(coh(\mathbb{P}^1))$. To show these monoidal triangulated
structures are not equivalent, one need to use some arguments
in the proof of Lemma \ref{xxlem5.9} (details are omitted).
\end{example}
\section{Proof of Theorems \ref{xxthm0.8}}
\label{xxsec8}
It is important and interesting to calculate explicitly
$\fpd(M)$ of some objects $M$ in
a monoidal abelian (or triangulated) category. Generally
this is very difficult task and dependent on complicated
combinatorial structures of the brick sets. In this section
we will work out one example. Note that some non-essential
details are omitted.
A type $\mathbb{A}_n$ quiver is defined to be a quiver of
form \eqref{E0.7.1}:
\begin{equation}
\nota
\xymatrix{
1 \ar@{-}[r]^{\alpha_1}&2\ar@{-}[r]^{\alpha_2}
&\cdots\ar@{-}[r]^{\alpha_{i-1}}&i\ar@{-}[r]^{\alpha_i}
&\cdots\ar@{-}[r]^{\alpha_{n-1}}&n}
\end{equation}
where each arrow $\alpha_i$ is either $\longrightarrow$ or
$\longleftarrow$. For each $n\geq 3$, there are
more than one isomorphism classes of type $\mathbb{A}_n$
quivers with $n$ vertices, though we denote all of them
by $\mathbb{A}_n$. In this section we provide
fairly detailed computation of $\fpd(M)$ for every indecomposable
object in the monoidal abelian category $\Repr(\mathbb{A}_n)$.
Using Lemma \ref{xxlem4.11}, we obtain $\fpd(M)$ for every
indecomposable object $M$ in the monoidal triangulated
category $D^b(\Repr (\mathbb{A}_n))$. The result is
summarized in Theorem \ref{xxthm0.8}. Throughout this
section, the tensor product is defined as in \eqref{E2.1.1}.
First we try to understand brick sets in $\Repr(\mathbb{A}_n)$.
Recall that $M\{i,j\}$, for $i\leq j$, denotes the representation
of $\mathbb{A}_n$ defined by
\begin{align}
\notag
(M\{i,j\})_s&=\begin{cases} \Bbbk & i\leq s\leq j,\\
0 & {\text{otherwise,}}\end{cases} \\
\notag
(M\{i,j\})_{\alpha_s}&=\begin{cases} Id_{\Bbbk} & i\leq s<j,\\
0& {\text{otherwise}}.\end{cases}
\end{align}
We start with easy observations.
\begin{lemma}
\label{xxlem8.1}
If $\{M\{1,m\},M\{k,l\}\}$ is a brick set and $m\geq k \geq 3$,
then $\{M\{2,m\}$, $M\{k,l\}\}$ also is a brick set.
\end{lemma}
\begin{proof}
This is clear since $k\geq 3$.
\end{proof}
\begin{lemma}
\label{xxlem8.2}
For any $1\leq i<j\leq n$, $\{M\{1,i\},M\{1,j\}\}$ is not a
brick set.
\end{lemma}
\begin{proof}
There are two cases.
Case 1: $s(\alpha_i)=i$.
Let $f:M\{1,j\}\rightarrow M\{1,i\}$ be
$(f)_k=\begin{cases}
Id & k\leq i\\
0 & k>i
\end{cases}.$
Then it is clear that $f\in \Hom(M\{1,j\},M\{1,i\})$
and $\Hom(M\{1,j\},M\{1,i\})\neq 0$.
Case 2: $t(\alpha_i)=i$.
Let $g:M\{1,i\}\rightarrow M\{1,j\}$ be
$(g)_k=\begin{cases}
Id & k\leq i\\
0 & k>i
\end{cases}.$
Then $g\in \Hom(M\{1,i\},M\{1,j\})$ and $\Hom(M\{1,i\},M\{1,j\})\neq 0$.
Combining these two cases, one sees that $\{M\{1,i\},M\{1,j\}\}$
is not a brick set.
\end{proof}
In the above, we can replace $1$ by any positive integer
no more that $i$.
\begin{lemma}
\label{xxlem8.3}
Suppose $i\leq j\leq k$. Then one of spaces
$\Hom(M\{i,j\},M\{i,k\})$ and $\Hom(M\{i,k\},M\{i,j\})$ is
isomorphic to $\Bbbk $ while the other is zero.
\end{lemma}
\begin{proof}
An idea similar to the proof of Lemma \ref{xxlem8.2} shows that
one of spaces is nonzero and the other is zero. For the one that
is nonzero, it must be $\Bbbk$ by Lemma \ref{xxlem4.2}.
\end{proof}
\begin{lemma}
\label{xxlem8.4}
If $f:M\{i,k\}\rightarrow M\{i,l\}$ is a non-zero morphism and $k\neq l$,
then for any $j\leq i$, $\Hom(M\{i,l\}, M\{j,k\})=0$ and
$\Hom(M\{j,l\}, M\{i,k\})=0$.
\end{lemma}
\begin{proof}
Assume that $g:M\{i,l\}\rightarrow M\{j,k\}$ is non-zero morphism, then
it can induce a non-zero morphism $\hat g:M\{i,l\}\rightarrow M\{i,k\}$.
By Lemma \ref{xxlem8.3}, $f=0$ which contradicts the assumption.
Therefore, $\Hom(M\{i,l\}, M\{j,k\})=0$. Similarly,
$\Hom(M\{j,l\}, M\{i,k\})=0$.
\end{proof}
Next we define a binary relation, denoted by $\succ$, that
does not necessarily satisfy the usual axioms of an order.
\begin{definition}
{\label{xxdef8.5}}
For $N,N'\in \Repr(\mathbb{A}_n)$, we write $N\succ N'$ if
$\Hom(N,N')\cong \Bbbk$. Usually we only consider
indecomposable objects $N,N'$.
\end{definition}
Another easy observation, following from Lemma \ref{xxlem8.3}, is
\begin{lemma}
\label{xxlem8.6}
Let $I\subset \{1,2,\cdots,n\}$ and
$\mathcal{S}_I=\{X_i\mid X_i=M\{1,i\}, i\in I\}$.
Then $(\mathcal{S}_I,\succ)$ is a totally ordered set.
Similarly, $\{Y_i\mid Y_i=M\{i,n\}, i\in I\}$
is a totally ordered set.
\end{lemma}
\begin{lemma}
{\label{xxlem8.7}}
Let $N=M\{i,j\}$, $N'=M\{k,l\}$ and $k\leq j< l$.
\begin{enumerate}
\item[(1)]
If $s(\alpha_j)=j$ and $i\leq k$,
then $\Hom(N',N\otimes N')\cong \Bbbk$ where
$N\otimes N'=M\{k,j\}$.
\item[(2)]
If $t(\alpha_j)=j$,
then for all $m\leq j$, $\Hom(N', M\{m,j\})=0.$
\end{enumerate}
\end{lemma}
\begin{proof}
(1) In this case, we have $i\leq k\leq j$. By definition,
$N'=M\{k,l\}$ and $N\otimes N'=M\{k,j\}$.
Let $f:N'\rightarrow N\otimes N$ be defined by
$(f)_s=\begin{cases}
Id & \mathrm{if} ~k\leq s\leq j\\
0 & \mathrm{otherwise}
\end{cases}.$
Then it is not hard to check $0\neq f\in \Hom(N', N\otimes N')$.
If $f'\in \Hom(N',N\otimes N')$, then there is a scalar $c\in \Bbbk$
such that $(f')_s=c Id$ for all $k\leq s\leq j$.
Then $f'=c f$ and $\Hom(N', N\otimes N')\cong \Bbbk$.
(2) Since $k\leq j<l$, $(N')_{j+1}=\Bbbk$. Let $f\in
\Hom(N',M\{m,j\})$. Then, for every $s>j$, $f_{s}=0$
as $(M\{m,j\})_s=0$. So we have
$$(f)_j (N')_{\alpha_j}=(M\{m,j\})_{\alpha_j} (f)_{j+1}=0.$$
Since $(N')_{\alpha_j}=Id_{\Bbbk}$, we obtain $(f)_j=0$.
Using a similar equation as above and induction, one sees
that $f_s=0$ for all $s<j$. Therefore $f=0$ as desired.
\end{proof}
For the rest of this section we use $\phi$ for a brick set in
$\Repr (\mathbb{A}_n)$. Given a brick set $\phi$ and an
indecomposable representation $M\{i,j\}$, we define three subsets
of $\phi$ according to $\{i,j\}$:
\begin{enumerate}
\item[(1)]
$\phi_i=\{N\in \phi \mid (N)_i\cong \Bbbk, (N)_j=0\},$
\item[(2)]
$\phi_j=\{N\in \phi \mid (N)_i=0, (N)_j\cong \Bbbk\},$
\item[(3)]
$\phi_{ij}=\{N\in \phi \mid (N)_i\cong \Bbbk, (N)_j\cong \Bbbk\}.$
\end{enumerate}
It is clear that $\phi$ contain the disjoint union of $\phi_i$,
$\phi_j$ and $\phi_{ij}$. Note that $\phi_l$, for $l$ being either
$i$ or $j$, can be divided into the following two parts:
\begin{equation*}
\begin{split}
\hat\phi_l &= \{N\in \phi_l \mid M\{i, j\}\otimes N\succ M\{i, j\}\},\\
\tilde\phi_l &= \{N\in \phi_l \mid M\{i, j\}\succ M\{i, j\}\otimes N\}.
\end{split}
\end{equation*}
\begin{lemma}
\label{xxlem8.8}
Let $N$ be an object in $\phi$ that satisfies either
$M\{i,j\}\otimes N=0$ or $M\{i,j\}\otimes N=N$. Then
$$\rho(A(\phi,M\{i,j\}\otimes -))=
\max\{a, \quad \rho(A(\phi\setminus \{N\},M\{i,j\}\otimes -))\}$$
where $a=\begin{cases}
0 & \text{if } M\{i,j\}\otimes N=0,\\
1 & \text{if } M\{i,j\}\otimes N=N.
\end{cases}$
\end{lemma}
\begin{proof}
Write $\phi=\{N_1, \cdots, N_m\}$ where $N_1=N$. By the
hypothesis on $N$,
$$\dim \Hom(N_k,M\{i,j\}\otimes N)=0$$
for $2\leq k\leq m$. Hence, in the matrix
$A(\phi,M\{i,j\}\otimes -)$, $a_{k1}=0$ for all $k\geq 2$.
As a consequence,
$$\rho(A(\phi,M\{i,j\}\otimes -))=
\max\{a, \quad \rho(A(\phi\setminus \{N_1\},M\{i,j\}\otimes -))\}$$
where $a:=a_{11}$ is the $(1,1)$-entry in $A(\phi,M\{i,j\}\otimes -)$.
Clearly $a$ has the desired property.
\end{proof}
\begin{lemma}
{\label{xxlem8.9}}
Let $N\in \phi_i$ and $N'\in \phi_j$. Then
$\{N, M\{i,j\}\otimes N'\}$ and $\{M\{i,j\}\otimes N, N'\}$ are
brick sets.
\end{lemma}
\begin{proof}
Write $N$ as $M\{i',j'\}$. Then $i'\leq i$ and $j'<j$.
Similarly, $N'=M\{k, l\}$ for some $k>i$ and $l\geq j$,
and consequently, $M\{i,j\}\otimes N'=M\{k, j\}$. A version
of Lemma \ref{xxlem8.1} shows that $\{M\{i',j'\},M\{k,l\}\}$
being a brick set implies that $\{M\{i',j'\}, M\{k,j\}\}$ is a
brick set. Therefore $\{N, M\{i,j\}\otimes N'\}$ is a
brick set. A similar argument shows that
$\{M\{i,j\}\otimes N, N'\}$ is brick set.
\end{proof}
\begin{lemma}
\label{xxlem8.10}
Let $j$ be a positive integer no more than $n$. If
$j=n$ or $s(\alpha_j)=j$, then $A(\phi_j, M\{i,j\}\otimes -)$ is similar
to an upper triangular matrix in which all diagonal entries are 1.
\end{lemma}
\begin{proof}
If $j=n$, then $|\phi_j|=1$ and $A(\phi_j, M\{i,j\}\otimes -)=(1)_{1\times 1}$
by Lemma \ref{xxlem8.2}.
If $j<n$ and $s(\alpha_j)=j$, by Lemma \ref{xxlem8.6}, the set
$(\{M\{i,j\}\otimes N \mid N\in \phi_j\}, \succ)$ is a totally
ordered set. Let $|\phi_j|=m$ and we can label the objects in
$\phi_j$ so that
$$M\{i,j\}\otimes N_1\succ \cdots\succ M\{i,j\}\otimes N_{m}.$$
By Definition \ref{xxdef8.5},
\begin{equation}
\label{E8.10.1}\tag{E8.10.1}
\Hom(M\{i,j\}\otimes N_k, M\{i,j\}\otimes N_l)\cong
\begin{cases}
0 & \mathrm{if} ~l< k,\\
\Bbbk & \mathrm{if} ~l\geq k.
\end{cases}
\end{equation}
And, by Lemma \ref{xxlem8.7}(1),
\begin{equation}
\label{E8.10.2}\tag{E8.10.2}
\Hom(N_k, M\{i,j\}\otimes N_k)\cong \Bbbk.
\end{equation}
Combine \eqref{E8.10.1} and \eqref{E8.10.2}, then
$$\dim \Hom(N_k,M\{i,j\}\otimes N_l)=
\begin{cases}
0 & \mathrm{if} ~l<k,\\
1 & \mathrm{if} ~l\geq k.
\end{cases}$$
The assertion follows.
\end{proof}
The next theorem is Theorem \ref{xxthm0.8}(2).
\begin{theorem}
\label{xxthm8.11}
Let $Q$ be a quiver of type $\mathbb{A}_n$ given in
\eqref{E0.7.1} for some $n\geq 2$. Then the following
hold in $\Repr(Q)$:
$$\fpd(M\{i,j\})=\begin{cases}
1 & {\text{if $M\{i,j\}$ is a sink}},\\
\min\{i, n-j+1\} & {\text{if $M\{i,j\}$ is a source}},\\
1 &{\text{if $M\{i,j\}$ is a flow}}.
\end{cases}$$
\end{theorem}
\begin{proof} First we show that
\begin{equation}
\label{E8.11.1}\tag{E8.11.1}
\fpd(M\{i,j\})\geq \begin{cases}
1 & {\text{if $M\{i,j\}$ is a sink}},\\
\min\{i, n-j+1\} & {\text{if $M\{i,j\}$ is a source}},\\
1 &{\text{if $M\{i,j\}$ is a flow}}.
\end{cases}
\end{equation}
Let $\phi$ be the singleton consisting of $M\{i,j\}$.
It is clear that $A(\phi, M\{i,j\}\otimes -)$ is $(1)_{1\times 1}$.
Hence $\fpd(M\{i,j\})\geq 1$. Now suppose that
$M\{i,j\}$ is a source. Let $d=\min\{i, n-j+1\}$.
We construct a brick set with $d$ elements as follows.
By Lemma \ref{xxlem8.6},
$(\{M\{k,i\}\mid 1\leq k\leq i\},\succ)$ and
$(\{M\{j,m\}\mid j\leq m\leq n\}, \succ)$
are two totally ordered sets. We list elements
in these two sets as
\begin{equation}
\label{E8.11.2}\tag{E8.11.2}
{\text{
$M\{k_1,i\}\succ \cdots\succ M\{k_i,i\}$ and
$M\{j,m_1\}\succ \cdots\succ M\{j,m_{n-j+1}\}$}}
\end{equation}
where $\{k_l\}_{l=1}^i$ and $\{m_l\}_{l=1}^{n-j+1}$
are distinct integers from $1$ to $i$ and
from $j$ to $n$ respectively.
Since $d=\min\{i,n-j+1\}$, we have a set of $d$ elements
$$\phi=\{M\{k_1,m_{n-j+1}\}, M\{k_2,m_{n-j}\}, \cdots,
M\{k_d, m_{n-j+2-d}\}\}.$$
We claim that $\phi$ is a brick set. If there is a nonzero
map from $M\{k_s,m_{n-j+2-s}\}$ to $M\{k_t,m_{n-j+2-t}\}$
for some $s<t$, then, when restricted to vertices
$\{j,j+1,\cdots,n\}$, we obtain a nonzero map from
$M\{j,m_{n-j+2-s}\}$ to $M\{j,m_{n-j+2-t}\}$. This
contradicts the second half of \eqref{E8.11.2}. Therefore
there is no nonzero morphism from $M\{k_s,m_{n-j+2-s}\}$ to
$M\{k_t,m_{n-j+2-t}\}$ for $s<t$. Similarly, there is
no nonzero morphism from $M\{k_t,m_{n-j+2-t}\}$ to
$M\{k_s,m_{n-j+2-s}\}$ for $s<t$, by using the first
half of \eqref{E8.11.2}. Thus we prove our claim.
Using this brick set, one see that every entry in
the matrix $A(\phi, M\{i,j\}\otimes -)$ is $1$,
consequently, $\rho(A(\phi, M\{i,j\}\otimes -))=d$.
Therefore $\fpd(M\{i,j\})\geq d$ if $M\{i,j\}$ is a
source. Combining with the inequality $\fpd(M\{i,j\})\geq 1$,
we obtain \eqref{E8.11.1}.
It remains to show the opposite inequality of
\eqref{E8.11.1}, or equivalently, to show that
\begin{equation}
\label{E8.11.3}\tag{E8.11.3}
\rho(A(\phi, M\{i,j\}\otimes -))\leq \begin{cases}
1 & {\text{if $M\{i,j\}$ is a sink}},\\
\min\{i, n-j+1\} & {\text{if $M\{i,j\}$ is a source}},\\
1 &{\text{if $M\{i,j\}$ is a flow}},
\end{cases}
\end{equation}
for every brick set $\phi$ in $\Repr(Q)$. We use induction
on the integer $|\phi|+n$. If $|\phi|+n$ is 1, nothing needs to
be proved. So we assume that $|\phi|+n\geq 2$.
If $|\phi|=1$, then $A(\phi, M\{i,j\}\otimes -)$
is either $(0)_{1\times 1}$ or $(1)_{1\times 1}$.
It is clear that the assertion holds. Now we assume that
$|\phi|\geq 2$. This forces that $n\geq 3$ (but we will
not use this fact directly). If there is an object $N\in
\phi$ such that either $M\{i,j\}\otimes N=0$ or
$M\{i,j\}\otimes N=N$, then \eqref{E8.11.3} follows
from Lemma \ref{xxlem8.8} and the induction
hypothesis.
For the rest of the proof we can assume that
$$N\not\cong M\{i,j\}\otimes N\neq 0$$
for every object $N\in \phi$. Note that the
above condition implies that $\phi$ is the disjoint
of $\phi_i$, $\phi_j$ and $\phi_{ij}$. Now it
suffices to consider $\phi$ satisfying the following
conditions:
\begin{enumerate}
\item[(*)] $\phi=\phi_i\cup \phi_j\cup \phi_{ij}$,
\item[(**)] for every $N\in \phi$, $M\{i,j\}\otimes N\not\cong N.$
\end{enumerate}
Let $w$ be the number of objects in $\phi$. Suppose that
$\phi_j$ is not empty. If there is an $N\in \phi_j$ such that
$N\otimes M\{i,j\} \succ M\{i,j\}$, we let $N_w$ be the object in
$\phi_j\cup \phi_{ij}$ such that $N_w\otimes M\{i,j\}$
is largest in the set
$$\{ N\otimes M\{i,j\}\mid N\in \phi_j \cup \phi_{ij}\}.$$
Such an object $N_w$ exists by a version of Lemma
\ref{xxlem8.6}. It is easy to see that $N_w\in \phi_j$.
By the choice of $N_w$, one can show that,
for every $N_k\in \phi_j \cup \phi_{ij}$ with $k\neq w$,
$$\Hom(N_k, N_w\otimes M\{i,j\})=0.$$
If $N_k\in \phi\setminus (\phi_j\cup\phi_{ij})$,
then, by Lemma \ref{xxlem8.9},
$$\Hom(N_k, N_w\otimes M\{i,j\})=0.$$
Therefore
$a_{kw}=0$ for all $k<w$ as an entry in the adjacency
matrix $A(\phi, M\{i,j\}\otimes -)$. As a consequence,
$$\rho(A(\phi, M\{i,j\}\otimes -))=\max\{1, \rho(A(\phi\setminus\{N_w\},
M\{i,j\}\otimes -))\}.$$
Assertion \eqref{E8.11.3} follows by induction hypothesis.
The other possibility is that for every $N\in \phi_j$ we
have $M\{i,j\}\succ N\otimes M\{i,j\}$. Now let $N_1$ be the object in
$\phi_j\cup \phi_{ij}$ such that $N_1\otimes M\{i,j\}$
is smallest in the set
$$\{ N\otimes M\{i,j\}\mid N\in \phi_j \cup \phi_{ij}\}.$$
Such an object $N_1$ exists by a version of Lemma
\ref{xxlem8.6}. It is easy to see that $N_1\in \phi_j$.
By the choice of $N_1$, one sees,
for every $N_k\in \phi_j \cup \phi_{ij}$ with $k\neq 1$,
$$\Hom(N_1, N_k\otimes M\{i,j\})=0.$$
If $N_k\in \phi\setminus (\phi_j\cup\phi_{ij})$,
then, by Lemma \ref{xxlem8.9}
$$\Hom(N_1, N_k\otimes M\{i,j\})=0.$$
Therefore
$a_{1k}=0$ for all $k>1$ as an entry in the adjacency
matrix $A(\phi, M\{i,j\}\otimes -)$. As a consequence,
$$\rho(A(\phi, M\{i,j\}\otimes -))=\max\{1, \rho(A(\phi\setminus\{N_1\},
M\{i,j\}\otimes -))\}.$$
Assertion \eqref{E8.11.3} follows by induction hypothesis.
Combining these two cases, we show that \eqref{E8.11.3}
holds by induction when $\phi_j$ is not empty.
Similarly, \eqref{E8.11.3} holds by induction when $\phi_i$
is not empty. The remaining case is when $\phi_i$ and
$\phi_j$ are empty, or
\begin{enumerate}
\item[$(^{\ast\ast\ast})$]
$\phi=\phi_{ij}$.
\end{enumerate}
We divide the rest of the proof into 5 small subcases.
Subcase 1: $t(\alpha_{i-1})=i$.
Pick any object in $\phi$, say $N$.
Suppose that $(N_1)_{i-1}\neq 0$. Then
$\Hom(N_1, M\{i,j\})=0$. Note that in
this case $M\{i,j\}=M\{i,j\}\otimes N$
for all $N\in \phi$. Therefore
$a_{1k}=0$ for all $k>1$ as an entry in the adjacency
matrix $A(\phi, M\{i,j\}\otimes -)$. As a consequence,
$$\rho(A(\phi, M\{i,j\}\otimes \rho(A(\phi\setminus\{N_1\},
M\{i,j\}\otimes -)).$$
Assertion \eqref{E8.11.3} follows by induction hypothesis.
Therefore, without loss of generality, we can assume that
$(N_1)_{i-1}=0$ for all $N_1\in \phi$. Now everything can be computed
in the subquiver quiver $Q\setminus\{1\}$. Then we reduce the number
of vertices from $n$ to $n-1$. Again the assertion follows from the
induction hypothesis.
Subcase 2: $t(\alpha_j)=j$. This is equivalent to Subcase 1 after one
relabels vertices of $Q$ by setting $i'=n+1-i$ for all
$1\leq i\leq n$.
Subcase 3: $i=1$. Since $\phi=\phi_{ij}$, by Lemma \ref{xxlem8.6},
$\phi$ consists of single object. As a consequence,
$A(\phi, M\{i,j\}\otimes -)$ is either $(0)_{1\times 1}$
or $(1)_{1\times 1}$. Then $\rho(A(\phi, M\{i,j\}\otimes -))
\leq 1$ and the assertion follows trivially.
Subcase 4: $j=n$. This is equivalent to Subcase 3 after one
re-labels vertices of $Q$ by setting $i'=n+1-i$ for all
$1\leq i\leq n$.
Subcase 5: Not cases 1-4, namely, $i>1$, $j<n$, $t(\alpha_{i-1})=i-1$
and $t(\alpha_j)=j+1$.
In this case $M\{i,j\}$ is a source. We list all objects in
$\phi=\phi_{ij}$ as
$$M\{i_1,j_1\}, \cdots, M\{i_w,j_w\}$$
where $1\leq i_s\leq i$ and $j\leq j_s\leq n$.
By Lemma \ref{xxlem8.3}, all $i_s$ are distinct.
The same holds true for $j_s$. Therefore $|\phi|=w\leq
d:= \min\{i,n-j+1\}$. Since every
entry of $A(\phi, M\{i,j\}\otimes -)$ is
at most 1, we obtain that
$\rho(A(\phi, M\{i,j\}\otimes -))\leq |\phi|\leq d$
as desired.
Combining \eqref{E8.11.1} with \eqref{E8.11.3},
we finish the proof.
\end{proof}
Note that, for $M,N\in \Repr(Q)$,
$$\Hom_{D^b(\Repr(Q))}(M[0], N[1])\cong
\Ext^1_{\Repr(Q)}(M,N).$$
For the rest of this section we use
$\Ext^1(M,N)$ instead of $\Ext^1_{\Repr(Q)}(M,N)$.
The {\it Euler characteristic} of two representations
$M$ and $N$ of $Q$ is defined to be
$$\langle\mathbf{dim} M,\mathbf{dim} N\rangle_{Q}
=\sum_{v\in Q_0}x_v y_v-\sum_{\alpha\in Q_1}
x_{s(\alpha)} y_{t(\alpha)}$$
where $\mathbf{dim}$ denotes the dimension vector and
$x_v=\dim((M)_v)$, $y_v=\dim ((N)_v)$ for any
$v\in Q_0$. By \cite[p.65]{GR1992}, we have
\begin{equation}
\label{E8.11.4}\tag{E8.11.4}
\dim \Hom(M,N)-\dim \Ext^1(M,N)=
\langle\mathbf{dim} M,\mathbf{dim} N\rangle_{Q}.
\end{equation}
One can verify the following.
\begin{lemma}
\label{xxlem8.12}
Assume $Q$ is of type $\mathbb{A}_n$. Let
$N=M\{i_1,j_1\},N'=M\{i_2,j_2\}$ and $i_1\leq i_2$.
\begin{enumerate}
\item[(1)]
If $j_1\leq i_2-2$, then $\Ext^1(N,N')=\Ext^1(N',N)=0.$
\item[(2)]
Suppose that $j_1=i_2-1$.
\begin{enumerate}
\item
If $s(\alpha_{j_1})=j_1$, then $\Ext^1(N,N')\cong\Bbbk$, $\Ext^1(N',N)=0$.
\item
If $s(\alpha_{j_1})=i_2$, then $\Ext^1(N,N')=0$, $\Ext^1(N',N)\cong\Bbbk$.
\end{enumerate}
\item[(3)]
Suppose either $i_1<i_2\leq j_1<j_2$ or $i_1<i_2\leq j_2<j_1$.
\begin{enumerate}
\item
If $\Hom(N,N')\cong\Bbbk$, then $\Ext^1(N,N')=0$, $\Ext^1(N',N)\cong\Bbbk$.
\item
If $\Hom(N',N)\cong\Bbbk$, then $\Ext^1(N,N')\cong\Bbbk$, $\Ext^1(N',N)=0$.
\item
If $\{N,N'\}$ is a brick set, then $\Ext^1(N,N')=\Ext^1(N',N)=0$.
\end{enumerate}
\item[(4)]
If $i_1=i_2$ or $j_1=j_2$, then $\Ext^1(M,N)=\Ext^1(N,M)=0$.
\end{enumerate}
\end{lemma}
\begin{proof}
When $j_1\leq i_2-2$, it is easy to see
\[
\dim \Hom(N,N')=\dim \Hom(N',N)=0
\]
and
\[
\langle\mathbf{dim} N,\mathbf{dim} N'\rangle_{Q}=
\langle\mathbf{dim} N',\mathbf{dim} N\rangle_{Q}=0.
\]
Therefore, $\Ext^1(N,N')=\Ext^1(N',N)=0.$
As for (2), (3) and (4), the proofs are similar and we omit them here.
\end{proof}
A direct corollary of Lemma \ref{xxlem8.12} is
\begin{corollary}
\label{xxcor8.13}
Assume $Q$ is of type $\mathbb{A}_n$.
If $\Hom(M\{i_1,j_1\},M\{i_2,j_2\})\cong \Bbbk$,
then \[\Ext^1(M\{i_1,j_1\},M\{i_2,j_2\})=0.\]
\end{corollary}
Any brick set $\phi$ in $\Repr(Q)$ is also a brick set in $D^b(\Repr(Q))$.
In the next lemma we are working with the category $D^b(\Repr(Q))$
and $\phi$ (respectively, $\phi_i$ and $\phi_j$) still denotes a brick
set in $\Repr(Q)$.
\begin{lemma}
\label{xxlem8.14}
Retain the notation above. Then $A(\phi_i, M\{i,j\}[1]\otimes-)$
is similar to a strictly lower triangular matrix.
\end{lemma}
\begin{proof}
By Lemma \ref{xxlem8.6}, $(\{M\{i,j\}\otimes N\mid N\in \phi_i\},\succ)$
is a totally ordered set, which can be listed as
\begin{equation}
\label{E8.14.1}\tag{E8.14.1}
M\{i, j_1\}\succ M\{i,j_2\}\succ \cdots M\{i,j_{|\phi|_i}\}.
\end{equation}
When we compute the adjacency matrix $A(\phi_i, M\{i,j\}[1]\otimes-)$,
we order elements in $\phi_i$ according to \eqref{E8.14.1}.
For any two objects $M\{i_{s_1}, j_{s_1}\},M\{i_{s_2}, j_{s_2}\}$ in
$\phi_i$ with $s_1< s_2$, we have $M\{i, j_{s_1}\}\succ M\{i, j_{s_2}\}$.
An easy analysis shows that either
$\{M\{i_{s_1}, j_{s_1}\}, M\{i, j_{s_2}\}\}$ is a brick set or
$\Hom(M\{i_{s_1}, j_{s_1}\}, M\{i, j_{s_2}\})\cong \Bbbk$.
By Lemma \ref{xxlem8.12}(3),
$$\Ext^1 (M\{i_{s_1}, j_{s_1}\}, M\{i,j\}\otimes M\{i_{s_2}, j_{s_2}\})=0.$$
By Lemma \ref{xxlem8.12}(4), we have
$$\Ext^1 (M\{i_{s_1}, j_{s_1}\}, M\{i,j\}\otimes M\{i_{s_1}, j_{s_1}\})=
\Ext^1 (M\{i_{s_1}, j_{s_1}\}, M\{i, j_{s_1}\})=0.$$
As a consequence, $A(\phi_i,M\{i,j\}[1]\otimes -)$
is a strictly lower triangular matrix.
\end{proof}
\begin{lemma}
\label{xxlem8.15}
Let $N\in \hat\phi_j$, $N'\in \phi_i\cup \phi_{ij}$ and
$N''\in \tilde\phi_j$. then
$$\Ext^1 (N, M\{i,j\}\otimes N')=\Ext^1 (N', M\{i,j\}\otimes N'')=
\Ext^1 (N, M\{i,j\}\otimes N'')=0.$$
\end{lemma}
\begin{proof}
Similar to the proof of Lemma \ref{xxlem8.12}, we only prove the first
equation and leave out the proof of the last two equations.
Write $N=M\{i_1, j_1\}$ and $N'=M\{i_2, j_2\}$. By definition,
$\hat\phi_j$ is nonempty. This implies that $s(\alpha_{i_1-1})=i_1-1$.
First we suppose that $N'\in \phi_i$. If $j_2\neq i_1-1$, then,
by Lemmas \ref{xxlem8.1} and \ref{xxlem8.12}(1,3c),
$\Ext^1 (N, M\{i,j\}\otimes N')=0$. If $j_2=i_1-1$, then
$\Ext^1 (N, M\{i,j\}\otimes N')=0$ by Lemma \ref{xxlem8.12}(2).
Therefore, $\Ext^1 (N, M\{i,j\}\otimes N')=0$ always holds for
$N'\in \phi_i$.
Next we suppose that $N'\in \phi_{ij}$. Then either $\{N,M\{i,j\}\}$
is a brick set or $\Hom(N,M\{i,j\})\cong \Bbbk$. By Lemma
\ref{xxlem8.12}(3), $\Ext^1 (N, M\{i,j\}\otimes N')=0$ since
$M\{i,j\}\otimes N'=M\{i,j\}$.
The assertion follows.
\end{proof}
Now, we prove Theorem \ref{xxthm0.8}(3).
\begin{theorem}
\label{xxthm8.16}
Let $Q$ be a quiver of type $\mathbb{A}_n$ given in
\eqref{E0.7.1} for some $n\geq 2$. Then
$$\fpd(M\{i,j\}[1])=\begin{cases}
\min\{i-1, n-j\} & {\text{if $M\{i,j\}$ is a sink}},\\
1 & {\text{if $M\{i,j\}$ is a source}},\\
1 &{\text{if $M\{i,j\}$ is a flow}}.
\end{cases}$$
\end{theorem}
\begin{proof} Since this is a statement about the derived
category $D^b(\Repr(Q))$, we need to consider all brick
objects in this derived category. However, by the
argument given in the proof of Lemma\ref{xxlem4.11} (2), we
only need to consider brick sets of the form
$$\phi=\{N_1, \cdots, N_m\mid N_s\in \Repr(Q)\}$$
which consists of objects in the abelian category $\Repr(Q)$.
The rest of the proof is somewhat similar to the proof of
Theorem \ref{xxthm8.11}.
If there exists an object $N_1=M\{i_0, j_0\}\in \phi$ satisfying
$M\{i,j\}\otimes N_1\cong N_1$, by Lemma \ref{xxlem8.2}, there
exist at most one object $N_2=M\{i_1,j_1\}\in \phi$ satisfying $j_1=i_{0} - 1$
and at most one object $N_3=M\{i_2,j_2\}\in \phi$ satisfying $i_2=j_0+1$.
Then, by Lemmas \ref{xxlem8.1} and \ref{xxlem8.12},
in the first column and the first row of $A(\phi, M\{i, j\}[1]\otimes-)$,
all entries are zero except for $a_{12}, a_{21}, a_{13}, a_{31}$, and
$a_{12} a_{21}=a_{13} a_{31}=0$.
No matter which case is, we always have
$$\rho(A(\phi,M\{i,j\}[1]\otimes -))
=\rho(A(\phi\setminus \{N_1\},M\{i,j\}[1]\otimes -)).$$
Also, if there is an object $N\in \phi$ satisfying
$M\{i,j\}\otimes N=0$, we also have
$$\rho(A(\phi,M\{i,j\}[1]\otimes -))
=\rho(A(\phi\setminus \{N\},M\{i,j\}[1]\otimes -)).$$
Similar to the proof of Theorem \ref{xxthm8.11}, it suffices
to consider the brick set $\phi$ satisfying the following conditions:
\begin{enumerate}
\item[(*)] $\phi=\phi_i\cup \phi_j\cup \phi_{ij}$,
\item[(**)] for every $N\in \phi$, $M\{i,j\}\otimes N\not\cong N.$
\end{enumerate}
By Lemma \ref{xxlem8.14}, if we re-arrange objects in
$\phi$ as $\hat\phi_j$, $\hat\phi_i$, $\phi_{ij}$, $\tilde\phi_i$
and $\tilde\phi_j$, then $A(\phi, M\{i, j\}[1]\otimes-)$ is
a block lower triangular matrix.
By Lemma \ref{xxlem8.15},
$$\rho(\phi, M\{i,j\}[1]\otimes-)=\rho(\phi_{ij}, M\{i,j\}[1]\otimes-).$$
Therefore, for the rest we consider the brick set $\phi$
satisfying $\phi_{ij}=\phi$.
We divide the rest of the proof into 3 small cases.
Case 1: $M\{i,j\}$ is a source. In this case, for any
$N\in \phi$, $\Hom(N, M\{i,j\})\cong \Bbbk$. Then by Lemma
\ref{xxlem8.12}(3), $\Ext^1 (N, M\{i,j\})=0$.
As a consequence, the adjacency matrix
$A(\phi,M\{i,j\}[1]\otimes -)$ is a zero matrix.
Therefore, in this case, $\fpd(M\{i,j\}[1])=0$.
Case 2: $M\{i,j\}$ is a flow, without loss of generality, assume that
$\alpha_{i-1}=\alpha_j=\longleftarrow$.
For any $N=M\{i_1,j_1\}\in \phi$,
if $i_1=i$, by Lemma \ref{xxlem8.12}(4),
$\Ext^1 (N,M\{i,j\})=0$.
If $i_1<i$, either $\Hom(N, M\{i,j\})\cong \Bbbk$ or
$\{N, M\{i,j\}\}$ is a brick set, then by Lemma \ref{xxlem8.12}(3),
$\Ext^1 (N,M\{i,j\})=0.$
As a consequence, the adjacency matrix
$A(\phi,M\{i,j\}[1]\otimes -)$ is a zero matrix.
Therefore, in this case, $\fpd(M\{i,j\}[1])=0$.
Case 3: $M\{i,j\}$ is a sink.
In this case, for any $N=M\{i_1,j_1\}\in \phi$,
if $i_1=i$, by Lemma \ref{xxlem8.12}(4),
$\Ext^1 (N,M\{i,j\})=0$.
If $j_1=j$, by Lemma \ref{xxlem8.12}(4),
$\Ext^1 (N,M\{i,j\})=0$.
Therefore, since $M\{i,j\}\otimes N=M\{i,j\}$,
we can assume that $i_1<i$ and $j_1>j$.
Now, it's easy to see $\Ext^1 (N,M\{i,j\})\cong \Bbbk$
by Lemma \ref{xxlem8.12}(3).
As a consequence, all entries in the adjacency matrix
$A(\phi,M\{i,j\}[1]\otimes -)$ are 1 and
$\rho(A(\phi,M\{i,j\}[1]\otimes -))=|\phi_{ij}|\leq \min\{i-1,n-j\}$.
On the other hand, by Lemma \ref{xxlem8.6},
$(\{M\{k,i\}\mid 1\leq k\leq i-1\},\succ)$ and
$(\{M\{j,m\}\mid j+1\leq m\leq n\}, \succ)$
are two totally ordered sets. We list elements
in these two sets as
\begin{equation*}
{\text{
$M\{k_1,i\}\succ \cdots\succ M\{k_{i-1},i\}$ and
$M\{j,m_1\}\succ \cdots\succ M\{j,m_{n-j}\}$}}
\end{equation*}
where $\{k_l\}_{l=1}^{i-1}$ and $\{m_l\}_{l=1}^{n-j}$
are distinct integers from $1$ to $i-1$ and
from $j+1$ to $n$ respectively.
Let $d=\min\{i-1,n-j\}$, then we have a set of $d$ elements
$$\phi=\{M\{k_1,m_{n-j}\}, M\{k_2,m_{n-j-1}\}, \cdots,
M\{k_d, m_{n-j+1-d}\}\}$$ which is a brick set.
Using this brick set, one see every entry in the
matrix $A(\phi, M\{i, j\}[1]\otimes-)$
is 1 by Lemma \ref{xxlem8.12}, consequently,
$\rho(A(\phi, M\{i, j\}[1]\otimes-))=d$.
Hence, in this case, $\fpd(M\{i,j\}[1])=\min\{i-1,n-j\}$.
\end{proof}
\begin{proof}[Proof of Theorem \ref{xxthm0.8}]:
(1) This follows from Lemma \ref{xxlem4.11}(1).
(2) This follows from Lemma \ref{xxlem4.11}(2)
and Theorem \ref{xxthm8.11}.
(3) This follows from Theorem \ref{xxthm8.16}.
\end{proof}
\subsection*{Acknowledgments}
The authors thank the referee for his/her very careful reading and
valuable comments and thank Professors Jianmin Chen and
Xiao-Wu Chen for many useful conversations on the subject.
J.J. Zhang was partially supported by the US National Science
Foundation (Grant Nos. DMS-1700825 and DMS-2001015). J.-H. Zhou
was partially supported by Fudan University Exchange Program
Scholarship for Doctoral Students (Grant No. 2018024).
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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\section{Introduction}
\label{sec:INTRO}
Heavy flavour physics is a corner of the Standard Model where chances are higher to uncover
signals of new physics~\cite{REVSM,UT}. However, to extract from experiments useful phenomenological
information, it is mandatory to have an accurate knowledge of the relevant hadronic matrix elements of the
effective weak Hamiltonian. For low mass states (up to around the charm mass) lattice QCD (LQCD) represents the ideal
framework where such calculations can be performed with well under control systematic errors~\cite{REVLAT}.
Due to present day computer limitations, it is not possible, however, to work directly with the heaviest quarks (as the
$b$-quark) propagating on the simulated lattice. Various strategies, more or less inspired to the heavy quark effective
theory (HQET)~\cite{HQET,HQET1}, have been devised to circumvent this intrinsic difficulty, which go from
non-perturbative matching of HQET onto QCD~\cite{SOMMER} to finite size scaling methods with relativistic heavy
quark(s)~\cite{FSSM}. Relativistic heavy-quark actions designed (highly tuned) to have reduced cutoff effects~\cite{FERMILAB}
have also been employed for this purpose. Encouraging results have been obtained by several groups~\cite{GAMIZLAT08}
though different is the level at which the various relevant systematic effects are controlled.
In this work we wish to present a novel approach to $B$-physics in which the $b$-mass point is attained by
interpolating from the charm region to the asymptotic infinite mass regime suitable ratios of heavy-light
($h\ell$) meson masses and decay constants, computed at a number of pairs of quark mass values lying
slightly below and somewhat above the charm mass. The key feature of the approach is the use of ratios of
physical quantities which by construction have a well defined and exactly known infinite $h$-quark mass
limit. Injecting knowledge of meson masses and decay constants at the charm region, their $h$-quark mass
evolution can be computed by a chain of successive steps
up to values as large as about twice the charm mass. The $b$-physics region is finally reached through
an interpolation from the simulated points to the exactly known infinite $h$-quark mass value.
A first test of the viability of the method is presented here. It has been carried out by exploiting the
unquenched $N_f=2$ data recently produced by the ETM Collaboration~\cite{ETMCD,VCS} which makes
use of maximally twisted Wilson fermions~\cite{TM}. The results obtained in this feasibility study are
very encouraging and compare nicely with the unquenched determinations today available in the
literature~\cite{LITERUQ} as well as with PDG numbers~\cite{REVSM}. We get
\beqn
&&\hat{\mu}^{\overline{MS},N_f=2}_b(\hat{\mu}^{\overline{MS},N_f=2}_b)=4.63(27)~{\mbox{GeV}}\, ,
\label{UQRES1}\\
&&f_B=194(16)~{\mbox{MeV}}\, ,\label{UQRES2}\\
&&f_{B_s}=235(12)~{\mbox{MeV}}\, ,\label{UQRES3}
\eeqn
where, as indicated explicitly in eq.~(\ref{UQRES1}), the $b$-mass has been run in a world with two
(active) flavours. The results in eqs.~(\ref{UQRES1}) to~(\ref{UQRES3}) represent a ``first principle''
determinations of $B$-physics parameters with errors whose magnitude
can be systematically reduced. The quoted uncertainty will be discussed in sects. 2 and 3
for eqs.~(\ref{UQRES1}) and (\ref{UQRES2})-(\ref{UQRES3}), respectively.
A few observations are in order here. First of all we would like to remark that the results above are
extracted from unquenched LQCD data where $u$ and $d$ light fermions are dynamical, while
heavier quarks are introduced only as valence quarks. This scheme is what goes under the name of ``partially
quenched'' setting (see ref.~\cite{FR2} for a discussion within the twisted mass regularization of QCD).
Systematic errors due to partial quenching are not included in the figures quoted in eqs.~(\ref{UQRES1}) to~(\ref{UQRES3}).
The second observation is that no complicated renormalization steps are required for the method to work,
because, as noted above, the necessary inputs are (ratios of) physical quantities ($h\ell$-pseudoscalar
meson masses or decay constants) evaluated at $h$-quark masses around the charm region which are extracted
from the existing (large volume) lattice configurations produced for the study of pion physics.
The central value of $\hat{\mu}^{\overline{MS},N_f=2}_b(\hat{\mu}^{\overline{MS},N_f=2}_b)$ in
eq.~(\ref{UQRES1}) may look somewhat higher (though still compatible within statistical errors) than the available
phenomenological estimates of the $\overline{MS}$ $b$-quark mass at its own scale, which lie in the range
4.2-4.3~GeV. However, it is not unlikely that, when the quenching of quarks heavier than $u$ and $d$ will be
removed with the inclusion of dynamical $s$ and, possibly, $c$ quarks, $m_b$ will receive corrections which one
can argue will tend to make the quantity $\hat{\mu}^{\overline{MS},N_f=4}_b(\hat{\mu}^{\overline{MS},N_f=4}_b)$
somewhat smaller than the number given in eq.~(\ref{UQRES1})~\footnote{Indeed, if we evolve the intermediate
result $\hat{\mu}_b^{\overline{MS},N_f=2}(2~{\rm GeV}) = 5.35(32)$~GeV from 2~GeV to the $b$-quark
mass scale by using anomalous dimension and $\beta$-function of the $N_f=4$ (rather than $N_f=2$) theory, the
value of the $b$-quark mass gets lowered by about 3\% compared to the value we give in~(\ref{UQRES1}).}.
The results~(\ref{UQRES2}) and~(\ref{UQRES3}), instead, are only affected at a level
of less than 1\% by our present uncertainties in the $b$-quark mass, because the $hu/d$-
and $hs$-meson decay constants happen to have a rather mild dependence on the $h$-quark mass.
The content of this paper is as follows. In sect.~\ref{sec:METHB} we discuss the theoretical basis
underlying the strategy that we propose to extract the value of the $b$-quark mass from present day
LQCD data and we provide a rather accurate determination of it with controlled errors. In sect.~\ref{sec:METHF}
we extend the method to the determination of the $f_B$ and $f_{B_s}$ decay constants. We conclude
in sect.~\ref{sec:CONC} with a few words on how to improve the quality of the numbers~(\ref{UQRES1})
to~(\ref{UQRES3}), and how to extend the present method to other $h\ell$-physics quantities the large
$h$-quark mass behaviour of which is known.
We defer to an Appendix some technical details concerning the way chiral and
continuum extrapolations of $h\ell$ meson masses and decay constants are
performed.
\section{$b$-quark mass}
\label{sec:METHB}
In this section we present a simple strategy aimed at determining the value of the $b$-quark mass through
a smooth interpolation of suitable ratios of $h\ell$ pseudoscalar lattice meson masses from the well accessible
charm region to the asymptotic (infinite mass) point where these quantities have an exactly known value.
Inspired by HQET results we consider the lattice ratios ($a=$ lattice spacing)
\beqn
&&y^L(x^{(n)},\lambda;\hat\mu_{\ell},a)=\nn\\
&&=\frac{M_{h\ell}^L(\hat\mu_h^{(n)};\hat\mu_\ell,a)}
{M_{h\ell}^L(\hat\mu_h^{(n-1)};\hat\mu_\ell,a)} \cdot
\frac{\rho(\log \hat\mu^{(n-1)}_h) \hat\mu^{(n-1)}_h}{\rho(\log \hat\mu^{(n)}_h)\hat\mu^{(n)}_h}
\, ,\quad n=2,\cdots,N \, .\label{RATM}\eeqn
In eq.~(\ref{RATM}) and in the following by a ``hat'' we denote quark masses renormalized at 2~GeV in the $\overline{MS}$
scheme. By $\hat\mu_\ell$ we indicate the renormalized light quark mass, while $\hat\mu_h^{(n)}>\hat\mu_h^{(n-1)}$
are pairs of (renormalized) ``heavy'' valence quark masses lying around (from below to somewhat above) the charm mass.
The function $\rho(\log\hat\mu_h)$ is the factor that ``transforms'' the renormalized $\overline{MS}$ quark mass
at 2~GeV scale into the so-called ``quark pole mass''. In formulae
\beq
\rho(\log\hat\mu_h) \hat\mu_h=\mu_h^{\rm{pole}}\, .
\label{PMA}
\eeq
In continuum perturbation theory (PT) $\rho$ is known up to N$^3$LL (i.e.\ up to next-to-next-to-next-leading-log)
order terms included~\cite{CR,POLEtoMSbarMASS}. Finally $N$ is the number of $h$-quark masses at which
the values of the $h\ell$ pseudoscalar lattice meson masses, $M_{h\ell}^L$, are supposed to have been measured.
The choice of the form of eq.~(\ref{RATM}) is suggested by the HQET (continuum) asymptotic equation~\cite{HQET,HQET1}
\beq
\lim_{\mu_h^{\rm{pole}}\to \infty} \frac{M_{h\ell}}{\mu_h^{\rm{pole}}}={\mbox{constant}}\neq 0\, .
\label{PM}
\eeq
Although the above constant is known to be 1, its value is not really needed here.
In order to simplify our subsequent analysis we keep fixed the ratio between two successive values of the
heavy quark masses in eq.~(\ref{RATM}). Calling it $\lambda>1$, we set
\beq
\lambda=\frac{\hat\mu^{(n)}_h}{\hat\mu^{(n-1)}_h}=\frac{\mu^{(n)}_h}{\mu^{(n-1)}_h}=
\frac{x^{(n-1)}}{x^{(n)}}\, , \qquad x^{(n)}=\frac{1}{\hat\mu^{(n)}_h}\, .\label{DEFS}
\eeq
Notice that in $\hat\mu_h^{(n)}/\hat\mu_h^{(n-1)}$ the mass renormalization constant factor,
$Z_P^{-1}$, cancels out~\footnote{We recall that in maximally twisted LQCD the twisted mass
renormalizes according to $\hat\mu=Z_P^{-1}\mu$. If standard Wilson fermions were to be employed,
the quantity $\hat{m}_h = Z_{S^0}^{-1}(m_{0h}-m_{\rm cr}$),
should be used in place of $\hat\mu_h$ in eq.~(\ref{RATM}).}.
Ratios of the kind defined in~(\ref{RATM}) are introduced with the idea that they might have a smoother
chiral ($\mu_\ell\to\mu_{u/d}$, with $\mu_{u/d}$ the light quark mass that yields the
physical value of the pion mass) and continuum limit than each of the individual factors. Setting
\beqn
&&y(x^{(n)},\lambda; \hat\mu_{u/d}) \equiv
\lim_{\hat\mu_\ell \to \hat\mu_{u/d}}\,\lim_{a\to 0}\, y^L(x^{(n)},\lambda;\hat\mu_{\ell},a) =\nn\\
&&= \lambda^{-1} \frac{M_{h{u/d}}(1/x^{(n)})}{M_{h{u/d}}(1/\lambda x^{(n)})}
\frac{\rho(\log\lambda x^{(n)})}{\rho(\log x^{(n)})} \, ,
\label{RATLIM}
\eeqn
where we have introduced the (continuum limit) shorthand notation
\[
M_{h{u/d}}(1/x)\equiv M_{hu/d}(1/x,\hat\mu_{u/d})\, ,
\]
we observe that (for all $\lambda>1$) eqs.~(\ref{PMA}) and~(\ref{PM}) imply the following exact property
\beq
\lim_{x\to 0} y(x,\lambda;\hat\mu_{u/d})=1\, . \label{RATLEY}
\eeq
{}From lattice data the function $y(x,\lambda;\hat\mu_{u/d})$ can be determined at certain discrete values of $x$ ($x^{(n)}$,
$n=2,\cdots,N$). In order to extend our knowledge outside these particular points, while at the same time fully exploiting
the strong constraining power provided by eq.~(\ref{RATLEY}), we imagine proceeding in the following way. Suppose
the perturbative expansion of $\rho$ has been computed and resummed up to N$^P$LL order.
Then we can define a tower of $y$-ratios, $y|_{p}$, $p=0,1,\dots,P+1$, such that
\beq
y(x,\lambda;\hat\mu_{u/d})\Big{|}_{p}-1
~\stackrel{x \to 0}{\sim}~ {\rm O}\Big{(}\frac{1}{(\log x)^{p+1}}\Big{)}\, , \label{LIM}
\eeq
provided $\rho$ in eq.~(\ref{RATM}) is correspondingly taken at tree-level in the case of $p=0$, or to N$^{p-1}$LL
order for $p>0$. Then for sufficiently small values of $x$ we parameterize $y|_{p}$ in the form
\beq
y(x,\lambda;\hat\mu_{u/d})\Big{|}_{p}=1+\eta_1(\log x,\lambda;\hat\mu_{u/d})x+
\eta_2(\log x,\lambda;\hat\mu_{u/d}) x^2\, ,\label{ANLYTICY}
\eeq
where the coefficients $\eta_j(\log x,\lambda;\hat\mu_{u/d})$, $j=1,2$, are $p$-dependent
(though to lighten the notation we do not display explicitly this dependence in the following),
smooth functions of $\log x$ which tend to zero as $\lambda \to 1$ and to some fixed constant
as $x\to 0$~\cite{HQET,HQET1}.
With the ansatz~(\ref{ANLYTICY}) and at any order where PT results for $\rho$ are available,
it is not difficult to determine the $\eta_j$ coefficients from lattice data, assuming that their
$\log x$-dependence can be ignored in the range of masses where the above formulae are used.
It is important to remark that the ansatz~(\ref{ANLYTICY}) is based on the same kind of
assumptions under which HQET is usually employed in the study of heavy quark physics. A posteriori,
we check that the best fit values taken by the coefficient functions $\eta_j$ come out of a
reasonable order of magnitude. Indeed we find that $\eta_1 r_0$ and $\eta_2 r_0^2$ are O(1)
quantities.
\subsection{Implementing the method}
\label{sec:LLO}
Let us start considering for concreteness the case where $\rho$ is taken up to LL order and
subsequently compare the results we get in this way with what one would obtain taking
$\rho$ at NLL-order or at tree-level (at tree-level $\rho=1$).
\begin{table}[!ht]
\begin{center}
\begin{tabular}{cccccccccc}
\hline \hline
$\beta$ && $a^{-4}(L^3 \times T)$ && $a\mu_{\ell}~=~a\mu_{sea}$ && $a\mu_{s}$ && $a\mu_{h}$ \\
\hline
3.80 && $24^3 \times 48$&& 0.0060, 0.0080 && 0.0200, 0.0250 && 0.2700, 0.3100 \\
&& && 0.0110, 0.0165 && 0.0300, 0.0360 && 0.3550, 0.4350 \\
&& && && && \hspace*{-1.4cm}0.5200 \\
\hline
3.90 && $24^3 \times 48$&& 0.0040, 0.0064 && 0.0220, 0.0270 && 0.2500, 0.3200 \\
&& && 0.0085, 0.0100 && \hspace*{-1.4cm}0.0320 && 0.3900, 0.4600 \\
&& && \hspace*{-1.4cm}0.0150 && && \\
3.90 && $32^3 \times 64$&& 0.0030, 0.0040 && 0.0220, 0.0270 && 0.2500, 0.3200 \\
\hline
4.05 && $32^3 \times 64$&& 0.0030, 0.0060 && 0.0150, 0.0180 && 0.2000, 0.2300 \\
&& && 0.0080, 0.0120 && 0.0220, 0.0260 && 0.2600, 0.3150 \\
\hline \hline
\end{tabular}
\end{center}
\caption{\it Lattice size, light ($=$~sea), strange- and charm-like bare quark mass values
used in the analysis presented in this work. The number of correlator measurements was 240
in all cases, but for $\beta=4.05$, where it was 130. The $r_0/a$-values $4.46(3)$, $5.22(2)$ and
$6.61(3)$ are employed at $\beta=3.8$, $\beta=3.9$ and $\beta=4.05$, respectively~\cite{DFHUW_Latt07}.
The overall scale and the light quark mass are set by the experimental values of $f_\pi$ and $m_\pi$
via chiral fits of the pseudoscalar meson mass and decay constant data in the light quark
sector~\cite{Latt08,DFHUW_Latt07}. Here we use $\hat\mu_{u/d} = 3.6(3)$~MeV and $r_0=0.433(14)$~fm.
}
\label{tab:simpar}
\end{table}
In order to determine the coefficient functions $\eta_j$ we proceed as follows. Let us make for the smallest
$\hat\mu_h$ value the choice $\hat\mu_h^{(1)}=1.230$~GeV (we recall, we are referring to the $\overline{MS}$
scheme at the scale of 2~GeV). Fixing $\lambda =1.278$ (see below) and, in this exploratory study, $N=4$,
we shall successively consider the $h$-quark masses
\beqn
&&\hat\mu_h^{(1)}= 1.230~{\mbox{GeV}}\, , \nn\\
&&\hat\mu_h^{(2)}= \lambda \hat\mu_h^{(1)} = 1.572~{\mbox{GeV}}\, , \nn\\
&&\hat\mu_h^{(3)}= \lambda^2 \hat\mu_h^{(1)} = 2.009~{\mbox{GeV}}\, ,\nn\\
&&\hat\mu_h^{(4)}= \lambda^3 \hat\mu_h^{(1)} = 2.568~{\mbox{GeV}}\, .
\label{MUV}\eeqn
Actually at each lattice spacing we will be dealing with the dimensionless quantities
$\hat\mu_h^{(j)}r_0$, $j=1,2,3,4$, of which the numbers quoted in eq.~(\ref{MUV})
represent the central values in physical units. Uncertainties on $r_0/a$ and $Z_P^{-1}$ (present
at the level of about 3\%) will be taken into account in the final error analysis.
\begin{figure}[!hbt]
\centerline{\includegraphics[scale=0.50,angle=-90]{fig_RATIO_M3ov2.ps}}
\caption{\it Lattice spacing and $\hat\mu_\ell$ dependence of the ratio
$M_{h\ell}^L(\hat\mu_h^{(3)};\hat\mu_\ell,a)/M_{h\ell}^L(\hat\mu_h^{(2)};\hat\mu_\ell,a)$.
The black square with its error is the combined continuum and chirally ($\hat\mu_\ell \to \hat{\mu}_{u/d}$)
extrapolated value. Here and in all the following figures uncertainties possibly affecting the value of the variable
in the horizontal axis are propagated to the quantity plotted on the vertical axis.}
\label{fig:Mrat3to2}
\end{figure}
{}From the set of the ETMC simulation data~\cite{ETMCD} with parameters detailed in Table~\ref{tab:simpar},
we extract the values of the $h\ell$ pseudoscalar meson masses that correspond to the $\hat\mu_h$ values
listed in~(\ref{MUV}). With these masses we construct the lattice ratios~(\ref{RATM}) on which a combined
continuum and chiral fit is performed. As we hoped, ratios appear to have a mild dependence on the light quark
mass $\hat{\mu}_\ell$ and small cutoff effects, as seen for instance in fig.~\ref{fig:Mrat3to2}. This makes our
continuum and chiral fit straightforward and numerically robust.
\begin{figure}[!hbt]
\centerline{\includegraphics[scale=1.0]{fig_2_NEW.ps}}
\caption{\it Continuum data for $y|_0$ (blue dots), $y|_1$ (red squares), $y|_2$ (green triangles).
The corresponding best fit curves are drawn with $\lambda=1.273$ (lower curve, in blue) and $\lambda=1.278$
(middle curve, in red and upper curve, in green). In all cases $\mu_\ell \to \mu_{u/d}$.}
\label{fig:fig1}
\end{figure}
The red squares in fig.~\ref{fig:fig1} represent the numbers $y^{(n)}_1=y(x^{(n)},1.278;\hat\mu_{u/d})|_1$,
$n=2,3,4$, computed at the $x^{(n)}=1/\hat\mu_h^{(n)}$ values in the list~(\ref{MUV}) with the ratios
${\rho(\log \hat\mu_h^{(n-1)})}/{\rho(\log \hat\mu_h^{(n)})}$ computed at LL order (i.e.\ $p=1$ in
eq.~(\ref{LIM})). The best fit through the red squares and the point at $x=0$ determines the values
of the $\eta_j$ coefficients ($j=1,2$) and yields the middle (red) curve in the figure.
We note that a second order polynomial in $x$ is necessary to get a good fit to the data
(a straight line forced to pass through the point $y=1$ at $x=0$ would have a very large $\chi^2$).
The quadratic fit gives for the quantities $r_0\eta_{1}$ and $r_0^2\eta_{2}$ numbers of order unity,
in agreement with the standard assumptions underlying HQET.
At this stage, having in our hands the quantities $y^{(n)}_1=y(x^{(n)},1.278;\hat\mu_{u/d})|_1$ for any $n$
(actually for any $x$), the iterative formula
\beq
y_1^{(2)} y_1^{(3)}\cdots y_1^{(K+1)}=\lambda^{-K}
\frac{M_{hu/d}(\hat\mu_h^{(K+1)})}{M_{hu/d}(\hat\mu_h^{(1)})} \cdot
\Big{[}\frac{\rho(\log \hat\mu_h^{(1)})}{\rho(\log \hat\mu_h^{(K+1)})}\Big{]}_{p=1}\, ,
\label{ITER}
\eeq
should be looked at as a relation between the mass of the $hu/d$-meson, $M_{hu/d}(\hat\mu_h^{(K+1)})$,
and the corresponding heavy quark mass $\hat\mu_h^{(K+1)}$, which is fully explicit if the initial,
triggering value $M_{hu/d}(\hat\mu_h^{(1)})$ is assigned. The latter can be accurately measured, as
$\hat\mu_h^{(1)}$ lies in the well accessible charm quark mass region. We show in fig.~\ref{fig:fitm}
the quality of the continuum and chiral extrapolation of the triggering mass lattice data. Once this
number is known, determination of the $b$-quark mass is tantamount to find the value of $K$ at which
$M_{hu/d}(\hat\mu_h^{(K+1)})$ takes the experimental $B$-meson mass value, $M_B$. Calling
$K_b$ the solution of the resulting eq.~(\ref{ITER}) (as shown in fig.~\ref{fig:fig2}, we find $K_b=6$),
one gets for $\hat\mu_b$ the simple formula (valid for renormalized as well as bare masses)
\beq
\hat\mu_b=\lambda^{K_b}\hat\mu_h^{(1)}\, .
\label{MB}
\eeq
\begin{figure}[!hbt]
\centerline{\includegraphics[scale=0.50,angle=-90]{fig_M1.ps}}
\caption{\it The $M_{h\ell}^L(\hat\mu_h^{(1)};\hat\mu_\ell,a)$ lattice data extracted from the
simulations detailed in Table~\ref{tab:simpar}. The black square with its error is the continuum and
chirally extrapolated value giving $M_{hu/d}(\hat\mu_h^{(1)})=1.89(10)$~GeV.}
\label{fig:fitm}
\end{figure}
A few related remarks are important here. 1) It is not really necessary to have the lattice
$h\ell$ pseudoscalar meson masses computed at values of $\hat\mu_h$ matched exactly as indicated
in eq.~(\ref{MUV}). A $\mu_h$ interpolation between nearby $M_{h\ell}^L$ masses can be carried out if
necessary. This is what we have actually done in the numerical study we present in this
paper. 2) It is not a priori guaranteed that eq.~(\ref{ITER}) can be solved for an integer value of the
exponent $K$. This is not a problem, however, as one can always retune the parameter $\lambda$
(and at the same time readjust the values in the sequence~(\ref{MUV})), so as to end up with an
integer for $K_b$ (this is the reason why the peculiar value $\lambda=1.278$ was chosen).
Alternatively one could adjust the starting value of the heavy quark mass or both.
3) A detailed discussion of the numerical analysis will be given in a forthcoming
publication~\cite{FUT}. Here we only mention that
a simple SU($N_f=2$) chiral perturbation theory NLO-formula was used to model the $\hat\mu_\ell$
dependence of the triggering $h\ell$ meson mass and $y$-ratios, while O($a^2$) effects have been
parameterized (at each $\hat\mu_h$) by $\hat\mu_\ell$ independent terms. A few further details
on this point are given in Appendix~A.
\begin{figure}[!hbt]
\centerline{\includegraphics[scale=1.0]{fig_findK.ps}}
\caption{\it The numerical solution of eq.~(\ref{ITER}) giving $K_b= 6$.}
\label{fig:fig2}
\end{figure}
Following the procedure outlined above, one finds the result given in eq.~(\ref{UQRES1}), or
equivalently the renormalization group invariant (RGI) value
\beq
\hat\mu_b^{RGI,N_f=2} = 7.6(5)~{\mbox{GeV}}\, ,
\label{MUBARE}
\eeq
where in the running only two flavours are assumed to be active and the conventions
of ref.~\cite{GL} for the RGI quark mass have been used.
\subsection{Discussion and error budget}
\label{sec:TLNLL}
It is important to check the degree of reliability of the key smoothness assumption we have been implicitly
making on the function $y(x)$ and test the sensitivity of the procedure and its result~(\ref{MB}) to the
order of PT at which the expansion of $\rho$ is truncated. To this end we have repeated the entire analysis
above using for $\rho$ both a lower (tree-level) and a higher (NLL) order perturbative approximation
in place of the previously employed LL order truncation. We recall that in the large $h$-quark mass
limit $y|_{0}=y(x,\lambda;\hat\mu_{u/d})|_{0}$ and $y|_{2}=y(x,\lambda;\hat\mu_{u/d})|_{2}$
approach 1 (see eq.~(\ref{LIM})) with corrections O($1/\log x$) and O($1/(\log x)^3$), respectively.
One finds a (very) little shift in the value of $\lambda$ necessary for the solution of the corresponding iterative
equation~(\ref{ITER}) to be an integer (from 1.278 to 1.273) if we go from $y|_1$ to $y|_0$. The shift is
instead totally negligible within our statistical accuracy if we move from $y|_1$ to $y|_2$.
The fits to $y|_0$ and $y|_2$ data are shown in fig.~\ref{fig:fig1} (lower blue and upper green curve) together
with the fit to $y|_1$ data (middle red curve). One clearly sees that the $y|_p$ curves tend to become flatter and
flatter as we move from $p=0$ to $p=2$. As for the values of the $b$-quark mass, instead, the number extracted
from $y|_0$-ratios is only about 2\% smaller than the one obtained using the $y|_1$-ratios. The difference between
the latter and the one extracted from $y|_2$-ratios is smaller than 1\%.
The stability of the value of the $b$-quark mass with varying $p$ should not come as a surprise.
It is enough to notice that, if the $y|_p$-ratios were exactly known, for a generic value of
$p$ one would get (recall eq.~(\ref{ITER}))
\beqn
&&\Big{[}\frac{\rho(\log \hat\mu_h^{(K+1)})}{\rho(\log \hat\mu_h^{(1)})}\Big{]}_{p} \cdot
y_p^{(2)} y_p^{(3)}\cdots y_p^{(K+1)}=\nn\\
&&=y_0^{(2)} y_0^{(3)}\cdots y_0^{(K+1)}=\lambda^{-K}
\frac{M_{hu/d}(\hat\mu_h^{(K+1)})}{M_{hu/d}(\hat\mu_h^{(1)})} \, ,
\label{ITER1}
\eeqn
as all the intermediate $\rho$ factors (except the first and the last) cancel out in the l.h.s.\ leaving
behind simply the product of the $y|_0$-ratios.
The small $p$ dependence we have found in the value of $\lambda$
(hence in $\hat\mu_b$) is due to the slightly different level of accuracy
by which the $y|_p$-ratios (which instead significantly depend on $p$)
can be described by a polynomial in $x$ with the lowest
order coefficient set to unity. In this respect, increasing $p$
is expected to improve the quality of the ansatz~(\ref{ANLYTICY}) and reduce
the systematic error associated to it. This is so until $p$ becomes so ``large''
that the accuracy of the $\rho$ estimate gets spoiled by
the renormalon ambiguity in its perturbative expansion~\cite{MarSac96}.
To account for the truncation to LL of the perturbative expansion for $\rho$ we have
conservatively decided to attribute to the $b$-quark mass value a systematic error of 1\%,
which is added in quadrature to the other errors discussed below, leading to the total error quoted
in eq.~(\ref{UQRES1}) (and~(\ref{MUBARE})).
\subsubsection{Error budget}
\label{sec:EB}
The total error we attribute to the $b$-quark mass results~(\ref{UQRES1}) and~(\ref{MUBARE})
takes into account a number of statistical and systematic effects which we now briefly illustrate.
The relative error on the product of the continuum $y$-ratios in the l.h.s.\ of eq.~(\ref{ITER}) is only about 1\%,
whereas the pseudoscalar meson mass in the charm region ($M_{hu/d}(\hat\mu_h^{(1)})$ in the r.h.s.\ of
eq.~(\ref{ITER})) contributes a relative error of about 5\%. These errors are the result of our statistically
limited knowledge of $h \ell$-meson correlators, $r_0/a$ and $Z_P$~\footnote{At the moment the statistical
error on $Z_P$ quoted by ETMC is about $3\%$ at the simulated lattice spacings.} as well as of a number of further
systematic errors. Among the latter we mention those coming from the fit ansatz underlying the combined
continuum and chiral ($\hat\mu_\ell \to \hat\mu_{u/d}$) extrapolation, the error due to the $x$-interpolation
to the $b$-mass point, as well as the (tiny) error inherent the numerical solution of eq.~(\ref{ITER})
(giving $K_b=6$ and $\lambda=1.278$). As we discussed above, the effect on $\hat\mu_b$ due to the truncation
of the $\rho$ perturbative series to order $p$ is very small, not larger than 1\%.
Another .5-1\% systematic error comes from the possible (neglected)
logarithmic dependence of the $\eta_j$, $j=1,2$ coefficients.
The relative uncertainty on $\eta_j$ associated with these effects can be estimated to be
O($\alpha_s(1/x))\sim 10-15$\%, a number which is never larger
than the statistical errors on their best fit values.
Finally cross-correlations between the different quantities (stemming from common
ensembles of gauge configurations) are as usual taken into account by a bootstrap error
analysis. Further technical aspects of the error analysis are deferred to ref.~\cite{FUT}.
The information provided in figs.~\ref{fig:Mrat3to2}, \ref{fig:fig1} and~\ref{fig:fitm} about the $a^2$,
$\hat\mu_\ell$ and $x$ dependence of the intermediate quantities entering our analysis as well
as about the precision in solving eq.~(\ref{ITER}) (see fig.~\ref{fig:fig2}) shows that the global
systematic uncertainty is well within (or below) our present statistical errors.
We conclude by observing that, as expected, our results for the $b$-quark mass
(and $f_B$ or $f_{B_s}$ discussed in the next section) do not significantly depend on the
value of the intermediate quantity $r_0$ which is only employed to ease continuum
extrapolations, while the physical scale is ultimately set by $f_\pi$.
\subsection{$b$ and $c$ quark masses}
\label{sec:BCQM}
Although not necessary, the phenomenological value of the $D$-meson mass could have been
used as a triggering mass. In this case $\mu_h^{(1)}$ would have to be identified with $\mu_c$.
We note in this context that, since we get (see the black square in fig.~\ref{fig:fitm}
$M_{hu/d}(\hat\mu_h^{(1)})=1.89(10)$~GeV, i.e.\ a number that practically coincides with
the experimental value of $M_D$ ($M_{D^0}=1.865$~GeV~\cite{REVSM}),
our method immediately yields for the charm mass the estimate $\hat\mu_c=1.23(06)$~GeV.
For the phenomenologically important $b$- over $c$-mass ratio we then get
\beq
\frac{\hat \mu_b}{\hat \mu_c}=4.31(24)\, ,
\label{BOCM}
\eeq
in very good agreement with other estimates~\footnote{It is interesting to compare our unquenched result for the ratio of RGI
masses $m_c^{RGI,N_f=2}/m_b^{RGI,N_f=2}=0.232(13)$ (the inverse of eq.~(\ref{BOCM})) with the corresponding quantity
$[m_c^{RGI,N_f=0}=1.654(45)~{\rm GeV}]/[m_b^{RGI,N_f=0}=6.758(86)~{\rm GeV}]=0.245(7)$
determined using the quenched data of ref.~\cite{RS} (for the $c$-mass) and~\cite{DELM} (for the $b$-mass).
More recently the work of ref.~\cite{CHENEW} has appeared where the number
$m_c^{\overline{MS},N_f=4}(3~{\rm GeV})/m_b^{\overline{MS},N_f=4}(10~{\rm GeV})=0.273(3)$
is quoted. This value is well consistent with our result~(\ref{BOCM}) which translates into
$m_c^{\overline{MS},N_f=2}(3~{\rm GeV})/m_b^{\overline{MS},N_f=2}(10~{\rm GeV})=0.274(15)$.}.
In closing this section we note that an independent determination of the $b$-quark mass can be
obtained repeating the same analysis as before but using $M_{B_s}$, instead of $M_B$, and replacing
$\hat\mu_{u/d}$ with $\hat\mu_s$. By doing that we find a result which is fully consistent with the
one in eq.~(\ref{MUBARE}). Alternatively, and perhaps more interestingly, one could use $K_b$ as
determined from $M_B$ to predict $M_{B_s}$, or better the ratio $M_{B_s}/M_B$, by the method we
are proposing in this paper. Such an analysis is in progress and will be presented elsewhere~\cite{FUT}.
\section{$f_B$ and $f_{B_s}$ decay constants}
\label{sec:METHF}
A strategy very similar to the one outlined in sect.~\ref{sec:METHB} can be employed to extract
accurate values of the $f_B$ and $f_{B_s}$ decay constants from available lattice data. In analogy
with what we have done before, one should now take
\beq
z(x,\lambda;\hat\mu_\ell)=\lambda^{1/2} \frac{f_{h\ell}(1/x)}{f_{h\ell}(1/x\lambda)}
\cdot\frac{C^{stat}_A(\log(x\lambda))}{C^{stat}_A(\log x)}
\frac{[\rho(\log x)]^{1/2}}{[\rho(\log \lambda x)]^{1/2}}\label{RATMZ}
\eeq
with the (continuum limit) shorthand notation
\[
f_{h\ell}(1/x)\equiv f_{h\ell}(1/x,\hat\mu_\ell)\, ,
\]
where the quark mass $\hat\mu_\ell$ must be extrapolated to either $\hat\mu_{u/d}$ or to the appropriate
strange quark mass value, $\hat\mu_s$, depending on whether one wants to compute $f_B$ or $f_{B_s}$.
\begin{figure}[!hbt]
\centerline{\includegraphics[scale=0.50,angle=-90]{fig_RATIO_F3ov2.ps}}
\caption{\it Lattice spacing and $\hat\mu_\ell$ dependence of the ratio
$f_{h\ell}^L(\hat\mu_h^{(3)};\hat\mu_\ell,a)/f^L_{h\ell}(\hat\mu_h^{(2)};\hat\mu_\ell,a)$.
The black square with its error is the combined continuum and chirally ($\hat\mu_\ell \to \hat{\mu}_{u/d}$)
extrapolated value.}
\label{fig:Frat3to2}
\end{figure}
The form of the function $z(x,\lambda;\hat\mu_\ell)$ is dictated by the continuum asymptotic formula
\beq
\lim_{x\to 0} \sqrt{\frac{\rho(\log x)}{x}}\frac{f_{h\ell}(1/x)}{C^{stat}_A(\log{x})}
= {\mbox{constant}} \neq 0\, ,
\label{HQM}
\eeq
which follows by matching HQET to QCD~\cite{HQET,HQET1}. The presence of the factor $C^{stat}_A$
comes from the fact that in HQET the axial (and vector) current needs to be renormalized.
The renormalization constant $C^{stat}_A$ is known in PT up to three loops~\cite{ZAPT}. The ratio of
$\rho$ factors (raised to the appropriate power) is there to convert $\overline{MS}$ heavy quark masses
to pole masses (see eq.~(\ref{PMA})).
As before, the function~(\ref{RATMZ}) has been defined so as to fulfill the exact asymptotic constraint
\beq
\lim_{x\to 0} z(x,\lambda;\hat\mu_{\ell})=1\, , \label{RATLEZ}
\eeq
from which the small $x$ expansion
\beq
z(x,\lambda,\hat\mu_{\ell})=1+\zeta_1(\log x,\lambda;\hat\mu_{\ell})x
+\zeta_2(\log x,\lambda;\hat\mu_{\ell}) x^2 \, , \label{ANLYTICF}
\eeq
follows. Again the coefficients $\zeta_j(\log x,\lambda;\hat\mu_{\ell})$, $j=1,2$, are
smooth functions of $\log x$ which tend to zero as $\lambda \to 1$.
In analogy with what we did in sect.~\ref{sec:METHB} in determining the $b$-quark mass,
with the purpose of
checking the robustness of the procedure, we shall take $C_A^{stat}$ and $\rho$ at increasing orders in PT,
from tree-level up to NLL order, and construct $z|_p$-ratios endowed with the asymptotic behaviour
\beq
z(x,\lambda;\hat\mu_{u/d})\Big{|}_{p}-1
~\stackrel{x \to 0}{\sim}~ {\rm O}\Big{(}\frac{1}{(\log x)^{p+1}}\Big{)}\, , \label{ZLIM}
\eeq
Just like in the case of the determination of the $b$-quark mass, the values of $f_B$ or $f_{B_s}$ that
we shall extract will be almost independent of the PT truncation order.
\begin{figure}[!hbt]
\centerline{\includegraphics[scale=1.0]{fig_6_NEW.ps}}
\caption{\it Continuum data for $z|_0$ (blue dots), $z|_1$ (red squares), $z|_2$ (green triangles).
The corresponding best fit curves are drawn with $\lambda=1.273$ (upper curve, in blue) and $\lambda=1.278$
(middle curve, in red and lower curve, in green). In all cases $\mu_\ell \to \mu_{u/d}$.
The blue and red vertical lines represent the location of the $b$-mass as extracted from $y|_0$
and $y|_1$ data (with $\lambda=1.273$ and $\lambda=1.278$), respectively. The green vertical line is
practically on top of the red line and it is not visible.}
\label{fig:fig3}
\end{figure}
\subsection{Implementing the method. The case of $f_B$}
\label{sec:IMFB}
The $z$-ratios~(\ref{RATMZ}) have been evaluated at the reference $h$-quark masses of the list~(\ref{MUV})
for each of the lattice spacings and light quark mass values given in Table~(\ref{tab:simpar}). When we
perform the continuum and chiral extrapolation of the ETMC lattice data for the ratios~(\ref{RATMZ}) of
$h\ell$ pseudoscalar meson decay constants (again based on simple chiral NLO-formulae
supplemented
with $\hat\mu_\ell$-independent O($a^2$) corrections -- see Appendix~A),
as hoped, a rather smooth behaviour is found
since most of the $a^2$ and $\hat\mu_\ell$ dependence gets canceled in taking the ratio. The observable
dependence on $\hat\mu_\ell$ and $a^2$ is mild and/or hardly significant within our present statistical
errors (see e.g.\ fig.~\ref{fig:Frat3to2}).
{}From the structure of eq.~(\ref{RATMZ}) one derives the iterative formulae (analogous to eq.~(\ref{ITER})
with $z^{(n)}_p\equiv z(x^{(n)},\lambda;\hat\mu_{u/d})|_p$)
\beqn
&&z_p^{(2)} z_p^{(3)}\cdots z_p^{(K+1)}=\label{ITERZ}\\
&&=\lambda^{K/2} \frac{f_{h\ell}(\hat\mu_h^{(K+1)})}{f_{h\ell}(\hat\mu_h^{(1)})} \cdot
\Big{[}\frac{C^{stat}_A(\log \hat\mu_h^{(1)})}{C^{stat}_A(\log\hat\mu_h^{(K+1)})}
\sqrt{\frac{\rho(\log\hat\mu_h^{(K+1)})}{\rho{(\log \hat\mu_h^{(1)})}}}\Big{]}_{p}\, ,\quad p=0,1,2\, .\nn
\eeqn
Similarly to what we did in fig.~\ref{fig:fig1}, we collect in fig.~\ref{fig:fig3} continuum and chirally
extrapolated data for $z|_p$, $p=0,1,2$ and best fit curves through these data and the value at $x=0$.
Thus, for instance, the middle (red) curve is the parabola (eq.~(\ref{ANLYTICF})) which best
fits the values of $z_1^{(n)}=z(x^{(n)},1.278;\hat\mu_{u/d})|_1$, $n=2,3,4$, at the heavy
quark masses~(\ref{MUV}). The red vertical line marks the position $x_b$ which corresponds to the
previously determined value of $\hat\mu_b$ (eq.~(\ref{MUBARE})) and crosses the curve at the
point $z_1^{(K_b)}=z(x_b,1.278;\hat\mu_{u/d})|_1$. With the help of this number and the values of
$z_1^{(j)} $ for $4<j\leq K_b+1$, eq.~(\ref{ITERZ}) provides a determination of $f_{hu/d}(\hat\mu_b)$
in terms of $f_{hu/d}(\hat\mu_h^{(1)})$ (with LL-accurate fit for the $z$-ratios).
As observed before, the latter does not necessarily has to be identified with the phenomenological
value of $f_D$ for the method to work, as what we actually need to know is the dependence
of $f_{hu/d}(\hat\mu_h)$ on $\hat\mu_h$ at around the charm mass. Nevertheless, since, as remarked
in sect.~\ref{sec:TLNLL}, $M_{hu/d}(\hat\mu_h^{(1)})$ coincides with the experimental value of $M_D$,
we are in position of evaluating $f_D$, obtaining $f_D=f_{hu/d}(\hat\mu_c)= 211(9)$~MeV,
compatible with the result $f_D= 197(9)$~MeV given in ref.~\cite{VCS}.
The latter was obtained in the standard way (see ref.~\cite{ETMCD}) from
the same ETMC gauge configuration ensembles, but with a rather different analysis
method where the meson masses rather than the renormalized quark masses were
kept fixed as $a \to 0$, resulting in somewhat different statistical (no use of $Z_P$)
and systematic errors as compared to the present study.
For the present computation of $f_{hu/d}(\hat\mu_h^{(1)})= f_D$ the
quality of the continuum and chiral extrapolation of our lattice data
is shown in fig.~\ref{fig:fitf}. Taking as triggering value the continuum and chirally extrapolated
value of the pseudoscalar decay constant computed at $\hat\mu_h^{(1)}$, we get
\beq
f_B=f_{hu/d}(\hat\mu_b)=194(16){\mbox{MeV}} \, ,
\label{FB}\eeq
which is precisely the result~(\ref{UQRES2}).
\begin{figure}[!hbt]
\centerline{\includegraphics[scale=0.50,angle=-90]{fig_F1.ps}}
\caption{\it The $f_{h\ell}^L(\mu_h^{(1)};\hat\mu_\ell,a)$ lattice data extracted from the
simulations detailed in Table~\ref{tab:simpar}. The black square
with its error is the continuum and chirally extrapolated value giving
$f_{hu/d}(\hat\mu_h^{(1)},\hat\mu_{u/d})= 211(9)$~MeV.}
\label{fig:fitf}
\end{figure}
\subsection{Discussion and $f_B$ error budget}
\label{sec:EBF}
To test the reliability of the interpolation of our trial functions, $z(x)$, to $b$-mass point,
we have explicitly checked the stability of the result~(\ref{FB}) to the order of PT at which
the expansion of $\rho^{{1/2}}/C_A^{stat}$ is truncated. For this purpose we have repeated
the whole previous analysis employing values of $\rho^{{1/2}}/C_A^{stat}$ computed at tree-level
($p=0$) and NLL ($p=2$) order. Upon comparing with the decay constant values obtained in these
other ways we see that numbers obtained using the $z|_0$-ratios (upper blue curve
in fig.~\ref{fig:fig3}) differ by less than 1\% from the value one gets from the red data (LL $z|_1$-ratios).
If one employs the lower green data (coming from the NLL $z|_2$-ratios) the difference with the previous
determination is totally negligible (about 0.1\%). This specific systematic effect on $f_B$ was hence
conservatively estimated to be $\sim 0.5\%$ and added quadratically to the full error.
As in the case of the determination of the $b$-quark mass, the remarkable numerical stability of $f_B$
with varying $p$ can be traced back to the good quality of the interpolation ansatz~(\ref{ANLYTICF})
and the relation (again valid for exactly known $z|_p$-ratios)
\beqn
&&\Big{[}\frac{C^{stat}_A(\log\hat\mu_h^{(K+1)})}{C^{stat}_A(\log \hat\mu_h^{(1)})}
\sqrt{\frac{\rho{(\log \hat\mu_h^{(1)})}}{\rho(\log\hat\mu_h^{(K+1)})}}\Big{]}_{p} \cdot
z_p^{(2)} z_p^{(3)}\cdots z_p^{(K+1)}=\nn\\
&&=z_0^{(2)} z_0^{(3)}\cdots z_0^{(K+1)}=
\lambda^{K/2} \frac{f_{h\ell}(\hat\mu_h^{(K+1)})}{f_{h\ell}(\hat\mu_h^{(1)})}\, .\label{ITERZ1}
\eeqn
\subsubsection{The $f_B$ error budget}
\label{sec:DEFB}
The total error we attribute to $f_B$ in eqs~(\ref{UQRES2}) and~(\ref{FB}) comes in almost equal
parts from the product of $z$-ratios in the l.h.s.\ of eq.~(\ref{ITERZ}) and the value of
$f_{hu/d}(\hat\mu_h^{(1)})$ and is a combination of statistical and systematic errors stemming
from the same sources already illustrated in the case of the $b$-quark mass in sect.~(\ref{sec:TLNLL}). As we saw
above, the systematic error stemming from the truncation of the PT expansion of $\rho^{{1/2}}/C_A^{stat}$
has a negligible impact on $f_B$.
Another 1-2\% systematic uncertainty comes from the possible (neglected)
logarithmic dependence of the $\zeta_j$, $j=1,2$ coefficients.
The relative uncertainty on $\zeta_j$ associated with these effects can be estimated to be
O$(\alpha_S(1/x))\sim 10-15$\%, a number which,
as in the case of the $\eta_j$'s entering our analysis for $\mu_b$,
is never larger than the statistical errors on their best fit values.
In any case inspection of figs.~\ref{fig:Frat3to2} to~\ref{fig:fitf}
shows that all systematic uncertainties are smaller than our current statistical errors.
\subsection{The case of $f_{B_s}$}
\label{sec:CFBS}
In order to come up with a determination of $f_{B_s}$ one has simply to repeat the whole procedure setting
$\mu_\ell\to\mu_s$. With reference to the value of $\hat\mu_s^{\overline{MS},N_f=2}(2~{\rm GeV})=99(7)$~MeV
given in~\cite{ETMC_m_strange}, one finds
(thanks to the equality of $\hat\mu_h^{(1)}$ with the charm quark mass)
\beq
f_{D_s} = f_{hs}(\hat\mu_h^{(1)}) = 252(7)~{\rm MeV}
\label{fDs}
\eeq
and the best fit $z$-ratio curves shown in fig.~\ref{fig:fig4}. We may quote
as our final result (see also eq.~(\ref{UQRES2}))
\beq
f_{B_s}=f_{hs}(\hat\mu_b)=235(12)~{\mbox{MeV}}\, ,
\label{FBS}\eeq
where errors are estimated as in the case of $f_B$. We also note that the result (\ref{fDs}) for
the decay constant of the $D_s$ meson is in agreement with that of ref.~\cite{VCS} and
contributes to further reduce the possible ``tension'' with the recent Cleo data reanalysis~\cite{CLEO_jan09}.
A more complete analysis of the many possibilities and refinements one can envisage will be presented in~\cite{FUT}.
\begin{figure}[!hbt]
\centerline{\includegraphics[scale=1.0]{fig_8_NEW.ps}}
\caption{\it Same as fig.~\ref{fig:fig3} for $\mu_\ell \to \mu_s$.}
\label{fig:fig4}
\end{figure}
As is clear by comparing the results for $f_B$ and $f_{B_s}$ (eqs.~(\ref{FB}) and~(\ref{FBS}),
respectively), our method yields a significantly smaller error for the decay constant of the strange
$B$-meson. The reason is that no large statistical fluctuations from the light ($u/d$) quark
propagators nor (valence) chiral extrapolation uncertainties enter the computation of $f_{B_s}$.
In view of this observation we remark that, if one would know with high accuracy
the ratio $f_B/f_{B_s}$, a more precise determination of $f_B$ could be obtained by
simply multiplying this number by $f_{B_s}$~\footnote{This observation is far from
original, see e.g.\ ref.~\cite{BECIR98}.}. Actually the quantity $f_B/f_{B_s}$
can be accurately computed by a simple generalization of the method discussed in this paper.
It is indeed sufficient to consider the double ratio
\beq
\hspace{-.02cm}
w(x,\lambda;\hat\mu_{u/d},\hat\mu_s)= [f_{h/ud}/f_{hs}](1/x) [f_{hs}/f_{hu/d}](1/ x\lambda ) =
\frac{z(x,\lambda;\hat\mu_{u/d})}{z(x,\lambda;\hat\mu_s)}\!\!
\label{FBOFBS}
\eeq
and follow the procedure we described before starting from the triggering quantity
$[f_{hu/d}/f_{hs}](\hat\mu_h^{(1)})$. This kind of analysis is under way and will be
discussed elsewhere~\cite{FUT}.
\section{Conclusions and outlook}
\label{sec:CONC}
In this paper we have proposed a novel strategy to determine $B$-physics parameters from currently
available Wilson fermion simulation data. As a first test of the method, we have computed in (the continuum
limit of) QCD with $N_f=2$ light dynamical quarks the (renormalized) $b$-quark mass as well as the
$B$-meson decay constants, $f_B$ and $f_{B_s}$, employing the gauge configurations
recently produced by the ETM Collaboration with maximally twisted Wilson fermion action~\cite{ETMCD}.
The method provides rather accurate numbers with errors that are dominated by the
uncertainties related to the limited statistical accuracy by which the (two-point) $h\ell$ pseudoscalar
meson correlators and the quark mass renormalization constant, $Z_P^{-1}$, are evaluated.
A better assessment of the systematic errors due to the limited knowledge of logarithmic
corrections can only come from data taken at quark masses larger than the ones displayed in eq.~(\ref{MUV}).
In several respects the present feasibility study could benefit from the nice properties (particularly
O($a$) improvement~\cite{FR1,FR2}) of maximally twisted Wilson fermions. Indeed, an important
feature of the present computation is the pretty good control we have of cutoff effects, which
(judging from the spread between values at the coarsest lattice spacing and those at the continuum limit)
are always smaller than 10\%. This is so both for the triggering quantities at the charm mass scale
and for the $y$- and $z$-ratios, which involve higher quark masses (up to twice the charm mass).
It is also interesting to note that the whole procedure only relies on the use of physical
quantities that can be easily determined from lattice simulations, while the need
for a renormalization step is limited to establishing the relation between the
renormalized charm-like mass and the values of the triggering pseudoscalar meson mass.
Fixing this relation requires the knowledge of $Z_P$. No extra renormalization factor is
needed for the calculation of the decay constants of interest if maximally twisted fermions
are used as the charged axial currents are exactly conserved at finite lattice spacing.
There is a lot of room for improvement in the application of the method, like reducing the
statistical error of the correlation functions, using several, suitably smeared meson sources,
increasing the accuracy by which $Z_P$ is known and incorporating in the analysis the new
ETMC set of data that are coming out at a finer lattice spacing ($\beta=4.2$).
Needless to say, the method can be straightforwardly extended to LQCD computations with
$u$, $d$, $s$ and possibly $c$ dynamical quarks where quenching uncertainties are virtually
absent. In this respect we wish to note that in simulations with $N_f=3$ dynamical quarks, although low
energy hadronic effects in the $B$-meson wave function are correctly treated,
a conflict remains between the number ($N_f=3$) of dynamical quarks running in the loops (and thus
relevant for the subtraction of UV divergencies) and the number ($N_f=4$) that instead should be used for
continuum RG-evolution at scales above, say, 1.5~GeV. This problem and the related RG-uncertainties
are completely removed if also the $c$ quark is made dynamical.
Finally, we remark that the strategy we have outlined
can be applied to any other $h\ell$ physical quantity the large $\mu_h$
behaviour of which is known (typically from large quark mass arguments).
\vspace{0.5cm}
{\bf{Acknowledgments - }} We wish to thank R. Sommer and N. Tantalo for useful
discussions and all the other members of ETMC for their interest in this work
and a most enjoyable and fruitful collaboration.
\vspace{1.2cm}
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"redpajama_set_name": "RedPajamaArXiv"
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Soul of Stars
(Heart of Iron, #2)
by Ashley Poston
Genres: science fiction > space opera, young adult
The highly awaited sequel to Heart of Iron, Soul of Stars is a thrilling sci-fi adventure packed with romance, shocking twists, and witty banter, perfect for fans of Six of Crows and Cinder.
Once, Ana was an orphaned space outlaw. Then she was the Empress of the Iron Kingdom. Now, thought dead by most of the galaxy after she escaped from the dark AI program called the HIVE, Ana is desperate for a way to save Di from the HIVE's evil clutches and take back her kingdom.
Ana's only option is to find Starbright, the one person who has hacked into the HIVE and lived to tell the tale. But when Ana's desperation costs the crew of the Dossier a terrible price, Ana and her friends are sent spiraling through the most perilous reaches of the Iron Kingdom to stop the true arbiter of evil in her world: an ancient world-ending deity called the Great Dark.
Their journey will take the sharp-witted pilot, Jax, to the home he never wanted to return to, and the dangerous fate he left behind. And when Robb finds out who Jax really is, he must contend with his own feelings for the boy he barely knows, and whether he truly belongs with this group of outcasts.
When facing the worst odds, can Ana and her crew of misfits find a way to stop the Great Dark once and for all?
About the Author :: Ashley Poston
Ashley Poston loves dread pirates, moving castles, and starry night skies. When not lost in a book, she's lost in real life, searching for her next great adventure. She is the author of Heart of Iron and Geekerella.
Ashley Poston >
Heart of Iron
|
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"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 5,332
|
{"url":"https:\/\/math.stackexchange.com\/questions\/2874467\/is-there-a-notion-above-that-of-perfect-numbers","text":"# Is there a notion \u201cabove\u201d that of perfect numbers?\n\nWhen trying to understand a notion, it often gives great insight to see it as the \"shadow\" of something bigger, carrying more information. The notion of categorification relies on this idea.\n\nA basic example, where hopefully the point is clearly seen: if $n$ is a natural number and $\\varphi$ denotes the Euler function, then the following identity holds: $$n=\\sum_{d\\mid n} \\varphi(d)\\tag{1}$$ Now if $\\Phi_k(X)$ denotes the $k$-th cyclotomic polynomial, one can write $$X^n-1=\\prod_{d\\mid n}\\Phi_d(X)\\tag{2}$$ Then $(1)$ is a \"shadow\" of $(2)$, as it is obtained by taking the degree of the polynomials on both sides. Note that $(1)$ can be (and originally was) proved by much more elementary means that building the whole theory of cyclotomic polynomials, otherwise this observation would somewhat lose interest.\n\nDefinition: a perfect number is a natural number that is equal to the sum of all of its proper positive divisors.\n\nQuestion: Is there something \"above\" this definition?\n\nAttempt: A number-theorist's-perfect group is a finite group whose order is equal to the sum of the orders of all of its proper subgroups.\n\nFor instance, cyclic groups with perfect order satisfy the above definition, since a cyclic group has one subgroup for each factor of its order. What is less easy, and the point of my question, is whether this notion is in any way actually interesting.\n\nPossibly more interesting if blanks can be filled: A nobody's-perfect group is a finite group satisfying [some conditions that could look interesting to a group-theorist and which imply that its order is equal to the sum of the orders of all of its proper subgroups].\n\nIn that last case one could start investigating the interest of that notion by trying to figure out whether there is a nobody's-perfect group of each perfect order.\n\n\u2022 Relevant: mathoverflow.net\/questions\/54851\/\u2026 \u2013\u00a0Steve D Aug 7 '18 at 2:01\n\u2022 @SteveD Thanks. The idea of restricting oneself to normal subgroups makes great sense given that we're after a natural construction. Of course I'd take any ideas, not necessarily related to my initial thought. \u2013\u00a0Arnaud Mortier Aug 7 '18 at 13:43\n\u2022 (+1) for the illustration of a \"shadow\", never heard of it before! \u2013\u00a0Peter Aug 8 '18 at 23:37","date":"2019-06-25 15:37:03","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9050576686859131, \"perplexity\": 371.89448070934765}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-26\/segments\/1560627999853.94\/warc\/CC-MAIN-20190625152739-20190625174739-00372.warc.gz\"}"}
| null | null |
<?php
/*
* This file is part of php-cache organization.
*
* (c) 2015 Aaron Scherer <aequasi@gmail.com>, Tobias Nyholm <tobias.nyholm@gmail.com>
*
* This source file is subject to the MIT license that is bundled
* with this source code in the file LICENSE.
*/
namespace Cache\Adapter\Memcache;
use Cache\Adapter\Common\AbstractCachePool;
use Cache\Adapter\Common\PhpCacheItem;
use Cache\Adapter\Common\TagSupportWithArray;
use Memcache;
class MemcacheCachePool extends AbstractCachePool
{
use TagSupportWithArray;
/**
* @type Memcache
*/
protected $cache;
/**
* @param Memcache $cache
*/
public function __construct(Memcache $cache)
{
$this->cache = $cache;
}
/**
* {@inheritdoc}
*/
protected function fetchObjectFromCache($key)
{
if (false === $result = unserialize($this->cache->get($key))) {
return [false, null, [], null];
}
return $result;
}
/**
* {@inheritdoc}
*/
protected function clearAllObjectsFromCache()
{
return $this->cache->flush();
}
/**
* {@inheritdoc}
*/
protected function clearOneObjectFromCache($key)
{
$this->cache->delete($key);
return true;
}
/**
* {@inheritdoc}
*/
protected function storeItemInCache(PhpCacheItem $item, $ttl)
{
$data = serialize([true, $item->get(), $item->getTags(), $item->getExpirationTimestamp()]);
return $this->cache->set($item->getKey(), $data, 0, $ttl ?: 0);
}
/**
* {@inheritdoc}
*/
public function getDirectValue($name)
{
return $this->cache->get($name);
}
/**
* {@inheritdoc}
*/
public function setDirectValue($name, $value)
{
$this->cache->set($name, $value);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,859
|
by Sears, Michael
Publisher: Soho Crime
Tower of Babel > ISBN13: 9781641291958
Shamus Award–winning author Michael Sears brings Queens, New York, to literary life in this crime series debut featuring a somewhat seedy lawyer with a heart of gold (or at least gold plate).
Queens, New York—the most diverse place on earth. Native son Ted Malloy knows these streets like the back of his hand. Ted was once a high-powered Manhattan lawyer, but after a spectacular fall from grace, he has found himself back on his home turf, scraping by as a foreclosure profiteer. It's a grubby business, but a safe one—until Ted's case sourcer, a mostly reformed small-time conman named Richie Rubiano, turns up murdered shortly after tipping Ted off to an improbably lucrative lead.
With Richie's widow on his back and shadows of the past popping up at every turn, Ted realizes he's gotten himself embroiled in a murder investigation. His quest for the truth will take him all over Queens, plunging him into the machinations of greedy developers, mobsters, enraged activists, old litigator foes and old-school New York City operators.
Michael Sears spent over twenty years on Wall Street, rising to become a managing director for Paine Webber and Jefferies Financial before leaving the business in 2005 to pursue writing full-time. His books, a number of which are national bestsellers, have been nominated for—and received—numerous awards, including the Edgar. An avid sailor, he lives in Sea Cliff, New York, with his wife, poet and artist Barbara Segal, and the cat Penelope.
Reviews for Tower of Babel (9781641291958)
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 3,381
|
Thanks to your tithes and offerings in September, Unity on the Bay was able to tithe outside our walls. Here's the breakdown of how we tithed 15% outside our walls.
Newer PostDaylight Savings Time begins Sunday, November 6!
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 1,078
|
The year, 2019, marks the 85th anniversary of Three Hills Brand Kunserva! This much-loved Maltese delicacy started way back in 1934, in Gozo, and till today it is still being produced according to the same original Gozitan recipe. The story all started by a humble businessman from Xewkija, Ganni Magro, who began his career as a general provision merchant in 1916. In the twenties, Gianni's three male sons, who by then had joined the firm with their father to form Magro Brothers, ventured into yet another field that would eventually become the firm's main business activity to present times; they started to contract and purchase tomatoes from Gozitan farmers. This pulpy fruit was already used in the local kitchen during the summer months when the crop was at its best, but it was not cultivated commercially. By 1934, the three Magro brothers had completely taken over the business from their father and established themselves as leading general merchants and food distributors in Gozo. The Magro Brothers decided to start processing tomatoes to produce Kunserva, tomato-paste – a totally new venture for their firm. In 1934, the first Kunserva production was canned in containers with a capacity of five and a half pounds (5 pounds 8 ounces), equivalent to around 3 kgs. Grocers would then sell the Kunserva by weight and roll it in a grease-proof paper. The Three Hills Brand was an immediate success and it was destined to become, in a few years' time, a household name in Gozo, in Malta, and even abroad. The ingredients used are all natural and its exceptional taste comes from the Maltese summer grown juicy tomatoes and the well-guarded, secret recipe and formulation created by the Magro family. Kunserva is used widely in the Maltese kitchen. Nothing tastes as delicious as hard-crust Maltese bread spread with Kunserva, or ravjul biz-zalza (ricotta-filled ravioli with a Kunserva and garlic sauce), not to mention the traditional culinary dishes such as stuffat tal-fenek, laham jew qarnit (rabbit, meat or octopus stews), soppa ta' l-armla (widow's soup), imqarrun- il forn (baked macaroni) and most pasta sauces! The addition of Kunserva to our dishes simply gives the dishes the signature of Maltese flavours! Today, the traditional Kunserva is available in 200g and 400g metal cans as well as for the catering sector. Kunserva is produced as well in glass jars and convenient squeezy tubes. Today's lifestyle demands a more health-conscious diet. In response Three Hills Kunserva can be enjoyed with no added salt and with 30% Less Sugar added. For the adventurous ones, one can also try Kunserva with added tastes including mint and onion, basil and garlic or the pungent version; the Kunserva Pikkanti. From 1934 till today, 85 years on, Three Hills Brand Kunserva is still very much "Fil-Qalb tal-Maltin" and will continue to be one of Malta's staple kitchen ingredient!
This year's annual Magro Christmas gathering was held on Saturday 15th December at Hotel Ta' Cenc in Sannat. All Magro Group employees celebrated this festive season together with good food, company and nice atmosphere.
Magro Brothers are currently participating in bi-annual international food fair in Paris. It is a place where one can discover products from all over the world, the latest culinary trends. For this year's marked dates 21–25 October 2018, SIAL Paris will be the largest international marketplace for food service professionals seeking inspiration. Magro Brother's stand is Hall 5B J074.
It was our pleasure welcoming Member of Parliament Dr Robera Metsola at the Magro Food Village in Xewkija. Dr Metsola was shown around the premises including Savina Creations, Farm Fresh and Magro premises.
Member of Parlament Dr. Miriam Dalli paid an official visit at The Magro Food Village in Xewkija, Gozo. Mr Christian Magro welcomed Dr Dalli and showed her around the various factories and workshops. Dr Dalli met a number of employees from the various divisions of the company.
The Directors of Magro Brothers closed this year's season 2018 with a grand BBQ offered to all the staff and their families from Malta and Gozo. The event took place at the Magro premises on Saturday 1st September and started with a mass. The mass was followed by the opening of various entertainment activities which included a bouncing castle, a children's water slide and many more. All guests, over 300, were entertained to music, lavish food buffet and drinks. The social gathering ended with a grand raffle for all those present.
Do you crave the taste of the orient? Pinto's Pride Brand is introducing a new range of Indian ready-made cooking sauces. Freshly made, convenient, and super easy to prepare! Simply stir fry some pieces of chicken or meat and add the vegetables of your choice in a little oil for three minutes. Add a jar of Pinto's Indian sauce of your choice and simmer until chicken or meat is cooked through. Simply serve with basmati rice. Three different flavors to choose from including Tikka Masala, Korma and Curry Sauce. Outstanding cuisine, ready in minutes!
Do you fancy a classic Italian pasta dish? Pinto's Pride Brand is introducing a new range of Italian ready-made cooking sauces. Freshly made, convenient, and super easy to prepare! Simply warm contents of jar over a low flame, stirring occasionally, until hot. Pour over freshly cooked pasta. Pinto's pride range of Italian sauces are ideal to be served with penne or fusilli. Three different flavors to choose from including Basil & Garlic, Spicy Arrabiata and Napoletana (onion & carrot). Outstanding cuisine, ready in minutes!
nd is difficult to digest lactose. To produce Hanini's Lactose Free* Gibniet, an enzyme is added to the milk during the production process that breaks Lactose into other simpler sugars which can be digested by lactose intolerant people. Fortunately this process does not effect the great taste of the traditional Gozitan cheeselets. Hanini's Gibniet (singular Gibna) are conveniently packed in packs of two cheeselets. Enjoy!
A delegation led by His Excellency Dr. Aklilu Hailemichael, State Minister for Business and Diaspora Affairs within the Ministry for Foreign Affairs. The Minister was accompanied by H.E. The Ambassador Zenebu Tadasse, other Embassy officials and the members of the Ethiopian press. The delegation was organized by Mr. Anton Buttigieg CEO of Trade Malta and H.E. Ronald Micallef Non-Resident Ambassador to Ethiopia and African Union. Mr Magro and Trading team has welcomed the delegation at our premises, and explored trading opportunities between our firm and Ethiopia. We will surely follow up this visit to establish business contacts in Ethiopia and expressed our interest to visit the country in the near future.
Magro Brothers is currently participating in the Gulfood Exhibition which is taking place in Dubai. This is the 2nd time our company is taking part in this exhibition. Gulfood is the world's largest annual food & beverage exhibition, welcoming professionals from all corners of the globe to meet for 5 days of business. Over 4000 exhibitors took part this year; each provide a showcase of tastes, trends and innovations that are shaping the future of food and beverage consumption worldwide. Magro's Brothers Stand is situated at Sheikh Saeed Hall Stand S-K37.
The Magro Group proudly presents the latest addition to their brand portfolio, Divini. Divini embraces the cooking concepts that have traditionally shaped the Maltese household's menu. The brand is all about bringing wholesome, genuine products to the tables of the general public through presence in retail outlets across the Maltese islands. Handmade in Gozo from fresh ingredients and traditional recipes, yet supplied in ultra-modern high convenience packaging, Divini products are a wonderful fusion of the old and the new. Our first product which has successfully been launched to market is Ravjul (Ravioli) which comes in two varieties – Irkotta and Irkotta with Parsley. The bag also comes with 2 separate pouches of traditional tomato and garlic sauce (Zalza tal-Kunserva) which are conveniently portioned and packed in "boil-in bags". Simply prepare a pot of boiling water and have yourself a delightful meal ready in just a few minutes!
At the end of each year as always, Magro Brothers celebrated Christmas and the New Year with a delicious dinner party for which all employees of the Magro Group attended. The management and families of all employees were invited. The event was held on Thursday 21st December at Calypso Hotel in Marsalforn. Children were entertained by their favorite cartoon figures and many other activities. Father Christmas distributed gifts to the delight of all, especially the young ones. The many families present together with the directors and management and their families looked like one big family gathered together.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 4,350
|
Laura Podalsky
podalsky.1@osu.edu
Latin American youth cultures
Latin American urban cultures
Latin American film and visual cultures
Ph.D., Latin American Studies, Tulane University, 1995
B.A., Latin American Studies, Yale University, 1986
Professor Podalsky specializes in Latin American film and cultural studies. Her research involves the relationship between Latin American culture, politics, and socio-historical formations, and she has developed projects on urban culture, questions of affect and, more recently, youth cultures. Her first book, Specular City: Transforming Culture, Consumption, and Space in Buenos Aires, 1955-1973 Temple University Press, 2004), was a substantive, interdisciplinary, cultural studies project. Through the analysis of new films, literature, magazines, advertising, architecture, and car culture, Specular City discusses the material and discursive transformation of the Argentine capital in relation to contemporary struggles between middle-class and working-class sectors in the aftermath of the first Peronist administration. The Politics of Affect and Emotion in Contemporary Latin American Cinema: Argentina, Brazil, Cuba, and Mexico (Palgrave Macmillan, 2011) is a more medium-specific study, exploring the evocation of affect and the deployment of emotion in contemporary film as a response to the adjudicating tendencies of postdictatorial politics and the hyper-rationalist discourses of neoliberalism. She is currently working on a monographic study of youth, modernity, and film, comparing Argentina and Mexico in the 1950s-1960s and in the 1990s-present.
Prof. Podalsky also has published essays on a wide variety of topics, including landscapes of masculinity in contemporary Mexican cinema, Mexican youth films, the work of Brazilian director Ana Carolina, telenovelas and globalization, cosmopolitanism in tango films, and pre-revolutionary Cuban cinema in journals such as New Cinemas, Studies of Hispanic Cinemas, Framework, Screen, Cinemais (Brazil), and Archivos de la Filmoteca (Spain).
She is an Associate Editor of the Journal of Spanish and Latin American Cinemas (Intellect).
Youth, Film, Youth Culture in Latin America
The Documentary Impulse in Latin American Film
Theories of Visual Cultures
Introduction to Latin American Film
Contemporary Argentine Cinema
History and Film
Cuban Cinema
Gender & Sexuality in Latin American Film
Latin American Cinemas at the Global Crossroads
Introduction to Methods of Film Analysis
2020. "Cosmopolitanism, Modernity and Youth in the 1960s: The Transnational Wanderings of Teen Idols from Argentina, Mexico and Spain." Transnational Screens 20 (2020): 1-19.
2017. "Unpacking Periodization." In The Routledge Companion of Latin American Cinemas. Marvin D'Lugo, Ana M. López, and Laura Podalsky, eds. London: Routledge.
2017. "The Affect Turn." In New Approaches to Latin American Studies: Culture and Power. Juan Poblete, ed. New York: Routledge.
2016. "Ponerse al día: los jóvenes y el cine argentino contemporáneo." Cine argentino contemporáneo: visiones y discursos. Bernhard Chappuzeau y Christian von Tschilschke, eds. Amsterdam: Iberoamericana/Vervuert.
2016. "Aesthetics of Detachment." Arizona Journal of Hispanic Cultural Studies (20): 10-26. Special volume edited by María del Carmen Caña Jiménez and Vinodh Venkatesh.
2016. "El cine, el rock, la televisión y las culturas juveniles en los 1960s en la Argentina." Actas del V Congreso Internacional de AsAECA. Universidad de Quilmes, Buenos Aires, March 9-11. Actas del V Congreso AsAECA
Public Interventions
"Still Moving? Violence, Visual Regimes and Affect" (38:50:00 to 58:38:00) Latin American and Caribbean Film in the Era of Neoliberalism (1985-2020), North Carolina Latin American Film Festival Conversations, October 2020.
"Juventud y cine en América Latina" Tardes de cine: Jóvenes de película: genealogía de la juventud a partir de la producción cinematográfica en Chile del siglo XX, Universidad de Chile, August 2020.
"The Politics of Affect and Emotion in Contemporary Latin American Cinema: Comments on a Book." Wexner Center for the Arts, The Ohio State University, January 2012.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 3,265
|
We are booked in today under the name Owen James. Where do we park please?
If we aren't lucky enough to get a parking space, where can we park? i.e. how far away, and at what cost?
Further to my previous answer, we have now secured some guest parking permits as well as our on site parking, so it is likely you would be able to have one of these which allows you to park for free in our area on the street or in a choice of 3 public car parks including Royal Yard the nearest car park to us.
"Il faut choisir : chambre avec vue et bruyante ou chambre sans vue calme. Evitez la chambre 7"
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,320
|
{"url":"http:\/\/math.stackexchange.com\/questions\/214428\/find-formulae-for-px-x-and-py-y-in-terms-of-f-and-g","text":"# Find formulae for $P(X=x)$ and $P(Y=y)$ in terms of $f$ and $g$\n\nSuppose that random variables $X$ and $Y$, each with a finite number of possible values, have joint probabilities of the form $$P(X=x, Y=y) = f(x)g(y)$$ for some functions $f$ and $g$. How in the world would you find formulae for this? That doesn't even make sense.\n\n-\n\nWe have \\begin{align*} P(X=x) &= \\sum_y P(X=x, Y=y)\\\\ &= \\sum_y f(x)g(y)\\\\ &= f(x) \\cdot \\sum_y g(y) \\end{align*} and analogously \\begin{align*} P(Y=y) &= \\sum_x P(X=x, Y=y)\\\\ &= \\sum_x f(x)g(y)\\\\ &= g(y) \\cdot \\sum_x f(x) \\end{align*} Summing over all $x$ and $y$ gives $1 = \\sum_x\\sum_y f(x)g(y) = \\sum_x f(x) \\cdot \\sum_y g(y)$ So $P(X=x) = \\frac{f(x)}{\\sum_{x'} f(x')}, \\quad P(Y=y) = \\frac{g(y)}{\\sum_{y'} g(y')}-$\n@martini Yes I definitely agree with Alex this is an outstanding answer thanks. Just one question. What is the last step you did there in the very last line? When you put $P(X=x) = \\frac {f(x)}{\\sum_x' f(x')}$ Where did the summation of $f(x')$ come from? \u2013\u00a0 TheHopefulActuary Oct 16 '12 at 2:49\n@Kyle When we summed over $x$ and $y$ the line before, we concluded that $(\\sum_x f(x))^{-1} = \\sum_y g(y)$. We want to use that in $P(X=x) = f(x) \\cdot \\sum_y g(y)$. There is an $x$ in this equation, so I renamed the summation variable in $\\sum_{x'} f(x')$ and got $f(x) \\cdot \\sum_y g(y) = f(x) \\cdot (\\sum_{x'} f(x'))^{-1}$ \u2013\u00a0 martini Oct 16 '12 at 4:56","date":"2015-04-21 09:58:03","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 1.0000029802322388, \"perplexity\": 416.6872905428479}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-18\/segments\/1429246641266.56\/warc\/CC-MAIN-20150417045721-00142-ip-10-235-10-82.ec2.internal.warc.gz\"}"}
| null | null |
.class public Landroid/graphics/drawable/AnimationDrawable;
.super Landroid/graphics/drawable/DrawableContainer;
.source "AnimationDrawable.java"
# interfaces
.implements Ljava/lang/Runnable;
.implements Landroid/graphics/drawable/Animatable;
# annotations
.annotation system Ldalvik/annotation/MemberClasses;
value = {
Landroid/graphics/drawable/AnimationDrawable$1;,
Landroid/graphics/drawable/AnimationDrawable$AnimationListener;,
Landroid/graphics/drawable/AnimationDrawable$AnimationState;
}
.end annotation
# instance fields
.field private mAnimating:Z
.field private mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
.field private mCurFrame:I
.field mListener:Landroid/graphics/drawable/AnimationDrawable$AnimationListener;
.field private mMutated:Z
.field private mRunning:Z
# direct methods
.method public constructor <init>()V
.locals 1
.prologue
const/4 v0, 0x0
.line 100
invoke-direct {p0, v0, v0}, Landroid/graphics/drawable/AnimationDrawable;-><init>(Landroid/graphics/drawable/AnimationDrawable$AnimationState;Landroid/content/res/Resources;)V
.line 101
return-void
.end method
.method private constructor <init>(Landroid/graphics/drawable/AnimationDrawable$AnimationState;Landroid/content/res/Resources;)V
.locals 3
.param p1, "state" # Landroid/graphics/drawable/AnimationDrawable$AnimationState;
.param p2, "res" # Landroid/content/res/Resources;
.prologue
const/4 v2, 0x0
.line 426
invoke-direct {p0}, Landroid/graphics/drawable/DrawableContainer;-><init>()V
.line 88
const/4 v1, -0x1
iput v1, p0, Landroid/graphics/drawable/AnimationDrawable;->mCurFrame:I
.line 427
new-instance v0, Landroid/graphics/drawable/AnimationDrawable$AnimationState;
invoke-direct {v0, p1, p0, p2}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;-><init>(Landroid/graphics/drawable/AnimationDrawable$AnimationState;Landroid/graphics/drawable/AnimationDrawable;Landroid/content/res/Resources;)V
.line 428
.local v0, "as":Landroid/graphics/drawable/AnimationDrawable$AnimationState;
invoke-virtual {p0, v0}, Landroid/graphics/drawable/AnimationDrawable;->setConstantState(Landroid/graphics/drawable/DrawableContainer$DrawableContainerState;)V
.line 429
if-eqz p1, :cond_0
.line 430
const/4 v1, 0x1
invoke-direct {p0, v2, v1, v2}, Landroid/graphics/drawable/AnimationDrawable;->setFrame(IZZ)V
.line 432
:cond_0
return-void
.end method
.method synthetic constructor <init>(Landroid/graphics/drawable/AnimationDrawable$AnimationState;Landroid/content/res/Resources;Landroid/graphics/drawable/AnimationDrawable$1;)V
.locals 0
.param p1, "x0" # Landroid/graphics/drawable/AnimationDrawable$AnimationState;
.param p2, "x1" # Landroid/content/res/Resources;
.param p3, "x2" # Landroid/graphics/drawable/AnimationDrawable$1;
.prologue
.line 84
invoke-direct {p0, p1, p2}, Landroid/graphics/drawable/AnimationDrawable;-><init>(Landroid/graphics/drawable/AnimationDrawable$AnimationState;Landroid/content/res/Resources;)V
return-void
.end method
.method private inflateChildElements(Landroid/content/res/Resources;Lorg/xmlpull/v1/XmlPullParser;Landroid/util/AttributeSet;Landroid/content/res/Resources$Theme;)V
.locals 10
.param p1, "r" # Landroid/content/res/Resources;
.param p2, "parser" # Lorg/xmlpull/v1/XmlPullParser;
.param p3, "attrs" # Landroid/util/AttributeSet;
.param p4, "theme" # Landroid/content/res/Resources$Theme;
.annotation system Ldalvik/annotation/Throws;
value = {
Lorg/xmlpull/v1/XmlPullParserException;,
Ljava/io/IOException;
}
.end annotation
.prologue
const/4 v9, 0x2
const/4 v8, 0x1
.line 296
invoke-interface {p2}, Lorg/xmlpull/v1/XmlPullParser;->getDepth()I
move-result v6
add-int/lit8 v4, v6, 0x1
.line 299
.local v4, "innerDepth":I
:cond_0
:goto_0
invoke-interface {p2}, Lorg/xmlpull/v1/XmlPullParser;->next()I
move-result v5
.local v5, "type":I
if-eq v5, v8, :cond_6
invoke-interface {p2}, Lorg/xmlpull/v1/XmlPullParser;->getDepth()I
move-result v1
.local v1, "depth":I
if-ge v1, v4, :cond_1
const/4 v6, 0x3
if-eq v5, v6, :cond_6
.line 300
:cond_1
if-ne v5, v9, :cond_0
.line 304
if-gt v1, v4, :cond_0
invoke-interface {p2}, Lorg/xmlpull/v1/XmlPullParser;->getName()Ljava/lang/String;
move-result-object v6
const-string v7, "item"
invoke-virtual {v6, v7}, Ljava/lang/String;->equals(Ljava/lang/Object;)Z
move-result v6
if-eqz v6, :cond_0
.line 308
sget-object v6, Lcom/android/internal/R$styleable;->AnimationDrawableItem:[I
invoke-static {p1, p4, p3, v6}, Landroid/graphics/drawable/AnimationDrawable;->obtainAttributes(Landroid/content/res/Resources;Landroid/content/res/Resources$Theme;Landroid/util/AttributeSet;[I)Landroid/content/res/TypedArray;
move-result-object v0
.line 311
.local v0, "a":Landroid/content/res/TypedArray;
const/4 v6, 0x0
const/4 v7, -0x1
invoke-virtual {v0, v6, v7}, Landroid/content/res/TypedArray;->getInt(II)I
move-result v3
.line 312
.local v3, "duration":I
if-gez v3, :cond_2
.line 313
new-instance v6, Lorg/xmlpull/v1/XmlPullParserException;
new-instance v7, Ljava/lang/StringBuilder;
invoke-direct {v7}, Ljava/lang/StringBuilder;-><init>()V
invoke-interface {p2}, Lorg/xmlpull/v1/XmlPullParser;->getPositionDescription()Ljava/lang/String;
move-result-object v8
invoke-virtual {v7, v8}, Ljava/lang/StringBuilder;->append(Ljava/lang/String;)Ljava/lang/StringBuilder;
move-result-object v7
const-string v8, ": <item> tag requires a \'duration\' attribute"
invoke-virtual {v7, v8}, Ljava/lang/StringBuilder;->append(Ljava/lang/String;)Ljava/lang/StringBuilder;
move-result-object v7
invoke-virtual {v7}, Ljava/lang/StringBuilder;->toString()Ljava/lang/String;
move-result-object v7
invoke-direct {v6, v7}, Lorg/xmlpull/v1/XmlPullParserException;-><init>(Ljava/lang/String;)V
throw v6
.line 317
:cond_2
invoke-virtual {v0, v8}, Landroid/content/res/TypedArray;->getDrawable(I)Landroid/graphics/drawable/Drawable;
move-result-object v2
.line 319
.local v2, "dr":Landroid/graphics/drawable/Drawable;
invoke-virtual {v0}, Landroid/content/res/TypedArray;->recycle()V
.line 321
if-nez v2, :cond_5
.line 322
:cond_3
invoke-interface {p2}, Lorg/xmlpull/v1/XmlPullParser;->next()I
move-result v5
const/4 v6, 0x4
if-eq v5, v6, :cond_3
.line 325
if-eq v5, v9, :cond_4
.line 326
new-instance v6, Lorg/xmlpull/v1/XmlPullParserException;
new-instance v7, Ljava/lang/StringBuilder;
invoke-direct {v7}, Ljava/lang/StringBuilder;-><init>()V
invoke-interface {p2}, Lorg/xmlpull/v1/XmlPullParser;->getPositionDescription()Ljava/lang/String;
move-result-object v8
invoke-virtual {v7, v8}, Ljava/lang/StringBuilder;->append(Ljava/lang/String;)Ljava/lang/StringBuilder;
move-result-object v7
const-string v8, ": <item> tag requires a \'drawable\' attribute or child tag"
invoke-virtual {v7, v8}, Ljava/lang/StringBuilder;->append(Ljava/lang/String;)Ljava/lang/StringBuilder;
move-result-object v7
const-string v8, " defining a drawable"
invoke-virtual {v7, v8}, Ljava/lang/StringBuilder;->append(Ljava/lang/String;)Ljava/lang/StringBuilder;
move-result-object v7
invoke-virtual {v7}, Ljava/lang/StringBuilder;->toString()Ljava/lang/String;
move-result-object v7
invoke-direct {v6, v7}, Lorg/xmlpull/v1/XmlPullParserException;-><init>(Ljava/lang/String;)V
throw v6
.line 330
:cond_4
invoke-static {p1, p2, p3, p4}, Landroid/graphics/drawable/Drawable;->createFromXmlInner(Landroid/content/res/Resources;Lorg/xmlpull/v1/XmlPullParser;Landroid/util/AttributeSet;Landroid/content/res/Resources$Theme;)Landroid/graphics/drawable/Drawable;
move-result-object v2
.line 333
:cond_5
iget-object v6, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
invoke-virtual {v6, v2, v3}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->addFrame(Landroid/graphics/drawable/Drawable;I)V
.line 334
if-eqz v2, :cond_0
.line 335
invoke-virtual {v2, p0}, Landroid/graphics/drawable/Drawable;->setCallback(Landroid/graphics/drawable/Drawable$Callback;)V
goto/16 :goto_0
.line 338
.end local v0 # "a":Landroid/content/res/TypedArray;
.end local v1 # "depth":I
.end local v2 # "dr":Landroid/graphics/drawable/Drawable;
.end local v3 # "duration":I
:cond_6
return-void
.end method
.method private nextFrame(Z)V
.locals 3
.param p1, "unschedule" # Z
.prologue
.line 248
iget v2, p0, Landroid/graphics/drawable/AnimationDrawable;->mCurFrame:I
add-int/lit8 v1, v2, 0x1
.line 249
.local v1, "next":I
iget-object v2, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
invoke-virtual {v2}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->getChildCount()I
move-result v0
.line 250
.local v0, "N":I
if-lt v1, v0, :cond_0
.line 251
const/4 v1, 0x0
.line 254
:cond_0
iget-object v2, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
# getter for: Landroid/graphics/drawable/AnimationDrawable$AnimationState;->mOneShot:Z
invoke-static {v2}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->access$100(Landroid/graphics/drawable/AnimationDrawable$AnimationState;)Z
move-result v2
if-eqz v2, :cond_1
add-int/lit8 v2, v0, -0x1
if-ge v1, v2, :cond_2
:cond_1
const/4 v2, 0x1
:goto_0
invoke-direct {p0, v1, p1, v2}, Landroid/graphics/drawable/AnimationDrawable;->setFrame(IZZ)V
.line 255
return-void
.line 254
:cond_2
const/4 v2, 0x0
goto :goto_0
.end method
.method private setFrame(IZZ)V
.locals 4
.param p1, "frame" # I
.param p2, "unschedule" # Z
.param p3, "animate" # Z
.prologue
.line 258
iget-object v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
invoke-virtual {v0}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->getChildCount()I
move-result v0
if-lt p1, v0, :cond_1
.line 277
:cond_0
:goto_0
return-void
.line 261
:cond_1
iput-boolean p3, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimating:Z
.line 262
iput p1, p0, Landroid/graphics/drawable/AnimationDrawable;->mCurFrame:I
.line 263
invoke-virtual {p0, p1}, Landroid/graphics/drawable/AnimationDrawable;->selectDrawable(I)Z
.line 264
if-nez p2, :cond_2
if-eqz p3, :cond_3
.line 265
:cond_2
invoke-virtual {p0, p0}, Landroid/graphics/drawable/AnimationDrawable;->unscheduleSelf(Ljava/lang/Runnable;)V
.line 267
:cond_3
if-eqz p3, :cond_4
.line 269
iput p1, p0, Landroid/graphics/drawable/AnimationDrawable;->mCurFrame:I
.line 270
const/4 v0, 0x1
iput-boolean v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mRunning:Z
.line 271
invoke-static {}, Landroid/os/SystemClock;->uptimeMillis()J
move-result-wide v0
iget-object v2, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
# getter for: Landroid/graphics/drawable/AnimationDrawable$AnimationState;->mDurations:[I
invoke-static {v2}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->access$000(Landroid/graphics/drawable/AnimationDrawable$AnimationState;)[I
move-result-object v2
aget v2, v2, p1
int-to-long v2, v2
add-long/2addr v0, v2
invoke-virtual {p0, p0, v0, v1}, Landroid/graphics/drawable/AnimationDrawable;->scheduleSelf(Ljava/lang/Runnable;J)V
goto :goto_0
.line 273
:cond_4
iget-object v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mListener:Landroid/graphics/drawable/AnimationDrawable$AnimationListener;
if-eqz v0, :cond_0
iget v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mCurFrame:I
iget-object v1, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
invoke-virtual {v1}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->getChildCount()I
move-result v1
add-int/lit8 v1, v1, -0x1
if-ne v0, v1, :cond_0
.line 274
iget-object v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mListener:Landroid/graphics/drawable/AnimationDrawable$AnimationListener;
invoke-interface {v0}, Landroid/graphics/drawable/AnimationDrawable$AnimationListener;->onAnimationEnd()V
goto :goto_0
.end method
.method private updateStateFromTypedArray(Landroid/content/res/TypedArray;)V
.locals 3
.param p1, "a" # Landroid/content/res/TypedArray;
.prologue
.line 341
iget-object v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
const/4 v1, 0x1
iget-object v2, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
iget-boolean v2, v2, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->mVariablePadding:Z
invoke-virtual {p1, v1, v2}, Landroid/content/res/TypedArray;->getBoolean(IZ)Z
move-result v1
iput-boolean v1, v0, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->mVariablePadding:Z
.line 344
iget-object v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
const/4 v1, 0x2
iget-object v2, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
# getter for: Landroid/graphics/drawable/AnimationDrawable$AnimationState;->mOneShot:Z
invoke-static {v2}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->access$100(Landroid/graphics/drawable/AnimationDrawable$AnimationState;)Z
move-result v2
invoke-virtual {p1, v1, v2}, Landroid/content/res/TypedArray;->getBoolean(IZ)Z
move-result v1
# setter for: Landroid/graphics/drawable/AnimationDrawable$AnimationState;->mOneShot:Z
invoke-static {v0, v1}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->access$102(Landroid/graphics/drawable/AnimationDrawable$AnimationState;Z)Z
.line 346
return-void
.end method
# virtual methods
.method public addFrame(Landroid/graphics/drawable/Drawable;I)V
.locals 2
.param p1, "frame" # Landroid/graphics/drawable/Drawable;
.param p2, "duration" # I
.prologue
const/4 v1, 0x0
.line 241
iget-object v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
invoke-virtual {v0, p1, p2}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->addFrame(Landroid/graphics/drawable/Drawable;I)V
.line 242
iget v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mCurFrame:I
if-gez v0, :cond_0
.line 243
const/4 v0, 0x1
invoke-direct {p0, v1, v0, v1}, Landroid/graphics/drawable/AnimationDrawable;->setFrame(IZZ)V
.line 245
:cond_0
return-void
.end method
.method public clearMutated()V
.locals 1
.prologue
.line 366
invoke-super {p0}, Landroid/graphics/drawable/DrawableContainer;->clearMutated()V
.line 367
const/4 v0, 0x0
iput-boolean v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mMutated:Z
.line 368
return-void
.end method
.method cloneConstantState()Landroid/graphics/drawable/AnimationDrawable$AnimationState;
.locals 3
.prologue
.line 359
new-instance v0, Landroid/graphics/drawable/AnimationDrawable$AnimationState;
iget-object v1, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
const/4 v2, 0x0
invoke-direct {v0, v1, p0, v2}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;-><init>(Landroid/graphics/drawable/AnimationDrawable$AnimationState;Landroid/graphics/drawable/AnimationDrawable;Landroid/content/res/Resources;)V
return-object v0
.end method
.method bridge synthetic cloneConstantState()Landroid/graphics/drawable/DrawableContainer$DrawableContainerState;
.locals 1
.prologue
.line 84
invoke-virtual {p0}, Landroid/graphics/drawable/AnimationDrawable;->cloneConstantState()Landroid/graphics/drawable/AnimationDrawable$AnimationState;
move-result-object v0
return-object v0
.end method
.method public getDuration(I)I
.locals 1
.param p1, "i" # I
.prologue
.line 215
iget-object v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
# getter for: Landroid/graphics/drawable/AnimationDrawable$AnimationState;->mDurations:[I
invoke-static {v0}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->access$000(Landroid/graphics/drawable/AnimationDrawable$AnimationState;)[I
move-result-object v0
aget v0, v0, p1
return v0
.end method
.method public getFrame(I)Landroid/graphics/drawable/Drawable;
.locals 1
.param p1, "index" # I
.prologue
.line 207
iget-object v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
invoke-virtual {v0, p1}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->getChild(I)Landroid/graphics/drawable/Drawable;
move-result-object v0
return-object v0
.end method
.method public getNumberOfFrames()I
.locals 1
.prologue
.line 200
iget-object v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
invoke-virtual {v0}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->getChildCount()I
move-result v0
return v0
.end method
.method public inflate(Landroid/content/res/Resources;Lorg/xmlpull/v1/XmlPullParser;Landroid/util/AttributeSet;Landroid/content/res/Resources$Theme;)V
.locals 3
.param p1, "r" # Landroid/content/res/Resources;
.param p2, "parser" # Lorg/xmlpull/v1/XmlPullParser;
.param p3, "attrs" # Landroid/util/AttributeSet;
.param p4, "theme" # Landroid/content/res/Resources$Theme;
.annotation system Ldalvik/annotation/Throws;
value = {
Lorg/xmlpull/v1/XmlPullParserException;,
Ljava/io/IOException;
}
.end annotation
.prologue
const/4 v2, 0x0
.line 282
sget-object v1, Lcom/android/internal/R$styleable;->AnimationDrawable:[I
invoke-static {p1, p4, p3, v1}, Landroid/graphics/drawable/AnimationDrawable;->obtainAttributes(Landroid/content/res/Resources;Landroid/content/res/Resources$Theme;Landroid/util/AttributeSet;[I)Landroid/content/res/TypedArray;
move-result-object v0
.line 283
.local v0, "a":Landroid/content/res/TypedArray;
invoke-super {p0, p1, p2, v0, v2}, Landroid/graphics/drawable/DrawableContainer;->inflateWithAttributes(Landroid/content/res/Resources;Lorg/xmlpull/v1/XmlPullParser;Landroid/content/res/TypedArray;I)V
.line 284
invoke-direct {p0, v0}, Landroid/graphics/drawable/AnimationDrawable;->updateStateFromTypedArray(Landroid/content/res/TypedArray;)V
.line 285
invoke-virtual {v0}, Landroid/content/res/TypedArray;->recycle()V
.line 287
invoke-direct {p0, p1, p2, p3, p4}, Landroid/graphics/drawable/AnimationDrawable;->inflateChildElements(Landroid/content/res/Resources;Lorg/xmlpull/v1/XmlPullParser;Landroid/util/AttributeSet;Landroid/content/res/Resources$Theme;)V
.line 289
const/4 v1, 0x1
invoke-direct {p0, v2, v1, v2}, Landroid/graphics/drawable/AnimationDrawable;->setFrame(IZZ)V
.line 290
return-void
.end method
.method public isOneShot()Z
.locals 1
.prologue
.line 222
iget-object v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
# getter for: Landroid/graphics/drawable/AnimationDrawable$AnimationState;->mOneShot:Z
invoke-static {v0}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->access$100(Landroid/graphics/drawable/AnimationDrawable$AnimationState;)Z
move-result v0
return v0
.end method
.method public isRunning()Z
.locals 1
.prologue
.line 175
iget-boolean v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mRunning:Z
return v0
.end method
.method public mutate()Landroid/graphics/drawable/Drawable;
.locals 1
.prologue
.line 350
iget-boolean v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mMutated:Z
if-nez v0, :cond_0
invoke-super {p0}, Landroid/graphics/drawable/DrawableContainer;->mutate()Landroid/graphics/drawable/Drawable;
move-result-object v0
if-ne v0, p0, :cond_0
.line 351
iget-object v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
# invokes: Landroid/graphics/drawable/AnimationDrawable$AnimationState;->mutate()V
invoke-static {v0}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->access$200(Landroid/graphics/drawable/AnimationDrawable$AnimationState;)V
.line 352
const/4 v0, 0x1
iput-boolean v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mMutated:Z
.line 354
:cond_0
return-object p0
.end method
.method public run()V
.locals 1
.prologue
.line 186
const/4 v0, 0x0
invoke-direct {p0, v0}, Landroid/graphics/drawable/AnimationDrawable;->nextFrame(Z)V
.line 187
return-void
.end method
.method public setAnimationListener(Landroid/graphics/drawable/AnimationDrawable$AnimationListener;)V
.locals 0
.param p1, "listener" # Landroid/graphics/drawable/AnimationDrawable$AnimationListener;
.prologue
.line 435
iput-object p1, p0, Landroid/graphics/drawable/AnimationDrawable;->mListener:Landroid/graphics/drawable/AnimationDrawable$AnimationListener;
.line 436
return-void
.end method
.method protected setConstantState(Landroid/graphics/drawable/DrawableContainer$DrawableContainerState;)V
.locals 1
.param p1, "state" # Landroid/graphics/drawable/DrawableContainer$DrawableContainerState;
.prologue
.line 419
invoke-super {p0, p1}, Landroid/graphics/drawable/DrawableContainer;->setConstantState(Landroid/graphics/drawable/DrawableContainer$DrawableContainerState;)V
.line 421
instance-of v0, p1, Landroid/graphics/drawable/AnimationDrawable$AnimationState;
if-eqz v0, :cond_0
.line 422
check-cast p1, Landroid/graphics/drawable/AnimationDrawable$AnimationState;
.end local p1 # "state":Landroid/graphics/drawable/DrawableContainer$DrawableContainerState;
iput-object p1, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
.line 424
:cond_0
return-void
.end method
.method public setOneShot(Z)V
.locals 1
.param p1, "oneShot" # Z
.prologue
.line 231
iget-object v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
# setter for: Landroid/graphics/drawable/AnimationDrawable$AnimationState;->mOneShot:Z
invoke-static {v0, p1}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->access$102(Landroid/graphics/drawable/AnimationDrawable$AnimationState;Z)Z
.line 232
return-void
.end method
.method public setVisible(ZZ)Z
.locals 6
.param p1, "visible" # Z
.param p2, "restart" # Z
.prologue
const/4 v3, 0x1
const/4 v2, 0x0
.line 118
invoke-super {p0, p1, p2}, Landroid/graphics/drawable/DrawableContainer;->setVisible(ZZ)Z
move-result v0
.line 119
.local v0, "changed":Z
if-eqz p1, :cond_5
.line 120
if-nez p2, :cond_0
if-eqz v0, :cond_2
.line 121
:cond_0
if-nez p2, :cond_1
iget v4, p0, Landroid/graphics/drawable/AnimationDrawable;->mCurFrame:I
if-ltz v4, :cond_1
iget v4, p0, Landroid/graphics/drawable/AnimationDrawable;->mCurFrame:I
iget-object v5, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimationState:Landroid/graphics/drawable/AnimationDrawable$AnimationState;
invoke-virtual {v5}, Landroid/graphics/drawable/AnimationDrawable$AnimationState;->getChildCount()I
move-result v5
if-lt v4, v5, :cond_3
:cond_1
move v1, v3
.line 123
.local v1, "startFromZero":Z
:goto_0
if-eqz v1, :cond_4
:goto_1
iget-boolean v4, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimating:Z
invoke-direct {p0, v2, v3, v4}, Landroid/graphics/drawable/AnimationDrawable;->setFrame(IZZ)V
.line 128
.end local v1 # "startFromZero":Z
:cond_2
:goto_2
return v0
:cond_3
move v1, v2
.line 121
goto :goto_0
.line 123
.restart local v1 # "startFromZero":Z
:cond_4
iget v2, p0, Landroid/graphics/drawable/AnimationDrawable;->mCurFrame:I
goto :goto_1
.line 126
.end local v1 # "startFromZero":Z
:cond_5
invoke-virtual {p0, p0}, Landroid/graphics/drawable/AnimationDrawable;->unscheduleSelf(Ljava/lang/Runnable;)V
goto :goto_2
.end method
.method public start()V
.locals 1
.prologue
.line 145
const/4 v0, 0x1
iput-boolean v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimating:Z
.line 147
invoke-virtual {p0}, Landroid/graphics/drawable/AnimationDrawable;->isRunning()Z
move-result v0
if-nez v0, :cond_0
.line 148
invoke-virtual {p0}, Landroid/graphics/drawable/AnimationDrawable;->run()V
.line 150
:cond_0
return-void
.end method
.method public stop()V
.locals 1
.prologue
.line 161
const/4 v0, 0x0
iput-boolean v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mAnimating:Z
.line 163
invoke-virtual {p0}, Landroid/graphics/drawable/AnimationDrawable;->isRunning()Z
move-result v0
if-eqz v0, :cond_0
.line 164
invoke-virtual {p0, p0}, Landroid/graphics/drawable/AnimationDrawable;->unscheduleSelf(Ljava/lang/Runnable;)V
.line 166
:cond_0
return-void
.end method
.method public unscheduleSelf(Ljava/lang/Runnable;)V
.locals 1
.param p1, "what" # Ljava/lang/Runnable;
.prologue
.line 191
const/4 v0, -0x1
iput v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mCurFrame:I
.line 192
const/4 v0, 0x0
iput-boolean v0, p0, Landroid/graphics/drawable/AnimationDrawable;->mRunning:Z
.line 193
invoke-super {p0, p1}, Landroid/graphics/drawable/DrawableContainer;->unscheduleSelf(Ljava/lang/Runnable;)V
.line 194
return-void
.end method
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,070
|
GIVE MORE INFORMATION OTHER THAN JUST YOUR QUESTION IF I SEE OTHER ISSUES AS IMPORTANT ARISE.
99 % accurate with predictions. I read your current situations to unveil the truth of how they feel about you and where your relationship is headed.
Some predictions will take time to come out, I always recommend you write things down and watch before assuming I am wrong. Be open to possibilities or it will be more difficult to read you. NOTE: I will not lie so you can feel good at the end of the reading, if you do not want to hear the possible truth, for better or worse, don't call me. Things are not always the way you want them to be nor are they as they appear.
Major credit cards accepted through Paypal. If you do not wish to pay through Paypal, we will allow personal checks, Western Union, money orders. Readings will be read within 24-48 hours after payment has been received.
Learn about Paypal and sign up for a free account!
J. E. Bowser is the artist who painted this wonderful painting.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,148
|
{"url":"https:\/\/backendtea.com\/post\/phpunit-test-warnings\/","text":"# Testing code that generates warnings\n\ntrigger_error isn\u2019t the end of the world\n\nOur code base has a lot of code that looks like this:\n\ntry {\n$this->doScaryThing(); } catch(Exception$e) {\ntrigger_error(\"Downgraded: \" . get_class($e) . \":\" .$e->getMessage(), E_USER_WARNING);\n}\n\n\nOr sometimes trigger_error is used as a way to log other thigns. This makes it rather difficult to test. Thankfully PHPUnit 8.4 has the expectWarning method, that allows us to check this:\n\npublic function testItTriggersWarning(): void\n{\n$object = new Danger();$this->expectWarning();\n$object->doWarningThing(); } This does mean that the execution stops after the warning is triggered, so we can\u2019t assert anything after that. Thankfully we can still do it in a bit of a \u2018hackish\u2019 way: public function testItHasCorrectValueAfterWarning(): void {$object = new Danger()\n$ret = @$object->doWarningThing();\n$this->assertSame('good_value',$ret);\n}\n\n\nPersonally i like to add an @depends on that second test, so that it requires the test that it triggers a warning to pass before it is executed. Of course this does mean we need two tests per case, one for the triggering of the warning\/notice, and one where it is silenced so we can check the output. But it allows us to test the code, and maybe move to a better logging situation in the future.\n\n##### Gert de Pagter\n###### Software Engineer\n\nMy interests include software development, math and magic.","date":"2019-12-15 21:06:12","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.4136829078197479, \"perplexity\": 2214.6586286948705}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-51\/segments\/1575541310866.82\/warc\/CC-MAIN-20191215201305-20191215225305-00125.warc.gz\"}"}
| null | null |
Q: DEM data - Central Europe - noise in heights I have downloaded DEM data from this page: http://www.viewfinderpanoramas.org/dem3.html. I have written simple program in C++ that takes "bricks" and build resulting height map.
Hovewer, I have problem with result. I am using Mercator projection and take every "gps pixel" from DEM data and recalculate its position to real pixels (same for border). It works fine (or at least it seams to).
As you can see on image, there is something weird. That "mess" in lower part is incorrect and I dont know, if data are incorrect, if I am using them incorrect (wrong bricks ?) or something in my program is wrong.
EDIT:
Here is algorithm for reading "bricks" heights:
//iterate all bricks and set its starting coordinates
double startLon = 19;
double startLat = 48;
///-------------------------
int tileSize = 1201;
double step = 1.0 / tileSize;
for (int y = 0; y < tileSize; y++)
{
for (int x = 0; x < tileSize; x++)
{
short height = brick[x + (tileSize - 1 - y) * tileSize];
//tileSize - 1 - y -> reverse brick coordinates
height = swap_endian<short>(height);
if (height == -32768)
{
height = 0;
}
lon = (startLon) + x * step;
lat = (startLat - 1) + y * step;
int pixelX = 0;
int pixelY = 0;
this->helper->ConvertCoordinates(lon, lat, &pixelX, &pixelY);
if (pixelX < 0) { continue;}
if (pixelY < 0) { continue;}
if (pixelX >= this->width) { continue;}
if (pixelY >= this->height) { continue;}
//write it to map
//if multiple height in same pixel, take only last one
this->heightMap[pixelX + pixelY * this->width] = height;
}
}
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 4,949
|
Order food online in Bristol! It's so easy to use, fast and convenient. Try our new, online website which contains our entire takeaway menu. Oh Calcutta is located in Bristol.
Here at Oh Calcutta we are constantly striving to improve our service and quality in order to give our customers the very best experience. As a result, we are finally proud to unveil and introduce our latest improvement, our new online ordering website! You can now relax at home and order your favourite, freshly prepared meals from Oh Calcutta, online. You can even pay online!
Oh Calcutta in Bristol will always be offering great food at affordable prices. Please feel free to browse our new website and place your order online. Remember to check our new online ordering site to get up to date prices and exclusive special offers, limited to our online customers only!
Thank you for visiting Oh Calcutta in Bristol. We hope you enjoy our online ordering website and your food.
There is no better lamb biriyani in Bristol.
Really good as usual. Delivered quickly too. Arrived 20 minutes before the estimated delivery time !
Fast delivery and tasty food. Will order again.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,320
|
La Grenade participe aux Jeux olympiques d'été de 2008 à Pékin.
Athlètes engagés
Athlétisme
Hommes
Femmes
Boxe
Rolande Moses
Grenade
2008
2008 à la Grenade
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,288
|
<?php
/*namespace raelgc\view {*/
/**
* Template Management for PHP5
*
* The Template engine allows to keep the HTML code in some external files
* which are completely free of PHP code. This way, it's possible keep logical
* programmin (PHP code) away from visual structure (HTML or XML, CSS, etc).
*
* If you are familiar with PHP template concept, this class includes these
* features: object support, auto-detect blocks, auto-clean children blocks,
* warning when user call for a non-existent block, warning when a mal-formed
* block is detected, warning when user sets a non existant variable, and other
* minor features.
*
* @author Rael G.C. (rael.gc@gmail.com)
* @version 2.2
*/
class Template {
/**
* A list of existent document variables.
* @var array
*/
protected $vars = array();
/**
* A hash with vars and values setted by the user.
* @var array
*/
protected $values = array();
/**
* A hash of existent object properties variables in the document.
* @var array
*/
private $properties = array();
/**
* A hash of the object instances setted by the user.
* @var array
*/
protected $instances = array();
/**
* List of used modifiers
* @var array
*/
protected $modifiers = array();
/**
* A list of all automatic recognized blocks.
* @var array
*/
private $blocks = array();
/**
* A list of all blocks that contains at least a "child" block.
* @var array
*/
private $parents = array();
/**
* List of parsed blocks
* @var array
*/
private $parsed = array();
/**
* List of blocks to finalize
* @var array
*/
private $finally = array();
/**
* Describes the replace method for blocks. See the Template::setFile()
* method for more details.
* @var boolean
*/
private $accurate;
/**
* Regular expression to find var and block names.
* Only alfa-numeric chars and the underscore char are allowed.
*
* @var string
*/
private static $REG_NAME = "([[:alnum:]]|_)+";
/**
* Creates a new template, using $filename as main file.
*
* When the parameter $accurate is true, blocks will be replaced perfectly
* (in the parse time), e.g., removing all \t (tab) characters, making the
* final document an accurate version. This will impact (a lot) the
* performance. Usefull for files using the <pre> or <code> tags.
*
* @param string $filename file path of the file to be loaded
* @param booelan $accurate true for accurate block parsing
*/
public function __construct($filename, $accurate = false){
$this->accurate = $accurate;
$this->loadfile(".", $filename);
}
/**
* Put the content of $filename in the template variable identified by $varname
*
* @param string $varname existing template var
* @param string $filename file to be loaded
*/
public function addFile($varname, $filename){
if(!$this->exists($varname)) throw new \InvalidArgumentException("addFile: var $varname does not exist");
$this->loadfile($varname, $filename);
}
/**
* Do not use. Properties setter method
*
* @param string $varname template var name
* @param mixed $value template var value
*/
public function __set($varname, $value){
if(!$this->exists($varname)) throw new \RuntimeException("var $varname does not exist");
$stringValue = $value;
if(is_object($value)){
$this->instances[$varname] = $value;
if(!isset($this->properties[$varname])) $this->properties[$varname] = array();
if(method_exists($value, "__toString")) $stringValue = $value->__toString();
else $stringValue = "Object";
}
$this->setValue($varname, $stringValue);
return $value;
}
/**
* Do not use. Properties getter method.
*
* @param string $varname template var name
*/
public function __get($varname){
if(isset($this->values["{".$varname."}"])) return $this->values["{".$varname."}"];
elseif(isset($this->instances[$varname])) return $this->instances[$varname];
throw new \RuntimeException("var $varname does not exist");
}
/**
* Check if a template var exists.
*
* This method returns true if the template var exists. Otherwise, false.
*
* @param string $varname template var name
*/
public function exists($varname){
return in_array($varname, $this->vars);
}
/**
* Loads a file identified by $filename.
*
* The file will be loaded and the file's contents will be assigned as the
* variable's value.
* Additionally, this method call Template::identify() that identifies
* all blocks and variables automatically.
*
* @param string $varname contains the name of a variable to load
* @param string $filename file name to be loaded
*
* @return void
*/
private function loadfile($varname, $filename) {
if (!file_exists($filename)) throw new InvalidArgumentException("file $filename does not exist");
// If it's PHP file, parse it
if($this->isPHP($filename)){
ob_start();
require $filename;
$str = ob_get_contents();
ob_end_clean();
$this->setValue($varname, $str);
} else {
// Reading file and hiding comments
$str = preg_replace("/<!---.*?--->/smi", "", file_get_contents($filename));
if (empty($str)) throw new InvalidArgumentException("file $filename is empty");
$this->setValue($varname, $str);
$blocks = $this->identify($str, $varname);
$this->createBlocks($blocks);
}
}
/**
* Check if file is a .php
*/
private function isPHP($filename){
foreach(array('.php', '.php5', '.cgi') as $php){
if(0 == strcasecmp($php, substr($filename, strripos($filename, $php)))) return true;
}
return false;
}
/**
* Identify all blocks and variables automatically and return them.
*
* All variables and blocks are already identified at the moment when
* user calls Template::setFile(). This method calls Template::identifyVars()
* and Template::identifyBlocks() methods to do the job.
*
* @param string $content file content
* @param string $varname contains the variable name of the file
*
* @return array an array where the key is the block name and the value is an
* array with the children block names.
*/
private function identify(&$content, $varname){
$blocks = array();
$queued_blocks = array();
$this->identifyVars($content);
foreach (explode("\n", $content) as $line) {
if (strpos($line, "<!--")!==false) $this->identifyBlocks($line, $varname, $queued_blocks, $blocks);
}
return $blocks;
}
/**
* Identify all user defined blocks automatically.
*
* @param string $line contains one line of the content file
* @param string $varname contains the filename variable identifier
* @param string $queued_blocks contains a list of the current queued blocks
* @param string $blocks contains a list of all identified blocks in the current file
*
* @return void
*/
private function identifyBlocks(&$line, $varname, &$queued_blocks, &$blocks){
$reg = "/<!--\s*BEGIN\s+(".self::$REG_NAME.")\s*-->/sm";
preg_match($reg, $line, $m);
if (1==preg_match($reg, $line, $m)){
if (0==sizeof($queued_blocks)) $parent = $varname;
else $parent = end($queued_blocks);
if (!isset($blocks[$parent])){
$blocks[$parent] = array();
}
$blocks[$parent][] = $m[1];
$queued_blocks[] = $m[1];
}
$reg = "/<!--\s*END\s+(".self::$REG_NAME.")\s*-->/sm";
if (1==preg_match($reg, $line)) array_pop($queued_blocks);
}
/**
* Identifies all variables defined in the document.
*
* @param string $content file content
*/
private function identifyVars(&$content){
$r = preg_match_all("/{(".self::$REG_NAME.")((\-\>(".self::$REG_NAME."))*)?((\|.*?)*)?}/", $content, $m);
if ($r){
for($i=0; $i<$r; $i++){
// Object var detected
if($m[3][$i] && (!isset($this->properties[$m[1][$i]]) || !in_array($m[3][$i], $this->properties[$m[1][$i]]))){
$this->properties[$m[1][$i]][] = $m[3][$i];
}
// Modifiers detected
if($m[7][$i] && (!isset($this->modifiers[$m[1][$i]]) || !in_array($m[7][$i], $this->modifiers[$m[1][$i].$m[3][$i]]))){
$this->modifiers[$m[1][$i].$m[3][$i]][] = $m[1][$i].$m[3][$i].$m[7][$i];
}
// Common variables
if(!in_array($m[1][$i], $this->vars)){
$this->vars[] = $m[1][$i];
}
}
}
}
/**
* Create all identified blocks given by Template::identifyBlocks().
*
* @param array $blocks contains all identified block names
* @return void
*/
private function createBlocks(&$blocks) {
$this->parents = array_merge($this->parents, $blocks);
foreach($blocks as $parent => $block){
foreach($block as $chield){
if(in_array($chield, $this->blocks)) throw new \UnexpectedValueException("duplicated block: $chield");
$this->blocks[] = $chield;
$this->setBlock($parent, $chield);
}
}
}
/**
* A variable $parent may contain a variable block defined by:
* <!-- BEGIN $varname --> content <!-- END $varname -->.
*
* This method removes that block from $parent and replaces it with a variable
* reference named $block.
* Blocks may be nested.
*
* @param string $parent contains the name of the parent variable
* @param string $block contains the name of the block to be replaced
* @return void
*/
private function setBlock($parent, $block) {
$name = $block.'_value';
$str = $this->getVar($parent);
if($this->accurate){
$str = str_replace("\r\n", "\n", $str);
$reg = "/\t*<!--\s*BEGIN\s+$block\s+-->\n*(\s*.*?\n?)\t*<!--\s+END\s+$block\s*-->\n*((\s*.*?\n?)\t*<!--\s+FINALLY\s+$block\s*-->\n?)?/sm";
}
else $reg = "/<!--\s*BEGIN\s+$block\s+-->\s*(\s*.*?\s*)<!--\s+END\s+$block\s*-->\s*((\s*.*?\s*)<!--\s+FINALLY\s+$block\s*-->)?\s*/sm";
if(1!==preg_match($reg, $str, $m)) throw new \UnexpectedValueException("mal-formed block $block");
$this->setValue($name, '');
$this->setValue($block, $m[1]);
$this->setValue($parent, preg_replace($reg, "{".$name."}", $str));
if(isset($m[3])) $this->finally[$block] = $m[3];
}
/**
* Internal setValue() method.
*
* The main difference between this and Template::__set() method is this
* method cannot be called by the user, and can be called using variables or
* blocks as parameters.
*
* @param string $varname constains a varname
* @param string $value constains the new value for the variable
* @return void
*/
protected function setValue($varname, $value) {
$this->values['{'.$varname.'}'] = $value;
}
/**
* Returns the value of the variable identified by $varname.
*
* @param string $varname the name of the variable to get the value of
* @return string the value of the variable passed as argument
*/
private function getVar($varname) {
return $this->values['{'.$varname.'}'];
}
/**
* Clear the value of a variable.
*
* Alias for $this->setValue($varname, "");
*
* @param string $varname var name to be cleaned
* @return void
*/
public function clear($varname) {
$this->setValue($varname, "");
}
/**
* Manually assign a child block to a parent block
*
* @param string $parent parent block
* @param string $block child block
*/
public function setParent($parent, $block){
$this->parents[$parent][] = $block;
}
/**
* Subst modifiers content
*
* @param string $value text to be modified
* @param $exp
* @return unknown_type
*/
private function substModifiers($value, $exp){
$statements = explode('|', $exp);
for($i=1; $i<sizeof($statements); $i++){
$temp = explode(":", $statements[$i]);
$function = $temp[0];
$parameters = array_diff($temp, array($function));
$value = call_user_func_array($function, array_merge(array($value), $parameters));
}
return $value;
}
/**
* Fill in all the variables contained in variable named $value.
* $value. The resulting string is not "cleaned" yet.
*
* @param string $value var value
* @return string content with all variables substituted.
*/
protected function subst($value) {
// Common variables replacement
$s = str_replace(array_keys($this->values), $this->values, $value);
// Common variables with modifiers
foreach($this->modifiers as $var => $expressions){
if(false!==strpos($s, "{".$var."|")) foreach($expressions as $exp){
if(false===strpos($var, "->") && isset($this->values['{'.$var.'}'])){
$s = str_replace('{'.$exp.'}', $this->substModifiers($this->values['{'.$var.'}'], $exp), $s);
}
}
}
// Object variables replacement
foreach($this->instances as $var => $instance){
foreach($this->properties[$var] as $properties){
if(false!==strpos($s, "{".$var.$properties."}") || false!==strpos($s, "{".$var.$properties."|")){
$pointer = $instance;
$property = explode("->", $properties);
for($i = 1; $i < sizeof($property); $i++){
if(!is_null($pointer)){
$obj = strtolower(str_replace('_', '', $property[$i]));
// Get accessor
if(method_exists($pointer, "get$obj")) $pointer = $pointer->{"get$obj"}();
// Magic __get accessor
elseif(method_exists($pointer, "__get")) $pointer = $pointer->__get($property[$i]);
// Property acessor
elseif(property_exists($pointer, $obj)) $pointer = $pointer->$obj;
else {
$className = $property[$i-1] ? $property[$i-1] : get_class($instance);
$class = is_null($pointer) ? "NULL" : get_class($pointer);
throw new \BadMethodCallException("no accessor method in class ".$class." for ".$className."->".$property[$i]);
}
} else {
$pointer = $instance->get($obj);
}
}
// Checking if final value is an object...
if(is_object($pointer)){
$pointer = method_exists($pointer, "__toString") ? $pointer->__toString() : "Object";
// ... or an array
} elseif(is_array($pointer)){
$value = "";
for($i=0; list($key, $val) = each($pointer); $i++){
$value.= "$key => $val";
if($i<sizeof($pointer)-1) $value.= ",";
}
$pointer = $value;
}
// Replacing value
$s = str_replace("{".$var.$properties."}", $pointer, $s);
// Object with modifiers
if(isset($this->modifiers[$var.$properties])){
foreach($this->modifiers[$var.$properties] as $exp){
$s = str_replace('{'.$exp.'}', $this->substModifiers($pointer, $exp), $s);
}
}
}
}
}
return $s;
}
/**
* Show a block.
*
* This method must be called when a block must be showed.
* Otherwise, the block will not appear in the resultant
* content.
*
* @param string $block the block name to be parsed
*/
public function block($block) {
if(!in_array($block, $this->blocks)) throw new \InvalidArgumentException("block $block does not exist");
// Checking finally blocks inside this block
if(isset($this->parents[$block])) foreach($this->parents[$block] as $child){
if(isset($this->finally[$child]) && !in_array($child, $this->parsed)){
$this->setValue($child.'_value', $this->subst($this->finally[$child]));
$this->parsed[] = $block;
}
}
$this->setValue($block.'_value', $this->getVar($block.'_value') . $this->subst($this->getVar($block)));
if(!in_array($block, $this->parsed)) $this->parsed[] = $block;
// Cleaning children
if(isset($this->parents[$block])) foreach($this->parents[$block] as $child) $this->clear($child.'_value');
}
/**
* Returns the final content
*
* @return string
*/
public function parse() {
// Auto assistance for parse children blocks
foreach(array_reverse($this->parents) as $parent => $children){
foreach($children as $block){
if(in_array($parent, $this->blocks) && in_array($block, $this->parsed) && !in_array($parent, $this->parsed)){
$this->setValue($parent.'_value', $this->subst($this->getVar($parent)));
$this->parsed[] = $parent;
}
}
}
// Parsing finally blocks
foreach($this->finally as $block => $content){
if(!in_array($block, $this->parsed)){
$this->setValue($block.'_value', $this->subst($content));
}
}
// After subst, remove empty vars
return preg_replace("/{(".self::$REG_NAME.")((\-\>(".self::$REG_NAME."))*)?((\|.*?)*)?}/", "", $this->subst($this->getVar(".")));
}
/**
* Print the final content.
*/
public function show() {
echo $this->parse();
}
}
/*}
*/
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,372
|
The UCI gem allows for a much more ruby-like way of communicating with chess
engines that support the UCI protocol.
## Installation
NOTE: No Chess engines are included. You must install an appropriate UCI-compatible engine first.
Standard installation applies. Either:
gem install uci
..or, in a bundled project, add this line to your application's Gemfile:
gem 'uci'
And then execute:
$ bundle
## Example
```ruby
require 'uci'
uci = Uci.new( :engine_path => '/usr/local/bin/stockfish' )
while !uci.ready? do
puts "Engine isn't ready yet, sleeping..."
sleep(1)
end
# this loop will make the engine play against itself.
loop do
puts "Move ##{uci.moves.size+1}."
puts uci.board # print ascii layout of current board.
uci.go!
end
```
## Docs
### ::new(options = {})
make a new connection to a UCI engine
<pre>
Uci.new(
:engine_path => '/path/to/executable',
:debug => false, # true or false, default false
:name => "Name of engine", # optional
:movetime => 100, # max amount of time engine can "think" in ms - default 100
:options => { "Navalov Cache" => true } # optional configuration for engine
)
</pre>
### #bestmove()
Ask the chess engine what the "best move" is given the current state of the
internal chess board. This does not actiually execute a move, it simply queries
for and returns what the engine would consider to be the best option available.
### #board(empty_square_char = '.')
ASCII-art representation of the current internal board.
<pre>
> puts board
ABCDEFGH
8 r.bqkbnr
7 pppppppp
6 n.......
5 ........
4 .P......
3 ........
2 P.PPPPPP
1 RNBQKBNR
</pre>
### clear_position(position)
Clear a position on the board, regardless of occupied state
### engine_name()
Return the current engine name
### fenstring()
Return the state of the interal board in a FEN (Forsyth–Edwards Notation)
string, SHORT format (no castling info, move, etc).
### get_piece(position)
Get the details of a piece at the current position raises
NoPieceAtPositionError if position is unoccupied.
Returns array of [:piece, :player].
<pre>
> get_piece("a2")
> [:pawn, :white]
</pre>
### go!()
Tell the engine what the current board layout it, get its best move AND
execute that move on the current board.
### move_piece(move_string)
Move a piece on the current interal board. Will raise NoPieceAtPositionError
if source position is unoccupied. If destination is occipied, the occupying
piece will be removed from the game.
move_string is algebraic standard notation of the chess move. Shorthand is
not allowed.
<pre>
move_piece("a2a3") # Simple movement
move_piece("e1g1") # Castling (king's rook white)
move_piece("a7a8q" # Pawn promomition (to Queen)
</pre>
Note that there is minimal rule checking here, illegal moves will be executed.
### new_game!()
Send "ucinewgame" to engine, reset interal board to standard starting layout.
### new_game?()
True if no moves have been recorded yet.
### piece_at?(position)
returns a boolean if a position is occupied
<pre>
> piece_at?("a2")
> true
> piece_at?("a3")
> false
</pre>
### piece_name(p)
Returns the piece name OR the piece icon, depending on that was passes.
<pre>
> piece_name(:n)
> :knight
> piece_name(:queen)
> "q"
</pre>
### place_piece(player, piece, position)
Place a piece on the board, regardless of occupied state.
* player - symbol: :black or :white
* piece - symbol: :pawn, :rook, etc
* position - a2, etc
<pre>
place_piece(:black, :rook, "h1")
</pre>
### ready?()
True if engine is ready, false if not yet ready.
### send_position_to_engine()
Write board position information to the UCI engine, either the starting
position and move log or the current FEN string, depending on how the
board was set up.
This does not tell the engine to execute a move.
### set_board(fen)
Set the board using Forsyth–Edwards Notation (FEN), LONG format including
current player, castling, etc.
* fen - rnbqkbnr/pppppppp/8/8/4P3/8/PPPP1PPP/RNBQKBNR b KQkq - 0 1 (Please
see en.wikipedia.org/wiki/Forsyth%E2%80%93Edwards_Notation)
## Supported Engines
In theory it can support any UCI-compatible engine (except for conditions outlined in the 'caveats' section). It has been tested with:
* Stockfish (Jan 11 2013 Github source)
* Fruit 2.3.1 (Mac)
## Caveats
#### No move checking
This gem assumes the engine knows what it's doing. If the gem wishes to place a illegal move it will be accepted.
#### Unix-style Line endings are assumed.
Current version assumes unix-style ("\n") line endings. That means running this under MS-DOS or Windows may barf.
#### Very limited command set.
Very few commands of the total UCI command set are currently supported. they are:
* Starting a new game
* Setting positions
* Getting best move
* Setting options
It DOES NOT _yet_ support:
* 'uci' command
* ponder mode / infinite mode
* ponderhit
* registrations
## Known Issues
When connecting to more than one engine from the same code, there is a problem where their input streams get crosses. This is an issue with Open3, but for some reason turning "debug" on seems to mitigate it.
Open3 is supposed to work under in Ruby 1.9.x in Windows, but this is currently untested.
## Contributing
Ruby UCI needs support for more features and to be tested with more chess
engines. To contribute to this project please fork the project and add/change
any new code inside of a new branch:
git checkout -b my-new-feature
Before committing and pushing code, please make sure all existing tests pass
and that all new code has tests. Once that is verified, please push the changes
and create a new pull request.
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{
"redpajama_set_name": "RedPajamaGithub"
}
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L'Orbital Piloted Assembly and Experiment Complex (, Orbitalnyj Pilotiruiemyj Sboročno-Ekspierimientalnyj Komplieks)
(ОПСЭК, OPSEK) és una proposta d'estació espacial modular de tercera generació en òrbita terrestre baixa. L'OPSEK estaria formada de mòduls del segment orbital rus de l'Estació Espacial Internacional (ISS). La proposta seria utilitzar l'OPSEK per muntar components de naus espacials tripulades interplanetàries destinades a Mart, la Lluna, i possiblement Saturn. La tripulació de tornada també es recuperaria a l'estació abans d'aterrar a la Terra. Aquesta estació espacial russa formaria part d'una xarxa d'espai profund, donant suport a l'exploració tripulada del sistema solar.
Referències
Enllaços externs
OPSEK information page
Presentation, by Head of Russian Federal Space Agency, June 17, 2009
Estació Espacial Internacional
Naus espacials proposades
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,898
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Surfnetkids » Resources » Language Arts, Reference » Reading » A Good Mystery
A Good Mystery
September 27, 2000 by Barbara Feldman
Readers of all ages love to be transported from everyday life, and a good mystery story is the perfect escape. In this limited space, though, I can't even begin to introduce authors such as Edgar Allen Poe, Sir Arthur Conan Doyle and Agatha Christie. But hopefully today's five sites will teach you a bit about this popular genre, and either introduce you to an new author or reacquaint you with one you've long ignored.
Cyber.Kdz4 stars
What if the Hardy Boys or Sherlock Holmes had Internet access? Bruce Balan's Cyber.Kdz series is the first juvenile mystery to include junior sleuths from around the world who use the Internet as a communication and research tool. At the Cyber.Kdz site you can read chapters from the six books, meet the seven characters and peruse the Cyber.Kdz slang dictionary. Working as I do on the Internet all day long, it's great to see the Net integrated into a good story line for cyber-saavy readers (grades three to six.)
Mystery Greats Time Line5 stars
"The fascination with mystery and crime can be traced back to Ancient Greece, where playwrights like Sophocles and Euripides enthralled the local citizenry with their plays combining mystery and drama. In first-century B.C. Rome, Cicero argued passionately in court in defense of accused criminals, captivating Romans with his speeches. Read our evolution of the mystery in Time Line, and you'll see that the Ancient Greeks and Romans weren't so different from modern-day mystery fans." This captivating time line is just a taste of all that the fabulous MysteryNet has to offer. It's my pick of the day!
Nancy Drew5 stars
"In 1930, an American heroine was born -- a teenage detective named Nancy Drew. In the nearly seven decades that have since passed, Nancy has matured from sixteen to eighteen years old while solving over 350 mysteries." I am one of the many generations of girls that loved Nancy's can-do attitude, and although my daughter has yet to be bitten by the Nancy Drew bug, I am hoping she will soon. NancyDrew.com features an interactive mystery, chapters from selected books, a Shockwave game, discussion board and Nancy Drew lesson plans.
Sherlockian
Feldman, Barbara. "A Good Mystery." Surfnetkids. Feldman Publishing. 27 Sep. 2000. Web. 17 Jan. 2021. <https://www.surfnetkids.com/resources/mystery/ >.
By Barbara J. Feldman. Originally published September 27, 2000. Last modified October 17, 2017.
Filed Under: Language Arts, Reference, Reading
A Good Mystery Reader Reviews
Web Search for A Good Mystery
Famous Mystery Authors & Characters Word Search
►History, Holidays (790)
▼Language Arts, Reference (391)
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
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William B. Thompson, husband of Delores (Burchfield) Thompson for 64 years, passed away July 18, 2018 at the age of 84. b Born February 1, 1934 in Steubenville, Ohio, son of the late Lawrence and Thelma Thompson.
He is survived by his wife and two children, Pennie L. Rayburn of Steubenville, OH and William Barry Thompson, Jr. of Deltona, FL.
William was preceded in death by one brother, Lawrence (Boog) L. Thompson.
William retired as treasurer of D. Russell Lee Vocational School. William was a member of Crestview Presbyterian Church, West Chester, OH and served as past treasurer and member of Empty Nesters. Bill was active at First Westminster Church in Steubenville, OH where he served as elder, trustee, clerk of session, deacon, and Sunday school teacher. William also served eight years on the Indian Creek Board of Education. Bill also served four years in the U.S. Navy Reserves.
A memorial service will be held 10 a.m. Friday, July 27, 2018, at the Crestview Presbyterian Church, 9463 Cincinnati-Columbus Road, West Chester, OH. Interment in the Memorial Garden at Crestview Presbyterian Church.
In lieu of flowers, memorial contributions may be sent to Crestview Presbyterian Memorial Garden or Queen City Hospice, 8250 Kenwood Crossing Way, Suite 200, Cincinnati, OH 45236.
|
{
"redpajama_set_name": "RedPajamaC4"
}
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\section{\label{intro}Introduction}
Anyons are quasiparticles with topological, and therefore non-local, properties \cite{Wilczek,Pachos2}, that may be realized on two-dimensional systems \cite{Laughlin,Read,Freedman,Wen,Levin,Fendley,Wootton}. There has been a number anyon-based proposals for the storage and manipulation of quantum information. Many of these proposals deal with so-called Abelian anyons, encoding quantum information in quasiparticle occupancies \cite{Lloyd,me,qpl} or ground state degeneracies \cite{Dennis}. Others utilize cluster state quantum computation \cite{Raussendorf}. In all cases one obtains a topologically protected quantum memory, but this protection does not extend to the processing of the stored information.
Non-Abelian anyon models possess quasiparticles with more complex behaviour than their Abelian counterparts \cite{Kitaev2}. Specifically, local measurements on two such quasiparticles cannot determine how they will behave if brought together as composite object. This non-local degree of freedom, known as the fusion channel of the two anyons, is ideal to encode quantum information, protecting against local errors as long as the nature of the anyons is not affected. The energy gap associated with the anyons ensures that there is a threshold error rate before this may occur. Furthermore, processing the information contained in non-Abelian anyons is possible while remaining within the energy gap, and so has the same advantages as adiabatic quantum computation \cite{gold}.
Computational schemes with non-Abelian anyons are usually presented at an abstract level \cite{Bravyi,Georgiev}, while those using Abelian anyons are often more explicit \cite{Dennis,Raussendorf}. This means that, though non-Abelian schemes provide the most promising proposals for fault-tolerant quantum computation, it is Abelian schemes that are better understood in terms of their underlying systems. Here we propose a quantum memory using non-Abelian anyons of the $D(S_3)$ model, expressed explicitly in terms of the underlying spin lattice. This provides an opportunity to perform in-depth studies of the non-Abelian storage. Universal quantum computation is possible when the full $D(S_3)$ model is used \cite{mochon,Aguado}, but we restrict ourselves to a non-universal sub-model. This is because the memory is our primary concern, which can be more thoroughly studied when less anyon types are considered. It also gives us an opportunity to consider how to achieve universality by non-topological operations \cite{Raussendorf,bk,Bravyi,qpl}, and to see how they these work in terms of the underlying spins.
\subsection{The $D(S_3)$ anyon model}
Stabilizer codes, strictly defined, are based on lattices of two level spins and the corresponding Pauli group of operators \cite{Gottesman}. The quantum double models of anyons, proposed by Kitaev \cite{Kitaev2}, use a generalization of this concept. Spins of higher dimensions are employed, with operators based upon group structures. Abelian groups give rise to Abelian anyons, while non-Abelian groups lead to non-Abelian anyons. Here we consider the simplest non-Abelian model, $D(S_3)$, whose explicit lattice realization was outlined in \cite{Aguado}. This provides the tools with which we build our computational scheme. The relevant aspects of the model are summarized below.
The $D(S_3)$ anyon model is defined on an oriented two-dimensional square lattice. On each edge there resides a six-level spin spanned by the states $\ket{g}$, where $g$ is an element of $S_3$, the permutation group of three objects. We express every element in terms of generators $t$ and $c$, which satisfy $t^2 = c^3 = e$ and $tc = c^2 t$. $e$ denotes the trivial element. Using this notation the six elements are given by $S_3 = \{ e, c, c^2, t, tc, tc^2 \}$.
\begin{figure}[ht]
\begin{center}
{\includegraphics[scale=.5]{fig1.eps} }
\caption{\label{fig1}A pictorial representation of the vertex operators $T_g (v)$.}
\end{center}
\end{figure}
Define a vertex operator acting on vertex $v$ by,
\begin{equation}
T_g(v) = R_g (e_1) R_g (e_2) L_{g^{-1}} (e_3) L_{g^{-1}} (e_4), \quad [T_g(v), T_h(v')] = 0,
\end{equation}
where the $e_i$ are the four edges connected to vertex $v$ (see Fig. \ref{fig1}). Here $R_g(e)$ and $L_g(e)$ denote the right and left multiplication, respectively, of the local spin state on edge $e$ by the element $g$. To be precise, they act as $R_g\ket{h} = \ket{hg}$ and $L_g\ket{h}=\ket{gh}$. For the purposes of our topological memory, we consider only the so-called charge anyons associated with the vertices of the lattice. There are two non-trivial charges, which we call $\Lambda$ and $\Phi$, and the trivial vacuum charge, $1$. When $\ket{\Psi}$ denotes a general state of the system, the presence of a charge of type $A$ at vertex $v$ is defined by $P_{A}\ket{\Psi}=\ket{\Psi}$, where the orthogonal projectors are given by,
\begin{eqnarray} \label{p} \nonumber
P_{1}(v) &=& \frac{1}{6}[T_e (v) + T_c (v) + T_{c^2} (v) + T_t (v) + T_{tc} (v) + T_{tc^2} (v))], \\ \nonumber
P_{\Lambda}(v) &=& \frac{1}{6}[T_e (v) + T_c (v) + T_{c^2} (v) - T_t (v) - T_{tc} (v) - T_{tc^2} (v)], \\ \nonumber
P_{\Phi}(v) &=& \frac{1}{3}[2T_e (v) - T_c (v) - T_{c^2} (v)]. \nonumber
\end{eqnarray}
Projectors are also defined for the states of flux anyons on plaquettes, but we need not give them here.
The stabilizer space consists of states with no anyons, i.e. those for which $P_1(v)\ket{\textrm{gs}}=\ket{\textrm{gs}}$ for all $v$, and a similar condition for the fluxes on plaquettes. The syndrome measurement is defined as a measurement of anyon occupancies, and so corresponds to the above projectors. A Hamiltonian may be defined to maintain the stabilizer space. This assigns energy to the states of the anyons, and thus suppresses their spontaneous creation. This may be expressed,
\begin{equation}
H = -\sum_v P_{1}(v) -\sum_p P_1 (p).
\end{equation}
Charge anyons are created from the stabilizer space by acting with the following operators on single spins,
\begin{eqnarray}
W_{\Lambda}(e) & = & \ket{e}\bra{e} + \ket{c}\bra{c} + \ket{c^2}\bra{c^2} \nonumber \\
\ & \ & \qquad - \ket{t}\bra{t} - \ket{tc}\bra{tc} - \ket{tc^2}\bra{tc^2}, \label{Wlambda} \\
W_{\Phi}(e) & = & 2 \ket{e}\bra{e} - \ket{c}\bra{c} - \ket{c^2}\bra{c^2} \label{Wphi}.
\end{eqnarray}
These create charges on the two vertices connected by the edge $e$. A protocol to create and move charges several edges apart is given in \cite{Aguado}.
When charges of different type are brought to the same vertex, the possible outcomes are given by the fusion rules,
\begin{equation}
\Lambda \times \Lambda = 1, \,\,\, \Lambda \times \Phi = \Phi, \,\,\, \Phi \times \Phi = 1 + \Lambda + \Phi.
\end{equation}
The last implies that the $\Phi$ charges have three possible fusion channels; a pair may fuse to the trivial charge $1$, a $\Lambda$ or a $\Phi$. We may utilize the encoding of topological quantum computation \cite{Pachos2}, associating each possible outcome with a quantum state and hence using them to store quantum information. This information will be topologically protected due to the finite energy gap and the non-local encoding. However, the charges have trivial mutual statistics meaning that information processing by purely topological means is not possible. To achieve universal quantum computation, we propose non-topological operations to harness the power of the underlying spin lattice. As stated in \cite{Bravyi}, abstract treatments of such quantum gates tend to be speculative. However, we have the means to study these gates explicitly in terms of spin operations.
\section{\label{lambda}The computation with $\Lambda$ charges alone}
Though we are using a stabilizer code, the encoding described above is not within the stabilizer space. This allows similar protection from errors, yet easier manipulation. The basic principles of our scheme for universal quantum computation are first presented using the $\Lambda$ charges alone. Topological protection is introduced later by encoding the $\Lambda$ charges within the fusion channels of $\Phi$'s, making the logical states indistinguishable by the stabilizer.
Consider two neighbouring vertices, $v_1$ and $v_2$, connected by the edge, $e_a$ (see Fig. \ref{fig2}(a)). The two vertices may be used to store a logical qubit $a$ by identifying trivial charge or a pair of $\Lambda$ charges at both $v_1$ and $v_2$ with the logical qubit states $\ket{0}_a$ and $\ket{1}_a$, respectively. Explicitly,
\begin{eqnarray} \nonumber
\ket{0}_a &=& \ket{\rm gs}, \\
\ket{1}_a &=& W_{\Lambda}(e_a) \ket{\rm gs}.
\end{eqnarray}
These states are also expressed in Fig. \ref{fig2}(b).
\begin{figure}[ht]
\begin{center}
{\includegraphics[scale=.75]{fig2.eps} }
\caption{\label{fig2}(a) Two vertices use to store a logical qubit. (b) The logical states are stored by placing the trivial charge, $1$, or the charge $\Lambda$ at each vertex.}
\end{center}
\end{figure}
Measurement in the $Z$ basis requires measurement of either vertex's occupancy, using the four-spin projectors of Eq.(\ref{p}). The logical $X$ is realized by $W_{\Lambda}(e_a)$, hence all operations diagonal in the $X$ basis act on the spin $e_a$ alone. The relation $\ket{\pm} \bra{\pm} = (I \pm X)/2$ may be used to write the $X$ basis projectors in terms of the lattice spins,
\begin{eqnarray} \nonumber
\ket{+}_a \bra{+} &=& \frac{I + W_{\Lambda}(e_a)}{2} = \ket{e}_{e_a}\bra{e} + \ket{c}_{e_a}\bra{c} + \ket{c^2}_{e_a}\bra{c^2}, \\
\ket{-}_a \bra{-} &=& \frac{I - W_{\Lambda}(e_a)}{2} = \ket{t}_{e_a}\bra{t} + \ket{tc}_{e_a}\bra{tc} + \ket{tc^2}_{e_a}\bra{tc^2}.
\end{eqnarray}
Measurement in the $X$ basis is therefore achieved by measuring the lattice spin in the above subspaces. Arbitrary phase gates in the $X$ basis may then be written,
\begin{eqnarray} \nonumber
U_{\theta}(e_a) &=& \ket{+}_a \bra{+} + e^{i \theta} \ket{-}_a \bra{-} \\ \nonumber
&=& \Big(\ket{e}_{e_a} \bra{e} + \ket{c}_{e_a}\bra{c} + \ket{c^2}_{e_a} \bra{c^2} \Big) \\
&+& e^{i \theta} \Big(\ket{t}_{e_a} \bra{t} + \ket{tc}_{e_a}\bra{tc} + \ket{tc^2}_{e_a}\bra{tc^2} \Big).
\end{eqnarray}
These may be easily performed with single spin rotations.
Entanglement with another logical qubit, $b$, stored on another pair of vertices with shared spin $e_b$, may be achieved by the phase-controlled-NOT gate. This is diagonal in the $X$ basis of both qubits, and acts only on $e_a$ and $e_b$. It may be expressed as follows,
\begin{equation}
K_{a,b} = \ket{+}_a \bra{+} \otimes I_b + \ket{-}_a \bra{-} \otimes X_b = I + W_{\Lambda}(e_a) + W_{\Lambda}(e_b) - W_{\Lambda}(e_b) W_{\Lambda}(e_b).
\end{equation}
These operations form a universal gate set for quantum computation. For example, a Hadamard may be implemented on an arbitrary state $\ket\psi = \alpha \ket{+}_a + \beta \ket{-}_a$ of qubit $a$ as follows. Firstly, qubit $b$ is prepared in the state $\ket{0}_b$, and then entangled to $a$ using $K_{a,b}$. The resulting state is,
\begin{eqnarray} \nonumber
\alpha \ket{+0}_{a,b} + \beta \ket{-1}_{a,b} &=& \frac{1}{\sqrt{2}} \Big( \alpha \ket{00}_{a,b} + \alpha \ket{10}_{a,b} + \beta \ket{01}_{a,b} - \beta \ket{11}_{a,b} \Big) \\
&=& \frac{1}{\sqrt{2}} \Big( \ket{0}_a (H\ket{\psi}_b) + \ket{1}_a (ZH\ket{\psi}_b) \Big).
\end{eqnarray}
Measuring qubit $a$ in the $Z$ basis then yields the state $H \ket{\psi}$ on qubit $b$, followed by a $Z$ if the outcome of the measurement is $\ket{1}_a$. In the latter case the process may be repeated until the error is corrected and a Hadamard alone is implemented. With this Hadamard and the arbitrary phase gates in the $X$ basis, arbitrary single qubit unitaries may be performed. With the entangling gate, this leads to universal quantum computation \cite{ike+mike}.
\section{\label{phi}Fault-tolerance using non-Abelian charges}
We will now extend the encoding by using $\Phi$ charges to hide the $\Lambda$'s. We first consider the most straightforward way of doing this, and then explore an alternative method.
Let us consider four neighbouring vertices, as shown in Fig. \ref{fig3}(a). Pairs of $\Phi$ charges carrying the trivial fusion channel may be created from the ground state with $W_{\Phi}$ (\ref{Wphi}).
Applying this to spins $e^{1,4}_a$ and $e^{2,3}_a$ creates a pair carrying the trivial fusion channel on $v_1$ and $v_4$, and another on $v_2$ and $v_3$. This state is identified with the logical qubit state $\ket{0}_a$. By applying $W_{\Lambda}(e^{1,2}_a)$, a $\Lambda$ charge is fused with a $\Phi$ from each pair again resulting in two $\Phi$ pairs except that they now belong to the $\Lambda$ fusion channel. This state is identified with the logical qubit state $\ket{1}_a$. Explicitly,
\begin{eqnarray} \label{log} \nonumber
\ket{0}_a &=& W_{\Phi}(e^{1,4}_a) W_{\Phi}(e^{2,3}_a) \ket{\rm gs}, \\
\ket{1}_a &=& W_{\Phi}(e^{1,4}_a) W_{\Phi}(e^{2,3}_a) W_{\Lambda}(e^{1,2}_a) \ket{\rm gs}.
\end{eqnarray}
These states are also expressed in Fig. \ref{fig3}(b). Further logical qubits may be stored on other sets of four $\Phi$ charges. The syndrome measurements will see only the $\Phi$ charges and not the $\Lambda$ charges they contain, making the logical states indistinguishable by local measurements alone, and degenerate under the Hamiltonian.
\begin{figure}[ht]
\begin{center}
{\includegraphics[scale=1]{fig3.eps} }
\caption{\label{fig3}(a) Four vertices use to store a logical qubit. These are labelled from $v_1$ to $v_4$, starting from the top left and proceeding anticlockwise. The spin along the side connecting the vertices $v_i$ and $v_j$ is denoted $e^{i,j}_a$. (b) Both logical states use a $\Phi$ charge at each vertex. The only difference is that two of these are fused with a $\Lambda$ charge in the $\ket{1}$ state. There is no local way to detect this, especially when the charges are separated.}
\end{center}
\end{figure}
We observe that $W_{\Lambda} W_{\Phi} = W_{\Phi}$, implying,
\begin{equation}
W_{\Lambda}(e^{1,2}_a) W_{\Lambda}(e^{1,4}_a) W_{\Phi}(e^{1,4}_a) = W_{\Lambda}(e^{1,2}_a) W_{\Phi}(e^{1,4}_a).
\end{equation}
Here the left-hand side creates a $\Phi$ pair on $v_1$ and $v_4$ and fuses a $\Lambda$ with the $\Phi$ on $v_1$. The right-hand side does the same except that the $\Lambda$ is fused with the $\Phi$ on $v_4$. The equality between these shows that the resultant state does not depend upon which $\Phi$ the $\Lambda$ was fused with, and holds even when they are well-separated, showing that the encoding of information in this way is indistinguishable by local operators alone.
Rather than keeping the $\Phi$ charges on neighbouring vertices, it is possible to move them apart. The single spins $e^{i,j}_a$ are then replaced by chains $C^{i,j}_a$ of $l$ spins, where $l$ is the new separation between the anyons. The logical states will be similar in form to those of Eq.(\ref{log}) except that operations acting on spins $e^{i,j}_a$ will instead act on the chains $C^{i,j}_a$. The operations $W_{\Phi}[C^{i,j}_a]$ take the form,
\begin{equation}
W_{\Phi}[C^{i,j}_a] = \sum_{g_n\times...\times g_1=c^k} (\omega^k + \omega^{-k}) \ket{g_1,...,g_n}\bra{g_1,...,g_n},
\end{equation}
where $g_1,...,g_n$ are the states of the spins within the chain $C^{i,j}_a$ and $\omega=e^{i 2 \pi /3}$. The operations $W_{\Lambda}[C^{i,j}_a]$ are simply the product of $W_{\Lambda}$ on each spin along a the chain. Just as in the previous section, this operation provides the logical $X$. Hence all $X$ basis operations determined there still apply unchanged, except that they must now act on $O(l)$ spins to be realized. Measurement in the $Z$ basis now requires the fusion of one or other of the $\Phi$ pairs and measurement of the result, the trivial charge implying $\ket{0}_a$ and $\Lambda$ implying $\ket{1}_a$. These operations achieve universal quantum computation in the same way as before.
Errors in the encoding come from fusion with stray charges or braiding with stray fluxes. Both are suppressed by the stabilizer code, since regular measurements of the syndrome can detect these anyons and allow for their annihilation. They are also suppressed by the Hamiltonian, since the creation of the stray anyons costs energy. To see how well the errors are suppressed, we will now consider them individually. Errors in the $X$ basis are caused by the creation of stray $\Lambda$ charges and their fusion with a $\Phi$ from each pair. This requires a string of errors to occur on the $l$ spins between the $\Phi$'s, a process whose probability is suppressed by $O(e^{-l})$ \cite{Kitaev2,Dennis}. Since the size of the logical operations only increases linearly with $n$, this is an efficient suppression of errors. Errors in the $Z$ basis come from fusion with stray $\Phi$'s, which can disrupt those used to encode and thus leave the logical information exposed to the stabilizer, and lose its degeneracy under the Hamiltonian. $Z$ basis errors can also come from braiding with stray fluxes. Additional protection can be given to this basis by using a repetition code, in which two sets of $n$ $\Phi$ charges are used to encode each qubit, rather than just two pairs \cite{qpl}. The probability of errors will then be suppressed by $O(e^{-n})$.
It is possible to move the $\Phi$ charges using either multi-spin operations \cite{Aguado} or local potentials \cite{me}. This gives the scheme a useful flexibility, since the charges may be moved apart to harness improved protection against errors and moved close so that logical operations may be performed on less spins.
\subsection{Relation to other topological memories}
The $\Lambda$ occupation of a vertex can be determined by measuring the observable $T_t (v)$, with the presence of the charge signalled by an outcome of $-1$. This is true even when a $\Phi$ is present on the vertex, since the measurement can even detect those $\Lambda$'s fused with $\Phi$'s. Consequently, making such a measurement on two $\Phi$ charges allows us to determine the number of $\Lambda$'s within the $\Phi$ pair. As one might expect, an even number will be found within any $\Phi$ pair that will fuse to vacuum, since the $\Lambda$'s will annihilate upon fusion. An odd number will be found within any $\Phi$ pair that will fuse to a $\Lambda$. The LOCC protocol of measuring $T_t (v)$ on each $\Phi$ and collecting the results is therefore sufficient to distinguish the logical states of Eq.(\ref{log}). Note that since these measurements only act on the spins directly around each $\Phi$, increasing their separation will not affect the complexity of the protocol.
Consider a modification to the syndrome measurement, in which the projectors $P_{\Lambda}(v)$ are replaced by $P'_{\Lambda}(v)=[T_e (v) + T_t (v)]/2$, and can therefore detect the $\Lambda$'s within $\Phi$'s. Since the syndrome measures each vertex and collects the results, it is able to count the number of $\Lambda$'s within each $\Phi$ pair, and thus distinguish the logical states. This shows that the encoding is equivalent to those in which Abelian anyons are stored in holes \cite{Raussendorf,qpl}, since using the standard syndrome is equivalent to using the modified syndrome with the $P'_{\Lambda}(v)$ projections suppressed on any vertex holding a $\Phi$. A exciting implication of this is that Abelian models may be used for non-Abelian-like encodings, using the principles of non-Abelian anyons to enhance the power of their memories \cite{qna,thesis}.
To see how a stronger encoding may be constructed, let us consider the single spin operation,
\begin{equation} \label{w'}
W'_{\Phi} = \ket{c}\bra{c} - \ket{c^2}\bra{c^2}.
\end{equation}
Like $W_{\Phi}$, this creates $\Phi$ charges on the vertices either side of the spin. However, measurements of $T_t (v)$ will give different results. An odd number of $\Lambda$'s will be found within a pair of $\Phi$ charges that fuse to vacuum, and an even number found within those that fuse to a $\Lambda$. This is opposite to what one would expect. The relative minus sign, coupled with the non-Abelian group multiplication underlying all operations on the spins, causes the $T_t (v)$'s to detect one more $\Lambda$ within a pair than is actually present. Using this property, the logical states may be made indistinguishable to the $T_t (v)$ measurements, and any LOCC protocol, by using differently defined $\Lambda$ pairs for the logical states. Explicitly,
\begin{eqnarray} \label{log2} \nonumber
\ket{0}_a &=& W_{\Phi}(e^{1,4}_a) W_{\Phi}(e^{2,3}_a) \ket{\rm gs}, \\
\ket{1}_a &=& W'_{\Phi}(e^{1,4}_a) W'_{\Phi}(e^{2,3}_a) W_{\Lambda}(e^{1,2}_a) \ket{\rm gs}.
\end{eqnarray}
With this encoding an even number of $\Lambda$'s is found within any pair, regardless of their fusion channel. They are then distinguishable only with non-local operations, such as the fusion of $\Phi$'s. This is the true non-Abelian encoding, whose protection goes above and beyond that of Abelian encoding with holes.
Note that the huge operational difference between this encoding and that of Eq. (\ref{log}) comes directly from the non-Abelian group multiplication underlying the model. It is only because of this that the relative minus sign in Eq. (\ref{w'}) has such an effect. Abelian group multiplication cannot provide tricks to fool the $T_t (v)$ observables in such a way.
The stronger encoding increases the complexity of the logical $X$ operation. The fusion of a $\Phi$'s with a $\Lambda$'s is no longer enough. The unitary operation,
\begin{equation}
U(v) = \frac{1}{3} T_e (v) - \frac{2}{3}[\omega \, T_c (v) + \omega^2 \, T_{c^2} (v)],
\end{equation}
must be applied to any vertex on which a fusion takes place to rotate from $W_{\Phi}$ type $\Phi$ pairs to $W'_{\Phi}$ type, or vice-versa. Rather than single spin operations, logical operations on neighbouring $\Phi$'s must then act on seven spins. For non-neighbouring $\Phi$'s, operations must also act on six more spins than the previous requirement. Though the size of logical operations still scales with $O(l)$, and so still gives efficient suppression of errors, it is not as accessible to actual experimental realization.
\section{\label{end}Conclusions and further work}
We have proposed a novel scheme for fault-tolerant quantum computation, utilizing a non-Abelian topological memory. As a result of this work, we have an explicit form for the logical states stored non-locally in terms of the physical states of the underlying lattice model, an understanding of what kinds of memories are possible and their relations to other topological memories. Specifically, we have found two means to encode qubits in the fusion channels of the model's anyons. Though both fault-tolerant and indistinguishable to local operations, these encodings have a crucial difference. One has states distinguishable to LOCC protocols, and is equivalent to encodings using Abelian anyons. The other has states distinguishable only to non-local operations. Hence, by showing exactly how these encodings differ, we have demonstrated the true difference between Abelian and non-Abelian anyons from a quantum information perspective.
Furthermore, we harness these states to give the non-topological operations required for universality while remaining below the energy gap. Our work allows the application of realistic error models and studies of how anyonic systems respond to practical experimental conditions \cite{topent}. There exist proposals on how to realize this and other lattice models in the laboratory \cite{Aguado,Doucot,Pachos,Yang,Zoller}. This exercise is a step towards physical realizations of simple non-Abelian systems to demonstrate aspects of quantum computation.
We also note that the use of single spin measurements on highly entangled states bears a similarity to measurement based quantum computation \cite{Briegel}. It would be beneficial to unify these formalisms.
\section*{Acknowledgements}
We would like to thank Gavin Brennen for inspiring conversations. This work was supported by the EU grants SCALA and EMALI, the EPSRC, the Finnish Academy of Science and the Royal Society.
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Home Community Journals offer affirmation on front, outlet inside
Journals offer affirmation on front, outlet inside
By Will Fairless
Khadijah Torbert, an Opelika native now living in Tuscaloosa, started a business this year that she hopes will affect more than just her wallet.
Made Worthy Journal Notebooks LLC was started by Torbert in June 2020, four years after she was divinely inspired to create such a line of journals.
"The idea to have my own journal notebook came to me in a dream," Torbert said. "I truly believe God was pushing me into creating this journal line in 2015-2016 after a terrible breakup."
She kept on journaling in other brands' notebooks until she got serious about starting her own business in 2019. The next year, Torbert thought it was the perfect time to introduce the world to her line of affirming notebooks.
"With everything that has gone on from a global pandemic to racial injustice to other things that just happen in life, I felt the time was now, this year, to create the journal in order for people to release in a safe manner," she said.
Torbert's "Made Worthy" journals, which are meant to be healthy outlets for pouring out one's emotions, are different in that they each have words of encouragement on their fronts. One cover reads, "It is well within my soul;" another displays on its front, "You are worthy."
"I feel that everyone could use reminders of who they are or just words of encouragement to see and read daily," Torbert said. "The more you see something and repeat it, you believe it."
There are nine different journals, eight of which simply have lined paper inside. The ninth is pre-prompted and has an outline for its user to follow. That ninth showcases Torbert's favorite bible verse, Galatians 6:9 ("Let us not become weary in doing good, for at the proper time we will reap a harvest if we do not give up.").
Torbert said that the first few months of sales have been tremendous.
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Made Worthy notebooks can be purchased at shor.by/MadeWorthyJournalNotebooks?fbclid=IwAR3yhZqhWLHe6tM48kaGJ4gF5Pq2Zgj9EGNptfPINiOKEkEL_Mu2VEowUF8.
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| 7,957
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EARLY CHINESE MEDICAL LITERATURE
THE SIR HENRY WELLCOME ASIAN SERIES
_Editors_
Lawrence I. Conrad, London
Paul U. Unschuld, München
Dominik Wujastyk, London
_Editorial Board_
Ronald E. Emmerick, Hamburg
Donald J. Harper, Tucson
Lutz Richter-Bernburg, Leipzig
_Already Published_
**Ibn al-Jazz ār on Forgetfulness and its Treatment**: Gerrit Bos
**Early Chinese Medical Literature** : Donald J. Harper
_Forthcoming_
**Ibn al-Jazz ār on Sexual Diseases and their Treatment**: Gerrit Bos
**Al-Kind ī on Weather-Forecasting**: Gerrit Bos and Charles Burnett
**A Soup for the Qan** : Paul D. Buell and Eugene N. Anderson
**Ibn al-Jazz ār on Fevers**: Gerrit Bos
EARLY CHINESE MEDICAL LITERATURE
The Mawangdui Medical Manuscripts
Translation and Study
by
DONALD J. HARPER
First published in 1998 by
Kegan Paul International Ltd
This edition first published in 2009 by
Routledge
2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
Simultaneously published in the USA and Canada
by Routledge
270 Madison Avenue, New York, NY 10016
_Routledge is an imprint of the Taylor & Francis Group, an informa business_
© Donald J. Harper 1998
Transferred to Digital Printing 2009
All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers.
_British Library Cataloguing in Publication Data_
A catalogue record for this book is available from the British Library
ISBN 10: 0-7103-0582-6 (hbk)
ISBN 13: 978-0-7103-0582-4 (hbk)
**Publisher's Note**
The publisher has gone to great lengths to ensure the quality of this reprint but points out that some imperfections in the original copies may be apparent. The publisher has made every effort to contact original copyright holders and would welcome correspondence from those they have been unable to trace.
To the Memory of Edward H. Schafer (1913–1991)
CONTENTS
List of Figures
Preface
**Prolegomena**
Introduction
Section One: Mawangdui Medical Manuscripts
Manuscript Discovery
List of Mawangdui Medical Manuscripts and Texts
Other Excavated Manuscripts Related to Medicine
Provenance and Hermeneutic Issues
Section Two: Medicine, Medical Literature, Medical Men
Recipes, Techniques, Calculations, Arts
Readership and Transmission
Section Three: Medical Ideas and Practices
Illness
Physiology
Therapy
Materia Medica
Section Four: Macrobiotic Hygiene
Intellectual Background
Body and Spirit
Techniques
Philosophy and Macrobiotic Hygiene
Section Five: Magic
Magical Recipes
Varieties of Magic
Recipes of Yue
**Translation**
Introduction
_MS_ I | | _MS_ I.A "Zubi shiyi mai jiujing" 足 臂 十 一 脈 灸 經 (Cauterization canon of the eleven vessels of the foot and forearm)
---|---|---
| | _MS_ I.B "Yin Yang shiyi mai jiujing," _jiaben_ 陰 陽 十 一 脈 灸 經 申 本 (Cauterization canon of the eleven Yin and Yang vessels, ed. A)
| | _MS_ I.C "Maifa" 脈 法 (Model of the vessels)
| | _MS_ I.D "Yin Yang mai sihou" 陰 陽 脈 死 候 (Death signs of the Yin and Yang vessels)
| | _MS_ I.E "Wushier bingfang" 五 十 二 病 方 (Recipes for fifty-two ailments)
_MS_ II | | _MS_ II.A "Quegu shiqi" 却 榖 食 氣 (Eliminating grain and eating vapor)
| | _MS_ II.C "Daoyin tu" 導 引 圖 (Drawings of guiding and pulling)
_MS_ III | | "Yangsheng fang" 養 生 方 (Recipes for nurturing life)
_MS_ IV | | "Zaliao fang" 雜 療 方 (Recipes for various cures)
_MS_ V | | "Taichan shu" 胎 産 書 (Book of the generation of the fetus)
_MS_ VI | | _MS_ VI.A "Shiwen" 十 問 (Ten questions)
| | _MS_ VI.B "He Yin Yang" 合 陰 陽 (Conjoining Yin and Yang)
_MS_ VII | | _MS_ VII.A "Zajin fang" 雜 禁 方 (Recipes for various charms)
| | _MS_ VII.B "Tianxia zhidao tan" 天 下 至 道 談 (Discussion of the culminant way in Under-heaven)
Appendix 1 Transcription of _MS_ I.B, _MS_ I.C, and _MS_ I.D
Appendix 2 Revisions to the Transcription of Graphs in _MWD,_ vol. 4
Han Weights and Measures
Bibliography
Index of Materia Medica
Index of Physiological Terms
Index of Ailments
General Index
FIGURES
1. _MS_ I.A.1–4 (facsimile)
2. _MS_ II.C.15 (facsimile)
3. _MS_ II.C.24 (facsimile)
4. _MS_ II.C.25 (facsimile)
5. _MS_ II.C.26 (facsimile)
6. _MS_ II.C.28 (facsimile)
7. _MS_ II.C.34 (facsimile)
8. _MS_ II.C.35 (facsimile)
9. _MS_ II.C.36 (facsimile)
10. _MS_ II.C.37 (facsimile)
11. _MS_ II.C.39 (facsimile)
12. _MS_ II.C.42 (facsimile)
13. _MS_ III.89–92 (facsimile)
14. _MS_ V.1 (line drawing with reconstruction)
15. _MS_ V.2 (line drawing)
16. _MS_ V.2 (line drawing with reconstruction and compass points)
17. _MS_ VI.A.1 (facsimile)
PREFACE
I began work on the Mawangdui 馬 王 堆 medical manuscripts in early 1977 when I examined partial transcriptions published in _Wenwu_ 文物 1975.6 and 1975.9. My 1982 dissertation is the product of the first stage of my manuscript research. At that time a reproduction of the original manuscripts was not yet published, transcriptions of several texts had not yet appeared in print, and most of the published transcriptions used simplified graphs. _MWD_ , vol. 4, published in Beijing in 1985, provided a photographic reproduction of the manuscripts and a transcription of all texts in modern _kaishu_ 偕 書 graphs. By 1986 I was gradually making my way through the as yet unseen texts and familiarizing myself with the original manuscripts (the physical relics as well as their script). While I was convinced that the manuscripts were a remarkable testament to early Chinese medicine, I was uncertain whether an annotated translation of the entire corpus would find a publisher. For a time I considered translating a selection of texts or writing a study based on the manuscripts. The decision to translate the entire corpus was made in the fall of 1990 while I was a guest at the Institute for the History of Medicine, Munich University. I am indebted to Professor Paul U. Unschuld, Director of the Institute, for encouraging me to undertake a complete translation; and for providing me with the ideal research environment in Munich as I began the task in earnest.
Professor Unschuld has continued to watch over the project at critical stages, from commenting on the work in progress to securing publication funds. I wish to offer heartfelt thanks to my friend and colleague for his enthusiastic and unstinting support. I am also grateful to Professor Li Xueqin, Director of the Institute of History, Chinese Academy of Social Sciences, Beijing. Professor Li is responsible for the final editing of the transcription in _MWD_ , vol. 4, and has encouraged me to pursue research on the medical manuscripts since 1985 when we discussed the manuscripts in Beijing. At Professor Li's invitation I spent January to March 1993 at the Institute of History, during which time I consulted with Professor Li on matters related to the manuscripts. The memory of our meetings in his home—looking at the photographic reproduction of the manuscripts through a magnifying glass and weighing the evidence for determining the correct transcription—remains fresh. During these meetings I learned important lessons in manuscript studies and the art of transcription. Professor Li's generosity continued through the final stages of translation in letters responding to further questions concerning the manuscripts.
In addition, I wish to thank Professor Ma Jixing of the Academy of Traditional Chinese Medicine (who was a member of the editorial committee that produced _MWD_ , vol. 4) and Professor Qiu Xigui of Peking University for their assistance during my 1993 stay in Beijing. Professor Ma kindly presented me with a publisher's advance copy of his own book on the Mawangdui medical manuscripts (Ma Jixing 1992) on the day before my departure from Beijing. A research fellowship from the Alexander von Humboldt Foundation and a Chiang Ching-kuo fellowship administered by the American Council of Learned Societies permitted me to spend most of the academic year 1990–91 in Munich. The Committee on Scholarly Communication with China awarded me a research grant to attend the International Symposium on Mawangdui Han Tombs in Changsha in August 1992 (at which time I was able to inspect the original medical manuscripts at the Hunan Provincial Museum) and to spend winter 1993 in Beijing. I thank the University of Arizona East Asian Studies Department for releasing me from teaching duties during Spring Semester 1993, permitting me to go to Beijing and then to make rapid progress on the translation after my return to Arizona. A grant from the University of Arizona College of Humanities enabled me to engage the services of Mr. Xu Datong, a graduate student at the University, to produce the excellent facsimiles of the manuscripts which appear in this book. Mr. Xu also wrote the Chinese title on the title page in script based on the Mawangdui medical manuscripts. The Alexander von Humboldt Foundation provided a publication grant for the preparation of the electronic layout, which has been skillfully executed by Bo and Christine Hu of Munich.
D.H.
June 1996
PROLEGOMENA
Introduction
Since the 1970s there has been a succession of manuscript discoveries in late-fourth to second century B.C. tombs in several regions of China, the provinces of Hubei and Hunan being particularly fertile ground for manuscripts. Han manuscripts later than the second century B.C. have also been discovered, but Warring States, Qin, and early Han manuscripts have been more numerous. It is evident that the manuscripts were selected from the book collections of the well-to-do tomb occupants; that is, they were not prepared solely as burial goods. Contemporary records are silent on the custom of book burial. Perhaps manuscripts were placed in tombs because they were intrinsically valuable objects that bespoke expertise and status, or because they were imbued with a magical efficacy that suited the underworld environment.1 Whatever the rationale was at the time, the modern consequence is the recovery of manuscripts from the very period when books and book collecting first became popular in China. The spread of literacy and the transmission of books were themselves manifestations of intellectual ferment, which reached a high point by the third century B.C. Each tomb has yielded a unique collection of manuscripts—no doubt a reflection of their owner's avocations—all of them containing editions of texts that circulated in the Warring States, Qin, and early Han periods. While some of the texts have been preserved in received literature, most are lost works.2 Collectively, the excavated manuscripts shed new light on a pivotal period in Chinese civilization. They may contain lacunae due to rotted bamboo, wood, or silk (the materials used for manuscripts), but the manuscripts have experienced none of the vicissitudes of transmission that led to the loss of most ancient literature, or that recast the original form and content of a book in a new edition. When the manuscripts restore texts that were either lost or significantly altered in the course of transmission, their importance for new interpretations of early Chinese civilization is particularly great.
Such is the case with the Mawangdui medical manuscripts. The medical manuscripts are part of a large cache of manuscripts discovered in 1973 in Mawangdui 馬 王 堆 tomb 3, situated in the northeastern part of the city of Changsha 長 沙, Hunan. Other Mawangdui manuscripts contain philosophical writings and historical anecdotes as well as works on calendrics, astrology, divination, and related occult subjects. The man buried in the tomb was a member of the locally prominent Li 利 family. Skeletal remains indicate that he was about thirty years old when he died; a wooden tablet placed in the tomb gives a burial date corresponding to 168 B.C.1 This date provides a firm _terminus ante quem_ for the excavated manuscripts. From analysis of the script and other textual evidence we know that some manuscripts were already over forty years old at the time of burial, while others were copied during the decade preceding the man's death. Most of the medical manuscripts are thought to have been copied nearer to 200 B.C. than to the date of burial. Earlier editions of the texts written on them must have circulated in the third century B.C.; some were surely well known.
Several texts contain material that is related to but older than textual parallels in the oldest received classic of medical theory, the _Huangdi neijing_ 黄 帝 内 經 (Inner canon of the Yellow Thearch; ca. first century B.C.), which is extant in three medieval recensions: the _Suwen_ 素 問, _Lingshu_ 靈 樞, and _Taisu_ 太 素.2 The Mawangdui texts provide evidence of an earlier stage in the formation of the physiological and pathological theories that support acupuncture therapy in the _Huangdi neijing_. In the manuscript texts there are eleven _mai_ 脈 (vessels) in the body that contain _qi_ 氣 (vapor), one less than the twelve vessels of the _Huangdi neijing_. The vessels are divided into Yin and Yang categories, but the theoretical conception of the system of vessels is less elaborate than the _Huangdi neijing_. The manuscript texts attribute illness to pathogenic conditions of vapor in the vessels, associate the occurrence of certain ailments with particular vessels, describe how to diagnose illness in the vessels, and recommend cauterizing the vessels to cure ailments.1 Acupuncture is not mentioned, nor is the therapy attested elsewhere in the Mawangdui medical manuscripts.2
In addition to this type of theoretical writing, there are texts representing a broad range of lost medical literature. Recipe literature predominates. In their current state of preservation, five texts contain between them over 425 recipes. One long recipe manual deals exclusively with the treatment of ailments. It provides detailed instructions for a variety of remedies, among them: drags, several forms of heat therapy including cauterization, surgical procedures, exorcistic incantations, and other magico-religious operations. The recipes in two of the texts focus on macrobiotic hygiene (which encompasses dietetics, breath cultivation, exercise, and sexual cultivation) with many recipes for tonics and aphrodisiacs. A text that describes gestation concludes with recipes related to childbirth. The shortest recipe text concerns philters and miscellaneous charms. The subject of the remaining texts is macrobiotic hygiene. One text is composed of ten dialogues in which different macrobiotic specialists respond to questions (the questioner in the first four dialogues is the Yellow Thearch, who plays the same role in much of the _Huangdi neijing_ ). The specialists expound teachings that include instructions for cultivation techniques. There is a breath cultivation text on the technique of ingesting vapor from the external atmosphere while abstaining from regular food; and on the same manuscript, a text with drawings of exercises used both to treat ailments and to cultivate the body. Two texts focus on the techniques of sexual cultivation. All of the material on macrobiotic hygiene belongs to a medical tradition of _yangsheng_ 養生 (nurturing life), but neither this term nor several related terms in received literature occur in the manuscripts.1
We always knew that these types of medical literature existed. Newly copied editions of thirty-six medical books were deposited in the Han court library at Chang'an around the end of the first century B.C.; only the _Huangdi neijing_ survives in truncated form. We know the other titles from the _Hanshu_ bibliographic treatise, which reproduces the general scheme of Liu Xin's 劉 歆 now lost catalogue of the library (Tsien 1962: 14). The division of medical literature, entitled "Fangji" 方 技 (Recipes and techniques), lists the thirty-six books in four sub-categories ( _Hanshu_ , 30.78b): "Yijing" 醫 經 (Physicians' canons; medical theory as represented by works like the _Huangdi neijing_ , which is listed first); "Jingfang" 經 方 (Canonical recipes; as is clear from the titles listed, collections of recipes to treat ailments); "Fangzhong" 房 中 (Intra-chamber; sexual cultivation); and "Shenxian" 神 僊 (Spirit transcendence; other types of macrobiotic hygiene). The classification no doubt reflects a physician's conception of medicine and medical literature in the first century B.C.: the physicians' canons, which ground the practice of medicine in theories of the vessels and vapor, are placed first; the diffuse recipe literature, which collects a wealth of medical knowledge that does not necessarily conform to theory, comes next; private hygienic practices are last, and macrobiotic hygiene is identified with the immortality beliefs of the _xian_ 仙 (transcendent) cult.1 While the classification and its medical assumptions post-date the Mawangdui medical manuscripts, we may surmise that the contents of the manuscripts typify early Chinese medical literature—albeit in capsule form.
Manuscripts from tombs present problems not so different from the problems of interpreting other excavated artifacts; and many questions concerning the Mawangdui medical manuscripts must be answered with a judicious conjecture. On balance, however, the manuscripts provide a new foundation for the history of early Chinese medicine and medical literature. They are older than the _Huangdi neijing_ ; and they reveal more of what medicine was like than the _Huangdi neijing_ , the contents of which center on the new, universal model of illness based on vessel theory along with the methods of diagnosis and treatment that accompany it. The only received medical literature that dates roughly to the time of the tomb 3 burial (168 B.C.) are selected writings of the physician Chunyu Yi 淳 于 意 (216-ca. 150 B.C.) quoted in chapter 105 of Sima Qian's 司 馬 遷 (ca. 145-ca. 86 B.C.) _Shiji_ 史 記. They consist of twenty-five medical case histories, eight explanations of his medical practice, and a personal history of his medical training. Chunyu Yi, who practiced medicine in Qi 齊 (present-day Shandong), originally submitted these writings to the Han court at Chang'an around 154 B.C. in order to vindicate his medical reputation. Like the _Huangdi neijing_ , Chunyu Yi's writings dwell on etiology, diagnosis, and treatment (however, his understanding of vessel theory is not identical to the _Huangdi neijing_ , and he favors drug treatments over cauterization or acupuncture).2 There are, of course, references to medicine in historical and philosophical texts as well as in belles lettres, but this material is mostly anecdotal and is not itself medical literature.1
There is an important difference between Chunyu Yi's writings and the Mawangdui medical manuscripts. In his personal history, Chunyu Yi names the medical books that were transmitted to him by his teacher Yang Qing 陽 慶 in 180 B.C., which he states were the foundation of his medical practice ( _Shiji_ , 105.8b; Bridgman 1952–55: 26). Except for occasional quotations from a _Maifa_ 脈 法 (Model of the vessels) in the medical case histories, Chunyu Yi's writings concern his own medical practice; that is, we know virtually nothing about his collection of medical books other than their titles. With the Mawangdui manuscripts, we have examples of third to early-second century B.C. medical books. Considering the other manuscripts on philosophy, calendrics, astrology, and divination, the man buried in tomb 3 was an avid book collector who patronized specialists in several fields of knowledge including medicine. He need not have been a physician to collect literature on medicine, nor have been an astrologer or diviner. His manuscripts reflect the same range of subject matter as the _Hanshu_ bibliographic treatise, which lists works on calendrics and the other subjects in a separate division—"Shushu" 數 術 (Calculations and arts; _Hanshu_ , 30.65a). Tomb 3 reveals that the pattern of book collecting exemplified in the _Hanshu_ bibliographic treatise was maintained by private individuals as well as by the Han thearchs.
The combined literature in the "Shushu" and "Fangji" divisions of the bibliographic treatise falls broadly into fields of knowledge that I identify as natural philosophy and occult thought. I refer to the literature itself as " _fang_ -literature," based on the significance of the concept of _fang_ 方 (recipe) in defining natural philosophy and occult thought. These matters are discussed in Section Two ("Recipes, Techniques, Calculations, Arts"), but it would be wise to broach now the subject of early Chinese medicine and other fields of knowledge that come within the purview of the modern discipline of history of science. The history of science has long since moved beyond the stage of vetting ancient knowledge of nature to separate the rational from the irrational and the science from the superstition. Lively debate continues to focus on the relation between science, magic, and religion in a premodern context and on the question of what constitutes rationality. A number of earlier theories and interpretations have been put to rest, among them: that magic and religion are fundamentally different; that magic is failed science; and that scientific "progress" already separated science from magic in ancient times (Tambiah 1990; Vickers 1984; Lloyd 1979). The term "science" itself is part of the problem of defining the quiddities under investigation, because it assumes certain categorizations of knowledge that were not acknowledged in the past. "Natural philosophy," in the sense of systems of thought that take nature as their primary object of investigation and that develop theories to explain phenomena in terms of perceived regularities in the operation of nature itself, is gaining currency among English writers (Lindberg 1992: 1–4). However, "natural philosophy" has a long history in the Western intellectual tradition; from the standpoint of current research in the history of science, the term leaves open the question of the evident interpenetration of natural philosophy, magico-religious belief, and other forms of occult thought. It seems that we must speak dually of "natural philosophy" and "occult thought" in order to refer to something that was undivided or was divided differently in either the ancient Mediterranean world or early China.1
When we look for an identifiable Chinese natural philosophy what we find are principally the theories of vapor, of Yin and Yang, and of the Five Agents ( _wuxing_ 五 行), which arose during the Warring States period and by the end of the third century B.C. coalesced into the system of thought that Graham refers to as "correlative cosmology"—a cosmology that establishes elaborate correspondences between nature, the individual human being, and society (1986; 1989: 313–70). Graham identifies the earliest exponents of cosmology as "court historiographers, astronomers, diviners, physicians, and musicmasters" (1989: 325); that is, what I tentatively call Warring States natural philosophy was originally the province of the practitioners of technical arts like calendrics, astrology, divination, and medicine.2 Calendrics, astrology, and divination appear to have been most influential in the new rationalization of nature; medicine, while offering physiological and etiological theories that made the body a microcosm of the cosmos, was incorporating Yin Yang and Five Agent theories in stages. There is scant evidence of the theories in the Mawangdui medical manuscripts, whereas by the time of the _Huangdi neijing_ (ca. first century B.C.) they have been assimilated; even then, assimilation was not absolute nor did it become so during the Han. Nevertheless, physicians (which translates _yi_ 醫) were clearly active in the same social and intellectual milieu as the diviners and other specialists, all of whom shared a common interest in understanding natural phenomena and their consequences for humankind.
This account of the genesis of Warring States natural philosophy stands in contrast to the Greek pattern, where it was philosophers who developed universal theories of nature and change, from which they fashioned an understandable cosmos; and practitioners (like physicians) who applied the philosophers' theories to their craft. The "masters" ( _zi_ 子) of Warring States philosophy did not ignore nature entirely, but politics and ethics were their main concern. The extant writings of the masters of philosophy rarely exhibit an interest in nature outside of its utility as an analogy for their particular philosophical argument.1 To be sure, nature-based political models figured prominently in philosophy by the third century B.C., and philosophical argumentation on _dao_ 道 (way) as an ultimate organizing structure both in nature and in human society became quite sophisticated. Moreover, the humanistic orientation of the philosophers undeniably contributed to the rationalizing of nature and to skepticism of magico-religious conceptions. But natural philosophy as such was not their invention.2
Knowledge of nature during this age of intellectual ferment obviously encompassed more than what was channeled into Yin Yang and Five Agent theories. In the case of medicine, popular lore (much of it based on magico-religious beliefs), practical experiences, and competition between several kinds of medical practitioners brought forth a diversity of data and viewpoints—all of them drawn upon in the formation of a learned medicine. Just as clearly, the medicine of Chunyu Yi and the _Huangdi neijing_ shows that some physicians were using Yin Yang and Five Agent theories to establish a medicine that in principle adhered to naturalistic theories and rejected the influence of spirits and the use of magic. It is significant, however, that despite a kind of rationalistic skepticism which accompanied Yin Yang and Five Agent theories in various fields of knowledge, the theories themselves were not like laws of nature; and there was not a clear break with magico-religious conceptions. A wholly naturalistic explanation of phenomena was, therefore, a relative interpretation made by the person applying the theories; the theories themselves did not exclude occult interpretation. In short, Yin Yang and Five Agent theories did not constitute a "natural philosophy" that was opposed to "occult thought."1
A single term for the whole enterprise of investigating nature (and not just Yin Yang and Five Agent theories) is needed—one that might serve to differentiate between this enterprise and that of the Warring States philosophers, while not excluding occult thought. My use of "natural philosophy" and "occult thought" (or "occult knowledge"), either singly or as a pair, is a heuristic device. The reader should understand that the usage is intended to facilitate the discussion of early Chinese medicine, and that the two terms do not define opposite categories in the early Chinese conception.
This translation of the Mawangdui medical manuscripts is the first complete translation in any language; it is based on the transcription and photographic reproduction of the original manuscripts in _MWD_ , vol. 4. Translation assumes the existence of a critical edition of the text to be translated. In working with lost texts copied on excavated manuscripts, I have been mindful of the principles of textual criticism. I offer a number of revisions of the transcription of individual graphs in _MWD_ , vol. 4, which are recorded in the Translation notes and listed in Appendix 2. In addition, editions of three of the medical texts were discovered in a manuscript excavated from Zhangjiashan 張 家 山 tomb 247, Hubei, in 1983 (burial dated to mid-second century B.C.); these editions were still unavailable when _MWD_ , vol. 4, was published. I have used the Zhangjiashan editions to prepare a new transcription of the Mawangdui texts, which appears in Appendix 1. The Translation notes also record other instances where my textual research has led to judgments that differ with _MWD_ , vol. 4. Thus, while I have not prepared a new transcription of the entire corpus, the Translation provides a necessary text-critical supplement to the transcription of the texts in _MWD_ , vol. 4.
The Introduction to the Translation reviews the conventions adopted in the translation. Interpretations and supporting documentation are set forth in the Translation notes. The Prolegomena situate the Mawangdui medical manuscripts in their social and intellectual context, with the aim of identifying their place in the history of medicine and in the history of ideas. Sections are devoted to: (1) the discovery of the manuscripts, contents, dating, and hermeneutic issues; (2) the manuscripts as _fang_ -literature, readership, and transmission; (3) medical ideas and practices; (4) macrobiotic hygiene; and (5) magic.
Manuscripts from several tombs in addition to Mawangdui tomb 3 are providing us with our first look at the early texts of Chinese natural philosophy and occult thought. This kind of _fang_ -literature probably began to circulate in the fourth century B.C. at the same time as philosophical literature burgeoned. Beyond the circle of specialists, the existence of a literate elite who collected books must have increased the demand for _fang_ -literature. As transcriptions and reproductions of the manuscripts are published and research on them progresses, we will gain a far better understanding of the traditions they represent than could have been imagined only several decades ago; and our view of early Chinese civilization as a whole will be changed by them.1 I must confess that I sometimes wish I might delay publication of my translation of the Mawangdui medical manuscripts until every textual problem is solved to my complete satisfaction and every interpretation offered with certitude. The discovery of the Zhangjiashan medical manuscripts alone has shed much light on the Mawangdui medical manuscripts, rendering lucid what was previously unclear. Given the record of the last two decades, new manuscript discoveries seem inevitable. One thought that recurs is how much more I will know about the Mawangdui medical manuscripts and early medicine in a decade's time. Despite its imperfections, I hope this translation of the medical manuscripts stimulates research in the history of Chinese medicine and helps to build a critical mass of scholarly research on excavated manuscripts related broadly to natural philosophy and occult thought.
1Harper (forthcoming) speculates on the magical properties attributed to manuscripts. Before the 1970s the bulk of early manuscript material consisted of Han administrative documents, which were ofter excavated at the remains of fortifications in several northwestern provinces (Tsien 1962: 90–102; Loewe 1967). The tomb manuscript discoveries which include an array of literature have mostly occurred since 1972 (Loewe 1977; Shaughnessy forthcoming).
2I follow the definitions of text and edition proposed by Roth (1993: 227): "A _text_ is the unique complex and expression of ideas of an author or authors, an _edition_ is a distinct record containing a unique state of a text." An edition of a text exists on a manuscript, which is the physical object. My application of Roth's definition of "text" to the excavated manuscripts is discussed more fully in Section One. In addition to the meaning given, I also refer to "text" in the ordinary sense of the words of something written.
1The tablet is reproduced in Fu and Chen 1992: 37. Chen Songchang convincingly argues that the inscription of the tablet concerns the official delivery of burial goods to the tomb on the burial date; and that it is not like the documents addressed to the underworld found in other second century B.C. tombs (1994: 64–69; Harper 1994:17–18).
2The _Huangdi neijing_ in eighteen _juan_ 卷 (rolls) is listed in the division of medical literature in the _Hanshu_ bibliographic treatise ( _Hanshu_ , 30.78b), meaning that a fair copy of the text was prepared and deposited in the Han court library sometime after 26 B.C. as part of the bibliographic project directed by Liu Xiang 劉 向 and Liu Xin 歆 (Tsien 1962: 14). The fate of this edition is not known. While there are differences of opinion regarding the priority of the three medieval recensions, which vary considerably from one to the other, there is a general consensus among modern scholars that the _Huangdi neijing_ was compiled during the Former Han period from a variety of textual sources (see Sivin 1993). Two recent studies approach the problem of the original compilation and subsequent history of the text differently. Yamada attributes the composite nature of the _Huangdi neijing_ to the influence of schools of Han physicians whose theoretical differences are preserved in the _Huangdi neijing_ ; and he regards the _Taisu_ as closest to the original text (1979: 67–68, 86–89). Keegan, in contrast, argues that the _Huangdi neijing_ came into being as a consequence of an ongoing process of physicians transmitting medical literature; pieces of medical texts were combined and recombined, and were transmitted as a corpus that came to be known as _Huangdi neijing_. According to Keegan, each of the medieval recensions is a reflection of one of the forms of this corpus; and it is impossible to say that one of them is closest to the original text, or indeed that an original text ever existed in the sense of a first recension produced by a single editor or editors (1988: 249–59).
1Cauterization therapy in the Mawangdui medical manuscripts is not solely practiced in conjunction with vessel theory; and several materials are used to cause the burn (see Section Three, "Therapy"). One of the materials is _ai_ 艾 (mugwort), but the use of mugwort tinder (moxa) is not attested. Thus, it is anachronistic to refer to cauterization therapy in the medical manuscripts as moxibustion.
2Acupuncture is a therapy that treats pathogenic conditions of vapor in the body by pricking the vessels with needles in accordance with theories related to the vessels and vapor. I follow Unschuld (1985: 92–99) in distinguishing between the use of lancing instruments for draining pus from purulent swellings and acupuncture. The therapeutic paradigm established first for vessel cauterization was the crucial precedent for the emergence of acupuncture; lancing along cannot have led directly to acupuncture. The earliest documentation of acupuncture is in second to first century B.C. sources (for similar judgments, see Liao Yuqun 1991: 272–74; and Yamada 1985a: 3–19, 57–72). I take exception to the views of Lu and Needham (1980: 69–88), who tend to equate medical lancing with acupuncture and read early references to lancing as evidence of acupuncture (even speculating that acupuncture might already have been known in Shang times).
1The most prominent occurrence of _yangsheng_ in early literature is undoubtedly in the section title and text of _zhuangzi_ 3, 54. Differences between the medical tradition of macrobiotic hygiene and Daoist thought are discussed in Section Four, "Intellectual Background."
1Ideas of health and longevity in the Mawangdui medical manuscripts appear to represent a tradition of macrobiotic hygiene that was older than the _xian_ cult, which became prominent in the late third century B.C. Cross-fertilization between macrobiotic hygiene and the _xian_ cult is well documented in Former Han sources, hence their fusion in the bibliographic classification. The classification may have been devised by Li Zhuguo 李 柱 國, the physician who was assigned the task of editing the medical books in the court library ( _Hanshu_ , 30.1b).
2Bridgman (1952–55) translates the _Shiji_ account of Chunyu Yi and discusses its significance for the study of early Chinese medicine; see also, Lu and Needham 1980: 106–110. The same chapter of the _Shiji_ opens with an account of the legendary physician Bian Que 扁 鵲 (whose historical existence during the Warring States period is doubtful). Yamada (1988) has shown that Sima Qian fashioned the account of Bian Que from earlier anecdotal literature and tailored it to better reflect the image of Bian Que as a patron of certain medical arts (including acupuncture) in Sima Qian's own time. It is an important document, but is not an example of medical literature.
1See Bridgman 1952–55: 6–17, for a survey of some of the pre-Han and Han literature that refers to medicine.
1The question of magic is discussed further in Section Five.
2Kalinowski is in basic agreement with Graham: "The doctrine of the Five Agents matured from the contacts between religious, philosophical, and scientific conceptions of the end of the Warring States and the Former Han. Spilling over from the context of divinatory practices, it very quickly attained a sufficient degree of generality to become the conceptual basis for all activity" (1991: 47).
1The exception were the Mohists, who for a brief time moved in the direction of causal explanations of natural phenomena (Graham 1989: 160–66).
2Sivin's review of Graham 1989 makes a spirted counter-argument that "cosmology entered the technical world from philosophy, not vice versa" (1992: 23). Sivin links the genesis of cosmology to the political theories of philosophers seeking to prove that "the state was natural" (1992: 24–25). On balance I think Graham's argument still stands.
1Kalinowski compares Yin Yang and Five Agent theories to the hermetic traditions of Greco-Roman times, and rejects the label "natural philosophy": "To reduce this to a system of natural philosophy does not take account of the extreme diversity of the elements of which it is composed and of its multiple applications not only in the realm of the investigation of things in general, but also in that of politics, religion, and the arts" (1991: 47).
1See Harper forthcoming for a survey of these manuscripts.
Section One
Mawangdui Medical Manuscripts
Manuscript Discovery
Mawangdui tomb 3 was excavated during November and December 1973, followed by the excavation of tomb 2 (which continued into January 1974). Mawangdui tomb 1 was excavated in 1972. All three tombs were of the vertical-pit type. In tomb 3 the pit was 17.7 meters deep. A wooden burial-chamber had been built at the bottom of the pit with a central area to hold the three internested coffins and with four surrounding storage areas containing the burial goods. There is a full archaeological excavation report for Mawangdui tomb 1 (Hunan sheng bowuguan and Zhongguo kexueyuan kaogu yanjiusuo 1973), but not yet for tombs 2 and 3. Although basic facts about the latter tombs have been published, the information available is often not as specific as one would like. In addition to a wealth of burial goods, tomb 1 yielded the well preserved corpse of a woman—about fifty years old at the time of death—who has been determined to be the wife of Li Cang 利 蒼, the occupant of tomb 2. Three seals discovered in tomb 2 (two of bronze and one of jade) confirm the identity of the occupant as Li Cang, who held the aristocratic rank of Lord of Dai 軚 侯 and was also a chancellor in the Kingdom of Changsha 長 沙 國. According to the _Shiji_ and _Hanshu_ , Li Cang was installed as Lord of Dai in 193 and died in 186 B.C. It is presumed that the roughly thirty-year-old man buried in 168 B.C. in tomb 3 was the son of Li Cang and the wife in tomb 1. Because the construction of tomb 1 damaged tombs 2 and 3, Li Cang's wife died last; she was probably buried not long after 168 B.C. Opinion differs over whether the son was Li Xi 豨, who succeeded Cang as the second Lord of Dai (the _Shiji_ and _Hanshu_ state that Xi died in 165 B.C.), or was another son who may have held a military position in the region of Changsha (as suggested by weapons and other artifacts related to military activity among the grave goods). The Li family continued to be prominent in the region at least until 110 B.C. when their aristocratic entitlement was eliminated by Thearch Wu 武 帝 (r. 141–87 B.C.).1
All of the tomb 3 manuscripts were found inside a rectangular lacquer box with a roof-shaped lid (sixty centimeters long, thirty centimeters wide, and twenty centimeters high) that lay in the storage area on the east side of the coffins. The majority of manuscripts are on sheets of silk of two widths: either approximately fifty centimeters wide (somewhat over two _chi_ in Qin and Han measurements), or twenty-four centimeters (just over one _chi_ ). Of various lengths, most of the silk manuscripts had been folded and placed in a large rectangular compartment (one of five compartments inside the box). The silk had rotted at the creases, resulting in stacks of leaves that the restorers pieced back together. At least one silk manuscript (twenty-four centimeter width) was rolled around a wooden slat (three centimeters wide) and had been placed in the narrow compartment running the length of one side of the box. Another folded silk manuscript ( _MS_ II of the medical manuscripts) was also found in the side-compartment. On top of these silk manuscripts in the side-compartment were one manuscript of bamboo slips and another of bamboo and wooden slips ( _MS_ VI and _MS_ VII of the medical manuscripts). The original binding cords were disintegrated. The slips of _MS_ VI are twenty-three centimeters long (one _chi_ ); the wooden slips of _MS_ VII are twenty-three centimeters, the bamboo slips are twenty-eight centimeters. _MS_ VII had been rolled around a core of two bamboo flutes. There are other sizes of silk manuscripts, mostly containing maps, diagrams, and pictures. The largest manuscripts found in the box are two maps, one a square of silk ninety-six centimeters on a side and the other a rectangle seventy-eight centimeters wide and ninety-eight centimeters long. At present we lack a detailed record of the exact position of every manuscript in the lacquer box at the time of excavation (one hopes that when the official excavation report for tomb 3 is published it will include this information). It is evident that the medical manuscripts were not all placed in the same compartment, but were divided between the side-compartment and the larger rectangular compartment which held most of the manuscripts.1
The original manuscripts are deposited in the Hunan Provincial Museum in Changsha. Shortly after excavation, the manuscripts were divided into categories by content and editorial committees were formed to restore and transcribe the manuscripts in each category. The work of transcription was—and is—done primarily with photographic reproductions.2 Some transcriptions, usually in simplified graphs and not accompanied by reproductions of the manuscripts, were published relatively early in _Wenwu_ and elsewhere. Full reproductions and transcriptions in modern _kaishu_ 楷 書 graphs are being published in individual volumes in _MWD_. These volumes provide a standard edition of the manuscripts for scholarly research. Publication has been gradual, leaving many manuscripts either inadequately represented or unpublished in any form.3
Because work on several categories of manuscripts is still on-going, it is possible that published figures for the number of manuscripts discovered and the total number of texts contained in them will be revised. According to current accounts, the manuscript corpus comprises thirty manuscripts and forty-five texts (including maps, diagrams, and pictures in the count). Some manuscripts contain only one text; others several. Several texts occur in two editions on separate silk manuscripts, most famously the two editions of the _Laozi_ 老 子. Only three texts are known in received literature: the _Laozi_ ; an edition of the hexagram text of the _Yijing_ 易 經; and an edition of the "Xici zhuan" 擊 辭 傳, the cosmological commentary on the hexagrams which forms part of the received text of the _Yijing_.1 The medical manuscripts account for a sizeable portion of the corpus: seven medical manuscripts contain fourteen texts (one text occurs in two editions on separate silk manuscripts) with roughly 22,000 extant graphs—about eighteen percent of the extant graph count for the whole corpus, which I estimate to be 125,000.2
Having stated that there are forty-five texts on thirty manuscripts in the Mawangdui manuscript corpus, I should explain my use of the term "text." First, "text" corresponds to _pian_ 篇 (roughly, "piece of writing"), which is the term used by the Mawangdui manuscript editorial committees when identifying the distinct "pieces of writing" on a particular manuscript. Second, I follow Roth's definition of a "text" as the "unique complex and expression of ideas of an author or authors" (1993: 227). The editorial committees base the identification of _pian_ on identity with a received text (like the _Laozi_ ), on titles that occasionally appear in a manuscript, on obvious divisions in the layout of a manuscript, or on a change of subject that warrants distinguishing one "piece of writing" from another. Taking the manuscript with the second _Laozi_ edition as an example, the _Laozi_ is preceded on the manuscript by four writings each of which has a title. Perhaps these four _pian_ should be grouped together and identified as one "text" on the assumption that they are inseparable parts of a single work like the _Laozi_. But without the additional testimony of other editions of the four _pian_ as a single work, it is equally probable that the four _pian_ circulated separately—or perhaps each _pian_ is an extract from other lost works unknown to us. Given our lack of knowledge of authorship and manuscript transmission before the editorial project carried out by Liu Xiang 劉 向 and Liu Xin 飲 in the first century B.C. (Tsien 1962: 14), I advise caution when dealing with lost literature on the manuscripts. Treating each _pian_ of the editorial committees as a "text" establishes a minimal identification, which can always be revised if new manuscript discoveries prove that several _pian_ form one text. In the case of the medical texts, the minimal identification—even when it results in texts of only several hundred graphs—accurately reflects how medical literature and _fang_ -literature in general were composed. Teachings and recipes belonged to a common pool of medical literature (with oral material being continually introduced); any one medical manuscript might have made a different selection of short texts from the available literature, creating what could be called a "composite text" out of "text components." One of the Zhangjiashan 張 家 山 medical manuscripts illustrates this phenomenon well, containing editions of Mawangdui texts in combination with other texts not found in the Mawangdui medical manuscripts (see "Other Excavated Manuscripts Related to Medicine" below).1
Twenty-eight of the thirty Mawangdui manuscripts are written on silk; excluding the famous Chu silk manuscript (ca. 300 B.C.), unearthed in the vicinity of Changsha in 1942, there have been no other discoveries of silk manuscripts in the recent spate of manuscript discoveries.2 Silk was a more costly book material than wood or bamboo. Silk also required greater care from the scribe. A miswritten graph or wrong phrase could always be scraped off a bamboo or wooden slip, and individual slips could be replaced, but once the ink saturated the silk the scribe could only blot out errors and proceed (as is evidenced in the Mawangdui manuscripts). Silk, of course, offered advantages. It was not bulky like wood or bamboo, and text and illustrations could be combined easily on the smooth surface. The Mawangdui manuscripts show how the format of bound-slip books continued to influence silk books. Many of the silk manuscripts are ruled with vertical lines in red ink to form columns that imitate the book-mat formed from bound slips of wood or bamboo; the graphs in black ink fill each column like one slip of a bound-slip book (in some cases extra ruled columns have been left blank). The two widths of silk used for most of the Mawangdui silk manuscripts are probably also related to book dimensions established for slips. The narrower width (twenty-four centimeters) corresponds to a common length of twenty-three to twenty-four centimeters for excavated Qin and Han slips, which in turn reflects a standard slip-length of one _chi_ (23.1 centimeters) mentioned in Han sources (Tsien 1962: 105; Sun Ji 1991: 281–85).1 The wider silk (fifty centimeters) probably corresponds to the two- _chi_ slips mentioned in Han sources (Tsien 1962: 105).2 Han sources associate the larger and smaller sizes of books with writings of greater or lesser importance. Considering the Mawangdui manuscript corpus as a whole, there is not a consistent correlation between the size of the manuscript and the relative significance of its contents. The choice of wider silk for two of the five medical manuscripts on silk was evidently to better accommodate the drawings included on those manuscripts.
The graphs in the Mawangdui manuscripts can be classified as either seal script ( _zhuanshu_ 篆 書) or clerical script ( _lishu_ 隸 書), or a hybrid in between; that is, the scribes wrote in the scripts used in Qin during the Warring States and promulgated as the standard for all regions of China following the Qin unification of 221 B.C. By Han times the script reform was complete and the different scripts that had been in use in feudal states like Chu 楚 and Qi 齊 were virtually forgotten.3 The oldest Mawangdui manuscripts are those written in script which is predominately seal or in a hybrid of seal and clerical script. They were probably copied ca. 220–190 B.C. The youngest manuscripts are in Han clerical script, and of course can be no younger than 168 B.C. (the burial date).1
Occasionally a manuscript avoids a graph that is the personal name of a Qin or early Han thearch. This evidence can sometimes supplement script analysis in dating a manuscript. For example, in one of the medical manuscripts the graph _chang_ 常 replaces _heng_ 恒, the latter graph being the personal name of Liu Heng 劉 恒, Thearch Wen 文 帝 (r. 180–157 B.C.). The manuscript must have been copied sometime after 180 and before 168 B.C. (see _MS_ VI.B in the "List of Mawangdui Medical Manuscripts and Texts" below). However, evidence of name avoidance or the lack of it is often inconclusive. The manuscript containing the second _Laozi_ edition avoids _bang_ 邦, the personal name of the Han founder Liu Bang 劉 邦 (the High Thearch 高 帝, r. 202–195 B.C.), replacing it with _guo_ 國. But the calligraphy looks identical to an astrological manuscript that refers to a date in the reign of Thearch Wen; both manuscripts were probably copied by a single scribe in the period 180–168 B.C. ( _MWD_ , vol. 1: "Chuban shuoming"). Curiously, the second _Laozi_ edition does not avoid Thearch Wen's personal name; yet the medical manuscript ( _MS_ VI.B), copied during the same period of years, does. We do not have any contemporary accounts of the rules governing name avoidance in Qin and early Han times. The assumption has been that the use of the graph was prohibited during the reign of the thearch in question and perhaps for some time after the reign ended. This is borne out in the case of the medical manuscript (the reigning thearch's personal name is avoided), while the _Laozi_ edition offers a counter-example. It is difficult to guess the factors that determined why one scribe observed the prohibition and another did not. And the example underscores the difficulty of relying on name avoidance to date any of the Mawangdui manuscripts copied before Thearch Wen's reign.1
Examples of old Chu graphs in several manuscripts indicate that those manuscripts could only have been copied by scribes educated in the Chu tradition (Qiu Xigui 1990: 66; Li Xueqin 1981: 36–37). Changsha was politically attached to Chu before the Qin conquest and also participated in Chu culture. Simply based on the circumstances of the tomb, we might have surmised that the Mawangdui manuscripts were copied locally; the script evidence reinforces the surmise. There is also good evidence that some of the manuscripts were copied by a single scribe employed by Li fils. Five manuscripts in what appears to be the same calligraphy, a form of Han clerical script, can be dated to ca. 175 B.C.: the manuscript containing the second edition of the _Laozi_ , the _Yijing_ manuscript, a manuscript on physiognomizing horses, and two astrological manuscripts. Some common errors in writing graphs also ran through all five manuscripts.2 As for the medical manuscripts, some are older by virtue of their script and no two manuscripts are in the calligraphy of the same scribe; several contain the calligraphy of a second scribe. The majority of medical manuscripts were copied either before Li fils was born or during his infancy (assuming that he was about thirty when he was buried in 168 B.C.); either he collected old medical manuscripts himself or perhaps the manuscripts were part of an inherited family collection. Of course, dating the medical texts copied on the manuscripts is a separate problem from dating the manuscripts. In my judgment the medical texts are no earlier than third century B.C., and the Mawangdui manuscript editions of them may be fairly close in time to the original editions (see "Provenance and Hermeneutic Issues" below).
List of Mawangdui Medical Manuscripts and Texts
Five of the seven medical manuscripts are silk manuscripts; one consists of two sets of bamboo-slips, bound separately and rolled together in a single bundle; one consists of a set of wooden slips and a set of bamboo slips, bound separately and rolled together. The manuscripts do not include general titles for a whole manuscript nor do they provide titles for any of the texts within a manuscript. _MWD_ , vol. 4, arranges the manuscripts in a sequence beginning with the longest silk manuscript and concluding with the two bamboo- and wooden-slip manuscripts; and assigns titles to the texts on each manuscript. The list of manuscripts and texts below follows the sequence of manuscripts in _MWD_ , vol. 4, and identifies the assigned titles. To facilitate citation, I assign roman numerals I-VII to the manuscripts. When a manuscript contains a single text, no further indication is given; multiple texts on a manuscript are assigned letters. This form of identification is followed in the Translation, with the addition of arabic numerals to identify subdivisions of the texts in the translation (based on subdivisions in the original texts, like individual recipes in a recipe text). All references to the medical texts in the Prolegomena and Translation are in this citation style. Following the listing of each manuscript are data on its physical appearance, script, and date; and a brief description of the contents of each text.1
_MS_ I |
---|---
_MS_ I.A | "Zubi shiyi mai jiujing" 足 臂 十 一 脈 灸 經 (Cauterization canon of the eleven vessels of the foot and forearm)
_MS_ I.B | "Yin Yang shiyi mai jiujing," _jiaben_ 陰 陽 十 一 脈 灸 經, 甲 本 (Cauterization canon of the eleven Yin and Yang vessels, ed. A)
_MS_ I.C | "Maifa" 脈 法 (Model of the vessels)
_MS_ I.D | "Yin Yang mai sihou" 陰 陽 脈 死 候 (Death signs of the Yin and Yang vessels)
_MS_ I.E | "Wushier bingfang" 五 十 二 病 方 (Recipes for fifty-two ailments)
_MS_ I is a silk manuscript approximately twenty-four centimeters wide and 450 centimeters long. The silk had been folded; when excavated, the silk at the creases had rotted, leaving a stack of over thirty leaves. _MS_ I.E, with roughly 9,950 extant graphs, is the longest text on the manuscript and in the entire medical manuscript corpus.1 It occupies approximately five sixths of _MS_ I. The entire manuscript is in the calligraphy of the same scribe, with the exception of some text added at the end of _MS_ I.E by a second scribe at a later date ( _MS_ I.E.283, and some fragments). The script used by the first scribe is a form of seal script that is older than the seal and clerical hybrid used in the manuscript containing the first edition of the _Laozi_. The script of the second scribe is similar to the script of the latter manuscript. The major portion of _MS_ I in seal script was probably copied during the Qin, ca. 215 B.C.; and the addition by the second scribe probably dates to ca. 205–195 B.C.
_MS_ I.A–B both describe the paths of eleven _mai_ 脈 (vessels) inside the body; each vessel description is followed by a list of ailments associated with that vessel. There are six leg vessels and five arm vessels, which occur symmetrically on the left and right side of the body to give a total of twenty-two vessels (the Ceasing Yin vessel of the arm attested in the _Huangdi neijing_ is absent). The arrangement of vessels in _MS_ I.A is leg vessels first followed by arm vessels; each group is further subdivided into Yang and Yin vessels. _MS_ I.B arranges the Yang vessels first and the Yin vessels second; within each group the leg vessels come before the arm vessels (the Yang arm-vessel names are "shoulder vessel," "ear vessel," and "tooth vessel," not the three technical names for the Yang vessels used elsewhere in _MS_ I.A–B). Cauterization ( _jiu_ 灸) is the only therapy mentioned in both texts (at the end of every vessel entry in _MS_ I.A, and once in _MS_ I.B.9). The vessel descriptions in _MS_ I.A are briefer and the listing of ailments is less elaborate than in _MS_ I.B. Also, _MS_ I.B contains more text parallels with the enumeration of vessels and ailments in the _Lingshu_ 10 essay entitled "Jingmai" 經 脈 (Conduit vessels). _MS_ II.B is another edition of _MS_ I.B. A third edition of _MS_ I.B occurs in the Zhangjiashan 張 家 山 manuscript _Maishu_ 脈 書 (Vessel book; see below). The _Maishu_ edition is the best preserved of the three.
_MS_ I.C is a brief discussion of vessel theory in three parts: the first discusses pathogenic conditions of _qi_ 氣 (vapor) in the vessels and cauterization, concluding with a reference to cutting vessels open with a lancing-stone; the second concerns lancing technique, using the draining of pus from abscesses with lancing-stones as a model for how to open vessels; the third discusses vessel diagnosis, performed at the ankle. _MS_ I.C was so severely damaged that it was largely unreadable before the discovery of a second edition in the Zhangjiashan _Maishu_.
_MS_ I.D is the shortest text on the manuscript (approximately eighty-nine extant graphs). It concerns fatal signs associated with the Yin and Yang vessels as well as with five body constituents: flesh, bone, vapor, blood, and muscle. A second edition occurs in the _Maishu_.
_MS_ I.E is a manual of recipes to treat ailments, arranged by categories of ailment. A list of the ailment categories at the beginning of the text gives fifty-two names. At the end of the text the second scribe added recipes for several more ailments which are not indicated in the original list. In its current state of preservation there are 283 recipes (nineteen fragments from the left end of _MS_ I are transcribed in _MWD_ , vol. 4: 76–82, but I do not translate them and do not include them in the recipe count). The ailments range from flesh wounds and warts to hemorrhoids, snake bites, and child sprites (a demonic affliction). The recipes sometimes are a brief sentence (to treat a snake bite, "daub mulberry liquid on it"), and sometimes include detailed descriptions of symptoms, drug preparation, and therapy. Nearly forty recipes detail exorcistic incantations and magico-religious operations; and they are interspersed among recipes for the same ailments which use drugs and other therapies.
_MS_ II |
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_MS_ II.A | "Quegu shiqi" 却 榖 食 氣 (Eliminating grain and eating vapor)
_MS_ II.B | "Yin Yang shiyi mai jiujing," _yiben_ 陰 陽 十 一 脈 灸 經, 乙 本 (Cauterization canon of the eleven Yin and Yang vessels, ed. B)
_MS_ II.C | "Daoyin tu" 導 引 圖 (Drawings of guiding and pulling)
_MS_ II is a silk manuscript forty-nine to fifty centimeters wide and 110 centimeters long. The manuscript was found beneath _MS_ VI and _MS_ VII in the side-compartment of the lacquer box. _MS_ II.A–B occupy roughly eighteen centimeters at the front of the manuscript, written on twenty-six columns ruled in red ink. Another twenty ruled columns which are blank follow (evidently more texts were planned for the manuscript than were actually copied onto it). The _MS_ II.C drawings begin immediately after the blank columns. _MS_ II.A–B are in the calligraphy of a single scribe; the script is a hybrid of seal and clerical. The manuscript was probably copied ca. 205–195 B.C.
_MS_ II.A concerns dietetics and breath cultivation in macrobiotic hygiene. The first part of the text discusses the technique of "eliminating grain" ( _quegu_ 却 穀; that is, eliminating ordinary foodstuffs) by consuming the herb _shiwei_ 石 韋 (pyrrosia) and by performing breathing exercises in the morning and evening. The second part discusses a seasonal regimen of breath cultivation, identifying five vapors in the external atmosphere to be avoided and six to be consumed by the practitioner. Seasonal cultivation of the "six vapors" is similar but not identical to breath cultivation in the lost _Lingyang Ziming jing_ 陵 陽 子 明 經, fragments of which are preserved in early commentaries. _MS_ II.B is another edition of _MS_ I.B, probably included in _MS_ II because of the importance of vessel theory for macrobiotic hygiene (I do not translate _MS_ II.B).
_MS_ II.C consists of forty-four drawings of human figures performing exercises. Many of the drawings are damaged and most of the original captions with the names of the exercises are missing. The extant names indicate that some exercises are intended to treat ailments while others are part of a program of hygienic cultivation. One or two of the exercise names are attested in received literature. The Zhangjiashan manuscript _Yinshu_ 引 書 (Pulling book; see below) provides written descriptions of many exercises, some of which have the same name as drawings in _MS_ II.C. However, the _Yinshu_ descriptions mostly do not match the _MS_ II.C drawings. _Yinshu_ and _MS_ II.C both exemplify the hygienic exercise tradition known as _daoyin_ 導 引 (guiding and pulling) in early sources.
_MS_ III |
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_MS_ III | "Yangsheng fang" 養 生 方 (Recipes for nurturing life)
_MS_ III is a silk manuscript approximately twenty-four centimeters wide. The silk is severely damaged, making it impossible to accurately estimate the length (the extant pieces in the reproduction measure roughly 140 centimeters). The script is a hybrid of seal and clerical similar to _MS_ II (the calligraphy is not identical); _MS_ III was probably also copied ca. 205–195 B.C.
_MS_ III is basically a recipe manual for macrobiotic hygiene. In its present state of preservation there are eighty-seven recipes, followed by several entries related to sexual cultivation and exercise. There is a list of recipe categories at the end. Recipes for tonic drugs, foods, and beverages occur throughout the text. Aphrodisiacs for men and women are grouped in the first half of the text, interspersed with other types of recipes. Two recipe categories near the end of the text concern travel, including recipes for increasing one's speed on the road. The travel recipes are about evenly divided between drugs and magical operations. The final entries related to sexual cultivation and exercise include several text parallels with _MS_ VI.A–B and _MS_ VII.B. _MS_ III.91 is a labeled diagram of the female genitals.
_MS_ IV |
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_MS_ IV | "Zaliao fang" 雜 療 方 (Recipes for various cures)
_MS_ IV is a silk manuscript approximately twenty-four centimeters wide. The silk is severely damaged (the extant pieces in the reproduction measure sixty-five centimeters). Following _MS_ IV.25 there are about six blank ruled columns before a major gap in the manuscript. The script of _MS_ IV.1–25 and _MS_ IV.26–42 (after the blank columns and gap) is similar—a seal script reminiscent of _MS_ I. However, the calligraphy of _MS_ IV.26–42 does not match _MS_ IV.1–25. The two sections were evidently copied by different scribes. The contents of the two sections are also sufficiently different to warrant identifying _MS_ IV.1–25 and _MS_ IV.26–42 as distinct texts on the manuscript. The title assigned to the whole manuscript in _MWD_ , vol. 4, reflects a judgment that the two sections constitute a single text of mixed content. While the grounds for a formal division into two texts are strong (especially the occurrence of blank columns separating the two sections), I refrain from altering the identification of _pian_ given in _MWD_ , vol. 4.1 Based on the similarity between the script of _MS_ I and _MS_ IV, _MS_ IV was probably copied ca. 215–205 B.C.
Most of the recipes in _MS_ IV.1–25 are similar to the aphrodisiacs and tonics of _MS_ III. _MS_ IV.22–23 concern burial of the afterbirth to ensure the well-being of the newborn infant. _MS_ IV.28–35 are recipes for venomous bites, in particular attacks by a deadly southern water creature named _yu_ 蜮 ( _yu_ lore is well represented in received sources, but the biological identity of the creature is unknown). Most of these recipes are magical.
MSV |
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_MS_ V | "Taichan shu" 胎 産 書 (Book of the generation of the fetus)
_MS_ V is a silk manuscript approximately forty-nine centimeters wide and forty-nine centimeters long. It was folded into quarters. The script is similar to the Qin clerical script of the Shuihudi 睡 虎 地 tomb 11 manuscripts (burial dated ca. 217 B.C.). The graph _zhi_ 雉 occurs in the text, which is the personal name of Dowager Lü 呂 太 后. Dowager Lü was the de facto ruler of the Han realm from 188–180 B.C. (Twitchett and Loewe 1986: 135–36). Both the type of clerical script and the lack of name avoidance suggest a date before 188 B.C. for _MS_ V, perhaps as much as several decades before.
The contents of _MS_ V all concern childbirth. The top half contains two drawings. The first drawing represents a technique for predicting the child's fortune at birth by consulting two human figures surrounded by the twelve Branch signs. The same drawing occurs in the first Shuihudi hemerological manuscript, which includes text to explain its use (see "Other Excavated Manuscripts Related to Medicine" below). The second drawing is a chart used to determine the most auspicious burial site for the afterbirth; the use of the chart is explained in _MS_ IV.22. _MS_ V.3 is a description of gestation with instructions for the care of the fetus during pregnancy. There are extensive text parallels in the medieval _Zhubing yuanhoulun_ 諸 病 源 候 論, "Renzhen hou" 妊 娠 候; and _Qianjin yao_ _fang_ 千 金 要 方, "Xu Zhicai zhuyue yangtai fang" 徐 之 才 逐 月 養 胎 方 (both texts are reproduced in _MWD_ , vol. 4: 140–41). _MS_ V.3 is clearly the textual antecedent of the medieval accounts of gestation. _MS_ V concludes with recipes for afterbirth burial, child conception, gender fixing, easing birth, and ensuring the child's vigor.
_MS_ VI |
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_MS_ VI.A | "Shiwen"十 問 (Ten questions)
_MS_ VI.B | "He Yin Yang" 合 陰 陽 (Conjoining Yin and Yang)
The 101 bamboo slips of _MS_ VI.A are approximately twenty-three centimeters long and .8 centimeters wide; the thirty-two bamboo slips of _MS_ VI.B are approximately twenty-three centimeters long and one centimeter wide. The two sets of slips were originally bound separately. _MS_ VI.A had been rolled first and _MS_ VI.B was rolled around the outside of _MS_ VI.A. The bundle was set on top of the silk manuscripts in the side-compartment of the lacquer box. The binding cords were disintegrated and the slips slightly jumbled. The exact position of each slip at the time of excavation and the contents of the texts were used to restore the correct sequence of slips (I differ with _MWD_ , vol. 4, over the sequence of slips in _MS_ VI.A). The script in both texts is Han clerical with a cursive quality to it; however, the calligraphy in each belongs to a different scribe ( _MS_ VI.B is more cursive than _MS_ VI.A). Perhaps these texts written by different scribes on separate sets of bound bamboo-slips were always kept as a single manuscript in Li fils' book collection; but it is also possible that they were first rolled together when they were placed in the lacquer box. In the case of _MS_ VII, it is very unlikely that the wooden and bamboo slips of _MS_ VII.A–B Were kept as a single manuscript prior to being placed in the box. However, rolling two sets of bound slips—each containing a different text—into a single bundle may have been a common practice when storing bound-slip books. Thus I concur with _MWD_ , vol. 4, which treats the two bundles of slips as two manuscripts ( _MS_ VI and _MS_ VII) with two texts each rather than break the two bundles into four separate manuscripts. _MS_ VI.B writes the name of Constancy Mountain (the northern of the five sacred peaks) as 常 山, replacing the original graph _heng_ 恒 in the name of the mountain with _chang_ 常 to avoid the personal name of Thearch Wen (the fact that _chang_ was first used in the mountain name because of Thearch Wen is well documented). It must be post-180 B.C. _MS_ VI.A is probably no older.
_MS_ VI.A contains ten dialogues in which ten macrobiotic specialists respond to questions. The Yellow Thearch is the questioner in the first four dialogues, a reflection of his role as a student of esoteric knowledge in third to first century B.C. literature (the _Huangdi neijing_ is the most notable example of the dialogue genre featuring the Yellow Thearch; Seidel 1969: 50–51). Rong Cheng 容 成 and Ancestor Peng 彭 祖, well-known exponents of macrobiotic hygiene in received literature, are among the specialists. The teachings include instructions for executing cultivation techniques, often describing the process in esoteric and metaphoric language. There are a number of text parallels with the sexual cultivation techniques in _MS_ VI.B and _MS_ VII.B.
_MS_ VI.B focuses on sexual cultivation. The text opens with an esoteric poem summarizing intercourse from foreplay to achieving the goal of sexual cultivation. Subsequent sections of the text analyze the sex act and classify its essential parts in order to make intercourse conform to a macrobiotic regimen. Both _MS_ VI.B and _MS_ VII.B are the textual antecedents of the medieval sex manuals preserved in chapter 28 of the tenth century Japanese medical compendium _Ishinpô_ 醫 心 方.
_MS_ VII |
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_MS_ VII.A | "Zajin fang" 雜 禁 方 (Recipes for various charms)
_MS_ VII.B | "Tianxia zhidao tan" 天 下 至 道 談 (Discussion of the culminant way in Under-heaven)
The eleven wooden slips of _MS_ VII.A are approximately twenty-three centimeters long and 1.2 centimeters wide; the fifty-six bamboo slips of _MS_ VII.B are approximately twenty-eight centimeters long and .5 centimeters wide. The two sets of slips were originally bound separately. _MS_ VII.B was rolled around two bamboo flutes (one about twenty-five centimeters long, the other about twenty-one centimeters) and _MS_ VII.A was rolled around the outside of _MS_ VII.B. The bundle was placed beside _MS_ VI in the side-compartment. As with _MS_ VI the sequence of the loose slips was reconstructed based on their position at the time of excavation and on the contents of the texts (I differ with _MWD_ , vol. 4, over the sequence of slips in _MS_ VII.A). The script in _MS_ VII.A is highly cursive Han clerical; _MS_ VII.B is written in a more regular Han clerical. Both texts were probably copied within a period of one or two decades before Li fils' burial.
The charms and philters in _MS_ VII.A reflect popular magic of the times. Crying infants and marital disharmony are among the daily problems that can be stopped by spreading a five- _chi_ band of mud at specified places. An opponent in a suit will be magically trampled if you write the person's name and put it in your shoe. Three of the four philter recipes are to seduce the object of desire; one is to split apart a married couple. This type of popular magic also occurs in medieval literature, as attested both in chapter 26 of the _Ishinpô_ and in the demonography _Baizetu_ 白 澤 圖.
_MS_ VII.B concerns primarily, but not exclusively, sexual cultivation. Numerous text parallels with _MS_ VI.B suggest that the contents of both texts were drawn from a common body of macrobiotic literature (which also accounts for the text parallels in _MS_ III and _MS_ VI.A). In addition to sections which classify parts of the sex act like _MS_ VI.B, there are several sections with brief essays that are unique to _MS_ VII.B. The assigned title in _MWD_ , vol. 4, is taken from a heading written on a separate slip at the beginning of _MS_ VII.B.3.
Other Excavated Manuscripts Related to Medicine
The Mawangdui medical manuscripts remain the largest single collection of third to second century B.C. medical literature currently known to us. However, bamboo- and wooden-slip manuscripts from five additional tombs (the earliest is ca. 230–220 B.C.; the latest is first century A.D.) supplement the Mawangdui medical manuscripts and broaden our knowledge of early Chinese medicine. Not all of them are exclusively medical manuscripts, but all fall within the category of _fang_ -literature. Still other tombs have yielded exemplars of _fang_ -literature exclusive of medical contents. Even these discoveries are significant because they testify to the dissemination of _fang_ -literature across the several geographical and cultural regions of ancient China. While we still cannot quantify exactly how popular _fang_ -literature was among the elite, we at least know that the Mawangdui collection of _fang_ -literature is not an isolated phenomenon.
Two medical manuscripts from Zhangjiashan 張 家 山 tomb 247 in Jiangling 江 陵, Hubei, are particularly important. The tomb, which was excavated in late 1983, dates to no later than the mid-second century B.C. The tomb is near in date to Mawangdui tomb 3 and is also situated in the old land of Chu. In addition to the medical manuscripts, tomb 247 contained judicial and administrative documents as well as works on military strategy and mathematical calculations. All of the manuscripts are written in Han clerical script.1 Titles written on the back side of the first slip of each manuscript are in the calligraphy of a single scribe, suggesting that the titles were not original but were added to the manuscripts as a group afterwards. Whether the titles represent the generally acknowledged name for the text(s) placed on a particular manuscript, whether the scribe added descriptive titles under instructions from the man buried in tomb 247, or whether the titles were added after his death when these manuscripts were selected as burial goods from his book collection is not certain.2
The medical manuscripts are titled _Maishu_ 脈 書 (Vessel book) and _Yinshu_ 弓 書 (Pulling book).3 _Maishu_ contains six texts for which I assign titles as follows: "Ailment List" (SS1–15); "Eleven Vessels" (SS16–47; another edition of _MS_ I.B); "Five Signs of Death" (SS48–51; another edition of _MS_ I.D); "Care of the Body" (SS51–52); "Six Constituents" (SS53–55); and "Vessels and Vapor" (SS55–65; another edition of _MS_ I.C). "Ailment List" contains sixty-seven ailment names, sometimes with a few phrases on the symptoms of an ailment (five of the ailment names are lost because of lacunae). Most of the list is arranged anatomically: beginning at the head and ending at the feet, fifty-seven ailments are associated with a specific part of the body. Ten additional ailments that are not readily attached to a single region of the body conclude the list. "Ailment List" includes ailment names that are attested in received literature as well as names that were previously known only in the Mawangdui medical manuscripts. Vessel theory pathology does not enter into the identification of ailments in "Ailment List." Thus I cite it whenever possible to identify ailments in the Mawangdui medical manuscripts; and I correspondingly avoid relying on the understanding of a particular ailment in the _Huangdi neijing_ , which represents a later understanding grounded in vessel theory.
There are minor differences between _MS_ I.B and "Eleven Vessels," which I attribute to the fact that "Eleven Vessels" is a younger edition. Several differences between _MS_ I.B and _MS_ II.B suggest to me that _MS_ I.B and "Eleven Vessels" are more closely related, while _MS_ II.B may represent a different line of transmission (see Appendix 1). "Care of the Body" begins without interruption following "Five Signs of Death" in S51. It is a short statement on macrobiotic hygiene and the vessels. "Six Constituents" is an account of the six basic constituents of the body: bone, muscle, blood, vessel, flesh, and vapor. Each constituent exhibits a characteristic form of pain; and pain is a forewarning of physical breakdown. Following "Six Constituents" "Vessels and Vapor" begins without interruption in the bottom of S55 and continues to the end of the manuscript. The manuscript itself does not indicate any division between the end of "Five Signs of Death" and the beginning of "Care of the Body," nor between "Six Constituents" and "Vessels and Vapor."
With the discovery of _Maishu_ we have confirmation that three of the texts oil _MS_ I circulated among physicians and the elite during the second century B.C. (recall that _MS_ I was probably copied before the end of the third century B.C.). While the two manuscripts share three texts in common, they have selected differently from the pool of written medical knowledge for their remaining texts. The combining of "Five Signs of Death" with "Care of the Body," and of "Six Constituents" with "Vessels and Vapor" in _Maishu_ is noteworthy for placing a greater emphasis on macrobiotic hygiene than is evident in _MS_ I. I view the combination of texts in _Maishu_ as indicative of the influence of macrobiotic hygiene in the development of vessel theory (see Section Three, "Physiology").
The entirety of _Yinshu_ may be a single text devoted to exercise theory and practice within macrobiotic hygiene.1 I divide the manuscript into three texts, partly to facilitate reference to it and partly because it seems possible that these three portions of the manuscript could have been combined with different works to fashion other manuscripts. The texts, with my assigned titles, are: "Seasonal Regimen" (SS1–7); "Exercises" (SS8–103); and "Cultivation of the Body" (SS104–113). "Seasonal Regimen" concerns the hygienic activity appropriate for each season, including the morning wake-up routine and the times of the day when sexual intercourse is permitted. The text is introduced as the way of Ancestor Peng. "Exercises" begins with basic exercise movements, most of which have names ("measuring worm," "tiger pulling," "pulling Yang," etc.). Next are descriptions of exercise routines used for specific conditions—mostly ailments with some hygiene mixed in. Breathing is an integral part of the exercise routines. "Exercises" ends with a list of exercises and the parts of the body each exercise benefits. "Cultivation of the Body" concerns hygienic theory and the nature of illness.
Shuanggudui 雙 古 堆 tomb 1 in Fuyang 阜 陽, Anhui, is the burial of Xiahou Zao 夏 侯 竈, the second Lord of Ruyin 汝 陰 侯, who died in 165 B.C. according to historical records. The tomb was excavated in 1977. The bamboo and wooden slips of the manuscripts were not well preserved, thus the greater part of the texts is lost. Among the texts identified are fragments of the _Shijing_ 詩 經 _Yijing_ 易 經 and _Chuci_ 楚 辭. There are also texts on physiognomizing dogs, astrology, and hemerology. Among literature related to medicine, little remains of a text on breath cultivation, which is unfortunate because it might have supplemented _Yinshu_ and the Mawangdui macrobiotic hygiene texts. However, another manuscript is a unique discovery for early Chinese medicine. The contents are not strictly medical. The manuscript lists various substances, and for each identifies its applications (Fuyang Han jian zhenglizu 1983).
The title _Wanwu_ 萬 物 (Myriad things) has been assigned to the manuscript, based on a reference to the necessity of "investigating the myriad things" on the first slip (Fuyang Han jian zhenglizu 1988; Hu and Han 1988). _Wanwu_ catalogues human curiosity about the products of nature: a horse-gullet tube can be used to breathe under water; metal from Yue 越 is best for working with jade; _banxia_ 半 夏 (pinellia) fattens pigs; alkaline soil prevents drowsiness; _shiwei_ 石 韋 (pyrrosia) cures urine retention. _Wanwu_ represents a type of _fang_ -literature similar to the _Huainan wanbishu_ 佳 南 萬 畢 術 (ca. first century B.C.) and to passages in the _Shanhaijing_ 山 海 經 (ca. fourth century B.C.) which enumerate substances and their uses, including drugs used to cure ailments or to enhance physical well-being.1 _Wanwu_ lists many drugs used for ailments or for hygienic cultivation. Moreover, it shares drug and ailment names in common with the Mawangdui medical manuscripts; and the specific applications of some drugs to either an ailment or a cultivation technique also match. Thus, we now know that the drug knowledge implicit in many of the Mawangdui recipes was being disseminated in digests like _Wanwu_ (and the site of Shuanggudui tomb 1 extends the range of dissemination beyond Chu and into the Yellow River region). _Wanwu_ provides a clear antecedent to the genre of materia medica, the oldest received text being the _Shennong bencaojing_ 神 農 本 草 經 (Divine Agrarian's canon of materia medica) from the first or second century A.D. (the term _bencao_ 本 草 denoting knowledge of materia medica is not attested before the second half of the first century B.C.)2
Another type of early _fang_ -literature are compilations combining astrology and hemerology with an assortment of material related to divination and magic. Two such third century B.C. manuscripts were excavated from Shuihudi 睡 虎 地 tomb II at Yunmeng 雲 夢, Hubei, in 1977. The tomb dates to ca. 217 B.C., and is the site more often noted for the discovery of Qin judicial and administrative manuscripts (Hulsewé 1985). The second manuscript bears the title _Rishu_ 日 書 (Day book) at the end, referring to hemerological arts. Han accounts attest to the popularity of hemerological treatises among the elite. They were one of the vehicles for the dissemination of Yin Yang and Five Agent theories, whose correlations lay at the base of many of the numerological systems that determined whether a particular time or location was lucky or unlucky. As evidenced by the Shuihudi hemerological manuscripts, they were also a grab bag of miscellaneous occult knowledge (Harper 1985: 462–70). Hemerological texts have been recovered from other third and second century B.C. tombs, most recently in 1986 from Fangmatan 放 馬 灘 tomb 1 at Tian-shui 天 水, Gansu—a tomb that probably dates to ca. 230–220 B.C.3
Sections on iatromancy in the Shuihudi and Fangmatan hemerological treatises suggest cross-influences between iatromantic prediction of the cause and course of an ailment and the vessel-based diagnosis performed by physicians like those whose ideas are contained in the _Huangdi neijing_. Perhaps the iatromantic systems—which utilize Yin Yang and Five Agent theories—preceded vessel-based diagnosis, which for the first time incorporated Yin Yang and Five Agent ideas into medical diagnosis.1 Iatromantic ideas are not evident in the Mawangdui medical manuscripts. However, other kinds of sharing between the Shuihudi and Mawangdui manuscripts are in evidence. The method for predicting the fortune of a child based on the Branch sign of the date of birth in the first Shuihudi hemerological manuscript ( _SHD_ : 206) occurs in _MS_ V.1. The belief that demons cause ailments, which are cured by exorcising the demons, is documented in a short demonography entitled "Jie" 詰 (Spellbinding) in the first hemerological manuscript; the same conception underlies the magical recipes in _MS_ I.E ( _SHD_ : 212–16; Harper 1985; Harper 1990: 217–25). And scattered throughout the Shuihudi and Fangmatan hemerological manuscripts is evidence of magic-incantations and other magico-religious acts—that has exact counterparts in the Mawangdui medical manuscripts. Thus, the hemerological manuscripts provide yet another context for occult knowledge which in the Mawangdui manuscripts is presented in a primarily medical context (see Section Five, "Magical Recipes" and "Varieties of Magic"). Evidently by the third century B.C. this kind of occult knowledge was being widely disseminated in _fang_ -literature, be it in medical books or in hemerological treatises. The geographic distribution of the excavated hemerological manuscripts from the north to the south once again attests to the broad dispersion of the knowledge contained in _fang_ -literature.
The final site to yield manuscripts related to medicine is a tomb near Wuwei 武 威, Gansu, excavated in 1972. The tomb dates to sometime in the first century A.D. Two sets of wooden slips were discovered—a total of seventy-eight slips—containing recipes to treat ailments. The binding cords had disintegrated; while it is not possible to reconstruct the original sequence of the slips in each set, the several slips recording a single recipe can be grouped together by context. Another fourteen wooden tablets were also discovered, most of which had several columns of text written on both surfaces of the tablet. One tablet concerns hemerological prohibitions related to medical treatment; one concerns astrology; and one is a drug price list. The remaining eleven tablets contain recipes similar to those in the wooden slips. The drugs, ailments, and treatments in the Wuwei recipes are quite similar to the Mawangdui recipes texts, in particular _MS_ I.E. In tracing developments in early Chinese medicine, the Wuwei medical manuscripts provide an important bridge between the Mawangdui medical manuscripts and later received medical literature.1 There have been other discoveries in the northwest of Later Han wooden slips and tablets with medical contents, but none comparable to the Wuwei manuscripts (Unschuld 1986a: 15).
Provenance and Hermeneutic Issues
In order to better situate the Mawangdui medical manuscripts in the overall scheme of early medicine and medical literature one Would like to know much more about their history before the manuscripts were packed in the lacquer box and buried. Speculation on the intellectual and social milieu in which medical and other manuscripts related to natural philosophy and occult thought circulated will occupy us in Section Two. The contents of the Mawangdui medical manuscripts are surveyed in the subsequent three sections. My purpose here is to raise briefly several textual questions concerning the manuscripts. How old are the texts? Who were the authors, the scribes, the collectors? Are the manuscripts representative of third to second century B.C. medical literature? What sort of interpretive principles are best applied to the manuscripts? There are, of course, no absolute answers to the questions, yet addressing them brings some clarity to the evaluation of the medical manuscripts.
For reasons discussed in Section Two I assume that physicians were primarily responsible for medical literature, of which the earliest examples are now the Mawangdui medical manuscripts. At the same time, the elite participated in medicine, and the probability is great that the elite contributed to the production and dispersion of medical literature. Moreover, oral medical knowledge of both the popular and esoteric varieties was being continually committed to writing in ways that we cannot trace exactly. Pronouncing final judgment on the provenance of the Mawangdui medical manuscripts is not feasible. But as indicated in the listing of the fourteen medical texts and in the survey of other excavated manuscripts above, the Mawangdui manuscripts exhibit a range of textual relations not only with the other manuscripts but also with later received medical literature. This alone justifies a presumption of representativeness for them.
Who copied the medical manuscripts and how they were acquired are matters for conjecture. Li fils' manuscript corpus includes many examples of _fang_ -literature in addition to the medical manuscripts. Other members of the Li family may have preceded Li fils in collecting _fang_ -literature. He himself no doubt patronized specialists in natural philosophy and occult knowledge. Perhaps the very specialists he patronized were the scribes of his manuscripts; he even might have copied several himself (the transmission of _fang_ -literature and elite patronage are examined in Section Two, "Readership and Transmission"). We also know that in the second century B.C. men of education were employed to "copy books" ( _xieshu_ 寫 書)for others. Thearch Wu established an office for "copying books" to supply his library with fair editions of all works of literature, presumably employing as scribes the same men who filled other positions in the bureaucracy by virtue of their literacy ( _Hanshu_ , 30.1b). The ruling family in the second century B.C. included several prominent book collectors. Liu De 劉 德, the King of Hejian 河 間 王 (r. 155–129 B.C.), acquired many valuable old manuscripts by offering rewards and promising to provide the donor with a "fair copy" 好 寫. He obviously maintained a staff of scribes. Liu An 劉 安 (179–122 B.C.), the King of Huainan 淮 南 王, was also "fond of books" and must have kept a staff of scribes to copy the _fang_ -literature for which he was renowned ( _Hanshu_ , 53.1b). In Li fils we witness the bibliophilia of a broader spectrum of the elite (silk manuscripts were a luxury). In any case, in the second century B.C. it is too early to speak of a commercial book trade (the earliest reference to something we might call a bookshop where books were sold is first century A.D.; Tsien 1962: 15).
Turning to the question of the age of the medical texts, one must keep in mind that private literature did not exist before the fifth century B.C. Earlier writing consisted primarily of official records and collections like the _Shijing_ , which by the age of Confucius were revered as canons ( _Tsien_ 1962: 9–11). The Warring States was a watershed for the rise of private literature, the most prominent received examples being the books of the philosophers. _Fang_ -literature surely circulated in the fourth century B.C., however I regard the third century B.C. as the upper limit for the Mawangdui medical texts (some must be early second century B.C.). My judgment is influenced both by simple skepticism and by the contents of the Mawangdui texts. The third century B.C. saw the rapid development of medical ideas (including ideas about macrobiotic hygiene) and of natural philosophy in general. For vessel theory texts like _MS_ I.A–B to be relevant to medicine in the early second century B.C., I doubt that they would not reflect third century B.C. developments. Macrobiotic teachings in _MS_ VI.A.9–10 are attributed to two physicians who flourished in the late-fourth and early-third centuries B.C. The teachings themselves were probably recorded somewhat later; and the entirety of _MS_ VI.A with its full cast of legendary specialists is best treated as third century B.C. The composition of the recipe texts would have been especially fluid, since any one text might have drawn its collection of recipes from a variety of written and oral sources. There is certainly old medical knowledge in the recipes of _MS_ I.E, but lacking clear textual evidence of their antiquity I do not think we are justified in dating the text earlier than the third century B.C.
My assessment might change were fourth century B.C. tombs to yield comparable texts, but to date manuscripts from the late fourth century have been markedly more lapidary than third and second century B.C. manuscripts. A prime example of what could be called _fang_ -literature is the divination manuscript from Baoshan 包 山 tomb 2, Hubei, excavated in 1987. Written in Chu script in a terse, hieratic style, the manuscript is a personal record of turtle-shell divination and hexagram divination performed for the benefit of the tomb occupant during his lifetime (Hubei sheng Jing Sha tielu kaogudui 1991: 32–37). The world of divination and religion reflected in the text belongs to a time preceding the pervasive influence of correlative cosmology reflected in the third century B.C. Fangmatan and Shuihudi hemerological manuscripts. To generalize from a single example is incautious, but significant spiritual and intellectual changes were clearly underway between the fourth and third centuries B.C. The changes produced a flowering of specialists in natural philosophy and occult knowledge in the third century B.C., as well as an explosion of _fang_ -literature. The Mawangdui medical texts belong to the third century B.C. explosion along with the hemerological literature.
Where are we to place the Mawangdui medical texts in relation to Chunyu Yi's 淳 于 意 medical writings and the _Huangdi neijing_? The simple answer is "before." Complications immediately arise. Certainly the vessel theory texts in _MS_ I reflect an earlier theoretical stage than the _Lingshu_ 10 essay and other writings on vessel theory in the _Huangdi neijing_. Placing the _Huangdi neijing_ after the Mawangdui texts makes sense, and for a variety of reasons the first century B.C. represents the best date for its composition. Yet Chunyu Yi's career in medicine overlapped the life of Li fils. His medical writings reflect an understanding of vessel theory different from the _Huangdi neijing_ , but definitely more theoretically elaborate than the Mawangdui texts. Moreover, while Chunyu Yi used acupuncture infrequently, he did know the therapy. How are we to explain the contemporaneous Mawangdui texts (and Zhangjiashan editions) which do not know acupuncture?
One could propose several explanations—differences between medicine in the south (Chu 楚) and northeast (Qi 齊), Chunyu Yi's superior medical knowledge, etc. I think this is not the best approach to take to the problem. Ultimately, between the Mawangdui texts, Chunyu Yi's writings, and the _Huangdi neijing_ , we still lack sufficient evidence to fashion a complete, diachronic account of the development of medicine from the Warring States to the Han. A synchronic account of medicine in the third and early-second centuries B.C. based on the Mawangdui texts would also be seriously flawed. The texts are representative of medicine at that time, but one cannot claim they are the totality of medicine—and except for the Zhangjiashan manuscripts, there is as yet no other evidence. If the texts do not directly explain the genesis of acupuncture and of _Huangdi neijing_ medicine, they are nevertheless examples of medical literature before the _Huangdi neijing_. They are an embarrassment of riches; they are invaluable historical documents. The factual information contained in the Mawangdui medical manuscripts—which was unknown before their discovery—restores a picture of early Chinese medicine that had vanished from the received tradition. The manuscripts provide the basis for investigating a broader range of issues in early Chinese medicine than was possible in the past.
As a collection of texts unedited since burial in 168 B.C., the Mawangdui medical manuscripts present interpretive difficulties. The texts predate script normalization which tended to designate specific graphs as the standard graphs for specific words; in numerous instances the words and meanings intended by the graphs written in the texts are not obvious. Vocabulary can be technical and arcane, some of it obsolete and unattested outside of the manuscripts. And the idiom is sometimes puzzling. In received texts many of these difficulties have been smoothed out over the centuries in editions which use standard graphs and in commentaries which intend to make the meaning of the old texts plain. Indeed, we are accustomed to viewing ancient literature through the hermeneutic lens of editors and commentators (often the same individual). Already accorded canonical status in Han times, the subsequent history of the _Huangdi neijing_ wedded the original text to the hermeneutic endeavors of its editors and commentators.
_Huangdi neijing_ hermeneutics is a complex subject that cannot be investigated here. I raise it because of a tendency among some scholars working on the Mawangdui medical manuscripts to rely overmuch on the _Huangdi neijing_ to interpret the Mawangdui texts; and to adopt the _Huangdi neijing_ as the standard against which the Mawangdui texts are to be judged. Unattested anatomical terms are sometimes identified by reading the graphs as equivalent to graphs used to name acupuncture points (even though the Mawangdui texts predate the existence of a system of named acupuncture points). Ailments may be explained according to _Huangdi neijing_ etiology; _Huangdi neijing_ theory read into passages in the Mawangdui texts; and _Huangdi neijing_ parallels used to edit (and "correct") the Mawangdui passage. I advocate extreme caution when comparing the Mawangdui medical manuscripts to the _Huangdi neijing_ , lest interpretation of the manuscripts become attached to _Huangdi neijing_ interpretation.
Of course the _Huangdi neijing_ must be consulted. It is a rich resource; and it is medical literature. We would be at an even greater loss to explain the Mawangdui texts without it. And I do not mean to slight the honest efforts of scholars to devise an interpretive framework for the Mawangdui medical texts. We are all finding our way hermeneutically in uncharted territory. My own working method has chiefly entailed continuous evaluation of my contextual reading of a passage in one of the Mawangdui medical texts while casting about widely for pieces of evidence to solve textual puzzles. At times the _Huangdi neijing_ provided the solution; at times the solution came from unexpected sources. The best claim I can make for the tightness of my solutions is that they appear most suited to the context; a subjective claim to be sure, but one that I think holds up under critical scrutiny. Naturally other scholars have eased my work. The transcription notes in _MWD_ , vol. 4, are always insightful. _KGS_ , vol. 1, does not include all of the texts since it is based on transcriptions published before _MWD_ , vol. 4, but the notes and Japanese translation are of high quality. Among the Chinese scholars working on Mawangdui medical manuscripts, Ma Jixing has written an encyclopedic book that exhibits both his philological expertise and his erudition as a medical historian (1992). Other major contributions to Mawangdui medical manuscript studies are Zhou and Xiao (1988); Wei and Hu (1992); and Li Ling (1993: 281–402). I have also benefited from Wile's translation and study of Chinese sexual cultivation literature (which includes a translation of _MS_ VI.B and _MS_ VII.B; 1992); from Li and McMahon's study of the Mawangdui sexual cultivation texts (1992); and from Qiu Xigui's critical review of _MWD_ , vol. 4 (1992). I have learned from them all even if I do not always agree with them.
1During the first half of the second century B.C. the Kingdom of Changsha belonged to Wu Rui 吳 芮 and his descendants (Twitchett and Loewe 1986: 124). The three seals from tomb 2 are reproduced in Fu and Chen 1992: 40. Hunan sheng bowuguan and Zhongguo kexueyuan kaogu yanjiusuo 1973, vol. 1: 157, gives the succession of the Lords of Dai based on the _Shiji_ and _Hanshu_. Riegel (1975) summarizes the information on tombs 2 and 3 in the early archaeological reports published in Chinese journals. Initially, Li Xi's death date in the historical records was judged to eliminate him as the occupant of tomb 3. Fu Juyou (1983) offers a counter-argument that tomb 3 could only be that of the second Lord of Dai, and that the records of his death in 165 B.C. may be in error. Arguments for and against Li Xi continue to be made. Some scholars identify a commander named Sima De 司 馬 得 in a military garrison map found among the tomb 3 manuscripts as the tomb 3 occupant, reading Sima as an official title not as De's surname; others reject the identification. See Liu Xiaolu (1994), who favors Li Xi.
1My account of the manuscript discovery is necessarily provisionl. There are contradictions in published accounts (Hunan sheng bowuguan and Zhongguo kexueyuan kaogu yanjiusuo 1974; Xiao Han 1974; Wang Shimin 1986). I am indebted to Li Xueqin (private communication) for providing me with the information be acquired from those directly involved in the excavation of the manuscripts. In identifying the manuscripts I exclude a bamboo-slip manuscript that inventories the burial goods in the tomb (it is worth noting that the inventory not list the lacquer box containing manuscripts). The inventory, which was placed in the storage area on the west side of the coffins, is a type of burial document prepared specifically for the tomb. In contrast, the manuscripts in the box represent items that we may presume to have been selected from an even large collection of manuscripts possessed by the occupant of tomb 3 during his life. I also exclude three paintings on silk: one draped over the innermost coffin and related to burial custom; and two paintings that were positioned on the eastern and western walls of the burial chamber (Fu and Chen 1992: 22–34).
2Li Xueqin and Ma Jixing, both members of the medical manuscript committee responsible for _MWD_ , vol. 4, described to me the working procedures of that committee in conversations in Beijing in winter 1993.
3Excellent reproductions of some manuscripts as yet unpublished in _MWD_ appear in Fu and Chen 1992.
1My figures for the Mawangdui manuscript corpus are derived from Wang Shimin's enumeration of the silk manuscripts and texts (1986), to which I add the two manuscripts written on bamboo and wooden slips that contain four texts. The two manuscripts containing _Laozi_ editions and several lost philosophical texts are published in _MWD_ , vol.1. Reproductions of the _yijing_ hexagram text and the "Xici zhuan" are in Fu and Chen 1992: 106–26.
2It should be emphasized that the extant graph counts are rough estimates only, and are not based on my own research. Wang Shimin gives 120,000 for the whole corpus (1986: 307), but he does not include the tow medical manuscripts on bamboo and wooden slips. The table in Ma Jixing 1992: 4–5, counts 4,616 extant graphs in these manuscripts; and the extant graphs in all the medical manuscripts add up to 22,314 (Ma's total of 23,707 includes editions of three Mawangdui medical texts written on one of the Zhangjiashan tomb 247 manuscripts—discussed below—which I omit). Ma estimates extant graphs in the whole corpus to be 130,000 versus my 125,000 (1992: 1). Allowing for imprecision in both estimates, the figure of eighteen percent is still a fair representation of the amount of medical literature in the corpus as a whole.
1Keegan argues that the extant recensions of the _Huangdi neijing_ are basically compilations of composite texts fashioned from what he calls "primary texts" (1988: 252–54).
2See Tsien 1962: 116–30, on silk as a material for written documents in early China, which began to be used around the fifth century B.C. Bamboo and wood were used as early as the Shang. The most recent monograph on the Chu silk manuscript is Li Ling 1985.
1Another standard slip-length is one _chi_ two _cun_ , represented in excavated slips by roughly twenty-eight centimenter slips like the bamboo slips in _MS_ VII.
2Two _chi_ four _cun_ slips (just over fifty-five centimeters, double the length of one _chi_ two _cun_ ) were also used. At fifty centimeters, it is also possible that the wider silk represents a standard width for silk used as a commodity of exchange. The Qin administrative documents from Shuihudi 睡 虎 地 tomb II (see below) stipulate a width of two _chi_ five _cun_ (just under fifty-eight centimeters) for cloth, while Han sources give two _chi_ two _cun_ (just under fifty-one centimeters; _SHD_ : 36).
3Qiu Xigui provides an excellent overview of Qin to Han seal script and clerical script, including relevant paleographic evidence (1990: 59–72). Seal script was regarded in Qin as more formal—the appropriate script for inscriptions—whereas clerical script was a more convenient script for every day use. Paleographic evidence indicates that clerical script was already developing in Qin in the fourth century B.C., contrary to received accounts that associate the invention of clerical script with the Qin unification.
1Discussions on dating the manuscripts tend to speak of Qin, late Qin, end of Qin and beginning of Han, early Han, etc. I find it more convenient to give approximate dates using multiples of five and ten years to replace the rough period designations.
1The argument has also been made that avoidance of a thearch's personal name was observed after the reign ended, not during (Mansvelt Beck 1987: 68–76). But _MS_ VI.B could only have been copied during Thearch Wen's reign (which ended after Li fills was buried). Lacking contemporary documentation of name-avoidance rules, it is best to approach all cases of name avoidance with caution and to consider this evidence in conjuction with other evidence for dating once of the manuscripts.
2One of the astrological manuscripts was used as evidence for dating the _Laozi_ manuscript to the period 180–168 B.C. ( _MWD_ , vol 1: "Chuban shuoming"). Li Xueqin identified the group of five manuscripts in private conversation in Beijing in winter 1993, judging them to have been written by the same scribe. Not all of the manuscripts have been published. For partial comparisons, see Fu and Chen 1992: 106 ( _Yijing_ hexagram text), 130 (second _Laozi_ edition), and 132 (astrological manuscript).
1Information on physical appearance, script, and dating is mostly taken from Ma Jixing 1992: 2–5, 8–11; and _MWD_ , vol. 4: "Chuban shuoming." The photographic reproduction of the medical manuscripts in _MWD_ , vol. 4, maintains the original size with the exception of _MS_ II, which is approximately sixty percent of original size. Emura et al. 1987 is an index of the graphs in the medical manuscripts. The index reproduces different forms of the graphs as they appear in the seven manuscripts, which greatly facilitates study of the script and calligraphy. The exact location of each manuscript inside the lacquer box has been identified only for _MS_ II, _MS_ VI, and _MS_ VII, which were in the long side-compartment. I presume that the other manuscripts (all silk) were folded and placed in the rectangular compartment.
1See Ma Jixing 1992: 4–5. Ma provides three graph-count estimates for the texts: extant graphs, graphs that can be added to fill lacunae, and the original number of graphs in each text (a judicious surmise). All three figures represent his editorial judgment, with which I am not always in agreement. However, his estimate of extant graphs is a useful indicator of the length of the texts relative to one another. I occasionally cite his estimates (especially for longer texts), but do not treat them as absolute figures.
1Emura et al. also note the calligraphic differences between the two sections of _MS_ IV and suggest that they are two _pian_ rather than one (1987: v).
1See Zhangjiashan Han mu zhujian zhengli xiaozu 1985. An inventory of burial goods includes the manuscripts in the list, which is the earliest example of manuscripts being included in an inventory (the Mawangdui tomb 3 inventory does not mention manuscripts).
2I am indebted to Li Xueqin for information regarding the manuscript titles. The work of editing the Zhangjiashan manuscripts is not yet finished, and only selected transcriptions have appeared in simplified graphs in _Wenwu_.
3 _Maishu_ contains sixty-five bamboo slips; it is transcribed in simplified graphs in _MSSW_ (the original slips are not reproduced). _Yinshu_ contains 113 slips; it is transcribed in simplified graphs in _YSSW_ (slips not reproduced). The transcriptions mark the end of each slip but do not number them. Printing errors in _MSSW_ affect both the identification of the individual slips and several graphs. I am indebted to Li Xueqin, one of the editors of the Zhangjiashan manuscripts, for re-checking the photographic reproduction of _maishu_ kept at the Bureau of Cultural Relics in Beijing and providing me with corrections of _MSSW_ (Professor Li's corrections have been incorporated in the transcriptions of _MS_ I.B, and _MS_ I.C, and _MS_ I.D in Appendix 1). I am not aware of errors in _YSSW_. However, it is best to regard both transcriptions as provisional until reproductions of the manuscripts have been published. I have assigned the slip numbers which I use to identify the separate texts contained in the two manuscripts. Lian shaoming (1989) and Ma Jixing (1992: 158–72) examine the contents of _Maishu_ ; Peng Hao (1990), Li Xueqin (1991), and Li Ling (1993: 335–46) do the same for _Yinshu_.
1Li Xueqin treats _Yinshu_ as one text whose contents he divides into six sections (1991: 8).
1The _Huainan wanbishu_ (current editions are reconstructions based on preserved quotations) is associated with the _fangshi_ 方 土 (recipe gentlemen) at the Huainan court of Liu An 藰 安 in the second century B.C. (Kusuyama 1987). Drugs and their uses in the _Shanhaijing_ , a work replete with magico-religious lore, are itemized in Zhao Pushan 1986.
2See the discussion of _bencao_ in Unschuld 1986a: 11–16. Unschuld does not refer to _Wanwu_ because he was writing before the transcription was published.
3Transcriptions and reproductions of the two Shuihudi hemerological manuscripts are in _SHD_. The contents of the two Fangmatan manuscripts are described in He Shuangquan 1989a and 1989b; a transcription in simplified graphs of the first manuscript (without reproduction) is in Qin jian zhengli xiaozu 1989. I follow Li Xueqin's judgment on the dating of the Fangmatan tomb (1990). To date, none of the second century B.C. hemerological treatises have been published.
1For iatromancy in the Shuihudi hemerological manuscripts, see _SHD_ : 193, 245–46. The passages identify the demonic origin of an ailment and predict its course based on the conquest sequence of the Five Agents. I am currently preparing a study of the relation between the Shuihudi iatromantic passages and prognosis in the _Huangdi neijing_. Yamada (1980) has already demonstrated the influence of wind divination involving the deity Taiyi 太 一 in the _Huangdi neijing_ (cf. Unschuld 1982a; Unschuld 1985: 68–71). The occult, hemerological elements are eliminated or marginalized in the _Huangdi neijing_. He Shuangquan (1989a: 27) refers briefly to the Fangmatan treatise with iatromantic material, but the manuscript is not yet published.
1 _WWYJ_ provides a photographic reproduction, facsimile, and transcription; _KGS_ , vol. 1: 363–404, gives a transcription and Japanese translation.
Section Two
Medicine, Medical Literature, Medical Men
_MS_ VI.A.9 offers a vignette of a physician at court in the second half of the fourth century B.C. The physician is Wen Zhi 文 摯, known in the _Lüshi chunqiu_ as the physician from Song 宋 who cured King Min of Qi 齊 湣 王 (r. 300–284 B.C.) at the cost of his life (causing the ruler to explode with anger was the only treatment; and King Min would not forgive the physician's offensive behavior, which was calculated to cure him). _MS_ VI.A.9 finds Wen Zhi in better times advising King Min's predecessor King Wei 威 王 (r. 357–320 B.C.), eminent patron of learning and founder of the Jixia 稷 下 Academy. King Wei would like to hear just "two or three words" summarizing the physician's "way." Wen Zhi responds, "Your Servant's practice of the way consists of three hundred fascicles, but sleep is foremost." Thus begins a discussion of physical regimen, diet, drugs, and health with King Wei an active participant (at one point the ruler demands explanation of a seeming inconsistency in the physician's teaching). The interview is idealized, but no more so than interviews between Mencius and King Xuan of Qi 齊 宣 王 (r. 319–301 B.C.) which figure prominently in the _Mengzi_ (Graham 1989: 112). Much of Warring States philosophical literature records the philosophers' speeches, and the dialogue between a philosopher and a ruler is conventional. The written rendition of a given interview may be suspect as a historical record—its purpose, after all, is to formalize the teaching for the philosopher's partisans (and his disciples probably composed the text)—but the depiction of rulers questioning and listening to the philosophers accurately reflects a prominent feature of Warring States intellectual history.
Wen Zhi's interview with King Wei bears witness to a state of medicine and medical men which crystallized during the Warring States. Like the philosophers, the physician ( _yi_ 醫) possessed a way ( _dao_ 道); this way was recorded in his medical books (Wen Zhi's "three hundred fascicles" is self-advertisement and signifies that the written record of his way of medicine is "complete"). To teach medicine was to give verbal amplification of the books. Medical literature proliferated in the fourth to third centuries B.C. as new ideas arose and the impetus for committing knowledge to writing grew. The transformation of medicine from an archaic craft dominated by magico-religious belief and practice into a theoretically-grounded discipline was as much a function of the new literacy as it was of the rationalizing tendencies in thought. Medicine became one of many fields of natural philosophy that were defined by the books the specialists transmitted. Of course, the knowledge committed to writing was diverse. As documented in the Mawangdui medical manuscripts, incantations and magico-religious operations were collected together with other medical recipes. If such practices had once been the preserve of religious officiants and shamans ( _wu_ 巫), or formed part of oral folklore, they acquired a new kind of prestige as they were incorporated into the books of specialists in natural philosophy and occult knowledge. Magic became a technique to be taught and transmitted in books along with other techniques; it became a segment of occult thought.
I attribute the emergence of a learned and literate medicine between the fourth and first centuries B.C. to the _yi_ 醫, the word I translate as "physician." The word antedates the Warring States; etymologically, _yi_ is related to words for exorcism in Shang inscriptions (see Section Five, "Varieties of Magic"). The notion of _yi_ as originally a medicine man is also evident in the Warring States legend that credits Shaman Peng 巫 彭 with creating the profession of physician in antiquity. Even during the Warring States and through the Han, the compound _wuyi_ 巫 醫 sometimes meant shamans and physicians collectively and sometimes was an epithet for a "shaman-physician." Received sources often contrast the methods of the _wu_ with those of the _yi_ , the former specializing in incantation and ritual and the latter in drugs and other therapies. The contrast is sometimes pejorative, but not always; that is, patients continued to believe in the efficacy of shamanic medicine, and physicians did not uniformly eschew magic (Harper 1982: 42–47). Despite the flexible attitudes, by Warring States times physicians participated in the new text-based alignment of knowledge, which distanced them socially and intellectually from shamans who formed part of the substratum of a popular religion about which we know little.1 Moreover, magico-religious skills were now part of an occult tradition; books of incantations and demonological lore circulated. Parallels between the forms of magic in the Mawangdui medical manuscripts and in the Shuihudi hemerological manuscripts suggest that in both cases the source of much of the magical lore was textual (Harper 1985; Harper 1990; Harper forthcoming). Occult literature certainly drew upon oral traditions of popular and shamanic religion; but it also changed the perception of magic among the elite and connected magic to natural philosophy.
Medicine was practiced by others besides physicians. Some participated in the same text-based traditions as the physicians. Diviners and astrologers practiced iatromancy; and popular iatromancy is recorded in the Shuihudi hemerological manuscripts ( _SHD_ : 193, 246). Macrobiotic hygiene was among the many specialties of the recipe gentlemen ( _fangshi_ 方 士). Cross-fertilization between medicine and other branches of natural philosophy led as well to the assimilation of Yin Yang and Five Agent theories. Oral medical traditions were probably transmitted not only by shamans, but also by drug gatherers,1 midwives,2 and wet nurses. No doubt some of the material in the Mawangdui medical manuscripts should be attributed ultimately to such sources. However, the formation of the discipline of medicine backed by medical literature was accomplished by physicians. By the fourth century B.C. physicians were transmitting a written "way" of medicine. Their organization placed them in a relationship with other specialists in natural philosophy and occult knowledge as well as with the philosophers. A physician taught his way to select disciples, to whom he also transmitted his books. And the elite were not simply patients; they patronized physicians and collected their books.
The Mawangdui medical manuscripts belonged to this social and intellectual milieu. The following account of medicine, physicians, and their literature is an attempt to reconstruct the world in which the manuscripts were produced. I begin with the concepts that defined medicine as a field of knowledge and linked medicine to other fields. Then I discuss the readership for and transmission of medical literature.
Recipes, Techniques, Calculations, Arts
_Yi_ 醫 can denote the field of medicine. When the First Qin Thearch 秦 始 皇 帝 banned literature in 213 B.C., books on _yi_ (medicine) and _yao_ 藥 (drugs) were exempted ( _Shiji_ , 6.22b). Chunyu Yi 淳 于 意 also writes of "medicine and drugs" ( _Shiji_ , 105.8b), but usually he refers to the practice of medicine using terms which emphasize medicine as a technical skill. _Fang_ 方, a word that refers to "methods" for carrying out a procedure and to "written recipes," is ubiquitous in his writings.1 To practice medicine is to "practice recipes" ( _wei fang_ 爲 方; _Shiji_ , 105.23a); medical books are "recipe books" ( _fangshu_ 方 書; _Shiji_ , 105.8b). One learns medicine by studying a physician's recipe books—which are "prohibited" ( _jin_ 禁), meaning they are secret ( _Shiji_ , 105.9a). Given Chunyu Yi's usage, the title of the division of medical literature in the _Hanshu_ bibliographic treatise clearly represents a label that physicians themselves would have applied to medicine. "Fangji" 方 技 (Recipes and techniques) pairs the "recipes" which are the core of medicine with a standard word for skillful "technique" in any endeavor.2
If recipes and techniques were what defined medicine for physicians, they were also what connected physicians to other specialists in natural philosophy and occult thought. The division in the _Hanshu_ bibliographic treatise entitled "Shushu" 數 術 (Calculations and arts) parallels "Fangji" ( _Hanshu_ , 30.78b). _Shu_ 數 must refer in part to cosmological "calculations," since "Shushu" is the location of books on astrology, the calendar and hemerology, and Yin Yang and Five Agent correlations; _shu_ "art" is the most common term for technical skill. At the same time, "Shushu" is a grab bag of occult literature, including divination, demonology, and incantation. What appears to be a heterogeneous mixture makes sense when one realizes the chief criterion for classifying these books in the same division: they all concern techniques applied to dealing with particular areas of the natural world and spirit world. Thus the specialists in various fields of natural philosophy and occult knowledge were appreciated above all for the results of their _shu_ "calculations" and _shu_ "arts"; simultaneously, physicians were known by their _fang_ "recipes" and _ji_ "techniques."
The picture that emerges of medicine in relation to natural philosophy and occult thought has several important features. To begin, physicians regarded themselves as part of a text- and technique-based tradition that extended to many kinds of specialists. Before the Warring States, the practice of medicine, astrology, or divination was often inherited within a family tradition.1 By the Warring States, medicine had become a field of knowledge alongside other fields. And general interest in techniques crossed the boundaries between fields. Although Chunyu Yi lived in the second century B.C., his experiences must have represented a common pattern for physicians by the third century B.C. Chunyu Yi did not come from a family of physicians. He was drawn to medicine because as a boy he "liked all matters related to recipes." Even before being accepted as a disciple by his first teacher Gongsun Guang 公 孫 光, Chunyu Yi had been collecting whatever recipes he could obtain and testing them ( _Shiji_ , 105.23a). One wonders whether the recipes were necessarily all medical. Perhaps his youthful curiosity was drawn to the myriad phenomena of the sort recorded in the Shuanggudui manuscript _Wanwu_. Later, when Gongsun Guang recommended Chunyu Yi to the son of his future teacher Yang Qing 陽 慶, he characterized Chunyu Yi as "fond of calculations" ( _Shiji_ , 105.24a). No doubt the phrase praises his talent for medical study; it also reflects the easy communication between the fields of natural philosophy and occult knowledge.
Ideas arise in an environment. Was it common interests and communication among physicians and the other specialists that produced theories of nature? If so, where are the Warring States philosophers in the picture of early Chinese natural philosophy and occult thought? By the third century B.C. the belief that all knowledge and action could be formulated as a technique was widespread, and the philosophers also used the vocabulary of "recipes" and "arts" to designate the techniques of statecraft, rhetoric, mind cultivation—virtually any significant activity had a skill particular to it.1 To be sure, _dao_ "way" as a central idea in philosophy was always more concerned with patterns of human behavior than with abstract questions of truth and reality; the aim of philosophy beginning with Confucius was to present a course for humans to follow.2 But the Warring States emphasis on defining techniques to quantify _dao_ reflects both rationalizing tendencies in thought and the increasing specialization of knowledge. The trend had its critics. A _Zhuangzi_ passage that is probably mid-second century B.C. assesses five groups of philosophers, opening with the statement: "Those who cultivate _fangshu_ 方 術 (recipe-art) have become numerous... but where can be found what of old was called _daoshu_ 道 術 (way-art)."3 Interestingly, all philosophy is assumed to be an art. The subsequent passage decries the fragmentation of _dao_ into the many _fang_ of the philosophers, who are treated as recipe peddlers ( _fangshu_ and _daoshu_ occur as synonyms for skillful knowledge in other philosophical writings, thus the pointed contrast between the philosophers' fragmented "recipes" and the undivided "way" in the _Zhuangzi_ was not the common understanding).4
The question remains, did the recipes or arts of the Warring States philosophers include the investigation of nature; did they have a hand in the development of Yin Yang and Five Agent theories which became the basis for what Graham calls correlative cosmology? First, we need to know who were recognized as philosophers in Warring States times. There are two sources of evidence: references to other philosophers and their followers in well-known Warring States philosophical books like _Mengzi, Zhuangzi, Xunzi_ , and _Hanfeizi_ ; and retrospective classifications of philosophical traditions in Han literature, in particular the "Zhuzi" 諸 子 (The masters) division of the _Hanshu_ bibliographic treatise ( _Hanshu_ , 30.27b–52a). Being known as _zi_ "master" was one criterion for philosopher status, whence the division title in the bibliographic treatise. "Zhuzi" includes a category for "Yin Yang jia" 陰 陽 彖 (Yin Yang specialists) which lists the writings of Zou Yan 騶 衍, the early third century B.C. man reputed to have explained change in nature according to cycles of Yin Yang and the Five Agents in order to predict the political fortunes of rulers (Graham 1986: 70–92; Graham 1989: 325–30). Graham notes that despite the listing in the bibliographic treatise and another Han reference to "Yin Yang specialists" in Sima Tan's 司 馬 談 (d. 110 B.C.) classification of philosophy, Zou Yan is ignored in the enumerations of philosophers in third and second century B.C. books of philosophy like _Xunzi, Zhuangzi, Lüshi chunqiu_ , and _Huainanzi_ (1989: 328–29). Zou Yan may have been what we would call a cosmologer, but it appears that in the third century B.C. Zou Yan and other Yin Yang specialists were not among the masters of philosophy; inclusion of Yin Yang specialists among the masters was first recognized in Han times, after the assimilation of cosmology into philosophy was an accomplished fact. Graham's judgment that down to the mid-third century B.C. "cosmological speculation... belongs to a world right outside the philosophical schools," and that Zou Yan "belongs to the world not of philosophers but of the court diviners and physicians" has justice (1989: 325, 328). The masters of philosophy knew of the theories about nature—at the courts of Warring States rulers they shared the stage with physicians like Wen Zhi and the other specialists—but they did not mastermind them.
It should be evident that in the Warring States the categories of master of philosophy on the one hand and physician, to name just one specialty, on the other do not correspond precisely to the division between philosophy and craft in Greek civilization.1 Unlike the Greek philosophers, speculation on natural phenomena was tangential to the way of the masters of philosophy until a late date. For physicians and the other specialists, interest in natural phenomena in general was a function of the specialties (frequently overlapping) they practiced; they shared text- and technique-based traditions; and theories developed among them without direction from the philosophers. With Zou Yan we appear to have a generalist—a cosmologer who formulated a body of theory, demonstrated its relevance to the state and the individual, and thereby made natural philosophy indispensable to all.
Yin Yang is one term for Zou Yan's kind of natural philosophy in Han literature, but terms like _fangshu_ or _daoshu_ and a variety of related compounds which refer broadly to natural philosophy and occult thought are more common (Chen Pan 1948). The same vocabulary continues to be used for other erudite skills; for example, the Han socio-intellectual orthodoxy grounded in canonical books like the _Yijing_ and _Shijing_ is termed _jingshu_ 經 術 (canonical art), which is sometimes contrasted with the dubious moral guidance provided by the books of the Warring States masters of philosophy.1 The multiple usages of the vocabulary of recipes and arts indicate that within the intellectual tradition no one attempted to formulate a restrictive concept of skill itself so as to privilege only certain types of knowledge and to exclude knowledge that failed to satisfy the definition of skill. Thus, fundamental ambiguities regarding recipes and arts remained unresolved: were they genuine or spurious; were they ethical or did they aim to deceive and mislead; did they appeal to rationalized principles or claim magical power? Suspicions and accusations were commonplace, especially by the arbiters of Han socio-intellectual orthodoxy against those whose ideas and activities did not conform, but their arguments were more _ad hominem_ attacks than reasoned critiques of the conceptual issues.2 In the area of natural philosophy and occult thought, where the vocabulary of skill was most frequently applied, there were skeptics for whom rationalized models replaced magic. In medicine, Chunyu Yi and the physicians whose views are represented in the _Huangdi neijing_ maintained a rationalistic skepticism in their application of Yin Yang and Five Agent theories to the understanding and treatment of illness. But it is evident from the magical contents of the Mawangdui medical manuscripts that there was not a dichotomy between natural philosophy and occult thought; the medical manuscripts simply bear out the evidence of the division "Shushu" in the _Hanshu_ bibliographic treatise.3
I have referred to Zou Yan as a generalist and a cosmologer. Based on the record of the _Shiji, fangshi_ 方 士 (recipe gentlemen) appeared near the end of the third century B.C., claiming to be followers of Zou Yan. The idea that Zou Yan spawned a new kind of practitioner in natural philosophy and occult knowledge is plausible. Perhaps in the context of third century B.C. natural philosophy and occult thought, Zou Yan stood out as master of the ultimate secrets of the cosmos. In addition to correlative cosmology, the _xian_ 仙 cult (which promised immortal life as a transcendent being) swept late third century B.C. elite society, adding yet another element to the already varied mixture of natural philosophy and occult thought. The recipe gentlemen described in the _Shiji_ catered to the demand for esoteric knowledge in these areas—magic, macrobiotics, alchemy, and _xian_ transformation their strong suit. The _Shiji_ first uses the title _fangshi_ for men who arrived at the court of the First Qin Thearch with recipes ( _fang_ ) for "the way of transcendence ( _xian_ 仙), release of the form, and fluxing transformation."1 They were, according to the _Shiji_ , mountebanks who "exploited demons and spirits":
Zou Yan gained fame with The Lords for the cycles of domination of Yin and Yang. The recipe gentlemen of Yan 燕 and Qi 齊 and along the sea transmitted his arts without being able to penetrate them; and thus there arose at this time the uncounted followers who mislead with marvels, toady, and connive. ( _Shiji_ , 28.10b.)
Similar recipe gentlemen continued to flourish through the second and first centuries B.C., finding in Thearch Wu 武 帝 (r. 141–87 B.C.) an enthusiastic patron. Li Shaojun 李 少 君 gained Thearch Wu's favor with "recipes for worship of the stove, the way of grain, and repelling age"; that is, he taught alchemy, dietetics, and longevity techniques. Even before arriving at Thearch Wu's court, Li Shaojun had made a circuit of the households of the elite with his recipes:
When people heard that he was able to command spirit beings and to not die, they every time fed and begifted him. He always possessed a surfeit of gold, cash, clothing, and food. People all thought that he did not engage in an occupation and yet he was richly provided for. Moreover, because they did not know where he came from their faith was all the greater and they vied to serve him. ( _Shiji_ , 28.21a.)
The _Shiji_ is a hostile witness, but revealing nonetheless. Unlike physicians and others who practiced recognized occupations, Li Shaojun increased his appeal to the elite by cultivating a mystique. Their generous contributions were intended to secure his agreement to teach them his secrets (by accepting them as disciples in his service).
Li Shaojun and the others mentioned in the _Shiji_ probably would have referred to themselves as _fangshi_ , but the title need not have applied exclusively to their kind of occult practitioner. According to the _Hanshu_ , the southern court of Liu An 劉 安 (179–122 B.C.) at Huainan 淮 南 was renowned for its assembly of several thousand "guests-in-residence" 賓 客 and "recipe-and-art gentlemen" 方 術 之 士. The latter title is usually equated with _fangshi_. These men participated in the compilation of the _Huainanzi_ 淮 南 子 with its several chapters devoted to cosmology, astrology, geography, and the human body. In addition to the _Huainanzi_ —the "inner book" 内 書 produced at Huainan—there were also a voluminous "outer book" 外 書 and the "middle fascicles" 中 篇, both now lost. The latter work comprised over 200,000 graphs and dealt with "spirit transcendence and the art of yellow and white."1 As a book of natural philosophy, the _Huainanzi_ undoubtedly distills the knowledge of Liu An's recipe-and-art gentlemen. And they must have been responsible for the clearly occult "middle fascicles," which was perhaps similar to the _Huainan wanbishu_ 淮 南 萬 畢 術 (Kusuyama 1987). These scholars of natural philosophy and occult knowledge were a different sort than the itinerant wonderworkers called recipe gentlemen in the _Shiji_.
The title _fangshi_ even occurs twice in the _Huangdi neijing_ denoting physicians ( _Suwen_ 11, 3.13b; 74, 22.24b). The physician-authors of the _Huangdi neijing_ obviously knew the association of the title with men like Li Shaojun. Did they borrow the title? I think not. More likely, _fangshi_ was a generic title appropriate for anyone whose knowledge centered on his _fang_ "recipes." In short, even though historical records dwell on the notoriety of a certain group of recipe gentlemen whose exploits also serve the purposes of historiography, the title _fangshi_ itself covered a range of specialists in natural philosophy and occult knowledge.1
The chief attribute of _fangshi_ is the possession of _fang_ —specifically the books that contain both their knowledge and their techniques. I adopt the term " _fang_ -literature" to refer to all literature produced in the milieu of the specialists in natural philosophy and occult knowledge during the Warring States, Qin, and Han. The amount of _Fang_ -literature in circulation by the first century B.C.—both among the specialists and the elite—was considerable. The divisions "Shushu" and "Fangji" in the _Hanshu_ bibliographic treatise contain roughly one third of the books in the whole treatise, and these books account for one fourth of the total amount of literature calculated in number of _juan_ 卷 (rolls) or _pian_ 篇 (fascicles).2 There was undoubtedly more literature in circulation than recorded in the bibliographic treatise, all of it virtually lost before the manuscript discoveries of the last several decades.3
There are parallels between the ideas that grew around the terms _fang_ "recipe," _ji_ "technique," _shu_ "calculation," and _shu_ "art" and arguments about _techne_ in Greek civilization. Originally _techne_ meant the skill of an artisan. By the fifth century B.C. it also denoted a "rational discipline." Gorgias introduced the idea of magic as a _techne_ into his theory of rhetoric and the power of words to influence human behavior, treating magic as a technique to be learned and thus "rationalizing" the "irrational" (Romilly 1975: 20–21). At roughly the same time, medicine was established as the _techne iatriche_ as reflected in the eponymous essay in the Hippocratic Corpus (Lloyd 1983: 12–14).4 For the Hippocratic writers their _techne_ left no place for supernatural explanation, while in the culture at large magical attitudes persisted.1 The fourth century B.C. witnessed philosophical debate over genuine and spurious _techne_. Plato, for example, reasoned that medicine was a genuine _techne_ because it concerned health, whereas the _techne_ of cooking—which aimed at pleasure not health—was spurious.2 After Plato and Aristotle, the philosophers' definition of _techne_ set its "rational discipline" apart from ordinary skill on the one hand and occult thought on the other.
To the extent that _techne_ in philosophy formally excluded occult thought from the realm of natural philosophy, the Greek term differs from Chinese ideas about "recipes" and "arts." However, occult thought and literature in the Greco-Roman world was nowise less flourishing than in Warring States, Qin, and Han China. The so-called Hermetic texts of late Hellenistic and Roman date bear witness to the vitality of the occult tradition (Scarborough 1988). Greek and Demotic magical papyri excavated in Egypt in the nineteenth and twentieth centuries have restored original fragments of magic handbooks and inscribed amulets of comparable date (Betz 1986; Faraone and Obbink 1991; Brashear 1992). Inscribed amulets of lead, silver, and gold unearthed around the Mediterranean, dating from the fourth century B.C. through Roman times, are yet another addition to the evidence for the occult tradition in Greco-Roman civilization (Kotansky 1991). Magical medicine is common in all of these materials. Studies of Greek and Roman medical literature are beginning to delineate the influence of occult thought on physicians as they formulated their _techne_ ; older arguments that neatly separated Greek and Roman medicine into the scientific tradition of the physicians and a popular occult tradition have given way to an awareness of a complex pattern of mingling between the two traditions.3
The conception of _fang_ -literature facilitated exchange between the literatures of natural philosophy and occult knowledge. Imagine combining parts of the Hippocratic Corpus with Hermetic texts and magical papyri and you would have something like the syncretic mixture of the Mawangdui medical manuscripts. The emphasis on texts over oral traditions—the expectation of mastering an esoteric specialty by receiving written _fang_ from a teacher and the popularity of _fang_ -literature among the elite—also seems more prominent in early China than in the Greco-Roman world. In regard to its popularity and its focus on recipes and arts, I am inclined to compare _fang_ -literature to the abundant _artes_ -literature of medieval Europe, which encompassed books in three categories of the medieval arts: liberal arts (including arithmetic and astrology), mechanical arts (including medicine), and occult arts (magic, divination, and the like).1
The characteristics of _artes_ -literature are exemplified by the _Secretum secretorum_ (Secret of secrets), which enjoyed wide circulation in Europe from the tenth to the seventeenth century. Translated into Latin from an Arabic original, the _Secretum secretorum_ purports to be the wisdom imparted by Aristotle to Alexander the Great; its contents range from statecraft to astrology, alchemy, divination, magic, and medicine—in short, it is an arcane miscellany whose attractiveness to medieval intellectuals lay in its claim to antique wisdom (Ryan and Schmitt 1982; Eamon 1990: 335–36). Similar miscellanies are common in _artes_ -literature, compiled with the intent of recording the secrets of nature. In fact, the secrets are often recipes and formulas collected from medicine and other crafts to serve everyday needs; miracles and home remedies share the quality of being secrets. And _artes_ -literature is the repository of oral traditions which would not have been admitted into the more theoretically-oriented books of natural philosophy.2 The Mawangdui medical manuscripts and Mawangdui manuscripts of literature classified in the "Shushu" division of the _Hanshu_ bibliographic treatise would fit nicely into the genre of _artes_ -literature.
Readership and Transmission
_MS_ I.C concludes with an exhortation:1 "The vessel connections—let it be written and thoroughly studied. Pupils, be devoted and respectful. Study [4] {4} [6] words, it is imperative to investigate them." The only explicit reference to medical training in the Mawangdui medical manuscripts, it captures the relationship between physician and disciple; and it enunciates the first task in medicine—"let it be written." Most likely Li fils was an elite aficionado of medical books and other _fang_ -literature (as was the man buried in the Zhangjiashan tomb) and never served a physician as disciple. In _MS_ I.C and the other vessel theory texts on _MS_ I, we have evidence that the elite read books on diagnosing vessels and appropriate therapy which formed part of the curriculum of the relatively new vessel-theory based medicine being taught by physicians like Chunyu Yi. Editions of _MS_ I.B, _MS_ I.C, and _MS_ I.D in the Zhangjiashan _Maishu_ show that the same texts circulated among physicians and the elite across geographical regions, with later parallels in the _Huangdi neijing_. Thus we can now trace the growth of vessel theory within the larger community of physicians and simultaneously observe its spread to an elite readership.
Chunyu Yi's medical writings and passages in the _Huangdi neijing_ treat disciples as the principal readership for medical literature, the assumption being that the physicians' books contain the crux of their "way"; the books introduce disciples to the profession and are the foundation of medical practice. Text-transmission customs observed by physicians are discussed below. The event of receiving medical books constituted an initiation which bound the disciple to the physician and sanctified the books, confirming the exclusiveness of the knowledge they contained. Like all _fang_ -literature, medical _fang_ were idealized as secrets intended for the enlightened few. It is clear from the Mawangdui medical manuscripts that the elite readership was perhaps equally influential in shaping the contents of medical literature; they also participated in its dispersion. Besides the elite's understandable concern over illness and the esoteric appeal of medicine, physicians possessed knowledge of many matters vital to their well-being: hygiene was foremost, followed by childbirth, relations between the sexes, everyday hazards, and the like. Medical literature addressed these subjects, much of it written expressly for the elite. They participated as well in the culture of secrecy created by specialists in natural philosophy and occult knowledge.
Let me illustrate some of the characteristics of the elite readership for medical literature with a brief review of the Mawangdui medical texts. Li fils probably did not diagnose vessels himself or cauterize them, but by reading the four vessel theory texts on _MS_ I he would have been more keenly aware of his own physical condition—especially when bothered by an ailment—and he would have had a standard for judging the physicians he consulted. Simply owning their theoretical texts identified him as a participant in their secrets. The only other text to deal extensively with illness is _MS_ I.E, the ailment recipe manual. _MS_ I.E contains rich detail on drugs and therapies, but is virtually unaffected by vessel theory; its conception of the ailments for which it provides treatments derives from older ontological ideas, which continued to exist alongside the physiological ideas derived from vessel theory even after the Han (see Section Three, "Illness"). A number of the recipes are simple to execute. However, the complicated technique for the surgical removal of an anal fistula ( _MS_ I.E.153) is but one of many recipes which reflect the skill of a physician. I doubt that Li fils would have attempted it.
But I see no reason why he would not have chanted the incantations and performed the exorcistic rituals described in some of the recipes. Magical operations in other Mawangdui medical manuscripts and in the Shuihudi and Fangmatan hemerological manuscripts indicate that these activities were customary for the elite (see Section Five, "Magical Recipes" and "Varieties of Magic"). By following the four vessel theory texts on the same sheet of silk, _MS_ I.E presents itself as yet another source of expertise for the treatment of ailments. The magical contents, including exact wording for incantations and instructions for exorcistic rituals, exemplify the sophisticated treatment of magic within the occult tradition; occult books with identical or similar contents must have circulated. Once again, the air of secrecy is manifest.
Macrobiotic hygiene was a drawing card for physicians by the third century B.C. All seven hygiene texts assume an elite readership, idealized in the figures of rulers like King Wei of Qi or the more archetypal Yellow Thearch. The aspect of these texts that warrants emphasis in the present context is the esoteric quality of the language, best illustrated by the many metaphors in which cultivation techniques are couched. The breath cultivation technique in _MS_ VI.A.1 instructs a person to "still your spirit wind" and "make fast your two racks," which will produce the "dark winepot." None of the terms are attested in a physiological denotation in received literature. The "two racks" might be the ribcage. "Dark winepot" is attested in the _Lüshi chunqiu_ as the name of a liquid used in religious worship; in _MS_ VI.A.1 it must be saliva. A sequence of metaphors for parts of the female anatomy in _MS_ VI.B.1 forms a coded description of intercourse. The denotation of the majority of the metaphors is unknown (although judicious guesswork is possible). Clearly in order to practice these techniques one must be taught the meanings of the metaphors, which constitute a secret language. Thus, through the practice of macrobiotic hygiene the elite were significant participants in the culture of secrecy and privileged knowledge.
Perhaps the charms for everyday use in _MS_ VII.A.1 will suffice to round out a picture of the Mawangdui medical texts as a mixture of home remedies, physicians' theories and skillful techniques, and knowledge both arcane and occult—all constituting varieties of _fang_ -literature transmitted within the field of medicine. Like medieval European _artes_ -literature, medical books and other _fang_ -literature attracted an elite readership with a promise of secret knowledge, even though the contents were not necessarily arcane.
The amount of _fang_ -literature recorded in the "Shushu" 數 術 and "Fangji" 方 技 divisions of the _Hanshu_ bibliographic treatise and unearthed from elite tombs suggests that anyone who could afford to own books would have been able to collect it. Exactly how they collected it is more problematic. Presumably elite patronage of men of learning (including philosophers and physicians), who provided patrons with knowledge and books in exchange for support, was the chief mechanism. However, the text-transmission customs of specialists and their disciples described in Han sources give the appearance of excluding anyone outside that relationship. The obvious question to consider here is whether medical literature transmitted between a physician and a disciple differed in kind and quality from what the elite could acquire. There is also the question of how freely medical literature circulated—how popular was it, really?
The Han accounts of text transmission between physicians and disciples are the best evidence we have for addressing both questions. By examining how the community of physicians was organized and the role of medical books, we can perhaps identify several motifs that also apply to the elite readership. Some of the accounts contain miraculous elements—as in the case of the legendary physician Bian Que 扁 鵲, who is said to have received his secret medical books from a spirit.1 Chunyu Yi's medical writings and passages in the _Huangdi neijing_ provide a more certain gauge of the physician/disciple relationship in connection with medical literature and secrecy.
Chunyu Yi describes his introduction to medical literature and medicine in three separate passages: twice in response to questions asking him to explain what he knows about the source of Yang Qing's medical knowledge, and why Yang Qing selected Chunyi Yi as the recipient of it; and once in his personal history of his medical training. I begin with the two questions and Chunyu Yi's explanations:
(1) Your servant Yi is asked: How did Teacher Qing receive it; was he renowned among the noble households of Qi or not? The response: (Yi) does not know from what teacher Qing received it. Qing's family was wealthy. Skilled in the practice of medicine, he was unwilling to treat ailments for other people. It must be for this reason that he was not renowned. Moreover, Qing instructed your servant Yi, "Becareful to not allow my sons and grandsons to know that you are studying my recipes."
(2) Your servant Yi is asked: What did Teacher Qing see in Yi that made him love Yi and want to teach Yi all of his recipes? The response: Your servant Yi had not heard that Teacher Qing was skilled in the practice of recipes. Yi came to know Qing because when Yi was young he liked all matters related to recipes. When your servant Yi tested the recipes the majority produced results which were truly excellent. Your servant Yi heard that Gongsun Guang of Tang Village in Zichuan 菑 川 was skilled in the practice of old transmitted recipes. Your servant Yi immediately went to visit him and was able to have an interview and serve him, receiving recipes for the transformations of Yin and Yang as well as the models of transmitted speech.2 Your servant Yi received them all and copied them. When your servant Yi wanted to receive all of the other fine recipes, Gongsun Guang said, "My recipes are exhausted with these. It is not that I am stingy with you sire. My body is already in decline and I have no means to once again serve (a teacher). These are the marvelous recipes which I received in my youth. I have given them all to you sire; do not teach them to others." Your servant Yi said, "To have been able to see and serve you sire, and obtain all the prohibited recipes, has been my great good fortune. Were Yi to die he would not dare recklessly transmit them to others." Some time later when Gongsun Guang was in his private chamber your servant Yi discussed the recipes in depth, speaking the finest words for a hundred generations. Teacher Guang was delighted and said, "You sire are certain to become a state craftsman. There are some whom I regard as skilled, but all are crude (compared to you). In my birthplace Linzi 臨 菑 there is someone skilled in the practice of recipes with whom I cannot compare. His recipes are very extraordinary—like nothing the world has heard of. In my middle years I once wanted to receive his recipes, but Yang Zhongqian1 was unwilling and said 'You are the wrong person.' I must go with you sire to see him. He ought to know that you sire delight in recipes. This man is also old now, and his family is furnished with wealth." We had not yet gone when just at that time Qing's son Yin arrived to offer a horse to the court. Through the assistance of Teacher Guang he presented the horse at the King's place.2 Thus Yi was able to become friendly with Yin. Moreover, Guang entrusted Yi to Yin saying, "Yi is fond of calculations. You sire should treat him with respect. This man is a sage _ru_."3 Then he wrote a letter entrusting Yi to Yang Qing, which is how I came to know Qing. Your servant Yi served Qing respectfully, which is why he loved Yi. ( _Shiji_ , 105.23a.)
The additional information in Chunyu Yi's personal history can be summarized briefly. Having been accepted as a disciple by Yang Qing, Yang Qing ordered him to "get rid of the entire lot of your recipe books, for they are incorrect." Yang Qing then promised to transmit to Chunyu Yi all of his "prohibited recipe books," which included the "vessel books of the Yellow Thearch and Bian Que." There followed a three year training period consisting of text recitation and explication as well as practical experience, after which Chunyu Yi "treated other people—examining ailments, judging death and life, and obtaining truly excellent results" ( _Shiji_ , 105.8b–9a).
Chunyu Yi's account offers remarkable details concerning three late-third to second century B.C. physicians and how they acquired their knowledge. First, Yang Qing did not even practice medicine as an occupation; family wealth made the "practice of recipes" unnecessary and undesirable. It appears that Yang Qing did not inherit his knowledge in a family tradition; if hereditary practice of medicine had been the source of family wealth he would have been less likely to transmit his books to an outsider. Although Yang Qing possessed many medical books, including vessel books attributed to the Yellow Thearch and Bian Que, Chunyu Yi does not know who Yang Qing's teacher was. Someone gave Yang Qing his books and taught him, but he did not identify a text or teacher lineage to Chunyu Yi. Gongsun Guang also did not name his teacher when he told Chunyu Yi that his medical skill was based on "marvelous recipes which I received in my youth." And like Chunyu Yi, Gongsun Guang studied medicine out of youthful curiosity. Three men—not one a hereditary physician, not one identified with a specific lineage of texts or teachers extending over several generations.
Apart from the importance both of texts and of the relationship between teacher and disciple, there is little evidence in Chunyu Yi's account of a larger organization binding physicians into exclusive brotherhoods. I suspect that the pattern for physicians and other specialists in natural philosophy and occult knowledge was similar to the philosophers. While we have good evidence of a type of school organization for followers of Confucius (the _ru_ ) and the Mohists, other philosophers and their philosophies cannot be said to represent schools. Equating the classification of books in the "Zhuzi" 諸 子 division of the _Hanshu_ bibliographic treatise with schools of philosophy is by now a well-known fallacy (Twitchett and Loewe 1986: 651–52; Graham 1989: 379–81). To be sure, certain books can be grouped together based on shared philosophical viewpoints, but the authors of the books did not see themselves as members of a school.
One should be equally cautious in considering whether there were medical schools between the fourth and first centuries B.C.; and if they existed, what the nature of their organization was. Yamada speculates that there were two kinds of physician: one a physician whose practice was hereditary and tied to the family's place of residence; and the other an itinerant physician who learned medicine from a teacher and then sought clients in various regions (similar to the philosophers and recipe gentlemen). According to Yamada, text and school lineages formed among the itinerant physicians, which by Han times influenced all of medicine. Thus the Bian Que school specialized in vessel diagnosis in the third and second centuries B.C., with theories paralleling the Yellow Thearch school; by the first century B.C. the texts of several branches of the Yellow Thearch school were combined in the _Huangdi neijing_ (1979: 87–89; 1988: 120–29; 1990). In all, Yamada identifies three major Han medical schools on the basis of three book titles in the "Yijing" 醫 經 category of the "Fangji" 方 技 division of the _Hanshu_ bibliographic treatise (one of which is the _Huangdi neijing_ ; 1979: 67; 1990: 66–67).
Insofar as Yamada associates physicians with text-based traditions similar to those of the other specialists in philosophy, natural philosophy, and occult knowledge, I am in basic agreement. But his argument regarding medical schools, which relies on the assumption that a book like the _Huangdi neijing_ was composed within a Yellow Thearch school, is no more certain than the assumption of philosophical schools.1 Between the fourth and first centuries B.C. the Yellow Thearch became prominent among specialists in natural philosophy and occult knowledge as well as among philosophers. He was the knowledge as well as among philosophers. He was the archetypal disciple to whom esoteric teachers revealed the secrets of the cosmos; books in the "Zhuzi," "Shushu," and "Fangji" divisions of the _Hanshu_ bibliographic treatise are attributed to him (Seidel 1969: 21–23, 50–52; Harper forthcoming). If we are going to equate books with schools, we find ourselves in the awkward position of supposing either that each set of Yellow Thearch books signifies yet another school which adopted the Yellow Thearch as school patriarch or that all the books together represent sub-groups of a single, large Yellow Thearch movement. It is more likely that the Yellow Thearch had become a legendary spokesman for a variety of esoteric knowledge, leading to a diverse body of literature attributed to him. As medical theory grew, physicians could have attributed many teachings and texts to both the Yellow Thearch and Bian Que. The formation of a Yellow Thearch or Bian Que medical literature would then have been the outcome of physicians sharing text traditions, not of medical schools with different legendary patriarchs.1
With a premium placed on "old transmitted recipes" and new medical texts continually appearing, the transmission of medical literature was probably more random than would be the case if the core medical literature were in the hands of schools. There was surely an element of chance in the selection of medical literature owned by any one physician. It was Chunyu Yi's "great good fortune" to have first served Gongsun Guang and under his auspices to have received superior books and instruction from Yang Qing. Chunyu Yi dates the beginning of his career as a practicing physician to after his tutelage under Yang Qing, as if his earlier study had been at the level of talented amateur. Chunyu Yi's experience was probably repeated many times over in different regions. The Mawangdui medical manuscripts give us a selection of the medical literature available in Changsha at roughly the same time.
Chunyu Yi's descriptions of the event of receiving medical books from his two teachers include several details concerning transmission etiquette and secrecy. A would-be disciple must first be accepted by (or allowed to serve) the physician. Having received Gongsun Guang's recipes, Chunyu Yi made his own copies of them. The verbal exchange between the two men after Chunyu Yi requested still more recipes should be read as part of the same event. It represents a formal vow: Gongsun Guang instructs Chunyu Yi to "not teach them to others"; Chunyu Yi, in possession of the "prohibited recipes" promises that "were Yi to die he would not dare recklessly transmit them to others." The source of Chunyu Yi's statement that Yang Qing instructed him to "not allow my sons and grandsons to know that you are studying my recipes" must be the time when he received Yang Qing's "prohibited recipes books." A physician could also refuse to teach a would-be disciple, as Yang Qing did when he stated that Gongsun Guang "was the wrong person" 非 其 人.
The vow of secrecy must have been common to all specialists in natural philosophy and occult knowledge when transmitting _fang_ -literature to disciples. The vow was the centerpiece of the initiation rite binding the disciple to the teacher. The best statement of the principle of secrecy occurs in the _Huangdi neijing_. In the words of the Yellow Thearch, "to obtain the right person and not teach him is called losing the way; to transmit (the way) to the wrong person is to wantonly divulge heaven's treasure" ( _Suwen_ 69, 20.1b). Other passages give evidence of precautions observed when handling medical books lest their privileged contents be abused (Harper 1982: 63). A model for a text-transmission rite is described in the _Lingshu_. The Yellow Thearch guides Thunder Sire 雷 公 through the rite, which begins with three days of ritual purification:
The Yellow Thearch then entered the purification chamber with him. They cut their forearms and smeared the blood on their mouths. The Yellow Thearch chanted this incantation: "Today is True Yang. Smearing the blood I transmit the recipes. He who dares to turn his back on these words will himself receive the misfortune." Thunder Sire bowed twice and said: "The little son receives them." The Yellow Thearch then with the left hand gripped his hand and with the right hand gave him the books, saying: "Take caution, take caution. I will explain it to you...." ( _Lingshu_ 48, 8.1a–b.)
The Yellow Thearch then lectures Thunder Sire on vessel theory and acupuncture.
Blood covenants ( _xuemeng_ 血 盟) originated in Zhou religious and political life (Lewis 1990: 43–50). The Yellow Thearch's incantation includes a standard curse on the person who breaks the covenant. Yamada doubts that the _Huangdi neijing_ passage can be read literally as evidence that Han physicians swore an oath in blood when transmitting books (1990: 83). However, in the fourth century A.D. blood oaths were still being used by Daoist adepts for oral transmission of secrets.1 Han popular and shamanic religion probably used blood oaths and were one source for the Daoist custom, but I suspect that blood oaths exchanged among specialists in natural philosophy and occult knowledge were another source. The question is not whether physicians used blood oaths when transmitting medical books but which physicians used them.
The text-transmission customs described above reflect widespread ideas about the value of books. Notions of secrecy fueled Han bibliophilia in general; books were regarded as objects of power. In this environment the concern that books might be misused by the "wrong person" and the desire to possess them were equally matched.2 Specialists and elite collectors like Li fils shared this mentality, which found concrete expression in the transmission customs for _fang_ -literature. Without minimizing the significance of vows of secrecy and blood oaths, I am not so sure that they severely constrained the actual dispersion of _fang_ -literature. Keep in mind that Chunyu Yi encountered no obstacles obtaining recipes as a youth, which led to more serious study with Gongsun Guang and Yang Qing. During his own career as a physician Chunyu Yi taught parts of his recipes to at least five pupils: two men from Linzi, one physician from the court of the King of jibei 濟 北, one physician from the court of the King of Zichuan, and a man from the household of the Lord of Gaoyong 高 永 who "delighted in vessel (theory)." Chunyu Yi lists what each pupil studied and for how long: two studied for over a year, one for two years, and one did not complete his course of study ( _Shiji_ , 105.24–b). The pupils seem to have been quasi-disciples in the sense that Chunyu Yi did not fully introduce them to the medical tradition he inherited from Yang Qing (there is no record whether near the end of his career Chunyu Yi found the "right" disciple to whom he gave everything as Yang Qing did to him). Yet we have no reason to doubt that he transmitted medical books to them related to their studies, which they probably copied themselves; Yang Qing's "prohibited recipe books" were transmitted to appropriate pupils.1
Of course, Chunyu Yi and all of his pupils belonged to the literate elite, who constituted the chief pool for disciples. One wonders whether a great distinction was made between elite patrons and elite disciples. We have already seen that the recipe gentleman Li Shaojun cultivated a clientele who, desiring to learn his secrets of immortality, "vied to serve him" (see above, "Recipes, Techniques, Calculations, Arts"); that is, they served him in the manner of disciples while generously rewarding him for his knowledge. The elite demand for medical knowledge encouraged a similar market for medical books. Writing of the situation in the first century A.D., Wang Chong 王 充 sardonically observed:
At present among the recipe-and-technique books2 written on bamboo and silk, if (a book) lacks attribution and provenance, those who see it dismiss it and waste no time on its remedies. But if (a book) bears the heading "so-and-so's recipes" or declares "already proven" and "previously tested,"3 people vie to engrave and copy it, regarding it as something treasured and secret. It is memorialized to the state, reported to the commandery, and recommended with praise to gentlemen and officials. ( _Lunheng_ , "Xusong," 20.406.)
The size of the market for medical books in the third and second centuries B.C. was smaller than the first century A.D. (by which time books could be purchased at a shop; see Section One, "Provenance and Hermeneutic Issues"). But I expect that "vessel books of the Yellow Thearch and Bian Que" or Wen Zhi's macrobiotic recipes were being touted by physicians—with discretion of course, and in accordance with transmission etiquette, but touted nevertheless.
Prohibitions on transmitting a recipe are written at the end of several recipes in the Wuwei medical recipes, also first century A.D. Among the phrases are "take caution, do not permit it to be revealed" and "this ointment drug is extremely good—do not permit it to be transmitted."1 The contents of the recipes with prohibitions are comparable to the other recipes. My impression is that the vow exchanged between physician and disciple has been popularized as a written formula attached to recipes which for various reasons were regarded as notable; that is, the prohibition on transmission identifies their excellence in the same way as phrases like "already proven" and "previously tested." This type of prohibition formula does not occur in the Mawangdui medical manuscripts; its use may have come later.2 However, the convention of secrecy noted by Wang Chong and evident in the Wuwei medical manuscripts probably existed earlier.
A convention of secrecy does not in itself trivialize the status and allure of secrets. Transmission customs perpetuated a tradition of professional secrecy; surely physicians had secrets which they shared with select disciples (or never revealed). And in the elite quest for knowledge, secrecy bespoke significance. My interpretation of the evidence given above is that transmission customs observed by specialists and their disciples formed the background for a more popular participation in natural philosophy and occult knowledge by the elite. Physicians cultivated the elite readership; segments of medical literature were directed to the elite (macrobiotic hygiene being the prime example), who were also encouraged to acquire knowledge of other areas of medicine. I expect that some medical books came to be well known among the elite and circulated independently of physicians. What would have prevented Li fils, however he originally acquired his medical books, from permitting an acquaintance to copy them (after, no doubt, extracting a promise to treasure them and keep them secret)? Perhaps it was in this way that editions of _MS_ I.B, _MS_ I.C, and _MS_ I.D were acquired by the man buried in the Zhangjiashan tomb.
In Section One ("Provenance and Hermeneutic Issues") I argued for treating the Mawangdui medical manuscripts as representative of third to early-second century B.C. medicine. Even though it is ultimately impossible to situate the manuscripts precisely in a synchronic or diachronic scheme, they belong ahead of the _Huangdi neijing_ in any historical investigation of early Chinese medicine. One part of that argument is based on the presumption that Li fils and other elite collectors could acquire the kind of medical literature used by physicians. Obviously, my examination of transmission customs and secrecy is influenced by my judgment that the contents of the manuscripts correlate with contemporary medical ideas and practices. Nevertheless, judicious review of the evidence simply does not support Liu Zonghan's counter-argument that physicians like Chunyu Yi did in fact observe strict professional secrecy with respect to their knowledge and their books; and that comparison of the Mawangdui vessel theory texts to Chunyu Yi's writings shows the former to be texts of the sort belittled by better physicians who possessed better medical books (1992b: 252–54). In addition to having pupils, Chunyu Yi was prepared to debate medical theory with other physicians, as when he criticized Physician Sui's 醫 遂 understanding of a homeopathic principle attributed to Bian Que: "Bian Que states 'treat Yin ailments with Yin minerals; treat Yang ailments with Yang minerals'" ( _Shiji_ , 105.19b). Both physicians knew and accepted the statement—it belonged to a common core of medical theory—but Chunyu Yi claimed that his interpretation was right and Physician Sui's was wrong. Medical discourse was not confined to confidences exchanged sub rosa.
Secrecy, disciples, debates over the interpretation of theory, derisive statements about the poor quality of others' books—all have a place in the social history of early Chinese medicine. I have not even discussed professional competition as a motive for physicians' conduct, and must leave it for future study (there are many relevant passages in the _Huangdi neijing_ ). In focusing on readership and transmission customs, I have aimed to underscore the dialogue that existed within the culture of secrecy in which physicians and elite participated. The Mawangdui medical manuscripts bear witness to this dialogue.
1The question of the _wu_ tradition is addressed in Section Five, "Magical Recipes."
1Several of the _xian_ adepts whose lives are recounted in the _Liexian Zhuan_ sold drugs, which they probably also gathered (Kaltenmark 1953: 116, 120).
2The Shuihudi text _Fengzhenshi_ 封 診 式 refers to an official dispatching a woman "who has given birth several times" to examine a woman who has aborted ( _SHD_ : 161; Hulsewé 1985: 205). No doubt such women also participated in childbirth.
1 _Fang_ has other meanings, but these are the meanings relevant to medicine as a skill. Harper 1982: 54–55, provides text citations, especially for the meaning "written recipe."
2 _Hanshu_ , 30.82b. Cf. Harper 1982: 52–54.
1 _Liji_ , 5.6b, cautions against taking the drugs of a physician who is not at least the third generation descendant of a physician; no doubt in Han times the idea that physicians who inherited the occupation were more trustworthy was still current.
1The emphasis on _shu_ "art" in philosophy is traceable to fourth century B.C. theories of statecraft (Graham 1989: 268).
2Graham touches on this aspect of _dao_ when he states: "Chinese thinkers want to know how to live, how to organize community and, at the very end of the pre-Han period, how to relate community to cosmos. As for what is real, what exists, visible to the eye, audible to the ear, solid to the touch, what questions does it raise? From the Western viewpoint, pre-Buddhist Chinese philosophy is epistemologically naive" (1989: 222–23).
3 _Zhuangzi_ 33, 461. I accept Graham's dating (1989: 374–76).
4See Chen Pan 1948: 17–18, for examples of synonymy between _fangshu_ and _daoshu_.
1Edelstein's statement of the influence of Greek philosophy on the craft of medicine is classic (1987: 349–66).
1Thearch Cheng 成 帝 (r. 33–7 B.C.) refused an uncle's request to be given copies of the books of the masters of philosophy ans Sima Quian's _Shiji_ after a court official warned him that such books were dangerous and inimical to "canonical art" ( _Hanshu_ , 80.8a).
2Cf. Ngo 1976: 64–66, for observations on differences between the Han _ru_ 儒 tradition (so-called Confusion orthodoxy) and the _fangshi_ 方 士 (recipe gentleman).
3Harper 1990: 211, cites several passages from the _Huangdi neijing_ which explicity reject the belief in demons and spirits as the cause of illness (without, however, denying their existence). The _Lunheng_ 論 衡 is remarkable for its skeptical scrutiny of all manner of ideas that Wang Chong 王 充 (A.D. 27-ca. 100) finds illogical (including the politics and ethics of the pre-Han philosophers). He lambasts what to him are superstitious ideas concerning Yin Yang and Five Agent theories as well as other occult beliefs. His own arguments, however, often rely on Yin Yang and Five Agent theories to explain phenomena that others would have believed to be magic; for example, Wang Chong argues that the correlation between the agent Fire and speech explains why incantations work (see Section Five, "Varieties of Magic").
1 _Shiji_ , 28.10b. The _xian_ cult and the concept of "release of the form" are discussed in Section Four, "Intellectual Background" and "Body and Spirit."
1 _Hanshu_ , 44.8b. Cf. Roth 1992: 12–26. The reference to "yellow and white" is alchemical, with significance for _xian_ transformation as well.
1The origin and application of the title _fangshi_ await definitive treatment. Chen Pan's classic study has not been surpassed (1948). In my judgment, Chen places too much emphasis on the philosophers and not enough on the tradition of natural philosophy and occult thought, even though the title itself seems to have mostly been significant in the latter tradition.
2The statistics are based on Gu Shi, who counts 226 titles in "Shushu" and "Fangji" out of a total of 677 in the bibliographic treatise; and 3,420 _juan/pian_ out of a total of 13,201. "Zhuzi" contains fewer titles (189) but more _juan/pian_ (4,541; 1924: 95, 173, 196, 213, 243, 254).
3There are received texts of two books in "Shushu" and "Fangji": the _Shanhaijing_ ( _Hanshu_ , 30.77a) and the _Huangdi neijing (Hanshu_ , 30.78b). Text parallels between excavated _fang_ -literature of Han and earlier date and medieval manuscripts from Dunhuang 敦 煌 confirm that old _fang_ -literature continued to be transmitted sub rosa without being recorded in bibliographies (see Harper 1988).
4 _Techne_ is usually translated as "skill," "art," or "science." Which translation is chosen often depends on the modern interpretation of the context in which _techne_ occurs, hence I refrain from translation.
1Lloyd 1979: 10–58, examines the Hippocratic criticism of magic.
2Romilly 1975: 48. Romilly describes in detail the fourth century B.C. debate over _techne_ , especially in connection with the status of rhetoric (1975: 47–66).
3Cf. Lloyd 1979. Scarborough (1991: 150–51) incisively critiques Edelstein's earlier arguments concerning Greek medicine and magic (1987: 205–46).
1The term _artes_ -literature and its denotation derive from the German discipline of _Fachprosaforschung_ as formulated by Eis (1967: 1). Major studies of medieval _artes_ -literature include Keil et al. 1968; Keil and Assion 1974; and Keil 1982.
2See Follan 1968 for a description of the contents of a popular German miscellany. Eamon characterizes the "books of secrets" in sixteenth century Italy as "technical 'how-to' books rather than works of theoretical science," and notes the source of many of the secrets in knowledge normally communicated orally (1985: 473).
1See the Introduction to the Translation for the use of brackets and braces to represent lacunae and untranslatable graphs.
1The _Shiji_ account of Bian Que and several other accounts of divine transmission are translated and discussed in Harper 1982: 59–62.
2"Models of transmitted speech" translates 傳 語 法, possibly referring to written records of oral instructions.
1I.e. Yang Qing.
2It is not certain at whose court the horse was presented. According to historical records, Zichuan did not become a kingdom until sometime during Thearch Wen's 文 帝 reign (180–157 B.C.), after the events described by Chunyu Yi.
3The exact sense of _ru_ 儒 is uncertain. _SW_ , 8A.3b–4a, identifies _ru_ as a title for an "art-gengleman" 術 士. Despite Chen Pan's lengthy argument linking the name for followers of Confucius with the notion of skillful techniques (1948: 33–40), the evidence for equating _ru_ with "art-gentleman" before the Han is not convincing. Gongsun Guang may be praising Chunyu Yi as "scholarly" in the manner of the _ru_ tradition.
1Explanations have been proposed for the composite nature of the _Huangdi neijing_ which do not assume the existence of various Yellow Thearch schools (Keegan 1988: 249–59). Yamada also bases his argument for medical schools on the speculation that the so-called itinerant physicians still associated their occupation with _wu_ 巫 (shaman) traditions and that schools of itinerant physicians preserved elements of _wu_ -style social organiziation which included rituals for transmitting the secrets of the group. Thus, as medicine went from magico-religious origins to become a field of natural philosophy, medical schools developed out of earlier _wu_ groups (1990: 62–64). I reject the sociological schema that equates Warring States specialists in natural philosophy and occult knowledge with shamans for reasons discussed in Section Five, "Magical Recipes," and thus do not find Yamada's speculation convincing.
1I should note that many historians of Chinese medicine share Yamada's basic identification of the _Huangdi neijing_ with a Yellow Thearch school. Liu Zonghan further identifies this Yellow Thearch school with the political philosophy known as Huang Lao 黄 老 (i.e. the Yellow Thearch and Laozi), citing those parts of the _Huangdi neijing_ which present the Yellow Thearch in his cosmo-political role (1992a: 97). Sivin similarly suggests that the use of Yin Yang theory in connection with macrobiotic hygiene in _MS_ VI.A appears to be associated with "Huang-Lao ideology" (1992: 23). To be sure, intellectual developments in the third century B.C. brought physicians into contact with political theory, and there are significant political elements in the _Huangdi neijing_ ; but evidence of cross-fertilization between medicine and politics does not support the hypothesis that either a school of medicine or of hygiene as a separate specialty grew under the aegis of "Huang-Lao ideology."
1See _Baopuzi_ , 18.92, describing the oral transmission of secret names for the sacred One: "These things, then, are important to adepts of the Dao, who for generations have smeared their mouths with blood and orally transmitted the surnames and private names."
2See Harper forthcoming on the value attached to possessing books. See p. 49, n.1, above for an example of refusal to transmit philosophy books out of concern for potential misuse of their contents.
1I do not accept Liu Zonghan's argument that Chunyu Yi taught parts of his medical knowledge to several pupils in order to prevent any one pupil from learning the whole of his medical secrets (1992b: 254).
2I.e. medical books.
3Both terms are used to evaluate recipes in _MS_ I.E (see _MS_ I.E.21, 197).
1 _WWYJ_ : 8a, 10a.
2Keegan misinterprets an incomplete phrase in _MS_ I.E.238 concerning medical prohibitions to be observed during treatment of the ailment as evidence of the prohibition formula in the Mawangdui medical manuscripts (1988: 239).
Section Three
Medical Ideas and Practices
The discussions in Sections Three, Four, and Five present an overview of the main features of medicine as revealed in the Mawangdui medical manuscripts. My purpose is not to write a history of early Chinese medicine, nor do I propose to examine in detail the relation between the Mawangdui texts and received medical literature. I have chosen to survey the texts from three interrelated perspectives. Section Three deals with the basics of medicine: illness, physiology, therapy, and materia medica. Macrobiotic hygiene, which flourished as a consequence of physiological speculation, was no less basic in Warring States medicine. Indeed, the Mawangdui and Zhangjiashan medical manuscripts indicate that vessel theory may have developed first in connection with hygienic theories, and was then applied to pathology. This is but one of the bridges linking the discussion of macrobiotic hygiene in Section Four to Section Three. The evidence of magic in the Mawangdui manuscripts is the subject of Section Five.
Although the Mawangdui medical manuscripts do not require an apology, a reminder of the single-minded viewpoint of the physician-authors of the _Huangdi neijing_ —for whom all of medicine depended on vessel theory—would not be out of place. Here is how the centrality of vessel theory in combination with acupuncture (as represented by the "nine needles" of acupuncture) is portrayed in the _Lingshu_ :
The Yellow Thearch said: "I have received the nine needles from the Master and privately examined the various recipes. Between guiding and pulling, circulating vapor, flexing and massage, cauterization and hot-pressing, needling and burning, and drinking drugs—is there perhaps just one which can be maintained singly, or should I practice them all?" Qi Bo said: "The various recipes are recipes for the masses. They are not all practiced by the singular man." The Yellow Thearch said: "This, then, is what is called 'guard the one without fail and the myriad things will be complete."' ( _Lingshu_ 42, 7.2a.)
Among the "various recipes" listed, the first three belong to hygiene while the remaining therapies evidently lack the sanction of the "nine needle" acupuncture theorists, who "guard" their one theory. The "various recipes" depreciated in the _Huangdi neijing_ are in some measure restored to us in the Mawangdui manuscripts.
Illness
Every society constructs its own ideas of illness, health, and disease out of a mixture of bodily discomfort, observed phenomena, and shared cultural experience.1 The idea that demons and the spirits of the dead sicken the living is in evidence in the earliest Chinese written records, the Shang inscriptions on bone and turtle shell (ca. thirteenth to eleventh century B.C.; Harper 1990). Demonic illness reflects the belief that something with an existence outside the body has relocated on or in the body; exorcism is a logical treatment. Warring States medicine added more agents and pathogens of a naturalistic origin, but the idea that an ailment was localized and attributable to an agent or agents was essentially the same. Stated in general terms, this represents an ontological explanation of illness—ailments are entities with an existence of their own (Unschuld 1987; Unschuld 1993: 21–22; Hudson 1993: 45–46).
Another explanation of illness emerged in tandem with the formulation of physiolgical theories. By the third century B.C., ideas concerning the _mai_ 脈 (vessels) filled with blood and _qi_ 氣(vapor) inside the body dominated physiological speculation; one definition of health was the maintenance of a constant supply of free-flowing blood and vapor in the vessels. Thus in _MS_ VI.A.8, the legendary flood-hero Yu 禹 is taught that "when blood and vapor ought to move yet do not move, this is called the calamity of blockage"; that is, stagnation in the vessels causes infirmity. As elaborated in the _Huangdi neijing_ , vessel theory is the basis for a universal model of illness which explains illness as a dysfunction of the human organism within the system of vessels and internal organs. What is perceived as illness, or as nameable ailments, is the manifestation of that dysfunction; the goal of therapy—principally acupuncture—is to re-establish the harmonious functioning of the organism, thereby eliminating the signs of illness. Unschuld describes this explanation of illness as "functional" (1987; 1993: 21); it is the Chinese counterpart to humoral pathology and other types of physiological explanation of illness in Western medicine (Hudson 1993).
The physiological explanation of illness based on vessel theory was championed earlier by Chunyu Yi, who claimed that vessel theory itself was created by ancient sages seeking to bring order to the identification of _bing_ 病 (ailments):
Ailment names are mostly alike and are unknowable. Thus the ancient sages created the model of the vessels (脈 法)1 for them.... They differentiated the vessels in man and named each one. Matching with heaven and earth, (the vessels) combine in man to form a trinity. Thus they then differentiated the hundred ailments, distinguishing between them. ( _Shiji_ , 105.21b.)
According to Chunyu Yi's medical case histories, vessel diagnosis is the only accurate way to determine the nature of a patient's illness; treatment focuses on ameliorating the morbid condition exhibited by the vessels.
Despite the privileging of vessel theory and the physiological explanation of illness in Chunyu Yi's writings and the _Huangdi neijing_ , ontological ideas were never supplanted in later Chinese medicine. In medieval recipe manuals and materia medica, ailments continued to be treated as localized entities which drugs and other therapies could control. As in _MS_ I.E, demonic illness and magical treatment remained part of the medicine practiced by physicians, demonic agents being comparable to the other entities responsible for illness.2 Moreover, medicine dealt with many matters besides the actual incidence of illness; the course of development in pharmacy and other medical practices was not determined solely by vessel theory and physiological pathology. Thus there is nothing unusual about the multifarious contents of the Mawangdui medical manuscripts. What is noteworthy about them is that the application of vessel theory to pathology is evidently at an early stage of development and is not yet established doctrine. It seems that in the second and first centuries B.C. Chunyu Yi and like-minded physicians were justifying a new understanding of illness based on vessel theory. Ailments—the majority of which already had proper names in contemporary language—were being redefined according to physiological pathology; the physicians had to demonstrate that ailments did not exist as discrete entities, but were in fact manifestations of a deeper disturbance in the human organism.
The ailment _tui_ 穨 (inguinal swelling) provides a convenient example. _Tui_ means literally "drop down," and is first attested as a word for a fiery, descending wind in received literature; the Mawangdui medical manuscripts provide the earliest attestation of _tui_ as a name for various kinds of swelling in the inguinal region, including hernias (Harper 1990: 219). The majority of recipes for _tui_ in _MS_ I.E.118–41 attribute the ailment to demonic agents who are exorcised; wind and vapor as pathogens may also be involved.1 _MS_ I.E.135 first recommends treating _tui_ with a lancing-stone and cauterizing the lance wound, and then states, "for an easy cure, cauterize the Great Yin and Great Yang (vessels)." Among the examples of cauterization therapy in _MS_ I.E, this is the only reference to cauterization in accordance with vessel theory, and is also the only indication of physiological pathology in the ailment recipe manual. However, _tui_ is not listed under any vessel in _MS_ I.A; in _MS_ I.B it is listed under the leg Ceasing Yin vessel ( _MS_ I.B.8). Although Chunyu Yi credited sages with inventing vessel theory precisely to resolve doubts, pathological theory was still evolving.
The ascendancy of vessel theory and physiological pathology was driven by correlative cosmology. Vessel theory provided a basic structure for the application of Yin Yang and Five Agent theories to the human organism; it allowed physicians to precisely classify the human microcosm and link its operation to phenomenal processes in the macrocosm (which is the essential point in Chunyu Yi's statement on the "model of the vessels"). And it gave rise to a dual view of illness, with earlier ontological explanations overlaid by physiological explanations. I leave further discussion of vessel theory for "Physiology" below. In _MS_ I.E we find evidence of the varied ontological pathology of third century B.C. medicine which preceded physiological pathology. Some ailment names in _MS_ I.E are attested in received literature, others are not. References to ailments in other excavated manuscripts, including some of the same unattested names, add to the record of ontological pathology in early Chinese medicine.
"Conditions requiring medical attention" might be a better term than "ailments" for the categories of _MS_ I.E. The recipe manual begins with seventeen recipes for flesh wounds, including techniques for staunching the flow of blood (in _MS_ I.E.7, scalp hair is used; in _MS_ I.E.9, an incantation) and relieving pain. Categories for burns ( _MS_ I.E.176–93) and animal bites (for example, dog bites and mad dog bites; _MS_ I.E.28–33) are of a similar nature. However, the boundary between such conditions and ailments is slight. Immediately following the recipes for wounds are recipes for "rigidity due to a wound"; two recipes specify that wind entering the wound is the pathogen causing rigidity ( _MS_ I.E.19, 21). The third recipe category is a single recipe for rigidity in infants, perhaps associated with the wound created by cutting the umbilical cord ( _MS_ I.E.25). Throughout _MS_ I.E there is a noticeable pattern in which conditions or ailments are treated as localized entities. Agents or pathogens may or may not be specified, and sometimes they are identical to the entity itself; that is, both conditions and ailments are given an ontological explanation.
Let me provide several examples. _MS_ I.E.178 treats a burn (a condition) with a curse in which the burn is reified in the form of a demonic agent who is expelled in the curse (the curse addresses the agent directly as "you"). In several recipe categories concerning bites, the creature that bit is thought to lodge in the bite, which explains the curses for scorpions ( _MS_ I.E.48–49) and lizards ( _MS_ I.E.56, 60). The rash caused by working with raw lacquer is reified as the lacquer spirit ( _MS_ I.E.235); inguinal swelling is reified as misbegotten sons of perverse parents in one recipe ( _MS_ I.E.120) and blamed on a fox demon in another ( _MS_ I.E.124). I draw examples from magical recipes because they vividly illustrate ontological thinking about illness, but pathogens like wind or vapor—or unnamed pathogens in the ailment categories of _MS_ I.E—are not unlike the demonic agents. The basic identity of an ailment as an entity permitted dual interpretation.1
The most common term denoting illness in the Mawangdui medical manuscripts is _bing_ 病; I translate the verb as "ail" and the noun as "ailment." The word is classificatory; a morbid condition which can be given a name is a _bing_.1 The origins of ailment names are as varied as the ailments themselves (and excavated manuscripts have increased the record of ailment nomenclature). Whatever their origins, we can safely say that before vessel theory and physiological pathology ailment names were devised under the influence of ontological ideas. One of the problems that physicians like Chunyu Yi had to confront was how to correlate the contemporary, multifarious ailment nomenclature with vessel theory; as Chunyu Yi phrased it, "ailment names are mostly alike and are unknowable." Part of the redefinition of illness was the "rectification" of ailment names in accordance with vessel theory. _MS_ I.A and _MS_ I __.B bear witness to this process with their lists of ailments associated with each vessel. The kinds of ailments listed reflect a new sensitivity to somatic condition; most are pain felt in parts of the body along the path of a given vessel (the significance of pain is discussed in "Physiology" below). Only four of the names which appear in these lists also occur in _MS_ I.E— _dian_ 癲 (seizure; _MS_ I.A.1; _MS_ I.E.71), _long_ (urine retention; _MS_ I.B.8; _MS_ I.E.88–114), _tui_ 穨 (inguinal swelling; _MS_ I.B.8; _MS_ I.E.118–41), _zhi_ 痔 (hemorrhoids; _MS_ I.A.1; _MS_ I.B.1; _MS_ I.E.142–54)—indicating gradual incorporation of traditional ailments coupled with elimination of ailments not susceptible to physiological explanation. The formula concluding each ailment list in _MS_ I.A suggests a lingering association with ontological ideas: "In all cases of ailing from these things ( _wu_ 物 that is, the ailments listed), cauterize (the designated vessel)." By referring to ailments as _wu_ , _MS_ I.A perhaps comes closest to verbalizing the ontological explanation of ailments as entities that underlies _MS_ I.E.
The majority of ailments in _MS_ I.E are external. In addition to wounds and bites, there are numerous flesh ailments: warts ( _MS_ I.E.64–70), several skin afflictions of uncertain nature ( _MS_ I.E.34–35, 36, 73–75), two categories of abscesses ( _MS_ I.E.157–73, 225–32), scabies ( _MS_ I.E.200–223), itch ( _MS_ I.E.249–56), scabbing ( _MS_ I.E.257–70), and the like. Inguinal swelling and urine retention are among the few clearly internal ailments. References to the inside of the body are also scant: the bladder is mentioned twice in connection with urine retention ( _MS_ I.E.95, 101); the heart once, but only to designate that region of the exterior of the body ( _MS_ I.E.153); _shen_ 腎 refers to testicles, not to the kidney ( _MS_ I.E.134, 137). Except for the lone mention of cauterizing the Great Yang and Great Yin vessels, there is no evidence of Yin Yang and Five Agent theories; hemorrhoids are divided into "female" and "male" types using the older gender vocabulary _pin_ 牝 and _mu_ 牡.The greater attention paid to the exterior suggests a view of the body as the place where ailments lodge—a host to ailments—rather than as a functioning organism subject to physiological breakdown.
The contents of _MS_ I.E must conform to a rubric shared with contemporary ailment recipe manuals: wounds come first, followed by wound-related rigidity; several categories of bites are grouped in sequence ( _MS_ I.E.44–63; but a single recipe for snake bite is placed near the end, _MS_ I.E.224); urine retention, inguinal swelling, and hemorrhoids follow one another ( _MS_ I.E.88–154). One wonders why the two categories of abscesses are separated ( _MS_ I.E.157–73, 225–32), which reinforces the impression that an element of randomness is also involved in the organization of ailment categories. I doubt that the kinds of ailments treated and the sequence of the ailment categories in _MS_ I.E are intended to communicate specific etiological or nosological ideas.1 This does not mean that there is no evidence of etiological ideas. I have already mentioned demons, wind, and vapor. More prevalent than these are the many bugs associated with ailments. I use the word "bug" to refer to a category of creatures that includes, at minimum, insects and reptiles as well as all of their demonic variations in early Chinese belief. The breadth of the category is indicated in the earliest etymology of _hui_ 虫, defined as a name for the viper and then explained as a general term for anything small that crawls or flies, is hairy or naked, or has shell-like plates or scales ( _SW_ , 13A.40b–41a). _Chong_ 蟲 denotes bugs with legs, but also connotes an infestation of bugs ( _SW_ , 13B.4b).
Bugs as both natural and demonic agents of destruction can be traced to the Shang inscriptions, which provide the first attestation of _gu_ 蠱 (pictographically a representation of bugs contained in a vessel). If later definitions of _gu_ are applicable to Shang usage, the word refers to a demonic potion prepared from bugs which sickens select victims. By extension, _gu_ refers to demonic evil and black magic in general. By Warring States times _gu_ was also applied to ailments involving infestations of bugs in the body. It has been hypothesized that _gu_ denoted ailments like schistosomiasis, yet the underlying conception of the ailment cannot be separated from the magico-religious significance of a demonic bug-attack (Harper 1990: 225; see _MS_ I.E.271).
_Gu_ is one of eight ailments in _MS_ I.E which can be classified as bug ailments simply on the basis of their names: _gu_ ( _MS_ I.E.271–75), scorpion ( _MS_ I.E.44–49), leeches bite ( _MS_ I.E.50–51), lizard ( _MS_ I.E.52–63), _ming_ 螟 ( _MS_ I.E.78), _quan_ 蠸 ( _MS_ I.E.79), snake bite ( _MS_ I.E.224), and chewing by bugs ( _MS_ I.E.240–48). The presence of bugs is noted in other ailments, like female hemorrhoids ( _MS_ I.E.149) and scabies ( _MS_ I.E.208); bug etiologies for both ailments are documented in later medical literature. Chunyu Yi regards bugs in certain ailments as a secondary phenomenon arising from pathogenic wind and vapor, not as the first cause.1 However, the ailment categories _ming_ and chewing by bugs make bugs the primary agents of decayed flesh. _Ming_ is only attested as an ailment name in _MS_ I.E, where it is plausible to associate it with leprosy. In received literature _ming_ is a crop pest regularly paired with _te_ 蟘, which is the bug named in chewing by bugs as the cause of chewed flesh around the mouth and nose ( _MS_ I.E.244) and of tooth decay ( _MS_ I.E.248). In Han times it was believed that a plague of _ming_ and _te_ bugs was an omen of moral corruption in government; in _MS_ I.E, both bugs plague the body, the ravages of the former more destructive than the latter. Although neither _ming_ nor _te_ occurs as an ailment name in received literature, there is ample testimony of the widespread fear of bugs and of their association with demonic activity and illness in Warring States, Qin, and Han times (Harper 1990: 225–30). The derivation of the ailment names _ming_ and _te_ is easy to trace. And the imprint of etiological ideas about bugs derived from ontological pathology in _MS_ I.E is easy to detect.
The "Ailment List" in the Zhangjiashan _Maishu_ represents an effort to bring nosological order to ailments from an ontological perspective. The body itself serves as the organizational principle. Beginning with the words, "when the ailment is located on the head," the text lists three head ailments, then continues downward to the bottom of the foot for a total of fifty-seven ailments. "Ailment List" concludes with ten ailments that affect the body generally ( _MSSW_ : 72). The text is notable for both the precision with which it localizes ailments and the specificity of the ailment names. The first ten ailments listed are representative:
When the ailment is located on the head and there is pus it is _qian_ ; when there are sores it is _tu_ 禿; when there is itching it is _qiang_ 鬙. When (the ailment) is located on the eye and tears come out it is _qin_ 浸; when a screen covers the pupil it is screen- _qin_. When (the ailment) is located on the canthii and spreads it is _fu_ 赧. When (the ailment) is located on the nose it is _qiu_ 肍; when there are painful scabs it is _te_ chewing. When (the ailment) is located on the ear it is _long_ 聾; when pus comes out it is _jiao_ 澆.
"Ailment List" includes a number of the ailments in _MS_ I.E; for example, it provides a valuable second attestation of " _te_ chewing," identified as painful scabs on the nose. Recall that "Ailment List" precedes the _Maishu_ edition of _MS_ I.B on the manuscript, thus both ontological and vessel-theory classifications of ailments are represented in _Maishu_.
Another example of ontological classification occurs in _Wanwu_ (from Shuanggudui) in the form of ailments identified according to the drugs that cure them. Among the fragmentary slips there are over thirty such entries, including drugs used for the same ailment in _MS_ I.E; for example, _shiwei_ 石 韋 (pyrrosia) cures urine retention (Fuyang Hanjian zhenglizu 1988: 36; _MS_ I.E.109; the importance of _Wanwu_ as a drug list is discussed in "Materia Medica" below).
Between _MS_ I.E, the _Maishu_ "Ailment List," and _Wanwu_ , we have evidence of refinements in ontological pathology which were contemporary with vessel theory and physiological pathology. Chunyu Yi's categorical statement that only vessel theory can explain illness and bring order to ailments is as much a criticism of ontological classifications like "Ailment List" as it is a paean to vessel theory. Because the _Huangdi neijing_ has served to make vessel theory the standard for pathology in Chinese medicine, we tend to overlook the fact that in the third and second centuries B.C. it was still new; the excavated manuscripts allow us to see some of the alternatives to vessel theory and to speculate on the debate among physicians over the issue of illness.
Physiology
The earliest explicit statement in received literature of the idea that _qi_ "vapor" flows along with blood through _mai_ "vessels" inside the body occurs in the _Guanzi_ , in an essay on water which probably dates to the first half of the third century B.C.: "Water is the blood and vapor of the earth—like what flows through the muscles and vessels."1 The idea that _qi_ and blood together are the essential components of human life is only reliably documented in fourth century B.C. sources, by which time _qi_ already referred to the omnipresent "basic stuff" of the phenomenal world. And between them, _qi_ was already seen to be more necessary to human existence than blood: it was the air man breathed, it was the nourishment extracted from food; it was what suffused the body and made man alive; it was what connected the human organism to the larger operations of nature. It is not clear whether _qi_ originated as a word for atmospheric vapors (clouds, steam, etc.) which was generalized to encompass the source of human vitality and everything else; or whether _qi_ was a term for the life-sustaining stuff received from food, drink, and air or breath, which was extended to the natural world. The graph 气, glossed as "cloud _qi_ " 雲 气 in _SW_ , 1A.39a, suggests the former derivation; but the meaning is not attested in the oldest uses of this graph in Shang and Zhou inscriptions (where it means "beseech," "end," "food donation"). The graph 氣一which became the standard graph for the word in its generalized meaning—may have had earlier associations with food and breath, from which the concept of "stuff" in nature arose. By the fourth century B.C. the word was already a fixture in discourse on nature; barring new evidence, the question of etymological derivation is moot.2
My decision to translate _qi_ as "vapor" is in part practical—why not translate such a basic concept in early Chinese thought, especially since modern use of the word _qi_ both in Chinese and in English has colored its original meaning? "Vapor" avoids potentially misleading associations with "air" or "pneuma" in Western thought while retaining the sense of _qi_ as something material but simultaneously volatile and pervasive. Its greatest flaw is old Western medical usage which applies "vapor" to injurious emanations of the internal organs; so long as one does not permit this denotation to intrude, the connotations of "vapor" are by and large transferable to _qi_. For those who believe that _qi_ cannot or should not be translated, it is always possible to pronounce "vapor" as _qi_.
Physiological ideas proliferated during the fourth century B.C. This was the century when maintaining one's own physical existence became a philosophical issue (Yang Zhu 楊 朱 is best known as the exponent of caring for life); and when the belief that the body was constituted of physical and spiritual/mental components led to a greater focus on the nature of the indwelling spirit. Building on ideas about vapor, it was thought possible to enhance physical and spiritual well-being through a program of cultivation. As evidenced in _Guanzi_ , "Neiye" 内 業, vapor was at the base of physio-spiritual transformations which concentrated _jing_ 精 (essence) and _shen_ 神 (spirit) inside the body to produce the physique of the sage (Graham 1989: 53–64, 100–105). The Mawangdui and Zhangjiashan medical manuscripts restore the earliest documentation of the physicians as exponents of physiological theory and macrobiotic hygiene. Cross-fertilization between the medical tradition of macrobiotic hygiene and philosophy is discussed in Section Four, "Intellectual Background." The following treatment of physiology considers primarily the evidence of vessel theory in the manuscripts.
Chunyu Yi gives us to think that physiological theory is vessel theory, that the vessels are the essential structure subsuming the other constituents of the body. This understanding of vessel theory is also characteristic of the _Huangdi neijing_. In contrast, there are two passages in the Mawangdui medical manuscripts that list five body constituents without naming vessel among them; a third passage in the Zhangjiashan _Maishu_ lists vessel as one among six constituents of the body. For obvious reasons I do not accept Chunyu Yi's statement that "ancient sages created the model of the vessels." Physiological speculation between the fourth and first centuries B.C. moved gradually towards the view that vessel and vapor constituted the body's core, and that constituents like bone, muscle, and flesh were subsidiary. While we cannot determine whether the three passages antedate the vessel theory texts like _MS_ I.A-B, they do document other physiological views and help to place vessel theory as described in the manuscripts in perspective.
The first passage occurs as part of the account of gestation in _MS_ V.3 and is notable for including the only reference to Five Agent theory in the Mawangdui medical manuscripts. After three months during which the fetus settles into the womb, from the fourth through the eighth months the fetus develops five essential constituents: Water produces blood in the fourth month; Fire produces vapor in the fifth month; Metal produces muscle in the sixth month; Wood produces bone in the seventh month; Earth produces skin in the eighth month (the constituents are produced following the conquest sequence of the Five Agents). Notice that blood and vapor are the first constituents produced, but that vessel is not listed. Perhaps the existence of blood and vapor assumes that vessels are present in the fetus to hold them, perhaps not. A similar list of constituents occurs in _MS_ I.D in connection with death. Five sets of physical symptoms signify that one of the constituents has "died first"; when all five sets of symptoms occur, the person cannot live. The constituents in the order listed in the text are: flesh, bone, vapor, blood, muscle.
Immediately preceding this passage in _MS_ I.D is a passage on the Yang vessels (Great Yang, Minor Yang, Yang Brilliance) and Yin vessels (Great Yin, Minor Yin, Ceasing Yin); the latter are called the "vessels of death." Thus _MS_ I.D presents two views of mortality: the first is based on disturbance in the Yin vessels; the second on failure of a body constituent. By virtue of their juxtaposition the two views are related, but there is no indication that the Yin vessels are to be correlated with the five constituents. The correlation of Yin vessels with body constituents first occurs in a parallel text in _Lingshu_ 10. Five Yin vessels (the hand Ceasing Yin vessel is not included) are correlated with flesh, bone, hair, blood, and muscle; the failure of one of the constituents is attributed to the "severing of vapor" 氣 絶 in the vessel associated with it ( _Lingshu_ 10, 3.7a-b). Yamada explains the substitution of hair for vapor as evidence that vapor "is no longer regarded as one of the constituents of the body parallel with the flesh and other elements but rather as a more fundamental source power of life" (1979: 77). In the _Huangdi neijing_ , body constituents are subsumed within vessel theory. _MS_ I.D represents physiological ideas at a time when vapor was still listed among the body constituents, and before vessel theory's predominance. The constituents are the constituents produced during gestation in _MS_ V.3 (associating flesh in _MS_ I.D with skin in _MS_ V.3), now observed in decay (note, however, that there is no evidence of Five Agent theory in _MS_ I.D).
The _Maishu_ "Six Constituents" similarly concerns signs of breakdown associated with body constituents. The constituents are identical to _MS_ I.D with the addition of vessel as the sixth constituent. Each constituent serves a function; and each manifests a distinctive feeling of pain, which is bred in it:
Now, bone is the pillar; muscle is the binding; blood is the moistener; vessel is the channel; flesh is the attachment; vapor is the exhalation. Thus, bone pain is like chopping; muscle pain is like binding; blood pain is like leaking; vessel pain is like flowing; flesh pain is like floating; when vapor moves there is anxiety.1 Now, the six pains all exist in the body and no one knows how to treat them. Thus, if the gentleman becomes fat and loses the standard measure, this is called "muscle and bone do not succeed in their responsibilities." His vapor then becomes abundant; his blood then becomes uncontrolled. Blood and vapor putrefy and rot; the hundred joints all collapse. They clog the twenty extremities2 and turn back, racing to the heart. If this is not treated in advance, one will hear the sound of weeping. ( _MSSW_ : 74.)
"Six Constituents" treats knowledge of pain in the constituents as the key to knowing the body; pain signifies a specific dysfunction which if not remedied leads to death. The "loss of the standard measure" due to obesity initiates a fatal scenario: muscle and bone are overtaxed (flesh, which is the "attachment," is too heavy for the bone "pillar" and muscle "binding" to support); blood and vapor are unleashed, causing general collapse throughout the body; and finally the blocked blood and vapor reverse their course and attack the heart.
"Care of the Body," the text preceding "Six Constituents" in _Maishu_ , offers the teaching that only things which maintain regular movement do not stagnate. Stagnation inside the body causes "the vessels to rot and flesh to die." The words vapor and blood do not occur in the text (as they do in _MS_ VI.A.8), but the conclusion implicitly understands either vapor alone or both: "When the vessels are brimful, drain them; when empty, fill them; when still, stay in attendance on them" ( _MSSW_ : 74). In "Care of the Body" and "Six Constituents" it is evident that among the constituents the vessels and their contents are the focal point of physiology; and that physiology is oriented towards hygiene rather than pathology. This orientation is confirmed in the opening of "Vessels and Vapor," the _Maishu_ edition of _MS_ I.C, which follows "Six Constituents":1
Now, the vessels are something the sage prizes. As for vapor, it benefits the lower part (of the body) and harms the upper part; it follows warmth and departs from coolness. Thus, the sage has a cold head and warm feet. To treat ailments, take away the surplus and increase what is insufficient. ( _MSSW_ : 74.)
To paraphrase, health depends on the condition of vapor in the vessels. Vapor should flow in a downward direction; upward movement is contrary movement and creates disturbance. The sage is the model of good hygiene; his cold head and warm feet ensure that vapor moves as it should. Applying the principles of hygiene to pathology, ailments can be treated by redistributing the vapor in the vessels; therapies designed to remove surplus and correct insufficiency are counterparts to the routine "draining" and "filling" of the vessels in hygiene. The remainder of both editions of _MS_ I __.C detail aspects of vessel theory in connection with illness, beginning with a description of cauterization to make vapor move downward in a vessel that has been diagnosed as having an excess of vapor.
Following the leads in the Mawangdui and Zhangjiashan medical manuscripts, we arrive once again at vessel and vapor as the core of physiology. But whereas Chunyu Yi proposes that "sages created the model of the vessels" in order to deal with human illness, the manuscripts present the vessels as idealized in the body of the sage; secondarily, they are the basis for diagnosing and treating illness. Formally, the evidence pits the word of Chunyu Yi and the _Huangdi neijing_ against the manuscripts. However, there is logic in supposing that vessel theory began in connection with hygienic theory and practice, and over time became the basis for a new understanding of health and illness—at which point the significance of vessel and vapor in physiological pathology led vessel theory in a new direction. Once health was defined in terms of the circulation of blood and vapor in the body, maintaining health was essentially monitoring the condition of the vessels; transposing this scheme to illness and pathology would have been a small step to take. The _Maishu_ "Six Constituents" suggests what the new index of illness was: pain. It is not coincidental that the great majority of ailments listed under each vessel in _MS_ I.A and _MS_ I.B (as well as in the parallels in _Lingshu_ 10) are related to pain. The standard ailment name in these texts is a compound composed of _tong_ 痛 (pain) and the name of the affected body part, which in almost every instance lies along the path of the vessel under discussion.
Hygiene is not ignored in the _Huangdi neijing_ , but for reasons discussed in Section Four ("Intellectual Background") the _Huangdi neijing_ affirms the ideal of health while at the same time insisting on the priority of vessel theory pathology and acupuncture; that is, the business of physicians is to treat illness, not to encourage their patients or patrons to undertake hygienic regimens. Chunyu Yi makes no references to hygiene at all. The Mawangdui and Zhangjiashan medical manuscripts present hygiene and pathology on more or less equal footing, and suggest historical priority for vessel theory in hygiene. Thus, there are two aspects to vessel theory to be considered: its continuing role in macrobiotic hygiene, and its development as part of pathology.
Keeping these two aspects in mind, let me turn to the question of how vessel theory developed from initial awareness of a physiological structure holding blood and vapor—and named _mai_ 脈—to become the foundation of physiological theory. The conception of the vessels in the body and the meaning of the word _mai_ were continually changing as physiological ideas flowered and interacted with correlative cosmology to produce a new image of the microcosmic body. Our knowledge of vessel theory before the _Huangdi neijing_ is still rough, but the differences between vessel theory in the Mawangdui and Zhangjiashan medical manuscripts and in the _Huangdi neijing_ shed light on a theory in the course of development.
Blood vessels are the obvious original referent of _mai_ 脈. The earliest attestation of the word is fourth century B.C., in a _Zuozhuan_ 左 傳 description of a horse: "chaotic vapor, untamed, erupts; dark blood1 springs forth, coursing; ridges of swollen vessels ( _mai_ ) bulge" ( _Zuozhuan_ , Xi 15, 14.3a). Blood continues to be the defining feature of _mai_ in the _SW_ gloss, listed in the form with 脈 given as an orthographic variant: "The distribution network for blood which angles through the body" 血 理 分 衷 行 體 中 者 ( _SW_ , 11B.6a). The graph is composed of two signifies, 血 and _pai_ 厎; the latter is the signific under which the _SW_ classifies _mai_ and it also serves as the phonetic of the graph.1 Thus _pai_ 厎 and its word family provide clues to the etymology of _mai_ "vessel." As a graph, the _SW_ identifies 厎 as the reverse image of the pictograph _yong_ 永: the gloss of the former is "water angling and flowing separately" 水 之 衷 流 別 也 ( _SW_ , 11B.6a); the latter is "water which is long; it depicts the long extension of the network of subterranean water-channels" 水 長 也 象 水 巠 理 之 長 永 也 ( _SW_ , 11B.5b).2 The _SW_ gloss of _jing_ 巠 (subterranean channel) is necessary to round out the etymological evidence: "Water vessels 水 . (The graph) is composed of 川 (stream) underneath 一, and 一 signifies earth; the phonetic is an abbreviation of 壬" ( _SW_ , 11B.3b).
Evidence from the _SW_ must be weighed carefully—its etymologies do not invariably yield the original meaning of a word. However, even cautious evaluation of the evidence for _mai_ would lead one to surmise that when the word was first adopted there already existed a conceptual correlation between the body and earth, and between blood vessels and streams. The idea of a "network" ( _li_ 理) of vessels is probably also significant in the original meaning of _mai_. I interpret two occurrences of _li_ in the Mawangdui macrobiotic hygiene texts as allusions to the "network of vessels" ( _MS_ VI.A.9; _MS_ VII.B. 19). Given the plurality of blood vessels, it would have been logical to conceive of them as a system, even if the exact nature of the system was not determined.3 The _Guanzi_ analogy comparing water flowing through the earth to blood and vapor flowing through the muscles and vessels can be read as an expression of the meaning of _mai_.4
The transition from the old idea of blood vessels to a physiological theory whose main purpose was to explain the movement of vapor in the body directed attention away from the blood-vascular system _per se_ and towards an idealized system which meshed with correlative cosmology. As vessel theory developed, what held vapor was not clearly distinguished from what held blood. _MS_ I.C does pair vessel and vapor as the principal terms of vessel theory, and the same can be assumed for _MS_ I.A and _MS_ I.B; but there are enough occurrences of "blood and vapor" or "vapor and blood" in the macrobiotic hygiene texts to indicate that the substances are inside the same vessels ( _MS_ III.89, _MS_ VIA.8, _MS_ VI.B.7, _MS_ VII.B.4). This is also true in the _Huangdi neijing_ , where the vessels contain both vapor and blood (Epler 1980: 339; Unschuld 1985: 74–76; Sivin 1987: 135–38).
Most attention has been given to comparing the system of vessels described in _MS_ I.A and _MS_ I.B with the _Huangdi neijing_ , in particular with _Lingshu_ 10. Both texts already know of the classification of the vessels into three types of Yang vessel and three types of Yin vessel; and each vessel has a name. Not enough attention has been paid to differences between the Mawangdui vessel theory texts and the macrobiotic hygiene texts. The hygiene texts understand that vapor circulates in the vessels; _MS_ VI.A.8 includes one of several generic references to the "hundred vessels." References to cultivating vapor sometimes specify Yin vapor (Yang vapor is not specified). But there is no evidence of vessel nomenclature nor of a vessel classification scheme; and the concept of Yin and Yang is understood as a complementariness grounded in physiological correlates other than the vessels themselves. The evidence suggests to me that macrobiotic hygiene was not the source of vessel nomenclature and classification. Rather, the Yang and Yin classification of vessels and their names arose in the context of pathology (hence the Yin vessels are the "vessels of death" in _MS_ I.D). This new elaboration of vessel theory probably explains Chunyu Yi's perception of it; and he is undoubtedly correct that "differentiating" and "naming" the vessels was accomplished as part of vessel-theory pathology.
Speculation on antecedents to vessel theory as presented in _MS_ I.A and _MS_ I.B is aided by intriguing evidence in the Zhangjiashan _Yinshu_. Although I still suspect that pathology had the greater influence, we may want to leave open questions regarding vessel classification and nomenclature. In an entry on exercises to treat _lou_ 瘦 (neck lumps), "Exercises" classifies the neck muscles into two Yang and two Yin types; and identifies vessels where the neck lumps appear by naming the muscles to which the vessels are attached. At this point I must offer a belated comment on _jin_ 筋 (muscle). The _SW_ defines _jin_ as "the strength of flesh" ( _SW_ , 4B.41a). There exists a separate word for "tendon" ( _jian_ ; _SW_ , 4B.41a), but _jin_ itself seems to have included any fibrous tissue binding flesh to bone and giving the body tensility. Muscles and vessels were associated; the _Guanzi_ refers to "muscles and vessels" when describing the flow of blood and vapor. And the _Huangdi neijing_ gives a separate classification of muscles which in its main features copies vessel classification ( _Lingshu_ 13, 4.1a). It has been thought that vessel theory combined ideas about muscles and blood vessels (and perhaps nerves) in producing an idealized vascular system (Yamada 1979: 80).
The neck muscles listed in _Yinshu_ are: Constant Yang 恒 陽 (right and left),1 Lateral Yang 側 陽 (right and left), Lateral Yin 側 陰 (right and left), and Front Yin 前 陰 ( _YSSW_ : 85). The vessels are identified as "vessel attached to the Lateral Yang muscle on the right," "vessel attached to the Lateral Yin muscle on the right," and so forth; the exception is the single Front Yin muscle which is itself the location of the neck lumps (and no vessel is mentioned). _SW_ , 10B.14b, analyzes _gang_ 亢 (throat) as a pictograph of the "form of the neck vessels." The most obvious blood vessels are the jugular veins, which do give the appearance of being attached to the sternocleidomastoid muscles. Given the conceptual pairing of muscles and vessels, whether the graph 亢 depicts vessels or muscles may be a moot question. The _Yinshu_ classification of muscles seems to be old; otherwise one would expect to find the muscles classified in terms of the vessels (as occurs in the _Huangdi neijing)_. Perhaps it represents early knowledge of the muscles in connection with hygienic exercises. Another _Yinshu_ exercise to cure pain in the malleolus refers to Yin and Yang muscles in the thigh. Pulling the thigh Yin muscle cures pain in the inner malleolus, pulling the thigh Yang muscle cures the outer malleolus—Yin and Yang clearly designate inner and outer sides of the leg as they do in _MS_ I __.A and _MS_ I.B ( _YSSW_ : 83).
_Yinshu_ does not describe a system of muscles throughout the body, thus we do not know if the classification of neck muscles was applied generally. However, ideas about a physiological structure running from head to foot would be as likely to focus on muscles as on vessels. I presume that ideas about muscles and vessels and their functions are implicit in the exercises described in _Yinshu_ even though there are few direct references to them; and I suspect that the early conception of a system of vessels was influenced by a parallel conception of muscles which connected the two ends of the body. One mention of vessels is particularly suggestive. It occurs in a list of hygienic exercises and their benefits at the end of "Exercises": "Make a circuit in the vessels and follow along the skin's webbed pattern to benefit the heels and head" ( _YSSW_ : 85). Recall that _MS_ I.C praises the sage's cold head and warm feet, which ensure that vapor travels in the proper downward direction. I submit that what is envisioned in _Yinshu_ and in _MS_ I.C is not a circulatory system in which vapor passes from one vessel to another in a single, continuous cycle. Rather, the vessels are individual channels (as stated in "Six Constituents") and the vapor circulates inside each channel. What is important is that "heels and head" are united as the result of vapor circulation, not that there is a centralized circulatory system.
This idea of vertical channels is in fact described in _MS_ I.A: all three Yang vessels of the foot pass from the foot (more precisely, the Great Yang and Minor Yang vessels begin near the outer malleolus, the Yang Brilliance vessel begins somewhere in the shin) to the head (ending at the nose, eyes, and nose respectively). Of the Yin vessels, only the Minor Yin vessel passes from the inner malleolus to the tongue, while the Great Yin and Ceasing Yin vessels pass from the big toe to the thigh and mid-body region respectively. The vessels are parallel channels which do not communicate with one another. Perhaps the idea of "making a circuit in the vessels... to benefit the heels and head" in _Yinshu_ centered on vessels which came to be classified as Yang vessels in _MS_ I.A. Referring to _MS_ I.B, which also represents the vessels as parallel channels, Unschuld suggests that the vessels may have been seen as "strings linking various sections of the body" (1986b: 283). The analogy is apt, and suggests the probable influence of muscles in the development of vessel theory.
Yamada concludes with good reason that vessel theory focused first on identifying and classifying the foot/leg vessels, and that the hand/arm vessels were added later (1985a: 69). The brevity of the accounts of the hand vessels in _MS_ I.A and _MS_ I __.B and the absence of a twelfth hand Ceasing Yin vessel is evidence enough, not to mention the obvious priority of the vessels rising from the lower limbs as outlined above. The key difference between vessel theory in the manuscripts and in _Lingshu_ 10 is in the basic structure of the system of vessels. In contrast to the parallel-channel system of vessels in _MS_ I.A and _MS_ I.B, _Lingshu_ 10 describes an interconnected circulatory system. Each vessel is linked to one of the internal organs, whose physiological function influences the vessel.1 The directionality of the vessels is no longer uniform as in _MS_ I.A (according to which the hand vessels also extend upwards from the hand and forearm); in _Lingshu_ 10 the twelve vessels are laid out so that they communicate with the organs and one another in a great, interconnected circuit. This interconnected circuit is the basis for applying a broad range of Yin Yang and Five Agent theories to physiology, as well as for applying the calendro-numerological correspondences which quantify correlative cosmology. Moreover, the _Huangdi neijing_ vessels are identified as _jing_ 經 (conduits), and these conduits are additionally linked by branch systems which contribute to the complexity of the overall system. There are holes ( _xue_ 穴) on the body located at precise points along the paths of the conduits which permit external access to them (chiefly using acupuncture). Vapor is also classified, with Yin and Yang among the several varieties. Some of these ideas were already known to Chunyu Yi; they represent a new level of theorization combined with idealization (Unschuld 1985: 73–91; Sivin 1987: 49–53, 117–39).
None of these ideas are present in the Mawangdui and Zhangjiashan medical manuscripts. The eleven vessels are not yet conceived as interconnected conduits; the five mentions of internal organs in describing the paths of the vessels in _MS_ I A and _MS_ I.B do not indicate any theoretical relation between the vessels and the organs, nor are the organs physiologically significant anywhere in the vessel theory texts;2 no vessel holes are identified; no varieties of vapor are described. In the absence of fuller theoretical explanations in the texts themselves, we are left to guess at their precise understanding of vessel theory and pathology. The following summary attempts to state what can be known from the texts. We clearly know that a six-fold classification of vessels into Yin and Yang types has been achieved; and that the vessel names are the same as those in the _Huangdi neijing_. Notably, _MS_ I.B does not use the names Great Yang, Minor Yang, and Yang Brilliance for the three hand Yang vessels, which instead are named shoulder vessel, ear vessel, and tooth vessel respectively. Whether these names represent the older anatomical names for the same vessels before Yin Yang classification, as has been generally thought, or whether the anatomical names are simply accepted alternate names of the hand Yang vessels is not certain (according to _MS_ I.B.7, the foot Great Yin vessel is also called the stomach vessel). I am wary of assuming that a definite system of vessels was already identified prior to Yin Yang classification, which then simply imposed itself onto the pre-existing system. Perhaps the system as we see it in _MS_ I.A and _MS_ I.B crystallized because of the stimulus of Yin Yang theory and the need to classify which it created.1
The Yang vessels are associated with the "vapor of heaven" and their ailments are less likely to be fatal than those of the Yin vessels, which are associated with the "vapor of earth" and are the "vessels of death" ( _MS_ I.D). The lists of ailments associated with the vessels in _MS_ I __.A and _MS_ I.B give nosological specificity to this basic principle of vessel theory pathology in the manuscripts.2 Pathogenic conditions of vapor in the vessels take several forms: surplus or insufficiency (in which case the vessel must be drained or filled); vapor which moves in the wrong direction; and blockage.3 Individual vessels can be diagnosed for signs of illness at the malleolus by applying pressure above the malleolus with the left hand and palpating it with the right hand ( _MS_ I.C).4 Cauterization is the only therapy mentioned specifically in _MS_ I.A, _MS_ I __.B __, and _MS_ I.C, although in an extreme situation a vessel can be lanced with a lancing-stone (see "Therapy" below).
The parallels shared between the vessel theory texts on _MS_ I and the _Huangdi neijing_ indicate a textual relation. The manuscript texts graphically confirm the hypothesis that the _Huangdi neijing_ is a summation of written medical knowledge edited so as to reframe older recorded teachings in terms of theoretical innovations (thus the _Lingshu_ 10 parallel to the account of the five constituents in _MS_ I.D additionally correlates each constituent with one of five Yin vessels). Despite the formal text parallels, it is difficult to trace the historical growth of vessel theory from one text to the next. Ma Jixing is one of several scholars who have argued for a developmental progression of vessel theory with _MS_ I.A representing the oldest attested stage and _MS_ I.B as the immediate antecedent to _Lingshu_ 10 (1992: 87–102). It is true that the vessel descriptions in _MS_ I.B contain more anatomical detail than _MS_ I.A; and the contents of the _MS_ I.B ailment lists are quite close to _Lingshu_ 10. However, Yamada and others have noted several features linking _MS_ I.A and _Lingshu_ 10 which are missing in _MS_ I.B. For example, _MS_ I.A consistently uses the technical names for all the vessels whereas _MS_ I.B uses anatomical names for the three hand Yang vessels; and _MS_ I.A describes branches of some vessels which relate well to the branches described in _Lingshu_ 10, but branches are missing entirely from the _MS_ I.B descriptions. The argument for a progression from _MS_ I.A to _MS_ I.B to _Lingshu_ 10 is weakened on both points. Yamada prefers to identify _MS_ I.B as the "direct archetype" of _Lingshu_ 10 and _MS_ I.A as the "collateral archetype" (1979: 72–73).1
Even speaking of both manuscript texts as archetypes of _Lingshu_ 10 without implying historical progression is problematic. The essential feature of vessel theory in _Lingshu_ 10 is the concept of a great circuit formed by twelve interconnected conduits, which is missing in _MS_ I.A and _MS_ I.B. Recall that _MS_ I.A represents the eleven vessels as parallel channels which all extend upwards from the extremities. _MS_ I.B is similar, except that two vessels extend in the opposite direction: the foot Great Yin vessel passes from the stomach down to the inner malleolus, and the shoulder vessel (corresponding to the forearm Great Yang vessel in _MS_ I.A) passes from the ear down to the back of the hand. A survey of the _Huangdi neijing_ shows that it does not present a unified vessel theory in accordance with _Lingshu_ 10. There are several references to eleven vessels (the hand Ceasing Yin vessel is regularly missing) and to vessel systems reminiscent of _MS_ I.A and _MS_ I.B. The directionality of the vessels in _Lingshu_ 17, 4.7a, coincides exactly with _MS_ I.A (Unschuld 1986b: 298–99). One might argue that the two vessels which extend downwards rather than upwards in _MS_ I.B indicate a stage in the transition from the idea of parallel channels to an interconnected circuit, but other factors—like connecting the organs into the system—are more probable inspirations for the _Lingshu_ 10 vessel system. Liu Zonghan argues convincingly that _MS_ I.A and _MS_ I.B are the prototypes of vessel theory not in _Lingshu_ 10, but in the other _Huangdi neijing_ passages which maintain older ideas; that is, the idea of an interconnected-circuit of conduits in _Lingshu_ 10 was not derived directly from the kind of parallel-channel system described in _MS_ I.A and _MS_ I.B, hence its origin is not explained by the manuscript texts (1992a).
Yamada observes that knowledge of internal organs and other parts of the body in _Lingshu_ 10 "clearly proves that there had been rapid development in anatomy" prior to its compilation (1979: 80). What we find in _MS_ I.A and _MS_ I.B is just as clearly a record of vessel theory pathology at a time when anatomical knowledge was more limited. Yet the idea of vessels which hold vapor has already resulted in a classified system of vessels, which serves as the basis for pathology. I find it noteworthy that so many theoretical pieces are already in place—in particular the detailed linkage between the vessels and ailments as indicated in the parallels between the vessel ailment lists in _MS_ I.B and _Lingshu_ 10. Speculation on the relation between physiology and illness was ahead of actual anatomical knowledge.
Therapy
The main evidence of therapy is in _MS_ I.E, whose basic view of illness is ontological not physiological. The only exception is the single inguinal swelling recipe in _MS_ I.E.135. Internal and external uses of drugs predominate, and are discussed in "Materia Medica." Magical therapy (primarily exorcistic) is discussed in Section Five. Medical theory is not discussed in _MS_ I.E, but there are examples of choosing drugs and applying therapy that reflect theoretical considerations, including: plants picked at the summer solstice or eggs collected in spring, which are understood to have solar, Yang potency (prior magico-religious belief regarding the solar virtues of drugs must also be taken into account); homeopathy;1 and environmental factors affecting treatment.2 In comparison with Chunyu Yi—who in his medical case histories only proceeds with treatment after diagnosing the vessels to determine the nature of the ailment—therapeutic principles in _MS_ I.E are fashioned from a combination of practical experience, magical belief, and naturalistic reasoning.
The inclusion of _MS_ II.B (the second edition of _MS_ I.B) ahead of the hygienic exercises in _MS_ II.C indicates a relation between the exercises used to cure ailments and vessel theory pathology. Of course the main evidence of therapy in combination with vessel theory pathology is in _MS_ I.A, _MS_ I.B, and _MS_ I.C. _MS_ I.A and _MS_ I.B specify cauterization as the therapy used with vessel theory pathology. _MS_ I.A concludes each vessel ailment list with the recommendation to treat the ailments by cauterizing the vessel. _MS_ I.B does not include the formulaic recommendation of cauterization, but does mention some precautions for the patient when cauterizing the foot Minor Yin vessel ( _MS_ I.B.9). Neither text describes how cauterization is performed and exactly where on a vessel it is applied. _MS_ I.C refers to cauterizing vessels near the waist; the actual technique is not described. The condition being treated is an excess of vapor in one of the vessels which causes "vapor to ascend and not descend." Cauterization near the waist is intended to redirect the vapor downwards (in the warm foot and cold head paradigm, vapor normally flows downwards in the vessels towards warmth). The condition is evidently serious, because the text recommends a second cauterization higher on the body than the first if the first cauterization is ineffective. Finally, if cauterization fails to work, it is necessary to cut open vessels at the elbow and knee with a lancing-stone ( _bian_ 砭) to release the vapor. As a rationale of lancing the vessels, _MS_ I.C recounts the principles which apply to lancing abscesses and other swellings in order to drain pus.
Both cauterization and lancing with a lancing-stone are included in _MS_ I.E; that is, both are older therapies which _MS_ I.C employs in the newer framework of vessel theory pathology. Before surveying therapy in _MS_ I.E, let me first examine these two therapies from the perspective of the vessel theory texts. _MS_ I.A clearly understands cauterization to be the ideal therapy for correcting pathogenic conditions of vapor in the vessels. Lancing, on the other hand, is still used primarily for draining pus; lancing vessels is an extreme measure, not the therapy of choice. The Mawangdui vessel theory texts confirm cauterization as the earlier therapy associated with vessel theory pathology. I concur with Yamada that the practice of cauterization contributed to the elaboration of vessel theory. Because cauterization applied externally affected the condition of vapor in the vessels internally, successful cauterization also confirmed the location of the vessels. And the knowledge that some places on the path of a vessel were more efficacious therapeutically than others certainly began with cauterization and culminated with the identification and naming of acupuncture pits ( _xue_ 穴) where needles were inserted. Yamada speculates that physicians began using metal needles ( _zhen_ 鍼) by the late third to early second century B.C., substituting the prick of a needle for the hot stimulus of cauterization. By the time of the _Huangdi neijing_ , acupuncture overshadowed cauterization (Yamada 1985a: 70–73).
The use of the _bian_ in _MS_ I.C seems to be transitional. Chunyu Yi's writings combine the word _bian_ for the lancing-stone in a compound with _jiu_ 灸 for cauterization, understanding _bian jiu_ to be the vessel-theory therapies "acupuncture and cauterization"; the lineage of the new acupuncture therapy is traced to the old lancing-stone ( _Shiji_ , 105.23a, 24b; Yamada 1985a: 37–39). We can be reasonably certain that Chunyu Yi pricked patients with metal needles ( _zhen_ ), especially in the light of the gold and silver needles discovered in 1968 in the tomb of Liu Sheng 劉 勝 (King of Zhongshan 中 山 王 from 154 B.C. to his death in 113 B.C.).1 The same tomb also contained two small ax-shaped blades of rock crystal which are thought to be lancing-stones. The blades are well suited for lancing abscesses as detailed in _MS_ I.C (Sun Ji 1991: 300). Which medical instrument—needle or blade—is understood in the _MS_ I.C description of lancing vessels with a _bian_ ; and what is the significance of attaching the account of lancing abscesses to drain pus?
Yamada characterizes the transition from cauterization to acupuncture as rapid, and speculates that early acupuncture needles imitated the forms of the older _bian_. The newer metal needles were also used for lancing abscesses, and—according to passages in the _Huangdi neijing_ —for bloodletting, although these uses did not fit into the theoretical framework of vessel theory and were abandoned except for some simple bloodletting techniques (1985a: 70–71). Perhaps _bian_ in _MS_ I.C refers to a metal needle rather than a stone blade. But even if it is a needle, its use still does not constitute a formal therapy grounded in vessel theory, for which the earliest evidence is Chunyu Yi's writings. In short, acupuncture as a therapy still did not exist at the time _MS_ I.C was composed.1
However, a parallel to the _MS_ I.C account of lancing vessels in _Lingshu_ 7 indicates that lancing abscesses was indeed one of the rationales of acupuncture which found its way into the _Huangdi neijing_. In the _Lingshu_ 7 passage, which concerns the proper use of the nine needles of acupuncture, every occurrence of _bian_ "lancing-stone" is replaced by _zhen_ "needle"; and every reference to _nong_ 膿 (pus) is replaced by _bing_ 病 (ailment). The technique of using lancing-stones to rid an abscess of pus has been transferred to the technique of using acupuncture needles to rid the patient of an ailment ( _Lingshu_ 7, 2.5b; Yamada 1985a: 44). The central idea is that the needle, like the lancing-stone, opens the vessel to "release" the ailment; that is, to release the pathogenic vapor which is the counterpart to pus. This idea is present in _MS_ I.C in embryonic form. Recall that the rationale for cauterization is the use of heat to correct the condition of pathogenic vapor inside the vessel. Lancing contributes a new element—the discharge of pathogenic vapor.
Since Epler's study of bloodletting in the _Huangdi neijing_ this practice has also been seen as belonging to the prehistory of acupuncture (1980). One of the problems with Epler's hypothesis is the lack of documentation of bloodletting in Chinese medicine before the _Huangdi neijing_ ; all references to _bian_ in Warring States, Qin, and early Han sources consistently associate the lancing-stone with the treatment of abscesses and other purulent swellings. Even with the archaeological discovery of medical manuscripts we have not found a single reference to bloodletting.1 The hypothesis remains plausible if only because of the importance of blood vessels in the development of vessel theory, and because bloodletting is known to have been practiced in other ancient cultures. However, one might argue that bloodletting as medical therapy in the _Huangdi neijing_ arose simultaneously with acupuncture as physicians began to insert needles into vessels.2 In any case, _MS_ I.C does not corroborate the bloodletting hypothesis and suggests an alternative to it.
Despite the association between vessel theory and cauterization in the Mawangdui vessel theory texts, cauterization did not monopolize therapeutic practice in the third and second centuries B.C. even within vessel theory pathology. The applicability of the newer acupuncture therapy was of course still being established. Chunyu Yi's writings provide the clearest evidence. Chunyu Yi states categorically that when he treats patients, "I invariably press their vessels first and then treat them" ( _Shiji_ , 105.24b). Thus vessel diagnosis is indispensable. But of the eighteen instances of therapy administered by Chunyu Yi in the medical case histories, fourteen are drug therapy, two are cauterization of vessels, and two are acupuncture (Yamada 1985a: 37–38). The only traditional ailment treated with cauterization or acupuncture is a case of cauterization for dental decay.3 Moreover, while Chunyu Yi uses both therapies, he explicitly cautions against using them when "according to the model one should not perform acupuncture and cauterization" ( _Shiji_ , 105.23a); that is, after diagnosing the vessels a physician had to additionally determine if acupuncture and cauterization should or should not be administered. Based on the medical case histories, Chunyu Yi favored drugs.
Chunyu Yi's medical practice apparently combined the older tradition of drug therapy with the new vessel theory pathology; and also utilized cauterization and acupuncture in accordance with vessel theory. Chunyu Yi was surely not alone, but the promotion of acupuncture at the expense of other therapies in the _Huangdi neijing_ suggests that many physicians ranked acupuncture well above the other therapies. Let me turn now to these other therapies (exclusive of drugs and magic) as represented in _MS_ I.E.
Cauterization is one of five forms of heat therapy in _MS_ I.E __. In the first of two descriptions of the technique in _MS_ I.E, a cord is ignited and pressed against a wart; once the wart is hot it is plucked off ( _MS_ I.E.64). In the second description (in _MS_ I.E.127), inguinal swelling is treated by cauterizing the center of the crown of the patient's head with a kind of lit cigarette until it blisters. The cigarette wrapper is made of _ai_ 艾 (mugwort) leaves, perhaps anticipating the later use of moxa (prepared mugwort leaves) for moxibustion. Cauterizing the center of the crown of the head has inspired conjectures about early knowledge of acupuncture pits, since it coincides with the location of the well-known _baihui_ 百 會 (hundred convergence) pit. However, the same spot is also where _ji_ 薊 (thistle) is pressed to treat a lizard bite in _MS_ I.E.53 (an example of counterirritation). The idea that therapy applied to one part of the body affects another part does not require an explanation based on vessel theory. Physicians probably discovered the therapeutic virtue of the crown of the head long before vessel theory.
The other four forms of heat therapy are: roasting ( _zhi_ 炙), literally roasting the affected part of the body over fire after first applying medicines to it; hot-pressing ( _yun_ 熨), most often pressing heated materials against the patient's body but there are variations; fumigation ( _xun_ 熏), in which heat and the steam or smoke of the fumigants play a role; and balneotherapy, immersing the affected part of the body in hot medicinal baths. The therapeutic use of heat in _MS_ I.E is sophisticated, and surely bears witness to a naturalistic rationale of heat in ontological pathology. Nevertheless, heat therapy has older magico-religious associations which were still very much alive in the third and second centuries B.C. The heat of fire is transformational, exorcistic, and prophylactic. It is not coincidental that _jiu_ "cauterize" is one of the verbs used to denote the act of thrusting the firebrand against the turtle shell to make it crack in the _SW_ gloss of _bu_ 卜 pyro-plastromancy; _SW_ , 3B.41b). The use of a burning cord or mugwort-wrapped cigarette in _MS_ I.E is analogous to the divination technique. The demonography "Jie" in the first Shuihudi hemerological treatise prescribes holding a burning torch aloft to bar revenants from entering the home ( _SHD_ : 213). The affinity between medical cauterization and magico-religious acts may be overlaid by naturalistic ideas, but it is definitely present in _MS_ I.E.
The affinity is even more evident in the examples of vermifugal roasting and fumigation in _MS_ I.E. _MS_ I.E.208 explicitly associates scabies with bugs which are expelled after the medicine-covered scabies are roasted. Scabies are treated by roasting in three more recipes ( _MS_ I.E.202, 204, 206) and other scabies recipes use well-known vermifugal drugs; for example, the feces of a ram and a rat ( _MS_ I.E.200, 211).1 Correspondingly, fumigation is used to expel bugs in recipes for hemorrhoids, which also have a bug etiology. Hemorrhoids swarming with pinworms are fumigated by burning an unidentified drug in a pit while the patient kneels over it in _MS_ I.E.149. The patient sits over a steaming jar of drugs boiled in urine in _MS_ I.E.147 (the steam is so irritating to the throat that the recipe includes a formula for a soothing beverage to counteract it). Fumigation is one of the most potent demonifuges, and occurs frequently in the Shuihudi "Jie." In one entry the Yang Demon 陽 鬼, a reification of Yang, prevents the kitchen stove from cooking food; the remedy is to "burn pig feces inside the house, then it will stop" ( _SHD_ : 212). When the Pestilence Demon 癘 鬼 occupies a home, causing the occupants to suffer from itching, the remedy is to "burn fresh _tong_ 桐 (paulownia) inside the house, then it will desist" ( _SHD_ : 216). These fumigations have parallels in received literature in _Zhouli_ accounts of the exorcistic responsibilities of certain state officers.2 Let me reiterate that fumigation and other forms of heat therapy in _MS_ I.E belong to a medical tradition in which naturalistic theories were developing rapidly, while at the same time the therapies applied to the body continued to be analogous to magico-religious activities.
Soaking in a hot bath of decocted _tao_ 桃 (peach) leaves to treat itch ( _MS_ I.E.255), and soaking a wounded shin in a pot of water with pulverized drugs which is kept hot all day ( _MS_ I.E.199) are the two examples of balneotherapy—which I distinguish from the more numerous examples of washing the body with medicinal liquids. _Yun_ "hot-pressing" occurs more frequently. The therapy takes its name from the instrument used to iron fabric. In _MS_ I.E.19, hot-pressing the body with scorched salt wrapped in cloth expels the cold and wind which are the cause of "rigidity due to a wound." The hot-press expellent in _MS_ I.E.25, used to treat rigidity in infants, is made of anthill loam and salt. There are two examples of hot-pressing hemorrhoids. In the first ( _MS_ I.E.146), oblong stones are burned in the fire, quenched in vinegar, and then used to hot-press the hemorrhoid.1 The second is, strictly speaking, fumigation; the hemorrhoid is "hot-pressed" with the vapor of a rat boiled in urine ( _MS_ I __.E.154). Equally unusual is the example of "hot-pressing" an abscess with _shanglao_ 商 牢 (pokeweed) soaked in vinegar ( _MS_ I.E.159)—perhaps the drug is understood to have "hot" properties.
Let me briefly mention several other forms of therapy in _MS_ I.E. Urine retention is treated by roasting the affected area and having two people massage the patient's buttocks in _MS_ I.E.104. _Yinshu_ , "Exercises," includes a similar entry for urine retention in which the patient stands erect, puts his arms around a pillar, and pulls his buttocks while another person apparently grips his waist (the verb describing the other person's action is illegible in the text; _YSSW_ : 84). Massage is of course related to the hygienic and therapeutic exercise tradition illustrated in _MS_ II.C (as best as can be determined from its current state of preservation, _MS_ II.C does not illustrate an exercise for urine retention). An anal fistula is surgically removed in a complicated procedure in _MS_ I.E.153. Hemorrhoidal surgery also occurs in _MS_ I.E.145–46. The first recipe seems to describe cupping the hemorrhoid before cutting it open.
As I stated at the outset, drugs alone or in combination with some of the therapies discussed above predominate in _MS_ I.E. In addition to the emphasis on drug therapy I would note a corresponding lack of surgical procedures. The only reference to lancing is in the inguinal swelling recipe ( _MS_ I.E.135). None of the abscess recipes mention lancing, even though this is the classic application of the lancing-stone. The lack of surgical procedures does not mean that painful therapies are avoided. The cauterization described is hardly painless; and in one of the roasting therapy recipes (for a skin ailment) the patient is instructed to get drunk before beginning the therapy, which is stopped when "the heat is unbearable" ( _MS_ I.E.74).
Materia Medica
_MS_ VI.A.9 includes the earliest drug descriptions attributed to a physician. Wen Zhi praises _jiu_ 韭 (leek) as the "thousand-year herb" which concentrates the vapor of heaven and earth; and he declares it to be the "king of the hundred herbs." The leek calms skittishness, improves vision and hearing, and prevents illness. Liquor is the "vapor-essence of the five grains" which penetrates the vessels and permeates the body, thus it is the "medium for the hundred drugs." And when King Wei asks about eggs, Wen Zhi identifies the chicken as a "Yang creature." The context for Wen Zhi's observations is chiefly dietetic, but they are applicable to materia medica in general. In _MS_ I.E as well as in the two macrobiotic hygiene recipe texts ( _MS_ III and _MS_ IV), drugs are typically added to liquor and drunk. Various forms of liquor are the most frequently used substances in the recipe texts, both internally and externally; liquor, itself a drug, is the ideal medium for the other drugs. Bird eggs gathered in the second and third months of spring (when their potency is great) are used to make a skin medicine in _MS_ I.E.74 (the medicine is applied before roasting the affected skin). "Spring-bird egg"—perhaps a dickeybird egg—is a tonic food in _MS_ III.17; and is used as a male aphrodisiac in _MS_ IV.4. Curiously, the leek does not occur in the recipe texts.
The three recipe texts and the section of recipes related to conception and childbirth in _MS_ V are the main documentation of materia medica in the Mawangdui medical manuscripts.1 Ma Jixing estimates the extant number of substances used in the manuscripts to be nearly four hundred, divided between plant, animal, mineral, and prepared substances (the last category covers condiments and food preparations as well as cloth, mats, and other manufactured goods).2 It is convenient to refer to the inventory of substances as materia medica or as drugs, keeping in mind that foods (grain, fruit, meat, etc.) and other goods are also drugs; and that in addition to therapeutic or hygienic uses, the substances are used in a range of applications loosely related to medicine by virtue of their inclusion in the manuscripts. For example, a woman's menstrual cloth is an ingredient in a medicine taken internally to treat inguinal swelling in _MS_ I.E.121; in _MS_ III.85, a virgin's menstrual cloth is part of a magical technique to hasten the speed of travel. A similar catholicity is evident in the Shuanggudui _Wanwu_ , whose significance for knowledge of early Chinese materia medica is discussed below.3
Information on the identity of the drugs or their properties is rarely included in the recipes. Two recipes in _MS_ I.E and two in _MS_ III are exceptions. _MS_ I.E.95 concludes with a detailed discussion of the plant _dujin_ 毒 堇 (identity uncertain). We learn that "the stalks are red and the leaves have vertical cords," that the fruit has a "bitter taste," and that the fruit forms shortly before the summer solstice. A fresh supply of _dujin_ must be gathered every year on the day of the summer solstice, dried in the dark (not in sunlight), and stored in a leather pouch. _MS_ I.E.147 describes a plant named _qu_ 屈 (identity uncertain). The recipe first gives the name for the drug in Jing 荆 (i.e. Chu 楚); then it notes that "its leaves can be boiled and are sour; its stalks have thorns" (the Jing name for a second plant is also given). _MS_ III.38 and 43, both aphrodisiacs, provide brief identifications for several ingredients (insects and plants); lacunae prevent clear understanding of the text.
A recipe which gives the name for a drug in Jing implies that for the most part the drug names in the text are generally known and are not local names; Chu names were added to editions copied in places like Changsha. Like other elements of medicine, knowledge of materia medica was shared across the cultural and geographical regions of China in the third and second centuries B.C. We have no information on drug production or commerce for this period. Presumably the majority of the drugs named in the recipe texts were obtainable in Changsha, although one wonders how many could be gathered locally like _dujin_. Yoneda identifies three names of drugs used in _MS_ I.E which had to have been imported from the north: _gancao_ 甘 草 (licorice), _fangfeng_ 防 風 (saposhnikovia), and _huangqi_ 黄 耆 (astragalus; 1988: 52).1 Several drugs are explicitly identified as imports: Rong salt in _MS_ I.E.97 is salt from Rong 戎, the northwestern borderlands; _MS_ III __.69 uses a stone found in the vicinity of Song Mountain 嵩 山(in present-day Henan); and the dark fungus in _MS_ III.77 comes from Luo 雒 (the Luo River 洛 水 region, Henan).
Unschuld (1982b) and Yoneda (1988) address the problem of identifying the precise botanical, zoological, or mineralogical referents of drug names in _MS_ I.E (the majority of drugs are plants and animals) as well as questions concerning the relation of drug knowledge in _MS_ I.E to the _Shennong bencaojing_ and later materia medica.2 As Yoneda wisely cautions, the correlation between drug names and their referents in the natural world has hardly been constant. Already in medieval times, Tao Hongjing 陶 弘 景 (456–536) complained that physicians did not themselves know drugs and instead listened to the drug sellers in the market; and the sellers' knowledge was also faulty since they relied in turn on the drug gatherers (Yoneda 1988: 48–49; Unschuld 1986a: 38). Yoneda lists several factors influencing which plants, animals, or minerals went by which names in traditional materia medica: either identifications were imprecise and resulted in several natural referents for a single drug name; a substitute supplanted the chief referent of the drug name; or the same name was applied to different things in different regions. Yoneda adds that unchanging identity between a drug name and its natural referent from antiquity to the present is not common in materia medica (1988: 49–52). Despite the twentieth century normalization of Chinese materia medica which includes scientific identifications, we should not become overconfident that we know the very plants, animals, and minerals named in the Mawangdui medical manuscripts. When the evidence is strong I provide a scientific identification using _ZY_ as the standard reference. This does not mean, however, that I am equally confident of all of the identifications, many of which I still regard as tentative.
Unschuld utilizes a statistical model to estimate the correlation between _MS_ I.E and later materia medica. Although my definition of materia medica is broader than Unschuld's, and my scientific identifications are not in complete agreement with his, Unschuld's conclusions bear repeating.1 Based on a count of 224 drugs in _MS_ I.E, Unschuld judges 27 to be unidentifiable, 109 to be identifiable with confidence, and another 47 to be identifiable with a fair degree of confidence. Thus, 156 out of 224 drugs (or roughly seventy percent) can be compared to later materia medica with relative confidence (1982b: 58). Comparing _MS_ I.E to Tao Hongjing's _Bencaojing jizhu_ 本 草 經 集 注 (the oldest extant recension of the _Shennong bencaojing_ ), Unschuld estimates that slightly more than half of the drugs in _MS_ I.E can be correlated with drugs listed in the _Bencaojing jizhu_ (1982b: 59). Even with generous margins of error for both figures, it is clear that _MS_ I.E bears witness to an early tradition of materia medica which resulted several centuries later in the compilation of the _Shennong bencaojing_.2
The other recipe texts include some of the same drugs found in _MS_ I.E along with additional drugs. I have not attempted to extend Unschuld's statistical analysis of _MS_ I.E to all drugs in the Mawangdui medical manuscripts, but the relation with later materia medica is equally evident. Most importantly, the other recipe texts document hygienic drug use which is missing in _MS_ I.E (it is wholly concerned with the use of drugs to treat ailments—ailments as understood in ontological pathology). To give two notable examples, _MS_ III.2 details a recipe for a fermented beverage with _dianji_ 顛 棘 (asparagus), which is a well-known longevity drug in the Later Han xian cult; and _MS_ III.71 provides the earliest record of micaingestion as part of macrobiotic dietetics. Thus, by the third century B.C. the therapeutic and hygienic uses of a variety of individual drugs were already determined. Moreover, the recipe texts sometimes call for as many as seven drugs in specified proportions, suggesting definite ideas about how drugs worked in combination.1
What kind of thinking or specific theories guided drug use? Unschuld estimates that among the _MS_ I.E drugs with correlates in the _Shennong bencaojing_ , about half show some degree of correspondence in terms of the ailments they treat; of course, the therapeutic indications for the other half are different (1982b: 59). Yet there is no evidence in the Mawangdui medical manuscripts of the _Shennong bencaojing's_ theoretical framework for materia medica.2 The fact that _dujin_ fruits are said to be "bitter" and _qu_ leaves "sour" ( _MS_ I.E.95, 147) is not evidence of the formal classification of drugs by taste (sour, salty, sweet, bitter, acrid) for therapeutic purposes. Nor is Wen Zhi's classification of the chicken as Yang evidence of systematic Yin Yang classification. Vessel theory, either in connection with pathology or hygiene, also does not play an identifiable role in materia medica in the manuscripts. For that matter, we do not know how Chunyu Yi combined vessel theory diagnosis with drug therapy. In the medical case histories he refers to drug formulas by proper names and does not mention individual drugs or discuss principles of materia medica (Yamada 1985a: 100–107). Materia medica is insignificant in the _Huangdi neijing_ , and drug theory in the _Shennong bencaojing_ is not based on _Huangdi neijing_ vessel theory pathology; in particular, the Yin Yang and Five Agent theories incorporated into vessel theory pathology do not figure in the _Shennong bencaojing_ (Unschuld 1986a: 26–27).
The drug monographs in the _Shennong bencaojing_ relate both hygienic and therapeutic information for individual drugs, which are additionally ranked in three grades and classified according to taste and warming or cooling properties. The ranking and classifications represent the application of theory to drugs already in use. Older drug knowledge was not discarded; it was simply incorporated into a new, more systematic materia medica. Theory is not needed to discover which substances in nature are medically effective; nor is theory a prerequisite for experimentation with combinations of drugs such as occur in the Mawangdui medical recipe texts. The recipe texts restore evidence of materia medica before the _Shennong bencaojing_ systematization. While the recipe texts do not reveal an underlying theory, there are indications of ideas which informed early knowledge of materia medica.
I would note first of all the strong magico-religious component. Many of the substances used in the recipe texts had dual uses in medicine and in popular religion or occult practice; naturalistic explanations of their properties which emerged in Warring States medicine built on and did not invalidate their magical properties. The magical properties of drugs continue to be noted in the _Shennong bencaojing_ and later materia medica, which identify certain drugs as demonifuges in addition to describing their properties according to naturalistic standards (Unschuld 1986a: 25–26). _Jiao_ 椒 (zanthoxylum) is one of the important aromatics in early Chinese religion, used to both attract spirits and expel demons (Mizukami 1977: 521–50). Zanthoxylum is used nine times in the medical manuscripts—several times in combination with two other pungent aromatics which are used even more frequently, _jiang_ 薑 (ginger) and _gui_ 桂 (cinnamon).1 Rationalization of the medicinal value of pungent substances was surely already accomplished in Warring States medicine, hence the frequency with which zanthoxylum, ginger, and cinnamon are used for therapeutic and hygienic purposes in the manuscripts. But their very prominence should be seen against the background of their prior and contemporary magico-religious uses.2
Magical properties are obviously foremost for the substances used in _MS_ I.E. for exorcistic operations, including feces ( _MS_ I.E.233, 235) and peachwood ( _MS_ I.E.137, 276). The use of such substances in other contexts is not unrelated; their exorcistic efficacy is simply an assumed property. Feces have already been mentioned as a vermifugal, demonifugal drug associated with bug-related ailments in _MS_ I.E. In _MS_ I.E.71, dog feces play an important role in treating "crazed seizure," evidently a demonically-inspired seizure. The feces are spread on an incision made along the back of the sufferer's head, which is then covered with a white chicken for three days. Afterwards the chicken is cooked and eaten by the sufferer. The therapy is like therapy in other recipes in which drugs are prepared and administered; yet it is barely one step removed from the overtness of an exorcistic ritual to drive the demon from the sufferer's body. The recipe represents a kind of sublimation of exorcistic behavior, which is replaced by the manipulation of drugs understood to be exorcistic. The exorcistic nature of consuming chicken flesh is best illustrated in _MS_ I.E.274, which treats the demonic _gu_ ailment by having the patient consume a medicine made from one black rooster and one snake. I suspect that the clay-wrapped baked chicken eaten to cure hemorrhoids in _MS_ I.E.150 is also exorcistic, as is the dog medicine used to treat rigidity in _MS_ I.E.22.1
Peachwood bows and figurines were a standard item in the Warring States magico-religious arsenal; their exorcistic properties were associated with the sun, Yang, and the east (see Section Five, "Varieties of Magic"). A bow is used exorcistically in _MS_ I.E.137; a figurine in _MS_ I.E.276. Perhaps the peach-leaf bath to treat itch in _MS_ I.E.255 shares some of the same efficacy. The use of peach fruit ( _MS_ III.23) and peach fuzz ( _MS_ III.43; _MS_ IV.3, 12) in aphrodisiacs may be due to their Yang potency, but magical associations are not absent. Eastward orientation alone is sufficient to render certain plants more efficacious, as in the case of the east-facing parts of _huai_ 槐 (pagoda tree) used in _MS_ I.E.264 to treat scabbing ( _MS_ I.E.265 uses an exorcistic incantation to treat the same ailment).
The variety of drugs and the elaborateness of their use indicate the other major aspect of ideas about materia medica in the Mawangdui medical manuscripts. Quite simply, within the community of physicians, knowledge of materia medica was organized; it was known that drug X was useful for application Y. Oral traditions—including those of drug gatherers and others—certainly played an important role in the diffusion of this knowledge, but I regard the Shuanggudui _Wanwu_ as evidence that physicians compiled lists of drugs which noted their applications. Such written lists would have provided much of the therapeutic and hygienic information later incorporated into the _Shennong bencaojing_. Of course, _Wanwu_ is not exclusively a drug list. In addition to physicians, other specialists in natural philosophy and occult knowledge had reasons to record the uses of substances in nature. I estimate that slightly more than a hundred names of substances are extant on the fragmentary slips of _Wanwu_ , of which at least one third can be identified with drugs named in the Mawangdui medical recipe texts (not all are used medicinally in _Wanwu_ ).
One drug, _wuhui_ 烏 喙 (monkshood), occurs four times in _Wanwu_ , the most separate entries of any substance: monkshood "stops _jie_ 節" (an ailment of uncertain identity);1 "ingested for one hundred days monkshood improves a person's ability to ran"; monkshood "makes horses run faster; the last entry only preserves the name _wuhui_ (Fuyang Han jian zhenglizu 1988: 36, 38, 39, 40). Notably, _wuhui_ is the second most used drug in the Mawangdui medical recipe texts (excluding liquors, vinegars, and fats) with twenty-one occurrences.2 In _MS_ I.E its main use is external, for wounds ( _MS_ I.E.12–13), abscesses ( _MS_ I.E.162, 227), and scabies ( _MS_ I.E.209, 212, 215–16); it is used once internally for hemorrhoids ( _MS_ I.E.151). Its use in _MS_ III is internal, chiefly in tonics and purgatives ( _MS_ III.60–61, 72, 74) as well as to increase one's speed when traveling by foot ( _MS_ III.77–80). The drug, an aconite, was one of the famous early Chinese poisons—a potion produced from it was used to coat arrowheads and other weapons ( _MS_ I.E.37–43 provide recipes for treating _wuhui_ poisoning). All aconites are a source of aconitine, a narcotic alkaloid still in use as a sedative and pain killer (Heywood and Chant 1982: 11, 26). Appreciation of its toxic and narcotic properties in early Chinese medicine is well documented in both _Wanwu_ and the Mawangdui medical manuscripts. _Wuhui_ and other aconite drugs continued to be used internally as purgatives and stimulants in later materia medica, although they were no longer the poison of choice in recipes for rapid travel. The _Shennong bencaojing_ assigns this use to _langdang_ 莨 菪 (henbane), which it states "makes a person walk vigorously, running in step with a galloping horse."3
I suspect that _yun_ 雲 is an abbreviation of _yunmu_ 雲 母 (mica) in the _Wanwu_ entry which states "to lighten the body use Yue Mountain _yun_ 越 山 之 雲" (Fuyang Han jian zhenglizu 1988: 38).1 As noted above, mica is one of the drugs in a medicine which "makes a person longlived and not become aged" in _MS_ III.71. _MS_ III also includes a category of recipes to "lighten the body and increase strength," but all drug names are missing from the single extant recipe in _MS_ III.45. Might not the original recipes have included mica? The conjectural nature of my argument notwith-standing, _Wanwu_ and _MS_ III can be seen to anticipate the _Shennong bencaojing_ monograph on mica, which is placed in the upper grade along with the hygienic information that "when ingested for a long time (mica) lightens the body and extends one's years of life" ( _GM_ , 8.44).
Unschuld notes the emphasis on the hygienic uses of drugs in the _Shennong bencaojing_. He tabulates eighty-four upper-grade drugs which "lighten the body," thirty-nine which "extend years of life," thirty-one which "eliminate agedness," and another thirty-one which are also useful macrobiotic drugs (1986a: 24). Some drugs in the middle and lower grades are used hygienically, but most are primarily used therapeutically. Thus the chief purpose of ranking the drugs into three grades is to privilege those used in macrobiotic hygiene. At the time of the compilation of the _Shennong bencaojing_ (roughly first century A.D.), the tradition of macrobiotic hygiene in medicine had already been influenced by teachings emanating from a kind of syncretistic Daoism and the _xian_ cult, which introduced new ideas about the care of the body and immortality (see Section Four, "Intellectual Background"). It is likely that the privileging of macrobiotic drugs in the _Shennong bencaojing_ derives from the cross-fertilization between medical hygiene and Daoist/ _xiaw_ macrobiotics at that time.2 The Mawangdui medical manuscripts and _Wanwu_ document the physicians' knowledge of materia medica in the third and second centuries B.C. Hygienic uses of drugs in the recipe texts are nearly as numerous as therapeutic uses; and the hygienic information anticipates the _Shennong bencaojing_ ("lightens the body," "increases strength," etc.). This is significant evidence of the importance of macrobiotic drug use in the medicine taught by Warring States physicians before Daoist or _xian_ -cult influences.3
Much research remains to be done on the drugs in the Mawangdui medical manuscripts. In the Translation and in the Index of Materia Medica I attempt a judicious evaluation of the drug names. I generally refrain from comparing their uses (assuming that a drug can be identified with certainty) with uses recorded in later materia medica. I lack the medical and anthropological expertise for critical evaluation of drug use in specific therapeutic contexts, which is made all the more difficult when the evidence is in the form of newly excavated manuscripts. Perhaps this is the place to mention that the Mawangdui medical manuscripts usually do not identify which part of a plant is used as the drug. We may presume the root, but stalks, leaves, flowers, fruits, seeds, and pods of many plants are equally usable (later materia medica is clearer on this point). I trust that these kinds of questions will be addressed by scholars more qualified than myself, and that they will find the Translation an accurate basic guide.1
Let me conclude with a brief account of drug processing and of the varieties of medicines or hygienic preparations in the Mawangdui medical recipe texts.2 The discussion of gathering and processing _dujin_ in _MS_ I.E.95 includes important details. We learn from it that the summer solstice—a significant day in magico-religious belief and the day the sun is at the peak of its Yang potency—was already an important day to gather certain plants by the third century B.C.; the earliest testimony of gathering plants on the summer solstice in received literature is sixth century A.D. The fifth month, the month of the summer solstice, is specified for the same reason in _MS_ III.6–8 (other months and seasons for gathering drugs are occasionally indicated in the recipe texts). _Dujin_ must be dried in the dark, not in the sun. The opposite instruction—to dry a plant in the sun or over heat—is given for other plants in other recipes. _Dujin_ is one of several drugs stored in a leather pouch; pouches of silk and plain cloth are also used.
Most drugs are pounded with mortar and pestle. The most common term used is _ye_ 冶, a word borrowed from metallurgy (where it means to cast metal or perhaps to hammer metal). _Ye_ denotes the fine pestling required to achieve a uniform powder before the introduction of sifting techniques (which were not common in medicine until after the Han). I adopt the translation "smith" for _ye_ in order to preserve the metallurgical connotation.1 Drugs are also chopped, minced, flaked, hammered, ground, and chewed.2 Fresh or dried, some drugs are allowed to soak before further use, often in liquor or vinegar; sometimes it is the infusion which is used. When drugs are cooked, the chief methods are boiling, steaming, incinerating, scorching, and frying. Many drugs are incinerated before being pulverized. Boiling, which forms part of the preparation of many decoctions, is the most varied of the cooking methods. Besides simply boiling substances until they are done or boiling to produce a reduced concentrate, there are examples of "thrice boiling" at three degrees of heat: the substances are brought to a certain temperature, allowed to cool, and then cooked again for a total of three times. The lowest temperature is indicated by the verb _wen_ 温 (heat), the highest by _fei_ 沸 (bubble). A third word written with the graph 扔 is unattested in received literature, but from the context it appears to represent a temperature in between the other two; I tentatively translate it as "scald."3
Therapeutic medicines which are to be drunk may be decoctions or infusions, but it is common to stir pulverized drugs into liquor, vinegar, or some other beverage. Hygienic drug use follows the same pattern. There are a few examples of forming the drugs into balls, which are either swallowed directly or are crashed and drunk in a beverage.4 Macrobiotic beverages and food preparations are discussed in Section Four, "Techniques." The relation between therapy, pharmacy, and cuisine is evident in _MS_ I.E recipes for baked chicken ( _MS_ I.E.150), a rich millet gruel ( _MS_ I.E.57), and a strained broth of chicken, rabbit, and grain ( _MS_ I.E.58).1 Most ointments for external application are prepared either by frying the drugs in lard or by blending pulverized drugs with lard without cooking. Decoctions, infusions, and drugs in solution are also used externally. One innovative form of external application is used in _MS_ III and _MS_ IV exclusively for aphrodisiacs, usually applied to the region of the genitals. Cloth is repeatedly soaked in a drug liquid, allowed to dry, and soaked again until the liquid is gone. The drug-impregnated cloth is then rubbed on the body ( _MS_ III.23, 37–43; _MS_ IV.3, 6, 7).2
1Hudson (1993) offers a concise statement on the concepts of illness, health, and disease in a Western setting which covers the basic issues.
1The same term is used in _MS_ I.C.
2Sun Simo's 孫 思 邈 (seventh century) _Qianjin yifang_ 干 金 冀 方 is notable for its two final chapters devoted to magical medicine ( _Qianjin yifang_ , 29–30).
1Pathogenic _qi_ represents ontological pathology, the vapor being the cause of a specific ailment rather than some other entity (Harper 1990: 217). On wind and vapor as pathogens, see Unschuld 1985: 67–73.
1The similarity between natural and demonic causes of illness in early Chinese belief is discussed in Harper 1990: 222–25.
1Its classificatory usage is perhaps best attested in _SW_ , 7B.26b–35b, which lists the names of ailments written with the signific 疒, many of which are simply identified as "a _bing_."
1Yamada argues that there is an etiological and nosological plan in _MS_ I.E, which he deduces by arranging the original fifty-two ailment categories into fourteen groups. He then identifies seven or eight combined groups within the fourteen, whose coherence he interprets in terms of four "images" of the body (1985b: 234–53). I am not convinced by Yamada's argument, especially given the uncertainty surrounding the identification of some of the ailment names and the ailments they designate.
1In diagnosing a case of intestinal parasites, Chunyu Yi argues that the pinworms are a natural transformation of cold, damp vapor ( _Shiji_ , 105.18a; pinworms are named in _MS_ I.E.149).
1 _Guanzi_ 39, 14–236. I concur with Graham's judgment that the essay pre-dates the crystallization of Yin Yang and Five Agent theories in the third century B.C. (1989: 356).
2The relevant etymological and textual evidence is conveniently summarized in Onozawa et al. 1978: 14–17, 30–34; see also Sivin 1987: 46–48. The compounds "blood and vapor" and "food vapor" occur in the _Lunyu_ 論 語, but in late chapters which are probably no earlier than fourth century B.C. Other occurrences in received literature also cannot be dated earlier than fourth century B.C.
1"Move" translates dong 動, which here signifies disturbance. In other contexts _dong_ can refer to the normal movement of blood and vapor in the vessels and to their pulse.
2Fingers and toes.
1The two editions are slightly different. For example, _MS_ I.C opens with the exhortation that the "model of the vessels be clearly taught," which is not included in the _Maishu_ edition.
1"Dark" translates _yin_ 陰, which is not used in the technical sense of Yin here.
1Phonetic contacts between words with initial * _p_ \- and initial * _m_ \- in Old Chinese are common.
2It is common to write _mai_ "vessel" using 永 rather than 厎 The scribal variant 温 is used for _mai_ in _MS_ I.A, but it appears to be simply a variant and does not contribute to etymological analysis of the word _mai_.
3Liu Zonghan notes several occurrences of the compound _mai li_ "vessel network" which are probably of Han date (1992b: 250).
4Yamada is skeptical of the _SW_ etymological evidence and considers the _Guanzi_ passage to be of Han date; he argues for a pristine idea of _mai_ as vessels in animals (based on the _Zuozhuan_ passage), which was extended to vessels in humans and only later acquired connotations relating blood vessels to streams in the earth (1985a: 64–67). I disagree with his argument and his dating of the _Guanzi_ passage.
1The word _jin_ "muscle" is not written after the name Constant Yang, but based on the subsequent names it must have been omitted by mistake.
1The organ forms part of the name of each vessel in _Lingshu_ 10.
2 _MS_ I.A.4 mentions the liver in describing the path of the foot Mino Yin vessel; in _MS_ I.A.7 the forearm Great Yin vessel ends at the heart; the kidney is on the path of the foot Minor Yin vessel in _MS_ I.B.9, coincidentally the organ associated with the foot Minor Yin vessel in _Lingshu_ 10; the forearm Great Yin and Minor Yin vessels both end at the heart in _MS_ I.B.10–11. _MS_ I.D contains the only reference to _zang_ 臟 (depot): the Yin vessels "putrefy the depots," presumably the five depots (heart, kidney, liver, lung, spleen). Yamada sees significance in the fact that _MS_ I.A and _MS_ I.B only mention organs in connection with Yin vessels, perhaps reflecting the special pathology of the Yin vessels as stated in _MS_ I.D (1979: 82). The macrobiotic hygiene texts do not mention specific organs other than the heart, but do include references to the five depots and six _fu_ 腑 (cavities) as storage areas inside the body (see Section Four, "Body and Spirit").
1The muscle nomenclature in _Yinshu_ also suggests that Yin Yang theory and correlative cosmology may have inspired systematic theorizing about physiology. This is not to say that there was no prior knowledge of muscles, but rather that the conception of a system of muscles may not have existed yet. My wariness may prove to be excessive if future manuscript discoveries clarify the issue.
2 _MS_ I.A.6 also associates of the three foot Yin vessels with death. _MS_ I.B.7–8 concur that the ailments of the foot Great Yin and Ceasing Yin vessels can be fatal.
3The first paragraph of _MS_ I.C refers to surplus and insufficiency, as does the third paragraph which describes ailing vessels as being empty or as having excess (manifested in pathogenic movement of vapor). Vapor moving in the wrong direction is described in _MS_ I.C when "vapor ascends and does not descend," and in the "reversal ailments" listed in _MS_ I.B. Blockage in mentioned in the third paragraph of _MS_ I.C.
4Diagnosis at the malleolus applies to the foot vessels. The _Maishu_ edition of _MS_ I.C concludes with several sentences, not found in _MS_ I.C, which confirm that vessels are diagnosed individually: "The method for treating ailments. Discern which (vessel) erupted first and treat it. When several vessels erupt in ailments together, pick the one that is most severe and treat it first" ( _MSSW_ : 74). There is no corresponding description of diagnosing vessels at the wrist.
1I should note that Yamanda consistently refers to the _Taisu_ edition of the vessel description text in _Lingshu_ 10, which he regards as the older edition.
1In _MS_ I.E.267, chilblain is treated by steaming frozen earth and hot-pressing the chilblain with it. The homoepathic treatment of facial pustules in _MS_ I.E.280 involves magical correspondence—the ailment name, _ma_ 瀌, is written with the graph for horse inside, and horse cheekbone is the drug used to treat it.
2 _MS_ I.E.188 forbids exposure to the night sky while treating scars lest the stellar and lunar essences interfere with the treatment.
1Ma Jixing associates the excavated needles with the "nine needles" of the _Huangdi neijing_ (1972).
1Lu and Needham (1980: 77–88) state that acupuncture is attested for the sixth century B.C. in two passages in the _Zuozhuan_ (whose information is best treated as fourth century B.C., the probable date of its compilation). They also conclude that the _Shiji_ account of Bian Que documents knowledge of the _xue_ "pits" in acupuncture theory by the fourth century B.C. Their interpretation of the _Zuozhuan_ passages is inaccurate (cf. Unschuld 1985: 94, n. 64; and Yamada 1985a: 6–11); and imputing a fourth century B.C. date to Bian Que and his practice of acupuncture is not credible (cf. Yamada 1988). Moreover, Yamada has shown that the interpretation of the term 三 陽 五 會 in the _Shiji_ as the name of an acupuncture pit is doubtful (1988: 130–32). Perhaps this is the place to state once again that lancing is not acupuncture; the latter began when the use of needles was adopted as a therapy in vessel theory pathology (see the Introduction, p.5, n.2). Chinese scholars may be correct when they speculate that certain neolithic, Shang, and Zhou needle- and blade-like instruments are medical instruments (Ma Jixing and Zhou Shirong 1978), and when they propose interpreting certain Shang graphs as related to the medical use of such instruments (Hu Houxuan 1984). However, the use of these instruments does not constitute acupuncture.
1Epler (1980: 349) relies on Miyashita's conjecture regarding bloodletting in the Shang bone and shell inscriptions as proof of the antiquity of bloodletting in China (1959: 235). Miyashita's interpretation of the inscriptional evidence as bloodletting is uncertain; and it certainly cannot be used to prove the existence of bloodletting in Warring States medicine in the absence of any evidence.
2Chunyu Yi states in one of his medical case histories that after inserting acupuncture needles into three places on the patient's foot he pressed on the spots to prevent bleeding ( _Shiji_ , 105.15b).
3 _Shiji_ , 105.16a. The other ailments concern: disturbance in the foot Ceasing Yin vessel, requiring cauterization of the vessel ( _Shiji_ , 105.15a); heat reversal ( _re jue_ 熱 蹶), treated by pricking the feet with needles ( _Shiji_ 105.15a); and ascending reversal ( _jue shang_ 蹶 上), treated by performing acupuncture on the foot Yang Brilliance vessel ( _Shiji_ , 105.17a). _Jue_ "reversal" is the same condition described in _MS_ I.C when vapor moves in the wrong direction.
1It is unlikely that the itch mite _Sarcoptes scabiei_ was already observed in early Chinese medicine. There is probably some other basis for the observation of bugs in scabies.
2Harper (forthcoming) discusses the relation between magico-religious fumigation and fumigation in _MS_ I.E.
1Ma Jixing and Zhou Shirong (1978) broaden the definition of _bian_ "lancing-stone" to include all stones used in therapy (they are used to massage in addition to hot-pressing). I find no written evidence that the term _bian_ refers to stone medical instruments other than a lance and am not convinced by their argument.
1In addition, _MS_ II.A names one drug; _MS_ VI.A includes occasional references to drugs; and the recipes for philters in _MS_ VII.A also provide evidence of drugs.
2Ma Jixing 1992: 123–26, 1073–98. Ma counts exactly 394; and he does not include some of the magical materials—like those used to exorcise ailments in _MS_ I.E and to produce philters in _MS_ VII.A—which brings the total to over four hundred.
3In the Index of Materia Medica I adopt a broad definition of material medica as nearly everything that forms part of the treatment of ailments or the execution of techniques (cooking pots, dishes, and sundry utensils used to prepare drugs are not included); that is, if something seems to me to be playing an active role in a recipe—be it the _ge_ 葛 (kudzu) used to make exorcistic arrows in _MS_ I.E.132 or the _bai_ 柏 (arbor-vitae) pestle used for exorcistic beating in _MS_ I.E.118—I include it.
1See the Index of Materica Medica for occurrences. _Fangfeng_ also occurs in _MS_ III.
2Other Mawangdui medical texts which utilize drugs were not available before publication of _MWD_ , vol. 4. Detailed studies of all materia medica in the Mawangdui medical manuscripts have not yet been published.
1Unschuld does not count as drugs substances which he judges to be carriers of the drugs (fats and various liquids), and does not include magical materials. It is well to remember that scienfitic identifications of drug names are subject to the caveats enumerated by Yoneda.
2Some drugs in _MS_ I.E not listed in the _Bencaojing Jizhu_ are included in other, later materia medica. For further discussion of the _Shennong bencaojing_ and Tao Hongjing's contribution to materia medica, see Unschuld 1986a: 17–43.
1 _MS_ I.E.157 describes a seven-drug compound as an internal medicine for _ju_ abscess; the proportions of the drugs vary depending on the location of the abscess.
2The classification of drugs and drug theory in the _Shennong bencaojing_ are discussed in detail in Unschuld 1986a: 18–27.
1For combinations of zanthoxylum, ginger, and cinnamon, see _MS_ I.E.2, 157, 171; _MS_ IV.5. There are more combinations of zanthoxylum with cinnamon, zanthoxylum with ginger, and ginger with cinnamon. Cinnamon—including _jungui_ 菌 桂 (curled cinnamon)—is used a total of twenty-three times; ginger a total of fifteen times.
2Mawangdui tomb 1 exemplifies the importance of aromatics in mortuary customs. The woman's corpse was holding in its hands silken pouches filled with zanthoxylum, cinnamon, and other aromatics. And all four storage areas in the burial chamber surrounding the coffins contained aromatics; notably six sacks in the storage area on the west side, five of which were filled with a mixture of zanthoxylum, cinnamon, ginger, and other aromatics (Huan yixueyuan 1980: 261–66).
1Dog and chicken are well-known sacrificial animals used for exorcistic purposes. See _Fengsu tongyi_ , 8.4a-b; and Bodde 1975: 317–25. The chicken is also Yang, another aspect of its exorcistic efficacy.
1The editorial committee reads it as _jie_ 癤 but I remain skeptical because this word is not attested as a name for a kind of swelling before medieval times.
2Cinnamon and curled cinnamon combined occur twenty-three times.
3 _GM_ , 17.20; _ZY_ : no. 0649, _Hyoscyamus niger_ L. (cf. Unschuld 1986a: 22). The _Shennong bencaojing_ also notes that eating too much henbane "makes a person run crazily."
1Minerals from Yue are noted in another entry which refers to working jade with Yue metal 越 金 (Fuyang Han jian zhenglizu 1988: 38).
2It is interesting that the materia medica specialists responsible for the _Shennong bencaojing_ embraced macrobiotic hygiene while the physician-authors of the _Huangdi neijing_ distanced themselves from it.
3Unschuld characterizes the _Shennong bencaojing_ as having a "Taoist orientation" (1986a: 24). I would argue that the intellectual affiliations of macrobiotic hygiene are complicated and are not simply Daoist (whether one means the philosophy associated primarily with the _Zhuangzi_ and _Laozi_ , the syncretistic Daoism of the Former Han, or the nascent religious Daoism of the Later Han). Again, see Section Four.
1In addition to Unschuld 1982b and Yoneda 1988, Morimura 1981 and Murakami 1985 represent ambitious preliminary assessments of materia medica in _MS_ I.E. Ma Jixing's survey of all Mawangdui materia medica is also a useful beginning (1992: 123–51, 1073–98).
2Ma Jixing's account is more detailed (1992: 128–51). Similar information in the _Shennong bencaojing_ and Tao Hongjing's additional notes is translated by Unschuld (1986a: 18–39).
1See the first occurrence of _ye_ in _MS_ I.E.3 for details. I disagree with Ma Jixing, who interprets _ye_ to mean grinding drugs (1992: 130).
2I assume that the many references to chopping, mincing, and flaking involve the use of knives, although it is not impossible that the terms might refer to pounding the drug to a certain degree of fineness as well. Drugs are chewed in the mouth in three recipes: _MS_ I.E.197, _MS_ III.74, _MS_ IV.3. See Ma Jixing 1992: 130–31, for further discussion of pulverization vocabulary.
3The three words are discussed in the notes to _MS_ I.E.102.
4Balls of a four-drug compound (including monkshood) are swallowed to treat hemorrhoids in _MS_ I.E.151; in _MS_ I.E.2, the balls are crushed and mixed into liquor. Macrobiotic balls are swallowed in _MS_ III.16–17 and _MS_ III.71 (where the main ingredient is mica); the balls swallowed in _MS_ III.77 (also containing monkshood) speed travel.
1Note also the frequent use of grain throughout the recipes in _MS_ I.E.
2In several recipes a mixture of drugs is spread on the cloth rather than the soaking method described. _Lingshu_ 6, 2.5a, details a similar preparation (the cloth is soaked in an infusion of liquor, zanthoxylum, ginger, and cinnamon!), which is used to _yun_ "hot-press" an ailment rather than as an aphrodisiac.
Section Four
Macrobiotic Hygiene
The first text in the Zhangjiashan _Yinshu_ , "Seasonal Regimen," opens with a hygienic maxim attributed to Ancestor Peng 彭祖, the paragon of longevity in late-fourth and third century B.C. received literature: "Spring, generate; summer, grow; fall, collect; winter, store—this is the way of Ancestor Peng" ( _YSSW_ : 82). The text continues with an amplification of the hygienic regimen appropriate to each season:
Spring days. After rising in the morning, eliminate water,1 scrub (the hands), rinse (the mouth), wash the teeth, and knock (the teeth);2 unfasten the hair, stroll to the lower end of the hall to meet the purest of dew and to receive the essence of heaven,3 and drink one cup of water—these are the means to increase accord. Enter the palace4 from evening until greater midnight;5 increasing it injures vapor.
Summer days. Wash the hair frequently, bathe rarely; do not rise late; eat many greens. After rising in the morning and eliminating water, scrub and rinse with water, and clean the teeth; unfasten the hair, walk to the lower end of the hall, and after a while drink one cup of water. Enter the palace from evening until midnight; increasing it injures vapor.
Fall days. Bathe and wash the hair frequently. With drink and food, let hunger or satiation be whatever the body desires. Enter the palace however often the body finds it beneficial and comfortable—this is the way of benefit.
Winter days. Bathe and wash the hair frequently. The hands should be cold, the feet warm, the face cold, the body warm.1 One should rise from sleep late, and while recumbent must stretch out straight. Enter the palace from evening until lesser midnight; increasing it injures vapor.
Ancestor Peng's way of hygiene is directed to an elite, male audience; and it encompasses various activities that promote a healthy, enjoyable, and long life—personal cleanliness, cultivation of vapor (or "dew" and "essence"), diet, and sexual intercourse. In _MS_ VI.A.6, Ancestor Peng teaches men to value the vapor associated with the penis, claiming that "longevity lies entirely with the penis." Daily exercise, breath cultivation, and diet serve to "secure" the penis and nurture its essential vitality. The final text in _Yinshu_ , "Cultivation of the Body," provides teachings on the nature of health and illness. A distinction is made between the noble and the ignoble in society. The ailments of the noble are caused by imbalances of vapor; the "person of the way" 道 者 prevents them from occurring by maintaining the proper balance of vapor with breathing techniques. Strenuous labor coupled with their ignorance (they do not even know about the breathing techniques!) make the ignoble prone to sickness and death ( _YSSW_ : 86). Similarly, "Care of the Body" in _Maishu_ assumes that its hygienic teachings are intended for "those who ride in carriages and eat meat" ( _MSSW_ : 74).
The Mawangdui and Zhangjiashan macrobiotic hygiene texts provide a remarkably full record of a tradition of macrobiotic hygiene which by all appearances was taught to the elite by physicians in the third and second centuries B.C. Writing without knowledge of the Mawangdui and Zhangjiashan medical manuscripts, Graham speculates that the philosophies of Yang Zhu 楊 朱 and Zhuangzi 莊 子 borrowed physiological concepts from medicine in the fourth century B.C. based on circumstantial evidence, chiefly in the _Zhuangzi_ (1989: 328). Graham seems to have in mind borrowing from basic medical ideas related to vapor and to Yin and Yang, not from a body of macrobiotic hygiene literature disseminated by physicians. Yet _MS_ VI.A.9 presents the fourth century B.C. physician Wen Zhi teaching his "way" of macrobiotic hygiene to the founder of the Jixia Academy, King Wei of Qi. The cross-fertilization between Warring States philosophy and medicine was far more extensive than even Graham thinks.
Intellectual Background
As the excavated macrobiotic hygiene texts make clear, the theory and practice of physical and spiritual cultivation were part of the medical knowledge that the elite acquired from physicians. We now know how philosophy came by the basic physiological ideas that underlie the philosophers' discussions of spiritual cultivation and meditation (none of the extant philosophical texts discuss physiological theory in any detail).1 To be sure, medicine was hardly isolated from Warring States philosophical discourse and the philosophers contributed to medical thought, especially during the third century B.C. when the nature of the body and spirit became a prominent philosophical issue. At the same time, there is esoteric knowledge in the Mawangdui and Zhangjiashan macrobiotic hygiene texts that has no counterpart in Warring States, Qin, and Han philosophical literature; nothing comparable exists before the cultivation literature of religious Daoism of roughly the third century A.D. and after (see "Techniques" below).
Physiological ideas are the basis for the conception of the sage in the _Guanzi_ , "Neiye," as the man who trains his heart to cultivate vapor ( _qi_ 氣), essence ( _jing_ 精), and spirit ( _shen_ 神)—these being the basic elements of human physiology. Meditation in the "Neiye" is this heart/mind training, which produces "perfect virtue" ( _cheng de_ 成 德) and consequently wisdom ( _Guanzi_ 49, 16.269). I concur with Graham that the "Neiye" is the oldest Chinese meditation text, probably composed in the late fourth century B.C. and associated with the Jixia Academy (1989: 100). The "Neiye" alternates between discussion of the mystical transformation wrought by the heart and concerns of a more hygienic nature. For example, the discussion of the "way of eating" 食 之 道 is reminiscent of passages in the Mawangdui and Zhangjiashan macrobiotic hygiene texts ( _Guanzi_ 49, 16.272; see "Philosophy and Macrobiotic Hygiene" below). As Graham notes, the "Neiye" is not a Daoist text. "Way" 道 has both cosmological and moral dimensions; and the goal of meditative cultivation is to perfect human potential (1989: 105). I would add that its hygienic concerns indicate an affinity with the hygienic teachings of contemporary physicians like Wen Zhi.
A focus on the spirit and meditative cultivation of the heart/mind is evident in the _Zhuangzi_ , which at the same time distances its more mystical understanding of cultivation from commonplace hygiene. "Xiaoyao yu" 遣 遙 遊—probably also late fourth century B.C.—pointedly belittles the ordinary folk who admire Ancestor Peng's longevity and try to emulate him ( _Zhuangzi_ 1, 7). The same essay later describes a "spirit-being" 神 人 who "does not eat the five grains, but sucks wind and drinks dew." His body rendered light by this diet, he "mounts clouds and vapor, driving flying dragons, and journeys beyond the four seas" ( _Zhuangzi_ 1, 15). The spirit-being's dietetics and breath cultivation have counterparts in macrobiotic hygiene; _MS_ II.A relates the technique of "eliminating grain" and "eating vapor." Cosmic flight as the result of long cultivation is described near the end of _MS_ VI.A.4; perhaps the _xian_ 仙 cult with its ideas about transcendence has influenced both the _Zhuangzi_ and _MS_ VI.A.4. However, I do not read the _Zhuangzi_ 's ideal of the spirit-being as condonation of macrobiotic hygiene or nascent _xian_ ideas, nor does it necessarily allude to the _Zhuangzi_ 's own program of cultivation. The spirit-being is fashioned to serve as yet another image of perfect freedom which stands in contrast to human endeavors (like the Peng bird which opens "Xiaoyao yu"). The _Zhuangzi_ is concerned with the cultivation of the spirit in connection with matters beyond bodily well-being, long life, and immortality; it does not share the goals of medical macrobiotic hygiene or the _xian_ cult. A program of cultivation is detectable in many _Laozi_ passages, which appear to encode specific teachings in verse and metaphor. The precise intent of these passages hinges on what the original frame of reference may have been. Similar use of verse and metaphor to encode techniques in the Mawangdui macrobiotic hygiene texts bear out the physio-spiritual interpretation of _Laozi_ passages in Han commentaries like the "Heshang gong" 河 上 公 and "Xianger" 想 爾 (see "Techniques" below). However, cultivation in the _Laozi_ is fused to a political plan in which longevity and immortality are not the central goals.1
The Mawangdui and Zhangjiashan macrobiotic hygiene texts describe a kind of baseline macrobiotic hygiene for the elite that focuses on care of the body, not on the more philosophical and mystical programs of the "Neiye," _Zhuangzi_ , or _Laozi_. In addition, the texts' goal of long life is not identical to the _xian_ -cult goal of immortality and transcendence. The formation of the _xian_ cult in the third and second centuries B.C. remains unclear. Eremitism, shamanic religion, and ideas about flight to spirit paradises each played a role, as did new ideas about a drug of deathlessness and alchemical elixirs which began to circulate in the third century B.C. Most importantly, the physiological theories on which macrobiotic hygiene was founded also furnished the rationale for immortality—to go from the belief that macrobiotic hygiene can lengthen life to the belief that an individual can create an imperishable body is in many respects a logical progression of ideas (all that is necessary is the assumption that humans can achieve perfection). The promise of immortality seems to have been instrumental in establishing the reputation of the _xian_ cult as a superior tradition of macrobiotic hygiene.2 Rather than adopt Ancestor Peng, the early _xian_ cult attributed its macrobiotic traditions to a new pair of legendary adepts, Chisongzi 赤 松 子 and Wangzi Qiao 王 子 喬. Their longevity is briefly noted in several third-century B.C. sources; second-century B.C. sources are more numerous and detailed, including references to immortality and cosmic flight.1 The word _xian_ does not occur in the Mawangdui and Zhangjiashan macrobiotic hygiene texts; the only mention of ideas related to immortality and other possibly _xian_ beliefs is the brief passage in _MS_ VI.A.4 (discussed in "Body and Spirit" below). Given the prominence of the _xian_ cult by the end of the third century B.C., we could expect to find signs of its influence in the excavated texts; what is surprising is how slight the influence is.2
By the time Li fils practiced the techniques of macrobiotic hygiene described in his manuscripts, the situation regarding physical and spiritual cultivation must have been complex. First, the Daoist authors of the probably second-century B.C. "Keyi" 刻 意 in the _Zhuangzi_ criticize people who strive to match Ancestor Peng's longevity by practicing breath cultivation ("spitting out the old and taking in the new" 吐 故 納 納) and exercises ("guiding and pulling" 道 引; _Zhuangzi_ 15, 237); a criticism which is seconded in a parallel passage in _Huainanzi_ , 7.105. In the words of the _Huainanzi_ , the "realized man" 真 人 focuses on the condition of the spirit; his spiritual communion with the ultimate does not depend on exertion to "nurture the form" 養 形 because he knows that physical decay is inevitable. Thus he is not distracted by the popular hygienic regimens. I expect that the criticism did little to dissuade the elite from practicing the techniques described in the Mawangdui and Zhangjiashan macrobiotic hygiene texts.
Then we have the syncretistic Daoism reflected in the _Huainanzi_ , which has a definite program of cultivation—an amalgam of Daoist, _xian_ , and medical ideas.3 Finally, there were people who declared themselves followers of Wangzi Qiao or Chisongzi. According to the _Shiji_ , Zhang Liang 張 良 (d. 187 B.C.) wished to "abandon affairs among men to wander with Chisongzi," which led him to study "avoidance of grain" ( _bigu_ 辟 榖), "guiding and pulling," and "body lightening" ( _Shiji_ , 55.12b). All three were also part of what I shall call standard second-century B.C. hygiene and are attested in the Mawangdui macrobiotic hygiene texts (see _MS_ II.A on "elimination of grain," _MS_ II.C on "guiding and pulling," and _MS_ III.45 for a tonic to "lighten the body"). I do not doubt Chisongzi's reputation among enthusiasts, but I wonder how different from standard hygiene the practices were. I also wonder whether everyone who professed admiration for the legendary _xian_ adepts actually participated in the _xian_ cult or whether it was the convention to glamorize any form of macrobiotic hygiene with a _xian_ pedigree.1
I assume that the hygienic practices in Li fils' manuscripts were customary rather than exceptional among people of his class; and that the "way of Ancestor Peng" in _Yinshu_ was a standard guide to healthful living. If a distinctive _xian_ macrobiotic hygiene literature was already circulating, I can only conclude that we have not recovered it in the manuscripts excavated to date. Yet there are signs of a trend to associate macrobiotic hygiene with _xian_ ideas by the first century B.C. The changing perception of hygiene is formalized in the rubric adopted for the subcategories of medical literature in the _Hanshu_ bibliographic treatise: sexual cultivation literature is placed in a separate category, even though sexual cultivation is one of the branches of macrobiotic hygiene; the rest of the macrobiotic hygiene literature is in a category entitled "Shenxian" 神 僊 (Spirit transcendence; _Hanshu_ , 30.82a). The summary appended to the category states that "Shenxian" literature, "provides the means to secure the real nature of life and to explore what lies beyond it," making _xian_ -style "exploration of the beyond" part of the definition of macrobiotic hygiene. The summary also strikes a note of warning to practitioners of macrobiotic hygiene: "Yet because some people devote themselves solely to this endeavor, grandiose, deceptive, weird, and obtuse texts proliferate all the more—this is not how the sage kings instructed. Confucius said, 'To seek the occult and engage in weird practices in order to leave a mark for later ages—this I will not do.'"
The accusation could have been leveled (and was) at all _fang_ -literature, which lay outside "canonical art" in Han intellectual and social orthodoxy (see Section Two, "Recipes, Techniques, Calculations, Arts"). Orthodox censure of both macrobiotic hygiene and the _xian_ cult focused on the issue of selfishness. Even the _Huainanzi_ gives voice to the orthodox complaint in a passage which states that for devotion to macrobiotic hygiene Chisongzi and Wangzi Qiao "can be said to have nurtured life, but cannot be said to have been filial sons" ( _Huainanzi_ , 20.354). Horiike surveys the attitudes of Han intellectuals towards macrobiotic hygiene and _xian_ ideas; unsurprisingly, expressions of skepticism and disapproval outnumber approval (1988: 298–311).
The physician-authors of the _Huangdi neijing_ acknowledge that according to physiological theory a person will not become ill so long as he maintains the natural harmony of the organism. This is the subject of _Suwen_ 2, which concludes with the dictum: "The sage does not treat those who are already ailing, he treats those who do not yet ail; he does not treat what is already chaotic, he treats what is not yet in chaos" ( _Suwen_ 2, 1.9b). The kind of preventive medicine implied in this statement is of course the individual practice of hygiene. Yet, vessel theory in the _Huangdi neijing_ is vessel theory pathology; and the physician uses vessel theory to diagnose illness, which he treats with the nine needles of acupuncture. The _Huangdi neijing_ physician does not necessarily condemn macrobiotic hygiene. _Suwen_ 2 opens with a discussion of harmonizing the body with the seasons which is clearly related to the "way of Ancestor Peng" in the _Yinshu_ ( _Suwen_ 2, 1.6a–7b). There is the same correlation of spring/generate, summer/grow, fall/collect, and winter/store; and there are recommendations about times for rising and going to bed. But the real point of _Suwen_ 2 is to demonstrate the correlation between the microcosmic body and macrocosmic processes across the seasons. Where the _Yinshu_ details a specific hygienic regimen, _Suwen_ 2 substitutes general principles. _Lingshu_ 55 increases the distance between vessel theory pathology and macrobiotic hygiene by quoting the dictum on "treating those who do not yet ail" in a new context. The ideal no longer concerns working to keep patients healthy, but rather concerns the physician's skill in diagnosing the entire course of a patient's illness. The superior physician "treats _what_ does not yet ail," meaning that his acupuncture therapy is applied not to the morbid condition which is already manifest in the organism ("what is already ailing")—it is too late for that—but to the next stage of the illness which he can expect to treat. Preventive hygiene has disappeared.1
In the midst of _xian_ -cult enthusiasm, Daoist critique, syncretistic-Daoist approval, orthodox disapproval, and neglect by the medical establishment represented in the _Huangdi neijing_ , I think a medical tradition of macrobiotic hygiene—a kind of standard hygiene—remained a part of everyday elite life. The _Lunheng_ attests to its continued vitality in the first century A.D. Wang Chong states that he himself wrote a "book on nurturing life" in sixteen fascicles which treated of "nurturing vapor and self-preservation," "ingesting drugs and pulling and guiding," and other subjects in hopes of extending his own life ( _Lunheng_ , "Ziji," 30.592). The book is lost, but Wang Chong's sympathy for macrobiotic hygiene comes out at various points in the _Lunheng_ , even as he savages what he regards as the unfounded belief in immortality and transcendents ( _xian_ ). According to Wang, "swallowing drugs and nurturing life can make a person free of ailments; they cannot increase his longevity to become a transcendent" ( _Lunheng_ , "Daoxu," 7.148). And again, "there has tended to be proof of ingesting drugs to lighten the body and increase vapor, but (the idea) that it extends your years so that you transcend ( _du_ 度) the world—of this the world has no verification" ( _Lunheng_ , "Daoxu," 7.157).
A distinction between the medical tradition of macrobiotic hygiene and the newer _xian_ -cult hygiene is not an issue in the Mawangdui and Zhangjiashan macrobiotic hygiene texts; it became an issue for Wang Chong because by the first century A.D. macrobiotic hygiene was so closely associated with _xian_ ideas in the popular mind. In subsequent centuries, religious Daoism developed its own macrobiotic theory and practice out of the legacy of Han medical and _xian_ ideas, while at the same time more popular hygienic traditions coexisted with and borrowed from religious Daoism. The Mawangdui and Zhangjiashan texts invite comparison to later popular and religious Daoist hygienic literature—a large-scale undertaking which I do not attempt here except for the occasional illustration. The following discussion focuses on the characteristics of early macrobiotic hygiene, of which the excavated texts are our first significant evidence.
Body and Spirit
The _Guanzi_ , "Neiye," provides the best testimony of the fourth century B.C. formulation of physiological theories which fused the physical and spiritual components of the human organism, and which made vapor the source of each. The "Neiye" opens with the declaration that _jing_ 精 (essence) is the source of life ( _Guanzi_ 49, 16.268). Then in a series of statements spread across its rhymed stanzas the text identifies the heart as the "abode of essence" 精 舍, defines essence as the "essence of vapor" 氣 之 精 者, and links essence with the indwelling _shen_ 神 (spirit)—which like essence comes to rest in the body so long as the body is cared for properly ( _Guanzi_ 49, 16.270). In later usage _jing_ and _qi_ , either singly or in compound form, are ubiquitous terms for the vital stuff which lies at the base of human existence. In the fourth century B.C., the physiological denotation of _jing_ was new. Like _shen_ , the original meaning of _jing_ was related to religious conceptions. Things that were pure and refined were considered "essence," be they the offerings presented to the external spirits or the potency of the spirits themselves.
Shibata (1984) discusses the religious background of essence and spirit, and their naturalization in the physiological theory of the "Neiye." In religion, external spirits were believed to descend to human beings; or humans might draw them down with the power of _de_ 德 (virtue; another philosophical concept with religious origins). The "Neiye" transfers this religious transaction to the physiological plane, and equates essence with vapor. Having opened with the statement on essence as life, the text shifts to a discussion of "human vapor" 民 氣, and identifies the role of virtue: "This vapor cannot be stopped with strength, yet it can be made to rest with virtue" ( _Guanzi_ 49, 16.269). The chief innovation in the "Neiye" is the equation of essence and vapor, which unites essence and spirit (with their old religious connotations) with vapor. Moreover, every human being possesses an indwelling spirit which is particular to the body in which it resides yet is similar in nature to the external spirits. Virtue serves to explain the mechanism by which vapor, essence, and spirit are drawn to the body and stored inside.
The "Neiye" mentions the combination of blood and vapor in passing ( _Guanzi_ 49, 16.271), but the focus throughout the essay is on the triad of vapor, essence, and spirit, which must be stored and concentrated inside the body in order to create a wellspring of vitality. If virtue is the philosophical explanation of how the three are cultivated, it is clear that at the very least the "Neiye" assumes the practice of breath cultivation. The same focus is evident in the Mawangdui macrobiotic hygiene texts. The breath cultivation technique in _MS_ VI.A.1 is entitled "the way of the Heavenly Teacher to eat spirit vapor." References elsewhere in _MS_ VI.A to "essence and spirit," "essence and vapor," and other combinations are frequent, as are references to wellsprings inside the body. The techniques of cultivation are breathing, sex, exercise, and diet; several paths to one goal. As already noted, the "Neiye" has a philosophical plan that goes beyond macrobiotic hygiene. One need not claim a fourth-century B.C. date for the Mawangdui and Zhangjiashan texts to argue that they restore examples of medical ideas that were part of the intellectual context within which "Neiye" physiological theory was formulated.
The physio-spiritual fusion in the Mawangdui macrobiotic hygiene texts is expressed most clearly in the term _shenming_ 神 明 (spirit illumination), used in _MS_ VI.A–B and _MS_ VII.B. The term already occurs with a physiological denotation in the "Neiye" where it means something like the divine spark of intelligence ( _Guanzi_ 49, 16.270). _Shenming_ originated in religion, referring to the external spirits or to the magical efficacy possessed by spirits or permeating sacred objects. The religious meanings continued to be used by Warring States philosophers alongside newer meanings referring to numinous powers in nature and to human intelligence.1 On the one hand, the idea of spirit illumination gave specificity to the mental faculties of the heart and the indwelling spirit, further rationalizing the conception of the human organism. Yet the ambiguity of the term admitted the possibility of a natural sympathy between man and external spirits. This sympathy is expressed in the "Neiye" in a passage which states that when meditative concentration fails to "penetrate" ( _tong_ 通), "demons and spirits will penetrate it"; followed by the explanation, "this is not due to the strength of the demons and spirits, but to the supremacy of essence and vapor" ( _Guanzi_ 49, 16.271). The idea that cultivation of essence and vapor leads to contact with external spirits recurs in the _Huainanzi_ , in praise for the person who "makes Yin and Yang his model": "His virtue forms a triad with heaven and earth, his illumination is a mate for the sun and moon, his _essence joins with demons and spirits_ " ( _Huainanzi_ , 8.120).1
The breath cultivation technique in _MS_ VI.A.1 is also called the "doubly marvelous recipe to penetrate spirit illumination." The remaining occurrences of spirit illumination are closely associated with sexual cultivation. Cultivating essence by thrusting his penis in the vagina without ejaculating culminates in "penetrating spirit illumination" in _MS_ VI.A.3, which has parallels in _MS_ VI.B.2 and _MS_ VII.B.3. Female orgasm in _MS_ VI.B.8 brings sexual cultivation to a successful conclusion, described as follows: "Essence and spirit enter and are deposited, then engendering spirit illumination." The direct references to sexual cultivation in _MS_ VI.A.3 and _MS_ VII.B.3 are preceded by more general statements regarding accumulating essence—in the words of _MS_ VII.B.3, "to cultivate the body the task lies in accumulating essence." And both refer to an internal space called the "jade enclosure" (a physiological metaphor of uncertain identity) where spirit illumination accumulates. Again, _MS_ VII.B.3 provides the more explicit statement:
The matter of spirit illumination lies in what is enclosed. Vigilently control the jade closure, and spirit illumination will arrive.
Spirit illumination in the Mawangdui macrobiotic hygiene texts is obviously related to spirit illumination in the "Neiye" and other Warring States philosophical texts. But whereas the philosophical texts use ideas of spirit and spirit illumination to speculate on the nature of mental faculties, in macrobiotic hygiene spirit illumination is a kind of mana which those who practice cultivation can concentrate in their body. I suspect that the macrobiotic concept of spirit illumination is older than the philosophical one, and that it retains a deeper awareness of the human organism as a sacred vessel. This awareness may explain some of the physiological metaphors in descriptions of techniques which are attested with a religious meaning in received literature, but not with a physiological meaning. As in later religious Daoist cultivation, the language for the body projects a vision of its divinity (see "Techniques" below).1
_Hun_ 魂 (ethereal-spirit) and _po_ 魄 (earthly-spirit) appear twice, in _MS_ VI.A.4 and _MS_ VI.A.10. The references are conventional; the view of human life as the fusion of ethereal-spirit and earthly-spirit is theoretically insignificant in the Mawangdui and Zhangjiashan macrobiotic hygiene texts. Yin and Yang are prominent. When Yao 堯 asks Shun 舜 how to cultivate life in _MS_ VI.A.5, Shun replies, "investigate Yin and Yang." In _MS_ VI.A.1, the Heavenly Teacher teaches the Yellow Thearch that, "when you examine heaven's nature, Yin and Yang are the rulers," then exhorts the Yellow Thearch to "eat Yin and secure Yang; attain spirit illumination." A rhymed breath-cultivation technique follows in the text, headed by the phrase "the way to eat Yin" (this is the same technique which at the end of _MS_ VI.A.1 is called the "doubly marvelous recipe to penetrate spirit illumination" and the "way of the Heavenly Teacher to eat spirit vapor"). Many passages in the Mawangdui and Zhangjiashan macrobiotic hygiene texts refer to cultivating vapor, essence, spirit, and the like without specific reference to Yin and Yang. But, whenever human life as a Yin Yang construct is at issue, the texts are unanimous in identifying Yin (or Yin vapor, Yin essence, etc.) as the primary element of life that must be cultivated.
_Yinshu_ , "Cultivation of the Body," provides the most theoretical statement on the subject:
The reason why people are prone to collapse and suffer early degeneration of Yin is because they are unable to regulate their vapor. Those who can regulate their vapor well and solidify Yin will then benefit their body. ( _YSSW_ : 86.)
Yin is associated with the body in general and with the genitals in particular (referred to as the Yin); at times the two referents are indistinguishable. Loss of Yin causes irreparable damage: "If there is a calamity for that life, it is invariably because Yin essence leaks out; and the hundred vessels are clogged and derelict" ( _MS_ VI.A.4). For those who fail to follow a regular program of cultivation, "at the age of forty, Yin vapor has halved itself" ( _MS_ VII.B.4). And impotency portends physical collapse. In _MS_ VI.A.5, Yao asks Shun, "why is it that the Yin is born together with a man and yet departs ahead of the body?" Shun replies that the Yin (the penis) is too often neglected, even shunned, except in times of unbridled lust. Shun instructs Yao to "cherish it and delight in it; instruct and counsel it; and give it drink and food"; that is, all hygienic activity should focus on nurturing the Yin. Ancestor Peng offers the same advice when he declares, "let penetrating breathing be together with the penis; let drinking and eating be together with the penis" ( _MS_ VI.A.6). In short, cultivation of Yin encompasses sexual cultivation, breath cultivation, exercise, and dietetics (see "Techniques" below). There is no Yang counterpart to the emphasis on Yin cultivation in the texts.1
The texts assume that vapor and essence are inside the vessels, which are sometimes referred to generically as the "hundred vessels." During intercourse, one of the stages the man achieves while thrusting his penis without ejaculating is referred to as "the hundred vessels pass clear through" in _MS_ VI.A.3; parallels in _MS_ VI.B.2 and _MS_ VII.B.3 refer to the same stage as "the waterway passes through." The meaning is that vapor and essence now move freely in the vessels; the idea of the vessels as a waterway reinforces the analogy between the body's vessels and water channels in the earth (see Section Three, "Physiology"). Conversely, when vapor is blocked, "the hundred vessels produce illness" ( _MS_ VI.A.6).
Except for the heart, none of the usual internal organs are mentioned by name. There are, however, references to the "five depots" ( _wu zang_ 五 臓) and "six cavities" ( _liu fu_ 六 腑). We can probably assume that the depots are the heart, kidney, liver, lung, and spleen. The cavities probably include gall bladder, stomach, large intestine, small intestine, and bladder; it is improbable that the sixth is the _Huangdi neijing_ 's "triple burner" ( _san jiao_ 三 焦; see _MS_ VI.A.4). The five depots and six cavities are not explicitly linked to the vessels in the Mawangdui and Zhangjiashan macrobiotic hygiene texts, but they are places where vapor and essence are stored (see _MS_ VI.A.1, 4, 10). More important as places for storage than the five depots or six cavities are places particular to macrobiotic hygiene: jade closure ( _MS_ VI.A.3, _MS_ VII.B.3), jade wellspring ( _MS_ VI.A.3, _MS_ VII.B.3), womb ( _MS_ VI.A.7–8; see "Techniques" below), progenitive gate ( _MS_ VI.B.1), central cavity ( _MS_ VI.B.7), central bourne ( _MS_ VI.B.8), blood gate ( _MS_ VII.B.13). Some of the places seem to have a closer association with one form of cultivation than another (progenitive gate and blood gate are evidently synonyms for the place where essence is stored following successful sexual cultivation), and some of the names are attested in later received literature. But we still know too little about early macrobiotic hygiene to be able to specify the exact location and function of the storage places named. A similar caution applies to many unattested physiological terms (some of which are discussed in "Techniques" below).
The conclusion to _MS_ VI.A.4 warrants separate discussion because it is the only passage in the Mawangdui and Zhangjiashan macrobiotic hygiene texts that reflects the likely influence of _xian_ or syncretistic-Daoist ideas about immortality. The regular perspective in the texts is on the care of the body and on longevity. The conclusion to _MS_ VI.A.4 begins with the unexceptional statement that "longevity is born of growth and accumulation." Then it moves in a new direction, declaring that "the person who is capable of it invariably becomes a spirit"; and that such a person achieves _xingjie_ 形 解. _Xingjie_ is attested in the _Shiji_ in connection with the _xian_ cult and recipe gentlemen during the reign of the First Qin Thearch. _Xingjie_ is thought to be synonymous with the term _shijie_ 尸 解, first attested in the first century A.D. _Shijie_ was understood to be the moment of _xian_ transformation, and became an important religious Daoist concept. Having fashioned the immortal body within the shell of the mortal body, the _xian_ adept's immortal body emerged from the mortal body, which it sloughed off. In this context _shijie_ seems to mean "release from the corpse." I am uncertain whether the concept of a second body—the immortal body—which sloughs off the mortal body was already the understanding of _xingjie_ in the third and second centuries B.C. _Xingjie_ is plausibly interpreted as "release of the form," meaning that cultivation renders the one body a person is born with imperishable and it is released from mortal constraints to live as the spirits. To me this is the more likely meaning in _MS_ VI.A.4. But I am uncertain of the connection between _xingjie_ in the Mawangdui text and in the _xian_ cult; and I am not entirely certain that the term originated in the _xian_ cult rather than in macrobiotic hygiene.1
Following a description of cosmic flight which is reminiscent of the spirit-being in _Zhuangzi_ , "Xiaoyao yu," and of _xian_ flight, _MS_ VI.A.4 rationalizes immortality based on Yin and Yang:
Wuchengzhao 巫 成 招 (identity uncertain) was born together with Yin and Yang. Yin and Yang do not die, and Wuchengzhao is coequal with them. The gentleman who possesses the way is also like this.
The "way" described here is in keeping with passages in the _Huainanzi_ which argue that death does not come to someone who is above life and death, someone who renders himself identical to the ultimate source of change which itself is eternally unchanging:
What gives life to living things has never died; the things that it gives life to are what die. The transformer of things has never transformed; the things that it transforms are what transform. ( _Huainanzi_ , 7.105.)
The promise of immortality is given in _MS_ VI.A.4; and one suspects the influence of literature more focused on that goal. Immortality is not the unifying theme of the Mawangdui and Zhangjiashan macrobiotic hygiene texts.
Techniques
The true focus of the Mawangdui and Zhangjiashan macrobiotic hygiene texts is on techniques. Unlike the "Neiye," which is a theoretical exposition on the physiology of the sage, the excavated texts are meant to teach how to do it—whether it be breath cultivation, exercise, sexual cultivation, or dietetics. Prior to their discovery, the only ancient example of a macrobiotic technique was a rhymed inscription on a dodecagonal block of jade bearing the title _xing qi_ 行 氣 (To circulate vapor). The artifact is thought to be late Warring States (perhaps late fourth or early third century B.C.). The technique is presented in nine trisyllabic phrases which describe the stages of breath cultivation from first swallowing the vapor to completion; four explanatory phrases conclude the text:1
Swallow, then it travels; traveling, it extends; extending, it descends; descending, it stabilizes; stabilizing, it solidifies; solidifying, it sprouts; sprouting, it grows; growing, it returns; returning, it is heaven. Heaven—its root is above; earth—its root is below. Follow the pattern and live; go against it and die.
The verbs that identify the stages of cultivation are not obscure words (travel, extend, descend, etc.), but neither is it obvious exactly how the technique is executed. Like the "Neiye" and the _Laozi_ , the text is an example of verse meant for recitation by initiates who would have received fuller knowledge of its meaning either orally or in ancillary texts. The verse itself is the verbal distillation of the technique, each verb an icon of the act of circulating vapor.1
The jade-inscription verse does, nevertheless, describe initial downward movement of vapor, followed by transformation and return upwards—the pattern of circulation recommended in _MS_ I.C. The verse has a counterpart in a longer, more esoteric verse on breath cultivation in _MS_ VI.A.1, and in another esoteric verse on sexual cultivation in _MS_ VI.B.1, as well as in numerous shorter technique records (often rhymed) in _MS_ II.A, _MS_ III, _MS_ VI.A–B, _MS_ VII.B, and the Zhangjiashan _Yinshu_. This trove of techniques is complemented by exact recipes for everyday tonics and aphrodisiacs in _MS_ III and _MS_ IV, and illustrations of exercises in _MS_ II.C. Esoterica mix easily in the texts with common knowledge in a way that is characteristic of other _fang_ -literature. With the "Neiye" or the single, contextless jade-inscription technique, one is inclined to think of Warring States cultivation theory and practice as an arcane matter with few actual practitioners. The Mawangdui and Zhangjiashan macrobiotic hygiene texts paint a rather different picture of the popularity of macrobiotic hygiene among the elite in the third and second centuries B.C. The techniques and recipes need not all have been practiced daily by everyone. But it is clear that macrobiotic hygiene literature was available, and that it represented the ideal which the elite emulated.
There is considerable overlap between the four main branches of macrobiotic hygiene: breath cultivation, exercise (and massage), sexual cultivation, and dietetics (which I define broadly to include aphrodisiacs and the like). The four were indivisible elements of a single enterprise. Breath cultivation sometimes occurs simultaneously with sexual intercourse; or a combination of breath cultivation with exercise may be a counterpart to sexual cultivation. The following discussion aims to give a summary of both the shared and distinctive features.
Let me begin with esoterica, using the verse in _MS_ VI.A.1 as my example.1 Encoding a technique in esoteric verse is a well-known feature of religious Daoist cultivation and meditation, beginning with the ca. third century A.D. _Huangting jing_ 黄 庭 經 (Scripture of the Yellow Court). The scripture uses a secret, metaphorical language to describe the inner regions of the body and the spirits who dwell there. Embedded within the text of the _Huangting jing_ are instructions for performing the practices essential to achieving the Daoist goal of corporeal perfection and spiritual transcendence, including sexual cultivation. Learning the physio-spiritual denotations of the metaphors was part of initiation into the secrets of the religion; current interpretation of the scripture relies on several extant medieval commentaries.2 Metaphorical language in certain _Laozi_ passages has also been interpreted to refer to physiological and meditative cultivation, although the passages do not describe actual techniques to be performed. The Later Han "Heshang gong" and "Xianger" commentaries provide the earliest evidence of this reading of the _Laozi_.3 In _MS_ VI.A.1, _MS_ VI.B.1, and other shorter technique passages in the excavated texts we have the oldest examples of recording cultivation techniques in esoteric verse. Ideas about secrecy and initiation must have been an important part of the social and intellectual background. At the same time, the metaphors made the body a more cosmic and spiritual site. Lacking a contemporary commentary, the metaphorical language is difficult to decipher. But occasionally the denotations are clear and their symbolic significance is evident.
Here is the core of the breath cultivation verse in _MS_ VI.A.1:
Still your spirit wind, make fast your two racks, triply pound, and let nothing escape. The spirit wind then is born; the five tones then are matched.
Suck it in not more than five times, bring it to the mouth, and still it with the heart—this being what the four assistants prize. The dark winepot then arrives.
Drink it not more than five times; the mouth invariably finds the taste sweet. Bring it to the five depots. The form then is extremely relaxed.
Make it spread to your flesh and skin, and reach to those hair tips. The hair vessels then are permeated. The Yin water then arrives, drenching that Yang blaze. Firm, sturdy, and undying; drink and food enter the body as guests.
A rough synopsis (see _MS_ VI.A.1 for fuller explanation): external vapor is inhaled, the two racks (the ribcage?) compress it to produce the spirit wind (an internal vapor?); the spirit wind is brought to the mouth where it is transformed into the dark winepot (saliva); the dark winepot is swallowed, stored in the five depots, and then circulated outward to the skin; an internal transformation produces Yin water, which tempers the Yang blaze inside the body; the body itself is now tempered and benefits from the drink and food introduced into it.
The only metaphor attested in third and second century B.C. sources is "dark winepot" ( _xuanzun_ 玄 尊), which is attested in a religious not a physiological meaning. Dark winepot is the name for holy water used to worship the _shenming_ —in religion, the glowing manifestation of the external spirits. The water was obtained from a Yin mirror-pan set beneath the moon; the condensation in the pan was regarded as Yin fluid from the moon. In the context of _MS_ VI.A.1, dark winepot certainly denotes saliva. The technique provides the earliest evidence of saliva ingestion, which was a regular practice in religious Daoism. The technique seems to understand a parallel between the holy water used in religion and saliva; the holy water given to the _shenming_ to drink becomes the ingested saliva which produces Yin water—a numinous internally generated fluid. Yang blaze evidently designates an alchemical zone in the abdominal region (anticipating later alchemical metaphors for the body, particularly in religious Daoism). Tempering it with Yin water prepares the body for realizing the full benefit of whatever drink and food are consumed; that is, the technique concerns dietetics as well.
Breath cultivation, exercise, sexual cultivation, and dietetics share the goal of continually replenishing and refining the body's supply of vapor and essence. The following statement in _MS_ VI.A.4 is representative:
The essence of cultivating vapor is to exit from death and enter into life. With zest and gusto, let the taste suckle. To fill the form with this is called "concentrating essence." To cultivate vapor there is a norm; the task lies in accumulating essence. When essence reaches fullness, it invariably drains; and when essence is lost, it must be replenished.
The activity of storing accumulated vapor and essence somewhere and the activity of circulating it throughout the body are equally important; one or both of the activities occur in many techniques (breath cultivation in _MS_ VI.A.1 above includes both). _MS_ VI.A.4 provides a statement related to breath cultivation:
It must be made to reach to the extremities1 so that essence is generated and not deficient.... He who is skilled at cultivating vapor lets the old vapor disperse at night and the new vapor gather at dawn, thereby penetrating the nine apertures2 and filling the six cavities.
Tonics contribute to vapor production, as evidenced by the medicine in _MS_ III.61 which "increases the vapor, and also makes a person's face lustrous"; and the liquor in _MS_ IV.25 which ensures that the interior of the body "has an abundance of essence-fluid."
"Eating vapor" 食 氣 is the usual expression for breath cultivation. The most common verb for inhaling vapor is _xi_ 噏 (suck). I identify the term "dual-entry doorway" in _MS_ VI.A.4 as the nostrils, providing the only direct reference to inhaling external vapor through the nose: "During the ingress, gauge that dual-entry doorway as if storing it in a deep pool." The nose is the port of entry for external vapor in the "Heshang gong" commentary to the _Laozi_ and in religious Daoist breath cultivation. There are three verbs for exhaling through the mouth: _hu_ 呼, _xu_ 呴, and _chui_ 吹. _Hu_ is both the usual word for "exhale" and one of the three manners of exhalation in breath cultivation technique. _Xu_ and _chui_ are more technical Based on their usage in _Yinshu, xu_ is associated with heat and Yang, _chui_ with dampness and Yin. In later breath cultivation _xu_ exhalation is performed with a round open mouth, _chui_ exhalation with lips spread flat (see _MS_ II.A for text citations). Exhalation technique is discussed in _MS_ II.A:
Those who eat vapor practice _xu_ exhalation and _chui_ exhalation when they first go to bed and first arise. Whenever doing _xu_ exhalation, in mid-breath change to _chui_ exhalation.
The passage continues with details on the timing of the exhalation routine and the number of repetitions during each performance (which is based on the age of the practitioner).
_MS_ II.A also details a seasonal routine for breath cultivation. The text identifies six types of vapor in the external atmosphere which the practitioner mixes with his breath in different combinations according to the season. A two-vapor mixture is inhaled in spring, summer, and fall; in winter, four of the six vapors are mixed and eaten. Dusk and dawn are the times of day when cultivation is allowed ( _MS_ VI.A.4 specifies dawn, daytime, dusk, and midnight as appropriate times). In addition, there are five harmful atmospheric vapors (one each in spring, summer, and winter; two in fall) which must be dispersed by the practitioner before breath cultivation can begin (four of the five are named in the parallel in _MS_ VI.A.4). Damage to the silk has destroyed most of the final section of _MS_ II.A. However, some of the fragments concern the characteristics of the vapors (atmospheric conditions which produce them, color, appearance, etc.). The knowledge of atmospheric vapors required to practice the technique is similar to the knowledge of the astrological specialists who interpreted the portents signified by similar kinds of atmospheric conditions. The technique is evidence of the specificity applied to the classification of atmospheric vapors for the purpose of "eating vapor."
_MS_ II.A several times contrasts "those who eat vapor" with "those who eat grain," expressed in cosmological terms near the end of the text:
Those who eat grain eat what is square; those who eat vapor eat what is round. Round is heaven; square is earth.
The contrast is not made elsewhere in the Mawangdui and Zhangjiashan macrobiotic hygiene texts; "eating vapor" is simply the term for breath cultivation and the regular consumption of drink and food is assumed. The contrast in _MS_ II.A is part of the rationale for the technique of "eliminating grain" which opens the text (and which only occurs in _MS_ II.A). Grain is, of course, the basis of the normal human diet, but is also associated with decay. This explains the _Huainanzi_ statement that, "those who eat vapor achieve spirit illumination and are long-lived; those who eat grain have quick minds and are short-lived" ( _Huainanzi_ , 4.60; a final phrase adds that, "those who do not eat do not die and are spirits"). The grain-elimination technique in _MS_ II.A involves daily consumption of the drug _shiwei_ 石 韋 (pyrrosia) in specified amounts over the course of a lunar cycle, which is obviously coupled with "eating vapor" as described later in the text. According to the text, _xu_ exhalation and _chui_ exhalation are used to counter some of the physical effects of grain elimination (heavy head, light feet, itchy body); the drug must have also ameliorated symptoms that accompanied grain elimination.
Han sources tend to associate grain elimination with the _xian_ cult, whose adepts eschewed human food in favor of macrobiotic drugs and the pure diet of the spirits. Wang Chong dismissed the idea as simply misguided starvation ( _Lunheng_ , "Daoxu," 7.156). In religious Daoism, grain elimination was additionally related to purging the corpse-worms inside the body—a necessary first step towards undertaking a Daoist program of cultivation (Maspero 1981: 333–35). I remain uncertain of the nature and purpose (or purposes) of grain elimination in _MS_ II.A. The text does not seem to be influenced by _xian_ ideas of immortality, nor is a belief in corpse-worms evident. No drug besides pyrrosia is mentioned. Yet the dietetics recommended to King Zhao of Qin 秦 昭 王 (r. 306–251 B.C.) in _MS_ VI.A.10 could be understood to be a grain-elimination regimen in which food is replaced by macrobiotic drugs like _song_ 松 (pine) and _bai_ 怕 (arbor-vitae):
You must face the sun and moon and suck in the rays of their essence; eat _song_ (pine) and _bai_ (arbor-vitae); and drink running beasts' wellspring blossom.
In both _MS_ II.A and _MS_ VI.A.10 it is not clear whether the macrobiotic diet cum breath cultivation is to be practiced in perpetuity (as in religious Daoism) or periodically (in _MS_ II.A the expectation may be to complete just one mensual cycle). Short-term practice might have served as a method of fasting with therapeutic benefits. Still, the contrast between vapor-eaters (who partake of heaven) and grain-eaters (who partake of earth) suggests a macrobiotic asceticism in which the former are more privileged (dietetics is discussed further below).
The drawing captioned "bear ramble" in _MS_ II.C.41 is one of the _daoyin_ 導 引 (guiding and pulling) exercises named in the _Zhuangzi_ criticism of macrobiotic hygiene ( _Zhuangzi_ 15, 237). There is no doubt that the forty-four drawings in _MS_ II.C represent the early _daoyin_ exercise tradition. The drawings are skillful, yet few of the captions remain and the original exercises are often difficult to reconstruct from the static poses of the figures. The descriptions of exercises in _Yinshu_ , "Exercises," are more informative. "Exercises" includes both single exercises and combinations of exercises in more complicated routines to achieve a specific purpose, often to treat an ailment. Although both the _Yinshu_ and _MS_ II.C refer only to _yin_ "pull," which probably has the sense of "physical exercise" in the compound _daoyin_ , breathing is an integral part of many routines in "Exercises."1 Some single exercises have animal names or are related to Yin and Yang: extending the lower leg and curling the toes thirty times is the "measuring worm";2 extending both feet out straight thirty times is "pulling the Yang muscles" ( _YSSW_ : 82); putting one foot forward, kneeling, raising one arm, and bending back is the "tiger pull"; clasping the hands with palms facing out, raising them, and bending down as low as possible—a basic toe-touch—is "pulling Yin"; clasping the hands with palms in and lifting them as high as possible is "pulling Yang" ( _YSSW_ : 83). "Exercises" concludes with a list of exercises that identifies what part of the body or physiological function they benefit. It is clear from the list that basic calisthenics was very much a part of the early _daoyin_ tradition.
The _Yinshu_ is a rich source; its documentation of exercise as a branch of macrobiotic hygiene far exceeds anything in the Mawangdui macrobiotic hygiene texts. A full study of the manuscript and its contribution to knowledge of early _daoyin_ cannot be undertaken here. I propose to examine just two exercise routines described in "Exercises." Their significance lies in their focus on Yin cultivation, and in their relation to several techniques in the Mawangdui macrobiotic hygiene texts that combine exercise with breath cultivation. Moreover, the Mawangdui techniques overlap with sexual techniques as a way of cultivating Yin and shed light on aspects of early sexual cultivation technique. The first _Yinshu_ exercise is called "increasing Yin vapor":
Increasing Yin vapor. Sit in the regular position with thighs straddled. Do not feel remorse for food. Press the left hand on the ground. Grasp cooked grain in the right hand and suspend it over the mouth. Then inhale the vapor of the cooked grain, doing it to the utmost. Then eat it. Let both thighs press down, bend the waist, and extend the lesser abdomen forward, using force to do it to the utmost. Do not drink or swallow. Repeat again, stopping after the third time. ( _YSSW_ : 84.)
This exercise routine, which combines dietetics (ingestion of the vapor of grain and the grain itself) with exercise and breath cultivation (clearly the Yin vapor is circulated internally), is a variation on another exercise called "pulling Yin" (not the toe-touch which is also called "pulling Yin"):
Pulling Yin. Sit squarely and spread both thighs. Place the left hand on the ground and reach up with the right hand. Bend the waist, extend the lesser abdomen forward, and use force to pull the buttocks. ( _YSSW_ : 84.)
The additional instruction to pull the buttocks suggests that anal constriction is used to propel the vapor being forcefully compressed in the lesser abdomen. The technique is similar to several passages in _MS_ VI.A and _MS_ VII.B which refer explicitly to anal constriction. _MS_ VII.B.7 describes "eight benefits," most of which arise from sexual cultivation. The first two, however, are techniques which do not involve intercourse:
To rise at dawn, sit upright, straighten the spine, open the buttocks, suck in the anus, and press it down is "cultivating vapor." When drinking and eating, to relax the buttocks, straighten the spine, suck in the anus, and let the vapor pass through is "bringing the fluid."1
The benefits from intercourse begin with the third technique; and the fourth once again concerns anal constriction: "While having intercourse, to relax the spine, suck in the anus, and press it down is 'gathering vapor.'" The specific role of anal constriction in sexual cultivation is discussed below. A parallel to _MS_ VII.B.7 occurs in _MS_ VI.A.7, where it is called the "way for coitus with Yin (sexual intercourse) and eating spirit vapor."1 Moreover, Yin is also understood as the Yin, the male genitals:
First, relax the limbs, straighten the spine, and flex the buttocks; second, spread the thighs, move the Yin, and contract the anus; third draw the eyelashes together, do not listen, and suck in the vapor to fill the womb;2 fourth, contain the five tastes and drink that wellspring blossom; fifth, the mass of essence all ascends, suck in the great illumination.
The second stage adds the instruction to "move the Yin" which suggests penile action during intercourse, but other aspects of the technique indicate a second, non-coital application similar to _MS_ VII.B.7 and to the two _Yinshu_ exercises.3 Of course, the dual technique is also evidence of the simultaneous practice of sexual cultivation and breath cultivation.4
There is an ambiguous reference to "pulling Yin" in _MS_ VI.A.8:
To awaken from sleep and pull Yin, this is called "refining the muscles." To first stretch and then curl, this is called "refining the bones."
More in the nature of a wake-up routine, "pulling Yin" is certainly not a sexual cultivation technique (besides, morning is not the recommended time for men to practice sexual cultivation).5 Is it the dawn exercise called "cultivating vapor" in _MS_ VII.B.7, which then corresponds to the _Yinshu_ technique of "pulling Yin"? Or is it something as simple as the toe-touch also called "pulling Yin" in the _Yinshu_? I remain uncertain. Still, the direct references to anal constriction in _MS_ VI.A.7 and _MS_ VII.B.7 are important evidence of a broader use of anal constriction in early macrobiotic hygiene beyond its role in male sexual cultivation.1
Sexual intercourse is denoted by the following terms in the Mawangdui macrobiotic hygiene texts: "coitus with Yin" ( _jie_ Yin 接 陰), "conjoin vapor" ( _heqi_ 合 氣), "conjoin Yin and Yang" ( _he_ Yin Yang 合 陰 陽), "conjoin male and female" ( _he nan nü_ 合 男 女), "conjoin forms" ( _jiexing_ 接 形), and "approach the inner (chamber)" ( _jin nei_ 近 内).2 Sexual relations are, of course, complicated by the matter of lust. The problem is addressed in _MS_ VII.B.9:
When a person is born there are two things that do not need to be learned: the first is to breathe and the second is to eat. Except for these two, there is nothing that is not the result of learning and habit. Thus, what assists life is eating; what injures life is lust. Therefore, the sage when conjoining male and female invariably possesses a model.
The summary appended to the sexual cultivation category of medical literature in the _Hanshu_ bibliographic treatise is in the same vein ( _Hanshu_ , 30.81a).
The literature recorded in the bibliographic treatise includes books like the _Rong Cheng Yindao_ 容 成 陰 道 (Rong Cheng's way of Yin), the _Yao Shun Yindao_ 堯 舜 陰 道 (Way of Yin of Yao and Shun), and the _Huangdi sanwang yang Yang fang_ 黄 帝 三 王 養 陽 方 (Recipes of the Yellow Thearch and the Three Kings for nurturing Yang). All of the books are lost. Rong Cheng, Yao, Shun, and the Yellow Thearch are associated with macrobiotic hygiene and sexual cultivation teachings in _MS_ VI.A. Presumably the books in the bibliographic treatise were also composed in dialogue form, but with far more detail—similar to the style of the _Huangdi neijing_. The oldest sex manuals in received literature are preserved in extensive quotations in chapter twenty-eight of the tenth century _Ishinpô_ 醫 心 方, compiled by the Japanese physician Tanba Yasuyori 丹 波 康 賴 from medieval Chinese sources. The _Sunü jing_ 素 女 經 (Scripture of the Immaculate Maid) and _Xuannü jing_ 玄 女 經 (Scripture of the Dark Maid), which may be as old as third century A.D., are composed as dialogues in which the Immaculate Maid and the Dark Maid teach the Yellow Thearch the principles of sexual cultivation. Ancestor Peng also offers occasional teachings.1
The medieval sex manuals provide theoretical background for sexual cultivation, but their chief objective is to translate the erotic subtleties of intercourse into a technique which, like other cultivation techniques, guides a man towards success. Each aspect and every stage of intercourse are analyzed, including: foreplay, sexual positions, signs of female arousal, the art of using the penis, and the culminating moment when the man successfully achieves his goal. And the analysis takes a numerical form: there are "five signs" to watch for in the woman as intercourse gets underway, "ten movements" to be made by the penis as it thrusts, "nine manners" in which to thrust it, etc. The same kind of analysis of sexual intercourse is detailed in _MS_ VI.B and _MS_ VII.B, minus the dialogue manner of presentation; both are realizations of the sage's "model for conjoining male and female."2 The parallels between _MS_ VI.B, _MS_ VII.B, and the medieval sex manuals show the Mawangdui texts to be the textual antecedents to the later literature.3 Previously, a lack of evidence led to speculation that the sexual cultivation technique of the later sex manuals was a Han development (Schipper 1969: 14). We now know that both the technique and the literature came into being as part of Warring States macrobiotic hygiene.
The goal in sexual cultivation is to generate vapor and essence, which the man absorbs and stores inside his body. The description of female orgasm in _MS_ VI.B.8 and the statement concerning "nurturing the woman's essence with my essence" in _MS_ VI.B.7 suggest that the woman may also benefit from intercourse, but the technique is designed for the man's benefit. The attention paid to the woman is a necessary part of realizing a true "conjoining of Yin and Yang"—the man must be certain that his mate reaches sexual climax. _MS_ VII.B.20 includes one of several statements on the male flaw of haste in intercourse:
If when having intercourse he is unsuccessful, the blame can be placed entirely on haste. The essential task in the pleasures of play is to be slow and prolonged. If only he can be slow and prolonged, the woman then is greatly pleased. She treats him with the closeness she feels for her brothers, and loves him like her father and mother.
In the later sex manuals male sexual cultivation takes several forms. The man might absorb the sexually generated essence and withdraw from the woman without reaching orgasm. Needham adopts the term _coitus conservatus_ for this technique. Alternatively, the man might reach climax but prevent ejaculation and retain the essence inside his body. Needham calls this _coitus thesauratus_. Needham associates _coitus thesauratus_ with a method of applying hand pressure to a spot between the anus and the scrotum, which prevents ejaculation by blocking the urethra and redirects the essence internally. He further equates _coitus thesauratus_ with the form of sexual cultivation called _huanjing bunao_ 還 精 補 腦 (returning the essence to replenish the brain). Needham notes that while the Chinese maintain that the essence passes up the spine to the brain, physiologically the ejaculate— _jing_ now become semen—passes to the bladder. In sexual cultivation without male orgasm, the man's _jing_ remains an internal essence similar in nature to _jing_ in breath cultivation; with male orgasm, _jing_ also becomes fluid semen. Whether what passes up the spine to the brain is _jing_ become semen or is the vaporous form of sexually generated _jing_ is variously understood in the sex manuals (1954–, vol. 5, part 5: 197–99).
Based on careful review of the medieval sex manuals, Wile objects to Needham's definitions on several grounds. First, causing _jing_ to ascend by means of "returning the essence" is not exclusively associated with Needham's _coitus thesauratus_ in the sex manuals; non-orgasmic _coitus conservatus_ also results in "returning the essence." Thus male orgasm is not the defining characteristic of "returning the essence to replenish the brain" as Needham proposes in his definition of _coitus thesauratus_. And the matter of the ejaculate—the _jing_ become semen—is less central to cultivation theory. The predominant view in the sex manuals is that whether or not male orgasm occurs, what ascends is vaporous _jing_. Furthermore, anal constriction is a common method for "returning the essence," with or without orgasm. Blocking the urethra with hand pressure is used only with orgasm. Wile prefers the term "retrograde ejaculation" for sexual cultivation in which male orgasm occurs (1992: 59).
In the Mawangdui macrobiotic hygiene texts _jing_ appears to consistently name something inside the body similar in nature to vapor; there are no examples of _jing_ denoting semen. In fact, no word for semen occurs. Semen is implicit in several passages in _MS_ III. An aphrodisiac recipe in _MS_ III.5 states that "if (the semen) is already spent, splash (the penis) with cold water," which is intended to cause detumescence. _MS_ III.63–64 are recipes for "if a man experiences scantness when engaging in intercourse and (the semen) is clear." But none of the passages on sexual cultivation use _jing_ or any other term to denote semen as distinct from vapor and essence. There were surely ideas about semen and _jing_ which are simply not elucidated by the Mawangdui macrobiotic hygiene texts. However, I suspect that the conception of _jing_ in connection with other forms of cultivation influenced the conception of _jing_ in sexual cultivation, not vice versa. I am inclined to think that Wile's understanding of _jing_ in the later sex manuals applies to the Mawangdui texts as well. Thus, rather than adopt Needham's "retention of semen" as a general term for male sexual cultivation (1954–, vol. 5, part 5: 30), I prefer "essence retention."
Whether essence retention in the Mawangdui macrobiotic hygiene texts includes both non-orgasmic cultivation ( _coitus conservatus)_ and orgasmic cultivation ( _coitus thesauratus_ , retrograde ejaculation) is not certain. The passages on thrusting the penis uniformly describe the benefits of repeated thrusting without ejaculating; none describe male orgasm, ejaculation, or retrograde ejaculation ( _MS_ VI.A.3, _MS_ VI.B.2, _MS_ VII.B.3). Passages which describe the culmination of intercourse and what actions the man takes are ambiguous. Let me cite two of the more ambiguous lines first:
Enter the dark gate (the vagina); ride the coital muscle; suck the essence and spirit upward. ( _MS_ VI.B.1.)
Conjoin forms after sunset; and send the vapor to the progenitive gate. ( _MS_ VI.B.1.)
The section on "cultivation of the eight benefits" in _MS_ VII.B.7 refers explicitly to anal constriction in connection with sexual cultivation:
While having intercourse, to relax the spine, suck in the anus, and press it down is "gathering vapor." While having intercourse, to not hurry and not be hasty, and to exit and enter with harmonious control is "harmonizing the fluid." When getting out of bed, to have the other person make it erect and let it subside when angered is "accumulating vapor." When nearly finished, to not let the inner spine move, to suck in the vapor and press it down, and to still the body while waiting for it is "awaiting fullness." To wash it after finishing and let go of it after becoming angered is "securing against upset."
This is from the same section quoted above which opens with the morning exercise: "To rise at dawn, sit upright, straighten the spine, open the buttocks, suck in the anus, and press it down is 'cultivating vapor.'" In both the exercise and in intercourse, the "it" in the phrase "press it down" 抑 下 之 refers to the vapor which is compressed by means of anal constriction; there is no evidence of hand pressure as in the one form of retrograde ejaculation. At the culmination of intercourse ("when nearly finished..."), the man once again "sucks in the vapor and presses it down" using anal constriction. Because anal constriction is used to influence the vapor at several stages during intercourse, anal constriction alone is not proof of orgasmic retrograde ejaculation in _MS_ VII.B.7; but neither is the occurrence of orgasm positively disproven. The text is simply not clear on the question of orgasm.
The same ambiguity applies to _MS_ VI.A.7 (quoted above), where the instruction to "contract the anus" occurs at the second stage of a five stage technique, followed in the third stage by the instruction to "suck in the vapor to fill the womb." The technique culminates in the fifth stage when "the mass of essence all ascends, suck in the great illumination." "Womb" translates _liu_ /* _lj əgw_ , which I read as a phonetic loan for _bao_ /* _pr əgw_ 胞 (womb, uterus) and understand as a womb-like organ where men as well as women store vapor and essence (see _MS_ VI.A.7 for details). Other scholars conjecture that the graph should be read as _nao_ 腦 (brain), and conclude that the passage is the earliest documentation of "returning the essence to replenish the brain." The conjecture is disproved by the passage itself. "Returning the essence to replenish the brain" culminates sexual cultivation. Assuming that the _MS_ VI.A.7 technique concerns sexual cultivation (recall that breath cultivation is also probable), filling the _liu_ takes place at the midpoint of the technique; culmination occurs in the fifth stage when "the mass of essence all ascends." In short, the internal place which is filled in the third stage of the technique is not the brain.
However, "sucking the essence and spirit upwards" ( _MS_ VI.B.1) and "sucking in the great illumination" ( _MS_ VI.A.7) are evidence of an early idea of "returning the essence," of using sexual cultivation technique to reverse the flow of essence as sexual climax nears and the imminence of ejaculation threatens. _MS_ VII.B.3 expresses the concern nicely:
Conjoin in a sitting position; tailbone, buttocks, nose, and mouth each participate at the proper time. Passing by fleetingly and coming momentarily, the culminant essence is about to be lost. How can I stay it?
Whether orgasm is part of male sexual cultivation in _MS_ VI.B and _MS_ VII.B or not, the texts do teach the technique of "staying the culminant essence."
_MS_ III and _MS_ IV devote considerable space to aphrodisiac recipes for both men and women. The use of aphrodisiacs to arouse desire, increase strength, and stimulate the genitals was evidently quite acceptable in sexual cultivation. Wasps are the basic ingredient in _MS_ III.12–13. Snails are used in many recipes, as in _MS_ III.14:
Pingling Lü's way of pleasure. Dry in the dark snails (removed) from the shell and smith. If you want twenty, use seven pinches; if you want ten, use three pinches—and one cup of liquor.
The frequency of intercourse and the number of different partners are not discussed in _MS_ VI.B and _MS_ VII.B. _MS_ III.14 is one of several recipes with numbers attached to the dosage ("if you want twenty, use seven pinches"). The numbers probably represent anticipated sexual conquests; the dosage gives a man the strength to finish. The recipe for dried dog-meat prepared with snails in _MS_ III.75 is clearer: "Eat one _cun_ of the dried-meat slices to overcome one person, and ten _cun_ to overcome ten people" (the recipe is intended to fortify a man for encounters with opponents, which is basically the same as encounters with sexual partners).
Turning to dietetics, the tonic drugs, beverages, and foods in _MS_ III and _MS_ IV supplement the usual diet; nothing in the recipes suggests the kind of ascetic dietetics represented by grain elimination. The recipe for drinking raw eggs in liquor ( _MS_ III.15) stipulates that the eggs are consumed before the morning meal; taking tonics after meals is more frequent (for example, _MS_ III.60–62). Several recipes describe foods that are simply meals in themselves. A dish of boiled _dianji_ 顛 棘 (asparagus), chicken parts, and dog parts in _MS_ III.34 is "eaten at the late afternoon meal, in whatever amount you wish." Its purpose is to "facilitate approaching the inner (chamber)"; that is, to prepare for sexual intercourse in the evening. _MS_ III.50 gives a recipe for boiled beef, concluding with the statement that "you may eat whatever amount of meat you wish" (it fortifies the body).
The _MS_ III recipes are grouped under headings, a number of which directly describe their hygienic purpose. Some of the headings, selected from the list in _MS_ III.92, are: non-erection due to agedness, cultivation, to lighten the body and increase strength, to purge the inside and increase vapor, to cultivate strength, mash-liquor to benefit the inside. These represent the kinds of properties associated with certain drugs in the _Shennong bencaojing_ (see Section Three, "Materia Medica") as well as in the Shuanggudui _Wanwu_ , which includes entries like: to firm the body, to double strength, to lighten the body, to increase vapor (Fuyang Han jian zhenglizu 1988: 36, 38, 39). Some of the drugs with macrobiotic properties in the _Shennong bencaojing_ figure in the _xian_ -cult dietetics of the Han period. The _Liexian zhuan_ often records the drugs consumed by famous _xian_ adepts, including: _songshi_ 松 實 (pine fruit), _songzhi_ 松 脂 (pine rosin), _yunmu_ 雲 母 (mica), and _gui_ 桂 (cinnamon; Kaltenmark 1953: 53, 59, 81–82). In the _xian_ cult, these drugs were claimed to replace food in a grain-elimination regimen. The recommendation to "eat _song_ (pine) and _bai_ (arbor-vitae); and drink running beasts' wellspring blossom" in _MS_ VI.A.10 suggests a similar ideal (see above). _MS_ III and _MS_ IV document the normal use of the drugs in the medical tradition of macrobiotic hygiene.
Two examples will suffice. In _MS_ III.71, equal amounts of pulverized mica and pine rosin are combined with whole-wheat flakes and made into balls (the heading under which the recipe comes is missing in the body of the text as well as in the list in _MS_ III.92). The recipe details the regimen for swallowing the balls. Beginning with one ball, for the first decade the person swallows an additional ball each day until on the tenth day he swallows ten. For the second decade he gradually decreases the number of balls until on the tenth day he swallows just one. Over successive decades the result is to "make a person longlived and not become aged." The mica-rosin-wheat balls do not replace meals; the mixture of horseflesh and drugs in _MS_ III.70 also "increases longevity," and is to be eaten in a dosage of "a three-fingered pinch after the meal." _MS_ III.74 is the best preserved of the fermentation recipes in _MS_ III and _MS_ IV.1 Received sources indicate that _lao_ 醪 (mash-liquor) is a liquor produced by adding a mash of freshly cooked grain to already fermented liquor for a second fermentation (see _MS_ III.10). The mash-liquor in _MS_ III.74 is a sophisticated and potent cordial worthy of Wen Zhi's praise for liquor ( _MS_ VI.A.9), and representative of the tradition of medicinal liquors among early physicians.2 _Wuhui_ , 烏 喙 (monkshood) is one of the drugs added during the fermentation process (see Section Three, "Materia Medica"). The finished cordial is a valued daily tonic:
Drink one cup at the late afternoon meal. After drinking, rub any places on the body that itch. When ingested for one hundred days, it makes the eyes bright and ears perceptive; the extremities all become strong.
Wen Zhi says of liquor:
Liquor is the vapor-essence of the five grains. When it enters the inside it disperses and flows; when it enters the internal network (of vessels) it penetrates and circulates.
Each afternoon to drink a cordial and massage the body as the liquory spirits circulate is nice macrobiotic work.
Philosophy and Macrobiotic Hygiene
The Mawangdui and Zhangjiashan texts restore the first examples of medical literature on macrobiotic hygiene of the third and second centuries B.C. Their significance for the study of Warring States thought is certain. We can no longer investigate knowledge of the human organism in philosophy without considering the interaction between philosophers and physicians. Physicians had the ear of the elite, who also collected their books—books which taught of the body and its care. And their hygienic ideas and techniques were put to use as the elite daily observed dietary recommendations and engaged in various forms of cultivation. Medical ideas and techniques belonged to a pool of knowledge of nature from which the philosophers drew in formulating their ideas about human existence. Philosophers might reject ideas—as did the author or authors of the _Zhuangzi_ essay "Keyi" in criticizing the practice of breath cultivation and exercise—and they might tacitly incorporate ideas into their philosophical program.
My purpose here is not to examine standpoints on macrobiotic hygiene among Warring States philosophers, nor to prove that one or another philosopher's ideas were borrowed from the medical tradition of macrobiotic hygiene. To the extent that medical knowledge was a common intellectual property, a philosopher was simply formulating his ideas within the intellectual framework of his time. Some ideas were ubiquitous by the third century B.C. Everyone was talking and writing about _shenming_ "spirit illumination," although its exact significance was understood differently in different contexts. Other ideas were better known in connection with a particular philosopher or philosophical book—or, as we now know, a particular physician or medical book. We are accustomed to examining Warring States philosophical literature for signs of cross-influences. We acknowledge that Mencius' idea of vapor owes something to the _Guanzi_ , "Neiye," and that the _Laozi_ is behind the mystical strain of thought in the political theory of the _Hanfeizi_ (Graham 1989: 126–27, 285–92). Because it was lost, medical literature has not been considered as a source of ideas paralleling philosophical literature.
Yet it is evident from the Mawangdui and Zhangjiashan macrobiotic hygiene texts that certain ideas were probably more widely known in medical literature than in philosophical literature. I suspect, for example, that the readership for texts like _MS_ VI.A was greater than for the _Guanzi_ , "Neiye." Moreover, there is evidence in the excavated texts of hygienic maxims which probably arose in a medical context but which have only been known to us through quotation in philosophical literature. Similarly, theoretical discussions of hygiene in philosophical literature sometimes incorporate phrases which I suspect are culled from accounts of macrobiotic techniques in medical literature. In a text like _MS_ VI.A, such phrases fit in a sequence which corresponds to stages of the actual technique. The same phrases in the philosophical literature are like shorthand allusions which assume that the reader already knows of the original technique. The Mawangdui and Zhangjiashan macrobiotic hygiene texts give us the techniques.
I identify several passages from the excavated texts below to illustrate ways in which philosophy may have drawn upon medicine. Again, my purpose is not to review philosophy, nor is it to make claims about textual borrowing. I simply wish to introduce a body of medical literature which, circulating concurrently with philosophical literature, played a role in the formation of ideas about physical and spiritual cultivation. Knowing what the physicians were teaching—which I would argue reflects the elite consensus—we gain a new perspective on the philosophers.
The Zhangjiashan _Maishu_ , "Six Constituents" (see Section Three, "Physiology") concludes with a warning against obesity:
Thus, if the gentleman becomes fat and loses the standard measure, this is called "muscle and bone do not succeed in their responsibilities." His vapor then becomes abundant; his blood then becomes uncontrolled. Blood and vapor putrefy and rot; the hundred joints all collapse. They clog the twenty extremities and turn back, racing to the heart. If this is not treated in advance, one will hear the sound of weeping. ( _MSSW_ : 74.)
_Maishu_ , "Care of the Body," precedes "Six Constituents" with a maxim and positive advice:
Now, the reason why flowing water does not become putrid and the doorway pivot is not devoured by bugs is because they move. By moving, you fill the four limbs and empty the five depots. When the five depots are empty, the jade body will benefit.
The discussion of the "way of eating" in the _Guanzi_ , "Neiye," warns against either overeating or undereating, observing that, "when overstuffed, injury results and the form does not store things; when undernourished, the bones wither and the blood cakes." Thus: " _When hunger and satiation lose the standard measure_ , devise a strategy for it. When over-sated, _move rapidly_ " ( _Guanzi_ 49, 16.272). I expect that such advice was common in medical literature. The key to health is to prevent stagnation of blood and vapor, lest they putrefy—a teaching which "Care of the Body" presents figuratively. In received literature the _locus classicus_ for the "flowing water" analogy is the _Lüshi chunqiu_ essay "Jinshu" 盡 數 (Fulfill the calculation):1
The reason why flowing water does not become putrid and the doorway pivot is not devoured by bugs is because they move. The form and vapor are also thus. If the form does not move, the essence does not flow. If the essence does not flow, the vapor clogs. ( _Lüshi chunqiu_ , 3.26.)
The passage continues with a list of specific ailments caused by vapor clogging in various parts of the body.
"Jinshu" is one of two essays in the third chapter of the _Lüshi chunqiu_ which treat of care of the body; it is followed by "Xianji" 先 己 (Put oneself first). The first and second chapters of the _Lüshi chunqiu_ are thought to contain four essays which represent the self-preservation philosophy associated with the figure of Yang Zhu: "Bensheng" 本 生 (Life as the root), "Zhongji" 重 己 (Emphasize self), "Guisheng" 貴 生 (Prize life), and "Qingyu" 情 欲 (Essential nature and desire; Graham 1989: 55). The titles of the chapter three essays (Fulfill the calculation, Put oneself first) appear thematically related to the Yangist essays. However, their emphasis on macrobiotic hygiene sets them apart from Yangist philosophical issues. In my judgment "Jinshu" reads like an adaptation of a medical text; "Xianji" opens with a passage straight from the medical tradition, and then moves on to other topics.
Let me be specific. "Jinshu" opens with Yin and Yang as the models for cultivating life (as does _MS_ VI.A.1), next discusses the importance of cultivating essence, and then presents the "flowing water" analogy—probably a well-known hygienic maxim in medicine (as we can see from the _Maishu_ , "Care of the Body"). Dietary advice follows the list of ailments, culminating with a statement on the "way of eating":
Be neither hungry nor sated—this is called the "treasure of the five depots." The mouth invariably finds the taste sweet. Blend the essence, right the figure, and fortify it with spirit vapor. The hundred joints rejoice and all advance to receive the vapor. Invariably drink in small swallows. Be square and erect, do not be hunched. ( _Lüshi chunqiu_ , 3.26.)
I note a marked similarity between this passage and the breath cultivation technique in _MS_ VI.A.1, which is a technique for "eating spirit vapor" (see "Techniques" above). The "Jinshu" passage appears to paraphrase a related technique. Do not "blending essence, righting the figure, and fortifying it with spirit vapor" parallel stages of the _MS_ VI.A.1 technique, as the practitioner first produces the spirit wind and then the dark winepot (saliva)? And after swallowing the dark winepot five times, "the mouth invariably finds the taste sweet." Is this not the sense of the same statement in "Jinshu"? "Drinking in small swallows" may refer to swallowing in breath cultivation. "The hundred joints advancing to receive the vapor" alludes to the circulation of the vapor (or saliva) after ingestion. Of course, "Jinshu" may still refer to eating and drinking. But eating and drinking are combined with cultivation activity in the Mawangdui and Zhangjiashan macrobiotic hygiene texts. I have no doubt that a late-third or second century B.C. reader of "Jinshu" knew of the cultivation technique underlying the passage, a full account of which was to be found in texts like _MS_ VI.A.
The medical passage in "Xianji" is an exchange between King Tang of the Shang 商 湯 王 and his minister Yi Yin 伊 尹 on how to become the supreme ruler.1 Yi Yin advises King Tang that the first order of business is to _zhi_ 洽 (order, cultivate) his body, for self-cultivation is the key to ordering the world. The idea was ubiquitous by the third century B.C.2 Yi Yin recommends a plan:
Utilize the new, discard the old, and the skin's webbed pattern is permeated. Essence-vapor is daily renewed; evil vapor is entirely eliminated. ( _Lüshi chunqiu_ , 3.27.)
Rong Cheng's "way to suck in vapor" in _MS_ VI.A.4 clarifies Yi Yin's intent:
It must be made to reach to the extremities, so that essence is generated and not deficient. Above and below are all essence; cold and warm are tranquilly generated. Breathing must be deep and long, so that the new vapor is easy to hold. The old vapor is that of agedness, the new vapor that of longevity. He who is skilled at cultivating vapor lets the old vapor disperse at night and the new vapor gather at dawn, thereby penetrating the nine apertures and filling the six cavities.
Yi Yin's recommendation and Rong Cheng's technique concern the practice of breath cultivation—"spit out the old and take in the new"—criticized in _Zhuangzi_ , "Keyi" ( _Zhuangzi_ 15, 237).
What we learn from the Mawangdui and Zhangjiashan texts is that the elite regarded macrobiotic hygiene as normal. Medical advice on the care of the body provided a common base of belief and practice. The philosophers addressed their ideas about the body and about heart/mind cultivation to a clientele already versed in the basics.
1 I.e. urinate.
2 Later in _Yinshu_ knocking the teeth when awaking is said to prevent tooth decay ( _YSSW_ : 85).
3 Perhaps breath cultivation.
4 "Enter the place" translates _rugong_ 人 宮, which from the context denotes sexual intercourse. The term also occurs in the demonography "Jie" on the first Shuihudi hemerological manuscript, where I previously interpreted it to mean "married" ( _SHD_ : 213; Harper 1985: 496). _Rugong_ is attested in received literature, but its proper denotation has not been recognized. An anecdote in _Hanfeizi_ , 11.200, mentions ritual purification in which, "for half a year you must not enter the palace ( _rugong_ ) nor drink liquor and eat meat." The phrase has been read as an injunction barring the ruler from entering his palace, but clearly it is sexual intercourse that is forbidden.
5 "Greater half" 大 半 and "lesser half" 少 半 refer to two thirds and one third respectively (see _MS_ I.E.90, 156). "Greater midnight" 夜 大 半 ought to be 1:00 A.M.; and "lesser midnight" 夜 少 半 11:00 P.M. (see below). Cf. Chen Mengjia 1965: 121, 126.
1 Compare these statements to the ideal of cold head and warm feet in _MS_ I.C. Perhaps exercise is understood as a way to maintain the proper temperatures.
1 Roth notes the absence of physiological theory in the philosophical literature, but like Graham is not aware of the excavated macrobiotic hygiene texts (1991: 602–603).
1 The scholarly convention is to treat the complex of ideas associated with both macrobiotic hygiene and the belief in _xian_ as aspects of a belief system loosely called Daoist. However, Graham notes that in the whole of the _Zhuangzi_ (which contains a variety of material down to the second century B.C.) there are only two passages concerning the pursuit of immortality; that is, even the later authors whose writings are incorporated in the received text of the _Zhuangzi_ were not preoccupied with the theme of immortality (1981: 176). The _Laozi_ is an equally unlikely point of origin for ideas about longevity and immortality. The Mawangdui and Zhangjiashan macrobiotic hygiene texts are evidence enough that macrobiotic hygiene did not originate in so-called Daoist philosophy. The case of the _Huainanzi_ is more complicated; most of its chapters appear to represent a syncretistic Daoism which crystallized in the second century B.C. Like the _Zhuangzi_ , the _Huainanzi_ focuses primarily on the more rarefied cultivation of the spirit, yet its rationale of spiritual cultivation incorporates elements from medical and _xian_ ideas (see below). This syncretistic Daoism clearly influenced second-century B.C. thought, but it is still difficult to gauge its influence on ideas about longevity and immortality. In short, efforts to understand the development of ideas concerning macrobiotic hygiene and the _xian_ cult are not well served by a too easy use of the label Daoist.
2 The basic elements of the _xian_ cult are well summarized in Kaltenmark 1953: 8–26; and Needham 1954–, vol. 5, part 2: 93–126. Qin and Han recipe gentlemen played a major role in the spread of the _xian_ cult.
1 A speech in _Zhanguoce_ , 5.13a, alludes to the "longevity of Qiao and Song." _Huainanzi_ , 11.178, enumerates the macrobiotic techniques of Wang Qiao and Chisongzi, which culminate in leaving behind the mortal form and taking flight. The _Chuci_ poem "Yuanyu" 遠 遊 is a kind of _xian_ -cult credo; Wangzi and Chisong are named along with others who became _xian_ ( _Chuci_ , 5.2b, 4b; cf. Hawkes 1985: 199–200).
2 Sakade notes the more medical orientation of macrobiotic hygiene in the Mawangdui texts; Sakade distinguishes between this type of hygiene, which he associates with the figure of Ancestor Peng, and the beliefs and practices of the _xian_ cult (1985: 426–29). It has been argued that Ancestor Peng's interlocutor in _MS_ VI.A.6, Wangzi Qiaofu 王 子 巧 父, is none other than Wangzi Qiao; I think the identification is doubtful (in any case, nothing in the content of the passage bespeaks _xian_ ideas). Parallels between the technique of breath cultivation in _MS_ II.A and _Chuci_ , "Yuanyu," also raise the possibility of _xian_ -cult influence, but it is possible that the technique was shared by both traditions.
3 Roth gives a thorough account of physiological and spiritual cultivation in the _Huainanzi_ (1991: 628–48).
1 The _Shiji_ account of Zhang Liang represents his "grain avoidance" dietetics as a kind of self-imposed starvation which Zhang abandoned at the behest of Dowager Lü 呂 太 后. Before assuming that all such dietetic practices were regarded as ascetic extremism—which is not the impression one gets from _MS_ II.A—we should consider Sima Qian's motive for portraying macrobiotic hygiene as he does (for the historian the issue is whether an official should quit government service for selfish reasons).
1 In vessel theory pathology individual ailments are manifestations of a physiological dysfunction whose location within the organism continues to shift, producing new manifestations until the physician intervenes. Unschuld discusses both passages and the elaboration on the _Lingshu_ meaning in the _Nanjing_ (1986b: 633–34).
1 The best account of the early history of the term _shenming_ , including complete text references, is Knoblock 1988: 252–55.
1 One of the effects of theorizing about vapor, essence, and spirit was to add another dimension to the understanding of the spirit world; manifestations of demons, spirits, and other things in nature were explained as functions of vapor and essence which could influence the human world. In medicine, the _Huangdi neijing_ denies the validity of such ideas. Its theories of vapor, essence, and spirit deal purely with the relation between the indwelling spiritual and mental elements of the individual and the physiological substrate; external spirit world is not relevant to the functioning of the human organism. This viewpoint was not universal. See Harper 1990: 224–25; and Ishida 1981.
1 This concept of spirit illumination is not the concept of the _Huangdi neijing_ , which is closer to the philosophical idea of mental Acuities (see Ishida 1981: 31).
1 Perhaps aphrodisiacs to stiffen the penis and tonics to increase strength in _MSS_ III-IV are understood to bolster the Yang element, but Yang is never mentioned. There is one passage in the _Yinshu_ which equates illness with imbalances of Yin and Yang vapor, manifested in the emotions of anger and joy respectively. Breathing techniques are used to remedy the excess of each vapor and restore somatic harmony ( _YSSW_ : 86).
1 See the notes to _MS_ VI.A.4 for text citations. Resurrection is also part of the background to _shijie_ , and is examined in Harper 1994.
1 Rubbings of the twelve faces were published over fifty years ago. The artifact has been referred to as either a jade hilt or a set of jade plaques. The artifact itself was lost and only recently resurfaced; it is indeed a dodecagonal block not twelve plaques. According to Chen Banghuai (1982) the jade is not a hilt and its original function remains uncertain. The inscription has been studied by a number of scholars. My tentative translation is based on Chen Banghuai's transcription. Cf. Li Ling 1993: 320–23.
1 For discussion of didactic verse in Warring States philosophy, see Harper 1987b: 560–64.
1 The verse in _MS_ VI.B.1 is analyzed in Harper 1987b.
2 I refer to the so-called "outer" scripture ( _Huangting waijing jing_ 黄 庭 外 景 經), not the later "inner" scripture ( _Huangting neijing jing_ 黄 庭 丙 景 經) which was probably composed within the Shangqing 上 情 sect of Daoism in the fourth to sixth centuries (see Schipper 1975: 1–11). Maspero's translation of passages related to breath cultivation and sexual cultivation in the _Huangting jing_ is classic (1981: 491–94, 524–28).
3 Needham translates the "Heshang gong" commentary for several such _Leozi_ passages (1954–, vol.5, part 5: 130–35)
1 I.e. the four limbs.
2 Mouth, eyes, nostrils, ears, genitals, anus.
1 Sakade (1980) examines the meaning of the term _daoyin_ beginning with Warring States occurrences. As a compound, _daoyin_ often seems to refer to exercise combined with breathing, but there are examples where _daoyin_ is exclusively exercise and others where is refers to breath cultivation. The _MS_ II.C drawing illustrate different mouth positions which must represent the specific manner of breathing performed along with the exercise.
2 Measuring worm is also the name of a sexual position in _MS_ VI.B.3.
1 "Sucking in the anus" refers to constriction, not to introducing vapor into body via an open anus. Similarly, "letting the vapor pass through" refer to transmitting vapor internally (the anus is not the port of entry). The sense of "pressing down" is discussed in connection with sexual cultivation below.
1 The sexual cultivation technique in _MS_ VI.A.3 is called "coitus with Yin and cultivating spirit vapor." The sense of "eating spirit vapor" may be purposefully ambiguous in _MS_ VI.A.7 (recall that the breath cultivation technique in _MS_ VI.A.1 is "eating spirit vapor," "eating Yin," and "penetrating spirit illumination").
2 "Womb" represents my identification of the graph 磂. The term is discussed under sexual cultivation below.
3 I have already noted above ("Body and Spirit") that cultivation of Yin is also cultivation of genitals, which must be included in all cultivation activity (as taught by Shun in _MS_ VI.A.5 and by Ancestor Peng in _MS_ VI.A.6).
4 _MS_ VI.A.10 and _MS_ VII.B.13 also combine sexual cultivation with breath cultivation.
5 See the statements on proper times for sexual intercourse in the _Yinshu_ , "Seasonal Regimen," quoted above; and _MS_ VI.B.1, _MS_ VII.B.13. _MS_ VI.A.6 also describes a morning routine of self-massage and breath cultivation.
1 Wile discusses anal constriction in later macrobiotic hygiene, in particular in sexual cultivation (1992: 59). See also, Li Ling 1993: 345.
2 For "conjoin vapor" see _MS_ III.89 and _MS_ VI.A.3; for "conjoin Yin and Yang," _MS_ VI.B.1; for conjoin male and female," _MS_ VII.B.9; for conjoin forms," _MS_ VI.B.1 and _MS_ VII.B.13; for "approach the inner (chamber)," _MS_ III.34. "Coitus with Yin" is used mostly in _MS_ VI.A. In addition, _MSS_ III-IV use _yong_ 用 and _wei_ 爲 idiomatically in the sense of "engage in intercourse, have intercourse" (see _MS_ III.23, 39)
1 Evidence of Han sexual cultivation literature is examined by Gulik, who traces the Immaculate Maid and Dark Maid to Later Han times (1961: 70–79); Gulik also discusses the medieval sex manuals in the _Ishinpô_ (1961: 121–60). Wile (1992) provides a fine translation of the _Ishinpô_ sex manuals along with a general study of traditional Chinese sexology. See also, Harper 1987b; Li McMahon 1992; and Li Ling 1993: 356–402.
2 There is a brief dialogue between the Yellow Spirit (the Yellow Thearch by another name) and the Left Spirit in _MS_ VII.B.1. For the "five signs," "ten movements," and "nine manners" and their counterparts in the Mawangdui texts, see _MS_ VI.B.1, 2, 4.
3 Passages on sexual cultivation in _MS_ III.88–89 and in _MS_ VI.A seem to borrow selectively from fuller accounts of sexual cultivation technique like _MS_ VI.B and _MS_ VII.B. _MS_ VIII.89 is notable for casting the ladies at Yu's court as instructresses, anticipating the role of the Immaculate Maid and Dark Maid in the later sex manuals.
1 These recipes are significant for the history of fermentation; the earliest received fermentation recipes are in the sixth century _Qimin yaoshu_ 齊 民 要 術.
2 This tradition is reflected in the word _yi_ 醫 (physician). _SW_ , 14B.40a, explains the lower part of the graph, which represents "liquor," in terms of the centrality of liquor to medical treatment.
1 The title refers to fulfilling one's allotted years of life.
1 Yi Yin is a legendary medical and culinary expert. The _Lüshi chunqiu_ essay "Benwei" 本 味 (Taste as the root) has Yi Yin teaching King Tang that cuisine is the key to becoming a true Son of Heaven ( _Lüshi chunqiu_ , 14–140). For Yi Yin in medicine, see Harper 1982: 44–46.
2 _MS_ VI.A.8 introduces the idea in the form of advice to Yu 禹, whose body is ravaged by his labors to control the flood: "As a rule, the mainstay for ordering government must begin from the body."
Section Five
Magic
_MS_ I.E.120 offers the following recipe for the treatment of inguinal swelling:
On the sixteenth day of the month when the moon first begins to deteriorate, perform the Pace of Yu thrice. Say: "Moon is matched against sun" and "Sun is matched against moon"—three times each. "Father is perverse, Mother is strong. Like other people they bore Sons, and only bore inguinal swelling bulges. Perverseness desist. Grasp the hammering stone and strike your Mother." Immediately, exorcistically beat and hammer the person twice seven times with an iron mallet. Do it at sunrise, and have the person with inguinal swelling face east.
In a magical operation which on one level might be construed as the conquest of Mother moon by Father sun, the time (sunrise of the day after full moon), the eastward orientation, the ritual acts, and the incantation all work in concert to overwhelm the demonic Mother blamed for giving birth to the ailment. A similar combination of magical elements is applied to a different end in _MS_ III.87:
If while traveling you wish to have your feet not hurt, face south, perform the Pace of Yu thrice, and say: "Whatever the water, no disaster; whatever the way, no withering. Give me [2]." When finished, take chimney soot [5] and insert it inside the shoe.
The Pace of Yu (Yu _bu_ 禹 步) and other magical devices are discussed below ("Varieties of Magic"). The point to be made now is that the Mawangdui medical manuscripts are perfect illustrations of the blending of natural philosophy and occult thought, and of the everyday uses of magic among the elite. Related magical material in the Shuihudi and Fangmatan hemerological manuscripts provides further proof that the Mawangdui medical manuscripts are not exceptional. Whatever the sources—religion, folklore, occult specialists—by the third century B.C. this material circulated in manuscript within the several geographical and cultural regions of the ancient Chinese world.
Any attempt to discuss magic encounters formidable problems of definition. Without minimizing the importance of theory and definitions, I propose to take a primarily descriptive approach with the Mawangdui medical manuscripts.1 One does not need a definition in order to recognize that the two recipes just cited are relevant to the investigation of magic in early China. Indeed, it is only with this kind of evidence that we will come to know more about the subject of early Chinese magic.
A few basic observations are necessary. I assume the relation between religion and magic in Chinese antiquity; were it not stylistically cumbersome I would consistently use the compound forms "magic and religion" and "magico-religious." Magic, whether from the perspective of ancient text sources or of modern investigation, concerned human actions undertaken in the belief that spirits and divine powers were present in nature. Having encountered particular circumstances, humans tapped the divine presence with voice, gesture, and select materials; likewise religion. Qualifications can be proposed, but it is difficult to justify the discreteness of religion except on relativistic grounds. When such grounds are expressed in an ancient text they are an invaluable record of how an individual or a group (religious or political) judged the action in question; they do not define the action absolutely. Astrology, divination, and other occult systems of knowledge arose in the same spiritual environment. I treat them as specialized systems alongside religion and magic. Astrology and divination blended with Warring States naturalistic theories—astrologers and diviners were among the formulators of correlative cosmology. The bond between Warring States natural philosophy and occult thought as represented by astrology and divination was one reason (but not the only reason) for the easy accommodation of magico-religious viewpoints. Knowledge of demons and deities, incantations, rituals, and sundry magico-religious devices became part of the occult knowledge dispersed in _fang_ -literature like the Mawangdui medical manuscripts and the hemerological manuscripts from Shuihudi and Fangmatan.
There is further discussion of these matters in "Magical Recipes" below. In studying a subject that has received scant attention in sinology, I am indebted to scholars investigating Greco-Roman occult thought and magic (see Section Two, "Recipes, Techniques, Calculations, Arts"). Their investigations reveal complex patterns of intellectual and spiritual syncretism in which magic plays an important role.1 The evidence of magic in the Mawangdui medical manuscripts is significant for ancient magic studies as well as for the history of early Chinese medicine.
Magical Recipes
I identify fifty-six entries in _MS_ I.E, _MS_ III, _MS_ IV, and _MS_ VII.A as magical. All are recipes that detail magical techniques. The thirty-nine magical recipes in _MS_ I.E involve incantations, ritual acts,2 or both: _MS_ I.E.9, 27, 34, 48–49, 56, 59–60, 65–70, 93, 107, 114, 118–20, 124–26, 128, 131–32, 134, 137–38, 178, 225, 229, 233–35, 265, 273, 276–77. With one exception ( _MS_ I.E.9) the recipes are exorcistic. _MS_ III includes a group of five magical recipes related to travel (protection when stopping overnight, increasing speed, and easing foot pain): _MS_ III.83–87. The six magical recipes in _MS_ IV all concern ways to avoid the attack of the venomous creature named _yu_ 蜮: _MS_ IV.28–29, 32–35. _MS_ VII.A.1 describes a charm and six applications (among them, to stop a dog's barking and an infant's crying). _MS_ VII.A.2 is an agonistic charm intended to magically defeat an adversary. _MS_ VII.A.3–6 are recipes for philters, which when administered serve to seduce or in one instance to separate. They form a set with the preceding charms and share with the charms a similar coercive effect (one of the applications of the charm in _MS_ VII.A.1 is for seduction).
The fifty-six magical recipes are not the only evidence of magic in the Mawangdui medical manuscripts. Except for the philters in _MS_ VII.A I have omitted other recipes in which the use of drugs is demonstrably magical. For example, _MS_ IV.30–31 prescribe chewing _suan_ 蒜 (garlic), _lan_ 蘭 (eupatorium), or _lingji_ 菱 芰 (water chestnut) every morning to avoid the _yu_ 's attack; the effect of the drugs is surely apotropaic. In _MS_ I.E.271–75, the ailment category _gu_ 蠱 is a demonic ailment, like the category "child sprite" which follows in _MS_ I.E.276–77 (both magical recipes). Why not identify all of the recipes for _gu_ as magical, not just _MS_ I.E.273 which uses talisman water? I have already noted in Section Three ("Materia Medica") the exorcistic nature of the rooster and snake medicine in _MS_ I.E.274. And why not include other recipes for ailments whose names suggest demonic possession, in particular the exorcistic dog feces cure for "crazed seizure" in _MS_ I.E.71 (see Section Three, "Materia Medica")?1
I restrict my identification of magical recipes to the fifty-six for several reasons. First of all, I wish to focus attention on the two things that for someone like Li fils were unambiguously magical: incantations and ritual acts. At a time when naturalistic explanations were forming the foundation for a rationalized understanding of the medical properties of drugs and of the effects of other therapies on illness, to chant an incantation or perform a ritual act was to align oneself with divine powers. Notably, stipulations regarding time in the magical recipes mostly relate to the positions of the sun and moon (as in _MS_ I.E.120). Only three magical recipes specify days in the sexagenary cycle based on hemerological ideas ( _MS_ I.E.107, 124, 126; see "Varieties of Magic" below). Because the evidence is so slight, the Mawangdui medical manuscripts do not require that we deal with the issue of whether hemerology and other occult knowledge ought to be called magic.2 The medical manuscripts themselves imply that incantations and ritual acts were the essence of magic.
Even though I call _gu_ a demonic ailment, I am wary of using the ailment name as the basis for identifying all _gu_ recipes as magical. I prefer to allow the possibility that any ailment might have been perceived at several levels (after all, the physician-authors of the _Huangdi neijing_ reject demonic causation). Perhaps a naturalistic understanding _of gu_ lies behind the two recipes which have the patient drink a medicine made from a woman's menstrual cloth ( _MS_ I.E.272, 275). A dual view combining naturalistic causation and demonic causation is even more likely for crazed seizure. Moreover, most of the ailment categories with magical recipes randomly intersperse them with non-magical recipes (twelve inguinal swelling recipes are magical, twelve are not). The same caveat applies to drugs, whose multiple uses were surely viewed multiply. To cure _gu_ , drink the ash of a woman's menstrual cloth ( _MS_ I.E.272); to speed travel, tie a virgin's menstrual cloth around the waist after first tossing it at a whirling wind ( _MS_ III.85); soak a menstrual cloth and spread the liquid on a burn ( _MS_ I.E.184); use the same liquid to boil meat, and consume both meat and liquid to treat inguinal swelling ( _MS_ I.E.121). Ailments and drugs considered individually lead us into a middle ground where magical and naturalistic conceptions overlap.
The philters in _MS_ VII.A.3–6 are, of course, drugs. They obviously belong together with the charms as examples of coercive magic. Just as obviously, magical ideas inform the use of drugs and therapies elsewhere in the Mawangdui medical manuscripts. The virtue of focusing primarily on incantations and ritual acts as the identifying sign of magic is that we are identifying clear-cut types of magical behavior from the perspective of those who performed the techniques. From the fifty-six magical recipes we learn something of the magico-religious side of their personality.
One of the surprises about the magical recipes is the knowledge that the Warring States, Qin, and Han elite were far more involved in a variety of magico-religious activities than we previously knew. Before recent archaeological discoveries, the conventional wisdom was that their religious beliefs and practices chiefly concerned family ancestral cults and ritual observances associated with state and family. If there was a popular religion, it was presumed to have been part of regional _wu_ 巫 (shaman) cults. The mechanisms of interaction with the spirit world (incantation, exorcism, and the like) were, so far as was recorded in received sources, in the hands of shamans and religious officiants, whose activities were paralleled by the astrologers and diviners. Other than that, general superstition was widespread but was not a defining characteristic of elite religious life.1
Seidel's investigation of Later Han religious life based on archaeological evidence changes this picture of popular religion during the time when religious Daoism was born. Demonstrating that first and second century A.D. popular religion revolved around notions of administrative procedures and judgments issued to individuals by a bureaucratic spirit world, Seidel observes that this religion—which was practiced at all levels of society—"is definitely not the mediumistic folk religion we assume to have preceded Taoism" (1987: 46). Basic religious ideas in the early Daoist communities were clearly derived from popular religion. Similar evidence of Warring States popular religion is now emerging in the archaeological record. Shamans were an important part of the religious scene (the core of Seidel's "mediumistic folk religion"), but the elite themselves were already engaged in transactions with a highly organized spirit world. The most intriguing find is a Fangmatan text recounting the resurrection of a man named Dan 丹 in 297 B.C. Written as a first person account, the text describes how Dan was released from the underworld because of a petition submitted by his former employer to the Scribe of the Director of the Life-mandate 司 命 史 (Li Xueqin 1990; Harper 1994; Harper 1995).
While the Fangmatan text attests to the bureaucratizing of the spirit world and to ideas about death in Warring States popular religion, the Mawangdui magical recipes (together with the Shuihudi and Fangmatan hemerological manuscripts) show the elite in another light utilizing incantations and ritual acts for everyday, personal needs. Some of the magic is simple folklore; for example, treating warts by rubbing them against something onto which the warts are magically transferred ( _MS_ I.E.65–70). But there are many examples of incantations and rituals like _MS_ I.E.120 and _MS_ III.87. The few references in received literature of the period only occur in the context of the performances of shamans and religious officiants. The magical recipes indicate that it was usual for the elite to perform comparable magico-religious techniques on their own.
The archaeological record is supplementing the received picture of Warring States elite society as religiously cool with a picture of religious engagement.1 And apart from religious life, magico-religious traditions were one element in the syncretistic mixing of ideas in natural philosophy and occult thought. Describing the whole of this complex phenomenon and determining precisely where within it the Mawangdui magical recipes fit is infeasible. Let me attempt to isolate a few distinctive features. By the third century B.C. popular religion as we now understand it emphasized individual magico-religious practices. Practices once left to shamans and religious officiants were in general use, and probably spawned a boom in magic which greatly enriched folkloristic practices. Concurrently, natural philosophy and occult thought were reshaping intellectual and spiritual conceptions. Rather than isolating a world of strictly natural phenomena from a world inhabited by spirits and demons, the two worlds were merged in varying composites fashioned by the specialists and recorded in _fang_ -literature. Books which treated magic as one among a number of techniques in the broad fields of natural philosophy and occult thought made magic all the more appealing.
The _Hanshu_ bibliographic treatise classifies books on demonology, exorcism, and incantation together with divination literature in the sub-category "Zazhan" 雜 占 (Assorted divination) of the "Shushu" 數 術 division. Titles include: _Rengui jingwu liuchu bianguai_ 人 鬼 精 物 六 畜 變 怪 (Human and demonic spectral entities and the mutant prodigies of the six domestic animals), _Zhi buxiang he guiwu_ 執 不 祥 劾 鬼 物 (Seizing the unpropitious and subjugating demonic entities), _Qingdao zhifu_ 請 禱 致 福 (Favor-granting prayers to bring good fortune; _Hanshu_ , 30.75a–76a). The demonography "Jie" in the first Shuihudi hemerological manuscript exemplifies occult literature on "spectral entities" and "mutant prodigies." "Jie" contains seventy entries which identify the causes of uncanny phenomena in everyday life, most attributed to demons, and provide remedies. Here is one of several entries dealing with domestic animals: "When people or birds and beasts as well as the six domestic animals continually go into a person's home—these are spirits from above who are fond of those below and enjoy entering." The remedy is to have virgin boys and girls beat drums, ring bells, and screech ( _SHD_ : 213; Harper 1985: 496). The Mawangdui magical recipes furnish the best examples of incantations and exorcistic rituals to "seize the unpropitious and subjugate demonic entities." Prayers to counteract the demonic evil of nightmares in both Shuihudi hemerological manuscripts exemplify the genre of "favor-granting prayers" ( _SHD_ : 210, 247; Harper 1987a: 270–71).
Part of the rationale behind the naturalistic/demonic composites in occult thought is expressed in the word _jing_ 精, which I translate both as "essence" and as "specter, spectral." In its origin _jing_ was understood to be the "stuff of spirits," which the _Guanzi_ , "Neiye," links to _qi_ "vapor" (see Section Four, "Body and Spirit"). In later use _jing_ continued to signify spectral qualities associated with the transmutability of things. With time the concentration of _jing_ in certain things became "spectral" and the thing became a "specter," as evidenced by the _SW_ definition of _mei_ 鬽 (a kind of goblin) as "the _jing_ of an aged entity" ( _SW_ , 9A.41a). Spectral manifestations of vapor itself are documented in "Jie" entries which blame uncanny phenomena on vapor. Vapor makes it possible for a demon to impinge on a person, either because vapor is the medium of transfer or because vapor is the stuff of demons just as it is the stuff of things that exist in the natural world.1 Theories of vapor as well as Yin Yang and Five Agent theories served to reanimate the world of spirits and demons in a more complex religious viewpoint.2
In the Mawangdui magical recipes and "Jie" we have the magic recommended to the elite by occult specialists ranging from recipe gentlemen to physicians. Much of it surely circulated orally in an environment that included shamans. However, the committing of magic to writing and the transmission of magical literature within _fang_ -literature set this magic apart from oral tradition and connected it to occult thought as a field of knowledge. Shamans also contributed to the dispersion of magico-religious practices among the elite (the fame of Yue 越 shamans and Thearch Wu's 武 帝 patronage of them in the second century B.C. is discussed in "Recipes of Yue" below). But their activities belonged more to the sphere of religion than to occult thought. Shamans were both admired and feared for their commerce with spirit powers. And the arbiters of socio-intellectual orthodoxy held their cults in low regard as a source of social unrest.1 Although all manner of occult practice was potentially suspect, shamanic activities were the most suspect, no doubt because shamans as a group were outside the elite mainstream and were predominately female. Whether perpetrated by shamans or not, Han terms for witchcraft or black magic tend to utilize the word _wu_ (see below).
The Mawangdui magical recipes provide techniques that like the other recipes are expected to work. The magical recipe for infant convulsions ( _MS_ I.E.27) concludes with word "excellent," one of several terms used in _MS_ I.E to indicate that certain recipes are known for their efficacy. Similarly, "Jie" concludes most entries with phrases like "it will stop," "it will desist," "it will not come," "it will leave," "it will die of terror." The idea is that the magical remedy "will work." We find in both texts a kind of everyman's magic, a magic that addresses the exigencies of everyday life. This continued to be the focus of medieval popular magic as we know it from works like the fourth century _Baopuzi_ and from Dunhuang 敦 煌 manuscripts of the Tang period like the _Baize tu_ 白 澤 圖 (Diagrams of White Marsh). Text parallels between these works and the newly excavated manuscripts testify to the durability of magical literature from its Warring States origins into the medieval period.2
The Mawangdui magical recipes do not treat of unusual feats of magic for which recipe gentlemen and their occult brethren as well as shamans were famed: conjuring up the dead, magic flight, invisibility, and various acts of magical transformation (assuming multiple forms, changing the forms of other things, and the like).3 The elite appreciated the difference between the kind of magic that they practiced ordinarily and the more powerful magic of those rare individuals who had a true calling. Yet their own involvement in magico-religious activity was not insignificant. Conditions favored a flourishing occult culture with the elite as active participants.
The approbation of magic evidenced in the excavated manuscripts helps to put the disapprobation of received sources in perspective; despite its problematic nature, everyone did it. Sima Tan 司 馬 談 (d. 110 B.C.) approves of the art of Yin Yang—by which he means cosmological and calendrical knowledge—for the order it brings to seasonal cycles, but he reproves it for "the multitude of prohibitions and avoidances, which cripple the people and increase their fears"; that is, he accuses the Yin Yang specialists of abetting superstition ( _Shiji_ , 130.3b). The summary of the Yin Yang specialists in the _Hanshu_ bibliographic treatise is even more explicit: "When (the Yin Yang art) is practiced in a crippling way, it becomes snarled in interdictions and prohibitions, and mired in specious calculations. It abandons the business of humankind and relies on demons and spirits" ( _Hanshu_ , 30.40a). Both criticisms are directed at popular hemerological books like those discovered at Shuihudi and Fangmatan (Harper 1985: 462–70). The _Hanshu_ objection does not concern ideas—that belief in demons and spirits is in principle wrong—but concerns the social consequences of the ideas. From the standpoint of the Han socio-intellectual orthodoxy expressed in the _Hanshu_ , if ideas encouraged undesirable behavior they had to be regulated. What was the basis for distinguishing between desirable and undesirable behavior? In Han times, one standard was established by _jingshu_ 經 術 (canonical art; see Section Two, "Recipes, Techniques, Calculations, Arts").
To be sure, anything perceived to be potentially damaging to the person and the authority of the Han thearch and to accepted social norms was suspect, including the Warring States philosophical books which a first century B.C. court official branded as inimical to "canonical art" ( _Hanshu_ , 80.8a). By engaging in religious practices other than approved state observances and in any form of occult practice one risked running afoul of the government, even though the practices themselves were customary and were not specifically outlawed. The fact that magic had been performed was not so important as the circumstances of its performance. For example, in the late first century B.C. Xifu Gong 息 夫 躬, dismissed from court for his involvement in political intrigues, was harassed by robbers at home and was taught a magical technique to keep them away:
He fashioned a ladle from a mulberry branch that faced southeast and drew the seven stars of the Northern Dipper on it. At night Gong unfastened his hair, stood in the central courtyard, and faced the Northern Dipper. He gripped the ladle and waved it while chanting the incantation against robbers. ( _Hanshu_ , 45.18a.)
The astrological and magical significance of the Northern Dipper (the Big Dipper) in Warring States, Qin, and Han times is well documented (Harper 1978–79; Kalinowski 1983). The description of Xifu's magical exploitation of the constellation to subdue robbers is comparable to techniques in the Mawangdui magical recipes. However, someone reported Xifu Gong to the authorities claiming that Xifu harbored hatred for his ruler; moreover, that Xifu was examining astrological signs to discover his ruler's fortune and was chanting "shaman curses" ( _wu zhuju_ 巫 祝 詛). Xifu was promptly arrested and died in jail. Perhaps his intent was sinister. The Mawangdui magical recipes indicate that the magical performance itself was not out of the ordinary. Might not Li fils have found himself in similar difficulty if his performance of one of the magical recipes were to have been viewed in the wrong light by a hostile party?
Ill-purposed magic or witchcraft—that is, magic perceived by others as witchcraft—is commonly denoted by compounds using _wu_ in Han sources. _Wu_ , the majority of them female shamankas, were known to aid people in achieving whatever goal they desired. The _Hanshu_ account of Liu Xu 劉 胥 (d. 54 B.C.), one of Thearch Wu's sons, must represent a common pattern. When Liu Xu did not succeed his father, he employed the shamanka Li Ruxu 李 女 須 to curse Thearch Zhao 昭 帝 (r. 87–74 B.C.). Ruxu first entered a shamanic trance. When she announced that Thearch Wu occupied her body, everyone present bowed while the deceased ruler declared, "I command that Xu become Son of Heaven" ( _Hanshu_ , 63.15a–b). Delighted, Liu Xu sent the shamanka to offer prayers to the spirits that he be granted a favor—the demise of Thearch Zhao and his own succession. Shortly thereafter, Thearch Zhao died. Although Liu Xu failed to succeed to the throne, he remained convinced of Ruxu's shamanic powers and continued to employ her to perform her "shaman curses" on other occasions (the same curses Xifu Gong was accused of performing).
Such activities contributed to a generalized notion of black magic or witchcraft as the work of women. Accounts of Thearch Wu's reign provide notable examples. In 130 B.C. it came to light that Dowager Chen 陳 皇 后 had been practicing the "women's way of seduction" ( _furen meidao_ 婦 入 媚 道) in her efforts to secure her uncertain position ( _Hanshu_ , 97A.11a; Twitchett and Loewe 1986: 174). Shortly thereafter the lady's daughter and others were arrested for attempting to aid her by practicing "shaman _gu_ ( _wugu_ 巫 蠱), sacrificial worship, and curses." Her daughter was beheaded. The lady was demoted in a decree that opened with the words, "the Dowager has failed to observe propriety and is deluded by shaman curses." Yet another more serious _wugu_ scandal occurred in the last years of Thearch Wu's reign (Loewe 1974: 37–90; Twitchett and Loewe 1986: 177–78).
The association of _gu_ with demonic evil and with female seduction was already made in the Warring States (see _MS_ I.E.271). The compound _wugu_ reflects the perception that women's magic was inherently dangerous (especially for men). As in all accusations of witchcraft, the deed and its name are defined by the accusers. I am particularly struck by the accusation that Dowager Chen practiced a "women's way of seduction," implying witchcraft. Did her "way of seduction" perhaps include the use of philters like those in _MS_ VII.A which ensure that "seduction will occur" ( _MS_ VII.A.4) or that the object of desire "will be obtained" ( _MS_ VII.A.5)? Was the use of philters by men to seduce women perceived differently from their use by women? As in the case of Xifu Gong, I suspect that some of the activities were not in themselves exceptional; it was simply riskier for women to engage in them.
Varieties of Magic
In the Han mind the south was where magico-religious traditions were strongest. Chu 楚 and Yue 越 shamans were the most powerful; inhabitants of Chu and Yue were most given to worship of spirits and demons; the southern genius for magic was attributed to the sultry environment itself. The contents of the Mawangdui magical recipes reflect in part southern magico-religious traditions. The prominence of spitting and spouting when chanting incantations in the magical recipes suggests the southern breath magic called "recipes of Yue" (Yue _fang_ 越 方) in Han sources. Breath magic is discussed below under incantation. My thesis regarding the Mawangdui magical recipes and the recipes of Yue is presented separately in "Recipes of Yue." Other aspects of the magical recipes clearly belong to beliefs and practices that were already common to magic in the north and south during the third century B.C. Parallels in the Shuihudi and Fangmatan hemerologieal manuscripts provide the proof, the Pace of Yu being the best single piece of evidence. There is evidence as well of deities in the Later Han popular religion reconstructed by Seidel (1987). In short, the Mawangdui magical recipes bear witness to widespread magico-religious traditions in the third to second centuries B.C.
Consequently, although the context is most often the treatment of specific ailments (the thirty-nine recipes in _MS_ I.E and the eight in _MS_ IV), the contents of the Mawangdui magical recipes are not exclusive to medicine. Li fils would have understood the magical recipes as the medical application of magico-religious techniques; we can use the same recipes to reconstruct magic and religion.1 My survey of the Mawangdui magical recipes is brief, more a list of salient details than an exegesis. I begin with incantation, followed by ritual acts and other magical devices. There is a slight amount of corroborative evidence in received literature. For the most part, the magical recipes themselves are our first records of the wording of incantations and of all the directions needed to actually work magic. The Shuihudi and Fangmatan hemerological manuscripts corroborate and supplement the Mawangdui magical recipes. I refer to the hemerological manuscripts on occasion, but I leave thorough treatment of them for another time.
The majority of incantations in the magical recipes are indicated as direct speech with the verb _yue_ 曰 (say), the standard verb for any kind of direct speech. Next in frequency is _zhu_ 祝 (chant the incantation; the right side of the graph signifies a mouth atop a human figure, the left side signifies the presence of the spirits). The texts of several incantations are simply prefaced by words for spitting and spouting, indicating breath magic (see below); and there are two examples of a word denoting "curse" (see _MS_ I.E.124). Mostly rhymed and occasionally punctuated by magical utterances, the Mawangdui incantations represent the third to second century B.C. manifestation of a long tradition of magical communication with the spirits.2
A feature shared by all of the incantations is their intelligibleness. Nonsense and phrases from other languages are not used.1 The purpose of the incantations is to deliver a particular kind of message, and most of them state their information in straightforward fashion. The magical recipe to stop bleeding in _MS_ I.E.9 includes the simplest, most direct incantation: "Man, staunch! Woman, vinegar!" The incantation conjures the presence of a man to stop the flow of blood and a woman to cleanse the wound with vinegar. An incantation may also take the form of a wish, as in the _MS_ III.87 recipe to prevent foot pain quoted at the beginning of this section ("Whatever the water, no disaster; whatever the way, no withering.").
The majority of the incantations occur in _MS_ I.E and are exorcistic curses. The curses typically threaten the demonic agent blamed for causing the ailment with mutilation and death if it does not leave the patient's body. The graphic quality of the phrases is illustrated by the following portion of the incantation in _MS_ I.E.229: "With a _zuo_ 柞 (oak) rod I stab you; with tiger claws I gouge and grab you; with a knife I butcher you; with _wei_ 葦 (reeds) I sever you.... If you do not depart, it will be bitter." Oak, tiger claws, and reeds are all exorcistic materials used in ritual acts; the use of the first person pronoun indicates that the very person chanting the incantation intends to punish the agent (the "you"). Usually the incantations request spirit assistance in dealing with the demonic agent; and an exorcistic act follows the chanting of the incantation, like flagellation (with an iron mallet in _MS_ I.E.120 quoted above) or spitting (see below).
This scenario for exorcism mirrors the one complete account of a Han state-sponsored exorcism in received literature, the Great Exorcism ( _da nuo_ 大 儺) performed at New Year's and recorded in the _Hou Hanshu_ treatise on ritual.2 The Great Exorcism clears away the pestilential evil of the old and dying year, inaugurating a new purified cycle of time. It is performed by the chief exorcist leading a troupe of youths and palace officiants. The curse comes at the climax of the ceremony when twelve spirit beasts—played by twelve costumed officiants—are commanded to each devour one of twelve evils (some illnesses, some demons) of the old year. Having conjured their assistance, the curse continues:
These twelve spirits are all charged to pursue the evil and baleful. May they scorch your carcass! May they rip apart your skeleton! May they strip away your flesh! May they tear out your lungs and guts! If you do not depart quickly, whoever remains will become food.
Brandishing torches, the exorcistic party passes through the palace, finally delivering the torches to horsemen outside the south gate who dispose of them (and the evil they contain) in the river ( _Hou Hanshu_ , "Zhi" 志, 5.10b; Bodde 1975: 81–82).
The _MS_ I.E incantations are the chief source for the names of spirits and demons, who are either invoked to assist or are the objects of the exorcism (similar to the Great Exorcism). The religious viewpoint reflected in the incantations is animistic. The ontological view of ailments as entities fuses with the belief that each entity has its spirit—which is one reason for alternation between treating ailments medically and treating them with exorcism. The scorpion spirit is cursed in _MS_ I.E.48–49; the lizard spirit in _MS_ I.E.56, 59–60; in _MS_ I.E.65 the person with warts plays the role of the wart spirit who is exorcised by being forced to name himself. Some of the spirits who assist are personifications of elements of nature. The incantation in _MS_ I.E.49 calls upon a spirit Father and Mother to trap the scorpion:
Father dwells in Shu. Mother is the Wind Bird who punishes. Do not dare flee up or down. The Wind Bird bores your heart.
Father, Mother, and Son groupings are sometimes associated with spirit powers in the environment (as above); and are sometimes part of the demonic etiology of an ailment (as in _MS_ I.E.120, in which the incantation commands the inguinal swelling Sons to attack the Mother who bore them).
There is evidence of a more formal pantheon. The magical recipes for the rash caused by lacquer include incantations which accuse the Lacquer King 漆 王 of failing to perform the tasks assigned to him by the Thearch of Heaven 天 帝 ( _MS_ I.E.233–35). The incantation in _MS_ I.E.124 calls upon the Spirit of Heaven 天 神 and Spirit Maids 神 女 to expel the fox blamed for inguinal swelling. The Yellow Spirit 黄 神 is summoned in _MS_ I.E.178 (a burn) and _MS_ I.E.265 (scabbing). The fox's demonic reputation in China is well known; _MS_ I.E.124 and 128 are now the earliest attestation of fox possession. Thearch of Heaven, Spirit of Heaven, and Yellow Spirit all refer to the same supreme deity in Han popular religion (Seidel 1987: 28–30). Spirit Maids are divine agents associated with hemerology ( _MS_ I.E.124 is to be performed on a specific day in the sexagenary cycle; see below); they figure prominently in religious Daoism. The bureaucratic aspect of human relations with this pantheon is reflected in two incantations that mimic the formula used by officials to address their superiors: "I dare to declare." The announcement of an abscess in _MS_ I.E.229 is made to Tai Mountain (the sacred peak of the east, in present-day Shandong, whose presiding deity was one of the arbiters of human fate): "I dare to declare to the Tai Mountain Barrow." A similar address is made to the East Lord and Bright Star 東 君 明星 (perhaps the astral deity Taiyi 太一) when securing a campsite in _MS_ III.84.
Let me turn to breath magic. The evidence is of two kinds: magical utterances and acts of spitting and spouting. The two are not unconnected. Like spitting and spouting, utterances concentrate the vapor which is the breath as it is ejected from the mouth. A vocabulary of utterances used by shamans and religious officiants can be traced to the Shang bone and shell inscriptions. Shirakawa demonstrates that _yi_ 殿—both a phonetic and signific in 醫 "physician"—belongs to a family of Shang words for exorcistic weapons, the sounds of exorcistic beating, and exorcistic utterances (1976, vol. 2: 232–33). The etymology of the word _yi_ "physician" as the "shaman who heals with exorcistic techniques" proposed by Shirakawa is convincing.1 Warring States ideas about vapor, breath, and saliva added to the magico-religious conception of magical utterances.
_MS_ I.E includes five magical utterances, each one occurring just once and always at the beginning of the incantation (I list them with Old Chinese reconstruction as they appear in the translation): * _tsjar_ 嗟 ( _MS_ I.E.56); * _gwjag_ 吁 ( _MS_ I.E.128); * _sjit_ * _sjit_ , * _khw ət_ * _khw ət_ 胖 胖 訕 訕 ( _MS_ I.E.178); * _k əgw_ 睪 ( _MS_ I.E.229); * _tsj əm_ * _tsj əm_, * _hj əkw_ * _hj əkw_ 浸 浸 爐 爐 ( _MS_ I.E.265). * _Gwjag_ * _tsjar_ is attested as a compound utterance in several _Shijing_ 詩 經 poems in which the utterance is part of the magic of conjuring spirit beasts (see _MS_ I.E.56). A variant of the first of the two four-syllable utterances is attested in the _Zuozhuan_ 左 傳 as a monitory prophecy; the graphs in _MS_ I.E.178 may additionally mean "swarm, submit." * _K əgw_ represents the sound of a cry that reaches into the spirit world. The utterance forms part of the _Yili_ 儀 禮 ritual of summoning back the soul of a person recently deceased; and it is used to summon assistance in exorcising nightmare demons in the two Shuihudi hemerological manuscripts. In _MS_ I.E.229 the cry reaches the Tai Mountain Barrow. One occurrence each hardly constitutes heavy usage, but the fact that the utterances occur indicates that the Mawangdui incantations utilize widely shared conventions of incantation.
The examples of spitting ( _tuo_ 唾) and spouting ( _pen_ 噴) I judge to be more characteristic of a southern style of breath magic. Let me inventory the occurrences. In _MS_ I.E.27 spitting precedes the incantation; the incantation first invokes a "spouter" to "spout ferociously" and continues with a typical curse of the demonic agent who is expelled by the spirit spouter (surely the act of invoking the spouter involves spouting action by the person chanting). The incantation in _MS_ I.E.48 is preceded by spitting and spouting; in _MS_ I.E.59 by spouting and blowing; in _MS_ I.E.93 by spouting and snorting thrice. The incantation in _MS_ I.E.118 again invokes a spouter to expel the demonic agent, as does the incantation in _MS_ I.E.277. In _MS_ I.E.178 the person spits thrice after the incantation; _MS_ I.E.229 says simply to spit after the incantation. Spitting precedes the incantation in _MS_ I.E.233, and the first word of the incantation is "spout" as the utterance * _p ə_n; * _p ən_ is again the initial utterance in the incantation in _MS_ I.E.235. Spitting follows the incantation in _MS_ I.E.234, seven times for men and twice seven times for women. In _MS_ I.E.48, 178, 229, and 234 the recipes instruct the person to spit on the ailments; that is, to spit on the demonic agent who is localized in the affected part of the body.
As a universal human custom spitting does not require elaborate explanation. The Chinese custom of spitting at demons is already well documented in post-Han sources (Liu Zhiwan 1974: 338–48; Harper 1982: 92–93). From the standpoint of the demons, the fact that they dislike being spat at is now on record for the third century B.C. in the Fangmatan resurrection account. The account concludes with a list of graveyard rules, including the following: "Let those who offer sacrifices at tombs not dare to spit. If they spit, the ghosts depart and flee in fright" (Harper 1994:14). Surely spitting and spouting were employed exorcistically in the north and south in the third century B.C. and earlier. My argument for a southern style of breath magic involving spitting and spouting is based on two forms of evidence: first, Wang Chong's 王 充 rationalization of incantation in the _Lunheng_ 論 衡, which uses vapor theory to explain what others would have understood to be breath magic; and second, accounts in the _Lunheng_ and elsewhere of the potent breath of the inhabitants of Chu and Yue, and of the techniques of the recipes of Yue. The Han tradition of the recipes of Yue probably grew out of the blending of magic and occult thought in the south during the Warring States. Originally a southern tradition, the recipes of Yue gained wider fame during the Han. I submit that the examples of spitting and spouting in the Mawangdui magical recipes are the breath magic of the recipes of Yue.
The southern tradition of breath magic is treated in "Recipes of Yue" below. Wang Chong's statements on why incantations work are necessary background information. Wang Chong's purpose is to demystify incantation by showing that it is a natural phenomenon involving vapor, Yin and Yang, and the Five Agents. His arguments shed light on probable ways in which Warring States naturalistic theories bolstered the magico-religious understanding of incantation and breath magic. Even in the first century A.D. I suspect that Wang Chong's rationalization served to justify the elite's belief in the magical efficacy of incantation.
Wang Chong's basic premise is that all phenomena can be explained as manifestations of vapor. What people take to be demons are momentary agglomerations of Yang vapor, which is volatile, fiery, and red. Yang vapor burns like fire and can harm people, but the harm of seeing a demon—that is, of encountering a mass of Yang vapor—is no different than the harm of being poisoned by certain substances, which Wang Chong explains as being burned by the Yang vapor concentrated in them. Wang Chong further equates speech and fire, citing as his authority the canonical "Hongfan" 洪 範 (Great plan) treatise of the _Shangshu_ 尚 書, which Graham dates to the fifth century B.C. (1989: 326). The "Hongfan" lists of symbolic correlations name Fire as the second of the Five Agents and Speech as the second of the Five Human Functions.1 The _Lunheng_ essay "Yandu" 言 毒 (Explanation of poison) appeals both to the "Hongfan" and to folk belief:
There is a folk saying, "A multitude of mouths melts metal." The mouth is Fire. Among the Five Agents the second is Fire; among the Five Human Functions the second is Speech. Speech is matched with Fire, hence the saying that it "melts metal." ( _Lunheng_ , "Yandu," 23.459.)
Wang Chong's argument weaves together his own ideas about Yang vapor, the "Hongfan" correlation of Fire and Speech, and folk belief. His argument continues with an explanation of why the folk saying must be grounded in Five Agent theory (according to which Fire conquers Metal), but this is part of his rationalization. The folk saying itself simply indicates a popular belief that breath works like fire, which probably reflects magico-religious ideas about the properties of fire prior to Five Agent theory (see Section Three, "Therapy"). Having provided a theoretically satisfying explanation, Wang Chong has no difficulty affirming that the incantations chanted by shamans are efficacious because shamans are naturally endowed with greater concentrations of Yang vapor. Moveover, the speech of the inhabitants of the south (which is a Yang region) is naturally more potent:
In the lands of Grand Yang the people are frenzied. When a person is frenzied his mouth and tongue become poisonous. Thus the people of Chu and Yue are frenzied and febrile. When they speak with another person and the saliva from their mouth strikes the person, then his vessels swell up and form sores. In the extremely hot lands of the Southern Commandery, when the inhabitants chant an incantation at a tree the tree dies, and when they spit at a bird the bird drops down. The reason why Shaman Xian was able to use incantations to alleviate the people's sicknesses and cure the people's misfortunes is because he was born in Jiangnan and possessed burning vapor. Now as for poison, it is the vapor of Yang. Thus when it strikes a person it is like fire scorching the person. ( _Lunheng_ , "Yandu," 23.457.)
Wang Chong rationalizes the effects of speech and incantation as natural phenomena. Others would have understood the words spoken in incantation to be oral fire, whose power was increased by the use of utterances, spitting, and spouting. Breath magic partook of the magic of fire.
The incantation in _M_ SIII.83 is a notable example of travel magic. The recipe is used "when traveling and stopping overnight," evidently when camping in the open. Both the incantation and the ritual acts which accompany it secure the campsite by creating a magically protected space. This kind of magic is well documented in the fourth century A.D. _Baopuzi_ 抱 朴 子 as part of the essential knowledge for anyone who would go into the wilds in search of spirits and the magical substances which confer immortality, and who must beware of tigers, wolves, and demonic machinations. _MS_ III does not explain why a traveler would find it necessary to camp; I presume that lodges even along better known routes were not plentiful in the third and second centuries B.C. No doubt the hazards of the road were similar to those experienced by the _Baopuzi_ traveler. Remarkably, there is a parallel version of the incantation in the _Baopuzi_ , which includes the same phrases "the Yang side of Tai Mountain" and "walls and ramparts that are not intact, seal with the metal bar." In _MS_ III.83, following the incantation the traveler performs the Pace of Yu and draws a circle on the ground saying, "With a stick of fresh _jing_ 荆 (vitex) two _cun_ long I draw a circle around the inside." In the _Baopuzi_ the traveler draws a square on the ground with a knife, and the knife is laid on the square at an astrologically significant position. The phrase "seal with the metal bar" suggests that in earlier versions of the technique a knife was also used, but has been replaced by a magical stick of vitex in _MS_ III.83. The parallel techniques may be due to oral transmission, but I think it probable that we are witnessing continuity in the transmission of _fang_ -literature.
Discussion of ritual acts and magical devices must begin with the Pace of Yu 禹 步. Prior to the evidence in the Mawangdui magical recipes and the Shuihudi and Fangmatan hemerological manuscripts, the earliest occurrence of the term was in the _Shizi_ 尸 子, in a description of the physical deformities suffered by Yu (the hero of the Chinese flood myth and legendary founder of the Xia ruling house) as a consequence of his labor to control the flood:
His hands did not have nails and his shins had no hair. He was afflicted with hemiplegia. One foot would not step past the other foot, which the people called the Pace of Yu. ( _Shizi_ , 1.16b.)
Granet (1925) adduces _Shizi_ and other passages in pre-Han philosophical literature that describe Yu's physical deformities (treated by the philosophers as an example of the ruler sacrificing himself for his people) as evidence of an underlying religious conception in which such traits constituted the mark of the shaman. Granet proceeds to hypothesize that the Pace of Yu, which was a trademark of religious Daoism during the centuries after the Han, originated in shamanistic traditions of early popular religion; and that key elements of religious Daoism were derived from this earlier popular religion. There is, of course, other evidence in the excavated manuscripts of the relation between ancient popular religion and religious Daoism. But the eight occurrences of the Pace of Yu in the Mawangdui magical recipes ( _MS_ I.E.60, 67, 118, 120, 128, 225, 276; _MS_ III.83) are the most striking proof, and confirm Granet's inspired hypothesis.1
I believe Granet is correct. However, the exact nature of its shamanic origin is not clarified in the manuscript evidence, in which the Pace of Yu is already part of the occult tradition transmitted in _fang_ -literature.2 In _MS_ I.E performing the Pace of Yu magically subdues; it always occurs at the beginning of a magical operation, either before or simultaneously with the incantation. _MS_ III.83, the first Shuihudi hemerological manuscript ( _SHD_ : 223), and the first Fangmatan hemerological manuscript (Qinjian zhengli xiaozu 1989: 5) all employ the Pace of Yu in magical techniques related to travel. The incantation accompanying the Pace of Yu in the Shuihudi technique declares the traveler's wish: "Let so-and-so travel and not suffer odium; he first acts as Yu to clear the road." The Pace of Yu clears away the hazards of the road, replicating Yu's taming of water, earth, spirits, and demons during his legendary travels. The legend of Yu's caldrons (magical talismans emblazoned with the images of the spirits and demons) and the talismanic _Shanhaijing_ (the prototypical demonography which enumerates the habitats and marvelous inhabitants of the earth) belong to the same Warring States occult tradition which made the Pace of Yu a popular magico-ritual step (Harper 1985: 479; Harper forthcoming; Kudô 1990: 44–57).
The regular instruction to perform the pace thrice in the manuscripts suggests that the early Pace of Yu was similar to the technique described in _Baopuzi_ , 17.78, which is the earliest extant account of how to execute it. Beginning with the right foot in front and the left foot behind, the performer steps ahead with the left foot and then again with the right foot, finally bringing the left foot even with the right foot—which concludes the first pace. The second pace continues by stepping ahead with the right foot, followed by the left foot, finally bringing the right foot even with the left foot. The third pace repeats the first pace.1
The inguinal swelling recipes in _MS_ I.E are notable for descriptions of exorcistic rituals and for references to ritual acts attested in received literature. Several provide precise stage directions, as in the _MS_ I.E.125 sunrise ritual: the patient faces east beneath the roof gutter; the designated officiant grasps a rammer and faces west opposite the patient; after chanting the first incantation (which blames the ailment on Father, Mother, and Sons), the officiant hits the patient twice seven times; finally, in a second incantation the officiant commands the patient to rise and inguinal swelling to desist. Archery is described in _MS_ I.E.132 and 137; the latter recipe uses a peach-branch bow, which is well attested in received descriptions of formal exorcistic rituals (see _MS_ I.E.132). Exorcistic archery with peachwood bow and jujube arrows (the material for arrows specified in received literature) also occurs in the Shuihudi "Jie" ( _SHD_ : 212; Harper 1985: 492–93). There are three occurrences of a rare, technical term for "exorcistic beating" ( _si_ 攺; see _MS_ I.E.118). Creating a magical, protected space by drawing on the ground in _MS_ III.83 has an exorcistic counterpart in _MS_ I.E.134. The patient kneels beneath a wall facing east and inserts his testicles and penis into a gourd. Then twice seven pegs made of oak are poked into the ground around him, creating a magical demon-trap. A similar technique using peach stakes to exorcise nightmare demons is described in "Jie" ( _SHD_ : 214).
The two recipes to exorcise the child sprite warrant mention, _MS_ I.E.276 for the use of peachwood figurines fastened above the door-way. The custom is associated with New Year's observances in received literature. The bundles of peachwood figurines placed in the coffin in Mawangdui tomb I (see _MS_ I.E.276) and the "Jie" recommendation to hit demons with a peachwood figurine ( _SHD_ : 215) attest to their wider use. _MS_ I.E.277 describes an exorcistic procession. A cart made from a winnowing basket mounted on gourds is harnessed to a black pig and led through the patient's home. The accompanying incantation declares that the Shamanka Mistress is searching for the child sprite, and that it will be cast into the water (recall that the Great Exorcism concludes with casting the torches into the river).
Synchronization of incantations, ritual acts, and magical devices into a whole operation must be examined for each magical recipe, which I will not do here. Nor will I inventory the magical recipes for everything that is magically significant. However, I would like to indicate representative magical devices employed in the recipes. Let me begin with the idea of magical transfer. Water, gourds, gourds filled with water, clods, brooms, and various plants are all used to trap and contain demonic pathogens, which are then discarded. The water is often a preparation called "silted water" (see _MS_ I.E.27). In _MS_ I.E.60 (a lizard bite), the designated officiant carries a gourd holding one cup of silted water in his left hand, faces north towards the patient to perform the Pace of Yu, chants incantations, and has the patient drink one half cup of the water in the gourd. The recipe concludes with the instruction, "cover the gourd flask and discard it." A gourd is placed over the man's genitals during the exorcism in two inguinal swelling recipes ( _MS_ I.E.134, 137). Clods, brooms, and plants are most common in the recipes for warts ( _MS_ I.E.65–70). And after brushing the warts with a broom in _MS_ I.E.66 the broom is discarded in an abandoned well.
Specifically demonifugal materials include peach and arbor-vitae wood. Both have well-known associations with the sun, Yang, and the east ( _MS_ I.E.118, 137, 276) which are usually cited in explanations of why these two kinds of wood are magical. Certainly the magical exploitation of the sun and the east in the inguinal swelling recipes ( _MS_ I.E.118–20, 125–26, 132, 134, 137) overlaps with the use of peach and arbor-vitae; and the peachwood figurines in _MS_ I.E.276 are made from a branch cut from the east side of the tree. Whether the woods are magical because of the sun and the east is another question. In discussing peachwood Bodde makes a useful distinction between the ancient belief that the wood _is_ magical and attempts to explain _why_ it is magical (1975: 128–34). Bodde cites the Han legend of the peach tree in the eastern sea which is a demon barrier. As demons pass through the barrier from the northeast, two spirit guards seize the evil ones and feed them to tigers. While the legend served in Han times to explain the tradition of the peachwood figurines (they are the two spirit guards), we still cannot say why the tree in the eastern sea is a peach and why peachwood is magical. The logic to why some materials are believed to be magical and others not remains unexplained (and there may not be an explanation).1
The demonifugal use of feces to expel the lacquer demon in _MS_ I.E.233 and 235 is supplemented in "Jie" by fumigation with feces (see Section Three, "Therapy"), throwing balls of dog feces at demons ( _SHD_ : 213; Harper 1985: 495), and bathing in dog feces to exorcise a demon ( _SHD_ : 215; Harper forthcoming). There are notable examples of prophylactic clothing to protect the wearer from the _yu_ in _MS_ IV 32–34, especially the red and black silk garments trimmed with horsehair in _MS_ IV.33. Similar attire is worn by the chief exorcist in the Great Exorcism and is used to dress the body of the deceased in the _Yili_.2
Timing and orientation have been in evidence throughout this section. Sunrise and east are preferred for exorcising inguinal swelling; night and north are preferred for warts.3 _MS_ I.E.120 schedules the exorcism of inguinal swelling to coincide with the waning moon in order to weaken the influence of the "Mother who is strong." The last day of the month, the point of juncture between one lunar cycle and the next, is usual for warts (except for _MS_ I.E.69 which schedules the exorcism on the first day of the month). The symbolism is reasonably clear. North is the realm of water and is where noxious things are imprisoned (the dead, demons, and the like). The act of "brushing the warts to the north" ( _MS_ I.E.66) on the last day of the month is a lesser version of the Great Exorcism at New Year's. East has its own exorcistic associations (including the peach tree legend); and the rising sun expels darkness and evil. In the third and second centuries B.C. Yin Yang classifications of spatial orientations and temporal cycles would have added to the rationale underlying the magical operations. It is worth noting, however, that none of the magical recipes refer to Yin and Yang or to the Five Agents.
Two inguinal swelling recipes ( _MS_ I.E.124, 126) and one urine retention recipe ( _MS_ I.E.107) are scheduled for specific days in the sexagenary cycle. The three days must be hemerologically significant, but I cannot explain their selection. Both days in the inguinal swelling recipes are in the _xin_ 辛 decade, and both incantations open with a declaration of cyclical day designation. The _MS_ I.E.123 incantation then exhorts Spirit Maids to "according to sequence hear the spirit pronouncement." The sequence must be the sequence of the sexagenary cycle, thus the Spirit Maids are the hemerological spirits associated with days. The day in _MS_ I.E.126 serves as the occasion for the patient to get rid of the ailment by changing his name to Yu, the flood hero.
The significant numbers in the magical recipes are three, seven, and twice seven (fourteen). Seven is odd and thus Yang; twice seven is Yin. In _MS_ I.E.67 a man rubs his warts with seven clods, a woman with twice seven; in _MS_ I.E.234 a man spits on the lacquer rash seven times, a woman twice seven times. The two examples are interesting, but gender is not a consideration in other occurrences. Moreover, all three numbers are used regularly in non-magical recipes (as well as in later medical recipe literature). Their use is important in the magical recipes, but is not a definitive sign of magic.
I conclude with an example of associative magic in _MS_ VII.A.6 involving words, materials, and objectives. The philter recipe is short:
Put the person's left eyebrow in liquor and drink it. You invariably obtain the person.
The word for eyebrow in _MS_ VII.A.6 is _mei_ 眉 (written 麋 in the recipe). Eyebrows figure in the etymology of the word for seduction, _mei_ 媚. In _MS_ VII.A.6, the object of desire's left eyebrow compels her or him to submit to the magic of your seduction.
Recipes of Yue
A scattering of received sources from the Han to the early twentieth century indicates the existence of a southern tradition of breath magic, called Yue _fang_ 越 方 (recipes of Yue) in Han times. According to the _Baopuzi_ , the technique "consists of augmenting the vapor (of the breath) and that is all" ( _Baopuzi_ , 5.24). Down the centuries, southern "vapor charms" ( _qijin_ 氣 禁) were associated with various legendary practitioners and were known by several names. And southern breath magic mingled with Daoist and popular occult traditions. The examples of spitting and spouting in _MS_ I.E are now the earliest documentation of this southern breath magic; several magical recipes are remarkably similar to much later received accounts. To show how breath magic in _MS_ I.E is related to the recipes of Yue I must first examine received documentation concerning the latter. Even without the new manuscript evidence, the history of the recipes of Yue demonstrates the durability of a distinctive tradition of magic which has been handed down in the region of the Yangzi River since Han times. With the discovery of _MS_ I.E we can verify its transmission in third century B.C. _fang_ -literature.
The term Yue _fang_ first occurs in the _Hou Hanshu_ account of two occult specialists: Xu Deng 徐 登 and Zhao Bing 趙 炳. Xu Deng was from Min 閩 (a region identified with Yue culture and peoples in Han times, situated in present-day Fujian); he "excelled in performing shaman arts ( _wushu_ 巫 術)." Zhao Bing was from Dongyang 東 陽 (in the old Yue heartland, present-day Zhejiang) and "was able to perform the recipes of Yue" ( _Hou Hanshu_ , 82B.9a; Ngo 1976: 127–28). The men, who lived during the Later Han, met at the Ji River 溪 水 (Zhejiang):
It was a time of war and chaos, and sickness was rampant. After meeting on the banks of the Ji River at Wushang the two men made a compact to use their arts to cure ailments. They said to one another, "Now that we share a mutual determination, let us each test our ability." Deng then charmed ( _jin_ 禁) the Ji River causing its water to not flow. Bing followed that by charming a dead tree, which immediately sprouted buds.
The account continues with details of their sometimes miraculous activities, noting that "solely by practicing these charms (the ailments) they treated were always eliminated." Xu Deng's and Zhao Bing's abilities are reminiscent of the southern incantation skills described by Wang Chong (see "Varieties of Magic"). I suspect that Wang Chong had knowledge of the recipes of Yue when he composed his argument concerning the south, Yang vapor, and human breath.
Xu Deng and Zhao Bing were Later Han inheritors of magico-religious traditions that were already highly regarded in the second century B.C. The _Huainanzi_ relates that "people of Jing 荆 (i.e. Chu 楚) worship demons, people of Yue are habitual demon-worshippers" ( _Huainanzi_ , 18.306). Han references to Jing/Chu designate a broad geographical and cultural sphere in the central and eastern regions of the Yangzi, tending to overlap with Yue and Wu 吳 in the southeast. In addition, the deep south which stretched from Min to Southern Yue 南 越 (including present-day Fujian and Guangdong, and extending into Vietnam) was known as the land of various groups of Yue people. Thus references to Yue apply both to the southeast Yangzi region and the deep south.1 Yue magic and religion were officially sponsored by Thearch Wu around 110 B.C. when the Yue shamanka Yongzhi 贵 之 convinced Thearch Wu that Yue magic was not only spiritually potent, but was also the key to longevity (the reason for Thearch Wu's active patronage of recipe gentlemen). Thearch Wu ordered Yue shamans to establish cult sites for Yue _zhu_ 越 祝 (Yue incantation) at Chang'an; Yue-style worship and divination with chicken bones are said to have become popular as a result ( _Shiji_ , 28.33b; _Hanshu_ , 25B.1a–b).2 Thearch Wu's faith in Yue shamans and their magic was reconfirmed in 104 B.C. when the Arbor-vitae Beam Terrace 柏 梁 臺 burned. Thearch Wu followed Yongzhi's counsel regarding the Yue custom of averting the danger of fire by replacing a burned structure with an even larger one; and he built the grandest of his palace complexes, the Establishing Brilliance Palace 建 章 宫 ( _Hanshu_ , 25B.4b).
Zhang Heng 張 衡 (78–139) makes a stock allusion to "Yue shamans putting forth recipes" 越 巫 東 方 in the "Xijing fu" 西 京 賦 account of the building of the Establishing Brilliance Palace ( _Wenxuan_ , 2.6a). A later passage on a man known as Yellow Sire 黄 公 from Donghai 東 海 (present-day Shandong) is more suggestive of the occult tradition represented by the recipes of Yue during the Han:
Donghai's Yellow Sire, he of the red knife and Yue incantations.
He hoped to subdue the white tiger, and in the end could not be rescued. ( _Wenxuan_ , 2.16a–b.)
According to the Li Shan 李 善 commentary (seventh century): "In Donghai there was a man who was able with a red knife and the Pace of Yu to use the incantation method of the Yue people to subdue tigers, and who was called Yellow Sire." Various post-Han sources give anecdotal accounts of Yellow Sire, explaining how in old age his powers weakened and how he was eaten by a tiger when his magic failed to work.
The Yellow Sire's technique of Yue incantation surely represents the same magical tradition as Zhao Bing's recipes of Yue. Moreover, while the existence of cult sites for Yue incantation at Chang'an is significant evidence of the dispersal of Yue magic, the man who went by the alias Yellow Sire and hailed from present-day Shandong was not a Yue shaman but was an occult specialist like Xu Deng and Zhao Bing. Called either recipes of Yue or Yue incantation, by the first century A.D. Yue magic was being transmitted orally and in writing among occult specialists. The magical recipes in _MS_ I.E reflect the knowledge of Yue-style incantation in _fang_ -literature collected by the elite several centuries earlier.
The terms "recipes of Yue" and "Yue incantation" became obsolete after Han times. However, the _Baopuzi_ proves that southern breath magic continued to be transmitted:
In Wu and Yue there is a method for charm spells ( _jinzhou_ 禁 呪)1 that produces very clear results. It consists of augmenting the vapor (of the breath) and that is all. Those who know it can enter into the midst of a great pestilence and share the bed with a sick person without themselves being infected. Again, in a group of several tens of travelers, all can be made to lose their fear. This demonstrates that vapor can exorcise heavenly calamity. It may happen that evil goblins and mountain specters invade the home, throwing tiles and stones at people or setting fire to the roof. At times they manifest their forms as they go and come; at times only the sound of their speech is heard. If someone skilled at charms charms them with vapor, they all cease immediately. This demonstrates that vapor can charm demons and spirits. When entering mountains and forests where the land abounds in streams and poisonous snakes, none who venture there will not be attacked and injured. If someone skilled at charms charms them with vapor, they can be repelled for over a distance of several tens of square _li_ ; and none of his companions will suffer harm. Moreover, he can charm tigers and leopards as well as snakes and wasps, causing them all to lie prostrate and be unable to rise. If he charms a metal wound with vapor the blood stops flowing the moment it wells up. Moreover, he can reattach bones and reconnect muscles. If he charms a bare blade with vapor he can stamp on it without injury, and stab without having it penetrate. If a person is struck by a snake or viper and charms it with vapor, it is immediately cured. In recent times Zuo Ci 左 慈, Zhao Ming 趙 明,1 and others have used vapor to charm water, making the water flow in the opposite direction for one or two _zhang_. Or again, lit a fire on a thatch roof; cooked food and eaten it; and the thatch roof was not singed.2 Or again, nailed a large nail into a pillar seven or eight _cun_ and blown on it with the vapor (of the breath); and the nail popped out as if shot from a bow. ( _Baopuzi_ , 5.24.)
The enumeration of southern breath magic concludes with several more examples of vapor charms.
The mention of charming tigers and leopards brings to mind Yellow Sire and his Yue incantations which failed to subdue the white tiger; Zhao Bing's well-known expertise in the recipes of Yue is referred to directly. The everyday aspect of vapor charms is evident in the passage on demonic nuisances in the home. The Shuihudi "Jie" provides remedies for the same kinds of hazards. I expect that the techniques of spitting and spouting in the _MS_ I.E magical recipes were also used to rid the home of demons (note especially the exorcistic procession through the home to capture the child sprite in _MS_ I.E.277, and the incantation which summons a "spouter"). Vapor charms to stop bleeding and to cure snake bites have counterparts in _MS_ I.E.9 (even though recipe does not include spouting and spitting)1 and in several recipes for bites by poisonous creatures ( _MS_ I.E.48, 59). In short, there is good evidence to link the fourth century A.D. southern breath magic in the _Baopuzi_ not only with the recipes of Yue and Yue incantation, but also with the techniques of spouting and spitting in _MS_ I.E.
After the _Baopuzi_ description of Wu and Yue vapor charms, I have found only two likely references to the transmission of southern breath magic prior to the seventeenth century. The Li Xian 李 賢 (seventh century) commentary to the _Hou Hanshu_ account of Xu Deng and Zhao Bing notes that, "it is said that in Jiangnan the charm method of Lord Zhao to cure sickness is still being transmitted" ( _Hou Hanshu_ , 82B.9b). And Xue Bozong 薛 伯 宗, a fifth century southerner, knew the art of vapor charms:
Gongsun Tai suffered from (an abscess) on his back. Bozong sealed it with the vapor (of his breath) and transferred it, lodging it on the willow in front of the studio. ( _Nanshi_ , 32.18a.)
Xie Zhaozhe 謝 筆 淛 (1567–1624), from a prominent Fujian family, picks up the thread of the tradition in the _Wuzazu_ 五 雜 俎. His discussion of vapor charms follows that of shamans in Jiangnan and Min:
In antiquity those skilled at vapor charms could extract a spearhead from bone and transfer an abscess to a tree in the courtyard.2 As for being able to drive dragons and bind goblins, such things were all the easier to do! This is, to be sure, the genuine talisman spell-casting ( _fuzhou_ 符 呎) and not an illusory art. The various kinds of talisman spell-casting are all to be found in the Daoist Canon ( _Daozang_ 道 藏). One must simply undergo a process of refinement and training (to practice them). At present there are certain wandering monks who singe their eyebrows, set fire to their fingers, and go for up to thirty-five days without starving. They are not genuine possessors of the way. They are also able to perform vapor charms, but the spuriousness of their practices needs no discussion. ( _Wuzazu_ , 6.32b.)
Extracting spearheads, transferring abscesses, and binding goblins are activities consistent with the Wu and Yue vapor charms discussed in the _Baopuzi_. By placing the entry after the entries on Jiangnan and Min shamans, Xie Zhaozhe appears to have a regional tradition in mind. However, he is quite definite in attributing the genuine art to talisman spell-casting in the scriptures of the Daoist Canon. The local "wandering monks"—no doubt popular occultists—practice a false art.
Xie Zhaozhe's evaluation suggests one answer to why the record of the recipes of Yue vanished in medieval times. Quite simply, the popular use of charms, spells, and talismans was subsumed by religious Daoism. The use of magic in Daoism and the record of it in the Daoist Canon came to represent the genuine source in the minds of the elite and of popular occultists who would have tended to identify their practices with the prestige of Daoism.1 Moreover, breath magic in the later occult tradition was regarded as an extension of breath cultivation; the ability to perform incantations and spells was one of the fruits of cultivating vapor (the refining and training referred to in the _Wuzazu_ ). Already in the _Baopuzi_ the purpose of discussing Wu and Yue vapor charms was not to describe a notable southern tradition of breath magic for its own sake; the passage follows a discussion of macrobiotic hygiene which advocates ingesting drugs, circulating vapor, and sexual cultivation. The purpose of the passage on Wu and Yue vapor charms is to illustrate the importance and utility of vapor cultivation with examples of vapor's magical potency (hence the refrain of "this demonstrates that vapor can exorcise heavenly calamity" and "this demonstrates that vapor can charm demons and spirits").
Ideas about vapor must have already influenced the Warring States conception of the power of incantation and breath magic. However, in the third century B.C. the acts of spitting and spouting in _MS_ I.E were likely to have still been regarded as magical acts in themselves, not yet assimilated with vapor theory. Southern breath magic was grounded in magico-religious tradition, not in naturalistic or occult theories concerning vapor. The _Lunheng_ offers the first explanation of breath magic based on vapor theory (see "Varieties of Magic"). In the _Baopuzi_ we have the first references to the idea that breath magic is "augmenting vapor" and "charming with vapor," and the oldest statement linking breath magic to hygiene (religious Daoism also assumes the connection). The new rationale of breath magic would have tended to diminish the significance of a regional tradition of breath magic, for now the regional tradition was one example among others of phenomena associated with vapor and its cultivation. Along with the rise of religious Daoism, changes in the perception of breath magic also affected the old southern breath magic called recipes of Yue. Nevertheless, neither Daoism nor changed perceptions stifled its continued transmission.
Writing in the first quarter of the twentieth century, Chai E 柴 萼 argues that the current name for the Han recipes of Yue is Chenzhou _fu_ 辰 州 符 (Chen District talismans; Chen District is present-day Yuanling 沅 陵, several hundred kilometers west of Changsha):
The _Hou Hanshu_ , "Account of Recipes and Arts," states that Zhao Bing was skilled at the recipes of Yue. I note: The former Chen District in Hunan is the ancient region of Southern Yue.1 Thus it is also called Chen District talismans. In the _Nanshi_ , Xue Bozong was skilled at transferring abscesses. When Gongsun Tai suffered from (an abscess) on his back, Bozong transferred it for him onto a tree. Something like one _dou_ of yellow-red liquid came out (from the tree) and the tree withered because of it. Thus one already sees the transfer of illness by means of _zhuyou_ 祝 由 (incantations for removal) in the Northern and Southern Dynasties. ( _Fantianlu conglu_ , 33.28a.)
Whereas Xie Zhaozhe attributes breath magic to sources in the Daoist Canon, Chai E argues that an old southern tradition of breath magic lies behind the Chen District talismans. Chai E deserves credit for being the first scholar to identify the recipes of Yue with the Chen District talismans. His reason for making the identification requires explanation.
Like other Qing writers, Chai E understood medicine to contain thirteen divisions of which the thirteenth is the division of magical medicine, called _zhuyou_ ke 祝 由 枓 (division of incantations for removal). The _locus classicus_ of _zhuyou_ is in the _Suwen_.1 The classification of medicine into thirteen divisions is first attested in the fourteenth century in the _Chuogenglu_ 輟 耕 錄, which attributes the classification to the twelfth century Song medical compendium _Shengji zonglu_ 聖 濟 總 錄 ( _Chuogenglu_ , 15.227; the classification does not appear in extant editions of the _Shengji zonglu_ ). Chai E and other writers discuss magical medicine under the heading _zhuyou ke_ , and their examples mostly date to the Song and later. By linking the recipes of Yue, the Chen district talismans, and Xue Bozong's magical removal of the abscess in his entry on _zhuyou ke_ , Chai E breaks new ground with his claim that "the transfer of illness by means of _zhuyou"_ can be traced to the Northern and Southern Dynasties (i.e. third to sixth centuries A.D.). Chai E's purpose is to clarify the history of the _zhuyou ke_. He cites magical traditions besides the Chen District talismans in the entry; other writers cite still other magical traditions in their entries on _zhuyou ke_.2
The virtue of the idea of the _zhuyou ke_ is that regional traditions of magic became the focus of attention; magical medicine was not treated as just an adjunct of religious Daoism. One must bear in mind, however, that the Qing writers did not pursue research on the Chen District talismans or other magical traditions beyond noting their significance for the history of the _zhuyou ke_ ; nor did they cast themselves in the role of ethnographers. My thesis regarding southern breath magic is supported chiefly by several accounts of specialists in the Chen District talismans and occultists from Yuanling (who presumably practice the Chen District talismans) in sources like the _Qingbai leichao_ 清 稗 類 鈔. Evidence that might provide us with a better picture of the Chen District talismans in more recent times is lacking, although I suspect that written materials exist and that oral traditions are still alive in Hunan and elsewhere.3 I do not doubt that there have been changes in the tradition of magic whose most recent name is Chen District talismans; and that the Chen District talismans incorporate much Daoist magic (especially the use of talismans). At the same time, comparison of the _MS_ I.E recipes which make use of spitting and spouting (see the list in "Varieties of Magic" above) with the _Qingbai leichao_ accounts indicates to me that we are dealing with the same core tradition of breath magic, which has been transmitted in the region of Hunan and elsewhere in the south since at least the third century B.C.
The plausibility of my thesis is best illustrated by one _Qingbai leichao_ account, which has a counterpart in _MS_ I.E.27. The specialist in the Chen District talismans was an anonymous salt official from Hangzhou 杭 州 (Zhejiang):
There was a local man who had a sore on his back. A physician diagnosed it for him and it did not get better. The oozing and rotting became increasingly severe and the mouth of the wound was already about three _cun_ across. Then he went to the gate of the salt official and sought a diagnosis from him. He examined it closely and said, "Sir, your coming is already ten days delayed. Nevertheless I must remove it for you. Just ten days will be needed, then it will be cured." Thereupon he hooked his finger and drew a talisman. At the same time he applied an ointment. Further, he got a cup of pure water for (the patient) to carry home and place on the stove as an offering. He instructed him saying, "Tomorrow morning when you come again for diagnosis, bring along the water. I will cure (the sore) for you." The next morning the man arrived bearing the cup of water. Then he had him sit with his back facing east. Once again he hooked his finger and drew a talisman. He sucked up the water in the cup and spouted ( _pen_ 噴) it. Then he pinched the wound with three fingers, hurled (his hand) towards the wall, and there seemed to be a sound.1 Continuing, he covered (the wound) with an ointment and the mouth of the wound subsequently closed. After that, he took a talisman and pasted it on, saying, "You are better now." As for the man at this point, his ailment was as if vanished. ( _Qingbai leichao_ , vol. 30: 154.)
The magical operation in _MS_ I.E.27 could easily be taken for yet another of the salt official's Chen District talisman cures. The ailment is infant convulsions and may be related to a tetanus infection. The treatment focuses on drawing the demonic pathogen out from the opening of a wound, like the removal of the cause of the festering sore above. Let me quote the relevant part of the recipe:
Take vegetation from the upturned slope of the roof. Incinerate it using kindling and [1] it in a ladle. Make silted water that is roiled thrice and fill a cup with it. Then spit on the ladle and chant this incantation over it: "Spouter, spout ferociously. On high be like the sweeper star. Down below be like congealed blood. You will be seized left of the gate. You will be cut apart right of the gate. Should you not desist, you will be quartered and exposed in the marketplace." Then stroke with the ladle in a circle around the spot where the infant convulsions are, and rinse it in the cup of water. Watch it. When there is blood like a fly wing, discard it by the wall. Take fresh water. Once again spit on the liquid in the ladle1 and stroke with it as before. There should be no trembling. Repeat it over and over again. When the trembling has ceased, stop. Excellent.
The salt official drew talismans, spouted consecrated water on the sore and extracted the demonic pathogen from the sore with his fingers, hurling it at the wall. The related sequence of actions in _MS_ I.E.27 is as follows: the designated officiant spits on the ladle filled with roof vegetation ash (perhaps the ash has solar, exorcistic properties) and chants an incantation over it; the incantation commands a spouter to spout and exorcise the demonic agent, who is directly threatened with execution; with the power of the spouter transferred to the ladle, the ladle is then used to stroke the spot where the ailment is located (probably a wound); the demonic agent is caught by the ladle; once caught, the agent becomes manifest as blood in the shape of a fly wing in the rinsing water; and the rinsing water is discarded by the wall. The sequence of actions is repeated until the demonic pathogen is entirely removed, as indicated by cessation of trembling.
The salt official also drew talismans with his finger and chanted spells to remove a writing brush lodged inside a man's throat—the counterpart to vapor charms for removing nails from pillars which the _Baopuzi_ associates with occult specialists like Zhao Bing ( _Qingbai leichao_ , vol. 30: 154).1 A skeptic may object that there is simply not enough evidence to prove that the Chen District talismans, the recipes of Yue, and _MS_ I.E belong to a continuous tradition of breath magic. I admit that my argument is conjectural and that we will probably never have better evidence. However, I think the similarity between _MS_ I.E.27 and the salt official's use of the Chen District talismans coupled with historical references to southern traditions of incantation, to the recipes of Yue, and to southern vapor charms satisfy the burden of proof; it is up to the skeptic to prove me wrong.
1I take for granted the obsolescence of earlier theories which attempt to relate magic developmentally to either the history of religion or of science (with the implicit understanding that religion and science are more evolved civilizational forms); nor is magic simply degenerate religion. The issues arising from the question "what is magic?" in the Greco-Roman context are ably set forth by Phillips (1991).
1For medicine, I would mention Scarborough's masterly study of Greek pharmacology and magico-religious assumptions (1991). Lloyd's investigations of the formation of scientific ideas (especially medical ideas) within a broad context of natural philosophy and occult thought give new direction to the history of ancient science (1979).
2I use "ritual act" as a broad term for gestures ranging from the most simple to elaborate rituals. Thus "using the hem-band term from a robe to bind the thumb of the left hand once" in _MS_ I.E.114 is a ritual act, as is "scratching twice seven times with the middle finger" in _MS_ I.E.131. I also use the term "magical device," which overlaps with "ritual act" but refers additionally to strategies like timing and orientation or the use of certain materials.
1Yamada's identification of magical recipes in _MS_ I.E is more inclusive, counting forty-nine magical recipes to my thirty-nine (1985b: 256).
2The techniques for determining a child's fortune and for burying the afterbirth in _MS_ V.1–2 are based on astrological, calendrical, and hemerological ideas. Magic does not seem like the best description of them.
1I follow Hawkes in rendering _wu_ as "shaman" in view of the importance of spirit mediumism as the chief _wu_ specialty (1985: 42–51). _Wu_ ideas are thought to lie behind the Shang concept of divine kingship (the classic statement of the thesis is Chen Mengjia 1936). The exact identity of the shamans in Shang and Zhou society is far from clear. Warring States legends trace the origins of medicine, divination, and other skills to them. However, in Warring States society shamans underwent a decline in status. With the intellectual transformations of the Warring States period, physicians ( _yi_ 醫) participated in the text-based traditions of the other specialists in natural philosophy and occult knowledge. As I argue below, it is important to distinguish the continuing religious role of the shamans from the activities of these specialists. The connotations of the word _wu_ also changed. By Han times _wu_ was applied to what in English could be called "witchcraft"; and what was perceived as witchcraft was not simply the activities of shamans.
Mair (1990) argues that _wu_ /* _mjag_ is a loan from Old Persian _magus_ , and speculates on archaic contacts between China and the Near East, including migration of foreign magi to China. Mair's ideas are provocative, but I remain skeptical. In any case, they pertain to religion and magic prior to the Warring States transformations that concern me here.
1 Graham sums up received opinion when he contrasts what he regards as the folk-religious beliefs of the Mohists (a reflection of their lower social origins) with the general tendency in Warring States thought: "The tendency throughout the classical age is to ignore the spirits of the dead and of the mountains and rivers after paying them their customary respects, and to regard Heaven as an impersonal power responsible for everything outside human control, including the undeserved misfortune to which you resign yourself as your destiny" (1989: 47). The archaeological record (in particular the manuscripts under discussion) suggests that the elite tendency deduced from received literature is less general than has been supposed.
1Cloud vapor which enters the home covertly is remedied by building a fire ( _SHD_ : 215); the vapor of "Bug-misfortune" ( _yang_ 恙) causes a person's hair to stand on end ( _SHD_ : 214; Harper 1990: 227); the vapor of the "Whirling Wind" ( _piaofeng_ 飄 風) causes animals to speak to people ( _SHD_ : 212; Harper 1985: 495). Several entries also reify Yin and Yang as demons ( _SHD_ : 212, 214). On this point and for further discussion of the bivalence of _qi_ and _jing_ , see Harper 1990: 224–25.
2Yin Yang and Five Agent cycles provided a new _modus operandi_ for spirits and demons. See the preceding note for reification of Yin and Yang.
1The _Shiji_ account of the Warring States official Ximen Bao 西 門 豹 is paradigmatic. As the newly installed magistrate in a Yellow River district, Ximen is credited with eliminating the annual bride sacrifice made to the river god by tossing the head shamanka and her cohorts into the river in place of the local virgin required by the cult ( _Shiji_ , 126.12b).
2A version of the nightmare prayer in the Shuihudi hemerological manuscripts occurs in the Dunhuang _Baize tu_ , which is a medieval demonographic counterpart to "Jie" (Harper 1985; Harper 1988). The incantation text shared between _MS_ III.83 and the _Baopuzi_ is discussed in "Varieties of Magic" below.
3See Ngo 1976: 160, 195–202.
1Of course, the belief that illness was demonically inspired made faith-healing a key element of shaman cults and popular religion.
2Harper summarizes some of the material relevant to the history of incantation in early Chinese religion, for which the Shang bone and shell inscriptions provide the earliest documentation (1982: 69–79). As early as the Shang, the act of speaking to the spirits in incantation was complemented by written communication with them. Evidence of oral and written communication is discussed in Harper 1985: 472–74. It is worth noting that most Shang vocabulary for speaking and writing was originally related to spirit communication in religion; application to human communication was secondary. I suspect that the fundamentally sacred nature of speech itself continued to inform ideas about the magic of speech in Warring States, Qin, and Han times. Vocabulary for different types of incantations and written documents is attested in ritual books like the _Zhouli_ , along with the hierarchy of officiants charged with executing them (Harper 1982: 71). The influence of incantation on the writing of poetry is studied in Harper 1987a.
1Chinese incantations were enriched by Indic speech and pseudo-Indic speech following the introduction of Buddhism. The use of foreign speech meshed with religious Daoist ideas about celestial speech and script known only to initiates (Bokenkamp 1983: 462–65).
2Bodde studies the account and reviews earlier scholarship on it (1975: 75–138).
1For further speculation on the early vocabulary of magical utterances, see Harper 1982: 76–79.
1These matters are discussed in two essays: _Lunheng_ , "Dinggui," 22.453–54; and "Yandu," 23.459. As explained by Graham, the lists of correlations in the "Hongfan" predate the concept of a five-fold cycle in later Five Agent theory (1989: 340–56)
1When I first examined a transcription of _MS_ I.E in 1977 the occurrence of the Pace of Yu immediately reminded me of Granet's hypothesis, launching my research on the Mawangdui medical manuscripts.
2Granet traces the Pace of Yu to the ancient royal cult in which the shaman-king controlled the world by virtue of his contact with the spirits. The pace represents the themes of initiatory sickness and ecstatic trance which are universal in shamanism. Evidence in Shang bone and shell inscriptions suggests that the Shang king was the chief shaman and experienced shamanic sickness as part of his kingship (Harper 1982: 99–100). The _Fayan_ notes a Han "shaman pace" ( _wubu_ 巫 步) attributed to Yu: "In the past the chief of the Yao clan (i.e. Yu) controlled the water and earth and the shaman pace makes much of Yu" ( _Fayan_ , "Chongli," 10.28; the word _wu_ in _wubu_ probably connotes popular magico-religious tradition, not just the shaman cults).
1Andersen (1989–90) surveys the Pace of Yu in religious Daoism, where it is identified with the cosmo-ritual practice of _bugang_ 步 綱 (walking the guideline). I do not agree with Andersen's assumption that the Pace of Yu in the excavated manuscripts is already a cosmo-ritual walk as in religious Daoism.
1Not wanting to belabor the point, let me just note that it would be incautious to assume that solar associations can be used as the primary criterion for classifying various materials as magical. Yin Yang and Five Agent correlations also influenced people's perceptions, yet why something is magical cannot be explained by reference to correlative cosmology. Faraone's observations on attempts to explain why Greco-Roman binding spells were inscribed on lead are instructive (1991: 7).
2There are standard correlations between red and fire, Yang, heaven, and life; between black and water, Yin, earth, and death. I will not try to explain how these correlations are related to warding off the _yu_ 's attack with red and black clothing.
3Actually, only _MS_ I.E.67 specifies that the technique be performed after dark. The preference for the last day of the month may imply the night of the last day.
1For a summary of the political geography of the south in Former Han times, see Twitchett and Loewe 1986: 451–57. The Kingdom of Southern Yue was independent of Han rule until its defeat by Thearch Wu in III B.C.
2Thearch Wu's conquest of Southern Yue in III B.C. was the prelude to his sponsorship of Yue magic and religion. The Yue cult sites are mentioned again in _Hanshu_ , 28A–1.30a, and were known for their exorcisms (see _MS_ I.E.124).
1 _Zhou_ 呪 (spell) is interchangeable with _zhu_ 祝 (incantation).
1I.e. Zhao Bing.
2This feat is attributed to Zhao Bing in the _Hou Hanshu_ account.
1It is tempting to speculate that the missing penultimate word in _MS_ I.E.9 might be "spit," making the sentence read, "Draw five lines on the ground and [spit] on it."
2Alluding to Xue Bozong's feat.
1I of course do not fault the received record for failing to provide the kind of information that interests me; writing about regional magico-religious customs would have been of minor interest to most Chinese authors.
1Chai E's claim that Chen District belonged to Southern Yue is plausible, however his geographical argument to prove the identity of the recipes of Yue and the Chen District talismans is not entirely convincing. In the second century B.C. the kingdom of Southern Yue extended northwards from its center in present-day Guangdong to a frontier with Changsha and the ancient Chu region. Riegel (1976) discusses the border between Changsha and Southern Yue based on maps discovered in Mawangdui tomb 3. As for the recipes of Yue, Zhao Bing was from Dongyang in the old Yue heartland (present-day Zhejiang). While the name Chen District talismans as well as the occurrence of spitting and spouting in _MS_ I.E are significant evidence of the distribution of this southern breath magic in the region of present-day Hunan, the later appearance of the name Chen District talismans is not likely to have been because Chen District was geographically part of ancient Southern Yue.
1The Yellow Thearch asks why drugs and other therapies are necessary in the present age whereas he has heard that in antiquity "incantations for removal" were sufficient to cure ailments. Qi Bo replies that people of old enjoyed a simpler life and that as a result evil did lodge in their bodies; incantations sufficed to remove an ailment ( _Suwen_ 13, 4.2b).
2The _zhuyou ke_ is also discussed in _Qingabi leichao_ , vol. 30: 102; _Kechuang xianhua xuji_ , 1.4b; and _Jianhu guangji_ , 1.3a.
3In a study of the interpretation of talismans Chen Xiangchun (1942) refers to a book entitled _Chenzhou zhenben lingyan fuzhou quanshu_ 辰 州 真 本 靈 驗 符 咒 全 書 (Complete book of divinely verified talisman-spells in the genuine edition of Chen District), published in 1922. I have not been able to examine the book. The talismans cited by Chen are Daoist in nature, but it is possible that other parts of the book contain material related to the breath magic of the Chen District talismans tradition. I delivered a paper on the magical recipes in _MS_ I.E, the recipes of Yue, and the Chen District talismans at the International Symposium on Mawangdui Han Tombs in Changsha in August 1992 (Xia De'an 1994). I did not acquire new evidence while in Hunan.
1The demonic pathogen hitting the wall is the source of the noise.
1See _MS_ I.E.27 for comments on the meaning of this phrase.
1According to the account, the brush slowly emerged from the patient's throat as the salt official chanted.
TRANSLATION
Introduction
The Translation is based on the photographic reproduction and transcription of the Mawangdui medical manuscripts in _MWD_ , vol. 4. _MWD_ , vol. 4, assigns column (C) or slip (S) numbers to all of the manuscripts (the numbers appear both in the transcription and the photographic reproduction, excepting _MS_ II and _MS_ V). I provide column or slip numbers for each entry in the texts in parentheses at the beginning of the entry. Citations to _MWD_ , vol. 4, "Transcription," are to the appropriate columns or slips in the transcription portion of _MWD_ , vol. 4.
Because _MWD_ , vol. 4, does not take account of the editions of _MS_ I.B, _MS_ I.C, and _MS_ I.D in the Zhangjiashan _Maishu_ , I have made a new transcription of the three texts in Appendix 1. I explain my transcription method there, but I would like to note here that I do not attempt to produce a collated edition of the texts in question. Rather, I have used the more complete _Maishu_ editions to fill lacunae in the _MS_ I editions ( _MWD_ , vol. 4, "Transcription," resorts to filling many of the lacunae in _MS_ I.B based on text parallels in _Lingshu_ 10). I trust that the transcription in Appendix 1 is a fairer representation of the texts.
In order to explain my translation conventions, I must briefly review the _MWD_ , vol. 4, transcription conventions (set forth in the "Fanli" 凡例 at the front of the volume). I am grateful to Professor Li Xueqin, who performed the final editing of the "Transcription," for clarifications. The "Transcription" uses modern _kaishu_ 楷 書 graphs, changing some graphs to conform with current convention ( is written 飲, 衝 becomes 衝, etc.). Modern punctuation is used throughout (which at times I judge to be incorrect). Of three text markers in the original manuscripts, the dot • is retained in the "Transcription" (it is used most often before new entries or to distinguish one passage from another within a single entry in the texts). Two other markers are excised in the "Transcription": a double-bar sign = placed at the bottom right of a graph meaning that the graph is repeated ("Transcription" writes the graph twice); and a hook-like sign ᄂ that is used occasionally to punctuate words or phrases within a line of text.
Lacunae in the texts are either graphs that are judged to be illegible or places where the material of the manuscripts (silk, bamboo, wood) is actually destroyed. When lacunae occur and it is possible to estimate the number of missing graphs, each missing graph is marked in the "Transcription" with a box; if the number is indeterminable, a box with a slash through it is used. Missing graphs in lacunae are sometimes restored based on parallels within the text, with other Mawangdui medical texts, or with received literature. These emendations are indicated by placing heavy brackets around the graph(s). The "Transcription" does not identify the basis for the emendation in each instance, but Li Xueqin informs me that emendations based on received literature affect only _MS_ I.B, _MS_ II.B (another edition of _MS_ I.B), _MS_ III.91, and _MS_ V.3. In addition, if a graph is barely legible in the text and the transcription necessarily tentative, the graph is placed in the same heavy brackets. Finally, the heavy brackets are also used to emend the text when the "Transcription" judges that a graph has been erroneously omitted by the scribe; these emendations are always identified in the "Transcription" notes. When the "Transcription" judges that the scribe miswrote a graph, the graph deemed correct is placed in caret-shaped brackets < > after the graph in question.
Most of the graphs are readily identifiable. Quite often they are written without the signific (or "radical") usually used in received literature, but there is little difficulty in reading the intended word. The "Transcription" places the fuller graph in parentheses after the graph as written in the text. Sometimes the graph as written in the text is attested for the appropriate word and meaning in received literature, but it is a rare usage or is a loan graph. To facilitate reading, the "Transcription" again uses parentheses to indicate a more usual graph for the word in question; the same is true of variant graphs and simple cases of unattested graphs. When identification of a graph is problematic the "Transcription" notes often propose a solution, but the proposed graph is not introduced parenthetically into the text.
My translation is complete but for _MS_ II.B. Although it differs in small details from _MS_ I.B (see Appendix 1), I have decided to let the latter edition represent the text (a major reason for my decision is the number of lacunae in both editions and my judgment that _MS_ I.B is more similar to the _Maishu_ edition, leaving me less certain of emending _MS_ II.B). I do not rely on the punctuation in the "Transcription" and usually do not comment when my own punctuation differs. As a rule I accept the "Transcription," minus any of the material placed in heavy brackets, caret-shaped brackets, and parentheses. Between forty and fifty graphs have been mistranscribed in the "Transcription." Some are obvious printing errors, some involve fine points of transcription. Qiu Xigui (1992) is responsible for identifying most of the incorrect graph transcriptions; I discovered some during the course of my research. The revisions are noted in the Translation and are also listed in Appendix 2. In several instances the correct transcription of a graph remains difficult to determine (I am grateful to Li Xueqin for re-examining the photographic reproduction and giving me his considered opinion).
I accept most of the "Transcription" emendations (graphs placed in heavy brackets and caret-shaped brackets). When I accept them, I simply translate without comment. When I do not, I note my reasons. Words placed in brackets [ ] in the Translation indicate either that my acceptance of the "Transcription" emendation is tentative or that I am introducing an emendation of my own. Again, I note my reasons. Lacunae are indicated in the Translation with brackets as well, the enclosed arabic numeral representing the estimated number of missing graphs; [?] means that the number is indeterminable. Whenever lacunae leave me perplexed as to the meaning of the graphs before or after, I indicate these graphs with braces { } enclosing the number of graphs involved. I use parentheses sparingly as needed to fill out the meaning; and also to provide common English names for the drugs which are given in romanization.
The parenthetical graphs in the "Transcription" lie at the heart of text explication. It would be a dry exercise to note every instance when my reading of a graph differs from the parenthetical graph-gloss given in the "Transcription"; and I do not do so. My reading and interpretation of difficult graphs are discussed in the Translation notes, including of course the unattested and other problematic graphs discussed in the "Transcription" notes.
Reconstructions of Old Chinese are based on Li Fang-kuei's system as represented in Schuessler 1987 (I have removed tone markers used by Li and Schuessler). At times I have had to improvise, usually a matter of using the phonetic of a graph in the manuscripts as the basis for determining the reconstruction; and I bear the responsibility for any errors committed. Mostly the reconstructions serve to test the probability of phonetic loan graphs and to identify rhyming words in the incantations in _MS_ I.E.
Materia medica presents special difficulties. Traditional Chinese drug names are not like modern botanical, zoological, and chemo-mineratogical nomenclature. Whether we can know exactly which plant, animal, or mineral is denoted by the name is frequently open to doubt. The situation is all the more uncertain for Materia medica in the Mawangdui medical manuscripts. Items like cultivated grains, domesticated animals, foods and food products, common minerals (soils, salt, mercury, etc.), and manufactured articles are simply translated. Where appropriate, a technical identification is provided in the Index of Materia Medica, using _ZY_ as the standard reference. Most other plant, animal, and mineral names are romanized. If I am sufficiently confident of its identity, a common English name is placed in parentheses in the Translation (often I adopt the expedient of using the genus of the item in question). The scientific name is provided in the Index of Materia Medica, based on _ZY_. Many of these identifications should, of course, still be regarded with suspicion, but the possible continuities in traditional knowledge of materia medica leading up to the compilation of works like _ZY_ outweigh my skepticism. Other names are left in romanization. If there is room for speculation, likely identifications are discussed in the Translation notes.
Facsimiles of portions of _MS_ I.A (Fig. 1), _MS_ III (Fig. 13), and _MS_ VI.A (Fig. 17) are the work of Mr. Xu Datong. They are based on the photographic reproduction in _MWD_ , vol. 4, which while discernible—especially with bright light and magnifying glass—loses considerable clarity when reproduced itself. The facsimiles both illustrate the manuscripts and exemplify several types of script and calligraphic styles. Fig. 13 was also chosen to illustrate the _MS_ III.91 drawing of the female genitals. In addition, Mr. Xu has made facsimiles of eleven of the _MS_ II.C exercise drawings (Figs. 2–). The photographic reproduction of _MS_ II.C in _MWD_ , vol. 4, was supplemented by color photographs in Fu and Chen 1992: 148–50; and in Mawangdui Han mu boshu zhengli xiaozu 1979. The original is severely damaged; of the forty-four drawings we chose eleven that lend themselves to accurate replication (captions are also copied when they are legible in the photographs). A reconstruction of _MS_ II.C in Mawangdui Han mu boshu zhengli xiaozu 1979 provides renderings of all forty-four drawings, even the most fragmentary, and should be regarded as conjectural in many details. My parenthetical description of the _MS_ II.C drawings in the Translation is based on photographic reproductions, not on this reconstruction.
_MS_ I.A
Zubi Shiyi Mai Jiujing
足臂十一脈灸經
Cauterization Canon of the Eleven Vessels of the Foot and Forearm
_MS_ I.A.1 (CC1–4)
Foot1
Foot Great Yang vessel.2 It emerges3 in the hollow by the outer malleolus.4 Ascending, it penetrates the calf and emerges at the poples.1 A branch goes to the lower _xun_.2 The direct path penetrates the [1] and presses laterally on the spine.3 It [2] and ascends to the head.4 A branch at the lower part of the center of the forehead goes to the ear. The direct path penetrates the inner canthus of the eye and goes to the nose.
The ailments: ailing from the loss of function in the little toe;5 calf pain; cramping in the poples; buttock pain;6 the occurrence of hemorrhoids;7 waist pain; pain pressing laterally on the spine; [1] pain; nape pain; hand pain;8 coldness in the center of the forehead; the occurrence of deafness; eye pain; stuffy nose and bloody nose;9 continual seizure sickness.1 In all cases of ailing from these things, cauterize the Great Yang vessel.
Fig.1 Facsimile of _MS_ I.A.1–4
_MS_ I.A.2 (CC5–9)
Foot Minor Yang vessel. It emerges in front of the malleolus.2 A branch is situated in the bone.3 (The direct path) ascends4 and penetrates the outer edge of the knee.5 It emerges at the outer edge of the thigh and emerges at the side. A branch goes to the shoulderblade. The direct path penetrates the underarm, emerges at the nape and at the ear, emerges at the _zhen_ ,6 and emerges at the outer canthus of the eye.
The ailments: ailing from the loss of function in the (toe) next to the little toe;7 pain in the outer edge of the shin; coldness in the shin; pain in the outer edge of the knee; pain in the outer edge of the thigh; pain in the outer edge of the ham;8 pain in the side; [1] pain; the occurrence of _ma_ ;9 pain in the broken basin;10 neck lumps;1 deafness; pain in the _zhen_ ; pain in the front of the ear; pain in the outer canthus of the eye; swelling in the outer part of the side. In all cases of (ailing from) these things,2 cauterize the Minor Yang vessel.
_MS_ I.A.3 (CC10–12)
Foot Yang Brilliance vessel. It follows along in the shin. Ascending, it penetrates the knee, emerges at the thigh, and presses laterally on the lesser abdomen.3 Ascending, it emerges at the inner edge of the breast and emerges at the throat. It presses laterally on the mouth and, ascending, goes to the nose.
The ailments: ailing from the loss of function in the middle toe; shin pain; swelling in the knee; swelling in the abdomen; pain in the inner edge of the breast; swelling in the outer part of the [1]; cheekbone pain; stuffy nose4 and bloody nose; continual hotness with sweating; loss of flesh at the _cuo_ ;5 coldness in the center of the forehead. In all cases of ailing from these things, cauterize the Yang Brilliance vessel.
_MS_ I.A.4 (CC13–15)
Foot Minor Yin vessel. It emerges in the hollow by the inner malleolus. Ascending, it penetrates the calf and enters the poples.1 It emerges at the thigh, enters the abdomen, and follows along the inner [1] edge of the spine. It emerges at the liver,2 enters the upper side,3 and is attached to the tongue [1].
The ailments: ailing from hotness in the foot; pain in the calf;4 pain in the thigh; pain in the abdomen crossroads5 and the inner edge of the spine; liver pain; heart pain; feverishness of the heart;1 throat [4];2 tongue splitting;3 [1] exhaustion;4 rising [vapor];5 [2]; being continually parched;6 coughing accompanied by muteness and a craving to sleep. (In all cases of)7 ailing from these things, cauterize the foot Minor Yin vessel.
_MS_ I.A.5 (CC16–18)
Foot Great Yin8 vessel. It emerges at the inner edge of the big toe alongside the bone and emerges at the upper edge of the inner malleolus. It follows along1 the inner edge of the shin, [1] the inner edge of the knee, and emerges at the inner edge of the thigh.
The ailments: ailing from the loss of function in the big toe; pain in the inner edge of the shin; pain in the thigh; abdomen pain; bloated abdomen; _fu_ [1];2 no craving to eat; a tendency to belch; heart [1];3 a tendency for _zhou_.4 In all cases of ailing from these things, cauterize the foot Great Yin vessel.
_MS_ I.A.6 (CC19–24)
Foot Ceasing Yin vessel. It follows along in the big toe and, ascending, emerges at the inner edge of the shin. Eight _cun_ up, it intersects the Great Yin vessel.5 It [1] the inner part of the thigh and, ascending, enters in the _cuo_.6
The ailments: ailing from loss of flesh at the _cuo_ ; frequent urination; a craving to drink; swelling in the back of the foot; affliction with numbness.7 In all cases of ailing from these things, cauterize the Ceasing Yin vessel.
In all cases of having these five ailments and in addition suffering feverishness of the heart, death occurs. When ailments of the three Yin (vessels) create disorder,1 death occurs within ten days. If when pressing a vessel it is like three men triply pounding,2 death occurs within three days. When the vessels are severed for the time it takes to eat,3 death occurs within three days. When there is feverishness of the heart and in addition bloating of the abdomen, death occurs. When unable to sleep and in addition suffering feverishness of the heart, death occurs. When muck and leaking slop continually come out, death occurs.4 When ailments of the three Yin (vessels) are mixed with ailments of the Yang (vessels), it can be treated. As for ailments of the Yang (vessels), when the back seems to be streaming with hot water,5 death occurs. In the case of Yang (vessel) ailments where bones are broken and muscles severed, yet there are not Yin (vessel) ailments, death does not occur.6
_MS_ I.A.7 (CC25–26)
Forearm7
Forearm Great Yin vessel. It follows along the upper edge of the muscle1 and runs along the inner part of the upper arm.2 It emerges at the inner edge of the underarm and goes to the heart.
The ailments: heart pain; feverishness of the heart with belching. In all cases of ailing from these things, cauterize the forearm Great Yin vessel.
_MS_ I.A.8 (CC27–28)
Forearm Minor Yin vessel. It follows along the lower edge of the muscle3 and emerges at the lower edge on the inner part of the upper arm. It emerges at the underarm and runs to the side.
The ailments: pain in the side. In all cases of ailing from (these)4 things, cauterize the forearm Minor Yin vessel.
_MS_ I.A.9 (CC29–30)
Forearm Great Yang vessel. It emerges at the little finger and follows along the lower edge of the bone.5 It emerges at the lower edge of the upper arm, emerges at the outer edge of the shoulder, and emerges at the nape. It [3] outer canthus of the eye.
The ailments: pain in the outer edge of the forearm. In all cases of ailing from these things, cauterize the forearm Great Yang vessel.
_MS_ I.A.10 (CC31–32
Forearm Minor Yang vessel. It emerges at the middle finger, follows along the lower edge of the upper bone of the forearm,6 and runs to the ear.
The ailments: the occurrence of deafness; [1] pain. In all cases of ailing from these things, cauterize the forearm Minor Yang vessel.
_MS_ I.A.11 (CC33–34)
Forearm Yang Brilliance vessel. It emerges in the middle finger, follows along the upper edge of the bone,1 and emerges at the [2] of the upper arm. Ascending,2 it runs to the _zhen_3 and goes to the mouth.
The ailments: ailing from tooth pain; [4]. In all cases of ailing from these things, cauterize the forearm Yang Brilliance vessel.
In the above, the foot vessels are six; the hand vessels are five.
1 _Zu_ 足 (foot) is written in a raised position about one centimeter above the main text in C1. It serves as the heading for _MS_ I.A.1–6. Each of the six foot vessels occurs symmetrically on the left and right side, for a total of twelve vessels.
2温 represents the word _mai_ "vessel," which is consistently written with this graph throughout _MS_ I.A. It is composed of three parts: 血 (blood); 水 (water); and 目 (eye). According to _MWD_ , vol. 4, "Transcription," n. 2, the graph is composed of a variant form of 衇 (the graph for _mai_ attested in _SW_ , 11B.6b) with the addition of 目. The "Transcription" also notes that the graph occurs on Warring States seals, and thus may be a Warring States seal script graph for the word _mai_. Two other graphs are used to write _mai_ on _MS_ I. _MS_ I.B consistently writes 脈 (still using 目); and _MS_ I.E.1 writes 脈 (attested in _SW_ , 11B.6b). The reason for writing the graph with _mu_ /* _mj əkw_ 目 is not clear (it is definitely not a phonetic for _mai_ /* _mrik)_.
3The verb _chu_ 出 occurs many times in _MS_ I.A–B when describing the path of the vessels. All occurrences are uniformly translated "emerge," in the sense of "rise forth." According to _SW_ , 6B.2b, _chu_ means "advance" and the graph depicts a plant rising. Like English "emerge," _chu_ includes the sense that something becomes apparent, that it "rises into notice." When _chu_ is used at the beginning of a vessel description, as in the present case, it designates the point from where the vessel arises (see _MS_ I.B.1 and _MS_ I.B.4 for examples of other words used to denote a vessel's point of origin). Ma Jixing argues that occurrences of _chu_ at subsequent points in a vessel description mean simply "ascend" or "reach" (1992: 176, n. 11). I suspect that the sense of "rise into notice" is applicable, and that _chu_ means not only that the path of the vessel reaches a particular point on the body, but also that the presence of the vessel is detectable at that point.
4 _Huai_ 踝 denotes the bony prominence on either side of the ankle (see _SW_ , 2B.24a); i.e. the malleolus. For the most part the use of "outer" and "inner" as well as "upper" and "lower" to designate positions on the body in _MS_ I.A–B is readily comprehensible. However, in some contexts the use of _nei_ 内 is ambiguous, since it also means "in" or "inside" in addition to designating an "inner" surface in contrast to an "outer" surface on the exterior of the body.
1胎 in _MWD_ , vol. 4, "Transcription," should be transcribed as 谻, which represents the word _xi_ , written 郄 in _Suwen_ 41, 11.7a. According to the Wang Bing commentary, _xi_ denotes the place at the center of the back of the knee where there is a fold in the skin; roughly the center of the poples.
2膓 is not attested in received literature; the reading _xun_ is conjectural, based on reading 旬 as the phonetic. Wei and Hu argue that the graph may be a phonetic loan for _tun_ 臀 (buttock; 1992, vol. 1: 2, n. 6). Phonological evidence does not support a loan between _xun_ /* _sgwjin_ and _tun_ /* _d ən_; hence I do not accept the proposed loan usage. It is worth noting that Li Fang-kuei's reconstruction of a velar in the Old Chinese initial of _xun_ departs from Karlgren (1957), who reconstructs a dental affricate. Ma Jixing argues that the graph is a phonetic loan for _shen_ /* _sthjin_ 胛, attested at _SW_ , 4B.23b, as a term for the flesh that presses laterally on both sides of the spine (1992: 177, n. 14). Thus the "lower _xun_ " would designate a point at the lower end of the spine. Ma's proposed loan usage is arguable and I am not firmly convinced. For the time being I leave the graph unidentified.
3"Press laterally" translates _jia_ 來. The meaning is that the left and right foot Great Yang vessels pass along either side of the spine. All other occurrences of _jia_ in describing the path of the vessels have the same meaning; e.g. _MS_ I.A.3, "press laterally on the lesser abdomen" and "press laterally on the mouth."
4I follow Ma Jixing in reading 豆 as _tou_ 頭 (head), and not as a word for the nape as suggested in _MWD_ , vol. 4, "Transcription" (1992: 177, n. 20).
5"Loss of function" translates _fei_ 癈. See _Lingshu_ 10, 3.8b, for an example of the medical sense of _fei_ in connection with the vessels: "When (the vessel) is full then the joints grow slack and the elbow has loss of function ( _fei_ )." The sense of _fei_ includes numbness as well as physical impairment.
6睢 (read _shui_ ) in _MWD_ , vol. 4, "Transcription," should be transcribed as 脽, which is attested in _SW_ , 8A.71b, as a variant graph for _tun_ "buttock." _Shui_ also denotes "buttock," and is glossed with _tun_ in _SW_ , 4B.25b.
7On hemorrhoids ( _zhi_ 痔) see _MS_ I.E.142.
8Because the hand does not lie on the path of the foot Great Yang vessel, Ma Jixing proposes reading _shou_ 丰 as the homophonous 首 "head" (1992: 181, n. 12). While there is reason for suspicion about the graph written in the text, the evidence is insufficient and I do not accept Ma's reading.
9尪 in _MWD_ , vol. 4, "Transcription," should be transcribed as 尪. The graph represents the word _qiu_ , written 鼽 in _SW_ , 4A.17a, a defined as "ailing from coldness affecting the nose so that it is blocked." _SW_ , 5A.51a, defines _niu_ 衄 as "blood coming out from the nose."
1"Seizure" translates _dian_ 癲 (see _MS_ I.E.71).
2The outer malleolus must be understood here.
3Ma Jixing suggests that the bone is the malleolus (1992: 184, n. 4), but the shinbone is also plausible. Ma also cites evidence for understanding _jian_ 間 in the sense of "in, inside."
4Usually _MS_ I.A explicitly distinguishes a branch path from the main path of the vessel with the phrase 其 直 者 "the direct path." I have added the phrase parenthetically for clarity.
5 _MS_ I.A–B regularly use _lian_ 廉 (edge) to add specificity to the identification of points on the exterior of the body.
6臈 is not attested in early sources. It is attested later as a variant graph for _nan_ 腩, which refers to a form of cooked meat (Morohashi 1957–60, vol. 9: nos. 29692–29693). The reading _zhen_ /* _tj əm_ is based on the phonetic 甚. _MWD_ , vol. 4, "Transcription," reads the graph as a phonetic loan for _zhen_ /* _tj əm_ 枕 (headrest), and interprets it as a reference to the occipital bone based on _Suwen_ 60, 16.4a. The argument is plausible. Equally plausible is the argument cited in _KGS_ , vol. 1: 90, n. 29, that the graph is a phonetic loan for _zhun_ /* _tj ən_ 肫, defined as "cheekbone" in _SW_ , 4B.20b. The difference of consonant *- _n_ in place of *- _m_ does not invalidate a phonetic loan. Luo and Zhou cite evidence which suggests that several groups of words with consonant *- _m_ already changed to *- _n_ in some Former Han dialects (1958: 53). Hence 臈 may have already been read * _tj ən_ in the dialect reflected in _MS_ I.
7I.e. the fourth toe. The phrase in the original text consists of three graphs 小 指 次, literally "(the one) next to the little toe." _MWD_ , vol. 4, "Transcription," emends the text by adding a fourth graph 指 "toe" to the end of this phrase, arguing that it was omitted due to scribal error. I judge the text to be acceptable as written.
8"Ham" translates _bi_ 髀, defined as "outer part of the thigh" in _SW_ , 4B.15a. My translation derives from the use of _bi_ to gloss _tun_ "buttock" in _SW_ , 8A.71b, which indicates that the "outer thigh" denotes the buttock and back part of the thigh; i.e. the ham.
9 _MWD_ , vol. 4, "Transcription," n. 4, and Ma Jixing (1992: 188, n. 7) both identify _ma_ 馬 as an abbreviation of _madao jiaying_ 馬 刀 倈 癭, which is attested in _Lingshu_ 10, 3.6a (in the description of the foot Minor Yang vessel), as the name for lumps (probably scrofula) that appear by the underarm ( _madao_ ) and the neck ( _jiaying_ ). _Ma_ also occurs as an ailment name in the Zhangjiashan _Maishu_ , "Ailment List": "When it is located below the underarm—it is _ma_ " ( _MSSW_ : 72). Although _ma_ and _madao_ are both said to occur in the underarm region, I remain skeptical of the identity between the two ailment names. The ailment name _madao_ was probably derived from the resemblance of the lump to a type of mussel known as _madao_. I question whether _ma_ in _MS_ I.A.2 and in "Ailment List" can be an abbreviation of the proper name of the mussel. Another possible explanation is to identify _ma_ with _ma_ 癜, which occurs in _MS_ I.E.280–82. From the descriptions there, the ailment is characterized by the formation of pustules on the face which burst.
10"Broken basin" _(quepen_ 缺盆) denotes the clavicle (see _Shiji_ , 105.20a, and commentary).
1 _Lou_ 瘦 is defined as "swellings on the neck" in _SW_ , 7B.29a—most likely scrofula. _Maishu_ , "Ailment List," also specifies that _lou_ is an ailment located on the neck ( _MSSW_ : 72). Ma Jixing cites evidence for identifying _lou_ as a kind of abscess and argues that _lou_ in _MS_ I.A.2 refers more generally to this condition rather than specifically to lumps on the neck (1992: 188, n. 10). Ma's identification of _lou_ is in part related to the fact that if _lou_ denotes "neck lumps" it overlaps with the same kind of scrofulous ailment that Ma has already identified with the ailment name _ma_ above.
2 _MWD_ , vol. _4_ , "Transcription," emends the text by adding 病 on the presumption that the final sentence in each vessel description in _MS_ I.A should begin 諸 病 此 物 者, as in _MS_ I.A.1. I judge the phrase as written to be scribal abbreviation and would not emend the text (adding words parenthetically for clarity).
3According to _Shiming_ , 3.61, _shaofu_ 少 腹 (lesser abdomen) is the name for the part of the abdomen that lies below the navel. Medical literature also refers to this region as the "small (小) abdomen."
4尪 in _MWD_ , vol. 4, "Transcription," should be transcribed as 尪 (see _MS_ I.A.1).
5From the context here and in two later occurrences in _MS_ I.A.6, _cuo_ 脞 is the name of a part of the body. The graph is attested in pre-Han literature meaning "small" or "chopped" (Morohashi 1957–60, vol. 9: no. 29508). _MWD_ , vol. 4, "Transcription," n. 4, argues that in all three occurrences the graph is a scribal error for _bi_ 陛. The earliest attestation of _bi_ is in medieval sources where it designates the upper thigh region. I am skeptical that a scribe would commit the same error thrice; and I suspect that the graph as written is a phonetic loan for an anatomical term. Zhou and Xiao (1988: 9, n. 13) cite an argument that _cuo_ /* _tshuar_ is a loan for _zui_ /* _tshu əd_ 睃, which is attested as a word for the penis (see _MS_ I.E.134). In _MS_ I.A.6 the path of the foot Ceasing Yin vessel terminates at the _cuo_ ; and according to _Lingshu_ 10, 3.6b, the foot Ceasing Yin vessel passes by the genitals on the way to the lesser abdomen, stomach and liver. Thus the argument is plausible. My own proposal is to identify _cuo_ /* _tshuar_ with _duo_ /* _duar_ 隋. The latter graph occurs several times in _MS_ I.E; although it is also unattested; it probably denotes the navel (see _MS_ I.E.88). This speculation receives added support from _Maishu_ , "Ailment List," where there is the following description of a type of _jia_ 瘕 (conglomeration): "When on the inside it constricts the _duo_ (navel?), so that there is no passage from above to below—it is feces conglomeration" ( _MSSW_ : 72). Assuming that cuo refers to the navel in _MS_ I.A.3, there remains the problem of explaining what it means to have a "loss of flesh at the navel." Perhaps it refers to an ailment similar to the one described in "Ailment List" when the _duo_ becomes "constricted." An analogous condition is described in _Lingshu_ 29, 6.1a: "When above the navel ( _ji_ 臍) the skin is hot and it is hot inside the intestines, then (the feces) expelled are yellow like gruel; when below the navel the skin is cold and it is cold inside the stomach, then the abdomen becomes bloated." Further speculation in the absence of more certain evidence seems unwise.
1谻 in _MWD_ , vol. 4, "Transcription," should be transcribed as 谻 (see _MS_ I.A.1).
2The reference to the liver is intended to describe the path that the vessel takes and is not related to the correlation between internal organs and vessels as described in _Lingshu_ 10. According to _Lingshu_ 10, 3.4b, the foot Minor Yin vessel is associated with the kidney. _KGS_ , vol. 1: 93, n. 43, argues that the reference to the liver should not be interpreted as meaning the internal organ itself, but rather a location on the surface of the body corresponding to the internal position of the liver. The argument is plausible since _MS_ I.A–B generally specify external points on the body or points near the surface when describing the path of a vessel; further, they treat the vessels as a set of separate paths in the body that are neither interconnected nor connected to the internal organs.
3According to _SW_ , 4B.24b, _qu_ 胠 specifies the region of the side below the underarm, hence the translation "upper side."
4Ma Jixing argues that _nei_ 内 in this phrase means the "inner surface" of the calf, not "in" the calf; and Ma adopts the same interpretation of _nei_ at various points below (1992: 194, n. 2). I agree that in the descriptions of the vessel paths, which locate a vessel mainly by reference to external points, _nei_ occurring by itself refers to the "inner surface"; e.g. _MS_ I.A.6 ("the inner part of the thigh") and _MS_ I.A.7 ("the inner part of the upper arm"). However, in the ailment lists I suspect that _nei_ alone simply means "in."
5The _term fujie_ 腹 街 (abdomen crossroads) is not attested in received literature. Ma Jixing (1992: 194, n. 4) associates the term with _qijie_ 氣 街 (vapor crossroads), which has two meanings in medical literature. It is used to name four regions of the body where vapor collects in the process of being transported, one of which is the abdomen (see _Lingshu_ 52, 8.7b). And it is the name of an acupuncture point on the groin (see _Lingshu_ 10, 3.2a). In either meaning, the concept of _qijie_ relies on medical theories that are absent from _MS_ I.A–B. In my judgment the term cannot be used to interpret _fujie_ in _MS_ I.A.4.
1"Feverishness of the heart" translates _fanxin_ 煩 心, an ailment name that also occurs as _xinfan_ (see _MS_ I.A.7). In _MS_ I.A.6, _MS_ I.B.7, and _MS_ I.B.8, _fanxin_ is associated with incurable, fatal conditions in the vessels. Although _fanxin_ occurs many times in the _Huangdi neijing_ , I am not convinced that its meaning there is the same (see Ma Jixing 1992: 250, n. 2, for one definition). It should also be noted that there was an older concept of _fanxin_ that did not rely on vessel theory. _Fan_ itself refers to a burning, feverish pain that disturbs a person's mental and physical composure (Yu Yan 1972: 172) _. Hanfeizi_ 34, 13.247, uses _fanxin_ to describe a condition of unbearable pain. And the Shuanggudui _Wanwu_ includes a fragment concerning a drug that _"stops fanxin"_ (Fuyang Han jian zhenglizu 1988: 36).
2I follow Ma Jixing in reading 洇 as _yan_ 咽 (throat; 1992: 195, n. 9). _MS_ I.B.9 includes throat-related ailments in the description of the foot Minor Yin vessel. The ailments following the lacuna contain more textual problems which may be resolved by referring to the text of _MS_ I.B.9.
3I follow Ma Jixing in reading _lu_ /* _glag_ 車各 as a phonetic loan for _ce_ /* _thrak_ 拆 (1992: 195, n. 10). While the phonological evidence is arguable, the parallel in _MS_ I.B.9 which reads _shece_ 舌 拆 (tongue splitting) is convincing.
4I follow Ma Jixing in reading _dan_ /* _tan_ 旦 as a phonetic loan for homophonic 癉 based on the parallel in _MS_ I.B.9 (1992: 195, n. 11). _SW_ , 7B.33b, glosses _dan_ as an "exhaustion ailment." For discussion of _dan_ as a type of exhaustion associated with hotness, see Yu Yan 1972: 144. Ma Jixing interprets the ailment differently (see _MS_ I.B.9).
5I follow Ma Jixing in filling the lacuna with 氣 based on the parallel in _MS_ I.B.9 (1992: 195, n. 12). The ailment concerns the contrary movement of vapor in the vessels (see _MS_ I.B.1).
6 _MWD_ , vol. 4, "Transcription," reads 臈 as _he_ 喝 (hoarse). I agree with Qiu Xigui that the graph should be read as _ke_ 渴 (parched, thirsty; 1992: 529).
7 _MWD_ , vol. 4, "Transcription," emends the text by adding 諸. The emendation is unnecessary.
8陽 in _MWD_ , vol. 4, "Transcription," is a printing error for 陰.
1循 in _MWD_ , vol. 4, "Transcription," should be transcribed as 楯; the meaning, however, is the same as other occurrences of _xun_ 循 (follow along).
2Wei and Hu argue that _fu_ 復 should be read as 腹 "abdomen" (1992, vol. 1: 10, n. 3). Even though the two previous occurrences of the word for "abdomen" are written with the usual graph, the reading is plausible.
3The ailment must be either "feverishness of the heart" or "heart pain."
4 _MWD_ , vol. 4, "Transcription," n. 1, suggests reading _zhou_ 肘 as _zhou_ 疛. The latter is glossed in _SW_ , 7B.29a, as "ailment of the heart and abdomen." _Maishu_ , "Ailment List," describes _zhou_ , written with the graph 肘, as a type of "vapor conglomeration" ( _qijia_ 氣 瘕): "As for _zhou_ , when it arises from the spine and chest causing the abdomen to become bloated, and it is eased slightly when vapor (i.e. breath) is obtained—it is vapor conglomeration" ( _MSSW_ : 72). The reference to "obtaining vapor" suggests that the ailment is accompanied by shortness of breath.
5Based on the description of the foot Ceasing Yin vessel in _MS_ I.B.8, the lower point of reference for the upward measurement of eight _cun_ must be the inner malleolus.
6See _MS_ I.A.3 on _cuo_ and my conjecture that it refers to the navel. In _MS_ I.B.8 the path of the foot Ceasing Yin vessel is said to pass from the lesser abdomen (located below the navel) upwards to the canthi. Although the identification of _cuo_ remains speculative, reference to the navel in _MS_ I.A.6 would be a logical counterpart to the lesser abdomen in _MS_ I.B.8.
7"Numbness" translates _bi_ 痹. _Maishu_ , "Ailment List," describes _bi_ as follows: "When it is located on the body, and (the person) is in a stunned state so when he is [1] he has no feeling—it is _bi_ " ( _MSSW_ : 72). For further discussion of the association of _bi_ with numbness, see Yu Yan 1972: 229–32.
1I.e. the foot Minor Yin, Great Yin, and Ceasing Yin vessels.
2The phrase likens the abnormal, erratic pulse in a vessel to the pounding action of pestle in mortar when three people pound simultaneously. The phrase "like triply pounding" also occurs in _Suwen_ 20, 6.10b, to describe an abnormal pulse.
3To say that the vessels are severed means that the pulse in the vessels ceases. The term _shiqing_ 食頃 in Han texts refers to the amount of time required to consume a meal, not to simply swallow a mouthful of food. I do not know how many minutes a meal was supposed to last, and depending on the context the exact duration of _shiqing_ seems to range from a few moments to a rather longer stretch of time. A passage in _Suwen_ 63, 18.2a–3a, describes the length of time following acupuncture therapy before the patient recovers using four terms to indicate relative time: _li_ 立 (immediately); _youqing_ 有 頃 (some time); _shiqing_ ; and _xing shili qing_ 行 十 里 頃 (the time it takes to travel ten _li_ ). By implication, "the time it takes to eat" is longer than "immediately" and "some time."
4"Muck and leaking slop" translates _tangxie_ 溏 泄, referring to diarrhea-like conditions. _Tang_ is glossed as "muck" in _Guangya_ , 5A.5b. I translate the two words as two ailment names because of _Maishu_ , "Ailment List," which describes two ailments, one _tangjia_ 溏 瘕 (muck conglomeration) and the other _xie_ : "When it is located in the intestines, is painful, nothing transforms, and slop leaks out _(xie_ ; here the word describes a symptom)—it is muck conglomeration"; "When immediately after eating (the food) is discharged—it is leaking slop" _(MSSW_ : 72). It is also possible that _tangxie_ is a single ailment name in _MS_ I.A.6, since the compound occurs in _Suwen_ 69, 20.3b; and in _Suwen_ 74, 22.6b.
5I.e. a hot sweat.
6The Yang vessels are associated with heaven and external things, hence the association of external injuries with the Yang vessels. This idea is stated explicitly in _MS_ I.D. However, in _MS_ I.D broken bones and severed muscles are regarded as fatal in connection with Yang vessel ailments.
7 _Bi_ 臂 (forearm) is written in a raised position about one centimeter above the main text in C25. It serves as the heading for _MS_ I A.7–11. _Bi_ can also refer to the entire arm. I adopt the narrower meaning because the vessel descriptions in _MS_ I.A–B regularly use _bi_ to specify the forearm and another word for the upper arm. Each of the five forearm vessels occurs symmetrically on the left and right side, for a total of ten vessels.
1The muscle is the muscle of the forearm, and the reference to the upper edge is to the radius (or thumb) side of the forearm (see Ma Jixing 1992: 208, n. 2; and _KGS_ , vol. 1: 97, n. 68).
2"Upper arm" translates _ru_ 臑, which usually denotes the forequarter of an animal in Han sources ( _SW_ , 4B.24b). _Lingshu_ 10, 3.1a, attests to medical usage denoting the arm from the elbow to the shoulder. _Zou_ 揍 is well attested in received literature in the sense of _zou_ 走 (run; see Ma Jixing 1992: 208, n. 3).
3The lower edge of the muscle is on the ulna (or little finger) side of the forearm (see Ma Jixing 1992: 210, n. 2; _KGS_ , vol. 1: 97, n. 68).
4 _MWD_ , vol. 4, "Transcription," emends the text by adding the graph 此. The emendation is unnecessary.
5The bone must be the ulna.
6I.e. the lower edge of the radius.
1I.e. the upper edge of the radius.
2 _MWD_ , vol. 4, "Transcription," places a comma after 上, connecting it to the preceding sentence. In this instance _shang_ clearly has the meaning "ascend," and should be read as translated.
3See _MS_ I.A.2.
_MS_ I.B
Yinyang Shiyi Mai Jiujing, Jiaben
陰陽十一脈灸經甲本
Cauterization Canon of the Elevenyin and Yang vessels, ED. A
_MS_ I.B.1 (CC35–38)
Great Yang vessel. It is attached to the heel, in the outer malleolus. It emerges in the poples. Ascending, it bores the buttock, emerges in the hip joint,1 and presses laterally on the spine. It emerges at the nape, ascends the corner of the head,2 descends the center of the forehead, presses laterally on the bridge of the nose, and is attached to the inner edge of the eye.
When this (vessel) is moved, one ails from:3 dashed head;4 the eye is as if being torn; the nape is as if being axed; chest pain; the waist is as if being snapped; the ham cannot rotate;1 the upper side is as if knotted; the calf is as if being ripped. These constitute heel reversal.2 For these (ailments), the Great Yang vessel controls the treatment.
The ailments that it produces are: head pain; ear deafness; nape pain; strain in the _qian_ ;3 cold and hot syndrome;4 back pain; waist pain; buttock pain; hemorrhoids; pain in the upper side;1 calf pain; numbness in the little toe—making twelve ailments.
_MS_ I.B.2 (CC39–42)
Minor Yang vessel. It is attached to the front edge of the outer malleolus. Ascending, it emerges at the outer part of the fish-thigh2 and emerges at the side. Ascending, it emerges at the front of the ear.
When this (vessel) is moved, one ails from: pain in the heart and side; inability to turn from side to side; when severe, lacking fat;3 the foot turning outward. These constitute Yang reversal.4 For these (ailments), the Minor Yang vessel controls the treatment.
The ailments that it produces are: [3] pain; nape pain; side pain; cold and hot syndrome; sweating; pain in all the joints; pain in the edge of the ham; pain in the fish-thigh; pain in the outer edge of the knee; shaking from coldness; numbness in the middle toe—making twelve ailments.
_MS_ I.B.3 (CC43–47)
Yang Brilliance vessel. It is attached to the outer edge of the shinbone and ascends following along the shin. It bores the kneecap and emerges at the edge of the fish-thigh. Ascending, it bores the breast, bores the cheek, emerges at the outer edge of the eye, and circles the center of the forehead.
When this (vessel) is moved, one ails from: shivers and ailing from coldness; fondness for stretching;1 continual yawning; blackness in the center of the forehead;2 ailing from swelling; when severe,3 detestation for people and fire; when hearing the sound of wood, panicked alarm;4 panicky heart; the desire to close doors and windows and dwell in isolation; when the ailment is severe, the desire to mount high and sing, and to cast off clothing and ran. These constitute shin reversal. For these (ailments), the Yang Brilliance vessel controls the treatment.
The ailments that it produces are: pain in the center of the forehead; stuffy nose; neck pain;5 breast pain; calf pain;6 pain in the heart and the upper side; swelling in the outer part of the abdomen; intestinal pain; knee rigidity;7 numbness in the back of the foot—making ten ailments.
_MS_ I.B.4 (CC48–49)
Shoulder vessel.8 It arises behind the ear, descends the shoulder, and emerges at the inner edge of the elbow.9 It emerges at [3],10 and mounts the back of the hand.
When this (vessel) is moved, one ails from: swelling and pain in the neck; inability to look back; the shoulder is as if being torn; the upper arm is as if being snapped. For these (ailments), the shoulder vessel controls the treatment.
The ailments that it produces are: neck pain; throat numbness; shoulder pain; pain in the outer part of the elbow—making four ailments.
_MS_ I.B.5 (CC50–51)
Ear vessel.1 It arises at the back of the hand and emerges at the outer part of the forearm between the two bones, at the lower edge of the upper bone.2 It emerges at the elbow and enters the ear.
When this (vessel) is moved, one ails from: ear deafness with blurring; swelling in the throat. For these (ailments), the ear vessel controls the treatment.
The ailments that it produces are: pain in the outer canthus of the eye; cheek pain; ear deafness—making three ailments.
_MS_ I.B.6 (CC52–53)
Tooth vessel.3 It arises at the index finger and thumb, emerges at the upper edge of the forearm, enters the elbow, and mounts the upper arm. It bores the cheek, enters the teeth, and presses laterally on the nose.
When this (vessel) is moved, one ails from: tooth pain; cheekbone swelling.4 For these (ailments), the tooth vessel controls the treatment.
The ailments that it produces are: tooth pain; cheekbone swelling; yellowing of the eye; dry mouth; upper arm pain—making five ailments.
_MS_ I.B.7 (CC54–57)
Great Yin vessel. This is the stomach vessel.1 It goes alongside the stomach,2 emerges at the lower edge of the Yin part of the fish-thigh3 and at the upper edge of the calf, and emerges at the upper edge of the inner malleolus.
When this (vessel) is moved, one ails from: (vapor) ascending [1] and racing to the heart;4 bloated abdomen; a tendency to belch; wanting to vomit after eating—when able to defecate and pass vapor5 there is welcome relief. For these (ailments), the Great Yin vessel controls the treatment.
The ailments that it produces are: feverishness of the heart by itself—death occurs; heart pain and bloated abdomen—death occurs; inability to eat, inability to sleep, and strained yawning—when the three are combined, death occurs; muck and leaking slop—death occurs; water and blockage—when combined, death occurs6—making ten ailments.
_MS_ I.B.8 (CC58–61)
Ceasing Yin vessel. It is attached to the clump of hair on the big toe. It mounts the upper edge of the back of the foot, one _cun_ away from the inner malleolus. It rises five _cun_ above the malleolus and emerges behind the Great Yin (vessel).1 Ascending, it emerges at the inner edge of the fish-thigh, encounters the lesser abdomen, and presses laterally2 on the canthi.
When this (vessel) is moved, one ails from: in men, inguinal swelling3 and _shan_ ;4 in women, swelling in the lesser abdomen; waist pain; inability to raise the head skyward; when severe, the throat is dry; facial blemish. For these (ailments), the Ceasing Yin vessel controls the treatment.
The ailments that it produces are: internal hotness; urine retention;5 inguinal swelling; _pian; shan_6—making five ailments. If in addition to these five ailments there is feverishness of the heart, death occurs—there is no treating it. If there are Yang vessels with ailments at the same time, it can be treated.
_MS_ I.B.9 (CC62–66)
Minor Yin vessel. It is attached to the outer edge of the inner malleolus, bores the calf, and emerges at the center of the poples. Ascending, it bores the inner edge of the spine, is attached to the kidney,1 and presses laterally on the tongue.
When this (vessel) is moved, one ails from: hoarse panting; when rising from a sitting position the eyes become clouded as if sightless; the heart is as if suspended; ailing from hunger; insufficiency of vapor;2 a tendency to become angry; paiucky heart with the fear that one is about to be seized by someone; no desire to eat; the face is moldy black3 like the color of lampblack; when coughing, there is blood. These constitute bone reversal. For these (ailments) the Minor Yin vessel controls the treatment.4
The ailments that it produces are: hotness in the mouth; tongue splitting; throat dryness; rising vapor;1 choking; pain in the throat; exhaustion;2 a craving to sleep; coughing; mutism—making ten ailments. When cauterizing the Minor Yin vessel, eat raw meat heartily, leave the belt loose and the hair unbound, and walk with a large stick wearing heavy shoes. The moment the cauterization is finished the ailment will desist.
_MS_ I.B.10 (CC67–69)
Forearm Great Yin vessel. It is situated in the palm of the hand and emerges at the inner Yin part (of the forearm)3 between the two bones, at the lower edge of the upper bone above the muscle.4 It emerges at the inner Yin part of the arm5 and enters the heart.
When this (vessel) is moved, one ails from: heart pain with throbbing;6 pain in the broken basin;7 when severe, one is shaking with both hands clasped.8 These constitute forearm reversal. For these (ailments) the forearm Great Yin vessel controls the treatment.
The ailments that it produces are: chest pain; pain in stomach sack;1 heart pain;2 pain in the four extremities; conglomeration3—making five ailments.
_MS_ I.B.I1 (CC70–71)
Forearm Minor Yin vessel. It arises in between the two bones of the forearm and goes along the upper edge of the lower bone below the muscle.4 It emerges at the inner Yin of the upper arm and enters the heart.5
When this (vessel) is moved, one ails from: heart pain; parched throat with the desire to drink. These constitute forearm reversal. For these (ailments) the forearm Minor Yin vessel controls the treatment.
The ailments that it produces are: side pain—making one ailment.
1 According to Wang Bing's commentary to _Suwen_ 58, 15.7b, _yan_ 厭—literally, "press down"—designates the space between the hip joint and the head of the femur. By analogy, the femur is likened to the pestle pressing on the hip-joint mortar.
2 The term _toujiao_ 頭 角 (corner of the head) is not attested in received literature. _MWD_ , vol. 4, "Transcription," n. 6, associates it with _ejiao_ 額 角, which is attested in _Lingshu_ 13, 4.1b, where it refers to the boundary formed by the hairline along the side of the forechead.
3 This phrase and the companion phrase "the ailments that it produces are" (see below) introduce separate lists of ailments for each vessel in _MS_ I.B. Additionally, a count for the number of ailments in the second list is recorded at the end of each vessel description. A similar form of listing ailments occurs in _Lingshu_ 10. Ma Jixing cites five different explanations of the two lists found in traditional medical commentaries, all of which assume that the two lists have a basis in etiological and nosological classification (1992: 221, n. 1). However, the explanations are based on a level of medical theory not yet in evidence in the Mawangdui medical manuscripts. My interpretation of the first ailment list in _MS_ I.B is that _dong_ 動 (move) connotes vascular disturbance arising from a contrary movement of vapor in the vessels, a condition also known as _jue_ 厥 (reversal). Significantly, it is stated below that the ailments in the first list in _MS_ I.B.1 "constitute heel reversal ( _jue_ )"; and five other vessel descriptions also attribute the ailments in the first list to "reversal" stemming from a part of the body with which the vessel is associated ( _MS_ I.B.2, which speaks of "Yang reversal," is an exception). _Shiming_ , 8.255, gives a basic definition of _jue_ which reflects ideas prior to the elaboration of _jue_ in the _Huangdi neijing_ : " _Jue_ is when contrary vapor rises from below in a reverse direction and goes upward to enter the heart and side" (cf. Yu Yan 1972: 233). The idea that vapor (especially vapor entering the body through respiration or eating) should move downward, and that a reversal of that pattern causes illness is the central point of _MS_ I.C (although the word _jue_ does not occur in _MS_ I.C). The first paragraph in _MS_ I.C explains that maintaining warm feet and a cool head ensures that vapor, which moves in the direction of warmth, will move downward. This was evidently a fundamental teaching in early hygiene.
But if the first ailment list is to be associated with vascular disturbance, what is the essential difference between it and the second list which enumerates ailments that are "produced by the vessel," especially when many of the ailments are forms of pain occurring in both lists? I agree with Liao Yuqun (1989: 21) that the two lists are not based on specific etiological or nosological theories. However, I disagree with Liao when he argues that the first list belongs to the older, core text; and that the second list arose as a form of commentary expanding on the core text. For Liao, the notion of canonical text and appended commentary explains the fact that _Lingshu_ 10 expands on the second list (often more than doubling the number of ailments) while leaving the first list relatively intact. I would attribute the existence of two kinds of concerns in early medicine. The first list may reflect a concept of the relation between the vessels and illness that arose in the context of early hygiene as documented in _Maishu_ and _Yinshu_ (Prolegomena, Section Three, "Physiology"). The prominence of _jue_ "reversal" in the first list might also be explained as the influence of hygiene, since the idea of _jue_ reflects early hygienic theory of how vapor should move in the vessels. In contrast, the second list appears to focus on counting the number of ailments in the second list in _MS_ I.B and for the expansion of the second list in _Lingshu_ 10 is because it was in this category that vessels were associated with ailments for diagnostic purposes. It is also noteworthy that most ailments with technical names occur in the second list (the exception is _MS_ I.B.8, which includes inguinal swelling and _shan_ in the first list); and that references to medical prognosis and treatment form part of the second list in _MS_ I.B.7–9. Thus, it is the second list that is comparable to the list of ailments in _MS_ I.A, whose diagnostic/therapeutic nature is evident in the conclusion to each vessel description which states that the vessel in question is to be cauterized whenever one of the ailments occurs.
4 Ma Jixing suggests that "dashed" ( _chong_ 冲) refers to vapor moving counter to the proper direction of flow and "dashing" against the head; i.e. that "dashed head" is a "reversal" ailment (1992: 222, n. 2).
1 No doubt due to pain in the thigh and hip joint.
2 _Maishu_ writes _zhong_ 踵 (heel). The graph in the corresponding position in the text of _MS_ I.B.1 is fragmentary. Undoubtedly because the _Lingshu_ 10, 3.4a, parallel writes _huai_ 踝 (malleolus), _MWD_ , vol. 4, "Transcription," writes the latter graph. On re-examination, the graph should be written 踵.
3 _Qian_ /* _dzji ǝm_ 灊 clearly represents an anatomical name, but I am unable to identify it. Ma Jixing argues that is a phonetic loan for _zhen_ /* _tj ǝm_ 枕 (headrest), referring to the occipital bone (1992: 224, n. 3; cf. _MS_ I.A.2). The parallel in _MS_ II.B writes _er_ 耳 (ear) in place of _qian_. As noted by Ma Jixing, _er_ undoubtedly resulted from miswriting the graph 灊 as _er_ , which was then altered to 耳.
4 _SW_ , 7B.31a, defines _nue_ 虐 as "the ailment when cold (chill) and hot (fever) stop and start." According to _Maishu_ , "Ailment List": "When the body is cold and hot, is parched, and the four limbs are painful—it is _nue_ " ( _MSSW_ : 72). The name _nue_ is also applied to malarial disease in early sources (Yu Yan 1972: 235).
1 _Maishu_ writes _qu_ 胠 (upper side; n.b., 胘 in the _MSSW_ transcription is a printing error). The graph in the corresponding position in the text of _MS_ I.B.1 is fragmentary and written _xi_ 胎 (poples) in _MWD_ , vol. 4, "Transcription." On re-examination, and also based on comparison with one occurrence of _qu_ in C46 and one of _xi_ in C62, the graph in _MS_ I.B.1 should be written 胠.
2 The term _yugu_ 魚 股 (fish-thigh) is not attested in received literature. However, there is evidence of anatomical names that liken parts of the body to the shape of a fish. For example, _Suwen_ 41, 11.8a, refers to the calf as the "fish belly" ( _yufu_ 魚 腹). _MWD_ , vol. 4, "Transcription," n. 1, suggests that "fish-thigh" refers to the quadriceps of the thigh.
3 The wording of the parallel at _Lingshu_ 10, 3.6a, indicates that the lack of fat refers to the body's loss of moisture and fat. Perhaps the fat is literally cooked out of the body by the heat of "Yang reversal" in the vessel.
4 The other "reversals" in _MS_ I.B are named according to a part of the body associated with the vessel in question. Yang Shangshan's commentary to _Taisu_ , 8.83, associates Yang reversal with morbific heat.
1 It is evident from the _Maishu_ text and from _MS_ II.B that the word in the text of _MS_ I.B.3 should be _shen_ 伸 (stretch) and not _long_ 巃 (dragon). _MWD_ , vol. 4, "Transcription," n. 5, argues that the original graph was probably 申, and speculates on how the graph 巃 came to be written in the text.
2 Yang Shangshan's commentary to _Taisu_ , 8.74, explains the blackness as the presence of Yin vapor.
3 I follow Yang Shangshan's gloss of _zhi_ 至 as "severe" in the commentary to _Taisu_ , 8.74. Ma Jixing interprets _zhi_ to mean "when (an ailment) arises" (1992: 234, n. 7).
4 Yang Shangshan's commentary to _Taisu_ , 8.74, explains the antipathy for fire and wood in terms of Five Agent theory. Since there is no evidence of Five Agent theory in _MS_ I.B, these antipathies have some other basis.
5 The text writes _ling_ 領 (neck). According to _MWD_ , vol. 4, "Transcription," this is a scribal error for _han_ 頷 (jaw). The apparent reason for emending _ling_ is the occurrence of _ling_ in _MS_ I.B.4, where the parallel in _Lingshu_ 10, 3.3b, writes _han_. However, _MS_ I.B, _MS_ II.B, and _Maishu_ consistently write _ling_. Given that the meaning "neck" fits in each context, I do not accept the proposed emendation.
6 For identification of _qi_ 晵 as a name for the calf, see _Guangya_ , 6B.9b. In _MS_ I.B.3 there is a lacuna in the text extending from "neck" above to "heart" below. The five graphs added from _Maishu_ easily fit the space left by the lacuna.
7 "Rigidity" translates _tiao_ 跳, which according to _SW_ , 2B.28a, refers to stiffness in the leg joints that causes stumbling.
8 The shoulder vessel corresponds to the forearm Great Yang vessel in _MS_ I.A.
9 _Maishu_ writes _zhou_ 肘 (elbow). The graph in the corresponding position in the text of _MS_ I.B.4 is fragmentary and is written _ru_ 臑 (upper arm) in _MWD_ , vol. 4, "Transcription." On re-examination, and comparing the graph to one occurrence of _zhou_ in C52, the graph in _MS_ I.B.4 should be written 肘. Similarly, the graph following _zhou_ is illegible and I follow the _Maishu_ text which writes _nei_ 內 (inner). The text of _MS_ II.B.4. appears to be different since it writes _wai_ 外 (outer; the graph is fragmentary and there is a lacuna above it).
10 At this point the _Maishu_ text writes four graphs 臂 外 捥 上 "the outer part of the forearm by the wrist." There is not space for four graphs in the lacuna in _MS_ I.B.4 (C48); and at the same time, I am unable to determine a plausible abbreviation of the four graphs in _Maishu_. Two possibilities occur to me. Perhaps the restored silk of _MS_ I as shown in the plate is inaccurate and the lacuna in C48 is larger than it appears to be; or perhaps the fourth graph was omitted from the text due to scribal error and must be added to the three graphs that fit the lacuna. I am unable to prove either possibility, and it is equally likely that the text of _MS_ I.B.4 is simply different.
1 The ear vessel corresponds to the forearm Minor Yang vessel in _MS_ I.A.
2 The upper bone is the radius.
3 The tooth vessel corresponds to the forearm Yang Brilliance vessel in _MS_ I.A.
4 _Zhuo_ 崸 refers to the cheekbone ( _SW_ , 9A.10b), and to the space above the cheekbone and below the eye.
1 The identification of the foot Great Yin vessel with the stomach is unrelated to the correlation between vessels and organs in _Lingshu_ 10.
2 "Go alongside" translates _pi_ 披, which represents my reading of _bi_ 彼 in the original text. For attestation of _pi_ in the sense of "go alongside," see _Shiji_ , 1.4b. and 1.28a. _MWD_ , vol. 4, "Transcription," n. 2, reads 彼 as _bei_ 被, glossed as "cover over." The phrase in _MS_ I.B.7 begins the description of the path of the vessel, and the meaning "cover the stomach" does not fit the context well. In addition, _Lingshu_ 10, 3.6b, describes the foot Ceasing Yin vessel as "pressing laterally on the stomach," which lends support to reading the phrase in _MS_ I.B.7 as translated.
3 Yin and Yang are used to refer to positions on the exterior of the body, corresponding to inner and outer respectively.
4The ailment name is composed of four graphs 上 [1] 走 心, with one graph missing in the lacuna at the bottom of C54. Perhaps the lacuna is _dang_ 當, which appears in the corresponding position in _MS_ II.B. The _Maishu_ text writes 上 走 心. I concur with _MWD_ , vol. 4, "Transcription," n. 4, that the ailment is a reversal ailment where vapor harms the heart by moving in a contrary direction.
5 I.e. intestinal gas.
6 Both "blockage" ( _bi_ 閉) and "water" ( _shui_ 水) are included in _Maishu_ , "Ailment List," the former referring to not being able to urinate and the latter to abdominal bloating: "When it is located at the forbidden spot (i.e. the genitals) and one is unable to urinate—it is blockage"; "When the abdomen is full while the body, face, feet, and legs all diminish—it is water" ( _MSSW_ : 72). For discussion of the two ailments in later medical literature, see Ma Jixing 1992: 250, n. 8.
1 The phrase "emerges behind the Great Yin (vessel)" is lost in the lacuna at the bottom of C58, and there is also a lacuna in the corresponding position in _Maishu_. Although there is only space for five graphs at the bottom of C58, I fill the lacuna with the six graph phrase from _MS_ II.B since either one of the two grammatical particles in this phrase (於, 之) can be omitted without affecting the meaning.
2 _Maishu_ writes _jia_ 夾 (press laterally). _MWD_ , vol. 4, "Transcription," writes _da_ 大 in the corresponding position in _MS_ I.B.8. On re-examination, and comparing it to _jia_ 夾 in C62, the graph in _MS_ I.B.8 should be written 夾.
3 For _tui_ 癪 (inguinal swelling), see _MS_ I.E.118.
4 _Shan_ 疝 is applied to several morbid conditions characterized by pain and swelling in the region of the heart and abdomen, and sometimes is treated synonymously with _tui_. Various meanings of _shan_ are discussed in Ma Jixing 1992: 253, n. 2; and Yu Yan 1972: 218–20, 225.
5 For _long_ (urine retention), see _MS_ I.E.88.
6 The last two ailment names pose a problem that is not easily resolved. They can be plausibly read as a single ailment name, _pianshan_ 偏 疝 (see below); but if they are read thus, there are only four ailments instead of the five stated in the text. Of course, the number five is only extant in _Maishu_ (there are lacuae in _MS_ I.B.8 and _MS_ II.B in the corresponding position), and we might feel justified in emending the text to read "four" on the presumption that _Maishu_ is in error. This solution seems unacceptable because of _MS_ I.A.6 which lists five ailments for the foot Ceasing Yin vessel and also describes the fatal prognosis when these ailments occur together with feverishness of the heart, providing a clear parallel to _MS_ I.B.8. To be sure, the ailments listed are not identical, but the number five undoubtedly has a significance of its own. Ma Jixing resolves the problem by reading _pianshan_ together and speculating that the fifth ailment name has been omitted in _MS_ I.B.8 as well as in the corresponding position in _MS_ II.B. and _Maishu_ (1992:255). My approach to the problem is to read the text as written and to treat _pian_ and _shan_ as two ailments. _Shan_ already appears in the first ailment list above. _Pian_ is attested in _Xunzi_ 5, 3.47, referring to hemiplegia, usually written _pianku_ 偏 枯 (withering on one side). _Lingshu_ 23, 5.4b, describes _pianku_ as follows: "The body is useless on one side and is painful. Speech is not altered and the will is not disordered."
Despite my skepticism of reading _pianshan_ as a single ailment in _MS_ I.B.8, the alternative merits careful consideration since the usage is attested in the _Huangdi neijing_ ; however, the first graph of the name has been altered in the received text. In the second ailment list of the foot Ceasing Yin vessel in _Lingshu_ 10, 3.6b, the ailment _hushan_ 狐 疝 (fox _shan_ ) occurs. Akahori argues that the _Lingshu hu_ 狐 is a corruption of _MS_ I.B.8 _pian_ 偏 (1989: 21). The Yang Shangshan commentary in _Taisu_ , 8.84, explains the ailment as follows: "The fox cannot urinate at night and is first able to do it at dawn. The human ailment resembles the fox. The list (in the description of the foot Ceasing Yin vessel) reads _hushan_ ; and there are editions that write _tuishan_ 頹 疝. It refers to the ailment _piantui_ 偏 頹." The name _hushan_ also occurs in _Lingshu_ 47, 7.9a; 49, 8.4b; and in _Suwen_ 64, 18.7a. And in medical literature after the _Huangdi neijing_ , "fox _shan_ " continues to be described as a distinctive type of _shan_ ailment associated with inguinal hernias (Yu Yan 1972: 228–29). Yang Shangshan's commentary is significant because it documents the name _piantui_ "inguinal swelling on one side" when identifying "fox _shan_." Evidently even after _hu_ "fox" replaced pian "on one side" in the name of the ailment—and the fox was introduced into its etiology—the identification of the ailment as a form of asymmetrical "inguinal swelling" was still understood.
1 The kidney happens to be the organ correlated with the foot Minor Yin vessel in _Lingshu_ 10. While reference to the kidney in _MS_ I.B.9 may have some bearing on the later vessel-organ correlations, it cannot be interpreted as evidence of such correlations in _MS_ I.B.
2 The ailment may refer to a general shortage of vapor in the body and its vessels as well as to shortness of breath. _Taisu_ , 8.79, connects this ailment to the next one, which is fear rather than anger: "When there is insufficiency of vapor, there is a tendency to become frightened." According to the Yang Shangshan commentary, the "insufficiency" is of the vapor in the foot Minor Yin vessel.
3 "Moldy black" translates _yan_ 黭, defined in _SW_ , 10A.59a, as the "deep black of (molded) fruit."
4 _Zhi_ 洽 (treatment) is not written in the text and should be regarded as a case of scribal omission.
1 I.e. a "reversal" of the movement of vapor in the vessels.
2 "Exhaustion" translates _dan_ 癅 (see _MS_ I.A.4). The second ailment list in _Lingshu_ 10, 3.4b, has the ailment _huangdan_ 黃 疸 (yellow _dan_ ; i.e. jaundice) instead. Ma Jixing argues that because received medical literature generally associates the foot Minor Yin vessel with jaundice the ailment in _MS_ I.B.9 should be understood as jaundice rather than as exhaustion (1992: 264, n. 7). In received literature the use of _dan_ 癅 and homophonous _dan_ 疸 is confused (see _SW_ , 7B.33b, and Duan Yucai commentary), so Ma's interpretation is plausible.
3 The forearm must be understood here (the word for forearm is written in _Maishu_ ). Inner and Yin are synonymous, both referring to the inner surface of the forearm.
4 The upper bone is the radius.
5 _Bi_ 臂, which in all other occurrences in _MS_ I.A–B refers to the forearm, is suspect. Although _bi_ can refer to the arm in general, which is how I have translated it here, it is likely that _bi_ is an error for _ru_ 臑 (upper arm). There is a lacuna in the corresponding position in _Maishu_ , while _MS_ II.B also writes _bi_. The best evidence for scribal error is the description of the path of the forearm Minor Yin vessel in _MS_ I.B.11 which is similar to _MS_ I.B.10, and which specifies the upper arm at this point.
6 _Pangpang_ 滂 滂 is a descriptive compound that suggests the quality of surging water ( _Guangya_ , 6A. 10b). The corresponding position in _MS_ II.B uses the same compound, but in _Maishu_ the compound is _pengpeng_ 彭 彭. _SW_ , 5A.34a, glosses _peng_ as the "sound of drumming."
7 I.e. the clavicle.
8 Even clasping one's hands cannot suppress the excruciating pain.
1 惌 is not attested in received literature (the same graph appears in the corresponding position in _MS_ II.B). I follow _MWD_ , vol. 4, "Transcription," in reading the graph as _wan_ 脘, for which the variant graph 腕 also occurs. _Wan_ refers to the stomach in its capacity as the receptacle for food (see _Suwen_ 33, 9.10b, which attributes the inability to get food to go down to blockage in the "stomach sack"). _Maishu_ writes _qi_ 晵 (calf). While the inclusion of "pain in the four extremities" just below in the second ailment list increases the plausibility of _qi_ , I suspect that _wan_ is the better reading.
2 I follow the emendation in _MWD_ , vol. 4, "Transcription," which adds _xintong_ 心 痛 (heart pain) to the text. The ailment is included in _Maishu_ and _MS_ II.B. It is a clear case of scribal omission since the text only names four ailments and yet gives a final count of five ailments.
3 "Conglomeration" translates _jia_ 瘕. _Jia_ refers to a variety of growths or internal blockages that occur primarily in the abdomen and intestines (Yu Yan 1972: 129). _Maishu_ , "Ailment List," gives the names of the following types: male conglomeration (intestinal), blood conglomeration (intestinal), vapor conglomeration (abdominal), fat conglomeration (abdominal), feces conglomeration, and muck conglomeration ( _MSSW_ : 72).
4 The lower bone is the ulna.
5 Both _Maishu_ and _MS_ II.B conclude the description of the vessel path with the pharse 人 心 中 "enters the heart." In _MS_ I.B.11 there is a lacuna at the bottom of C70 that begins where this phrase should be and extends into the beginning of the next paragraph. I differ with _MWD_ , vol. 4, "Transcription," which omits this phrase and adds only the subsequent five graphs to fill the lacuna. According to my calculations there is sufficient space to add all eight graphs as written in the corresponding positions in _Maishu_ and _MS_ II.B.
_MS_ I.C
Maifa
脈 法
Model of the Vessels
_MS_ I.C (CC72–83)
May the model of the vessels be clearly taught to those below.1 The vessels are also something the sage prizes. As for vapor, it goes to the lower part (of the body) and harms the upper part;2 it follows warmth and departs from coolness. The sage has a cold head and warm feet.3 To treat ailments, take away the surplus and increase what is insufficient.1 When vapor ascends and does not descend, discern which vessel has excess and cauterize it at the ring.2 If the ailment is severe, go up two _cun_ above the ring and perform an additional cauterization.3 If vapor emerges, lance the vessels at the poples and elbow with a lancing-stone.4
The use of the lancing-stone to open vessels must conform to the plan. When an abscess or swelling has pus, gauge its size and then lance it. When lancing there are four harms.1 When the pus is deep and lancing is shallow, it is called "not reaching"—the first harm. When the pus is shallow and the lancing is deep, it is called "exceeding"—the second harm. When the pus is large and the lancing-stone is small, it is called "seeping"; when seeping occurs, the pollution is not eliminated—the third harm.2 When the pus is small and the lancing-stone is large, it is called "overflow"; when overflow occurs, good flesh is injured—the fourth harm. When pus is abundant and deep, the top is black and large. When pus is slight and deep, the top is black and small. When pus is abundant and shallow, the top is white and large. When pus is slight and shallow, the top is white and small. It is imperative to investigate this. When there is pus, cauterization cannot be used.1
The way to examine the vessels. Place the left [hand five _cun_ up from the malleolus] and press on it.2 Place the right hand at the malleolus and palpate it.3 If other vessels are full and this one alone is empty, it controls the ailment. If other vessels flow evenly1 and this one alone is blocked,2 it controls the ailment. If other vessels are still and this one alone is moved, it controls the ailment. Now, the vessels that have constant movement are the Minor Yin of the shin and the Great Yin and Minor Yin of the forearm. These (vessels) normally have movement;3 and when it is rapid, ailments occur. These provide the basis for deciding when there is excess in the vessels. For the remainder, carefully discern the excess in the corresponding vessel.4 The vessel connections5—let it be written and thoroughly studied. Pupils, be devoted and respectful. Study [4] {4} [6] words, it is imperative to investigate them.
1This sentence is not included in _Maishu_. The term _maifa_ 脈 法 (model of the vessels) refers to the physiological theory of the vessels and its medical application as well as to a genre of medical literature. Both meanings occur in the _Shiji_ account of Chunyu Yi. Beginning with the first of Chunyu Yi's medical case histories, at _Shiji_ , 105.9b, Chunyu Yi regularly quotes from a _Model of the Vessels_ to provide theoretical support for his diagnoses. And at _Shiji_ , 105.21b, Chunyu Yi refers to the "model of the vessels" as the invention of ancient sages for the purpose of elucidating the structure of the body and classifying the ailments that effect it. See also, _Suwen_ 4, 1.15b, which concludes a discussion of the effects of the seasons on the body and its ailments with the statement, "this is the model of the vessels for the average person"; and _Suwen_ 67, 19.9b, which quotes from a work entitled _Model of the Vessels_ to demonstrate an argument.
2"Goes to the lower part" translates _dao xia_ 到 下. The corresponding position in _Maishu_ writes _li xia_ 利 下 (benefits the lower part). Since "benefit" is the standard antonym of "harm," it is tempting to emend _dao_ in _MS_ I.C. I hesitate to make the emendation for several reasons. _Dao_ is grammatically acceptable and to reject it solely because it does not form the standard antonym pair is incautious. In addition, _dao_ does express the contrast between where the vapor should go and the harm it causes if it ascends instead. Given other instances where _Maishu_ adds rhetorical words and rewords difficult phrases, it is possible that an earlier _dao_ was altered to _li_.
3This observation on the physiology of the sage concludes the brief paean to the theory of the vessels, and _MS_ I.C next shifts to a discussion of how to apply vessel theory to treating ailments. The image of the sage, whose warm feet ensure that vapor is drawn downward, is related to Warring States ideas about macrobiotic hygiene. Similar ideas occur in the Warring States jade inscription on circulating vapor, in which downward movement is the key (see Prolegomena, Section Four, "Techniques"). The sage's warm feet also call to mind the passage in _Zhuangzi_ 6, 103, which speaks of the "perfected man of antiquity" who "breathes with the heels." Both the warm feet theory of _MS_ I.C and the _Zhuangzi's_ "heel-breathing" have their origins in forms of breath cultivation designed to circulate vapor by generating warmth in the lower limbs.
The idea of a cold head to balance the warm feet in _MS_ I.C differs from _Huangdi neijing_ passages that refer to the face as able to withstand coldness because it is the place where all Yang vessels meet. See Ma Jixing 1992: 281, for relevant citations; and Unschuld 1986b: 446, for a translation of the _Nanjing_ passage concerning the face (Ma's interpretation of _MS_ I.C based on the _Huangdi neijing_ misses the significance of the idealized physiology of the sage described in _MS_ I.C).
1The principle of treating ailments by restoring equilibrium in the vessels is standard in the _Huangdi neijing_. For example, _Suwen_ 60, 16.1a, states that, "to regulate the Yin and Yang, replenish when there is insufficiency and drain when there is surplus." The same principle also existed in ancient macrobiotic hygiene as attested in the _Maishu_ , "Care of the Body," passage which states that, "when the vessels are brimful, drain them; when empty, fill them; when still, stay in attendance on them" ( _MSSW_ : 74).
2 _Suwan_ 80, 24.5b, discusses "having surplus" and "vapor ascending and not descending" as aspects of the morbid condition of _jue_ 厥 (reversal). In my judgment, the condition described in _MS_ I.C is comparable to the reversal ailments of _MS_ I.B (see _MS_ I.B.1). The part concerning cauterization is more problematic—especially the interpretation of the word _huan_ 環, which I translate as "ring." The grammer of the phrase "cauterize it at the ring" 當 環 而 灸 之 is parallel to the phrase below, "lance the vessels at the poples and elbow with a lancing-stone" 胎 與 肘 之 脤 而 砈 之; and I am convinced that the best explanation of the two occurrences of _huan_ in _MS_ I.C is to treat the word as a noun for a part of the anatomy. Ma Jixing cites the acupuncture point named _huangu_ 環 谷 located in the navel and suggests that _huan_ in _MS_ I.C refers to the navel region (1980: 23). My own speculation is that _huan_ "ring" refers to the waist ( _yao_ 要). A related term in _MS_ VI.B.1, _zhouhuan_ 周 環 (encircling ring), I also identify as the waist. Although this usage is unattested in received literature, the idea of the waist as the central ring around the body is well documented. _SW_ , 3A.39b, glosses _yao_ "waist" as the "middle of the body," and explains the graph as a depiction of a person clasping both hands around the waist. The _Huangdi_ neijing acknowledges the importance of the waist for vessel theory by including a special vessel that rings the waist even with the navel called the _daimai_ 帶 脤 (belt vessel). Its nature and function differ from the twelve Yin and Yang vessels of the hands and feet (cf. Unschuld 1986b: 322) yet _Suwen_ 44, 12.10a, states that the Yin and Yang vessels "belong to the belt vessel" 屬 於 帶脤. The idea in _MS_ I.C is to correct the ascending vapor in the vessels by cauterizing a central point on the body that might induce the vapor to re-descend (since vapor "follows warmth"). Even though one is supposed to determine which vessel "has excess," I doubt that cauterization was performed at discrete places around the waist corresponding to the path of each vessel (impossible in any case for the hand vessels). The treatment appears to be relatively simple and unrelated to the vessel theory and therapy found in the _Huangdi neijing_. Ma Jixing (1992: 282–83) rejects his earlier identification of _huan_ as an anatomical term in favor of a more theoretically elaborate interpretation of _MS_ I.C. His new understanding of _huan_ is grammatically implausible, and I am skeptical of his general interpretation.
3Presumably when the reversal ailment is severe, a single cauterization at the waist is insufficient to induce the vapor to descend and a second cauterization must be performed higher on the body than the first. I interpret _yang_ 陽 in the sense of "rise, go up," not as a reference to Yang.
4For the phrase 氣 出 "if vapor emerges," the corresponding position in _Maishu_ writes 氣 一 上 下 "if vapour now ascends and now descends." I suspect that the latter version is a paraphrase of the former. The grammatical use of _yi_ 一 in the sense of "either/or" or "now/now" when referring to an unstable physiological condition is attested in _Suwen_ 62, 17.4a: "Blood and vapor leave their abodes, _now full and now empty_. Blood bonds to Yin and vapor bonds to Yang, thus causing panicky wildness." For "vapor to emerge" or "vapor to now ascend and now descend" appears to designate the most severe form of the reversal ailment, one where treatment with cauterization is inadequate. Perhaps the ailment is similar to the ailment suffered by the Prince of Guo 虢 太 子 as described in _Shiji_ , 105.3b–6a. According to the account, the palace experts believe that he has died of "violent reversal" ( _baojue_ 暴 憠): "The Prince was ailing from blood and vapor being untimely so that they crossed one another and could not be drained. When it violently erupted to the outside, this caused internal harm. The essence and spirit were unable to stop the evil vapor so that the evil vapor accumulated and could not be drained. Therefore Yang was slack while Yin was tense. Thus he experienced violent reversal and died." While Bian Que's diagnosis is that the Prince's ailment is "corpse reversal" ( _shijue_ 尸 憠) and that the patient is still alive, his description of the ailment continues to focus on disorder among the vessels: "The Yang vessels plummet downward and the Yin vessels fight upward. The converging vapor is blocked and does not pass through." It is plausible to interpret "vapor emerging" in _MS_ I.C as related to the "violent eruption which caused internal harm" in the _Shiji_ account, the idea being that a morbid condition (perhaps vapor that ascends and descends) makes it impossible for vapor to flow normally and that even cauterization does not prevent it from erupting. Under these circumstances _MS_ I.C introduces the use of the lancing-stone ( _bian_ 砈, more often written 砭) to cut open vessels at the poples and elbow and allow the vapor to drain.
_SW_ , 9B.32a, defines _bian_ as a verb meaning "lance an ailment with a stone"; and the word is used both as a verb and a noun in _MS_ I.C. _MS_ I.C and the single occurrence of _bian_ in _MS_ I.E.135 confirm pre-Han and Han sources that describe the use of sharpened stones to drain pus from abscesses and to relieve pressure in swellings. The significance of the lancing-stone in _MS_ I.C in connection with the transition from cauterization to acupuncture is discussed in the Prolegomena, Section Three, "Therapy."
1See the Prolegomena, Section Three, "Therapy," for discussion of a _Lingshu_ parallel to this account of draining pus with the lancing-stone, which speaks instead of acupuncture needles.
2"Seeping" translates _lan_ 澰, which is listed among words meaning _zi_ 漬 (soak) in _Guangya_ , 2B.7a. The third and fourth harms concern the choice of a lancing-stone, which depends on the amount of pus to be drained: large lancing-stones for large amounts of pus and small lancing-stones for small amounts. If the lancing-stone is too small for the amount of pus, the undrained pus "seeps" and the abscess continues to fester.
1Due to the fragmentary condition of the silk, _MWD_ , vol. 4, "Transcription," errs in identifying a single column in this part of the text as two columns (CC79–80). _Maishu_ permits correction of the error ("Transcription," n. 4 states that CC79–80 may be a single column). The error is corrected in my transcription. In _MWD_ , vol. 4, "Transcription," C81 should be renumbered C80 and so forth to the end of the numbering sequence with C88 in _MS_ I.D, which should be renumbered C87.
2The bracketed words represent lacunae in both _MS_ I.C and _Maishu_ that have been filled in accordance with the emendation proposed by Ma Jixing, who adds the graphs 手 上 去 踝 五 寸 from a parallel passage in _Taisu_ , 14.185 (1992: 292, n. 2). Textual parallels also occur in _Suwen_ 20, 6.11a; and _Zhenjiu jiayi jing_ , 4.27a. The lacuna in _MS_ I.C has sufficient space for the six graphs. _MWD_ , vol. 4, "Transcription," and the new transcription of _MS_ I.C appended to _MSSW_ : 74, do not include this emendation; but both transcribe two graphs 走 而 at the end of the lacuna, which conflict with the proposed emendation. On re-examination, I find that 而 is in fact the top of 案 ( _an_ "press") below, As for 走, I am unable to discern the graph written in the text.
3"Palpate" translates _tan_ 撢, glossed with _tan_ 探 in _SW_ , 12A.44b. While the primary meaning of both words is "search out," they are also used to refer to grasping something and feeling it with the hand ( _Erya_ , 2.10b, and commentary). The parallels in _Taisu_ , _Suwen_ , and _Zhenjiu jiayi jing_ all write _dan_ 弹 (strike), meaning that the right hand should strike the malleolus with a tapping motion. Ma Jixing argues convincingly that _tan_ "palpate" is the best reading (1992: 108).
_MS_ I.C and the parallels in received medical literature present a paradigm of vessel diagnosis, but none specify which vessel is being diagnosed. According to the Yang Shangshan commentary in _Taisu_ , 14.185, the vessel is the foot Great Yin vessel because it emerges at the upper part of the inner malleolus and then intersects the foot Ceasing Yin vessel eight _cun_ above the malleolus. The diagnostic technique as described in the _Taisu_ text and explained by Yang Shangshan entails tapping the vessel at the malleolus with the right hand while the left hand feels for a response up above. It is likely that _MS_ I.C also understands the foot Great Yin vessel as the one being diagnosed. According to _MS_ I.B.7, the path of the foot Great Yin vessel descends from the stomach and ends at the "upper edge of the inner malleolus"; and in _MS_ I.B.8, the foot Ceasing Yin vessel "rises five _cun_ above the malleolus and emerges behind the Great Yin vessel." Thus in _MS_ I.C, the left hand is pressing precisely at the intersection of the Great yin and Ceasing Yin vessels while the right hand is probably palpating the Great Yin vessel at the malleolus. The similarity between _MS_ I.C and received medical literature ends here. In the sentences below, _MS_ I.C judges the condition of the vessel by comparing the vessel being diagnosed—called "this one" ( _ci_ 此)—to "other vessels" ( _tuo mai_ 它 脈), whereas received medical literature looks at the response within the vessel being diagnosed. Ma Jixing interprets _mai_ in the sense of the "pulse" in the vessel and argues that _tuo mai_ refers to the "other pulse," meaning the pulse where the right hand is positioned, while "this one" refers to the pulse where the left hand is positioned (1992: 295, nn. 1–2). Thus he argues that the diagnostic technique is basically similar to the received medical literature. Even if one accepts the identification of _mai_ as the pulse (which is unlikely here, and occurs nowhere else in the Mawangdui medical manuscripts), the grammar of _tuo mai_ and _ci_ requires considerable forcing to produce Ma's interpretation. I think it best to simply acknowledge that the diagnostic technique described in _MS_ I.C is different.
1"Flow evenly" translates _gu_ /* _kw ǝt_ 汩, glossed in _SW_ , 11A–2.43a "well-ordered water." The corresponding position in _Maishu_ writes _gu_ /* _kw ǝt_ 滑 (smooth).
2"Blocked" translates _shuai_ /* _slj ǝt_ 率, glossed in _SW_ , 13A.40b as a "bird-catching net" (the graph is explained as a depiction of a net on a pole). This meaning is not attested outside of the _SW_ , and my speculation that it may have the extended meaning of "block" is tentative (most occurrences of _shuai_ borrow the graph to represent a word meaning "lead" or "follow"). _Shuai_ /* _slj ǝt_ contrasts with _gu_ "smooth" in _Maishu_ (the first word is missing in _MS_ I.C). The _SW_ includes two words that both are glossed as "not smooth," i.e., "rough, blocked"; _SW_ , 2A.40b, _se_ /* _srj ǝp_ 歰; and _SW_ , 11A–2.11b, _se_ /* _srj ǝk_ 瀒. Although they are phonetically distinct, the two words were used interchangeably in Han texts as antonyms of _gu_ "smooth." Perhaps _shuai_ /* _slj ǝt_ represents a third previously unattested antonym of _gu_.
3The blood pulse is responsible for the idea that certain vessels "normally have movement."
4 _MS_ I.C leaves many matters unexplained. Assuming that the technique for diagnosing the foot Great Yin vessel has been described above, details concerning where and how to diagnose the other foot vessels are missing; and nothing is said about diagnosing the hand vessels. After this sentence _Maishu_ has a different conclusion which does not include the final sentences of _MS_ I.C: "The method for treating ailments. Discern which (vessel) erupted first and treat it. When several vessels erupt in ailments together, pick the one that is most severe and treat it first."
5"Connection" translates _xuan_ /* _gwian_ 縣, glossed in _SW_ , 9A.17b, as _xi_ 繫 (attach, connect). The term "vessel connections" probably designates the set of vessels "attached" to the body along paths described in _MS_ I.A–B. I reject _MWD_ , vol. 4., "Transcription," which reads 縣 as a phonetic loan for _xuan_ /* _gwin_ 玄 (darkness, subtlety). The phonological evidence is arguable, and the meaning "subtlety of the vessels" has nothing to recommend it.
_MS_ I.D
Yin Yang Mai Sihou
陰 陽 脈 死 候
Death Signs of the Yin and Yang Vessels
_MS_ I.D (CC84–87)
All three Yang (vessels) are the vapor of heaven. Among their ailments, only the cases where bones are broken and skin is ripped are the sole occasion when death occurs.1 All three Yin (vessels) are the vapor of earth, and are the vessels of death. When ailments of the Yin (vessels) create disorder, death occurs within ten days.2 The three Yin (vessels) putrefy the depots and rot the intestines, and they control killing.3
[2] the five forms of death.4 When the lips turn outward and the groove beneath the nose is full,5 flesh has died first. When the gums become level and the teeth long,6 bone has died first. When the face is black and the eyes—fixed with fear7—gaze obliquely, vapor has died first. When floss-like strands of sweat emerge that stick and do not flow, blood has died first.1 When the tongue binds and the testicles curl up,2 muscle has died first. When all five occur, he will not live.3
1Compare the statement in _MS_ I.A.6 on the Yang vessels.
2Compare the statement in _MS_ I.A.6 on the Yin vessels.
3The sentence identifies the Yin vessels as the source of decay in the body. Reference to the depots (liver, heart, spleen, lung, kidney) and intestines (large and small) is metonymy for the body and does not imply àny theoretical correspondence between the Yin vessels and these organs. In _Maishu_ this sentence occurs ahead of the previous sentence ("When ailments of the Yin....").
4 _Maishu_ has a different opening sentence: "Whenever discerning the signs of death." _Lingshu_ 10, 3.7a–b, lists fatal signs for five Yin vessels (the hand Ceasing Yin vessel is not included) using language that is sometimes similar to _MS_ I.D. For example, when "the vapor is severed in the foot Great Yin (vessel)," one of the signs is that "the lips turn outward"; and the conclusion is that "flesh has died first." The contents of _MS_ I.D reflect older physiological ideas which were later subsumed within _Huangdi neijing_ vessel theory (see Prolegomena, Section Three, "Physiology").
5I translate _ren_ 人 as "groove beneath the nose" on the basis of _Lingshu_ 10, 3.7a, which has the compound _renzhong_ 人 中 (human middle). The compound denotes the nasolabial groove (see Ma Jixing 1992: 308, n. 4).
6I.e. the guns recede, exposing the teeth.
7I follow _MWD_ , vol. 4, "Transcription," in reading 環 (i.e. _huan_ "ring") as _qiong_ 睘 (also written 睘), glossed in _SW_ , 4A.5b, as "eyes gazing startledly."
1 _Maishu_ reverses the third and fourth signs, making the third a sign of blood dying first and the fourth a sign of vapor dying first.
2"Bind" translates _jun_ 稛, glossed in _SW_ , 7A.48a, as "bind with a cord." The graph is written 捆 in _MS_ I.D, and is miswritten as 掐 in _MWD_ , vol. 4, "Transcription," which reads the latter graph as _xian_ 陷 (drop down). _Lingshu_ 10, 3.7b, uses the phrase "the tongue curls up and the testicles contract" to describe "muscle dying first." In _MS_ I.D, "bind" refers to the stiffening of the tongue as it contracts, and it is the testicles that "curl up."
3 _Maishu_ has a different conclusion: "In all, the signs are five. When one signs appears, act first to keep the person alive."
_MS_ I.E
Wushier Bingfang
五 十 二 病 方
Recipes for Fifty-Two Ailments
_MS_ I.E.I
Various Wounds ( _MS_ I.E.2–18)
Rigidity Due to a Wound ( _MS_ I.E.19–24)
Infant-cord Rigidity ( _MS_ I.E.25)
Infant Ailing from Spasms ( _MS_ I.E.26)
Infant Convulsions ( _MS_ I.E.27)
Mad Dog Bites a Person ( _MS_ I.E.28–30)
Dog Bites a Person ( _MS_ I.E.31–33)
Nest ( _MS_ I.E.34–35)
_Xixia_ ( _MS_ I.E.36)
_Wuhui_ (Monkshood) Poisoning ( _MS_ I.E.37–43)
Scorpion ( _MS_ I.E.44–49)
Leeches Bite ( _MS_ I.E.50–51)
Lizard ( _MS_ I.E.52–63)
Warts ( _MS_ I.E.64–70)
Seizure Sickness ( _MS_ I.E.71–72)
_Baichu_ ( _MS_ I.E.73–75)
_Dadai_ ( _MS_ I.E.76–77)
_Ming_ ( _MS_ I.E.78)
_Quan_ ( _MS_ I.E.79)
[1] _zhe_ ( _MS_ I.E.80–83)
_Yun_ ( _MS_ I.E.84–85)
To Make a Person Ailing from the Horse not Have Spasms ( _MS_ I.E.86)
To Make a Person Ailing from the [1] not Have Spasms
To Make a Person Ailing from the Sheep not Have Spasms
To Make a Person Ailing from the Snake not Have Spasms
Various Eating Ailments
Various [1] Ailments
Urine Retention Ailment ( _MS_ I.E.88–114)
When Urine Has [1] Sediment ( _MS_ I.E.115)
Lard Urine ( _MS_ I.E.116)
Swollen Scrotum ( _MS_ I.E.117)
Intestine Inguinal Swelling ( _MS_ I.E.118–41)
Vessel Hemorrhoid ( _MS_ I.E.142)
Male Hemorrhoid ( _MS_ I.E.143–46)
Female Hemorrhoid ( _MS_ I.E.147–54)
Anus Itchiness ( _MS_ I.E.155–56)
_Ju_ Abscess Ailment ( _MS_ I.E.157–73)
[2] ( _MS_ I.E.I74–75)
[1] Burns ( _MS_ I.E.176–93)
Shin Burns ( _MS_ I.E.194–97)
Shin Wounds ( _MS_ I.E.198–99)
Scabies ( _MS_ I.E.200–223)
Snake Bite ( _MS_ I.E.224)
Abscess ( _MS_ I.E.225–32)
Lacquer ( _MS_ I.E.233–39)
Chewing by Bugs ( _MS_ I.E.240–48)
Dry Itch ( _MS_ I.E.249–56)
Old Scabbing ( _MS_ I.E.257–70)
_Gu_ ( _MS_ I.E.271–75)
Child Sprite ( _MS_ I.E.276–77)
Removing a Person's Horse Warts ( _MS_ I.E.278–79)
Treating Facial Pustules ( _MS_ I.E.280–82)
Altogether Fifty-two
_MS_ I.E.2 (CC1–2)
Various Wounds
[2] lard and _gancao_ (licorice), two portions of each; _gui_ (cinnamon), _jiang_ (ginger), _jiao_ (zanthoxylum), [22]. Crush one ball in a cup of liquor and drink it. Drink once daily. {1} [1] {1} [?].
_MS_ I.E.3 (CC3–4)
Another. [4] _qu_ , made to be the size of small beans. Then combine with one _dou_ of _chida_ (adzuki beans) and [1]. Again smith [11] {1} [3]. Drink the liquid, entirely consuming the dregs along with the liquid. Eat it as you wish. It relieves pain {1} [?].
_MS_ I.E.4 (CC5–7)
Another. Smith _ji_ [2] soak using pure liquor, and shape into wafers. Bake in a pottery kettle, using charcoal [13] soak [1]. Bake as [before]. Then smith. Put a three-fingered pinch into a half cup of warmed liquor. [15] ones, smith one hundred times; for large [1] ones, (smith) eighty times; and for small ones, (smith) forty times. Smith until fine.
_MS_ I.E.5 (CC8–9)
Another. Incinerate the feathers of a white chicken and scalp hair. Smith each in equal amounts. Smith eight times that amount of hundred-grass-residue ash and [6]. [Crush] one ball in one cup of warmed liquor and drink it.
_MS_ I.E.6 (C10)
Another. For a blade wound, incinerate sheep feces and spread (the feces) on it.
_MS_ I.E.7 (C11)
Another. To stop blood from coming out, incinerate scalp hair and press it on the wound.
_MS_ I.E.8 (C12)
Another: To cause the wounded person not to feel pain and not to have blood coming out, take an old cattail mat {1} [3] incinerate [4] the wound.
_MS_ I.E.9 (C13)
Another. When blood is coming out of the wounded person, chant this incantation: "Man, staunch! Woman, vinegar!" Draw five lines on the ground and [1] it.
_MS_ I.E.10 (C14)
Another. To cause the wound to not form a scar, take pig lard and [1] _yan_. Smith together and spread (the salve) on it.
_MS_ I.E.11 (C15)
Another. Spread a man's slime on it. Every time, a scar does not form.
_MS_ I.E.12 (C16)
Another. For a metal wound, use lard, _wuhui_ (monkshood), and [2] {2} [1] fry. Apply (the salve) to it.
_MS_ I.E.I3 (CC17–18)
Another. For a wound, use one handful of _xuduan_ (teazel), two long sticks of _du_ [1], two sticks of _huangqin_ (skullcap), [1] sticks of _gancao_ (licorice), two [1] of autumn _wuhui_ (monkshood), and two saucers of [4]. Then _fry_ together [1] cooked. Wring it in a cloth to obtain the liquid. Use old hemp-wadding [2]. Spread (the salve) on it.
_MS_ I.E.14 (CC19–20)
Another. For [1], smith _huangqin_ (skullcap) and [5] pig lard [2] it. Then wring it in a cloth [8]. Swab (the salve) on it.
_MS_ I.E.15 (C21)
Another. For an old wound, mince _xing_ (apricot) pit kernels. Beat in rancid lard and seal the wound. The bugs then come out. Previously tested.
_MS_ I.E.16 (C22)
Another. Put _xiaoshi_ (niter) in hot water and wash the abscess with it.
_MS_ I.E.17 (CC23–24)
Another. Recipe to cause a metal wound not to be painful. Take a _fenshu_ (mole), and dry and smith it. Take a _zhiyu_ , and incinerate and smith it. [2] _xinyi_ (magnolia bud) and _gancao_ (licorice), each in the same amount as the _fenshu_ (mole). Combine them all, stirring. Take one three-fingered pinch, put it in one cup of warmed liquor, and drink it. If this does not work, increase the medicine a bit. Stop when it is no longer abscessed. Excellent.
_MS_ I.E.18 (CC25–29)
Another. To cause a metal wound not to be painful. Take one portion of the thoroughly dried fruits of _ji_ (capsella), scorched until blackened and smithed; and two portions of _zhu_ (atractylodes) root, peeled and smithed. Blend the two substances together. Take one three-fingered pinch reaching to the knuckles and put the medicine into one brimming-full cup of pure liquor. Stir and drink. For those who do not (usually drink), use one half cup of liquor. Having drank it, after some time there is no pain. If pain occurs again, drink the medicine following the same procedure. If there is no pain, do not drink the medicine. (Take) the medicine before eating or after eating as you wish. While treating the ailment, do not eat fish, pork, horseflesh, turtles, snakes, odorous foods, and _mazhu_ greens. Do not approach the inner (chamber). When the ailment desists, (you may do things) as before. While treating the ailment, there are no temporal (restrictions). Smith enough medicine to treat the ailment. After smithing the medicine, store it in a silk pouch. When smithing the _zhu_ (atractylodes), let it dry by putting it in the sun or by some other means, then smith. Excellent.
_MS_ I.E.19 (CC30–33)
Rigidity Due to a Wound
Rigidity occurs when there is a wound, wind enters the wound, and then the body becomes straight and cannot bend. To treat it, scorch salt until it turns yellow. Wrap one _dou_ of it in a cloth. Quench it in pure liquor, dipping it in and then immediately taking it out. Cover it with an apron, and hot-press the head with it. If it is too hot, lift it off and lower it when all right. {1} [1] {1} and once again hot-press. When the hot-press becomes cold, once again scorch salt and use it to hot-press. Continue hot-pressing without interruption. With the first hot-pressing, cold and sweat come out. After a great amount of sweat has come out, and (the body) can bend and straighten, stop. While hot-pressing as well as for four days after hot-pressing, [2] clothing, and do not let (the body) be exposed to wind. After four days (the body) feels good again. Hot-press before eating or after eating as you wish. There are no prohibitions and no temporal (restrictions). Excellent.
_MS_ I.E.20 (CC34–36)
Another. For rigidity due to a wound, boil _li_ (plum) fruit in a sufficient amount of water. Let it bubble rapidly and then remove (the liquid). Sieve (the fruit) to obtain the liquid. When cooled to lukewarm, give it to the ailing person to drink. When drinking, take [2] as the measure. If the ailment is severe and (the ailing person) cannot drink, open his mouth forcibly and pour it in for him. If at the time there is no _li_ (plum) fruit, [6] boil, and drink the liquid following the same procedure as for the fruit. There are no prohibitions. Previously tested. Excellent.
_MS_ I.E.21 (CC37–40)
Another. For various wounds when wind enters the wound, which becomes abscessed and painful. Treat it using wadded hemp to make {1} [3] the wound. Soak [5] pig lard {2} [3] {1} continually [1] pour the lard downward without interruption, thereby expelling the cold vapor. [4] {1} [5] and spread it on the opening of the wound. Cover with a napkin [1] {3} [20] {1} [5]. Spread the medicine on (the wound) before eating or after eating as you wish. There are no prohibitions and no temporal (restrictions). [1] _yu_ (arsenopyrite) {1} [3] {1} [1].
_MS_ I.E.22 (CC41–42)
Another. For rigidity due to a wound, chop finely one dog and allow it to rot with one half _dou_ of malt. Do not remove its feet. Place both in a [1] and soak at the bottom of a well. [3] and take it out. Dry in the dark for one hundred days. Then if someone has rigidity, smith, blend one three-fingered pinch into one cup of warmed liquor, and drink it.
_MS_ I.E.23 (C43)
Another. For rigidity due to a wound. Take one handful of _xie_ (scallions) and boil in one half _dou_ of pure liquor until it bubbles. Drink it, and immediately sit with warm clothing pressed around all four sides. When sweat comes out and reaches the feet, then [1].
_MS_ I.E.24 (C44)
Another. Smith _huartgqin_ (skullcap) and _gancao_ (licorice), half and half. Then fry it in a sufficient amount of pig lard. Fry it until it bubbles, then wring it in a cloth to remove the liquid. [1] spread [1].
_MS_ I.E.25 (CC45–47)
Infant-cord Rigidity
Cord rigidity occurs if at the time of birth (the infant) remains on damp ground for a long time. The flesh by the bones stiffens and the mouth locks; the muscles cramp and are hard to straighten. Take anthill loam and smith it. [2], two portions; and salt, one portion. Combine them, stirring, and steam. Use it to hot-press all round the areas of stiffened flesh and cramped muscles. Starting from the head gradually [1] the hands and feet and no more. When the hot-press becomes cold [2] and steam it again. When the hot-press dries out, make a new one. Excellent.
_MS_ I.E.26 (CC48–50)
Recipe for Infant Ailing from Spasms
Take three nodules of _leishi_ (bamboo truffle) and smith. Blend fried pig lard into it. For a small infant use one half _dou_ of water, and for a large one use one _dou_. Divide the blended mixture into three parts. Place one part in the water, stir, and bathe the infant with it. When bathing, begin at the top of the head and proceed downward over the entire body, without letting the four limbs get wet. Bathe once a day for three days. It desists after three days. After bathing always discard the water immediately in the privy. When spasms occur the body is hot and continually trembles. The neck and spine are rigid and the abdomen is enlarged, [1] spasms are many and various. Using this medicine, they all desist.
_MS_ I.E.27 (CC51–55)
Infant Convulsions
When infant convulsions occur, the eyes are fixed in a sidelong gaze. The sides are painful, the breath is quick and shrill, and the feces remain green without transforming. Take vegetation from the upturned-slope of the roof. Incinerate it using kindling and [1] it in a ladle. Make silted water that is roiled thrice and fill a cup with it. Then spit on the ladle and chant this incantation over it:
"Spouter, spout ferociously. On high be like the sweeper star. Down below be like congealed blood. You will be seized left of the gate. You will be cut apart right of the gate. Should you not desist, you will be quartered and exposed in the marketplace." Then stroke with the ladle in a circle around the spot where the infant convulsions are, and rinse it in the cup of water. Watch it. When there is blood like a fly wing, discard it by the wall. Take fresh water. Once again spit on the liquid in the ladle and stroke with it as before. There should be no trembling. Repeat it over and over again. When the trembling has ceased, stop. Excellent.
_MS_ I.E.28 (C56)
Mad Dog Bites a Person
Take two _hengshi_ and grind them against each other. Take the bits which are ground to the consistency of gruel and spread them on the dog bite. It will desist.
_MS_ I.E.29 (CC57—59)
Another. When a mad dog bites a person, thoroughly clean silted water. Pour it into a cup, the amount equivalent to the second serving of beverage, Take a three-fingered pinch of stove residue ash and [2] in the water. Give it to the ailing person to drink. After drinking, have him vigorously shake both hands, like [2] {2} [1] {1} [9] the person bitten by the mad dog [3] spread nothing on it.
_MS_ I.E.30 (C60)
Another. When a mad dog wounds a person, smith _yu_ (arsenopyrite) and _tuomo_. Drink it in one half cup of gruel vinegar. Women use the same medicine. {1} [?].
_MS_ I.E.3I (CC61–62)
Wound Caused by a Dog Biting a Person
Take two _sheng_ of earthworm excrement along with an equal amount of dirt deposited at the bottom of the water jar kept by the well. Scorch them together and take fine gruel vinegar [4] it. Shape roughly into balls and hot-press the wound with them. When the dog for is completely removed, spread (the medicine balls) on the wound and it desists.
_MS_ I.E.32 (C63)
Another. Boil stalks. Wash it with the liquid. During winter days, boil the root.
_MS_ I.E.33 (CC64–65)
Another. Recipe to make a dog bite not be painful and to make it easy to cure. Have the person who was bitten lie down and have someone else pour a sufficient amount of liquor over the wound. After pouring, [1] {1} it. Previously tested. There are no prohibitions.
_MS_ I.E.34 (C66)
Nest
Watch for lightning in heaven; then rub both hands together, face the lightning, and chant this incantation: "Eastern Quarter Sovereign, Western Quarter [4] preside over the dark. Darken this person's stars." Do it twice seven times and [1].
_MS_ I.E.35 (C67)
Another. Take choice beef, _wuhui_ (monkshood), and _gui_ (cinnamon). Smith in equal amounts and blend, [1] fumigate, thereby [1] the ailment.
_MS_ I.E.36 (CC68–70)
_Xixia_
Take a three- _cun_ long piece of _huangqin_ (skullcap) and thirty _helu_ the size of [2] beans, skins removed; and smith them together. [7]. Pestle, and boil until it bubbles. Squeeze to remove the dregs. Then using the liquid [2] chill the _xixia_. When finished, use suet [7] the smithed medicine and spread (the medicine) on it. If you are going to spread (the medicine) on it again, chill and spread as before. When finished, the _xixia_ vanishes.
_MS_ I.E.37 (C71)
_Wuhui_ (Monkshood) Poisoning
Roast [2]. Drink the urine of a young boy or fresh _jichi_ , and then with water drink [?].
_MS_ I.E.38 (C72)
Another. Flake _shaoyao_ (peony). With one half cup of [1] take a large three-fingered pinch and drink it.
_MS_ I.E.39 (C73)
Another. Take a _one-chi_ long piece of _qi_ (lycium) root the thickness of a finger. Peel it. Pound it in a wooden mortar. Boil in liquor [?].
_MS_ I.E.40 (C74)
Another. Using [1] liquid, swallow soybeans or _ku_. It desists.
_MS_ I.E.41 (C75)
Another. Boil iron and drink it.
_MS_ I.E.42 (C76)
Another. When there is an occurrence of a person being poisoned, take _miwu_ (lovage) root or [1] _ji_ , one [9]. Spread (the medicine) on the wound.
_MS_ I.E.43 (C77)
Another. Dig up the ground to a depth of [1] _chi_ , and then boil one jar of water [11] one cup.
_MS_ I.E.44 (C78)
Scorpion
[7] {3} _xie_ (scallion) [?]
_MS_ I.E.45 (C79)
Another. [?].
_MS_ I.E.46 (C80)
Another. Moisten, spread salt on it, and have a cow lick it.
_MS_ I.E.47 (C81)
Another. Seal it with _jili_ (caltrop) and _baihao_ (artemisia).
_MS_ I.E.48 (CC82–83)
Another. Spit on it and spout: "Elder Brother and Father live on Tai Mountain. You dwell down in [1] Ravine. [3] {2} [4] {1} Wind Bird [6] flee. Flee, and its beak will bore your heart."
_MS_ I.E.49 (C84)
Another. "Father dwells in Shu. Mother is the Wind Bird who punishes. Do not dare flee up or down. The Wind Bird bores your heart."
_MS_ I.E.50 (C85)
Leeches Bite a Person's Shin, Thigh, and Knee
When they appear in these places, combine glutinous panicled millet, soybeans, and glutinous spiked millet—three (substances). Cook them. Steam [4] ailment.
_MS_ I.E.51 (C86)
Another. Mince _gui_ and spread (the _gui_ ) on it.
_MS_ I.E.52 (C87)
Lizard
Mince _lan_ (eupatorium). Pour liquor over it. Drink the liquid and seal the wound with the dregs. Change it continually. {2} [?].
_MS_ I.E.53 (C88)
Another. Press _ji_ (thistle) into the center of the crown of the head.
_MS_ I.E.54 (C89)
Another. Rub it with a raw suckling pig snout.
_MS_ I.E.55 (C90)
Another. Take one piece _of jin_ and beat it into bits. Seal it (with the medicine). Then incinerate deer horn and drink it with urine.
_MS_ I.E.56 (C91)
Another. Blow: "Tsjar Nien bites. The killed man now criesout." Repeat it again.
_MS_ I.E.57 (CC92–93)
Another. Make gruel with blue choice millet grains. Use fifteen parts water to one part grain to produce five _dou_ of gruel. Remove it, let the vapor steam away, and fill a new pottery water jar with it. Cover the mouth with three layers of cloth. Then seal it with mud two _cun_ thick. Bake until the mud is completely fired, and drink it. The wound desists.
_MS_ I.E.58 (CC94–95)
Another. Boil two roosters that have been aged for three nights, pouring three _dou_ of water (into the kettle). Remove when done. Scoop out the liquid and pour it over (the roosters) again. Set a [metal] [1] beneath a slotted steaming-pot and cook the five grains. Drop rabbit [1] flesh into the slotted steaming-pot. Gradually pour the liquid on top, letting it collect in the bowl below. When done, drink the liquid.
_MS_ I.E.59 (C96)
Another. Spout and blow: "Hidden eater. Father's dwelling is at the north. Mother's dwelling is to the south. Together they gave birth to three men who do not treat people virtuously. Desist. If you do not desist, _qing_ (azurite) will be spread on it."
_MS_ I.E.60 (CC97–98)
Another. Put one cup of silted water into a large-bellied gourd. Carry it in the left hand. Facing north, face towards the person and perform the Pace of Yu thrice. Ask his name. Then say: "So-and-so was [1] by a certain Nien and now [1]." Have (the person) drink one half cup and say: "Ailment [2] desist; slowly leave, slowly desist." Then cover the gourd flask and discard it.
_MS_ I.E.6I (C99)
Another. Boil deer flesh or wild pig flesh. Eat it and drink the liquid. Superb.
_MS_ I.E.62 (C100)
Another. Incinerate the skin of a _li_ (raccoon-dog). Smith the ash. Put it into liquor and drink. Large amounts are permitted and do not harm the person. Boil sheep flesh. Take the liquid and [1] it.
_MS_ I.E.63 (C101)
Take mud from inside a well. Surround and seal the wound with it. It desists.
_MS_ I.E.64 (C102)
Warts
Take a worn-out cattail mat or the soft leaves of a cattail bedmat and make them into a cord. Then light the tip and cauterize the tip of the wart with it. When it becomes hot, pluck off the wart and discard it.
_MS_ I.E.65 (C103)
Another. Have the person with warts clasp grain plants. Have other people shout: "Why do you do this." Respond: "I am the wart." Set the grain plants down and leave without looking back.
_MS_ I.E.66 (C104)
Another. On the last day of the month go to an abandoned well that has water in it. Brush the warts twice seven times with a worn out broom and chant this incantation: "Today is the last day of the month. I brush the warts to the north." Drop the broom into the well.
_MS_ I.E.67 (CC105–107)
Another. On the last day of the month at the end of the late afternoon, take clods the size of a chicken egg—men seven and women twice seven. First set the clods down behind the house, arranging them in a line from south to north. When dark, go to the place where the clods are. Perform the Pace of Yu thrice. Starting from the southern quarter, pick up a clod and say: "Today is the last day of the month. I rub the warts to the north." Rub the [1] once with the clod. After rubbing, set the clod back in its place and leave without looking back.
_MS_ I.E.68 (C108)
Another. On the last day of the month, go behind the inner (chamber). Say: "Today is the last day of the month. I rub the warts north of the inner (chamber)." Rub the warts on the wall of the inner (chamber) twice seven times.
_MS_ I.E.69 (CC109–110)
Another. On the first day of the month, rub the warts twice seven times with _kui_ (mallow) stalks. Say: "Today is the first day of the month. I rub the warts with a _kui_ (mallow) halberd." In addition, take _sha_ root or _jian_ root from the side of the road—twice seven in number—and toss them into a marsh or deep pool. If it is a "removal day," (wait until) after mid-month.
_MS_ I.E.70 (C111)
Another. To treat warts by incantation, go to the north of the house on the last day of the month. Rub the warts—men seven times and women twice seven times. Say: "Today is the last day of the month. I rub the warts north of the house." The warts desist within a month.
_MS_ I.E.71 (CC112–13)
Seizure Sickness
First have ready a white chicken and dog feces. When it occurs, use a knife to cut open his head from the crown to the nape. Then moisten that with the dog feces and halve the chicken. [1] cover the place that was moistened with dog feces. Stop after three days. After stopping, cook the chicken that was used to cover and eat it. [1] desists.
_MS_ I.E.72 (C114)
Another. For seizure sickness, take _quanwei_ and grain plants that are on the wall of the animal pen. Smith it, hammering. Drink with silted water.
_MS_ I.E.73 (CC115–16)
Recipe for _Baichu_
Take Guan _qing_ (azurite), another name for which is Guan laminar—using (an amount) like [2]; salt, one twentieth of a _dou_ ; and yellow earth from the stove, one tenth of a _sheng_. Smith all and [2] {I} and drink it before eating. If it does not desist, repeat it again and [1] the Guan _qing_ (azurite). Drink a second time and it desists. Excellent.
_MS_ I.E.74 (CC117–29)
Another. [2] {1} [5] {3} [2]. To treat it, take one half _dou_ of unbroken bird eggs, [1] sweet salt [15] {1} [6] into it. The eggs come second. {1} [5]. Cover the water jar with four [layers] of cloth [16] three [6] {1}. After daubing (the medicine) on it, hang (the medicine) in the [place] for drying in the dark. [20]. Cover the flesh thickly, completely covering the areas with _chu_ and no more. [5] {2} [4]. Stop when the heat is unbearable. Having stopped, the _chu_ [2]. Even though it responds, do not remove the medicine. The medicine [2] {2} [1]. [2] {1} [1]. When roasting it, [1] eat very [3] {1}, and do not spread (the medicine) on it with the hands. Spread the medicine at dawn before eating. After spreading the medicine, drink good liquor, stopping when very sated. Then roast [1]. After roasting [1] it and rise. When you want to eat, eat. Goings and comings as well as drink and food are all as you wish. Apply the medicine at dawn. Beforehand, do not eat [1] for two to three days. While applying the medicine, do not eat fish. When the ailment desists, (you may do things) as before. While treating the ailment there are no temporal (restrictions).
Collect the bird eggs between the fifteenth and seventeenth of the second and third months. After [1], then use them. [2] bird. Even though the eggs have kernels they are still usable. When this medicine is finished, even if it sits for over ten years up to [1] years, it continues to get better. [1] becomes dry and cannot be daubed on the body, take a small amount of the medicinesufficient to daub on the _chu_ —and [1] it in a shallow pottery bowl with fine gruel vinegar. Let it soak [1] and it can be blended, gradually returning to its regular (consistency). Boil gelatin. Then set the bowl over a fire of grain chaff until the medicine is finished and remove it. After removing it [4] daubing, cover with cloth, use a shallow bowl as a lid, and hang it in the place for drying in the dark. Medicine made ten years previous becomes dry.
_MS_ I.E.75 (CC130–31)
Another. _Baichu_. When _baichu_ occurs, there is whiteness and no webbed pattern. Take cinnabar granules and _zhanyu_ (sturgeon) blood or chicken blood—either one is permissible. Leave a chicken to soak for two [2] it [1]. Scratch the _chu_ with the claws until they redden, and [spread] (the medicine) on them. Wash after two days and wipe thoroughly with new cloth. Spread (the medicine) again following this procedure, stopping after thirty days. Excellent.
_MS_ I.E.76 (C132)
_Dadai_
Incinerate _dang_. Combine with old lard and spread (the medicine) on it.
_MS_ I.E.77 (C133)
Another. Boil gelatin in clear (liquor). Daub (the medicine) on it.
_MS_ I.E.78 (CC134–36)
Recipe for _Ming_ Ailment
_Ming_ is a bug. The places where it chews holes [1]. It does not emerge at a regular spot. Sometimes it is located at the nose, sometimes at the side of the mouth, sometimes at the teeth and gums, sometimes at the hands and fingers [1]. It causes a person's nose to be gouged out and his fingers to break off. To treat it, take fresh raw fish [1] and blend a sufficient amount of salt with it. Spread (the medicine) where the bug has chewed [6] it, stopping when the ailment desists. Previously tested. There are no prohibitions. Excellent.
_MS_ I.E.79 (C137)
[1] Quan
[2] put one _quan_ into an egg [4] it.
_MS_ I.E.80 (CC138–39)
Put in [?] rabbit skin [?].
_MS_ I.E.81 (C140)
Another. Mince _lan_ (eupatorium) [?].
_MS_ I.E.82 (C141)
Another. Use pure liquor [?].
_MS_ I.E.83 (C142)
Another. Pour hot water over [?].
_MS_ I.E.84 (C143)
_Yun_
Take _lan_ (eupatorium) [?].
_MS_ I.E.85 (C144)
Another. Roast _hua_ (birch) [?] _yun_.
_MS_ I.E.86 (CC145–47)
To Make a Person Ailing from the Horse not Have Spasms
[?]. Bathe the ailing person with it. If the ailing person is a woman [1], and if a man [?]. Then incinerate a woman's first (menstrual) cloth [?].
_MS_ I.E.87 (CC148–49)
[?] drink. Use cloth [?] in liquor and drink [?].
_MS_ I.E.88 (CC150–51)
[6] dried _cong_ (onion) [?] salt the _duo_ (navel) and roast the buttocks.
_MS_ I.E.89 (C152)
Another. Seal the _duo_ (navel) and lesser abdomen with _chuohua_ [?].
_MS_ I.E.90 (C153)
Another. Smith one third _sheng of ximing_ (pennycress) and one [1] of old _kui_ (mallow) seeds and [?].
_MS_ I.E.91 (C154)
Another. Boil one bunch of _longxu_ (bog rash) in three _dou_ of silted water.[?].
_MS_ I.E.92 (C155)
Another. Cauterize the middle toe of the left foot.
_MS_ I.E.93 (CC156–57)
Another. [Perform the Pace of Yu] thrice. Take a cup of silted water. Spout and snort three times. Say: "Above there is [10] spearhead. So-and-so [5] drink it and cover the cup.
_MS_ I.E.94 (CC158–60)
Another. Recipe for when [2] and dries up so that it does not come out. Put pure liquor into a [1]. Boil gelatin, {1} [7] incinerate {1} [4] fire and quench in the liquor. When the bubbling stops, remove it. Have the ailing person drink the liquor. [8] drink it, until [3] and rise as you wish. If it does not desist, repeat [it] again following this procedure. Excellent.
_MS_ I.E.95 (CC161–65)
Another. Urine retention. There is pain in the bladder and the inside. The pain is intense, and when urinating [1] the pain is even more intense. [4]. To treat it boil three _sheng_ of black soybeans in three [1] of fine gruel vinegar. Cook rapidly. When it bubbles, stop the fire. When the bubbling subsides, cook again, stopping after it bubbles for the third time. Sieve to obtain the liquid. Use one portion of oysters and three of smithed _dujin_—altogether two substances—[2]. Take one three-fingered pinch reaching to the knuckles, put it into lukewarm gruel vinegar, [1] drink it. Drink before eating or after eating as you wish. After drinking it once the ailment responds. Drink it once a day. After three days the ailment desists and a stream of stones like rice slop comes out of the front. There are no prohibitions and no temporal (restrictions). Smith the oysters. Do not dry the _dujin_ in the sun. On the day of the summer solstice go to [2] the _dujin_. Dry it in the dark. Smith the leaves and fruits together and store in a leather pouch. When (you need to) use it, take it (from the pouch). Collect _dujin_ again every year. _Dujin_ [3] _jin_ leaves are different and smaller. The stalks are red and the leaves have vertical cords. [1] leaves and fruit have a bitter taste. It forms fruit about six or seven days before the summer solstice. [4] by the side of a marsh. Excellent.
_MS_ I.E.96 (C168)
Another. Boil one _dou_ of _kui_ (mallow) seeds in one _dou_ of water. Sieve to obtain the liquid. Boil one and a half sticks of gelatin in the liquid to produce one third _dou_ of liquid and [?].
_MS_ I.E.97 (C169)
Another. Fill the _duo_ (navel) with a small cup of Rong salt or fine salt. In addition, daub it [1] the _duo_ (navel) from the bottom reaching to the top, and dry in the sun {1} [?].
_MS_ I.E.98 (C170)
Another. Boil _kui_ (mallow) and drink the liquid. In the winter [2] the root. Pour [2].
_MS_ I.E.99 (C171)
Another. Boil _kui_ (mallow) and drink the liquid. Then [2] {1}, taking a large amount as the standard, and [2] the buttocks.
_MS_ I.E.100 (C172)
Another. Soak the neckband of an undershirt and dandruff in one cup of liquor. Let it bubble and drink it.
_MS_ I.E.101 (CC173–75)
Another. Urine retention. Recipe for when urination is difficult and the bladder is full. Take two _sheng_ of coarsely flaked _zao_ (jujube) seeds and one _sheng_ of _kui_ (mallow) seeds. Combine them, stirring. Divide into three portions. Boil one portion in one and a half _dou_ of water. When done, remove the dregs and again boil one portion, proceeding like this until all three portions are used up. Sieve to obtain the liquid. Blend in honey until it is just sweet. When lukewarm [1] drink it. When the medicine is used up, make it again. Stop when the ailment desists. Excellent.
_MS_ I.E.102 (CC 176–77)
Another. Urine retention. Take one large bunch of _one-chi_ long _jingtian_ (stonecrop) and divide into three parts. Scald it thrice in one half _dou_ of pure liquor. When done, sieve to obtain the liquid, and drink it. If it does not desist, repeat it. After no more than the third time of drinking, it desists. Do not eat the evening before. Drink the medicine at dawn. Excellent.
_MS_ I.E.103 (CC178–79)
Another. Urine retention. Make a square pit one and a half _chi_ to a side and as deep as your elbow. Then burn old straw in it until the ash is not quite one half _chi_ deep. Lightly sprinkle fine liquor on it. [1] one _zaojia_ (honey locust), fourteen _zao_ (jujubes), _yi_ style _zhuyu_ (evodia), and _jiao_ (zanthoxylum). Combine, deposit in one spot in the pit, and burn it. Drop the lower (body) into it. When it desists, rinse.
_MS_ I.E.104 (C180)
Another. Urine retention. Incinerate old fodder or old kindling. Have the ailing person turn his back to the fire and roast it. Have two people rub his buttocks for him. The urine retention desists.
_MS_ I.E.105 (C181)
Another. Boil one third _dou_ of gelatin and one _sheng_ of rice in one _dou_ of water. When cooked, eat it. Do not eat at night.
_MS_ I.E.106 (C182)
Another. Take snails, twice seven in number, and one small bunch of _xie_ (scallions). Boil them together in liquor and drink it.
_MS_ I.E.107 (C183)
Another. At daybreak on a _jisi_ day, shout. Face east and urinate. If it does not desist, repeat it.
_MS_ I.E.108 (C184)
Another. Bloody urine retention. Boil _jing_ (vitex). Heat it thrice, and drink it.
_MS_ I.E.109 (C185)
Another. Stone urine retention. Boil _shiwei_ (pyrrosia) and liquor, heating it thrice, and drink it.
_MS_ I.E.110 (C186)
Another. Lardy urine retention. Use _zaoshi_ the size of a plum pit. Drink it after eating. If it does not desist, repeat it.
_MS_ I.E.111 (C187)
Another. Female urine retention. Take three-year-old bean leaves. Steam and obtain the liquid. [1] and drink it.
_MS_ I.E.112 (C188)
Another. Female urine retention. Boil _yinfu mu_ , and drink it. Wait one day. Mince _yang_ [1] and make it into a boiled-dish.
_MS_ I.E.113 (C189)
Another. Boil glutinous panicled millet and panicled millet in gruel vinegar and liquor, scalding thrice, and drink the liquid. All [2].
_MS_ I.E.114 (C190)
Another. Use the hem-band from a robe to bind the thumb of the left hand once. In three days [1].
_MS_ I.E.115 (C191)
Recipe for When Urine Has [1] Sediment
Take [6] {1} [4] {1} take _hao_ from under a magpie dwelling.
_MS_ I.E.116 (C192)
Lard Urine
This is called Internal Return. Boil old _kui_ (mallow) seeds in water and urine, and drink it. In addition, mince _yang_ [1] and make it into a boiled-dish.
_MS_ I.E.117 (CC193–94)
Swollen Scrotum
When swollen scrotum occurs, the scrotum is black and distended, and it does not go away. To treat it, take three _dou_ of coarse horse manure. Break it up thoroughly. Pour water over it, stopping when the water is clear. Sieve to remove the liquid. Pour in [1] _dou_ of _suattjiang_. Take _jie zhong jia_. After using once, it responds. After using four or five times, the swelling goes away. There are no prohibitions and no temporal (restrictions). Excellent.
_MS_ I.E.118 (CC 195–97)
Inguinal Swelling
Grasp a _bai_ (arbor-vitae) pestle. Perform the Pace of Yu thrice. Say: "Spouter expel the Hu once. Spouter expel the Hu twice. Spouter expel the Hu thrice. The _bai_ (arbor-vitae) pestle bores through the mortar. There is one Mother and one [Father; Sons] there are only three. Spouter, for these swellings you use the _bai_ (arbor-vitae) pestle seven times and let not a single one of so-and-so's inguinal swellings remain." Members of the same clan must be made to carry [1] the person with inguinal swelling, set him down by an east-facing window looking out, and beat him with the exorcising rod.
_MS_ I.E.119 (C198)
Another. At the time of clear brightness have someone whose foot has been cut off face east and stamp on the person twice-seven times with the amputee peg.
_MS_ I.E.I20 (CC 199–200)
Another. For prostration. On the sixteenth day of the month when the moon first begins to deteriorate, perform the Pace of Yu thrice. Say: "Moon is matched against sun" and "Sun is matched against moon"—three times each. "Father is perverse, Mother is strong. Like other people they bore Sons, and only bore inguinal swelling bulges. Perverseness desist. Grasp the hammering stone and strike your Mother." Immediately, exorcistically beat and hammer the person twice seven times with an iron mallet. Do it at sunrise, and have the person with inguinal swelling face east.
_MS_ I.E.121 (C201)
Another. Soak a woman's (menstrual) cloth. Boil meat in the liquid. Eat it, and drink the liquid.
_MS_ I.E.122 (C202)
Another. Break an egg into a cup of gruel vinegar. Drink it.
_MS_ I.E.123 (C203)
Another. Roast silkworm eggs until they sizzle and turn yellow. Smith them. Put a three-fingered pinch reaching to the knuckles into one half cup of liquor. Drink it for three or four days.
_MS_ I.E.124 (CC204–205)
Another. On. a _xinsi_ day utter this curse: "The day is _xinsi_ " _—_ three times. Say: "Spirit of Heaven send down the sickness-shield. Spirit Maids according to sequence hear the spirit pronouncement. A certain fox has seized a place where it does not belong. Desist. If you do not desist, I hack you with an ax." Immediately grasp a cloth and exorcistically beat the person twice seven times.
_MS_ I.E.125 (CC206–207)
Another. At sunrise have the person with inguinal swelling face east beneath the roof gutter. Have another person grasp a rammer, face west, and chant this incantation: "Today [1]. So-and-so's inguinal swelling bulges today desist. So-and-so's inguinal swelling desist. [1] your Father and Mother. Both are expired— _bai_ (arbor-vitae) rammed them. Throwing down Father and hitting the Sons, how can there not be desistance." Hit the inguinal swellings twice seven times with the rammer. After completion, immediately say: "So-and-so rise. Inguinal swelling desist."
_MS_ I.E.I26 (C208)
Another. On a _xinmao_ day, stand at the foot of the hall facing east toward the sun. Have someone lift the person with inguinal swelling by both arms. Say: "Today is _xinmao_. His name is changed to Yu."
_MS_ I.E.127 (C209)
Another. Take _xi_ (hemp) refuse and wrap in _ai_ (mugwort). Use this to cauterize the center of the crown of the head of the person with inguinal swelling. Let it blister and no more.
_MS_ I.E.128 (C210)
Another. Have the person with inguinal swelling look north and lie down facing north in a hall with a four-slope roof. Perform the Pace of Yu thrice. Shout: "Gwjag. Fox _piao_ "—thrice. "You know so-and-so ails from fox [?].
_MS_ I.E.129 (C211)
Another. Inguinal swelling and goiter. Steam the food sacrifice of a dead person and wrap it in new cloth. Use a sack [4] {2} [?].
_MS_ I.E.130 (C212)
Another. Wrap hive-bee eggs that have been dried in the dark in cloth [2].
_MS_ I.E.131 (C213)
Another. When there are inguinal swellings as well as thigh abscesses and rat bellies, [1] scratch twice seven times with the middle finger. It is invariably cured.
_MS_ I.E.132 (C214)
Another. Use straw to make a bow, the cord handle from a slotted steaming-pot to make a bowstring, _ge_ (kudzu) to make arrows, and [feather them] with [1] feathers. Shoot at dawn. At sunset [1] become small.
_MS_ I.E.133 (CC215–16)
Another. Take a _one-chi_ square (sheet) of dark silkworm eggs, once seven clothes-eating _baiyu_ (silverfish), and twice seven _changzu_ (spiders). Scorch the silkworm eggs until they turn yellow and grind. Smith the silkworm eggs. Also grind the _baiyu_ (silverfish) and _changzu_ (spiders). Measure the three proportionately and combine. Blend with two _sheng_ of gruel vinegar. Drink it before eating. Infants use one _sheng_.
_MS_ I.E.134 (CC217–20)
Another. Bore into a small gourd, making the hole (large enough) to completely contain the testicles and penis of the person with inguinal swelling. Then have the person with inguinal swelling cup the gourd in his hands, face east, and kneel beneath an old eastern wall. Then insert his testicles and penis into the hole in the gourd. Make _four-cun_ long pegs from _cai_ (oak), twice seven in number. Then chop at them with a _cai_ (oak) mallet, once [2] and twice smoothing them. After they are chopped, immediately poke the pegs (into the ground) beneath the wall, stopping when all twice seven pegs have been exhausted. Always do it when the moon is waning on the sixteenth day [2] exhausted. Do it once a day. [1] do it a second time. Always do it when the stars come out. Wait for the inguinal swelling to desist and then stop.
_MS_ I.E.135 (CC221–22)
Another. Inguinal swelling. First raise the testicles and pull down the skin. Pierce the side of the _duo_ (navel) with a lancing-stone. [2] liquid and lard [1] stir with pure [liquor]. In addition, cauterize the wound. Do not allow the wind to reach it. For an easy cure, cauterize the Great Yin and Great Yang [2]. Excellent.
_MS_ I.E.136 (CC223–24)
Another. Recipe for treating inguinal swellings when they first erupt, and there is humping and cramping but they are not yet large. Take one whole bug slough and [3] incinerate both. [8] liquor , drinking a sufficient amount to become intoxicated. Allowed for men and women. Excellent.
_MS_ I.E.137 (CC225–26)
Another. Inguinal swelling. Cover the testicles with a large-bellied gourd. Then take _tao_ (peach) branches that face east and make a bow with them. Take [1] {I} [11] {I}. On the last day of the month shoot three arrows in one shot. [2] drink the medicine. The medicine is called "yellow cow gall dried in the dark." When it has dried, gradually [9] drink it.
_MS_ I.E.138 (CC227–31)
Another. Smith one _chi_ of _jungui_ (curled cinnamon) and one _sheng_ of _du_ [1]. Smith them together and place inside a bamboo tube. Fill the bamboo tube [18]. Then cover with cloth. Spread it below the _duo_ (navel) in two places. {3} [17] it. {6}. Wait for his body to become calm and stable. [18]. When inguinal swelling desists, reverently perform the requital rite with a suckling pig. If this is considered inhumane, use _bai_ [19]. Hang the _mao_ (woolly grass) in the place for the pig sacrifice and requite the favor {2} [?]
_MS_ I.E.139 (CC232–34)
Another. [1]. Take a woman's menstrual cloth. Soak it, and roast until it becomes warm [24] [vegetation] from the four up-turned slopes of the roof. Incinerate _lianghuang_. Smith five _cun_ of _gui_ (cinnamon). [?] {1} [?]
_MS_ I.E.140 (C235)
Inguinal swelling [1]. Cauterize the left shin. [?]
_MS_ I.E.141 (C236)
Another. Do not eat at night. At dawn take one bee egg. Soak it in one cup of fine gruel vinegar and give it to the person to drink.
_MS_ I.E.142 (CC237–38)
Vessel Hemorrhoid
Take equal amounts of the fur from five kinds of wild animals whose flesh is eaten. Incinerate and smith. Combine them, stirring [1]. Every dawn before eating take three large three-fingered pinches and blend in one cup of warm liquor. Drink it. At sunset drink it again before eating, following the previous procedure. Continue ingesting the medicine for twenty days. Even an old ailment invariably [1]. While ingesting the medicine it is prohibited to eat pork and fresh fish. Previously tested.
_MS_ I.E.143 (CC239–40)
Male Hemorrhoid
There is snail-like flesh protruding, sometimes like the shape of a rat teat. The tip is large and the base small, and there is a hole in it. [1] it, heat it quickly using cauterization, grasp the small base, and twist until it breaks off. Take the millet food sacrifice from the offering niche by the entrance to the inner (chamber) and incinerate the head of a dead person. Smith both, moisten with rancid lard, and put it into the hole.
_MS_ I.E.144 (CC241–43)
Another. For when there are many holes. Boil fatty black ewe and use the liquid to soak three _dou_ of fine glutinous panicled millet. Cook it, and moisten with (ewe liquid). When done, divide into two portions. Use [3] {1} one portion. Then take copper bits and the dregs of soybean sauce, half and half. Pestle together. Spread (a layer) as thick as a _jiu_ (leek) leaf on the holes. Then wrap with thick cloth. [2] warm it anew. In two days it desists.
_MS_ I.E.145 (CC244–45)
Another. Recipe for male hemorrhoids lodged on the side of the anus—large ones like a _zao_ (jujube) and small ones like a _zao_ (jujube) pit. Use a small horn to perform horn treatment for the time it takes to cook two _dou_ of rice and lift off the horn. Bind it with a small cord and cut it open with a knife. Inside there is something like a _tu_ fruit. If hardened blood comes out like it is breaking open the tip (of the hemorrhoid), then it desists. Excellent.
_MS_ I.E.146 (CC246–47)
Another. Recipe for male hemorrhoids the size of a _zao_ (jujube) pit lodged on the edge of the anus which at times itch and at times are painful. First cut it off. If it cannot be cut off, [take] turtle brain and _didan chong_ (oil beetles), half and half. Blend and spread on (the hemorrhoid). Burn small oblong stones. Quench them in gruel vinegar and use them to hot-press. If it does not desist, repeat it again following this procedure. Excellent.
_MS_ I.E.147 (CC248–52)
Female Hemorrhoid
Recipe for (female hemorrhoids) that are one _cun_ inside the anus, are shaped like a cow louse, {1} [2] {1}, burst and ooze blood when defecating, and face upward when not defecating. Take five _dou_ of urine. Use it to boil two large handfuls of _qinghao_ (wormwood), seven _fuyu_ (golden carp) the size of a hand, a six _cun_ piece of smithed _gui_ (cinnamon), and two nodules of dried _jiang_ (ginger). Let it bubble ten times. Remove (the liquid) and put it in a water jar. Bury (the jar) under a sitting mat, make an opening in it, and fumigate the hemorrhoids. Stop when the medicine becomes cold. Fumigate thrice a day. When the throat becomes choked, drink medicinal beverage and do not drink anything else.
The recipe for making medicinal beverage. Take two _sheng_ of the dried and smithed stalks of _qu_. Soak it in two _dou_ of _shuluo_ (yam) liquid to make a beverage. Drink it, stopping when the ailment desists. The Jing name for _qinghao_ (wormwood) is _qiu_. The Jing name for _qu_ is _luru_. Its leaves can be boiled and are sour; its stalks have thorns. Excellent.
_MS_ I.E.148 (C253)
Another. Recipe for female hemorrhoids that have holes, are curved, and ooze blood. Incinerate a woman's (menstrual) cloth. Set it in a vessel and fumigate the hemorrhoids with it, stopping after three days. Excellent.
_MS_ I.E.149 (CC254–57)
Another. Recipe for female hemorrhoids that have numerous openings with _rao_ (pinworms), white and swarming, coming out. First introduce a slick _xia_ (catalpa) rod to let out the blood. Dig a hole in the ground one and a half _chi_ deep, one _chi_ long, and three _cun_ across. Incinerate [1] charcoal in it. Dry one third _dou_ of _luomart_ and distribute it on the charcoal. Cover the entire top with cloth and kneel to fumigate the anus. When the fumes are extinguished, take fatty [1] flesh and set it in the fire. From time to time, (have the person) open the anus himself. [2] burn [1] {1} fire is extinguished [1] {1} [1]. Fumigate once a day. {1} [2] {1} [1] five to six days {1} [4]. Other names for _luoruan_ are _baiku_ and _kuqin_.
_MS_ I.E.150 (C258)
Another. For hemorrhoids. Pour sauce into a yellow hen until it dies on its own. Wrap it in _jian_ (miscanthus), daub mud on it, and bake it. When the mud has dried, eat the chicken. Use the feathers to fumigate the perineum.
_MS_ I.E.151 (CC259–60)
Another. Smith _miwu_ (lovage), _fangfeng_ (saposhnikovia), _wuhui_ (monkshood), and _gui_ (cinnamon)—all in equal amounts. Soak in pure liquor and form them into balls the size of a black soybean. Then swallow them. At the beginning, eat one. If it does not respond, increase by one, with [1] as the upper limit. It may also be used to master wounds. Always eat them before eating.
_MS_ I.E.152 (C261)
Another. For before there is a nest. Boil one _dou_ of _zao_ (jujubes) and one _dou_ of lard to produce four _dou_ of liquid. Put it in a basin and squat in it. The worms come out.
_MS_ I.E.153 (CC262–63)
Another. For when a nest obstructs the rectum. Kill a dog. Take its bladder and insert it through (the end of) a bamboo tube. Insert the tube into the rectum and blow on it. Draw it out and slowly cut off the nest with a knife. Smith _huangqin_ (skullcap) and spread it on repeatedly. If the person's anus is prolapsed and cannot be put back inside, grease the part that is prolapsed with lard and suspend the person upside down. Throw cold water on his heart and abdomen and it will go back inside.
_MS_ I.E.154(C264)
Bloody hemorrhoid. Boil thoroughly one male rat in urine. Hot-press with the vapor.
_MS_ I.E.155 (CC265–69)
Anus Itchiness
For when hemorrhoids occur and small holes protrude like cones on the side of the rectum of the person with hemorrhoids. At times white worms emerge from the holes, and the burning pain in the rectum is caustic. To treat it use one portion of _liuxun_ (willow fungus) and two of crumbled _ai_ (mugwort), altogether two substances. Dig a hole in the ground, making the width and depth the same size as a small saucer. Burn the earth inside the hole until it is dry, and put the _ai_ (mugwort) in it. Put the _liuxun_ (willow fungus) on top of the _ai_ (mugwort) and burn the _ai_ (mugwort) and fungus. Then take a small saucer. Bore a hole in the bottom one _cun_ in diameter, and cover (the hole in the ground) with it. Mound up earth around the saucer, and seal it [so that] smoke cannot leak out. Then cover the saucer with a garment without covering the hole in the saucer. Then have the person with hemorrhoids squat on the saucer with his rectum directly over the hole in the saucer, and let the smoke fumigate the rectum. When fumigating the rectum, raise it when it gets hot and lower when it gets cold. Stop when exhausted.
_MS_ I.E.156 (C270)
Another. Take stones the size of a fist, twice seven in number. Thoroughly burn them. Have two thirds _sheng_ of well beaten rice and eight times that amount of water, and put the stones into it. [2] cooked, then drink it, and it desists.
_MS_ I.E.157 (CC271–72)
_Ju_ Abscess Ailment
Smith _bailian_ (ampelopsis), _huangqi_ (astragalus), _shaoyao_ (peony), _gui_ (cinnamon), _jiang_ (ginger), _jiao_ (zanthoxylum), and _zhuyu_ (evodia)—altogether seven substances. For _ju_ abscesses of the bone, double the _bailian_ (ampelopsis). For _ju_ abscesses of the flesh, double the _huangqi_ (astragalus). For _ju_ abscesses of the testicles, double the _shaoyao_ (peony). Use one portion of each of the others. Combine, and put one large three-fingered pinch into a cup of liquor. Drink it five or six times a day. Wait for it to desist [?].
_MS_ I.E.158 (C273)
Another. Boil _penglei_ (raspberry), scalding thrice. Use four _dou_ of the liquid to wash the _ju_ abscess.
_MS_ I.E.159 (C274)
Another. When a _ju_ abscess first occurs, soak _shanglao_ (pokeweed) in gruel vinegar, and hot-press the swollen spot with it.
_MS_ I.E.160 (CC275–76)
Another. Take _bailian_ (ampelopsis), _huangqi_ (astragalus), _shaoyao_ (peony), and _gancao_ (licorice)—and boil the four substances, [1], _jiang_ (ginger), Shu _jiao_ (Shu zanthoxylum), and _zhuyu_ (evodia)—(use an amount of) the four substances equivalent to one of the (first four) substances. The first is bone [3] {1} [2] using one cup of liquor [4] muscle type, which glares and glitters. [2] {2} [5]. Drink four times a day. Once it is ready to burst, stop.
_MS_ IE.161 (CC277–79)
Another. Recipe for [25]. Use [2] _dou_ [20] {1} wash the _ju_ abscess [5] {2} [?].
_MS_ I.E.162 (CC280–82)
Another. When a _ju_ abscess has not yet [4] fourteen nodules of _wuhui_ (monkshood). Use one half _sheng_ of fine gruel vinegar [6] two thirds _dou_ of grain-cleaning slop, and put the medicine into it. [3] until it is like [5] roast the hand {2} [3] spread [5] it. Seal with the remaining medicine and wrap [4] not be painful. When it desists [2]. Excellent.
_MS_ I.E.163 (C283)
Another. For a _ju_ abscess of the throat. Smith together three portions of _bailian_ (ampelojpsis) and one portion of _bahe_. [7] drink it.
_MS_ I.E.164 (CC284–85)
Another. Suppurating abscess. When a suppurating abscess [2] occurs and [8] and smith. Take pig lard that has not been rendered, melt it by roasting, and blend it with [1]. Spread (the medicine) on it. Spread the medicine once a day. Before spreading the medicine, wash with warm water. Apply the medicine for thirty days. [1] desists. Previously tested. Excellent.
_MS_ I.E.165 (CC286–88)
Another. When various _ju_ abscesses first appear. Thoroughly scorch one _dou_ of soybeans. Then quickly remove them and set in a slotted steaming-pot. [9] {2} [2]. Pour one _dou_ of pure liquor over it. [2], then drink the entire amount of liquid. If after drinking once the ailment has not desisted, [11] drinking it is permitted. After just several times of drinking (the medicine), the ailment desists. There are no prohibitions. Previously tested. Excellent.
_MS_ I.E.166 (CC289–91)
Another. When a blood _ju_ abscess first appears, is glaringly hot, and the pain is unrelenting. [6] _ju_ abscess [12] _daishen_ (astragalus), _huangqin_ (skullcap), and _bailian_ (ampelopsis)—leaving them all for three days. [19] it, until sweat flows down to the feet. It desists.
_MS_ I.E.167 (CC292–93)
Another. When a vapor _ju_ abscess first appears, forming a volatile callus in the shape of a [1]. If rubbed [1] and [16], two nodules, until smashed; soybeans, [1] scorched {1} [1]. Pour liquor over it, then sieve [16] comes out and stop.
_MS_ I.E.168 (CC295–96)
Another. When a [1] _ju_ abscess appears, protruding from the body like the [1] of a person who has died. If someone jostles it, it is extremely [19] one half _dou_ , and boil to produce three _sheng_. Drink it. Dress warmly and lie down [?].
_MS_ I.E.169 (C297)
Another. [10] {1} [?].
_MS_ I.E.170 (C298)
[?] although [?].
_MS_ I.E.171 (CC299–300)
Another. [?] _ju_ abscess. _Jiang_ (ginger), _gui_ (cinnamon), _jiao_ (zanthoxylum), [1]—leaving them for four [?] one half _dou_ of pure liquor. Boil until it produces three _sheng_.[?].
_MS_ I.E.I72 (CC301–302)
Another. [?] three small bunches, and chop finely. One _dou_ of pure liquor [?], then sieve and [drink] it. Dress warmly [?].
_MS_ I.E.I73 (C303)
Another. [?] _gui_ (cinnamon), _jiao_ (zanthoxylum) [?].
_MS_ I.E.174 (C304)
Another. Boil wheat. When the wheat is cooked, wash it with the liquid. [3] lard [?].
_MS_ I.E.175 (C305)
Another. Roast _zi_ (catalpa) leaves, and warm it.
_MS_ I.E.I76 (C306)
Recipe for [1] Burns
Daub human sludge on it, and seal with dog or sheep fur. If it does not desist, again use [?].
_MS_ I.E.177 (C307)
Another. When a burn occurs, masticate malt, wring (in a cloth) to obtain the liquid, and fry until it resembles gelatin. Then smith _houpu_ (magnolia bark). Blend. Spread (the medicine on the burn).
_MS_ I.E.I78 (C308)
Another. When a burn occurs, utter this curse: "Sjit sjit, khwjət khwjət. Come out from the stove and do not spread. The Yellow Spirit is about to speak with you." Immediately spit on it thrice.
_MS_ I.E.179 (C309)
Another. Boil a sufficient amount of glutinous spiked millet. When just cooked, sieve, and scorch it until it becomes ash. Spread (the ash) on it for several days. If (the ash) becomes dry, beat liquid into it.
_MS_ I.E.180 (C310)
Another. Beat a chicken egg into rabbit fur, and spread (the medicine) on it.
_MS_ I.E.181 (C311)
Another. Smith malt, blend breast milk into it, and spread (the medicine) on it. It is not painful and does not scar.
_MS_ I.E.182 (C312)
Another. Incinerate _yuyi_ (algae), and spread the ash on it.
_MS_ I.E.183 (C313)
Another. Incinerate worn out plaited hemp and smith. Spread (the ash) on it with a cloth.
_MS_ I.E.184 (C314)
Another. Soak a menstrual cloth, and spread the liquid on it.
_MS_ I.E.185 (C315)
Another. Steam alkaline soil and wrap. Hot-press it with (the wrapped soil).
_MS_ I.E.186 (C316)
Another. When a burn from scalding bath water occurs, scorch pig feces, soak in gruel vinegar, and seal it (with the medicine).
_MS_ I.E.187 (C317)
Another. When a serious burn from scalding water occurs, scorch pig feces, moisten with liquor, and seal it (with the medicine).
_MS_ I.E.188 (CC318–19)
Another. For scars. Use two portions of mercury, four portions of a man's muck, and one portion of cinnabar. Blend together, and set on the stove flue for two or three days. When it is finished, then [3] sack, and spread (the medicine) on it. (During the time the medicine) is being spread, remain indoors. Block the windows, bar the entry, and do not go out. Perform private functions in the inner (chamber), and do not look at the stars and moon for one month. In a hundred days, it desists.
_MS_ I.E.189 (CC320–21)
Another. To remove old scars, carefully split open a large melon and (?) the seeds. Cut the melon, and use the [1] the size of two fingers to rub the scar until [2] it. Use [2] to spread on it. When dry, spread again. After the third time it desists. One must carefully observe ritual abstinence and restrictions without [1] and it desists.
_MS_ I.E.190 (C322)
Another. For [2]. {1} [2] {1} [1]. Spread the liquid on it, and skin grows.
_MS_ I.E.191 (C323)
Another. For a scar [12]. Incinerate it until ashed. Use it to [2] like the old skin.
_MS_ I.E.192 (C324)
Another. [?]
_MS_ I.E.I93 (C325)
Another. Boil autumn bamboo, and fumigate the wound with the vapor. It desists.
_MS_ I.E.194 (C326) Shin Burns
To treat shin burns, smith old glutinous panicled millet and soybeans. Blend with dog bile, and spread it (on the burn).
_MS_ I.E.I95 (C327)
Another. Smith the pits inside _wuyi_ (stinking elm fruits). Heat the firm lard of a castrated pig and pour it into the smithed (pits). Blend, and spread it (on the burn).
_MS_ I.E.196 (C328)
Another. Thoroughly boil two pheasants at a very fast boil. When the bird quill feathers loosen on their own and drop from the tail [5]. Incinerate both and smith. Blend the ash with pig lard, and spread.
_MS_ I.E.197 (C329)
Another. On summer days use _jin_ leaves, and on winter days use the root. Chew either one in the mouth and seal it. When it dries, immediately seal on top of that. This is all already proven.
_MS_ I.E.198 (CC330–31) Shin Wounds
Carefully pick out the grass and grit from old urine sludge. Put the sludge in a vessel. At dawn, use bitter liquor [2]. Spread the sludge on the wound. Spread [2] it, and the wound desists. Already used.
_MS_ I.E.I99 (CC332–36)
Another. Old shin wound. When an old shin wound becomes abscessed, the abscess bursts, and the liquid is like gruel. To treat it, boil two _dou_ of water. Have one third _dou_ of _yu_ (tumeric), one third _dou_ of _zhu_ (atractylodes), and one third _dou_ of [1]—altogether three substances—and smith both the _yu_ (tumeric) and the _zhu_ (atractylodes). [Put] them into the hot water and heat. When the water cools sufficiently to permit putting the foot into it, set a small piece of wood in the water. Then [2] {1} [2]. Put the foot into the water, step on the piece of wood, and slide [1]. When the water gets cold, heat it; and when it is hot, stop the fire and wait for the temperature to adjust itself. Put (the foot) into the water in the morning after eating, and remove it in the late afternoon. The ailment will then be cured. If the ailment is not [severe], it is cured after putting it into the water once. If severe, it is cured after putting it into the water five or six times. When it is cured, [1] abscess. [1] abscess and new flesh grows. When new flesh grows, stop putting (the foot) into the water. Then it will close itself and be cured. When applying the medicine there are no prohibitions, and in treating the ailment there are no temporal (restrictions). Excellent.
_MS_ I.E.200 (C337)
Scabies
Soak the feces of a black ram in the urine of an infant. Leave for one whole day. Spread (the medicine) on it.
_MS_ I.E.201 (C338)
Another. Smith realgar. Moisten with pig lard, and blend in a little gruel vinegar. Let (the medicine) [cool] to lukewarm, and spread it on it. When (the medicine) is spread, do not clean it off First wash the scabies thoroughly with hot water, and then spread (the medicine).
_MS_ I.E.202 (C339)
Another. Smith _pulei_. Work hub grease into it, and spread (the medicine on the scabies). Spread and then roast it, spreading for three or four times.
_MS_ I.E.203 (C340)
Another. Slit the throat of a red lizard, and daub the blood on it.
_MS_ I.E.204 (C341)
Another. Smith _tingli_ and _wuyi_. Scorch soybeans [2]. Using equal amounts of all, work in male [pig] lard and _zhan_ (sturgeon) blood. First wash (the scabies) with liquor. Burn bark to roast it, and then spread (the medicine).
_MS_ I.E.205 (CC342–43)
Another. Smith _niuxi_ (achyranthes) and the ash of incinerated loose hair in equal amounts, and combine [2]. Thoroughly wash the scabies and spread (the medicine) on it. Roast beef, and daub the old suet on top of (the medicine). Even when it desists, spread (the medicine) again without stopping.
_MS_ I.E.206 (C344)
Another. Use [1] suet or leopard lard. [1] and roast it. [3] and is not painful. Repeat it over and over again. First drink fine liquor until the body becomes warm, then [?].
_MS_ I.E.207 (C345)
Another. Carefully wash, and rub to make it bleed. Spread mercury on it. Also take equal amounts of smithed bronze and copper bits, work in pig lard, and spread (the medicine) on it.
_MS_ I.E.208 (C346)
Another. Pound _qianglang_ (dung beetles), and work in gruel vinegar. Seal (the scabies with the medicine) and roast it. The bugs come out from all sides.
_MS_ I.E.209 (C347)
Another. Remove the carapace and feet from one _dou_ of _qianglang_ (dung beetles), and combine with five nodules of _wuhui_ (monkshood) and a piece of _yu_ (arsenopyrite) the size of a plum. Boil in [1] _dou_ of vinegar until the liquid evaporates. Spread (the medicine) on it.
_MS_ I.E.210 (C348)
Another. Cover with large-bark _tong_ (paulownia) and bind. Superb.
_MS_ I.E.211 (C349)
Another. Incinerate the feces of a male rat and smith. Work in good vinegar, and seal it.
_MS_ I.E.212 (C350)
Another. Incinerate _yu_ (arsenopyrite). Smith one _ge_ each of _wuhui_ (monkshood), _lilu_ (black veratrum), Shu _shu_ , _zhe_ , Shu _jiao_ (Shu zanthoxylum), and _gui_ (cinnamon). Blend them together. Take dandruff [3] cloth. Roast, and hot-press with it. Stop when exhausted.
_MS_ I.E.213 (C351)
Another. Soak _lingji_ (water chestnuts) in the urine of a young boy. Put it in a pottery vessel, cover with cloth, and place it on the stove flue for five or six days. [1] spread (the medicine) on it.
_MS_ I.E.214 (C352)
Another. Smith _wuyi_ and _kuhu_ (bitter gourd) seeds. Combine, and beat in pig lard. Spread (the medicine) on it. Wrap with cloth and bind.
_MS_ I.E.215 (C353)
Another. Smith four nodules of _wuhui_ (monkshood) and one and a half _sheng_ of _lingji_ (water chestnuts). Combine with one and a half _dou_ of the urine of a male youth and [1]. Boil until done. Put in one _sheng_ of [1] grain, and stir. Spread (the medicine) on it.
_MS_ I.E.216 (C354)
Another. Smith _wuhui_ (monkshood). Roast black ram suet and beat (it in). Spread (the medicine) on it while hot.
_MS_ I.E.217 (C355)
Another. Incinerate old _kui_ (mallow) stalks and smith. Blend rancid pig lard into it, beating. Spread (the medicine) on the wound.
_MS_ I.E.218 (CC356–57)
Another. Moist scabies. Smith one sixth _dou_ of _wuyi_. Take castrated pig lard that is fatty, firm, and glistening [1] {1} [7]. Wash the scabies well with water. When dry, spread (the medicine) on it and bind with cloth. [2] the shinbone of a dead person. Incinerate and smith it. Using rancid lard [?].
_MS_ I.E.219 (C358)
Another. Fresh scabies. First wash well with water; and roast snake lard until it melts, and spread. Spread thrice [?].
_MS_ I.E.220 (C359)
Another. Recipe for scabies. Spread three-year-old rancid pig lard on it. Incinerate a rotted _jing_ (vitex) winnowing basket. Take the ash [2] {1} [2] desists. Excellent.
_MS_ I.E.221 (C360)
Another. Dry scabies. Smith _shechuang_ (cnidium) fruits, and work in male pig lard. First scrape the scabies. When it bursts, then spread (the medicine) and [2] {2} [1] {1} [?].
_MS_ I.E.222 (C361)
Another. Blend mercury with _gu_ (paper mulberry) liquid, and spread (the medicine) on it. First use vinegar to cleanse [3] spread.
_MS_ I.E.223 (C362)
Another. Recipe for scabies. Smith a sufficient amount of _lilu_ (black veratrum). Blend it with bee larvae, beating. Then thoroughly [4] scabies [1] and it desists. Previously tested. There are no prohibitions.
_MS_ I.E.224 (C363)
Snake Bite
Daub _sang_ (mulberry) liquid on it.
_MS_ I.E.225 (C364)
Abscess
Take [2] feather [1] {1} [1] {1}. Perform the Pace of Yu thrice. [2] one cup [?].
_MS_ I.E.226 (C365)
Another. When an abscess appears on its own, take about one joint of _tong_ (paulownia) root. Boil in grain-cleaning slop [?].
_MS_ I.E.227 (CC366–67)
Another. When abscess swellings occur, smith _wuhui_ (monkshood) and _lilu_ (black veratram). [10] it. Use it to hot-press the places with swellings. {2} [2] {1}, making the abscess swellings all desist.
_MS_ I.E.228 (C368)
Another. Head abscess. Chop finely one half _dou_ of _zi_ , and using six _dou_ of good vinegar [6] {2} [2] {5} [?].
_MS_ I.E.229 (CC369–71)
Another. When there is an abscess on the body, say: "Kəgw. I dare to [declare] to the Tai Mountain Barrow. So-and-so [un]fortunately ails from an abscess. I direct the [1] of the hundred illnesses. With the bright moon I irradiate you; with the cold [4] with a _zuo_ (oak) rod I stab you; with tiger claws I gouge and grab you; with a knife I butcher you; with _wei_ (reeds) I sever you. [Today] [1]. If you do not depart, it will be bitter." Spit. [5] at dawn before [eating], face [east] and spit on it.
_MS_ I.E.230 (CC372–75)
Another. _Baizhi_ (angelica), _baiheng_ , _jungui_ (curled cinnamon), dried _jiang_ (ginger), and _xinzhi_ (magnolia bud)—altogether five substances in equal amounts. After smithing the five substances [3]. Take beef suet [3] fine cloth. Combine and bake in a metal chafing dish over _sang_ (mulberry) charcoal. When it barely bubbles, uncover and let the vapor escape. Once again bake and allow to bubble like this [3] cloth to remove and obtain the liquid. Then crumble mercury in the palms and blend it into the medicine. Spread. At dawn use {3} [3] {1} [5]. While spreading the medicine do not eat [1] pork and fish, and do not (have intercourse) with women. When it desists, the face resembles that of [2].
_MS_ I.E.231 (CC376–77)
Another. Recipe for when there are abscess swellings on the body. Take one male [1] and gut it. {1} [8]. Cook it. Watch for when the broth is reduced to just under one _dou_. Remove and store it. Use a small amount to daub on the places on the body where there are swellings, and roast it. [6] the abscess swellings entirely depart, and it desists. Previously tested. Excellent.
_MS_ I.E.232 (CC378–79)
Another. When a chin abscess occurs, combine in a caldron one portion of smithed _banxia_ (pinellia), two of rendered beef suet, and six of gruel vinegar. [3] {1} [1] {1}. Spread (the medicine). Do not spread it all over, but rather make a ring that extends for one _cun_. When dry, spread (the medicine) on it again, and wash off the medicine with hot water. It will desist.
_MS_ I.E.233 (C380)
Lacquer
Spit and say: "Pən, Lacquer"—thrice. Then say: "The Thearch of Heaven sent you down to lacquer bows and arrows. Now you cause scabby sores for the people down below. I daub you with pig feces." Rub and slap it with the sole of a shoe.
_MS_ I.E.234 (C381)
Another. Chant this incantation: "The Thearch possesses the five weapons. You, begone. If you do not go, I will spew knives to coat you." Then spit on it, men seven times and women twice seven.
_MS_ I.E.235 (C382)
Another. "Pən, Lacquer King. You are incapable of lacquering armor and weapons, and have caused so-and-so to be wounded. Chicken feces and rat detritus are daubed on the Lacquer King."
_MS_ I.E.236 (C383)
Another. [3] rat [1] {1}. Drink the [1], one cup. It will make a person not have lacquer (rash) for his whole life.
_MS_ I.E.237 (C384)
Another. [12]. Spread (the medicine) on it.
_MS_ I.E.238 (CC385–87)
Another [31]. Spread at dawn before eating. [21]. The ailment desists and (the body) is as it was before. When treating the ailment there are no temporal (restrictions). When treating the ailment it is prohibited to [?].
_MS_ I.E.239 (CC388–89)
Another. [2]. Cook five _dou_ of rice using wood kindling. When done, [1] it. Then [17] {1}, use _langya_ root.
_MS_ I.E.240 (CC390–97)
Chewing by Bugs
[2] located on the throat or located at another place. The place where the ailment is located is called [9] {4} [2] {1} [2]. Wash it with [1] until irritated, then spread (the medicine). When spreading [9] hot water, and rub with a feather [5]. Then spread the medicine. When spreading the medicine, let it just fill the holes and no more. [9]. The next day wash again with hot water and spread the medicine as before. Wash once a day, and spread the medicine once a day. In three [9] {1} flesh grows {1} [2] flesh and stop. Then wash off the medicine. After washing off the medicine, use pig [11] the scabs are cured and stop. [2] three days and flesh grows. In about eight or nine days, the wound is level. When the wound is level [7]. In somewhat more than ten days it is cured and (the body) is as it was before. The wound [2]. If one wants to wrap it, then wrap it. If one [1] want [1], do not [9]. When spreading the medicine, first at dawn before spreading [2] spread the medicine. If one wants to eat, eat. While the medicine is being applied [9].
_MS_ I.E.241 (C398)
Another. Incinerate _loulu_ , and smith it. Use male pig lard [?].
_MS_ I.E.242 (CC399–400)
Another. Incinerate rooster feces, and fumigate the wound with it. [10] rat until it dies on its own. Boil in water. [1] cloth in the liquid and spread (the liquid) on it. Do not rub the wound with the hands.
_MS_ I.E.243 (C401)
Another. When there is chewing by bugs, take Yu stove [2] to fill the wound [8]. Excellent.
_MS_ I.E.244 (C402)
Another. When the _te_ eats the mouth and nose, smith _jinkui_ [3] incinerate using _sang_ (mulberry) kindling. [2] {1} [2] until the liquid comes out. Use a feather to take [?].
_MS_ I.E.245 (C403)
Another. Quickly split a carriage's lacquered _guo_ [?].
_MS_ I.E.246 (CC404–405)
Another. [1] eating. Use fatty pork [?] {1} [?].
_MS_ I.E.247 (C406)
Another. Smith old _kui_ (mallow). Use [?].
_MS_ I.E.248 (C407)
Another. When the _te_ eats the teeth, take _yu_ (elm) bark, _bai_ [1], and fine _gui_ (cinnamon), and combine [4]. Spread (the medicine) on the holes [?].
_MS_ I.E.249 (CC408–409)
Recipe For Dry Itch
Use two _liang_ of realgar, one third _liang_ of mercury, and one _sheng_ of dandruff [1] the realgar, and crumble the mercury [in] the hands [6] the realgar and stir it thoroughly. First thoroughly wash the itch with hot water so that the washed places burst. Wipe with a cloth until [2] and spread (the medicine) on it. For one night and one [?].
_MS_ I.E.250 (C410)
Another. Scorch one third _dou_ of _lingji_ (water chestnuts) until they yellow. Boil in one half _dou_ of pure liquor. Let it bubble thrice and stop. Clarify the liquid. In the evening do not eat, and drink (the liquid).
_MS_ I.E.251 (C411)
Another. Use _fuling_ (pine truffle). Select one that is large and pound it. Pound in a mortar, beat in suet, and form into large balls. Rub (the itch with the balls).
_MS_ I.E.252 (C412)
Another. Mince _rulu_ (madder) root, and soak in liquor. After a day and a night, daub (the medicine) on it. It desists.
_MS_ I.E.253 (CC413–14)
Another. Take two measures of _lilu_ (black veratrum), one measure of _wuhui_ (monkshood), one measure of _yu_ (arsenopyrite), [1] measure of _quju_ , and one measure of _yuanhua_ (daphne). Blend them together using old carriage grease. {1} [3] wrap. Carefully wash and dry. Then roast the wrapped medicine and rub the itch with it. [1] rub suet [2] suet. The itch then desists.
_MS_ I.E.254 (CC415–16)
(Another. Take one _sheng_ of _lan_ (eupatorium) root and of _baifu_ chopped into small pieces. Pound, and pour vinegar and grain rinse —half and half—into it until just [2]. Set in a warm place for three days, and put one _ge_ of pig lard that is [2] into it. Then cook, letting it bubble thrice. Spread (the medicine) on the rash and roast it. When dry, spread again [1]. Leave for two days, then bathe. The rash desists. Excellent.
_MS_ I.E.255 (C417)
Another. Boil _tao_ (peach) leaves, scalding thrice, to make hot bath water. Go to a warm inner (chamber), drink hot liquor, and afterward get into the hot bath water. Drink hot liquor again in the bath. Even old itch desists.
_MS_ I.E.256 (C418)
Another. Dry itch. Boil two _dou_ of urine until it reduces to two _sheng_. Combine with one _sheng_ of pig lard and two _sheng_ of _lilu_ (black veratrum), and spread (the medicine) on it.
_MS_ I.E.257 (C419)
Body Scabbing
When there is no name for the scabbing but it itches, scorch and smith _lingji_ (water chestnuts). Blend with dog bile, and spread (the medicine) on it. When spreading (the medicine) for a long time, always stop for three days. After the third time, the scabbing desists. Previously tested. Excellent.
_MS_ I.E.258 (C420)
Another. Scabbing. Mince _kui_ (mallow), and soak in water. During summer days do not soak. Spread (the medicine) on it. The hundred types of scabbing all desist.
_MS_ I.E.259 (C421)
Another. Blend two portions of _lilu_ (black veratrum) with one portion of _yu_ (arsenopyrite), and _suo_. Hot-press the scabbing with it.
_MS_ I.E.260 (C422)
Another. When old scabbing does not desist, soak the dry matter scraped from the stove. Spread (the medicine) on it. It desists.
_MS_ I.E.261 (C423)
Another. When scabbing like cow eyes appears on the body while traveling in the mountains, this is called "day [?].
_MS_ I.E.262 (C424)
Another. Exposed scabbing. Incinerate the charred crust of cooked rice. Smith, blend with old lard, and spread.
_MS_ I.E.263 (C425)
Another. [?]
_MS_ I.E.264 (C426)
Another. Use the east-facing root, branches, and leaves of _huai_ (pagoda tree). Boil, scalding thrice. Use the liquid [?].
_MS_ I.E.265 (C427)
Another. The incantation is: "Tsjəm tsjəm, hjəkw hjəkw bugs. The Yellow Spirit is in the stove. [2] {1}. Yellow Spirit arise. [?].
_MS_ I.E.266 (CC428–30)
Another. Chilblain. First wash the chilblain thoroughly with glutinous panicled millet slop. Then incinerate straw that is several years old. [Take] the ash and smith. [3] spread on the chilblain. After spreading the ash, soak the ash entirely [3] and wipe to scrape it away. After scraping, immediately spread ash again and scrape as before. When the liquid is used up, then even old chilblain will be cured. When spreading the medicine it is prohibited [4]. Previously tested. Excellent.
_MS_ I.E.267 (C431)
Another. Steam frozen earth, and use (the earth) to hot-press it.
_MS_ I.E.268 (C432)
Another. Daub fresh rabbit brain on it.
_MS_ I.E.269 (C433)
Another. Chew _xie_ (scallions), and seal it.
_MS_ I.E.270 (C434)
Another. When being barefoot results in chilblain, burn the inside of a pit in the ground and put the foot into it for the time it takes to eat and no more. Then [1] _cong_ (onions) and seal it, or hot-press it with steamed _cong_ (onions).
_MS_ I.E.271 (C435)
[1] _Gu_
Incinerate a bat using _jing_ (vitex) kindling, then feed it to the accursed person.
_MS_ I.E.272 (C436)
Another. Incinerate a woman's (menstrual) cloth, and have (the person) drink it.
_MS_ I.E.273 (C437)
When someone ails from [1] _gu_ , incinerate a north-facing paired talisman. Then steam sheep buttock, drop (the buttock) into hot bath water, and toss in the talisman ash. Then [2] the ailing person, and wash the hair and body to treat the _gu_.
_MS_ I.E.274 (CC438–40)
Another. When ailing from _gu_ combine one black rooster and one snake in a red pottery kettle. Then cover, and use [2] to cook it on an east-facing stove until the rooster and snake are completely charred. Then remove and smith. Have the ailing person put three three-fingered pinches of the medicine into one cup of liquor or el every morning at dawn, and drink it. Drink once a day. When medicine is used up, it desists.
_MS_ I.E.275 (C441)
Another. _Gu_. Soak the menstrual cloth of a woman who has never had a husband [2] cup. Smith _gui_ (cinnamon), put it in until the odor is gone, and give the [1] to the person to drink.
_MS_ I.E.276 (C442)
Child Sprite
Perform the Pace of Yu thrice. Take a branch from the east side of a _tao_ (peach). In the middle separately fashion [3] figurines, and fasten them above the doorway, one on each side.
_MS_ I.E.277 (CC443–45)
Another. Chant this incantation: "Spouter. Child Sprite Father. Child Sprite Mother. Do not hide [3] north. [1] Shamanka Mistress searches for you and certainly catches you. She [1] your four limbs, plaits your ten fingers, and casts you [1] water. Being human, being human—you join demons." Each time travel [1] with large-bellied gourds for axles and a worn out winnowing basket for the chassis. Harness it to the person's black pig and travel through the person's home. [9] {1} [2] {2} child sprite [1] child sprite [4] place.
_MS_ I.E.278 (CC446–48)
Recipe for Removing a Person's Horse Warts
Take iron forging ash, three [20]. Boil in a wide-mouthed kettle. Cook gently, without letting it bubble rapidly. When about one _sheng_ of the [1] remains, [3] {2} [10] and remove it. Spread it over and over again on this spot, and it desists. Previously tested. There are no prohibitions. Excellent.
_MS_ I.E.279 (CC449–50)
Another. Removing a person's horse warts. The tip of the wart is large and the base is smallTreating Facial Pustule. [2], take _jia_ [1] and _baifu_ [1]. Tie with a cord, binding it firmly. [2] {2} [3] warts will go away. There are no prohibitions. Previously tested. Excellent.
_MS_ I.E.280 (CC451–53)
Treating Facial Pustules
When facial pustules occur the abscess is painful and bursts. If the pustule is situated on the right, [use] the right cheekbone of a horse; if situated on the left, [use] the left cheekbone. Incinerate and smith. Boil soybeans, and wash the [1] with the liquid. Anoint it with already rendered pig lard, and take the smithed horse cheekbone [3] spread on a cloth [1] lard [3] and wrap again. Again anoint (with lard), spread (the medicine), and wash with the soybean liquid. In twenty days the facial pustules desist. Previously tested. Excellent.
_MS_ I.E.281 (CC454–55)
Another. Facial pustules. There are female and male types of facial pustules. In the male type the skin swells. The female type has a hole. Treat it with cinnabar [10] {2}. Combine, stirring, and blend in rancid pig lard. Spread (the medicine) on it. If some comes off, immediately reapply it. Do not wash [10]. The redness of the facial pimples desists.
_MS_ I.E.282 (CC456–57)
Another. Facial pustules. When facial pustules occur there is an abscess that bursts. Use good soybeans and _leishi_ (bamboo truffle), each [10] and pound them. Spread it in the hole of the abscess. When spreading the medicine, (the abscess) must first be washed. Wash and spread the medicine once a day. After spreading the medicine for sixty days, the facial pustules [?].
_MS_ I.E.283 (CC458–62)
[1] Bite
[1] take _mei_ (berry) vine. Dry it in the sun [?]. Do not [2]. After drinking this he should go to sleep. When he awakens, he should again [6] {3} [9] dried _mei_ (berry) {2} [2] root. Dry it. Peel to obtain the skin. [2] {2} [?] ten _dou_. Use fine [?].
The names of the fifty-two ailment categories that form the main contents of _MS_ I.E are listed in four registers. Throughout _MS_ I.E these names (or slight variations) appear as headings written just above the first column of the first recipe in a given ailment category. When there is more than one recipe in an ailment category, subsequent recipes are usually headed by _yi_ — (another).
The recipes for this ailment category as well as for the next four ailment categories are missing in the text.
Judging from _MS_ I.E.6, 12, 17, and 18—which all refer specifically to "blade wounds" or "metal wounds"—this category is mainly concerned with stab wounds and accidental cuts. The usual term for such wounds in Han and post-Han medical nomenclature is _jin chuang_ 金 創 (metal injuries). A recipe manual for treating "metal injuries" is listed in the _Hanshu_ bibliographic treatise ( _Hanshu_ , 30.80a); and the Wuwei recipes include "metal injuries" ( _WWYJ_ : 2b–3a, 8a–b).
_Gao_ 膏 (lard) and _zhi_ 脂 (suet) are the two standard terms in the Mawangdui medical manuscripts for animal fat. Li Zhongwen (1980) examines the use of both words in _MS_ I.E and concludes that their meaning corresponds to the definition in _SW_ , 4B.36b. _Gao_ is the soft fat from animals without horns, principally the pig (i.e. lard); _zhi_ is the hard fat from horned animals, principally oxen and sheep (i.e. suet).
_Jiao_ 椒 refers to several species in the genus _Zanthoxylum_. _MS_ I.E occasionally specifies Shu _jiao_ 蜀 椒, which is the drug name listed in _BC_.
The standard practice in _MS_ I.E is to form medicine balls which are crushed before using; _MS_ I.E.151 provides the only example of swallowing the balls directly. Balls are also swallowed in _MS_ III.71.
_Qu_ /* _gjug_ 朐 is glossed in _SW_ , 4B.33b, as "strips of dried meat." I doubt the graph has this meaning in _MS_ I.E.3 and suspect that it is a loan for a herbal drug name. One possibility is _ju_ /* _kjug_ 蒟. _Ju_ is glossed in _SW_ , 1B.31b, as "a fruit"; and is also mentioned as the chief ingredient of a spicy sauce produced in Shu 蜀 in _Shiji_ , 116.2b. Hui-lin Li presents evidence for identifying _ju_ as the word for black pepper ( _Piper nigrum_ ) in Former Han times (1979: 46–53).
_Da_ 荅 (small bean) is the adzuki bean, also called _xiaodou_ 小 豆 and _chi xiaodou_ 赤 小 豆 (see _chida_ ). In _MS_ I.E.3, "small bean" is used as a relative measure of size in drug preparation. A similar usage occurs in the Wuwei recipes, which mention making medicine balls "the size of _chidou_ 赤 豆" ( _WWYJ_ : 3b). The use of the adzuki bean as a metrological standard in early medicine is confirmed by Tao Hongjing, who explains that references in old medical recipes to a measurement "like a small bean" are to the _chi xiaodou_ of his day, and that the measurement is equivalent to three large hemp seeds ( _GM_ , 1.38).
_Ye_ 佁 is used regularly in _MS_ I.E to denote the fine pounding of a drug. My literal translation "smith" is based on Akahori (1985), who argues that _ye_ —which means to cast metal according to _SW_ , 11B.8b—also had the sense of hammering metal; and was then extended to the pestling of drugs. As noted by Akahori, sifting techniques were not common in medicine until after the Han period. Before that time, long pestling was necessary to reduce a drug to a uniform powder; and _ye_ "smith" was borrowed from metallurgy to denote the pounding process. _Ye_ appears frequently in the Wuwei recipes, but it is rare in later medical literature (and when it does occur in received literature it is regularly miswritten as _zhi_ 治). Evidently the word _ye_ became obsolete once sifting simplified the process of pulverizing drugs.
It is probable that 齊 should be read as _ji_ 薺 (see _MS_ I.E.18).
_Chunjiu_ 淳 酒 (pure liquor) is undiluted liquor (see the definition of _chun_ 醇 in _SW_ , 14B.35a).
The repetition of the words "soak" and "bake" following the thirteen-graph lacuna above suggests that there is a second drug prepared in the same fashion as the first. Filling the lacuna here with "before" is based on the repeated use of the phrase _ru qian_ 如 前 (as before) in _MS_ I.E.
_SW_ , 12A.32b, glosses _cuo_ 撮 (pinch) as "four spatulas" and as "a three-fingered pinch" i.e. the amount of medicine that can be picked up using the thumb, index, and middle fingers. Measurement by spatulas is not mentioned in the Mawangdui medical manuscripts, and measuring drugs was undoubtedly still performed with the fingers. _MS_ I.E.18 provides a more precise indication of the measurement when it specifies using "one three-fingered pinch reaching to the knuckles." The three-fingered pinch also occurs in _Suwen_ 46, 13.2b; and in the Wuwei recipes ( _WWYJ_ : 3a, 8b).
Despite the lacuna, it is evident that the conclusion of _MS_ I.E.4 discusses the technique of pestling relative to the size of the drug being powdered. Determining the fineness of a drug by counting the number of times it is pounded was probably a standard procedure in early medicine, although this is the only place in the Mawangdui medical manuscripts that specifies a pounding count.
In materia medica _fa_ 髮 refers to hair clipped from the scalp as distinct from loose hair that collects in brushes and combs ( _GM_ , 52.81). Loose hair is specified in _MS_ I.E.205.
_Baicao_ mo 百 草 末 (hundred grass residue) is not attested in received literature. _MWD_ , vol. 4, "Transcription," n. 3, suggests that it may be similar to _baicao shuang_ 百 草 霜 (hundred grass frost), which is the name for the soot that collects in the stove flue in later medical literature ( _GM_ , 7.87). Wei and Hu argue that _ba_ /* _priat_ ハ is not the number eight, but rather is a phonetic loan for _ba_ /* _briat_ 坺, glossed in _SW_ , 10A.44a, as "fire vapor" (1992, vol. 1: 48, n. 3). _Ba_ is unattested outside of the _SW_ , but the reading _bahui_ 坺 灰 (fire-vapor ash) is plausible; in which case the translation would be, "Smith hundred-grass-residue fire-vapor ash."
Filling the lacuna here with "crush" ( _hui_ 毁), based on _MS_ I.E.2.
The ashes of the cattail mat are probably pressed on the wound, like the scalp hair in _MS_ I.E.7.
"Vinegar" translates _dai_ 酨, glossed in _SW_ , 14B.41a, as "vinegar beverage." _Dai_ was a common beverage in Han times, made by allowing rice-preparation water to ferment (see Hayashi 1975: 69). Elsewhere in _MS_ I.E rice-cleaning water is used as a bathing solution. In the incantation, I interpret "vinegar" as a verb meaning "apply vinegar to the wound." The incantation conjures a man to stop the bleeding and a woman to apply the vinegar.
The act of drawing five lines on the ground creates a magical diagram. _MS_ III.83 describes a magical technique to project a traveler from harm at night that includes drawing a circle on the ground. A similar procedure is described in the first Shuihudi hemerological manuscript, which gives instructions for a ritual to be performed before departing on a journey. The last part of the ritual entails drawing five lines on the ground, picking up soil from the center of the lines, and carrying it in the bosom ( _SHD_ : 223). The exact manner of executing the five-line diagram remains unclear. Perhaps it is a kind of magic square composed of five lines. Kudô examines the Mawangdui and Shuihudi manuscript evidence in the light of later religious Daoist practices; he speculates that the five lines may be related to a Daoist cross-hatch design consisting of four vertical lines and five horizontal lines (1990: 50–57). I would prefer better evidence. In _MS_ I.E.9 the five-line diagram is intended to create a magical space that protects the wounded person from further harm.
The drug name [1] _yan_ 衍 is unidentified.
"Slime" translates _ji_ 洎, which has two attested meanings: "pour water into a vessel" ( _SW_ , 11A–2.30b); and "juice from meat" ( _Zuozhuan_ , Xiang 28, 38.13b). Both meanings occur in _MS_ I.E. Although the meaning is unattested, _MWD_ , vol. 4, "Transcription," n. 1, argues that _ji_ refers to semen in _MS_ I.E.11, citing as support later medical literature that records the use of semen to prevent scars. Qiu Xigui argues that 洎 should be read as _yi_ 侇 (snot) in _MS_ I.E.11, citing as evidence the Mawangdui _Yijing_ manuscript in which the text for the hexagram Cui 卒 writes 洎 instead of in the received text (1992: 530; the Mawangdui graph could be analyzed literally as "fluid that comes from the nose"). Ma Jixing accepts the identification with semen and rejects snot, in part because he questions why _MS_ I.E.11 should distinguish between a man's snot and a woman's (1992: 339–40). I am inclined to agree that in _MS_ I.E.11 _ji_ refers to a substance like semen or snot (both viscous fluids, one from the nose and the other from the penis). Rather than pass judgment on the relative probability of semen or snot, I use "slime" in the sense of a viscous body fluid.
_Jian_ 煎 (fry) means to cook something until the liquid is cooked away. Fat may or may not be used for frying.
According to _SW_ , 6A.23b, _ting_ 挺 is a measure word for stick-like objects. The scribe failed to write the complete graph in this occurrence in _MS_ I.E.I3, for there is merely an oblique stroke 乀 in the text. The subsequent two occurrences are written 挺 and 廷 respectively.
_Du_ [1] 獨 also occurs in _MS_ I.E.138; unfortunately the second graph is again missing. The drug may be the herb _duhuo_ 獨 活, listed in _BC_ and recommended for "metal injuries" ( _GM_ , 13.49). _ZY_ : no. 3510, lists seven plants identified with this drug name.
Reference to autumn probably specifies when the drug is to be gathered.
Probably two saucers of lard are added.
_Bu_ 布 refers to cloth woven from hemp or kudzu fibers ( _SW_ , 7B.54a, and Duan Yucai commentary). The practice of squeezing a lard-based medicine through cloth is explained by Tao Hongjing, who recommends using the dregs separately ( _GM_ , 1.40). In _MS_ I.E.13 the "liquid" is probably liquid fat being squeezed through a cloth to separate out the fried debris of the drugs. Other recipes in _MS_ I.E describe the preparation of lard salves that are not strained before use.
_SW_ , 13A.38a equates _yun_ with _fu_ , which is glossed as "matted hemp fiber." The main uses of hemp-wadding were as padding for clothing, as tinder for starting fires, and for twine.
_Wei/*mj əd_ is attested as a variant graph for _mei/*m əd_ 浼 ( _Shijing_ , Mao 43, 2c.9a, and commentaries). _Mei_ is glossed with _wu_ 污 in _SW_ , 11A–2. 40a; and the third of three glosses for _wu_ in _SW_ , 11A–2. 29a, is _tu_ 涂 (daub). Like _tu_ , which occurs frequently in _MS_ I.E, _wei_ must mean "daub, swab."
"Mince" translates _ji_ 韲, which refers to the fine mincing of ingredients for relishes ( _SW_ , 7B.3b, and Duan Yucai commentary; the _SW_ records several graphs used to write the word, and several variants also occur in _MS_ I.E). It is likely that "mincing" could also be accomplished with a mortar and pestle.
"Rancid" translates _zhi_ 膱. The zheng Xuan commentary in _Zhouli_ , 42.9b, explains _zhi_ as "grease that is rancid and spoiled." The same word is written 殖 in _SW_ , 4B.13a, and glossed as "grease that is old and rancid". _MS_ I.E often calls for rancid lard in preparing salves because it is more viscous than fresh lard. I read text 弁 as _pan_ 拚, which _SW_ , 12A.42b, glosses as "clapping the hands." _KGS_ , vol. 1:148, n.64, argues that in _MS_ I.E _pan_ refers to a kneading action with the hands necessitated by the stiffness of the ingredients (other occurrences of _pan_ in _MS_ I.E also involve rancid lard or thick substances). I suspect that _pan_ may also refer to beating something with a stick, hence the translation "beat in."
_Changshi_ 嘗 試 (previously tested) is one of several terms used in _MS_ I.E to praise the effectiveness of a recipe. Wang Chong alludes to the term in the _Lunheng_ in his criticism of those who exploited the demand for secret recipes (see Prolegomena, Section Two, "Readership and Transmission").
Needham examines the evidence concerning various soluble salts in early China, and concludes that the name _xiaoshi_ 消 石 (solvent mineral) was applied to niter (1954–, vol. 5, part 4: 179–94).
"Abscess" translates _yong_ 癰, which is also the name of the ailment category beginning in _MS_ I.E.225. In _MS_ I.E. 16–17 _yong_ probably refers to a wound that becomes abscessed. _Yong_ occurs in the Shuihudi text _Fengzhen shi_ meaning "wound" ( _SHD_ : 162, n. 8). Thus it is possible that _yong_ in _MS_ I.E.16–17 refers to wound, not an abscessed wound. It is also possible that _yong_ in this context refers to ulceration.
_SW_ , 10A.37a, identifies _fen_ 鼢 as _yanshu_ 偃 鼠, the latter being the name listed in _BL_ ( _GM_ , 51.67).
_Zhi_ /* _drjad_ 彘 means "pig." _MWD_ , vol. 4, "Transcription," n.2, proposes reading it as a phonetic loan for _ti_ /* _di əd_ 鮧. _Tiyu_ 鮧 魚 is the name of a fish listed in _BL_ ( _GM_ , 44.114); identified in _ZY_ : no. 5359, as _Parasilurus asotus_ (L.). Althought the phonological evidence supports the proposed loan, I hesitate to make a conclusive identification. _Zhiyu_ might also mean "pig fish" and represent a name that is not recorded in received literature.
For the use of _cai_ 財 (also written 裁 and 才) to mean "a few, a bit," see _Hou Hanshu_ , 17.6a, and commentary. In other contexts in _MS_ I.E _cai_ has the sense of "a sufficient amount."
_Ling_ 令 (excellent) is another term of praise for a recipe that occurs frequently in _MS_ I.E.
In _BC_ only _zhu_ 术 is listed. Tao Hongjing ( _GM_ , 12B.4) distinguishes between _baizhu_ 白 术 ( _Atractylodes macrocephala_ ) and _chizhu_ 赤 术 (i.e. _cangzhu_ 蒼 术; _Atractylodes lancea_ and other spp.).
I interpret _zhong bei_ 衷 杯 to mean a "brimming cup." For the use of _zhong_ , written 衷 or 中, in the sense of a full measure, see _Hanshu_ , 8.18a, and the Yan Shigu commentary.
The expression _ru shu_ 如 數 occurs six more times in _MS_ I.E (with slight variations depending on the context): _MS_ I.E.20 (C36), 75 (C131), 94 (C160), 142 (C238), 146 (C247), and fragment 1 ( _MWD_ , vol. 4: 76). _Shu_ means literally "a calculation." Considered in isolation, _shu_ in _MS_ I.E.18 might seem to mean "amount" (making the translation read, "drink the medicine using the same amounts"). However, judging from all seven occurrences, _shu_ refers to the steps involved in executing a particular operation, hence my translation "following the same procedure."
Instructions concerning whether to take medicine before or after eating a meal occur a number of times in _MS_ I.E; and _MS_ III contains similar instructions for tonics. I believe the meaning of the expressions _xian shi_ 先 食 (before eating) and _hou shi_ 後 食 (after eating) is as translated. Curiously, the Wang Bing commentary in _Suwen_ 46, 13.2b, explains the expression _hou fan_ 後 飯 to mean, "make the meal come after and the medicine come before"—exactly the opposite of my translation. However, the Yang Shangshan commentary to the parallel passage in _Taisu_ , 30.450, corresponds to my interpretation.
_Xun_ 葷 refers to strong-smelling, sharply-flavored vegetables like onions and garlic (see _SW_ , 1B.7b)
The term _mazhu_ 麻 诛 is also used in the Wuwei recipes ( _WWYJ_ : 6a). It clearly denotes a food preparation that was known in the cuisine of the Former and Later Han periods, yet there is no mention of it in received literature.
I.e. entry to the bedroom for sexual intercourse is forbidden. For _jin nei_ 近 内 (approach the inner chamber) as a term for sexual intercourse, see _MS_ III.34.
_MS_ I.E gives few examples of what constitute temporal restrictions, the statement that there are none being the usual formula. There is one calendrical prohibition in _MS_ I.E.69, and it is probable that the restrictions derive from hemerological and astrological symbolism.
Other methods of drying drugs besides in the sun are leaving them in a dark place or drying them over a fire.
In _SW_ , 7B.33a, _jing_ 俓 (rigidity) is glossed simply as "acute stiffness." The etiology of _jing_ "rigidity" in _MS_ I.E is consistently linked to the prior existence of a wound, which permits wind to enter the body—and it is the wind that causes _jing_ to occur. The third ailment category ( _MS_ I.E.25) is a kind of _jing_ that affects infants, apparently occurring when the removal of the umbilical cord permits the pathogen to enter; and the fifth ailment category ( _MS_ I.E.27) is similar in that the treatment focuses on drawing the pathogen out of the opening of a wound. In the discussion of "rigidity" brought on by "metal injuries" in _Chaoshi zhubing yuanhoulun_ , 36.12a, wind is also the pathogen. It is difficult to judge what modern ailments might correspond to _jing_ , although tetanus is one likely choice (Yu Yan 1972: 142).
The _fu_ 巿 (apron) was a regular article of clothing in male and female dress (Hayashi 1976: 16–17).
"Hot-press" translates _yun_ 熨, glossed in _SW_ , 10A.46b, as "pressing down from above" and "what one smooths silk with." Several specimens of the _yundou_ 熨 斗 (iron) of Han date have been discovered (Sun Ji 1991: 346). They have shallow flat-bottomed pans to hold hot coals and are attached to long handles. As a form of medical therapy, _yun_ is attested in _Hanfeizi_ 21, 7.118, where Bian Que recommends "hot-pressing" when an ailment first lodges on the surface of the body and has not penetrated deeply inside (see also _Shiji_ , 105.6b). _MS_ I.E provides the earliest descriptions of the methods of hot-pressing; and the frequency of hot-pressing in _MS_ I.E suggests that it was a common form of therapy in the third and second centuries B.C. A variety of materials are used, from the salt in _MS_ I.E.19 to hot stones in _MS_ I.E.146 (see Prolegomena, Section Three, "Therapy").
I.e. the fruit is placed in a sieve and strained separately to obtain the liquid still in it. This is the only recipe where _shu_ 抒 (remove) and _jun_ 浚 (sieve) occur together. Other recipes either say to "sieve (a boiled decoction) to obtain the liquid" (thereby removing the solid matter) or say to "remove the liquid" (apparently without straining it through a sieve). In just one instance, _MS_ I.E.117 says to "sieve to remove the liquid" when it is the solid matter that is wanted for the recipe.
_MS_ I.E.99 contains the phrase "take a large amount as the measure," which is syntactically the same as the fragmentary phrase here.
Missing in the lacuna is the drug to be substituted for plum fruit when the latter is unavailable. According to the recipe, the preparation and consumption of the substitute drug follow the procedure already described for plum fruit.
Obviously arsenopyrite is used in preparing a medicine earlier in the recipe. The occurrence of the word at the end of the recipe is part of an added comment on the drug and its use in medicine
_Nie_ 糱 (malt) is sprouted grain used for fermentation ( _SW_ , 7A.60b). "Allow to rot" is a tentative translation of _beng_ 湍, which is not attested in received literature until well after the Han period; and not in a meaning appropriate to _MS_ I.E.22. Perhaps it is related to the primary graph _beng_ 崩, glossed in _SW_ , 9b.8a, as "destruction of a mountain" and also used in the sense of "ruin, spoil." I suspect that in _MS_ I.E.22 _beng_ refers to the degenerative effect of the malt on the chopped dog.
Evidently the "rotting" process involves packing the chopped dog together with the malt in a vessel.
occurs again in _MS_ I.E.31 where the context also suggests the meaning is "bottom"; and the same meaning is indicated for _duan_ 斷 in _MS_ I.E.155. The meaning "bottom" for _duan_ is not attested in received literature.
_ZY_ : no. 5545, lists _Allium chinense_ G. Don and _A. macrostemon_ Bge. as the two main plants for the onions identified by the name _xie_ 薤. However, as with English "scallion," _xie_ has been applied to several other small onions.
Probably the liquid obtained after wringing the lard medicine is spread on the affected part of the body.
_MWD_ , vol. 4, "Transcription," n. 1, argues that the ailment is a female ailment that occurs in women after childbirth, and then offers the alternative explanation that it is an infant ailment. The fourth and fifth ailment categories ( _MS_ I.E.26–27) are both related infant ailments, a good indication that _MS_ I.E.25 is also an infant ailment and not a post-partum female ailment. _Yinger suo_ 嬰 兒 索 (infant cord) is not attested in received literature, but there is no difficulty identifying it as a term for the umbilical cord. _MS_ I.E.27 treats of the ailment _chi_ 瘛 (convulsions) in infants. _SW_ , 7B.35a, glosses _chi_ as "the ailment _chizong_ 瘛 瘲 in infants." Yu Yan hypothesizes that _chi_ refers specifically to infections like tetanus that often occur when the newborn infant's umbilical cord is cut (1972: 115). Although the umbilical cord is not mentioned in _MS_ IE.27, there is reference to "stroking around the spot where the infant convulsions are"—perhaps a wound where the umbilical cord was cut. _MS_ I.E.25 does not mention the cutting of the umbilical cord as a factor contributing to the occurrence of the ailment, but the umbilical cord or navel might still have been regarded as the point of entry for the pathogen.
"Lock" translates _kou_ 釦 which means literally "metal plating around the mouth of a vessel" ( _SW_ , 14A.8a).
_Feng_ 封 could have several meanings, but the meaning "anthill" is attested in _Fangyan_ , 10.6a, as a Chu dialect word, which is probably the correct meaning of _feng_ in _MS_ I.E.25. The friable soil from anthills is included in _GM_ , 7.77.
_Xian_ 癇 (spasms) refers to an ailment characterized by spasmodic fits. According to _Chaoshi zhubing yuanhoulun_ , 45.7a, _xian_ is the name for the ailment when it occurs in children younger than ten, and the same ailment is called _dian_ 癒 when it occurs in someone older. It is unlikely that the twinned identity and age-based differentiation apply to _xian_ and _dian_ in _MS_ I.E. Besides this recipe for Infant Ailing from Spasms, _MS_ I.E.86 is the only extant recipe in _MS_ I.E of what was originally a sequence of four categories of _xian_ ailments; and age is apparently not a factor. _Maishu_ , "Ailment List," also makes no mention of age when it identifies _xian_ : "When (the body) snaps in a reverse direction, it is _xian_ " ( _MSSW_ : 72). Although the ailment is not described, _MS_ I.E.71–72 treat of _dian_ as a separate ailment category. _Dian_ was associated with mental derangement in Han times, and perhaps included epileptic seizure (see _MS_ l.E.71).
_MWD_ , vol. 4, "Transcription," n. 4, argues that _san_ 三 (three) is excrescent, making the line read, "bathe once a day." I suspect that the original wording is an elliptical way of saying that for a duration of three days the infant should be bathed once each day.
See _MS_ I.E.25 for the association of _chi_ 瘛 (convulsions) with tetanus. The exorcistic removal of the pathogen in _MS_ I.E.27 focuses on a wound from which blood is magically expelled. Although the umbilical cord is not mentioned, cutting the umbilical cord is a likely cause for a wound on a newborn infant. Among the symptoms described in _MS_ I.E.27 are pain in the sides and shortness of breath. "Inability to breath" is also one of the signs of _chi_ in _Maishu_ , "Ailment List" ( _MSSW_ : 72); and _Yinshu_ specifies the sides as the location of _chi_ when describing an exercise routine to alleviate it ( _YSSW_ : 85; it is highly unlikely that _chi_ in the _Yinshu_ passage has any connection with tetanus).
_Jie_ /* _krig_ 繲, which I translate as "fixed," was previously a _hapax legomenon in zhuangzi_ 4, 82. Commentaries gloss the word as "wash clothes." However, the textual variant _xian_ 鮮 (thread) occurs in some _zhuangzi_ editions. This variant must also reflect the correct meaning of _jie_ , which I interpret as "thread-work, sewing" in the _Zhuangzi_ passage (complementing the reference to "wielding the needle" immediately preceding in the _zhuangzi_. _Jie_ /* _krig_ is undoubtedly cognate with _xi_ /* _kig_ 係 (bind) and other words meaning to fasten with a cord. Ma Jixing interprets _mu jie_ 目 繲 as equivalent to _mu xi_ 目 系, a term for an attanchment at the back of the eye attested in _Lingshu_ 10, 3.6b (1992: 375, n. 2). I doubt that this technical denotation applies to _MS_ I.E.27. 郰, which I read as _xie_ , is not attested in received literature. Either it is a specialized word for oblique gazing, or perhaps a fusion of two graphs written by the scribe as one (目 and 邪).
_Rong_ 榮 is an architectural term that refers to the upturned edges of the roof by the eaves—also known as _wuyi_ 屋 翼 (roof wing; _SW_ , 6A. 18b,) and Duan Yucai commentary). "Vegetation from the upturned-slope of the roof" is probably the various plants that can still be seen today sprouting from the roof tiles of Chinese buildings. The use of roof vegetation in _MS_ I.E.27 must have symbolic significance related to the solar potency of something that grows on the roof, which makes roof vegetation an appropriate exorcistic material.
Ma Jixing argues that _xin_ 薪 forms a compound with _cai_ 蔡 (vegetation) in the previous sentence, meaning "vegetation and grassy material" (1992: 377, n. 12). However, _MS_ I.E.244 and _MS_ I.E.271 exhibit similar grammar in which _xin_ "kindling" refers to the kindling used to incinerate the drug.
"Silted water" translates _yanji_ 潭 汲, which means literally " make freshly-drawn water silty." It is used often in _MS_ I.E. _MWD_ , vol. 4, "Transcription," n. 4, identifies _yanji_ with _dijiang_ 地 漿 (earth juice), which is listed in _BL (GM_ , 5.51). Tao Hongjing describes the method for preparing it as follows: "Dig a pit three _chi_ deep in ground where there is yellow earth. Pour freshly drawn water into it and stir until turbid. After a little while, take the clear part and use it." The term _san hun_ 三 渾 (roiled thrice) in _MS_ I.E.27 must mean that the water is stirred together with the dirt and allowed to clarify thrice before use.
A purely exorcistic act of spouting through the mouth or nostrils (the word is _pen_ /* _p ən_ 噴) often precedes the chanting of an incantation in _MS_ I.E; and sometimes the first utterance in the incantation is the word for "spout" (in which case I adopt the reconstructed sound of the word to reflect its value as an exorcistic utterance). The person chanting the incantation in _MS_ I.E.27 is undoubtedly spouting while uttering the words "Spouter, spout ferociously." The distinctive element in _MS_ I.E.27 is that the person summons a "spouter"—a spirit—to assist in the expulsion of the demonic agent responsible for the ailment.
I.e. a comet.
_SW_ , 5A.50b, glosses _pei_ 衃 as "The compound _pei xie_ 衃 血 is used to describe the bloody blob of an aborted fetus in the Shuihudi _Fengzhen shi_ (SHD: 161; cf. Hulsewé 1985: 205). The word is cognate with _pei_ 肧, glossed in _SW_ , 4B.20a, as "first month of a pregnancy"; i.e. the stage when the fetus is still an amorphous blob. In _MS_ I.E.27 it appears that the "spouter" is ordered to enter the infant's body and assume the form of "congealed blood" to expel the demonic agent.
"You" represents a direct address to the demonic agent who is threatened with death.
"Liquid in the ladle" renders the grammar of the text and agrees with the earlier instruction to spit on the ladle (and not on the cup of silted water); yet why would the ashed vegetation in the ladle would be referred to as a "liquid"? Another possible interpretation is that the person spits on both the ladle and the cup of water, referred to here as the "liquid."
"Trembling" translates _zheng_ 徴. The graph is often used for _zheng_ 征, which occurs in compounds for extreme fright; e.g. _zhengying_ 征 營 (trembling and shaking), a conventional expression used by court officials in addressing the monarch (see _Hou Hanshu_ , 60B. 16a: "Your servant trembles and shakes with alarm and terror"). _Fangyan_ , 10.5b, identifies _zhengzhong_ 征 忪 as another expression for terrified trembling used in the region of the Yangzi and Xiang Rivers (i.e. around Changsha). Ma Jixing interprets _zheng_ to mean " a sign of being cured"; and the phrase to mean "if there are no signs" (1992: 379, n. 34). However, the second occurrence of _zheng_ in the phrase _zheng jin_ 徴 盡 below leads Ma into the forced interpretation, "when the signs of cure are completed."
_MWD_ , vol. 4, "Transcription," n. 2, identifies _hengshi_ 恒 石 with _changshi_ 長 石, which is listed in _BC (GM_ , 9.75). The identification is plausible, but uncertain. _ZY_ : no. 0915, identifies _changshi_ as anhydrite.
_SW_ , 11A-2.37a, glosses _sao_ 澡 as " wash the hands." In _MS_ I.E.29 _sao_ refers to "cleaning" the silted water, probably to make it more suitable for dingking. _KGS_ , vol. 1:164, n. 173, reads _sao_ as _lao_ 摷, in the sense of "pick out floating debris." _MWD_ , vol. 4, "Transcription," reads _sao_ as _cao_ 操, which Ma Jixing interprets to mean "manage, prepare" (1992: 381, n. 3). I reject the latter reading; the first reading is more plausible in that it still relates to cleaning the silted water.
A "second serving of beverage" clearly represents a form of measure (perhaps related to rules governing the serving of drink at rituals and banquets), but there is no record of it in received literature.
"Stove residue ash" is one of several terms used in the Mawangdui medical manuscripts for ash removed from the stove. _MWD_ , vol. 4, "Transcription," n. 4, identifies "stove residue ash" with _fulong gan_ 伏 龍 肝, which Tao Hongjing identifies as the yellow soil that accumulates inside the stove ( _GM_ , 7.81).
_MWD_ , vol. 4, "Transcription," n. 1, identifies _tuomo_ 橐 莫, with _tuomu_ 橐 吾, which is undoubtedly correct. _BC_ gives _tuowu_ as an alternate name for _kuandong_ 款 冬 ( _GM_ , 16.102), identified in _ZY_ : no. 4782, as _Tussilago farfara_ L. However, the Wuwei recipes indicate that in Han times _tuowu and kuandong_ were two distinct plants. Akahori demonstrates that _tuowu_ was the name for _T. farfara_ , while the early identity of _kuandong_ is not known (1978: 104, nn. 191–92).
_Xi_ 醯 is a rich vinegar made from rice gruel fermented in liquor ( _SW_ , 5A.48a).
Earthworm excrement is the fine soil produced by earthworms. Tao Hongjing discusses this substance in his commentary to the entry on earthworms ( _GM_ , 42.40), and observes that it was a regular ingredient in the lute used to seal alchemical vessels.
_MWD_ , vol. 4, "Transcription," n. 1, notes that the name of the plant whose stalks are used must have been omitted by the scribe. Ma Jixing argues that _jing_ 莖 (stalk) should be read as _jing_ 勁, which is the name of a kind of wild onion (1992: 385, n. 1). The instruction below to boil the root in winter leads me to doubt Ma's interpretation.
The ailment name _chao_ 巢 (nest) is not attested in received literature. _Chao_ occurs again in _MS_ I.E.152–53 below designating an anal fistula. The ailment denoted by _chao_ in _MS_ I.E.34–35 is uncertain. It is probably a condition affecting the skin and flesh. _MWD_ , vol. 4, "Transcription," n. 1, speculates that _chao_ /* _dzragw_ might represent a phonetic loan for _sao_ /* _tshagw_ 臊, and that the ailment is "body odor." Continuing with this speculation, it is suggested that _xing_ 星 (star) in the incantation should be read as _xing_ 腥, interpreted as "stench." I agree with the reading of the word _xing_ in the incantation, but not the meaning "stench." _SW_ , 4B.36a-b, distinguishes between the _xing_ written 胜, which means "stench of dog fat"; and written 腥, which means "small hard growths produced in the flesh of pigs when they are fed while the stars are out." The Duan Yucai commentary notes several passages in the _Liji_ that apply this word to hard, inedible lumps in pork. I would argue that in _MS_ I.E.34 _xing_ represents a pun which links the ailment to the influence of stars on the body. It seems likely that a transfer of stellar essence was believed to produce small growths in the flesh, and that these growths had the appearance of a "nest." Thus I reject the identification of the ailment as body odor in favor of some kind of growth, perhaps including polyps. It is because of the astral etiology that _MS_ I.E.34 exploits a flash of lightning and an incantation ordering spirits to "darken the stars/growths."
Spirits from the east and west who "preside over the dark" may be deities of the sun and moon. The incanted request to "darken the stars" refers both to the stars that have caused the growths and the growths themselves. The rhyming words in the incantation are _ming/*ming_ 冥 (dark) and _xing/*sing_ 星 (star).
"Choice" translates _niu_ 扭, glossed in _SW_ , 14B.28b as "edubile meat" (i.e. a choice cut of meat for fine eating).
Apparently the blend of beef, _wuhui_ , and _gui_ is burned as a fumigant to treat the ailment.
The name _xixia_ 夕 下 is not attested in received literature. It appears to be another skin or flesh ailment. Reading the name literally, it might refer to "darkening" or "dark blotches" on the skin. _MWD_ , vol. 4, "Transcription," n. 1, notes that _xi/*rjiak_ might be a phonetic loan for yi/ _*rak_ 腋 (underarm), in which case it would be an ailment that affects the underarm region—perhaps a scrofular condition.
_Helu_ 台 盧 is an unidentified herbal drug. The quantity thirty, the size indication, and the instruction to remove the skins suggest that the drug is a fruit or seed.
There are two different drug preparations used to treat _xixia_. The first is a salve of _huangqin_ and _helu_ —apparently mixed with suet and spread on the affected area (see below). In addition, there is a decoction whose ingredients are missing in the seven-graph lacuna above. This decoction is strained and applied to the affected area before the salve. _Jin_ 湝, translated as "squeeze," is not attested in received literature. _MWD_ , vol. 4, "Transcription," n. 3, reads the word as _jin_ 晉, glossed as "restrain, press" in the zheng xuan commentary in _zhouli_ , 32.10b (the passage concerns horsemanship). My guess is that with the addition of "water," the word means to press the liquid out of something. The instruction to "squeeze to remove the dregs" suggests the technique of straining a decoction through cloth as described by Tao Hongjing: "Use a new cloth. Two men wring it using a piece of wood that is one _chi_ long" ( _GM_ , 1.39).
"Chill" is a literal translation of _qi_ /* _tshi əd_ 凄 _MWD_ , vol. 4, "Transcription," n. 4, proposes reading it as a phonetic loan for _kai_ /* _kr əd_ 谐 (rub), which is phonologically inadmissible—and besides, it is unlikely that a decoction would be "rubbed" on the body. Perhaps _qi_ refers to cooling the _xixia_ by bathing it with the decoction (and the unknown ingredients of the decoction also may have had cooling properties).
_Wuhui_ is an aconite and was a well-known poison in early China. Presumably incidents of poisoning could have been accidental or purposeful. _MS_ I.E.42 describes applying medicine to a wound, providing the earliest evidence of the practice of coating weapons—especially arrow tips—with the poison (called _shewang_ 射 罔 by Tao Hongjing; _GM_ , 17.46).
_Jichi_ 薺 赤 is an unidentified drug name. For several guesses, see Ma Jixing 1992: 392, nn. 5–6; and _KGS_ , vol. 1: 169, n. 203.
_Shu_ 菽 sometimes serves as a general term for bean plants, but regularly denotes _dadou_ 大 豆 (soybean; _Guangya_ , 10A.34b). In _MS_ I.E, _shu_ consistently refers to the soybean.
_Ku_ 苦 is a herbal drug of uncertain identity. I favor identifying it with _kucai_ 苦 荚, listed in _BC (GM_ , 27.103); and identified in _ZY_ : no. 2627, as _Sonchus oleraceus_ L. This plant was a regular seasoning in ancient Chinese cuisine, adding a pungent bitter taste to dishes. Han textual sources and the modern botanical identification are discussed in the transcription notes to the grave inventory document from Mawangdui tomb 1, which lists a beef stew and a dog stew flavored with _ku_ (Hunan sheng bowuguan and zhongguo kexueyuan kaogu yanjiusuo 1973, vol. 1: 133). _MWD_ , vol. 4, "Transcription," n. 1, associates _ku_ with _daku_ 大 苦, interpreted as name for the fermented soybean condiment known as _shi_ 豉. Ma Jixing gives three other possible identifications for _daku_ (1992: 395, n.3).
[1] _ji_ 薺 is an unidentified herbal drug.
The wound was probably caused by an arrow or weapon coated with aconite poison.
There is another occurrence of Tai Mountain 大 山 (the Great Mountain) in _MS_ I.E.229. In the latter recipe, the mountain is definitely the sacred peak of the east situated in present-day Shandong; perhaps this denotation applies to _MS_ I.E.48 as well. Part of the incantation's efficacy derives from creating a magical space under the dominion of those who occupy the Great Mountain (hence the scorpion spirit blamed for the sting is at their mercy down below).
豙 is used regularly in _MS_ I.E to write _hui_ 喙 (snout, beak) in the drug name _wuhui_ 烏 喙.
_MWD_ , vol. 4, "Transcription," n. 3, notes that _fengniao_ 鳯 烏 (Wind Bird) is written in the text as a fusion graph 鳯 (the sign = indicates that 烏 is to be repeated). The incantation in _MS_ I.E.49 pairs the Wind Bird as Mother with a Father who dwells in Shu. Thus in both incantations it is the Wind Bird/Mother who eliminates the scorpion spirit with her lethal beak. Rather than understand the Wind Bird as the so-called Chinese phoenix, I suspect that it is the kite ( _yuan_ 鳶. A discussion of ritual banners used in funeral processions in L _iji_ , 3.5a, mentions a banner with a "crying kite" emblem; the Zheng Xuan commentary explains the symbolism equating the crying of the kite with wind. A southern tradition of the kite as a wind spirit is indicated in the ca. tenth century _Qinjing_ : "The Wind Bird is a kite. The people of Yue call it the Wind Elder. When it soars in flight there is a great wind in the heavens" ( _Qinjing_ , 11b). Known for its ability to drop from the sky like an arrow to attack its prey—and known as the Wind Elder among the people of Yue—the kite is a likely candidate for the Wind Bird in _MS_ I.E.48–49. The extant rhyming words in the incantation are _xun_ /* _rj əm_ 尋 (flee) and _xun_ /* _sj əm_ 心 (heart).
My guess is that Father controls the ground (specifying the southwestern region of Shu suggests a southern tradition of magic) and Mother/Wind Bird controls the air, making escape impossible for the scorpion spirit. Translating _ru_ 蓐 as "punish" is based on reading the word as _ru_ 蓐, which in _SW_ , 14B.30b is glossed as "humiliate." The _SW_ etymologizes the word as signifying the execution of men who fail to observe the seasonal regulations for agricultural work. "The Wind Bird who punishes" undoubtedly reflects a popular religious belief similar to the belief in Rushou 蓐 收, the bird-headed divinity of the east who punishes misdeeds (see Riegel 1989–90: 58).
The rhyming words in the incantation are Shu/*Djuk 蜀 and _ru_ /* _njuk_ 蓐 (punish); and _xun_ /* _rj əm_ 尋 (flee) and _xin_ /* _sj əm_ 心 (heart).
l _SW_ , 13A.58b, glosses _gui_ 跪 as "crab." Song sources cited in _GM_ , 45.17, identify _gui_ as a poisonous crab with six legs.
_MWD_ , vol. 4. "Transcription," n. 1, identifies _yuan_ as the name of a poisonous snake. _Yuan_ occurs as the name of a type of viper in _BL_ ( _GM_ , 43.80), but this usage appears to be post-Han. Besides, the recipes to treat the ailment in _MS_ I.E do not describe the kind of emergency treatment that would be expected if the ailment were the lethal bite of the viper. _SW, 1_ 3A.43a, glosses _yuan_ with _rongyuan_ 蝶 and _sheyi_ 它 醫. Both names are applied to various lizards. According to the fourth century _Gujinzhu_ , 2.5b, _rongyuan_ is the name for large lizards which can be as long as three _chi_ ; and the dark purplish black ones like to bite people. The Shuanggudui _Wanwu_ also identifies _yuan_ "lizard" as the name of an ailment (Fuyang Han jian zhenglizu 1988: 39).
薊 is an attested variant graph for _ji_ 薊 (see _Shanhaijing_ , 5.23a). _BL_ lists a large and a small _ji_ ( _GM_ , 15.34); the former identified as _Cirsium japonicum_ DC ( _ZY_ : no. 0191), and the latter as _Cephalanoplos segetum_ (Bge.) Kitam. ( _ZY_ : no. 0479). _MWD_ , vol. 4, "Transcription," n. 1, reads the graph as _jie_ 芥 ( _Brassica juncea_ mustard), noting the use of mustard plasters as a counterirritant in medicine. The textual evidence is not convincing, and I do not accept the reading;.
_MWD_ , vol. 4, "Transcription," reads 豙 as _yi_ , identified as a name for the herb _zhuyu_ 茱 萸. This reading is clearly justified in _MS_ I.E.103 where 豙 occurs together with the drug name _zhuyu_. However, the weight of evidence in _MS_ I.E.54 is far from convincing. Han ritual literature stating that a condiment of _yi_ is eaten with the "three sacrificial animals" (cow, sheep, pig) is adduced in the "Transcription," n. 1, to explain the term "suckling pig _yi_." Ma Jixing offers a different argument—that _chan tun_ 産 豚 means "fresh and plump" (referring to the _zhuyu_ fruit) not "raw suckling pig" (1992: 406, nn. 2–3). Despite additional circumstantial evidence concerning the later use of _zhuyu_ as a drug, Ma's interpretation of _chan tun_ remains unconvincing and I still question reading 豙 as _yi_. I provisionally adopt the argument in Qiu Xigui 1992: 531, and read the graph 豙 as _hui_ 喙 (snout) in _MS_ I.E.54 (see _MS_ I.E.48). Perhaps this treatment is similar to _MS_ I.E.46, which treats a scorpion sting by having a cow lick it.
"Beat into bits" translates _yang zhu_ 陽 筑. I am guessing that _yang_ modifies _zhu_ to indicate the manner in which the drug is beaten. Lacking an appropriate meaning for _yang_ itself in this context, perhaps it can be read as _dang_ 蕩 (broken apart, scattered). _KGS_ , vol. 1: 178, n. 243, proposes this reading, but interprets _dang_ to mean "clean" and translates _dang zhu_ as "clean (the _jin_ ) and beat it." The identification of _jin_ 堇 is uncertain. _MWD_ , vol. 4, "Transcription," n. 1, equates it with _jincai_ 堇 莱. According to Miao Qiyu's commentary in _Qimin yaoshu_ 28, 3.161, the plant denoted by this name is a viola, perhaps _Viola yedoensis_ Makino or _V. verucunda_ A. Gray. Several other possible identifications for _jin_ are summarized in Ma Jixing 1992: 408, n. 1.
_Jie_ /* _tsjar_ 暛 is one of several incantatory utterances in the _MS_ I.E incantations. In _MS_ I.E.128, _yu_ /* _gwjag_ 吁 is the first word uttered in the incantation, followed by the name of an animal demon. The _locus classicus_ for the compound utterance * _gwjag_ * _tsjar_ is _Shijing_ , Mao 11, 1C.7a; and Mao 25, 1E.8b. The themes of both poems concern auspicious animals—the _lin_ 麟 in the former and the _zouyu_ 騶 虞 in the latter—and the utterances are followed immediately by the animal names. The purpose of the utterances is to conjure the animal spirits. In _MS_ I.E these utterances are used in a specifically exorcistic manner to magically force the demon responsible for the ailment into submission.
Although _nien_ 年 is not attested as the name of a spirit in received literature, I suspect that in the incantations in _MS_ I.E.56 and _MS_ I.E.60 the lizard spirit blamed for the ailment is named Nien. The verb _he_ 蛬 is used when a venomous bug or scaly creature delivers a bite or sting ( _SW_ , 13A.53b).
I read _zi_ 兹 in the text as _zi_ 嗞 (cry out). The latter word is glossed in _SW_ , 2A.25a, with _jie/*tsjar_. _Zi_ is another word used in _MS_ I.E to denote the action of calling upon spirits—I suspect in this case to call upon other spirits to aid the "killed man" (i.e. the wounded man). The rhyming words in the incantation are: _he/*hrjiag_ 蛬 (bite) and _zi/*tsj əg_ 嗞 (cry out). See Luo and Zhou 1958: 81, for evidence that these words rhymed in southern dialects in Han times.
"Choice millet" translates _liang_ 梁, which refers to the choicest grade of _su_ 粟 ( _ZY_ : no. 4841, _Setaria italic_ [L.] Beauv.; spiked millet). _BL_ classifies the large seeds of _liang_ according to color: white, yellow, and blue (i.e. a dark bluish-black hue; _GM_ , 23.75).
Ma Jixing interprets this to mean that one _dou_ of millet is cooked in fifteen _dou_ of water (1992:410).
_Su_ 宿 means literally "pass the night." In _MS_ IV.7 a drug is soaked in vinegar for "five nights ( _su_ )"; that is, for a five day period counted by nights. In _MS_ I.E.58 I assume that the roosters are killed and then allowed to age for a three day period before cooking. A similar use of _su_ occurs in _MS_ III.54, which calls for "three-night-old rooster blood." Ma Jixing argues that _su_ in _MS_ I.E.58 refers to "years of age," and that the recipe calls for "three-year-old roosters (1992: 412, n. 2). But Ma does not provide sufficient evidence to support this interpretation _of su_.
I read text _ji_ 及 _as ji_ 汲 (draw water, scoop).
The graph in C94 is fragmentary and is transcribed as 食 in _MWD_ , vol. 4, "Transcription." Qiu Xigui argues that the graph in the text looks like _jin_ 金 (metal; 1992: 531). Comparing the fragmentary graph to other occurrences of 食 and 金 in _MS_ I.E, I am inclined to agree with Qiu.
At the end of the recipe the broth from the boiled roosters is poured into the steaming apparatus and drops into a bowl. I suspect that the graph missing in the preceding lacuna is _yu_ 盂 (bowl). It appears that a metal bowl is set beneath the _yan_ 甗 (slotted steaming-pot), which itself rests on top of the _fu_ 釜 (kettle) holding the water for steaming. Sun Ji reviews the archaeological evidence for the steaming apparatus in Han times, which consisted of an upper pot with a slotted bottom that fit into the mouth of the kettle below (1991: 332).
There are differing lists of which grains constitute the "five grains" in Han sources. The various identifications are discussed in Hayashi 1975: 10. Millet, barley, soybean, rice, and hemp could all be among the grains called for in _MS_ I.E.58.
I do not accept _MWD_ , vol. 4, "Transcription," which reads _tuo_ 陀 (drop) as _tuo_ 他 (another). The graph in the lacuna is fragmentary. The "Transcription," n. 2, states that it might be _tou_ 頭; and further speculates that _tutou_ 兔 頭 (rabbit head) might be the name of a kind of melon.
The recipe involves rather complicated cookery to produce a rich broth. First the roosters are boiled; and when they are done, the broth is poured over them once again. Having placed a bowl beneath the slotted steaming-pot (perhaps attached to the bottom of the pot or resting on the kettle below), grain is cooked and "rabbit [1] flesh" is added to the cooked grain in the slotted steaming-pot. Finally, the rooster broth is poured over and the liquid collects in the bowl.
_Qing_ 青 refers primarily to azurite ( _ZY_ : no. 3062), but is applied to malachite and other copper ores. It is listed in _BC_ ( _GM_ , 10.11). In addition to the natural ores, verdigris ( _tongqing_ 銅 青) was also used in medicine. _Qianjin yaofang_ , 76.3a, provides a recipe for treating snake, reptile, and insect bites by simply spreading verdigris over the wound. In _MS_ I.E.59 the incantation threatens the lizard spirit with the three rough men and in addition names the drug that will be applied to the wound to expel it. _Qing_ itself was probably applied to the bite wound at the conclusion of the incantation. The incantations in _MS_ I.E.233 and _MS_ I.E.235 employ a similar strategy, concluding with the threat to apply feces to the skin to expel the spirit blamed for the ailment. The rhyming words in the incantation are: _shi/*dj ək_ 食 (eater), _zai_ /* _dj əg_ 在 (is at), _zhi/*krj əg_ 止 (is to), _de/*t ək_ 德 (virtuously), _yi/*r əg_ 已 (desist), and _zhi/*tj əg_ 之 (it).
The _jili_ 奚 蠡 (large-bellied gourd) is identified as a water vessel with a capacity of up to one _dou_ in _mozi_ 52, 14.309. _jili_ is synonymous with _huli_ 瓠 蠡 as a name for gourds used as containers. The gourd is either _hulu_ 壺 盧 ( _ZY_ : no. 3683, _Lagenaria siceraria_ [Molina] Standl. var. _depressa_ Ser.) or _ku hulu_ 苦 壺 盧 (ZY: no. 2653, _L_. _siceraria_ [Molina] Standl. Var. _gourda_ Ser.) For another gourd container, see _MS_ I.E.134.
There are seven additional occurrences of the Pace of Yu 禹 步: _MS_ I.E.67, 118, 120, 128, 225, 276, and _MS_ III.83. See the discussion in the Prolegomena, Section Five, "Varieties of Magic."
Based on the parallel with the incantation in _MS_ I.E.56, the incantation might read: "So-and-so was [bitten] by a certain Nien and now [cries out]."
I accept Schafer's judgment that _li_ 貍 refers to the raccoon-dog ( _Nyctereutes procyonoides_ ; 1987: 29). The Asian raccoon-dog is a small fox-like animal with dark fur by the eyes resembling raccoon markings (see Tate 1947: 162). In _Huainanzi_ , 10.514, _li_ is said to belong to the same category of animal as the fox ( _hu_ 抓), the two animals being easily mistaken for one another. _Li_ is commonly identified as wild cat ( _ZY_ : no.3904, _Felis bengalensis_ Kerr).
The usual "another" does not occur at the head of _MS_ I.E.63.
For the identification of _you_ 抚 with warts, see Yu Yan 1972: 243.
_Jie_ 藉 (cattail bedmat) is synonymous with _jian_ 薦, the doublefaced mat filled with straw used for sleeping. _SW_ , 1B.14a, glosses _ruo_ 蒻 as the soft young leaves of the cattail which are suitable for covering a bedmat. The ancient vocabulary for mats and relevant archaeological data are summarized in Hayashi 1976: 203–204.
Judging from this description of how to perform cauterization and one other description in _MS_ I.E.127, early cauterization treatment entailed touching the person's skin with a brand-like material: a burning cattail cord in _MS_ I.E.64, and a kind of cigarette wrapped in _ai_ (mugwort) leaves in _MS_ I.E.127. Presumably the technique used was similar whenever cauterization is mentioned in the Mawangdui medical manuscripts. The mugwort cigarette in _MS_ I.E.127 is not moxa, and its use should not be construed as moxibustion.
_He_ 禾 was a general term for grain plants in Han times. Perhaps it refers to spiked millet, as it did in Shang and Zhou times (see Hayashi 1975: 4).
_Hui_ 晦 denotes the day when the moon is darkest preceding the appearance of the new moon.
The rhyming words in the incantation are: _hui/*hm əg_ 晦 (last day of month) and _bei/*p ək_ 北 (north).
Bu 鋪 refers the time of day when the sun is low on the western horizon and is used to designate a division of the day corresponding to 3:00–5:00 p.m. This is also the time of one of the standard meals. _Xiabu_ 下 餔 (end of the late afternoon) corresponds to a time around 5:00 P.M. (see Chen Mengjia 1965: 123).
_MWD_ , vol. 4, "Transcription," emends the text by adding _yi_ 以 before the word for "cold." The meaning of the text is clear as written, and I do not accept the emendation.
The phrase 塊 訁 日 is written twice in the text, an obvious scribal error.
The rhyming words are the same as _MS_ I.E.66.
The lacuna is probably you 疣 (warts).
I.e. the bedroom.
The rhyming words are the same as _MS_ I.E.66.
_Shuo_ 朔 denotes the day of the new moon.
Presumably the mallow halberd represents the nature of the mallow stalks as an exorcistic weapon. The rhyming words in the incantation are _shuo_ /* _sngrawk_ 朔 (first day of month) and _ji_ /* _kjiak_ 戟 (halberd).
_SW_ , 6A.14a, describes _sha_ 樧 as a plant that "resembles _zhuyu_ (evodia) and comes from Huainan." Other sources simply identify _sha_ as _zhuyu_. Ma Jixing discusses two additional identification (1992: 423, n.6).
_MWD_ , vol. 4, "Transcription," reads _jian_ 煎 as _jian_ 前. The latter graph is glossed with _wanghui_ 王 蔧 in _Erya_ , 8.1b; and _wanghui_ is an alternate name for _difu_ 地 膚, listed in _BC (GM_ , 16.105) and identified as broomplant ( _ZY_ : no 1635, _Kochia scoparia_ [L.] Schrad.). The dried stalks of _difu_ were commonly used to make brooms. Perhaps _jian_ in _MS_ I.E.69 refers to this plant.
The reference to a "removal day" is to a hemerological system known as _jianchu_ 廪 除 (establishment and removal). According to the description of the system in _Huainanzi_ 3.48, each of the twelve Branches of the sexagenary cycle is correlated with one of twelve divinatory signs, among which _jian_ "establishment" is the first in the sequence and _chu "_ removal" the second. To give an example, the first lunar month is assigned the Branch _yin_ 寅, making the Branch _yin_ the sign of "establishment" and the following Branch _mao_ 卯 the sign of "removal" during the course of the first month. If during the first month, a day which includes the Branch _mao_ in its cyclical designation occurs, this day is a "removal" day and is unlucky. The earliest records of the _jianchu_ system are in the Shuihudi and Fangmatan hemerological manuscripts. Kalinowski analyzes the Shuihudi evidence (1986: 198–99). In _MS_ I.E.69 the restriction prohibits a person from performing the ritual and incantation on the first day of the month if that day happens to have a "removal" Branch in its cyclical designation for the month in question; as would be the case if the first day of the first month happened to be _guimao_ 癸 卯. When this circumstance arises, the person must wait until after mid-month; i.e. after the fifteenth day which is the day of the foil moon ( _wang_ 望).
The rhyming words are the same as _MS_ I.E.66.
Yu Yan reviews references to _dian_ 癲 in received literature, concluding that the ailment encompasses epileptic fits as well as fits of craziness (1972: 109–113). In _MS_ I.E.71 the ailment name is written 顛, literally "crown of the head." There is evidently an etymological and etiological link between the ailment and the head, since the treatment described in the recipe involves making an incision from the crown to the nape of the afflicted person's head. _Dian_ also means "fall over," which is often cited in explanations of the ailment in received literature and is the basis for Yu Yan's identification with epilepsy.
I.e. when the seizure occurs.
The graph in the lacuna is fragmentary. Ma Jixing writes _zhi_ 致 without explanation (1992: 426). Having examined the manuscript, the fragments are not decipherable and I do not accept Ma's emendation.
_MWD_ , vol. 4, "Transcription," n. I, suggest that _quanwei_ 犬 尾 may be the same as _gouwei cao_ 狗 尾 草 ( _ZY_ : no. 2959, _Setaria viridus_ [L.] Beauv.) listed in later material media ( _GM_ , 16.120).
The ailment name _baichu_ 白 處 is not attested in received literature. According to _MS_ I.E.75, "whiteness and no webbed pattern (on the skin)" is a sign of the occurrence of the ailment. _Baichu_ can be translated "white patches," and perhaps the ailments is vitiligo. However, the meaning of the ailment name is complicated by the fact that _MS_ I.E.74–75 use three different graphs to represent the second word: 施, 瘧, and 虗 On the assumption that all four graphs are intended to represent the same word, I provisionally read them all as _chu_. The probability that _chu_ itself denotes a specific ailment—and does not simply mean "patch"—is increased by the occurrence of the ailment name in 沱 _Wanwu_ , where it is not preceded by _bai_ "white" (Fuyang Han jian zhenglizu 1988: 37). 沱 and the variant graph 沱 occur in medieval rhyming dictionaries, but the meaning is uncertain (Morohashi 1957–60, vol. 7: no. 22101).
It is likely that Guan 灌 is a toponym identifying the source of the mineral. The alternate name Guan _ceng_ 曾 (laminar) indicates that the azurite to be used is a stratified variety.
I.e. stove ash.
Because the recipe below specifies the exact time in spring to gather the eggs, they may be the eggs of sparrows and other small wild birds, known generically as _que_ 雀 (dickeybird). See _MS_ III.16.
The complete phrase _yinzao suo_ 陰 燥 所 occurs below, so there is no difficulty filling the lacuna here with _suo_ "place." The reference to a room for drying and storing drugs suggests that such rooms were to be found in elite households. Perhaps the _yinzao suo_ in _MS_ I.E.74 is related to the palace _pushi_ 暴 室 (drying chamber). The Yan Shigu commentary in _Hanshu_ , 8.2a, derives the name from the activity of processing and dyeing silk, but his explanation has been discounted several times (cf. Goodrich 1966). The _pushi_ was also the infirmary and place of detention for the ladies of the palace, a use that would fit well with a place a used primarily for processing drugs.
Repetition of 而 上 in the text is an obvious scribal error. It becomes clear a little later in the recipe that the egg-base medicine is daubed on the skin with _chu_ , which is then roasted over a fire. To help alleviate the pain of the roasting treatment the recipe tells the patient to first get drunk on good liquor.
"Respond" translates _yu_ 愈, which is one of two words used in _MS_ I.E to indicate that the medicine or therapy has taken effect, and that the patient is moving toward full recovery. _MS_ I.E.95 states that the ailment _yu_ "responds" after one treatment, and that it is finally cured after three days of repeating the treatment once a day. In _MS_ I.E.117 _zhi_ 智 is the word used to mean that the ailment responds to the treatment.
I.e. fertilized eggs. _Ren_ 仁 (kernel) referring to the embryo in a fertilized egg also occurs in "Jie" in the first Shuihudi hemerological manuscript ( _SHD_ : 212; Harper 1990: 223).
The gelatin must be added to the egg medicine after it boils. _BC_ lists gelatin made from various animal hides ( _GM_ , 50.93) and gelatin made from deer horn ( _GM_ , 51.28). _MS_ I.E.96 calls for adding gelatin in the form of sticks. The production of dried gelatin wafers is described in _Qimin yaoshu_ 90, 9.550–52.
It is not clear what is done with the chicken, unless it was soaked just to prepare the claws for scratching the affected skin.
_Dadai_ 大 帶 is not attested in received literature and we can only surmise that it refers to a skin ailment.
挡 is unattested in received literature. _MWD_ , vol. 4, "Transcription," n. 2, suggests that the right side may be a variant of _dang_ 當, but 壋 is also unattested. The romanization _dang_ is used for lack of another way to represent the unknown drug.
Qing 清 refers to _qingjiu_ 清 酒 (clear liquor), one of three grades of liquor listed in _Zhouli_ , 5.6b. According to the Zheng Xuan commentary, clear liquor is brewed in winter and is ready to drink the next summer. The name also indicates that it is a filtered liquor (see Hayashi 1976: 74). _MWD_ , vol. 4, "Transcription," n. 1, suggests an alternative interpretation that the recipe calls for boiling the liquor "until gelatinous" rather than boiling gelatin in liquor.
_Ming_ 螟 is one of two crop pests that are regularly paired in early literature, the second being _te_ 蟘. The modern identification of both insects is uncertain. Zhou Yao has proposed that _ming_ may refer to _Diatraea shariinensis_ or _D. venosata_ , insects that infest millet and sorghum crops (1957: 43). _Te_ has been identified with the locust, but this is clearly inapplicable to pre-Han and Han usage in which _te_ is paired with _ming_ (the locust constituted a category of pest unto itself). Neither _ming_ nor _te_ are attested as ailment names in received literature. Yet _MS_ I.E.244 and _MS_ I.E.248 treat damage caused by the _te_ bug: the first for when the _te_ chews at the mouth and nose, and the second for when it chews at the teeth. In addition, _Maishu_ , "Ailment List," records the name _teshi_ 蟘 食 (chewing by _te_ ) for an ailment characterized by painful scabs on the nose ( _MSSW_ : 72). Identifying crop-destroying pests as the source of decay on the body is not merely figurative, but reflects the belief that the very bugs that destroy crops also afflict the body. In applying the classical pairing of _ming_ and _te_ to ailments, it is evident in _MS_ I.E that the _ming_ ailment is the more major and life-threatening of the two. Based on the symptoms in _MS_ I.E.78 it has been suggested that the ailment is leprosy, even though two names for an ailment that is definitely associated with leprosy are attested in Qin and Han texts: _li_ 癘 (also a word for pestilence) and _eji_ 惡 疾 (foul sickness; also applied to disabling afflictions like blindness or deafness). I think the identification is plausible. For further analysis of the _ming_ -bug ailment, see Harper 1990: 227–30.
_MWD_ , vol. 4, "Transcription," n. 2, notes that there is a break in the next following C137; it is not clear how many columns might be missing. _SW_ , 13A.43b, glosses _quan_ 蠸 as follows: "It is a bug. Another meaning is a major poisonous bite." _Erya_ , 9.7a, glosses _quan_ as _shougua_ 守 瓜 (melon guardian), a bug that infests melons. There are several possible ways to interpret the ailment name and the fragment of the one extant recipe. Assuming that the [1] _quan_ ailment is similar to the _ming_ ailment, it is another case of bug etiology. When the recipe calls for mixing a _quan_ bug with egg, perhaps we have a case of homeopathic medicine in which the bug that caused the ailment is used to treat it. Alternatively, the ailment is some kind of poisonous bite that can be treated with its namesake, the _quan_ bug.
_MS_ I.E.80–83 must belong to the unknown ailment category [1] _zhe_ 者 listed in _MS_ I.E.1.
is not attested in received literature, and the reading _yun_ is based on the phonetic 云. _MWD_ , vol. 4, "Transcription," n. 1, offers two tentative identifications of the ailment name: perhaps it is equivalent to _yun_ , glossed in _SW_ , 7B.27b, as "an ailment" and associated in later sources with dizzyness (Yu Yan 1972: 113); or it may be a scribal miswriting of _jie_ 痎, identified in _SW_ , 7B.31b, as a form of _nue_ 瘧 (cold and hot syndrome; see _MS_ I.B.1).
_SW_ , 6A.13b, glosses _hua_ as follows: "A tree. The bark is used to wrap pine pitch." The Duan Yucai commentary adduces early sources to identify this name with _hua_ 樺, the Chinese white birch ( _ZY_ : no. 3657, _Betula platphylla_ Suk). _GM_ 35.38, includes references to the use of birch bark to make torches of the type described in _SW_. Ma Jixing offers a second identification as _shu_ 樗 (1992: 441, n. 2); but the Duan Yucai commentary in _SW_ , 6A.6b, indicates that the two graphs were confused for one another and that the identification is invalid.
For _xian_ 癇 see _MS_ I.E.26. According to _MS_ I.E.1 there are four categories of _xian_ ailments in this section of the text, all named after animals: horse, [1] (the name of the animal is not written in the text, a clear case of scribal error), sheep, and snake. _MS_ I.E.86 is the only recipe that can be placed with certainty in the horse type of _xian_ , and recipes for the latter three categories are no longer extant (unless the fragmentary phrases in _MS_ I.E.87 represent recipes for a subsequent category. _Qianjin yaofang_ , 10.15a, describes a classification of _xian_ according to the six domestic animals: horse, cow, sheep, pig, dog, and chicken. The sounds emitted by the afflicted person and the contortions of his body during an attack of spasms are the bases for naming each type. The four categories of _xian_ ailments in _MS_ I.E seem to have a similar basis.
_MWD_ , vol. 4, "Transcription," n. 1, notes that there is a break in the text following C149; it is not clear how many columns might be missing. In addition to the three types of _xian_ , two other ailment categories are lost: Various Eating Ailments and Various [1] Ailments.
On the basis of _MS_ I.E.1 and the fact that the recipes following _MS_ I.E.88 open with the conventional "another," _MS_ I.E.88 is the first extant recipe in the ailment category Urine Retention ( _long_ ). _Long_ is identified as an ailment characterized by "prostration" in _SW_ , 7B.34b), and this seems to be the meaning of _long_ in _MS_ I.E.120. _Suwen_ 23, 7.8b, provides positive identification of _long_ as retention of urine in the bladder. In _Maishu_ , "Ailment List," inability to urinate is called _bi_ 閉 (blockage; _MSSW_ : 72). _Wanwu_ records the name _long_ along with the fact that it can be cured with _shiwei_ (pyrrosia), the drug used to treat urine retention in _MS_ I.E.109 (Fuyang Han jian zhenglizu 1988: 36). _Long_ is also the name used in the Wuwei recipes, which record four types of urine retention also treated in _MS_ I.E: bloody ( _MS_ I.E.108), stone ( _MS_ I.E.109), lardy ( _MS_ I.E.110), and rice slop ( _MS_ I.E.95 describes stones that come out "like rice slop" after treatment; _WWYJ_ : 2a). The standard name for difficulty in urination in later medical literature is _lin_ 淋 (Yu Yan 1972: 239).
_Duo_ /* _duarx_ 隋 is not attested as an anatomical name in received literature. I accept Zhao Youchen's argument that it represents a word meaning "navel" (1981). _MWD_ , vol. 4, "Transcription," reads it as a phonetic loan for _shui_ /* _dj əd_ 雎 (buttock). Phonological evidence does not support the loan. Reviewing the related occurrences of _duo_ in _MS_ I.E.89, 97, 135, and 138, Zhao cites evidence from later medical literature to show that the navel is the logical referent of _duo_ in these recipes. Additional support for Zhao's identification comes from _Maishu_ , "Ailment List" (see the discussion of _cuo_ in _MS_ I.A.3). _Duo_ has the meaning "oblong" (as in _MS_ I.E.146), and this sense may account for its use as a name for the navel. Although unattested, the possibility of an anatomical application is suggested by the Zheng Xuan commentary in _Liji_ , 16.13b, which glosses _dou_ 寶 as a hole in the ground "with an oblong shape ( _duo_ )."
_Chuohua_ 逸 華 is unknown. 逸 is also unattested in received literature (the reading _chuo_ assumes as phonetic).
Performing cauterization on the middle toe of the left foot does not appear to be related to vessel theory.
The context clearly indicates that the two-graph lacuna is 禹 步.
"Snort" translates _gu_ 鼔. _Gu_ was used idiomatically to refer to blowing the nose in Han times, as attested in the _SW_ , 2A.24a, gloss of _pen_ 噴: "Another meaning is to blow ( _gu_ ) the nose."
The conclusion of the incantation is missing in the lacuna. It appears that the cup of silted water is used to magically remove the ailment (similar to the gourd of silted water in _MS_ I.E.60).
癟 appears to be a variant graph for _bi_ 癟. _Bi_ is listed in later dictionaries with a meaning of "withered" (Morohashi 1957–60, vol. 7: no. 22588). The word has been linked with _bi_ 秕, which _SW_ , 7A.49a, glosses as "unformed millet"; i.e. millet that shrivels on the stalk. I suspect that in _MS_ I.E.94 _bi_ refers to being unable to urinate because the urine "dries up" internally—perhaps forming the kind of bladder stone mentioned in _MS_ I.E.95 and 109. _MWD_ , vol. 4, "Transcription," n. 1, offers an alternative interpretation by simply reading the graph as a phonetic loan for _bi_ 閉 (blocked).
It appears that a solid object has been heated and plunged into the liquor to quench it. Then the person drinks the liquor.
The graph in the lacuna ought to be 之.
"Inside probably refers to the lower abdominal region around the bladder.
The herb _dujin_ 毒 堇 does not appear in later materica medica. _MWD_ , vol. 4, "Transcription," n. 4, suggests identifying it with _zijin_ 紫 堇 ( _ZY_ : no. 4867, _Corydalis edulis_ Maxim.; see _GM_ , 26.84. The description of the herb at the end of _MS_ I.E.95 supports rather than negates the identification, but it remains uncertain.
_Gan_. 泔 (rice slop) is one of several words that refer to the liquid left over from cleaning grain to prepare it for cooking (see _SW_ , 11A–2.33a).
_Qian_ 前 (front) refers to the genitals. See _MS_ IV.3.
_MS_ I.E.95 provides the earliest testimony to the custom of gathering herbs on the day of the summer solstice, celebrated on the fifth day of the fifth month. In received literature the custom is first mentioned in the sixth century _Jing Chu suishi ji_ (Moriya 1963: 353), although the gathering of artemisia to serve as a protective amulet on this day is attested earlier. The summer solstice is the day when the solar power culminates, and herbs gathered on this day swell with potency. Special notice is accorded to red colored plants. The red stalks of _dujin_ mentioned below may account for the association with the solstice, although it is equally probable that the fruit is reddish.
I suspect that _dujin_ is being compared to another type _of jin_ in this sentence; that is, the leaves of _dujin_ are smaller than the leaves of the other unknown jin.
_Xi_ is literally the main-cord on a net ( _SW_ , 13A.25a). Here it refers to the distinctive veins on the leaves.
Rong 戎 refers to the northwestern borderlands. This is the source of Rong salt, which is listed in _BC (GM_ , 11.41).
Because of the lacuna the grammar of the sentence and precise area to be coated with salt are uncertain, but it is somewhere in the vicinity of the _duo_ (navel).
The same idiomatic phrase occurs in _MS_ III.5, where yan 厭 (satiation replaced duo 多 (large amount). The use of gu 故 to mean "standard" is attested in Lüshi chunqiu, 17.209.
Ru 襦 is an undershirt that fits closely around the neck and goes down to the waist. For early text references and archaeological data, see Hayashi 1976: 9–10. Jing 頸 (neck) probably refers to the neckband of the undershirt. Another possibility is that rujing is a compound meaning "undershirt." Fangyan, 4.2b, gives quling 曲 領 (neck wrapper) as a name for ru in the southwest region; and another synonym of ru, yan 褗, is glossed as yanling 褗 領 (shirt that wraps around the neck) in SW, 8A.51b. However, one cup of liquor seems like too little liquid to soak the whole undershirt. Hanshan 汗 衫 (sweatshirt) is listed in GM, 38.31.
扔 is not attested in early literature, and it is difficult to determine a reading for it. Ma Jixing cites the graph in recent sources, but they are inapplicable to the occurrence of the graph in _MS_ I.E (1992: 459, n.4). _MWD_ , vol. 4, "Transcription," n. 2, suggests that it be reas as _zheng_ 蒸 (steam), which is doubtful. The word appears to represent a method of boiling that contrasts with _fei_ 沸 (bubble; i.e. a full bubbling boil) and _wen_ 溫 (heat). Since wen probably refers to cooking a liquid until hot (see _MS_ I.E.108–109), I suspect that 扔 represents a stage in between "heating" and "bubbling"; hence the provisional translation "scald."
I follow _KGS_ , vol. 1: 205, n. 399, in identifying _zhuyu_ 茱 萸 as Wu _zhuyu_ 吳 茱 萸 ( _ZY_ : no. 2280, _Evodia rutaecarpa_ [Juss.] Benth.), listed in _BC_ ( _GM_ , 32.37). _Yi_ 蘋 in one usage refers to the _zhuyu_ fruit, but most often is the name of a spicy condiment prepared from the fruit. In _MS_ I.E.103 _yi_ may refer to the condiment, but I suspect that it is part of the name of the herb itself. There is considerable confusion in materia medica between Wu _zhuyu_ and _shi zhuyu_ 食 茱 萸 ( _ZY_ : no. 3504, _Zanthoxylum ailanthoides_ Sieb. et Zucc.), described in _GM_ , 32.41. Ma Jixing argues for the latter identification in _MS_ I.E.103 (1992: 461, n. 4).
SW, 6B.9a, glosses _jian_ as a "small bunch ( _shu_ 束)."
_Jisi_ 己 巳 is the sixth cyclical designation in the sexagenary cycle of Stems and Branches. Two other cyclical days are indicated in _MS_ I.E: _MS_ I.E.124 specifies the day _xinsi_ 辛 巳 (eighteenth in the cycle) for an exorcistic cure; and _MS_ I.E.126 specifies _xinmao_ 辛 卯 (twenty-eighth in the cycle). In all three cases I am unable to determine the precise symbolism of selecting these days. However, there must have been a reason for choosing them. The Shuihudi and Fangmatan hemerological manuscripts provide abundant data on calculations involving the sexagenary cycle (see _MS_ I.E.69).
I accept Qiu Xigui's argument that the graph transcribed as in _MWD_ , vol. 4, "Transcription," should be 虎, read as _ti_ 嗁 (shout; 1992: 531).
_Ruo_ 若 functions as a conjunction in this sentence.
The name _zaoshi_ 澡 右 does not occur in received literature. It might be an unattested name for huashi 滑 右 ( _ZY_ : no. 5037, talc), which is listed in _BC_ ( _GM_ , 9.77) and recommended for curing urine retention. Other identifications are proposed in Ma Jixing 1992: 466, n. 2; and in Wei and Hu, vol. 1: 92, n. 2. _KGS_ , vol. 1: 207, n. 409, doubts that _zaoshi_ is a drug name and translates the sentence literally: "Cleanse a stone the size of a plum pit."
If _zaoshi_ is a mineral drug, it is probably powdered first. If it is simply a "cleansed stone," perhaps it can be swallowed whole.
_Huo_ 藿 is a general term for the leaves of bean plants (see _Guangya_ , 10A.42b). Perhaps soybean or adzuki bean are intended in _MS_ I.E.111.
The identity of _yinfu mu_ 隱 夫 木 is not known. It appears to be a single drug, undoubtedly a tree. The compound _yinfu_ occurs in _Hanshu_ , 57A.34b, identified as two plant names in the Wang Xianqian commentary: _yin_ 檃 and _fu_ 枎. Neither of these names can be identifies with certainty, and the commentary may be incorrect in reading the graphs as two names rather than as a single compound name.
_Yang_ [1] 陽 occurs again in _MS_ I.E.116 with the second graph still missing. Judging from the fact that it is made into a _geng_ 羹 (boiled-dish"), it may be a food plant.
I interpret _renzi_ 衽 緇 as a compound meaning "the band that forms the hem of a robe." _Ren_ refers to the band of cloth attached to the collar and front edge of a wrap-around robe ( _SW_ , 8A.51b). Archaeological evidence shows that the wrap-around robe had a long flap on the left that was wrapped across the right and around the back, which explains the association of _ren_ with the fastening of the robe (Sun Ji 1991: 241). The identity of _zi_ is problematic. _KGS_ , vol. 1: 208, n. 418, reads _zi_ in its original meaning "black"; and interprets the compound as "a band of black (material)." I suspect that _zi_ /* _tsrj_ ə _g_ is a phonetic loan for another word, most likely the word _zhi_ /* _drj_ ə _k_ 値 used in _Liji_ , 29.6b, to denote the trim attached to ritual banners. This was evidently a rare usage because the Zheng Xuan commentary supplies a sound gloss and defines it as _yuan_ 緣 (edge). _MWD_ , vol. 4, "Transcription," n. 1, proposes a different solution to reading the compound _renzi_ that I find unacceptable.
This recipe and _MS_ I.E.116 treat ailments where the discharge of urine is abnormal. One of the meanings _of lun_ 淪 in _SW_ , 11A–2.7a, is "sink." I follow _KGS_ ' vol. 1: 209, n. 420, in interpreting _lun_ in _MS_ I.E.115 as "sunken matter, sediment."
The drug is unknown and the translation is conjectural. The main conjecture is reading _tang_ 棠 (the name of a species of pear) as _tang_ 堂 (dwelling), and guessing that this refers to the magpie nest. Perhaps the compound _quetang_ 鵲 堂 (magpie dwelling) is related to the magpie nest as a metaphor for the ideal conjugal dwelling, the _locus classicus_ of which is _Shijing_ , Mao 12, 1C.7b. _Hao_ 嵩 might be artemisia in _MS_ I.E.115, but perhaps it should be read as _gao_ 稾 (straw)—and the drug is grassy material taken from the magpie nest. Other conjectures are possible.
Whereas lardy urine in _MS_ I.E.110 is a form of urine retention (perhaps the urine does not flow because it is congealed), lard urine suggests a thick, milky discharge. _Maishu_ , "Ailment List," lists an ailment that may be related: "When the urine comes out and is white like hair-washing rinse—it is white conglomeration" ( _MSSW_ : 72).
The meaning of the second name for the ailment is unclear. Perhaps _fu_ 復 (return) represents _fu_ 腹 (abdomen).
橐 in _MWD_ , vol. 4, "Transcription," should be transcribed as _nang_ , 囊 (the meaning "scrotum" is well attested for the latter). The same correction applies to the ailment name in _MS_ I.E.1. Later medical literature usually includes this type of ailment under the category _tui_ 穨 (inguinal swelling), which is the next ailment category beginning in _MS_ I.E.118 (Yu Yan 1972: 225). A similar classification occurs in _Maishu_ , "Ailment List": "When the scrotum has a swelling—it is blood inguinal swelling" ( _MSSW_ : 72).
_Suanjiang_ 酸 漿 is a liquid added to the manure after the water is drained away. The compound might refer to a "vinegar beverage," similar to the _cujiang_ 酢 漿 (vinegar beverage) given in _SW_ , 11A-2.34b, as a gloss of _jiang_ ; and related to the _suanjiang_ listed among medicinal liquids in _GM_ , 5.54. However, _suanjiang_ is also the name of a herb identified as _Physalis alkekengi_ L. var. _franchetii_ (Mast.) Mak. ( _ZY_ : no. 5287, listed in _BC_ ( _GM_ , 16.97).The liquid extracted from the plant is commonly used in medicine.
The interpretation of _jie zhong jia_ 芥 衷 莢 is problematic. _MWD_ , vol. 4, "Transcription," n. 6, identifies _jie_ as mustard ( _ZY_ : no. 2173, _Brassica juncea_ [L.] Czern. et Coss.); and suggests that _jia_ "pod" may refer to the fruit body, usually called _jiao_ 角. To accept this interpretation one must assume that the recipe is incomplete, for there is no indication of show the newly introduced ingredient is used. _KGS_ , vol. 1: 210, n. 431, reads _jie_ in the sense of " refuse matter"—referring to the manure. For attestation of _jie_ as "grassy matter, refuse," see _Zuozhuan_ , Ai 1, 57.3b. In this interpretation, the recipe would have the person pick out the "pods" from the refuse/manure (either undigested pods that are still in the manure or pod-like pieces of the manure). The problem of whether the therapy is internal or external remains, since the recipe does not say.
Tui 穨 means literally "drop down," and is attested first as a word for a fiery, descending wind in received literature (Harper 1990: 219). The Mawangdui and Zhangjiashan medical manuscripts provide the earliest attestation of _tui_ as a name for various kinds of swellings in the inguinal region, including hernias. Several of the magical treatments in _MS_ I.E provide evidence of a demonic etiology for _tui_. A naturalistic conception related to pathogenic vapor is also evident; e.g. in _MS_ I.E.135, which recommends cauterizing the foot Great Yin and Great Yang vessels. For discussion of the ailment in Han and later received sources, see Yu Yan 1972: 225–29. The name of this ailment category as given in _MS_ I.E.1 is _changtui_ 腸 穨 (intestine _tui_ ). Intestine _tui_ is included in _Maishu_ , "Ailment List": "When there is a screeching noise above and below the swelling—it is intestine _tui_ " ( _MSSW_ : 72). _Yinshu_ also describes an exercise routine to treat intestine _tui_ and muscle _tui_ ( _YSSW_ : 84). The description does not appear to match the illustration of the exercise to treat _tui_ in _MS_ II.C. Many of the recipes in _MS_ I.E refer to the male genitals and possibly concern a scrotal hernia.
The patient is beaten with the pestle at the end of the recipe. Arbor-vitae wood has associations with the east and solar potency that make it and appropriate material for an exorcistic instrument.
The use of Hu 胡 in the incantation probably involves a pun. _KGS_ , vol. 1: 211, n. 435, interprets the word literally as "cow dewlap"—the gloss in _SW_ , 4B.31b. Hence the swellings to be exorcised are likened to the excrescent skin of the dewlap. At the same time, it appears that Hu designates a demon, and that the three Hu are the trio mentioned below ("there are only three"). Hu/*Gag was a generic term for northern barbarians, but I suspect that the pun involves the fox ( _hu_ /* _gwag_ 柧). The earliest attestation of fox possession in China is found in _MS_ I.E.124 and 128, where a fox is named in the incantations as the cause of the inguinal swellings. Post-Han sources tell of were-foxes disguising their identity by adopting the surname Hu (see Groot 1892–1910, vol. 4: 195). Perhaps the Hu in _MS_ I.E.118 represent fox demons.
The two-graph lacuna is probably 父 子. The incantations in _MS_ I.E.120 and 125 attribute inguinal swellings to the Sons born of a Mother and Father.
漳 in _MWD_. vol. 4, "Transcription," should be written 撞, and read as _zhong_ 腫 (swellings).
The rhyming words in the incantation are: Hu/*Gag 胡 (all three occurrences) and _fu_ /* _bjag_ 父 (father); and _qi_ /* _tshjit_ 七 (seven) and _yi_ * _?jit_ 一 (one).
_Si chui_ 椎 (beat with an exorcising rod) refers in this case to beating the person with the pestle. _Si_ occurs again as a verb in _MS_ I.E.120, where the person is exorcistically beaten with an iron mallet; and in _MS_ I.E.124, where a cloth is used. _Si_ was already a rare word in Han times. The only attestation is the definition in _SW_ , 3B.40a: "It is a _haisi_ 毅 改, which is a large _gangmao_ 剛 卯 used to expel demonic apparitions." The definition indicates that _si_ was only known as a member of the compound _haisi_ the name of an apotropaic amulet related to the _gangmao_ amulet (for which see Bodde 1975: 304–306). The use of _si_ in _MS_ I.E to denote the action of exorcistic beating is an archaic usage that can be traced back to the Shang bone and shell inscriptions. Shirakawa demonstrates that _si_ is to be identified with a Shang graph that depicts a hand holding a rod and beating a snake or bug-like creature (i.e. a demonic creature). In Shang inscriptions the word is used both as a verb and as a noun (meaning the rite of beating with an exorcising rod; 1974: 462–70). The word _chui/*tj əd_ ("to hammer, mallet")either as verb or noun—also has particular relevance to the treatment of the ailment _tui/*d əd_, since the two words are homophonous. The word magic involved in the pun on the name of the ailment and the instrument or method used to exorcise it may account for the prevalence of exorcistic beating to treat _tui_ in _MS_ I.E. The same kind of word magic figures in later magical treatments for inguinal swelling. _Qianjin yaofang_ , 74.19b, includes recipes for treating inguinal swelling that make use of a treadle mill ( _dui_ 碓), another homophone of the name of the ailment.
_Qingmin_ 清 明 (clear brightness) refers to dawn in this context. See the Kong Yingda commentary in _Shijing_ , Mao 236, 16B.7a.
_Tong_ 筩 is glossed in _SW_ , 5A.11b, as a tube of cut bamboo. In the context of _MS_ I.E.119 it is clear that the graph is to be read as _yong_ 踊 in the sense of the prosthetic device used by foot-amputees (foot amputation was one of the mutilation punishments). See _Zuozhuan_ , Zhao 3, 42.6a.
In the context of the ailment _tui_ it is probable that _long_ 洚—which refers to urine retention above—should be understood in the sense glossed in SW, 7B.34b, "prostration ailment."
九 in _MWD_ , vol. 4, "Transcription," should be transcribed as _gang_ 亢. I understand the word in the sense of "high" (Guangya, 4B.7a), referring to the "bulges" of the ailment.
I follow _KGS_ , vol. 1: 213, n. 450, in interpreting duanshi 鍛 石 as "a stone used for hammering." The rhyming words in the incantation are: _qiang_ /* _gjang_ 强 (strong) and _kang_ /* _khang_ 亢 (bulges); and _zi_ /* _tsj əg_ 子 (Sons), _yi_ /* _r əg_ 已 (desist), and _mu_ /* _m əg_ 母 (Mother).
Silkworm eggs ( _luan_ 卵) are silkworm larvae. In _MS_ I.E.133 the recipe calls for "dark silkworm eggs ( _zhong_ 種)" and the measurement is stated in terms of the length of cloth on which silkworm larvae are cultivated. In later material medica the measurement of silkworm larvae are cultivated. In later materica medica the measurement of silkworm larvae is by the sheets of paper containing the larvae (see _GM_ , 39.78). I follow _MWD_ , vol. 4, "Transcription," n.1, in reading 簍 簍 as _shushu_ 數 數, attested in _Zhuangzi_ 1 10, in the sense of "urgent, hasty." In _MS_ I.E.123 it refers to the movement of the silkworm eggs as they roast.
_Xinsi_ 辛 巳 is the eighteenth cyclical designation in the sexagenary cycle (see _MS_ I.E.107). The word _gu_ 古 occurs again in _MS_ I.E.178, and in both occurrences has the sense of "utter a curse." _MWD_ , vol. 4, "Transcription", n. 1, identifies it with _gu_ 辜 glossed in _SW_ , 14B.22b, as _zui_ 辠 (guilty of a crime). Duan Yucai traces the etymology of the word to execution by dismemberment, as attested in _Zhouli_ , 36.8a; and the word is also associated with the exorcistic rite of dismembering an animal to neutralize demonic danger, as attested in _Zhouli_ , 18.3b. The words of the incantations in _MS_ I.E.124 and 178 are the verbal counterpart of exorcistic dismemberment. It is possible that the use _of gu_ in _MS_ I.E is related to a specifically southern tradition of exorcistic magic. According to _Hanshu_ , 28A–1.30a, there were three cult sites established near Han-time Chang'an where Yue shamans performed their exorcisms, known as _gurang_ . It has been argued that the graph is an error for , given as a variant orthography of 辜 in _SW_. However, the Yue shamans were renowned for their methods of incantation. I suspect that _gu_ refers to a type of malediction practiced by the Yue shamans and now attested in _MS_ I.E. Another word for exorcistic malediction, _liu_ 馏 ( _SW_ , 1A.12b), may be related to _gu_ (graphically if not phonologically).
Sickness-shield" translates _ganji_ 干 疾. It is a verb-object compound functioning as a noun ("that which shields sickness"), similar to the well-known compound _bixie_ 辟 邪 (that which wards off evil). Spirit of Heaven 天 神 is the same chief deity referred to as Yellow Spirit in _MS_ I.E.178 and as Thearch of Heaven in _MS_ I.E.233. On the relation between these names and the concept of a chief deity in Han popular religion, see Seidel 1987.
The Spirit Maids (or perhaps Maid) appealed to in this incantation appear to be spirits associated with the cyclical designations; that is, the appeal is being addressed to the spirit(s) who presides over the _xinsi_ day. The belief in spirits of the cyclical designations is attested in _Lunheng_ , "Jieshu," 25.499 (Wang Chong makes disparaging remarks about the belief). Summoning Jade Maids of the cyclical designations for assistance is described in the _Baopuzi_ and in many religious Daoist scriptures of the post-Han period (see Schipper 1965: 34–38).
The incantations in _MS_ I.E.124 and 128 are the earliest attestation of fox possession in China. The fox's demonic reputation is indicated in the gloss in _SW_ , 10A.36a: "It is an ill-omened creature, one that demons ride." Malicious and cunning, the fox is frequently blamed for sickness and mental derangement in post-Han sources (see Groot 1892–1910, vol. 4: 188–96; and vol. 5: 576–600). I reject the argument in _MWD_ , vol. 4, "Transcription," n. 2, that _huzhao_ 狐 叉 should be read as _hushan_ 狐 疝 (referring to a type of hernia). See _MS_ I.B.8 for evidence that the ailment name _hushan_ in the _Huangdi neijing_ is a corruption of _pianshan_ 偏 疝.
The rhyming words in the incantation are: _yu/*ngjag_ 語 (pronouncement), _suo/*skrjag_ 所 (place), _yi/*r_ ə _g_ 已 (desist; two occurrences), and _ruo/*njak_ 若 (you). See _MS_ I.E.56 for rhyming between *-ə _g_ and *- _ag_.
"Roof gutter" translates _wuliu_ 屋 霤. The compound must be the equivalent of _chengliu_ 承 霤, which refers to rain gutters attached to the outer edge of the roof (see Hayashi 1976: 193, for discussion of _chengliu_ ). The symbolic significance of placing the person beneath the center of the house that constituted a central axis connection the house to heaven and the spiritual realm.
_Zhu_ 築 (rammer) may refer to a pestle, or perhaps to the tool used in rammed earth construction.
九 in MWD, vol. 4, "Transcription," should be transcribed as gang 亢 (see _MS_ I.E.120).
I follow the punctuation of the incantation proposed by Qiu Xigui which is based on the sequence of rhyming words (1992: 532): _yi_ /* _r əg_ 己 (desist; two occurrences), mu/*məg 母 (Mother), zhi/*tjəg 之 (them), zi/*tsjəg 孑 (Son), and you/*gwjəg 有 (there is).
I place the words "inguinal swelling desist" within the incantation because of the continuation of the rhyming pattern: qi/* _khj əg_ 赽 (rise) and yi/* _r əg_ 己 (desist). It is also possible that they belong outside the incantation as the conclusion to the recipe, indicating that the magical treatment will cure the ailment.
_Xinmao_ 辛 卯 is the twenty-eighth cyclical designation (see _MS_ I.E.107).
The incantation reveals yet another magical element in Yu's identity. The ritual of name changing, like the Pace of Yu, is an efficacious way to deal with demonic entities.
_Xi_ 枲 is a general name for hemp (see _SW_ , 7B.1a, and Duan Yucai commentary). _Xi gou_ 枲 垢 must refer to the refuse produced when hemp is processed to obtain the fibers.
_Ai_ 艾 (mugwort) is associated with cauterization therapy in _Suwen_ 14, 4.5b; and _Lingshu_ 51, 8.6b. While the use of moxa (prepared _ai_ leaves) which is burned on the skin is implied in _Lingshu_ 51, there is no Han period description of moxa (Lu and Needham 1980: 175–76). The earliest description of a method of performing cauterization with _ai_ is _MS_ I.E.127, which describes not moxa but a kind of cigarette with hemp filling rolled in _ai_ leaves. Yamada 1985a: 58–63, speculates that the use of _ai_ in cauterization is related to its earlier use as an exorcistic fumigant (see _MS_ I.E.155, which uses _ai_ as a fumigant). Perhaps the use of _ai_ leaves in _MS_ I.E.127—in contrast to _MS_ I.E.64 where warts are cauterized with a cattail cord—is related to the strong association between the ailment _tui_ and demonic causation in _MS_ I.E.
The center of the crown of the head is also used for a counter-irritant treatment in _MS_ I.E.53. While this is the location of a well-known acupuncture point—the _baihui_ 百 會 (hundred convergence; see Lu and Needham 1980: 80–83)—there is no indication in _MS_ I.E.127 that performing cauterization there is related to vessel theory, just as there is no evidence of vessel theory in _MS_ I.E.53.
For identification of _wu_ 廡 as a building with a four-sloped roof, see Hayashi 1976: 190; and Sun Ji 1991: 164.
See _MS_ I.E.56 on the use of the utterance _yu/*gwjag_ 吁.
I assume that _hupiao_ 狐 鹿 (fox _piao_ ) is a compound name for a demonic animal ( _piao_ is attested as a variety of deer), but I have found no supporting references. It is also possible that _piao_ should be read as another word that I am unable to identify.
The fact that the rest of the incantation is missing makes it difficult to interpret the opening fragment. Other translations are possible.
Early glosses consistently identify _ying_ 瘦 as a growth by the throat, which Yu Yan shows refers to goiter (1972: 212). The identification is also confirmed by _Maishu_ , "Ailment List": "When located beneath the chin—it is _ying_ " ( _MSSW_ : 72). _MS_ I.E.129 doubles as a treatment for goiter.
_Zhui_ 腏 is food prepared for a sacrificial offering ( _SW_ , 5B.15a, and Duan Yucai commentary). _MS_ I.E.I43 calls for millet food sacrifice as well as the head of a dead person. The earliest occurrences of _zhui_ are in the Fangmatan resurrection account (the passage concerns the proper way to offer _zhui_ to the dead in the graveyard; Li Xueqin 1990: 43; Harper 1994) and in the first Shuihudi hemerological manuscript (where setting out _zhui_ forms part of a prayer ritual to the guardian deity of horses; _SHD_ : 228). As distinct from the ritual feeding of ancestors in ancestor worship, _zhui_ appears to have been part of the growing mortuary cult centered on the graveyard in the late Warring States period. This custom is reflected in _MS_ I.E.129 when the recipe specifies the "food sacrifice of a dead person." _MS_ I.E.143 identifies the source for _zhui_ as the "offering niche by the entrance to the inner chamber," which might be a household offering site or a cult site (in the graveyard?).
_Nang_ 囊 (sack) might refer to the scrotum.
I.e. the larvae.
I follow _MWD_ , vol. 4, "Transcription," in reading 復 as _fu_ 腹 (belly). "Rat belly" describes the shape of a swelling, similar to the use of the term _yufu_ 魚 腹 (fish belly) to refer to the calf (see _Suwen_ 41, 11.8a). Ma Jixing reads the graph as _fu_ 伏 (crouch), citing _Suwen_ 52, 14.3b, which uses the compound _shupu_ 鼠 僕 (1992: 485, n. 2). The Wang Bing commentary explains the compound as "a swelling like the shape of a crouching ( _fu_ ) rat." In _Suwen_ 52 the "crouching rat" swelling is caused by improper acupuncture, whereas in _MS_ I.E.131 the "rat belly" is a third type of swelling along with inguinal swelling and thigh abscess.
The lacuna is probably 以.
The compound yanyi 甗 衣—literally, "slotted steaming-pot garb"—must be equivalent to zengdai 甑 帶, the cord handle attached to the steaming-pot. _KGS_ , vol. 1: 218, n. 481, argues that _yi_ /*? _j əd_ is a phonetic loan for _wa_ /*? _wjar_ 瓾. The latter word occurs in _Huainanzi_ , 16.284, and is glossed in the Gao Yu commentary as _zengdai_. The argument is plausible. _Yanyi_ occurs again in _MS_ V.5. _Zengdai_ is among the items listen in _Wanwu_ (Fuyang Han jian zhenglizu 1988: 39). The item is also listed in later materica medica ( _GM_ , 38.50)
The text is not clearly visible, but I suspect that there is a graph-repeat sign following yu 羽 (the first occurrence is the noun "feather" and the repeat is the verb "attach feathers"), and that the lacuna following 羽 is 之 "them." The kind of feather used in missing in the lacuna preceding yu. Exorcistic archery is also employed in _MS_ I.E.137, which uses the peachwood bow attested in descriptions of formal exorcistic rituals in received literature (see Bodde 1975: 127, 134) See the Prolegomena, Section Five, "Varieties of Magic."
The measurement "one-chi square" means that the silkworm larvae are measured by the length of the cloth on which the larvae are deposited (see _MS_ I.E.123). The meaning of ming 冥 (dark) with reference to the silkworm larvae is uncertain. Ma Jixing proposes reading ming as mu 暮 (1992: 487, n. 1. but his argument is implausible.
BC gives the names yiyu 衣 魚 (clothes fish) and baiyu 白 魚 (white fish; GM, 41.18). The "clothes-eating baiyu" in _MS_ I.E.133 must represent a long form of the name for the silverfish.
_Changzu_ 長 足 must be equivalent to _changyi_ 長 . The latter name occurs in _Erya_ , 9.9a, and is glosed in the Guo Pu commentary as a kind of long-legged spider. For spiders in materia medica, see _GM_ , 40.97.
Hu 瓠 and hu 壺 are synonyms for a gourd used as a vessel (SW, 7B.5a, and Duan Yucai commentary). In _MS_ I.E.134 they must represent a compound referring to a gourd similar to the one used in _MS_ I.E.60.
_Zui_ /* _tsuad_ 嘬 represents the same word as _zui_ /* _tsu əd_ 脧, which refers to the male genitals. Rhyming between words with final *- _ad_ and *- _ə d_ in the _Huainanzi_ corroborates the phonological identity in southern speech (Luo and Zhou 1958: 254). _SW_ , 4B.40b, glosses _zui_ as "the Yin (i.e. genitals) of the red infant." The locus classicus is _Laozi_ , par. 55, as confirmed by the Mawangdui Laozi manuscripts ( _MWD_ , vol. 1: 105). The graph 最 is used in _MS_ III.33; and the same graph is used in the medieval sex manual _Dongxuanzi_ 洞 玄 子, cited in _Ishinpô_ , 28.47b. _Zui_ refers generally to the male genitals as well as more narrowly to the penis.
I read text _fan_ 煩 as _fan_ , 蹞 which is given as a variant graph for _fan_ 番 (animal paw) in _SW_ , 2A.4a. The person is supposed to "cup" the large end of the gourd in his hands as a bear would hold something in its front paws.
_Cai_ 采 occurs in _Shiij_ , 87.12b, and is glossed in the commentary as another name for _li_ 櫟 ( _ZY_ : no. 5433, _Quercus acutissima_ Carr.).
"Chop at" translates _duo_ 剟. The exact procedure described is unclear because of the lacuna, but the act of chopping at the pegs with a mallet of the same material must form part of the overall exorcistic ritual that culminates with the insertion of the pegs beneath the wall. _MWD_ , vol. 4, "Transcription," n. 5, argues that _duo_ means "knock, hit," even though this meaning is not attested for _duo_. I suspect that the instruction to "chop" with a mallet is intentional, and that it has magical significance. Perhaps the tips of the pegs are splintered with a chopping action and then the splintered wood is "smoothed."
"Exhausted" may refer to the moon waning, meaning that the exorcistic treatment continues over the last half of the month.
I suspect that the lacuna is a negative indicating that the treatment is not to be performed twice in one day.
_Bian_ (lancing-stone) is discussed in _MS_ I.C. The initial treatment in _MS_ I.E.135 focuses on the _duo_. Although the treatment does not rely on vessel theory, Zhao Youchen (1981) cites later medical literature in which acupuncture points near the navel are used to treat _tui_ —which at least lends credibility to identifying _duo_ with the navel.
From the context, the final lacuna must be 酒. The preceding lacunae make it impossible to follow the recipe at this point, other than to surmise that a slave is prepared and applied to the spot that was lanced.
Presumably the spot that was lanced.
The text writes 易 廖 ﹂ 而, placing the hook-sign after the phrase "easy to cure." In my reading, er 而 functions grammatically like nai 乃 (then; a common usage in early texts), and I understand the phrase "easy to cure" to be logically linked to what follows. Ma Jixing links "easy to cure" to what precedes in his translation and does not account for _er_ (1992: 492). The hook-sign is used in the Mawangdui manuscripts mostly to break phrases where confusion might occur (e.g. in lists of drug names), not to mark the end of a sentence or logical unit. In the case at hand I suspect that the hook-sign marks "easy to cure" as a topic, followed by the statement concerning cauterizing the Great Yin and Great Yang vessels; that is, cauterizing the two vessels is represented as easier than the complicated procedure just described (Ma's interpretation is that the preceding treatment "makes the ailment easy to cure").
Great Yin and Great Yang must refer to the foot Great Yin and Great Yang vessels. This is the only occurrence of vessel names in _MS_ I.E, and the only clear instance of a treatment based on vessel theory. It is worth noting that _MS_ I.A-B do not associate the foot Great Yin and Great Yang vessels with _tui_ (nor is the association made in _Lingshu_ 10). In _MS_ I.B.8, _tui_ is one of the ailments listed under the foot Ceasing Yin vessel. Perhaps _MS_ I.E.135 reflects an earlier association between _tui_ and these vessels that was already discarded in _MS_ I.A-B; or perhaps it is simply a different medical tradition that found its way into _MS_ I.E.
I interpret "humping and cramping" as describing the condition of the swellings as they first erupt, before becoming large. Ma Jixing interprets "humping and cramping" as describing the body of the patient hunched over in pain; and "not yet large" as meaning that the ailment is "not yet severe" (1992: 493).
The second ingredient is missing in the lacuna. Depending on the identification of 虫, the first drug is either the sloughed skin of a snake—the interpretation in _MWD_ , vol. 4, "Transcription," n. 1, which reads the graph as _hui_ "snake" or the slough of an insect (reading the graph as _chong_ "bug"); e.g. cicada slough (chantuo 蟬 蜕) Both are listed in materia medica: GM, 43.67 (snake slough), and GM, 41.10 (cicada slough). Fragment 1 of _MS_ I.E ( _MWD_ , vol. 4: 76) records snake slough by the name shetuo 蛇 蜕 (it is uncertain in which ailment category the fragment belongs).
See _MS_ I.E.132 for exorcistic archery.
The cow gall medicine is probably first mentioned in the long lacuna at the beginning of the recipe. Gall is listed along with other parts of the cow in _BC (GM_ , 50.70). It is usually dried and then broken into pieces when used. The lacuna at the end of the recipe may describe how to process the gall.
"Curled cinnamon" refers to the curled bark used as a drug.
己 in _MWD_ , vol. 4, "Transcription," should be transcribed as _yi_ 已 (desist).
The lengthy lacunae make it impossible to discern the treatment. The reference to the "requital rite" (sai 塞) indicates that at some point above there should be a "ritual requesting a favor from the spirits," called dao 檮. The purpose of the sai is to present spirits with the sacrificial offerings that were pledged to them when the person first requested a favor in the form of a dao. Thus the dao constitutes the promise of a bribe to the spirits, which must be paid when the spirits fulfill the requested favor. The use of dao and sai to deal with illness is documented in Hanfeizi 35, 14.253, where a cow is the promised offering. The earliest attestation of sai and dao in popular Warring States religion is in the fourth century b.c. divination records from Baoshan (Li Ling 1990: 84). The Shuihudi hemerological manuscripts include the text of a dao prayer to alleviate nightmares in which the spirit who controls nightmare demons is offered material goods as payment (Harper 1987a: 270).
I follow _KGS_ , vol. 1: 223, n. 515, in reading bi 比, as bi 秕, glossed in _SW_ , 1A.9b, as "sacrificing a pig to the Director of the Life-mandate 司 命. Other Han sources cited in the Duan Yucai commentary describe the cult of the Director of the Life-mandate in popular religion, including the pig sacrifice. Perhaps the dao prayer in _MS_ I.E.138 is directed to him. _Mao_ 茅 is _Imperta cylindrica_ (L.) P. Beauv. var. _major_ (Nees) C. E. Hubb. ( _ZY_ : no. 1435), llisted in _BC_ ( _GM_ , 13.64). The plant is commonly called _baimao_ 白 茅 (hence _bai_ preceding the lacuna is undoubtedly followed by _mao_ , naming the plant). For a study of the religious use of _mao_ in the pre-Han period, see Mizukami 1977: 615–26. It was regarded as a receptacle for spirits, as evidenced in the _SW_ , 14A.51b, definition of a roadway ritual known as _ba_ 軷: "When a person is about to embark and engage in affairs on the roadway, he must first make a declaration to the spirit (of the roadway). The altar is placed at a crossroads. _Mao_ is set up, thereby providing a prop for the spirit. This is _ba_." _MS_ I.E.138 indicates that _mao_ might be substituted for animal sacrifices in the event that the person is loath to kill an animal as an offering to the spirits.
"Requite the favor" translates _saidao_.
灸 in MWD, vol. 4, "Transcription," should be transcribed as _zhi_ 炙 (roast).
Qiu Xigui identifies the fragmentary graph following 四 榮 (four up-turned slopes of the roof) as _cai_ 蔡 (vegetation; 1992: 531). It appears to be the same material used in _MS_ I.E.27.
The drug _lianghuang_ 量 簧 is unknown.
The customary "another" does not occur at the head of _MS_ I.E.140.
脈 者 denotes the "vessel" type of hemorrhoid. The standard name for hemorrhoids is _zhi_ 痔. Later medical literature recognizes five types: male hemorrhoid, female hemorrhoid, vessel hemorrhoid, intestine hemorrhoid, and bloody hemorrhoid ( _Chaoshi zhubing yuanhoulun_ , 34.14a). The name vessel hemorrhoid is probably derived from the appearance of the swollen vein of the hemorrhoid. Male hemorrhoid is the next ailment category in _MS_ I.E; followed by female hemorrhoid, within which are recipes for bloody hemorrhoid as well as a condition called "nest" (i.e. anal fistula). _Maishu_ , "Ailment List," also lists male and female hemorrhoids: "When it is located in the perineum and forms a swelling like a jujube—it is male hemorrhoid"; "When the swelling has holes that ooze liquid—it is female hemorrhoid" ( _MSSW_ : 72). Early etiological theories attribute the swollen veins of hemorrhoids to the chewing of bugs (Yu Yan 1972: 232). Worms are mentioned in the description in _MS_ I.E.149. The elaborate fumigation treatments described in several recipes in _MS_ I.E are undoubtedly intended as vermifuges to kill the bugs.
The lacuna must be one of the several words meaning "cured."
The description is similar to that of male hemorrhoid in _Chaoshi zhubing yuanhoulun_ , 34.14a: "On the side of the anus a rat teat appears and emerges outward."
See _MS_ I.E.129 on the food sacrifice. "Offering niche by the entrance to the inner chamber" translates 内 户 旁 柌 空 中. _MWD_ , vol. 4, "Transcription," n. 6, suggests that 空 中 (niche) may be excrescent (perhaps a case of dittography since the two graphs conclude the recipe). But we are still left with an "offering (place) by the entrance to the inner chamber." If there were "offering places" near the bedroom in early China, this recipe is the first evidence of them. I suspect that there may be a technical denotation that is unknown to me. For example, _neihu_ 内 户 seems to mean "entrance to the inner chamber" (there are corroborative uses of _hu_ in _MS_ VII.A), but perhaps it is an unattested compound for a cult site. Because the recipe also calls for the head of a dead person, and _MS_ I.E.129 calls for the food sacrifice of a dead person, the "entrance to the inner chamber" may refer to a structure located in the graveyard.
"Black ewe" translates _yu_ 输, which is the gloss given in _SW_ , 4A.34a.
I read _xiu_ 滫 as a verb meaning "moisten." According to SW, 11A–2.33a, xiu is the slop left over from cleaning grain to prepare it for cooking, specifically aged slop that has soured. The word is also used like sou 溲 to refer to moistening flour to make a paste; and is attested in the sense of moistening a dish with the addition of liquid (see the Duan Yucai commentary). _MWD_ , vol. 4, "Transcription," n. 2, interprets xiu as a noun meaning "grain slop" and proposes that the sentence is missing a verb to indicate that the grain slop is added to the millet while it is cooking. Given the attested meaning of xiu as "moisten," the argument for the missing verb is weak.
"Copper bits" translates _yumo_ 鋊 末. _Yu_ is glossed as "copper flakes" in _SW_ , 14A.7b; and the term refers specifically to the bits of copper scraped of coins. Copper flakes are listed in material medica ( _GM_ , 8.9).
The recipe specifies _shujiang_ 菽 醤, so it is clear that the main ingredient of the sauce is soybeans. Besides soybeans, fish and meat were also fermented to produce _jiang_ in Han times; and it is possible that _jiang_ was the name for a mixture combining these thick sauces with gruel vinegar (Hayashi 1975: 58–60).
"Perform horn treatment" translates _jiao_ 角. _Waitai biyaofang_ , 13.9a, contains a description of cupping by Zhang Wenzhong 張 文 仲 (fl. 685) that uses _jiao_ as the verb for cupping. The cups are short sections of bamboo that are boiled and then pressed on the skin. _MS_ I.E.145 seems to concern the same general therapy, making it the oldest record of cupping in Chinese medical literature. The recipe indicates neither how to fashion the horn-cup nor how to apply it to the skin. Ma Jixing interprets the lack of details as sign that cupping was already commonly practiced and did not require explanation (1992: 507). Given that _MS_ I.E.145 provides the only evidence of cupping in early Chinese medicine, I am skeptical that it was a common therapy and am inclined to regard its use in _MS_ I.E to treat a hemorrhoid as an exceptional case. There is no comparison between early Chinese medicine and Greco-Roman medicine, where the popularity of cupping is well documented from the fifth century B.C. Used most often in conjunction with blood-letting, the cups came to serve as symbols of the medical profession. In China, on the other hand, there is no evidence that cupping was integrated into medical theory and therapeutics. The most likely explanation of the cupping technique in _MS_ I.E.145 that I have found is given by the first century A.D. Roman physician Celsus Most Greek and Roman cups were bronze, but Celsus also describes a horn cup that is open at the large end with a small hole in the tip. The horn is placed on the skin, the air sucked out, and the small hole sealed with wax to make the cup adhere (Jackson 1988: 72–73).
_MWD_ , vol. 4, "Transcription," n. 3, reads 髕 (unattested in received literature) as _shi_ 實 (fruit), and compares the compound _tushi_ 兔 實 to _tuxi shi_ 兔 系 實 in the Wuwei recipes ( _WWYJ_ : 2a). The latter drug can be equated with _tusi zi_ , 菟 絲 子 which refers to dodder seeds ( _ZY_ : no. 4125, _Cuscuta chinensis_ Lam., C. _japonica_ Choisy).
The lacuna must be 以 or 取.
Identification of _qu_ 屈, which is not attested as a drug name in received literature, and its alternate name given below, _luru_ 盧 茹, is problematic. _MS_ I.E.253 uses the drug _quju_ 屈 居, which is glossed with _luru_ in _Guangya_ , 10A.24b. This drug is listed in materia medica. However, I doubt that _qu_ in _MS_ I.E.147 can be equated with _quju_ in _MS_ I.E.253; and given that _qu_ is supposed to be the name with wider currency, I doubt that the Jing (i.e. Chu) name _luru_ can be identified with the name attested in materia medica. _MWD_ , vol. 4, "Transcription," n. 7, argues that _luru_ is a scribal metathesis of _rulu_ "madder" ( _ZY_ : no. 3276, _Rubia cordifolia_ L.). _Rulu_ occurs in _MS_ I.E.252. Ma Jixing reviews other speculations regarding the alternate name and continues to regard _rulu_ as the best (1992: 513, n. 23). I think it advisable to refrain from a positive identification.
I accept the judgment of _MWD_ , vol. 4, "Transcription," n. 5, that _shuluo_ 署 蓏 is equivalent to _shuyu_ 署 預 ( _ZY_ : no. 0319, _Dioscorea opposita_ Thunb.). _Luo_ refers to edible tubers ( _SW_ , 1B.3a, and Duan Yucai commentary), in this case the yams.
Jing 荆 designates the region of Chu 楚. _SW_ , 1B.28b, also glosses _qiu_ 萩 as a variety of artemisia.
_SW_ , 13A.42b, glosses rao 蟯 as "a short worm inside the abdomen." The worm is the pinworm, Enterobius vermicularis. Several pinworm eggs were found in the lower intestinal tract of the corpse buried in Mawangdui tomb I (Hunan yixueyan 1980: 202); and in shiji, 105.18a, Chunyu Yi diagnoses an ailment he calls raojia 蟯 瘕 (pinworm conglomeration). _MS_ I.E.149 associates female hemorrhoids with the presence of the pinworms, reflecting the belief that chewing bugs cause hemorrhoids. Chaoshi Zhubing Yuanhoulun, 18.5a, explicitly names pinworms as the culprits: "Pinworms inhabit the colon. When numerous, they cause hemorrhoids."
_Xia_ 夏 should be read as xia 榎, a variant graph for _jia_ 檟 ( _SW_ , 6A.8a, and Duan Yucai commentary). It refers to the catalpa ( _ZY_ : no. 4091, _Catalpa ovata_ G. Don).
"Dry" translates xia 煆, which is the gloss for xia in _Fangyan_ , 7.5b (especially to dry something by heating it).
_Luoruan_ 駱 阮 is not attested in received literature. Ma Jixing reviews arguments for identifying the plant based on the second of the two alternate names given below, _kuqin_ 苦 浸 (1992: 519, n. 12). Reading qin/*tshjəm as a phonetic loan for shen/*tshəm 参, the name is equivalent to kushen 苦 参 ( _ZY_ : no. 2624, _Sophora flavescens_ Ait.), listed in _BC_ ( _GM_ , 13.54). The identification if plausible.
Fat is added to generate more fumes.
Mizukami presents conclusive evidence that _jian_ 菅 should be identified as _Miscanthus sinensis_ (1977: 558–60). The grass is similar to _mao_ "woolly grass," and the two are often confused.
_MWD_ , vol. 4, "Transcription," emends text _shang_ 上 to _tu_ 土, claiming scribal error. Since the meaning "to daub (something) with mud" is already implicit in the preceding word _tu_ 涂, the emendation is unnecessary.
"Bake" translates _bao_ 炮, a popular Han method of baking whole animals wrapped in clay without removing the fur or feathers ( _SW, 10_ A.45a, and Duan Yucai commentary).
以 in _MWD_ , vol. 4, "Transcription," should be transcribed as _wei_ 爲.
The medicine in _MS_ I.E.151 is similar to some of the medicines in the first ailment category, Various Wounds.
I follow _MWD_ , vol. 4, "Transcription," n. 1, in identifying _chao_ 巢 (nest) as an anal fistula; and in associating the name with the presence of worms "nesting."
"Anus" translates 朐, for which _MWD_ , vol. 4, "Transcription," n. 1, offers two possible readings. The first is based on the Mawangdui manuscript of the _Yijing_ hexagrams. The text of the hexagram Jung 井 writes _lou_ /* _kug_ 句, whereas in the received _Yijing_ the graph in the corresponding position is _lou_ /* _lug_ 漏. Since _lou_ denotes anal fistula in medical usage (Yu Yan 1972: 120), perhaps the graph 朐 is a phonetic loan for _lou_ and means "fistula." The argument is plausible, but flawed. In the Mawangdui _Yijing_ text, _gou_ is not a phonetic loan for _lou_ , but is part of a phrase whose grammar and meaning differ from the received text. For the phrase 甕 敝 漏 ("the jar is worn out and leaks") in the received text, the Mawangdui text has 唯 敝 句. Han Zhongmin compares _bigou_ 敝 句 to _bigou_ 敝 笱 in the _Shijing_ , in which case the phrase means, "it is a worn out fish-trap basket" (1992: 139). The second "Transcription" reading equates the graph 朐 with _gouzi_ 鉤 子, a word meaning "anus" in Shaanxi dialect that is related to other similar vernacular terms for the buttocks and anus. I tentatively accept the second reading.
The worms are undoubtedly the pinworms mentioned in _MS_ I.E.149. The phrase 脖 從 其 空 出 "at times emerge from the holes" is written twice in the text before and after 有 白 蟲 "there are white worms." The first occurrence is excrescent. I suspect that the scribe initially erred by not writing 有 白 蟲 before writing 脖 從 其 空 出; and after correcting himself by writing, the whole again, he then forgot to blot out the now excrescent phrase.
_Xun_ 蕈 is the fungus known as "wood ear" ( _ZY_ : no. 0701, _Auricularia auricula_ [L. ex Hook.] Underw.). Wood ear is listed in _BC_ ( _GM_ , 28.23). _Liu_ 柳 ( _ZY_ : no. 3175, _Salix babylonica_ L.) is one of five trees from which wood ears are harvested according to _GM_.
"Crumbled" translates _nuo_ 捼, glossed in _SW_ , 12A.45a, as "break up by rubbing the hands together." Duan Yucai regards 捼, as a miswriting of 挼, but _MS_ I.E.155 shows that first graph is also correct. _MWD_ , vol. 4, "Transcription," n. 5, interprets _nuo_ as a measure word for the amount of _liuxum_ ("one _nuo_ of _liuxum_ "), in which case it does not modigy _ai_. Ma Jixing proposes reading 捼 as _rui_ 捼, which is attested in medieval sources as a measure word meaning "four handfuls of grain" (1992: 529, n. 10). I am not convinced by either argument.
The lacuna is undoubtedly 今.
_Fa_ 伐 (beaten) is not attested as a term for grain preparation. It probably refers to polishing the rice.
The hot stones cook the rice.
According to _SW_ , 7B.30a, _ju_ 疽 refers to "an old _yong_ 癰," _yong_ being the more general term for an abscess. Duan Yucai interprets the gloss to mean that _ju_ is an abscess that becomes _ju_ 沮 (rotted, leaky). A separate ailment category for _yong_ begins in _MS_ I.E.225. The _SW_ definition of _ju_ as "an old _yong_ " does not seem to apply in _MS_ I.E because a number of recipes treat _ju_ "when it first appears." The distinction between _yong_ and _ju_ in _Lingshu_ 81, 12.10b, also cannot be applied to _MS_ I.E. _MS_ I.E.158 uses the compound _juyong_ —meaning the " _ju_ type of _yong_ "—whereas _ju_ is not mentioned in the section of recipes which treat _yong_. In light of this usage, and lacking better evidence, I adopt the expedient of translating _yong_ as "abscess" and _ju_ as " _ju_ abscess."
_Penglei_ 蓬 藁 is listed in _BC_ ( _GM_ , 18.6). There is much scholarly discussion over the question of whether the name refers to the vine and root or to the berries of the raspberry ( _ZY_ : no. 0964, _Rubus tephrodes_ Hance). Tao Hongjing identifies it as the root.
_MWD_ , vol. 4, "Transcription," n.1, equates _Shand lao_ /* _l əgw_ 商 牢 with _shang lu_ /* _lj əkw_ 陸 ( _ZY_ : no. 4664, _Phytolacca acinosa_ Roxb.; pokeweed), listed in _BC_ ( _GM_ , 17.7).
The lacuna must be the name of a drug because the recipe specifies that there are also four substances in the second list of drugs.
The extensive lacunae prevent a clear understanding of the recipe. The latter part of the recipe appears to discuss two types of abscess—bone and muscle—and to give a description of the appearance of the muscle abscess. _Shu_ 倏 (glare) is attested as an orthographic variant of 倏 (Mmorohashi 1957–60, vol. 1: no. 763). The reduplicated compound _shushu_ is glossed in _Guangya_ , 6A.8a, as "radiant." In _MS_ I.E.160 and again in _MS_ I.E.166, the compound describes the inflamed appearance of the abscess. The second compound, _didi_ 翟 翟 (glitter), represents a term for the glistening quality of light and is written with a number of related graphs: 嚁 嚁, 耀 耀, 燿 燿, 濯 濯. In _MS_ I.E.160 _didi_ refers to the shiny swollen surface of the abscess.
The word "recipe" occurs near the bottom of C277, meaning that there must be an extended description of the kind of _ju_ abscess being treated.
_Shi_ 釋 refers to the action of soaking and washing grain ( _SW_ , 7A.61a); and gan 泔 is the grain slop left over from the cleaning process ( _SW_ , 11A–2.33a).
灸 in _MWD_ , vol. 4, "Transcription," should be transcribed as _zhi_ 灸 (roast).
己 in _MWD_ , vol. 4, "Transcription," should be transcribed as _yi_ 己 (desist).
_Bahe_ 罷 合 is not attested in received materia medica. Ma Jixing equates _ba_ /* _pr əg_ with _bai_ /* _prak_ 百—which is phonologically plausible (1992: 539, n. 2). _Baihe_ 百 合 is listed in _BC_ ( _GM_ , 27.121) and refers to _Lilium brownii_ F.E. Brown var. _colchesteri_ Wisl., and other species ( _ZY_ : no. 1728).
Evidently pig fat was usually rendered before being used in medicine.
灸 in _MWD_ , vol. 4., "Transcription," should be transcribed as _zhi_ 灸 (roast).
The lacuna probably details the increased dosages, including the maximum dosage permited.
條 must be an orthographic variant of _shu_ 條 (see _MS_ I.E.160).
_Daishen_ 戴 糁 is given as an alternate name for _huangqi_ (astragalus) in _BC_ ( _GM_ , 12A.85).
I read the unattested graph 庰 as _pian_ 聠. _Pian_ occurs frequently in pre-Han and Han literature with the meaning "callus" (e.g. _Xunzi_ 29, 29.348). While the graph in _MS_ I.E.167 is not an attested variant for _pian_ , the significs 疒 and 月 are often interchangeable ( _you_ "wart" is written 疣 and 肬). In _MS_ I.E.167 _pian_ refers to the layer of skin covering the abscess. "Volatile" translates _yun_ 溳, attested in the sense of agitated, choppy water in Guo Pu's 郭 璞 "Jiang fu" 江 賦 ( _Wenxuan_ , 12.7b). _SW_ , 6B.14a, glosses a related word, _yun_ , as describing a chaotic, turbulent condition.
I read the unattested graph as _hu_ 惚. The phonetic 訒 can be equated with _hu_ 曶. The interchangeability of 曶 and 忽 as the phonetic in certain graphs is noted in the Duan Yucai commentary in _SW_ , 5A.28b. Thus (the bottom represents hands) is probably a variant of 惚. According to _Fangyan_ , 10.9b, the later word means "strike, beat" in southern Chu, which suggests that the use of in _MS_ I.E.167 is an example of regional dialect.
The abscess is being compared to some noticeable feature of a corpse.
I.e. the liquid is reduced from one half _dou_ ( _five sheng_ ) to three _sheng_.
_MWD_ , vol. 4, "Transcription," n. 1, notes that there is a break in the text after C297; it is not clear how many columns might be missing.
As in _MS_ I.E.168 the liquid is reduced to three _sheng_.
I suspect that the unattested graph 糉 is a scribal miswriting of _jun_ 浚 (sieve); and that the lacuna is _yin_ 飮 (drink). Ma Jixing reads the unattested graph as _zong_ 惾, with the meaning "gather" (1992: 546, n. 2). However, the context suggests that a liquid medicine is sieved and drunk (compare the fragmentary _MS_ I.E.167, which mentions sieving; and several recipes in which the medicine for _ju_ abscess is drunk).
_MWD_ , vol. 4, "Transcription," n. 1, notes that there is a break in the text after C303; it is not clear how many columns might be missing.
According to _MS_ I.E.1 there is one ailment category between _Ju_ Abscesses and [1] Burns. The name is missing both in _MS_ I.E.1 and in the body of the text. Since [1] Burns begins in _MS_ I.E.176, and _MS_ I.E.174–175, both open with the formula "another (recipe)," the latter two recipes must belong to the unknown ailment category.
There is ambiguity as to whether _mai_ 麥 refers to _damai_ 大 麥 ( _ZY_ : no. 0186, _Hordeum vulgare_ L.; barley) or _xiaomai_ 小 麥 ( _ZY_ : no. 0474, _Triticum aestivum_ L.; wheat). Based on archaeological evidence and received sources, Hayashi argues for barley (1975: 8). However, I am inclined to identify _mai_ as wheat on the basis of a hemp sack labeled _mai_ that was excavated from Mawangdui tomb 1 and that contained a quantity of _Triticum turgidum_ L. mixed with which were a very few grains of _Hordeum vulgare_ L. (Hunan nongxueyuan et al. 1978: 4–5). The occurrence of _mai_ in recipes for liquors in _MS_ III.10 and _MS_ III.74 also suggests wheat. Wheat and barley are listed in materia medica ( _GM_ , 22.53, 58).
I.e. wash the affected part of the body.
灸 in _MWD_ , vol. 4, "Transcription," should be transcribed as _zhi_ 炙 (roast).
I.e. use the roasted leaves to warm the affected part of the body.
_MWD_ , vol. 4, "Transcription," n. 1, states that judging from the remaining fragment of the graph in the lacuna it might be _huo_ 火 (fire). In any case, _lan_ 爛 is attested meaning a skin burn in _Zuozhuan_ , Ding 3, 54.5a.
_Rentti_ 人 泥 (human sludge) is not attested in materia medica. _MS_ I.E.198 calls for "sludge ( _ni_ ) from old urine," which can be equated with a urine product in received materia medica. _MWD_ , vol. 4, "Transcription," n. 2, suggests that "human sludge" might refer to body sweat and grime. Dandruff occurs elsewhere in _MS_ I.E, but other waxy, grimy matter that collects on the body might all come under the heading "human sludge." Compare _GM_ , 52.86 (ear dirt, dirt from the kneecap); and 52.102 (dental detritus, body sweat). _KGS_ , vol. 1: 245, n. 660, suggests feces as one referent for "sludge," but given other words for feces in _MS_ I.E I doubt the identification.
On wringing a medicine through a cloth, see _MS_ I.E.13.
The utterance _xi xi, qu qu_ 肸 肸 詘 詘 (represented in reconstructed form in the translation) must be related to the utterance _xi xi, chu chu_ 譆 譆 出 出 recorded in _Zuozhuan_ , Xiang 30, 40.3b. The utterance is shouted anonymously in the Great Temple of the state of Song. According to the commentary, _xi_ signifies a fire omen and _chu_ is monitory ("get out"); and in the _Zuozhuan_ narrative the utterance anticipates a conflagration in Song. In _MS_ I.E.178 the phrase is written using the repeat-graph sign, mistranscribed in _MWD_ , vol. 4, "Transcription," as 肸 詘 肸 詘. Qiu Xigui notes the _Zuozhuan_ parallel and corrects the "Transcription" (1992: 532). In _MS_ I.E.178 _xi_ 肸 refers literally to a swarm of bugs rising like a cloud ( _SW_ , 3A.6a, and Duan Yucai commentary), an image that might also suggest fire. _Qu_ probably has the sense of "submit." In context, the utterance seems to express the idea that "the burn submit"; which is then explicitly stated in the following line of the incantation: "Come out from the stove and do not spread." The connection between the use of the utterance to treat a skin burn in _MS_ I.E.178 and its premonitory use in the _Zuozhuan_ is obvious. Together with a similar four syllable utterance in _MS_ I.E.265 (in an incantation that also names the Yellow Spirit) we have evidence of multi-syllabic utterances that belonged to a common stock of incantatory speech.
The rhyming words in the incantation are: _yan_ /* _ran_ 延 (spread) and _yan_ /* _ngjan_ 訁 (speak). The incantation in _MS_ I.E.265 also invokes the Yellow Spirit 黄 神. The Yellow Spirit is the same deity as the Yellow Thearch 黄 帝 (see _Huainanzi_ , 6.96), whose identity in received literature as a mythical culture hero and patron of esoteric arts is being expanded through archaeological evidence that reveals him as a supreme deity in popular religion. Seidel discusses the nature of the Yellow Spirit as a supreme deity as it is currently known from Han archaeological evidence, which is mostly related to mortuary customs (1987: 28–34). The invocations in _MS_ I.E.178 and 265 clearly relate to the religious aspects of the Yellow Spirit identified by Seidel. Another reference to the Yellow Spirit in _MS_ VII.B.L in a dialogue concerning sexual hygiene serves to indicate that the images of supreme deity and patron of esoteric arts are not independent traditions, and that they can probably be traced to a common magico-religious source. It is also noteworthy that the Yellow Thearch as culture hero has the name Yellow Progenitor 黄 宗 in the cosmo-political writings that precede the second Mawangdui edition of _Laozi_ , where the Yellow Tearch's emergence in the world is described as an act of cosmic self-creation ( _MWD_ , vol. 1: 61). While a complete understanding of the multifaceted Yellow Tearch in pre-Han and Han belief still eludes us, the archaeological and manuscript evidence regarding his role in religion sheds new light on the subject.
_Ruzhi_ 乳 汁 (breast milk) is a general term for milk, as attested in _SW_ , 11A–2.40a, which glosses _dong_ 湩 which _ruzhi_. It is probable that _ruzhi_ in _MS_ I.E.181 refers specifically to milk from a woman's breast.
The Zheng Sinong commentary in _Zhouli_ , 6.1b, identifies _tai_ 箈 as " _yuyi_ 魚 衣 (fish garment which is in the water." _SW_ , 1B.32b, glosses _tai_ similarly as " _qingyi_ 青 衣 (green garment) in the water." _Tai_ also refers to moss and lichens, but it is evident that in Han times algae was the primary referent; and that _yuyi_ was one of several names comparing the algae to a garment. The algae called _zhili_ 陟 釐 in _BL_ ( _GM_ , 21.17) appears to represent the type denoted by such names. It is described as a hair-like algae usually found growing on submerged rocks. Although the name _zhili_ is also applied to some seaweeds, it is unlikely that _yuyi_ in _MS_ I.E.182 is a seaweed.
_He_ 楬 is glossed in _SW_ , 8A.65a, both as plaited hemp footwear and as a coarse garment. Hayashi identifies the hemp footwear mentioned in _SW_ as a shoe sole, and shows that the hemp garment was also made of plaited material rather than woven fabric (1976: 43–44, 141).
is a variant of _lu_ 鹵. Wei and Hu cite Li Xuequin, who states that the identification is confirmed by occurrences of the graph in Zhangjiashan manuscripts and pottery inscriptions (1992, vol. 1: 124, n. 1). The name _lutu_ 鹵 土 suggests that the substance is raw alkaline soil and not the salt purified from it. _Lutu_ is also listed in _Wanwu_ , where it is recommended for treating drowsiness (Fuyang Han jian zhenglizu 1988: 38).
_E_ 惡 is used in _Wu Yue chunqiu_ , 7.6a, to denote human feces (the passage concerns diagnosis by tasting faces). Perhaps "a man's muck" in _MS_ I.E.188 refers to feces. _MWD_ , vol. 4, "Transcription," n. 1, argues that the name denotes semen; and that it is related to the name "a man's slime" in _MS_ I.E.11. The basis for the identification is the use of semen to treat scars in later medical literature, which is not incontrovertible proof of the meaning of _e_ in _MS_ I.E.188. The early textual evidence favors feces, but I would not rule out semen as a possible identification. _SW_ , 13B.25b, glosses _e_ 堊 as "white daub" (the white plaster applied to walls); perhaps semen is the corresponding male substance.
月 in _MWD_ , vol. 4, "Transcription," should be transcribed as _ri_ 曰 (day).
_Si_ 私 (perform private functions) is glossed as "urinate" in the commentary in _Zuozhuan_ , Xiang 15, 32.13b.
The prohibition on looking at the night sky might be related to a belief that scar tissue, like the growths in _MS_ I.E.34, is affected by the essence from the stars and moon.
己 in _MWD_ , vol. 4, "Transcription," should be transcribed as _yi_ 己 (desist).
I am unable to offer a grammatical analysis of the sentence as written, and I suspect that the scribe omitted the verb from the phrase 而 其 瓣 (attempting to link the phrase as written with the sentence that follows also results in syntactic difficulty). The missing verb must indicate that the seeds are to be removed.
_Zhaijie_ 齋 戒 is the standard term for ritual purification preceding sacrifices to the spirits.
Autumn must refer to the season in which the bamboo is gathered.
"Firm" translates _man_ 滿, which is attested in medieval rhyme dictionaries with the meaning "congealed gruel" (see Morohashi 1957–60, vol. 8: no. 27099). _Man_ occurs again in _MS_ I.E.218, where it also refers to the firmness of castrated pig lard.
_Yiyan_ 已 験 (already proven) is one of the terms for tauting recipes mentioned in _Lunheng_ (see _MS_ I.E.15).
_Niaozhong ni_ 溺 中 泥 (urine sludge) can be equated with _niao baiyin_ 溺 白 近 (white sediment in urine) in materia medica ( _GM_ , 52.93). It is the sediment that precipitates out of human urine ( _ZY_ : no. 0056).
_Kujiu_ 苦 酒 (bitter liquor) refers to vinegar—because vinegar has a bitter taste according to Tao Hongjing ( _GM_ , 25.23).
I.e. the recipe has been used previously with good results.
_Jiu_ 久 occurs in several other recipes to indicate ailments that persist for a long time. Ma Jixing favors reading the graph as _jiu_ 灸 (cauterize), and understands the ailment as "cauterization wounds on the shin" (i.e. eschars that do not heal following cauterization; 1992: 567, n. 1). Eschar scars are mentioned in a description of a corpse in the Shuihudi _Fengzhen shi_ : "On his belly were old scars from cauterization in two places" ( _SHD_ : 157).
Judging from the context, the lacuna should be _ru_ 人.
It appears that the person slides the piece of wood with his foot in order to move the shin around in the water while it soaks.
"Late afternoon" translates _bushi_ 餔 時, which corresponds to 3:00–5:00 P.M. (see _MS_ I.E.67).
Judging from the context, the lacuna should be _shen_ 甚.
By translating _jia_ 痂 as "scabies," I understand scabies in the older sense of a scabby itch, not as the parasitic skin disease caused by the itch mite _Sarcoptes scabiei_. _MS_ I.E.208 does refer to expelling bugs from the scabies, and many of the treatments in _MS_ I.E are clearly vermifugal. But associating the ailment with bugs does not necessarily indicate early Chinese knowledge of the itch mite. _MS_ I.E evidences a similar association between hemorrhoids and bugs, including vermifufal treatments and observation of pinworms (see _MS_ I.E.149). _Chaoshi zhubing yuanhoulun_ , 50.9a, provides more definite evidence of the observation of the itch mite when discussing _jie_ 疥 (the standard name for the ailment in later medical literature): "The _Discourse on the Nine Bugs_ states that pinworms undergo manifold transformations, and that they also transform to become _jie_. There are tiny bugs in the sores that are extremely hard to see." While _jie_ and _jia_ were synonymous in Han times ( _SW_ , 7B.30b), _jie_ replaced _jia_ as the name for the ailment in the post-Han period; and _jia_ came to refer only to a scab that forms on a wound (Yu Yan 1972: 128, 235). _Jia_ is the name for scabies recorded in _Maishu_ , "Ailment List": "When it is located on the body, the scabs spread in channels, and it itches—it is _jia_ " ( _MSSW_ : 72). _MS_ I.E includes a separate category for other types of itch beginning in _MS_ I.E.249.
_Zu qi shi_ 卒 其 時 is equivalent to _zu shi_ 碎 時, which is defined by Tao Hongjing as "the period of time from dawn today until dawn tomorrow" ( _GM_ , 1.40).
Judging from the context, the lacuna must be _han_ 寒. The literal meaning of the whole phrase is "let it be balanced between cold and warm."
It is not certain whether _pulei_ 僕 喿 is an herbal or animal drug. _MWD_ , vol. 4, "Transcription," n. 1, identifies it as one of the alternate names of _mai mendong_ 麥 門 冬 ( _ZY_ : no. 2082, _Ophiopogon japonicus_ Ker-Gawl.), listed in _BC_ ( _GM_ , 16.84). However, _pulei_ is also attested in _Shanhaijing_ , 5.6b, and _Guanzi_ 58, 19.314 (written 僕 累), as the name of a kind of snail.
Hayashi shows that _gang_ 釭 refers to an iron ring placed inside the hub to reduce friction between the axle and the hub (1976: 300). _MS_ I.E.253 calls for "old grease from a carriage." Carriage grease ( _chezhi_ 車 脂) is listed in materia medica ( _GM_ , 38.48). _Shan_ 饍, which I have translated as "work in," is attested as a variant of _shan_ 膳 (Morohashi 1957–60, vol. 12: no. 44390); but the word is not attested in an appropriate meaning in received literature. The translation is based on my conjecture that _shan_ refers to mixing a liquid or soft substance into a medicine to make it malleable, the sense which it appears to have in _MS_ I.E.202 and other occurrences in _MS_ I.E.204, 207, 208, 211.
As in the treatment in _MS_ I.E.74, a medicine is first applied and then that part of the body is roasted.
I have not found specific reference to a red lizard in received literature, nor does materia medica mention lizard blood as a drug.
_Tingli_ 葶 藶 is listed in _BC_ ( _GM_ , 16.111). The seeds are the drug. _ZY_ : no. 4818, lists several plants in the genus _Lepidium_ as well as several other genera. _KGS_ , vol. 1: 256, n. 715, names _Draba nemorosa_ and various species of the genus _Brassica_. It is not clear which plants were the source of _tingli_ in early medicine.
The identity of the drug _wuyi_ 莁 荑 is not known. In materia medica it has been treated as an alternate name for _wuyi_ 蕪 荑 (stinking elm fruit; see _MS_ I.E.195). However, the two names are glossed separately in _Erya_ , 8.4a and 9.3a. Evidently the names originally referred to two different plants and were conflated in later material medica.
Judging from the context, the lacuna should be _zhi_ 彘.
"Bark" is the gloss for _pu_ 朴 in _SW_ , 6A.22b. _MWD_ , vol. 4, "Transcription," n. 2, plausibly equates the word with _pumu_ 朴 木, the magnolia from which the drug _houpu_ 厚 樸 is obtained (see _MS_ I.E.177).
_SW_ , 9A.26a, glosses _rong_ 髶 as "disheveled hair" ( _luanfa_ 亂 髶). In material medica, _luanfa_ is the loose hair that drops from the head and collects in brushes and combs (see _MS_ I.E.5).
Based on other recipes for scabies, the lacuna might be _fu_ 傅 (spread).
Since the recipe specifies equal amounts of two substances, _jin_ 金 must refer to a second source of metal in addition to _yu_ 鋊 (copper hits; see _MS_ I.E.144). The translation "bronze" reflects my speculation that the metal bits are obtained from bronzeware.
Perhaps the conclusion to _MS_ I.E.208 indicates that the itch mite was already observed in early Chinese medicine, but I remain skeptical. Several other recipes conclude with similar statements that following the treatment, "the bugs come out" (of a wound in _MS_ I.E.15, and of hemorrhoids in _MS_ I.E.152). Like hemorrhoids, the etiology of _jia_ is grounded in early Chinese ideas about bugs and disease that do not correspond to modern parasitology. Without additional evidence it is difficult to determine what bugs are seen coming out in _MS_ I.E.208.
_Dai_ 戴 as a Han word for vinegar is discussed in _MS_ l.E.9.
I agree with _MWD_ , vol. 4, "Transcription," n. 1, that _dapi tong_ 大 皮 桐 may refer to a kind of _tong_ (paulownia), but the name "large-bark paulownia" is not attested in received literature.
Identification of Shu _shu_ 蜀 叔 is problematic. Presumably _shu_ is to be read as _shu_ 菽, referring to some kind of bean. Ma Jixing reviews several proposed identifications, concluding that the name refers to a bean from the region of Shu and that its identity is not known (1992: 581, n. 4). I tend to agree with Ma in rejecting the proposed equation between Shu _shu_ and Ba _dou_ 巴 豆 ( _ZY_ : no. 1028, seed of _Croton tiglium_ L.), listed in _BC_ ( _GM_ , 35.63). The geographic proximity of Shu and Ba is insufficient evidence to justify equating the two different drug names.
_MWD_ , vol. 4, "Transcription," n. 1, proposes reading _zhe_ 庶 as _zhe_ 庶 ( _ZY_ : no. 1190, _Saaharum sinensis_ Roxb.; sugar cane; _GM_ , 33.58). However, Liu Junzheng (1989) proposes reading it as _zhe_ 廑 ( _ZY_ : no. 5633, _Eupolyphaga sinensis_ Walker; cockroach), listed in _BC_ ( _GM_ , 41.21). Liu cites several occurrences of _zhe_ "cockroach" in the Wuwei recipes to support his identification.
It appears that the medicine is wrapped in cloth, roasted until hot, and then used to hot-press the scabies.
I am uncertain of the sense of _chan_ 産, which means "live, grow, raw, fresh." Perhaps it refers to a fresh outbreak of scabies.
I follow Ma Jixing (1992: 589, n. 2) in reading _gu_ 穀 as _gu_ 穀, paper mulberry ( _ZY_ : no. 4754, _Broussonetia papyrifera_ [L.] Vent.), which is listed in _BC_ ( _GM_ , 36.78). _MWD_ , vol. 4, "Transcription," n. 1, plausibly interprets _guzhi_ 榖 汁 as referring to "grain" cooking liquid; but occurrences of the term in _MS_ III.38 and _MS_ IV.5–6 suggest that the substance is a liquid prepared from the tree not from cooked grain. Whether the liquid is sap or a decoction is not certain.
倏 in _MWD_ , vol. 4, "Transcription," should be transcribed as _xiu_ 滫. Qiu Xigui notes that this is the only instance in _MS_ I.E where the signific for water is written with three short bars rather than with the older seal-script style water signific ( ; 1992: 532). Qiu speculates that the scribe initially wrote the graph without the water signific, and when he corrected the graph there was only room to write the abbreviated three bar form. For attestation of _xiu_ in the sense of "cleanse," see _SW_ , 3B.9b, where _zhi_ 敲 is glossed as "the vessel for cleaning ( _xiu_ ) grain."
I read 駘 as _tai_ 胎, literally "embryo." I accept the suggestion in _MWD_ , vol. 4, "Transcription," n. 1, that the word refers to the same substance as the "bee eggs" already used in _MS_ I.E.130 and 141. Twenty wasp _tai_ are used in _MS_ III.12. It has been argued that the graph should be read as _yi_ 餄 (malt sugar), and that the substance is bee sugar (i.e. honey). I agree with Ma Jixing that wasps do not produce honey, therefore the word cannot be _yi_ (1992: 590, n. 4).
The liquid is probably mulberry sap, but it could also be a decocted liquid.
For identification of _yong_ 廱 with abscess, see Yu Yan 1972: 238. Etymologically the word connotes a "walled-up" place where pus collects.
The "feather" might be related to exorcistic archery preceding the Pace of Yu.
潼 in _MWD_ , vol. 4, "Transcription," should be transcribed as 穜, and read as _zhong_ 腫 (swellings).
_Zi_ 茈 is glossed as _zicao_ 茈 艸 in _SW_ , 1B.19b, which is listed in _BC_ ( _GM_ , 12B.26; _ZY_ : no. 4863, _Lithospermum erythrorhizon_ Sieb. Et Zucc. And several other plants). _MWD_ , vol. 4, "Transcription," n. 1, reads _zi_ as referring to _chaihu_ 柴 胡 (also written 茈 胡). _Chaihu_ ( _ZY_ : no. 3763, _Bupleurum chinense_ DC. and other spp.) is listed in _BC_ ( _GM_ , 13.43). Either identification is plausible.
自 in _MWD_ , vol. 4, "Transcription," should be transcribed as _yue_ 日 (say); and 取 should be transcribed as _gan_ 敢 (dare). Qiu Xigui (1992: 532–33) compares the opening formula of the incantation to an incantation recorded in the Shuihudi hemerological manuscripts (translated and studied in Harper 1987a: 270–71; the same formula occurs in other incantations). I agree with Qui's speculation that in _MS_ I.E.229, the scribe omitted the word _gao_ 告 (declare), which invariably follows _gan_ "dare" in the formula (in incantations as well as in the speech of government officials addressing superiors). The scribe left out another word in the following sentence. The scribe also omitted a word from the incantation in _MS_ I.E.233, but there he corrected the omission. The utterance at the beginning of the incantation, _gao_ /* _k əgw_ 皋 (also written 睪), is attested both in Han ritual literature and in the Shuihudi hemerological manuscripts. Zheng Xuan glosses * _k əgw_ as "an extended cry" in the commentary in _Yili_ , 35.2b, where the utterance forms part of the ritual of summoning back the soul of a person recently deceased. In _MS_ I.E.229 the "extended cry" is directed toward Tai Mountain Barrow 大 山 陵, the sacred peak of the east located in present-day Shandong. For the role of the spirit of Tai Mountain in Han popular religion, see Seidel 1987: 30; and Ngo 1976: 111. Tai Mountain was regarded as the abode of the dead, and the presiding deity was one of the arbiters of human fate who could be entreated to intervene in matters concerning illness and death. The appeal to Tai Mountain in _MS_ I.E.229 is similar to the one made to the Spirit of Heaven in _MS_ I.E.124; and in both cases the request for help is followed by cursing the demonic agent responsible for the ailment.
The scribe omitted 木 in the text.
炻 is not attested in received literature, and the translation "irradiate" is based on my judgment that the word probably has the sense of attacking the demon with moonrays. The phonetic indicates a pronunciation _shi_ /* _djiak_. _KGS_ , vol. 1: 264, n. 771, suggests reading the graph as _yi_ /* _dag_ 燡 (shine), which is phonologically plausible but unlikely because the word is attested just once in Han literature. Ma Jixing argues that the graph is a scribal miswriting of _zhao_ 炤 (i.e. 照; 1992: 595, n. 5), but I think _KGS_ must be basically correct in proposing a phonological solution to the identity of the graph.
根 is not attested in received literature. I propose the pronunciation _shi_ /* _dj ək_, perhaps a phonetic loan for _zhi_ /* _tj ək_ 樴 (pole, road). 桯 in _MWD_ , vol. 4, "Transcription," should be transcribed as _zhu_ 柱. _Zhu_ is commonly used for _zhu_ 拄 in Han literature (see _SW_ , 6A.31b, and Duan Yucai commentary); and the latter word is attested in the sense of "strike, stab" in _Hanshu_ , 67.5b.
Tiger claws symbolize the punishment inflicted on demons by the tiger ( _hu_ 虎), the demon-queller par excellence in early China (Bodde 1975: 129). In analyzing _wei_ 葦 畏 (fearsome), _SW_ , 9A.43a, identifies the top as the head of a demon and the bottom as an abbreviation of 虎 The significance of its composition is explained as follows: "To have a demon head and tiger _claws_ is to be something that can be feared."
The common reed, _wei_ 葦 ( _ZY_ : no. 2191, _Phragmites communis_ Trin.), played a significant role in Han exorcistic practices, including the New Year's customs of presenting reed halberds at the Great Exorcism and hanging reed cords over doorways (Bodde 1975: 82, 128–30). The Shuihudi "Jie" states that a spirit who harasses a woman can be expelled by striking it with reeds, followed by bathing in feces ( _SHD_ : 215). The punctuation of this part of the incantation in _MWD_ , vol. 4, "Transcription," is incorrect. Each phrase should end with the word _ruo_ 若 (you).
肉 in _MWD_ , vol. 4, "Transcription," should be transcribed as _jin_ 今 (today). The bottom part of the graph is missing, but enough remains to compare with other occurrences of the two graphs in _MS_ I.E and to confirm the correct identity. The lacuna below might be _qu_ 去 (depart), making the incantation read: "Today depart. If you do not depart, it will be bitter." Compare the formula using "today" in _MS_ I.E.125. Li Xueqin (private communication) suggests that perhaps the silk fragment should be moved up slightly, leaving no lacuna between 今 and 若 (in which case the incantation would read, "Today if you do not depart it will be bitter").
Based on remaining fragments of the first graph and on the context, Qiu Xigui fills the two-graph lacuna with _shi_ 食 (eat) and _dong_ 東 (east; 1992: 533).
_Baiheng_ 自 衡 is not attested in materia medica. _MWD_ , vol. 4, "Transcription," n. 1, suggests identifying the name with _duheng_ 杜 衡 ( _ZY_ : no. 2094, _Asarum forbesii_ Maxim.; _GM_ , 13.70).
_Xinzhi_ 薪 雉 is for _xinyi_ 辛 夷 in _Wenxuan_ , 7.3a ( _zhi_ /* _drjid_ and _yi_ /* _r əd_ are homophones).
Archaeological evidence indicates that the _diao_ 銚 was a shallow, flat-bottomed bowl that could be placed directly on the fire to warm food and drink (Hayashi 1976: 230–31).
The cloth is probably used to strain the cooked medicine as in _MS_ I.E.13.
Evidently the recipe concerns an abscess on the face.
I read 夸 as _ku_ 刳 For examples of _ku_ in the sense of cutting out the inside of something, see _SW_ , 4B.45a, and Duan Yucai commentary.
_SW_ , 6B.8a, glosses _xiu_ with _qi_ 桼 ( _ZY_ : no. 0131, _Rhus verniciflua_ Stokes), the tree that produces the sap for lacquer. Duan Yucai cites evidence that _xiu_ refers to applying lacquer to objects. Thus the ailment category in _MS_ I.E probably refers to the rash caused by working with lacquer, a reflection of the lacquer industry in the region of Changsha.
The incantation portrays a pantheon in which the Thearch of Heaven 天 帝 presides over lesser nature spirits like the lacquer spirit. On the Thearch of Heaven in Han popular religion, see Seidel 1987: 28.
_Bi_ 疕 refers to thin scabs that spread across the skin (Yu Yan 1972: 117). _Bi_ occurs as a separate ailment category beginning in _MS_ I.E.257.
_Min_ 民 (people) was initially omitted by the scribe, who then corrected the error by writing the graph in tiny script on the left beside the graphs between which it should be inserted.
The rhyming words in the incantation are: _shi_ /* _hrj əd_ 矢 (arrow), _bi_ /* _pji əd_ 疕 (scabby sore), and _shi_ /* _hrj əd_ 矢 (feces).
The text writes _di_ 抵, but apparently means _zhi_ 抵, glossed in _SW_ , 12A.51a, as "strike with a sideways blow." Duan Yucai notes that the use of 抵 to write _zhi_ is a common error in received editions of Han texts; _MS_ I.E.233 suggests that the error may have already been a scribal convention in Han times.
It is likely that the incanted threat to daub feces on the lacquer spirit was fulfilled by actually slapping feces on the lacquer rash after the incantation. On the exorcistic nature of feces in early magico-religious belief, see Harper 1985: 495.
There are several different lists of the five weapons. One legend has it that weapons were invented by the war-like Chiyou 尤, who was defeated by the Yellow Thearch. The pairing of the two figures and the role of Chiyou as a demon-queller are examined in Bodde 1975: 120–27; and Lewis 1990: 185–95. Seidel 1987: 34–39, examines the parallel relationship between the Thearch of Heaven and his weapon-bearing envoy in popular Han religion.
The incantation likens the exorcistic saliva to knives. The rhyming words in the incantation are: _bing_ /* _pjiang_ 兵 (weapon), _wang_ /* _mjang_ 亡 (begone), and _zhuang_ /* _tsijang_ 裝 (coat).
As in _MS_ I.E.233, chicken feces and rat detritus are probably daubed on the lacquer rash following the incantation. _Rang_ 壤 (detritus) refers to the soil from a rat burrow. The rhyming words in the incantation are: _wang_ /* _gwjang_ 王 (king; two occurrences), _bing_ /* _pjiang_ 兵 (weapon), _shang_ /* _hrjang_ 傷 (wound), and _rang_ /* _njang_ (detritus).
_Langya_ 狼 牙 is listed in _BC_ ( _GM_ , 17.11). Its botanical identification is uncertain. Ma Jixing offers two possibilities: _Potentilla cryptotaenia_ Maxim.; and _Agrimonia pilosa_ Ledeb (1992: 605, n. 2).
_MS_ I.E.244 and _MS_ I.E.248 specifically mention _te_ 蟘 as the bug that damages the mouth, nose, and teeth with its chewing. It appears that this chewing is of the same nature as, but less serious than, the chewing by the _ming_ bug in _MS_ I.E.78. Other recipes are less specific, but clearly reflect the belief that bugs chew holes into the surface of the body. Treatment in _MS_ I.E.240 consists of filling the chew-holes with medicine and getting new flesh to grow. As noted in _MWD_ , vol. 4, "Transcription," n. 1, later medical literature deals with a similarly broad range of body decay ailments under the category _ni_ 蠹 (hidden bugs).
_Pupu_ 僕 僕 is used in _Mengzi_ 5B, 10.423, to refer to feverish activity. In _MS_ I.E.240, the term must refer to scrubbing until the skin is irritated.
While it is difficult to guess the exact words of the phrase preceding the nine-graph lacuna, it must state that not wrapping the wound is also all right.
_Loulu_ 漏 蘆 is listed in _BC_ ( _GM_ , 15.38). _ZY_ : no. 5397, gives two principal identifications, _Rhaponticum uniflorum_ (L.) DC.; and _Echinops Latifolius_ Tausch. _BL_ ( _GM_ , 15.39) identifies _loulu_ as an alternate name for _feilian_ 飛 廉 ( _ZY_ : no. 0567, _Carduus crispus_ L.), also listed in _BC_.
I.e. the medicine must be applied with the cloth just mentioned (the lacuna preceding "cloth" should be a verb meaning to dip the cloth into the liquid).
I suspect that the first graph in the lacuna belongs to the name of the preceding substance; and that the substance may be another form of stove ash. _MS_ IV. 7–8 record the name Yu _xun_ 禹 熏, which may be stove soot.
Ma Jixing discusses several possible indentifications for _jinkui_ 堇 葵 (1992: 611, n. 4). None permit certain identification of the drug in _MS_ I.E.244.
_KGS_ , vol. 1: 273, n. 827, suggests reading _guo_ 椁 as _kuo_ 鞹; and conjectures that the next missing graph might be _hong_ 鞃. _Kuohong_ is the name for a horizontal leather piece that is attached to the front of the carriage chassis.
_Sao_ 慅 means literally "scratch" ( _SW_ , 12A.36a), and by extension refers broadly to skin itch (Yu Yan 1972: 128). Sao is included in Maishu, "Ailment List": "When the body ails from itch and pus oozes—it is sao" ( _MSSW_ : 72).
Judging from the context and from the parallel in _MS_ I.E.230, the lacuna should be 中.
The reading for is problematic. Based on _SW_ , 13A.53a, and Duan Yucai commentary, I propose the pronunciation _che_ /* _thijat_. I suspect that the graph is a phonetic loan for _shui_ /* _sthjuad_ 涚, which refers to a filtration process using ash that is mentioned in Han ritual literature ( _SW_ , 11A–2.31a, and Duan Yucai commentary; and Hayashi 1975: 77). Ma Jixing proposes a phonetic loan for _che_ /* _thijat_ 澈 (clear), understanding the word to mean "clarify" in _MS_ I.E.250 (1992: 615, n. 3). I am skeptical of Ma's reading because the word is rare and is not attested in Han sources, whereas _shui_ is well attested in the sense of "clarify."
後 in _MWD_ , vol. 4, "Transcription," should be transcribed as 后.
_Quju_ 屈 居 is identified as _luru_ 盧 茹 in _Guangya_ , 10A.24b. _Luru_ can be identified with _lüru_ 蕳 茹, which is listed in _BC_ ( _GM_ , 17.12). _ZY_ does not give a botanical identification.
The itch is rubbed with the roasted, wrapped medicine below. The lacuna probably describes wrapping the medicine to prepare it for use in hot-pressing.
The identification of baifu 白 付 is problematic. MWD, vol. 4, "Transcription," n. 1, offers two suggestions. First, it may be bai fuzi 白 附 子, which is listed in _BL_ ( _GM_ , 17.50). Tao Hongjing already does not know what the drug is. In later materia medica it is sometimes identified as a variety of fuzi (g. Aconitum), but Li Shizhen pointedly notes that it is not an aconite. Alternatively, the drug in _MS_ I.E.254 may be baifu 白 符, which belongs to the so-called wuse fu 五 色 符. The name is associated with the wuse shizhi 五 色 石 脂, five kinds of clay classified by color that are listed in _BC_ ( _GM_ , 9.80). The red and white varieties of fu occur in _MS_ III.62.
_Mu_ 沐 is the verb for washing the hair, but also denotes the grain-cleaning liquid used for hair-washing (see _Shiji_ , 49.6a).
In received literature _bi_ 疕 refers broadly to any rash that forms scabs. Yu Yan associates the word with conditions like eczema (1972: 117). _MS_ I.E.266–270 concern chilblain, which is not classified under _bi_ in received medical literature.
I.e. spread the medicine, stop for three days, and spread again.
膆, which I pronounce _suo_ , is not attested in received literature. It must be a verb describing what is done with the medicine. _MWD_ , vol. 4, "Transcription," n. 1, simply reads the graph as _suo_ 索 in the sense of "gather up"; and interprets the line to mean that the medicine is gathered in something so that it can be used for hot-pressing.
This appears to be another form of stove ash.
"Exposed" translates _lou_ 露. I am uncertain of the meaning of "exposed scabbing." Perhaps _lou_ refers to a kind of open sore; perhaps it has the sense of "protruding," describing a pattern of raised bumps with scabs.
Ma Jixing associates the name _fanjiao_ 飯 焦 with _guojiao_ 鍋 焦 in later medical literature, which refers to the charred crust of rice that sticks to the cookpot (1992: 626, n. 1).
搐 is not attested in received literature. It may be related to _chu_ /* _hj əkw_ 稸, which is the basis for the pronunciation. The utterance _qin qin, chu chu_ 浸 浸 焴 焴 is similar but not identical to the utterance in _MS_ I.E.178 (the repetition of syllables in _MWD_ , vol. 4, "Transcription," should be corrected as in _MS_ I.E.178). I am not able to identify the symbolic significance of the choice of words for the utterance. 虫 is read _chong_ "bug" here, as confirmed by the rhyming words.
The extant rhyming words in the incantation are: _chong_ /* _drh əngw_ 虫 (bug), _zhong_ /* _trkdngw_ 中 (in), and _xing_ /* _hj əng_ 興 (arise). On the Yellow Spirit, see _MS_ I.E.178.
_SW_ , 7B.32a, glosses _zhu_ 瘃 as "swollen lumps due to being struck by coldness." For identification with chilblain, see Yu Yan 1972: 67, 136.
The lacuna should be 取 or 以.
I read _li_ 捏 as _li_ 裡 (also pronounced _si_ ), given as a variant graph for _si_ 梠 in _SW_ , 6A.42a. It is the name of kind of spade (see Sun Ji 1991: 2, for archaeological artifacts). In _MS_ I.E.266, the word is used verbally to denote the action of "scraping away" the layer of ash.
I suspect that the "liquid" and the "medicine" refer to the same thing. The two three-graph lacunae earlier in the recipe must identify the medicine, which is applied simultaneously with the ash.
The Shang bone and shell inscriptions provide the first attestation of _gu_ 蠱, pictographically a representation of bugs in a vessel. If later explanations of _gu_ are applicable to Shang usage, the etymology of the word goes back to a demonic potion prepared from bugs that the manufacturer uses to sicken chosen victims. See, for example, _Chaoshi zhubing yuanhoulum_ , 25.1a: "They mostly use kinds of bugs and serpents, and keep them in a vessel until they eat one another. There is just one creature remaining, which is then called the _gu_." By extension, _gu_ refers to demonic evil and to black magic in general. Shirakawa 1976, vol. 1: 250–51, discusses Shang and later evidence. _Zuozhuan_ , Zhao 1, 41.13b, records the diagnosis of the ruler of Jin 晉 by Physician He 醫 和, who declares that the ruler has an ailment caused by sexual excess that is "like _gu_." The passage includes Physician He's etymology of _gu_ ("buge inside a vessel") and two denotations: the bugs that are generated from grain, and delusions arising from female seduction. The idea of internal bugs is the basis for the _SW_ , 13B.5b, gloss: " _Gu_ is when the abdomen is attacked by bugs." Lu and Needham suggest schistosomiasis as one identification for _gu_ (1967: 225), but associating the ailment with a modern parasitic disease is highly questionable given early Chinese notions about bugs and illness. The aspect of female seduction in _gu_ etiology is very much alive in Han accounts that associate _gu_ with female witchcraft and with the use of voodoo-like objects to harm victims (see Loewe 1974: 81–90). The recipes in _MS_ I.E do not describe _gu_ , but demonic bugs or female witchcraft are likely factors in the identity of the ailment.
"Paired talisman" translates _bingfu_ 并 符. It seems likely that the talismans of wood, bamboo, or fabric inscribed with magical images and script are involved, similar to talismans of later times. The earliest archaeological specimens of talismanic writing occur on burial writs dating to the Later Han period (Sun Ji 1991: 404–407; and Wang Yucheng 1991).
"Toss" translates _dui_ 敦, which is attested in this sense in _Huainanzi_ , 15.266, in the phrase 敦 六 博 "toss (the die to play) _liubo_."
It is possible that the lacuna has the patient first drink the water, followed by bathing with it. Water containing talisman ash anticipates the _fushui_ 符 水 (talisman water) used to cure ailments in the second century A.D. politico-religious movement headed by Zhang Jue 張 角 (see _Hou Hanshu_ , 71.la); and widely used in later religious Daoism.
The medicine seems to be an antidote whose production imitates the production of the _gu_ potion.
_SW_ , 9A.41b, glosses _qi_ 鬾 as "child demon." A number of Han sources identify the child demon as the third of Zhuan, Xu's 顓 頊 three children who died after birth and became disease demons. Whereas the first two demons inhabit rivers, the child demon occupies the home and likes to frighten people, especially children (see the Duan Yucai commentary in _SW_ ; and _Lunheng_ , "Dinggui," 22.450). Both of the recipes in _MS_ I.E involve exorcistic magic performed in the home, confirming the received account of the child demon.
倡 in _MWD_ , vol.4, "Transcription," should be transcribed as _Kuai_ 儈. _Kuai_ is not attested in the sense of "figurine," but it must represent a word similar to _geng_ 梗, which is attested in pre-Han and Han sources as the term for a figurine of wood or clay. Perhaps the figurines in _MS_ I.E.276 are like the apotropaic peachwood figurines placed in the coffin in Mawangdui tomb 1, which are made from short pieces of peach branch cut in half lengthwise. The upper end of each piece is carved into a triangular shape, and painted with a nose and two eyes (Hunan sheng bowuguan and Zhongguo kexueyuan kaogu yanjiusuo 1973, vol. 1: 100). _MS_ I.E.276 is the earliest account of hanging peachwood figurines over the doorway (see Bodde 1975: 127–38, for further discussion of the custom).
The Shamanka Mistress is invoked to apprehend the child sprite, perhaps with assistance from the "parents." Disposing of demons in water is a common device. I cannot claim to have understood the conclusion of the incantation. The rhyming words are: _mu_ /* _m əg_ 母 (Mother), _bei_ /* _pǝk_ 北 (north), _de_ /* _t ək_ 得 (catch); and _ti_ /* _hli əd_ 體 (limb), _zhi_ /* _krjid_ 指 (finger), _shui_ /* _hwrjid_ 水 (water), _gui_ /* _kwjed_ 鬼 (demon).
_MWD_ , vol.4, "Transcription," n.2, argues that _cai_ 采 is a scribal error for _ji_ 奚. I accept the emendation. For _jili_ 奚 蠡******* (large-bellied gourd) see _MS_ I.E.60.
I suspect that a second incantation is lost in the lacunae in the latter part of the recipe.
_Mayou_ 馬 疣 (horse wart) probably refers to some kind of tumor or polyp. _MWD_ , vol.4, "Transcription," n.1, cites a passage from the _Huangdi hama jing_ 黄 帝 蝦 蟆 經 that mentions the ailment name alongside abscess and fistula, but _mayou_ is otherwise unattested in received medical literature.
Ma Jixing (1992: 639, n.3) equates this substance with _tieluo_ 鐵 落 ( _ZY_ : no.3812, oxidized iron produced during forging), listed in _BC_ ( _GM_ , 8.29).
_Baifu_ 白 柎 may represent the same substance as _baifu_ 白 付 in _MS_ I.E.254 (identity uncertain).
_SW_ , 7B.28b, lists three denotations for ma 瘍: an eye ailment, noxious vapor adhering to the body, and a festering wound. Because of the use of horse cheekbone as a drug in _MS_ I.E.280 as the reference to facial _pao_ 皰 in _MS_ I.E.281 ( _pao_ is well attested for acne-like pustuales), _ma_ evidently denotes facial pustules in _MS_ I.E.
The two lacunae should be either 以 or 取. The use of horse ( _ma_ 馬) cheekbone to treat the _ma_ ailment exemplifies the same homeopathic principle as _MS_ I.E.79 where the _quan_ insect is used to treat the _quan_ ailment. Using the cheekbone also suggests the ailment is located on the patient's face.
The lacuna must contain a reference to the pustules.
Perhaps the horse cheekbone medicine is applied with a cloth.
_Pao_ 靤 (pimple) is attested as an orthographic variant of _pao_ 皰, which is glossed in _SW_ , 3B.31a, as "an outbreak of vapor on the face" (see Yu Yan 1972:72–73, for identification with acne).
_MWD_ , vol.4, "Transcription," n.1, notes that the graph in the lacuna may be _she_ 它 (snake). CC458–62, as well as fragment 7–19 ( _MWD_ , vol. 4: 79–81), are in the hand of different scribe and were evidently added at the end of the silk sheet subsequent to the original redaction of the text. The ailment names are also not recorded in _MS_ I.E.1.
_Mei_ 苺 is glossed as _mamei_ 馬 莓 in _SW_ , 1B.10a, but this name is not found in later sources and its identity is unknown. _Mei_ 莓 is a general term for berry vines, and perhaps the reference to _mei_ in _MS_ I.E.283 is also nonspecific.
_MS_ II.A
Quegu Shiqi
却 榖 食 氣
Eliminating Grain and Eating Vapor
_MS_ II.A (CC1–9)
Those who eliminate grain eat _shiwei_ (pyrrosia).1 On the first day of the month eat the base. Daily add one joint, stopping on the fifteenth day.2 On the sixteenth day begin to decrease. Daily [1] one joint,1 returning to the base on the last day of the month. Advance and retreat together with the moon. If the head becomes heavy, the feet become light, and the body has itchy swellings,2 practice _xu_ exhalation and _chui_ exhalation—stopping when the benefit is realized.3 Those who eat grain eat the base and [1]; those who eat vapor practice _xu_ exhalation and _chui_ exhalation when they first go to bed and first arise.4 Whenever doing _xu_ exhalation, in mid-breath change to _chui_ exhalation. A twenty year old does it twenty times at dawn, twenty times at dusk, and two hundred times every second day at dusk. A thirty year old does it thirty times at dawn, thirty times at dusk, and three hundred times every third day at dusk. Use this calculation to extrapolate.
For spring eating, eliminate entirely Turbid Yang; blend with Waning Light and Dawn Aurora.1 Dusk and dawn are allowed. For summer eating, eliminate entirely Scalding Wind; blend with Dawn Aurora and Drifting Flow. Dusk and dawn are allowed. For autumn eating, eliminate entirely [Cool Wind] and Frost Mist;1 blend with Resurgent Yang and Waning [Light].2 Dusk and dawn are allowed. For winter eating, eliminate entirely Frozen Yin; blend with True Yang, Waning Light, Resurgent Yang, and Resurgent Yin. Dusk and dawn are allowed.
[3] As for [Cool Wind],3 [1] permeates the four directions.4 Cool Wind (is a vapor) that snaps the head. Frost Mist [7]. As for Turbid Yang, black permeates the four directions. It is heaven's chaotic vapor, and becomes mist when the sun rises. Scalding Wind is [1] wind. It is (a vapor) that is hot and strikes people. {1} [1]. Frozen Yin enters the bones [2]. These five cannot be eaten.
Dawn Aurora [13]. As for [Resurgent Yang],5 when the sun ascends the height of two poles6 it becomes turbid [5]7 clouds are like a cover that veils [4] {2} [2] {2} [6]1 is the cool wind of summer dusk.
Whenever eating [19]. Those who eat grain eat what is square; those who eat vapor eat what is round. Round is heaven; square is earth. [3] {1} face north [8] eat a large amount.2 [21] then blend with True Yang. {3} [13] is mostly Yin. Day and night are divided [31] [is]3 the blue adjunct. The blue adjunct is mostly Dawn Aurora. The dispersed vapor of dawn is the white adjunct. The white adjunct is mostly Waning Light. The dispersed vapor of dusk is the black adjunct. The black adjunct is mostly Resurgent [10] {2} [?].4
1"Eliminate grain" translates _quegu_ 却 穀. The term refers to a dietetic regimen that shuns ordinary foodstuffs, which are replaced by drugs and by breach cultivation. Comparable terms in received literature of the Han period are _bigu_ 辟 穀 (avoid grain) and _juegu_ 絶 穀 (abstain from grain. The former is attested in _Shiji_ , 55.12a–b, in the account of Zhang Liang 張 艮 d. 187 B.C.), who is said to have practiced "avoidance of grain," "guiding and pulling" ( _daoyin_ 道 引), and "lightening of the body" ( _qingshen_ 輕 身). The latter is attested in Lu Jia's 阹 (fl. 200–180 B.C.) _Xinyu_ , 1.11a, which criticizes the man who, hoping to achieve _shenxian_ 神 仙 (divine transcendence), "abstains from the five grains" and "strains his body and exhausts his physique" while abandoning parents and family. I regard _MS_ II.A and the other Mawangdui medical texts that treat of macrobiotic hygiene to be representative of a medical tradition of macrobiotic hygiene which was related to, but not identical with, Daoist ideas and _xian_ -cult hygiene in the third and second centuries B.C. These matters are discussed in the Prolegomena, Section Four, "Intellectual Background" and "Body and Spirit."
_Shiwei_ (pyrrosia) is used in _MS_ I.E.109 to treat urine retention; eating the drug in _MS_ II.A is surely intended to ameliorate some of the physical effects of not eating regular foodstuffs, which include abnormal urination. Descriptions of initial symptoms experienced by the adept who eliminates grain while ingesting vapor in later religious Daoist literature are relevant to _MS_ II.A. Here, for example, is the description of the first two decades of a hundred day regimen from _Yunji qiqian_ , 57.10b: "During the first decade essence and vapor are weak and slight; facial coloration is wan and yellow. During the second decade movements are lurching, the limbs and joints ache, defecation is difficult, and urine is red-yellow. At times there is dysentery that at first is firm and then turns to muck."
2The precise denotation of _zhi_ 質 (base) and _jie_ 節 (joint) in relation to the herb _shiwei_ (pyrrosia) is uncertain. _MS_ I.E.226 use _jie_ as a measure for the root of a herb, and _jie_ is sometimes used as a measure for sections of the stalk. _Shiwei_ (pyrrosia) grows mainly in rocky places, spreading by means of a rhizome that sends out single leaves at intervals. I suspect that _zhi_ refers to the end of the rhizome—the "base"—as the primary unit of the herb, and that the _jie_ are the sections between leaves. Perhaps a whole herb was measured out in this fashion at the time of use, but it seems likely that there was an established equivalence between this form of measurement and a volumetric measurement.
1The lacuna is a word meaning to decrease the amount of the drug.
2"Itchy swellings" translates _zhen_ 軫. _Zhen_ is attested for _chen_ 疹 in _Suwen_ 64, 18.7a. For discussion of early glosses of the ailment name, see Yu Yan 1972: 196 (Yu gives hives as one identification).
3 _Xu_ 呴, _chui_ 吹, and _hu_ 呼 are the tree methods of exhaling vapor in early breath cultivation. The manner of executing them is not described in Mawangdui and Zhangjiashan medical manuscripts, but passages in the _Yinshu_ indicate certain characteristics of each. When the body is affected by heat, it is vented by _xu_ exhalation; when affected by dampness, by _chui_ exhalation; and when affected by dryness, by _hu_ exhalation. When a person is joyful, Yang vapor is abundant; and the somatic disharmony is corrected by venting the excess Yang vapor using _xu_ exhalation. Anger represents an excess of Yin vapor; and _chui_ exhalation restores balance. As part of a daily regimen of breathing, a person should adhere to the following seasonal schedule: in spring, _xu_ twice, and _hu_ and _chui_ once each; in summer, _hu_ twice, and _xu_ and _chui_ once each; in winter, _chui_ twice, and _xu_ and _hu_ once each (autumn is not mentioned in the text; _YSSW_ : 86). Summing up the data, _xu_ is associated with heat, Yang, and spring, _chui_ with dampness, Yin, and winter, _hu_ with dryness and summer. Ma Jixing discusses several later explanations of _xu_ and _chui_ in connection with breath cultivation (1992: 825, n. 17). Ma notes that _xu_ is performed with a round open mouth while _chui_ is performed with lips spread flat. I suspect that _hu_ exhalation is with the mouth in a regular breathing position. The illustrations of exrcises in _MS_ II.C depict many mouth positions from wide open to closed, which undoubtedly represent _xu, chui_ , and _hu_ exhalation (precise identification is, however, not possible). In _MS_ II.A, heavy head, light feet, and itchy body are to be treated with _xu_ or _chui_ (the text below describes a combination beginning with _xu_ exhalation and changing midway to _chui_ ).
4The "base" must refer to _shiwei_ (pyrrosia). The outcome of eating the herb for "those who eat grain" ( _shigu zhe_ 食 穀 者) is lost in the lacuna. The sentence probably underscores the difference between the ordinary use of the herb and its use as part of a program of breath cultivation cum grain-elimination diet. The contrast between grain-eaters and "those who eat vapor" ( _shiqi zhe_ 食 穀 者) is made again below, where it is stated in cosmological terms: eating grain is linked to the symbolism of square and earth; eating vapor to round and heaven. The contrast parallels the "Heshang gong" 河 上 公 commentary to _Laozi_ , par.6, which identifies heaven with the nose and earth with the mouth. Thus, according to the commentary, "heaven feeds man with five vapors which enter through the nose and are deposited in the heart," while "earth feeds man with the five tastes which enter through the mouth and are deposited in the stomach" ( _Daode zhenjing zhu_ , 1.5a). _Shiqi_ "eating vapor" is the usual term for breath cultivation in _MS_ VI.A, and does not assume simultaneous grain-elimination dietetics (see Prolegomena, Section Four, "Techniques").
1The remainder of _MS_ II.A concerns a tradition of breath cultivation for which parallels exist in Han received literature. This first paragraph specifies five vapors in the external atmosphere to be avoided and six to be ingested during each season. The next two paragraphs describe first the five harmful vapors (four of the five also occur in _MS_ VI.A.4), and next the six vapors to be ingested. The five harmful vapors are not attested in received literature, but the other set of six can be associated with the _liuqi_ 六 氣 (six vapors) in Han sources. _Chuci_ , "Yuan you" 遠 遊, 5.4a, incorporates them into the narrative of the poem: "I will follow Wang Qiao to find pleasurable entertainment. Consume the six vapors and drink Drifting Flow ( _hangxie_ 沆 韰) ah! Rinse the mouth with True Yang ( _zheng_ Yang 正 陽) and swallow Dawn Aurora ( _chaoxia_ 朝 霞)." The Wang Yi commentary identifies the six vapors by quoting the lost _Lingyang Ziming jing_ 陵 陽 子 明 經 (Lingyang Ziming is a personage associated with the Han _xian_ cult; see Kaltenmark 1953: 183). According to the _Lingyang Ziming jing_ : "In spring eat Dawn Aurora; Dawn Aurora is the red-yellow vapor when the sun is just about to rise. In autumn eat Sunken Yin ( _lun_ Yin 倫 陰); Sunken Yin is the red-yellow vapor after the sun has set. In winter eat Drifting Flow; Drifting Flow is the midnight vapor of the northern quarter. In summer eat True Yang; True Yang is the midday vapor of the southern quarter. Together with Heaven's and Earth's Dark and Yellow vapors, these are the six vapors." In the _Lingyang Ziming jing_ each of the vapors corresponds precisely to one of the four seasons, heaven, and earth—the final two vapors being Heaven Dark ( _tianxuan_ 天 玄) and Earth Yellow ( _dihuang_ 地 黄).
The parallel with _MS_ II.A is obvious, but the correspondence is not complete. Both texts share the names Dawn Aurora, Drifting Flow ( _hanggai_ 行 曁 in _MS_ II.A, which is equivalent to _hanggai_ 坑 溉 in _Hanshu_ , 57A.21b), and True Yang ( _duan_ Yang 端 陽 in _MS_ II.A). They are the vapors of dawn, midnight, and midday respectively. That leaves three names in _MS_ II.A without direct counterparts in the _Lingyang Ziming jing_ : Resurgent Yin ( _shu_ Yin 輸 陰), Resurgent Yang ( _shu_ Yang 輸 陽) and Waning Light ( _kuangguang_ 銧 光). I agree with Ma Jixing (1992: 833, n. 5) that 銑 should be read as _kuang_ 匡 in the sense of "wane, decrease." Waning Light is probably a vapor produced as the sun declines in the sky. In translating _shu_ as "resurgent" I rely on the interpretation in Ma Jixing 1992: 838, n. 13. _Shu_ connotes renewal, and Ma suggests that Resurgent Yin is the vapor produced as day shifts to night and Yin is ascendant; in contrast, Resurgent Yang is the vapor produced as night turns to day. I further agree with Ma (1992: 839, n. 17) that Resurgent Yin is probably equivalent to Sunken Yin in the _Lingyang Ziming jing_ ; and that it is probably the vapor produced after sunset.
While it is reasonable to associate the four vapors Dawn Aurora, True Yang, Resurgent Yin, and Drifting Flow with seasons and times of day, their use does not match with the _Lingyang Ziming jing_. For example, Drifting Flow is not consumed in winter, but in summer; and True Yang is consumed in winter rather than in summer. The differences are greater than simple seasonal switches, for in _MS_ II.A at least two vapors are consumed in each season, and as many as four in winter. In short, _MS_ II.A does not exhibit the kind of formal cosmo-seasonal correspondence that is laid out in the _Lingyang Ziming jing_. The understanding of the vapors and their cultivation in _MS_ II.A may predate the categorical correspondences of the _Lingyang Ziming jing_. Moreover, the _Lingyang Ziming jing_ was most likely associated with _xian_ -cult hygiene. Explaining unclear parts of the admittedly fragmentary text of _MS_ II.A by making its contents conform to the _Lingyang Ziming jing_ is, in my judgment, unwise. I am skeptical of the equation that Ma makes between Resurgent Yang in _MS_ II.A and Earth Yellow, as well as between Waning Light and Heaven Dark (1992: 840). Until more manuscripts are discovered that might shed additional light on the subject of early breath cultivation, the most that I would conclude is that _MS_ II.A lists the names of six vapor to be ingested in different combinations in each season, that three of the names correspond to names in lost _Lingyang Ziming jing_ , and that a fourth can be correlated as well.
1I follow Ma Jixing (1992: 837, n.11) in filling the lacuna with Cool Wind ( _quingfeng_ 清 風). The emendation is tentative, but justifiable. Cool Wind is the first vapor named in the paragraph below. Unless the first of the five harmful vapors is not mentioned in this paragraph (which is unlikely) it can only occur here.
2I emend the text by adding _guang_ 光 (light), which was clearly omitted by the scribe.
3I follow Ma Jixing (1992: 842, n. 2) in filling the final two graphs of the five-graph lacuna in _MWD_ , vol.4, "Transcription," with 清 風. The other four harmful vapors are all listed below. The formulaic language used to introduce the other vapor names corroborates the emendation.
4Comparison with the description of Turbid Yang indicates that the lacuna is a color word. _Sisai_ 四 塞 (permeates the four directions) is attested in connection with the reporting of portentous mists in the _Hanshu_. See, for example, _Hanshu_ , 27C–1.6a: "On the night of _xinchou_ (of the fourth month, in the year corresponding to 32 B.C.) there was something like fire light in the northwest. At dawn on _renyin_ , a great wind arose from the northwest. The cloud vapor was red-yellow and _permeated_ under-heaven _in the four directions_. After a whole day and night, what dropped to the ground was yellow dust." The precise knowledge of atmospherics necessary for the practice of breath cultivation no doubt paralleled the expertise of the portent interpreters.
5I follow Ma Jixing (1992: 845, n.2) in filling the final two graphs of the fifteen-graph lacuna in _MWD_ , vol.4, "Transcription" with 輸 陽. The name of a third vapor between Dawn Aurora and Resurgent Yang is lost in the lacuna. The emendation is tentative, but I agree with Ma that the reference below to a time when the sun has risen above the horizon can only match Resurgent Yang.
6I follow Ma Jixing (1992: 845, n.3) in reading _gan_ 干 as _gan_ 竿 (pole). Ma adduces several medieval sources in which the height of the ascending the sun is measured in "poles." _MS_ II.A indicates that this form of measurement was already in use by the second century B.C.
7The name of the fourth vapor is lost in the lacuna. Ma Jixing conjectures that it is Waning Light (1992: 845, n. 5), but I am skeptical of the identification.
1The names of the fifth and sixth vapors are lost in the lacunae. Ma Jixing conjectures that the sixth vapor is Drifting Flow (1992: 846, n. 9). As with the fourth vapor, I remain skeptical.
2There is a large dot in the text at this point, indicating a change of topic. It appears that discussion of the manner of eating vapor is lost in the lacunae.
3I fill the last graph of the thirty-two graph lacuna in _MWD_ , vol.4, "Transcription," with 爲, which is clearly indicated by the grammatical parallels below.
4Color-coded "adjuncts" ( _fu_ 附) that designate the "dispersed vapor" ( _yiqi_ 佚 氣) of different times of the day are clearly related to the six vapors, since the composition of each adjunct is "mostly" one of the six vapors. And there is probably a "yellow adjunct" and a "red adjunct" in addition to the blue, white, and black adjuncts. However, the idea of "dispersed vapor" and "adjuncts" has no counterpart in received literature, and the text of _MS_ II.A is too fragmentary to interpret. Wei and Hu offer a tentative interpretation based on cosmo-seasonal correspondences in _Huainanzi_ (1992, vol. 2: 9), but I am skeptical of their reasoning.
_MS_ II.C
Daoyin Tu
導 引 圖
Drawings of Guiding and Pulling
_MS_ II.C.11
(The caption is missing. The figure is in profile and is bent at the waist, performing a toe-touch.)
_MS_ II.C.2
(The caption is fragmentary. Little of the drawing remains.)
_MS_ II.C.3
(The caption is fragmentary. The figure is in profile and is standing upright, arms pressed against the sides.)
_MS_ II.C.4
(The caption is missing. The figure is in half profile and is standing upright with the right arm bent back level with the shoulders. The left arm is missing.)
_MS_ II.C.5
(The caption is missing. The figure is standing upright, forearms bent up in front of the chest.)
_MS_ II.C.6
Snapping Yin (The figure is in half profile. The head and arms are missing; the left foot appears to be behind and raised.)2
_MS_ II.C.7
(The caption is missing. Little of the drawing remains.)
_MS_ II.C.8
[1] _lang_ (The figure is standing with arms raised above the head, the upper body twisting backward, and the face looking down at an oval object behind, perhaps a lacquer dish.)1
_MS_ II.C.9
(The caption is missing. The figure is standing, but most of the drawing is missing.)
_MS_ II.C.10
(The caption is fragmentary. The figure is in profile and is standing upright with the left arm hanging down by the side and the right arm raised straight up.)2
_MS_ II.C.11
(The caption is missing. The figure is standing with the left arm curved down and away from the body. The right arm is missing, but evidently curves up.)
_MS_ II.C.I23
(The caption is missing. The figure is in profile and the arms are raised straight overhead. The left leg is missing except for the tip of the foot, but evidently it is striding forward or kicking.)
_MS_ II.C.13
Pain [1] (The figure is in half profile and is stepping forward with arms extended straight in front. The mouth is open wide.)4
_MS_ II.C.14
(The caption is missing. The figure is in profile and is bending forward from the shoulders with arms hanging down in front.)
_MS_ II.C.15
Pulling Inguinal Swelling (The figure is standing with legs spread and knees slightly bent. The arms are hanging away from the body.)1
_MS_ II.C.16
(The caption is missing. The figure is standing, but most of the drawing is missing.)
_MS_ II.C.17
(The caption is missing. The figure is in profile and is standing with hands in front of the chest holding a pole vertically.)
_MS_ II.C.18
Inside the Abdomen (The figure is standing. The arms are missing, but evidently they are stretched out on either side.)2
_MS_ II.C.19
(The caption is missing. The figure is in profile and is standing with arms pressed against the sides.)
_MS_ II.C.20
Pulling Deafness (The figure is standing with legs apart. The arms are missing except for a small fragment of the right arm, but evidently they are stretched out on either side.)3
_MS_ II.C.21
(The caption is missing. The figure is in half profile and is bending over at the waist with the left arm reaching straight up and the right arm reaching straight down. A round object, perhaps a ball, is beneath the figure.)4
_MS_ II.C.22
Feverishness (The figure is evidently standing, but little of the drawing remains.)1
_MS_ II.C.232
Pulling Knee Pain (The figure is in profile. Only the front part remains, minus the legs and arms. The figure might be kneeling.)3
_MS_ II.C.24
Pulling Upper Side Accumulation (The figure is in profile and is standing with the left foot placed behind, hands holding an object by the waist, and head looking down.)4
_MS_ II.C.25
Crane [1] (The figure is in half profile and is standing with the left foot placed slightly behind, arms stretched horizontally to the front and rear, and head looking up.)5
_MS_ II.C.26
(The caption is fragmentary. The figure is in half profile and is standing with the right arm reaching up at an angle and the left arm exactly opposite stretching back.)
_MS_ II.C.27
Dragon Ascending (The figure is standing with arms raised at an angle on either side.)6
_MS_ II.C.28
Bending Down for Reversal (The figure is in profile and is bending over from the waist with the back rigid and the arms touching the ground in front.)7
_MS_ II.C.29
Pulling the Nape (The figure is in half profile. The right arm is extended downward in front; the left arm is missing as are the lower legs, which may be bent.)1
_MS_ II.C.30
Penetrating Yin and Yang with a Pole (The figure is in half profile and is bending over at the waist with the hands gripping a pole at either end. The left arm is missing, but it is surely reaching straight up and the right arm straight down.)2
_MS_ II.C.31
Swinging the Upper Arms (The figure is standing with the arms stretched out at shoulder level on either side.)3
_MS_ II.C.32
Stretch (The figure is in profile and is bending over from the waist with the back rigid and parallel to the ground, and the arms hanging down in front.)4
_MS_ II.C.33
(The caption is missing. The middle section of the figure is missing, including the arms, but it is evident that figure is standing in half profile and that the arms are in front.)
_MS_ II.C.341
Looking Up and Shouting (The figure is in profile and is standing with both arms flung straight back over the head. The face is looking straight ahead with mouth open.)
_MS_ II.C.35
Monkey Bawling to Pull Internal Hotness (The figure is in half profile and is standing with fisted hands held near the belly. The mouth is open wide.)2
_MS_ II.C.36
Pulling the Warm Ailment (The figure is standing with arms crossed above the head.)3
_MS_ II.C.37
Sitting and Pulling the Eight Radial-cords (The figure is in half profile and is kneeling in a sitting position with both arms held away from the body.)4
_MS_ II.C.38
(The caption is missing. The lower body is missing except for the feet. The figure is in profile and is standing with the arms extended down in front away from the body.)
_MS_ II.C.39
Pulling Ham Pain (The figure is in profile and is sitting with knees tucked up against the chest and arms wrapped around the knees.)5
_MS_ II.C.40
Gibbon Shouting (Little of the drawing remains except for a fragment of the left side of the face and of the right hand, which is reaching at an angle above the head.)1
_MS_ II.C.41
Bear Ramble (The figure is standing with arms at the sides away from the body and bent at the elbows.)2
_MS_ II.C.42
[1] _hen_3 (The figure is in half profile and is standing with arms extended straight in front at shoulder level.)
_MS_ II.C.43
(The caption is missing. The hands and trunk of the figure are extant; the head, arms, and most of the lower body are missing. The figure appears to be bending at the waist and shoulders, with the arms hanging in front.)
_MS_ II.C.44
Merlin (Much of the drawing is missing. The figure is in profile and appears to be springing forward with the left leg extended in front and bent at the knee, and the right arm curving back above the head.)4
Fig.2 Facsimile of _MS_ II.C.15
Fig.3 Facsimile of _MS_ II.C.24
Fig.4 Facsimile of _MS_ II.C.25
Fig.5 Facsimile of _MS_ II.C.26
Fig.6 Facsimile of _MS_ II.C.28
Fig.7 Facsimile of _MS_ II.C.34
Fig.8 Facsimile of _MS_ II.C.35
Fig.9 Facsimile of _MS_ II.C.36
Fig.10 Facsimile of _MS_ II.C.37
Fig.11 Facsimile of _MS_ II.C.39
Fig.12 Facsimile of _MS_ II.C.42
1The forty-four human figures are arranged in four registers, eleven figures in each register. For each drawing I translate the caption, if extant, and provide a brief parenthetical description of the figure. _MS_ II.C.1–11 are drawn in the first register of the manuscript.
2 _Zhe_ 折 means "snap" or "bend sharply." _Yinshu_ includes a "snapping Yin" exercise, but it is performed by bending down with hands clasped ( _YSSW_ : 82). _MS_ II.C.6 is a different exercise.
1Fragments of the first graph remain. _MWD_ , vol. 4, "Transcription," writes tang 螳, giving the caption _tanglang_ 螳 狼. Ma Jixing reads the caption as homophonous 螳 螂 (praying mantis), and argues that the exercise _dulang_ 度 狼 in the _Yinshu_ represents the same name (1992: 850). Tang Lan suspects that the first graph is _hu_ 虖; the exercise name would then be "shouting wolf" (1979: 7). Given the high degree of uncertainty about the graph, I treat it as illegible and ark a lacuna. The _Yinshu_ exercise _dulang_ is performed by placing the hands in the armpits ( _YSSW_ : 83). _MS_ II.C.8 is a different exercise. The oval object appears to belong to _MS_ II.C.8 rather than to _MS_ II.C.19 beneath it. Assuming it is a lacquer dish, there may be a connection with the Han style of dance performed with dishes placed on the ground (for archaeological evidence, see Hayashi 1976: 395).
2Li Xueqin thinks the exercise depicted might be the exercise named _zhiluo_ 支 落 (meaning uncertain, perhaps "limbs dropping") in the _Yinshu_ ; and Li suspects that the fragmentary caption might be _zhiluo_ (1991: 9). The _Yinshu_ ; text is fragmentary, but does refer to placing one hand at the waist and raising the other arm ( _YSSW_ : 82).
3 _MS_ II.C.12–22 are drawn in the second register of the manuscript.
4The second graph is written _ming_ 明 in _MWD_ , vol.4, "Transcription," giving the name _tongming_ 痛 明 (meaning uncertain). Tang Lan writes _le_ 肋 for the second graph, glossed in _SW_ , 4B.23b, as "bones of the sides" (i.e. the ribs); the exercise name would then be "pain in the ribs" (i.e. the ribs); the exercise name would then be "pain in the ribs" (1979: 8). Examining the fragments of the graph in question, Tang Lan's transcription appears to be the more plausible one; but the graph is best treated as illegible.
1See _MS_ I.E.118 for the ailment. The _Yinshu_ includes an exercise with the same name, but the description does not relate to the drawing in _MS_ II.C.15 ( _YSSW_ : 84).
2The _Yinshu_ includes exercises for both abdomen pain and bloated abdomen, but neither is related to the drawing ( _YSSW_ : 84).
3An exercise of the same name is included in the _Yinshu_ , but it is not related to the drawing ( _YSSW_ : 85).
4The position of the arms does not seem to represent a throwing motion. It is not clear how the round object—if it is indeed a ball—is used.
1 _Fan_ 煩 (feverishness) may be related to "feverishness of the heart" (see _MS_ I.A.4).
2 _MS_ II.C.23–33 are drawn in the third register of the manuscript.
3An exercise of the same name is included in the _Yinshu_ , but it does not seem to be related to the drawing ( _YSSW_ : 83).
4 _Ji_ 積 (accumulation) probably refers to a blockage, perhaps of vapor.
5The second graph is fragmentary. The left side is 訁. Tang Lan suspects that graph is _ting_ 聽 (listen; 1979: 9); i.e. that the right side is 悪, which is unlikely. Shen Shou thinks the graph is _tan_ 譚, meaning the sound of the crane as represented by the onomatopoetic word _li_ 唳 in the _Lunheng_ and later sources (1980: 72). Ma Jixing accepts the transcription _ting_ , and also argues that it should be read as _li_ (1992: 855, n. 1). The graph probably represents a word for the call of the crane, rather than the crane "listening," but the transcription of the graph itself remain uncertain.
6The _Yinshu_ includes an exercise with a similar name, but it is not related to the drawing ( _YSSW_ : 82).
7慲 is not attested in received literature. I tentatively accept _MWD_ , vol. 4, "Transcription," which identifies the graph with _mian_ 俛. The latter graph is given as an orthographic variant _mian_ 頫 in _SW_ , 9A.10a, glossed as "lower the head." _Jue_ 欮 (reversal) is an ailment caused by vapor moving contrary to the proper direction of flow (see _MS_ I.B.1). The exercise for treating the reversal ailment (written 厥) in the _Yinshu_ is not related to the drawing ( _YSSW_ : 84).
1The exercise for treating nape pain in the _Yinshu_ is not related to the drawing ( _YSSW_ : 83)
2The exercise position is similar to _MS_ II.C.21, with the addition of the pole.
3The first graph in the caption is _yao_ . The second graph is fragmentary; and is written _bei_ 北 in _MWD_ , vol.4, "Transcription," read as _bei_ 背 (back). Li Xuequin (1991: 9) compares _MS_ II.C.31 to the _Yinshu_ exercise written _yaohong_ 榣 弘, read as _yaohong_ 摇 肱 (swinging the upper arms; _YSSW_ : 83). It is probable that the fragmentary second graph in the caption should be written 弘, as in the _Yinshu_. The _Yinshu_ exercise may be related to the drawing: "Swing both upper arms in front, like the hitting position."
4The caption is the single word _shen_ 信 (stretch). Ma Jixing suspects that the scribe omitted _niao_ 烏 above _shen_ (1992: 859, n. 1). While I would not emend the caption, the exercise is probably related to the _niaoshen_ 烏 伸 (bird stretch) mentioned in _Zhuangzi_ 15, 237; and _Huainanzi_ , 7.105. The Cheng Xuanying commentary in _Zhuangzi_ explains _niaoshen_ as an imitation of a bird in flight with feet extended. The _Yinshu_ includes an exercise named _jishen_ 鷄 信 (chicken stretch), which it says "benefits the shoulder and ham" ( _YSSW_ : 86). Altough the text does not describe how to execute the exercise, the therapeutic indications seem relevant to the figure in _MS_ II.C.32.
1 _MS_ II.C.34–44 are drawn in the fourth register of the manuscripts.
2熱 in _MWD_ , vol.4, "Transcription," should be transcribed as 旲, which is scribal error for _jiong_ 炅 (hotness; see Tang Lan 1979: 10). _Jiong_ is often used synonymously with _re_ 熱 in the sense of hot. _Jiongzhong_ 炅 中 (internal hotness) in _MS_ II.C.35 is equivalent to _rezhong_ 熱 中, which occurs as an ailment name in _MS_ I.B.8 (see also the occurrence of _jiongzhong_ for _rezhong_ in _Suwen_ 62, 17.4a).
3 _Wenbing_ 溫 病 (warm ailment) occurs as a generic term for ailments that arise due to unseasonal warmth in _Suwen_ 71, 21.3b. The ailment in _MS_ II.C.36 may be related to _wen_ as described in _Maishu_ , "Ailment List": "When the head and body are painful and sweat dries up before coming out—it is _wen_ " ( _MSSW_ : 72).
4"Radial-cord" translates _wei_ 維. The eight radial-cords denote the eight compass directions in terms of the analogy between net-cords radiating from a center and the axial structure of the cosmos. The cosmological exercise in _MS_ II.C.37 must be related to the exercise named _bajing zhi yin_ 八 經 之 引 (pulling the eight warps-strings) in the _Yinshu_ (the manner of performing the exercise is not described; _YSSW_ : 86). The exercise also forms part of an allusion to macrobiotic hygiene in the poem "Zibei" 自 悲 in the poem cycle "Qijian" 七 諫 in _Chuci_ , 13.15a: "I pull the eight radial-cords to guide myself, ah! I swallow Drifting Flow to prolong life."
5I read 睤 as _bi_ 髀 (ham); the same usage is attested in _MS_ I.B.2.
1I read 摢 as _hu_ 謼 (shout). _Huainanzi_ , 7.105, includes an exercise named _yuanjue_ 蝯 躩 (gibbon jumping). Perhaps the graph in _MS_ II.C.40 should be read as a word meaning to jump, but I do not know what the word might be and the drawing is too fragmentary to help in determining the nature of the exercise.
2The _xiongjing_ 熊 經 (bear ramble) is mentioned in _Zhuangzi_ 15, 237; and in _Huainanzi_ , 7.105. Commentators have identified the exercise as imitating a bear climbing a tree (Cheng Xuanying in _Zhuangzi_ ) or as bear-like movement (Gao Yu in _Huainanzi_ ). Judging from the figure in _MS_ II.C.41, the exercise imitates a bear's gait.
3The transcription of the first graph in the caption is uncertain. Tang Lan surmises that the first graph is the name of an animal (1979: 10). Ma Jixing identifies the graph as a variant of _gui_ 龜 (turtle), but gives no philological demonstration of the identification (1992: 865, n. 1). The second graph is _hen_ 恨, meaning uncertain.
4"Merlin" translates _zhan_ 鸇, glossed in _SW_ , 4A.52a, as _chenfeng_ 鷐 風, literally "bird of the morning wind." The rapid flight of the _chenfeng_ is the opening image in _Shijing_ , Mao 132, 6D.4b. Commentaries all identify _zhan_ / _chenfeng_ as a type of hawk that preys on pigeons and other small birds, undoubtedly a merlin. The exercise in _MS_ II.C.44 evidently imitates a merlin in flight.
_MS_ III
Yangsheng Fang
養 生 方
Recipes For Nurturing Life
_MS_ III.1 (CC1–2)
Non-erection Due to Agedness1
[9] aroma2 {1} [29] blended, then [1] then [6] {1} [?].
_MS_ III.2 (CC3–8)
Another. [2], recipe for making fermented beverage3 with _dianji_ (asparagus).4 Cut up three _dou_ of _dianji_ (asparagus) into one- _cun_ long [1] segments [8] it. Cook using firm reeds with close-set joints (as fuel).5 When it comes to a full boil, stop the fire. When the boil subsides, cook again. If you do not wish to do it like this, two and a half _dou_ [6].1 Put into an old pottery vessel, [1] prepare two _dou_ of glutinous spiked millet, cooking vigorously, and wring it.2 When the vapor is spent, [1] ten days [1] cold [1], then dry [5] and pour over it. Let it sit for two days and [1] fermented beverage, and then it is finished.3 Drink one _sheng_ of this fermented beverage when approaching the inner (chamber).4 The fermented beverage [13]. Store the liquid. {2} [2] and pour over it, until the sourness and sweetness [2] and drink it. Even [20]. It makes a man immediately have an erection. {2} [?].
_MS_ III.3 (CC9–10)
Another. [5] {2} [?] {2} [?].5
_MS_ III.4 (CC11–12)
To Make Sweet-liquor6
To make sweet-liquor take glutinous panicled millet and rice [24] rice. When the sweet-liquor is done, then every morning drink your fill. [6] {1} [?].
_MS_ III.5 (CC13–17)
Non-erection
To treat non-erection, at dawn prepare gruel made with excellent water and [2]. Take satiation as the standard.7 [15], and [1] take it out. Twice like this, and it will become erect. Do not [2] {6} [2] {1} [1] water [1] it. [6] handful, use [2]. After that, drink one (dose) a second time. And after that [1] a third time, not exceeding three drinks. After it becomes a jade rod,8 engage in intercourse9 [2]. When drinking it, do not follow with [8] drink. If (the semen) is already spent, splash with cold water,1 without [2] you must drink again. Drink and food [3]. After eliminating water,2 you must use [5] the vapor, make the mouth round3 and raise it, {1} [1]. Gradually exhale the vapor through the nose. [2] {2} [1] {2} [?].
_MS_ III.6 (CC18–20)
Augmentation4
Collect _lai_ (chenopodium) and _xian_ (eupatorium)5 in the fifth month on the full-moon day.6 Dry them in the dark and smith. Also smith _bai songzhi_ (white pine rosin)7 that is [14], using half of each. Wrap well in leather. Drink it once a day. Each time you drink, put a three-fingered pinch into liquor. [13] strength and excel in traveling. Drunk either at dawn or at dusk, (both) are permissible.
_MS_ III.7 (CC21–23)
Pliancy8
Collect swarming beetle larvae1 in the fifth month on the full-moon day. Put them in a bamboo tube2 [1] full. The length of the bamboo tube should be five [15] it. Set it in a slotted steaming pot, laid on [1],3 and cook. When moisture rises [2] and take it out. Once again [16]. If it does not take effect, then take some medicine the size of a grain of glutinous panicled millet from inside the bamboo tube [?].4
_MS_ III.8 (CC24–25)
Another. In the fifth month [1] _fuling_ (pine truffle) that is just yellowed. Then [22] {4} [?]
_MS_ III.9 (CC26–27)
Another. To cultivate the inside, pound _wu_ [27] {2} [?].5
_MS_ III.10 (CC28–29)
To Make Mash-liquor1
Use three _dou_ of fine liquor to soak wheat [16] it becomes mash-liquor, and drink it. A man [3] boil _xie_ (scallions) in formula sweet-liquor2 [?].
_MS_ III. 11 (CC30–31)
Cultivation3
Take4 one rooster, pluck it alive, and [1] wash it. [9]. Dry in the dark and smith, using the same amount as the chicken.5 [1], making them the size of [9]6 medicine. [1] the liquid to soak dried-meat slices for three days. Eat four _cun_ of the dried-meat slices. Sixty-five.7
_MS_ III.12 (C32)
Another. Take twenty wasp larvae1 and place them in one cup of sweet-liquor. [2] and drink it at midday. Ten.2
_Yi_3
_MS_ III.13 (C33)
Another. Soak one hundred wasps in one cup of fine sauce. Remove them after one day and one night. Use the liquid to soak two-ninths _sheng_ of thick roasted-grain meal.4 Each time you eat (the medicine), drink a three-fingered pinch in liquor.
_MS_ III.14 (C34)
Another. Pingling Lü's way of pleasure.5 Dry in the dark snails (removed) from the shell and smith. If you want twenty, use seven pinches; if you want ten, use three pinches—and one cup of liquor.6
_MS_ III.15 (CC35–36)
Wheat-and-egg7
At dawn regularly break a chicken egg and put it in liquor. Drink before (the meal). The next day, drink two (eggs), and the next drink three. Then begin anew drinking one (egg), the next day two, and the next three. In this fashion use up forty-two eggs. It makes a man strong and increases the beauty of his complexion.8
_MS_ III.16 (CC37–38)
Another. In the eighth month collect _tulu_ (dodder) fruit. Dry in the dark. When dry, split and remove the grains. Smith and wrap in leather. When spring arrives, beat in virile-bird egg liquid.1 Make balls the size of rat feces and dry in the dark, [1] put eight balls into soybean sauce and eat.
_MS_ III. 17 (C39)
Another. [1] one spring-bird egg.2 Break, and toss it into roasted-grain meal made from malt. Make it into balls the size of a large cow-louse. Eating many is good.
_MS_ III. 18 (CC40–41)
Another. [?].3 {1} [1] {1} [1] {1} [?].
_MS_ III. 19 (C42)
Another. To cultivate Yin, use sauce to soak [18] in it.
_MS_ III.20 (C43)
Washing the Male Organ4
[16] three _dou_ , and soak one _dou_ of _zi_ (catalpa) fruit for five days. Wash the male organ with it, and the male organ becomes strong.
_MS_ III.21 (C44)
To Cause Burning5
Collect snails1 in the fifth month on the full-moon day. Soak [5] cloth [1] {1}. Dry in the dark. Use [2] becomes hot.
_Yi_2
_MS_ III.22 (CC45–46)
Another. Take dried _jiang_ (ginger), _gui_ (cinnamon), _yaotiao_ ,3 _shechuang_ (cnidium), and [2]. Smith all of them. (Taking) equal amounts of each, blend with honey or _zao_ (jujube) fat4 and make balls the size of a fingertip. Wrap in loose-weave cloth and insert into the inside.5 The hotness is subtle.
_MS_ III.23 (CC47–50)
Another. In the fifth month collect three _dou_ of snails and two _dou_ of _tao_ (peach) fruits. Stir together and put into a crock. Pour in three _dou_ of fine vinegar. Cover and seal with mud. Bury inside the stove, making it [2] three _cun_. Fill in the top until level with the ground.6 Cook over it during the day; the fire [1] be extinguished.7 Remove after four days. Filter8 and discard the dregs. Use the liquid to dye a three _chi_ piece of cloth. Dry in the dark, then immediately dye again. When the liquid is used up, wrap the cloth well—do not let it be loosely [1]. When engaging in intercourse,1 take a piece the size of the palm and insert it in a nostril. It itches slightly and is hot. If pressed on the arm, the arm itches greatly and is fiercely hot. Do not let it touch the face. If it touches the face, the itching is unbearable.2 Whatever amount of cloth you make, use this to determine the proportions.
_MS_ III.24 (CC51–52)
Increasing Craving3
[1] _fuling_ (pine truffle) and discard the dregs.4 Use the liquid to fatten a suckling pig. Feed it to the woman.5 It makes her increase in sweetness and makes her inside6 become fine. Incinerate and smith the inner part of cow horn. [1] dried _jiang_ (ginger) and _jungui_ (curled cinnamon). Combine them [3] put in a sack. Soak it in gruel vinegar and insert into the inside.
_MS_ III.25 (C53)
Another. Blend [1] liquid with choice beef or venison.7 Have the woman insert it herself deep inside her prohibited part.8 [?].
_MS_ III.26 (CC54–56)
Another. Pare _xu_ (oak) wood, removing the bark and bad spots, and hurriedly chop it. Boil in water [2] vapor [12] and becomes clear. Take the liquid and discard the sediment. Once again boil the clear liquid until it is evaporated.1 When dry, [16] {1}, for the time it takes to eat, and wash with water. It keeps for seven or eight [3].2 Previously [?].3
_MS_ III.27 (CC57–58)
Another. Take a stillborn chick.4 {5} [24] moisten, and dry in the dark. When dry [?].5
_MS_ III.28 (CC59–60)
Play6
[2], take a gecko [1] {1} [3] deep.7 When finished, bury it beneath the mouth of the stove, in depth [5] water, and dye it in the liquid. Dye the woman's arm with it.1 If the woman plays with a man, the [1] then cracks and breaks. If [1] sleeps, then it vanishes.2
_MS_ III.293
Take a gecko, place it in a new jar, and place cinnabar in the jar. Have the gecko eat it. Wait for it to die, then smith, [1] to paint the woman's arm or body. If she plays with a man, it instantly loses its brightness.[?]
_MS_ III.30 (C61)
To Remove Hair4
If you want to remove hair—when (a woman) who has newly given birth shaves5 for the first time, if she first shaves the lower (body) and then shaves her hole, the hair will be removed.6
_MS_ III.31 (C62)
Another. Fry white-necked earthworms.7 Blend in spider webs and _kuhu_ (bitter gourd), and quench iron (in the liquid).8 Then spread the liquid on it.
_MS_ III.32 (C63)
Another. Pluck out (the hair) in the fifth month, and spread formula sweet-liquor on it.1
_MS_ III.33 (C64)
Ailing from Genital Swelling2
Beat _liufu_ (willow catkins).3 Combine with rancid lard and knead until blended. Spread it on the swellings. When finished, wrap with cloth.
_MS_ III.34 (CC65–69)
To Facilitate Approaching the Inner (Chamber)4
Recipe to facilitate approaching the inner (chamber). Cut up two thirds _dou_ of _dianji_ (asparagus) root into pieces one _cun_ long, and wash well. Also take a whole black rooster, closing the wings to make [3] the heart, brain, and breast of three chickens. Pour two _sheng_ of water into an old iron kettle, and boil them together. Cook using firm reeds with close-set joints (as fuel). Let it come to a full boil once, then [3] and discard the dregs.5 Use the clear liquid to boil the heart, lung, liver, and [1] of a black male dog that is one whole year old or older. Use firm reeds with close-set joints [8] _jue_6 [4] five substances [2] {1} [6], Eat it at the late afternoon meal,7 in whatever amount you wish.[?].
_MS_ III.35 (CC70–73)
Another. To approach the inner (chamber) [29] _wuhui_ (monkshood)8 that are large, four [19]. Take two large handfulls of fresh steamed _chejian_ (plantain).1 The vapor [12] _chejian_ (plantain) [3]. Put it in a cloth sack or (?).2 When you want to engage in intercourse, then eat [1] it.
_MS_ III.36 (CC74–76)
Another. To cultivate the inside.3 Collect bulging fungi4 that have just started to bulge forth, and dry them in the dark [without]5 letting them see the daylight. Wait until they are dry. [1] take five _bai_ [1],6 two _mendong_ ,7 and one _fuling_ (pine truffle). Then pestle them together. Soak in water, using just enough to cover. [1] and press8 to obtain the liquid. Use it to soak the bulging fungi, again using just enough to cover. Then remove and dry them. Let them become completely dry, then smith. Drink a three-fingered pinch in one half cup of [1].
_MS_ III.37 (CC77–80)
[?] Napkin9
Take a chicken that is just able to produce eggs.1 Pluck it alive, completely removing the feathers except at the tip of both wings. Tie it so it hangs from a pole, [4] the chicken rub against a large bee hive, and let the bees sting it. When (the bees) are spent, shift the chicken again until it is stung to death.2 When it dies, remove and discard its [4] its flesh, and smith well. Sift through cloth.3 When finished, mix it with _yi zao_ (jujube) fat,4 and daub it on a cloth napkin. Then rub the feet with the napkin [3] four or five and then repeat. Stop after using two napkins. [1] the feet have little vapor, this makes a person have an abundance of vapor.5
_MS_ III.38 (CC81–84)
Another. To prepare napkins. Take one _sheng_ of _yangsi_ ,6 one _sheng_ of red ants, and twenty _banmao_ (blister beetles). Soak them together in one half _dou_ of fine [1], covering [4] the liquid. Soak one _chi_ of finely woven cloth in it. After it has soaked, dry over heat. When dry, soak again. When the liquid is gone, take _gu_ (paper mulberry) and _yitong_ (paulownia) liquid [5], and daub it on the cloth that was soaked. Dry it, then store well. When engaging in intercourse, rub the jade whip with it, and the horse will then be startled.1 _Yangsi_ [5]. Its shape is like a small [2] and bites2 people.
_MS_ III.39 (CC85–87)
Another. [2] _shechuang_ (cnidium), two ninths _dou; lin_ root,3 two and a half _dou; fanshi_ ,4 one three-fingered pinch; _one-chi_ long _gui_ (cinnamon), five sticks; [5] {3} [2], one small bunch. Use grass-filtered vinegar produced in the third month5 to [1], and boil until done. Let it come to the boil, and steep6 the cloth napkin in the [3] liquid. When having intercourse7 [12] it. It makes the skin taut and not sag. Moreover, it makes the man {1} [?].
_MS_ III.40 (C88)
Another. Take two _zaojia_ (honey locust fruits).8 Smith, and pour one third _dou_ of water onto it. Stir well, then soak a napkin in it. Leave for one whole day and take it out. [3] dry, immediately soak it again.
_MS_ III.41 (C89)
Another. Dry rat testes in the dark, and smith. Crack open _yi_ bird eggs,1 combine (with the smithed testes), and daub it on a new cloth napkin. When going to bed,2 wipe the male organ and the female organ with it.3
_MS_ III.42 (CC90–91)
Another. Take one _dou_ of snails and divide into two portions. Soak one portion in vinegar and dry in the sun. During the winter set it on the stove until it bubbles very rapidly, then remove the snails. [4] the remainder as before. Then soak a napkin in it until the liquid is gone. When finished, use a soaked napkin when going to bed to wipe the male organ. It also makes the female organ [?].4
_MS_ III.43 (CC92–95)
Another. Four _dou_ of snails; four _dou_ of fine fermented milk; one fourth _sheng_ of _tianmu_ ;5 _taoke_ (peach fuzz)6 the size of a _zao_ (jujube); twice seven _mulou_ heads;7 [9], one half _sheng_. Soak together in the fermented milk. When finished, take the liquid and use it to [3] cloth [2] soak, stopping when the liquid is gone. [1] engaging in intercourse, dampen [2] and rub the jade whip, and the horse will then become unrestrained. The substance called _tianmu_ is [3] and eats _tao_ (peach) and _li_ (plum) flowers. _Taoke_ is the fuzz from peach fruits when they are small. As for _mulou, jiequan_ [12] {2} [2] is the shape of the skin of a _gan_ (Job's tears fruit).8
_MS_ III.44 (CC96–97)
Another. Incinerate [1] _fu_. Spread out a napkin in the [11] {1} [5]. Rub1 the female organ with the napkin, and the horse just then [?].2
_MS_ III.45 (CC98–101)
[To Lighten the Body and Increase Strength]3
Another. If you wish to lighten the body, take {2} [24] {1} [1]. Use after the meal. In spring and autumn [29] them, four _dou_ each, {1} [3] {1} [?].
_MS_ III.46 (C102)
To Purge the Inside and Increase Vapor4
[2] _zi_ meat5 that is fat [3] lard. Dry them all in the dark and smith. Use one three-fingered pinch [?].
_MS_ III.47 (CC103–104)
Another. [1] {2}. The medicine uses bird [3], _zixie_ (water plantain), _sui_ ,6 _suanzao_ (sour jujube), [12] in equal amounts, and smith. Then blend with _songzhi_ (pine rosin) and make balls. Use after the meal, the amount as you [?].
_MS_ III.48 (CC105–106)
Another. In spring and fall collect _yuan_.1 Dry it in the dark and smith. Take winter _kui_ (mallow) seeds and smith. Combine them. Use a three-fingered pinch [12] increases the inside.
_MS_ III.49 (C107)
Another. [2], _fangfeng_ (saposhnikovia), and [1]—all three in equal amounts. Use _jie_2 in an amount that matches the three substances. Smith. Use a three-fingered pinch after the meal [?].
_MS_ III.50 (CC108–109)
Another. Slice beef thinly. Then take a one _cun_ piece of _beixie_ (yam)3 and set [2] in the beef. Cook until it bubbles, stop, cook again until it bubbles, and stop again. After the third time remove the meat and eat it. Store the liquid and _beixie_ (yam) to reuse for boiling meat, discarding them after the third use. [2] the person's ring becomes increasingly strong4 and it does not harm a person. You may eat whatever amount of meat you wish.
_MS_ III.51 (C110)
Another. Take _baiyuan_ (daphne) root. Dry in the dark and smith. Blend with horse sauce. [1] balls, the size of a finger-tip. [6] hole. It swells and becomes large.5
_MS_ III.52 (C111)
Another. _Mandong_ ,6 _shu_ ,7 and _fangfeng_ (saposhnikovia): smith separately in equal amounts. Combine them [?].
_MS_ III.53 (C112)
Another. Take two portions of _jungui_ (curled cinnamon), four of _xixin_ (asarum), one of _qiu_ (wormwood),1 one of oyster, and two of Qin _jiao_ (Qin zanthoxylum). Use a three-fingered pinch after the meal. It makes a person strong.2
_MS_ III.54 (CC113–14)
Another. Grind _ru_3 while wet and put it in a container. Eat and drink liquor until full, [2], and sniff it. [2]; smith well, separately, and combine both. Three-night-old rooster blood [6].4 Pack it in silk. {3} [1] {2} [1] {1} [1] {1} [3] {1}. One section of bamboo with widely spaced joints and a diameter of three _cun_ [?] __.
_MS_ III.55 (C115)
Another. In autumn collect [ _ban_ ] _mao_ (blister beetle)5 [2] head [5] three [3] it. You become strong.
[1]6
_MS_ III.56 (C116)
Another. Take [16] strong.
_MS_ III.57 (C117)
Another. [2] liquid and set it in a bamboo tube. Virile-bird [9]7 put it in water, and drink it.
_MS_ III.58 (CC118–19)
Another. Use pig lard the size of a hand. Have bees [17] four _dou_ of pure liquor lees. Smith well [1]. When you do not want it, wash it off.8
_MS_ III.59 (C120)
Another. [5] in equal amounts. Also take [2], and use after the meal.
_MS_ III.60 (CC121–23)
Another. [3] large male rabbit. Skin and remove the intestines. Take _four-cun_ long _beixie_ (yam), one handful; _zhu_ (atractylodes), one handful; and _wuhui_ (monkshood), ten [3] pare the skin and chop finely. Add the large male rabbit meat to the medicine, mix completely, and dry without letting it see the sun. After one hundred days wrap in [1]. Use one three-fingered pinch after the meal for one hundred days. It keeps for six or seven years. [1] eating it is allowed. Use as you wish.
_MS_ III.61 (CC124–25)
Another. Take _xixin_ (asarum); dried _jiang_ (ginger); _jungui_ (curled cinnamon); and _wuhui_ (monkshood)—altogether four substances. Smith separately. Take four parts of _xixin_ (asaram) to two each of dried _jiang_ (ginger), _jungui_ (curled cinnamon), and _wuhui_ (monkshood). Combine them. Use a three-fingered pinch after the meal. It increases the vapor, and also makes a person's face lustrous.
_MS_ III.62 (CC126–30)
Another. Take two _liang_ each of _baifu_ , _hongfu_ ,1 and _fuling_ (pine truffle); ten nodules of _jiang_ (ginger); and three _chi_ of _gui_ (cinnamon). Smith each separately. Blend them with two _dou_ of fine gruel vinegar. Then take butchered horse loin, ten [1]. Prepare fine dried-meat slices with it, making them the thickness of three fingers. Then soak in gruel vinegar, stirring over and over again. Then drain. After draining, dry in the dark over heat. [4] bubble. Once again soak and dry over heat as before, stopping2 when the liquid is gone. Dry over heat [1] jerky.3 Then pound with a mallet until thin and lustrous, and again dry over heat [3] them, until [1] lustrous. [13] lacquer it with _qi_ (lacquer). When dry, then store them well. Eat three _cun_ at each of the dawn, daytime [1], and evening meals, always before the meal [15] smith separately in equal amounts. Use after the meal.1
_MS_ III.63 (CC131–32)
Scantness When Engaging in Intercourse2
If a man experiences scantness when engaging in intercourse and (semen) is clear, [16] male bird. Blend with the blood of the two to make balls the size of a _suanzao_ (sour jujube).3 Use after the meal. {2}, then [?].
_MS_ III.64 (CC133–34)
[7] _dou_ [15] _. Use_ [1] _hua_ , one half _dou, mula_ [9] _sheng_ [?].4
_MS_ III.65 (CC135–36)
To Cultivate Strength5
[30] the body seems to itch but does not itch,6 {1} [?].
_MS_ III.66 (CC 13 7–40)
To blacken the hair and increase the vapor, take [25] {7} [23] {1}, without letting the fire go out. Thirty [2] smith. Use [2] to wrap. [18]. Prepare the medicine in the eighth month.
_MS_ III.67 (CC141–43)
To prepare sweet-liquor.1 Use one and a third _jin_ of _shigao_ (gypsum); _gaoben_ (lovage), _niuxi_ (achyranthes), [21] two _dou_. {1} [1] the liquid. {1} [?].
_MS_ III.68 (CC144–45)
To increase strength and thoroughly purge foul vapor from the [1], heart, and chest. Take the fruits inside _huai_ (pagoda tree) pods. Set on the stove [13] five fruits. The itching is intense. [1] it and there is no itching, increase it until the body seems to itch but does not itch. [13].
_MS_ III.69 (CC146–47)2
[1] valley, are the places named Great Chamber and Lesser Chamber.3 There are stones there named _pianshi_.4 Take small ones [13] illness and increases longevity.
_MS_ III70 (CC148–51)
Take a butchered horse, dress it, and prepare dried-meat slices. Pound one _sheng_ of _wuhui_ (monkshood)5 and soak it in pure liquor. [1] discard the dregs.6 [10] _yu_ , _mendong_ ,7 each [2]; _beixie_ (yam) and _niuxi_ (achyranthes), five small bunches of each; [1] _jia_ , _jiegeng_ (balloon flower), and _hou_ [1], two _chi_ ; and _wuhui_ (monkshood), ten nodules. Combine and smith. Soak in four _dou_ of pure liquor. Do not discard the dregs. Use [2] {2}. [3] wrap in a leather sack. Eat a three-fingered pinch after the meal. Ingesting it makes the six extremities8 strong and increases longevity.
_MS_ III.71 (CC152–53)
Smith _yunmu_ (mica)1 and melt _songzhi_ (pine rosin) in equal amounts. Combine with whole-wheat flakes2 to make balls, without [1] the hands, making them the size of a _suanzao_ (sour jujube). [1] it. Swallow3 one ball. Daily increase by one ball until the tenth day. The day after, daily eliminate one ball until the tenth day. The day [6] increase and decrease [5]. It makes a person longlived and not become aged.
_MS_ III.72 (CC154–58)
Mash-liquor to Benefit the Inside4
Take _qi_ and [1] stalks5 in equal amounts and [13] four and a half _dou_ of the clear liquid [3] {5} [17] and ferment it. Take blackened _wuhui_ (monkshood), eight nodules;6 [1] take _qi_ and _jie_7 [16] beneath the fermented (grain).8 Seal the mouth of the jar well, so that [25] it is done {3} [26].
MSIII.73 (CCI59–61)
Another. [1], nine _dou_. First [26], two _sheng_ , in it for ten days. Smith [10] remove from the vessel [9] {1}. When ingested for one hundred days, it makes the intestines be without ailments.
_MS_ III.74 (CC162–68)
Another. To prepare mash-liquor. Finely chop _qi_ and _jie_ , one _dou_ of each. Use water, five [4] sieve. Use the liquid to boil _ziwei_ (trumpet-flower) [8] sieve again. Yeast and wheat yeast, one _dou_ of each, [3]. Leave for one whole day, then sieve.1 [4] glutinous panicled millet, rice [3], one _dou_ of each. Combine [1], and rinse it with the yeast liquid, like the usual method for cooking grain.2 Take _wuhui_ (monkshood), three nodules; dried _jiang_ (ginger), five; and _jiao_ [2]—altogether three substances. Chew3 [2] and toss them in. First put the [1] in the jar, and then the fermented glutinous millet on top of that. [1] liquid and pour over it evenly; then pour ten _dou_ of fine liquor over it. Do not stir, [3] daub it with mud.4 In eleven [1] it will be done. Then open and do not filter. Gradually [2] the clear liquid is gone. Once again use [2] liquor to pour over it. Do it like this thrice, and [2].5 Drink one cup at the late afternoon meal. After drinking, rub any places on the body that itch. When ingested for one hundred days, it makes the eyes bright and ears perceptive; the extremities all become strong; and [2] ailments and withering on one side.6
_MS_ III.75 (CC169–70)
Cultivation
Soak four _dou_ of snails in vinegar for two days. Remove the snails and use the liquid to soak [1] meat that has been pounded.7 [1] dog dried-meat slices [2], and soak again in the liquid [2]. Eat one _cun_ of the dried-meat slices to overcome one person, and ten _cun_ to overcome ten people.1
_MS_ III.76 (C171)
To Snap Horns2
Incinerate _chou_3 and smith. Wrap the ash to [1] a bull, and it can snort [flagons]4 and snap horns. Increases strength.
_MS_ III.77 (CC172–74)
Striding5
_Feilian_ , _6 fangkui_, _7 shiwei_ (pyrrosia), _jiegeng_ (balloon flower), and _ziwei_ (trumpet-flower), one small bunch each; _wuhui_ (monkshood), three nodules; [9] large [3] bamboo skin, five _cun; bai tengshe_ or _zang gengshe_ that is three to four _cun_ long,8 or [8]. Smith separately, and combine with [1] or _zao_ (jujube) fat to make balls the size of sheep feces. Eat once every fifty _li_. Dark fungus comes from Luo [8].1 Seven hundred.2
_MS_ III.78 (CC175–77)
Another. _Wuhui_ (monkshood), five parts; _longkai_ ,3 three parts; _shiwei_ (pyrrosia), _fangfeng_ (saposhnikovia), and _futu_ ,4 each [1]. Dry in the dark [8] remove the {1} [2] smith the five substances. Put into liquor for one day and one night. Sieve and discard the dregs. Use the liquid to soak saturated cooked-grain for the time it takes to eat.5 [2] dry. When dry, once again [2] dry. When the liquid is used up, it is finished.
_MS_ III.79 (CC178–81)
Another. _Wuhui_ (monkshood), two parts; north-south facing Yang [1] _gu_ , one part. Smith. Combine and wrap in three layers of finely-woven new white cloth. Horse lard [4] {1} fat chicken [4]. Then boil roof-tile lichen6 that is the length of the middle finger. Put [4] liquid. Remove the lichen and put it in a sack. [4] days discard and bury [2] dregs. When traveling, soak it, scoop7 one cup of east-flowing water, put [14] {3} [3] see the sun, drink it.8
_MS_ III.80 (CC182–84)
Another. [2] dog {2} [?] _wuhui_ (monkshood), one half. Smith them. [?] {1} [?].
_MS_ III.8I (CC185–86)
Another. For striding, take a woman's [28]1 {1} one _dou_. Take [?].
_MS_ III.82 (CC187–88)
Another. [2] {1} [20]. Soak it during the night and dry it during the day. Having used up [3] travel one hundred _li_.
_MS_ III.83 (CC189–90)
Another. When traveling and stopping overnight, call out to yourself: "The Yang side of Tai Mountain. Heaven [5] first [1]. Walls and ramparts that are not intact, [seal] with the metal bar"2 Then perform the Pace of Yu thrice and say: "With a stick of fresh _jing_ (vitex) two _cun_ long I draw a circle around the inside."3
_MS_ III.84 (C191)
Face east and shout: "I dare to declare to the East Lord and Bright Star.4 The person who [1] comes and dares to reach the encircled place, and who beds down on those broken tiles—who is he?" Then return inside the circle.
_MS_ III.85 (CC192–93)
Another. If while striding you are in a hurry and wish to stay ahead, take the cloth of a woman who has never been with a man.1 Tie with hemp and keep it by your breast. When you see a whirling wind, throw (the cloth) at it. When the wind stops, [2] and attach it to your waist.
_MS_ III. 86 (C194)
To Travel Quickly2
Take the hemp thill-rope from an ox-cart and attach it to your waist. If you wish to hurry, bind it once around.3
_MS_ III.87 (CC195–96)
Another. If while traveling you wish to have your feet not hurt, face south, perform the Pace of Yu thrice, and say: "Whatever the water, no disaster; whatever the way, no withering. Give4 me [2]." When finished, take chimney soot [5] and insert it inside the shoe.
_MS_ III.88 (CC 197–204)5
[4] Under-heaven [10] {1}. Possessing vapor you live; lacking6 vapor you die. This [6]. When it is angered yet not large, skin has not arrived;7 when large yet not firm, muscle has not arrived; when firm yet not hot, vapor has not arrived. If you engage in intercourse when skin has not arrived, it droops. If you engage in intercourse when muscle has not arrived, it retreats. If you engage in intercourse when vapor has not arrived, it collapses. Therefore, the sage must [2] it.
Tang journeyed to the Blue-gem Terrace.8 Chen [2] at the South Palace,9 and (Tang) asked: "When man and woman achieve unison and are a matched pair, how can it be accomplished without injuring the body?"1 (Chen) replied: "What assists life is eating; what diminishes life is lust. Therefore, the sage must have a model.2 The first is 'river deer [butting]';3 the second is 'gibbon grabbing': the third is 'cicada clinging'; the fourth is 'toad'; the fifth is 'fish gobbling'; the sixth is '[dragonfly].' The first is 'cloud stone';4 the second is 'dry gourd';5 the third is 'glistening plug';6 the fourth is 'crouching [1]';7 the fifth is '[2].' The first is 'go up';8 the second is 'go down'; the third is 'go to the left'; the fourth is 'go to the right'; the fifth is 'enter deeply'; the sixth is 'enter shallowly'; the seventh is 'rabbit bolting.' The first is 'blowing'; the second is 'biting.'1 The first is '[2]'; the second is 'shaking.'2 The first is 'secure the taste';3 the second is 'bring vapor'; the third is 'exercise the fruit';4 the fourth is 'attend to the joints.'"5
_MS_ III.89 (CC205–217)
[1] Discourse6
[1] {1} the auspicious day7 of the third month at [1]. Yu then [2] and entered the Circular-jade Chamber.8 His shape was transformed and his complexion was extremely virile and beautiful, like someone in the vigor of manhood. The flock of beauties9 beheld him [16] {3} [1] {4} [1] {10} [21]. My whiskers and eyebrows had already changed, blood and vapor was not sufficient, and I felt no pleasure.10 [25] {5} [1] {1} [29] at dusk awoke. South Beauty [4] {3} [31] not able to desist. West Beauty [12] {2} [16]1 severe ailment and [1] and did not desist. I feared suffering excess and not awakening. Young Beauty [1] {3} [15] {1} [1] {8}. Young Beauty came forward and replied: "The woman's [pleasure]2 is [13] suffer illness in youth. If you advance violently and withdraw violently, the good vapor is not maintained."3 Yu said: "Well spoken, indeed!4 [16]. I wish to conjoin vapor so that man and woman propagate.5 How is it to be accomplished?" Young Beauty said: "The way of conjoining vapor must always [11]6 {2} [1] {1}, vapor is not [1] clogged." Yu said: "Well spoken, indeed! Now my blood and vapor collect outside [11]7 said: "Why does Milord not make a boiled-dish of _mao_ (woolly grass) and _ai_ (mugwort), take the broth {7} [15] {7} Ascend on the left and descend on the right; and do not reach completion violently."8
_MS_ III.90 (CC218–19)
Eating and Pulling1
To assist in increasing vapor, when eating and drinking always shift the Yin and move it. When in bed once again pull it.2 Thus it is said: "Give it drink [2]; and also instruct and counsel it."3 Pull on the right and bend the left foot.4
_MS_ III.915
(Right side, inside the drawing)
red bead6
[1] strings7
(Left side, inside the drawing)
attached [1]1
(right side, outside the drawing)
hairpin light2
[1] rat3
[2]4
wheat teeth
grain fruit5
_MS_ III.926
Non-erection Due to Agedness ( _MS_ III. 1–3)
To Make Sweet-liquor ( _MS_ III.4)
Non-erection ( _MS_ III.5)
Augmentation ( _MS_ III.6)
Pliancy ( _MS_ III.7–9)
To Make7 Mash-liquor ( _MS_ III. 10)
Cultivation ( _MS_ III.11–14)
Wheat-and-egg ( _MS_ III. 15–19)
Washing the Male Organ ( _MS_ III.20)
To Cause Burning ( _MS_ III.21–23)
Increasing Craving ( _MS_ III.24–27)
Play ( _MS_ III.28–29)
To Remove Hair ( _MS_ III.30–32)
Ailing from Genital Swelling ( _MS_ III.33)
To Facilitate Approaching the Inner (Chamber) ( _MS_ III.34–36)
[?] Napkin ( _MS_ III.37–44)
To Lighten the Body and Increase Strength ( _MS_ III.45)
To Purge the Inside and Increase Vapor ( _MS_ III.46–62)
Scantness ( _MS_ III.63–64)
To Cultivate Strength ( _MS_ III. 65)
[?]
[?]
[?]
[?]
Mash-liquor to Benefit the Inside ( _MS_ III.72–74)
Cultivation ( _MS_ III.75)
To Snap Horns ( _MS_ III.76)
Striding ( _MS_ III.77–85)
To Travel Quickly ( _MS_ III.86–87)
[?] ( _MS_ III.88)
[1] Discourse ( _MS_ III.89)
Eating and Pulling ( _MS_ III.90)
Fig. 13 Facsimile of _MS_ III.89 (partial) – 92
1 _MWD_ , vol. 4, "Transcription," n. 2, notes that the right end of the silk sheet is damaged. It is not certain if _MS_ III. 1 is the first recipe; and the numbering of columns begins with the first extant fragments of text. The "Transcription" adds the heading for the first recipe category at the beginning of C1 based on the list in _MS_ III.92. The headings are written above the first column of text of the first recipe in a given category. "Non-erection" translates _buqi_ 木 起. _Buqi_ is a standard term for impotence in later medical literature. For example, a recipe for pills to bolster the vapor of the kidneys in _Qianjin yaofang_ , 60.22b, includes "when the Yin (i.e. penis) shrivels and does not become erect ( _buqi_ )" among the many conditions treated by the pills.
2The reference to "aroma" suggests that the recipe concerns a fermented beverage as in _MS_ III.2.
3醬 in _MWD_ , vol. 4, "Transcription," should be transcribed as _jiang_ 漿. _Jiang_ (fermented beverage) is named as one of the "four beverages" in _Zhouli_ , 5.7a. According to the Zheng Xuan commentary, " _jiang_ is the vinegar beverage ( _daijiang_ 酨 漿) of today (second century A.D.)."
4Tao Hongjing identifies _dianji_ 顛 棘 as an alternate name for _tian mendong_ 末 釁 冬 which is listed in _BC_ (GM, 18.37). _Dianji_ is evidently synonymous with _dianle_ 顛 勒 which is given as an alternate name in BC. _Tian mendong_ is asparagus (ZY: no. 0645, _Asparagus cochinchinensis_ [Lour.] Merr. And other spp.). The use of _tian mendong_ in Han _xian_ -cult dietetics is attested in the _Liexian zhuan_ (Kaltenmark 1953: 136).
5 _Huan_ 雚 is a reed (genus _Phragmites_ ) that is smaller than _wei_ 葦 ( _GM_ , 15.59, and Li Shizhen commentary).
1Presumably the recipe gives an alternative method for preparing the _dianji_ , and two and a half _dou_ refers to the amount of the drug.
2I read 足 as _zhuo_ 捉 (wring). A cloth is used to separate the liquid from the millet by wringing (see _MS_ I.E.13).
3Presumably the millet and boiled _dianji_ are combined and left to ferment for two days.
4I.e. before sexual intercourse (see _MS_ III.34).
5 _MWD_ , vol. 4, "Transcription," n. 1, notes that there is a break in the text between C9 and C10; it is not clear how many columns might be missing.
6"Sweet-liquor" translates _li_ 醴. _SW_ , 14B.34b, describes _li_ as a liquor that is ready to drink after fermenting overnight. _Zhouli_ , 5.6a, includes _li_ as one of five liquors known as _ji_ 齊 (a reference to the "proportionate measuring" of the grain and other ingredients); and the Zheng Xuan commentary describes _li_ as a sweet, unfiltered liquor.
7I.e. drink until sated. For the idiomatic use of _gu_ 故 meaning "standard," see _MS_ I.E.99.
8 _Ting_ 珵 is attested as an orthographic variant of _ting_ 挺. See _SW_ , 1A.25a, and Duan Yucai commentary. The _SW_ glosses _ting_ as follows: "It is a large scepter ( _gui_ 圭), three _chi_ long and tapered on the upper part, with a hammer-shaped head." The ritual "jade rod" with ts hammer-shaped head denotes the erect penis in _MS_ III.5.
9I suspect that _yong_ 用 has the sense of engaging in intercourse here (see _MS_ III.23).
1"Spend" translates _shi_ 施, denoting ejaculation. The sexual denotation of _shi_ is common in later sexual literature; see, for example, the passage concerning the number of ejaculations permitted depending on the man's age and physical condition in _Ishinp ô_, 28.23b. _MS_ IV.3 describes washing the penis to cause detumescence after having used an aphrodisiac to make it erect, which probably explains the use of cold water in _MS_ III.5.
2 _Qishui_ 棄 水 (eliminate water) is an idiom for urination attested in the _Yinshu_ ( _YSSW_ : 82).
3I read _gou_ 鉤 as synonymous with _gui_ 規 (compass, round). The usage is attested in _Hanshu_ , 87A.4a. _MWD_ , vol. 4, "Transcription," n. 3, suggests reading the graph as _xu_ 呴. While the end of _MS_ III.5 is concerned with some kind of breathing exercise, _xu_ does not make sense grammatically here.
4I agree with Li and McMahon that _jia_ 加 (augmentation) refers to increasing the size of the erect penis (1992: 151), rather than to increasing vitality with tonics as suggested in _MWD_ , vol. 4, "Transcription," n. 1. This denotation is unmistakable in the recipes for _neijia_ 内 加 (inside augmentation) in _MS_ IV. 3–7. The references to "strength" and "traveling" at the end of _MS_ III.6 suggest that what is good for the male organ is also good for male vitality in general.
5蕳 in _MWD_ , vol. 4, "Transcription," should be transcribed as _xian_ 閒. I nevertheless agree that the graph is to be read as _xian_ 蕑, another name for _lan_ 蘭 (eupatorium).
6I.e. the fifteenth day of the lunar month. The fifth month is the time of the summer solstice when Yang potency peaks, making it an optimal time to collect drugs possessing Yang properties (see _MS_ I.E.95).
7For the use of pine rosin in Han _xian_ -cult dietetics, see Kaltenmark 1953: 54, n. 2.
8The recipe category is entitled _suan/*suan_ 筭. I suspect that the graph is to be read as a phonetic loan for _sun_ /* _sjuan_ 巽, in the sense of "pliant." Confirmation of this loan usage occurs in the Mawangdui manuscript of the _Yijing_ hexagrams, which writes _suan_ 筭 for the name of the hexagram written _sun_ 巽 in the received _yijing_ (Han Zhongmin 1992: 175). References to a position "beneath the bed" in the hexagram text hint at a possible sexual connotation for _suan/sun_. And a textual variant in the Mawangdui manuscript makes a sexual interpretation entirely plausible. The explanation of the bottom line of the hexagram in the received _Yijing_ is, "In advancing and retreating ( _jintui_ 進 退) it is beneficial to have the rectitude of the military man." The corresponding text in the Mawangdui manuscript is, "In advancing inside ( _jinnei_ 進 内) it is beneficial to have the rectitude of the military man." The words "advance inside" suggest sexual intercourse; and in this context perhaps _zhen_ 貞 should be rendered "erection" rather than "rectitude." Coming after Augmentation, which concerns increasing the size of the penis, the category Pliancy is concerned with impotence. Significantly, _suan_ occurs in _MS_ I.E, fragment 7 ( _MWD_ , vol. 4: 79), in a recipe to treat _wei_ 痿 (impotence). The recipe is one of several added to the end of _MS_ I.E after the original redaction. The meaning of _suan_ is not clear in the fragment, but I would guess that it is related to _suan_ in _MS_ III.7.
1I read _xiang_ 鄉 as _xiang_ 蠁 and _rong_ /* _njung_ 軵 as a phonetic loan for _yong_ /* _rung_ 蛹. The compound _xiangyong_ is not attested in received literature, but I suspect that it refers to the larva of an insect, probably the scarab beetle. _Guangya_ , 10B.11a, glosses _tuyong_ 土 蛹 (earth _yong_ ) with _xiangchong_ 蠁 蟲 ( _xiang_ bug). _GM_ , 41.3, associates these names with a type of grub that is cultivated by digging a pit and filling it with grain and manure; the larva produced is comparable to _qicao_ 螬, the larva of the scarab beetle ( _ZY_ : no. 4934, _Holotrichia diomphalia_ Bates).The method is first described in _Huainan wanbishu_ , 1.11a: "In autumn and winter put mixed glutinous millet in a ditch and _qicao_ are produced." The adjective _cheng_ 蚕 (swarming) constitutes additional confirmation that _xiangyong_ in _MS_ III.7 is an insect drug; _SW_ , 13A.53a, glosses _cheng_ as "bugs swarming."
2 _MWD_ , vol. 4, "Transcription," erroneously transcribes 籥 人 籥 The first _yao_ 籥 is not written in the text and should be excised from the transcription.
3 _MWD_ , vol. 4, "Transcription," writes 笇 for the frangmentary graph in the lacuna, which it reads as _ce_ 策 (bamboo strip). Both the transcription and reading are doubtful. Qiu Xigui suggesests that the graph in question might be _ji_ 箕 (winnowing basket; 1992: 534). I treat the graph as illegible and mark a lacuna.
4Presumably it may be necessary to use the medicine more than once before the desired effect (an erect penis) is achieved.
5 _MWD_ , vol. 4, "Transcription," n. 1, notes a break in the text between C27 and C28; it is not clear how many columns might be missing.
1"Mash-liquor" translates _laozhuo_ 醪 酌 _Zhuo_ is a verb meaning "pour liquor," but here it is a generic term for liquor. _SW_ , 14B.35a, describes _lao_ as a liquor in which the liquid and dregs are combined. Judging from the recipes for making _bailao_ 白 醪 in _Qimin yaoshu_ , 7.394, the liquor is filtered after an initial period of fermentation, then a mash of freshly cooked grain is added. The liquor is ready to drink when the mash floats to the surface of the fermentation jar. According to one recipe, the liquor is "sweet like milk." _MS_ III.74 provides a recipe for _lao_ that is a potent herbal cordial unlike the _Qimin yaoshu_ recipes.
2"Formula sweet-liquor" translates _chengli_ 稱 醴. I suspect that _cheng_ refers to the fact that the ingredients of the liquor are balanced according to a formula; and that _chengli_ is synonymous with _liji_ 醴 齊, the name for _li_ as one of the five _ji_ (liquors made with "balanced proportions") in _Zhouli_ , 5.6a (see _MS_ III.4).
3 _MWD_ , vol. 4, "Transcription" restores the recipe heading _zhi_ 治 to the text based on the list in _MS_ III.92. In _MS_ III.92, the scribe evidently forgot once again to record this recipe category, since the graph in written in smaller script above the first register between the names of the sixth and eighth categories. Besides _MS_ III.11–14, _MS_ III.75 also belongs to the category Cultivation. The recipes concern increasing Yang vitality—as indicated by the use of substances like roosters and wasps—but it is not entirely clear whether the intended result is related to physical strength or to sexual prowess. I suspect that the two are not distinguished.
4以 in _MWD_ , vol. 4, "Transcription," should be transcribed as _qu_ 取.
5The drug or drugs used in the recipe are lost in the lacuna.
6The medicine is probably formed into balls of a certain size.
7Despite the lacunae, it is evident that dried meat is soaked in a medicinal liquid and eaten. The number sixty-five probably refers to people. _MWD_ , vol. 4, "Transcription," n. 4, speculates that the number is related to sexual prowess and refers specifically to multiple female partners, citing a recipe in _Ishinp_ ô, 28.40b, entitled, "recipe for cultivating the man with the goal of vigorously engaging in bedroom activity so that in one night he (has intercourse) over ten times without stopping." The conclusion to the recipe states that, "Sire Cao consumed this and in one night passed through seventy women" (cf. Wile 1992: 101). The speculation is plausible. Similar use of numbers occurs in _MS_ III.12, 14, and 75. The wording in _MS_ III.75 suggests that physical strength to overpower opponents is the objective, which indicates to me that the category Cultivation concerns both physical strength and sexual prowess.
1I read 駘 as _tai_ 胎 (embryo, larva; see _MS_ I.E.223).
2I.e. the tonic is good for entertaining ten partners, for sex or physical combat.
3 _Yi_ 易 is written in large script below the recipe. The graph occurs again at the bottom of C44 in _MS_ III.21. A second large-script graph, which is unidentified, is written at the bottom of C115 in _MS_ III.55. I do not know why the graphs are written on the manuscript in the way that they are, nor do I know what _yi_ means—other than to guess at a meaning like "easy."
4According to _SW_ , 7A.62b, _qiu_ 糗 is a food made by first roasting and then grinding various grains. _Shiming_ , 4.129, describes _qiu_ as grain that is cooked, dried, and ground, which is probably another Han-time method for preparing _qiu_. This type of converted grain provision played an increasingly important role in the Han diet (Ying-shih Yu 1977: 76–77). Former Han measuring spoons of a type that could have been used to measure two-ninths _sheng_ have been recovered archaeologically (Qiu et al. 1984: 78).
5Pingling 平 陵 must refer to the Dong Pingling 東 平 陵 recorded in _Hanshu_ , 28A–2.72b; and situated east of present-day Jinan, Shandong. I interpret Pingling Lü 呂 as the moniker of a Mr. Lü from Pingling; and _ledao_ 樂 道 as his "way of (sexual) pleasure." _MWD_ , vol. 4, "Transcription," n. 1, interprets Lü Le as the man's name, and understands _dao_ as "say, state"; giving the translation, "Lü Le of Pingling states."
6A three-fingered pinch must be understood. The dosage is determined by the anticipated number of sexual partners.
7The recipe category concerns vitalizing tonics based on eggs and several other ingredients.
8The raw egg immersed in liquor and swallowed whole has a place in many cuisines. In North America it is the "prairie oyster," especially recommended for hangover. In _MS_ IV.23 the eggs are drunk in an ascending and descending progression (1:2:3:2:1), and are stirred.
1 _MWD_ , vol. 4, "Transcription," n. 2, surmises that _muniao_ 牡 鳥 (virile-bird) refers to _que_ 雀 (dickeybird). The identification is plausible. _MS_ III.17 and _MS_ IV.4 call for "spring-bird eggs"; and _MS_ VI.A.2 for "spring dickeybird eggs." _Que_ flesh and eggs are associated with male potency in later materia medica ( _GM_ , 48.97–98), which perhaps accounts for the name "virile-bird" in _MS_ III.16.
2I.e. a dickeybird egg.
3 _MWD_ , vol. 4, "Transcription," n. 1, notes a break in the text between C40 and C41; it is not clear how many columns might be missing.
4 _Nan_ 男 denotes the male genitals. The usage occurs again in _MS_ III.41–42.
5I follow the interpretation in _MWD_ , vol. 4, "Transcription," n. 1, that 勺 be read as _zhuo_ 灼 with the sense of a "burning" sensation. The reading depends largely on the context of _MS_ III.21–23, all of which describe medicines that stimulate sexual excitement by causing an itchy, burning sensation. Li and McMahon argue for reading the graph as _yue_ 約 with the sense of "contract" (1992: 152). The latter interpretation is supported by _MS_ IV.8–12 in which _yue_ refers to contracting the vagina (the counterpart to _MS_ IV.3–7 which deal with penile erection). However, in addition to the contextual evidence for associating _MS_ III.21–23 with "burning," _MS_ III.23 describes inserting the medicine in a nostril, which has little connection with tightening the vagina and could be applied to the man as well as the woman.
1The name _boluo_ 勃 蠃 is equivalent to _fuluo_ 蚹 蠃 in _Erya_ , 9.12a, identified in the Guo Pu commentary as "snail." Two variations on the name are used in _MS_ III: 蠃 ( _MS_ III.23) and 岪 選 ( _MS_ III.42).
2See _MS_ III.12.
3 _MWD_ , vol. 4, "Transcription," n. I, reads _yao_ 要 as _piao_ 票, and cites _Erya_ , 8.9b: " _Tiao_ 苕 is _lingtiao_ 陵 苕. With yellow flowers it is called _piao_ ; with white flowers it is called _ba_ 苃." _Piao_ is glossed in _SW_ , 1B.34a, as " _tiao_ with yellow flowers," but Duan Yucai suspects textual corruption and argues that the original gloss read "a plant with yellow flowers." In either case, if one accepts the "Transcription" reading _piao_ , _piaotiao_ in _MS_ III.22 could be interpreted as a compound for a variety of _tiao_ with yellow flowers. The botanical identity of _tiao_ is based on BC, which gives _lingtiao_ as an alternate name for _ciwei_ 紫 葳 ( _GM_ , 18.23; _ZY_ : no. 3947, _Campsis grandiflora_ [Thunb.] Loisel.). The "Transcription" identification is plausible, but uncertain. _Ciwei_ occurs in _MS_ III.73, which suggests that _yao/piaotiao_ is not the same plant. While I am inclined to agree that the two graphs are a compound drug name, _yao_ 要 and _tiao_ are each glossed as plant names in _SW_ , 1B.31a, and 1B.51b, respectively.
4I.e. a paste prepared from jujube fruits.
5 _Zhong_ 中 (inside) refers to the vagina. The usage occurs again in _MS_ III.24.
6The pot is buried so that the top is three _cun_ lower than the ground, and the space is then filled with soil.
7The lacuna must be an injunctive negative: "do not" let the fire be extinguished.
8 _MWD_ , vol.4, "Transcription," reads _l ü_ 閭 as _l ü_ 濾 (strain, filter), which would be plausible were it not for the fact that the latter word is not attested before the Tang period. I read _l ü/_* _gljag_ 閭 as a phonetic loan for _shi/_ * _srjag_ 釃, glossed in _SW_ , 14B.34b, as "send down (i.e. filter) liquor." _Shi_ occurs in _MS_ III.74, and 麗 in _MS_ III.37 should probably be read as _shi_ as well.
1"Engage in intercourse" translates _yong_ 用, which is used idiomatically to refer to having sexual intercourse in several recipes in _MS_ III, as well as in _MS_ IV, _MS_ VI.A, and _MS_ VII.B. The usage is attested in _Suwen_ 5, 2.7a, where the Wang Bing commentary explains _yong_ as having a sexual meaning. In _MS_ III.35, 38, and 43 the expression 用 之 occurs, which seems to have a double sense of "using" the prepared sexual excitant to "engage in intercourse." _Yong_ occurs in the text with its usual meaning as well, and it is sometimes difficult to be certain when the idiomatic usage applies.
2"Itch" translates _yang_ 癢, referring to the itching associated with sexual excitation.
3The recipe category concerns increasing the woman's sexual desire. _Gan_ 甘 in the sense of "crave" is common in early literature; e.g., in _Huainanzi_ , 6.97, where those who eat human flesh, pickle the human liver, and drink human blood are said to "crave it more than grass and grain fed animals." At the same time, _gan_ "sweet" connotes succulence; and the recipes are probably intended to stimulate the woman to produce an abundant flow of sexual fluids during intercourse.
4The drug must be boiled.
5I agree with Ma Jixing that the phrase 以 汁 肥 豯 means that liquid is fed to the pig, which is then cooked and fed to the woman (1992: 681). _MWD_ , vol.4, "Transcription," n. 2, interprets the phrase as an elliptical way of saying that the suckling pig is cooked in the liquid.
6I.e. vagina.
7For the translation of _niu_ as "choice," see _MS_ I.E.35.
8"Prohibited part" translates _jie_ 戒, referring to the vagina. The usage is also attested in _Maishu_ , "Ailment List," where it denotes either the male or female genitals: "When it is located in the prohibited part and the person cannot urinate—it is blockage" ( _MSSW_ : 72).
1Other drugs are probably lost in the lacuna above. A purified medicine is produced by continuous boiling and clarifying until the liquid has boiled away.
2Judging from other contexts, the period of time the medicine keeps is probably measured in years.
3試 is probably the first graph in the lacuna. _Changshi_ 嘗 試 occurs several times in _MS_ I.E to praise the effectiveness of a recipe.
4I interpet the phrase 鳥 産 不 鷇 to mean a chick that was born but did not live to be nurtured by its mother, understanding _kou_ 鷇 as glossed in _SW_ , 4A.56a, "a chick whose food is chewed and fed to it." _MWD_ , vol. 4, "Transcription." n. 1, interprets _kou_ in the sense of a chick about to hatch from the egg, citing the term _kouyin_ 鷇 音 in _Zhuangzi_ 2, 30. Despite the commentary that defines the term as "the sound of a chick emerging from the egg," it is better understood as the sound of chicks chirping for their food. Thus I am not convinced by the "Transcription" argument that the phrase in _MS_ III.27 refers to an unhatched egg.
5 _MWD_ , vol. 4, "Transcription," n. 3, notes a break in the text between C58 and C59; it is not clear how many columns might be missing.
6The two recipes in this category corroborate the recipes for a gecko and cinnabar compound used to detect illicit sexual activity in _Huainan wanbishu_ , 1.4b. While we cannot know how often and in what circumstances the compound was actually used, the recipes suggest that marking a woman's skin with the compound was an ordinary feature of private life. The recipes should also dispel the skepticism of many later Chinese scholars concerning the veracity of received accounts of the practice.
7The name used for the gecko is _shougong_ 守 宮 (guard of the palace), referring both to the gecko's habit of climbing walls and to its application in preventing the occurrence of illicit sexual activity in the sleeping quarters. Because of the lacunae it is not clear whether cinnabar is also added in this recipe (some of the _Huainan wanbishu_ passages only use gecko to produce the potion).
1The lacuna makes the meaning unclear, but I suspect that a cloth is dipped in a liquid preparation of gecko and then the dyed cloth is applied to the woman's arm.
2The recipe distinguishes between sexual play and actual intercourse; in the former case the compound on the arm has cracks, and in the latter it disappears entirely.
3The recipe is written in the space beneath the main text in CC60–63, and is blocked off from the main text by a horizontal line. It was evidently added after the original redaction of the text.
4The recipe category concerns the removal of body hair, especially pubic hair. _Ishinp ô_, 28.34b, testifies to the disapproval of body hair with the statement that a man should not have intercourse with a woman who "has hair on her thighs and lower legs"; and also warns of the harm a man suffers if he has intercourse with a woman whose pubic hair is "both coarse and stiff, and mostly grows in the opposing direction." Ideally, according to _Ishinp ô_, 28.33b, the woman's "genitals and underarms should not have hair; and if there is hair, it must be made to be fine and smooth."
5"Shave" translates _mu_ 沐. From a literal meaning of "cleanse the hair (on the head)," _mu_ has the extended meaning of clearing away plants or debris ( _SW_ , IIA-2.36b, and Duan Yucai commentary). Since the goal in _MS_ III.30 is hair-removal—and given the reference to "plucking" the hair in _MS_ III.32— _mu_ is best interpreted in its extended meaning.
6"Hole" translates _xu_ 洫, here referring to the female genitals. _Xu_ is glossed in _SW_ , IIA-2.17b, as a ditch with specified dimensions; my translation is based on _Guangya_ , 9B.14b, which groups _xu_ together with words all meaning "hole in the ground." My understanding of the recipe is that removing the hair from her lower body and genitals after childbirth is supposed to keep the woman free of this unwanted hair.
7According to Tao Hongjing, old earthworms have white necks ( _GM_ , 42.40).
8Water must be added to the earthworms, spider webs, and bitter gourd at some point before the iron is quenched in the medicine.
1See _MS_ III.10 for formula sweet-liquor.
2For _zui_ 最 (also written 嘬) as a term for the male genitals, see _MS_ I.E.134. Li and McMahon express the opinion that in _MS_ III.33 _zui_ denotes the female genitals (1992:152), but do not offer a supporting argument. Occurrences of _zui_ in received literature and in _MS_ I.E.134 all indicate that the referent is the male genitals.
3I follow Ma Jixing (1992: 688, n. 2) in reading _fu_ 付 as _fu_ 柎; and identifying it as a term for a catkin. The identification is based on _Shanhaijing_ , 2.12b, and Guo Pu commentary.
4 _Jinnei_ 近 内 (approach the inner chamber) as a euphemism for sexual intercourse also occurs in _MS_ I.E.18, where intercourse is one of the prohibited activities during treatment for an ailment. It is likely that _nei_ has a double reference that includes the female genitals.
5I.e. the decocted medicine is strained.
6Max Jixing identified _jue_ 芵 as part of the drug name _beijue/xie_ 草 薢 (1992: 691, n. 17; se _MS_ III.50).
7 _Bu_ 餔 refers to a time in the late afternoon between 3:00–5:00 P.M. (see _MS_ I.E.67).
8In the text there is a twenty-eight graph lacuna in C70 and a one graph lacuna at the top of C71. _MWD_ , vol. 4, "Transcription," n. 1, notes that there may be a break in the text between C70 and C71.
1 _MWD_ , vol. 4, "Transcription." n. 2, equates the drug name _chejian_ 車 踐 with _cheqian_ 車 前.
2The grammar of the sentence, in which _ruo_ 若 means "or," indicates that words naming the alternative to the cloth sack were omitted from the text by the scribe.
3 _Zhong_ 中 (inside) occurs in _MS_ III.46, 71, and _MS_ IV.23 referring to the inside of the body as a region to be cultivated, not necessarily for the purpose of sexual intercourse.
4I follow _MWD_ , vol. 4, "Transcription," in reading 囷 as _jun_ 菌; and indentifying _fenjun_ 菌 as the name of a type of mushroom ( _fen_ is well attested in the sense of something that swells and bulges).
5Judging from the context the lacuna should be an injunctive negative.
6 _Bai_ 稗 is glossed in _SW_ , 7A.44a, as "grain of a different sort" (i.e. a grain-like plant; see Duan Yucai commentary). _Bai_ is listed in material medica ( _GM_ , 23.80; _ZY_ : no. 5199, _Echinochloa crusgalli_ [L.] Beauv.). Ma Jixing reads _bai_ as _bei_ 草; and indentifies bei [1] as the drug name _beixie_ (1992: 692, n. 5; see _MS_ III.50).
7 _Mendong_ 門 冬 is the same drug name written _mandong_ 慲 冬 in _MS_ III.52 and _mendong_ 釁 冬 in _MS_ III.70. _Mendong_ is the gloss given for _qiangmi_ 靡 in _Erya_ , 8.7a; and in _SW_ , 1B.29a. According to the Duan Yucai commentary it is not certain whether the gloss refers to _tian mendong_ 天 釁 冬 (i.e. the same drug already identified with the name _dianji_ ; see _MS_ III.2) or to _mai mendong_ 麥 釁 冬. _Mai mendong_ is listed in _BC_ ( _GM_ , 16.84; _ZY_ : no. 2082, _Ophiopogon japonicus_ Ker-Gawl., and plants in the genus _Liriope_ ). Primarily because of the occurrence of _dianji_ in _MS_ III, I suspect that _mendong_ refers to _mai mendong_.
8I read _bi/_ * _pji əd_ 枇 as phonetic loan for _bi/_ * _pji ət_ 潷, glossed in _Guangya_ , 2B.12b, as a synonym for "strain." The Wang Niansun commentary supplies additional glosses indicating that _bi_ refers to "pressing" the liquid out of something.
9"Napkin" translates _jin_ 巾, which according to _SW_ , 7B.44b, is a napkin worn at the waist. The Duan Yucai commentary outlines the use of the _jin_ to wipe things (its use as a head covering is later). The recipe category concerns cloth saturated with medicine and used to rub the body—in particular the genitals—as a sexual stimulant.
1"Produce eggs" represents my interpretation of _juan_ 卷. The phonetic _juan_ 关 is glossed in _SW_ , 3A.37a, as "rolling cooked grain into a ball ( _zhuanfan_ 摶 飯)." The practice of serving oneself by taking a handful of cooked grain from the pot and rolling it into a ball is attested in _Liji_ , 2.12a, where it is prohibited. I suspect that in _MS_ III.37 the sense of _juan_ is extended to a bird laying eggs. It is equally likely that _juan/_ * _kwjian_ is a phonetic loan for _wan/_ * _gwan_ 丸 (ball), which is attested in the sense of "egg" in _L üshi chunqiu_, 14.141. The speculation in _MWD_ , vol. 4, "Transcription," n. 1, that _juan/_ * _kwjian_ is a phonetic loan for _huan/_ * _gwan_ 讙 (shout, cry) is phonologically possible, but in my judgment is the less likely alternative.
2I.e. set the chicken against another bee hive.
3I read 麗 as _shi_ 釃, the word for filtering a liquid in _MS_ III.74. In _MS_ III.37, it is likely that the chicken flesh has been dried or incinerated before being smithed; and then it is sifted through a cloth before being mixed with jujube fat. This is the only reference to sifting a drug powder in the Mawangdui medical manuscripts. _MWD_ , vol. 4, "Transcription," n. 2, reads the graph as _shai_ 矖 (dry in the sun), which is possible but unlikely in my judgment.
4I am uncertain of the meaning of _yi_ 邑. The same graph modifies bird eggs in _MS_ III.41. _MWD_ , vol. 4, "Transcription," n. 3, suggests that _yi/_ * _?j əp_ may be a phonetic loan for _za/_ * _dz əp_ 雜 (mixed, assorted); _ji/_ * _dzj əp_ 集 (collected, gathered) is another possibility.
5Increasing the vapor in the feet may be related to the idea expressed in _MS_ I.C that vapor should flow towards the feet and that the feet should be warm.
6From the description at the end of the recipe _yangsi_ 楊 思 refers to a bug, but the name is not attested in received literature and its identity is not known.
1"Jade whip" translates _yuce_ 玉 策, denoting the penis. The term, which is not attested in received literature, occurs four more times in the Mawangdui medical manuscripts: _MS_ III.43, _MS_ VI.A.2, _MS_ VI.A.10, and _MS_ VI.B.6. The female counterpart to the jade whip in _MS_ III.38 and 43 is _ma_ 馬 (horse), denoting the female genitals (the term also occurs in _MS_ III.44 where it is paired with _pin_ 牝, which denotes the female genitals as well). _Ma_ is attested for female genitals in Yuan to Ming drama and fiction; see, for example, the Ming collection _Gujin xiaoshuo_ , 3.7b, where sexual intercourse is referred to as _ruma_ 人 馬 (entering the horse). The analogy between horseriding and intercourse evident in _MS_ III.38 and 43 also occurs, but the word for the whip/penis is _bian_ 鞭. The Yuan drama _Shanshenmiao Pei Du huan dai_ , 46a, plays on the image of the male horserider holding a silk whip, who after dismounting is promptly seduced—at which point the whip image shifts to the penis: "When (the women) got a glimpse of the First Candidate's whip those in the front of the hall were delighted." Given the horseriding analogy in _MS_ III.38 and 43, the Han term _yun ü_ 鞭 女 clearly refers to the man "riding the woman/horse" (see _MS_ VI.B.1).
2 _MWD_ , vol. 4, "Transcription," transcribes 紇, read as _he_ 齕 (bite, chew). Qiu Xigui suggests the transcription 赦, read as _shi_ 螫 (bit, sting; 1992: 534).
3Identification of _lin_ is uncertain. _MWD_ , vol. 4, "Transcription," n. 1, suggests equating it with _lin_ 菻 glossed as a plant related to artemisia in _SW_ , 1B.28a.
4Identification of _fanshi_ 潘 石 is uncertain. The same mineral name is written _fanshi_ 蕃 石 in _MS_ IV.8, 9, 11, and 12. _MWD_ , vol. 4, "Transcription," n. 1, reads _fan_ as _fan_ 礬, identifying the mineral as alunite ( _ZY_ : no. 1383; _GM_ , 11.68). However, _BL_ gives _fanshi_ 番 石 as an alternate name for _huashi_ 滑 石 ( _GM_ , 9.77), which is talc ( _ZY_ : no. 5037).
5"Grass-filtered" translates _you_ 莤, glossed in _SW_ , 14B.40b, as a ritual of preparing liquor for sacrifices by filtering it through mao 茅 (woolly grass). _MS_ III.39 testifies to the use of this filtering process outside of religion.
6I read 曼 as man 漫, glossed in _Fangyan_ , 13.4a, as "soak until decomposed."
7爲 之 is another expression meaning to have intercourse, similar to 用 之.
8 _MWD_ , vol. 4, "Transcription," n. 1, identifies 萩 莢 as equivalent to _zaojia_ 皂 莢 ( _qiu/_ * _tshi əgw_ 萩 is a phonetic loan for _zao/_ * _dz əgw_ 皂). The name occurs written 蕉 莢 in _MS_ IV.5.
1See _MS_ III.37 for a possible interpretation of _yi_.
2I.e. having sexual intercourse.
3The genitals are referred to as _nan_ 皂 and _n ü_ 女 respectively.
4The genitals are referred to as _nan_ 皂 and _pin_ 牝 respectively.
5Identification of _tianmu_ 天 牡 is uncertain. _MWD_ , vol. 4, "Transcription," n. 2, proposes reading _mu_ 牡 as a scribal error for _she_ 社 and identifying the drug as the insect _tianshe chong_ 天 社 蟲, listed in _GM_ , 41.14 (a kind of beetle).
6Identification of _taoke_ 桃 可 is based on the description at the end of the recipe. _Taomao_ 桃 毛 is the name for peach fuzz in _GM_ , 29.48, and is the name used in _MS_ IV.3.
7Identification of _mulou_ 牡 螻 is uncertain. _MWD_ , vol. 4, "Transcription," n. 4, associates the name with _bai mugou_ 白 牡 拘 in _MS_ V.6; and cites _Fangyan_ , 11.2a, where _dugou_ 牡 拘 is given as a Southern Chu name for _lougu_ 螻 蛄 _Lougu_ is the molecricket ( _ZY_ : no. 5477, _Gryllotalpa africana_ Pal. de Beauvois; _GM_ , 41.15). The identification is plausible, but at the end of the recipe the unidentified bug name _jiequan_ 頡 蠸 occurs in a context where it might form part of a definition of _mulou_ , which in turn casts doubt on the identification with _lougu_.
8I follow _MWD_ , vol. 4, "Transcription," n. 5, in reading 贛 as _gan_ 贛, and alternate name for _yiyi_ 薏 苡 ( _ZY_ : no. 5548, _Coix lachryma_ - _jobi_ L.; _GM_ , 23.83). The reference to the "skin" must be to the outer covering of the fruit; thus it is the fruit that is denoted by _gan_ in _MS_ III.43.
1玩 in _MWD_ , vol. 4, "Transcription," should be transcribed as _wan_ 抏. The graph is attested in the meaning "rub" in _Shiji_ , 105.3b (the graph is erroneously written 抗 in the _Shiji_ edition cited).
2 _MWD_ , vol. 4, "Transcription," n. 1, notes that there is a break in the text between C97 and C98; it is not clear how many columns might be missing.
3All other recipes in this category are lost in the preceding break in the text. I add the category name from the list in _MS_ III.92 for reference purposes only.
4 _MWD_ , vol. 4, "Transcription," provisionally adds the name of this recipe category from the list in _MS_ III.92 to the beginning of _MS_ III.46. The recipes seem to be primarily concerned with tonics for bolstering physical vitality, but several are sexual ( _MS_ III.51, 58).
5 _MWD_ , vol. 4, "Transcription," n. 2, suggests reading _zi_ 兹 as _zi_ 牸, listed in _Guangya_ , 10B.37b, as one of the words for the female of animals. The "Transcription" note argues that the word denotes a female cow in _MS_ III.46, but both the reading of the graph in the text and the interpretation are uncertain.
6 _MWD_ , vol. 4, "Transcription," n. 1, argues that _sui/_ * _sdj əd_ 遂 represents the same plant name as _shu/_ * _dj ət_ 蒁 in _MS_ III.52; and that both should be understood as _zhu/_ * _dj ət_ 术 (atractylodes). The argument is plausible but uncertain.
1 _MWD_ , vol. 4, "Transcription," n. 1, reads _yuan_ 冤 as _wan_ 菀 and identifies the plant as _ziwan_ 紫 菀 ( _ZY_ : no. 4866, Aster _tataricus_ L. f; _GM_ , 16.82). However, _SW_ , 1B.19b, glosses _yuan_ 蒬 as _jiyuan_ 棘 蒬, which is equivalent to _jiwan_ 棘 菀 ( _ZY_ : no. 2087, _Polygala tenuifolia_ Willd.; _GM_ , 12B.15). Materia medica assigns tonic properties to both drugs; which one is the referent of _yuan_ in _MS_ III.48 is uncertain.
2 _MWD_ , vol. 4, "Transcription," n. 1, suggests reading _jie_ 界 as _jie_ 芥 ( _ZY_ :no. 2173, _Brassica juncea_ [L.] Czern. et Coss.; _GM_ , 26.62). The identification is plausible.
3I follow _MWD_ , vol. 4, "Transcription," n. 1, in reading 萆 芵 as equivalent to _beixie_ 萆 薢 in _MS_ III.70. The drug is listed in _GM_ , 18.44 ( _ZY_ : no. 4120, _Dioscorea hypoglauca_ Palib., and other spp.). The name is written 萆 蒵 in _MS_ III.60.
4"Ring" translates _huan_ 環, which I believe is an idiomatic term for the waist region in the Mawangdui medical manuscripts (see _MS_ I.C). It is also possible that in _MS_ III.50 _huan_ means "all around" (i.e. the whole body).
5The end of the recipe suggests that the medicine is used to stimulate the penis. Perhaps the hole is the navel (see _MS_ IV.5).
6See _MS_ III.36.
7See _MS_ III.47.
1See _MS_ I.E.147.
2Being strong might refer to penile erection in addition to physical strength (see _MS_ III.20).
3 _MWD_ , vol. 4, "Transcription," reads _ru_ 如 as _ru_ 茹, which n. 1 identifies as _rucao_ 茹 草 ( _GM_ , 13.43; _ZY_ : no. 3763, _Bupleurum chinense_ DC. and other spp.). However, _ru_ occurs in other plant names; e.g. _rugen_ 茹 根, which is the name for the root of _baimao_ 白 茅 ( _GM_ , 13.64; _ZY_ : no. 1435, _Imperata cylindrical_ [L.] P. Beauv. var. _major_ [Nees] C.E. Hubb.).
4The two-graph lacuna must name two drugs, which are mixed with rooster blood. It is not clear how this preparation relates to the _ru_ above or to the end of the recipe.
5I fill the lacuna with _ban_ 螌 based on the context (see _MS_ III.38).
6 is written in large script beneath the text in C115 (compare _MS_ III.12 and 21). Perhaps the graph is a variant of _dun_ 盾, but this seems unlikely.
7 _MS_ III.16 calls for "virile-bird egg liquid," possible dickeybird eggs.
8The instruction to wash the medicine off suggests that the recipe concerns stimulation of the penis (see _MS_ IV.3).
1 _Baifu_ 白 符 and _hongfu_ 紅 符 represent the white and red varieties of the _wuse fu_ 五 色 符 ( _fu_ of the five colors). Wu Pu 吳 普 (d. 250 A.D.) equates _wuse fu_ with _wuse shizhi_ 五 色 石 脂, which is a name for five varieties of clay classified by color ( _GM_ , 9.80). However, Tao Hongjing lists _wuse fu_ in a separate entry under mineral drugs, noting that the substance was no longer used and that no one in his time had knowledge of it (see _Bencaojing jizhu_ , 2.33). Since _MS_ IV.2 calls for [1] _shizhi_ ([1] clay), it is possible that _fu_ in _MS_ III.62 represents a different, unidentified mineral.
2止 in _MWD_ , vol. 4, "Transcription," should be transcribed as _yi_ 已.
3"Jerky" translates _xiu_ 脩, glossed in _SW_ , 4B.33a with _fu_ 脯 (dried-meat slice). According to the Duan Yucai commentary, _fu_ is the basic term for a slice of dried meat while _xiu_ refers to meat strips that are beaten and coated with ginger and cinnamon.
1The lacuna evidently contains a second medicine that is eaten after the meal (the dired meat is eaten before the meal).
2The heading _yongshao_ 用 少 is elliptical. _MWD_ , vol. 4, "Transcription," n. 1, explains the sense by comparison with a passage in _Qianjin yaofang_ , 60.18b, listing the "seven injuries" associated with intercourse, among which the second is "essence/semen ( _jing_ 精) is clear" (see the first line of the recipe below) and the third is "essence/semen is scant." The list of the seven injuries in a parallel account in _Waitai biyaofang_ , 17.3a, is different, but still gives "essence/semen is clear" and "essence/semen is scant" as the third and fourth injuries.
3The drugs used to make the medicine are lost in the lacuna. The reference to _xiong_ 雄 (male bird) and to blending the drugs with the "blood of the two" suggests that the blood of two birds is used.
4The occurrence of the volumetric measure _sheng_ as the final extant graph in _MS_ III.64 suggests that the listing of drugs and amounts continues at least to this point. _MWD_ , vol. 4, "Transcription," n. 1, notes that there is a break in the text between C134 and C135; it is not clear how many columns might be missing.
5 _MWD_ , vol. 4, "Transcription," provisionally adds the heading for this recipe category from the list in _MS_ III.92, until _MS_ III.72 which can be restored based on _MS_ III.92. The "Transcription" provisionally marks lacunae for the missing headings, which I omit.
6I.e. there should be a stimulating sensation of itching. The same phrase occurs again in _MS_ III.68.
1See _MS_ III.4.
2 _MWD_ , vol. 4, "Transcription," treats CC144–47 as one entry. I follow Ma Jixing in making CC146–47 a separate recipe (1992: 721).
3Great Chamber 泰 室 and Lesser Chamber 少 室 designate the site of Song Mountain 山 in present-day Henan, which is the central peak in the system of the five sacred peaks. See _Huainanzi_ , 4.64.
4The term _pianshi_ 駢 石 is attested in _Guanzi_ 58, 19.312, where it refers to stones that are joined to form a solid layer. Perhaps in _MS_ III.69 _pianshi_ refers to some kind of conglomerate, or perhaps it is a technical term whose meaning is unknown. In any case, the recipe calls for stones that come from Song Mountain.
5"Pound" translates _tuan_ 段. Ma Jixing argues that _duan_ could also be read as _duan_ 煅, and understood as a heating process used to cook the monkshood (1992: 722, n. 2). The argument for cooked monkshood is more plausible in _MS_ III.72, where the word is _xun_ 熏.
6The recipe probably states that the dregs should not be discarded.
7See _MS_ III.36.
8 _Simo_ 四 末 (four extremities) is a standard term for the arms and legs; _liumo_ 六 末 is not attested in received literature. _MWD_ , vol. 4, "Transcription," n. 3, identifies the additional two extremities as the genital and anal regions.
1 _MS_ III.71 provides the earliest documentation of mica ingestion in Chinese macrobiotic dietetics. See Kaltenmark 1953: 59, for mica in _xian_ -cult dietetics; and Schafer 1955: 282, for discussion of the earliest references in the received literature.
2"Whole-wheat flakes" translates _maizhi_ 麥 . _Zhi_ refers to coarsely milled whole grains of wheat, including the bran ( _SW_ , 5B.34a, and Duan Yucai commentary).
3各 in _MWD_ , vol. 4, "Transcription," should be transcribed as _tun_ 吞.
4See _MS_ III.10 for an earlier recipe for _lao_ 醪. Of the three recipes in this category, only _MS_ III.74 is well enough preserved to provide a fair description of the method of production.
5Based on _MS_ III.74, The lacuna might be _jie_ 節. See below for the possible identity of _qi_ 漆 and _jie_.
6"Blackened" translates _xun_ 熏. _Xun_ usually means "fumigate," but is attested in the sense of "sear, roast" ( _Shijing_ , Mao 258, 18B.11a, and Mao commentary). In _MS_ III.72 _xun_ refers to preparatory cooking of the monkshood.
7In _MS_ III.74, _MWD_ , vol. 4, "Transcription," n. 1, suggests identifying _qi_ 漆 as _zeqi_ 澤 漆; and _jie_ 節 as _dijie_ 地 節. For _zeqi_ , see _GM_ , 17.15 ( _ZY_ : no. 3047, _Euphorbia heliostopia_ L.). _Diji_ is probably the plant listed in _GM_ , 12.105 ( _ZY_ : no. 1156, _Polygonatum odoratum_ [Mill.] Druce var. _pluriflorum_ [Miq.] Ohwi.). However, it may also refer to the plant listed in _GM_ , 36.107 ( _ZY_ : no. 1640, _Lycium chinense_ Mill.).
8In _MS_ III.74 the herbal ingredients are set in the fermentation jar first and the fermented grain is placed on top. _MS_ III.72 probably describes a similar procedure.
1This appears to represent the first stage of production. A decoction of _qi_ and _jie_ is used to cook trumpet-flower, and two kinds of yeast are left to ferment in the second decoction for twenty-four hours.
2In the second stage millet and rice are prepared using the fermented yeast brew. Combing cooked grain with a partially fermented brew is characteristic of mash-liquor (see _MS_ III.10).
3I follow Ma Jixing in reading 甫 as _fu_ 呚 (1992:729, n. 13). The compound _fuju_ 呚 咀 (chew) occurs in _MS_ IV.3.
4In the third stage a layer of chewed herbs is placed in the fermenting jar first, followed by the grain and the liquid in which it was fermenting, and finally by a quantity of liquor. At this point the fermentation jar is sealed.
5Evidently the fermentation jar is opened and the liquid allowed to drain naturally without filtration. Then more liquor is poured into the jar and the process of sealing and fermenting is repeated a second time. After the third time the mash – liquor is ready to drink.
6For _pianku_ 偏 枯 (withering on one side), see _MS_ I.B.8.
7The meat is probably dog meat, which is then used to prepare the dried-meat slices mentioned below.
1See _MS_ III.11 on the connection between dosage and the number of people whom the user can successfully encounter.
2Evidently a reference to fighting bulls, since the recipe indicates that the medicine is used on a bull. For animal combat and man-animal combat in early China, see Hayashi 1976: 411–12; and Lewis 1990: 157–60. The end of the recipe indicates that the medicine can also be used by humans.
3The insect _chou_ 螑 is unknown.
4Qiu Xigui suggests that the fragmentary graph marked as a lacuna in _MWD_ , vol. 4, "Transcription," may be _hu_ 壺 (flagon; 1992: 534). My translation is based on the guess that a raging bull "snorting flagons" is intended to suggest its brute energy.
5The recipe category is principally concerned with speeding travel by foot. _MS_ III.77–80 all include monkshood in the medicine, which is the drug mentioned in _Wanwu_ : "Ingested for one hundred days _wuhui_ improves a person's ability to run" (Fuyang Han jian zhenglizu 1988: 38). According to _Huainan wanbishu_ , 1.7b, one ball of medicine containing monkshood and crane embryo enables a person to travel one thousand _li_ in one day. _MS_ III.83–84 concern magic to secure a campsite at night.
6 _MWD_ , vol. 4, "Transcription," n. 2, reads _feilian_ 非 廉 as _feilian_ 蜚蠊 ( _GM_ , 41.22; _ZY_ : no. 5625, _Blatta orientalis_ L.; flying cockroach). It is equally likely that the name refers to _feilian_ 飛 廉 ( _GM_ , 15.39; _ZY_ : no. 0567, _Carduus crispus_ L.; thistle).
7 _Fangkui_ 防 赛 is listed in _GM_ , 17.10 (not identified in _ZY_ ).
8 _Bai tengshe_ 白 膉 蛇 is unknown, but may be a southern dialect name. Most early glosses of _tengshe_ identify it as a fantastic, flying dragon-like serpent. However, the Guo Pu commentary in _Erya_ , 9.13a, seems to indicate that in Huainan dialect _tengshe_ referred to _mangshe_ 莽 蛇 (python; my uncertainty is due to the possibility that _mang_ is a textual error for _ben_ 奔). _Huainan wanbishu_ , 1.7b, lends support to the identification by recommending that _tengshe_ bile be added to the monkshood and crane medicine for rapid travel (python bile is highly tauted in materia medica; _GM_ , 43.68). _Zang gengshe_ 蒼梗 蛇 is unknown. Perhaps both names refer to snakes, although the short length (three to four _cun_ ) suggests something besides a snake.
1The fungus must have been mentioned in one of the lacunae above. Luo 雒 probably refers to the region of the Luo River 洛 水 in present-day Henan.
2Presumably the number of _li_ that the medicine balls enable a person to travel in one day.
3The identity of _longkai_ 龍 慨 is uncertain. _MWD_ , vol. 4, "Transcription," n. 1, suggests equating the name with _longkui_ 龍 葵 ( _GM_ , 16.95; _ZY_ : no. 1286, _Solanum nigrum_ L.). But the name is not attested in material medica before the Tang.
4 _Futu_ 伏 兔 is probably another name for _fuling_ 茯 苓 (pine truffle) as indicated in _GM_ , 37.2. However, _futu_ is also an alternate name for _feilian_ (thistle; see _MS_ III.77).
5"Saturated cooked-grain" translates _xiufan_ 茯 苓. The compound is written 脩 飯 in _SW_ , 5B.6b, where it occurs as the gloss for fen 饙. _Fen_ is a thick porridge made by saturating cooked-grain with additional liquid. In _MS_ III.78 the grain is saturated with the medicinal liquid, allowed to dry, and then saturated again until there is no more liquid.
6I follow _MWD_ , vol. 4 "Transcription," n. 1, in reading _chi_ /* _khrj ǝg_ 茞 as a photetic loan for _tai_ /* _hr ǝg_ 苔. _Tai_ is a general term for various mosses and lichens, and several algae ( _GM_ , 21.17; roof-tile lichen is described in _GM_ , 21.21).
7扺 is not attested in received literature; the graph is used to write _jian_ 菄 (small bunch) in _MS_ III.39. The translation "scoop" is a guess based on the idea of using the hand to gather a bunch of something, or in this case to scoop water.
8Perhaps the medicine is drunk at sunrise before setting off on the day's journey.
1The missing drug at the beginning of the lacuna is probably a menstrual cloth.
2A similar incantation is recorded in _Baopuzi_ , 17.89, where it also forms part of a magical ritual to secure a campsite for the night: "The Yin side of Heng Mountain. The Yang side of Tai Mountain. Let robbers and plunderers not arise. Let tigers and wolves not move. Walls and ramparts that are not intact, seal with the metal bar." The incantation in _MS_ III.83 is clearly the antecedent to the _Baopuzi_ incantation; and the latter incantation can be used to fill the final lacuna with _bi_ 閉 (seal). For Tai Mountain, see _MS_ I.E.229. The rhyming words in the incantation are: _wan_ /* _gwan_ 完 (intact) and _guan_ /* _kwran_ 關 (bar).
3The person states aloud that he is creating a magic circle as he draws the circle on the ground. In the _Baopuzi_ the person draws a square on the ground with a knife, and after the incantation is finished the knife is laid on the square at the astrological position of the White Tiger 白 虎.
4East Lord 東 君 is a solar deity in the seventh of the "Jiuge" 九 歌 in _Chuci_ , 2.16a. However, I suspect that East Lord and Bright Star 東君 明 星 is a name for Taiyi 太 一, who is called the Shining One of the East and Grand Monad 東 皇 太 一 in the first of the "Jiu ge" in _Chuci_ , 2.2a. In heaven, Taiyi is a polar star whose nature is revealed astrologically in the movement of the Big Dipper. Recent archaeological evidence indicates the existence of a Taiyi cult in the Chu region in the third to second centuries B.C., most strikingly the Mawangdui painting of Taiyi flanked by the Rain Master 雨 師 and the Thunder Sire 雷 公 (Li Ling 1991; the best photographic reproduction of the painting is Fu and Chen 1992: 35). Inscriptions on the Mawangdui painting are related to military astrology, which represents a significant aspect of the Taiyi cult. Among powerful spirits to whom a person might announce the securing of a campsite, Taiyi would be a logical choice.
1I.e. the menstrual cloth of a virgin.
2 _Wanwu_ uses the same term when it states that using spiders enables a person to "travel quickly" ( _jixing_ 疾 行; Fuyang Han jian zhenglizu 1988: 37).
3I.e tie a loop of rope all the way around the waist.
4 _Xi_ 氣 means "give provisions"; the graph was subsequently used to write _qi_ "vapor" ( _SW_ , 7A.63b, and Duan Yucai commentary).
5 _MS_ III.88 represents the third from last category in the _MS_ III.92 list. The entry is a pastiche of information on sexual cultivation. In every instance there is a fuller account in _MS_ VI.B or _MS_ VII.B.
6無 in _MWD_ , vol. 4, "Transcription," should be transcribed as 无.
7The "it" with which the remainder of the paragraph is concerned is the penis. The closest parallel to this passage on the arousal of the penis is _MS_ VII.B.2; there is a partial parallel in _MS_ VII.B.18.
8 _Yao_ 搖 (move) should definitely be read as _yao_ 搖 (blue-gem) in _MS_ VI.A.4. However, the original graph may be intended in _MS_ III.88, giving the translation Moving Terrace. The name occurs as Blue-gem Terrace in _Huainanzi_ , 8.118, explained in the Gao You commentary as a structure decorated with blue-gem. It is one of several royal structures associated in received literature with the legendary degenerate rulers Jie 桀 of the Xia and Zhou 紂 of the Shang (rather than with Tang, 湯, the Shang founder). The Gao You commentary additionally gives _yao_ 搖 (move) as a textual variant of _yao_ 搖 (blue-gem), along with the alternative explanation of the structure as a marvel of mechanical engineering. Similarly, the chamber mentioned in _MS_ III.89 occurs in received literature in forms that mean either a chamber of precious stone or a revolving chamber. Whether constructed of precious materials or engineered to move in harmony with the cosmos, these structures symbolized the ideal site for a ruler—conceptually identical to the Bright Hall 明 堂 (Rickett 1985: 149). While received literature treats the Blue-gem Terrace as an example of royal excess, _MS_ III.88 presents it as the natural site for a ruler.
9Chen 陳 is probably the surname of a master of sexual cultivation. In the exchange that follows I assume that Tang seeks instruction from Chen, which is the rhetorical pattern of the dialogues in _MS_ VI.A.
1I.e. how can intercourse fulfill the goal of macrobiotic cultivation?
2There is a parallel to these lines in _MS_ VIII.B.8, which is a fuller statement of the need for a program of sexual cultivation.
3This begins a list of six names of sexual positions. Two lacunae have been filled on the basis of the parallel in _MS_ VI.B.3 (a list similar to _MS_ VI.B.3 also occurs in _MS_ VII.B.10).
4This begins a list of five names for parts of the female genitals. There is a labeled drawing of the female genitals in _MS_ III.91 in which seven names are extant; and a list of twelve names in _MS_ VII.B.19. None of the names in _MS_ III.88 have exact counterparts in _MS_ III.91 or _MS_ VII.B.19; and the connection between the names in _MS_ III.88 and in later sexual literature is extremely uncertain. Reading _yun_ 云 in the sense of "cloud" is merely a guess. The name _yunshi_ 云 石 may be related to _zaoshi_ 躁 石 in _MS_ VII.B.19.
5I read 拮 as _ku_ 枯, again merely a guess. The name _jianhu_ 澗 瓠 occurs in _MS_ VII.B.19 and may be related.
6"Glistening plug" is a literal rendering of _zhuogua_ 濯 昏.
7The first graph is _fu_ 伏; the name may be related to _fu_ [1] 付 in _MS_ III.91.
8This begins a list of seven ways for the man to move his penis inside the vagina. Parallels occur in _MS_ VI.B.4 and _MS_ VII.B.12. "Rabbit bolting" appears to be out of place in _MS_ III.88, since it is given as the name of a sexual position in _MS_ VI.B.3 and _MS_ VII.B.10.
1These refer to the woman's state of arousal as exhibited by signs coming from the mouth. "Blowing" and "biting" are given along with three other signs in _MS_ VI.B.6, _MS_ VII.B.15, and _MS_ VII.B.20.
2"Shaking" is one of eight ways the woman moves her body during intercourse as described in _MS_ VI.B.5 and _MS_ VII.B.16.
3The final list of four has a parallel in _MS_ VII.B.11 which names ten aspects of intercourse that the man must master. _MS_ VII.B.11 places "bring vapor" first and "secure the taste" second.
4"Exercise the fruit" is fourth in _MS_ VII.B.11.
5 _Shijie_ 侍 節 (attend to the joints) corresponds to _zhijie_ 治 節 (control the joints) in _MS_ VII.B.11.
6Despite the extensive lacunae, the general format of _MS_ III.89 is discernible. Yu 禹, who has regained the vigor of youth, engages in a discussion of sexual cultivation with the females at his court. The passage is notable for presenting women in the role of the experts who instruct their lord. While this is a standard form for later sexual cultivation, literature, it occurs nowhere else in the Mawangdui medical manuscripts.
7The _jiri_ 吉 日 can refer to any auspicious day chosen in accordance which hemerological principles, but it also denotes the first day of the month ( _Zhouli_ , 12.5a).
8 _Xuanfang_ 璇 房 is equivalent to _xuanshi_ 琁 室 in _Huainanzi_ , 8.118; like the Blue-gem Terrace it exemplifies the architectural excesses of Jie and Zhou in received literature. I follow _MWD_ , vol. 4, "Transcription", which reads the original 靛 as 琁, but 旋 is also possible. Both readings are indicated in the Gao You commentary in _Huainanzi_ , which identifies the chamber either as decorated with a jade-like stone called _xuan_ or as built to revolve ( _xuan_ 旋; see _MS_ III.88).
9I follow _MWD_ , vol. 4, "Transcription," n. 2, in reading _he_ /* _gar_ 河 as a phonetic loan for _e_ /* _ngar_ 娥. The compound _jing'e_ 娙 娥 is glossed in _SW_ , 12B.11b, as a term for a beautiful woman; and the same compound occurs written 娙 何 in _Shiji_ , 49.13a, where it refers to one of the grades of consorts at the court of Thearch Wu (r.141–87 B.C.).
10Yu is evidently describing a time when old age descended on him, before his rejuvenation.
1It is probable that South Beauty and West Beauty both speak to Yu, their words lost in the lacunae.
2I follow Qiu Xigui in filling the lacuna with _le_ 樂 based on the fragments of the graph (1992: 534).
3I.e. aggressive behavior by the man during intercourse nullifies the possible benefits of cultivation.
4也 in _MWD_ , vol. 4, "Transcription," should be transcribed as _hu_ 虖.
5"Conjoin vapor" translates _heqi_ 合 氣, which is attested in _Lunheng_ , "Wushi," 3.68, in two senses: the union of the vapor of heaven and earth (which by coincidence engendered humankind); and the union of the vapor of man and wife (which by coincidence engenders offspring). As evidenced by _MS_ III.89, _heqi_ was one of several standard terms for sexual intercourse in the third to second centuries B.C. _Guanzi_ 39, 14.236, also speaks of "essence and vapor conjoining" 精 氣 合 when intercourse between a man and a woman leads to the conception of a child. _Heqi_ acquired special meaning in later religious Daoism, where it was the name of a group sexual rite practiced by Daoists as early as the Later Han (Rao Zongyi 1991: 142; Maspero 1981: 533–41; Schipper 1969: 27–31; and Kalinowski 1985: 781–85).
6The lacuna extends to the bottom of C215. After C215 _MWD_ , vol. 4 "Transcription," erroneously omits an entire column of text. My transcription of the missing column (C215a) is based on Qiu Xigui (1992: 534–35): 必 至 [1] 思 氣 不 [1] 鬱 禹 曰 善 戏 訁 庠 今 我 血 氣 外 揖 [11].
7The lacuna extends to the bottom of C215a. Since the lacuna begins at the same point on the manuscript as the eleven-graph lacuna in C215, I estimate the same number of missing graphs in C215a. It is evident that Yu has finished speaking and that one of the females now begins to speak.
8The final sentence refers to procedures for sexual intercourse. I do not know the significance of ascending on the left and descending on the right.
1 _MS_ III.90 joins diet with exercise ( _yin_ 引) in cultivating the Yin element of the body. The genitals are a prime but not the sole referent of Yin in the passage.
2Compare _MS_ VI.A.6, which describes the cultivation of "penile vapor" through diet and exercise. _MS_ VI.A.8 mentions a morning exercise called "pulling Yin" ( _yin_ Yin 引 陰) which serves to "refine the muscles." It seems to refer to an exercise rather than to sexual activity; that is, Yin does not simply denote the genitals. Cultivating the Yin element of the body is the object of two techniques for "pulling Yin" described in the _Yinshu_ , one a simple toe-touch and the other a procedure involving anal constriction (see the Prolegomena, Section Four, "Techniques," for details).
3In the parallel in _MS_ VI.A.5 the "it" in the quotation is indisputably the penis.
4The sentence seems to be a fragment from a description of an exercise (for cultivating Yin?).
5Following C219 a heavy vertical line separates the main text from the list of recipe categories in _MS_ III.92. The line ends about eight centimeters above the bottom of the silk sheet; a full-face drawing of the female genitals with names identifying the parts occupies the space directly beneath it (C218 contains a short column of text in order to make room for the right side of the diagram; see Fig. 13). Only one name is partially extant inside the drawing on the left side of the diagram. On the right side there is evidence of seven names: two inside the drawing; and five outside the drawing, one now completely illegible. Because of the parallel in _MS_ VII.B.19 which lists twelve names, _MWD_ , vol. 4, "Transcription," n. 1, suggests that the diagram in _MS_ III.91 might originally have included twelve names as well. Li and McMahon argue that the diagram originally contained nine names (1992: 164); but this is based on the symbolic significance of the number nine in connection with vaginal penetration in later sexual literature that I doubt is applicable to _MS_ III.91. Li and McMahon provide a table comparing names for parts of the female genitals in _MS_ III.91 and _MS_ VII.B.19 with later sexual literature. Ma Jixing also provides a table of all of the names that occur in the manuscripts and in received sexual literature; and speculates on possible identifications of the manuscript names (1992: 1063–65).
6 _Chizhu_ 赤 珠. "Red bead" is written at the top beside two dots on either side of what must represent the labia major. I assume that the dots represent the two corpora cavernosa of the clitoris. Li and McMahon also identify _chizhu_ as the clitoris (1992; 164). The name occurs in later sexual literature.
7[1] _xian_. 弦. The name is written beneath "red bead." There is no counterpart in _MS_ VII.B.19, but based on the occurrence of _qinxian_ 琴 弦 (zither strings) in later sexual literature the lacuna is probably _qin_. Li and McMahon identify "zither strings" as the labia minor (1992: 164); Wile concurs (1992: 236, n. 73).
1 _Fu_ [1] 付. Li and McMahon identify this as a name for the labia major (1992: 164). The identification is plausible.
2The names outside the drawing represent points inside the vagina. In later sexual literature such names identify successively deeper points and serve as landmarks for the depth of penile penetration (see the table in Li and McMahon 1992: 164). I translate the names in a sequence from upper right to lower left, beginning with _jiguang_ 笄 光 (hairpin light) and concluding with _gushi_ 糓 實 (grain fruit), written two columns to the left near the base of the drawing. _Jiguang_ is the first of the twelve names in _MS_ VII.B.19, but is not attested in later sexual literature. In later sexual literature _maichi_ 麥 齒 (wheat teeth) is the first interior point after passing the labia minor, and _gushi_ is deeper than _maichi_ (see Wile 1992: 255, n. 42; and Li and McMahon 1992: 164). If one assumes that _MS_ III.91 follows a sequence from shallow to deep and that this sequence corresponds to later sexual literature, the names in _MS_ III.91 ought to be listed beginning with _maichi_ on the left and concluding with _jiguang_. That would make _jiguang_ the deepest point in the vagina. The list in _MS_ VII.B 19 does not help resolve the matter, since the names there do not follow any particular sequence. I leave the question of the location of _jiguang_ inside the vagina and the sequence of the names written outside the drawing in _MS_ III.91 unresolved. It occurs to me that the names may not be written in a strict shallow to deep or deep to shallow sequence.
3[1] _shu_ 鼠. The name is written in a column to the left of _jiguang_. The compound _shufu_ 鼠 婦 (rat wife) in _MS_ VII.B.19 may be related to "[1] rat." Several names with "rat" as the second word of the compound occur in later sexual literature. The lacuna in _MS_ III.91 may be _chou_ 臭 (odorous) or _yu_ 俞. _Choushu_ is identified in later sexual literature as the next point deeper than _gushi_ ; _yushu_ is a point between _maichi_ and _gushi_.
4The two graphs written beneath [1] _shu_ are illegible.
5 _Maichi_ 麥 齒 (wheat teeth) and _gushi_ 毂 實 (grain fruit) are written in a column to the left of [1] _shu_. Both names occur in _MS_ VII.B.19 and in later sexual literature. For discussion of the meaning of "wheat teeth" (which refers to irregular teeth, and by extension to a similar-appearing part of the vagina) see Wile 1992: 243, n. 129.
6The recipe categories of _MS_ III are listed in four registers.
7I follow Ma Jixing (1992: 654, n. 3) in reading _sui_ /* _stj ǝd_ 虽 as a phonetic loan for _wei_ /* _r ǝd_ 惟; and understanding it as synonymous with _wei_ 爲 (make) in the heading as written in _MS_ III. 10.
_MS_ IV
Zaliao Fang
雜 療 方
Recepies for Various Cures
_MS_ IV.1 (CC1–2)
[18] bird egg [1]{1}[19] {2}.1
_MS_ IV.2 (C3)
[2] increase vapor. Take _bai songzhi_ (white pine rosin), _duyu_ ,2 and [1] _shizhi_ (clay)3 in equal amounts. Smith and mix together. Then put a large three-fingered pinch [?].
_MS_ IV.3 (CC4–7)
Inside augmentation and contraction.4 Take two _dou_ of _konglei_ ,5 chew, and pound. [2] {2} or soak it in two _dou_ of fine gruel-vinegar. [4] and remove the palms. Put two _sheng_ of _tao_ (peach) fuzz into [1] and stir [1]. Soak two _chi_ of excellent cloth in the [1]. Dry in the dark. [7] cloth. When engaging in intercourse rub the mid-body and the front with the cloth.6 When (the penis) rises, remove it. If you wish to stop it, wash with glutinous panicled millet slop or flowing water.1
_MS_ IV.4 (C8)
Inside augmentation. Put spring-bird eggs between _sang_ (mulberry) branches and steam them, [1] in glutinous panicled millet and eat. Consume one egg; do not eat more. If you eat more [?].
_MS_ IV.5 (CC9–10)
Inside augmentation. Take _gui_ (cinnamon), _jiang_ (ginger), _jiao_ (zanthoxylum), and _zaojia_ (honey locust)2 in equal amounts. Smith all of them, and mix together. Make balls using _gu_ (paper mulberry) liquid, and roll them with _yu_ (elm) [1] the size of [3]. Store in a bamboo tube and do not let them lose their moisture. Then put them into the mid-body hole.3 When (the penis) rises, remove.
_MS_ IV.6 (C11)
Inside augmentation. Soak two _chi_ of excellent white cloth in one _dou of gu_ (paper mulberry) liquid. [2] steam until the liquid is gone. Store well until ready to engage in intercourse. Moisten4 the mid-body with the cloth. When (the penis) rises, remove.
_MS_ IV.7 (CC12–15)
Inside augmentation. Put a dog liver in a bee hive and let the bees [1] sting it on all sides, running through over ten hives.5 Smith one _sheng_ of _linggao_ (spurge). Soak in one _sheng_ of fine gruel-vinegar for five nights, and remove the _linggao_ (spurge). Then take one large three-fingered pinch each of Yu soot1 and [2]. Combine with the liver in gruel-vinegar. Then [5] good wadding [6] the gruel-vinegar is gone.2 Store well in a bamboo tube and do not let it lose its moisture. When engaging in intercourse, wrap the mid-body with it. When (the penis) rises, remove.
_MS_ IV.8 (CC16–17)
Contraction. Take _fanshi_ ,3 _zaojia_ (honey locust), and Yu soot––the three substances in equal amounts. [3] one substance. Smith all of them, and mix together. When having intercourse, prepare a small sack. Insert it into the front4 for the time it takes to eat, and remove.
_MS_ IV.9 (CC18–19)
Contraction. Take one part each of _gui_ (cinnamon) and dried _jiang_ (ginger); two parts of _fanshi_ ; and three parts of _zaojia_ (honey locust). Smith all of them and mix. Wrap in plain silk, making it the size of a finger. Insert into the front. When it takes effect, take it out.
_MS_ IV.10 (CC20–21)
Contraction. Take three parts of Ba _shu_ (croton);5 two parts of _shechuang_ (cnidium); one part each of _gui_ (cinnamon) and _jiang_ (ginger); and four parts of _zaojia_ (honey locust). Smith all of them and mix together. Blend with honey or _zao_ (jujube) fat. Make balls the size of a _gan_ (Job's tears fruit) to insert into the front. When having intercourse, put them in a small sack and stuff into the front. When it takes effect, take it out.
_MS_ IV.11 (CC22–23)
Contraction. Take two parts each of incinerated dog bone and _fanshi_ ; one part each of _gui_ (cinnamon) and _jiang_ (ginger); and three parts of _zaojia_ (honey locust). Smith all of them and mix together. Use _zao_ (jujube) fat [3] the front. When it takes effect, take it out.
_MS_ IV.12 (CC24–25)
Contraction. Take one part each of _fanshi_ and _tao_ (peach) fuzz; and two parts of Ba _shu_ (croton). Smith all three substances and mix. Blend with _zao_ (jujube) fat. Make balls the size of a _gan_ (Job's tears) fruit. Insert [4] for the time it takes to cook a meal.1 Then [8] in the recess.2
_MS_ IV.13 (CC26–27)
[1] excitation.3 Sheep head [9].4 Dry in the sun until solidified. Blend with honey, making them the size of [5] fingertip [?].
_MS_ IV.14 (C28)
[14] {1}. The woman feels pleasure and desires it.
_MS_ IV.15 (C29)
[?].5
_MS_ IV.16 (C30)
[?] it.
_MS_ IV.17 (CC31–32)
[?] all in equal amounts. Mix together. Yin [?] pinch. Insert into the front. The woman feels intense pleasure and desires it.
_MS_ IV.18 (CC33–34)
[?] half. Smith all of them and mix together, making them the size of [1]. Put into good gruel [?].
_MS_ IV.19 (C35)
[?] fine gruel-vinegar [1] and eat. {2} [4] do not eat more than thrice [?].
_MS_ IV.20 (C36)
[?] three _cun_. Incinerate and smith. [4], for the time it takes [to eat].6 [?].7
_MS_ IV.21 (CC37–39)
[4] {2} [24]. When finished, take the [1] {1} [9] three days [14]. If {5}, a small three-fingered pinch is also all right. Already tested.1
_MS_ IV.22 (C40)
The method of the afterbirth-burial chart for entombment according to Yu.2 When burying the afterbirth, avoid the location of the Small Period and the Great Period. According to the month of birth, look for the number that is highest to bury the afterbirth [1].3
_MS_ IV.23 (CC41–42)
After having given birth, thoroughly wash the afterbirth with clear flowing water and well water. Wipe thoroughly until there is no liquid. Put it in an old pottery slotted steaming-pot1 that is free of grime. Cover very tightly with a pottery bowl so that bugs cannot enter. Bury it in unspoiled ground in a Yang position at a place where the sun shines long. This ensures that the infant has excellent heart-knowledge,2 a good complexion, and few ailments.
_MS_ IV.24 (CC43–47)
To increase the inside and benefit the interior. Warm one half cup of pure liquor without letting it get hot. Break a chicken egg and pour the liquid into the liquor. Stir, and drink it. Always drink it at dawn before eating. When you begin to drink, drink one egg; the next day drink two eggs; and the day after drink three eggs. On the day after that again drink two eggs, and the next day drink one egg. Always decrease after reaching three eggs; and after decreasing to one egg, again increase.3
Always begin ingesting (the eggs) on the first day of the eighth and second months. Drink [5]. Ingesting in these two seasons4 makes a person's face not become wizened;5 the mouth and lips are not dry; and it benefits the interior and increases the inside.
Always ingest [?].
_MS_ IV.25 (CC48–53)
[3] tonic sweet-liquor.6 Take {1} [69] {1} the amount [2] _sheng_ and boil [2] {1} [1] above it. [11] to make five _sheng_. Combine the five substances with _bi_ [1] root, set in a slotted steaming-pot, and collect the liquid in the small cup below.7 [11] the taste is completely extracted and stop.8 Then boil the liquid. When it bubbles once, the sweet-liquor is finished. Then drink it gradually, until [1] body [8] the inside, and at the same time the interior has an abundance of essence-fluid.1 {2} [?].
_MS_ IV.26 (CC54–55)2
[?] {1} [?] {2} [1] {1} [?]
_MS_ IV.27 (CC56–57)
[?] {1} [?]
_MS_ IV.28 (CC58–60)
[2] arrive at a place where the _yu_3 [9] name is _nüluo_.4 {1} [9] {3} [12]. Yi makes you not5 [8] {1} makes the _yu_ not shoot.
_MS_ IV.29 (C61)
To make the _yu_ not shoot. When you arrive at water, throw a handful of grain at it.6
_MS_ IV.30 (C62)
Another. Every morning chew two or three nodules of _suan_ (garlic),1 and ingest them.
_MS_ IV.31 (C63)
Another. Every morning chew three _lan_ (eupatorium) fruits, and chew _lingji_ (water chestnut).
_MS_ IV.32 (C64)
Another. Wear a silkworm cocoon or a silk-trimmed garment.
_MS_ IV.33 (C65)
Another. Dress in a red coarse-silk garment and a black alum-dyed garment.2 Trim the collarband and sleeves with horsehair,3 or use [1] and [1] to fill in the underarms.
_MS_ IV.34 (C66)
Another. Trim the collarband and sleeves of the garment with wild4 pig bristles. It makes the _yu_ and venomous snakes not dare to shoot.
_MS_ IV.35 (CC67–70)
If by misfortune you are shot by the _yu_ , venomous snakes, and bees, chant an incantation and spit at it thrice. Name the creature that did the shooting with its name, saying: "So-and-so. You five brothers, so-and-so knows all your names.5 You who dwell in the water are the fish- _qi_. You who dwell on the land are the bug- _qi_.6 Those lodged in trees are the bee and _ransi_ (catepillar).1 The one who flew to Jing-in-the-South is the _yu_. You advance2 [1] not [1]. You instruct the clan grandsons. So-and-so is a murderer. If you do not cause so-and-so's ailment to desist, once again [14].3
_MS_ IV.36 (C71)
[19] root, one third _dou_ and add it. Sieve thoroughly, and drink.4
_MS_ IV.37 (CC72–73)
[?] dry. When dry, smith [?].
_M5_ IV.38 (CC74–75)
Another. Take [11] fish. Do not eat that evening, and eat it at dawn.5 Take satiation as the standard. Do not drink the liquid.
_MS_ IV.39 (C76)
Another. Butcher a _bie_ (soft-shelled turtle), and drink the blood. Steam the flesh and eat it.
_MS_ IV.40 (C77)
Another. Soak yellow earth from the stove in gruel-vinegar. Steam, and hot-press the spot with it.
_MS_ IV.41 (C78)
Another. Pound _lan_ (eupatorium) leaves while fresh. Steam, and hot-press it.
_MS_ IV.42 (C79)
Another. Steam earthworm excrement, and hot-press the spot with it.
1 _MWD_ , vol. 4, "Transcription," n. 1, notes that the right end of the silk sheet is damaged. The numbering of columns begins with the first extant fragments of text.
2Ma Jixing (1992: 750, n. 3) argues that _duyu/*ngwjag_ 杜 虞 is _duruo/*njak_ 杜 若 (listed in _GM_ , 14.23, botanical identity uncertain). The argument is phonologically plausible.
3 _Wuse shizhi_ 五 色 石 脂 is listed in _GM_ , 9.80, and refers to five types of cay classified by the five colors blue, yellow, black, white, and red. The lacuna must be the word for the color of the clay.
4I.e. recipes for increasing the size of the erect penis (augmentation) and reducing the size of the vaginal opening (contraction: see _MS_ III.6, 21). _MS_ IV.3–7 concern the penis and _MS_ IV.8–12 the vagina.
5 _Konglei_ 空 壘 is unknown.
6I interpret the term _zhongshen_ 中 身 (mid-body) to refers to the region between the waist and the navel; and _qian_ 前 (front) to refer to the genitals, in this case the male genitals. _Zhongshen_ is attested in _Zhanguoce_ , 25.1a, in a passage that compares the strategic position of Liang 梁 to the body of a snake: "Using the examples of a snake, strike the tail and the head comes to the rescue; strike the head and the tail comes to the rescue; strike the head and the tail comes to the rescue; strike the mid-body ( _zhongshen_ ) and the head and tail both come to the rescue. At present the King of Liang is the mid-body of Under-heaven." The ancient division of the body into head, foot, and waist is indicated in the _SW_ , 3A.39b, gloss of _yao_ 要 (waist) as _shenzhong_ 身 中 (middle of the body). _MS_ IV.5 refers specifically to the _zhongshen kong_ 中 身 空 (mid-body hole), which is the navel. I do not accept the argument in Li and McMahon (1992: 161) that _zhongshen_ denotes the "shaft of the penis"; and _zhongshen kong_ the "urinary opening" (the passage cited from _Ishinpô_ , 28.12a, to support the latter identification does not contain the term _zhongshen kong_ ; the _Sunzi_ passage adduced for _zhongshen_ parallels the _Zhanguoce_ passage quoted above, and the denotation "penis" is implausible). _Zunsheng bajian_ , 860 (高 子 論 房 中 藥 物 之 害), lists four aphrodisiac drugs that are put in the navel and two that are applied to the waist. Thus there is no need for concern that the waist and navel are improbable locations for the application of aphrodisiacs in the Chinese tradition. Since _MS_ IV.3 is concerned with penile erection, _qian_ is best understood as male genitals; _qian_ refers to the vagina in _MS_ IV.8–11and _MS_ IV.17.
1 _Ishinpô_ , 28.40b, also recommends washing the penis with water if an aphrodisiac-induced erection does not stop. Napkins impregnated with aphrodisiac drugs and applied to both male and female genitals are described in _MS_ III.38–39 and _MS_ III.41–44.
2I follow _MWD_ , vol. 4, "Transcription," in reading _jiao/*tsjagw_ 焦 as a phonetic loan for _zao/*ts əgw_ 皂.
3I.e. the navel.
4"Moisten" translates _wen_ 慍, glossed in _SW_ , 12A.53b, as "immerse." Perhaps the cloth remains moist with the aphrodisiac like the wadding in _MS_ IV.7. Alternatively, the word may simply mean "rub" (attested in Song and later sources).
5Compare _MS_ III.37.
1Yu _xun_ 禹 熏 may be the same substance as Yu _zao_ [1] 禹 竈 in _MS_ I.E.243, probably stove soot.
2The wadding is soaked in the aphrodisiac until the liquid is completely adsorbed.
3The mineral denoted by _fanshi_ 蕃 石 is uncertain (see _MS_ III.39).
4I.e. the vagina.
5Ba _shu_ 巴 菽 is synonymous with Ba _dou_ 巴 豆.
1I assume that 熟 食 refers to cooking food, undoubtedly grain. Alternatively, 熟 食 頃 refers to an "extension" 熟 of the "time it takes to eat" 食 頃.
2"Recess" translates _bi_ 庳, glossed in _SW_ , 9B.16b, as "house with a sunken area in the center." In _MS_ IV.12 it is evidently another name for the vagina.
3I follow Ma Jixing in reading 痒 as _yang_ 癢, referring to the excitation associated with sexual arousal (1992: 761, n. 1).
4Sympathetic magic based on punning between _yang_ 療 (itching) and _yang_ 羊 (sheep) is probably the reason for using sheep head in the aphrodisiac.
5 _MWD_ vol. 4, "Transcription," n. 1, notes that there is a break in the text between C29 and C30; it is not clear how many columns might be missing.
6Judging from the context the lacuna must be _shi_ 食.
7 _MWD_ , vol. 4, "Transcription," n. 1, notes that there is a break in the text between C36 and C37; it is not clear how many columns might be missing.
1 _Yishi_ 已 試 is the same kind of term as _changshi_ 嘗 試 (previously tested; see _MS_ I.E.15).
2"Afterbirth" translates _bao_ 胞, strictly speaking the placenta (see _SW_ , 9A.38b; _bao_ 包 is the original graph for the womb). _MS_ IV.22–23 concern proper burial of the afterbirth, which is essential to the well-being of the newborn infant. _MS_ V.2 is a drawing of the chart referred to in _MS_ IV.22, identified there as "Entombment according to Yu, with south orientation". (南 方 禹 臧). Yu is also the recipient of the teaching on gestation in _MS_ V.3. Yu's association with childbirth continued into the medieval period as reflected in a quotation from the pre-Tang _chanjing_ 産 經 (Childbirth canon) in _Ishinpô_ , 23.19a: "In the past when Yu was at Thunder Marsh there was a woman who approached him sorrowfully wailing. Yu asked the reason and she replied, 'Your maid has given birth to numerous children who all died young. Not one is alive, and that is why I am sorrowfully wailing.' Yu taught her this method, and her children were all long-lived. None were lost young." The method subsequently described is similar to _MS_ V.4–7. In all, quotations from the _Chanjing_ on afterbirth burial occupy _Ishinpô_ , 23.18b–23a.
3Small Period ( _xiaoshi_ 小 時) and Great Period ( _dashi_ 大 時) refer to calendro-astrological calculations based on the rotation of the Big Dipper and the Jupiter cycle respectively. The compass points on earth that correspond to the positions of the two astrological bodies for each month are unlucky. The chart in _MS_ V.2 consists of twelve small squares arranged around the perimeter of a large square. Each small square represents one of the twelve months and is marked with twelve compass points. Two of the points are labeled _si_ 死 (death), representing the positions of Small Period and Great Period for the month in question, and ascending numbers are written by the other points. As explained in _MS_ IV.22, the afterbirth should be buried in the direction indicated by a point labeled "death" (see _MS_ V.2 for further explanation of the calendro-astrological symbolism and use of the chart). A similar method was still in use in medieval times, as indicated in _Ishinpô_ , 23.33b: "Whenever you wish to bury the afterbirth you should first examine the chart of the twelve months. The location with the highest number means (the infant) will not be long-lived. If a place with the highest number is simultaneously occupied by an ill-omened spirit, you must avoid it. If you choose the location with the next highest number that will also be lucky."
1It is curious that the slotted steaming-pot ( _yan_ 甗) is specified, since the afterbirth is supposed to be tightly sealed inside. I suspect that the kettle ( _fu_ 釜) that sits beneath the slotted steaming-pot is the intended vessel (see _MS_ I.E.58).
2I.e. a bright mind.
3Compare _MS_ III.15.
4I.e. autumn and spring.
5"Wizened" translates _jiao_ 焦, attested in _Suwen_ 1, 1.3b, as the dark, wrinkled appearance of the face that comes with age.
6A recipe for _li_ 醴 (see _MS_ III.4).
7I read 贛 as _gan_ 匿 (small cup), as in _MS_ I.E.97. I am guessing that the solid ingredients from the preceding decoction are put into the slotted steaming-pot and the liquid allowed to drain into a cup placed below. _MWD_ , vol. 4, "Transcription," n. 2, reads the graph as _gan_ , glossed in _SW_ , 146.36a, as liquor with a potent taste; giving the translation, "collect the potent-tasting liquid below."
8Perhaps liquor is poured over the ingredients in the steaming-pot to extract their essence.
1"Essence-fluid" translates _jingzhi_ 精 汁, which refers to vital juices generated inside the body as the result of drinking the liquor.
2 _MWD_ , vol. 4, "Transcription," n.1, notes that there is a break in the text between C53 and C54, and again between C55 and C56; it is not clear how many columns might be missing on either side of CC54–55. The "Transcription" does not note another aspect of the silk sheet, which is that after C53 there are about six blank ruled columns before the break. Moreover, the calligraphy beginning in CC54–55 is different. The blank columns and change of calligraphy indicate that _MS_ IV.26–42 were added to the silk sheet by another scribe after _MS_ IV.1–25.
3 _Yu_ 蜮 is the name of a deadly water creature that was an ever-present hazard for inhabitants of Chu and Yue. _SW_ , 13A.58b, glosses _yu_ with one of its several names, _duanhu_ 短 狐 (short fox); describes it as "resembling a turtle with three legs"; and notes that it "shoots vapor to injure people." Early _yu_ lore is summarized in Eberhard 1968: 193–95. It was believed to have a mouth in the form of a bow, from which it shot vapor "arrows" at its victims. And shooting someone's reflection in the water was sufficient to mortally wound the person standing on the blank. The notion of the _yu_ as an evil omen is first indicated in _Zuozhuan_ , Zhunang 18.9.8a. In the first century B.C. Liu Xiang expressed the opinion that the _yu_ was locally generated from chaotic vapor in Southern Yue, and that it was a manifestation of the excessive sexuality of the women of Yue ( _Hanshu_ , 27C–1.13b). There is little solid information regarding its biological identity. _SW_ gives as an orthographic variant of _yu_. The same graph was understood as a name for the toad, but that does not mean that the _yu_ was considered to be a toad (see the Duan Yucai commentary). In medieval times––when the southern yu was still feared––many regarded it as a kind of water insect (Schafer 1967: 111). The recipes in _MS_ IV.28–35 focus on preventing the _yu_ from shooting, no doubt because its wound is believed to be mortal and prophylaxis is the best remedy.
4 _Nüluo_ 女 籮 is the name of a parasitic plant, probably tree moss ( _GM_ , 37.12). Its use in _MS_ IV.28 is not clear.
5Yi 羿 refers to the master archer who appears in a number of early legends associated with exorcistic themes. His image in myth is reviewed in Eberhard 1968: 80–87. The direct form of address "you" indicates that these words belong to an incantation.
6The purpose of throwing grain is probably twofold: to appease the _yu_ with an offering, and to break the smooth surface of the water so that the _yu_ cannot shoot at the person's reflection.
1I read as _suan_ 蒜. For the use of 林 as a signific element in place of 艹 in Warring States script, see He Linyi 1989: 207 (the example given is 楚 to write _xun_ 輩). I do not accept the reading _nai_ 柰 (crab apple) in _MWD_ , vol. 4, "Transcription," n. 1. Also, _suan_ refers to the native Chinese garlic, _Allium scorodoprasum_ L. (ZY: no. 0478), not to _A. sativum_ L., the garlic with multiple-clove heads that was introduced from the West.
2This prophylactic attire must be related to the black upper garment and red lower garment worn by the chief exorcist in the Great Exorcism ( _Hou Hanshu_ , "Zhi" 志, 5.Ioa; cf. Bodde 1975: 81). Similar black and red attire is used to clothe the body of the deceased in _Yili_ , 40.6b. According to the Zheng Xuan commentary the colors symbolize heaven and earth.
3 _Lai_ 處 is glossed in _SW_ , 2A.11a, as bristly hair used to pad clothing. The horsehair is probably stuffed inside the collarband and sleeves.
4"Wild" translates 田 啺 (I read _chang_ 啺 as _chang_ 場 in the sense of "unarable land"; see _SW_ , 13B.39a, and Duan Yucai commentary).
5The first "so-and-so" represents the name of the creature, the second the name of the person.
6 _Qi_ 蚑 is given as an alternate name for _zhi_ 蛭 (leech) in BL; and Tao Hongjing notes that there are many varieties of qi both in the water and out ( _GM_ , 40.104). Perhaps the unattested graph 鮍 in _MS_ IV.35 (which I render as "fish- _qi_ ") signifies the leech; and 蚑 "bug- _qi_ " signifies another blood-sucking creature on land.
1Tao Hongjing states that the hair on the _ransi_ 蛅 嘶 stings ( _GM_ , 39.77).
2I translate _jin_ 晉 as glossed in _SW_ , 7A.4b, "advance." _MWD_ , vol. 4, "Transcription," n.5, argues that _jin_ /* _tsjin_ is a phonetic loan for _jian_ /* _tsjan_ 前 (arrow). The loan usage is phonologically plausible, but the following lacunae make it impossible to determine whether the meaning "arrow" is justified by the context.
3The first "so-and-so" is the creature, the second the person. _Qianjin yifang_ , 30.357, records a similar incantation that first identifies the stinging creatures by their location and then concludes: "You five brothers, I know you all. Collect your five poisons, let no one transmit them. If you do not collect poison, (I) destroy your clan." Several incantations in _MS_ I.E also liken the agents blamed for the ailment to a family (for example, _MS_ I.E.120).
4 _MWD_ , vol. 4, "Transcription," n.1, notes that there is a break in the text between C71 and C72; it is not clear how many columns might be missing. It is a also no longer clear what the recipes in _MS_ IV.36–42 are intended to treat.
5I understand this to mean that the person should not eat a meal the night before taking the medicine; and that he should eat the medicine the next morning at dawn.
_MS_ V
Taichan Shu
胎 産 書
Book of the Generation of the Fetus
_MS_ V.1 (Upper Half, Right Side)
_Explanation_
The two human figures are placed sideways on the manuscript; each one stands with legs spread and arms raised (Fig. 14). Despite the poor preservation of the drawing, the extant Branch signs can be seen to be written on top of the head, by the sides of the head, by the shoulders, on the hands, by the underarms, beneath the feet, and in the crotch. Comparing _MS_ V.1 with the drawing in the first Shuihudi hemerological manuscript ( _SHD_ : 206), the arrangement of Branch signs on the top figure matches the Shuihudi figure representing spring and summer; the bottom figure matches the Shuihudi figure representing fall and winter. The child's fortune is determined by consulting the figure for the appropriate season and locating the Branch sign in the cyclical designation of the date of birth on it. According to the explanatory text in the Shuihudi manuscript, if the Branch sign is atop the head the child will be extremely wealthy; by the neck (the Branch signs written by the sides of the head in _MS_ V.1), noble; in the crotch, wealthy; by the underarms, the child will be loved; at the hands, he will be a thief; beneath the feet, ignoble; and on the "outside" ( _wai_ 外; the Branch signs written above the arms on the Shuihudi figures and by the shoulders on the _MS_ V.1 figures), he will be a vagabond. Thus, a child born on a _mao_ 卯 day in summer will be wealthy ( _mao_ is atop the head of the top figure); a child born on a _mao_ day in winter will be a vagabond ( _mao_ is by the right shoulder of the bottom figure).
Fig.14 Line drawing of _MS_ V.1, with reconstruction; from _MWD_ , vol.4: 133
_MS_ V.2 (Upper Half, Left Side)
_Explanation_
The name of the chart is written in the center: "Entombment according to Yu, with south orientation" 南 方 禹 臧 (Figs. 15–16). Its use in the method for burying the afterbirth is explained in _MS_ IV __.22 __. Looking at the chart, each square representing a month is marked with twelve points corresponding to the twelve Branch signs and compass directions (south is at the top): _zi_ 子 (N), _chou_ 丑 (N-NE), _yin_ 寅 (E-NE), _mao_ 卯 (E), _chen_ 辰 (E-SE), _si_ 巳 (S-SE), _wu_ 午 (S), _wei_ 未 (S-SW), _shen_ 申 (W-SW), _you_ 酉 (W), _xu_ 戍 (W-NW), _hai_ 亥 (N-NW). According to _MS_ IV.22 the directions corresponding to Small Period ( _xiaoshi_ 小 時) and Great Period ( _dashi_ 大 時) must be avoided when burying the afterbirth. These points are labeled _si_ 死 (death) on the chart. As explained in _Huainanzi_ , 3.42, Small Period corresponds to the handle of the Big Dipper, which shifts clockwise one position per month beginning at _yin_ (E-NE) in the first month. The points marked "death" on the chart corresponding to the positions of Small Period are: first month, E-NE; second month, E; third month, E-SE; fourth month, S-SE; fifth month, S; sixth month, S-SW; seventh month, W-SW; eighth month, W; ninth month, W-NW; tenth month, N-NW; eleventh month, N; twelfth month, N-NE. Having established the positions of Small Period on the chart, the positions of Great Period are: first month, E; second month, S; third month, W; fourth month, N; fifth month, E; sixth month, S; seventh month, W; eighth month, N; ninth month, E; tenth month, S; eleventh month, W; twelfth month, N. The _Huainanzi_ passage just cited identifies Great Period as another name for one of the cycles associated with _taisui_ 太 歲 (Grand Year). In calendro-astrological calculations Grand Year represents a planet that moves clockwise in opposition to counter-clockwise rotating _suixing_ 歲 星 (Year Star; i.e. Jupiter). However, the Great Period cycle described in _Huainanzi_ moves counter-clockwise, beginning from _mao_ (E) in the second month and shifting to the successive cardinal compass points in subsequent months (N in the third month, W in the fourth month, etc.). Later sources show that the _Huainanzi_ text is corrupt and that the cycle should begin at _mao_ (E) in the first month rather than in the second month, in agreement with the chart in _MS_ V.2 (Zhang Peiyu 1989: 137–38). But the later sources still indicate a counter-clockwise direction for the Great Period cycle, rather than the clockwise direction in the chart. The Great Period cycle indicated in _MS_ V.2 does, however, correspond to the cycle of _sui_ (Jupiter) described in the first Shuihudi hemerological manuscript ( _SHD_ : 190).
Fig.15 Line drawing of _MS_ V.2, from _MWD_ , vol.4: 134
Fig.16 Line drawing of _MS_ V.2, with reconstruction and compass points
I know of no other examples of the numbering system used on the chart. The lowest number is 20, and the numbers increase clockwise by tens until interrupted by a "death" point, after which the numbering begins again with 20. There are three exceptions to this pattern. In the second month the number 40 appears at S-SW, followed by 30, 40, and 50 on the west side of the square (the numbers are missing in _MS_ V.2, but can be restored based on the sequence 60, 70, 80 on the north side of the square). This is clearly scribal error, writing 廿廿 (40) instead of 廿(20). In the ninth month, the number 30 appears at E-SE instead of 20 following the position of Great Period at E, and the numbering continues 40, 50, 60 on the south side of the square. Similarly, in the first month 20 appears at E-SE, followed by 40, 50, 60 on the south side. According to the regular progression, 110 is the highest number that can be reached in the chart, but the first month records a 120 at N-NE. There must be a reason for skipping from 20 to 40 in the first month in order to reach a high number of 120; and the ninth month sequence beginning with 30 at E-SE is probably also intentional, not scribal error. Besides choosing the highest number to determine the burial site for the afterbirth, I do not know what other significance the numbers may have. I doubt that they represent a prediction of the lifespan of the child as suggested in Ma Jixing 1992: 820. The appropriate burial sites by month are: first month, 120 (N-NE); second month, 90 (E-NE); third month, 70 (E); fourth month, 70 ((N-NW); fifth month, 90 (E-NE); sixth month, 110 (S-SE); seventh month, 110 (S-SW); eighth month, 90 (W-SW); ninth month, 80 (W); tenth month, 70 (S-SE); eleventh month, 90 (W-SW); twelfth month, 110 (N-NW).
_MS_ V.3 (Lower Half, CC1–13)
Yu asked Youth Multiplier:1 "I wish to propagate people and engender children. How is it that this occurs?"
Youth Multiplier replied: "After menstruation2 is finished and the fluid [1],3 have intercourse with her over the next three days and there will be a child. If on the first day, it is a boy; if on the second day, a girl.4 Thus when human beings are engendered, having entered into obscure darkness and exited from obscure darkness, they first become humans.5 In the first month it is called 'flowing into the form.'6 Food and drink must be the finest; the sour boiled dish must be thoroughly cooked. Do not eat acrid or rank foods. This is called 'initial fixture.' In the second month it first becomes lard.7 Do not eat acrid or stinking foods. The dwelling place must be still. For a boy there must be no exertion, lest the hundred joints all ail.1 This is called 'first deposition.'2 In the third month it first becomes suet, and has the appearance of a gourd. During this time it does not yet have a fixed configuration, and if exposed to things it transforms. For this reason lords, sires, and great men must not employ dwarves. Do not observe monkeys. Do not eat _cong_ (onion) and _jiang_ (ginger); and do not eat a rabbit boiled dish.3 [1] you wish to give birth to a boy, set out bow and arrow, [1] male pheasant, mount a male horse, and observe the male tiger. If you wish to give birth to a girl, wear hairpins and earrings at the waist, and wear a pearl belt.4 This is called 'inner imaging to complete the child.'5 In the fourth month Water is bestowed on it, and blood first forms.6 The appropriate foods are rice, wheat, _shanyu_ (mud eel) [2], which clarify the blood and brighten the eyes. In the fifth month Fire is bestowed on it, and vapor first forms. Rise late and [1] wash the hair. Wear a thick layer of clothing and remain inside the house. At dawn inhale heaven's rays and avoid harm from the cold. The appropriate foods are [rice] and wheat;1 the appropriate boiled dishes are beef and mutton, mixed with _zhuyu_ (evodia); and do not eat [1], thereby nurturing the vapor. In the sixth month Metal is bestowed on it, and muscle first forms. Exercise [3]; [go out] to wander [in the countryside; frequently]2 observe running dogs and horses. You must eat [2] without [3]. This is called 'changing the skin's webbed pattern and [1] muscle.' [4]. In the seventh month Wood is bestowed on it, and [bone] first forms.3 Occupy heated places, and do not become [immobilized].4 [12]. [With drink and food]5 avoid (things that have a) cooling effect. [9] and fine teeth. In the eighth month Earth is bestowed on it, and [skin and hide] first form.1 [8]. This is called 'tightening the [skin's webbed pattern].' In the ninth month [stone] is bestowed on it, and filament hairs first form.2 [28] await it. In the tenth month the vapor spreads [2] to form [?]."
_MS_ V.4 (Lower Half, C14)
Whenever attending to a birth, wash the afterbirth with clear water [?].
_MS_ V _.5_ (Lower Half, CC15–16)
Another. You must thoroughly wash the afterbirth, and wash it again with liquor.3 [8] {1} [13] pottery bowl, so that bugs and ants cannot enter. Then [8] a place where the sun shines. This ensures that the infant does not have scabbing, has lustrous skin, and is longlived [1].4
_MS_ V.6 (Lower Half, C17)
Another. Bury the afterbirth beneath a mat to prevent scabby itch. Inside the inner (chamber) [4], and drink on an "establishment day."5
_MS_ V.7 (Lower Half, CC18–19)
If when giving birth you have mostly boys and no girls, and you wish to have a girl, after [4] bury the afterbirth beneath a Yin oriented wall. If you have mostly girls and no boys, bury the afterbirth beneath a Yang oriented wall.
Another. Bind the afterbirth with the cord handle from a slotted steaming-pot,6 and bury it.
_MS_ V.8 (Lower Half, C20)
If a pregnant woman prepares boiled _bai mugou_ heads7 and she alone eats them, the child is beautiful and radiant, and also emerges easily. If you want to make the child vigorous, at the time of [1] eat the flesh of a mother horse.
_MS_ V.9 (Lower Half, C21)
If a woman who is still within the third month of pregnancy swallows two _jueweng_ (caterpillar cocoons), the child is a boy.
Another. If you swallow alive three blue-backed bugs from inside _jueweng_ (caterpillar cocoons), you invariably give birth to a boy. Myriad perfection.1
_MS_ V.10 (Lower Half, C22)
Another. When (the fetus) is just at the stage of the "chewed mass"2 take _hao_ (artemisia), mu,3 and _pixiao_ (mantis egg-case)—three substances. Smith and drink them; and you invariably give birth to a boy. Already tested.
Another. Pass one half _sheng_ of urine [2] is firm and has little fluid.4
_MS_ V. 11 (Lower Half, C23)
Another. Take larvae from a beehive and the Yin5 of a dog. Dry and smith them. Have the pregnant woman drink them, and she gives birth to a boy.
Another. [1] fresh fish [2] eat it.
_MS_ V.12 (Lower Half, C24)
[8] dry and smith them. Toss into liquor [3], and the pregnant woman gives birth to [3] the third month you cannot [1].
_MS_ V.13 (Lower Half, C25)
[8] {1} [14] gives birth to a boy.
_MS_ V.14 (Lower Half, C26)
Another. Take a black [4] the man alone eat the meat and drink the liquid. The woman sits on a mat of fine reeds [?].6
_MS_ V.15 (Lower Half, C27)
If you wish to give birth to a girl, boil a black hen; have the woman alone eat the meat and drink the liquid; and sit on a mat [?].
_MS_ V.16 (Lower Half, C28)
The way to seek a child. Search for _jiuzong_ herb.1 Then the husband and wife together make liquor with it and drink it.
_MS_ V.I7 (Lower Half, CC29–30)
When the birth is about to take place, first take moist, clean earth from the marketplace. [1] it in a square of three to four _chi_ that is three to four _cun_ high. After the child is born, set it on the earth. Do not [1], and let the infant [1] on it. When its body is completely covered with earth, bathe it. This makes (the child) vigorous and strong.2
_MS_ V.18 (Lower Half, CC31–32)
After having given birth, incinerate the straw bedding. Put it in water, and [2] the infant to prevent scabby itch.3 In addition, have the mother drink one half cup of the water used to bathe the infant and the mother will have no further ailments.
_MS_ V.19 (Lower Half, CC33–34)
When a woman who has few children gives birth, have another person carry the [1] and leave [2] wash the afterbirth. Wrap in new cloth; seal by binding it thrice around; and put it into [1]. Have the mother hold it herself; enter a stream-gulch [3] it thrice; set it down and leave; and return home without looking back. Then have someone else bury it well.
1A literal translation of the name You Pin 幼 頻, which suggests someone who produces a continuous line of offspring. I assume that Youth Multiplier is a male expert on childbirth. _MWD_ , vol. 4, "Transcription," emends lacunae in _MS_ V.3 based on the _Chaoshi zhubing yuanhoulun_ and _Qianjin yaofang_ parallels (printed in _MWD_ , vol. 4: 140–41).
2"Menstruation" translates _yueshuo_ 月 朔, which is related to the term _shuoshi_ 朔 事 used for menstruation in the Shuihudi _Fengzhen shi_ ( _SHD_ : 162). _Yueshi_ 月 事 (menstrual activity) is the term used in _Shiji_ , 105.18a. The use of _shuo_ in the Mawangdui and Shuihudi manuscripts specifically correlates menstruation with the spring tide that accompanies the new moon.
3The fluid must be the menstrual blood, which no longer flows.
4There is probably a symbolic connection between odd numbers which are Yang and a male birth; and between Yin, even numbers and a female birth. _Waitai biyaofang_ , 33.3b–4a, states that insemination on the first, third, and fifth days after menstruation produces a boy; insemination on the second, fourth, and sixth days produces a girl.
5"Obscure darkness" translates _mingming_ 冥 冥. _Mingming_ forms part of an epithet for _dao_ 道—Way as the source of all phenomena—in _Shiji_ , 130.6a. A writing entitled "Daofa" 道 法 (Model of Way) preceding the second Mawangdui _Laozi_ edition also uses the compound: "The empty and formless its central seam is obscurely dark ( _mingming_ ); it is the place from which the myriad creatures come into being" ( _MWD_ , vol. 1: 43). Perhaps "entering and exiting obscure darkness" alludes to the action of the penis in the vagina. In any case, conception is likened to the emergence of living things from the empty place that is Way.
6The "it" is the newly conceived entity inside the womb. _Liuxing_ 留 刑 occurs written 流 形 in _Guanzi_ 39, 14.236, where it introduces the passage on gestation: "The essence and vapor of man and woman conjoin and water flows into the form ( _liuxing_ )." The term likens the creation of the embryo to the flowing of fluid into a mold where it acquires its distinctive shape.
7I.e. the embryo is a soft mass like lard ( _gao_ 膏). Lard is the term for the first month of gestation in _Huainanzi_ , 7.99.
1Presumably the pregnant woman already has an idea about the gender of the child to be born, and must take care not to exert herself if she is expecting a boy.
2I.e. a matrix now exists for the growth of the fetus.
3As explained in _Bowuzhi_ , 2.1b, the prohibition of rabbit and ginger during the malleable third month is to prevent harelip and hand deformities: "A pregnant woman can neither eat rabbit nor look at a rabbit, for it causes the infant to have a split lip; moreover, she cannot eat fresh ginger, which causes the infant to have many fingers."
4I follow _MWD_ , vol. 4, "Transcription," in reading _shen_ 呻 as _shen_ 紳, glossed in _SW_ , 13A.20b, as "large belt." _SW_ , 1A.34b, glosses _zhu_ 珠 as "Yin essence inside the oyster," making pearls an ideal material for inducing the development of a female in the fetus. It is possible that _shen_ /* _stjin_ 呻 is a phonetic loan for _tun_ 吞 (swallow; the graph is also pronounced like its phonetic _tian_ /* _thin_ 天). This usage occurs in _MS_ V.9; and is also attested in _MWD_ , vol. 3: 68. However, all of the other items used to induce male or female gender affect the fetus from the outside; none are ingested by the pregnant woman. Thus it is more likely that she wears the pearls rather than swallowing them. The parallels in the later descriptions of gestation use the verb _long_ 弄 (fiddle with).
5The impressionability of the fetus during the third month is also evident in _MS_ V.9–10, which specify that medicines to guarantee the birth of a boy should be taken no later than the third month of pregnancy.
6From the fourth to eighth months the fetus receives the Five Agents, each of which is responsible for a physiological constituent: Water produces blood; Fire produces vapor; Metal produces muscle; Wood produces bone; Earth produces skin. Underscoring the elemental nature of the Agents, a sixth material Stone follows Earth in the ninth month to produce hair. The enumeration of the Five Agents in m _MS_ V.3 follows the order of the "conquest sequence" given in Han sources, which usually begin with Wood: Wood conquers Earth; Earth conquers Water; Water conquers Fire; Fire conquers Metal; Metal conquers Wood (Kalinowski 1991: 247). The first Shuihudi hemerological manuscript lists the "conquest sequence" in the order: Metal conquers Wood: Fire conquers Metal; Water conquers Fire; Earth conquers Water; Wood conquers Earth ( _SHD_ : 223) It is interesting that _MS_ V.3 applies the "conquest sequence" of the formulation of a cosmo-physiological model of creation (the "generation sequence" to Wood, Fire, Earth, Metal, Water was known in the third century B.C.) There is a definite logic to the correlations between Agents and constituents. Water producing blood and Fire producing vapor situates the Yin Yang duality of blood and vapor at the beginning of the process. The reasons for associating Metal with muscle, Wood with bone, and Earth with skin can also be deduced without stretching the imagination. By implication, the correlations described for the fetus ought to apply to human physiology. However, such correlations are not mentioned in the Mawangdui medical manuscripts; and there are few counterparts to _MS_ V.3 in extant writings related to physiology. Later received literature on physiology also correlates the constituents differently; for example, Fire is correlated with muscle, Metal with bone, and Wood with hair and skin (Kalinowski 1991: 222). In the _Huangdi neijing_ , constitutents like muscle and bone are subsumed under the larger category of the vessels and the internal organs; and the primary correlates of the Five Agents are the Five Depots (liver, heart, lung, kidney, spleen; these correlations are also not in evidence in the Mawangdui medical manuscripts). Antecedents to the _Huangdi neijing_ emphasis on internal organs occur in _Guanzi_ 39, 14.236, which describes gestation as a process in which the Five Tastes produce the Five Depots, which in turn produce constituents like bone and flesh (the Five Agents are not mentioned); and in third century B.C. calendars that include internal organs among the manifold Five Agent correlations operating in nature (Rickett 1985: 158–61). To sum up, _MS_ V.3 represents an early attempt at applying Five Agent theory to physiology in the context of fetal development, but its physiological correlations were not generally adopted in latter medical literature except as a conventionally accepted account of gestation itself.
1 _MWD_ , vol. 4, "Transcription," fills a three-graph lacuna based on the context and on the fact that the later parallels give rice and wheat as appropriate foods for the fifth month. I bracket [rice] because it is added to the text on the basis of the later parallels. The use of brackets in the remainder of _MS_ V.3 follows the same principle.
2 _MWD_ , vol. 4, "Transcription," fills the two lacunae on the basis of the later parallels.
3 _MWD_ , vol. 4, "Transcription," fills a five-graph lacuna based on the context and the later parallels; the bracketed word is based on the later parallels.
4Filling the lacuna is based on the later parallels.
5Filling the lacuna is based on the later parallels.
1 _MWD_ , vol.4, "Transcription," fills a six-graph lacuna based on the context and the later parallels; the bracketed words are based on the later parallels.
2 _MWD_ , vol. 4, "Transcription," fills an eleven-graph lacuna based on the context and the latter parallels; the bracketed words are based on the later parallels.
3酒 in _MWD_ , vol. 4, "Transcription," should be transcribed as _jiu_ 酒 (liquor).
4Compare _MS_ IV.23.
5The hemerological system underlying the designation of certain days as "establishment days" is explained in _MS_ I.E.69. Perhaps the liquid drunk is water that was used to bathe the infant (see _MS_ V.18).
6This cord is also used to string an exorcistic bow in _MS_ I.E.132.
7 _Bai mugou_ 甶 牡 狗 is an insect of uncertain identity (perhaps molecricket; see _MS_ III.43).
1Another term praising the efficacy of a medicine or treatment.
2I.e. the third month of pregnancy. _Guanzi_ 39, 14.236, describes the fetus in the third month as resembling a _ju_ 咀 (chewed mass).
3 _MWD_ , vol. 4, "Transcription," n. 2, reads _mu_ 牡 as _du_ 杜, citing the Guo Pu commentary in _Erya_ , 8.9b, which identifies _du_ as _duheng_ 杜 衡 ( _GM_ , 13.70; _ZY_ : no. 2094, _Asarum forbesii_ Maxim.). _SW_ , 6A.4a, glosses _du_ as a kind of pear. The reading is plausible, but I also suspect that the scribe might have omitted a graph or graphs following _mu_ , meaning that _mu_ could designate a male creature or be part of an insect name as in _MS_ V.8.
4Perhaps the urine is drunk.
5I.e. the penis.
6 _MS_ V.14 must be for giving birth to a boy. Compare _MS_ V.15 for giving birth to a girl.
1 _Jiuzong_ 九 宗 means "nine lineages," connoting fecundity. _MWD_ , vol. 4, "Transcription," n. 1, suggests two interpretations of the unknown drug name. It might represent a variant of _guizong_ 軌 鬷, an unidentified plant name listed in _Erya_ , 8.10a. Alternatively, and less plausibly in my mind, there is a Jiu Zong Mountain 九 嵕 山 in present-day Huberi that has the alternate form 九 宗 山 (Morohashi 1957–60, vol. 1: no. 167.421).
2 _MS_ V.17 describes the preparation of a mound of earth on which the newborn infant is placed and left to move about until coated with the earth. The passage provides remarkable confirmation of Granet's thesis concerning the ritual of placing the newborn infant on the ground for a period of time immediately after birth. Granet uses Han ritual literature and related sources that describe separate rituals for boys and girls to reconstruct an original ritual in which all newborn infants, male and female, are placed on the ground to receive the Yin nurture of "mother" earth (1953: 159–202). According to the ritual literature the infant is left for three days before being taken up by the wetnurse, which Granet identifies as a type of initiatory exposure that precedes the infant's acceptance into the family. We do not know whether the ritual prescriptions were followed to the letter by elite families. However, _MS_ V.17 shows that the custom of placing the newborn infant on a mound of earth was practiced; and there can be no doubt that its symbolic significance was as proposed by Granet.
3The infant must be bathed in the water, since the mother then drinks some of the bath water.
_MS_ VI.A
Shiwen
十 問
Ten Questions
_MS_ VI.A.1 (SS1–7)
The Yellow Thearch asked the Heavenly Teacher:1 "The myriad creatures, how are they able to move? Grasses and wood, how are they able to grow? The sun and moon, how are they able to glow?"
The Heavenly Teacher said: "When you examine heaven's nature, Yin and Yang are the rulers. Having lost them, the myriad creatures are discontinued; having obtained them, they thrive. Eat Yin and secure Yang; attain spirit illumination.2
"The way to eat Yin:3 Empty your five depots and disperse your three malignancies,4 as if unable to evacuate them––this being what is prized in the diet of elemental stuff.5
"Still your spirit wind, make fast your two racks, triply pound, and let nothing escape.1 The spirit wind then is born; the five tones then are matched.2
"Suck it in not more than five times, bring it to the mouth, and still it with the heart—this being what the four assistants prize.3 The dark winepot then arrives.4
"Drink it not more than five times; the mouth invariably finds the taste sweet.1 Bring it to the five depots. The form then is extremely relaxed.2
"Make it spread3 to your flesh and skin, and reach to those hair tips. The hair vessels then are permeated.4 The Yin water then arrives, drenching that Yang blaze.5 Firm, sturdy, and undying; drink and food enter the body as guests.6
"This is called the 'doubly marvelous recipe to penetrate spirit illumination.'"1
The way of the Heavenly Teacher to eat spirit vapor.2
_MS_ VI.A.2 (SS8–14)
The Yellow Thearch asked Great Perfection:3 "What do people lose so that their facial complexion is coarse and dun, blackened and dark green? What do people obtain so that the skin's webbed pattern is smooth and lustrous, freshly white and glowing?"
Great Perfection replied: "If your lordship wishes to refine a complexion that is freshly white, then examine the measuring worm. The measuring worm recipe for eating penetrates Yin and Yang. When it eats something dark green it becomes dark green; when it eats something yellow it becomes yellow. Solely on the basis of what your lordship eats you will turn into the five colors.4
"Your lordship must make eating Yin your constant; supplementing it with _bai_ (arbor-vitae) fruit is quite excellent. By drinking running beasts' wellspring blossom5 you can repel agedness and restore vigor, becoming lustrous and glowing.
"When coitus with Yin1 is expected to be frequent, follow it with flying creatures. The spring dickeybird's round egg arouses that crowing cock. The crowing cock has an essence. If you are truly able to ingest this, the jade whip is reborn.2 Best is engaging the member.3 Block that jade hole.4 When brimming then have intercourse, and bid farewell with round eggs. If the member is not engaged, conserve it with roasted-wheat meal.5 If truly able to ingest this, you can raise the dead."6
Great Perfection's way to raise the dead and eat bird essence.
_MS_ VI.A.3 (SS15–22)
The Yellow Thearch asked Cao Ao:7 "What do people lose so that they die? What do people obtain so that they live?"
Cao Ao replied: "[5] and take the essence. Attend to that conjoining of vapor and lightly move her form.8 When able to move her form and bring forth the five tones, then absorb her essence.9 Those who are empty can be made brimming full; the vigorous can be made to flourish lastingly; the aged can be made to live long.
"The procedure for living long is to carefully1 employ the jade closure.2 When at the right times the jade closure enfolds,3 spirit illumination arrives and accumulates. Accumulating, it invariably manifests radiance. When the jade closure firms the essence, this invariably ensures that the jade wellspring is not upset.1 Then the hundred ailments do not occur; thus you can live long.
"In the way of coitus with Yin, stay the heart, settle and secure it; and the form and vapor secure one another.2 Thus it is said: at the first arrival without emission, ears and eyes are perceptive and bright;3 at the second arrival without emission, the voice's vapor rises high;4 at the third arrival without emission, skin and hide glow; at the fourth arrival without emission, spine and upper side suffer no injury; at the fifth arrival without emission, buttock and ham can be squared; at the sixth arrival without emission, the hundred vessels pass clear through;5 at the seventh arrival without emission, your entire life is without calamity; at the eighth arrival without emission, you can have a lengthy longevity; at the ninth arrival without emission, you penetrate spirit illumination."
Cao Ao's way for coitus with Yin and cultivating spirit vapor.
Fig.17 Facsimile of _MS_ VI.A.1
_MS_ VI.A.4 (SS23–39, SS52–59)
The Yellow Thearch asked Rong Cheng:1 "When people first dispense the purity that flows into the form, what is obtained so that life occurs?2 When flowing into the form produces a body, what is lost so that death occurs? Among people of the age, why are some foul while others are fair; why do some die young while others are longlived? I wish to hear the reason why people's vapor thrives or shrinks, why it slackens or expands."
Rong Cheng replied: "If your lordship wishes to be longlived, then comply with and examine the way of heaven and earth. The vapor of heaven is monthly exhausted and monthly replenished; thus it is able to live long. The vapor of earth during the year is cold and hot, and the precipitous and the gentle complement one another; thus the earth endures and does not deteriorate. Your lordship must examine the nature of heaven and earth, and put it into practice with your body.3
"There are signs that can be known. At present it is not within the ability of even the sage. Only the person of the way knows it.4 The culminant essence of heaven and earth is born in the signless, grows in the formless, and is perfected in the bodiless. He who obtains it has a lengthy longevity, he who loses it dies young.1 Thus he who is skilled at cultivating vapor and concentrating essence accumulates the signless. Essence and spirit overflow like a wellspring.2 Suck in the sweet dew and have it accumulate. Drink the blue-gem wellspring and numinous winepot and make it circulate.3 Eliminate the foul and love the habitual,4 and spirit then flows into the form.5
"The way to suck in vapor: it must be made to reach to the extremities, so that essence is generated and not deficient. Above and below are all essence; cold and warm are tranquilly generated.6 Breathing must be deep and long, so that the new vapor is easy to hold. The old vapor is that of agedness, the new vapor that of longevity. He who is skilled at cultivating vapor lets the old vapor disperse at night and the new vapor gather at dawn,1 thereby penetrating the nine apertures and filling the six cavities.2
"When eating vapor there are prohibitions. In spring avoid Turbid Yang; in summer avoid Scalding Wind; in autumn avoid Frost Mist; in winter avoid Frozen Yin. You must eliminate the four malignancies, then breathe deeply to become longlived.3
"The goal of dawn breathing: during the egress, endeavor to join with heaven. During the ingress, gauge that dual-entry doorway4 as if storing it in a deep pool. Then the stale vapor is daily exhausted, and the new vapor is daily replenished. Then the form possesses billowing radiance and is filled with essence; thus it is able to last long. The goal of daytime breathing: exhaling and inhaling must be light, and ears and eyes are perceptive and bright. Spreading1 vapor permeates,2 and inside there is neither blockage3 nor decay; thus the body is without affliction and calamity. The goal of dusk breathing: breathe deeply, long and slow, causing the ears to not hear; and when tranquil go to bed. The ethereal-spirit and earthly-spirit are at ease in the form; thus you can live long. When breathing at midnight: after awakening do not change from the sleeping posture; do it deeply and slowly, without exertion,4 and the six cavities all open. Make long duration your ideal. If you wish to make the spirit longlived, you must breathe with the skin's webbed pattern.
"The essence5 of cultivating vapor is to exit from death and enter into life. With zest and gusto, let the taste suckle.6 To fill the form with this is called concentrating essence. To cultivate vapor there is a norm; the task lies in accumulating essence. When essence reaches fullness, it invariably drains; and when essence is lost, it must be replenished.7 As for the time to replenish what drained, coordinate it with sleep.8 Exit and enter, thereby improving the skin's webbed pattern.1 When the firm and white is perfected inside, what ailment can occur?2
"If there is a calamity for that life, it is invariably because Yin essence leaks out; and the hundred vessels are clogged and derelict. Joy and anger are untimely, the person is ignorant of the great way, and the vapor of life departs from him. The vulgar man lives blindly, and then relies on shaman physicians. Before reaching middle age,3 his form invariably is buried young. To kill yourself by toiling at affairs4 is truly a grievous and sorrowful thing.
"Wherever life and death lie, the penetrating gentleman controls it. By filling what lies below and enclosing essence, vapor does not leak out. When the heart controls death and life, who is defeated by them? Carefully hold it and do not lose it, and long life continues across ages. For continuous ages you are peaceful and joyous, and possess longevity.
"Longevity is born of growth and accumulation. As for the fullness of that life: above it scans heaven and below it spreads over earth.1 The person who is capable of it invariably becomes a spirit. Thus he is capable of achieving release of the form.2 The person who perceives the great way skims the clouds as he moves. From Piled Blue-gem above,3 like water flowing he can range far; like the dragon ascending he can rise high. Quick and untiring in strength [7] Wuchengzhao1 [2] did not die. Wuchengzhao makes the four seasons his assistants and heaven and earth his constants. Wuchengzhao was born together with Yin and Yang. Yin and Yang do not die, and Wuchengzhao is coequal with them.2 The gentleman who possesses the way is also like this."
_MS_ VI.A.5 (SS42–47)
Yao asked Shun: "In Under-heaven what is most valuable?"
Shun replied: "Life is most valuable."
Yao said: "How can life be cultivated?"
Shun said: "Investigate Yin and Yang."
Yao said: "Man possesses nine apertures and twelve joints,3 each one situated in its place. Why is it that the Yin is born together with a man and yet departs ahead of the body?"4
Shun said: "When drinking and eating it is not used; it is not utilized for counseling and thinking.5 Its name is avoided and its body concealed, yet it is employed very frequently with neither leniency nor ritual.1 Thus while it is born together with the body, it dies ahead of the body."
Yao said: "How can it be cultivated?"
Shun said: "You must cherish it and delight in it; instruct and counsel it; and give it drink and food. Make the prong at its tip2 firm and strong, and employ it slackly. You must imbibe, but do not dispense;3 you must be joyful, but do not allow emission. The stuff will accumulate and vapor grow. On reaching the age of one hundred, you will be more sterling than in the past."
Shun's way for coitus with Yin and cultivating vapor.
_MS_ VI.A.6 (SS48–51, S41)
Wangzi Qiaofu asked Ancestor Peng:4 "Of man's vapor, which is the most essential?"
Ancestor Peng replied: "Of man's vapor none can compare with penile essence.5 When the penile vapor is clogged and blocked, the hundred vessels produce illness. When the penile vapor is not perfected, you cannot procreate. Thus longevity lies entirely with the penis. When the penis is secured and cherished, its simultaneous giving becomes an aid.
"For this reason, at the first light of day1 the person of the way spits on his hands and strokes his arms. He rubs the abdomen, following the Yin and following the Yang.2 He must first spit out the stale, then suck in the penile vapor.3 Let penetrating breathing be together with the penis; let drinking and eating be together with the penis. Drink and food consummate the penis, like nurturing the red infant.4 When the red infant5 is boisterous and brash and repeatedly becomes erect, be careful to not burden it with labor.6 Then he can have lasting coitus7 and can travel distantly; thus he is able to have a lengthy longevity."
_MS_ VI.A.7 (SS60–65)
Thearch Pan Geng asked Wizen-faced Oldster:1 "I have heard that the Master practices coitus with Yin to become strong, and sucks in heaven's essence to achieve lengthy longevity. What might I undertake so that the way can be put into practice?"
Wizen-faced Oldster replied: "Your lordship must prize that which is born together with the body and yet grows old ahead of the body.2 The weak, it makes them strong; the short, it makes them tall; the poor, it guarantees them abundant provisions. The regimen involves both emptying and filling, and there is a precise procedure for cultivating it.3 First, relax the limbs, straighten the spine, and flex the buttocks; second, spread the thighs, move the Yin,4 and contract the anus;5 third, draw the eyelashes together, do not listen, and suck in the vapor to fill the womb;6 fourth, contain the five tastes and drink that wellspring blossom;1 fifth, the mass of essence all ascends, suck in the great illumination.2 After reaching the fifth, stop. Essence and spirit grow daily more blissful."
Wizen-faced Oldster's way for coitus with Yin and eating spirit vapor.
_MS_ VI.A.8 (SS66–72, S40, S73)
Yu asked Teacher Gui:3 "I put forth the wisdom of my ears and eyes to order Under-heaven. Above, I made the submerged land level; below, I followed the course of the Jiang River and reached Kuaiji Mountain. I have spent ten years controlling the water; and now my four limbs are useless and my household is in disorder. How can they be put into order?"4
Teacher Gui replied: "As a rule, the mainstay for ordering government must begin from the body.5 When blood and vapor ought to move yet do not move, this is called the calamity of blockage; and is something that controls the six extremities.6 So, the continuity of vapor and blood and the meshing of muscles and vessels can- not be set aside and forgotten. As for the womb, dispense to it; as for the tastes, transmit them.1 Guide it with the will, and use the regimen to move it. Were it not for the tastes there would be nothing filling the inside and making the joints grow. Were it not for the will there would be no means of knowing whether the inside is empty or full. Were it not for the regimen there would be no means to move the four limbs and to dispatch illness. Thus to awaken from sleep and pull Yin, this is called refining the muscles.2 To first stretch and then curl, this is called refining the bones.3 Movement and activity must be fitting; essence, thus, comes forth like a wellspring. By practicing this way, what age would not have perfect specimens?"4
Thereupon Yu drank fermented milk5 and ate the five tastes. With the will he cultivated vapor. His eyes became bright and his ears perceptive; skin and hide glowed; the hundred vessels were fulland replete. The Yin then [1] born, thereby pacifying Queen Yao.1 The household then was tranquil again.
Teacher Gui's way for cultivating spirit vapor.
_MS_ VI.A.9 (SS74–93)
Wen Zhi saw King Wei of Qi.2 King Wei asked him about the way: "The Deficient Man3 has heard that the Master and Great Man4 has broad knowledge of the way. Due to the sacrifices of the ancestral temple, the Deficient Man does not have the leisure to listen to all of it. I would like to hear the crux of the way in two or three words and no more."
Wen Zhi replied: "Your Servant's practice of the way consists of three hundred fascicles,5 but sleep is foremost."
King Wei said: "Let the Master elaborate; when engaging in sleep what should be eaten?"
Wen Zhi replied: "Pure liquor and clumped _jiu_ (leeks)."6
King Wei said: "Why does the Master advocate _jiu_ (leeks)?"
Wen Zhi replied: "When Lord Millet sowed and tilled,1 the herb that lived a thousand years was _jiu_ (leek) alone; thus, it was named for this.2 It receives heaven's vapor early, and its receipt of earth's vapor is secure. Thus, those who are skittish, timid,3 dispirited,4 and frightened eat it and regain regular strength; those whose eyes do not see clearly eat it and regain regular brightness; those whose ears do not hear eat it and regain regular perceptivity. Eat it during the three months of spring and neither affliction nor illness arises; and muscle and bone grow ever stronger. For these reasons it is called king of the hundred herbs."
King Wei said: "Excellent. Why does the Master advocate liquor?"
Wen Zhi replied: "Liquor is the vapor-essence of the five grains.5 When it enters the inside it disperses and flows; when it enters the internal network6 it penetrates and circulates. It permeates the internal network without the need for sleep. Thus it serves as the medium for the hundred drags."
King Wei said: "Excellent. But there is something that is not consistent with what the Master has stated. Now then, when _jiu_ (leek) is offered for the spring-feast collation, why is it not together with liquor but always together with egg?"1
Wen Zhi replied: "Also permissible. Now then, the chicken is a Yang creature; one that at the first light of day rouses the sense of hearing, with its head extended and feathers cocked. During the three 'returned Yin' months it is combined with _jiu_ (leek).2 Thus, the person of the way eats it."
King Wei said: "Excellent. Why does the Master advocate sleep?"
Wen Zhi replied: "Now then, sleep is not merely a matter that concerns living people. Ducks and geese, swans and _sushuang_ ,1 earthworms,2 fish and turtles, and the whole horde of mobile creatures need to eat in order to live. And having eaten, they need to sleep in order to be perfected. Now then, sleep is what causes food to disintegrate and dissolve, and what disperses drags to flow through the form. The relation of sleep to eating is analogous to that of fire to metal. Thus, if for a single night you do not sleep, for a hundred days you do not recover. When food does not transform, you invariably become like a stuffed leather ball. This generates craving in the heart with clogging; and discomfort in the intestines with malaise.3 Thus, the person of the way reveres sleep."
King Wei said: "Excellent. The Deficient Man is habitually fond of drinking at sunset and continuing into the night; that is, if it does not cause sickness."
Wen Zhi replied: "There is no harm. By analogy it is like birds and beasts. Those that go to sleep early rise early; those that go to sleep late rise late.4 Heaven receives light; earth receives darkness. The person of the way does no more than investigate the matter thoroughly. Now then, when eating vapor let it sink in and spread in blackness.5 At midnight [5] vapor, and bring it to the six extremities.1 The six extremities are firm with essence, hence the inside is full and the outside even. Pustules and neck lumps have no place to lodge; not a single abscess appears. This is the culmination of the way."
King Wei said: "Excellent."
_MS_ VIA.10 (SS94–101)
Wang Qi saw King Zhao of Qin, who asked him about the way:2 "The Deficient Man has heard that the Guest3 eats Yin to become active and strong, and sucks in vapor to achieve essence illumination.4 What might the Deficient Man undertake so that longevity can be prolonged?"
Wang Qi replied: "You must face the sun and moon and suck in the rays of their essence; eat _song_ (pine) and _bai_ (arbor-vitae);5 and drink running beasts' wellspring blossom.6 You can repel agedness and restore vigor, becoming lustrous and glowing. In the three summer months eliminate fire and use the sun to cook and boil.7 Then the spirit becomes keen, (the ears) perceptive, and (the eyes) bright.
"The way of coitus with Yin uses stillness to become strong. Make the heart even like water; store the numinous dew inside.1 Be relaxed in using the jade whip;2 do not let the heart be nervous and flurried. The five sounds arise in response, both the short and the long.3 Suck in the spirit mist; drink that heavenly beverage.4 Bring it to the five depots, with the aim of storing it deeply.
"Perform dragon breathing at dawn;5 the vapor and form, then, become hard. {1} [5] nears water. Essence and vapor are congealed,6 hardy, and long lasting. Spirit harmony is obtained inside; ethereal-spirit and earthly-spirit are gleaming [1]. The five depots become firm and white, their jade color having a renewed glow. Your longevity forms a triad with the sun and moon; and you become the blossom of Under-heaven."
King Zhao said: "Excellent."
1Heavenly Teacher ( _tianshi_ 天 肺) is a title by which the Yellow Thearch's teacher Qi Bo 岐 伯 is known in the _Huangdi neijing_ (see _Suwen_ 1, 1.1b). The title occurs elsewhere in early literature; for example, the Yellow Thearch honors a sagacious youngster as Heavenly Teacher in _Zhunangzi_ 24, 361. The person addressed as Heavenly Teacher in _MS_ VI.A.1 is not known (Qi Bo is an extremely unlikely candidate). In Later Han religious Daoist movements the title _tianshi_ (usually translated Celestial Master) acquired added significance (Seidel 1969: 74–84, 112–14).
2The idea that the Yin element of the body—especially the male body—is most vulnerable to decay runs through the Mawangdui macrobiotic hygiene texts. Sexual cultivation is one, but not the only, way to ensure that the fullness of Yin is maintained (see Prolegoment, Section Four, "Body and Spirit").
3The Heavenly Teacher's method of eating Yin is breath cultivation technique written in verse.
4"Disperse" translates _guang_ 廣. I interpret the word like _kuang_ 曠, meaning "abandon, discard" (see _Lüshi chunqiu_ , 22. 287). The denotation of the term "three malignancies" (sanjiu 三 咎) is not known. In _MS_ VI.A.4 the "four malignancies" refer to four harmful vapors that must be avoided when practicing breath cultivation. Presumably anything harmful to physical and spiritual well-being constitutes a "malignancy."
5"Evacuate" translates _chu_ /* _thj әd_ 出, which rhymes with _gui_ /* _gwji әd_ 貴 (prize) in the final phrase. I follow MWD, vol. 4, "Transcription," n. 2, in reading _wu_ /* _?uk_ 楃 as a phonetic loan for _pu_ /* _phuk_ 樸 (elemental stuff). The loan usage is confirmed by the use of 楃 to write 樸 in the first Mawangdui Laozi edition ( _MW_ D, vol. 1: 12; corresponding to _Laozi_ , par. 28, in the received text). The interchange between a glottal/velar initial and a labial is unusual, but not unknown. For example, _SW_ , 7B.17a, explains that _ba_ /* _priat_ 八 is the phonetic in _xue_ /* _gwit_ 穴. My punctuation differs from the "Transcription," which fails to recognize the rhyming between _chu_ /* _tjk әd_ and _gui_ /* _gwji әd_. _Pushi_ 樸 食 as a term for some kind of macrobiotic diet may be related to _sushi_ 素 食, which refers to a diet of plants gathered from the wild in Mozi 6, 1.20, and other early sources.
1Beginning with "spirit wind" ( _shenfeng_ 神 風), much of the technique is presented in metaphorical language. The spirit wind seems to refer to a quality of breath that exists internally and is at the same time linked to the external atmosphere. It is activated by forcefully holding the breth—for "triply pound" see _MS_ I.A.6—so that "nothing escapes." _Zhi_ 恃 (rack) is glossed in _SW_ , 6A.47b, as a name for the vertical rack used for silkworm cultivation. I suspect that the "two racks" denote the ribcage.
2The "five tones ( _wusheng_ 五 聲) being matched" signifies perfect harmony in the cosmos (see the use of the synonymous _wuyin_ 五 咅 in _Lüshi chunqiu_ , 3.33). I understand the birth of the spirit wind and the matching of the five tones to mean that there is consonance between the internal and external, and the person can begin to inhale external vapor. _Wusheng_ and _wuyin_ have another denotation in _MS_ VI.A.3, 10; _MS_ VI.B.6; and _MS_ VII.B.15, 20. There they refer to signs of arousal coming from the woman's mouth during intercourse.
3Having inhaled vapor through the nose, it is brought to the mouth. "Still" translates _mei_ 枚, which as a noun refers to a wooden bit placed in the mouth to block unwanted speech (see _Zhouli_ , 34.6a, and Zheng Xuan commentary). I understand "still it with the heart" to mean that the person subjects the vapor in the mouth to the "stilling device" of the heart _Sifu_ 四 輔 (four assistants) is well attested as a term for the ruler's chief administrators; and also occurs in this sense in one of the writings preceding the second Mawangdui _Laozi_ edition ( _MWD_ , vol. 1: 66). In _MS_ VI.A.1 the term must be related to the heart's function as the ruler of the body; and I identify the "four assistants" as the four limbs. _MWD_ , vol. 4, "Transcription," n. 5, interprets _mei_ in the sense of "gather, collect"; giving the translation, "collect it (i.e. the vapor) in the heart." The interpretation is grammatically acceptable, but the technique at this point focuses on vapor in the mouth that is in the process of being transformed into saliva and swallowed. In my judgment the technique uses the heart/ruler to effect this transformation in the mouth, whereas the collection of vapor in the heart seems out of place in the overall progression of the technique.
4"Dark winepot" translates _xuanzun_ 玄 尊, attested in _Lüshi chunqiu_ , 5.50, and glossed in the Gao You commentary as _mingshui_ 明 水 (bright water; a name for a holy water used in worship). The synonymous xuanjiu 玄 酒 (dark liquor) is described as the highest grade of _mingshui_ in _Liji_ , 26.7a, in a passage concerning various items appropriate for worshipping the _shenming_ 神 明 (in this context not the physio-spiritual "spirit illumination," but the glowing manifestation of the spirits of the other world). According to the Zheng Xuan commentary, the liquid is "water obtained from the moon using the Yin mirror (a metal pan in which moon dew condenses)." Although not attested as a physiological metaphor in received literature, it is clear that "dark winepot" denotes saliva in _MS_ VI.A.1. This saliva is a purified concentrate produced inside the mouth from the inhaled vapor. A related term _lingzun_ 靈 尊 (numinous winepot) occurs in MSVI.A.4. Saliva ingestion was regularly practiced in religious Daoist hygiene (Maspero 1981: 489–94; Needham 1954, vol. 5, part 5: 150–51).
There is an interesting parallel between the technique and religious worship, since the final result of swallowing the saliva is to "penetrate spirit illumination ( _shenming_ )," just as the final result of worship is communication with the _shenming_. The religious interaction between human and spirit worlds has become in macrobiotic hygiene an individualized internal transformation.
1The dark winepot/saliva is swallowed, its taste sweet like liquor. The phrase 口 必 甘 味 "the mouth invariably finds the taste sweet" also occurs in _Lüshi chunqiu_ , 3.26, in a passage related to dietetics (see the discussion in the Prolegomena, Section Four, "Philosophy and Macrobiotic Hygiene").
2For _tui_ 退 in the sense of "relaxed," see _Liji_ , 10.16a, and Zheng Xuan commentary.
3 _MWD_ , vol. 4, "Transcription," transcribes 搏, read as _fu_ 薄 (spread). Qiu Xigui argues that the graph is 摶, read as _zhuan_ 摶 (concentrate; 1992: 535). Li Xueqin (personal communication) suggests 摶. Distinguishing between 尃 and 專 in Qin and Han manuscripts is often difficult, and there is also the possibility of the scribe having erroneously written one when the other was intended. The word _fu_ 薄 best fits the context of _MS_ VI.A.1, thus I follow Li Xueqin's transcription of the graph and the "Transcription" reading.
4The term _maomai_ 毛 脈 (hair vessels) occurs in _Guoyu_ , 17.8a, in a context where it seems to denote hair (hair perceived as fine thread-like extrusions of the body's vessels). _Suwen_ 21, 7.2a, uses _maomai_ in a more technical sense in a description of the circulation of vapor in the body; after the lungs distribute vapor to the skin and hair, the "hair vessels" transmit the vapor to a central cavity. While the concept of "hair vessels" in _Suwen_ theories of vapor circulation cannot be applied directly to _MS_ VI.A.1, it is evident that by "permeating the hair vessels" the vapor/saliva has been distributed to the outer limits of the body.
5"Yin water" (Yin _shui_ 陰 水) and "Yang blaze" (Yang _fu_ 陽 炥) are the complementary elements of water and fire in the body of the person practicing the technique, the latter evidently pre-existing as a kind of central forge and the former generated by the technique. According to the Duan Yucai commentary in _SW_ , 10A.42b, _fu_ is an orthographic variant of _fu_ , which refers to a conflagration. I have not found either term attested in received literature. Although their precise denotations are unknown, using the cooling Yin water to temper the Yang heat of the internal blaze is clearly the actualization of the Heavenly Teacher's instruction to "consume Yin and secure Yang." As physiological metaphors, Yang blaze and Yin water anticipate the alchemical imagery of religious Daoist hygiene.
6Having prepared the body according to the technique, the person now realizes the ultimate benefit: all food and drink brought into this revitalized body "enter as guests" ( _bin_ 賓), meaning that they provide the ideal nurture. It is possible that 賓 should be read as _shi_ 實, giving the translation "drink and food fill the body." _Wanwu_ contains a clear case of scribal error in the drug name _lanbin_ 蘭 賓, which should be _lanshi_ 蘭 實 (eupatorium fruit; see Fuyang Han jian zhenglizu 1988: 37). _Bin_ and _shi_ fit the context in _MS_ VI.A.1 equally well, making it difficult to judge whether scribal error has occurred.
1In my judgment _fuqi_ 復 奇 (doubly marvelous) adds embellishment to a recipe for "penetrating spirit illumination." The compound _qifang_ 奇方 (marvelous recipe) is attested in _Shiji_ , 28.31b, in connection with occult arts. Ma Jixing interprets _fuqi_ to mean "recovering from irregularity" (1992: 877, n. 8); and Wei and Hu offer the interpretation "replenish Yang" (equating _qi_ with Yang; 1992, vol. 2: 97, n. 25).
2The concluding line serves as a title for the technique described by the Heavenly Teacher. The same formula occurs in _MS_ VI.A.2, 3, 5, 7, 8.
3Great Perfection 大 成 is attested as both an epithet and proper name in early sources. _Zhuangzi_ 20, 298, attributes a teaching to the "man of Great Perfection"; and _Xinxu_ , 5.71, recounts that Yu 禹 studied with Great Perfection.
4The measuring worm ( _chihuo_ 尺 蠖) is a caterpillar most often noticed for its movement—a contraction followed by a stretch that matches the ideal of _qushen_ 屈 伸 (curling and stretching) in macrobiotic hygiene (see _MS_ VI.A.8). There is a measuring worm exercise in the _Yinshu_ ; and a measuring worm sexual position in _MS_ VI.B.3 and _MS_ VII.B.10 (see _MS_ VI.B.3). _Yanzi chunqiu_ , 8.219, and _Shuoyuan_ , 1.12b, record the same figurative use of the measuring worm's diet as in _MS_ VI.A.2. However, the that its body becomes yellow and dark green when it eats yellow and dark green things serves as an analogy for court sycophants (who "eat", the ruler and become exactly like him) rather than to make the point that you are what you eat.
5"Wellspring blossom" translates _quanying_ 泉 英. The term is attested in _Guanzi_ 58, 19.312, as a technical name for a type of high mountain with a wellspring at the summit. In _MS_ VI.A.7 _quanying_ denotes an internal fluid (neither saliva nor semen) that the practitioner "drinks" in the course of cultivation. The usage indicates an analogy between human physiology and mountain topography. _MWD_ , vol. 4, "Transcription," n. 4, suggests that "running beasts' wellspring blossom" refers to cow and sheep milk. While the identification is plausible (and horse might also be added to the list of milk-producing "running beasts"), I suspect that wellspring blossom may not be restricted to milk alone. Zhou and Xiao suggest that animal semen and decoctions of male animal genitals might also be included (1988: 370, n. 8); and animal saliva is not improbable.
1 _Jie_ Yin 接 陰 (coitus with Yin) is a standard term for sexual intercourse in received literature.
2The jade whip is the penis (see _MS_ III.38). Eating eggs and the flesh of fowl to bolster Yang vitality is described in several recipes in _MSS_ III-IV; e.g. _MS_ III.11, 15, 17; and MSIV.4, 24. Crowing cock ( _mingxiong_ 鳴 雄) appears to have a double reference to the rooster and to the male genitals. Rooster is the chief ingredient in _MS_ III. 11 for a food that increases a man's endurance during sexual encounters. At the same time _MS_ VI.A.6 teaches that the ideal diet combines eating with cultivating "penile vapor." Thus the crowing cock's essence may be that of the man's own genitals, which the man cultivates while eating dickeybird egg to revitalize the jade whip.
3I follow Ma Jixing (1992: 885, n. 1) in reading 埶 as shi 勢, and interpreting it as the male genitals (member). The usage is attested in the Han period prophecy text _Shangshu xingde fang_ 尚 書 刑 德 放 (Yasui and Nakamura 1971–92, vol. 2: 65).
4I.e. the vagina.
5"Roasted-wheat meal" translates _feng_ 麷, which refers to a form of _qiu_ 糗 (roasted-grain meal) using wheat (see _SW_ , 5B.34b, and Duan Yucai commentary). Receipes for bolstering Yang vitality that include roasted-grain meal are in _MS_ III.13, 17.
6The limp penis is often described as "dead." Thus to "raise the dead" is to revitalize the penis.
7The name Cao Ao 曹 熬 is not attested in received literature.
8 _Heqi_ 合 氣 (conjoin vapor) refers to sexual intercourse; see _MS_ III.89.
9The _wusheng_ 五 聲 (five tones) and the similar _wuyin_ 五 音 (five sounds) in _MS_ VI.A.10 refer to sounds made by the woman during intercourse. They are probably to be identified with the _wuyin_ in _MS_ VI.B.6 and _MS_ VII.B.15, which refer to five signs of arousal coming from the woman's mouth (mostly audible, but biting is included as one of the "sounds"). _MS_ IV.A.3 and _MS_ VI.A.10 both portray the man as actively stimulating the woman to produce the "five tones/sounds," which constitute positive evidence of the harmonization at work in sexual cultivation (similar to the harmonization of the "five tones" in the breath cultivation technique in _MS_ VI.A.1).
1傎 in _MWD_ , vol. 4, "Transcription," should be transcribed as _shen_ 傎 (carefully).
2"Jade closure" translates _yubi_ 玉 閉. The term is not attested in received literature. _Bi_ , however, is a standard term for concentrating vapor and essence inside the body by "enclosing" them. In later religious Daoist hygiene this usually involved holding one's breath according to a specified technique, followed by exhalation (Maspero 1981: 463, 495). The same verbal usage if _bi_ occurs in _MS_ VI.A.4, which states: "By filling what lies below and enclosing essence ( _bi jing_ 閉 精), vapor does not leak out." The "jade closure" appears to be a physiological metaphor designating a place inside the body where vapor and essence are physiological metaphor designating a place inside the body where vapor and essence are enclosed. The term appears again in _MS_ VII.B.3: "The matter of spirit illumination lies in what is enclosed ( _bi_ ). Vigilantly control the jade closure, and spirit illumination will arrive." As in _MS_ VI.A.3, careful use of the jade closure to "enclose" facilitates the arrival of spirit illumination. In addition, both passages concern sexual cultivation as well as breath cultivation; thus there are two sources for the vapor and essence being enclosed inside the body. Wei and Hu compare the "jade closure" to the _guan_ 關 (barrier; 1992, vol.2: 102, n. 4). _Guan_ is attested in _Shenjian_ 3, 17, as a term for an internal barrier located near the navel where Han-time practitioners of macrobiotic hygiene stored vapor and essence; and this meaning of guan entered the terminology of religious Daoist physiology (Maspero 1981: 491). I agree that the idea of the "jade closure" may be similar to the later-attested "barrier," and that it is probably in the abdominal region, but I would refrain from identifying the former exactly with the latter. It is also possible that the "jade closure" is not an anatomical term, but rather designates the act of "enclosing vapor/essence." To "employ the jade closure" might then mean to practice the technique of either holding the breath or enclosing vapor in some other fashion (this is the interpretation in Ma Jixing 1992: 890, n. 2).
3I read _bi_ /* _pjik_ 辟 as _bi_ 襞, glossed in _SW_ , 8A.62a, as "fold clothing" (the use of the former graph in the sense of the latter is also attested in Han sources). The word is not attested in a physiological denotation, but I suspect that the extended meaning "enfold" is similar to _bi_ / _pid_ 閉 (enclose; for which it cannot be a phonetic loan). _Bi_ 辟 might also be understood in its sense of "wall, embankment" (as in _biyong_ 辟 廱, the "moated enclosure" in the ideal plan of a royal capital) to refer to the enclosing function of the jade closure. Wei and Hu understand _bi_ in the sense of "open"; giving the translation, "the jade closure open" (1992, vol.2: 102, n. 5). However, this meaning does not best fit the context of _MS_ VI.A.3 or _MS_ VII.B.3, which both focus on an act of "enclosing" that causes vapor and essence to accumulate and spirit illumination to arrive.
1 _Yuquan_ 玉 泉 (jade wellspring) occurs again in association with the jade closure, breath cultivation, and sexual cultivation in _MS_ VII.B.3. In religious Daoist hygiene _yuquan_ is sometimes identified as the pool of saliva beneath the tongue and sometimes as the _bao_ 胞 (the bladder or a place where essence is stored; see the Liangqiuzi commentary to the _Huangting neijing jing_ in _Yunji qiqian_ , 11.17a and 12.20a). _Zhenjiu jiayi jing_ , 3.34b, gives _yuquan_ as another name for _zhongji_ 中 極 (inner bourne), which it identifies as the chief acupuncture point associated with the bladder (see _MS_ VI.B.8 for other denotations of _zhongji)_. Based on the location of the jade wellspring inside the jade closure and the later identifications, I would identify the jade wellspring in _MS_ VI.A.3 as a reservoir in the abdominal region where vapor and essence are stored. "Upsetting" the jade wellspring would result in the loss of vapor and essence.
2The reference to "staying the heart" is reminiscent of _Guanzi_ 49, 16.270: "When a stable heart is situated inside, the ears and eyes are perceptive and bright; the four limbs are firm and solid; and you can be an abode for essence." The role of the heart (in the form of the will) in overseeing the body's needs is mentioned in _MS_ VI.A.8.
3"Arrival" ( _zhi_ 至) refers to thrusting the penis inside the vagina. Parallels in _MS_ VI.B.2, and _MS_ VII.B.3 refers to thrusting the penis as "movement" ( _dong_ 動). According to _MS_ VI.B.2, ten thrusts constitute one movement and there are ten movements for a total of one hundred thrusts. For every movement (ten thrusts) through the tenth (one hundred thrusts) that the man prolongs intercourse without ejaculating the benefits of sexual cultivation grow ever greater. The parallel in _MS_ VII.B.3 concludes the passage concerning the jade closure, just as the listing of nine "arrivals" concludes Cao Ao's teaching.
4I.e. the voice has beauty and clarity.
5I.e. vapor passes freely through the vessels.
1The _Liexian zhuan_ identifies Rong Cheng 容 成 as the Yellow Thearch's teacher; and describes his mastery of the full range of macrobiotic hygiene (Kaltenmark 1953: 55–58). Rong Cheng's role as a patron of sexual cultivation is attested in the book _Rong Cheng Yin dao_ 容 成 陰 道 (Rong Cheng's way of Yin), whose title is recorded in _Hanshu_ , 30.80b.
2 _Liuxing_ 溜 刑 (flow into the form) is the term for the first month of gestation in _MS_ V.3. The Yellow Thearch is asking how intercourse and conception lead to the production of a life.
3The description of the vapor of earth is reminiscent of a passage in the _Yijing_ , "Xicizhuan," 8.6a: "When coldness goes, heat comes; when heat goes, coldness comes. Cold and hot succeed one another and the year is thereby completed." For the use of _xianyi_ 險 馬 in the sense of "precipitous and gentle (terrain)," see _Shiji_ , 71.8a; for _xiangqu_ 相 取 in the sense of "complement one another," see _Yijing_ , 8.14b.
4"The person of the way" ( _daozhe_ 道 者) is mentioned again in _MS_ VI.A.6 and _MS_ VI.A.9. Presumably the way is the "way of macrobiotic hygiene." At the same time, the concept of Way as the ultimate quiddity was already accepted doctrine in the third century B.C., giving rise to a new form of cosmo-political thought. In referring to the _daozhe_ there is a connotation of universality that extends beyond macrobiotic hygiene. The ability to achieve universality is the reason for ranking the person of the way above the sage ( _sheng_ 聖).
1 _Huainanzi_ often uses "formless" ( _wuxing_ 無 形) as an epithet for Way or One ( _yi_ 一). For example, _Huainanzi_ , 1.10: "Now then, the formless is the great ancestor of creatures"; and 1. 11: "The term 'formless' refers to One; and One means that it is something without peer in Under-heaven." _Huainanzi_ , 7.104, describes the person who cultivates the Way as "bodiless" ( _wuti_ 無 體) as well as formless: "When moving he is formless; when still he is bodiless" (according to the Gao Yu commentary, "being formless and bodiless is the manner of Way"). _Guanzi_ 49, 16.272, attests to the notion of Way as "signless" ( _wuzheng_ 無 徵): "It is ever so that when a person is born heaven puts forth the essence and earth puts forth the form, and that these are conjoined to make the person. If harmonized, birth occurs; if not harmonized, it does not. Examining the way of harmonization, the essence is not visible and the signs ( _zheng_ ) are not manifest: "And _Guanzi_ 49, 16.269, provides the oldest statement of obtaining Way as the key to life: "(Way) is something that when people lose it, they die; and when they obtain it, they live."
2The _locus classicus_ for _zhuan_ 搏 in the sense of "concentrate (vapor/essence)" is _Guanzi_ 49, 16.271: "Concentrate vapor spirit-like, and store the myriad creatures in their entirety." _Guanzi_ 49, 16.270 is the source of the wellspring as a physiological metaphor: "When essence is stored it gives birth of itself. The outside is peaceful and flourishing; inside it is deposited to form a wellspring source. Flood-like, harmonious, and even, it becomes a deep pool of vapor. When the pool does not go dry, the four limbs are solid; when the wellspring is not exhausted, the nine apertures penetrate."
3The _locus classicus_ for "sweet dew" ( _ganlu_ 甘 露) is _Laozi_ , par. 32 ( _MWD_ , vol. 1: 123): "Heaven and earth conjoin and send down sweet dew." Rong Cheng's teaching demonstrates the incorporation of sweet dew into breath cultivation terminology. I suspect that sweet dew refers to a particular form of inhaled vapor (compare the "spirit wind" in _MS_ VI.A.1). Once the sweet dew accumulates, saliva forms—referred to as the "blue-gem wellspring" ( _yaoquan_ 瑶 泉) and the "numinous winepot" ( _lingzun_ 靈 尊). The "numinous winepot" is synonymous with the "dark winepot" in _MS_ VI.A.1. The "blue-gem well-spring" suggests the "blue-gem pool" ( _yaochi_ 瑶 池) at Mount Kunlun 崑 崙 where the Queen Mother of the West exchanged a toast with King Mu of the Zhou ( _Mu tianzi zhuan_ , 3.1a). Tang Daoist adepts also associated the mythical geography of Kunlun with breath cultivation. Schafer explains the use of the term _bijin_ 碧 津 (cyan exudates) to denote saliva as an allusion to the blue-gem pool at Kunlun (1981: 405, n. 110).
4I understand _su_ 俗 (habitual) in the sense of good habits that are treated as norms and regularly cultivated (see _SW_ , 8A.23b, and Duan Yucai commentary).
5Since "flowing into the form" is what occurs during the first month of gestation, for breath cultivation to result in "spirit flowing into the form" suggests a kind of rebirth.
6For cold and warm to be tranquilly ( _an_ 安) generated suggests the natural alternation between cold and hot that is characteristic of the vapor of earth (see above). _MWD_ , vol. 4, "Transcription" understands _an_ as an interrogative, giving the translation "how would cold and warm occur." In my judgment the notion of cold and warm as pathogenic conditions is improbable in the present context.
1I.e. old vapor must be voided from the body at night in preparation for inhaling new vapor at dawn. The passage on "dawn breathing" below similarly describes "daily exhausting stale vapor" and "daily replenishing new vapor." I suspect that the technique involves a nighttime exhalation exercise followed by a morning inhalation exercise. Rong Cheng's teaching anticipates religious Daoist hygiene, which divides the day into periods of daytime "living vapor" and nighttime "dead vaor"—daytime being defined either as sunrise to sunset or as midnight to noon. Breath cultivation should only be practiced during the time of "living vapor" (Maspero 1981: 500–501). Rong Cheng's teaching also exemplifies the slogan "spit out the old and ingest the new" associated with macrobiotic hygiene in _Zhuangzi_ 15, 237.
2The nine apertures are the mouth, ears, eyes, nostrils, genitals, and anus. The six cavities ( _liufu_ 六 腑) are identified in _Suwen_ 4, 1.16a, as: gall bladder, stomach, large intestine, small intestine, bladder, and "triple burner" ( _sanjiao_ 三 焦; the only cavity that is more a theoretical construct than a readily identifiable part of the body). The _Suwen_ classifies the six cavities as Yang, complementing the five depots ( _wuzang_ ; liver, heart, spleen, lung, kidney) which are Yin. There is no evidence in the Mawangdui medical manuscripts of the physiological theories involving depots and cavities that are detailed in the _Huangdi neijing_. And while the "triple burner" is also attested in _Shiji_ , 105.5b, it is doubtful that it is one of the six cavities in the Mawangdui manuscripts. A quotation from the _Hanshi waizhuan_ in _Taiping yulan_ , 363.2b, gives "gullet" as the sixth cavity instead of "triple burner."
3The four vapors to be avoided are the same vapors described in _MS_ II.A.
4I read as _liang_ 兩 (dual); and I identify the "dual-entry doorway" ( _guiliang_ 閨 兩) as the nostrils. _SW_ , 12A.8a, glosses _gui_ as follows: "It is a doorway that stands singly. The top is round and the bottom square, like the shape of the _gui_ 圭 (jade tablet)." The nostrils constitute a pair of single-entry doorways of the same shape, hence the physiological metaphor _guiliang_. In addition, the etymological analysis of _liang_ (originally written 兩) in _SW_ , 7B.39a–b, suggests that the graph itself might be seen to depict the nose: "It is composed of 冂 (the cover), of 从 (two points of entry), and of 丨 (the divider between the two points of entry)." Received sources indicate that vapor is supposed to be inhaled through the nose during breath cultivation, and supply other metaphors for the nostrils. According to the "Heshang gong" commentary to _Laozi_ , par. 10, the term _tianmen_ 天 門 (heaven gate) refers both to the entrance to heaven and to the nostrils (Daode zhening zhu, 1.8a). For the role of the nose in religious Daosit breath cultivation, see Maspero 1981: 491–94.
1孷 in _MWD_ , vol.4, "Transcription," should be transcribed as , an unattested graph. I read it as ao 敖 glossed in SW, 6B.2b, with you 遊 (travel, drift, spread).
2"Permeates" translates _yinyin_ 陰 陰. For use of the compound in the sense of "pervasive" (literally, something that "overshadows" everything else), see _Hanshu_ , 22.20b.
3"Blockage" translates _hui_ 薈, based on the gloss in _Guangya_ , 2B.6b.
4執 in _MWD_ , vol.4, "Transcription," should be transcribed as 埶 and read as _shi_ 勢, in the sense of "exert."
5This is one of the rare occasions when _jing_ 精 means the "essential thing" rather than physio-spiritual essence.
6I read _mi_ /* _mi əd_ 味 as a phonetic loan for _wei_ /* _mj əd_ 味 (taste). Nou 彀 is glossed as "suckle" in SW, 14B.25a.
7The same hygienic principle of replenishment is enunciated in the _Maishu_ : "When the vessels are brimful, drain them; when empty, fill them; when still, stay in attendance on them" ( _MSSW_ : 74). The passage in _MS_ VI.A.4 is also reminiscent of _Suwen_ 17, 5.3b: "When replenishing and draining do not fail to be as one with heaven and earth. To grasp the nature of One is to know death and life. Therefore, tones conjoin with the Five Sounds, colors conjoin with the Five Agents, and the vessels conjoin with Yin and Yang."
8The end of the sentence coincides with the bottom of S39. S40 is clearly misplaced in _MWD_ , vol. 4, "Transcription," and I follow Qiu Xigui in moving S40 to _MS_ VI.A.8 between S72 and S73 where the text fits the context perfectly (1992: 525–27). I further agree with Qiu that the text of S41 does not connect well with S39 as the conclusion to _MS_ VI.A.4. Based on consideration of the overall content of _MS_ VI.A.4, to follow S51 as the conclusion to _MS_ VI.A.6. Although not noted by Qiu, there is a parallel to his rearranged text of _MS_ VI.A.4 in _MS_ VII.B.3 that adds support to his argument. The parallel begins with the exact statement concerning cultivation give above: "The task lies in accumulating essence"; continue with a similar discussion of the need to drain and replenish essence; and proceeds to a description of sexual cultivation that includes the instruction to "lightly exit and lightly enter" (referring to the penis in the vagina). The instruction to "coordinate (replenishment) with sleep" at the bottom of S39 followed by "exit and enter" at the top of S52 makes the same transition to a description of sexual cultivation. In addition, S41 appears to provide a satisfactory conclusion to _MS_ VI.A.6. Although the basis for the rearrangement is contextual, the diagram of the original positions of the bamboo slips when the manuscript was first excavated (in _MWD_ , vol. 4: 152) does not defintely prove the sequence of the slips in _MWD_ , vol. 4, nor does it disprove Qiu's rearrangement. It is also possible that the manuscript as excavated is defective, that a slip or slips with text belonging to _MS_ VI.A.4 or _MS_ VI.A.6 were missing when the bound manuscript was put into the tomb. Qiu himself regards his rearrangement of the slips as tentative, but superior to MWD, vol. 4; and I accept the rearrangement with same sense of caution.
1美 in _MWD_ , vol. 4, "Transcription," should be transcribed as zou 奏, read as _zou_ 腠 (skin's webbed pattern). The top part of the original graph is indistinct and may have been miswritten by the scribe, but the graph itself is clearly not 美 (and is very close to the writing of _zou_ in S38).
2 _MS_ VI.A.10 describes the five depots as "becoming firm and white, their jade color having a renewed glow." The meaning in _MS_ VI.A.4 must be similar, referring to the jade-like condition of the body resulting from the cultivation of vapor and essence.
3泰 十 in _MWD_ , vol. 4, "Transcription," should be transcribed as _weiban_ 未 半 (not yet half; referring to age).
4"Toil at affairs" translates _songshi_ 頌 事. I follow _MWD_ , vol. 4, "Transcription," n. 8, in reading _song_ as _yong_ 庸, whose interchangeability is attested in _Yili_ , 16.4a, and Zheng Xuan commentary. I understand _yong_ as glossed in _Erya_ , 2.3b: "toil ( _lao_ 勞)." The synonymous compound _laoshi_ 勞 事 occurs in _Shiji_ , 105.21a, where the physician Chunyu Yi warns a patient to not "toil at laborious affairs (勞 力 事)."
1The expression of universality in this sentence is reminiscent of language in the writings that precede the second Mawangdui _Laozi_ edition, as well as language in _Guanzi_ and _Huainanzi_. _MWD_ , vol. 1: 72, has the sentence: "The explication of One scans( _cha_ 察) heaven and earth." The parallel in _Huainanzi_ , 1.12, is: "The explication of One reaches( _ji_ 際) heaven and earth." Both sentences are anticipated in _Guanzi_ 49, 16.270: "The explication of One Word, above scans( _cha_ ) heaven and below extends to earth." Replace "One Word" with "life" and we have the sentence in _MS_ VI.A.4.
2"Release of the form" translates _xingjie_ 形 解. The term is attested in _Shiji_ , 28.10b, in a passage concerning occult specialists from the region of Yan who arrived at the court of the First Qin Thearch with recipes for "the way of transcendence( _xiandao_ 僊 道)" as well as "release of the form and fluxing transformation( _xingjie xiaohua_ 形 解 銷 化)." The commentary cites Fu Qian 服 虔 (second century A.D.), who equates _xingjie_ with _shijie_ 尸 解 (release of the corpse). _Shijie_ is best known in connection with religious Daoism. For the Daoist believer, _shijie_ marked the moment when a new, immortal physique was perfected and the mortal body sloughed off, leaving behind a husk-like corpse (or an object such as a sword or staff) as evidence of the adept's achievement of _shijie_ (Maspero 1981: 445–48).
While _xingjie_ and _shijie_ are surely related, it is evident that _xingjie_ in _MS_ VI.A.4 does not represent the identical concept as _shijie_ in religious Daoism. The occurrence of _xingjie_ in MSVI.A.4 along with the references to "becoming a spirit" above and rising "like the dragon" below suggest cross-influences between the medical tradition of macrobiotic hygiene and the _xian_ -cult, but I am uncertain what the nature of the influences is (see Prolegomena, Section Four, "Body and Spirit").
3 _MWD_ , vol. 4, "Transcription," n. 10, reads 麇 as _jun_ /* _kwji әn_ 麇, which it identifies as a phonetic loan for _qun_ /* _gwji әn_ 群 (the loan usage is attested in _Zuozhuan_ , Zhao 5, 43.6b). The name Piled Blue-gem ( _qunyao_ 群 瑶) is similar to the Piled Jade Mountain 群 玉 之 山 mentioned in _Mu tianzi zhuan_ , 2.4a, as the domain of Rong Cheng where Mu stops on his westward journey to the land of the Queen Mother of the West. While there is no evidence that Piled Blue-gem is another name for Piled Jade Mountain, the identification is plausible and adds to contextual evidence for making SS52–59 part of Rong Cheng's teaching in _MS_ VI.A.4. Alternatively, Jade Mountain 玉 山 is identified as the dwelling place of the Queen Mother of the West in _Shanhaijittg_ ; 2.19a. It is also possible that Piled Blue-gem alludes to the Blue-gem Pool at Kunlun Mountain where Mu met the Queen Mother of the West (see above).
1 _MWD_ , vol. 4, "Transcription," n. 11, identifies the name Wuchengzhao 巫 成 柖 with Wuchengzhao 務成 昭. According to _Xunzi_ 27, 19.323, the latter was Shun's teacher. Hanshu, 30.81a, records the _Wuchengzi Yin_ dao 務 成 子 陰 道 (Wuchengzi's way of Yin) among books on sexual cultivation; and this same Wuchengzi laer gained prominence in religious Daoism. If the "Transcription" identification is accepted, one might then question whether the mention of Shun's teacher in a dialogue between the Yellow Thearch and Rong Cheng constitutes historical anachronism (assuming, that is, that the chronology of figures in old legends was a settled issue by the third century B.C.); which could cast doubt on the rearrangement of SS52–59 (there is less of a problem in _MS_ VI.A.6, since tradition places Pengzu in historical proximity to Shun). In my judgement anachronism is not a significant issue. I am also skeptical of the "Transcription" identification. _Zhuangzi_ 14,219, mentions a Wuxiantiao 巫 咸 柖, who imparts cosmological wisdom. 咸 in the _Zhuangzi_ version of the name is probably to be equated with 成 in _MS_ VI.A.4, providing a second possible referent for the name (I disagree with the Zhuangzi commentaries which identify Wuxiantiao as the shaman Wuxian 巫 咸, who is credited with the invention of divination). All three names may have some connection in legends that are only imperfectly recorded in Warring states philosophical texts.
2The idea of immortality expressed here is discussed in the Prolegomena, Section Four, "Body and Spirit."
3I follow the interpretation of the twelve joins in the Yang Shangshan commentary in _Taisu_ 3.26: "The four limbs each have three large joints" (i.e. ankle, knee, hip, wrist, elbow, and shoulder). The Wang Bing commentary in _Suwen_ 3, 1.9b, identifies the twelve joints as the twelve vessels, but this denotation is clearly inapplicable to the Mawangdui medical manuscripts, which describe only eleven vessels.
4The Yin refers to the penis as the chief Yin component of the body. Given that Yin vitality of the body depends above all on the care of the penis, Yao is requesting instruction on how to prevent its early demise. A parallel passage occurs in _MS_ VII.B.1.
5 _MS_ VI.A.6 offers further discussion of the necessity of including the penis and its vitality in an overall hygienic regimen.
1Perhaps _kuanli_ 寬 禮 should be read as compound meaning "lenient ritual" similar to _kuanzheng_ 寬 政 (lenient government) in _Zuozhuan_ , Zhuang 22, 9.12b.
2I follow _MWD_ , vol. 4, "Transcription," n. 3, in reading as _cui_ 顇. The scribe probably erred in writing 衣 instead of 卒. Cui should be understood as _cui_ 崒, in the sense of the tip of a peak (see _SW_ , 9B.5b, and Duan Yucai commentary). In _MS_ VI.A.5 the word serves as a euphemism for the head of the penis, hence my translation "prong." _Cui_ /(dzjәd also puns with zui/(tsuәd 脧, which refers to the genitals or penis (see _MS_ VI.A.6).
3I.e. the man should absorb the woman's essence during intercourse without releasing any of his own.
4Ancestor Peng 彭 祖 as a legendary figure in Warring States macrobiotic hygiene is discussed in the Prolegomena, Section Four, "Intellectual Background." _MWD_ , vol. 4, "Transcription," n. 1, identifies the name Wangzi Qiaofu 王 子 巧 父 with Wangzi Qiao 王 子 喬, the legendary xian-cult adept (see Prolegomena, Section Four, "Intellectual Background"). I would treat the identification as an unverified as an unverified probability rather than a proven fact.
5I follow _MWD_ , vol. 4, "Transcription," in reading 竣 as _zui_ 脧, referring to the genitals or penis (see MSI.E.134). _MS_ VI.A.6 concerns the need to cultivate the vapor and essence of the penis by various means other than sexual intercourse. The conclusion does not that proper cultivation of the vitality of the penis permits "lasting coitus."
1"First light of day" translates _faming_ 發明, which occurs again in _MS_ VI.A.9 describing the time when the rooster crows. The term is attested in _Shuoyuan_ , 18.6b, as the name for the call made by the mythical _feng_ 鳳 bird at dawn (there are three other names for the call of the _feng_ in the daytime, while in flight, and while perching). According to _SW_ , 4A.4oa, _faming_ is one of the five spirit birds, and is associated with the east (the _feng_ is the bird of the center). See Chen Mengjia 1965: 122, for other Han terms denoting the break of day in which _ming_ is the second member of the compound.
2Yin and Yang refer to inner and outer surface on the body. According to _Suwen_ 4, 1.16a–b, the abdomen is Yin and the back is Yang. Perhaps the rubbing motion in _MS_ VI.A.6 moves between the abdomen and the back. However, I suspect that the person is supposed to stroke in a circular motion from the center of the abdomen (the Yin inner part) towards the edges (the Yang outer part).
3Ejecting stale vapor is discussed in _MS_ VI.A.4. Perhaps sucking in penile vapor is related to the practice of contracting the anus described in _MS_ VI.A.7.
4The _locus classicus_ for the "red infant" ( _chizi_ 赤 子; i.e. the newborn infact) is _Laozi_ , par. 55, which also refers to the infant's sexual potency: "The fact that without knowing of the conjoining of female and male its penis ( _zui_ 朘) rises is the culmination of essence" ( _MWD_ , vol. 1: 105). Comparing the cultivation of the penis to nurturing the red infant suggest an analogy between macrobiotic hygiene and infact care—or, as I think is more likely, gestation. The analogy becomes a reality in the following sentence which uses "red infant" as a euphemism for the penis. In religious Daoist hygiene, "nurturing the red infant" refers to the inner cultivation of a perfected being through a process equivalent to gestation. Six Dynasties Daoist sources locate the red infant in the "cinnabar field" ( _dantian_ 丹 田) by the navel, which functions as the womb (Schipper 1978: 370–71). The cultivation of the red infant/penis is not equivalent to the Daoist cultivation of the red infant/perfected being. But the idea of gestation prominent in the Daoist sources must also be present in _MS_ VI.A.6 (the idea of cultivation as gestation is also evident in _MS_ VI.A.7).
5Here referring to the penis itself.
6The injunction "be careful to not" marks the bottom of S51, followed at the top of S41 by the compound _yaoshi_ 使, which is a standard compound meaning "corvée lanor" in Han sources (see, for example, _shiji_ , 7.12b). The idea that the penis should not be "burdened with labor" paralles the idea in _MS_ VI.A.5 that the penis is too often "employed without leniency."
7立 in _MWD_ , vol. 4, "Transcription," should be transcribed as _jiao_ 交 (coitus).
1 _Qi_ is glossed in _SW_ , 8A.68a, as "face of an old man that looks frozen and blackened like refuse," hence my translation "wizen-faced." The Wizen-faced Oldster 老 is not attested in received literature. Pan Geng 盤庚 reigned in the middle years of the Shang period. The book _Tang Pan Geng Yin dao_ 湯 盤 庚 陰 道 (Way of Yin of Tang and Pan Geng) in _Hanshu_ , 30.81a, indicates his association with sexual cultivation.
2I.e. the penis (as in _MS_ VI.A.5).
3The five part procedure described below is similar to the description of the "eight benefits" in _MS_ VII.B.7. The "eight benefits" are eight ways to cultivate the vapor and essence associated with the genitals, some of them involving sexual intercourse. _MS_ VI.A.7 differs in that the Wizen-faced Oldster appears to be describing a single technique in five linked stages, from "relaxing the limbs" to "sucking in the great illumination." The technique seems to accompany sexual intercourse, but it may also be accomplished without intercourse, as suggested by the concluding sentence that labels _MS_ VI.A.7 the "Wizen-faced Oldster's way for coitus with Yin and eating spirit vapor."
4Presumably the Yin refers to the penis. "Move the Yin"suggests sexual stimulation, but assuming that the technique is not solely a method for intercourse some form of exercise may also be intended (like "pulling Yin" in _MS_ VI.A.8).
5For _zhou_ 州 in the sense of "anus," see _MS_ I.E.153. Instead of _suo_ 縮 (contract), _MS_ VII.B.7 uses the verb _xi_ 口翕 (suck in). _Ishinp_ ô, 28.22b, recommends "contracting the lower region" to help stabilize the essence being generated during intercourse so that it is not lost by ejaculation of semen. The use of anal constriction in both coital and non-coital cultivation techniques is discussed in the Prolegomena, Section Four, "Techniques."
6The person concentrates meditatively. I read _liu_ /* _ljdgw_ as a phonetic loan for _bao_ /* _pr ǝgw_ 胞 (womb, uterus), which I understand to mean a "womb-like organ" where men as well as women store vapor and essence. The word occurs again in _MS_ VI.A.8 in a passage that alludes to the third and fourth stages of the technique in _MS_ VI.A.7.胞 pronounced _pao_ also denotes the bladder (written 脬 in _SW_ , 4B.22b), but in my judgment the bladder—even though it is a receptacle for water—is not the referent of _liu_ / _bao_ ( _pao_ 脬 occurs in _MS_ I.E.95 and _MS_ I.E. 101 denoting the bladder). Two _Suwen_ passages support the identification of _bao_ as an organ possessed by men and women in early physiological theory. _Suwen_ 37, 10.10a, notes that "when the womb ( _bao_ ) transfers heat to the bladder ( _pangguang_ 膀 腕), there is urine retention and bloody urine." According to the Wang Bing commentary, "the bladder is the cavity for fluids; the womb oversees receiving and injecting." _Suwen_ 48, 13.8a, attributes a certain morbid condition of the vessels to insufficient transmission of "womb essence," and Wang Bing notes that "the womb vessel is attached to the kidney." Other occurrences of _bao_ in the _Huangdi neijing_ denote the uterus, although it is possible that some of the statements concerning the _bao_ are applicable to male as well as female anatomy. _Nanjing_ , 3.30b, is the earliest source to distinguish between the left kidney, which it identifies as the location of the depot named _shen_ 賢 (also a water receptacle), and the right kidney, which is the organ where vapor and essence are stored: "The right one is the gate of life ( _mingmen_ 命 門). The gate of life is the place where all spirit essence lodges, and where the original vapor is attached. Thus the man stores essence in it and the woman attaches it to the womb ( _bao_ )" (cf. Unschuld 1986b: 382). The _Nanjing_ passage appears to resolve ambiguity in the _Huangdi neijing_ concerning the function of the two kidneys as well as the status of the _bao_ : the latter is a female organ subordinated to the right kidney which is the gate of life proper. I think that _liu_ / _bao_ in the Mawangdui manuscripts serves the function of what the _Nanjing_ calls the _mingmen_ (and the lack of references in the manuscripts to the kidney as a place for storing vapor and essence is probably because this function is performed by the _bao_ ). Significantly, _MS_ VI.B.I identifies the place where a man sends the essence generated during sexual intercourse as the _zong_ \- men 宗 門 (progenitive gate); and the same place is called _xuemen_ 血 門 (blood gate) in _MS_ VII.B.13. I suspect that both terms are related to the later _mingmen_ ; and I would argue for associating them with _bao_ in _MS_ VI.A.7–8. Although my interpretation of the manuscript evidence is contextual and circumstantial, I believe that it is sufficient to support my speculation that early macrobiotic hygiene theory included the idea that men as well as women possessed a womb/progenitive gate.
Religious Daoist hygiene makes a similar correlation between the _bao_ and the _mingmen_ —which is situated at the navel (the terminus of the life-cord of birth). For example, the _Lingshu ziwen_ , 1.11b–12a, provides the following identifications: "The gate of life ( _mingmen_ ) is the navel. The dark barrier ( _xuanguan_ 玄 關) is the passageway to the womb ( _bao_ ) and intestines from the original time of birth. Within it there is a palace of life.... To replenish the fetus and return to the womb, at sunset first enclose vapor, breathing twenty-four times...." Robinet 1984, vol. 2: 109–110, dates this text to the original Shangqing revelations in the fourth century A.D. I am grateful to Stephen Bokenkamp for drawing my attention to this example of the pairing of _bao_ and _mingmen_. For additional discussion of the significance of gestation as a model for breath cultivation and sexual cultivation in religious Daoist hygiene, see Schipper 1978: 370–71. The occurrence of _liu_ / _bao_ and the references to "nurturing the red infant" in _MS_ VI.A.6 indicate that the idea of gestation was already part of early macrobiotic hygiene.
Other arguments have been made for the identification of _liu_ 月留. _MWD_ , vol. 4, "Transcription,"n. 3, proposes reading the graph as _nao_ /* _nagw_ 月甾 (brain). In Han texts examples of rhyming between Old Chinese *-ǝgw and *-agw are common (Luo and Zhou 1958: 19). Thus an argument that _liu_ /* _lj ǝgw_ is a loan for _nao_ /* _nagw_ is phonologically tenable. I am not persuaded by Ma Jixing's claim that 月留 is a scribal error for 月甾 (1992: 937, n. 4). The flaw in the argument is, in my judgment, the a priori assumption that the passage concerns the later sexual technique of "returning the essence to replenish the brain" ( _huanjing bunao_ 還 精 補 月甾); thus the graph in question must be the word for brain. The sequence of the technique itself belies this speculation. In the later technique, "replenishing the brain" culminates sexual cultivation. In _MS_ VI.A.7 "filling the _liu_ " occurs in the third stage, and cultivation (which may be non-coital as well as coital) culminates in the fifth stage when the "essence ascends." "Filling the _liu_ " as the third stage in _MS_ VI.A.7 cannot be equated with "replenishing the brain." Matters related to the culmination of sexual cultivation in the Mawangdui medical manuscripts are discussed in the Prolegomena, Section Four, "Techniques."At present the earliest attestation of _huanjing bunao_ is ca. second century A.D., in the "Xianger" commentary to _Laozi_ , par. 9, which condemns the practice of "lying with women without ejaculating, thinking to return the essence and replenish the brain" (Rao Zongyi 1991: 11). Based on a quotation in the _Hou Hanshu_ , it has been argued that _bunao_ occurred in the original version of the _Liexian zhuan_ account of Rong Cheng; but Kaltenmark 1953: 58, correctly notes that the _bunao_ reference belongs to the commentary and not to the text of the _Liexian zhuan_.
Ishida proposes identifying _liu_ /* _lj ǝgw_ as the male genitals by reading it as a phonetic loan for _gao_ /*kǝgw 峯 (testicle; 1991: 15). The phonological probability of the loan is good, but "sucking in vapor to fill the testicles/genitals" is an unlikely interpretation of the text.
1"Wellspring blossom" is obviously an internally produced fluid, unlike the "running beasts' wellspring blossom" in _MS_ VI.A.2 and 10.
2See the parallel in _MS_ VI.B.1 which also describes the ascent of essence.
3Teacher Gui 師 癸 is not attested in received literature. Yu 禹 discusses sexual cultivation with court ladies in _MS_ III.89.
4Descriptions of Yu's labors to tame the flood waters occur in numerous pre-Han sources, including the physical impairments that serve as the rationale for the Pace of Yu in the _Shizi_ (see _MS_ I.E.60). _Shiji_ , 2.26a, identifies Kuaiji 會 稽 as the mountain in the southeast where Yu convened his lords and then died. "Order" translates _zhi_ 治, elsewhere translated as "cultivate." Yu is asking how to restore his health and bring order to his household simultaneously.
5I.e. to "order" (zhi) the state a ruler must "cultivate" ( _zhi_ ) his body.
6 _Liuji_ 六 (six extremities) refers to the four directions as well as up and down in _Zhuangzi_ 7,132. In _MS_ VI.A.9, _liuji_ appears to be equivalent to _liumo_ 六末 in _MS_ III.70, denoting the four limbs as well as the genital and anal regions. To say that the "calamity of blockage controls ( _zong_ 宗) the six extremities" means that when stagnation of blood and vapor causes internal blockage, this morbid condition affects the entire body (and by extension, the entire state). _MWD_ , vol. 4, "Transcription," n. 4, proposes a different meaning for _liuji_ in _MS_ VI.A.8, referring to a list of six harmful things called _liuji_ in _Shangshu_ , "Hong fan," 12.14b. Ma Jixing cites several examples of _liuji_ referring to maladies in medieval medical literature (1992: 942, n. 9). In their interpretation the translation would be, "this is called the calamity of blockage, which is the source ( _zong_ ) of the six extremities." The interpretation is plausible, but I regard the occurrence of _liuji_ in _MS_ VI.A.9 as decisive.
1The sentence alludes to the third and fourth stages in the technique described in _MS_ VI.A.7.
2"Pulling Yin" ( _yin_ Yin 引 陰) is the name for two exercises in the _Yinshu_ , one a simple toe-touch and the other a procedure involving anal constriction (see the Prolegomena, Section Four, "Tecniques," for details). Ma Jixing understands "pulling Yin" in _MS_ VI.A.8. to refer to exercicing the genitals (1992: 947, n. 1). While not impossible, this is probably not the intended meaning.
3 _Qushen_ 屈 伸 (curl and stretch) as a term connoting the ability to conform to the pattern of nature is ubiquitous in early lieterature. The regular occurrence of _qu_ and _shen_ in the exercise instructions in the _Yinshu_ best illustrates the application of the concept of "curl and stretch" to macrobiotic hygiene.
4 _Buwu_ 不 物 occurs in _Zhongjiu_ , 15.3a, in the sense of an "abnormal creature." In _MS_ VI.A.8 I understand _wu_ as a verb meaning "be a normal creature," embellished as "be a perfect specimen."
5" Fermented milk" translates _zhonjiju_ 酒 ( _zhong_ occurs at the bottom of S72, and _jiu_ at the top of S40). I suspect that _zhongjiu_ is a variant of _zhonglao_ 酪 (kumiss), the favored beverage of the Xiongnu 匈 奴 ( _Shiji_ , 110.15a).
1I surmise from the context that Yin refers to the genitals. The lacuna may be _fu_ 復, making the genitals "reborn." Queen Yao 后 J兆 is not attested as the name of Yu's wife. Qiu Xigui notes that the graph transcribed as _yao_ 姚 is difficult to decipher and recommends further investigation (1992: 525–26). Assuming that it is _yao_ , Qiu suggests that Queen Yao is equivalent to Woman Qiao 女 the name of Yu's wife given in _Hanshu_ , 20.20b (there is phonological similarity: _yao_ /* _dagw_ and _qiao_ /* _gjagw_ ).
2King Wei of Qi 齊 威 主 (r. 357–320 B.C.) is credited with establishing the Jixia 稷 下 Academy, the pre-eminent center of learning of the day (Rickett 1985: 18–19; Knoblock 1988: 54–55). Wen Zhi 文 摯 is identified in _Lüshi chunqiu_ , 11.107, as a physician from Song 宋 who treated the illness of King Min 滑 王 of Qi (r. 300–284 B.C.). The only cure was to anger the king, and once the king recovered he could not be dissuaded from executing Wen Zhi: "So they boiled Wen Zhi alive in a caldron. It cooked for three days and three nights, and his facial complexion was unchanged. Wen Zhi said, 'If you genuinely wish to kill me, why not cover it to cut off the vapor of Yin and Yang.' The king had the caldron covered, and Wen Zhi then died." _Lunheng_ , "Dao xu," 7.151, presents a detailed refutation of the truth of the story in order to dismiss the popular belief that Wen Zhi was a "person of the way." The format of the exchange between master and student changes in _MS_ VI.A.9–10 to the interview style characteristic of Warring States rhetoric. A specialist gains an interview with a ruler; he responds to the ruler's questions; and the ruler caps the response with the formulaic "excellent."
3A humilific form of self address commonly used by Warring States rulers.
4Master ( _zi_ 子) is a respectful form of address, but the additional Great Man ( _daju_ 大夫) suggests that Wen Zhi was a man of rank in court hierarchy (in Song or perhaps in Qi).
5I read _bian_ 编 as pian 篇, referring to a bundle of bound bamboo slips (fascicle). The statement is self-advertisement, and "three hundred fascicles" is an idealized number implying perfection. See, for example _Shiji_ , 130.12a, where the three hundred songs of the _Shijing_ are referred to as the "three hundred fascicles," meaning that they are the cynosure of the moral feelings of the sages of old.
6"Clumped" translates _du_ 毒, glossed as follows in _SW_ , 1B.2a: "Thick; grass that harms people continually growing." "Harmful, poisonous" is an extended meaning. For the development of the word _du_ in medical usage, see Unschuld 1975. In _MS_ VI.A.9. it simply describes the rowth of leeks in clumps.
1Lord Millet 后 稷 is an agricultural deity and legendary founder of the Zhou lineage. I read 半 as _ban_ 尘, meaning "toss" and here used in the sense of "sow" ( _see Guangya_ , 1a.13a, and Wang Niansun commentary). I follow _MWD_ , vol. 4, "Transcription," n. 4, in reading _rou_ /* _nj ǝgw_ 稷 as a phonetic loan for _you_ /*? _j ǝgw_ 稷, glossed in _SW_ , 6A.43a, as "implement for tilling fields."
2The gloss of _jiu_ /* _kj ǝgw_ 韭 in _SW_ , 7B.3b, also traces the origin of the same for the leek to the fact that it is _jiu_ /* _kj ǝgw_ 久 (long lasting): "planted once, it lives long ( _jiu_ 久); thus it is called _jiu_."
3I follow _MWD_ , vol. 4, "Transcription," in reading _zhe_ 聶 as _zhe_ 懾 (timid). "Skittish" translates _bi_ 辟, in the sense of "evasive, nervous." The "Transcription," n. 6, additionally cites the compound _zhebi_ 辟 as a technical term in _Suwen_ 62, 17.5a, but _bi_ and _zhe_ are best interpreted as single descriptive words in _MS_ VI.A.9.
4I give the pronunciation _ljang_ /* _gljang_ to the unattested graph ; and read it as a phonetic loan for _liang_ /* _ljang_ 悢, glosses as "dispirited" in _Guangya_ , 3A.4b. The compound _kuang-liang_ 懭 悢 is attested with the same meaning in _Chuci_ , "Jiubian," 8.2a. _MWD_ , vol. 4, "Transcription," n. 6, reads the graph as a phonetic loan for rang/* _njang_ 懭 (abhor), but in my judgement _liang_ "dispirited" is a better reading phonologically and semantically.
5I.e. it is the most refined form of the vapor of the five grains.
6"Internal network" translates _li_ 理, here alluding to the vessels.
1The phrase 春 寫人人以韭 in the first half of the sentence requires textual commentary. I read 人as _ru_ 人, a simple scribble miswriting that also occurs in the preceding paragraph. I read , glossed in _SW_ , 5B.12b, as "feast." I understand the "spring feast" to be the spring festival when the populace makes offerings of agricultural products; and I understand _xieru_ 人 as a compound to the collection of offerings at an offering site, hence the translation "collation." The custom of offering the leek at the spring festival is described in _Liji_ , 12.12b (which also lists the appropriate offerings for the summer, autumn, and winter festivals): "In the spring the populace offers leek, in the summer wheat, in the autumn millet, and in the water rice. Egg accompanies leek, fish accompanies wheat, pork accompanies miller, and goose accompanies rice." King Wei's question to Wen Zhi confirms that the combination of leek and egg was a well established custom; and he wants Wen Zhi to justify the difference between medical Knowledge and popular custom.
2I am not certain which season is specified by Wen Zhi, but I suspect summer. _Fu_ Yin (returned Yin) can be interpreted in two ways: as the time during the annual Yin Yang cycle when Yin beings to flourish while Yang recedes; or as the time when Yin "returns back" to its optimal state of fullness. There is evidence for both interpretations in received sources. _Xijing zaji_ , 5.16, records a statement attributed to Dong Zhongshu 董 仲 舒 that the latent " return to Yin" becomes manifest; and Yin continues to grow during the months after the fourth month until it peaks in the tenth month. In contrast, the Wang Bi commentary in _Yijing_ , "Fu," 3.12a, understands the winter solstice to be the time of _fu_ Yin, when yin "returns back" to its origin and is at rest. The winter solstice carr be equated with the eleventh month. Ectrapolating from the _Xijing zaji_ , Wen Zhi's three _fu_ Yin months ought to be the summer months (the fourth through the sixth). Extra polating from the Wang Bi commentary, the _fu_ Yin months might be either the winter months (the tenth through the first). It is also possible that received sources fail to indicate the meaning of the term _fu_ Yin as used by Wen Zhi, and that it refers isiomatically to the spring months. I am skeptical of the third possibility, and prefer to think that Wen Zhi is providing a medical rationale for the third possibility, and prefer to think that Wen Zhi is providing a medical rationale for the combination of leek and chicken that is based on yin Yang classification (leek was probably also considered Yang as it was later; see _GM_ , 26.40) instead of folk custom. Since spring and summer are the seasons for fresh leeks, I favor interpreting _fu_ Yun as understood in the _Xijing zaji_ and identifying the season as summer.
1I am not certain which bird is denoted by the name _sushuang_ 鷫 鸘. According to _SW_ , 4A.40a, it is one of the five spirit birds, and is associated with the west. The Duan Yucai commentary cites several sources that describe the bird as goose-like with a long neck and green feathers.
2I follow Ma Jixing (1992: 962, n. 3) in reading _yuan_ 蚖 as _wan_ 蜿, and understanding _wanshan_ 蜿 蟺 as a compound denoting the earthworm (see _Guangya_ , 10B.9b).
3The phrase 桅 湯 劓 惑 in the second half of the sentence requires textual commentary. I assume that the phrase is grammatically parallel to the precending phrase. Thus, I read 湯 as _chang_ 卼 (intestine), parallel to "heart" above. I read 桅 as _nie_ 臲. The compound _niewu_ 臲 is attested in _Yijing_ , "Kun," 5.8b, with the meaning "uneasy, uncomfortable." _SW_ , 6B.2b, records a variant written 槷 . I understand _yi_ 劓 in the sence of the compound _yiyue_ 劓 刖 (literally, the mutilation punishments of cutting off the nose and the feet) in _Yijing_ , "Kun," 5.8a, where it is similar in meaning to _niewu_. I suspect that _yihuo_ 劓 惑 the compound for "clogging" in the preceding phrase.
4Presimably the king belongs to the latter category.
5"Blackness" translates _yi_ 黟, glossed in _SW_ , 10A.59a, as "black tree" _MWD_ , vol. 4, "Transcription," reads the graph as _mei_ 鏘 without comment, evidently regarding the former as scribal error for the latter. I prefer to interpret the original graph in the sense of the "blackness" of the body's interior.
1I.e. the four limbs as well as the genital and anal regions (see _MS_ VI.A.8). Using breath cultivation to transport vapor to the limbs is mentioned in _MS_ VI.A.4.
2Wang Qi 王 期 is not attested in received literature. The Qin ruler is King Zhaoxiang 昭 襄 王 (r. 306–251 B.C.). Presumably Wang Qi was a physician who was patronized by the Qin elite.
3The title indicates that Wang Qi belonged to the rank of Guest (ke 客)) in the court hierarchy.
4"Essence illumination" translates jingming 精 明 which I assume to be similar in meaning to _shenming_ 神 明 (spirit illumination). The religious sense of the compound is attested in _Guoyut_ 18.3a: "Now as for spirits, they are what approach people with essence illumination." As a component of human physiology, _Suwen_ 17, 5.1a–2b, associates essence illumination with the eyes and vision, and states that "the head is the cavity of essence illumination."
5See _MS_ III.6, 47, 71 for dietetic use of pine rosin. Pine and arbor-vitae also figure in _xian_ \- cult dietetics (see Kaltenmark 1953: 54, 81).
6See _MS_ VI.A.2.
7Wang Qi recommends solar cookery during the summer. There is no evidence of solar cookery in received literature or in the archaeological record. _MWD_ , vol. 4, "Transcription," n. 1, speculates that "using the sun to cook" refers to using the Yang _sui_ 陽 縫, a kind of burning-lens that was believed to draw true Yang fire down from heaven (on the Yang _sui_ , see Needham 1954–, vol. 4, part 1: 111–13). However, using a burning-lens to produce the fire is still cooking with fire. I prefer to think that a solar cooker existed, perhaps utilizing the technology of the Yang _sui_ , and that food was cooked without fire in the reflected rays of the sun.
1Perhaps "numinous dew" ( _linglu_ 靈 露) is similar to "sweet dew" in _MS_ VI.A.4.
2I understand _kuan_ 款 in the sense of "relaxed" as attested in _Hou Hanshu_ , 24.9a. An occurrence of _kuan_ in _shiji_ , 130.11b, is glossed by Ru Chun 如 淳 (third century) as _kuan_ 巬 (relax) and by Ying Shao 應 (second century) as _kou_ 扣 (knock). While it is possible that Wang Qi is saying to "Knock" with the jade whip (i.e. to hit the vagina with the penis), I think the meaning "relaxed" is the best in this context.
3See _MS_ VI.A.4.
4The vitalizing fluids must be the simultaneously generated products of sexual cultivation in combination with breath cultivation.
5I follow _MWD_ , vol. 4, "Transcription," n. 2, in reading 蠪 as _long_ 龍 (dragon).
6"Congealed" translates _ling_ 淩, which is equivalent to _ling_ 淩, literally "blocks of ice" ( _SW_ , 11B.9a, and Duan Yucai commentary).
_MS_ VI.B
He Yin Yang
合 陰 陽
Conjoining Yin and Yang
_MS_ VI.B.I (SS102–111)
The recipe for whenever you will be conjoining Yin and Yang:1
Grip the hands,2 and emerge at the Yang side of the wrists;3
Stroke the elbow chambers;4
Press the side of the underarms;5
Ascend the stove trivet;6
Press the neck zone;1
Stroke the receiving canister;2
Cover the encircling ring;3
Descend the broken basin;4
Cross the sweet-liquor ford;5
Skim the Spurting Sea;
Ascend Constancy Mountain;1
Enter the dark gate;2
Ride the coital muscle;3
Suck the essence and spirit upward.1
Then you can have lasting vision2 and exist in unison with heaven and earth.
The coital muscle is the coital vessel inside the dark gate. When you are able to rub and stroke it,3 it causes both bodies to experience ecstatic excitation and to exude beauty that is joyful and lustrous.4 Although desirous, do not act. Perform mutual exhalation5 and mutual embracing, following in sequence the way of play.6 The way of play: the first is "vapor rises and her face is flushed—slowly exhale";7 the second is "the nipples harden and her nose sweats—slowly embrace"; the third is "the tongue spreads and becomes slippery—slowly press";1 the fourth is "the fluid flows below and her thighs are damp—slowly rub";2 the fifth is "her throat is dry, swallowing saliva—slowly rock." These are the "signs of the five desires." When the signs are complete, ascend. Jab upward but do not penetrate inside, thereby bringing the vapor. When the vapor arrives penetrate deeply inside and thrust it upward, thereby dispensing the heat.3 Then once again bring it back down. Do not let the vapor spill out, lest the woman become greatly parched.4 Afterward practice the ten movements;5 conjoin in the ten postures;6 and intersperse the ten refinements.7 Conjoin forms after sunset; and send the vapor to the progenitive gate.8 Then observe the eight movements;9 listen to the five sounds;10 and examine the signs of the ten pauses.11
_MS_ VI.B.2 (SS112–15)
The ten movements: commence with ten, followed by twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety, and one hundred—exiting and entering without spilling.1 At the first movement without spilling, ears and eyes are perceptive and bright; at the second, the voice's sound is brilliant; at the third, skin and hide glow; at the fourth, spine and side are strong; at the fifth, buttock and ham are squared; at the sixth, the waterway passes through;1 at the seventh, you achieve culminant firmness and strength; at the eighth, the skin's webbed pattern glows; at the ninth, you penetrate spirit illumination; at the tenth, the body achieves constancy. These are the ten movements.
_MS_ VI.B.3 (SS116–17)
The ten postures:2 the first is "tiger roving";3 the second is "cicada clinging";4 the third is "measuring worm";5 the fourth is "river deer butting";6 the fifth is "locust splayed"; the sixth is "gibbon grabbing";7 the seventh is "toad"; the eighth is "rabbit bolting";8 the ninth is "dragonfly"; the tenth is "fish gobbling."9
_MS_ VI.B.4 (SS118–19)
The ten refinements:1 the first is "go up"; the second is "go down"; the third is "go to the left"; the fourth is "go to the right"; the fifth is "thrust rapidly"; the sixth is "thrust slowly"; the seventh is "thrust rarely"; the eighth is "thrust frequently"; the ninth is "enter shallowly"; the tenth is "enter deeply."
_MS_ VI.B.5 (SS120–24)
The eight movements:2 the first is "clasping hands"; the second is "extending elbows"; the third is "straightening heels"; the fourth is "hooking the flanks"; the fifth is "hooking up above"; the sixth is "crossing thighs"; the seventh is "level upspring"; the eighth is "shaking." When she clasps hands, she wants her abdomen pressed; when she extends elbows, she wants the upper part rubbed and scratched;3 when she straightens heels, entry is insufficiently deep; when she hooks the flanks, she wants the sides rubbed; when she hooks up above, she wants the lower part rubbed; when she crosses thighs, penetration is excessive; when she makes a level upspring, she wants shallow entry; when she shakes, she wants the man to continue holding for a long time.
_MS_ VIB.6 (SS125–26)
When there is convulsive breathing, the inside is tense;4 when there is panting, she feels culminant delight; when there is continual moaning,1 the jade whip has entered and excitation then commences; when there is blowing, rapturous craving is intense;2 when there is biting, her body shakes and she wants the man to continue for a long time.
_MS_ VI.B.7 (SS127–28)3
In the evening the man's essence flourishes; in the morning the woman's essence accumulates. By nurturing the woman's essence with my essence, muscles and vessels4 both move; skin, vapor, and blood are all activated. Thus, you are able to open blockage and penetrate obstruction. The central cavity receives the transmission and is filled.5
_MS_ VI.B.8 (SS129–33)
The signs of the ten pauses:6 at the first pause, clear coolness emerges; at the second pause, the odor is like burning bones; at the third pause, it is freshened;1 at the fourth pause, it is viscid; at the fifth pause, it is fragrant; at the sixth pause, it is slippery; at the seventh pause, it is congealed;2 at the eighth pause, it is tallowy; at the ninth pause, it is gelatinous; at the tenth pause, it clusters.3 After clustering it becomes slippery again, and the clear coolness emerges once again. This is called "great completion."4 The signs of great completion: the nose sweats and the lips are white; the hands and feet all twitch; the buttocks do not adhere to the bedmat, but rise up and away.5 When she becomes corpse-like, there is spreading.6 Precisely at this time vapor expands in the central bourne. Essence and spirit enter and are deposited, then engendering spirit illumination.1
1He Yin Yang 合 陰 陽 (conjoin Yin and Yang) is a standard term for sexual intercourse in received literature. It is synonymous with "conjoin vapor" in _MS_ III.89. The "recipe for conjoining Yin and Yang" that follows is a verse composed primarily of trisyllabic phrases in which monosyllabic verbs are followed by anatomical terms referring to parts of the woman's body. The verbs tell the man what action to perform and the objects indicate where on the woman's body to perform the action. The verse, which begins with foreplay and concludes with achieving the goal of sexual cultivation, is rich in physiological metaphors.
2Presumably the man grips the woman's hands. However, _wo_ 握 (grip) could also be interpreted as an instruction to the man to "fist" his own hands (and then stroke the woman's body with fisted hands). In religious Daoist hygiene the term _wogu_ 握 固 (grip the fist firmly) refers to a fist position in which the adept lays the thumb in the palm of the hand and wraps the fingers around it ( _see Ishinpô_ , 27.20b). The _locus classicus_ for the term is _Laozi_ , par. 55 ( _MWD_ , vol. 1: 105). It is likely that the fist position was already current in early macrobiotic hygiene.
3I.e. the outside of the wrists by the back of the hand. I read 土 as a scribal miswriting of _chu_ 出 (emerge). The two graphs are written similarly in Qin and Han manuscripts (see Qiu Xigui 1992: 535). _Chu_ is used in _MS_ I.A–B to designate the place on the body where the path of a vessel first "emerges" (or "arises"; see _MS_ I.A.1). In _MS_ VI.B.1 _chu_ indicates where the man begins his path around the woman's body.
4The term _rufang_ 乳 房 (breast chamber) is attested in _Suwen_ 52, 14.4a, referring to the mammary gland. Although I have not found _fang_ suffixed to other anatomical names in received sources, I suspect that _zhoufang_ 肘 房 (elbow chamber) refers to the elbow as a "chamber-like"joint. Alternatively, _fang_ should be read as _pang_ 旁 (side).
5"Press" translates _di_ 抵, which could also be understood as "go to." The tactile and directional connotations of the word are probably both intended in the verse.
6"Stove trivet" translates _zaogang_ 寵 綱. Han tombs have yielded numerous specimens of a metal trivet used to hold a kettle over an open fire. Sun Ji (1991: 335) demonstrates that _jiong_ 挂 was a contemporary name for this trivet (glossed in _SW_ , 10A.44b, as "traveling stove"). I suspect that _zaogang_ refers to the same cooking apparatus, hence my translation of _gang_ as "trivet." Applied to female anatomy, the term suggests a triangular configuration. Keeping in mind that the previous line names the underarms and the following line the neck, I would suggest identifying the "stove trivet" with the upper chest between the neck and the two breasts.
1"Neck zone" translates _lingxiang_ 領 鄉. I do not know of other examples of _xiang_ suffixed to an anatomical name. _Lingxiang_ may be a technical term whose nuances escape me. However, I suspect that it may be a nonce word created to fill out the rhird syllable with an *- _ang_ rhyme word.
2"Receiving canister" translates _chengkuank_ 拯 匡. The term is attested in _Yijing_ , "Guimei," 5.20a; and in _Shijing_ , Mao 161, 9B.1b. The _kuang_ "canister" is a square basket (which adds to its earth, Yin, feminine symbolism); and both occurrences of _chengkuang_ use the canister image to suggest female sexuality. The usage is consistent with other _Shijing_ basket imagery in which baskets suggest the female genitals. Given the square shape of the canister, I would suggest identifying the "receiving canister" with the pelvic region—the osseous basket that holds the genitals. For further discussion, see Harper 1987b: 570–75. Having moved across her upper body, the man now touches the genital region.
3"Encircling ring" translates _zhouhuan_ 周 擐, which I identify as the waist—the band that encircles the body at its midpoint. The identification is based primarily on another use of _huan_ "ring" in _MS_ I.C. The first Shuihudi hemerological manuscript uses _zhouhuan_ to describe a road that "makes an encircling ring around a house" (an unlucky sign when siting a house; _SHD_ : 210). The synonymous 周 瞏 occurs in _Hou Hanshu_ , 88.12b, with the meaning "circumference." I suspect that the instruction to "cover the encircling ring" means that the man mounts the woman at the waist; and that there is a shift from massage-like foreplay to more direct sexual action.
4The clavicle (see _MS_ I.A.2). Li and McMahon situate _chengkuang_ at the shoulders (because the shoulders hold the head) and _zhouhuan_ at the breasts (because they are round), assuming that they must be located in the vicinity of the clavicle in order for the man to touching that they must be located in the vicinity of the clavicle in order for the man to touch all three in succession as part of foreplay (1992: 167–68). I find the argument unpersuasive, especially given the strong evidence for associating _chengkuang_ with the genitals. Because the metaphors that follow the descent from the broken basin are geographical in their inspiration and the verbs no longer connote hand touching, I suspect that this part of theverse is intended more as a survey of the sexual topography of the women's body than as a literal route for the man to follow with his hands (it is of course the penis that "enters the dark gate").
5"Sweet-liquor ford" translates _lijin_ 醴 津. The term is similar to _liquan_ 醴 泉 (sweet-liquor wellspring), which denotes saliva in religious Daoist hygiene (Maspero 1981:508). Harper cites Han sources for the belief that the emergence of a _liquan_ from the earth was an auspicious portent, a manifestation of the cosmic axis joining heaven and earth (1987b: 576–77). The terrestrial location of the cosmic axis was also conceived as a navel. According to _Shiji_ , 28.9b, "heaven's navel" ( _tianji_ 天 齊) was a spring situated at the base of a mountain in the southern suburb of Linzi 臨 菑 (which accounts for the tradition that the ancient state of Qi 齊 was so named because it was the _ji_ "navel" of heaven). The human navel is the corresponding axial point on the body. Perhaps the _lijin_ is situated by the navel (a central location for storing vapor and essence as well). It is also possible that the term refers to the mammae. _Taipingjing_ , 45.123, identifies the mammae as wellsprings ( _quan_ ) that provide drink for a child in the same way that the wellsprings of the earth provide life-sustaining water.
1The Spurting Sea (Bohai 勃 海) is the body of water into which the Yellow River drains. Constancy Mountain (Changshan 常 山) is the sacred peak of the north, in present-day Hebei (the verse uses 常 rather than the usual _heng_ 恒 in the name of Constancy Mountain to avoid the personal name of Thearch Wen 文 帝). Context justifies identifying constancy Mountain as the rise of the female genitals, the _mons veneris_. By implication, the head and upper body must be situated in the south in the verse's geography. Pondering the physiological analogue to the Spurting Sea, the Liaodong and Shandong peninsula give this sea the appearance of an enclosure. I suspect that this enclosure is to be correlated with a location for storage of vapor in the body. If, purely for the sake of speculation, we assume that the "sweet-liquor ford" has a geographical location as "heaven's navel" in Qi, the Spurting Sea ought to be the region to the north of (beneath) the navel. If, however, the "sweet liquor ford" refers to the mammae, it would be equally plausible to situate the Spurting Sea below the breast. In my reading of the verse, I prefer situating the Spurting Sea closer to the genitals and thus I favor a location below the navel. In Tang and later religious Daoist hygiene the term _qihai_ 氣 海 (vapor sea) refers to a place beneath the navel (also the location of the lower cinnabar field; Maspero 1981: 459, 488). This would appear to corroborate my preference for the location of the Spurting Sea were it not for the fact that the earliest attested usage, in _Lingshu_ 33, 6.5a, identifies the _qihai_ as one of four "seas" in the body and situates it in the upper chest (the stomach is the location of the "water and grain sea," and the brain of the "water and grain sea," and the brain of the "marrow sea"). While confirming the notion of seas in the body, _qihai_ in _Lingshu_ might be used to justify the alternative interpretation of the "Sweet lilquor ford" as the mammae with the Spurting Sea underneath. In short, the physiological denotation of Spurting Sea remains uncertain.
2I.e. the penis penetrates the vagina. The term "dark gate" ( _xuanmen_ 玄 門) must be derived from the "gate of the dark feminine" (玄 牝 之 門) in _Laozi_ , par. 6 ( _MWD_ , vol. 1: 115). The "Xianger" commentary interprets the _Laozi_ phrase as a reference to the vagina (Rao 1991:9).
3The "coital muscle" ( _jiaojin_ ) is defined in the prose text below as the "coital vessel" ( _jiaomai_ 交 筋) inside the vagina that can be stimulated by the penis, "causing both bodies to experience ecstatic excitation." Neither term is attested in received literature, but _jiaojin_ also occurs in _Yinshu_ ( _YSSW_ : 85). While it is evident that the terms refer to a physiological structure in the vagina that is probably responsible for what we call female orgasm, I would refrain from making specific correlations between the "coital muscle/vessel" as identified in _MS_ VI.B and modern research on the psycho-physiological elements of female orgasm (in which the role of the vagina is generally discounted). Moreover, the concept of the women's "coital muscle/vessel" is uniquely Chinese in that the man's penis is stimulated by it simultaneously. The _Huangdi neijing_ locates both muscles and vessels in the male and female genitals. According to _Suwen_ 60, 16.2a–b, the _ren_ 任 and _du_ 督 vessels pass through the genitals (for discussion of the role of these vessels in later sexual cultivation, see Needham 1954–, part 5: 202). _Suwen_ 45, 12.11a, states that the genitals are "where the manifold muscles ( _zongjin_ 宗 筋) are gathered"; and in _Suwen_ 44, 12.9a, "manifold muscles" refers to the penis.
"Ride" translates _yu_ 御, which analogizes sexual intercourse to horse-riding (see _MS_ III.38, where the man's penis/jade whip contrasts with the women's vagina/horse).The standard term for intercourse, _yunü_ 御 女, has been understood to mean simply "lie with the woman" based on _Duduan_ , 1.4a, which explains that _yu_ refers generally to the downward-directed actions of the monarch including his sexual relations with consorts. However, "riding the coital muscle" is clearly an act of penile horsemanship which probably reveals the original meaning of _yunü_.
1"Suck" translates _xia_ 欱, glossed in _SW_ , 8B.24b, as "drink." According to the Duan Yucai commentary _xia_ is the antonym of _pen_ 歕 (spout out), hence my translation "suck" for the action of drawing the sexually generated essence upward. The culmination of intercourse/cultivation for the man _MS_ VI.A.7 is similar: "the mass of essence all ascends, suck in ( _xi_ 噏) the great illumination." While the man obviously practices some form of essence retention, it is unclear whether orgasm occurs (see Prolegomena, Section Four, "Techniques").
2The earliest citation I have found for "lasting vision" ( _jiushi_ 久 視) is _Laozi_ , par. 59 ( _MWD_ , vol. 1: 107), where it is paired with "extended life" ( _changsheng_ 長 生) in the phrase "the way of extended life and lasting vision."
3I.e. stimulate it with the penis.
4Similar language is used in _Ishinpô_ , 28.7b–8a (sec. "Yang Yin"), to describe the benefits of essence retention for the woman; and in _Ishinpô_ , 28.6a (sec. "Yang Yang"), for the man.
5 _Xu_ 呴 (exhalation) is one of the forms of exhalation used in breath cultivation (see _MS_ II.A). Here it refers to a kiss in which the partners suck in the exhaled breath of their mate and thus mingle Yin and Yang essences. This mingling of breaths while kissing is referred to in the Gao You commentary in _Huainanzi_ , 2.24. For the phrase "that into which Yin and Yang exhale," the commentary notes, "the word _xu_ is read like the word _xu_ 吁 as in mouths exhaling into each other." _Ishinpô_ , 28.8b (sec. "Hezhi"), provides a detailed description of the kissing technique (cf. Wile 1992: 108).
6The five stage "way of play" detailed below (also called the "signs of the five desires") concerns foreplay. There is a parallel text in _MS_ VII.B.17. The language of a passage on the "five signs" in _Ishinpô_ , 28.12b (sec. "Wuzheng"), is clearly related to the manuscript, but the actions performed by the man in response to the signs exhibited by the woman are not limited to foreplay (cf. Wile 1992:87).
7I.e. kiss.
1I translate _tun_ 屯 as "press" primarily on the basis of the parallel _fu_ 俜 in _MS_ VII.B.17. I suspect that _tun_ in the sense of "press" is an extension from the meaning "amass" (see _Guangya_ , 3B.4a). The actions denoted by "press" as well as by "rub" and "rock" below probably involve the man's hands against the woman's body, but whole body action and penile action are also possible. In any case, penetration does not occur.
2For other occurrences of _cao_ 僺 in the meaning "rub," see _MS_ I.E.242, 251; _MS_ III.38, 43. _Xi_ 夕 and the parallel _xi_ 夕 in _MS_ VII.B.17 probably refer to tidal flow, a meaning first attested in received literature in Guo Pu's 郭 樸 (276–324) "Jiang fu" 江 賦, _Wenxuan_ , 12.6b. _Xi_ denotes the evening or neap tide in contrast to _chao_ 溯, the morning or spring tide (Needham 1954–, vol. 3: 484–85). In _MS_ VI.B.1 the "fluid flowing" is vaginal secretion (compare _MS_ V.3 where menstrual blood is associated with spring tide). _MWD_ , vol. 4, "Transcription," n. 6, reads _xi/*rjiak_ 汐 as a phonetic loan for _ye/*rag_ 液 (fluid), which is phonologically and semantically plausible. However, I think the analogy between vaginal secretion and tidal flow favors reading the graph as written (the fact that the first attestation of this meaning if _xi_ in received literature is post-Han is not in itself cause for rejecting the graph as written).
3Having completed foreplay, the man jabs at the vagina with the penis until he "brings the vapor", and then penetrates after "the vapor arrives." The vapor referred to might be the woman's, but in my interpretation it is the vapor of the penis. _MS_ VII.B.2 and _MS_ VII.B.18 describe the penis' "three arrivals": to become large, flesh or skin must arrive first; to become hard, muscle must arrive next; and to become hot, vapor must arrive before the penis can finally enter the vagina. The references to "bringing the vapor" and "dispensing the heat" in _MS_ VI.B.1 indicate the same concern for achieving full arousal of the male organ before penetration.
4I.e. the penis must still block the vaginal opening in order to seal the sexually generated essence inside.
5The "ten movements" refer to the technique of thrusting the penis without ejaculating. See _MS_ VI.B.2.
6The ten positions for intercourse are listed in _MS_ VI.B.3.
7The "ten refinements" refers to the ways to move the penis in the vagina. See _MS_ VI.B.4.
8 _MS_ VII.B.13 provides a parallel to this sentence in which the words _yihun_ 以 昏 (in the evening) appear in place of _yimo_ 已 伇". The parallel leads me to interpret _mo_ as elliptical for _rimo_ 日 没 (sunset; _yimo_ could mean "at sunset" rather than "after sunset"). Without the parallel, _mo_ might easily be understood as "finish", giving the translation "after finishing the conjoining of forms." For me the statement in _MS_ VI.B.7 that the man's essence flourishes in the evening while the woman's essence accumulates in the morning is decisive confirmation of evening as the recommended time for the man to practice sexual cultivation. In addition, _Yinshu_ , "Seasonal Regimen," recommends evening hours for intercourse (translated at the beginning of Section Four in the Prolegomena).
For _zongmen_ 宗 門 (progenitive gate), _MS_ VII.B.13 has _xuemen_ 血 門 (blood gate). In my judgment both terms refer to a place where the man stores vapor and essence; perhaps related to the _mingmen_ 命 門 (gate of life) in received literature, and to the womb in _MS_ VI.A.7. And I suspect that "filling the womb" in _MS_ VI.A.7 and "dispensing to the womb" in _MS_ VI.A.8 correspond to "sending the vapor to the progenitive gate" in _MS_ VI.B.I. Li and McMahon translate the sentence differently as the vapor "passing through the master gate ( _zongmen_ )" of the woman after intercourse is finished ( _sui_ 遂 in intransitive usage means "pass through" and in transitive usage means "send"); and further claim that both this sentence and the parallel in _MS_ VII.B.13 are descriptions of "sexual climax in the woman" (1992: 178). While the _zongmen_ was surely a part of female anatomy as well, the sentence occurs at the conclusion of a series of actions performed by the man for his own benefit. It is clearly the man who is the focus of attention; and it is his _zongmen_ that receives vapor.
9The "eight movements" refer to body movements made by the woman that indicate to the man what she wants him to do in order to satisfy her sexually. See _MS_ VI.B.5. Similarly, the "five sounds" and "ten intermissions" below concern the woman's state of arousal, something that the man must carefully monitor if he is to bring her to orgasm (and then store the sexually generated essence in his body). Their placement at the end of the passage is simply a matter of describing a technique in a text: those items concerning the man himself are listed first, including essence retention when "vapor is sent to the progenitive gate"; and those concerning the woman are appended at the end. During actual intercourse the man's observation of the woman's reactions would be part of process leading up to the moment of successful sexual cultivation.
10Signs of arousal coming from the woman's mouth. See _MS_ VI.B.6.
11The "ten pauses" refers to stages of transformation as the woman moves toward orgasm. See _MS_ VI.B.8.
1"Movement" refers to thrusting the penis inside the vagina. As detailed in _MS_ VI.B.2, ten thrusts constitute one movement and there are ten movements for a total of one hundred thrusts. There are text parallels in _MS_ VII.B.3 and _MS_ VI.A.3. The latter refers to "nine arrivals" rather than "ten movements"; and _MS_ VI.B.2 is the only passage to explicitly state that each movement consists of ten thrusts. None of the passages on penile "movements" specify whether the man should finally reach orgasm. I reject the argument in Li and McMahon (1992: 175) that the numbers ten and one hundred should be understood figuratively as signifying fullness and not as a literal count of the number of thrusts. To be sure, one hundred is an ideal number, but ideal numbers can be counted and often were in religious Daoist hygiene. There is no reason to assume that early macrobiotic hygiene was different. The longer intercourse continues without ejaculation, the greater the benefit for the man. _Ishinpô_ , 28.22a (sec. "Huanjing"), describes a sequence often movements without ejaculation (the number of thrusts in a movement is not specified) with benefits similar to those identified in the Mawangdui texts (cf. Wile 1992: 92).
1For "waterway" ( _shuidao_ 水 道), _MS_ VI.A.3 has "hundred vessels." _Huangdi neijing_ also uses _shuidao_ to refer to the course followed by fluids in the body (not necessarily just the vapor and blood in the vessels); see, for example, _Suwen_ 8, 3.1b. There is an obvious analogy between waterways through the earth and through the body.
2There are parallel lists of sexual positions in _MS_ VII.B.10 and _MS_ III.88. Li and McMahon discuss each position and its possible correlation with positions in later sexual literature (1992: 170).
3"Tiger roving" ( _huyou_ 虎 游) may be related to "tiger pace" ( _hubu_ 虎) 步 in _Ishinpô_ , 28.14b (sec. "Jiufa"). In the latter position the woman bends over on all fours, buttocks raised and head lowered; the man kneels and performs rear entry (cf. Wile 1992: 89).
4"Cicada clinging" ( _chanfu_ 蟬 附 附) appears as a sexual position in _Ishinpô_ , 28.15a (sec. "Jiufa"). The woman lies prone; the man lies on top of her and enters from the rear (cf. Wile 1992: 89).
5"Measuring worm" ( _chihuo_ 尺 蠖) is the name of an exercise in the _Yinshu_. The person extends his lower leg and curls his toes thirty times ( _YSSW_ : 82). As a sexual position, measuring worm must involve bending and stretching.
6I follow _MWD_ , vol. 4, "Transcription," n. 2, in reading 桷 as _jue_ 角. Perhaps the man and woman face one another in "river deer butting" ( _junjue_ 庸 角). There may be a connection with the sport known as _juedi_ 角 抵 (horn butting; see Lewis 1990: 157–60), but it should be noted that the water deer lacks antlers in both sexes (Tate 1947: 331).
7"Gibbon grabbing" ( _yuanju_ 據 援) may be related to "gibbon striking" ( _yuanbo_ 辕 搏) in _Ishinpô_ , 28.15a (sec. "Jiufa"). In the latter position the woman lies supine; the man raises her legs over his shoulders until her buttocks and back are raised off the ground, and performs front entry (cf. Wile 1992: 89).
8 "Rabbit bolting" ( _tuwu_ 兔 騖) may be related to "rabbit licking hair" ( _tu shunhao_ 兔 吮 豪) in _Ishinpô_ , 28.15b (sec. "Jiufa"). In the latter position the man lies supine; the woman straddles him facing his feet, and he enters from the rear (cf. Wile 1992: 89).
9"Fish gobbling" ( _yuzuo_ 魚 嘬) may be related to "fish touching scales" ( _yu jielin_ 魚 接 鱗) in _Ishinpô_ , 28.15b (sec. "Jiufa"). In the latter position, the man lies supine; the woman straddles him facing his head, and after he inserts his penis she alone makes a rocking movement (cf. Wile 1992: 89).
1There are parallels for the ways a man moves his penis in the vagina in _MS_ VII.B.12 and _MS_ VIII.88. A related passage in _Ishinpô_ , 28.18a–b (sec. "Jiuzhuang"), is more descriptive, often comparing the thrusting of the penis to the actions of various creatures with indications like "rapidly" and "slowly" incorporated into the description (cf. Wile 1992: 111).
2For parallels see _MS_ VII.B.14, 16; and _MS_ VIII.88. According to _MS_ VII.B.15, the man observes the woman's movements during intercourse in order to "know what gives her pleasure and gets through to her." There is a related passage in _Ishinpô_ , 28.13a–b (sec. "Shidong"; cf. Wile 1992:88).
3From "extend elbows" through "level upspring" the woman's movements communicate to the man how he should stimulate her vagina with his penis.
4 _MS_ VI.B.6 concerns the "five sounds"—signs emanating from the woman's mouth that are indicative of her state of arousal during intercourse. For parallels see _MS_ VII.B.15, 20; and _MS_ III.88. Judging from the descriptions of what each sound indicates in _MS_ VI.B.6 and _MS_ VII.B.20, the sequence of the five sounds reflects the progressive intensification of her passion. There is nothing comparable in received sexual literature. "Convulsive breathing" translates _chixi_ 瘛 息. I understand the breathing to be like the description of the ailment _chi_ "convulsions" in _MS_ I.E.27 ("the breath is quick and shrill"). The parallels in _MS_ VII.B.15 and 20 give the first sound as "throaty breathing."
1I follow _MWD_ , vol. 4, "Transcription," n. 2, in reading _ji/*kj ǝd_ 機 as a phonetic loan for _ai_ /*?ǝd 哀 (moan; the latter graph occurs in the _MS_ VII.B parallels).
2"Blowing" translates _he_ 映, literally denoting a kind of hot exhalation. The word is also used for chanting incantations in _MS_ I.E.56 and _MS_ I.E.59. "Rapturous craving" translates _yangan_ 鹽 甘. For _gan_ in the sense of craving see _MS_ III.24. _Yan_ occurs in _Liji_ , 25.14b, where it is glossed as _yan_ 艷 (rapturous) in the Zheng Xuan commentary.
3 _MWD_ , vol. 4, "Transcription," n. 2, indicates that **SS** 127–28 may belong to the end of the text, after _MS_ VI.B.8.
4前 in _MWD_ , vol. 4, "Transcription," should be transcribed as _jin_ 筋 (muscle). The top part of the graph looks like 斗 (the signifies 斗 and _kk_ are sometimes used interchangeably in the manuscripts); but the graph is otherwise similar to _jin_ in S104 and S105, and is clearly unlike other occurrences of 前. Because of the transcription error Li and McMahon incorrectly identify _qianmai_ 前 脈 as a term for genitals (translated "front artery"; 1992: 163).
5 _Zhongfu_ 中 府 occurs in a plural sense in _Suwen_ 27, 8.11b, referring to the internal organs in general. _MS_ VI.B.7 concerns the man's achievement in sexual cultivation. While it is possible that the sexually generated essence goes to the "inner cavities," I think the reference is to a "central cavity" inside both the male and female body where vapor and essence are stored (like the "progenitive gate" in _MS_ VI.B.1 and the "central bourne" in _MS_ VI.B.8).
6"Pause" translates _yi_ 已. The conclusion of _MS_ VI.B.8 describes female orgasm and successful sexual cultivation. At each of the "ten pauses" a transformation occurs, and the cyclical return to the condition of the first pause corresponds to female orgasm. I think the transformation involves the fused essence of the man and woman generated through intercourse. There are parallels in _MS_ VII.B.18–19. The parallel for the sixth pause in _MS_ VII.B. 18 explicitly refers to "the essence being like choice glutinous millet" (in _MS_ VI.B.8 the characteristic is "slippery"). Alternatively, Li and McMahon interpret the pauses as corresponding to sensations that accompany states of arousal rather than to the transformation of essence (1992: 177–78; this is also the interpretation in Ma Jixing 1992: 1000, n. 2). Wile misunderstands the meaning of _yi_ and mistranslates all three passages (1992:79, 82–83). The parallel in _MS_ VII.B.19 add a crucial piece of evidence concerning the ten pauses. Following a description of female orgasm similar to _MS_ VI.B.5, the text states "the count has already reached one hundred" One hundred is, course, the ideal number of penile thrusts in the "ten pauses" are correlated with the "ten movements"; and the man's completion of the movements coincides with female orgasm (the "great completion" that occurs when the cycle of pauses is complete). I would argue that the words _dong_ 動 (movement) and _yi_ 已 (pause) should be understood as relating sexual intercourse to the process of _dongjing_ 動 靜 (movement and stillness) in nature as described in the opening of _Yijing_ , "Xici zhuan," 7.1b: "When movement and stillness have constancy, hard and pliant will be determined." In intercourse it is the Yang man who favors movement and the Yin women who favors stillness; it is his hard penis that encounters her pliant vagina. _MS_ VII.B.20 elaborates on precisely these kinds of correlations, which are called "the calculation of Yin and Yang." The same passage states that in order to delight a women, intercourse "must be slow and prolonged... _as if pausing but not pausing_ (如 已 不 已)." Pausing is to female arousal what movement is to male arousal. The cycle of the "ten pauses" formalizes the value attached to female arousal in sexual cultivation technique.
1"Freshened" translates _zao_ 燥. I reject _MWD_ , vol. 4, "Transcription," which reads _zao_ 燥 (scorched, dry).
2遅 in _MWD_ , vol. 4, "Transcription," should be transcribed as 遲, pronounced _chi/*drid_. The parallel graph in _MS_ VII.B.18 is _di/*drjad_ 慸, which the "Transcription" reads as _zhi/*drjad_ 僀 (congealed; see _SW_ , 11A–2.27b). I suspect that _chi/*dried_ is a phonetic loan for _zhi/*drjad_ (see Luo and Zhou 1958:253, for examples of rhyming between _*-id_ and _*-ad_ in _Huainanzi)_ ; hence the translation "congealed."
3 in _MWD_ , vol. 4, "Transcription," should be transcribed as _qiu_ , which is attested as an orthographic variant of 絤 (Morohashi 1957–60, vol. 8: no. 27661). I read the graph as _jiu_ 牺, glossed in _SW_ , 12A.39a, as "cluster."
4I understand _zu_ 卒 (completion) to signify completing a cycle, like in the idiomatic phrase 卒 其 時 (leave for one whole day; see _MS_ I.E.200; and _MS_ III.40, 74).
5Similar physiological changes during female orgasm are noted in Kinsey 1953: 613–23; and Masters and Johnson 1966: 128–34.
6The sentence 成 死 爲 薄 is difficult to interpret. The parallel in _MS_ VII.B.19 is 成 死 有 薄. I am convinced that the sentence concludes the physiological description of the woman. I understand _si_ 死 to be equivalent to _shi_ 屍 (corpse). The usage is attested in _Hanshu_ , 70.7a, as well as in Shuihudi _Fengzhen Shi_ (SHD: 157–58). I suspect that "corpse-like" describes the relaxed state following orgasm rather than the muscle tension that accompanies it (Kinsey 1953:627; Masters and Johnson 1966: 276–77). A description of female arousal in _Sunü miaolun_ , 128–29, concludes with: "When her body is hot and soaked with sweat, her feet are relaxed, and her hands are languid—it is a sign that her feelings have culminated and her desires are satisfied" (cf. Wile 1992: 128). If I may be allowed the conjecture that "corpse-like" refers to this relaxed state, _pu_ 溥 seems to refer to the subsequent "spreading" of the sexually generated essence in the same way that the breath cultivation technique in _MS_ VI.A.1 describes the transformed vapor "spreading ( _pu_ ) to your flesh and skin, and reaching to those hair tips." In the MSVII.B.19 parallel the spreading is further decribed as "racing to the internal network hairs and settling in the waist and heart." The parallel leads me to reject translating the sentence as "spread our like a corpse," which might otherwise seem as plausible as the translation I offer. I also reject Ma Jixing's interpretation that _si_ refers to the penis gone limp (1992: 1002.n. 14). Ma understands the last several sentences to mean something like: "... the buttocks do not adhere to the bedrnat. (The man) should withdraw (his penis) and leave. When (the penis) dies there is injury." _Si_ has this meaning, as indicated in Ishinpô, 28.11b (sec. "Linyu"): "When the woman"s fuluids are overflowing, the man must retreat (i.e. withdraw his penis). He cannot come back dead ( _si_ ), but must return alive (i.e. with the penis still erect). Exiting dead does great injury to a man." This meaning does not fit the context of _MS_ VI.B.8 well, and Ma's interpretation is forced. The passage is an integrated description of female orgasm that concludes below with the successful completion of sexual cultivation. _MS_ VII.B.19 concludes similarly with the man achieving a count of one hundred thrusts of the penis.
1I understand the conclusion to be a description of the man successfully completing sexual cultivation when the woman reaches orgasm. I also assume that spirit illumination occurs when the essence and spirit are concentrated in a location like the "progenitive gate" ( _MS_ VI.B.1) or the "central cavity" ( _MS_ VI.B.7). Thus I translate 藏 verbally as _cang_ "deposit" rather than adopting the translation "essence and spirit the depot (s)." I suspect that _zhongji_ 中 極 (central bourne) denotes this storage location in the man's body. _Suwen_ 60, 16.2a, gives _zhongji_ as the name of an acupuncture point, and locates the origin of the _ren_ vessel (see _MS_ VI.B.1) beneath it. In religious Daoist hygiene _zhongji_ is one of the names for the navel region, which links it to the lower cinnabar field and the womb (see _MS_ VI.A.7). The earlist citation is in _Laozi zhongjing_ , par. 14 ( _Yunji qiqian_ , 18.10b). If _zhongij_ in _MS_ VI.B.8 refers to a location in the man's body, the phrase "vapor expands in the central bourne" probably means that his _zhongji_ opens to receive the inflow of sexually generated essence. Alternatively, _zhongji_ may belong to female physiology. _Zhongji_ is attested as the name of a point inside the vagina in _Ishinpô_ , 28.14b (sec. "Jiufa"); and it is not implausible for the term to have been applied to the vagina itself. Perhaps "vapor expanding in the central bourne" refers to the release of sexually generated essence from her _zhongji_ , which is then absorbed by the man. I favor the first interpretation, but in either case it is the man who receives the benefit of sexual cultivation. My interpretation is at odds with Li an McMahon, who understand this passage as a description of the woman achieving spirit illumination (1992: 178).
_MS_ VII.A
Zajin Fang
雜 禁 方
Recipes for Various Charms
_MS_ VII.A.1 (SS1–5)
When there is a dog that likes to bark in the courtyard and gate, daub mud on the well in a rectangular band five _chi_ long.1 When husband and wife dislike one another, daub mud on the doorway [1]2 in a rectangular band five _chi_ long. When you wish to seduce a noble person, daub mud on the left and right sides of the gate in a rectangular band five _chi_ long.3 When you have frequent foul dreams, daub mud beneath the bed in a rectangular band seven _chi_ long. When the husband's mother and his wife like to fight, daub mud on the doorway in a rectangular band five _chi_ long. When an infant likes to cry, daub mud on the window in a rectangular band five _chi_ long.
_MS_ VII.A.2 (S6)
When involved in a suit with another person, write the person's name and set it inside a shoe.4
_MS_ VII.A.3 (S8)
Take _quantou_ that faces east-west. Incinerate and smith. Give it to the husband and wife to drink, and they will be driven apart.1
_MS_ VII.A.4 (S7)
Incinerate and smith the tails of two female doves. Drink it yourself, and seduction will occur.2
_MS_ VII.A.5 (SS9–10)
Take four nails from the left claw of a male dove and four nails from the left hand of a young girl. Scorch in a saucepan, combine, and smith. Apply it to the person and the person will be obtained.3
_MS_ VII.A.6 (S11)
Put the person's left eyebrow in liquor and drink it.4 You invariably obtain the person.
1 _Tu_ alone means to "daub something with mud." _MS_ VII.A.1 indicates that daubing mud at specified locations in the house was an all-purpose magical act. I assume that the phrase 方 五 尺 refers to daubing a rectangular band of mud that is one _chi_ wide and five _chi_ long, rather than to daubing an area of five square _chi_. The medieval demonography _Baizetu_ 白 includes examples of the same type of magic. The following is representative: "Whenever a rat causes a prodigy it is called Yin murder. [2] blend with yellow earth and daub it inside the chamber on the ground near the bed in a rectangular band three _chi_ long. Make a six _cun_ high dog of yellow earth and set it on the (band of) earth. On an Earth day (in the cycle of the Five Agents), take the dog and throw it in a crossroad. The calamity will be eliminated" (Rao Zongyi 1969: pl. 6; Mastumoto 1956: 147, no.27). A second example is simpler: "When a person's clothing shines at night, daub the wall of the inner chamber with mud in a rectangular band three _chi_ long, and whatever you are searching for will be obtained" (Rao Zongyi 1969: p1. 7; Matumoto 1956: 147, no. 59)
2Based on the remaining traces of the graph, _MWD_ , vol. 4, "Transcription," n. 2, suggests that it might be _mei_ 楣 (lintel).
3These two applications of daubing mud are related to the examples of love magic below.
4The expectation is that by treading on your opponent's name in your shoe, you will magically emerge the winner in the suit. The same type of agonistic magic is attested in the Greek magical papyri (Betz 1986: 142–43). A similar charm used for seduction occurs in _Ishinpô_ , 26.19b (sec. "Xiang'ai"): "On a _wuzi_ 戊 子 day write the person's surname and name and set it beneath your foot. The persoji is invariably obtained."
1 _Quantou_ 犬 頭 (dog head) must be the name of an herbal drug. Choosing the part that grows east-west has the magical effect of sending husband and wife in opposite directions. _Ishinpô_ , 26.19b (sec. "Xiang'ai"), states that placing horsehair and dog fur in the husband's and wife's bed will make them dislike one another. I agree with Qiu Xigui that the sequence of the wooden slips as given in _MWD_ , vol. 4, "Transcription," is incorrect (1992: 527–29). We both agree that S8 should follow S6, and that the text following S6 is concerned with love magic (the "Transcription" misinterprets S7 as related to the suit in S6). I place S7 after S8. Both _MS_ VII.A.3 (S8) and _MS_ VII.A.4 (S7) involve drinking a potion. There is a clear contextual relation between surreptitiously giving a potion to the husband and wife in order to separate them in _MS_ VII.A.3 and drinking a potion yourself in order to magically seduce the object of desire in _MS_ VII.A.4. Qiu interprets the context differently and places S7 at the end of the text.
2In _MS_ VII.A.I, _MWD_ , vol. 4, "Transcription," n. 3, reads _wei_ /* _mj ǝd_ 微 as a phonetic loan for _mei_ /* _mj ǝd_ 媚 (seduce). The reading is the same in _MS_ VII.A.4 (the "Transcription" understands the graph differently here because of the error in the sequence of the wooden slips).
3There is a similar philter recipe in _Ishinpô_ , 26.19b (sec. "Xiang'ai"): "Take the nails from the left claw of a rooster and the nail from the middle finger of the right hand of a never married woman. Burn to ash and apply it to that person's clothing." The result, of course, is that the object of desire will be obtained.
4 _Mei_ 康 (eyebrow; usually written 眉) and _mei_ 媚 (seduction) are etymologically related (eyebrows are literally bewitching in early religious belief; see Shirakawa 1974: 443–57). Ingesting the left eyebrow of the object of desire gives you a magical hold on the person.
_MS_ VII.B
Tianxia Zhidao Tan
天 下 至 道 談
Discussion of the Culminant Way in Under-Heaven
_MS_ VII.B.I (SS12–14)
The Yellow Spirit asked the Left Spirit:1 "Why is it that the Yin is born together with the nine apertures and twelve joints, yet it alone dies first?"2
The Left Spirit replied:3 "It is not utilized in strenuous activity; when there is sorrow and joy it is not used; it does not assist when drinking and eating.4 It dwells in deepest Yin and does not see Yang.5 Suddenly it is violently employed6 without waiting for it to become vigorous. It cannot withstand the double hotness,7 and therefore is severely injured. Its name is avoided and its body concealed, yet it engages frequently in violent activity without ritual. Therefore it is born together with the body, yet it alone dies first."
_MS_ VII.B.2 (SS15–16)
When it is angered yet not large, flesh has not arrived; when large yet not firm, muscle has not arrived; when firm yet not hot, vapor has not arrived.1 If you engage in intercourse2 when flesh has not arrived, it collapses.3 If you engage in intercourse when vapor has not arrived, it retreats.4 When all three arrive this is called "triple coming."
_MS_ VII.B.3 (SS17–24)
Discussion of the Culminant Way in Under-heaven5
Like bubbles in the water's torrent, like the vapor of spring and autumn—what has passed by I do not see, and I do not obtain its benefits; I do not espy what is coming, yet I enjoy its fruits.6 O be careful indeed! The matter of spirit illumination lies in what is enclosed. Vigilently control the jade closure, and spirit illumination will arrive.7 As a rule, to cultivate the body the task lies in accumulating essence. When essence reaches fullness, it invariably is lost; when essence is deficient, it must be replenished. As for the time to replenish a loss, do it when essence is deficient. To do it, conjoin in a sitting position; tailbone, buttocks, nose, and mouth each participate at the proper time.1 Passing by fleetingly and coming momentarily, the culminant essence is about to be lost. How can I stay it? Emptiness and fullness have a constant; carefully employ it without negligence. Do not thwart, do not deplete; muscle and bone are bulging and strong.2 Move the jade wellspring and eat the fragrant aroma.3 Lightly exit and lightly enter; await fullness—this is the constant.4 When the three harmonious vapors arrive you become firm, vigorous, and strong.5 When you wish to cultivate it, you must avoid verbalization.6 Move the jade closure, and you can unite with the changes.7 At the first movement, ears and eyes are perceptive and bright;8 at the second movement, the voice's sound is brilliant; at the third movement, skin and hide glow; at the fourth movement, the spine is strong; at the fifth movement, buttock and ham are squared; at the sixth movement, the waterway passes through; at the seventh movement, you achieve culminant firmness and strength; at the eighth movement, the will soars boisterously; at the ninth movement, you conform to that heavenly blossom;9 at the tenth movement, spirit illumination is engendered.
_MS_ VII.B.4 (SS25–30)
Vapor has eight benefits and also has seven detriments.1 If you are unable to utilize the eight benefits and eliminate the seven detriments, at the age of forty, Yin vapor has halved itself;2 at fifty, mobility deteriorates; at sixty, ears and eyes are not perceptive and bright; at seventy, the lower body withers and the upper body shrinks, the Yin's vapor is useless, and effluvia and tears flow out.3 There is a way to restore its vigor. Eliminate the seven detriments, thereby shaking off its ailments. Utilize the eight benefits, thereby assisting its vapor. Therefore, the aged are restored to vigor, and the vigor does not deteriorate.4
The gentleman dwells in peace and happiness. Drinking and eating as he pleases, the skin's webbed pattern is lustrous and taut; vapor and blood are replete; and the body is light and lithe. But if he has intercourse impulsively,1 he is unable to effect the passage (of vapor) and becomes ill. Sweating and panting, the inside is feverish and the vapor disordered. When not treated, internal hotness is produced. He drinks medicine and undergoes cauterization to bring forth the vapor; and he practices dietetics2 to bolster his exterior. If he forces intercourse,3 he is unable to effect the passage (of vapor), producing pustules and swollen scrotum.4 Vapor and blood are replete while the nine apertures are not clear; the upper and lower body are useless, producing pustules and _ju_ abscesses.5 Thus, when you are skilled at utilizing the eight benefits and eliminating the seven detriments, the five ailments do not arise.
_MS_ VII.B.5 (S31)
The eight benefits:6 first is "cultivate vapor"; second is "bring the fluid";7 third is "know timing"; fourth is "gather vapor"; fifth is "harmonize the fluid"; sixth is "steal vapor"; seventh is "await fullness"; eighth is "secure against upset."8
_MS_ VII.B.6 (S32)
The seven detriments: first is "blockage"; second is "leakage"; third is "parching"; fourth is "incapacity"; fifth is "feverishness"; sixth is "curtailment"; seventh is "wastage."
_MS_ VII.B.7 (SS33–36)
Cultivation of the eight benefits. To rise at dawn, sit upright, straighten the spine, open the buttocks, suck in the anus, and press it down is "cultivating vapor."1 When drinking and eating, to relax the buttocks, straighten the spine, suck in the anus, and let the vapor pass through is "bringing the fluid."2 To first play until each is delighted and to have intercourse when both are desirous is "knowing timing."3 While having intercourse, to relax the spine, suck in the anus, and press it down is "gathering vapor." While having intercourse, to not hurry and not be hasty,4 and to exit and enter with harmonious control is "harmonizing the fluid." When getting out of bed, to have the other person make it erect and let it subside when angered is "accumulating vapor."5 When nearly finished, to not let the inner spine move,6 to suck in the vapor press it down, and to still the body while waiting for it is "awaiting fullness."1 To wash it after finishing and let go of it after becoming angered is "securing against upset."2 These are the eight benefits.
_MS_ VII.B.8 (SS37–39)
The seven detriments. To have acute pain during intercourse is "internal blockage."3 To sweat during intercourse is "external leakage."4 To have intercourse without pausing is "parching."5 To desire it but to be unable is "incapacity."6 To pant and suffer internal disorder during intercourse is "feverishness."7 To force it when desire is lacking is "curtailment."8 To become ill from intercourse is "wastage."9 These are the seven detriments. Thus, when you are skilled at utilizing the eight benefits and eliminating the seven detriments, ears and eyes are perceptive and bright; the body is light and lithe; Yin vapor grows increasingly strong; your years are extended and longevity increased; and you dwell in continuing happiness.
_MS_ VII.B.9 (SS40–41)
When a person is born there are two things that do not need to be learned: the first is to breathe and the second is to eat. Except for these two, there is nothing that is not the result of learning and habit. Thus, what assists life is eating; what injures life is lust. Therefore, the sage when conjoining male and female invariably possesses a model. Thus.1
_MS_ VII.B.I0 (SS42–43)
The first is "tiger roving";2 the second is "cicada clinging"—focus on the outside;3 the third is "measuring worm"; the fourth is "river deer butting";4 the fifth is "locust splayed"—breath on the inside; the sixth is "gibbon grabbing"5 —focus on the outside; the seventh is "toad"; the eighth is "rabbit bolting"; the ninth is "dragonfly"一 focus on the outside; the tenth is "fish gobbling." These are the ten positions.
_MS_ VIIB.11 (SS44–45)
The first is "bring vapor";1 the second is "secure the taste";2 the third is "control the joints";3 the fourth is "exercise the fruit";4 the fifth is "perfect timing"; the sixth is "transport material";5 the seventh is "move lightly"; the eighth is "await fullness";6 the ninth is "equalize life";7 the tenth is "rest the form."8 These are the ten refinements.
_MS_ VII.B.12 (S46)
The first is "go up";9 the second is "go down"; the third is "go to the left"; the fourth is "go to the right"; the fifth is "enter deeply"; the sixth is "enter shallowly"; the seventh is "thrust rapidly"; the eighth is "thrust slowly." These are the eight ways.
_MS_ VII.B.13 (SS47–48)
The ten refinements have already been completed, the ten positions displayed in advance, and the eight ways interspersed. Conjoin forms in the evening. Sweat should not begin to flow; and send the vapor to the blood gate.10 Suck in and swallow the blue-gem well-spring to penetrate the vessels and benefit the muscles.11 Then examine the eight movements, and observe where vapor lies. Then know the five sounds,1 both the later and the earlier.2
_MS_ VII.B.14 (S49)
The eight movements:3 the first is "clasping hands"; the second is "extending elbows"; the third is "level upspring"; the fourth is "straightening heels"; the fifth is "crossing thighs"; the sixth is "shaking"; the seventh is "hooking the flanks"; the eighth is "hooking up above."
_MS_ VII.B.I5 (SS50–51)
The five sounds:4 the first is "throaty breathing";5 the second is "panting"; the third is "continual moaning"; the fourth is "blowing"; the fifth is "biting." Examine the five sounds to know her heart; investigate the eight movements to know what delights and affects her.
_MS_ VII.B.16 (SS52–53)
When she clasps hands, she wants her abdomen pressed;6 when she extends elbows, she wants the upper part rubbed and scratched;7 when she hooks the flanks, she wants the sides rubbed; when she crosses thighs, penetration is excessive; when she straightens heels, entry is insufficiently deep; when she hooks up above, the lower part is not reaching the heart;1 when she makes a level upspring, she wants shallow entry; when she shakes, superbness is culminant. These are the eight observations.2
_MS_ VII.B.17 (SS54–55)
Vapor rises and her face is flushed—slowly exhale. The nipples harden and her nose sweats—slowly embrace. The tongue spreads and becomes slippery—slowly press. The fluid flows below and her thighs are damp—slowly rub. Her throat is dry, swallowing saliva—slowly rock. These are the "five signs"; these are the "five desires." When the signs are complete, ascend.3
_MS_ VII.B.18 (SS56–58)
When it is angered yet not large, skin has not arrived; when large yet not firm, muscle has not arrived; when firm yet not hot, vapor has not arrived. When the three arrive, enter.4 At the first pause, clear coolness emerges;5 at the second pause, the odor is like rotting bones; at the third pause, it is freshened; at the fourth pause, it is viscid; at the fifth pause, it is fragrant; at the sixth pause, the essence is like choice glutinous millet; at the seventh pause, it is congealed; at the eighth pause, it is tallowy; at the ninth pause, it is pasty;6 at the tenth pause, it matures.7 After maturing it becomes slippery again, and dawn vapor then emerges.8
_MS_ VII.B.I9 (SS59–61)
The first is "hairpin light";1 the second is "sealing cord";2 the third is "dry gourd";3 the fourth is "rat wife"; the fifth is "grain fruit"; the sixth is "wheat teeth";4 the seventh is "infant girl";5 the eighth is "depart to return";6 the ninth is "why remain";7 the tenth is "red thread";8 the eleventh is "red bead";9 the twelfth is " _zao_ stone."10 Obtain it and do not release it.11 When she becomes corpse-like, there is spreading that races to the internal network hairs and settles in the waist and heart.12 The lips are completely white; sweat flows down to the hollow at the back of the knees;1 and the count has already reached one hundred.2
_MS_ VII.B.20 (SS62–67)
What all men enjoy without exception is women. Possessing a woman, the skilled man alone is capable.3 Do not give, but do not control;4 do not initiate, but do not hesitate.5 It must be slow and prolonged, and must be light and sustained—as if pausing but not pausing. The woman then is greatly delighted.
When there is throaty breathing, the lower body is stimulated, spitting Yin and radiating Yang.6 When there is panting, the vapors ascend to touch one another, expanding out from the palace.7 When there is continual moaning, she quickens her buttocks and he has moved the sealing cord.8 When there is blowing, rapturous craving is intense and excitation then commences. When there is biting, her body shakes1 and he times pausing to continue for a long time.
Therefore, what is masculine belongs to the category male and is Yang; and what is Yang is external. What is feminine belongs to the category female and is Yin; and what is Yin is internal. Everything belonging to the category male is rubbed outside; everything belonging to the category female is rubbed inside. This is called the calculation of Yin and Yang, and the intrinsic pattern of female and male.2 If when having intercourse he is unsuccessful, the blame can be placed entirely on haste.3 The essential task in the pleasures of play is to be slow and prolonged. If only he can be slow and prolonged, the woman then is greatly pleased. She treats him with the closeness she feels for her brothers, and loves him like her father and mother. Whoever is capable of this way is designated "heaven's gentleman."4
1The Yellow spirit 黄 神 is the yellow Thearch (see _MS_ I.E.178). Ma Jixing cites an argument identifying Left spirit 左 神 as a name for Goumang 句芒, the spirit who presides over the east (associated with left and Wood; 1992: 1012, n.1). I doubt the identification is correct. In the absence of positive evidence, I simply treat Left Spirit as another of the Yellow Thearch's teachers in the Mawangdui medical manuscripts. The Left Spirit named in _Huangting neijing jing_ , par.17 ( _Yunji qiqian_ , II.42a), cannot be related.
2The Yin is the penis. Yao asks the same question of Shun in _MS_ VI.A.5.
3Much of the content of the Left Spirit's reply also occurs in _MS_ VI.A.5.
4See _MS_ VI.A.5–6 on the necessity of "feeding" the penis. I am uncertain why the penis is not involved in situations of sorrow and joy, unless formal, ritual occasions of sorrow and joy are intended(funerals, births, etc.).
5I.e. the penis is kept hidden and not ecposed to view.
6 _Yong_ 用 (employ) refers specifically to engaging in intercourse as in _MS_ VII.B.2.
7I.e. the hotness emanating from the man and the woman.
1The "it" is the penis. _MS_ VII.B.2 describes three stages necessary for the penis to become fully aroused and ready for intercourse. There is a parallel in _MS_ III.88 (MSVII.B.18 also includes a brief parallel). _Ishinpô_ , 28.13b (sec. "Sizhi"), discusss four stages of arousing the penis in similar terms, and the stage when the penis is "hot" marks the arrival of "spirit vapor" (cf. Wile 1992: 88).
2For the use of _yong_ 用 to mean "engage in intercourse," see _MS_ III.23.
3遺 in _MWD_ , vol. 4, "Transcription," should be transcribed as 遀, equivalent to _duo_ 隋 (collapse) in _MS_ III.88 (where it describes the consequence of attempting intercourse when vapor has not arrived).
4The text omits reference to the consequence of engaging in intercourse when muscle has not arrived.
5This heading is written at the top of S17; the text begins in S18. A dot mark • appears above the graphs of the heading in S17. Each new entry in _MS_ VII.B is marked with a dot in this fashion. It is probable, therefore, that the heading in S17 serves as a title for _MS_ VII.B.3. _MWD_ , vol. 4, "Transcription," n. 1, argues that the dot at the top of S17 represents scribal error; and that the heading should be understood as the general title for the remainder of _MS_ VII.B.
6The thought is reminiscent of _Zhuangzi_ 20, 297, which concerns the spontaneity of a bell-maker: "Clustering! Billowing! Such is his sending off what passes by and his greeting what is coming. What is coming, do not bar; what passes by, do not stay." The point is that a person must plunge unreservedly into the activity at hand without dwelling on opportunities already lost and ever aware of the shape of things to come. In _MS_ VII.B.3 the activity is sexual cultivation; and the remainder of the passage concerns what to do so that when "the culminant essence is about to be lost" the techniques of sexual cultivation can be used to "stay it."
7On the jade closure, see _MS_ VI.A.3.
1I.e. engage in sexual intercourse. The statements concerning accumulating essence and replenishing loss through sexual cultivation are paralleled in _MS_ VI.A.4.
2凌 in _MWD_ , vol. 4 __, "Transcription," should be transcribed as 洚. Qiu xigui reads the graph as _long_ 隆, citing the compound _longqiang_ 隆 彊 (bulging and strong; 1992: 535). _Longqiang_ is attested in _shiming_ , 7.232, as a name for the braces of a carriage canopy.
3On the jade wellspring, see _MS_ VI.A.3.
4Exiting and entering refers to penile action.
5I am uncertain of the referents for the "there harmonious vapors."
6The meaning of the phrase _hai qi yan_ 害 其 言 is uncertain. My "avoid verbalization" assumes that the instruction is related to the idea of being spontaneous expressed above. _MWD_ , vol 4, "Transcription," n. 4. Suspects that 害 is scribal error for _shen_ 審 (examine), which would give the translation "examine the words (of the sexual cultivation technique?)."
7"Unite with the changes" translates _yiqian_ 一 遷. Sima Tan's assessment of the daoists in Shiji, 130.4a, praises their ability to "change and shift ( _qianyi_ 遷 移) with the times." _Yijing_ , "Xici zhuan," 8.11a, also refers to "repeated changing" ( _lüqian_ 麜 遷) as a characteristic of the hexagrams. Management of the jade closure is evidently the key to success in sexual cultivation; and the "ten movements" described below (matched by the "ten pauses" in _MS_ VII.B.18) represent a specific technique that enable a person to "unite with the changes." _MWD_ , vol.4, "Transcription" reads 遷 as _xian_ 僊 (transcendent), which I reject. Nothing in _MS_ VII.B.3 suggests a connection with the concept of _xian_ or with any practices associated with the _xian_ cult.
8On the ten movements, see _MS_ VI.B.2.
9I do not know the referent of "heavenly blossom" ( _tianying_ 天 英).
1The "eight benefits" ( _bayi_ 八 益)and "seven detriments" ( _qisun_ 七 損) all concern the man. They are listed in _MS_ VII.B.5–6, and are further described in _MS_ VII.B.7–8. While the emphasis is on sexual intercourse, the first two benefits described in _MS_ VII.B.7 concern cultivation practices similar to the cultivation of "penile essence" in _MS_ VI.A.6 and the five-stage technique described in _MS_ VI.A.7. The detriments described in _MS_ VII.B.8 concern conditions that must be avoided lest intercourse be injurious to health. _Ishinpô_ , 28.19a–21b (sees. "Bayi" and "Qisun"), also describes a system of "eight benefits".and "seven detriments" related to intercourse. Each benefit or detriment involves practicing a specific sexual technique to either achieve the benefit or eliminate the detriment (cf. Wile 1992: 89–91). The eight benefits in _MS_ VII.B and in the _Ishinpô_ are dissimilar. The names and characteristics of the seven detriments in the two sources bear comparison, but _MS_ VII.B does not mention sexual techniques to alleviate the detriments. _Suwen_ 5, 2.7a–b, discusses the "seven detriments and eight benefits" without listing their names or describing their nature. Given the general absence of references to sexual cultivation in the _Huangdi neijing_ , I suspect that these detriments and benefits concern some other aspect of hygiene. The _Suwen_ passage is notable for its parallel account of the decade by decade aging process described immediately below in _MS_ VII.B.4. To sum up, _MS_ VII.B provides the earliest documentation of the idea of "eight benefits" and "seven detriments" as part of sexual cultivation theory, which continues in a different form in later sexual literature. The _Suwen_ parallel suggests that a more general notion of cultivating "eight benefits" and eliminating "seven detriments" was also current in Han medicine.
2Yin vapor is the essential complement to Yang vapor. The connection between loss of Yin vapor and aging is mentioned in _MS_ VI.A.4.
3The description of the body at seventy is similar to the description of the body at sixty in _Suwen_ 5, 2.7b. In the _Suwen_ it is the Yin (i.e. penis) that becomes impotent, hence 陰 氣 in _MS_ VII.B.4 must refer to the penis and its vapor and not to Yin vapor in general. _Guan_ 深 (usually written 棵) refers to the ritual of pouring liquor on the ground after it has been offered to the impersonator of the dead in ancestral worship ( _SW_ , 1A.11b, and Duan Yucai commentary). The word as used in _MS_ VII.B.4 probably refers to the spent vapor or fluid given off by the aging body, hence my impressionistic translation "effluvia." The parallel word in the _Suwen_ is _ti_ 涕 (snot).
4According to _MWD_ , vol. 4, "Transcription," n. 3, the context requires adding 者 to the text following 狀 and the emendation is made in the transcription, which would give the translation "the vigorous do not deteriorate." From the standpoint of grammar and meaning there is no reason to assume that the phrase necessarily contrasts "the vigorous" with "the aged" above, and I reject the emendation.
1I understand _shinei_ 使 内 to be similar to _jinnei_ 近 内, which refers to sexual intercourse in _MS_ III.34.
2I read 司 as _si_ 飼 (also written 飤), meaning "feed" ( _SW_ , 5B.10a, and Duan Yucai commentary). The compound 服 飼 refers to dietetics.
3"Forcing intercourse" refers to having intercourse when the condition of the penis is unfit, as when impulsive intercourse results in illness.
4槖 in _MWD_ , vol. 4, "Transcription," should be transcribed as _gao_ 槖, attested as a word for a "large sack" in _SW_ , 6B.9b. Qiu Xigui argues that _gao_ is equivalent to _gao_ 睾, still in use in the compound _gaowan_ 睾 丸 (testicles; 1992: 536). The same graph is used for the scrotum in _Maishu_ , "Ailment List" ( _MSSW_ : 72). On the ailment "swollen scrotum," see _MS_ I.E.117.
5For _ju_ 疽 as a type of abscess, see _MS_ I.E.157.
6The names of some of the benefits are similar to the "ten refinements" in _MS_ VII.B.11, however the latter are all concerned with sexual intercourse.
7"Fluid" translates _mo_ 沫, which is primarily the word for water bubbles (see _MS_ VII.B.3). Association with saliva is indicated in _Zhuangzi_ 6, 109; and 18, 277. The descriptions of the second and fifth benefits in _MS_ VII.B.7 associate _mo_ with fluids generated in the lower body rather than the mouth.
8 _Guoyu_ , 21, 1a, gives "securing against upset" ( _dingqing_ 定 傾) as one of a state's three central concerns.
1"Cultivating vapor" appears to be a kind of morning exercise routine whereby vapor is generated and sent to an internal storage area using anal constriction. The description is reminiscent of _MS_ VI.A.7, which describes "contracting the anus" (equivalent to "sucking in the anus") and "sucking in the vapor to fill the womb." _Yi_ 抑 refers literally to "pressing (something) with the hand"; and _yi_ is the verb used for pressing behind the scrotum with the middle fingers to block the urethra in the description of "returning the essence to replenish the brain" in _Ishinpô_ 28.22b (sec. "Huanjing bunao"). Although "returning the essence" in later sexual cultivation made use of both anal constriction and pressure applied to the urethra (Wile 1992: 59), I think the three occurrences of the phrase 抑 下 之 (press it down) in _MS_ VII.B.7 are best understood as referring to pressure applied by means of anal constriction to force vapor to flow toward its destination inside the body. The "it" in each case is, then, vapor. In short, the practice of applying pressure to the urethra at the moment of male orgasm is not mentioned in the Mawangdui medical manuscripts (and in any case, the first benefit is not directly concerned with sexual intercourse).
2"Bringing the fluid" appears to represent a technique for "drinking and eating together with the penis" as recommended in _MS_ VI.A.6.
3For the use of 爲 之 to mean "have intercourse," see _MS_ III.39.
4"Hasty" translates _shu_ 數, glossed in _Erya_ , 2.2b, as "rapid."
5The "it" is clearly the penis. I am uncertain whether the phrase "get out of bed" (出 ) refers to getting up in the morning or to rising from bed after intercourse. In either case, the female partner is supposed to stimulate the penis until erect in order to invigorate the man's vapor. In _MS_ VII.B.5 this benefit is called "stealing vapor," implying that the man's gain is the woman's loss.
6"Inner spine" translates _neiji_ 内 脊. I think the phrase refers to the cessation of movement on the side of the spine where the man's genitals lie as the climax of intercourse approaches, presumably in order to delay or prevent ejaculation. It is also possible that _nei_ should be understood as a verb with spine as the direct object, but I am not satisfied by the possible verbal renderings of _nei_ in this context.
1"Fullness" ( _Ying_ 贏) is, of course, the goal of sexual cultivation. The seventh benefit concerns the critical stage of intercourse when the women reaches orgasm and the man absorbs the sexually generated essence. This is the point at which the man "sends the vapor to the blood gate" in _MS_ VII.B.13. The descriptions of the "ten pauses" and female orgasm in _MS_ VII.B.18–19 are also related.
2Washing the penis is done to bring about detumescence. _MS_ III.5 describes washing the penis after ejaculation when an aphrodisiac has been used to induce an erection; and _MS_ IV.3 similarly describes washing the penis to cause detumescence. The eighth benefit appears to equate this post-coital washing (which returns the penis to its ordinary condition) with the principle of preventing ejaculation during intercourse by allowing the erect penis to subside each time it is "angered"—thereby "securing against upset." Li and McMahon mistranslate the eighth benefit as "finally to ejaculate" ( _qing_ 傾 does not denote ejaculation as claimed); and misinterpret the seventh and eighth benefits as referring to the man's sexual climax and ejaculation respectively (1992: 173). The text itself does not mention whether ejaculation occurs.
3The first detriment in _MS_ VII.B is related to the sixth in the _Ishinpô_ —"hundred blockages."
4Related to the fourth detriment in the _Ishinpô_ —"leakage of vapor."
5"Parching" ( _jie_ 偈; my reading for text 楬) refers to the desiccation of vapor that occurs when intercourse is practiced immoderately. The phenomenon of parching is mentioned in _MS_ VI.B.1, which warns the man to not let vapor leak out after the penis enters the vagina, "lest the woman become greatly parched ( _jie_ )"; and is alluded to in _MS_ VII.B.1, which warns of the damage done when the penis is unprepared for intercourse and "cannot withstand the double hotness" generated by the man and woman. The seventh detriment in the _Ishinpô_ is "blood parching."
6I.e. impotence. This is probably related to the third detriment in the _Ishinpô_ —"vessel disarmament" (which also concerns impotence).
7Probably related to the second detriment in the _Ishinpô_ —"overflowing essence."
8The first detriment in the _Ishinpô_ is "curtailment of vapor," referring to "forcing intercourse when the heart and thoughts are not desirous." Compare _MS_ VII.B.4, which describes the consequences of "forcing intercourse" when the penis is unfit.
9Related to the fifth detriment in the _Ishinpô_ —"reversal and injury of the vital joints" (which concerns illness arising from intercourse).
1The eight graphs written on S41, concluding with _gu_ 故 (thus), occupy only the top one fourth of the bamboo slip. _MWD_ , vol. 4, "Transcription," places a colon after _gu_ , evidently regarding the word as introducing the lists of sexual procedures that follow in subsequent sections of _MS_ VII.B. I suspect that having written 故, the scribe omitted the text for what should have been a conclusion for _MS_ VII.B.9.
2See _MS_ VI.B.3 for the sexual positions listed in _MS_ VII.B.10.
3I am uncertain of the meaning of the added instruction to "focus on the outside" ( _siwai_ 思 外), which occurs again following "gibbon grabbing" and "dragonfly." The related instruction "breath on the inside" ( _xinei_ 息 内)follows "locust splayed." Wei and Hu conjecture that _siwai_ refers to the man positioning himself behind the woman (the interpretation involves reading 思 as _si_ 司) and _xinei_ to the man and woman positioned face to face (1992, vol. 2: 153, n. 6). Li and McMahon conjecture differently, associating _siwai_ with meditation during intercourse and _xinei_ with breathing methods (1992: 171). The content of _MS_ VII.B.10 does not provide enough evidence to reach a definite conclusion. I am partial to the idea that _siwai_ is related to the man's mental state, but it might simply mean that he should pay attention to external matters; and in contrast, _xinei_ might mean that he should pay attention to internal matters. Whether or not the interpretation in Wei and Hu is correct, the idea that the two terms specify how the man and woman are positioned also has merit. It would be logical for a list of sexual positions to include details of this sort, whereas references to the man's mental state when using certain positions for intercourse áre less easily explained.
4I _read ju/*kjug_ 暴 as a phonetic loan for _jue/* kruk_ 角 (butt; see _MS_ VI.B.3).
51 read 居 as _ju_ 据 (grab).
1The "ten refinements" listed in _MS_ VII.B.11 concern the actions that the man must accomplish during intercourse. _MS_ VII.B provides only the names of these actions without detailing their exact nature. The names reflect a system similar to but not identical with the eight benefits. Perhaps the action of "bringing vapor" is related to _MS_ VI.B.1, where the penis jabs at the entrance to the vagina without penetrating in order to "bring the vapor." However, it just as likely refers to breath cultivation, one form of which is kissing.
2Perhaps a reference to swallowing saliva or strong sexually generated fluids internally. The fourth stage in the five-stage cultivation technique described in _MS_ VI.A.7 is "contain the five tastes and drink that wellspring blossom."
3Perhaps a reference to skill in moving the body during intercourse.
4The "fruit" ( _shi_ 簣) probably refers to a point inside the vagina, as it does in _Ishinpô_ , 28.15b (sec."Jiufa").
5I read 才 as _cai_ 材 (material). Since the seventh refinement is to have the penis "move lightly," the material that is transported may be the penis being brought into the vagina.
6Compare the seventh benefit in _MS_ VII.B.7.
7Perhaps a reference to the successful accomplishment of sexual cultivation.
8Perhaps similar to the eighth benefit in _MS_ VII.B.7, which concerns refraining from ejaculation and post-coital conduct.
9See _MS_ VI.B.4 for a list of ten ways to move the penis ("thrust rarely" and "thrust frequently" are not included in _MS_ VII.B.12).
10Compare the parallel passage in _MS_ VI.B.1.
11I read 榣 as _ _(blue-gem); and _qian/* dzian_ 前 as a phonetic loan for _quan/* dzjuan_ 泉 (wellspring). The loan usage is comparable to the standard Qin and Han use of _qian/* dzjan_ for _quan/* dzjuan_ in the sense of "currency" ( _SW_ , 14A.10b, and Duan Yucai commentary). The "blue-gem wellspring" occurs as a metaphor for saliva in the description of breath cultivation in _MS_ VI.A.4 ("Drink the blue-gem wellspring and numinous winepot and make it circulate"). In my interpretation, swallowing saliva coincides with sending vapor to the blood gate; and both actions have the effect of invigorating the man's body. The combining of sexual intercourse with breath cultivation in _MS_ VI.A.10 is comparable. Alternatively, _qian_ may refer to the female genitals (see _MS_ IV.8), making "blue-gem front" an elegant term for the vagina. However, there is no other attestation of this usage in the Mawangdui medical manuscripts; and I cannot explain what it would mean in sexual cultivation technique to have the man "suck in and swallow the blue-gem front." It makes better sense for him to be swallowing the same "blue-gem wellspring" attested in _MS_ VI.A.4. _MWD_ , vol. 4,"Transcription," reads 榣 as _yao_ 搖 (shake, wave), which I reject (the "Transcription" reads the same graph as _yao_ 瑶 in _MS_ VI.A.4). And I do not accept the interpretation of Li and McMahon, which errs in treating _MS_ VII.B.13 as a description of sexual climax for the woman rather than for the man; and understands 搖 前 as the woman who "sways her vagina" (1992: 178).
1音 in _MWD_ , vol. 4, "Transcription," should be transcribed as 言; however, the latter graph is a scribal error for the former (the same scribal error occurs in _MS_ VII.B.15).
2Compare _MS_ VI.A.10, which includes the sentence, "The five sounds arise in response, both the short and the long."
3These are movements made by the woman during intercourse that indicate what she wants the man to do. See _MS_ VI.B.5.
4I.e. signs that emanate from the woman's mouth. See _MS_ VI.B.6.
5The parallel in _MS_ VI.B.6 is "convulsive breathing."
6This continues the discussion of the eight movements from _MS_ VII.B.14 (see _MS_ VI.B.5).
7From "extend elbows" through "level upspring" the woman's movements communicate to the man how he should stimulate her vagina with his penis.
1The parallel in _MS_ VI.B.5 is "she wants the lower part rubbed," referring to the lower part of the vagina. "The lower part is not reaching the heart" must mean that she wants that part to be stimulated by the penis.
2Another name for the "eight movements" based on the fact that it is the man who must "observe" the movements and react appropriately.
3The "five signs" constitute stages to be followed in foreplay (see the parallel in _MS_ VI.B.1).
4The "it" is the penis (see the parallels in _MS_ VII.B.2 and _MS_ III.88).
5The remainder of _MS_ II.B.18 concerns the "ten pauses" that lead up to female orgasm. _MS_ VII.B.19 concludes with a description of female orgasm. The pauses and description of female orgasm are combined in the parallel in _MS_ VI.B.8.
6"Pasty" translates _li_ 黎, glossed in _SW_ , 7A.57b, as the paste used to glue shoes. The parallel graph in _MS_ VI.B.8 is _jiao_ 膠 (gelatinous).
7I read 愾 as _kai_ 愾 in the sense of "full, mature" ( _Guangya_ , 1A.10a). The parallel graph in _MS_ VI.B.8 is _jiu_ (cluster).
8The reference to the emergence of dawn vapor must be related to the statement in _MS_ VI.B.7 that "in the morning the woman's essence accumulates." After the tenth pause in _MS_ VI.B.8 there is a return to the condition of the first pause, "clear coolness."
1 _MS_ VII.B.19 lists twelve names for parts of the female genitals, both external and internal. Some of the names also occur in _MS_ III.91; and some may be related to names in _MS_ III.88. The names in _MS_ VII.B.19 do not follow an identifiable sequence from the exterior to the interior of the vagina. See _MS_ III.91 for discussion of the problems involved in associating the names with later sexual literature. _Jiguang_ 笄 光 (hairpin light) occurs in _MS_ III.91 as the name of a point inside the vagina. I am unsure of its location. _MWD_ , vol. 4, "Transcription," n. 1, notes that the scribe of _MS_ VII.B writes _mai_ 辰 in a style that is indistinguishable from _guang_ 光. It is possible that the graph in _MS_ VII.B. 19 should be identified as 辰 and read as _mai_ 脈 (vessel; see the occurrence of 辰 for 脈 in _MS_ VII.B.13). The graph transcribed as 光 in _MS_ III.91 is fragmentary, and the scribe of _MS_ III may have followed the same calligraphic convention as the scribe of _MS_ VII.B.
2 _Fengji_ 封 紀. The name occurs again in _MS_ VII.B.20, but the latter occurrence does not help to identify the part of the vagina denoted by the name. I assume that _feng_ refers to the "sealing" of documents and letters, however I do not know of the use of a sealing cord.
3 in _MWD_ , vol. 4, "Transcription," should be transcribed as _jian_ 澗. _Jianhu_ 澗 may be related to _kuhu_ (dry gourd) in _MS_ III.88, which leads me to suspect that _jian/*krian_ may be a phonetic loan for _gan/*kan_ (dry).
4See _MS_ III.91 for the names "grain fruit" and "wheat teeth" and their identification in later sexual literature.
5 _Yingnu_ 嬰 女. The name is attested in later sexual literature as a point inside the vagina between "wheat teeth" and "grain fruit" (see the table in Li and McMahon 1992: 164).
6A literal rendering of _fanqu_ 反 去. Perhaps it identifies a point inside the vagina beyond which the penis should not penetrate.
7A literal rendering of _heyu_ 何 寓, perhaps so named because the penis should not be there.
8I read 繖 as _lü_ 縷 (thread). "Red thread" may refer to a part of the external genitals (the name for the clitoris follows).
9I.e. the clitoris (see _MS_ III.91).
10 _Zaoshi_ 燥 石. Perhaps related to _yunshi_ 云 石 in _MS_ III.88. The name _kunshi_ 昆 石 occurs in later sexual literature for a point deep inside the vagina (Li and McMahon 1992: 164).
11I understand this line to mean that the man's penis should continually stimulate the inside of the vagina to bring about female orgasm. Compare the passage concerning the "coital muscle" in _MS_ VI.B.1.
12See the parallel description of female orgasm in _MS_ VI.B.8. For _li_ 理 in the sense of the "internal network" of vessels in the body, see _MS_ VI.A.9. _Mao_ 毛 (hair) is probably related to the idea of _maomai_ 毛 脈 (hair vessels) in _MS_ VI.A.1. I understand the sentence to mean that the woman's vapor and essence circulate to the outer limits of her body (compare the breath cultivation technique in _MS_ VI.A.1) and then return to concentrate in the midsection of her body.
1 _Guo_ 膕 is the standard anatomical term for the popliteal space behind the knee (see _Suwen_ 60, 16.4a, and Wang Bing commentary).
2I.e. when the woman reaches orgasm the man simultaneously completes the count of the "ten movements" (see _MS_ VI.B.8).
3 _MWD_ , vol.4, "Transcription," n.1, suspects that there are errors and perhaps omitted text in the above sentences, but I think the text is intelligible as written. There is a play on the word _shan_ 善, which in its first occurrence refers to what all men "enjoy" and in its second occurrence refers to the man who is "skilled" at sexual cultivation.
4Even though the man's goal is to retain the sexually generated essence for his own benefit, he should not be domineering.
5Undoubtedly an exhortation to the man to proceed with intercourse based on his observations of the woman's responses.
6The "five sounds" are reprised in order to underscore the need for the man to observe the woman. I follow _MWD_ , vol. 4, "Transcription," in reading 士 as _tu_ 吐 (spit). I understand _guang_ 光 to have a parallel meaning, hence my translation "radiating." The description of what the first sound indicates about the woman's state of arousal is different in the parallel in _MS_ VI.B.6, which states that "the inside is tense" (the sound is also different, "convulsive breathing"). Subsequent descriptions in _MS_ VII.B.20 tend to give more physiological detail than _MS_ VI.B.6.
7I.e. Yin and Yang vapors begin to fuse. I read 窝 as _gong_ 宮 ( __palace), which _MWD_ , vol. 4, "Transcription," n. 3, gives as an alternative reading to its preferred reading _rong_ 容 (perhaps "contain" or "absorb"). I suspect that _gong_ refers to the vagina. The best evidence I can adduce fir this meaning is the term _rugong_ 入 宮 (enter the palace), which denotes sexual intercourse in _Yinshu_ , "seasonal regimen" ( _YSSW_ : 82; Prolegomena, Section Four). I am unable to find early attestation of the term _Zigong_ 子 宮 for the womb.
8In the phrase 尻 彼 疾, I understand _kao_ 尻 (buttocks) as the object of _ji_ 疾 (quicken), and _bi_ 彼 as an emphatic demonstrative marking the exposed placement of _kao_ at the head of the phrase. The grammar pattern is noted in Yang Shuda 1986: 5. For "sealing cord" as a name for a part of the vagina see _MS_ VII.B.19.
1While the term _zhenhan_ 振 寒 (shaking with cold) might refer to shivering from sexual arousal, I follow _MWD_ , vol. 4, "Transcription," n. 5, in reading 寒 as a scribal error for _dong_ 動. The parallel graph in _MS_ VI.B.6 is 動.
2See _MS_ III.42 for an example of _pin_ 牝 (female) denoting the female genitals.
3There is a play on the word _shu_ 數, which in the previous sentence is the "calculation" of Yin and Yang and here is "haste" (the latter meaning is also attested in _MS_ VII.B.7).
4 _Tianshi_ 天 士 (heaven's gentleman) is attested in _Shiji_ , 28.25b, as part of the honorary title inscribed on a seal granted to the recipe gentleman Luan Da 變 大 by Thearch Wu:"At his waist he wore the seals of the General who is Heaven's Gentleman, the General who is Earth's Gentleman, and the General of Great Penetration." _Tianshi_ is also used as a title for an astrological specialist in _Hanshu_ , 75.24a.
Appendix 1
Transcription of _MS_ I.B, _MS_ I.C, _MS_ I.D
The transcription of _MS_ I.B, _MS_ I.C, and _MS_ I.D given below is based on the reproduction and transcription of the three texts in _MWD_ , vol. 4, and on the revised transcription of _MS_ I.C appended to _MSSW_. In place of the emendations of lacunae in the _MWD_ , vol. 4, transcription, which does not take account of the Zhangjiashan _Maishu_ editions of the three texts ("Eleven Vessels," "Vessels and Vapor," and "Five Signs of Death" respectively), my transcription fills lacunae using _MSSW_ whenever possible. _MSSW_ transcribes _Maishu_ in simplified graphs, which I write with modern _kaishu_ 措 書 graphs. A reproduction of _Maishu_ has not yet been published, and I have seen neither the original manuscript nor photographs (several of the bamboo slips are reproduced in Zhangjiashan Han mu zhujian zhengli xiaozu 1985). There are errors in the identification of the original slips in _MSSW_ , which does not compromise its general reliability. More serious are several mistranscribed graphs in _MSSW_. Li Xueqin, who participated in the preparation of the _MSSW_ transcription, kindly reviewed his own handwritten transcription of _Maishu_ and checked photographs of the original manuscript kept at the Bureau of Cultural Relics in Beijing in order to confirm the correct identification of slips and of graphs (the errors occurred at the stage of typesetting, and the editorial committee was not able to correct them before publication). I have confidence in the accuracy of _MSSW_ as corrected by Professor Li, but a reproduction of _Maishu_ needs to be published before this confidence can be completely justified.
Lacunae due to damaged silk and illegible graphs are extensive: two columns of text are missing at the beginning of _MS_ I.B, and significant gaps occur throughout; much of _MS_ I.C was unreadable before the _Maishu_ edition came to light; _MS_ I.D, the shortest text, suffered the least. The _MWD_ , vol. 4, transcription emends _MS_ I.B using the _MS_ II.B edition and parallels in _Lingshu_ 10 ( _MS_ II.B is moderately damaged); little could be done for lacunae in _MS_ I _.C_ and _MS_ I.D. Comparison of _MS_ I.B and _MS_ II.B with _Maishu_ , "Eleven Vessels," reveals a closer correspondence between _MS_ I.B and "Eleven Vessels." Both editions arrange the vessels in the same order, whereas _MS_ II.B differs by placing the foot Minor Yin vessel ahead of the foot Ceasing Yin vessel. Occasional differences in wording also separate _MS_ I.B and "Eleven Vessels" from _MS_ II.B. Comparing _MS_ I.B to "Eleven Vessels," the latter shows signs of being a younger edition. Most obvious is the addition of ailments at the end of certain vessel entries in "Eleven Vessels" using the formula "and also including ( _ji_ 及) ailment X." My judgment that _MS_ I.B and "Eleven Vessels" are more closely related editions is the basis for my decision to emend lacunae in _MS_ I.B using "Eleven Vessels" whenever possible. I have not collated the two editions; "Eleven Vessels" is used only to emend lacunae in _MS_ I.B. I make two exceptions where it is obvious that the scribe of _MS_ I.B omitted graphs that occur in "Eleven Vessels." And because of lacunae in "Eleven Vessels" six emendations rely on _MS_ II.B. The result is a reasonable approximation of _MS_ I.B in its original condition.
Like "Eleven Vessels," the _Maishu_ "Vessels and Vapor" and "Five Signs of Death" give evidence of being younger editions of _MS_ I.C and _MS_ I.D. For example, "Vessels and Vapor" uses _gu_ 故 (thus) several times to accentuate the discursive tone of a passage; the same passage without _gu_ in _MS_ I.C is older. For the _MS_ I.C phrase 氣 出 ("if vapor emerges") "Vessels and Vapor" writes 氣 一 上 一 下 ("if vapor now ascends and now descends"), the latter a paraphrase of the former. Similarly, _gu_ 滑 (smooth) in "Vessels and Vapor" is a _lectio facilior_ for _gu_ 汩 (flow evenly) in _MS_ I.C. "Vessels and Vapor" being the younger edition, I refrain from emendation of _MS_ I.C other than to fill lacunae (in one case using a parallel in _Taisu_ when a lacuna also occurs in "Vessels and Vapor"). There are few lacunae in _MS_ I.D; "Five Signs of Death" is worded somewhat differently, but the only significant difference is its reversing of the signs of death associated with vapor and with blood.
The transcription does not include the three text markers used in the original manuscripts. Graphs followed by the double-bar repeat sign are written twice. For convenience I add periods corresponding to the periods in the sentences of the Translation. Emended lacunae are indicated with brackets. When emendation is not possible, the number of graphs estimated to be missing is enclosed in the brackets. The source of bracketed emendations (mostly _MSSW_ ) is given parenthetically following the emendation. Notes on emendations (including several exceptions to the standard emendation of lacunae) are provided separately as needed. Additional textual notes are in the Translation.
The transcription uses modern _kaishu_ graphs, adopting the conventions of the _MWD_ , vol. 4, transcription. For example, 撞 is written 種 (however, I retain 撞 if it is used in the _MWD_ , vol. 4, transcription). Graphs in emendations are not changed to reflect the orthography of _MS_ I.B, _MS_ I.C, and _MS_ I.D. For example, all three _MS_ I texts write 脈 for _mai_ "vessel"; _Maishu_ writes 脈, and this graph is used directly in emendations. Graphs that are not attested for the appropriate word and meaning in received literature (including graphs the scribe miswrote) are followed by a standard attested graph placed in parentheses in the form (:). Any mistranscribed graphs in the _MSSW_ transcription (see above) are written as corrected by Li Xueqin and noted. In some cases a barely legible graph in one of the three _MS_ I texts is mistranscribed in the _MWD_ , vol. 4, transcription. Based on the reproduction of _MS_ I and on _MSSW_ it is possible to determine the correct graph (the revised transcription of _MS_ I.C appended to _MSSW_ supplies a number of such corrections). My transcription records the correct graph without note.
_MS_ I.B
CC35–36
[鉅 陽 之脈。觳 (:繫) 於 踵 外 踝 中。出 胳 衷。上 穿 臀 出 攀 (:厭) 中 夾 脊。出 於 項 上 頭 角 下 顏 夾 頦觳(: 繫) 目 内 廉。 是 動 則 病 冲 頭 目以 (:似) 脱 項 以(:似) 伐 胸 痛 要 以 (:似) 折 脾 (:髀) 不 可 以 運肤
C37
如 結] ( _MSSW_ ) 踹 如 [裂。此] ( _MSSW_ ) 爲 踵 蹶 (: 厥)。 是 鉅 陽哌 (:脈) [主 治。其 所 之 (:産) 病 頭 痛 耳 聾 項 痛 鬵
C38
强] ( _MSSW_ ) 瘧 北(:背) 痛 要 痛 尻 痛 時 (:痔) 肤1 痛踹 痛 [足 小 指鎅 (: 痹) 爲 十] ( _MSSW_ ) 二 病。
C39
[少] ( _MSSW_ ) 陽哌(:脈)。 軗 (:繫) 於 外 踝 之 前 廉。 上 出 魚 股 之 [外 出 脅。] ( _MSSW_ ) 上 [出 耳 前。] ( _MSSW_ ) 是 動 則 病 [心 與 脅 痛
C40
不] ( _MSSW_ ) 可 以 反 稷 (: 側)甚 則 无 膏 足 外 反。 此 爲 陽 厥。 是 少 陽 [脈 主] ( _MS_ II.B)治。 其 所 産 病 [3] [痛
C41
項] ( _MSSW_ ) 痛 脅 痛 瘧 汗 出 節 盡 痛 脾 (:髀) 廉 痛魚 股 痛 [厀 外 廉] ( _MSSW_ ) 痛 振 寒 [足 中 指] ( _MSSW_ )
C42
踝 (:痹) 爲 十 二 病。
C43
陽 明脈 (:脈)。軗 (:繫) 於 肝 骨 外 廉 循 肝 而 上。 穿 臏 出 魚 股 [之 廉。 上] ( _MSSW_ ) 穿 [乳] ( _MSSW_ ) 穿 頰 [出 目 外] ( _MSSW_ )
C44
廉 環 顏。 是 動 則 病 洒 酒 病 寒 喜 龍 婁 (:數) 吹 (:欠) 顏 [墨 (:黑) 病 種 (:腫) 至 則 惡 人 與 火聞] ( _MSSW_ )
C45
木 音 則 憊 (:惕) 然 驚 心 腸 (:惕) 欲 獨 閉 户 牖 而 處 [病 甚] ( _MSSW_ ) 則 欲 [乘 高 而 歌 棄] ( _MSSW_ ) 衣 [而 走。 此 爲] ( _MSSW_ )
C46
肝 蹶 (:厥)。 是 陽 明 脈 (:脈) 主 治。 其 所 産 病 顏 痛 鼻 肌 (:鼽) 領 [庆 (:痛) 乳 痛 膂 痛] ( _MSSW_ ) 心 與 肤 痛
C47
腹 外 撞 (:膨) 陽 (:腸) 痛 翱 跳 付(:谢) 上 鎅 (:搏) 爲] ( _MSSW_ ) 十 [病。
C48
肩脈 (:脈)。 起 於 耳 後 下 肩 出 肘 [内 廉。] ( _MSSW_ ) 出 [3] 乘 手 北 (:背)。 是 [動 則 病 領 種 (:腫) 痛] ( _MSSW_ ) 不 可 以 顧 肩
C49
以 (:似) 脱 臑 以 (:似) 折。 是 肩 哌 (:脈) 主 治。[ 其 所 産 病] ( _MSSW_ ) 領 [痛 餱 (:喉) 蹐 (:痹) 肩 痛 肘 外] ( _MSSW_ ) 痛 爲 四 病。
C50
耳哌 (:脈)。 起 於 手 北(:背) 出 臂 外 兩 骨 之 間[上 骨] ( _MSSW_ ) 下 廉。 [出 肘 中] ( _MSSW_ ) 入 耳 中。 是 動 則 病 耳 聾
C51
揮 焊 膊 脖 嗌 撞 (:腫)。 是 耳 哌 (:脈) 主 治。 其 所 産 病 目 外 漬 (:营) 痛 頰 [痛] ( _MSSW_ ) 耳 聾 爲 三 病
C52
齒脈 (:脈)。 起 於 次 指 與 大 指 上 出 臂 上 廉 人 肘 中 乘 臑。 [穿] ( _MSSW_ ) 頰 入 齒 中 夾 鼻。 是 [動] ( _MSSW_ )
C53
則 病 齒 痛 肶 (:頓)潼 (:腫)。 是 齒 哌 (:脈) 主 治。 其 所 産 病 齒 痛 肺 (:頓)潼 (:腫) 目 黄 口 乾 臑 痛 爲 五 [病。 ] ( _MSSW_ )
C54
大 陰 哌 (:脈)。 是 胃 哌 (:脈) 殹。 彼 (:披) 胃 出 魚 股 陰 下 廉 踹 上 廉 出 [内] ( _MSSW_ ) 踝 之 上 廉。 是 動 則 病 上[1]
C55
走 心 使 復 (:腹) 張 (:脹) 善 噫 食 欲 歐 (: 嘔) 得 後 與 氣 則 佚 然 衰。 是 鉅 陰 脈 (:脈) 主 治。 其 所 [産
C56
病 獨] ( _MSSW_ ) 心 煩 死 心 痛 與 復 (:腹) 張 (:脹) 死 不 能 食 不 能 卧 强 吹 (:欠) 三 者 同 則 死 唐 (:溏) 泄 死 [水 與] ( _MSSW_ )
C57
閉 同 則 死 爲 十 病。
C58
厥 陰 脈 (:脈)。毄 (:繫) 於 足 大 指 敢 (:叢) [毛] ( _MSSW_ ) 之 上。 乘 足 [拊 (:谢) 上 廉] ( _MSSW_ ) 去 内 腺 (:踝)一 寸。 上 [牒 (:踝)] ( _MS_ II. B) 五 寸 而 [出 於 大 陰 之 後。] ( _MS_ II. B)
C59
上 出 魚 股 内 廉 觸 少 腹 夾 漬 (:营) 旁。 是 動 則 [病 丈] ( _MSSW_ ) 夫嘖 (:癩) [山 (:沛) 婦 人 則 少 腹 種 (:腫) 要 翻痡] ( _MSSW_ )
C60
不 可 以 卬 (:仰) 甚 則 嗌 乾 面 疵。 是 厥 陰 哌 (:脈) 主 治。 [其] ( _MSSW_ ) 所 産 病 熱 中 [瘁 饋 扁 (:偏)山 (:疝) 爲 五 病。 五 病] ( _MSSW_ )
C61
有 而 心 煩 死 勿 治 殹。 有 陽 哌 (:脈) 與 之 [俱] ( _MSSW_ ) 病 可 治 殿。
C62
少 陰 脈 (:脈)。 觳 (:繫) 於 内 腺 (:碟) 外 廉 穿 踹 出 胳 [中] ( _MSSW_ ) 央。 上 穿 脊 之 [内] ( _MSSW_ ) 廉 數 (:繫) 於 腎 夾 舌。 [是 動 即 (:則) 病] ( _MSSW_ )
C63
恂 (:喝) 恂 (:喝) 如 喘 坐 而 起 則 目 膜 (:硭) 如 毋 見 心 如 縣 (:懸) 病 飢 氣 [不 足] ( _MSSW_ ) 善 怒 心 腸 (:惕) 恐 [人 將 捕 之] ( _MSSW_ )
C64
不 欲 食 面若 馳 (:姗) 色 效 則 有 血。 此 爲 骨 蹶 (:厥)。 是 少 [陰] ( _MSSW_ ) 哌 (:脈) 主 [治。] ( _MSSW_ )1 其 [所 産 病 口 熱] ( _MSSW_ )
C65
舌 柝 (:坼) 嗌 乾 上 氣 饈 (:噎) 嗌 中 痛 癉 耆 (:嗜) 卧 欸 音 (:瘠) 爲 十 病。[少] ( _MSSW_ ) 陰 之 哌 (:脈) [久 (:灸) 則 强 食 産 肉 缓 帶] ( _MSSW_ )
C66
皮 (:被) 髪 大 丈 (:杖) 重 履 而 步。 久 (:灸) 幾 息 則 病 已 矣。
C67
臂 鉅 陰 脈 (:脈)。 在 於 手 掌 中 出 内 陰 兩 骨 之 間 上 骨 下 廉 筋 之 上。 出 臂 [内 陰 入 心 中。] ( _MS_ II. B)
C68
是 動 則 病 心 滂 滂 如 痛 缺 盆 痛 甚 [則] ( _MS_ II. B) 交 兩 手 而 戰。 此 爲 臂 蹶 (:厥)。 [是 臂 巨 陰 脈 主] ( _MS_ II. B)
C69
治。 其 所 産 病 脑 (:胸) 痛 癒 (:院) 痛 [心 痛] ( _MSSW_ )1 四 末 痛 叚 (:瘕) 爲 五 病。
C70
臂 少 陰 脈(:脈)。 起 於 臂 兩 骨 之 間 之 間2 之 下 骨 上 廉 筋 之 下。 [出] ( _MSSW_ ) 臑 内 陰 [入 心 中。 是 動 則 病 心] ( _MSSW_ )
C71
痛 益 (:嗌) 渴 欲 飲。 此 爲 臂 蹶 (:厥)。 是 臂 少 陰 哌 (:脈) 主 治。 其 所 産 [病 脅] ( _MSSW_ ) 痛 爲 [一 病。] ( _MSSW_ )
_MS_ I.C
C72
以脈(:脈) 法 明 教 下。 脈 (:脈) 亦 聽 (:聖) 人 之 所 貴 殹。 氣 殹 者 到 下 而 [害] ( _MSSW_ ) 上 [從 煖 而 去 清] ( _MSSW_ )
C73
焉。 聽 (:聖) 人 寒 頭 而 煖 足。 治 病 者 取 有 餘 而 益 不 足 殹 。 [氣] ( _MSSW_ ) 上 而 不 下 [則 視 有] ( _MSSW_ )
C74
過 之脈 (:脈) 當 環 而 久 (:灸) 之。 病 甚 陽 上 於 環 二 寸 而 益 爲 一 久 (:灸)。 氣 出 胳 與 肘 之脈 (:脈) 而 [砈 之。] ( _MSSW_ )
C75
用 (:砈) 啓 脈 (:脈) 者 必 如 式。 壅 (:癰) 潼 (:腫) 有 臘 (:膿) 則 稱 其 小 大 而 [爲] ( _MSSW_ ) 之 [石[砈。 砈] ( _MSSW_ ) 有 四 [害。] ( _MSSW_ ) 臘 (:膿) 深 [而] ( _MSSW_ )
C76
(:砈) 輚 (:淺) 謂 上 (:之) 不 遝 一 害。 臘 (:膿) 輚_(:淺) 而 裝 (:石G) 深 胃 (:謂) 之 過二 害。 臘 (:膿) 大 [而 砠 小 胃 (:謂) 之 渝 渝 者 惡
C77
不 畢] ( _MSSW_ ) 三 [害。 農 (:膿)] ( _MSSW_ ) 小 而 (砈) 大 胃 (:謂) 之 l (:泛) (:泛) 者 傷 良 肉 殹 四 害。 臘 (:膿) [多 而 深 者 上 黑] ( _MSSW_ ) 而 大。[農 (:膿))
C78
少 而 深 者 上 黑 而 小。 農 (:膿) 多 而 淺 者 上 白 而 大。] ( _MSSW_ ) 臘 (:膿) 少 [而] ( _MSSW_ ) 輚 (:淺) [者 上 白 而 小。 此 不 可 不] ( _MSSW_ ) 察 殹。 [肴] ( _MSSW_ )
C79
臘 (:膿) 者 不 [可 久 (:灸) 殹。 相 脈 之 道。 左] ( _MSSW_ ) [手 上 去 踝 五 寸] ( _Taisu_ ) 案 之。右 [手 直 踝 而 簟 (:撢) 之。它脈] ( _MSSW_ ) 盈 此
C80
獨 虚 則 主 病。 它 脈 (:脈) 汩 此 獨 [衛 (:率)] ( _MSSW_ ) 則 主 [病。] ( _MSSW_ ) 它脈 (:脈) [靜 此 獨 動 則 生 (:主) 病。 夫 脈 固 有 動 者 酐] ( _MSSW_ )
C81
之 少 陰 臂 之 大 陰 少 陰。 氏 (:是) 主 [動 疾] ( _MSSW_ ) 則 [病。] ( _MSSW_ ) 此 [所 以 論 有 過 之 脈 殹。 其 餘 謹 視 當 脈 之 過。] ( _MSSW_ )
C82
脈 (:脈) 之 縣 書 而 熟 學 之。 季 子 忠 謹。 學[4] 見 於 爲 人 [6]
C83
言 不 可 不 察 殹。
_MS_ I. D
C84
凡 三 陽 天 氣 殹。 其 病 唯 折 骨 列 (:裂) 膚 一 死。 凡 三 陰 地 氣 殹 死 脈 (:脈) 殹。 [陰] ( _MSSW_ ) 病 而 亂 則 [不] ( _MSSW_ )
C85
過 十 日 而 死。 三 陰 怤 (:腐) 臧 (:臟) 煉 (:爛) 腸 而 主 殺 。 [2] 五 死。 唇 反 人 盈 則 肉 [先 死。 龈 齊 齒 長 則] ( _MSSW_ )
C86
骨 先 死。 面 黑 目 環 (:袁) 視 襄 (:裏) 則 氣 先 死。 汗 出 如 絲 傅 而 不 流 則 血 先 死。 舌 捆 (:糊)橐 (:卵) 卷 [則 筋] ( _MSSW_ )
C87
先 死。 五 者 扁 (:徧) 有 則 不 沽 (:活) 矣。
1See _MS_ I.B.1, p. 205, n. 1.
1The scribe of _MS_ I. B omitted 洽.
1The scribe of _MS_ I. B. omitted 心 痛. See _MS_ I. B. 10, p. 212, n. 2.
2The scribe of _MS_ I. B. worte 之 間 twice; the second occurence is excrescent.
Appendix 2
Revisions To the Transcription of Graphs in _MWD_ , Vol. 4
The revisions are based on Qiu Xigui (1992), my own research, and consultation with Li Xueqin, who is responsible for the final editing of the transcription in _MWD_ , vol. 4. I am indebted to Professor Li for personally checking the revisions and indicating his general agreement with them. In several instances the correct transcription remains open to argument; I bear sole responsibility for the revisions proposed in the list below (each revision is also noted in the Translation). Because the transcription of _MS_ I.B, _MS_ I.C, and _MS_ I.D in Appendix 1 replaces the transcription in _MWD_ , vol. 4, revisions are not given for those texts.
Han Weights and Measures
Equivalents*
*See Twitchett and Loewe 1986: xxxviii. Only those weights and measures that occur in the Prolegomena and Translation are included.
Bibliography
Only works cited are included. Abbreviated titles appear at the appropriate alphabetic position. Traditional works in Chinese and Japanese are listed by title. Authors or compilers are identified following the title when possible; dates are often approximate (detailed information on Han and pre-Han works may be found in Loewe 1993). In addition, commentaries to which specific reference is made are identified.
Andersen, P. 1989–90. "The Practice of _Bugang_." _Cahiers d'Extr ême-Asie_ 5. 15–53.
Akahori, Akira 赤 堀 昭. 1978. "Bu-i Kandai ikan ni tsuite" 武 威 漢 代 醫 簡 に つ ぃ て. _T ôhô gakuhô_ 東方學報 50. 75–107.
Akahori, Akira 赤 堀 昭. 1985. "Yahô o meguru mondai" 冶 法 め ぐ ろ 問 題. _KGS_ , vol. 2. 123–165.
Akahori, Akira 赤 堀 昭. 1989. "The Interpretation of Classical Chinese Medical Texts in Contemporary Japan: Achievements, Approaches, and Problems." _Approaches to Traditional Chinese Medical Literature_. Ed. P. Unschuld. Dordrecht: Kluwer Academic Publishers. 19–27.
Akizuki, Kan'ei 秋 月 觀 暎, ed. 1987. _D ôkyô to shûkyô bunka_ 道 教 と 宗 教 文 化. Tokyo: Hirakawa shuppansha.
_BC. Shennong bencaojing_ 神 農 本 草 經. First to second centuries A.D. References are to citations of _BC_ in _GM_.
_BL. Mingyi bielu_ 名 醫 別 錄. Ca. sixth century. References are to citations of _BL_ in _GM_.
_Baopuzi_ 抱 朴 子. Ge Hong 葛 洪 (283–343). _Zhuzi jicheng_ ed.
_Bencaojing jizhu_ 本 草 經 集 注. Tao Hongjing (456–536). References are to _Honz ôkyô shûchû_ 本 草 經 集 注. Ed. Mori Risshi 森 立 之 (between 1849 and 1852) and Okanishi Tameto 岡 西 爲 人. Osaka: Minami Ôsaka insatsu sentâ, 1972.
Betz, H., ed. 1986. _The Greek Magical Papyri in Translation_. Chicago: University of Chicago Press.
_Biji xiaoshuo daguan_ 筆 記 小 説 大 觀. Taibei: Xinxing shuju, 1973.
_Biji xiaoshuo daguan xubian_ 筆 記 小 説 大 觀 續 編. Taibei: Xinxing shuju, 1973.
Bodde, D. 1975. _Festivals in Classical China: New Year and Other Annual Observances during the Han Dynasty 206 B.C.–A.D. 220_. Princeton: Princeton University Press.
Bokenkamp, S. 1983. "Sources of the _Ling-pao_ Scriptures." __Tantric and Taoist Studies in Honour of R.A. Stein_ , vol. 2 ( _M élanges chinois et bouddhiques_ 21)_. Ed. M. Strickmann. 434–486.
_Bowuzhi_ 博 物 志. Zhang Hua 張 華 (232–300). _Sibu beiyao_ ed.
Brashear, W. 1992. "Magical Papyri: Magic in Bookform." _Das Buck ah magisches und als Repr äsentationsobjekt_. Ed. P. Ganz. Wiesbaden: Harrassowitz. 25–57.
Bridgman, R. 1952–55. "La medicine dans la Chine antique." _M élanges chinois et bouddhiques_ 10. 1–213.
_Chaoshi zhubing yuanhoulun_ 巢 氏 諸 病 源 候 論. Chao Yuanfang 巢 元 方 (fl. 610). _Siku quanshu_ ed.
Chen, Banghuai 陳 邦 懷. 1982. "Zhanguo 'Xingqi yuming' kaoshi" 戰 國 行 氣 玉 銘 考 釋. _Guwenzi yanjiu_ 古 文 字 研 究 7. 187–193.
Chen, Mengjia 陳 夢 家. 1936. "Shang dai de shenhua yu wushu" 商 代 的 神 話 與 巫 術. _Yanjing xuebao_ 燕 京 學 報 20. 485–576.
Chen, Mengjia 陳 夢 家. 1965. "Han jian nianli biaoxu" 漢 簡 年 曆 表 叙. _Kaogu xuebao_ 考 古 學 報 1965.2. 103–149.
Chen, Pan 陳 槃. 1948. "Zhanguo Qin Han jian fangshi kaolun" 戰 國 秦 漢 間 方 士 考 論. _Zhongyang yanjiuyuan lishi yuyan yanjiusuo jikan_ 中 央 研 究 院 歷 史 語 言 研 究 所 集 刊 17. 7–57.
Chen, Songchang 陳 松 長. 1994. "Mawangdui sanhao Han mu mudu sanlun" 馬 王 堆 三 號 漢 墓 木 牘 散 論. _Wenwu_ 文 物 1994.6. 64–70.
Chen, Xiangchun. 1942. "Examples of Charm against Epidemics with Short Explanations." _Folklore Studies_ 1. 37–54.
_Chuci_ 楚 辭. Contents of various dates, from late fourth century B.C. to second century A.D. _Sibu beiyao_ ed. Commentaries cited: Wang Yi 王 逸 (ca. 89–ca. 158).
_Chuogenglu_ 輟 耕 錄. Tao Zongyi 陶 宗 儀 (ca. 1316–ca. 1402). _Congshu jicheng_ ed.
_Congshu jicheng_ 叢 書 集 成. Shanghai: Shangwu yinshuguan, 1935–1937.
_Daode zhenjing zhu_ 道 德 真 經 註 (with the Heshang gong 河 上 公 commentary). _Daozang_ ed. ( _HY_ 682).
_Daozang_ 道 藏. Taibei: Yiwen yinshuguan, 1977 (reprint of the 1926 Hanfenlou reproduction of the woodblock ed. housed in the Baiyunguan, Beijing; the latter based on eds. of 1444–45 and 1607).
Dubs, H. 1938–55. _The History of the Former Han Dynasty_. 3 vols. Baltimore: Waverly Press.
_Duduan_ 獨 斷. Cai Yong 蔡 邕 (133–192). _Han Wei congshu_ 漢 魏 叢 書 ed. Shanghai: Hanfen lou, 1925 (reproduction of 1592 woodblock ed.).
Eamon, W. 1985. "Science and Popular Culture in Sixteenth Century Italy: The 'Professors of Secrets' and Their Books." _The Sixteenth Century Journal_ 16. 471–485.
Eamon, W. 1990. "From Secrets of Nature to Public Knowledge." _Reappraisals of the Scientific Revolution_. Ed. D. Lindberg and R. Westman. Cambridge: Cambridge University Press. 333–365.
Eberhard, W. 1968. _The Local Cultures of South and East China_. Trans. A. Eberhard. Leiden: E.J. Brill.
Edelstein, L. 1987. _Ancient Medicine: Selected Papers of Ludwig Edelstein_. Ed. O. Temkin, and C. Temkin. Baltimore: Johns Hopkins University Press.
Eis, G. 1967. _Mittelalterliche Fachliteratur_. Stuttgart: Sammlung Metzler.
Emura, Haruki 江 村 治 樹 et al., eds. 1987. _Ma- ô-tai shutsudo isho jikei bunrui sakuin_ 馬 王 堆 出 土 醫 書 字 形 分 類 索 引. Private publication.
Epler, D. 1980. "Bloodletting in Early Chinese Medicine and Its Relation to the Origin of Acupuncture." _Bulletin of the History of Medicine_ 54. 337–367.
_Erya_ 爾 雅. Ca. third century B.C. _Shisanjing zhushu_ ed. Commentaries cited: Guo Pu 郭 璞 (276–324).
_Fangyan_ 方 言. Yang Xiong 揚 雄 (58 B.C.–A.D. 18). _Sibu beiyao_ ed.
_Fantianlu conglu_ 梵 天 廬 叢 錄. Chai E 柴 萼 (1892-?). Author's preface dated 1925, n.p.
Faraone, C. 1991. "The Agonistic Context of Early Greek Binding Spells." Faraone and Obbink 1991. 3–32.
Faraone, C. and D. Obbink, eds. 1991. _Magika Hiera: Ancient Greek Magic and Religion_. Oxford: Oxford University Press.
_Fayan_ 法 言. Yang Xiong 揚 雄 (58 B.C.–A.D. 18). _Zhuji jicheng_ ed.
_Fengsu tongyi_ 風 俗 通 義. Ying Shao 應 劭 (ca. 140–ca. 200). _Sibu beiyao_ ed.
Follon, J. 1968. "Manuscripts of Ortolf von Bayerlants 'Arzneibuch'. Their Contents, Exemplifying German Mediaeval Artes Literature." Keil et al. 1968. 31–52.
Fu, Juyou 傅 舉 有. 1983. "Guanyu Changsha Mawangdui sanhao Han mu de muzhu wenti" 關 於 長 沙 馬 王 堆 三 號 漢 墓 的 墓 主 問 題. _Kaogu_ 耉 古 1983.2. 165–172.
Fu, Juyou 傅 舉 有 and Chen Songchang 陳 松 長. 1992. _Mawangdui Han mu wenwu_ 馬 王 椎 漢 墓 文 物. Changsha: Hunan chubanshe.
Fuyang Han jián zhenglizu 阜 陽 漢 簡 整 理 組. 1983. "Fuyang Han jian jianjie" 阜 陽 漢 簡 簡 介. _Wenwu_ 文 物 1983.2. 21–23.
Fuyang Han jián zhenglizu 阜 陽 漢 簡 整 理 組. 1988. "Fuyang Han jian _Wanwu_ " 阜 陽 漢 簡 萬 物. _Wenwu_ 文 物 1988.4. 36–47.
_GM. Bencao gangmu_ 本 草 綱 目. Li Shizhen 李 時 珍 (1518–1593). Taibei: Hongye shuju, 1985.
Gansu sheng wenwu kaogu yanjiusuo 甘 肅 省 文 物 考 古研 究 所. 1989. _Qin Han jiandu lunwenji_ 秦 漢 簡 牘 論 文 集. Lanzhou: Gansu renmin chubanshe.
Goodrich, C. 1966. "Two Chapters in the Life of an Empress of the Later Han (II)." _Harvard Journal of Asiatic Studies_ 26. 187–210.
Graham, A. 1981. _Chuang Tzu: The Inner Chapters_. London: George Allen and Unwin.
Graham, A. 1986. _Yin-Yang and the Nature of Correlative Thinking_. Singapore: Institute of East Asian Philosophies.
Graham, A. 1989. _Disputers of the Tao_. La Salle: Open Court.
Granet, M. 1925. "Remarques sur le taoisme ancient." _Asia Major_ 2. 146–151.
Granet, M. 1953. "Le dépôt de l'enfant sur le sol: rites anciens et or-dalies mythiques." _É tudes sociologiques sur la Chine_. By M. Granet. Paris: Presses Universitaires de France. 159–202.
de Groot, J. 1892–1910. _The Religious System of China_. 6 vols. Leiden: E.J. Brill.
Gu, Shi 顧 實. 1924. _Hanshu yiwenzhi jiangshu_ 漢 書 藝 文 志 講 疏. Shanghai: Shangwu yinshuguan.
_Guangya_ 廣 雅. Zhang Yi 張 揖 (fl. 227–232). References are to the _Sibu beiyao_ ed. of _Guangya shuzheng_ 廣 雅 疏 證. Ed. Wang Niansun 王 念 孫 (1742–1832). Commentaries cited: Wang Niansun.
_Guanzi_ 管 子. Fourth to first centuries B.C. _Zhuzi jicheng_ ed.
_Gujin xiaoshuo_ 古 今 小 説. Feng Menglong 傌 夢 龍 (1574–1645) Taibei: Shijie shuju, 1958.
_Gujinzhu_ 古 今 注. Cui Bao 催 豹 (fl. 290–306). _Sibu beiyao_ ed.
van Gulik, R. 1961. _Sexual Life in Ancient China_. Leiden: E.J. Brill.
_Guoyu_ 國 語. Ca. third century B.C. _Sibu beiyao_ ed.
_HY. Daozang zimu yinde_ 道 藏 子 目 引 得. Harvard-Yenching Institute Sinological Index Series, no. 25. Taibei: Cheng-wen Publishing Company, 1966. Works in the _Daozang_ are further identified by their _HY_ number.
Han, Zhongmin 韓 仲 民 (see also Xiao Han). 1992. _Bo Yi shuol üe_ 帛 易 説 略. Beijing: Beijing Shifan daxue chubanshe.
_Hanfeizi_ 韓 非 子. Han Fei 韓 非 (d. 233 B.C.) and others. _Zhuzi jicheng_ ed.
_Hanshu_ 漢 書. Ban Gu 班 固 (32–92). References are to _Hanshu buzhu_ 漢 書 補 注. Ed. Wang Xianqian 王 先 謙 (1842–1918). Taibei: Xinwenfeng chuban gongsi, 1975 (reproduction of 1900 woodblock ed.). Commentaries cited: Yan Shigu 顏 師 古 (581–645); Wang Xianqian.
Harper, D. (see also Xia De'an). 1978–79. "The Han Cosmic Board." _Early China_ 4. 1–10.
Harper, D. (see also Xia De'an). 1982. "The _Wu Shih Erh Ping Fang_ : Translation and Prolegomena." Diss. University of California, Berkeley. Ann Arbor: University Microfilms International. 8312837.
Harper, D. (see also Xia De'an). 1985. "A Chinese Demonography of the Third Century B.C." _Harvard Journal of Asiatic Studies_ 45. 459–498.
Harper, D. (see also Xia De'an). 1987a. "Wang Yen-shou's Nightmare Poem." _Harvard Journal of Asiatic Studies_ 47. 239–283.
Harper, D. (see also Xia De'an). 1987b. "The Sexual Arts of Ancient China as Described in a Manuscript of the Second Century B.C." _Harvard Journal of Asiatic Studies_ 47. 539–593.
Harper, D. (see also Xia De'an). 1988. "A Note on Nightmare Magic in Ancient and Medieval China." _T'ang Studies_ 6. 69–76.
Harper, D. (see also Xia De'an). 1990. "The Conception of Illness in Early Chinese Medicine, as Documented in Newly Discovered 3rd and 2nd Century B.C. Manuscripts." _Sudhoffs Archiv_ 74. 210–235.
Harper, D. (see also Xia De'an). 1994. "Resurrection in Warring States Popular Religion." _Taoist Resources_ 5.2. 13–28.
Harper, D. (see also Xia De'an). 1995. "Warring States, Ch'in and Han Periods." In "Chinese Religions: The State of the Field." Ed. D. Overmyer. _Journal of Asian Studies_ 51.1. 152–160.
Harper, D. (see also Xia De'an). Forthcoming. "Warring States, Qin, and Han Manuscripts Related to Natural Philosophy and the Occult." Shaugh-nessy forthcoming.
Hawkes, D. 1985. _The Songs of the South: An Anthology of Ancient Chinese Poems by Qu Yuan and Other Poets_. Harmonds-worth: Penguin Books.
Hayashi, Minao 林 巳 奈 夫. 1975. "Kandai no inshoku" 漢 代 の 飲 食. _T ôhô gakuhô_ 東 方 學 報 48. 1–98.
Hayashi, Minao 林 巳 奈 夫. 1976. _Kandai no bunbutsu_ 漢 代 の 文物. Kyoto: Kyôto daigaku jinbun kagaku kenkyûjo.
He, Linyi 何 琳 儀. 1989. _Zhanguo wenzi tonglun_ 戰 國 文 字 通 論. Beijing: Zhonghua shuju.
He, Shuangquan 何 雙 全. 1989a. "Tianshui Fangmatan Qin jian zongshu" 天 水 放 馬 灘 秦 簡 綜 述 _Wenwu_ 文 物 1989.2. 23–31.
He, Shuangquan 何 雙 全. 1989b. "Tianshui Fangmatan Qin jian jiazhong _Rishu_ kaoshu" 天 水 放 馬 灘 秦 簡 甲 種 日 書 考 述. Gansu sheng wenwu kaogu yanjiusuo 1989. 7–28.
Heywood, V. and S. Chant, eds. 1982. _Popular Encyclopedia of Plants_. Cambridge: Cambridge University Press.
Horiike, Nobuo 堀 池 信 夫. 1988. "Kandai no shinsen yôsei-setsu, igaku to chishikijin" 漢 代 の 神 仙 養 生 説 醫學 と 知 識 人. Sakade 1988. 296–321.
_Hou Hanshu_ 後 漢 書. Fan Ye 范 曄 (398–446) and others. References are to _Hou Hanshu jijie_ 後 漢 書 集 解. Ed. Wang Xianqian 王 先 謙 (1842–1918). Taibei: Xinwenfeng chuban gongsi, 1975 (reproduction of 1915 woodblock ed.).
Hu, Houxuan 胡 厚 宣. 1984. "Lun Yin ren zhiliao jibing zhi fangfa" 論 殷 人 治 療 疾 病 之 方 法. _Zhongyuan wenwu_ 中 原 文 物 1984.4. 27–30.
Hu, Pingsheng 胡 平 生 and Han Ziqiang 韓 自 强. 1988. " _Wanwu_ lüeshuo" 禽 物 略 説. _Wenwu_ 文 杨 1988.4. 48–54.
_Huainan wanbishu_ 淮 南 萬 畢 術. Ca. first century B.C. References are to the reconstructed text in _Guangutang suo zhushu_ 觀 古 堂 所 著 書. Ed. Ye Dehui 葉 德 輝 (1864–1927). _Congshu jicheng xubian_ 叢 書 集 成 續 编. Taibei: Yiwen yinshuguan, 1970 (reproduction of the 1902 woodblock ed. of _Guangutang suo zhushu_ ).
_Huainanzi_ 淮 南 子. Liu An 劉 安 (179–122 B.C.) and others. _Zhuzi jicheng_ ed. Commentaries cited: Gao You 高 誘 (ca. 160–220).
_Huangdi neijing_ 黄 帝 内 經. Ca. first century B.C. See _Lingshu, Suwen, Taisu_.
_Huangting neijing jing_ 黄 庭 内 景 經. Fourth to sixth centuries A.D. References are to the edition in _Yunji qiqian_. Commentaries cited: Liangqiuzi 梁 丘 子 (Tang period).
_Huangting waijing jing_ 黄 庭 外 景 經. Ca. third century. References are to the edition in _Yunji qiqian_.
Hubei sheng Jing Sha tielu kaogudui 湖 北 省 荆 沙 鐵 路 考 古 隊. 1991. _Baoshan Chu jian_ 包 山 楚 簡. Beijing: Wenwu chubanshe.
Hudson, R. 1993. "Concepts of Disease in the West." Kiple 1993. 45–52.
Hulsewé, A. 1985. _Remnants of Ch'in Law: An Annotated Translation of the Ch'in Legal and Administrative Rules of the 3 rd Century B.C. Discovered in Yün-meng Prefecture, Hu-pei Province, in 1975_. Leiden: E.J. Brill.
Hunan nongxueyuan 湖 南 農 學 院 et al., eds. 1978. _Changsha Mawangdui yihao Han mu chutu dongzhiwu biaoben de yanjiu_ 長 沙 馬 王 堆 一 號 漢 墓 出 土 動 植 物 標 本 的 研 究. Beijing: Wenwu chubanshe.
Hunan sheng bowuguan 湖 南 省 博 物 館 and Zhonggo kexueyuan kaogu yanjiusuo 中 國 科 學 院 考 古 研 究 所. 1973. _Changsha Mawangdui yihao Han mu_ 長 沙 馬 王 堆 一 號 漢 墓. 2 vols. Beijing: Wenwu chubanshe.
Hunan sheng bowuguan 湖 南 省 博 物 館 and Zhonggo kexueyuan kaogu yanjiusuo 中 國 科 學 院 考 古 研 究 所. 1974. "Mawangdui er, san hao Han mu fajue jianbao" 馬 王 堆 二三 號 漢 墓 發 掘 簡 報. _Wenwu_ 文 物 1974.7. 39–48, 63.
Hunan yixueyuan 湖 南 醫 學 院. 1980. _Changsha Mawangdui yihao Han mu gushi yanjiu_ 長 沙 馬 王 堆 一 號 漢 墓 古 尸 研 究. Beijing: Wenwu chubanshe.
Ishida, Hidemi 石 田 秀 實. 1981. "Chûgoku kodai ni okeru sei-shin shippei kan" 中 國 古 代 に お け る 精 神 疾 病 觀. _Nihon ch ûgoku gakkai hô_ 曰 本 中 國 學 會 報 33. 29–42.
Ishida, Hidemi 石 田 秀 實. 1991. "Shoki no bôchû yôsei shisô to sensetsu" 初 期 の 房 中 養 生 思 想 と 僊 説. _T ôhô Shûkyô_ 東 方 宗 教 77. 1–21.
_Ishinp ô_ 醫 心 方. Tanba Yasuyori 丹 波 康 賴 (912–995). Tokyo: Kôdansha, 1973 (reproduction of 1854 Japanese woodblock ed.).
Jackson, R. 1988. _Doctors and Diseases in the Roman Empire_. London: British Museum Publications.
_Jianhu guangji_ 堅 瓠 廣 集. Chu Jiaxuan 褚 稼 軒 (fl. 1695). _Biji xiaoshuo daguan xubian_ ed.
_Jing Chu suishi ji_ 荆 楚 歲 時 記. Zong Lin 宗 懍 (sixth century). References are to the edition in Moriya 1963.
_KGS. Shin hatsugen ch ûgoku kagakushi shiryô no kenkyû_ 新發 現 中 國 科 學 史 資 料 の 研 究. Ed. Yamada Keiji 山 田 麁 兒. 2 vols. (vol. 1, _Yakuch û hen_ 譯 注 篇; vol. 2, _Ronk ô hen_ 論 考 篇). Kyoto: Kyôto daigaku jinbun kagaku kenkyûjo, 1985.
Kalinowski, M. 1983. "Les instruments astro-calendériques des Han et la méthode _liuren_." _Bulletin de l' École Frangaise d'Extrême-Orient_ 72. 309–419.
Kalinowski, M. 1985. "La transmission du dispositif des neuf palais sous les Six Dynasties." _Tantric and Taoist Studies in Honour of R.A. Stein_ , vol. 3 ( _M êlanges chinois et bouddhiques_ 22). Ed. M. Strickmann. 773–811.
Kalinowski, M. 1986. "Les traités de Shuihudi et l'hémérologie chinoise à la fin des Royaumes Combattants." _T'oung Pao_ 72. 175–228.
Kalinowski, M. 1991. _Cosmologie et divination dans la Chine ancienne_. Paris: École Française d'Extrême-Orient.
Kaltenmark, M. 1953. _Le Lie-sien tchouan_. Bejing: Université de Paris, Centre d'Etudes sinologiques de Pekin.
Karlgren, B. 1957. _Grammata Serica Recensa_. Stockholm: Museum of Far Eastern Antiquities.
_Kechuang xianhua xuji_ 客 窗 閒 話 續 集. Wu Xianghan 吳 薌 厈 (fl. 1875–1908). _Biji xiaoshuo daguan_ ed.
Keegan, D. 1988. "The 'Huang-ti Nei-ching': The Structure of the Compilations; The Significance of the Structure." Diss. University of California, Berkeley. Ann Arbor: University Microfilms International. 8916728.
Keil, G., ed. 1982. _Fachprosa-Studien: Beitr äge zur mittelalterlichen Wissenschajis- und Geistesgeschichte_. Berlin: Erich Schmidt Verlag.
Keil, G. and P. Assion, eds. 1974. _Fachprosaforschung: Acht Vortr äge zur mittelalterlichen Artesliteratur_. Berlin: Erich Schmidt Verlag.
Keil, G. et al., eds. 1968. _Fachliteratur des Mittelalters: Festschrift fur Gerhard Eis_. Stuttgart: J.B. Metzlersche Verlagsbuchhandlung.
Kinsey, A. 1953. _Sexual Behavior in the Human Female_. Philadelphia: Saunders.
Kiple, K., ed. 1993. _The Cambridge World History of Human Disease_. Cambridge: Cambridge University Press.
Knoblock, J. 1988. _Xunzi: A Translation and Study of the Complete Works_ , vol. 1. Stanford: Stanford University Press.
Kotansky, R. 1991. "Incantations and Prayers for Salvation on Inscribed Greek Amulets." Faraone and Obbink 1991. 107–137.
Kudô, Motoo 工 藤 元 男. 1990. "Un-bô Sui-ko-chi Shin bo chikukan nissho to dôkyô teki shûzoku" 雲 夢 睡 虎 地 秦 墓 竹 簡 日 書 と 道 教 的 習 俗. _T ôhô shûkyô_ 東 方 宗 教 76. 43–61.
Kusuyama, Haruki 楠 山 春 樹. 1987. " _Enan ch ûhen_ to _Enan man-hitsu_ " 淮 南 中 篇 と 淮 南 萬 畢. Akizuki 1987. 27–44.
_Laozi_ 老 子. Ca. third century B.C. References are to various editions as cited.
_Laozi zhongjing_ 老 子 中 經. Second to third centuries A.D. References are to the edition in _Yunji qiqian_.
Lewis, M. 1990. _Sanctioned Violence in Early China_. Albany: State University of New York Press.
Li, Hui-lin. 1979. _Nan-fang ts'ao-mu chuang: A Fourth Century Flora of Southeast Asia_. Hong Kong: Chinese University Press.
Li, Ling 李 零. 1985. _Changsha Zidanku Zhanguo Chu boshu yanjiu_ 長 沙 子 彈 庫 戰 國 楚 帛 書 研 究. Beijing: Zhonghua shuju.
Li, Ling 李 零. 1990. "Formulaic Structure of the Chu Divinatory Bamboo Slips." _Early China_ 15. 71–86.
Li, Ling 李 零. 1991. "Mawangdui Han mu 'Shenqi tu' ying shu bibing tu" 馬 王 堆 漢 墓 神 祗 圖 應 屬 辟 兵 圖. _Kaogu_ 考 古 1991.10. 940–942.
Li, Ling 李 零. 1993. _Zhongguo fangshu kao_ 中 國 方 術 考. Beijing: Ren-min Zhongguo chubanshe.
Li, Ling and K. McMahon. 1992. "The Contents and Terminology of the Mawangdui Texts on the Arts of the Bedchamber." _Early China_ 17. 145–185.
Li, Xueqin 李 學 勤. 1981. "Xin chu jianbo yu Chu wenhua" 新 出 簡 帛 與 楚 文 化. _Chu wenhua xintan_ 楚 文 化 新 探. Ed. Hubei sheng shehui kexueyuan lishi yanjiusuo 湖 北 省社 會 科 學 院 歷 史 研 究 所. Wuhan: Hubei renmin chubanshe. 28–39.
Li, Xueqin 李 學 勤. 1990. "Fangmatan jianzhong de zhiguai gushi" 放 馬 灘 簡 中 的 志 怪 故 事. _Wenwu_ 文 物 1990.4. 43–47.
Li, Xueqin 李 學 勤. 1991. " _Yinshu_ yu _Daoyin tu_ " 引 書 與 導 引 圖. _Wenwu tiandi_ 文 物 天 地 1991.2. 7–9.
Li, Zhongwen 李 鐘 文. 1980. " _Wushier bingfang_ zhong gaozhi lei yaowu de tantao" 五 十 二 病 方 中 膏 脂 類 藥 物 的 探 討. _Mawangdui yishu yanjiu zhuankan_ 馬 王 堆 醫 書 研 究 專 刊 1. 43–48.
Lian, Shaoming 連 劭 名. 1989. "Jiangling Zhangjiashan Han jian _Maishu_ chutan" 江 陵 張 家 山 漢 簡 脈 書 初 探. _Wenwu_ 文 物 1989.7. 75–81.
Liao, Yuqun 廖 育 群. 1989. " _Yin Yang shiyi mai jiujing_ yanjiu: jian-lun jingluo tixi de xingcheng yu fazhan" 陰 陽 十一 脈 灸 經 研 究 兼 論 經 絡 體 系 的 形 成 與 發 展. _Zhonghua yishi zazhi_ 中 華 醫 史 雜 志 1989.1. 20–24.
Liao, Yuqun 廖 育 群. 1991. "Qin Han zhi ji zhenjiu liaofa lilun de jianli" 秦 漢 之 際 緘 灸 療 法 理 論 的 建 立. _Ziran kexue yanjiu_ 自 然 科 學 研 究 10. 272–279.
_Liexian zhuan_ 列 仙 傳. Ca. second century A.D. References are to Kaltenmark 1953.
_Liji_ 禮 記. Han period. _Shisanjing zhushu_ ed. Commentaries cited: Zheng Xuan 鄭 玄 (127–200).
Lindberg, D. 1992. _The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, 600 B.C. to A.D. 1450_. Chicago: University of Chicago Press.
_Lingshu_ 靈 樞. Tang period recension of Han period _Huangdi neijing_. _Sibu beiyao_ ed.
_Lingshu ziwen_ 靈 書 紫 文. Fourth century. _Daozang_ ed. ( _HY_ 639).
Liu, Junzheng 劉 均 正. 1989. " _Wushier bingfang_ 'zhe' kao" 五 十 二 病 务 庶 考. _Zhonghua yishi zazh_ 中 華 醫 史 雜 志 1989.2. 75.
Liu, Xiaolu 劉 曉 路. 1994. "Cong Mawangdui sanhao mu chutu ditu kan muzhu guanzhi" 從 馬 王 堆 三 號 墓 出 土 地 圖 看 墓 主 官 彘. _Wenwu_ 文 杨 1994.6. 59–62.
Liu, Zhiwan 劉 枝 萬. 1974. _Zhongguo minjian xinyang lunji_ 中 國 民 間 信 仰 論 集. Taibei: Zhongyang yanjiuyuan min-zuxue yanjiusuo.
Liu, Zonghan 劉 宗 漢. 1992a. "Changsha Mawangdui chutu boshu _Jingmai shu_ yanjiu zhi yi" 長 沙 馬 王 堆 出 土 帛 書 經 脈 書 研 究 之 一. _Wenshi_ 文 史 36. 91–100.
Liu, Zonghan 劉 宗 漢. 1992b. "Changsha Mawangdui chutu boshu _Jingmai shu_ yanjiu zhi er" 長 沙 馬 王 堆 出 土 帛 書 經 脈 書 研 究 之 二. _Yazhou wenming_ 亞 洲 文 明 2. 249–254.
Lloyd, G. 1979. _Magic, Reason and Experience_. Cambridge: Cambridge University Press.
Lloyd, G. ed. 1983. _Hippocratic Writings_ , Harmondsworth: Penguin Books.
Loewe, M. 1967. _Records of Han Administration_. 2 vols. Cambridge: Cambridge University Press.
Loewe, M. 1974. _Crisis and Conflict in Han China_. London: George Allen and Unwin.
Loewe, M. 1977. "Manuscripts Found Recently in China: A Preliminary Survey." _T'oung Pao_ 63. 99–136.
Loewe, M., ed. 1993. _Early Chinese Texts: A Bibliographic Guide_. Berkeley: Society for the Study of Early China and Institute of East Asian Studies, University of California, Berkeley.
Lu, G. and J. Needham. 1967. "Records of Diseases in Ancient China." _Diseases in Antiquity_. Ed. D. Brothwell and A. Sandison. Springfield: Charles C Thomas. 222–237.
Lu, G. and J. Needham. 1980. _Celestial Lancets: A History and Rationale of Acupuncture and Moxa_. Cambridge: Cambridge University Press.
_Lunheng_ 論 衡. Wang Chong 王 充 (A.D. 27–ca. 100). References are to _Lunheng jijie_ 論 衡 集 解. Ed. Liu Pansui 劉 盼 遂. Beijing: Guji chubanshe, 1957.
Luo, Changpei 羅 常 培 and Zhou Zumo 周 祖 誤. 1958. _Han Wei Jin Nan Bei chao yunbu yanbian yanjiu_ 漢 魏 晉 南 北 韻 部 演 變 研 究. Beijing: Kexue chubanshe.
_L üshi chunqiu_ 呂 氏 春 秋. Lü Buwei 呂 不 韋 (d. 235 B.C.) and others. _Zhuzi jicheng_ ed. Commentaries cited: Gao You 髙 誘 (ca. 160–220).
_MSSW_. Jiangling Zhangjiashan Han jian zhengli xiaozu 江 陵 張 家 山 漢 簡 整 理 小 組. "Jiangling Zhangjiashan Han jian _Maishu_ shiwen" 江 陵 張 家 山 漢 簡 脈 書 釋 文. _Wenwu_ 文 物 1989.7: 72–74.
_MWD. Mawangdui Han mu boshu_ 馬 王 堆 漢 墓 帛 書. Ed. Mawangdui Han mu boshu zhengli xiaozu 馬 王 堆 漢 墓 帛 書 整 理 小 組. 3 vols. to date. Beijing: Wenwu chubanshe. Vol. 1, 1980 (philosophical texts); vol. 3, 1983 (historical and anecdotal texts); vol. 4, 1985 (medical texts).
Ma, Jixing 馬 繼 興 (see also Zhong Yiyan). 1980. " _Maifa_ kaoshi" 脈 法 考 釋 _Mawangdui yishu yanjiu zhuankan_ 馬 王 堆 醫 書 研 究 專 刊 1. 21–26.
Ma, Jixing 馬 繼 興 (see also Zhong Yiyan). 1992. _Mawangdui gu yishu kaoshi_ 馬 王 堆 古 醫 書 考 釋. Changsha: Hunan kexue jishu chubanshe.
Ma, Jixing 馬 繼 興 and Zhou Shirong 周 世 榮. 1978. "Kaogu fajuezhong suo jian bianshi de chubu tantao" 考 古 發 掘 中 所 見 砭石 的 初 步 探 討. _Wenwu_ 文 物 1978.11. 80–82.
Mair, V. 1990. "Old Sinitic * _Myag_ , Old Persian _Magus_ , and English 'Magician.'" _Early China_ 15. 27–47.
Mansvelt Beck, B. 1987. "The First Emperor's Taboo Character and the Three Day Reign of King Xiaowen." _T'oung Pao_ 73. 68–85.
Maspero, H. 1981. _Taoism and Chinese Religion_. Trans. F. Kierman. Amherst: University of Massachusetts Press.
Masters, W. and V. Johnson. 1966. _Human Sexual Response_ , Boston: Little, Brown and Company.
Matsumoto, Eiichi 松 本 榮 一. 1956. "Tonkô hon _Haku-taku seikai zu_ kan" 敦 煌 本 白 澤 精 怪 圖 卷. _Kokka_ 國 華 770. 135–147.
Mawangdui Han mu boshu zhengli xiaozu 馬 王 堆 漢 墓 帛 書 整 理 小 組, ed. 1979. _Daoyin tu_ 導 引 圖. Beijing: Wenwu chubanshe.
_Mengzi_ 孟 子. Meng Ke 孟 軻 (ca. 372–ca. 289 B.C.) and others. _Zhuzi jicheng_ ed.
Miyashita, Saburo 宫 下 三 郎. 1959. "Chûgoku kodai no shippeikan to ryôhô" 中 國 古 代 の 疾 病 觀 と 療 法. _T ôhô gakuhô_ 東 方 學 報 30. 227–252.
Mizukami, Shizuo 水 上 靜 夫. 1977. _Ch ûgoku kodai no shokubu- tsugaku no kenkyû_ 中 國古代 の 植 物 學 の 研 究. Tokyo: Kadokawa shoten.
Morimura, Ken-ichi 森 村 謙 一 1981. "Shin shutsudo iyaku shiryô ni okeru shizen himmoku no tankyû" 新 出 土 醫 藥資 料 に お け る 自 然 品 目 の 探 究. _T ôhô gakuhô_ 東 方 學 報 53. 341–385.
Moriya, Mitsuo 守 屋 美 都 雄. 1963. _Ch ûgoku ko saijiki no kenkyû_ 中 國 古 歲 時 記 の 研 究. Tokyo: Teikoku shoin.
Morohashi, Tetsuji 諸 橋 轍 次. 1957–60. _Dai Kan-Wa jiten_ 大 漢 和 辭 典. 13 vols. Tokyo: Taishûkan shoten.
_Mozi_ 墨 子. Mo Di 墨 翟 (ca. 479–ca. 381 B.C.) and others. _Zhuzi jicheng_ ed.
_Mu tianzi zhuan_ 穆 天 子 傳. Ca. fourth century B.C. _Sibu beiyao_ ed.
Murakami, Yoshimi 村 上 嘉 實. 1985. " _Goj ûni byôhô_ no jin-buyaku" 五 十 二 病 方 の 人 部 藥. _KGS_ , vol. 2. 167–223.
_Nanjing_ 難 經. First century A.D. _Sibu beiyao_ ed.
_Nanshi_ 南 史. Li Yanshou 李 延 壽 (600–680) and others. Taibei: Xinwenfeng chuban gongsi, 1975 (reproduction of 1739 Palace woodblock ed.).
Needham, J. 1954–. _Science and Civilisation in China_ , 6 vols, to date. Cambridge: Cambridge University Press.
Ngo, Van Xuyet. 1976. _Divination, magie et politique dans la Chine ancienne_. Paris: Presses Universitaires de France.
Onozawa, Sei-ichi 小 野 沢 精 一 et al., eds. 1978. _Ki no shis ô: Chûgoku ni okeru shizenkan to ningenkan no tenkai_ 氣 の 思 想: 中 國 に お け る 自 然 觀 と 人間 觀 の 展 開. Tokyo: Tôkyô daigaku shuppankai.
Peng, Hao 彭 浩. 1990. "Zhangjiashan Han jian _Yinshu_ chutan" 張 家 山 漢 簡 引 書 初 探. _Wenwu_ 文 物 1990.10. 87–91.
Phillips, C. 1991. " _Nullum Crimen sine Lege_ : Socioreligious Sanctions on Magic." Faraone and Obbink 1991. 260–276.
_Qianjin yaofang_ 千 金 藥 方. Sun Simo 孫 思 邀 (seventh century). _Daozang_ ed. ( _HY_ 1155).
_Qianjin yifang_ 千 金 翼 方. Sun Simo 孫 思 邀 (seventh century). Taibei: Guoli Zhongguo yiyao yanjiusuo, 1965 (reproduction of 1829 Japanese woodblock ed.).
_Qimin yaoshu_ 齊 民 要 術. Jia Sixie 賈 思 勰 (sixth century). References are to _Qimin yaoshu jiaoshi_ 齊 民 要 術 校 釋. Ed. Miao Qiyu 谬 啓 愉. Beijing: Nongye chubanshe, 1982.
Qin jian zhengli xiaozu 秦 簡 整 理 小 組. 1989. "Tianshui Fangmatan Qin jian jiazhong _Rishu_ shiwen" 天 水 放 馬 灘 秦 簡 甲 種 日 書 釋 文. Gansu sheng wenwu kaogu yanjiusuo 1989. 1–6.
_Qingbai leichao_ 清 稗 類 鈔. Xu Ke 徐 珂 (1869–1928). Taibei: Shangwu yinshuguan, 1966 (reprint of 1917 ed.).
_Qinjing_ 禽 經. Ca. tenth century. _Tang Song congshu_ 唐 宋 灇 書. Jingde tang 經 德 堂 woodblock ed. (n.p., n.d).
Qiu, Long 邱 隆 et al., ed. 1984. _Zhongguo gudai du liang heng tuji_ 中 國 吿 代 度 量 衡 圖 集. Beijing: Wenwu chubanshe.
Qiu, Xigui 裘 錫 圭. 1990. _Wenzixue gaiyao_ 文 字 學 概 要. Beijing: Shangwu yinshuguan.
Qiu, Xigui 裘 錫 圭. 1992. "Mawangdui yishu shidu suoyi" 馬 王 堆 醫 書 釋 讀 瑣 議. _Gu wenzi lunji_ 古 文 字 論 集. By Qiu Xigui. Beijing: Zhonghua shuju.
Rao, Zongyi 饒 宗 頥. 1969. "Ba Dunhuang ben _Baize jingguai tu_ liang canjuan" 跋 敦 煌 本 白 澤 精 怪 圖 兩 殘 卷. _Zhong yang yanjiuyuan lishi yuyan yanjiusuo jikan_ 中 央 研 究 院 歷 史 語 言 研 究 所 集 刊 41. 539–543.
Rao, Zongyi 饒 宗 頥. 1991. _Laozi "Xianger zhu" jiaozheng_ 老 子 想 爾 住 校 證. Shanghai: Guji chubanshe.
Rickett, A. 1985. _Guanzi: Political, Economic, and Philosophical Essays from Early China; A Study and Translation_. Princeton: Princeton University Press.
Riegel, J. 1975. "A Summary of Some Recent _Wenwu_ and _Kaogu_ Articles on Mawangdui Tombs Two and Three." _Early China_ 1. 10–15.
Riegel, J. 1976. "Mawangdui Tomb Three: Documents, II. The Maps." _Early China_ 2. 69–72.
Riegel, J. 1989–90. "Kou-mang and Ju-shou." _Cahiers d'Extr ême-Asie_ 5. 55–83.
Robinet, I. 1984. _La r êvelation du Shangqing dans l'histoire du taoisme_. 2 vols. Paris: École Française d'Extrême-Orient.
de Romilly, J. 1975. _Magic and Rhetoric in Ancient Greece_. Cambridge: Harvard University Press.
Roth, H. 1991. "Psychology and Self-cultivation in Early Taoistic Thought." _Harvard Journal of Asiatic Studies_ 51. 599–650.
Roth, H. 1992. _The Textual History of the Huai-nan Tzu_. Ann Arbor: Association for Asian Studies.
Roth, H. 1993. "Text and Edition in Early Chinese Philosophical Literature." _Journal of the American Oriental Society_ 113. 214–227.
Ryan, W. and C. Schmitt, eds. 1982. _Pseudo-Aristotle The Secret of Secrets: Sources and Influences_. London: Warburg Institute.
_SHD. Shuihudi Qin mu zhujian_ 睡 虎 地 秦 墓 竹 簡. Ed. Shuihudi Qin mu zhujian zhengli xiaozu 睡 虎 地 秦 墓 竹 簡 整 理 小 組. Beijing: Wenwu chubanshe, 1990.
_SW. Shuowen jiezi_ 説 文 解 字. Xu Shen 許 慎 (d. A.D. 146). References are to _Shuowen jiezi zhu_ 説 文 解 字 注. Ed. Duan Yucai 段 玉 裁 (1735–1815). Shanghai: Guji chubanshe (reproduction of 1872 woodblock ed.).
Sakade, Yoshinobu 坂 出 祥 伸. 1980. "Dô-in kô" 導 引 考. _Ikeda Suetoshi hakuse koki kinen t ôyôgaku ronshû_ 池 田 末 利 博 士 古 稀 記 念 東 洋 學 論 集. Hiroshima: Ikeda Suetoshi hakuse koki kinen jigyôkai. 225–239.
Sakade, Yoshinobu 坂 出 祥 伸. 1985. "Hôso densetsu to _H ôso kei_" 彭 祖 傳 説 と 彭 祖 經. _KGS_ , vol. 2. 405–462.
Sakade, Yoshinobu 坂 出 祥 伸, ed. 1988. _Ch ûgoku kodai yôsei shisô no sôgôteki kenkyû_ 中 國 古 代 養 生 思 想 の 総 合 的 研 究. Tokyo: Hirakawa shuppansha.
Scarborough, J. 1988. "Hermetic and Related Texts in Classical Antiquity." _Hermetisicm and the Renaissance: Intellectual History and the Occult in Early Modem Europe_. Ed. I. Merkal and A. Debus. Cranbury: Associated University Presses. 19–44.
Scarborough, J. "The Pharmacology of Sacred Plants, Herbs, and Roots." Faraone and Obbink 1991. 138–174.
Schafer, E. 1955. "Notes on Mica in Medieval China." _T'oung Pao_ 43. 265–286.
Schafer, E. 1967. _The Vermilion Bird: T'ang Images of the South_. Berkeley: University of California Press.
Schafer, E. 1981. "Wu Yün's 'Cantos on Pacing the Void.'" _Harvard Journal of Asiatic Studies_ 41. 377–415.
Schafer, E. 1987. _Consolidated Supplements to Mathews_. Berkeley: private publication.
Schipper, K. 1965. _L'empereur Wou des Han dans la l égende taoiste: Han Wou-ti Nei-tchouan_, Paris: École Française d'Extrême-Orient.
Schipper, K. 1969. "Science, Magic, and the Mystique of the Body." _The Clouds and the Rain: The Art of Love in China_. Ed. M. Beurdeley. London: Hammond and Hammond. 14–20.
Schipper, K., ed. 1975. _Concordance du Houang-t'ing king_. Paris: École Française d'Extrême-Orient.
Schipper, K. 1978. "The Taoist Body." _History of Religions_ 17. 355–386.
Schuessler, A. 1987. _A Dictionary of Early Zhou Chinese_. Honolulu: University of Hawaii Press.
Seidel, A. 1969. _La divinisation de Lao Tseu dans le taoisme des Han_. Paris: École Française d'Extrême-Orient.
Seidel, A. 1987. "Traces of Han Religion in Funeral Texts Found in Tombs." Akizuki 1987. 21–57.
_Shangshu_ 尚 書. Contents of various dates, from the early Zhou period to the fourth century A.D. (the forged sections). _Shisanjing zhushu_ ed.
_Shanhaijing_ 山 海 經. Contents of various dates, from ca. fourth century B.C. to ca. first century A.D. _Sibu beiyao_ ed. Commentaries cited: Guo Pu 郭 撲 (276–324).
_Shanshenmiao Pei Du huan dai_ 山 神 廟 裴 度 還 帶. Yuan period. _Quan Yuan zaju chubian_ 全 元 雜 劇 初編. Ed. Yang Jialuo 楊 家 駱. Taibei: Shijie shuju, 1962.
Shaughnessy, E., ed. Forthcoming. _New Sources of Early Chinese History: An Introduction to Reading Inscriptions and Manuscripts_. Berkeley: Society for the Study of Early China.
Shen, Shou 沈 壽. 1980. "Xi Han bohua _Daoyin tu_ jiexi" 西 漢 帛 晝 導 引 圖 解 析. _Wenwu_ 文 物 1980.9. 70–76.
_Shenjian_ 申 鑒. Xun Yue 荀 悦 (148–209). _Zhuzi jicheng_ ed.
Shibata, Kiyotsugu 柴 田 清 繼. 1984. " _Kanshi_ shihen ni okeru shin to dô" 管 子 四 篇 に お け る 神 と 逪. _Nihon Ch ûgoku gakkai hô_ 日 本 中 國 學 會 報 36. 12–24.
_Shiji_ 史 記. Sima Qian 司 馬 遷 (ca. 145–ca. 86 B.C.). Taibei: Xin-wenfeng chuban gongsi, 1975 (reproduction of 1739 Palace woodblock ed.).
_Shijing_ 詩 經. Contents of various dates, from ca. 1000 to ca. 600 B.C. _Shisanjing zhushu_ ed. Commentaries cited: Kong Yingda 孔 穎 達 (574–648).
_Shiming_ 釋 名. Liu Xi 劉 熙 (fl. 200). _Congshu jicheng_ ed.
Shirakawa, Shizuka 白 川 靜. 1974. _K ôkotsu kinbungaku ronshû_ 甲 骨 金 文 學 論 集. Kyoto: Hôyû shoten.
Shirakawa, Shizuka 白 川 靜. 1976. _Kanji no sekai_ 漢 字 の 世 界. 2 vols. Tokyo: Heibonsha.
_Shisanjing zhushu_ 十 三 經 注 疏. Ed. Ruan Yuan 阮 元 (1764–1849). Shanghai: Zhonghua shuju, 1957 (reprint of _Sibu beiyao_ ed.).
_Shizi_ 尸 子. Ca. third to first centuries B.C. _Sibu beiyao_ ed.
_Shuoyuan_ 説 苑. Liu Xiang 劉 向 (79–78 B.C.). _Sibu beiyao_ ed.
_Sibu beiyao_ 四 部 備 要. Shanghai: Zhonghua shuju, 1927–35.
_Sibu congkan_ 四 部 叢 刊 3 ser. Shanghai: Shangwu yinshuguan, 1920–36.
_Siku quanshu_ 四 庫 全 書. Taibei: Shangwu yinshuguan (reproduction of 1782 Wenyuange woodblock ed.).
Sivin, N. 1987. _Traditional Medicine in Contemporary China_. Ann Arbor: University of Michigan Center for Chinese Studies.
Sivin, N. 1992. "Ruminations on the Tao and Its Disputers" (rev. of Graham 1989). _Philosophy East and West_ 42. 21–29.
Sivin, N. 1993. " _Huang ti nei ching_." Loewe 1993. 196–215.
Sun, Ji 孫 僟. 1991. _Han dai wuzhi wenhua ziliao tushuo_ 熯 代 物 質 文 化 資 科 圖 説. Beijing: Wenwu chubanshe.
_Sun ü miaolun_ 素 女 妙 論. Ming period. References are to the edition in R. van Gulik, _Erotic Colour Prints of the Ming Period, with an Essay on Chinese Sexual Life from the Han to the Ch 'ing Dynasty, B.C. 206-A.D. 1644_. 3 vols. Tokyo: private publication, 1951. Vol. 2. 115–139.
_Suwen_ 素 問. Tang period recension of Han period _Huangdi neijing_. _Sibu beiyao_ ed. Commentaries cited: Wang Bing 王冰 (eighth century).
_Taiping yulan_ 太 平 御 覽. Li Fang 李 昉 (925–96) and others. Beijing: Zhonghua shuju, 1960 (reproduction of Song woodblock ed.).
_Taipingjing_ 太 平 經. Ca. second century A.D. References are to _Taipingjing hejiao_ 太 平 經 合 校. Ed. Wang Ming 王 明. Beijing: Zhonghua shuju, 1979.
_Taisu_ 太 素. Sui period recension of Han period _Huangdi neijing_. _Congshu jicheng_ ed. Commentaries cited: Yang Shangshan 楊 上 善 (fl. 610).
Tambiah, S. 1990. _Magic, Science, Religion, and the Scope of Rationality_. Cambridge: Cambridge University Press.
Tang, Lan 唐 蘭. 1979. "Shilun Mawangdui sanhao Han mu chutu _Daoyin tu_ " 試 論 馬 王 堆 三 號 漢 墓 出 土 導 引 圖. Mawangdui Han mu boshu zhengli xiaozu 1979. 1–10.
Tate, G. 1947. _Mammals of Eastern Asia_. New York: Macmillan Company.
Tsien, T. 1962. _Written on Bamboo and Silk: The Beginnings of Chinese Books and Inscriptions_. Chicago: University of Chicago Press.
Twitchett, D. and M. Loewe, eds. 1986. _The Cambridge History of China_ , vol. 1 (The Ch'in and Han Empires, 221 B.C.-A.D. 220). Cambridge: Cambridge University Press.
Unschuld, P. 1975. "Zur Bedeutung des Terminus _tu_ in der traditionellen medizinisch-pharmazeutischen Literatur Chinas." _Sudhoffs Archiv_ 57. 165–183.
Unschuld, P. 1982a. "Der Wind als Ursache des Krankseins: Einige Gedanken zu Yamada Keijis Analyse der _Shao-shih_ Texte des _Huang-ti nei-ching_." _T'oung Pao_ 68. 91–131.
Unschuld, P. 1982b. "Ma-wang-tui _Materia Medica_ : A Comparative Analysis of Early Chinese Pharmaceutical Knowledge." _Zinbun: Memoirs of the Research Institute for Humanistic Studies, Kyoto University_ 18. 11–63.
Unschuld, P. 1985. _Medicine in China: A History of Ideas_. Berkeley: University of California Press.
Unschuld, P. 1986a. _Medicine in China: A History of Pharmaceutics_. Berkeley: University of California Press.
Unschuld, P, trans. 1986b. _Nan-ching: The Classic of Difficult Issues_. Berkeley: University of California Press.
Unschuld, P. 1987. "Traditional Chinese Medicine: Some Historical and Epistemological Reflections." _Social Science and Medicine_ 24. 1023–1029.
Unschuld, P. 1993. "History of Chinese Medicine." Kiple 1993. 20–27.
Vickers, B. 1984. Introduction. _Occult and Scientific Mentalities in the Renaissance_. Ed. B. Vickers. Cambridge: Cambridge University Press.
_WWYJ. Wuwei Handai yijian_ 武 威 漢 代 醫 簡. Ed. Gansu sheng bowuguan 甘 肅 省 博 物 館 and Wuwei xian wen-huaguan 武 威 縣 文 化 館. Beijing: Wenwu chubanshe, 1975
_Waitai biyaofang_ 外 臺 秘 要 方. Wang Tao 王 壽 (eighth century). _Siku quanshu_ ed.
Wang, Shimin 王 世 民. 1986. "Mawangdui boshu" 馬 王 堆 帛 書. _Zhongguo da baike quanshu: kaoguxue_ 中 國 大 百 枓 全 書: 考 古 學. Beijing: Zhongguo da baike quanshu chubanshe. 307–309.
Wang, Yucheng 王 育 成. 1991. "Dong Han daofo shili" 東 漢 道 符 釋 例. _Kaogu xuebao_ 考 古 學 報 1991.1. 45–56.
Wei, Qipeng 魏 啓 鵬 and Hu Xianghua 胡 翔 驊. 1992. _Mawangdui Han mu yishu jiaoshi_ 馬 主 堆 漢 墓 醫 書 校 釋. 2 vols. Chengdu: Chengdu chubanshe.
_Wenxuan_ 文 選. Xiao Tong 蕭 統 (501–531). _Sibu beiyao_ ed.
Wile, D. 1992. _Art of the Bedchamber: The Chinese Sexual Yoga Classics Including Women's Solo Meditation Texts_. Albany: State University of New York Press.
_Wuzazu_ 五 雜 俎. Xie Zhaozhe 謝 肇 淛 (1567–1624). 1795 Japanese woodblock ed.
Xia, De'an 夏 德 安 (D. Harper). 1994. " _Wushier bingfang_ yu Yue fang" 五 十 二 病 方 與 越 方. _Mawangdui Han mu yanjiu wenji_ 馬 王 堆 漢 龛 研 究 文 集. Ed. Hunan sheng bowuguan 湖 南 省 博 物 館. Changsha: Hunan chubanshe. 118–124.
Xiao Han 曉 菌 (pen name for Han Zhongmin, which also see). 1974. "Changsha Mawangdui Han mu boshu gaishu" 長 沙 馬 王 堆 漢 夢 帛 書 概 述. _Wenwu_ 文 物 1974.9. 40–44.
_Xijing zaji_ 西 京 雜 記. Ca. fourth century. _Sibu congkan_ ed.
_Xinxu_ 新 序. Liu Xiang 劉 向 (79–8 B.C.). _Congshu jicheng_ ed.
_Xinyu_ 新 語. Lu Jia 陸 賈 (fl. 200–180 B.C.). _Sibu beiyao_ ed.
_Xunzi_ 荀 子. Xun Qing 荀 (ca. 298–ca. 238 B.C.). _Zhuzi jicheng_ ed.
_YSSW_. Zhangjiashan Han jian zhenglizu 張 家 山 漢 簡 整 理 組. "Zhangjiashan Han jian _Yinshu_ shiwen" 張 家 山 漢 簡 引 書 釋. _Wenwu_ 文 物 1990.10. 82–86.
Yamada, Keiji 山 田 慶 兒. 1979. "The Formation of the _Huang-ti Nei-ching_." _Acta Asiatica_ 36. 67–89.
Yamada, Keiji 山 田 慶 兒. 1980. "Kyû-ku hachi-fu setsu to shôshiha no tachiba" 九 宫 八 風 説 と 少 師 派 の 立 場. _T ôhô gakuhô_ 東 方 學 報 52. 199–242.
Yamada, Keiji 山 田 慶 兒. 1985a. "Shinkyû to tôeki no kigen" 緘 灸 湯 液 と 起 の. _KGS_ , vol. 2. 3–122.
Yamada, Keiji 山 田 慶 兒. 1985b. "Ma-o-tai Kan bo shutsudo isho sansoku" 馬 王 堆 漢 墓 出 土 醫 書 三 則. _KGS_ , vol. 2. 225–262.
Yamada, Keiji 山 田 慶 兒. 1988. "Hen Shaku densetsu" 扁昔 傳 説. _T ôhô gakuhô_ 東 方 學 報 60. 73–158.
Yamada, Keiji 山 田 慶 兒. 1990. "Igaku no denju" 醫 學 の 傳 授. _Ya naku tori: igaku, jujutsu, densetsu_ 夜 鳴 〱 鳥: 醫 學 说 術 傳 説. By Yamada Keiji. Tokyo: Iwanami shoten. 55–96.
Yang, Shuda 楊 樹 逢. 1986. _Ciquan_ 詞 詮. Shanghai: Guji chubanshe.
_Yanzi chunqiu_ 晏 子 春 秋. Ca. fourth century B.C. _Zhuzi jicheng_ ed.
Yasui, Kôzan 安 居 香 山 and Nakamura Shôhachi 中 村 璋 八. 1971–92. _J ûshû isho shûsei_ 重 修 緯 書 集 成. 6 vols. Tokyo: Meitoku shuppansha.
_Yijing_ 烏 經. Zhou period. _Shisanjing zhushu_ ed. Commentaries cited: Wang Bi 王 弼 (226–249).
_Yili_ 儀 禮. Ca. third to second centuries B.C. _Shisanjing zhushu_ ed. Commentaries cited: Zheng Xuan 鄭 玄 (127–200).
Yoneda, Kaisuke 米 田 該 典. 1988. "Chûgoku kodai isho chû no yakubutsu no bussanshi teki kôsatsu" 中 國 古 代 醫 書 中 の 寿 物 の 物 産 誌 的 考 察. Sakade 1988. 45–63.
Yu, Yan 余 嚴. 1972. _Gudai jibing minghou shuyi_ 古 代 疾 病 名 候 疏 義. Taibei: Ziyou chubanshe.
Yu, Ying-shih. 1977. "Han." _Food in Chinese Culture: Anthropological and Historical Perspectives_. Ed. K. Chang. New Haven: Yale University Press. 55–83.
_Yunji qiqian_ 雲 发 七 籤. Zhang Junfang 張 君 房 (fl. first quarter of the eleventh century). _Daozang_ ed. ( _HY_ 1026).
_ZY. Zhongyao dacidian_ 中 藥 大 辭 典. Ed. Jiangsu xin yixueyuan 江 蘇 新 醫 學 院. 3 vols. Shanghai: Shanghai kexue jishu chubanshe, 1977–79.
Zhang, Peiyu 張 培 瑜. 1989. "Chutu Han jian boshu shang de li zhu" 出 土 瘼 簡 帛 書 上 的 曆 注. _Chutu wenxian yanjiu xuji_ 出 土 女 獻 研 究 續 集. Ed. Guojia wenwuju gu-wenxian yanjiushi 國 家 文 物 局 古 文 獻 研 究 室. Beijing: Wenwu chubanshe.
Zhangjiashan Han mu zhujian zhengli xiaozu 張 家 山 漢 墓 竹 簡 整 理 小 組. 1985. "Jiangling Zhangjiashan Han jian gaishu" 江 陵 張 家 山 漢 簡 概 述. _Wenwu_ 文 物 1985.1. 9–15.
_Zhanguoce_ 戰 國 策. Third century B.C. _Sibu beiyao_ ed.
Zhao, Pushan 趙 璞 珊. 1986. " _Shanhaijing_ jizai de yaowu, jibing he wuyi" 山 海 經 記 載 的 藥 物 疾 病 和 巫 醫. _Shanhaijing xintan_ 山 海 系 坐 新 探. Ed. Zhongguo _Shanhaijing_ xueshu taolunhui 中 國 山 海 經 學 術 討 論 會. Chengdu: Sichuan sheng shehui kexueyuan chubanshe.
Zhao, Youchen 趙 有 臣. 1981. " _Wushier bingfang_ zhong 'duo' zi de kaoshi" 五 十 二 病 方 中 隋 字 的 考釋. _Wenwu_ 文 物 1981.3. 22.
_Zhenjiu jiayi jing_ 緘 灸 甲 乙 經. Huangfu Mi 皇 甫 謐 (third century). _Siku quanshu_ ed.
Zhong, Yiyan 鐘 依 研 (pen name for Ma Jixing, which also see). 1972. "Xi Han Liu Sheng mu chutu de yiliao qiju" 西 漢 劉 勝 墓 出 土 的 臀 療 器 具. _Kaogu_ 考 古. 1972.3. 49–53
Zhou, Yao 周 堯. 1957. _Zhongguo zaoqi kunchongxue yanjiushi_ 中 國 早 期 昆 蟲 學 研 究 史. Beijing: Kexue chubanshe.
Zhou, Yimou 周 一 謀 and Xiao Zuotao 蕭 佐 兆, eds. 1988. _Mawangdui yishu kaozhu_ 馬 王 堆 醫 書 考 注. Tianjin: Tianjin kexue jishu chubanshe.
_Zhouli_ 周 禮. Third to second centuries B.C. _Shisanjing zhushu_ ed. Commentaries cited: Zheng Xuan 鄭 玄 (127–200); Zheng Sinong 鄭 司 農 (d. A.D. 83).
_Zhuangzi_ 莊 子. Zhuang Zhou 莊 周 and others, fourth to second centuries B.C. References are to _Zhuangzi jishi_ 莊 子 集 釋. Ed. Guo Qingfan 郭 享 艮 慶 藩 (1844–1896). _Zhuzi jicheng_ ed. Commentaries cited: Cheng Xuanying 成 玄 英 (fl. 631).
_Zhuzi jicheng_ 諸 子 集 成. Beijing: Zhonghua shuju, 1954.
_Zunsheng bajian_ 遵 生 ハ 箋. Gao Lian 高 濂 (fl. 1570–1591). Chengdu: Ba Shu shushe, 1992.
_Zuozhuan_ 左 傳. Fourth century B.C. _Shisanjing zhushu_ ed.
Index of Materia Medica
Materia medica is indexed by entry in the Translation. The name of a substance may occur more than once in the same entry; the index does not provide a lexical count of the total number of occurrences of a given name in the manuscripts. Materia medica is defined broadly to include nearly everything that forms part of the treatment of ailments or the execution of techniques; cooking pots, dishes, and sundry utensils used solely in the preparation of drags are excluded. A few fragmentary drug names have been omitted. An asterisk following an entry indicates further discussion in a footnote in that entry. If the names of plants, animals, and minerals can be identified with a high degree of certainty, relevant citations to _GM_ and _ZY_ are provided (those occurring in _BC_ are also noted; reference to _ZY_ is omitted for some common animals and minerals). If the identification is uncertain, likely identifications are often discussed in the footnotes. Citations to _ZY_ are to the entry that provides the basic description of the plant, animal, or mineral, which may be the source of several drags having separate _ZY_ entries; the _ZY_ entry cited may not correspond to the specific drug in the manuscripts. Similarly, the index does not correlate every drag in the manuscripts (e.g. the various parts of a plant or animal) with a corresponding drug in _BC_ or _GM_ ; most _GM_ citations are to the main entry for a plant, animal, or mineral, not to the individual drags listed after the main entry in _GM_ (see also the index of materia medica in Ma Jixing 1992: 1073–98, which notes likely correlations between the Mawangdui medical manuscripts and later materia medica). Some headings in the index provide subheadings for the parts of a substance used as drags in the manuscripts. However, occasional references in the manuscripts to the root, fruit, leaf, stalk, or other parts of many substances are not specified in the index. Chinese graphs are provided selectively; they often represent a standard graph in received literature, not the graph written on the original manuscripts.
**ai** 艾 (mugwort). _GM_ , 15.7. _ZY_ : no. 1175, _Artemisia argyi_ Lévl, et Vant.
I.E.127,* I.E.155, III.89
**alkaline soil**
I.E.185*
**ant**. _GM_ , 40.106
red ant
III.38
anthill loam ( _GM_ , 7.77)
I.E.25*
**amputee peg**
I.E.119*
**Ba** **_shu_** 巴 寂 (croton). _GM_ , 35.63. _ZY_ : no. 1028, _Croton tiglium_ L.
IV.10,* IV.12
**_bahe_** 罷 合
I.E.163*
**_bai_** 柏 (arbor-vitae). _BC. GM_ , 34.78. _ZY_ : no. 2840, _Biota orientalis_ (L.) Endl.
VI.A.10
_bai_ (arbor-vitae) fruit. Kernels of arbor-vitae ( _ZY_ : no. 3154)
VI.A.2
_bai_ (arbor-vitae) pestle
I.E.118
**_bai mugou_** 白 牡 狗
V.8*
**_bai tengshe_** 白 臜 蛇
III.77*
**_baifu_** 白 付
I.E.254*
**_baifu_** 白 拊
I.E.279*
**_baifu_** 白 符
III.62*
**_baihao_** 白 嵩 (artemisia; see also **_hao, qinghao_** ). _BC. GM_ , 15.15. _ZY_ : no. 1392, _Artemisia sieversiana_ Ehrh. ex Willd.
I.E.47
**_baiheng_** 白 衡
I.E.230*
**_bailian_** 白 蔽 (ampelopsis). _BC_. _GM_ , 18.48. _ZY_ : no. 1393, _Ampelopsis japonica_ (Thunb.) Mak.
I.E.157, I.E.160, I.E.163, I.E.166
**_baiyu_** 白 魚 (silverfish)
I.E.133*
**_baizhi_** 白 宦 (angelica). _BC. GM_ , 14.11. _ZY_ : no. 1380, _Angelica dahurica_ (Fisch. ex Hoffm.) Benth. et Hook. f. ex Franch. et Sav. and other spp.
I.E.230
**bamboo**. _BC. GM_ , 37.15
autumn bamboo
I.E.193
**_banmao_** 螌 畺 (blister beetle). _GM_ , 40.93. _ZY_ : no. 4730, _Mylabris phalerata_ Pall. and _M. cichorii_ L. (drag known as Spanish fly)
III.38, III.55
**_banxia_** 半 夏 (pinellia). _BC. GM_ , 17.57. _ZY_ : no. 1550, _Pinellia ternata_ (Thunb.) Breit.
I.E.232
**bark**
I.E.204
**bat**. _BC. GM_ , 48.102. _ZY_ : no. 5479.
I.E.271
**bean leaves**
I.E.111*
**bee**
III.58
bee egg, bee larva ( _BC. GM_ , 39.61)
I.E.130, I.E.141, I.E.223,* V.11
bee (venom)
III.37, IV.7
**beetle larva**
III.7*
**_beixie_** 萆 藓 (yam). _GM_ , 18.44. _ZY_ : no. 4120, _Dioscorea hypoglauca_ Palib. and other spp.
III.50,* III.60, III.70
**_bie_** 驚 (soft-shelled turtle). _GM_ , 44.11. _ZY_ : no. 5707, _Amyda sinensis_ (Wiegmann)
IV.39
**bird egg** (see also **spring-bird egg, virile-bird egg** )
I.E.74,* III.41, IV.1
**bird feathers**
I.E.132
**bronze bits**
I.E.207*
**broom**
worn out broom
I.E.66
**bulging fungus**
III.36*
**cai** 采 (oak)
_cai_ (oak) mallet
I.E.134
_cai_ (oak) peg
I.E.134*
**cattail mat**. _GM_ , 38.45
I.E.8
soft leaves from cattail mat
I.E.64
worn out cattail mat
I.E.64
**_changzu_** 長 足 (spider; see also **spider web** )
I.E.133*
**_chejian_** 車 踐 (plantain). _GM_ , 16.113. _ZY_ : no. 0799, _Plantago asiatica_ L.
III.35*
**chicken**. _BC. GM_ , 48.69
III.37, III.79
white chicken
I.E.71
yellow chicken
I.E.150
chicken blood
I.E.75
chicken brain
III.34
chicken breast
III.34
chicken egg
I.E.180, III.15, IV.24, VI.A.9
chicken feathers
I.E.5, I.E.150
chicken feces
I.E.235
chicken heart
III.34
black hen
V.15
rooster
I.E.58, III.11
black rooster
I.E.274, III.34
rooster blood
III.54
rooster feces
I.E.242
stillborn chick
III.27*
**_chida_** 赤 荅 (adzuki bean). _BC_. _GM_ , 24.94. _ZY_ : no. 2222, _Phaseolus calcaratus_ Roxb.
I.E.3*
**_Chou_** 螑
III.76*
**cinnabar**. _BC_. _GM_ , 9.51
I.E.75, I.E.188, I.E.281, III.29
**clod**
I.E.67
**cloth**
I.E.124
**_cong_** 葱 (onion). _BC_. _GM_ , 26.44. _ZY_ : no. 4813, _Allium fistulosum_ L.
I.E.88, I.E.270
**copper bits**
I.E.144,* I.E.207
**cord handle from steaming-pot**
I.E.132,* V.7
**cow**. _BC. GM_ , 50.64
beef
III.50, V.3
choice beef
I.E.35,* III.25
beef suet
I.E.205, I.E.230, I.E.232
cow gall
I.E.137*
cow horn
III.24
cow saliva
I.E.46
**_daishen_** 戴 糝 (astragalus; see also **_huangqi_** _)_
I.E.166*
**dandruff** (see **human** )
**_dang_** 壋
I.E.76*
**deer**. _BC. GM_ , 51.24
I.E.61
choice venison
III.25
deer horn
I.E.55
**_dianji_** 顛 棘 (asparagus). _GM_ , 18.37. _ZY_ : no. 0645, _Asparagus cochinchinensis_ (Lour.) Merr. and other spp.
III.2,* III.34
**_didan chong_** 地 膽 蟲 (oil beetle). _BC_. _GM_ , 40.96. _ZY_ : no. 1611, _Meloë coarctatus_ Motsch.
I.E.146
**dirt from bottom of water jar**
I.E.31
**dog**. _BC_. _GM_ , 50.43
I.E.22, 111.75, III.80
dog bile
I.E.194, I.E.257
dog feces
I.E.71
dog fur
I.E.176
dog heart
III.34
dog liver
III.34
dog lung
III.34
dog penis
V.11
**dove**. _GM_ , 49.2. _ZY_ : no. 4728
female dove tail
VII.A.4
male dove claw
VII.A.5
**_du_** [1] 獨
I.E.13,* I.E.138
**_dujin_** 毒 董
I.E.95*
**_duyu_** 杜 虞
IV.2*
**earth**
earth from marketplace
V.17
frozen earth
I.E.267
**earthworm**. _GM_ , 42.40
white-necked earthworm
III.31*
earthworm excrement
I.E.31,* IV.42
**egg**
I.E.79, I.E.122
**ewe** (see **sheep** )
**eyebrow** (see **human** )
**_fangfeng_** 防 風 (saposhnikovia). _BC. GM_ , 13.47. _ZY_ : no. 1985, _Saposhnikovia divaricata_ (Turcz.) Schischk. and other plants
I.E.151, III.49, III.52, III.78
**_fangkui_** 防 葵
III.77*
**_fanshi_** 潘 石, **_fanshi_** 蕃 石
III.39,* IV.8, IV.9, IV.11, IV.12
**_feilian_** 非 廉
III.77*
**_fenshu_** 鼢 鼠 (mole). _GM_ , 51.67. _ZY_ : no. 5763, _Scaptochirus moschatus_ Milne-Edwards and _Mogera robusta_ Nehring
I.E.17*
**fermented beverage** ( _jiang_ 獎)
III.2*
**fingernail** (see **human** )
**fish**
I.E.78
**food sacrifice**
I.E.129,* I.E.143
**_fuling_** 苻 苓 (pine truffle). _BC. GM_ , 37.2. _ZY_ : no. 3314, _Poria cocos_ (Schw.) Wolf
I.E.251, III.8, III.24, III.36, III.62
**_futu_** 伏 兔
III.78*
**_fuyu_** 鮒 魚 (golden carp). _GM_ , 44.98. _ZY_ : no. 5510, _Carassius auratus_ (L.)
I.E.147
**_gancao_** 甘 草 (licorice). _BC. GM_ , 12A.81. _ZY_ : no. 1187, _Glycyrrhiza uralensis_ Fisch.
I.E.2, I.E.13, I.E.17, I.E.24, I.E.160
**_gaoben_** 藥 本 (lovage). _GM_ , 14.10. _ZY_ : no. 5616, _Ligusticum sinense_ Oliv. and other spp.
III.67
**_ge_** 葛 (kudzu). _BC_. _GM_ , 18.33. _ZY_ : no. 4796, _Pueraria lobata_ (Willd.) Ohwi
_ge_ (kudzu) arrow
I.E.132
**gecko**. _GM_ , 43.63. _ZY_ : no. 5604, _Gekko swinhoana_ Günther and other spp.
III.28,* III.29
**gelatin**
I.E.74,* I.E.77, I.E.94, I.E.96, I.E.105
**gourd**
I.E.60,* I.E.134, I.E.137, I.E.277
**grain**
IV.29
grain plants
I.E.65,* I.E.72
five grains
I.E.58*
cooked grain
III.78
grain rinse
I.E.254*
grain-cleaning slop ( _GM_ , 22.68)
I.E.162,* I.E.226
**grease**
carriage grease ( _GM_ , 38.48)
I.E.253
hub grease
I.E.202*
**gruel**
I.E.274, III.5
**_gu_** 毂 (paper mulberry). _BC. GM_ , 36.78. _ZY_ : no. 4754, _Broussonetia papyrifera_ (L.) Vent.
_gu_ (paper mulberry) liquid
I.E.222,* III.38, IV.5, IV.6
**_gui_** 桂 (cinnamon). _BC. GM_ , 34.88. _ZY_ : no. 1790, _Cinnamomum cassia_ Presl.
I.E.2, I.E.35, I.E.139, I.E.147, I.E.151, I.E.157, I.E.171, I.E.173, I.E.212, I.E.248, I.E.275, III.22, III.39, III.62, IV.5, IV.9–11 _jungui_ 菌 桂 (curled cinnamon)
I.E.138,* I.E.230, III.24, III.53, III.61
**_gui_** 跪
I.E.51*
**hair** (see **human** )
**_hao_** 嵩 (artemisia; see also **_baihao, qinghao_** )
V.10
**_hao_** 蒿 **from under magpie dwelling**
I.E.115*
**_helu_** 合 盧
I.E.36*
**hemp thill-rope**
III.86
**hen** (see **chicken** )
**_hengshi_** 恒 石
I.E.28*
**honey**. _BC. GM_ , 39.56
III.22, IV.10, IV.13
**_hongfu_** 紅 符
III.62*
**horse**. _BC. GM_ , 50.76
III.62, III.70, V.8
horse cheekbone
I.E.280
horsehair
IV.33
horse lard
III.79
horse manure
I.E.117
horse sauce
III.51
**_houpu_** 厚 撲 (magnolia bark). _BC. GM_ , 35.6. _ZY_ : no. 3366, bark _of Magnolia officinalis_ Rehd. et Wils.
I.E.177
**_hua_** 裤 (birch)
I.E.85*
**_huai_** 槐 (pagoda tree). _BC. GM_ , 35.25. _ZY_ : no. 5078, _Sophora japonica_ L.
I.E.264, III.68
**_huangqi_** 黄 耆 (astragalus; see also **_daishen_** ). _BC. GM_ , 12A.85. _ZY_ : no. 4153, _Astragalus membranaceus_ (Fisch.) Bge. and other spp.
I.E.157, I.E.160
**_huangqin_** 黄 芩 (skullcap). _BC. GM_ , 13.49. _ZY_ : no. 4147, _Scutellaria baicalensis_ Georgi and other spp.
I.E.13, I.E.14, I.E.24, I.E.36, I.E.153, I.E.166
**human**
dandruff ( _GM_ , 52.85)
I.E.100, I.E.212, I.E.249
dead person's head ( _GM_ , 52.105)
I.E.143
dead person's shinbone ( _GM_ , 52.104)
I.E.218
eyebrow
VII.A.6
fingernail ( _GM_ , 52.86)
VII.A.5
hair (loose hair, scalp hair; _GM_ , 52.81)
I.E.5,* I.E.205*
human sludge
I.E.176*
man's slime
I.E.11*
man's muck
I.E.188*
menstrual cloth ( _GM_ , 52.99)
I.E.86, I.E.121, I.E.139, I.E.148, I.E.184, I.E.272, I.E.275, III.85
milk ( _GM_ , 52.97; see also **milk** )
I.E.181*
spit
I.E.27, I.E.48, I.E.178, I.E.229, I.E.233, I.E.234
urine ( _GM_ , 52.90)
I.E.55, I.E.116, I.E.147, I.E.154, I.E.256, V.10
urine of infant
I.E.200
urine of young boy
I.E.37, I.E.213, I.E.215
sludge from urine
I.E.198*
**hundred grass residue** (see also **stove** **ash** )
I.E.5*
**iron**. _BC. GM_ , 8.26
I.E.41, III.31
iron forging ash
I.E.278*
iron mallet
I.E.120
**_ji_** 薺 (capsella). _GM_ , 27.94. _ZY_ : 3328, _Capsella bursa-pastoris_ (L.) Medic.
I.E.4,* I.E.18
**_ji_** 薊 (thistle)
I.E.53*
**_jichi_** 齊 赤
I.E.37*
**_jili_** 後 藜 (caltrop). _BC. GM_ , 16.140. _ZY_ : no. 2602, _Tribulus terrestris_ L.
I.E.47
**_jian_** 煎
I.E.69*
**_jian_** 菅 (miscanthus)
I.E.150*
**_jiang_** 墓 (ginger). _BC. GM_ , 26.76. _ZY_ : no. 1358, _Zingiber officinale_ Rosc.
I.E.2, I.E.147, I.E.157, I.E.160, I.E.171, I.E.230, 111.22, 111.24, III.61, III.62, III.74, IV.5, IV.9–11
**_jiao_** 椒 (zanthoxylum). _BC. GM_ , 32.29. _ZY_ : no. 2152, _Zanthoxylum bungeanum_ Maxim. and other spp.
I.E.2,* I.E.103, I.E.157, I.E.171, I.E.173, IV.5
Qin _jiao_ 秦 椒 (Qin zanthoxylum)
III.53
Shu _jiao_ 蜀 椒 (Shu zanthoxylum)
I.E.160, I.E.212
**_jie_** 界
III.49*
**_jie_** 節
III.72,* III.74
**_jie zhong jia_** 芥 衷 莢
I.E.117*
**_jiegeng_** 桔 梗 (balloon flower). _GM_ , 12.100. _ZY_ : no. 3642, _Platy-codon grandiflorum_ (Jacq.) A. DC.
III.70, III.77
**_jin_** 堇
I.E.55,* I.E.197
**_jing_** 荆 (vitex). _GM_ , 36.114. _ZY_ : no. 2295, _Vitex negundo_ L. var. _cannabifolia_ (Sieb. et Zucc.) Hand.-Mazz.
I.E.108, III.83
_jing_ (vitex) winnowing basket
I.E.220
**_jingtian_** 景 天 (stonecrop). _BC. GM_ , 20.6. _ZY_ : no. 4937, _Sedum erythrostictum_ Miq.
I.E.102
**_jinkui_** 堇 葵
I.E.244*
**_jiu_** 韭 (leek). _GM_ , 26.40. _ZY_ : no. 3394, _Allium tuberosum_ Rottler
VI.A.9
**_jiuzong_** 九 宗 **herb**
V.16*
**_jueweng_** 爵 饔 (caterpillar cocoon). _GM_ , 39.77. _ZY_ : no. 4311, cocoon and larva of _Monema flavescens_ Walker
V.9
**_konglei_** 空 壘
**_ku_** 苦
I.E.40*
**_kuhu_** 苦 瓠 (bitter gourd). _BC. GM_ , 28.6. _ZY_ : no. 2653, _Lagenaria siceraria_ (Molina) Standi, var. _gourda_ Ser.
I.E.214, III.31
**_kui_** 葵 (mallow). _BC. GM_ , 16.88. _ZY_ : no. 1536, _Malva verticillata_ L.
I.E.98, I.E.99, I.E.247, I.E.258
_kui_ (mallow) seed
I.E.90, I.E.96, I.E.101, I.E.116, III.48
_kui_ (mallow) stalk
I.E.69, I.E.217
**lacquered** **_guo_** 椁
I.E.245*
**_lai_** 萊 (chenopodium). _GM_ , 27.115. _ZY_ : no. 5651, _Chenopodium album_ L.
III.6
**_lan_** 蘭 (eupatorium; see also **_xian_** ). _BC. GM_ , 14.56. _ZY_ : no. 2841, _Eupatorium fortunei_ Turcz.
I.E.52, I.E.81, I.E.84, I.E.254
_lan_ (eupatorium) fruit
IV 31
_lan_ (eupatorium) leaf
IV.41
**_langya_** 狼 牙
I.E.239*
**lard** ( _gao_ 膏)
I.E.2,* I.E.12, I.E.135, I.E.152, I.E.174
old lard
I.E.76, I.E.262
rancid lard
I.E.15,* I.E.143, I.E.218, III.33
horse lard
III.79
leopard lard ( _GM_ , 51.8)
I.E.206
pig lard
I.E.10, I.E.14, I.E.21, I.E.24, I.E.26, I.E.164, I.E.196, I.E.201, I.E.204, I.E.207, I.E.221, I.E.241, I.E.254, I.E.256, I.E.259, I.E.280, III.58
castrated pig lard
I.E.195, I.E.218
rancid pig lard
I.E.214, I.E.217, I.E.220, I.E.281
snake lard
I.E.219
**_leishi_** 雷 (bamboo truffle). _BC. GM_ , 37.10. _ZY_ : no. 5148, _Polyporus mylittae_ Cook, et Mass.
I.E.26, I.E.282
**leopard** (see **lard** )
**_li_** 李 (plum). _GM_ , 29.33. _ZY_ : no. 2247, _Prunus salicina_ Lindl.
I.E.20
**_li_** 貍 (raccoon-dog)
I.E.62*
**_lianghuang_** 量 賛
I.E.139*
**lichen**. _GM_ , 21.17
III.79*
**_lilu_** 藜 盧 (black veratrum). _BC. GM_ , 17.30. _ZY_ : no. 5652, _Veratrum nigrum_ and other spp.
I.E.212, I.E.223, I.E.227, I.E.253, I.E.256, I.E.259
**_lin_** 臨
III.39*
**_linggao_** 陵 藁 (spurge). _GM_ , 17.16. _ZY_ : no. 1188, _Euphorbia kansui_ Liou
IV.7
**_lingji_** 菱 芰 (water chestnut). _GM_ , 33.69. _ZY_ : no. 4100, _Trapa bispinosa_ Roxb.
I.E.213, I.E.215, I.E.250, I.E.257, IV.31
**liquor** ( _jiu_ 酒).
I.E.5, I.E.17, I.E.18, I.E.22, I.E.33, I.E.52, I.E.62, I.E.74, I.E.100, I.E.103, I.E.106, I.E.109, I.E.113, I.E.123, I.E.136, I.E.142, I.E.167, I.E.171, I.E.187, I.E.204, I.E.206, I.E.252, I.E.255, I.E.274, III.6, III.10, III.13, III.15, III.54, III.74, III.78, V.5, V.12, V.16, VI.A.9, VII.A.6
clear liquor ( _qing_ 清)
I.E.77*
mash-liquor ( _laozhuo_ 醪 酌)
III.10,* III.72–74, III.92
pure liquor ( _chunjiu_ 淳 酒)
I.E.4,* I.E.18, I.E.19, I.E.23, I.E.82, I.E.94, I.E.102, I.E.135, I.E.164, I.E.172, I.E.250, III.70, IV.24
pure liquor lees
III.58
sweet-liquor ( _li_ 醴)
III.4,* III.10, III.12, III.32, III.67, III.92, IV.25
**_liu_** 柳 (willow). _GM_ , 35.45. _ZY_ : no. 3175, _Salix babylonica_ L.
_liufu_ 柳 柎 (willow catkin)
III.33*
_liuxun_ 柳 輩 (willow fungus)
I.E.155*
**lizard**
red lizard blood
I.E.203*
**_longkai_** 龍 慨
III.78*
**_longxu_** 龍 須 (bog rush). _BC. GM_ , 15.69. _ZY_ : no. 1227, _Juncus effusus_ L. var. _decipiens_ Buchen. f. _utilis_ Mak.
I.E.91
**_loulu_** 漏 蘆
I.E.241*
**_luoruan_** 騎 阮
I.E.149*
**malt** ( _nie_ ) _GM_ , 25.19
I.E.22,* I.E.177, I.E.181
roasted-grain meal of malt (see also **roasted-grain meal** )
III.17
**man** (see **human** )
**_mao_** 茅 (woolly grass). _BC_. _GM_ , 13.64. _ZY_ : no. 1435, _Imperata cylindrica_ (L.) P. Beauv. var. _major_ (Nees) C. E. Hubb.
I.E.138,* III.89
**meat**
I.E.121
**_mei_** 莓 (berry)
_mei_ (berry) vine
I.E.283*
**melon**
I.E.189
**_mendong_** 門 冬
III.36,* III.52, III.70
**menstrual cloth** (see **human** )
**mercury**. _BC. GM_ , 9.56
I.E.188, I.E.207, I.E.222, I.E.230, I.E.249
**milk** (see **also human** )
fermented milk ( _lao_ 酪, _zhongjiu_ 湩 酒)
III.43, VI.A.8*
**millet**
blue choice millet
I.E.57*
panicled millet ( _ji_ 稷). _GM_ , 23.69. _ZY_ : no. 5003, _Panicum miliaceum_ L.
I.E.113
glutinous panicled millet ( _shu_ 黍). _GM_ , 23.71. _ZY_ : no. 5003, _Panicum miliaceum_ L., glutinous var.
I.E.50, I.E.113, I.E.144, I.E.194, III.4, III.74, IV.4
glutinous panicled millet slop
I.E.266, IV.3
glutinous spiked millet ( _shu_ 秫). _GM_ , 23.78. _ZY_ : no. 4841, _Setaria italica_ (L.) Beauv., glutinous var.
I.E.50, I.E.179, III.2
**_miwu_** 蘼 蕪 (lovage). _BC_. _GM_ , 14.5. _ZY_ : no. 0452, _Ligusticum wallichii_ Franch.
I.E.42, I.E.151
**_mu_** 牡
V.10*
**_mulou_** 牡 螻
III.43*
**mud**
VII.A.1*
mud from well
I.E.63
**_niuxi_** 牛 膝 (achyranthes). _BC. GM_ , 16.79. _ZY_ : no. 0833, _Achyranthes bidentata_ Bl.
I.E.205, III.67, III.70
**_nüluo_** 女 羅
IV.28*
**oblong stone**
I.E.146
**oyster**. _BC. GM_ , 46.21
I.E.95, III.53
**_penglei_** 蓬 躉 (raspberry). _BC. GM_ , 18.6. _ZY_ : no. 0964, _Rubus tephrodes_ Hance
I.E.158*
**pheasant**. _GM_ , 48.87
I.E.196
**_pianshi_** 駢 石
III.69*
**pig** (see also **lard** ). _BC. GM_ , 50.26
pork
I.E.246
black pig
I.E.277
pig feces
I.E.186, I.E.187, I.E.233
suckling pig
I.E.138, III.24
suckling pig snout
I.E.54*
wild pig
I.E.61
wild pig bristles
IV.34
**_pixiao_** 蜱 蛸 (mantis egg-case). _GM_ , 39.75. _ZY_ : no. 4048
V.10
**plaited hemp**
I.E.183*
**_pulei_** 僕 員
I.E.202*
**_qi_** 滚
III.72,* III.74
**_qi_** 杞 (lycium). _BC. GM_ , 36.107. _ZY_ : no. 1640, _Lycium chinense_ Mill.
I.E.39
**_qianglang_** 蜣 螂 (dpng beetle). _BC. GM_ , 41.12. _ZY_ : no. 5174, _Catharsius molossus_ L.
I.E.208, I.E.209
**_qing_** 青 (azurite)
I.E.59*
Guan 灌 _qing_ (azurite)
I.E.73*
**_qinghao_** 青 蒿 (wormwood; see also **_baihao, hao_** ). _BC. GM_ , 15.13. _ZY_ : no. 2491, _Artemisia apiacea_ Hance
I.E.147, III.53
**_qu_** 朐
I.E.3*
**_qu_**
I.E.147*
**_quan_** 罐
I.E.79*
**_quantou_** 犬 頭
VII.A.3*
**_quanwei_** 犬 尾
I.E.72*
**_quju_** 屈 居
I.E.253*
**rabbit**. _GM_ , 51.53
III.60
rabbit brain
I.E.268
rabbit fur
I.E.180
rabbit skin
I.E.80
**rabbit** **[1] flesh**
I.E.58*
**ram** (see **sheep** )
**rammer**
I.E.125*
**rat**. _GM_ , 51.63
I.E.154, I.E.242
rat detritus
I.E.235
rat feces
I.E.211
rat testes
III.41
**realgar**. _BC. GM_ , 9.65
I.E.201, I.E.249,
**_rice_** ( _dao_ 稻, _mi_ 米). _GM_ , 22.66. _ZY_ : no. 5242, _Oryza sativa_ L.
I.E.105, I.E.156, I.E.239, III.4, III.74, V.3
charred crust of cooked rice
I.E.262*
**roasted-grain meal** ( _qiu_ 模; see also **malt, wheat** )
III.13*
**rooster** (see **chicken** )
**_ru_** 茹
III.54*
**_rulu_** 茹 蘆 (madder). _BC_. _GM_ , 18.59. _ZY_ : no. 3276, _Rubia cordifolia_ L. and other spp.
I.E.252
**running beasts' wellspring blossom**
VI.A.2*
**salt**. _BC. GM_ , 11.37
I.E.19, I.E.25, I.E.46, I.E.73, I.E.78, I.E.88, I.E.97
Rong 戎 salt
I.E.97*
sweet salt
I.E.74
**_sang_** 桑 (mulberry). _BC. GM_ , 36.71. _ZY_ : no. 4030, _Morns alba_ L.
IV.4
_sang_ (mulberry) liquid
I.E.224*
**sauce** ( _jiang_ 醫; see also **horse, soybean** )
I.E.150, III.13, III.19
**_sha_** 椴
I.E.69*
**_shanglao_** 商 牢 (pokeweed)
I.E.159*
**_shanyu_** 鱒 魚 (mud eel). _GM_ , 44.110. _ZY_ : no. 5725, _Monopterus albus_ (Zuiew)
V.3
**shaoyao** 芍 藥 (peony). _BC. GM_ , 14.14. _ZY_ : no. 1412, _Paeonia lactiflora_ Pall.
I.E.38, I.E.157, I.E.160
**_shechuang_** 蛇 牀 (cnidium). _BC. GM_ , 14.8. _ZY_ : no. 4345, seed of _Cnidium monnieri_ (L.) Cusson
I.E.221, III.22, III.39, IV.10
**sheep**. _BC. GM_ , 50.50
I.E.62, V.3
sheep buttock
I.E.273
sheep feces
I.E.6
sheep fur
I.E.176
sheep head
IV.13
black ewe
I.E.144*
black ram feces
I.E.200
black ram suet
I.E.216
**_shigao_** 石 膏 (gypsum). _GM_ , 9.71. _ZY_ : no. 1214
III.67
**_shiwei_** 石 韋 (pyrrosia). _BC. GM_ , 20.4. _ZY_ : no. 1202, _Pyrrosia lingua_ (Thunb.) Farw. and other spp.
I.E.109, II.A,* III.77, III.78
**_Shizhi_** 石 脂 (clay). _GM_ , 9.80
IV.2*
**shoe sole**
I.E.233
**_shu_** 蒁
III.52*
**Shu** **_shu_** 蜀 菽
I.E.212*
**_shuluo_** 署 蓏 (yam). _BC. GM_ , 27.119. _ZY_ : no. 0319, _Dioscorea opposita_ Thunb.
I.E.147*
**silk garment**
IV.32, IV.33*
**silkworm**. _BC_. _GM_ , 39.78. _ZY_ : no. 1468, _Bombyx mori_ L.
silkworm cocoon
IV.32
silkworm eggs
I.E.123,* I.E.133
**silted water**
I.E.27,* I.E.29, I.E.60, I.E.72, I.E.91, I.E.93
**slough**
I.E.136*
**snail**. _GM_ , 42.43
I.E.106, III.14, III.21,* III.23, III.42, III.43, III.75
**snake**
I.E.274
snake lard
I.E.219
**_song_** 松 (pine). _GM_ , 34.81. _ZY_ : no. 1549, _Pinus tabulaeformis_ Carr. and other spp.
VI.A.10
_songzhi_ 松 脂 (pine rosin; _GM_ , 34.82; _ZY_ : no. 2552)
III.6, III.47, III.71, IV.2
**soybean** ( _shu_ 寂). _BC. GM_ , 24.89. _ZY_ : no. 4941, _Glycine max_ (L.) Merr.
I.E.40,* I.E.50, I.E.165, I.E.167, I.E.194, I.E.204, I.E.280, I.E.282
black soybean
I.E.95
soybean sauce
I.E.144,* III.16
**spider web** (see also **_changzu_** )
III.31
**spring-bird egg, spring dickeybird egg** (see also **virile-bird egg** )
III.17,* IV.4, VI.A.2
**stove ash** (various names; see also **hundred grass residue** )
chimney soot
III.87
dry matter from stove
I.E.260
stove residue ash
I.E.29*
yellow earth from stove
I.E.73, IV.40
Yu 禹 soot
IV.7, IV.8
Yu stove [1]
I.E.243*
**straw**
I.E.266
straw bedding
V.18
straw bow
I.E.132
**_suan_** 蒜 (garlic). _GM_ , 26.52. _ZY_ : no. 0478, _Allium scorodoprasum_ L.
IV.30*
**_suanjiang_** 酸 聚
I.E.117*
**suet** ( _zhi_ 脂; see also **lard** )
I.E.206, I.E.251
beef suet
I.E.205, I.E.230, I.E.232
black ram suet
I.E.216
**_sui_** 蓬
III.47*
**talisman**
I.E.273*
**_tao_** 桃 (peach). _BC. GM_ , 29.45. _ZY_ : no. 3664, _Prunus persica_ (L.) Batsch and _P. davidiana_ (Carr.) Franch.
_tao_ (peach) branch bow
I.E.137
_tao_ (peach) branch figurine
I.E.276*
_tao_ (peach) fruit
III.23
_tao_ (peach) fuzz
IV.3, IV.12
_taoke_ 桃 可 (peach fuzz)
III.43*
_tao_ (peach) leaf
I.E.255
**_tianmu_** 天 牡
III.43*
**_tingli_** 專 藶. _BC. GM_ , 16.111. _ZY_ : no. 4818, seeds of several plants
I.E.204*
**_tong_** 桐 (paulownia). _BC. GM_ , 35.18. _ZY_ : no. 3648, _Paulownia fortunei_ (Seem.) Hemsl. and other spp.
I.E.226
large-bark _tong_ (paulownia)
I.E.210*
_yitong_ 椅 桐 (paulownia) liquid
III.38
**_tulu_** 冤 盧 (dodder). _GM_ , 18.2. _ZY_ : no. 4123, _Cuscuta chinensis_ Lam. and _C. japonica_ Choisy
III.16
**_tuomo_** 囊 莫
I.E.30*
**turtle**. _BC. GM_ , 45.2
turtle brain
I.E.146
**undershirt**
I.E.100*
**urine** (see **human** )
**vegetation from roof**
I.E.27,* I.E.139
**Vinegar** ( _dai_ 酨)
I.E.209,* I.E.211, I.E.222, I.E.228, I.E.254, III.23, III.39, III.42, III.75
gruel vinegar ( _xi_ 酸)
I.E.30,* I.E.74, I.E.95, I.E.113, I.E.122, I.E.133, I.E.141, I.E.159, I.E.162, I.E.186, I.E.201, I.E.208, I.E.232, III.24, III.62, IV.3, IV.7, IV.19
bitter liquor ( _kujiu_ 苦 酒)
I.E.198*
**virile-bird egg** (see also **spring-bird egg** )
III.16*
**_wasp_** ( _huangfeng_ 黄 蜂) _GM_ , 39.63. _ZY_ : no. 5741, _Polistes mandarinus_ Saussure
III.13
wasp larva
III.12
**wheat** ( _mai_ 麥; the referent may be barley; see also **yeast** )
I.E.174,* III.10, V.3
roasted-wheat meal ( _feng_ 麷)
VI.A.2*
whole-wheat flakes ( _maizhi_ 麥 )
III.71*
**wild animal fur**
I.E.142
**winnowing basket**
I.E.277
**_wuhui_** 烏 喙 (monkshood). _BC. GM_ , 17.46. _ZY_ : nos. 0456 and 3287, _Aconitum carmichaeli_ Debx., _A. kusnezoffii_ Rchb., and other spp.
I.E.12, I.E.13, I.E.35, I.E.151, I.E.162, I.E.209, I.E.212, I.E.215, I.E.216, I.E.227, I.E.253, III.35, III.60, III.61, III.70, III.72, III.74, III.77–80
**_wuyi_** 蕪 荑 (stinking elm fruit). _BC. GM_ , 35.56. _ZY_ : no. 2137, fruit of _Ulmus macrocarpa_ Hance
_wuyi_ (stinking elm fruit) pit
I.E.195
**_wuyi_** 莁 荑
I.E.204,* I.E.214, I.E.218
**_xi_** 枲 (hemp). _BC_. _GM_ , 22.49. _ZY_ : no. 1019, _Cannabis sativa_ L.
I.E.127*
**_xian_** 藺 (eupatorium; see also **_lan_** )
III.6*
**_xiaoshi_** 消 石 (niter). _BC. GM_ , 11.54. _ZY_ : no. 3959
I.E.16*
**_xie_** 薤 (scallion). _BC. GM_ , 26.50. _ZY_ : no. 5545, _Allium chinense_ G. Don and _A. macrostemon_ Bge.
I.E.23,* I.E.44, I.E.106, I.E.269, III.10
**_ximing_** 菥 蓂 (pennycress). _BC. GM_ , 27.95. _ZY_ : no. 4107, _Thlaspi arvense_ L.
I.E.90
**_xing_** 杏 (apricot) **pit kernel**. _BC. GM_ , 29.36. _ZY_ : no. 2240, kernel of _Prunus armeniaca_ L.
I.E.15
**_xinyi_** 辛 夷 (magnolia bud). _BC. GM_ , 34.96. _ZY_ : no. 2354, flower bud _of Magnolia liliflora_ Desr. and _M. denudata_ Desr.
I.E.17, I.E.230
**_xixin_** 細 辛 (asaram). _GM_ , 13.69. _ZY_ : no. 3082, _Asarum heterotropoides_ F. Schm. var. _mandshuricum_ (Maxim.) Kitag. and _A. sieboldii_ Miq.
III.53, III.61
**_xu_** 柔 (oak). _GM_ , 30.102. _ZY_ : no. 5433, _Quercus acutissima_ Carr.
III.26
**_xuduan_** 續 斷 (teazel). _BC. GM_ , 15.36. _ZY_ : no. 4706, _Dipsacus asper_ Wall, and D. _japonicus_ Miq.
I.E.13
**_yangsi_** 楊 思
III.38*
**_yaotiao_** 要 苕
III.22*
**yeast**
III.74
wheat yeast
III.74
**_yin fu mu_** 隱 夫 木
I.E.112*
**_yu_** 礜 (arsenopyrite). _BC. GM_ , 10.18. _ZY_ : no. 2728
I.E.21, I.E.30, I.E.209, I.E.212, I.E.253, I.E.259
**_yu_** 鬱 (tumeric). _GM_ , 14.38. _ZY_ : no. 2708, _Curcuma aromatica_ Salisb. and other spp.
I.E.199
**_yu_** 榆 (elm). _BC. GM_ , 35.53. _ZY_ : no. 5088, _Ulmuspumila_ L.
IV.5
_yu_ (elm) bark
I.E.248
**_yuan_** 冤
III.48*
**_yuanhua_** 芫 花 (daphne). _BC. GM_ , 17.73. _ZY_ : no. 2135, _Daphne genkwa_ Sieb. et Zucc.
I.E.253
_baiyuan_ 自 芫 (daphne)
III.51
**_yunmu_** 雲 母 (mica). _BC. GM_ , 8.44. _ZY_ : no. 0692
III.71*
**_yuyi_** 魚 衣 (algae)
I.E.182*
**_zang gengshe_** 蒼 梗 蛇
III.77*
**_zao_** 棗 (jujube). _BC. GM_ , 29.57. _ZY_ : no. 0187, _Ziziphus jujuba_ Mill. var. _inermis_ (Bge.) Rehd.
I.E.101, I.E.103, I.E.152
_suanzao_ 酸 東 (sour jujube)
III.47
_zao_ (jujube) fat
III.22,* III.37, III.77, IV.10–12
**_zaojia_** 皂 莢 (honey locust). _BC. GM_ , 35.33. _ZY_ : no. 2326, _Gledit-sia sinensis_ Lam.
I.E.103, III.40, IV.5, IV.8–11
**_zhanyu_** 鱣 魚 (sturgeon). _GM_ , 44.112. _ZY_ : no. 5751, _Huso dauricus_ (Georgi)
_zhanyu_ (sturgeon) blood
I.E.75, I.E.204
**_zhe_** 庶
I.E.212*
**_zhiyu_** 彘 魚
I.E.17*
**_zhu_** 术 (atractylodes). _BC. GM_ , 12B.3. _ZY_ : no. 1376, _Atractylodes macrocephala_ Koidz.; and _ZY_ : no. 2174, _Atractylodes lancea_ (Thunb.) DC. and other spp.
I.E.18,* I.E.199, III.60
**_zhuyu_** 茱 萸 (evodia)
I.E.103,* I.E.157, I.E.160, V.3
**_zi_** 梓 (catalpa). _BC. GM_ , 35.16. _ZY_ : no. 4091, _Catalpa ovata_ G. Don
I.E.175, III.20
**_zi_** 茈
I.E.228*
**_ziwei_** 紫 葳 (trumpet-flower). _GM_ , 18.23. _ZY_ : no. 4899, _Campsis grandiflora_ (Thunb.) Loisel.
III.74, III.77
**_zixie_** 澤 瀉 (water plantain). _GM_ , 19.89. _ZY_ : no. 3046, _Alisma plantago-aquatica_ L. var. _orientate_ Samuels
III.47
Index of Physiological Terms
Physiological terms are indexed by entry in the Translation. A term may occur more than once in the same entry; the index does not provide a lexical count of the total number of occurrences of a given term in the manuscripts. When the same English translation is used for several Chinese terms, the Chinese terms are recorded separately under the main heading (there are exceptions; e.g. the heading **body** , in which the two Chinese terms occasionally occur in compound form in the manuscripts). Some headings in the index list related terms as subheadings. The graphs for the Chinese terms often represent a standard graph in received literature, not the graph written on the original manuscripts. An asterisk following an entry indicates that the term is discussed in a footnote in that entry.
**abdomen**
_fu_ 腹: I.A.3, I.A.4, I.A.5, I.A.6, I.B.3, I.B.7, I.E.26, I.E.153, II.C.18, VI.A.6, VI.B.5, VII.B.16
lesser abdomen
_shaofu_ 少 腹: I.A.3,* I.B.8, I.E.89
abdomen crossroads
_fujie_ 腹 街: I.A.4*
**afterbirth**
_bao_ 胞: IV.22* IV.23, V.4, V.5, V.6, V.7, V.19
**anus**
_qiao_ 竅: I.E.145, I.E.146, I.E.147, I E. 149
_zhou_ 州: I.E.153, VI.A.7, VII.B.7
_gou_ 朐: I.E.1, I.E.155*
**aperture**
nine apertures
_jiuqiao_ 九 竅: VI.A.4,* VI.A.5, VII.B.1, VII.B.4
**arm**
_bi_ 臂: III.23, III.28, III.29, VI.A.6
forearm
_bi_ 臂: I.A.7* I.A.8, I.A.9, I.A.10, I.A.11, I.B.5, I.B.6, I.B.10, I.B.11, I.C
upper arm
_ru_ 臑: I.A.7* I.A.8, I.A.9, I.A.11, I.B.4, I.B.6, I.B.11
_hong_ 肱: II.C.31
**back**
_bei_ 背: I.A.6, I.B.1
**bladder**
_pao_ 脬: I.E.95, I.E.101
**blood**
_xue_ 血: I.D, I.E.9, I.E.27, I.E.145, I.E.147, I.E.148, I.E.149, I.E.166, III.89, V.3, VI.A.8, VI.B.7, VII.B.4
**blood gate**
_xuemen_ 血 門: VII.B.13*
**blue-gem wellspring**
_yaoquan_ 瑤 泉: VI.A.4* VII.B.13*
**body** (see also **form** )
_shen_ 身, _ti_ 體: I.E.19, I.E.26, I.E.74, I.E.138, I.E.168, I.E.206, I.E.229, I.E.231, I.E.261, II.A, III.29, III.45, III.65, III.68, III.74, III.88, V.17, VI.A.1, VI.A.4, VI.A.5, VI.A.8, VI.B.1, VI.B.2, VI.B.6, VII.B.1, VII.B.3, VII.B.4, VII.B.7, VII.B.8, VII.B.20
**bone** (general reference and specific reference by context)
_gu_ 骨: I.A.2, I.A.5, I.A.6, I.A.9, I.A.10, I.A.11, I.B.5, I.B.10, I.B.11, I.D, I.E.157, I.E.160, II.A, V.3, VI.A.8, VI.A.9, VII.B.3
**breast** (see also **nipple** )
_ru_ 乳: I.A.3, I.B.3
**broken basin** (clavicle)
_quepen_ 缺 盆: I.A.2,* I.B.10, VI.B.1
**buttock**
_tun_ 臀, 準: I.A.1, I.B.1
_kao_ 尻: I.E.88, I.E.104, VI.A.3, VI.A.7, VI.B.2, VI.B.8, VII.B.3, VII.B.7, VII.B.20
**calf**
_chuai_ 腨: I.A.1, I.A.4, I.B.1, I.B.7, I.B.9
_qi_ : I.B.3
**cavity**
six cavities
_liufu_ 六 腑: VI.A.4*
central cavity
_zhongfu_ 中 府: VI.B.7*
**central bourne**
_zhongji_ 中 極: VI.B.8*
**cheek**
_jia_ 頰: I.B.3, I.B.5, I.B.6
cheekbone
_kui_ 頮: I.A.3
_zhuo_ : I.B.6*
**chest**
_xiong_ 胸: I.B.1, I.B.10, III.68
**chin**
_yi_ 頤: I.E.232
**cloud stone** (part of female genitals)
_yunshi_ 云 石: III.88*
**coital muscle**
_jiaojin_ 交 筋: VI.B.1*
**coital vessel**
_jiaomai_ 交 脈: VI.B.1*
**Constancy Mountain** ( _mons veneris_ )
Changshan 常 山: VI.B.1*
**cord** (umbilical cord)
_suo_ 索: I.E.1, I.E.25*
**crowing cock** (male genitals)
_mingxiong_ 嗚 雄: VI.A.2*
**_cuo_**
脞: I.A.3,* I.A.6
**dark gate** (vagina)
_xuanmen_ 玄 門: VI.B.1*
**dark winepot** (saliva; see also **numinous winepot** )
_xuanzun_ 玄 尊: VI.A.1*
**depart to return** (part of female genitals)
_fanqu_ 反 去: VII.B.19
**depot**
five depots
_wuzang_ 五 臟: VI.A.1, VI.A.10
**dual-entry doorway** (nostrils)
_guiliang_ 閨 兩: VI.A.4*
**_duo_** (navel; see also **mid-body hole** )
隋: I.E.88* I.E.89, I.E.97, I.E.135, I.E.138
**dry gourd** (part of female genitals)
_kuhu_ 枯 瓠: III.88*
_ganhu_ 亁 瓠: VII.B.19*
**ear**
_er_ 耳: I.A.1, I.A.2, I.A.10, I.B.1, I.B.2, I.B.4, I.B.5, III.74, VI.A.3, VI.A.4, VI.A.8, VI.A.9, VI.B.2, VII.B.3, VII.B.4, VII.B.8
**earthly spirit**
_po_ 魄: VI.A.4, VI.A.10
**elbow**
_zhou_ 肘: I.B.4, I.B.5, I.B.6, I.C, I.E.103, VI.B.1, VI.B.5, VII.B.14, VII.B.16
**encircling ring** (waist; see also **ring** )
_zhouhuan_ 周 環: VI.B.1*
**essence**
_jing_ 精: VI.A.3, VI.A.4, VI.A.7, VI.A.8, VI.A.9, VI.A.10, VI.B.1, VI.B.7, VI.B.8, VII.B.3, VII.B.18
essence-fluid
_jingzhi_ 精 汁: IV.25*
essence illumination
_jingming_ 精 明: VI.A.10*
penile essence
_zuijing_ 胺 精: VI.A.6
Yin essence
Yin _jing_ 陰 精: VI.A.4
**ethereal spirit**
_hun_ 魂: VI.A.4, VI.A.10
**extremities**
_mo_ 末: II.74, VI.A.4
four extremities
_simo_ 四 末: I.B.10
six extremities
_liumo_ 六 末: III.70*
_liuji_ 六 極: VI.A.8,* VI.A.9
**eye**
_mu_ 目: I.A.1, I.B.1, I.B.3, I.B.6, I.B.9, I.D, I.E.27, III.74, V.3, VI.A.3, VI.A.4, VI.A.8, VI.A.9, VI.B.2, VII.B.3, VII.B.4, VII.B.8
canthus of eye
_muzi_ 目 眥: I.A.1, I.A.2, I.A.9, I.B.5, I.B.8
eyebrow
_mei_ 眉: III.89, VII.A.6
eyelash
_jie_ 睫: VI.A.7
**face**
_mian_ 面: I.B.8, I.B.9, I.D, I.E.230, III.23, III.61, IV.24, VI.B.1, VII.B.17
**female organ** (female genitals)
_nü_ 女: III.41
_pin_ 牝: III.42, III.44
**finger**
_zhi_ 指: I.E.78, I.E.277
index finger
_cizhi_ 次 指: I.B.6
little finger
_xiaozhi_ 小 指: I.A.9
middle finger
_zhongzhi_ 中 指: I.A.10, I.A.11, I.E.131
thumb
_dazhi_ 大 指: I.B.6, I.E.114
**flank**
_ce_ 側: VI.B.5, VII.B.14, VII.B.16
**flesh**
_rou_ 肉: I.C, I.D, I.E.74, I E.157, I.E.199, I.E.240
_ji_ 肌: VI.A.1, VII.B.2
**flesh by bones**
_ken_ 肎: I.E.25
**forehead**
center of forehead
_yan_ 顏: I.A.1, I.A.3, I.B.1, I.B.3
**form** (see also **body** )
_xing_ 形: V.3, VI.A.1, VI.A.3, VI.A.4, VI.A.9, VI.A.10, VI.B.1, VII.B.11, VII.B.13
**foot**
_zu_ 足: I.A.1, I.A.2, I.A.3, I.A.4, I.A.5, I.A.6, I.A.11, I.B.2, I.C, I.E.23, I.E.25, I.E.92, I.E.119, I.E.166, I.E.199, I.E.270, II.A, III.37, III.87, III.90, VI.B.8
back of foot
_zufu_ 足 跗: I.A.6, I.B.3, I.B.8
**four assistants** (limbs)
_sifu_ 四 輔: VI.A.1*
**front** (female or male genitals by context)
_qian_ 前: I.E.95, IV.3* IV.8, IV.9, IV.10, IV.11, IV.17
**fruit**
_shi_ 實: VII.B.11*
**_fu_** 膽 (see **cavity** )
**genitals**
female genitals (see **dark gate, female organ, front, hole, horse, inside, jade hole, prohibited part** , recess)
male genitals (see also **front, jade whip, male organ, member, penis, red infant, testicle** )
_zui_ 臈: III.33*
**glistening plug** (part of female genitals)
_zhuogua_ 濯 : III.88
**grain fruit** (part of female genitals)
_gushi_ 榖 實: III.91,* VII.B.19
**great illumination**
_darning_ 大 明: VI.A.7
**gums**
_yin_ 齦: I.D, I.E.78
**hair**
body and genital hair
_mao_ 毛: III.30, V.3, VI.A.1
scalp hair
_fa_ 髮: I.B. 9, III.66
**hairpin light** (part of female genitals)
_jiguang_ 笄 光: III.91,* VII.B.19
**ham**
_bi_ 碑: I.A.2* I.B.1, I.B.2, II.C.39, VI.A.3, VI.B.2, VII.B.3
**hand**
_shou_ 手: I.A.1, I.A.11, I.B.10, I.C, I.E.25, I.E.29, I.E.34, I.E.74, I.E.78, I.E.114, I.E.162, I.E.242, I.E.249, VI.A.6, VI.B.1, VI.B.5, VI.B.8, VII.B.14, VII.B.16
back of hand
_shoubei_ 手 背: I.B.4, I.B.5
palm of hand
_shouzhang_ 手 掌: I.B.10
**head**
_tou_ 頭: I.A.1, I.B.1, I.C, I.E.19, I.E.25, I E.26, I.E.71
_shou_ : I.E.228, II.A
corner of head
_toujiao_ 頭 角: I.B.1*
crown of head
_dian_ 顛: I.E.53, I.E.71, I.E.127
**heart**
_xin_ 心: I.A.4, I.A.5, I.A.6, I.A.7, I.B.2, I.B.3, I.B.7, I.B.8, I.B.9, I.B.10, I.B.11, I.E.153, III.68, VI.A.1, VI.A.3, VI.A.4, VI.A.9, VI.A.10, VII.B.15, VII.B.19
**heavenly beverage**
_tianjiang_ 天 漿: VI.A.10
**heel**
_zhong_ 踵: I.B.1, VI.B.5, VII.B.14, VII.B.16
**hip joint**
_yan_ 厭: I.B.1*
**hole** (vagina)
_xu_ : III.30*
**horse** (female genitals)
_ma_ 馬: III.38,* III.43, III.44
**_hun_** 魂 (see **ethereal spirit** )
**infant girl** (part of female genitals)
_yingnü_ 嬰 女: VII.B.19*
**inside** (vagina)
_zhong_ 中: III.22, III.24
**internal network**
_li_ 理: VI.A.9*
internal network hairs
_limao_ 理 毛: VII.B.19*
**interstine**
_chang_ 腸: I B.3, I.D, I.E.1, III.73, VI.A.9
**jade closure**
_yubi_ 玉 閉: VI.A.3,* VII.B.3
**jade hole** (vagina)
_yudou_ 玉 寳: VI.A.2
**jade wellspring**
_yuquan_ 玉 泉: VI.A.3,* VII.B.3
**jade whip** (penis)
_yuce_ 玉 策: III.38,* III.43, VI.A.2, VI.A.10, VI.B.6
**_jing_** 精 (see essence)
**joints**
_jie_ 節: I.B.2, III.88, VI.A.8, VII.B.11
hundred joints
_baijie_ 百 節: V.3
twelve joints
_shier jie_ 十 二 節: VI.A.5,* VII.B.1
**kidney**
_shen_ 腎: I.B.9
**knee**
_xi_ 膝: I.A.2, I.A.3, I.A.5, I.B.2, I.B.3, I.E.50, II.C.23
kneecap
_bin_ 髖: I.B.3
hollow at back of knee (see also **poples** )
_guo_ 膕: VII.B.19
**limb**
_zhi_ 肢: VI.A.7
four limbs
_sizhi_ 四 肢: I.E.26, VI.A.8
_siti_ 四 體: I.E.277
**male organ** (penis)
_nan_ 男: III.20, III.41, III.42
**malleolus**
_huai_ 踝: I.A.1,* I.A.2, I.A.4, I.A.5, I.B.1, I.B.2, I.B.7, I.B.8, I.B.9, I.C
**member** (male genitals)
_shi_ 勢: VI.A.2*
**menstruation**
_yueshuo_ 月 朔: V.3*
**mid-body**
_zhongshen_ 中 身: I V.3,* IV.6, IV. 7
**mid-body hole** (navel)
_zhongshen kong_ 中 身 孔: IV.5
**mouth**
_kou_ 囗: I.A.3, I.A.11, I.B.6, I.B.9, I.E.20, I.E.25, I.E.78, I.E.197, I.E.244, III.5, IV.24, VI.A.1, VII.B.3
**muscle**
_jin_ 筋: I.A.6, I.A.7, I.A.8, I.B.11, I.D, I.E.25, I.E.160, III.88, V.3, VI.A.8, VI.A.9, VI.B.7, VII.B.2, VII.B.3, VII.B.13, VII.B.18
**nape**
_xiang_ 項: I.A.1, I.A.2, I.A.9, I.B.1, I.B.2, I.E.71, II.C.29
**neck**
_ling_ 領: I.B.3, I.B.4, VI.B.1
_jing_ 頸: I.E.26
**nipple** (see also breast)
_ru_ 乳: VI.B.1, VII.B.17
**nose**
_bi_ 鼻: I.A.1, I.A.3, I.B.3, I.B.6, I.E.78, I.E.244, III.5, VI.B.1, VI.B.8, VII.B.3, VII.B.17
bridge of nose
_e_ 頞: I.B.1
groove beneath nose
_ren_ 人: I.D*
nostril
_bikong_ 鼻 孔: III.23
**numinous dew**
_linglu_ 靈 露: VI.A.10*
**numinous winepot** (saliva; see also **dark winepot** )
_lingzun_ 靈 尊: VI.A.4*
**palace**
_gong_ 宮: VII.B.20*
**penis**
_zui_ 胺: I.E.134,* VI.A.6
**perineum**
_zuan_ 簒: I.E.150
**_po_** 魄 (see **earthly spirit** )
**poples**
_xi_ 郄: I.A.1,* I.A.4, I.B.1, I.B.9, I.C
**progenitive gate**
_zongmen_ 宗 門: VI.B.1*
**prohibited part** (female genitals)
_jie_ 戒: III.25*
**_qi_** 氣 (see **vapor** )
**_qian_**
鬵: I.B.1*
**rat wife** (part of female genitals)
_shufu_ 鼠 婦: VII.B.19
**receiving canister**
_chengkuang_ 拯 匡: VI.B.1*
**recess** (vagina)
_bi_ 庳: IV.12*
**rectum**
_zhi_ : I.E.153, I.E.155
**red bead** (part of female genitals)
_chizhu_ 赤 珠: III.91,* VII.B.19
**red infant** (penis)
_chizi_ 赤 子: VI.A.6*
**red thread** (part of female genitals)
_chilü_ 赤 縷: VII.B.19
**release of the form**
_xingjie_ 形 解: VI.A.4*
**ring** (waist)
_huan_ 環: I.C,* III.50*
**scrotum**
_nang_ 囊: I.E.1, I.E.117
_gao_ 橐: VII.B.4
**sealing cord** (part of female genitals)
_fengji_ 封 紀: VII.B.19,* VII.B.20
**shin**
_xing_ 胻: I.A.2, I.A.3, I.A.5, I.A.6, I.E.1, I.E.50, I.E.140, I.E.194, I.E.198, I.E.199
_gan_ 骭: I.B.3, I.C
shinbone
_gangu_ 骭 骨: I.B.3
**shoulder**
_jian_ 肩: I.A.9, I B.4
shoulderblade
_jianbo_ 肩 髆: I.A.2
**side**
_xie_ 脅: I.A.2, I.A.8, I.B.2, I.B.11, I.E.27, VI.B.2
upper side
_qu_ 胠: I.A.4* I.B.1, I.B.3, II.C.24, VI.A.3
**skin**
_fu_ 膚: I.D, I.E.190, I.E.191, I.E.281, III.39, III.88, VI.A.1, VI.B.7, VII.B.18
_pi_ 皮: I.E.135, VI.B.7
skin and hide
_fuge_ 膚 革: V.3, VI.A.3, VI.A.8, VI.B.2
_pige_ 皮 革: VII.B.3
skin's webbed pattern
_zou_ 腠, _zouli_ 腠 理: I.E.75, V.3, VI.A.2, VI.A.4, VI.B.2, VII.B.4
**spine**
_ji_ 脊: I.A.1, I.A.4, I.B.1, I.B.9, VI.A.3, VI.A.7, VI.B.2, VII.B.3, VII.B.7
**spirit**
_shen_ 神: VI.A.4, VI.A.7, VI.A.10, VI.B.1, VI.B.8
**spirit illumination**
_shenming_ 神 明: VI.A.1, VI.A.3, VI.B.2, VI.B.8, VII.B.3
**spirit mist**
_shenwu_ 神 霧: VI.A.10
**spirit wind**
_shenfeng_ 神 風: VI.A.1,*
**spirit vapor** (see **vapor** )
**Spurting Sea**
Bohai 勃 海: VI.B.1*
**stomach**
_wei_ 胃: I.B.7
stomach sack
_wan_ 腕: I.B.10*
**stove trivet**
_zaogang_ 竈 綱: VI.B.1*
**sweet dew**
_ganlu_ 甘 露: VI.A.4*
**sweet-liquor ford**
_lijin_ 醴 津: VI.B.1*
**tailbone**
_jue_ 鱖: VII.B.3
**testicle**
_shen_ 腎: I.E.134, I.E.137, I.E.157
_luan_ 卵: I.D, I.E.135
**thigh**
_gu_ 股: I.A.2, I.A.3, I.A.4, I.A.5, I.A.6, I.E.50, I.E.131, VI.A.7, VI.B.1, VI.B.5, VII.B.14, VII.B.16, VII.B.17
fish-thigh
_yugu_ 魚 股: I.B.2* I.B.3, I.B.7, I.B.8
**throat**
_yi_ 溢: I.A.3, I.B.5, I.B.8, I.B.9, I.B.11, I.E.283, VI.B.1, VII.B.17
_yan_ 咽: I.A.4, I E.147
_hou_ 喉: I.B.4, I.E.240
**toe**
big toe
_dazhi_ 大 指: I.A.5, I.A.6, I.B.8
little toe
_zu xiaozhi_ 足 小 指: I.A.1, I.A.2, I.B.1
middle toe
_zu zhongzhi_ 足 中 指: I.A.3, I.B.2, I.E.92
**tongue**
_she_ 舌: I.A.4, I.B.9, I.D, VI.B.1, VII.B.17
**tooth**
_chi_ 齒: I.A.11, I.B.6, I.D, I.E.78, I.E.244, V.3
**two racks**
_liangzhi_ 兩 持: VI.A.1*
**underarm**
_ye_ 腋: I.A.2, I.A.7, I.A.8, IV.33, VI.B.1
**vapor**
_qi_ 氣: I.B.7, I.B.9, I.C, I.D, I.E.21, I.E.167, II.A, III.5, III.37, III.46, III.61, III.66, III.68, III.88, III.89, III.90, IV.2, V.3, VI.A.3, VI.A.4, VI.A.5, VI.A.6, VI.A.8, VI.A.9, VI.A.10, VI.B.1, VI.B.7, VI.B.8, VII.B.2, VII.B.3, VII.B.4, VII.B.5, VII.B.7, VII.B.11, VII.B.13, VII.B.17, VII.B.18, VII.B.20
vapor of life
_shengqi_ 生 氣: VI.A.4
penile vapor
_zuiqi_ 脧 氣: VI.A.6
spirit vapor
_shenqi_ 神 氣: VI.A.1, VI.A.3, VI.A.7, VI.A.8
Yin vapor
Yin _qi_ 陰 氣: VII.B.4, VII.B.8
**vessel**
_mai_ 脈: I.A.6, I.A.11, I.C, I.D, I.E.1, I.E.142, VI.A.8, VI.B.7, VII.B.13
Ceasing Yin vessel
_jue_ Yin _mai_ 厥 陰 脈: I.A.6, I.B.8
ear vessel
_ermai_ 耳 脈: I.B.5*
Great Yang vessel
_tai_ Yang _mai_ 太 陽 脈, _ju_ Yang _mai_ 鉅 陽 脈: I.A.1, I.A.9, I.B.1, I.E.135
Great Yin vessel
_tai_ Yin _mai_ 太 陰 脈, _ju_ Yin _mai_ 鉅 陰 脈: I.A.5, I.A.6, I.A.7, I.B.7, I.B.8, I.B.10, I.C, I.E.135
hair vessel
_maomai_ 毛 脈: VI.A.1*
hundred vessels
_baimai_ 百 脈: VI.A.3, VI.A.4, VI.A.6, VI.A.8
Minor Yang vessel
_shao_ Yang _mai_ 少 陽 脈: I.A.2, I.A.10, I.B.2
Minor Yin vessel
_shao_ Yin _mai_ 少 陰 脈: I.A.4, I.A.8, I.B.9, I.B.11, I.C
shoulder vessel
_jianmai_ 肩 脈: I.B.4*
stomach vessel
_weimai_ 胃 脈: I.B.7
tooth vessel
_chimai_ 齒 脈: I.B.6*
Yang vessel
Yang _mai_ 陽 脈: I.B.8
Yang Brilliance vessel
Yang _ming mai_ 陽 明 脈: I.A.3, I.A.11, I.B.3
**waist**
_yao_ 腰: I.A.1, I.B.1, I.B.8, VII.B.19
**waterway**
_shuidao_ 水 道: VI.B.2,* VII.B.3
**wellspring blossom**
_quanying_ 泉 英: VI.A.7*
**wheat teeth** (part of female genitals)
_maichi_ 麥 齒: III.91,* VII.B.19
**whiskers**
_xu_ 鬚: III.89
**why remain** (part of female genitals)
_heyu_ 何 寓: VII.B.19
**will**
_zhi_ 志: VI.A.8, VII.B.3
**womb**
_liu_ 榴/ _bao_ 胞: VI.A.7* VI.A.8
**wrist**
_wan_ 腕: VI.B.1
**_xun_**
: I.A.1*
**Yang** (various senses by context)
陽: I.A.6, I.B.2, I.D, II.C.30, VI.A.1, VI.A.2, VI.A.4, VI.A.5, VI.B.1, VII.B.1, VII.B.20
Yang blaze
Yang _fu_ 陽 佛: VI.A.1*
Yang vessel (see **vessel** )
**Yin** (various senses by context)
陰: I.A.6, I.B.7, I.B.10, I.B.11, I.D, II.C.6, II.C.30, III.90,* VI.A.1, VI.A.2, VI.A.3, VI.A.4, VI.A.5, VI.A.7, VI.A.8, VI.A.10, VI.B.1, VII.B.4, VII.B.20
Yin vapor (see **vapor** )
Yin water
Yin _shui_ 陰 水: VI.A.1*
**_zang_** 臓 (see **depot** )
**_zao_** **stone** (part of female genitals)
_zaoshi_ 磉 石: VII.B.19
**_zhen_**
腦: I.A.2,* I.A.11
Index of Ailments
Ailments are indexed by entry in the Translation. An ailment name may occur more than once in the same entry; entries known to treat a given ailment, yet in which the ailment name is not written in the text, are also included (e.g. recipes arranged by category of ailment in _MS_ I.E). Note that "ailment" is understood to refer broadly to "a condition warranting medical attention." Ailments which focus on parts of the body (back pain, cheekbone swelling, throat numbness, etc.) are arranged under the appropriate part. Some headings in the index bring together several related ailments under one category. Graphs are provided selectively; they often represent a standard graph in received literature, not the graph written on the original manuscripts. An asterisk following an entry indicates that the ailment is discussed in a footnote in that entry.
**abdomen**
abdomen pain: I.A.5
bloated abdomen: I.A.5, I.A.6, I.B.7
swelling in abdomen: I.A.3
swelling in outer part of abdomen: I.B.3
lesser abdomen
swelling in lesser abdomen: I.B.8
abdomen crossroads
pain in abdomen crossroads: I.A.4
**abscess**
_yong_ 癰: I.C, I.E.1, I.E.16,* I.E.17, I.E.131, I.E.199, I.E.225*–32, VI.A.9
_ju_ 疽: I.E.1, I.E.157*–73, VII.B.4
**alarm**
panicked alarm: I.B.3
**angry**
tendency to become angry: I.B.9
**anus**
anus itchiness: I.E.1, I.E.155,* I.E.156
**arm**
arm as if being snapped: I.B.4
arm pain: I.B.6
forearm
pain in outer edge of forearm: I.A.9
**back**
back pain: I.B.1
**_baichu_**
白 處: I.E.1, I.E.73*–75
**belch**
tendency to belch: I.A.5, I.B.7
**blockage**
_bi_ 閉: I.B.7*
**breast**
breast pain: I.B.3
pain in inner edge of breast: I.A.3
**broken basin** (clavicle)
pain in broken basin: I.A.2, I.B.10
**bugs**
chewing by bugs: I.E.1, I.E.240*–48
**burns**
I.E.1, I.E.176–197
**buttock**
buttock pain: I.A.1, I.B.1
**calf**
calf as if being ripped: I.B.1
calf pain: I.A.1, I.A.4, I.B.1, I.B.3
**cheek**
cheek pain: I.B.5
**cheekbone**
cheekbone pain: I.A.3
cheekbone swelling: I.B.6
**chest**
chest pain: I.B.1, I.B.10
**chilblain**
_zhu_ 瘃: I.E.266*–70
**child sprite**
_qi_ 魅: I.E.1, I.E.276* I.E.277
**choking**
I.B.9
**cold and hot syndrome**
_nue_ 瘧: I.B.1,* I.B.2
**coldness**
shaking from coldness: I.B.2
shivers and ailing from coldness: I.B.3
**conglomeration**
_jia_ 瘕: I.B.10*
**convulsions** (see **infant convulsions** )
**coughing**
I.B.9
coughing with blood: I.B.9
coughing with muteness and craving to sleep: I.A.4
**_cuo_**
loss of flesh at _cuo_ 脞: I.A.3,* I.A.6
**_dadai_**
大 帶: I.E.1, I.E.76,* I.E.77
**deafness**
_long_ 聾: I.A.1, I.A.2, I.A.10, I.B.1, I.B.5, II.C.20
**detestation**
detestation for people and fire: I.B.3
**dog**
dog bite: I.E.1, I.E.31–33
mad dog bite: I.E.1, I.E.28–30
**drink**
craving to drink: I.A.6
**ear**
pain in front of ear: I.A.2
**eat**
inability to eat: I.B.7
no craving to eat: I.A.5
no desire to eat: I.B.9
wanting to vomit after eating: I.B.7
**elbow**
pain in outer part of elbow: I.B.4
**exhaustion**
_dan_ 癉: I.A.4* I.B.9*
**extremities**
pain in the four extremities: I.B.10
**eye**
eye as if being torn: I.B.1
eye pain: I.A.1
eyes clouded as if sightless: I.B.9
yellowing of eye: I.B.6
canthus of eye
pain in outer canthus of eye: I.A.2, I.B.5
**face**
face is mouldy black: I.B.9
facial blemish: I.B.8
facial pustules
_ma_ 癄: I.E.1, I.E.280*–82
**feverishness** (see also **heart** )
II.C.22*
**foot**
foot turning outward: I.B.2
hotness in foot: I.A.4
back of foot
numbness in back of foot: I.B.3
swelling in back of foot: I.A.6
**forehead**
center of forehead
blackness in center of forehead: I.B.3
coldness in center of forehead: I.A.1, I.A.3
pain in center of forehead: I.B.3
**genital swelling**
III.33, III.92
**goiter**
_ying_ 癭: I.E.129*
**_gu_**
蠱: I.E.1, I.E.271*–75
**ham**
ham cannot rotate: I.B.1
ham pain: II.C.39
pain in edge of ham: I.B.2
pain in outer edge of ham: I.A.2.
**hand**
hand pain: I.A.1
**head**
head pain: I.B.1
dashed head: I.B.1*
inability to raise head: I.B.8
**heart**
heart as if suspended: I.B.9
heart pain: I.A.4, I.A.7, I.B.7, I.B.10, I.B.11
heart pain with throbbing: I.B.10
feverishness of heart: I.A.4,* I.A.6, I.A.7, I.B.7, I.B.8
pain in heart and side: I.B.2
pain in heart and upper side: I.B.3
panicky heart: I.B.3, I.B.9
(vapor) ascending and racing to heart: I.B.7
**hemorrhoid**
_zhi_ 痔: I.A.1, I.B.1, I.E.1, I.E.142*–54
**hotness**
hotness with sweating: I.A.3
internal hotness: I.B.8, II.C.35, VII.B.4
**hunger**
I.B.9
**inability**
inability to look back: I.B.4
inability to turn from side to side: I.B.2
**infant convulsions**
_yinger chi_ 嬰 兒 瘛: I.E.1, I.E.27*
**inguinal swelling**
_tui_ 癪: I.B.8, I.E.1, I.E.118*–41, II.C.15
**intestinal pain**
I.B.3
**isolation**
desire to dwell in isolation: I.B.3
**itch**
_sao_ 瘙: I.E.1, I.E.249*–56
**itchy swellings**
_chen_ 疹: II.A*
**joints**
pain in all joints: I.B.2
**knee**
knee pain: II.C.23
knee rigidity: I.B.3
pain in outer edge of knee: I.A.2, I.B.2
swelling in knee: I.A.3
**lacquer**
I.E.1, I.E.233*–39
**leaking slop**
_xie_ 泄: I.A.6,* I.B.7
**leeches**
I.E.1, I.E.50, I.E.51
**liver**
liver pain: I.A.4
**lizard**
I.E.1, I.E.52*–63
**_ma_**
馬: I.A.2*
**_ming_**
螟: I.E.1, I.E.78*
**mouth**
dry mouth: I.B.6
hotness in mouth: I.B.9
**muck**
_tang_ 溏: I.A.6* I.B.7
**mutism**
_yin_ 瘖: I.B.9
**nape**
nape as if being axed: I.B.1
nape pain: I.A.1, I.B.1, I.B.2
**neck**
neck pain: I.B.3, I.B.4
swelling and pain in neck: I.B.4
neck lumps
_lou_ 瘻: I.A.2,* VI.A.9
**nest**
_chao_ 巢: I.E.1, I.E.34,* I.E.35
**non-erection** (of penis)
III.1*–3, III.5, III.92
**nose**
bloody nose
_niu_ 衄: I.A.1,* I.A.3
stuffy nose
_qiu_ 鼽: I.A.1,* I.A.3, I.B.3
**numbness**
_bi_ 痹: I.A.6*
**panting**
hoarse panting: I.B.9
**parched**
I.A.4
**_pian_** (see also **withering on one side** )
偏: I.B.8*
**pliancy** (of penis)
III.7*–9, III.92
**poples**
cramping in poples: I.A.1
**prostration**
_long_ : I.E.120*
**pustules**
_cuo_ 痤: VI.A.9, VII.B.4
**_qian_**
strain in the _qian_ 鬵: I.B.1*
**_quan_**
蠸: I.E.1, I.E.79*
**rat belly**
I.E.131*
**rigidity**
_jing_ 痙: I.E.1, I.E.19*–24, I.E.25*
**scabbing**
_bi_ 疕: I.E.1, I.E.257*–70, V.5
**scabby itch**
_bisao_ 疕 瘙: V.6, V.18
**scabies**
_jia_ 痂: I.E.1, I.E.200*–223
**scantness** (of semen)
III.63,* III.64, III.92
**scorpion**
I.E.1, I.E.44–49
**scrotum**
swollen scrotum: I.E.1, I.E.117,* VII.B.4
**seizure sickness**
_dianji_ 癲 疾: I.A.1, I.E.1, I.E.71,* I.E.72
**_shan_**
疝: I.B.8*
**shin**
shin burns: I.E.1, I.E.194–197
shin wounds: I.E.1, I.E.198, I.E.199
coldness in shin: I.A.2
pain in inner edge of shin: I.A.5
pain in outer edge of shin: I.A.2, I.A.3
**shoulder**
shoulder as if being torn: I.B.4
shoulder pain: I.B.4
**side**
side pain: I.A.2, I.A.8, I.B.2, I.B.11
swelling in outer part of side: I.A.2
upper side
upper side accumulation: II.C.24
upper side as if knotted: I.B.1
pain in upper side: I.B.1
**sing**
desire to sing (and cast off clothing and run): I.B.3
**sleep**
craving to sleep: I.B.9
inability to sleep: I.B.7
**snake**
snake bite: I.E.1, I.E.224
**spasms**
_xian_ 癎: I.E.1, I.E.26* I.E.86*
**spine**
pain in inner edge of spine: I.A.4
pain pressing laterally on spine: I.A.1
**stomach sack**
pain in stomach sack: I.B.10
**stretching**
fondness for stretching: I.B.3
**sweating**
I.B.2
**swelling**
I.B.3
**thigh**
pain in thigh: I.A.4, I.A.5
pain in outer edge of thigh: I.A.2
fish-thigh
fish-thigh pain: I.B.2
**throat**
throat numbness: I.B.4
dry throat: I.B.8, I.B.9
pain in throat: I.B.9
parched throat: I.B.11
**toe**
loss of function in big toe: I.A.5
loss of function in little toe: I.A.1*
loss of function in middle toe: I.A.3
loss of function in toe next to little toe: I.A.2
numbness in little toe: I.B.1
numbness in middle toe: I.B.2
**tongue**
tongue splitting: I.A.4, I.B.9
**tooth**
tooth pain: I.A.11, I.B.6
**urine**
urine has sediment: I.E.1, I.E.115*
lard urine: I.E.1, I.E.116*
frequent urination: I.A.6
urine retention
_long_ : I.B.8, I.E.1, I.E.88*–114
**vapor**
insufficiency of vapor: I.B.9*
rising vapor: I.A.4,* I.B.9
**waist**
waist as if being snapped: I.B.1
waist pain: I.A.1, I.B.1, I.B.8
**warm ailment**
II.C.36*
**warts**
_you_ 疣: I.E.1, I.E.64–70
horse warts
_mayou_ 馬 疣: I.E.1, I.E.278,* I.E.279
**water**
_shui_ 水: I.B.7*
**withering on one side**
_pianku_ 偏 枮: III.74
**wounds**
I.E.1, I.E.2*–18
**_wuhui_** **(monkshood) poisoning**
I.E.1, I.E.37*–43
**_xixia_**
夕下: I.E.1, I.E.36*
**yawning**
I.B.3, I.B.7
**_yu_**
蜮: IV.28*–35
**_yun_**
痃: I.E.1, I.E.84* I.E.85
**_zhen_**
pain in _zhen_ : I.A.2
**_zhou_**
tendency for _zhou_ 肘: I.A.5*
General Index
Important terms, subjects, persons, and books mentioned in the Prolegomena are indexed.
Acupuncture, , 5n.2, , , , –, –; needles in the tomb of Liu Sheng,
Ailment identification, –, –,
Anal constriction, –, –
Ancestor Peng, , , –, , –, ,
Aphrodisiacs, –, , ,
Aristotle, –
_Artes_ -literature, ,
Baoshan tomb divination manuscript,
Bian Que, 7n.2, , –, ,
Blood, –, –, –, ,
Bloodletting, –
Body, metaphorical language for, –, , , –
Books, –; copying and collecting of, , –, _See also_ Medical books
Breath cultivation, , –, –, , , –, –, –, –
Bugs and illness, –,
Cauterization, , 5n.1, , , , , –. _See also_ Heat, therapeutic use of
Chen District talismans, –
Childbirth, –
Chisongzi, –
Chu silk manuscript,
Chunyu Yi, –, , –, , , –, –, , –, , –, , –, –,
_Coitus conservatus and coitus thesauratus_ , –. _See also_ Essence retention
Correlative cosmology, , –, , . _See also_ Five Agent theory, Natural philosophy, Yin Yang theory
Cupping,
_Dao_ (way), , , , , ,
Daoism, early, –, 114n.1, , ; religious, , , , –, , , , , , –
_Daoyin_ (guiding and pulling), , , –, –, 132n.1. _See also_ Exercise
Dietetics, –, , , , , –, –
Drugs, –, , –, –; processing of, –
Essence ( _jing_ ), , , –, , , , –, –, ; retention of, . _See also Jing_
Exercise, , –, , , , , –. _See also Daoyin_
_Fang_ (method, recipe), , , –; and medicine, ,
_Fang_ -literature, , , –, –, –, , –, , , , , –,
"Fangji" (Recipes and techniques) division in the _Hanshu_ bibliographic treatise, –, , , ,
Fangmatan tomb , hemerological manuscripts, –, , –, , , , –; resurrection account, , –
_Fangshi. See_ Recipe gentleman
Five Agent ( _wuxing_ ) theory, –, 9n.2, 11n.1, –, , , , , –, , , –, 171n.1,
Fox demon, ,
Gestation, –, –
Great Exorcism ( _da nuo_ ), –, –
Greek and Demotic magical papyri,
Heat, therapeutic use of, –
Heavenly Teacher ( _tianshi_ ),
Hermetic texts,
Hippocratic Corpus, –
_Huainan wanbishu_ , ,
_Huainanzi_ , , , 114n.1, , –, ,
Huangdi. _See_ Yellow Thearch
_Huangdi neijing_ , , 4n.2, –, –, –, , –, , , 52n.3, , , –, 61n.1, 62n.1, –, –, , –, –, –, , –, 121n.1, , , 180n.1
_Huangting jing_ , , 127n.2
_Huanjing bunai_ (returning the essence to replenish the brain), –
_Hun_ (ethereal-spirit) and _po_ (earthly-spirit),
Iatromancy, ,
Illness, –; demonic, –, , –, –; ontological explanation of, –, –, , ; physiological explanation of, –, , , ,
Immortality, –, –
_Ishinpô_ , –, –
_Jing_ , as specter, . _See mainly_ Essence
Jixia Academy in Qi, ,
King Tang of Shang,
King Wei of Qi, , , ,
King Zhao of Qin,
Lancing-stone ( _bian_ ) __,, , –; in the tomb of Liu sheng,
_Laozi_ , –, 114n.1, –, , ; "Heshang gong" commentary, , , ; "Xianger" commentary, ,
Li Shaojun, –,
_Liexian zhuan_ , 44n.1,
_Lingyang Ziming jing_ ,
Liu An, King of Huainan, ,
Liu De, King of Hejian,
_Lüshi chunqiu_ , macrobiotic hygiene in, –
Macrobiotic hygiene, , –, –, , –, , , –, –, , –, –, –; in _xian_ cult, –; literature, –; medical tradition of, –, , –. _See also_ Breath cultivation, Dietetics, Exercise, Sexual cultivation
Magic, –, , , , –, , –, –, , , –, , –; and drags, , –, , ; and incantation, , , –, ; and religion, , –, –; and ritual acts, , , –, –; black, , –; breath, –, –, –, –; literature, –
_Mai_ (vessel), definition of, –. _See mainly_ Vessel theory
Medical books, –, –, , –; transmission of, , , –, –. _See also_ "Fangji"
Medicine, as a technical skill, ; training, , –
Meditation, –
Mencius, ,
Moxibustion, 5n.1, . _See also_ Cauterization
Natural philosophy and occult thought, –, –, –, , –, , , –, . _See also_ Correlative cosmology
"Neiye" chapter in the _Guanzi_ , , –, –, –, ,
Northern Dipper,
Orgasm, –
Pace of Yu (Yu _bu_ ), , , –,
Pain, , –
Pengzu. _See_ Ancestor Peng
Pharmacy, , –. _See also_ Drugs
Philosophy, , –, –; as a _shu_ (art), –; masters ( _zi_ ) of, , , –, –, , –
Philter, , , , ,
Physician ( _yi_ ), –, , , –, –, –, –, , , , , , –, –, –, ,
Physiological theory, , –, , , –
Plato,
Poison, aconite,
_Qi_ (vapor), definition of, . _See mainly_ Vapor
Recipe gentleman ( _fangshi_ ), , –, –
Retrograde ejaculation, –
Rong Cheng, , , –
Saliva, , , , . _See also_ Spitting
Science, –
Secrecy, , , –, –, –
_Secretum secretorum_ ,
Semen, –; retention of, . _See also_ Essence, retention of Sexual cultivation, , , –, , , –, –, , –, ; literature, , , , –
Shaman ( _wu_ ), –, 61n.1, –, 152n.1, –, , , –,
Shaman Peng,
Shang bone and shell inscriptions, , , , 160n.2,
_Shanhaijing_ , ,
_Shen. See_ Spirit
_Shenming_ (spirit illumination), –, , . _See also_ Spirit
_Shennong bencaojing_ , , –,
_Shu_ (art), –, , –
Shuanggudui tomb manuscript _Wanwu_ , –, , , , –,
Shuihudi tomb hemerological manuscripts, –, , , –, –, , –, ,
Shun, –,
"Shushu" (Calculations and arts) division in the _Hanshu_ bibliographic treatise, , , , , , ,
Sima Tan, ,
Smith ( _ye_ ), as a term for pulverizing drugs,
Spirit ( _shen_ ) __,, , –,
Spirits and demons, identification of, –, –
Spitting, , –, –, –
Surgery, , –
Tao Hongjing, –
_Techne_ , –
Text, definition of, 3n.2, –
Vapor ( _qi_ ) __,–, –, , , –, –, , –, –, –, –, –, –, , –, –; Warring States jade inscription on circulation of, –. _See also Qi_
Verse, esoteric, –
Vessel ( _mai_ ) theory, , –, , , , –, –, , , . _See also Mai_ , Physiological theory
Wang Chong, and incantation, –, , ; and macrobiotic hygiene,
Wangzi Qiao, –,
Wen Zhi (pre-Qin physician), , , , , , –,
_Wu. See_ Shaman
Wuwei medical manuscripts,
_Wuxing. See_ Five Agent theory
_Xian_ (transcendent) cult, , 44n.1, , , –, –, ,
Yang Zhu, , ,
Yao, –,
Yellow Thearch, , , –, , –, 180n.1
Yi Yin, –
Yin and physiology, –, –
Yin Yang theory, –, –, –, , , , –, , , –, , , , , , –, 171n.1,
Yu, , –, . _See also_ Pace of Yu
Yue, magic of, , –; recipes of, , , –
Zhang Liang, , 116n.1
Zhangjiashan tomb medical manuscripts _Maishu_ and _Yinshu_ , –, –, –, , , , –, –, –, , –, , , –, , –, –
Zhou inscriptions,
Zhuangzi,
_Zhuangzi_ , –, 114n.1, ,
Zou Yan, ,
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Николáй Николáевич Чхеи́дзе (26 октября 1909, Новый Торъял, Уржумский уезд, Вятская губерния, Российская империя — 28 октября 1996, Марий Эл, Россия) — советский деятель сельского хозяйства, учёный-агроном. Заместитель директора Марийской сельхозопытной станции (1946—1949), начальник инспектуры Государственной комиссии по сортоиспытанию сельскохозяйственных культур по Марийской АССР (1953—1981). Заслуженный агроном РСФСР (1976). Участник Великой Отечественной войны. Член ВКП(б).
Биография
Родился 26 октября 1909 года в п. Новый Торъял ныне Новоторъяльского района Марий Эл.
В 1930—1932 годах служил в рядах РККА.
В 1933 году окончил Нартасский сельскохозяйственный техникум, по окончании — преподаватель, завуч этого техникума. В 1936 году окончил Казанский сельскохозяйственный институт, в 1941 году — аспирантуру при нём.
В 1941 году вновь призван в РККА Йошкар-Олинским военкоматом. Участник Великой Отечественной войны: заместитель командира бронепоезда 39 отдельного дивизиона бронепоездов на Сталинградском фронте, лейтенант. В июне 1944 года завершил военную службу. Награждён орденом Отечественной войны II степени.
В 1946—1949 годах был заместителем директора Марийской сельхозопытной станции. В 1953—1981 годах — начальник инспектуры Государственной комиссии по сортоиспытанию сельскохозяйственных культур по Марийской АССР.
За вклад в развитие сельского хозяйства в 1960 году ему присвоено почётное звание «Заслуженный агроном Марийской АССР», в 1976 году — почётное звание «Заслуженный агроном РСФСР». Награждён орденом «Знак Почёта», медалями, в том числе медалью «За трудовую доблесть» и серебряной медалью ВДНХ, а также Почётной грамотой Президиума Верховного Совета Марийской АССР (трижды).
Скончался 28 октября 1996 года в Йошкар-Оле.
Звания и награды
Заслуженный агроном РСФСР (1976)
Заслуженный агроном Марийской АССР (1960)
Орден Отечественной войны II степени (06.04.1985)
Орден «Знак Почёта» (1966)
Медаль «За трудовую доблесть» (1946)
Серебряная медаль ВДНХ
Медаль «За доблестный труд. В ознаменование 100-летия со дня рождения Владимира Ильича Ленина»
Почётная грамота Президиума Верховного Совета Марийской АССР (1946, 1957, 1968)
Примечания
Литература
Сухин В. И. Развитие сельского хозяйства Марийской АССР в 1965—1975 гг.: автореферат диссертации кандидата исторических наук: 07.00.02 / АН СССР. Институт истории СССР. — Москва, 1987. — 15 с.
Выпускники Казанского государственного аграрного университета
Заслуженные агрономы Республики Марий Эл
Военные железнодорожники Великой Отечественной войны
Лейтенанты (СССР)
Члены ВКП(б)
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\section{Introduction}
Product formulas in the literature of Gromov--Witten (GW) theory started
with \cite{KM} for the genus zero Gromov--Witten invariants.
It was soon generalized in \cite{B} to (absolute) GW invariants
in any genus.
There is also an orbifold version in \cite{AJT}.
In this paper, we extend the product formula to the setting of
\emph{relative GW theory} or more generally \emph{log GW theory}.
The absolute Gromov--Witten theory studies the intersection theory
on the moduli stacks of stable maps $\overline{\mathcal{M}}_{g,n}(X, \beta)$
from an $n$-pointed curve with arithmetic genus $g$
to a fixed nonsingular projective variety $X$ with a fixed degree $\beta$
in the Mori cone $NE(X)$ of effective curves in $X$
\[
f\colon (C, x_1, x_2, \ldots, x_n) \to X, \, \text{such that }\,
f_*([C]) = \beta.
\]
For notational convenience, we denote such a class by $[f]$.
Intuitively, GW invariants count the numbers of curves passing through
$n$ fixed cycles $\alpha_1, \ldots, \alpha_n$ in $X$
with the above given conditions.
To put it on a mathematically sound setting, one defines the
invariants as intersection numbers on $\overline{\mathcal{M}}_{g,n}(X, \beta)$
in the following way.
By the functorial properties of the moduli stacks, there are the
\emph{evaluation morphisms}
\[
ev_i \colon \overline{\mathcal{M}}_{g,n}(X, \beta) \to X, \, i= 1, \ldots, n,
\]
and \emph{stabilization morphism}
\[
\pi \colon \overline{\mathcal{M}}_{g,n}(X, \beta) \to \overline{\mathcal{M}}_{g,n},
\]
where $\overline{\mathcal{M}}_{g,n}$ is the moduli stack of stable genus $g$,
$n$-pointed curves and
\[
ev_i ([f]) = f(x_i) \in X, \quad
\pi ([f]) = [(\overline{C}, \overline{x}_1, \overline{x}_2, \ldots,
\overline{x}_n)] \in \overline{\mathcal{M}}_{g,n},
\]
where $\overline{C}$ is the stabilization of the source curve $C$.
The GW invariants can be defined as
\[
\int_{[\overline{\mathcal{M}}_{g,n}(X, \beta)]^{vir}} \pi^*(\gamma) \prod_i ev_i^*(\alpha_i),
\]
where $[\overline{\mathcal{M}}_{g,n}(X, \beta)]^{vir}$ is the \emph{virtual fundamental class}.
One can rephrase these invariants in terms of the cohomological field theory
\[
R^X_{g,n,\beta} \colon H^*(X)^{\otimes n} \to H^*(\overline{\mathcal{M}}_{g,n})
\]
via
\[
\int_{[\overline{\mathcal{M}}_{g,n}(X, \beta)]^{vir}} \pi^*(\gamma) \prod_i ev_i^*(\alpha_i)
= \int_{\overline{\mathcal{M}}_{g,n}} \gamma . R^X_{g,n,\beta} ( \prod_i \alpha_i ) .
\]
The details can be found in \cite{B} and references therein.
Intuitively, the \emph{relative} invariants
as defined in \cite{LR} and \cite{jL} can be considered as refined counting.
Let $(X, D)$ be a pair consisting of a nonsingular projective variety $X$ and a smooth
divisor $D$ in $X$.
If the curve $C$ does not lie in $D$, it intersects with $D$ at $\rho$ points
with multiplicities $\mu_1, \ldots, \mu_{\rho}$ such that
\[
\sum_j \mu_j = \int_\beta [D].
\]
The refined counting is to fix the profile $(\mu_1, \ldots, \mu_{\rho})$ and
constraint the $\rho$ points to lie in chosen cycles $\{ \delta_j \}$ in $D$.
Similarly, one can define the relative invariants as intersection
numbers on relative moduli stacks as above.
See \cite{jL} and \cite{LR} for details.
There is also a similar reformulation in terms of cohomological field theory.
See Section~\ref{s:3}.
The divisor $D$ in $X$ gives rise to a divisorial log structure on X.
Recently relative invariants have been generalize to the setting of \emph{log} GW (\cite{AC,C,GS}).
See Section~\ref{s:1} for a brief summary of log geometry and log GW theory.
In a sense, the study of Gromov--Witten theory is the study
of the virtual fundamental classes.
The \emph{product formula} is a statement that
\emph{GW invariants of $V$ and $W$ determine the invariants of $V \times W$}.
See Equation~\eqref{e:3}.
It can be written in the form of certain
functorial properties of virtual classes.
In \cite{B}, K.~Behrend proves a product formula for absolute
GW invariants by first establishing a corresponding functorial property
of virtual fundamental classes.
In this note, we approach the product formula in the relative and log
settings in a similar way.
The \emph{main results} are Theorem~\ref{t:main} and Corollary~\ref{c:2.2},
which \emph{expresses the log/relative invariants of $X \times (Y,D)$ by
invariants of $X$ and of $(Y,D)$}.
The logarithmic approach to relative GW invariants of Abramovich-Chen and Gross-Siebert (\cite{AC,C, GS}) avoids the expanded degenerations of Li (\cite{jL}) and allows us to adapt
Behrend's original proof, but it also presents new technical difficulties.
We were not able to prove the product formula in the
general log setting and we have to assume the log structure on one of the factors
to be trivial. For the general case, see Section \ref{s3} for some initial attempts and speculations.
This product formula could be useful in the study of Gromov--Witten theory, even when no explicit product or log geometry is involved in the statement. For example, it plays a role in proving the crepant transformation conjecture for ordinary flops with non-split vector bundles in \cite{LLQW}. There the degeneration technique is extensively employed and the product
formula is applied to treat fiber integrals which naturally occur in the degeneration process.
\section{Preliminaries} \label{s:1}
\subsection{Log geometry}
We work over the base log scheme $\spec \mathbb{C}$ with the trivial log structure.
We refer to \cite[Sections~1-4]{K} for general background on
log structures on schemes, and \cite[Section~5]{O2} for log stacks.
For the reader's convenience, we recall
the basic properties we need about
Olsson's Log stack and
saturated morphisms.
\subsubsection{$\Tor_X$}
Denote by $\mathbf{LogSt}$ the category of fine saturated (fs) log algebraic stacks, and $\mathbf{St}$ the category of algebraic stacks.
\footnote{In a higher categorical sense.
In other words, $\mathbf{LogSt}$ and $\mathbf{St}$ are 2-categories, or (2,1) categories.}
For a fs log stack $X$, $\Tor_X$ is introduced in \cite[Remark 5.26]{O2} to parametrize all fs log schemes over $X$. It follows from the definition of $\Tor_X$ that a map $S \to X$ in $\mathbf{LogSt}$ factors
as
$
S \to \Tor_X \to X.
$
We can view $X$ as an open substack of $\Tor_X$ parametrizing strict maps $S \to X$.
Note that $\Tor_X$ has a natural fs log structure so that the factorization $S \to \Tor_X$ above is strict, and $\Tor_X \to X$ is log \'{e}tale.
It is easy to check when $X$ is log smooth, it is open dense in $\Tor_X$.
In particular if $X$ is log smooth and irreducible, $\Tor_X$ is irreducible.
\begin{remark}
Let $\mathbf{Sch}$ be the category of schemes over $\mathbb{C}$, $\mathbf{Grpd}$ the category of (small) groupoids.
Recall a stack is a functor
$\mathbf{Sch} \to \mathbf{Grpd}$ that satisfies certain 'sheaf' condition. A log stack is a stack with a log struture,
and a log structure can be understood as a map from the stack to $\Log_\mathbb{C}$.
It is more natural to describe a fs log moduli stack $X$ by its functor of points than
specifying its underlying stack and log structure.
As the Yoneda embedding for the (2,1) category $\mathbf{LogSt}$ is fully faithful, an object $X$ in $\mathbf{LogSt}$
is uniquely determined by:
\[
\hom_{\mathbf{LogSt}}(-, X)\colon \mathbf{LogSch} \to \mathbf{Grpd}.
\]
Here the stack condition for $X$ allows us to restrict $\hom_{\mathbf{LogSt}}(-, X)$ from $\mathbf{LogSt}$
to its full subcategory $\mathbf{LogSch}$ of fs log schemes.
Given a log moduli functor $\mathbb{X} \colon \mathbf{LogSch} \to \mathbf{Grpd}$ such that it is isomorphic to
$\hom_{\mathbf{LogSt}}(-, X)$ for some fs log stack $X$, one
might recover $X$ by considering the stack $\Tor_\mathbb{X}\colon \mathbf{Sch} \to \mathbf{Grpd}$ which corresponds to
$\Tor_X$, then the underlying stack $\underline{X}$ of $X$ is the substack of
$\Tor_\mathbb{X}$ satisfying a minimal condition, and the log structure of $X$
is the restriction of the natural log structure on $\Tor_\mathbb{X}$. See \cite{G1} for details.
\end{remark}
\subsubsection{Saturated morphisms}
\begin{defn}
Let $P, Q$ be saturated monoids, a \emph{map $P \to Q$ is saturated},
if it is integral and the push out of
\[
\xymatrix{
P \ar[r]\ar[d] & Q \\
R
}
\]
is saturated when $R$ is saturated.
\end{defn}
\begin{defn}
Let $(X, \M_X), (Y, \M_Y) $ be fs log schemes,
a map $f \colon (X, \M_X) \to (Y, \M_Y)$ is called \emph{saturated},
if for any $x \in X, y=f(x)$, the induced map between characteristics
$\overline{\M}_{Y,\bar{y}} \to \overline{\M}_{X, \bar{x}}$ is saturated.
\end{defn}
\begin{remark}
Given the above definition, a saturated morphism between fs log stacks can be
defined locally with respect to the lisse-\'{e}tale topology.
\end{remark}
It follows from the definition that saturated morphisms satisfy the following properties:
\begin{itemize}
\item They are stable under composition and base change in $\mathbf{LogSt}$.
\item
For a cartesian square
\[
\xymatrix{
(W,\M_W) \ar[r]\ar[d] & (X,\M_X) \ar[d]^f\\
(Z, \M_Z) \ar[r] &(Y, \M_Y)\\
}
\]
in $\mathbf{LogSt}$, when $f$ is saturated, the underlying diagram of stacks
\[
\xymatrix{
W \ar[r]\ar[d] & X\ar[d] \\
Z \ar[r] & Y
}
\]
is cartesian in $\mathbf{St}$.
\end{itemize}
\subsection{Log Gromov--Witten theory}
\subsubsection{Log curves}
Let $\overline{\mathcal{M}}_{g,n}$ (resp.\ $\mathfrak{M}_{g,n}$) be the algebraic stack of stable
(resp.\ prestable) curves of genus $g$ with $n$ marked points.
The log structure of $\overline{\mathcal{M}}_{g,n}$ is the divisorial log structure associated
with its boundary consisting of singular curves.
The log structure of $\mathfrak{M}_{g,n}$ is determined from the smooth chart
$\sqcup_{m}\overline{\mathcal{M}}_{g,n+m} \to \mathfrak{M}_{g,n}$, where the map from
$\overline{\mathcal{M}}_{g,n+m} \to \mathfrak{M}_{g,n}$ is forgetting the extra m marked points
without stabilizing. We view $\overline{\mathcal{M}}_{g,n}$ and $\mathfrak{M}_{g,n}$ as log stacks from now on using the same notation.
Note that the forgetful map $\overline{\mathcal{M}}_{g,n+1} \to \overline{\mathcal{M}}_{g,n}$ is saturated,
as it can be identified as the universal log curve. This implies the stabilization map
$\mathfrak{M}_{g,n} \to \overline{\mathcal{M}}_{g,n}$ is saturated.
\subsubsection{Log stable maps}
For a projective log smooth scheme $V$, let $\mathscr{M}_{g,n}(V)$ be the fs log stack
parameterizing stable log maps from log curves of genus $g$ with $n$ marked
points (see \cite{AC,ACMW,C,GS} for more details).
For a fs log scheme $S$, a log map from $S$ to $\mathscr{M}_{g,n}(V)$ corresponds to a
stable log map:
\begin{equation} \label{e:1}
\xymatrix{
C \ar[r]\ar[d] & V\\
S &.
}
\end{equation}
We note that the underlying map of the diagram is a usual stable map.
A log map $ V \to W$ induces a stabilization map $\mathscr{M}_{g,n}(V) \to \mathscr{M}_{g,n}(W)$.
Given $S \to \mathscr{M}_{g,n}(V)$ which corresponds to a diagram \eqref{e:1},
the composition $S \to \mathscr{M}_{g,n}(V) \to \mathscr{M}_{g,n}(W) $ corresponds to
\[
\xymatrix{
\overline{C} \ar[r]\ar[d] & W\\
S &.
}
\]
where the underlying map of $\overline{C} \to W$ is the stabilization of
the underlying map $ C \to V \to W$, and the log structure on $\overline{C}$
is the push forward of the log structure on $C$ with respect to the partial
stabilization $C \to \overline{C}$.
(See \cite[appendix B]{AMW}.)
\subsubsection{Perfect obstruction theories}
We have a natural log map $\mathscr{M}_{g,n}(V) \to \mathfrak{M}_{g,n}$ forgetting the map to $V$.
As log deformations for $\mathscr{M}_{g,n}(V) \to \mathfrak{M}_{g,n}$ is the same as
deformations for the underlying map
of $\mathscr{M}_{g,n}(V) \to \Tor_{\mathfrak{M}_{g,n}}$, a (relative) perfect obstruction theory for the log map
$\mathscr{M}_{g,n}(V) \to \mathfrak{M}_{g,n}$
is by definition a perfect obstruction theory for the underlying map of $\mathscr{M}_{g,n}(V) \to \Tor_{\mathfrak{M}_{g,n}}$.
A perfect obstruction theory for $\mathscr{M}_{g,n}(V) \to \mathfrak{M}_{g,n}$
is defined in \cite[Section~5]{GS},
tangent space and obstruction space at $[f\colon C \to V] \in \mathscr{M}_{g,n}(V)$
are given by $H^0(f^*T_V)$ and $H^1(f^*T_V)$ respectively, where
$T_V$ is the log tangent bundle of V.
If we have a factorization $\mathscr{M}_{g,n}(V) \to \mathfrak{N} \to \mathfrak{M}_{g,n}$,
and $\mathfrak{N} \to \mathfrak{M}_{g,n}$ is log \'{e}tale,
a perfect obstruction theory for $\mathscr{M}_{g,n}(V) \to \mathfrak{M}_{g,n}$
induces a perfect obstruction theory for $\mathscr{M}_{g,n}(V) \to \mathfrak{N}$ since
$\Tor_{\mathfrak{N}} \to \Tor_{\mathfrak{M}_{g,n}}$ is \'etale.
\section{Product formula in terms of virtual classes} \label{s:2}
\subsection{Setup}
We start by introducing relevant commutative diagrams, which are the log enhancement
of those in \cite{B}.
We define a fs log stack $\mathfrak{D}$
by its functor of points. Given any fs log scheme $S$, a map $S \to \mathfrak{D}$ corresponds
to the data consisting of $n$-pointed
prestable log curves $C, C', C''$ of genus $g$ over $S$,
together with partial stabilizations $p'\colon C \to C'$ and $p''\colon C \to C''$,
such that no component of $C$ is contracted by both $p',p''$. Note that as log curves over $S$, the log structure of $C'$ resp. $C''$
is given by the pushforward of the log structure of $C$ along $p'$ resp. $p''$.
Define $e\colon \mathfrak{D} \to \mathfrak{M}_{g,n}$ as the forgetful morphism taking
$(p',p'')$ to $C$.
It is proved in \cite[Lemma 4]{B} that the underlying map of $e$ is \'{e}tale.
As $e$ is strict, it is log \'{e}tale.
We claim that the following commutative diagram is cartesian
in $\mathbf{LogSt}$,
\begin{equation} \label{e:2}
\xymatrix{
\mathscr{M}_{g,n}(V \times W) \ar[r]\ar[d] & \mathscr{M}_{g,n}(V) \times
\mathscr{M}_{g,n}(W) \ar[d]\\
\mathfrak{D} \ar[r] &\mathfrak{M}_{g,n} \times \mathfrak{M}_{g,n}
}
\end{equation}
Here the top horizontal arrow is determined by stabilization maps
$\mathscr{M}_{g,n}(V \times W) \to \mathscr{M}_{g,n}(V)$,
$\mathscr{M}_{g,n}(V \times W) \to \mathscr{M}_{g,n}(W)$
induced from the projections $\mathrm{pr}_1\colon V \times W \to V$,
$\mathrm{pr}_2\colon V \times W \to W$.
The left vertical arrow is defined by retaining the curve together with
its partial stabilizations with respect to $\mathrm{pr}_1,\mathrm{pr}_2$.
The reason for the diagram being cartesian is essentially the same as that
in \cite[Proposition 5]{B}. For a fs log scheme S,
a commutative diagram
\[
\xymatrix{
S \ar[r]\ar[d] &\mathscr{M}_{g,n}(V) \times \mathscr{M}_{g,n}(W) \ar[d] \\
\mathfrak{D} \ar[r] &\mathfrak{M}_{g,n} \times \mathfrak{M}_{g,n}\\
}
\]
corresponds to stable log maps $C' \to V, C'' \to W$ over $S$,
together with stabilization between log curves $C \to C', C \to C''$.
\footnote{Note that $\mathscr{M}_{g,n}(V)(S)\to \mathfrak{M}_{g,n}(S)$ and $\mathscr{M}_{g,n}(W)(S)\to \mathfrak{M}_{g,n}(S)$ are iso-fibrations of groupoids.}
This recovers a stable log map $C \to C'\times C'' \to V \times W$.
Indeed, $\mathfrak{D}$ is constructed to make \eqref{e:2} cartesian.
We then extend the above cartesian diagram
in $\mathbf{LogSt}$ to
\[
\xymatrix{
\mathscr{M}_{g,n}(V \times W) \ar[r]^-h \ar[d]^c & P\ar[r]\ar[d] & \mathscr{M}_{g,n}(V) \times \mathscr{M}_{g,n}(W) \ar[d]^a\\
\mathfrak{D} \ar[r]^l\ar[d]^e & \mathfrak{P} \ar[r]^-\phi \ar[d]& \mathfrak{M}_{g,n} \times \mathfrak{M}_{g,n} \ar[d] \\
\mathfrak{M}_{g,n} & \overline{\mathcal{M}}_{g,n} \ar[r]^-\Delta & \overline{\mathcal{M}}_{g,n} \times \overline{\mathcal{M}}_{g,n} \, .
}
\]
Here all squares are constructed by taking fiber product. If $V$ and $W$ have trivial log structures, this reduces to Diagram (2) of \cite{B}.
\begin{defn}
We say that the product formula (of virtual fundamental classes) holds for $V$ and $W$ if
\begin{equation} \label{e:3}
h_*([\mathscr{M}_{g,n}(V \times W)]^{\mathrm{vir}})
=\Delta^!([\mathscr{M}_{g,n}(V)]^{\mathrm{vir}} \times [\mathscr{M}_{g,n}(W)]^{\mathrm{vir}}).
\end{equation}
\end{defn}
In \cite{B}, Behrend showed that the
product formula holds for $V$ and $W$ when $V$ and $W$ are smooth projective schemes, or log smooth schemes with
trivial log structures, our goal of this paper is to
extend his result to the case when $W$ has nontrivial log structure.
\subsection{Product formula in log GW theory} \label{QQQ}
When $W$ has nontrivial log structure, %
we factor
\[
a\colon \mathscr{M}_{g,n}(V) \times \mathscr{M}_{g,n}(W) \to \mathfrak{M}_{g,n} \times \mathfrak{M}_{g,n}
\]
into
\[
\mathscr{M}_{g,n}(V) \times \mathscr{M}_{g,n}(W) \overset{a'}{\to} \mathfrak{M}_{g,n} \times \Tor_{\mathfrak{M}_{g,n}}
\to \mathfrak{M}_{g,n} \times \mathfrak{M}_{g,n}.
\]
We then have the following commutative diagram in which
all squares are cartesian in $\mathbf{LogSt}$,
\begin{equation} \label{e:4}
\xymatrix{
\mathscr{M}_{g,n}(V \times W) \ar[r]^-h \ar[d]^{c'} & P\ar[r]\ar[d] & \mathscr{M}_{g,n}(V) \times \mathscr{M}_{g,n}(W) \ar[d]^{a'}\\
\mathfrak{D}' \ar[r]^{l'}\ar[d] & \mathfrak{P}' \ar[r]^-{\phi'} \ar[d]& \mathfrak{M}_{g,n} \times \Tor_{\mathfrak{M}_{g,n}} \ar[d] \\
\mathfrak{D} \ar[r]^l\ar[d] & \mathfrak{P} \ar[r]^-\phi \ar[d]& \mathfrak{M}_{g,n} \times \mathfrak{M}_{g,n} \ar[d] \\
\mathfrak{M}_{g,n} & \overline{\mathcal{M}}_{g,n} \ar[r]^-\Delta & \overline{\mathcal{M}}_{g,n} \times \overline{\mathcal{M}}_{g,n} \, .
}
\end{equation}
\begin{mlemma} \label{l:main}
\begin{enumerate}[(I)]
\item The underlying square diagrams in $\mathbf{St}$ are all cartesian.
\item The relative perfect obstruction theories for $a'$ and $c'$ are compatible.
\item $\mathfrak{D}', \mathfrak{P}'$ are irreducible, and $l'$ is of degree 1.
\item $\phi'$ is a l.c.i. and is compatible with $\Delta$ in the sense that the cotangent complex
$\mathcal{L}_{\Delta}$ pulls back
to $\mathcal{L}_{\phi'}$.
\end{enumerate}
\end{mlemma}
\begin{thm} \label{t:main}
Using the notations in \eqref{e:4}, we have
\[
h_*([\mathscr{M}_{g,n}(V \times W)]^{\mathrm{vir}})
=\Delta^!([\mathscr{M}_{g,n}(V)]^{\mathrm{vir}} \times [\mathscr{M}_{g,n}(W)]^{\mathrm{vir}})
\]
in the log GW setting, assuming the trivial log structure on $V$.
\end{thm}
\begin{proof}
We have virtual pullbacks $c'^!, a'^!, \phi'^!,$ and $\Delta^!$. (See \cite[Section 3.1]{M1})
For the upper left square of diagram \eqref{e:4},
we have $$h_*([\mathscr{M}_{g,n}(V \times W)]^{\mathrm{vir}})=a'^![\mathfrak{P}'],$$
by (II), (III), and Costello's pushforward theorem \cite[Theorem 5.0.1]{Co}.
For the upper right square of diagram \eqref{e:4},
note that $\phi'^!([\mathfrak{M}_{g,n}] \times [\Tor_{\mathfrak{M}_{g,n}}])$ equals $[\mathfrak{P}']$,
and $a'^!([\mathfrak{M}_{g,n}] \times [\Tor_{\mathfrak{M}_{g,n}}])$ is $[\mathscr{M}_{g,n}(V)]^{\mathrm{vir}} \times [\mathscr{M}_{g,n}(W)]^{\mathrm{vir}}$.
By \cite[Theorem 4.3]{M1}, we know that $a'^!\phi'^!=\phi'^!a'^!$, so
$$a'^![\mathfrak{P}']=\phi'^!([\mathscr{M}_{g,n}(V)]^{\mathrm{vir}} \times [\mathscr{M}_{g,n}(W)]^{\mathrm{vir}}).$$
Now (IV) gives
$$\phi'^!([\mathscr{M}_{g,n}(V)]^{\mathrm{vir}} \times [\mathscr{M}_{g,n}(W)]^{\mathrm{vir}}]) =
\Delta^!([\mathscr{M}_{g,n}(V)]^{\mathrm{vir}} \times [\mathscr{M}_{g,n}(W)]^{\mathrm{vir}}),$$
and we can complete the proof by combining these equations.
\end{proof}
\subsection{Proof of Main Lemma}
\subsubsection*{(I)}
As $a'$ is strict, the first row of squares are cartesian.
Since $\mathfrak{M}_{g,n} \to \overline{\mathcal{M}}_{g,n}$ is saturated, the bottom square is cartesian.
For the second row, to prove the two squares are cartesian is the same
as showing the squares in the following diagram are cartesian in $\mathbf{St}$.
\begin{equation} \label{e:5}
\xymatrix{
\mathfrak{D}' \ar[r]^{l'} \ar[d] & \mathfrak{P}' \ar[r]^-{\mathrm{pr}_2\circ\phi'} \ar[d] & \Tor_{\mathfrak{M}_{g,n}} \ar[d]\\
\mathfrak{D} \ar[r]^l & \mathfrak{P} \ar[r]^-{\mathrm{pr}_2\circ\phi} \ar[r] & \mathfrak{M}_{g,n} .
}
\end{equation}
We claim that $l \circ \mathrm{pr}_2\circ\phi$ and $\mathrm{pr}_2\circ\phi$ are both saturated.
$l \circ \mathrm{pr}_2\circ\phi$ is saturated because a partial stabilization map locally
is given by forgetting marked points.
(See the proof of \cite[Proposition 3]{B}.
What we need is that Diagram (4) there to be commutative.)
$\mathrm{pr}_2\circ\phi$ is saturated as it is the base change by
$\mathfrak{M}_{g.n} \to \overline{\mathcal{M}}_{g,n}$
\[
\xymatrix{
\mathfrak{P} \ar[r]^-{\mathrm{pr}_2\circ\phi} \ar[d] & \mathfrak{M}_{g,n} \ar[d]\\
\mathfrak{M}_{g.n}\ar[r] & \overline{\mathcal{M}}_{g,n} .\\
}
\]
Thus, both squares in \eqref{e:5} are cartesian.
\subsubsection*{(II)}
We remark that as $\Tor_{\mathfrak{M}_{g,n}} \to \mathfrak{M}_{g,n}$ is log \'{e}tale,
$\mathfrak{D}'$ is log \'{e}tale over $\mathfrak{D}$.
Thus the relative perfect obstruction theory for the log map
$\mathscr{M}_{g,n}(V \times W) \to \mathfrak{M}_{g,n}$ can be viewed as a
relative perfect obstruction theory for the underlying map of $c'$.
Compatibility check is the same as in \cite[Propsition 6]{B}.
\subsubsection*{(III)}
Start with Diagram \eqref{e:5}.
The open embedding
$\mathfrak{M}_{g,n} \to \Tor_{\mathfrak{M}_{g,n}}$ induces
\begin{equation} \label{e:6}
\xymatrix{
\mathfrak{D} \ar[r]^l \ar[d] & \mathfrak{P} \ar[r]^-{\mathrm{pr}_2\circ\phi}\ar[d] & \mathfrak{M}_{g,n} \ar[d]\\
\mathfrak{D}' \ar[r]^{l'} \ar[d] &\mathfrak{P}' \ar[r]^-{\mathrm{pr}_2\circ\phi'} \ar[d] & \Tor_{\mathfrak{M}_{g,n}} \ar[d]\\
\mathfrak{D} \ar[r]^l & \mathfrak{P} \ar[r]^-{\mathrm{pr}_2\circ\phi} & \mathfrak{M}_{g,n} \, .\\
}
\end{equation}
$\mathfrak{M}_{g,n}$ being log smooth, it is open and dense in $\Tor_{\mathfrak{M}_{g,n}}$.
Note that both
$\mathrm{pr}_2\circ\phi, l\circ\mathrm{pr}_2\circ\phi$ are flat surjective, we conclude
$\mathfrak{D}$(resp. $\mathfrak{P}$) are open dense substacks of $\mathfrak{D}'$ (resp.\ $\mathfrak{P}'$).
(III) then follows from properties of $\mathfrak{D}, \mathfrak{P}$ and $l$. (See \cite[Proposition 3]{B}).
\subsubsection*{(IV)}
We factor $\mathfrak{M}_{g,n} \times \Tor_{\mathfrak{M}_{g,n}} \to \overline{\mathcal{M}}_{g,n} \times \overline{\mathcal{M}}_{g,n}$
into
\[
\mathfrak{M}_{g,n} \times \Tor_{\mathfrak{M}_{g,n}} \to \overline{\mathcal{M}}_{g,n} \times \Tor_{\mathfrak{M}_{g,n}} \to
\overline{\mathcal{M}}_{g,n} \times \Tor_{\overline{\mathcal{M}}_{g,n}} \to \overline{\mathcal{M}}_{g,n} \times \overline{\mathcal{M}}_{g,n}.
\]
First arrow is saturated and flat, and second arrow strict and smooth.
For the third arrow, note that
\begin{equation*}
\xymatrix{
\Tor_{\overline{\mathcal{M}}_{g,n}} \ar[r]\ar[d] & \overline{\mathcal{M}}_{g,n} \times \Tor_{\overline{\mathcal{M}}_{g,n}} \ar[d]\\
\overline{\mathcal{M}}_{g,n}\ar[r]^-\Delta & \overline{\mathcal{M}}_{g,n} \times \overline{\mathcal{M}}_{g,n}\\
}
\end{equation*}
is cartesian in $\mathbf{LogSt}$ as well as in $\mathbf{St}$, and horizontal
arrows are compatible l.c.i.\ maps. It is then easy to see $\phi'$ and $\Delta$ are compatible.
\subsection{Product formula for families}
As we need the product formula for equivariant invariants in \cite{LLQW}, we will adapt the arguments
above to families.
Let $X \to S$ and $Y\to T$ be two families of log smooth projective varieties over log smooth and irreducible bases. We would like to relate GW invariants of the family $X\times Y \to S \times T$ to those of $X\to S$ and $Y\to T$.
Denote by $\mathscr{M}_{g,n}(X/S), \mathscr{M}_{g,n}(Y/T),\mathscr{M}_{g,n}(X\times Y/S\times T)$ log stacks of stable log maps from genus $g$ curves with $n$ marked points to these families.
\begin{remark}
Let $X \to S$ be a family of log smooth projective varieties over a log stack $S$.
As a cartesian digram
\[\xymatrix{
X' \ar[r]\ar[d] & X \ar[d]\\
S' \ar[r] & S
}\] in $\mathbf{LogSt}$
induces a cartesian diagram
\[
\xymatrix{
\mathscr{M}_{g,n}(X'/S') \ar[r]\ar[d] & \mathscr{M}_{g,n}(X/S)\ar[d]\\
S' \ar[r] & S
}
\] in $\mathbf{LogSt}$.
It follows that
$\mathscr{M}_{g,n}(X/S)$ is an algebraic stack locally of finite type over $S$ by \cite[Theorem 0.1]{GS}.
\end{remark}
It is easy to see we have a cartesian diagram in $\mathbf{LogSt}$
\[
\xymatrix{
\mathscr{M}_{g,n}(X\times Y/S\times T) \ar[r]\ar[d]
& \mathscr{M}_{g,n}(X/S) \times \mathscr{M}_{g,n}(Y/T) \ar[d]\\
\mathfrak{D} \ar[r] &\mathfrak{M}_{g,n} \times \mathfrak{M}_{g,n}\ ,
}
\]
and we consider the diagram
\[
\xymatrix{
\mathscr{M}_{g,n}(X\times Y/S\times T) \ar[r]^-h \ar[d]^c
& P\ar[r]\ar[d]
& \mathscr{M}_{g,n}(X/S) \times \mathscr{M}_{g,n}(Y/T) \ar[d]^a\\
\mathfrak{D} \ar[r]^l\ar[d]^e & \mathfrak{P} \ar[r]^-\phi \ar[d]& \mathfrak{M}_{g,n} \times \mathfrak{M}_{g,n} \ar[d] \\
\mathfrak{M}_{g,n} & \overline{\mathcal{M}}_{g,n} \ar[r]^-\Delta & \overline{\mathcal{M}}_{g,n} \times \overline{\mathcal{M}}_{g,n} \, .
}
\] as before.
\begin{thm}
Let $X \to S$ be
a family of smooth projective varieties over a smooth, pure dimensional stack $S$,
and $Y \to T$ a family of log smooth projective varieties over a stack $T$ which is log smooth and irreducible.
Then we have \[
h_*([\mathscr{M}_{g,n}(X \times Y/S\times T)]^{\mathrm{vir}})
=\Delta^!([\mathscr{M}_{g,n}(X/S)]^{\mathrm{vir}} \times [\mathscr{M}_{g,n}(Y/T)]^{\mathrm{vir}})
\]
\end{thm}
\begin{proof}
Consider the cartesian diagram in $\mathbf{LogSt}$,
\[
\xymatrix{
\mathscr{M}_{g,n}(X\times Y/S\times T) \ar[r]\ar[d]
& \mathscr{M}_{g,n}(X/S) \times \mathscr{M}_{g,n}(Y/T) \ar[d]\\
\mathfrak{D}\times (S\times T) \ar[r]\ar[d] &(\mathfrak{M}_{g,n} \times S) \times (\mathfrak{M}_{g,n} \times T) \ar[d]\\
\mathfrak{D} \ar[r] &\mathfrak{M}_{g,n} \times \mathfrak{M}_{g,n}\ .
}
\]
As $T$ is log smooth,
$\Tor_{\mathfrak{M}_{g,n} \times T} \to \Tor_{\mathfrak{M}_{g,n}}$ is smooth, the perfect obstruction theory for
$\mathscr{M}_{g,n}(Y/T) \to \mathfrak{M}_{g,n} \times T$ then induces a perfect obstruction theory for the composition
\[
\mathscr{M}_{g,n}(Y/T) \to \mathfrak{M}_{g,n} \times T \to \mathfrak{M}_{g,n}
\] by the arguments in \cite[Appendix B]{GP}.
Similarly, we have a perfect obstruction theory for
\[
\mathscr{M}_{g,n}(X/S) \to \mathfrak{M}_{g,n}\times S \to \mathfrak{M}_{g,n},
\]
and
\[
\mathscr{M}_{g,n}(X\times Y/S\times T) \to \mathfrak{D}\times (S\times T) \to \mathfrak{D}
\]
Now we are in the same situation as in Section \ref{QQQ},
identical arguments finish the proof.
Note that (II) follows from standard properties of cotangent complexes of algebraic stacks.
\end{proof}
\section{Remarks for the general case} \label{s3}
\subsection{}
When $V$ has nontrivial log structure, we might consider factoring $a$ by
\[
\mathscr{M}_{g,n}(V) \times
\mathscr{M}_{g,n}(W) \to \Tor_{\mathfrak{M}_{g,n}} \times \Tor_{\mathfrak{M}_{g,n}}.
\]
In this case, the underlying diagram of
\begin{equation*}
\xymatrix{
\Tor_{\overline{\mathcal{M}}_{g,n}} \times_{\overline{\mathcal{M}}_{g,n}} \Tor_{\overline{\mathcal{M}}_{g,n}} \ar[r]\ar[d] &
\Tor_{\overline{\mathcal{M}}_{g,n}} \times \Tor_{\overline{\mathcal{M}}_{g,n}}\ar[d]\\
\overline{\mathcal{M}}_{g,n} \ar[r]^-\Delta & \overline{\mathcal{M}}_{g,n} \times \overline{\mathcal{M}}_{g,n}
}
\end{equation*}
is no longer cartesian in $\mathbf{St}$.
If it is true that $\mathscr{M}_{g,n}(V) \to \mathfrak{M}_{g,n}$ is saturated,
we can replace $\Tor_{\mathfrak{M}_{g,n}}$ by its open substack parameterizing saturated
maps and the argument we used can be adapted to this more general setting.
However, the map $\mathscr{M}_{g,n}(V) \to \mathfrak{M}_{g,n}$ is not even integral in general, and
further understanding concerning the log structure of $\mathscr{M}_{g,n}(V)$ seems necessary.
\subsection{}
To prove the product formula holds for $V$ and $W$, we can assume $V$ and $W$ are smooth and log smooth.
This is achieved by using desingularizations of log smooth schemes and invariance of virtual classes under certain log modifications.
By \cite[Theorem 5.10]{Ni}, for any log smooth variety $X$, there exists a log blow up $\pi\colon Y \to X$
such that $Y$ is smooth, log smooth and $\pi$ is birational. In particular, $\pi$ is proper, birational, and log \'etale.
\begin{lemma}
Let $\Phi\colon \widetilde{V} \to V$ and $\Psi\colon \widetilde{W} \to W$ be proper, birational, log \'etale maps between log smooth projective varities.
If the product formula holds for $\widetilde{V}$ and $\widetilde{W}$,
then it holds for $V$ and $W$.
\begin{proof}
Consider the diagram
\[
\xymatrix{
\mathscr{M}_{g,n}(\widetilde{V} \times \widetilde{W}) \ar@/^/[rrd]^-{\widetilde{h}} \ar@/_/[rdd]_{\mathscr{M}(\Phi\times \Psi)}\\
&
& \widetilde{P}\ar[r]\ar[d]
& \mathscr{M}_{g,n}(\widetilde{V}) \times \mathscr{M}_{g,n}(\widetilde{W}) \ar[d]^{\mathscr{M}(\Phi)\times\mathscr{M}(\Psi)}\\
&\mathscr{M}_{g,n}(V \times W) \ar[r]^-h
& P\ar[r]\ar[d] & \mathscr{M}_{g,n}(V) \times \mathscr{M}_{g,n}(W) \ar[d] \\
&
& \overline{\mathcal{M}}_{g,n} \ar[r]^-\Delta
& \overline{\mathcal{M}}_{g,n} \times \overline{\mathcal{M}}_{g,n} \, ,
}
\]
where
\[
\mathscr{M}(\Phi)\colon \mathscr{M}_{g,n}(\widetilde{V}) \to \mathscr{M}(V),
\]
\[
\mathscr{M}(\Psi)\colon \mathscr{M}_{g,n}(\widetilde{W}) \to \mathscr{M}(W),
\]
and
\[
\mathscr{M}(\Psi\times \Psi)\colon \mathscr{M}_{g,n}(\widetilde{V}\times \widetilde{W}) \to \mathscr{M}(V\times W)
\]
are maps between moduli stacks induced by $\Phi,\Psi$ and $\Phi\times\Psi$ respectively.
As $\Phi$ is proper, birational, log \'etale, by \cite[Theorem 1.1.1]{AW},
\[
\mathscr{M}(\Phi)_*[\mathscr{M}_{g,n}(\widetilde{V})]^\mathrm{vir} =[\mathscr{M}_{g,n}(V)]^\mathrm{vir}.
\]
Similarly, we have
\[
\mathscr{M}(\Psi)_*[\mathscr{M}_{g,n}(\widetilde{W})]^\mathrm{vir} =[\mathscr{M}_{g,n}(W)]^\mathrm{vir},
\]and
\[
\mathscr{M}(\Psi\times \Psi)_*[\mathscr{M}_{g,n}(\widetilde{V}\times \widetilde{W})]^\mathrm{vir}= [\mathscr{M}(V\times W)]^\mathrm{vir}.
\]
Now
pushforwarding the relation
\[
\widetilde{h}_*[\mathscr{M}_{g,n}(\widetilde{V}\times \widetilde{W})]^\mathrm{vir} =
\Delta^!([\mathscr{M}_{g,n}(\widetilde{V})]^\mathrm{vir} \times [\mathscr{M}_{g,n}(\widetilde{W})]^\mathrm{vir})
\] along $\widetilde{P} \to P$ gives
\[
h_*([\mathscr{M}_{g,n}(V \times W)]^{\mathrm{vir}})
=\Delta^!([\mathscr{M}_{g,n}(V)]^{\mathrm{vir}} \times [\mathscr{M}_{g,n}(W)]^{\mathrm{vir}}).
\]
\end{proof}
\end{lemma}
\begin{remark}
Let $V$ be a smooth projective variety with log structure coming from a simple normal crossing divisor $\cup D_i$.
Motivated by the results proved in \cite{ACW, AMW}, we expect that genus zero log GW invariants of $V$ are related to orbifold GW invariants of root stacks $V(\sqrt[r]{D_i})$.
If this naive expectation is valid, then the product formula for orbifolds proved in \cite{AJT} would imply the product formula of log GW invariants in genus zero.
\end{remark}
\section{Applications to relative Gromov--Witten invariants} \label{s:3}
We apply this to the \emph{relative GW} invariants as defined by
A.~Li and Y.~Ruan \cite{LR}, and J.~Li \cite{jL}.
Let $X$ and $Y$ be nonsingular projective varieties,
and $D$ a a smooth divisor in $Y$.
We further assume $H^1(Y)=0$, so a curve class of $X\times Y$ is of the form $(\beta_X, \beta_Y)$
where $\beta_X$ (resp.\ $\beta_Y$) is a curve class of $X$ (resp.\ $Y$).
Let $\overline{\mathcal{M}}_{\Gamma_Y}(Y,D)$ be the relative moduli stack.
Here $\Gamma_Y=(g,n,\beta_Y,\rho, \mu)$ encodes the discrete data:
$g$ for the genus, $n+\rho$ for the number of marked points, $\beta_Y$ the curve class,
$\mu= (\mu_1, ...\mu_{\rho})$ an ordered partition of $\int_{\beta_Y} [D]$.
We have evaluation maps
\[
ev_Y \colon \overline{\mathcal{M}}_{\Gamma_Y}(Y,D) \to Y^n, \quad
ev_D\colon \overline{\mathcal{M}}_{\Gamma_Y}(Y,D) \to D^{\rho}
\]
and the stabilization map
\[
\pi\colon \overline{\mathcal{M}}_{\Gamma_Y}(Y,D) \to \overline{\mathcal{M}}_{g,n+\rho}.
\]
Relative GW invariants can be viewed as the
\emph{Gromov--Witten transformation}
\[
R_{\Gamma_Y}\colon H^*(Y)^{\otimes n} \otimes H^*(D)^{\otimes \rho} \to H^*(\overline{\mathcal{M}}_{g,n+\rho})
\]
defined as
\[
\operatorname{PD} \left( \pi_* \left( ev_Y^*(\alpha ) ev_D^*( \delta )
\cap [\overline{\mathcal{M}}_{\Gamma_Y}(Y,D)]^{vir} \right) \right),
\]
where $\operatorname{PD}$ stands for the Poincar\'e duality.
Let $\Gamma_{X \times Y} =(g,n,(\beta_X,\beta_Y),\rho,\mu)$.
Similarly we have
\[
R_{\Gamma_{X \times Y}}\colon
H^*(X \times Y)^{\otimes n} \otimes H^*(X \times D)^{\otimes \rho} \to H^*(\overline{\mathcal{M}}_{g,n+\rho}).
\]
Let $\Gamma_X=(g,n+\rho, \beta_X)$.
The map
\[
R_{\Gamma_X}\colon H^*(X)^{\otimes (n+\rho) } \to H^*(\overline{\mathcal{M}}_{g,n+\rho})
\]
is the Gromov--Witten correspondence $R^X_{g,n+\rho,\beta_X}$,
defining a cohomological field theory.
\begin{corollary} \label{c:2.2}
\[
\begin{split}
&R_{\Gamma_{X \times Y}}
((\alpha_1 \otimes \alpha'_1) \otimes ... \otimes (
(\alpha_n \otimes \alpha'_n));
(\alpha_{n+1} \otimes \delta_1) \otimes ... \otimes ((\alpha_{n+\rho} \otimes \delta_\rho)) \\
= &R_{\Gamma_X} (\alpha_1 \otimes ... \otimes \alpha_{n+\rho})
R_{\Gamma_Y} (\alpha'_1 \otimes ... \otimes \alpha'_n;
\delta_1\otimes ...\otimes \delta_\rho),
\end{split}
\]
where $\alpha_i \in H^*(X)$, $\alpha'_i \in H^*(Y)$ and
$\delta_j \in H^*(D)$.
\end{corollary}
\begin{proof}
This follows directly from Theorem~\ref{t:main} and the comparison result
between relative and log GW invariants in \cite[Theorem 1.1, Section 2.3]{AMW}.
\end{proof}
\subsection*{Acknowledgements}
We wish to thank Q.~Chen, W.~D.~Gillam, and S.~Marcus for helpful discussions, and the referee for valuable comments.
This research is supported in part by the NSF.
|
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| 4,871
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{"url":"https:\/\/www.transtutors.com\/questions\/the-firm-sos-sounds-of-silence-prepares-to-launch-a-revolutionary-system-of-bluetoot-5396650.htm","text":"# The firm SoS (Sounds of Silence) prepares to launch a revolutionary system of bluetooth- enabled noi\n\nThe firm SoS (Sounds of Silence) prepares to launch a revolutionary system of bluetooth- enabled noise-cancellation headphones. There are two types of consumers in the market: 400,000 \u201chigh-end\u201d consumers and 750,000 \u201cnormal\u201d consumers. It is estimated that high-end consumers are willing to pay $450 for these headphones, whereas normal consumers are willing to pay only$250. SoS is also considering selling a stripped-down version of the headphones (the stripped-down version uses wires instead of bluetooth). The high-end consumers are only willing to pay $325 for the stripped-down version. The normal consumers don't particularly care about bluetooth vs. wire connections, and they are willing to pay the same$250 for either version of headsets. Both the bluetooth version and the stripped-down version cost the same to produce: \\$100 per unit. 1. Determine the optimal pricing policy assuming that SoS only sells bluetooth-enabled headphones. (3 points) 2. Determine the optimal pricing policy assuming that SoS offers for sale both versions of headphones. (Remember: when both versions are offered for sale, consumers can choose the version they prefer, which may depend on the prices charged). (4 points) 3. Suppose that SoS finds out that its estimate of the number of normal consumers was way off: in fact, there are only 250,000 such consumers. How would you change your answer to #1 and #2 in light of this information? Explain. (3 points)\n\n## Plagiarism Checker\n\nSubmit your documents and get free Plagiarism report\n\nFree Plagiarism Checker","date":"2020-11-24 17:40:23","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.1970033347606659, \"perplexity\": 3746.3792799126127}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-50\/segments\/1606141176922.14\/warc\/CC-MAIN-20201124170142-20201124200142-00063.warc.gz\"}"}
| null | null |
Learn more at http://urinx.github.io/app/iconista/
The best & most beautiful way to set your Mac OS X beautiful!
What
----
It's easy, save, and fast tool that helps you to change your Mac Os X default applications icon, for it looks like horrible and ugly.
Which can do the followings:
* Replace the system applications icon with default themes
* Replace the some third part apps icon
* Set the files or folders icon
* Set the wallpaper
El Capitan
----------
> In OS X 10.11(El Capitan) and up, Apple add a new 'Rootless' feature -- System Integrity Protection(SIP).
>
> SIP is protecting the core apps which OS X installs into Applications and Applications Utilities. This means it will no longer be possible to change the applications which OS X installs, even from the command line when using root privileges.
>
> You can find all protected directories in /System/Library/Sandbox/rootless.conf
>
> So we cant change the icon of core apps in Applications and Applications Utilities.
>
> **Or:**
>
> If you really want to change the default apps icon, you can disable SIP. Currently this requires rebooting into recovery mode and running the command `csrutil disable`.
Install
-------
You can download it [here](https://github.com/Urinx/Iconista/releases) or just clone the soure code and then unzip it.
```
git clone https://github.com/Urinx/Iconista/archive/master.zip
```
Go to `build` folder, and `Iconista` is the main program.
```
cd build/
sudo ./Iconista
```
That's all, it's very easy, right?
How
---
For help, you can do this:
```
sudo ./Iconista -h
```
Install the default icon theme:
```
sudo ./Iconista -i
```
Restore the origin system icon:
```
sudo ./Iconista -r
```
Delete/hide the app in Launchpad:
```
sudo ./Iconista -d "Safari"
```
Set icon for file or folder:
```
sudo ./Iconista -f /path/to/file /path/to/icon
```
Install the specified theme:
```
sudo ./Iconista -s "theme_name"
```
If you disable the SIP, you can change the icon of apps which OS X installs:
```
sudo ./Iconista -i -rootless
```
Demo
----
Screenshots
-----------
Themes
------
There is only a default theme for now, but more themes will be added in the furtrue.
The icon of default theme is come from [BlackVariant (Patrick)](http://blackvariant.deviantart.com), free for non-commercial use.
License
-------
> Copyright (C) 2013-2015 Eular <uri.lqy@gmail.com>
> Licensed under the Apache License, Version 2.0 (the "License");
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 782
|
{"url":"https:\/\/www.math.tohoku.ac.jp\/tmj\/abs\/abs61_2_2.html","text":"## Tohoku Mathematical Journal 2009 June SECOND SERIES VOL. 61, NO. 2\n\n Tohoku Math. J. 61 (2009), 205-212\n\nTitle RICCI SOLITONS AND REAL HYPERSURFACES IN A COMPLEX SPACE FORM\n\nAuthor Jong Taek Cho and Makoto Kimura\n\n(Received June 19, 2008, revised August 26, 2008)\nAbstract. We prove that a real hypersurface in a non-flat complex space form does not admit a Ricci soliton whose potential vector field is the Reeb vector field. Moreover, we classify a real hypersurface admitting so-called \u201c$\\eta$-Ricci soliton\u201d in a non-flat complex space form.\n\n2000 Mathematics Subject Classification. Primary 53C20; Secondary 53C15, 53C25.","date":"2018-02-18 21:55:29","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5180444717407227, \"perplexity\": 798.3588208922165}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-09\/segments\/1518891812259.30\/warc\/CC-MAIN-20180218212626-20180218232626-00129.warc.gz\"}"}
| null | null |
Canadian Chains will strive to manufacture and distribute the highest quality Logging, Industrial, Trucking and Agricultural chain products in our marketplace. We work to meet our customer's needs by listening, responding quickly, and leading our Industry with innovative ideas and products.
When Roger Gower put some steel chain together in his backyard shop in Canaan, ME, little did he know that the chains he made with an investment of over $1200, which he later sold for a mere $250, would revolutionize the forest industry as much as the skidder itself. Roger's ring-style tire chain came from a chain he had seen in Quebec, Canada in 1962. The chains were produced out of horse shoes and made for the farm industry. After seeing this type of chain in Canada, Roger decided to name the company Canadian Chains.
In 1968, the company moved to Skowhegan, ME. In 1980, Canadian Chains made its fourth expansion, bringing its plant to 42,000 square feet. At that time, four forging hammers for making alloy fittings were added. The company had 33 employees, though peak demands brought as many as 67 people working on three shifts.
Over the span of two decades Canadian Chains became a well-known name in the industry. At the time, they produced the only forestry tire chain made in the USA. At its peak, the company had six distributors working with over four hundred dealers in North America, South America, Panama, Mexico, Australia and New Zealand. The company changed hands three times over the next decade and today is still producing a superior tire chain to compete with foreign products.
In the summer of 2000, Canadian Chains was purchased by the current owners. The new ownership believes as Roger did, that Canadian Chains was - and still is - the best tire chain made in the USA. We still produce all of our forestry tire chains with steel and chain made in the USA, and are proud to be the only company who can say our forestry chains are truly American Made. We feel our strong growth in sales since our purchase in 2000 is because of this. Canadian Chains has gone back to its roots to give customers a superior chain made to the highest standards in the industry today.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 439
|
COLUMN | Container losses [The Wet Detective]
By Mike Wall - January 5, 2021
Written by Mike Wall on January 5, 2021 . Posted in Boxship World, Ship World Features, Ship World Vessel Reviews, Work Boat World Features.
Three of the approximately 270 containers that fell overboard from the Panama-flagged MSC Zoe after it sailed through bad weather in the North Sea on January 2, 2019 (Photo: Netherlands Coastguard)
More than 80 per cent of goods traded worldwide travel on one of the more than 90,000 cargo vessels plying the world's oceans. At the heart of it all is the freight container, one of the most important inventions for global trade.
Little did we know when freight containers first came into being back in the 1960s just how widespread they would become in cargo operations. In 2019, the international liner shipping industry transported approximately 226 million containers, with cargo transported valued at more than US$4 trillion.
The first truly successful container shipping company dates to 1956, when American trucking entrepreneur McLean put 58 trailer vans, later called containers, aboard a refitted tanker ship, Ideal X, sailing them from Newark, New Jersey to Houston, Texas.
However, the first truly international transport of containers was by Atlantic Container Line, which was formed in 1965 by a consortium of four shipping companies: Wallenius Lines, Swedish America Line, the Transatlantic Steamship Company and Holland America Line. These were joined by Cunard and CGT in 1967.
The initial reason for implementing container carriage was to reduce the high rates of pilferage and damage to general cargo. However, the other advantages of shipping freight in containers were soon found to be:
Reduced ship time in port
Better berth utilisation
Improved trans‑shipment and inter‑modal operations
Reduced time between producer and consumer
Less physical handling of cargo, less damage
Good security, less pilferage
Protection against weather and detrimental atmosphere
Quality control to improve shelf life of perishables
Improved safety for personnel, cargo and equipment
Reduced tallying costs
It was about this time that I was serving as an apprenticed marine engineer aboard Cunard cargo vessels on the transatlantic route from Liverpool. Whilst in New York on one trip we were having a beer in the ward room with the stevedore foreman who was asked how containerisation would affect him. "What the hell, we'll just take a whole container!" he responded.
Reasons for cargo losses
Cargo theft is seen by the perpetrators as a low-risk, high-reward crime carrying minor criminal penalties. The FBI reports that less than 20 per cent of stolen cargo is ever recovered.
During the 1990s there was a proliferation of container thefts in southern Chinese ports. Thugs would regularly board container vessels with bolt-cutters and, clearly having inside information, open selected containers to steal any valuable contents.
Cargo is also lost when a container is lost at sea. During a twelve-year period (2008-2019), the World Shipping Council has estimated that there were on average a total of 1,382 containers lost at sea each year. Thankfully, the trend is downwards.
Losses may be caused by fires and explosions that can happen both on deck and underdeck. The rules state that dangerous cargoes (DG) should be stowed on deck, usually outboard near the bow flare. This is so that they can be easily jettisoned.
However, DG containers are often mis-declared and stowed underdeck. This can result in catastrophic consequences, the Hyundai Fortune fire and explosion being a classic example.
Losses of deck stowed containers due to freak waves and parametric rolling are becoming more frequent.
Freak or rogue waves are just that – unpredictable and spasmodic. Meteorologists and oceanographers have been unable to find any patterns. Rogues, called "extreme storm waves" by scientists, are those waves that are greater than twice the size of surrounding waves being very unpredictable and often coming unexpectedly from directions other than prevailing wind and waves.
Parametric rolling is an unstable phenomenon that can quickly generate large roll angles coupled with significant pitch motions. The rolling occurs in phase with pitch, and on containerships introduces high loads in the containers and their lashing systems. It appears that post-Panamax containerships may be particularly prone to this behaviour. This is an important issue considering the large number of these vessels scheduled for delivery in the next few years.
Parametric rolling is experienced only on container ships. It occurs when natural roll period is between 1.8 to 2.1 times the encounter period, normally associated with the pitching period. The larger the flare the more likely is the parametric roll angle and wider range of resonance. It requires a group of waves above a threshold or critical height for parametric roll to be initiated and sustained; the threshold depends on size and shape of the hull.
Addressing the problems
The size of container ships is still increasing. The new container ships coming into service have large bow flare and wide beam to decrease the frictional resistance generated when the ship fore end passes through the water. As a wave crest travels along the hull, it results in flare immersion in the wave crest and the bow comes down.
The stability (GM) varies as a result of pitching and rolling of the ship. The combination of buoyancy and wave excitation forces creates rapid rolling with larger than normal rolling angles with resultant increased and excessive rolling loads on the containers.
Container stacks that have not been stowed in an appropriate manner on deck will increase the loads on stacking cones and twistlocks, particularly when heavier loads are stowed higher in the stack where the accelerating forces are also higher. This is evidenced by the base cone pieces failing whilst the container twistlocks remain in place. Poor stowage and misdeclaration of container contents weights exacerbate this situation.
When vessels are built or modified their container lashing plan must be approved and endorsed by Class. Class carries out calculations where the worst possible conditions are used to find the maximum loading on lashings. If they are within limits, the lashing plan is approved. When container lashings fail, marine consultants use similar calculations to find the loads in the lashings.
Actual conditions experienced by the vessel when the lashings failed are entered into the calculations. The results show where the loads in lashings exceed Class limits.
If the stability of the vessel is correct there should be no lashing failures. However, lashing failures are also common on the smaller container feeder trades. One of the most common causes is poor stability where the vessel is too stiff with a large GM. This is caused by the crew failing to deballast tanks for a loaded passage. Losses also tend to be more attributable to human error, for example:
Missing lashing gear and/or lashing gear not fitted appropriately
Heavy corrosion/wastage fittings
Mixing manual and semi-automatic twistlocks
Using left- and right-hand twistlocks together
The containers lost overboard will usually sink very quickly. However, those that have lighter cargoes may float just below the sea surface, presenting a navigational hazard. There are many cases of smaller vessels' hulls being holed by contact with floating containers. Insurance losses are therefore significantly increased by the loss of the containers and damage to other vessels.
Nobody could have foreseen the hazards now facing the container shipping industry back in the 1960s. As these hazards are becoming more frequent perhaps it is time for a rethink and assessment of current lashing arrangements. Recommendations have been made by various organisations with a stake. These include:
Providing better information to the shippers on the consequences of misdeclaration of goods, especially dangerous goods
Promotion of the CTU code and improvement of its content regarding safe packing of containers
Constant review and maintenance of the equipment including corn castings, lashing materials and twist locks
Constant operational dialogue between owners and charterers on vessel capacity and stowage plans
Weather tracking and passage planning reviews
Amendment of the IMO guidelines for inspection programs for cargo transport units, including containers
Revision of the IMO's guidelines for the inspection programs for cargo transport units
Exploring the use of satellite tracking of containers
Mandatory reporting of containers lost at sea
A review of container lashing arrangements
Most major catastrophes can be shown to be caused by a number of smaller problems contributing to the final event with the possible loss of a ship, its cargo and crew. A misdeclared dangerous goods cargo in a container stowed below deck has been shown to be a classic case. A well-publicised prosecution of those responsible would go a long way to reducing such incidents.
Mike Wall
Mike Wall has been a marine educationalist for more than 50 years, writing training modules and books on various shipping technical subjects. Mike has also been a marine surveyor and consultant for more than 30 years, operating his own company in New Zealand, Fiji and Hong Kong. Due to his qualifications and experience he has been appointed to carry out many varied investigations and to give expert opinions. He is also an accredited mediator.
SITC orders two container ships
DP World reduces Australian container terminal workforce by ten per cent
Big plans for autonomous container ship
COLUMN | The ubiquitous marine surveyor [The Wet Detective]
Smart container use on the rise
Tags: Atlantic Container Line CGT China Cunard Line Holland America Line Hyundai Fortune Ideal X Swedish America Line Transatlantic Steamship Company United Kingdom USA Wallenius Lines World Shipping Council
Newbuild gas carrier handed over to Flex LNG
New Year's Day armed robbery attempt foiled on berthed car carrier in Casablanca
Ship World, launched in 1986, is your window into the ups and downs of the containership, tanker, dry cargo and port sectors.
All the latest news, opinion and speculation from the industry that drives the world economy.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,067
|
We are seeking to appoint a full time Mainscale Teacher to start in the Summer Term.
Beacon Primary is an ambitious, successful and inclusive primary school with a growing reputation in Willenhall. Our staff are highly committed, hardworking and motivated. Due to increasing numbers, we are seeking to appoint a main scale teacher to help us provide a supportive, stimulating environment and to share our high expectations of achievement for all our children.
To arrange a visit to the school, please contact the school office on 01922 710874.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 4,081
|
\section*{Introduction}
Photonic crystal (PhC) nanoresonators exhibit exceptional capability of controlling light confinement and light-matter interactions in the sub-wavelength scale, which forms a crucial foundation for many applications such as signal processing \cite{Notomi10}, information storage \cite{Notomi14}, bio-sensing \cite{Fan08}, nonlinear photonics \cite{Soljacic04}, cavity quantum electrodynamics \cite{Lodahl15}, among many others. Among various photonic crystal structures, two-dimensional (2D) photonic crystal slabs exhibit significant advantage in the engineering of the density of photonic states, the flexibility of device structure design, the scalability of optoelectronic integration, and the compatibility with current nanofabrication technology. These excellent characteristics have excited tremendous interest in recent years to develop 2D PhC slab nanoresonators on a variety of material platforms \cite{Notomi10, Notomi14, Fan08, Soljacic04, Lodahl15, Noda05, Noda07, Benisty08, Eggleton11, Trivino14, Debnath17}.
Lithium niobate (LN), known as ``silicon of photonics," \cite{Buse09} exhibits outstanding electro-optic, nonlinear optical, acousto-optic, piezoelectric, photorefractive, pyroelectric, and photoconductive properties \cite{Gaylord85}, promising for broad applications \cite{Arizmendi04}. The great application potential has attracted significant attention recently to develop LN photonic devices on chip-scale platforms \cite{Gunter07, Fathpour13, Reano14, Loncar14, Cheng15, Pertsch15, Xu15, Hu15, Shayan16, Jiang16, Bower16, Fathpour17, Loncar17, Luo17, Sun17, Luo172, Amir17, Liang17, Buse17, Loncar173, Peruzzo17, Loncar172}. However, realizing high-quality 2D LN PhC structures remains significant challenge \cite{Baida05, Gu06, Salut06, Gunter09, Pertsch10, Laude10, Baida11, Bernal12, Diziain13, Wang14, Pertsch14}, which becomes the major obstacle hindering the exploration of optical phenomena in the nanoscopic scale that would potentially result in intriguing device characteristics and novel functionalities inaccessible by conventional means.
\begin{figure*}[hbtp]
\centering\includegraphics[width=2.0\columnwidth]{fig_1.pdf}
\caption{\label{Fig1} Properties of the photonic band structure and line-defect cavity modes of the designed 2D LN photonic crystal slab. \textbf{a.} Dispersion property of the fundamental transverse-electric-like (TE-like) guided mode inside the designed 2D photonic crystal slab. {\bf b.} Schematics showing the top view and cross section of the 2D PhC slab with a line defect waveguide. {\bf c.} Lattice constant as a function of position, which is optimized for high radiation-limited optical Q. {\bf d-f.} The optical mode field profiles of the fundamental (${\rm TE_{01}^0}$ and ${\rm TE_{10}^0}$) and second-order (${\rm TE_{01}^1}$) TE cavity modes, with electric field dominantly lying in the device plane. The mode field profiles are simulated by the finite element method. The left inset shows the orientation of crystal where the optical axis is along the $z$ direction. The right inset shows the ${\rm E_{z}}$ cavity fields as a function of transverse position, at the cross sections indicated by the dashed lines. }
\end{figure*}
In this paper, we demonstrate 2D LN PhC slab nanoresonators with optical Q up to $3.51\times 10^5$, about three orders of magnitude higher than other 2D LN photonic crystal nanocavities reported to date \cite{Baida05, Gu06, Salut06, Gunter09, Pertsch10, Laude10, Baida11, Bernal12, Diziain13, Wang14, Pertsch14}. The high optical Q together with the tiny effective mode volume supports extremely strong nonlinear optical interactions, which results in interesting third harmonic generation, for the first time in on-chip LN nanophotonic devices \cite{Gunter07, Fathpour13, Reano14, Loncar14, Cheng15, Pertsch15, Xu15, Hu15, Shayan16, Jiang16, Bower16, Fathpour17, Loncar17, Luo17, Sun17, Luo172, Amir17, Liang17, Buse17, Loncar173, Peruzzo17, Loncar172}. In particular, the pure polarization characteristics of the cavity modes enabled us to reveal peculiar anisotropy of photorefraction quenching and unique anisotropic thermo-optic nonlinear response, both of which have never been reported before. It also allowed us to observe strong orientation-dependent generation of second harmonic. The demonstrated high-Q 2D LN PhC nanoresonators not only offer an excellent device platform for the exploration of extreme nonlinear and quantum optics at single-photon and few-photon level, but also open up up a great avenue towards future development of energy efficient nonlinear photonic and electro-optic signal processing.
\section*{Device design and fabrication}
\begin{figure*}[htbp]
\centering\includegraphics[width=2.0\columnwidth]{fig_2.pdf}
\caption{\label{Fig2} Fabricated device structure and experimental testing setup. {\bf a.} Scanning electron microscopic image of a fabricated 2D LN PhC slab. {\bf b.} Zoom-in image of a section of the photonic crystal slab. {\bf c.} Schematic of the experimental testing setup. MZI: Mach-Zehnder interferometer, used to calibrate the laser wavelength; VOA: variable optical attenuator; WDM: wavelength-division multiplexed filter; OSC: oscilloscope. The inset shows an optical microscopic image of a device side coupled to a tapered optical fiber. }
\end{figure*}
The major challenge in making high quality 2D LN photonic crystal structure lies in the complexity of device structures and the stringent requirement on fabrication precision which are significantly beyond current technology to define LN nanophotonic structures. For example, current plasma etching approaches generally produce a slant angle on the device sidewall \cite{Loncar14, Jiang16}. Although such a slant angle can be incorporated into the design of 1D LN photonic crystal \cite{Liang17}, it imposes serious challenge in both the design and fabrication of 2D structures which has much more stringent requirement on the sidewall verticality. On the other hand, LN is a ferroelectric crystal with strong material anisotropy, which leads to significant etching anisotropy in the device plane, making it challenging to define nanoscopic circular hole structures required by 2D photonic crystals \cite{Baida05, Gu06, Salut06, Gunter09, Pertsch10, Laude10, Baida11, Bernal12, Diziain13, Wang14, Pertsch14}.
We overcame all these challenges by optimizing the fabrication processes, which were able to produce a sidewall angle of about ${\rm 85^o}$ uniformly across the whole device structure (Fig.~\ref{Fig1} and \ref{Fig2}). Such a nearly vertical device sidewall enabled us to design well-defined photonic guided modes, as shown in Fig.~\ref{Fig1}a. We optimized the layer thickness $t$, hole radius $r$, and lattice constant $a$ of a hexagonal structure to enlarge the photonic bandgap. Detailed simulations by the finite element method shows that a layer thickness of 270~nm, a hole radius of 145~nm, together with a lattice constant of 620~nm is able to achieve an optimized bandgap of 28.1 THz in the telecom band, with the fundamental transverse-electric (TE) polarized guided mode well confined below the light line (Fig.~\ref{Fig1}a).
To produce a well-confined line-defect cavity, we employed the multi-heterostructure design \cite{Noda05}, by gradually varying the lattice constant from 620~nm to 613 nm around the center of the line-defect waveguide (Fig.~\ref{Fig1}b and c) and optimizing the waveguide width $w$ to minimize the radiation leakage. Figure \ref{Fig1}d-e show the simulated optical mode field profiles of the fundamental (${\rm TE_{01}^0}$ and ${\rm TE_{10}^0}$) and second-order (${\rm TE_{01}^1}$) TE-like cavity modes, which exhibit radiation-limited optical Qs of $1.5 \times 10^6$, $5 \times 10^5$, and $3 \times 10^5$, respectively, with effective mode volumes of 2.43$(\lambda/n)^3$, 3.06$(\lambda/n)^3$, and 4.63$(\lambda/n)^3$. In particular, the nearly vertical device sidewalls here significantly decrease the polarization hybridization, in contrast to the 1D photonic crystal nanobeams demonstrated recently \cite{Liang17}. For example, the fundamental cavity mode ${\rm TE_{01}^0}$ shown in Fig.~\ref{Fig1}d exhibits 62.5\% of its energy in the $z$-polarization lying in the device plane, and almost zero in the $x$-direction. Such a pure polarization enables us to explore intriguing anisotropy of optical phenomena, by making the line-defect cavity either in parallel with or perpendicular to the optical axis, as we will show below. For convenience, we denote the one perpendicular to the optical axis as an \emph{e-cavity} since the dominant electric field polarizes along the optical axis, corresponding to the extraordinary polarization (see Fig.~\ref{Fig1}d). Accordingly, we denote the one in parallel with the optical axis as an \emph{o-cavity} as the dominant cavity field polarizes along the ordinary polarization.
Our devices were fabricated on a $270$-nm-thick X-cut single-crystalline LN thin film sitting on a 2-${\rm \mu m}$ silicon dioxide layer on a silicon substrate. To define the photonic crystal structure, we deposited first a $400$-nm thick amorphous silicon as a hard-etching mask through plasma enhanced chemical vapor deposition. The device structure was patterned with ZEP-$520$A positive resist via electron-beam lithography, which was then transferred to the amorphous silicon mask layer with a standard reactive ion etching process. It was in turn transferred to the LN layer with an Ar$^+$ plasma etching process. The residual mask was removed by a $30$\% KOH resolvent at 70 $^{\rm o}$C. Finally, we use diluted hydrofluoric acid to undercut the buried oxide layer to form a suspended photonic crystal membrane structure (Fig.~\ref{Fig2}a and b).
\section*{Optical properties}
Figure \ref{Fig2}a and b show an example of a fabricated device. It shows clearly that we achieved a nearly vertical device sidewall both inside and outside the circular holes, uniformly across the entire device structure. The circular shape of holes is well defined and the hexagonal lattice structures is accurately patterned. To characterize the optical property of the device, we launched a continuous-wave tunable laser into the device via evanescent side-coupling with a tapered optical fiber. Figure \ref{Fig2}c shows the schematic of the experimental testing setup, where the optical wave transmitted out from the device is detected by a photodetector whose output is characterized by an oscilloscope. In the case of harmonic generation, the harmonic light was separated by a dichroic filter and then recorded by a spectrometer.
\begin{figure*}[t!]
\centering \includegraphics[width=1.550\columnwidth]{fig_3.pdf}
\caption{\label{Fig3} Linear optical properties of 2D LN PhC slab nanoresonators. {\bf a.} Laser-scanned transmission spectrum of an e-cavity. The inset shows the top-view schematic of the e-cavity device orientation with respect to the optical axes. {\bf b and c.} Detailed transmission spectra of the ${\rm TE_{10}^0}$ and ${\rm TE_{01}^0}$ cavity modes, respectively, with the experimental data shown in blue and the theoretical fitting shown in red. {\bf d.} Detailed transmission spectrum of the fundamental ${\rm TE_{01}^0}$ cavity mode in an o-cavity, with the experimental data shown in blue and the theoretical fitting shown in red. The inset shows the top-view schematic of the o-cavity device orientation. {\bf e.} Optical Qs of the ${\rm TE_{01}^0}$ mode in e-cavities as a function of the width of line-defect waveguide. The blue dots show the experimental data and the solid line shows the theoretical results simulated by the finite element method. The fluctuations on the theoretical curve are primarily due to the precision of numeric simulations, which is limited by the finite size of the computer memory. The dashed line is used for eye guidance only. }
\end{figure*}
Figure \ref{Fig3}a shows the transmission spectrum of an e-cavity device recorded when we scanned the laser over a telecom band. It shows that the devices exhibit five cavity modes located at two spectral regions between 1535 and 1541~nm and between 1572 and 1582~nm, with the mode species identified on the figure. Detailed characterizations (Fig.~\ref{Fig3}b and c) show that the fundamental cavity mode ${\rm TE_{ 01}^0}$ located at 1578.96~nm exhibits an intrinsic optical Q as high as $3.34 \times 10^5$, while the second-order mode ${\rm TE_{10}^0}$ at 1539.36~nm has an optical Q about one order of magnitude lower. The o-cavity devices exhibit same magnitude of optical quality. One example is shown in Fig.~\ref{Fig3}d, which shows an optical Q of $3.51 \times 10^5$ that is even higher than that of the e-cavity. These optical Qs are about three orders of magnitude higher than other 2D LN photonic crystal nanocavities reported to date \cite{Baida05, Gu06, Salut06, Gunter09, Pertsch10, Laude10, Baida11, Bernal12, Diziain13, Wang14, Pertsch14}. They are only about five times lower than the theoretically designed values, indicating the high quality of device fabrication. They are even more than three times higher than the 1D LN nanoresonators we demonstrated very recently \cite{Liang17}, although the 2D device structure here is significantly more complicated.
To obtain the dependence of optical Q on the width of line-defect waveguide, we characterized more than 50 e-cavity nanoresonators with varied waveguide width. Figure \ref{Fig3}e shows the results for the ${\rm TE_{01}^0}$ mode. It shows clearly that the experimentally recorded optical Q maintains above $1.5 \times 10^5$ for a large range of waveguide width between 1.10 and 1.33~${\rm \mu m}$, with a peak value appearing at $w= 1.27$ $\mu$m. This trend agrees well with the numerical simulations shown in the solid line. The o-cavities exhibit similar dependence on the waveguide width, while the waveguide width leading to the peak optical Q shifts to $w = 1.18$ ${\rm \mu m}$, simply due to the birefringence of LN crystal.
\section*{Photorefraction}
\begin{figure*}[t!]
\centering\includegraphics[width=2.0\columnwidth]{fig_4.pdf}
\caption{\label{Fig4} Laser-scanned cavity transmission spectrum as a function of input power. The input optical power remains first at 2 mW for about 15 minutes (gray region) to quench the photorefraction before we started recording the transmission spectra at different power levels. The input power corresponding to each scanning spectrum is shown in the middle. The laser wavelength is periodically scanned back and forth in a triangular fashion over a spectral range of 230~pm, with a scanning period of 100 ms. The cavity transmission spectra are shifted with each other along the vertical axis for convenient comparison. The left panel is recorded for an e-cavity (indicated on the top), where the dashed line indicates the left edge of the cavity resonance which remains unchanged with optical power. The right panel is for an o-cavity, where the red and blue dashed lines show the red and blue shifts, respectively, of the left edge of the cavity resonance. }
\end{figure*}
The high quality and the small effective mode volume of the 2D LN photonic crystal slab nanoresonators would result in dramatic enhancement of optical energy density inside the cavity, which would thus support strong nonlinear optical interaction. In particular, the pure polarization of the cavity modes in these devices enables us to explore the potential anisotropy of nonlinear optical phenomena. This anisotropy is challenging to access in 1D LN photonic crystal nanobeams \cite{Liang17} that exhibit significant polarization hybridization due to the specific shape of the device cross section. In the following, we explore photorefractive effect, thermo-optic bistability, and harmonic generation, which show intriguing behaviors in the nanoscopic scale that do not appear in any other LN photonic devices.
To do so, we selected an e-cavity and an o-cavity with the same intrinsic optical Q of $3.3 \times 10^5$ for the fundamental ${\rm TE_{01}^0}$ cavity mode. For a fair comparison between the two devices, we maintained exactly same operation conditions for the two devices, by positioning the coupling tapered fiber to maintain a same external coupling efficiency of $70$\% for both devices (accordingly, same loaded optical Q around $2.1 \times 10^5$ for both cavities). To explore the photorefractive effect, we increased the input optical power to 2 mW, at which the photorefraction is quenched in both devices, an intriguing phenomena we also observed previously in the 1D LN photonic crystal nanobeams \cite{Liang17}. We maintained the devices at this condition for about 15 minutes to stabilize the photorefraction quenching. After that, we varied the optical power and monitored the transmission of the devices when we continuously scanned the laser wavelength across the cavity resonances back and forth in a periodic triangular fashion.
Figure \ref{Fig4} shows the laser-scanned transmission spectra of the cavities at different optical power levels. The quenching of photorefraction behaves very differently in the two cavities. In the e-cavity, Fig.~\ref{Fig4}a shows that the left edge of the cavity resonance remains unchanged when the input power is varied between the whole range from 2 $\mu$W to 0.8 mW, as indicated by the dashed line. Since the left edge of the cavity resonance indicates the spectral location of the passive cavity (in the absence of optical wave), this implies a complete quenching of the photorefraction. In the o-cavity, surprisingly, Fig.~\ref{Fig4}b shows that the left edge of the cavity resonance shifts towards red when the input power increases from 0.08 mW to 0.32 mW, as indicated by the red dashed line. However, it shifts backwards towards blue when the optical power increases further from 0.32 mW to 0.8 mW, as indicated by the blue dashed line. The whole process is reversible when the optical power changes. To the best of our knowledge, this is the first time to observe such peculiar anisotropic behavior of photorefraction quenching. The underlying mechanism is not clear at this moment. One potential reason is likely related to the photovoltaic property of lithium niobate, which tends to produce photocurrent preferably along certain crystographic axis \cite{Gaylord85}. However, the exact physical nature requires further exploration in the future.
\section*{Thermo-optic nonlinearity}
\begin{figure*}[t!]
\centering\includegraphics[width=2.0\columnwidth]{fig_5.pdf}
\caption{\label{Fig5} Second harmonic generation in 2D LN PhC slab nanoresonators. {\bf a and b.} Optical microscopic images of an e-cavity and o-cavity, respectively, showing bright spots appearing when the pump wave is launched into the cavities. {\bf c.} Spectrum of generated second harmonic, with a pump wave at 1557.45 nm. {\bf d.} Recorded power of the generated second harmonic wave as a function of that of the fundamental pump wave, where the blue and purple dots are experimental recorded data for an e-cavity and o-cavity, respectively. The solid lines show quadratic fitting to the experimental data. }
\end{figure*}
Figure \ref{Fig4}a and b show clear thermo-optic bistability when the input optical power becomes significant, as expected. However, it is interesting to note that, at a same power level, the thermo-optic bistability in the o-cavity is considerably larger than that in the e-cavity. This is surprising since the two devices exhibit identical intrinsic optical Q and operates with exactly same external coupling condition, from which we expect a same temperature change due to photothermal heating. As the thermo-optic coefficient for the extraordinary polarization ($\frac{dn_e}{dT} = 3.34 \times 10^{-5}{\rm /K}$) is significantly greater than that for the ordinary light ($\frac{dn_o}{dT} = 0{\rm /K}$) at room temperature in the telecom band, and the thermal expansion along the optical axis ($\alpha^{(z)} = 0.75 \times 10^{-5} {\rm /K}$) is only slightly smaller than that along the orthogonal direction ($\alpha^{(x,y)} = 1.54 \times 10^{-5} {\rm /K}$)), we shall expect a larger thermo-optic bistability in the e-cavity instead.
The peculiar thermo-optic nonlinear behavior is likely due to the pyroelectricity of lithium niobate \cite{Gaylord85}, which produces an electric field along the crystal axis when temperature increases. The induced electric field in turn decreases the refractive index via the Pockels effect, which compensates the refractive index increase induced by the thermo-optic effect. As the Pockels effect is dominant along the optical axis, the e-cavity will experience more the pyroelectricity-induced refractive index change, leading to a smaller net increase of refractive index. Note that the time response of the pyroelectricity is primarily determined by that of the temperature variation which is the same as a normal thermo-optic effect. Consequently, the combined thermo-optic nonlinearity and the pyroelectricity-induced effect would manifest as a net thermo-optic bistability, which is smaller in an e-cavity than an o-cavity, as we observed in Fig.~\ref{Fig4}.
\section*{Harmonic generation}
\begin{figure*}[htpb]
\centering\includegraphics[width=2.0\columnwidth]{fig_6.pdf}
\caption{\label{Fig6} Third-harmonic generation in 2D LN PhC slab nanoresonators. {\bf a.} Spectrum of the generated third harmonic, with a pump wave at 1557.45 nm. {\bf b.} Recorded power of the generated third harmonic wave as a function of the fundamental pump wave, where the blue and purple dots are experimental recorded data for an e-cavity and o-cavity, respectively. The solid lines show cubic fitting to the experimental data. }
\end{figure*}
Lithium niobate exhibits significant second-order optical nonlinearity. Therefore, the strong nonlinear optical interactions in the 2D LN PhC slab nanoresonators would enable us to observe second-harmonic generation (SHG). Figure \ref{Fig5} shows an example. When we increased the optical power dropped into the e-cavity, a bright spot appeared at the center of the device structure where the nanoresonator is located, which is clearly visible in the optical microscopic image (Fig.\ref{Fig5}a). As the imaging camera has a spectral response in the visible and near infrared, the bright spot implies the generation of second harmonic. This is verified by the emission spectrum shown in Fig.~\ref{Fig5}c which shows a clear coherent emission line at 778.73 nm when we launched a pump wave into the cavity mode at 1557.45 nm. The SHG exhibits a quadratic power dependence, as shown in Fig.~\ref{Fig5}d, which is a typical signature of second harmonic generation. Figure \ref{Fig5}d shows a conversion efficiency of 0.078~${\rm \%/W}$. The small value is primarily due to the SHG frequency which is well above the light line of the 2D photonic crystal (Fig.~\ref{Fig1}a) that was designed only for high-Q cavities in the telecom band, leading to low optical Q around the second harmonic with significant radiation leakage into free space. On the other hand, the coupling tapered optical fiber was designed for operating in the telecom band, which exhibits very low coupling efficiency at shorter waveband. Future optimization of the device design and the coupling waveguide would help improve the nonlinear conversion efficiency.
We also characterized the second harmonic generation in an o-cavity, as shown in Fig.~\ref{Fig5}d. Compared with the e-cavity, the o-cavity exhibits an efficiency about 4 times lower. It is possibly because the SHG in the e-cavity is likely to be a type-0 process since the dominant cavity field polarizes along the optical axis where the nonlinear susceptibility is maximum, while that in the o-cavity is likely to be a type-II process since the cavity field is dominantly along the ordinary polarization. Interestingly, Fig.~\ref{Fig5}a and b show that SHG in the e-cavity tends to be spatially located towards the side of the line-defect cavity, while that in the o-cavity tends to be located at the center. The exact physical reason is not clear at this moment, which requires further exploration.
Of particular interest is that the nonlinear optical interaction is enhanced so much in the 2D LN PhC slab nanoresonators that we were even able to observe third-harmonic generation. This is shown in Fig.~\ref{Fig6}, where a clear emission line appears at a wavelength of 519.15 nm, which corresponds directly to the third harmonic of the pump wave at 1557.45 nm. We recorded the power dependence of the third harmonic, which is plotted in Fig.~\ref{Fig6}b. It shows a clear cubic dependence on the pump power, an intrinsic signature of third harmonic generation. To the best of our knowledge, this is the first time to observe third-harmonic generation in on-chip LN nanophotonic devices \cite{Gunter07, Fathpour13, Reano14, Loncar14, Cheng15, Pertsch15, Xu15, Hu15, Shayan16, Jiang16, Bower16, Fathpour17, Loncar17, Luo17, Sun17, Luo172, Amir17, Liang17, Buse17, Loncar173, Peruzzo17, Loncar172}. Similar to the case of the second harmonic generation, the third-harmonic generation is considerably weaker in the o-cavity (Fig.~\ref{Fig6}b, purple curve), which is likely due to the tensorial nature of the third-order nonlinear susceptibility of lithium niobate.
\section*{Discussion}
We have demonstrated 2D LN PhC slab nanoresonators with optical Q up to $3.51 \times 10^5$ that is about three orders of magnitude higher than other 2D LN PhC nanoresonators reported to date \cite{Baida05, Gu06, Salut06, Gunter09, Pertsch10, Laude10, Baida11, Bernal12, Diziain13, Wang14, Pertsch14}. The high optical Q together with tight optical mode confinement results in intriguing nonlinear optical interactions. We have observed second-harmonic generation, particularly third harmonic generation that is the first time to be observed in on-chip LN nanophtonic devices \cite{Gunter07, Fathpour13, Reano14, Loncar14, Cheng15, Pertsch15, Xu15, Hu15, Shayan16, Jiang16, Bower16, Fathpour17, Loncar17, Luo17, Sun17, Luo172, Amir17, Liang17, Buse17, Loncar173, Peruzzo17, Loncar172}. Moreover, the devices exhibits pure polarization of the cavity modes, which enabled us to probe the intriguing anisotropy of nonlinear optical phenomena. We have revealed the peculiar anisotropy of photorefraction quenching and the unique anisotropic thermo-optic nonlinear response, which have never been reported previously.
With the significant optical nonlinearity of lithium niobate material, the demonstrated high-Q 2D LN PhC nanoresonators offer an excellent device platform for exploring extreme nonlinear and quantum optical phenomena in the regime inaccesible to conventional means. For example, the low nonlinear conversion efficiency in our current devices is primarily due to the low optical Q and external coupling at the second and third harmonic. Therefore, future design to minimize the radiation leakage at the second (and/or third) harmonic frequency would significantly improve the optical Q. Moreover, appropriate design of on-chip coupling waveguide would optimize the external coupling to these waveband. The resulting device platform would further dramatically enhance nonlinear wave interactions, which would enable exploration of nonlinear and quantum optics at single and few photon levels, which would open up broad nonlinear and quantum photonic applications \cite{Lukin14}.
On the other hand, 2D PhC slab resonators are particularly suitable for optoelectronic integration \cite{Painter11, Baba12} and for scaling up to large-scale photonic integrated circuits \cite{Notomi14}. As lithium niobate exhibits strong piezoelectric effect, electro-optic effect, and electromechanical coupling, the demonstration of high-Q 2D LN PhC slab nanoresonators thus open the door towards developing large-scale electro-opto-mechanically hybrid integrated LN circuits for broad applications in communication, computing, signal processing, sensing, and energy harvesting.
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{
"redpajama_set_name": "RedPajamaArXiv"
}
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One of my favorite collecting - and selling - areas is vintage ephemera. I particularly love vintage dog ephemera.
I collect vintage Dachshund ephemera (especially Valentines and Christmas cards) but that is another blog entry - or perhaps a whole separate blog!
I love the cute, often whimsical vintage dog illustrations, of course. But it is also fun to peek into another time and see people with their pets.
My axiom as an eBay seller has always been: if it has a dog, mention the dog. Prominently. In the title and in the description.
I also recommend being as specific as possible -- not just Cute Dog Card, but Cute Poodle Card, or better yet, Cute BLACK STANDARD POODLE Card.
Although I started on line selling vintage children's books (and that will always be my first love), over time I've also come to really enjoy vintage ephemera. I have a big box of it here waiting to be listed (perhaps 400 - 500 pieces). It's a little like a treasure hunt; you never know what goodies you will find!
I certainly hope there are more vintage dogs waiting for me in my ephemera box.
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{
"redpajama_set_name": "RedPajamaC4"
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Sir Roger Blakemore Sands, (born 6 May 1942) is a British retired public servant who served as Clerk of the House of Commons from 2003 to 2006.
Sands attended University College School in Hampstead, followed by Oriel College, Oxford. He joined the House of Commons as a parliamentary clerk in 1965. In the 2006 Queen's Birthday Honours, Sands was appointed a Knight Commander of the Order of the Bath (KCB) in recognition of his service as Clerk of the House and Chief Executive of the House of Commons.
References
1942 births
Living people
Clerks of the House of Commons
Knights Commander of the Order of the Bath
Alumni of Oriel College, Oxford
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{
"redpajama_set_name": "RedPajamaWikipedia"
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Thibron (; died 391 BC) was a Spartan general. He was sent out as harmost in 400 BC, with an army of about 5,000 men, composed of 1,000 emancipated helots and 4,000 other Peleponesians, to aid the Ionians against Tissaphernes, who wished to bring them into subjection. In addition to this force, Thibron recruited 2,000 local troops upon his arrival, but was initially unable to face the Persian army in the field. However, after he was joined by elements of the Ten Thousand, he was able to seize several cities. He then, according to Xenophon, settled in to besiege Larissa, but this proved fruitless, and Thibron was ordered to abandon it. Diodorus suggests that at some point, after taking Magnesia, Thibron attempted to conquer Tralles in Ionia, but was unsuccessful and returned to Magnesia. He is then said to have withdrawn to Ephesus after Tissaphernes arrived with a large force of cavalry. In any case, Thibron was recalled to Sparta and replaced by another general, Dercylidas, before he could launch his next campaign. Upon his return to Sparta Thibron was tried and exiled for allowing his troops to plunder Sparta's allies in the region.
In 391 BC, during the Corinthian War, Thibron was again dispatched to Ionia with orders to take aggressive action against the Persian satrap Struthas, who was pursuing a pro-Athenian, anti-Spartan policy. He was given an army of 8,000 men and launched a number of successful raids into Persian territory. His raids tended to be poorly organized, however, and Struthas took advantage of this to ambush one of these expeditions. Struthas successfully lured Thibron and his men into ideal cavalry terrain before launching the attack. The Spartan army was routed and most of them, including Thibron, were killed. One source even indicates that Thibron was slain in personal combat by Struthas himself. What was left of his army was subsequently incorporated into a new army under Diphridas. It is likely that this Thibron is the same one mentioned by Aristotle as writing a treatise on the Spartan Constitution.
Notes
References
Fine, John V.A. The Ancient Greeks: A Critical History (Harvard University Press, 1983)
Tober, Daniel. ""Politeiai" and Spartan Local History" in Historia: Zeitschrift für Alte Geschichte 59.4 (2010), 412 - 431.
Year of birth unknown
391 BC deaths
4th-century BC Spartans
Ancient Greeks killed in battle
Anabasis (Xenophon)
Harmosts
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{
"redpajama_set_name": "RedPajamaWikipedia"
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cargo install bat
cargo install exa
cargo install fd-find
cargo install tealdeer
cargo install skim
cargo install thumbs
cargo install nu
cargo install git-delta
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"redpajama_set_name": "RedPajamaGithub"
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{"url":"http:\/\/tex.stackexchange.com\/questions\/84404\/page-number-in-outer-margin-affects-vertical-ruler","text":"# Page number in outer margin affects vertical ruler\n\nI adapted the idea from here to place the page numbers in the outer margin. However, by doing so, the vertical ruler disappears. I first thought that adjusting the horizontal spacing parameters for the ruler might bring it back, but it doesn't seem so. How can this be fixed?\n\n\\documentclass{scrartcl}\n\n\\usepackage[T1]{fontenc}\n\\usepackage{lmodern}\n\\usepackage[american]{babel}\n\\usepackage{scrpage2}\n\\usepackage{vruler}\n\n% comment this paragraph out and see that the ruler appears again\n\\rofoot{foo\\ \\ \\textbullet\\,\\ bar\\pageno{o}}% right odd\n\\lefoot{\\pageno{e}Foo\\ Bar}% left even\n\\def\\pageno#1{\\leavevmode\n\\vbox to 0pt{\n\\vss\n\\hbox to 0pt{%\n\\if#1o\\kern 2em\\else\\hss\\fi\\thepage\n\\if#1o\\hss\\else\\kern2em\\fi}}}\n\n\\begin{document}\n\\setvruler[10pt][1][1][4][1][10pt][10pt][-24pt][\\textheight]%\nFoo Bar\n\\clearpage\nFoo Bar\n\\end{document}\n\n-\n\nQuite subtle. :)\n\nThe vruler package distinguishes between LaTeX and Plain TeX by looking whether the \\pageno macro is defined. So with that code it guesses wrongly that the document is a Plain TeX one.\n\nChange \\pageno into \\xpageno or whatever.\n\nHere's the relevant part from vruler.sty\n\n141 \\ifx\\pageno\\undefined % this is considered as LaTeX\n142 % we assume all LaTeX versions have \\@outputpage in the form of\n143 % \\@outputpage= ...\\vbox{ ... \\vbox{...}...}... , where 2nd \\vbox\n144 % contains the true content.\n\n-\nMany thanks, that's indeed quite subtle :-) \u2013\u00a0 Marius Hofert Nov 27 '12 at 0:59","date":"2015-05-25 11:53:42","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9919742345809937, \"perplexity\": 7601.140834380137}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-22\/segments\/1432207928486.86\/warc\/CC-MAIN-20150521113208-00013-ip-10-180-206-219.ec2.internal.warc.gz\"}"}
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\section{Introduction}
Micro- and nanostructured interfaces for electromagnetic scattering continue to play a major role in photonics due to their particularly wide range of existing as well as prospective applications, e.g. for light management in solar cells\cite{spinelli2012,Otto2015,Schneider2020} and solid-state lighting devices\cite{Son2012,Park2020}, spectral molecular fingerprint detection\cite{Ding2016,Langer2020}, or colored surfaces in architecture and design\cite{Chung2012,Blaesi2017,Liu2020}.
The key challenge in ongoing research is the ability to tailor the optical response from these interfaces in a quite sophisticated manner to meet the demands of specific applications.
This fundamental scientific goal is accompanied by the engineering challenge of scalable fabrication of nanophotonic interfaces.
As today's manufacturing capabilities fall far behind proposed theoretical approaches due to the costs and complexity of their fabrication, prevalent structures are those of highest feasibility instead, e.g. in crystalline silicon solar cells pyramidal surface textures by alkaline etching still are industry standard.\cite{Wilson_2020}
While advanced techniques such as electron beam lithography provide high flexibility in terms of producing nanostructures with quite a deterministic geometry, these fabrication technologies are generally slow and expensive, thus, e.g. applied to solar cells at most feasible for proof-of-concept or research purposes.
In this work, we focus on the implementation of photonic scattering interfaces consisting of an array of identical scatterers.
The angle-resolved scattering ($ARS$) response of such a structure generally depends (a) on the arrangement of the scatterers, e.g. regularity of the array and distances between the scatterers, as well as (b) on the properties of the scatterers it is made of, e.g. size, shape, and involved materials.
The first property is described by the structure factor $S$, the latter property by the form factor $\bm{f}$, and under the assumption of the first Born approximation, it is $ARS\propto \left|\bm{f}\right|^2 S$.\cite{born_wolf1999,Zemb2002}
However, either of these two quantities usually determines the angular scattering profile of established scattering interfaces almost completely.
The strong spatial correlations present in a periodic array cause the structure factor to compact into a Dirac delta distribution.
Hence, scattering from periodic arrays is only allowed into a small fraction of all available angular directions, the well-defined diffraction orders, while any other direction is prohibited as $S$ is zero otherwise.
A fully random arrangement of scatterers is here in stark contrast.
There, no particular direction is enhanced nor suppressed due to the arrangement of the scatterers and the scattering response of the array essentially becomes identical to that of the individual scatterer.
Between these two diametrically opposed types of spatial configurations lies the parameter space of correlated disorder, which received increased interest from the photonics community in recent years.\cite{vynck2012,wiersmas2013,rockstuhlAmorphousNanophotonics2013,Riboli2014,Yu2020}
On the one hand, a spectrally broadband operation and robustness in fabrication makes the use of disorder attractive.
On the other hand, structural correlations enable effective means for directional and spectral enhancement or suppression of scattering.
A special class of disorder is the \textit{hyperuniform disordered} (HuD) case for which large-scale density fluctuations vanish as they do in periodic systems but a disordered and isotropic spatial configuration is maintained.\cite{torquato2018,Yu2020}
HuD structures have recently seen increasing interest in applications and experimental realizations due to their unique properties such as isotropic band gap formation\cite{torquato2018,Yu2020,sun2018,sapienza2017,leseur2016,florescu2009,Man2013,Florescu2013,Milosevic2019}.
In this work, we will show how a hyperuniform configuration of scatterers enables a new leverage to tailor light scattering by enabling both $S$ and $\bm{f}$ to significantly shape the resulting scattering response of the array.
The lack of large-scale density fluctuations
represents a hidden symmetry and, just as long-range translational symmetry in periodic systems, leads to a strong suppression of small-angle scattering.
However, the disorder present in our structures on short length-scales relaxes the bounds of $S$ for larger scattering angles up to the extend of random structures, thus leaving the composition of the scattering pattern to $\bm{f}$.
As scattering elements we choose TiO$_2$ nanodisks.
Low-loss high refractive index nanoparticles are renowned for their large scattering cross sections, thus constitute ideal scattering elements for this study\cite{Kuznetsovaag2016}.
Furthermore, high-index nanoparticles have received considerable attention from the metamaterials community in recent years as they allow, e.g., the study of magnetic in addition to electrical resonances at optical frequencies.\cite{Decker2013,Kuznetsovaag2016,Kruk2017}
These Mie-type resonances give rise to novel ways for near and far field manipulation such as nonlinear frequency generation\cite{Kruk2017,Koshelev2020} and wavefront shaping\cite{Jang2018,Wang2018}.
Nanodisks have been investigated in particular due to their rather simple fabrication while allowing good control over spectral features via the geometry of the disks.
Based on findings of our previous work\cite{piechulla2018}, in addition to the above we report on a novel scalable method to fabricate substrates covered with TiO$_2$ nanodisk arrays of tailored nearly hyperuniform disorder by a self-organized nanosphere deposition process.
\section{Sample fabrication scheme}
The procedure to fabricate large-scale TiO$_2$ arrays of tailored disorder relies on a nanosphere deposition technique that we have published elsewhere\cite{piechulla2018}.
By exploiting the nanospheres as a template in a subsequent dry-etching process, we significantly extend our approach by the ability to obtain disk-shaped nanoparticles.
The developed process scheme allows controlled etching of TiO$_2$, which is a material of particular interest to the photonics community due to its high refractive index in the visible spectral range, and is, to the best of our knowledge, here reported on for the first time.
The fabrication scheme (see Figure~\ref{fig:process}) starts with standard microscopic slides that are functionalized with a Al$_2$O$_3$/TiO$_2$/Al$_2$O$_3$ multilayer with thickness 13.8\,nm, 231.0\,nm and 19.5\,nm, respectively.
We use atomic layer deposition (ALD) since this method allows great control over film thickness and produces dense layers.
The thin top layer serves a double purpose.
Firstly, the surface charges of the Al$_2$O$_3$ film are essential for immobilizing the nanospheres in the subsequent nanosphere deposition.
Second, this layer transforms into a hard mask imprinted by the nanospheres.
The thick TiO$_2$ layer provides the material of the nanodisks.
The thin bottom layer serves as an etch stop to prevent overetching and damage to the substrate.
\begin{figure}[t]
\includegraphics[width=1.0\textwidth]{processScheme.pdf}
\caption{Fabrication scheme of disordered TiO$_2$ nanodisk arrays: (a) The substrate is functionalized with a Al$_2$O$_3$/TiO$_2$/Al$_2$O$_3$ layer stack. (b) Then a self-organized nanosphere deposition process is applied and the substrate is (c) tempered. The resulting domes serve as a template for the following (d) 2-step dry-etching process after which (e) arrays of TiO$_2$ nanodisks are obtained.}
\label{fig:process}
\end{figure}
In the next step we apply our nanospheres deposition using PMMA nanospheres (diameter $D=499\pm 10$\,nm) in aqueous dispersion.
In short, this technique exploits the electrostatic interactions of surface-charged nanospheres with each other and with the top Al$_2$O$_3$ layer.
The nanospheres (negatively charged) are driven towards the substrate (positively charged) and are immobilized as soon as they adsorb on the substrate surface.
The nanospheres repel each other, thus modifying the probability of the location of adsorption for another nanosphere.
After a certain density of adsorbed nanospheres is reached, no more nanospheres will attach since the repelling forces due to already adsorbed nanospheres become dominant.
Therefore, our deposition process is not only self-organized but also self-limiting, which makes it very cost-effective.
A prepared dispersion can be applied multiple times since only a tiny fraction of nanospheres is used up during one deposition.
By precisely setting the ionic strength of the dispersion, here via the addition of KCl, screening of the nanosphere surface charges within the aqueous dispersion can be controlled, providing an effective lever to control the resulting nanosphere density on the substrate.
Details and theoretical background of our nanosphere deposition method are presented elsewhere\cite{piechulla2018}.
After the nanosphere deposition, the substrate is rinsed in deionized water and directly transferred to ethylene glycol and heated to 144$^\circ$C to slightly soften the nanospheres and increase the particle-substrate bond.
This step prevents particle aggregation due to surface tension of the liquid film during drying.
After rinsing with water and drying in air, the samples undergo an additional tempering step (30\,min at 155$^\circ$C) to change the nanospheres' shape to a dome-like structure such that the area below a nanosphere is fully covered with PMMA (Figure~\ref{fig:process}c).
The transition from the nanosphere pattern to a Al$_2$O$_3$ hard mask is performed via reactive ion-etching (RIE).
As shown by Dekker {\it et al.}, Al$_2$O$_3$ prepared by ALD provides an excellent hard mask for dry etching processes due to its chemical stability and superior film quality even in thin layers.\cite{DekkerAl2O3mask}
Due to the low volatility of AlF$_3$, Al compounds can not be etched by fluorine-based dry chemistry without a significant physical component.
However, they are readily etched in chlorine chemistry.\cite{Powell1984,KooAlox2005,YunAlox2008,DekkerAl2O3mask}.
Based on this, we developed the hard mask patterning process (see methods section for technical details).
The plasma is ignited in a BCl$_3$/Ar atmosphere with a low DC bias to achieve a sufficient Al$_2$O$_3$ over PMMA etching selectivity of $\approx 0.4$ \cite{YunAlox2008}.
The etch rate of Al$_2$O$_3$ was found to be $\approx 1.1$\,nm/s and the etch time was chosen to be 29\,s, which results in slightly overetching the hard mask layer while keeping the PMMA nanospheres sufficiently intact, which are afterwards removed in a pure O$_2$ plasma.
Unlike Al$_2$O$_3$, TiO$_2$ is etched by fluorine chemistry.
Based on the work of Choi {\it et al.},\cite{ChoiDryetchingproperties2013} a CF$_4$-O$_2$-based process has been developed resulting in a TiO$_2$ etch rate of $\approx 1.5$\,nm/s and a TiO$_2$ over Al$_2$O$_3$ selectivity of $\approx 29$.
Hence, the top hard mask layer was sufficiently thick.
For the 231.0\,nm TiO$_2$ layer, we etched for 240\,s, i.e. longer than actually needed.
However, the Al$_2$O$_3$ etch stop layer beneath limits the etch depth and thereby increases repeatability of the manufacturing process (Figure~\ref{fig:process}e).
The requirements of high selectivity, high aspect ratios and smooth surfaces are difficult to meet in fluorine-based TiO$_2$ etching compared to, e.g., silicon processes \cite{GarayInductivecoupleplasma2015,Jansenblacksiliconmethod1995}, as parameters for vertical sidewalls and good selectivity also lead to self-masking effects and, thus, rough surfaces.
In our case, etching down to the etch stop layer reduces the roughness to an acceptable level for our investigations and produced relatively smooth surfaces (see Figure~\ref{fgr:SEM}b) compared to previously published results\cite{HotovyDryetchingcharacteristics2014,AdzhriReactiveIonetching2015a}.
We note that reactive ion etching processes have been successfully applied in industrial process chains and therefore do not principally impede the scalability of our fabrication method \cite{piechullaIncreasedIonEnergies2011,volkHoneycombStructureMulticrystalline2015}.
\section{Results and discussion}
The key objective of this study is to combine scattering properties of the individual TiO$_2$ nanodisk (form factor $\bm{f}$) with those introduced by positional correlations of their disordered arrangement (structure factor $S$).
Therefore, we choose the dimensions of the nanodisks, diameter $D$ and height $h$, and the characteristic distance $r_0$ of the array, i.e. the typical next-neighbor center-to-center distance defined as the first maximum of the pair correlation function $g_2(r)$ of the array\cite{torquato2018}, such that the resulting spectral features overlap.
Given the refractive index of our amorphous TiO$_2$, $n\approx$ 2.54 - 2.31 for a wavelength range of $\lambda=450-1000\,\text{nm}$, preliminary calculations using the finite-element method (FEM) predict a number of multipolar resonances in the visible and near-infrared spectral region for individual nanodisks of about 230\,nm height and 500\,nm diameter.
Accordingly, the nearest available particles size from stock, $D=499$\,nm, was chosen for the template fabrication.
For the structural resonances to spectrally coincide with the resonances of the individual nanodisks, $r_0$ needs to be of the same order as the wavelength.
We have previously demonstrated how $r_0$ can be varied by the deposition conditions.
Furthermore, we are able to statistically predict particle patterns based on a modified random sequential adsorption (RSA) model of soft spheres near the saturation density.\cite{piechulla2018}
Thus, we experimentally fabricated a set of samples comprising glass substrates covered with disordered TiO$_2$ nanodisk patterns with desired geometrical dimensions.
Additionally, one pattern that ideally shows no structural correlations, i.e. of random disorder, was fabricated by exposing the functionalized substrate to the nanosphere dispersion for only a short period of time such that the particle density is far from saturation.
In the following we discuss the properties of such samples first from a structural and later from an optical perspective.
\subsection{Structural properties}
\begin{figure}[t]
\includegraphics[width=1.0\textwidth]{SEM.pdf}
\caption{Scanning electron micrographs of a fabricated TiO$_2$ nanodisk array on glass substrate in a) top view and b) viewed at 52$^\circ$ inclination from normal. The disk density of this sample is 1.15 $\mu$m$^{-2}$ and the characteristic center-to-center distance is $r_0=828\,$nm.
}
\label{fgr:SEM}
\end{figure}
We successfully fabricated disordered arrangements of TiO$_2$ nanodisks.
Exemplary images of the fabricated TiO$_2$ nanodisk structures are shown in Figure~\ref{fgr:SEM}.
We determine an average nanodisk diameter of 455.0\,$\pm$\,5.4\,nm and an average height of 231.0\,nm.
We attribute the nanodisk diameter dispersion to the size dispersion of the nanospheres used to prepare the mask template.
In comparison to the nanospheres (499\,nm diameter), the disks are around 10\,\% smaller in diameter, which is a result of the tempering process prior to pattern transfer.
The error on disk height is negligible due to the excellent control of ALD deposition over layer thickness.
\begin{figure}[t]
\includegraphics[width=1.0\textwidth]{structureFactors.pdf}
\caption{a) Typical structure factor $S(\bm{q})$ for a fabricated disordered pattern.
b)-d) Angular average $S(q)$ for the uncorrelated pattern and two correlated patterns from experiment (dots) and simulations (solid black lines).
e)-g) Exemplary electron micrographs (detail) corresponding to structure factors to their left (scale bar: 2\,$\mu$m).}
\label{fgr:Sq}
\end{figure}
The disks are homogeneously distributed across the entire substrate surface in a disordered pattern (see characterization methods for pattern extraction)
The statistics of our patterns can be appropriately captured in Fourier space.
We consider the size dispersion of the disks sufficiently small to consider the structure factor instead of the spectral density.
However, the latter would be a more appropriate quantity to characterize polydisperse particle patterns \cite{dreyfus_diagnosing_2015}.
The (static) structure factor of a $N$-point pattern $\bm{r}_i$ is \cite{liu_direct_2016, allen1999}
\begin{equation}
S(\bm{q})=\frac{1}{N}\sum\limits_{i,j}^{N} e^{-i\bm{q}(\bm{r}_{i}-\bm{r}_{j})}
\label{eqn:Sq}
\end{equation}
with wave vectors $\bm{q}$.
In this work, we write $\bm{q}$ for wave vectors that lie in the plane of the nanodisk array and $\bm{k}$ for wave vectors of propagating free-space light modes which in general have a component perpendicular to the array plane.
The point patterns are isotropic, thus $S$ is rotationally symmetric, exemplary shown in Figure~\ref{fgr:Sq}a.
The angular average $S(q)=S(|\bm{q}|)$ is plotted for typical samples in Figure~\ref{fgr:Sq}b-d together with $S(q)$ of predicted patterns.
Figure~\ref{fgr:Sq}b shows $S(q)$ for the sample on which the nanosphere deposition was stopped prior saturation.
As a result, spatial correlations are negligible and $S(q)\approx1$ for all $q$ and we will refer to this pattern in the following as \textit{uncorrelated}.
The deviation from unity near $q=0$ stem from the fact that particles maintain a minimum distance, which becomes relevant at finite densities.
However, the random nature of the process prevails.
The particle patterns of the samples corresponding to Figures~\ref{fgr:Sq}c and d are saturated and reveal strong correlations, i.e. $S(q)$ clearly deviates from unity.
Each structure factor $S(q)$ of these patterns holds a characteristic peak $S_\text{max}=S(q_0)$ at around $q_0=7.5\,\mu$m$^{-1}$ and $q_0=10.6\, \mu$m$^{-1}$, corresponding to a characteristic next-neighbor distance of about $r_0=828$\,nm and $r_0=604$\,nm, respectively, that is also indicated in the figure.
For the sparsely coated saturated sample (Figure~\ref{fgr:Sq}c,f), we find excellent agreement between our modified RSA model \cite{piechulla2018} and experiment, whereas for the densely coated sample (Figure~\ref{fgr:Sq}d,g) a lower value of $S_\text{max}$ and a slight shift of about $-0.1\,\mu$m$^{-1}$ compared to the prediction can be observed.
A possible explanation for this deviation in the denser sample is the occurrence of aggregates, i.e. touching particles, which is not accounted for in our deposition model.
To experimentally achieve a certain characteristic distance $r_0$, we carefully adjust the electrostatic potential landscape in which the nanospheres move through during the deposition process and a rather shallow potential minimum (in the order of $-k_\text{B}T$) gives rise to a preferred next neighbor distance.\cite{piechulla2018}
However, as soon as two spheres touch each other, irreversible aggregation occurs.
Thus, the smaller the characteristic distance aimed for, the higher the probability of aggregate formation, which is supported by our observations in numerous other experiments.
Furthermore, aggregates would also explain increased values of $S(q)$ for $0<q<q_0$ in comparison to our model, as aggregate formation occurs in a random Poisson-like manner and, therefore, enhances long-range particle density fluctuations.
Therefore, aggregation and its effect on the resulting structure factor should be taken into account when considering high particle densities.
For the samples used in this work, the number share of particles present in configurations of two or more touching particles was found to be 2.6\,\%, 3.0\,\%, 9.5\,\%, and 31.2\,\% for $r_0=828$\,nm, 713\,nm, 649\,nm, and 604\,nm, respectively.
Due to the strong increase in aggregation for $r_0=604$\,nm, the pattern may be dubbed over-saturated.
Nevertheless, the general shape of the structure factor is still preserved (Figure~\ref{fgr:Sq}d).
Furthermore, we note that the final structure was obtained by patterning a flat layer.
Therefore, all nanosphere aggregates result in in-plane nanodisk aggregates, i.e. a binary height profile with no component in the third dimension.
For our samples of correlated disorder, $S(q)$ becomes small for $q$ approaching zero, which is equivalent to a suppression of density fluctuations on large length scales.
When ${S(q\rightarrow0)=0}$, structures are referred to as \textit{hyperuniform}, and \textit{stealthy hyperuniform} when $S(q)$ vanishes for an entire range of $q$ around the origin.\cite{torquato2003, torquato2018}
In real world structures, the strict criterion of $S(q\rightarrow 0)=0$ can obviously not be achieved due to fundamental aspects such as finite size and temperature effects to the least.
A practical criterion that has recently been proposed is the hyperuniformity metric\cite{kim_effect_2018,torquato2018}
\begin{equation}
H=\frac{S(q\rightarrow 0)}{S_\text{max}}.
\label{eqn:H}
\end{equation}
A system is considered as \textit{effectively} hyperuniform if $H$ is of the order of $10^{-4}$\cite{kim_effect_2018}, which is stricter than the requirement for \textit{nearly} hyperuniform patterns with $H$ on the order of $10^{-2}$\cite{torquatoRSA2006}.
In our case, $H\approx 0.032$ and the lower limit of the structure factor is $S(q\rightarrow 0)\approx 0.05$, which is slightly lower than values found for 2D random sequential adsorption of hard sphere patterns\cite{zhangPreciseAlgorithmGenerate2013}.
Therefore, we consider the structures shown here nearly hyperuniform disordered.
Besides fundamental reasons, we suspect further limitations similar to those applying to conventional RSA patterns hindering the achievement of lower degrees of hyperuniformity.
In RSA patterns, a strictly sequential adsorption of particles onto the substrate surface is assumed and except the condition that particles must not overlap no interaction potential is accounted for.
Thus, the precise position of an adsorbed particle carries a rather large amount of randomness leading to density fluctuations at large length scales, i.e. $S(q\rightarrow 0)>0$.
In our case, the particles interact with each other via repulsive electrostatic and attractive van-der-Waals forces\cite{piechulla2018}.
The probability for a particle to adhere in the vicinity of already attached particles with a characteristic distance -which we are able to set experimentally- is therefore modulated and leads to increased correlations of particle positions.
Additionally, the adsorption of particles is not strictly sequential so there might be some degree of coordination while particles are mobile.
However, the particle ensemble cannot achieve a collective configuration to minimize potential energy since they are immobilized as soon as they touch the substrate.
Thus, density fluctuations are not fully suppressed and it can therefore be assumed that $H$ in our nanosphere deposition will be at least identical or, as observed here, smaller to the RSA case.
At this point, the limits of $H$ in self-organized bottom-up techniques like ours are still an open question.
Nevertheless, the relative stealthiness of our patterns, i.e. $S(q)$ being rather small for a range of $q$'s around the origin, has a strong impact on their scattering properties as we will show in the next section.
\subsection{Optical properties}
\subsubsection{Numerical method}
To numerically reproduce the optical response of our fabricated TiO$_2$ nanodisk arrays, we apply the first Born approximation,\cite{born_wolf1999} i.e. the exciting light field for each scatterer is assumed to be the unperturbed incoming light field $\bm{E}_\text{in}$.
Throughout this work we consider plane wave irradiation through a transparent substrate of refractive index $n^- = 1.52$ occupying the $z \leq 0$ half space.
The $z > 0$ half space is vacuum with $n^+ = 1$, see Figure\,\ref{fgr:notation} for notation.
The plane wave with field amplitude $\bm{E_0}$ is $x$-polarized and normally incident onto an infinite array of identical scatterers covering the substrate, i.e. $\bm{E}_\text{in}(\bm{r}) = E_0\hat{\bm{x}}\, e^{i(k_0 z-\omega t)}$.
\begin{figure}
\includegraphics[width=0.3\textwidth]{sketch.pdf}
\caption{Sketch of the notation used throughout this work.
The nanodisk array lies in the $xy$-plane on a glass substrate and the incoming light is travelling through the substrate at normal incidence with regard to the array plane.
}
\label{fgr:notation}
\end{figure}
The scattered far field ($kr \gg 1$) of an individual scatterer can be expressed as an outgoing spherical wave (we omit the harmonic time dependence $e^{-i\omega t}$ in the following)
\begin{equation}\label{sph_wav}
\bm{E}_\text{s}(\bm{r}) = E_0 \frac{e^{ i\bm{k}\cdot\bm{r} }}{r} \bm{f}.
\end{equation}
$\bm{f}=\bm{f}(\hat{\bm{E}}_0,\bm{k}_0,\bm{k})$ is the \textit{form factor} and describes the normalized scattered field amplitude of an individual scatterer for a given polarisation $\hat{\bm{E}}_0=\bm{E}_0/|\bm{E}_0|$ and incoming and scattered wave vectors $\bm{k}_0$ and $\bm{k}$, respectively.
Furthermore, $|\bm{f}|^2=\frac{\text{d}\sigma}{\text{d}\Omega}$ is the differential scattering cross section or radiation pattern of the individual particle.
$\bm{f}$ can be readily obtained by various means, e.g. analytically by Mie theory in case of a spherical particle, or by rigorously solving Maxwell's equations with techniques such as FEM.
We write $\bm{f}_0$ for $x$-polarized irradiation normal to the array plane, i.e. $\bm{f}_0(\bm{k})=\bm{f}(\hat{\bm{x}},k\hat{\bm{z}},\bm{k})$.
Using the angular spectrum representation of Equation\,\ref{sph_wav} in its asymptotic limit ($kr\rightarrow\infty$),\cite{wolf1995} we find the normal incidence transmission and reflection of an infinite array of identical scatterers in terms of the form factor to be
\begin{eqnarray}
\label{T} T & = \frac{n^+}{n^-} & \left| t\hat{\bm{E}}_0 + \rho \frac{2\pi}{ik^+}\bm{f}_0^+\right|^2 \\
\label{R} R & = & \left| r\hat{\bm{E}}_0 + \rho \frac{2\pi}{ik^-}\bm{f}_0^-\right|^2
\end{eqnarray}
with areal density of scatterers $\rho$, Fresnel's transmission and reflection coefficients $t$ and $r$ of the bare substrate interface, wave numbers $k^+$ and $k^-$ in
substrate and vacuum, and $\bm{f}_0^\pm = \bm{f}_0 (\bm{k}=\pm\bm{k}_0)$, respectively.
Scattering into the directions normal to the array plane, $\bm{k}=\pm k\hat{\bm{z}}$,
depends on $\bm{f}_0$ and $\rho$, but not on the particular spatial arrangement of scatterers.
Interference of these fields with $t\hat{\bm{E}}_0$ and $r\hat{\bm{E}}_0$ (Equations\,\ref{T} and \ref{R}) determines the normalized power $P_\text{sca}$ that undergoes off-normal scattering,
$P_\text{sca}=1-T-R$ (neglecting absorption).
However, for off-normal scattering structural phase relations have to be accounted for by modulating
$\left|\bm{f_0}\right|^2$ by the structure factor $S(q=k_\parallel)$, with the projection $k_\parallel$ of the scattered wave vector $\bm{k}$ onto the array plane.\cite{Zemb2002}
Using $P_\text{sca}=\int_\Omega ARS\, \text{d}\Omega$, with integration of the angle-resolved scattering $ASR$ over the unit sphere $\Omega$ except for $\text{d}\Omega = \text{d}\Omega(\bm{k} \pm k\hat{\bm{z}})$, we can now write down the $ARS$ response of the array at normal incidence as
\begin{equation}\label{Born1}
ARS
= \frac{P_\text{sca}}{\int_\Omega\left|\bm{f_0}\right|^2 S\,\text{d}\Omega} \cdot \left|\bm{f_0}(\bm{k})\right|^2 S(k_\parallel)
\hspace{1cm} \bm{k}\neq \pm k\hat{\bm{z}\, }.
\end{equation}
The numerical approach described here significantly simplifies the computational efforts to predict the optical response of our structures.
The structure factor $S$ in Equation~\ref{Born1} can be taken either from experiment, e.g. by evaluating SEM pictures, or, if sufficient knowledge of the fabrication process is available, from theoretical modelling such as our modified RSA approach.\cite{piechulla2018}
Instead of numerically solving Maxwell's equations for a computational domain large enough to sufficiently approximate the statistics of a disordered array of scatterers, only the scattering response of the individual scatterer is calculated rigorously.
We shortly discuss the applicability of the first Born approximation to our structures at the end of the discussion, see below.
\begin{comment}
In the first Born approximation (Equation~\ref{Born1}), near-field coupling between neighboring particles and multiple scattering are neglected.
The near-fields of high index nanodisk resonances are mostly confined to the inside, thus, coupling only occurs for particles very close to each other.
It has been shown for Si nanoparticles with resonances in the visible that substantial coupling starts for surface-to-surface distances smaller than 25\,nm to 100\,nm.\cite{VandeGroep2016a}
Here, smallest typical surface-to-surface distances are 149\,nm, hence we conclude that the assumption of negligible near-field interaction is justified.
Multiple scattering can be neglected as we consider out-of-plane scattering of a nanodisks array at normal incidence.
\end{comment}
\begin{comment}
\begin{figure}
\includegraphics[width=1.0\textwidth]{scatterFotos.png}
\caption{Photographed forward scattering of TiO$_2$ nanodisks arranged in an (a) uncorrelated and (b) correlated pattern illuminated with collimated laser light ($\lambda=520$\,nm, normal incidence, unpolarized) onto a screen.
(c) The observed ring-shaped pattern (thick green line) evolves from light waves scattered by each individual disk (thin green line) interfering constructively or destructively as prescribed by the structure factor (orange line) of the disks' spatial arrangement (Equation~\ref{eqn:scatter}).}
\label{fgr:scatfoto}
\end{figure}
\end{comment}
\subsubsection{Angle-resolved scattering response}
\begin{figure}[t]
\includegraphics[width=1.0\textwidth]{polarplots_B.pdf}
\caption{Measured and calculated $ARS(\theta,\varphi)$ in forward direction of an uncorrelated (top row) and nearly HuD array of nanodisks (bottom row). $S$ and SEM of the uncorrelated and correlated sample are shown in Figure\,\ref{fgr:Sq}b,e and c,d, respectively.
The incoming light is $x$-polarized.
}
\label{fgr:polar}
\end{figure}
Figure~\ref{fgr:polar} illustrates how arranging identical TiO$_2$ nanodisks into a nearly HuD pattern has a remarkable impact on the resulting angular scattering response.
For two different wavelengths we compare the $ARS$ of the uncorrelated pattern in the top row and a nearly HuD pattern (characteristic distance $r_0=828$\,nm) in the bottom row.
Additionally, corresponding numerical results after the approach described above are plotted using $\bm{f_0}$ calculated by FEM and $S$ taken from our modified RSA modelling algorithm.
For the uncorrelated sample, it is $S\approx1$ for all $q$'s (see Figure\,\ref{fgr:Sq}b), thus its $ARS$ essentially remains that of the individual nanodisk but scaled by the number of illuminated particles.
Scattering is strongest at $\theta = 0^\circ$ and quickly decreases as $\theta$ increases.
In contrast to this, scattering is very different for the nearly HuD pattern with a maximum at significantly larger angles and being mostly confined within a ring-shaped area.
Spatial correlations in these structures, e.g. expressed through the existence of the characteristic distance of neighbors $r_0$, leads to similar optical phase differences for off-normal scattered light waves.
Thus, destructive as well as constructive interference occurs and even though translational symmetry is missing, intensity maxima (ring-shaped area) or minima (angular area inside ring) appear well pronounced.
Opposed to the well-know diffraction of an optical grating, which is based on interference as well, constructive interference occupies a much larger solid angle due to a range of similar but not exactly equal distances between scatterers.
E.g., for ${\lambda=540}$\,nm we find that $\int_{\theta}\int_{\varphi=0}^{2\pi}ARS\,\text{d}\Omega=80$\,\% of forward scattering is confined within $\theta < 48^\circ$ for the uncorrelated case, while the same amount is confined within $25^\circ<\theta<56^\circ$ for the nearly HuD case.
In contrast to irradiation with unpolarized light, we here observe experimentally as well as numerically a $\varphi$-dependency of the scattering response, which is very subtle for most part of the investigated spectral range but is slightly visible at $\lambda = 470$\,nm and well observed for $\lambda = 540$\,nm.
In particular, for the nearly hyperuniform sample it can be seen that for $\lambda = 470$\,nm scattering reaches out further into the $y$- than into the $x$-direction, and even more pronounced for $\lambda = 540$\,nm but perpendicular to the former, i.e. reaching out further into the $x$- than into the $y$-direction.
The same anisotropy is also present for the uncorrelated sample, but less pronounced.
\begin{figure}[t]
\includegraphics[width=\textwidth]{polarization.pdf}
\caption{Forward scattering $P(\varphi_0,\lambda)$ into the plane defined by $\varphi_0 = 0^\circ$ ($xz$-plane) and $\varphi_0 =90^\circ$ ($yz$-plane).
Experimental data of the uncorrelated sample together with simulations of a TiO$_2$ nanodisk on glass substrate as well as without substrate.
Additionally, $P_\text{el}(\varphi_0,\lambda)$ and $P_\text{mag}(\varphi_0,\lambda)$ is plotted, i.e. the radiation power of the sum of electric and magnetic dipole, quadrupole, and octupole, respectively, derived from multipole expansion analysis of the same nanodisk without substrate (see also \textit{supporting information}).
}
\label{fgr:mulipoles}
\end{figure}
To elucidate our observations, we look into the $\varphi$-dependency in more detail in Figure\,\ref{fgr:mulipoles}.
Plotted is the power scattered into the $xy$- and $yz$-plane in forward direction, $P(\varphi_0,\lambda)=\int_{\theta=0}^{\nicefrac{\pi}{2}}\int_{\varphi=\varphi_0-\Delta\nicefrac{\varphi}{2}}^{\varphi_0+\Delta\nicefrac{\varphi}{2}}ARS(\lambda)\,\text{d}\Omega$ with $\varphi_0=0^\circ$ and 90$^\circ$, respectively, and $\Delta\varphi = 3.5^\circ$, and of the uncorrelated sample together with FEM simulations of a single TiO$_2$ nanodisk on glass substrate.
Furthermore, we performed a multipole expansion analysis of a single TiO$_2$ nanodisk.
As multipole expansion is only defined for a scatterer embedded in a homogeneous medium, we analyse a TiO$_2$ nanodisk with identical geometrical dimensions in vacuum (dashed lines).
Comparing $P(\varphi_0,\lambda)$ for the isolated disc in vacuum with the case of the disk on glass substrate, we find only minor deviations, particularly for the spectral feature at $\lambda = 540$\,nm.
This indicates that the removal of the substrate has only little impact on the optical properties of the disk and insights obtained from the multipole expansion considering the isolated disc can be applied to the substrate case.
The multipole expansion reveals that for our chosen nanodisk dimensions a plethora of modes ranging from magnetic and electric dipoles up to octupoles contribute significantly to the scattering response withinin the spectral range of interest (see Figure S1 in \textit{supporting information}). None of the spectral features found in the scattering spectra can be accounted to a single mode but a mix of several modes.
However, comparing the power emitted by the sum of electric dipole, quadrupole, and octupole with the sum of their magnetic counterparts, $P_\text{el}(\varphi_0,\lambda)$ and $P_\text{mag}(\varphi_0,\lambda)$, respectively (colored dashed lines in Figure\,\ref{fgr:mulipoles}), reveals that scattering at $\lambda = 470$\,nm is predominately caused by electric modes, whereas at $\lambda = 540$\,nm it is predominately caused by magnetic modes.
The electric moments excited in the nanodisks share an equatorial plane that is oriented perpendicular to the one shared by the magnetic moments, according to the geometry of our experiment the $yz$- and the $xz$-plane, respectively.
Therefore, since their equatorial planes are also the planes of preferred scattering, excitation of these two kind of modes explains the observed $\varphi$-anisotropy observed in Figure~\ref{fgr:polar}.
However, as both kind of modes emit into small $\theta$s, the discussed effect is only significant at larger $\theta$s.
As scattering concentrates at rather small $\theta$s for the uncorrelated case, the dependency of the scattering pattern on the nature of the excited mode is only weak.
But arranging the same nanodisks into a nearly HuD pattern strongly emphasizes this effect.
Due to its structure factor, small-angle scattering is suppressed, hence giving an enhanced spatial contrast to differentiate between the nature of the excited modes.
To be specific, for TiO$_2$ disks arranged in an uncorrelated pattern the ratio $P(\varphi_0=0^\circ,\lambda)/P(\varphi_0=90^\circ,\lambda)$ at $\lambda=540$\,nm is 2.2, but it more than doubles to 5.2 in the nearly HuD case.
\begin{comment}
\begin{figure}[t]
\includegraphics[width=1\textwidth]{radiation_patterns.png}
\caption{Radiation intensity patterns from multipole expansion analysis of a TiO$_2$ nanodisk in vacuum (diameter 455\,nm, height 231\,nm) for $\lambda=470$\,nm (upper row) and $\lambda=540$\,nm (lower row).
(a) and (d): Radiation patterns of the sum (dipole, quadrupole, and octupole) of electric ($y>0$) and magnetic ($y<0$) modes. (b) and (e): Sum of all modes. (c) and (f): Same as (b) and (d) but multiplied by the structure factor of a nearly-hyperuniform arrangement of the scatterers.
Incoming light is travelling along the $+z$-direction and polarized along the $x$-axis.}
\label{fgr:rad_pat}
\end{figure}
With the coefficients obtained by multipole expansion analysis one can also plot the corresponding angular-resolved radiation intensity patterns.
In Figure\,\ref{fgr:rad_pat}a and d we plot the radiation patterns after summing up the fields of the electric and magnetic modes, respectively.
In this representation it becomes visible that the radiation pattern of the nanodisk at $\lambda=470$\,nm is dominated by electric modes which results in scattering that reaches out to larger $\theta$ into the $\varphi=90^\circ$-direction than into the $\varphi=0^\circ$-direction (Figure\,\ref{fgr:rad_pat}b).
The opposite is the case for $\lambda=540$\,nm as now radiation from magnetic modes dominate.
Since the magnetic moments are oriented perpendicular with regard to the electric moments, the radiation pattern of the magnetic modes is rotated by $90^\circ$, and thus the direction of preferred scattering (Figure\,\ref{fgr:rad_pat}d).
\end{comment}
\subsubsection{Spectral dependence of scattering response}
\begin{figure}
\includegraphics[width=.65\textwidth]{uncorrelated_vs_correlated.pdf}
\caption{Measured (left column) and calculated (right column) $\varphi$-averaged angle-resolved scattering response $ARS(\theta,\lambda)$ in forward direction of (top row) the uncorrelated TiO$_2$ nanodisk array, and the nearly HuD array with (centre row) $r_0 = 828$\,nm, and (bottom row) $r_0 = 604$\,nm.
Color scaling is identical for (a) and (b) and (c)-(f), respectively.
}
\label{fgr:corr_vs_uncorr}
\end{figure}
In Figure~\ref{fgr:corr_vs_uncorr}, we capture the spectral dependence of scattering in near HuD TiO$_2$ nanodisk arrays by plotting the calculated and experimentally measured $ARS$ against wavelength $\lambda$ and forward scattering angle $\theta$.
As the $\varphi$-dependency was discussed in the previous section and for the sake of clarity, the values are averaged over $\varphi$.
The top row shows the scattering response of the uncorrelated array, i.e. essentially the unmodified response of the individual TiO$_2$ nanodisk, the centre and bottom rows show the scattering response of two nearly HuD arrays with different characteristic distances $r_0 = 828$\,nm, and $r_0 = 604$\,nm, respectively. Both of them have been discussed in Figure~\ref{fgr:Sq}.
As indicated above for single wavelengths, experimental and calculated ARS agree as well for the whole considered spectral range.
The unmodified scattering response of the uncorrelated pattern is characterized by spectrally broadband forward scattering with its maximum at $\theta=0$.
The strongest scattering response is around $\lambda=560$\,nm, which can be attributed to the simultaneous excitation of the magnetic dipole, quadrupole, and octupole mode (see also \textit{supporting information}, Figure \ref{si:multipoles}).
The center row of Figure~\ref{fgr:corr_vs_uncorr} shows the scattering response of the nearly HuD sample that was also under study in the previous section.
In accordance to the observations for single wavelengths, the ARS is modified for the whole considered spectral range as well, i.e. transformed into a ring-shaped pattern with a scattering maximum $\theta \neq 0$.
Surprisingly, the angular range covered by the ring stays almost constant for a rather large spectral bandwidth.
To be precise, for $\lambda = 450 - 750$\,nm the major part of scattered light stays within $30^\circ < \theta < 50^\circ$, for $\lambda = 800 - 1000$\,nm, the ring radius rather abruptly increases to occupy an angular range of $50^\circ < \theta < 70^\circ$.
Scattering in both periodic and (nearly) HuD structures is based on structural phase-induced interference, therefore it is intuitive to compare the two.
In Figure\,\ref{fgr:S_and_FF}a we plot the same $S$ as in Figure\,\ref{fgr:Sq}c but converted $q$ to the corresponding scattering angle $\theta$ for each wavelength $\lambda$.
Since $S$ is a property of the arrangement of scatterers within the array, it is invariant with regards to constant $q$'s, and, thus, its course for varying $\theta$ and $\lambda$ is determined through $\theta = \arcsin{(\nicefrac{\lambda \, q}{2 \pi} )}$ (assuming normal incidence).
This general relation is fundamental for periodic structures, such as optical gratings, since it sets the only angular directions periodic structures are allowed to scatter into as long as $q$ exactly equals a multiple of reciprocal grating vectors.
The black line in Figure\,\ref{fgr:S_and_FF}a follows $S_\text{max}=S(q_0)$ of the HuD array.
Considering a periodic pattern with periodicity $a=r_0$, this line would also represent its (first) diffraction order.
The most distinct difference between $S$ of a periodic and a HuD structure is that the first consists of a set of Dirac delta functions while the latter is a continuous function.
This implies the existence of a cutoff wavelength $\lambda_\text{c}=a$ for the periodic structure, i.e. for wavelengths $\lambda>\lambda_\text{c}$, off-normal scattering is disabled since then all scattered waves become evanescent in the normal direction.
In contrast to this, the continuous nature of $S$ of a HuD structure leads to a pronounced spectral broadening of any features of $S$ as clearly visible in Figure\,\ref{fgr:S_and_FF}a.
For $\lambda_\text{c}>r_0$, i.e. when light with wavelengths longer than the one corresponding to $S_\text{max}$, non-vanishing values of $S$ still stretch over a considerable angular and spectral range enabling scattering.
For example, light waves corresponding to $S(q=6\,\mu\text{m}^{-1})=0.5\cdot S_\text{max}$ are able to propagate in free space up to $\lambda=1050$\,nm.
In case of a truly stealthy HuD structure, for which $S(q)=0$ for some finite $q<Q$, a cutoff wavelength exists as well, but in contrast to the periodic case, this wavelength can in principle be much longer than the characteristic next-neighbor distance of scatterers within the array.
\begin{figure}[!t]
\includegraphics[width=1\textwidth]{S_and_FF_2.pdf}
\caption{(a) $S(\lambda,\theta)$ of our nearly HuD pattern with $r_0 = 828$\,nm.
(b) $\varphi$-averaged $\left|\bm{f}_0\right|^2$ normalized by its maximum value for each wavelength.
The overlayed white line indicates the contribution of electric and magnetic dipole modes, $|a_1|^2+|b_1|^2$, the dashed line the contribution of higher order modes, $\sum_{i=2,3}|a_i|^2+|b_i|^2$.
(c) $ARS$ of the nearly HuD array normalized by its maximum value for each wavelength.
The dashed black line indicates a contour line of the data shown in (b) at $\left|\bm{f}_0\right|^2 =0.35$.
(d) Experimental (circles) and calculated (black) $ARS$, $\left|\bm{f}_0\right|^2$, and $S$ (all for $\lambda=700$\,nm) of the sample shown bottom in Figure\,\ref{fgr:corr_vs_uncorr}. Full and dashed lines of $ARS$ and $S$ indicate use of simulated and experimental array patterns, respectively.
(e) Experimental (circles) and calculated (lines) $1-T-R$ of different nearly HuD samples with characteristic next-neighbor distances $r_0$.}
\label{fgr:S_and_FF}
\end{figure}
However, by comparing Figure~\ref{fgr:corr_vs_uncorr}c/d and Figure\,\ref{fgr:S_and_FF}a, the $ARS$ cannot be traced back to the structure factor alone.
Indeed, we find that the form factor $\bm{f}$ has to be taken into account as well.
In Figure\,\ref{fgr:S_and_FF}b we plot the radiation pattern $\left|\bm{f}_0\right|^2$ of the individual nanodisk.
Since we focus on the angular dependence for now, $\left|\bm{f}_0\right|^2$ is normalized by its maximum value for each wavelength, i.e. by its value in forward direction ($\theta=0$).
In this representation, the angular dependencies of the different involved multipoles become visible.
For $\lambda<800$\,nm, scattering is confined roughly within $\theta< 45^\circ$ but abruptly widens up to $\theta=75^\circ$ for $\lambda>800$\,nm.
Multipole expansion analysis reveals that this is due to the electric and magnetic dipole modes being the dominant modes excited in our nanodisks for $\lambda>800$\,nm (see overlayed full and dashed white lines in Figure\,\ref{fgr:S_and_FF}b).
The resulting scattering pattern of the individual nanodisk depends on the detailed interference of all excited multipoles\cite{Mie1908}.
In contrast to higher order modes, such as quadrupole and octupole modes, the radiation pattern of pure dipole modes does not hold a $\theta$-dependence, i.e. does not posses any radiation lobes.
Therefore, as long as dipole modes are dominant their radiation pattern is only little affected by interference with higher-order modes and they keep their angularly broad scattering.
This is not the case for $\lambda<800$\,nm, as electric and magnetic quadrupoles as well as octupoles are excited, resulting in a scattering pattern that is confined to a smaller $\theta$-range.
The final $ARS$ of scatterers with form factor $\bm{f}$ arranged into an array with structure factor $S$ is proportional to their product, $\left|\bm{f}_0\right|^2 \cdot S$ (Equation\,\ref{Born1}), which we plot in Figure\,\ref{fgr:S_and_FF}c.
Essentially, this is the same data as shown in Figure~\ref{fgr:corr_vs_uncorr}d, but again we normalize to the maximum value at each wavelength to better visualize the resulting main direction of scattering.
Additionally, a contour line of the normalized radiation pattern of the individual nanodisk (Figure\,\ref{fgr:S_and_FF}c) is overlayed following the value of $\left|\bm{f}_0\right|^2$ at the absolute scattering maximum of this sample, ($\lambda=560$\,nm, $\theta=35^\circ$, see Figure~\ref{fgr:corr_vs_uncorr}d).
In this representation, it becomes visible that the angular scattering properties of our nearly HuD structures is indeed not only governed by $S$.
Comparing the contour line and the course of maximum scattering (light-yellow regions in Figure\,\ref{fgr:S_and_FF}c) reveals that the angular dependence of the individual scatterer is clearly imprinted into the angular dependence of the array.
This is in stark contrast to diffraction in periodic structures.
In these, the impact of $\bm{f}$ is limited to the intensity of a diffraction order, but $\bm{f}$ never affects the direction of propagation.
However, our observations are as well in contrast to truly random structures, in which $\bm{f}$ alone determines the scattering pattern since in those structures is $S=1$.
In fact, instead either $S$ or $\bm{f}$ dominating the scattering response, tailored disorder structures such as our HuD structures enable a precise interplay between $\bm{f}$ and $S$.
An example of how delicate this interplay can be reveals another sample with the same TiO$_2$ nanodisks but different characteristic distance $r_0=604$\,nm.
Its experimentally measured $ARS$ is plotted in Figure~\ref{fgr:corr_vs_uncorr}e and we observe a rather uniform scattering response with regards to $\lambda$ and $\theta$.
With $S$ from our modified RSA modelling we were not able to theoretically reproduce the $ARS$ as good as it is the case for the other samples.
We found better agreement using the experimentally evaluated $S$ (deduced from SEM pictures), the resulting $ARS$ is shown in Figure~\ref{fgr:corr_vs_uncorr}e.
This can also be observed in Figure\,\ref{fgr:S_and_FF}d, where we plot $\left|\bm{f}_0\right|^2$, $S$, and the resulting $ARS$ for $\lambda=700$\,nm.
It can be recognized how the slight deviations between simulated (full line) and experimental (dashed) $S$ lead to a closer agreement between $ARS$ of theory and experiment.
The need to use the experimental $S$ is due to the high share of aggregates (30.2\%) in this sample as pointed out above in the discussion on structural properties.
The occurence of aggregates is random, which shifts $S$ slightly towards unity and, for the case shown in Figure\,\ref{fgr:S_and_FF}d, increases scattering up to $\theta=70^\circ$.
We point out that many experimentally obtained disordered interfaces generally carry intrinsic correlations to some extend due to fabrication conditions and constraints, i.e. $S$, or any other appropriate representation of a structure in Fourier space, deviates from the value of a truly random structure.
As an example, it is known that black silicon surface textures prepared by dry-etching have certain correlation lengths that can be controlled through fabrication parameters, moreover, it has been shown that their correlation length correlates with the light-trapping abilities of these kind of textures in solar cells\cite{Steglich2014,Otto2015}.
However, as long as $S$ has no tendency towards zero for $q\rightarrow 0$ and $\bm{f}$ concentrates scattering into an angular region of small $\theta$'s, which is the case for most nanoparticles commonly used in the field of nanophotonics, these structures will still scatter mostly into the forward direction since their $\left|\bm{f}_0\right|^2$ and $S$ are both large.
To suppress scattering into small $\theta$s, $S$ has to be as small as possible in the corresponding $q$-range, but large otherwise, which essentially describes $S$ of a nearly HuD structure.
Therefore, we can identify (nearly) HuD as a key element to achieve high efficiency large-angle scattering.
Concerning array properties, specular transmission and reflection depend only on the areal nanodisk density $\rho$ but are independent of $S$, see Equations\,\ref{T} and \ref{R}.
This counter-intuitive result is a direct consequence of the first-Born approximation which we apply within the framework of our numerical approach, as it neglects any kind of coupling between scatterers that could change $\bm{f}$ in, e.g., dependence of distance to neighboring scatterers.
However, throughout this work and also in Figure\,\ref{fgr:S_and_FF}e, where we plot $P_\text{sca}=1-R-T$ for different nearly HuD samples made of the same nanodisks but different $S$ and $\rho$, we find good agreement between numerical and experimental results.
We take the observed agreement as a strong indication that the assumption of negligible inter-particle coupling in our samples is sufficiently justified.
We attribute the deviations between the numerical and experimental values in case of the dense sample (orange) in Figure\,\ref{fgr:S_and_FF}e to the high number of aggregates in this sample.
However, since $P_\text{sca}$ depicts the amount of light scattered, but does not imply how the angular scattering response looks like, Figure\,\ref{fgr:S_and_FF}e also reveals the potential of (nearly) HuD structures to built highly efficient scattering interfaces with a scattering response on demand (see also \textit{supporting information}).
The scattering response is up to the interplay between $\bm{f}$ and $S$ and can be tailored by adapting both precisely.
It implies that one could change $\bm{f}$ by using another scatterer geometry, and $S$ by refining the fabrication process to suppress the occurrence of aggregates at high densities and enhance hyperuniformity, or use even another suitable process to enable the fabrication of desired $S$.
\section{Conclusion}
In summary, we achieved to prepare high-index nanodisk arrays of strong correlated disorder with a novel fabrication method.
The developed technique is scalable and allows control over important properties of the array, such as nanodisk height and diameter, and characteristic next-neighbor distance, through easy-to-access experimental parameters.
Moreover, we could show that the disorder of the arrangement of the nanodisks is nearly hyperuniform, leading to rather unusual light scattering properties.
While control over the angular scattering response of conventional scattering interfaces, either periodic or random, is essentially limited by either the structure or the form factor, near hyperuniform disorder enables both quantities to substantially impact the response.
This particular ability, in consequence, leads to a fundamentally novel approach to tailor light scattering through tailoring both structure and form factor towards a scattering response on demand and paves the way to a new class of optical materials.
\section{Methods}
\subsection{Nanodisk array fabrication}
Standard 1\,mm thick 76\,x\,26\,mm object slides (soda-lime glass) were coated by thermal atomic layer (ALD) deposition in a Beneq TFS-200 ALD tool.
First, the 13.8\,nm etch stop layer of Al$_2$O$_3$ was deposited by alternating pulses of trimethylaluminum (Al(CH$_3$)$_3$) and water (250\,ms pulse duration, 100 pulses per precursor, 3\,s purge) at 180$^\circ$C\cite{otto_alox2012}. Then, a 231.0\,nm layer of TiO$_2$ was deposited at 120$^\circ$C by 3633~alternating pulses of TiCl$_4$ and water (pulse duration 200\,ms).
This layer provides the material the nanodisks are made of.
In more detailed studies on the optical properties of ALD grown TiO$_2$ found in literature,\cite{aarik1995,aarik1997,saha2014} deposition temperatures below $\approx 165^\circ$C produce smooth, amorphous films with negligible optical losses in the visible spectrum compared to higher deposition temperatures, which agrees well with our observations by electron microscopy and spectroscopic ellipsometry.
To complete the layer stack (please note Figure~\ref{fig:process}a), a layer of 19.5\,nm Al$_2$O$_3$ was deposited by ALD (165 cycles, otherwise same deposition parameters as above).
A dispersion of PMMA nanospheres with diameter of 499\,$\pm$\,10\,nm (microParticles GmbH, Berlin, Germany) was first treated in an ultrasonic bath for 30\,min to break up reversible aggregates and then diluted with a mixture of MicroPure$^{\text{TM}}$ water (18\,M$\Omega$cm) and 30\,\% isopropyl alcohol (p.a.\,grade).
Potassium chloride (KCl) was used to carefully adjust the ionic strength of the dispersion (typically in the range of $10^{-5}$\,M to $10^{-3}$\,M).
The ALD coated substrates were exposed to the dispersion for 18 hours and rinsed in deionized water afterwards.
The samples were then rinsed in ethylene glycol multiple times to remove all water since Al$_2$O$_3$ surfaces can degrade in hot aqueous solutions during the subsequent tempering step \cite{tadanaga2008}.
Pattern transfer was performed via RIE in an Oxford Plasmalab 100 System.
For the Al$_2$O$_3$ etch process, BCl$_3$ and Ar were used in a ratio of 30:20 sccm at a pressure of 10 mTorr.
The inductively coupled plasma (ICP) power was 2500\,W and the capacitively coupled plasma (CCP) power was 63\,W, resulting in a dc-bias of -89\,V \cite{YunAlox2008}.
For the TiO$_2$ etch process the gas of CF$_4$:O$_2$:Ar was 40:6:10\,sccm with the pressure kept constant at 15\,mTorr.
The ICP power was 1800\,W and the CCP power was 41\,W, resulting in a dc-bias of -81\,V.
\subsection{Characterization}
For the microstructural characterization, SEM images were recorded with a field emission microscope (FEI Versa 3D) at 4 kV.
Disk positions were extracted from images of 104\,x\,70\,$\mu$m$^2$ areas via template matching\cite{piechulla2018,opencv}.
Some disk pairs exhibit nominal surface-to-surface distances $\leq 0$\,nm (see e.g. Figure~\ref{fgr:Sq}g) due to slight merging of the PMMA particles during tempering.
Those pairs were defined as disks in aggregates.
The ALD layers were optically characterized on Silicon reference samples using a spectroscopic ellipsometer (J.A.~Woollaam M2000V). Due to the low absorption of TiO$_2$ the refractive index could reasonably approximated by Cauchy's equation with $n(\lambda_{\mu m})=2.281+0.024/\lambda_{\mu m}^2+0.006/\lambda_{\mu m}^4$, e.g. $n(\lambda=0.45\,\text{$\mu$m})\approx$\,2.54 and $n(\lambda=1.0\,\text{$\mu$m})\approx$\,2.31.\cite{aarik1997,saha2014}
Angular resolved scattering measurements were performed using a custom-made goniometer setup.
White light of a halogen lamp was collimated, linearly polarized (where applicable) and directed onto the respective sample.
The scattered light was collected and focused onto a fiber bundle by a single lens with an aperture corresponding to an acceptance angle of $\approx3.5^\circ$.
Accordingly, the lense-fiber setup was rotated about the sample from $\theta=4^\circ$ (to avoid recording the directly transmitted light) to $\theta=90^\circ$ in steps of $\Delta\theta=3^\circ$.
A monochromator (Horiba iHR550) in conjunction with a silicon photodetector (Thorlabs DET210) and a lock-in amplifier (Stanford Research Systems SR830) was used to detect the light at the fiber output in the range of 450\,nm to 1000\,nm.
Directly transmitted light at $\theta=0^\circ$ without sample was recorded as reference $I_\text{ref}(\psi,\lambda)$ for each linear polarization angle $\psi$ and for unpolarized light, in order to characterize the system response.
The presented data are $I(\theta,\psi,\lambda)=(I_\mathrm{raw}(\theta,\psi,\lambda)-I_\mathrm{dark})/(I_\mathrm{ref}(\psi,\lambda)-I_\mathrm{dark})$.
Integrations over the forward-scattering half-space were $\int_{4^{\circ}}^{90^{\circ}} I(\theta,\psi,\lambda) \sin{\theta} d\theta $, where the $\sin{\theta}$ accounts for stronger representations of larger angles.
\subsection{Numerical methods}
Point configurations were predicted via a random sequential adsorption scheme in a Monte Carlo type code.
The soft-sphere behavior of the charged colloidal particles was taken into account by modulating the probability of a particle to adhere on the substrate at a given random position within an extended radius of neighboring particles\cite{piechulla2018}.
Considering the extended radius, the saturation density in the experiment was slightly higher than in the hard-sphere case but approximately constant over a variety of number densities.
It could therefore be kept constant for the prediction of patterns.
Optimizations of the algorithm regarding computation time were inspired by the work of Zhang {\it et al.}\cite{zhangPreciseAlgorithmGenerate2013}
To calculate the angular resolved scattering response of a single nanodisk, the form factor $\bm{f(\hat{\bm{E}},\bm{k}_0,\bm{k}})$, we rigorously solved Maxwell's equations in 3D with appropriate source, material, and boundary condition settings using the time-harmonic finite-element solver \textit{JCMsuite}\cite{Pomplun2007}.
To obtain the angular resolved scattering response of an infinitely extended array of identical nanodisks, $\bm{f}$ is combined with the structure factor $S(q)$ of the point configuration of the particular array via our numerical approach based on Born's approximation (Equations\,\ref{T}-\ref{Born1}).
Multipole decomposition was performed using an integrated function of \textit{JCMsuite} that applies the multipole expansion to the scattered fields and solves for the corresponding coefficients using an algorithm presented by Santiago \textit{et al.}\cite{Santiago2019}
\begin{acknowledgement}
This work was funded by the Deutsche Forschungsgemeinschaft (DFG) through program DFG-SPP 1839 "Tailored Disorder", second period (RO 3640/6-2 and WE4051/19-2, project 278744673).
The authors thank Claudia Stehr for her excellent technical support.
\end{acknowledgement}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 7,505
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Not to be confused with survey township.
A civil township is a widely-used unit of local government in the United States that is subordinate to a county. The term town is used in New England, New York, and Wisconsin to refer to the equivalent of the civil township in these states. Specific responsibilities and the degree of autonomy vary based on each state. Civil townships are distinct from survey townships, but in states that have both, the boundaries often coincide and may completely geographically subdivide a county. The U.S. Census Bureau classifies civil townships as minor civil divisions. Currently, there are 20 states with civil townships.
Township functions are generally overseen by a governing board (the name varies from state to state) and a clerk or trustee. Township officers frequently include justice of the peace, road commissioner, assessor, constable, and surveyor. In the 20th century, many townships also added a township administrator or supervisor to the officers as an executive for the board. In some cases, townships run local libraries, senior citizen services, youth services, disabled citizen services, emergency assistance, and even cemetery services. In some states, a township and a municipality that is coterminous with that township may wholly or partially consolidate their operations.
Depending on the state, the township government has varying degrees of authority.
In the Upper Midwestern states near the Great Lakes, civil townships (known in Michigan as general law townships and in Wisconsin as towns), are often, but not always, overlaid on survey townships. The degree to which these townships are functioning governmental entities varies from state to state and in some cases even within a state. For example, townships in the northern part of Illinois are active in providing public services — such as road maintenance, after-school care, and senior services — whereas townships in southern Illinois frequently delegate these services to the county. Most townships in Illinois also provide services such as snow removal, senior transportation, and emergency services to households residing in unincorporated parts of the county. The townships in Illinois each have a township board, whose board members were formerly called township trustees, and a single township supervisor. In contrast, civil townships in Indiana are operated in a relatively consistent manner statewide and tend to be well organized, with each served by a single township trustee and a three-member board.
Civil townships in these states are generally not incorporated, and nearby cities may annex land in adjoining townships with relative ease. In Michigan, general law townships are corporate entities (e.g. they can be the subject of lawsuits), and some can become reformulated as charter townships, a status intended to protect against annexation from nearby municipalities and which grants the township some home rule powers similar to cities. In Wisconsin, civil townships are known as "towns" rather than townships, but they function essentially the same as in neighboring states. In Minnesota, state statute refers to such entities as towns yet requires them to have a name in the form "Name Township". In both documents and conversation, "town" and "township" are used interchangeably. Minnesota townships can be either Non-Urban or Urban (giving the township government greater power), but this is not reflected in the township's name. In Ohio, a city or village is overlaid onto a township unless it withdraws by establishing a paper township. Where the paper township does not extend to the city limits, property owners pay taxes for both the township and municipality. Ten other states also allow townships and municipalities to overlap.
In Kansas, some civil townships provide services such as road maintenance and fire protection services not provided by the county.
In New England, the states are subdivided into towns, which are fully functioning municipal corporations that provide most local services. While counties exist in New England, for the most part they serve as dividing lines for state judicial systems. With the exception of a few remote areas of New Hampshire, Vermont and Maine, every square foot of New England lies within the borders of an incorporated town. New England also has cities, most of which are towns whose residents have voted to replace the town meeting form of government with a city form.
In portions of New Hampshire, Vermont and Maine, county subdivisions that are not incorporated are occasionally referred to as townships, or by other terms such as "gore", "grant", "location", "plantation", or "purchase".
In New York, counties are further subdivided into towns and cities, the principal forms of local government. Towns fulfill a function similar to those of townships in other states. As is the case in New England, every square foot of New York's territory is incorporated; all New York residents who do not live in a city or a Native American reservation live in a town. New York towns contain one or more incorporated villages, and village residents pay both town and village taxes. Towns also include a number of unincorporated hamlets.
A Pennsylvania township is a unit of local government, responsible for services such as police departments, local road and street maintenance. It acts the same as a city or borough. Townships were established based on convenient geographical boundaries and vary in size from six to fifty-two square miles (10–135 km²). A New Jersey township is similar, in that it is a form of municipal government equal in status to a village, town, borough, or city, and provides similar services to a Pennsylvania township.
In the South, outside cities and towns there is generally no local government other than the county.
North Carolina is no exception to that rule, but it does have townships as minor geographical subdivisions of counties, including both unincorporated territory and also land within the bounds of incorporated cities and towns (as well as the extraterritorial jurisdiction of municipalities). Every county is divided into townships as mandated since the North Carolina Constitution of 1868. Some urbanized counties such as Mecklenburg County (Charlotte) now number their townships (e.g. "Township 12") rather than using names. Townships all over the state used to have some official organization and duties but now are only considered ceremonial divisions of each county. Township names are still used quite extensively at the county government level in North Carolina as a way of determining and dividing up areas for administrative purposes; primarily for collecting county taxes, determining fire districts (e.g. Lebanon Township in Durham County gives its name to the Lebanon Volunteer Fire Department), for real estate purposes such as categorizing land deeds, land surveys and other real estate documents, and for voter registration purposes. In most areas of North Carolina that are outside any municipal limit (outside cities or towns), townships are used to determine voter polling places, and in most instances county election boards divide up their voter precincts by township. However, there is no government per se at the township level in North Carolina, and there are no elected or appointed offices associated with townships.
Iowa had 1,608 townships in 1942. By 1952, their responsibilities and functions had essentially been absorbed by their counties, were considered "vestigal", and were no longer counted.
Missouri had 329 townships in 1952, with "limited powers", primarily limited to local roads and bridges.
Oklahoma did have civil townships statewide upon statehood. On August 5, 1913, Oklahoma voters passed the Oklahoma Township Amendment, also known as State Question 58. This allowed the creation or abolishment of townships on a county by county basis. By the mid 1930s, all counties had voted to abolish them. Their former names and boundaries were used for United States census counting purposes and census documentation through 1960, after which Census Counting Divisions (CCDs) were used.
South Carolina had 2 townships in 1952, those of Folly Island, and Sullivan's Island.
The 1870 Constitution of Virginia required the division of counties into townships, but an amendment in 1874 converted those townships into magisterial districts.
Washington had 70 townships in 1952, in only Spokane and Whatcom counties, for administration of local roads.
Township for other divisions called "township"
↑ "What is a Township?". Michigan Township Association. 2006-12-05. Retrieved 2007-01-24.
↑ "Minnesota Statutes 368.01: Powers of Certain Metropolitan Area Towns". Retrieved 2008-06-04.
↑ "Commissioners Meeting" (PDF). Medina, Ohio: Medina County, Ohio. 2005-05-23. p. 5. Retrieved 2009-10-22. Lynda Bowers, Lafayette Township Trustee, noted that we already have property that is dual citizenship and they pay taxes in 2 places. There is Chippewa Lake in Lafayette Township, Westfield Village in Westfield Township and Lodi in Harrisville Township.
↑ "Municipalities and Townships". Lists & Structure of Governments. Washington, D.C.: United States Census Bureau. 2009-06-08. Retrieved 2009-10-22.
1 2 United States Census Bureau. 2012 Census of Governments: Individual State Descriptions: 2012, Washington, DC: U.S. Department of Commerce, p. viii.
↑ State and Local Government Special Studies: 1948-1961. U.S. Department of Commerce [and] U.S. Department of Labor. 1982.
↑ "Oklahoma Township Government, State Question 58 (August 1913) - Ballotpedia". Retrieved 2017-11-03.
↑ "Wagoner County - 1928 - 1937". www.ok.gov. Retrieved 2017-11-02.
↑ "NUMBER OF INHABITANTS - OKLAHOMA (1960)" (PDF).
↑ "NUMBER OF INHABITANTS - OKLAHOMA (1970)" (PDF).
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{
"redpajama_set_name": "RedPajamaC4"
}
| 799
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IZ est une abréviation, qui signifie :
Iž est une île de Croatie ;
Iz est un des surnoms d'Israel Kamakawiwoʻole, musicien et chanteur hawaïen (1959-1997) ;
( en anglais) est un groupe musical sud-coréen ;
IZ est également un code, qui signifie :
Irak, selon la liste des codes pays utilisés par l'OTAN, code alpha-2,
Arkia (Israël), selon la liste des codes AITA des compagnies aériennes.
Code
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 7,846
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The push comes after a "waste audit" of dumpsters at two on-campus locations conducted by the school's Office of Sustainability.
Students are now looking to pressure food trucks to give up their Styrofoam containers, which may prove difficult as food trucks at one of the locations park on a public street.
The dining halls at Yale University do not use Styrofoam containers, but local food trucks do, and they are now being targeted by student leaders in the interest of promoting sustainability.
Three student government organizations—the Yale College Council, the Graduate Student Assembly, and the Graduate and Professional Student Senate (GPPS)—have now passed resolutions to form a committee that will be tasked with examining the feasibility of banning Styrofoam containers on campus, The Yale Daily News reported Tuesday.
"Sustainability is a mission that the entire generation of students feels very passionate about."
The resolution was first passed by the GPPS in May, with the other two bodies following suit last week. Whereas the GPPS resolution only envisions a reduction in Styrofoam use, though, the GSA resolution sets a goal of banning the substance altogether.
The GSA resolution identifies the motivation behind the effort, crediting a recent "waste audit" of dumpsters at two on-campus locations conducted by the Yale Office of Sustainability. The dumpsters, located on Science Hill and on the Medical School campus, were chosen for their proximity to areas where privately-owned food trucks do business on or near the campus.
One difficulty the initiative will likely face is that Yale only has the power to enforce the ban on the food trucks on Science Hill, because vendors in that area rent parking spaces from the university while those near the Medical School campus park on a public street.
The GSA resolution also acknowledges that many food vendors might be reluctant to switch to higher-cost materials, especially if their competitors do not make the transition as well, prompting Yoon to suggest that the committee could exert institutional pressure on the vendors while also working with them to find affordable alternatives.
"Although businesses on Yale campus properties … are not run by Yale, we should use our institutional leverage to change New Haven," Yoon said, proposing as an example that compliant vendors could be rewarded with "Yale Green Badges" that might encourage environmentalists on campus to patronize them more frequently.
Somewhat ironically, given that one of the primary objections to Styrofoam is that it is non-biodegradable, the YCC and GSA resolutions were passed less than two weeks after the publication of two research papers reporting a promising new technique for decomposing the plastic-based material based on research pioneered at Yale in 2011.
According to Fast Company, a self-described progressive business media website, Stanford researcher Wei-Min Wu published a pair of research papers on September 21 claiming that wax-worms and mealworms are adept at breaking down Styrofoam products, converting them into carbon dioxide and tiny shreds that Wu suggests might be useful in soil.
The concept Wu describes is similar to one identified in a 2011 study by researchers from Yale, who discovered a certain type of fungus in the Amazon rainforest that produces enzymes capable of breaking down plastics, which they proposed adapting for commercial use.
Spokespersons for Yale did not respond by press time to requests for comment from Campus Reform.
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Ministri del tesoro del Regno d'Italia
Ministri del tesoro della Repubblica Italiana
Ministri del tesoro, del bilancio e della programmazione economica della Repubblica Italiana
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"redpajama_set_name": "RedPajamaWikipedia"
}
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'The Iron Lady' (Blu-ray/DVD Combo + Digital Copy)
(Meryl Streep, Jim Broadbent, et al / 3-Disc Blu ray+DVD / PG-13 / 2012 / The Weinstein Company)
Overview: 'The Iron Lady' is a surprising and intimate portrait of Margaret Thatcher (Two-time Oscar� winner Meryl Streep), the first and only female Prime Minister of The United Kingdom. One of the 20th century�s most famous and influential women, Thatcher came from nowhere to smash through barriers of gender and class to be heard in a male-dominated world.
DVD+Blu Ray Verdict: Margret Thatcher (Meryl Streep) is in the final years of her life. She suffers from dementia and often carries on conversations with her husband who has been dead for 8 years. She has many flashbacks to her younger years when she went to Oxford University and had a desire to go into politics. She was the daughter of a grocer who was also the mayor in the town in which they lived.
She had a hard and focused personality but she has declined to the point where she needs constant care, supervision and protection. Her political successes came as she won three elections for Prime Minister of England and the leader of the Conservative Party for over 11 years.
This movie has a major asset, the acting of Meryl Streep, who once again proves that she is possibly the best character actor of all time. Beyond her amazing performance this movie suffers for many reasons. Hollywood likes to take pot shots at leaders and this is no different. Margret Thatcher hated Socialism and Communism and fought to keep England a democratic and market driven country thriving on the intellect and inventiveness of its people. In the movie she is vilified (as she was during her career) but unfortunately this movie only seems to focus on vilifying her and illustrating her Alzheimer's and dementia.
The most powerful women in political history also had as many admirers as those who hated her policies. She broke the unions and fought the government from printing money just to be more socialistic. The unions wanted a 30% pay increase. England was going into debt and high inflation was rampant. She helped lead them back to stability and financial security. She believed in taking action and fighting for what was right. She wanted to do something to make the world better rather than just trying to be someone.
This movie was focused on belittling Margret Thatcher and depicting her as an old lady severely ill and as a bully when she was Prime Minister. Over 50% of the film was focused on her dementia instead of the powerful influence she had on the world. She was one of the leaders who helped stop the cold war with Russia but this topic was hardly even touched!
The acting of Meryl Streep was superb but the script and story line was shameful. Hollywood does it again! This movie is not worth seeing for the story but the acting of Streep is the hook that will make you want to see it! This is a Widescreen Presentation (1.85:1) enhanced for 16x9 TVs and comes with the Blu ray Special Features of:
Making The Iron Lady (12:20)
Recreating The Young Margaret Thatcher (2:44)
Denis: The Man Behind The Woman (2:33)
Battle In The House Of Commons (2:28)
Costume Design: Pearls And Power Suits (2:43)
History Goes To The Cinema (18:04)
DVD Copy + Digital Copy
www.weinsteinco.com/sites/iron-lady
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
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\section{Introduction}\label{intro}
We prove a Harnack inequality for distributional solutions to the degenerate elliptic PDE
\begin{equation}\label{5.1}
\Delta_y u+\beta(y)u_x+\gamma(x,y)u=0
\end{equation}
in cylindrical domains in $\mathbb{R}^N$ with axes in the direction of the first variable $x$. Here $\gamma$ is bounded measurable and $\beta$ is a smooth function such that the operator
\begin{equation}\label{5.1a}
L =\sum_{n=1}^{N-1} X_n^2 + X_0 := \sum_{n=1}^{N-1} (\partial_{y_n})^2 + \beta(y)\partial_x = \Delta_y + \beta(y)\partial_x
\end{equation}
satisfies H\" ormander's hypoellipticity condition. That is, vector fields $\{X_n\}_{n=0}^{N-1}$ and their commutators up to certain order span the whole tangent space $\mathbb{R}^N$ at each $(x,y)$. Moreover, $\beta$ changes sign so that $L$ is not parabolic, since then the ``elliptic'' Harnack inequality \eqref{5.3} below would not hold in general. These conditions on $\beta$ are equivalent to hypothesis \eqref{5.2} below and our result is then as follows:
\begin{theo}\label{T.5.1}
Let $D\subseteq \mathbb{R}^{N-1}$ be open connected and $u:(a,b)\times D\to[0,\infty)$ a bounded distributional solution of \eqref{5.1}
with $\gamma$ bounded measurable and $\beta$ satisfying for some $r\in\mathbb{N}$,
\begin{equation}\label{5.2}
\beta\in C^{\infty}(D), \ \ {\inf_{D}\,\beta<0<\sup_{D}\,\beta}, \ \ \text{and} \ \
\sum_{0\le |\zeta|\le r} |D^\zeta \beta(y)|>0 \text{ for all $y\in D$}.
\footnote{For $\zeta=(\zeta_1,\ldots,\zeta_{N-1})\in\mathbb{N}^{N-1}$, we let $|\zeta|=\zeta_1+\cdots+\zeta_{N-1}$ and $D^{\zeta}\beta(y)=\frac{\partial^{|\zeta|}\beta}{\partial y_1^{\zeta_1}\cdots\partial y_{N-1}^{\zeta_{N-1 }}}(y)$.}
\end{equation}
Then for each $[a',b']\subseteq (a,b)$ and bounded open $D'$ with $\overline{D'}\subseteq D$, there is $C>0$, depending only on $D$, $D'$, $\beta$ and an upper bound on $(a'-a)^{-1},(b-b')^{-1},b'-a'$, and $\|\gamma\|_\infty$, such that
\begin{equation}\label{5.3}
\sup_{(a',b')\times D'} u \le C \inf_{(a',b')\times D'} u.
\end{equation}
\end{theo}
{\it Remark.} We note that $\Delta_y$ could be replaced by any $x$-independent, uniformly elliptic in $y$ operator on $D$, but for the sake of simplicity we state the theorem with $\Delta_y$ instead.
\smallskip
This result is motivated by its application in our work \cite{hz} on large amplitude $A\to\infty$ asymptotics of traveling fronts in the $x$-direction, and their speeds, for the reaction-advection-diffusion equation
\begin{equation}\label{eqv}
v_t+A\,\alpha(y)\,v_x=\Delta_{x,y} v+f(v)
\end{equation}
on $\mathbb{R}^{N+1}$, with the first order term representing a shear flow in the $x$-direction and $f$ a non-negative reaction function vanishing at 0 and 1. The front speeds in question are proved to satisfy $\lim_{A\to\infty}c^*(A\alpha,f)/A= \kappa(\alpha,f)$ for some constant $\kappa(\alpha,f)\ge 0$, so after substituting the front ansatz $v(t,x,y)=u(x-c^*(A\alpha,f)t,y)$ into \eqref{eqv} and scaling by $A$ in the $x$ variable, one formally recovers \eqref{5.1} in the limit $A\to\infty$, with $\beta(y):=\kappa(\alpha,f)-\alpha(y)$ and $\gamma(x,y):=-f(u(x,y))/u(x,y)$.
The study of hypoelliptic operators of the form
$$L=\sum_{n=1}^{M} X_n^2 + X_0$$
(where $X_n$ are first order differential operators with smooth coefficients), possibly with an additional potential term,
has been systematically pursued since H\" ormander's fundamental paper \cite{Hor}. Although various regularity and maximum principle results have been obtained soon thereafter (see, e.g., \cite{Bony,FP,Fol,NSW,rs,sv}), Harnack inequalities and related heat kernel estimates for such operators have initially been proved only in the case when the tangent space at each point is spanned by the fields $\{X_n\}_{n=1}^{M}$ and their commutators, sometimes with $X_0$ either zero or a linear combination of $\{X_n\}_{n=1}^{M}$ \cite{Bony,Jer,JS,KS,KS2}.
More recently, Harnack inequalities have been obtained without this assumption for certain special classes of operators, not including \eqref{5.1} with general $\beta,\gamma$. Specifically, some operators with constant and linear coefficients, such as the Kolmogorov operator $L=\partial^2_{yy} + y\partial_x -\partial_t$, were considered in \cite{GL,PP}, and cases of more general coefficients satisfying somewhat rigid structural assumptions (see hypothesis [H.1] in \cite{PP2}) were studied in \cite{KL,PP2} and with a potential term in \cite{PR}. The domains involved in the obtained inequalities have to depend on the metrics associated to the operators rather than the Euclidian metric, as shows a counter-example to a Harnack inequality in \cite{GL}. This is related to the need for the sign-changing assumption on $\beta$ here. We also note that the operators considered in these papers involve the term $\partial_t$ and appropriate ``parabolic-type'' Harnack inequalities are obtained, but corresponding ``elliptic'' inequalities follow from these.
It was a mild surprise to us that we were not able to find in the literature a sufficiently general result which would include our case \eqref{5.1}. It appears that Harnack inequalities and heat kernel estimates become much more involved when the field $X_0$ is required for H\" ormander's condition to be satisfied. One hint in this direction is the fact that the sign-changing hypothesis on $\beta$ is necessary for \eqref{5.3} to hold, so hypoellipticity of $L$ is in itself not a sufficient condition.
We therefore believe that our method of proof of Theorem \ref{T.5.1} in the next section is itself also a valuable contribution to the problem of quantitative estimates for hypoelliptic operators. The proof is based on the Feynman-Kac formula for the stochastic process associated with the operator $L$, and uses the independence of $L$, and thus also of the stochastic process, on $x$. It is not immediately obvious whether this requirement can be lifted and replaced, for instance, by some assumption on the relation of the stochastic processes associated to $L$ and starting from two different points which can be connected by a path with tangent vector $X_0$ at each point. We leave this as an open problem.
We thank Luis Caffarelli, Nicola Garofalo, Nicolai Nadirashvili, Brian Street, and Daniel Stroock for useful discussions and pointers to references. FH is indebted to the Alexander von~Humboldt Foundation for its support. His work was also supported by the French {\it Agence Nationale de la Recherche} through the project PREFERED. AZ was supported in part by NSF grants DMS-1113017 and DMS-1056327, and by an Alfred P. Sloan Research Fellowship. Part of this work was carried out during visits by FH to the Departments of Mathematics of the Universities of Chicago and Wisconsin and by AZ to the Facult\'e des Sciences et Techniques, Aix-Marseille Universit\'e, the hospitality of which is gratefuly acknowledged.
\section{Proof of Theorem \ref{T.5.1}}\label{proof}
Without loss we can assume ${\inf_{D'}\,\beta<0<\sup_{D'}\,\beta}$ and $D'$ connected, after possibly enlarging $D'$.
We will also assume $a=-5$, $a'=0$, $b'=1$, $ b=6$, $D=B_3(0)$, $D'=B_1(0)$, and $\|\gamma\|_\infty\le 1$, with $C$ then only depending on $\beta$, because the general case is analogous. We also note that \cite[Theorem 18(c)]{rs} and boundedness of $u$ show that $u$ is actually continuous.
We first claim that for each $d>0$ there is $C_{d,\beta}\ge 1$ such that
\begin{equation}\label{5.4}
\sup_{{[0,1]}\times A_d} u \le C_{d,\beta} \inf_{{[0,1]}\times B_1(0)} u,
\end{equation}
with $A_d:=A_d^+\cup A_d^-$ and $A_d^\pm := \{ y\in B_1(0) \,\big|\, \pm\beta(y)> d \}$. Clearly it suffices to show this for all small enough $d$ such that $A_d^\pm\neq \emptyset$, which we shall assume.
To this end, note that parabolic regularity theory with $x$ as the time variable, applied on $[-1,5]\times \{ y\in B_2(0) \,\big|\, -\beta(y)> d/2 \}$, yields
\begin{equation}\label{5.5}
\sup_{[0,1]\times A_d^-} u \le C_{d,\beta}' \inf_{[2,5]\times A_d^-} u,
\end{equation}
where $C'_{d,\beta}>0$ depends only on $d$ and $\beta$.
Similarly, we obtain
\begin{equation}\label{5.6}
\sup_{[3,4]\times A_d^+} u \le C_{d,\beta}' \inf_{[-1,2]\times A_d^+} u,
\end{equation}
Next, consider the stochastic process $(X_t^{x,y},Y_t^{x,y})$ starting at $(x,y)\in\mathbb{R}\times B_2(0)$ and satisfying the stochastic differential equation
\[
(dX_t^{x,y},dY_t^{x,y})= (\beta(Y^{x,y}_t)dt, \sqrt{2}\,dB_t) , \qquad (X_0^{x,y},Y_0^{x,y})=(x,y).
\]
Here $t$ is a new time variable and $B_t$ is a normalized Brownian motion on $\mathbb{R}^{N-1}$ with $B_0=0$ (defined on a probability space $(\Omega,\mathcal{B},\mathbb{P})$). We then have
\begin{equation}\label{5.8b}
(X_t^{x,y},Y_t^{x,y}) = (X_t^{0,y}+x, \sqrt 2 B_t +y).
\end{equation}
for any $(x,y)\in\mathbb{R}\times B_2(0)$, in particular, $Y_t^{x,y}$ is independent from $x$. For any $y\in B_2(0)$ we also define the stopping time
\[
\tau=\tau_y:=\inf \big\{t>0\,\big|\, Y_t^{x,y}\notin B_2(0) \big\}.
\]
If $t\wedge \tau:=\min\{t,\tau\}$, then by the Feynman-Kac formula, $\|\gamma\|_\infty\le 1$, and the parabolic comparison principle, we have for each $t\ge 0$ and $(x,y)\in\mathbb{R}\times B_2(0)$,
\begin{equation} \label{5.8}
e^{-t} \mathbb{E}(u(X_{t\wedge \tau}^{x,y},Y_{t\wedge \tau}^{x,y})) \le u(x,y) \le e^{t} \mathbb{E}(u(X_{t\wedge \tau}^{x,y},Y_{t\wedge \tau}^{x,y})).
\end{equation}
(The Feynman-Kac formula is usually stated for $C^2$ functions so we provide a proof of \eqref{5.8} in Lemma \ref{L.5.2} below.)
Here
\begin{equation} \label{5.8a}
\mathbb{E}(u(X_{t\wedge \tau}^{x,y},Y_{t\wedge \tau}^{x,y})) = \int_\Omega u(X_{t\wedge \tau}^{x,y}(\omega),Y_{t\wedge \tau}^{x,y}(\omega)) d\mathbb{P}(\omega) = \int_{\mathbb{R}\times \overline{B_2(0)}} u(x',y') d\mu_t^{x,y}(x',y'),
\end{equation}
with the probability measure $\mu_t^{x,y}$ on $\mathbb{R}\times \overline{B_2(0)}$ such that $\mu_t^{x,y}(A) = \mathbb{P}((X_{t\wedge \tau}^{x,y},Y_{t\wedge \tau}^{x,y})\in A)$ for Borel sets $A\subseteq\mathbb{R}\times\overline{B_2(0)}$. Notice that $\mu_t^{x,y}$ is supported on $[x-\|\beta\|_\infty t, x+\|\beta\|_\infty t] \times \overline{B_2(0)}$ and $\mu_t^{x,y}(\mathbb{R} \times\partial B_2(0)) = \mathbb{P}(\tau_y\le t)$.
By \eqref{5.8b}, translation in $x$ equally translates the $\mu_t^{x,y}$, and the ($x$-independent) measure on $\overline{B_2(0)}$ given by $\nu_t^y(A)=\mu_t^{x,y} (\mathbb{R}\times A)$ is just the law of $\sqrt 2 B_{t\wedge\tau_y} +y$, the Brownian motion on $B_2(0)$ starting at $y$, with stopping time $\tau_y$, and with time scaled by a factor of two. In particular for each $t>0$ there is $h_t>0$ such that for any $y_1,y_2\in B_1(0)$ and any Borel sets $A_1\subseteq B_1(0)$ and $A_2\subseteq \overline{B_2(0)}$,
\begin{equation}\label{5.8c}
h_t \nu_t^{y_1}(A_2) \le \nu_t^{y_2}(A_2)\le h_t^{-1} \nu_t^{y_1}(A_2) \qquad \text{and} \qquad h_t |A_1|\le \nu_t^{y_1}(A_1) \le h_t^{-1}|A_1|.
\end{equation}
From this it follows for $t:=\|\beta\|_\infty^{-1}$ that
\begin{equation} \label{5.9}
\inf_{[0,1]\times B_1(0)} u \ge C_{d,\beta}'' \inf_{[-1,2]\times A_d^+} u
\end{equation}
with $C_{d,\beta}'':=e^{-t}h_t \min\{|A_d^+|,|A_d^-|\}$ and, similarly, we obtain
\begin{equation} \label{5.10}
\inf_{[3,4]\times B_1(0)} u \ge C_{d,\beta}'' \inf_{[2,5]\times A_d^-} u.
\end{equation}
Using \eqref{5.5}, \eqref{5.10}, \eqref{5.6}, and \eqref{5.9} (in that order) yields
\[
\sup_{[0,1]\times A_d^-} u \le C_{d,\beta} \inf_{[0,1]\times B_1(0)} u,
\]
with $C_{d,\beta}>0$ depending only on $d$ and $\beta$. An analogous argument gives
\[
\sup_{[0,1]\times A_d^+} u \le C_{d,\beta} \inf_{[0,1]\times B_1(0)} u,
\]
and \eqref{5.4} follows.
Next we let $v(x,y):=\int_{-z}^z u(x+s,y)ds$ for some $z\in(0,1/3]$
\begin{equation}\label{5.14}
\sup_{[0,1]\times B_1(0)} v \le \widetilde C_{z,\beta} \inf_{[0,1]\times B_1(0)} u
\end{equation}
holds for some $\widetilde C_{z,\beta}\ge 1$. Indeed, it follows from \eqref{5.8b}, \eqref{5.8}, \eqref{5.8a} that for each $(x,y)\in\mathbb{R}\times B_2(0)$,
\[
e^{-t} \int_{\mathbb{R}\times\overline{B_2(0)}} u(x',y') d\mu_t^{x,y;z}(x',y') \le v(x,y) \le e^t \int_{\mathbb{R}\times\overline{B_2(0)}} u(x',y') d\mu_t^{x,y;z}(x',y'),
\]
where $\mu_t^{x,y;z}(x',y') = \mu_t^{x,y}(x',y') * ( \chi_{[-z,z]}(x')dx'\delta_0(y'))$. The above claims about $\mu_t^{x,y}$ and the definition of $\nu_t^y$ imply that
\[
\mu_t^{x,y;z}(x',y') \le \kappa^{x;z}_{t}(x')\times \nu_t^y(y') \le \sum_{m=-M}^M \mu_t^{x+2mz,y;z}(x',y'),
\]
where $\kappa^{x;z}_{t}$ is the measure on $\mathbb{R}$ with $\kappa^{x;z}_{t}(B)=|B\cap [x-z-\|\beta\|_\infty t,x+z+\|\beta\|_\infty t]|$ for any Borel set $B\subseteq\mathbb{R}$, and $M$ is such that $(2M+1) z \ge 2(z+ \|\beta\|_\infty t)$, for instance, $M:=\lceil 1/2+\|\beta\|_\infty t/z \rceil$. This and the first claim in \eqref{5.8c} means that
\begin{equation}\label{5.16}
v(x,y_1) \le e^{2t} h_t^{-2} \sum_{m=-M}^M v(x+2mz,y_2)
\end{equation}
for any $x\in\mathbb{R}$, $y_1,y_2\in B_1(0)$ and $t>0$.
Now we take any $x\in[0,1]$, $y_1\in B_1(0)$, and $y_2\in A_d$ for some fixed $d>0$ such that $A_d^\pm\neq \emptyset$. Pick $t:= (2\|\beta\|_\infty)^{-1}z$ and $M=1$ to obtain using \eqref{5.16},
\[
v(x,y_1) \le e^{2t} h_t^{-2} \int_{-3z}^{3z} u(x+s,y_2) ds \le e^{2t} h_t^{-2} \int_{-1}^{2} u(x',y_2) dx'.
\]
Since \eqref{5.4} and its shifts in $x$ give for $c=-1,0,1$,
\[
\sup_{[c-1,c]\times A_d} u \le C_{d,\beta} \inf_{\{c\}\times A_d} u \le C_{d,\beta} \sup_{[c,c+1]\times A_d} u,
\]
\[
\sup_{[c-1,c]\times A_d} u \le C_{d,\beta} \inf_{\{c-1\}\times A_d} u \le C_{d,\beta} \sup_{[c-2,c-1]\times A_d} u,
\]
we obtain \eqref{5.4} with $[0,1]$ and $C_{d,\beta}$ replaced by $[-1,2]$ and $C_{d,\beta}^3$. This proves \eqref{5.14}.
Similarly, \eqref{5.14} with $[-1,0]$ and $[1,2]$ in place of $[0,1]$, together with \eqref{5.4}, yield
\[
\sup_{[-1,2]\times B_1(0)} v \le \widetilde{C}_{z,\beta}C_{d,\beta} \inf_{[0,1]\times B_1(0)} u.
\]
In a similar way one can also obtain
\begin{equation}\label{5.17}
\sup_{[-1,2]\times \overline{B_2(0)}} v \le C_{z,d,\beta} \inf_{[0,1]\times \overline{B_2(0)}} u.
\end{equation}
for some $C_{z,d,\beta}>0$ (recall that $B_2(0)\subset\subset D=B_3(0)$).
We will now need to use \eqref{5.2} to finish the proof. This assumption makes the differential operator on the left-hand side of \eqref{5.1} hypoelliptic in the sense of H\" ormander. It follows that for $t>0$, the measure $\mu_t^{x,y}$ is absolutely continuous when restricted to $\mathbb{R}\times B_2(0)$ and also to $\mathbb{R}\times \partial B_2(0)$ (as an $(N-1)$-dimensional measure in the latter case), with densities $p_t(x,y,\cdot,\cdot),q_t(x,y,\cdot,\cdot)\ge 0$ such that
$$p_t(x,y,x',y')=p_t(0,y,x'-x,y'),$$
$$q_t(x,y,x',y')=q_t(0,y,x'-x,y'),$$
and $p_t,q_t$ are bounded functions when restricted to $y\in B_1(0)$ (with $y'\in B_2(0)$ for $p_t$ and $y'\in \partial B_2(0)$ for $q_t$). For $p_t$ this follows from the same claim for the corresponding measure $\widetilde\mu_t^{x,y}$ on $\mathbb{R}^N$ given by \eqref{5.8a} with $t$ in place of $t\wedge\tau$ and $\beta$ smoothly extended to a periodic function on $\mathbb{R}^{N-1}$ (whose density is smooth in all arguments, \cite[Theorem 3]{IK}). This is because $\widetilde\mu_t^{x,y}(A)\ge \mu_t^{x,y}(A)$ for any Borel set $A\subseteq \mathbb{R}\times B_2(0)$.
For $q_t$ this would follow from the same claim for the corresponding escape measure $\widetilde\mu_{\tau}^{x,y}$ on $\mathbb{R}\times \partial B_2(0)$ given by \eqref{5.8a} with $\tau=\tau_y$ in place of $t\wedge\tau$. We know of such a result for bounded domains only \cite[Corollary 2.11]{BKS} but since $\mu_t^{x,y}$ is supported on a bounded cylinder, it applies in our case as well. Specifically, take any $a_- < - \|\beta\|_\infty t$ and $a_+ > \|\beta\|_\infty t$. There is a convex open domain $G$ with a smooth boundary whose intersection with $[a_-, a_+] \times \mathbb{R}^{N-1}$ is $[a_-, a_+] \times B_2(0)$, and the intersection with $[(-\infty, a_-)\cup(a_+,\infty)] \times \mathbb{R}^{N-1}$ are two smooth ``slanted'' conical caps $G_\pm\subseteq \mathbb{R}\times B_2(0)$ over the $(N-1)$-dimensional balls $\{a_\pm\}\times B_2(0)$ with the two (rounded) tips at points with $y'$ coordinates $y'_{\pm}$ such that $\pm \beta(y'_{\pm})>0$ and sufficiently long so that for any $(x',y')\in\partial G_\pm\cap\partial G$, the unit outer normal vector $n(x',y')$ to $\partial G_\pm$ at $(x',y')$ satisfies
$$|n(x',y')\cdot (1,0,\cdots,0)| \le \tfrac 12 (\|\beta\|_\infty^{-1}+1)\ \hbox{ whenever }\pm\beta(y')\le 0.$$
Then $G$ satisfies the hypotheses of \cite[Corollary 2.11]{BKS} (it satisfies the escape condition and all points of $\partial G$ are $\tau'$-regular). It follows that the escape measure $\widetilde\mu_{\tau}^{x,y}$ has a density $\widetilde q_\tau(x,y,\cdot,\cdot)$ which is a continuous function of $(x,y,x',y')\in G\times\partial^* G$, where $\partial^* G$ is the set of ``good'' points of $\partial G$, that is, all $(x',y')\in\partial G$ except of the two cone tips, where $n(x',y')=(\pm 1,0,\cdots,0)$. Thus $\widetilde q_\tau$ is bounded on $S:=\{0\}\times B_1(0)\times(a_-,a_+)\times\partial B_2(0)$. Since $\{X^{0,y}_s\}_{s\le t\wedge \tau}$ almost surely stays in $(a_-,a_+)$, we obtain $q_t\le \widetilde q_\tau$ on $S$ and $q_t=0$ on $[\{0\}\times B_1(0)\times\mathbb{R} \times\partial B_2(0)] \setminus S$. Finally, $q_t(x,y,x',y')=q_t(0,y,x'-x,y')$ shows that $q_t$ is bounded on $\mathbb{R}\times B_1(0)\times \mathbb{R} \times\partial B_2(0)$.
Let $d>0$ be such that $A_d^\pm\neq \emptyset$, let $z:=1/3$, $t:=\|\beta\|_\infty^{-1}$, and
\[
C_t:=\max\{ \sup_{\mathbb{R}\times B_1(0)\times \mathbb{R} \times B_2(0)} p_t, \sup_{\mathbb{R}\times B_1(0)\times \mathbb{R} \times\partial B_2(0)} q_t\} <\infty.
\]
Then $p_t(x,y,x',y'),q_t(x,y,x',y')\le C_t \chi_{[x-1,x+1]}(x')$ because the measure $\mu_t^{x,y}$ is supported on $[x-1, x+1] \times \overline{B_2(0)}$, so we obtain from \eqref{5.8} and \eqref{5.8a}
\begin{align*}
\sup_{[0,1]\times B_1(0)} u & \le C_t e^t\int_{[-1,2]\times B_2(0)} u(x',y') dx'dy' + C_t e^t\int_{[-1,2]\times \partial B_2(0)} u(x',y') dx'dy'
\\ & \le 10C_te^t \sup_{[-1,2]\times \overline{B_2(0)}} v
\\ & \le 10C_t C_{z,d,\beta} e^t \inf_{[0,1]\times B_1(0)} u
\end{align*}
by using $[-1,2]=[-1,-1/3]\cup[-1/3,1/3]\cup[1/3,1]\cup[1,5/3]\cup[4/3,2]$ and \eqref{5.17}. This is \eqref{5.3}, so the theorem will be proved once we establish \eqref{5.8}.
\begin{lem} \label{L.5.2}
If $u,\beta,\gamma,X^{x,y}_t,Y^{x,y}_t,\tau_y$ are as in the proof of Theorem \ref{T.5.1} (in particular, $\|\gamma\|_\infty\le 1$), then \eqref{5.8} holds for $(x,y)\in \mathbb{R}\times B_2(0)$.
\end{lem}
\noindent{\bf{Proof.}}
Let $Z^{x,y}_t=t$ so that $dZ^{x,y}_t=dt$ and $K:=\Delta_y+\beta(y)\partial_x+\partial_z$ is the generator of the process $(X^{x,y}_t,Y^{x,y}_t,Z^{x,y}_t)$. If we let $v(x,y,z):=e^{z}u(x,y)$, then $Kv\ge 0$ on $\mathbb{R}\times B_3(0)\times\mathbb{R}$ in the sense of distributions, that is,
\[
\int_{\mathbb{R}\times B_3(0)\times\mathbb{R}} v K^*\phi\, dxdydz \ge 0
\]
for any $\phi\in C^\infty_0(\mathbb{R}\times B_3(0)\times\mathbb{R})$, with $K^*:= \Delta_y-\beta(y)\partial_x-\partial_z$ the adjoint of $K$.
For any $\epsilon>0$ let $\delta_\epsilon\in(0,1/2\sqrt{N-1})$ be such that $|\beta(y)-\beta(y')| \le \epsilon^2$ whenever $y,y'\in B_{5/2}(0)$ and $|y-y'|\le \sqrt{N-1}\,\delta_\epsilon$. Let $\eta:\mathbb{R}\to [0,1]$ be a smooth non-negative function supported in $[-1,1]$, with $\int_{-1}^1\eta(x')dx'=1$ and $\|\eta'\|_\infty\le 2$. For $\epsilon>0$ define the mollifier
\[
\eta^{\epsilon}(x,y,z) :=
\epsilon^{-2}\delta_\epsilon^{1-N} \eta \left( \displaystyle{\frac x\epsilon} \right) \eta \left( \displaystyle{\frac z\epsilon} \right) \displaystyle{\mathop{\prod}_{n=1}^{N-1}} \eta \left( \displaystyle{\frac {y_n}{\delta_\epsilon}} \right),
\]
and let $v^{\epsilon}:= v*\eta^\epsilon$ and $\phi^{\epsilon;x,y,z}(x',y',z'):=\eta^\epsilon(x-x',y-y',z-z')$.
For $\epsilon\in(0,1)$ the smooth function $v^\epsilon$ then satisfies on $\mathbb{R}\times B_2(0)\times\mathbb{R}$
\begin{align*}
(Kv^{\epsilon}) (x,y,z) = & \int_{\mathbb{R}\times B_3(0)\times\mathbb{R}} vK^*\phi^{\epsilon;x,y,z} \, dx' dy' dz'
\\ + & \int_{\mathbb{R}\times B_3(0)\times\mathbb{R}} v(x',y',z')[\beta(y')-\beta(y)] \phi^{\epsilon;x,y,z}_{x'}(x',y',z') \, dx' dy' dz'.
\end{align*}
The first integral is non-negative. The integrand in the second vanishes when $|x'-x|>\epsilon$ or $|y'_n-y_n|> \delta_\epsilon$ for some $n$ or $|z'-z|>\epsilon$, and $|\phi^{\epsilon;x,y,z}_{x'}(x',y',z')|\le 2 \epsilon^{-3}\delta_\epsilon^{1-N}$, so we have
\[
(Kv^{\epsilon}) (x,y,z) \ge - 2^{N+2} \epsilon e^{z+\epsilon} \|u\|_\infty.
\]
We next apply Dynkin's formula \cite[Theorem 7.4.1]{Oks} to the smooth function $v^\epsilon$, the process $(X^{x,y}_t,Y^{x,y}_t,Z^{x,y}_t)$, and stopping time $t\wedge \tau$ (with $\tau=\tau_y$), to obtain
\begin{align*}
\mathbb{E} \left[ v^\epsilon(X^{x,y}_{t\wedge \tau},Y^{x,y}_{t\wedge \tau},Z^{x,y}_{t\wedge \tau}) \right] & = v^\epsilon(x,y,0)+ \mathbb{E}\left[ \int_0^{t\wedge \tau} (Kv^\epsilon) (X^{x,y}_s,Y^{x,y}_s,Z^{x,y}_s) ds \right]
\\ & \ge v^\epsilon(x,y,0) - 2^{N+2} \epsilon e^{t+\epsilon} \|u\|_\infty t.
\end{align*}
Since $v^\epsilon\to v$ uniformly on $[x-\|\beta\|_\infty t, x+\|\beta\|_\infty t]\times \overline{B_2(0)}\times [0,t]$ as $\epsilon\to 0$ (by continuity of $v$) and $Z^{x,y}_{t\wedge \tau}\le t$, it follows that
\[
e^t \mathbb{E} \left[ u(X^{x,y}_{t\wedge \tau},Y^{x,y}_{t\wedge \tau}) \right] \ge \mathbb{E} \left[ v(X^{x,y}_{t\wedge \tau},Y^{x,y}_{t\wedge \tau},Z^{x,y}_{t\wedge \tau}) \right]\ge u(x,y).
\]
This is the second inequality in \eqref{5.8}. The first inequality is obtained in the same way, this time with $v(x,y,z):=e^{-z}u(x,y)$, so that $Kv\le 0$ on $\mathbb{R}\times B_3(0)\times\mathbb{R}$ and
\[
(Kv^{\epsilon}) (x,y,z) \le 2^{N+2} \epsilon e^{-z+\epsilon} \|u\|_\infty.
\]
\hfill$\Box$
|
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News Sports Mesquite Cedar City Life Opinion Obituaries eNewspaper Legals
Springdale bracing for road construction
Jud Burkett
jburkett@thespectrum.com
Residents in Springdale and Rockville are begrudgingly bracing for the impending challenge of dealing with major road construction along their stretch of state Route 9.
The Utah Department of Transportation has determined that the road needs to be resurfaced in Rockville, while in Springdale the road needs to be completely replaced.
The project is currently in the design phase with construction set to begin in January 2017.
"There's a lot of places through town where there's no road base and other places where there's only 2 inches of road base," said Springdale Mayor Stan Smith. "With all the traffic in the canyon, the road's being torn up, and it just can't handle the traffic."
Smith also owns the Bumbleberry Inn in Springdale.
While business owners and residents are concerned about what impact road construction along the only traffic corridor through the two towns will have on their day-to-day activities, they recognize the need to resurface SR-9, Smith said.
"It's our livelihood, but when the finished product is done, that's also our livelihood. It's kind of like birthing a child; are you worried about the labor pains? Yeah. But once the baby's here, you have a baby. I am concerned about the impact of the construction, but we are going to do everything we can so it doesn't have that much of an impact," Smith said.
"We've tried to be sensitive to the communities needs," said Kevin Kitchen, the communications manager for UDOT's Region 4. "Especially, where it's the gateway to the national park; we're looking at construction starting in January, trying to avoid the tourist season as much as possible."
The project includes plans to save as much of the historic irrigation ditch system along the sides of the road in Rockville and Springdale as feasibly possible; a widening of the road between Rockville and Springdale; parking improvements for the roadway; and adding a bike lane that will run from the west end of Springdale to the gates of Zion National Park.
UDOT originally planned to begin construction in October of 2016, but a number of issues pushed back that timetable, officials said.
"The town really has some concerns at Lion Boulevard, especially with the growth going up that road, so we want to do a traffic study on the Lion Boulevard intersection to see if we can improve the functionality of that," said Branden Anderson, UDOT's project manager for the SR-9 resurfacing. "Combined with the environmental schedule with the ditches we're going to preserve, the best thing to do is to get the right project in there, so it's been pushed back."
Rather than complete the project all at once as they had originally planned, Anderson said UDOT now plans to use two phases — one stretching from January through April followed by a second phase from October through December of 2017.
Nate Wells, the general manager of Zion Canyon Village, said even with the added tourist traffic Zion Canyon is seeing due to the National Park Service's 100th Anniversary, he's anticipating a slight downturn in winter business.
"There will be some impact," Wells said. "Thinking about five or six years ago when they did the Mount Carmel Highway reconstruction, there was an impact then. It was slight, but it (seemed) like there was a slow down during that period. Certain tours won't come through during that time, which is just the way things work. It has to happen, and it was just our turn to have to take a break."
Springdale resident Marcel Rodriguez said he thinks most of his neighbors recognize the need for the road construction.
"From my talking to the people on the Town Council, people in town, business people, I think everybody regards it as an inevitable disaster," he said. "It has got to be done, but it ain't gonna be fun. Most of us that live along the road are not looking forward to not being able to get out of our driveways very easily, but it's got to be done."
While the irrigation ditches are being preserved, one thing that will go away once the road is resurfaced is the red tint.
The roadways through Zion National Park all have a red colored surface and the roads through Springdale and Rockville are currently made of the same material. However, Andersen said they don't last as long as the black pavement planned for the project.
"We discussed that with the Town of Springdale and just for a more viable long term pavement, we've decided to go back to black to help extend the pavement life of the road," Anderson said. "The red chip and seal doesn't have as long a life, so for a more sustainable pavement, it has to be black."
Anderson said things went well during a Thursday night meeting in Springdale where UDOT officials were on hand to provide information on the project and to hear the concerns of the residents.
"A lot of ideas were discussed, and there was a lot of education from both sides, so it was pretty good," he said. "For the most part, people were accepting of the designs knowing they were going to get a longer life out of the pavement."
Smith, who was also on hand for UDOT's open house, agreed that the discussion with the public went well.
"We had a good conversation," Smith said. "Everybody was able to see whats going on and it went really well. I was mostly listening and waiting to see if (people) had questions for me, but nobody did. There were a couple of people that stated their concerns (to UDOT) — everybody is concerned about how disruptive it's going to be, and it is going to be disruptive, but we're attempting to minimize it as much as possible."
Follow reporter Jud Burkett on Twitter and Instagram @judburkett. Email him atjburkett@thespectrum.com or call him at 435-674-6262.
Then and Now - Bumbleberry Inn
Tour of Utah start in Springdale has some residents irked, others, excited
Surviving Springdale's winter tourism slowdown
Earth Day festival in Springdale
© 2023 www.thespectrum.com. All rights reserved.
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| 2,760
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Ендрю Луїс Прайн (; 14 лютого 1936, Дженнінґс, Флорида — 31 жовтня 2022, Париж) — американський актор театру, кіно та телебачення.
Життєпис
Ендрю Прайн народився 14 лютого 1936 року в місті Дженнінґс, штат Флорида. Закінчив середню школу Ендрю Джексона у Маямі. Навчався в Маямському університет, але покинув навчання та переїхав у Нью-Йорк, щоб почати акторську кар'єру.
У 1956 році Ендрю Прайн дебютував на Бродвеї.
З кінця 1950-х років він також працював на телебаченні, 1959 року дебютував у кіно.
Особисте життя
У 1962 році Ендрю Прайн одружився з акторкою Шерон Фаррелл, але шлюб тривав лише кілька місяців. 1973 року він вдруге одружився, його обраницею стала американська акторка Бренда Скотт. Подружжя розлучилося через місяць, але наступного року знову одружилися. У 1986 році Ендрю Прайн одружився з акторкою Гізер Лав, з якою донині перебуває у шлюбі.
Фільмографія
— За межами найдальшої зірки / Beyond the Farthest Star — сенатор Джон Каттер
— Повелителі Салема / The Lords of Salem — преподобний Джонатан Ґоторн
- — Врятувати Ґрейс / Saving Grace — Еверет Маршалл
— Долтрі Келгун / Daltry Calhoun — шериф Кабот
— CSI: Місце злочину / CSI: Crime Scene Investigation — Роджер Стокс
— Скляний мурашник / Glass Trap — шериф Ед
— Клієнт завжди мертвий / Six Feet Under — Ед Кіммель
— Хлопчик з рентгенівськими очима / The Boy with the X-Ray Eyes — Малкольм Бейкер
— Люди-тіні / The Shadow Men — людина в чорному
— Вокер, техаський рейнджер / Walker, Texas Ranger — Тім Кінґстон
— Район Мелроуз / Melrose Place — Такер
— Зоряний шлях: Глибокий космос 9 / Star Trek: Deep Space Nine — легат Таррел
— Одружені... та з дітьми / Married… with Children — батько
— V / V — Стівен
Премії та номінації
Примітки
Посилання
Уродженці Флориди
Американські телеактори
Американські кіноактори
Американські театральні актори
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| 5,716
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As a resident of any of our Brookline apartments, you'll be able to take advantage of refreshing essentials. Each of our apartments features abundant natural light and memorable views. With ten foot ceilings, hardwood flooring (select apartments), and efficient kitchens equipped with dishwashers, it will be easy to feel at home at Princeton on Beacon Street. For more information about our available floor plans, stop by our office today!
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| 1,318
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Q: Display Array of arrays in a table I have an Array of arrays in my data, they look like this :
And now I want to display this array in a table, but all I get is empty page, this is my html for the table (because of code length I added only the first column code :
<table mat-table [dataSource]="dataPur" class="mat-elevation-z8" matSort>
Name Column
<ng-container matColumnDef="name">
<th mat-header-cell *matHeaderCellDef> Type </th>
<td mat-cell *matCellDef="let element; let i = index"> {{element.name}} </td>
</ng-container>
<tr mat-header-row *matHeaderRowDef="displayedColumns"></tr>
<tr mat-row *matRowDef="let row; columns: displayedColumns;"></tr>
</table>
Component.ts :
name:string[] = [];
iItem:number[] = [];
iTotal:number[] = [];
qty:number[] = [];
dataPur:any[] = [];
displayedColumns: string[] = ['name','iItem', 'iTotal','pretemp', 'qty'];
ngAfterViewInit() {
for(var i = 0; i < this.data.docDetailes.length; i++){
this.dataPur[i] = [
this.name[i] = this.data.docDetailes[i].name,
this.iItem[i] = this.data.docDetailes[i].iItem,
this.iTotal[i] = this.data.docDetailes[i].iTotal,
this.qty[i] = this.data.docDetailes[i].qty
]
}
console.log(this.dataPur);
}
Someone can help?
A: generally a datasource of a mat-table is an array of object (not an array of arrays) so, should be
for(var i = 0; i < this.data.docDetailes.length; i++){
this.dataPur[i] = {
name:this.data.docDetailes[i].name,
iItem: this.data.docDetailes[i].iItem,
iTotal: this.data.docDetailes[i].iTotal,
qty: this.data.docDetailes[i].qty
}
}
But really you can use an array of arrays, the only is that your td should be like
<ng-container *ngFor="let column of displayedColumns;let index=index"
[matColumnDef]="column">
<th mat-header-cell *matHeaderCellDef>{{column}}</th>
<td mat-cell *matCellDef="let element; let i = index">
{{element[index]}}
</td>
</ng-container>
see that it's not magic. "element" is the "row", so if we has an array of object we use element.[name of property] if we has an array of array simple use element[index]
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The Blériot 290 was a 1930s French sesquiplane flying-boat designed by Filippo Zappata, only one was built and it was not ordered into production.
Design and development
The 290 was designed by Zappata as a three-seat touring amphibian flying-boat, it had a streamlined single-step hull and an enclosed cabin. Powered by a Salmson 9Ab radial piston engine with a two-bladed pusher propeller. It first flew in October 1931 and as a result of tests was re-designed with a second step in the hull. The 290 was underpowered and over priced and did not enter production, the prototype was scrapped in April 1937.
Specifications
See also
References
Notes
Bibliography
1930s French civil utility aircraft
Flying boats
290
Sesquiplanes
Single-engined pusher aircraft
Aircraft first flown in 1931
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\section{I. INTRODUCTION} \label{sec:intro}
There has been steady progress over the past few decades in terms of understanding the spin structure of the nucleon, one of the fundamental questions in nuclear physics. In the relativistic quark parton model, the spin of the proton was naively explained~\cite{dis:rqpModel} by the alignment of spins of the valence quarks. However, as of our current knowledge~\cite{dis:EMU}, the valence quarks, sea quarks, gluons and their possible orbital angular momenta are all expected to contribute to the overall spin of the proton. Despite this significant progress, the individual polarizations of quarks and antiquarks are yet to be understood precisely.\\
\indent
According to the spin sum rule introduced by Jaffe and Monahar~\cite{dis:sumrule} in 1990, the spin of the proton can be written in terms of its contributions from the intrinsic quark and antiquark polarizations, intrinsic gluon polarization and their orbital angular momenta. Polarized inclusive deep-inelastic scattering (DIS) experiments were able to strongly constrain the total quark contribution to the proton spin~\cite{dis:global}. However, DIS experiments were not sensitive to the flavor separated individual quark spin contributions. These were then measured by polarized semi inclusive DIS experiments (SIDIS), where a specific hadron is tagged in the final state. The helicity-dependent parton distribution functions (PDF)~\cite{dis:global} were extracted from global analyses using the world data of both DIS and SIDIS. Relatively large uncertainties remain in the polarized antiquark PDFs in comparison to quark PDFs mainly due to the large uncertainties found in the fragmentation functions~\cite{dis:frag} which were used in the global analysis. Over the years however, progressively more precise polarized SIDIS data, covering an enhanced kinematic range has become available~\cite{dis:newdata1, dis:newdata2, dis:newdata3}. Moreover the knowledge of the fragmentation process has increased, leading to the extraction of rather precise fragmentation functions~\cite{dis:FFs}. Furthermore, the global fitting tools used in various global analyses has improved over the years. Despite this significant progress, the current knowledge of antiquark helicity PDFs is still less precise in comparison to the valence sector~\cite{dis:lss10}. \\
\indent
The production of $W^\pm$ bosons in longitudinally polarized $p+p$ collisions at RHIC provides a unique and powerful tool to probe the individual helicity PDFs of light quarks and anti quarks at much larger $Q^2$ scale ($\sim$ 6400 $GeV^2$) set by the W mass. Due to the maximal parity violating nature of the weak interaction, $W^{-(+)}$ bosons couple to the left handed quarks and right-handed anti quarks and hence offer direct probes of their respective helicity distributions in the nucleon. These distributions can be extracted by measuring the parity violating $A_L$, as a function of the decay electron (positron) pseudo rapidity, $\eta_e$. The longitudinal single-spin asymmetry is defined as $A_L =(\sigma_+-\sigma_- )/ (\sigma_++\sigma_-)$, where $\sigma_{+(-)}$ is the cross section when the helicity of the polarized proton beam is positive (negative). At leading order, $W^+$ $A_L$ is directly related to polarized anti d and u quark distributions ($\Delta \bar d$, $\Delta u$) while $W^-$ $A_L$ is directly related to polarized anti u and d quark distributions ($\Delta \bar u$, $\Delta d$)~\cite{dis:rhicW}. \\
\indent
Considering the SU(3) flavor symmetry, since the mass difference of up and down quarks is small, equal numbers of up and down quark-antiquark pairs are expected to be produced perturbatively in the nucleon sea from gluon splitting. However in 1970's the first indication of up-down asymmetric sea came through early SLAC data suggesting the violation of the Gottfried Sum Rule (GSR)~\cite{dis:GSR}. Later on more concrete evidence supported the up-down asymmetric sea with surprising results from the FNAL E866 Drell-Yan (DY) Experiment~\cite{dis:E866}. The E866 data clearly showed that $\bar d \neq \bar u$, suggesting a non perturbative origin of the nucleon sea. However, theoretical calculations failed to explain the $\bar d / \bar u$ behavior at higher Bjorken-x values~\cite{dis:FAtheory}. Moreover, the most recent preliminary results of the SeaQuest E906~\cite{dis:seaquest} experiment where DY measurements have extended to larger $x$ values deviates from E866 results at higher $x$ values. \\
\indent
At leading order, the ratio of W cross sections, $\sigma^+_W / \sigma^-_W$ in $p+p$ collisions provides a direct measurement of the unpolarized flavor structure of the sea as shown in equation~\ref{eq:xsection} which is expressed in terms the unpolarized PDFs of up, down quarks and antiquarks.\begin{equation}
\frac{\sigma ^+_W} {\sigma ^-_W} = \frac{u(x_1)\bar{d}(x_2) + \bar d(x_1)u(x_2)}{\bar u(x_1)d(x_2) + d(x_1)\bar{u}(x_2)}
\label{eq:xsection}
\end{equation}
The RHIC kinematic range is highly sensitive to the particular $x$ region where the two DY results disagree and the steadily increasing behavior of $\bar d / \bar u$ changes~\cite{dis:FAtheory}. Hence, measurements of W cross section ratio at RHIC provide an important and completely independent cross check of the up-down flavor asymmetry of the sea at much larger $Q^2$ values than the DY measurements.\\
\indent
This paper is organized as follows: section II provides a brief overview of the experimental aspects focusing on the use of various detector elements at STAR in terms of reconstructing and extracting W signal spectra from the data set. This section also explains the estimation and subtraction of the background from the W signal spectra. In section III we discuss the calculation of the W single spin asymmetry and W cross section ratio and present the preliminary results comparing to several theoretical calculations. Finally the last section provides a summary and outlook.
\section{II. ANALYSIS}\label{ana}
The data analyzed here for W $A_L$, were collected by the STAR experiment in RHIC 2013 running of longitudinally polarized $p+p$ collisions at $\sqrt{s}=510$ GeV. The total integrated luminosity of the data are 246.2 pb$^{-1}$, with an average beam polarization of 54\%. The data used for the W cross section analysis is the combination of data collected by the STAR experiment in RHIC 2011 and 2012 running of $p+p$ collisions at $\sqrt{s}$ = 500 and 510 GeV with a total integrated luminosity of 25 pb$^{-1}$ and 77 pb$^{-1}$ respectively. Both asymmetry and cross-section analyses whose final results are presented as a function of $\eta_e$, followed largely the same analysis procedure. The data were selected online using the same high energy trigger requirement in the calorimeter for both analyses. Next, similar steps for the reconstruction, extraction of the W signal, and the estimation and subtraction of backgrounds were followed. However, an additional step of correction for W detection efficiencies was involved for the cross section analysis. As for the cross-section analysis as a function of $y_W$, the details of the W reconstruction algorithm can be found in Ref.~\cite{run11paper}.\\
\indent
The STAR experiment~\cite{dis:starNIM} is well equipped to measure $A_L$ for $W^\pm$ boson production within a pseudorapidity range of $|\eta|<1$. $W^\pm$ bosons are detected via their $W^\pm \rightarrow e^\pm \nu$ decay channels. A subsystem of the STAR detector, the Time Projection Chamber (TPC) is used to measure the transverse momentum ($p_T$) of decay electrons and positrons and to separate their charge sign. Two other subsystems, Barrel and Endcap Electromagnetic Calorimeters (BEMC, EEMC) are used to measure the energy of decay leptons. A well developed algorithm~\cite{dis:run12paper} is used to identify and reconstruct $W^\pm$ candidate events by removing QCD type background events. In this algorithm, various cuts are applied at each level of the selection process based on the kinematics and topological differences between the electroweak process of interest and QCD processes. For example, tracks associated with $W^\pm$ candidate events can be identified as isolated tracks in the TPC that point to an isolated EMC cluster in the calorimeter. However, QCD type events have several TPC tracks point to several EMC clusters. In contrast to QCD background events, a large missing transverse energy opposite in azimuthal direction ($\phi$) can be observed for $W^\pm\rightarrow e^\pm \nu$ candidate events, due to the undetected neutrinos in the final state. This leads to a large imbalance in the vector $p_T$ sum of all reconstructed final-state objects in W candidate events, which is expressed as $\vec{p}^{~balance}_T$ in equation~\ref{eq:signPt1}.
\begin{equation}
\vec{p}^{~balance}_T=\vec{p}^{~e}_T+\sum\limits_{\Delta R > 0.7} \vec{p}^{~jets}_T
\label{eq:signPt1}
\end{equation}
\begin{figure}[H]
\centering
\includegraphics[width=0.48\textwidth]{signPt.pdf}
\caption{Signed $p_T$-balance vs $E^e_T$ for data (a) and $W \rightarrow e\nu$ MC (b).}
\label{Fig:signPt}
\end{figure}
Here, the $\vec{p}^{~e}_T$ is the $p_T$ of the candidate lepton. The transverse momentum of jet like events, $\vec{p}^{~jets}_T$ is determined using the anti-$\it{k}_T$ algorithm~\cite{dis:antikt}, by reconstructing the $p_T$ from all reconstructed jets outside a cone of radius of 0.7 in $\eta-\phi$ space which is centered around the candidate lepton. A strong correlation is observed between $E^e_T$ and the scalar quantity, signed $p_T$ balance, which is defined in equation~\ref{eq:signPt2}. This can be seen clearly in Fig~\ref{Fig:signPt} (b) which shows the MC results simulating $W^\pm\rightarrow e\nu$ decays. \\
\begin{figure}[H]
\centering
\includegraphics[width=0.45\textwidth]{Et.pdf}
\caption{Candidate $E^e_T$ distribution from the data after various selection cuts.}
\label{Fig:Et}
\end{figure}
\indent
After initially requiring reconstructed TPC tracks to have $p_T > 10$ GeV, candidate tracks were matched to a BEMC tower. The transverse energy, $E_T$ of each of four possible $2\times2$ clusters which contain the pointed track was computed and the cluster with largest summed $E_T$ was assigned as the candidate cluster. The energy corresponding to the candidate cluster was considered as the energy of the candidate, $E^e_T$ and was required to be greater than 14 GeV. Next, two isolation requirements were imposed. First, the ratio of $E^e_T$ to total energy of the $4\times4$ BEMC cluster surrounding the candidate cluster, was required to be grater than $95\%$. Second isolation requirement demanded that the ratio of $E^e_T$ to $E_T$ sum of the area within a cone of radius of 0.7 around the candidate track ($E^{\Delta R < 0.7}_T$) to be greater than $88\%$. As the final requirement, the signed-$p_T$ balance mentioned in equation~\ref{eq:signPt2} was required to be greater than 14 GeV, which is indicated by the red line in Fig.~\ref{Fig:signPt} (a). After all the selection cuts have been applied, the characteristic Jacobean peak in the $E_T$ distribution for mid-rapidity $W^\pm$ candidate events was observed near the half of the $W^\pm$ mass, as shown in Fig.~\ref{Fig:Et}.
\begin{equation}
signed\:{p_T}\:balance=\frac{(\vec{p}^{~e}_T).\vec{p}^{~balance}_T}{|\vec{p}^{~e}_T|}
\label{eq:signPt2}
\end{equation}
\begin{figure*}
\centering
\includegraphics[width=0.99\textwidth]{bg.pdf}
\caption{$E^e_T$ distribution of $W^-$ (top) and $W^+$ (bottom) candidate events (black), various background contributions and sum of backgrounds and $W\rightarrow e\nu$ MC signal (red-dashed).}
\label{Fig:bg}
\end{figure*}
$W^\pm$ candidates were charge separated based on $e^\pm$ track curvature measured in the TPC. The charge separated $W^\pm$ yields as a function of $E^e_T$ are shown in Fig.~\ref{Fig:bg} for four different $\eta$ bins, along with the estimated residual background contributions from electroweak processes and QCD processes.
The $W^\pm\rightarrow\tau^\pm\nu_\tau$ and $Z/{\gamma^*}\rightarrow e^+ e^-$ electroweak background contributions were estimated from Monte-Carlo (MC) samples.
The MC samples were simulated by generating the respective events using PYTHIA 6.422~\cite{dis:pythia} and passing through the STAR GEANT\cite{dis:geant} model and embedding into STAR zero-bias triggered events. In comparison to QCD, relatively small electroweak background contributions were estimated.\\
\indent
The selection process of W candidate events described above is designed to remove significant amount of QCD type background events. However a certain amount of QCD background will still be present in the signal region. This contribution originates primarily from events which satisfy candidate $W^\pm$ isolation cuts but contain jet fragments which escape the detection outside the STAR acceptance. Two procedures referred as ``Second EEMC" and ``Data-driven QCD", were used to estimated these backgrounds associated with the acceptance ranges $-2<\eta < -1.09$ and $|\eta|>2$ respectively. The backgrounds treated with the Second EEMC procedure refers to the $e^\pm$ candidate events that satisfy W isolation requirement which had an opposite-side jet fragment in the range $-2 < \eta < -1.09$, where an EEMC does not exist in opposite to the real EEMC ($1.09<\eta < 2.0$) at STAR. Therefore, this opposite-jet fragment had escaped the detection leading respective events to satisfy W candidate requirements. The magnitude of this background contribution was estimated using the real EEMC~\cite{dis:run9paper}. The backgrounds treated with Data-driven QCD procedure were referred to QCD background events that satisfied W candidate selection criteria due to the escape of detection of a jet fragment similar to the Second EEMC case, but in the range of $\eta < |2|$. This component of the background was estimated using a data-driven procedure~\cite{dis:run9paper} as a function of $E^{e}_{T}$.
\section{III. RESULTS}\label{results}
The $W^\pm$ single-spin asymmetries were calculated using the formula as shown in equation~\ref{eq:AL},
\begin{equation}
A^W_L=\frac{A_L - \alpha}{\beta}
\label{eq:AL}
\end{equation}
where $A_L$ is the parity violating single spin asymmetry which is dominated by the signal but still contain some residual background. This raw asymmetry was calculated separately for each RHIC beam for a given $\eta$ bin at STAR in terms of luminosity corrected yields, $N_i$ corresponds to four RHIC helicity states, $+ +,+ -,- + and - -$ and average beam polarization of the beam $P_{1,(2)}$. The polarized background correction $\alpha$, was determined using the fraction of Z background component contained in the signal yield and its respective longitudinal single-spin asymmetry, $A^Z_L$ which was estimated using full next-to-leading (NLO) order framework~\cite{dis:run9paper}. This contribution was found to be negligible within the statistical uncertainty due to the small ($<$1 \%) fraction of Z background contribution as shown in Fig.~\ref{Fig:bg}. The unpolarized background correction, $\beta$ for $A_L$ is calculated independently for $W^+$ and $W^-$ for each $\eta$ bin. This dilution factor is due to background events as shown in Fig.~\ref{Fig:bg} and is determined by $\beta = S / (S+B) $, where $S (B)$ is the number of signal (background) events for $25 < E^e_T < 50$ GeV. \\
\begin{figure}[!h]
\centering
\includegraphics[width=0.49\textwidth]{results.pdf}
\caption{Longitudinal single-spin asymmetries for $W^\pm$ production as a function of lepton pseudorapidity, $\eta_e$ in comparison to theory predictions}
\label{Fig:results}
\end{figure}
\indent
The STAR 2012 published~\cite{dis:run12paper} $W^\pm$ single-spin asymmetry results (open and closed black squares) measured for $e^\pm$ are shown in Fig.~\ref{Fig:results} along with recently released STAR 2013 preliminary results (open and closed red circles) as the function of decay $e^\pm$ pseudorapidity, $\eta_e$ in comparison to theoretical predictions based on DSSV08~\cite{dis:dssv08} and LSS10~\cite{dis:lss10} helicity-dependent PDF sets, using both CHE (next-to-leading order)~\cite{dis:rhicW} and RHICBOS (fully resummed) frameworks~\cite{dis:rhicbos}. The new 2013 preliminary results are consistent with published 2012 results which measured larger $A^{W^-}_L$ than the central value of the theoretical predictions. The enhancement at large negative $\eta_e$, in particular is sensitive to the polarized anti u quark distribution, $\Delta\bar u$. $A^{W^+}_L$ is negative as expected and consistent with theoretical predictions. The total uncertainties in both results are completely statistically driven while systematic uncertainties are well under control. Vertical error bars include statistical uncertainty as well as systematic uncertainties due to the unpolarized background dilutions ($<$10 \% of statistical uncertainty). Horizontal error bars of each point represented the width of the $\eta_e$ distributions within the bin. In 2013 results, systematic uncertainty due to the BEMC calibration is represent by the thickness of the horizontal bar which is in the same order of the relative luminosity systematic, represent by the grey band. The total systematic of 2013 results are on the same order of published 2012 results despite significant enhancement in luminosity in RHIC 2013 running in comparison to previous years. The uncertainty of new 2013 preliminary results is reduced by 40\% in comparison to published results making new results the most precise measurement in the world to date. The STAR 2012 preliminary $A^{W^\pm}_L$ results~\cite{dis:global} are included in the DSSV++ global analysis~\cite{dis:dssv++} from the DSSV group and recent NNPDF~\cite{dis:nnpdf} global analysis. Both analyses show that the STAR W $A_L$ results provide a significant constraint on $\Delta\bar u$ and $\Delta\bar d$ quark polarizations. We expect new STAR 2013 preliminary results to further constrain anti u ($\Delta\bar u$) and anti d ($\Delta\bar d$) quark polarizations. \\
\indent
The charged W cross section ratio can be measured experimentally as
\begin{equation}
\frac{\sigma _{W^+}}{\sigma _{W^-}} = \frac{N^+_i - N^+_B }{N^-_i - N^-_B}\frac{\varepsilon^-}{\varepsilon^+}
\label{eq:Xsection}
\end{equation}
where $\pm$ corresponds to positively or negatively charged lepton, $N_i$ are reconstructed $W^\pm$ yields from decay $e^\pm$, $N_B$ are estimated background yields and $\varepsilon$ is the efficiency at which W events are detected. The detection efficiencies which account for all cut and detector efficiencies are calculated using Monte Carlo based on PYTHIA 6.422 and GEANT simulations. However there was only a small ($\sim 1-2\%$) charge dependence measured between the $W^+$ and $W^-$ efficiencies leading to a negligible contribution to the charged W cross section ratio. Figure~\ref{Fig:results2}(\ref{Fig:results3}) shows the charged W cross section ratio for the combined 2011 and 2012 runs, computed using equation~\ref{eq:Xsection} as a function of the electron pseudo-rapidity $\eta_e$ (W boson rapidity, $y_W$). More information on how the W boson kinematics were reconstructed can be found in \cite{dis:wrapidity}.
\begin{figure}[!h]
\centering
\includegraphics[width=0.48\textwidth]{results2.pdf}
\caption{$W^+ / W^-$ cross section ratio as a function of electron pseudo-rapidity.}
\label{Fig:results2}
\end{figure}
The error bars on data points represent the statistical uncertainty, while the shaded boxes correspond to the systematic uncertainty. The yellow band and colored curves serve as a comparison to different PDF sets \cite{dis:XsecPDF1,dis:XsecPDF2} and theory frameworks \cite{dis:XsecTheory1,dis:XsecTheory2}. The systematic uncertainties for the charged W cross section ratios as a function of $\eta_e$ are due to the background subtraction~\cite{dis:matt} and are well under control similar to the asymmetry analysis. The systematic uncertainty of the result as a function of $y_W$ is contributed both by the background subtraction and W reconstruction smearing~\cite{dis:wrapidity} where the latter provided the leading contribution. Further studies into this newly established W boson kinematics reconstruction process~\cite{dis:wrapidity} should reduce the systematic uncertainties on the $W^\pm$ cross-section ratio dependence on the boson kinematics.
\begin{figure}[!h]
\centering
\includegraphics[width=0.48\textwidth]{results3.pdf}
\caption{$W^+ / W^-$ cross section ratio as a function of W boson rapidity}
\label{Fig:results3}
\end{figure}
\section{IV. SUMMARY AND OUTLOOK}
We present the STAR 2013 preliminary results of measurements of single spin asymmetries for $W^\pm$ boson production in longitudinally polarized p+p collisions and STAR 2011+2012 W cross section ratios $W^+ / W^-$, at $\sqrt{s}=510$ GeV. The new 2013 $A^{W^-}_L$ results are consistent with STAR published 2012 $A^{W^-}_L$ results, further confirming the measured large $W^-$ asymmetry compared to the theoretical prediction indicating a large anti u quark polarization. Furthermore, the uncertainty of new 2013 results is reduced by 40\% in comparison to published results making the STAR 2013 preliminary results the most precise measurements of $A^{W^-}_L$ in the world up to date. The uncertainties are purely statistical driven while systematics are well under control. With the reduced uncertainty, we expect our new results to further constrain the antiquark helicity distribution functions. Analysis is ongoing to measure the asymmetry in the forward rapidity region from $1<\eta<1.4$ using STAR EEMC subsystem and further extend using STAR Forward Gem Tracker (FGT) which covers the acceptance between $1<\eta<2$. This enhances the sensitivity to $\bar u$ and $\bar d$ quark polarizations. We expect to include these measurements in the publication from STAR 2013 data. STAR has also measured and presented charged W cross section ratios from combined 2011 and 2012 proton-proton STAR data at $\sqrt{s}$ = 500 and 510 GeV. The inclusion of this data into global PDF analysis should help constrain the sea quark distributions and provide additional insight into the $\bar d / \bar u$ ratio at relatively higher Bjorken-x values where the behavior of $\bar d / \bar u$ is not clearly understand yet.
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{
"redpajama_set_name": "RedPajamaArXiv"
}
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package driver
type UbuntuSystemdDriver struct {
ubuntuBaseDriver
systemdBaseDriver
systemdUnitOverwriteDriver
}
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{
"redpajama_set_name": "RedPajamaGithub"
}
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He was born Oct. 22, 1926, in Fayette, Alabama, to Sherman Martin Webster and Nancy Alice Mills Webster.
Survivors include one son, Roderick Kelly Webster of Grand Bay, Alabama; one daughter, Donna Webster Goodlett of Auburn, Alabama; Dorothy's children, Wanda Woods, Teresa Edwards, and Danny Webster; nine grandchildren; 15 great-grandchildren.
A celebration of life will be 2 p.m. Friday, March 22, at Tanner United Methodist Church. Visitation will be 1-2 p.m. Friday at the church. Burial will be at Roselawn Cemetery.
In lieu of flowers, make memorials to Tanner United Methodist Church, 19607 Huntsville Browns Ferry Road, Tanner, AL 35671 or Philadelphia Missionary Baptist Church, 10890 Lockwood Drive, Grand Bay, AL 36541.
McConnell Funeral Home is directing services.
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{
"redpajama_set_name": "RedPajamaC4"
}
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Q: How to download only particular folder files of sub-folders from FTP site in command line in linux I had tried using this command
"wget -r ftp://ftptrace.ncbi.nlm.nih.gov/giab/ftp/data/AshkenazimTrio/HG004_NA24143_mother/NIST_HiSeq_HG004_Homogeneity14572558/HG004_HiSeq300x_fastq/140818_D00360_0046_AHA5R5ADXX/Project_RM8392/Sample_4A1/"
but in this case it takes huge time and morover it download all the folders starting from ftp-trace.ncbi.nlm.nih.gov - Sample_4A1. So, in this case whether there is any other commands or way to download only particular folder? In my mycase i wish to fetch (download) only this last folder files "Sample_4A1"
is there any script or command to do this? So, by doing this I can make download my required folder by excluding other unnecessary folders files.
Thanks in advance.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
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# THE REDHEADED OUTFIELD
### AND OTHER BASEBALL STORIES
## * * *
## ZANE GREY
#
## *
_The Redheaded Outfield_
_And Other Baseball Stories_
First published in 1920
ISBN 978-1-775453-01-7
© 2011 The Floating Press
_While every effort has been used to ensure the accuracy and reliability of the information contained in The Floating Press edition of this book, The Floating Press does not assume liability or responsibility for any errors or omissions in this book. The Floating Press does not accept responsibility for loss suffered as a result of reliance upon the accuracy or currency of information contained in this book. Do not use while operating a motor vehicle or heavy equipment. Many suitcases look alike._
_Visitwww.thefloatingpress.com_
# Contents
## *
_The Redheaded Outfield_
_The Rube_
_The Rube's Pennant_
_The Rube's Honeymoon_
_The Rube's Waterloo_
_Breaking into Fast Company_
_The Knocker_
_The Winning Ball_
_False Colors_
_The Manager of Madden's Hill_
_Old Well-Well_
# The Redheaded Outfield
## *
There was Delaney's red-haired trio—Red Gilbat, left fielder; Reddy Clammer, right fielder, and Reddie Ray, center fielder, composing the most remarkable outfield ever developed in minor league baseball. It was Delaney's pride, as it was also his trouble.
Red Gilbat was nutty—and his batting average was .371. Any student of baseball could weigh these two facts against each other and understand something of Delaney's trouble. It was not possible to camp on Red Gilbat's trail. The man was a jack-o'-lantern, a will-o'-the-wisp, a weird, long-legged, long-armed, red-haired illusive phantom. When the gong rang at the ball grounds there were ten chances to one that Red would not be present. He had been discovered with small boys peeping through knotholes at the vacant left field he was supposed to inhabit during play.
Of course what Red did off the ball grounds was not so important as what he did on. And there was absolutely no telling what under the sun he might do then except once out of every three times at bat he could be counted on to knock the cover off the ball.
Reddy Clammer was a grand-stand player—the kind all managers hated—and he was hitting .305. He made circus catches, circus stops, circus throws, circus steals—but particularly circus catches. That is to say, he made easy plays appear difficult. He was always strutting, posing, talking, arguing, quarreling—when he was not engaged in making a grand-stand play. Reddy Clammer used every possible incident and artifice to bring himself into the limelight.
Reddie Ray had been the intercollegiate champion in the sprints and a famous college ball player. After a few months of professional ball he was hitting over .400 and leading the league both at bat and on the bases. It was a beautiful and a thrilling sight to see him run. He was so quick to start, so marvelously swift, so keen of judgment, that neither Delaney nor any player could ever tell the hit that he was not going to get. That was why Reddie Ray was a whole game in himself.
Delaney's Rochester Stars and the Providence Grays were tied for first place. Of the present series each team had won a game. Rivalry had always been keen, and as the teams were about to enter the long homestretch for the pennant there was battle in the New England air.
The September day was perfect. The stands were half full and the bleachers packed with a white-sleeved mass. And the field was beautifully level and green. The Grays were practicing and the Stars were on their bench.
"We're up against it," Delaney was saying. "This new umpire, Fuller, hasn't got it in for us. Oh, no, not at all! Believe me, he's a robber. But Scott is pitchin' well. Won his last three games. He'll bother 'em. And the three Reds have broken loose. They're on the rampage. They'll burn up this place today."
Somebody noted the absence of Gilbat.
Delaney gave a sudden start. "Why, Gil was here," he said slowly. "Lord!—he's about due for a nutty stunt."
Whereupon Delaney sent boys and players scurrying about to find Gilbat, and Delaney went himself to ask the Providence manager to hold back the gong for a few minutes.
Presently somebody brought Delaney a telephone message that Red Gilbat was playing ball with some boys in a lot four blocks down the street. When at length a couple of players marched up to the bench with Red in tow Delaney uttered an immense sigh of relief and then, after a close scrutiny of Red's face, he whispered, "Lock the gates!"
Then the gong rang. The Grays trooped in. The Stars ran out, except Gilbat, who ambled like a giraffe. The hum of conversation in the grand stand quickened for a moment with the scraping of chairs, and then grew quiet. The bleachers sent up the rollicking cry of expectancy. The umpire threw out a white ball with his stentorian "Play!" and Blake of the Grays strode to the plate.
Hitting safely, he started the game with a rush. With Dorr up, the Star infield played for a bunt. Like clockwork Dorr dumped the first ball as Blake got his flying start for second base. Morrissey tore in for the ball, got it on the run and snapped it underhand to Healy, beating the runner by an inch. The fast Blake, with a long slide, made third base. The stands stamped. The bleachers howled. White, next man up, batted a high fly to left field. This was a sun field and the hardest to play in the league. Red Gilbat was the only man who ever played it well. He judged the fly, waited under it, took a step hack, then forward, and deliberately caught the ball in his gloved hand. A throw-in to catch the runner scoring from third base would have been futile, but it was not like Red Gilbat to fail to try. He tossed the ball to O'Brien. And Blake scored amid applause.
"What do you know about that?" ejaculated Delaney, wiping his moist face. "I never before saw our nutty Redhead pull off a play like that."
Some of the players yelled at Red, "This is a two-handed league, you bat!"
The first five players on the list for the Grays were left-handed batters, and against a right-handed pitcher whose most effective ball for them was a high fast one over the outer corner they would naturally hit toward left field. It was no surprise to see Hanley bat a skyscraper out to left. Red had to run to get under it. He braced himself rather unusually for a fielder. He tried to catch the ball in his bare right hand and muffed it, Hanley got to second on the play while the audience roared. When they got through there was some roaring among the Rochester players. Scott and Captain Healy roared at Red, and Red roared back at them.
"It's all off. Red never did that before," cried Delaney in despair. "He's gone clean bughouse now."
Babcock was the next man up and he likewise hit to left. It was a low, twisting ball—half fly, half liner—and a difficult one to field. Gilbat ran with great bounds, and though he might have got two hands on the ball he did not try, but this time caught it in his right, retiring the side.
The Stars trotted in, Scott and Healy and Kane, all veterans, looking like thunderclouds. Red ambled in the last and he seemed very nonchalant.
"By Gosh, I'd 'a' ketched that one I muffed if I'd had time to change hands," he said with a grin, and he exposed a handful of peanuts. He had refused to drop the peanuts to make the catch with two hands. That explained the mystery. It was funny, yet nobody laughed. There was that run chalked up against the Stars, and this game had to be won.
"Red, I—I want to take the team home in the lead," said Delaney, and it was plain that he suppressed strong feeling. "You didn't play the game, you know."
Red appeared mightily ashamed.
"Del, I'll git that run back," he said.
Then he strode to the plate, swinging his wagon-tongue bat. For all his awkward position in the box he looked what he was—a formidable hitter. He seemed to tower over the pitcher—Red was six feet one—and he scowled and shook his bat at Wehying and called, "Put one over—you wienerwurst!" Wehying was anything but red-headed, and he wasted so many balls on Red that it looked as if he might pass him. He would have passed him, too, if Red had not stepped over on the fourth ball and swung on it. White at second base leaped high for the stinging hit, and failed to reach it. The ball struck and bounded for the fence. When Babcock fielded it in, Red was standing on third base, and the bleachers groaned.
Whereupon Chesty Reddy Clammer proceeded to draw attention to himself, and incidentally delay the game, by assorting the bats as if the audience and the game might gladly wait years to see him make a choice.
"Git in the game!" yelled Delaney.
"Aw, take my bat, Duke of the Abrubsky!" sarcastically said Dump Kane. When the grouchy Kane offered to lend his bat matters were critical in the Star camp.
Other retorts followed, which Reddy Clammer deigned not to notice. At last he got a bat that suited him—and then, importantly, dramatically, with his cap jauntily riding his red locks, he marched to the plate.
Some wag in the bleachers yelled into the silence, "Oh, Maggie, your lover has come!"
Not improbably Clammer was thinking first of his presence before the multitude, secondly of his batting average and thirdly of the run to be scored. In this instance he waited and feinted at balls and fouled strikes at length to work his base. When he got to first base suddenly he bolted for second, and in the surprise of the unlooked-for play he made it by a spread-eagle slide. It was a circus steal.
Delaney snorted. Then the look of profound disgust vanished in a flash of light. His huge face beamed.
Reddie Ray was striding to the plate.
There was something about Reddie Ray that pleased all the senses. His lithe form seemed instinct with life; any sudden movement was suggestive of stored lightning. His position at the plate was on the left side, and he stood perfectly motionless, with just a hint of tense waiting alertness. Dorr, Blake and Babcock, the outfielders for the Grays, trotted round to the right of their usual position. Delaney smiled derisively, as if he knew how futile it was to tell what field Reddie Ray might hit into. Wehying, the old fox, warily eyed the youngster, and threw him a high curve, close in. It grazed Reddie's shirt, but he never moved a hair. Then Wehying, after the manner of many veteran pitchers when trying out a new and menacing batter, drove a straight fast ball at Reddie's head. Reddie ducked, neither too slow nor too quick, just right to show what an eye he had, how hard it was to pitch to. The next was a strike. And on the next he appeared to step and swing in one action. There was a ringing rap, and the ball shot toward right, curving down, a vicious, headed hit. Mallory, at first base, snatched at it and found only the air. Babcock had only time to take a few sharp steps, and then he plunged down, blocked the hit and fought the twisting ball. Reddie turned first base, flitted on toward second, went headlong in the dust, and shot to the base before White got the throw-in from Babcock. Then, as White wheeled and lined the ball home to catch the scoring Clammer, Reddie Ray leaped up, got his sprinter's start and, like a rocket, was off for third. This time he dove behind the base, sliding in a half circle, and as Hanley caught Strickland's perfect throw and whirled with the ball, Reddie's hand slid to the bag.
Reddie got to his feet amid a rather breathless silence. Even the coachers were quiet. There was a moment of relaxation, then Wehying received the ball from Hanley and faced the batter.
This was Dump Kane. There was a sign of some kind, almost imperceptible, between Kane and Reddie. As Wehying half turned in his swing to pitch, Reddie Ray bounded homeward. It was not so much the boldness of his action as the amazing swiftness of it that held the audience spellbound. Like a thunderbolt Reddie came down the line, almost beating Wehying's pitch to the plate. But Kane's bat intercepted the ball, laying it down, and Reddie scored without sliding. Dorr, by sharp work, just managed to throw Kane out.
Three runs so quick it was hard to tell how they had come. Not in the major league could there have been faster work. And the ball had been fielded perfectly and thrown perfectly.
"There you are," said Delaney, hoarsely. "Can you beat it? If you've been wonderin' how the cripped Stars won so many games just put what you've seen in your pipe and smoke it. Red Gilbat gets on—Reddy Clammer gets on—and then Reddie Ray drives them home or chases them home."
The game went on, and though it did not exactly drag it slowed down considerably. Morrissey and Healy were retired on infield plays. And the sides changed. For the Grays, O'Brien made a scratch hit, went to second on Strickland's sacrifice, stole third and scored on Mallory's infield out. Wehying missed three strikes. In the Stars' turn the three end players on the batting list were easily disposed of. In the third inning the clever Blake, aided by a base on balls and a hit following, tied the score, and once more struck fire and brimstone from the impatient bleachers. Providence was a town that had to have its team win.
"Git at 'em, Reds!" said Delaney gruffly.
"Batter up!" called Umpire Fuller, sharply.
"Where's Red? Where's the bug? Where's the nut? Delaney, did you lock the gates? Look under the bench!" These and other remarks, not exactly elegant, attested to the mental processes of some of the Stars. Red Gilbat did not appear to be forthcoming. There was an anxious delay Capt. Healy searched for the missing player. Delaney did not say any more.
Suddenly a door under the grand stand opened and Red Gilbat appeared. He hurried for his bat and then up to the plate. And he never offered to hit one of the balls Wehying shot over. When Fuller had called the third strike Red hurried back to the door and disappeared.
"Somethin' doin'," whispered Delaney.
Lord Chesterfield Clammer paraded to the batter's box and, after gradually surveying the field, as if picking out the exact place he meant to drive the ball, he stepped to the plate. Then a roar from the bleachers surprised him.
"Well, I'll be dog-goned!" exclaimed Delaney. "Red stole that sure as shootin'."
Red Gilbat was pushing a brand-new baby carriage toward the batter's box. There was a tittering in the grand stand; another roar from the bleachers. Clammer's face turned as red as his hair. Gilbat shoved the baby carriage upon the plate, spread wide his long arms, made a short presentation speech and an elaborate bow, then backed away.
All eyes were centered on Clammer. If he had taken it right the incident might have passed without undue hilarity. But Clammer became absolutely wild with rage. It was well known that he was unmarried. Equally well was it seen that Gilbat had executed one of his famous tricks. Ball players were inclined to be dignified about the presentation of gifts upon the field, and Clammer, the dude, the swell, the lady's man, the favorite of the baseball gods—in his own estimation—so far lost control of himself that he threw his bat at his retreating tormentor. Red jumped high and the bat skipped along the ground toward the bench. The players sidestepped and leaped and, of course, the bat cracked one of Delaney's big shins. His eyes popped with pain, but he could not stop laughing. One by one the players lay down and rolled over and yelled. The superior Clammer was not overliked by his co-players.
From the grand stand floated the laughter of ladies and gentlemen. And from the bleachers—that throne of the biting, ironic, scornful fans—pealed up a howl of delight. It lasted for a full minute. Then, as quiet ensued, some boy blew a blast of one of those infernal little instruments of pipe and rubber balloon, and over the field wailed out a shrill, high-keyed cry, an excellent imitation of a baby. Whereupon the whole audience roared, and in discomfiture Reddy Clammer went in search of his bat.
To make his chagrin all the worse he ingloriously struck out. And then he strode away under the lea of the grand-stand wall toward right field.
Reddie Ray went to bat and, with the infield playing deep and the outfield swung still farther round to the right, he bunted a little teasing ball down the third-base line. Like a flash of light he had crossed first base before Hanley got his hands on the ball. Then Kane hit into second base, forcing Reddie out.
Again the game assumed less spectacular and more ordinary play. Both Scott and Wehying held the batters safely and allowed no runs. But in the fifth inning, with the Stars at bat and two out, Red Gilbat again electrified the field. He sprang up from somewhere and walked to the plate, his long shape enfolded in a full-length linen duster. The color and style of this garment might not have been especially striking, but upon Red it had a weird and wonderful effect. Evidently Red intended to bat while arrayed in his long coat, for he stepped into the box and faced the pitcher. Capt. Healy yelled for him to take the duster off. Likewise did the Grays yell.
The bleachers shrieked their disapproval. To say the least, Red Gilbat's crazy assurance was dampening to the ardor of the most blindly confident fans. At length Umpire Fuller waved his hand, enjoining silence and calling time.
"Take it off or I'll fine you."
From his lofty height Gilbat gazed down upon the little umpire, and it was plain what he thought.
"What do I care for money!" replied Red.
"That costs you twenty-five," said Fuller.
"Cigarette change!" yelled Red.
"Costs you fifty."
"Bah! Go to an eye doctor," roared Red.
"Seventy-five," added Fuller, imperturbably.
"Make it a hundred!"
"It's two hundred."
"ROB-B-BER!" bawled Red.
Fuller showed willingness to overlook Red's back talk as well as costume, and he called, "Play!"
There was a mounting sensation of prophetic certainty. Old fox Wehying appeared nervous. He wasted two balls on Red; then he put one over the plate, and then he wasted another. Three balls and one strike! That was a bad place for a pitcher, and with Red Gilbat up it was worse. Wehying swung longer and harder to get all his left behind the throw and let drive. Red lunged and cracked the ball. It went up and up and kept going up and farther out, and as the murmuring audience was slowly transfixed into late realization the ball soared to its height and dropped beyond the left-field fence. A home run!
Red Gilbat gathered up the tails of his duster, after the manner of a neat woman crossing a muddy street, and ambled down to first base and on to second, making prodigious jumps upon the bags, and round third, to come down the home-stretch wagging his red head. Then he stood on the plate, and, as if to exact revenge from the audience for the fun they made of him, he threw back his shoulders and bellowed: "HAW! HAW! HAW!"
Not a handclap greeted him, but some mindless, exceedingly adventurous fan yelled: "Redhead! Redhead! Redhead!"
That was the one thing calculated to rouse Red Gilbat. He seemed to flare, to bristle, and he paced for the bleachers.
Delaney looked as if he might have a stroke. "Grab him! Soak him with a bat! Somebody grab him!"
But none of the Stars was risking so much, and Gilbat, to the howling derision of the gleeful fans, reached the bleachers. He stretched his long arms up to the fence and prepared to vault over. "Where's the guy who called me redhead?" he yelled.
That was heaping fuel on the fire. From all over the bleachers, from everywhere, came the obnoxious word. Red heaved himself over the fence and piled into the fans. Then followed the roar of many voices, the tramping of many feet, the pressing forward of line after line of shirt-sleeved men and boys. That bleacher stand suddenly assumed the maelstrom appearance of a surging mob round an agitated center. In a moment all the players rushed down the field, and confusion reigned.
"Oh! Oh! Oh!" moaned Delaney.
However, the game had to go on. Delaney, no doubt, felt all was over. Nevertheless there were games occasionally that seemed an unending series of unprecedented events. This one had begun admirably to break a record. And the Providence fans, like all other fans, had cultivated an appetite as the game proceeded. They were wild to put the other redheads out of the field or at least out for the inning, wild to tie the score, wild to win and wilder than all for more excitement. Clammer hit safely. But when Reddie Ray lined to the second baseman, Clammer, having taken a lead, was doubled up in the play.
Of course, the sixth inning opened with the Stars playing only eight men. There was another delay. Probably everybody except Delaney and perhaps Healy had forgotten the Stars were short a man. Fuller called time. The impatient bleachers barked for action.
Capt. White came over to Delaney and courteously offered to lend a player for the remaining innings. Then a pompous individual came out of the door leading from the press boxes—he was a director Delaney disliked.
"Guess you'd better let Fuller call the game," he said brusquely.
"If you want to—as the score stands now in our favor," replied Delaney.
"Not on your life! It'll be ours or else we'll play it out and beat you to death."
He departed in high dudgeon.
"Tell Reddie to swing over a little toward left," was Delaney's order to Healy. Fire gleamed in the manager's eye.
Fuller called play then, with Reddy Clammer and Reddie Ray composing the Star outfield. And the Grays evidently prepared to do great execution through the wide lanes thus opened up. At that stage it would not have been like matured ball players to try to crop hits down into the infield.
White sent a long fly back of Clammer. Reddy had no time to loaf on this hit. It was all he could do to reach it and he made a splendid catch, for which the crowd roundly applauded him. That applause was wine to Reddy Clammer. He began to prance on his toes and sing out to Scott: "Make 'em hit to me, old man! Make 'em hit to me!" Whether Scott desired that or not was scarcely possible to say; at any rate, Hanley pounded a hit through the infield. And Clammer, prancing high in the air like a check-reined horse, ran to intercept the ball. He could have received it in his hands, but that would never have served Reddy Clammer. He timed the hit to a nicety, went down with his old grand-stand play and blocked the ball with his anatomy. Delaney swore. And the bleachers, now warm toward the gallant outfielder, lustily cheered him. Babcock hit down the right-field foul line, giving Clammer a long run. Hanley was scoring and Babcock was sprinting for third base when Reddy got the ball. He had a fine arm and he made a hard and accurate throw, catching his man in a close play.
Perhaps even Delaney could not have found any fault with that play. But the aftermath spoiled the thing. Clammer now rode the air; he soared; he was in the clouds; it was his inning and he had utterly forgotten his team mates, except inasmuch as they were performing mere little automatic movements to direct the great machinery in his direction for his sole achievement and glory.
There is fate in baseball as well as in other walks of life. O'Brien was a strapping fellow and he lifted another ball into Clammer's wide territory. The hit was of the high and far-away variety. Clammer started to run with it, not like a grim outfielder, but like one thinking of himself, his style, his opportunity, his inevitable success. Certain it was that in thinking of himself the outfielder forgot his surroundings. He ran across the foul line, head up, hair flying, unheeding the warning cry from Healy. And, reaching up to make his crowning circus play, he smashed face forward into the bleachers fence. Then, limp as a rag, he dropped. The audience sent forth a long groan of sympathy.
"That wasn't one of his stage falls," said Delaney. "I'll bet he's dead.... Poor Reddy! And I want him to bust his face!"
Clammer was carried off the field into the dressing room and a physician was summoned out of the audience.
"Cap., what'd it—do to him?" asked Delaney.
"Aw, spoiled his pretty mug, that's all," replied Healy, scornfully. "Mebee he'll listen to me now."
Delaney's change was characteristic of the man. "Well, if it didn't kill him I'm blamed glad he got it.... Cap, we can trim 'em yet. Reddie Ray'll play the whole outfield. Give Reddie a chance to run! Tell the boy to cut loose. And all of you git in the game. Win or lose, I won't forget it. I've a hunch. Once in a while I can tell what's comin' off. Some queer game this! And we're goin' to win. Gilbat lost the game; Clammer throwed it away again, and now Reddie Ray's due to win it.... I'm all in, but I wouldn't miss the finish to save my life."
Delaney's deep presaging sense of baseball events was never put to a greater test. And the seven Stars, with the score tied, exhibited the temper and timber of a championship team in the last ditch. It was so splendid that almost instantly it caught the antagonistic bleachers.
Wherever the tired Scott found renewed strength and speed was a mystery. But he struck out the hard-hitting Providence catcher and that made the third out. The Stars could not score in their half of the inning. Likewise the seventh inning passed without a run for either side; only the infield work of the Stars was something superb. When the eighth inning ended, without a tally for either team, the excitement grew tense. There was Reddy Ray playing outfield alone, and the Grays with all their desperate endeavors had not lifted the ball out of the infield.
But in the ninth, Blake, the first man up, lined low toward right center. The hit was safe and looked good for three bases. No one looking, however, had calculated on Reddie's Ray's fleetness. He covered ground and dove for the bounding ball and knocked it down. Blake did not get beyond first base. The crowd cheered the play equally with the prospect of a run. Dorr bunted and beat the throw. White hit one of the high fast balls Scott was serving and sent it close to the left-field foul line. The running Reddie Ray made on that play held White at second base. But two runs had scored with no one out.
Hanley, the fourth left-handed hitter, came up and Scott pitched to him as he had to the others—high fast balls over the inside corner of the plate. Reddy Ray's position was some fifty yards behind deep short, and a little toward center field. He stood sideways, facing two-thirds of that vacant outfield. In spite of Scott's skill, Hanley swung the ball far round into right field, but he hit it high, and almost before he actually hit it the great sprinter was speeding across the green.
The suspense grew almost unbearable as the ball soared in its parabolic flight and the red-haired runner streaked dark across the green. The ball seemed never to be coming down. And when it began to descend and reached a point perhaps fifty feet above the ground there appeared more distance between where it would alight and where Reddie was than anything human could cover. It dropped and dropped, and then dropped into Reddie Ray's outstretched hands. He had made the catch look easy. But the fact that White scored from second base on the play showed what the catch really was.
There was no movement or restlessness of the audience such as usually indicated the beginning of the exodus. Scott struck Babcock out. The game still had fire. The Grays never let up a moment on their coaching. And the hoarse voices of the Stars were grimmer than ever. Reddie Ray was the only one of the seven who kept silent. And he crouched like a tiger.
The teams changed sides with the Grays three runs in the lead. Morrissey, for the Stars, opened with a clean drive to right. Then Healy slashed a ground ball to Hanley and nearly knocked him down. When old Burns, by a hard rap to short, advanced the runners a base and made a desperate, though unsuccessful, effort to reach first the Providence crowd awoke to a strange and inspiring appreciation. They began that most rare feature in baseball audiences—a strong and trenchant call for the visiting team to win.
The play had gone fast and furious. Wehying, sweaty and disheveled, worked violently. All the Grays were on uneasy tiptoes. And the Stars were seven Indians on the warpath. Halloran fouled down the right-field line; then he fouled over the left-field fence. Wehying tried to make him too anxious, but it was in vain. Halloran was implacable. With two strikes and three balls he hit straight down to white, and was out. The ball had been so sharp that neither runner on base had a chance to advance.
Two men out, two on base, Stars wanting three runs to tie, Scott, a weak batter, at the plate! The situation was disheartening. Yet there sat Delaney, shot through and through with some vital compelling force. He saw only victory. And when the very first ball pitched to Scott hit him on the leg, giving him his base, Delaney got to his feet, unsteady and hoarse.
Bases full, Reddie Ray up, three runs to tie!
Delaney looked at Reddie. And Reddie looked at Delaney. The manager's face was pale, intent, with a little smile. The player had eyes of fire, a lean, bulging jaw and the hands he reached for his bat clutched like talons.
"Reddie, I knew it was waitin' for you," said Delaney, his voice ringing. "Break up the game!"
After all this was only a baseball game, and perhaps from the fans' viewpoint a poor game at that. But the moment when that lithe, redhaired athlete toed the plate was a beautiful one. The long crash from the bleachers, the steady cheer from the grand stand, proved that it was not so much the game that mattered.
Wehying had shot his bolt; he was tired. Yet he made ready for a final effort. It seemed that passing Reddie Ray on balls would have been a wise play at that juncture. But no pitcher, probably, would have done it with the bases crowded and chances, of course, against the batter.
Clean and swift, Reddie leaped at the first pitched ball. Ping! For a second no one saw the hit. Then it gleamed, a terrific drive, low along the ground, like a bounding bullet, straight at Babcock in right field. It struck his hands and glanced viciously away to roll toward the fence.
Thunder broke loose from the stands. Reddie Ray was turning first base. Beyond first base he got into his wonderful stride. Some runners run with a consistent speed, the best they can make for a given distance. But this trained sprinter gathered speed as he ran. He was no short-stepping runner. His strides were long. They gave an impression of strength combined with fleetness. He had the speed of a race horse, but the trimness, the raciness, the delicate legs were not characteristic of him. Like the wind he turned second, so powerful that his turn was short. All at once there came a difference in his running. It was no longer beautiful. The grace was gone. It was now fierce, violent. His momentum was running him off his legs. He whirled around third base and came hurtling down the homestretch. His face was convulsed, his eyes were wild. His arms and legs worked in a marvelous muscular velocity. He seemed a demon—a flying streak. He overtook and ran down the laboring Scott, who had almost reached the plate.
The park seemed full of shrill, piercing strife. It swelled, reached a highest pitch, sustained that for a long moment, and then declined.
"My Gawd!" exclaimed Delaney, as he fell back. "Wasn't that a finish? Didn't I tell you to watch them redheads!"
# The Rube
## *
It was the most critical time I had yet experienced in my career as a baseball manager. And there was more than the usual reason why I must pull the team out. A chance for a business deal depended upon the good-will of the stockholders of the Worcester club. On the outskirts of the town was a little cottage that I wanted to buy, and this depended upon the business deal. My whole future happiness depended upon the little girl I hoped to install in that cottage.
Coming to the Worcester Eastern League team, I had found a strong aggregation and an enthusiastic following. I really had a team with pennant possibilities. Providence was a strong rival, but I beat them three straight in the opening series, set a fast pace, and likewise set Worcester baseball mad. The Eastern League clubs were pretty evenly matched; still I continued to hold the lead until misfortune overtook me.
Gregg smashed an umpire and had to be laid off. Mullaney got spiked while sliding and was out of the game. Ashwell sprained his ankle and Hirsch broke a finger. Radbourne, my great pitcher, hurt his arm on a cold day and he could not get up his old speed. Stringer, who had batted three hundred and seventy-one and led the league the year before, struck a bad spell and could not hit a barn door handed up to him.
Then came the slump. The team suddenly let down; went to pieces; played ball that would have disgraced an amateur nine. It was a trying time. Here was a great team, strong everywhere. A little hard luck had dug up a slump—and now! Day by day the team dropped in the race. When we reached the second division the newspapers flayed us. Worcester would never stand for a second division team. Baseball admirers, reporters, fans—especially the fans—are fickle. The admirers quit, the reporters grilled us, and the fans, though they stuck to the games with that barnacle-like tenacity peculiar to them, made life miserable for all of us. I saw the pennant slowly fading, and the successful season, and the business deal, and the cottage, and Milly—
But when I thought of her I just could not see failure. Something must be done, but what? I was at the end of my wits. When Jersey City beat us that Saturday, eleven to two, shoving us down to fifth place with only a few percentage points above the Fall River team, I grew desperate, and locking my players in the dressing room I went after them. They had lain down on me and needed a jar. I told them so straight and flat, and being bitter, I did not pick and choose my words.
"And fellows," I concluded, "you've got to brace. A little more of this and we can't pull out. I tell you you're a championship team. We had that pennant cinched. A few cuts and sprains and hard luck—and you all quit! You lay down! I've been patient. I've plugged for you. Never a man have I fined or thrown down. But now I'm at the end of my string. I'm out to fine you now, and I'll release the first man who shows the least yellow. I play no more substitutes. Crippled or not, you guys have got to get in the game."
I waited to catch my breath and expected some such outburst as managers usually get from criticized players. But not a word! Then I addressed some of them personally.
"Gregg, your lay-off ends today. You play Monday. Mullaney, you've drawn your salary for two weeks with that spiked foot. If you can't run on it—well, all right, but I put it up to your good faith. I've played the game and I know it's hard to run on a sore foot. But you can do it. Ashwell, your ankle is lame, I know—now, can you run?"
"Sure I can. I'm not a quitter. I'm ready to go in," replied Ashwell.
"Raddy, how about you?" I said, turning to my star twirler.
"Connelly, I've seen as fast a team in as bad a rut and yet pull out," returned Radbourne. "We're about due for the brace. When it comes—look out! As for me, well, my arm isn't right, but it's acting these warm days in a way that tells me it will be soon. It's been worked too hard. Can't you get another pitcher? I'm not knocking Herne or Cairns. They're good for their turn, but we need a new man to help out. And he must be a crackerjack if we're to get back to the lead."
"Where on earth can I find such a pitcher?" I shouted, almost distracted.
"Well, that's up to you," replied Radbourne.
Up to me it certainly was, and I cudgeled my brains for inspiration. After I had given up in hopelessness it came in the shape of a notice I read in one of the papers. It was a brief mention of an amateur Worcester ball team being shut out in a game with a Rickettsville nine. Rickettsville played Sunday ball, which gave me an opportunity to look them over.
It took some train riding and then a journey by coach to get to Rickettsville. I mingled with the crowd of talking rustics. There was only one little "bleachers" and this was loaded to the danger point with the feminine adherents of the teams. Most of the crowd centered alongside and back of the catcher's box. I edged in and got a position just behind the stone that served as home plate.
Hunting up a player in this way was no new thing to me. I was too wise to make myself known before I had sized up the merits of my man. So, before the players came upon the field I amused myself watching the rustic fans and listening to them. Then a roar announced the appearance of the Rickettsville team and their opponents, who wore the name of Spatsburg on their Canton flannel shirts. The uniforms of these country amateurs would have put a Philadelphia Mummer's parade to the blush, at least for bright colors. But after one amused glance I got down to the stern business of the day, and that was to discover a pitcher, and failing that, baseball talent of any kind.
Never shall I forget my first glimpse of the Rickettsville twirler. He was far over six feet tall and as lean as a fence rail. He had a great shock of light hair, a sunburned, sharp-featured face, wide, sloping shoulders, and arms enormously long. He was about as graceful and had about as much of a baseball walk as a crippled cow.
"He's a rube!" I ejaculated, in disgust and disappointment.
But when I had seen him throw one ball to his catcher I grew as keen as a fox on a scent. What speed he had! I got round closer to him and watched him with sharp, eager eyes. He was a giant. To be sure, he was lean, rawboned as a horse, but powerful. What won me at once was his natural, easy swing. He got the ball away with scarcely any effort. I wondered what he could do when he brought the motion of his body into play.
"Bub, what might be the pitcher's name?" I asked of a boy.
"Huh, mister, his name might be Dennis, but it ain't. Huh!" replied this country youngster. Evidently my question had thrown some implication upon this particular player.
"I reckon you be a stranger in these parts," said a pleasant old fellow. "His name's Hurtle—Whitaker Hurtle. Whit fer short. He hain't lost a gol-darned game this summer. No sir-ee! Never pitched any before, nuther."
Hurtle! What a remarkably fitting name!
Rickettsville chose the field and the game began. Hurtle swung with his easy motion. The ball shot across like a white bullet. It was a strike, and so was the next, and the one succeeding. He could not throw anything but strikes, and it seemed the Spatsburg players could not make even a foul.
Outside of Hurtle's work the game meant little to me. And I was so fascinated by what I saw in him that I could hardly contain myself. After the first few innings I no longer tried to. I yelled with the Rickettsville rooters. The man was a wonder. A blind baseball manager could have seen that. He had a straight ball, shoulder high, level as a stretched string, and fast. He had a jump ball, which he evidently worked by putting on a little more steam, and it was the speediest thing I ever saw in the way of a shoot. He had a wide-sweeping outcurve, wide as the blade of a mowing scythe. And he had a drop—an unhittable drop. He did not use it often, for it made his catcher dig too hard into the dirt. But whenever he did I glowed all over. Once or twice he used an underhand motion and sent in a ball that fairly swooped up. It could not have been hit with a board. And best of all, dearest to the manager's heart, he had control. Every ball he threw went over the plate. He could not miss it. To him that plate was as big as a house.
What a find! Already I had visions of the long-looked-for brace of my team, and of the pennant, and the little cottage, and the happy light of a pair of blue eyes. What he meant to me, that country pitcher Hurtle! He shut out the Spatsburg team without a run or a hit or even a scratch. Then I went after him. I collared him and his manager, and there, surrounded by the gaping players, I bought him and signed him before any of them knew exactly what I was about. I did not haggle. I asked the manager what he wanted and produced the cash; I asked Hurtle what he wanted, doubled his ridiculously modest demand, paid him in advance, and got his name to the contract. Then I breathed a long, deep breath; the first one for weeks. Something told me that with Hurtle's signature in my pocket I had the Eastern League pennant. Then I invited all concerned down to the Rickettsville hotel.
We made connections at the railroad junction and reached Worcester at midnight in time for a good sleep. I took the silent and backward pitcher to my hotel. In the morning we had breakfast together. I showed him about Worcester and then carried him off to the ball grounds.
I had ordered morning practice, and as morning practice is not conducive to the cheerfulness of ball players, I wanted to reach the dressing room a little late. When we arrived, all the players had dressed and were out on the field. I had some difficulty in fitting Hurtle with a uniform, and when I did get him dressed he resembled a two-legged giraffe decked out in white shirt, gray trousers and maroon stockings.
Spears, my veteran first baseman and captain of the team, was the first to see us.
"Sufferin' umpires!" yelled Spears. "Here, you Micks! Look at this Con's got with him!"
What a yell burst from that sore and disgruntled bunch of ball tossers! My players were a grouchy set in practice anyway, and today they were in their meanest mood.
"Hey, beanpole!"
"Get on to the stilts!"
"Con, where did you find that?"
I cut short their chaffing with a sharp order for batting practice.
"Regular line-up, now no monkey biz," I went on. "Take two cracks and a bunt. Here, Hurtle," I said, drawing him toward the pitcher's box, "don't pay any attention to their talk. That's only the fun of ball players. Go in now and practice a little. Lam a few over."
Hurtle's big freckled hands closed nervously over the ball. I thought it best not to say more to him, for he had a rather wild look. I remembered my own stage fright upon my first appearance in fast company. Besides I knew what my amiable players would say to him. I had a secret hope and belief that presently they would yell upon the other side of the fence.
McCall, my speedy little left fielder, led off at bat. He was full of ginger, chipper as a squirrel, sarcastic as only a tried ball player can be.
"Put 'em over, Slats, put 'em over," he called, viciously swinging his ash.
Hurtle stood stiff and awkward in the box and seemed to be rolling something in his mouth. Then he moved his arm. We all saw the ball dart down straight—that is, all of us except McCall, because if he had seen it he might have jumped out of the way. Crack! The ball hit him on the shin.
McCall shrieked. We all groaned. That crack hurt all of us. Any baseball player knows how it hurts to be hit on the shinbone. McCall waved his bat madly.
"Rube! Rube! Rube!" he yelled.
Then and there Hurtle got the name that was to cling to him all his baseball days.
McCall went back to the plate, red in the face, mad as a hornet, and he sidestepped every time Rube pitched a ball. He never even ticked one and retired in disgust, limping and swearing. Ashwell was next. He did not show much alacrity. On Rube's first pitch down went Ashwell flat in the dust. The ball whipped the hair of his head. Rube was wild and I began to get worried. Ashwell hit a couple of measly punks, but when he assayed a bunt the gang yelled derisively at him.
"What's he got?" The old familiar cry of batters when facing a new pitcher!
Stringer went up, bold and formidable. That was what made him the great hitter he was. He loved to bat; he would have faced anybody; he would have faced even a cannon. New curves were a fascination to him. And speed for him, in his own words, was "apple pie." In this instance, surprise was in store for Stringer. Rube shot up the straight one, then the wide curve, then the drop. Stringer missed them all, struck out, fell down ignominiously. It was the first time he had fanned that season and he looked dazed. We had to haul him away.
I called off the practice, somewhat worried about Rube's showing, and undecided whether or not to try him in the game that day. So I went to Radbourne, who had quietly watched Rube while on the field. Raddy was an old pitcher and had seen the rise of a hundred stars. I told him about the game at Rickettsville and what I thought of Rube, and frankly asked his opinion.
"Con, you've made the find of your life," said Raddy, quietly and deliberately.
This from Radbourne was not only comforting; it was relief, hope, assurance. I avoided Spears, for it would hardly be possible for him to regard the Rube favorably, and I kept under cover until time to show up at the grounds.
Buffalo was on the ticket for that afternoon, and the Bisons were leading the race and playing in topnotch form. I went into the dressing room while the players were changing suits, because there was a little unpleasantness that I wanted to spring on them before we got on the field.
"Boys," I said, curtly, "Hurtle works today. Cut loose, now, and back him up."
I had to grab a bat and pound on the wall to stop the uproar.
"Did you mutts hear what I said? Well, it goes. Not a word, now. I'm handling this team. We're in bad, I know, but it's my judgment to pitch Hurtle, rube or no rube, and it's up to you to back us. That's the baseball of it."
Grumbling and muttering, they passed out of the dressing room. I knew ball players. If Hurtle should happen to show good form they would turn in a flash. Rube tagged reluctantly in their rear. He looked like a man in a trance. I wanted to speak encouragingly to him, but Raddy told me to keep quiet.
It was inspiring to see my team practice that afternoon. There had come a subtle change. I foresaw one of those baseball climaxes that can be felt and seen, but not explained. Whether it was a hint of the hoped-for brace, or only another flash of form before the final let-down, I had no means to tell. But I was on edge.
Carter, the umpire, called out the batteries, and I sent my team into the field. When that long, lanky, awkward rustic started for the pitcher's box, I thought the bleachers would make him drop in his tracks. The fans were sore on any one those days, and a new pitcher was bound to hear from them.
"Where! Oh, where! Oh, where!"
"Connelly's found another dead one!"
"Scarecrow!"
"Look at his pants!"
"Pad his legs!"
Then the inning began, and things happened. Rube had marvelous speed, but he could not find the plate. He threw the ball the second he got it; he hit men, walked men, and fell all over himself trying to field bunts. The crowd stormed and railed and hissed. The Bisons pranced round the bases and yelled like Indians. Finally they retired with eight runs.
Eight runs! Enough to win two games! I could not have told how it happened. I was sick and all but crushed. Still I had a blind, dogged faith in the big rustic. I believed he had not got started right. It was a trying situation. I called Spears and Raddy to my side and talked fast.
"It's all off now. Let the dinged rube take his medicine," growled Spears.
"Don't take him out," said Raddy. "He's not shown at all what's in him. The blamed hayseed is up in the air. He's crazy. He doesn't know what he's doing. I tell you, Con, he may be scared to death, but he's dead in earnest."
Suddenly I recalled the advice of the pleasant old fellow at Rickettsville.
"Spears, you're the captain," I said, sharply. "Go after the rube. Wake him up. Tell him he can't pitch. Call him 'Pogie!' That's a name that stirs him up."
"Well, I'll be dinged! He looks it," replied Spears. "Here, Rube, get off the bench. Come here."
Rube lurched toward us. He seemed to be walking in his sleep. His breast was laboring and he was dripping with sweat.
"Who ever told you that you could pitch?" asked Spears genially. He was master at baseball ridicule. I had never yet seen the youngster who could stand his badinage. He said a few things, then wound up with: "Come now, you cross between a hayrack and a wagon tongue, get sore and do something. Pitch if you can. Show us! Do you hear, you tow-headed Pogie!"
Rube jumped as if he had been struck. His face flamed red and his little eyes turned black. He shoved his big fist under Capt. Spears' nose.
"Mister, I'll lick you fer thet—after the game! And I'll show you dog-goned well how I can pitch."
"Good!" exclaimed Raddy; and I echoed his word. Then I went to the bench and turned my attention to the game. Some one told me that McCall had made a couple of fouls, and after waiting for two strikes and three balls had struck out. Ashwell had beat out a bunt in his old swift style, and Stringer was walking up to the plate on the moment. It was interesting, even in a losing game, to see Stringer go to bat. We all watched him, as we had been watching him for weeks, expecting him to break his slump with one of the drives that had made him famous. Stringer stood to the left side of the plate, and I could see the bulge of his closely locked jaw. He swung on the first pitched ball. With the solid rap we all rose to watch that hit. The ball lined first, then soared and did not begin to drop till it was far beyond the right-field fence. For an instant we were all still, so were the bleachers. Stringer had broken his slump with the longest drive ever made on the grounds. The crowd cheered as he trotted around the bases behind Ashwell. Two runs.
"Con, how'd you like that drive?" he asked me, with a bright gleam in his eyes.
"O-h-!—a beaut!" I replied, incoherently. The players on the bench were all as glad as I was. Henley flew out to left. Mullaney smashed a two-bagger to right. Then Gregg hit safely, but Mullaney, in trying to score on the play, was out at the plate.
"Four hits! I tell you fellows, something's coming off," said Raddy. "Now, if only Rube—"
What a difference there was in that long rustic! He stalked into the box, unmindful of the hooting crowd and grimly faced Schultz, the first batter up for the Bisons. This time Rube was deliberate. And where he had not swung before he now got his body and arm into full motion. The ball came in like a glint of light. Schultz looked surprised. The umpire called "Strike!"
"Wow!" yelled the Buffalo coacher. Rube sped up the sidewheeler and Schultz reached wide to meet it and failed. The third was the lightning drop, straight over the plate. The batter poked weakly at it. Then Carl struck out and Manning following, did likewise. Three of the best hitters in the Eastern retired on nine strikes! That was no fluke. I knew what it meant, and I sat there hugging myself with the hum of something joyous in my ears.
Gregg had a glow on his sweaty face. "Oh, but say, boys, take a tip from me! The Rube's a world beater! Raddy knew it; he sized up that swing, and now I know it. Get wise, you its!"
When old Spears pasted a single through shortstop, the Buffalo manager took Clary out of the box and put in Vane, their best pitcher. Bogart advanced the runner to second, but was thrown out on the play. Then Rube came up. He swung a huge bat and loomed over the Bison's twirler. Rube had the look of a hitter. He seemed to be holding himself back from walking right into the ball. And he hit one high and far away. The fast Carl could not get under it, though he made a valiant effort. Spears scored and Rube's long strides carried him to third. The cold crowd in the stands came to life; even the sore bleachers opened up. McCall dumped a slow teaser down the line, a hit that would easily have scored Rube, but he ran a little way, then stopped, tried to get back, and was easily touched out. Ashwell's hard chance gave the Bison's shortstop an error, and Stringer came up with two men on bases. Stringer hit a foul over the right-field fence and the crowd howled. Then he hit a hard long drive straight into the centerfielder's hands.
"Con, I don't know what to think, but ding me if we ain't hittin' the ball," said Spears. Then to his players: "A little more of that and we're back in our old shape. All in a minute—at 'em now! Rube, you dinged old Pogie, pitch!"
Rube toed the rubber, wrapped his long brown fingers round the ball, stepped out as he swung and—zing! That inning he unloosed a few more kinks in his arm and he tried some new balls upon the Bisons. But whatever he used and wherever he put them the result was the same—they cut the plate and the Bisons were powerless.
That inning marked the change in my team. They had come hack. The hoodoo had vanished. The championship Worcester team was itself again.
The Bisons were fighting, too, but Rube had them helpless. When they did hit a ball one of my infielders snapped it up. No chances went to the outfield. I sat there listening to my men, and reveled in a moment that I had long prayed for.
"Now you're pitching some, Rube. Another strike! Get him a board!" called Ashwell.
"Ding 'em, Rube, ding 'em!" came from Capt. Spears.
"Speed? Oh-no!" yelled Bogart at third base.
"It's all off, Rube! It's all off—all off!"
So, with the wonderful pitching of an angry rube, the Worcester team came into its own again. I sat through it all without another word; without giving a signal. In a way I realized the awakening of the bleachers, and heard the pound of feet and the crash, but it was the spirit of my team that thrilled me. Next to that the work of my new find absorbed me. I gloated over his easy, deceiving swing. I rose out of my seat when he threw that straight fast ball, swift as a bullet, true as a plumb line. And when those hard-hitting, sure bunting Bisons chopped in vain at the wonderful drop, I choked back a wild yell. For Rube meant the world to me that day.
In the eighth the score was 8 to 6. The Bisons had one scratch hit to their credit, but not a runner had got beyond first base. Again Rube held them safely, one man striking out, another fouling out, and the third going out on a little fly.
Crash! Crash! Crash! Crash! The bleachers were making up for many games in which they could not express their riotous feelings.
"It's a cinch we'll win!" yelled a fan with a voice. Rube was the first man up in our half of the ninth and his big bat lammed the first ball safe over second base. The crowd, hungry for victory, got to their feet and stayed upon their feet, calling, cheering for runs. It was the moment for me to get in the game, and I leaped up, strung like a wire, and white hot with inspiration. I sent Spears to the coaching box with orders to make Rube run on the first ball. I gripped McCall with hands that made him wince.
Then I dropped back on the bench spent and panting. It was only a game, yet it meant so much! Little McCall was dark as a thunder cloud, and his fiery eyes snapped. He was the fastest man in the league, and could have bunted an arrow from a bow. The foxy Bison third baseman edged in. Mac feinted to bunt toward him then turned his bat inward and dumped a teasing curving ball down the first base line. Rube ran as if in seven-league boots. Mac's short legs twinkled; he went like the wind; he leaped into first base with his long slide, and beat the throw.
The stands and bleachers seemed to be tumbling down. For a moment the air was full of deafening sound. Then came the pause, the dying away of clatter and roar, the close waiting, suspended quiet. Spears' clear voice, as he coached Rube, in its keen note seemed inevitable of another run.
Ashwell took his stand. He was another left-hand hitter, and against a right-hand pitcher, in such circumstances as these, the most dangerous of men. Vane knew it. Ellis, the Bison captain knew it, as showed plainly in his signal to catch Rube at second. But Spears' warning held or frightened Rube on the bag.
Vane wasted a ball, then another. Ashwell could not be coaxed. Wearily Vane swung; the shortstop raced out to get in line for a possible hit through the wide space to his right, and the second baseman got on his toes as both base runners started.
Crack! The old story of the hit and run game! Ashwell's hit crossed sharply where a moment before the shortstop had been standing. With gigantic strides Rube rounded the corner and scored. McCall flitted through second, and diving into third with a cloud of dust, got the umpire's decision. When Stringer hurried up with Mac on third and Ash on first the whole field seemed racked in a deafening storm. Again it subsided quickly. The hopes of the Worcester fans had been crushed too often of late for them to be fearless.
But I had no fear. I only wanted the suspense ended. I was like a man clamped in a vise. Stringer stood motionless. Mac bent low with the sprinters' stoop; Ash watched the pitcher's arm and slowly edged off first. Stringer waited for one strike and two balls, then he hit the next. It hugged the first base line, bounced fiercely past the bag and skipped over the grass to bump hard into the fence. McCall romped home, and lame Ashwell beat any run he ever made to the plate. Rolling, swelling, crashing roar of frenzied feet could not down the high piercing sustained yell of the fans. It was great. Three weeks of submerged bottled baseball joy exploded in one mad outburst! The fans, too, had come into their own again.
We scored no more. But the Bisons were beaten. Their spirit was broken. This did not make the Rube let up in their last half inning. Grim and pale he faced them. At every long step and swing he tossed his shock of light hair. At the end he was even stronger than at the beginning. He still had the glancing, floating airy quality that baseball players call speed. And he struck out the last three batters.
In the tumult that burst over my ears I sat staring at the dots on my score card. Fourteen strike outs! one scratch hit! No base on balls since the first inning! That told the story which deadened senses doubted. There was a roar in my ears. Some one was pounding me. As I struggled to get into the dressing room the crowd mobbed me. But I did not hear what they yelled. I had a kind of misty veil before my eyes, in which I saw that lanky Rube magnified into a glorious figure. I saw the pennant waving, and the gleam of a white cottage through the trees, and a trim figure waiting at the gate. Then I rolled into the dressing room.
Somehow it seemed strange to me. Most of the players were stretched out in peculiar convulsions. Old Spears sat with drooping head. Then a wild flaming-eyed giant swooped upon me. With a voice of thunder he announced:
"I'm a-goin' to lick you, too!"
After that we never called him any name except Rube.
# The Rube's Pennant
## *
"Fellows, it's this way. You've got to win today's game. It's the last of the season and means the pennant for Worcester. One more hard scrap and we're done! Of all the up-hill fights any bunch ever made to land the flag, our has been the best. You're the best team I ever managed, the gamest gang of ball players that ever stepped in spikes. We've played in the hardest kind of luck all season, except that short trip we called the Rube's Honeymoon. We got a bad start, and sore arms and busted fingers, all kinds of injuries, every accident calculated to hurt a team's chances, came our way. But in spite of it all we got the lead and we've held it, and today we're still a few points ahead of Buffalo."
I paused to catch my breath, and looked round on the grim, tired faces of my players. They made a stern group. The close of the season found them almost played out. What a hard chance it was, after their extraordinary efforts, to bring the issue of the pennant down to this last game!
"If we lose today, Buffalo, with three games more to play at home, will pull the bunting," I went on. "But they're not going to win! I'm putting it up to you that way. I know Spears is all in; Raddy's arm is gone; Ash is playing on one leg; you're all crippled. But you've got one more game in you, I know. These last few weeks the Rube has been pitching out of turn and he's about all in, too. He's kept us in the lead. If he wins today it'll be Rube's Pennant. But that might apply to all of you. Now, shall we talk over the play today? Any tricks to pull off? Any inside work?"
"Con, you're pretty much upset an' nervous," replied Spears, soberly. "It ain't no wonder. This has been one corker of a season. I want to suggest that you let me run the team today. I've talked over the play with the fellers. We ain't goin' to lose this game, Con. Buffalo has been comin' with a rush lately, an' they're confident. But we've been holdin' in, restin' up as much as we dared an' still keep our lead. Mebbee it'll surprise you to know we've bet every dollar we could get hold of on this game. Why, Buffalo money is everywhere."
"All right, Spears, I'll turn the team over to you. We've got the banner crowd of the year out there right now, a great crowd to play before. I'm more fussed up over this game than any I remember. But I have a sort of blind faith in my team.... I guess that's all I want to say."
Spears led the silent players out of the dressing room and I followed; and while they began to toss balls to and fro, to limber up cold, dead arms, I sat on the bench.
The Bisons were prancing about the diamond, and their swaggering assurance was not conducive to hope for the Worcesters. I wondered how many of that vast, noisy audience, intent on the day's sport, even had a thought of what pain and toil it meant to my players. The Buffalo men were in good shape; they had been lucky; they were at the top of their stride, and that made all the difference.
At any rate, there were a few faithful little women in the grand stand—Milly and Nan and Rose Stringer and Kate Bogart—who sat with compressed lips and hoped and prayed for that game to begin and end.
The gong called off the practice, and Spears, taking the field, yelled gruff encouragement to his men. Umpire Carter brushed off the plate and tossed a white ball to Rube and called: "Play!" The bleachers set up an exultant, satisfied shout and sat down to wait.
Schultz toed the plate and watched the Rube pitch a couple. There seemed to be no diminution of the great pitcher's speed and both balls cut the plate. Schultz clipped the next one down the third-base Line. Bogart trapped it close to the bag, and got it away underhand, beating the speedy runner by a nose. It was a pretty play to start with, and the spectators were not close-mouthed in appreciation. The short, stocky Carl ambled up to bat, and I heard him call the Rube something. It was not a friendly contest, this deciding game between Buffalo and Worcester.
"Bing one close to his swelled nut!" growled Spears to the Rube.
Carl chopped a bouncing grounder through short and Ash was after it like a tiger, but it was a hit. The Buffalo contingent opened up. Then Manning faced the Rube, and he, too, vented sarcasm. It might not have been heard by the slow, imperturbable pitcher for all the notice he took. Carl edged off first, slid back twice, got a third start, and on the Rube's pitch was off for second base with the lead that always made him dangerous. Manning swung vainly, and Gregg snapped a throw to Mullaney. Ball and runner got to the bag apparently simultaneously; the umpire called Carl out, and the crowd uttered a quick roar of delight.
The next pitch to Manning was a strike. Rube was not wasting any balls, a point I noted with mingled fear and satisfaction. For he might have felt that he had no strength to spare that day and so could not try to work the batters. Again he swung, and Manning rapped a long line fly over McCall. As the little left fielder turned at the sound of the hit and sprinted out, his lameness was certainly not in evidence. He was the swiftest runner in the league and always when he got going the crowd rose in wild clamor to watch him. Mac took that fly right off the foul flag in deep left, and the bleachers dinned their pleasure.
The teams changed positions. "Fellers," said Spears, savagely, "we may be a bunged-up lot of stiffs, but, say! We can hit! If you love your old captain—sting the ball!"
Vane, the Bison pitcher, surely had his work cut out for him. For one sympathetic moment I saw his part through his eyes. My Worcester veterans, long used to being under fire, were relentlessly bent on taking that game. It showed in many ways, particularly in their silence, because they were seldom a silent team. McCall hesitated a moment over his bats. Then, as he picked up the lightest one, I saw his jaw set, and I knew he intended to bunt. He was lame, yet he meant to beat out an infield hit. He went up scowling.
Vane had an old head, and he had a varied assortment of balls. For Mac he used an under hand curve, rising at the plate and curving in to the left-hander. Mac stepped back and let it go.
"That's the place, Bo," cried the Buffalo infielders. "Keep 'em close on the Crab." Eager and fierce as McCall was, he let pitch after pitch go by till he had three balls and two strikes. Still the heady Vane sent up another pitch similar to the others. Mac stepped forward in the box, dropped his bat on the ball, and leaped down the line toward first base. Vane came rushing in for the bunt, got it and threw. But as the speeding ball neared the baseman, Mac stretched out into the air and shot for the bag. By a fraction of a second he beat the ball. It was one of his demon-slides. He knew that the chances favored his being crippled; we all knew that some day Mac would slide recklessly once too often. But that, too, is all in the game and in the spirit of a great player.
"We're on," said Spears; "now keep with him."
By that the captain meant that Mac would go down, and Ashwell would hit with the run.
When Vane pitched, little McCall was flitting toward second. The Bison shortstop started for the bag, and Ash hit square through his tracks. A rolling cheer burst from the bleachers, and swelled till McCall overran third base and was thrown back by the coacher. Stringer hurried forward with his big bat.
"Oh! My!" yelled a fan, and he voiced my sentiments exactly. Here we would score, and be one run closer to that dearly bought pennant.
How well my men worked together! As the pitcher let the ball go, Ash was digging for second and Mac was shooting plateward. They played on the chance of Stringer's hitting. Stringer swung, the bat cracked, we heard a thud somewhere, and then Manning, half knocked over, was fumbling for the ball. He had knocked down a terrific drive with his mitt, and he got the ball in time to put Stringer out. But Mac scored and Ash drew a throw to third base and beat it. He had a bad ankle, but no one noticed it in that daring run.
"Watch me paste one!" said Captain Spears, as he spat several yards. He batted out a fly so long and high and far that, slow as he was, he had nearly run to second base when Carl made the catch. Ash easily scored on the throw-in. Then Bogart sent one skipping over second, and Treadwell, scooping it on the run, completed a play that showed why he was considered the star of the Bison infield.
"Two runs, fellers!" said Spears. "That's some! Push 'em over, Rube."
The second inning somewhat quickened the pace. Even the Rube worked a little faster. Ellis lined to Cairns in right; Treadwell fouled two balls and had a called strike, and was out; McKnight hit a low fly over short, then Bud Wiler sent one between Spears and Mullaney. Spears went for it while the Rube with giant strides ran to cover first base. Between them they got Bud, but it was only because he was heavy and slow on his feet.
In our half of that inning Mullaney, Gregg and Cairns went out in one, two, three order.
With Pannell up, I saw that the Rube held in on his speed, or else he was tiring. Pannell hit the second slow ball for two bases. Vane sacrificed, and then the redoubtable Schultz came up. He appeared to be in no hurry to bat. Then I saw that the foxy Buffalo players were working to tire the Rube. They had the situation figured. But they were no wiser than old Spears.
"Make 'em hit, Rube. Push 'em straight over. Never mind the corners. We don't care for a few runs. We'll hit this game out."
Shultz flied to Mac, who made a beautiful throw to the plate too late to catch Pannell. Carl deliberately bunted to the right of the Rube and it cost the big pitcher strenuous effort to catch his man.
"We got the Rube waggin'!" yelled a Buffalo player.
Manning tripled down the left foul line—a hit the bleachers called a screamer. When Ellis came up, it looked like a tie score, and when the Rube pitched it was plain that he was tired. The Bisons yelled their assurance of this and the audience settled into quiet. Ellis batted a scorcher that looked good for a hit. But the fast Ashwell was moving with the ball, and he plunged lengthwise to get it square in his glove. The hit had been so sharp that he had time to get up and make the throw to beat the runner. The bleachers thundered at the play.
"You're up, Rube," called Spears. "Lam one out of the lot!"
The Rube was an uncertain batter. There was never any telling what he might do, for he had spells of good and bad hitting. But when he did get his bat on the ball it meant a chase for some fielder. He went up swinging his huge club, and he hit a fly that would have been an easy home run for a fast man. But the best Rube could do was to reach third base. This was certainly good enough, as the bleachers loudly proclaimed, and another tally for us seemed sure.
McCall bunted toward third, another of his teasers. The Rube would surely have scored had he started with the ball, but he did not try and missed a chance. Wiler, of course, held the ball, and Mac got to first without special effort. He went down on the first pitch. Then Ash lined to Carl. The Rube waited till the ball was caught and started for home. The crowd screamed, the Rube ran for all he was worth and Carl's throw to the plate shot in low and true. Ellis blocked the Rube and tagged him out.
It looked to the bleachers as if Ellis had been unnecessarily rough, and they hissed and stormed disapproval. As for me, I knew the Bisons were losing no chance to wear out my pitcher. Stringer fouled out with Mac on third, and it made him so angry that he threw his bat toward the bench, making some of the boys skip lively.
The next three innings, as far as scoring was concerned, were all for Buffalo. But the Worcester infield played magnificent ball, holding their opponents to one run each inning.
That made the score 4 to 2 in favor of Buffalo.
In the last half of the sixth, with Ash on first base and two men out, old Spears hit another of his lofty flies, and this one went over the fence and tied the score. How the bleachers roared! It was full two minutes before they quieted down. To make it all the more exciting, Bogart hit safely, ran like a deer to third on Mullaney's grounder, which Wiler knocked down, and scored on a passed ball. Gregg ended the inning by striking out.
"Get at the Rube!" boomed Ellis, the Bison captain. "We'll have him up in the air soon. Get in the game now, you stickers!"
Before I knew what had happened, the Bisons had again tied the score. They were indomitable. They grew stronger all the time. A stroke of good luck now would clinch the game for them. The Rube was beginning to labor in the box; Ashwell was limping; Spears looked as if he would drop any moment; McCall could scarcely walk. But if the ball came his way he could still run. Nevertheless, I never saw any finer fielding than these cripped players executed that inning.
"Ash—Mac—can you hold out?" I asked, when they limped in. I received glances of scorn for my question. Spears, however, was not sanguine.
"I'll stick pretty much if somethin' doesn't happen," he said; "but I'm all in. I'll need a runner if I get to first this time."
Spears lumbered down to first base on an infield hit and the heavy Manning gave him the hip. Old Spears went down, and I for one knew he was out in more ways than that signified by Carter's sharp: "Out!"
The old war-horse gathered himself up slowly and painfully, and with his arms folded and his jaw protruding, he limped toward the umpire.
"Did you call me out?" he asked, in a voice plainly audible to any one on the field.
"Yes," snapped Carter.
"What for? I beat the ball, an' Mannin' played dirty with me—gave me the hip."
"I called you out."
"But I wasn't out!"
"Shut up now! Get off the diamond!" ordered Carter, peremptorily.
"What? Me? Say, I'm captain of this team. Can't I question a decision?"
"Not mine. Spears, you're delaying the game."
"I tell you it was a rotten decision," yelled Spears. The bleachers agreed with him.
Carter grew red in the face. He and Spears had before then met in field squabbles, and he showed it.
"Fifty dollars!"
"More! You cheap-skate you piker! More!"
"It's a hundred!"
"Put me out of the game!" roared Spears.
"You bet! Hurry now—skedaddle!"
"Rob-b-ber!" bawled Spears.
Then he labored slowly toward the bench, all red, and yet with perspiration, his demeanor one of outraged dignity. The great crowd, as one man, stood up and yelled hoarsely at Carter, and hissed and railed at him. When Spears got to the bench he sat down beside me as if in pain, but he was smiling.
"Con, I was all in, an' knowin' I couldn't play any longer, thought I'd try to scare Carter. Say, he was white in the face. If we play into a close decision now, he'll give it to us."
Bogart and Mullaney batted out in short order, and once more the aggressive Bisons hurried in for their turn. Spears sent Cairns to first base and Jones to right. The Rube lobbed up his slow ball. In that tight pinch he showed his splendid nerve. Two Buffalo players, over-anxious, popped up flies. The Rube kept on pitching the slow curve until it was hit safely. Then heaving his shoulders with all his might he got all the motion possible into his swing and let drive. He had almost all of his old speed, but it hurt me to see him work with such desperate effort. He struck Wiler out.
He came stooping into the bench, apparently deaf to the stunning round of applause. Every player on the team had a word for the Rube. There was no quitting in that bunch, and if I ever saw victory on the stern faces of ball players it was in that moment.
"We haven't opened up yet. Mebbee this is the innin'. If it ain't, the next is," said Spears.
With the weak end of the batting list up, there seemed little hope of getting a run on Vane that inning. He had so much confidence that he put the ball over for Gregg, who hit out of the reach of the infield. Again Vane sent up his straight ball, no doubt expecting Cairns to hit into a double play. But Cairns surprised Vane and everybody else by poking a safety past first base. The fans began to howl and pound and whistle.
The Rube strode to bat. The infield closed in for a bunt, but the Rube had no orders for that style of play. Spears had said nothing to him. Vane lost his nonchalance and settled down. He cut loose with all his speed. Rube stepped out, suddenly whirled, then tried to dodge, but the ball hit him fair in the back. Rube sagged in his tracks, then straightened up, and walked slowly to first base. Score 5 to 5, bases full, no outs, McCall at bat. I sat dumb on the bench, thrilling and shivering. McCall! Ashwell! Stringer to bat!
"Play it safe! Hold the bags!" yelled the coacher.
McCall fairly spouted defiance as he faced Vane.
"Pitch! It's all off! An' you know it!"
If Vane knew that, he showed no evidence of it. His face was cold, unsmiling, rigid. He had to pitch to McCall, the fastest man in the league; to Ashwell, the best bunter; to Stringer, the champion batter. It was a supreme test for a great pitcher. There was only one kind of a ball that McCall was not sure to hit, and that was a high curve, in close. Vane threw it with all his power. Carter called it a strike. Again Vane swung and his arm fairly cracked. Mac fouled the ball. The third was wide. Slowly, with lifting breast, Vane got ready, whirled savagely and shot up the ball. McCall struck out.
As the Buffalo players crowed and the audience groaned it was worthy of note that little McCall showed no temper. Yet he had failed to grasp a great opportunity.
"Ash, I couldn't see 'em," he said, as he passed to the bench. "Speed, whew! look out for it. He's been savin' up. Hit quick, an' you'll get him."
Ashwell bent over the plate and glowered at Vane.
"Pitch! It's all off! An' you know it!" he hissed, using Mac's words.
Ashwell, too, was left-handed; he, too, was extremely hard to pitch to; and if he had a weakness that any of us ever discovered, it was a slow curve and change of pace. But I doubted if Vane would dare to use slow balls to Ash at that critical moment. I had yet to learn something of Vane. He gave Ash a slow, wide-sweeping sidewheeler, that curved round over the plate. Ash always took a strike, so this did not matter. Then Vane used his deceptive change of pace, sending up a curve that just missed Ash's bat as he swung.
"Oh! A-h-h! hit!" wailed the bleachers.
Vane doubled up like a contortionist, and shot up a lightning-swift drop that fooled Ash completely. Again the crowd groaned. Score tied, bases full, two out, Stringer at bat!
"It's up to you, String," called Ash, stepping aside.
Stringer did not call out to Vane. That was not his way. He stood tense and alert, bat on his shoulder, his powerful form braced, and he waited. The outfielders trotted over toward right field, and the infielders played deep, calling out warnings and encouragement to the pitcher. Stringer had no weakness, and Vane knew this. Nevertheless he did not manifest any uneasiness, and pitched the first ball without any extra motion. Carter called it a strike. I saw Stringer sink down slightly and grow tenser all over. I believe that moment was longer for me than for either the pitcher or the batter. Vane took his time, watched the base runners, feinted to throw to catch them, and then delivered the ball toward the plate with the limit of his power.
Stringer hit the ball. As long as I live, I will see that glancing low liner. Shultz, by a wonderful play in deep center, blocked the ball and thereby saved it from being a home run. But when Stringer stopped on second base, all the runners had scored.
A shrill, shrieking, high-pitched yell! The bleachers threatened to destroy the stands and also their throats in one long revel of baseball madness.
Jones, batting in place of Spears, had gone up and fouled out before the uproar had subsided.
"Fellers, I reckon I feel easier," said the Rube. It was the only time I had ever heard him speak to the players at such a stage.
"Only six batters, Rube," called out Spears. "Boys, it's a grand game, an' it's our'n!"
The Rube had enough that inning to dispose of the lower half of the Buffalo list without any alarming bids for a run. And in our half, Bogart and Mullaney hit vicious ground balls that gave Treadwell and Wiler opportunities for superb plays. Carl, likewise, made a beautiful running catch of Gregg's line fly. The Bisons were still in the game, still capable of pulling it out at the last moment.
When Shultz stalked up to the plate I shut my eyes a moment, and so still was it that the field and stands might have been empty. Yet, though I tried, I could not keep my eyes closed. I opened them to watch the Rube. I knew Spears felt the same as I, for he was blowing like a porpoise and muttering to himself: "Mebee the Rube won't last an' I've no one to put in!"
The Rube pitched with heavy, violent effort. He had still enough speed to be dangerous. But after the manner of ball players Shultz and the coachers mocked him.
"Take all you can," called Ellis to Shultz.
Every pitch lessened the Rube's strength and these wise opponents knew it. Likewise the Rube himself knew, and never had he shown better head work than in this inning. If he were to win, he must be quick. So he wasted not a ball. The first pitch and the second, delivered breast high and fairly over the plate, beautiful balls to hit, Shultz watched speed by. He swung hard on the third and the crippled Ashwell dove for it in a cloud of dust, got a hand in front of it, but uselessly, for the hit was safe. The crowd cheered that splendid effort.
Carl marched to bat, and he swung his club over the plate as if he knew what to expect. "Come on, Rube!" he shouted. Wearily, doggedly, the Rube whirled, and whipped his arm. The ball had all his old glancing speed and it was a strike. The Rube was making a tremendous effort. Again he got his body in convulsive motion—two strikes! Shultz had made no move to run, nor had Carl made any move to hit. These veterans were waiting. The Rube had pitched five strikes—could he last?
"Now, Carl!" yelled Ellis, with startling suddenness, as the Rube pitched again.
Crack! Carl placed that hit as safely through short as if he had thrown it. McCall's little legs twinkled as he dashed over the grass. He had to head off that hit and he ran like a streak. Down and forward he pitched, as if in one of his fierce slides, and he got his body in front of the ball, blocking it, and then he rolled over and over. But he jumped up and lined the ball to Bogart, almost catching Shultz at third-base. Then, as Mac tried to walk, his lame leg buckled under him, and down he went, and out.
"Call time," I called to Carter. "McCall is done.... Myers, you go to left an' for Lord's sake play ball!"
Stringer and Bogart hurried to Mac and, lifting him up and supporting him between them with his arms around their shoulders, they led him off amid cheers from the stands. Mac was white with pain.
"Naw, I won't go off the field. Leave me on the bench," he said. "Fight 'em now. It's our game. Never mind a couple of runs."
The boys ran back to their positions and Carter called play. Perhaps a little delay had been helpful to the Rube. Slowly he stepped into the box and watched Shultz at third and Carl at second. There was not much probability of his throwing to catch them off the base, but enough of a possibility to make them careful, so he held them close.
The Rube pitched a strike to Manning, then another. That made eight strikes square over the plate that inning. What magnificent control! It was equaled by the implacable patience of those veteran Bisons. Manning hit the next ball as hard as Carl had hit his. But Mullaney plunged down, came up with the ball, feinted to fool Carl, then let drive to Gregg to catch the fleeting Shultz. The throw went wide, but Gregg got it, and, leaping lengthwise, tagged Shultz out a yard from the plate.
One out. Two runners on bases. The bleachers rose and split their throats. Would the inning never end?
Spears kept telling himself: "They'll score, but we'll win. It's our game!"
I had a sickening fear that the strange confidence that obsessed the Worcester players had been blind, unreasoning vanity.
"Carl will steal," muttered Spears. "He can't be stopped."
Spears had called the play. The Rube tried to hold the little base-stealer close to second, but, after one attempt, wisely turned to his hard task of making the Bisons hit and hit quickly. Ellis let the ball pass; Gregg made a perfect throw to third; Bogart caught the ball and moved like a flash, but Carl slid under his hands to the bag. Manning ran down to second. The Rube pitched again, and this was his tenth ball over the plate. Even the Buffalo players evinced eloquent appreciation of the Rube's defence at this last stand.
Then Ellis sent a clean hit to right, scoring both Carl and Manning. I breathed easier, for it seemed with those two runners in, the Rube had a better chance. Treadwell also took those two runners in, the Rube had a way those Bisons waited. They had their reward, for the Rube's speed left him. When he pitched again the ball had control, but no shoot. Treadwell hit it with all his strength. Like a huge cat Ashwell pounced upon it, ran over second base, forcing Ellis, and his speedy snap to first almost caught Treadwell.
Score 8 to 7. Two out. Runner on first. One run to tie.
In my hazy, dimmed vision I saw the Rube's pennant waving from the flag-pole.
"It's our game!" howled Spears in my ear, for the noise from the stands was deafening. "It's our pennant!"
The formidable batting strength of the Bisons had been met, not without disaster, but without defeat. McKnight came up for Buffalo and the Rube took his weary swing. The batter made a terrific lunge and hit the ball with a solid crack It lined for center.
Suddenly electrified into action, I leaped up. That hit! It froze me with horror. It was a home-run. I saw Stringer fly toward left center. He ran like something wild. I saw the heavy Treadwell lumbering round the bases. I saw Ashwell run out into center field.
"Ah-h!" The whole audience relieved its terror in that expulsion of suspended breath. Stringer had leaped high to knock down the ball, saving a sure home-run and the game. He recovered himself, dashed back for the ball and shot it to Ash.
When Ash turned toward the plate, Treadwell was rounding third base. A tie score appeared inevitable. I saw Ash's arm whip and the ball shoot forward, leveled, glancing, beautiful in its flight. The crowd saw it, and the silence broke to a yell that rose and rose as the ball sped in. That yell swelled to a splitting shriek, and Treadwell slid in the dust, and the ball shot into Gregg's hands all at the same instant.
Carter waved both arms upwards. It was the umpire's action when his decision went against the base-runner. The audience rolled up one great stentorian cry.
"Out!"
I collapsed and sank back upon the bench. My confused senses received a dull roar of pounding feet and dinning voices as the herald of victory. I felt myself thinking how pleased Milly would be. I had a distinct picture in my mind of a white cottage on a hill, no longer a dream, but a reality, made possible for me by the Rube's winning of the pennant.
# The Rube's Honeymoon
## *
"He's got a new manager. Watch him pitch now!" That was what Nan Brown said to me about Rube Hurtle, my great pitcher, and I took it as her way of announcing her engagement.
My baseball career held some proud moments, but this one, wherein I realized the success of my matchmaking plans, was certainly the proudest one. So, entirely outside of the honest pleasure I got out of the Rube's happiness, there was reason for me to congratulate myself. He was a transformed man, so absolutely renewed, so wild with joy, that on the strength of it, I decided the pennant for Worcester was a foregone conclusion, and, sure of the money promised me by the directors, Milly and I began to make plans for the cottage upon the hill.
The Rube insisted on pitching Monday's game against the Torontos, and although poor fielding gave them a couple of runs, they never had a chance. They could not see the ball. The Rube wrapped it around their necks and between their wrists and straight over the plate with such incredible speed that they might just as well have tried to bat rifle bullets.
That night I was happy. Spears, my veteran captain, was one huge smile; Radbourne quietly assured me that all was over now but the shouting; all the boys were happy.
And the Rube was the happiest of all. At the hotel he burst out with his exceeding good fortune. He and Nan were to be married upon the Fourth of July!
After the noisy congratulations were over and the Rube had gone, Spears looked at me and I looked at him.
"Con," said he soberly, "we just can't let him get married on the Fourth."
"Why not? Sure we can. We'll help him get married. I tell you it'll save the pennant for us. Look how he pitched today! Nan Brown is our salvation!"
"See here, Con, you've got softenin' of the brain, too. Where's your baseball sense? We've got a pennant to win. By July Fourth we'll be close to the lead again, an' there's that three weeks' trip on the road, the longest an' hardest of the season. We've just got to break even on that trip. You know what that means. If the Rube marries Nan—what are we goin' to do? We can't leave him behind. If he takes Nan with us—why it'll be a honeymoon! An' half the gang is stuck on Nan Brown! An' Nan Brown would flirt in her bridal veil! ... Why Con, we're up against a worse proposition than ever."
"Good Heavens! Cap. You're right," I groaned. "I never thought of that. We've got to postpone the wedding.... How on earth can we? I've heard her tell Milly that. She'll never consent to it. Say, this'll drive me to drink."
"All I got to say is this, Con. If the Rube takes his wife on that trip it's goin' to be an all-fired hummer. Don't you forget that."
"I'm not likely to. But, Spears, the point is this—will the Rube win his games?"
"Figurin' from his work today, I'd gamble he'll never lose another game. It ain't that. I'm thinkin' of what the gang will do to him an' Nan on the cars an' at the hotels. Oh! Lord, Con, it ain't possible to stand for that honeymoon trip! Just think!"
"If the worst comes to the worst, Cap, I don't care for anything but the games. If we get in the lead and stay there I'll stand for anything.... Couldn't the gang be coaxed or bought off to let the Rube and Nan alone?"
"Not on your life! There ain't enough love or money on earth to stop them. It'll be awful. Mind, I'm not responsible. Don't you go holdin' me responsible. In all my years of baseball I never went on a trip with a bride in the game. That's new on me, an' I never heard of it. I'd be bad enough if he wasn't a rube an' if she wasn't a crazy girl-fan an' a flirt to boot, an' with half the boys in love with her, but as it is—"
Spears gave up and, gravely shaking his head, he left me. I spent a little while in sober reflection, and finally came to the conclusion that, in my desperate ambition to win the pennant, I would have taken half a dozen rube pitchers and their baseball-made brides on the trip, if by so doing I could increase the percentage of games won. Nevertheless, I wanted to postpone the Rube's wedding if it was possible, and I went out to see Milly and asked her to help us. But for once in her life Milly turned traitor.
"Connie, you don't want to postpone it. Why, how perfectly lovely! ... Mrs. Stringer will go on that trip and Mrs. Bogart.... Connie, I'm going too!"
She actually jumped up and down in glee. That was the woman in her. It takes a wedding to get a woman. I remonstrated and pleaded and commanded, all to no purpose. Milly intended to go on that trip to see the games, and the fun, and the honeymoon.
She coaxed so hard that I yielded. Thereupon she called up Mrs. Stringer on the telephone, and of course found that young woman just as eager as she was. For my part, I threw anxiety and care to the four winds, and decided to be as happy as any of them. The pennant was mine! Something kept ringing that in my ears. With the Rube working his iron arm for the edification of his proud Nancy Brown, there was extreme likelihood of divers shut-outs and humiliating defeats for some Eastern League teams.
How well I calculated became a matter of baseball history during that last week of June. We won six straight games, three of which fell to the Rube's credit. His opponents scored four runs in the three games, against the nineteen we made. Upon July 1, Radbourne beat Providence and Cairns won the second game. We now had a string of eight victories. Sunday we rested, and Monday was the Fourth, with morning and afternoon games with Buffalo.
Upon the morning of the Fourth, I looked for the Rube at the hotel, but could not find him. He did not show up at the grounds when the other boys did, and I began to worry. It was the Rube's turn to pitch and we were neck and neck with Buffalo for first place. If we won both games we would go ahead of our rivals. So I was all on edge, and kept going to the dressing-room to see if the Rube had arrived. He came, finally, when all the boys were dressed, and about to go out for practice. He had on a new suit, a tailor-made suit at that, and he looked fine. There was about him a kind of strange radiance. He stated simply that he had arrived late because he had just been married. Before congratulations were out of our mouths, he turned to me.
"Con, I want to pitch both games today," he said.
"What! Say, Whit, Buffalo is on the card today and we are only three points behind them. If we win both we'll be leading the league once more. I don't know about pitching you both games."
"I reckon we'll be in the lead tonight then," he replied, "for I'll win them both."
I was about to reply when Dave, the ground-keeper, called me to the door, saying there was a man to see me. I went out, and there stood Morrisey, manager of the Chicago American League team. We knew each other well and exchanged greetings.
"Con, I dropped off to see you about this new pitcher of yours, the one they call the Rube. I want to see him work. I've heard he's pretty fast. How about it?"
"Wait—till you see him pitch," I replied. I could scarcely get that much out, for Morrisey's presence meant a great deal and I did not want to betray my elation.
"Any strings on him?" queried the big league manager, sharply.
"Well, Morrisey, not exactly. I can give you the first call. You'll have to bid high, though. Just wait till you see him work."
"I'm glad to hear that. My scout was over here watching him pitch and says he's a wonder."
What luck it was that Morrisey should have come upon this day! I could hardly contain myself. Almost I began to spend the money I would get for selling the Rube to the big league manager. We took seats in the grand stand, as Morrisey did not want to be seen by any players, and I stayed there with him until the gong sounded. There was a big attendance. I looked all over the stand for Nan, but she was lost in the gay crowd. But when I went down to the bench I saw her up in my private box with Milly. It took no second glance to see that Nan Brown was a bride and glorying in the fact.
Then, in the absorption of the game, I became oblivious to Milly and Nan; the noisy crowd; the giant fire-crackers and the smoke; to the presence of Morrisey; to all except the Rube and my team and their opponents. Fortunately for my hopes, the game opened with characteristic Worcester dash. Little McCall doubled, Ashwell drew his base on four wide pitches, and Stringer drove the ball over the right-field fence—three runs!
Three runs were enough to win that game. Of all the exhibitions of pitching with which the Rube had favored us, this one was the finest. It was perhaps not so much his marvelous speed and unhittable curves that made the game one memorable in the annals of pitching; it was his perfect control in the placing of balls, in the cutting of corners; in his absolute implacable mastery of the situation. Buffalo was unable to find him at all. The game was swift short, decisive, with the score 5 to 0 in our favor. But the score did not tell all of the Rube's work that morning. He shut out Buffalo without a hit, or a scratch, the first no-hit, no-run game of the year. He gave no base on balls; not a Buffalo player got to first base; only one fly went to the outfield.
For once I forgot Milly after a game, and I hurried to find Morrisey, and carried him off to have dinner with me.
"Your rube is a wonder, and that's a fact," he said to me several times. "Where on earth did you get him? Connelly, he's my meat. Do you understand? Can you let me have him right now?"
"No, Morrisey, I've got the pennant to win first. Then I'll sell him."
"How much? Do you hear? How much?" Morrisey hammered the table with his fist and his eyes gleamed.
Carried away as I was by his vehemence, I was yet able to calculate shrewdly, and I decided to name a very high price, from which I could come down and still make a splendid deal.
"How much?" demanded Morrisey.
"Five thousand dollars," I replied, and gulped when I got the words out.
Morrisey never batted an eye.
"Waiter, quick, pen and ink and paper!"
Presently my hand, none too firm, was signing my name to a contract whereby I was to sell my pitcher for five thousand dollars at the close of the current season. I never saw a man look so pleased as Morrisey when he folded that contract and put it in his pocket. He bade me good-bye and hurried off to catch a train, and he never knew the Rube had pitched the great game on his wedding day.
That afternoon before a crowd that had to be roped off the diamond, I put the Rube against the Bisons. How well he showed the baseball knowledge he had assimilated! He changed his style in that second game. He used a slow ball and wide curves and took things easy. He made Buffalo hit the ball and when runners got on bases once more let out his speed and held them down. He relied upon the players behind him and they were equal to the occasion.
It was a totally different game from that of the morning, and perhaps one more suited to the pleasure of the audience. There was plenty of hard hitting, sharp fielding and good base running, and the game was close and exciting up to the eighth, when Mullaney's triple gave us two runs, and a lead that was not headed. To the deafening roar of the bleachers the Rube walked off the field, having pitched Worcester into first place in the pennant race.
That night the boys planned their first job on the Rube. We had ordered a special Pullman for travel to Toronto, and when I got to the depot in the morning, the Pullman was a white fluttering mass of satin ribbons. Also, there was a brass band, and thousands of baseball fans, and barrels of old foot-gear. The Rube and Nan arrived in a cab and were immediately mobbed. The crowd roared, the band played, the engine whistled, the bell clanged; and the air was full of confetti and slippers, and showers of rice like hail pattered everywhere. A somewhat dishevelled bride and groom boarded the Pullman and breathlessly hid in a state room. The train started, and the crowd gave one last rousing cheer. Old Spears yelled from the back platform:
"Fellers, an' fans, you needn't worry none about leavin' the Rube an' his bride to the tender mercies of the gang. A hundred years from now people will talk about this honeymoon baseball trip. Wait till we come back—an' say, jest to put you wise, no matter what else happens, we're comin' back in first place!"
It was surely a merry party in that Pullman. The bridal couple emerged from their hiding place and held a sort of reception in which the Rube appeared shy and frightened, and Nan resembled a joyous, fluttering bird in gray. I did not see if she kissed every man on the team, but she kissed me as if she had been wanting to do it for ages. Milly kissed the Rube, and so did the other women, to his infinite embarrassment. Nan's effect upon that crowd was most singular. She was sweetness and caprice and joy personified.
We settled down presently to something approaching order, and I, for one, with very keen ears and alert eyes, because I did not want to miss anything.
"I see the lambs a-gambolin'," observed McCall, in a voice louder than was necessary to convey his meaning to Mullaney, his partner in the seat.
"Yes, it do seem as if there was joy aboundin' hereabouts," replied Mul with fervor.
"It's more spring-time than summer," said Ashwell, "an' everything in nature is runnin' in pairs. There are the sheep an' the cattle an' the birds. I see two kingfishers fishin' over here. An' there's a couple of honey-bees makin' honey. Oh, honey, an' by George, if there ain't two butterflies foldin' their wings round each other. See the dandelions kissin' in the field!"
Then the staid Captain Spears spoke up with an appearance of sincerity and a tone that was nothing short of remarkable.
"Reggie, see the sunshine asleep upon yon bank. Ain't it lovely? An' that white cloud sailin' thither amid the blue—how spontaneous! Joy is a-broad o'er all this boo-tiful land today—Oh, yes! An' love's wings hover o 'er the little lambs an' the bullfrogs in the pond an' the dicky birds in the trees. What sweetness to lie in the grass, the lap of bounteous earth, eatin' apples in the Garden of Eden, an' chasin' away the snakes an' dreamin' of Thee, Sweet-h-e-a-r-t—"
Spears was singing when he got so far and there was no telling what he might have done if Mullaney, unable to stand the agony, had not jabbed a pin in him. But that only made way for the efforts of the other boys, each of whom tried to outdo the other in poking fun at the Rube and Nan. The big pitcher was too gloriously happy to note much of what went on around him, but when it dawned upon him he grew red and white by turns.
Nan, however, was more than equal to the occasion. Presently she smiled at Spears, such a smile! The captain looked as if he had just partaken of an intoxicating wine. With a heightened color in her cheeks and a dangerous flash in her roguish eyes, Nan favored McCall with a look, which was as much as to say that she remembered him with a dear sadness. She made eyes at every fellow in the car, and then bringing back her gaze to the Rube, as if glorying in comparison, she nestled her curly black head on his shoulder. He gently tried to move her; but it was not possible. Nan knew how to meet the ridicule of half a dozen old lovers. One by one they buried themselves in newspapers, and finally McCall, for once utterly beaten, showed a white feather, and sank back out of sight behind his seat.
The boys did not recover from that shock until late in the afternoon. As it was a physical impossibility for Nan to rest her head all day upon her husband's broad shoulder, the boys toward dinner time came out of their jealous trance. I heard them plotting something. When dinner was called, about half of my party, including the bride and groom, went at once into the dining-car. Time there flew by swiftly. And later, when we were once more in our Pullman, and I had gotten interested in a game of cards with Milly and Stringer and his wife, the Rube came marching up to me with a very red face.
"Con, I reckon some of the boys have stolen my—our grips," said he.
"What?" I asked, blankly.
He explained that during his absence in the dining-car someone had entered his stateroom and stolen his grip and Nan's. I hastened at once to aid the Rube in his search. The boys swore by everything under and beyond the sun they had not seen the grips; they appeared very much grieved at the loss and pretended to help in searching the Pullman. At last, with the assistance of a porter, we discovered the missing grips in an upper berth. The Rube carried them off to his stateroom and we knew soon from his uncomplimentary remarks that the contents of the suitcases had been mixed and manhandled. But he did not hunt for the jokers.
We arrived at Toronto before daylight next morning, and remained in the Pullman until seven o'clock. When we got out, it was discovered that the Rube and Nan had stolen a march upon us. We traced them to the hotel, and found them at breakfast. After breakfast we formed a merry sight-seeing party and rode all over the city.
That afternoon, when Raddy let Toronto down with three hits and the boys played a magnificent game behind him, and we won 7 to 2, I knew at last and for certain that the Worcester team had come into its own again. Then next day Cairns won a close, exciting game, and following that, on the third day, the matchless Rube toyed with the Torontos. Eleven straight games won! I was in the clouds, and never had I seen so beautiful a light as shone in Milly's eyes.
From that day The Honeymoon Trip of the Worcester Baseball Club, as the newspapers heralded it—was a triumphant march. We won two out of three games at Montreal, broke even with the hard-fighting Bisons, took three straight from Rochester, and won one and tied one out of three with Hartford. It would have been wonderful ball playing for a team to play on home grounds and we were doing the full circuit of the league.
Spears had called the turn when he said the trip would be a hummer. Nan Hurtle had brought us wonderful luck.
But the tricks they played on Whit and his girl-fan bride!
Ashwell, who was a capital actor, disguised himself as a conductor and pretended to try to eject Whit and Nan from the train, urging that love-making was not permitted. Some of the team hired a clever young woman to hunt the Rube up at the hotel, and claim old acquaintance with him. Poor Whit almost collapsed when the young woman threw her arms about his neck just as Nan entered the parlor. Upon the instant Nan became wild as a little tigress, and it took much explanation and eloquence to reinstate Whit in her affections.
Another time Spears, the wily old fox, succeeded in detaining Nan on the way to the station, and the two missed the train. At first the Rube laughed with the others, but when Stringer remarked that he had noticed a growing attachment between Nan and Spears, my great pitcher experienced the first pangs of the green-eyed monster. We had to hold him to keep him from jumping from the train, and it took Milly and Mrs. Stringer to soothe him. I had to wire back to Rochester for a special train for Spears and Nan, and even then we had to play half a game without the services of our captain.
So far upon our trip I had been fortunate in securing comfortable rooms and the best of transportation for my party. At Hartford, however, I encountered difficulties. I could not get a special Pullman, and the sleeper we entered already had a number of occupants. After the ladies of my party had been assigned to berths, it was necessary for some of the boys to sleep double in upper berths.
It was late when we got aboard, the berths were already made up, and soon we had all retired. In the morning very early I was awakened by a disturbance. It sounded like a squeal. I heard an astonished exclamation, another squeal, the pattering of little feet, then hoarse uproar of laughter from the ball players in the upper berths. Following that came low, excited conversation between the porter and somebody, then an angry snort from the Rube and the thud of his heavy feet in the aisle. What took place after that was guess-work for me. But I gathered from the roars and bawls that the Rube was after some of the boys. I poked my head between the curtains and saw him digging into the berths.
"Where's McCall?" he yelled.
Mac was nowhere in that sleeper, judging from the vehement denials. But the Rube kept on digging and prodding in the upper berths.
"I'm a-goin' to lick you, Mac, so I reckon you'd better show up," shouted the Rube.
The big fellow was mad as a hornet. When he got to me he grasped me with his great fence-rail splitting hands and I cried out with pain.
"Say! Whit, let up! Mac's not here.... What's wrong?"
"I'll show you when I find him." And the Rube stalked on down the aisle, a tragically comic figure in his pajamas. In his search for Mac he pried into several upper berths that contained occupants who were not ball players, and these protested in affright. Then the Rube began to investigate the lower berths. A row of heads protruded in a bobbing line from between the curtains of the upper berths.
"Here, you Indian! Don't you look in there! That's my wife's berth!" yelled Stringer.
Bogart, too, evinced great excitement.
"Hurtle, keep out of lower eight or I'll kill you," he shouted.
What the Rube might have done there was no telling, but as he grasped a curtain, he was interrupted by a shriek from some woman assuredly not of our party.
"Get out! you horrid wretch! Help! Porter! Help! Conductor!"
Instantly there was a deafening tumult in the car. When it had subsided somewhat, and I considered I would be safe, I descended from my berth and made my way to the dressing room. Sprawled over the leather seat was the Rube pommelling McCall with hearty good will. I would have interfered, had it not been for Mac's demeanor. He was half frightened, half angry, and utterly unable to defend himself or even resist, because he was laughing, too.
"Dog-gone it! Whit—I didn't—do it! I swear it was Spears! Stop thumpin' me now—or I'll get sore.... You hear me! It wasn't me, I tell you. Cheese it!"
For all his protesting Mac received a good thumping, and I doubted not in the least that he deserved it. The wonder of the affair, however, was the fact that no one appeared to know what had made the Rube so furious. The porter would not tell, and Mac was strangely reticent, though his smile was one to make a fellow exceedingly sure something out of the ordinary had befallen. It was not until I was having breakfast in Providence that I learned the true cause of Rube's conduct, and Milly confided it to me, insisting on strict confidence.
"I promised not to tell," she said. "Now you promise you'll never tell."
"Well, Connie," went on Milly, when I had promised, "it was the funniest thing yet, but it was horrid of McCall. You see, the Rube had upper seven and Nan had lower seven. Early this morning, about daylight, Nan awoke very thirsty and got up to get a drink. During her absence, probably, but any way some time last night, McCall changed the number on her curtain, and when Nan came back to number seven of course she almost got in the wrong berth."
"No wonder the Rube punched him!" I declared. "I wish we were safe home. Something'll happen yet on this trip."
I was faithful to my promise to Milly, but the secret leaked out somewhere; perhaps Mac told it, and before the game that day all the players knew it. The Rube, having recovered his good humor, minded it not in the least. He could not have felt ill-will for any length of time. Everything seemed to get back into smooth running order, and the Honeymoon Trip bade fair to wind up beautifully.
But, somehow or other, and about something unknown to the rest of us, the Rube and Nan quarreled. It was their first quarrel. Milly and I tried to patch it up but failed.
We lost the first game to Providence and won the second. The next day, a Saturday, was the last game of the trip, and it was Rube's turn to pitch. Several times during the first two days the Rube and Nan about half made up their quarrel, only in the end to fall deeper into it. Then the last straw came in a foolish move on the part of wilful Nan. She happened to meet Henderson, her former admirer, and in a flash she took up her flirtation with him where she had left off.
"Don't go to the game with him, Nan," I pleaded. "It's a silly thing for you to do. Of course you don't mean anything, except to torment Whit. But cut it out. The gang will make him miserable and we'll lose the game. There's no telling what might happen."
"I'm supremely indifferent to what happens," she replied, with a rebellious toss of her black head. "I hope Whit gets beaten."
She went to the game with Henderson and sat in the grand stand, and the boys spied them out and told the Rube. He did not believe it at first, but finally saw them, looked deeply hurt and offended, and then grew angry. But the gong, sounding at that moment, drew his attention to his business of the day, to pitch.
His work that day reminded me of the first game he ever pitched for me, upon which occasion Captain Spears got the best out of him by making him angry. For several innings Providence was helpless before his delivery. Then something happened that showed me a crisis was near. A wag of a fan yelled from the bleachers.
"Honeymoon Rube!"
This cry was taken up by the delighted fans and it rolled around the field. But the Rube pitched on, harder than ever. Then the knowing bleacherite who had started the cry changed it somewhat.
"Nanny's Rube!" he yelled.
This, too, went the rounds, and still the Rube, though red in the face, preserved his temper and his pitching control. All would have been well if Bud Wiler, comedian of the Providence team, had not hit upon a way to rattle Rube.
"Nanny's Goat!" he shouted from the coaching lines. Every Providence player took it up.
The Rube was not proof against that. He yelled so fiercely at them, and glared so furiously, and towered so formidably, that they ceased for the moment. Then he let drive with his fast straight ball and hit the first Providence batter in the ribs. His comrades had to help him to the bench. The Rube hit the next batter on the leg, and judging from the crack of the ball, I fancied that player would walk lame for several days. The Rube tried to hit the next batter and sent him to first on balls. Thereafter it became a dodging contest with honors about equal between pitcher and batters. The Providence players stormed and the bleachers roared. But I would not take the Rube out and the game went on with the Rube forcing in runs.
With the score a tie, and three men on bases one of the players on the bench again yelled "Nanny's Goat!"
Straight as a string the Rube shot the ball at this fellow and bounded after it. The crowd rose in an uproar. The base runners began to score. I left my bench and ran across the space, but not in time to catch the Rube. I saw him hit two or three of the Providence men. Then the policemen got to him, and a real fight brought the big audience into the stamping melee. Before the Rube was collared I saw at least four blue-coats on the grass.
The game broke up, and the crowd spilled itself in streams over the field. Excitement ran high. I tried to force my way into the mass to get at the Rube and the officers, but this was impossible. I feared the Rube would be taken from the officers and treated with violence, so I waited with the surging crowd, endeavoring to get nearer. Soon we were in the street, and it seemed as if all the stands had emptied their yelling occupants.
A trolley car came along down the street, splitting the mass of people and driving them back. A dozen policemen summarily bundled the Rube upon the rear end of the car. Some of these officers boarded the car, and some remained in the street to beat off the vengeful fans.
I saw some one thrust forward a frantic young woman. The officers stopped her, then suddenly helped her on the car, just as I started. I recognized Nan. She gripped the Rube with both hands and turned a white, fearful face upon the angry crowd.
The Rube stood in the grasp of his wife and the policemen, and he looked like a ruffled lion. He shook his big fist and bawled in far-reaching voice:
"I can lick you all!"
To my infinite relief, the trolley gathered momentum and safely passed out of danger. The last thing I made out was Nan pressing close to the Rube's side. That moment saw their reconciliation and my joy that it was the end of the Rube's Honeymoon.
# The Rube's Waterloo
## *
It was about the sixth inning that I suspected the Rube of weakening. For that matter he had not pitched anything resembling his usual brand of baseball. But the Rube had developed into such a wonder in the box that it took time for his let-down to dawn upon me. Also it took a tip from Raddy, who sat with me on the bench.
"Con, the Rube isn't himself today," said Radbourne. "His mind's not on the game. He seems hurried and flustered, too. If he doesn't explode presently, I'm a dub at callin' the turn."
Raddy was the best judge of a pitcher's condition, physical or mental, in the Eastern League. It was a Saturday and we were on the road and finishing up a series with the Rochesters. Each team had won and lost a game, and, as I was climbing close to the leaders in the pennant race, I wanted the third and deciding game of that Rochester series. The usual big Saturday crowd was in attendance, noisy, demonstrative and exacting.
In this sixth inning the first man up for Rochester had flied to McCall. Then had come the two plays significant of Rube's weakening. He had hit one batter and walked another. This was sufficient, considering the score was three to one in our favor, to bring the audience to its feet with a howling, stamping demand for runs.
"Spears is wise all right," said Raddy.
I watched the foxy old captain walk over to the Rube and talk to him while he rested, a reassuring hand on the pitcher's shoulder. The crowd yelled its disapproval and Umpire Bates called out sharply:
"Spears, get back to the bag!"
"Now, Mister Umpire, ain't I hurrin' all I can?" queried Spears as he leisurely ambled back to first.
The Rube tossed a long, damp welt of hair back from his big brow and nervously toed the rubber. I noted that he seemed to forget the runners on bases and delivered the ball without glancing at either bag. Of course this resulted in a double steal. The ball went wild—almost a wild pitch.
"Steady up, old man," called Gregg between the yells of the bleachers. He held his mitt square over the plate for the Rube to pitch to. Again the long twirler took his swing, and again the ball went wild. Clancy had the Rube in the hole now and the situation began to grow serious. The Rube did not take half his usual deliberation, and of the next two pitches one of them was a ball and the other a strike by grace of the umpire's generosity. Clancy rapped the next one, an absurdly slow pitch for the Rube to use, and both runners scored to the shrill tune of the happy bleachers.
I saw Spears shake his head and look toward the bench. It was plain what that meant.
"Raddy, I ought to take the Rube out," I said, "but whom can I put in? You worked yesterday—Cairns' arm is sore. It's got to be nursed. And Henderson, that ladies' man I just signed, is not in uniform."
"I'll go in," replied Raddy, instantly.
"Not on your life." I had as hard a time keeping Radbourne from overworking as I had in getting enough work out of some other players. "I guess I'll let the Rube take his medicine. I hate to lose this game, but if we have to, we can stand it. I'm curious, anyway, to see what's the matter with the Rube. Maybe he'll settle down presently."
I made no sign that I had noticed Spears' appeal to the bench. And my aggressive players, no doubt seeing the situation as I saw it, sang out their various calls of cheer to the Rube and of defiance to their antagonists. Clancy stole off first base so far that the Rube, catching somebody's warning too late, made a balk and the umpire sent the runner on to second. The Rube now plainly showed painful evidences of being rattled.
He could not locate the plate without slowing up and when he did that a Rochester player walloped the ball. Pretty soon he pitched as if he did not care, and but for the fast fielding of the team behind him the Rochesters would have scored more than the eight runs it got. When the Rube came in to the bench I asked him if he was sick and at first he said he was and then that he was not. So I let him pitch the remaining innings, as the game was lost anyhow, and we walked off the field a badly beaten team.
That night we had to hurry from the hotel to catch a train for Worcester and we had dinner in the dining-car. Several of my players' wives had come over from Worcester to meet us, and were in the dining-car when I entered. I observed a pretty girl sitting at one of the tables with my new pitcher, Henderson.
"Say, Mac," I said to McCall, who was with me, "is Henderson married?"
"Naw, but he looks like he wanted to be. He was in the grand stand today with that girl."
"Who is she? Oh! a little peach!"
A second glance at Henderson's companion brought this compliment from me involuntarily.
"Con, you'll get it as bad as the rest of this mushy bunch of ball players. We're all stuck on that kid. But since Henderson came she's been a frost to all of us. An' it's put the Rube in the dumps."
"Who's the girl?"
"That's Nan Brown. She lives in Worcester an' is the craziest girl fan I ever seen. Flirt! Well, she's got them all beat. Somebody introduced the Rube to her. He has been mooney ever since."
That was enough to whet my curiosity, and I favored Miss Brown with more than one glance during dinner. When we returned to the parlor car I took advantage of the opportunity and remarked to Henderson that he might introduce his manager. He complied, but not with amiable grace.
So I chatted with Nan Brown, and studied her. She was a pretty, laughing, coquettish little minx and quite baseball mad. I had met many girl fans, but none so enthusiastic as Nan. But she was wholesome and sincere, and I liked her.
Before turning in I sat down beside the Rube. He was very quiet and his face did not encourage company. But that did not stop me.
"Hello, Whit; have a smoke before you go to bed?" I asked cheerfully.
He scarcely heard me and made no move to take the proffered cigar. All at once it struck me that the rustic simplicity which had characterized him had vanished.
"Whit, old fellow, what was wrong today?" I asked, quietly, with my hand on his arm.
"Mr. Connelly, I want my release, I want to go back to Rickettsville," he replied hurriedly.
For the space of a few seconds I did some tall thinking. The situation suddenly became grave. I saw the pennant for the Worcesters fading, dimming.
"You want to go home?" I began slowly. "Why, Whit, I can't keep you. I wouldn't try if you didn't want to stay. But I'll tell you confidentially, if you leave me at this stage I'm ruined."
"How's that?" he inquired, keenly looking at me.
"Well, I can't win the pennant without you. If I do win it there's a big bonus for me. I can buy the house I want and get married this fall if I capture the flag. You've met Milly. You can imagine what your pitching means to me this year. That's all."
He averted his face and looked out of the window. His big jaw quivered.
"If it's that—why, I'll stay, I reckon," he said huskily.
That moment bound Whit Hurtle and Frank Connelly into a far closer relation than the one between player and manager. I sat silent for a while, listening to the drowsy talk of the other players and the rush and roar of the train as it sped on into the night.
"Thank you, old chap," I replied. "It wouldn't have been like you to throw me down at this stage. Whit, you're in trouble?"
"Yes."
"Can I help you—in any way?"'
"I reckon not."
"Don't be too sure of that. I'm a pretty wise guy, if I do say it myself. I might be able to do as much for you as you're going to do for me."
The sight of his face convinced me that I had taken a wrong tack. It also showed me how deep Whit's trouble really was. I bade him good night and went to my berth, where sleep did not soon visit me. A saucy, sparkling-eyed woman barred Whit Hurtle's baseball career at its threshold.
Women are just as fatal to ball players as to men in any other walk of life. I had seen a strong athlete grow palsied just at a scornful slight. It's a great world, and the women run it. So I lay awake racking my brains to outwit a pretty disorganizer; and I plotted for her sake. Married, she would be out of mischief. For Whit's sake, for Milly's sake, for mine, all of which collectively meant for the sake of the pennant, this would be the solution of the problem.
I decided to take Milly into my confidence, and finally on the strength of that I got to sleep. In the morning I went to my hotel, had breakfast, attended to my mail, and then boarded a car to go out to Milly's house. She was waiting for me on the porch, dressed as I liked to see her, in blue and white, and she wore violets that matched the color of her eyes.
"Hello, Connie. I haven't seen a morning paper, but I know from your face that you lost the Rochester series," said Milly, with a gay laugh.
"I guess yes. The Rube blew up, and if we don't play a pretty smooth game, young lady, he'll never come down."
Then I told her.
"Why, Connie, I knew long ago. Haven't you seen the change in him before this?"
"What change?" I asked blankly.
"You are a man. Well, he was a gawky, slouchy, shy farmer boy when he came to us. Of course the city life and popularity began to influence him. Then he met Nan. She made the Rube a worshipper. I first noticed a change in his clothes. He blossomed out in a new suit, white negligee, neat tie and a stylish straw hat. Then it was evident he was making heroic struggles to overcome his awkwardness. It was plain he was studying and copying the other boys. He's wonderfully improved, but still shy. He'll always be shy. Connie, Whit's a fine fellow, too good for Nan Brown."
"But, Milly," I interrupted, "the Rube's hard hit. Why is he too good for her?"
"Nan is a natural-born flirt," Milly replied. "She can't help it. I'm afraid Whit has a slim chance. Nan may not see deep enough to learn his fine qualities. I fancy Nan tired quickly of him, though the one time I saw them together she appeared to like him very well. This new pitcher of yours, Henderson, is a handsome fellow and smooth. Whit is losing to him. Nan likes flash, flattery, excitement."
"McCall told me the Rube had been down in the mouth ever since Henderson joined the team. Milly, I don't like Henderson a whole lot. He's not in the Rube's class as a pitcher. What am I going to do? Lose the pennant and a big slice of purse money just for a pretty little flirt?"
"Oh, Connie, it's not so bad as that. Whit will come around all right."
"He won't unless we can pull some wires. I've got to help him win Nan Brown. What do you think of that for a manager's job? I guess maybe winning pennants doesn't call for diplomatic genius and cunning! But I'll hand them a few tricks before I lose. My first move will be to give Henderson his release."
I left Milly, as always, once more able to make light of discouragements and difficulties.
Monday I gave Henderson his unconditional release. He celebrated the occasion by verifying certain rumors I had heard from other managers. He got drunk. But he did not leave town, and I heard that he was negotiating with Providence for a place on that team.
Radbourne pitched one of his gilt-edged games that afternoon against Hartford and we won. And Milly sat in the grand stand, having contrived by cleverness to get a seat next to Nan Brown. Milly and I were playing a vastly deeper game than baseball—a game with hearts. But we were playing it with honest motive, for the good of all concerned, we believed, and on the square. I sneaked a look now and then up into the grand stand. Milly and Nan appeared to be getting on famously. It was certain that Nan was flushed and excited, no doubt consciously proud of being seen with my affianced. After the game I chanced to meet them on their way out. Milly winked at me, which was her sign that all was working beautifully.
I hunted up the Rube and bundled him off to the hotel to take dinner with me. At first he was glum, but after a while he brightened up somewhat to my persistent cheer and friendliness. Then we went out on the hotel balcony to smoke, and there I made my play.
"Whit, I'm pulling a stroke for you. Now listen and don't be offended. I know what's put you off your feed, because I was the same way when Milly had me guessing. You've lost your head over Nan Brown. That's not so terrible, though I daresay you think it's a catastrophe. Because you've quit. You've shown a yellow streak. You've lain down.
"My boy, that isn't the way to win a girl. You've got to scrap. Milly told me yesterday how she had watched your love affairs with Nan, and how she thought you had given up just when things might have come your way. Nan is a little flirt, but she's all right. What's more, she was getting fond of you. Nan is meanest to the man she likes best. The way to handle her, Whit, is to master her. Play high and mighty. Get tragical. Then grab her up in your arms. I tell you, Whit, it'll all come your way if you only keep your nerve. I'm your friend and so is Milly. We're going out to her house presently—and Nan will be there."
The Rube drew a long, deep breath and held out his hand. I sensed another stage in the evolution of Whit Hurtle.
"I reckon I've taken baseball coachin'," he said presently, "an' I don't see why I can't take some other kind. I'm only a rube, an' things come hard for me, but I'm a-learnin'."
It was about dark when we arrived at the house.
"Hello, Connie. You're late. Good evening, Mr. Hurtle. Come right in. You've met Miss Nan Brown? Oh, of course; how stupid of me!"
It was a trying moment for Milly and me. A little pallor showed under the Rube's tan, but he was more composed than I had expected. Nan got up from the piano. She was all in white and deliciously pretty. She gave a quick, glad start of surprise. What a relief that was to my troubled mind! Everything had depended upon a real honest liking for Whit, and she had it.
More than once I had been proud of Milly's cleverness, but this night as hostess and an accomplice she won my everlasting admiration. She contrived to give the impression that Whit was a frequent visitor at her home and very welcome. She brought out his best points, and in her skillful hands he lost embarrassment and awkwardness. Before the evening was over Nan regarded Whit with different eyes, and she never dreamed that everything had not come about naturally. Then Milly somehow got me out on the porch, leaving Nan and Whit together.
"Milly, you're a marvel, the best and sweetest ever," I whispered. "We're going to win. It's a cinch."
"Well, Connie, not that—exactly," she whispered back demurely. "But it looks hopeful."
I could not help hearing what was said in the parlor.
"Now I can roast you," Nan was saying, archly. She had switched back to her favorite baseball vernacular. "You pitched a swell game last Saturday in Rochester, didn't you? Not! You had no steam, no control, and you couldn't have curved a saucer."
"Nan, what could you expect?" was the cool reply. "You sat up in the stand with your handsome friend. I reckon I couldn't pitch. I just gave the game away."
"Whit!—Whit!—"
Then I whispered to Milly that it might be discreet for us to move a little way from the vicinity.
It was on the second day afterward that I got a chance to talk to Nan. She reached the grounds early, before Milly arrived, and I found her in the grand stand. The Rube was down on the card to pitch and when he started to warm up Nan said confidently that he would shut out Hartford that afternoon.
"I'm sorry, Nan, but you're way off. We'd do well to win at all, let alone get a shutout."
"You're a fine manager!" she retorted, hotly. "Why won't we win?"
"Well, the Rube's not in good form. The Rube—"
"Stop calling him that horrid name."
"Whit's not in shape. He's not right. He's ill or something is wrong. I'm worried sick about him."
"Why—Mr. Connelly!" exclaimed Nan. She turned quickly toward me.
I crowded on full canvas of gloom to my already long face.
"I'm serious, Nan. The lad's off, somehow. He's in magnificent physical trim, but he can't keep his mind on the game. He has lost his head. I've talked with him, reasoned with him, all to no good. He only goes down deeper in the dumps. Something is terribly wrong with him, and if he doesn't brace, I'll have to release—"
Miss Nan Brown suddenly lost a little of her rich bloom. "Oh! you wouldn't—you couldn't release him!"
"I'll have to if he doesn't brace. It means a lot to me, Nan, for of course I can't win the pennant this year without Whit being in shape. But I believe I wouldn't mind the loss of that any more than to see him fall down. The boy is a magnificent pitcher. If he can only be brought around he'll go to the big league next year and develop into one of the greatest pitchers the game has ever produced. But somehow or other he has lost heart. He's quit. And I've done my best for him. He's beyond me now. What a shame it is! For he's the making of such a splendid man outside of baseball. Milly thinks the world of him. Well, well; there are disappointments—we can't help them. There goes the gong. I must leave you. Nan, I'll bet you a box of candy Whit loses today. Is it a go?"
"It is," replied Nan, with fire in her eyes. "You go to Whit Hurtle and tell him I said if he wins today's game I'll kiss him!"
I nearly broke my neck over benches and bats getting to Whit with that message. He gulped once.
Then he tightened his belt and shut out Hartford with two scratch singles. It was a great exhibition of pitching. I had no means to tell whether or not the Rube got his reward that night, but I was so happy that I hugged Milly within an inch of her life.
But it turned out that I had been a little premature in my elation. In two days the Rube went down into the depths again, this time clear to China, and Nan was sitting in the grand stand with Henderson. The Rube lost his next game, pitching like a schoolboy scared out of his wits. Henderson followed Nan like a shadow, so that I had no chance to talk to her. The Rube lost his next game and then another. We were pushed out of second place.
If we kept up that losing streak a little longer, our hopes for the pennant were gone. I had begun to despair of the Rube. For some occult reason he scarcely spoke to me. Nan flirted worse than ever. It seemed to me she flaunted her conquest of Henderson in poor Whit's face.
The Providence ball team came to town and promptly signed Henderson and announced him for Saturday's game. Cairns won the first of the series and Radbourne lost the second. It was Rube's turn to pitch the Saturday game and I resolved to make one more effort to put the love-sick swain in something like his old fettle. So I called upon Nan.
She was surprised to see me, but received me graciously. I fancied her face was not quite so glowing as usual. I came bluntly out with my mission. She tried to freeze me but I would not freeze. I was out to win or lose and not to be lightly laughed aside or coldly denied. I played to make her angry, knowing the real truth of her feelings would show under stress.
For once in my life I became a knocker and said some unpleasant things—albeit they were true—about Henderson. She championed Henderson royally, and when, as a last card, I compared Whit's fine record with Henderson's, not only as a ball player, but as a man, particularly in his reverence for women, she flashed at me:
"What do you know about it? Mr. Henderson asked me to marry him. Can a man do more to show his respect? Your friend never so much as hinted such honorable intentions. What's more—he insulted me!" The blaze in Nan's black eyes softened with a film of tears. She looked hurt. Her pride had encountered a fall.
"Oh, no, Nan, Whit couldn't insult a lady," I protested.
"Couldn't he? That's all you know about him. You know I—I promised to kiss him if he beat Hartford that day. So when he came I—I did. Then the big savage began to rave and he grabbed me up in his arms. He smothered me; almost crushed the life out of me. He frightened me terribly. When I got away from him—the monster stood there and coolly said I belonged to him. I ran out of the room and wouldn't see him any more. At first I might have forgiven him if he had apologized—said he was sorry, but never a word. Now I never will forgive him."
I had to make a strenuous effort to conceal my agitation. The Rube had most carefully taken my fool advice in the matter of wooing a woman.
When I had got a hold upon myself, I turned to Nan white-hot with eloquence. Now I was talking not wholly for myself or the pennant, but for this boy and girl who were at odds in that strangest game of life—love.
What I said I never knew, but Nan lost her resentment, and then her scorn and indifference. Slowly she thawed and warmed to my reason, praise, whatever it was, and when I stopped she was again the radiant bewildering Nan of old.
"Take another message to Whit for me," she said, audaciously. "Tell him I adore ball players, especially pitchers. Tell him I'm going to the game today to choose the best one. If he loses the game—"
She left the sentence unfinished. In my state of mind I doubted not in the least that she meant to marry the pitcher who won the game, and so I told the Rube. He made one wild upheaval of his arms and shoulders, like an erupting volcano, which proved to me that he believed it, too.
When I got to the bench that afternoon I was tired. There was a big crowd to see the game; the weather was perfect; Milly sat up in the box and waved her score card at me; Raddy and Spears declared we had the game; the Rube stalked to and fro like an implacable Indian chief—but I was not happy in mind. Calamity breathed in the very air.
The game began. McCall beat out a bunt; Ashwell sacrificed and Stringer laced one of his beautiful triples against the fence. Then he scored on a high fly. Two runs! Worcester trotted out into the field. The Rube was white with determination; he had the speed of a bullet and perfect control of his jump ball and drop. But Providence hit and had the luck. Ashwell fumbled, Gregg threw wild. Providence tied the score.
The game progressed, growing more and more of a nightmare to me. It was not Worcester's day. The umpire could not see straight; the boys grumbled and fought among themselves; Spears roasted the umpire and was sent to the bench; Bogart tripped, hurting his sore ankle, and had to be taken out. Henderson's slow, easy ball baffled my players, and when he used speed they lined it straight at a Providence fielder.
In the sixth, after a desperate rally, we crowded the bases with only one out. Then Mullaney's hard rap to left, seemingly good for three bases, was pulled down by Stone with one hand. It was a wonderful catch and he doubled up a runner at second. Again in the seventh we had a chance to score, only to fail on another double play, this time by the infield.
When the Providence players were at bat their luck not only held good but trebled and quadrupled. The little Texas-league hits dropped safely just out of reach of the infielders. My boys had an off day in fielding. What horror that of all days in a season this should be the one for them to make errors!
But they were game, and the Rube was the gamest of all. He did not seem to know what hard luck was, or discouragement, or poor support. He kept everlastingly hammering the ball at those lucky Providence hitters. What speed he had! The ball streaked in, and somebody would shut his eyes and make a safety. But the Rube pitched, on, tireless, irresistibly, hopeful, not forgetting to call a word of cheer to his fielders.
It was one of those strange games that could not be bettered by any labor or daring or skill. I saw it was lost from the second inning, yet so deeply was I concerned, so tantalizingly did the plays reel themselves off, that I groveled there on the bench unable to abide by my baseball sense.
The ninth inning proved beyond a shadow of doubt how baseball fate, in common with other fates, loved to balance the chances, to lift up one, then the other, to lend a deceitful hope only to dash it away.
Providence had almost three times enough to win. The team let up in that inning or grew over-confident or careless, and before we knew what had happened some scratch hits, and bases on balls, and errors, gave us three runs and left two runners on bases. The disgusted bleachers came out of their gloom and began to whistle and thump. The Rube hit safely, sending another run over the plate. McCall worked his old trick, beating out a slow bunt.
Bases full, three runs to tie! With Ashwell up and one out, the noise in the bleachers mounted to a high-pitched, shrill, continuous sound. I got up and yelled with all my might and could not hear my voice. Ashwell was a dangerous man in a pinch. The game was not lost yet. A hit, anything to get Ash to first—and then Stringer!
Ash laughed at Henderson, taunted him, shook his bat at him and dared him to put one over. Henderson did not stand under fire. The ball he pitched had no steam. Ash cracked it—square on the line into the shortstop's hands. The bleachers ceased yelling.
Then Stringer strode grimly to the plate. It was a hundred to one, in that instance, that he would lose the ball. The bleachers let out one deafening roar, then hushed. I would rather have had Stringer at the bat than any other player in the world, and I thought of the Rube and Nan and Milly—and hope would not die.
Stringer swung mightily on the first pitch and struck the ball with a sharp, solid bing! It shot toward center, low, level, exceedingly swift, and like a dark streak went straight into the fielder's hands. A rod to right or left would have made it a home run. The crowd strangled a victorious yell. I came out of my trance, for the game was over and lost. It was the Rube's Waterloo.
I hurried him into the dressing room and kept close to him. He looked like a man who had lost the one thing worth while in his life. I turned a deaf ear to my players, to everybody, and hustled the Rube out and to the hotel. I wanted to be near him that night.
To my amaze we met Milly and Nan as we entered the lobby. Milly wore a sweet, sympathetic smile. Nan shone more radiant than ever. I simply stared. It was Milly who got us all through the corridor into the parlor. I heard Nan talking.
"Whit, you pitched a bad game but—" there was the old teasing, arch, coquettishness—"but you are the best pitcher!"
"Nan!"
"Yes!"
# Breaking into Fast Company
## *
They may say baseball is the same in the minor leagues that it is in the big leagues, but any old ball player or manager knows better. Where the difference comes in, however, is in the greater excellence and unity of the major players, a speed, a daring, a finish that can be acquired only in competition with one another.
I thought of this when I led my party into Morrisey's private box in the grand stand of the Chicago American League grounds. We had come to see the Rube's break into fast company. My great pitcher, Whittaker Hurtle, the Rube, as we called him, had won the Eastern League Pennant for me that season, and Morrisey, the Chicago magnate, had bought him. Milly, my affianced, was with me, looking as happy as she was pretty, and she was chaperoned by her mother, Mrs. Nelson.
With me, also, were two veterans of my team, McCall and Spears, who lived in Chicago, and who would have traveled a few miles to see the Rube pitch. And the other member of my party was Mrs. Hurtle, the Rube's wife, as saucy and as sparkling-eyed as when she had been Nan Brown. Today she wore a new tailor-made gown, new bonnet, new gloves—she said she had decorated herself in a manner befitting the wife of a major league pitcher.
Morrisey's box was very comfortable, and, as I was pleased to note, so situated that we had a fine view of the field and stands, and yet were comparatively secluded. The bleachers were filling. Some of the Chicago players were on the field tossing and batting balls; the Rube, however, had not yet appeared.
A moment later a metallic sound was heard on the stairs leading up into the box. I knew it for baseball spiked shoes clanking on the wood.
The Rube, looking enormous in his uniform, stalked into the box, knocking over two chairs as he entered. He carried a fielder's glove in one huge freckled hand, and a big black bat in the other.
Nan, with much dignity and a very manifest pride, introduced him to Mrs. Nelson.
There was a little chatting, and then, upon the arrival of Manager Morrisey, we men retired to the back of the box to talk baseball.
Chicago was in fourth place in the league race, and had a fighting chance to beat Detroit out for the third position. Philadelphia was scheduled for that day, and Philadelphia had a great team. It was leading the race, and almost beyond all question would land the flag. In truth, only one more victory was needed to clinch the pennant. The team had three games to play in Chicago and it was to wind up the season with three in Washington. Six games to play and only one imperatively important to win! But baseball is uncertain, and until the Philadelphians won that game they would be a band of fiends.
"Well, Whit, this is where you break in," I said. "Now, tip us straight. You've had more than a week's rest. How's that arm?"
"Grand, Con, grand!" replied the Rube with his frank smile. "I was a little anxious till I warmed up. But say! I've got more up my sleeve today than I ever had."
"That'll do for me," said Morrisey, rubbing his hands. "I'll spring something on these swelled Quakers today. Now, Connelly, give Hurtle one of your old talks—the last one—and then I'll ring the gong."
I added some words of encouragement, not forgetting my old ruse to incite the Rube by rousing his temper. And then, as the gong rang and the Rube was departing, Nan stepped forward for her say. There was a little white under the tan on her cheek, and her eyes had a darkling flash.
"Whit, it's a magnificent sight—that beautiful green field and the stands. What a crowd of fans! Why, I never saw a real baseball crowd before. There are twenty thousand here. And there's a difference in the feeling. It's sharper—new to me. It's big league baseball. Not a soul in that crowd ever heard of you, but, I believe, tomorrow the whole baseball world will have heard of you. Mr. Morrisey knows. I saw it in his face. Captain Spears knows. Connie knows. I know."
Then she lifted her face and, pulling him down within reach, she kissed him. Nan took her husband's work in dead earnest; she gloried in it, and perhaps she had as much to do with making him a great pitcher as any of us.
The Rube left the box, and I found a seat between Nan and Milly. The field was a splendid sight. Those bleachers made me glow with managerial satisfaction. On the field both teams pranced and danced and bounced around in practice.
In spite of the absolutely last degree of egotism manifested by the Philadelphia players, I could not but admire such a splendid body of men.
"So these are the champions of last season and of this season, too," commented Milly. "I don't wonder. How swiftly and cleanly they play! They appear not to exert themselves, yet they always get the ball in perfect time. It all reminds me of—of the rhythm of music. And that champion batter and runner—that Lane in center—isn't he just beautiful? He walks and runs like a blue-ribbon winner at the horse show. I tell you one thing, Connie, these Quakers are on dress parade."
"Oh, these Quakers hate themselves, I don't think!" retorted Nan. Being a rabid girl-fan it was, of course, impossible for Nan to speak baseball convictions or gossip without characteristic baseball slang. "Stuck on themselves! I never saw the like in my life. That fellow Lane is so swelled that he can't get down off his toes. But he's a wonder, I must admit that. They're a bunch of stars. Easy, fast, trained—they're machines, and I'll bet they're Indians to fight. I can see it sticking out all over them. This will certainly be some game with Whit handing up that jump ball of his to this gang of champs. But, Connie, I'll go you Whit beats them."
I laughed and refused to gamble.
The gong rang; the crowd seemed to hum and rustle softly to quiet attention; Umpire McClung called the names of the batteries; then the familiar "Play!"
There was the usual applause from the grand stand and welcome cheers from the bleachers. The Rube was the last player to go out. Morrisey was a manager who always played to the stands, and no doubt he held the Rube back for effect. If so, he ought to have been gratified. That moment reminded me of my own team and audience upon the occasion of the Rube's debut. It was the same only here it happened in the big league, before a championship team and twenty thousand fans.
The roar that went up from the bleachers might well have scared an unseasoned pitcher out of his wits. And the Quakers lined up before their bench and gazed at this newcomer who had the nerve to walk out there to the box. Cogswell stood on the coaching line, looked at the Rube and then held up both arms and turned toward the Chicago bench as if to ask Morrisey: "Where did you get that?"
Nan, quick as a flash to catch a point, leaned over the box-rail and looked at the champions with fire in her eye. "Oh, you just wait! wait!" she bit out between her teeth.
Certain it was that there was no one who knew the Rube as well as I; and I knew beyond the shadow of a doubt that the hour before me would see brightening of a great star pitcher on the big league horizon. It was bound to be a full hour for me. I had much reason to be grateful to Whit Hurtle. He had pulled my team out of a rut and won me the pennant, and the five thousand dollars I got for his release bought the little cottage on the hill for Milly and me. Then there was my pride in having developed him. And all that I needed to calm me, settle me down into assurance and keen criticism of the game, was to see the Rube pitch a few balls with his old incomparable speed and control.
Berne, first batter for the Quakers, walked up to the plate. He was another Billy Hamilton, built like a wedge. I saw him laugh at the long pitcher.
Whit swayed back, coiled and uncoiled. Something thin, white, glancing, shot at Berne. He ducked, escaping the ball by a smaller margin than appeared good for his confidence. He spoke low to the Rube, and what he said was probably not flavored with the milk of friendly sweetness.
"Wild! What'd you look for?" called out Cogswell scornfully. "He's from the woods!"
The Rube swung his enormously long arm, took an enormous stride toward third base, and pitched again. It was one of his queer deliveries. The ball cut the plate.
"Ho! Ho!" yelled the Quakers.
The Rube's next one was his out curve. It broke toward the corner of the plate and would have been a strike had not Berne popped it up.
Callopy, the second hitter, faced the Rube, and he, too, after the manner of ball players, made some remark meant only for the Rube's ears. Callopy was a famous waiter. He drove more pitchers mad with his implacable patience than any hitter in the league. The first one of the Rube's he waited on crossed the in-corner; the second crossed the out-corner and the third was Rube's wide, slow, tantalizing "stitch-ball," as we call it, for the reason that it came so slow a batter could count the stitches. I believe Callopy waited on that curve, decided to hit it, changed his mind and waited some more, and finally the ball maddened him and he had to poke at it, the result being a weak grounder.
Then the graceful, powerful Lane, champion batter, champion base runner, stepped to the plate. How a baseball crowd, any crowd, anywhere, loves the champion batter! The ovation Lane received made me wonder, with this impressive reception in a hostile camp, what could be the manner of it on his home field? Any boy ball-player from the lots seeing Lane knock the dirt out of his spikes and step into position would have known he was a 400 hitter.
I was curious to see what the Rube would pitch Lane. It must have been a new and significant moment for Hurtle. Some pitchers actually wilt when facing a hitter of Lane's reputation. But he, on his baseball side, was peculiarly unemotional. Undoubtedly he could get furious, but that only increased his effectiveness. To my amazement the Rube pitched Lane a little easy ball, not in any sense like his floater or stitch-ball, but just a little toss that any youngster might have tossed. Of all possible balls, Lane was not expecting such as that, and he let it go. If the nerve of it amazed me, what did it not do to Lane? I saw his face go fiery red. The grand stand murmured; let out one short yelp of pleasure; the Quaker players chaffed Lane.
The pitch was a strike. I was gripping my chair now, and for the next pitch I prophesied the Rube's wonderful jump ball, which he had not yet used. He swung long, and at the end of his swing seemed to jerk tensely. I scarcely saw the ball. It had marvelous speed. Lane did not offer to hit it, and it was a strike. He looked at the Rube, then at Cogswell. That veteran appeared amused. The bleachers, happy and surprised to be able to yell at Lane, yelled heartily.
Again I took it upon myself to interpret the Rube's pitching mind. He had another ball that he had not used, a drop, an unhittable drop. I thought he would use that next. He did, and though Lane reached it with the bat, the hit was a feeble one. He had been fooled and the side was out.
Poole, the best of the Quaker's pitching staff, walked out to the slab. He was a left-hander, and Chicago, having so many players who batted left-handed, always found a southpaw a hard nut to crack. Cogswell, field manager and captain of the Quakers, kicked up the dust around first base and yelled to his men: "Git in the game!"
Staats hit Poole's speed ball into deep short and was out; Mitchell flew out to Berne; Rand grounded to second.
While the teams again changed sides the fans cheered, and then indulged in the first stretch of the game. I calculated that they would be stretching their necks presently, trying to keep track of the Rube's work. Nan leaned on the railing absorbed in her own hope and faith. Milly chattered about this and that, people in the boxes, and the chances of the game.
My own interest, while it did not wholly preclude the fortunes of the Chicago players at the bat, was mostly concerned with the Rube's fortunes in the field.
In the Rube's half inning he retired Bannister and Blandy on feeble infield grounders, and worked Cogswell into hitting a wide curve high in the air.
Poole meant to win for the Quakers if his good arm and cunning did not fail him, and his pitching was masterly. McCloskey fanned, Hutchinson fouled out, Brewster got a short safe fly just out of reach, and Hoffner hit to second, forcing Brewster.
With Dugan up for the Quakers in the third inning, Cogswell and Bannister, from the coaching lines, began to talk to the Rube. My ears, keen from long practice, caught some of the remarks in spite of the noisy bleachers.
"Say, busher, you 've lasted longer'n we expected, but you don't know it!"
"Gol darn you city ball tossers! Now you jest let me alone!"
"We're comin' through the rye!"
"My top-heavy rustic friend, you'll need an airship presently, when you go up!"
All the badinage was good-natured, which was sure proof that the Quakers had not arrived at anything like real appreciation of the Rube. They were accustomed to observe the trying out of many youngsters, of whom ninety-nine out of a hundred failed to make good.
Dugan chopped at three strikes and slammed his bat down. Hucker hit a slow fly to Hoffer. Three men out on five pitched balls! Cogswell, old war horse that he was, stood a full moment and watched the Rube as he walked in to the bench. An idea had penetrated Cogswell's brain, and I would have given something to know what it was. Cogswell was a great baseball general, and though he had a preference for matured ball-players he could, when pressed, see the quality in a youngster. He picked up his mitt and took his position at first with a gruff word to his players.
Rand for Chicago opened with a hit, and the bleachers, ready to strike fire, began to cheer and stamp. When McCloskey, in an attempt to sacrifice, beat out his bunt the crowd roared. Rand, being slow on his feet, had not attempted to make third on the play. Hutchinson sacrificed, neatly advancing the runners. Then the bleachers played the long rolling drum of clattering feet with shrill whistling accompaniment. Brewster batted a wicked ground ball to Blandy. He dove into the dust, came up with the ball, and feinting to throw home he wheeled and shot the ball to Cogswell, who in turn shot it to the plate to head Rand. Runner and ball got there apparently together, but Umpire McClung's decision went against Rand. It was fine, fast work, but how the bleachers stormed at McClung!
"Rob-b-ber!"
Again the head of the Quakers' formidable list was up. I knew from the way that Cogswell paced the coaching box that the word had gone out to look the Rube over seriously. There were possibilities even in rubes.
Berne carefully stepped into the batter's box, as if he wanted to be certain to the breadth of a hair how close he was to the plate. He was there this time to watch the Rube pitch, to work him out, to see what was what. He crouched low, and it would have been extremely hard to guess what he was up to. His great play, however, was his ability to dump the ball and beat out the throw to first. It developed presently, that this was now his intention and that the Rube knew it and pitched him the one ball which is almost impossible to bunt—a high incurve, over the inside corner. There was no mistaking the Rube's magnificent control. True as a plumb line he shot up the ball—once, twice, and Berne fouled both—two strikes. Grudgingly he waited on the next, but it, too, was over the corner, and Berne went out on strikes. The great crowd did not, of course, grasp the finesse of the play, but Berne had struck out—that was enough for them.
Callopy, the famous spiker, who had put many a player out of the game for weeks at a time, strode into the batter's place, and he, too, was not at the moment making any funny remarks. The Rube delivered a ball that all but hit Callopy fair on the head. It was the second narrow escape for him, and the roar he let out showed how he resented being threatened with a little of his own medicine. As might have been expected, and very likely as the Rube intended, Callopy hit the next ball, a sweeping curve, up over the infield.
I was trying to see all the intricate details of the motive and action on the field, and it was not easy to watch several players at once. But while Berne and Callopy were having their troubles with the Rube, I kept the tail of my eye on Cogswell. He was prowling up and down the third-base line.
He was missing no signs, no indications, no probabilities, no possibilities. But he was in doubt. Like a hawk he was watching the Rube, and, as well, the crafty batters. The inning might not tell the truth as to the Rube's luck, though it would test his control. The Rube's speed and curves, without any head work, would have made him a pitcher of no mean ability, but was this remarkable placing of balls just accident? That was the question.
When Berne walked to the bench I distinctly heard him say: "Come out of it, you dubs. I say you can't work him or wait him. He's peggin' 'em out of a gun!"
Several of the Quakers were standing out from the bench, all intent on the Rube. He had stirred them up. First it was humor; then ridicule, curiosity, suspicion, doubt. And I knew it would grow to wonder and certainty, then fierce attack from both tongues and bats, and lastly—for ball players are generous—unstinted admiration.
Somehow, not only the first climaxes of a game but the decisions, the convictions, the reputations of pitchers and fielders evolve around the great hitter. Plain it was that the vast throng of spectators, eager to believe in a new find, wild to welcome a new star, yet loath to trust to their own impulsive judgments, held themselves in check until once more the great Lane had faced the Rube.
The field grew tolerably quiet just then. The Rube did not exert himself. The critical stage had no concern for him. He pitched Lane a high curve, over the plate, but in close, a ball meant to be hit and a ball hard to hit safely. Lane knew that as well as any hitter in the world, so he let two of the curves go by—two strikes. Again the Rube relentlessly gave him the same ball; and Lane, hitting viciously, spitefully, because he did not want to hit that kind of a ball, sent up a fly that Rand easily captured.
"Oh, I don't know! Pretty fair, I guess!" yelled a tenor-voiced fan; and he struck the key-note. And the bleachers rose to their feet and gave the Rube the rousing cheer of the brotherhood of fans.
Hoffer walked to first on a base on balls. Sweeney advanced him. The Rube sent up a giant fly to Callopy. Then Staats hit safely, scoring the first run of the game. Hoffer crossed the plate amid vociferous applause. Mitchell ended the inning with a fly to Blandy.
What a change had come over the spirit of that Quaker aggregation! It was something to make a man thrill with admiration and, if he happened to favor Chicago, to fire all his fighting blood. The players poured upon the Rube a continuous stream of scathing abuse. They would have made a raging devil of a mild-mannered clergyman. Some of them were skilled in caustic wit, most of them were possessed of forked tongues; and Cogswell, he of a thousand baseball battles, had a genius for inflaming anyone he tormented. This was mostly beyond the ken of the audience, and behind the back of the umpire, but it was perfectly plain to me. The Quakers were trying to rattle the Rube, a trick of the game as fair for one side as for the other. I sat there tight in my seat, grimly glorying in the way the Rube refused to be disturbed. But the lion in him was rampant. Fortunately, it was his strange gift to pitch better the angrier he got; and the more the Quakers flayed him, the more he let himself out to their crushing humiliation.
The innings swiftly passed to the eighth with Chicago failing to score again, with Philadelphia failing to score at all. One scratch hit and a single, gifts to the weak end of the batting list, were all the lank pitcher allowed them. Long since the bleachers had crowned the Rube. He was theirs and they were his; and their voices had the peculiar strangled hoarseness due to over-exertion. The grand stand, slower to understand and approve, arrived later; but it got there about the seventh, and ladies' gloves and men's hats were sacrificed.
In the eighth the Quakers reluctantly yielded their meed of praise, showing it by a cessation of their savage wordy attacks on the Rube. It was a kind of sullen respect, wrung from the bosom of great foes.
Then the ninth inning was at hand. As the sides changed I remembered to look at the feminine group in our box. Milly was in a most beautiful glow of happiness and excitement. Nan sat rigid, leaning over the rail, her face white and drawn, and she kept saying in a low voice: "Will it never end? Will it never end?" Mrs. Nelson stared wearily.
It was the Quakers' last stand. They faced it as a team that had won many a game in the ninth with two men out. Dugan could do nothing with the Rube's unhittable drop, for a drop curve was his weakness, and he struck out. Hucker hit to Hoffer, who fumbled, making the first error of the game. Poole dumped the ball, as evidently the Rube desired, for he handed up a straight one, but the bunt rolled teasingly and the Rube, being big and tall, failed to field it in time.
Suddenly the whole field grew quiet. For the first time Cogswell's coaching was clearly heard.
"One out! Take a lead! Take a lead! Go through this time. Go through!"
Could it be possible, I wondered, that after such a wonderful exhibition of pitching the Rube would lose out in the ninth?
There were two Quakers on base, one out, and two of the best hitters in the league on deck, with a chance of Lane getting up.
"Oh! Oh! Oh!" moaned Nan.
I put my hand on hers. "Don't quit, Nan. You'll never forgive yourself if you quit. Take it from me, Whit will pull out of this hole!"
What a hole that was for the Rube on the day of his break into fast company! I measured it by his remarkable deliberation. He took a long time to get ready to pitch to Berne, and when he let drive it was as if he had been trifling all before in that game. I could think of no way to figure it except that when the ball left him there was scarcely any appreciable interval of time before it cracked in Sweeney's mitt. It was the Rube's drop, which I believed unhittable. Berne let it go by, shaking his head as McClung called it a strike. Another followed, which Berne chopped at vainly. Then with the same upheaval of his giant frame, the same flinging of long arms and lunging forward, the Rube delivered a third drop. And Berne failed to hit it.
The voiceless bleachers stamped on the benches and the grand stand likewise thundered.
Callopy showed his craft by stepping back and lining Rube's high pitch to left. Hoffer leaped across and plunged down, getting his gloved hand in front of the ball. The hit was safe, but Hoffer's valiant effort saved a tie score.
Lane up! Three men on bases! Two out!
Not improbably there were many thousand spectators of that thrilling moment who pitied the Rube for the fate which placed Lane at the bat then. But I was not one of them. Nevertheless my throat was clogged, my mouth dry, and my ears full of bells. I could have done something terrible to Hurtle for his deliberation, yet I knew he was proving himself what I had always tried to train him to be.
Then he swung, stepped out, and threw his body with the ball. This was his rarely used pitch, his last resort, his fast rise ball that jumped up a little at the plate. Lane struck under it. How significant on the instant to see old Cogswell's hands go up! Again the Rube pitched, and this time Lane watched the ball go by. Two strikes!
That whole audience leaped to its feet, whispering, yelling, screaming, roaring, bawling.
The Rube received the ball from Sweeney and quick as lightning he sped it plateward. The great Lane struck out! The game was over—Chicago, 1; Philadelphia, 0.
In that whirling moment when the crowd went mad and Milly was hugging me, and Nan pounding holes in my hat, I had a queer sort of blankness, a section of time when my sensations were deadlocked.
"Oh! Connie, look!" cried Nan. I saw Lane and Cogswell warmly shaking hands with the Rube. Then the hungry clamoring fans tumbled upon the field and swarmed about the players.
Whereupon Nan kissed me and Milly, and then kissed Mrs. Nelson. In that radiant moment Nan was all sweetness.
"It is the Rube's break into fast company," she said.
# The Knocker
## *
"Yes, Carroll, I got my notice. Maybe it's no surprise to you. And there's one more thing I want to say. You're 'it' on this team. You're the topnotch catcher in the Western League and one of the best ball players in the game—but you're a knocker!"
Madge Ellston heard young Sheldon speak. She saw the flash in his gray eyes and the heat of his bronzed face as he looked intently at the big catcher.
"Fade away, sonny. Back to the bush-league for yours!" replied Carroll, derisively. "You're not fast enough for Kansas City. You look pretty good in a uniform and you're swift on your feet, but you can't hit. You've got a glass arm and you run bases like an ostrich trying to side. That notice was coming to you. Go learn the game!"
Then a crowd of players trooped noisily out of the hotel lobby and swept Sheldon and Carroll down the porch steps toward the waiting omnibus.
Madge's uncle owned the Kansas City club. She had lived most of her nineteen years in a baseball atmosphere, but accustomed as she was to baseball talk and the peculiar banterings and bickerings of the players, there were times when it seemed all Greek. If a player got his "notice" it meant he would be released in ten days. A "knocker" was a ball player who spoke ill of his fellow players. This scrap of conversation, however, had an unusual interest because Carroll had paid court to her for a year, and Sheldon, coming to the team that spring, had fallen desperately in love with her. She liked Sheldon pretty well, but Carroll fascinated her. She began to wonder if there were bad feelings between the rivals—to compare them—to get away from herself and judge them impersonally.
When Pat Donahue, the veteran manager of the team came out, Madge greeted him with a smile. She had always gotten on famously with Pat, notwithstanding her imperious desire to handle the managerial reins herself upon occasions. Pat beamed all over his round ruddy face.
"Miss Madge, you weren't to the park yesterday an' we lost without our pretty mascot. We shure needed you. Denver's playin' at a fast clip."
"I'm coming out today," replied Miss Ellston, thoughtfully. "Pat, what's a knocker?"
"Now, Miss Madge, are you askin' me that after I've been coachin' you in baseball for years?" questioned Pat, in distress.
"I know what a knocker is, as everybody else does. But I want to know the real meaning, the inside-ball of it, to use your favorite saying."
Studying her grave face with shrewd eyes Donahue slowly lost his smile.
"The inside-ball of it, eh? Come, let's sit over here a bit—the sun's shure warm today.... Miss Madge, a knocker is the strangest man known in the game, the hardest to deal with an' what every baseball manager hates most."
Donahue told her that he believed the term "knocker" came originally from baseball; that in general it typified the player who strengthened his own standing by belittling the ability of his team-mates, and by enlarging upon his own superior qualities. But there were many phases of this peculiar type. Some players were natural born knockers; others acquired the name in their later years in the game when younger men threatened to win their places. Some of the best players ever produced by baseball had the habit in its most violent form. There were players of ridiculously poor ability who held their jobs on the strength of this one trait. It was a mystery how they misled magnates and managers alike; how for months they held their places, weakening a team, often keeping a good team down in the race; all from sheer bold suggestion of their own worth and other players' worthlessness. Strangest of all was the knockers' power to disorganize; to engender a bad spirit between management and team and among the players. The team which was without one of the parasites of the game generally stood well up in the race for the pennant, though there had been championship teams noted for great knockers as well as great players.
"It's shure strange, Miss Madge," said Pat in conclusion, shaking his gray head. "I've played hundreds of knockers, an' released them, too. Knockers always get it in the end, but they go on foolin' me and workin' me just the same as if I was a youngster with my first team. They're part an' parcel of the game."
"Do you like these men off the field—outside of baseball, I mean?"
"No, I shure don't, an' I never seen one yet that wasn't the same off the field as he was on."
"Thank you, Pat. I think I understand now. And—oh, yes, there's another thing I want to ask you. What's the matter with Billie Sheldon? Uncle George said he was falling off in his game. Then I've read the papers. Billie started out well in the spring."
"Didn't he? I was sure thinkin' I had a find in Billie. Well, he's lost his nerve. He's in a bad slump. It's worried me for days. I'm goin' to release Billie. The team needs a shake-up. That's where Billie gets the worst of it, for he's really the makin' of a star; but he's slumped, an' now knockin' has made him let down. There, Miss Madge, that's an example of what I've just been tellin' you. An' you can see that a manager has his troubles. These hulkin' athletes are a lot of spoiled babies an' I often get sick of my job."
That afternoon Miss Ellston was in a brown study all the way out to the baseball park. She arrived rather earlier than usual to find the grand-stand empty. The Denver team had just come upon the field, and the Kansas City players were practising batting at the left of the diamond. Madge walked down the aisle of the grand stand and out along the reporters' boxes. She asked one of the youngsters on the field to tell Mr. Sheldon that she would like to speak with him a moment.
Billie eagerly hurried from the players' bench with a look of surprise and expectancy on his sun-tanned face. Madge experienced for the first time a sudden sense of shyness at his coming. His lithe form and his nimble step somehow gave her a pleasure that seemed old yet was new. When he neared her, and, lifting his cap, spoke her name, the shade of gloom in his eyes and lines of trouble on his face dispelled her confusion.
"Billie, Pat tells me he's given you ten days' notice," she said.
"It's true."
"What's wrong with you, Billie?"
"Oh, I've struck a bad streak—can't hit or throw."
"Are you a quitter?"
"No, I'm not," he answered quickly, flushing a dark red.
"You started off this spring with a rush. You played brilliantly and for a while led the team in batting. Uncle George thought so well of you. Then came this spell of bad form. But, Billie, it's only a slump; you can brace."
"I don't know," he replied, despondently. "Awhile back I got my mind off the game. Then—people who don't like me have taken advantage of my slump to—"
"To knock," interrupted Miss Ellston.
"I'm not saying that," he said, looking away from her.
"But I'm saying it. See here, Billie Sheldon, my uncle owns this team and Pat Donahue is manager. I think they both like me a little. Now I don't want to see you lose your place. Perhaps—"
"Madge, that's fine of you—but I think—I guess it'd be best for me to leave Kansas City."
"Why?"
"You know," he said huskily. "I've lost my head—I'm in love—I can't think of baseball—I'm crazy about you."
Miss Ellston's sweet face grew rosy, clear to the tips of her ears.
"Billie Sheldon," she replied, spiritedly. "You're talking nonsense. Even if you were were that way, it'd be no reason to play poor ball. Don't throw the game, as Pat would say. Make a brace! Get up on your toes! Tear things! Rip the boards off the fence! Don't quit!"
She exhausted her vocabulary of baseball language if not her enthusiasm, and paused in blushing confusion.
"Madge!"
"Will you brace up?"
"Will I—will I!" he exclaimed, breathlessly.
Madge murmured a hurried good-bye and, turning away, went up the stairs. Her uncle's private box was upon the top of the grand stand and she reached it in a somewhat bewildered state of mind. She had a confused sense of having appeared to encourage Billie, and did not know whether she felt happy or guilty. The flame in his eyes had warmed all her blood. Then, as she glanced over the railing to see the powerful Burns Carroll, there rose in her breast a panic at strange variance with her other feelings.
Many times had Madge Ellston viewed the field and stands and the outlying country from this high vantage point; but never with the same mingling emotions, nor had the sunshine ever been so golden, the woods and meadows so green, the diamond so smooth and velvety, the whole scene so gaily bright.
Denver had always been a good drawing card, and having won the first game of the present series, bade fair to draw a record attendance. The long lines of bleachers, already packed with the familiar mottled crowd, sent forth a merry, rattling hum. Soon a steady stream of well-dressed men and women poured in the gates and up the grand-stand stairs. The soft murmur of many voices in light conversation and laughter filled the air. The peanut venders and score-card sellers kept up their insistent shrill cries. The baseball park was alive now and restless; the atmosphere seemed charged with freedom and pleasure. The players romped like skittish colts, the fans shrieked their witticisms—all sound and movements suggested play.
Madge Ellston was somehow relieved to see her uncle sitting in one of the lower boxes. During this game she wanted to be alone, and she believed she would be, for the President of the League and directors of the Kansas City team were with her uncle. When the bell rang to call the Denver team in from practice the stands could hold no more, and the roped-off side lines were filling up with noisy men and boys. From her seat Madge could see right down upon the players' bench, and when she caught both Sheldon and Carroll gazing upward she drew back with sharply contrasted thrills.
Then the bell rang again, the bleachers rolled out their welcoming acclaim, and play was called with Kansas City at the bat.
Right off the reel Hunt hit a short fly safely over second. The ten thousand spectators burst into a roar. A good start liberated applause and marked the feeling for the day.
Madge was surprised and glad to see Billie Sheldon start next for the plate. All season, until lately, he had been the second batter. During his slump he had been relegated to the last place on the batting list. Perhaps he had asked Pat to try him once more at the top. The bleachers voiced their unstinted appreciation of this return, showing that Billie still had a strong hold on their hearts.
As for Madge, her breast heaved and she had difficulty in breathing. This was going to be a hard game for her. The intensity of her desire to see Billie brace up to his old form amazed her. And Carroll's rude words beat thick in her ears. Never before had Billie appeared so instinct with life, so intent and strung as when he faced Keene, the Denver pitcher. That worthy tied himself up in a knot, and then, unlimbering a long arm, delivered the brand new ball.
Billie seemed to leap forward and throw his bat at it. There was a sharp ringing crack—and the ball was like a white string marvelously stretching out over the players, over the green field beyond, and then, sailing, soaring, over the right-field fence. For a moment the stands, even the bleachers, were stone quiet. No player had ever hit a ball over that fence. It had been deemed impossible, as was attested to by the many painted "ads" offering prizes for such a feat. Suddenly the far end of the bleachers exploded and the swelling roar rolled up to engulf the grand stand in thunder. Billie ran round the bases to applause never before vented on that field. But he gave no sign that it affected him; he did not even doff his cap. White-faced and stern, he hurried to the bench, where Pat fell all over him and many of the players grasped his hands.
Up in her box Madge was crushing her score-card and whispering: "Oh! Billie, I could hug you for that!"
Two runs on two pitched balls! That was an opening to stir an exacting audience to the highest pitch of enthusiasm. The Denver manager peremptorily called Keene off the diamond and sent in Steele, a south-paw, who had always bothered Pat's left-handed hitters. That move showed his astute judgment, for Steele struck out McReady and retired Curtis and Mahew on easy chances.
It was Dalgren's turn to pitch and though he had shown promise in several games he had not yet been tried out on a team of Denver's strength. The bleachers gave him a good cheering as he walked into the box, but for all that they whistled their wonder at Pat's assurance in putting him against the Cowboys in an important game.
The lad was visibly nervous and the hard-hitting and loud-coaching Denver players went after him as if they meant to drive him out of the game. Crane stung one to left center for a base, Moody was out on a liner to short, almost doubling up Crane; the fleet-footed Bluett bunted and beat the throw to first; Langly drove to left for what seemed a three-bagger, but Curtis, after a hard run, caught the ball almost off the left-field bleachers. Crane and Bluett advanced a base on the throw-in. Then Kane batted up a high foul-fly. Burns Carroll, the Kansas City catcher, had the reputation of being a fiend for chasing foul flies, and he dashed at this one with a speed that threatened a hard fall over the players' bench or a collision with the fence. Carroll caught the ball and crashed against the grand stand, but leaped back with an agility that showed that if there was any harm done it had not been to him.
Thus the sharp inning ended with a magnificent play. It electrified the spectators into a fierce energy of applause. With one accord, by baseball instinct, the stands and bleachers and roped-in-sidelines realized it was to be a game of games and they answered to the stimulus with a savage enthusiasm that inspired ballplayers to great plays.
In the first half of the second inning, Steele's will to do and his arm to execute were very like his name. Kansas City could not score. In their half the Denver team made one run by clean hitting.
Then the closely fought advantage see-sawed from one team to the other. It was not a pitchers' battle, though both men worked to the limit of skill and endurance. They were hit hard. Dazzling plays kept the score down and the innings short. Over the fields hung the portent of something to come, every player, every spectator felt the subtle baseball chance; each inning seemed to lead closer and more thrillingly up to the climax. But at the end of the seventh, with the score tied six and six, with daring steals, hard hits and splendid plays, enough to have made memorable several games, it seemed that the great portentous moment was still in abeyance.
The head of the batting list for Kansas City was up. Hunt caught the first pitched ball squarely on the end of his bat. It was a mighty drive and as the ball soared and soared over the center-field Hunt raced down the base line, and the winged-footed Crane sped outward, the bleachers split their throats. The hit looked good for a home run, but Crane leaped up and caught the ball in his gloved hand. The sudden silence and then the long groan which racked the bleachers was greater tribute to Crane's play than any applause.
Billie Sheldon then faced Steele. The fans roared hoarsely, for Billie had hit safely three times out of four. Steele used his curve ball, but he could not get the batter to go after it. When he had wasted three balls, the never-despairing bleachers howled: "Now, Billie, in your groove! Sting the next one!" But Billie waited. One strike! Two strikes! Steele cut the plate. That was a test which proved Sheldon's caliber.
With seven innings of exciting play passed, with both teams on edge, with the bleachers wild and the grand stands keyed up to the breaking point, with everything making deliberation almost impossible, Billie Sheldon had remorselessly waited for three balls and two strikes.
"Now! ... Now! ... Now!" shrieked the bleachers.
Steele had not tired nor lost his cunning. With hands before him he grimly studied Billie, then whirling hard to get more weight into his motion, he threw the ball.
Billie swung perfectly and cut a curving liner between the first baseman and the base. Like a shot it skipped over the grass out along the foul-line into right field. Amid tremendous uproar Billie stretched the hit into a triple, and when he got up out of the dust after his slide into third the noise seemed to be the crashing down of the bleachers. It died out with the choking gurgling yell of the most leather-lunged fan.
"O-o-o-o-you-Billie-e!"
McReady marched up and promptly hit a long fly to the redoubtable Crane. Billie crouched in a sprinter's position with his eye on the graceful fielder, waiting confidently for the ball to drop. As if there had not already been sufficient heart-rending moments, the chance that governed baseball meted out this play; one of the keenest, most trying known to the game. Players waited, spectators waited, and the instant of that dropping ball was interminably long. Everybody knew Crane would catch it; everybody thought of the wonderful throwing arm that had made him famous. Was it possible for Billie Sheldon to beat the throw to the plate?
Crane made the catch and got the ball away at the same instant Sheldon leaped from the base and dashed for home. Then all eyes were on the ball. It seemed incredible that a ball thrown by human strength could speed plateward so low, so straight, so swift. But it lost its force and slanted down to bound into the catcher's hands just as Billie slid over the plate.
By the time the bleachers had stopped stamping and bawling, Curtis ended the inning with a difficult grounder to the infield.
Once more the Kansas City players took the field and Burns Carroll sang out in his lusty voice: "Keep lively, boys! Play hard! Dig 'em up an' get 'em!" Indeed the big catcher was the main-stay of the home team. The bulk of the work fell upon his shoulders. Dalgren was wild and kept his catcher continually blocking low pitches and wide curves and poorly controlled high fast balls. But they were all alike to Carroll. Despite his weight, he was as nimble on his feet as a goat, and if he once got his hands on the ball he never missed it. It was his encouragement that steadied Dalgren; his judgment of hitters that carried the young pitcher through dangerous places; his lightning swift grasp of points that directed the machine-like work of his team.
In this inning Carroll exhibited another of his demon chases after a foul fly; he threw the base-stealing Crane out at second, and by a remarkable leap and stop of McReady's throw, he blocked a runner who would have tied the score.
The Cowboys blanked their opponents in the first half of the ninth, and trotted in for their turn needing one run to tie, two runs to win.
There had scarcely been a breathing spell for the onlookers in this rapid-fire game. Every inning had held them, one moment breathless, the next wildly clamorous, and another waiting in numb fear. What did these last few moments hold in store? The only answer to that was the dogged plugging optimism of the Denver players. To listen to them, to watch them, was to gather the impression that baseball fortune always favored them in the end.
"Only three more, Dal. Steady boys, it's our game," rolled out Carroll's deep bass. How virile he was! What a tower of strength to the weakening pitcher!
But valiantly as Dalgren tried to respond, he failed. The grind—the strain had been too severe. When he finally did locate the plate Bluett hit safely. Langley bunted along the base line and beat the ball.
A blank, dead quiet settled down over the bleachers and stands. Something fearful threatened. What might not come to pass, even at the last moment of this nerve-racking game? There was a runner on first and a runner on second. That was bad. Exceedingly bad was it that these runners were on base with nobody out. Worst of all was the fact that Kane was up. Kane, the best bunter, the fastest man to first, the hardest hitter in the league! That he would fail to advance those two runners was scarcely worth consideration. Once advanced, a fly to the outfield, a scratch, anything almost, would tie the score. So this was the climax presaged so many times earlier in the game. Dalgren seemed to wilt under it.
Kane swung his ash viciously and called on Dalgren to put one over. Dalgren looked in toward the bench as if he wanted and expected to be taken out. But Pat Donahue made no sign. Pat had trained many a pitcher by forcing him to take his medicine. Then Carroll, mask under his arm, rolling his big hand in his mitt, sauntered down to the pitcher's box. The sharp order of the umpire in no wise disconcerted him. He said something to Dalgren, vehemently nodding his head the while. Players and audience alike supposed he was trying to put a little heart into Dalgren, and liked him the better, notwithstanding the opposition to the umpire.
Carroll sauntered back to his position. He adjusted his breast protector, and put on his mask, deliberately taking his time. Then he stepped behind the plate, and after signing for the pitch, he slowly moved his right hand up to his mask.
Dalgren wound up, took his swing, and let drive. Even as he delivered the ball Carroll bounded away from his position, flinging off the mask as he jumped. For a single fleeting instant, the catcher's position was vacated. But that instant was long enough to make the audience gasp. Kane bunted beautifully down the third base line, and there Carroll stood, fifteen feet from the plate, agile as a huge monkey. He whipped the ball to Mahew at third. Mahew wheeled quick as thought and lined the ball to second. Sheldon came tearing for the bag, caught the ball on the run, and with a violent stop and wrench threw it like a bullet to first base. Fast as Kane was, the ball beat him ten feet. A triple play!
The players of both teams cheered, but the audience, slower to grasp the complex and intricate points, needed a long moment to realize what had happened. They needed another to divine that Carroll had anticipated Kane's intention to bunt, had left his position as the ball was pitched, had planned all, risked all, played all on Kane's sure eye; and so he had retired the side and won the game by creating and executing the rarest play in baseball.
Then the audience rose in a body to greet the great catcher. What a hoarse thundering roar shook the stands and waved in a blast over the field! Carroll stood bowing his acknowledgment, and then swaggered a little with the sun shining on his handsome heated face. Like a conqueror conscious of full blown power he stalked away to the clubhouse.
Madge Ellston came out of her trance and viewed the ragged score-card, her torn parasol, her battered gloves and flying hair, her generally disheveled state with a little start of dismay, but when she got into the thick and press of the moving crowd she found all the women more or less disheveled. And they seemed all the prettier and friendlier for that. It was a happy crowd and voices were conspicuously hoarse.
When Madge entered the hotel parlor that evening she found her uncle with guests and among them was Burns Carroll. The presence of the handsome giant affected Madge more impellingly than ever before, yet in some inexplicably different way. She found herself trembling; she sensed a crisis in her feelings for this man and it frightened her. She became conscious suddenly that she had always been afraid of him. Watching Carroll receive the congratulations of many of those present, she saw that he dominated them as he had her. His magnetism was over-powering; his great stature seemed to fill the room; his easy careless assurance emanated from superior strength. When he spoke lightly of the game, of Crane's marvelous catch, of Dalgren's pitching and of his own triple play, it seemed these looming features retreated in perspective—somehow lost their vital significance because he slighted them.
In the light of Carroll's illuminating talk, in the remembrance of Sheldon's bitter denunciation, in the knowledge of Pat Donahue's estimate of a peculiar type of ball-player, Madge Ellston found herself judging the man—bravely trying to resist his charm, to be fair to him and to herself.
Carroll soon made his way to her side and greeted her with his old familiar manner of possession. However irritating it might be to Madge when alone, now it held her bound.
Carroll possessed the elemental attributes of a conqueror. When with him Madge whimsically feared that he would snatch her up in his arms and carry her bodily off, as the warriors of old did with the women they wanted. But she began to believe that the fascination he exercised upon her was merely physical. That gave her pause. Not only was Burns Carroll on trial, but also a very foolish fluttering little moth—herself. It was time enough, however, to be stern with herself after she had tried him.
"Wasn't that a splendid catch of Crane's today?" she asked.
"A lucky stab! Crane has a habit of running round like an ostrich and sticking out a hand to catch a ball. It's a grand-stand play. Why, a good outfielder would have been waiting under that fly."
"Dalgren did fine work in the box, don't you think?"
"Oh, the kid's all right with an old head back of the plate. He's wild, though, and will never make good in fast company. I won his game today. He wouldn't have lasted an inning without me. It was dead wrong for Pat to pitch him. Dalgren simply can't pitch and he hasn't sand enough to learn."
A hot retort trembled upon Madge Ellston's lips, but she withheld it and quietly watched Carroll. How complacent he was, how utterly self-contained!
"And Billie Sheldon—wasn't it good to see him brace? What hitting! . .. That home run!"
"Sheldon flashed up today. That's the worst of such players. This talk of his slump is all rot. When he joined the team he made some lucky hits and the papers lauded him as a comer, but he soon got down to his real form. Why, to break into a game now and then, to shut his eyes and hit a couple on the nose—that's not baseball. Pat's given him ten days' notice, and his release will be a good move for the team. Sheldon's not fast enough for this league."
"I'm sorry. He seemed so promising," replied Madge. "I liked Billy—pretty well."
"Yes, that was evident," said Carroll, firing up. "I never could understand what you saw in him. Why, Sheldon's no good. He—"
Madge turned a white face that silenced Carroll. She excused herself and returned to the parlor, where she had last seen her uncle. Not finding him there, she went into the long corridor and met Sheldon, Dalgren and two more of the players. Madge congratulated the young pitcher and the other players on their brilliant work; and they, not to be outdone, gallantly attributed the day's victory to her presence at the game. Then, without knowing in the least how it came about, she presently found herself alone with Billy, and they were strolling into the music-room.
"Madge, did I brace up?"
The girl risked one quick look at him. How boyish he seemed, how eager! What an altogether different Billie! But was the difference all in him! Somehow, despite a conscious shyness in the moment she felt natural and free, without the uncertainty and restraint that had always troubled her while with him.
"Oh, Billie, that glorious home run!"
"Madge, wasn't that hit a dandy? How I made it is a mystery, but the bat felt like a feather. I thought of you. Tell me—what did you think when I hit that ball over the fence?"
"Billie, I'll never, never tell you."
"Yes—please—I want to know. Didn't you think something—nice of me?"
The pink spots in Madge's cheeks widened to crimson flames.
"Billie, are you still—crazy about me? Now, don't come so close. Can't you behave yourself? And don't break my fingers with you terrible baseball hands.... Well, when you made that hit I just collapsed and I said—"
"Say it! Say it!" implored Billie.
She lowered her face and then bravely raised it.
"I said, 'Billie, I could hug you for that!' ... Billie, let me go! Oh, you mustn't!—please!"
Quite a little while afterward Madge remembered to tell Billie that she had been seeking her uncle. They met him and Pat Donahue, coming out of the parlor.
"Where have you been all evening?" demanded Mr. Ellston.
"Shure it looks as if she's signed a new manager," said Pat, his shrewd eyes twinkling.
The soft glow in Madge's cheeks deepened into tell-tale scarlet; Billie resembled a schoolboy stricken in guilt.
"Aha! so that's it?" queried her uncle.
"Ellston," said Pat. "Billie's home-run drive today recalled his notice an' if I don't miss guess it won him another game—the best game in life."
"By George!" exclaimed Mr. Ellston. "I was afraid it was Carroll!"
He led Madge away and Pat followed with Billie.
"Shure, it was good to see you brace, Billie," said the manager, with a kindly hand on the young man's arm. "I'm tickled to death. That ten days' notice doesn't go. See? I've had to shake up the team but your job is good. I released McReady outright an' traded Carroll to Denver for a catcher and a fielder. Some of the directors hollered murder, an' I expect the fans will roar, but I'm running this team, I'll have harmony among my players. Carroll is a great catcher, but he's a knocker."
# The Winning Ball
## *
One day in July our Rochester club, leader in the Eastern League, had returned to the hotel after winning a double-header from the Syracuse club. For some occult reason there was to be a lay-off next day and then on the following another double-header. These double-headers we hated next to exhibition games. Still a lay-off for twenty-four hours, at that stage of the race, was a Godsend, and we received the news with exclamations of pleasure.
After dinner we were all sitting and smoking comfortably in front of the hotel when our manager, Merritt, came hurriedly out of the lobby. It struck me that he appeared a little flustered.
"Say, you fellars," he said brusquely. "Pack your suits and be ready for the bus at seven-thirty."
For a moment there was a blank, ominous silence, while we assimilated the meaning of his terse speech.
"I've got a good thing on for tomorrow," continued the manager. "Sixty per cent gate receipts if we win. That Guelph team is hot stuff, though."
"Guelph!" exclaimed some of the players suspiciously. "Where's Guelph?"
"It's in Canada. We'll take the night express an' get there tomorrow in time for the game. An' we'll hev to hustle."
Upon Merritt then rained a multiplicity of excuses. Gillinger was not well, and ought to have that day's rest. Snead's eyes would profit by a lay-off. Deerfoot Browning was leading the league in base running, and as his legs were all bruised and scraped by sliding, a manager who was not an idiot would have a care of such valuable runmakers for his team. Lake had "Charley-horse." Hathaway's arm was sore. Bane's stomach threatened gastritis. Spike Doran's finger needed a chance to heal. I was stale, and the other players, three pitchers, swore their arms should be in the hospital.
"Cut it out!" said Merritt, getting exasperated. "You'd all lay down on me—now, wouldn't you? Well, listen to this: McDougal pitched today; he doesn't go. Blake works Friday, he doesn't go. But the rest of you puffed-up, high-salaried stiffs pack your grips quick. See? It'll cost any fresh fellar fifty for missin' the train."
So that was how eleven of the Rochester team found themselves moodily boarding a Pullman en route for Buffalo and Canada. We went to bed early and arose late.
Guelph lay somewhere in the interior of Canada, and we did not expect to get there until 1 o'clock.
As it turned out, the train was late; we had to dress hurriedly in the smoking room, pack our citizen clothes in our grips and leave the train to go direct to the ball grounds without time for lunch.
It was a tired, dusty-eyed, peevish crowd of ball players that climbed into a waiting bus at the little station.
We had never heard of Guelph; we did not care anything about Rube baseball teams. Baseball was not play to us; it was the hardest kind of work, and of all things an exhibition game was an abomination.
The Guelph players, strapping lads, met us with every mark of respect and courtesy and escorted us to the field with a brass band that was loud in welcome, if not harmonious in tune.
Some 500 men and boys trotted curiously along with us, for all the world as if the bus were a circus parade cage filled with striped tigers. What a rustic, motley crowd massed about in and on that ball ground. There must have been 10,000.
The audience was strange to us. The Indians, half-breeds, French-Canadians; the huge, hulking, bearded farmers or traders, or trappers, whatever they were, were new to our baseball experience.
The players themselves, however, earned the largest share of our attention. By the time they had practiced a few moments we looked at Merritt and Merritt looked at us.
These long, powerful, big-handed lads evidently did not know the difference between lacrosse and baseball; but they were quick as cats on their feet, and they scooped up the ball in a way wonderful to see. And throw!—it made a professional's heart swell just to see them line the ball across the diamond.
"Lord! what whips these lads have!" exclaimed Merritt. "Hope we're not up against it. If this team should beat us we wouldn't draw a handful at Toronto. We can't afford to be beaten. Jump around and cinch the game quick. If we get in a bad place, I'll sneak in the 'rabbit.'"
The "rabbit" was a baseball similar in appearance to the ordinary league ball; under its horse-hide cover, however, it was remarkably different.
An ingenious fan, a friend of Merritt, had removed the covers from a number of league balls and sewed them on rubber balls of his own making. They could not be distinguished from the regular article, not even by an experienced professional—until they were hit. Then! The fact that after every bounce one of these rubber balls bounded swifter and higher had given it the name of the "rabbit."
Many a game had the "rabbit" won for us at critical stages. Of course it was against the rules of the league, and of course every player in the league knew about it; still, when it was judiciously and cleverly brought into a close game, the "rabbit" would be in play, and very probably over the fence, before the opposing captain could learn of it, let alone appeal to the umpire.
"Fellars, look at that guy who's goin' to pitch," suddenly spoke up one of the team.
Many as were the country players whom we seasoned and traveled professionals had run across, this twirler outclassed them for remarkable appearance. Moreover, what put an entirely different tinge to our momentary humor was the discovery that he was as wild as a March hare and could throw a ball so fast that it resembled a pea shot from a boy's air gun.
Deerfoot led our batting list, and after the first pitched ball, which he did not see, and the second, which ticked his shirt as it shot past, he turned to us with an expression that made us groan inwardly.
When Deerfoot looked that way it meant the pitcher was dangerous. Deerfoot made no effort to swing at the next ball, and was promptly called out on strikes.
I was second at bat, and went up with some reluctance. I happened to be leading the league in both long distance and safe hitting, and I doted on speed. But having stopped many mean in-shoots with various parts of my anatomy, I was rather squeamish about facing backwoods yaps who had no control.
When I had watched a couple of his pitches, which the umpire called strikes, I gave him credit for as much speed as Rusie. These balls were as straight as a string, singularly without curve, jump, or variation of any kind. I lined the next one so hard at the shortstop that it cracked like a pistol as it struck his hands and whirled him half off his feet. Still he hung to the ball and gave opportunity for the first crash of applause.
"Boys, he's a trifle wild," I said to my team-mates, "but he has the most beautiful ball to hit you ever saw. I don't believe he uses a curve, and when we once time that speed we'll kill it."
Next inning, after old man Hathaway had baffled the Canadians with his wide, tantalizing curves, my predictions began to be verified. Snead rapped one high and far to deep right field. To our infinite surprise, however, the right fielder ran with fleetness that made our own Deerfoot seem slow, and he got under the ball and caught it.
Doran sent a sizzling grasscutter down toward left. The lanky third baseman darted over, dived down, and, coming up with the ball, exhibited the power of a throwing arm that made as all green with envy.
Then, when the catcher chased a foul fly somewhere back in the crowd and caught it, we began to take notice.
"Lucky stabs!" said Merritt cheerfully. "They can't keep that up. We'll drive him to the woods next time."
But they did keep it up; moreover, they became more brilliant as the game progressed. What with Hathaway's heady pitching we soon disposed of them when at the bat; our turns, however, owing to the wonderful fielding of these backwoodsmen, were also fruitless.
Merritt, with his mind ever on the slice of gate money coming if we won, began to fidget and fume and find fault.
"You're a swell lot of champions, now, ain't you?" he observed between innings.
All baseball players like to bat, and nothing pleases them so much as base hits; on the other hand, nothing is quite so painful as to send out hard liners only to see them caught. And it seemed as if every man on our team connected with that lanky twirler's fast high ball and hit with the force that made the bat spring only to have one of these rubes get his big hands upon it.
Considering that we were in no angelic frame of mind before the game started, and in view of Merritt's persistently increasing ill humor, this failure of ours to hit a ball safely gradually worked us into a kind of frenzy. From indifference we passed to determination, and from that to sheer passionate purpose.
Luck appeared to be turning in the sixth inning. With one out, Lake hit a beauty to right. Doran beat an infield grounder and reached first. Hathaway struck out.
With Browning up and me next, the situation looked rather precarious for the Canadians.
"Say, Deerfoot," whispered Merritt, "dump one down the third-base line. He's playin' deep. It's a pipe. Then the bases will be full an' Reddy'll clean up."
In a stage like that Browning was a man absolutely to depend upon. He placed a slow bunt in the grass toward third and sprinted for first. The third baseman fielded the ball, but, being confused, did not know where to throw it.
"Stick it in your basket," yelled Merritt, in a delight that showed how hard he was pulling for the gate money, and his beaming smile as he turned to me was inspiring. "Now, Reddy, it's up to you! I'm not worrying about what's happened so far. I know, with you at bat in a pinch, it's all off!"
Merritt's compliment was pleasing, but it did not augment my purpose, for that already had reached the highest mark. Love of hitting, if no other thing, gave me the thrilling fire to arise to the opportunity. Selecting my light bat, I went up and faced the rustic twirler and softly said things to him.
He delivered the ball, and I could have yelled aloud, so fast, so straight, so true it sped toward me. Then I hit it harder than I had ever hit a ball in my life. The bat sprung, as if it were whalebone. And the ball took a bullet course between center and left. So beautiful a hit was it that I watched as I ran.
Out of the tail of my eye I saw the center fielder running. When I rounded first base I got a good look at this fielder, and though I had seen the greatest outfielders the game ever produced, I never saw one that covered ground so swiftly as he.
On the ball soared, and began to drop; on the fielder sped, and began to disappear over a little hill back of his position. Then he reached up with a long arm and marvelously caught the ball in one hand. He went out of sight as I touched second base, and the heterogeneous crowd knew about a great play to make more noise than a herd of charging buffalo.
In the next half inning our opponents, by clean drives, scored two runs and we in our turn again went out ignominiously. When the first of the eighth came we were desperate and clamored for the "rabbit."
"I've sneaked it in," said Merritt, with a low voice. "Got it to the umpire on the last passed ball. See, the pitcher's got it now. Boys, it's all off but the fireworks! Now, break loose!"
A peculiarity about the "rabbit" was the fact that though it felt as light as the regulation league ball it could not be thrown with the same speed and to curve it was an impossibility.
Bane hit the first delivery from our hoosier stumbling block. The ball struck the ground and began to bound toward short. With every bound it went swifter, longer and higher, and it bounced clear over the shortstop's head. Lake chopped one in front of the plate, and it rebounded from the ground straight up so high that both runners were safe before it came down.
Doran hit to the pitcher. The ball caromed his leg, scooted fiendishly at the second baseman, and tried to run up all over him like a tame squirrel. Bases full!
Hathaway got a safe fly over the infield and two runs tallied. The pitcher, in spite of the help of the umpire, could not locate the plate for Balknap, and gave him a base on balls. Bases full again!
Deerfoot slammed a hot liner straight at the second baseman, which, striking squarely in his hands, recoiled as sharply as if it had struck a wall. Doran scored, and still the bases were filled.
The laboring pitcher began to get rattled; he could not find his usual speed; he knew it, but evidently could not account for it.
When I came to bat, indications were not wanting that the Canadian team would soon be up in the air. The long pitcher delivered the "rabbit," and got it low down by my knees, which was an unfortunate thing for him. I swung on that one, and trotted round the bases behind the runners while the center and left fielders chased the ball.
Gillinger weighed nearly two hundred pounds, and he got all his weight under the "rabbit." It went so high that we could scarcely see it. All the infielders rushed in, and after staggering around, with heads bent back, one of them, the shortstop, managed to get under it. The "rabbit" bounded forty feet out of his hands!
When Snead's grounder nearly tore the third baseman's leg off; when Bane's hit proved as elusive as a flitting shadow; when Lake's liner knocked the pitcher flat, and Doran's fly leaped high out of the center fielder's glove—then those earnest, simple, country ballplayers realized something was wrong. But they imagined it was in themselves, and after a short spell of rattles, they steadied up and tried harder than ever. The motions they went through trying to stop that jumping jackrabbit of a ball were ludicrous in the extreme.
Finally, through a foul, a short fly, and a scratch hit to first, they retired the side and we went into the field with the score 14 to 2 in our favor.
But Merritt had not found it possible to get the "rabbit" out of play!
We spent a fatefully anxious few moments squabbling with the umpire and captain over the "rabbit." At the idea of letting those herculean railsplitters have a chance to hit the rubber ball we felt our blood run cold.
"But this ball has a rip in it," blustered Gillinger. He lied atrociously. A microscope could not have discovered as much as a scratch in that smooth leather.
"Sure it has," supplemented Merritt, in the suave tones of a stage villain. "We're used to playing with good balls."
"Why did you ring this one in on us?" asked the captain. "We never threw out this ball. We want a chance to hit it."
That was just the one thing we did not want them to have. But fate played against us.
"Get up on your toes, now an' dust," said Merritt. "Take your medicine, you lazy sit-in-front-of-the-hotel stiffs! Think of pay day!"
Not improbably we all entertained the identical thought that old man Hathaway was the last pitcher under the sun calculated to be effective with the "rabbit." He never relied on speed; in fact, Merritt often scornfully accused him of being unable to break a pane of glass; he used principally what we called floaters and a change of pace. Both styles were absolutely impractical with the "rabbit."
"It's comin' to us, all right, all right!" yelled Deerfoot to me, across the intervening grass. I was of the opinion that it did not take any genius to make Deerfoot's ominous prophecy.
Old man Hathaway gazed at Merritt on the bench as if he wished the manager could hear what he was calling him and then at his fellow-players as if both to warn and beseech them. Then he pitched the "rabbit."
Crack!
The big lumbering Canadian rapped the ball at Crab Bane. I did not see it, because it went so fast, but I gathered from Crab's actions that it must have been hit in his direction. At any rate, one of his legs flopped out sidewise as if it had been suddenly jerked, and he fell in a heap. The ball, a veritable "rabbit" in its wild jumps, headed on for Deerfoot, who contrived to stop it with his knees.
The next batter resembled the first one, and the hit likewise, only it leaped wickedly at Doran and went through his hands as if they had been paper. The third man batted up a very high fly to Gillinger. He clutched at it with his huge shovel hands, but he could not hold it. The way he pounced upon the ball, dug it out of the grass, and hurled it at Hathaway, showed his anger.
Obviously Hathaway had to stop the throw, for he could not get out of the road, and he spoke to his captain in what I knew were no complimentary terms.
Thus began retribution. Those husky lads continued to hammer the "rabbit" at the infielders and as it bounced harder at every bounce so they batted harder at every bat.
Another singular feature about the "rabbit" was the seeming impossibility for professionals to hold it. Their familiarity with it, their understanding of its vagaries and inconsistencies, their mortal dread made fielding it a much more difficult thing than for their opponents.
By way of variety, the lambasting Canadians commenced to lambast a few over the hills and far away, which chased Deerfoot and me until our tongues lolled out.
Every time a run crossed the plate the motley crowd howled, roared, danced and threw up their hats. The members of the batting team pranced up and down the side lines, giving a splendid imitation of cannibals celebrating the occasion of a feast.
Once Snead stooped down to trap the "rabbit," and it slipped through his legs, for which his comrades jeered him unmercifully. Then a brawny batter sent up a tremendously high fly between short and third.
"You take it!" yelled Gillinger to Bane.
"You take it!" replied the Crab, and actually walked backward. That ball went a mile high. The sky was hazy, gray, the most perplexing in which to judge a fly ball. An ordinary fly gave trouble enough in the gauging.
Gillinger wandered around under the ball for what seemed an age. It dropped as swiftly as a rocket shoots upward. Gillinger went forward in a circle, then sidestepped, and threw up his broad hands. He misjudged the ball, and it hit him fairly on the head and bounced almost to where Doran stood at second.
Our big captain wilted. Time was called. But Gillinger, when he came to, refused to leave the game and went back to third with a lump on his head as large as a goose egg.
Every one of his teammates was sorry, yet every one howled in glee. To be hit on the head was the unpardonable sin for a professional.
Old man Hathaway gradually lost what little speed he had, and with it his nerve. Every time he pitched the "rabbit" he dodged. That was about the funniest and strangest thing ever seen on a ball field. Yet it had an element of tragedy.
Hathaway's expert contortions saved his head and body on divers occasions, but presently a low bounder glanced off the grass and manifested an affinity for his leg.
We all knew from the crack and the way the pitcher went down that the "rabbit" had put him out of the game. The umpire called time, and Merritt came running on the diamond.
"Hard luck, old man," said the manager. "That'll make a green and yellow spot all right. Boys, we're still two runs to the good. There's one out, an' we can win yet. Deerfoot, you're as badly crippled as Hathaway. The bench for yours. Hooker will go to center, an' I'll pitch."
Merritt's idea did not strike us as a bad one. He could pitch, and he always kept his arm in prime condition. We welcomed him into the fray for two reasons—because he might win the game, and because he might be overtaken by the baseball Nemesis.
While Merritt was putting on Hathaway's baseball shoes, some of us endeavored to get the "rabbit" away from the umpire, but he was too wise.
Merritt received the innocent-looking ball with a look of mingled disgust and fear, and he summarily ordered us to our positions.
Not far had we gone, however, when we were electrified by the umpire's sharp words:
"Naw! Naw, you don't. I saw you change the ball I gave you fer one in your pocket! Naw! You don't come enny of your American dodges on us! Gimmee thet ball, an' you use the other, or I'll stop the game."
Wherewith the shrewd umpire took the ball from Merritt's hand and fished the "rabbit" from his pocket. Our thwarted manager stuttered his wrath. "Y-you be-be-wh-whiskered y-yap! I'll g-g-give—"
What dire threat he had in mind never materialized, for he became speechless. He glowered upon the cool little umpire, and then turned grandly toward the plate.
It may have been imagination, yet I made sure Merritt seemed to shrink and grow smaller before he pitched a ball. For one thing the plate was uphill from the pitcher's box, and then the fellow standing there loomed up like a hill and swung a bat that would have served as a wagon tongue. No wonder Merritt evinced nervousness. Presently he whirled and delivered the ball.
Bing!
A dark streak and a white puff of dust over second base showed how safe that hit was. By dint of manful body work, Hooker contrived to stop the "rabbit" in mid-center. Another run scored. Human nature was proof against this temptation, and Merritt's players tendered him manifold congratulations and dissertations.
"Grand, you old skinflint, grand!"
"There was a two-dollar bill stickin' on thet hit. Why didn't you stop it?"
"Say, Merritt, what little brains you've got will presently be ridin' on the 'rabbit.'"
"You will chase up these exhibition games!"
"Take your medicine now. Ha! Ha! Ha!"
After these merciless taunts, and particularly after the next slashing hit that tied the score, Merritt looked appreciably smaller and humbler.
He threw up another ball, and actually shied as it neared the plate.
The giant who was waiting to slug it evidently thought better of his eagerness as far as that pitch was concerned, for he let it go by.
Merritt got the next ball higher. With a mighty swing, the batsman hit a terrific liner right at the pitcher.
Quick as lightning, Merritt wheeled, and the ball struck him with the sound of two boards brought heavily together with a smack.
Merritt did not fall; he melted to the ground and writhed while the runners scored with more tallies than they needed to win.
What did we care! Justice had been done us, and we were unutterably happy. Crabe Bane stood on his head; Gillinger began a war dance; old man Hathaway hobbled out to the side lines and whooped like an Indian; Snead rolled over and over in the grass. All of us broke out into typical expressions of baseball frenzy, and individual ones illustrating our particular moods.
Merritt got up and made a dive for the ball. With face positively flaming he flung it far beyond the merry crowd, over into a swamp. Then he limped for the bench. Which throw ended the most memorable game ever recorded to the credit of the "rabbit."
# False Colors
## *
"Fate has decreed more bad luck for Salisbury in Saturday's game with Bellville. It has leaked out that our rivals will come over strengthened by a 'ringer,' no less than Yale's star pitcher, Wayne. We saw him shut Princeton out in June, in the last game of the college year, and we are not optimistic in our predictions as to what Salisbury can do with him. This appears a rather unfair procedure for Bellville to resort to. Why couldn't they come over with their regular team? They have won a game, and so have we; both games were close and brilliant; the deciding game has roused unusual interest. We are inclined to resent Bellville's methods as unsportsmanlike. All our players can do is to go into this game on Saturday and try the harder to win."
Wayne laid down the Salisbury Gazette, with a little laugh of amusement, yet feeling a vague, disquieting sense of something akin to regret.
"Pretty decent of that chap not to roast me," he soliloquized.
Somewhere he had heard that Salisbury maintained an unsalaried team. It was notorious among college athletes that the Bellville Club paid for the services of distinguished players. And this in itself rather inclined Wayne to sympathize with Salisbury. He knew something of the struggles of a strictly amateur club to cope with its semi-professional rivals.
As he was sitting there, idly tipped back in a comfortable chair, dreaming over some of the baseball disasters he had survived before his college career, he saw a young man enter the lobby of the hotel, speak to the clerk, and then turn and come directly toward the window where Wayne was sitting.
"Are yon Mr. Wayne, the Yale pitcher?" he asked eagerly. He was a fair-haired, clean-cut young fellow, and his voice rang pleasantly.
"Guilty," replied Wayne.
"My name's Huling. I'm captain of the Salisbury nine. Just learned you were in town and are going to pitch against us tomorrow. Won't you walk out into the grounds with me now? You might want to warm up a little."
"Thank you, yes, I will. Guess I won't need my suit. I'll just limber up, and give my arm a good rub."
It struck Wayne before they had walked far that Huling was an amiable and likable chap. As the captain of the Salisbury nine, he certainly had no reason to be agreeable to the Morristown "ringer," even though Wayne did happen to be a famous Yale pitcher.
The field was an oval, green as an emerald, level as a billiard table and had no fences or stands to obstruct the open view of the surrounding wooded country. On each side of the diamond were rows of wooden benches, and at one end of the field stood a little clubhouse.
Wayne took off his coat, and tossed a ball for a while to an ambitious youngster, and then went into the clubhouse, where Huling introduced him to several of his players. After a good rubdown, Wayne thanked Huling for his courtesy, and started out, intending to go back to town.
"Why not stay to see us practice?" asked the captain. "We're not afraid you'll size up our weaknesses. As a matter of fact, we don't look forward to any hitting stunts tomorrow, eh, Burns? Burns, here, is our leading hitter, and he's been unusually noncommittal since he heard who was going to pitch for Bellville."
"Well, I wouldn't give a whole lot for my prospects of a home run tomorrow," said Burns, with a laugh.
Wayne went outside, and found a seat in the shade. A number of urchins had trooped upon the green field, and carriages and motors were already in evidence. By the time the players came out of the dressing room, ready for practice, there was quite a little crowd in attendance.
Despite Wayne's hesitation, Huling insisted upon introducing him to friends, and finally hauled him up to a big touring car full of girls. Wayne, being a Yale pitcher, had seen several thousand pretty girls, but the group in that automobile fairly dazzled him. And the last one to whom Huling presented him—with the words: "Dorothy, this is Mr. Wayne, the Yale pitcher, who is to play with Bellville tomorrow; Mr. Wayne, my sister"—was the girl he had known he would meet some day.
"Climb up, Mr. Wayne. We can make room," invited Miss Huling.
Wayne thought the awkwardness with which he found a seat beside her was unbecoming to a Yale senior. But, considering she was the girl he had been expecting to discover for years, his clumsiness bespoke the importance of the event. The merry laughter of the girls rang in his ears. Presently, a voice detached itself from the others, and came floating softly to him.
"Mr. Wayne, so you're going to wrest our laurels from us?" asked Miss Huling.
"I don't know—I'm not infallible—I've been beaten."
"When? Not this season?" she inquired quickly, betraying a knowledge of his record that surprised and pleased him. "Mr. Wayne, I was at the Polo Grounds on June fifteenth."
Her white hand lightly touched the Princeton pin at her neck. Wayne roused suddenly out of his trance. The girl was a Princeton girl! The gleam of her golden hair, the flash of her blue eyes, became clear in sight.
"I'm very pleased to hear it," he replied.
"It was a great game, Mr. Wayne, and you may well be proud of your part in winning it. I shouldn't be surprised if you treated the Salisbury team to the same coat of whitewash. We girls are up in arms. Our boys stood a fair chance to win this game, but now there's a doubt. By the way, are you acquainted in Bellville?"
"No. I met Reed, the Bellville captain, in New York this week. He had already gotten an extra pitcher—another ringer—for this game, but he said he preferred me, if it could be arranged."
While conversing, Wayne made note of the fact that the other girls studiously left him to Miss Huling. If the avoidance had not been so marked, he would never have thought of it.
"Mr. Wayne, if your word is not involved—will you change your mind and pitch tomorrow's game for us instead of Bellville?"
Quite amazed, Wayne turned squarely to look at Miss Huling. Instead of disarming his quick suspicion, her cool, sweet voice, and brave, blue eyes confirmed it. The charms of the captain's sister were to be used to win him away from the Bellville nine. He knew the trick; it had been played upon him before.
But never had any other such occasion given him a feeling of regret. This case was different. She was the girl. And she meant to flirt with him, to use her eyes for all they were worth to encompass the Waterloo of the rival team.
No, he had made a mistake, after all—she was not the real girl. Suddenly conscious of a little shock of pain, he dismissed that dream girl from his mind, and determined to meet Miss Huling half way in her game. He could not flirt as well as he could pitch; still, he was no novice.
"Well, Miss Huling, my word certainly is not involved. But as to pitching for Salisbury—that depends."
"Upon what?"
"Upon what there is in it."
"Mr. Wayne, you mean—money? Oh, I know. My brother Rex told me how you college men are paid big sums. Our association will not give a dollar, and, besides, my brother knows nothing of this. But we girls are heart and soul on winning this game. We'll—"
"Miss Huling, I didn't mean remuneration in sordid cash," interrupted Wayne, in a tone that heightened the color in her cheeks.
Wayne eyed her keenly with mingled emotions. Was that rose-leaf flush in her cheeks natural? Some girls could blush at will. Were the wistful eyes, the earnest lips, only shamming? It cost him some bitterness to decide that they were. Her beauty fascinated, while it hardened him. Eternally, the beauty of women meant the undoing of men, whether they played the simple, inconsequential game of baseball, or the great, absorbing, mutable game of life.
The shame of the situation for him was increasingly annoying, inasmuch as this lovely girl should stoop to flirtation with a stranger, and the same time draw him, allure him, despite the apparent insincerity.
"Miss Huling, I'll pitch your game for two things," he continued.
"Name them."
"Wear Yale blue in place of that orange-and-black Princeton pin."
"I will." She said it with a shyness, a look in her eyes that made Wayne wince. What a perfect little actress! But there seemed just a chance that this was not deceit. For an instant he wavered, held back by subtle, finer intuition; then he beat down the mounting influence of truth in those dark-blue eyes, and spoke deliberately:
"The other thing is—if I win the game—a kiss."
Dorothy Huling's face flamed scarlet. But this did not affect Wayne so deeply, though it showed him his mistake, as the darkening shadow of disappointment in her eyes. If she had been a flirt, she would have been prepared for rudeness. He began casting about in his mind for some apology, some mitigation of his offense; but as he was about to speak, the sudden fading of her color, leaving her pale, and the look in her proud, dark eyes disconcerted him out of utterance.
"Certainly, Mr. Wayne. I agree to your price if you win the game."
But how immeasurable was the distance between the shy consent to wear Yale blue, and the pale, surprised agreement to his second proposal! Wayne experienced a strange sensation of personal loss.
While he endeavored to find his tongue, Miss Huling spoke to one of the boys standing near, and he started off on a run for the field. Presently Huling and the other players broke for the car, soon surrounding it in breathless anticipation.
"Wayne, is it straight? You'll pitch for us tomorrow?" demanded the captain, with shining eyes.
"Surely I will. Bellville don't need me. They've got Mackay, of Georgetown," replied Wayne.
Accustomed as he was to being mobbed by enthusiastic students and admiring friends, Wayne could not but feel extreme embarrassment at the reception accorded him now. He felt that he was sailing under false colors. The boys mauled him, the girls fluttered about him with glad laughter. He had to tear himself away; and when he finally reached his hotel, he went to his room, with his mind in a tumult.
Wayne cursed himself roundly; then he fell into deep thought. He began to hope he could retrieve the blunder. He would win the game; he would explain to her the truth; he would ask for an opportunity to prove he was worthy of her friendship; he would not mention the kiss. This last thought called up the soft curve of her red lips and that it was possible for him to kiss her made the temptation strong.
His sleep that night was not peaceful and dreamless. He awakened late, had breakfast sent to his room, and then took a long walk out into the country. After lunch he dodged the crowd in the hotel lobby, and hurried upstairs, where he put on his baseball suit. The first person he met upon going down was Reed, the Bellville man.
"What's this I hear, Wayne, about your pitching for Salisbury today? I got your telegram."
"Straight goods," replied Wayne.
"But I thought you intended to pitch for us?"
"I didn't promise, did I?"
"No. Still, it looks fishy to me."
"You've got Mackay, haven't you?"
"Yes. The truth is, I intended to use you both."
"Well, I'll try to win for Salisbury. Hope there's no hard feeling."
"Not at all. Only if I didn't have the Georgetown crack, I'd yell murder. As it is, we'll trim Salisbury anyway."
"Maybe," answered Wayne, laughing. "It's a hot day, and my arm feels good."
When Wayne reached the ball grounds, he thought he had never seen a more inspiring sight. The bright green oval was surrounded by a glittering mass of white and blue and black. Out along the foul lines were carriages, motors, and tally-hos, brilliant with waving fans and flags. Over the field murmured the low hum of many voices.
"Here you are!" cried Huling, making a grab for Wayne. "Where were you this morning? We couldn't find you. Come! We've got a minute before the practice whistle blows, and I promised to exhibit you."
He hustled Wayne down the first-base line, past the cheering crowd, out among the motors, to the same touring car that he remembered. A bevy of white-gowned girls rose like a covey of ptarmigans, and whirled flags of maroon and gray.
Dorothy Huling wore a bow of Yale blue upon her breast, and Wayne saw it and her face through a blur.
"Hurry, girls; get it over. We've got to practice," said the captain.
In the merry melee some one tied a knot of ribbon upon Wayne. Who it was he did not know; he saw only the averted face of Dorothy Huling. And as he returned to the field with a dull pang, he determined he would make her indifference disappear with the gladness of a victory for her team.
The practice was short, but long enough for Wayne to locate the glaring weakness of Salisbury at shortstop and third base. In fact, most of the players of his team showed rather poor form; they were overstrained, and plainly lacked experience necessary for steadiness in an important game.
Burns, the catcher, however, gave Wayne confidence. He was a short, sturdy youngster, with all the earmarks of a coming star. Huling, the captain, handled himself well at first base. The Bellville players were more matured, and some of them were former college cracks. Wayne saw that he had his work cut out for him.
The whistle blew. The Bellville team trotted to their position in the field; the umpire called play, and tossed a ball to Mackay, the long, lean Georgetown pitcher.
Wells, the first batter, fouled out; Stamford hit an easy bounce to the pitcher, and Clews put up a little Texas leaguer—all going out, one, two, three, on three pitched balls.
The teams changed from bat to field. Wayne faced the plate amid vociferous cheering. He felt that he could beat this team even without good support. He was in the finest condition, and his arm had been resting for ten days. He knew that if he had control of his high inshoot, these Bellville players would feel the whiz of some speed under their chins.
He struck Moore out, retired Reed on a measly fly, and made Clark hit a weak grounder to second; and he walked in to the bench assured of the outcome. On some days he had poor control; on others his drop ball refused to work properly; but, as luck would have it, he had never had greater speed or accuracy, or a more bewildering fast curve than on this day, when he meant to win a game for a girl.
"Boys, I've got everything," he said to his fellow-players, calling them around him. "A couple of runs will win for us. Now, listen, I know Mackay. He hasn't any speed, or much of a curve. All he's got is a teasing slow ball and a foxy head. Don't be too anxious to hit. Make him put 'em over."
But the Salisbury players were not proof against the tempting slow balls that Mackay delivered. They hit at wide curves far off the plate and when they did connect with the ball it was only to send an easy chance to the infielders.
The game seesawed along, inning after inning; it was a pitcher's battle that looked as if the first run scored would win the game. Mackay toyed with the Salisbury boys; it was his pleasure to toss up twisting, floating balls that could scarcely be hit out of the diamond. Wayne had the Bellville players utterly at his mercy; he mixed up his high jump and fast drop so cleverly, with his sweeping out-curve, that his opponents were unable to gauge his delivery at all.
In the first of the seventh, Barr for Bellville hit a ball which the third baseman should have fielded. But he fumbled. The second batter sent a fly to shortstop, who muffed it. The third hitter reached his base on another error by an infielder. Here the bases were crowded, and the situation had become critical all in a moment. Wayne believed the infield would go to pieces, and lose the game, then and there, if another hit went to short or third.
"Steady up, boys," called Wayne, and beckoned for his catcher.
"Burns, it's up to you and me," he said, in a low tone. "I've got to fan the rest of these hitters. You're doing splendidly. Now, watch close for my drop. Be ready to go down on your knees. When I let myself out, the ball generally hits the ground just back of the plate."
"Speed 'em over!" said Burns, his sweaty face grim and determined. "I'll get in front of 'em."
The head of the batting list was up for Bellville, and the whole Bellville contingent on the side lines rose and yelled and cheered.
Moore was a left handed hitter, who choked his bat up short, and poked at the ball. He was a good bunter, and swift on his feet. Wayne had taken his measure, as he had that of the other players, earlier in the game; and he knew it was good pitching to keep the ball in close to Moore's hands, so that if he did hit it, the chances were it would not go safe.
Summoning all his strength, Wayne took his long swing and shot the ball over the inside corner with terrific speed.
One strike!
Wayne knew it would not do to waste any balls if he wished to maintain that speed, so he put the second one in the same place. Moore struck too late.
Two strikes!
Then Burns signed for the last drop. Wayne delivered it with trepidation, for it was a hard curve to handle. Moore fell all over himself trying to hit it. Little Burns dropped to his knees to block the vicious curve. It struck the ground, and, glancing, boomed deep on the breast protector.
How the Salisbury supporters roared their approval! One man out—the bases full—with Reed, the slugging captain, at bat!
If Reed had a weakness, Wayne had not discovered it yet, although Reed had not hit safely. The captain stood somewhat back from the plate, a fact that induced Wayne to try him with the speedy outcurve. Reed lunged with a powerful swing, pulling away from the plate, and he missed the curve by a foot.
Wayne did not need to know any more. Reed had made his reputation slugging straight balls from heedless pitchers. He chopped the air twice more, and flung his bat savagely to the ground.
"Two out—play the hitter!" called Wayne to his team.
Clark, the third man up, was the surest batter on the Bellville team. He looked dangerous. He had made the only hit so far to the credit of his team. Wayne tried to work him on a high, fast ball close in. Clark swung freely and cracked a ripping liner to left. Half the crowd roared, and then groaned, for the beautiful hit went foul by several yards. Wayne wisely decided to risk all on his fast drop. Clark missed the first, fouled the second.
Two strikes!
Then he waited. He cooly let one, two, three of the fast drops go by without attempting to hit them. Burns valiantly got his body in front of them. These balls were all over the plate, but too low to be called strikes. With two strikes, and three balls, and the bases full, Clark had the advantage.
Tight as the place was, Wayne did not flinch. The game depended practically upon the next ball delivered. Wayne craftily and daringly decided to use another fast drop, for of all his assortment that would be the one least expected by Clark. But it must be started higher, so that in case Clark made no effort to swing, it would still be a strike.
Gripping the ball with a clinched hand, Wayne swung sharply, and drove it home with the limit of his power. It sped like a bullet, waist high, and just before reaching the plate darted downward, as if it had glanced on an invisible barrier.
Clark was fooled completely and struck futilely. But the ball caromed from the hard ground, hit Burns with a resounding thud, and bounced away. Clark broke for first, and Moore dashed for home. Like a tiger the little catcher pounced upon the ball, and, leaping back into line, blocked the sliding Moore three feet from the plate.
Pandemonium burst loose among the Salisbury adherents. The men bawled, the women screamed, the boys shrieked, and all waved their hats and flags, and jumped up and down, and manifested symptoms of baseball insanity.
In the first of the eighth inning, Mackay sailed up the balls like balloons, and disposed of three batters on the same old weak hits to his clever fielders. In the last of the eighth, Wayne struck out three more Bellville players.
"Burns, you're up," said Wayne, who, in his earnestness to win, kept cheering his comrades. "Do something. Get your base any way you can. Get in front of one. We must score this inning."
Faithful, battered Burns cunningly imposed his hip over the plate and received another bruise in the interests of his team. The opposing players furiously stormed at the umpire for giving him his base, but Burns' trick went through. Burnett bunted skilfully, sending Burns to second. Cole hit a fly to center. Then Huling singled between short and third.
It became necessary for the umpire to delay the game while he put the madly leaping boys back off the coaching lines. The shrill, hilarious cheering gradually died out, and the field settled into a forced quiet.
Wayne hurried up to the plate and took his position. He had always been a timely hitter, and he gritted his teeth in his resolve to settle this game. Mackay whirled his long arm, wheeled, took his long stride, and pitched a slow, tantalizing ball that seemed never to get anywhere. But Wayne waited, timed it perfectly, and met it squarely.
The ball flew safely over short, and but for a fine sprint and stop by the left fielder, would have resulted in a triple, possibly a home run. As it was, Burns and Huling scored; and Wayne, by a slide, reached second base. When he arose and saw the disorderly riot, and heard the noise of that well-dressed audience, he had a moment of exultation. Then Wells flew out to center ending the chances for more runs.
As Wayne received the ball in the pitcher's box, he paused and looked out across the field toward a white-crowned motor car, and he caught a gleam of Dorothy Huling's golden hair, and wondered if she were glad.
For nothing short of the miraculous could snatch this game from him now. Burns had withstood a severe pounding, but he would last out the inning, and Wayne did not take into account the rest of the team. He opened up with no slackening of his terrific speed, and he struck out the three remaining batters on eleven pitched balls. Then in the rising din he ran for Burns and gave him a mighty hug.
"You made the gamest stand of any catcher I ever pitched to," he said warmly.
Burns looked at his quivering, puffed, and bleeding hands, and smiled as if to say that this was praise to remember, and reward enough. Then the crowd swooped down on them, and they were swallowed up in the clamor and surge of victory. When Wayne got out of the thick and press of it, he made a bee line for his hotel, and by running a gauntlet managed to escape.
Resting, dressing, and dining were matters which he went through mechanically, with his mind ever on one thing. Later, he found a dark corner of the porch and sat there waiting, thinking. There was to be a dance given in honor of the team that evening at the hotel. He watched the boys and girls pass up the steps. When the music commenced, he arose and went into the hall. It was bright with white gowns, and gay with movement.
"There he is. Grab him, somebody," yelled Huling.
"Do something for me, quick," implored Wayne of the captain, as he saw the young people wave toward him.
"Salisbury is yours tonight," replied Huling
"Ask your sister to save me one dance."
Then he gave himself up. He took his meed of praise and flattery, and he withstood the battery of arch eyes modestly, as became the winner of many fields. But even the reception after the Princeton game paled in comparison with this impromptu dance.
She was here. Always it seemed, while he listened or talked or danced, his eyes were drawn to a slender, graceful form, and a fair face crowned with golden hair. Then he was making his way to where she stood near one of the open windows.
He never knew what he said to her, nor what reply she made, but she put her arm in his, and presently they were gliding over the polished floor. To Wayne the dance was a dream. He led her through the hall and out upon the balcony, where composure strangely came to him.
"Mr. Wayne, I have to thank you for saving the day for us. You pitched magnificently."
"I would have broken my arm to win that game," burst out Wayne. "Miss Huling, I made a blunder yesterday. I thought there was a conspiracy to persuade me to throw down Bellville. I've known of such things, and I resented it. You understand what I thought. I humbly offer my apologies, and beg that you forget the rude obligation I forced upon you."
How cold she was! How unattainable in that moment! He caught his breath, and rushed on.
"Your brother and the management of the club have asked me to pitch for Salisbury the remainder of the season. I shall be happy to—if—"
"If what?" She was all alive now, flushing warmly, dark eyes alight, the girl of his dreams.
"If you will forgive me—if you will let me be your friend—if—Miss Huling, you will again wear that bit of Yale blue."
"If, Mr. Wayne, you had very sharp eyes you would have noticed that I still wear it!"
# The Manager of Madden's Hill
## *
Willie Howarth loved baseball. He loved it all the more because he was a cripple. The game was more beautiful and wonderful to him because he would never be able to play it. For Willie had been born with one leg shorter than the other; he could not run and at 11 years of age it was all he could do to walk with a crutch.
Nevertheless Willie knew more about baseball than any other boy on Madden's Hill. An uncle of his had once been a ballplayer and he had taught Willie the fine points of the game. And this uncle's ballplayer friends, who occasionally visited him, had imparted to Willie the vernacular of the game. So that Willie's knowledge of players and play, and particularly of the strange talk, the wild and whirling words on the lips of the real baseball men, made him the envy of every boy on Madden's Hill, and a mine of information. Willie never missed attending the games played on the lots, and he could tell why they were won or lost.
Willie suffered considerable pain, mostly at night, and this had given him a habit of lying awake in the dark hours, grieving over that crooked leg that forever shut him out of the heritage of youth. He had kept his secret well; he was accounted shy because he was quiet and had never been able to mingle with the boys in their activity. No one except his mother dreamed of the fire and hunger and pain within his breast. His school-mates called him "Daddy." It was a name given for his bent shoulders, his labored gait and his thoughtful face, too old for his years. And no one, not even his mother, guessed how that name hurt Willie.
It was a source of growing unhappiness with Willie that the Madden's Hill boys were always beaten by the other teams of the town. He really came to lose his sadness over his own misfortune in pondering on the wretched play of the Madden's Hill baseball club. He had all a boy's pride in the locality where he lived. And when the Bogg's Farm team administered a crushing defeat to Madden's Hill, Willie grew desperate.
Monday he met Lane Griffith, the captain of the Madden's Hill nine.
"Hello, Daddy," said Lane. He was a big, aggressive boy, and in a way had a fondness for Willie.
"Lane, you got an orful trimmin' up on the Boggs. What 'd you wanter let them country jakes beat you for?"
"Aw, Daddy, they was lucky. Umpire had hay-seed in his eyes! Robbed us! He couldn't see straight. We'll trim them down here Saturday."
"No, you won't—not without team work. Lane, you've got to have a manager."
"Durn it! Where 're we goin' to get one?" Lane blurted out.
"You can sign me. I can't play, but I know the game. Let me coach the boys."
The idea seemed to strike Capt. Griffith favorably. He prevailed upon all the boys living on Madden's Hill to come out for practice after school. Then he presented them to the managing coach. The boys were inclined to poke fun at Daddy Howarth and ridicule him; but the idea was a novel one and they were in such a state of subjection from many beatings that they welcomed any change. Willie sat on a bench improvised from a soap box and put them through a drill of batting and fielding. The next day in his coaching he included bunting and sliding. He played his men in different positions and for three more days he drove them unmercifully.
When Saturday came, the day for the game with Bogg's Farm, a wild protest went up from the boys. Willie experienced his first bitterness as a manager. Out of forty aspirants for the Madden's Hill team he could choose but nine to play the game. And as a conscientious manager he could use no favorites. Willie picked the best players and assigned them to positions that, in his judgment, were the best suited to them. Bob Irvine wanted to play first base and he was down for right field. Sam Wickhart thought he was the fastest fielder, and Willie had him slated to catch. Tom Lindsay's feelings were hurt because he was not to play in the infield. Eddie Curtis suffered a fall in pride when he discovered he was not down to play second base. Jake Thomas, Tay-Tay Mohler and Brick Grace all wanted to pitch. The manager had chosen Frank Price for that important position, and Frank's one ambition was to be a shortstop.
So there was a deadlock. For a while there seemed no possibility of a game. Willie sat on the bench, the center of a crowd of discontented, quarreling boys. Some were jealous, some were outraged, some tried to pacify and persuade the others. All were noisy. Lane Griffith stood by his manager and stoutly declared the players should play the positions to which they had been assigned or not at all. And he was entering into a hot argument with Tom Lindsay when the Bogg's Farm team arrogantly put in an appearance.
The way that team from the country walked out upon the field made a great difference. The spirit of Madden's Hill roused to battle. The game began swiftly and went on wildly. It ended almost before the Hill boys realized it had commenced. They did not know how they had won but they gave Daddy Howarth credit for it. They had a bonfire that night to celebrate the victory and they talked baseball until their parents became alarmed and hunted them up.
Madden's Hill practiced all that next week and on Saturday beat the Seventh Ward team. In four more weeks they had added half a dozen more victories to their record. Their reputation went abroad. They got uniforms, and baseball shoes with spikes, and bats and balls and gloves. They got a mask, but Sam Wickhart refused to catch with it.
"Sam, one of these days you'll be stoppin' a high inshoot with your eye," sagely remarked Daddy Howarth. "An' then where'll I get a catcher for the Natchez game?"
Natchez was the one name on the lips of every Madden's Hill boy. For Natchez had the great team of the town and, roused by the growing repute of the Hill club, had condescended to arrange a game. When that game was scheduled for July Fourth Daddy Howarth set to driving his men. Early and late he had them out. This manager, in keeping with all other famous managers, believed that batting was the thing which won games. He developed a hard-hitting team. He kept everlastingly at them to hit and run, hit and run.
On the Saturday before the Fourth, Madden's Hill had a game to play that did not worry Daddy and he left his team in charge of the captain.
"Fellers, I'm goin' down to the Round House to see Natchez play. I'll size up their game," said Daddy.
When he returned he was glad to find that his team had won its ninth straight victory, but he was not communicative in regard to the playing of the Natchez club. He appeared more than usually thoughtful.
The Fourth fell on Tuesday. Daddy had the boys out Monday and he let them take only a short, sharp practice. Then he sent them home. In his own mind, Daddy did not have much hope of beating Natchez. He had been greatly impressed by their playing, and one inning toward the close of the Round House game they had astonished him with the way they suddenly seemed to break loose and deluge their opponents in a flood of hits and runs. He could not understand this streak of theirs—for they did the same thing every time they played—and he was too good a baseball student to call it luck.
He had never wanted anything in his life, not even to have two good legs, as much as he wanted to beat Natchez. For the Madden's Hill boys had come to believe him infallible. He was their idol. They imagined they had only to hit and run, to fight and never give up, and Daddy would make them win. There was not a boy on the team who believed that Natchez had a chance. They had grown proud and tenacious of their dearly won reputation. First of all, Daddy thought of his team and their loyalty to him; then he thought of the glory lately come to Madden's Hill, and lastly of what it meant to him to have risen from a lonely watcher of the game—a cripple who could not even carry a bat—to manager of the famous Hill team. It might go hard with the boys to lose this game, but it would break his heart.
From time out of mind there had always been rivalry between Madden's Hill and Natchez. And there is no rivalry so bitter as that between boys. So Daddy, as he lay awake at night planning the system of play he wanted to use, left out of all account any possibility of a peaceful game. It was comforting to think that if it came to a fight Sam and Lane could hold their own with Bo Stranathan and Slugger Blandy.
In the managing of his players Daddy observed strict discipline. It was no unusual thing for him to fine them. On practice days and off the field they implicitly obeyed him. During actual play, however, they had evinced a tendency to jump over the traces. It had been his order for them not to report at the field Tuesday until 2 o'clock. He found it extremely difficult to curb his own inclination to start before the set time. And only the stern duty of a man to be an example to his players kept Daddy at home.
He lived near the ball grounds, yet on this day, as he hobbled along on his crutch, he thought the distance interminably long, and for the first time in weeks the old sickening resentment at his useless leg knocked at his heart. Manfully Daddy refused admittance to that old gloomy visitor. He found comfort and forgetfulness in the thought that no strong and swift-legged boy of his acquaintance could do what he could do.
Upon arriving at the field Daddy was amazed to see such a large crowd. It appeared that all the boys and girls in the whole town were in attendance, and, besides, there was a sprinkling of grown-up people interspersed here and there around the diamond. Applause greeted Daddy's appearance and members of his team escorted him to the soap-box bench.
Daddy cast a sharp eye over the Natchez players practicing on the field. Bo Stranathan had out his strongest team. They were not a prepossessing nine. They wore soiled uniforms that did not match in cut or color. But they pranced and swaggered and strutted! They were boastful and boisterous. It was a trial for any Madden's Hill boy just to watch them.
"Wot a swelled bunch!" exclaimed Tom Lindsay.
"Fellers, if Slugger Blandy tries to pull any stunt on me today he'll get a swelleder nut," growled Lane Griffith.
"T-t-t-t-t-te-te-tell him t-t-t-to keep out of m-m-m-my way an' not b-b-b-b-bl-block me," stuttered Tay-Tay Mohler.
"We're a-goin' to skin 'em," said Eddie Curtis.
"Cheese it, you kids, till we git in the game," ordered Daddy. "Now, Madden's Hill, hang round an' listen. I had to sign articles with Natchez—had to let them have their umpire. So we're up against it. But we'll hit this pitcher Muckle Harris. He ain't got any steam. An' he ain't got much nerve. Now every feller who goes up to bat wants to talk to Muck. Call him a big swelled stiff. Tell him he can't break a pane of glass—tell him he can't put one over the pan—tell him it he does you'll slam it down in the sand bank. Bluff the whole team. Keep scrappy all the time. See! That's my game today. This Natchez bunch needs to be gone after. Holler at the umpire. Act like you want to fight."
Then Daddy sent his men out for practice.
"Boss, enny ground rules?" inquired Bo Stranathan. He was a big, bushy-haired boy with a grin and protruding teeth. "How many bases on wild throws over first base an' hits over the sand bank?"
"All you can get," replied Daddy, with a magnanimous wave of hand.
"Huh! Lemmee see your ball?"
Daddy produced the ball that he had Lane had made for the game.
"Huh! Watcher think? We ain 't goin' to play with no mush ball like thet," protested Bo. "We play with a hard ball. Looka here! We'll trow up the ball."
Daddy remembered what he had heard about the singular generosity of the Natchez team to supply the balls for the games they played.
"We don't hev to pay nothin' fer them balls. A man down at the Round House makes them for us. They ain't no balls as good," explained Bo, with pride.
However, as Bo did not appear eager to pass over the balls for examination Daddy simply reached out and took them. They were small, perfectly round and as hard as bullets. They had no covers. The yarn had been closely and tightly wrapped and then stitched over with fine bees-waxed thread. Daddy fancied he detected a difference in the weight of the ball, but Bo took them back before Daddy could be sure of that point.
"You don't have to fan about it. I know a ball when I see one," observed Daddy. "But we're on our own grounds an' we'll use our own ball. Thanks all the same to you, Stranathan."
"Huh! All I gotta say is we'll play with my ball er there won't be no game," said Bo suddenly.
Daddy shrewdly eyed the Natchez captain. Bo did not look like a fellow wearing himself thin from generosity. It struck Daddy that Bo's habit of supplying the ball for the game might have some relation to the fact that he always carried along his own umpire. There was a strange feature about this umpire business and it was that Bo's man had earned a reputation for being particularly fair. No boy ever had any real reason to object to Umpire Gale's decisions. When Gale umpired away from the Natchez grounds his close decisions always favored the other team, rather than his own. It all made Daddy keen and thoughtful.
"Stranathan, up here on Madden's Hill we know how to treat visitors. We'll play with your ball.... Now keep your gang of rooters from crowdin' on the diamond."
"Boss, it's your grounds. Fire 'em off if they don't suit you.... Come on, let's git in the game. Watcher want—field er bat?"
"Field," replied Daddy briefly.
Billy Gale called "Play," and the game began with Slugger Blandy at bat. The formidable way in which he swung his club did not appear to have any effect on Frank Price or the player back of him. Frank's most successful pitch was a slow, tantalizing curve, and he used it. Blandy lunged at the ball, missed it and grunted.
"Frank, you got his alley," called Lane.
Slugger fouled the next one high in the air back of the plate. Sam Wickhart, the stocky bowlegged catcher, was a fiend for running after foul flies, and now he plunged into the crowd of boys, knocking them right and left, and he caught the ball. Whisner came up and hit safely over Griffith, whereupon the Natchez supporters began to howl. Kelly sent a grounder to Grace at short stop. Daddy's weak player made a poor throw to first base, so the runner was safe. Then Bo Stranathan batted a stinging ball through the infield, scoring Whisner.
"Play the batter! Play the batter!" sharply called Daddy from the bench.
Then Frank struck out Molloy and retired Dundon on an easy fly.
"Fellers, git in the game now," ordered Daddy, as his players eagerly trotted in. "Say things to that Muckle Harris! We'll walk through this game like sand through a sieve."
Bob Irvin ran to the plate waving his bat at Harris.
"Put one over, you freckleface! I 've been dyin' fer this chanst. You're on Madden's Hill now."
Muckle evidently was not the kind of pitcher to stand coolly under such bantering. Obviously he was not used to it. His face grew red and his hair waved up. Swinging hard, he threw the ball straight at Bob's head. Quick as a cat, Bob dropped flat.
"Never touched me!" he chirped, jumping up and pounding the plate with his bat. "You couldn't hit a barn door. Come on. I'll paste one a mile!"
Bob did not get an opportunity to hit, for Harris could not locate the plate and passed him to first on four balls.
"Dump the first one," whispered Daddy in Grace's ear. Then he gave Bob a signal to run on the first pitch.
Grace tried to bunt the first ball, but he missed it. His attempt, however, was so violent that he fell over in front of the catcher, who could not recover in time to throw, and Bob got to second base. At this juncture, the Madden's Hill band of loyal supporters opened up with a mingling of shrill yells and whistles and jangling of tin cans filled with pebbles. Grace hit the next ball into second base and, while he was being thrown out, Bob raced to third. With Sam Wickhart up it looked good for a score, and the crowd yelled louder. Sam was awkward yet efficient, and he batted a long fly to right field. The fielder muffed the ball. Bob scored, Sam reached second base, and the crowd yelled still louder. Then Lane struck out and Mohler hit to shortstop, retiring the side.
Natchez scored a run on a hit, a base on balls, and another error by Grace. Every time a ball went toward Grace at short Daddy groaned. In their half of the inning Madden's Hill made two runs, increasing the score 3 to 2.
The Madden's Hill boys began to show the strain of such a close contest. If Daddy had voiced aloud his fear it would have been: "They'll blow up in a minnit!" Frank Price alone was slow and cool, and he pitched in masterly style. Natchez could not beat him. On the other hand, Madden's Hill hit Muck Harris hard, but superb fielding kept runners off the bases. As Daddy's team became more tense and excited Bo Stranathan's players grew steadier and more arrogantly confident. Daddy saw it with distress, and he could not realize just where Natchez had license for such confidence. Daddy watched the game with the eyes of a hawk.
As the Natchez players trooped in for their sixth inning at bat, Daddy observed a marked change in their demeanor. Suddenly they seemed to have been let loose; they were like a band of Indians. Daddy saw everything. He did not miss seeing Umpire Gale take a ball from his pocket and toss it to Frank, and Daddy wondered if that was the ball which had been in the play. Straightway, however, he forgot that in the interest of the game.
Bo Stranathan bawled: "Wull, Injuns, hyar's were we do 'em. We've jest ben loafin' along. Git ready to tear the air, you rooters!"
Kelly hit a wonderfully swift ball through the infield. Bo batted out a single. Malloy got up in the way of one of Frank's pitches, and was passed to first base. Then, as the Natchez crowd opened up in shrill clamor, the impending disaster fell. Dundon hit a bounder down into the infield. The ball appeared to be endowed with life. It bounded low, then high and, cracking into Grace's hands, bounced out and rolled away. The runners raced around the bases.
Pickens sent up a tremendous fly, the highest ever batted on Madden's Hill. It went over Tom Lindsay in center field, and Tom ran and ran. The ball went so far up that Tom had time to cover the ground, but he could not judge it. He ran round in a little circle, with hands up in bewilderment. And when the ball dropped it hit him on the head and bounded away.
"Run, you Injun, run!" bawled Bo. "What'd I tell you? We ain't got 'em goin', oh, no! Hittin' 'em on the head!"
Bill dropped a slow, teasing ball down the third-base line. Jake Thomas ran desperately for it, and the ball appeared to strike his hands and run up his arms and caress his nose and wrap itself round his neck and then roll gently away. All the while, the Natchez runners tore wildly about the bases and the Natchez supporters screamed and whistled. Muck Harris could not bat, yet he hit the first ball and it shot like a bullet over the infield. Then Slugger Blandy came to the plate.
The ball he sent out knocked Grace's leg from under him as if it were a ten-pin. Whisner popped a fly over Tay Tay Mohler's head. Now Tay Tay was fat and slow, but he was a sure catch. He got under the ball. It struck his hands and jumped back twenty feet up into the air. It was a strangely live ball. Kelly again hit to shortstop, and the ball appeared to start slow, to gather speed with every bound and at last to dart low and shoot between Grace's legs.
"Haw! Haw!" roared Bo. "They've got a hole at short. Hit fer the hole, fellers. Watch me! Jest watch me!"
And he swung hard on the first pitch. The ball glanced like a streak straight at Grace, took a vicious jump, and seemed to flirt with the infielder's hands, only to evade them.
Malloy fouled a pitch and the ball hit Sam Wickhart square over the eye. Sam's eye popped out and assumed the proportions and color of a huge plum.
"Hey!" yelled Blandy, the rival catcher. "Air you ketchin' with yer mug?"
Sam would not delay the game nor would he don the mask.
Daddy sat hunched on his soap-box, and, as in a hateful dream, he saw his famous team go to pieces. He put his hands over his ears to shut out some of the uproar. And he watched that little yarn ball fly and shoot and bound and roll to crush his fondest hopes. Not one of his players appeared able to hold it. And Grace had holes in his hands and legs and body. The ball went right through him. He might as well have been so much water. Instead of being a shortstop he was simply a hole. After every hit Daddy saw that ball more and more as something alive. It sported with his infielders. It bounded like a huge jack-rabbit, and went swifter and higher at every bound. It was here, there, everywhere.
And it became an infernal ball. It became endowed with a fiendish propensity to run up a player's leg and all about him, as if trying to hide in his pocket. Grace's efforts to find it were heartbreaking to watch. Every time it bounded out to center field, which was of frequent occurrence, Tom would fall on it and hug it as if he were trying to capture a fleeing squirrel. Tay Tay Mohler could stop the ball, but that was no great credit to him, for his hands took no part in the achievement. Tay Tay was fat and the ball seemed to like him. It boomed into his stomach and banged against his stout legs. When Tay saw it coming he dropped on his knees and valorously sacrificed his anatomy to the cause of the game.
Daddy tried not to notice the scoring of runs by his opponents. But he had to see them and he had to count. Ten runs were as ten blows! After that each run scored was like a stab in his heart. The play went on, a terrible fusilade of wicked ground balls that baffled any attempt to field them. Then, with nineteen runs scored, Natchez appeared to tire. Sam caught a foul fly, and Tay Tay, by obtruding his wide person to the path of infield hits, managed to stop them, and throw out the runners.
Score—Natchez, 21; Madden Hill, 3.
Daddy's boys slouched and limped wearily in.
"Wot kind of a ball's that?" panted Tom, as he showed his head with a bruise as large as a goose-egg.
"T-t-t-t-ta-ta-tay-tay-tay-tay—" began Mohler, in great excitement, but as he could not finish what he wanted to say no one caught his meaning.
Daddy's watchful eye had never left that wonderful, infernal little yarn ball. Daddy was crushed under defeat, but his baseball brains still continued to work. He saw Umpire Gale leisurely step into the pitcher's box, and leisurely pick up the ball and start to make a motion to put it in his pocket.
Suddenly fire flashed all over Daddy.
"Hyar! Don't hide that ball!" he yelled, in his piercing tenor.
He jumped up quickly, forgetting his crutch, and fell headlong. Lane and Sam got him upright and handed the crutch to him. Daddy began to hobble out to the pitcher's box.
"Don't you hide that ball. See! I've got my eye on this game. That ball was in play, an' you can't use the other."
Umpire Gale looked sheepish, and his eyes did not meet Daddy's. Then Bo came trotting up.
"What's wrong, boss?" he asked.
"Aw, nuthin'. You're tryin' to switch balls on me. That's all. You can't pull off any stunts on Madden's Hill."
"Why, boss, thet ball's all right. What you hollerin' about?"
"Sure that ball's all right," replied Daddy. "It's a fine ball. An' we want a chanst to hit it! See?"
Bo flared up and tried to bluster, but Daddy cut him short.
"Give us our innin'—let us git a whack at that ball, or I'll run you off Madden's Hill."
Bo suddenly looked a little pale and sick.
"Course youse can git a whack at it," he said, in a weak attempt to be natural and dignified.
Daddy tossed the ball to Harris, and as he hobbled off the field he heard Bo calling out low and cautiously to his players. Then Daddy was certain he had discovered a trick. He called his players around him.
"This game ain't over yet. It ain't any more'n begun. I'll tell you what. Last innin' Bo's umpire switched balls on us. That ball was lively. An' they tried to switch back on me. But nix! We're goin' to git a chanst to hit that lively ball, An' they're goin' to git a dose of their own medicine. Now, you dead ones—come back to life! Show me some hittin' an' runnin'."
"Daddy, you mean they run in a trick on us?" demanded Lane, with flashing eyes.
"Funny about Natchez's strong finishes!" replied Daddy, coolly, as he eyed his angry players.
They let out a roar, and then ran for the bats.
The crowd, quick to sense what was in the air, thronged to the diamond and manifested alarming signs of outbreak.
Sam Wickhart leaped to the plate and brandished his club.
"Sam, let him pitch a couple," called Daddy from the bench. "Mebbe we'll git wise then."
Harris had pitched only twice when the fact became plain that he could not throw this ball with the same speed as the other. The ball was heavier; besides Harris was also growing tired. The next pitch Sam hit far out over the center fielder's head for a home run. It was a longer hit than any Madden's Hill boy had ever made. The crowd shrieked its delight. Sam crossed the plate and then fell on the bench beside Daddy.
"Say! that ball nearly knocked the bat out of my hands," panted Sam. "It made the bat spring!"
"Fellers, don't wait," ordered Daddy. "Don't give the umpire a chanst to roast us now. Slam the first ball!"
The aggressive captain lined the ball at Bo Stranathan. The Natchez shortstop had a fine opportunity to make the catch, but he made an inglorious muff. Tay Tay hurried to bat. Umpire Gale called the first pitch a strike. Tay slammed down his club. "T-t-t-t-to-to-twasn't over," he cried. "T-t-t-tay—"
"Shut up," yelled Daddy. "We want to git this game over today."
Tay Tay was fat and he was also strong, so that when beef and muscle both went hard against the ball it traveled. It looked as if it were going a mile straight up. All the infielders ran to get under it. They got into a tangle, into which the ball descended. No one caught it, and thereupon the Natchez players began to rail at one another. Bo stormed at them, and they talked back to him. Then when Tom Lindsay hit a little slow grounder into the infield it seemed that a just retribution had overtaken the great Natchez team.
Ordinarily this grounder of Tom's would have been easy for a novice to field. But this peculiar grounder, after it has hit the ground once, seemed to wake up and feel lively. It lost its leisurely action and began to have celerity. When it reached Dundon it had the strange, jerky speed so characteristic of the grounders that had confused the Madden's Hill team. Dundon got his hands on the ball and it would not stay in them. When finally he trapped it Tom had crossed first base and another runner had scored. Eddie Curtis cracked another at Bo. The Natchez captain dove for it, made a good stop, bounced after the rolling ball, and then threw to Kelly at first. The ball knocked Kelly's hands apart as if they had been paper. Jake Thomas batted left handed and he swung hard on a slow pitch and sent the ball far into right field. Runners scored. Jake's hit was a three-bagger. Then Frank Price hit up an infield fly. Bo yelled for Dundon to take it and Dundon yelled for Harris. They were all afraid to try for it. It dropped safely while Jake ran home.
With the heavy batters up the excitement increased. A continuous scream and incessant rattle of tin cans made it impossible to hear what the umpire called out. But that was not important, for he seldom had a chance to call either ball or strike. Harris had lost his speed and nearly every ball he pitched was hit by the Madden's Hill boys. Irvine cracked one down between short and third. Bo and Pickens ran for it and collided while the ball jauntily skipped out to left field and, deftly evading Bell, went on and on. Bob reached third. Grace hit another at Dundon, who appeared actually to stop it four times before he could pick it up, and then he was too late. The doughty bow-legged Sam, with his huge black eye, hung over the plate and howled at Muckle. In the din no one heard what he said, but evidently Muck divined it. For he roused to the spirit of a pitcher who would die of shame if he could not fool a one-eyed batter. But Sam swooped down and upon the first ball and drove it back toward the pitcher. Muck could not get out of the way and the ball made his leg buckle under him. Then that hit glanced off to begin a marvelous exhibition of high and erratic bounding about the infield.
Daddy hunched over his soap-box bench and hugged himself. He was farsighted and he saw victory. Again he watched the queer antics of that little yarn ball, but now with different feelings. Every hit seemed to lift him to the skies. He kept silent, though every time the ball fooled a Natchez player Daddy wanted to yell. And when it started for Bo and, as if in revenge, bounded wickeder at every bounce to skip off the grass and make Bo look ridiculous, then Daddy experienced the happiest moments of his baseball career. Every time a tally crossed the plate he would chalk it down on his soap box.
But when Madden's Hill scored the nineteenth run without a player being put out, then Daddy lost count. He gave himself up to revel. He sat motionless and silent; nevertheless his whole internal being was in the state of wild tumult. It was as if he was being rewarded in joy for all the misery he had suffered because he was a cripple. He could never play baseball, but he had baseball brains. He had been too wise for the tricky Stranathan. He was the coach and manager and general of the great Madden's Hill nine. If ever he had to lie awake at night again he would not mourn over his lameness; he would have something to think about. To him would be given the glory of beating the invincible Natchez team. So Daddy felt the last bitterness leave him. And he watched that strange little yarn ball, with its wonderful skips and darts and curves. The longer the game progressed and the wearier Harris grew, the harder the Madden's Hill boys batted the ball and the crazier it bounced at Bo and his sick players. Finally, Tay Tay Mohler hit a teasing grounder down to Bo.
Then it was as if the ball, realizing a climax, made ready for a final spurt. When Bo reached for the ball it was somewhere else. Dundon could not locate it. And Kelly, rushing down to the chase, fell all over himself and his teammates trying to grasp the illusive ball, and all the time Tay Tay was running. He never stopped. But as he was heavy and fat he did not make fast time on the bases. Frantically the outfielders ran in to head off the bouncing ball, and when they had succeeded Tay Tay had performed the remarkable feat of making a home run on a ball batted into the infield.
That broke Natchez's spirit. They quit. They hurried for their bats. Only Bo remained behind a moment to try to get his yarn ball. But Sam had pounced upon it and given it safely to Daddy. Bo made one sullen demand for it.
"Funny about them fast finishes of yours!" said Daddy scornfully. "Say! the ball's our'n. The winnin' team gits the ball. Go home an' look up the rules of the game!"
Bo slouched off the field to a shrill hooting and tin canning.
"Fellers, what was the score?" asked Daddy.
Nobody knew the exact number of runs made by Madden's Hill.
"Gimme a knife, somebody," said the manager.
When it had been produced Daddy laid down the yarn ball and cut into it. The blade entered readily for a inch and then stopped. Daddy cut all around the ball, and removed the cover of tightly wrapped yarn. Inside was a solid ball of India rubber.
"Say! it ain't so funny now—how that ball bounced," remarked Daddy.
"Wot you think of that!" exclaimed Tom, feeling the lump on his head.
"T-t-t-t-t-t-t-ta-tr—" began Tay Tay Mohler.
"Say it! Say it!" interrupted Daddy.
"Ta-ta-ta-tr-trimmed them wa-wa-wa-wa-with their own b-b-b-b-b-ba-ba-ball," finished Tay.
# Old Well-Well
## *
He bought a ticket at the 25-cent window, and edging his huge bulk through the turnstile, laboriously followed the noisy crowd toward the bleachers. I could not have been mistaken. He was Old Well-Well, famous from Boston to Baltimore as the greatest baseball fan in the East. His singular yell had pealed into the ears of five hundred thousand worshippers of the national game and would never be forgotten.
At sight of him I recalled a friend's baseball talk. "You remember Old Well-Well? He's all in—dying, poor old fellow! It seems young Burt, whom the Phillies are trying out this spring, is Old Well-Well's nephew and protege. Used to play on the Murray Hill team; a speedy youngster. When the Philadelphia team was here last, Manager Crestline announced his intention to play Burt in center field. Old Well-Well was too ill to see the lad get his tryout. He was heart-broken and said: 'If I could only see one more game!'"
The recollection of this random baseball gossip and the fact that Philadelphia was scheduled to play New York that very day, gave me a sudden desire to see the game with Old Well-Well. I did not know him, but where on earth were introductions as superfluous as on the bleachers? It was a very easy matter to catch up with him. He walked slowly, leaning hard on a cane and his wide shoulders sagged as he puffed along. I was about to make some pleasant remark concerning the prospects of a fine game, when the sight of his face shocked me and I drew back. If ever I had seen shadow of pain and shade of death they hovered darkly around Old Well-Well.
No one accompanied him; no one seemed to recognize him. The majority of that merry crowd of boys and men would have jumped up wild with pleasure to hear his well-remembered yell. Not much longer than a year before, I had seen ten thousand fans rise as one man and roar a greeting to him that shook the stands. So I was confronted by a situation strikingly calculated to rouse my curiosity and sympathy.
He found an end seat on a row at about the middle of the right-field bleachers and I chose one across the aisle and somewhat behind him. No players were yet in sight. The stands were filling up and streams of men were filing into the aisles of the bleachers and piling over the benches. Old Well-Well settled himself comfortably in his seat and gazed about him with animation. There had come a change to his massive features. The hard lines had softened; the patches of gray were no longer visible; his cheeks were ruddy; something akin to a smile shone on his face as he looked around, missing no detail of the familiar scene.
During the practice of the home team Old Well-Well sat still with his big hands on his knees; but when the gong rang for the Phillies, he grew restless, squirming in his seat and half rose several times. I divined the importuning of his old habit to greet his team with the yell that had made him famous. I expected him to get up; I waited for it. Gradually, however, he became quiet as a man governed by severe self-restraint and directed his attention to the Philadelphia center fielder.
At a glance I saw that the player was new to me and answered the newspaper description of young Burt. What a lively looking athlete! He was tall, lithe, yet sturdy. He did not need to chase more than two fly balls to win me. His graceful, fast style reminded me of the great Curt Welch. Old Well-Well's face wore a rapt expression. I discovered myself hoping Burt would make good; wishing he would rip the boards off the fence; praying he would break up the game.
It was Saturday, and by the time the gong sounded for the game to begin the grand stand and bleachers were packed. The scene was glittering, colorful, a delight to the eye. Around the circle of bright faces rippled a low, merry murmur. The umpire, grotesquely padded in front by his chest protector, announced the batteries, dusted the plate, and throwing out a white ball, sang the open sesame of the game: "Play!"
Then Old Well-Well arose as if pushed from his seat by some strong propelling force. It had been his wont always when play was ordered or in a moment of silent suspense, or a lull in the applause, or a dramatic pause when hearts heat high and lips were mute, to bawl out over the listening, waiting multitude his terrific blast: "Well-Well-Well!"
Twice he opened his mouth, gurgled and choked, and then resumed his seat with a very red, agitated face; something had deterred him from his purpose, or he had been physically incapable of yelling.
The game opened with White's sharp bounder to the infield. Wesley had three strikes called on him, and Kelly fouled out to third base. The Phillies did no better, being retired in one, two, three order. The second inning was short and no tallies were chalked up. Brain hit safely in the third and went to second on a sacrifice. The bleachers began to stamp and cheer. He reached third on an infield hit that the Philadelphia short-stop knocked down but could not cover in time to catch either runner. The cheer in the grand stand was drowned by the roar in the bleachers. Brain scored on a fly-ball to left. A double along the right foul line brought the second runner home. Following that the next batter went out on strikes.
In the Philadelphia half of the inning young Burt was the first man up. He stood left-handed at the plate and looked formidable. Duveen, the wary old pitcher for New York, to whom this new player was an unknown quantity, eyed his easy position as if reckoning on a possible weakness. Then he took his swing and threw the ball. Burt never moved a muscle and the umpire called strike. The next was a ball, the next a strike; still Burt had not moved.
"Somebody wake him up!" yelled a wag in the bleachers. "He's from Slumbertown, all right, all right!" shouted another.
Duveen sent up another ball, high and swift. Burt hit straight over the first baseman, a line drive that struck the front of the right-field bleachers.
"Peacherino!" howled a fan.
Here the promise of Burt's speed was fulfilled. Run! He was fleet as a deer. He cut through first like the wind, settled to a driving strides rounded second, and by a good, long slide beat the throw in to third. The crowd, who went to games to see long hits and daring runs, gave him a generous hand-clapping.
Old Well-Well appeared on the verge of apoplexy. His ruddy face turned purple, then black; he rose in his seat; he gave vent to smothered gasps; then he straightened up and clutched his hands into his knees.
Burt scored his run on a hit to deep short, an infielder's choice, with the chances against retiring a runner at the plate. Philadelphia could not tally again that inning. New York blanked in the first of the next. For their opponents, an error, a close decision at second favoring the runner, and a single to right tied the score. Bell of New York got a clean hit in the opening of the fifth. With no one out and chances for a run, the impatient fans let loose. Four subway trains in collision would not have equalled the yell and stamp in the bleachers. Maloney was next to bat and he essayed a bunt. This the fans derided with hoots and hisses. No team work, no inside ball for them.
"Hit it out!" yelled a hundred in unison.
"Home run!" screamed a worshipper of long hits.
As if actuated by the sentiments of his admirers Maloney lined the ball over short. It looked good for a double; it certainly would advance Bell to third; maybe home. But no one calculated on Burt. His fleetness enabled him to head the bounding ball. He picked it up cleanly, and checking his headlong run, threw toward third base. Bell was half way there. The ball shot straight and low with terrific force and beat the runner to the bag.
"What a great arm!" I exclaimed, deep in my throat. "It's the lad's day! He can't be stopped."
The keen newsboy sitting below us broke the amazed silence in the bleachers.
"Wot d'ye tink o' that?"
Old Well-Well writhed in his seat. To him if was a one-man game, as it had come to be for me. I thrilled with him; I gloried in the making good of his protege; it got to be an effort on my part to look at the old man, so keenly did his emotion communicate itself to me.
The game went on, a close, exciting, brilliantly fought battle. Both pitchers were at their best. The batters batted out long flies, low liners, and sharp grounders; the fielders fielded these difficult chances without misplay. Opportunities came for runs, but no runs were scored for several innings. Hopes were raised to the highest pitch only to be dashed astonishingly away. The crowd in the grand stand swayed to every pitched ball; the bleachers tossed like surf in a storm.
To start the eighth, Stranathan of New York tripled along the left foul line. Thunder burst from the fans and rolled swellingly around the field. Before the hoarse yelling, the shrill hooting, the hollow stamping had ceased Stranathan made home on an infield hit. Then bedlam broke loose. It calmed down quickly, for the fans sensed trouble between Binghamton, who had been thrown out in the play, and the umpire who was waving him back to the bench.
"You dizzy-eyed old woman, you can't see straight!" called Binghamton.
The umpire's reply was lost, but it was evident that the offending player had been ordered out of the grounds.
Binghamton swaggered along the bleachers while the umpire slowly returned to his post. The fans took exception to the player's objection and were not slow in expressing it. Various witty enconiums, not to be misunderstood, attested to the bleachers' love of fair play and their disgust at a player's getting himself put out of the game at a critical stage.
The game proceeded. A second batter had been thrown out. Then two hits in succession looked good for another run. White, the next batter, sent a single over second base. Burt scooped the ball on the first bounce and let drive for the plate. It was another extraordinary throw. Whether ball or runner reached home base first was most difficult to decide. The umpire made his sweeping wave of hand and the breathless crowd caught his decision.
"Out!"
In action and sound the circle of bleachers resembled a long curved beach with a mounting breaker thundering turbulently high.
"Rob—b—ber—r!" bawled the outraged fans, betraying their marvelous inconsistency.
Old Well-Well breathed hard. Again the wrestling of his body signified an inward strife. I began to feel sure that the man was in a mingled torment of joy and pain, that he fought the maddening desire to yell because he knew he had not the strength to stand it. Surely, in all the years of his long following of baseball he had never had the incentive to express himself in his peculiar way that rioted him now. Surely, before the game ended he would split the winds with his wonderful yell.
Duveen's only base on balls, with the help of a bunt, a steal, and a scratch hit, resulted in a run for Philadelphia, again tying the score. How the fans raged at Fuller for failing to field the lucky scratch.
"We had the game on ice!" one cried.
"Get him a basket!"
New York men got on bases in the ninth and made strenuous efforts to cross the plate, but it was not to be. Philadelphia opened up with two scorching hits and then a double steal. Burt came up with runners on second and third. Half the crowd cheered in fair appreciation of the way fate was starring the ambitious young outfielder; the other half, dyed-in-the-wool home-team fans, bent forward in a waiting silent gloom of fear. Burt knocked the dirt out of his spikes and faced Duveen. The second ball pitched he met fairly and it rang like a bell.
No one in the stands saw where it went. But they heard the crack, saw the New York shortstop stagger and then pounce forward to pick up the ball and speed it toward the plate. The catcher was quick to tag the incoming runner, and then snap the ball to first base, completing a double play.
When the crowd fully grasped this, which was after an instant of bewilderment, a hoarse crashing roar rolled out across the field to bellow back in loud echo from Coogan's Bluff. The grand stand resembled a colored corn field waving in a violent wind; the bleachers lost all semblance of anything. Frenzied, flinging action—wild chaos—shrieking cries—manifested sheer insanity of joy.
When the noise subsided, one fan, evidently a little longer-winded than his comrades, cried out hysterically:
"O-h! I don't care what becomes of me—now-w!"
Score tied, three to three, game must go ten innings—that was the shibboleth; that was the overmastering truth. The game did go ten innings—eleven—twelve, every one marked by masterly pitching, full of magnificent catches, stops and throws, replete with reckless base-running and slides like flashes in the dust. But they were unproductive of runs. Three to three! Thirteen innings!
"Unlucky thirteenth," wailed a superstitious fan.
I had got down to plugging, and for the first time, not for my home team. I wanted Philadelphia to win, because Burt was on the team. With Old Well-Well sitting there so rigid in his seat, so obsessed by the playing of the lad, I turned traitor to New York.
White cut a high twisting bounder inside the third base, and before the ball could be returned he stood safely on second. The fans howled with what husky voice they had left. The second hitter batted a tremendously high fly toward center field. Burt wheeled with the crack of the ball and raced for the ropes. Onward the ball soared like a sailing swallow; the fleet fielder ran with his back to the stands. What an age that ball stayed in the air! Then it lost its speed, gracefully curved and began to fall. Burt lunged forward and upwards; the ball lit in his hands and stuck there as he plunged over the ropes into the crowd. White had leisurely trotted half way to third; he saw the catch, ran back to touch second and then easily made third on the throw-in. The applause that greeted Burt proved the splendid spirit of the game. Bell placed a safe little hit over short, scoring White. Heaving, bobbing bleachers—wild, broken, roar on roar!
Score four to three—only one half inning left for Philadelphia to play—how the fans rooted for another run! A swift double-play, however, ended the inning.
Philadelphia's first hitter had three strikes called on him.
"Asleep at the switch!" yelled a delighted fan.
The next batter went out on a weak pop-up fly to second.
"Nothin' to it!"
"Oh, I hate to take this money!"
"All-l o-over!"
Two men at least of all that vast assemblage had not given up victory for Philadelphia. I had not dared to look at Old Well-Well for a long, while. I dreaded the nest portentious moment. I felt deep within me something like clairvoyant force, an intangible belief fostered by hope.
Magoon, the slugger of the Phillies, slugged one against the left field bleachers, but, being heavy and slow, he could not get beyond second base. Cless swung with all his might at the first pitched ball, and instead of hitting it a mile as he had tried, he scratched a mean, slow, teasing grounder down the third base line. It was as safe as if it had been shot out of a cannon. Magoon went to third.
The crowd suddenly awoke to ominous possibilities; sharp commands came from the players' bench. The Philadelphia team were bowling and hopping on the side lines, and had to be put down by the umpire.
An inbreathing silence fell upon stands and field, quiet, like a lull before a storm.
When I saw young Burt start for the plate and realized it was his turn at bat, I jumped as if I had been shot. Putting my hand on Old Well-Well's shoulder I whispered: "Burt's at bat: He'll break up this game! I know he's going to lose one!"
The old fellow did not feel my touch; he did not hear my voice; he was gazing toward the field with an expression on his face to which no human speech could render justice. He knew what was coming. It could not be denied him in that moment.
How confidently young Burt stood up to the plate! None except a natural hitter could have had his position. He might have been Wagner for all he showed of the tight suspense of that crisis. Yet there was a tense alert poise to his head and shoulders which proved he was alive to his opportunity.
Duveen plainly showed he was tired. Twice he shook his head to his catcher, as if he did not want to pitch a certain kind of ball. He had to use extra motion to get his old speed, and he delivered a high straight ball that Burt fouled over the grand stand. The second ball met a similar fate. All the time the crowd maintained that strange waiting silence. The umpire threw out a glistening white ball, which Duveen rubbed in the dust and spat upon. Then he wound himself up into a knot, slowly unwound, and swinging with effort, threw for the plate.
Burt's lithe shoulders swung powerfully. The meeting of ball and bat fairly cracked. The low driving hit lined over second a rising glittering streak, and went far beyond the center fielder.
Bleachers and stands uttered one short cry, almost a groan, and then stared at the speeding runners. For an instant, approaching doom could not have been more dreaded. Magoon scored. Cless was rounding second when the ball lit. If Burt was running swiftly when he turned first he had only got started, for then his long sprinter's stride lengthened and quickened. At second he was flying; beyond second he seemed to merge into a gray flitting shadow.
I gripped my seat strangling the uproar within me. Where was the applause? The fans were silent, choked as I was, but from a different cause. Cless crossed the plate with the score that defeated New York; still the tension never laxed until Burt beat the ball home in as beautiful a run as ever thrilled an audience.
In the bleak dead pause of amazed disappointment Old Well-Well lifted his hulking figure and loomed, towered over the bleachers. His wide shoulders spread, his broad chest expanded, his breath whistled as he drew it in. One fleeting instant his transfigured face shone with a glorious light. Then, as he threw back his head and opened his lips, his face turned purple, the muscles of his cheeks and jaw rippled and strung, the veins on his forehead swelled into bulging ridges. Even the back of his neck grew red.
"Well!—Well!—Well!!!"
Ear-splitting stentorian blast! For a moment I was deafened. But I heard the echo ringing from the cliff, a pealing clarion call, beautiful and wonderful, winding away in hollow reverberation, then breaking out anew from building to building in clear concatenation.
A sea of faces whirled in the direction of that long unheard yell. Burt had stopped statue-like as if stricken in his tracks; then he came running, darting among the spectators who had leaped the fence.
Old Well-Well stood a moment with slow glance lingering on the tumult of emptying bleachers, on the moving mingling colors in the grand stand, across the green field to the gray-clad players. He staggered forward and fell.
Before I could move, a noisy crowd swarmed about him, some solicitous, many facetious. Young Burt leaped the fence and forced his way into the circle. Then they were carrying the old man down to the field and toward the clubhouse. I waited until the bleachers and field were empty. When I finally went out there was a crowd at the gate surrounding an ambulance. I caught a glimpse of Old Well-Well. He lay white and still, but his eyes were open, smiling intently. Young Burt hung over him with a pale and agitated face. Then a bell clanged and the ambulance clattered away.
## * * *
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Валентин Миколайович Уланов ( , село Велика Чернігівка, тепер Станично-Луганського району Луганської області) — український діяч, заступник начальника відділу слідчого управління Луганського обласного Управління внутрішніх справ, пенсіонер МВС. Народний депутат України 2-го скликання.
Біографія
У вересні 1954—1955 роках — учень Ворошиловського (тепер — Алчевського) технічного училища № 3.
У 1955—1956 роках — машиніст баштових кранів тресту «Ворошиловськбуд» Ворошиловградської області.
У липні 1956 — жовтні 1959 року — служба в Радянській армії.
У 1959—1960 роках — машиніст баштових кранів тресту «Ворошиловськбуд» Луганської області.
У червні 1960 — лютому 1970 року — дільничий уповноважений, слідчий, старший слідчий Комунарського (тепер — Алчевського) міського відділу внутрішніх справ Луганської області. Член КПРС.
Закінчив заочно Харківський юридичний інститут імені Дзержинського, юрист-правознавець.
У лютому 1970 — січні 1993 року — старший інспектор, старший слідчий з особливо важливих справ, заступник начальника чергової частини, заступник начальника відділу кадрів, заступник начальника відділу слідчого управління Луганського обласного Управління внутрішніх справ.
З січня 1993 року — пенсіонер МВС. Член КПУ.
Народний депутат України 2-го демократичного скликання з .04.1994 (2-й тур) до .04.1998, Станично-Луганський виборчий округ № 258, Луганська область. Секретар Комітету з питань законності і правопорядку. Член депутатської групи «Відродження та розвиток агропромислового комплексу України» (до цього — член депутатської фракції комуністів).
Звання
полковник міліції
Нагороди та відзнаки
п'ять медалей
Посилання
Уланов Валентин Миколайович
Уланов Валентин Миколайович
Уродженці Станично-Луганського району
Народні депутати України 2-го скликання
Члени КПРС
Члени КПУ
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Q: how to add pre-made database .db file to Android using LibGDX I am programming Android using LibGDX. I have pre-made database file. I can make database on android at runtime using this wraper, but I can't figure out how to use already made one.
I tried 2 ways to get it done:
1. To use this DataBaseHelper class example, but while in Android, I would just write:
DataBaseHelper myDbHelper = new DataBaseHelper(this);
in LibGDX I run into problem:
DataBaseHelper myDbHelper = new DataBaseHelper(); <--requires variable "android.content.Context"
2. Using internal file handler of LibGDX:
FileHandle mHandle = Gdx.files.internal("list.db");
mydb1 = DatabaseFactory.getNewDatabase(DATABASE_NAME,DATABASE_VERSION, DATABASE_CREATE, null);
but I don't know how to make contact between mHandle and mydb1.
Any ideas welcome how to do it in LibGdx, thanx
|
{
"redpajama_set_name": "RedPajamaStackExchange"
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Episode 8 - Apple Accessibility: Sarah Herrlinger
Episode Expert: Sarah Herrlinger
Sarah Herrlinger is the Director of Global Accessibility Policy & Initiatives at Apple.
Sarah leads Accessibility for Apple — including Apple's award winning VoiceOver screenreader software for people who are blind, Made for iPhone Hearing Aids, and other initiatives that support Apple's culture of inclusion. At Apple, Accessibility is championed as a basic human right and influences all Apple platforms.
Since joining Apple in 2003, Sarah has served in several key Accessibility roles, including in Apple's Education organization, focusing on the use of Apple technology to support all learners, as well as defining the Accessibility product strategy across the Apple ecosystem.
Sarah holds a Bachelor of Arts degree from DePauw University and a Master of Business Administration from the Stanford Graduate School of Business, and serves on the board of directors of the American Foundation for the Blind.
Connect with Sarah on LinkedIn
Overview of Apple accessibility: Apple Accessibility
Playlist of Apple Accessibility Features Explained: How To's
Video created by filmmaker Sady Paulson: Apple Accessibility Sady
About recent initiatives:
Apple Celebrates Global Accessibility Awareness Day
Apple Art of Autism Gallery
For Apple Accessibility Awareness Happens All Year Long
Meet the Blindness Consultant Ensuring Apple TV Plus Show See Respects Accessibility
Overview of iOS14: iOS Preview
Apple has a dedicated team for accessibility support available to customers 24/7 at 877-204-3930, as well as online, through chat, or from Contact section of the Apple Support app.
Email: accessibility@apple.com
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"redpajama_set_name": "RedPajamaCommonCrawl"
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Yurts, Polo, And Georgian Wine Vie For UNESCO Recognition
The UN's cultural and educational organization, UNESCO, meets on December 2-7 to grant special designation to examples of intangible cultural heritage -- traditions, crafts, and rituals passed from generation to generation. Dozens of countries and communities are seeking recognition for their cultu
EU Not Losing Hope For Ukraine, Yet
The president of the European Parliament, Martin Schulz, says he expects Ukraine to play its "game" with the EU until the very last minute.
Explainer: What Exactly Is An EU Association Agreement?
Ukraine may or may not sign one. Georgia and Moldova are due to initial theirs. But what exactly are these Association Agreements with the European Union that are causing such a ruckus in the run-up to the EU's Eastern Partnership summit in Vilnius?
Starving To Death
In 1932-33, Soviet authorities took all the grain from Ukrainian villagers and left them with nothing. More than 3 million people died in the resulting famine. Survivors talk about the horror of the tragedy known as the Holodomor.
Amnesty Urges Kyiv To Eradicate Torture
Rights group Amnesty International is urging Ukraine to eliminate torture and other ill-treatment of detainees as the European Union is mulling offering Kyiv closer ties with the bloc.
New 'Tymoshenko Bill' Delay
The European Union has conditioned the signing of a key free-trade agreement with Kyiv later this month on the release for medical treatment abroad of Tymoshenko, whose conviction on abuse-of-office charges is seen by Brussels as "selective justice."
Unclear Kyiv 'Willing' To Sign EU Pact
German Chancellor Angela Merkel says it remains unclear whether Ukraine is "willing" to meet the criteria needed for a key free-trade deal with the European Union.
EU Issues 'Urgent Appeal' To Ukraine
EU foreign ministers have called on Kyiv to take action over jailed former Prime Minister Yulia Tymoshenko as they gathered in Brussels to discuss Ukraine ahead of an EU summit in Vilnius later this month.
Opposition Head Denied Tymoshenko Visit
The leader of the Ukrainian opposition in parliament has not been allowed to meet with jailed former Prime Minister Yulia Tymoshenko.
Ukraine's Choice: East Or West?
The EU's Eastern Partnership summit is less than two weeks off, and it still unclear whether Ukraine will sign a long-negotiated Association Agreement with the bloc. What are the pressures on Ukrainian President Viktor Yanukovych and why might the matter not be settled until at least 2015?
Gazprom Warns Over Ukraine Gas Transit
Gazprom has warned that Ukraine's decision to halt most of its Russian natural-gas imports through the end of the year could disrupt energy supplies for Western and Central Europe.
Ukraine Could Lose EU Deal 'Indefinitely'
A senior EU envoy has warned Ukraine not to miss its chance to sign a key deal with the bloc at a Vilnius summit on November 28-29.
|
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| 0
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\subsection{Tree construction and setup}
Let $N_p$ denote the number of processes used in the computation. We initially distribute the $N_s$ particles evenly across all processes and determine the diameter $D_0$ of the cube bounding the entire computational domain. Given the finest box diameter $D(L)$, the number of levels in the tree is then calculated as the smallest integer $L$ such that $L\geq \log_2(D_0/D(L))+1$. Once the number of levels and therefore the position of the leaf nodes are known, every particle is assigned a key based on the Morton-Z order traversal of the H-FMM tree \cite{warren1993parallel}. A parallel bucket sort on the Morton keys is then used to roughly equally distribute particles across processes at the granularity of leaves. This is done by selecting $N_p-1$ Morton keys, or ``splitters'', which chop the Morton Z-curve into $N_p$ contiguous segments. Leaves are uniquely assigned to processes using these splitters. (Note that this partitioning can be significantly different from the initial one, as the initial partitioning randomly assigns each input particle to a process.) Given a contiguous segment of leaf nodes, each process determines all ancestor keys of the leaves up to the root. The leaves and ancestors are stored in post-order, comprising the \emph{local subtree}.
\paragraph{Plural Nodes}
Despite the non-overlapping partitioning of leaf nodes, overlaps among different processes at the higher level nodes are inevitable as illustrated in Fig.\,\ref{fig:tree}. Such nodes shared by multiple processes are called \emph{plural nodes}. While there are no limitations to the number of processes that can share a plural node, we designate a particular process, i.e., the right-most process sharing the plural node in the H-FMM tree, as its \emph{resident process}. We refer to the resident process' copy of a plural node as a \emph{shared node} and all other copies of this node residing on other processes as \emph{duplicate nodes}. We call the set of processes that own these duplicate nodes as \emph{users} of the shared node, denoted by $U(s)$, where $s$ is the shared node.
One notable advantage provided by plural nodes is storage of the node can be split between multiple processes. This means that rather than completely storing very large nodes at the high level of the tree, the memory needed for a plural node is only the size of the node, divided by the number of processes sharing the node. As the entire node is not stored in any process, a fine grain parallel method to process each plural node is necessary. A simple method of storing the local subtree is as a post-order traversal array. Accessing a single node quickly requires an indexer into this array. If the memory is reduced to only store the portion of a plural node that each process owns, the indexer will additionally need to store what part of a node the current process actually stores in the array.
\subsection{Parallel Evaluation}
\begin{figure}
\centering
\includegraphics[width=0.9\linewidth]{figs/FMMTraversalParallel.png}
\caption{Parallel Farfield MLFMA.}
\label{fig:tree}
\end{figure}
As shown in the diagram in \ref{fig:tree} the Farfield MLFMA execution is as follows:
\begin{enumerate}
\item Compute Charge to Multipole for each leaf (C2M).
\item Compute the expansions, for each non-leaf box, from all of the children boxes (M2M).
\item Translate expansions for each box from sources to observers (M2L).
\item Distribute observer expansions to children (L2L).
\item Distribute leaf box expansions to observers (L2O).
\end{enumerate}
The fine grain parallel algorithm will focus on M2M, M2L and L2L. C2M and L2O occur at the leaf level of the tree, where course grain parallel is trivial to implement due to the high leaf node to process ratio, and plural nodes will not occur.
\paragraph{M2M}
\begin{algorithm}
\caption{Multipole-to-multipole interpolation}
\begin{algorithmic}[1]
\For{each box in post-order traversal}
\For{each child box}
\If{Child is plural}
\State perform parallel fft interpolation
\Else
\State perform serial fft interpolation
\EndIf
\State Shift interpolated data to the parent node's position.
\EndFor
\State Aggregate all interpolated and shifted child data to the parent node.
\EndFor
\end{algorithmic}
\end{algorithm}
M2M creates multipole expansions of non-leaf boxes by combining multipole expansions of their children. First all boxes are interpolated to the level of the parent box. Next each interpolated child box is shifted from the center of of the child box to the center of the parent box. Finally every shifted child box is summed together to form the parent box. This section will describe the impact of splitting plural nodes among processes and the fine grained parallel algorithm.
\paragraph{Interpolation}
\paragraph{Parallel FFT}
\begin{algorithm}
\caption{Parallel FFT interpolation}
\begin{algorithmic}[1]
\For{$\phi$ vector}
\State FFT\_Interpolate()
\EndFor
\State Transpose\_And\_Fold()
\State AlltoAll()
\For{$\theta$ vector}
\State FFT\_Interpolate()
\EndFor
\State Transpose\_And\_Fold()
\State AlltoAll()
\end{algorithmic}
\end{algorithm}
Interpolation is performed using a Fast Fourier transform (FFT)-based interpolation \cite{Sarvas2003}. For interior nodes, the entire node is owned by a single process, thus the FFT interpolation can be performed entirely using local data. For plural nodes, the node data is split among multiple processes. Because interpolation is performed along the $\phi$ direction as well as the $\theta$ direction, there is no way to divide multipole samples among processes that does not place interdependent data on separate processes. Thus to perform parallel FFT interpolation with each process only storing the portion of a plural node it owns, communication between the processes is required.
\begin{figure}
\centering
\includegraphics[width=\linewidth]{figs/FFT.png}
\caption{Graphical illustration of the transposition and folding operation within the parallel FFT interpolation of radiation pattern $a$ to $A$ for $N_\theta=3,N_\phi=4,M_\theta=5,M_\phi=6$. The data from (a) is interpolated serially along $\phi$ to obtain the data in (b). The folding operation acting on this data is shown by the placement of the elements in (c). The hash marks show how the folded data is stored on the wrong processes, and must be communicated to the correct process in (d). With the entire $\theta$ direction stored on each process, the data is then interpolated serially along $\theta$ (e), which is then transposed and folded to the final node data (e) which must be communicated to the processes that own each $\theta$ vector (f) and can be shifted to the center of the parent box and added to each process' local copy of its radiation pattern in accordance with the spherical symmetry condition.}
\label{fig:parallel_interpolation}
\vspace{-0.15in}
\end{figure}
(Should a paper be referenced for this FFT method?)
Parallel interpolation is performed on plural nodes, which are split among multiple processes. First each process is assigned an equal number of columns of $\phi$ data. Then each process is assigned an extra column of $\phi$ data, until all remaining vectors have been assigned. So the first $n$ processes will each own $\ceil{\frac{N_\theta}{P}}$ columns of $\phi$ data where $n=remainder of \frac{N_\theta}{P}$ and the remaining processes will each own $\floor{\frac{N_\theta}{P}}$ columns of $\phi$ data.
The parallel interpolation begins with a standard 1d FFT along the columns to interpolate the $\phi$ direction. The next step would be interpolating data along the $\theta$ rows, but this data is split between processes owning the node. So the interpolated data is transposed and folded, see figure \ref{fig:parallel_interpolation}, placing the $\theta$ rows in locally owned columns. The transpose and fold results in each process storing data in columns outside those assigned to the process, and some data in each process' columns being owned by other processes. So the folded and transposed data outside of each process' columns is communicated to the process that will own the samples. Now each process is storing full columns of $\theta$ samples the data can be interpolated along the $\theta$ columns. A second fold and transpose is performed to return the data to a $\phi \times \theta$ matrix and the folded and transposed data is again communicated to the process that owns the corresponding multipole samples.
Interpolated data for a given node will require more memory than the original data. If enough memory is allocated to store all samples of each plural node at every level, the interpolated data can be stored in the memory for the parent box to later be shifted and aggregated. Instead if only enough memory is allocated to store the portion of a plural node each process owns, this memory may not be sufficient to store interpolated data. For any given node, it is guaranteed (more details?) that the parent node will be shared among at least the same number of processes as the child node. This means when allocating only enough memory to store the local portion of a plural node, it can only be guaranteed (better description that the lower level has a node shared among say 2 processes, so allocating half the node is sufficient, but the parent node may be shared among say 4 processes, so the data interpolated by the two processes sharing the child node will be two large to store when 4 processes share the parent node?) there will be at most enough memory to store the interpolated data in the local subtree array, but in many cases there will be less memory. Since the local subtree array may not be large enough, temporary memory is allocated during the parallel M2M process to store the interpolated node data for shifting and aggregation. The amount of memory allocated is equal to the twice the interpolated size of the locally owned portion of any plural node. This is because each process can have up to two plural nodes per level, and allows for (is this the wrong place to be talking about this?) local shifting and aggregation operations to be performed, before the portions of the aggregated node owned by other processes are communicated to the other processes (primarily because a process might own two children nodes for the same parent).
\paragraph{Shifting Interpolated Data}
Shifting of nodes simply shifts all multipole samples of a node owned by a process from the child node's center to the parent node's center. All samples are independent during this operation so parallelization is trivial.
\paragraph{Aggregation}
When all children are owned by the same process, aggregation simply requires adding all of the corresponding samples from each interpolated and shifted child together. When children are owned by separate processes, aggregation requires communications to aggregate the child nodes, such as a reduce operation. Finally if the children are owned by different processes, the parent is going to be plural, so each process will only own a portion of this parent node. A reduce/scatter can perform both the aggregation and distributing the appropriate portion of the aggregated node to the process that owns the corresponding portion.
One complication is that the reduce/scatter implementations, such as MPI\_reducescatter, require memory to be allocated for the full interpolated and shifted data from the child node, even if the parts not owned by the process are simply filled with 0s. In place of allocating enough memory for the fully interpolated node, a custom point to point method is used for aggregation. In this method, the interpolated and shifted multipole samples are communicated to the process that owns the corresponding samples of the parent node. If the source and destination are the same process, no communication is necessary. Each process sharing the parent node then sums up the corresponding multipole samples from each child, local and communicated. This method both reduces the amount of memory necessary to store the interpolated and shifted data, as well as reduces the communication to only what is necessary to aggregate the node.
\paragraph{Process Alignment}
\begin{figure}
\centering
\includegraphics[width=0.75\linewidth]{figs/ProcessAlignment.png}
\caption{This image shows how multipole samples, ordered clockwise starting at 12 o'clock, are assigned to processes owning child nodes (C1-C5) align with processes owning parent nodes (P1-P5) when assigned in process order on the left, and realigned on the right. The darker portions on the parent are regions where the portion of a parent node the process owns corresponds with the portion of a child node owned by the same process.}
\label{fig:process_alignment}
\vspace{-0.15in}
\end{figure}
The performance impact of the order of the processes that share a plural node also needs to be considered. During M2M of plural nodes, interpolated nodes are aggregated together, then distributed among the processes that share the node. If the some of the multipole samples of the parent node a process owns corresponds with the samples the process owns in the child node, the corresponding interpolated and shifted samples from child node are already local to this process. So this data does not need to be communicated to another process to aggregate the data into the parent node. If the process owns no samples in the parent node that correspond with any of the samples the process owns in a child node, all interpolated and shifted child node samples must be communicated to another process to be aggregated to the parent node. When the processes owning a node are simply ordered by process index, see the left side of figure \ref{fig:process_alignment}, some processes will own samples of a parent node that correspond with none of the samples of the child node which the process owns. For example, while process 1 owns overlapping samples in both the child and the parent, process 2 and 3 own no samples in the parent node that correspond with the samples this process owns in the child.
To optimize the alignment of parent and child node samples owned by each process, the process ordering within a node is sorted so that the portion of the parent node owned by each corresponds optimally with the portion of the child node owned by the process. The processes are first ordered by the following priorities:
\begin{enumerate}
\item Order by process owning the lowest sample in the child node.
\item Order by process with the least number of samples.
\item Order by process PID.
\end{enumerate}
In figure \ref{fig:process_alignment} both process 1 and 3 own samples starting at the beginning of the node, but process 3 has a smaller number of samples so is assigned the first portion of the parent node with process 1 being assigned the second portion. After this processes 4 owns the lowest multipole sample in a child, followed by 2, then 5, so the remaining portions of the parent node are assigned in this order. As can be seen in the figure, all samples each process owns in the parent node correspond with samples that process owns in a child node, despite the layout being non-uniform. Further, process 3 will still need to communicate some samples to process 1 to be aggregated, but over half of the interpolated child samples owned by process 3 can be aggregated locally. While ordering process by PID meant the entire portion of the child owned by process 3 would have been communicated to process 1 and 2. Now nearly all processes in the entire parent node can use interpolated samples from part of a child node without needing to communicate the samples. While this works best with a perfectly balanced tree, this approach will still help to lower the communication requirements during aggregation.
\paragraph{M2L}
\begin{algorithm}
\caption{M2L Translation}\label{M2LTrans}
\begin{algorithmic}[1]
\State Determine the union of data owned by both source and target.
\Procedure{M2L}{}
\For{each source box}
\For{each farfield interaction target}
\If{Target box is not local}
\For{each process sharing target box}
\State Add source multipole data in union of data owned by both source and target to buffer.
\EndFor
\EndIf
\EndFor
\EndFor
\State Communicate buffers between processes.
\For{each target box}
\For{each farfield interaction source}
\If{Source box is local}
\State Load source multipole data from local memory.
\State Translate source multipole data to target and add to existing translated data for target node
\Else
\For{each process sharing source box}
\State Read source multipole data from communication.
\State Translate source multipole data to target and add to existing translated data for target node
\EndFor
\EndIf
\EndFor
\EndFor
\EndProcedure
\end{algorithmic}
\end{algorithm}
During translation, each target node loops through all farfield source nodes, translates the source multipole data to the location of the observer node and the observer node aggregates this translated data together. When the source data is on the same process as the target, this data can simply be read from memory. When the source data is on another process, the data much be communicated. At levels where a process owns multiple nodes, remote source nodes may translate to multiple observer nodes owned by the process. Before the tree traversal a communication list is precalculated to determine which source nodes are needed by target nodes for each process, rather than for each interaction. This makes the communications as efficient as possible by sending the a node's data to each process that needs the data only once. Further if the source node is plural, and/or all target nodes on each target process are plural, then the precalculated list will calculate the union of the node data owned on both the source and target process, so only the range of data owned by both will be communicated.
\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{figs/Translation.png}
\caption{This figure shows how translation communications occurs between nodes owned by different numbers of processes.}
\label{fig:process_alignment}
\vspace{-0.15in}
\end{figure}
Fig. \ref{fig:Translation} provides a representation of how data is communicated between a plural source and observer node, where samples start at the top of each circle and increase clockwise. Here the source node is owned by by three processes (S1, S2 and S3) and the observer node is owned by two (O1 and O2). Process S1 and O1 both own multipole samples starting at the beginning of the node, while S1 owns less samples than O1. For this interaction, S1 can send all samples that it owns to O1, and during the initialization phase S1 and O1 will communicate that S1's communication will begin with the first sample for the node and end with the last sample S1 owns. S3 and O2 both own samples at the end of the node, while the first ample of S3 is later than the first ample of O2. Here S3 will send all of its samples to O2, and during initialization S3 and O2 communicate that S1's communication begins with the first sample it owns and ends with the last sample of the node. Finally S2 owns samples that correspond to samples owned by both O1 and O2. During translation S2 must send half of its samples to O1 and half to O2. During initialization S2 will communicate with both O1 and O2. S2 will communicate with O1 that it will send samples starting with the first sample S2 owns, and the last sample O1 owns. S2 will communicate with O2 that it will send samples starting with the first sample O2 owns, and ending with the last sample S2 owns. During the actual translation process, the initialization allows a process to determine the start and end sample either to send for each source node the process owns, or to translate and apply for each observer node the process owns.
To perform the actual translation, first a send buffer for each process is filled and transmitted based on the communication list. The size of the send buffer is limited to avoid excessive memory use and maximize communication overlap. The communications are performed point to point, as opposed to an All to All, because there are significant differences in the amount of data sent to one process vs another. Because of these differences, we process receive data from multiple processes communicating smaller amounts of data, during the time other processes with larger amounts of data complete their communications. Further, during the time communications are completing, we process local translations.
\paragraph{Translation Operators}
Translation of source to target node data is performed by multiplying each direction of the source node by a translation operator to calculate the impact of the source potential on the target observer. When the geometry is static, the translation operators can be precalculated to improve performance. These precalculated translation operators take up a significant amount of memory. This memory use is limited by each process only storing precalculated translation operators for the local and remote translation directions the process will actually perform. These translations are determined from the M2L precalculated communication list.
\paragraph{L2L}
L2L reverses the operations of M2L to distribute the interpolated and translated data out to the child nodes. First each node is shifted to each child node, then anterpolated, finally the anterpolated data is summed with the data previously anterpolated to the child node.
\paragraph{Shift}
When a child node is an internal node, shifting the parent data to the child node is not significantly different from M2M shifting, each multipole sample in the parent node is shifted from the parent node's center to the child node's center. When a child node is a plural node, the parent node data must be communicated from each process that owns part of the parent node to each process that owns part of the child node. This is most easily done before the data has been shifted, as the parent will not need to know the position of the child node. This data can be communicated via an AlltoAll between all processes sharing the parent node. In most cases, only a subset of the parent processes will share a child node. Because of this, a point to point communications method is used here so messages are only sent from processes owning a piece of the parent node to a process owning that piece of the child node. Once a process owns all of the necessary samples of the parent node, the process can shift all multipole samples from the parent node's center to the child node's center.
\paragraph{Anterpolate}
Parallel anterpolation is exactly the same as parallel interpolation, except the number of multipole samples is reduced, rather than increased.
\paragraph{Sum}
Adding the anterpolated and translated child node together is trivial as all samples are already stored locally.
\end{document}
\subsection{Tree construction and setup}
Let $N_p$ denote the number of processes used in the computation. We initially distribute the $N_s$ particles evenly across all processes and determine the diameter $D_0$ of the cube bounding the entire computational domain. Given the finest box diameter $D(L)$, the number of levels in the tree is calculated as the smallest integer $L$ such that $L\geq \log_2(D_0/D(L))+1$. Once the number of levels and therefore the position of the leaf nodes are known, every particle is assigned a key based on the Morton-Z order traversal of the MLFMA tree \cite{Warren1993}. A parallel bucket sort on the Morton keys is then used to roughly equally distribute particles across processes at the granularity of leaves. This is done by selecting $N_p-1$ Morton keys, or ``splitters'', which chop the Morton Z-curve into $N_p$ contiguous segments. Whole leaves are uniquely assigned to processes using these splitters. Given a contiguous segment of leaf nodes, each process determines all ancestor keys of its leaves up to the root. The leaf through ancestor nodes are used to construct the \emph{local subtree}. A simple method of storing the local subtree is as a post-order traversal array. To quickly access a random node, we use an indexer into this local subtree array.
\paragraph{Plural Nodes}
Despite the non-overlapping partitioning of leaf nodes, overlaps among different processes at the higher level nodes are inevitable (and in fact, are desirable) as illustrated in Fig.\,\ref{fig:tree}. Details and associated proofs on such partitioning can be found in \cite{melapudi2011scalable}. We call such nodes shared by multiple processes as \emph{plural nodes}. While there are no limitations to the number of processes that can share a plural node, we designate a particular process, i.e., the right-most process sharing the plural node in the MLFMA tree, as its \emph{resident process}. We refer to the resident process' copy of a plural node as a \emph{shared node} and all other copies of this node residing on other processes as \emph{duplicate nodes}. We call the set of processes that own these duplicate nodes as \emph{users} of the shared node, denoted by $U(s)$, where $s$ is the shared node.
One notable advantage provided by plural nodes is that storage of the node is split between multiple processes. In this case, the indexer additionally stores which \emph{slice} of a tree node the current process actually stores in its local subtree array. As the information content for a node is not available to any single process in its entirety, a fine grain parallelization is necessary to perform computations associated with plural nodes. We note that a process can have at most two plural nodes per level in its local tree (essentially one to the ``left'', and another to the ``right'').
\subsection{Parallel Evaluation}
\begin{figure}
\centering
\includegraphics[width=0.9\linewidth]{figs/FMMTraversalParallel.png}
\caption{Parallel Farfield MLFMA.}
\label{fig:tree}
\end{figure}
\subsubsection{C2M}
\label{sec:m2m}
C2M is unchanged from our previous works \cite{melapudi2011scalable,hughey2019parallel}.
As each process is assigned a contiguous segment of whole leaf nodes, each process handles the C2M phase for its assigned leaf nodes in parallel independently.
\subsubsection{M2M}
\label{sec:m2m}
In a nutshell, M2M creates multipole expansions of non-leaf boxes from the multipole expansions of their children. This first requires multipole expansions of all children to be \emph{interpolated} to the size of the parent box. Next, each interpolated child box is \emph{shifted} from the center of the child box to the center of the parent box. Finally, multipole contributions of every shifted child box are \emph{aggregated} to form the multipole expansion for the parent box.
M2M computations start at the leaf level and proceed upwards in the tree following a post-order traversal of the local tree. Our parallelization of \emph{M2M} depends on the level of the node and is described in Alg.\,\ref{alg:m2m}. The approach is as follows: i) Non-plural tree nodes (that are typically found at lower levels of the tree) are handled by their owner processes in parallel independently, ii) for plural nodes without any plural children, \emph{interpolation} and \emph{shift} steps for child nodes are performed sequentially, and the aggregation step is performed as a reduce-scatter operation among processes sharing the plural node, iii) plural nodes with plural children (which typically are located at the higher levels of the tree and incur significant computational and storage costs) are processed using a fine-grained parallel algorithm that we discuss in more detail below.
\begin{algorithm}
\caption{Multipole-to-multipole interpolation}
\begin{algorithmic}[1]
\Require $p.center$ coordinates of the parent box center
\Ensure $pmp$ is parent's multipole representation
\For{each box $p$ in post-order traversal}
\For{each child box $c$}
\If{$c$ is plural}
\State $mp[c]\gets$ parallel\_interpolation($c$)
\Else
\State $mp[c]\gets$ serial\_interpolation($c$)
\EndIf
\State $smp[c]\gets$ shift($mp$, $p.center$)
\EndFor
\If{$p$ is plural}
\State reduce\_scatter($smp$, $users(p)$)
\Else
\For{each child box $c$}
\State aggregate($pmp$,$smp[c]$)
\EndFor
\EndIf
\EndFor
\end{algorithmic}
\label{alg:m2m}
\end{algorithm}
\paragraph{Fine-grained Parallel Interpolation}
For plural nodes that necessitate fine-grained parallelization of M2M, the multipole data of the child nodes needed for FFTs are themselves split among multiple processes as indicated in Alg.\,\ref{alg:m2m}. Prior to elucidating our parallel algorithm, we note that our M2M implementation uses a Fast Fourier Transform (FFT)-based interpolation over the uniformly spaced multipole expansions of the child nodes \cite{Sarvas2003}. FFT-based interpolation on the Fourier sphere requires equispaced samples along $\theta$ (vertical) and $\phi$ (horizontal) directions. Due to the inter-dependencies of the FFT algorithm, there is no way to partition the data so as to avoid communication.
\begin{comment}
\paragraph{Parallel FFT}
\begin{algorithm}
\caption{Parallel FFT interpolation}
\begin{algorithmic}[1]
\For{$\phi$ vector}
\State FFT\_Interpolate()
\EndFor
\State Transpose\_And\_Fold()
\State AlltoAll()
\For{$\theta$ vector}
\State FFT\_Interpolate()
\EndFor
\State Transpose\_And\_Fold()
\State AlltoAll()
\end{algorithmic}
\end{algorithm}
\end{comment}
Our approach is as follows: First, each process is assigned a (roughly) equal number of contiguous columns of multipole data (which correspond to groups of samples along the $\phi$ direction).
The operation begins with a set of independent FFTs along these columns for interpolation in the $\phi$ direction, performed the same as the basic Sarvas approach. Then, the interpolated columns are shifted into rows (see Fig.\,\ref{fig:parallel_interpolation}), transposing and folding the samples in the $\theta$ direction into individual columns. The next step with serial processing would be FFT interpolation in the $\theta$ direction, but this data is split between processes sharing the plural node.
Therefore, each process is communicated the $\theta$ samples they need to complete their assigned columns using an \verb|MPI_Alltoallv| collective call. Now that each process is storing full columns of $\theta$ samples, these multipole data can be interpolated. The fully-interpolated multipole data is transposed and folded back to its original form ($\phi$ samples along columns, $\theta$ samples along rows). The data are again communicated back to the processes that own the corresponding multipole samples via another \verb|MPI_Alltoallv|. These major steps are illustrated in Figure\,\ref{fig:parallel_interpolation}.
\begin{figure}
\centering
\includegraphics[width=\linewidth]{figs/FFT.png}
\caption{Graphical illustration of the transposition and folding operations during fine grained parallel interpolation of multipole data of child node $c$ to parent node $p$ for $N_\theta=3,N_\phi=4$ (for $c$) and $M_\theta=5,M_\phi=6$ (for $p$) using 3 processes each of which owns a column of the initial multipole data as indicated by the hashmarks. Multipole data from (a) is interpolated along the $\phi$ dimension locally, leading to the multipole expansions in (b). The folding operation acting on the interpolated data is shown by the repositioning of the data as in (c). The hash marks show how the folded data is stored on the wrong processes, and must be communicated to the correct process as shown in (d). With the entire multipole data columns in the $\theta$ direction being available on each process, another set of interpolations are performed locally (e), which is then transposed and folded to yield the final multipole expansions (f). A final communication step is needed to send each $\theta$ vector to their owner processes (g) which can then be shifted to the center of the parent box and added to the parent's multipole expansions in accordance with the spherical symmetry condition.}
\label{fig:parallel_interpolation}
\end{figure}
\paragraph{Shifting of Interpolated Data}
Shifting of multipole data is simply the translation of the interpolated samples from the child node's center to the parent node's center. Translation of each multipole data is independent of others and trivially parallelizable even in the case of fine-grained parallel M2M.
\paragraph{Aggregation}
Aggregation requires adding all corresponding samples from each interpolated and shifted child node together to form the multipole expansion of a parent node (step (g) in Fig.\,\ref{fig:parallel_interpolation}). When children are owned by separate processes (as is the case for plural nodes), reduction communications are required. Note that in fine-grained parallel M2M for a plural node, each process owns only a portion of the parent node's multipole data. A reduce/scatter operation (for instance using \verb|MPI_Reduce_scatter|) could perform both the aggregation and distribution of the appropriate portions of the aggregated multipole data to the processes sharing a plural node. One complication here is that the reduce/scatter operation would require memory to be allocated to the full-size of the parent node by each user process through padding the parts not owned by a process with 0s. Clearly, this would lead to significant memory and computational overheads, especially at the highest levels of the H-FMM tree (due to the large sizes of the plural nodes there). Therefore, we opt for a custom point-to-point aggregation scheme where the interpolated and shifted multipole samples from child nodes are communicated directly (via \verb|MPI_Send| and \verb|MPI_Recv|s) to the process that owns the corresponding samples of the parent node. If the source and destination are the same process, obviously no communication is performed. Each process sharing the parent node then adds up the corresponding multipole samples it receives from each child node, local or communicated. This method reduces both the amount of temporary memory necessary for aggregation and the overall communication volume.
\paragraph{Process Alignment}
In fine-grained parallel M2M, performance impact of how the multipole data of child and parent plural nodes are mapped to processes sharing those nodes also needs to be considered. From the description of our custom point-to-point aggregation scheme above, it is evident that increasing the overlap of the multipole sample regions owned by a process in the child and parent nodes is critical for reducing the communication volume.
As an extreme example, if a process owns no samples in the parent node that correspond with any of the samples it owns in the child node, all its interpolated and shifted child node samples would have to be communicated to another process for aggregation. In fact, this extreme example is not uncommon when multipole data of a node is simply partitioned into blocks and mapped to user processes according to their process ranks. This situation is illustrated on the left side of Fig.\,\ref{fig:process_alignment}; some processes own samples of a parent node that has no overlap with the samples they own in the child node. Specifically, while process 1 owns overlapping samples in the child and parent nodes, process 2 and 3 own no overlapping samples.
As a heuristic to minimize the communication volume, we order processes within a parent node such that the parent node samples are assigned by following the priorities below to ensure maximal overlap with their child node samples:
\begin{enumerate}
\item Index of the lowest sample they own in the child nodes (lower comes first),
\item number of samples they own in the child nodes (fewer comes first),
\item process rank.
\end{enumerate}
\begin{figure}
\centering
\includegraphics[width=0.75\linewidth]{figs/ProcessAlignment.png}
\caption{This image shows how multipole samples, ordered clockwise starting at 12 o'clock, are assigned to processes owning the children nodes (C1-C5) overlap with processes owning the parent node (P1-P5) when assigned in process rank order on the left, and with our realignment scheme on the right. The darker portions on the parent samples show the regions where the parent node data overlap with the child node data, and are essentially local data that do not require communication.}
\label{fig:process_alignment}
\end{figure}
In the example given in Fig.\,\ref{fig:process_alignment}, both process 1 and process 3 own samples with index 0 in the child nodes, but process 3 has a smaller number of samples so it is assigned the first portion of the parent node samples with process 1 being assigned the second portion. Following processes 3 and 1, process 4 owns the multipole sample with the lowest index in the child nodes, followed by process 2, and then process 5. As such, remaining portions of the parent node samples are assigned in this order. As can be seen in the figure, all samples each process owns in the parent node fully overlap with samples that they own in the child nodes, despite the non-uniform layout. With the proposed process alignment scheme, process 3 will still need to communicate some samples to process 1 for aggregation, but over half of the child samples interpolated by process 3 remains local. Note that with the straight-forward ordering of processes by their ranks, the entire child data interpolated by process 3 would have to be communicated to processes 1 and 2. In the new scheme, all processes use interpolated samples from their part of a child node without having to communicate. While this scheme would work best with a perfectly balanced tree, this approach will still be effective in reducing the communication volume during aggregation with any tree structure.
\subsubsection{M2L}
\label{sec:m2l}
The M2M step builds the multipole expansions of all tree nodes owned/shared by a process, starting from the leaves all the way up to the root (or the highest level of computation).
During M2L each observer node loops through all source nodes in its far-field and translates the source multipole data to its locale, aggregating the effects from all its far-field interactions in the process. When the source-observer node pair is on the same process, this interaction is handled purely locally. However, when the source node data is on another process (or a set of processes), one needs a load balanced algorithm that is communication efficient.
To understand the scope of the problem, consider Figure \ref{fig:Translation}. Here, the source node is a plural node shared by three processes (S1, S2 and S3); the observer node is shared by two processes (O1 and O2). Multipole samples for both are shared starting at the top of each circle and increasing clockwise (consistent with the process alignment scheme utilized during M2M). Process S1 and O1 both own multipole samples with the lowest indices, with S1 having less samples than O1. For this far-field interaction, S1 would need to send all samples that it owns to O1. S3 and O2 both own samples with the highest indices; here S3 would need to send all of its samples to O2. Finally, S2 owns samples that are needed by both O1 and O2, therefore S2 must send half of its samples to O1 and the other half to O2. Since each node in the H-FMM tree interacts with several others ($\approx$27 for surfaces and up to 189 for volumes) each of which may be shared by a varying number of different processes, it is evident that coordination of all communications that must take place during an H-FMM evaluation is non-trivial.
\begin{figure}
\centering
\includegraphics[width=0.35\linewidth]{figs/Translation.png}
\caption{A translation operation between two plural nodes shared by different numbers of processes.}
\label{fig:Translation}
\end{figure}
In an initialization step before the actual M2L operations, all processes discover the owner process(es) of the tree nodes (i.e., observers) which will need the multipole data for the source nodes they own, given the partitioning of leaf nodes (for load balancing purposes) and process alignments for plural nodes. This pre-calculated list is formed to carry out the actual communications that will take place during the ensuing H-FMM potential evaluations. If a source node or the corresponding observer node is plural, then the pre-calculated communication list will include only the intersection of the multipole data owned by both the source and target processes. When a source node on a process is needed by multiple observers on another process, it is sufficient to include the source node in the communication list to that other process only once. Also, multipole data for multiple source nodes residing on one process that are needed by another can be combined into a single message in this communication list, even if the source nodes are at different levels.
Note that the tree structure in most H-FMM applications are fixed. As such, the overheads associated with such an initialization stage is minimal.
\begin{algorithm}
\caption{M2L Translation}\label{M2LTrans}
\begin{algorithmic}[1]
\State Determine the union of data owned by both source and target.
\Procedure{M2L}{}
\For{each source box}
\For{each farfield interaction target}
\If{Target box is not local}
\For{each process sharing target box}
\State Add source multipole data in union of data owned by both source and target to buffer.
\EndFor
\EndIf
\EndFor
\EndFor
\State Communicate buffers between processes.
\For{each target box}
\For{each farfield interaction source}
\If{Source box is local}
\State Load source multipole data from local memory.
\State Translate source multipole data to target and add to existing translated data for target node
\Else
\For{each process sharing source box}
\State Read source multipole data from communication.
\State Translate source multipole data to target and add to existing translated data for target node
\EndFor
\EndIf
\EndFor
\EndFor
\EndProcedure
\end{algorithmic}
\end{algorithm}
While plural node to plural node far field interactions (which constitute the most expensive communications in an H-FMM evaluation) could actually be carried out using all-to-all communications that involve only the users of the two corresponding plural nodes, due to the excessive number of M2L interactions present in large-scale computations (and hence the large number of different communicators that must be created), we choose to perform these communications using non-blocking point-to-point send/recv operations (i.e., MPI-Isends and MPI-Irecvs) in the default global communicator. Another reason for opting for a point-to-point scheme is that there are significant differences in the amount of data that must be sent to one process compared to another. As part of the initialization step then, each process allocates a message buffer for every other process that it will communicate with. The size of the send buffer is limited to avoid excessive memory use and maximize communication overlap.
To perform communications during M2L, every process first fills their send buffers for each process based on the pre-calculated communication list and initiates the message transmission using \verb|MPI_Isend|s. Immediately after initiating the sends, each process starts waiting for their expected messages using \verb|MPI_Irecv|s. The status of these communications are checked periodically. Computations are overlapped with M2L communications in two ways. First, blocks of translations that are entirely local (which is actually common at the lower tree levels) are processed while the non-blocking send/recvs are taking place. Second, translation data that is detected as received during the periodic checks are applied immediately, overlapping the corresponding computational task with communications underway. Due to the limit we impose on the message buffer sizes, communications with processes that involve a large amount of data transfer need to be performed in multiple phases. Hence, upon reception/delivery of a message from another process, if there is more data to be transferred, a new non-blocking recv/send operation is initiated.
\paragraph{Translation Operators}
Source node data is translated to the target node by multiplying it with a translation operator. The translation operators can be pre-calculated to reduce computational costs. As these can potentially take significant memory, we limit such memory use by each process by having them store the pre-calculated operators only for translation of the local and remote samples that they will actually need. This information can be determined from the pre-calculated M2L communication list. In case the memory available is not sufficient to store the needed operators, we use techniques outlined in \cite{hughey2019parallel} to sample and interpolate translation operators.
\subsubsection{L2L}
\label{sec:l2l}
To anterpolate and distribute the translated local expansions down to the child nodes, L2L applies the operations in M2M in reverse order. First, local expansions at the parent node are shifted to the center of each child node, they are then anterpolated and percolated down the tree. Finally, the anterpolated data is aggregated with local expansions previously translated to the child node during the M2L stage.
Much like M2M, L2L operation is parallelized in three different ways: i) Non-plural parent tree nodes at the lower tree levels are processed independently in parallel by their owner processes, ii) for a plural node with a non-plural child, shifts involve communications, but the ensuing anterpolation and aggregation (with translated local expansions) are performed sequentially by the process owning the child node, iii) plural nodes with plural children require fine-grained parallelization.
\paragraph{Shift}
In a parallel shift operation, parent node samples corresponding to those of the child node must be communicated by the processes sharing the parent node to the process(es) owning the child node. This is most easily done before the data has been shifted, as the parent will not need to know the position of the child node. In case of plural parent and non-plural child, this communication would essentially be a \emph{gather}, and in case of plural parent with a plural child, it would be an \emph{all-to-all}, in both cases involving all processes sharing the parent node. However, only a subset of the processes sharing the parent node will actually share the child node. To avoid non-trivial issues that would arise from having to coordinate several collective calls among different subsets of processes, we again resort to point-to-point communications instead. Consequently, messages are only sent from processes owning a piece of the parent node to a process owning the corresponding piece of the child node. Once a process gathers all of necessary samples of the parent node, it applies the shift operation to all its multipole samples independently.
\paragraph{Anterpolation}
Anterpolation would have to be performed in parallel only if the child node is a plural node. The procedure for parallel anterpolation is exactly the same as that of the parallel interpolation, except that the number of multipole samples is reduced (rather than increased).
\paragraph{Aggregation}
Aggregating the shifted and anterpolated parent data with translated local expansions is trivial. Even in the case of plural child nodes, all required data is already available locally.
\subsubsection{L2O}
\label{sec:m2m}
As in C2M, each process handles the L2O computations of its assigned leaf nodes in parallel independently.
\end{document}
\subsection{Interpolation (M2M)}
\paragraph{Computational Complexity}
M2M is performed for each node, starting from the leaf level up to the highest level $N_L$. The dominant component in the computational complexity for $M2M$ is FFT-based interpolation. Shifting and aggregation are $O(K(l)^2)$ operations each, while interpolation for a given node costs $O(K(l)^2 \log^2{(K(l)))}$. This gives a total computational complexity of
\begin{equation}
C \propto \sum_{l=1}^{N_L}G(l)K(l)^2 \log^2 (K(l))
\end{equation}
Plugging in the equations \eqref{eq:gl} and \eqref{eq:kl} and simplifying the summation, we obtain the computational complexity for a surface to be:
\begin{equation}
C \propto O(N_s \log^2 N_s),
\end{equation}
and for a volume to be:
\begin{equation}
C \propto O(N_s)
\end{equation}
\paragraph{Number of Messages (Latency)}
Communication in $M2M$ happens during aggregations for both coarse-grained and fine-grained parallel $M2M$s, as well as the FFTs of the fine-grained parallel $M2M$s. As described in Sect.\,\ref{sec:m2m}, we perform aggregations (which are effectively reduce-scatter operations) using point-to-point communications. In an ideal tree, every source and observer node will be divided among the same number of nodes. This means the portion of a source node owned by any process will only be owned by a single process in the observer node, limiting the communication for each source node process to one process in each observer node. Since this is done for each group at each level, the total message count for aggregations can be written as:
\begin{equation}
M_{Ag} \propto \sum_{P_L}^{N_L} G(l) P_N(l+1).
\end{equation}
Using expressions for $P_N(l+1)$ and $G(l)$, yields the number of messages for aggregation
\begin{equation}
M_{Ag} = O(P \log (N_S) 2^d).
\end{equation}
Here, we ignore aggregations that would be needed for plural nodes (located at process boundaries) below level $P_L$. Note that there may only be two such plural nodes per level for each process and these aggregations will involve only two processes. As such, their contribution to the number of messages during aggregations is of a lower order term.
Next, consider the parallel FFTs in fine-grained parallel $M2M$s. In this case, an all-to-all communication is performed after each of the two fold and transpose operations. As we implement these all-to-all communications using point-to-point calls, the message count for FFTs is then:
\begin{equation}
M_{FFT} = \sum_{l=P_L}^{N_L} G(l) P_N(l)^2 \propto O(P^2).
\end{equation}
Consequently, the total number of messages for $M2M$ is:
\begin{equation}
M_{M2M} = O(P^2 + P \log(N_s)). \label{eq:m2m}
\end{equation}
Note, the $N_s$ portion of the equation above is only going to matter when $P_L$ is greater than the number of levels in the tree. In all other cases, increasing the height of the tree does not increase the number of levels with plural nodes. Given that it is practically useless to have more processes than the number of leaf nodes (which is the condition required for $P_L$ to be more than the tree height), the message count can be simplified to $M_{M2M} = O(P^2)$.
\paragraph{Communication Volume (Bandwidth)}
Bandwidth during interpolation is due to all to all communications during interpolation, and a reduce scatter during the aggregation. Each of these operation communicates up to the entire node, resulting in a bandwidth that can be written as:
\begin{equation}
B \propto \sum_{l=1}^{N_L} G(l) K(l)^2
\end{equation}
Applying the previous definitions for $G(l)$ and $K(l)$ yields a communication bandwidth of $B \propto N_s \log N_s$ for the surface geometry, and $B \propto N_s$ for the volume geometry.
\subsection{Translation (M2L)}
\paragraph{Computational Complexity}
The complexity for the translation operation at a given level is directly proportional to the number of multipole samples for nodes, the average number of interactions per node (denoted by $I(l)$ for level $l$), and the number of nodes at that level. Summing these costs across all levels, we obtain:
\begin{equation}
C \propto \sum_{l=1}^{N_L} K(l)^2 I(l) G(l).
\label{eq:mMapping}
\end{equation}
While the number of interactions for a node changes based on its exact position in the geometry (for instance, corner or edge nodes), the upper limit is the constant $6^d-3^d$. Using the equations for $K(l)$ and $G(l)$, computational complexity of the translation step can be simplified to $O(N_s \log N_s)$ for the surface structure, and to $O(N_s)$ for the volume structure.
\paragraph{Number of Messages (Latency)}
At level $P_L$ or above, a process can have multipole samples for only one node. Since a process owns at most part of a single node, each of its interactions will require a separate communication because the nodes in its far-field will all reside on different processes. Assuming an ideal tree partitioning where the source and target nodes are shared among the same number of processes, the $k$th process for the target node will only need the source node data from the $k$th process of the source node. As we limit the size of each translation message, the number of messages will then be proportional to the communication volume between a pair of processes divided by the message buffer size $M_S$. At levels below $P_L$, a process can own multiple nodes. Here groups of nodes can be communicated to the same process, if all source nodes reside on one process and all observer nodes reside on another. In this case, the interaction count is going to be based on the total amount of data communicated between the two interacting processes, divided by the message buffer size, summed up for all interacting processes.
Considering contributions at/above $P_L$ and below $P_L$ gives a total message count of:
\begin{equation}
M \propto \sum_{l=P_L}^{N_L} P I(l) \frac{K(l)^2}{P_N M_S} + P I(l) \ceil{\frac{\sum_{l=1}^{P_L - 1} K(l)^2 \frac{G(l)}{P}}{M_S}}
\label{eq:mMapping}
\end{equation}
where $M_S$ is the size of message buffers. For the surface geometry, this can be simplified to $M \propto O(N_s \log N_s) + O(N_S)$ (where the first term is for levels $\ge P_L$ and the second term is for levels $<P_L$), and for the volume geometry it can be simplified to $M \propto O(N_s)$ (with both below and above $P_L$ having the same impact).
\paragraph{Communication Volume (Bandwidth)}
Similarly, communication volume can be analyzed in two parts as well. At and above $P_L$, all multipole data for every source node must essentially be communicated to every target node as no process contains any multipole data other than its own. Even if the number of processes increases, still the same amount of data needs to be transmitted, just among an increased number of nodes. Therefore, for level at or above $P_L$, the communication volume is independent of the number of processes:
\begin{equation}
B \propto \sum_{l=P_L}^{N_L} K(l)^2 G(l) I(l)
\end{equation}
This expression simplifies to $O(N_s \log N_s)$ for the surface geometry and to $O(N_s)$ for the volume geometry.
Below $P_L$, each process will own more than one node, nodes will be interacting with nodes on the same process, or multiple nodes owned by a neighboring process. In fact, only nodes within two nodes off the edge of process boundaries will require communications with other processes. Total communication bandwidth can then be expressed as:
\begin{equation}
B \propto \sum_{l=1}^{P_L - 1}P K(l)^2 (S_N)
\end{equation}
where $S_N$ is the number of nodes that have nodes in its far-field from at least one (out of the 8 possible neighboring processes for the surface and 26 for the volume) other processes touching them and can be represented as $S_N = \frac{G(l)}{P}^{\frac{d-1}{d}} = \frac{1}{P}(\frac{N_s}{(2^d)^{(l-1)}})^{\frac{d-1}{d}}$.
With this definition of $S_N$, the total communication volume for M2L below $P_L$ becomes
\begin{equation}
B \propto O(N_S)
\end{equation}
for the surface, and
\begin{equation}
B \propto O(N_S^{\frac{2}{3}})
\end{equation}
for the volume, due to the lower portion of the tree dominating.
\subsection{Anterpolation (L2L)}
As mentioned before, L2L is the reverse operation for M2M. Similar to M2M, anterpolation dominates the computational complexity for L2L. Computational complexity for anterpolations is the same as that of interpolations, so L2L's computation complexity is the same as M2M's.
Likewise, communications performed are the same but in reverse order. Therefore, the latency and bandwidth costs of L2L are the same as those of M2M.
\end{document}
\subsection{Remedies for plural node bottlenecks}
We will first examine the performance gains in the M2M and L2L stages from parallelizing the Fourier interpolation/anterpolation operators for plural nodes.
We first consider a sphere of diameter $320\lambda$ discretized using 241,920,000 dipoles on the surface. The leaf box is chosen as $d_0=0.2\lambda$, yielding a 12-level tree. The transition level is chosen such that the finest five levels of computation use spherical sampling and the top five levels use uniform.
Timings for M2M and L2L for different numbers of processes $N_p$ up to 2048 are given in Table \ref{fig:pfft_timings_table_sphere}. As with the grid geometry, performance gains using PFFT become increasingly evident with increasing $N_p$, culminating in speedups of over $3\times$ on 2048 processes. The scalability of the traversal operations thus improves dramatically. A more intimate perspective is offered by Figs. \ref{fig:BigSphereOverview}-\ref{fig:BigSphere}, which present per-process timings for M2M and L2L in both the original and PFFT-augmented algorithms. Unlike the grid geometry, a sphere does not conform directly to the octree structure so imbalances in these operations are to be expected. This is evident from the timings shown in Fig. \ref{fig:BigSphere}a), which shows timings of individual components of M2M and L2L for the original algorithm. Here, a large amount of time is spent waiting in M2M at an \texttt{MPI\_Waitall} as other processes finish their portion of the serial interpolations. L2L also suffers from a load imbalance resulting from uneven distribution of high-level serial anterpolations. These effects are highlighted by the extreme imbalance of composite serial interpolation and anterpolation (int/ant) timings. Parallelization of these operations, as shown in Fig. \ref{fig:BigSphere}b), significantly reduces both the computation and wait times. The serial interpolation and anterpolation are reduced to about one second overall in the worst case, and the overall distribution is much more balanced. The difference in the shapes of the M2M and L2L timings is due to the fact that M2M has a synchronization barrier at the end, while L2L does not.
We next consider a $512\lambda\times512\lambda$ grid of particles in the $z=0$ plane with a grid spacing of $\lambda/32$ with 268,435,456 points. The box size is chosen to be $0.25\lambda$, resulting in a 12-level tree with 10 levels of computation. For the hybrid implementation, we empirically set the bottom 6 levels of the tree to employ the spherical scheme, while the top 4 levels of computation employ the uniform scheme. The oversampling parameter $\chi$ is chosen to be 1.
The regularity of the grid geometry helps to highlight load imbalances inherent to the original algorithm and to illustrate the benefits of the PFFT algorithm. A study of the timings for M2M and L2L for both the original and PFFT schemes is shown in Table \ref{fig:pfft_timings_table}. We observe bigger gains in performance relative to the original scheme as the number of processes $N_p$ increases. This is due to the increasing number of plural nodes to be parallelized. PFFT also facilitates significant improvements in the M2M and L2L parallel efficiency (\emph{strong scaling}), defined as
\begin{equation}
\text{Eff.}\left[N_q\right] (\%) \doteq \frac{N_p T_{N_p}}{N_q T_{N_q}} \times 100 \%,
\end{equation}
where $N_p,T_{N_p}$ are the reference process count and computation time, and $N_q,T_{N_q}$ are the process count and computation time for which the efficiency is being calculated.
We now consider the case of a $1024\lambda\times1024\lambda$ grid lying in the $z=0$ plane with a regular spacing between points of $\lambda/32$ in each dimension. The total number of particles in this geometry is 1,073,741,824. The leaf box size is chosen as $\lambda/4$, resulting in a 13-level tree (with 11 levels of computation). The finest six levels of the tree employ spherical interpolation/anterpolation and the coarsest five levels employ uniform interpolation/anterpolation.
Figure \ref{fig:BigGridOverview} provides a comparison of tree traversal timings for 2048 processes both with and without the PFFT scheme. Specific timings for the run without the PFFT scheme are shown in Figure \ref{fig:BigGrid}a), while those for the run with the PFFT scheme are given in Figure \ref{fig:BigGrid}b). As with the previous grid example, the apparently well-balanced load in M2M for the former case is shown to be misleading, as most processes spend approximately 23 seconds in M2M waiting for nodes with larger than average amounts of serial interpolations to finish their serial computations. The load imbalance is also clear in the timings for L2L, which lacks an explicit synchronization step at the end.
The PFFT scheme, in contrast, results in much better load balance in both M2M and L2L stages, along with reduced run-times due to the parallelization of some previously serial computations. The time spent in M2M is reduced from 46.2 seconds for the original algorithm to 7.65 seconds with the PFFT scheme, a speedup of over 6$\times$. Similarly, the maximum time spent in L2L decreases from 35.0 seconds to 5.44 seconds for a speedup of 4.6$\times$
\begin{table*}
\centering
\rowcolors{2}{gray!30}{white}
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|}
\multicolumn{1}{c}{} & \multicolumn{2}{c}{\textbf{Orig} (s)} & \multicolumn{2}{c}{\textbf{PFFT} (s)} & \multicolumn{2}{c}{\textbf{Speedups}} & \multicolumn{2}{c}{\textbf{Orig Eff. (\%)}} & \multicolumn{2}{c}{\textbf{PFFT Eff. (\%)}}\\\hline
$N_p$ & M2M & L2L & M2M & L2L & M2M & L2L & M2M & L2L & M2M & L2L\\\hline
32 & 78.6 & 62.6 & 73.9 & 71.9 & 1.06 & 0.87 & 100 & 100 & 100 & 100\\
64 & 43.7 & 34.4 & 41.3 & 38.5 & 1.06 & 0.89 & 89.9 & 91.0 & 89.5 & 93.4\\
128 & 28.9 & 22.0 & 26.2 & 20.0 & 1.10 & 1.10 & 68.0 & 71.1 & 70.5 & 89.9\\
256 & 16.7 & 12.4 & 13.9 & 10.5 & 1.20 & 1.18 & 58.8 & 63.1 & 66.5 & 85.6\\
512 & 12.5 & 9.16 & 9.08 & 6.87 & 1.38 & 1.33 & 39.4 & 42.7 & 50.9 & 65.4\\
1024 & 18.6 & 14.7 & 6.38 & 4.78 & 2.92 & 3.08 & 13.2 & 13.3 & 36.2 & 47.0\\
2048 & 12.7 & 9.22 & 3.80 & 2.97 & 3.34 & 3.10 & 9.67 & 10.6 & 30.4 & 37.8\\\hline
\end{tabular}
\caption{Comparison of original algorithm with PFFT for $320\lambda$ diameter sphere geometry.}
\label{fig:pfft_timings_table_sphere}
\end{table*}
\begin{table*}
\centering
\rowcolors{2}{gray!30}{white}
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|}
\multicolumn{1}{c}{} & \multicolumn{2}{c}{\textbf{Orig} (s)} & \multicolumn{2}{c}{\textbf{PFFT} (s)} & \multicolumn{2}{c}{\textbf{Speedups}} & \multicolumn{2}{c}{\textbf{Orig Eff.} (\%)} & \multicolumn{2}{c}{\textbf{PFFT Eff.} (\%)}\\\hline
$N_p$ & M2M & L2L & M2M & L2L & M2M & L2L & M2M & L2L & M2M & L2L\\\hline
32 & 45.4 & 38.0 & 44.5 & 37.4 & 1.02 & 1.02 & 100 & 100 & 100 & 100\\
64 & 25.8 & 21.2 & 24.9 & 20.3 & 1.04 & 1.04 & 88.0 & 89.6 & 89.4 & 92.1\\
128 & 18.5 & 14.3 & 12.9 & 10.5 & 1.43 & 1.36 & 61.4 & 66.4 & 86.2 & 89.0\\
256 & 13.5 & 9.9 & 7.4 & 5.7 & 1.82 & 1.74 & 42.0 & 48.0 & 75.2 & 82.0\\
512 & 12.1 & 8.5 & 4.4 & 3.4 & 2.75 & 2.5 & 23.5 & 27.9 & 63.2 & 68.8\\
1024 & 11.4 & 7.7 & 3.0 & 2.3 & 3.80 & 3.35 & 12.4 & 15.4 & 46.4 & 50.8\\\hline
\end{tabular}
\caption{Comparison of PFFT with original algorithm for $512\lambda$ grid geometry.}
\label{fig:pfft_timings_table}
\end{table*}
\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{figs/BigSphereOverview.pdf}
\caption{Timing comparison of M2M and L2L operations for $320\lambda$ diameter sphere on 2048 cores with and without PFFT.}
\label{fig:BigSphereOverview}
\end{figure}
\begin{figure*}
\centering
\subfloat[Without PFFT]{\includegraphics[width=0.49\linewidth]{figs/BigSphereNoPFFT.pdf}}
\subfloat[With PFFT]{\includegraphics[width=0.481\linewidth]{figs/BigSpherePFFT.pdf}}
\caption{Timing breakdown for M2M/L2L with and without PFFT for the 320$\lambda$ sphere.}
\label{fig:BigSphere}
\end{figure*}
\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{figs/BigGridOverview.pdf}
\caption{Timing comparison of M2M and L2L operations for $1024\lambda$ diameter grid on 2048 cores with and without PFFT.}
\label{fig:BigGridOverview}
\end{figure}
\begin{figure*}
\centering
\subfloat[Without PFFT]{\includegraphics[width=0.49\linewidth]{figs/BigGridNoPFFT.pdf}}
\subfloat[With PFFT]{\includegraphics[width=0.481\linewidth]{figs/BigGridPFFT.pdf}}
\caption{Timing breakdown for M2M/L2L with and without PFFT for the 1024$\lambda$ grid.}
\label{fig:BigGrid}
\end{figure*}
\begin{figure}
\centering
\subfloat[]{\label{fig:boeingUniNU}\includegraphics[width=0.485\linewidth]{figs/Boeing1024proc_Uni_vs_NU.pdf}}
\hfill
\subfloat[]{\label{fig:boeingLB}
\includegraphics[width=0.485\linewidth]{figs/Boeing_1024proc_LB.pdf}}
\caption{Per-process timings for far-field matvec stages for the airplane geometry (a) with uniform vs. non-uniform tree and (b) with and without load balancing (LB) for non-uniform tree on 1024 processes.}
\label{fig:boeing1024}
\end{figure}
Finally, we examine the effects of merging the tree for non-uniform distributions and load balancing. We consider a geometry containing 175,764,666 points on the surface of an aircraft which fits into a bounding box of dimensions $693.5\lambda\times200.2\lambda\times754.8\lambda$. The minimum leaf box diameter was set to $\lambda/32$ resulting in a 16-level tree, and the densest box contains 56 points. The four coarsest levels of computation use uniform sampling, and the remaining seven MLFMA levels use spherical sampling. ACE is used for boxes of diameter smaller than $\lambda/4$. The non-uniform tree is merged with $s_{max}=40$, resulting in leaves containing 20 points on average distributed over the bottom five levels of the tree, and an almost twenty-fold reduction in leaf boxes. For accuracy on the order of $10^{-3}$, we set $\chi=1.0,P=3$ \cite{vikram2009novel}. This supposition is backed up by randomly selecting a point on each process to ensure good spatial distribution, computing the exact observed field, and comparing with the computed value; the average relative error at these observers is $3.98\times10^{-3}$.
With this setup, we examine the trade-offs for non-uniform trees vs. uniform trees and the beneficial effects of load balancing for parallel matvecs. Fig. \ref{fig:boeingUniNU} shows the time taken per process for the far-field matvec using 1024 processes using a uniform tree and a non-uniform tree. The time drops from 61 seconds on average for the uniform tree to 38 seconds for the non-uniform tree. Load balancing is employed in both instances. Much of the speedup is achieved in the translation stages. The flatness of portions of the M2L timings for the uniform tree are caused by synchronization barriers. Fig. \ref{fig:boeingLB} details the effectiveness of load balancing, showing per-process timings for the tree traversal (M2M+L2L) and translation ($V,W,X-$lists) both with and without load balancing with exactly the same parameters. Without load balancing, the translation stage alone takes ten seconds longer than the entire matvec with load balancing.
\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{figs/arrow_scaling.pdf}
\caption{Parallel efficiency of the complete \emph{matvec} for the 286M-point arrow geometry with reference to 256 processes. Colorization of geometry solely to illustrate depth.}
\label{fig:arrow_scaling}
\end{figure}
Next, we consider a collection of 286,312,650 points distributed uniformly on a surface geometry with an arrow-like shape, yielding high variation in point density over the surface. The bounding box for the arrow measures $234.9\lambda\times77\lambda\times39.32\lambda$, and we choose the minimum box size to be $\lambda/64$, resulting in a 15-level tree. As always, ACE is used for boxes smaller than $\lambda/4$. The three coarsest MLFMA levels of computation employ uniform sampling, while the rest employ spherical sampling. The tree is merged using $s_{max}=25$, resulting in 9 points per leaf box on average.
The parallel efficiency of the complete \emph{matvec} (both near- and far-field together) is given in Fig. \ref{fig:arrow_scaling} with reference to 256 processes. Memory limitations prevented us from running the code under the same memory-per-core conditions beneath 256 processes. Up to 1,024 processes the \emph{matvec} exhibits good scaling, but drops precipitously for 2,048 processes. This appears to be associated with synchronization steps within the parallel interpolation/anterpolations.
\end{document}
\subsection{Fine grain algorithm balance}
\begin{figure}[H]
\centering
\includegraphics[width=.5\textwidth]{figs/GridProcessBalance.png}\hfill
\includegraphics[width=.5\textwidth]{figs/SphereProcessBalance.png}\hfill
\caption{Process execution times for a grid and a sphere geometry.}
\label{fig:computational_complexity}
\vspace{-0.15in}
\end{figure}
The intent of the find grain parallel algorithm is to provide improved balance at the upper levels of the tree where a lower number of much larger nodes reside. First we look at the performance of a $512\lambda\times512\lambda$ grid of particles in the $z=0$ plane with a grid spacing of $\lambda/4$ with 4,194,304 particles. The box size is chosen to be $0.25\lambda$, resulting in a 12-level tree with 10 levels of computation. With this geometry, each leaf contains a single particle. This minimizes the nearfield execution time as we are focusing on the performance of the farfield tree traversal. The resulting time of execution is very balanced across the process ranks. Total execution of the farfield tree traversal takes up to 21.3 seconds for the worst case process and 21.0 second for the best case process. Balance of total time can be a little misleading as M2L cannot progress until all processes a given process interacts with have completed their M2M processing. However the M2M execution times are also very balanced, ranging from at most 4.43 seconds to as little as 4.21 seconds. This means at most a process would have to wait 0.22 seconds to begin communicating with the other processes.
Next we look at the performance of a sphere of diameter $384\lambda$ discretized using 4,542,208 dipoles on the surface. The leaf box is chosen as $d_0=0.25\lambda$, yielding an 11-level tree. Again, this geometry produces one particle per leaf box so the performance analysis can focus on the farfield tree traversal. This geometry far less balanced than the grid geometry. High level nodes can range from having no children due to no particles in that part of the geometry at the leaf level, up to having a completely filled quad tree from the leaf level up to a high level node. This results in notable imbalance at the M2M level, which as discussed before, results in delays in the M2L execution. The M2M execution ranges from as long as 11.4 seconds to as short as 6.2 seconds. Despite this noticeable imbalance, the long execution times are not clustered among a small group of nodes as you would see if each of the 16 nodes at the highest level of computation was being handled by a single process. So even in this unbalanced geometry, the find grain parallel algorithm is helping to maintain a better balance across process ranks.
\subsection{Performance}
The previous section showed the balance provided by the fine grain parallel algorithm, in this section we will look at what this means for performance.
\begin{table*}
\centering
\rowcolors{2}{gray!30}{white}
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|}
\multicolumn{1}{c}{} & \multicolumn{4}{c}{\textbf{Grid} (s)} & \multicolumn{1}{c}{\textbf{Speedup}} & \multicolumn{4}{c}{\textbf{Par Eff.} (\%)}\\\hline
$N_p$ & M2M & M2L & L2L & Tot & Tot & M2M & M2L & L2L & Tot\\\hline
128 & 5.80 & 5.30 & 5.30 & 18.55 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00\\
256 & 3.06 & 4.13 & 2.66 & 11.21 & 1.65 & 0.95 & 0.64 & 0.99 & 0.83\\
512 & 1.52 & 2.76 & 1.31 & 6.42 & 2.89 & 0.95 & 0.48 & 1.01 & 0.72\\
1024 & 0.81 & 2.12 & 0.69 & 4.05 & 4.58 & 0.89 & 0.31 & 0.95 & 0.57\\\hline
2048 & 0.43 & 1.31 & 0.37 & 2.38 & 7.78 & 0.84 & 0.25 & 0.89 & 0.49\\\hline
\end{tabular}
\caption{Performance of the MLFMA algorithm $512\lambda$ grid geometry.}
\label{fig:pfft_timings_table}
\end{table*}
First we look at the same $512\lambda\times512\lambda$ grid. An analysis of the parallel efficiency (\emph{strong scaling}), defined as
\begin{equation}
\text{Eff.}\left[N_q\right] (\%) \doteq \frac{N_p T_{N_p}}{N_q T_{N_q}} \times 100 \%,
\end{equation}
where $N_p,T_{N_p}$ are the reference process count and computation time, and $N_q,T_{N_q}$ are the process count and computation time for which the efficiency is being calculated, shows where the parallel execution is performing well and where it is performing more poorly. Both the interpolation and anterpolation (M2M and L2L) perform very well as the number of processes increase, while M2L performance falls off more rapidly. There are a couple of factors that contribute to this. First is M2M and L2L only communicate at the highest level nodes. With M2L communication occurs at every level where the source and observer nodes are on separate processes, which can occur all the way down to the leaf nodes. As a result, M2L initial bandwidth is much higher. Secondly the worst case M2L bandwidth estimate shows a only dependent on the number of samples, but this is not the full story. Once there are enough processes that every leaf is on a separate process, increasing the number of processes would not increase M2L bandwidth. For a 12 level tree of a surface geometry, this would require 4,194,304 processes. So as the number of processes increases toward the number of leaf nodes, the M2L bandwidth trends toward the worst case bandwidth. Support for this can be seen by noting that while parallel efficiency drops off drastically from 128 to 256 processes, but less so from 1024 to 2048 processes. Despite M2L not scaling as well, the scalability still provides good speedups, nearly a full 8x when going from 128 to 2048 processes.
\begin{table*}
\centering
\rowcolors{2}{gray!30}{white}
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|}
\multicolumn{1}{c}{} & \multicolumn{4}{c}{\textbf{Volume} (s)} & \multicolumn{1}{c}{\textbf{Speedup}} & \multicolumn{4}{c}{\textbf{Par Eff.} (\%)}\\\hline
$N_p$ & M2M & M2L & L2L & Tot & Tot & M2M & M2L & L2L & Tot\\\hline
128 & 0.527 & 2.15 & 0.526 & 3.26 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00\\
256 & 0.266 & 1.10 & 0.263 & 1.68 & 1.94 & 0.99 & 0.97 & 0.99 & 0.97\\
512 & 0.14 & 0.679 & 0.135 & 0.99 & 3.27 & 0.93 & 0.79 & 0.97 & 0.82\\
1024 & 0.079 & 0.380 & 0.084 & 0.574 & 5.68 & 0.83 & 0.71 & 0.78 & 0.71\\\hline
2048 & 0.051 & 0.271 & 0.058 & 0.406 & 8.03 & 0.65 & 0.50 & 0.57 & 0.50\\\hline
\end{tabular}
\caption{Performance of the MLFMA algorithm $32\lambda$ volume geometry.}
\label{fig:pfft_timings_table}
\end{table*}
Next we look at a $32\lambda\times32\lambda\times32\lambda$ volume. While real world Helmholtz FMM applications rarely work with volumes, a complicated enough surface may act like a volume over part of the geometry. From 128 to 512 processes the scaling is very strong but then it drops off quickly. The optimal execution happens when the nodes of a given level are distributed evenly among the processes, ie when the number of processes divides evenly into the number of nodes in a level or vice versa. This does not occur at 1024 or 2048 processes with a volume. (is that the reason? think more...) Still the overall speedup remains around 8x when going from 128 to 2048 processes, so the parallel execution is still providing value.
\begin{table*}
\centering
\rowcolors{2}{gray!30}{white}
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|}
\multicolumn{1}{c}{} & \multicolumn{4}{c}{\textbf{Sphere} (s)} & \multicolumn{1}{c}{\textbf{Speedup}} & \multicolumn{4}{c}{\textbf{Par Eff.} (\%)}\\\hline
$N_p$ & M2M & M2L & L2L & Tot & Tot & M2M & M2L & L2L & Tot\\\hline
128 & 6.71 & 13.54 & 5.29 & 26.76 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00\\
256 & 3.86 & 10.05 & 2.7 & 18.00 & 1.49 & 0.87 & 0.67 & 0.97 & 0.74\\
512 & 2.34 & 6.20 & 1.46 & 11.04 & 2.42 & 0.72 & 0.55 & 0.91 & 0.61\\
1024 & 1.23 & 4.32 & 0.72 & 7.70 & 3.47 & 0.68 & 0.39 & 0.92 & 0.43\\\hline
2048 & 0.92 & 3.19 & 0.416 & 5.58 & 4.79 & 0.46 & 0.26 & 0.79 & 0.30\\\hline
\end{tabular}
\caption{Performance of the MLFMA algorithm $384\lambda$ diameter sphere geometry.}
\label{fig:pfft_timings_table}
\end{table*}
Finally we look at the performance of the $384\lambda$ sphere for something closer to a real world geometry. As seen in the load balance analysis, the unbalanced tree results in the faster processes having to wait for slower processes to complete at times. This results in a noticeable drop in efficiency in M2M time, where the imbalance has the greatest impact, and the M2L time, where some M2L processes have to wait for other processes to complete their M2M processing. This also has an impact on the overall speedup. While increasing the number of processes continues to improve execution times, the speedup when going from 128 to 2048 processes is just under 5x in the unbalanced geometry.
\subsection{Complexity Analysis}
To obtain the complexity analysis, the software was instrumented to report eh number of computations, complex packets and messages sent. This was run on the $512\lambda$ grid and the $32\lambda$ volume geometries as these geometries produce perfect 4 or 8 dimensional trees. Runs ranged from 256 to 2048 processes, the number of processes being doubled each run, surface geometries ranging from 9 to 13 levels and volume geometries ranging from 7 to 11 levels.
\begin{figure}[H]
\centering
\includegraphics[width=.5\textwidth]{figs/ComplexitySurface.png}\hfill
\includegraphics[width=.5\textwidth]{figs/ComplexityVolume.png}\hfill
\caption{Computational Complexity vs expected Big-O complexity. The left diagram shows analysis of a surface geometry, while the right diagram shows analysis of a volume geometry.}
\label{fig:computational_complexity}
\vspace{-0.15in}
\end{figure}
Figure \ref{fig:computational_complexity} shows the actual complexity vs the estimated worst case complexity. The actual complexities match the expected complexities very closely. If the algorithm was causing duplicate computations, the complexity would not scale as expected. This shows that the parallel execution does not negatively impact overall computation.
\begin{figure}[H]
\centering
\includegraphics[width=.5\textwidth]{figs/M2ML2LBandwidthSurface.png}\hfill
\includegraphics[width=.5\textwidth]{figs/M2ML2LBandwidthVolume.png}\hfill
\caption{M2M and L2L Bandwidth vs expected Big-O bandwidth. The left diagram shows analysis of a surface geometry, while the right diagram shows analysis of a volume geometry.}
\label{fig:m2m_l2l_bandwidth}
\vspace{-0.15in}
\end{figure}
Figure \ref{fig:m2m_l2l_bandwidth} shows the actual bandwidth vs the estimated worst case bandwidth for M2M and L2L. Of note is how the measured bandwidth drops off relative to the estimate. This is thought to be due to the number of samples producing a tree with more nodes at lower levels than the number of processes. Thus many nodes are fully owned by a single process, and require no communication during M2M or L2L. Increasing the number of processes would lead to more levels with plural nodes, bringing the bandwidth up closer to the estimated worst case.
\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{figs/M2LBandwidthComplexity.png}\hfill
\caption{M2L Bandwidth vs expected Big-O bandwidth.}
\label{fig:m2l_bandwidth}
\vspace{-0.15in}
\end{figure}
Figure \ref{fig:m2l_bandwidth} shows the measured bandwidth vs the estimated worst case bandwidth for M2L. M2L does not show the same bandwidth falloff as M2M and L2L vs the expected bandwidth, because fully owned nodes still require data from the source nodes to be communicated to the process owning the observer node. This communication will be required all the way down to the leaf node.
\begin{figure}[H]
\centering
\includegraphics[width=1.\textwidth]{figs/M2ML2LMessages.png}\hfill
\caption{M2M and L2L Messages vs expected Big-O messages.}
\label{fig:m2m_l2l_messages}
\vspace{-0.15in}
\end{figure}
Figure \ref{fig:m2m_l2l_messages} shows the measured worst case messages vs the estimated worst case messages for M2M and L2L. Message counts are dominated by the $P^2$ complexity of the all to all communications and the actual message count reflects this.
\begin{figure}[H]
\centering
\includegraphics[width=.5\textwidth]{figs/M2LMessageProcessComplexityGrid.png}\hfill
\includegraphics[width=.5\textwidth]{figs/M2LMessageProcessComplexityVolume.png}\hfill
\caption{M2L Messages vs expected Big-O messages for changes in process counts.}
\label{fig:m2l_messages_process}
\vspace{-0.15in}
\end{figure}
Figure \ref{fig:m2l_messages_process} shows the actual vs expected message count based on increasing process counts. The prediction simplifies a very complex process that results in the number of M2L messages that are communicated.
\begin{figure}[H]
\centering
\includegraphics[width=.5\textwidth]{figs/M2LMessageSampleComplexityGrid.png}\hfill
\includegraphics[width=.5\textwidth]{figs/M2LMessageSampleComplexityVolume.png}\hfill
\caption{M2L Messages vs expected Big-O messages for changes in particle counts.}
\label{fig:m2l_messages_sample}
\vspace{-0.15in}
\end{figure}
Figure \ref{fig:m2l_messages_sample} shows how the actual number of M2L messages compares with the expected number. This analysis is a bit skewed as we limit the size of the communication buffer in order to save memory. Thus more messages are sent than would be necessary if all source nodes with observer nodes in a given process could be communicated in a single message, but this message is split up into multiples.
\subsection{Process Alignment}
\begin{table*}
\centering
\rowcolors{2}{gray!30}{white}
\begin{tabular}{|r|r|r|r|r|r|r|}
\hline
N_P & & 128 & 256 & 512 & 1024 & 2048\\\hline
PID Ordered & M2M Bandwidth & 1714 & 1872 & 3009 & 3126 & 4246\\
& L2L Bandwidth & 1206 & 1166 & 2429 & 2382 & 3649\\
& Combined Bandwidth & 2920 & 3038 & 5438 & 5508 & 7895\\\hline
Process Aligned & M2M Bandwidth & 1468 & 1662 & 2711 & 3272 & 4412\\
& L2L Bandwidth & 960 & 955 & 2131 & 2104 & 3338\\
& Combined Bandwidth & 2428 & 2617 & 4842 & 5376 & 7750\\\hline
Delta & & -492 & -421 & -596 & -132 & -145\\\hline
\end{tabular}
\caption{Comparison of packets sent between PID and Process Aligned nodes for the $512\lambda$ grid geometry in millions of packets sent.}
\label{fig:grid_memory_table}
\end{table*}
Initial investigation into process alignment shows a notable reduction in bandwidth for lower process counts and continued reduction in bandwidth at higher process counts. This approach appears to be worth continued investigation.
\subsection{Memory Scaling}
\begin{table*}
\centering
\rowcolors{2}{gray!30}{white}
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|}
\hline
$N_p$ & S/R Buffs & Tdir & Trans Ops & Tree Mem\\\hline
128 & 5.0 & 34.352 & 107.479 & 52.741\\
256 & 20.0 & 68.704 & 141.006 & 61.953\\
512 & 800.0 & 137.409 & 162.204 & 52.768\\
1024 & 3200.0 & 274.818 & 199.047 & 62.028\\
2048 & 12800.0 & 549.636 & 221.362 & 52.809\\\hline
\end{tabular}
\caption{Memory Scaling of the MLFMA algorithm $512\lambda$ grid geometry in GB.}
\label{fig:grid_memory_table}
\end{table*}
Figure \ref{fig:grid_memory_table} shows the memory scaling of the four largest memory users. The memory used for tree storage (Tree Mem) has no scaling with process count, despite some fluctuations when doubling the process count imbalances the tree that grows by 4x per level slightly, which shows the tree is not being duplicated across the processes. Translation operators do increase a little with process count, a bit more than doubling in memory from 128 to 2048 processes. This is because we distribute the nodes spatially, so the multiple source observer pairs with the same translation in the tree may belong to different processes. Particularly as the process count increases and the number of nodes in a process decreases. This results in some processes storing some of the same translation operators as other processes. Finally the greatest memory increase is in Tdir and the S/R Buffs. The first is our temporary memory to store temporary calculations of the largest size node and each process allocates one of these temporary storage locations, so this memory doubles as node count doubles. This is a tradeoff of only allocating the necessary memory in the tree, so memory improvements in the tree allocation have a cost of additional temporary memory storage. Second the translation send and receive buffers (S/R Buffs) are used to store the source nodes that are observed by nodes within another process. Single node communications for each source and observer pair would eliminate the need for this buffer, but would result in drastically more translation messages which would degrade performance. So the translation message buffers are maximized to use any remaining memory to limit the number of translation messages that must be sent.
\begin{table*}
\centering
\rowcolors{2}{gray!30}{white}
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|}
\hline
$N_p$ & S/R Buffs & Trans Ops & Tree Mem & Tdir\\\hline
128 & 5.0 & 6.559 & 5.012 & 0.146\\
256 & 20.0 & 10.095 & 5.161 & 0.292\\
512 & 800.0 & 16.301 & 5.457 & 0.585\\
1024 & 3200.0 & 21.396 & 5.102 & 1.170\\
2048 & 12800.0 & 30.390 & 5.414 & 2.340\\\hline
\end{tabular}
\caption{Memory Scaling of the MLFMA algorithm $32\lambda$ volume geometry in GB.}
\label{fig:volume_memory_table}
\end{table*}
On the other end of what can be performed with MLFMA is the volume geometry. Here the number of nodes per level is significantly increased due to using an oct tree, as opposed to a quad tree for a surface geometry, but the maximum height of a tree that can be computed is reduced. Most memory is reduced due to the shorter height of the tree, which reduces the size of the nodes at the top of the tree. However the translation message buffers still use up as much memory as possible to improve translation communication performance.
\end{document}
\subsection{Load balance with the fine grain parallel algorithm}
The intent of the fine-grain parallel algorithm is to provide improved balance at the upper levels of the tree where a lower number of much larger nodes reside. First, we look at the performance of a planar grid of particles (in the $z=0$ plane) of dimensions $512\lambda\times512\lambda$ with a grid spacing of $\lambda/4$ and 4,194,304 particles in total. The box size is chosen to be $0.25\lambda$, resulting in a 12-level tree with 10 levels of computation. As can be seen in the left subfigure of Fig.\,\ref{fig:computational_complexity}, the resulting execution profile is very balanced across process ranks. Execution time of the fastest to the slowest process varies by only 1.43\%. Balance of total time can be a little misleading as M2L cannot progress until all processes that a given process interacts with have completed their M2M processing. However, the M2M execution times are also very balanced, varying from slowest to fastest process by 5.23\%.
\begin{figure}[H]
\centering
\includegraphics[width=.5\textwidth]{figs/GridProcessBalance.png}\hfill
\includegraphics[width=.5\textwidth]{figs/SphereProcessBalance.png}\hfill
\caption{Process execution times for a grid and a sphere geometry.}
\label{fig:computational_complexity}
\end{figure}
Next, we look at the performance for a sphere of diameter $384\lambda$ discretized using 4,542,208 dipoles on the surface with a leaf box size of $d_0=0.25\lambda$, yielding an 11-level tree. This geometry is less balanced than the grid geometry (see the right subfigure of Fig.\,\ref{fig:computational_complexity}) as high level nodes can range from having no children due to no particles being in that part of the geometry at the leaf level, up to having a completely filled quad tree from the leaf level up to a high level node. This results in notable imbalance at the M2M level, which as discussed before, results in delays in the M2L execution. Note that there is an implicit barrier at the beginning of M2L processing, as an M2L interaction communication cannot proceed until both interacting processes have completed their M2M phases (though the faster process can perform local translations while waiting). Another (less significant) implicit barrier occurs at the beginning of L2L where nodes that are fully owned by a process must have all of the data from the translated parent node to perform anterpolation on this parent node. The M2M execution range from the fastest to the slowest processes varies by as much as 84.5\%. Despite this noticeable imbalance, the long execution times are not clustered among a small group of processes as one would see if each of the highest level tree nodes were to be handled by a single process without fine-grain parallelization. So even in this unbalanced geometry, the fine-grain parallel algorithm is helping to maintain a good load balance across process ranks.
\subsection{Scalability}
Next, we investigate the strong scaling efficiency of our parallel Helmholtz FMM algorithm, first on a surface and then on a volumetric structure.
For the 2D surface structure, we use the same $512\lambda\times512\lambda$ planar grid as above. As our base case for strong scaling efficiency, we use the performance on 128 cores because this is the smallest number of cores that this problem can be executed on due to its memory requirements. As seen in Table\,\ref{fig:pfft_grid_timings_table}, both the interpolation and anterpolation phases (M2M and L2L) perform very well with the increasing process counts, while M2L's performance falls off rapidly (down to 25\% efficiency on 2048 cores). There are a couple of factors that contribute to this difference we observe in scaling characteristics. First factor is that M2M and L2L incur significant communications only at the highest level nodes, while M2L communications occur at every level where the source and observer nodes are on separate processes, which may essentially happen all the way down to the leaf nodes. Secondly, and more importantly, M2M and L2L computations involve relatively computation-heavy FFTs in between its communication steps. When the number of nodes in a level exceeds the number of processes, no process can own both a source and observer node of any translation, so all node data must be communicated. As the number of processes approaches the number of leaf nodes, the M2L communication bandwidth asymptotically approaches the worst case estimate. This means the increase in M2L bandwidth exceeds the worst case estimate increase as the number of processes approaches the number of leaf nodes.
Despite M2L not scaling very well, the fine grained parallel algorithm presented still provides good speedups, nearly an 8x speedup when going from 128 to 2048 processes without showing any performance stagnation.
\begin{table*}
\centering
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|}
\multicolumn{1}{c}{} & \multicolumn{4}{c}{\textbf{Grid} (s)} & \multicolumn{1}{c}{\textbf{Speedup}} & \multicolumn{4}{c}{\textbf{Par Eff.} (\%)}\\\hline
$N_p$ & M2M & M2L & L2L & Tot & Tot & M2M & M2L & L2L & Tot\\\hline
128 & 5.80 & 5.30 & 5.30 & 18.55 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00\\
256 & 3.06 & 4.13 & 2.66 & 11.21 & 1.65 & 0.95 & 0.64 & 0.99 & 0.83\\
512 & 1.52 & 2.76 & 1.31 & 6.42 & 2.89 & 0.95 & 0.48 & 1.01 & 0.72\\
1024 & 0.81 & 2.12 & 0.69 & 4.05 & 4.58 & 0.89 & 0.31 & 0.95 & 0.57\\
2048 & 0.43 & 1.31 & 0.37 & 2.38 & 7.78 & 0.84 & 0.25 & 0.89 & 0.49\\\hline
\end{tabular}
\caption{Performance of the MLFMA algorithm on the $512\lambda$ grid geometry.}
\label{fig:pfft_grid_timings_table}
\end{table*}
Next, we examine strong scaling on a $32\lambda\times32\lambda\times32\lambda$ volumetric structure (Table\,\ref{fig:pfft_vol_timings_table}). From 128 to 512 processes, we observe very good scaling (80\% overall efficiency), but then parallel efficiency drops off quickly (down to 50\% overall at 2048 cores). In a volumetric problem, each tree node has a large number of nodes in its far-field (up to 189). Therefore the overall execution time is largely dominated by the M2L stage which does not manifest good scaling. The ideal scenario for our fine-grained parallel algorithm is when the nodes of a given level are distributed evenly among the processes, i.e., when the number of processes divides evenly into the number of nodes in a level or vice versa. This does not occur at 1024 or 2048 processes for this particular volumetric problem. Nevertheless, the overall speedup remains at around 8x when going from 128 to 2048 processes.
\begin{table*}
\centering
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|}
\multicolumn{1}{c}{} & \multicolumn{4}{c}{\textbf{Volume} (s)} & \multicolumn{1}{c}{\textbf{Speedup}} & \multicolumn{4}{c}{\textbf{Par Eff.} (\%)}\\\hline
$N_p$ & M2M & M2L & L2L & Tot & Tot & M2M & M2L & L2L & Tot\\\hline
128 & 0.527 & 2.15 & 0.526 & 3.26 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00\\
256 & 0.266 & 1.10 & 0.263 & 1.68 & 1.94 & 0.99 & 0.97 & 0.99 & 0.97\\
512 & 0.14 & 0.679 & 0.135 & 0.99 & 3.27 & 0.93 & 0.79 & 0.97 & 0.82\\
1024 & 0.079 & 0.380 & 0.084 & 0.574 & 5.68 & 0.83 & 0.71 & 0.78 & 0.71\\
2048 & 0.051 & 0.271 & 0.058 & 0.406 & 8.03 & 0.65 & 0.50 & 0.57 & 0.50\\\hline
\end{tabular}
\caption{Performance of the MLFMA algorithm on the $32\lambda$ volumetric geometry.}
\label{fig:pfft_vol_timings_table}
\end{table*}
Finally, we look at scaling on the $384\lambda$ sphere (Table\,\ref{fig:pfft_sphere_timings_table}). As seen in the load balance analysis of the previous subsection, load imbalances result in the faster processes having to wait for slower processes. This results in a noticeable drop in scaling efficiency of the M2M phase, where the imbalance has the greatest impact, as well as the M2L phase, where some processes that are already in their M2L phase have to wait for others that are still in their M2M phase. This also has an impact on the overall speedup. While increasing the number of processes continues to improve execution times, the speedup when going from 128 to 2048 processes is just under 5x in the sphere case.
\begin{table*}
\centering
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|}
\multicolumn{1}{c}{} & \multicolumn{4}{c}{\textbf{Sphere} (s)} & \multicolumn{1}{c}{\textbf{Speedup}} & \multicolumn{4}{c}{\textbf{Par Eff.} (\%)}\\\hline
$N_p$ & M2M & M2L & L2L & Tot & Tot & M2M & M2L & L2L & Tot\\\hline
128 & 6.71 & 13.54 & 5.29 & 26.76 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00\\
256 & 3.86 & 10.05 & 2.7 & 18.00 & 1.49 & 0.87 & 0.67 & 0.97 & 0.74\\
512 & 2.34 & 6.20 & 1.46 & 11.04 & 2.42 & 0.72 & 0.55 & 0.91 & 0.61\\
1024 & 1.23 & 4.32 & 0.72 & 7.70 & 3.47 & 0.68 & 0.39 & 0.92 & 0.43\\
2048 & 0.92 & 3.19 & 0.416 & 5.58 & 4.79 & 0.46 & 0.26 & 0.79 & 0.30\\\hline
\end{tabular}
\caption{Performance of the MLFMA algorithm on the $384\lambda$ diameter sphere geometry.}
\label{fig:pfft_sphere_timings_table}
\end{table*}
\subsection{Complexity Analysis}
To help validate the complexity analysis presented in Sect.\,\ref{sec:complexity}, the software was instrumented to report the computational cost, the number of messages sent and the size of these messages. In accordance with the geometries analyzed in Sect.\,\ref{sec:complexity}, data was collected on the grid geometries ranging from $64\lambda$ to $1024\lambda$ and volume geometries ranging from $16\lambda$ to $16\lambda$ to as these geometries produce perfect quadtrees of heights ranging from 9 to 13 levels and octrees of heights ranging from 7 to 11 levels, respectively. As complexity estimates are asymptotic, they are scaled by least-squares fit to help visualize how well the estimates match the actual measurements.
\begin{figure}
\centering
\begin{tikzpicture}
\begin{semilogyaxis}[cycle list/Set1,
grid=both,
xlabel={Particles},
ylabel={Operations},
ytick pos=left,
xtick pos=left,
xtick={0,5000000,10000000,15000000},
xticklabels={0,5M,10M,15M},
ymin=900000000,ymax=1000000000000,
legend style = {legend cell align=left,/tikz/every even column/.append style={column sep=0.25cm},at={(0.01,0.01)},anchor=south west},
legend image post style={scale=1.5},
legend style={at={(0.5,1.05)},anchor=south},
legend columns=2,
set layers,mark layer=axis background,
width=0.45\textwidth
]
\addplot+[gray, line width=1mm, style={mark size=1.0},mark size=1.0,mark=square*,mark options=solid]
table[scatter, x index={0},y index={1}]
{Data/GridComplexity.txt};
\addplot+[black,dash pattern=on 6pt off 6pt on 6pt off 6pt, line width=0.5mm]
table[scatter, x index={0},y index={2}]
{Data/GridComplexity.txt};
\addplot+[black,dash pattern=on 3pt off 3pt on 3pt off 3pt, line width=0.5mm]
table[scatter, x index={0},y index={3}]
{Data/GridComplexity.txt};
\addplot+[gray, line width=1mm, style={mark size=1.0},mark size=1.0,mark=triangle*,mark options=solid]
table[scatter, x index={0},y index={4}]
{Data/GridComplexity.txt};
\addplot+[black,dash pattern=on 2pt off 6pt on 6pt off 6pt, line width=0.5mm]
table[scatter, x index={0},y index={5}]
{Data/GridComplexity.txt};
\legend{M2M/L2L Est,M2M Act,L2L Act,M2L Est,M2L Act};
\end{semilogyaxis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{semilogyaxis}[cycle list/Set1,
grid=both,
xlabel={Particles},
ytick pos=left,
xtick pos=left,
xtick={0,5000000,10000000,15000000},
xticklabels={0,5M,10M,15M},
ymin=400000000,ymax=400000000000,
legend style = {legend cell align=left,
/tikz/every even column/.append style={column sep=0.25cm},at={(0.01,0.01)},anchor=south west},
legend image post style={scale=1.5},
legend style={at={(0.5,1.05)},anchor=south},
legend columns=2,
set layers,mark layer=axis background,
width=0.45\textwidth
]
\addplot+[gray, line width=1mm, style={mark size=1.0},mark size=1.0,mark=square*,mark options=solid]
table[scatter, x index={0},y index={1}]
{Data/VolumeComplexity.txt};
\addplot+[black,dash pattern=on 6pt off 6pt on 6pt off 6pt, line width=0.5mm]
table[scatter, x index={0},y index={2}]
{Data/VolumeComplexity.txt};
\addplot+[black,dash pattern=on 3pt off 3pt on 3pt off 3pt, line width=0.5mm]
table[scatter, x index={0},y index={3}]
{Data/VolumeComplexity.txt};
\addplot+[black,dash pattern=on 3pt off 6pt on 6pt off 6pt, line width=0.5mm]
table[scatter, x index={0},y index={4}]
{Data/VolumeComplexity.txt};
\legend{M2M/L2L Est,M2M Act,L2L Act,M2L Act};
\end{semilogyaxis}
\end{tikzpicture}
\caption{Actual vs. estimated computational complexity. The left subfigure shows results for the surface geometry, while the right subfigure is for the volume geometry.}
\label{fig:computational_complexity}
\end{figure}
Figure \ref{fig:computational_complexity} shows the actual vs. the estimated overall computational complexities for the surface and volume geometries. The actual complexities match the estimates very closely. This indicates that the implementation of this algorithm does not have any unnecessary overhead costs in computation as computation is near to the ideal for Helmholtz FMM.
\begin{figure}
\centering
\begin{tikzpicture}
\begin{semilogyaxis}[cycle list/Set1,
grid=both,
xlabel={Particles},
ylabel={Bandwidth},
ytick pos=left,
xtick pos=left,
xtick={0,5000000,10000000,15000000},
xticklabels={0,5M,10M,15M},
ymin=59000000,ymax=65000000000,
legend style = {legend cell align=left,/tikz/every even column/.append style={column sep=0.25cm},at={(0.01,0.01)},anchor=south west},
legend image post style={scale=1.5},
legend style={at={(0.5,1.05)},anchor=south},
legend columns=2,
set layers,mark layer=axis background,
width=0.50\textwidth
]
\addplot+[gray, line width=1mm, style={mark size=1.0},mark size=1.0,mark=square*,mark options=solid]
table[scatter, x index={0},y index={1}]
{Data/SurfaceBandwidth.txt};
\addplot+[black,dash pattern=on 6pt off 6pt on 6pt off 6pt, line width=0.5mm]
table[scatter, x index={0},y index={2}]
{Data/SurfaceBandwidth.txt};
\addplot+[black,dash pattern=on 3pt off 3pt on 3pt off 3pt, line width=0.5mm]
table[scatter, x index={0},y index={3}]
{Data/SurfaceBandwidth.txt};
\addplot+[gray, line width=1mm, style={mark size=1.0},mark size=1.0,mark=triangle*,mark options=solid]
table[scatter, x index={0},y index={4}]
{Data/SurfaceBandwidth.txt};
\addplot+[black,dash pattern=on 2pt off 6pt on 6pt off 6pt, line width=0.5mm]
table[scatter, x index={0},y index={5}]
{Data/SurfaceBandwidth.txt};
\legend{M2M/L2L Est,M2M Act,L2L Act,M2L Est,M2L Act};
\end{semilogyaxis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{semilogyaxis}[cycle list/Set1,
grid=both,
xlabel={Particles},
ytick pos=left,
xtick pos=left,
xtick={0,5000000,10000000,15000000},
xticklabels={0,5M,10M,15M},
ymin=1800000,ymax=9000000000,
legend style = {legend cell align=left,
/tikz/every even column/.append style={column sep=0.25cm},at={(0.01,0.01)},anchor=south west},
legend image post style={scale=1.5},
legend style={at={(0.5,1.05)},anchor=south},
legend columns=2,
set layers,mark layer=axis background,
width=0.50\textwidth
]
\addplot+[gray, line width=1mm, style={mark size=1.0},mark size=1.0,mark=square*,mark options=solid]
table[scatter, x index={0},y index={1}]
{Data/VolumeBandwidth.txt};
\addplot+[black,dash pattern=on 6pt off 6pt on 6pt off 6pt, line width=0.5mm]
table[scatter, x index={0},y index={2}]
{Data/VolumeBandwidth.txt};
\addplot+[black,dash pattern=on 3pt off 3pt on 3pt off 3pt, line width=0.5mm]
table[scatter, x index={0},y index={3}]
{Data/VolumeBandwidth.txt};
\addplot+[gray, line width=1mm, style={mark size=1.0},mark size=1.0,mark=triangle*,mark options=solid]
table[scatter, x index={0},y index={5}]
{Data/VolumeBandwidth.txt};
\addplot+[black,dash pattern=on 3pt off 6pt on 6pt off 6pt, line width=0.5mm]
table[scatter, x index={0},y index={5}]
{Data/VolumeBandwidth.txt};
\legend{M2M/L2L Est,M2M Act,L2L Act,M2L Est,M2L Act};
\end{semilogyaxis}
\end{tikzpicture}
\caption{Actual vs estimated communication volume. The left subfigure shows results for the surface geometry, while the right subfigure is for the volume geometry.}
\label{fig:m2m_l2l_bandwidth}
\end{figure}
Figure \ref{fig:m2m_l2l_bandwidth} shows the actual vs the estimated communication volumes for each phase separately. Of note is how the measured communication volume drops off relative to the estimate. We believe this is due to the number of samples producing a tree with more nodes at lower levels than the number of processes. Hence, many nodes are fully owned by a single process and require no communication during M2M or L2L. Increasing the number of processes would lead to more levels with plural nodes, bringing the communication volume closer to our estimates. M2L does not show the same communication volume falloff as M2M and L2L compared to the estimated volume because fully owned nodes still require data from the source nodes to be communicated to the process owning the observer node. Such communications will be required all the way down to the leaf nodes.
\begin{figure}
\centering
\begin{tikzpicture}
\begin{semilogyaxis}[cycle list/Set1,
grid=both,
xlabel={Processes},
ylabel={Messages},
ytick pos=left,
xtick pos=left,
xtick={0,250,500,1000,2000},
xticklabels={0,250,500,1000,2000},
ymin=4000,ymax=1750000,
legend style = {legend cell align=left,/tikz/every even column/.append style={column sep=0.25cm},at={(0.01,0.01)},anchor=south west},
legend image post style={scale=1.5},
legend style={at={(0.5,1.05)},anchor=south},
legend columns=2,
set layers,mark layer=axis background,
width=0.50\textwidth
]
\addplot+[gray, line width=1mm, style={mark size=1.0},mark size=1.0,mark=square*,mark options=solid]
table[scatter, x index={0},y index={1}]
{Data/SurfaceMessages.txt};
\addplot+[black,dash pattern=on 6pt off 6pt on 6pt off 6pt, line width=0.5mm]
table[scatter, x index={0},y index={2}]
{Data/SurfaceMessages.txt};
\addplot+[black,dash pattern=on 3pt off 3pt on 3pt off 3pt, line width=0.5mm]
table[scatter, x index={0},y index={3}]
{Data/SurfaceMessages.txt};
\addplot+[gray, line width=1mm, style={mark size=1.0},mark size=1.0,mark=triangle*,mark options=solid]
table[scatter, x index={0},y index={4}]
{Data/SurfaceMessages.txt};
\addplot+[black,dash pattern=on 2pt off 6pt on 6pt off 6pt, line width=0.5mm]
table[scatter, x index={0},y index={5}]
{Data/SurfaceMessages.txt};
\legend{M2M/L2L Est,M2M Act,L2L Act,M2L Est,M2L Act};
\end{semilogyaxis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{semilogyaxis}[cycle list/Set1,
grid=both,
xlabel={Processes},
ytick pos=left,
xtick pos=left,
xtick={0,250,500,1000,2000},
xticklabels={0,250,500,1000,2000},
ymin=200,ymax=650000,
legend style = {legend cell align=left,
/tikz/every even column/.append style={column sep=0.25cm},at={(0.01,0.01)},anchor=south west},
legend image post style={scale=1.5},
legend style={at={(0.5,1.05)},anchor=south},
legend columns=2,
set layers,mark layer=axis background,
width=0.50\textwidth
]
\addplot+[gray, line width=1mm, style={mark size=1.0},mark size=1.0,mark=square*,mark options=solid]
table[scatter, x index={0},y index={1}]
{Data/VolumeMessages.txt};
\addplot+[black,dash pattern=on 6pt off 6pt on 6pt off 6pt, line width=0.5mm]
table[scatter, x index={0},y index={2}]
{Data/VolumeMessages.txt};
\addplot+[black,dash pattern=on 3pt off 3pt on 3pt off 3pt, line width=0.5mm]
table[scatter, x index={0},y index={3}]
{Data/VolumeMessages.txt};
\addplot+[gray, line width=1mm, style={mark size=1.0},mark size=1.0,mark=triangle*,mark options=solid]
table[scatter, x index={0},y index={5}]
{Data/VolumeMessages.txt};
\addplot+[black,dash pattern=on 3pt off 6pt on 6pt off 6pt, line width=0.5mm]
table[scatter, x index={0},y index={5}]
{Data/VolumeMessages.txt};
\legend{M2M/L2L Est,M2M Act,L2L Act,M2L Est,M2L Act};
\end{semilogyaxis}
\end{tikzpicture}
\caption{Message counts vs expected Big-O message counts. The left diagram shows analysis of a surface geometry, while the right diagram shows analysis of a volume geometry.}
\label{fig:m2m_l2l_messages}
\end{figure}
Figure \ref{fig:m2m_l2l_messages} shows the measured worst case messages vs the estimated worst case messages for M2M and L2L. M2M and L2L Message counts are dominated by the $P^2$ complexity of the all to all communications and the actual message count reflects this. The M2L prediction simplifies a very complex process that results in the number of M2L messages that are communicated.
\subsection{Process Alignment}
In Table\,\ref{fig:process_alignment_table}, we compare the number of packets sent between Rank Ordered and Process Aligned schemes during M2M and L2L phases for the $512\lambda$ grid geometry. We observe a notable reduction in the number of messages exchanged, and hence the overall bandwidth, for lower process counts and continued reduction at higher process counts as expected. This reduction is likely to be effective in the relatively good scaling characteristics of M2M and L2L phases.
\begin{table*}
\centering
\begin{tabular}{|r|r|r|r|r|r|r|}
\hline
{\bf $N_P$} & & {\bf 128} & {\bf 256} & {\bf 512} & {\bf 1024} & {\bf 2048}\\\hline
{\bf Rank Ordered} & M2M Bandwidth & 1714 & 1872 & 3009 & 3126 & 4246\\
& L2L Bandwidth & 1206 & 1166 & 2429 & 2382 & 3649\\
& Combined Bandwidth & 2920 & 3038 & 5438 & 5508 & 7895\\\hline
{\bf Process Aligned} & M2M Bandwidth & 1468 & 1662 & 2711 & 3272 & 4412\\
& L2L Bandwidth & 960 & 955 & 2131 & 2104 & 3338\\
& Combined Bandwidth & 2428 & 2617 & 4842 & 5376 & 7750\\\hline
{\bf Delta} & & -492 & -421 & -596 & -132 & -145\\\hline
\end{tabular}
\caption{Comparison of the number of packets sent between Rank Ordered and Process Aligned schemes for the $512\lambda$ grid geometry in millions of packets sent.}
\label{fig:process_alignment_table}
\end{table*}
\subsection{Memory Utilization}
\begin{table*}
\centering
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|}
\hline
{\bf $N_p$} & {\bf S/R Buffs} & {\bf Trans Ops} & {\bf Tree Mem}\\\hline
128 & 1.652 & 107.479 & 52.741\\
256 & 4.487 & 141.006 & 61.953\\
512 & 102.661 & 162.204 & 52.768\\
1024 & 256.982 & 199.047 & 62.028\\
2048 & 431.797 & 221.362 & 52.809\\\hline
\end{tabular}
\caption{Total memory utilization (in GBs) by the three largest data structures for the $512\lambda$ grid geometry.}
\label{fig:grid_memory_table}
\end{table*}
Table \ref{fig:grid_memory_table} shows the memory utilization of the three data structures with largest memory needs with increasing process counts. As expected, the memory used for tree storage (Tree Mem) does not increase with process count, despite some fluctuations due to different partitionings of the leaf nodes. This shows that the tree data structure is being nicely partitioned across processes. Size of the translation operators (Trans Ops) increase slowly with process count, slightly more than doubling going from 128 to 2048 processes. This is due to the spatial distribution of the tree nodes; multiple source observer pairs with the same translation in the tree may belong to different processes. Particularly, as the process count increases and the number of nodes in a process decreases. This results in some processes storing some of the same translation operators as the other processes. The greatest memory increase is in the message buffers (S/R Buffs). The translation send and receive buffers (S/R Buffs) are used to communicate the data for source nodes that interact with nodes in another process. Single node communications for each source and observer pair would eliminate the need for this buffer, but would result in drastically more translation messages which would degrade performance. So the translation message buffers are maximized to use any remaining memory to limit the number of translation messages that must be sent.
\begin{table*}
\centering
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|}
\hline
{\bf $N_p$} & {\bf S/R Buffs} & {\bf Trans Ops} & {\bf Tree Mem}\\\hline
128 & 3.110 & 6.559 & 5.012\\
256 & 8.402 & 10.095 & 5.161\\
512 & 22.264 & 16.301 & 5.457\\
1024 & 31.889 & 21.396 & 5.102\\
2048 & 51.736 & 30.390 & 5.414\\\hline
\end{tabular}
\caption{Total memory utilization (in GBs) by the three largest data structures for the $32\lambda$ volume geometry.}
\label{fig:volume_memory_table}
\end{table*}
On the other end of what can be performed with H-FMM is the volume geometry. Here the number of nodes per level is significantly increased due to the underlying full oct-tree structure (as opposed to a quad tree for a surface geometry), but the maximum height of a tree that can be computed is reduced. Most memory is reduced due to the shorter height of the tree, which reduces the size of the nodes at the top of the tree. However, the translation message buffers still use up as much memory as possible to improve translation communication performance.
\subsection{Performance Comparison with Other Codes}
Finally, we seek to compare our approach against those code that are available in the public domain. We note that open-source H-FMM codes are almost non-existent, with Abduljabbar et al. \cite{abduljabbar2019extreme} being a recent exception. Their BEMFMM code discretizes a mesh; the discretized points are used as particle inputs to our H-FMM code in order to compare processing of the same geometry. We ran a spherical geometry with 240 thousand mesh elements that produces 1.44 million points. Both codes are configured to produce a 6 level tree with slightly over 4100 leaf nodes with this sphere geometry and run with 64 nodes and 2048 MPI ranks. With this configuration, the BEMFMM implementation runs a single FMM iteration in 18.686 while our fine grain parallel FMM runs in 0.483 seconds. Our fine grain parallel Helmholtz FMM algorithm shows significantly faster performance in comparison.
\end{document}
\section{Introduction}
\label{sec:intro}
\subfile{Introduction/Introduction0.2}
\section{Problem Statement and Background}
\label{sec:background}
\subfile{ProblemStatement/ProblemStatement0.2}
\section{Parallel Algorithms and Implementations}
\label{sec:algo_base}
\subfile{Algorithms/Algorithms0.2}
\section{Computational and Communication Complexity Analysis}
\subfile{NumericalMethods/NumericalMethods0.2}
\section{Performance Evaluation}
\subfile{NumericalResults/NumericalResults0.3}
\section{Conclusions and Future Work}
\subfile{Conclusions/Conclusions0.2}
\section*{Acknowledgment}
This research has in part been funded by the NSF Grant CCF-1822932. It has used computational resources at the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, and at the High Performance Computing Center at Michigan State University.
\bibliographystyle{ACM-Reference-Format}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 3,902
|
<?php
/**
* This file is part of Bldr.io
*
* (c) Aaron Scherer <aequasi@gmail.com>
*
* This source file is subject to the MIT license that is bundled
* with this source code in the file LICENSE
*/
namespace Bldr\Block\Core\Command;
use Bldr\Application;
use Bldr\Block\Core\Service\Builder;
use Bldr\Command\AbstractCommand;
use Bldr\Definition\JobDefinition;
use Bldr\Definition\TaskDefinition;
use Bldr\Exception\BldrException;
use Bldr\Registry\JobRegistry;
use Symfony\Component\Console\Helper\FormatterHelper;
use Symfony\Component\Console\Input\InputArgument;
/**
* @author Aaron Scherer <aequasi@gmail.com>
*/
class RunCommand extends AbstractCommand
{
/**
* @var Builder $builder
*/
private $builder;
/**
* @var JobRegistry $registry
*/
private $registry;
/**
* {@inheritDoc}
*/
protected function configure()
{
$this->setName('run')
->setDescription("Runs the project for the directory you are in. Must contain a config file.")
->addArgument('profile', InputArgument::OPTIONAL, 'Profile to run')
->setHelp(
<<<EOF
The <info>%command.name%</info> builds the current project, using the config file in the root directory.
To use:
<info>$ bldr %command.name% <profile_name></info>
EOF
)
;
}
/**
* {@inheritDoc}
*/
protected function doExecute()
{
$this->registry = $this->container->get('bldr.registry.job');
$this->builder = $this->container->get('bldr.builder');
$profileName = $this->input->getArgument('profile') ?: 'default';
$this->output->writeln(["\n", Application::$logo, "\n"]);
$profile = $this->getProfile($profileName);
$projectFormat = [];
if ($this->container->getParameter('name') !== '') {
$projectFormat[] = sprintf("Building the '%s' project", $this->container->getParameter('name'));
}
if ($this->container->getParameter('description') !== '') {
$projectFormat[] = sprintf(" - %s - ", $this->container->getParameter('description'));
}
$profileFormat = [sprintf("Using the '%s' profile", $profileName)];
if (!empty($profile['description'])) {
$profileFormat[] = sprintf(" - %s - ", $profile['description']);
}
$this->output->writeln(
[
"",
$projectFormat === [] ? '' : $this->formatBlock($projectFormat, 'blue', 'black'),
"",
$this->formatBlock($profileFormat, 'blue', 'black'),
""
]
);
$this->fetchJobs($profile);
$this->builder->runJobs($this->registry);
$this->output->writeln(['', $this->formatBlock('Build Success!', 'green', 'white', true), '']);
}
/**
* @param string|array $output
* @param string $background
* @param string $foreground
*
* @return string
*/
private function formatBlock($output, $background, $foreground, $large = false)
{
/** @var FormatterHelper $formatter */
$formatter = $this->getApplication()->getHelperSet()->get('formatter');
return $formatter->formatBlock($output, "bg={$background};fg={$foreground}", $large);
}
/**
* @param array $profile
*/
private function fetchJobs(array $profile)
{
if (!empty($profile['uses']) && !empty($profile['uses']['before'])) {
foreach ($profile['uses']['before'] as $name) {
$this->fetchJobs($this->getProfile($name));
}
}
$this->buildJobs($profile['jobs']);
if (!empty($profile['uses']) && !empty($profile['uses']['after'])) {
foreach ($profile['uses']['after'] as $name) {
$this->fetchJobs($this->getProfile($name));
}
}
}
/**
* @param string[] $names
*
* @throws \Exception
* @return array
*/
private function buildJobs(array $names)
{
$jobs = $this->container->getParameter('jobs');
foreach ($names as $name) {
if (!array_key_exists($name, $jobs)) {
throw new BldrException(
sprintf(
"Job `%s` does not exist. Found: %s",
$name,
implode(', ', array_keys($jobs))
)
);
}
$jobInfo = $jobs[$name];
$description = isset($jobInfo['description']) ? $jobInfo['description'] : "";
$job = new JobDefinition($name, $description);
foreach ($jobInfo['tasks'] as $taskInfo) {
$task = new TaskDefinition($taskInfo['type']);
$task->setContinueOnError(isset($taskInfo['continueOnError']) ? $taskInfo['continueOnError'] : false);
unset($taskInfo['type'], $taskInfo['continueOnError']);
$task->setParameters($taskInfo);
$job->addTask($task);
}
$this->registry->addJob($job);
}
}
/**
* @param $name
*
* @return mixed
* @throws \Exception
*/
private function getProfile($name)
{
$profiles = $this->container->getParameter('profiles');
if (!array_key_exists($name, $profiles)) {
throw new \Exception(
sprintf(
'There is no profile with the name \'%s\', expecting: (%s)',
$name,
implode(', ', array_keys($profiles))
)
);
}
return $profiles[$name];
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,818
|
\section{Discussion}
Antineutrinos from the decay chains of $^{238}$U and $^{232}$Th existing
in the Earth interior (the so called geo-neutrinos)
have been recently detected both by Kamland \cite{kamland} and by Borexino \cite{borexino} experiments.
Future experiments for geo-neutrinos detection have been proposed (or starting) in several
location in the world (e.g. SNO+ in Canada \cite{SNO+}, Lena project in Europe \cite{lena} and
Hawaii Anti-Neutrino Observatory\cite{hawaii}).
The main source of background of such experiments is given by antineutrino produced
by nuclear plants. These particles account for a signal almost always larger than geo-neutrinos one,
see Table \ref{table}. So a detailed calculation of reactor antineutrino
flux in mandatory for an accurate measurements of geo-neutrinos.
With this aim, we performed a calculation of reactor antineutrinos flux all over the world.
Previus analysis has been presented, for instance, in ref. \cite{report} and \cite{geoscience2010}.
Now we will show an updated estimate of reactor antineutrino signal,
with particular attention to the sites proposed for the new geo-neutrino experiments.
In our calculation we take into account the most updated data on Thermal Power for each nuclear plant,
on reactor antineutrino spectra and on three neutrino oscillation mechanism.
The expected reactor antineutrino signal has been calculated as follows:
\begin{equation}
N_{ev}= \epsilon N_p \tau
\sum_{r=1}^{N_{react}}
\frac {P_{r}}{4 \pi L_{r}^{2}} <LF_r>
\int dE_{\bar{\nu}_e}
\sum_{i=1}^4
\frac {f_{i}}{E_{i}} \phi_{i}(E_{\bar{\nu}_e})
\sigma(E_{\bar{\nu}_e})
P_{ee}(E_{\bar{\nu}_e};\hat\theta, L_r)
\label{Eq:ReactorFlux}
\end{equation}
where $\epsilon$ is detector efficiency,
$N_p$ is the number of target proton,
$\tau$ is period of data taking,
index $r$ cycles over the $N$ reactors considered,
$L_{r}$, $P_{r}$ and $<LF_r>$
are the distance, the nominal thermal power and the averaged Load Factor of reactor
$r$, respectively.
The index $i$ stands for the i-th spectral component in the set
($^{235}$U, $^{238}$U, $^{239}$Pu, and $^{241}$Pu), $f_{i}$ is the power fraction of the component $i$,
as reported in\cite{borexino},
$E_i$ is the average antineutrino energy per fission of the component $i$ \cite{huber},
$\phi(E_{\bar{\nu}})$ is the anti-neutrino flux per fission of the $i^{\rm th}$ component,
as recently calculated in ref.\cite{mueller},
$\sigma(E_{\bar{\nu}})$ is the inverse beta decay cross section\cite{vissani}
and $P_{ee}$ is the survival probability of the reactor antineutrinos of energy
$E_{\bar{\nu}}$ traveling the baseline $L_r$,depending on the mixing parameters $\hat\theta$.
In Eq. (\ref{Eq:ReactorFlux}) we assume a 100\% detection efficiency, for a detector containing
$10^{32}$ target protons and operating continuously for 1 year.
In particular we consider the nuclear cores all over the world,
operating in the year 2012. Information on the nominal thermal power and monthly load factor for each
nuclear cores originates from International Agency of Atomic Energy (IAEA)~\cite{iaea}.
Concerning survival probability, we assumed a three flavour vacuum oscillation mechanism with $P_{ee}$ as in
in ref.\cite{fiorentini2012}, and mixing parameters from ref.\cite{fogli2012}.
The results of our calculation are reported in Table\ref{table} and in Fig.\ref{mappa}.
We also performed a analysis on the sources of uncertainty in reactor signal prediction, see\cite{geoscience2010} for details.
The total uncertainty is of the order of 5\%, the main contributions (i.e. greater than 2\%)
arising from $\theta_{12}$ mixing angle, antineutrino spectrum, fuel composition and thermal power.
One can see that, due to reactors shutdown occurred in 2012,
Kamioka became a suitable site for detecting geo-neutrinos, comparable to LNGS.
A new European geo-neutrino detector located at Frejus Laboratory
requires a detailed knowledge of closeby reactors;
the choice of Phyasalmi looks better in this respect.
Of course Hawaii and Curacao are wonderful places for geo-neutrino studies due to their position
far away from any nuclear plants of the world. The same holds for Homestake.
In the near future, the SNO+ experiment, with a quite reasonable ratio
R$_G$/G, will provide more information about Earth's interior.
\begin{figure}
\center
\includegraphics[width=.9\textwidth]{mappa.pdf}
\caption{A worldwide map of reactor antineutrinos signal. 1 TNU= 1 events/yr/10$^{32}$ target protons}
\label{mappa}
\end{figure}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 8,671
|
Q: Windows Anytime upgrade not available in this edition of Windows 7 (Starter) even though I live in the U.S I have a laptop with Windows 7 Starter and a key for Windows 7 Home Premium. I'd like to upgrade the system to the Home Premium. When I try to use the Windows Anytime Upgrade, it informs me that "Windows Anytime Upgrade not available in this edition of Windows".
I'm confused because I thought this limitation shouldn't exist for laptops in the U.S. Is there a setting somewhere that is causing this error?
A: It may be trying to upgrade you to Win 8 64 bit, you would need 32 bit Win 8. You won't be able to upgrade to 7 as it isn't available to buy from Microsoft any more, only Win 8.1 is.
If you have already bought it, try a clean install.
http://technet.microsoft.com/en-us/library/jj203353.aspx#editions
This should help you out with any luck. Happy upgrading!
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 8,638
|
The beautiful small island paradise of Isla Mujeres is just a 25 minute ferry ride from the Cancun Hotel Zone. Here you'll find the area's finest dolphin swims, including the only Dorsal Tow activity in Cancun, as well as the spectacular Garrafon Park. The ferry to Isla Mujeres is included in your dolphin swim, so what you see is what you get! Add dolphins to your memorable day in Cancun!
CHOOSE YOUR DOLPHIN EXPERIENCE ON ISLA MUJERES!
Scroll Down to See All 8 Dolphin Swim Options!
Isla Mujeres is a great place for people staying in Cancun to do a dolphin swim. Every dolphin swim here is ALL-INCLUSIVE, with open bar, lunch, breakfast, round-trip boat ride to Isla Mujeres, beach club, fantasy snorkel with sharks and stingrays, a bike tour, and a downtown tour of Isla Mujeres all included with the price of the dolphin swim, a great deal!
By far the most popular dolphin swimming activity in Isla Mujeres is the Royal Dolphin Swim. This fast and exciting activity features the famous foot push, where you're pushed across the pool by the dolphins at such speeds you actually lift out of the water like Superman! Also featured in the Royal Swim is the Dorsal Tow, where you are pulled across the pool at a high speed by two dolphins - the only dolphin activity in Cancun to feature this. To really get the most bang for your buck, we recommend the Royal Garrafon Tour with Royal Dolphin Swim. You'll SAVE UP TO 25% on your dolphin swim when booked together with the all-inclusive tour - a great day in Isla Mujeres! Another great option is the new Sea Life Discovery Plus, where you not only get the Royal Dolphin Swim, but you get to swim with manatees and sea lions too!
For families and small kids under 8 years old, we recommend the Dolphin Encounter - kids as small as 1 year old can do this activity. Adults who don't swim, are on a budget, or are afraid of deep water also should book this activity. The Dolphin Swim Adventure is a great bargain at only $119.00, and is the only activity in Cancun where you can actually snorkel with live dolphins!
IMPORTANT: It is very important to reserve your Isla Mujeres dolphin swim online before you leave for Cancun. This is a hugely popular activity, and especially in high season, if you wait until you get to Isla Mujeres and try to sign up, you will almost certainly not get to swim with the dolphins. We offer you every choice possible above, and with us you can get special prices on packages as well as every possible promotion and sale price.
You can ride the ferry over from the Aquatours Marina at Km 6.5 of the Cancun Hotel Zone. The ferry is included in the price of your dolphin swim, just show up and ride on over.
IMPORTANT: Garrafon Park will not allow you to bring your regular sunblock into the park, as part of the ongoing effort to protect the environment. It will be confiscated at the gate unless it is biodegradable. See Biodegradable Sunscreen.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,015
|
\section*{Introduction}
Ants are social insects that typically use pheromone traces to
self-organize long foraging lines without any centralized
organization \cite{Holldobler1990}. However, a very basic question
arises: how a single ant explores new territories without any chemical
or ``topographical" clues? To the authors knowledge, the question is
unanswered in the literature. In this paper, we offer a preliminary
quantification of the free exploration of the Cuban leaf-cutter ant
{\it Atta insularis} (known as {\it bibijagua} in Cuba)
\cite{Altshuler2005,Noda2006,Nicolis2013,Tejera2014,Reyes2016}.
A typical experiment can be described as follows. A single
individual of {\it Atta insularis} is collected from a foraging line
in natural conditions, immediately taken to the laboratory, and
released at the center of a 1-meter-diameter circular area made of
white plastic. The trajectory of the ant is then followed by a
digital camera located 1.8 meters above the center of the arena,
until the ant reaches the edge of the circular platform. The
illumination is provided by a 250-watt incandescent lamp located
near the camera, equipped with a light diffusor, as sketched in the
left panel of Fig.\ref{Experimental schemme}. Then, the individual
is released back in its natural foraging area. The experiment is
replicated for several individuals collected in the same way,
thoroughly cleaning the plastic arena with ethanol between
repetitions.
Images were averaged and the result was subtracted from each
photogram, in order to distinctly visualize the moving object (i.e.,
the ant), on an immobile and homogeneous background. Then, images were binarized
using an appropriately threshold, so the ant trajectory can be
easily converted into a list of positions and times. The right panel
of Fig.\ref{Experimental schemme} shows a typical trajectory.
\begin{figure}[h]
\begin{center}
\includegraphics[width=10cm]{Fig1FreeExploration.png}
\caption{{\bf Experimental setup.} Left panel: sketch of the
experimental set up. The camera was a CANON EOS Rebel T3. Videos
were taken at 25 frames per second, with a resolution of 4272 pixels
$\times$ 2848 pixels. Right panel: Actual photogram of the
experimental arena, where an experimental trajectory of a single ant
is represented as a dotted line. The starting point of the
trajectory is at the geometrical center of the circular arena.}
\label{Experimental schemme}
\end{center}
\end{figure}
The first parameter we measured was the position of the ants as time
goes by, which was used to calculate the Mean Squared Displacement
(MSD), shown in Fig.\ref{MSD}. In the figure, it is included the data of 25
experiments (corresponding to 25 ants). The straight line fitting
the data can be described as $\left\langle r{}^{2}\right\rangle\sim t^{\gamma}$
with $\gamma=1.74$ (here, {\it r} is the absolute distance from the ants to the center of the arena).
Since the value of the exponent is bigger than 1, the motion
can be classified as {\it super-diffusive} --i.e., there is a
direction persistence beyond a pure random walk. Super-diffusive
behavior is expected when animals move in an ``anisotropic"
environment. For example, bacteria moving ``chemotactically" in a
chemical gradient of nutrients, or ``phototactically" in a light
gradient \cite{Berg2004}. In the case of ants, we would expect a
direction-biased walk if our arena was illuminated from one side
(ants would try to escape from light), but that is not the case. A
strongly super-diffusive behavior could be also expected if many
ants were released on the arena at the same time, since they would
chase each other due to the deposition of pheromone tracks --but
that is neither our case. The super-diffusive behavior we have found
in isolated ants might be related to ``direction memory" of the
individuals, or perhaps a short range (but not long range) lack of
memory (``Alzheimer walk", \cite{Viswanathan2011}).
\begin{figure}[h]
\begin{center}
\vspace{0.5cm}
\includegraphics[width=8.5cm]{Fig2LogLog_MSD.png}
\caption{{\bf Mean Squared Displacement (MSD).} The figure shows the
logarithm of the MSD of the ants against the logarithm of time. The
graph comprises the data from a sample of 25 experiments with
individual ants. The straight line corresponds to a Log-Log graph of the
power law $\left\langle r{}^{2}\right\rangle\sim t^{\gamma}$ where the exponent
$\gamma=1.74 > 1$, suggests {\it super-diffusion}.}
\label{MSD}
\end{center}
\end{figure}
The second element we have computed is the statistics of turn
angles of the ant. The inset of Fig.\ref{FrecuencyAngles} illustrates how it was
measured. First, the trajectory of one ant was divided into straight
segments connecting two consecutive positions of the individual, separated
by a time interval of 0.8 seconds (20 frames). The turn angle was
defined as the deviation angle from one trajectory segment, to the
next.
The main frame of Fig.\ref{FrecuencyAngles} shows the statistical distribution of the
resulting angles, comprising all trajectories measured on 25
different experiments on 25 different ants. It can be immediately
seen the dominance of small turn angles: most of the time, ants
explore through smooth curves, and just eventually stop and perform
a major turn. A subtler observation is that the distribution is
slightly skewed to the left and the height of the right bars is considerable
near zero, i.e., left turns are more probable (due to our
sign convention, it corresponds to a ``thicker" right side of the statistical
distribution shown in Fig.\ref{FrecuencyAngles}). That opens the question if ants are
``intrinsically left handed", so to speak.
Some authors have proposed that this asymmetry can result in
adaptive advantages. Studies with {\it Temnothorax albipennis}
ants show that they apparently use their right eye more the left eye to recognize
reference points \cite{Basari2014} (however, as we mentioned before, {\it Atta insularis} ants
are practically blind , so they are not likely to use any reference points
in our experiments). Another example of these antecedents
is illustrated in \cite{Hunt2014}, also with {\it Temnothorax albipennis}, showing more
left turns when ants explore new territories for the construction of a nest.
The continuous line in Fig.\ref{FrecuencyAngles} corresponds to a fit of a $\alpha$-stable
distribution (see, for example, \cite{Mandelbrot1960})which is able
to reproduce the ``power-law-like" tails of the bell-shaped
distribution.
\begin{figure}[h]
\begin{center}
\vspace{0.5cm}
\includegraphics[width=12cm]{Fig3FrecuencyDistribution.png}
\caption{{\bf Frequency distribution of turn angles} The figure
represents the statistical distribution of turn angles, and comprise
the angles measured in all trajectories of all individual ants. The
inset indicates how the turn angle is defined.}
\label{FrecuencyAngles}
\end{center}
\end{figure}
During exploration, every few seconds ants stop and perform bigger
turns whose average is of the order of 90 degrees. In analogy with
the ``run-and-tumble" motion of {\it E. coli}
\cite{Berg2004,Altshuler2013,Figueroa2013,Figueroa2015} we define a
``tumble" as a bigger turn and a {\it run} as the fast
segment between two consecutive tumbles. Then, we have found that
the statistical distribution in the durations of runs follows an
exponential law, as ``classically" expected for bacteria. However,
more statistics must be collected to completely discard a power law.
In summary, we have preliminarily characterized the free exploration
of a social insect (the Cuban endemic ant {\it Atta insularis})
using parameters typically used in the area of micro-swimmers. On
the one hand, we have found a super-diffusive behavior in the
individual ants --which implies a certain level of direction
preference of unknown origin. Secondly, we have found clues
indicating that free-exploring ants are slightly ``left-handed",
i.e., they prefer to turn left instead of right during exploration.
These results --especially the latter-- must be corroborated by a
larger statistical sample of individuals, and should be extrapolated
to other, non-social, insect species.
\bibliographystyle{naturemag}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 5,272
|
/**
* ag-grid - Advanced Data Grid / Data Table supporting Javascript / React / AngularJS / Web Components
* @version v5.0.0-alpha.5
* @link http://www.ag-grid.com/
* @license MIT
*/
var __decorate = (this && this.__decorate) || function (decorators, target, key, desc) {
var c = arguments.length, r = c < 3 ? target : desc === null ? desc = Object.getOwnPropertyDescriptor(target, key) : desc, d;
if (typeof Reflect === "object" && typeof Reflect.decorate === "function") r = Reflect.decorate(decorators, target, key, desc);
else for (var i = decorators.length - 1; i >= 0; i--) if (d = decorators[i]) r = (c < 3 ? d(r) : c > 3 ? d(target, key, r) : d(target, key)) || r;
return c > 3 && r && Object.defineProperty(target, key, r), r;
};
var __metadata = (this && this.__metadata) || function (k, v) {
if (typeof Reflect === "object" && typeof Reflect.metadata === "function") return Reflect.metadata(k, v);
};
var context_1 = require("../../context/context");
var gridOptionsWrapper_1 = require("../../gridOptionsWrapper");
var sortController_1 = require("../../sortController");
var valueService_1 = require("../../valueService");
var utils_1 = require("../../utils");
var SortStage = (function () {
function SortStage() {
}
SortStage.prototype.execute = function (rowNode) {
var sortOptions;
// if the sorting is already done by the server, then we should not do it here
if (!this.gridOptionsWrapper.isEnableServerSideSorting()) {
sortOptions = this.sortController.getSortForRowController();
}
this.sortRowNode(rowNode, sortOptions);
};
SortStage.prototype.sortRowNode = function (rowNode, sortOptions) {
var _this = this;
// sort any groups recursively
rowNode.childrenAfterFilter.forEach(function (child) {
if (child.group) {
_this.sortRowNode(child, sortOptions);
}
});
rowNode.childrenAfterSort = rowNode.childrenAfterFilter.slice(0);
var sortActive = utils_1.Utils.exists(sortOptions) && sortOptions.length > 0;
if (sortActive) {
rowNode.childrenAfterSort.sort(this.compareRowNodes.bind(this, sortOptions));
}
this.updateChildIndexes(rowNode);
};
SortStage.prototype.compareRowNodes = function (sortOptions, nodeA, nodeB) {
// Iterate columns, return the first that doesn't match
for (var i = 0, len = sortOptions.length; i < len; i++) {
var sortOption = sortOptions[i];
// var compared = compare(nodeA, nodeB, sortOption.column, sortOption.inverter === -1);
var isInverted = sortOption.inverter === -1;
var valueA = this.valueService.getValue(sortOption.column, nodeA);
var valueB = this.valueService.getValue(sortOption.column, nodeB);
var comparatorResult;
if (sortOption.column.getColDef().comparator) {
//if comparator provided, use it
comparatorResult = sortOption.column.getColDef().comparator(valueA, valueB, nodeA, nodeB, isInverted);
}
else {
//otherwise do our own comparison
comparatorResult = utils_1.Utils.defaultComparator(valueA, valueB);
}
if (comparatorResult !== 0) {
return comparatorResult * sortOption.inverter;
}
}
// All matched, these are identical as far as the sort is concerned:
return 0;
};
SortStage.prototype.updateChildIndexes = function (rowNode) {
if (utils_1.Utils.missing(rowNode.childrenAfterSort)) {
return;
}
rowNode.childrenAfterSort.forEach(function (child, index) {
child.firstChild = index === 0;
child.lastChild = index === rowNode.childrenAfterSort.length - 1;
child.childIndex = index;
});
};
__decorate([
context_1.Autowired('gridOptionsWrapper'),
__metadata('design:type', gridOptionsWrapper_1.GridOptionsWrapper)
], SortStage.prototype, "gridOptionsWrapper", void 0);
__decorate([
context_1.Autowired('sortController'),
__metadata('design:type', sortController_1.SortController)
], SortStage.prototype, "sortController", void 0);
__decorate([
context_1.Autowired('valueService'),
__metadata('design:type', valueService_1.ValueService)
], SortStage.prototype, "valueService", void 0);
SortStage = __decorate([
context_1.Bean('sortStage'),
__metadata('design:paramtypes', [])
], SortStage);
return SortStage;
})();
exports.SortStage = SortStage;
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,444
|
Die einundzwanzigste Staffel der deutschen Krimiserie SOKO LeipzigDie einundzwanzigste Staffel von SOKO Leipzig umfasst 22 Episoden und feierte ihre Premiere am 28. August 2020 im ZDF. Das Finale wurde am 5. März 2021 gesendet. Alle Episoden wurden eine Woche vor TV-Ausstrahlung in der ZDFmediathek veröffentlicht.
Die Episoden der Staffel wurden auf dem freitäglichen 21:15-Uhr-Sendeplatz erstausgestrahlt.
Darsteller
Episoden
Weblinks
Staffel 21 in der Internet Movie Database (englisch)
Episodenliste der einundzwanzigsten Staffel von SOKO Leipzig bei fernsehserien.de
Einzelnachweise
Staffel einer Fernsehserie
SOKO Leipzig
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 9,852
|
Q: Django url patterns, redirect from root to other url This should be an easy enough problem to solve for you guys:
I just started working with Django, and I'm doing some routing. This is my urls.py in the root of the project:
urlpatterns = [
path('admin/', admin.site.urls),
path('', include('dashboard.urls')),
]
This is the routing in my dashboard app:
urlpatterns = [
path('dashboard', views.index, name='index'),
path('', views.index, name='index'),
]
Now let's say I want my users to be redirected to /dashboard if they go to the root of the website. So I would use '' as a route in the urls.py in the root, and then have everyone sent to /dashboard from the urls.py in the dashboard app. But when I do this I get the following warning:
?: (urls.W002) Your URL pattern '/dashboard' [name='index'] has a route beginning with a '/'. Remove this slash as it is unnecessary. If this pattern is targeted in an include(), ensure the include() pattern has a trailing '/'.
So I tried to use '/' instead of '', but since a trailing / is automatically removed from an url, the url wouldn't match the pattern. Should I ignore/mute this warning or is there another way to go about it?
This is the code that worked perfectly but gave me a warning earlier:
urlpatterns = [
path('/dashboard', views.index, name='index'),
path('', views.index, name='index'),
]
urlpatterns = [
path('admin/', admin.site.urls),
path('', include('dashboard.urls'))
]
A: You can use RedirectView to redirect from / to /dashboard/. Then use 'dashboard' when including the dashboard urls.
urlpatterns = [
path('admin/', admin.site.urls),
path('', RedirectView.as_view(pattern_name='dashboard:index')
path('dashboard/', include('dashboard.urls')),
]
You can then remove 'dashboard' from the path in dashboard/urls.py, as it is already in the include().
app_name = 'dashboard'
urlpatterns = [
path('', views.index, name='index'),
]
I've added app_name='dashboard' to match the namespace used above in pattern_name='dashboard:index'.
Note that Django projects usually use URLs with a trailing slash, e.g. /dashboard/ instead of dashboard.
If you really want to use URLs like /dashboard without a trailing slash, then the include should be
path('dashboard', include('dashboard.urls')),
If you do this, I suggest you set APPEND_SLASH to False in your settings.
A: You can try something like this:
from django.conf import settings
from django.conf.urls import include, url
from django.contrib import admin
from django.views.generic import RedirectView
urlpatterns = [
url(r'^admin/', include(admin.site.urls)),
url(r'^contacts/', include('appname.contacts.urls')),
url(r'^comments/', include('appname.urls')),
url(r'^subscriptions/', include('appname.partner.urls')),
url(r'^', RedirectView.as_view(url="/admin/"))
]
This is what I've done in my project so whenever the user go to 127.0.0.1:8000 it redirects to /admin
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,501
|
The Boston Palestine Film Festival (BPFF) is an annual film festival held in Boston, MA that was established in 2007. The festival brings Palestine-related cinema, narratives, and culture to New England audiences with the mission to "showcase the extraordinary narrative and culture of Palestinians through cinema and art." The thirteenth annual festival took place October 18–27, 2019.
Overview
Run by volunteers and co-presented by the Museum of Fine Arts, Boston, BPFF features documentaries, features, rare early works, video art pieces, as well as new films by emerging artists and youth. The selected works from directors around the world offer views of Palestine and its history, culture, and geographically dispersed society.
Each year, guest filmmakers from various countries and expert commentators are invited to be part of the festival and discuss their work with audiences. Since its founding in 2007, BPFF has presented over 300 Palestine-related films, as well as numerous major concerts, workshops, and art exhibits.
Winners
See also
Chicago Palestine Film Festival
DC Palestinian Film and Arts Festival
References
External links
Official website for the Boston Palestine Film Festival
Fifth Annual Boston Palestine Film Festival (2011) - Jadaliyya
Arab-American culture in Massachusetts
Film festivals in Boston
Palestinian-American culture
Cinema of the State of Palestine
Film festivals established in 2007
2007 establishments in Massachusetts
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 8,536
|
It looks like you have javascript turned off. This What are 'Stackers' and Will They Help Us Lose Weight? page on EmpowHER Women's Health works best with javascript enabled in your browser.
What are 'Stackers' and Will They Help Us Lose Weight?
By Alison Stanton
Stackers, also known as the ECA stack, are a drug combination that is used as both a stimulant and a way for people to lose weight. The "ECA" portion stands for ephedrine, caffeine, and aspirin, and since the three drugs are taken at once, or "stacked" together, they have earned the nickname of stackers. They apparently decrease the appetite and help keep food cravings under control. With the combination of ephedrine and caffeine, it seems stackers also rev up your energy and metabolism, which may also lead to weight loss.
From my research, it seems like stackers are definitely a "good news/bad news" type of product. The good news? Studies indicate that they might actually work to help you lose weight, which is a relative rarity in the world of diet pills. The bad news?
The main ingredient in stackers, ephedrine, comes with a pretty hefty laundry list of dangers and potential side effects, especially those involving the heart.
First, let's look at the research. Placebo-based studies have found that ephedrine taken in combination with caffeine can lead to fat loss. Also, plain supplements with just ephedrine and no caffeine have shown the same result. A meta-analysis, which is when researchers look at a bunch of similar studies all at once, concluded that using ephedrine in some combination leads to an average weight loss of about one kilogram more a month than just a placebo. Just as a side note, some ads for stackers claim that they will help with your athletic endurance too, but this has not been proven in medical studies.
Again, this weight loss can definitely come at a price. Ephedrine has been shown to be especially dangerous for people who have pre-existing heart problems and heart disease. But it can also cause heart attacks and other problems in young people who had no previous health conditions.
Most people who use stackers taken them two to three times a day in a ratio of one part ephedrine to 10 parts caffeine and 10 parts aspirin. In order to avoid sleep problems, many people take their stackers before mid to late afternoon. Some people buy them already stacked, so to speak.
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I was introduced to stackers in 2000. Having been really healthy for most of my life. I lost 2 and a half stone in weeks. My head was buzzing like pins and needles. I was shaking , couldn't sleep, couldn't sit down was on the go all the time. The sweating was really bad too. I stopped taking them after 6 months after I was stood in a pool of sweat and realised this wasn't good. I then put on 3 stone and was tired all the time, sleeping lathagic and more. Two years later I was diagnosed with an under active thyroid and after scan ion my throat it showed I had scarring that you would get only from having been over active. I know these tablets caused my thyroid to go over and then under.. and I've been so unhealthy since. I would never recommend them
July 20, 2017 - 2:57am
Improved My Health 1
Alison Stanton View Profile Send Message
We value and respect our HERWriters' experiences, but everyone is different. Many of our writers are speaking from personal experience, and what's worked for them may not work for you. Their articles are not a substitute for medical advice, although we hope you can gain knowledge from their insight.
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 3
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{
"redpajama_set_name": "RedPajamaC4"
}
| 4,872
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Łukasz Kubot and Oliver Marach were the defending champions; however, they lost to Santiago González and Máximo González in the quarterfinals.
Victor Hănescu and Horia Tecău won the final against Marcelo Melo and Bruno Soares 6–1, 6–3.
Seeds
Bob Bryan / Mike Bryan (first round)
Łukasz Kubot / Oliver Marach (quarterfinals)
Mark Knowles / Michal Mertiňák (first round)
Marcelo Melo / Bruno Soares (final)
Draw
Draw
External links
Main Draw
Abierto Mexicano Telcel - Doubles
2011 Abierto Mexicano Telcel
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 7,372
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namespace org
{
namespace w3c
{
namespace dom
{
namespace bootstrap
{
std::u16string CSSValueImp::getCssText()
{
// TODO: implement me!
return u"";
}
void CSSValueImp::setCssText(const std::u16string& cssText)
{
// TODO: implement me!
}
unsigned short CSSValueImp::getCssValueType()
{
// TODO: implement me!
return 0;
}
}
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 971
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Q: Updating to font awesome 5 in backpack I see laravel-backpack comes with font awesome 4.
I would like to update it to font-awesome 5. But I can't find the file where I must change it.
Has anybody updated font-awesome to v5?
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 4,246
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\section{Introduction}
Throughout the information era, we have seen a shift in human-computer interactions, from clicks to chats. Conversational agents and dialogue systems are becoming prominent with the daily advances in the field of Artificial Intelligence. Technology will be effective if it can reach for the vaster population, by building computational models for popular languages. According to \cite{Ethnologue:19}, Telugu, which belongs to the Dravidian family, is one of the active growing languages and is ranked 16 among 7,111 living languages with 93 million speakers universally. Despite such attention, Telugu has inadequate resources when compared to its counter-partners. And also, with the advent of deep learning, many recent works are producing promising results for many languages.
In a discourse, anaphora is a lexical device which acts as a substitution for an entity mentioned earlier. As shown in example (\ref{ex1}) it is complicated to define a computable representation of the resolution process because humans personally deal with it subconsciously and mostly oblivious of the particularities.
\begin{description}
\label{ex1}
\setlength{\itemsep}{0pt}
\setlength{\parskip}{0pt}
\setlength{\parsep}{0pt}
\item {
Example 1:
Shyam: Will Ram come to our school tomorrow for the competition?
Prem: It is too far from his house.
Here the pronouns 'his' refers to Ram, 'it' refers to school and 'our' refers to both Shyam and Prem.}
\end{description}
\noindent Despite the involvement of such intricacy, these systems are yet crucial in dialogue systems, machine translation, and information extraction. In this paper, we build a system that resolves the anaphora in Telugu dialogues. In contrast to syntactic and rule-based systems, which are approximate solutions, our method uses few handcrafted features appended to the word embeddings, focusing on semantic features and works excellently on real conversations. We present a new strategy to resolve speaker-hearer mentions and plural mentions, which were never tackled before. To the best of our knowledge, it is the first time deep learning has successfully implemented in Telugu dialogue NLP research.
\section{Related Work}
\citet{Hobbs:78} was one of the first persons to pioneer in the area of anaphora resolution focusing on early syntactic heuristics. His algorithm takes sentences up to target pronoun as input, and as it traverses backward it finds the noun phrases with same gender and number. Hobbs evaluated his algorithm manually and reported an accuracy of 88.3 percent. Then \cite{Hirst:81} directed the anaphora problem towards resolving it in discourse. \cite{leass:94,Denber:98} described several syntactic heuristics for reflexive, reciprocal and pleonastic anaphora. \cite{Grosz:95} claimed that at any given point there is a single entity being centered. Using this claim they proposed a centering algorithm which finds an entity which is divergent from other evoked entities. \cite{Mitkov:98} proposed a robust, knowledge-poor multilingual approach in resolving pronouns where each entity is provided a score based on indicators and entity with high score is considered antecedent. \cite{Ng:02} suggested a machine learning approach to anaphora resolution. However, statistical learning methods suffer from the difficulties of small corpora and corpus dependent learning.
Most of the work in Indian languages has been done in Hindi, Bengali, and Tamil. \cite{Praveen:2013} built a hybrid approach for anaphora resolution in Hindi using dependency parser and a decision tree classifier. \cite{Hemanth:15} proposed a rule-based system for anaphora resolution in Telugu dialog systems, After preprocessing the data using Morphological analyzer and POS tagger they used a set of hard-coded rules to deal with different types of pronouns.
\citet{Clark:2015} has done pioneering work in coreference resolution using deep learning that automatically learns dense vector representations for mention pairs for English and Chinese. He built them using the word embeddings in the mention and surrounding context, which will maintain the semantic similarity. Despite using a few hand-engineered features, he trained an incremental coreference system that can utilize entity-level information. His mention pair model acted as an inspiration for our feature representations, and we updated it for free word order languages. In free word order languages, despite changing the order of words in a sentence the overall meaning of the sentence will not change. As shown in Example (\ref{ex2}) telugu is a free word order language. Later, \cite{Clark:2016} used reinforcement learning to optimize a neural mention ranking model for coreference resolution.
\begin{description}
\label{ex2}
\setlength{\itemsep}{0pt}
\setlength{\parskip}{0pt}
\setlength{\parsep}{0pt}
\item {
Example 2:
Ram gave Nikhil a book.
S1: rAmu nikhilki pustakam icchADu
(Ram Nikhil book gave)
S2: rAmu pustakam nikhilki icchADu.
(Ram book Shyam gave)
Here the order of the words doesn't affect the meaning of the Telugu sentence.}
\end{description}
\section{Anaphora Resolution in Telugu Language}
In Telugu, the verbs are formed by adding the grammatical information as suffixes. Along with gender, number and pronoun (GNP), the verb also agrees with tense, aspect, and modality (TAM), which makes the complete structure of the verb as verb root + TAM suffix + GNP suffix. The pronoun should agree with all the components in order to refer to an entity in previous utterances. There are three genders (male, female, nonhuman), three persons (first, second and third) and two numbers (singular and plural) in Telugu. Example (\ref{ex3}) shows the variations produced by changing GNP variables for a common root word 'icchaa'(gave). The subject verb agreement becomes more complex because of honorifics, proximity and formality features attached to the subject in Telugu culture \cite{Subbarao_2000}.
\begin{description}
\label{ex3}
\setlength{\itemsep}{0pt}
\setlength{\parskip}{0pt}
\setlength{\parsep}{0pt}
\item{Example 3:
For Verb 'gave' when subject is:
\begin{tabular}{lclclclc}
Male&1st&singular:&icchaanu \\
Male&2nd&singular:&icchaavu\\
Male&3rd&singular:&icchaaDu \\
Female&3rd&singular:&icchindi \\
Any &3rd&plural: &iccharu \\
\end{tabular}
}
\end{description}
\subsection{Types of Anaphora}
When two or more entities refer to the same person or thing then it is known as coreference \cite{yale:97,Jurafsky:2000:SLP:555733}. Coreference is of two types exophoric and endophoric. In Exopheric coreference, words or entities refer to something which is outside text or discourse. Whereas in Endophoric coreference, entities refer to words which are present in the text. Endophoric coreference is further divided into two types: Anaphora and Cataphora.
In anaphoric reference, words refer to entities which are earlier mentioned in the discourse, whereas in cataphoric reference words refer to entities which are mentioned later in discourse. Anaphoric references are of different types such as repeated, pronominal, lexical and one anaphora.
\subsection{Types of Pronouns in Telugu}
There is a wide variety of pronouns in Telugu. These pronouns differ in their usage based on gender, number, person or other semantic variables. Listed below are few commonly used types of pronouns in Telugu:
\begin{itemize}
\setlength{\itemsep}{0pt}
\setlength{\parskip}{0pt}
\setlength{\parsep}{0pt}
\item \textbf{Personal Pronouns}: Telugu pronouns that are used as substitutes for known noun phrases. Ex:
nEnu (I), manamu (we), nIvu (you), vAru (they).
\item \textbf{Interrogative Pronouns}: Telugu pronouns that indicate questions. Ex: EmI (what), Edi (which), EvaDu (who).
\item \textbf{Possessive Pronouns}: Telugu pronouns that indicate ownership. Ex: nA (my), atani (his), Amedi (Hers).
\item \textbf{Adverbial Pronouns}: Telugu adverbs that are formed by combining a pronoun with a preposition. Ex: imducEta (whereby), anduvaLa (whereby), imdulO (wherein).
\item \textbf{Reflexive Pronouns}: These pronouns are used when subject and object are same in a sentence. Ex: tAnu (oneself), tAmu (themself).
\item \textbf{Demonstrative Pronouns}: Pronouns that point to specific things. Ex: I (This | These), A (That | Those).
\item \textbf{Reciprocal Pronouns}: Reciprocal pronouns are used to indicate that both the parties got benefited by performing certain action or task. Ex: Okarikokaru (Each other).
\end{itemize}
\section{Methodology}
According to Clark\shortcite{Clark:2015}, the primary motive of a neural mention pair model is to perform a binary classification, predicting whether two vectors are co-referent or not. The vectors should be able to learn the linguistic phenomena that appears in the nominal and pronominal mentions in the dialogues. We call these linguistic devices as features. Since Telugu is verb-final language and verbs are strongly inflected than in English, the noun and verb mentions agree more on gender, number, and person. Therefore, in contrast to the 17 features applied by Clark\shortcite{Clark:2015}, we suggest only 6 features:
\begin{itemize}
\setlength{\itemsep}{0pt}
\setlength{\parskip}{0pt}
\setlength{\parsep}{0pt}
\item Word embeddings (100 Dim)
\item Gender, Number, Person (10 Dim)
\item Part-of-Plural (1 Dim)
\item Speaker-Hearer (2 Dim)
\end{itemize}
This section introduces our framework to build the feature vectors and the deep learning model which associates anaphora with its antecedent. Our methodology can be mainly classified into three stages:
\begin{itemize}
\setlength{\itemsep}{0pt}
\setlength{\parskip}{0pt}
\setlength{\parsep}{0pt}
\item Parsing the dialogues
\item Feature vector generation
\item Neural network model
\end{itemize}
\subsection{Parsing the dialogues}
\label{sec:vg}
As Telugu is an agglutinative language to get the mentions from the utterances, we need to use a tokenizer and a sandhi splitter which breaks the complex terms into individual stems or root words. Then use a parts of speech tagger to detect the mentions. Then we need to do morph analysis of each word to extract the Gender, Number and Person features from Telugu dialogues. We used an online shallow parser build by LTRC center at IIIT Hyderabad. This shallow parser takes a text sentence as an input in the form of UTF-8 or WX format and generates an output in the form of Shakti Standard Format (SSF) given by \cite{Bharati:14}. This SSF acts as a common format of data for all the Indian languages. See example 4 for output in SSF format.
\begin{description}
\setlength{\itemsep}{0pt}
\setlength{\parskip}{0pt}
\setlength{\parsep}{0pt}
\item{Example 4:
unnADu VM $<$fs af='unDu,v,m,sg,3,,A,A' name="$unnaaDu$"$>$
}
\end{description}
\noindent In the above example, we are able to capture parts of speech of the given word which is 'VM' gender which is 'm'(Male), number which is 'sg'(Single) and person which is 3(Third Person). Gender is of three types $any$, $male$, and $female$. Number is of 3 types $zero$, $singular$ and $plural$. Person is of three types $none$, $1st$, $2nd$ and $3rd$. To encode these into the vector we need to hot encode them. So the GNP vector will be a vector of 10 dimensions. In this way, we are extracting three important features of our model i.e., Gender, Number and Person. The shallow parser also helps us the nouns, pronouns and verb phrases in the dialogues, which are potential mentions of real entities.
\subsection{Feature Vector Generation}
For generating the word embeddings for Telugu, we scraped Telugu pages in Wikipedia and Andhrajyothi newspaper. From Andhrajyothi website we scrapped all the telugu articles published between 2015 and 2017. This accounted to a total of around 133148 articles. Using Gensim, a word representation tool, we trained our own word2vec model using the scraped data. After training, we obtained 23,000 unique words (types) in our vocabulary. Each vector is of 100 dimensions. Since the data collected from these sources is vast and a mixture of several domains, the vectors have a rich semantic description. Since the conversations involve plenty of 1st and 2nd person mentions, we suggest an experimental feature called $Speaker-Hearer$. It easily discriminates between the two actors by assigning its value to $-1, 1$ respectively. Plural mention discontinuity is popular in coreference resolution systems, but no work has tackled it. Here we introduce a feature called $Part-of-Plural$ that will allow the model to treat plural definite noun mentions as single mentions. For each mention in the dialogue, we will generate the feature vector by appending all the features making it a 113-dimensional vector.
\subsection{Neural Network Model}
The model we build is a Binary Classification Multilayer Perceptron that classifies the pair as a true or false antecedent and anaphora pair. The input is a feature vector that is created by appending vectors of two mentions making it a 226-dimensional mention pair vector. Given the small dimension of the input, there is no expensive computation involved. So we are using a dense neural network.
\subsubsection{Architecture}Let $m_i$ be the mention feature vector of the mention $i$ and $p_{(i,j)}$ be the mention pair vector that represents the antecedent-anaphora pair. Now we will send this $p_{(i,j)}$ vector into a fully connected dense neural network with two hidden layers.
\begin{flalign*}
&Input Layer: x = p_{(i, j)} = [ m_i, m_j ]& \\
&Hidden Layer 1: h^1 = relu(w^1x + b^1)& \\
&Hidden Layer 2: h^2 = relu(w^2h^1 + b^2)& \\
&Output Layer: o_{(i, j)} = sigmoid(w^Th^2)&
\end{flalign*}
The output layer consists of a single value which denotes the probability of the pair to be a true antecedent-anaphora pair. We calculate the loss using a binary cross entropy function.
\begin{flalign*}
&L(\theta) = -\sum_{i,j\epsilon M,i<j}( y_{(i, j)}\log(o_{(i, j)})+(1-y_{(i, j)})&\\
&\log(1- o(i, j)))&
\end{flalign*}
Here $M$ are all the annotated mentions in the data set and $y_{(i,j)}$ represents the actual labels of the mention pairs. Here $0$ represents a false pair and $1$ represents a true pair. See figure \ref{fig:model} for the complete model.
\begin{figure}[htp]
\centering
\includegraphics[width=6cm]{finalmodel}
\caption{Neural Network Model}
\label{fig:model}
\end{figure}
\subsubsection{Hyper Parameters}
After each hidden layer, a dropout layer of $0.5$ probability for regularization is added. Regularization helps in over-fitting of the model. Then each epoch of the training phase is optimized using the Adam optimizer \cite{kingma2014adam}. Adam is a momentum based gradient descent optimization technique. We are using a mini-batch of size $128$ pairs in each training epoch. The first hidden layer has $512$ units and the second hidden layer has $128$ units. We use Rectified Linear Unit $(relu)$ activation functions in both the hidden layers and Sigmoid for the last layer.
\section{Corpus and Annotation}
Telugu is a digital resource-limited language. Most of the research for Telugu was done in sentiment analysis, POS tagging, NER, and text summarization. Publicly available annotated dialogue dataset for Telugu is not available. However, we built a corpus of 157 conversations, consisting of simple to complex dialogues that we hear in our daily life. We collected the corpus in such a way that it consists of all the possible pronoun types and mentions are balanced in gender, number, and person. About 50\% of the conversations are hand engineered, and the remaining 50\% is a translation from English and online scraping. To translate conversations from English to Telugu we are using Google translate API and on top of it a reviewer will evaluate the correctness of the translation, These conversations are then parsed using the shallow parser discussed in section \ref{sec:vg}. The total number of mentions in the corpus is 775.
After the corpus is ready, the conversations are annotated using a web application we have built specifically for annotating the mentions. The annotator allows you to make a pair of antecedent and anaphora mentions in the conversation. If both the mentions are a single real entity, then they are labeled true, else, they are labeled false. There are 642 true mention pairs and 1818 false mention pairs. The total number of mention pairs in the corpus after oversampling is 3636. Note that the LTRC shallow parser for Telugu is far from human-level performance. So, for enhancing training, the semantic features are corrected and manually tagged with the help of annotator. Each conversation is annotated by two reviewers and in case if there is any conflict, then the conversation is sent to a third reviewer.
\section{Results}
Consider that, in a given context, if there are $n$ mentions, where $n\geq2$, $k$ mentions among them are referring the same entity, where $0\leq k\leq n$. Then there are $k(k-1)/2$ pairs which are true coreference mention pairs and $(n-k)(n+k-1)/2$ pairs which are false coreference mention pairs. After observing the graph constructed based on these two equations for a given $n=5$ and $0\leq k\leq 5$, there are more possibilities of the false pairs dominating the true pairs. In figure \ref{fig:graph}, we can interpret from the region bounded by the two curves that the true and false mention pairs are unbalanced. This leads to bias while training the model on this corpus.
\begin{figure}[htp]
\centering
\includegraphics[width=6cm]{graph}
\caption{True vs False mention pairs}
\label{fig:graph}
\end{figure}
To fix this we followed sampling strategies. There are two strategies for balancing the data. In undersampling, we will reduce the number of false pair instances randomly. In oversampling, we inflate the number of true pair instances, by generating synthetic samples using a distance-based technique called SMOTE \cite{Chawla_2002}. For testing, a separate set of dialogues are used. See the comparison of the model for both the strategies in table \ref{tab:1}.
To check the performance of the model with features as part of the embedding, we compared the model to the baseline model. A baseline model is a naive model assuming to be the least possible intelligent system. Here we achieved the baseline model by training the neural network only on the 100-dimensional word embeddings. To understand the significance of every feature, we trained the model considering a feature at a time. See table \ref{tab:2} for the comparison based on features.
\begin{table}
\begin{tabular}{ |c|c|c|c|c| }
\hline
Sampling & Loss & Precision & Recall & F1\\
\hline
Under & 1.8\% & 50.4 & 42.8 & 43.8\\
Over & 0.6\% & 83.3 & 90.0 & \textbf{86.0}\\
\hline
\end{tabular}
\caption{Comparison between the sampling strategies}
\label{tab:1}
\end{table}
\begin{table}
\begin{tabular}{ |c|c|c|c|c| }
\hline
Features & Loss & Precision & Recall & F1\\
\hline
None & 0.9\% & 67.6 & 79.1 & 71.3 \\
Gender & 0.7\% & 80.09 & 86.8 & \textbf{82.5} \\
Number & 0.7\% & 78.2 & 85.7 & 80.8 \\
Person & 0.7\% & 80.0 & 86.2 & 82.3 \\
PoP & 0.7\% & 76.9 & 85.2 & 79.7\\
\hline
\end{tabular}
\caption{Comparison based on features}
\label{tab:2}
\end{table}
\section{Issues}
\subsection{Reporting Speech}
The word vector representation we chose cannot deal with reporting speech. See example (5).
\begin{description}
\setlength{\itemsep}{0pt}
\setlength{\parskip}{0pt}
\setlength{\parsep}{0pt}
\item {
Example 5:
Speaker: Ram said, 'I am the king of the world'.
Here the pronouns 'I' refers to Ram. But our feature representation will refer to speaker because it is 1st person.}
\end{description}
\subsection{Parser}
When using the system in real conversations, the parser may not give correct GNP tags. These affects the predictions. Also, the morph analyzer gives unnecessary tokenization which leads to unresolved mentions.
\subsection{Sandhi}
Sometimes the pronoun will be a part of the compound word, which is difficult to split with any computational sandhi splitter in Telugu.
\begin{description}
\setlength{\itemsep}{0pt}
\setlength{\parskip}{0pt}
\setlength{\parsep}{0pt}
\item {
Example 6:
Only he came.
atanokkaDocchADu
atanu + okkaDu + vacchADu
he + alone + came
Here `he` is part of the compound word which cannot be split and resolved.
}
\end{description}
\section{Conclusion and Future work}
This model is the best anaphora resolution system for Telugu dialogues. It can be used to build more natural conversational agents in Telugu. Since most of the linguistics of the Dravidian language family are similar, we can extend this work for other south Indian languages. The feature vectors are constructible for any language. Our system has surpassed the recent state of the art in Telugu anaphora resolution \cite{Hemanth:15}, whose accuracy is 61.1\%. With more data and discovering more useful features we can further improve this system.
\bibliographystyle{acl_natbib}
|
{
"redpajama_set_name": "RedPajamaArXiv"
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We work directly with Product teams to implement an evidence-based approach to creating valuable solutions. Some call this process Market Validation or Customer Development. No matter what it's called, the key to success is deeply involving the Product team and translating relevant and frequent feedback into the product itself.
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Why you should watch this video: Michael Sippey of First Round Capital is an original practitioner of Product Discovery. He's concise. His advice is timeless and cuts to the core of how Product teams should spend their time and energy. Don't write the MRD, PRD, Jira, whatever. Talk to customers. Now. Only 13 min long when you watch at 1.5x speed.
Why you should read this book: Sprint is a recipe-like guide to running your own design sprint. Think of it as "Design Sprints for Dummies." The exercises are valuable and repeatable making this book indispensable for product teams.
Most companies have tried a form of Product Discovery to include the voice of the customer. Often the initial attempt was not impactful and took too much work. And, they end up struggling to make it a regular part of their process. Bringing in an experienced outsider who can spot areas of improvement, suggest process and organizational changes and focus on the most important techniques can effect the cultural change needed to get the benefits of Product Discovery for the long-term.
Lack of knowledge about customers leaves Product teams guessing. Bring confidence to product development by using Product Discovery techniques. Engage with a Product Discovery Coach to quickly teach these skills and create a lasting culture change.
Product Management is a hard job. Most PMs come from other disciplines and learn on the fly. A mentor brings the experience of dozens of companies and can distill the latest trends into manageable topics for these busy professionals.
Design Sprints don't produce better ideas; they just produce them faster. Get both valuable ideas and an accelerated process by learning how to focus on problems and value.
Jim Morris founded the Product Discovery Group in 2015 to bring predictability and process to innovation and development.
He graduated from Stanford University with a degree in Computer Science and immediately joined in the first wave of Internet startups. Since then he's had two successful exits with Fogdog Sports going public on the Nasdaq exchange in 1999 and PowerReviews getting bought in 2012 for $168 million. He started PowerReviews with three others in 2005.
In the past few years, Jim has advised Product teams at over 20 companies in a variety of industries, business models, business types, and product types.
Reach out to discuss your specific needs. Typically, we get on a video chat and explore how our services can be useful to your Product organization.
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\section{Introduction }
\label{sec:intro}
Non-equilibrium kinetics of diffusion-limited reactions has been the subject
of much recent interest
\cite{vanKampen,Haken,Nicolis,Ligget,reaction-reviews,JStatPhys}. In contrast
to equilibrium systems --- which are best analyzed with standard thermodynamics
--- or reaction-limited processes --- whose kinetics is well described by
classical rate equations \cite{Laidler,Benson}--- there is no general approach
to non-equilibrium, diffusion-limited reactions.
In this letter we study a diffusion-limited coalescence process in one
dimension: $A+A\rightleftharpoons A$, which can be analyzed {\it exactly\/}
\cite{Coalescence,Doering}. When a trap is introduced, the resulting steady
state is a non-equilibrium state. We derive an exact description of this state
and compare it to the prediction from a reaction-diffusion equation --- the
standard approximation method of choice. The exact solution allows us
to determine the appropriate rate constants of the reaction-diffusion equation
directly. Normally, this feat requires a renormalization group analysis.
The rest of this letter is organized as follows. In
Section~\ref{sec:formulation} we present a lattice model of diffusion-limited
reversible coalescence, along with the exact method of analysis; the method of
Empty Intervals, also known as the method of Inter-Particle Distribution
Functions. The stationary state in the presence of a trap is derived and
analyzed in Section~\ref{sec:trap}.
In Section~\ref{sec:mean-field} we
compare the exact solution to that of a reaction-diffusion equation, and
devise strategies to determine the appropriate rate coefficients. We conclude
with a discussion and open questions in Section~\ref{sec:discussion}.
\section{Reversible Coalescence}
\label{sec:formulation}
Our model \cite{Coalescence,Doering} is defined on a one-dimensional lattice of
lattice spacing
$a$. Each site is in one of two states: occupied by a particle $A$, or empty.
Particles hop randomly into nearest neighbor sites, at rate
$D/a^2$. A particle may give birth to an additional particle, into a
nearest neighbor site, at rate $v/2a$ (on either side of the particle).
If hopping or birth occurs into a site which is already occupied, the target
site
remains occupied. The last rule means that coalescence, $A+A\to A$, takes
place
{\it immediately\/} upon encounter of any two particles. Thus, together with
hopping and birth, the system models the diffusion-limited reaction process
$A+A\rightleftharpoons A$.
An exact treatment of the problem is possible through the method of
Inter-Particle Distribution Functions (IPDF). The key concept is
$E_{n,m}(t)$ --- the probability that sites $n,n+1,\cdots,m$ are empty at time
$t$. The probability that site $n$ is occupied is
\begin{equation}
\label{disc-conc}
{\rm Prob}({\rm site\ }n{\rm\ is\ occupied})=1-E_{n,n}\;.
\end{equation}
The event that sites $n$ through $m$ are empty (prob. $E_{n,m}$) consists of
two
cases: site $m+1$ is also empty (prob. $E_{n,m+1}$), or it is occupied. Thus
the probability that sites $n$ through $m$ are empty, but site
$m+1$ is occupied is $E_{n,m}-E_{n,m+1}$. With this (and with a similar rule
for
when the particle is to the left of the empty segment) one can write down
a rate equation for the evolution of the empty interval probabilities:
\begin{eqnarray}
\label{mastereq}
&&{\partial E_{n,m}\over\partial t}
= {D\over a^2}(E_{n,m-1}-E_{n,m})\nonumber\\
&&- {D\over a^2}(E_{n,m}-E_{n,m+1})\nonumber\\
&&- {D\over a^2}(E_{n,m}-E_{n-1,m})\nonumber\\
&&+ {D\over a^2}(E_{n+1,m}-E_{n,m})\nonumber\\
&&- {v\over2a}[(E_{n,m}-E_{n,m+1})+(E_{n,m}-E_{n-1,m})]\;.
\end{eqnarray}
Eq.~(\ref{mastereq}) is valid for $m>n$. The special case of $m=n$ yields the
boundary condition
\begin{equation}
\label{discBC}
E_{n,n-1}=1\;.
\end{equation}
The fact that the $\{E_{n,m}\}$ represent {\it probabilities\/} implies the
additional condition that $E_{n,m}\geq 0$. Finally, if the system is not empty
then $E_{n,m}\to 0$ as $n\to-\infty$ and $m\to\infty$.
In many applications, it is simpler to pass to the continuum limit. We write
$x=na$ and $y=ma$, and replace $E_{n,m}(t)$ with $E(x,y;t)$. Letting $a\to 0$,
Eq.~(\ref{mastereq}) becomes
\begin{equation}
\label{eqE}
{\partial E\over\partial t}=D({\partial\over\partial x^2}
+{\partial\over\partial y^2})E - {v\over 2}({\partial E\over\partial x}
-{\partial E\over\partial y}) \;,
\end{equation}
with the boundary conditions,
\begin{eqnarray}
\label{BC1}
E(x,x;t) &=& 1\;,\\
\label{BCpositive}
E(x,y;t) &\geq& 0\;,\\
\label{BC0}
\lim_{{x\to-\infty\atop y\to+\infty}}E(x,y;t) &=& 0\;.
\end{eqnarray}
The concentration of particles is obtained using Eqs.~(\ref{disc-conc}) and
(\ref{discBC}), and passing to the continuum limit:
\begin{equation}
\label{conc}
c(x,t)=-{\partial E(x,y;t)\over\partial y}|_{y=x}\;.
\end{equation}
It can also be shown \cite{Coalescence,Doering} that the conditional joint
probability for having particles at $x$ and $y$ but none in between, is
\begin{equation}
\label{IPDF}
P(x,y;t)=-{\partial^2E(x,y;t)\over\partial x\,\partial y}\;.
\end{equation}
Given a particle at $x$, the probability that the next nearest particle is at
$y$, {\it i.e.}, the IPDF, is $p(x,y;t)=(1/c)P$.
\section{Steady state with a trap}
\label{sec:trap}
The steady state of Eq.~(\ref{eqE}), with the boundary conditions (\ref{BC1})
--
(\ref{BC0}), when $\partial E/\partial t=0$, is
\begin{equation}
\label{E_eq}
E_{eq}=e^{-{v\over2D}(y-x)}\;.
\end{equation}
This corresponds to the equilibrium concentration of particles (using
Eq.~\ref{conc})
\begin{equation}
\label{ceq}
c_{eq}={v\over2D}\equiv\gamma\;.
\end{equation}
Another trivial solution is $E(x,y)=1$; it represents a totally empty system.
But the solution~(\ref{E_eq}) is stable, while the vacuum state is not. In
fact, when the initial state of the system is a mixture of the two phases:
$c(x,t\!=\!0)=0$ for $x<0$, and $c(x,t\!=\!0)=c_{eq}$ for $x>0$, say, then the
stable phase invades the unstable phase. The front between the two phases
propagates at a constant speed, similar to the case of Fisher waves
\cite{waves}. Here we wish to study another inhomogeneous situation, where
there
is a perfectly absorbing trap at the origin instead of the initial empty
half-space. The trap depletes its immediate neighborhood, but a non-trivial
steady state is expected as the depletion zone created by the trap is
continually replenished by a stream of particles from the stable phase.
To derive the appropriate boundary condition, we turn back to the discrete
representation. In the presence of a perfect trap at $n=0$,
Eq.~(\ref{mastereq}) is then limited to $0<n<m$. The special equation for
$n=0$ is
\begin{eqnarray}
{\partial E_{0,m}\over\partial t} &=&
{D\over a^2}(E_{0,m-1}+E_{0,m+1}+E_{1,m}-3E_{0,m})\nonumber\\
&-& {v\over 2a}(E_{0,m}-E_{0,m+1})\;.
\end{eqnarray}
Comparison to Eq.~(\ref{mastereq}) yields the discrete boundary condition
\begin{equation}
E_{-1,m}=E_{0,m}\;,
\end{equation}
which in the continuum limit becomes
\begin{equation}
\label{BCtrap}
{\partial E(x,y;t)\over\partial x}|_{x=0}=0\;.
\end{equation}
In addition, the boundary condition~(\ref{BC0}) is now replaced by
\begin{equation}
\label{BC0trap}
\lim_{y\to\infty}E(0,y;t) = 0\;.
\end{equation}
The stationary solution to Eq.~(\ref{eqE}), confined to the wedge ($0\leq
x\leq y$), which satisfies the boundary conditions (\ref{BC1}),
(\ref{BCpositive}), (\ref{BCtrap}) and (\ref{BC0trap}), is
\begin{equation}
\label{Es}
E_s(x,y)=e^{-\gamma(y-x)}+\gamma(y-x)e^{-\gamma y}\;.
\end{equation}
Far away from the trap, as $x,y\to\infty$, this converges to the equilibrium
result of Eq.~(\ref{E_eq}). From~(\ref{conc}), we obtain the stationary
concentration profile:
\begin{equation}
\label{cs-true}
c_s(x)=\gamma(1-e^{-\gamma x})\;.
\end{equation}
As expected, there is a depletion zone of size $1/\gamma=2D/v$ near the trap,
and the concentration grows asymptotically to $c_{eq}$ as $x\to\infty$.
The IPDF between nearest particles is surprising. From Eqs.~(\ref{IPDF}) and
(\ref{Es}) we obtain the conditional joint probability
\begin{equation}
\label{jointPs}
P_s(x,y)=\gamma^2 e^{-\gamma y}(e^{\gamma x}-1)\;.
\end{equation}
Dividing $P_s(x,y)$ by $c_s(x)$ yields the ``forward" IPDF --- the
probability that given a particle at $x$ the next nearest particle {\it to its
right\/} is at $y$:
\begin{equation}
\label{ps}
p_s(z)=\gamma e^{-\gamma z}\;;\qquad z\equiv y-x\;.
\end{equation}
The notation chosen here emphasizes the unexpected result that $p_s$ is
translationally invariant. What is more, this Poissonian IPDF is
characteristic of particles at {\it equilibrium\/}, when there are no
correlations between their various positions. Indeed, exactly the same IPDF is
obtained for the equilibrium state of Eq.~(\ref{E_eq}), without the trap!
To obtain the ``backward" IPDF --- the probability that given a particle at
$y$ the next nearest particle {\it to its left\/} is at a distance $z$ --- we
divide $P_s(x,y)$ by $c_s(y)$:
\begin{equation}
q_y(z)=\gamma{e^{-\gamma z}-e^{-\gamma y}\over 1-e^{-\gamma y}}\;.
\end{equation}
The fact that $q_y(z)$ is not translationally invariant comes as no surprise,
because of the trap at $x=0$. However, $q_y(z)$ does not normalize properly!
The reason for that is that there is a finite
chance that there are no particles between the particle at $y$ and
the trap; {\it i.e.}, the particle at $y$ is the nearest
particle to the trap. The probability that this happens is $p_0(y)=-\partial
E/\partial y|_{x=0}$, or
\begin{equation}
p_0(y)=\gamma^2ye^{-\gamma y}
\end{equation}
With this understanding, the proper normalization condition is
\begin{equation}
c_s(y)\int_0^y q_y(z)dz+p_0(y)=c_s(y)\;,
\end{equation}
which is indeed met.
\section{Reaction-diffusion equation}
\label{sec:mean-field}
So far, we have presented an exact solution to the problem of
diffusion-limited reversible coalescence with a trap. Exactly solvable
models of diffusion-limited reactions, however, are rare. We now wish to
discuss one of the most widely used approximation methods, in light of the
exact
results.
The method is that of reaction-diffusion equations. Here one assumes
the existence of a {\it mesoscopic\/} length scale within which the system is
homogeneous and well mixed, and where the reaction rates can be accounted for
as in classical rate equations. At longer length scales, variations in the
concentration, $c(x,t)$, give rise to diffusion. In our case, the
appropriate reaction-diffusion equation is
\begin{equation}
\label{diff-reac}
{\partial c(x,t)\over\partial t}=D{\partial^2c\over\partial x^2}+k_1c-k_2c^2\;,
\end{equation}
where $k_1$ and $k_2$ represent the ``effective" rates of birth and
coalescence, respectively. The trap at the origin imposes the boundary
condition:
\begin{equation}
\label{c=0}
c(0,t)=0\;.
\end{equation}
An alternative approach is that of writing down an infinite hierarchy of rate
equations for the $n$-point density correlation functions, and truncating the
hierarchy with a Kirkwood ansatz at some convenient stage. In the simplest
case, one truncates the hierarchy at the level of single-point density
functions. This is achieved by neglecting all correlations, and by expressing
multiple-point density functions as products of single-point densities. In
view of the peculiar IPDF in our problem (Eq.~\ref{ps}), this seems a
promising approximation.
Let the probability of having a particle at site
$n$ be
$\rho_n(t)$, then the joint probability of having particles at both $n$ and
$m$ at time $t$ may be approximated as
$\rho^{(2)}_{n,m}(t)\approx\rho_n(t)\rho_m(t)$. In this fashion, our model is
described by the equation
\begin{eqnarray}
\label{rho}
{\partial\rho_n\over\partial t} = &&
{D\over a^2}[-2\rho_n+(1-\rho_n)(\rho_{n-1}+\rho_{n+1})]\nonumber\\
&& +{v\over 2a}(1-\rho_n)(\rho_{n-1}+\rho_{n+1})\;,
\end{eqnarray}
and the boundary condition $\rho_0(t)=0$.
Notice that in the stationary limit, and without the trap, Eq.~(\ref{rho}) is
{\it exact\/}, since in the equilibrium state of the infinite system the
particles really are uncorrelated! Indeed, solving~(\ref{rho}) when
$\partial\rho_n/\partial t=0$ yields $c=\rho/a=v/(2D+av)$, which agrees with
$c_{eq}$ of Eq.~(\ref{ceq}) when $a\to 0$.
It is tempting to try and connect Eq.~(\ref{rho}) to the reaction-diffusion
approach, by passing to the continuum limit. This, however, does not work:
writing $c(x,t)=\rho_n(t)/a$, and letting $a\to 0$ while keeping only up to
first-order terms in $a$, yields
\begin{equation}
\label{rho_limit}
{\partial c\over\partial t}=D{\partial^2c\over\partial x^2}
+{v\over a}c - ({2D\over a}+v)c^2\;.
\end{equation}
Thus, it is impossible to identify $k_1$ and $k_2$ in this manner, and one is
forced to work with the discrete equation~(\ref{rho}). (An approximate
solution could be found by proceeding with Eq.~(\ref{rho_limit}) anyway,
ignoring the fact that $a$ is supposed to be infinitesimally small.)
We now use the exact solution of Section~\ref{sec:trap} to attempt and
determine $k_1$ and $k_2$. We note that without the birth and coalescence
reactions the particles would simply diffuse with a diffusion constant
$D$ --- the same $D$ as in the hopping rate $D/a^2$ of the microscopic rules.
First consider the stationary solution of Eq.~(\ref{diff-reac}), for an
infinite system without the trap: $c_{eq}=k_1/k_2$. To conform with the
exact solution of~(\ref{ceq}), we must have
\begin{equation}
\label{k1/k2}
{k_1\over k_2}={v\over2D}\;.
\end{equation}
The stationary solution to
Eq.~(\ref{diff-reac}) with the trap --- the boundary condition~(\ref{c=0})
--- is
\begin{equation}
\label{tanh}
{c_s(x)\over c_{\infty}}={3\over2}\tanh^2\Big(\sqrt{{k_1\over3D}}x
+ \tanh^{-1}\sqrt{{1\over3}}\,\Big)-{1\over2}\;,
\end{equation}
where $c_{\infty}=c_{eq}$ is the concentration of particles infinitely far away
from the trap.
The concentration profile described by Eq.~(\ref{tanh}) looks
similar to the exact result of Eq.~(\ref{cs-true}). One could now use
different criteria to further constrain $k_1$ and $k_2$. Demanding the same
asymptotic behavior far away from the trap;
$\lim_{x\to\infty}\ln[1-c_s(x)/c_{eq}]/x=-v/2D$, we get
\begin{equation}
k_1={3\over8}{v^2\over2D}\;.
\end{equation}
On the other hand, if we require the same behavior close to the trap;
$(\partial c_s/\partial x)_{x=0}=(v/2D)^2$, we get
\begin{equation}
k_1={9\over8}{v^2\over2D}\;.
\end{equation}
Clearly, it is impossible to fix the short range behavior and the long range
behavior simultaneously. Instead, one may write
\begin{equation}
k_1=\alpha{v^2\over 2D}\;,{\rm\ \ and\ \ } k_2=\alpha v\;,
\end{equation}
where $\alpha$ is a single fitting parameter of order unity. A
least square fit in the range $0\leq c_{eq}x\leq 5$ is achieved with
$\alpha=0.889\,$.
\section{Discussion}
\label{sec:discussion}
We have solved the problem of diffusion-limited reversible coalescence with a
trap, in one dimension, exactly. The result is tantalizingly simple: the
stationary concentration profile is exponential. Moreover, the distribution of
distances between nearest particles (the IPDF) is also exponential, similar to
that of particles in an {\it equilibrium\/} process --- the same process in the
absence of the trap. This does not mean, however, that the
distribution of particles in the two cases is identical: it
is just a peculiarity of the IPDF in this particular model. To be sure, the
distribution of particles in the equilibrium situation is fully random and
uncorrelated, whereas in the presence of the trap it is not!
We have also contrasted the exact solution with the alternative, traditional
approach of reaction-diffusion equations, highlighting the fact that the latter
is merely an approximation method. Our model provides a clear example where
the
effective rates of the reaction-diffusion equation can be related to the
microscopic rates of the underlying process, without appealing to
renormalization.
An interesting open question is at what dimension reaction-diffusion
equations accurately describe the kinetics of the system. Previously, we
had conducted numerical studies of Fisher waves in the coalescence
process, suggesting that the critical dimension is $d_c=3$ \cite{waves}. The
present model could present an advantage in future numerical studies, because
of its non-trivial {\it stationary\/} state.
Future work will also include the investigation of two-point density
correlation functions, as well as the influence of a drift away from the
trap. Both problems can be formulated rigorously within the framework of
the IPDF method \cite{Doering}. Multiple-point density correlation functions
would shed further light on the breakdown of reaction-diffusion equations in
low
dimensions. Drift away from the trap could potentially give rise to an
interesting phase transition: from a system with a non-trivial steady state
(such as in our case, when the drift is zero), to a system with only a trivial
steady state (the vacuum), as the drift increases beyond a critical point.
\acknowledgments
I thank L.~Glasser, P.~Krapivsky, S.~Redner, and L.~Schulman for valuable
discussions.
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THE SECRET GARDENER
DUMSNÅLA TIPS FÖR NYGAMLA ODLARE
JAG SKRIVER DET HÄR SITTANDE PÅ KNÄ PÅ EN ISKALL KYRKOGÅRD I PARIS. Det är mitt i vintern men jag är ändå svettstressad över att molnen vägrar skingra sig tillräckligt mycket för att jag ska hinna få en skymt av månen innan de flera meter höga portarna till kyrkogården stängs och jag blir kvar här resten av natten. Och jag tänker för mig själv att det här aldrig hänt om jag inte blivit odlingsintresserad.
För då blir det så här: ena dagen står man och sköljer ur äggskal i köket, eller försöker få rucola att gro ("Rucola, det är ju ett ogräs, växer var som helst!"), men innan man vet ordet av hukar man på en lerig grusgång ett stenkast från Jim Morrisons grav och funderar på om de där avlägsna koskällorna betyder att man håller på att bli inlåst.
Allt började den där sommaren när jag blev förälskad i en vackert övervuxen kolonilott strax utanför Stockholm. I två år läste jag allt jag kunde om odling medan kön till lotten långsamt ringlade sig framåt. Jag läste Lena Israelsson och upptäckte att tomater inte är allt. Jag läste Ruth Stout, en tant som älskade täckodling (vi återkommer till det) och som under ett helt år levde enbart på grönsaker från sin egen odling. Jag läste Dolly Freed, en 18-åring som strävade efter att kunna göra samma sak, och John Seymour som lyckades bättre än de båda tillsammans. Nästan exakt när vår lott blev ledig kände jag mig fullärd. Jag hade läst allt om odling, det enda som återstod var att använda kunskapen till att göra mig och min man självförsörjande på grönsaker.
Nu, ett gäng odlingsår senare, har jag lärt mig den kanske allra viktigaste läxan om självförsörjning: Det är omöjligt. Det existerar inte. I alla fall inte i moderna städer. Jag bryr mig inte om vad John säger: Ruth åt inget annat än rå, gul lök på vintern och Dolly ägnar ett helt kapitel i sin bok _Possum Living_ åt hur man hotar kommunalpolitiker på ett sätt som gör att de slutar kräva en på skatt. Det är inget liv för mig. Det är inte ens eftersträvansvärt. Men jag har också lärt mig att det finns delar av det livet som inte bara är eftersträvansvärda, utan fullkomligt livsomvälvande och nödvändiga.
Kockar och matskribenter brukar uppskatta att vitlök dök upp på trendkänsliga svenska middagar i slutet av 70-talet. Först kring 1993–94 upptäckte moderiktiga svennar italienska specialiteter som basilika och rucola. Sen dess, sägs det, har svenskarnas grönsaksmedvetenhet och trendkänslighet bara vuxit. Samtidigt har den vilda formen av rucola ett gammelsvenskt namn: sandsenap — visst fattar man både hur den smakar och var den ska växa? Och tuvor av förvildad vitlök hittas då och då bakom gamla torp som stått övergivna i decennier.
Så när jag hör hur trendigt det är med grönsaksodling blir jag skeptisk. Jag tror att det går mycket djupare än så. Det är en verklig, bestående förändring. Det är inte trendigt att odla grönsaker. Att påstå det är bara närsynt. Det är ju uppenbart att den verkliga modenycken är den här industrialiseringstrenden som varit så het de senaste 60–70 åren.
Numera ser jag mig själv som en del av en nygammal odlingsrörelse där ilskna miljötanter och -farbröder möter orediga nyodlare, långt ifrån mossfria villaträdgårdar.
Vi nygamla odlare är snåla, envisa, skeptiska, nyfikna och bryr oss inte så mycket om vad andra tycker (man kan inte hänga upp sig på det där med skam när man gödslar sina grönsaker med kiss). Vi odlar för att äta och för att känna oss oberoende men även för att grönsaker är fascinerande och vackra, och att dra stenhårda gränser mellan det vackra och det funktionella är ändå ointressant eftersom vi vet att de flesta blommor är ätliga och dessutom har medicinska egenskaper.
Våra odlingstrick kommer från västerländska forskare lika gärna som från gamla urfolk och afrikanska skolträdgårdar. Så länge det maxar skörden är det skitsamma vem som kom på det. I den här boken har jag försökt samla så många av de tricken som möjligt.
XOXO
ELIN
Groddar = årets första odlingsprojekt.
MÅNRIT FÖR GOD SKÖRD. Januari är en tung tid för odlare. Jag känner inga odlare som får höstdepressioner, vårdepressioner däremot står som spön i hypotalamus. Det här är månaden när groddar och, framförallt, böcker kommer att hålla dig vid liv. För när du väl blivit odlingsintresserad – vilket inträffar, utan undantag, första gången ett frö du stoppat i jorden gror – finns det många coola flummerier att sätta sig in i. Flummigast av dem alla är månodling, en sorts mellanting mellan astrologi, astronomi och bondepraktikan. För mig ballade månodlingen snabbt ur i total vidskepelse och plötsligen satt jag där, ensam på en fransk kyrkogård, mitt i vintern eftersom det är då månritualen jag fastnat för ska utföras.
#### Gör så här:
Utför ritualen under första nymånen efter vintersolståndet – nyårsnyet. Det är då, enligt den danska häxan Dannie Druehyld, grunden för ditt kommande år läggs. Du utformar riten själv, genom att ta med dig det du vill fokusera på under året ut i månljuset. Vill du att det ska gå bra för ditt band tar du med dig instrument, vill du ha en bra skörd, fokusera på frön och trädgårdsverktyg. Det finns spår av ritualen även i gammel-Sverige, där bönder sägs ha hållit fram nåt långt i månskenet för att garantera en god linskörd. Dannie föreslår också att du tar med dig lite pengar ut i natten för att kunna leva i överflöd under resten av året.
Och jag blev inte inlåst. Jag släntrade ut mellan två förfallna sarkofager precis när kyrkovaktmästaren hängde undan koskällan för att putta igen de enorma grindarna och samtidigt som en liten japansk man kom rusande, 100 meter längre in på kyrkogården, panikslaget skrikande åt mig att hålla porten.
## (GRODDAR)
När odlingsabstinensen blir övermäktig är groddar ett bra vinteralternativ. De behöver inte ljus för att gro och är supernyttiga under en period när de enda svenska grönsakerna i säsong ser ut och smakar som jordklumpar.
I vanliga fall är jag emot att köpa odlingsprylar – de är för livsstilsodlarna, inte för oss nyodlare. Men helt ärligt så revolutionerades mitt groddliv av ett riktigt groddtråg. Det vanliga gör det själv-tipset är att lägga de fuktiga groddfröerna i en glasburk och trä muslintyg över mynningen. Ställ sen glasburken uppochner, lite på sniskan, på ett fat för att vattnet ska kunna rinna ut. Mer än en gång har jag efter en veckas pyssel stått med en handfull mögliga frön insnodda i en bit sönderklippt örngott.
Mitt köpetråg, däremot, är gammalt och fult men funkar hundra gånger bättre än alla hemgjorda försöksburkar jag byggt.
#### Gör så här:
• Börja med nån matsked frö – storleken kommer att öka i kvadratcentimeter på ett overkligt sätt.
• Om du är otålig, lägg fröerna i blöt över natten, det snabbar på groningen.
• Stjälp över fröerna i tråget och skölj dem.
• Ha tråget i rumstemperatur. Ställ det mörkt om du vill ha bleka, snygga groddar eller ljust om du vill ha klorofylligt gröna groddar. Groddar med klorofyll är nyttigare men fulare.
• Skölj morgon och kväll med ljummet vatten så att groddarna varken torkar ut eller möglar.
• Efter nån vecka är groddarna klara. Ställ dem i kylen så gror de inte vidare.
• Skölj alltid groddarna innan du äter dem – de lever fortfarande (freaky) och fröet kan bära på bakterier.
ALTERNATIVA GRODDAR. Det finns ett trick för att få mungböngroddar att se sådär proffsiga ut, som i kinaaffären. Skölj groddarna extra försiktigt och låt bli att vända, flytta eller skaka runt dem när du sköljer. Precis som alla andra växter strävar groddarna mot ljuset och om ljuskällan hela tiden flyttar sig vrider de på sig och blir krokiga. Det ständiga vridandet gör också att grodden försvagas och lättare blir dålig och går sönder.
Testa experimentgroddning. En kväll när jag hade extra svår odlingsabstinens men alla fröbutiker var stängda började jag maniskt leta igenom skafferiet efter groddmaterial. Och insåg att där finns hur mycket odlingsbart som helst: quinoa, linser, råa mandlar (alltså såna som inte värmts upp eller pastöriserats) och kryddan bockhornsklöver är alla levande fröer som funkar asbra att grodda.
Istället för groddar. Solrosfröer och gula ärter – helt vanliga ärtsoppeärter alltså – blir fina, ätliga skott. De funkar på samma sätt som smörgåskrasse: Lägg dem i blöt över natten, sprid ut över ett tunt lager jord och spänn en genomskinlig plastpåse med några hål i över så att jorden inte torkar ut med en gång. Klipp och ät råa.
En varning. Gamla grönsaksfröer du vill bli av med går också att grodda, men det finns risker. Även om det är helt ätligt kanske inte själva fröet hanterats på ett sätt som passar människoföda, och olika magbakterier kan följa med under groddningsprocessen.
Och en lösning. Färdiggroddade böngroddar går att hetta upp snabbt, då dör alla bakterier. Kasta ner dem i kokande vatten och skölj dem sen i kallt vatten med en gång. Blanda med lite sesamolja och sesamfrön och ät omedelbart.
Låt bli linfröna. Testa inte ens, lita bara på mig.
GODA GREJER ATT GRODDA. Så länge de inte är för gamla, utan fortfarande lever, går fröer från alla dessa växter att grodda.
• Bockhornsklöver • Rädisa • Fänkål • Alfalfa • Anis • Klöver
• Kålväxter som rucola, broccoli, grönkål.
• Men även linser, mung- och sojabönor, korn, icke-polerat brunt ris och bovete.
RIVSTARTA DINA ÄRTSKOTT. Lägg torra ärter och bönor i hett vatten, omkring 60 grader, över natten så gror de extra snabbt. Tricket funkar oavsett om du ska så dem i grönsakslandet, odla ärtskott eller förbereda ärter för ärtsoppa (behandla dem i så fall som groddar tills de fått en liten svans och koka dem sen som vanligt, då blir soppan mer lättsmält). Ärt- och solrosskott är dessutom lätta att odla som hydrokultur: i speciella vattenfyllda tråg, utan jord.
## (JULBLOMMOR I REPRIS)
Som nyodlare tänker du alltid snålt och smart. Sen jag började odla klarar jag inte längre av att slänga blommor och jord i soporna. Därför återanvänder jag julblommorna. En bonus med den övervintrade amaryllisen är ju också att du slipper ha en nyköpt och alltså nybesprutad växt hängande över frukostmackan varenda vintermorgon. Att övervintra ekologiska, giftfria växter är såklart ännu lyxigare.
DRIV HYACINTEN SOM ETT PROFFS. Övervintra och plantera om din hyacint på samma sätt som amaryllis (se sidan 20), men istället för att genast flytta in den nyplanterade löken i ljuset och värmen i lägenheten ställer du den mörkt och svalt i ytterligare åtta veckor. När löken skjutit ett blekt toppskott flyttar du den till ett ljust lägenhetsfönster. På det här sättet tvingar du fram blomstängeln snabbare och risken att det bara blir en massa långa blad minskar. Det här är dock en ganska brutal metod, så den funkar bara ett år. Sen behöver löken ta igen sig med en massa ljus och näring, i en rabatt till exempel.
JULROSOR går att plantera ut när frostrisken är över. Gärna under en buske – dels för att det blir snyggt, dels för att julrosor gillar porös lövig jord. Passa på att blanda ner lite lövkompost i planteringsgropen också. Har du tur sticker det upp vackra blommor ur snön under buskens kala grenar redan nästa senvinter.
JULGRANEN går att klippa ner och återanvända. Om snön ännu inte lagt sig vid tjugondag Knut, klipp av kvistarna med en sekatör och lägg dem som skydd över känsliga grejer i trädgården. Om snön redan ligger, luta istället grenarna som en kåta runt extra utsatta växter: stark vårsol kan vara lika skadlig som vinterns iskyla.
JULSTJÄRNAN kan du övervintra genom att... Hmm... Äh, skit i julstjärnor, de är jättekrångliga att få sådär röda och snygga igen. Köp en julros istället, de är coolare.
## (HEMMAGJORDA BIVAXLJUS)
En vinter fick jag dille på att köpa bivaxljus: Jag är ensambarn och känner att om jorden går under [1] kan det potentiellt bero på att jag inte styrt upp grejer ordentligt. Efter att ha letat som en galning hittade jag en tant på internet som sålde värmeljus av bivax. Men när jag skickade in beställningen sa hon att hon bara hade ett kvar, för 15 kronor plus frakt på 35 kronor, och frågade om jag ville ha det ändå. Jag sa tack men nej tack.
Så i ren desperation upptäckte jag att det är svinlätt att göra egna bivaxljus. Hemmagjorda bivaxljus luktar sjukt gott och är billiga. Jämfört med stearinljus tillverkade av palmolja (som gör livet surt för folk i Malaysia och Indonesien) och paraffinljus (som osar farliga ämnen) är det en no-brainer.
Köp inte ditt bivax från hälsokostbutikerna, de tar ut ockerpriser. Det är mycket billigare att köpa i butikerna där biodlarna själva handlar eller direkt från en biodlare. Om du inte redan känner nån kan du hitta lokala biodlare genom Sveriges Biodlares Riksförbund.
[1] Om våra bin försvinner kraschar pretty much allt i världen. Kostnaderna för att utföra det jobb som bin och andra flygfän gör gratis i kommersiella frukt- och bärodlingar skulle bli astronomiska och konsekvenserna för både vår vilda och tama miljö skulle vara dystopiska. Att inte bespruta kommersiella odlingar är ett bra sätt att skydda bin. Men du kan även stödja lokala biodlare genom att köpa biprodukter, som äkta, svensk honung (till skillnad från en del annan honung är den inte gjord på socker som smaksatts med honung) och just bivax.
DE BÄSTA, SNÅLASTE LJUSSTAKELJUSEN. En vinternatt när jag och min man satt och drack vin och rullade ljus tills händerna var lena av vax och köket luktade varm honung kom min kompis Martin på besök. Han har långa, smala pianofingrar och hårda små gubbanypor och rullade ett ljus som blev stenhårt och inte tjockare än en blyertspenna. När vi tände ljusen brann Martins dubbelt så länge som våra fluffiga, slapprullade ljus. Ju mindre luft det är mellan varven på ditt ljus, desto mer ekonomiskt blir det alltså. De hardcorerullade hemmaljusen blir till och med bättre än svindyra köpebivaxljus eftersom du kommer vara mycket mer noggrann när du gör dem än vad professionella bivaxljustillverkare är. Det enda som behövs är bivax och veke.
#### Gör så här:
• Lägg veken längsmed ena långsidan på bivaxkakan.
• Nyp/rulla in veken i kakan tills du har något som ser ut som en smal hushållspappersrulle med en veke i ena änden.
LJUS I GLAS är ännu lättare att göra, men kräver fler tillbehör. Du behöver ett dricksglas eller liknande, veke, klister, drinkpinne och bivax.
#### Gör så här:
• Ta ett gammalt glas, en burk eller ett utbränt, urdiskat doftljusglas.
• Limma fast veken i botten på glaset – ibland är det lättare om du först knyter fast veken i en sån där metallplupp som finns i botten på vanliga värmeljus.
• Fäst veken på en drinkpinne eller penna eller nåt som du lägger tvärsöver glaset, så att veken löper rakt upp i mitten av glaset.
• Smält bivaxet försiktigt i en gammal kastrull som du inte kommer att behöva använda till nåt annat än ljustillverkning i framtiden. Det går åt ungefär två vaxkakor till ett glas stort som ett vanligt doftljus.
• Fyll glaset till nån centimeter från kanten.
• När vaxet stelnat är ljuset klart att tända.
Beeatches.
GJUTNA LJUS går att tillverka med hjälp av en gjutform. Jag har en formad som en stegrande kattunge. Tyvärr brinner konstigt formade ljus väldigt snabbt, men gillar du tanken på att bränna kattungar så är det ett lågt pris att betala.
## (SÅ MYCKET BÄTTRE)
Ett frö är resultatet av att två blommor har legat med varandra (eller att en blomma legat med sig själv). Det kan ju verka som skäl nog att så egna fröer istället för att köpa färdiga plantor, men det finns faktiskt fler anledningar. Dels är fröer billigare, dels har färdiga plantor ofta färdats långt vilket tar bort lite av syftet med att snålodla sin egen mat precis runt hörnet. Om du inte kan köpa ekologiskt odlade plantor vet du inte heller hur jorden, gödseln, djuren som bajsat ur sig gödseln eller plantan behandlats innan den kommit till dig. För att få reda på exakt hur du gör när du sår, se sidan 18.
AVMYSTIFIERING AV STRATIFIERING. Fröer styrs av hormoner, och hormonerna triggas av omständigheterna runt omkring fröet. Det är bland annat det som gör att de inte vaknar mitt i vintern eller på hösten eller vid nåt annat helt opassande tillfälle. Vissa växter har specialkrav. Det finns de vars väckarklocka sätts igång av växlande perioder av värme och kyla (här kan man tänka att fröet planerat att överleva både skogsbränder och midvinter). Andra har hårda skal som behöver öppnas med en skalpell för att fukt ska nå in till fröet (det här kan vara ett frö som tänkt ta över världen genom att åka snålskjuts i djurs magar, eller flyta över hav). Och så finns det de som stimuleras om de märker att det hunnit vara riktigt kallt ett par månader. Det är inte alltid skitlätt att få den här grejen – som kallas för stratifiering – att funka men det finns ändå några väldigt odlingsvärda växter att testa köldbehandlingen på.
Eftersom det går lång tid från sådd till grodd när man köldbehandlar brukar jag så alla dessa kinkiga fröer i krukor på gården, inte direkt i jorden. Om du är alls lik mig finns det annars en överhängande risk att du glömmer var du sått dyrgriparna och sen, när våren kommer, helt övernitiskt rensar bort dem i tron att de är ogräs.
#### Gör så här:
• Fyll små krukor med såjord. Släpp krukorna från låg höjd ett par gånger – som folk på film släpper handrullade cigaretter i bordet – så att jorden packas lätt.
• Så ett par frön per kruka.
• Täck stora frön med fint grus eller vermikulit (en sorts specialsubstrat som säljs på odlingsställen). Täck små frön mycket tunt.
• Vattna försiktigt så att fröna inte sköljs omkring.
• Ställ krukorna i ett minidrivhus eller täck dem med genomskinlig plast för att minska avdunstningen.
• Ställ ut alltihopa i vinterkylan minst 2 månader.
• Se till att jorden inte torkar ut, särskilt på våren när värmen kommer och fröna förhoppningsvis gror.
• När plantorna har två riktiga blad (mer än det där allra första bladparet, som kallas hjärtblad) planterar du om dem i enskilda krukor och sköter dem som vanligt tills du planterar ut dem i rabatten nån gång framåt våren.
• Om du har plats, och en fördomsfri hemmamiljö, går det att göra samma sak i kylen.
• Vissa fröer går också att köldbehandla genom att du lägger dem direkt i en hopknuten plastpåse fylld med fuktig sand eller vermikulit.
• Förvara påsen i kylen och så fort du ser att fröna börjat gro sår du dem – mycket försiktigt – i krukor med fuktig såjord som sen placeras i ett ljust fönster i väntan på våren.
### HYACINT [ _Hyacinthus orientalis_ ]
Julens pynthyacinter klarar sig asbra i svenskt klimat. Jag fattar inte varför inte fler odlar dem som rabattblommor, istället för att bara kasta. Det känns som ytterligare en sån där grej som ingen gör bara för att ingen gjort det tidigare. Hyacintens enda nackdel är att den får rabatten att lukta jul i april, vilket kan vara den absolut sista månad på året man vill bli påmind om vintern. Gud, vad jag hatar april.
#### Gör så här:
• När hyacintlöken blommat över, ställ den ljust och vattna med svag näring nån gång i veckan. Löken är inte död bara för att blasten vissnar, den bara vilar lite.
• När våren kommer, och det går att gräva i jorden utan att det känns som en kamp, planterar du ut löken. Gödsla försiktigt i gropen – det finns specialblandad lökgödsel som passar extra bra – och låt eventuell blast sticka upp ur jorden.
• Ge lökgödsel varje höst så blommar löken förhoppningsvis år efter år. Vill du fortsätta ha din hyacint inomhus följer du istället instruktionerna för övervintring av amaryllis som kommer här.
### AMARYLLIS [ _Hippeastrum x horturum_ ]
Till skillnad från hyacinten klarar amaryllisen inte den svenska vintern och går alltså inte att lämna i rabatten året runt. Och de är pyssliga, men roliga, att övervintra inomhus. Allra lättast är det (som alltid) om du har en jordkällare. Jag har ingen jordkällare och därför har jag i flera år – säg det inte till nån – gömt mina amaryllisar i bostadsrättsföreningens lyxiga vinkällare. Amaryllis och dyra viner vill ha samma klimat.
Ett år drog jag till Frankrike på hösten och glömde lökarna där nere under vintern. När jag kom ihåg dem igen, på sommaren nästa år, var jag säker på att jag bara skulle hitta en liten hög mögel/damm plus arg lapp i vinkällaren. Istället låg där två friska men extremt otåliga lökar, varav den ena gett upp hoppet om min återkomst och börjat skjuta ut blast i mörkret. Hur de kan veta att det är sommar, i en källare där både temperatur och ljus är helt reglerat, övergår mitt förstånd. Jag planterade ut lökarna på kolonilotten och den ena, peppad på gränsen till övertänd, blommade på bara några veckor.
#### Gör så här:
• Köp en amaryllis.
• Om löken är på bar rot – alltså inte planterad i en kruka utan med de feta, nakna rötterna hängande löst på undersidan – placerar du den med rumpan ner i ett glas vatten. Ställ lökglaset på ett ljummet element över natten, då vaknar både rötterna och löken till.
• Plantera, gärna i näringsfattig såjord, och vattna.
• Ställ på valfritt snyggt ställe i lägenheten och ge ungefär en liten snaps vatten i veckan.
• När amaryllisen blommat över ställer du den i ett soligt fönster och vattnar som vilken växt som helst. Ge lite näring med varje vattning, det är bättre än mycket då och då.
• När blasten vissnat plockar du upp löken och pillar bort jorden. Försök att inte få panik över att rötterna ser ut som utomjordingstentakler.
• Slå in löken i skrynklat tidningspapper eller nåt liknande som kan suga upp lite fukt så löken inte möglar.
• Lägg i jordkällaren/göm i vinkällaren, eller var som helst där det är mörkt och omkring 12–15 grader.
• I oktober–november nästa år börjar du om från steg 2 igen.
### VIOL [ _Viola odorata_ ]
En vårdag för några år sen, helt utan förklaring, blev jag besatt av violer. Efter att i flera år ha skrivit "blommor är töntiga" i profilen på min blogg kunde jag nu bara tänka på denna blomma. Men violer går att både äta och göra medicin av. Violämnet, det man gör godis av, ska enligt en icke-expert till kompis vara lite lätt beroendeframkallande. Det senare skulle kunna förklara varför jag en dag fann mig själv i en växtbutik, lätt omtöcknad och med famnen full av violplantor, vilt stirrande och hojtande: "Men jag vill ju stoppa dom i MUNNEN!" till en stackars kvinna i personalen.
Mitt problem – just då i alla fall – var att hon precis berättat att typ alla plantor som inte säljs som grönsaker är så hårt besprutade att de inte är tjänliga som människoföda. Hennes rekommendation, om man inte känner för att äta pesticider och svampgift, var att vänta i ett år med att äta krukväxter. Men till och med då går det inte att vara säker på hur jorden och växten behandlats, eller om skadliga ämnen finns kvar. Orka liksom.
Kruxet med violer är att även om du sår dina egna plantor från frö så måste de stratifieras vilket alltså innebär en hel del väntan det med. Därför är det smart att så violer nu med en gång, vare sig du känner dig intresserad av dem eller inte, bara för att undvika att nån gång i framtiden behöva vara jag i den där växtbutiken.
#### Gör så här:
• Så mörkt.
• Stratifiera sådden 2 månader (se sidan 17).
• När miniviolerna är stora nog att hantera, plantera om dem i varsin kruka, ställ de nya krukorna ljust och håll jorden fuktig.
• Plantera i rabatten när jorden är varm nog att gräva i, gärna i halvskugga.
• Violer blommar redan första året efter sådd.
• Plocka blommorna varma dagar. Torka eller använd färska, i sallader, efterrätter eller gör eget violgodis (se sidan 154).
#### Superkrafter
• Viol är antiinflammatorisk.
• Te gjort på violblommor kan lösa bronkit.
• I hudkrämer eller blomsteroljor (se sidan 171) används viol mot eksem, akne och allmänt irriterad hud.
• Vissa violer går också att föröka genom så kallade avläggare. Låt en utlöpare (en sorts reva) rota sig, klipp sen av den från moderplantan, gräv upp lillplantan och stoppa ner den där du vill ha den.
• Violer uppskattas av pärlemorfjärilens larver (mer om varför det är bra att odla käk till larver på sidan 43).
### JULROS [ _Helleborus niger_ ]
Prydnadsblommor är som sagt töntiga, men det finns undantag och julrosen är helt klart ett av dem. Dels är den en av de allra första växterna att skvallra om våren i denna gudsförgätna, polcirkelskramande del av världen: bara det måste räknas som en närmast medicinsk egenskap. Dels har julrosen även ett mörkt förflutet. På den tiden när man tyckte att det var en bra idé att stänga in folk som var lite galna i trånga lådor för att de skulle sluta psykosa sig och istället börja må bättre brukade doktorer använda ett pulver av julrosens rot (svart prustrot) som medicin. Pulvret, som framkallar kraftiga nysningar, blåstes in i den stängda lådan så att hen därinne skulle ha nåt att göra/klarna till lite snabbare.
#### Gör så här:
• Så fröerna, ett par stycken i en mindre kruka, och täck med fint grus eller vermikulit.
• Stratifiera ett par månader (se sidan 17).
• När plantorna är stora nog att hantera, plantera om i varsin kruka i väntan på att utomhusjorden ska bli varm nog att gräva i.
• Plantera i utkanten av buskar eller buskage, gärna i halvskugga, när våren kommer.
• Välj planteringsplats väl: när julrosen etablerat sig vill den inte bli störd. När den väl börjat blomma kan den helt komma av sig och blomstervägra i flera år om du flyttar den.
• Luckra jorden djupare än vad odlingsgropen kräver och fyll på med löv eller lövmull (löv som fått förmultna) i botten av gropen.
• Plantera pytteplantan, ge den näring under sommaren och håll rent från ogräs så att den får kraft och utrymme att växa till sig.
• Täck gärna med granris eller liknande under vintern, för extra skydd.
#### Superkrafter
• Blommar först av alla, ibland redan innan snön smält.
• Hela växten är giftig och innehåller glykosider och kan framkalla kräkningar, yrsel och diarré.
Tack till Pia, Trinidad, Ragnar, Stajn & Lars!
Jag har vid i alla fall ett tillfälle i mitt odlarliv skottat snö ur grönsakslandet, frustrerad på gränsen till Homer Simpson. Jag la ner när jag insåg att jag inte hade nån annanstans att lägga snön än
1. i nåt av mina andra grönsaksland eller
2. på grannens lott.
Med andra ord, om du tyckte att januari var en hård månad, då har du aldrig upplevt februari. Jag vet inte om det egentligen är så konstruktivt – eller om det mer är som nån med beroendepersonlighet som helt självdestruktivt lockar sig själv med sin favoritdrog – men jag brukar använda februari till att planera. Vilken odlare vill du vara i år? Hur ska din trädgård se ut? Och vilken metod vill du använda för att komma dit?
## (DAGS ATT VÄLJA ODLINGSTEKNIK)
Att börja odla är lite som att spela tv-spel. Du kastar dig in på nybörjarnivå utan att riktigt veta vad du håller på med, och allteftersom du hajar tricken rör du dig framåt. Och då är du fast. Det finns svåra bossar och bonusbanor att låsa upp på vägen, men i grunden är det enkelt. Allt utöver att stoppa ett frö i jorden och vattna är egentligen bara lullull, sånt man lägger sig till med för att det blivit just ett tv-spel – det räcker inte bara med att klara banan, man vill få full poäng och hitta det hemliga svärdet så att man kan dräpa regnbågsdraken också. Nu vet jag inte om liknelsen höll hela vägen, men poängen är att du kan odla precis så lätt eller svårt du själv vill.
PLANERA GRÖNSAKSLANDET. Skaffa en odlingskalender, den kommer vara din livlina. Att skriva ner vad du gör, när du sått och planterat, hur mycket och när du skördat, är enda sättet att lära sig av misstagen. Rita sen en karta över hela din odling. Glöm inte att rita in skuggande träd och värmande väggar. Om du har flera olika grönsaksland eller rabatter, döp dem. Dels gör det att man känner sig som en engelsk stately home-ägare, men framförallt blir det lättare att prata om och föra anteckningar kring landen. Skriv in mått.
Spara den här tomma grundkartan och utgå från den när du planerar varje vårs sådd. Spara sen även ifyllda kartor – de gör det lättare att hålla koll på växtföljden (se sidan 131).
Grönsakslanden kan vara hur långa som helst men gör dem inte bredare än 90 cm, annars blir du galen av att aldrig nå ordentligt in till mitten. Se också till att rita in gångar mellan remsorna. Gångarna behöver varken vara tjusiga eller permanenta: en planka eller två, tidningspapper täckt med flis eller en tjock markduk gjord speciellt för trädgårdsgångar funkar lika bra.
Sen är det bara att välja – utifrån vilken odlare du är och hur kaotisk din lott är – vilken metod du vill använda för att fylla dina land med grönsaker.
KVADRATODLING OCH/ELLER PALLKRAGEODLING är turbometoden för dig som står mitt i ett totalkaos. En pallkrage är en stapelbar, fyrkantig träram som är tänkt att användas inom godstransport, men som nu kidnappats av brutalistiska, effektivitetstörstande nyodlare som använder kragarna som stora, bottenlösa krukor.
Mel Bartholemew är i sin tur en säljig amerikansk odlingsfarbror som på 80-talet startade en veritabel presidentkampanj för odlingsmetoden square foot gardening, vilket i själva verket bara är pallkrageodling med en annan form: ett grönsaksland i en liksidig odlingslåda istället för en avlång.
Kvadratodling är lätt att ta till sig eftersom den är i det närmaste matematiskt exakt. Utgå från en upphöjd odlingslåda där varje sida är 90 cm. Den kvadraten delas i sin tur upp i 30 gånger 30 cm stora småkvadrater (använd snören eller vad som helst för att skapa rutmönstret). Bädden kan placeras på i stort sett vilken mark som helst, fyllas med jord och odlas upp väldigt intensivt med minimalt spill eftersom Mel har räknat ut exakt hur många grönsaker av varje art som får plats per kvadrat. Om du nånsin känt dig aningens aning dampig (och vem har inte det) är det här perfekt – det finns ingen osäkerhet, inga gråzoner. Det ska vara exakt 9 spenatplantor per kvadrat, på pricken 16 rädisor och varken mer eller mindre än 1 pumpa. Det finns till och med mjukvara som kan göra matten åt dig.
Det finns flera fördelar med den upphöjda odlingslådan, oavsett om du väljer Mels matematiska kvadrat eller en skruttig pallkrage du hittat i ett dike. En upphöjd odlingsbädd blir varm snabbare på våren (särskilt om den är målad i en mörk färg), regnvatten rinner undan lättare vilket gör att bädden inte blir blöt på samma sätt som ett lerigt trädgårdsland, jorden blir inte heller hård eller tillplattad och behöver därför inte grävas, ogräsrensandet minskar och du kan sitta på kanten när du pysslar med grönsakerna.
Nackdelen, som alltid med saker som går snabbt, är att du behöver skaffa rätt mycket grejer för att komma igång. Antingen färdiga pallkragar eller plankor för att bygga en egen bädd och – om du inte har tillgång till en stor, allmän kompost – en hel massa jord och gödsel. Om du inte täckodlar (läs mer om det här nedan) kommer du också att behöva vattna oftare än om du har ett trädgårdsland i markplan.
Ställer du lådan direkt på ogrästäckt jord är det smart att göra den lite högre, två kragar på varandra till exempel, och grunda med nåt som kväver ogräset: ett tjockt lager tidningspapper eller markduk till exempel.
Om du vill göra dig till kan du lägga ett gammalt fönster ovanpå ramen, då blir din bädd till en drivbänk på våren.
TÄCKODLING är en av de mest miljövänliga odlingsmetoderna. I huvudet är odling ofta detsamma som grävning. Men grävandet skadar maskarna och gör att växthusgaser som lagrats i jorden släpps ut i luften. Undersökningar visar dessutom att det inte alls är säkert att ständigt grävande förbättrar jorden, tvärtom. Genom att istället täcka marken behöver du inte vattna och rensa ogräs lika ofta, och redan lucker odlingsjord hålls mjuk. Med tiden bryts täckmaterialet ner och blir till näringsrik kompost i jorden.
För att bli en framgångsrik täckodlare krävs det dock att ditt startläge är ok. Om din jord är hårt packad, näringsfattig eller täckt av ogräs är det lättare att börja med konventionell grävodling. Fast med grep istället för spade, för maskarnas skull.
Bra täckmaterial
• Kompost, helt eller halvt nerbruten
• Gräs
• Halm (läs vidare för noggranna instruktioner)
• Äggskal
• Löv eller kompost gjord på löv
• Flis
• All of the above, blandat med strimlade dagstidningar
• Det går också att använda markduk, presenningar eller svarta sopsäckar, men då missar du näringstillskottet som det organiska materialet ger.
HALM ÄR ETT GRYMT TÄCKMATERIAL. Men halmen behöver brinna, alltså förmultna, för att bli maxad och inte utveckla elakt mögel när den bäddar in grönsakerna.
#### Gör så här:
• Lägg ut dina balar på hösten.
• Boosta dem med guldvatten – urin (se sidan 89). Det gör att de bryts ner snabbare och dessutom laddas halmen med extra näring.
• Låt balarna ligga ute ett år, då blir de riktigt saggiga och eländiga, precis som de ska vara.
• På hösten sprider du halmen i ett 10 cm tjockt lager över hela den tomma köksträdgården.
• På våren, när solen tittar fram, makar du halmen åt sidan. Då blir jorden varm snabbare.
• När det är dags att så makar du tillbaka halmen, men lämna såraderna nakna: några centimeter brett räcker för att grönsaksfröerna ska hitta upp till solen.
• Så som vanligt.
• När plantorna är 10 cm höga bäddar du försiktigt in dem i halm på samma sätt som du drar ett täcke över nån som somnat för snabbt för sitt eget bästa. Låt täcket ligga till nästa vår och börja om från punkt 5.
MÅNODLING är odlingstekniken som på mycket lösa grunder fick mig att utföra fruktbarhetsritualer på en fransk kyrkogård mitt i vintern. Månodling är både flummigt och komplicerat, men även för skeptiker finns fördelar med en metod som anpassar sådd och skörd efter månens cykler. Du kommer till exempel att kunna sprätta omkring och säga saker som "Det vet väl alla att man inte ska så på drakens svans?" Vilket betyder att månen precis har passerat den södra noden på ekliptikaplanet. Tror jag.
För att veta exakt när du ska så och plantera olika saker behöver du en månodlingskalender. Jag gillar _Gardening and Planting by the Moon_ som går att köpa via de engelska snobbodlarna Royal Horticultural Society. Det går också att använda en månmatrix, alltså ett datorprogram som berättar allt sånt för dig.
Några grundläggande, allmängiltiga regler inom månodling är:
• Så eller plantera aldrig vid extrema astronomiska händelser, som mån- eller solförmörkelser.
• Skörda grönsaker som är saftiga (gurka, sallat, tomat) vid fullmåne. Frukt och blad är mer vätskefyllda då eftersom fullmånen lockar upp vattnet ur växternas rötter.
• Skörda grejer du ska torka, som chili och örter, vid nymåne. Då funkar det tvärtom: vattnet är i roten, koncentrationen av aktiva ämnen blir högre i växtdelarna ovan jord och dina örter torkar snabbare vilket gör att risken för att de ska bli dåliga minskar.
• Av samma anledning skördar du frukt som ska vinterförvaras vid nymåne – då håller sig skadad frukt längre.
PETTRICKET passar norrlänningar och otåliga. Börja spara på petflaskor nu och när odlingssäsongen kommer igång använder du dem som en modern variant på viktorianernas odlingskupor. (Du vet vilka jag menar, de där glaskupolerna folk säljer som cupcakevitriner nuförtiden.) De största flaskorna är bäst men 50-centiliters funkar också. De hemmagjorda petväxthusen ger sådden en supersnabb start och extra skydd under den opålitliga svenska låtsasvåren.
#### Gör så här:
• Skölj ur flaskan, ta bort etiketten och korken.
• Skär av botten.
• Placera flaskan över det nysådda fröet i ditt grönsaksland. Det här funkar bäst med stora, ensamma frön, som bönor och majs.
• Om du har sniglar, knyt en liten bit växtväv över öppningen. Det gör också att nyvakna humlor inte drullar ner och fastnar i flaskan.
• Plocka bort flaskan när växten slår i taket, men gör det försiktigt så att du inte sliter upp eller skadar växtens rötter.
### CHILI [ _Capsicum annuum_ ]
Chili är den perfekta självhushållningsgrödan. Den är lättodlad, klarar sig i flera år som krukväxt och frukterna är svinenkla att torka och förvara. Dessutom använder man så lite åt gången att bara ett par plantor gör att du aldrig mer behöver gå till affären för att få tag på chili.
Några roliga sorter är 'Anaheim' (supermild, funkar på friland i alla fall till zon 2), 'Peruvian Purple' (nästan svarta frukter), 'Serrano' (helt vanlig stark), 'Bulgarian Carrot' (stark och gul) och 'Penispeppar' (ja, det är en barnslig gimmickpeppar, så skjut mig). Men låt bli att köpa en påse frö av varje sort: det är dyrt med frö och du kommer garanterat inte att hinna göra slut på dem innan de blir gamla och trötta. Det är slugare att starta upp fler plantor än vad du behöver av en och samma sort och sen byta till dig småplantor av andra sorter från kompisar.
#### Gör så här:
• Så som vanligt, inomhus, mycket tidigt på våren – chili gror vid 21 grader.
• När plantorna är några centimeter höga planterar du om dem, en och en, i 8–10 cm vida krukor.
• Ställ ljust och svalt, gärna kring 15 grader, och håll jorden fuktig.
• Plantera om i större krukor allteftersom plantorna växer, de gillar inte att få för mycket plats på en gång. Ställ eller plantera ut när dygnets lägsta temperatur är över 8 grader, i skyddat, soligt läge – gärna mot en vägg.
• Om plantan blir hög och gänglig, stötta den och nyp av toppen, då blir den buskigare.
• Om du har en kanna solvarmt vatten stående nånstans i trädgården trivs chilin med en ljummen dusch på kvällen.
• Efter 12–14 veckor borde de första frukterna vara klara att skörda.
• Skörda gröna, omogna frukter om du vill ha mild chili, de blir starkare ju mognare de är.
#### Superkrafter
• Chili har antiseptiska egenskaper.
• Kan förökas genom sticklingar (se nästa sida).
• Ettårig i det fria, men lever flera år som krukväxt. Ta in krukan när den lägsta dygnstemperaturen återigen börjar närma sig 8 grader på hösten.
• Stark chili ökar blodcirkulationen och olja som hettas upp tillsammans med chili blir till en värmande massageolja för onda muskler och kalla fötter. Tvätta händerna efter smörjet (man glömmer det bara en gång).
Skönhetstipset. En snygg kombo i kruka är chili och citrongräs. Köp färskt citrongräs på våren, använd den översta blastbiten som vanligt men spara den nedersta decimetern, den del av växten där rötterna ska komma ut, och tryck ner den i chilikrukan. Håll jorden fuktig så rotar sig citrongräset och börjar skjuta ny blast på några veckor.
Sticklingar är ett alternativt sätt att föröka chili. Det är hyfsat lätt att odla plantor från frö, men samtidigt är det så jämrans mycket som kan gå fel med grejer som måste sås inomhus i februari innan man ställer ut dem i typ juni eller nån annan deprimerande sen månad. När du väl har en fungerande chiliplanta är det enkelt att föröka den genom att ta sticklingar. Och det är hur som helst bra att klippa ner övervintrade plantor, på samma sätt som din mamma brukade göra med pelargonerna, på vårkanten. Då kommer du helt naturligt att få ett gäng sticklingar över, som sen kan förvandlas till nya plantor.
#### Gör så här:
• I slutet av sommaren, i god tid innan första frosten, plockar du in din chili och behandlar den som en krukväxt. Mycket ljus men mindre näring, värme och vatten under de mörka månaderna.
• När våren närmar sig ökar du näringsdosen (lite näring i varje kanna vatten är lagom) och gärna ljuset också om du kan.
• Ljus och näring bör få plantan att vakna till liv och när det händer väljer du ut ett nytt, färskt skott som verkar extra på gång. Undvik äldre, träiga skott. Om du klipper ner din planta sparar du de finaste, färskaste bortklippta skotten.
• Klipp av skottet snett, strax under ett bladpar.
• Plocka bort de två nedersta bladen på sticklingen.
• Stoppa ner varje stickling i fuktig såjord, så att de nedersta kvarvarande bladen hamnar i jordhöjd. Sätt dem en och en i specialgjorda såbrätten med små celler, eller flera stycken längs kanten på en större kruka, då rotar de sig bättre.
• Ställ i ett miniväxthus eller dra en genomskinlig plastpåse över krukan, så att vattnet inte avdunstar så snabbt.
• På lite över 20 dagar borde dina sticklingar få rötter och då planterar du dem i vanlig jord, en och en i lite större krukor, och så börjar allt om igen.
### BASILIKA [Ocimum basilicum]
Du vet hur mataffärsbasilika alltid dör när man har skördat den, även om man planterat om den jättenoga i en ny stor kruka? Det beror på att köpebusken egentligen inte alls är en buske, utan bara en kruka fullknökad med frön och uppstressade småplantor. Och precis som med alla småplantor dör de om man nyper av stjälken. Riktig, vuxen basilika går däremot att skörda gång på gång, och varje gång du knipsar av den – strax ovanför ett bladfäste – kommer två nya skott, vilket gör den större och buskigare ju mer pesto du äter.
Basilika trivs inomhus i en rejäl kruka eller ute i ett mycket skyddat läge, men motsägelsefullt nog inte på en stekig balkong eftersom den samtidigt är lite känslig för att torka ut. Om plantan börjar få svarta blad betyder det att den fryser. Den grekiska varianten av basilika är extra smakrik.
### Gör så här:
• Så som vanligt inomhus tidigt på våren: basilika har inget emot att stå i kruka under längre tid.
• När basilikan är stor nog att hantera planterar du om den. Det går att sätta flera småplantor i samma kruka, så länge det finns gott om vatten och näring är basilika helt ok med att trängas.
• När sommaren kommit, eller när det inte blir kallare än 13 grader under ett dygn, plantera ut basilikan i ett varmt skyddat läge. Busken kan också växa vidare i en rejäl kruka.
#### Superkrafter
• Basilika ska fungera som ett insektsmedel och en kruka på fönsterblecket eller vid balkongdörren sägs avskräcka flugor.
• Kan hjälpa mot illamående och kräkningar.
### HELIG BASILIKA [Ocimum tenuiflorum]
Under flera år lagade min man phở åt mig till frukost. Det är en nästan överjordisk soppa som vietnameser äter istället för frukost, mellanmål, fika, lunch och middag. Den jagar bort bakfylla, förkylning och ångest, och förutom silkiga nudlar, chili, mungböngroddar och salladslök brukar jag krydda den med färsk holy basil, som ibland kallas för helig eller stark basilika på svenska.
Det här var när jag fortfarande jobbade 18-timmarsdagar på en livsstilstidning, och vid ett tillfälle skulle jag producera en modefotografering med en albinistisk supermodell från Hongkong. Vi ville ta några bilder inne i en asiatisk butik, och medan jag letade efter lämpliga kinaaffärer upptäckte jag Livsmedelsverkets "svarta lista". Det är en lista på olika livsmedel som förbjudits i Sverige för att de innehåller rester av olagliga bekämpningsmedel och annat som gör att ens barn föds utan njurar. Till exempel.
Det kändes extra spännande att just thai- och helig basilika toppade listan över flest svartlistade importörer. Även affären där vi brukade handla nämndes. Det var så jag bestämde mig för att börja odla min egen basilika. Mat utan acetamiprid och klorpyrifos smakar helt enkelt bättre.
Helig basilika sås på samma sätt som vanlig basilika, men tar riktigt lång tid på sig att gro. Ibland tycker jag också att fröna gror bättre i lite halvmörker, och till skillnad från vanlig basilika, som trivs med trängsel, vill helig basilika vara ensam om sin kruka. Trivs absolut inte utomhus i Sverige.
Ser basilikan hängig ut? Min kompis Tobias, som är snickare halva året och surfare andra halvan, är en mästare på att odla helig basilika. Han kallar växten tulsi, eftersom han och hans bräda hängt mycket i södra Asien, och hos honom blir örten till en vedartad buske. När jag frågade vad hans trick är berättade han att det är viktigt att tillbe plantan litegrann, i alla fall nån gång om dan, annars vantrivs den.
... eller inte.
Är du inne på ditt andra eller tredje år som odlare är det ofta nu du börjar ÄLSKA din odlingskalender. Under mitt andra odlingsår skrattade jag läppen av mig när jag upptäckte att jag året innan, andra veckan i mars, hade börjat förodla rosenbönor inomhus. När de kommit upp, vilket hände efter cirka två dagar, växte de märkbart varje dag ända fram till mitten av juni när det faktiskt är dags att sätta ut dem. Hela min odlingspyramid och ganska stora delar av resten av köket var insnärjda i blommande rosenbönor som – med ungefär två undantag – stendog när jag och min man försökte snurra loss dem för att ta dem på pakethållaren ut till lotten. Läxan är: Håll i hatten, sitt i båten, det är inte dags att så riktigt än. Men du kan ändå börja skaffa fröer. Det kan man ju å andra sidan nästan jämt.
## (GRÖNSAKER FÖR SJÄLVFÖRSÖRJARE)
När du fortfarande är en lättpåverkad odlingsrookie kommer folk att säga åt dig att satsa på ovanliga grödor som inte går att lagra. Svårlagrade grönsaker är både dyra och ovanliga i grönsaksdisken – alltså blir din förtjänst större om du satsar på haverrot istället för rädisor. Men eftersom jag odlar för basbehovet tänker jag annorlunda.
Det största problemet med självförsörjning i moderna svenska städer är förvaring. Eller bristen på den. Vår odlingssäsong är så kort att vi måste ha hela skörden liggande i typ sex månader för att inte få skörbjugg framåt maj. Och så länge din kommun inte planerar att bygga en stor, kollektiv jordkällare, eller du är beredd att leva som en hoarder inbäddad i grönsaker, är det kört.
Men vissa saker går ändå att bli självförsörjande på. Sånt du bara använder väldigt lite av till exempel, som chili. Eller bara äter precis när det är som bäst, i rätt säsong, som jordärtskockor. Men även allt som är lätt att torka, sylta, lägga in eller helt enkelt spara som det är utan att det blir dåligt. Tänk örter och kryddor, ärter och bönor, ätliga fröer, all sorts lök men framförallt vitlök, pumpor, frukter och bär.
VÄLJ GRÖNSAKSFRÖ NOGA. En kommersiell odlare och en hobbyodlare har helt olika krav på sina grödor. Den som ska sälja grönsaker i mataffärer struntar i smaken så länge grönsaken kan festa med kackerlackorna efter ett kärnvapenkrig och fortfarande se ok ut. Dessutom kommer storodlaren att föredra grönsaker som mognar helt synkroniserat så att vändorna på åkern blir så få som möjligt. Du, däremot, kommer att behandla din potatis som ägg, du bryr dig enbart om smaken och vill helst att saker ska mogna lite åt gången, för att slippa drunkna i sallat ena månaden och squash nästa.
Välj därför grönsaker noga, undvik de namnlösa, kommersiella sorterna från storfirmorna och sök istället upp specialiserade fröfirmor med väl utvalda sorter. Eller byt till dig fröer från andra odlare – det finns ingen idag levande grönsaksodlare som inte har ett frööverskott.
ATT SAMLA EGET FRÖ är klassiskt trädgårdsnörderi. Om du precis börjat odla och inte hunnit skörda några fröer än, eller om du känner att du inte har tillräckligt bra koll, finns det andra som kan göra det åt dig. Föreningen Sesam, till exempel, är en tajt medlemsklubb där folk får kalla sig roliga saker som "ålderman" och "gesäll" men där du även, helt gratis, kan beställa en massa coola och ovanliga grönsaksfröer. De kan också lära dig skörda, förvara och förädla eget frö.
DU VILL INTE VARA DEN DÄR KIRSKÅLSMUNKEN. Enligt odlingsmyten fanns det, nån gång på medeltiden, en svensk munk som var tröttare på kål än nån annan nånsin varit tidigare. Han var beredd att testa vad som helst för att slippa äta mer svennekål. Tyvärr så var det nya fräscha som han föll för kirskål, som han plockade med sig hem från Tyskland. Nu, några hundra år senare, är det ett av våra mest outrotningsbara ogräs.
Det här blev jag påmind om en dag när jag läste en artikel om hur det är lika bra att sälja huset och flytta om man råkat få in pepparrot i trädgården, sittande bara nån meter från en pepparrotsplanta som jag stoppat i jorden några veckor tidigare. Jag grävde upp den på en gång, och varje år sen dess har den kommit tillbaka som en trogen katt som vägrar överge platsen den från och med nu och i all evighet kommer att kalla sitt hem.
Location, location, location är alltså inte bara ditt mantra när det gäller fastighetsspekulation. Rätt växt på fel plats blir snabbt invasiv och börjar bete sig som en makthungrig fältherre. Läs på, på mer än ett ställe, och om du är osäker, plantera i kruka istället.
Några saker man ska vara extra försiktig med är just pepparrot, maskros (det finns faktiskt odlade maskrosor), mynta, bambu och lupin.
EXPERIMENTSTICKLINGAR är ett alternativ till frö när du vill skaffa växter. Sticklingar är ett bra sätt att föröka till exempel pelargon, chili och tomat. Det går att klippa av sticklingar på det traditionella sättet (se sidan 33), men du kan även göra sticklingen direkt på plantan.
#### Gör så här:
• Vänta tills solen återvänder på våren och din övervintrade planta börjar vakna till liv.
• Ta en mindre plastpåse och klipp upp den i botten.
• Välj ut ett ungt, färskt skott och pilla försiktigt loss några av bladen närmast toppen så att skottet får en kal hals med två, tre blad som sticker ut högst upp.
• Trä påsen över skottet och knyt med ett snöre längst ner så att det bildas en liten strut runt skottet.
• Fyll struten med fuktig jord.
• Knyt även ihop påsen upptill så att den är stram kring jorden och bara toppbladen sticker ut. Det ska se ut som om skottet har en tajt badring full med jord runt midjan.
• Efter en månad eller två kommer rötter att börja växa ut direkt ur de tomma bladfästena på skottets hals. Då klipper du bara av skottet under plastpåsebadringen och planterar om det i en kruka.
## (GLASRABARBER OCH GRATISBÄR)
Rabarber är nåt så coolt som en perenn grönsak. Det betyder att den kommer tillbaka år efter år, oavsett om du gör nåt med den eller inte. Men vi är ju bara människor, och människor älskar att göra saker med saker. Och av alla människor genom tiderna var viktorianerna bland de allra mest ovilliga att bara låta saker vara. Det fanns inget de älskade så mycket som att bleka, driva och bara i största allmänhet undertrycka naturliga beteenden. En av de mer lyckade kvarlevorna är glasrabarber, som bleks och drivs för extra tidig, god skörd.
#### Gör så här:
• Märk ut din rabarber på hösten. Eftersom den vissnar ner helt är det lätt att glömma var den är.
• Så fort snön smält bort på våren täcker du rabarbern med nåt mörkt. Jag använder en gammal uppochnervänd, svart plastkruka med en
botten som jag skurit loss för att det ska gå att tjuvkika på rabarbern utan att behöva lyfta hela krukan.
• Fös upp ett berg av obrunnen – alltså färsk – gödsel runt hela krukan (ridstall och kobönder brukar kunna ge bort hur mycket som helst). När du gödslar trädgårdslandet använder du alltid brunnen gödsel, men den här gången är det inte näringen vi är ute efter, utan värmen.
• För att få extra sprutt på uppdrivningen, toppa din gödselinbäddade kruka med fuktig halm som du förberett på samma sätt som inför täckodling (se sidan 28).
• Meningen med hela den här illaluktande processen är att skapa en rabarberkuvös. Den mörka krukan blir snabbt varm i vårsolen, men den ser också till att rabarbern inte kan göra fotosyntes. När den obrunna gödseln börjar brytas ner avger den värme som förstärker bastueffekten ännu mer.
• Stjälkarna som dyker upp därinne i mörkret, flera veckor innan rabarbern på friland är skördeklar, blir knalligt klarröda, supermilda och nästan söta. Blekningen gör också att den lite lätt giftiga oxalsyran, som finns i all rabarber, minskar och man slipper bli sådär sträv om tänderna.
• När stjälkarna slår i taket skördar du dem genom att rycka loss dem – det är bättre än att klippa av dem eftersom en kvarlämnad stump kan börja ruttna.
• Ät de blekta, sköra stjälkarna som de är, råa och doppade i lite socker, och tacka Gaia för att hon skapat en vårpresent som på bara några tuggor suddar ut alla minnen av vintereländet.
• När rabarbern börjar bli kraftig tar du bort täckningen och skördar som vanligt fram till midsommar. Efter det behöver plantan ta igen sig och göra fotosyntes – alltså äta solljus.
Rabarbersvaj?
BÄRBUSKAR OCH FRUKTTRÄD behöver beskäras för att skörden ska maximeras. Vissa saker är känsliga för beskärning och blöder om de klipps vid fel tid. Andra grejer är mer robusta och då kan du välja tidpunkt för beskärning utifrån vad du vill ska hända. JAS-beskärning (under juli, augusti och september) stimulerar tillväxt: Skär dina trötta vinbär på hösten om du vill att busken ska få extra mycket fart. Beskärning under vårvintern, innan busken blivit grön, är inte lika stimulerande och passar därför om busken redan har en bra form – en vinbärsbuske spaljerad som en solfjäder till exempel – och bara behöver fräschas upp lite.
GRATIS SVARTA VINBÄR är lätt att få tag på. Om du, eller nån annan, beskär en svartvinbärsbuske på vårvintern sparas ett par grenar. Antingen sticker du ner dem i en kruka med såjord som hålls fuktig, eller så lägger du dem i en blomlåda eller halverat stuprör och täcker med såjord. Låt toppen på kvisten sticka upp ur jorden. Kvisten skjuter sen rötter längs hela den jordtäckta biten. Till sommaren har du en helt ny planta som du kan plantera ut eller ge bort. Samma sak går även att göra med till exempel lavendel, som kan vara eländigt svårsådd.
SVARTVINBÄRSTRÄD är både bonsaisöta och yteffektiva. En avklippt vårkvist är den perfekta starten om du vill designa ditt eget träd. Sätt kvisten i en kruka eller direkt i rabatten om tjälen släppt taget. Fäst den vid ett rakt växtstöd, en rejäl pinne som är djupt förankrad i jorden till exempel, så att trädet bara kan växa rakt uppåt och inte dra iväg åt sidan. När kvisten börjar växa klipper du bort alla skott som kommer från roten och längsmed stammen, så att den fortsätter se ganska pinnig ut. Till hösten klipper du toppen rakt av, på den höjd du vill att miniträdets krona ska börja förgrena sig. Om trädet inte är tillräckligt högt väntar du ett år till. Följande vår kommer det nya grenar under det ställe där du klippt av toppen. Fortsätt sen att klippa bort rot- och stamskott och klipp av kronkvistarna på hälften, så att kronan förgrenar sig ännu mer.
När du väl stammat upp bärbusken kommer det resulterande miniträdet att ta mindre plats i trädgården än de buskar som får växa fritt. Du kan odla andra saker direkt under trädet och det skuggar inte lika mycket som en rufsig buske men ger fortfarande massor med bär. Samma sak går att göra med andra sorters bärbuskar, men även lavendel och rosmarin (om du är ihärdig och pyssligt lagd). Prova dig fram bara.
FJÄRILAR är både snygga och nyttiga i trädgården. Tillsammans med allt annat fladder i naturen hjälper de till att pollinera växterna. Dessutom är det roligt att skrämma slag på sig själv genom att plocka upp dem i handen och titta nära, nära på deras läskiga små sabeltandade ansikten. Man läser ofta om fjärilsrestauranger: odlingar med till exempel buddleja och stjärnflocka, växter rika på nektar, som är säkra kort om du vill flörta till dig lite prydnadsinsekter. Men egentligen spelar det ingen roll om du har en massa fjärilskrubb i din trädgård. Om inte larverna har nåt att äta är det ändå status quo: då har du bara lockat till dig nån annans fjärilar, inte fött upp några egna. Så om du gillar snyggläskiga insekter, avsätt utrymme till (eller låt bli att rensa bort) larvföda i trädgården redan på våren.
Växterna som fjärilarna lägger sina ägg på, och som larverna lever på, kallas värdväxter och helt naturligt är de ofta inhemska svenska växter.
### Några bra barnkammarväxter:
• Orörda nässlor i soligt läge – värdväxt för nässelfjäril, påfågelöga, tistelfjäril och vinbärsfuks.
• Viol – värdväxt för pärlemorfjäril.
• Kärleksört – värdväxt för apollofjäril.
• Gräs och starr som får växa sig höga – värdväxt för kamgräsfjäril, luktgräsfjäril, skogsgräsfjäril.
• Brakved – värdväxt för blåvinge och citronfjäril.
Kronärtskocka (Cynara cardunculus scolymus-gruppen)
### EPAZOTE [ _Chenopodium ambrosioides_ ]
Enligt internet är epazote – citronmålla på svenska – helt oumbärlig i äkta mexikansk frijoles, alltså svartbönröra. Dels för smaken, dels för att örten motverkar de, eh... matsmältningsproblem som bönor ger. Vissa använder den istället för citron eller lime i matlagning men det är jag skeptisk till.
Kruxet är bara att epazote inte går att köpa färsk i Sverige, så om du älskar frijoles lika mycket som jag (och om du inte gör det utgår jag från att du aldrig ätit frijoles) är det bara att börja odla. Nordisk litteratur svämmar inte direkt över av odlingstips, men efter en del experimenterande lyckades vi till slut få upp en blyg liten skörd.
Vi sådde de pyttesmå fröna inomhus tidigt på våren och planterade ut dem när sommaren kom. Efter cirka fyra månader av intensivt curlande, i hård kamp mot sniglarna, stod till slut en handfull centimeterhöga plantor med förskrämd uppsyn i trädgårdslandet, helt uppenbart missnöjda med att det inte var Mexiko som dök upp ovanför jordytan. Min man, amatörkocken, provsmakade ett miniatyrblad, gjorde en konstig min och sa: "Smakar som fingrarna luktar när man mekat med moppen." Och beskrivningen stämmer: den här märkliga lilla örtens smak börjar med en lätt dusch av rengöringsmedel följt av en lamslående, metallisk smak av diesel.
Men nåt skumt händer när epazoten möter sin bästis, de svarta bönorna. Då försvinner dieselsmaken och kvar blir nåt nästan rökigt, vilket är perfekt om du inte vill ha djur i maten – och rengöringsmedlet blir till en mild citrussmak. En enda liten kvist räcker till en hel gryta frijoles, och med en påse epazote i frysen kan du utan problem göra bönröra ett helt år.
### KRONÄRTSKOCKA [Cynara cardunculus scolymus-gruppen]
Kronärtskocka är krävande och ger ganska lite mat för mödan, men den kan ändå vara självhushållarens vän eftersom vissa sorter är perenna, alltså fleråriga. Det betyder att du sätter plantan ena året och med lite (ok, mycket) pyssel så dyker den upp igen nästa år. Det här funkar dock inte på alla sorter, och för att få tag på ett flerårigt exemplar, sorten 'Herrgård' till exempel, behöver du skaffa en färdig planta eller en stickling. Frösådda plantor är inte fleråriga, men kan istället ge större blomknoppar.
Kronärtskocksblommorna tar lång tid på sig att utvecklas men klarar tacksamt nog lite frost på hösten: de fortsätter dyka upp långt efter att andra känsligare saker somnat in och du kommer att ha jacka på dig när du skördar de sista.
#### Gör så här:
• Så som vanligt, inomhus tidigt på våren, en och en i varsin kruka.
• Skola om när plantorna är 1 dm höga i 10–15 cm vida krukor och ställ svalt och ljust, kring 10–18 grader.
• Plantera ut när risken för frost är över, på en varm, skyddad plats med mycket lucker jord – kronärtskockan ruttnar oftare än den fryser.
• Framåt hösten utvecklas blomknopparna. Skörda dem när de nedersta fjällen på knoppen börjar vika sig utåt.
• Efter allt väntande är den bästa belöningen att äta knopparna som de är, kokta i saltat vatten, tillsammans med extrasaltat franskt smör.
### Superkrafter
• Kronärtskocka kan hjälpa till att sänka lätt förhöjt kolesterol.
• Innehåller stora mängder antioxidanter.
• Ett extrakt gjort på kronärtskockans blad kan lindra IBS, irritabel tarm.
### KARDON [Cynara cardunculus]
Om du bor längre norrut eller bara är otålig, testa den andra tistelsläktingen, kardon, istället för kronärtskocka. Den här grönsaken är lite som ett hemligt handslag bland grönsaksodlare och matnördar. Första gången jag såg ett knippe kardon på en svensk marknad och gick fram för att fråga om den blev den söte mannen som sålde ruggen så uppspelt att han ropade till sin kollega: "Hon här vet vad det är, hon VET vad det ÄR!"
Kardon ser ut som arg selleri och stammarna måste blekas, sen smakar de kronärtskockshjärta. Den odlas också på samma sätt som kronärtskocka, men du behöver alltså inte vänta på blommorna.
När hösten närmar sig sätter du igång och bleker. Knyt ihop plantan i toppen och svep in den i juteväv eller flera lager tidningspapper och svart plast. Efter nån månad skördar du genom att skära av plantan vid roten. Skörda inte fler plantor än du behöver – de förfaller snabbt i kylen men knorrar inte över lite kyla om de får stå kvar utomhus.
En blöt dag i april när luften luktade jord och alla bussar var försenade fick vi den där lilla jordbiten vi så nervöst köat till. Trots att vi kärleksfullt kallade den "favelan på risfältet" var vi övertygade om att alla andra ville ha exakt samma kolonilott som vi (det ville de inte). När allt var påskrivet kastade jag mig in i odlandet med en energi matchad enbart av min praktiska okunskap. En okunskap som gjorde att jag sen februari haft köket täckt av bönor och helt elakt planterade ut pumpaplantorna i det iskalla duggregnet så fort vi fick tillträde till lotten. April, eller när sälgen blommar, är deppigt nog rätt månad att börja så. Inomhus alltså.
## (TORRT, KALLT OCH GRATIS)
Om du är en snål, smart nyodlare föredrar du fröer. Fröer är billigt eller gratis (se sidan 38) medan plantor som du köper i affären har färdats långt, ofta är stressade och om du gillar att äta även sånt som traditionellt inte anses ätligt, typ violer och pelargoner, riskerar du att få i dig svamp- och ogräsgift. Att odla långsamt – istället för att bara rusa ut på helgen och kompensationsshoppa till sig ett odlingsliv – är bättre för både miljön och själen. För att dina fröer ska hålla så länge som möjligt bör de förvaras torrt och svalt i väntan på sådden.
GRUNDFÖRUTSÄTTNINGARNA, det du kan påverka i din odling, är inte fler än tre: vatten, näring och ljus. Resten kommer naturen ändå att bestämma över huvudet på dig.
1. Vatten. För ett litet frö finns bara ett fokus: fukt. Sår du på friland, alltså direkt i trädgårdslandet, måste jorden hållas fuktig tills fröet kommit upp. Sår du inomhus tidigt på våren är det viktigt att minska avdunstningen från jorden. Ställ småkrukorna i minidrivhus, täck dem med genomskinliga plastpåsar eller använd en speciell odlingsmodul med plasttak.
2. Näring. Frön kräver nästan ingen näring: som små tyska tågluffare har de med sig allt de behöver. Det är också därför sådden trivs bra i näringsfattig såjord eller kaktusjord. Specialjorden är dock inget krav och för den verkligt sparsamma går det lika bra att sterilisera helt vanlig utomhusmatjord (det finns proffsiga instruktioner på internet). I grönsakslandet behöver jorden vara fet och näringsrik för att dina växande grönsaker ska må bra (mer om gödsling hittar du på sidan 88). Om du sår utomhus, på friland, istället för att förkultivera hemma kan du därför fylla såfåran med nån centimeter såjord, så att fröerna inte får en näringschock när de börjar gro.
3. Ljus. Grönsaker älskar sol. Odla inte på baksidan av skuggande hus eller plank och aldrig under träd – de där giriga kolosserna snor dessutom all näring ur jorden. De allra flesta grönsaker vill växa precis på den plats dit du själv drar fram stolen för att götta dig i vårsolen.
Håll koll på väderstrecken i din trädgård. En mur eller vägg i söderläge är gräddhyllan reserverad för grönsakernas primadonnor: chili, tomat och kronärtskocka. Sätt höga växter som bondbönor eller jordärtskockor längst bak, i norr, så att deras skugga faller bort från odlingarna.
Sår du inomhus tidigt på våren kommer sådden att behöva extra ljus. Växande plantor ska se ut som motsatsen till fotomodeller. Långa, gängliga, bleka plantor är ett tecken på att det är för mörkt och varmt.
PROBLEM MED HJÄRNSLÄPP? Om du sår väldigt små frön på friland kan det vara smart att blanda fröerna med fin, ljus sand. Det gör att de fördelas jämnt och att du ser var du redan sått. Annars brukar det här hända: du tar blicken från såfåran i en sekund och sen ser hela landet osått ut, du strösslar ett varv frö till för säkerhets skull och fyra veckor senare står du inför gallringen från helvetet.
FÖRKULTIVERING, förodling av grejer inomhus, görs för att vissa grönsaker är långsamma och inte hinner klart på en kort svensk sommar (jag tittar på dig nu, chili), för att du själv är otålig eller när du bor så långt norrut att du behöver ha färdiga plantor att sätta ut så fort frostrisken är över.
Min erfarenhet från mitten av landet, zon 2 på odlingsspråk, är att man egentligen inte tjänar så mycket på att förkultivera: hur mycket du än duttar med pytteplantorna är utomhusklimatet så mycket bättre att de grönsaker du sår direkt i jorden väldigt snabbt kommer ikapp de inomhusodlade, som dessutom ofta är lite medtagna. För extra snabb utomhussådd, använd pettricket (se sidan 30). Men trots alla de här helt relevanta och sanna argumenten ockuperas mitt kök varje vår av tonårsaktigt krävande småplantor.
Gör så här:
• Lägg alla fröer utom de allra minsta i blöt i ljummet vatten över natten.
• Hitta nåt att odla i. Nästan vad som helst med ett hål i botten funkar: såna där plastaskar som affärens grönsaker ligger i, äggskal (se sidan 69) eller ursköljda, halverade mjölkpaket, precis som på dagis. Vissa använder toarullar, men jag har aldrig fått det att funka. Helt vanliga krukor går såklart också bra.
• Fyll dina krukor med såjord och släpp dem i bordet några gånger: på det sättet blir jorden lagom kompakt och alla luftfickor försvinner.
• I stora askar kan du så många frön med några centimeters mellanrum. I en mindre kruka sår du ett par frön per kruka. I specialtillverkade pluggbrickor eller odlingsmoduler sår du bara ett frö per hål. Tro mig, du kommer ångra dig om du följer lockelsen att tömma hela fröpåsen i en och samma odlingsbytta.
• Stora fröer sås djupt och små fröer grunt. Regeln är dubbelt så djupt som fröet är stort, men pyttesmå fröer kan även sås direkt på jordytan, eller täckas med ett mycket tunt lager av fin sand.
• Du kan även täcka med vermikulit eller en blandning av vermikulit och jord. Vermikulit är en sorts mineralgryn som håller fröet fuktigt, fördelar näring och släpper igenom ljus. Nackdelen är att det blir svårare att se om sådden torkar ut.
• Vattna försiktigt eller duscha med sprayflaska tills jorden är ordentligt fuktig.
• Täck med plastfolie, gummibanda fast genomskinliga plastpåsar med några hål i över krukorna eller ställ sådden i minidrivhus.
• Krukor kan också ställas på fat eller i formar fyllda med grus som hålls fuktigt. Det är bättre än att vattna i krukan. Grustricket funkar för alla inomhusväxter – det ökar luftfuktigheten och gör att rötterna söker sig neråt mot gruset utan att behöva mötas av den syrefria kallsup som ett vanligt vattenfyllt fat innebär.
• Ställ sådden varmt, 20–30 grader. Har du ett kylskåp som läcker värme uppåt brukar det vara lagom svettigt.
• Vissa emofröer gror bara i mörker, men de allra flesta vill ha det ljust och varmt.
• När fröerna grott vill samtliga ha det ljust och svalt. Ju ljusare och svalare, desto kraftigare blir de, men i brist på annat brukar ett ljust fönster med avstängt element funka. Jag vet en odlare som smäller upp frigolitskivor på insidan av sina fönsterkarmar för att skapa ett kallväxthus på fönsterbrädan. Precis som han kommer du så småningom till en punkt där du är tvungen att välja hur mycket av dina egna livsbehov du är beredd att kompromissa bort för plantornas skull.
• När småplantorna fått två riktiga blad, eller känns tillräckligt stora för att du ska klara av att hantera dem utan att förlora förståndet, är det dags att plantera om dem till större krukor. Se till att jorden är fuktig och skaka sen försiktigt ut plantorna ur krukorna, eller gröp ur dem med en sked eller penna. Det gör inget om jorden ramlar av rötterna, men hantera plantan genom att lyfta den i bladen. Om du lyfter den i stjälken är det lätt att nypa till för hårt och då är det hejdå lillplantan.
• Stoppa ner plantorna i nya krukor, en och en. De flesta vill placeras så pass djupt att de får jord ända upp till de två första riktiga bladen. Inga nakna halsar alltså.
• Ställ tillbaka krukorna på faten med fuktigt grus i det svala, ljusa fönstret.
• Allteftersom utomhusjorden värms upp härdar du av plantorna, alltså vänjer dem vid utetemperaturen och -ljuset stegvis. Efter det är de redo att planteras ut på sina slutgiltiga platser.
## (EXTRALJUS)
Eftersom jag bor i ett av de sista överlevande husen i Stockholms gamla Klarakvarter, och det alltså är mörkt som på 1800-talet hos oss, måste jag använda extrabelysning 12–16 timmar om dan till min sådd. Den här kunskapen utbyts framförallt av gräsrökande programmerare på internetforum, så därför sker all kommunikation om extraljus medelst förkortningar.
LE, lågenergilampor, är bäst för hobbyodlaren. Det viktigaste med lampan är att färgtemperaturen blir rätt. Den anges i kelvin och skrivs ut som "K". Småväxter som drivs upp inomhus trivs bäst i en färgtemperatur kring 6 200–6 500 K. Näst viktigast är lumen, alltså styrkan på ljuset. Ju högre lumen (lm) och watt (W) en lampa har desto bättre. MEN om det är fel K spelar varken lm eller W nån roll.
MH, metallhalogenlampor, är egentligen bättre än LE-lampor. De ger buskigare plantor och om du till exempel vill odla tomater inomhus på vintern är det en MH-lampa som gäller. Men eftersom den är så mycket starkare avger den också mer värme och kräver ventilation. Alltså enbart för den riktigt seriösa odlingsnörden.
HPS, högtrycksnatriumlampor, används inomhus när du vill att dina växter ska blomma eller bära frukt, men blir varma, precis som MH-lamporna.
LED-LAMPOR utgör ett undantag från lumenregeln. Eftersom färgtemperaturen i en LED-lampa är mycket mer exakt behöver du inte alls lika högt lm. Jag har till exempel sett folk bygga om tomma pc-hårddiskar till miniväxthus med hjälp av två stycken LED-lampor på 25 watt och 1 400 lumen. Bara på internet i och för sig. Men ändå.
LYSRÖR, alltså såna vanliga som finns ovanför diskbänken, är den kanske allra mest funktionella extrabelysningen för hobbyodlaren. För att uppskatta ungefärlig kelvin räcker det att kolla på ljuset. Är ljusskenet kallt gillar växterna det, är det varmt blir det till att läsa om stycket här ovan från början igen.
Om du har ett tomt akvarium funkar både lysröret och terrariemiljön bra för växter.
Det finns också speciella växtlysrör att köpa. De är dyra men brukar finnas begagnade på internet. Växtlampor ska hängas minst 25–30 cm ovanför bladen på växterna, annars blir de stekta. En timer gör att du inte behöver komma ihåg att tända på morgonen och släcka på kvällen.
## (KÖP SÄLG)
Min pappa är skogshuggare och jag är skogsmulle. Det låter besläktat, men inget kunde vara mer fel. I en av åsiktsklyftorna mellan skogshuggare och skogsmullar frodas sälgen, alltså den där busken som får videkissar på våren. För en skogsbrukare är den ett ogräs, men av ekoflummare (samt bin) ses den som en livsviktig måltid. Sälgen är bland det första som blommar under vårens tidiga, tafatta försök och för gubbvaknande pollinerare betyder det en enda sak: frukost. Första gången jag såg en riktigt stor ensamt blommande sälg en tidig vårdag kunde jag inte sluta kolla efter helikoptern. Tills jag fattade att det var den flygande maskrosbollen av brunchande insekter som fick själva trädet att surra.
Det är först när du fäller sälgträd som du får den där eländiga kvasten av rotskott som skogsbönder älskar att hata. Låt därför stora träd vara, och sätt ett nytt om du vill bli binas bästa vän.
Den bästa sorten är helt vanlig sälg, _Salix caprea_ , av hankön. Köp ett färdigt träd eller gräv upp en planta på en plats där de finns i överflöd. Plantera på solig plats så de nyvakna flygfäna inte behöver frysa, gärna nära en bikupa.
## (PERENNA GRÖNSAKER)
Om grönsaker är coolare än blommor så är fleråriga grönsaker Miles Davis. Ascoola. Fleråringar, perenner, brukar dyka upp i så kallade skogsträdgårdar – grönsaksodlingar som ser ut som skogsdungar. En av de vackraste trädgårdar jag varit i såg ut som om nån från filmen _Mad Max_ hade designat den: omgivna av rangligt hönsnät och två meter höga grindar gjorda av vässade trästörar frodades de fleråriga grönsakerna. Strandkål och jordärtskockor, bärbuskar, frukt- och nötträd och örter växte huller om buller längs smala, ringlande stigar. Marken var täckt av bark och sönderrivna tidningar och i en grund göl låg brandgula brödbackar med flytväxter i.
Att skapa en egen skogsträdgård är skitsvårt, men det finns flera fördelar med perenna grönsaker. Du slipper skaffa frö, så, härda av och plantera om varje år. Dessutom blir plantan starkare och ofta går det att skörda tidigare än om du börjat från scratch.
Förutom de verkliga perennerna, de växter som vissnar ner helt på hösten men sen återföds från den övervintrade roten, finns det grönsaker som går att låtsasodla som perenner.
Persilja, mangold och svartrot är tvååriga grönsaker. Första året dyker de helt vanliga bladen och rötterna upp, som du skördar efter behov. När hösten kommer lämnar du några rötter i jorden och täcker bladväxterna med fluffiga löv, halm och kanske en nerklippt julgran.
Följande vår brukar de första bladen dyka upp så fort solen värmt upp jorden. Under det andra årets sommar blommar plantorna. Om du låter naturen ha sin gång kommer de att släppa sina frön där de står, och den tredje sommaren har du ett helt land fullt av självsådda småplantor som du kan låta växa vidare eller gräva upp och flytta till en annan plats i trädgården (det sista är ett måste om du odlar kålväxter som mangold, grönkål eller pak choi).
Knölar av jordärtskocka och potatis som lämnas i jorden kommer tillbaka år efter år, precis som kvarglömda vitlökar. Den snygga perennen egyptisk luftlök får små, lila lökar uppe i luften, på själva blasten. Lökarna är ovärt pilliga att skala, men hela i en gryta eller inläggning funkar de bra. Faller lökarna till marken sprider sig plantan.
En nackdel med den här metoden är att den strider mot en av de heliga grundprinciperna inom ekologisk odling: växelbruk – att aldrig odla samma växt på samma plats flera år i rad.
Särskilt kålväxter kan dra på sig fruktansvärda krämpor, klumprotsjuka till exempel, som effektivt avslutar all framtida kålodling i din trädgård. Så om du odlar kål som perenn, se alltid till att flytta småplantorna till nya land.
### Fleråringar
• Strandkål • Kronärtskocka • Pepparrot – planteras med försiktighet • Ramslök, kajplök, gräslök och luftlök • Trädgårdssyra, sköldsyra, harsyra och alla andra syror • Rabarber • Vild rucola, alias sandsenap • Sparris • Vinterkrasse, en sorts vattenkrasse som ska vara härdigare, alltså köldtåligare, än vattenkrasse • Kardon i milda klimat, eller vinterförvarad i kallgaraget
Bondböna (Vicia faba)
### JORDÄRTSKOCKA [Helianthus tuberosus]
Jordärtskockan är härdig – den överlever alltså vintern – och går att behandla som perenn. Lämna några knölar i jorden när du skördar så kommer plantan tillbaka år efter år. Man brukar få rådet att odla sorter med släta knölar, som 'Fuseau' eller 'Sugarball', eftersom skockorna kan vara meckiga att skala annars. Men det går lika bra att låta bli att skala dem och istället bara skrubba dem med rotborste innan du grillar, bakar eller hyvlar dem råa i en sallad. Skrubbade skockor funkar såklart i soppor också, så länge ditt estetiska sinne är mer... öppet. Om keso är gjord på malda mumintroll så är oskalad jordärtskockssoppa samma sak fast med de 101 dalmatinerna i huvudrollen.
Jordärtskockor är årets första skörd: du kan plocka upp dem så fort tjälen gått ur jorden. De håller sig allra bäst i grönsakslandet, ta bara upp så mycket du behöver och fortsätt skörda resten av året.
Placera jordärtskockslandet i norr så att stjälkarnas skugga faller bort från trädgården (eller välj en dvärgsort som 'Dwarf Sunray'). Skockorna är också lite lätt aggressiva, ett avgränsat land är bäst. Jag föredrar sorten 'Bianca' eftersom den blommar med gula, solrosliknande blommor.
#### Gör så här:
• Sätt knölarna så fort jorden går att arbeta på våren. Det gör inget om de fått ögon, på samma sätt som potatis.
• Om knölarna är stora som ägg planterar du dem som de är. Större knölar kan du dela, men se till att varje del har i alla fall ett par ögon.
• Gör ett dike som är 13–15 cm djupt, placera skockorna med 30 cm mellanrum och täck med jord.
• Kupa jorden runt stjälkarna när de växt till sig och vattna om sommaren är torr.
• På hösten klipper du ner stjälkarna och lägger dem över marken. Det skyddar mot första tjälen och gör det lättare att hitta skocklandet på våren när trädgården ser ut som en blöt öken.
• I november, eller följande vår om du bor där vintern kommer tidigt, är skockorna skördeklara. Lyft dem försiktigt med en grep och lämna några att växa vidare.
### Superkrafter
• Rätt placerade funkar jordärtskockorna som skydd mot vind och insyn.
• Kan odlas enligt tre systrar-principen: tillsammans med bönor eller ärter, som klättrar på de höga stjälkarna, och squash eller pumpa som täcker marken med sina yviga blad.
• Är söta men inte onyttiga för diabetiker.
### BONDBÖNOR [ _Vicia faba_ ]
När jag fick min första påse bondbönor i present hade jag aldrig tidigare hört talas om dem. Nu vet jag att det är en gammal svensk kulturväxt som man brukade torka och sen koka till en simmig bönsupa, ett mellanting mellan gröt och ärtsoppa (många gamlingar verkar ha ett totalt pölsaförhållande till rätten). Samt att den i Italien, enligt hörsägen, räknas som en vårdelikatess och äts under kräftskiveliknande former: bönskidor hälls i stora högar på långbord där man själv spritar, skalar, doppar i olja och sköljer ner med prosecco. Jag gillar den bilden så mycket att jag vägrar kolla om det stämmer.
Bondbönor kan ge väldigt mycket skörd på liten yta (så är det ju ofta med de gamla svenska godingarna). De är magnifika färska men går bra att torka och spara hela året.
Min favoritsort heter 'Green Hangdown', den blommar med fina svartvita blommor och får skidor stora som en barnarm.
#### Gör så här:
• Välj ett land som du vet är relativt ogräsfritt – bönor och andra baljväxter ogillar konkurrens.
• Så de första bönorna när jorden känns grävbar. Lägg dem i blöt i ljummet vatten kvällen innan så gror de snabbare.
• Så också en andra omgång bönor några veckor senare, då sprider du ut skörden mer.
• Skörda genom att klippa av bönskidorna med sekatör och dubbelskala dem: sprita först ut bönorna ur skidorna och skala sen av det yttre membranet på själva bönan.
• Ät bönorna råa (med måtta) eller lätt blancherade. Om du kokar dem kan du vänta med den andra skalningen: det är lätt att pluppa ut bönorna ur det innersta skalet efter att du sköljt dem i kallt vatten.
• När skörden från den första omgången bönor börjar avta klipper du av stjälkarna en dryg decimeter från marken. Med lite tur och en lång, mild höst växer det upp en ny bönplanta från stumpen, och du får ytterligare en liten skörd.
Superkrafter
• Väldigt lätt att ta eget frö från. Låt några av de först mognande bönskidorna sitta kvar på busken: när de börjat svartna plockar och torkar du dem.
• Bondbönor är okänsliga för kall jord och lätt frost.
• Bönorna har en förmåga att binda kväve i sina rötter, vilket gödslar jorden till glädje för efterföljande grödor.
### LÖK [Allium cepa]
Det går att så lök, men det är inte lätt. Problemet är att lökens utveckling styrs av dagslängden. Ett vanligt beteende hos lök är att den slutar skjuta blast när dagarna blir längre än 16 timmar. Då byter växten fokus och satsar istället på själva löken. Men lökens storlek avgörs av hur mycket blast den hunnit få. Och eftersom vårt nordliga land tänder lampan långt innan elementen går igång hinner löken inte göra tillräckligt mycket blast. Allt det här hade inte behövt vara ett problem – det skulle ju gå att förodla lök på samma sätt som chili eller basilika – men löken hatar dessutom att ha nån som pillar med rötterna. Avskyr det. Tappar takten och kommer av sig. Men för all del, testa att så några lökfrön ändå, precis i början av våren. Det är experimenten som gör att vi rör oss framåt. En annan experimentell metod är att så lökfrön på friland redan på hösten.
Det vanligaste är dock att sätta lök från lök. Det kan låta meningslöst: du stoppar ner en lök och plockar – med lite tur – upp en lök. Men allt tvivel försvinner när du väl smakar en hemmaodlad lök och blir helt: "Jaha, dom ska smaka gott. Varför har ingen sagt nåt?!"
Min erfarenhet är att det går att sätta lök precis hur tidigt som helst på året. Flera vårar har jag hittat små, övervintrade lökar som klarat kölden hur bra som helst och som glatt fortsätter växa när värmen kommer.
Ytterligare ett alternativ är att göra som gammelsvenskarna och plantera potatislök. Potatisen i namnet kommer av sättet den växer på: du stoppar ner en lök och skördar sen ett helt gäng, precis som med potatis.
Potatislök går just nu inte att köpa kommersiellt. Gå med i föreningen Sesam och byt till dig några lökar, och låt sen alltid några stå kvar i jorden vid varje skörd så att du inte behöver skaffa nya. Eller bli trädgårdsdetektiv. Fråga runt på stan. Kolla forum. Glöm inte att prata med tanterna i hembygdsföreningen. Du kommer att få både utsäde, fler historier än du kan hantera och ett gäng hängivna fans som älskar dig över allt annat eftersom du är en "ung" odlare (citattecken här eftersom det kommer att vara din USP långt upp i 40-årsåldern).
#### Gör så här:
• Välj lökland med omsorg, det ska vara den plats i trädgården som är bäst rensad från ogräs. Löken hatar som sagt när nån pillar med rötterna, oavsett om det är människor eller andra växter. Det bästa är om du gödslade eller odlade bönor på samma plats året innan: löken klarar inte för mycket näring.
• Sätt löken tidigt på våren, när jorden känns ok, med 5–10 cm mellanrum. Lämna toppen kvar precis över ytan.
• Rensa ogräs under sommaren utan att hacka. Ryck inkräktarna rakt upp bara.
• Skörda på sensommaren, när blasten börjat gulna.
• Häng på tork under taknocken, där solen värmer men regnet inte kommer åt.
• Att spara hemmaodlad lök är inga problem, den ruttnar inte som köpelök. Lägg eller häng dem luftigt. Skilj ut och ät upp skadade lökar först, så att inte mögel eller annat otyg sprider sig.
### Superkrafter
• Rå, gul lök har visat sig vara nyttigare än till och med vitlök.
• Hela löksläktet sägs ha en avskräckande effekt på bladlöss.
NORRLÄNDSK VÅR. Det finns vissa grödor som du kan så på chans tidigt på våren och som självmant vaknar till när de tycker att läget känns gynnsamt. Vintersallat, pak choi, salladslök och persilja är exempel på tåliga typer som inte kräver särskilt mycket mer än en skvätt vatten om våren är torr.
På långt håll är vi två ett stiligt par.
Nu är det dags, nu får du så! Kör!
## (GRUNDRECEPT PÅ SÅDD)
Det är som sagt lätt att odla. Folk har listat ut hur man gör på egen hand sen tidens början. Men för att minimera riskerna för totalfejl finns det lite rekommendationer att förhålla sig till.
I stort sett alla grönsaker, bär och örter vill ha djup, näringsrik, fuktig jord, som inte får vara för blöt. Att skapa den jorden är ett ständigt pågående jobb som påbörjades av de där allra första människorna som listade ut hur man odlar.
Börja med att rensa grönsakslandet från ogräs. Om du aldrig odlat på platsen tidigare gräver du igenom hela landet med en grep och plockar bort alla rötter du hittar (det finns en massa lathundstrick för ogräsrens, som du hittar om du läser vidare). Har du mull från egen kompost blandar du i den allteftersom du gräver dig framåt. Har du halvt brunnen kompost – där delar av växterna ännu inte förmultnat – gräver du en ränna i landet, gärna två spadtag djup, stoppar ner komposten i rännan och täcker över med jorden igen. Fortsätt så, med parallella rännor, över hela landet. Där nere under ytan kommer maskarna att avsluta jobbet och du har gjort jorden luftig och skapat utrymme för skyfall att rinna undan. Gödsla (se sidan 88).
När landet är grävt (från och med då är det förbjudet att gå på jorden) krattar du det plant. Sen är du redo att så.
Människor som blivit hårt pottränade gillar att dra upp snören för att få riktigt raka sårader, mer frihetliga personer bredsår (strösslar ut fröer över hela landet) och pyntiga overachievers sätter olikfärgade grönsaker i rutmönster och lär sig att "trädgård" heter "potager" på franska.
För nybörjaren är dock den mer anala metoden bäst. Då fattar man att allt som dyker upp i raka rader är grönsaker och allt annat är ogräs som man lik förbannat inte fått bort.
Lägg stora fröer i blöt över natten före sådd.
Dra ut dina sårader djupare än de behöver vara, gärna som ett decimeterdjupt dike. Grunda med såjord för överkursodling.
Om du sår väldigt små frön kan du blanda dem med ljus sand i handen, då sprids de jämnt och du ser var du sått.
Personligen ser jag mitt liv passera förbi i revy av tristess om jag blir tvungen att gallra, därför sår jag lika många frön som jag vill ha färdiga plantor. Det spar tid men gör min odling känslig för angrepp. Vill du försäkra dig om skörd kan du vräka på lite mer frikostigt och sen rycka bort överskottet när plantorna kommit upp.
Täck fröerna med jord – följ instruktionen på påsen, eller följ regeln om ett sådjup på fem gånger fröets storlek – och märk ut raderna med pinnar med namn.
Vattna försiktigt – om du gjorde decimeterdiken rinner vattnet rätt av sig självt – och håll sen sådden fuktig tills plantorna kommit upp.
Stora fröer och snigelfavoriter som sallat gynnas av pettricket (se sidan 30).
## (OGRÄS EXISTERAR INTE)
Inte egentligen. Det är en definition som du gör i ditt eget huvud. Ett ogräs är en växt som befinner sig på en plats där du inte vill att den ska vara, på samma sätt som en inbjuden gäst kan bli till en pina när han druckit upp allt ditt naturvin och vägrar sluta spela halva låtar på stereon medan han pratar om att han ångrar att han gjorde slut med sitt ex.
Så det allra enklaste sättet att rensa ogräs på är att tänka att alla växter är precis där de ska vara. På mindre än en sekund är dina land helt fria från ogräs.
Om du är en aningens mer, vadskamansäga, ickefilosofisk odlare har ogräset faktiskt några negativa egenskaper. Den största, i alla fall för nybörjaren, är att det blir svårt att skilja fingröda från fulgröda. Med tiden lär du dig känna igen grönsaksskott i landet, men sådär precis i början, när naturen ännu bara är ett stort grönt brus, försvinner de i mängden, som wallflowers i gyttret av bjudna och objudna partyprissar. Om du sår dina fröer direkt i jorden, inte inomhus i förväg, kan ogräset dessutom skugga och sno näring.
OGRÄS MED RÖTTER OCH FRÖN. Man skiljer på ogräs som sprider sig med frö (det snälla ogräset) och det som sprider sig med rötter (det dumma, dumma ogräset). Växter som sprider sig med frö – som våtarv och vitgröe – blir du av med lätt. Ryck upp dem innan de fröat av sig bara. Eller klipp av fröställningen: även om det är en flerårig växt, som lupiner, stoppar du dem på det sättet från att sprida sig vidare. Rotogräset struntar däremot helt i om du rafsar bort den ovanjordiska delen. De växterna vilar under vintern och kommer tillbaka starkare än nånsin på våren, och du måste därför plocka bort varenda eländig liten rotbit.
Rotogräset har dock en akilleshäl, eller kompensationspunkt som den kallas bland odlingsnördar (jag kände det som om jag anlänt i trädgårdsvärlden när jag en sen kväll i maj ledigt stod och diskuterade olika växters kompensationspunkter med två jämnåriga odlare på ett trädgårdsmingel). Kompensationspunkten är den brytpunkt när växten skickat maximalt av den näring som sparats i roten under vintern upp i bladen, men innan den hunnit göra tillräckligt mycket fotosyntes för att skapa en ny energireserv. Rycker du bort ogräset då kommer det att försvagas lite mer för varje år, även om du lämnar roten i jorden. Våren är den bästa tiden att rensa bort ogräsrötter på. Kompensationspunkten inträffar dock lite senare – läs på om just ditt rotogräs för att tajma den perfekt.
LÅT GRÄSET GÖRA JOBBET. Kirskål är min fiende. I april–maj gör det ständiga rensandet att jag ser de långa, blekfeta, sköra rötterna till och med när jag blundar. Trots att jag älskar antropomorfism lika mycket som alla andra är jag i grunden emot bambifiering – att ge naturen mänskliga egenskaper. Men jag är beredd att göra ett undantag för kirskål. Den VET. Den snirklar sig runt rötterna på värdefulla växter bara för att jag inte ska kunna rensa bort den utan att samtidigt skada _my precious._ Därför blev jag så glad när jag läste nånstans att kirskål går att trötta ut bara genom att klippa av bladen, kompensationspunkterad eller ej. Sen läste jag att det tar ungefär 300 klipp innan den tröttnat. Om kirskålen fick ett nytt blad varje dag, vilket den absolut inte får, och jag aldrig missade ett enda av dem, skulle det alltså krävas ungefär ett års oavbrutet växande och klippande för att bli av med den.
Många andra ogräs är dock inte lika ihärdiga. En av få växter, förutom kirskål, som klarar ständigt klippande är (trumvirvel!) gräs. Därför kan en gräsmatta vara en effektiv ogräsbekämpare.
#### Gör så här:
• Börja på hösten, för regnets skull.
• Gräv upp och omplacera värdefulla växter och sånt du vill spara.
• Rensa bort så mycket ogräs du kan/orkar från den utsatta plätten.
• Luckra och gödsla.
• Kratta jorden jämn.
• Så gräs, räfsa runt lite lätt och vattna. Om det är höst brukar naturen göra jobbet efter det.
• Till våren kommer ogräset att stå som en kvast i skyn och du kommer att misströsta. Men sen, i maj nån gång, när du bara kör rakt över ogräskaoset med gräsklipparen (åh, lyckan) kommer en vacker, slät, sprillans ny gräsmatta att visa sig därunder. Efter ett par somrars klippande börjar ogräset ge upp.
• Fortsätt då genom att skära loss grässvålen och dra bort den.
• Du kan antingen omplacera ditt fina gräs till nån annan plätt som du vill rensa från ogräs, eller så lägger du svålen uppochner i komposten för återanvändning som jord.
• Rensa bort eventuella maskrosrötter från din nya, tomma jordplätt.
• Odla som om inget hade hänt.
LÅT POTATISEN GÖRA JOBBET. Potatis är en riktig pionjärväxt. Den är så oöm att den kan etablera sig typ var som helst där det finns jord. Sättet som den växer på, med stora knölar som expanderar och spränger upp jorden, i kombination med kupandet (när du puttar upp ny jord mot de växande stjälkarna) och den yviga blasten, gör att ogräset får svårt att hänga med. Om du har ett grönsaksland som är extra infekterat, börja med att sätta potatis så slipper du lite av rensandet.
#### Gör så här:
• Sätt tidig potatis (se sidan 72).
• Kupa två gånger under odlandet.
• Skörda.
• Innan hösten kommer hinner du odla ännu en snabb gröda, rädisor eller sallat, i ditt nyrensade land.
• Upprepa följande vår.
• Egentligen får man inte odla samma sak i samma land flera år i rad men om du gör så här några år på raken, och sen byter gröda, brukar ogräset vara borta och jorden fin och lucker.
PROFFSENS METOD går ut på att du spänner genomskinlig, isolerande fiberduk över grönsakslandet på våren, redan innan sådden. Duken värmer jorden och ogräset kommer igång långt innan det är dags att så. Försprånget blir ogräsets fall, och du kan lätt rycka upp de första, övermodiga plantorna redan innan säsongen kommit igång. Sen sår du i ditt nyrensade land och då får grönsakerna istället fördelen av odlingsduken.
KUNSKAP FÖR DEN SOM TAPPAT GEISTEN. En bedrövande/trösterik sak är att all matjord fungerar som en enorm fröbank. Det finns oändliga mängder "sovande" fröer i varje kubikmeter jord. Varje gång du vänder jorden exponeras nya fröer som sätter igång och gror. Du KAN alltså inte rensa bort alla fröer ur jorden, och även om du rent teoretiskt skulle kunna det så fyller fåglar, sorkar och vinden på med nya hela tiden.
Däremot kan du låta bli att vända jorden. Det minskar dessutom läckaget av jordlagrade växthusgaser ut i luften. Hackor och ogräsöglor tar bort ogräset på ytan men väcker också många nya fröer. Om du istället bara lite slött rycker upp det ogräs som syns väcker du inte det frö som sover precis under. Med den här kunskapen blir det också vettigt att täckodla (se sidan 28).
MER BEDRÖVELSE/TRÖST. Potatis är alltså en pionjär. Men det är ogräset också. Ogräs är naturens förtrupp, de växter som etablerar sig först, för att skapa trevligare förutsättningar för andra, känsligare och roligare växter. Om du skulle lämna din odling vind för våg i några år skulle allt ogräs vara borta, antagligen ersatt av tjusiga ängsväxter som gråbo, rölleka och johannesört.
## (ANGÅENDE ÄGGSKALETS FÖRTRÄFFLIGHET)
När odlingsintresset väl vaknar kan det hända oväntade saker. Som den där gången på kyrkogården. Eller som när man står en gråmulen dag i mars och diskar äggskal. För sån är odlingens makt – du slutar plötsligen skygga för märkligheter.
När säsongen kommer igång får du betalt för mödan. Äggskal är nämligen fantastiska i odling. Dels är de rika på kalk, vilket är godis för kalkälskande växter. Dels verkar det som om sniglarna tvekar lite om man sprider äggkross längsmed såfårorna. Jag tror att de tycker att det rifsar på magen eller nåt.
Som odlingsrookie har man dessutom ett ständigt underskott på krukor. Och jord. Men mest krukor. Det var så jag först började experimentera med äggskal. Äggskalskrukor är långt ifrån perfekta, men de funkar i brist på annat.
#### Gör så här:
• Innan du kokar eller knäcker ägget pickar du det med en nål eller äggpickare (i början fattade jag inte att det var smartare att göra det här på förhand, utan sparade ihop ett tjugotal tomma skal som jag sen pickade hål på med min egen tumme som motstånd, en tumme som ganska snart närmade sig ett kallbrandsliknande stadium).
• När du använt ägget sköljer du ur skalet, då åldras det luktfritt. Samma sak gäller om du kastar skalen i en utomhuskompost, de drar inte till sig skadedjur om de är rena.
• Placera skalen i en form som gärna får ha ett genomskinligt tak. Jag använder de där plastbyttorna som affärerna envisas med att stoppa ekologisk frukt i. Om du köpt en bytta med smörgåskrasse är det plasttråget perfekt. Stöd skalen mot varandra så de inte vippar.
• Fyll äggen med jord, pilla ner fröet och toppa med vermikulit eller mer jord.
• Bäst funkar fröer till ganska stora, ensamväxande grönsaker, typ chili, majs eller pumpa.
• Spraya eller vattna försiktigt.
• Sätt på det genomskinliga locket. Lite jord = snabb avdunstning. Utan lock måste du spraya flera gånger varje dag.
• När växten grott och det är dags för omplantering klämmer du bara försiktigt till äggskalet i handen så att det spricker och stoppar sen ner alltihop i en ny, större kruka eller direkt i jorden.
ÄGGSKAL SOM GÖDSEL. Jag tycker det är snyggt med mycket krafs i landet och därför har jag inte nåt emot söndersmulat äggskal bland grönsakerna. Är du mer pedantiskt lagd kan du istället lägga skalen i vatten. Husmorsknepet är att låta skalvattnet stå i några dagar och sen vattna ut det kalkrika vattnet i trädgårdslandet. För att vara säker på att få ett berikat vatten, låt stå så länge som 1 månad.
### SOLROS [ _Helianthus annuus_ ]
Solrosen har setts som en avgudablomma eftersom den helt fräckt vänder ansiktet mot solen istället för att stirra blint mot Gud. Humlor och bin gillar blommorna, och de stora blomskivorna går att skörda när fröerna mognat fram, för att sen torkas inomhus. Lämnar du dem ute blir de vintermat åt fåglarna. Knopparna ska gå att äta på samma sätt som kronärtskockor, men det krävs _mycket_ viljestyrka för att klippa av dem precis innan blommorna slår ut.
#### Gör så här:
• Så på friland enligt grundreceptet (se sidan 64), eller inomhus några veckor före sista frosten.
• Planterar du väldigt höga solrosor, välj ett läge i norr, så att deras skugga faller bort från övriga land.
• Solrosor går också att odla enligt tre systrar-principen, tillsammans med en marktäckande slingerväxt och klättrande bönor som använder solrosens stjälk som stöd.
• Låt stå till hösten.
• När fröerna mognat skär du av hela den stora skivan och eftertorkar inomhus.
### Superkrafter
• Extremt snygg.
• Har så stark sugförmåga att den ibland används för att torka upp sanka områden.
• Solrosfröer innehåller ungefär 40 procent olja och är extra nyttiga för folk som älskar fisk (och därför inte äter upp de små liven).
### POTATIS [ _Solanum tuberosum_ ]
Rekommendationen är att sätta potatis när jordtemperaturen är minst 7 grader. Men min erfarenhet är att det går att sätta potatis nästan hur tidigt som helst. Som den där hösten när vi hittade fem kilo pinfärsk mandelpotatis medan vi tömde en vilande kompostbinge.
Potatisskörden det året hade varit eländig: brunrötan hade löpt amok och sorken hade snacksat upp resten. Vi kunde inte förstå var den här kompostpotatisen, som inte ens avslöjat sig med blast under sommaren, kommit ifrån. Till slut pinpointade vi sådden till en surströmmingsskiva några somrar tidigare, när vi köpt en påse mandelpotatis i affären och sen kastat de gröna knölarna i den då helt nya komposten. Sommar efter sommar hade de sen förökat sig, i flera våningar, ostörda i den rika kompostjorden medan vi täckt dem med lager på lager av nytt växtrens. Det här betyder alltså att potatis är så tuff att den går att så redan på hösten. Det betyder även att min kompost inte funkade, men skitsamma.
Om du ändå vill vara försiktig kan du förgro potatisarna inomhus några veckor innan du planterar ut dem.
#### Gör så här:
• Ta en stor form, grunda med tidningspapper, fyll på med några centimeter jord och tryck ner knölarna sida vid sida i jorden.
• Placera formen ljust och håll jorden fuktig. Försten med ett riktigt blad vinner.
• Sätt ut potatisarna högst sex veckor senare.
• Gör 15 cm djupa diken med 50–60 cm mellanrum och placera försiktigt ut knölarna med cirka 30 cm mellanrum. Bryt inte av nya blad eller rötter, då måste potatisen börja om från början. Stora potatisar som fått många ögon går att dela, se bara till att varje del har minst ett öga.
• Vill du skörda stora och tidiga potatisar? Nyp i så fall bort alla ögon utom tre. Låter du alla ögon vara får du istället en skörd bestående av många potatisar, men senare på året: ju fler tillväxtställen, desto fler färdiga potatisar.
• Fyll igen dina diken med jord – oroa dig inte för att bladen hamnar i underjorden, de gillar det.
• Dra fiberduk över odlingen och låt duken sitta tills frostrisken är över.
• När blasten är ett par decimeter hög kupar du potatisen – putta upp jord mot stjälkarna så att de täcks till hälften. Om du orkar upprepar du samma sak några veckor senare. Kupandet skyddar potatisen från solljus som kan få knölarna att utveckla giftet solanin (fun fact: det är inte det gröna som är giftigt, det är bara resultatet av helt vanlig fotosyntes, men färgen skvallrar om att knölen utsatts för ljus, vilket i sin tur kan leda till giftig potatis).
• När potatisen blommat kan du tjuvkika i jorden genom att rota runt med handen och känna om där finns nåt att skörda.
• Om det gör det lyfter du försiktigt hela beståndet med en grep.
• För potatis med längre hållbarhet låter du plantorna växa vidare. Klipp ner blasten på hösten, lämna cirka 5 cm, och låt sen potatisen ligga kvar i marken några veckor till. Då tjocknar skalet och potatisen kan lagras längre.
• Skörda på varma dagar, långt efter det senaste regnet. Låt potatisen ligga i solen ett par timmar innan du tar in den. Det allra bästa stället för förvaring är en jordkällare, då klarar sig skörden hela vintern. Näst bäst är alla platser som liknar en jordkällare. Om ingen sån plats finns får du nöja dig med nåt mörkt, svalt hörn.
DEN BÄSTA KNÖLEN. Att skaffa sig en favoritpotatissort och sen med en dåres envishet hävda att den är bättre än alla andra är lite som odlandets version av att lära sig spotta långt på skolgården. Få det överstökat bara.
Konsensus just nu är att 'Amandine' är bäst, så jag föredrar 'Rocket' och 'Asterix', men även skotska 'Saxon'. De är alla utsökt smöriga och nästan självsaltande, men inte så förbannat paranta som 'Amandine', 'Cherie' och de andra fransyskorna.
SUPERSNABB POTATISSKÖRD. Om du känner dig äventyrlig finns det ett avancerat sätt att skaffa extra tidig potatis på. Det här funkar dessutom om du till exempel har en gräsplätt du inte orkar gräva upp, eller nåt annat totalt igenvuxet ställe som du vill börja odla på. Antingen kan du täckodla potatisen direkt på marken. Lägg ut knölarna och täck dem mycket tjockt med ditt favoritmaterial (se sidan 28). Eller använd den här mer högteknologiska metoden som jag lärde mig i en av den engelska trädgårdsmästaren Rosemary Vereys böcker. På det här sättet kan du börja odla väldigt tidigt på våren, särskilt om du lägger ut den svarta plasten i förväg, så att marken tinar och värms upp före plantering.
#### Gör så här:
• Gräv igenom jorden med en grep och fyll på med kompostmull. Om du vill. Eller strunta i det.
• Vattna så att landet är fuktigt utan att vara dyngsurt.
• Fäst tjock, svart, ogenomskinlig plast eller mörk marktäckväv över jordplätten.
• Skär kryss i plasten, 10 cm breda, med 30 cm mellanrum.
• Stoppa ner en förgrodd potatis precis vid jordytan under varje kryss. Välj en sort som blir klar tidigt – det är meckigt att vattna med plasten på plats så en snabb tillväxt är viktig.
• Fyll på med mull eller kompostjord så att krysset och potatisen är helt täckta och inget ljus riskerar att nå knölen.
• Fäst fiberduk över alltihop.
• Höj fiberduken allteftersom blasten växer eller, om risken för frost är över, ta bort den.
• Om det behövs, fyll på med mer täckmaterial omkring blasten allteftersom den växer. Om du skördar mycket rabarber är rabarberblad i lager på lager utmärkta att täcka med.
• När potatisen är redo att skörda behöver du bara lyfta på plasten och rafsa åt dig det du behöver, och sen täcka igen.
### GRÄSLÖK [ _Allium schoenoprasum_ ]
Trots allt tjat om frö köper jag ofta perenner som färdiga plantor. Visst, det kan vara en sport att stratifiera, pyssla och dutta, passa och vattna, för att inom ett till två år ha en liten förskrämd lavendelplanta som sen tar ytterligare fyra år på sig innan du får nåt som ens liknar en skörd. Men samtidigt finns det folk som har allt det här som jobb. Att odla egna perenner från frö är som att stjäla brödet ur deras munnar (det är i alla fall så jag rationaliserar bort denna inkonsekvens).
Gräslök är just en sån perenn som är värd att köpa färdig. Den är aslätt att dela och föröka på det sättet, men det är stor skillnad på smak mellan olika plantor så om du tar en bit av nån annan, gör ett smaktest först. Stråna ska vara saftiga och ha en kraftfull men inte skarp löksmak.
I övrigt är gräslöken kravlös. När jag var liten hade vi en speciell gräslökssten mitt i gräsmattan (i efterhand har jag förstått att hela mattan förmodligen varit en köksträdgård med ett hav av gräslök och att stenen varit enda platsen som min pappa inte kunde köra över med gräsklipparen). På den solvarma stenen, i några centimeter djup jord, tillsammans med kvickrot och lavar, dök gräslöken upp tidigt, tidigt varje vår.
När löken går i blom blir stjälkarna träiga, men då är blommorna desto godare. Minst dubbelt så lökiga men med en lätt touch av nektar. Gräslöken har dessutom lökens medicinska egenskaper, bara i lite mildare form.
### STRANDKÅL [ _Crambe maritima_ ]
Strandkål är ännu en perenn hjälte. Den har blågröna, vackra blad och blir till en stor kålbuske. Enda kruxet är att strandkålsfrön vägrar gro. I alla fall hemma hos mig. Men på egen hand frösår sig växten vilt. Tänk dig lyckan när en granne med kålöverskott bjöd in mig att ogräsrensa självsådda småplantor ur hans kålland. Om du inte har en granne som kan avvara en hel planta räcker det med en rotbit. Begrav den i jorden åt rätt håll (den tjockaste delen uppåt) och vattna. Låt bli att gräva upp vilda plantor eller rötter, de kan vara fridlysta.
Efter att du satt din planta eller rotbit låter du den växa till sig i några år. Sen driver du den på samma sätt som rabarber (se sidan 40).
Driven strandkål skördas redan i mars–april. Om du enbart bleker kålen, utan att lägga till den obrunna gödseln, är de späda skotten klara att plocka nån månad senare. Efter blekning och skörd måste plantan vila och hålla på med växters favoritgrej, fotosyntes. Under tiden går dock blommorna att äta, på samma sätt som broccoli.
Kålen växer vild längs stränder och passar därför bra nära sparris. Dels ser de snygga ut ihop, dels vill de ha ungefär samma förhållanden: luftig, sandig, mullig jord och gärna ett täcke av tång.
ÄR DIN KÅL STEKT? Alla jordar är olika, och vår har bestämt sig för att vi inte är värda att äta kål. Jag vet inte om det är jordloppornas, kålflugornas eller sniglarnas fel, eller om det kanske är en sorts skuldcocktail. Däremot vet jag att färskt gräsklipp – eller vilket grönt rens som helst – runt plantorna hjälper. Det gröna håller jorden fuktig, släpper ifrån sig näring som stärker växterna och det verkar dessutom förvirra skadedjuren tillräckligt mycket för att plantan ska hinna växa till sig. Numera spar jag alltid en extra stor rugge av den tråkiga oreganon (den där namnlösa sorten som inte alls smakar oregano när den torkas) i ett hörn av lotten så att jag alltid har nåt att klippa ner och täcka kålen med.
### TAGETES [Olika sorter]
Tagetes, denna tråkiga, tråkiga blomma, är ytterligare en av trädgårdens hemliga superhjältar. Dels motar den skadliga nematoder i dörren, och den passar därför bra vid potatis och tomater som kan råka ut för dessa fula rundmaskar. Dels finns det tecken på att den motarbetar ogräs som kirskål, kvickrot och rotvinda. Det har med rötter och utsöndring och en extremt cool grej som kallas biologisk kemi att göra. Rejält med tagetes runt odlingen kan alltså minska ogräsinvasionen och hålla skadedjur borta.
Tagetes älskas av sniglar, så du kan även använda den på samma sätt som mc-gäng använder målvakter: för att ta smällen när ryktet sprids om vad du egentligen håller på med.
Den mest kraftfulla tagetessorten, där forskningen pekar på allt det här, är mexikansk tagetes ( _Tagetes minuta_ ). Men även andra sorter, som snygg 'Linnétagetes' ( _Tagetes patula_ ) till exempel, verkar ha liknande, bara lite svagare egenskaper. Tagetes går att så på friland, enligt grundreceptet (se sidan 64), men du får längre blomning om du startar den inomhus, tidigt på våren.
### SALLAT [ _Lactuca sativa_ med flera]
Sallat, som alltså är grönsaken medan sallad är maträtten (en grönsakshatande vän till mig föredrar till exempel sin sallad helt utan sallat), är hemmaodlingens vattendelare. När du väl ätit din egen kan du inte gå tillbaka. Du har stirrat ner i sallatsavgrunden, och sallaten har stirrat tillbaka. Det gröna bruset i matbutikens hyllor kommer inte längre att registreras. För medan köpesallatens geggiga blad har två smaker – besk eller urvattnat besk – kommer din sallat att smaka allt. Rucola så pepprig att ögonen tåras, nötig mâche som smakar solsken och smör, krispig romansallat och bitter endive som ger hår på bröstet kalla höstdagar.
Romansorterna (som även kallas cos eller gem) behöver inte mer än 5 grader i jorden vid sådd och mâche går att så hur tidigt som helst. Så i omgångar enligt grundreceptet (se sidan 64), då har du blad i olika stadier hela sommaren.
Den allra godaste trädgårdslunchen är den när du inser att det räcker att ta ett varv runt odlingen och rafsa åt dig några nävar blad – alla med olika smak och struktur, lägga till lite grillad potatis eller zucchini och avsluta med det enda som inte kommer från din egen hand och jord: olja och salt. "Rik" kommer inte ens i närheten av att beskriva känslan.
Under högsommaren kan värmen göra att fröna ogärna gror. Lägg dem i så fall i kylen över dan och så när kvällen svalnar, i skuggigt, fuktigt läge.
### SPARRIS [ _Asparagus officinalis_ ]
Att börja odla sparris är lite som att ställa sig i bostadskön (eller varför inte i kolonilottskön). Du gör det inte för att du är sugen på sparris, utan för att du inte kan utesluta möjligheten att du om fem, sex år kommer att bli sugen på sparris. Den tar för evigt att bli skördeklar. Köp några plantor nu med en gång, så har du framtiden säkrad.
Sparris är lätt att odla från frö men tar då ännu längre tid på sig. De nakna rotkronorna, som alltså säljs utan jord, är roliga och ser läskigt alienaktiga ut men behöver planteras på ett speciellt sätt (ovanpå underjordiska åsar så att deras tentakler riktas utåt, neråt). Plantor i kruka, med jord, är lättast.
#### Gör så här:
• När du köper sparris, försök välja ut hanplantor. Inte alla plantskolor vet skillnaden, men honplantor får små röda frön på hösten – frön som är lite giftiga och som sprider sparrisen över hela odlingen. Hanplantor struntar i att göra frön och ger istället fler stjälkar.
• Var noga när du väljer ut och förbereder växtplatsen: sparris är ännu en perenn, och ju djupare, fluffigare och bättre jorden är när du planterar den, desto bättre kommer dina årtionden av skörd att bli. Ogräs kan bli ett problem så undvik delar av trädgården där det finns kirskål, åkerfräken och andra grejer med rötter djupare än helvetet. Sparris trivs extra bra i upphöjda bäddar.
• Placera plantorna med 30 cm mellanrum och låt dem växa till sig under några år. När de ser pigga och starka ut och producerar rejält med stjälkar kan du börja skörda ett par stycken. Efter ytterligare ett par år kan du ta några fler. Skörda från att de första stjälkarna visar sig och sex veckor framåt. Efter det behöver växten vila.
• Sparris – med eller utan bär – blir också en extremt snygg häck. Placera den nånstans där dina kompisar kan gå förbi och häpna över hur konstigt din grönsak beter sig på hösten.
• Hemodlad sparris, skördad och sen direkt serverad, är så god att den går att äta rå – smakar som äpple ungefär. Den går att blanchera och frysa, men jag föredrar att leva i avhållsamhet för att sen delikatessfrossa i en månad.
### NÄSSLOR [ _Urtica dioica_ ]
Folk tycker att man gör sig till när man tjatar om nässlor, men jag kan inte hjälpa det: jag älskar dem. Jag älskar smaken och jag älskar de medicinska egenskaperna. Jag älskar ritualen som det är att plocka dem, daggiga och sprängfyllda med vitaminer till soppan, eller i stekande sol för att hänga upp och torka i stora ruggar inför vintern. Nässlor renar blodet, stärker själen och gör att håret växer snabbare. Det är en av världens mest klorofyllrika växter och om du hittar nässlor i skogen är det ett tecken på att nån bott där: växten älskar den feta jord som människors rester och avfall skapar. Plocka dem på våren, då är de som mest potenta, eller på hösten, när nya, späda nässlor dyker upp under de gamla, träiga. När de går i blom är det för sent att plocka mer, då kan du istället vänta in fröna som går att grodda eller äta färska. Men undvik vägrenens nässlor, de kan innehålla farligheter och tungmetaller.
Jag brukar förvälla och frysa in en omgång, men inte mer. Bladen från torkade plantor smulas ner i burkar eller bruna papperspåsar och används till teer och hårskölj hela vintern.
### Superkrafter
• Förutom allt ovan har nässlor även använts som smärtstillande medel, mot till exempel ledvärk och reumatism, i en massa olika kulturer. Precis som med medicinen amylnitrit, poppers, brukar det få mig att fundera över hur överjävlig sjukdomen måste vara, om det är så botemedlet känns. Om du inte heller tycker att nässelbränna fungerar smärtstillande kan du testa att krossa ett groblad mellan fingrarna och stryka mot stället där du bränt dig – det mildrar svedan.
### DJUNGELGURKA [ _Melothria scabra_ ]
Gurka är en sån där sak som svenskar odlar mot bättre vetande. Djungelgurka däremot, eller musmelon som de kallar den i England, vilket gör att man fattar både storlek och utseende, ger stor skörd för liten ansträngning. Eftersom gurkan är nästan rund och vitgrönt zebrarandig ser den spexig ut inlagd i glasburkar.
#### Gör så här:
• Så några fröer inomhus på våren. Du behöver inte särskilt många plantor och de blir lättare att hålla reda på om du förodlar dem.
• Placera småplantorna vid en spaljé, ett hönsnät eller liknande – de slingrar sig vilt – i varmt, skyddat läge.
• Håll jorden fuktig och skydda mot sniglar tills plantorna kommit igång.
• Skörda genom att nypa bort minigurkorna allteftersom. Fröna blir mycket större än i en vanlig gurka, så ju längre gurkfrukten får växa, desto mer framträdande blir fröna.
• Gurkorna fortsätter att mogna fram i överflöd, som små gröna julgranskulor, till långt in på hösten.
• Ät frukterna färska, lätt wokade eller inlagda surt eller sött beroende på smak.
• Har du en jordkällare, eller ett utrymme med samma ljus och temperatur som en jordkällare, kan du vinterförvara plantans rötter. Klipp ner plantan och gräv upp rötterna före sista frosten. Förvara dem svalt och mörkt, täckta med sand eller torv. Plantera ut igen efter sista frosten på våren så får din planta en flygande start.
### RINGBLOMMA [ _Calendula officinalis_ ]
Ringblomma och johannesört är de två medicinalväxter som jag inte klarar mig utan. Och som jag dessutom medicinerar vänner med när de inte beter sig som de ska. Utanpå kroppen, i en blomsterolja (se sidan 171), fungerar ringblomman vårdande för inflammerad hud. Inuti kroppen, drucken som te (se sidan 169) mildrar den pms och livmoderbesvär, rätar ut tarmar och mjukar upp magknip.
#### Gör så här:
• Så ringblomma i överflöd, enligt grundreceptet (se sidan 64), gärna på en solig plats för att få blommor med riktigt mycket aktiva substanser. De är extra snygga som en häck runt grönsakslandet.
• Skörda genom att nypa av blommorna i torrt, varmt väder, mitt på dan. En del använder bara själva kronbladen, men jag får bra resultat av hela blomman, korg och allt.
• Torka på en torkolla (en ställning för örttorkning) eller utspridda på skrynkligt tidningspapper.
• När blommorna är helt torra förvarar du dem i burkar eller mörka papperspåsar.
### Superkrafter
• Antiseptisk och antiinflammatorisk.
• Innehåller salicylsyra.
• I hudkräm, använd under en längre period, kan ringblomma hjälpa mot akne.
• Ringblommete hjälper mot kramp i livmodern. Samma te, avkylt, kan användas utvärtes för att svalka solbränd hud.
• Färska kronblad, mosade mot huden, lugnar bett och stick.
### SQUASH OCH PUMPA [ _Cucurbita pepo, C moschata, C argyrosperma, C maxima_ ]
De flesta som odlar squash slutar köpa squash. Efter att plantorna matat ut så mycket frukt att det känns som att vara med i en squashätartävling under sommaren är det ett hån att under vintern krävas på betalning för dem. Hemma hos oss ersätter sommarsquashen allt från gurkan på mackan till köttet i chilin, osten på grillen och pumpan i soppan.
Pumpa, i sin tur, mognar senare men det hårda skalet gör att den kan sparas hela vintern. De två växterna vill ha ungefär samma odlingsförhållanden.
#### Gör så här:
• Förbered växtplatsen väl: jorden ska vara djupgrävd, mullig och välgödslad. Har du en vilande kompostbinge, boostad med guldvatten (se sidan 89), är det ett perfekt squashland.
• Så två fröer, enligt grundreceptet (se sidan 64), i varje planteringshål och nyp sen bort den svagaste plantan. Använd pettricket (se sidan 30).
• Placera fröerna i en grop eller använd kruktricket (se sidan 99) för att göra vattnandet enklare.
• Squash- och pumpaplantor tar mycket plats. Använd dem som marktäckare, bind upp dem mot en spaljé eller låt dem ringla över en pergola och ge skugga till dig därunder. Det är dessutom extra roligt att skörda pumpor som hänger ner från himlen.
• Vattna hela sommaren och guldvattna då och då.
• Squash har både hon- och hanblommor. Honorna ger frukt men hanarna går också att äta. Doppa de råa blommorna i frityrsmet och fritera dem, eller fyll dem med en blandning av äggstanning, ricotta och chili och baka dem i ugnen. För den som älskar just blommorna finns sorter som producerar enbart hanar.
• Skörda squashen beroende på smak – från babygrönsak till mastodont. Ju oftare du skördar, desto mer frukt får du.
• Pumpor med tjockt skal lämnas på plantan hela sommaren.
När pumpan vuxit klart och plantan börjar vissna kapar du hela stjälken, med pumpa och allt, och lämnar i höstsolen för att eftermogna.
• Ta in före första frosten. Knipsa av den intorkade stjälken och förvara torrt och luftigt.
• I det här tillståndet går pumpan att spara på köksbänken hela vintern, medan squash som skördas färsk blir dålig snabbare. Men om du får panik, sådär mitt i sommaren när squashen hotar att ta över ditt liv, går det att lämna den färska squashen på stjälken, precis som med pumpan, för att mogna vidare. Då höjs också hållbarheten på samma sätt. Smaken försämras en del men du kommer att ha färsk squash kvar ända tills symtomen på att du förätit dig börjar lägga sig.
Strax efter att min kompis Marie fått barn frågade hon mig hur säkert det egentligen är att plocka vilda växter och äta sina egna, stadsodlade grönsaker. Hur är det egentligen med vägar och markföroreningar? Och man vet ju faktiskt inte var de vilda växterna varit.
Jag tyckte att jag gav ett väldigt balanserat och informativt svar. Hon tyckte att hon fick en utskällning. Det var ju såklart inte meningen, men varför är vi så säkra på att allt som ligger inslaget i plast i affären är rent, medan allt som vuxit ute i öppen jord är smutsigt? Skillnaden är att du inte vet var köpegrönsakerna vuxit och att du, möjligtvis, kan stämma nån om du får salmonella. För det är ju inget som säger att köpebladen inte vuxit en spottloska från en flygplats, under ett stilla regn av jetbränsle och rabiesmättat vildhunddrägel. Och även om det inte är så extremt: du har ingen aning om var konstbevattningen kommit ifrån, vilka gifter just den bonden måste använda för att hålla liv i sin monokultur eller vilken antibiotika som korna som (i bästa fall) gödslat odlingen ätit. Alla de här sakerna blir lite mer överskådliga när grönsaken vuxit upp i ditt närområde. Dessutom finns det nåt så genomlogiskt i att faktiskt använda kroppen och göra av med (samt få) energi samtidigt som middagen eller efterrätten samlas in i en gammal papperskasse. Att komma hem, jordig och utpumpad och med rivsår i ansiktet, har aldrig känts så bra som när belöningen är egenplockad nässel- eller jordärtskockssoppa, och ingen hemmaodlad soppa har nånsin smakat så bra som när den äts med arbetsblåsiga händer.
SÄKER SAMLARE I STAD OCH SKOG. Om du håller dig till de här rekommendationerna ska det vara helt lugnt att skörda vilda samt stadsodlade grödor och låna fritt av naturens överflöd.
1. Plocka bara saker du är helt säker på att du identifierat korrekt. Flera av grejerna vi äter har släktingar som är dödligt giftiga. En av mina favoritfamiljer är till exempel _Solanaceae,_ som innehåller både potatis och belladonna. Inte för att nån nånsin blandat ihop just de två, men du fattar: i naturen existerar verkligen den onda tvillingen.
2. Odla och plocka grödor med ett säkerhetsavstånd på 25 meter till närmaste hårt trafikerade gata. Om du odlar på balkongen i ett höghus kan du även räkna med höjdmeter. Skölj alltid grönsakerna, annars kan du få med dig tungmetaller och grejer (en bra verklighetskoll är dock att titta ut genom fönstret när du tar en roadtrip genom södra Sverige, chansen är stor att du är omgiven av växande mat på båda sidor av vägen).
3. Om du odlar i jord som inte är gammal kulturmark utan kanske använts till nåt annat stadsrelaterat (bebyggelse, industri eller parkering till exempel), odla för säkerhets skull i upphöjda bäddar. Förorenad matjord är oftast inte förstörd för evigt, det finns icke-ätliga hjältegrödor som kan ta hand om miljögifter, men det är en ganska avancerad process som kräver att du först gör ett jordtest och analyserar om nåt, och i så fall vad, behöver rensas bort.
FLÄDER är en sån där härlig sak som naturen bjuder på. Alla delar av fläderträdet är användbara och att begränsa sig till blommorna gör försommaren stressig. Hur många gånger har jag hetsat fram och tillbaka längs cykelstigar i söderförort bara för att inse att alla blommor inom tanthöjd sen länge rensats från träden och bara några insektsbitna, höga exemplar finns kvar? Lyckan var total när jag, efter att ha krupit genom ett hål i ett trasigt staket, upptäckte ett övergivet äventyrsbad översållat med orörd fläder. I ruset plockade jag och mannen en hel Icakasse full av fläderbär, bara för att inse att plockandet är semestern medan rensandet är det riktiga jobbet. Sen dess har jag lärt mig att det går att rispa av bären med en gaffel (frys först klasarna om bären är för mosiga). Samma metod ska funka på blommorna, men många blomsterrecept har faktiskt inget emot stjälkarna.
Fläderblommor blir inte bara god saft och blomsterchampagne (se sidan 168, och byt ut älggräset mot fläder), ett te på blommorna är också en klassisk förkylningskur. Invärtes hjälper blommorna mot hosta, utvärtes mot fet eller stressad hud. Frys eller torka skörden så har du resten av året.
Omogna bär kan läggas in som kapris (se sidan 161) och de mogna bären används mot hosta och förkylning, i sylt eller te.
Både rötter och bark har traditionellt använts mot allt från epilepsi till ödem. Såpvatten blandat med ett te gjort på fläderträdets blad fungerar mot insekter och svampangrepp på andra växter.
Fläderns enda problem (förutom att den har dödsgiftiga släktingar) är att trädet kan bli en riktig mastodont. Om du har en liten odlingsyta men tillgång till nån form av allmän mark, föreslå ett gemensamt flädersnår. Då får du också en bra referens och risken för farliga misstag när du skördar fläder i det vilda minskar.
## (GÖDSEL)
När vi i grupp promenerade runt på vår första lottvisning var det en sak som var väldigt förvirrande.
Det här var i mars–april nån gång, och varje gång vi kom fram till en lott som såg ut som en leråker började gruppledaren ooha och aaha och säga saker som: "Oj oj, en av våra äldsta kolonister, 90 i år, orkar inte längre." Man ba: "Nä, jag ser det..." Och sen la hon alltid till: "Men vilken fantastisk lott han lämnar efter sig!"
Då trodde jag hela tiden att det var falsk marknadsföring, ett sätt att lämpa över ett omöjligt uppdrag på okunniga nykomlingar.
Numera är jag också intresserad av jordförbättring – att få en maxad skörd genom att lägga till näring, gödsel och mull i matjorden.
Gödslar gör du framförallt tidigt på våren, när du förbereder grönsakslanden för sådden genom att gräva ner och fylla på med organiskt material som ko- eller hästgödsel. Kompost är ofta näringsfattigt men förbättrar istället strukturen på jorden.
När de sådda grödorna väl kommer igång och börjar suga i sig av näringen behöver även den mest välförberedda jorden gödselvattnas. Har du helt glömt att gödsla kan en mager jord faktiskt fungera minst lika bra som fullt grundgödslad jord så länge du gödselvattnar klokt och sparsamt, lite vid varje bevattningstillfälle. Om du inte tror mig, testa odling i grus och gräs, där du planterar grönsakerna direkt i grus täckt av färskt gräsklipp. Så länge gräset är grönt släpper det ifrån sig lite plantmat ner i gruset varje gång du vattnar, och grödorna frodas trots att de står med rötterna i helt näringsfri låtsasjord.
Det finns flera olika sorters gödselvatten, men de flesta odlare blir efter nåt år enorma fans av metod nummer fyra, framförallt tack vare den mycket fria tillgången på grundråvaran.
1. Vallörtsnäring. Packa en dunk eller gammal plasthink med färska blad av uppländsk vallört. Borra hål i bottnen på kärlet och ställ eller häng det över en behållare. Efter några dagar börjar din vallörtsnäring sippra ut. Konceptet är detsamma som när din hushållskompost läcker lakvatten, och de två vätskorna går att använda på samma sätt: som krukväxtnäring fast i större dimensioner. Häll nån liter i din stora vattenkanna och fyll upp med färskt vatten (de exakta delarna är 1 till 10). Väl grundgödslad jord behöver bara gödselvattnas nån gång då och då. Mager jord gödslas med en svag blandning varje gång du vattnar. Allra bäst tas näringen upp om jorden redan är fuktig – efter regn eller vanlig bevattning. Obs! Vallört kan bli ett klängigt och aggressivt ogräs så välj odlingsplats väl och se till att hen inte kan rymma.
2. Nässelvatten. Det finns olika avancerade sätt att göra nässelvatten på, men det mest grundläggande är att låta sönderklippta nässlor dra i en hink med vatten tills de soppat till sig rejält. Det brukar ta nån vecka. Rör om varje dag. När nässlorna fallit sönder – mycket eller lite beroende på ditt tålamod – silar du sörjan och späder den 50/50 med vatten i vattenkannan. Det går åt ungefär 1,5 liter outspätt nässelvatten per kvadratmeter och vecka, och det fungerar lika bra att använda torkade nässlor. Skörda stora ruggar under våren och häng på tork mot en solig vägg. Varning för denna metod dock: ganska snabbt brukar hinken börja bubbla som en häxkittel. Vid några tillfällen har vår lott luktat så mycket gödsel att vi smugit in bakvägen av skam.
Det går även att förbättra jordstrukturen genom att gräva ner färska nässlor nån decimeter i jorden. Gör det tidigt på våren, längsmed raderna där du tänker plantera ut förodlade grejer, så hinner maskarna börja tugga i sig bladen och bajsa ut den fina nässelnäringen i jorden.
3. Hönsgödsel. Mät upp en näve ungefär, lös upp i vatten, sila och späd sen till en teliknande färg, ungefär 1 till 10.
4. Guldvatten. Om du vet vad en golden shower är så kan du räkna ut hur man tillverkar guldvatten. Så länge du och övriga familjemedlemmar inte är sjuka eller äter medicin är det här växternas favoritregn. Urin är dock ett starkt gödselmedel. En av min farfars favoritföreteelser var att snacka skit om skogsturisterna som tältade på hans mark och kissade ihjäl en ny gran varje år eftersom de gick till samma ställe varje morgon. När man gödselvattnar späs därför urinen med vatten för att det ska bli lättare att dosera ut en lagom liten skvätt till extra hungriga växter. Späd i 1 till 10 och vattna på samma sätt som med övriga gödselvatten. Det går dock alldeles utmärkt att även använda outspädd urin, enda skillnaden är att doseringen blir svårare eftersom det krävs så lite. Därför passar den bra till grundgödslingen – den där första, rejäla givan på våren, innan växterna hunnit ut. En outspädd liter per kvadratmeter är rekommendationen.
Komposten, som inte nödvändigtvis innehåller så mycket näring, blir också mer potent av guldvatten. Placera komposten lite i skymundan så kommer den, under ljusa, susiga juninätter när en förrädiskt rosig natthimmel gör att ingen fattar att det är dags att gå hem, få så att den klarar sig resten av året.
5. Kol. I Amazonområdet i Sydamerika har man hittat flera meter djup, mycket bördig och nästan svart matjord fylld av kol. Kol är näringsfattigt och bäst blir resultatet om du laddar det innan du använder det. Låt kolet ligga och dra i näringslösningen som du får innan du blandar till ditt vallörts-, nässel- eller guldvatten och vänd sen ner det i jorden.
## (FYLL HUNGERLUCKAN)
Jag hatar att gallra mina grönsaksland. Avskyr det. Därför föredrar jag att så ett eller två frön per slutgiltig växtplats, plonka ner en avsågad petflaska över paret och sen lägga armarna i kors i väntan på hösten.
Men gallrandet har faktiskt fördelar. Bland annat ger det en första försmak av kommande klorofyll under den där hungriga månaden i början av sommaren, då allt är i jorden men inget hunnit bli skördeklart. När du för tredje gången sprätt jord i ditt eget öga och händerna är fulla av greprelaterade blåsor kan en macka med extrasaltat smör och den allra första grönsaksskörden, bestående av utgallrade ärtskott, göra underverk för moralen.
#### Gör så här:
• Bredså över hela landet. Det betyder att du struntar i raderna och istället slösar med frö i kvadrat.
• När de första pytteplantorna kommer upp gallrar du lite lätt, men lämnar ändå en majoritet av växterna.
• Det här första steget sker redan några veckor efter sådd, och de utrensade mikrogrönsakerna passar bra i sallader eller på mackan, sköljda, hela och råa (tänk smörgåskrasse, fast med andra smaker).
• Efter ytterligare sex till åtta veckor gallrar du en andra gång och lämnar precis så mycket grödor som det ska vara i slutändan. Gillar du raka rader skapar du dem nu, genom hård gallring, annars låter du landet vara fyllt i kvadrat.
• Babygrönsakerna som du rycker upp vid den här gallringen använder du råa i sallader eller snabbt och försiktigt uppvärmda. Lite beroende på vad du odlar funkar både blast och rot.
_Ätlig blast och rot_ : morötter, rödbetor, rädisor, koriander, persiljerot. _Enbart blad:_ krasse, spenat, sallat, senap, mangold, grönkål, kålrabbi, fänkål, pak choi, ärter och bönor (du vet, som i ärtskott).
### DILL [ _Anethum graveolens_ ]
Dill är en kinkig växt, men den är snygg och mäktig och att kunna lägga in egna höstgrönsaker med eget dillfrö motiverar odlandet. Jag tycker den är ovärd att slösa en egen rad på i grönsakslandet, precis som med okynnes-OSA:re kan du aldrig vara riktigt säker på om den dyker upp eller ej. Men strösslad lite här och där, i rabatter och bland bärbuskar (men inte mellan morötterna), kan den komma som en rolig överraskning på skördefesten. En enda rejäl dillkrona ger allt frö du behöver. Får du flera kronor, lämna en eller ett par till självföryngring.
När fröna börjat mogna och ändra färg klipper du av kronorna och buntar ihop ett par stycken som du fäster med huvudet neråt i en papperspåse. Häng upp papperspåsen nånstans med bra ventilation och lämna i några veckor. När du skakar påsen borde fröna lossna av sig själva och falla ner på bottnen. Dillfrön passar bra i hårt och mjukt bröd och till oliver. Om du inte orkar vänta på torrt frö går de att använda färska också, i potatissallader och soppor till exempel.
#### Superkrafter
• Fröerna, krossade och bryggda till te, hjälper mot matsmältningsbesvär, kolik och gas. Viktorianerna var så kära i just den sista egenskapen att de skrev dillhyllande sånger.
• Vill du dra ner på saltet i kosten är dillfrö perfekt: fröerna är så rika på mineraler och salter att de funkar som substitut.
• Tuggade, några stycken efter maten, kan de hjälpa mot dålig andedräkt.
• Stärker naglar och hår.
### KORIANDER [ _Coriandrum sativum_ ]
Jag är ett levande bevis för att det går att sluta hata koriander. Jag vet att det finns många persiljeälskare där ute som börjat tycka illa om koriander bara för de två växternas förvillande likhet (åh, besvikelsen när man tror att man tar en stor, krispig tugga slätbladig persilja och möts av parfymerad koriander!). Jag känner er smärta. Men försök igen. Med öppet sinne. Till asiatiska rätter. För dig som behöver medicinsk motivation har jag ett ord: alfakaroten. I många år trodde folk att betakaroten var det magiska ämnet som gjorde morötter nyttiga. Nu lutar det istället åt att just alfakaroten är grejen. Det här illustrerar också problemet med syntetiska kosttillskott kontra riktiga grönsaker: vi är sällan helt och hållet säkra på exakt vad, eller vilka ämnen i kombination med varandra, som faktiskt gör en viss grönsak nyttig.
Enligt en amerikansk undersökning sänker man risken att dö i förtid med 39 procent om man äter grönsaker som innehåller alfakaroten. Enligt den här helt och hållet seriösa undersökningen är det inte bara risken att dö i förtid av sjukdomar utan risken att dö, lite i största allmänhet, som sjunker. Alltså, du cyklar inte omkull lika ofta, blir inte påkörd lika ofta, stoppar inte fingrarna i vägguttaget lika ofta om du äter morötter. En av få alfakarotenrika grönsaker, förutom just morot och pumpa, är koriander. Linné sa också att korianderblad fördriver vägglöss och "är goda för okyskhet". Det känns som om det blir nån sorts dubbelnegation där i slutet, lite oklart om koriander gör en mer eller mindre okysk, men jag tycker ändå det låter bra. Dessutom går alla delar av växten att äta: bladen, stjälkarna (hacka dem fint – de är krispigare och friskare än bladen), roten, blommorna och fröna.
#### Gör så här:
• Så koriander, enligt grundreceptet (se sidan 64), i fjolårsgödslad jord eller i djupa krukor.
• Skörda ett fåtal blad så fort de dyker upp, öka sen skörden allteftersom.
• När växten blommar kan du skörda blommorna och använda i sallader, men låt ett gäng plantor blomma ostört, från början till slut.
• Glöm helt bort en eller ett par av de plantorna. Låt dem blomma över, gå i frö och självså sig utan att du lägger dig i, så har du sådden fixad inför nästa år.
• Två andra plantor passar du som en hök.
• När de blommat över och fröet torkat – det byter färg och blir mer väldoftande – klipper du av stjälken och hänger frökronan uppochner på ett torrt, varmt, dammfritt ställe i ungefär 10 dagar.
• Pilla loss fröna och förvara dem hela, i en gammal kryddburk eller papperspåse.
• När du ska använda fröna optimerar du smaken genom att rosta dem lite snabbt i torr panna innan du mal dem i en kvarn eller mortel. De har en fascinerande smak: tuttifrutti med citroninslag, typ.
• Använd i frijoles (mexikansk svartbönröra) eller indiska rätter.
#### Superkrafter
• Ät korianderfrö före måltider för att förbättra matsmältningen.
### JOHANNESÖRT [ _Hypericum perforatum_ ]
Det lättaste sättet att fatta hur en växt vill ha det är att tänka på hur den växer vilt: johannesört är den där gula, halvhöga, ostyriga blomman som växer i solstekta vägrenar. Den sprider sig snabbt och en enda köpt planta fyller ett land på några år.
Om du plockar den vild vet du att du fått tag på rätt växt om du får fläckar på fingrarna när du nyper av blommorna. Det är samma färg som Ulf Lundell får på sitt brännvin efter att han låtit blommorna dra i vodka några veckor.
Örten slår ut lagom till midsommarblotet – med blommor gula som sommarsolståndet och olja röd som blod – och fortsätter sen blomma långt in på hösten. De skördade blommorna, färska eller torkade, är starkt lugnande. De hjälper mot sömnlöshet, oro och ångest, och gör tråkiga filmer lite, lite bättre. De är också lätt beroendeframkallande och kan slå ut effekten av p-piller, så visa respekt.
Blommorna har liknande effekt om de används utvärtes: lugnande, läkande och sammandragande. En blomsterolja (se sidan 171) gjord på johannesört hjälper mot torr hy, inflammationer och solsveda.
### BÖNOR & ÄRTER [Familjen _Fabaceae_ ]
Tumregeln, som en äldre dam gav mig, är att så eller sätta ut bönorna först när det är så varmt att du kan tänka dig att gå ut i morgonrock på morgonen. Är det för kallt i jorden ruttnar de bara. Ärter kan däremot sås redan när jorden är 8–10 grader.
Bönor och ärter är bra grödor eftersom flera av dem kan ätas i många olika stadier: som späd balja, som färsk böna eller torkad och sparad till långt in på vintern. Så go crazy: odla buskbönor med haricots verts-baljor i gult eller grönt, störbönor med svarta skidor, italienska vaxvarianter med stora, spräckliga bönor eller engelska rosenbönor som kan klä in en hel husvägg på nolltid och blommar lika vackert som vilken prydnadsväxt som helst. Samtliga går att så enligt grundreceptet (se sidan 64) en och en och passar därför utmärkt till att petodla (se sidan 30).
Både ärter och bönor kan binda kväve i jorden, vilket fungerar som gödsel för andra växter, och de passar extra bra att odla ihop med squash eller pumpa (vars stora blad skuggar jorden åt de törstiga bönorna) och majs eller höga solrosor (som blir till klätterstöd). Vill du torka bönorna låter du dem sitta kvar på busken till hösten, annars skördar du allteftersom. Ju mer du skördar, desto fler skidor dyker upp.
### SENAP [ _Brassica juncea, B nigra_ ]
Senap, sån du köper på burk, är gjord på senapsfrö. Senapsfrö kommer från senapsplantan, en rucolaliknande, ogräsaktig växt som är väldigt god i sallad. Senapsplantan finns i sin tur i tre olika varianter, med svarta, gula eller vita frön. De svarta är de starkaste – dijonsenap görs av svarta, skalade frön.
Så senap enligt grundreceptet (se sidan 64) och skörda blad genom hela säsongen, utan att slakta hela plantan. Ät bladen råa eller tillaga dem försiktigt, på samma sätt som du skulle behandla babyspenat. Låt sen växten gå i blom och sätta frö. Skörda fröbaljorna när de börjat mogna, eftertorka dem inomhus på en torkolla och pilla ut fröerna ur skidorna när de är helt torra. Använd i inläggningar eller gör din egen senap: det enda som krävs är en skvätt vatten och en gammal kanonkula (se sidan 160).
### LIN [ _Linum usitatissimum_ ]
I Hälsingland är både bergen och fälten blånande på hösten. Men linet som växer på åkrarna istället för säd är inte bara bra till tyg, det är dessutom en tjusig och nyttig växt. Hela frön är bra för matsmältningen, de bryts inte ner utan utvecklar en sorts slajmigt hölje (vilket jag förskräckt upptäckte av misstag, när jag experimentgroddade) som gör att de passerar genom kroppen hela. Malda, i filen på morgonen, ger de ett tillskott av nyttiga fetter. Ät inte mer än 1–2 matskedar om dan och mal inte fröerna förrän du äter dem: nyttigheterna är känsliga för både ljus och syre.
Fyll en hel rabatt med linfrö, inte i rader utan på bredden, täck tunt med jord och håll fuktigt tills det grott. Några månader senare har du ditt eget blåskimrande linfält och sen gulnande frökapslar som går att skörda och eftertorka, hängande uppochner på en torr dammfri plats inomhus.
Högsommaren är framförallt en blomsterfest. Grönsaksfröerna är i jorden, solstolen är insutten och varenda fertil växt i hela trädgården slår på stort för att locka till sig så många pollinerande flygfän som möjligt. Från början tyckte jag att blommor var töntiga. Men när de ändå stod där och skräpade, mitt i sommaren till ingen nytta, började jag skörda dem. Och ganska snart upptäckte jag att de har en massa medicinska egenskaper. När solen står som högst är många av dem också mycket potenta. Under juli brukar man därför se mig, som en grinch som stjäl sommaren, kutryggigt rensa rabatterna på nyutslagna lavendelblommor, skyar av älggräs och små tajta rosenknoppar. Blommorna blir till teer, salvor och snapsar som både smakar pollen och botar snuva.
Högsommaren är också den tid på året när du, till slut, kan ta några första självförsörjande steg på din odling. Fixa lunch genom att promenera genom grönsakslandet med utsträckta armar. Äta sockerärter istället för godis. Leva på potatis (kokt med smör, friterad, kanarisk), och bota fotsvampen med ringblommor.
ATT UTAN FÖRVARNING PLÖTSLIGEN BLI VITA SACKVILLE-WEST. Halvvägs igenom sommaren händer nåt annat också. Kroppen, den som under våren kändes på gränsen till bruten under grepens tyngd, är stärkt och sinnet lätt. Träningsvärken har försvunnit och den rödheta nacken har mörknat. Allt i naturen verkar berusat och berusande. På dagarna doftar älggräset så starkt och sött att de blankgröna skalbaggarna som klamrar sig fast vid de nyplockade flockarna ser kalejdoskopiska ut och det kan inte bara vara salicylsyran i bladen som gör att du känner dig avdomnad. På kvällarna verkar växterna så besjälade att du skulle ha varit mörkrädd om det nånsin blev mörkt och till och med nattljuset är varmt. Det var under en sån yr natt som jag kände mig så nykär att jag blev tvungen att skriva en dikt till trädgården. Naturen–jag, 100–0.
Gör inte för mycket nu. Vattna smart. Så det lilla som trivs i torkan. Fyll på vätskereserverna med fläderchampagne. Var fulländad: det är lätt när potatisen svullnar i jorden och humlorna raglar omkring i blomsterkorgarna med fejorna fulla av pollen som fulla engelsmän på Ibizasemester.
## (BEVATTNING)
I början när jag odlade tänkte jag att jag matade blommorna när jag vattnade dem. Men det stämmer inte. Blommor äter inte vatten, de äter solljus. Vattnet är mer som en sorts blodomlopp/skelett. Det fraktar runt näring i plantan och fungerar samtidigt som luften i en sån där uppblåsbar fladderfigur som ibland finns på fotbollsmatcher. Rötterna suger i sig vatten ur jorden snabbare än vad de små hålen i växtens blad hinner släppa ut det. Det skapar ett tryck som gör att plantan kan hålla sig upprätt. Det är därför blommor slokar när de är törstiga. Det är inte för att de är hungriga utan för att de saknar ryggrad.
Mitt under högsommaren, när värmen ritar vingliga streck genom luften, händer det att avdunstningen ur bladhålen går snabbare än vad rötterna hinner suga upp nytt vatten. Då hjälper det inte hur mycket du än vattnar – växten kommer att sloka även i ett dyblött land. Men de allra flesta grönsaker gillar sol och värme, och så fort kvällssvalkan kommer återhämtar de sig. Då, eller på morgonen om du har problem med sniglar, är bästa tiden att vattna.
BEVATTNINGSREKOMMENDATIONEN brukar ligga kring 30 liter per kvadratmeter och vecka, det motsvarar 30 mm regn. Men innan du okynnesvattnar, kolla hur det står till i jorden genom att sticka ner fingrarna några centimeter under det allra översta jordlagret.
Det är bättre att vattna sällan och mycket än ofta och lite. Växande grödor blir stressade av torka, men en fuktig jordyta sänker växtens motivation att borra rötterna djupt ner i jorden. Där nere är det nästan alltid lite fuktigt. Med snål skvättbevattning blir rotsystemet istället grunt och därför ännu känsligare än om du inte vattnat alls. Undersökningar visar också att växter som försiktigt vänjs av inte behöver alls lika mycket vatten som grödor som skämts bort med ständig väta.
Om du vattnar för hand, istället för att fuska med vattenspridare eller droppslang, kommer du på ett nästan zenaktigt vis att inse fördelarna med täckodling (se sidan 28).
KRUKTRICKET. När du planterar lite större växter, som pumpor eller kronärtskockor, kan du samtidigt gräva ner en kruka precis intill växten. Grunda med grus under krukan och låt krukans överkant vara parallell med jordytan, eller nån centimeter lägre i en mjukt sluttande grop. Sen vattnar du bara rakt ner i krukan. Du behöver inte ens använda stril, så som man brukar göra för att jorden inte ska spolas bort av strålen. Krukan kommer att leda vattnet direkt till plantans rötter och du slipper de där tjuriga rännilarna som kilar bort i landet till ingen nytta. Samma sak går att göra i större skala – med en rejälare kruka – vid nyplanterade bärbuskar eller större perenner.
Nyplanterade fruktträd kräver mycket vatten för att rota sig på sin nya plats. Snabba på bevattningen genom att gräva ner en tät ring av korrugerad plast eller nåt annat som är böjbart och vattentätt runt trädets rötter. Det räcker om ringen sitter några centimeter ner i jorden, sticker upp nån halvmeter ur jorden och är nån halvmeter i diameter. Röret kan snabbt fyllas med hinkvis med vatten som sen i sakta mak rinner rakt ner till trädets rötter. När trädet rotat sig tar du bort ringen.
## (BESKÄRA TRÄD)
Första gången jag var med på beskärningskurs frågade kursledaren (en fantastisk gammal arborist som fyllt sin trädgård med stenhårt spaljerade träd och kallar sin kiwi för Kivikfrukt, som en sorts exotiskt äpple) om han fick använda vårt 'Victoria'-plommon som träningsobjekt. Han var helt lyrisk över trädet. "Det var ju fantastiskt att vi kunde hitta ett träd i det här skicket! Verklig tur!" sa han och jag kände mig väldigt smickrad.
Fruktträd växer sällan på sin egen rot. Träden har istället en grundstam – nåt sorts närbesläktat fulträd – som det ädla, framavlade trädet ympats in på. Under kursen förstod jag för första gången vad den spännande, taggiga busken runt vårt plommonträd var. Den där yviga kvasten som jag och mannen försökt artbestämma genom att jämföra med olika exotiska växter vi hittat i andra trädgårdar. Det var rotskott. Oäkta rotskott. Vi hade vårdat och vattnat oäkta rotskott en hel sommar, medan de söta damerna på området promenerat förbi och nickat och lett överseende. Arboristen var så till sig i trasorna eftersom det är ovanligt att nån faktiskt vet _så_ lite om trädvård. För en gångs skull hade han hittat ett avskräckande skolexempel.
Det finns många olika skolor i hur man beskär fruktträd (en favorit är till exempel Brommaklippningen, där det ser ut som äppelträdets krona plötsligen nått upp till ett osynligt glastak och sen bara fortsatt växa utåt som ett platt paraply). Men den enklaste grundregeln är att spara de kvistar som är riktade åt det håll som du vill att trädet ska växa åt. Vill du ha ett lågt, vidsträckt träd sparar du grenar som går neråt och utåt. Vill du höja kronan och få mer plats under trädet lämnar du kvar grenarna som går uppåt, utåt. Alla grenar som går in mot kronan ska bort så det blir luftigt och fint därinne. Och om du har två grenar som tävlar om att vara mittenstammen, så att de tillsammans bildar ett V mot himlen, tar du bort den ena.
På drift mot Idaho.
JAS – juli, augusti, september – är en bra klipptid, men det finns undantag så dubbelkolla alltid vad just ditt fruktträd föredrar.
Det är bäst att forma trädet när det är litet, gärna med hjälp av en trädkunnig arborist, och sen hålla efter det. Inte, som vi gjorde under den där kursen, slakta en stackars förvuxen 25-åring. Efter en rejäl klippning dyker nämligen vattenskotten upp som en extra utmaning. Vattenskott är de där unga kvistarna som liksom sprutar rakt ut från stam och grenar och inte ser ut att vara det minsta intresserade av att göra frukt. Tar du bort alla vattenskott på en gång kommer lika många till. Nyp istället bort alla som växer på helt fel ställe, korta in några andra och låt ytterligare ett gäng sitta kvar orörda. Nästa år gör du samma sak igen. På det sättet kan du förhoppningsvis klippa lite försiktigare varje år.
ATT JOBBA UNDER STRESS är negativt för i stort sett alla utom just fruktträd. Om du har ett fruktträd som bara skjuter en massa nya, färska grenar och inte verkar ha en tanke på att producera frukt kan du stressa fram fruktsättningen genom att böja ner grenarna. Bind fast tyngder längst ut i de mjukaste kvistarna, eller spänn ner dem med snören mot marken (snörena kan även funka som stöd för bönor eller klätterväxter, som i sin tur liknar lianer när de växer upp i trädkronan). Nedåtböjningen gör att trädet byter fokus, från tillväxt till produktion av frukt. Dessutom får du ett träd som ser coolt och skrotigt ut, som nån sorts övergiven totem från den amerikanska södern.
## (BURKSAMLARE)
Under högsommaren tornar skörden upp sig vid horisonten och om du inte redan gjort det är det dags att börja spara på gamla glasburkar. I början kan du spara på vad som helst, även om du med åren kommer att bli mer kräsen. Bara spara på burkar med extra fina lock till exempel, kanske såna med en rolig teckning föreställande en polsk pelikan som äter pickels. Redan i affären kommer du att välja burkar med tjusig form eller seriefigurstryck (i Frankrike säljer man bland annat dijonsenap med hjälp av smurfar), eller prioritera märken med etiketter som är extra lätta att diska bort. Du kommer att hamstra italienska sardellburkar eftersom så små burkar är ovanliga och det är irriterande att fylla kryddhyllan med stora burkar innehållande enbart en bottenskyla kryddiga frön. Men till att börja med går det alltså bra att spara varenda glasburk som passerar hemmet.
Förbered glasburkarna genom att diska dem noga. Etiketter brukar lossna efter några timmar i ljummet vatten. När du gör pickels och sura inläggningar passar de bäst i burkar med lock som är gjorda för att tåla syra. Det sista du gör innan du fyller burkarna med årets skörd är att sterilisera dem. Koka snabbt locken och låt burkarna stå fulla med kokhett vatten i 10–15 minuter. Töm ur vattnet och fyll på med inkokta körsbär, picklad pepparrot och koreansk surkål.
## (FATTIGMANSSPENAT)
Det var min enormt glamorösa vän Behnaz som, under en semestervecka på Öland, skakade uppgivet på huvudet åt mig när jag kastade rödbetsblast. Hon samlade ihop de slitna bladen ur komposthinken och efter 15 minuter i iskallt vatten var de som nya. Sen snodde Behnaz ihop en enkel men fantastisk sallad som hennes persiska mamma lärt henne. Nuförtiden tycker ingen i den lokala öländska ladubutiken att det är konstigt att jag varje sommar dyker upp och krafsar runt på det stampade jordgolvet efter blasten de precis skurit bort från nån annans betor.
Och ändå blev jag lika glatt chockad när min redaktörsvän Anna berättade att samma sak gäller morötter, och så ännu en gång när jag läste att det finns rädisor som odlas enbart för blasten. Du hajar poängen. Många ätliga rötter har ätlig blast. Späda, sparsamt plockade innan roten är skördeklar, går bladen att äta råa. Har den vuxit till sig klarar vissa rotfrukters blast att behandlas mer som fullvuxen spenat, blancherad lite snabbt i buljongvatten, sen fräst i smör och vitlök till exempel. Slå i några matskedar av det buljongiga kokvattnet när du fräser bladen så får du en såsigare konsistens.
Och håll i dig, för nu blir det spinn: på samma sätt som många rotfrukter har ätlig blast har många blastväxter – som persilja och koriander – ätlig rot. Men visst, det är som min experimenttrötte man säger ett litet men viktigt smakglapp mellan "ej direkt giftigt" och "svingott". Därför har också många grönsaker förädlats med särskilt fokus på antingen den ovanjordiska eller underjordiska växtdelen. Som persiljerot och bladpersilja till exempel. Dessa två är dock extremt goda grannar i maten. Gör persiljerotpuré på samma sätt som du gör potatismos och avsluta med massor av färsk eller fryst bladpersilja för en dubbelt smakrik persiljeröra.
Stängde jag verkligen av plattan?
### PAK CHOI [ _Brassica rapa var chinensis_ ]
Pak choi är den ödmjuka lilla asiatiska kålväxten som många dystopiskt lagda odlare hoppas ska säkra mattillgången i världens städer ifall infrastrukturen skulle falla samman över en natt. Jag har skördat den, lika hurtigt grön som alltid, med ett tjockt lager frost på bladen så sent som i november. Om jag sår den tidigt på våren, utomhus i krukor medan snön fortfarande ligger, ger den en första skörd redan i juni. Det innebär en imponerande skördeperiod på hela fem månader.
Pak choi är ettårig och ibland går den i blom snabbt – då blir bladen små och tråkiga. Men om du fortsätter så enligt grundreceptet (se sidan 64) hela sommaren blir tillgången konstant. Har du kålflugor som tuggar hål på bladen hjälper det att lägga färskt gräsklipp runt plantorna. I övrigt är växten oöm. Jag odlar sorten 'Prize Choi', som var den enda icke-hybrid jag hittade när jag först köpte mitt frö. Hybrider är hårt avlade plantor som ofta är sterila, som mulor, medan min choi är härligt lösaktig och sprider sig över hela odlingen, till och med till gräsmattan.
### PERSILJA [ _Petroselinum crispum_ ]
För mig – och för många av mina bleka, blodfattiga systrar – kan persilja bli lite av en besatthet. Jag har svårt att komma på en enda maträtt som inte förbättras av persilja. Och kanske är det lite som när hundar instinktivt vet att de ska äta gräs när de fått i sig nåt skräp: persilja är inte bara rik på järn, örten hjälper också till när kroppen ska ta upp järn ur annan föda.
Det går bra att så persilja mitt i sommaren, bara du ser till att hålla jorden fuktig och fortsätter vattna ordentligt tills plantorna tagit sig. Örten är tvåårig och även om du inte hinner få en urstor skörd samma år kommer den tillbaka extra tidigt följande vår. Däremot tar persilja tid på sig att gro och processen går snabbare om du blötlägger fröerna i varmt vatten. Så enligt grundreceptet (se sidan 64), gärna i en remsa runt hela grönsakslandet: persilja kan ha en avskräckande effekt på skadedjur och om inte annat får du en tjusig liten persiljehäck.
Andra året blommar plantan. Fåglarna gillar fröerna men det brukar bli tillräckligt många över för att den ska föröka sig av sig själv. När de nya plantorna börjar titta upp här och där i grönsakslandet är det bara att gräva upp dem och flytta dem dit du vill.
Fransmännen torkar persilja, på samma sätt som oregano, men jag tycker bättre om den hackad och fryst, eller bevarad i olja eller vinäger (se sidan 160). När frosten kommer går det också att klippa ner en planta, gräva upp roten, plantera om den i en djup kruka och flytta in den på fönsterbrädan för vinterskörd.
### SUPERKRAFTER
• Hela plantan är ätlig: blad, stjälkar, rötter och frön.
• Rik på C- och A-vitamin och järn.
• Frön och rötter har använts framförallt till att rena njurar och urinvägar.
Garlic & shots.
Det finns teorier som pekar på att kunskapen om hur jobbigt det faktiskt är att odla påverkar hur gärna eller ogärna vi slänger grönsaker. Det finns inga bevis men dock en stark känsla av att odlare tar tillvara sina grönsaker bättre än ickeodlare. Så ju mindre mat och grönsaker som produceras i det egna landet, desto svårare blir det för oss som äter maten att förstå hur krävande det varit och hur mycket mark det krävts för att odla maten. Eller så här: det verkar som om matslöseriet ökar exponentiellt med avståndet till ursprungslandet. Siffrorna skiljer sig lite åt, men i Sverige slängs ungefär 30 procent av all mat som köps. Potatis är till exempel en av de grönsaker som slängs mest. Potatis är också en av de mest besprutade grönsaker vi har – gamle, trötte 'King Edward' drabbas av så mycket krämpor att han måste medicineras som en skröplig farbror. En knöl sväljer dessutom sex hinkar vatten under sin livstid.
Problemet med slängd mat är dubbelt: dels kräver grönsaksodling en massa energi (och vatten), dels bygger det på sopberget.
Hemmaodling löser båda problemen.
En enkel kompost tar bort all framtida mat från sopberget. Över en natt är det problemet löst. Och, här kommer en impopulär åsikt, 30 procent är egentligen inte jättemycket. 30 procent kan vi radera genom att äta 10 procent mindre (ingen av oss skulle må dåligt) och odla 20 procent mer. 20 procent av din årliga potatiskonsumtion är 10 kilo potatis. Det odlar du lätt under en sommar, oavsett hur liten din trädgård är.
Så här i skördetider är det också helt uppenbart varför folk förr i tiden gick till marknaden för att köpa framförallt tre saker: olja, socker och salt. Allt annat kan du just nu hämta från naturens ymnighetshorn.
## (FLÄTA VITLÖK)
Är du inne på ditt andra år som odlare har du nu ett lyxigt överflöd av vitlök att ta hand om. Vitlöksflätandet (eller, som jag är säker på att de kallar det i Frankrike, "datorteket") är en extremt tidskrävande och fullkomligt onödig aktivitet. Ändå står jag där varje höst, borstar lök och svettas, tjatar mig igenom en monoton "Mitten, höger, vänster. Mitten, höger, vänster"-ramsa och svär över mitt eget skrytiga behov att förvandla mina grönsaker till superstjärnor. För herregud så snyggt det blir.
#### Gör så här:
• Vitlöken är klar när blasten slutat växa och börjat gulna.
• Gräv upp lökarna, försiktigt, en torr dag.
• Häng lökarna på en väl ventilerad plats, under tak, för att torka några dagar.
• När det yttersta, smutsiga skalet är torrt är det hyfsat lätt att få bort genom att bara försiktigt krama och gnugga löken med händerna.
• Trimma rötterna med en sax till nån centimeters längd och borsta bort den sista jorden från rottrådarna med en torr rotborste.
• Odlar du nån av de tjusigt lila, franska sorterna borde dina lökar nu vara vackert vit- och lilaspräckliga, med ett tajt, torrt, glansigt ytterhölje.
• Har blasten hunnit bli snustorr är den svårare att fläta. Mjuka upp den genom att låta den dra mellan två fuktiga handdukar i nån halvtimme.
• Om du redan vet hur man gör en vanlig inbakad fläta kan du också fläta vitlök: vänd den inbakade flätan uppochner i huvudet och fläta sen vitlöken på samma sätt.
• Har du haft oturen att aldrig lära dig göra inbakade flätor när du var liten: sök på internet efter videoinstruktioner och förbered dig på en lång kväll.
### PEPPARROT [ _Armoracia rusticana_ ]
Pepparrot är alltså en väldigt aggressiv växt. Den är flerårig och härdig och får den växa ostört sprider den sig som en gräsbrand. Så den här beskrivningen är framförallt för dig som redan har ogräset i din trädgård. Men just för att pepparroten är så invasiv finns den förmodligen redan i din närhet. Lär dig känna igen bladen – stora, djupt mörkgröna och lite rynkiga med en grov nerv – så kommer du se dem överallt. På våren går de unga bladen att äta som pepprig sallat eller snabbt uppvärmda. På hösten skördas de feta rötterna som är så starkt antibiotiska att de till och med kan skydda tarmen från de parasiter som ibland överlever i försiktigt uppvärmd eller rå fisk.
För att få fram en rejäl rot, inte bara en lurvig rottuss som är omöjlig att skrubba eller riva, krävs lite pyssel. Jag har märkt att mina försök att utrota pepparroten (som jag själv förde in på vår lott) i själva verket är ett väldigt effektivt sätt att få fram bra pepparrötter på. Ena året gräver jag så djupt det går för att få bort växten, nästa år tror jag att jag lyckats och året därpå växer en perfekt, tjock, skördeklar pålrot i den djupgrävda, luftiga jorden. Men det finns även ett mindre destruktivt sätt att odla pepparrot på. För extra snabb fuskodling, hitta ett förvildat bestånd och hoppa direkt till punkt fem.
#### Gör så här:
• På våren gräver du upp en 30 cm lång pepparrot, tjock som ett finger ungefär.
• Rensa roten från smårötter och liknande, allt utom den översta, grövsta biten ska vara slät (det är där uppe bladen sen ska komma).
• Skapa en upphöjd bädd. Gräv också ner en rotbarriär runt bädden så att det blir svårare för plantan att rymma.
• Plantera rotbiten i 45 graders vinkel, med den översta, grova toppen några centimeter under jorden.
• I slutet av högsommaren, juli–augusti ungefär, ska roten snyggas till. När det är fuktigt i jorden, gärna efter ett duggregn, gräver du fram den översta halvan av roten och putsar den med en vass kniv. Låt den understa biten sitta kvar i jorden och lämna bladen orörda. Fyll sen på med jord igen.
• Till hösten skördar du all rot.
• Förvara pepparrot på samma sätt som potatis.
• När våren kommer börjar du om från början.
#### Superkrafter
• Pepparrot stärker immunförsvaret (hej pepparrotssnaps på vintern!).
• Den fungerar konserverande och motverkar mögel och passar alltså extra bra i inläggningar.
### MANGOLD [ _Beta vulgaris_ ]
Mangold är tvåårig och klarar temperaturer ner till minus 14 men plantan är såklart extra tacksam om den får ett täcke av fluffig halm under vintern.
Växten går att skörda gång på gång: från de allra första, späda bladen som äts råa, fram tills frosten sätter stopp för den på hösten. Och sen igen, tidigt följande vår innan plantan går i blom. Mangold går att så enligt grundreceptet (se sidan 64) hela året, men allra bäst växer den i temperaturer kring 16–18 grader.
På sensommaren blir stjälkarna grövre. Då kan de skäras loss från bladen, kokas 5–10 minuter, hackas upp i munsbitar, slungas i smör och sen går det väldigt bra att låtsas att de är vårprimörer. Bladen förvälls eller steks.
### GRÖNKÅL [ _Brassica oleracea_ ]
Jag ska inte ljuga: kål är svårt. Allt som nånsin flugit, krälat, krupit eller hoppat in i en trädgård äter kål. Men belöningen, i smak, i mineraler och i längd på skördesäsongen, är massiv.
Hos oss är en av de största kålbovarna små djur som äter hål på bladen. När plantorna är små är det så illa att inget mer än taniga nerver, helt rensade på bladmassa, står som antenner i kålgården. Färskt grönt gräsklipp runt småplantorna förvirrar just de djuren, pettricket (se sidan 30) skyddar mot snigelattacker. Platta, runda kragar av takpapp kan också hjälpa och på hösten är väl förankrad fiberduk eller hönsnät mot harar och rådjur ett måste.
Grönkål trivs bra i land där du precis skördat nåt annat: växten gillar inte nygödslad jord och är dessutom helt ok med att marken packats en del, och därför ger lite stöd, till skillnad från de flesta andra grönsaker som kräver superfluffig jord. Däremot måste du flytta kålgården vid varje sådd, annars kan du dra på dig svåra och obotliga kålsjukdomar.
Kålen är tvåårig, den blommar andra året och om du vinterförvarat den, eller om den överlevt på egen hand, kan du skörda blomknopporna och använda dem som minibroccoli.
Allra godast blir kålen efter första frosten och den är en av få grönsaker som går att skörda rakt igenom den svenska vintern. Om du nån gång kring vintersolståndet äter kål förvälld i skinkspad och sen kokad i grädde som reducerats till en sås upprätthåller du en tradition som hållit liv i många svenskar före dig.
### LAVENDEL [ _Lavandula angustifolia_ ]
Sen jag fattade att det går att skörda blommor får jag kli i fingrarna när jag går förbi ambitiösa trädgårdar där nån prydnadsodlar häckar av lavendel runt sina grönsaksland. Jag har också lavendelhäckar, men varje sommar slåss jag med fjärilarna om vem av oss som ska roffa åt sig flest blommor. Jag klipper blomsterstjälkarna vid stammen, buntar ihop dem tio och tio med ett hårt knutet jutesnöre och hänger dem på tork några veckor innan jag rispar ner blommorna i burkar. Till vintern används blommorna i olja för att lugna lidande hud och i te för att lätta tunga sinnen.
Att så lavendel från frö är pilligt: gör det på vintern, då hjälper naturen till med stratifieringen (se sidan 17). Det lättaste är att plantera en liten köpebuske när de första höstregnen börjar falla, då etablerar den sig bra. Precis som de flesta örter vill lavendel ha djup, luftig och gärna sandblandad jord. Den blir extra potent i ett läge där den riktigt steks av solen.
När busken väl etablerat sig är den lätt att föröka. Ta sticklingar när du beskär den eller, ännu lättare, föröka den på samma sätt som svarta vinbär (se sidan 43). Böj ner en av de yttersta grenarna under jorden och lägg en sten ovanpå. Låt toppen på grenen sticka upp ur jorden. Nästa vår har den underjordiska delen rotat sig. Klipp navelsträngen till moderplantan, gräv upp den nya plantan och placera den en bit bort så att den får gott om plats att buska till sig. Fortsätt på samma sätt i några år så har din enda buske blivit till en hel häck.
Minns du hur det var i våras? Ett totalt jävla kaos av fröer och småplantor i köket och gödsel hit och dit och för tidiga starter och för sena järnnätter. På hösten känns allt annorlunda – det är egentligen en mycket lugnare tid att så. Men kanske märker du också skillnad för att ditt hjärta slår långsammare, ditt immunförsvar är starkare, din hjärna yngre och halten av stresshormoner i ditt blod har sjunkit under sommaren. Grönska gör sånt med en.
## (VÄLKOMMEN TILL SKÖRDEFESTEN)
Under den tidiga hösten möts sensommarens överflöd av nåt mer bitterljuvt. Skördemånen, den fullmåne som inträffar närmast höstdagjämningen, är så stor och låg att det reflekterade solljuset hjälper de sista grönsakerna att mogna fram, trots de allt kortare dagarna. Det är squash överallt, plommon och äpplen rasar från träden och det börjar märkas hur mycket du faktiskt kommer få betalt för vårens och sommarens ansträngningar.
Skörda försiktigt. Allt från äpplen till potatis ska helst behandlas som ägg, då håller de sig längre. Ät skadad frukt med en gång och förvara resten svalt och mörkt. Låna en bok om jordkällare och fundera på om du vill bygga en stuka (en jordkällare i miniatyr) innan tjälen kommer. Låt halloweenpumpor och squash mogna på sina stjälkar tills skalen är hårda och blanka, och klipp bort överflödiga och skuggande blad för att få ut maximal effekt av de sista solstrålarna.
Ofta består överflödet i en enda grej åt gången, så passa på att byta till dig en mer varierad kost från andra odlare. Squash mot honung, äpplen mot körsbär, potatis mot chili. Inget gör odlare så glada som att få dela med sig av sitt överskott till nån som uppskattar hemmaodlade grönsaker lika mycket som de själva.
SKÖRDA GRÖNSAKSFRÖ och bli din egen Darwin. Välj ut de plantor som verkar trivas och frodas allra bäst hos dig och låt dem gå i blom. Samla in de mogna fröerna, torka, rensa, förvara i kylen och så dem nästa år. Gör sen samma sak igen, följande höst. På det sättet kan du med lite tur och mycket tålamod förädla fram plantor som är som gjorda för just din jord och ditt klimat.
## (ATT SÅ PÅ HÖSTEN)
Hösten är inte endast skördens tid, återfödsel och sådd är nästan lika närvarande. Alla grönsaker går inte att så på hösten, men några grejer trivs alldeles utmärkt när temperaturen sjunker och regnet åter faller.
TIDIG HÖST sår du:
• Salladslök, vintersallat och spenat. De är så tåliga att de fortsätter växa rakt in i kylan.
• Pak choi, mizuna och annan tålig asiatisk kål fungerar på samma sätt.
• Rädisor är så snabba att de hinner bli skördeklara före vintern.
• Persilja både hinner med att ge en liten skörd under hösten och klarar att övervintra till nästa år.
SEN HÖST sätter du:
• Jordärtskockor som skördas följande år.
• Vallmo sås riktigt sent och kan till och med strösslas ovanpå ett tunt snötäcke.
• Dill och koriander, morot, rödbeta och palsternacka har alla fröer som klarar vintern och gror extra tidigt på våren om de kommit i jorden redan på hösten.
• Vitlök är en klassisk höstgrönsak. Vi återkommer till det lite senare.
## (PLANTERA BÄRBUSKAR)
Bärbuskar är till och med mer tacksamma än perenna grönsaker och örter. Välj sort noga – det är stor skillnad på smaken mellan olika namnsorter, även inom en och samma bärfamilj. Du kommer att skörda från samma buske i årtionden så det är bortkastat att impulsköpa en namnlös bärplanta på Ica bara för att komma igång snabbt.
Förbered växtplatsen väl. Gräv ett spadtag djupt och luckra ännu ett med en grep, så att plantan har gott om plats för sina rötter. Blanda upp jorden med kompost, grus eller småsten och lite höstgödsel. Men låt bli kväverikt gödsel – det är alldeles strax läggdags för växterna och kväve fungerar som sockervadd för en treåring.
Ta bort allt flerårigt ogräs från odlingsplatsen: när kirskålen väl slingrat sig runt rötterna på din nya svartvinbärsbuske får du aldrig bort den. Om du känner dig extra lat kan du sätta en liten barriär runt planteringsgropen så att ogräsrötterna får det svårare att ta sig in även i framtiden.
Sätt busken på en svag upphöjning om du har en fuktig trädgård och i en grop om du har det torrt. Platta till jorden med hälen. När du planterar busken ska det vara riktigt dyngsurt och geggigt i gropen, men efter det kan du använda kruktricket (se sidan 99) för att göra bevattningen mer effektiv. Vill du spaljera busken som en solfjäder eller stamma upp den så att den ser ut som ett litet träd kan du göra det nu.
PÅLITLIGA SVENNEBUSKAR är svarta vinbär (goda både färska och i sylt), röda vinbär (för geléns skull), krusbär (till att moffas fritt under sommaren) och hallon (med stenhårt kontrollerade rötter, så de inte rymmer och invaderar resten av odlingen).
LITE MER ÄVENTYRLIGA BUSKAR är björnbär (för anglofilen), blåbär (välj hybriden half-high, de är inte riktigt lika goda som de vilda, svenska men inte heller fullt lika menlösa som de amerikanska), vindruvor (för att köpedruvor är råbesprutade) och hassel (för att kunna äta egna nötter till jul).
KNASBUSKARNA är kiwi (i alla fall i södra Sverige), mispel (för att frukterna, som ser ut som små hundrumpor, måste ruttna innan de går att äta) och rosenkvitten. Det finns två sorters kvitten, och rosenkvitten blommar i knallrött på våren. Frukterna går inte att äta råa men luktar som liljor och opium om du tar in dem i värmen på hösten. De är även så rika på pektin att de fungerar som vegetariskt gelatin i sylt som vägrar stelna.
## (OCH SÅ SNIGLARNA)
Jag började odla med en sorts live and let live-, här finns plats för oss alla-inställning. Så länge man odlar tillräckligt mycket av en gröda, tyckte jag, gör det ju inget om den naggas lite i kanten. Vi är alla här på samma villkor. Och det heter faktiskt "spansk skogssnigel".
Jag var en blåögd hippie.
Året då mördarsniglarna slaktade allt från pumpor till chili och kronärtskockor (som jag hade pysslat med sen i mars, skitsniglar!) ändrades min inställning till nåt mer i linje med Bushadministrationens. "Döda varenda jävel" helt enkelt.
Sniglar vaknar på våren (från och med att vitsipporna blommar ungefär) och håller igång så länge temperaturen inte sjunker under 5 grader. På hösten lägger de ägg som ser ut som vit fiskrom. De är aktiva, precis som alla som trampat barfota på en i mörkret vet, på natten. Och om du har dem i din odling är det bara att lämna karman vid dörren: att plocka dem för hand och klippa isär dem – vid de där prickarna på huvudet där deras öron skulle ha suttit – är en effektiv bekämpning. Men det finns även andra metoder.
Kaffe & kaffesump. Enligt vissa undersökningar är kaffe giftigt för sniglar. Om inte annat verkar sniglarna ogilla stark lukt och därför borde en lätt dusch med gammalt kallt kaffe fungera som första hjälpen för en extra hårt attackerad eller känslig växt.
På samma sätt borde kaffesump runt växten fungera avskräckande, särskilt eftersom sniglarna verkar ogilla att få skräp på magen.
Upphöjda bäddar. Det finns teorier om att sniglar är slöa djur som hellre går runt ett hinder än forcerar det. En upphöjd bädd kan alltså hjälpa, särskilt om du omger bädden och växterna med vasst grus eller sand.
Koppar verkar ha en avskräckande effekt på sniglar. Det finns både kopparbarriärer, som du monterar på kanten av en upphöjd bädd och som boostar effekten av slöhetsprincipen, och kopparspray för enskilda växter.
Ölfällor. Det finns fantastiskt uppfinningsrika hemmagjorda ölfällor på internet (nergrävda pepparkaksburkar och uppochnervända, avsågade petflaskor till exempel). Principen bakom ölfällorna bygger på att sniglar älskar öl så mycket att de blir redlöst berusade och sen drunknar i samma öl. Hade det inte varit så fruktansvärt frånstötande att tömma avsågade petflaskor fulla av härsket öl och snigellik hade den här metoden varit perfekt.
Järnfosfat. Järn är giftigt för sniglar men nyttigt eller ofarligt för nästan alla andra, därför kan det vara smart att ersätta ölet i fällorna med snigelpellets gjorda på järnfosfat. Vissa använder järntillskott avsett för grisar eftersom det är billigare än de pellets som säljs specifikt för snigelbekämpning.
Örter. En koloniträdgård som jag slank in på i Paris hade en stor binge fylld med torkade, starkt luktande örter. Örterna hackades upp och spreds sen runt grönsakerna. Enligt kolonisterna förvirrade örternas lukt sniglarna.
Nematoder, som även kallas rundmaskar, är en liten parasit som fungerar som dödlig LSD för sniglarna. Maskarna sipprar in genom molluskernas hud och pajar deras inre organ. Du beställer nematoderna, levande och inpackade i kylklampar, på internet. Sen vattnar du ut dem i trädgårdslandet. I Norge har man kommit fram till att den allra mest effektiva metoden är att även doppa några sniglar i nematodvatten, klippa isär dem och sen sprida dem i odlingen. Sniglar äter nämligen inte bara alla dina växter, de äter också varandra. Och genom kannibalismen sprids parasitsmittan. Som sagt, ingen sa att det här skulle bli en snygg kamp.
Pantersnigeln. Ibland, när man väl bestämt sig för att lämna sin karma vid dörren, kan saker gå lite över styr. Som den där sommaren när jag hittade en enorm snigel vid vattentunnan. Under dramatiska former fick mannen bära iväg och döda den. När jag lugnat mig lite insåg jag att snigeln hade ett väldigt speciellt utseende. Helt fläckig och faktiskt väldigt snygg. En sökning senare visste jag att vi precis dödat en pantersnigel. Pantersnigeln är en sorts hjältemollusk som inte äter levande grödor och som konkurrerar med, till och med attackerar, spansk skogssnigel. Kunskap är allt. Sök först, klipp sen.
Morotsbitar och/eller maskar. Börje Remstam är en old school odlingsnörd som täckodlat i årtionden. Det har givit honom en nästan overkligt rik jord dit maskarna vallfärdar. När jag träffade honom i hans överdådiga trädgård tittade han mig djupt i ögonen och sa, så övertygad att jag just då trodde honom, att täckodling inte leder till fler sniglar. Jag frågade honom om han inte bekämpar dem alls och han svarade: "Jovisst bekämpar jag dem. Jag lägger ut morotsbitar längs gångarna. De älskar morot och tack vare färgen ser man dem tydligt."
"Och sen då", frågade jag, "klipper du dem sen?" Börje blinkade lite förvirrat och skakade på huvudet.
"Så", fortsatte jag, "egentligen kan man inte säga att du bekämpar sniglar. Det är mer som om du utfodrar dem?" Börje nickade nöjt och sa: "Ja, jo, det stämmer nog."
Att det här faktiskt skulle fungera låter ju som nån sorts urban odlingsmyt, men undersökningar visar att en stor andel maskar i jorden sammanfaller med färre sniglar. Så även om täckodling på kort sikt leder till snigelinvasion verkar det som om Börjes teori faktiskt stämmer, i alla fall på lång sikt.
Obs! När du odlat ett tag kan det hända att du blir lite... avtrubbad inför naturen. Som den där gången när jag jobbade som redaktionschef på en modetidning och beställde nematoder till redaktionens kontor. Helt logiskt eftersom paketet inte får ligga och svettas hos nåt postombud utan måste in i kylen med en gång, annars kan nematoderna skadas av värmen. Förutom att alla inte verkade se logiken och att jag – efter att högt och glatt förklarat hur extremt uppspelt jag var över att mina sniglar snart skulle ha rundmaskar insipprande genom porerna – blev utkastad då de övriga modeskribenterna förstod att den vita lådan i kylen inte innehöll min lunch.
### TIDLÖSA [ _Colchicum autumnale_ ]
Med odlingsåren har min inställning till blommor kontra grönsaker blivit mindre och mindre separatistisk. Och med den nya toleransen har blomsterlökar blivit mer intressanta. De mest kända lökarna blommar på våren, men några av de bästa blommar på hösten. Som halvlöken tidlösa till exempel. Tidlösan är dödligt giftig och fantastiskt vacker. Växten är inte en krokus rent tekniskt, men den ser ut som en. Och eftersom den inte blommar på våren, som de andra krokusarna, har man i folktron spekulerat kring huruvida häxor åt blommorna under valborg och använde bladen i farliga häxsallader. Tidlösans aktiva substans heter kolchicin och ämnet har en effekt som liknar – håll i dig nu – radioaktiv strålning. Växter som behandlas med kolchicin får ett fördubblat antal kromosomer och det används därför både till växtförädling och under behandling av leukemi. Jag skulle kunna fortsätta räkna upp bisarra och spännande egenskaper som tidlösan besitter, men egentligen räcker det med att stirra på den sköra, bleka blomman, som är uppe när nästan alla andra gått och lagt sig, för att förälska sig i den.
Det är bättre att sätta tidlösa under sommaren, när den vilar, men eftersom blomman och de tulpanliknande bladen aldrig syns tillsammans är växten svår att identifiera om du aldrig odlat den. På hösten, när de nakna blommorna sträcker sig efter dig från rabatterna, är den plötsligen överallt. Då brukar det vara lätt att hitta vänner eller grannar att byta till sig lökknölar från.
Som alltid när du flyttar växter från en plats till en annan är det lag på god växthygien. Välj friska, starka blommor och skölj bort all jord från knölarna redan när du gräver upp dem, annars riskerar du att släpa med dig skadedjur och jordsmittor till din odling.
Gräv ner knölarna djupt (20 cm) och vattna. Det kan ta nåt år innan växten återhämtar sig så ha tålamod och låt blasten växa och vissna ostört.
### SAFFRANSKROKUS [ _Crocus sativus_ ]
Saffran är en liten lök som sätts djupt ner i jorden (cirka 15 cm). På våren sticker det upp några nåltunna blad med en ensam ljusgrön strimma. Under sommaren vissnar bladen och på hösten (om allt går som det ska) blommar krokusen med en pistill så överdimensionerad att växten ser ut som en utmattad tecknad hund med en knallröd tunga hängande ur mungipan.
Berätta inte för dina persiska vänner att du odlar saffranskrokus. De kommer att skratta dig i ansiktet och sen erbjuda dig stora mängder saffran till lågt pris, vilket gör hela det här experimentet ännu mer fåfängt.
Min saffran har aldrig blommat, men det finns svenskar som svär att det ska funka. Det största problemet verkar inte vara de kalla vintrarna (löken övervintrar utan problem), utan de milda somrarna. När löken vilar, i juli–augusti, behöver den ungefär sex veckor av temperaturer över 20 grader. Om du kan skapa den typen av ihållande värmebölja för dina lökar finns potential för en egen saffransskörd. Det går åt ungefär 80 pistillmärken till ett halvt gram färdig krydda, och ungefär ett gram saffran till en normalstor sats lussekatter. Den ekvationen talar för att du parallellt med odlandet bör fortsätta vårda de där persiska kontakterna.
Motgångar är en naturlig del av odlandet. Det är så du lär känna din jord. Allt jag är bra på att odla har jag nån gång misslyckats med. Kommer du ihåg tv-spelsliknelsen från februarikapitlet? Tänk på den om inte alla odlingsprojekt går som du tänkt dig. Du kommer att klara nya bossar – det är bara att det tar typ ett år att spela sig igenom en bana. Tålamod är naturens present till odlaren. Och när du väl klarat av de där första, grundläggande grejerna finns det så mycket coolt att ge sig in i: gröna blad som smakar biffstek, pumpor som väger 300 kilo och björkar som kan prata med varandra.
## (KRUKVÄXTER)
Om du inte är beredd att överge odlingen bara för att vintern närmar sig finns det växter som går att gräva upp och flytta in i krukor. Testa till exempel att driva rabarber inomhus. Om allt går som det ska kan du skörda gnistrande knallröd, färsk glasrabarber mitt i vintern (mer om vad som är speciellt med glasrabarber hittar du på sidan 40).
#### Gör så här:
• På hösten, när plantan vissnat men innan tjälen kommit, gräver du upp en eller ett par rejäla rabarberrötter. Se till att få med minst en tillväxtpunkt per rot.
• Plantera rötterna i individuella krukor och lämna dem utomhus. När temperaturen sjunker till minus 2–10 grader somnar plantorna. För att de ska gå med på att vakna behöver de luras att tro att vintern är över.
• Efter 6–8 veckor av ihållande utomhuskyla är rabarbern – helt okunnig om det eländiga svenska klimatet – övertygad om att vintern haft sin gång. Då kan du börja driva den.
• Plocka in en kruka och ställ mörkt och svalt, 7–16 grader är lagom.
• Vattna försiktigt, rabarbern ska vara fuktig men inte blöt. I den här miljön börjar plantan gro utan att för den skull göra fotosyntes.
• Efter omkring 5 veckor kan du skörda din egen färska vårprimör, helt obrydd om snöstormar och en halv meter tjäle.
• Det går också bra att plantera rabarber på hösten. Sorten 'Rosenhagen' är mild men med mycket rabarbersmak och låg halt av oxalsyra, och 'Barbro' är en ny sort som tagits fram speciellt av Elitplantstationen i Balsgård.
Obs! Den här brutala metoden kräver en gammal, väletablerad planta. Förvuxna gamlingar kan till och med må bra av att begränsas lite. Unga plantor måste ha lugn och ro för att kunna etablera sig.
ANNAT SOM KAN PLOCKAS IN på vintern är mynta, persilja och gräslök. Gräv upp en eller par tuvor, plantera i krukor med köpejord (så du inte får med dig maskar av misstag) och klipp ner örten. Plocka in i värmen, ställ på fönsterbrädan och vattna med näring. Eller lämna krukorna ute i några månader tills du är i desperat behov av färskt grönt. Tänk bara på att rotbiten är känsligare för sträng kyla när den står i kruka och att plantor i kruka inte alls klarar lika låga temperaturer som de i marken.
## (VÄXELBRUK)
När jag var liten odlade vi potatis i slänten bakom farfarshuset och tomater mot söderväggen på stallet. År ut och år in, utan minsta problem. Att odla potatis nån annanstans än i potatislandet? Ja, du hör ju själv hur det låter.
Men på maximalt uppodlade koloniområden och mellan tajta villatomter hoppar sjukdomar, virus, skadedjur och annat skräp från grönsaksland till grönsaksland på bara några år. Därför är det bra att hålla hårt på växthygienen. Sätt presentplantor i karantän och rensa noga köpeplantor från sniglar. En av de tråkigaste grejerna som hänt min inomhusodling var till exempel den där gången när jag fick sniglar i köket. Nej förresten, det tråkigaste var att upptäcka det med foten (varför alltid med foten?).
Och skaffa ett schema för hälsosam växtföljd. Enligt växelbruket följer en grupp växter på en annan efter ett bestämt mönster. Hungriga växter följer på bönor, som hjälper till att gödsla jorden, och kålsläktingar separeras med flera år för att minska risken för klumprotsjuka.
Om ett enda land får representera hela schemat kan det landet till exempel odlas så här:
ÅR 1: _Solanaceae_ & co (potatis, tomater, physalis, selleri, svartrot, morot, rödbeta). Gödsla med ko- eller hästgödsel inför sådden.
ÅR 2: Baljväxter (blomsterbönor, sockerärter, okra, haricots verts). Innan du sår baljväxterna kan du tillföra lite kalk: det gynnar de kvävefixerande bakterierna kring växternas rötter.
ÅR 3: Kål- och bladväxter (till exempel grönkål, broccoli och mizuna, men även kålrot och -rabbi eftersom de också kan dra på sig klumprotsjuka, samt pumpa och squash eftersom de gillar mycket näring). Kalken från förra året gynnar också kålen, men inför sådden krävs också mer kogödsel.
ÅR 4: Lökväxter (till exempel potatislök, schalottenlök och salladslök men även sallat). Gödsla ej, de här grönsakerna trivs bäst i fjolårsgödsel.
SAMTLIGA ÅR: Öppen jord är alltid dåligt. Jordstrukturen försämras och näringen i jorden nöts bort av sol och spolas ut i vattendrag av regn. När du tömt ett land kan du så gröngödsling för att skydda och boosta jorden. Lin är en cool kulturväxt med rötter som hämtar näring från långt ner i jorden, honungsört är snygg, perserklöver luktar overkligt gott. Till våren vänds resterna av gröngödslingen ner i jorden och blir till näring och mull.
### VITLÖK [ _Allium sativum_ ]
Jag slutar aldrig förundras över hur mycket bättre jag är på att göra mat jämfört med affären. Vitlök är ett av de bästa bevisen på det. Två sättlökar, uppdelade i klyftor och satta på hösten, gör oss dessutom helt och hållet självförsörjande på vitlök, både till matlagning och till utsäde nästa år.
Det mest fantastiska med hemmagjord vitlök är:
1. Hållbarheten. Hemmaodlad vitlök håller rakt genom vintern, hela vägen fram till dess att följande års skörd grävs upp. Du vet hur köpelök liksom skrumpnar ihop och blir lite brun? Hemmaodlad vitlök är kritvit och sprängfylld med godsaker ända till sista klyftan.
2. Konsistensen. Jag tänkte aldrig på det förrän jag började odla, men köpevitlök är torr. Den går knappt ens att pressa (om man nu skulle vilja det, vilket min man säger att man inte får för att det förstör löken) eftersom det inte finns nån saft i den. Och skär man den fint till en tomat- och vitlökssallad är varje skiva som ett segt bakplåtspapper. Skivor av vår egen vitlök är däremot nästan genomskinliga av saft och så spänstiga att de säger "snäpp" om de bryts.
3. Smaken. Riv vitlöken, med rivjärn eller i ett specialdesignat vitlöksfat med räfflad botten, slå över fin, spansk olivolja, doppa en bit nybakat, vitt bröd i blandningen och förundras över att du skapat nåt så smakrikt med dina egna händer och bara lite hjälp av naturen.
#### Gör så här:
• Välj ett generöst land: djupgrävt, tömt på ogräs och med rik, lerig jord full av kompost och mull. Vitlöken är extremt härdig men kan ruttna om det blir för blött i jorden över vintern.
• Sätt löken sent på hösten. Den ska bara precis hinna rota sig och jordtemperaturen ska helst ligga kring 10 grader.
• Sätt de separerade klyftorna dubbelt så djupt som de är stora, ungefär 7 cm, med 18 cm mellanrum. Om du har mycket tung och våt jord kan du sätta klyftorna en och en i små krukor istället. Låt krukorna stå ute över vintern och plantera lökarna så fort tjälen gått ur marken på våren.
• Täck gärna jorden med ett lager torv, kompost eller löv – lökarna kommer att växa här länge och täckningen hjälper mot ogräs.
• När våren kommer dyker de första vitlöksskotten upp. Om du absolut inte kan hålla dig, skörda genom att bara klippa av dem (läs vidare för fler instruktioner). Under försommaren skördas små lökar med kort hållbarhet färska och används på samma sätt som purjolök. Först framåt sensommaren, när blasten börjat gulna och vissna, är det dags att testskörda. När löken ser rejält mogen ut, men innan det yttre skalet fallit sönder och börjat ruttna, gräver du försiktigt upp dem och hänger dem på tork under tak.
• Gör en vitlöksfläta (se sidan 110) eller förvara löken på en torr plats i köket – eftersom kyla fungerar stimulerande är rumstemperatur helt rätt vid förvaring.
#### Superkrafter
• Egentligen för många att räkna upp här – örtidolen Juliette de Bairacli Levy anser till exempel att vitlök är bra mot allt som kan drabba den mänskliga kroppen, från mask och mjäll till cancer.
• En enormt potent växt som är naturligt antiseptisk och allmänt stärkande för immunförsvaret.
• Kan lindra förkylningar, bronkit, katarr och andra infektioner och inflammationer.
• Kan sänka högt kolesterol och tunna ut blodet.
• Starka svamphämmande egenskaper gör att vitlök är ett bra tillskott i en blomsterolja gjord för fotsmörj (se sidan 171).
Lökskott à la Yayoe. Min japanska kompis Yayoe har övertygat mig om att överplantera en rad vitlök som sen offras som vitlöksskott.
• Skörda vitlöksstråna så fort de kommer upp, som en vårprimör, och fortsätt sen klippa så mycket du vill hela året.
• Koka skotten i saltvatten några minuter och använd dem i wok eller slunga dem i smör.
• Lämna lökarna i jorden och ge dem lite lökgödsel så kan du göra samma sak igen nästa år.
Att föda sig själv är stärkande på en massa andra sätt än bara rent näringstekniskt. Jag kan bli yr av lycka och stolthet när jag inser att jag ätit en hel lunch av saker jag rafsat åt mig i trädgården.
Men en lika viktig sak med modern, urban självförsörjning är att den tvingar oss att inse att vi inte klarar oss själva. Hela grejen med Earthships, där människor isolerar sig och försöker skapa ett perfekt mikrokosmos, eller folk som drar off-the-grid till stugor i skogen för att leva självhushållande, faller på att vi aldrig blir helt ensamma. Vi kan inte skapa en perfekt avskärmad värld. Fråga bara de kaliforniska bönderna som hittade radioaktivt cesium i sina navelapelsiner efter kärnkraftsolyckan i Fukushima, Japan.
Men den här sårbarhetsinsikten är positiv. Den gör att jag lånar en dehydrator av en skönhetsskribents gröna vågen-mamma när jag ska torka svamp. Den innebär att Lovisa, som bor i en jurta i Spanien och duschar i ett vattenfall, ger mig sitt överskott av ljuvliga, opastöriserade mandlar (och som den moderna människa jag är utbrast jag första gången jag åt en: "Det smakar precis som mandelessens!"). Den gör att Johan skickar en medicinflaska örtsalt från sin villaodling i Göteborg, att hårdrockarna Adam och Susanna delar med sig av den kolsvarta potatisen som deras familj alltid odlat i Born och att Per bjuder på en prilla av sitt hemmaodlade snus när det är fest.
Medberoendet gör oss inte mer sårbara utan mindre. Det får oss att inse att vi inte är maktlösa, att vi är många och att vi kan skapa kraftfulla förändringar. Och allt det här bara för att man under en hel sommar inte behövt köpa sallat i affären en enda gång.
VÄGEN TILL SJÄLVFÖRSÖRJNING kan sammanfattas i ett enda ord: sparsamhet. Ju mindre du gör av med, desto mindre behöver du producera. Samma sak gäller ekonomiskt oberoende. Många tänker att ett liv i ekonomiskt oberoende innebär att du har väldigt, väldigt mycket pengar. Men allt är relativt. Det kan lika gärna innebära att du gör av med väldigt, väldigt lite pengar. När det du gör av med ställs i relation till vad du har, och den spenderade summan procentuellt sett är minimal, blir du automatiskt rik. Sluga, snåla nyodlare vet att det mest ekologiska shoppingtipset är att inte köpa nåt alls.
MOSSBEKÄMPNING – särskilt om den involverar trädgårdsbranschens storsäljare ogräsgift – är egentligen helt överflödig. Mossa är vacker, den älskar skugga och kräver ingen näring från jorden. Den håller sig grön rakt igenom vintern och ju mer mossa du har i gräsmattan, desto mindre gräs behöver du klippa.
Mossa skiljer sig från de flesta andra trädgårdsväxter på det sätt att den inte sprider sig med frön eller rötter. Den är mer lik en alg eller en ormbunke, med rhizoider istället för rötter och sporer istället för frön. Det gör att den kan växa även på ställen där det inte finns nån jord – den suger i sig vatten på andra sätt än från rötter i jorden. Det går också ganska enkelt att sprida mossan i din trädgård. Om du redan har mossa i gräsmattan kan det räcka att kratta ut tussar av mossan i resten av mattan. Då vet du ju också att just den mossan redan trivs hos dig. Vissa sorters mossa kan också lockas upp på stenbänkar och fuktiga stammar eller ut över skuggiga, stenlagda trädgårdsgångar på det här lite mer brutala sättet.
#### Gör så här:
• Ta en tuss torr, brun mossa – bara om du har lov såklart, och plocka aldrig känsliga eller ovanliga arter. Kolla alltid upp vilken mossa det är du har spanat in innan du börjar.
• Det är bäst att plocka mossan i närheten av där den ska växa, så att miljön matchar.
• Blanda mossan med en kopp fil och kör i en mixer.
• Sprid mossfilen på ytan där du vill att växten ska sprida sig (filen gör miljön sur, vilket mossan gillar).
• Eftersom mossa inte har några rötter är den extremt känslig för torka, så växtplatsen bör vara halvskuggig och naturligt fuktig. Innan mossan tagit sig behöver plätten också försiktigt blötas nån gång om dan.
• När mossan väl fått fäste och börjat växa – räkna med att det tar lång tid – kan den bli brun under torrperioder. Det behöver inte betyda att den dött, den sover bara, och så fort höstregnen kommer kan den vakna till liv.
## (FÅGELMATNING)
Fåglar är inte bara roligt slapsticksällskap – som mitt i sommaren, när tonåriga talgoxar är så sällskapssjuka att de sätter sig på våra fötter och tjattrar med i samtalen medan vi dricker kaffe. De hjälper dessutom till att hålla efter trädgårdens skadedjur och äter allt från bladlöss och mygg till snäckor och sniglar. Men när vintern kommer blir maten svårare att få tag på.
Du kan enkelt hjälpa fåglarna genom att inte göra nånting alls. Undertryck din inre pedant och städa så lite som möjligt när hösten kommer. Låt solrosorna stå kvar som de är, syrenen får förbli obeskuren med frökapslarna i behåll, persiljan, kålväxterna, till och med sallaten som gått i blom får spendera vintern i grönsakslandet. Nån majsplanta, med de torkande kolvarna kvar på stammen, offras till naturen.
Har du plats över kan du plantera några av fåglarnas favoriter: yviga buskar eller träd där de kan gömma sig och äta bär, som berberis, nypon, oxbär, eldtorn, enbuskar eller ett rönnbärsträd med en slingrande kaprifol i.
Vill du mata fåglarna mer aktivt är det viktigt att deras matplats inte samtidigt blir katternas och rovfåglarnas matplats. Sätt upp foderautomater i skydd av buskar. Häng fågelmatare på grenar som är så tunna att katten inte klarar av att balansera ut till spetsen.
När du väl börjat mata, samtidigt som första snön kommer, måste du fortsätta konsekvent genom hela vintern. Du vill inte lura nån vintersvulten mes att göra av med viktig energi genom att flyga över halva stan bara för att upptäcka att det vanliga matstället plötsligen är tomt.
Fortsätt sen att fylla på med fågelmat ända in i maj. Annars finns det risk att käket inte räcker genom äggläggningen och då kläcker fåglarna små taniga indieungar istället för rejäla, livsdugliga jocks.
Under sommaren kan du också så ettåriga fågelfavoriter som blåklint, solros, ringblomma, hirs, raps och lin. Låt växterna stå som de är när de blommat över, eller skörda fröerna och gör din egen fågelblandning som du portionerar ut under vintern.
PAVLOVS FÅGLAR. De flesta fåglar, utom möjligtvis myskankans ungar, är hopplösa mördarsnigelkramare. För att ändra på det har en odlare jag känner (som jobbat som psykolog) försökt skapa en betingad reflex hos småfåglarna i trädgården genom att vända halshuggna spanska skogssniglar i fågelfrö. Enligt henne verkar fåglarna sakta men säkert vara på gång att ändra åsikt om sniglarnas ätbarhet.
### VALLMO [ _Papaver somniferum_ ]
Vallmofrön är pyttesmå och rätt pilliga att så inomhus på våren, men när växten väl fått fäste i trädgården sprider den sig gärna. Om nån annan i närheten också odlar vallmo är dock chansen stor att sorterna korsar sig. Mina två vallmosorter – den ena brukade vara en magnifik, djupt svartlila fylld pionvallmo och den andra en enkel röd fjädervallmo – korsar sig fram och tillbaka på ett sätt som gör att de för varje år mer och mer ser ut som ett misslyckat experiment på rymmen från Doktor Moreaus ö.
För att vara säker på att din vallmo är ren och alltså har just de egenskaper som _Papaver somniferum_ besitter, måste du börja från början varje år.
#### Gör så här:
• Vallmo går att så tidigt på våren enligt grundreceptet (se sidan 64). Men fröna är tuffa och går också att strössla direkt på vinterskaren.
• Täck med ett tunt lager jord så att inte djur och vind drar iväg med dem. Alltihop smälter sen ner genom snön och under tiden får fröna en rejäl köldbehandling.
• När våren kommer gror fröna och under högsommaren blommar de vackert i grönsaksland och rabatter.
• Vallmons omogna frökapslar innehåller en vit vätska som är full av alkaloider – i _Game of Thrones_ kallas vätskan för vallmomjölk och används för att stilla smärta. I stora doser är mjölken dock ett gift som kan leda till både koma och dödsfall.
• För ett tryggare sätt att använda vallmon, låt frökapslarna mogna helt och skörda fröna istället. De går att hälla direkt ur de vackra, torra frökapslarna som fungerar som naturens egna sockerströare. Vallmofrön är en klassisk topping på bagels men funkar också bra i filen på morgonen. Precis som många andra fröer är de rika på nyttiga oljor och bara en tesked tillför din kropp mätbara nivåer av kalcium, järn och zink.
• Till och med fröna är dock så potenta att många fängelser förbjudit dem som brödingrediens av rädsla för att de skulle kunna leda till ett positivt utslag vid ett drogtest.
### ENDIVE [ _Cichorium intybus, Foliosum_ -gruppen]
Bara helt nyligen började svenskar odla sallat som människoföda. Och fortfarande för några årtionden sen fanns det äldre människor som sockrade bladen. Så vi har en ursäkt om vi inte har fullt lika äventyrliga smaklökar som till exempel fransmännen.
Det var just en fransk vän som fick mig att förstå den märkliga, märkliga grönsaken endive. Han snodde ihop en minutsnabb middag till ett tiotal vinterhungriga vänner genom att skiva endive mycket tunt och blanda den med roquefort, päron och valnötter. Det var himmelskt. Men lyssna på hur man odlar endive: På våren sår du växten som vanligt. Välj frö som heter något med Belgien, Bryssel eller witloof så får du rätt. Den blir sen till en sorts blå blomma. När hösten kommer klipper du ner plantan och gräver upp roten. Roten planterar du sen i en kruka eller bytta med sandig jord. Ställ kallt, mörkt och fuktigt. Några veckor innan du blir sugen på att äta sallad flyttar du roten till en varmare plats (15–20 grader ungefär). Det ska fortfarande vara mörkt och fuktigt. Då börjar det istället växa ut ett tajt, vitt, slutet sallatshuvud där det förut satt gröna spretiga blad. Jag fattar inte ens hur det går att sälja en sån grönsak. Den borde kosta flera tusen. Hur som helst är den fantastiskt god, besk och frisk och en av få grönsaker som är i säsong mitt i vintern.
Efter att jag råkat köpa ett lite väl äventyrligt sallatsfrö i Paris använder jag nu samma metod för att göra den bittra fransosen mer svensk: klipper ner, gräver upp, planterar om och ställer in i skafferiet. Resultatet är en blekt rosa sallat som smakar spännande men acceptabelt.
När jag blev odlingsintresserad var det lite som jag tänker mig att en benign psykos känns. Allt utom odling blev overkligt. Om jag var i sällskap där det pratades om nåt annat än odling hände det att jag kände mig som om jag tittade på film. Och i hjärnan rullade det under tiden bara "Bönor samodlas med vinterkyndel i Italien. Pumpa går att odla i halmbalar. Testa friterad rölleka till smörslungade morötter. Spara äggskal. Gör snaps på gullviva. Be dem som krattar kyrkogården om löv till täckodlingen." Jag tänkte bara på odling, läste bara om odling och pratade bara om odling.
För att inte driva min man från vettet startade jag en blogg. Men jag var för fåfäng för att skriva okunnigt om odling under mitt riktiga namn. Så jag skaffade en pseudonym, inspirerad av en favoritodlingsbok, och började leva ett hemligt dubbelliv som onlineodlare. Det tog inte så jättelång tid innan det livet helt tog över och konkurrerade ut mitt andra, vanliga liv.
OCH NÄR JAG ÅTERVÄNDE TILL DEN DÄR KYRKOGÄRDEN i Paris hade nåt förändrats, inte bara i livet och inuti huvudet utan också utanför mig. Naturen var inte längre ett grönt brus. Prydnadsväxterna mellan de förfallna gravarna var som ledtrådar i en pågående deckare. Jag kunde se en mänsklig hand här, en självsådd mistel där. Och i skuggan av en stor sarkofag – grönstrimmig av ålder och med en vacker gråterska i två gånger mänsklig storlek lutande över kistlocket – fick jag syn på några buskar. Helt klart planterade där, men mer i hemlighet än som prydnad, stod två små järnekar och försökte smyga undan runt varsitt hörn på graven. Bladen var taggiga, blanka och klargröna fastän det var mitt i vintern. De frodades inte direkt i halvskuggan, men de verkade inte heller helt missnöjda. Jag blev stående där, fascinerad, och funderade över vilken sorts andar den som planterat buskarna haft problem med. För järneken har, förutom att bladen använts medicinskt, framförallt planterats på ställen där osaliga väsen behöver lockas tillbaka ner i jorden. Som på kyrkogårdar till exempel. Enligt folktro är järneken markens växt, en sorts portal som sammanbinder vår verklighet med underjorden. Den är också en favorit hos dödsrikets gudinna, Hel. Och där, mitt i det moderna Paris, runt hörnet från vattenpipekaféer tapetserade med aluminiumfolie och nattöppna kebabhak, var det nån som inte velat chansa och istället skaffat sig en extra försäkring mot eventuella besök från förfäderna.
Rulla hatt.
### JÄRNEK [ _Ilex aquifolium_ ]
Järneken har vuxit vild i Sverige. Nu är den i stort sett utdöd. Men en tam, tuktad köpeplanta (den ska klara sig i landets sydligare delar) fungerar fortfarande som en påminnelse om den makt som naturen haft, och har, över oss.
Plantera busken på våren, i sol eller halvskugga, i djupt grävd, lucker jord som är rik på mull och ruttnande växtdelar.
Vattna ordentligt under det första året och täck jorden med löv för att minska avdunstningen. Sen klarar sig busken själv och när vintern är som kallast festar fåglarna på de röda bären som mjukats upp av köldknäpparna.
#### Superkrafter
• Busken har använts medicinskt men både blad och bär är giftiga.
### MISTEL [ _Viscum album_ ]
I den icke helt faktabaserade bokserien _Discworld_ beskrivs druider som ett gäng präster som gillar att bränna folk på bål närhelst de inte är upptagna med att bränna folk på bål. Nåt vi faktiskt vet om druiderna – de var keltiska hedningar – är att de såg misteln som en helig växt och att de odlade den på ekar.
Om järneken är underjordens växt så kommer misteln från himmeln. Den är en parasit som bor i trädkronorna och den rör inte marken under hela sin livstid, inte ens när den sprider sig till nya träd. Istället svävar den genom luften med hjälp av fåglar. Den vissnar aldrig utan är grön året om och inom folktron var misteln en fruktbarhetssymbol. Vissa kelter ansåg att buskens vita, klibbiga bär var sädesdroppar från en kosmisk oxe. Det lite mer städade arvet efter den uppfattningen lever fortfarande kvar i kyssen under kvisten på jul. Upphängd i taket var misteln inte bara en chans för ogifta tjejer att slampa ur utan att riskera repressalier, den ger också himmelskt beskydd under vinterblotet. Kombinera misteln i taket med några kvistar järnek på bordet så har du ett heltäckande skydd, från underjorden och uppåt.
Misteln är numera ovanlig i Sverige. Märkligt nog verkar den lilla växten ovillig att leva på platser dit den inte sprids av människor och de mest misteltäta platserna i England är kommersiella äppellundar. Det ska även gå att sprida misteln till den egna trädgården.
#### Gör så här:
• Förutom just ekar är till exempel apel (alla sorters äppelsläktingar) och lind lämpliga som värdträd.
• Plocka ett par mogna bär – be alltid om lov och plocka bara på platser där misteln redan växer i överflöd.
• Medan bäret fortfarande är färskt klibbar du fast det i ditt träd. Det ska sitta halvvägs ut på en ganska ung gren. Resten är upp till de gamla gudarna.
• Efter att mistelbäret fått grepp om grenen och skickat ut sitt sugorgan kommer växten att sno en liten gnutta näring från värdträdet, men den gör sällan nån skada.
• Druiderna använde en skära av guld för att skörda kvistarna, men om du har svårt att få tag på en sån verkar i stort sett alla överens om att verktyget inte är så viktigt så länge misteln inte vidrör marken vid skörden, då förlorar den sin kraft.
#### Superkrafter
• Förutom det där med fertiliteten och gudomligheten har misteln använts inom folkmedicin, framförallt som en nervlugnare. Men det finns många olika sorters mistel, samtliga är giftiga och vissa är dödliga, så låt busken vara en strikt esoterisk närvaro i din trädgård.
Strandkål (Crambe maritima)
Spagettipumpa (Cucurbita pepo)
Ringblomma (Calendula officinalis)
### DET ENKLASTE SÄTTET
ATT TORKA FRUKT-, grönsaks- och svampskörden på är i en elektrisk frukt- och grönsakstork. Gå ihop flera stycken och köp en tillsammans, du kommer inte använda den mer än några gånger om året. Det går också att torka grönsaker i ugn på mycket låg värme, men det tar 8–15 timmar (beroende på hur blöt frukten eller grönsaken är) och under tiden måste du ha luckan på glänt så att fukten slipper ut. Örter torkas enklast och energisnålast på en torkolla – en sorts gammeldags torknät – eller upphängda i små buketter. Knyt hårt eller använd gummiband så buketterna inte rasar isär när de torkat.
#### SOMMARSNACKS
Under högsommar kan det funka att soltorka mindre bär, som röda och svarta vinbär. Har du ett solstekt skjul eller garage eller en outhärdligt varm, inglasad veranda är det perfekt. Sprid ut bären över brickor (de ska ligga ett och ett, inte i högar) och lämna dem där tills de skrumpnat ihop så mycket som du vill: ju torrare, desto längre blir hållbarheten. Om du bara semitorkar bären kan du förvara dem i kylen för att förlänga hållbarheten.
Äppelringar går att torka i vanligt inomhusklimat. Ta bort kärnhuset med en urkärnare, skär äpplet i centimetertjocka rundlar och trä upp de ihåliga skivorna på ett snöre som du spänner upp framför ett fönster till exempel. När skivorna torkat förvarar du dem i papperspåsar eller burkar.
Egna katrinplommon gör du genom att dela plommonen och pilla ur kärnorna. Pensla snittytan med honung om du känner dig vågad och torka sen frukten i en grönsakstork 12–20 timmar.
Torkad frukt går att äta som snacks, i fil eller müsli. Den kan även blötläggas över natten och användas till helt vanliga syltkok.
#### CHILIFLARN
Skörda chilin mitt på dagen en varm, solig dag, långt efter närmaste regnperiod och gärna när det är nymåne – då torkar den snabbare, och ju snabbare tork, desto mindre risk att den blir dålig.
• Häng upp frukterna på ett varmt, torrt och dammfritt ställe, eller dela dem på mitten och torka på ugnsgaller eller torkolla.
• Vänta tills chilin är snustorr, 1–2 veckor. Spara som den är, i burkar eller papperspåsar.
• För att använda, lägg ett par torkade chilisar i en pepparkvarn eller kaffekvarn och mal vid behov. Detta blir extra coolt om du använder en genomskinlig pepparkvarn och blandar frukter med olika färg. Trilskas de kan du mortla dem lite innan du finmal dem.
#### VIOLGODIS
Använd luktviol och undvik köpevioler i matlagning, de kan vara besprutade på ett sätt som gör dem oätliga. De här frostade violerna går att äta som godis och smakar lite, lite som violtabletter. Samma sak går att göra med alla ätliga blommor, som rosenblad eller lavendel till exempel.
• Plocka blommorna när det är varmt ute, gärna på en plats långt från vägar och andra dåligheter: de ska helst inte sköljas.
• Pensla varje blomma med lite lagom uppvispad äggvita.
• Strö över vanligt strösocker.
• Låt blommorna torka, gärna liggande på ett finmaskigt nät, nånstans där det inte dammar.
• När blommorna är helt torra, efter ett par dar, går de att stapla lager på lager, med bakplåtspapper mellan varje omgång, i burkar.
• De håller sig några månader.
#### KÄLCHIPS
Grönkål är en stadig kålväxt och den klarar tuff kärlek, som att torkas i ugn och ätas som chips. Alla sorters kål – svart, röd eller grön – går att använda.
• Skär bort mittennerven och riv kålbladen i chipsstora bitar.
• Blanda bladen med olivolja, salt och eventuella kryddor (chili är alltid pålitlig, muskot är en bra kålkompis och dill är ett roligt experiment).
• Lägg bladen på en plåt täckt med bakplåtspapper.
• Torka mitt i ugnen på 200 grader tills bladen är krispiga. Det tar inte mer än 5–10 minuter och på slutet måste du stirra på ugnen som om den vore en tv, en sekund för länge på plåten så byter chipsen vokal, från kål till kol.
• Ta ut dem ur ugnen och fös genast bort dem från plåten så att de inte fortsätter torka.
• Moffa i dig chipsen och förundras över att sjukt gott och nyttigt faktiskt kan mötas.
#### SEMITORKADE GRÖNA TOMATER
I södra USA måste man plocka omogna, gröna tomater hela sommaren eftersom skörden är så stor att grenarna annars kan knäckas. Här plockar vi omogna tomater för att det är vad vi får. Men det betyder inte att vi inte kan njuta av dem lika mycket. I södern doppar man tomatskivor i kärnmjölk och majsmjöl och friterar dem i baconfett. Gröna körsbärstomater går att semitorka, precis som de gör med mogna tomater i Italien. De blir både sötare och mer smakrika och passar som snacks, i sallader eller i varma rätter där man annars skulle använt färska tomater.
• Halvera tomaterna.
• Strö över några nypor salt så håller de smaken bättre.
• Peppra och ringla över lite god olivolja.
• Sprid ut halvorna med snittytan uppåt på en plåt med bakplåtspapper.
• Torka i ugn på 100 grader med luckan på glänt.
• Ta ut tomaterna när de torkat lagom mycket, några timmar för semitorkade, men ju torrare de är, desto längre håller de.
• Lägg i en burk och fyll på med olivolja om du känner dig lyxig eller en neutral matolja om du gör en större sats. Stoppa eventuellt ner lite färska kryddor (oregano eller salvia till exempel) eller halverade vitlöksklyftor. Se till att allt täcks av oljan.
• Förvara svalt. Håller sig i några veckor (för tomater som torkat kort tid) upp till flera månader.
#### TORKADE NYPON
På hösten, när skörden ligger i skafferiet och den första frosten har tagit kål på allt utom persiljan och vintersallaten, är nyponen perfekta. Bären innehåller mer C-vitamin än citrusfrukt men är gratis och finns i nästan varje skogsbryn eller lite vildare park. Vanlig nyponros eller vresros (den där supertaggiga busken som är så aggressiv att den används mot jorderosion) är de vanligaste soppnyponen, men de flesta sorter funkar. Undvik dem som växer i vägrenar eller på förorenad mark.
• Plocka så mycket du orkar och gör sen en liter nyponsoppa på de färska bären. Det är viktigt att komma ihåg den där omedelbara gratifikationen, det är den som gör att alla med beroendepersonlighet faktiskt får arslet ur vagnen och fixar saker. Torka sen resten av skörden så har du en lättillgänglig C-vitamindepå resten av vintern.
• Plocka bären innan den värsta frosten gjort dem mosiga. Det är inget fel på de mjuka bären, de är bara svårare att hantera.
• Skölj bären och skär bort kvistar och fnas. Du behöver inte ta bort det där klipulvret inuti bären, det silas bort senare.
• Torka bären på en torkolla, från några dagar upp till några veckor beroende på hur blöta de är. I slutändan ska de vara snustorra. Det går också att sprida ut bären på en plåt och ställa i ugnen på lägsta möjliga värme, med luckan på glänt 5–8 timmar.
#### NYPONSOPPA
• Ta 5 dl färska, rensade nypon till 1 liter vatten.
• Koka upp nyponen i vattnet och låt dem sjuda tills de faller sönder, 20–30 minuter. Mosa med en slev på slutet om du är otålig.
• Passera nyponkoket genom en trådsil eller liknande, så att soppan skiljs från de små nyponnötterna.
• Om det fortfarande är mycket nyponmassa kvar efter första omgången kan du koka upp den överblivna massan med lite nytt vatten.
• Passera sen en gång till.
• Koka upp den silade soppan under omrörning tillsammans med 1 dl strösocker.
• För soppa på torkade nypon, gör som ovan men minska mängden nypon, 3 dl till 1 liter vatten räcker. Lägg nyponen i blöt över natten eller öka koktiden efter behov.
• Servera soppan varm med groddade mandlar till frukost, eller kall med vaniljglass och mandelbiskvier till efterrätt.
Radis noir (Raphanus sativus niger)
### FULLA AV NÄRING,
VITAMINER OCH NYTTIGA MJÖLKSYREBAKTERIER: det enda syrade grönsaker snålar med är kalorier. De är bra för matsmältningen och funkar alltså perfekt ihop med fet vintermat. Vill du veta mer, sök på internet eller läs det lilla hippiehäftet _Mjölksyrejäsning av grönsaker._ Hardcorefansen säger att man till och med kan äta surkål istället för penicillin (Obs! Stäm mig inte om du testar och det inte funkar).
Jäsningsprocessen som leder fram till att mjölksyran bildas har fyra behov: salt, syrefri miljö, tryck och kontrollerad temperatur. Du kan mjölksyra gurka, tomat, pepparrot, all sorts lök, morötter, svamp – nästan vad som helst.
Att syra med ättika eller vinäger är inte fullt lika nyttigt som mjölksyrning, men nästan, och risken att misslyckas är betydligt mindre.
* * *
#### SURKÅL
Den allra enklaste grönsaken att mjölksyra är vitkål, eftersom den bär på en inbyggd mjölksyrekultur. Det är viktigt med rena verktyg, burkar och händer, annars kan dåliga bakterier sjanghaja hela satsen.
1 kg ekologisk vitkål
2 msk grovt havssalt
ev smaksättning: torkade eller färska enbär, dill- eller korianderfrön, kummin eller lagerblad, torkade eller färska hallon- eller vinbärsblad (har du varken eller och det är vinter kan du ta in ris och sätta i vatten så dyker färska blad upp på nån vecka).
• Dela kålen och skär bort men spara den grova rotbiten – det är där många av mjölksyrebakterierna bor.
• Ta av de allra yttersta bladen och släng i komposten. Ta av ytterligare några stora blad och spara.
• Strimla kålen fint, det är lättast med en mandolin eller osthyvel. Riv rotbiten och blanda allt med saltet.
• Byttan som kålen ska syras i behöver steriliseras med hett vatten innan du går vidare.
• Knåda kålblandningen. Ta i så mycket att det bildas kåljuice och packa sen blandningen hårt i botten på byttan. Varva med eventuella kryddor. Kålen ska bilda ett tajt lager och vätskan ska lägga sig på toppen.
• Ta de stora bladen du sparade i steg två och lägg dem som ett lock på kålen.
• Lägg en tallrik eller nåt annat i rätt storlek över kålen och toppa med en tyngd. Om du gör kålen i en burk skruvar du på ett tättslutande lock. Använder du ett öppet kärl stoppar du in det i en plastpåse och stänger till så att inte syret kommer åt kålen.
• Låt stå mörkt men i rumstemperatur 2 dygn så att nedbrytningsprocessen kommer igång.
• Flytta sen byttan till ett svalare ställe (gärna kring 15 grader): ett förråd, en veranda eller, som jag, göm den under en bänk i en annars väldigt lyxig vinkällare.
• Vänta 2–6 veckor. Tjuvkika inte.
• När kålen är klar kan du ha den i kylen. Oöppnad håller den mycket länge (några år enligt Tore Wretman, vilket är så länge att jag inte kan bekräfta det). När burken öppnats och kålen kommit i kontakt med syre behöver den ätas inom cirka 4 veckor.
• Om det bildas lite vit gucka på toppen, toppjäst, är det bara att plocka bort den.
#### Att tänka på:
• Använd ekologisk vitkål – ostressade, näringsrika växter som vuxit i jord med rikt mikroliv är lättare att syra.
• Om du syrar grejer du odlat själv, undvik att skörda direkt efter en regnig period, då kan viktiga mikroorganismer ha sköljts bort.
• Använd havssalt, det innehåller mycket naturliga mineraler.
• Det finns särskilda jäsningskrukor, men det går också bra att använda vanliga glasbyttor eller Höganäskrus. Undvik plast (det är i och för sig en bra regel rent allmänt i livet).
• Om du har problem att få igång syrningen går det att blanda lite vassle med kålen.
#### Juggetipset
Den strimlade surkålen är typiskt tysk. Min kompis Fredrik, som har en jugoslavisk mamma, tipsade mig en gång om att hans morfar istället brukar syra hela vitkålshuvuden. Det syrade huvudet ska gå att baka helt i ugn, men du kan också ta loss bladen och göra serbiska surkålsdolmar, sarma. När surkål hettas upp dör mycket av mikrolivet, men allt annat nyttigt finns kvar. Så här går det till enligt morfarn.
• Koka upp vatten med salt, cirka 15 g salt per liter vatten, och låt svalna.
• Ta av de allra yttersta bladen på kålhuvudet.
• Gör ett hål in i kålhuvudet där rotbiten är och fyll med salt.
• Lägg huvudet i en bytta, fyll på med saltvattnet så att kålen täcks och se till att det hålls under ytan med en tyngd (allt måste såklart vara kliniskt rent). Lägg på ett lock.
• Låt stå svalt minst 2 veckor och förvara sen i kylen.
#### Chins Kim-Tje
En av de bästa grejerna med att bli odlingsintresserad är att det inte längre är svårt att veta vad som är i säsong i grönsaksdisken. En tråkig grej med att bli odlingsintresserad är att man inser att nio månader av tolv är den grejen typ vitkål och nånting man inte kan namnet på men som ser ut som en jordhög.
Eftersom folk förr i tiden nästan bara åt sånt som var i säsong finns det en massa grymma, gammelsvenska sätt att laga till just vitkål på. Men den kålrätt som jag minns från min barndom, som jag fortfarande inte kan fira en äkta svensk jul utan, är kimchi. På hösten brukade min pappa fylla en hel diskbalja med salladskål, vitlök, morot och kryddor. Sen ställde han ut hela schabraket på förstukvisten för att jäsa. Under vintern var alltid en hel vägg i matkällaren fylld med stinkande, hårt packade kimchiburkar. Perfekt till fet, svensk julmat.
Att en bonde i Hälsingland står och packar fermenterad, koreansk kål på trelitersburkar låter ju såklart exotiskt, men när jag mejlade och frågade sa min pappa: "Kim-Tje-receptet har jag fått av en äkta koreanska som heter Chin och bor i Björklinge norr om Uppsala." Kimchi kan ätas som den är men passar också i soppor och grytor, som koreansk chige. Kryddningen sätter smak på soppan och kålen blir istället söt och mild.
Det här receptet är en hälsingsk basvariant, det finns en massa andra sätt att syra kål och göra kimchi på. En kompis till mig fyller till exempel en stor hink med kål och sen packar han den, på samma sätt som man kärnar smör, med ett baseballträ. Ett alternativ till kålen är rättika (eller radis noir, se foto sidan 156) skuren i kuber och en alternativ krydda är fisksås.
1 ½ kg salladskål
2 dl grovt havssalt
3 msk koreanskt chilipulver i flingform (kallas också kodjokaro)
3 purjolökar (gärna späda) eller salladslökar, hackade
6 rejäla vitlöksklyftor, rivna övrigt grönt som passar – morötter, rädisor, kinesisk gräslök, färsk ingefära – som hackas eller strimlas fint.
• Ta bort fula och grova blad.
• Renskär salladskålen genom att skära bort den grövsta delen av rotfästet. Märgen, inuti det grova fästet, går att riva och inkludera i blandningen.
• Lägg salladskålen i en stor skål. Häll över saltet och fyll på med vatten så att kålen täcks. Lägg på en tyngd och låt stå över dagen eller natten i rumstemperatur.
• Häll bort vätskan, skölj rent med friskt vatten och låt rinna av.
• Varva kålen med chili, purjo och vitlök i en stor glasburk med skruvlock.
• Låt stå minst 1 dygn i kylen, men gärna upp till 10 dar, innan du äter. Håller sig i veckor.
#### Spartips från norr
Om du skulle få för dig att till exempel göra halva satsen av det här receptet – vilket fortfarande är tillräckligt mycket för att imponera på en koreansk husmor – kommer du stå där med en halv bit sträv vinterpurjo till ingen nytta.
Hälsingepappans trick är att kasta in restbiten i frysen, delad i lagom stora portionsbitar (kvartar till exempel). När det är dags att använda purjon, till soppa eller gratäng, rekommenderar han att banka den lite lätt med en hammare medan den fortfarande är djupfryst i sin påse. "Blir precis lika bra som finhackat." Detta är även mannen som klyver sina cigarrer på hälften i vedkapen eftersom han blir yr av att röka en hel, men tobaken blir sur om han spar en halvrökt.
#### NYTTIG PICKLAD PEPPARROT
Pepparrotens rötter går omöjligt djupt, så försök att få upp så mycket som möjligt när du skördar den. Vänta med att gräva upp roten tills du ska använda den och skala den inte: det starka i pepparroten är en lättflyktig olja som det finns mest av i det yttre skalet.
• Ta en rejäl rot, skrubba den lite lätt och skär bort eventuella skador.
• Gör en saltad vinäger av 1 tsk salt och 3 dl ljus vinäger.
• Riv roten eller kör den i en mixer.
• Packa löst i små burkar och toppa upp med vinägern.
• Skruva på ett tättslutande lock och ställ svalt.
• Använd som du skulle ha använt färsk pepparrot.
• Roten går också att lägga in hel, rengjord som ovan och nerstoppad som den är i en flaska vitvinsvinäger.
#### ONYTTIG PICKLAD PEPPARROT
I södra USA gör folk en typiskt slö/genialisk rätt genom att ta en burk saltgurka, lyfta ur gurkan, fylla på med några rejäla matskedar färsk riven pepparrot, sockra och sen stoppa tillbaka gurkan i burken. Skruva på locket och skaka om ordentligt ett par gånger så att sockret löser upp sig. Efter nån vecka i kylen har gurkan blivit sötstark. Passar bra, som nästan allt annat i södra USA, till grillat.
#### ÖRTVINÄGER
Under varma, torra dagar är örterna packade med smak. Vinäger är ett bra sätt att bevara den smaken på. Använd vinägern till marinader, såser och dressingar. Örtvinäger passar också perfekt när du ska lägga in grönsaksskörden och med en flaska dragonvinäger i skafferiet kan du laga bearnaisesås med färsk dragonsmak hela vintern.
• Plocka örterna innan de gått i blom, då ligger fokus fortfarande på bladen.
• Mortla dem lite lätt och packa i en burk eller i en flaska med vid hals.
• Värm upp vitvinsvinäger utan att koka den, fyll burken eller flaskan till brädden och korka till.
• Låt stå ljust och varmt, till exempel på fönsterkarmen, ett par veckor. Skaka dagligen.
• Smaka av. Om du vill ha mer smak byter du till nya, färska örter. Gör sen samma sak en gång till: låt stå ljust och varmt ytterligare 2 veckor och skaka dagligen.
• Fortsätt så tills vinägern fått den smak du vill ha. Då silar du av örterna och stoppar tillbaka en tjusig, omortlad kvist i flaskan – det funkar lika bra som klisterlapp med namn.
#### SENAP
Helt senapsfrö smakar inte senap, det är först när du maler och blöter det som senapssmaken uppstår. Det coolaste sättet att göra senap på är som förr: att sätta en vid bytta mellan knäna, plonka ner en kanonkula i byttan och sen luta benen från höger till vänster så att kanonkulan rullar som en roulettekula längs kanten och mal senapsfröet lite finare för varje varv. Men det går såklart att mala senap i en helt vanlig mortel också.
• Börja mala fröna med lite kallt vatten. Kokande vatten, salta och sura ingredienser dödar enzymet som ger senapen den där näskittlande smaken, så vänta med kryddorna.
• Tillsätt vatten allteftersom och fortsätt hela tiden mala fröna tills du har en bra konsistens, grov eller fin beroende på smak.
• Låt senapen stå till sig lite (10 minuter eller längre beroende på hur bråttom du har), smaka och när du fått den senapssmak du vill ha kryddar du. Efter egen smak tillsätter du vitt vin eller vitvinsvinäger, sötar med honung, kryddar med dragon, salt, peppar eller vad som helst som du gillar.
#### FLÄDERKAPRIS
Omogna, gröna fläderbär (eller omogna krassefrön) går att förvandla till nordisk kapris. Jag förälskade mig i dem redan första gången jag åt dem på Stockholmsrestaurangen Volt.
Var noga med att bara plocka fläderbär från träd som du vet att du identifierat som äkta fläder, _Sambucus nigra._ Och använd små burkar: när du väl öppnat en burk är det bäst att göra slut på kaprisen ganska snabbt.
Om du gjort din egen örtvinäger (se sidan bredvid) är det nu den får sin chans att briljera. Du kan också koka ihop en kryddig vinäger inför steg fem i det här receptet.
• Plocka och rensa bären en torr dag.
• Varva dem med finmalt havssalt i en glasburk med tättslutande lock. Ta 1/3 salt i förhållande till bärmängden.
• Låt stå i kylen 3 veckor. Rör om varje dag.
• Skölj slarvigt.
• Packa bären i rena, steriliserade burkar och fyll ända upp med örtvinäger eller äppelcidervinäger. För extra mycket smak, koka ihop en snabb kryddvinäger*.
• Låt stå i kylen ytterligare 3 veckor.
• Använd på samma sätt som vanlig kapris.
#### *SNABB KRYDDVINÄGER
Börja med att välja smak på din vinäger: 2 vitlökar, 1 gul lök och 2 lagerblad är en bra grund till 3 dl vitvinsvinäger (eller 1 ½ dl ättika blandad med 1 ½ dl vatten). Lägg till ett par centimeter pepparrot och någon tesked kryddpepparkorn om du vill att din vinäger ska smaka svenskt. Byt ut mot ett par teskedar dragon och rosmarin om du känner dig mer kontinental. Eller experimentera med sånt du har hemma: senapsfrön, rostade korianderfrön eller hackad chili. Torkade kryddkorn kan krossas men mal dem inte, då blir lagen grumlig.
• Halvera vitlökarna och klyfta den gula löken.
• Koka under lock, tillsammans med dina utvalda kryddor, i vinägern 10–15 minuter.
• Plocka bort lökbitarna ur grytan och använd den heta vinägern genom att slå den över det du vill lägga in: fläderbär eller grönsaker. Pilla ner ett lagerblad, en vitlöksbit eller nåt kryddkorn i varje burk så att de fortsätter ge ifrån sig smak.
Pepparrot (Armoracia rusticana)
### FÖRR I TIDEN
KUNDE ÖL OCH SPRIT VARA BLAND DE BÄST filtrerade och nyttigaste dryckerna det gick att få tag på. Då låg i och för sig medellivslängden i Stockholm kring 20 år och vattenkvaliteten var kanske inte riktigt på samma nivå som idag. Snapsen sågs ibland som en form av medicin och flera av medicinalörterna i våra trädgårdar – johannesört, malört, älggräs – passar fortfarande väldigt bra i sträv, katarsisk snaps.
* * *
#### HIRKUM PIRKUM
En del tror att namnet på johannesörtssnaps är en sorts bonnig felhörning av örtens latinska namn: _Hypericum perforatum._ Snapsen kan göras på både färska och torkade blommor. Den har en lätt beska, smakar örter, jord och hedendom och är tjusigt mörkröd.
• Fyll en vidhalsad flaska (en gammal vinägerflaska till exempel) ända upp med färska blommor, eller till hälften med torkade blommor.
• Toppa upp med en neutral vodka och korka till.
• Låt dra minst några dagar, gärna upp till 1 månad. Under högsommaren, när du använder färska blommor plockade på varma dagar och flaskan får stå och steka i solen, blir smaken ännu djupare och starkare.
• Sila av blommorna och drick iskall.
#### PEPPARROTSSNAPS
Vällagrad pepparrotssnaps har en smak som bäst beskrivs som "slagborr". Ögon tåras, lungor drar ihop sig, bihålor expanderar, hattar rullar. Låter det spännande? Den är enkel att göra.
• Skär mynt av 5–10 cm färsk pepparrot.
• Stoppa ner i en gammal glasflaska (helst genomskinlig, så att du ser när färgen förändras).
• Toppa upp med en kvarting vodka. Nån månad senare, när vätskan börjat gulna, är du framme vid slagborr.
Tips! För en snaps som är mer uppfriskande och förkylningsdämpande, men fortfarande drickbar, bör du testa vodkan redan efter några dagar. När du fått rätt styrka silar du bort roten. Smaka av med honung om du vill ha en riktigt len snaps.
#### ROMTOPF
När jag var liten var min farfar skibum i Österrike, och kanske var det därför vi alltid åt romtopf på julafton. Jag älskar fortfarande den här tyska efterrätten, men numera eftersom den är en skördetrött odlares bästa vän. Romtopf sväljer all överbliven frukt med minimal anstränging.
• Ta en stor glasburk, större än den aktuella skörden kräver.
• Skölj frukten. Bär som körsbär och druvor, lingon och björnbär rensas och snoppas men kärnas ej ur. Plommon och aprikoser delas och kärnas ur. Äpplen och päron kärnas ur med en urkärnare och klyftas eller skärs i tjocka rundlar.
• Varva frukten med hälften så mycket socker (gå på vikten) i burken och ställ svalt över natten.
• Följande dag toppar du upp med Strohrom 60 % och ställer tillbaka i kylen, eller ännu hellre i en sval källare. Har du inte så stark rom kan du använda vanlig, mörk rom. Öka i så fall på sockermängden, för hållbarhetens skull.
• Vänd eller skaka försiktigt burken nån gång då och då så att sockret löser upp sig.
• När nästa omgång frukt eller bär är mogen gör du samma sak igen: blanda skörden med socker, lägg den nya frukten ovanpå den gamla
i burken, toppa upp med rom.
• Fortsätt så tills hösten är kommen och du kan dra en bitterljuv suck av lättnad över att ingen frukt längre finns kvar att ta hand om. Nu borde du ha en burk fylld med lager på lager av frukter och bär, simmande under ett värmande täcke av rom.
• Vänta minst 1 månad innan du provsmakar, gärna längre. Julafton brukar vara lagom. Öppna andaktsfullt burken och ät frukten med lättvispad grädde eller vaniljglass.
STENFRUKT KÄRNAS LÄTTAST UR genom att du skär ett snitt på längden, 360 grader runt hela frukten. Skruva försiktigt de två delarna i motsatta riktningar tills den ena delen lossnar från kärnan. Är frukten mogen går det lätt. Pilla sen in en smal, vass kniv under kärnan och sprätta bort den från den andra delen av frukten.
#### SPRITKOKTA KÖRSBÄR
Körsbär finns i två versioner, sura och söta. Med surkörsbär blir det här en klassisk vuxenefterrätt. Folk med mycket tålamod och lite karpaltunnelsyndrom brukar kärna ur körsbär med ett gem. Jag kärnar ur dem på samma brutala sätt som oliver: lägger dem på en skärbräda och använder en kniv med bred klinga för att platta till dem (skär inte, lägg klingan över bären och tryck till med handen). Kärnan lossnar från köttet och blir lätt att pilla ur. Med den här metoden får bären en rufsigare look, men som de brukade säga på dagis: de går ju ändå sönder i magen. Det går att använda bär med kärnorna kvar också, enda skillnaden är att du måste ha en spottkopp när du serverar dem.
1 liter körsbär
2 dl strösocker
1 dl vatten
ev en bit vaniljstång
1 ½ dl konjak eller rom
• Koka upp socker, vatten och eventuellt vaniljstång.
• Lägg i bären och koka 10–15 minuter. Håll koll på bären, de ska inte koka sönder.
• Ta grytan från värmen och rör i spriten.
• Lyft över bären i rena, steriliserade burkar och fyll ända upp med sockerlagen.
• Låt stå i kylen minst ett par dar innan du äter dem med vispad grädde, syrlig crème fraiche eller vaniljglass. Håller sig i alla fall till jul.
#### MALÖRTSSNAPS
Malörten är besläktad med johannesörten på det sätt att de båda tillhör en svensk snapstradition där man accepterat smaker som idag kan uppfattas som lätt brutala. Det är lite som att ta medicin – strävheten i örten stärker både kropp och själ, vilket ju är bra eftersom du samtidigt dricker ren vodka.
Men malörten har också mer konkreta medicinska egenskaper: bitterämnet i örten kan förbättra matsmältningen och öka aptiten (och no offence svensk julmat, men det är en väldigt användbar egenskap).
Dessutom är örten perfekt om du till exempel vill skydda dig från osaliga havsdemoner. I alla fall enligt John Ajvide Lindqvist samt den svenska skrocken.
Jag har älskat malört, _Artemisia absinthium,_ ända sen jag var en gotisk 16-åring och läste novellen _And His Mouth Will Taste of Wormwood,_ om en oerhört dekadent vampyr som älskar absint. Tujon, ämnet i absinten som brukar skyllas för både avskurna öron och grönskimrande hallucinationer, kommer från malörten. En del modern forskning lutar dock åt att koncentrationen av ämnet i absinten är så låg att du dragit på dig fylledille långt innan tujonen börjar kittla ditt centrala nervsystem. Men precis som med johannesört är det alltså bäst att behandla malört med respekt.
• Fyll en glasburk med späda malörtsblad och/eller blommor, beroende på vilken tid på året det är. Ta bort kvistarna.
• Toppa upp med en neutral vodka.
• Skruva på locket.
• Vänta 1–2 veckor, sila bort örten och drick, antingen som snaps eller blandat till en grogg.
#### DAGENS MALGRÄS
Den här groggen är en version på drinken dagens. Den går att blanda med antingen älggrässaft eller flädersaft som båda är söta på gränsen till kvalmiga, medan malörten kan vara väldigt bitter.
• Börja med att göra malörtssnaps.
• När örtinfusionen är klar gör du malgräsgroggen genom att ta fyra delar saft, sex delar torrt vitt vin och en del malörtssnaps.
• Blanda och drick med mycket is.
Jordärtskocksblomma (Helianthus tuberosus)
För söt för att syltas.
### SOCKER KONSERVERAR
PÅ ETT LIKNANDE SÄTT SOMI SALT. I sockrade, inkokta körsbär eller plommon bevaras till exempel C-vitamin bättre än i osockrade bär och frukter. Ju mer socker, desto längre hållbarhet. Om du ändå vill hålla igen på sockret går det att frysa in burkar och flaskor efter att du syltat eller saftat för att få grejerna att hålla bättre.
* * *
RABARBERKOMPOTT
Den här efterrätten blir extra god om du drivit fram egen glasrabarber (se sidan 40), då behöver du inte ens skala stjälkarna.
1 ½ liter rabarber
2 ½ dl vatten
2 dl strösocker
ev skal från ½ ekologisk citron
ev några strimlor färsk ingefära
ev 1 msk potatismjöl + ½ dl vatten
• Koka upp en sockerlag på vatten och socker.
• Lägg eventuellt till citronskal och ingefära för smakens skull.
• Skär rabarberstjälkarna i nån god storlek - jag gillar typ 5 cm för då får man in hela i munnen i en tugga och kan äta med en hand.
• Lägg ner stjälkarna sida vid sida i sockerlagen och låt dem sjuda några minuter tills de mjuknat men inte lösts upp. Skillnaden brukar vara hårfin.
• Plocka upp dem med en tång eller hålslev och lägg på ett serveringsfat. Fortsätt sen med nästa omgång stjälkar.
• När rabarbern är färdigkokt kan du antingen reda av lagen med lite potatismjöl utrört i kallt vatten eller bara koka upp lagen ordentligt och sen hälla den över rabarbern. Låt citron- och ingefärsstrimlorna följa med.
• Servera med vispad grädde, vaniljsås eller glass. Får du lag över går den att spara och använda till andra saker som behöver en smak av söt rabarber.
RABARBERVARIATION
Jag är inget jättefan av rabarberpaj, men älskar helt vanlig saft gjord på rabarber. Kasta i nån näve röda vinbär för knalligare färg eller svarta vinbär för en mer gotisk ton. En standardlagad rabarbermarmelad tar sig upp på en ny nivå med ett tillägg av strimlad ingefära och jordgubbar – smakkombinationen är skamligt inställsam. Några sönderrivna pelargonblad samt saft och skal av blodapelsin gör marmeladen exotisk på ett engelskt sätt. Och barndomsfrukosten rabarberkräm blir extra god om den kokas med en kanelstång.
ÄLGGRÄSSAFT
Den här saften är andra chansen för dig som missade fläderblommorna! Älggräs växer vilt och blommorna har samma somrigt kvalmiga, sött pollendruckna smak som fläder.
50 klasar älggräsblommor
3 ekologiska citroner
2 liter vatten
2 kg strösocker
½ msk citronsyra
ev 1 msk vitvinsvinäger
• Plocka blommorna i varmt väder och låt dem ligga ett tag så att småkrypen hinner ta sig därifrån. Flytta blommorna till en stor bytta, gärna med ett passande lock. Skiva citronerna och kasta i dem på toppen.
• Koka ihop en sockerlag på vatten och socker, blanda ut lite av lagen med citronsyran och slå sen alltihop över blommorna. Täck med lock, plast eller en handduk så det inte drunknar en massa flugor i saften och låt stå upp till 1 vecka. Rör om varje dag.
• Nöjer du dig med alkofritt, sila bort blommor och citron, tappa saften på flaskor och förvara svalt.
• För att göra ett bubbligt vin av saften, tillsätt vitvinsvinäger samtidigt som citronerna och dra ner på sockret till omkring 300 g. Sila bort blommorna som ovan men var noga med att tappa på glasflaskor med starka lock (tänk Grolschflaska). Låt stå ytterligare 3 veckor och drick väl kyld. Om älggräschampagnen inte vill fermentera kan du tillsätta en nypa vinjäst medan blommorna fortfarande ligger och drar i sockerlagen.
Praktmålla (Chenopodium giganteum)
Johannesört (släktet Hypericum)
### JAG KAN BLI SÅ TRÖTT
PÄ ATT MAN ALLTID MÄSTE lägga till en disclaimer när man skriver om medicinalörter och förklara att inget är bevisat och att du alltid ska prata med din doktor innan du tar örter mot en krämpa. Örter ÄR medicin. Inte på nåt flummigt, avlägset, hypotetiskt sätt utan helt konkret: de ämnen som finns i örterna är desamma som syntetiseras och används i "riktig" medicin. Så visa respekt och behandla örterna som de kraftfulla läkeväxter de är. Men med det sagt: alla örter funkar inte för alla. Hitta din egen väg. Experimentera på ett klokt, empiriskt sätt. Då bygger du samtidigt vidare på den hedniska, folkliga DIY-tradition som brukade ledas av kvinnor som kyrkan gillade att bränna.
#### BLOMSTEROLJA
Jag får eksem och utslag av allt från luft och vatten till hög puls och dåliga tv-serier. När jag blev gammal nog att fatta att livet inte behöver vara en kamp började jag smörja in mig. Men eftersom jag har hippiepåbrå blir jag stressad över att det är så mycket mysko grejer i krämerna man köper. Då är egentillverkad kroppsolja lugnande på flera sätt.
• Skörda blommor under varma, torra dagar och välj dem som bara precis slagit ut, innan de tömts på nektar och pollen. Ignorera de sura blickarna från fjärilar och humlor.
• Fyll en glasburk med blommor. Det går att använda torkade blommor också, dra ner lite på mängden i så fall.
• Toppa upp med olja och se till att alla blommor är täckta, annars kan de bli dåliga. Många använder olivolja men jag föredrar mandelolja, den känns lättare på huden och kostar knappt nåt alls på apoteket.
• Skruva på ett tättslutande lock och låt stå minst 2 veckor, gärna längre. Skaka burken nån gång om dan. Om det är sommar blir oljan extra stark om den får stå och steka i fullt solljus ute på trappen. På vintern går det att försiktigt värma oljeburken (om den är i glas) i vattenbad några gånger under processen.
• För ännu mer styrka, byt blommor varannan vecka.
• Pressa ur eller sila av blommorna (med kaffefilter till exempel) och tappa oljan på flaska, gärna en med pump eller droppmynning så den inte blir så slabbig att hantera. Blanda, om du vill, i några droppar eterisk olja.
• Använd oljan som en mäktig hudkräm. På vintern kan du använda den för att boosta din vanliga lätta ansiktskräm: blanda några droppar olja med krämen direkt i handen. Oljan funkar även istället för raklödder. Direkt efter duschen, när huden och håren är mjuka och fuktiga, stryker du på 3–4 droppar och rakar som vanligt.
• Det går att blanda olika blommor i en burk, eller så kan du göra rena oljor baserade på en blomma och sen blanda oljorna med varandra utifrån behov.
• Håller sig lika länge som vanlig olja.
#### FAVORITBLOMMOR
Ringblomma – bra för den sportiges fötter, ringblomma kan motverka svampangrepp.
Citronmeliss – kan dämpa herpesinfektioner och passar extra bra till läpparna.
Johannesört – när du somnat i solen.
Fläder – samma som ovan, men också mot helt vanlig rosighet.
Viol – mot kliande eksem och hudinflammationer.
Pelargon – särskilt Doktor Westerlunds blad kan hjälpa mot akne.
Lavendel – allmänt läkande och lugnande.
Ros – doftande blommor smittar av sig på oljan så kasta i några precis utslagna rosenknoppar också.
#### LAVENDELTONIC
Det här hårsköljet gör håret strävt och starkt. Det gör också att du inte behöver tvätta håret riktigt lika ofta, så yay för att slippa gnugga in sulfiter i huvudsvålen varje dag!
Jag brukade använda sköljet utan att fatta varför det funkade. Sen berättade blomsterbarnet/skönhetsredaktören Filippa att kranvattnets pH-värde inte matchar skalpens pH-värde och att en hårtonic gjord på vinäger alltså kan rätta till obalansen.
Skölj håret med tonic direkt efter duschen, innan du torkar det. Eller massera in några stänk i hårbotten på kvällen innan du går och lägger dig. Om du ställer dig med huvudet neråt medan du masserar så växer håret dessutom snabbare.
• Blanda en flaska ljus vinäger med lika mycket vatten och koka upp.
• Kasta ner en ordentlig näve färska vårnässlor, eller lite färre torkade.
• Sjud försiktigt under lock upp till 2 timmar.
• Ta av grytan från plattan och blanda ner en halv näve lavendelblommor. Om jag precis rensat ogräs brukar jag lägga i några strån åkerfräken också – de innehåller en massa silica som stärker både hår och naglar (dricker du te på åkerfräken har det samma effekt).
• Låt stå ett par timmar, eller tills blandningen svalnat, med locket på.
• Sila genom dubbla kaffefilter och tappa på en ren flaska. Sköljet brukar ha reducerats till ungefär hälften så det går att återanvända den tomma vinägerflaskan till förvaring. Diska bort etiketten så känns det mindre som att hälla salladsdressing i håret.
• Sätt på lock och förvara i kylen. Håller upp till ett par månader.
### JULIETTES MEDICINSKA TE
För en svag, daglig dos av din favoritört är det lättast att bara stoppa några blommor eller blad i tevattnet eller kaffefiltret på morgonen – ringblomma mot pms, nässlor mot hösnuva, lavendel mot dåligt morgonhumör, johannesört mot lakansskräck. För en mer koncentrerad behandling är örtkvinnan och vagabonden Juliette de Bairacli Levys medicinska te bra.
• Ta en rejäl handfull örter eller blommor till 2 koppar vatten. Torkade örter är mer koncentrerade än färska, så anpassa mängden.
• Koka upp vattnet, ta det av värmen och lägg ner örten.
• Använd lock så att de aktiva substanserna inte smiter ut.
• Håll teet strax under kokpunkten ytterligare 3 minuter.
• Ta av från värmen och låt dra minst 3 timmar.
• Du behöver inte sila bort örterna, teet blir starkare ju längre de ligger i.
• Förvara svalt upp till 3 dagar och ta några matskedar vid behov, upp till ett par gånger om dan.
## LÄSLISTA
_Common Herbs for Natural Health_ av Juliette de Bairacli Levy
Nomaden Juliette går igenom i stort sett alla vanliga vilda och tama växter, hur de använts inom folkmedicinen och vilken effekt hon själv märkt att växterna har.
Bra tips: Att gnida färska, krossade ringblommor direkt på huden för att stilla inflammationer eller för att rena och påskynda läkning av sår. Och att dricka lavendelte mot svimningar.
_Den arbetsfria trädgården_ av Ruth Stout
Ruth Stout är en äkta OG – original gardener. Drottningen av täckodling är rolig, vresig, effektivitetstörstande och generös, en typisk nygammal odlare, och hennes bok är lika stärkande som lärorik.
Bra tips: Att man får göra precis så som man själv tycker är bäst, oavsett vad det står i böckerna.
_The Royal Horticultural Society Encyclopedia of Gardening_
Om du som jag gillar tanken på att även under ett strömavbrott kunna läsa extremt noggranna instruktioner om hur man ympar tomater så är en trädgårdsencyklopedi ett måste. Enda nackdelen med den här tegelstenen är att den är brittisk och alltså hela tiden påminner om att vi hade kunnat skörda egna fikon om inte våra förfäder så enträget gnetat sig allt längre norrut.
Bra tips: Att samplantera sallat och majs – bladen kan skördas redan efter några veckor och gör att grönsakslandet ger avkastning även under sommarmånaderna då majsen fortfarande mognar.
_Gardening and Planting by the Moon_ från RHS eller Maria Thuns _Så- och skördekalender_ från Biodynamiska Föreningen
En månkalender är ett måste om du vill hänga med i månsvängarna.
Bra tips: Att undvika att så, plantera eller skörda i närheten av extrema astronomiska händelser, som månförmörkelse till exempel.
_Häxans handbok_ av Dannie Druehyld
Fint magisamlingsverk för barn. För vuxna läsare är det fortfarande en vacker och underhållande cyprianus och Dannie är så nära en nordisk Patti Smith vi kommer.
Bra tips: Att strö linfrö över markerna under första fullmånen efter vårdagjämningen, då blidkas den fornnordiska gudinnan Hild och linet växer bra.
_Possum Living_ av Dolly Freed
18-åriga Dolly skrev det här mästerverket strax efter att hon bestämt sig för att lämna gården där hon och hennes sjukligt snåla pappa förfinat den moderna självhushållningskonsten. Här samlar hon instruktioner kring allt från hur man botar pms till hur man bränner hemma (det första löses med hjälp av det andra).
Bra tips: Att ifrågasätta all konventionell kunskap. Och att köpa utsäde och liknande grejer där yrkesbönder handlar – priset är garanterat lägre.
_Runåbergs fröer_ av Johnny Andreasson Allt du nånsin velat veta men inte ens varit smart nog att fråga om frö.
Bra tips: Att använda en fön inställd på låg värme för att försiktigt blåsa bort skräp och uppbrutna frökapslar från skördat, torkat frö.
_Square Foot Gardening_ av Mel Bartholomew Mannen som får idén om ett kvadratiskt grönsaksland att låta som upptäckten av penicillin är faktiskt väldigt konkret. Han ger närmast matematiska instruktioner kring allt från plantavstånd till skördetider.
Bra tips: Angivelserna för antalet veckor det tar från att fröet hamnat i jorden till att grönsaken ligger på bordet (tomater 17 veckor; ärter 10 veckor; squash 8 veckor; rädisor 4 veckor).
_The Complete Book of Self-Sufficiency_ av John Seymour
Om du till exempel vill veta hur du på egen hand får bort en enorm sten ur en åker eller hur du bevarar egenslaktat kött med hjälp av en nypa salpeter och några kilo salt.
Bra tips: Att använda den tjusiga, vilda ärtsläktingen kråkvicker till gröngödsling.
_The Secret Garden_ av Frances Hodgson Burnett Den här underbara barnboken om två hemska ungar läste jag under en period när jag var rädd att alla odlingsböcker för vuxna höll på att ta slut. Lustigt nog har den påverkat min syn på odling lika mycket som nånsin en faktabok.
Bra tips: Att under årstider när växterna har fällt sina blad kontrollera om det är liv i en till synes död buske genom att försiktigt skava ett litet snitt i barken. Är det grönt därunder kan växten prunka till våren, oavsett hur illa däran den verkar.
Vad som helst av Lena Israelsson
Dagen efter att jag ställt mig i kö till kolonilotten gick jag till bibblan och sa "Ge mig en bok om det härna med odling". En snäll bibliotekarie stack Lena Israelssons _Jordens täppor_ i mina händer och på den vägen är det.
Bra tips: Att låta alla delar av trädgården vara både ätliga och vackra – gör en häck av sparris och sätt styvmorsviol i grönsakslandet.
_Vilda grannar_ av Maria Lewander och Per Bengtsson
En bok om hur du lockar olika djurarter till trädgården. Söt, praktisk och dessutom enormt ickerasistisk: det enda djur som inte har ett eget kapitel är rådjuret. Till och med sniglar och ormar har egna avsnitt om hur just de gynnas.
Bra tips: Att samla jorden från perfekt smuliga mullvadshögar i gräsmattan och använda som blomkruksjord.
www.nok.se
info@nok.se
© ELIN UNNES 2014
NATUR & KULTUR, STOCKHOLM
Text & recept: _Elin Unnes_ | Form: _Stefan Fält_
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Fotografi: _Calle Stoltz_ | Faktagranskare: _Lars-Erik Läck_
Redaktör: _Maria Nilsson_ | E-boksproduktion: _Elib AB, 2014_
ISBN 978-91-27-14027-1
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