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Tag: rub and release
The Aroma Company get down and dirty in 'Filthy Cities' of the past with the BBC's 'Dirt Season'.
Viewers of BBC's Dirt Season series can get closer to the action with a Touch to Smell (advanced version of scratch and sniff) card that brings the pungent smells of yesteryear into the living room.
The interactive card, created by The Aroma Company, will be available in the latest edition of the Radio Times and from your local library from 1st April and should be used whilst watching 'Filthy Cities' on BBC Two. Viewers just rub the indicated area on the card, to the release the smells.
BBC Filthy Cities scratch card
The Aroma Company was approached by the BBC to bring the stinky cities of 'Medieval London' and 'Revolutionary Paris' to life for a two part documentary.
The series will excavate the murky past of the filthiest cities in gruesome detail, offering viewers the chance to immerse in the sights, sounds and SMELLS of defining periods in history.
The Aroma Company's first challenge was to recreate the 'stink' of Sewage Sludge, 18th Century Tannery, Pong de Paris and Marie Antoinette's Perfume. By blending a repertoire of disgusting fragrances and a strong nose, The Aroma Company created 4 unique fragrances that will evoke all the viewers' senses and take them back in time like never before.
The second challenge was to bring these 'Filthy Cities' to the living rooms of the nation. Using Touch to Smell technology, The Aroma Company produced a 'scratch and sniff' card that allows the viewer to rub and release the fragrance whilst following the documentary.
For a preview and in depth look at how the 'scratch and sniff' cards were made, join The Aroma Company Managing Director, Val Lord and presenter Dan Snow on The One Show, 7.00pm, 1st April *.
* NOW AVAILABLE: Watch The One Show feature on our YouTube channel.
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{"url":"https:\/\/oqtavetech.com\/a-lot-more-might-possibly-be-created-from-this\/","text":"Select Page\n\nA lot more might possibly be created from this time for the Section step 3 whenever we really explain related amount known as trigonometric characteristics\n\nThe fresh angle ? that appears on these significance must sit anywhere between 0 rad (0\u00b0) and you can ?\/dos rad (90\u00b0), however, afterwards in this module we shall extend brand new meanings in buddygays order to the bases. It needs to be showcased that value of a particular trigonometric proportion would depend merely to your property value ?, so the sine, cosine and you will tangent try effortlessly attributes of perspective ?.\n\nIt\u2019s very beneficial to remember the meanings of your trigonometric rates. You may find it beneficial to denote new sine, cosine and tangent by the characters s, c and you can t following, having fun with h, o and you will a toward portray hypotenuse, contrary and adjoining, the 3 affairs see, kept to help you right and you will top to bottom, since soh, cah and you can toa.\n\nYou should use an excellent calculator to discover the sine, cosine otherwise tangent from a direction conveyed in both values or radians, provided you first turn it on the appropriate form \u2013 normally, this is done-by clicking a button designated \u2018DRG (or something like that equivalent) up until both \u2018degree or \u2018radians looks on the monitor. Then type in the newest perspective followed closely by among the mode tactics sin, cos or tan.\n\n## People triangle having two sides of equal size is known as a keen isosceles triangle, and people isosceles triangle must include two equivalent indoor angles\n\n?) letter (to have confident philosophy of n) might be made use of. Equivalent events can be used for another trigonometric services. The latest notation can not be used in negative thinking of letter as the sin ?1 ? is usually used in new inverse sine means, and that i thought after in this component. The aforementioned loved ones can also be ergo be authored since the:\n\nSince there are two identities related the latest trigonometric percentages, it observe one one ratio was independent hence given one to proportion we could find the other several. (Which assumes on your trigonometric rates is self-confident, which is genuine having 0\u00b0 ? ? ? 90\u00b0.)\n\nThe brand new perspective ? for the Figure 9 comes with their sine, cosine and you can tangent. But the contrary and you will surrounding corners appropriate so you\u2019re able to ? is interchanged having ? and you can, for this reason we can make\n\nThe isosceles triangle of Figure 10 is special because it is also a right\u2013angled triangle. Since the interior angles of any triangle add up to 180\u00b0, the angles of this particular triangle must be 45\u00b0, 90\u00b0, 45\u00b0. Also, since the two equal sides of this particular triangle are both of unit length it follows from Pythagorass theorem that the length of the hypotenuse is $\\sqrt <1^2>= \\sqrt<2\\os>$ and so we can write down the following results:\n\nProfile 11 reveals a keen equilateral triangle, we.age. one to which have around three edges away from equivalent length and hence around three equal indoor basics and this need to be equal to sixty\u00b0. A column could have been taken from vertex (i.age. corner) into middle of your own other side, therefore the perspective amongst the range in addition to top try 90\u00b0 (that\u2019s, brand new range are an everyday to the side).\n\nOf the given Figure 11, discover thinking away from sin ?, cos ? and you can bronze ? having ? comparable to 29\u00b0 (?\/six rad) and you may 60\u00b0 (?\/step three rad), thus complete the trigonometric rates in Table dos.\n\n## Clearly, composing powers of trigonometric qualities might be alternatively cumbersome and so the new conference you to sin letter ? function (sin\n\nBy Pythagorass theorem, the perpendicular has length, $\\sqrt <2^2-1>= \\sqrt<3\\os>$. Therefore the completed table is as given in Table 4.\n\nFigure 12 shows a graph of sin ? for 0 ? ? < ?\/2. i Using Table 2, your answer to Question T5, and any other relevant information given in this subsection, sketch corresponding graphs for cos ? and tan ?.","date":"2023-03-30 18:37:42","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\": 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\": 0.7657785415649414, \"perplexity\": 1812.3152344161504}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"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-2023-14\/segments\/1679296949355.52\/warc\/CC-MAIN-20230330163823-20230330193823-00131.warc.gz\"}"}
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\section{Introduction and overview of main results}
Sign covariances such as Kendall's tau ($\tau$) are especially useful for testing independence when (i) the data are ordinal (whether continuous or discontinuous) and the ordinary covariance is inappropriate, (ii) the data are heavy tailed and the ordinary covariance may not be defined, or (iii) the data are contaminated and robustness is needed. Kendall's tau ($\tau$), however, has the possible drawback that it may be zero when there is association present. To achieve power against broader alternatives, the chi-square test can be used; it is directly applicable to categorical data and can be used for continuous data after a suitable categorization. However, the chi-square test for data with ordered outcomes does not take the ordinal nature of the data into account, leading to potential power loss for `ordinal' alternatives; effectively the chi-square test treats the data as nominal rather than ordinal (see also \citeNP{agresti10}).
As a possible substitute for these two tests, we consider a modification of $\tau^2$, which we call $\tau^*$. Tests based on the sample value of $\tau^*$ yield power against a broad range of ordinal alternatives. Below, we first derive $\tau^*$, then summarize its properties and provide a probabilistic interpretation in terms of concordance and discordance probabilities.
Regarding notation, we denote iid sample values by $(x_1,y_1),\ldots,(x_n,y_n)$, but will also use $\{(X_i,Y_i)\}$ to denote iid replications of $(X,Y)$ in order to define population coefficients. For the most part of this paper we assume all variables are real, but briefly touch upon more general metric sample spaces.
The empirical value $t$ of Kendall's tau is
\begin{eqnarray*}
t =
\frac{1}{n^2}{\sum_{i,j=1}^n\sign(x_i-x_j)\sign(y_i-y_j)}
\end{eqnarray*}
and its population version is
\begin{eqnarray*}
\tau =
{E\sign(X_1-X_2)\sign(Y_1-Y_2)}
\end{eqnarray*}
\cite{kruskal58,kg90}. With
\begin{eqnarray*}
s(z_1,z_2,z_3,z_4)
&=& \sign(z_1-z_3)(z_2-z_4)\\
&=& \sign(|z_1-z_2|^2+|z_3-z_4|^2-|z_1-z_3|^2-|z_2-z_4|^2)
\end{eqnarray*}
we obtain
\begin{eqnarray*}
t^2 =
\frac{1}{n^4}{\sum_{i,j,k,l=1}^n s(x_i,x_j,x_k,x_l)s(y_i,y_j,y_k,y_l)}
\end{eqnarray*}
and
\begin{eqnarray*}
\tau^2
=
{Es(X_1,X_2,X_3,X_4)s(Y_1,Y_2,Y_3,Y_4)}
\label{tdef}
\end{eqnarray*}
Replacing squared differences in $s$ by absolute values of differences, we define
\begin{eqnarray}
a(z_1,z_2,z_3,z_4) =
\sign
\left(|z_1-z_2|+|z_3-z_4|-|z_1-z_3|-|z_2-z_4|\right)
\label{sdef}
\end{eqnarray}
This leads to a modified version of $t^2$,
\begin{eqnarray*}
t^*
=
\sum_{i,j,k,l}a(x_i,x_j,x_k,x_l)a(y_i,y_j,y_k,y_l)
\label{tdef2}
\end{eqnarray*}
and the corresponding population coefficient
\begin{eqnarray*}
\tau^* = \tau^*(X,Y)
=
{Ea(X_1,X_2,X_3,X_4)a(Y_1,Y_2,Y_3,Y_4)}
\label{tdef3}
\end{eqnarray*}
The quantities $t^*$ and $\tau^*$ are new, and the main result of the paper is the following:
\begin{theorem}\label{th1}
Let $X$ and $Y$ be real continuous random variables. Then
$\tau^*(X,Y)\ge 0$ with equality if and only if $X$ and $Y$ are independent.
\end{theorem}
The proof is given in Section~\ref{app-cvm}. We conjecture that the continuity condition is not needed, and have the following partial proofs of this: (i) Lemma~\ref{lem2} in Section~\ref{cvmsec} shows that if $X$ is binary and $Y$ continuous or discrete, the theorem holds; (ii) the code for a computational `proof' of nonnegativity of $\tau^*$ using {\em Mathematica} for $3\times 3$ contingency tables with given marginals is given in Appendix~\ref{app-math}.
If the sign functions are omitted from $\tau^*$, we obtain the covariance $\kappa$ introduced by \citeA{bergsma06}. He showed that for arbitrary real random variables $X$ and $Y$, $\kappa(X,Y)\ge 0$ with equality if and only if $X$ and $Y$ are independent.
We now give a probabilistic interpretation of $\tau^*$. A pair of points $\{(x_1,y_1),(x_2,y_2)\}$ is called concordant if
$(x_1-x_2)(y_1-y_2)>0$ and discordant if $(x_1-x_2)(y_1-y_2)<0$, as illustrated in Figure~\ref{concdisc2}.
Denoting the probabilities that two randomly chosen points
are concordant by $\Pi_{C_2}$ and that they are discordant by $\Pi_{D_2}$, Kendall's tau has the well-known probabilistic interpretation
\begin{eqnarray*}
\tau =
\Pi_{C_2}-\Pi_{D_2}
\end{eqnarray*}
An analogous interpretation of $\tau^*$ can be given. A set of four points is concordant if there exist vertical and
horizontal axes such that two opposing open quadrants contain two points
each (Figure~\ref{concdisc}(a)). The set is discordant if there exist vertical and
horizontal axes such that every open quadrant contains a single point (Figure~\ref{concdisc}(b)).
Note that the axes must strictly separate the points, i.e., no points can fall on the axes.
In mathematical notation, a set of four points $\{(x_1,y_1),\ldots,(x_4,y_4)\}$
is concordant if there is a permutation $(i,j,k,l)$ of $(1,2,3,4)$ such that
\begin{eqnarray*}
(x_i,x_j<x_k,x_l) \wedge \left[(y_i,y_j<y_k,y_l)\vee (y_i,y_j>y_k,y_l)\right]
\end{eqnarray*}
and discordant if there is a permutation $(i,j,k,l)$ of $(1,2,3,4)$ such that
\begin{eqnarray*}
\left[(x_i,x_j<x_k,x_l)\vee(x_i,x_j>x_k,x_l)\right] \wedge \left[(y_i,y_k<y_j,y_l)\vee (y_i,y_k>y_j,y_l)\right]
\end{eqnarray*}
It is straightforward to verify that
\begin{eqnarray*}
a(z_1,z_2,z_3,z_4) &=& I(z_1,z_2<z_3,z_4) + I(z_1,z_2>z_3,z_4) \\
&&- I(z_1,z_3<z_2,z_4) - I(z_1,z_3>z_2,z_4)
\end{eqnarray*}
where $I$ is the indicator function and $I(z_1,z_2<z_3,z_4)$ is shorthand for $I(z_1<z_3\wedge z_1<z_4\wedge z_2<z_3\wedge z_2<z_4)$. Hence,
\begin{eqnarray}
\tau^*
&=& 2P(X_1,X_2<X_3,X_4\wedge Y_1,Y_2<Y_3,Y_4) +\nonumber\\
&& 2P(X_1,X_2<X_3,X_4\wedge Y_1,Y_2>Y_3,Y_4) -\nonumber\\
&& 4P(X_1,X_2<X_3,X_4\wedge Y_1,Y_3<Y_2,Y_4)
\label{tauprob1}
\end{eqnarray}
Denoting the probability that four randomly chosen points are concordant as $\Pi_{C_4}$ and the probability that they are discordant as
$\Pi_{D_4}$, we obtain that the sum of the first two probabilities on the right hand side of~(\ref{tauprob1}) equal $\Pi_{C_4}/6$, while the last probability equals $\Pi_{D_4}/24$.
Hence,
\begin{eqnarray}
\tau^* = \frac{2\Pi_{C_4} - \Pi_{D_4}}{6}\label{tau-int}
\end{eqnarray}
The reason that $\Pi_{C_4}$ is given twice as much weight as $\Pi_{D_4}$ is related to there being twice as many discordant as concordant patterns in Figure~\ref{concdisc}.
It can be seen that $t^*$ and $\tau^*$ do not depend on the scale at which the variables are measured, but only on the ranks or grades of the observations.
Four points are said to be {\em tied} if they are neither concordant nor discordant.
Clearly, for continuous distributions the probability of tied observations is zero. Hence, under independence, when all configurations are
equally likely, $\Pi_{C_4}=1/3$ and $\Pi_{D_4}=2/3$, and if one variable is a strictly monotone function of the other, then
$\Pi_{C_4}=1$ and $\Pi_{D_4}=0$.
The definition of $\tau^*$ can easily be extended to $X$ and $Y$ in arbitrary metric spaces, but unfortunately Theorem~\ref{th1} does not extend then, as it is possible that $\tau^*<0$. This is shown by the following example. Consider a set of points $\{u_1,\ldots,u_8\}\subset\bR^8$, where $u_i=(u_{i1},\ldots,u_{i8})'$ such that $u_{ii}=3$, $u_{ij}=-1$ if $i\ne j$ and $i,j\le 4$ or $i,j\ge 5$, and $u_{ij}=0$ otherwise. Suppose $Y$ is uniformly distributed on $\{0,1\}$, and given $Y=0$, $X$ is uniformly distributed on $u_1,\ldots,u_4$, and given $Y=1$, $X$ is uniformly distributed on $u_5,\ldots,u_8$. Then $\tau^*=-1/64$.
Still, for $X$ and $Y$ in arbitrary metric spaces, the following result suggests that a test that $\tau^*=0$ against the alternative $\tau^*>0$ can have power for certain interesting alternatives: if $(X,Y)$ is the mixture of a non-degenerate independence model and a point mass, then $\tau^*(X,Y)>0$ (Theorem~\ref{mix-th} in Appendix~\ref{mix-app}).
By the Cauchy-Schwarz inequality, the normalized value
\begin{eqnarray*}
\tau_b^* = \frac{\tau^*(X,Y)}{\sqrt{\tau^*(X,X)\tau^*(Y,Y)}}
\end{eqnarray*}
does not exceed one. (Note that this notation is in line with Kendall's $\tau_b$, defined analogously.)
Note that $\tau^*(X,Y)$ is a function of the copula, which is the joint distribution of $F_X(X)$ and $F_Y(Y)$, where $F_X$ and $F_Y$ are the cumulative distribution functions of $X$ and $Y$. \citeA[Chapter~5]{nelsen06} explores the way in which copulas can be used in the study of dependence between random variables, paying particular attention to Kendall's tau and Spearman's rho.
The remainder of the paper is organized as follows.
In Section~\ref{sec-alt}, a comparison is given with some other approaches in the literature. In particular, the \cvm\ test is essentially a special case and there are interesting similarities with a test devised by Hoeffding.
In Section~\ref{sec-applic} we give a description of independence testing with an artificial and a real data example, briefly comparing the tests described in Section~\ref{sec-hoeff} with a test based on Kendall's tau and the chi-square test.
\begin{figure}[tbp]
\centering
\subfigure[Concordant pair]
{\hspace*{5mm}\includegraphics[width=20mm]{concordant2dim2.eps}\hspace*{5mm}}
\hspace{8mm}
\subfigure[Discordant pair]
{\hspace*{5mm}\includegraphics[width=20mm]{discordant2dim2.eps}\hspace*{5mm}}
\caption{Concordant and discordant pairs of points
associated with Kendall's tau}\label{concdisc2}
\end{figure}
\begin{figure}[tbp]
\centering
\subfigure[Concordant quadruples]
{\includegraphics[width=120mm]{concordant2dim.eps}}
\\
\subfigure[Discordant quadruples]
{\includegraphics[width=120mm]{discordant2dim.eps}}
\caption{Configurations of concordant and discordant quadruples of points associated
with $\tau^*$. The dotted axes indicate strict separation of points in different quadrants; within a quadrant, no restrictions apply.}\label{concdisc}
\end{figure}
\section{Proof of Theorem~\ref{th1}}\label{app-cvm}
For the proof of Theorem~\ref{th1}, we need Lemma~\ref{lem2}, which covers the case that one of the variables is binary. Note that Lemma~\ref{lem2} provides an extension of Theorem~\ref{th1}, which does not cover the discrete case.
\begin{lemma}\label{lem2}
If $X$ is binary and $Y$ given $X$ is continuous or discrete, then $\tau^*\ge 0$ with equality if and only if $X$ and $Y$ are independent.
\end{lemma}
Before giving the proof, let us first look at the form of $\tau^*$ when one of the variables is binary.
Suppose $X\in\{0,1\}$ and $Y\in\bR$ and denote $U\equiv(Y|X=0)$, $V\equiv(Y|X=1)$, and $p=P(X=0)$. Then using~(\ref{tauprob1}) it is straightforward to verify that
\begin{eqnarray}
\tau^* = 2p^2(1-p)^2
\left[
P(U_1,U_2<V_1,V_2) + P(V_1,V_2<U_1,U_2) - 2 P(U_1,V_1<U_2,V_2)
\right]
\label{cvm1}
\end{eqnarray}
Note that in this case, independence of $X$ and $Y$ is equivalent to $U$ and $V$ having identical distributions (see Section~\ref{cvmsec} for comments on the resulting two-sample test).
Below, we first prove Lemma~\ref{lem2} separately for the continuous and the discrete case, then we prove Theorem~\ref{th1}.\\
\noindent\proof{Proof of Lemma~\ref{lem2} (the continuous case)}
Continuity implies
\begin{eqnarray*}
P(U_1,U_2<V_1,V_2) + P(V_1,V_2<U_1,U_2) + 4 P(U_1,V_1<U_2,V_2) = 1
\end{eqnarray*}
so by~(\ref{cvm1}), $\tau^*\ge 0$ reduces to
\begin{eqnarray*}
P(U_1,U_2<V_1,V_2) + P(V_1,V_2<U_1,U_2) \ge \frac13.
\end{eqnarray*}
Now, with $G$ and $H$ the distribution functions of $U$ and $V$, respectively,
\[ P \left( U_1, U_2 < V_1, V_2 \right) + P \left( V_1, V_2 < U_1, U_2 \right)
= \]
\[ 2 \int_{\mathbbm{R}} G^2 \left( 1 - H \right) \tmop{dH} + 2
\int_{\mathbbm{R}} \left( 1 - G \right)^2 H \tmop{dH} = \]
\[ 2 \int_{\mathbbm{R}} \left( G^2 + H - 2 H G \right) \tmop{dH} = \]
\[ 2 \int_{\mathbbm{R}} \left( H - H^2 \right) \tmop{dH} + 2
\int_{\mathbbm{R}} \left( H - G \right)^2 \tmop{dH} \geq \frac{1}{3} \]
with equality if and only if $H \equiv G$.
\endproof
\noindent\proof{Proof of Lemma~\ref{lem2} (the discrete case)}
The lemma is true for random variables that take two values each (by inspection).
Assume now it is true for random variables with $k$ values. Let $A_k$ be $P
\left( U_1, U_2 < V_1, V_2 \right) + \text{$P \left( U_1, U_2 > V_1, V_2
\right)$}$ and $B_k$ be $P \left( U_1, V_1 > U_2, V_2 \right)$ for some
random variables with $k$ values.
Suppose now that $U_i^{\ast}$ has a mixed distribution: it has the same
distribution as $U_i $with probability $1 - \alpha$ and takes a different
value larger than all previous possible values of $U_i$ with probability
$\alpha$.
Similarly $V_i^{\ast}$ has a mixed distribution: it takes the same distribution
as $V_i $ with probability $1 - \beta$ and takes the different value
mentioned before with probability $\beta$.
We now have
\[ \left. \text{$P \left( U^{\ast}_1, U_2^{\ast} < V_1^{\ast}, V_2^{\ast}
\right) + \text{$P \left( U^{\ast}_1, U_2^{\ast} > V_1^{\ast}, V_2^{\ast}
\right)$} = \alpha^2$} \beta^2 \text{$A_k + \beta^2 \left( 1 - \alpha^2
\right) + \alpha^2 \left( 1 - \beta^2 \right.$} \right) \]
and
\[ P \left( U_1, V_1 > U_2, V_2 \right) = \alpha^2 \beta^2 \text{$B_k +$}
\alpha \beta \left( 1 - \alpha \beta \right) . \]
Hence
\[ \text{$P \left( U^{\ast}_1, U_2^{\ast} < V_1^{\ast}, V_2^{\ast} \right) +
\text{$P \left( U^{\ast}_1, U_2^{\ast} > V_1^{\ast}, V_2^{\ast} \right)$} -
2$} P \left( U_1, V_1 > U_2, V_2 \right) = \]
\[ \alpha^2 \beta^2 \left( A_k - 2 B_k \right) + \beta^2 \left( 1 - \alpha^2
\right) + \alpha^2 \left( 1 - \beta^2 \right) - 2 \alpha \beta \left( 1 -
\alpha \beta \right) = \]
\[ \alpha^2 \beta^2 \left( A_k - 2 B_k \right) + \left( \alpha - \beta
\right)^2 . \]
But $A_k \geq 2 B_k$ with equality if and only if the distributions are identical, so
now for random variables taking $k + 1$ values the statement is true with equality if and only if $A_k
= 2 B_k$ and $\alpha = \beta$, that is, when the distributions are identical.
\endproof
\noindent\proof{Proof of Theorem~\ref{th1}}
We assume the distribution of $\left(X_i,Y_i\right) $ is
continuous. We can see that we need to prove that
\[ P \left( Y_1, Y_2 < Y_3, Y_4 \&X_1, X_2 < X_3, X_4 \right) + P \left( Y_1,
Y_2 > Y_3, Y_4 \&X_1, X_2 < X_3, X_4 \right) \geq \]
\[ \frac{1}{3} P \left( X_1, X_2 < X_3, X_4 \right) . \]
This is because
\[ P \left( Y_1, Y_2 < Y_3, Y_4 \&X_1, X_2 < X_3, X_4 \right) + P \left( Y_1,
Y_2 > Y_3, Y_4 \&X_1, X_2 < X_3, X_4 \right) + \]
\[ 4 P \left( Y_1, Y_3 > Y_2, Y_4 \&X_1, X_2 < X_3, X_4 \right) = 1. \]
We now have that
\[ P \left( Y_1, Y_2 < Y_3, Y_4 \&X_1, X_2 < X_3, X_4 \right) + P \left( Y_1,
Y_2 > Y_3, Y_4 \&X_1, X_2 < X_3, X_4 \right) = \]
\[ 2 \int \int \int_{\mathbbm{R}^3} P \left( Y < y | X = x_1 \right) P \left(
Y < y | X = x_2 \right) \left( 1 - P \left( Y < y | X > x_1 \vee x_2
\right) \right) \cdot \]
\[ \left( P \left( X > x_1 \vee x_2 \right) \right)^2 P \left( Y \in \tmop{dy}
| X > x_1 \vee x_2 \right) P \left( X \in \tmop{dx}_1 \right) P \left( X
\in \tmop{dx}_2 \right) + \]
\[ 2 \int \int \int_{\mathbbm{R}^3} \left( 1 - P \left( Y < y | X = x_1
\right) \right) \left( 1 - P \left( Y < y | X = x_2 \right) \right) P
\left( Y < y | X > x_1 \vee x_2 \right) \cdot \]
\[ \left( P \left( X > x_1 \vee x_2 \right) \right)^2 P \left( Y \in \tmop{dy}
| X > x_1 \vee x_2 \right) P \left( X \in \tmop{dx}_1 \right) P \left( X
\in \tmop{dx}_2 \right) = \]
\[ 2 \int \int \int_{\mathbbm{R}^3} \left\{ P \left( Y < y | X = x_1 \right) P
\left( Y < y | X = x_2 \right) + P \left( Y < y | X > x_1 \vee x_2 \right)
\right. \]
\[ \left. - P \left( Y < y | X = x_1 \right) P \left( Y < y | X > x_1 \vee x_2
\right) - P \left( Y < y | X = x_2 \right) P \left( Y < y | X > x_1 \vee
x_2 \right) \right\} \cdot \]
\[ \left( P \left( X > x_1 \vee x_2 \right) \right)^2 P \left( Y \in \tmop{dy}
| X > x_1 \vee x_2 \right) P \left( X \in \tmop{dx}_1 \right) P \left( X
\in \tmop{dx}_2 \right) = \]
We now rewrite the quantity in brackets as
\[ 2 \int \int \int_{\mathbbm{R}^3} \left\{ P \left( Y < y | X > x_1 \vee x_2
\right) - \left( P \left( Y < y | X > x_1 \vee x_2 \right) \right)^2
\right\} \cdot \]
\[ \left( P \left( X > x_1 \vee x_2 \right) \right)^2 P \left( Y \in \tmop{dy}
| X > x_1 \vee x_2 \right) P \left( X \in \tmop{dx}_1 \right) P \left( X
\in \tmop{dx}_2 \right) + \]
\[ 2 \int \int \int_{\mathbbm{R}^3} \left( P \left( Y < y | X > x_1 \vee x_2
\right) - P \left( Y < y | X = x_1 \right) \right) \left( P \left( Y < y |
X > x_1 \vee x_2 \right) - P \left( Y < y | X = x_2 \right) \right) \cdot
\]
\begin{eqnarray}
\left( P \left( X > x_1 \vee x_2 \right) \right)^2 P \left( Y \in \tmop{dy}
| X > x_1 \vee x_2 \right) P \left( X \in \tmop{dx}_1 \right) P \left( X
\in \tmop{dx}_2 \right)
\label{pthm1}
\end{eqnarray}
Now \
\[ \int_{\mathbbm{R}^{}} \left\{ P \left( Y < y | X > x_1 \vee x_2 \right) -
\left( P \left( Y < y | X > x_1 \vee x_2 \right) \right)^2 \right\} P
\left( Y \in \tmop{dy} | X > x_1 \vee x_2 \right) = \frac{1}{6} \]
so the first of the two integrals in (\ref{pthm1}) is equal to
\[ \frac{2}{6} \int \int_{\mathbbm{R}^2} \left( P \left( X > x_1 \vee x_2
\right) \right)^2 P \left( X \in \tmop{dx}_1 \right) P \left( X \in
\tmop{dx}_2 \right) = \frac{1}{3} P \left( X_1, X_2 < X_3, X_4 \right) . \]
It remains to show that the second integral is non-negative (with 0 for
independence). We have
\[ \int \int \int_{\mathbbm{R}^3} \left( P \left( Y < y | X > x_1 \vee x_2
\right) - P \left( Y < y | X = x_1 \right) \right) \left( P \left( Y < y |
X > x_1 \vee x_2 \right) - P \left( Y < y | X = x_2 \right) \right) \cdot
\]
\[ \left( P \left( X > x_1 \vee x_2 \right) \right)^2 P \left( X \in
\tmop{dx}_1 \right) P \left( X \in \tmop{dx}_2 \right) P \left( Y \in
\tmop{dy} | X > x_1 \vee x_2 \right) = \]
\[ \int \int \int_{\mathbbm{R}^3} \left( P \left( Y < y, X > x_1 \vee x_2
\right) P \left( X \in \tmop{dx}_1 \right) - P \left( Y < y, X \in
\tmop{dx}_1 \right) P \left( X > x_1 \vee x_2 \right) \right) \cdot \]
\[ \left( P \left( Y < y, X > x_1 \vee x_2 \right) P \left( X \in \tmop{dx}_2
\right) - P \left( Y < y, X \in \tmop{dx}_2 \right) P \left( X > x_1 \vee
x_2 \right) \right) P \left( Y \in \tmop{dy} | X > x_1 \vee x_2 \right) .
\]
The integrand of the expression above has the same sign as
\[ \int \int_{\mathbbm{R}^2} \left( P \left( X > x_1 \vee x_2 | Y < y \right)
P \left( X \in \tmop{dx}_1 \right) - P \left( X \in \tmop{dx}_1 | Y < y
\right) P \left( X > x_1 \vee x_2 \right) \right) \cdot \]
\begin{eqnarray}
\left( P \left( X > x_1 \vee x_2 | Y < y \right) P \left( X \in \tmop{dx}_2
\right) - P \left( X \in \tmop{dx}_2 | Y < y \right) P \left( X > x_1 \vee
x_2 \right) \right) \frac{P \left( X > x_1 \vee x_2 | Y = y \right)}{P
\left( X > x_1 \vee x_2 \right)}.
\label{pthm2}
\end{eqnarray}
To simplify notation, we now define $P \left( X < x \right) = G \left( x
\right)$, $P \left( X > x \right) = \overline{G} \left( x \right)$, $P \left( X \in
\tmop{dx} \right) = g \left( x \right) \tmop{dx}$, $P \left( X < x | Y < y
\right) = H \left( x \right)$, $P \left( X > x | Y < y \right) = \overline{H}
\left( x \right)$, $P \left( X \in \tmop{dx} | Y < y \right) = h \left( x
\right) \tmop{dx},$ $P \left( X < x | Y = y \right) = F \left( x \right)$, \
$P \left( X > x | Y = y \right) = \overline{F} \left( x \right)$ and $P \left( X
\in \tmop{dx} | Y = y \right) = f \left( x \right) \tmop{dx}$. We rewrite
(\ref{pthm2}) as
\[ \int \int_{\mathbbm{R}^2} \left( \overline{H} \left( x_1 \vee x_2 \right) g
\left( x_1 \right) - \overline{G} \left( x_1 \vee x_2 \right) h \left( x_1
\right) \right) \cdot \]
\[ \left( \overline{H} \left( x_1 \vee x_2 \right) g \left( x_2 \right) - \overline{G}
\left( x_1 \vee x_2 \right) h \left( x_2 \right) \right) \frac{\overline{F}
\left( x_1 \vee x_2 \right)}{\overline{G} \left( x_1 \vee x_2 \right)}
\tmop{dx}_1 \tmop{dx}_2 = \]
\[ 2 \int_{\mathbbm{R}} \int_{- \infty}^{x_2} \left( \overline{H} \left( x_2
\right) g \left( x_1 \right) - \overline{G} \left( x_2 \right) h \left( x_1
\right) \right) \tmop{dx}_1 \left( \overline{H} \left( x_2 \right) g \left( x_2
\right) - \overline{G} \left( x_2 \right) h \left( x_2 \right) \right)
\frac{\overline{F} \left( x_2 \right)}{\overline{G} \left( x_2 \right)} \tmop{dx}_2 =
\]
\[ 2 \int_{\mathbbm{R}} \left( \overline{H} \left( x_2 \right) G \left( x_2 \right)
- \overline{G} \left( x_2 \right) H \left( x_2 \right) \right) \left( \overline{H}
\left( x_2 \right) g \left( x_2 \right) - \overline{G} \left( x_2 \right) h
\left( x_2 \right) \right) \frac{\overline{F} \left( x_2 \right)}{\overline{G} \left(
x_2 \right)} \tmop{dx}_2 = \]
\[ 2 \int_{\mathbbm{R}} \left( G \left( x_2 \right) - H \left( x_2 \right)
\right) \left( \overline{H} \left( x_2 \right) g \left( x_2 \right) - \overline{G}
\left( x_2 \right) h \left( x_2 \right) \right) \frac{\overline{F} \left( x_2
\right)}{\overline{G} \left( x_2 \right)} \tmop{dx}_2 = \]
\[ 2 \int_{\mathbbm{R}} \left( G \left( x_2 \right) - H \left( x_2 \right)
\right) \left( \overline{H} \left( x_2 \right) g \left( x_2 \right) - \overline{G}
\left( x_2 \right) g \left( x_2 \right) + \overline{G} \left( x_2 \right) g
\left( x_2 \right) - \overline{G} \left( x_2 \right) h \left( x_2 \right)
\right) \frac{\overline{F} \left( x_2 \right)}{\overline{G} \left( x_2 \right)}
\tmop{dx}_2 = \]
\[ 2 \int_{\mathbbm{R}} \left( G \left( x_2 \right) - H \left( x_2 \right)
\right) \left( \overline{H} \left( x_2 \right) - \overline{G} \left( x_2 \right)
\right) g \left( x_2 \right) \frac{\overline{F} \left( x_2 \right)}{\overline{G}
\left( x_2 \right)} \tmop{dx}_2 + \]
\[ 2 \int_{\mathbbm{R}} \left( G \left( x_2 \right) - H \left( x_2 \right)
\right) \left( g \left( x_2 \right) - h \left( x_2 \right) \right) \overline{G}
\left( x_2 \right) \frac{\overline{F} \left( x_2 \right)}{\overline{G} \left( x_2
\right)} \tmop{dx}_2 = \]
\[ \]
\[ 2 \int_{\mathbbm{R}} \left( G \left( x_2 \right) - H \left( x_2 \right)
\right)^2 g \left( x_2 \right) \frac{\overline{F} \left( x_2 \right)}{\overline{G}
\left( x_2 \right)} \tmop{dx}_2 + \]
\[ 2 \int_{\mathbbm{R}} \left( G \left( x_2 \right) - H \left( x_2 \right)
\right) \left( g \left( x_2 \right) - h \left( x_2 \right) \right)
\int_{x_2}^{\infty} f \left( z \right) \tmop{dzdx}_2 = \]
\[ 2 \int_{\mathbbm{R}} \left( G \left( x_2 \right) - H \left( x_2 \right)
\right)^2 g \left( x_2 \right) \frac{\overline{F} \left( x_2 \right)}{\overline{G}
\left( x_2 \right)} \tmop{dx}_2 + \]
\[ 2 \int_{\mathbbm{R}} \int_{- \infty}^z \left( G \left( x_2 \right) - H
\left( x_2 \right) \right) \left( g \left( x_2 \right) - h \left( x_2
\right) \right) \tmop{dx}_2 f \left( z \right) \tmop{dz} = \]
\[ 2 \int_{\mathbbm{R}} \left( G \left( x_2 \right) - H \left( x_2 \right)
\right)^2 g \left( x_2 \right) \frac{\overline{F} \left( x_2 \right)}{\overline{G}
\left( x_2 \right)} \tmop{dx}_2 + \int_{\mathbbm{R}} \left( G \left( z
\right) - H \left( z \right) \right)^2 f \left( z \right) \tmop{dz} \]
which is non-negative and can only be $0$ if $G \left( x_{} \right) = H \left(
x_{} \right)$ for all $x$, that is if $P \left( X < x \right) = P \left( X < x
| Y < y \right)$ for (almost) all $x$ and $y$, which is equivalent to
independence.
\endproof
\section{Comparison to other approaches}\label{sec-alt}
If one of the variables is binary, our approach leads to the \cvm\ test, as described in Section~\ref{cvmsec}. In Sections~\ref{sec-hoeff} and~\ref{sec-dewh} the two direct competitors to tests based on $\tau^*$ known to the authors, one originally by \citeA{hoeffding48ind} and another originally by \citeA{dewet80} and \citeA{deheuvels81}, are discussed. Both these competitors share the property of our approach that they are rank-based and consistent for all alternatives.
Useful and extensive discussions of other ordinal data and nonparametric methods for independence testing are given \citeA{agresti10,hw99} and \citeA{sheskin07}.
\subsection{The two-sample case and relation to the \cvm\ test}\label{cvmsec}
The two-sample \cvm\ test is used to test whether or not two samples are drawn from the same distribution, and is consistent for any alternative.
We show that if one of the variables is binary and the conditional distribution of the other variable is continuous, a test based on $\tau^*$ coincides with the \cvm\ test.
We argue that the test based on $\tau^*$ has a possible advantage for discrete distributions.
We now give the relationship with the \cvm\ test.
Let $G$ be the distribution function of $U$ and let $H$ be the distribution function of $V$. With $F_\alpha=\alpha G+(1-\alpha)H$ let
\begin{eqnarray}
C_\alpha = \int (G-H)^2dF_\alpha\label{cvm2}
\end{eqnarray}
Then $C_\alpha$ is zero if and only if $G=H$, i.e., if and only if $X$ and $Y$ are independent. The \cvm\ test statistic is based on an estimate of $C_p$. First, note:
\begin{lemma}\label{lem5}
For $\alpha\in\bR$, $C_\alpha$ does not depend on $\alpha$.
\end{lemma}
\proof{Proof} The lemma is implied because
\[\int(G-H)^2dH - \int(G-H)^2dG = \int(G-H)^2d(G-H) = \left[\frac13(G-H)^3\right]^\infty_{-\infty} = 0\]
\endproof
The relationship between the \cvm\ test, which is based on $C_p$, and $\tau^*$ is given by the following:
\begin{lemma}\label{lem1a}
If $X$ is binary and $Y$ given $X$ is continuous, then $\tau^* = 6p^2(1-p)^2C_p$.
\end{lemma}
\proof{Proof}
First note that
\begin{eqnarray}
\int HdH = \frac12 \hspace{6mm}\mbox{and}\hspace{6mm} \int H^2dH = \frac13 \label{sqint}
\end{eqnarray}
Now continuity implies
\begin{eqnarray*}
P(U_1,U_2<V_1,V_2) + P(V_1,V_2<U_1,U_2) + 4 P(U_1,V_1<U_2,V_2) = 1
\end{eqnarray*}
Hence by~(\ref{cvm1}) and~(\ref{sqint}),
\begin{eqnarray*}
\tau^*
&=& 2p^2(1-p)^2
\left[
\frac32 P(U_1,U_2<V_1,V_2) + \frac32 P(V_1,V_2<U_1,U_2) - \frac12
\right]\\
&=& 2p^2(1-p)^2
\left[
3\int G^2HdH + 3\int (1-G)^2HdH - \frac12
\right]\\
&=& 2p^2(1-p)^2
\left[
3\int (G^2-2GH+H)dH - \frac12
\right]\\
&=& 2p^2(1-p)^2
\left[
3\int (G^2-2GH+H^2)dH
\right]\\
&=& 2p^2(1-p)^2
\left[
3\int (G-H)^2dH
\right]
\end{eqnarray*}
The lemma now follows from Lemma~\ref{lem5}
\endproof
Note that, for discrete distributions, the definition of $C_p$ unsatisfactorily depends on the way $G$ and $H$ are defined, e.g., whether we define $G(u)=P(U<u)$ or $G(u)=P(U\le u)$. Since $\tau^*$ deals naturally with discreteness of random variables, tests based on $\tau^*$ might serve as an alternative for the \cvm\ test if discreteness is present.
\subsection{Hoeffding's $H$}\label{sec-hoeff}
Hoeffding's \citeyear{hoeffding48ind} coefficient for measuring deviation from independence for a bivariate distribution function $F_{12}$ with marginal distribution functions $F_1$ and $F_2$ is defined as
\begin{eqnarray*}
H = \int (F_{12}-F_1F_2)^2dF_{12}
\end{eqnarray*}
(See also \citeNP{bkr61,hw99} and \citeNP{wm08}.) An alternative formulation given by Hoeffding is
\begin{eqnarray*}
H = \frac14 E\phi((X_1,X_2,X_3)\phi((X_1,X_4,X_5)\phi((Y_1,Y_2,Y_3)\phi((Y_1,Y_4,Y_5)
\end{eqnarray*}
where $\phi(z_1,z_2,z_3)=I(z_1\ge z_2)-I(z_1\ge z_3)$.
Interestingly, Hoeffding's $H$ has an interpretation in terms of concordance and discordance probabilities closely related to the interpretation of $\tau^*$.
With
\begin{eqnarray*}
F_{12}(x,y) &=& P(X\le x,Y\le y)\\
F_{1\overline 2}(x,y) &=& P(X\le x,Y> y) = F_1(x)-F_{12}(x,y)\\
F_{\overline 12}(x,y) &=& P(X> x,Y\le y) = F_2(y)-F_{12}(x,y)\\
F_{\overline 1\overline 2}(x,y) &=& P(X>x,Y>y) = 1-F_1(x)-F_2(y)+F_{12}(x,y)
\end{eqnarray*}
we have the equality
\begin{eqnarray}
F_{12}-F_1F_2 = F_{12}F_{\overline1\overline2} - F_{1\overline2}F_{\overline12}\label{f12}
\end{eqnarray}
Let five points be $H$-concordant if four are configured as in Figure~\ref{concdisc}(a) and the fifth is on the
point where the axes cross and, analogously, five points are $H$-discordant if four are configured as in Figure~\ref{concdisc}(b) and the fifth is on the
point where the axes cross. Denote the probabilities of $H$-concordance and discordance by $\Pi_{C_5}$ and $\Pi_{D_5}$.
Then
\begin{eqnarray*}
\int \left(F_{12}^2F_{\overline1\overline2}^2+F_{1\overline 2}^2F_{\overline 12}^2\right)dF_{12} = \frac{2!2!}{5!}\Pi_{C_5} = \frac1{30}\Pi_{C_5}
\end{eqnarray*}
and
\begin{eqnarray*}
\int F_{12}F_{1\overline 2}F_{\overline 12}F_{\overline1\overline2}dF_{12} = \frac1{5!}\Pi_{D_5} = \frac1{120}\Pi_{D_5}
\end{eqnarray*}
Hence, using~(\ref{f12}),
\begin{eqnarray*}
H = \int\left(F_{12}F_{\overline1\overline2} - F_{1\overline2}F_{\overline12}\right)^2dF_{12} = \frac{2\Pi_{C_5}-\Pi_{D_5}}{60}
\end{eqnarray*}
\subsection{De Wet and Deheuvels' $D$}\label{sec-dewh}
A coefficient related to Hoeffding's $H$ is
\begin{eqnarray*}
D = \int (F_{12}-F_1F_2)^2dF_{1}F_{2}
\end{eqnarray*}
Tests based on estimators of this coefficient were studied by \citeA{dewet80} and \citeA{deheuvels81}.
\citeA{bergsma06} showed that in the continuous case, with
\begin{eqnarray*}
h(z_1,z_2,z_3,z_4) = |z_1-z_2|+|z_3-z_4|-|z_1-z_3|-|z_2-z_4|,
\end{eqnarray*}
\begin{eqnarray*}
D = Eh(F_1(X_1),F_1(X_2),F_1(X_3),F_1(X_4))h(F_2(Y_1),F_2(Y_2),F_2(Y_3),F_2(Y_4))
\end{eqnarray*}
The latter definition is suitable for discontinuous $X$ and $Y$ as well and has the advantage that it does not depend on the way $F_{12}$ is defined.
\subsection{Comparison of $\tau^*$, $H$, and $D$}
Hoeffding's $H$ is more complex than $\tau^*$ in that it is based on concordance and discordance of five points rather than four.
See also \citeA{kruskal58}, who compares Kendall's tau and Spearman's rho which are based on concordance and discordance probabilities of two and three points respectively and for this reason expresses some tentative preference for the simpler Kendall's tau.
A possible drawback of $D$ is that there seems to be some arbitrariness in the use of rank scores; for example, one might also use normal scores.
Of the three coefficients, $\tau^*$ may thus have some advantage. Tests based on $\tau^*$ are discussed in the next section, which includes a remark on power.
\section{Testing independence}\label{sec-applic}
A suitable test for independence is a permutation test which rejects the independence hypothesis for large values of $t^*$. For every permutation $\pi$ of the observed $y$-values, the sample $\tau^*$-value $t_\pi^*$ is computed, and the $p$-value is the proportion of the $\{t_\pi^*\}$ which exceed $t^*$. As is well-known, the permutation test conditions on the empirical marginal distributions, which are sufficient statistics for the independence model. In categorical data analysis, it is usually referred to as an exact conditional test. In practice, the number of permutations may be too large to compute and a random sample of permutations is taken, which is also called a resampling test.
Note that there doesn't seem to be a need for an asymptotic approximation to the sampling distribution of $t^*$.
Direct evaluation of $t^*$ requires computational time $O(n^4)$, which may be practically infeasible for moderately large samples, but $t^*$ can be well-approximated by taken a random sample of subsets of four observations. The proof of Theorem~\ref{th1} suggests that the complexity can be reduced to $O(n^3)$. An open problem is what the minimum computational complexity of computing $t^*$ is.
Below, we compare various tests of independence using an artificial and a real data set.
An artificial multinomial table of counts is given in Table~\ref{ct1}, where $X$ and $Y$ are ordinal variables with~5 and~7 categories. Visually, we can detect an association pattern, but as it is non-monotonic a test based on Kendall's tau does not yield a significant $p$-value. The chi-square test also yields a non-significant $p=0.253$ (based on $10^6$ resamples), while a permutation test based on $t^*$ yields $p=0.035$ ($10^4$ resamples), giving evidence of an association. We also did tests based on $D$, which yields $p=0.045$ ($10^4$ resamples), and the test based on Hoeffding's $H$ yields $p=0.028$ ($4000$ resamples).
In this example, using a test designed for ordinal data with power against broad alternatives, evidence for an association can be found, which is not possible with a nominal data test like the chi-square test or with a test based on Kendall's tau.
\begin{table}
\begin{center}
\begin{tabular}{|ll|ccccccc|}
\hline
&& \multicolumn{7}{l|}{$Y$}\\ \
& & \,1\, & \,2\, & \,3\, & \,4\, & \,5\, & \,6\, & \,7\, \\ \hline
$X$ & 1 & 2 & 1 & 0 & 0 & 0 & 1 & 2 \\
& 2 & 1 & 2 & 0 & 0 & 0 & 2 & 1 \\
& 3 & 0 & 0 & 2 & 1 & 2 & 0 & 0 \\
& 4 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\
& 5 & 0 & 0 & 1 & 2 & 1 & 0 & 0 \\ \hline
\end{tabular}
\end{center}
\caption{Artificial contingency table containing multinomial counts. Kendall's tau and the chi-square test do not yield a significant association, but a permutation test based $t^2$ yields $p=0.035$}
\label{ct1}
\end{table}
\begin{table}
\begin{center}
\begin{tabular}{|ll|cccc|}
\hline
&& \multicolumn{4}{l|}{Change in size of Ulcer Crater ($Y$)}\\ \
& & Larger & Healed ($<\frac23$) & Healed ($\ge\frac23$) & Healed \\ \hline
Treatment group ($X$) & $A$ & 6 & 4 & 10 & 12 \\
& $B$ & 11 & 8 & 8 & 5 \\ \hline
\end{tabular}
\end{center}
\caption{Results of study comparing two treatments of gastric ulcer}
\label{ct2}
\end{table}
Table~\ref{ct2} shows data from a randomized study to compare two treatments for a gastric ulcer crater, and was previously analyzed in \citeA{agresti10}. Using $10^5$ resamples, the chi-square test yields $p=0.118$, Kendall's tau yields $p=0.019$, $t^*$ yields $p=0.028$, $D$ yields $p=0.026$, and using $10^4$ resamples Hoeffding's $H$ yields $p=0.006$.
For future research, more understanding is needed concerning the power of the tests based on $t^*$, $H$, $D$, and the chi-square test. We have done some limited simulations and, unsurprisingly, found that for all four there are alternatives for which they are most powerful. However, so far we were unable to detect any patterns which can lead to useful advice on when to use which test; it appears we need a better understanding than we currently appear to have of the types of alternatives that might be of most interest.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 5,138
|
Q: JSON::ParserError in Ruby Am trying to read data I just stored in the .json file, when running the script, am getting this error:
/Users/topazjos/.rvm/gems/ruby-3.0.0/gems/json-2.6.1/lib/json/common.rb:216:in `parse': 859: unexpected token at '[] (JSON::ParserError)
from /Users/topazjos/.rvm/gems/ruby-3.0.0/gems/json-2.6.1/lib/json/common.rb:216:in `parse'
from /Users/topazjos/Documents/SQL & Ruby Projects/school-library/savedata.rb:48:in `fetch_people_datas'
it is showing that the error is coming from thefecth_people_datas method
class IOmanager
def save_people(persons)
file = File.open('./people.json', 'a')
person_data = persons.map do |person|
if person.instance_of?(Teacher)
{ occupation: 'Teacher', name: person.name, age: person.age, specialization: person.specialization }
else
{ occupation: 'Student', name: person.name, age: person.age, parent_permission: person.parent_permission }
end
end
file.puts(JSON.generate(person_data))
end
def fetch_people_datas
return [] unless File.exist?('./people.json')
file = File.read('./people.json')
array = []
if file.empty?
array
else
person_data = JSON.parse(file)
person_data.map do |data|
if data['occupation'] == 'Teacher'
teacher = Teacher.new(data['age'], data['specialization'], data['name'])
array.push(teacher)
else
student = Student.new(data['age'], data['classroom'], data['name'], data['parent_permission'])
array.push(student)
end
end
end
array
end
end
then am calling that method like this
class CreatePeople
def initialize
@iomanager = IOmanager.new
@books = @iomanager.fetch_book_data
@persons = @iomanager.fetch_people_datas
@rentals = []
end
def create_student
puts 'Create a new student'
print 'Enter student age: '
age = gets.chomp.to_i
print 'Enter name: '
name = gets.chomp
print 'Has parent permission? [Y/N]: '
parent_permission = gets.chomp.downcase
case parent_permission
when 'n'
Student.new(age, 'classroom', name, parent_permission: false)
@persons << student
puts 'Student doesnt have parent permission, cant rent books'
when 'y'
student = Student.new(age, 'classroom', name, parent_permission: true)
@persons << student
puts 'Student created successfully'
end
end
def create_teacher
puts 'Create a new teacher'
print 'Enter teacher age: '
age = gets.chomp.to_i
print 'Enter teacher name: '
name = gets.chomp
print 'Enter teacher specialization: '
specialization = gets.chomp
teacher = Teacher.new(age, specialization, name)
@persons << teacher
puts 'Teacher created successfully'
end
def json_runner
@iomanager.save_book(@books)
@iomanager.save_people(@persons)
@iomanager.save_rental(@rentals)
end
end
I have used the same way to read from the previous file fecth_book_data inside the same class and it has worked but I don't understand what went wrong here
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 621
|
Q: Error on HTTPS based service: Underlying connection was closed, an unexpected error occured I am getting an error while send the dataset to https based web service. The error is underlying connection was closed; An unexpected error occured on a send.
Kindly suggest me the appropriate solution.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 3,355
|
Jammz is a grime MC and record producer from Hackney, East London and the founder of the record label I Am Grime.
Career
Although he had already released an early mixtape, Jammz started to make a proper name for himself in 2014, and was frequently cited as part of grime's "radio renaissance" of those years due to his appearances on radio stations such as Rinse FM, BBC Radio 1xtra, NTS and Radar Radio.
His single 'Hit Then Run', released in 2015, was voted as Noisey's Third Best Grime Track of that year and was playlisted on BBC Radio 1xtra. He also collaborated with Plastician on the single 'London Living', and Finn & Fallow on the single 'Final Warning'.
In March 2016, Jammz supported Kano on the UK leg of his Made In The Manor tour and featured on the front cover of the Observer Music Magazine, alongside Krept & Konan, Stormzy, Novelist and Little Sims as part of an article titled 'How British MCs Found a Voice of Their Own'. In July 2016, he featured in GQ's documentary The Business of Grime.
In November 2016 Jammz released his Warrior EP to acclaim from Fader, Complex, FACT Mag, Noisey and more, and he performed at his first London headline show in December of that year.
In 2017 he collaborated with DJ Q on the single 'Who's That Girl', an answer song to Dizzee Rascal's "I Luv U", and released the singles 'Oh Please' and 'Know Yourself' (with Westy).
Personal life
Jammz is of Jamaican and Vincentian descent.
References
External links
1991 births
People from the London Borough of Hackney
Grime music artists
Living people
English people of Jamaican descent
English people of Saint Vincent and the Grenadines descent
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 9,351
|
Due unità della United States Navy hanno portato il nome di USS Boise:
– incrociatore leggero della classe Brooklyn, varato nel 1936, ceduto all'Argentina nel 1951 e rinominato Nueve de Julio, radiato nel 1978
– sottomarino nucleare d'attacco della classe Los Angeles, varato nel 1991 e ancora in servizio attivo
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 2,769
|
If Your Weight Is Bringing You Down, This Is the Pill to Take to Feel Happier and Speed Slimming
By Linda Rodgers
It's no secret that some medications have unintended side effects, good and bad. But when you have a chronic health condition, you usually have to put up with these unwanted consequences, until science comes along with a better pill.
RELATED: These Common Anti-Heartburn Drugs Have Serious Side Effects--and May Not Keep Your Heartburn Away
This is especially true for people suffering from depression. Taking an antidepressant usually lifts your mood, but the life-saving drug can wreak havoc with your metabolism--and cause you to pack on some unwanted pounds.
One antidepressant doesn't have that side effect, according to a new study. Researchers from Group Health Research Institute, a Seattle-based nonprofit consumer health group, found that after two years, people taking bupropion (Wellbutrin) were more likely to lose weight, not gain it. And the antidepressant worked just as well as the others in improving a person's outlook. (It also is effective in helping people quit smoking.)
RELATED: This Major News Will Change How Depression Is Treated From Now On
The evidence was so clear that the doctors involved in the study recommended that bupropion be the antidepressant of choice for depressed people who were obese or overweight. "It makes sense for doctors and patients to choose antidepressants on the basis of their side effects, costs, and patients' preferences--and, now, on whether patients are overweight or obese," one of them said in a statement.
So if you're depressed and overweight, talk to your doctor about whether it makes sense for you to start--or switch to--bupropion.
via EurekAlert!
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,528
|
'use strict';
exports.inject = function (app) {
app.factory('UserService', exports.service);
return exports.service;
};
exports.service = function ($http) {
return {}
};
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,157
|
B-29 "Dauntless Dotty". This print renders both aircraft faithfully that was personally approved by Morgan. Matted and framed in a beautiful dark stained wood frame.
B-29 "Dauntless Dotty". This print renders both aircraft faithfully that was personally approved by Morgan. Available signed and unsigned.
Although Boyington did not fly in this a/c, it has been the subject of many artists. I thought I would follow in the masters footsteps and render one myself for my small mini reunions.
With a score of 40 kills, Bong became Americas 'Ace of Aces'. Maj. Bong had his sweetheart Marge Vettendahl's photo applied to his P-38 with the name "Marge" painted next to it. During his second leave back to the states, Bong gave Marge a 'piggyback' ride in a P-38 to show her what it was like to fly in a high performance fighter. This sketch design was approved by Marge for a print.
can offer them to you for framing. These are the first few available by us.
An 8"x10" glossy print reproduced from the original negative.
B-24 (F-7) 20th Combat Map. Sq.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 5,190
|
{"url":"https:\/\/blog.paperspace.com\/filters-in-convolutional-neural-networks\/","text":"# Filters In Convolutional Neural Networks\n\nThis blog details different techniques for filtering image data and explores what these filters actually do to an image as it passes through the layers of a Convolutional Neural Network (CNN). https:\/\/blog.paperspace.com\/filters-in-convolutional-neural-networks\/\n\n4 months ago \u00a0 \u2022 \u00a0 9 min read\n\nBring this project to life\n\nIn Multi Layer Perceptrons (MLP), learnable parameters are the network's weights which map to feature vectors. In the context of Convolutional Neural Networks however, learnable parameters are termed filters, filters which are 2-dimensional matrices\/arrays commonly square in size.\n\nIn my previous article, we developed a bit of our intuition on how these filters are used with images via a process called convolution. In this article, we are going to explore what these filters actually do to an image as it passes through the layers of a Convolutional Neural Network (CNN).\n\n### Neural Nets and Feature Extraction\n\nAn essential capability of neural networks is their ability to extract features from data so as to then use them in archiving a certain goal, be it classification, regression etc. In MLPs, this process is easy to conceptualize, data points which are often times attributes of a particular instance of data are mapped to trained weights in order to combine or transform them in some form into essential features. On the other hand, feature extraction is not as clear cut when it comes to CNNs as they do not deal with a vector of attributes rather they deal with images which are a 2-dimensional matrix of attributes (pixels).\n\nBesides, what would represent a feature when it comes to images anyway? When talking about a tabular dataset of houses for instance, columns which hold attributes such as number of bedrooms or size of living room are said to be features of a particular house instance. So what about an enhanced definition (480p) image of a cat which has a size of (640, 480) pixels? This image has 640 columns and 480 rows, a total of 307,200 attributes (pixels), what represents features in this case?\n\n### Images On Edge\n\nA lot of the details of what makes up an image is actually contained in its edges or outlines. It's one of the reasons why we can easily distinguish objects in cartoon sketches. In fact, there are numerous studies to suggest that edge perception is one of the first techniques utilized by the human brain when processing visual cues coming from the eyes (Willian Mcllhagga, 2018). Edge perception is not just limited to human vision, some studies have argued that it is one of the reasons why Avians (birds) are so adept at dodging obstacles mid-flight at such high speeds as well as landing on small targets from so far away with pinpoint accuracy (Partha Bhagavatula et al, 2009).\n\n### CNNs and Human Vision\n\nThere has been a lot of talk about how neural networks mimic the human brain. One scenario that gives some credence to this is the fact that just as the human brain begins to process visual cues coming from the eyes by perceiving edges, Convolutional Neural Networks also begin to extract features from images by detecting edges, in fact it can be said that edges represent image features. The tools it uses for this purpose are its learnable parameters, its filters.\n\nThat is specifically the purpose served by filters in a Convolutional Neural Network, they are there to help extract features from images. While the first few layers of a CNN are comprised of edge detection filters (low level feature extraction), deeper layers often learn to focus on specific shapes and objects in the image. For the purpose of this article, I will be focusing on edge detection in the first few layers as it is quite an intriguing process and the filters are easily comprehensible.\n\n### Filtering Out Edges\n\nThe cool thing about Convolutional Neural Networks is that they can learn custom edge detection filters based on the probability distribution of pixels in a certain dataset and the network's specific objective. Notwithstanding, there are some classic manually formulated edge detection filters which can be used to develop an intuition of what edge detection looks like in a computer vision context. They are the Prewitt, Sobel, Laplacian, Robinson Compass and Krisch Compass filters.\n\nTo really examine what these filters do let's do some grunt work by applying them unto images using the manually written convolution function given below.\n\nThis function replicates the convolution process with an additional step of ReLU activation as expected in a typical convnet. Utilizing this function, we will be detecting edges in the image below using the filters listed above.\n\nBring this project to life\n\n#### Prewitt Filters\n\nThe Prewitt operator is comprised of two filters which help to detect vertical and horizontal edges. The horizontal (x-direction) filter helps to detect edges in the image which cut perpendicularly through the horizontal axis and vise versa for the vertical (y-direction) filter.\n\n# utilizing the horizontal filter\nconvolve('image.jpg', horizontal)\n# utilizing the vertical filter\nconvolve('image.jpg', vertical)\n\n#### Sobel Filters\n\nJust like the Prewitt operator, the Sobel operator is also made up of a vertical and horizontal edge detection filter. Detected edges are quite similar to results obtained using Prewitt filters but with a distinction of higher edge pixel intensity. In other words, edges detected using the Sobel filters are sharper in comparison to Prewitt filters.\n\n# utilizing the horizontal filter\nconvolve('image.jpg', horizontal)\n# utilizing the vertical filter\nconvolve('image.jpg', vertical)\n\n#### Laplacian Filter\n\nUnlike the Prewitt and Sobel filters, the Laplacian filter is a single filter which detects edges of different orientation. From a mathematical standpoint, it computes second order derivatives of pixel values unlike the Prewitt and Sobel filters which compute first order derivatives.\n\n# utilizing the filter\nconvolve('image.jpg', filter)\n\nThe Robinson Compass masks are edge detection filters which are made up of 8 different filters accounting for the 8 geographical compass directions as shown in the image above. These filters help to detect edges oriented in those compass directions. For brevity, just two of the filters are used for illustration purposes.\n\n# utilizing the north_west filter\nconvolve('image.jpg', north_west)\n# utilizing the north_east filter\nconvolve('image.jpg', north_east)\n\nSimilar to the Robinson Compass masks, the Krisch Compass mask is also comprised of 8 filters which help to detect edges in geographical compass directions. two of the filters are used below.\n\n# utilizing the south_west filter\nconvolve('image.jpg', south_west)\n# utilizing the south_east filter\nconvolve('image.jpg', south_east)\n\n### Filter Notations\n\nThere's a pretty important statement above which you most likely missed,\n\nThe horizontal (x-direction) filter helps to detect edges in the image which cut perpendicularly through the horizontal axis and vice versa for the vertical (y-direction) filter.\n\nThat statement might seem a bit confusing but I'll break it down further in this section. Consider the image below, the figure on the right is what the human eye sees while the figure on the left is what a computer perceives. As evident in the image, the white line delineates a clear vertical edge on the black 'canvas', to the human eye this is evident because of the contrast between that line and its surroundings (In the same vane, a computer needs to be able to perceive this change in contrast on a pixel level and that's essentially what edge detection entails).\n\nIn order to physically encounter this edge however, one would need to run a finger from left to right (horizontally) or vice versa. The same applies to edge detection filters, to detect a vertical edge you need to utilize an horizontal filter.\n\nLet's attempt to detect edges in the image using both the horizontal and vertical Prewitt filters, the math behind the edge detection process is illustrated in the image below. The math behind the convolution process is quite easy to follow as outlined;\n\n1. Place the filter at the top left corner.\n2. Perform element-wise multiplication.\n3. Compute a cumulative sum.\n4. Return obtained sum as a corresponding pixel in an empty array.\n5. Shift the filter to the right by one pixel and repeat steps 1 - 4 as you continue to populate the first row in the empty array towards the right.\n6. Stop when the filter falls out of bounds.\n7. Shift the filter downwards by one pixel to the second row.\n8. Repeat steps 1 - 6 as you populate the second row in the empty array.\n9. Do the same for all rows until the filter falls out of bounds in the vertical axis (dim 1).\n\nActivation is done using the ReLU function which simply casts any negative pixel to 0. After convolution and activation, the vertical edge is highlighted by the horizontal filter while the vertical filter returns a blacked out image (all zero pixels) meaning it has detected no edge.\n\nThe resulting detected edge is visualized below. Following the same logic, if the line were to be horizontal, representing an horizontal edge, the vertical filter would highlight the horizontal edge while the horizontal filter returns a blacked out image.\n\n### Using The Convolution Function\n\nFor those who might want to use the convolution function above on a different image or to test out different filters for edge detecting or other image processing tasks, this section is a quick guide on how to do so.\n\nThe function takes 3 parameters namely, 'image_filepath', 'filter' and 'title'.\n\n#### 'Image_filepath'\n\nThis refers to the location of the desired image on your local drive or cloud. In a case where your image is in the current working directory, all you need to do is enter the image name complete with its file extension. If not, you'll need to provide an absolute path, something of the form 'C:\/Users\/Username\/Downloads\/image_name.jpg' (forward slash in this case since we are working in Python).\n\n#### Filter\n\nThis is in fact the filter you would like to use in the convolution process. Filters are quite easy to make using NumPy as demonstrated below. All you need to do afterwards is to supply the filter object in the function.\n\n# creating a Prewitt horizontal filter\nprewitt_x = np.array(([-1, 0, 1],\n[-1, 0, 1],\n[-1, 0, 1]))\n\n# creating a laplacian filter\nlaplacian = np.array(([-1, -1, -1],\n[-1, 8, -1],\n[-1, -1, -1]))\n\n#### Title\n\nThis will be the title of the image visualization provided when the function is used. It's an empty string by default but feel free to provide a suitable title as desired.\n\n### Final Remarks\n\nWhat makes Convolutional Neural Networks special is their ability to extract features from a 2-dimensional representation of data such as image pixels. The features are extracted as edges using tools contained in the neural network called filters.\n\nIn this article, we have examined what edge detection\/feature extraction looks like from a computer vision point of view using some predefined filters. It is worthy of note however that a CNN will not be using these predefined filters for edge detection, it will rather learn the best filters to detect edges and extract features in the dataset of interest.","date":"2022-11-27 05:40:27","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\": 0.47141510248184204, \"perplexity\": 1020.3926844763685}, \"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-2022-49\/segments\/1669446710192.90\/warc\/CC-MAIN-20221127041342-20221127071342-00854.warc.gz\"}"}
| null | null |
Charm City Roller Derby (CCRD), is a flat track roller derby league in Baltimore, Maryland. Founded in 2005, Charm City is a member of the Women's Flat Track Derby Association (WFTDA).
History and league structure
The league was established in 2005 as Charm City Roller Girls, when Caroline Donaghy returned to Baltimore from Houston, where she had skated with the Space City Roller Girls, and began promoting the intention to start a league in Baltimore. The first public Charm City game was held in 2006 at Skateland in Putty Hill. Upon the league's formation, it comprised four teams: the Junkyard Dolls, the Mobtown Mods, the Night Terrors and the Speed Regime. As early as 2008, games were being held at the Fifth Regiment Armory in Baltimore, and by 2009, the league was holding games at Du Burns Arena in Canton before sellout crowds of 2,000 fans.
As of 2017, Charm City has three travel teams: the All-Stars represent the league in WFTDA competition, and Female Trouble and the Trouble Makers are B and C teams, respectively. A three-team home league features the Dundalk Deviants, Hampden Hons and Pigtown Butchers. The All-Stars are known for wearing helmets that feature elements of the state flag of Maryland, which they first donned in 2008. Charm City Roller Derby operates as a limited liability company.
League member Joy Collision was a member of Team USA, representing the United States at the 2011 Roller Derby World Cup.
WFTDA competition
Charm City was announced as a new member of the WFTDA in May 2007. The Charm City All-Stars first competed at WFTDA Playoffs in 2008 as the sixth seed at the Eastern Regional, where they won their opening game against Cincinnati Rollergirls, lost their quarterfinal to the Windy City Rollers but recovered to defeat Detroit to finish in fifth place. In 2009 at the Eastern Regional, Charm City won their opener against DC Rollergirls but then lost their semifinal to Philly Roller Girls to put them in the third-place game, which they lost 156-143 to Boston to finish in fourth place.
In 2010, an opening round win over Steel City was followed by a loss to Gotham Girls Roller Derby to put them in the third-place game again, this time beating Boston 162-128 to finish third and qualify for WFTDA Championships for the first time. At Championships, Charm City won their opening game against Minnesota Rollergirls 249-118, but then lost their quarterfinal to Rocky Mountain Rollergirls 165-103 to end their weekend. At the 2011 East Regional (co-hosted by Charm City and DC Rollergirls at Du Burns Arena), the All-Stars defeated Steel City 189-94 to again finish in third place and advance to Championships. At Championships, Charm City lost 160-121 to Minnesota in the opening round. At the 2012 East Regional, Charm City finished in third place for the third straight year, via a 183-159 victory over London Rollergirls, and again qualified for Championships. At Championships, a 268-141 loss to Denver in the opening round eliminated the All-Stars.
In 2013, the WFTDA restructured the Playoff system, and Charm City qualified as the ninth seed for Division 1 Playoffs in Salem, Oregon, where upset losses to Detroit and Sacred City Derby Girls put the All-Stars in the ninth-place game against the Chicago Outfit, which they won, 189-177. At the 2014 Division 1 Playoff in Salt Lake City, fourth-seeded Charm City finished in fourth place with a 183-156 loss to Rocky Mountain. In 2015 at Tucson, Charm City was the fifth seed but dropped down to an eighth-place finish with a 191-165 loss to Team United Roller Derby. In 2016, Charm City dropped into Division 2 for the first time, albeit as the top seed at the Playoff in Lansing, but were eliminated from Division 2 Championships contention with an upset loss to Calgary, 216-191. Charm City earned third place with a narrow 197-194 win over Wasatch Roller Derby. Charm City returned to Division 1 Playoffs in 2017 at Malmö as the twelfth seed, but lost both their games to Helsinki Roller Derby (308-144) and Rainy City Roller Derby (258-78) to finish outside of the medals.
In 2018, Charm qualified for the WFTDA North American East Continental Cup held in Kalamazoo, Michigan as the eighth seed, but after losing their opening game to North Star Roller Derby 259-176 finished out of the medals.
Rankings
CR = consolation round
References
External links
Official website
Roller derby leagues in Maryland
Roller derby leagues established in 2005
Sports competitions in Baltimore
Women's Flat Track Derby Association Division 1
Women's sports in Maryland
2005 establishments in Maryland
|
{
"redpajama_set_name": "RedPajamaWikipedia"
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| 1,886
|
**ALSO BY JOHN C. MAXWELL**
RELATIONSHIPS
_Encouragement Changes Everything_
_Everyone Communicates,_
_Few Connect_
_Relationships 101_
_Winning with People_
EQUIPPING
_The 15 Invaluable Laws of Growth_
_The 17 Essential Qualities_
_of a Team Player_
_The 17 Indisputable_
_Laws of Teamwork_
_Developing the Leaders Around You_
_Equipping 101_
_Intentional Living_
_Learning from the Giants_
_Make Today Count_
_Mentoring 101_
_My Dream Map_
_Put Your Dream to the Test_
_Running with the Giants_
_Talent Is Never Enough_
_Today Matters_
_Wisdom from Women in the Bible_
_Your Road Map for Success_
ATTITUDE
_Attitude 101_
_The Difference Maker_
_Failing Forward_
_How Successful People Think_
_Sometimes You Win—_
_Sometimes You Learn_
_Sometimes You Win—Sometimes_
_You Learn for Teens_
_Success 101_
_Thinking for a Change_
_The Winning Attitude_
LEADERSHIP
_The 21 Irrefutable Laws_
_of Leadership_
_The 21 Indispensable_
_Qualities of a Leader_
_The 360 Degree Leader_
_Developing the Leader_
_Within You 2.0_
_Good Leaders Ask Great Questions_
_The 5 Levels of Leadership_
_Leadership 101_
_Leadership Promises for Every Day_
© 2019 by John C. Maxwell
All rights reserved. No portion of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, scanning, or other—except for brief quotations in critical reviews or articles, without the prior written permission of the publisher.
Published by HarperCollins Leadership, an imprint of HarperCollins Focus LLC.
Published in association with Yates & Yates, www.yates2.com.
Scripture quotations are from _The Message_. Copyright © by Eugene H. Peterson 1993, 1994, 1995, 1996, 2000, 2001, 2002. Used by permission of Tyndale House Publishers, Inc.
Epub Edition December 2018 9780718098605
ISBN 978-0-7180-9860-5 (eBook)
ISBN 978-0-7180-9850-6 (HC)
ISBN 978-1-4002-1294-1 (IE)
ISBN 978-1-4002-1539-3 (signed)
**Library of Congress Cataloging-in-Publication Data**
Library of Congress Control Number: 2018957778
_Printed in the United States of America_
19 20 21 22 23 LSC 10 9 8 7 6 5 4 3 2 1
Ebook Instructions
In this ebook edition, please use your device's note-taking function to record your thoughts wherever you see the bracketed instructions [Your Notes]. Use your device's highlighting function to record your response whenever you are asked to checkmark, circle, underline, or otherwise indicate your answer(s).
Information about External Hyperlinks in this ebook
Please note that endnotes in this ebook may contain hyperlinks to external websites as part of bibliographic citations. These hyperlinks have not been activated by the publisher, who cannot verify the accuracy of these links beyond the date of publication.
This book is dedicated to Ed Bastian.
The day I met you, I could see you were a leader of the highest caliber. _Fortune_ has called you one of the world's greatest leaders. As chief executive officer of Delta Air Lines, you lead one of the world's most admired companies. For more than a decade, I have watched you lead with integrity, respect, perseverance, and a servant's heart in the midst of extraordinary global change. I know of no one better at leadershifting than you. Thank you for your friendship and the way you model leadership to the world.
CONTENTS
ACKNOWLEDGMENTS
CHAPTER 1: WHY EVERY LEADER NEEDS TO LEADERSHIFT
CHAPTER 2: SOLOIST TO CONDUCTOR
CHAPTER 3: GOALS TO GROWTH
CHAPTER 4: PERKS TO PRICE
CHAPTER 5: PLEASING PEOPLE TO CHALLENGING PEOPLE
CHAPTER 6: MAINTAINING TO CREATING
CHAPTER 7: LADDER CLIMBING TO LADDER BUILDING
CHAPTER 8: DIRECTING TO CONNECTING
CHAPTER 9: TEAM UNIFORMITY TO TEAM DIVERSITY
CHAPTER 10: POSITIONAL AUTHORITY TO MORAL AUTHORITY
CHAPTER 11: TRAINED LEADERS TO TRANSFORMATIONAL LEADERS
CHAPTER 12: CAREER TO CALLING
ABOUT THE AUTHOR
NOTES
ACKNOWLEDGMENTS
I want to say thank you to Charlie Wetzel and the rest of the team who assisted me with the formation and publication of this book. And to the people in my organizations who support it. You all add incredible value to me, which allows me to add value to others.
Together, we're making a difference!
CHAPTER 1
WHY EVERY LEADER NEEDS TO LEADERSHIFT
_Change or die._
—THOMAS EDGLEY
I've been wanting to write a book on the idea of _leadershifts_ for a long time because a lot has changed in the decades I've been studying and practicing leadership. In the 1970s when I was new to my career, I could find very few books on leadership. Back then, _management_ ruled the business world and Peter Drucker was the king. That started to change toward the end of the 1980s, as a few authors were starting to write leadership books. People eagerly bought and read them. Why? Because they could feel that life was moving faster, change was becoming normal, and they needed a way to navigate the world's complexities, which were becoming more challenging.
People need to learn leadership to be successful. The principles of management, which had been taught for years, depended on stability and known factors. As expressed by Eric J. McNulty, director of research at the National Preparedness Leadership Initiative:
Management systems and processes tend to be linear. They assume that similar inputs will result in similar outputs. In many situations, this holds true. Leadership, however, requires a more nuanced view of the world because it involves people: what motivates them, what their interests are, and how engaged they become. Mechanical systems may be linear but as soon as the human element becomes involved the system becomes both complex and adaptive.
Where management took stability for granted, leadership provides principles that work in the face of the unknown. Back in the eighties, people were looking for leaders to guide them, and people running organizations recognized the need to become leaders themselves. As they began to apply leadership principles to their world, they thrived. That's why for the last thirty years, leadership has ruled the business world.
FAST IS FASTER—FORWARD IS SHORTER
As fast as the pace was in the 1980s, when I look back it seems slow by today's standards. Life moves _much_ faster now. The rate at which we must deal with change and uncertainty can seem insane.
For several years one of my organizations, the John Maxwell Team, has asked me to do short videos they post daily called Minute with Maxwell. My team will set me up in front of a camera and then give me a word or phrase, asking me to react to it or teach on it for a minute or so. It's fun and the video gets posted online as a kind of mentoring moment. Recently, for one of these sessions, the phrase they gave me was _fast forward_. What immediately came to my mind were the words _faster_ and _shorter_. Here's what I mean.
The future seems to be coming at us faster than ever. It is not going to slow down. Would anybody seriously consider the idea that tomorrow will be at a slower pace than today? Technology, social media, and the rate of change will never allow that to happen. To go forward, we need to move faster. And as leaders, we need to stay ahead, we need to see more than others, and we need to see before others.
Because of the pace of change, we also need to be flexible. Do you remember the old Mother Goose rhyme "Jack Be Nimble"?
Jack be nimble,
Jack be quick,
Jack jump over
The candlestick.
The more nimble, adaptable, and flexible we are, the more quickly we can move and change.
Traditionally, in athletic races, the first three finishers are recognized, and all three receive prizes. Today, outside of sports, it seems as though only winners get recognized and rewarded. As the saying goes, coming in second means you're the first loser. That's why speed and agility are so important.
A few years ago I saw an article in the _New York Times_ on cheetahs, which can teach us a lot about the importance of agility when it comes to success.
Anyone who has watched a cheetah run down an antelope knows that these cats are impressively fast. But it turns out that speed is not the secret to their prodigious hunting skills: a novel study of how cheetahs chase prey in the wild shows that it is their agility—their skill at leaping sideways, changing directions abruptly and slowing down quickly—that give those antelope such bad odds. . . .
The cheetahs ran as fast as 58 miles an hour, and their average speed was 33 mph. High-speed runs accounted for only a small portion of the total distance covered by the cheetahs each day, the researchers found.
They also found that a cheetah can slow down by as much as 9 mph in a single stride—a feat that proves more helpful in hunting than the ability to break highway speed records. A cheetah often decelerates before turning, the data showed, and this enables it to make the tight turns that give it an advantage over its fast and nimble prey.
Forward is also shorter. As a young leader, I was taught that to be effective in leading my organization, I should create a long-range plan of ten years, a medium-range plan of five years, and a short-range plan of two years. That seems absurd now. Today a long-range plan may be two years. Technology and innovation move so quickly that everything is going forward in a shorter time frame. As leaders, we can't drag our feet or take too long making assessments. We have to change, reread our situation, and change again. And _continue_ changing.
How does a leader do more than just hang on and survive in such an environment? The key is to learn how to continually make _leadershifts_. What is a leadershift? It is an ability and willingness to make a leadership change that will positively enhance organizational and personal growth.
Educator and author Bruna Martinuzzi cited a study conducted by an organization called the Economist Intelligence Unit. It identified the top three leadership qualities that will be important in the years ahead: "the ability to motivate staff (35 percent); the ability to work well across cultures (34 percent); and the ability to facilitate change (32 percent)." All three of these qualities require adaptability. Martinuzzi likened this to the Chinese proverb that says that the wise adapt themselves to circumstances, as water molds itself to the pitcher. Perhaps at no other time in recent history has adaptability been more important than it is now. " _Adaptability_ —the ability to change (or to be changed) to fit new circumstances—is a crucial skill for leaders."
A more recent study conducted by Right Management and published in _The Flux Report_ made it clear that the need for adaptability is only increasing. They asserted that 91 percent of future recruiting in the workplace will be based on people's ability to deal with change and uncertainty.
* * *
LEADERSHIFTING IS THE ABILITY AND WILLINGNESS TO MAKE A LEADERSHIP CHANGE THAT WILL POSITIVELY ENHANCE ORGANIZATIONAL AND PERSONAL GROWTH.
* * *
Good leaders adapt. They shift. They don't remain static because they know the world around them does not remain static. This has always been true, but it's never been more obvious than today, nor has the ability to change quickly been more important. And when I say that good leaders adapt, I don't mean that they conform. As success coach Dave Martin pointed out:
There is a profound difference between adaptability and conformity. The "greats" seem to instinctively understand this difference, and while they disdain conformity, they cherish the courageous ability to adjust to changing circumstances. Conformity is the negative quality of blending in, becoming average, refusing to stand out or capitalize on one's uniqueness. Adaptability is the positive quality of being able to sense the shift in wind direction and proactively adjust one's course to take advantage of that wind shift. While conformity is a weakness based upon fear of rejection, adaptability is a strength based upon confidence in oneself and in one's own judgment and abilities.
In the face of uncertainty, people who conform pull away to a safe place to protect themselves. Adaptable leaders who make leadershifts lean into uncertainty and deal with it head on. I like what Paul Karofsky, executive director emeritus of Northeastern University's Center for Family Business, said about this, though he used the word _ambiguity_ instead of _uncertainty_ :
Ambiguity may keep people up nights, but anyone seeking exquisite simplicity in his or her career ought to look for a non-leadership position.
Leaders, by definition, have followers. Followers need direction. Direction requires decision-making. Decision-making requires consideration of options. And consideration of options involves dealing with uncertainty.
If you want to be successful as a leader, you need to learn to become comfortable with uncertainty and make shifts continually. You need to be flexible and deal with uncertainty without losing focus. Leaders who leadershift must be like water. They have to be fluid. Water finds a way, then makes a way. First it changes with its circumstances. The environment dictates the change. But moving water is also forceful. It first moves around an object, but at the same time it begins moving the object. It can wear down solid rock over time. A seemingly small shift can make a big difference. Simple and obvious it may be. Trivial it is not.
The truth is this: _every advance you make as a leader will require a leadershift that changes the way you think, act, and lead._ If you want to be an effective leader, you must leadershift. You cannot be the same, think the same, and act the same if you hope to be successful in a world that does not remain the same.
* * *
YOU CANNOT BE THE SAME, THINK THE SAME, AND ACT THE SAME IF YOU HOPE TO BE SUCCESSFUL IN A WORLD THAT DOES NOT REMAIN THE SAME.
* * *
As Malcolm Gladwell said, "That's your responsibility as a person, as a human being—to constantly be updating your positions on as many things as possible. And if you don't contradict yourself on a regular basis, then you're not _thinking_." Maybe as leaders we need to recognize the value of "mental floss." Dentists encourage us to use dental floss daily to promote the health of our teeth; we need to use mental floss to get rid of old thinking and promote the health of our leadership.
In my twenties, I was inspired by the words of nineteenth-century preacher Phillips Brooks, the author of the famous hymn "O Little Town of Bethlehem." He wrote:
Sad will be the day for every man when he becomes absolutely contented with the life he is living, with the thoughts that he is thinking, with the deeds that he is doing, when there is not forever beating at the doors of his soul some great desire to do something larger, which he knows that he was meant and made to do.
I memorized those words and have often used them to move me toward greater growth and achievement.
Leadershifting moves us forward in the face of the natural temptation to be mentally rigid. It prompts us to become more innovative and get out of our comfort zones, question conventional wisdom, and welcome change. Every leadershift you make has the potential to make you a better leader.
ARE YOU READY TO SHIFT AS A LEADER?
Before I talk about the practices involved in leadershifting, I want to lay the groundwork by describing the mind-set needed to leadershift. How open are you to change? Are you willing to start asking more questions instead of giving more answers? Are you willing to become a better listener, a better observer?
Are you willing to rely more on your intuition and your creativity? Leadershifting will require you to rely on values, principles, and strategy, but it will also push you to rely on innovation, to seek out options, to harness creativity. You'll also need to let go of some things and be dedicated to getting better.
Leadershifting is not easy, especially when you first start doing it. Often you leave behind something that has worked to pursue something untested. You'll have to deal with the tension between the stability that gives security and the adaptability that opens up opportunity. That will empower you to get better, to become someone new before you can grow into something new. The desire to improve will drive you to keep learning. But here's the good news: learning to leadershift will make you a better leader!
* * *
YOU'LL HAVE TO DEAL WITH THE TENSION BETWEEN THE STABILITY THAT GIVES SECURITY AND THE ADAPTABILITY THAT OPENS UP OPPORTUNITY.
* * *
HOW TO LEADERSHIFT
If you answered yes to the previoius questions—or you're willing to move in the direction where you'll be able to answer yes—then you're ready to take steps forward and start leadershifting. As we move forward in this book, I'll take you through eleven major leadershifts I've made in my leadership journey. But before we do that, I want to teach you seven things you must do to leadershift successfully. Embrace these practices daily, and you will be ready to face every leadershift situation with flexibility and confidence.
**1. C ONTINUALLY LEARN, UNLEARN, AND RELEARN**
I've already discussed the pace at which our world is changing. I recently read an article published by the World Economic Forum that brought light to this.
To quote Harvard Business Review's "Mind the (Skills) Gap": "The lessons learned in school can become outdated before student loans are paid off." As it points out, the skills college graduates acquire during a bachelor's degree that used to provide enough basic training to last a career, today have an expected shelf life of only five years.
In turn, studying the impact of disruptive change on existing skill sets in its recent report "The Future of Jobs," the World Economic Forum discovered that: "On average, by 2020, more than a third of the desired core skill sets of most occupations will be comprised of skills that are not yet considered crucial to the job today." Or, as lynda.com author Mark Niemann-Ross states bluntly: "In four years, you'll have to relearn 30% of your job."
How are leaders to thrive in this environment? We must learn, unlearn, and relearn. This process is essential for leadershifting. We have to embrace change every day. We must be willing to let go of what worked yesterday and learn new ways of seeing, doing, and leading. We cannot afford to be in love with any one technology or methodology. We keep learning and changing, or our leadership dies.
**2. V ALUE YESTERDAY BUT LIVE IN TODAY**
Baseball great Babe Ruth is rumored to have said, "Yesterday's homerun doesn't win today's game." Isn't that fantastic? It's a good reminder to focus on today. What we did in the past may look good on a resume, but it won't help us win today.
For years I had a sign in my office that said, "Yesterday Ended Last Night." I put it there to remind me that all the good I did yesterday won't guarantee a good day for me today, nor will all the bad that happened yesterday mean that today has to be bad. Today stands on its own. If I want a great today, I need to do what's necessary now. I can and should be grateful for yesterday, but I have to focus on today.
When I was a young author, I was mentored by a very successful writer. I will always be indebted to him for the help he gave me. One evening we were having dinner, and I shared that I was writing another book. He inquired about the thesis and content and then asked me, "John, is this going to be your best book?"
"Yes, it is!" I replied.
"Good," he said. "Because you are only as good as your last book. If you disappoint your readers, they'll always wonder if they should buy your next one."
I've never forgotten that advice. I've written and sold a lot of books over the years, but I can't rest on my past reputation. People may honor you for what you did yesterday, but they respect you for what you're doing now. I value yesterday but I live in today.
**3. R ELY ON SPEED, BUT THRIVE ON TIMING**
Having to move quickly in today's climate isn't really a choice if you want to succeed. However, timing is. As a leader who leadershifts, you need to understand the context of your environment. What is happening around you determines whether you hold fast or move forward. Leading is like knowing when to eat a pear. It's said that there is only one day in the life of a pear when it is perfect to eat. As a leader you must be able to recognize the right timing of leadershift moments. When does a team member need an encouraging pep talk and when do they need to be challenged to step up? When is the right time to add a new product or to retire an existing one that has already seen its best days? When should your organization use some of its cash to seize an opportunity, and when is that a bad idea?
For leaders, timing is critical. Good timing enables leaders to seize the moment and gain the victory for their team. That sense of timing is especially important when leadershifting. To paraphrase financier James Goldsmith, when the leader sees the bandwagon, it's too late to lead.
* * *
WHEN THE LEADER SEES THE BANDWAGON, IT'S TOO LATE TO LEAD.
* * *
**4. S EE THE BIG PICTURE AS THE PICTURE KEEPS GETTING BIGGER**
My journey leading people really began when I first understood that everything rises and falls on leadership. This truth became the foundation upon which I built my life. It continues to be the catalyst for my personal development and my training of others.
When people started asking me to speak on leadership, I didn't have much to teach. Later when I decided to write a book on the subject, I thought it would be my only one. Now I've been leading people and training leaders for more than forty-five years, and my perspective has been enlarged tremendously. The more I learn about the subject, the more I recognize I don't know enough about it. The more leadership experiences I gain, the more I realize I would benefit from more experience. There is no finish line when it comes to improving, and there is no complete picture of leadership that can be mastered. As long as I'm growing, my leadership picture will continue to enlarge. If you keep growing, yours will too.
I like to think of this process as layered learning. Each time we learn a new lesson and connect it with the many things we've already learned on the same subject, we gain depth and we see more of the big picture. This process requires time; no one can learn all the lessons at once. Putting together lessons requires intentionality, but when you do, you expand your knowledge.
My first formal leadership role was in a church in southern Indiana, in a farming community. I developed a friendship with the community banker, who one day explained to me how he decided whether or not to loan farmers money. He would ask them if they were fencing in or fencing out. If they were fencing in, they were done expanding their farm. They were intent on holding on to what they had and doing only minor improvements to their property. However, if they were fencing out, it indicated they were expanding, wanting more land for crops or livestock. They were extending their reach and striving to do more. My banker friend said, "I loan money to those who are fencing out. They need help to get bigger and better." Leadershifting is all about fencing out. It's about seeing a bigger picture and getting better.
**5. L IVE IN TODAY BUT THINK ABOUT TOMORROW**
Leaders have a natural bias toward action. They have to be proactive today for the sake of tomorrow. However, the longevity of their leadership is determined by how they think and see the future. Staying ahead of the team comes from thinking ahead of the team. If you think ahead, you can stay ahead. As political columnist George Will said, "The future has a way of arriving unannounced." We cannot recover yesterday but tomorrow is ours to win or lose.
How can we do that as leaders? What can we do today to ensure we have what we need to lead tomorrow? We have to practice what I call advance attraction, which I discovered in the 1980s. I concluded that I could experience a positive future only if I had a good dream and a good team. At that time, my dream excited me, but my team did not. How was I going to attract the team I needed to fulfill my dream?
When you become aware of what you need or want, you're better able to see it—and attract it. If you think about blue, you will see blue everywhere you look. If you start noticing blue, you will see even more blue. What you focus on expands. Awareness allows you to bring into your future the people and resources you need. It enables you to lead your life instead of merely accepting it.
Being unaware has exactly the opposite effect. Unawareness lets you see nothing, attract nothing, and receive nothing that will enhance your future. Leaders who are unaware wonder why they don't have access to the resources they need to ensure a better tomorrow. They cannot leadershift; their tomorrow will not be any better than their today.
Going back to what I did in the eighties, the first step toward getting a better team for the future was to know what I wanted and needed. I started by writing down the qualities of the team I wanted to have. This developed an increased awareness in me that promoted advance attraction. Here's how this works.
When you know who you are and you know what you want, you then know the kind of people you will attract, and the things you will discover.
Your mind will think things that will help you get what you want.
Your eyes will see things that will help you get what you want.
Your heart will feel things that will help you get what you want.
Your attitude will believe things that will help you get what you want.
Your mouth will say things that will help you get what you want.
Your actions will attract things that will help you get what you want.
As I attracted and discovered the kinds of team members I needed to realize my dream, I began to experience positive results. Today I'm abundantly reaping the benefits of this leadershift.
**6. M OVE FORWARD COURAGEOUSLY IN THE MIDST OF UNCERTAINTY**
Life expands or shrinks in proportion to our courage. When leaders fail to make a necessary leadershift because of fear or uncertainty, it only increases their fear, which results in frustration. The greater the inaction of the leaders, the more opportunities they lose because opportunities are always surrounded by uncertainty. All good things include uncertainty, and overcoming uncertainty requires courage.
I like what Brad Lomenick said about courage in his book _The Catalyst Leader_. He quoted my friend Andy Stanley, a wonderful leader who founded North Point Church. Andy was speaking to Catalyst leaders, but his words also described leaders who leadershift:
Many, many great things have begun with a single act of courage, throughout history and today. A person steps out and makes one courageous decision and that one domino starts many other dominoes falling. We have to step out and take that first step, and we may never know the ripple effect of that one courageous decision. Catalyst leaders—your decision to do something courageous may result in something greater than you ever imagined. Step out. . . .
Fear in leadership usually is connected to the uncertainty about the future. But uncertainty about the future is never going to go away. I tell leaders all the time—uncertainty is why there are leaders. Uncertainty gives you job security. Wherever there is uncertainty, there will always be a need for leaders, which means always stepping out into the unknown, always requiring courage.
Betty Bender, former president of the Library Administration and Management Association, said, "Anything I've ever done that ultimately was worthwhile initially scared me to death." When faced with uncertainty, as leaders we need to move forward courageously.
**7. R EALIZE TODAY'S BEST WILL NOT MEET TOMORROW'S CHALLENGES**
If you want to become good at leadershifting, you need to keep getting better, because tomorrow's challenges will not be won with today's abilities. Here's my strategy for getting better. My goal at the end of each day is to feel satisfied because I gave my very best, but my goal at the beginning of each day is to be dissatisfied enough to try to improve on yesterday. This interplay of dissatisfaction and satisfaction creates a tension that makes me want to improve.
As I approach a new day, I try to be my best. That will make tomorrow better. The best way to have good choices tomorrow is to make the right choices today. The best way to realize the changes we want tomorrow is to make the needed changes today. The best way to meet the challenges of tomorrow is to do our best in the challenges of today. I can't skip today and hope tomorrow is better. So every day I ask myself, "Is this the best I can do today?" In this way, I'm following the advice of my hero and mentor John Wooden, who said to make today your masterpiece.
At the same time, I don't rest on my best. You've heard that good is the enemy of great, but best is the enemy of better. I have to cultivate the dissatisfaction required to get better. I purposely create that tension every day. The question, "Is this the best I can do today?" helps me to make the most of today. The question, "Am I getting better?" spurs me on to change. I want to grow into tomorrow's challenges, not just go into them. If I keep getting better, I can leadershift better tomorrow. Yesterday's best is the foundation for tomorrow's improvement.
If you want to keep getting better so that you can become a better leadershifter, then
• **L EARN SOMETHING NEW**—Ask yourself, "When's the last time I learned something for the first time?"
• **T RY SOMETHING DIFFERENT**—Ask yourself, "When's the last time I did something for the first time?"
• **F IND SOMETHING BETTER**—Ask yourself, "When's the last time I found something better for the first time?"
• **S EE SOMETHING BIGGER**—Ask yourself, "When's the last time I saw something bigger for the first time?"
Keep in mind: everyone can improve, and everything can be improved. Every day has improvement possibilities.
Now you understand the framework for leadershifting:
• Continually Learn, Unlearn, and Relearn
• Value Yesterday but Live in Today
• Rely on Speed but Thrive on Timing
• See the Big Picture As the Picture Keeps Getting Bigger
• Live in Today but Think About Tomorrow
• Move Forward Courageously in the Midst of Uncertainty
• Realize Today's Best Will Not Meet Tomorrow's Challenges
The rest of this book focuses on the most important leadershifts I have made over the years. Without a doubt, these shifts have strengthened and sustained my leadership. Each has changed my course, setting me in a new and better direction. Each has allowed me to gain new leadership territory and grow inwardly. Each has shed light on my leader ship journey, and I believe they will help yours. Even a small shift can make a big difference.
However, these are _examples_ of leadershifting, not a blueprint. The leadershifts you need to make will be unique to your journey. While it's true that some of yours may be similar to mine, many will not be. But don't forget: _every advance you make as a leader will require a leadershift that changes the way you think, act, and lead._ When you make a leadershift, it will make you a better leader.
As you read this book, you will need to continually shift from action to reflection. I will ask questions and present challenges so that your best leader can emerge. The leadershifts in this book will not take you from bad to good. They will take you from good to better. If you try to make some small shift in that direction every day, you can and will reach your leadership potential.
CHAPTER 2
SOLOIST TO CONDUCTOR
_The Focus Shift_
_One is too small a number to achieve greatness._
—THE LAW OF SIGNIFICANCE
One of the first and most important shifts anyone must make to become a leader is from soloist to conductor. You can be a successful person on your own, but not a successful leader. I began to learn this lesson and make this shift in 1974 when I heard Zig Ziglar for the first time. Zig, who later became a good friend, made a positive impact on millions of lives, and mine was one of them.
That first time I went to see him speak, I was mesmerized. He was so dynamic. I had been trained to speak and had been speaking for about five years, but Zig was different. He moved back and forth on the stage. His delivery was distinctive with his Southern drawl. He paced his words for impact. He had charm. At one point, he even knelt to make a point and connect with us.
I loved everything about what he did that day, but what made the greatest impression on me was a statement he made. It became the catalyst for taking my leadership mind-set from soloist to conductor. Zig said, "You can get everything in life you want if you will just help enough other people get what they want."
Those words struck me like a bolt of lightning. Immediately I realized that my leadership focus was wrong. I was like a soloist who wanted the entire orchestra to serve me and my agenda. Instead, I needed to act like a conductor who worked to bring out the best in everyone around me. My agenda needed to change to how I could help others, not just myself.
Over the next couple of years, my focus shifted from me to we and I made a discovery. My increased effort to first focus on others and add value to them increased the energy of those I led—and it increased my energy while I was leading them. That's when I discovered that it's wonderful when the people help their leader, but it's even more wonderful when the leader helps the people.
* * *
MY INCREASED EFFORT TO FIRST FOCUS ON OTHERS AND ADD VALUE TO THEM INCREASED THE ENERGY OF THOSE I LED—AND IT INCREASED MY ENERGY WHILE I WAS LEADING THEM.
* * *
Recently I read an article about four musical soloists who have transitioned to become conductors. South Korean Han-Na Chang, who has enjoyed a successful international career as a cellist, recently became a full-time conductor. When asked why she began conducting, she replied:
I am drawn to the great symphonic and operatic literature, and also by the music-making and collaboration that exists between the conductor and the orchestra. . . . Collaborating with the orchestra is tremendously rewarding: Every orchestra is different, so the conductor is always trying to find the most effective way of conducting that particular orchestra, in order to unite the group behind a common vision and interpretation.
Chang pointed out that conducting is completely different from being a soloist. "When I play my instrument," she said, "what I think quite naturally and instantaneously translates into sound; when conducting, I'm making sound with a group of individuals. The possibilities and the potential of the sound of an orchestra are virtually limitless, and this is truly fascinating to me."
Eric Jacobsen, an American violinist who began conducting, spoke about the role and impact of being a conductor: "Ideally a conductor is a catalyst for mutual understanding, with the orchestra becoming greater than the sum of its parts." And Gemma New, a violinist from New Zealand who recently began conducting, said, "I became fascinated by the way orchestral music unifies and inspires everyone involved. Experiencing music together creates a strong human bond between us, no matter who we are or where we come from."
CHALLENGES LEADERSHIFTING FROM SOLOIST TO CONDUCTOR
The potential of a group is always greater than that of an individual. People working together possess limitless possibilities. They can work together to do something greater than themselves. And when they bond, they enjoy the journey of working even more. However, that doesn't mean that working together doesn't have its own challenges. When you transition from soloist to conductor, there are some realities you have to face:
**1. G OING SLOWER SO YOU CAN GO FARTHER**
You've probably heard the old expression "it's lonely at the top" applied to leadership. But think about that statement. If you're at the top all alone, where are the people you're supposed to be leading? Shouldn't they be at the top with you? If you're at the top alone, it means you took off ahead of your people and left them behind. If you climb the peaks of success alone, you're not a leader. You're a hiker. You're a leader only if you have your people with you. Your pace will be slower, but you will journey together.
Good leaders don't go to the top alone and then yell down, "Hey, people, come on up—if you can figure out how to make the climb." They make a conscious decision to slow down. They carefully choose their steps so that they can help others make the climb with them.
Think about how this must have been for cellist Han-Na Chang when she shifted from soloist to conductor. As a musician she could pick up her instrument anytime she wanted, play any music she wanted, and do so however long she wanted. She could focus on any part of the music desired or on any aspect of her technique, with no regard for others. Now, as a conductor, she can't do that. She has to make arrangements. She has to be on other people's schedules. She has to take into consideration the abilities and personalities of a large group of people. She has to communicate her vision. And in the end, she bears responsibility for their success or failure.
As I've already mentioned, leaders have a natural bias for action. Good leaders see more than others do, and they see before others do. It's in their DNA to move quickly and decisively. So their natural inclination is often to run fast on their own, to climb as high as they can. But to lead others successfully, leaders need to travel with their people, not run or climb ahead of them.
This requires a leader to do what I call the leadership dance. As you lead, your position in a group can't be static. Remember, leadership, unlike management, is dynamic. It expects change. So to do the leadership dance, you must . . .
• step _ahead_ of people, staying close enough for them to see you,
• step _beside_ people, listening to them and talking about the journey, and
• step _behind_ people, sharing words of encouragement to keep them going.
Doing this dance keeps you connected to your people and energizes everyone. And that's important, because healthy organizations are not about the one person who leads them—they are about everyone who's in them. Being a good leader is about helping people reach their potential. That doesn't happen unless the leader is willing to slow down and take the journey with them.
* * *
HEALTHY ORGANIZATIONS ARE NOT ABOUT THE ONE PERSON WHO LEADS THEM—THEY ARE ABOUT EVERYONE WHO'S IN THEM.
* * *
**2. R ECOGNIZING THAT YOU NEED OTHERS**
Another reality you must recognize when transitioning from soloist to conductor is your need for other people. You can't produce the music of an orchestra when you're trying to be a one-man (or one-woman) band. Before I heard Zig Ziglar speak and realized I needed to make a leadershift, I only thought of how people needed me. I believed I was the key to their success. But after I started focusing on helping others, I began to understand how much I needed them. Only by working together and helping one another would we be able to become successful.
Once I made that discovery, I began creating an environment where people worked together to add to one another's strengths and offset one another's weaknesses. I asked others to come alongside me and make up for my leadership deficits. I, in turn, worked to apply my strengths to their weaker areas. I made it my goal to cultivate an environment where we put completing one another ahead of competing with one another. Notice the difference between the two attitudes:
**COMPETING** | **COMPLETING**
---|---
Has a Scarcity Mind-set | Has an Abundance Mind-set
Thinks Win-Lose | Thinks Win-Win
Practices Single Thinking | Practices Shared Thinking
Excludes Others | Includes Others
A completing culture creates wins for everyone. It lifts morale. It encourages team members to make one another better. People enjoy working in such an environment.
As I worked to create a culture and environment where completing was valued, I better understood how I needed others. I also began enjoying what we were doing together.
**3. M AKING THE EFFORT TO UNDERSTAND OTHERS**
Many entrepreneurs and high achievers are able to work alone. Like good soloist musicians who choose to play in the subway, they can create music without the assistance of any other musicians. It's also true that some soloists are so talented that others are willing to work with them, even if the soloist is egotistical and inconsiderate. But no one can become a good conductor without making the effort to understand other people.
When people lead without taking the time or making the effort to understand those who are trying to follow them, the results can be tragic or comic. Several years ago, I witnessed a funny incident that occurred with my grandchildren. When they were young, we often vacationed in Coeur d'Alene, Idaho. No matter where we vacation, I always look for opportunities to do something fun with the kids. This particular year, I decided that we should organize the grandchildren into a marching band. The kids were excited as we handed out kazoos, maracas, and tambourines. We worked together on a song, and they were having a wonderful time.
When they were ready to march, I held up a whistle and baton and explained that the leader would use these to lead the band. I, of course, became the first leader to demonstrate how to direct the band. The whistle was the signal for them to get ready to march. Then when I pointed the baton forward, that was their signal to play and march. When they heard the whistle again, that was the signal to stop. For the next few minutes, I led them around the pool as they marched and made music.
As soon as I saw that they had it, I let the grandchildren take turns being the leader. They were enjoying themselves, and all was well until four-year-old John Porter was given the whistle and put in charge. He loved the idea of being in control, so he would blow the whistle to start everyone marching, but after only a few steps he would blow the whistle again to stop them. Then he'd start them. Then stop them. Start-stop. Start-stop. The kids weren't marching—they were lurching!
All the children began to protest, but John didn't care. He liked the feeling of power. It may have been the first time all of his siblings and cousins had ever done what he said.
As we watched, the adults couldn't help laughing, but the truth is that a lot of leaders in organizations employ little John's style of leadership. They like the power of bossing others around, and rarely do they think about how the people they're leading feel or what they think.
I have to confess, I was one of those leaders in my early years. As a soloist leader, I thought the symphony was there simply to accompany me. I only wanted people to understand and embrace my vision, my agenda, my journey, my talents, my heart. I was like little John, leading my team around the pool, and I was whistle happy! To make the leadershift from soloist to conductor, I had to consider everyone else. I needed to understand and embrace their thoughts, desires, talents, contribution, and journey.
Several years ago I was speaking in Buenos Aires, Argentina. One evening my host took me to a large ballroom where we watched a huge exhibition of people dancing the tango. There must have been two hundred people out on the floor in beautiful costumes. They were fantastic. Their sense of movement and rhythm was wonderful. I greatly enjoyed watching them.
Years before, my wife, Margaret, and I had taken ballroom dance lessons, so I had a little bit of appreciation for how difficult dancing is. The tango looked very complicated and difficult to execute with precision. I knew that my host was an excellent dancer, so I asked him, "What enables them to dance so flawlessly and effortlessly?"
He said the key was understanding your partner's point of view. "To be able to lead properly," he said, "you want to understand how it feels to be led. In the tango, you cannot lead without having the sense of the follower." That made sense to me. The follower has to be able to trust the leader, and she must be able to move with him in time with the music. Only together can they accomplish the dance. That cooperation and understanding also applies equally to good leadership.
**4. W ANTING OTHERS TO SHINE MORE THAN YOU DO**
My host in Argentina also shared another insight about the tango that applies to leaders who shift from soloist to conductor. He explained that the dancer who leads sets up the dancer who follows for success. The leader provides the foundation and makes it possible for both of them to successfully execute the intricate serpentine steps and kicks. As a result, the follower gives the tango its full expression. The more secure and solid the leader is, the more the follower is able to shine.
Good leaders who conduct rather than go solo want the people who work with them to shine. How do they do that? They follow this thinking:
Before I say, "Follow me," I find you.
Before I ask you to listen to me, I listen to you.
When I show you the Big Picture, you are in it.
When I point to success, I point to you.
Often you hear me say, "I need you."
Often you discover, he needed me!
After the journey, we are both exhausted.
After the victory, you hold the trophy!
Good leaders do what they can to put others in position to win. As the cofounder of the John Maxwell Team, I try to do that for the coaches who become certified through our organization. Twice a year we host a training conference for new coaches. For three days, the faculty and I get to teach attendees how to make a difference with their lives and the lives of others through coaching, training, and speaking. It's so much fun.
* * *
GOOD LEADERS DO WHAT THEY CAN TO PUT OTHERS IN POSITION TO WIN.
* * *
One of the teaching sessions I do at every conference is a lesson I call JMT-DNA. It helps coaches understand the culture of the John Maxwell Team, and it encourages them to embrace the values and behavior I embrace as a leader who wants to add value to others. In recent years, I've chosen veteran coaches and invited them to join me onstage. We talk about how they flesh out the Team values. This gives those coaches a chance to shine and helps the new coaches understand how to conduct themselves with integrity as they start their coaching and speaking careers.
After one of these sessions, a couple of coaches gave me a special gift: a Montblanc highlighter. Engraved on the side were the words, "You highlight our lives." What a wonderful gesture that was to me, because I do strive to highlight others. Every day I look for opportunities to lift up people. To do it, I follow a simple formula:
• see the possibilities in all people,
• honor them in front of others,
• invite them to help achieve the vision,
• notice what they do well and compliment them, and
• thank them to make sure they know they're valued.
I strive to do this every day. As you can see, none of these actions takes brilliance or a high degree of skills. But they do all require intentionality. If you want to become a good conductor, give them a try. Help others to shine.
**5. H ELPING OTHERS TO BECOME BETTER EVERY DAY**
To become a successful leadership conductor, you must go slower so you can go farther, recognize that you need others, make the effort to understand others, and want others to shine more than you do. But you will also need to learn how to do things every day that help the people you lead to improve. This requires taking the focus off yourself and looking for ways you can help others reach their potential. Sometimes that can be a challenge.
A few years ago, I was getting ready to speak to a large group in Kiev, Ukraine, and my interpreter and I were in the green room getting acquainted. We had never worked together, but as we chatted, it became clear that he was familiar with me because he had read a lot of my books.
About ten minutes before I was scheduled to go out onstage, I could tell he was wanting to communicate something important to me. He said, "I know you teach a lot about leaders adding value to others, but you need to know that message will not work here. For three generations, people here have been under leadership that has taken value from them, not added value to them."
As he left to prepare for our time onstage, I sat in my chair and realized that I had a big challenge ahead of me. How could I expect the people to help others when the only model of leadership they'd ever seen had leaders who took from them and added value only to themselves? How could I connect with them?
That night I walked out onstage and asked, "How many of you are suspicious of leaders?" It looked like every hand was raised.
"How many of you have been hurt by leaders?" Once again, hands were raised everywhere. Then I said to the audience, "Everything rises and falls on leadership. For three generations, you have experienced leadership that makes everything fall. Tonight I'm going to help you learn how to help people, add value to them, and help them rise under your leadership."
I went on to give them the three questions followers ask of their leaders:
1. Do you care for me?
2. Can I trust you?
3. Can you help me?
As I said each question, I asked if it resonated with them, and each time they affirmed that it did.
Making the shift so that you're doing something every day to add value to others makes good leadership possible. A few years ago, my organizations partnered with Rob Hoskins, the CEO of One Hope, to develop curriculum to teach leadership to high school students. The program was piloted in Ghana.
Before the course was taught to a group of teenagers, the participants were asked to complete a survey. One question asked was, "Do you want to become a leader?" When they were asked before going through the curriculum, 95 percent of the respondents answered no. Their opinion of leadership and leaders was negative because most of them had observed corrupt and manipulative leaders taking from others rather than adding to them. Their leaders didn't care about them, so they didn't care to become leaders. However, after taking the course, their attitudes about leadership had shifted. When asked the same question, 85 percent of them responded with a yes. Why? They had been taught that leadership was about helping people, adding value to them, and using influence to improve their community. That's something they wanted to be a part of.
CHANGE YOUR FOCUS FROM RECEIVING TO GIVING
As I've already mentioned, as a young leader I was focused on how people could help me, not on how I could help them and add value to them. My thinking was selfish. It was also shortsighted. Having lived in a farming community early in my career, I should have known better. I should have thought about the sowing and reaping principle: sowing always precedes reaping.
As leaders, our question each day should not be, "Will I reap a harvest?" Instead, it should be, "Have I sowed seeds today?" I know—I'm changing my metaphor from music to farming, but stay with me. Said another way, am I trying to add value or take value? Am I focused on receiving or giving? As a soloist, it's very easy to make everything about myself: How am I performing? Is the orchestra making me sound good? Is my technique as good as I want it to be? Is my audience appreciating me and my performance? Is this moment helping my career?
Good leaders shift from being self-focused to others-focused. They give more than they take. They focus on sowing not reaping. As leaders, we need to maintain a seed-sowing mind-set. What does that mean? It means we should . . .
• Focus on adding value daily.
• Add as much value as possible as often as possible.
• Never wait to add value.
• Give without keeping score so motives stay pure.
• Welcome any return as an unexpected blessing.
I want to spend the remainder of this chapter on the idea of adding value to those we "conduct." I want to drill down on each aspect of this mind-set so that you can embrace and practice it as a leader. So let's tackle each one in turn:
**1. F OCUS ON ADDING VALUE DAILY**
Every day I look at my calendar and ask myself, _Where can I add value today?_ This question prepares me mentally to be ready to add value to others within the framework of my day. I review the scheduled meetings and activities to discover where I can be intentional about helping people.
I also ask myself, _What additional opportunities to help others will be given to me today?_ When I ask myself this question in the morning, I usually don't know what the answer will be. But by asking it, I create positive anticipation, which prepares me mentally and emotionally to seek out and identify moments when I will be able to sow positive seeds in the lives of others.
My experience over the years has convinced me that we receive what we believe, and that applies to opportunities to add value to others. Because I expect to have many opportunities, I'm able to act on them. This is part of a positive cycle, a circle of action that makes the world a better place. It looks like this:
Belief encourages anticipation. Anticipation creates intention. Intention helps us prioritize focus. Focus helps us see opportunity. Only when we see the opportunity are we able to take action on it. When we do, it inflames our passion to do more good. That in turn fuels belief. And the cycle begins all over again. This is a circle you definitely want to keep unbroken!
**2. A DD AS MUCH VALUE AS POSSIBLE AS OFTEN AS POSSIBLE**
It's clear that there is a direct relationship between the seeds we sow and the harvest we reap. The amount of value we add to others determines the possible return. The fewer the seeds, the smaller the harvest. The more seeds, the greater the harvest. This seems obvious. So, I have a question for you. Why do so many people sow so few seeds? Why do people not give more generously to others? Why do people not help others more? Everyone would like to reap a great harvest. I would, wouldn't you? How can you hope to have a big return with a small investment? The foundation and core of every realized dream come from sowing positive seeds. As leaders, we must stop wishing and start working. Instead of looking for the "secret sauce" of success, we must start sowing seeds of success.
* * *
AS LEADERS, WE MUST STOP WISHING AND START WORKING. INSTEAD OF LOOKING FOR THE "SECRET SAUCE" OF SUCCESS, WE MUST START SOWING SEEDS OF SUCCESS.
* * *
My friend James Crocker, a successful entrepreneur, recently shared a story with me. He had agreed to be a sponsor for a charity event and had decided along with his wife that the money they gave for sponsorship would be the extent of their contribution. But when they attended the banquet that was part of the event and heard the organization's vision and needs, they decided to give more money to the cause. Later that night after he got home, James wondered if they had given too much.
As he processed this question, he thought about something that had occurred to him several months before. James and a few of his friends went out on a boat trip to fish for lobsters and had succeeded in gathering a massive catch of 125 lobsters. When he got home, he had a freezer full of lobsters—more than enough to last him an entire year.
The day after James got home, his friend Jeff dropped by the house, and James offered him a lobster. Jeff was delighted.
This interaction prompted James to ask himself, _Who else do I know who might like to have a lobster?_ James got so excited by the idea of giving friends lobsters that by the end of the week, he had given away 122 lobsters, leaving only three for himself. He had such a great time giving, he didn't even mind that his supply had dwindled from enough for a year to enough for a meal.
A few days later, James went into his garage and was assaulted by a terrible stench. He followed his nose to the freezer and opened it to find that the electricity had gone out, and his remaining three lobsters had spoiled.
As he cleaned up the mess, he felt sorry for himself. But then he remembered all the lobsters he had given away, and it gave him great joy. If he hadn't shared his bounty with others, all of it would have been wasted.
James applied his lobster lesson to his donation at the charity event, and he was glad to have given more. He discovered that you don't lose the seeds you sow. The only ones wasted are the ones you don't sow. He had embraced the truth of this paradoxical statement: what you keep you lose, and what you lose you keep.
**3. N EVER WAIT TO ADD VALUE**
Too many people wait to do good. It's as though they're waiting for permission. Or inspiration. But we should never delay sowing seeds that benefit others. Instead, we should follow the motto: be the first to give or add value to another person when you can.
When you add value to others—especially when you do it early and unprompted—you inspire others with your example. I know I've been inspired by the positive actions of others. For example, when my mentor Les Parrott shared with me that the reason he wrote books was to add value to people, I was inspired to start doing the same. Going back to my childhood, when I watched my father walk slowly through the crowd to touch the lives of others, I could see how people positively responded to him, and I wanted to do the same. These examples inspired me to be more giving, to sow seeds into the lives of others.
There's another good reason not to wait to help others. People remember those who added value to them, and they're especially grateful to those who helped them first. I know I am. Thousands of people have sowed positive seeds into my life—too many to count. However, I remember many of those who were the first to sow into my life in a particular way. My fourth-grade teacher, Mr. Horton, was the first person to tell me I was a leader. Glen Leatherwood, my junior high Sunday school teacher, was the first to share with me that there was a calling in my life. My mother was the first person to unconditionally love me. Professor Don Brown was the first person who told me I was gifted, and pastor Paul Dorsey was the first one to say my future held great promise.
Should I continue? I could name a hundred people who were the first to sow positive seeds in my life in a particular area. I remember so many of them. Why? They were first. We can remember hundreds of firsts in our lives, yet we have difficulty remembering even a handful of people who added value second in a given area. Being first sets givers apart.
Don't hesitate to help another person by sowing a positive seed in his or her life. Add value as early and often as you can. Help others to "play music better." You just might become the leader someone remembers for encouraging them to greatness.
**4. G IVE WITHOUT KEEPING SCORE SO MOTIVES STAY PURE**
I know that I've already explained how we can't reap a harvest if we don't sow seeds, and we can't get a return without first giving. But receiving should not be our motive for giving. We live in a tit-for-tat culture. People are willing to scratch our backs if we're willing to scratch theirs. As leaders who add value to others, we should never keep score. We should sow seeds because it's the right thing to do. That's the only way to be sure our motives remain pure.
My thinking has changed over the years in this area. In the beginning, I was motivated by the return I would receive. I was focused on the harvest. I already shared how Zig Ziglar's quote about helping others changed my focus. But over time, I realized that placing emphasis on the return was diminishing the joy of helping others. I was thinking about how much and how long I had to give, not on how I was helping. Besides, when you add value to others, there isn't a guaranteed return.
At that time, my focus began to shift from return to recognition. I realized that even if I never saw a return, I could at least receive recognition for the effort I was making. After all, abundant seed sowers are not common. When they show up, they stand out. And I liked being recognized for giving. But again, I realized that my quest for recognition undermined my efforts to help others. I'm sorry to say that there were times I'd hesitate to give unless someone was watching to see it. Anonymous givers don't get the photo op. I know—it's unfortunate, but that's the way I thought.
My attitude began shifting when I remembered the words of Jesus, who said: "Whenever you did one of these things to someone overlooked or ignored, that was me—you did it to me." Because I'm a person of faith, those words convicted me. But they also assured me. God sees the value we add to others, and it's like we did it for him. That finally brought me to the correct belief about helping others—that it is the right thing to do. It's always the right thing to do—anytime, anyplace, anyone. And the right way to do it is any way you can. Any day we are giving is a good day—and we should never keep score.
**5. W ELCOME ANY RETURN AS AN UNEXPECTED BLESSING**
When my leadership mind-set began focusing on adding value by sowing positive seeds in the lives of others, I became more creative about how I could do that. I started my career by speaking once a week to my tiny congregation. Soon I started creating resources and sharing them. In time, I added writing. I started teaching at conferences, and later I started hosting my own events. I trained leaders so that they could train the people who followed them. Beginning in 2009, I expanded to include social media. I started companies that develop leaders in businesses and corporations. And I started training coaches.
All that time, my focus was on adding value. My goal was only to sow seeds, but I have to say, the return has been incredible. The influence I have been given and the value I've added is far greater than I ever imagined it could be. And it feels as though the harvest has multiplied way beyond the seeds I've sown. That has been a great blessing. If you keep sowing seeds and you do it while focused on the giving rather than the receiving, I believe you, too, will receive a harvest of unexpected blessings.
These are my thoughts on adding value. And that's what leaders do who shift from soloist to conductor. They focus on helping others to be their best. In the end, can you be a successful person as a soloist? The answer is undoubtedly yes. Can you be a successful leader? I would say maybe, but only in a very limited way. To reach your leadership potential—and more importantly, to help others reach their individual and team potential—you need to make the shift from soloist to conductor. If you are willing to make that shift and do the work of leading others well, then you might have the opportunity to live a life like the one described by author Matthew Kelly, who wrote:
In a land where there are no musicians;
In a land where there are no storytellers, teachers, and poets;
In a land where there are no men and women of vision and leadership;
In a land where there are no legends, saints, and champions;
In a land where there are no dreamers,
The people will most certainly perish.
But you and I, we are the music makers;
We are the storytellers, teachers, and poets;
We are the men and women of vision and leadership;
We are the legends, the saints, and the champions;
And we are the dreamers of the dreams.
I would add that we are the conductors, who help others make beautiful music together.
CHAPTER 3
GOALS TO GROWTH
_The Personal Development Shift_
_Improving yourself is the first step in improving everything else._
—UNKNOWN
When I started my leadership career, I had two goals. I wanted to help the people in my congregation, and I hoped to someday—by the end of my career—grow a church to an attendance of five hundred people. I had a pretty good sense of how to accomplish the first task. I had watched my father help people every day of my life, plus I had natural people skills. But I had no idea how to go about accomplishing the second task other than to work hard.
In _The 15 Invaluable Laws of Growth_ , I wrote about a meeting I had in 1972 with Curt Kampmeier, a salesman from Success Motivation. Curt introduced me to a personal growth kit that cost a whopping $799. It took Margaret and me six months to scrape together the money, and I bought the kit.
I look back now at what that kit taught, and it was really simple: the basics of goal-setting and follow-through. But it was significant to me because it helped me to create a track to run on for identifying goals, breaking them down into manageable steps, and following through with the disciplines to get them done. I spent three years working from that growth kit, and hitting goals became a consistent part of my professional life.
During that period, I read an article about the fastest-growing churches in the country, and I got excited. _What if we could make our church one of them? What if we could become the fastest-growing church in the state of Ohio_ , I thought. That became my goal. It was a big goal, a huge goal for me. The church was already close to my lifetime goal of five hundred people, and I was only in my twenties. But I was willing to strive for it. I won't bore you with all the details, but we succeeded in doubling the size of the congregation in one year, and in 1975 we were recognized as the fastest-growing church in Ohio. And we all celebrated.
When you hit a goal like that, once the celebration is done, you start asking yourself the question, _What's next?_ And that's what I started to do. I wondered what I should try to do next. Did I want to attempt the same thing next year? Was there a different goal I should be going after?
As I reflected and explored ideas, I came to a realization. The lessons I'd learned while working to grow the church were actually more important—and more valuable to me—than hitting any numbers or achieving the goal. In that moment, I made a shift: the personal development shift from goals to growth. The goals I set and achieved were nice, but they weren't as significant as the growth I experienced. Goals helped me to _do_ better. But growth helped me to _become_ better. The growth experience was giving me greater satisfaction than reaching individual goals.
* * *
GOALS HELPED ME TO _DO_ BETTER. BUT GROWTH HELPED ME TO _BECOME_ BETTER.
* * *
There was also another great benefit. Soon other leaders began asking me how I had accomplished the growth of the church, and I started teaching what I had learned. That was the start of my career as a leadership trainer and speaker. Achieving a goal had opened the door to the opportunity, but my ongoing ability to train others and develop my career as a trainer and speaker came as the fruit of my personal growth. And I've been able to continue speaking because personal development became my focus.
GROWTH CHANGES
As I look back at the time I was making this personal development leadershift from goals to growth, I can see that I made three significant shifts in the way I approached becoming a better leader:
**1. G ROWTH OUTWARD TO GROWTH INWARD**
A little second-grade student raised his hand in class to ask his teacher a question. "What did I learn today?" the boy inquired as the teacher was ending her session on basic addition and subtraction.
"That's an odd question, Johnny," the teacher replied. "Why would you ask me that?"
"Because that's what my parents will ask me when I get home," Johnny replied.
That's what I would call outward motivation. To make the shift from goals to growth, you need to find inward motivation.
* * *
GROWTH ON THE INSIDE FUELS GROWTH ON THE OUTSIDE.
* * *
When I started my career, I was motivated by my desire to meet numerical goals, and every year I set those kinds of goals for myself. I'd look at every area of my career, break each large goal down into smaller, achievable goals, and attack them. I believed that hitting numbers would automatically make me better. And I hoped that external production would increase my internal motivation. But I discovered that it didn't. Instead, the focus on hitting numbers started to wear me down. That prompted me to realize that growth on the inside fuels growth on the outside, not the other way around. I recognized I needed to make a leadershift.
**2. G ROWTH IN EVERYTHING TO GROWTH IN A FEW VITAL THINGS**
When I understood that my focus needed to be internal rather than external, I began thinking about where and how I wanted to grow. That made me realize how unfocused I was. At age twenty-six, my hunger to grow was greater than my willingness to get specific in my areas of growth. If you'd asked me where I wanted to improve, I'd have said, "Everywhere." But it's impossible to grow everywhere all at once. So how would I proceed?
I decided to study success. My desire was to spend a year examining what made people successful and try to discover what all of them had in common. Even as I started this process, I knew what the first quality was: attitude. My father had taught me that. Not a naturally optimistic person, Dad had studied successful people as a youth and found that a positive attitude was something they all had in common. Dad had made it a regular practice to read books that promoted a positive attitude, such as the works of Norman Vincent Peale, and had paid me to read those same books as I was growing up. I would become intentional about continuing to improve in this area.
The second characteristic I quickly attributed to successful people was the ability to develop strong relationships. This was a natural strength of mine. As a teenager I had observed that people go along with people when they get along with them. I liked people and found that they usually responded well to me. So I determined to leverage this natural strength and keep building upon it.
While I recognized that attitude and relationships were vital to success, I also recognized that they weren't enough to make a person successful. I've known plenty of relational people with good attitudes who never accomplished anything, haven't you? I wanted to figure out what the key factor was.
It took time to figure it out, but when I did, it changed my life. I read _Spiritual Leadership_ by J. Oswald Sanders, which helped me understand the impact of good leadership. It was then that I recognized that everything rises and falls on leadership.
The last piece of the success puzzle to fall into place for me took even longer to recognize, and its discovery came through failure. In my first leadership position, I had helped my organization to grow, but within six months of my departure, the organization had regressed. I studied that leadership failure for six months before I figured out the reason: I had not equipped a single person to carry on without me. Realizing this made me change the way I led, and it prompted me to start learning and developing myself as a trainer and coach.
Since then I've focused my growth on these four key areas, which I later turned into the acronym R-E-A-L so that I could teach it to others: Relationships, Equipping, Attitude, and Leadership. Those are my focus when I read books and articles, listen to podcasts, and attend conferences. Those areas have also become the focus of my teaching and my writing. Look at any speech I've given or book I've written, and you will be able to place it into one of those four categories. If you want to grow to your potential and become a better leader, you need to grow in these four areas. You may also want to identify any other top growth needs your specific career requires and add them too.
**3. G ROWTH WITH A TIMELINE VERSUS GROWTH WITHOUT A FINISH LINE**
As a young leader, I was focused on achieving goals. One of the questions I continually asked myself as I set a goal was, _How long will this take?_ I'm naturally impatient and I was often preoccupied by how long any given task would take. But as I shifted from goals to growth, my mind-set changed. My thinking shifted onto the bigger picture, and I became less impatient. (I won't say I became _patient_ because everyone I know would call me on it!)
As I made this shift, instead of worrying about how long something might take, I started asking, _How far can I go?_ Instead of thinking about what I was getting and how much I had to pay to get it, I started to think about who I was becoming and the impact I could make because of it. I recognized I was on a growth journey. And I started to fall in love with personal development. What's more, at age seventy-one, I'm still in love with it.
In my organizations, I try to cultivate that same love. I do that by promoting a culture focused on growth, not goals. Here's the difference.
**GOAL-ORIENTED CULTURE** | **GROWTH-ORIENTED CULTURE**
---|---
Values Achievement | Values Development
Focuses on Status | Focuses on Stretching
Honors Privilege | Honors Serving
Emphasizes the Teacher | Emphasizes the Student
Target Is Arrival | Target Is Growth
Nowhere has my leadershift from a defined timeline to an undefined finish line been more evident or more rewarding than in my writing career. I wrote my first book at age thirty-two because I wanted to make an impact on people I would never meet or get to speak to. The book was called _Think on These Things_. I can honestly say that I gave it my best, but the end result was not very impressive. It was only about a hundred pages. But that was okay. I hadn't written it to impress anyone. I had written it to make a difference.
After that first book, I continued writing. I contributed a chapter to a book on time management. I did a book based on questions and answers. I worked on a Bible commentary. None of the books sold especially well, but I was happy to be learning how to write better and to reach new audiences.
During this early season, I was talking with Elmer Towns, a professor at Liberty University who was one of my heroes, and I found out that the lifetime sales of all his books was 110,000 copies. This was back in the early eighties. He has since sold many more books, but that was a staggering figure to a small-time author like me at the time. And I found myself wondering, _Would it be possible for me to match that? Could I ever hope to sell 110,000 copies of my books in my lifetime?_ For a short time, that became my goal. But it wasn't long before I replaced that goal with the desire to grow as an author—to keep improving my writing as well as what I had to say.
Years later my assistant, Linda Eggers, called to tell me that Thomas Nelson, my publisher, had sent me a gift. When I got to the office, I discovered a beautiful crystal eagle. Engraved in its base were the words "John C. Maxwell: 1 Million Books Sold." I was amazed. Somewhere along the line, I had passed my old sales goal, and I hadn't even been aware of it. Making growth your focus is like having your cake and eating it too. Growth's highest reward is not what we get from it, but what we become by it.
There was a time when people in the inner circle of Truett Cathy, the founder of Chick-fil-A, were pressing him to expand the organization. "We need to get bigger," they kept telling him. I've always loved Truett's response: "If we get better, our customers will demand that we get bigger." That's how I feel about personal growth. When you get better, it makes you bigger. Growth is sustaining. Growth is the only guarantee that tomorrow will be better than today.
* * *
IF WE GET BETTER, OUR CUSTOMERS WILL DEMAND THAT WE GET BIGGER.
—TRUETT CATHY
* * *
HOW TO BECOME A GROWTH-ORIENTED PERSON
Making the leadershift from goal-oriented to growth-oriented isn't complicated, but it isn't easy either. It requires a shift in mind-set. It takes time, but it's well worth it. If you shoot for goals, you'll achieve your goals but you may not grow. If you shoot for growth, you'll grow _and_ you'll achieve goals. To start making that shift, do these seven things:
**1. E MBRACE CHANGE**
In 1974 I heard Olan Hendrix, currently the CEO of the Leadership Resource Group, say, "Growth means change." That has always stuck with me, because I think it's human nature to desire improvement and resist change at the same time. And that's impossible.
If you want to become a better leader, a better employee, a better person, you must shift from a fixed mind-set to a growth mind-set. Why?
**A FIXED MIND-SET** | **A GROWTH MIND-SET**
---|---
Believes Intelligence | Believes Intelligence
Is Static | Can Be Developed
|
Avoids Challenges | Embraces Challenges
|
Gives Up | Persists When Faced
Too Easily | with Setbacks
Sees Effort as Fruitless | Sees Effort as a Path to Mastery
|
Ignores | Learns from
Constructive Criticism | Constructive Criticism
|
Feels Threatened by the | Finds Lessons and Inspiration
Success of Others | in the Success of Others
|
Plateaus Early and Achieves | Reaches Higher Levels
Less Than Full Potential | of Achievement
A fixed mind-set results in an early plateau, achieves less, and hinders people from reaching their full potential, whereas a growth mind-set fuels people to a higher level of achievement. Beverly Sills said, "There are no shortcuts to any place worth going." That's certainly true when it comes to growth. It's a long, slow road, but it's a highly rewarding one. And it requires us to stretch.
I wanted to illustrate this to my grandchildren one year when we were on vacation in Vail, Colorado. The first evening I placed rubber bands of different sizes and colors around the dinner table. Our discussion that evening was about the value of being stretched beyond our comfort zones. I asked all of them to place a rubber band around their wrists as a reminder to stretch and grow during their week snow skiing. The next evening, Ella, our youngest granddaughter, came up to me and showed me her wrist. She had two rubber bands on it. "This morning I looked on the ground and saw this other rubber band," she said. "I felt that it was a sign for me to be stretched twice as much!"
I loved her attitude. That's how we need to approach every day, because stretching is the ongoing lifestyle of a person of growth. That means continually changing when we don't feel like it because we know it's going to lead us to the life we really want.
**2. A DOPT A TEACHABLE SPIRIT**
Growth begins with having a teachable spirit. What does that entail? It means having a passion to learn, possessing the intention to learn every day, and reflecting on what you learn so that you know how to apply it. It's a bit like gardening. A garden doesn't spring to life on its own. It requires planning, hard work, and the right environment. A gardener must do the work: prepare the soil, plant the seeds, water the plants, then feed, mulch, and weed. It's an intentional process, and it must occur every day.
I try to cultivate a growth environment and maintain a teachable spirit. How do I do that?
• **I M AKE GROWTH MY NUMBER-ONE PRIORITY.** I am conscious of my need to learn 24/7 because a day without growth is not a good day for me.
• **I L OOK FOR GROWTH POSSIBILITIES IN EVERY SITUATION.** No matter what I'm doing, whether succeeding or failing, opportunities to grow are there. The question is, do I see it and take advantage of it?
• **I A SK QUESTIONS THAT WILL HELP ME GROW.** Growth doesn't find me. I must find it. The fastest way to find out what I don't know is to ask questions. The best way to dig deeper and learn more is to ask questions. Are you getting the picture?
• **I F ILE WHAT I HAVE LEARNED.** People forget a lot of what they learn. If they want to recall it, they can't. Or they can't find it. When I find articles of value, I clip them and put them in folders by subject. When I find quotes I like, I add them to index cards filed by topic. I file what I learn so that I can always regain access to it quickly.
• **I P ASS WHAT I LEARN ON TO OTHERS.** Sharing something I learn reinforces growth and prompts me to make it my own. It also allows me to help others.
I encourage you to find your own ways to remain teachable and facilitate learning. It will open you up to amazing new possibilities.
**3. M AKE YOUR LOVE FOR LEARNING GREATER THAN YOUR FEAR OF FAILURE**
Over the years, I have experienced the fruits of failure. I don't count my losses; I count the lessons I've learned from them. I wrote _Sometimes You Win, Sometimes You Learn_ to help people to learn from their losses. Even failure isn't failure if you learn something from it. That's how you can make failure your friend.
I can remember the day that fear of failure became my friend. It occurred in Los Angeles when I was asked to speak at a conference. Every speaker on the program was more successful, experienced, mature, and recognized than I was. I was less in every way, and I was feeling it. Finally, in the green room, I confided with one of the best speakers.
"I don't feel qualified to be speaking here," I told him. I think I was hoping for reassurance. Instead, his reply startled me.
"You're not," he said. "Speak afraid. Be willing to do it afraid, and eventually you will become qualified."
That was a revelation, and it created a leadershift in me. I spoke afraid, did my best, and here is what I discovered: action reduces fear and increases courage. That realization was a major step toward increasing my love for learning and decreasing my fear of failure.
Don't allow failure to be a bully in your life. It will, if you let it. Many people get intimidated by failure every day. Instead, you need to make failure your friend. How? Fail early, fail often, and fail forward.
In this season of my life, my greatest goal is to become a catalyst for the transformation of a nation. I'm spending a significant amount of time in South and Central America trying to add value to people and teach them how to raise one another up. Recently I was asked by a reporter if I thought I would achieve that goal. My answer was, "Probably not."
* * *
ACTION REDUCES FEAR AND INCREASES COURAGE.
* * *
The expression on the interviewer's face indicated surprise. "Really?"
"Yes. I probably won't live to see it. But I would rather try something bigger than my capabilities with high odds of failure than attempt something smaller that I know I could achieve." The fear of failure is no longer a bully in my life. I'm not afraid of failing as long as I'm stretching and growing.
**4. D EVELOP RELATIONSHIPS WITH OTHER GROWING PEOPLE**
It's much easier to become a growing person if you're in a positive growth environment. I realized this when I was in my twenties, and it inspired me to write out a description of a growth environment. I observed that such environments have ten characteristics. Recently I was looking at this list and I realized that five of the ten involve other people. (I italicized them for emphasis.)
1. _Others are ahead of me._
2. I am continually challenged.
3. My focus is forward.
4. _The atmosphere is affirming._
5. I am often out of my comfort zone.
6. I wake up excited.
7. Failure is not my enemy.
8. _Others are growing._
9. _People desire change._
10. _Growth is modeled and expected._
Much of my personal growth has come as a direct result of having the opportunity to spend time with growing people. Earlier I mentioned Elmer Towns. He is one of the growing people who was an early mentor in the formative years of my life. One of the things he taught me was what he called the hot poker principle. He used to say that if you keep the poker near the fire it remains hot. Remove it and over time it becomes cold. He likened growing people to fire and would often remind me, "John, stay close to the fire."
That is exactly what I have tried to do. Stay close to the "fire" of growing people. Few things in life are better than conversation with people who are growing. Those conversations have been a great catalyst for my growth. I'm indebted to so many who have walked the growth journey with me and from whom I've learned so much.
**5. D EVELOP GREATER HUMILITY**
"Humility is not denying your strengths," said pastor and author Rick Warren. "Humility is being honest about your weaknesses." The essence of humility is being unafraid to admit when we're wrong. It's like saying we want to be wiser tomorrow than we are today. And the more we learn and grow, the more we recognize what we don't know.
Leaders who possess humility are confident yet feel no need to draw attention to themselves. They are comfortable with themselves yet acknowledge that they need to improve. They have self-awareness. They gratefully receive criticism. And they are not threatened when others shine. They are happy for them.
Are you willing to be criticized for the sake of improvement? Are you willing to admit you're wrong in deference to your desire to change and grow? Are you willing to drop bad habits, change wrong priorities, and embrace new ways of thinking? That's what it will take to make the leadershift to growth. You must be willing to admit where you're wrong so that you can discover what is right. Anyone can make that choice, but it requires humility.
**6. B ELIEVE IN YOURSELF**
The Law of the Mirror in my book _The 15 Invaluable Laws of Growth_ states: "You must see value in yourself to add value to yourself." What you think about yourself determines the investment you will make in yourself. If your self-worth is low, then your investment in yourself will be low. If you see yourself as a two (out of ten), then you'll make a two-level investment. If you see yourself as an eight, you'll make an eight-level investment. That matters because your growth return will not exceed your growth investment.
* * *
WHAT YOU THINK ABOUT YOURSELF DETERMINES THE INVESTMENT YOU WILL MAKE IN YOURSELF.
* * *
Benjamin Franklin said, "Empty the coins of your purse into your mind and your mind will fill your purse with coins." What a great way to think about it. Be willing to invest in yourself.
**7. E MBRACE LAYERED LEARNING**
In 1954, politician Adlai Stevenson addressed the senior class at Princeton University. Here, in part, is what he said:
What a man knows at fifty that he did not know at twenty is, for the most part, incommunicable. The laws, the aphorisms, the generalizations, the universal truths, the parables and the old saws—all the observations about life which can be communicated handily in ready, verbal packages—are as well known to a man at twenty who has been attentive as to a man at fifty. He has been told them all, he has read them all, and he has probably repeated them all before he graduates from college; but he has not lived them all.
What he knows at fifty that he did not know at twenty boils down to something like this: The knowledge he has acquired with age is not the knowledge of formulas, or forms of words, but of people, places, actions—a knowledge not gained by words but by touch, sight, sound, victories, failures, sleeplessness, devotion, love—the human experiences and emotions of this earth and of oneself and other men; and perhaps, too, a little faith, and a little reverence for things you cannot see.
At the time Stevenson made these statements, he was in his mid-fifties, and what he describes is what I would call layered learning—one life lesson applied upon another and another, each gaining greater insight, depth, and weight. It is wisdom acquired and applied over time, and I believe it is the best kind of learning.
If you desire to grow to your maximum potential as a person and a leader, embrace layered learning. As you do, know these things about it:
_Layered Learning Requires Time and Intentionality_
Any gardener knows you can't force a seed to grow faster than nature intended it to. You can't make trees bear good fruit before they're mature. You can't rush the season. Plants need to grow, and though they may grow every day, it will not show every day. It takes a lot of growing to do a little showing.
That doesn't mean we shouldn't cultivate growth every day. Small improvements over time make a big difference. Knowledge gives us a layer of learning, increasing with each added layer until it turns into wisdom. It takes years, decades, sometimes a lifetime for a person to become an overnight success.
The _21 Irrefutable Laws of Leadership_ has been one of my most successful books. It was the product of layered learning. I spent decades intentionally learning about leadership. I read hundreds of books. I sat with dozens of mentors. I listened to hundreds of messages. I daily applied what I learned. I failed and succeeded, time after time. And slowly, painstakingly, I learned enough about leadership to write the book. It was the product of layered learning.
_Layered Learning Gives You a Bigger Picture_
Layered learning is like building a picture one piece at a time. It's like receiving additional pieces of the jigsaw puzzle of leadership and putting them in place so that the picture enlarges. What you see becomes more relevant. It also enlarges you as a leader because the more pieces you receive, the better your perspective and the greater your understanding of the principles involved in leadership.
• Layered learning determines the depth of a principle.
• Layered learning determines the length of a principle.
• Layered learning determines the consistency of a principle.
• Layered learning determines the compounding impact of a principle.
You are capable of adding layers and acquiring more of the big picture than you possess today.
_Layered Learning Gives You a Better Picture_
Recently I received the opportunity to revise my book _Developing the Leader Within You_ on the occasion of its twenty-fifth anniversary. My publisher requested that I revise at least 15 percent of it so that they could call it a new edition. I relished the thought of updating the book and dove in. By the time I was done, I hadn't rewritten 15 percent; I'd rewritten 85 percent! I changed so much, my publisher decided to call it _Developing the Leader Within You 2.0._
How was I able to make so many changes to a book that was already highly successful? Layered learning. In the twenty-five years since I had written the original version, I had continued to grow in leadership.
When you make the personal development shift from goals to growth and embrace the process of layered learning, you will never stop getting better. And your level of success can keep expanding.
I like to think of layered learning the way C. S. Lewis talked about learning. He said that learning isn't so much like a train going from one station to the next, so that we leave one place and move on to somewhere else. Instead, our growth is similar to that of a tree. As we learn and grow, we add new rings of understanding without giving up the older ones. We build, using the past to strengthen us. And create something new.
GROWTH PERSPECTIVE
Few things have a greater positive impact than shifting from goals to growth. Why do I say that? Because the benefits are so numerous. Make growth your priority and . . .
• You will unlock and achieve your potential.
• You will feel good about yourself.
• You will strengthen your values and abilities.
• You will grow in humility and self-awareness.
• You will _become_ more so you can _do_ more.
• You will be an example for others to follow.
I want to say one more thing about shifting from goals to growth before we move on to the next leadershift. Being a goal-oriented person means having more of a short-term mind-set. We often reach for goals because we want the positive feelings that come from quick achievements. But when we make the shift to focusing on growth, it means we've begun to adopt a long-term mind-set. By focusing on growth, we go from improving in spurts to improving day after day to reach our potential. That consistency compounds. And that's important because your level of success will never exceed your level of personal development.
CHAPTER 4
PERKS TO PRICE
_The Cost Shift_
_Strength and growth come through continuous effort and struggle._
—NAPOLEON HILL
I've met a lot of people who desire to become leaders. That's only natural since I do so much teaching and writing on the subject. When I get the chance to interact with people one-on-one, I often ask them why they want to be leaders. Sometimes their answers reveal that their motivation is really about the perks of leading. They want to be in control. They want others to do what they say. They want a nicer office. They want a higher income. They want a better parking place.
When I started out as a young leader, my thoughts were similar. I was enamored with my title of pastor. It conveyed to me that I was the shepherd of the flock, and I thought people would automatically follow me because they needed me. They would rely on me for direction and be grateful for everything I did for them. It seemed simple.
Then reality hit. The people of the church were kind to me, but they didn't automatically follow me. That's when I learned what I later called the Law of E. F. Hutton: when the real leader speaks, people listen. The title that I expected to be so important didn't come with any of the perks I anticipated. I learned that I would have to earn influence myself along the way.
Fifty years later, I can say that in my career as a leader, I've received just about every kind of perk imaginable. I've received titles, recognition, honorary degrees, authority, nice offices, good parking places, money, preferential treatment—you name it, I've had it! However, none of these things motivates me as a leader. I lead because of what I can do for other people. That's the best motivation to lead others. It took time to get there, but I made the shift from being focused on what I can receive as a leader (the perks) to what I can give as a leader (the price).
Take a look at the kinds of questions leaders ask themselves based on where they focus:
**LEADERS WHO FOCUS ON PERKS** | **LEADERS WHO FOCUS ON PRICE**
---|---
What will I receive? | What can I give?
How will this decision affect me? | How will this decision affect others?
How long will this take me? | How far can we go?
What will you give me to stay in the game? | What must I give to stay in the game?
The choice to lead because of benefits, benefits no one, not even the leader. Focusing on perks won't take you anywhere worthwhile because deep inner fulfillment never comes from perks. What they offer is ultimately hollow. And they have never helped a leader to reach his or her potential. Leaders who focus on perks end up misusing their leadership, and because they love perks more than people, they are continually tempted to misuse people to receive, maintain, or improve their perks.
If you want to reach your potential, become the best leader you can be, and make the greatest impact, then you must shift from perks to price in your leadership. A price is what stands between you and your potential. If you want to be a better leader, you need to pay for it.
YOUR PRICE POINTS
While many of the specifics of the price will be unique to each individual leader, there are some common costs that every leader needs to take into account. I want to discuss three that should be part of every leader's shift from perks to price:
**1. R EALITY—LEADERS RECOGNIZE THAT EVERYTHING WORTHWHILE IS UPHILL**
Max De Pree, CEO of the furniture giant Herman Miller, said, "The first responsibility of a leader is to define reality." Let me define the reality of your leadership potential: it's uphill all the way. No one ever coasted to success. No successful person has ever experienced accidental achievements. Nothing of genuine value is easy, quick, and downhill. All the precious things in life require that we pay a price. Contrary to the line in the old song, the best things in life are not free. Or as someone told me once during a break in one of my speeches, "If it doesn't suck, it's not worth doing."
There's a lot of difference between what we can't do and what we won't do. What we _won't_ do will keep us from being successful a lot more than what we _can't_ do. Poor choices, not lack of talent and ability, are the greatest hindrances to most people's success. If we want to succeed in leadership, we must do what we don't want to do, so we can do what we need to do. We must be willing to pay the price. Early American missionary Adoniram Judson is rumored to have said, "There is no success without sacrifice. If you succeed without sacrifice it is because someone has suffered before you. If you sacrifice without success it is because someone will succeed after."
As a leader, how can you prepare yourself to pay the price required to reach your potential? How do you get ready for the long uphill journey? I think you can learn a lesson from Navy Vice Admiral James Stockdale. In his book _Good to Great_ , Jim Collins writes about Stockdale and what Collins calls the Stockdale Paradox.
Stockdale was a pilot who spent eight years imprisoned in North Vietnam's notorious Hanoi Hilton after he was shot down during the Vietnam War. He was frequently tortured and abused. When Collins interviewed Stockdale, the former admiral said his imprisonment was "the defining event of my life," explaining, "I never lost faith in the end of the story. . . . I never doubted not only that I would get out, but also that I would prevail."
Collins was intrigued by this man whose body, decades later, still showed signs of being broken but whose spirit was as indomitable as ever.
"Who didn't make it out?" Collins asked a little hesitantly.
"Oh, that's easy," he said. "The optimists." When a confused Collins asked him to explain, Stockdale said, "Oh, they were the ones who said, 'We're going to be out by Christmas.' And Christmas would come, and Christmas would go. Then they'd say, 'We're going to be out by Easter.' And Easter would come, and Easter would go. And then Thanksgiving, and then it would be Christmas again. And they died of a broken heart."
What Stockdale said next gave Collins the idea for the Stockdale Paradox: "This is a very important lesson. You must never confuse faith that you will prevail in the end—which you can never afford to lose—with the discipline to confront the most brutal facts of your current reality, whatever they might be." Here's how Collins states the Stockdale Paradox:
Retain faith that you will prevail in the end,
regardless of the difficulties.
_AND at the same time_
Confront the most brutal facts of your current reality,
whatever they might be.
These twin expectations of faith and fact help us to believe we can prevail in the end but remind us that the process won't be easy.
I express these twin expectations to myself using different words. As I prepare to lead, I think of _hope_ and _hard_. These words help me personally to handle the very different expectations needed for leadership. _Hope_ empowers me to believe that I can make the climb. It fuels me with energy to continue when I get tired. And it enables me to speak hope into the lives of the people who are journeying with me. I cannot give hope to others if I do not possess it myself. It must come from a place of authenticity because you can't fake hope. As you encourage yourself, your people feel that encouragement too. As you encourage them, you also become encouraged. It creates a positive cycle that keeps everyone moving forward.
While I love the encouragement of _hope_ , I also value the level-setting word _hard_. It balances my expectations and prevents me from being naively optimistic. I remind myself that the leadership journey is often difficult. Much of success lies in possessing right expectations.
I confess that during the early years of my leadership, I possessed an excess of hope but had very little knowledge or expectation for how hard leading would be. As a result, I set myself and those I led up for disappointment. We expected the best, and that's the only thing we prepared ourselves for. When things got hard and didn't go perfectly, we weren't ready for it. When you don't prepare for the worst, the worst wins!
* * *
WHEN YOU DON'T PREPARE FOR THE WORST, THE WORST WINS.
* * *
Nowhere was my experience more challenging than at Skyline Church in Lemon Grove, California. I began my leadership there in 1981. The church's attendance had plateaued for quite some time but soon started growing again, and it quickly became clear that we would need to relocate. Our current facilities were dated, we were using every inch of space we had, there was no room for expansion, and the neighborhood where the church was located was becoming less safe.
I had initiated the construction of new buildings at both of the previous churches I had led, so I didn't go into this process blindly. I knew it would not be easy. And I knew that relocating the whole church to a new campus would be more difficult than the other projects I had overseen.
I began working with my board and processing them through the decision to relocate. We also started doing our due diligence. It took some time, but we made the decision, planned the process, and in October of 1987, we asked the congregation to vote on our decision to buy eighty acres of land in nearby El Cajon.
When we started, we expected the whole process from land purchase to relocation to take four years and cost $25 million. To say that we underestimated it would be a huge understatement. After we bought the land for $1.8 million and the survey revealed it was actually 110 acres—plus we gained access to additional acreage totaling 130 acres—we thought things were going our way. But then the trouble started.
The land was declared a protected habitat for two species of birds, severely restricting where and when construction could be done. Environmental officials also discovered coastal sage on the land and declared that we could not build anywhere it grew. The local water district required the church to purchase additional water rights. A local commission opposed the construction plan and forced the church to change the location of the first building and redraw its plans. The state insisted that the church pay for improvements on the highway that bordered the property. The county refused to issue building permits. Huge amounts of granite were discovered on the property, requiring major demolition. Building requirements for earthquakes changed, raising construction costs significantly. And on it went.
I fought these battles from 1987 until 1995, when I stepped down from leadership of the church. My successor, Jim Garlow, continued to fight them until the church finally entered their new building in April of 2000. What I thought would take four years and $25 million took thirteen years and more than $36 million. And Jim continued to build and battle for another decade after that!
During that season, I continually had to balance _hope_ and _hard_ while communicating to the congregation. They needed to be encouraged enough to hold on to the vision, passionate enough to overcome all the obstacles we were facing, and inspired enough to stay engaged in the process and continue supporting it emotionally and financially. They also needed to be apprised of the obstacles and setbacks. If they understood how difficult the process was, they would be more understanding. But I didn't want them to become discouraged. That season was one of my most challenging as a leader. And it taught me lessons about communicating expectations up-front.
Management consultant and business visionary Peter Drucker said, "A time of turbulence is a dangerous time, but its greatest danger is the temptation to deny reality." As leaders we can't deny reality, nor should we try to sugarcoat it when communicating with our people. We need to bring reality into the conversation as soon as possible. In other words, we should strive to be up-front with the hard part of any journey we plan to take others on.
I used to wait for a good time to share hard realities with others, and then I realized that there's never a good time to share hard news, and the longer I waited, the harder it was to talk about it. Since then I've made it a regular practice to look for and mention any downside to a process I'm trying to communicate. I want people to know there is a price to pay for progress.
No matter what you want to do in life, you have to face reality, and you have to be willing to pay the price required to go uphill. The sooner you start climbing and the more you're willing to pay, the higher you can go.
**2. E XAMPLE—LEADERS ACKNOWLEDGE THEY MUST CLIMB THE HILL FIRST**
All people with leadership ability have one perspective in common: before and more. They see things _before_ other people do, and they see _more_ than other people do. However, what sets great leaders apart from all other leaders is this: they _act before_ others and they _do more_ than others. Great leaders face their uncertainty and doubt, and they move through it to pave the way for others. And because they are willing to pay the price first and often pay more than others do, they can say with moral authority, "Follow me."
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WHAT SETS GREAT LEADERS APART FROM ALL OTHER LEADERS IS THIS: THEY _ACT BEFORE_ OTHERS AND THEY _DO MORE_ THAN OTHERS.
* * *
This doesn't mean great leaders don't have all the same human failings as everyone else. I suspect that even Moses, as he started to walk across the bed of the Red Sea, asked himself, _Why must I always go first?_
When times are tough and challenges are difficult, being first isn't a perk. It's a cost that has to be paid. In the uphill climb to achieving something worthwhile, leaders have to pay that price by climbing first and leading the way. There is no elevator to the top. Someone has to find the path and set the example.
A person's title or position doesn't help here. The climb isn't enhanced by college degrees. Or material possessions. No one is inspired by any of those things. It's the actions leaders take that inspire others to follow and to rally to the vision. Great leaders take action. They move out front, staying ahead but within sight of their people, and they say "follow me." The example of a good leader continually inspires people.
Follow-me leaders know it's their responsibility to set the example. Over the years, I've observed that they share three common before-and-more characteristics:
_Follow-Me Leaders Believe in Themselves Before and More Than Others Do_
I've observed a lot of successful people whom others have not believed in, but I've yet to meet a successful person who did not believe in him-or herself. Self-belief comes first. As leaders, we cannot give to others what we do not possess ourselves.
Speaker and author Bob Burg told a great story that sheds light on the power of belief:
A defense attorney was arguing a case for his client, who was charged with murder. Despite the fact that the victim's body was never discovered, the circumstantial evidence was overwhelming, and everyone in the courtroom, including the jurors, knew that the defendant was guilty. The clever lawyer decided to go for broke. As he addressed the jury in his closing argument, he pointed toward the courtroom doors and said, "Ladies and gentlemen, in exactly _60_ seconds, the so-called corpse, the man you _believe_ is dead, is going to come walking into this courtroom—right through those very doors. We can begin counting now."
Immediately, the eyes of all the jurors went to the door.
The time ticked by: 1 second, 2 seconds, 3 seconds, 10 seconds, 20 seconds, 45 seconds, 55 seconds, 56, 57, 58, 59 seconds—finally, one minute. And at exactly the one-minute mark, wouldn't you know it, but who should come striding in through those doors?
Absolutely no one. Certainly not the victim.
The lawyer now faced the jury again and spoke in a conciliatory, reasoning, almost patronizing tone: "Now, ladies and gentlemen, I must apologize. I told you something that clearly did not come true. However, you will have to admit that the mere fact that each and every one of you looked toward those doors as you did, showed me and showed you and showed everyone in this courtroom that _you had some doubt_. And as the judge will instruct you, if there is any doubt in your minds, any doubt at all, you must— _you must_ —return a verdict of not guilty and set my client free."
The jury went into the jury room to deliberate and came back out just five minutes later to render their verdict. The foreman stood up, faced the defendant, and when asked by the judge what their verdict was, said that they declared the defendant—GUILTY!
The defense attorney was enraged. "How could you?!" he stammered. "I saw you all watching those doors."
The foreman glanced at the defense attorney and replied, "Yes, sir, we did. But we were also watching you and your client—and you did _not_ watch the door; your client did not watch the door. And that's because neither of you believed for even a moment that anyone was actually going to be walking in through there."
The moral of the story?
Don't expect anyone to believe in something you don't believe in yourself.
Self-belief is more than saying positive words to myself or receiving them from others. As radio broadcaster Paul Harvey said, "If you don't live it, you don't believe it." Words of affirmation without the work of accomplishment are hollow. Even if others believe in you, their borrowed belief must be activated by success and become self-belief if it is to be sustained. Borrowed belief without results soon loses its power. A leader's self-belief must be authentic, and it must be backed up with successful action.
* * *
IF YOU DON'T LIVE IT, YOU DON'T BELIEVE IT.
—PAUL HARVEY
* * *
_Follow-Me Leaders Set Expectations for Themselves Before and More Than Others Do_
I mentioned in chapter 2 that I teach a lesson called JMT-DNA to my new John Maxwell Team coaches every time we meet. One of the values I personally embrace that I also want them to embrace is exceeding expectations. I want my coaches to expect more of themselves than others do. As speaker and author Brian Tracey said, "Your success in your career will be in direct proportion to what you do after you've done what you are expected to do."
Leaders are in trouble when they need someone else to set the level of expectations. If that continues, they will cease to lead others. Sadly, there are a lot of people who go in the opposite direction, trying to do as little as they can to stay afloat in their careers. It's like they're treading water in the pool during an Olympic swimming race. They're like these employees described in what are said to be actual employee evaluations:
• "Since my last report, this employee has reached rock bottom and has started to dig."
• "Works well when under constant supervision and cornered like a rat in a trap."
• "He would be out of his depth in a parking lot puddle."
• "This young lady has delusions of adequacy."
• "He sets low personal standards and consistently fails to achieve them."
• "This employee should go far, and the sooner he starts, the better."
• "He brings a lot of joy whenever he leaves the room."
• "If you see two people talking and one looks bored, he's the other one."
• "Gates are down, the lights are flashing, but the train isn't coming."
• "If you give him a penny for his thoughts, you'd get change."
• "Some drink from the fountain of knowledge; he only gargled."
I don't know whether these lines come from real-life evaluations as claimed, but you get the idea. You can't set a low standard of performance for yourself and expect to lead others effectively. If you want to be a good leader, you must have high expectations for yourself. I like the advice given by Dianne Snedaker, executive vice president and chief marketing officer of First Republic Bank, who said:
Set your standards high and keep them high. If you are interested in success, it's easy to set your standards in terms of other people's accomplishments. And then let other people measure you by those standards. But the standards you set for yourself are always the more important. They should be higher than the standards anyone else would set for you, because in the end you have to live with yourself, and judge yourself, and feel good about yourself. And the best way to do that is to live up to your highest potential. So set your standards high and keep them high, even if you think no one else is looking. Somebody out there will always notice, even if it's just you.
If you're a leader, you must set the standards high for yourself before anyone else does.
_Follow-Me Leaders Make Commitments to Themselves Before and More Than to Others_
To be successful, leaders must continually make commitments. Commitment is key. But the first and most important commitment that any leader makes is to him-or herself: a commitment to integrity, responsibility, and selflessness. Good leaders promise themselves they will pay the price and follow through regardless of the circumstances.
One of the leaders I most admire is Abraham Lincoln. Before Lincoln became president, few people expected him to be one of the nation's greatest leaders. In fact, the _New York Times_ said he was unqualified for the presidency of the United States. But Lincoln was committed to helping the nation. He later revealed his mind-set of commitment: "I have never done an official act with a view to promote my own personal aggrandizement, and I don't like to begin now."
If you're a leader, or you desire to become one, you must always be ready, willing, and committed to climbing the hill first. Climb first, setting the example, and call out "follow me." If you're willing to do that, there's still one more quality you must display as you pay the price of leadership.
**3. C ONSISTENCY—LEADERS UNDERSTAND THEY NEVER GET TO STOP CLIMBING**
I have another confession to make. Early in my leadership, I thought that if I led well for a season, I could earn the right to take shortcuts and quit making sacrifices. I thought I could pay the price for a little while, be done paying, and then enjoy the good life—the perks that came with having paid a price. That created a blind spot in my leadership and led to "destination disease." I thought I could arrive at a time, place, and situation that would give me the greatest of all perks—recognition without responsibility.
There is no such place—unless you get out of the game. But I don't want out of the game. I'm more than seventy years old, and I still like the game. What I've discovered is that I had to give up to go up, and I have to give up even more if I want to stay up!
There is a reason that sports teams seldom have back-to-back championships. The perks that come with the first championship often become a hindrance to achieving the next one. When a team earns the first championship, they don't get the next one free. Dwight D. Eisenhower, whose leadership experience included serving as both a general and the president of the United States, said, "There is no victory at bargain basement prices."
If you desire to go to higher levels of leadership, you need to keep paying the price. That price will be higher than you think, and it will have to be paid continually and consistently. Jim Collins said, "The signature of mediocrity is chronic inconsistency." A corollary to that would be that the signature of excellence is relentless consistency. But excellence doesn't show up quickly. And you have to work at it to sustain it.
It has been my privilege to play a few rounds of golf with several PGA players. One of them explained to me the reason most tournaments consist of several rounds. He said that almost any good professional golfer can shoot one good round. Having to shoot a second good round typically knocks out half of the competitors. The third round eliminates another half of the remaining players. The fourth round is the real test of consistency for a golfer. Anyone who can sustain that consistency rises above the rest and deserves to be rewarded.
Bill Bradley was a great basketball player who later became a US senator. In his memoir, he recounted his basketball mentor, Ed Macaulay, telling him, "If you're not practicing, remember someone somewhere is practicing, and, given roughly equal ability, if you two ever meet, he will win." Bradley took that advice and determined that in his basketball career, there would be no off season. That's how leaders need to see it too. There is no off season for leadership. As long as you're in the game, you need to keep working and keep climbing. You'll be glad to know that your efforts will be rewarded. Here are some of the ways consistency will help you as a leader.
_Consistency Provides Security for Others_
Anthropologist Margaret Mead observed, "What people say, what they do, and what they say they do are entirely different things." If you're consistent as a leader, that should not be true of you. Your words, intentions, and actions should all line up. People know where you stand and how you deliver. Others can depend on you, which is perhaps the highest compliment you can receive as a leader.
_Consistency Establishes Your Reputation_
Just about everyone can be good every once in a while. It's more difficult to be good every time. Consistency lifts people above the crowd and sets them apart. It can make you someone that others notice. And that's important in leadership because the people you lead are always watching you. When you deliver time after time, you develop a reputation for coming through when needed. Not only does that help you to influence people, it also sets the tone for your team. People do what people continually see. The more consistent you are, the more consistent they will want to be.
_Consistency Keeps You in the Leadership Game_
When you're consistent, it means never having to restart or get back "into the swing of things." You're already swinging. Your constant progress keeps morale high, keeps enthusiasm brimming, and increases your investment in whatever goal you're pursuing. Author and speaker Michael Angier said, "If you develop the habits of success, you'll make success a habit." If you consistently stay on top of your game, you never have to gear up to get back into the game.
_Consistency Compounds_
What did genius Albert Einstein call the greatest mathematical discovery of all time? Not Arabic numerals. Not calculus. Not the theory of relativity. Compound interest—wealth that grows based on continual reinvestment. And what's the secret to compound interest? Consistency! It never stops growing.
One of my favorite examples of the compounding power of consistency occurred in the world of professional baseball in the 1980s and '90s with Cal Ripken Jr. He is in the Hall of Fame, but he isn't there because he was the best hitter, best fielder, or best base stealer. He's there because of consistency.
Ripken played in 2,632 consecutive games, the major league baseball record by a long shot. Only one other player passed the 2,000 mark: Lou Gehrig, with 2,160. For more than forty years, baseball fans believed Gehrig's record would never be broken. The rarity of that kind of consistency becomes clearer when you recognize that only five other players in major league history have ever played in more than a thousand consecutive games. Maybe that's why the game in which Ripken passed Gehrig's record was voted the most memorable in MLB history, ahead of Gehrig's farewell speech in 1939, ahead of Hank Aaron's home run record, and ahead of Jackie Robinson breaking the color barrier in 1947.
Ripken was quick to say that his success didn't come from being more talented than everyone else. When asked if he was a superstar, he responded, "Superstar? Oh, no. . . . I don't think I stack up with the great talents in the league. I have talent, no doubt. My advantage is that I know the game well. The reason is that I grew up in it and had a good teacher in my father. I'm sure that whatever I am as a man and as a ballplayer comes from the way I was raised." Years later, Ripken said of his record:
The streak was really born out of a very simple and honest approach. Dad always taught me to show up at the ballpark each and every day ready to play, and if the manager believes you are one of the nine guys who can help the team win that day, he knows he can count on you and will put you in the lineup. That's simply how the streak started and grew over the years.
In other words, he showed up, worked hard, played hurt, and gave his best—every day for sixteen years straight. He was the definition of consistency.
Recently I was backstage before a speaking engagement, waiting to be introduced to the audience. The host described me as "an amazing leader." I mention this only because I know I'm _not_ amazing. Rather, I'm experienced as a leader, and I've stayed consistent. I'm just experiencing the compounding effect of having paid the price to improve as a leader for a really long time. So at this point in my career, I look better than I actually am.
If you want to have an amazing impact as a leader, you need to make the shift from perks to price and do many unamazing things as you make the difficult uphill climb of leadership and set the example for your team. The reality is that
• Practicing is not amazing.
• Studying is not amazing.
• Showing up is not amazing.
• Working hard is not amazing.
• Asking questions is not amazing.
• Changing is not amazing.
• Trying is not amazing.
• Failing is not amazing.
• Trying again is not amazing.
But every one of these things is necessary. They are the price you must pay every day to reach your potential. If you pay that price and do it consistently, the final result can be amazing.
CHAPTER 5
PLEASING PEOPLE TO CHALLENGING PEOPLE
_The Relational Shift_
_You cannot lead people if you need people._
Pleasing people is not the same as leading people. That was one of the first important lessons I had to learn in leadership. It defined a new reality for me, and it was very difficult for me to learn. Early in my life I realized that most people liked me. My relational connections with others were strong. My teachers liked me. Kids wanted to hang out with me and be around me in the classroom and on the playground. Intuitively, I knew what mattered to people and was able to please them. So naturally, I worked hard at developing my people-pleasing skills. I felt like my leadership mojo was making everyone happy. And doing it made _me_ happy.
During those early years, I might have defined leadership as, "Make people happy and they will follow you." I was continually asking myself one question: "Is everybody happy?" But if you're a leader, the answer is no. You can never make _everyone_ happy. And wanting to do so is a setup for disappointment or failure.
WHO NEEDS A WAKE-UP CALL?
I started my professional leadership career at the age of twenty-two. As already mentioned, I was the leader of a small congregation in Indiana. For the first six months, I felt that everybody was happy. The people there liked me, and I liked them. It was all Kum ba ya.
Then one day I created trouble in paradise. There was an ugly painting in the small lobby of the church. I had noticed it before and thought about how it needed to go, but it hadn't been a priority. I didn't say anything about it to anyone, but I got around to removing it. I considered it a small improvement that I was glad to make.
The reaction was immediate and negative. You'd have thought that I called somebody's baby ugly. Right away I learned that two members of the congregation had given that painting as a gift to the church and had placed it in a prominent spot themselves. When they learned that I had removed it, to say they were not happy is a gross understatement.
I quickly apologized and put the painting back. Whew! That was close. I had dodged the bullet and gone from bad leader to good leader because everyone was happy again.
But a few weeks later, I faced another problem. The youth of our church were playing in a basketball game, and I had promised to attend. But then a member of the church called me with an emergency situation, and I missed the game. The coach of our team and a few of the parents were not happy about it. Uh-oh. I needed do something. So I explained the situation, and the parents got happy again.
But the coach still wasn't happy.
I went to work pleasing him. I visited him twice to smooth things over. And attended the next two games, even though I hadn't promised to. Finally, I had won him back over to the happy side. Yay. I'd succeeded. But boy was this happy stuff beginning to wear me out. How could I possibly keep up with making everybody happy?
For two years I did everything I could to try to make everyone I led happy. I sincerely believed that if my leadership was good, everybody would like me and everything I did. And if someone—anyone—didn't like me or something I did, then it must mean there was something wrong with my leadership and I needed to fix it. That thinking motivated every action I took and every decision I made.
What a mistake! No leader can please everyone all the time. Even history's greatest leaders had their opponents. But back then, I hadn't yet realized that. When the reality struck me that _everyone_ wasn't happy _all_ the time, I hit an emotional wall. I believed that I was a bad leader, and I even wondered if I should resign from my position and try to lead somewhere else.
But then I got wise counsel from leaders with more experience. They helped me to understand that it's impossible to please everyone. Then they taught me an even more important insight about myself. I was doing things backward. My goal had been to get people to like me enough so that I could gain the confidence to ask them for commitment. If they declined, I simply worked harder to try to get them to like me more, thinking that would solve the problem. Worse still, I gave the most time and energy to the unhappiest and least-committed people, even though they were not contributing to the vision or helping to move the organization forward. I was letting the tail wag the dog.
I finally realized that I wasn't leading people. I was trying to make them and myself feel good. I wasn't moving the organization forward. I was in the friendship business, not the leadership business. I wasn't taking people anywhere or helping them to do better and get better. I was trying to live in Happyville.
To get the best out of people, leaders must ask for the best from people. I wasn't doing that at all. Once I realized this, I wish I could say that I shifted from pleasing people to challenging people quickly and easily, but I can't. The process of change for me was very slow. My desire to be liked by others was deeply rooted within me to the point where my best days in leadership were the ones when people affirmed me. I craved that affirmation every day. But I recognized that affirmation doesn't equal leadership accomplishment, so I vowed to change. Step by step, I talked myself out of the idealistic thoughts and feelings I had as a young leader and coached myself to try to become the leader that the people really needed, not just the one they wanted. I made the leadershift from pleasing people to challenging them.
* * *
TO GET THE BEST OUT OF PEOPLE, LEADERS MUST ASK FOR THE BEST FROM PEOPLE.
* * *
HOW TO SHIFT FROM PLEASER TO LEADER
I don't know whether you have the people-pleasing tendencies I once had. If so, you need to make the same leadershift I did, because you can never really lead your organization, serve your people, or reach your leadership potential if you're always trying to make others happy. You have to put _doing_ what's right for your people and organization ahead of what _feels_ right for you. To make that shift, you need to do these seven things:
**1. C HANGE YOUR EXPECTATIONS TOWARD LEADERSHIP**
The heart of my people-pleasing problem was a desire to do what made me feel good. That included an unwillingness to deal with difficult issues. To fix this I had to change the way I thought about leadership and the way I interacted with others. I had to stop seeking affirmation. I had to stop trying to be everyone's buddy.
One of the people who helped me improve in this area was my mentor, Fred Smith (the consultant, not the founder of FedEx). Once while we were discussing how to handle difficult situations with people, he said, "Always separate what's best for you from what's best for the organization." That statement felt like a smack in the face, because too often I had put myself first. I had always thought about what was best for me. Fred gave me a new perspective and suggested that I think about things in a different order:
1. What's best for the organization?
2. What's best for other people within the organization?
3. What's best for me?
By learning to ask myself these three questions in this order, I was able to clarify my motives for leadership decisions.
I must say that during this relational leadershift from pleasing people to challenging people, I felt great loneliness as a leader. The affirmation that had been such a wonderful sound to my ears went silent during this season. The people who used to seek me out for consensus avoided me when they were unhappy. Some of the people who used to "toast" me now wanted to "roast" me. But as I stepped back from the crowd, I started to find myself. I discovered that if I _needed_ people, I probably couldn't lead them well. That gave me determination to shift from making them happy to helping them get better.
Eventually I began to desire what was best for the people I led more than what made me feel good about myself. As the pull for approval lessened, I felt released to do the right thing as a leader. I shared the vision, raised the bar, challenged others, showed the way, asked for commitment, and stopped waiting for consensus. The organization was able to take ground, and I was able to help people start reaching their God-given potential. Those who didn't want to go with me, I allowed to go their own way without expending all my energy trying to win them back.
It took time, but I learned to love the new leader I was becoming. No longer did I wait and worry about having everyone on board. The days of allowing unhappy people to manipulate me and steal my joy were over. The first question I asked would no longer be, "Are we all okay?" Instead, I began to consistently ask, "Are we committed?"
One of the greatest lessons I learned in this season was that you never know if people are really with you until you ask them for commitment. When you ask others for commitment, you lose the uncommitted people and you gain the committed ones. When you don't ask for commitment, you keep the uncommitted and lose the committed. You choose who you lose. I also learned that respect is most often earned on difficult ground. People respect leaders who make the hard decisions, who lead by example in tough times instead of just giving orders, who put others first, and who value people enough to ask them to rise up to the greatness that is within them. It's been forty-five years since I made that leadershift, but I still feel how it changed me and my leadership.
* * *
YOU NEVER KNOW IF PEOPLE ARE REALLY WITH YOU UNTIL YOU ASK THEM FOR COMMITMENT.
* * *
If your leadership is motivated by pleasing others or receiving approval, you need to change your expectations. Shift your focus from what you gain to how you can help people, improve your organization, and achieve your vision. Otherwise, your leadership will always be limited.
**2. V ALUE PEOPLE AS MUCH AS YOU VALUE YOURSELF**
Valuing people is a high priority in my life; every day I intentionally add value to others. For me, this always starts with valuing myself. We see others as we see ourselves, and if we value ourselves, we are able to value others.
Your value assessment of yourself determines your personal investment in others. If you feel that you are worthy of opportunity, you will give others opportunities. If you feel that you are worthy of being developed, you will be willing to develop others. If you see yourself as a 9 (out of 10), you will be more likely to value others highly. If you devalue yourself, you will probably devalue others too. And that's critical because you can't devalue others and be a good leader. Look at how this works:
• Leaders who value their people give them their best effort.
• Leaders who devalue their people give them little effort.
• Leaders who value their people serve them.
• Leaders who devalue their people want to be served by them.
• Leaders who value their people empower them.
• Leaders who devalue their people control them.
• Leaders who value their people motivate them.
• Leaders who devalue their people manipulate them.
To get the best out of people, you need to _believe_ the best about people. Only then will you give them your best—and ask them to give you their best.
**3. W ORK TO ESTABLISH EXPECTATIONS UP FRONT**
In my people-pleasing years, I never established expectations up front. I'd tell myself that sometime, somewhere, somehow, I'd broach the topic of expectations _when the time was right_. But the time was never right, and I never initiated those conversations. Instead, I would work hard to win people over relationally, hoping that they would guess what I wanted from them and that when the tough times came, they would hang with me. But assumptions are never a good method of operation in the leadership world. They always lead to unfulfilled expectations and disappointment.
As a leader, you can either set expectations on the front end and set up the working relationships for success or leave expectations unstated and deal with disappointment on the back end for both you and the people you're leading.
Today, I see the sharing and setting of expectations on the front end as the litmus test for a leader. I go out of my way to be up-front with people.
• Up-front _appreciation_ places value on the person and increases the value of our time together.
• Up-front _expectations_ increase the value of any meeting. (The sooner I set expectations, the quicker and easier the meeting.)
• Up-front _questions_ are the quickest way for people to understand one another and increase the value of our time together.
• Up-front _discussion_ influences the way and direction we lead others.
• Up-front _decisions_ increase the value of our time together.
Being up-front means you're out in front.
When I'm preparing to have an up-front conversation with someone, I work to level-set the interaction with one question and seven statements. First, the question:
_What Are Your Expectations for Our Interaction?_
When I have a conversation with someone, I always invite the other person to go first. It's not only polite but it's smart. Asking a good question without a slanted preamble is good because you can find out what the other person is really thinking, and that's more important than what I want them to think. In addition, if I listen first, the odds increase for the other person to listen to me, because he or she has already been heard.
When I start a professional relationship with someone, the most important thing to establish up-front is our expectations for each other. What does the other person expect of me? What do I expect of him or her? That way we can find out if our desires are compatible. We may need to adjust our expectations to bring them into alignment so that we can both sign off on them. And if I'm the leader in this relationship, the better I know the person, the better I'll know how to lead them.
Once I've learned the other person's expectations up front by asking questions, I set expectations for the other person by communicating these statements:
_It's Not About Me—It's Not About You—It's About the Big Picture_
A mature person has the ability to see and respect different perspectives. However, when you're leading a team, department, or organization, you must always keep your eye on the big picture. And maybe you're aware of what I call the Law of the Big Picture in my book _The 17 Indisputable Laws of Teamwork_ : the goal is more important than the role. Each person has a role on a team. Why? To help the team accomplish its goal. To fulfill the bigger picture, no individuals—not any team member and not the leader—can lose sight of the goal and get consumed by themselves.
This statement has power only when I start with the part that says it's not about me. I may be the owner of my companies, but I need to remember that it really isn't about me. I don't need to make every leadership decision. I don't need to have my idea win in every meeting. The organization needs to be successful. And if others know that it's not about me, then they should be willing to accept that it's also not about them. This can be difficult for some people, especially if they are very talented and have star potential. But high talent with low self-awareness requires a lot of maintenance. That's why it's important to get expectations settled up front. The team doesn't play its best when its best player thinks it's all about them.
* * *
THE TEAM DOESN'T PLAY ITS BEST WHEN ITS BEST PLAYER THINKS IT'S ALL ABOUT THEM.
* * *
_You Must Value Other People_
All leaders are in the people business. If we want to work well with people, we need to value them and add value to them. And here's the good news: adding value to people is also good for business.
Anyone who works with me needs to value people. That's the core of who I am and it's the core of all my companies. We must be willing to serve others, and servant leadership isn't difficult if we value people. When we value people, they feel valued. And we are able to succeed in our mission.
_You Are Expected to Keep Growing_
How do you grow an organization? Through the growth of its individual members. The future of any organization can be found in the growth of the people who are a part of it, and especially the people who lead it. As the Law of the Lid says, leadership ability determines a person's level of effectiveness.
I am a lifelong learner who is intentional about learning something every day of my life. I'm also attracted to people who grow. My best friends are the ones who are continually developing themselves. Our conversations are stimulated by our growth journey.
I expect anyone who joins my team to be intentional about personal and professional growth. Growing together is even better than growing alone. Teams either grow together or they grow apart. Making a commitment to grow every day and then developing relationships with growing people will keep us on the growth track.
_You Must Be Prepared to Change_
There is a vast difference between conceding that change is inevitable and believing change is essential. The person who concedes that change is inevitable becomes resigned to it and is reactive, thinking, _Change is going to happen, so what can I do?_ The individual who believes change is essential is proactive and thinks, _I will make change happen so that our team can improve._ If growth is expected then change is essential. We cannot grow without changing. The very fact that I do something better today means that I learned and improved something yesterday.
* * *
THERE IS A VAST DIFFERENCE BETWEEN CONCEDING THAT CHANGE IS INEVITABLE AND BELIEVING CHANGE IS ESSENTIAL.
* * *
_Everyone Has to Earn My Time_
There are a lot of things I freely give to everyone in my organizations: vision, belief, resources, support, and leadership. One thing that must always be earned is my time. That is the most limited of my personal resources, so it must be earned before I give it. How does someone do that? By being a productive member on the team. In this, I practice the 80-20 principle. I give 80 percent of my time to the 20 percent of the team that produces 80 percent of the results.
Earlier in my career I spent a lot of time with unproductive people, thinking I could change them. I was so naïve. As I mentioned, at first I just wanted to win everyone over. Later, I started to think about people's potential, and I would ask: _Will they do it? Can they do it? Is it worth the effort to ask them?_
Today I'm very pragmatic, and I don't ask those questions, because they are too subjective and rely too much on speculation. Now I ask myself just one question: _Are they productive?_
I place this same standard on myself. Just because I enjoy a friendship with someone doesn't mean I get a pass on productivity. For example, for several years Tom and Todd Mullins included me on the teaching team of Christ Fellowship Church. Tom is founding pastor and Todd, his son, is the lead pastor. Both are good friends, and I have loved every minute of my time teaching. However, every year I ask them this question: "Do you want me on the team again this year, or do you want to make a change?" They know I am always ready to step down for the sake of the team. If I can't be productive for them, it's time for me to go.
If you work for someone, value that person's time and be aware that you need to earn it. If others work for you, give your own time only to those who are productive and who are willing to learn, grow, and keep earning it.
_Always Take Responsibility_
Most people want empowerment when what they need first are responsibility and accountability. As Kevin Turner, who is vice chairman of the board of managers of Albertsons and senior advisor to the company's chairman and CEO, said, "People want to be judged by their intentions not by their actions." But results are what make a difference, not good intentions. And results come only when people take responsibility for themselves.
I like what business executive Seth Godin said about this:
Employees wait to be picked for promotion, or to lead a meeting or to speak up at a meeting.
"Pick me, pick me" acknowledges the power of the system and passes responsibility to someone to initiate. Even better, "pick me, pick me" moves the blame from you to them.
If you don't get picked, it's their fault, not yours.
If you do get picked, well, they said you were good, right? Not your fault anymore.
Reject the tyranny of picked. Pick yourself.
That's what taking responsibility is. It's picking yourself. It's motivating yourself. It's bringing intentionality and energy to everything you do.
Speaking of energy, that's an area where I especially expect people to take responsibility because, sadly, the lowest energy level often brings down the team. People with negative energy and attitudes can take the team lower faster than people with positive energy can take it up. This is especially true in meetings. How does a leader deal with this problem?
I start by having energy check-ins at the beginning of meetings. I simply ask each person in the room what their energy level number is as I start a meeting. This motivates everyone to be fully present in the room. If needed, I put everyone's name and number on the board, and then I let them know what level of energy is needed from everyone in the room for us to be successful in the meeting. People usually take responsibility to raise their energy to the level of expectations, and it helps the meeting to have high energy and positive results.
_We Will Not Avoid Tough Conversations_
Leadership demands that we tackle the problems. That includes tough conversations. And their difficulty increases when the issue is not easy and it involves people on our team. But we should never delay tough conversations. The more you wait, the more difficult they become. Why?
• Silence to most people means approval.
• When people have to fill in the blanks themselves, they do so negatively.
• Problems left unaddressed have a snowball effect: they become larger and gain momentum.
• Problems left unaddressed cause inner erosion: we lose respect for ourselves internally.
• The Law of Diminishing Intent is in effect: The longer you wait to do something you should do now, the greater the odds that you will never do it. One of these days becomes none of these days.
Back in the days when I directly supervised a lot of staff, I used to tell them, "Never worry about how you are doing. I will let you know immediately if there's a problem." I don't sit on issues. If I need to have a tough conversation, I have it as soon as humanly possible.
You've probably heard the saying that all's well that ends well. I also believe that all's well that begins well. That's what establishing up-front expectations does for you as a leader. It helps you begin well so that you can challenge people to become their best.
**4. A SK YOURSELF THE HARD QUESTIONS BEFORE ANY POTENTIALLY DIFFICULT CONVERSATION**
As I grew in my leadershift from pleasing people to challenging people, I had to work hard at becoming better at difficult conversations. One of the questions I began asking myself was, _What is the source of the problem prompting the need for this challenging conversation? Is it an external issue, is it a problem within the other person, or is it me?_ If the issue was external, like poor communication, a bad system, or an external problem, it would be easy to solve. If it was a problem related to the person's attitude or actions, it would be more difficult. If the fault was mine, then I might not need to meet with the other person at all. I just needed to own up to it and fix myself! If it was any combination of the three, then the conversation would be very difficult because of the complexity.
As you think about any difficult conversation you are getting ready to have, I want to give you some help. Here is a checklist I've used _before_ having difficult conversations to help me prepare:
**QUESTIONS TO CONSIDER:** | **YES** | **NO**
---|---|---
Have I invested in the relationship enough to be candid with them? | |
Do I demonstrate that I value them as individuals? | |
Am I sure this is their issue and not mine? | |
Am I sure I'm not speaking up because I feel threatened? | |
Is the issue more important than the relationship? | |
Does this conversation clearly serve their interests and not just mine? | |
Am I willing to invest time and energy to help them change? | |
Am I willing to show them how to do something and not just say what's wrong? | |
Am I willing and able to set clear, specific expectations? | |
Have I previously addressed the issue or problem in a less formal setting? | |
Total: | |
Take a look at the tally of _yes_ or _no_ responses. If you have one or more _no_ responses to any of these questions, consider what steps you need to take to make that _no_ become a _yes_ before you conduct that crucial conversation.
**5. W HEN A TOUGH CONVERSATION IS NEEDED, DO IT RIGHT**
Because it was once so difficult for me, I want to give you some advice about how to make a tough conversation less tough. First, remember why you are having the conversation. It's because you care about the other person; you care enough to confront them. Your goal is to help that person.
Having the right attitude is essential because your actions often carry more weight than your words, and a negative attitude can cause more damage. People remember how they felt long after they have forgotten what you said. You can communicate the right attitude by seeking to understand. Here is a road map for the conversation:
• State the issue clearly at the beginning. Use the phrase, "Are you aware that. . .?"
• Ask them to tell you their perspective. Start with the phrase, "I need you to help me understand your situation."
• Ask questions. Say, "Am I hearing you correctly?"
• Repeat back what you heard.
• Allow them to respond.
• Try to find common ground.
• Arrive at an agreement on what's best for both of you.
• If you cannot come to an agreement on the issue and solution, agree to meet again.
• See the growth opportunity that lies within the tough conversation.
• Seek to maintain a positive relationship.
* * *
HAVING THE RIGHT ATTITUDE IS ESSENTIAL BECAUSE YOUR ACTIONS OFTEN CARRY MORE WEIGHT THAN YOUR WORDS.
* * *
Following this pattern and arriving at a positive outcome is not always possible, but it's worth trying to attain. You're always better off having the tough conversation and finding out where you stand rather than avoiding it and hoping the problem will resolve itself, because it never does.
**6. U NDERSTAND THE 25-50-25 PRINCIPLE**
Good leadership always challenges people to rise to the occasion, become their best, and achieve more. Some people accept the challenge and help the team to win. Others don't. As a leader, you have to manage the process that people go through. You can use the 25-50-25 principle to help you. I learned about it years ago when I attended a leadership roundtable in Los Angeles.
Here's how it goes: Whenever you cast vision and challenge people to become part of achieving an endeavor, they tend to fall into one of three groups. Typically, 25 percent of the people will support your efforts, 50 percent will be undecided, and 25 percent will resist change. Your job is to help the middle 50 percent join the first 25 percent. Here are tips for doing that and working with all three groups:
• Understand that the resistant bottom 25 percent are not going to join you, no matter what you do. The greatest leader in the world could be leading them, and they would still resist change. Accept that.
• Don't waste your effort trying to make this bottom 25 percent happy. They are not going to get happy. Trying to placate them will only encourage their resistance.
• Don't give the bottom 25 percent a platform or credibility. If you believe you're doing the right thing, why would you help them undermine that?
• Try to keep the bottom 25 percent away from the 50 percent who have not yet made up their minds. As baseball manager Casey Stengel said, "The secret of managing is to keep the guys who hate your guts away from the guys who haven't made up their minds yet."
• Ask the 25 percent who support you to help positively influence the middle 50 percent who are undecided.
• Give the supportive 25 percent credibility and a platform to speak. They will help you help the organization move forward.
Any movement you can create in the middle 50 percent toward your leadership and the vision is a win because it takes the organization in the right direction. Celebrate that and keep moving forward.
**7. B ALANCE CARE WITH CANDOR**
I want to give you one more piece of advice related to challenging people, and it's an important one. As a leader, you need to bring both caring and candor into the relationship. I'll explain why that's so important in a moment. But first, let me set it up for you by explaining one of the core teachings I use to develop leaders. It's called the 5 Levels of Leadership. It illustrates a process whereby people can develop influence with others. Here is a brief description of each of the five levels:
1. **P OSITION** (based on rights), where people follow you because they have to.
2. **P ERMISSION** (based on relationships), where people follow you because they want to.
3. **P RODUCTION** (based on results), where people follow you because you help improve the team.
4. **P EOPLE DEVELOPMENT** (based on reproduction), where people follow you because you improve them personally.
5. **P INNACLE** (based on respect), where people follow you because you help them become leaders at Level 4 themselves.
In the forty years I've used the 5 Levels of Leadership to train and develop leaders, I've observed that the most difficult step for most leaders to take is from Level 2 to Level 3. Almost any likable person can develop relationships with people on Level 2, caring about them and connecting with them. But Level 3 is about production. Making the transition from getting people to like you to getting people to produce better results can be daunting. And reproducing yourself on Level 4 by investing in another person and helping him or her become a good leader is even more difficult.
How does a leader move others from "I like being on the team," to "I need to produce for the team"? The answer is to balance care and candor. I mention this because most people naturally default to one or the other. But here's why it's important for you to practice both:
• Care without candor creates dysfunctional relationships.
• Candor without care creates distant relationships.
• Care balanced with candor creates developing relationships.
Care and candor are like the two wings of a plane; you can't fly with only one. They must work together.
**CARE** | **CANDOR**
---|---
Values the Person | Values the Person's Potential
Establishes the Relationship | Expands the Relationship
Shores Up Weaknesses | Brings Out Strengths
Offers Comfort | Offers a Challenge
Makes the Team Pleasant | Makes the Team Productive
Caring should never suppress candor, while candor should never displace caring. When I have the responsibility for leading people, I must care for them, but I must also challenge them by initiating honest conversations to help them improve. My mind-set should be, "I love you too much to let you stay where you are." That thinking was difficult for me when I was a young leader. Caring was easy; candor was difficult. Today I'm able to sit down with people and have honest, tough conversations with them. But the principle that guides me is a saying I adopted long ago: people don't care how much you know until they know how much you care. That helps me to keep the right balance of care and candor.
It's been almost fifty years since I made the leadershift from pleasing people to challenging them. It's been one of the most difficult changes I've had to make in my leadership, but it has also been one of the most rewarding. If I hadn't been willing to face up to the need to change, I'd have gotten stuck in my leadership.
I don't know how much difficulty people pleasing has given you. Maybe it's not an issue at all. I hope that's the case. But no matter what, you need to learn how to positively challenge people if you desire to become the best leader you can be. If you can help people to positively reach their potential, you help them, your team, and yourself.
CHAPTER 6
MAINTAINING TO CREATING
_The Abundance Shift_
_The joy is in creating—not maintaining._
—VINCE LOMBARDI
Have you ever thought about the expectations your profession or industry places on you? Are people in your leadership position expected to hold the line? Maintain the course? Change direction? Get out of the box? Blow up the box?
When I started my career, it never occurred to me to think about such things. I knew from a fairly early age that I was going to become a pastor. That determined my course of study in college, and after I graduated, I was happy to get my first job in rural Indiana. A few weeks after Margaret and I got married, we moved there and off we went. That was back in 1969. In those days, the role of pastors was pretty set. We were expected to be shepherds, and our main job was to feed and care for the flock. The whole mind-set was _maintaining_. As much as I loved the people in my congregation and had looked forward to being a pastor, it wasn't long before I started to feel unsettled.
Each year the organization I belonged to held a meeting for the pastors and leaders of all the churches. Toward the end of my first year on the job, I went to my initial meeting as the leader of my own church. It was good to see some friends from college and to catch up with them. But what struck me most was how _traditional_ everything was. The highlight of the meeting was when the pastor of the year was recognized. For the first time, it struck me. The people they honored were always the ones with the longest tenure, the leaders who were faithful—the maintainers.
I did not want to be a maintainer. Tenure wasn't my goal. I began to feel like a misfit among a group of people who valued tradition and conformity, and my sense of unsettledness only increased. And the way the organization worked, if you were a faithful shepherd at a small church and didn't rock the boat, you were eventually invited to pastor a larger church. If you were faithful there, you would get offered a denominational position. The recognized pastors maintained their way to the top. And on it went until you received recognition toward the end of your career as you approached retirement. I could see the whole path ahead of me. I was beginning to suspect that it wasn't a good fit for me. I wanted to innovate. I wanted to reach people. I wanted to build a great church.
Years later, someone in the ministry world pointed out that not all pastors are actually shepherds. He referred instead to another analogy: church leader as rancher. He described the difference this way: while shepherds are maintainers who care for the sheep they already have, ranchers are leaders who pioneer new ideas and build. Now, I'm not saying that people are livestock. But there's a difference in mind-set between these two types of people, and it was clear which type I was. I wanted to build.
There's an old saying: don't tear down a fence until you know why it's there. Within my organization, I wasn't someone who was itching to tear down fences, but I _was_ a questioner. I was very quick to ask why a fence had been put up. And whether it still needed to be there. And if it could be replaced by something better. If the reason something was done was reasonable, then I'd leave it alone. If not, then I started asking, "Why not do it another way—a better way?"
Asking questions and exploring ignited my creativity. Although, within my organization, it seemed like I was the only one doing that. In fact, my questions annoyed them. They questioned my questions—they couldn't understand _why_ I was asking them at all. It eventually became clear to me that I wasn't compatible with the culture, and I needed to make a change. So I left the organization.
RECOGNIZE WHAT ZONE YOU'RE IN
I don't want to put down the organization I was a part of or the people I grew up with. They were good people. However, I believe the culture they were part of was working against them. It's difficult overcoming a maintaining culture. And if you also happen to have an inherent tendency toward inactivity when it comes to innovation, you have even more to overcome.
I've observed that we all tend to fall into one of four different zones when it comes to innovation, which impacts how we live, how we lead, and what we achieve. Here are the zones, along with attitude statements that represent them:
1. **T HE COASTING ZONE—**"I do as little as possible."
2. **T HE COMFORT ZONE—**"I do what I have always done."
3. **T HE CHALLENGE ZONE—**"I attempt to do what I haven't done before."
4. **T HE CREATIVE ZONE—**"I attempt to think what I have never thought before."
To which zone do you naturally gravitate? Do you tend to live in the coasting zone, casually—even passively—doing as little as possible? Do you tend to stay in the comfort zone, avoiding risks? Do you connect with the challenge zone, where you try new things and willingly risk failure? Or do you try to stretch yourself the furthest by living in the creative zone, where you explore new ideas, seek out other perspectives, and cross bridges in your imagination long before you physically reach them?
The good news is that we have the ability to choose a zone different from our natural one. And I recommend the creative zone, because it is where we experience abundance and expand our potential. If you want to take your leadership to ever-higher levels, you need to make the leadershift from maintaining to creating and try to live in the creative zone.
UNLOCK THE MENTAL BLOCKS THAT KEEP YOU OUT OF THE CREATIVE ZONE
How can you make the shift from maintaining to creating? I believe you must start the process from the inside out. Begin by removing some of the mental blocks that cripple so many people's creative potential. Roger von Oech wrote extensively about many of them in his book _A Whack on the Side of the Head_. I've included some of my favorites. Which of these phrases do you find yourself thinking or saying?
**M ENTAL BLOCK #1: "FIND THE RIGHT ANSWER"**
It's wrong to believe there is only one right answer to any question. There are always other solutions. If we believe they are there and we're willing to look for them, we will find them.
**M ENTAL BLOCK #2: "THAT'S NOT LOGICAL"**
Albert Einstein said, "Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world." Imagination turns possibilities into reality. It's willing to take leaps that logic can't. While logic does have great value and you should keep it, you should intentionally add creativity.
**M ENTAL BLOCK #3: "FOLLOW THE RULES"**
I've always loved this quote from Thomas Edison: "There ain't no rules around here! We are tryin' to accomplish some[thing]!" Most revolutionary ideas have been disruptive violations of set rules.
**M ENTAL BLOCK #4: "AVOID AMBIGUITY"**
Life is complex. It's messy. It's contradictory and paradoxical. Why in the world would we think we should—or could—avoid ambiguity? There is never one fixed way to understand something—everything can be understood in more than one way.
**M ENTAL BLOCK #5: "FAILURE IS BAD"**
Creative people don't avoid failure. They see it as a friend. They know that if they are to experiment, innovate, and create, they will fail. They embrace risk.
**M ENTAL BLOCK #6: "DON'T BE FOOLISH"**
To stand up is to stand out. You have to stick your neck out to put your head above the crowd. If others don't at first understand or accept you, so what? All the great dreamers looked foolish to someone. How you are perceived by others is less important than how effective you can be.
**M ENTAL BLOCK #7: "I'M NOT CREATIVE"**
The mental block that most keeps us from being creative is believing we don't possess creativity. This self-perception is a barrier to talent, opportunity, and intelligence. But the truth is that everyone can learn to be creative. The only real block to creativity is our disbelief.
I love what blogger Hugh MacLeod said about this: "Everyone is born creative; everyone is given a box of crayons in kindergarten. Then when you hit puberty they take the crayons away and replace them with dry, uninspiring books on algebra, history, etc. Being suddenly hit years later with the 'creative bug' is just a wee voice telling you, 'I'd like my crayons back, please.'"
CREATIVE PRINCIPLES TO LEARN AND LIVE BY
If you want to shift from maintaining to creating in your life and leadership, then you need to take your crayons back. Here's how:
**1. B UILD A CREATIVE CULTURE**
If you lead a team, department, or organization, take responsibility for promoting creativity and building a creative culture. Several years ago, I read an article in _Forbes_ that took tips from _Disciplined Dreaming_ by Josh Linkner, and they provide great insight in how to make your organization's culture more creative. I've interpreted his ideas, plus added a few of my own.
_Fuel Passion_
Creativity requires time, tenacity, testing, options, U-turns, imagination, questions, failure, and change. All these things require a lot of energy. Passion provides the fuel.
_Celebrate Ideas_
What gets celebrated gets done. If you reward ideas with money, praise, and opportunity, people will come to value ideas and work toward generating and sharing them.
_Foster Autonomy_
George S. Patton said, "Never tell people _how_ to do things. Tell them _what_ to do and they will surprise you with their ingenuity." What he was really talking about was allowing people to have enough autonomy to be creative. Micromanagement undermines creativity while freedom and flexibility foster it.
_Encourage Courage_
Creativity requires risk, and taking risks requires courage. As a leader, you need to model it and encourage it. As Daniel R. Denison of IMD Business School said, "There is always a premium on being able to deal with the unknown. People will venture there if they feel they'll be secure in doing it. It's the leader's job to create that sense of security."
_Minimize Hierarchy_
In creative environments, decisions are made closest to the problems. For that to happen, leaders need to minimize the number of layers between the top and the bottom. A few years ago, I read an article by Robert Kaplan in which he interviewed now-retired General Stanley McChrystal, who said, "Any complex task is best approached by flattening hierarchies. It gets everybody feeling like they're in the inner circle, so that they develop a sense of ownership."
_Reduce Rules_
Author Henry David Thoreau wrote, "Any fool can make a rule and every fool will mind it." Creativity gets stifled when everyone expends too much energy worrying about following rules. Too many rules cause idea anemia. General Douglas MacArthur said, "You are remembered for the rules you break." I like that idea.
_Fail Forward_
I once saw a sign that said, "Company Motto: We make _new_ mistakes." I love that. I'm a huge supporter of the idea of failing forward. So much that I wrote an entire book on the subject. If you fall down, you should learn from it, get up, and step forward. Any time you learn what doesn't work, you're a step closer to what does work.
_Start Small_
Too often we want huge breakthroughs and innovations when we should be looking for small ones. If you want one great idea, look for a lot of good ideas. If you want to create something significant, build it in small increments. Do that consistently, and you make creative progress.
The more you foster creativity in the environment you influence, the more you instill an abundance mind-set. That's why I call this leadershift the abundance shift. It's like poet Maya Angelou said, "You can't use up creativity. The more you use, the more you have. Sadly, too often creativity is smothered rather than nurtured. There has to be a climate in which new ways of thinking, perceiving, questioning are encouraged." As a leader, you have the influence and an obligation to try to create that climate.
**2. M AKE EVERYTHING BETTER**
You've probably heard the expression, "It doesn't get any better than this." Well, I have news for you. It _can_ get better. Everything can get better. And as leaders, we should be catalysts for improvement. We need to champion the idea expressed by poet James Russell Lowell, who said, "Creativity is not the finding of a thing, but making something out of it after it is found."
* * *
CREATIVITY IS NOT THE FINDING OF A THING, BUT MAKING SOMETHING OUT OF IT AFTER IT IS FOUND.
—JAMES RUSSELL LOWELL
* * *
I have a process for making things better that I use with my team. I call it 10-80-10. Whenever we start on a task or project, the first thing I do is identify the target, which represents approximately 10 percent of the process. So, the first 10 of 10-80-10 focuses on _knowing_ what we want to accomplish. After all, how can I find what I don't know that I'm looking for? This sets up the next part of the process, which is the 80 percent. The focus here is production. Now that the task has been set in the right direction, the team finds the way to execute it. Sometimes they have to try things out, practice different approaches, find out what works.
I've observed that when most teams reach this point, the leader is done. However, there's still one more step to take things to a whole new level. This is the final 10 in 10–80–10. This last 10 percent is like putting the cherry on top. Once the team has the strategy and process down and everything's working, I see if there's a way to make it even better.
Can we take an idea to the next level? Can we target a message even more sharply? Can we make a client's experience even better? Can we add something to an event to make it spectacular? Is there anything important that the rest of the team didn't see because they were too far into the weeds and didn't have perspective? What can we do to go the extra mile? This phase is where great innovation often occurs and we are able to maximize ideas. It's also the reason we as a team are so often able to exceed expectations.
**3. M AKE PLANS BUT LOOK FOR OPTIONS**
No doubt good leaders use plans to get things done. But planning is not the end-all and be-all of leadership. Leaders who cling too inflexibly to a plan stifle creativity and miss opportunities. To be creative, leaders need to add options to their planning. I think of this as moving from Plan A to Option A. I'll explain that in a moment, but first I want to talk about planning. The first definition of planning that I ever learned was this: planning is predetermining tomorrow's results today. I love that definition. It is so specific. It offers a promise of control over tomorrow through what you're doing right now. As a young leader, I wanted and needed some certainties in my life that I could rely upon, and planning looked like it would be one of them.
Every day I would plan my work and work my plan. I even thought of myself as a man with a plan. Ten-year plan? I had it. Five-year plan? Check. Two-year plan? On paper. In detail. I was ready to let anybody read it. My personality was controlling, and planning put me in control. I was also aided by living in Hillham, Indiana, a small farming community where very little changed. I felt on top of everything.
As I progressed in my leadership, planning became more complicated. But my understanding of it also dealt with that complexity. A decade into my leadership career, I was teaching a seminar entitled PLAN AHEAD. Here's what I taught other leaders to do:
• Predetermine your course of action.
• Lay out your goals.
• Adjust your priorities.
• Notify key personnel.
• Allow time for acceptance.
• Head into action.
• Expect problems.
• Adjust your plan.
• Daily review your plans.
Notice, my planning formula now included, "Adjust your priorities," "Allow time for acceptance," "Expect problems," "Adjust your plan," and "Daily review your plans." Why? I had begun to learn that there was no perfect plan. You can't just sit down and plan tomorrow with certainty. You have no control over it. You don't control other people. Even controlling yourself can be a challenge. I had begun to make a leadershift from rigidly working on a set plan to regularly adapting my plan to deal with unaccounted problems, uncooperative people, and unexpected opportunities. I was growing, but I still had a long way to go.
More than two thousand years ago, Publilius Syrus wrote, "It is a bad plan that admits of no modifications." I believe what he really meant is that it's a bad _leader_ whose plans don't allow modifications. Good leaders are flexible and their plans are fluid. They allow for creativity. They plan, but they look for options. And that's important. Options always present themselves soon after action is taken on a plan. If we don't open ourselves up to those options, we miss the chance to innovate, to create, and—sometimes—to win.
In football, there is the game plan. It is developed before the game starts. For example, the offensive coordinator for a pro football team plans how the offense will attack, and before the game he will often script the first twenty plays. Meanwhile, the defensive coordinator creates his plan against the other team's offense. But their plans don't always work, or they work less effectively than was hoped. That's why coaches have to make adjustments. On his blog, author and speaker Steve Pavlina wrote about how good leaders look for options and make adjustments:
Stephen Covey often used the expression, "Integrity in the moment of choice." What that means is that you should not follow your plans blindly without conscious awareness of your goals. For instance, let's say you're following your plans nicely—so far so good—and then an unforeseen opportunity arises. Do you stick to your original plan, thereby missing the opportunity, or do you stop and go after the opportunity, thereby throwing yourself off schedule? This is where you have to stop and reconnect with your goals to decide which is the better course. No plan should be followed blindly.
As a young leader, I needed to learn to seek out options. Too often, I sought great security in my plan. I identified a single, solitary pathway. The good news is that I held to my plan and made progress. The bad news is that because I held to that plan, I missed opportunities that would have expanded my plans and my potential. Being inflexible and sticking to my plan put a lid on me and my organization.
I'm not disparaging planning. It is essential for success. As the old Yogi Berra quote says, "You've got to be careful if you don't know where you are going because you might not get there." But the best leaders also adapt. They use options to their advantage. The more they've invested in their plans the more likely they are to defend and hold on to them too long. It's a natural reaction, but not allowing themselves to see and explore options isn't creative, and it isn't good leadership.
The best leaders are flexible. As leadership author Warren Bennis said, "Adaptive capacity allows leaders to respond quickly and intelligently to constant change. It is the ability to identify and seize opportunities. It allows leaders to act and then evaluate results instead of attempting to collect and analyze all the data before acting."
One of the instances when I recognized the need to search for options came in my writing career. When I first started writing, I found it very difficult. The only way I wrote my first few books was through sheer discipline. I planned my work and then forced myself to follow it. Jeff Fisher said, "Discipline is doing what you really don't want to do so you can do what you really want to." That described me. When it came to writing, I really didn't want to do it!
I wondered if there were any other options besides gritting my teeth and forcing myself to write. The first thing I did was ask myself why I enjoyed speaking. I was able to answer that in a single word: _anticipation_. Whenever I spoke, I anticipated a positive response from the audience. That immediate feedback was missing when I wrote. If you're familiar with the traditional publishing process for books, you know that after you finish a manuscript, you must wait an entire year before the book is published and your audience gets to read it.
I asked myself, _Is there a creative way to create anticipation for my writing?_ Soon the ideas began to flow. I found a picture of an audience I had spoken to, printed a quote from a writing mentor, and placed them both at my desk so that I'd see them every day as I wrote. The quote said, "I write books to extend my influence to people beyond my personal touch." Seeing the picture and the quote helped inspire me and build positive anticipation of my work's results.
Today I don't need those prompts to inspire me to write. I'm at my desk at 5:30 most mornings, anxious to put words to paper. But if I encounter another problem, I'll go looking for options. Multiple options always help us find solutions. Creativity is the joy of not knowing all the answers but of knowing the answers are out there. We just need to find them.
* * *
CREATIVITY IS THE JOY OF NOT KNOWING ALL THE ANSWERS BUT OF KNOWING THE ANSWERS ARE OUT THERE.
* * *
**4. P LACE HIGH VALUE ON IDEAS**
Harvey Firestone, one of the most successful businessmen of the nineteenth and early twentieth centuries, said, "Capital isn't so important in business. Experience isn't so important. You can get both of these things. What is important is ideas. If you have ideas you have the main asset you need, and there isn't any limit to what you can do with your business and your life. They are any man's greatest asset—ideas." If you want to be creative, you must place high value on ideas and learn how to generate them. You can by following this process:
_Start Gathering Ideas_
I have been a collector of ideas all my life, and this practice has been the foundation for my ability to keep writing, speaking, and leading. I encourage you to look for ideas everywhere and glean them from everyone. Whenever you are successful in gathering ideas, do two things. File those you don't intend to use right away by title. And keep in front of you any ideas you're currently giving consideration. The first practice keeps you from losing ideas while seeking new ones. The second practice enables you to look for connections between the ideas you've found and whatever you are currently working on.
_Test Every Idea That You Gather_
The more ideas you test, the more likely you are to find one that works. Remember, just as there isn't one right answer to a problem, there isn't just one good idea. There are many. And when ideas are tested and put together, there might be many great ideas. Test every idea to see if it is—or could be made to be—great.
_Analyze Your Failures_
Analyzing my failures has been a major help to me—maybe because I've experienced so many failures, flops, and fumbles. When an idea falls apart, take time to consider what went wrong and how you can learn from it. The only truly bad ideas are those that die without giving rise to other ideas. Great ideas are often nothing more than the restructuring of ideas that failed.
_Adapt Other Ideas_
Stanley Weston, creator of the action figure G. I. Joe said, "Truly groundbreaking ideas are rare—but you don't necessarily need one to make a career out of creativity. My definition of creativity is the logical combination of two or more existing elements that result in a new concept. The best way to make a living with your imagination is to develop innovative applications, not imagine completely new concepts." Every successful idea is based on other ideas that precede and surround it. Taking existing ideas and adding to them is how the human race has made progress.
_Question All Assumptions_
Assumptions are creativity killers. If you assume there is not a better way, you won't find one. Assume that you have found the answer, and you won't find a better answer. Assume that it's never going to get any better, and it won't. When you're working to be creative, don't take anything for granted. Question. Wonder. Challenge. Go back to the beginning if necessary. The more open the mental playing field, the better your odds of finding new and better ideas.
**5. S EEK OUT AND LISTEN TO DIFFERENT VOICES**
Creativity thrives when one subject is approached from many different perspectives. It short-circuits the kind of one-way thinking that interferes with better solutions. If we get into single-perspective thinking, we find ourselves in ruts. If we see things from a new perspective, we can be like the mechanic who told his customer, "I couldn't repair your brakes, so I just made the horn louder."
* * *
CREATIVITY THRIVES WHEN ONE SUBJECT IS APPROACHED FROM MANY DIFFERENT PERSPECTIVES.
* * *
Norman Vincent Peale said, "Ask the God who made you to keep remaking you." I do that. I try to remain teachable, and I listen to many different voices and perspectives to try to improve myself. That's why I always try to surround myself with the best and the brightest people I can find. I like nothing more than to bring together a group of leaders, young and old, new and experienced, and ask them for their perspectives on a question, problem, or project. I'm a firm believer in the T-E-A-M principle: Together Everyone Accomplishes More. I want others' assessment. And I love that word: _assessment_. It comes from the Latin _assidere_ , which means "to sit beside." I want people willing to sit beside me, share their perspectives, give their insights, add their ideas to mine, and make all of us better.
From about the age of forty, I have greatly valued the help of my inner circle, the people closest to me in life and in business. These individuals compensate for my weaknesses, focus on today, and implement much of the work in my organizations. Most of these people have worked with me for many years, some for more than two decades. But over the last few years, I have intentionally cultivated another group that I call my outer circle. These people have fresh eyes and can speak to me from a different perspective. They enhance my strengths, help me focus on tomorrow, and give me creative ideas. The people in this group change frequently, based on time and opportunities. Together, both circles complement or empower each other and complete me.
A couple of years ago, I felt I needed new input in my writing. I wanted an outsider's fresh perspective on how to improve. I invited someone into my outer circle to challenge me. The result? My writing became more reflective and personal. Conventional wisdom would warn not to mess with success. I disagree. If you want to bless your success, mess with it. Get another perspective. Listen to other voices. Have the courage to let go of your certainties, challenge your assumptions, and change your way of doing things. It will make you more creative.
**6. T AKE RISKS**
I witnessed a fantastic example of creative risk-taking on January 8, 2018, in a college football playoff National Championship game between the University of Alabama Crimson Tide and the University of Georgia Bulldogs. At the end of the first half, coach Nick Saban's Alabama team was losing 13–0, because his offense was having no success against the tough defense of Georgia. That point spread may not sound like much, but in a game that was expected to be a defensive battle, two touchdowns seemed like a lot to overcome. Alabama's quarterback, Jalen Hurts, the sophomore who had started every game and set many Alabama records the previous year, didn't look like he would be capable of winning a shootout. So what could Saban do?
Some coaches would have ramped up their defense to try to stop their opponent. Others might have tried running different offensive plays. Saban made another choice that was a huge risk. Thinking outside of the box, Saban started the second half with an untested freshman quarterback, Tua Tagovailoa. What a bold move! Tagovailoa had never started a college game and had very little playing time, yet he was asked to lead the team in the most pressure-filled game of the season.
I've never before seen a coach change from a tested quarterback to an inexperienced freshman quarterback during the most important game of the season. Had Alabama lost, Saban would have been criticized mercilessly. But they didn't lose. Saban's creative risk changed the outcome of the game. Alabama ended up winning the game 26–23 in overtime when they scored a touchdown on a pass by the freshman quarterback. That creative move was praised as the key to victory.
**7. L IVE ON THE OTHER SIDE OF "YES"**
Recently I was casting vision to a large group of leaders. There was a great sense of anticipation as I shared the possibilities and opportunities that could be before us if we partnered together and joined hands to accomplish this vision. After that session, I met in the green room with the top leaders of that organization, continuing to discuss the possibilities of working together. One of those leaders, Larry Stockstill, interrupted the discussion and said, "John, the answer is yes. Count me in. Whatever this means, I am a 'yes.'" His response energized the room and everyone followed his positive lead.
After the meeting when Larry and I were together, I thanked him for his positive response. I was curious, so I asked what made him respond so boldly.
"I live on the other side of 'yes,'" Larry said, "That's where I find abundance and opportunity. It's where I become a better and bigger self. The opportunity of a lifetime must be seized within the lifetime of the opportunity. So I try to say 'yes' whenever I can."
Larry's statement made a strong impression on me, and I love his phrase: live on the other side of "yes." I believe what he's talking about is seizing opportunities. When we do that, we're like Lori Greiner who wrote,
Dear Optimist, Pessimist and Realist—
While you guys were busy arguing about the glass of [water], I drank it!
Sincerely,
The Opportunist
How can you become more opportunistic and live on the other side of "yes"?
_Imagine Opportunities Everywhere_
Everything mankind has accomplished existed in someone's imagination before it became a reality. We create what we imagine, and imagination is one of the last remaining legal means you have to gain what feels like an unfair advantage over your competition. You can cultivate this imagination by:
• **A SKING QUESTIONS:** Curious people are imaginative people, and questions are doorways to opportunity. I love the story Tim Sanders tells about a little girl who kept asking her mother question after question. Finally, her mother cried, "For heaven's sake, stop asking so many questions. Curiosity killed the cat." After two minutes of thinking, the girl asked, "So what did the cat want to know?" Curiosity doesn't kill cats. It kills the competition because it identifies opportunities.
• **N ETWORKING:** You are only a few people away from a wonderful opportunity. Right now, someone knows something you should know, and someone is doing something you should do. Once you believe this, you will begin asking others, "Who do you know that I should know?" Don't settle for who you already know and what you already know. Don't be like Yogi Berra, who said, "I'm in favor of leaving the status quo as it is." People you haven't yet met but can meet will help you get on the other side of "yes."
• **T AKING ACTION:** Action creates opportunities. The best opportunity is seldom behind the first door you come to, but going through that first door will be essential to get to the other doors that present the better opportunities. As Dr. Jonas Salk said, "The greatest reward for doing is the opportunity to do more."
Opportunities are like rabbits. You get a couple and learn to handle them, and pretty soon you have a dozen. An opportunity grasped and used produces another opportunity. The more successful you are, the more opportunities will be given to you.
* * *
IMAGINATION IS ONE OF THE LAST REMAINING LEGAL MEANS YOU HAVE TO GAIN WHAT FEELS LIKE AN UNFAIR ADVANTAGE OVER YOUR COMPETITION.
* * *
_Prepare for Opportunities_
In addition to looking for opportunities, you also need to prepare for them. One of my all-time favorite quotes is by legendary UCLA basketball coach John Wooden, who said, "When opportunity comes, it's too late to prepare." These words have inspired me to keep working and growing, because I never know when the door of opportunity is going to open wide. But I know that those who become successful are ready when it does.
To be prepared for opportunity, you must produce results and make sure that you are the most qualified when the door opens. Are you working as hard as you can? Are you learning as much as you can? Are you connecting with others as often as you can? Are you building a team as well as you can? All these things make you ready and put you closer to the door when it opens.
Do you hear that? That's the sound of your door opening. Will you be ready?
_Activate Your Current Opportunities_
It's always easier to see opportunities we've missed, the ones that are behind us, than to see the ones in front of us now. To live on the other side of "yes," we need to be like my friend Larry Stockstill. We need to focus on the current moment and activate whatever opportunity is presenting itself. We need to open the door before us, not lament the doors behind us that we missed. As Mother Teresa said, "Yesterday is gone. Tomorrow has not yet come. We have only today. Let us begin." If we activate the opportunities we have now and keep pursuing them, we will eventually cultivate success momentum. To do that, we must stay hungry, believe we will have opportunities, seize the small ones when we find them, and build upon them until we are ready for even bigger challenges.
Robert Lynch, president and CEO of Americans for the Arts, said, "Creativity is the most effective response to rapid change." Why? Because creativity always adds. Leadershifting from maintaining to creating allows you to lead people into the land of abundance and opportunity. And that's especially important if you are operating in an environment that does not value or cultivate creativity, as I was early in my career.
In his book _The Creative Priority_ , Jerry Hirshberg wrote,
No one in a corporation deliberately sets out to stifle creative thought. Yet, a traditional bureaucratic structure, with its need for predictability, linear logic, conformance to accepted norms, and the dictates of the most recent "long-range" vision statement, is a nearly perfect idea-killing machine. People in groups regress toward the security of the familiar and the well-regulated. Even creative people do it. It's easier. It avoids the ambiguity, the fear of unpredictability, the threat of the unfamiliar, and the messiness of intuition and human emotion.
If you desire to be successful and to be the best leader you can possibly be, you cannot settle for the familiar. You cannot live in your comfort zone. You need to be willing to be uncomfortable. You need to embrace the words of American Giant, the manufacturer of what they call the greatest sweatshirt ever made. In an ad highlighting their own willingness to be uncomfortable in order to achieve excellence, they say:
Comfortable isn't comfortable
Comfortable never got up before dawn
Comfortable won't get its hands dirty
Comfortable has nothing to prove
Comfortable can't get the job done
Comfortable doesn't have new ideas
Comfortable won't dive in head first
Comfortable isn't the American dream
Comfortable has no guts
Comfortable never dares to be great
Comfortable falls apart at the seams
Don't get comfortable
Don't ever get comfortable. Make the shift to abundance. Get out on the edge. Break new ground. Seize opportunity. Get creative.
CHAPTER 7
LADDER CLIMBING TO LADDER BUILDING
_The Reproduction Shift_
_If I have seen farther than others, it is by standing on the shoulders of giants._
—ISAAC NEWTON
I've always been a talker, from the time I was a child, through high school, in college, and into my career as a pastor. That trait, coupled with a desire to improve as a communicator and a degree of success in leadership, landed me some big opportunities to speak at a relatively young age. Sometimes I got to speak before large crowds alongside some amazing speakers.
When I started getting these great opportunities for speaking gigs, my excitement was always mixed with fear. My eagerness to get out and speak was often tempered by worry because of my lack of experience. I was glad for the exposure and the chance to teach new audiences, but I was also aware that I was in over my head. Early in my speaking career, at most events, I was at the bottom of the class.
I told you about one of those experiences in Los Angeles, where I learned to embrace fear and speak anyway. But I also started to do something else. Whenever I got invited to speak, I became the chief cheerleader of all the other speakers. I sat in the front row. I laughed at their stories. I wrote down all their insights. I stood and cheered as they walked offstage. And I stood in line to thank them for helping me after the event.
The speakers were very accepting of me, even though most of them were old enough to be my father. I was invited into the green room with the other speakers, and I often found myself mixing with them, asking questions and getting feedback on what they were learning. They embraced me as one of their own and took me under their wing. I was grateful to be with them and to learn from them on the speaker circuit. And I felt like I was headed for the top.
After the thrill of being part of such wonderful speaking teams started to wear off, I began to analyze my communication and my impact on my audiences. Here's what I discovered: after I was done speaking, there was lots of inspiration but not a lot of application. People who heard me speak were glad they came, but they weren't sure what to do with anything I said when they got home. I was encouraging everybody, but I wasn't helping anybody.
TIME TO MAKE A CHANGE
It took me a while to figure out my problem, but after asking experienced communicators questions and listening to their responses, I realized what was wrong. My focus was totally on myself. The experience was more about me than the people I was there to help. My subject matter, my stories, my points, my thoughts, my delivery—it was all for me. After I spoke, the questions I was asking myself afterward were, _How did I do? Did they like me? Did they like what I said? Did they clap for me? Were they impressed by my talent? Do they admire me?_
When I realized what I had been doing, I felt exposed and saw the error of my ways. And I knew that I had to make a shift. My speaking had to change. So did my attitude. It was wrong of me to try to gain fans. Instead, I needed to make friends. I needed to focus on others and on adding value to them when I spoke.
I took some time to reflect. I wondered how I could make the changes needed in this area. So I wrote something to help me. This is what I wrote:
• It's not about me—it's about them.
• Success is not a standing ovation—it's people walking out with a game plan.
• My talk is not to help me look good—it's to help them get good.
• If they can't relate to what I want to say—I shouldn't say it.
• If they can't apply what I say to their lives—I shouldn't say it.
• When I'm done, don't expect them to give me a hand—invite them to come shake my hand.
• When they walk away, hope that they say, "His name is John and he's my friend."
Eventually, this shift started to bleed into my leadership, where it wasn't ever supposed to be about me. Leadership should always be about others.
Before this, I was a ladder climber. Nearly everything I did was motivated by the question, "How high can I go?" But making this shift helped me to realize that there was more to life than getting to the top. Instead of just trying to be successful personally, I could help others. And over the years, I realized that there were a series of shifts I could make, and they came in stages.
1. Ladder Climbing—"How high can I go?"
2. Ladder Holding—"How high will others go with a little help?"
3. Ladder Extending—"How high will others go with a lot of help?"
4. Ladder Building—"Can I help them build their own ladder?"
This leadershift is about changing from being a personal producer to an equipper of others. It's a shift that takes your leadership math from addition to multiplication. It takes you from the solitary climb to the top of your ladder, where you might enjoy the view and wave to the people down below, to watching many people climb to the top of their own ladders, and you all enjoy the view from the top together.
LADDER STAGES
I want to explain the four stages I went through to help you make this shift in your leadership:
**1. L ADDER CLIMBING—"HOW HIGH CAN I GO?"**
Wanting to climb the ladder yourself isn't a bad thing, because credibility in leadership is often built on personal success. No one wants to follow a leader who cannot succeed. People want to be on a team only if they know they have a chance to win. So the first step in leadership is not leading others. It's leading yourself; it's showing you are capable of climbing the ladder yourself.
Speaker Glen Turner once told me, "The hardest challenge of getting to the top of the ladder was getting through the crowd at the bottom." Being able to climb the ladder yourself is the first step in separating yourself from the rest of the crowd. If you need help in figuring out how to do that, ask yourself these three questions:
* * *
THE HARDEST CHALLENGE OF GETTING TO THE TOP OF THE LADDER WAS GETTING THROUGH THE CROWD AT THE BOTTOM.
—GLEN TURNER
* * *
_1. What Are My Strengths?_
Success comes from building upon your strengths and making the most of them, not from bringing your weaknesses up to par. For example, three of my top strengths are strategy, activation, and Woo (from StrengthsFinder). Where am I weak? I don't do well with tasks related to administration or maintenance. And I'm absolutely terrible when it comes to anything technical. Any time or energy spent in these areas would be a total waste. Know what your strengths are and start developing them.
_2. What Are My Opportunities?_
I believe everyone has opportunities. I do, and I'm convinced you do. The opportunities you receive may not be as big as you want. They may not be the kind that you want. But they are opportunities. What should you do with them? Apply your strengths to them and make the most of them. The meeting of your strengths with an opportunity is where you get the chance to start climbing the ladder. Make the most of it. Even if it's not the perfect opportunity—and trust me, it won't be, because there is no such thing—you can start the climb. Once you climb up out of the crowd, you'll discover other, better opportunities.
_3. Am I Taking Steps Every Day?_
When you seize an opportunity and apply your strengths to it, you still have to do the work. If you can't answer yes to the question of whether you're taking steps every day, you won't succeed, and you'll have to forget about taking the next step toward becoming a ladder builder. How high do you need to climb? My answer is that you need to get to the top 10 percent. That's the magic number. That's where you become set apart from all the rest in the areas of money, influence, opportunity, and relationships. That's where the quality of people who want to be on your team changes drastically. So as you work to climb the ladder yourself, one of the things you need to ask yourself is whether you can get to that top 10 percent. If you can, then you will be able to start holding the ladder for others.
As you climb the ladder of success, here's some advice for making sure you're doing it as effectively as possible:
• Make sure your ladder is on a firm foundation of integrity and strong character.
• Make sure your ladder is leaning against the right "building" for your purpose.
• Never step on other people while climbing up.
• Don't skip any rungs of the ladder.
• Step back down occasionally to rest, reflect, and gain perspective.
• Don't step on anyone while descending either.
• Each time you start to climb back up, make sure you improve.
• Always value the people who are holding the ladder for you.
The better you are at climbing the ladder yourself, the more you will have to give others when you move on to the next phases.
**2. L ADDER HOLDING—"HOW HIGH WILL OTHERS GO WITH A LITTLE HELP?"**
My friend Kevin Myers, the leader of 12Stone Church, said, "Leaders should want far more _for_ their people than _from_ their people." I talked a little about that in chapter 1 on shifting from soloist to conductor. When you want more for others and you're willing to give them some help, it's like holding the ladder for another person, giving them a secure base, empowering them to take moderate risks, and allowing them to climb higher.
* * *
LEADERS SHOULD WANT FAR MORE _FOR_ THEIR PEOPLE THAN _FROM_ THEIR PEOPLE.
—KEVIN MYERS
* * *
I've benefited from many people who were willing to hold the ladder for me as I climbed, especially when I was younger. Their initial support was key to my success. They made me better. And their help inspired me to want to help others. If you've been successful, you're ready to begin helping others by holding the ladder for them. Here are the things you need to know to get started:
_Ladder Holding Begins with a Serving Attitude_
Ralph Waldo Emerson said, "Our chief want in life is somebody who shall make us do what we can." Adopting a serving attitude so that we will hold the ladder for others helps us to do what we can. Plus, living out an attitude of service sets a good example to the team and is a visual reminder of the importance of servanthood. When you show the people you work with that you are willing and able to serve, then they will be willing and able to serve.
_Ladder Holding Requires Availability_
To become a ladder holder, you must be open to people and willing to give of yourself. When someone asks a question, you must be willing to answer. If you're asked for an opinion, you need to be willing to talk. When people want your ideas, you need to jump in. If they want your endorsement, give it. Ladder holding is simply one leader helping another leader. When you engage with young leaders, value them, believe in them, encourage them, and give resources to them. Make yourself available to them.
_Ladder Holding Attracts People Who Want to Climb_
The greatest way to raise up good leaders is to recruit people with good leadership potential. How do you attract those kinds of individuals? Develop a reputation for investing in others. Young, talented people who desire to achieve will begin seeking you out if you become known for giving others a leg up.
_Ladder Holding Is a Pre-Qualifier for Discovering a Person's Potential_
How do you gauge others' ability to grow? How do you determine whether they can become good or even great leaders? By watching how they perform when given opportunities. By holding the ladder and offering them the chance to climb, you find out whether they take the steps they can and how quickly and easily they perform. You get a sense of their ability and desire. And that gives you insight into their eventual potential.
_Ladder Holding Over Time Multiplies Effectiveness_
Business magnate and philanthropist Andrew Carnegie said, "It marks a big step in your development when you come to realize that other people can help you do a better job than you could do alone." I've discovered that helping others helps me. Over the years, being a ladder holder has given me a huge ROI (return on investment).
My friend Chris Hodges said, "A dream is a compelling vision you see in your heart that is too big to accomplish without the help of others." When you start holding the ladder for others, you enlist their help. To take them to an even higher level, you need to do more.
**3. L ADDER EXTENDING—"HOW HIGH WILL OTHERS GO WITH A LOT OF HELP?"**
The next step in the process is to extend the ladder for others. When you do that, you empower them to climb higher and go to entirely new levels. How do you do that? By intentionally and strategically mentoring them.
Over the years I've sought out a lot of mentors who have extended the ladder for me. I've also been a mentor to many leaders, so I know this territory pretty well. Whether you're in the stage of your leadership to be extending the ladder to others, or you're looking for someone to help you develop, here are the criteria for being a good mentor:
_Ladder Extenders Are Successful_
Who you learn from is as important as what you learn. Good mentors are successful. Since the word _mentor_ is both a verb, something you do, and a noun, something you are, a good mentor must exhibit ability in both areas. In the area of doing, this means they are productive. When it comes to being, good mentors possess strong character. If both components aren't there, don't consider asking them to mentor you.
* * *
SINCE THE WORD _MENTOR_ IS BOTH A VERB, SOMETHING YOU DO, AND A NOUN, SOMETHING YOU ARE, A GOOD MENTOR MUST EXHIBIT ABILITY IN BOTH AREAS.
* * *
_Ladder Extenders Are Specialists_
A mentor ought to be very skilled in just a few areas. Often, people seek out a mentor to help them in all areas of their lives. That's not realistic. No one can help you with everything. Instead of looking for one mentor, seek out several for each key area in your life that you're working on. For example, I have sought different mentors for the following areas: relationships, equipping, attitude, leadership, communication, health, and faith. You'll notice the first four are the areas I identified as essential for success when I leadershifted from goals to growth. Communication is my greatest strength, so I'm continually trying to build upon that. The last two—health and faith—are areas that I consider essential to who I am as a person. I think it's obvious that one person would not be able to help me with all seven of these areas.
That said, when you're first starting out and learning the basics, one solid leader may be a sufficient help to you. As you advance and become more specialized in your growth, your mentors will need to be more specialized.
_Ladder Extenders Are Mature_
The whole idea of working with a mentor implies that the person is ahead of you. He or she is bigger, faster, more knowledgeable, and more experienced. It means the person possesses maturity. Here's how I would describe that:
• The ability to make decisions based on the big picture, not just the immediate one.
• The capacity to face unpleasantness, frustration, discomfort, and defeat without complaint or collapse.
• The choice to live up to responsibility and do the right thing, not the convenient thing.
• The willingness to stick with a task, project, or situation until it comes to completion.
• The discipline to harness abilities and energies to do more than is expected.
• The ability to take in difficult information and keep things confidential.
• The openness to share personal difficulties when appropriate and helpful.
• The compassion to connect with others without trying to correct them.
Why is maturity essential in a mentor's life? Because we teach what we know, but we reproduce who we are.
_Ladder Extenders Are Practiced in the Art of Asking Great Questions_
Good mentors don't jump to conclusions. They ask questions and explore ideas to unlock doors that would otherwise remain locked. I emphasize this because I have not always been good at asking questions. I used to be very quick with answers and had to slow down to become a better listener. Today when I work with someone, I try to follow this process:
• **A SK QUESTIONS:** In a mentoring situation, the first questions I ask are often preset and focus on basic information. They are designed to learn about the person's background, history, strengths, and aspirations.
• **L ISTEN:** I work hard to be fully engaged, not only because listening used to be a weakness of mine but because the answers I receive enable me to ask a second set of questions. Listening to the answers to the first set of questions expands my understanding and connects me with the person.
• **A SK FOLLOW-UP QUESTIONS:** At this stage I have the information I need to ask better questions. This is when I discern how to really help the other person. I equate this process to making half-time adjustments, the way a coach does during a ballgame. If the answers to the first set of questions represent the pre-game plan, then answers to the second set of questions are like halftime, allowing me to make adjustments.
• **L EARN:** The second set of questions deepens my understanding and allows me to create a specific, individual game plan for the person to take them from where they are to where I believe they could be.
• **L EAD:** I'm now ready to challenge, encourage, and coach them to their potential.
A lot of leaders are too quick to give direction when what they need to do is ask questions. If you're in a place to start extending the ladder for others, develop the ability to ask questions and carefully listen. And if you are working with a mentor and the person isn't asking you any questions, be aware that he or she may not be able to take you very far in the process.
_Ladder Extenders Are Humble_
The mentoring relationship is at its best when both people meet and interact on common ground. This is especially important since the mentor is usually working from the position of greater strength, position, and experience. How is this common ground maintained? Through the humility of the mentor. If he or she maintains an openness to sharing failures, disappointments, and losses, the person being mentored benefits tremendously.
When I was younger and began mentoring others, I naturally wanted to share my successes. As I got older, I realized that we may impress people with tales of our successes, but we can impact them when we share our failures. The more successful the mentor, the more important it is to share weaknesses as well as strengths. Nobody has all good days, and nobody has all bad days. Life for everyone is a daily mix of highs and lows, pleasure and pain, gains and losses, ups and downs. Humility and authenticity from both the ladder extender and the emerging leader create a strong foundation where growth is possible.
**4. L ADDER BUILDING—"CAN I HELP THEM BUILD THEIR OWN LADDER?"**
Once you've climbed the ladder of success yourself, begun to hold it for others, and then learned how to extend it for emerging leaders by mentoring them, there's still another level you can go to as a developer of people. You can become a ladder builder. One of the best ladder-building leaders I know is Sam Chand. He has written several books that contain the word _ladder_ in the title: _Who's Holding Your Ladder?_ , _What's Shaking Your Ladder?_ , and _Who Moved Your Ladder?_ Sam's license plate is LDDRMAN, and he was my inspiration for the title of this chapter.
Ladder building is all about giving another leader the permission, equipment, and empowerment to create their own ladder. As a leader, if you surround yourself with excellent people with high potential, there will be a time when you should allow them to build their own ladders. That's the time when you release them to lead on their own.
It is my joy in this season of life to focus on ladder building. For the last twenty years my nonprofit organizations, EQUIP and the John Maxwell Leadership Foundation, have trained leaders around the world so that they are equipped to build their own ladders. And for almost a decade, we have been able to give thousands of coaches around the world a platform through the John Maxwell Team. The training and support they receive empowers them to build their own ladders by starting or improving their careers as coaches, trainers, and speakers. And the best thing about it is that ladder building has no limitations imposed. People can build and climb as high as their talent and work ethic will take them. I have to say, I find it very rewarding to "kick leaders out of the nest" and watch them succeed.
To lay the groundwork for becoming a ladder builder, start by asking yourself some questions:
• Do I develop leaders to benefit others, not just for myself?
• Do I relinquish control and give other leaders the freedom to be themselves and develop their own process?
• Am I happy for a leader I help to move on without me or to enlist other mentors?
• Am I willing to help other leaders build their own ladders and then genuinely root for them?
• Am I willing to keep helping many leaders build their own ladders without expecting to receive any credit?
If you can answer yes to these questions, and you've climbed up the ladder enough yourself to have earned credibility, then you are ready to start your journey to becoming a ladder builder. Start helping others and mentoring them. And when you see an opportunity to encourage others to build their own ladders, don't hesitate to give them a hand.
QUESTIONS TO ASK BEFORE YOU MENTOR SOMEONE
Andy Stanley often says, "Do for one what you wish you could do for many." That's great advice. And when it comes to investing in and helping someone by holding, extending, and building his or her ladder, it's important who you choose as that one. Your time is limited, and if you can spend time with only one person, it has to be the right one. With that in mind, ask the following questions about anyone you are considering helping:
**1. I S THIS PERSON HUNGRY TO LEARN?**
Author Napoleon Hill said, "Strong, deeply rooted desire is the starting point of all achievement." Much of what people accomplish in their lives is based more on how much they want it than on how easy it was to get. Hope says, "There must be a way," while hunger says, "I will make a way." People with hope are many; people with hunger are few. I want to mentor one of the few. If you have to talk the person into being helped or convince him or her to follow through on your advice, that may not be someone you should be investing in. As poet Rudyard Kipling said, "If you don't get what you want it is either a sign that you did not seriously want it, or that you tried to bargain over the price."
**2. W HAT IS THIS PERSON'S CAPACITY?**
Hunger is easy to evaluate. Capacity is much more difficult. When I'm considering whether to mentor someone, I use the seven capacities that I wrote about in my book _No Limits_ to evaluate him or her:
1. Energy Capacity—their ability to push on physically
2. Emotional Capacity—their ability to manage emotions
3. Thinking Capacity—their ability to think effectively
4. People Capacity—their ability to build relationships
5. Creative Capacity—their ability to see options and find answers
6. Production Capacity—their ability to accomplish results
7. Leadership Capacity—their ability to lift and lead others
I want anyone I mentor to show plenty of potential to grow in all seven areas. As David Salyers of Chick-fil-A said, "The mentor pours into the student knowing that as that person grows the return will be greater than the investment." People cannot show a great return if they don't have adequate capacity.
**3. A RE THIS PERSON'S VALUES COMPATIBLE WITH MINE?**
Shared values give you a track to run on with someone you intend to mentor. They provide a very important common ground and philosophical foundation. When I prepare to mentor people, I want to know that they . . .
• **A DD VALUE TO PEOPLE—**They must be givers who want to help others, as I do.
• **V ALUE PERSONAL GROWTH—**They must demonstrate a lifestyle of learning.
• **L EAD BY EXAMPLE—**They understand that _follow me_ are the best words a leader can say to a follower.
• **E XCEED EXPECTATIONS—**They stand out and receive 80 percent of life's ROI.
• **L IVE INTENTIONALLY—**They know that everything worthwhile is uphill, and they climb intentionally every day.
Only if we share these common values will I invest time in them. Do you know what your values are? Identify them clearly so that you know whether or not you should invest in a potential candidate.
**4. I S THIS INDIVIDUAL A LEADER?**
Because my particular calling is to add value to leaders who multiply value to others, I will not invest in a person who is not a leader. I know that may sound very narrow, but it's focused and strategic. I discovered that when I mentor a leader, the ROI is much greater than if I pour myself into a follower. With a leader, I truly can do for one what I wish I could do for many, because that leader will influence many. With followers, that is not necessarily true.
What do leaders need from a mentor? I like what Tim Elmore, the founder and president of Growing Leaders, says about this. Tim is one of the emerging leaders I helped more than thirty years ago. First I helped hold his ladder, then extend it. And more than twenty years ago, I helped him build his own ladder and cheered him on. He speaks extensively on mentoring and has written about it too. Some of the things Tim says a successful mentor gives to the person being mentored are: handles, laboratories, road maps, roots, and wings. Let me explain:
_Handles_
Good mentors distill truths from complexity and divide the information into bite-sized principles that others can apply. All good mentors can put life lessons into a nutshell that is transferable. Are you willing to do the homework necessary to do that?
_Laboratories_
Good mentors provide a safe place where learners can practice the principles they're learning. Are you willing to create such a safe environment where people you're developing can take risks?
_Road Maps_
Good mentors give learners direction for life and provide roadmaps of options for how to proceed to their destination. Are you willing to follow through with a good game plan for the people you mentor?
_Roots_
Good mentors provide learners with a solid relational foundation. Giving stability and security makes it possible for other people to grow and flourish. Are you willing to extend love and acceptance to the people you mentor, and hang in there with them when they face difficulties?
_Wings_
Good mentors help people to see new horizons and fly to places beyond where they imagined they could go. This is true empowerment. Are you willing to celebrate when people you mentor fly higher or farther than you have?
_Whys_
I want to add one more quality to Tim's list. One of the most important things you can do for potential leaders is to help them see the big picture by teaching them the _why_ s. This gives them context. It reveals to them the thinking and reasons behind your decisions. It teaches them decision-making. If you want learners to follow directions, you only need to provide the _what_. If you want them to lead others and give directions, they must also have the _why_. Are you willing to take the time and trouble to give them the _why_ behind every _what_?
* * *
IF YOU WANT LEARNERS TO FOLLOW DIRECTIONS, YOU ONLY NEED TO PROVIDE THE _WHAT_. IF YOU WANT THEM TO LEAD OTHERS AND GIVE DIRECTIONS, THEY MUST ALSO HAVE THE _WHY_.
* * *
I've already mentioned that one of my mentors was Fred Smith. He was a model to me in the leadershift from climbing to building ladders. By the time I met him, he had already made that transition. Early in my relationship with him, I watched as every month for three years he met with a group of twenty young CEOs and poured himself into them. When he sensed that it was time for them to move ahead without him, he ended his ladder-extending time with them and encouraged them to build ladders of their own.
A year after he formally disbanded the group, those leaders asked to meet with Fred one evening. One by one over dinner, the CEOs shared with Fred all that he had done for them and how he had helped them become better leaders. At the close of the evening they presented him with a beautiful piece of Baccarat crystal with the following words etched in it: "He stretched us."
That's what all leaders do who shift from ladder climber to ladder builder. They help new leaders stretch to their potential. That's what I hope to do for the rest of my life and to leave as my legacy. And I invite you to do the same. You'll never regret investing in another leader who makes a positive difference in this world. It's the best way to extend your influence and achieve significance.
CHAPTER 8
DIRECTING TO CONNECTING
_The Communication Shift_
_You don't lead by hitting people over the head—that's assault, not leadership._
—DWIGHT D. EISENHOWER
All of the leadershifts in my life have not occurred in the same way or on the same timetable. Some have occurred gradually while others were almost instantaneous. Many were prompted by my leadership intuition, which has often been the catalyst for the changes I made. But some, like the communication shift from directing to connecting, went against my natural grain. This was a shift in the opposite direction of my experience, and it required time to develop.
I grew up in a home where directing was the practiced style of communication and leadership. In our family culture, everyone had assignments. We each had chores to do and times to do them. And my father was always certain to explain why we were required to do everything we did. My parents provided clarity, purpose, and a schedule. My brother, sister, and I were expected to understand and obey their direction with promptness.
My college theological training in communication and leadership reinforced this directing methodology. In communication, we were taught to preach with boldness and passion. My style had both of these qualities in abundance. Plus, when I preached I also added application—which is another way of giving direction. I worked to make every message I preached practical and to always provide a game plan to the people I was addressing. I felt good if, at the end of the service, everyone left with something to do that week.
In leadership, the authority in our ecclesiastical world was top-down. The constitution and by-laws of the organization stated that as the pastor, I was chairman of the board, and the governing rules made it clear that everything was supposed to begin with me: the agenda, the church's leadership, and the spiritual authority. People in my role were given the position of leadership in the boardroom, and if that didn't make it clear enough that they were supposed to be the leader of the pack, then they would use the sermon to reinforce the idea. And I have to admit, I was guilty of that too. I may not have been Moses coming down from Mount Sinai with the Ten Commandments to give to the people, but upon occasion I acted like Moses Jr.!
So I came from an upbringing and training that emphasized directing. On top of all this, my temperament is choleric, which means I love to be in charge and tell others what to do. I know where I want to go, and I'm not shy about saying how we should get there. If you have a question, I've got an answer. If you're not sure about what you want to do, I can give you a plan for your life.
Directing others was a very natural leadership style for me. But what's natural for me is not necessarily what's best for others. Nobody wants to be bossed around. Many times I could sense that people were following me only because they had to, not because they wanted to. Even those who wanted to follow me didn't always buy into the vision and direction I was communicating as strongly as I had hoped. Intuitively, I began to understand that I needed to move away from directing. I no longer wanted to be a "leadership cop" standing at the intersection of my organization and directing traffic all the time. But at the same time, I didn't know what else to do. What better way was there to lead people?
WELCOME TO A NEW PARADIGM
Two experiences functioned as catalysts to help me reshape my communication and leadership style. The first occurred in 1988. That was the year I hired Bobb Biehl as a consultant. At that time, I was leading a large high-profile church, and my influence was growing nationally and even internationally. I was getting a tremendous number of requests to speak to other organizations and to help them by providing resources. My sense was that I needed to create an organization to handle these requests, and I wanted it to pay for itself, not make it a nonprofit. But back then I had no personal experience in the business world, so I asked Bobb to answer questions and give me some needed direction.
This was my first experience hiring a business consultant, and it was before I had developed much experience as a ladder builder, so the way Bobb started the process took me totally by surprise. We spent two days together and the entire first day Bobb asked me questions. The entire day! He'd ask a question, I'd answer, and he'd ask follow-up questions based on my answers. He worked with flip charts, writing the questions and the answers. At the end of the day, every wall in my office was covered with sheets of paper containing everything we had talked about. I was exhausted yet fulfilled. In those hours Bobb had drawn out my innermost thoughts, hopes, and aspirations in a way that never had been done before. With each question, he had peeled away another layer, revealing the depth of my thinking and feelings. It was exhilarating.
I learned an important lesson that day. Bobb had to _find_ me—who I was, where I was, where I had been, where I hoped to go—before he could _lead_ me. That opened my eyes to a better way of leading, and the discovery became the foundation of my practice of connecting with others. From then on, I started working to find people by asking questions before trying to lead them.
The second experience that impacted me greatly occurred in 2003. I was invited to attend a basketball game of the University of Tennessee Lady Volunteers coached by the great Pat Summitt. I attended their pre-game and sat right behind the bench. At halftime, I was able to go into the locker room and observe how Pat coached the team.
When we got to the locker room, Pat and the other coaches huddled together away from the players, while the players immediately sat in a semicircle around a whiteboard that had three questions written on it:
1. What did we do right in the first half?
2. What did we do wrong?
3. What do we need to change?
For five minutes, the players discussed their answers to those three questions while one player wrote down their responses. I sat behind the players and watched. I was fascinated.
Then Pat walked over to the marker board and looked at the answers. She made a couple of comments related to what they had written, and then she sent the players back out on the floor to warm up for the second half.
After the game I asked Pat about it, and her answer was stunning.
"John, too many leaders lead by assumption," she said. "They assume they know where their people are. That halftime exercise lets me find my players so I can lead them. That can only be done by asking questions and listening to their answers."
That was a huge "aha" moment for me and was the second bookend in my leadershift from directing to connecting. I was determined from that moment forward to use connecting as the basis for my leadership and communication style.
Take a moment and look at the contrast between these two styles:
**DIRECTING** | **CONNECTING**
---|---
Authoritative | Collaborative
Talking | Listening
Top Down | Side by Side
Enlisting | Empowering
Assuming | Understanding
Gives Answers | Asks Questions
My Agenda | Your Agenda
The goal of connecting is to find common ground with the leader initiating. This is the place where . . .
• both people meet;
• both people are valued;
• both people share;
• both people listen and learn;
• both people adjust;
• both people settle on a game plan;
• both people take ownership of the game plan; and
• both people move together to higher ground.
Learning to connect is one of the most important things you can ever do in life. In my book _Winning with People_ , I assert that people can usually trace their successes and failures to their relationships. This is especially evident in leadership.
MAKE THE LEADERSHIFT TO CONNECTING
If you want to become the best leader you're capable of being, you must learn to connect with people. To do that, you must find ways to overcome the challenges of connecting and finding common ground. This can often be a difficult process, especially with a varied team. Here are the seven things I have found to be most important to a leader who wants to connect with others:
**1. H UMILITY—LET PEOPLE KNOW YOU NEED THEM**
I had the privilege of meeting one of my heroes, John Wooden, and being mentored by him during his later years. Back in 2001, I came across a piece written about him by Michael Josephson, president and founder of the Josephson Institute of Ethics. I can't recall where I found it, but I love it. Coach was a great connector, and I think Josephson's piece gives wonderful insight about him:
One of my personal heroes turned 91. He's not a general or a politician or a movie star; he's a teacher. Oh, I'll admit he's not an ordinary teacher—he's also the world's most successful and famous basketball coach—but John Wooden is, above all, a teacher. Even more, he's a homespun philosopher.
His thoughts and theories have been recorded in dozens of books, but reading John Wooden doesn't hold a candle to hearing from the man himself. The power of his words is amplified by his extraordinary character. You don't just meet the coach; you experience him. The man exudes an inner dignity and moral strength that makes you feel both worthy and humble at the same time. When he tells you what he knows, you believe it's because he cares about you and hopes it will be helpful.
Integrity, respect and kindness pervade everything he says. But more striking, it seems so effortless. He has received more awards and accolades than any ten of his peers, yet he is genuinely humble. I had to insist that he call me by my first name so he'd stop calling me Mr. Josephson. He talks about issues of honor, hard work, preparation and self-discipline as if there were no other choices.
This both inspires and humbles me. You see, for me, trying to be a person of character involves a daily struggle. Sometimes it feels as if I am acting the part of a good person rather than really being one. I don't think I will ever be as gracefully authentic as Coach Wooden. Yet if I told him this I think he would smile and say something like, "Michael, never underestimate what you can do. Why don't you keep trying? You'll get better."
Those words echo how I felt when I was with Coach. No man in my life helped me more or connected with me better than he did. The core of that connection was his humility. John Wooden knew his strengths and used them to help others. He was not preoccupied with himself. Instead, he focused on helping others, including me. When I was with him, he brought out the best in me. When I left him, I wanted to be like him and bring out the best in others.
Coach never talked about himself, but in every one of our sessions, all I could think about was him—his wonderful qualities, his values, his consistency, his kindness. I was aware of the gap between where he was and where I was, but he always made me feel that I wasn't too far behind him. That always encouraged me and made me want to improve.
Humility is essential in connecting with people. It took me a while to learn this. In my younger years, I would ask God to help me be successful, but secretly I hoped that people would think I did it all myself. I possessed more human frailty than humility. To help me, God gave me a dream bigger than myself. It was so intimidating that I had only two choices: give up or get help. I chose to ask for help, which at first felt very humbling. But I quickly discovered how much I needed other people. And as a result, my leadership actually got better, not worse.
* * *
GOD GAVE ME A DREAM BIGGER THAN MYSELF. IT WAS SO INTIMIDATING THAT I HAD ONLY TWO CHOICES: GIVE UP OR GET HELP.
* * *
Good leaders are aware that they need other people, and they let them know that. There really is no downside. It keeps the leader's ego in check, it connects the leader and the people on the team, it draws team members into the center, and it better enables them to fulfill the vison. So, if you want to be a connector, acknowledge your shortcomings and need for others, and be willing to ask for help.
**2. C URIOSITY—ASK PEOPLE QUESTIONS**
I'm known for asking questions. Whether I'm at dinner with friends, taking my grandchildren on a trip, or leading a business meeting, people know I'll be asking them questions. But I got my start as a questioner by asking myself questions. One of the things that stirred me to start asking myself better questions was Bob Buford's book _Halftime_. He had an important question for someone who is middle-aged, which I was at the time I first read the book more than twenty years ago. His question: "What kind of second half are you going to live?" Buford wrote:
You will not get very far in your second half without knowing your life mission. Can yours be stated in a sentence or two? A good way to begin formulating one is with some questions (and nakedly honest answers). What is your passion? What have you achieved? What have you done uncommonly well? How are you wired? Where do you belong? What are the "shoulds" that have trailed you during the first half? These and other questions like them will direct you toward the self your heart longs for; they will help you discover the task for which you were especially made.
These questions helped me at mid-life to set myself up for potentially a good second half.
Today I'm in my seventies, and I haven't stopped asking questions. I'm still curious, and I want to remain that way. Why? Because without asking questions, I can easily become comfortable, stagnant. Entropy can easily set in. I would start to accept the status quo without asking if there were a better way. I would fail to recognize opportunities.
Too many leaders don't ask enough questions—of themselves or others. This happens for a variety of reasons:
• They assume they have the answers.
• They value what _they_ think more than what _others_ think.
• They prioritize directing others over understanding others.
• They don't recognize the need to find common ground.
• They don't understand that questions help to manage expectations.
I want to take a moment to address this final point. As leaders, we must manage expectations all the time. We have to deal with expectations we have for ourselves, expectations we have for others, and expectations others have for us. Any time our expectations or those of others don't align with what's actually happening, there are problems. In fact, I believe that disappointment is the gap between expectations and reality. How do we close that gap? By asking questions so that we can adjust our expectations. Knowing the expectations I have of myself makes me more self-aware, which paves the way for me to improve myself and become better. Knowing the expectations I have of others makes me better able to communicate with people and face reality. And knowing the expectations others have of me makes me better able to lead them. All of these connections are made when we use questions to build bridges with others.
**3. E FFORT—GO OUT OF YOUR WAY TO CONNECT WITH PEOPLE**
Oprah Winfrey said, "The big secret in life is that there is no big secret. Whatever your goal, you can get there if you are willing to work." That is certainly true in connecting with people—you have to make the effort.
My grandson, John, started taking golf lessons when he was twelve. After months of lessons, it finally became time for him to play on a golf course, and I wanted to be the one to take him. Before we began I said, "John, I want you to try to get a par on one of the holes. If you are able to get on the green and putt for par, I'll take a video of you taking the shot and dropping the ball into the hole. That way we can show it to the family."
For two days, we played golf and worked on getting John his first par on a golf course. Every time he putted for a par, I pulled out my phone and videoed him. Four different times, he got on the green and had a chance to putt for par and missed it. But late on the second day on the sixteenth hole, John attempted his par putt and rolled the ball into the cup. And I had it on video! The first par he ever made.
We celebrated on the green, and then I immediately shared the video with the rest of the family right then and there. I also got a picture of John holding up his scorecard, proudly showing off his par, with his arm around me.
Now, why did I do that when it was so much work? Well, first of all, it was fun. But more importantly, I wanted to make a meaningful memory with my grandson. It's something both of us will always remember. And it created a special connection between us—one that will last well beyond our time on the golf course.
I've done a variety of things to connect with people over the years. For about two years I hosted intimate dinner parties at my home with people Margaret and I wanted to connect with. So that we could focus on the relational side of things, I hired my writer, Charlie Wetzel, whose first career was as a chef, to do the cooking for us. Once or twice a month we'd have three couples join us for a five-course meal where the only agenda was connecting and enjoying one another's company. We spent a lot of time deciding who we wanted to attend these meals. For example, Anne Beiler, the founder of Auntie Anne's Pretzels, had always wanted to meet Truett Cathy, her idol. So we arranged for Anne and her husband, Jonas, to have dinner with Truett Cathy and his son Dan. That was a very memorable evening.
Every relational connection starts with the decision to make the effort to connect. It ends with what I call the mirror test: Can you look into the mirror and say to yourself that you did your best? If so, you have passed the test. As my friend Art Williams said, "All you can do is all you can do, but all you can do is enough."
* * *
ALL YOU CAN DO IS ALL YOU CAN DO, BUT ALL YOU CAN DO IS ENOUGH.
—ART WILLIAMS
* * *
If you care about people, you will be capable of coming up with ways to create connecting experiences with others. But it will take effort. And it will take even _more_ effort to follow through on those ideas. But if you don't, you're not really doing all you can to connect—or to become the best leader you can be.
**4. T RUSTWORTHINESS—BE SOMEONE OTHERS CAN COUNT ON**
People do not connect with someone they don't trust. They connect with someone they can count on. Author and speaker Simon Sinek addressed this issue when he said, "People don't buy what you do, they buy why you do it." The _why_ deals with motives. Those motives come from the heart and play out as trustworthiness if the motives are good and right.
As a leader, I know I have to keep my motives right. If my primary motivation is to add value to people and help them, then all is good. If not, I'll get off track. And I'm continually aware that to remain trustworthy in the eyes of others, I have to work at being continually successful in three areas:
1. Integrity in my life
2. Consistency in my actions
3. Competence in my work
When I do these things well, I become more trustworthy and am able to connect with people—and build the relationship. When I fail in one or more of these, I lose trust and have to work to regain the trust I've lost. Because I'm only human, I do fail sometimes. How do I regain lost trust? By following this process:
• I fully acknowledge what I have done wrong.
• I explain exactly what I am going to do to try to make things right.
• I give them an opportunity to share their perspective and add anything to what I shared with them.
• I do the work to fix the problem.
• I follow up with them to confirm that the problem was fixed to their satisfaction.
The bottom line is that I do what I can to make it right. And trust me: I've had to do this too many times to count. But it works. And it's always amazing to me how forgiving people are when I follow this process with them. What's even more amazing is how often the relationship is strengthened and improved. It's often even better than it was before. I think there is a valuable lesson from this about trustworthiness. We often lose trust and connection with one another not because of an occasional failing, but because we neglect to take the right steps afterward to restore the relationship. Don't allow that to happen to you. Make the effort to be trustworthy, and when you fail, do what's in your power to make things right.
**5. G ENEROSITY—GIVE FIRST, GIVE CONTINUALLY**
Albert Einstein said, "A person first starts to live when he can live outside of himself." It could also be said that a person starts to give when he lives outside himself. And giving is a good way to connect with others.
* * *
A PERSON FIRST STARTS TO LIVE WHEN HE CAN LIVE OUTSIDE OF HIMSELF.
—ALBERT EINSTEIN
* * *
Roger Breland, dean emeritus of the Alabama School of the Arts, demonstrated this to me at a conference where we were speaking together. He pulled me aside and gave me a beautiful Montblanc pen as a gift. It was out of the blue, so I was surprised.
"I want you to have it because you're a special friend," he said, "and I also have a request. Every time you write with that pen, would you pray for me?"
I gladly said yes, and for more than a year I used that pen at my desk, and every time I did I prayed for Roger. His generosity to me and my prayers for him increased our connection as friends over time.
I have never known a stingy person with a scarcity mind-set who was able to connect well with other people. They are too often self-driven and make decisions based on self-preservation. As theologian Henri Nouwen said, "When we refrain from giving, with a scarcity mentality, the little we have will become less. When we give generously, with an abundance mentality, what we give away will multiply."
A few years ago I came across a transcript of the commencement address given by author Stephen King to the 2001 graduating class of Vassar College. As you might expect, it's written eloquently. In his address, he talked about money and generosity:
That human life is brief when placed in time's wider perspective is something we all know. I am asking you to consider it on a more visceral level, that's all. . . . What are you going to do? Well, I'll tell you one thing you're not going to do, and that's take it with you. . . .
We come in naked and broke. We may be dressed when we go out, but we're just as broke. Warren Buffett? Going to go out broke. Bill Gates? Going to go out broke. President Ferguson? Going to go out broke. Steve King? Broke. You guys? Broke. Not a crying dime between you. And how long in between? How long have you got to be in the chips? . . . Just the blink of an eye. . . .
Should you give away what you have? Of course you should. I want you to consider making your lives one long gift to others, and why not? All the other stuff you have is just on loan. All you want to get at the getting place, from the Maserati you may dream about to the retirement fund some guy will try to sell you on sooner or later—none of that is real. All that lasts in this world is what you pass on. The rest is smoke and mirrors. . . .
Giving isn't about the receiver or the gift but the giver. It's for the giver. One doesn't open one's wallet to improve the world, although it's nice when that happens. One opens one's wallet to improve one's self. I give because it's the only concrete way I have of saying I'm glad to be alive and that I can earn my daily bread doing what I love. I hope you will be similarly grateful to be alive and that you will also be glad to do whatever it is you wind up doing. . . . Giving is a way of taking the focus off the money we make and putting it back where it belongs—on the lives we lead, the families we raise, and the communities that nurture us. . . .
So I ask you to begin the next great phase of your life by giving, and to continue as you begin. I think you'll find that in the end you get far more than you ever had and do more good than you ever dreamed.
Generosity makes you a better person, it helps you to become a better leader, and it paves the way for you to connect with other people. If you're not already someone who gives first and gives continually, then I encourage you to try it.
**6. L ISTENING—OPEN THE BEST DOOR TO CONNECTING WITH PEOPLE**
I once read a story about a tennis pro who was giving a lesson to a new student. After watching the student take several swings at the tennis ball, the instructor began to suggest ways the man might improve his stroke. But every time the instructor made a suggestion, the student interrupted him with his own diagnosis of the problem and how he might fix it.
After being interrupted yet again, the pro simply nodded in agreement and let the player continue on his own.
When the lesson was over, a woman—who observed the lesson, was familiar with the pro, and had seen the whole thing—asked, "Why did you go along with that arrogant man's stupid suggestions?"
The old pro smiled and answered, "I learned a long time ago that it's a sheer waste of time to try to sell answers to a person who only wants to buy echoes."
If you never listen, before long the people around you will stop talking to you, and you'll become isolated as a leader. If you _do_ listen, not only will they tell you things you need to know but they will also connect with you because they see that you care and that you value what they have to say.
It took me a while to learn this myself. As a young leader I was like the tennis student who didn't listen. My highest priority was expressing my ideas and convincing others to buy into them, not listening to feedback or learning what others had to say. After a series of leadership misses, I recognized the problem in my unwillingness to make listening a priority, and I began shifting to do things differently. But it was hard fought. I struggled to change, but I eventually succeeded. Here's how I did it.
_I Made a List of the Negatives of Not Listening Well_
The first thing I did to get on the right track was sit down with my legal pad and list the ways not listening was hurting my leadership. At the top of the list I wrote the following:
• Few people had anything to share with me.
• My leadership was based on assumption.
• My ideas were the only ideas being implemented.
• No one was taking ownership of tasks except me.
• My team lacked connection.
I could see this was not a recipe for success, and this evidence helped me to _want_ to change and make the effort to do things differently.
_I Reminded Myself Daily to Listen Well_
Most leaders spend a lot of time in meetings. That was true for me at the time I was trying to change. I decided that every time I would meet with someone—and I mean every time—I would take out a legal pad to take notes, and I would write a large letter _L_ on the top of the page. That _L_ stood for _listen_. It was my reminder to shut up and listen.
_I Stopped Interrupting_
That brings me to my next point. I had to stop interrupting people. I used to do it because I was focused on what I wanted to communicate. And I also often thought I already knew what others were going to say. But interrupting someone is like saying, "What I want to say is more important than what you're saying." That was wrong, and I needed to stop doing it.
_I Started Asking Questions_
One of the ways I stopped myself from interrupting others was to start asking questions. I found that one of the best ways is to invite the other person to talk. I've already discussed the value of asking questions, so I don't need to say much here. But I will say this: I discovered that my ears never got me into trouble.
_I Invited People to Hold Me Accountable for Listening_
My final step in the process was to ask others to let me know any time I wasn't listening to them. There's nothing like accountability to keep you honest. Whenever anyone called me out for not listening, I apologized, closed my mouth, and listened.
If you want to be a connecting leader, become a better listener. Invite others to hold you accountable. If you have the courage, meet with your team members, colleagues, friends, and family, and ask them how good a listener you are on a scale of one to ten. If your score is low, you might need to take the same steps I did.
**7. E NCOURAGEMENT—GIVE PEOPLE OXYGEN FOR THEIR SOUL**
More than twenty years ago, I read an article by Greg Asimakoupoulos, which he wrote to encourage leaders. In it he included an illustration that has continued to stick with me:
One of the more obscure exhibits in the Smithsonian Institution displays the personal effects found on Abraham Lincoln the night he was shot. They include a small handkerchief embroidered _A. Lincoln_ , a country boy's pen knife, a spectacle case repaired with cotton string, a Confederate five-dollar bill, and a worn-out newspaper clipping extolling his accomplishments as president. It begins, "Abe Lincoln is one of the greatest statesmen of all time. . . ."
Why would our nation's sixteenth president carry around a clipping like that? History remembers Lincoln as a folk hero and a president's president. Was Lincoln an ego-maniac?
Hardly. When Lincoln was president, he wasn't as popular as he became after his death. The nation was bitterly divided, and Lincoln's leadership was constantly threatened. He was the object of a critical press. So Abraham Lincoln needed something in his pocket to remind himself that his critics were not his only observers. So he carried an icon [symbol] of affirmation, something that reminded him someone believed in him.
As leaders, we must never underestimate the value of reminding others that we believe in them. If even the greatest of leaders need encouragement, then everyone does. That's why George M. Adams called encouragement oxygen for the soul.
When you interact with others as a leader, what is your mind-set? Is your intention to correct them or connect with them? Do you keep them down, or lift them up? You have that choice every day—with those you lead, with those who lead you, with your friends, family, and colleagues.
* * *
WHEN YOU INTERACT WITH OTHERS AS A LEADER, WHAT IS YOUR MIND-SET? IS YOUR INTENTION TO CORRECT THEM OR CONNECT WITH THEM?
* * *
If you're a fan of the _Lord of the Rings_ books, and _The Hobbit_ , you might be surprised that their author, J. R. R. Tolkien, required the encouragement of a friend and fellow writer to keep him going in the early stages of his work on those books. C. S. Lewis and Tolkien used to gather, along with a few other friends, in a group they called the Inklings. They met weekly to share what they were working on and to encourage one another. Tolkien credited Lewis as the person who kept him going when he felt discouraged. In an article about the two writers, Mark Moring said:
Had it not been for Lewis, Tolkien wouldn't have written _The Lord of the Rings._ Tolkien wrote in a letter, "The unspeakable debt I owe him cannot be fathomed. For long, he was my only audience." Several times Tolkien really threw in the towel, and each time Lewis said, "Tollers, where's that next chapter? You can't give up now." Lewis was the only one who kept him going.
Everyone in your life could use the encouragement that only you can give. At home, I've always tried to provide encouragement, first to my children and now also to my grandchildren. When my daughter Elizabeth was young, every Thanksgiving I would offer to pull the turkey's wishbone with her. If you're not familiar with this tradition, here's how it works. Two people each grab an end of the wishbone, make a wish, and pull until the bone breaks. Whoever ends up with the larger part is the winner and gets his or her wish. What Elizabeth didn't know was that I always looked over the bone beforehand and made sure to give her the part that would make her the winner and have her wish come true.
One Thanksgiving after a succession of years when she always won, she said to me, "Dad, you never get to make a wish and have it come true. What do you wish for?"
"My wish is that you always get your wish," I answered. She gave me a big hug when she realized I always wanted what was best for her. She was encouraged, and so was I.
I also take the mind-set of an encourager onto the stage when I speak. As a communicator, I can either try to be a _sage on the stage_ or a _guide by their side_. A sage looks down on others and tries to impress them with wisdom. A guide comes alongside, shares the journey, and encourages them to go the distance with him. I don't want to impress others; I want to connect with them and help them.
Billionaire investor and philanthropist Charles Schwab said, "I have yet to find the man, however great or exalted his station, who did not do better work and put forth greater effort under a spirit of approval than he would ever do under a spirit of criticism." I believe most people are under-encouraged. You can correct that deficit by becoming an encouraging leader.
Changing from directing to connecting is one of the most valuable shifts you will ever make as a leader. When you direct, it's like building a bridge to others, but the traffic only goes one way. When you connect, it's a two-way street. And because of that, everything improves. Not only are relationships better, but ideas improve because they're flowing in both directions. People work better together, and the team gets stronger. Problems get solved more quickly because communication is better, people know one another better, and they start pulling together. And the environment improves too.
Will it take time to build these connections? The answer is yes. But don't let that stop you. In the long run, you'll save time. Your team will get better. And so will you.
CHAPTER 9
TEAM UNIFORMITY TO TEAM DIVERSITY
_The Improvement Shift_
_Our differences can make a positive difference._
Of all the leadershifts I've made, this required the greatest leap. I say that because there is nothing diverse about my background. I grew up in Circleville, Ohio. It was in the middle of the country. The community was almost entirely white. And my family was lower middle class. There was nothing cutting-edge about the church I grew up in. We were conservative and old-fashioned. Even the theological and ministry training I received at the college in Circleville emphasized that Christians should separate themselves from the culture of society in some ways. We set ourselves apart and were comfortable spending all our time with people like us.
My early days as a pastor were equally vanilla. The church I led was filled with farmers and their families. They were good-hearted, hardworking, salt-of-the-earth types of people. But they were not diverse or forward-looking. While I was at the church, NASA put the first man on the moon. The people in my church were not convinced that it had actually happened. Many believed it was a hoax that had been staged in the desert of the American West with trampolines placed underground and covered with sand. Really? Yes, really!
All the leaders in the church were old white men. They all seemed to be cut from the same cloth, adhering to the same rules, following the same model of leadership. They even looked like one another. As a pastor, I was expected to conform to the way other churches in our organization operated and follow all the same rules and guidelines everyone else did. As I already mentioned in chapter 6 on the abundance shift, the emphasis was on tradition and conformity. When it was time for me to hire my first staff member, the advice I received was to try to find a "John Jr.": someone exactly like me. Their concept of progress was moving backward slowly, and their idea of innovation was _more of the same_.
GETTING OUTSIDE OF THE BUBBLE
The improvement shift from uniformity to diversity occurred slowly for me. The seeds were sown for it while I was still in college. It started because I was coaching a basketball team at a Catholic school. This was my first exposure to and long-term interaction with Catholics. At that time, I also met the first priest I ever got to know: Father Mike Elifritz. He was wonderful. After I was done coaching and I was getting ready to graduate from college, I had a lunch with Father Mike. I shared with him some of my apprehension about the next steps I would be taking in life. I'll never forget what he told me: "John, trust your future to God." Those words helped me to be more confident as I moved into the next phase of living.
Why were those words so significant? After all, I was a person of faith who was actually going into ministry! They resonated strongly with me because a Catholic was adding value to a Protestant. In my small sheltered world, that wasn't supposed to happen. Those two groups stayed on opposite sides of the line and were suspicious of one another. But his heart and support changed my thinking. It was catalytic for me and started to show me a bigger, more diverse world.
That occurred in 1969 and was the start of a long journey toward the appreciation of diversity that would take almost thirty years. Along the way, there were a lot of experiences that challenged my narrow, naïve thinking, and a lot of lessons that I learned. Here are the headlines from just a few:
• **A L IFELONG FARMER TAUGHT ME MY GREATEST LEADERSHIP LESSON:** Claude, an unassuming, ordinary middle-aged farmer from rural Indiana helped me learn that leadership isn't position; it's influence.
• **A N IMPOVERISHED WOMAN TAUGHT ME GENEROSITY:** Helen, a member of my church, exhibited an extraordinary spirit of generosity and showed me it had nothing to do with wealth.
• **A N ON-LEADER TAUGHT ME NOT TO PIGEON-HOLE PEOPLE:** Brent, who modeled servanthood to me, helped me to understand that a person didn't have to be a classic leader type to make a valuable contribution to an organization.
• **A L ARGE-CHURCH LEADER SHOWED ME HOW TO GO FROM SHEPHERD TO RANCHER:** Jerry, the pastor of a large church, helped me to understand how to equip people to become leaders, grow my small church, and think like a rancher who pioneers and builds, not just a shepherd who maintains a flock.
• **A S PEAKER HELPED ME UNDERSTAND THAT MY WAY WASN'T THE ONLY WAY:** Florence, who wrote a book about the four different temperaments, helped me appreciate the differences and strengths of people unlike me.
• **A L AYPERSON GAVE ME THE IDEA TO RAISE MONEY:** I had thought the best ideas related to church leadership came from vocational ministers, but Bill, who was a businessman, was the one who came up with the idea of raising money for a church building program ourselves, instead of borrowing it from a bank.
There are hundreds more people different from me who made a positive difference in my life. They . . .
• challenged my assumptions,
• changed my thinking,
• showed me better ways of doing things,
• helped me remove my prejudices,
• taught me to value everyone, and
• made me a better person.
Slowly I moved from valuing sameness to questioning its value. Diversity slowly marked me with this thought: people different from me could make a positive difference in me.
* * *
PEOPLE DIFFERENT FROM ME COULD MAKE A POSITIVE DIFFERENCE IN ME.
* * *
This shift, which started subtly and grew over time, culminated when I relocated myself and my companies to Atlanta, Georgia, in 1997. Atlanta is a city rich in African-American influence and history. That was new to me. I'd lived in small-town Ohio, rural Indiana, and sunny San Diego. I knew there was a gap between me and the African-American community and their experiences, and I wanted to close that gap.
To help me, I enlisted the assistance of my friend Sam Chand, the president emeritus of Beulah Heights University, a predominantly African-American institution in Atlanta. Sam was born in India, but he was well-connected in our community. He arranged lunches every other month for two years where I got to meet more than three hundred local leaders. Overall, their journey was different from mine. I asked a lot of questions and requested that people tell me their stories. I'm happy to say that I was able to connect with most of the people I met. They reshaped my attitude, challenged my thinking, and touched my soul. I became a better person because of these experiences, and I made many new friends.
THE ADVANTAGES OF TEAM DIVERSITY
I saw a definition of _team_ in the _Harvard Business Review_ that I really like: "A team is a small number of people with complementary skills who are committed to a common purpose, set of performance goals, and approach for which they hold themselves mutually accountable." This definition assumes that there is a variety of skills. That implies diversity.
Our differences really can make a difference in our teams, our organizations, and our individual lives. Once we find common ground and commit to bringing the best out of people who are diverse, good things will begin to happen. This is what I am discovering now.
**1. D IVERSE TEAMS FILL IN THE KNOWLEDGE GAP**
As a leader, it's important to know what you don't know. How? By engaging with diverse people on your team. If you include a variety of people, then _someone_ on your team will be able to help you. That's why I frequently ask members of my team, "What am I missing?" I assume that I'm always missing something, and I believe someone can help me. When they do, then I'm freed up to focus on what I do know and what I do well.
When you don't fill in the knowledge gap, you can end up like the professor in this old story I read. He was traveling by train with a farmer. After several days together, they tired of talking and reading, so the professor suggested they play a game of riddles.
"Every time you miss a riddle, you give me a dollar, and every time I miss a riddle, I'll give you a dollar," said the professor.
"You're better educated than I am," the farmer pointed out. "I'll give you 50 cents." The professor agreed, and the farmer made up the first riddle.
"What has three legs walking and two legs flying?" he asked.
The professor didn't know, so he gave the farmer a dollar. The farmer didn't know either, so he gave the professor 50 cents.
**2. D IVERSE TEAMS FILL IN THE PERSPECTIVE GAP**
Malcolm Forbes said diversity is the art of thinking independently together. I love that because getting good independent thinkers to work together is the leadership challenge I love tackling. When everyone thinks and says the same things, it's the end of creativity and death to an entrepreneurial environment.
As a leader, it is my responsibility to encourage and engage in conversations that draw out different perspectives. I don't need or want my team members to parrot back to me what I think, or to try to guess what I want. I want to know what _they_ think. I want my team to "take me on" when they see things differently. I want them to challenge me just like I challenge them. It is only then that we get the most out of one another. That's called win-win.
**3. D IVERSE TEAMS FILL IN THE EXPERIENCE GAP**
A little bit of experience outweighs a whole lot of theory as far as I'm concerned. The greater the differences in personal experiences, the greater the team's ability to achieve, and the greater number of "tools" the team has at its disposal. As the saying goes, if all you have is a hammer, everything looks like a nail. Diversity helps prevent us from hammering away at things that need a screwdriver approach.
GOOD LEADERS EMBRACE DIVERSITY IN THEIR TEAMS
The topic of diversity is not a simple one, and people have a wide variety of reactions toward it. For some people, it conjures demographic studies, awkward interactions, relational minefields, and diversity training sessions in the workplace. For others it represents good-old-boy networks, glass ceilings, and privilege. But good leaders see diversity as one of the best ways to build a world-class team. When properly led, motivated, and unleashed, a diverse group of professionals can give your leadership team an uncommon advantage over your competitors.
One of the most impacting leadership books I've ever read is _Team of Rivals_ by Doris Kearns Goodwin. It tells the story of Abraham Lincoln's presidency and how he created his cabinet from a highly diverse group for its time. The members of his cabinet were his fierce rivals, not allies. Why did he choose people who were so different from himself? The demands of the Civil War required Lincoln to harness the skills of the best leaders and thinkers if the Union were to succeed. And President Lincoln used his greatest leadership skills and political insights to get the most out of the people holding different perspectives in the cabinet.
The book made quite an impression on me. When I finished reading _Team of Rivals_ , I wrote these words inside the front cover:
If you ever have to:
Handle tasks of great difficulty and diversity
Lead during a crisis
Place yourself beneath the burden of a higher cause
Carry the mantle of leadership with dignity . . .
Then, read this book.
—JCM, 11-09-2008
BARRIERS TO DIVERSITY
The greatest of leaders seem to do this instinctively. Winston Churchill, who masterfully led the United Kingdom during the difficult years of World War II, brought political adversaries like Clement Attlee into his strategy meetings in the underground bunker in London. Churchill knew the crisis demanded extraordinary talent, not just the skills of the people he would be comfortable with. Yet, if inviting diversity is such a valuable practice, why don't more leaders embrace it? Because diversity is uncomfortable. Many leaders fail to deal with that discomfort and have a difficult time overcoming these common barriers to diversity:
**1. F EAR OF CONFLICT**
A diverse team will naturally possess differences of opinion, perspective, and worldview. That almost inevitably leads to conflict. Many people are afraid of that, yet it's a necessary part of life. Conflict can actually help us. Author and consultant Patrick Lencioni wrote about this in his book _The Five Dysfunctions of a Team_ :
All great relationships, the ones that last over time, require productive conflict in order to grow. This is true in marriage, parenthood, friendship, and certainly business.
Unfortunately, conflict is considered taboo in many situations, especially at work. The higher you go up the management chain, the more you find people spending inordinate amounts of time and energy trying to avoid the kind of passionate debates that are essential to any great team.
Lencioni teaches that productive conflict has one purpose: "To produce the best possible solution in the shortest period of time."
When different people with different experiences sharing different opinions all sit at the table with the same objective, you can produce extraordinary results. But it requires people to set aside their titles and positions, personal agendas, and preferences. Everyone must want the best ideas to win, not just their own or their group's.
A marriage counselor once shared something with me about resolving the conflicts in marriage. People usually enter a marriage with different personalities, different experiences, different perspectives, and different expectations. Whatever differences existed before the wedding are intensified as the couple lives together for the first time. But happy marriages are based less on compatibility and more on how they deal with incompatibility. Rather than allowing the relationship to get tied up in knots, they need to learn to loosen the knot a bit—to face and resolve conflict.
**UNHEALTHY CONFLICT** | **HEALTHY CONFLICT**
---|---
Takes Differences Personally | Sees Differences Impartially
Dumps Personal Baggage | Desires to Know the Person
Searches for Retaliation | Searches for Resolution
Results in Hurt | Results in Helpfulness
Seeks Quick Conclusions | Seeks Understanding
Holds Back from the Conversation | Becomes Part of the Conversation
Values Self Above Solutions | Values Solutions Above Self
Defends Their Territory | Opens Up New Territory
Makes the Team Worse | Makes the Team Better
What people often fear most are breakdowns and that irreparable harm may occur in relationships. But when you value diversity and are genuinely open to the ideas and insights of other people, you open up the possibility of discovering fresh ideas, building a better team, and taking new ground.
**2. I NSUFFICIENT PERSONAL NETWORK**
Most people spend time with others like themselves. That often isn't out of prejudice. It's just how people act. When I was growing up, my mother used to tell me, "Birds of a feather flock together." She said it because she wanted me to spend time with other boys of high character, not kids who made bad choices and got into trouble. But the old adage she used to quote also is an indication that people naturally gravitate toward others of similar background, age, and race.
I recently read an article about Cheryle Moses, the founder and CEO of Urban MediaMakers in Lawrenceville, Georgia, which is not far from the John Maxwell Company headquarters. While planning an event to celebrate the sixteenth anniversary of her organization, Moses read a study that said 75 percent of white Americans don't have any nonwhite friends, and 65 percent of African-Americans don't have any white friends. Those statistics struck her so hard that she decided to turn the anniversary celebration into an event called "Come Meet a Black Person." Said Moses, "How can you learn about a person if you've never had that person in your life?" The event was well attended, and Moses thought it was a start toward a conversation between two groups that too often keep apart from one another.
Take an honest look at your peers, friends, and colleagues. If most of the people you know look like you, vote like you, and listen to the same music as you, you probably need to put some work into expanding your network, as I did when I moved to Atlanta. I've also taken other steps to expand my network. When I was a pastor, I spent much of my time outside the church networking with and talking to other pastors. After I transitioned out of full-time ministry, I started spending time with more business people from a wide variety of industries. I connected with Kevin Turner when he was at Walmart; Dan Cathy, the CEO of Chick-fil-A; Ed Bastian, the CEO of Delta; and many others. And I've traveled a lot more internationally to learn about different regions and cultures, from Venezuela to Nigeria to Saudi Arabia and the Philippines. And I can't even count the number of times I've been to China. All of this has stretched me and made me a better person and leader.
If you need to expand your personal network, as I did, keep these things in mind:
_Expanding Your Network Requires Humility_
When I started my leadership career, I thought I was always right. My greatest discovery as I started to meet people unlike myself was that they had so much to offer. Before making the improvement shift, I had shortchanged myself. Realizing that was humbling. When I recognized that others knew what I didn't, and that they had as much to contribute as I did, I could leave my world and enter new ones. Instead of fearing loss, I was anticipating what I would gain from our interaction.
_Expanding Your Network Requires Intentionality_
If you wait for connections with dissimilar people to happen on their own, they will never happen. You need to get out of your own natural "flock" and migrate to where other birds live and work. It will be uncomfortable, and anything uncomfortable or unusual must be done with high intentionality.
_Expanding Your Network Requires Energy_
Any time you try something new, it's going to take extra energy. That probably seems like common sense. However, people don't plan for it. If you want to make your team more diverse, gear up for it. Plan to keep going when you're too tired or don't feel like moving forward.
* * *
ANY TIME YOU TRY SOMETHING NEW, IT'S GOING TO TAKE EXTRA ENERGY.
* * *
_Expanding Your Network Requires Time_
The same can be said of time. It will take you time to build a diversified team. On top of that, it will take time (and energy) to see the benefits of diversity. You'll need to demonstrate patience as you start the "diversity dance," where you take two steps forward and one step back. It will take time for people to get to know one another. Everyone won't play nice at first. You'll encounter speed bumps and detours. That's true for any good team. But can you get there? Yes, if you give the time and energy required.
_Expanding Your Network Requires Love_
This one may be a surprise, especially in a business context, but I'm going to tell it like it is. Love makes all things work, and the foundation of love is being willing to value people—including people different from you and people you don't like. I've discovered that the more I value people, the more I add value to them. And the more I add value to them, the more value they return to the team. What gets appreciated, appreciates.
**3. U NWILLINGNESS TO DEAL WITH PREJUDICE**
I didn't grow up trying to isolate myself from people who were different from me—I just didn't know many. When I did eventually seek out relationships with people who were different, as I began connecting with the African-American business community in Atlanta, I discovered that I possessed a passive prejudice against people who were unlike me. Because of my ignorance, I had a blind spot. I assumed that people like me had good ideas that worked better than anyone else's. Exposure to different people from different backgrounds revealed my prejudice.
There's a saying I came across that really opened my eyes to what happens when you're prejudiced. I don't know who said it, but it's true: "The world is like a hand and all of the people its fingers. If you hate and destroy one group of people, you lose a finger, and the grasp of the world is less."
* * *
THE WORLD IS LIKE A HAND AND ALL OF THE PEOPLE ITS FINGERS. IF YOU HATE AND DESTROY ONE GROUP OF PEOPLE, YOU LOSE A FINGER, AND THE GRASP OF THE WORLD IS LESS.
—UNKNOWN
* * *
Embracing diversity has allowed me to have a better grasp of the world around me. One of the best ways I do this is through the John Maxwell Team. The Team's thousands of coaches are a mosaic of diverse people with different faiths from a broad range of countries—more than a hundred—each with its own culture. These coaches bring their different perspectives, gifts, and experiences together that provide us with a bigger picture and greater opportunities. Let me tell you about just five of them:
1. Gaby is from Paraguay; she has been the catalyst for transformation in her country.
2. Sorin is from Romania and leads more than one thousand coaches in that country who daily add value to many citizens.
3. Mfon, from Nigeria, trains people in leadership for the United Nations.
4. Rudolfo, who lives in Houston, has translated all the John Maxwell Team training materials into Spanish so that they will benefit millions of people in Latin America.
5. Dr. Saroja, in Saudi Arabia, teaches twenty-seven thousand high school students leadership values.
These are only five "fingers," but I know many more. I could fill this chapter with the names of difference-makers from various countries, but that's not the point. My perspective has been changed. Does yours need to be? What prejudices, whether conscious or unknown, do you possess that are keeping you from connecting with people unlike you and diversifying your team? You need to identify whatever is holding you back and work to resolve it.
**4. A RROGANCE**
I once read that the knights of the Middle Ages used to own a variety of horses for different uses. They rode smaller horses, called palfreys or amblers, for everyday use such as traveling. But when dressed in full armor, ready for battle or jousting, knights needed massive war horses, called coursers or destriers, which could support the weight of a rider, his armor and weapons, a saddle, and the horse's extensive armor. Those horses might have been as many as twenty hands high at the withers. For those of us who aren't horse people, that means seven feet tall at the horse's shoulder!
Why do I mention this? Because that's where the expression "get off your high horse" comes from. A mounted knight in full armor looked down upon everyone else—not just the peasants on the ground but even others on horseback. And that's what many people do, especially leaders who have achieved a certain rank. They arrogantly look down on others from their high horse. This prevents them from appreciating others, particularly those who are different from them.
Some leaders are so confident in their own genius that they can't imagine other people adding value to their work. They believe the less similar others are, the less they can contribute. And sadly, the farther down in the organization people are, the more they are ignored. But the reality is that no leaders are so good that they can afford to ignore the contributions of others. No one is indispensable.
Years ago I came across a poem by Saxon White Kessinger called "The Indispensable Man." I thought it expressed the plight of the arrogant:
Sometime when you're feeling important;
Sometime when your ego's on bloom;
Sometime when you take for granted,
You're the best qualified in the room.
Sometime when you feel that you're going
Would leave an unfillable hole;
Just follow this simple instruction,
And see how it humbles your soul.
Take a bucket and fill it with water,
Put your hand in it up to the wrist;
Pull it out and the hole that's remaining,
Is a measure of how you'll be missed.
You may splash all you please when you enter,
You can stir up the water galore;
But stop and you'll find in a minute,
That it looks quite the same as before.
The moral in this quaint example
Is to do just the best that you can;
Be proud of yourself, but remember
There's no indispensable man
If you dismiss the ideas of and potential contributions of others, especially of those offered by people different from you, you will never reach your potential and neither will your team. And, sadly, you will never even know it!
**5. P ERSONAL INSECURITIES**
There's an old joke that the CEO of an organization met one day with the head of HR and said, "Search the organization for an alert, aggressive young leader who could step into my shoes, and when you find him, fire him." Just as the CEO in that joke felt threatened by strong young leaders, there are people who feel threatened or uncomfortable around those who are different. That personal insecurity is easily sensed by others and puts them off.
* * *
THE BEST ANTIDOTE I'VE EVER FOUND FOR PERSONAL INSECURITY IS TO THINK ABOUT HELPING OTHER PEOPLE AND PUTTING THEM FIRST.
* * *
The topic of insecurity is a complex one, and if you're an insecure leader, you may need to get help dealing with it. But I will say this: the best antidote I've ever found for personal insecurity is to think about helping other people and putting them first. When you do that, you stop worrying about trying to look good, and you put your attention on making others look good.
I learned this lesson a couple of years after graduating from college. For two years I played on a good amateur basketball team where all the players in our starting lineup were better than I was. I have to admit, this intimidated me and made me feel a little insecure, because I was a pretty decent player back in those days. At first my competitive nature kicked in during our practices, but that only made things worse.
Before our first game, I made a decision, and it changed everything for me. Instead of trying to be better than them, I decided to focus on making the other players better. And I told them so. The moment my playing became about them and not about me, my insecurity faded, and I became a better contributor to our team.
If you have insecurities, especially those driven by other's strengths or differences, start working on them. If you don't, your leadership will harm—not help—the team.
**6. F AILING TO BE INCLUSIVE**
The final common barrier to promoting team diversity is the leader and team members' failure to be inclusive. When people are on your team but don't feel like they belong or contribute, they disconnect. And they don't bring their best gifts and talents to the table.
For many years I've taught people to seek common ground with others as the way to start the connection process, and to further that process by valuing people and adding value to them. I still believe this is the way to start. But the whole idea of _inclusion_ and how it relates to diversity is changing because of millennials. I recently read a study about the approach millennials take to the workplace, and I thought, _No wonder the number one question I'm asked in the business community is how to interact with millennials._
The study was called "The Radical Transformation of Diversity and Inclusion: The Millennial Influence" and was published by Deloitte University. It said that my generation of baby boomers as well as Generation Xers see _inclusion_ as a function of morality—the right thing to do. We would define it in terms of representation, or ensuring fair inclusion of "gender, race, religion, ethnicity, and sexual orientation." Baby boomers might not see practical value in diversity and inclusion; their focus would be on compliance, ethics, and equality.
In contrast, millennials see diversity and inclusion as having intrinsic value. They allow voices to be heard that have a tangible and beneficial impact on business. The goal isn't just bringing together people of different races, religions, and genders; instead, they want to bring together people with differences in background, personal experience, style, and perspective.
How those people are brought together is also important to millennials. As the study's authors, Christie Smith and Stephanie Turner, explained:
When it comes to defining inclusion, millennials focus primarily and extensively on teaming, valuing a culture of connectivity, and using collaborative tools to drive business impact. Older generations instead defined inclusion in terms of equality, fairness, and the integration, acceptance, and tolerance of gender, racial, and ethnic diversity within the organization.
Millennials are just happy to have people at the table. They want everyone to be seen as a contributor, and inclusion hasn't occurred until that's been empowered to happen.
These differences in thinking and approach have a huge impact in the workplace, and that impact will only increase. By 2025, 75 percent of the workforce will be made up of millennials. Currently, the majority of millennials feel less included and connected than people in the workplace from other generations.
• Millennials are 13 percent more likely to disagree with the statement that they feel excited to go to work.
• Overall, millennials are 13 percent more likely to disagree with the statement that they feel attached to the organization.
• Millennials are 33 percent more likely to disagree with the statement that their work has an impact on the organization.
Smith and Turner suggested that good leadership supporting inclusion and diversity will help millennials to become fully engaged. Leaders can do that by providing "a collaborative environment in which employees can see the impact of their work, understand the value they bring to the organization, and are recognized for their efforts. Leaders believe in openness and transparency and demonstrate that a cognitively diverse team is better for business."
HOW TO LEADERSHIFT TO DIVERSITY AND INCLUSION
If you're a millennial, you're probably saying, "Amen." If you're a boomer or Gen Xer, you're likely supportive of creating an environment that's diverse and inclusive, but you aren't sure what to do with these different ways of thinking and alternate perspectives. I have three suggestions:
**1. C REATE A CULTURE OF SHARING**
No matter how diverse the workplace is, teams will not embrace creativity unless there is a culture conducive to interaction and sharing of knowledge. This requires de-emphasizing titles, positions, and roles. It means inviting everyone to speak up. It means giving people opportunities to lead before they have an official role—and sometimes even before you feel they are fully ready. And it means being more open to differences. Smith and Turner pointed out:
Millennials yearn for self-expression and acceptance of their thoughts and opinions, but compared to older generations, they feel it's unnecessary to downplay their differences in order to get ahead. Millennials are refusing to check their identities at the doors of organizations today, and they strongly believe these characteristics bring value to the business outcomes and impact.
When you share space, share responsibility, share ownership, and share rewards, everyone wants to contribute.
**2. B ROADEN YOUR PERSPECTIVE ON DIVERSITY**
In an article in _Harvard Business Review_ , business psychology professor Tomas Chamorro-Premuzic wrote, "Most discussions about diversity focus on demographic variables (e.g., gender, age, and race). However, the most interesting and influential aspects of diversity are psychological (e.g., personality, values, and abilities)." This is also the way millennials see it.
Equality isn't just about giving everyone the same things; it's also about giving unique people what they need. Bernard Tyson, CEO of Kaiser Permanente, said, "We've evolved from equality to equity. Equality says everybody gets equal. Equity says no, everybody gets what they need. Part of building an inclusive environment is not how you're going to change the person. It's how you're going to change yourself and the environment in which the person is going to be successful." That requires us to think differently and treat diversity differently.
**3. P ROVIDE SOLID LEADERSHIP FOR DIVERSITY TO BE EFFECTIVE**
As much as diversity can help a team, it can also challenge a team. Bringing together a diverse group of people isn't easy. And as Chamorro-Premuzic pointed out, too great a diversity on a team can be problematic. I think of it as the Samson Syndrome—the pairing of great strength with great weakness. The strength of diversity is problem solving and idea creation. The weakness comes in decision-making and implementation. Tomas Chamorro-Premuzic stated:
There's a difference between generating ideas and implementing ideas. While diverse team composition does seem to confer an advantage when it comes to generating a wider range of original and useful ideas, experimental studies suggest that such benefits disappear once the team is tasked with deciding which ideas to select and implement, presumably because diversity hinders consensus.
He went on to say that "the creativity gains produced by higher team diversity are disrupted by the inherent social conflict and decision-making deficits that less homogeneous teams create." Good leadership can help bring strength to both ideation and implementation.
I'm still on the journey when it comes to shifting from uniformity to diversity. Why? Because the way people think is still changing, and I have to change to become a better leader. The greatest shift was from thinking I was right to realizing that people are different but they're not wrong. Once I was able to see from their perspective, I better saw their value, and I became open to it.
There's something of a paradox in all this. To embrace diversity, we must celebrate our differences. But I still believe the way we get there is to look for common ground. In the end, I think we all want the same things: to be heard, to value one another, to work together, to be successful, and to make a difference. If we can connect where we're similar and contribute using our differences, we can accomplish great things.
CHAPTER 10
POSITIONAL AUTHORITY TO MORAL AUTHORITY
_The Influence Shift_
_The true measure of leadership is influence—nothing more, nothing less._
—THE LAW OF INFLUENCE
I've been known for my definition of leadership for more than forty-five years: leadership is influence. If you've led people for any length of time, you probably know instinctively that this is true. But have you ever wondered where the influence comes from?
NO AUTHORITY
I found myself asking that question in my first leadership job. Just a few weeks out of college, I became the pastor of a small rural church in the farming community of Hillham, Indiana. The word _community_ almost makes it sound bigger than it really was: eleven houses, two gas stations, and a little country store.
It was a job I thought I could handle in an environment where I could learn the ropes. The church wasn't big, it wasn't in a city, and there were no titans of industry to deal with. I would be a medium fish in a small pond. The bylaws of the organization said that I was the leader of the congregation and the chairman of the organization's board. I thought that made me a leader.
The first time I met with the board, I prepared for it. I thought about the vision and how I would articulate it. I thought about how I wanted the meeting to go, and I wrote a detailed agenda.
I knew that, as the chairman, I was supposed to open the meeting and run it. So after the introductions and greetings were finished and we were sitting around the table, I prepared to start. But before I could say or do anything, Claude, one of the board members, said, "Pastor, why don't you open us in prayer?"
_That's a good idea_ , I thought, so I prayed.
I opened up the file folder with copies of my agenda in it and was about to hand them out, when Claude said, "There are a couple of things I think we ought to talk about tonight."
_Oh_ , I thought, _okay. We can take care of those things first. Then we can get to my agenda._
Claude led the discussion and asked questions while the other men responded. I listened and tried to follow along. Most of the things they were dealing with were the kind of mundane, everyday items that need to be done in an organization, so there was nothing earth-shattering.
After about an hour, Claude said, "Well, that about does it. Pastor, why don't you close us in prayer?"
So I said a prayer, everybody got up, shook hands, said their goodbyes, and went home. And I thought to myself, _What just happened?_
WHERE DOES AUTHORITY COME FROM?
That's the day I learned that a leadership position does not give someone leadership authority. And having a title is not the same as having influence. I had the title, but everyone followed Claude. His opinion was the one that mattered at the table. Everyone agreed with everything he said. And they were glad to do what he said.
* * *
A LEADERSHIP POSITION DOES NOT GIVE SOMEONE LEADERSHIP AUTHORITY.
* * *
Back then, I had not yet discovered my definition of leadership, but after that board meeting, I began thinking about the topic. And I started trying to figure out why all the board members followed Claude. He was a middle-aged farmer who also worked at the nearby power plant. He wasn't an especially impressive man. He wasn't educated. But he had influence.
I look back now, and I realize that in the small world of Hillham, Claude had a degree of moral authority. To the people in that church and on that board, his words carried great weight. Why? Because of the way he lived his life. He was a good man. He was honest, fair, and hardworking. His word and actions lined up, and that had been true for decades. He cared for the congregation and was always ready to help. Claude would not have recognized himself as a leader or called himself a leader, yet he had earned the right to be followed.
When it comes to leadership, I think there are all kinds of authority. Here are some examples:
• **N ATURAL AUTHORITY:** Some people naturally lead better than others and therefore step into leadership roles.
• **P OSITIONAL AUTHORITY:** This kind of authority comes with a title or a formal position in an organization and is the lowest level of leadership.
• **K NOWLEDGE AUTHORITY:** Knowing more than others do or having specific information can give people an influence edge.
• **S ITUATIONAL AUTHORITY:** A certain circumstance can arise that requires the most qualified person to lead in that situation.
• **R ELATIONAL AUTHORITY:** When people have built relationships with others, that gives them influence to lead.
• **P ROXIMITY AUTHORITY:** When individuals are close to the real leader or authority figure, they can borrow from that leader's influence to lead others.
• **S UCCESS AUTHORITY:** Success gives people credibility, and others want to be on their team to be part of their success.
• **M ENTORING AUTHORITY:** Developers of other people increase their influence with the people they mentor and gain a reputation for credibility.
• **S ENIORITY AUTHORITY:** In some cultures, being an elder or having seniority in an organization gives authority.
My experience with Claude started me on a journey toward understanding different kinds of leadership authority. It helped me settle my definition of leadership. It prompted me to develop the 5 Levels of Leadership, which I mentioned in chapter 5 on the leadershift from pleasing people to challenging people. And it ultimately led me to the concept of moral authority, which is the highest level of influence. For fifty years I have been in the process of the influence shift, from positional authority to moral authority. It's a journey I'm still on, and a shift I'm still working to make.
What is moral authority? It can be difficult to define. On his blog, Theodore Brown acknowledges that the term is used a lot, but he also states how difficult _moral authority_ is to define. One example he gives is what he calls the John McCain effect, which he says is "the capacity to convince others of how the world _should_ be.
Here's another perspective from Harvard Business School professor Kevin Sharer. He wrote:
Moral authority is not easy to define precisely, but like many things, you know it when you see it, or especially when you do not. Lack of moral authority in leaders breeds distrust, creates cynicism and kills initiative throughout the organization. Over time, the lack of strong moral authority in the leadership is fatal to the enterprise or country.
These perspectives make moral authority sound grandiose. It can be, but it doesn't have to be. Claude had moral authority and didn't even know it. But so did Nelson Mandela and Mother Teresa. So what is moral authority? Here's my definition:
Moral authority is the recognition of a person's leadership influence based on who they are more than the position they hold. It is attained by authentic living that has built trust and it is sustained by successful leadership endeavors. It is earned by a lifetime of consistency. Leaders can strive to earn moral authority by the way they live, but only others can grant them moral authority.
Moral authority is truly the highest level of leadership influence, and many people recognize it. It comes from possessing good values. It adds value to others. It inspires people. It helps the leader to make the right decisions for the right reasons. It marks a life of words and actions that line up. We know when we're in the presence of someone who has moral authority, and we want to follow them!
In "4 Ways to Build Moral Authority," Chuck Olson said,
People follow people, not positions. Your business card may say you're a leader and in-charge, but if your bank account of moral authority is overdrawn, you will be forced to rely on extrinsic factors to rally your followers. No amount of skill, wealth, personality, education, or accomplishment can compensate for the absence of moral authority. Perks and paychecks are the currency required to enlist people in a project, but moral authority is the currency required to enlist people in a movement. Andy Stanley in his book, _Next Generation Leader_ , observes: "Your position will prompt people in your organization to lend you their hands. . . . But your moral authority will inspire them to lend you their hearts."
Moral authority has the implicit power to transform what is into what can be. It takes people to higher levels of living and leading. It's inspirational, yet at the same time it is grounded and credible. It makes leaders better because they desire to do better. Moral authority brings out the best in teams because of the respect team members have for the leaders and the desire team members have to live up to and follow their example.
THE PATHWAY TO MORAL AUTHORITY
One of the dangers when anyone begins discussing moral authority is that it can sound mystical and out of reach. However, it is grounded in four things: competence, courage, consistency, and character. I believe anyone can pursue moral authority and develop greater influence by developing in all four of these areas. Let's take a look at each of them.
**1. C OMPETENCE—THE ABILITY TO LEAD WELL**
Everything starts here. Competence is the core of moral authority. If you can't do your job, if you can't deliver the goods, if you can't lead the team well, why would anyone want to follow you? You can't cultivate moral authority unless people respect you. Author George L. Davis observed, "Authority is not something we buy, are born with, or even have delegated to us by our superiors. It is something we earn—and we earn it from our subordinates. No manager has any real authority over his people until he has proved himself worthy of it—in the eyes of his people—not his own, nor those of his superiors."
* * *
COMPETENCE IS THE CORE OF MORAL AUTHORITY.
* * *
How do you build a foundation of competence? By giving your best, starting with the small stuff. Dale Carnegie said, "Don't be afraid to give your best to what seemingly are small jobs. Every time you conquer one it makes you that much stronger. If you do the little jobs well, the big ones tend to take care of themselves."
Doing work with excellence to full completion helps a person develop a reputation for competence. Oscar Hammerstein II was one of the great lyricists of the American theater. He wrote songs for shows such as _The Sound of Music_ , _The King and I_ , _Oklahoma_ , and _South Pacific_. His advice to writers and artists is equally valuable for business people and leaders:
This is a very important thing for writers to remember. You never know when you will be found out if your work is careless. A year or so ago, on the cover of the New York _Herald Tribune_ Sunday Magazine, I saw a picture of the Statue of Liberty. It was a picture taken from a helicopter and it showed the top of the statue's head. I was amazed at the detail there. The sculptor had done a painstaking job with the lady's coiffure, and yet he must have been pretty sure that the only eyes that would ever see this detail would be the uncritical eyes of sea gulls. He could not have dreamt that any man would ever fly over this head and take a picture of it. He was artist enough, however, to finish off this part of the statue with as much care as he had devoted to her face and her arms and the torch and everything that people can see as they sail up the bay. He was right. When you are creating a work of art, or any other kind of work, finish the job off perfectly.
Doing your work with devotion to excellence and the will to follow through will give you a positive reputation for competence. That's true in any profession. But leaders need to also cultivate influence with others and demonstrate competence in their ability to engage with people and motivate and inspire them to work together. Forty years ago, I started teaching the 5 Levels of Leadership to help people understand how influence worked and to teach them a growth process they could follow to become better leaders. I write about this more fully in my book _Developing the Leader Within You 2.0_ , but I want to summarize it here to help you get a feel for how you can develop your leadership competence.
_Level 1: Position—People Follow Because They Have To_
The authority someone receives at this level is very limited and is restricted to the leader's job description. A leader need not be competent to receive a leadership appointment. In some organizations, that person doesn't even have to be competent to _retain_ a leadership position.
_Level 2: Permission—People Follow Because They Want To_
A leader begins to develop authority at this second level. When the leader builds relationships, people are willing to work with them because they like them and enjoy spending time with them. They are beginning to give permission for the person to lead them.
_Level 3: Production—People Follow Because You Demonstrate Competence_
On this third level a leader begins to demonstrate genuine competence. Being productive is a big step in gaining moral authority with others. People follow because the leader has produced results and is successful, and they want to be on a winning team.
_Level 4: People Development—People Follow Because You Help Them Become Competent_
When you start to invest in people and help them to become successful personally, your level of authority rises dramatically, the lives of the people you help improve, and this gives you a level of credibility you can gain no other way.
_Level 5: Pinnacle—People Follow Because You Have a Reputation for Excellence_
When you live a life of competence, influence people at each of the first four levels, and develop leaders over a long period of time, you can approach the pinnacle of leadership. This is where true moral authority is established.
Moral authority is not based on position, but you must learn the skills of each level of leadership and master them to be seen as highly competent in leadership. However, competence alone is not enough to earn moral authority.
**2. C OURAGE—MOVING FORWARD IN THE FACE OF FEAR**
Leadership authority shrinks or expands with a person's courage. Author and professor C. S. Lewis said, "Courage is not simply one of the virtues but the form of every virtue at the testing point." Without courage, you can't live any other virtue consistently. With courage, especially when facing great obstacles, you begin to gain moral authority.
I think everyone admires courage, and intuitively we understand that it carries weight. We can follow a leader who is courageous. More specifically, here's how courage relates to moral authority:
_Courage Encourages People During Difficult and Uncertain Times_
There is perhaps no greater need for courage from a leader than during difficult times. Poet Ralph Waldo Emerson is rumored to have said:
Whatever you do, you need courage. Whatever course you decide upon, there is always someone to tell you [that] you are wrong. There are always difficulties arising, which tempt you to believe that your critics are right. To map out a course of action and follow it to the end, requires some of the same courage which a soldier needs. Peace has its victories, but it takes brave men [and women] to win them.
The courage that people need to see and feel during difficult times does not have to be loud and dramatic, though many times it is. The difficulties of our everyday lives often require us to find and display courage. Author and artist Mary Anne Radmacher said, "Courage doesn't always roar. Sometimes courage is the quiet voice at the end of the day saying, 'I will try again tomorrow.'"
* * *
COURAGE DOESN'T ALWAYS ROAR. SOMETIMES COURAGE IS THE QUIET VOICE AT THE END OF THE DAY SAYING, "I WILL TRY AGAIN TOMORROW."
—MARY ANNE RADMACHER
* * *
_Courage Enables People to Maximize Their Potential_
In _Making the Courage Connection_ , Doug Hall wrote, "Courage has a tangible quality. You can't touch it, but you can feel it. It feels like positive acceleration. Courage sends a rush of energy through your body. It makes you wake up in the morning with a feeling of wanting to wrap your hands around the day." Being courageous not only fires you up but also fires up others and makes them more courageous. That's important, because nobody ever reached his or her potential by cowering in fear. Fortune favors the bold.
One of my favorite stories of courage is about David of Israel before he became king. Most people are aware that David fought Goliath with a sling and defeated him. But many people know little more than that about the story. When David stepped out to battle Goliath, the rest of Israel's army, including King Saul and David's older brothers, were cowering in fear. None of them had the courage to face Goliath, who had challenged their army and taunted them daily, waiting for a champion to meet him. David, a boy with no military experience, had the courage to fight the Philistine giant, took him down with a stone, and then cut off his head with the warrior's own sword. In that moment, the entire army of Israel found their courage because of David's heroic act. They attacked and routed the Philistine army.
Time after time, before he was king and during his reign, David's courage inspired his people to do their best. His closest allies were men who also became great warriors because they were inspired by his courage. Under David's leadership, the nation expanded its borders, conquered its enemies, and achieved peace.
_Courage Helps Leaders Find Their Voice_
As leaders display courage in crisis, they often find their voices. During World War II, when England stood alone against Nazi Germany, Winston Churchill found his voice. In 1940 while addressing Parliament, he told his countrymen, "We shall never surrender." Martin Luther King Jr. found his voice during the civil rights struggle of the 1960s. His words still resound today: "Our lives begin to end the day we remain silent about things that matter."
A remarkable story of a leader who found his voice is told in _Profiles in Courage_ by John F. Kennedy. When Andrew Johnson became president following the assassination of Abraham Lincoln, Johnson was determined to carry out Lincoln's policies regarding the South. It was Lincoln's desire to bring healing quickly to the nation after the Civil War, and Johnson, who was from Tennessee, recognized Lincoln's policy as the best course of action.
Johnson's fellow Republicans in Congress desired a different path. They wanted to punish the Southern states for seceding, and when Johnson resisted their policies and vetoed much of the legislation they passed, the most radical wing of the Republican party became determined to impeach Johnson and remove him from office.
All the Democrats in the Senate opposed impeachment, as did six Republicans. If all the remaining Republicans voted in favor, then Johnson would be removed from office. But one senator from Kansas, Edmund G. Ross, who was believed to be a supporter of the radicals, would not vote to impeach the president because he believed it would signal the end of the divided powers of government and permanently damage the country, turning the United States into "a partisan Congressional autocracy."
Ross later commented, "I almost literally looked down into my open grave. Friendships, positions, fortune, everything that makes life desirable to an ambitious man were about to be swept away by the breath of my mouth, perhaps forever." When asked how he voted, he answered, "Not guilty," and Johnson was not impeached. Shortly after the trial, he said to his wife, "Millions of men cursing me today will bless me tomorrow for having saved the country from the greatest peril through which it has ever passed, though none but God can ever know the struggle it has cost me." And it did cost him. At the next election, he was voted out of office. When he returned home after his term, he was ostracized and attacked and lived in near poverty.
Every leader who possesses moral authority has had to stand alone at some point in time. Such moments make leaders. Such stands are often very difficult, but when leaders look back afterward, they often see those as their proudest moments.
* * *
EVERY LEADER WHO POSSESSES MORAL AUTHORITY HAS HAD TO STAND ALONE AT SOME POINT IN TIME. SUCH MOMENTS MAKE LEADERS.
* * *
We don't choose the times or the circumstances we must face in life, but we do choose our responses. I love the prayer of the Special Olympics because I think it represents the mind-set we should embrace as leaders: "Let me win, but if I cannot win, let me be brave in the attempt."
**3. C ONSISTENCY—DOING WELL ALL THE TIME, NOT JUST SOMETIMES**
In his fantastic book _Visioneering_ , Andy Stanley described the value of consistency related to moral authority. He wrote:
It is the alignment between a person's convictions and his behavior that makes his life persuasive. Herein is the key to sustained influence.
The phrase that best captures this dynamic is moral authority. To gain and maintain your influence you must have moral authority. Moral authority is the critical, non-negotiable, can't-be-without ingredient of sustained influence. Without moral authority, your influence will be limited and short-lived.
Moral authority is the credibility you earn by walking your talk . . . It is the relationship other people see between what you say and what you do, between what you claim to be and what you are. A person with moral authority is beyond reproach. That is, when you look for a discrepancy between what he says he believes and what he does, you come up empty. There is alignment between conviction and action, belief and behavior.
Nothing compensates for a lack of moral authority. No amount of communication skills, wealth, accomplishment, education, talent, or position can make up for a lack of moral authority. We all know plenty of people who have those qualities but who exercise no influence over us whatsoever. Why? Because there is a contradiction between what they claim to be and what we perceive them to be.
What Stanley described is internal consistency between values and actions, which is essential to a leader's success if he or she desires to gain moral authority. Equally important is the ability to be consistent over time.
Now that I'm in my seventies, people have started to ask me questions that prompt me to think back on my life. Probably the most common question is, "John, now that you're in your seventies, what has been your greatest surprise in life?" I think of these as "old man questions" because nobody asks them of young leaders. They make me chuckle, because they mean that I look much older than I feel, but I attempt to answer them honestly.
There are two things that surprise me. The first is how fast time has gone by. I still can't believe I'm over seventy. The second is the value of consistency. Consistency compounds in a way I never realized. If you do the right things when you're young, it mostly goes unnoticed and unrecognized. But if you do the right things and lead well over decades, it becomes recognized, and you get more credit than you feel you deserve. That's the power of what I call layered living. If you embrace layered learning (as I described in chapter 3 on shifting from goals to growth) and you practice layered leadership (by consistently living out your values and performing with excellence), then your reward can be layered living, where you reap the benefits of moral authority.
Consistency is so valuable to a leader that it's difficult to list all its benefits. Here are just a few:
• **C ONSISTENCY ESTABLISHES YOUR REPUTATION.** Nearly anyone can be good once. Being good continually is difficult. However, continued repetition leads to a positive reputation.
• **C ONSISTENCY MAKES TEAM MEMBERS MORE SECURE.** Perhaps the greatest compliment a person can receive is, "I can depend on you." A consistent leader inspires team members to become more confident.
• **C ONSISTENCY ALLOWS FOR ACCURATE MEASUREMENT OF YOUR GROWTH.** It's difficult to gauge the progress of inconsistent people. The track record we establish shows what we have done and how far we have come.
• **C ONSISTENCY MAKES YOU RELEVANT.** People who bounce back and forth between engagement and disengagement always have to play catch-up. By staying consistently engaged, you don't fall behind.
• **C ONSISTENCY MODELS YOUR EXPECTATIONS FOR OTHERS.** When you consistently model your values and work ethic, team members know what you expect of them because they've seen it every day. Consistency always reinforces expectations.
• **C ONSISTENCY MAINTAINS YOUR MESSAGE.** When a leader communicates a vision but acts in ways that are inconsistent with that vision the result is confusion. It distracts from the message and makes it more difficult for everyone on the team.
Consistency, along with competence and courage, is vital to a leader's ability to develop moral authority, but there's still one more component without which moral authority is impossible to earn.
**4. C HARACTER—BEING BIGGER ON THE INSIDE THAN THE OUTSIDE**
Moral authority is a result of right intentions, right values, right beliefs, right actions, right relationships, and right responses. There is a lot to do right to develop moral authority. That doesn't mean perfection. We are all human and make mistakes. But to have moral authority, our intentions must be right; the motives of the heart must be good.
While much of leadership is outward and public, the right motives and the good character traits we need to become leaders with moral authority are won in private. These two aspects of leadership, public and private, resemble the two parts of a tree. One part you see: our public leadership is like a tree's trunk and branches. That's the part that bears fruit. However, who leaders are in private is what can't be seen, like a tree's roots. If the roots are shallow, then the tree won't survive. Drought will dry it up. A storm will knock it down. But if the roots are deep, the tree can thrive in almost any circumstance.
What does it mean to develop deep roots as a leader? It means having strong character. What kind of character does a leader need to have? I believe good character demonstrates these four characteristics:
_Integrity_
I define integrity two ways. First, it's the alignment of your values and actions. You know what's right and you do it. Integrity has consistency, as I discussed earlier in this chapter, but the consistency is specific to what's right and wrong, not just what's good and best. Leaders with moral authority hold themselves to a high standard of conduct.
* * *
LEADERS OF INTEGRITY DO THE RIGHT THING, EVEN WHEN IT'S HARD, EVEN WHEN IT'S NOT BEST FOR THEM PERSONALLY.
* * *
The second definition has to do with decision-making. Leaders of integrity do the right thing, even when it's hard, even when it's not best for them personally. They put the team, the organization, and the vision ahead of themselves.
_Authenticity_
Author and spiritual leader Mark Batterson said, "Authenticity is the new authority in leadership." I agree, because I believe that is an essential part of moral authority. People do not want to follow leaders who pretend to be what they're not. They don't expect perfection—just honesty.
This can be a real struggle for many leaders. They want to meet others' expectations and can be tempted to compromise their beliefs or standards. I felt this pull early in my career as a young pastor. The organization I was a part of held some theological positions that I was personally uncomfortable with. For a couple of years, I felt an obligation to teach on these issues, but I always felt as though I was promoting something I didn't believe in, and it made me miserable.
Then one day, as I was preparing a message that I was struggling with, I resolved to change. I marked my resolve by writing down these three statements:
1. I will only teach what I believe—passion.
2. I will only teach what I experience—confidence.
3. I will only teach what I live—authenticity.
I have followed those guidelines ever since. Those decisions made me not only a better communicator but also a better leader. To be the best leader you can be, you need to acknowledge who you really are and be willing to let people witness your authenticity.
* * *
HUMILITY IS MAKING THE EVERYDAY CHOICE TO CREDIT GOD FOR YOUR BLESSINGS AND TO CREDIT OTHERS FOR YOUR SUCCESSES.
* * *
_Humility_
I believe humility is an essential quality for a leader who possesses moral authority. In his book _Good to Great_ , Jim Collins called this "a compelling modesty." He wrote:
We were struck by how the good-to-great leaders didn't talk about themselves. . . . When pressed to talk about themselves, they'd say things like, "I hope I'm not sounding like a big shot. . . ."
It wasn't just false modesty. Those who worked with or wrote about the good-to-great leaders continually used words like _quiet, humble, modest, reserved, shy, gracious, mild-mannered, self-effacing, understated, did not believe his own clippings_ ; and so forth.
As a person of faith, I see humility as making the everyday choice to credit God for my blessings and to credit others for my successes. How would you describe it? My friend Rick Warren said, "Humility is not denying your strengths. Humility is being honest about your weaknesses." No matter how you define _humility_ , know that it means three things. First, you possess self-awareness and can criticize yourself. Second, you are confident and comfortable enough that you don't feel any need to draw attention to yourself. And third, you revel in the accomplishments of others and are eager to help them shine.
_Love_
The final character quality to embrace as a leader in order to have moral authority is love. You must care about people. You must respect them. You must value them. People can always tell when you don't, and that creates an instant disconnection that short-circuits moral authority.
I've talked a bit about the John Maxwell Team. Our motto is, "People of Value, Who Value People." I want our coaches to have resources and expertise to offer, and I want them to value others so that their character and attitude are right when working with people. They need to love people and care about them enough to help them.
What do you want to do with your leadership? I think every leader wants to make an impact, a difference. It's the reason we get up in the morning. It's why we work with people. It's why we create teams or build organizations. Do you have it in you to do something big? Do you want to change your organization, or your community, or your culture, or your country? How big are your dreams? The bigger they are, the more you need moral authority to accomplish them.
When I was in my early thirties, I started to get the sense that my leadership could be impactful and my life could make a difference. That prompted me to make some personal decisions. At the time, I simply thought they were the right things to do to be a better leader. Today, I can see that they helped me in the four areas I've written about in this chapter: competence, courage, consistency, and character. I decided to:
1. Always put people first.
2. Live to make a difference, not to make money.
3. Be myself, but be my best self possible.
4. Express gratitude—reject entitlement.
5. Be willing to be misunderstood and lonely for the right reasons.
I've worked hard to follow these guidelines for the last forty years.
In the end, you don't get to grant yourself moral authority. You can choose to strive for it, but only others can give it to you, and they must do so freely. But that should not stop you from doing everything right that you can to earn it. Because if you gain moral authority, it makes you worthy of respect, inspires trust and confidence, and enables you to lead at the highest standards of performance. This leadershift will increase your influence, giving you buy-in not only from the people on your team but from others who aren't under your formal leadership. And with that influence, there's no telling what you can help people accomplish.
CHAPTER 11
TRAINED LEADERS TO TRANSFORMATIONAL LEADERS
_The Impact Shift_
_If your actions inspire people to dream more, learn more, do more, and become more, then you are a transformational leader._
Of all the chapters in this book, this one is the most important. Why do I say that? Because if you make only one leadershift in your life, this is the one I would wish for you to choose. The impact shift from trained leaders to transformational leaders will bring the greatest change to your life and the lives of those around you.
If your actions inspire people to dream more, learn more, do more, and become more, then you are a transformational leader. You influence people to think, speak, and act in ways that make a positive difference in their lives and the lives of others. That kind of leadership can change the world!
MY CHANGE IN LEADERSHIP PERSPECTIVE
My leadershift from trained leader to transformational leader occurred early. This story is very personal to me, and it had a dramatic effect on my life. At the heart of this shift was my faith, which is at the foundation of who I am. However, I value you whether or not you are a person of faith. No matter what your perspective is about faith, I don't want you to miss this, so I'll condense my story down to its essence.
At the beginning of my career, I cared mostly about myself and building my organization. Sadly, people were not my top priority. And I regret to say that my selfishness sometimes kept me from doing the right thing. There was one particular incident that made me realize that my priorities were wrong. I failed to help a man because I was focused on myself. And then the man died. My selfish decision meant that he never got the help I should have given him, and there was nothing I could do to fix that.
I can't express the devastating impact this had on me. I felt terrible, and it caused me to spend several months reevaluating myself as a leader. For the first time in my life, I started to ask myself the hard questions about my motives and methods that every leader ought to ask. And I was not satisfied with my answers.
During the next few months, I spent a lot of time in prayer and reflection, and I resolved to become a different kind of leader—someone different from who I had been up to that time. Thankfully my heart was changed, and my actions started following my heart. I became a person who valued other people and demonstrated that through my leadership decisions, which made others my top priority. The change within me was deep and made a difference that still influences me today. If I hadn't made this shift, my leadership would have been hollow and self-centered. I credit this with making possible whatever difference I've made with my leadership.
ESSENTIALS FOR TRANSFORMATIONAL LEADERSHIP
I'm a firm believer in training in leadership. I've done it myself for fifty years and helped others for more than forty years. But I also recognize there's a huge difference between trained leaders and leaders who are transformational. Take a look at how they compare:
**TRAINED LEADERS** | **TRANSFORMATIONAL LEADERS**
---|---
Know How to Lead | Know Why They Lead
Are Liked | Are Contagious
Influence Today | Influence Today and Tomorrow
Ask People to Follow | Ask People to Make a Difference
Love to Lead | Love the People They Lead
Are Trained | Are Trained and Transformed
Help People | Help People Change
Have a Career | Have a Calling
Impact a Few | Impact Many
For many years I have studied transformational movements and the people who led them. I've identified five actions common to all of them. If you desire to make the impact shift from trained leader to transformational leader, start doing these too.
**1. P OSSESS A CLEAR PICTURE OF WHAT TRANSFORMATIONAL LEADERS DO**
On the surface, all transformational leaders look different from one another. They come in all sizes and shapes, from many races and nationalities, and with a variety of skills and talents. Their differences are many. However, there are a few characteristics that all of them share, and if you desire to become transformational, you must embrace them, too, so that you know what you're striving for:
_Transformational Leaders See Things Others Do Not See_
Many people see problems and shake their heads. They experience adversity and throw up their hands. They look at challenges and ask "Why?"—not seeking a solution, just venting frustration. When they encounter problems, they see no possibilities. They become victims of negative circumstances and cannot help themselves or others.
Transformational leaders see things differently. They ask, "Why not?" because they're always thinking about trying to create a better future. They see more than others see. Of course, they see the problems. They may even be surrounded by them. But they also see potential in those problems. They believe there is always an answer, a solution, a better way, a brighter future. That belief creates anticipation, not desperation, during the darkest of hours.
How we view things determines how we do things. When I put myself first as a leader, I saw everything through the filter of my own selfishness. After my leadershift, I started to see through the lens of service. I started to ask, _How can I help more people, and how can I help people more?_ My friend Dave Ramsey said, "Organizations are not limited by their opportunity; they are limited by their leader." If we don't see the things others don't, how can we lead them to a better future?
* * *
ORGANIZATIONS ARE NOT LIMITED BY THEIR OPPORTUNITY; THEY ARE LIMITED BY THEIR LEADER.
—DAVE RAMSEY
* * *
_Transformational Leaders Say Things Others Do Not Say_
Transformational leaders speak up. They leverage their influence by speaking bold words about a better future. Their voice becomes a tool of transformation. Think of the bold words said by transformational leaders who were willing to describe a better future. Martin Luther King Jr. said, "I have a dream." It took courage for him to be the voice of change when others opposed him.
As I have become a better communicator, I've tried to use my voice to facilitate positive change. At times I was misunderstood. But I made decisions that I believed were right, such as when . . .
• I stood on the floor of a national meeting and promoted a policy of inclusiveness that I knew had no chance of passing.
• I said no to becoming the new host of a prestigious national radio show because I declined to sign a doctrinal statement I didn't agree with.
• I handed back a million-dollar gift given to my nonprofit organization because I proposed going in a direction that the donor did not like.
• I changed the nonprofit EQUIP from a training organization to a transformational one.
None of these decisions was popular when I shared it, and not everyone understood. But sometimes that's what a leader must do. Say things others won't.
_Transformational Leaders Believe Things Others Do Not Believe_
Transformational leaders believe that they can make a difference. That becomes their passion. President John F. Kennedy said he believed that everyone had a change-the-world speech in them. I was thirteen years old when he said it, and I can still remember how I felt when I heard those words. Although I was only a young teenager, I felt that he was talking directly to me. I believed him—because he believed it. When I reached my middle twenties, I concluded that everything rises and falls on leadership. Over time, that belief has been a conviction that I lived and taught. Today it is a cause that I have given my life to. It is the subject of my change-the-world speech.
* * *
EVERYONE HAS A CHANGE-THE-WORLD SPEECH IN THEM.
—JOHN F. KENNEDY
* * *
Believing you can make a difference changes everything. When transformational leaders believe that their cause can make a difference, then they bring conviction to their leadership. Without this conviction, you may be able to get people to follow you, and you will be a good leader. But only when you understand that the higher calling of leadership is to get people to follow your cause can you become a great leader.
Transformational leaders believe in others. They are belief magnets. People are drawn to them because they believe in their message and believe it will help people. They realize one is too small a number to achieve greatness, so they rally people together to make a difference; they extend their hand and ask others to join them in their mission. Abraham Lincoln said, "I am a success today because I had a friend who believed in me and I didn't have the heart to let them down." Transformational leaders are belief-makers who help people to believe in themselves.
_Transformational Leaders Feel Things Others Do Not Feel_
Peter Marshall said, "A different world cannot be built by indifferent people." Passion creates energy and tenacity in people. It fires up leaders and the people who join them for their cause. That fire helps them endure, the way Gandhi did in his fight for Indian independence. It was a process that took fifty-four years. During that time Gandhi was attacked, rejected, imprisoned, misrepresented, sick with malaria—and then was finally victorious. Passion carried him forward.
* * *
A DIFFERENT WORLD CANNOT BE BUILT BY INDIFFERENT PEOPLE.
—PETER MARSHALL
* * *
I've seen passion emerge in the lives of people I lead, and it has changed their lives and the way they lead. This happens every time I invite a group of John Maxwell Team coaches to go with me to another country to train roundtable facilitators. Hundreds of coaches have volunteered to travel overseas, paid all their own expenses, trained twelve hours a day, then traveled in less-than-ideal circumstances to help others. They give up their time, their money, and their energy to do it. And they love it! They tirelessly give of themselves, and yet at the end I hear over and over that they feel they've received more than they gave. And they want to do it again. Paul Martinelli, president of the John Maxwell Team, said, "When the light goes on in your life, you want to turn everyone else's light on." I love that, and it's true. Transformational leaders have their lights on, and they want to help others turn theirs on.
_Transformational Leaders Do Things Others Do Not Do_
Do you know what happens when a procrastinator has something to do? Nothing. Do you know what happens when a transformational leader has something to do? They get moving. In fact, they are often so eager that their actions follow this pattern: "Ready—Fire—Aim."
While fear causes many people to shrink back from the unknown and avoid challenges that lie ahead, it causes transformational leaders to prepare and work harder. How do they overcome their fears? By tapping into their sense of purpose and by believing in a cause that is much bigger than themselves. They want to make a difference, and the only questions they need to answer are, "What kind of difference can I make?" and "How big of a difference can it be?" Their strong sense of purpose propels them to do what others aren't willing to do.
I've already mentioned that my greatest desire is to see a country transformed so much that the leaders and citizens acknowledge the positive change. That is a BHAG (Big Hairy Audacious Goal). And I may not live to see it happen. So why am I doing everything I can to be part of this? Because I would rather try something big that is almost impossible than something small that won't make a difference. If you want to make the leadershift from trained to transformational leadership, I encourage you to have a similarly audacious attitude.
**2. F OCUS ON YOUR OWN TRANSFORMATION BEFORE LEADING OTHERS TO IT**
In chapter 3 I discussed how I developed the acronym R-E-A-L, with the _E_ representing _equipping_. As soon as I understood how important equipping was, I studied the process and discovered the best way to train others. I came up with a five-step process that works no matter what task you're trying to equip another person to do.
1. I do it.
2. I do it, and you are with me.
3. You do it, and I am with you.
4. You do it.
5. You do it, and someone is with you.
Why do I mention this? Because I want you to notice that the process begins with _I do it._ If I want to help others be transformational, I must first be transformed. I cannot give what I do not have. Neither can you.
The first person you must lead will always be you. If you want to see positive changes in your world, the first person you must change is you. As leaders, you and I have to be changed to bring change. We teach what we know, but we reproduce who we are.
* * *
AS LEADERS, YOU AND I HAVE TO BE CHANGED TO BRING CHANGE. WE TEACH WHAT WE KNOW, BUT WE REPRODUCE WHO WE ARE.
* * *
Before I personally experienced the transformation of shifting from a desire to make my life successful to a desire to help other people's lives improve, it never entered my mind that I could be a catalyst for positive change. It never entered my heart either. There was no passion within me to help others experience positive change. However, when I began to experience positive change in my life and became less selfish, I was eager to share what was happening with others. Knowing that I was changing got me excited about helping others change too.
For nearly twenty years, volunteer associate trainers for my nonprofit training organization EQUIP have traveled to countries around the world to teach people how to become better leaders. In recent years, we shifted from a classroom model of teaching to a roundtable method of facilitation. And we've placed a greater emphasis on asking the trainers to live the transformation before they travel overseas to train others in it. Specifically, before they go train others to lead roundtables, we ask them to gather a group in their own community and facilitate a roundtable there. We want them to experience for themselves what they intend to teach others. Why? Because we know transformation must occur in us before we can take it to others.
If you want to lead any positive change, you need to realize this: transformation begins with you. If you are not willing to change, you are not going to be able to help anyone else.
Philosopher and author James Allen wrote, "Men are anxious to improve their circumstances, but are unwilling to improve themselves; they therefore remain bound." If you want to lead positive change, don't remain bound. Be willing to change within. Start with you. That's always the first step to making a difference.
**3. T AKE POSITIVE ACTION BASED ON YOUR INTERNAL CHANGES**
An essential step in the leadershift from trained to transformational is a commitment to taking action. For real change to occur, we must go from knowing to doing. It's at this point that transformation becomes difficult, yet the results are so beautiful. It's difficult because saying is always easier than doing. It's beautiful because action is what brings transformation.
Everything worthwhile in life is uphill—all the way. Transformation requires us to walk uphill. Everyday. All the way. Most people are unwilling to commit to that. Instead of climbing, they would rather be . . .
• Talking: "Let's discuss uphill climbing."
• Thinking: "Let's contemplate uphill climbing."
• Planning: "Let's strategize about uphill climbing."
• Surveying: "Let's ask others what they think about uphill climbing."
• Studying: "Let's examine what uphill climbing looks like."
• Resting: "Let's conserve energy before we start climbing."
Transformation is a result of application, not education. That's why Gandhi said, "An ounce of practice is worth more than tons of preaching." To lead transformationally, you must first live transformed. That takes courage, the courage to let go of the familiar and set off on a better way.
**4. C REATE AN ENVIRONMENT THAT PROMOTES POSITIVE CHANGE**
For years I have encouraged people to embrace positive change. More recently my nonprofit organizations have dedicated themselves to promoting transformation. Our experience working with tens of thousands of people has helped us to understand what creates an ideal environment. These are the essentials:
_Leaders Who Are Passionate About Transformation_
Jim Collins said, "Transformational movements require transformational leaders." Only transformational leaders can bring about transformation. What I've said for years is true: everything rises and falls on leadership.
This poem by Lawrence Tribble really says it all:
One man awake, awakens another.
The second awakens his next-door brother.
The three awake can rouse a town
By turning the whole place upside down.
The many awake can cause such a fuss
It finally awakens the rest of us.
One man up with dawn in his eyes
Surely then multiplies.
Some man or woman has to start that process. The person who does is a transformational leader.
_Resources That Teach Good Values_
Many people are unaware that there is a better way to live. They are stuck in the life they have because they are not sure where to go, nor do they know how to move beyond their current situation. I'm convinced from personal experience and observation that good values are the road to a better life. And placing resources that teach good values in the hands of people turns the light on for them so that they can see a better way.
Good values are teachable and reachable. Just one good value in a person's life can bring great benefit. Here are some of the values my nonprofit organizations have helped people to understand and embrace over the years:
• **A TTITUDE:** your attitude colors everything in your life
• **C OMMITMENT:** it separates doers from dreamers
• **C OMPETENCE:** the shortest path to credibility is competence
• **F ORGIVENESS:** forgiveness empowers you to live with a light heart
• **I NITIATIVE:** you cannot experience success unless you start
• **I NTEGRITY:** living with integrity leads to a life of wholeness
• **P ERSONAL GROWTH:** people who keep learning always have a future
• **P RIORITIES:** clear priorities show you what to do and where to go
• **R ELATIONSHIPS:** the quality of your relationships determines the quality of your life
• **W ORK ETHIC:** working hard brings inner satisfaction every day
We've created resources to help people explore ideas, examine themselves, and decide how they will take action to embrace good values and change their lives. If you desire to shift from trained leader to transformational leader, you need to give people resources to help them. Most people cannot find the pathway to a better life without help.
_Small Groups Where People Learn and Participate_
Too often, training that begins in our heads stays in our heads. We learn something new, but we don't apply it to our lives or put it into practice. That's why transformation needs a living laboratory to be effective. That occurs best in a small group of people where all the members of the group share ideas, speak about themselves with candor and honesty, state their intentions, and hold one another accountable.
EQUIP and the John Maxwell Leadership Foundation, the two nonprofit organizations I founded, use roundtables in small groups to facilitate change. We've found that groups of four to ten can create the perfect environment for people to develop relationships, get to know themselves and others, and experience growth. Most people do not have a high level of self-awareness. They spend so much time and energy projecting a positive image that they don't examine themselves and their motives as much as they could. A safe small-group environment where people see the others as peers, everyone is asked to participate, and the leader of the group is open and authentic about his or her shortcomings encourages everyone to participate, ask questions, listen, share, reflect, and commit to taking action. And if members of the group report back the next time they meet to honestly share both failures and success, everyone is encouraged to grow and change.
I've experienced the positive power of participating in small groups in my own life. Some of the greatest changes that have determined my most important decisions occurred in small-group settings:
• I accepted the challenge to practice daily personal growth.
• I was encouraged to start writing books.
• I was inspired to start developing resources for leaders.
• I was energized to start developing leaders.
• I felt stirred to try leading a transformational movement.
All those things occurred—and more. I wasn't _expecting_ any of those things to happen before I joined those groups. But once I committed to a group and fully engaged in the process, good things began to happen. Small groups can bring big growth.
_Commitment to Reproduce Leaders_
By definition, for someone to be a leader, he or she must have followers. If you think you're leading but no one is following you, then you're only taking a walk. However, it's not enough to gather followers. To be transformational, leaders must develop and reproduce leaders.
I started to learn this lesson more than thirty years ago when I was leading Skyline Church. We recognized the transformative power of small groups, so we started a small-group program. Naively, we thought we could simply put people together in groups and they would flourish. We quickly discovered that if we didn't train leaders, the groups didn't succeed. So we dismantled the program, started training leaders, and relaunched. We were successful this second go-round, but then we learned something else: trained leaders could sustain a group, but transformed leaders could gather, grow, and reproduce groups. They could train other leaders who reached other people and trained other leaders.
My nonprofit organizations have embraced this model of growth for transformation. In each roundtable group, we invite participants to start and facilitate other roundtable groups when they have experienced positive change themselves. They pass on what they've learned, help facilitate transformation in others, and invite new leaders to rise up and lead groups of their own. In this way we continually equip leaders to reproduce themselves. When this happens repeatedly, individual transformation leads to group transformation which leads to community transformation. It starts with transformed leaders who want to lead others to transformation.
**5. C OMMIT TO MAKING A DIFFERENCE WITH OTHERS IN YOUR COMMUNITY**
Making positive changes requires commitment from leaders who want to make a difference. Civil rights leader Walter E. Fauntroy eloquently expressed this in an inspiring speech he delivered at Howard University. He said:
The past is yours. Learn from it. The future is yours. Fulfill it. Knowledge is yours. Use it. Cancer is yours. Cure it. Racism is yours. End it. Injustice is yours. Correct it. Sickness is yours. Heal it. Ignorance is yours. Banish it. War is yours. Stop it. Hope is yours. Confirm it. America is yours. Save it. The world is yours. Serve it. The dream is yours. Claim it.
Don't be blinded by prejudice, disheartened by the times, or discouraged by the system. Face the system. Challenge it. Change it. Confront it. Correct it. Don't let anything paralyze your mind, tie your hands, or defeat your spirit. Take the world—not to dominate it, but to deliver it. Not to exploit it, but to enrich it—take your dream and inherit the earth.
Change does not happen unless transformational leaders commit themselves to making a difference in their community and invite others to join them in the process. All transformational movements follow a pattern. They occur:
**T OP-DOWN—**Leadership influence filters down, not up.
**S MALL TO BIG—**Mass movements begin with a few people.
**I NSIDE OUT—**Inner values determine outward behavior.
If you're willing to commit to changing yourself, inviting a small group of people to join you in the process, and preparing other leaders to become agents of transformation, you can change your world.
AMAZING TRANSFORMATION
I want to close this chapter with a story told to me by my good friend Jerry Anderson. Jerry was a serial entrepreneur who kept failing until he met John Schrock, a successful businessman who lived his life in accordance with positive values he'd learned by reading Proverbs. Jerry was mentored by John, and it transformed his life. Jerry went on to become highly successful himself, and out of gratitude and a desire to make a difference, he started teaching the values he had learned from John to others. When his efforts started to gain momentum, Jerry founded the nonprofit organization La Red to multiply his efforts.
In the early 2000s, Jerry's organization was invited to Colombia. The reason? The prisons of Colombia were notoriously corrupt at that time. They were run by organized crime and the most powerful inmates. The prisoners were organized and often armed. Money flowed into the prisons. Some of the more powerful inmates had set up suites. A few were even equipped with doors to the outside so that associates and women could come and go at will, bringing money and drugs, among other things.
This criminal environment bred corruption among the guards. Since they could not beat the inmates, they simply joined them. They served the wealthiest criminals and treated the other inmates like slaves. The prison system was brutal. On average, there was a murder every day within the 143 prisons. Jerry said in one instance, a man's head had been cut off and used as a soccer ball in the prison yard.
The Colombian government desired change, but they weren't sure what to do or how to start. They decided to coax General Ricardo Cifuentes out of retirement. Cifuentes knew he would not be able to change the prison with more guns or new buildings. What he needed to do was change the hearts and minds of the leaders. To do that, he invited Jerry's organization La Red into the prison system to work with the guards. Jerry said that soon after the decision was made to bring in La Red, General Cifuentes called a press conference to announce that change had begun in the country.
La Red introduced character development and values into 143 prisons, believing they could transform the culture of the prison by teaching the guards and other prison employees character-based values. They met regularly in small roundtable groups. Any employee who refused to participate in the weekly meeting lost his job.
Slowly, the culture of the prison began to change. The eleven thousand guards in the prisons were changing. They no longer embraced corruption. They started treating people better. They asked others to forgive their previous behavior. They started to regain their dignity. The change was so dramatic that prisoners started writing letters to the director asking for the same training that the guards were receiving.
What happened next was remarkable. The guards started to allow one prisoner to become part of a roundtable group of guards. To participate, that inmate had to agree to lead his own group with other prisoners in his cell block. The process began with fifty-six prisoners. As these individuals were trained in values, their thinking changed. Their values changed. Their actions changed. They were transformed by the time they started their own groups in their cell blocks. As they led their groups, many of the inmates who were receiving training in the small roundtable groups started to change too. Over several years the entire prison system and its eighty thousand inmates were transformed. Many of the inmates expressed that if they had learned these values earlier in life, they probably would not have ended up in prison.
The most impacting value that the inmates embraced was forgiveness. The ability to forgive others allowed them to break the cycle of revenge and freed them from the chains of hatred and bitterness. Jerry said one inmate exclaimed that forgiving the person who had wrongfully put him in jail was the most freeing experience of his life. The man said that before, he had felt handcuffed to that person. Forgiving made him feel free. Perhaps most remarkable of all, the murder rate in the prison went from an average of one per day down to one per year!
The success Jerry had in the prisons was so dramatic that the Colombian military invited La Red to train their military troops in character development. The governments of other countries contacted him too. The last time I asked Jerry, he said La Red has helped people in forty-four nations. He estimates that more than one million people have participated in the transformational small groups they form and been trained in values-based principles. And they're still going strong. That's the power of the impact shift. If you leadershift from trained to transformational leadership, there's no telling what kind of impact you can make or how far your influence will go.
CHAPTER 12
CAREER TO CALLING
_The Passion Shift_
_Some wake up to an alarm. Some wake up to a calling._
—UNKNOWN
This last leadershift should be the most natural shift a person can make, yet many people miss it. They are so busy with their day-to-day existence and with making a living that they don't think about it. Or they've been told that life has no greater meaning—and they actually believed it. I'm here to tell you that this leadershift is available to you if you're willing to reach for it.
WHAT DO YOU DO?
I want to start by asking you a question: How do you currently think about what you do for a living? Yale professor Amy Wrzesniewski has done research with employees in the workplace and observed that people tend to fall into three groups. What's remarkable is that individuals fall into these three categories regardless of the industry they work in, the social status of their profession, their pay, or their title. For example, in a study, roughly equal numbers of administrative assistants surveyed fell into these three categories. And employees who mopped floors in a hospital were equally likely to fall evenly into these three groups. Think about which best describes you.
**1. Y OU DO A JOB**
When you have a job, your main goal is often to earn a living and support your family. You may not think beyond the time you spend on the clock. You may do your job with excellence or you may simply mark time, but either way, when you finish your day or your shift, you walk away and don't think about it. Satisfaction and fulfillment for people who have a job-only mind-set comes from activities outside of work. And while people in this group may hope to advance, they don't think in terms of a strategy of career building.
It's been said that if you choose a job you love, you will never have to work a day in your life. I think that's good advice, but it should be a starting point, not an ending goal. A job is not your calling, no matter how much money it will allow you to make or how it allows you to serve people. A job is merely a vehicle with the potential to take you toward your calling. That's the way you should think of it.
**2. Y OU BUILD A CAREER**
Most people would acknowledge that it's a step forward to think in terms of developing a career rather than just holding a job. When you have a career, the implication is that you are headed in a direction. You're making progress attaining positive achievements. An upward trajectory of skill mastery, larger responsibilities, and greater earnings are all marks of a successful career.
**3. Y OU FULFILL YOUR CALLING**
Author Frederick Buechner said that our purpose is at "that place where your deep gladness meets the world's deep need." Your calling, when you find and embrace it, will result in the merging of your skills, talents, character traits, and experiences. It will make use of your experience, your gifts, and the lessons you've learned. It will be represented by a deep desire to create, lead, inspire, and make a difference. Take a look at the difference between a career and a calling:
**CAREER** | **CALLING**
---|---
Mainly About You | Mainly About Others
Something You Choose | Something Chosen for You
Separated from Your Best Life | Integrated into Your Entire Life
You Can Take or Leave It | Never Leaves You
Something You Can Do | Something You Must Do
Measured by Success | Measured by Significance
Wouldn't you like to find and fulfill a calling that makes a difference and gets you excited every day for the rest of your life? Finding your calling is like finding your _why—_ the reason you exist, your purpose for living. When you do, it changes everything:
When you find your Why—you find your Way.
When you find your Why—you find your Will.
When you find your Why—you find your Wings.
Your life will never be the same once you know what you're called to do and are working to fulfill it every day.
WE ARE ALL SEARCHERS
I believe _everyone_ has the potential to find and fulfill his or her purpose. Everyone has the ability to be called. In each of us there is a desire to know more and be more. There is something in us that calls to something bigger. Richard Leider, author, coach, and founder of Inventure, the Purpose Company, has written extensively on the subjects of purpose and calling. He said:
The search for callings is not a trend. It is something much deeper. If it needs a label, it is searcher. James Kavanaugh captured the essence of the drive when he wrote, "I am one of the searchers. There are, I believe, millions of us. We are not unhappy, but neither are we really content. We continue to explore life, hoping to uncover its ultimate secret."
We humans are searchers for meaning. . . . Work has meaning if it serves others. Calling joins self and service. As Aristotle said, "Where our talents and the needs of the world cross, there lies our vocation."
When I turned seventy, I was asked what I found the most surprising about life. I answered, "The brevity of it." I don't feel seventy. I don't look—well, let's not go there. It's hard to believe I've lived seven decades and been married more than fifty years. It's remarkable that some of Margaret's and my _grandchildren_ are almost grown. I feel like I just started life's journey, yet I passed the halfway point quite a while ago. Life is short, and its brevity makes the message of this chapter important. The passage of time makes your search for your calling a high priority.
* * *
WHERE OUR TALENTS AND THE NEEDS OF THE WORLD CROSS, THERE LIES OUR VOCATION.
—ARISTOTLE
* * *
As you read this, you may be older, as I am. Or you may be in high school with your entire life and working career ahead of you. Either way, you can find your purpose, your calling. It's never too early, nor is it ever too late.
THE DAY I WAS CALLED
I consider myself to be fortunate. I received my calling when I was twenty-nine years old. I was old enough to appreciate it and young enough to have plenty of time to make the most of it. I want to tell you about the experience. Because I'm a person of faith, my experience involves God. However, you do not need to be a person of faith to receive a calling. You just need to be open and watchful.
Before I tell you the story, I want to say something meant for followers of Christ, in the event that you happen to be one. For all Christians there is a general calling meant for everyone. Jesus said, "Let me tell you why you are here. You're here to be salt-seasoning that brings out the God-flavors on this earth. . . . Here's another way to put it: You're here to be light, bringing out the God-colors in the world." Christ followers are in this world to be salt and light. Salt makes things better. Light makes things brighter. The wallpaper on my iPhone has a picture of a salt shaker and a light bulb with the words "Be These" to remind me every day to try to make the world better and brighter.
There is also often a specific calling—a compulsion to do something unique. Here God calls people to himself and to a cause so decisively that everything they are, everything they do, and everything they have is invested for him in that cause. Mother Teresa described this as "the call within a call." When she felt it on September 10, 1946, on a train ride from Kolkata to Darjeeling, she knew her life purpose was to serve the poorest of the poor. She immediately set on a course to fulfill that calling, serving poor people in Kolkata, and in time she was able to establish the Missionaries of Charity.
I experienced such a calling on July 4, 1976. I was speaking in celebration of the United States' bicentennial, and suddenly I had a clear and compelling sense that God wanted me to invest my life in developing leaders and teaching leadership. It was perhaps the greatest moment of clarity I've ever had in my life.
On the drive home, I told Margaret about it. She listened, as she always does when I'm excited by an idea. She asked, "What are you going to do?"
"Nothing," I answered.
She was surprised, because back then I usually dove right into strategy mode and started creating my plans. (This was back before I had fully leadershifted from planning to looking at options.) But this was different from any other experience I'd had. Yes, I was excited. I couldn't wait to train leaders for the rest of my life. At the same time, I was also patient, and I felt very settled—calm.
"If this is a calling," I told her, "then doors will open." And they did. Before the week was out, two different groups called to ask me to speak to their leaders.
In most areas of my life at that time, I was very ambitious. Earlier in this book I discussed how goal-oriented I was and how much I paid attention to stats and progress. This was different. This was God's personal invitation for me to work on his agenda, using the talents he'd given me, doing work that I sensed would be eternally significant. I felt grateful to be called to something important, but I wasn't thinking in terms of goals or timelines. I just wanted to be my best and do my best. I can honestly say that today, more than forty years later, I'm just as excited as I was that first day. I'm still thrilled to have been called to teach leadership and develop leaders. I want to add value to leaders who multiply value to others. That's my calling and purpose in life.
THE CHARACTERISTICS OF A CALLING
You have a purpose in life, too, and you can receive a sense of calling. I don't want you to miss this just because I'm telling you about my calling in the context of my faith. You can be of a different faith than me or have no faith at all, and you can still be called. Your calling can give you a fruitful and fulfilling life, one that fills you with passion and motivates you to make a difference. When it is your calling, you won't have to chase it. You will be _captivated_ by it.
* * *
WHEN IT IS YOUR CALLING, YOU WON'T HAVE TO CHASE IT. YOU WILL BE _CAPTIVATED_ BY IT.
* * *
I want to help you to understand calling so that you can find yours if you haven't already done so. I want you to be ready when it comes.
**1. Y OUR CALLING MATCHES WHO YOU ARE**
No one has ever been called to do something he or she wasn't suited for. Calling always matches who you are. For that reason, it's important for you to be self-aware as you stay attentive to finding your calling. Here are some questions that can help you think about calling:
• If you could do one thing for the rest of your life, even if you never got paid for it, what would you do?
• What do people often ask for your help with?
• What experiences have you had that you desire to help others with?
• What lights you up?
• What do you love learning about?
• What could you talk about for hours and hours?
• What activities are you always self-motivated to do?
• What can you do to make a positive difference in the lives of others?
• What would you like to do that would live beyond you?
The calling you receive often taps into not just one or two of these things but _all_ of them.
**2. Y OUR CALLING TAPS INTO YOUR PASSION**
Impacting the world is hard. If you lack passion for the call, your energy will fizzle out. You should use the sleepless night test for this one. Is there a cause you want to pursue that is consuming you so much that you can't sleep at night? That's a sign that you might be called to it. I like the advice of author, philosopher, and civil rights leader Howard Thurman, who said, "Don't ask what the world needs. Ask what makes you come alive and go do it. Because what the world needs is people who have come alive."
Passion is a great driver toward calling. If you're not sure about where your passion lies, ask yourself some of these questions:
• How do my strengths fuel my passion?
• What experiences inform my passion?
• What opportunities align with my passion?
• How does what I love to do point to my passion?
• How does what I do well contribute to my passion?
• How does what others say point to my passion?
• How does my history of success coincide with my passion?
• Where does my desire to grow increase my passion?
Talent, skills, experience, and opportunities all align with calling, but passion provides the fuel to pursue your calling.
**3. Y OUR CALLING IS IMPORTANT _TO_ YOU, BUT IT'S NOT _A BOUT_ YOU**
A true calling is never about the person being called. It's about helping others. A calling moves us from the center of everything in our world to becoming the channel through which good things come to others. As Nelson Mandela said, "What counts in life is not the mere fact that we have lived. It is what difference we have made to the lives of others that will determine the significance of the life we lead." When you're called, you have an important role to play, but it's never about you.
I wrote a lot about the subject of significance in my book _Intentional Living_. The book is about how significance comes from making a difference with others wherever you are, with whatever you have, day by day. In other words, significance means:
• giving beyond yourself,
• serving beyond yourself,
• thinking beyond yourself,
• loving beyond yourself, and
• seeing beyond yourself.
What do all these things have in common? They require you to live beyond _yourself_.
**4. Y OUR CALLING IS BIGGER THAN YOU**
A calling always involves something that feels big, something that's bigger than you are. It may intimidate you. It may even seem impossible. Yet you feel compelled to get out of your comfort zone to fulfill it. You are willing to stretch to complete it. You keep moving forward despite the odds.
There's an old story about vision that I came across many years ago. A passerby was looking at a building site during the Middle Ages and saw a craftsman working. "What are you doing?" asked the passerby.
"I'm laying stone," the craftsman replied.
The passerby continued on his way and saw a second craftsman doing the same kind of work. "What are you doing?" he asked.
"I'm building a wall," answered the second craftsman.
The passerby was nearly past the building site when he spotted a third man working. Like the other two, he was a stonemason. "What are you doing?" the passerby asked.
"I'm building a magnificent cathedral," the third craftsman answered. He saw the size of his task and knew what his contribution was. I think you could call that a _cathedral calling_. That's when you recognize that you are doing something bigger than you, and it may never be completed in your lifetime. But you know you are a part of something big and beautiful. Everyone should be part of a cathedral calling because we were meant for more than simply doing work or building careers. We were made for significance—for making a difference.
**5. Y OUR CALLING CHANGES YOUR PERSPECTIVE**
Having a calling makes you see your world differently. Where you once saw only obligations and responsibilities, you will begin to see options and opportunities. No longer will you be focused on the tasks you are required to do. A whole new world will open up to you of things you _want_ to do. Take a look at the difference between the two perspectives:
**RESPONSIBILITY PERSPECTIVE** | **OPPORTUNITY PERSPECTIVE**
---|---
Feels Heavy | Feels Light and Exciting
Is a Burden | Is a Privilege
Consumes Energy | Creates Energy
Can Seem Meaningless and Rote | Feels Purposeful and Meaningful
Is Driven by a Sense of Duty | Is Driven by a Sense of Optimism
Is Something We Have to Do | Is Something We Want to Do
Leads to Routine and Repetition | Inspires Creativity
Discourages Efficiency | Inspires Efficiency
Tends to Drag Out Tasks | Desires Bang for Our Buck
Repels Others with Negativity | Attracts Others with Positivity
Gives a Sense of Completion | Gives a Sense of Possibility
Is Associated with Pushing | Is Associated with Inspiring
Leads to Success in 10% of Our Lives | Leads to Success that Opens Up the Hidden 90%
A calling lifts our hearts and expands our options. It can make even the mundane meaningful. It drastically changes our perspective for the better.
**6. Y OUR CALLING GIVES YOU PURPOSE**
Sheri Riley is a John Maxwell Team coach who has worked for many years with professional athletes and celebrity entertainers. She recently published her first book, called _Exponential Living_. In it she wrote about how many people get so caught up in the grind of life that they lose track of why they do it. She said:
Many high achievers are so focused on working that work becomes an end in itself. They become addicted to the demands, the stress, and the sense of accomplishment they get from working hard, even if their hard work isn't leading them anywhere they want to go. Often, high achievers don't even realize they have achieved what they are working for and that it's time to move on to something else.
Work is labor, folks. That's all it is. It has value only to the extent that it accomplishes something you truly desire. Many of us high achievers operate under some version of the Puritan work ethic. That is, we believe that work has value in and of itself. So therefore, if we do a lot of it, _we_ must be valuable. So we take on lots of work, and keep ourselves very busy, but not necessarily as productive as we could. We exhaust ourselves because we confuse work with value. At the end of a tiring workweek, we look back and say, "Well, at least I did _that_." We may not be any closer to our dreams, but we sure did work.
At one end of the spectrum are people like the ones Sheri described, the high achievers who work for the sake of work. On the other end are people who work because they have to but find no fulfillment in what they do. Author Seth Godin was talking to these people when he said, "Instead of wondering what your next vacation is, maybe you should set up a life you don't need to escape from."
The answer for both types of people is the sense of purpose that comes with a calling. Take a look at the benefits of the strong sense of purpose that accompanies calling:
• Purpose will motivate you—Passion
• Purpose will keep your priorities straight—Discipline
• Purpose will develop your potential—Stretch
• Purpose will give you power to live in the present—Awareness
• Purpose will help you elevate your progress—Growth
• Purpose will direct your habits—Consistency
• Purpose will perpetuate an intentional lifestyle—Significance
Parker Palmer, the founder of the Center for Courage and Renewal, said, "Before I can tell my life what I want to do with it, I must listen to my life telling who I am." What he's talking about is calling and the purpose we derive from it.
**7. Y OUR CALLING HELPS YOU TO OVERCOME OBSTACLES**
What do you draw upon when you hit a wall in your life or your leadership? Do you rely on grit? Do you draw upon discipline? Do you work harder? All of these things are good, but they can't compare to the power of calling to keep you going.
My friend Dave Ramsey said, "Higher calling matters. When you care so deeply about the why—why you're doing what you're doing—then and only then are you operating in a way that allows you to overcome the obstacles."
**8. Y OUR CALLING BRINGS FULFILLMENT**
Nothing in life is as rewarding as fulfilling your calling—nothing. Wealth, fame, achievement, recognition: all of them fall short. Why do you think so many celebrities and athletes champion causes? They're looking for the fulfillment that comes only from pursuing a calling.
I've observed and known many who lived without a calling. As the years pass, their deepest needs and desires go unexplored. They are busy, but they develop a vague anxiety that their life has not achieved its ultimate meaning and significance. They live with a restlessness because they are not firmly attached to the moral purposes that give life its worth. Because they don't follow a calling, they lack the internal compass to make unshakable commitments. They never develop the inner consistency that they long for. Every day they come up short in obtaining the fulfillment they crave, and it frustrates them.
Calling changes everything. It's the missing piece in the puzzle. The plot in a good story. The musical note that completes the piece. Every day I experience the euphoric feeling of fulfillment as I write, speak, and lead. When I'm engaged in my calling, the sense that I experience is, "I was born for this!"
FINDING YOUR CALLING
So, what is your calling? Have you already discovered it? Or do you need some help finding your way? Fred Swaniker, the founder of the African Leadership Group, said, "Every now and then, we come to a fork in the road that requires us to either stay on our current life path, or change course and do something radically different." If you have not already found your calling, then you are at the fork in the road. I hope you will take the bold way, the radically different path that represents your calling. It may be frightening. It may be uncomfortable. It may feel uncertain. But I can assure you, if you find your calling, you will never regret the difficult journey taken to pursue it, because there's nothing else like it.
When I was in a class in college, a professor asked three questions to help us understand ourselves and find the pathway for our lives. Since I first heard them, I have asked them of myself repeatedly. Those three questions are:
1. What do I sing about? What fills my heart?
2. What do I cry about? What breaks my heart?
3. What do I dream about? What lifts my heart?
These questions set me on the journey that enabled me to discover my calling. As time went by, I experienced moments that spoke to me at a deep level of purpose:
• **S INGING MOMENTS—**Times when I knew that my leadership was making a positive difference for people.
• **C RYING MOMENTS—**Times when I wept because I saw that bad leadership misused or abused people.
• **D REAMING MOMENTS—**Times when I dreamed of training leaders who would make a significant impact on people.
You'll notice that all these moments related to leadership because that's where my calling is. So I ask you: Where do you experience singing, crying, and dreaming moments in your life?
As you think about these questions, you may be wondering, _How do I know the difference between_ calling _and_ ego? That's a fair question. Shelley Prevost, cofounder and CEO of Torch, wrote about this in _Inc_. Here are the main differences she pointed out between the two:
**EGO** | **CALLING**
---|---
Fears Not Possessing Something | Fears Not Expressing Something
Focuses on Doing | Focuses on Being
Needs Anxiety to Survive | Needs Silence to Survive
Manifests as Burnout | Manifests as Fulfillment
Focuses on the Result | Focuses on the Process
Wants to Preserve Self | Wants to Impact Others
Prevost went on to say that calling is discovered through observation and reflection, through self-discovery and the unfolding of your life. Another way to say it is that ego _drives_ you. Calling _draws_ you.
* * *
EGO _DRIVES_ YOU. CALLING _DRAWS_ YOU.
* * *
You may find your calling in a moment as I did, but I don't think you can force it to appear immediately if you haven't already discovered it. It usually takes time to unfold. I can look back at years of leadership moments, good and bad experiences, feelings of both discontent and contentment that set me up for my calling and prepared me for it. My best advice is to be attentive. Pay attention to your feelings. Take time to reflect. Learn from your experiences. Never dismiss your dreams. And when your moment comes, embrace it.
HOW TO MAXIMIZE YOUR CALLING
I don't know what phase of life you're in as you read this book. Maybe you're simply doing a job and hoping for more. Perhaps you've developed a career yet still long for something more. If either of these is true, keep working your way toward your calling. However, you might be in the season of life where you know your calling and you're working out what to do with it. If that describes you, then I want to give you some advice. And if this does not yet describe you, then mark these words for when you do enter your calling season:
**1. I NTEGRATE A DAILY FOCUS WITH A LONG-TERM PERSPECTIVE**
In his book _The Life Cycle Completed_ , Erik Erikson told a joke about a man who is on his deathbed. As he lay there with his eyes closed, his wife whispered to him, naming every member of the family who was there to wish him shalom. "And who," he suddenly asked, sitting up abruptly, "who is minding the store?"
People who have a sense of calling need to maintain a daily focus without losing their long-term perspective. I think of this as using both the clock and the compass. The clock helps me to stay on track with what I'm doing today. It encourages me to invest in my daily activities and to keep appointments. It allows me to fulfill the mission of the moment.
The compass helps me to stay on track with my destiny. It allows me to focus on the vision. It helps me know where I'm going. I maintain my overall values. I keep the vision before me. It allows me to fulfill the mission of my calling.
* * *
EXPECT TO WRITE YOUR STORY IN PENCIL—ONE THAT HAS AN ERASER!
* * *
In terms of my faith, the clock helps me to remember that I have a contribution to make. The Bible verse that speaks to me on this is 1 Corinthians 12:7, which says, "Each person is given something to do that shows who God is. Everyone gets in on it, everyone benefits." The compass reminds me that I have a destiny to fulfill. The verse that speaks to me on this is Psalm 139:16, which says, "Like an open book, you watched me grow from conception to birth; all the stages of my life were spread out before you, The days of my life all prepared before I'd even lived one day." And in terms of my calling, I have a legacy to leave that relates to leadership. The verse that speaks to this is 2 Timothy 2:2: "Pass on what you heard from me . . . to reliable leaders who are competent to teach others." As I've already mentioned, you don't need to be a person of faith to follow a calling. But if you are, I encourage you to examine Scripture to receive wisdom, deepen your understanding, and increase your commitment.
**2. S ET A CLEAR PATH IN A WORTHWHILE DIRECTION**
When you die, if people were to describe your life in a single sentence, what would you want it to be? The direction of your life and the journey you fulfill will write that sentence. You cannot choose where your life will end up. But you can determine the direction you take today.
One of the paradoxes of life is that you must follow your calling with clarity and purpose while living with uncertainty. So go forward in a direction that is worthy of the expenditure of your life, and go with confidence, but expect to write your story in pencil—one that has an eraser! I say that because as you pursue your calling, your life will be written and rewritten. Some experiences will end in a period—a full stop. Others will need the pause of a comma. You will have exclamation mark moments of victory and contentment. And of course, there will be many question marks.
People have asked me what I want on my tombstone. "He finally ran out of breath," I sometimes joke. But sincerely, my desire is that my one sentence would say, "He still lives on in this world." My hope is that what I taught leaders will be woven into their lives and continue to help others after I'm dead and gone. The goal in life is not to live on forever but to create something that does.
Where will you end up if you follow your calling? Only time will tell. But the journey will be worth it, and the story will be amazing.
**3. A SK OTHERS TO JOIN WITH YOU AND YOUR CALLING**
Because every person's true calling is bigger than the one who has been called, it always requires the aid of others to fulfill it. If you've found your calling and not yet asked others to join you in it, you have neglected a crucial step, and it's time to start enlisting help. People who are successful often leave an inheritance for others. People who fulfill a calling leave a legacy _in_ others.
In their book _Strengths Based Leadership_ , authors Tom Rath and Barry Conchie wrote about the impact that leaders have when they recruit people to their calling and empower them to their cause. They said:
Perhaps this is why the most extraordinary leaders do not see personal success as an end in itself. They realize that their impact on this world rests in the hands of those who follow. Martin Luther King, Jr. preached on the evening of April 3, 1968, "I may not get there with you. But I want you to know tonight that we, as a people, will get to the Promised Land." The next day, Dr. King was assassinated. Yet his influence on the world had just begun.
The day after his death, millions already stood on King's shoulders. By the turn of the 20th century, that number had increased to hundreds of millions. At the end of this century, whether they realize it or not, billions will lead better lives due to Dr. King's efforts during his all-too-brief 39 years.
You and I may not be able to make the kind of impact that Martin Luther King Jr. did, but that shouldn't stop us from giving ourselves fully to our calling and asking others to join us. Our calling is the gift we give the world while we are still alive. Our legacy is our gift to the world after we die.
I hope you will do whatever you can to search for your calling, and then work with everything you have to fulfill it. And I hope that you will embrace not only this leadershift but all the other ones I've discussed in this book. Remember, every advance you make as a leader will require a leadershift that changes the way you think, act, and lead. You can only reach your potential if you embrace these leadershifts:
• Soloist to Conductor—The Focus Shift
• Goals to Growth—The Personal Development Shift
• Perks to Price—The Cost Shift
• Pleasing People to Challenging People—The Relational Shift
• Maintaining to Creating—The Abundance Shift
• Ladder Climbing to Ladder Building—The Reproduction Shift
• Directing to Connecting—The Communication Shift
• Team Uniformity to Team Diversity—The Improvement Shift
• Positional Authority to Moral Authority—The Influence Shift
• Trained Leaders to Transformational Leaders—The Impact Shift
• Career to Calling—The Passion Shift
Are there other leadershifts that you'll have an opportunity to make? Probably. I haven't yet discovered them, but if they're out there, I intend to. Why? Because long ago I made the personal development shift from goals to growth, and I'm still growing as a leader. If you're growing, you will discover them too. When you do, let me and others know about them. The better we can lead and help others to lead, the greater and more fulfilling our impact will be.
ABOUT THE AUTHOR
John C. Maxwell is a #1 _New York Times_ bestselling author, coach, and speaker who has sold more than 30 million books in fifty languages. He has been identified as the #1 leader in business by the American Management Association and the most influential leadership expert in the world by _Business Insider_ and _Inc._ magazines. He is the founder of the John Maxwell Company, the John Maxwell Team, EQUIP, and the John Maxwell Leadership Foundation, organizations that have trained millions of leaders. The recipient of the Mother Teresa Prize for Global Peace and Leadership from the Luminary Leadership Network, Dr. Maxwell speaks each year to _Fortune_ 500 companies, presidents of nations, and many of the world's top business leaders. He can be followed at Twitter.com/JohnCMaxwell. For more information about him visit JohnMaxwell.com.
NOTES
**C HAPTER 1: WHY EVERY LEADER NEEDS TO LEADERSHIFT**
. Eric J. McNulty, "Thinking Like a Leader: Three Big Shifts," Strategy and Business, July 28, 2015, https://www.strategy-business.com/blog/Thinking-Like-a-Leader-Three-Big-Shifts.
. Katie Hiler, "Cheetahs' Secret Weapon: A Tight Turning Radius," _New York Times_ , June 12, 2013, http://www.nytimes.com/2013/06/13/science/agility-not-speed-is-cheetahs-meal-ticket-study-says.html.
. Bruna Martinuzzi, "The Agile Leader: Adaptability," Mindtools, accessed October 6, 2017, https://www.mindtools.com/pages/article/newLDR_49.htm.
. _The Flux Report: Building a Resilient Workforce in the Face of Flux_ (London: Right Management, 2014), 6, https://www.rightmanagement.co.uk/wps/wcm/connect/350a18c6–6b19–470d-adba-88c9e0394d0b/Right+Management+Flux+Report+Spread.pdf?MOD=AJPERES.
. Dave Martin, _The 12 Traits of the Greats: The Twelve Undeniable Qualities of Uncommon Achievers, and How You Can Master Them in Your Life . . . Right Now!_ (Tulsa, OK: Harrison House, 2011), Kindle location 2707.
. Paul Karofsky, quoted in Eric Yaverbaum, _Leadership Secrets of the World's Most Successful CEOs: 100 Top Executives Reveal the Management Strategies That Made Their Companies Great_ (Chicago: Dearborn Trade, 2004), 161.
. Maria Popova, "Malcolm Gladwell on Criticism, Tolerance, and Changing Your Mind," Brain Pickings, June 24, 2014, https://www.brainpickings.org/2014/06/24/malcolm-gladwell-nypl-interview/ (emphasis original).
. Phillips Brooks, _Addresses by the Right Reverend Phillips Brooks_ (1893, Los Angeles: Hard Press, 2006), 25.
. C. Vijayakumar, "3 Key Steps to Making Sure Your Skills Stay Relevant," World Economic Forum, May 24, 2017, https://www.weforum.org/agenda/2017/05/3-key-steps-to-making-sure-your-skills-stay-relevant/.
. Brad Lomenick, _The Catalyst Leader: 8 Essentials for Becoming a Change Maker_ (Nashville: Thomas Nelson, 2013), 111–12.
**C HAPTER 2: SOLOIST TO CONDUCTOR**
. Laurence Vittes, "4 Soloists Talk About Stepping Up to the Conductor's Podium," _Strings_ , March 11, 2016, http://stringsmagazine.com/4-soloists-talk-about-stepping-up-to-the-conductors-podium/.
. Vittes, "4 Soloists."
. Matthew 25:40.
. Matthew Kelly, _The Four Signs of a Dynamic Catholic: How Engaging 1% of Catholics Could Change the World_ (Hebron, KY: Beacon Publishing, 2012), Kindle location 2382 of 2488.
**C HAPTER 3: GOALS TO GROWTH**
. Andy Stanley, "Better Before Bigger," Andy Stanley Leadership Podcast, May 3, 2013, MP3 audio, https://store.northpoint.org/better-before-bigger.html.
. Adlai E. Stevenson, "The Educated Citizen," speech at Princeton University, March 22, 1954, transcript accessed January 10, 2018, http://infoshare1. princeton.edu/libraries/firestone/rbsc/mudd/online_ex/stevenson/adlai1954. html.
. C. S. Lewis, _Of Other Worlds: Essays and Stories_ (1966, New York: Houghton Mifflin Harcourt, 2002), 26.
**C HAPTER 4: PERKS TO PRICE**
. Jim Collins, _Good to Great: Why Some Companies Make the Leap . . . and Others Don't_ (New York: Harper Business, 2001), 85.
. Collins, _Good to Great_ , 86.
. Bob Burg, _Endless Referrals: Network Your Everyday Contacts into Sales_ , 3rd ed. (New York: McGraw-Hill, 2005), 190.
. Andris A. Zoltners, "Sales Management in Practice: Sales Humor," Kellogg School of Management, accessed December 7, 2017, http://www.kellogg.northwestern.edu/faculty/zoltners/htm/oneliners.html.
. Original source unknown.
. Douglas L. Wilson and Rodney O. Davis, eds., _Herndon's Informants: Letters, Interviews, and Statements About Abraham Lincoln_ (Champaign, IL: University of Illinois Press, 1998), 164.
. Bill Bradley, _Time Present, Time Past: A Memoir_ (New York: Vintage, 1997), 362.
. "Cal Ripken's 2,131st Consecutive Game Is Major League Baseball's Most Memorable Moment," mlb.com, accessed December 11, 2017, http://www.mlb.com/mlb/events/memorable_moments/mlb_memorable_moments.jsp.
. Ralph Wiley, "Second to One the Pressure Was Building When Ripken Took His Place Behind Gehrig, as This 1990 SI Story Attests," _Sports Illustrated_ , September 15, 1995, archived in the _Sports Illustrated_ Vault, https://www.si.com/vault/1995/09/15/207898/second-to-one-the-pressure-was-building-when-ripken-took-his-place-behind-gehrig-as-this-1990-si-story-attests.
. Bucky Fox, "Cal Ripken Wields an Iron Will While Winning in Baseball," _Investor's Business Daily_ , August 26, 2017, https://www.investors.com/news/management/leaders-and-success/cal-ripken-wields-an-iron-will-while-winning-in-baseball/.
**C HAPTER 5: PLEASING PEOPLE TO CHALLENGING PEOPLE**
. Seth Godin, _Poke the Box_ (New York: Penguin, 2015), 25.
. For more information, refer to John C. Maxwell, _The 5 Levels of Leadership_ (New York: Center Street, 2011).
**C HAPTER 6: MAINTAINING TO CREATING**
. Roger von Oech, _A Whack on the Side of the Head: How You Can Be More Creative_ , 3rd ed. (New York: Warner Books, 1998).
. Jeff Nilsson, "Albert Einstein: 'Imagination Is More Important Than Knowledge,'" _Saturday Evening Post_ , March 20, 2010, http://www.saturdayeveningpost.com/2010/03/20/history/post-perspective/imagination-important-knowledge.html.
. M. A. Rosanoff, "Edison in His Laboratory," _Harper's Magazine_ 135 (September 1932), 403 col. 2.
. Hugh MacLeod, _Ignore Everybody: And 39 Other Keys to Creativity_ (New York: Portfolio, 2009), 26.
. As summarized in Martin Zwilling, "Follow Seven Rules for a Creative Startup Culture," _Forbes_ , April 10, 2011, https://www.forbes.com/sites/martinzwilling/2011/04/10/follow-seven-rules-for-a-creative-startup-culture/.
. Robert D. Kaplan, "Man Versus Afghanistan," _The Atlantic_ , April 2010, https://www.theatlantic.com/magazine/archive/2010/04/man-versus-afghanistan/307983/.
. Mary Ardito, "Creativity: It's the Thought That Counts," _Bell Telephone Magazine_ , 61 (1): 33, https://quoteinvestigator.com/2014/03/03/creative-maya/.
. Steve Pavlina, "Do It Now," StevePavlina.com (blog), November 28, 2005, https://www.stevepavlina.com/blog/2005/11/do-it-now/.
. Quoted in Max Cates, _Seven Steps to Success for Sales Managers: A Strategic Guide to Creating a Winning Sales Team Through Collaboration_ , 1st ed. (Indianapolis: Pearson FT Press, 2015), 26.
. Jerry Hirshberg, _The Creative Priority: Driving Innovative Business in the Real World_ (New York: HarperCollins, 1999), 16.
. "The American Giant Way," American Giant, accessed January 18, 2018, https://www.american-giant.com/ag-ethos.html.
**C HAPTER 7: LADDER CLIMBING TO LADDER BUILDING**
. Lead Through Strengths, "Explore the Clifton Strengthfinder Talent Theme—Woo," Strengthsfinder, accessed May 16, 2018, http://leadthrough strengths.com/woo/.
. Napoleon Hill, _The Law of Success_ (New York: Penguin, 2008), 420.
. Tim Elmore, "Becoming a Life Giving Mentor," October 19, 2012, _Growing Leaders: Ready for Real Life_ , https://growingleaders.com/blog/life-giving-mentor/.
**C HAPTER 8: DIRECTING TO CONNECTING**
. Original source unknown. Used with the author's permission.
. Bob Buford, _Halftime: Moving From Success to Significance_ (Grand Rapids: Zondervan, 2008), 118.
. Stephen King, commencement address, Poughkeepsie, NY, Vassar College, May 20, 2001. Transcribed from "Vassar College Commencement," video, C-SPAN, May 20, 2001, https://www.c-span.org/video/?164360–1/vassar-college-commencement.
. Greg Asimakoupoulos, "Icons Every Pastor Needs," _Christianity Today_ , Winter 1993, http://www.christianitytoday.com/pastors/1993/winter/93l4108.html.
. Mark Moring, "Chronicling Caspian," Christianity.com, May 1, 2008, https://www.christianity.com/11622775/.
. Charles M. Schwab, "Mr. Carnegie Understood This Great Thing," _System_ (June 1922), 679, accessed May 17, 2018, https://books.google.com/books?id=rQRKAQAAMAAJ&dq=System%20Charles%20Schwab%20exalted&pg=PA679.
**C HAPTER 9: TEAM UNIFORMITY TO TEAM DIVERSITY**
. Jon R. Katzenbach and Douglas K. Smith, "The Discipline of Teams," _Harvard Business Review_ , March–April 1993, https://hbr.org/1993/03/the-discipline-of-teams-2.
. Submitted by "Grapevine" from Duncan, Oklahoma, to the column "Twice Told Tales," _The Rotarian_ , April 1956, 64.
. Patrick Lencioni, _The Five Dysfunctions of a Team: A Leadership Fable_ (San Francisco: Josey-Bass, 2002), 202.
. Lencioni, _Five Dysfunctions of a Team_ , 202–3.
. Amber Ferguson, "'Come Meet a Black Person,' Says the Invitation to a Georgia Networking Event," _Washington Post_ , November 15, 2017, https://www.washingtonpost.com/news/morning-mix/wp/2017/11/15/come-meet-a-black-person-says-the-invitation-to-a-georgia-networking-event/.
. Amanda C. Coyne, "Guests Hope to Bridge Gaps at 'Come Meet a Black Person' Mixer," _Atlanta Journal–Constitution_ , updated November 19, 2017, http://www.ajc.com/news/local/guests-hope-bridge-gaps-come-meet-black-person-mixer/MQoZHq3IJb4CXguWHdUGBP/.
. Saxon White Kessinger, "Indispensable Man," AppleSeeds, accessed May 9, 2018, http://www.appleseeds.org/indispen-man_saxon.htm.
. Christie Smith and Stephanie Turner, _The Radical Transformation of Diversity and Inclusion: The Millennial Influence_ (Westlake, TX: Deloitte University, 2015), 7, https://www2.deloitte.com/content/dam/Deloitte/us/Documents/about-deloitte/us-inclus-millennial-influence-120215.pdf.
. Smith and Turner, _Radical Transformation_ , 5.
. Smith and Turner, 11.
. Smith and Turner, 3.
. Smith and Turner, 13.
. Smith and Turner, 13.
. Smith and Turner, 15.
. Tomas Chamorro-Premuzic, "Does Diversity Actually Increase Creativity?" _Harvard Business Review_ , June 28, 2017, https://hbr.org/2017/06/does-diversity-actually-increase-creativity.
. Stefanie K. Johnson, "What 11 CEOs Have Learned About Championing Diversity," _Harvard Business Review_ , updated August 29, 2017, https://hbr.org/2017/08/what-11-ceos-have-learned-about-championing-diversity.
. Chamorro-Premuzic, "Does Diversity Actually Increase Creativity?"
**C HAPTER 10: POSITIONAL AUTHORITY TO MORAL AUTHORITY**
. Theodore Brown, "What Is Moral Authority?" Big Think, accessed January 31, 2018, http://bigthink.com/articles/what-is-moral-authority.
. Kevin Sharer, "How Moral Authority Manifests in Truly Impactful Leaders," _The Harbus_ , March 17, 2017, http://www.beatthegmat.com/mba/2017/03/17/moral-authority-in-truly-impactful-leader.
. Chuck Olson, "4 Ways to Build Moral Authority," Lead with Your Life (website), January 5, 2016, https://leadwithyourlife.com/4-ways-to-build-moral-authority/.
. George Lewis Davis, _Magic Shortcuts to Executive Success: 37 Ways and Timely Moves That Can Smooth the Path and Lead to More Rapid Promotion and More Important Jobs_ (Upper Saddle River, NJ: Prentice Hall, 1962), 110.
. Oscar Hammerstein II, _Lyrics_ (Milwaukee: Hal Leonard Books, 1985), 45–46.
. Doug Hall with David Wecker, _Making the Courage Connection: How People Get from Fear to Freedom—and How You Can Too_ (New York: Fireside, 1997), 47.
. John F. Kennedy, _Profiles in Courage_ (New York: Harper Perennial, 2003), 129.
. Kennedy, _Profiles in Courage_ , 115.
. Kennedy, 131.
. Kennedy, 130.
. Andy Stanley, _Visioneering: God's Blueprint for Developing and Maintaining Vision_ (Colorado Springs: Multnomah, 1999), 179.
. Jim Collins, _Good to Great_ (New York: Harper Business, 2001), 27 (emphasis original).
**C HAPTER 11: TRAINED LEADERS TO TRANSFORMATIONAL LEADERS**
. Lawrence Tribble, "Awaken" (c. 1780), Push Back Now (website), October 31, 2011, http://pushbacknow.net/2011/10/31/awaken-a-1700s-poem-by-lawrence-tribble/comment-page-1/.
. Quoted in Pat Williams with Jim Denney, _The Pursuit: Wisdom for the Adventure of Your Life_ (Ventura, CA: Regal, 2008), 196.
**C HAPTER 12: CAREER TO CALLING**
. Amy Wrzesniewski et al., "Jobs, Careers, and Callings: People's Relations to Their Work," _Journal of Research in Personality_ 31 (1997): 21–33, http://faculty.som.yale.edu/amywrzesniewski/documents/Jobscareersandcallings.pdf.
. Richard Leider, "Is Leading Your Calling?" _Leader to Leader_ , Winter 2004, http://www.geneva.edu/graduate/assets/msol_writing_sample_article.pdf, 2.
. Matthew 5:13–14.
. "Mother Teresa of Calcutta (1910–1997)," The Holy See (website), accessed February 15, 2018, http://www.vatican.va/news_services/liturgy/saints/ns_lit_doc_20031019_madre-teresa_en.html.
. Sheri Riley, _Exponential Living: Stop Spending 100% of Your Time on 10% of Who You Are_ (New York: New American Library, 2017), 191.
. Shelley Prevost, "5 Ways to Distinguish Your Calling from Your Ego," _Inc._ , December 12, 2013, https://www.inc.com/shelley-prevost/5-ways-to-distinguish-your-calling-from-your-ego.html.
. Quoted in Emily Esfahani Smith, "Psychology Shows It's a Big Mistake to Base Our Self-Worth on Our Professional Achievements," Quartz, May 24, 2017, https://qz.com/990163/psychology-shows-its-a-big-mistake-to-base-our-self-worth-on-our-professional-achievements/.
. Tom Rath and Barry Conchie, _Strengths Based Leadership: Great Leaders, Teams, and Why People Follow_ (New York: Gallup Press, 2008), 94.
CONTENTS
1. Contents
2. Acknowledgments
3. Chapter 1: Why Every Leader Needs to Leadershift
4. Chapter 2: Soloist to Conductor
5. Chapter 3: Goals to Growth
6. Chapter 4: Perks to Price
7. Chapter 5: Pleasing People to Challenging People
8. Chapter 6: Maintaining to Creating
9. Chapter 7: Ladder Climbing to Ladder Building
10. Chapter 8: Directing to Connecting
11. Chapter 9: Team Uniformity to Team Diversity
12. Chapter 10: Positional Authority to Moral Authority
13. Chapter 11: Trained Leaders to Transformational Leaders
14. Chapter 12: Career to Calling
15. About the Author
16. Notes
# Guide
1. Cover
2. Contents
3. CHAPTER 1: WHY EVERY LEADER NEEDS TO LEADERSHIFT
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|
{
"redpajama_set_name": "RedPajamaBook"
}
| 416
|
Q: Tensorflow libcublas 10.0 Issue Hi I've been using Adrian's guide from https://www.pyimagesearch.com/2020/03/25/how-to-configure-your-nvidia-jetson-nano-for-computer-vision-and-deep-learning/
I'm attempting to run Tensorflow 1.13.1 on a Jetson Nano. When I go to initiate python and import tensorflow I get the following error:
Python 3.6.9 (default, Apr 18 2020, 01:56:04)
[GCC 8.4.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
import tensorflow
Traceback (most recent call last):
File "/home/zachwad/.virtualenvs/py3cv4/lib/python3.6/site-packages/tensorflow/python/pywrap_tensorflow.py", line 58, in
from tensorflow.python.pywrap_tensorflow_internal import *
File "/home/zachwad/.virtualenvs/py3cv4/lib/python3.6/site-packages/tensorflow/python/pywrap_tensorflow_internal.py", line 28, in
_pywrap_tensorflow_internal = swig_import_helper()
File "/home/zachwad/.virtualenvs/py3cv4/lib/python3.6/site-packages/tensorflow/python/pywrap_tensorflow_internal.py", line 24, in swig_import_helper
_mod = imp.load_module('_pywrap_tensorflow_internal', fp, pathname, description)
File "/usr/lib/python3.6/imp.py", line 243, in load_module
return load_dynamic(name, filename, file)
File "/usr/lib/python3.6/imp.py", line 343, in load_dynamic
return _load(spec)
ImportError: libcublas.so.10.0: cannot open shared object file: No such file or directory
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
File "", line 1, in
File "/home/zachwad/.virtualenvs/py3cv4/lib/python3.6/site-packages/tensorflow/init.py", line 24, in
from tensorflow.python import pywrap_tensorflow # pylint: disable=unused-import
File "/home/zachwad/.virtualenvs/py3cv4/lib/python3.6/site-packages/tensorflow/python/init.py", line 49, in
from tensorflow.python import pywrap_tensorflow
File "/home/zachwad/.virtualenvs/py3cv4/lib/python3.6/site-packages/tensorflow/python/pywrap_tensorflow.py", line 74, in
raise ImportError(msg)
ImportError: Traceback (most recent call last):
File "/home/zachwad/.virtualenvs/py3cv4/lib/python3.6/site-packages/tensorflow/python/pywrap_tensorflow.py", line 58, in
from tensorflow.python.pywrap_tensorflow_internal import *
File "/home/zachwad/.virtualenvs/py3cv4/lib/python3.6/site-packages/tensorflow/python/pywrap_tensorflow_internal.py", line 28, in
_pywrap_tensorflow_internal = swig_import_helper()
File "/home/zachwad/.virtualenvs/py3cv4/lib/python3.6/site-packages/tensorflow/python/pywrap_tensorflow_internal.py", line 24, in swig_import_helper
_mod = imp.load_module('_pywrap_tensorflow_internal', fp, pathname, description)
File "/usr/lib/python3.6/imp.py", line 243, in load_module
return load_dynamic(name, filename, file)
File "/usr/lib/python3.6/imp.py", line 343, in load_dynamic
return _load(spec)
ImportError: libcublas.so.10.0: cannot open shared object file: No such file or directory
A: Seems related to the following problem.
Make sure that a compatible cuda version (in this case cuda 10) is installed on your system and that the linker can find the library: libcublas.so.10.0
Tensorflow often uses older cuda versions.
Keep also in mind that tensorflow released version 2.0, which is very different from version 1.13.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 5,990
|
// Copyright 2016, Santosh Kalidindi, All rights reserved.
import irc from 'irc';
import MessageHandler from '../services/message-handler';
const twitchIrcEndpoint = 'irc.twitch.tv';
const twitchIrcPort = 6667;
class SkalBot {
/**
* For reference:
* https://github.com/justintv/Twitch-API/blob/master/IRC.md
*/
constructor(oAuthToken, channel, botname) {
const handler = new MessageHandler();
const client = new irc.Client(twitchIrcEndpoint, botname, {
channels: [`#${channel}`],
port: twitchIrcPort,
showErrors: true,
debug: true,
autoConnect: false,
});
client.addListener('message', (from, to, message) => {
console.log(`${from} says from channel ${to} => ${message}`);
handler.parseMessage(client, channel, message, from);
});
client.addListener(`join#${channel}`, (user) => {
console.log(`${user} has joined channel!`);
});
client.addListener('error', (message) => {
console.log('error: ', message);
});
this.client = client;
this.oAuthToken = oAuthToken;
}
connect() {
this.client.connect();
this.client.send('PASS', `oauth:${this.oAuthToken}`);
this.client.send('CAP', 'REQ', ':twitch.tv/membership');
}
}
export default SkalBot;
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,021
|
This easy-to-use software is designed to you give full control of BitStream Pro. You can configure it, send previously downloaded libraries, edit and create your own libraries.
This Windows software allows to configure BitStream Pro MIDI Controller.
Each Potentiometer, Slider, and Switch can be configured via this software. This means any user defined MIDI string (up to 24 bytes) can be assigned to each control. Also, the user can assign an Alpha-Numeric String to each control, that will be displayed on the LCD, when tweaking the corresponding control.
This Software is easy to use, anyway, if troubles are encountered, contact Wave Idea Support.
This Software requires a PC or a Mac, with a Sound card featuring MIDI Input/Output, Windows 95 or later, and the BitStream MIDI controller connected to the PC (MIDI In & Out).
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 1,408
|
Оліас-дель-Рей () — муніципалітет в Іспанії, у складі автономної спільноти Кастилія-Ла-Манча, у провінції Толедо. Населення — осіб (2010).
Муніципалітет розташований на відстані близько 60 км на південний захід від Мадрида, 10 км на північ від Толедо.
На території муніципалітету розташовані такі населені пункти: (дані про населення за 2010 рік)
Оліас-дель-Рей: 4037 осіб
Ель-Беато: 1367 осіб
Каміно-Баргас-а-Масаррасін: 243 особи
Каньяда-де-Маган: 143 особи
Сан-Франсіско-Каверо: 1077 осіб
Демографія
Галерея зображень
Посилання
Провінційна рада Толедо
Оліас-дель-Рей
Примітки
Муніципалітети провінції Толедо
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 8,482
|
\section{Introduction}
Supervised learning, in its deterministic formulation, involves learning a mapping $f:\mathcal{X} \rightarrow \mathcal{Y}$ given observed data $\mathcal{D}_N=\{x_i, y_i\}_{i=1}^N=\{\boldsymbol{X}_D, \boldsymbol{y}_D\}$. In a Deep Learning context, $f$ is parametrized by a neural network whose architecture expresses convenient inductive biases for the task of interest and whose training consists on optimizing a loss function with respect to its parameters by using stochastic optimization techniques. Despite its widespread empirical success, Deep Learning approaches are hardly ever transparent, so that in certain domains, such as medical diagnosis or self-driving vehicles, it becomes unclear how to map predictions on unseen inputs to a non-catastrophic decision. Thus much research has been focused on obtaining uncertainties from deep models for common computer vision tasks such as semantic segmentation \cite{kampffmeyer2016semantic,huang2018efficient,mukhoti2018evaluating}, depth estimation \cite{kendall2017uncertainties,laidlowtowards}, visual odometry \cite{Bhattacharyya_2018_CVPR,wang2018end,clark2017vinet,clark2017vidloc}, SLAM \cite{czarnowski2020deepfactors} and active learning \cite{gal2017deep}.
The most reliable approach is to consider a Bayesian probabilistic formulation of deep supervised learning, also known as Bayesian Deep Learning \cite{mackay1992practical,neal1996}, so that all forms of predictive uncertainty may be quantified. There are two types of uncertainty one may encounter: $\textit{epistemic}$ and $\textit{aleatoric}$ \cite{kendall2017uncertainties}, both which are naturally accounted for in a Bayesian framework. Epistemic uncertainty is associated with a model's inability of finding a meaningful mapping from inputs to outputs and will eventually vanish as it is trained on a large and diverse dataset. Epistemic uncertainty becomes particularly relevant when the trained model has to make predictions on input examples which, in some sense, differ significantly from training data: out-of-distribution (OOD) inputs \cite{hafner2018ncp}. Aleatoric uncertainty is associated to noise contained in the observed data and cannot be reduced as more data is observed, nor does it increase on OOD inputs, so that it is not able to detect these by itself. Modelling the combination of epistemic and aleatoric uncertainties is therefore key in order to build deep learning based systems which are transparent about their predictive capabilities.
\subsection{General background}
Denoting all parameters of a neural network as $W$, Bayesian Deep Learning starts with positing a prior distribution $\pi(W)$, typically multivariate normal, and a likelihood $p(y|T(x;W))$, where $T(.;W)$ is a neural network with weights $W$. The solution to this bayesian inference problem is the posterior over weights $p(W|\mathcal{D}_N)$, which is unknown due to the intractable computation of marginal likelihood $p(\mathcal{D}_N)$. Stochastic variational inference (SVI) \cite{graves2011practical,hoffman2013stochastic} allows one to perform scalable approximate posterior inference, hence being the dominant paradigm in Bayesian Deep Learning. Denoting $q(W)$ as the variational distribution and $\mathcal{D}_B$ as a mini-batch of size $B$, the following training objective is considered:
\begin{multline}
\frac{N}{B} \sum_{i=1}^B \mathbb{E}_{q(W)}\left [ \log p(y_i|T(x_i;W))\right]
- \mathrm{KL}\left(q(W)||\pi(W)\right)
\label{elbo_weight_vi}
\end{multline}
This quantity is denoted as evidence lower bound (ELBO), given that it is bounded above by $\log p(\mathcal{D}_N)$. By choosing a convenient family of distributions for $q(W)$ and suitably parametrizing it with neural network mappings, approximate bayesian inference amounts to maximizing the ELBO with respect to its parameters over multiple mini-batches $\mathcal{D}_B$. The success of variational inference (VI) depends on the expressive capability of $q(W)$, which ideally should be enough to approximate $p(W|\mathcal{D}_N)$. Even though considerable work has been done in designing various variational families for BNN posterior inference \cite{blundell2015weight,louizos2016structured,louizos2017multiplicative,shi2018kernel}, these are not easily applicable in computer vision tasks which require large network architectures.
Alternatively, a nonparametric formulation of probabilistic supervised learning is obtained by introducing a stochastic process over a chosen function space. An $\mathcal{F}$ valued stochastic process with index set $\mathcal{X}$ is a collection of random variables $\{f(x)\}_{x \in \mathcal{X}}$ whose distribution is fully determined by its finite $n$-dimensional marginal distributions $p(f^{\boldsymbol{X}})$, for any $\boldsymbol{X} = (x_1, ..., x_n) \in \mathcal{X}^n$, $n \in \mathbb{N}$, and where $f^{\boldsymbol{X}} = (f(x_1), ..., f(x_n))$. An important class are Gaussian Processes (GPs) \cite{rasmussen2003gaussian}, which are defined by a mean function $m(.)$ and covariance kernel $k(.,.)$, and all its finite dimensional marginal distributions are multivariate gaussians: $p(f^{\boldsymbol{X}}) = \mathcal{N}(m(\boldsymbol{X}), k(\boldsymbol{X}, \boldsymbol{X}))$, where $m(\boldsymbol{X})$ is a mean vector and $k(\boldsymbol{X}, \boldsymbol{X})$ a covariance matrix.
Bayesian Neural Networks (BNNs) may also be viewed as prior distributions over functions by means of a two-step generative process. Firstly one draws a prior sample $W \sim \pi(W)$, and then a single function is defined by setting $f(.) = T(.;W)$. BNNs are an example of implicit stochastic processes \cite{ma2019variational}, where for any finite set of inputs $\boldsymbol{X}$ its distribution may be written as follows:
\begin{equation}
p\left(f^{\boldsymbol{X}} \in A\right) = \int_{\{T(\boldsymbol{X};W)=f^{\boldsymbol{X}} \in A\}} \pi(W) dW
\end{equation}
Where $p(.)$ is a probability measure and $A$ is an arbitrary measurable set. Even though it is easy to sample from $p(.)$, it is not generally possible to exactly compute its value due to non-invertibility of $T(.;W)$. Note that in this formulation the dimensionality of the BNN prior does not depend on the dimensionality of weight space, meaning that posterior inference over a BNN with millions of weights only depends on the number of inputs $n$ and dimensionality of $\mathcal{F}$, which is significantly smaller. Moreover, while $p(W|\mathcal{D}_N)$ may have complex structure due to the fact that many different values of $W$ yield the same output values, this can largely be avoided if one performs VI directly in function space \cite{ma2019variational}.
\subsection{List of contributions}
Our contributions are the following:
\begin{enumerate}
\item Given any loss function of interest for regression tasks, we provide sufficient conditions for constructing well-defined likelihoods which are compatible with aleatoric uncertainty quantification, and provide a practically relevant example based on the reverse Huber loss \cite{lambert2016adaptive,laina2016deeper}.
\item Leveraging the functional VI framework from \cite{sun2018functional}, we propose a computationally scalable variant which uses a suitably parametrized GP as the variational family. Following \cite{aga2018cnngp}, we are able to associate certain Bayesian CNN priors with a closed-form covariance kernel, which we then use to define a GP prior. Assuming the prior is independent across its output dimensions, we propose an efficient method for obtaining its inverse covariance matrix and determinant, hence allowing functional VI to scale to high-dimensional supervised learning tasks. After training, this constitutes a practically useful means of obtaining predictive uncertainty (both epistemic and aleatoric) at the cost of a single forward pass through the network architecture, hence opening new directions for encompassing uncertainty quantification into real-time prediction tasks \cite{kendall2017uncertainties}.
\item We apply this approach in the context of semantic segmentation and depth estimation, where we show it displays well-calibrated uncertainty estimates and error metrics which are comparable with other approaches based on weight-space VI objectives.
\end{enumerate}
\section{Functional Variational Inference}
\subsection{Background}
Even though GPs offer a principled way of handling uncertainty in supervised learning, performing exact inference carries a cubic cost in the number of data points, thus preventing its applicability to large and high-dimensional datasets. Sparse variational methods \cite{titsias2009variational,hensman2013gaussian} overcome this issue by allowing one to compute variational posterior approximations using subsets of training data, but it is difficult to choose an appropriate set of inducing points in the context of image-based datasets \cite{shi2019scalable}.
Functional Variational Bayesian Neural Networks (FVBNNs) \cite{sun2018functional} use BNNs to approximate function posteriors at finite sets of inputs. This is made possible by defining a KL divergence on general stochastic processes (see \cite{sun2018functional} for the definition and proof). Building upon such divergence, and defining $\boldsymbol{X'} \in \mathcal{X}^{n'}$, where $n'$ is fixed, and setting $\boldsymbol{X} = \boldsymbol{X}_D \cup \boldsymbol{X'}$, it is possible to obtain a practically useful analogue of ELBO in function space:
\begin{equation}
\sum_{i=1}^N \mathbb{E}_{q(f(x_i))} \left[\log p(y_i|f(x_i)) \right] - \mathrm{KL}\left(q(f^{\boldsymbol{X}})||p(f^{\boldsymbol{X}})\right)
\label{elbo_fvbnn}
\end{equation}
We refer to this equation as the \textit{functional VI} objective, whose structure will be discussed and simplified during the next sections in order to yield a more computationally feasible version which does not use BNNs as the variational family nor does so explicitly for its prior.
This objective is valid since it is bounded above by $\log p(\mathcal{D}_N)$ for any choice of $\boldsymbol{X'}$ \cite{sun2018functional}. In practice $\mathcal{D}_N$ is replaced by an expectation over a mini-batch $\mathcal{D}_B$, so that the corresponding ELBO is only a lower-bound to $\log p(\mathcal{D}_B)$ and not $\log p(\mathcal{D}_N)$. During training $\boldsymbol{X'}$ may be sampled at random in order to cover the input domain, such as adding gaussian noise to the existing training inputs. Whenever $\boldsymbol{X'}$ are far from training inputs, $q(.)$ will be encouraged to fit the prior process, whereas the data-driven term will dominate on input locations closer to training data. In this way, the question of obtaining reliable predictive uncertainty estimates on OOD inputs gets reduced to choosing a meaningful prior distribution over functions. In this work we will be choosing $p(.)$ to be Bayesian CNNs, which constitute a diverse class of function priors on image space.
\subsection{Logit attenuation for classification in functional VI}
We now consider classification tasks under the functional VI objective (\ref{elbo_fvbnn}), where we assume that $\mathcal{Y} = \{0,1\}^K$, $K$ is the number of distinct classes and $\mathcal{F}=\mathbb{R}^K$. One of the limitations of this objective is that it is not a lower bound to the log-marginal likelihood of the training dataset. When the true function posterior is not in the same class as $q(.)$, there is no guarantee that this procedure will provide reasonable results \cite{shi2019scalable}. We have observed this when we have first tried it in our segmentation experiments, which has caused model training to converge very slowly.
In order to mitigate this issue, we consider the following discrete likelihood under the functional VI framework:
\begin{equation}
p(y_k|f(x)) = \frac{\mathrm{exp} \left(f_k^{'}(x)\right)}{\sum_{k=1}^K \mathrm{exp} \left(f_k^{'}(x)\right)}
\label{boltzmann_likelihood}
\end{equation}
Where $f_k^{'}(x) = f_k(x)/\sigma^2_k(x)$, so that $p(y_k|f(x))$ is a Boltzmann distribution with re-scaled logits, where scale parameter $\sigma^2_k(x)$ weighs its corresponding logit $f_k(x)$. When included into the functional VI objective (\ref{elbo_fvbnn}), this parametrization enables the model to become robust to erroneous class labels contained in the training data, while also avoiding over-regularization from the function prior which may lead to underfitting. This effect of logit attenuation naturally yields a change in aleatoric uncertainty, as measured in entropy. Moreover, we note that each $\sigma^2_k(x)$ is not easily interpretable in terms of inducing higher or smaller aleatoric uncertainty according to its respective magnitude, so that one has to rely on measuring the total predictive uncertainty in terms of the predictive entropy. Additionally, when encompassed into deterministic models or the weight-space ELBO in (\ref{elbo_weight_vi}), re-scaling logits brings no added flexibility.
\section{Functional VI with general regression loss functions}
It is often the case that best-performing non-probabilistic approaches in computer vision tasks not only have carefully crafted network architectures, but also task-specific loss functions which allow one to encode relevant inductive biases. The most standard examples are the correspondence between gaussian likelihood and $\mathcal{L}_2$ loss, and also between laplacian likelihood and $\mathcal{L}_1$. However, various loss functions of interest are not immediately recognized as being induced by a known probability distribution, so that it would be of practical relevance to start with positing a loss function and then derive its corresponding likelihood model. Given any additive loss function $\ell : \mathcal{Y} \times \mathcal{F} \rightarrow \mathbb{R}_{\geq 0}$, we define its associated likelihood as follows:
\begin{equation}
p(y|f(x)) = \frac{\mathrm{exp} \left(-\ell(y, f(x)) \right)}{Z}
\label{gibbs_likelihood}
\end{equation}
This is known as the Gibbs distribution with energy function $\ell$ and temperature parameter set to 1. $Z = \int_{\mathcal{Y}} \mathrm{exp} \left(-\ell(y, f(x)) \right) dy$ is its normalization constant, potentially depending on $f(x)$, which can either be computed analytically or using numerical integration. Any loss function $\ell(.,.)$ for which $Z$ is finite can be made into a likelihood model, hence being consistent with Bayesian reasoning. Moreover, any strictly positive probability density can be represented as in (\ref{gibbs_likelihood}) for some appropriate choice of $\ell$, which follows from the Hammersley-Clifford theorem \cite{besag1974spatial}. In the context of computer vision, typically involving large amounts of labelled and noise-corrupted data, aleatoric uncertainty tends to be the dominant component of predictive uncertainty \cite{kendall2017uncertainties}. This means that, for each task of interest, one needs to restrict from choosing arbitrary likelihoods to the ones which are compatible with modelling this type of uncertainty. In the following subsection we provide a means of doing so for the task of regression.
\subsection{Aleatoric uncertainty for regression}
Without loss of generality, we assume that $\mathcal{Y}=\mathcal{F}=\mathbb{R}$, so that $p(y|f(x))$ is a univariate conditional density. This covers most practical cases of interest, including per-pixel regression tasks such as depth estimation, and simplifies the notation considerably.
In regression tasks, we are typically interested in writing loss functions of the form $\ell(y, f(x)) = \ell\left(\frac{y - f(x)}{\sigma(x)}\right)$, where $f(x)$ and $\sigma(x)$ are location and scale parameters, respectively. Writing $\ell(y)$ as the standardized loss, we define the standard member of its family of Gibbs distributions as $p_0(y) = \frac{1}{Z_0} \mathrm{exp}(-\ell(y))$. Then $p(y|f(x))=\frac{1}{Z} \mathrm{exp}\left(-\ell \left(\frac{y - f(x)}{\sigma(x)}\right)\right)$, where $Z = \sigma(x) Z_0$, defines a valid location-scale family of likelihoods. Moreover, we require its first and second moments to be finite, so that we may compute or approximate means and variances of the predictive distribution. For instance, this excludes using the Cauchy distribution as a likelihood. Substituting into equation \ref{elbo_fvbnn} and ignoring additive constants, we obtain the following training objective:
\begin{multline}
-\sum_{i=1}^n \left( \mathbb{E}_{q(f(x_i))} \left[\ell\left(\frac{y_i - f(x_i)}{\sigma(x_i)}\right) \right] + \mathrm{log}\left(\sigma(x_i)\right) \right) \\ - \mathrm{KL}\left(q(f^{\boldsymbol{X}})||p(f^{\boldsymbol{X}})\right)
\label{elbo_fvbnn_regression_losses}
\end{multline}
Similarly to \cite{kendall2017uncertainties,kendall2017multi}, we interpret each $\sigma(x_i)$ as a loss attenuation factor which may be learned during training and $\mathrm{log}(\sigma(x_i))$ as its regularization component.
In order to display the practical utility of this loss-based construction, we consider the reverse Huber (berHu) loss from \cite{lambert2016adaptive}, which has previously been considered in \cite{laina2016deeper} for improving monocular depth estimation, and derive its probabilistic counterpart, which we denote as berHu likelihood (see supplementary material).
\section{Scaling Functional VI to high-dimensional tasks}
Various priors of interest in computer vision applications, including Bayesian CNNs, are implicitly defined by probability measures whose value is not directly computable. \cite{sun2018functional} have considered BNNs both as priors and variational family, where the ELBO gradients have been estimated using Stein Spectral Gradient Estimator \cite{shi2018spectral}. However, due to its reliance on estimating intractable quantities from samples, this approach is not viable for computer vision tasks such as depth estimation, semantic segmentation or object classification with large number of classes, all of which display high-dimensional structure in both its inputs and outputs. In order to overcome this issue, we propose to first associate implicit priors with a Reproducing Kernel Hilbert Space (RKHS) and then defining a multi-output GP prior.
We consider $\mathcal{X} \subseteq \mathbb{R}^d$, where $d = C H W$ pertains to input images having $C$ channels and $H \times W$ resolution, and $\mathcal{F} \subseteq \mathbb{R}^P$, where $P$ is the output dimension depending on the task. For example, $P=H W$ for monocular depth estimation and $P$ equal to the number of distinct classes for object classification. Without loss of generality, we define $p(f(.))$ as a zero-mean multi-output stochastic process on $\mathcal{L}^2(\mathcal{F})$ whose index set is $\mathcal{X}$. Given two images $x_i$ and $x_j$, $K(x_i,x_j):=\int f(x_i)^T f(x_j) dp(f(x_i), f(x_j))$ is the covariance function of the process, which is a $P \times P$ symmetric positive semi-definite matrix for each pair $(x_i,x_j)$. We then posit a GP prior $\hat{p}(f(.))$ with zero mean and covariance function $K(.,.)$, and write its pair-wise joint distribution $\hat{p}(f(x_i), f(x_j))$ as follows:
\begin{equation}
\begin{pmatrix}
f(x_i) \\
f(x_j)
\end{pmatrix}\sim \mathcal{N}\left(\begin{pmatrix}
0 \\
0
\end{pmatrix},\begin{pmatrix}
K(x_i, x_i) & K(x_i, x_j) \\
K(x_i, x_j) & K(x_j, x_j)
\end{pmatrix}\right).
\end{equation}
Writing the joint multivariate gaussian distribution for a batch of $B>2$ images is straightforward: it is $BP$ dimensional with zero mean vector, and its $BP \times BP$ covariance matrix contains $B^2$ blocks of $P\times P$ matrices, each of which is the evaluation of $K(.,.)$ at the corresponding pair of images. Matrices across the diagonal in the block describe the covariances between pixel locations for each image, whereas the off-diagonal ones describe the correlation between pixel locations of different images.
In the dense case, obtaining the inverse of the full covariance matrix is of complexity $O(B^3 P^3)$ and carries a memory cost of $O(B^2 P^2)$. Even if one is able to choose small $B$ under the functional VI framework, this case would still be intractable for large $P$. A promising way of overcoming this would be to construct prior covariance functions with special structure across the $P$ output dimensions. Recent work done in \cite{aga2018cnngp,novak2019bayesian,yang2019scaling,yang2019wide} has highlighted that Bayesian CNNs do converge to Gaussian Processes as the number of channels of the hidden layers tends to infinity. In cases where activation functions such as relu and tanh are considered, and the architecture does not contain pooling layers, \cite{aga2018cnngp} shows that it is possible to exactly compute a covariance kernel which emulates the same behaviour as the Bayesian CNN, which is denoted as the \textit{equivalent kernel}. In other words, given any Bayesian CNN of this form, in the limit of large number of channels, the function samples they generate come from a zero-mean Gaussian Process given by this covariance function (see \cite{aga2018cnngp} Figure 2 for an example). This covariance kernel can be computed very efficiently at cost which is proportional to a single forward pass through the equivalent CNN architecture with only one channel per layer, which is due to the fact that the resulting GP is independent and identically distributed over the output channels. Moreover, in the absence of pooling layers \cite{novak2019bayesian}, the resulting kernel only contains the variance terms in its diagonal and all pixel-pixel covariances are 0. Thus, given a mini-batch of $B$ input images, the corresponding prior kernel matrix $\boldsymbol{K}$ has only $O(B^2P)$ non-zero entries and can be written in block structure as follows:
\begin{equation}
\begin{pmatrix}
K_{1,1} & \cdots & K_{B,1} \\
\vdots & \ddots & \vdots \\
K_{B,1} & \cdots & K_{B,B}
\end{pmatrix}
\label{kernel_mat}
\end{equation}
Each sub-matrix $K_{i,j}=K(x_i, x_j)$ is diagonal, hence easy to invert and store. Let $\boldsymbol{K}_{:n,:n}$ denote the $nP \times nP$ sub-matrix obtained by indexing from the top-left corner of $\boldsymbol{K}$, where $n=1,...,B$, and consider the following block sub-matrix $\boldsymbol{K}_{:n+1,:n+1}$:
\begin{equation}
\begin{pmatrix}
\boldsymbol{K}_{:n,:n} & \boldsymbol{K}_{:n,n+1} \\
\boldsymbol{K}_{:n,:n+1}^T & K_{n+1,n+1}
\end{pmatrix}
\end{equation}
Using the block-matrix inversion formula, we may write $\boldsymbol{K}_{:n+1,:n+1}^{-1}$ as follows:
\begin{align}
\begin{split}
& \begin{pmatrix}
\boldsymbol{A}_{:n,:n} & \boldsymbol{B}_{:n,n} \\
\boldsymbol{B}_{:n,n}^T & S_{n,n}^{-1}
\end{pmatrix},
\\
& \boldsymbol{A}_{:n,:n}=\boldsymbol{K}_{:n,:n}^{-1}(\boldsymbol{I} + \boldsymbol{K}_{:n,n+1} S_{n,n}^{-1} \boldsymbol{K}_{:n,n+1}^T\boldsymbol{K}_{:n,:n}^{-1}),
\\
& \boldsymbol{B}_{:n,n}=\boldsymbol{K}_{:n,:n}^{-1} \boldsymbol{K}_{:n,n+1} S_{n,n}^{-1},
\\
& S_{n,n} = K_{n+1,n+1} - \boldsymbol{K}_{:n,:n+1}^T \boldsymbol{K}_{:n,:n} \boldsymbol{K}_{:n,n+1}
\end{split}
\end{align}
Where $S_{n,n}$ is the Schur-complement of $\boldsymbol{K}_{:n+1,n+1}$. This equivalence holds because $\boldsymbol{K}_{:n+1,:n+1}^{-1}$ is invertible if and only if $\boldsymbol{K}_{:n,:n}$ and $S_{n,n}$ are invertible. Starting from $n=1$, $\boldsymbol{K}_{:n+1,:n+1}^{-1}$ can be recursively computed from $\boldsymbol{K}_{:n,:n}^{-1}$, so that we obtain $\boldsymbol{K}^{-1}$ in the last iteration. This algorithm is of complexity $O(B^2 P)$, where $B$ is much smaller than P since it is a batch-size, hence making functional VI applicable in the context of dense prediction tasks such as depth estimation and semantic segmentation. Additionally, the determinant of $\boldsymbol{K}$ may also be obtained efficiently by noting the following recurrence relation \cite{powell2011calculating}:
\begin{equation}
\mathrm{det}(\boldsymbol{K}_{:n+1,:n+1}) = \mathrm{det}(\boldsymbol{K}_{:n,:n}) \mathrm{det}(S_{n,n})
\end{equation}
By efficiently and stably computing inverse covariance matrices with the same block structure as $\boldsymbol{K}$ and its respective determinants, we are able to replace $p(f^{\boldsymbol{X}})$ in (\ref{elbo_fvbnn}) with the more convenient multi-output GP surrogate $\hat{p}(f^{\boldsymbol{X}})$. In this work we will only consider Bayesian CNN priors without pooling layers, which are most convenient in dense prediction tasks, in order to yield the structural advantages discussed above and leverage the methodology from \cite{aga2018cnngp,novak2019bayesian}. Nevertheless, given any square-integrable stochastic process, it is possible to estimate $K(x_i, x_j)$ using Monte Carlo (MC) sampling and then associating a GP prior with the estimated multi-output covariance function. This has been done in \cite{novak2019bayesian} in order to handle the cases where Bayesian CNN priors do contain pooling layers. Note that any cost involved in computing $\hat{p}(f^{\boldsymbol{X}})$ is only incurred during training.
\begin{figure}[h!]
\centering
{{\includegraphics[width=\columnwidth]{sivi.pdf} }}%
\caption{Overview of our functional VI approach. $X_B$ is a batch of rgb inputs, $x_n$ a newly generated one and $D_0$ is the mean function of the GP prior.}%
\label{fig_fvi}%
\end{figure}
Similarly, by choosing $q(f^{\boldsymbol{X}})$ to be a multi-output GP with mean function $h(.)$ and covariance function $\Sigma(.)$ parametrized by CNN mappings, we are able to compute the corresponding Gaussian KL divergence term in closed form. The expected log-likelihood term may be approximated with MC sampling, but in case of gaussian likelihood it can also be computed in closed form. For each pair of inputs $(x_i, x_j)$, we parametrize the covariance kernel as follows:
\begin{align}
\Sigma(x_i, x_j)= \frac{1}{L} \sum_{k=1}^L g_k(x_i) \odot g_k(x_j) + D(x_i, x_j) \delta(x_i, x_j)
\label{q_covariance}
\end{align}
Where each $g_k(x_i), g_k(x_j)$ is a $P$ dimensional feature mapping, $\odot$ denotes the element-wise product and $L<P$, so that the left-term is the diagonal part of a rank-$L$ parameterization. For example, in depth estimation these can be obtained by defining $g(.)$ as a CNN having its output resolution associated with the $P$ pixels and $L$ output channels. $D(x_i,x_j)$ is a diagonal $P \times P$ matrix containing per-pixel variances which is considered only when $x_i=x_j$. This parametrization yields a $P\times P$ diagonal matrix for each pair of inputs, so that the full $BP \times BP$ covariance matrix has the same block structure as in (\ref{kernel_mat}). In this way $q(f^{\boldsymbol{X}})$ is able to account for posterior correlations between different images while being practical to train with mini-batches. Additionally, if one considers regression tasks whose likelihoods are of location-scale family, predictive variances can be computed in closed-form at no additional sampling cost (see supplementary material for an example under the berHu likelihood). In the case of discrete likelihoods, which includes semantic segmentation, computing entropy or mutual-information of the predictive distribution may also be done with a single forward pass plus a small number of gaussian samples, which adds negligible computational cost and is trivially paralellizable.
In practice, for each input image $x$, we may obtain all quantities of interest as an $R \times (LC + 3C)$ tensor by splitting the output channels of any suitable CNN architecture, where $R$ is the desired output resolution, $C=1$ for tasks such as monocular depth estimation or $C$ equal to the number of classes for tasks such as semantic segmentation. In Figure \ref{fig_fvi} we display a more clear overview of the different components which form our proposed functional VI approach.
\section{Related work}
Monte Carlo Dropout (MCDropout) \cite{gal2016dropout} interprets dropout as positing a variational family in weight-space and uses it at test time in order to compute epistemic uncertainty estimates. MCDropout has since then yielded applications in semantic segmentation tasks \cite{kendall2015bayesian,kampffmeyer2016semantic,kendall2017uncertainties,huang2018efficient,mukhoti2018evaluating}, moncular depth estimation \cite{kendall2017uncertainties}, visual odometry \cite{Bhattacharyya_2018_CVPR} and active learning \cite{gal2017deep}. Despite being convenient to implement during training, the need for multiple forward passes at test time renders MCDropout impractical for both large network architectures (with many dropout layers) and tasks requiring high throughput, such as real-time computer vision. Alternatively, our proposed method allows one to obtain predictive epistemic uncertainty with a single forward pass and to consider a broad range of loss functions whose probabilistic counterparts are consistent with aleatoric uncertainty quantification.
In the ML literature, various approaches which consider the function space view of BNNs have been discussed in \cite{hafner2018ncp,wang2019function,ma2019variational,pearce2019expressive,khan2019approximate}. Gaussian Process Inference Networks (GPNet) \cite{shi2019scalable} constitutes an alternative to inducing point methods on GPs, and shares some of the motivation of our work in that it also leverages the functional VI objective from \cite{sun2018functional} and chooses both variational family and prior to be GPs. In contrast to any of these, our work focuses on making training and inference practical in the context of dense prediction tasks, which is enabled by suitably parametrizing the variational GP approximation and exploiting special structure in the covariance matrices.
Recently \cite{postels2019sampling} have proposed a scalable method which yields predictive epistemic uncertainty at the cost of a single forward pass. In contrast to it, ours naturally handles all forms of uncertainty, both at training and test times.
\section{Results}
\begin{figure*}[h!]
\centering
\qquad{{\includegraphics[width=17cm]{camvid_camvid_segmentation_mcd_results_test_pred_112.pdf} }}%
\qquad{{\includegraphics[width=17cm]{camvid_camvid_segmentation_gp_bnn_results_test_pred_112.pdf} }}%
\caption{Semantic segmentation on CamVid. MCDropout-Boltzmann (top) and Ours-Boltzmann (bottom). From left to right: rgb input, ground truth, predicted, entropy, calibration plot (as depicted in \cite{kendall2017uncertainties})}%
\label{fig_camvid}%
\vspace{-5mm}
\end{figure*}
In order to parametrize the variational GP approximation, we use the FCDenseNet 103 architecture \cite{jegou2017one} without dropout layers. We also adopt this architecture for all other baselines and experiments, using a dropout rate of $0.2$. Even though our initial goal was to closely mimic the setup from \cite{kendall2017uncertainties}, we were not able to reproduce their RMSprop results. Thus, in order to perform a clear comparison, we have decided to compare all methods with the exact same optimizer configurations. For MCDropout, we compute predictions using $S=50$ forward passes at test time.
We choose $L=20$ for the covariance parametrization in (\ref{q_covariance}) and add a constant of $10^{-3}$ to its diagonal during training in order to ensure numerical stability. In order to implement the prior covariance kernel equivalent to a densely connected Bayesian CNN, which has been discussed in section 3, we use the PyTorch implementation made available by the authors in \cite{aga2018cnngp}. For both the segmentation and depth estimation experiments, we compute the equivalent kernel of a densely connected CNN architecture, composed of various convolutions and up-convolutions (see supplementary material), and add a white noise component of variance $0.1$. For the depth experiments, we posit a prior mean of $0.5$ while for segmentation we set it to $1.0$. In order to generate the inducing inputs $\boldsymbol{X'}$ included in the KL divergence term from equation (\ref{elbo_fvbnn}) during training, we randomly pick one image in the mini-batch and add per-pixel gaussian noise with variance $0.1$.
\subsection{Semantic Segmentation}
In this section, we consider semantic segmentation on CamVid dataset \cite{brostow2009semantic}. All models have been trained with SGD optimizer, momentum of $0.9$ and weight decay of $10^{-4}$ for $1000$ epochs with batches of size $4$ containing randomly cropped images of resolution $224\times224$, with an initial learning rate of $10^{-3}$ and annealing it every epoch by a factor of $0.998$. Then we finish with training for one epoch on full-sized images with batch size of $1$. We have considered this setup because, while performing our initial experiments by monitoring on the validation set, we have observed that our approach, even though it consistently benefits from fine-tuning on full-sized images in terms of its accuracy measures, the quality of its uncertainty estimates (in terms of calibration score \cite{kuleshov2018accurate}) has degraded significantly.
For our proposed method, we have used the Boltzmann likelihood with re-scaled logits as given in equation (\ref{boltzmann_likelihood}), which we denote as Ours-Boltzmann. Even though re-scaling logits provides no increase in flexibility to non-functional VI approaches, in order to have the same comparison setup, we chose to parametrize it in the same way for both the deterministic baseline and MCDropout: Deterministic-Boltzmann and MCDropout-Boltzmann, respectively.
From Table \ref{table_camvid} we observe that our method performs best, both in terms of IoU score (averaged over all classes) and accuracy. In Figure \ref{fig_camvid} we display a test example of MCDropout-Boltzmann (top) and Ours-Boltzmann (bottom), where we have masked-out the void class label as yellow. We can see that the uncertainty estimates are reasonable, being higher on segmentation edges and unknown objects. We also include the calibration curve, as computed in \cite{kendall2017uncertainties}, where the green dashed line corresponds to perfect calibration. In order to assess the overall quality of the uncertainty estimates, it is common to compute calibration plots for all pixels in the test set \cite{kendall2017uncertainties,kuleshov2018accurate}. Unfortunately, this is not feasible to compute for our functional VI approach, due to the fact that it captures correlations between multiple images, so that approximating the predictive distribution would require sampling from a high-dimensional non-diagonal gaussian. Thus, in order to enable a simple comparison which works for both Ours-Boltzmann and MCDropout-Boltzmann, we compute the calibration score (see \cite{kuleshov2018accurate}) for each image in the test set and then average, which is given in Table \ref{table_calibration_camvid}.
\begin{table}[h!]
\centering
\caption{Results from training and testing on CamVid.}
\label{table_camvid}
\scalebox{0.70}{
\begin{tabular}{|l|l|l|l|l|}
\hline
& \textbf{IoU} & \textbf{Accuracy} \\ \hline
Deterministic-Boltzmann & 0.568 & 0.895 \\ \hline
MCDropout-Boltzmann & 0.556 & 0.893 \\ \hline
Ours-Boltzmann & \textbf{0.623} & \textbf{0.905} \\ \hline
\end{tabular}
}
\vspace{-5mm}
\end{table}
\begin{table}[h!]
\centering
\caption{Mean calibration score, computed with 10 equally spaced intervals, averaged over all test set examples. Lower is better.}
\label{table_calibration_camvid}
\scalebox{0.70}{
\begin{tabular}{|l|l|l|l|l|}
\hline
& \textbf{Mean Calibration} \\ \hline
MCDropout-Boltzmann & 0.058 \\ \hline
Ours-Boltzmann & \textbf{0.053} \\ \hline
\end{tabular}
}
\vspace{-5mm}
\end{table}
\subsection{Pixel-wise Depth Regression}
\begin{figure*}[h!]
\centering
\qquad{\includegraphics[width=17cm]{results_make3d_mcd_results_test_pred_82.pdf}}%
\qquad{\includegraphics[width=17cm]{make3d_make3d_fvi_laplace_gp_bnn_results_test_pred_82.pdf}}%
\caption{Depth estimation on Make3d. MCDropout-Laplace (top) and Ours-Laplace (bottom). From left to right: rgb input, ground truth, predictive mean, predictive standard deviation, calibration plot (as depicted in \cite{kuleshov2018accurate})}%
\label{fig_depth}%
\vspace{-5mm}
\end{figure*}
In this section, we consider depth estimation on Make3d dataset \cite{saxena2008make3d}. All models have been trained with AdamW optimizer \cite{adamw2019} with constant learning rate and weight decay set to $10^{-4}$. We have re-sized all images to a resolution of $168\times224$, and trained with a batch size of $4$ for $3000$ epochs. We consider our approach using 3 different likelihoods: Ours-Laplace, Ours-Gaussian and Ours-berHu (as derived in section 3.1.1). We compare with MCDropout-Laplace and two deterministic baselines: Deterministic-$\mathcal{L}_1$ and Deterministic-berHu using the reverse Huber loss \cite{laina2016deeper}.
Test results are displayed in Table \ref{table_make3d}, where MCDropout performs best on all accuracy metrics. To a certain extent, this happened because our proposed method is more sensitive to the choice of batch-size, due to the fact that the functional VI objective is not a lower bound to the log marginal likelihood of the dataset, so that it has underfitted slightly more than MCDropout-Laplace and deterministic methods. Additionally, we had to use a learning rate of $10^{-4}$, as higher values would result in more unstable training for all our functional VI approaches.
In Figure \ref{fig_depth} we plot one test prediction for MCDropout-Laplace (top) and Ours-Laplace (bottom). In this case, we observe one of the benefits of our approach: around the sky area in the image, MCDropout-Laplace is overconfident about its predicted depth map, while ours correctly outputs high predictive uncertainty. Note that this is not reflected in the calibration curves, as all pixels with depth greater than 70m are masked out due to long-range inaccuracies in the dataset \cite{laina2016deeper}.
In Table \ref{table_calibration_make3d} we display the calibration scores for the probabilistic methods (see \cite{kuleshov2018accurate}), averaged over all test images, where Ours-Laplace performs slightly better than MCDropout-Laplace, despite not faring so well in terms of accuracy metrics.
\begin{table}[h!]
\centering
\caption{Results from training and testing on Make3d dataset.}
\label{table_make3d}
\scalebox{0.70}{
\begin{tabular}{|l|l|l|l|}
\hline
& \textbf{rel} & \textbf{log10} & \textbf{rms} \\ \hline
Deterministic-$\mathcal{L}_1$ & 0.212 & 0.085 & 5.29 \\ \hline
Deterministic-berHu & 0.222 & 0.084 & 5.08 \\ \hline
MCDropout-Laplace & \textbf{0.210} & \textbf{0.081} & \textbf{5.05} \\ \hline
Ours-Laplace & 0.264 & 0.092 & 5.74 \\ \hline
Ours-berHu & 0.237 & 0.088 & 5.68 \\ \hline
Ours-Gaussian & 0.254 & 0.089 & 5.65 \\ \hline
\end{tabular}
}
\vspace{-5mm}
\end{table}
\begin{table}[h!]
\centering
\caption{Mean calibration score, computed with 10 equally spaced intervals, averaged over all test set examples. Lower is better.}
\label{table_calibration_make3d}
\scalebox{0.70}{
\begin{tabular}{|l|l|l|l|l|}
\hline
& \textbf{Mean Calibration} \\ \hline
MCDropout-Laplace & 0.427 \\ \hline
Ours-Laplace & \textbf{0.409} \\ \hline
Ours-berHu & 0.631 \\ \hline
Ours-Gaussian & 0.491 \\ \hline
\end{tabular}
}
\vspace{-5mm}
\end{table}
\subsection{Inference time comparison}
Let $F$ be the inference time of one forward pass from a neural network on a RGB input. Our method's inference time (for obtaining predictive mean and uncertainty) is then $F + c_1$, while for MCDropout is $SF + c_2$, where $c_1,c_2$ are extra time costs needed to obtain the predictive uncertainties. In computer vision $F$ is often the dominant term, since it often involves large network architectures, of which the FCDenseNet 103 architecture is an example. We have tested these claims by performing multiple runs on an NVIDIA RTX6000 GPU, the same device in which all models have been trained and tested. The inference times for depth estimation and semantic segmentation are displayed in Table \ref{table_runtime_make3d} and Table \ref{table_runtime_camvid}, respectively. On depth estimation our method and deterministic had equivalent inference times. On segmentation $c_1$ depends on the number of gaussian samples taken, but is significantly cheaper than $F$ and trivially amenable to parallelization, so that our method still displayed cost of same order as deterministic model. In both cases, MCDropout was approximately $S=50$ times slower than its deterministic counterpart.
\begin{table}[h!]
\centering
\caption{Depth estimation on Make3D. Inference time comparison over 100 independent runs.}
\label{table_runtime_make3d}
\scalebox{0.70}{
\begin{tabular}{|l|l|l|l|l|}
\hline
& \textbf{mean $\pm$ std (ms)} \\ \hline
Deterministic-$\mathcal{L}_1$ & 51.29 $\pm$ 1.88 \\ \hline
Deterministic-berHu & 51.28 $\pm$ 1.62 \\ \hline
MCDropout-Laplace & 2615.65 $\pm$ 13.75 \\ \hline
Ours-Laplace & 50.98 $\pm$ 1.74 \\ \hline
Ours-berHu & 51.43 $\pm$ 2.12 \\ \hline
Ours-Gaussian & 51.13 $\pm$ 2.20 \\ \hline
\end{tabular}
}
\vspace{-5mm}
\end{table}
\begin{table}[h!]
\centering
\caption{Semantic segmentation on CamVid. Inference time comparison over 100 independent runs.}
\label{table_runtime_camvid}
\scalebox{0.70}{
\begin{tabular}{|l|l|l|l|l|}
\hline
& \textbf{mean $\pm$ std (ms)} \\ \hline
Deterministic-Boltzmann & 111.64 $\pm$ 0.27 \\ \hline
MCDropout-Boltzmann & 5763.63 $\pm$ 1.95 \\ \hline
Ours-Boltzmann & 128.59 $\pm$ 1.86 \\
\hline
\end{tabular}
}
\vspace{-5mm}
\end{table}
\section{Conclusion}
We have proposed a method which, by leveraging the functional VI objective from \cite{sun2018functional}, enables efficient training of Bayesian Deep Learning models and whose predictive inference requires only one forward pass, for any supervised learning task and network architecture. This is made possible by replacing the intractable BNN prior by a GP with covariance kernel as derived in \cite{aga2018cnngp}, parametrizing the variational family as a GP with a suitably structured covariance kernel and by leveraging efficient algorithms for matrix inversion and determinant computation during training. Furthermore, we have discussed how to start with a well-defined loss function in regression and then derive its probabilistic counterpart in a way which is consistent with aleatoric uncertainty quantification, having provided the derivation of the berHu likelihood as an example.
Our framework may readily be applied to other pixel-wise supervised learning tasks. Extending to tasks which benefit from having pooling layers, such as object classification, is also possible but requires some caution. This is because Bayesian CNN priors which contain pooling layers no longer induce GPs which have the special covariance structure displayed in (\ref{kernel_mat}), given that pooling induces local correlations between different pixel locations \cite{novak2019bayesian}.
As a direction of future work, it would be relevant to extend our proposed methodology to account for temporal information. This would be particularly important in monocular depth estimation, which is naturally prone to display high aleatoric uncertainty and would benefit from refined uncertainty estimates over consecutive time-frames \cite{liu2019neural}. Another direction of future work would be to overcome any potential underfitting occurring in pixel-wise regression tasks, as observed in our Make3D depth regression experiment, in which choosing more meaningful function priors and better variational distribution's covariance parametrizations could help.
\textbf{Acknowledgements}
Eduardo is supported by an EPSRC Industrial CASE scheme in collaboration with Arup. Paul is supported by EPSRC grant reference EP/P010040/1. We would like to thank Jan Czarnowski, Sajad Saeedi, Tristan Laidlow and all our reviewers for helpful insights and comments.
\bibliographystyle{ieee_fullname}
\section*{Supplementary material}
\subsection*{a) Reverse Huber (berHu) likelihood}
The reverse Huber (berHu) loss is defined as follows:
\begin{equation}
\ell (y) = |y| \mathcal{I}(|y| \leq c) + \left(\frac{y^2 + c^2}{2c}\right) \mathcal{I}(|y| > c)
\label{berhu_loss}
\end{equation}
Where $\mathcal{I}(.)$ is the indicator function and $c>0$ is an appropriately chosen threshold. $\ell (y)$ yields a balance between $\mathcal{L}_1$ and $\mathcal{L}_2$ losses: for smaller residuals, $\mathcal{L}_1$ is considered in order to yield gradients with larger magnitudes, whereas the $\mathcal{L}_2$ component provides an increased penalty to large residuals so that the network also accounts for these.
In this case, it can be shown that $Z_0 = 2 \left(1 - e^{-\mathrm{c}} + e^{-\mathrm{c}/2} (2 \pi \mathrm{c})^{1/2} \Phi(-c^{1/2})\right)$, where $\Phi(.)$ is the standard normal CDF, and taking $c \rightarrow \infty$ recovers the Laplace distribution. Given a new input $x^*$, the predictive mean $m(x^*)$ and variance $\mathbb{V}(x^*)$ can be written as follows:
\begin{align}
\label{berhu_pred}
\begin{split}
& m(x^*) = m \left( q(f(x^*)) \right) ,
\\
& \mathbb{V}(x^*) = \underbrace{w(c) \sigma^2(x^*)}_{\text{aleatoric}} + \underbrace{\mathbb{V}(q(f(x^*))}_{\text{epistemic}} ,
\\
& w(\mathrm{c}) = \frac{-4 (\mathrm{c} + 1) e^{-\mathrm{c}} + 4 + 2 e^{-\mathrm{c}/2} (2 \pi)^{1/2} (\mathrm{c})^{3/2} \Phi(-c^{1/2})}{Z_0}
\end{split}
\end{align}
$m(x^*)$ is the mean of the variational distribution $q(f(x^*))$, which follows from the law of conditional expectation, and the decomposition of its variance as sum of epismetic and aleatoric components follows from the law of total variance. Compared to choosing gaussian or laplacian likelihoods, berHu yields a weighted version of $\sigma^2(x^*)$ which depends on the choice of $c$. We choose $c = \frac{1}{5} \mathrm{max}_i \mathbb{E}_{q(f(x_i))} \left( |y_i - f(x_i)| \right)$ during training, where $i$ indexes all output feature maps in a mini-batch and the inner expectation is replaced by a monte carlo estimate. In order to compute the predictive distribution at test time, we record the maximum value of $c$ across all batches in the final training epoch.
\section*{b) Bayesian CNN GP prior}
In Figure \ref{fig:prior} we display the Bayesian CNN architecture, with weight prior variance of $0.2$ and bias' prior variance of $0.08$, using relu activations, from which the equivalent kernel was derived. This covariance kernel encompasses the behaviour of this Bayesian CNN architecture in the limit where the number of channels in its hidden layers, $C$, tends to infinity, which we denote as Bayesian CNN GP prior. The red and gray blocks correspond to linear interpolation followed by a convolution layer. The sequence of output resolutions for linear interpolation are $20,40,60,80,100$ percent of the desired output resolution.
\begin{figure}[h!]
\centering
\includegraphics[width=0.5\textwidth]{BNN_gp.pdf}
\caption{Architecture of the Bayesian CNN GP prior.}
\label{fig:prior}
\end{figure}
\section*{c) Semantic segmentation on CamVid}
During training, for all methods, we augment the CamVid dataset by performing random horizontal flips with $0.5$. For our approach (Ours-Boltzmann) we estimate the expected log-likelihood term using $20$ monte carlo samples from the variational distribution.
We select and discuss two test cases in order to compare our method (Ours-Boltzmann) and MCDropout-Boltzmann. Unknown segmentation classes have been masked out as yellow in the plots corresponding to ground truth and predicted classes. In Figure \ref{fig_seg}, MCDropout-Boltzmann (top) is wrongly overconfident that the left sidewalk is part of the road, while ours correctly accounts for this difference by outputting higher predictive entropy. Figure \ref{fig_seg_failure} displays a failure test case from our method, in which it displays high confidence (low-entropy) that the bus-stop is part of the housing lots. MCDropout-Boltzmann does a better job at flagging out this unknown segmentation class by outputting higher entropy on several of its regions.
\begin{figure*}[h!]
\centering
\hspace{-7mm}\qquad{{\includegraphics[width=15cm]{camvid_camvid_segmentation_mcd_results_test_pred_117.pdf}}}
\qquad{{\includegraphics[width=15cm]{camvid_camvid_segmentation_gp_bnn_results_test_pred_117.pdf} }}%
\caption{Semantic segmentation on CamVid. MCDropout-Boltzmann (top) and Ours-Boltzmann (bottom). From left to right: rgb input, ground truth, predicted, entropy, calibration plot}%
\vspace{-5mm}
\label{fig_seg}
\end{figure*}
\begin{figure*}[h!]
\centering
\hspace{-7mm}\qquad{{\includegraphics[width=15cm]{camvid_camvid_segmentation_mcd_results_test_pred_122.pdf}}}
\qquad{{\includegraphics[width=15cm]{camvid_camvid_segmentation_gp_bnn_results_test_pred_122.pdf} }}%
\caption{Semantic segmentation on CamVid. MCDropout-Boltzmann (top) and Ours-Boltzmann (bottom). From left to right: rgb input, ground truth, predicted, entropy, calibration plot}%
\vspace{-5mm}
\label{fig_seg_failure}
\end{figure*}
\section*{d) Depth estimation on Make3d}
During training, for all methods, we augment the Make3d dataset with random horizontal flips (with probability $0.5$), and randomly adjust brightness, saturation, contrast and hue of rgb inputs by a factor of $0.1$. For Ours-Laplace and Ours-berHu, we estimate the expected log-likelihood term using $50$ monte carlo samples from the variational distribution.
We select and discuss two test cases in order to compare our methods (Ours-Laplace, Ours-Gaussian and Ours-berHu) with MCDropout-Laplace. In Figure \ref{fig_depth} we display an example where all methods perform well in terms of the predicted depth map. We can observe that both the predicted depth maps and uncertainty from our methods have a sharper aspect than MCDropout-Laplace, which we have consistently observed for most predictions. In Figure \ref{fig_depth_failure} we display a failure case for all methods, in terms of predicting inaccurate depth maps. Predictive uncertainty, both its epistemic and aleatoric components, is expected to be higher around the blue sky region. Our methods deliver this effect, while MCDropout-Laplace is overconfident about the predicted depth maps in this region.
\begin{figure*}[h!]
\centering
\hspace{-7mm}\qquad{{\includegraphics[width=15cm]{results_make3d_mcd_results_test_pred_56.pdf} }}%
\qquad{{\includegraphics[width=15cm]{make3d_make3d_fvi_laplace_gp_bnn_results_test_pred_56.pdf} }}%
\qquad{{\includegraphics[width=15cm]{make3d_make3d_fvi_gaussian_gp_bnn_results_test_pred_56.pdf} }}%
\qquad{{\includegraphics[width=15cm]{make3d_make3d_fvi_berhu_gp_bnn_results_test_pred_56.pdf} }}%
\caption{Depth estimation on Make3d. MCDropout-Laplace (first row), Ours-Laplace (second row), Ours-Gaussian (third row), Ours-berHu (fourth row). From left to right: rgb input, ground truth, predictive mean, predictive standard deviation, calibration plot.}
\vspace{-5mm}
\label{fig_depth}
\end{figure*}
\begin{figure*}[h!]
\centering
\hspace{-7mm}\qquad{{\includegraphics[width=15cm]{results_make3d_mcd_results_test_pred_70.pdf} }}%
\qquad{{\includegraphics[width=15cm]{make3d_make3d_fvi_laplace_gp_bnn_results_test_pred_70.pdf} }}%
\qquad{{\includegraphics[width=15cm]{make3d_make3d_fvi_gaussian_gp_bnn_results_test_pred_70.pdf} }}%
\qquad{{\includegraphics[width=15cm]{make3d_make3d_fvi_berhu_gp_bnn_results_test_pred_70.pdf} }}%
\caption{Depth estimation on Make3d. MCDropout-Laplace (first row), Ours-Laplace (second row), Ours-Gaussian (third row), Ours-berHu (fourth row). From left to right: rgb input, ground truth, predictive mean, predictive standard deviation, calibration plot.}
\vspace{-5mm}
\label{fig_depth_failure}
\end{figure*}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 3,131
|
namespace app { namespace Uno { namespace Collections { struct Dictionary__Outracks_Simulator_Bytecode_Variable__object; } } }
namespace app {
namespace Uno {
namespace Collections {
struct Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object;
struct Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object__uType : ::uStructType
{
::app::Uno::Collections::IEnumerator__object __interface_0;
::app::Uno::IDisposable __interface_1;
::app::Uno::Collections::IEnumerator __interface_2;
};
Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object__uType* Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object__typeof();
void Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object___ObjInit(Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object* __this, ::app::Uno::Collections::Dictionary__Outracks_Simulator_Bytecode_Variable__object* source);
void Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object__Dispose(Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object* __this);
::uObject* Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object__get_Current(Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object* __this);
bool Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object__MoveNext(Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object* __this);
Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object__New_1(::uStatic* __this, ::app::Uno::Collections::Dictionary__Outracks_Simulator_Bytecode_Variable__object* source);
void Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object__Uno_Collections_IEnumerator_Reset(Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object* __this);
struct Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object
{
::uStrong< ::app::Uno::Collections::Dictionary__Outracks_Simulator_Bytecode_Variable__object*> _source;
::uStrong< ::uObject*> _current;
int _iterator;
int _version;
void _ObjInit(::app::Uno::Collections::Dictionary__Outracks_Simulator_Bytecode_Variable__object* source) { Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object___ObjInit(this, source); }
void Dispose() { Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object__Dispose(this); }
::uObject* Current() { return Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object__get_Current(this); }
bool MoveNext() { return Dictionary2_ValueCollection_Enumerator__Outracks_Simulator_Bytecode_Variable__object__MoveNext(this); }
};
}}}
#endif
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,215
|
Ту́мба () — місто та адміністративний центр комуни Ботчирка в лені Стокгольм, Швеція. Населення — 38852 жителів у 2010 році. Одна його частина знаходиться в комуні Салем. Банкноти шведської крони друкуються компанією Crane AB в Tumba Bruk. Тумба розташована на півдорозі між Стокгольмом і Седертельє і вважається Стокгольмським передмістям. У Тумбі в Реннінге є станції на Стокгольмській передміської залізниці.
Тумба також має гимназію (Tumba gymnasium) з майже 1000 студентів. Компанія Alfa Laval Group була заснована в Тумбі Густафом де Лавалем і залишається в передмісті, так само, як і ДеЛаваль, яка була створена з Альфа Лаваль у 1991 році.
Гурт Amon Amarth, що грає мелодійний дез-метал, також походить з Тумби.
Історія
Що відрізняє Тумбу від інших комун у північній частині Ботчирка є те, що вона не походить від великої ферми з історичними коріннями. Доісторичні люди переважно жили близько до берегів, а Тумба знаходиться у глибині країни, ось чому сліди людської діяльності під час передісторії відносно рідкі. Велика зміна відбулася протягом 1755 року, коли банк Швеції купив невелику ферму і почав виробництво паперу тут. Навколо паперового млину зросла громада, з якою з'явились школа і будинки для працівників. Наступний великою подією став прихід сюди залізниці 1860 року. Після цього місто почало рости навколо станції, внаслідок чого з'явились комерційні установи, поліція і кінотеатр. У 1894 році Де Лаваль купив Гамра Гард і перетворив його на ферму, що спеціалізується на переробці молока. Ферма згодом перетворилась на велике виробництво.
Примітки
Населені пункти лену Стокгольм
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 2,523
|
{"url":"http:\/\/openstudy.com\/updates\/525d3461e4b002bdb090eac2","text":"## anonymous 2 years ago Help with these:\/ I don't understand\n\n1. anonymous\n\n2. hartnn\n\ncan you find slope of any given line ?\n\n3. hartnn\n\nlike say , x-5y = -10 is a line. can you find slope of this line first ?\n\n4. anonymous\n\nUh no not really... with a quick review I probably can\n\n5. hartnn\n\ngood, so i have x-5y =-10 i will try to isolate y and bring it in the form y=mx+c where m=slope so, x=5y-10 5y = x+10 y= (1\/5)x +2 got this ?\n\n6. anonymous\n\nYeah I got it\n\n7. hartnn\n\ncool, so can you find the slope of x -3y=9 line ? in same way\n\n8. hartnn\n\noh and i forgot to mention, y= (1\/5)x +2 comparing with y=mx+c gives, m=slope = 1\/5\n\n9. anonymous\n\nx-37=9 -3y=x+9 Y=(1\/3)x+3\n\n10. anonymous\n\nSo slope would be 1\/3 I assume?\n\n11. hartnn\n\ncorrect! :) now try to find slopes of other 3 lines also! and tell me, so that i will verify :)\n\n12. anonymous\n\n4x+2y=5 2y=-4x+5 Y-(-1\/2)x+2.5 ?\n\n13. hartnn\n\n2y=-4x+5 is correct, but then divide both sides by 2 what u get ?\n\n14. anonymous\n\n10x-5y=8 -5y=10x+8 Y=-2x+1.6?\n\n15. hartnn\n\n10x-5y=8 -5y=10x+8 <<<<<<NO! -5y = -10x +8\n\n16. anonymous\n\nand you would get y=-2+2.5\n\n17. anonymous\n\nAhh okay -10 so the problem would come out with a positive 2x\n\n18. hartnn\n\nyes, so the slope will be m= 2 , right ?\n\n19. anonymous\n\nYes\n\n20. hartnn\n\n4x+2y=5 slope = -2 make a note of all slopes, we'll need them\n\n21. hartnn\n\nand what about last line ?\n\n22. anonymous\n\n4x+y=-1 Y=-4x-1\n\n23. hartnn\n\nso, slope =?\n\n24. anonymous\n\n-4\n\n25. hartnn\n\nGood! now here's the rule : slope of parallel lines are equal! so, for the last one, slope of line parallel to 4x+y=-1 will also be m=-4 :) so, for last, the correct option will be C) m=-4 got this ? in same way, can you match the 2nd last and 3rd last ?\n\n26. anonymous\n\nYeah I got it, Thanks a ton man. You need to be my teacher xD\n\n27. hartnn\n\nhaha, :) but we still require to do the 1st 2 !\n\n28. hartnn\n\nanother rule, product of slopes of perpendicular lines = -1 so, for 1st one we had slope = 1\/5 let slope of perpendicular line be m. so, $$\\Large m\\times (1\/5)=-1$$ find m from here :)\n\n29. anonymous\n\n1st one is m=1\/5? 2cnd one is m=1\/3? It seems like these would be the answers but they are not possible to be selected.\n\n30. anonymous\n\nAhhhh okay\n\n31. hartnn\n\nbecause perpendicular lines follow different rule :)\n\n32. anonymous\n\nWell I still don't exactly get how it goes from (1\/5) to -1...\n\n33. hartnn\n\nproduct of slopes = -1 is the rule so, m (1\/5) =-1 multiplying by 5, m = -5 got this ?\n\n34. hartnn\n\nmultiplying by 5 on both sides.\n\n35. anonymous\n\nI'm confused on the product of slopes part, I get the multiplying on both sides. So like can you explain the product of slopes rule.. I tried looking it up on google but nothing I can comprehend really comes up.\n\n36. hartnn\n\nif say line 1 has slope M1 and line 2 has slope M2 now if these 2 lines are perpendicular to each other, then M1*M2 =-1\n\n37. hartnn\n\nanother way to remember the same thing is, the slope of line is negative reciprocal of the perpendicular line, so, slope of line perpendicular to line with slope 1\/5 will be - (1\/(1\/5)) = -5\n\n38. hartnn\n\nso, thats your 1st one, m =-5 for 2nd one, we had slope = 1\/3, so m *(1\/3) = -1 so, m=-3 is the answer to 2nd one :)\n\n39. anonymous\n\nOkay, so basically whenever there is a fraction just take (1\/_) blank space number lol\n\n40. hartnn\n\nyou forgot the negative :P -1\/ stuff\n\n41. hartnn\n\nbut this only applies to perpendicular lines\n\n42. hartnn\n\nfor parallel lines, slope are equal\n\n43. anonymous\n\nOh I see says the blind man\n\n44. hartnn\n\nwhat who ?\n\n45. hartnn\n\nlol\n\n46. hartnn\n\ni hope you got the entire problem clearly ?\n\n47. hartnn\n\n48. anonymous\n\nYeah I get it now man thanks a ton\n\n49. hartnn\n\nwelcome ^_^","date":"2016-09-27 10:38:50","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\": 1, \"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\": 0.7958492040634155, \"perplexity\": 4503.0101071096215}, \"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-2016-40\/segments\/1474738661023.80\/warc\/CC-MAIN-20160924173741-00144-ip-10-143-35-109.ec2.internal.warc.gz\"}"}
| null | null |
Do what you love; the money will follow.
printer's apprentice in Gap, Pennsylvania.
he accepted a job with a local caramel manufacturer.
fresh milk was used in the caramel-making process.
his reputation as a candy-maker—the Lancaster Caramel Company.
In 1900, Mr. Hershey sold the Lancaster Caramel Company for $1 million.
proceeded to prove his case.
to make fine milk chocolate.
office building for the chocolate factory.
Hersheys were anxious to put their growing fortune to good use.
an inspiration to all who worked with him.
company, community, and school a living legacy.
success and happiness fill your life.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 4,375
|
package ccm.nucleumOmnium.commands;
import net.minecraft.command.CommandBase;
import net.minecraft.command.ICommandSender;
import net.minecraft.server.MinecraftServer;
import net.minecraft.util.ChatMessageComponent;
import net.minecraftforge.common.DimensionManager;
import java.text.DecimalFormat;
import java.util.List;
/**
* Copy from N-O 1
*/
public class CommandTps extends CommandBase
{
private static final DecimalFormat timeFormatter = new DecimalFormat("########0.000");
@Override
public String getCommandName()
{
return "tps";
}
@Override
public String getCommandUsage(ICommandSender icommandsender)
{
return "/tps [worldID]";
}
@Override
public void processCommand(ICommandSender sender, String[] args)
{
int dim = 0;
boolean summary = true;
if (args.length > 0)
{
dim = parseInt(sender, args[0]);
summary = false;
}
if (summary)
{
for (Integer dimId : DimensionManager.getIDs())
{
double worldTickTime = mean(MinecraftServer.getServer().worldTickTimes.get(dimId)) * 1.0E-6D;
double worldTPS = Math.min(1000.0 / worldTickTime, 20);
sender.sendChatToPlayer(ChatMessageComponent.createFromTranslationWithSubstitutions("commands.forge.tps.summary", String.format("Dim %d", dimId), timeFormatter.format(worldTickTime), timeFormatter.format(worldTPS)));
}
double meanTickTime = mean(MinecraftServer.getServer().tickTimeArray) * 1.0E-6D;
double meanTPS = Math.min(1000.0 / meanTickTime, 20);
sender.sendChatToPlayer(ChatMessageComponent.createFromTranslationWithSubstitutions("commands.forge.tps.summary", "Overall", timeFormatter.format(meanTickTime), timeFormatter.format(meanTPS)));
}
else
{
double worldTickTime = mean(MinecraftServer.getServer().worldTickTimes.get(dim)) * 1.0E-6D;
double worldTPS = Math.min(1000.0 / worldTickTime, 20);
sender.sendChatToPlayer(ChatMessageComponent.createFromTranslationWithSubstitutions("commands.forge.tps.summary", String.format("Dim %d", dim), timeFormatter.format(worldTickTime), timeFormatter.format(worldTPS)));
}
}
@Override
public boolean canCommandSenderUseCommand(final ICommandSender sender)
{
return true;
}
private static long mean(long[] values)
{
long sum = 0l;
for (long v : values)
{
sum += v;
}
return sum / values.length;
}
@Override
public List addTabCompletionOptions(final ICommandSender sender, final String[] args)
{
if (args.length == 1)
{
String[] strings = new String[DimensionManager.getIDs().length];
for (int i = 0; i < DimensionManager.getIDs().length; i++)
strings[i] = DimensionManager.getIDs()[i].toString();
return getListOfStringsMatchingLastWord(args, strings);
}
return null;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,090
|
1113 Katja, provisional designation , is a background asteroid from the outer regions of the asteroid belt, approximately 39 kilometers in diameter. It was discovered by Pelageya Shajn at the Simeiz Observatory in 1928, and named after Ekaterina Iosko, a staff member at the discovering observatory.
Discovery
Katja was discovered on 15 August 1928, by Soviet astronomer Pelageya Shajn at the Simeiz Observatory on the Crimean peninsula. Nine nights later, it was independently discovered by Max Wolf at the German Heidelberg Observatory on 24 August 1928. The Minor Planet Center only recognizes the first discoverer. The asteroid was first observed as at Heidelberg on February 1909.
Orbit and classification
Katja is a non-family asteroid of the main belt's background population. It orbits the Sun in the outer asteroid belt at a distance of 2.7–3.6 AU once every 5 years and 6 months (2,004 days; semi-major axis of 3.11 AU). Its orbit has an eccentricity of 0.14 and an inclination of 13° with respect to the ecliptic. The body's observation arc begins at Heidelberg, 10 days after its official discovery observation at Simeiz.
Physical characteristics
Although Katja is an assumed, carbonaceous C-type asteroid, it is rather of stony composition due to its high albedo.
Rotation period
Between 2002 and 2011, several rotational lightcurves of Katja were obtained from photometric observations by French amateur astronomers Maurice Audejean, René Roy and Laurent Brunetto (). Best rated lightcurve, however, was obtained at the Sunflower (), Blackberry () and Universidad de Monterrey () observatories in January 2002. Lightcurve analysis gave a well-defined synodic rotation period of 18.465 hours with a brightness amplitude of 0.17 magnitude ().
Diameter and albedo
According to the surveys carried out by the Infrared Astronomical Satellite IRAS, the Japanese Akari satellite and the NEOWISE mission of NASA's Wide-field Infrared Survey Explorer, Katja measures between 38.20 and 51.949 kilometers in diameter and its surface has an albedo between 0.1144 and 0.211.
The Collaborative Asteroid Lightcurve Link derives an albedo of 0.2253 and a diameter of 38.65 kilometers based on an absolute magnitude of 9.3.
Naming
This minor planet was named for Ekaterina ("Katja") Iosko, a laboratory assistant and orbit calculator at the discovering Simeiz Observatory (). She was the daughter of Iosif Gavrilovich Iosko, who also worked as a mechanician at the observatory.
References
External links
Asteroid Lightcurve Database (LCDB), query form (info )
Dictionary of Minor Planet Names, Google books
Asteroids and comets rotation curves, CdR – Observatoire de Genève, Raoul Behrend
Discovery Circumstances: Numbered Minor Planets (1)-(5000) – Minor Planet Center
001113
Discoveries by Pelageya Shajn
Named minor planets
19280815
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,353
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{"url":"https:\/\/gea.esac.esa.int\/archive\/documentation\/GDR1\/Data_processing\/chap_astpre\/sec_cu3pre_prop.html","text":"# 2.2 Properties of the input data\n\nAuthor(s): Uli Bastian\n\nThis section describes the input data from which the astrometric and photometric pre-processing \u2014 and thus the DPAC data processing as a whole \u2014 starts. The input data largely fall into two categories: Telemetry data from the Gaia satellite, and auxiliary data prepared by the DPAC in advance of the mission.\n\n## 2.2.1 Overview\n\nAuthor(s): Uli Bastian\n\nThe most important and biggest input of course is the telemetry data from the Gaia satellite. Originating from the spacecraft they enter the data processing after several transmission and transformation steps: through the telemetry spacecraft-to-Earth telemetry link, the three ESA ground station antennas at Cebreros (Spain), New Norcia (Australia) and Malarg\u00fce (Argentina) to the Mission Operations Centre (MOC) at ESOC, Darmstadt (Germany), into the Telemetry Archive at the Science Operations Centre (SOC) at ESAC, Villafranca (Spain) and into the DPAC\u2019s live pre-processing database via the DPAC\u2019s MOC\u2013SOC Interface Task (MIT) software.\n\nThe telemetry consists of housekeep and science data. The former contains a huge variety of on-board status information, subsystems working logs etc., including the autonomous on-board attitude determination results. It is not described further in the present chapter, although it enters the processing in many critical ways.\n\nThe science telemetry data are described in Section\u00a02.2.2. The subsequent subsections, from Section\u00a02.2.3 to Section\u00a02.2.5, explain three auxiliary star catalogues prepared before the mission and used in the pre-processing: the Initial Gaia Source List (IGSL) for the preliminary assignment of Gaia observations to celestial objects, the Ecliptic-Poles Catalogue (EPC) for the initial in-orbit performance verification and calibration after launch, and the Attitude Star Catalogue (ASC) for the continual on-ground attitude reconstruction.\n\n## 2.2.2 The raw science telemetry data\n\nAuthor(s): Jordi Portell\n\nThe Gaia spacecraft, and specifically its focal plane through the Video Processing Units (VPUs), generate a variety of raw data packets which are down-linked to the ground and must be processed by DPAC. These packets include the astrometric, photometric and spectroscopic measurements, but they are not self-contained \u2014 in the sense that their measurement features are provided through separate packets. This is done for down-link optimisation reasons. Probably the most important task in the astrometric and photometric pre-processing is the reconstruction of self-contained individual measurements.\n\nRaw data is organized in Star Packets (SP) and Ancillary Science Data packets (ASD). The former contain the science data in itself, such as the pixels acquired from the CCDs, whereas the latter contain shared data needed for the reconstruction of raw measurements, such as information on the measurement coordinates through the focal plane or the integration time of each image.\n\nThere are 9 types of Star Packets, identified as SP1 to SP9, plus 7 types of Ancillary Science Data packets, identified as ASD1 to ASD7. There is yet another type of data packet, called Service Interface Packet (SIF), but that is only used for payload diagnostics and extended, on-demand data acquisition.\n\n### Generation\n\nTypically, one SP of one or more type is generated for every astronomical source transit across the Gaia focal plane. That is to say, every time that a VPU detects, confirms and measures the transit of a source with enough brightness and sharpness. Some of these packets are only generated during special calibration or non-nominal activities. We can classify Star Packets as follows:\n\n\u2022 Nominal astronomical packets:\n\n\u2022 SP1, the most numerous ones, with one packet generated for each astronomical source transit across the SM, AF and BP\/RP CCDs. These form the main data input to all Gaia data processing systems.\n\n\u2022 SP2, same as for SP1 but only for those sources detected in the focal plane rows that have RVS CCDs, and only for sources which are bright enough for being measured there.\n\n\u2022 SP3, generated only for SP1 packets for which a significant across-scan motion has been autonomously detected on board. These are called Suspected Moving Objects (SMO).\n\n\u2022 Nominal instrumental packets:\n\n\u2022 SP4, with regular (periodic) measurements from the Basic Angle Monitoring (BAM) device. That is, although these are labelled as \u2018Star Packets\u2019, these do not contain any astronomical information, but instrumental information instead.\n\n\u2022 Non-nominal astronomical packets:\n\n\u2022 SP6 and SP7, with SM and AF1 measurements of bright stars, which are only generated when the on-board Attitude and Orbit Control System (AOCS) is being initialised and when it loses convergence momentarily. These are mainly down-linked for further analysis and checks, but they do not enter the main data processing pipelines.\n\n\u2022 SP8 and SP9, with AF1 or SM measurements of bright stars, also only generated in special on-board conditions and not entering the main data processing pipelines.\n\n\u2022 Non-nominal instrumental packets:\n\n\u2022 SP5, with measurements from the Wave Front Sensor (WFS) monitoring device. As with SP4, these do not actually contain any astronomical information, but instrumental only.\n\nRegarding the ASD packets, they are generated as follows:\n\n\u2022 ASD1, with the across-scan window position information for most CCDs, generated every second for each VPU.\n\n\u2022 ASD2, with electronic bias data (pre-scan pixels), generated periodically (about once per minute per VPU).\n\n\u2022 ASD3, with information on the RVS resolution changes, generated every time that a bright-enough star is observed in an RVS CCD. Note that very early in the mission it was decided to use always the high-resolution acquisition mode in those CCDs, and thus these packets are not available for most of the mission.\n\n\u2022 ASD4, with statistical information and counters on some on-board events, generated periodically (once every number of seconds).\n\n\u2022 ASD5, with the times when the artificial Charge Injections (CI) have been applied on the CCDs, generated at a quite regular pace (once every number of seconds).\n\n\u2022 ASD6, with the information on the gates activation in the CCDs (to reduce the integration time). These are generated every time that a bright-enough star (about $G<$12) is observed in a CCD.\n\n\u2022 Finally, ASD7, with information (time and position) when any SP1, SP2 or SP3 measurement was acquired by any VPU. Therefore, these ASD7 packets are generated for each source transit (although an ASD7 packet actually contains information on a set of transits).\n\n### Contents\n\nThe following are the specific contents of each of the raw telemetry packets down-linked by Gaia:\n\n\u2022 SP1: These are the most important data packets. One SP1 packet contains the SM, AF, BP and RP samples from one source transit over the focal plane. Only small \u2018windows\u2019 of samples are acquired and transmitted, centred by the VPU algorithms on the astronomical source detected.\n\n\u2022 For SM, windows of 40$\\times$6 samples (each 2$\\times$2 pixels) are sent, thus covering an area of about 4.7$\\times$2.1\u00a0arcsec${}^{2}$.\n\n\u2022 For AF CCDs, the exact shape of the windows depends on the CCD (AF1 to 9) and on the source brightness, but typically, windows of 12$\\times$12 pixels are sent (with the AC pixels binned into one single sample, thus providing only 12 samples in the AL or scanning direction). Bright stars ($G<$16) are acquired with slightly larger windows (18$\\times$12 pixels), with the brightest sources ($G<$13) being acquired in full 2D resolution. Thus, AF windows typically cover about 700$\\times$2100\u00a0mas${}^{2}$ (raising to about 1$\\times$2.1\u00a0arcsec${}^{2}$ for bright sources).\n\n\u2022 Finally, BP and RP windows cover 60$\\times$12 pixels, with 2D resolution only for the brightest sources ($G<$11).\n\n\u2022 Besides the raw samples, these packets also include the time, FOV, CCD Row and AC pixel where the source was detected (all based on the AF1 CCD), an on-board estimated magnitude, and information about the exact sampling scheme used \u2014 including information on possible window overlaps with (or by) another source.\n\n\u2022 SP2: These packets also include the basic detection and measurement information as SP1 packets, but the only sample data included is from the RVS CCDs. Three windows are included (for each of the 3 along-scan RVS CCDs used for a spectroscopic transit), each covering a large area of 1296$\\times$10 pixels (about 76.4$\\times$1.8\u00a0arcsec${}^{2}$). Full 2D resolution is only used for the brightest stars.\n\n\u2022 SP3: These packets are complementary to SP1 packets for Suspected Moving Objects (objects for which the VPU has detected an AC motion from SM to AF1). Here, only basic detection information is included (as in SP2), and the only sample data is that from additional BP and RP windows placed on top (or bottom) of the nominal BP\/RP windows already included in the associated SP1 packet.\n\n\u2022 SP5: WFS data packets include windows of about 682$\\times$120 pixels plus timing and position information.\n\n\u2022 SP6, SP7, SP8 and SP9 packets are non-nominal. They include, besides timing, position and measurement information, windows of SM and AF samples (SP6 and SP7), AF1 samples (SP8) or SM samples (SP9).\n\n\u2022 ASD1: Each of these packets includes, besides a reference time and the CCD row number, the across-scan (AC) shift in pixels with respect to the AF1 reference coordinate for each of the CCDs (except AF1) and for each field of view, indicated in pixels. Thus, combining the adequate ASD1 packet with an SP1 (or SP2 or SP3) packet one can determine the absolute AC position where each window was acquired.\n\n\u2022 ASD2: Each ASD2 packet contains a \u2018burst\u2019 of pre-scan samples acquired on a given CCD. Thus, these contain a CCD identifier, a reference time, and a set of typically 1024 samples.\n\n\u2022 ASD3: These contain a reference time and CCD identifier, plus the resolution switch type (low-to-high or high-to-low).\n\n\u2022 ASD4: There are two variants of these packets, both containing a large set of on-board counters (per VPU), such as the number of detected, confirmed and allocated objects (that is, transits of astronomical sources) for the different types of windows and per field of view, or the number of packets generated of each SP\/ASD type.\n\n\u2022 ASD5: Each of these packets holds a number of times when a charge injection was generated (w.r.t. a packet reference time) for a given CCD. One of these packets can cover a few seconds (up to some 1\u20132 minutes, depending on the configuration).\n\n\u2022 ASD6: Each ASD6 packet indicates the gate configuration that was active for a given CCD at a given time. Thus, a new ASD6 packet is generated every time that a gated window (a window acquired with a shorter integration time, for a bright source) is started or finished. Note that it means that a given bright star, causing the activation of some gate, will also affect other sources being observed on the same CCD at and immediately around that time.\n\n\u2022 ASD7: Finally, each ASD7 (or object log) packet contains a reference time plus a set of up to 3071 entries, each corresponding to one SP1, SP2 or SP3 packet allocated on board for the measurement of a source transit. Each of such entries indicates the detection features (time, coordinate, FOV, acquisition mode, etc.) and the brightness of the source.\n\nIt is worth noting that, besides the raw data from the spacecraft in itself, other ancillary data is also needed when performing the raw measurements reconstruction. Such data is stored in the so-called Calibration DataBase (CDB), which contains, for example, the Along-scan Phasing Table (ALPT) from which, when combined with an AF1 detection time, we can determine the absolute measurement times for each of the windows in an SP1, SP2 or SP3 packet. Several other tables are also needed from the CDB, such as those that indicate the exact configuration for the Gates, Charge Injections, etc. Needless to say, the CDB must be perfectly synchronised with the actual configuration active on board Gaia.\n\n### Usage in Gaia processing\n\nAll the raw science telemetry data previously described is only used in the very first pre-processing stages of the Gaia DPAC \u2014 mainly in the Initial Data Treatment system (IDT) (see Section\u00a02.4.2). Such a system takes care of combining all these data packets to generate self-consistent measurement records, which become the basic input data to further downstream systems \u2014 be these for astrometric, photometric or spectroscopic processing. For more details see Section\u00a02.4.3.\n\n## 2.2.3 The Initial Gaia Source List (IGSL)\n\nAuthor(s): Ricky Smart\n\n### Construction\n\nThe Initial Gaia Source List (IGSL) was commissioned by the Gaia Data Processing and Analysis Consortium (DPAC) in 2006 to be a combination of the best optical astrometry and photometry information on celestial objects available at the Gaia launch: A snapshot of the sky as we know it before Gaia. The method adopted was to crossmatch large-area star catalogues into one database, then select the best parameters based on the typical precisions for each contributing catalogue. The 3rd delivery of the IGSL was made in late 2012, and it was at that point frozen to be fully integrated into the MDB before launch.\n\nThe formal DPAC mandate for the IGSL was to fulfil the following broad requirements: provide all-sky positions, proper motions, and magnitudes for objects to a limit of Gaia magnitude $G$=21 where possible, e.g., where there are large ($>$10\u2009000 square degrees) catalogues that reach that limit. The proper motions and magnitudes are to be provided on a best-effort basis, nominally with precisions of 10\u2009mas\u2009yr${}^{-1}$and 0.3 magnitudes, respectively, but obviously limited by the currently available large catalogues. The DPAC Core Processing Coordination Unit (CU3) catalogues of quasi-stellar objects (QSOs) and the Ecliptic Poles catalogue should be included (with no selection on magnitudes) to directly support the CU3 processes that require those resources. The Hipparcos objects were included with no selection on magnitudes to aid in the production of the Hundred Thousand Proper Motions Catalogue (de Bruijne and Eilers 2012; Michalik et al. 2014).\n\nThe format and contents of the IGSL are described in Smart and Nicastro (2014). After extensive use within the mission a number of problems were discovered. Such known problems are collected and made available in the documentation on the IGSL webpage.\n\n### Contents\n\nThe contents of the IGSL are a compilation of the following catalogues:\n\n\u2022 GSC2.3 \u2014 The Second Guide Star catalogue version 2.3 (Lasker et al. 2008);\n\n\u2022 Tycho-2 \u2014 (H\u00f8g et al. 2000);\n\n\u2022 UCAC4 \u2014 USNO CCD Astrograph catalogue version 4 (Zacharias et al. 2013);\n\n\u2022 2MASS \u2014 Two Micron All-Sky Survey Point Source catalogue (Skrutskie et al. 2006);\n\n\u2022 PPMXL \u2014 Positions and Proper Motions \u2018Extra Large\u2019 catalogue (Roeser et al. 2010);\n\n\u2022 LQRF \u2014 The CU3 early version of Large Quasar Reference Frame (Andrei et al. 2009);\n\n\u2022 OGLE \u2014 Optical Gravitational Lensing Experiment version III (Udalski et al. 2008a);\n\n\u2022 Hipparcos Perryman et al. (1997); van Leeuwen and Fantino (2005); van Leeuwen (2007);\n\n\u2022 Sky2000 the SKYMAP Master catalogue of bright stars, Version 4 (Myers et al. 2001);\n\n\u2022 SPSS the Gaia spectrophotometric standard star catalogue (Pancino et al. 2012).\n\nFor details see Smart and Nicastro (2014).\n\n### Usage in Gaia processing\n\nThe IGSL was and is being used for the initial (partly preliminary) assignment of individual Gaia observations to known astronomical objects in the sky (not including solar-system objects). The process doing this assignment is called crossmatch (or sometimes crossmatching) in the Gaia jargon.\n\nAlthough Gaia in the end will create a completely independent and self-contained all-sky inventory of astronomical objects \u2014 not relying on any pre-launch knowledge \u2014 it was deemed useful to have such an initial list, for two main reasons:\n\n\u2022 An assignment to known celestial objects is needed internally for the initial calibration and verification of the spacecraft and instruments.\n\n\u2022 Giving pre-defined Gaia source identifiers to known celestial sources (and publishing these in the form of the IGSL) will allow the members of the external scientific community to prepare specific object lists and auxiliary data for specific research topics \u2014 and then easily identify these objects in the Gaia catalogue by just using those pre-known \u2019names\u2019 (source identifiers).\n\n### Known issues with the IGSL\n\nThe IGSL was first delivered in 2007 and two other versions were delivered before the frozen version in 9\/2013. Subsequent use has revealed a number of problems. Most would be relatively simple to fix but there was no provision made for updating the IGSL hence all downstream Gaia processing had to deal with these problems and we collect the known issues here to have them in a central location.\n\n#### Duplicate entries\n\nDuplicate Hipparcos\/Tycho-2 entries: The Hipparcos catalogue was not one of the defining catalogues for the IGSL but after the catalogue was made there was a request to make sure all the Hipparcos stars were nevertheless included. Those that were not included as part of the other catalogues were added in patch as a \u2019fake\u2019 Tycho-2 star with the Tycho-2 ID = 9999999000000+HIP_Number. Subsequent work has shown that because of a bug in the matching procedures approximately 12000 Hipparcos stars were entered twice. These can be identified as the objects with auxHIP = 1 and idTYCHO $>$ 9999999000000. They should not be used for any purpose.\n\n#### RA or Dec values are out of range\n\nFor the GSC23 and SDSS objects when there is a proper motion from the PPMXL it was applied to bring the positions from the epoch of observation to 2000. These new positions were not normalised to be within normal RA\/Dec ranges and 34 have remained outside the nominal range. They should be normalised.\n\n#### Classification problems\n\nThe 197921 non-stars in the GEPC were classified as 3 or 27 rather than 1 as in other catalogues. The classification of a star is correctly listed as 0.\n\nThe 167055567 SDSS objects have their classification inverted, that is stars are classed as 1 and non-stars as 0 or -1.\n\nWhen the sourceClassification is 0 it is because none of the catalogues with that object provided a Classification which should be set to null.\n\n#### Ecliptic coordinate errors (thanks to S.\u00a0Roser)\n\nThe ecliptic coordinates were calculated with a 1950B rather than J2000 transformation.\n\n#### Proper motion null values\n\nThe null value for proper motions are not consistent as they are derived from the null values in the original catalogues. Objects with proper motions and errors of 0 or \u2019null\u2019 can be considered not provided with two exceptions: QSOs in the LQRF which is a defaulted value and UCAC objects where the null errors are set to zero but the proper motions maybe real.\n\n#### HEALPix in name\n\nFor $\\sim$30000 entries from the GSC23 the name (sourceID) which is made up of the 12th level HEALPix of the first instance and the running number in the 6th level HEALPix has sometimes the incorrect 12th level HEALPix. As a name they are still valid but generally the user is encouraged not to use the HEALPix part of the sourceID as an indication of the position in the sky.\n\n#### General magnitude transformations\n\nThe calculation of magnitudes from the transformations sometimes gives unreasonable numbers because of problems with the input catalogue or working outside the range of the transformations.\n\nSome examples:\n\n\u2022 IGSL sourceid = 2641188455049732224 has a bright $G$ but it is not real but due to noise in the SDSS that has a large g$-$r (SDSS ID 1237656906352361542) and so this makes the $G$ bright.\n\n\u2022 IGSL sourceid = 1339762992985816960 has a magBJ = 27.5297, magRF = 13.35 and gives $G$ = 17.713, all magnitudes are unrealistic. The B is a transform from the SDSS so the problem is probably in the SDSS original data.\n\n\u2022 IGSL sourceid = 5283973366647424768 has a $G$ = 7.6 but no bright source is present. The magnitudes come from the PPMXL and has ${\\rm m_{B}}=18.8$ and ${\\rm m_{R}}=13.0$ transforming to G the error is very large.\n\nApproximately 80% of the $G$ estimates come from transforms of R, B and the distribution in B$-$R for the IGSL is given in Table\u00a02.1\n\nMost objects outside of B$-$R = -1 to 4 are probably unreal and the transformation is only good from -1 to 2.5 so around 20% probably have large errors.\n\nVery wrong $G$\/$G_{\\rm RVS}$looking at 88000 HIP stars $\\sim$5% of them have very wrong $G_{\\rm RVS}$. A limit bad case HIP-112306 that has in IGSL $G_{\\rm RVS}$= -0.885 and G = 5.57 and in literature V = 10.89 I = 8.44 or HIP-114598 that has $G_{\\rm RVS}$= 20.11 and G = 16.299 and in literature V = 8.1 and I = 8.12. The error in IGSL (of $\\sim$0.5) are not indicative of these errors. Again this is due to transformation or input errors.\n\nFinally, all objects from the HIP, SPSS, SKY2000, LQRF and GEPC catalogues were included even if the magnitude information was incomplete. So for example if these objects had OGLE\/Tycho-2 magnitudes the relations 10, 13, 16 and 17 are only valid to B$-$V or BT$-$VT of 2.5 so objects outside that were not assigned $R_{F}$ & $B_{J}$ magnitudes and included nevertheless.\n\n#### Magnitude errors\n\nNo check was made on the magnitude errors in the IGSL and they are usually just a simple function of the input catalogue errors, so if the inputs were high so the IGSL ones will be high. So for example the IGSL object 9698311034780416 has an unrealistic error in $R_{F}$:\n\n RAJ2000 DEJ2000 ${\\rm magB_{J}}$ emag ${\\rm magR_{F}}$ emag 051.794675 +06.859480 19.720 0.450 24.160 27.506\n\nthat comes directly from the SDSS the source of the magnitude:\n\n ra dec g r err_g err_r 51.794674912 6.859479824 19.90372 24.14491 0.4029701 27.50531\n\nfor SDSS id = 1237673328683844256.\n\nThe Tycho-2 catalogue sometimes did not include the blue or red magnitudes and they were taken from Hipparcos, unfortunately in these cases the errors were not updated and they have remained zero as published in Tycho-2.\n\n#### Position errors\n\nNo check was made on the error of the positions, if the catalogue provides 0 or a number that is less than 0.5 mas rounds to 0 when stored in mas then it\u2019s error is listed as 0. An example from the Gaia EPC catalogue, described in Section\u00a02.2.4, is the object GEPCJ055642.10-665127.5:\n\n # Cat_name RA HH MM SS.SSSS error DEC sDD MM SS.SSS error GEPCJ055642.10 -665127.5 5 56 42.0998 0.0176 -66 51 27.451 0.0\n\nthis also happened a lot in the SDSS where a number of objects had errors less than 0.5 mas and these got rounded to 0.\n\n#### GRVS magnitudes\n\nFor the objects with GRVS magnitudes coming from Tycho-2, e.g. sourceGrvs = 29, there is an error in the equation of the GRVS, we used:\n\n ${\\rm GRVS}={\\rm VT}-.1313-1.3422({\\rm BT}-{\\rm VT})-0.09316({\\rm BT}-{\\rm VT})% ^{2}-0.0663({\\rm BT}-{\\rm VT})^{3}$ (2.1)\n\nwhile it should have been:\n\n ${\\rm GRVS}={\\rm VT}-.1313-1.3422({\\rm BT}-{\\rm VT})-0.07918({\\rm BT}-{\\rm VT})% ^{2}-0.04790({\\rm BT}-{\\rm VT})^{3}$ (2.2)\n\nFor large colours this becomes a problem at the 1\u20133 magnitude level,\n\n#### OGLE entries\n\nOGLE was considered on average to have better photometry than other catalogues so estimates of the G magnitude were taken from those values. We were provided with the deep catalogues of the OGLE surveys which did not have stars brighter than around 13. This means that when a faint OGLE star was matched to a bright input, because the OGLE magnitudes override others, these objects were sometimes dropped or assigned under estimated magnitudes. For example the 13th magnitude star at 91.9967388, -70.9623672 in the UCAC catalogue was matched to a faint nearby star in the OGLE deep catalogues and assigned a G fainter than 21 so was dropped. This occurred in the 5 OGLE regions which are small parts of the sky (a few square degrees in total). How many stars in this region that were mistakenly removed is not easy to estimate.\n\n#### Altitude star catalogue II\n\nAs this catalogue was made in a significantly different way the object sourceIds were not consistent. We matched the ASC II to the IGSL source database to try and obtain consistent sourceIds but there will be cases of mismatches as they are fundamentally two different catalogues. In particular we did not use the SDSS in the production of the ASC so the magnitudes are often based on different source catalogues.\n\n#### High proper motion objects\n\nAny objects with proper motions higher than 3276.7 \u2009mas\u2009yr${}^{-1}$ that were taken from the UCAC catalogue had their proper motions put to 3276.7, 3276.7 due to a bug in the read program. For the IGSL this occurred for the 17 sources where their proper motions should have been those listed in Table\u00a02.2.\n\n## 2.2.4 The Gaia Ecliptic Poles Catalogue (GEPC)\n\nAuthor(s): Martin Altmann, Uli Bastian\n\nThe Gaia Ecliptic Poles Catalogue (GEPC, formerly known as EPC (Ecliptic Poles Catalogue) was assembled primarily to utilise the two Ecliptic Poles fields (SEP: 06:00:00 $-$66:33:41, NEP: 18:00:00 +66:33:41, see Figure\u00a02.1) which are scanned by Gaia twice every rotation (once with each field of view) when the satellite operates in EPSL (Ecliptic Poles Scan Law) mode, which mainly happened during the commissioning time. These frequent observations yield data with a density which would only be reached for other parts of the sky after significantly more time, therefore allowing to evaluate the Gaia performance in a much more realistic way than with other methods. While the fields are located at similar Galactic latitudes, the makeup of both fields is very different, since the southern field is dominated by LMC field stars at fainter magnitudes (it lies in the outskirts of the LMC). The northern field is a normal low-density star field at high galactic latitude. This difference allows to analyse the properties of Gaia under two very distinct stellar environments.\n\n### Construction\n\nThe GEPC consists of two $\\simeq$1\u00a0square degrees fields centred on the ecliptic poles themselves.\n\nThe southern field, or SEP-field, was observed with the MPIA 2.2\u00a0m telescope at La Silla in Chile and its WFI detector, which covers $\\simeq 0.5$${}^{\\circ}$$\\times 0.5$${}^{\\circ}$. To fully cover the 1\u00a0square degree field as required, observations were done using 5 pointings, one centred on the pole and the other four being tiled so that they fill $\\simeq 60$${}^{\\prime}$$\\times 60$${}^{\\prime}$with some degrees of overlap between them. Observations were done in Bessel $BVRI$ and calibrated to Landolt Standard fields into the Vega magnitude system and then transformed to Gaia magnitudes ($G,G_{\\rm BP},G_{\\rm RP},G_{\\rm RVS}$).\n\nThe limiting magnitude in $V$ and $R$ and thus $G$ is roughly 22.5\u00a0mag. Centred on $G\\simeq$\u00a018.5 there is a peak in the magnitude distribution, see Figure\u00a02.2. This peak is real, it is caused by the LMC\u2019s Red Clump gint stars, which is a very prominent population in this field.\n\nThe northern field was observed with the 3.6\u2009m CFHT located on Mauna Kea (Hawaii, USA) and its MEGACAM detector. As the field of view of this device is already one square degree, observations were carried out without a pointing pattern, only a five-times dithering pattern. Filters used were SDSS $ugri$ in this case, and the $z$\u00a0band was incorporated from Hwang et al. (2007). Our own data was calibrated into the system of Hwang et al. (2007). In contrast to the SEP-field, the photometric zero points are for the $AB$ system, as generally in SDSS-type photometric fields. Again, the photometry is transformed into Gaia magnitudes. Due to the larger telescope the faint limiting magnitude for the NEP-field is about 26 in $g^{\\prime}$ and $r^{\\prime}$ and thus $G$, the limit of completeness being about 24 mag. For some stars the NEP field has proper motions, which were derived using the first epoch material from the POSS, taken from the Minnesota Automated Plate Scanner (MAPS), see Pennington et al. (1993); Cabanela et al. (2003). The plate in question (P72) was taken on August 18, 1952, allowing for a epoch baseline of roughly 56 years.\n\nBoth fields have some gaps, as can be seen in Figure\u00a02.1. In the case of the northern field these gaps are caused by the 5 point dither pattern which is not sufficient to close all gaps in this $4\\times 8$ detector array. Other gaps in the north and also those present in the southern field are due to matching criterion used in assembly. These gaps appear where the gaps between detectors are least covered by the dithering, and objects are partly only on one image of a set of five. In order to prevent too many false positives, which would have been detrimental for the commissioning process of Gaia, objects only on one image were discarded.\n\n#### Data reduction\n\nThis part deals with the data reduction steps from data treatment to photometric calibration.\n\n\u2022 Image reduction and source extraction: The northern field was delivered with the basic de-trending (de-biassing, flat-fielding, etc.) done by the Elixir-pipeline (see e.g. Magnier and Cuillandre (2004)). Further steps including the source extraction was conducted with the Theli program (Schirmer 2013), available here, based on the Astromatix Suite (Bertin et al. 2012), see also here, which includes well-known programs such as Sextractor (Bertin and Arnouts 1996). The final assembly and matching of the extracted catalogues including the calibration to Hwang et al. (2007) was done using TOPCAT, a VO-compatible table calculation and plotting tool or the underlying stilts routines, see Taylor (2005), see here respectively here. Since Theli delivers flux conserving images, the source extraction was done using the sky projected images, with the centre being the nominal coordinates of the NEP-field. This means that in contrast to the southern part, the source coordinates were already in one common plane\/projection and did not need to be transformed further.\n\nThe WFI-data was delivered as raw data including calibration data, and had to be reduced from scratch. Calibration data used, are the usual sets of bias and twilight flat data, as well as sky flats derived from the longer exposed science data. Additionally so called \u2018beta\u2019-images were used to save some of the unfortunately rather frequent \u2018bad columns\u2019. These images were images exposed to different exposures of $\\beta$-radiation which allow the correction of some of the bad columns, namely those which do show a signal response (opposed to those which do not, i.e. dark or hot dead columns). Nonetheless this did not completely work in every case, so some residual columns remain, which leads to the detection of spurious objects along these columns. As a consequence we decided to use harsher rejection methods in the matching process, eliminating the vast majority of such objects, at the cost of missing some others. For the Gaia commissioning, the catalogue is optimised for as few false positives as possible. The reduction of the SEP-data was done using MPIAphot (Meisenheimer, Roeser, priv comm.) a Midas based routine suite developed at the MPIA mainly for reduction of MPIA instruments, such as those on Calar Alto and the 2.2\u00a0m MPI-telescope on ESO\u2019s La Silla observatory, including the WFI detector used here. The photometry was derived from the non sky projected images (The sky projected images made with MPIAphot are not flux conserving), sources were again extracted with Sextractor (Bertin and Arnouts 1996). The extracted sources were then brought into one gnomonic plane centred on the centre of the first image of the central pointing using Midas routines.\n\n\u2022 Stacking and matching: The stacking and matching of individual images was done in a similar fashion for both fields; Therefore this step is described in one part. This process was not done using the actual images, but the extracted sources. After matching and before combining the data, photometric offsets were determined, and an r.m.s. error was derived. One image (usually the first in the sequence) was chosen to be the reference image, and the others were corrected for the offset to match the reference. Then the stacking of the images was done the following order and the standard deviations of magnitudes and gnomonic coordinates $\\Xi,\\eta$ were derived for error determination, and Equation\u00a02.10. The optimum matching radius was determined to be 0.6\u2009${}^{\\prime\\prime}$\u00a0for both fields. This is not surprising since the average seeing was 1\u2009${}^{\\prime\\prime}$\u00a0in both cases. For the next steps after the first match (where applicable) the errors were calculated by error propagation:\n\n1. (a)\n\nall images of one exposure time and one pass band (and one pointing in the case of the south).\n\n2. (b)\n\nall results from step 1 for all pointings (only for the south, since the north only has one pointing)\n\n3. (c)\n\nall results from step 1 (north) or step 2 (south) from one pass band\n\n4. (d)\n\nall pass bands were matched (not stacked, of course)\n\n\u2022 Photometric calibration: Please note that the two regions use different filter systems, the South, Johnson\u2013Cousins\u2013Bessel (JCB), and the North Sloan filters. These are similar but have distinct differences. Sloan does not have a $B$-band and JCB does not have $z$. The Sloan $g$ band is actually roughly speaking a combined $B+V$ JCB filter. The current version GEPC3.0 has $BVRI$ in the SEP-field and $u^{*}g^{\\prime}r^{\\prime}i^{\\prime}z^{\\prime}$ in the north, the $z$ is not our own data but taken from (Hwang et al. 2007). Please also note that the northern field is calibrated into the $AB$-system, and the southern field into the Vega-system. The reason for this is that those are the customary photometric zero point systems for each of these filter systems and moreover the relations are calculated this way.\n\nFor the northern field, we calibrated our photometry to that of (Hwang et al. 2007), since we had this data set at our disposal which also happened to be observed with the same instrument than our data. The conversion to G-mag was done using the $g,r$-bands and the latest version of the conversion functions. The data for the southern field contains four colour BVRI photometry calibrated to the Landolt secondary standard system. The filters used are Johnson\u2013Cousins resp. Bessel filters, available for the WFI instrument. Since all filters deviate a little from the original, and filter throughput are changed in time by oxidation and other degrading effects, there will always be small residual systematic effects, most of which can be dealt with during calibration, some however will remain.\n\nFor this release, individual photometric errors have been derived. These reflect the internal errors only, there are more uncertainties introduced by calibration and various effects, such as filter degradation and others. The true photometric error will thus be larger than the errors listed.\n\nBecause of the lack of suited calibration data in the data set on which the GEPC1.x was based on, it only has a rough photometric calibration based on the position of the LMC Red Clump. This has been changed in this version, the photometry is now calibrated to the Landolt secondary standards. The standard field used for the photometric calibration were T\u2013PHE, PG0231+051, SA95\u201342, and RU\u2013149. The magnitudes are of Vega type (rather than AB). For the northern part, the SDSS type magnitudes are AB by definition.\n\nThe calibration coefficients for the southern field are given in Table\u00a02.3\n\nThe calibration was conducted using the following calibration equations:\n\n $\\displaystyle(B-V)_{\\rm cal}=\\frac{(B-V)_{\\rm inst}-(B1-V1)-B2\\cdot AM_{B}+V2% \\cdot AM_{V}}{1+(B3-V3)}$ (2.3) $\\displaystyle B_{\\rm cal}=B_{\\rm inst}-B1-B2\\cdot AM_{B}-B3\\cdot(B-V)_{\\rm cal}$ (2.4) $\\displaystyle V_{\\rm cal}=V_{\\rm inst}-V1-V2\\cdot AM_{V}-V3\\cdot(B-V)_{\\rm cal}$ (2.5) $\\displaystyle(V-R)_{\\rm cal}=\\frac{(V-R)_{\\rm inst}-(V1-R1)-V2\\cdot AM_{V}+R2% \\cdot AM_{R}}{1-R3}$ (2.6) $\\displaystyle R_{\\rm cal}=R_{\\rm inst}-R1-R2\\cdot AM_{R}-R3\\cdot(V-R)_{\\rm cal}$ (2.7) $\\displaystyle(V-I)_{\\rm cal}=\\frac{(V-I)_{\\rm inst}-(V1-I1)-V2\\cdot AM_{V}+I2% \\cdot AM_{I}}{1-I3}$ (2.8) $\\displaystyle I_{\\rm cal}=I_{\\rm inst}-I1-I2\\cdot AM_{I}-I3\\cdot(V-I)_{\\rm cal}$ (2.9)\n\nThe following numbers show the zero point shifting between the data and the calibration images, and the measurements of the latter with Sextractor and PHOT (from the daophot package). The according errors show the shift errors and are almost negligible.\n\nShift within calibration images between sextractor and PHOT (instr, $mag_{\\rm sex}-mag_{\\rm phot}$):\n$B$: $-0.674$ ($\\sigma$=0.029, $\\Delta$=0.0017), 275 stars $V$: $-0.029$ ($\\sigma$=0.018, $\\Delta$=0.0013), 179 stars $R$: $-0.016$ ($\\sigma$=0.015, $\\Delta$=0.0008), 331 stars $I$: $+0.226$ ($\\sigma$=0.013, $\\Delta$=0.0008), 276 stars\n\nShift between calibration images (sextr) and data zero level (instr $mag_{\\rm corr}-mag_{\\rm sex}$):\n$B$: -0.050 ($\\sigma$=0.016, $\\Delta$=0.0009), 299 stars $V$: -0.038 ($\\sigma$=0.017, $\\Delta$=0.0008), 476 stars $R$: -0.148 ($\\sigma$=0.032, $\\Delta$=0.0014), 481 stars $I$: -0.136 ($\\sigma$=0.019, $\\Delta$=0.0011), 279 stars\n\nTotal shift between data zero level and aperture photometry:\n$B$: $-0.724$, ($\\Delta$=0.0019) $V$: $-0.067$, ($\\Delta$=0.0015) $R$: $-0.164$, ($\\Delta$=0.0016) $I$: $+0.090$, ($\\Delta$=0.0014)\n\nSince the northern part could be calibrated by differential photometry using data from Hwang et al. (2007) meaning only a magnitude shift was applied, we do not give the details here, since they are irrelevant.\n\nThe magnitude errors are computed by deriving the scatter and then the errors of the single values for each star. The according standard equation is:\n\n $dMag=\\sqrt{\\frac{1}{n}}\\cdot\\sigma_{Mag}=\\sqrt{\\frac{1}{n(n-1)}}\\sqrt{\\sum_{i=% 1}^{n}(\\overline{Mag}-Mag_{i})}$ (2.10)\n\nwith $n$ being the number of detections and $\\sigma_{Mag}$ the standard deviation. When combining data of different exposure Equation\u00a02.10 was carried out for every set separately and the error of the combined data was derived by error propagation.\n\nA note of caution: Stars with only one or two detections will have an error of zero, or a quite unrealistic one. Some (a few) objects have a RMS error much larger than others of comparable magnitude. In most cases this hints at variability, taking into account that most of the data were not observed on the same day, and in some cases a year lie between different parts of a dither series, etc.\n\nThe photometry errors given in the catalogue are internal RMS errors only. They do not include other systematic sources of error, such as calibration errors, photometry errors of non-point sources, brightness\/colour related errors, etc. At least in the southern field, zonal errors, which may be caused by non-prefect flat fielding are partly taken into account due to the 5 point pointing pattern. As a conservative assumption a systematic accuracy of 0.1\u00a0mag is mandated.\n\n\u2022 Astrometry: The astrometry was improved, so that systematic astrometric inaccuracies, as present in GEPC1.x have been corrected. Analysis shows no detectable mid frequency systematics to our precision scale. Accuracy is now mainly limited by the underlying reference catalogue, which for the GEPC2\/3 is the PPMXL (Roeser et al. 2010), while the earlier versions are based on the UCAC 2 catalogue (Zacharias et al. 2004). While the PPMXL is newer, the reference catalogue was not expected to have a large influence on the astrometry. However our experience shows that this is indeed the case. First of all, all available reference catalogues do have systematic differences, as is explained later in this text. Apparently not only the accuracy (i.e. systematic) effects, but also the precision plays a role and can lead to systematic effects in the reduced data. The reason for this is at current only partially understood, however most of the stars in the EPC field which are also in the reference catalogues, are in the faint part of the latter, consequently with a large error range, which will lead to \u2018sloppy\u2019 fits.\n\nThe registration and astrometric solution was done for each chip and each frame separately using the PPMXL as a reference and using 3rd order polynomials. An iterative method was used clipping 3-sigma outliers after the first round. The final positions were obtained using all of the good positional data, from all filters. This way we could ensure that every star has a valid position. We could not detect any sign of DCR. However since especially the U-band is prone to DCR, an alternative assembly of the final values might be considered in a future minor release.\n\nFor the NEP, we also excluded the long $i$-band images, since these produced large problems in the astrometry. For proper motions, we also added scans taken from the Minnesota Automated Plate Scanner (MAPS) Catalogue of POSS I. The MAPS database is supported by the University of Minnesota, available here. Pennington et al. 1993; Cabanela et al. 2003, See of the relevant POSS I-plate (P72, taken 18. August 1952), in order to get a longer baseline, than the two years for which we have baselines. In order to also include high proper motions stars, we chose a large matching radius of 5\u2009${}^{\\prime\\prime}$. In the current version we do not give errors for the proper motions, the according columns are thus completely filled. The scatter of the proper motions of the NEP field shows a sigma of about 10\u2009mas\u2009yr${}^{-1}$. This may well serve as an upper limit for the overall precision of the proper motions, since this value includes the proper motion and the positional error.\n\nConcerning the astrometric precision, the error given for in the relevant columns for right ascension and declination reflect the RMS error only, i.e. the scatter between the positions of all positions used to compile the position. The overall derivation of these errors is similar to those of the photometry, see Equation\u00a02.10. As in the case of most small field astrometry, we used a reference catalogue, which itself contains systematic errors to some degrees. These are not reflected in the errors as given in the EPC. One can presume zonal medium scale errors of about 50\u2013100\u00a0mas. As an example, the PPMXL and 2MASS catalogues (which build up partially on the same data!) show a residual slope against each other of up to 50\u00a0mas. Therefore the absolute astrometric positional accuracy cannot be better than this value. For proper motions, using the same reference catalogue for all epochs largely cancels out the systematic error introduced by the reference CATALOGUES. For the NEP-field, which currently has proper motions, these show a sigma of about 10\u2009mas\u2009yr${}^{-1}$. This may well serve as an upper limit for the overall precision of the proper motions, since this value includes the proper motion and the positional error.\n\nIt should also be noted that neither the instruments used, i.e. mosaic detectors nor the available software are optimised for high precision astrometry, since they have largely been conceived and developed for extra galactic work, where the demands are much lower. Therefore some areas with additional systematics will exist, especially near chip edges, dither gaps etc.\n\n\u2022 Stellarity: Another quantity added to the GEPC is also the stellarity index also known as CLASS-parameter (Bertin and Arnouts 1996). This is created during the source extraction from the 2d images using SExtractor. It is a measure for the \u2018stellarity\u2019 of an object, i.e. how star like it is. The stellarity index relies on a combined analysis of the measured morphological parameters, also employing neural networks. Values near 1 mean that it is very likely that this object is a point source like a star (it could of course also be the stellar nucleus of an AGN, etc., the stellarity index doesn\u2019t say anything about the physical nature of an object). In reality one could consider all values below about 0.3 to be galaxies, i.e. non point source-like objects. $S>$\u00a00.85 is a good lower limit for stars. At bright magnitudes, i.e. significantly above the detection limit, this classification works quite well, both object types are well separated, however about 2\u00a0mag above the detection limit it starts to break down, and soon the objects will not be classified correctly. This magnitude regime is also where most of the values between 0.3 and 0.85 occur. For saturated objects CLASS is also to be used with caution.\n\nThe northern field has a larger pixel scale than most other detectors, i.e. less angle per pixel. The neural networks on which the determination of the CLASS parameter of Sextractor is based are optimised for a FWHM of about 3 pixels. This means that the more the data deviates from this value, the less reliable the resulting CLASS value will be. This is not a linear process, but rather happens more or less suddenly \u2014 that it at least in this case already appears in the case of the NEP data is somewhat surprising. The networks can be trained for other FWHM values, however since this parameter was for the GEPC a secondary quantity, we did not embark on this tedious and difficult process.\n\n### Contents\n\nThe GEPC contains positional astrometry (and proper motions for a smaller subset in the NEP-field, see Sect. Section\u00a02.2.4.) and multi-pass-band photometry of 612,946 objects, of these 448,478 are located in the southern field, and 164,468 in the north. This discrepancy is caused by the presence of the LMC in the south, which outweighs the significantly fainter magnitude limit in the north. Note that the photometry has different characteristics in the two fields (filter pass band system, magnitude system), as described in Sect. Section\u00a02.2.4. The Gaia magnitudes however are comparable. The current version is GEPC3.0 which has been incorporated into the IGSL, and with the IGSL into the Main Database. For details of the IGSL, see Section\u00a02.2.3 and Smart and Nicastro (2014).\n\nThe format of GEPC3.0 is given in Table\u00a02.4.\n\n### Usage in Gaia processing\n\nThe EPC was most prominently used in the commissioning phase via the Ecliptic-Poles Scanning Law and the First-Look software system\n\n\u2022 to verify and quantify the efficiency of the on-board star image detection algorithms and Sky Mapper CCDs,\n\n\u2022 to perform initial measurements of the photometric throughput of the telescopes, CCDs and pre-amplifier electronics\n\n\u2022 to adjust the lower threshold of the on-board star image detection algorithms\n\nSince the start of the nominal mission, the first and third of these items are re-checked whenever the scanning law touches the ecliptic poles \u2014 which is quite regularly about once per month for 1\u20132 scans per pole and field of view each \u2014 while the second item is now being covered by a daily comparison of bright-star measurements with independent Tycho-2 magnitudes. All this is part of the daily First-Look data processing.\n\n## 2.2.5 The Attitude Star Catalogue (ASC)\n\nAuthor(s): Ricky Smart\n\nThe Attitude Star Catalogue (ASC) was commissioned by the Gaia Data Processing and Analysis Consortium (DPAC) in 2006 to allow a first reconstruction of the attitude of Gaia. Eventually it will be replaced by a catalogue constructed from the Gaia observations but for at least the first two years a precompiled ground based catalogue was needed. The ASC entries were required to be of a high astrometric precision, isolated from other bright $G>13.7$ objects, and, brighter than the 2D window threshold of the Gaia instrument.\n\nThe first version delivered to the DPAC in September 2013 was simply a subset of the Initial Gaia Source List (IGSL) described in Smart and Nicastro (2014) identified by the parameter toggleASC=1. Early commissioning usage and an examination of the ASC subset revealed a number of repeat entries for the same object and entries that did not meet the isolation requirements. Since the reliability of the ASC was fundamental to the Gaia mission a new re-compilation was requested in January 2014. The new separate ASC was delivered to DPAC in April 2014 and is available from the IGSL website.\n\n### Construction\n\nThe source catalogues used and their order of inclusion were:\n\n\u2022 Hipparcos (Perryman et al. 1997): The photometry from the original Hipparcos Catalogue and the astrometric parameters from the update by van Leeuwen (2007) when published. Initially all entries were included regardless of the known errors, e.g. also for entries that are considered erroneous. Since inclusion in the ASC requires an estimate of the $G$-mag the unreal entries were excluded as part of the cleaning phase.\n\n\u2022 Tycho-2 (H\u00f8g et al. 2000): This catalogue forms the backbone of all the major ground based catalogues currently available. It was made from a combination of the Tycho star mapper observations on the Hipparcos satellite (H\u00f8g et al. 1997), the Astrographic Catalogue and 143 other ground-based catalogues.\n\n\u2022 Sky2000 (Myers et al. 2001): The SKYMAP Star Catalogue System is a list of all stars with either measured Johnson blue or visual magnitudes brighter than 9.0. The version used here had 299167 entries of which 212 were not in the combined Hipparcos + Tycho-2 catalogues. Sky2000 provides positions at 2000, proper motions and a blue and visual magnitude. We assumed the positions to have an error of 100\u00a0mas, the proper motions an error of 10\u2009mas\u2009yr${}^{-1}$, and an error of 0.6 in the ASC magnitudes derived from the Sky2000 values.\n\n\u2022 UCAC4 (Zacharias et al. 2013): The USNO CCD Astrograph Catalogue version 4 is the most precise all-sky astrometric catalogue in the range V=10\u201316 currently available. There are no original standard magnitudes in this catalogue.\n\n\u2022 GSC2.3 (Lasker et al. 2008): The Second Guide Star Catalogue version 2.3 forms the bulk of the photometry and defines the red and blue magnitudes ($B_{J}$ and $R_{F}$) as this is the sky survey with the largest coverage on a precise homogeneous photometric system. The only variation with the public version is that we removed the multiple entries discussed in section 4.2 of Lasker et al. (2008). This was done by insisting that only one entry from any objects with position differences of less than 10\u00a0mas were kept selecting Tycho-2 or Sky2000 over other entries.\n\n\u2022 PPMXL (Roeser et al. 2010): The Positions and Proper Motions \u2018Extra Large\u2019 Catalogue,produced from a combination of the USNO\u2013B (Monet et al. 2003) and the Two Micron Sky Survey point source catalogue (Epchtein et al. 1999). This catalogue was included to provide magnitudes for those entries that did not have them in the previous catalogues.\n\nIn addition any objects in the Washington Double Star catalogue (Mason et al. 2010) or the Tycho Double Star catalogue (Fabricius et al. 2002) were indicated as probable members of a binary system.\n\nThe first version of the ASC was a subset of the IGSL and consequently was derived using the procedure in Smart and Nicastro (2014). In summary we produced a master list of objects starting with the large faint catalogues, progressively adding other catalogues and increasing the master list as entries from new catalogues were unmatched. The catalogues of bright objects were then matched to a large master list which resulted in mismatches of the bright objects to noise or faint objects near the true bright objects. Also it was found that the large Schmidt catalogues in the overlap region between plates often had many multiple entries of the same objects, this can be seen in the sky plot of the PPMXL. These multiple entries, if they were bright enough, were included as ASC sources.\n\nThe first on-ground attitude reconstruction of Gaia is described in detail in Gaia\u00a0DR1 papers. The goal of this attitude reconstruction is to provide the attitude with an accuracy of 50\u00a0mas for the first year when the ASC will be the primary source of reference objects. Later in the mission it is planned to replace this catalogue with one produced by Gaia with an expected accuracy of 5\u00a0mas. This reconstruction requires at least one 2D measurement per second and per field of view which equates into a minimum density of 75 stars per square degree.\n\nTo be automatically assigned a 2D window the star must have a $G<$\u00a013 but this does not provide enough calibration sources especially near the galactic poles. The compromise was to provide a list of faint calibration stars to a $G$=13.4 which sets the limiting magnitude of the ASC. Note that, originally the limit of the ASC was set to $G$=14.0 however a change of the procedure allowed a relaxation of that requirement to $G$=13.4.\n\nThe crossmatching radius in the first on-ground attitude reconstruction will be between 20\u201330\u2009${}^{\\prime\\prime}$, the precise value to be optimized during the commissioning phase. Hence we conservatively require that all ASC sources are isolated at the level of 40\u2009${}^{\\prime\\prime}$. This would potentially allow up to 8000 ASC entries per square degree and not violate the isolation criteria. Following this consideration, in the original subset of the IGSL that constituted the ASC, we just lowered the magnitude limit to reduce the number of stars to less than 1000. We then assumed the isolation criteria would always be met when there were this many objects per square degree. However, because of the multiple entries, uncatalogued binary systems and general non uniform distribution it was found that the isolation requirement of the ASC subset was violated.\n\nTo address the isolation and duplicate entry issues the ASC was reproduced from scratch using the catalogues listed above in the order given. The production of the ASC starts with all objects in the Hipparcos catalogue as a master list, the other catalogues are input and matched to this master list with a matching radius of 5\u2009${}^{\\prime\\prime}$. All entries from the input catalogue not matched are included as new master list objects. If more than one entry from the input catalogue matches the master list only the closest is considered matched and a new entry is generated for the others.\n\nIn this way the master list grows with each included catalogue. Since the first catalogues are composed of bright objects they are sparse and the chances of a mismatch between the input catalogues and the master list was reduced. The confusion at the bright end of the master list was in this way minimized. When the large, dense Schmidt plate based catalogues are included there is still the possibility that non-real entries are matched to bright objects and the real bright object in the GSC23\/PPMXL enter as new entries. However, the Schmidt data is only used to provide photometric information and to clean up the ASC list we drop any objects that are not in either UCAC4, Tycho-2, sky2000 or the Hipparcos catalogues under the assumption that the union of these catalogues are complete to fainter than the Gaia isolation limit of $G$=13.7.\n\nOnce the master list was completed with the compilation of all the catalogues we estimated the red $R_{F}$, blue $B_{J}$, Gaia $G$ and Gaia $G_{RVS}$ using the relations and priorities in Smart and Nicastro (2014) with the photometry from the contributing catalogues. We then dropped any objects fainter than $G$=13.7. This compilation and selection criteria results in 15 million objects. We assume all objects are stellar and then examine each object one-by-one and indicate for each object the number of neighbours within 40\u2009${}^{\\prime\\prime}$.\n\nFrom this list we drop any star with a (i) neighbour, (ii) $G<7.0$ or $G>13.4$ or (iii) in the Washington Double Star or Tycho Double Star catalogues.\n\n### Contents\n\nThe Attitude Star Catalogue was made by combining 7 all sky catalogues and selecting entries based on magnitude, isolation and astrometric precision criteria. The catalogue has 8\u2009173\u2009331 entries with estimates of the positions at 2000, proper motions and magnitudes (Gaia $G$, Gaia $G_{rvs}$, red $R_{F}$ & blue $B_{J}$) in the magnitude range $7.0.\n\n### Usage in Gaia processing\n\nThroughout the commissioning phase and scientific mission of Gaia, the ASC is used as the astrometric reference in the first on-ground attitude reconstruction, OGA1, see Section\u00a02.4.5. At some time the ASC as described above will be replaced by a similar star catalogue derived from Gaia observations, i.e.\u00a0as an excerpt from one of the early Gaia catalogues.","date":"2020-09-21 06:08:00","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 235, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"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\": 0.6113109588623047, \"perplexity\": 2598.1478198027917}, \"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-2020-40\/segments\/1600400198942.13\/warc\/CC-MAIN-20200921050331-20200921080331-00036.warc.gz\"}"}
| null | null |
\section{Introduction}
\label{Sec_Intro}
It is well known that, in biology, rhythmic locomotion is produced by a neural structure called \ac{CPG} \cite{ijspeert2008central}. This structure is located at the spinal cord and it usually comprises of two neural populations which produce an alternating output of spikes. Eventually, these output spikes are used to activate the muscles fibers.
This approach of using \acp{CPG} can be borrowed to create locomotion in robotics. There are several possibilities to implement a \ac{CPG}: using coupled-oscillators, using \acp{ANN} or using \acp{SNN}. The closest biological implementation is to use an \ac{SNN}. These networks are based on neuron models and synaptic connections that implement biological features. The field of research called neuromorphic engineering aims to implement these networks on electronics, mimicking the way living beings have solved complex problems by using both analog and digital circuits. The neuromorphic robotics field puts together both the neuromorphic engineering and the roboticists communities \cite{krichmar2011neuromorphic}. The use of neural structures made of spiking neurons, coming from the neuromorphic engineering field, within robotics results in the need for less resources, less power consumption and a simplification of the algorithms \cite{indiveri2011neuromorphic}.
One of this neural structures is the \ac{CPG}. This structure generates a rhythmic pattern at its output, which can be used within robotics to generate locomotion. Thus, a \ac{CPG} creates gaits that are suitable to use within a robotic platform. These structures can generate a very stable pattern even without sensory information or brain activity \cite{Vogelstein2008}.
As briefly shown, there is a growing community of researchers that are exploring the possibility of using a \ac{CPG} to create locomotion in robots \cite{ijspeert2008central}. Most of the previous works in the literature present an open-loop \ac{CPG} which does not include any sensory information: in \cite{Donati2014}, the actuation of a lamprey-like robot is done by using an open-loop \ac{CPG} and neuromorphic hardware. Then, in \cite{rostro2015cpg} and \cite{Brayan_2017}, the authors proposed a \ac{CPG} implemented on an \ac{FPGA} and the SpiNNaker platform \cite{furber2014spinnaker}; these three works do not offer the possibility of changing the originally produced pattern in real time. However, they showed that implementing \acp{CPG} using spiking neurons uses less power. There is a more recent paper which allows both real time functioning and pattern variation but without including any sensory information \cite{gutierrez2020neuropod}. In \cite{Polykretis2020}, the open-loop \ac{CPG} is implemented on Loihi \cite{davies2018loihi} using an astrocytic network, producing two different gaits with 24 motor neurons.
However, the most recent work \cite{Strohmer2020}, proposes the implementation of a \ac{CPG} with the possibility of changing the amplitude, frequency and phase online without any sensory input required. The authors also pointed out that the architecture should include sensory feedback to modify the behavior of the \ac{CPG}. That is the objective presented in this paper. We propose an \ac{SNN} that, using the sensory information, adapts the behavior of the \ac{CPG}.
Regarding works that include sensory information, in \cite{Sartoretti2018}, the \ac{CPG} is built using coupled-oscillators instead of spiking neurons and the feedback to the \ac{CPG} is included into the control loop of the equations of the \ac{CPG}. In \cite{Spaeth2020}, 12~simulated neurons modulated by sensory feedback are used to build the \ac{CPG}. Instead of what we propose, an adaptation \ac{SNN}, they achieve different gaits by either moving the location or increasing the number of neural structures. The neuron model used is Izhikevich instead of the \ac{LIF} model proposed in this work to reduce the computational resources used. The sensory information is used to adapt the time duration of each phase of the frequency switching to enable the actuators to reach the commanded position. Finally, in \cite{gutierrez2019live}, a neuromorphic sensor has been used to select which predefined gait of the \ac{CPG} should be activated. In most of these works, the use of an external input to the \ac{CPG} changes the performance of it. This performance can be defined as a neuromodulation. It has been shown that this modulation is essential to alter the behavior of a neural structure by modifying the synaptic connections \cite{harris2011neuromodulation}.
Finally, there are works where the main focus is on the learning process of the robotic platform: in \cite{Lele2020}, the authors proposed a rewarding-learning process to teach a hexapod robot how to walk without any previous knowledge. A couple of sensors (a standard camera and a gyroscope) are used to provide the rewarding signal to the neural network based on a \ac{CPG}. Although they used a digital version model neuron of the \ac{LIF}, they do not use neuromorphic hardware to implemented the neural architecture; a Raspberry Pi is used instead. A similar approach based on reinforcement learning, but without using spiking neurons, was proposed to improve the locomotion of the NAO robot \cite{li2013humanoids}.
Another approach is used in \cite{Ting}, where the authors have two hexapod robots: an expert and a student. The student learns or imitates the gait of the expert by using a one-layer feedforward \ac{SNN} and a \ac{DVS} camera as input. However, the possibility for the robot to adapt to its environment is not implemented.
The objective of this paper is to design and deploy a spiking architecture that makes the interaction of a spiking \ac{CPG} with its environment possible. An external agent. i.e. a \ac{FSR}, is introduced as the feedback stimulus to the network. This agent can modify the gait generated by the \ac{CPG}. Therefore, the locomotion of the end robotic platform (any legged robot) can be adapted to the terrain. Furthermore, the spiking network presented in this paper allows the introduction of the feedback sensory information on the loop of the \ac{CPG} to provide adaptation. This adaptation \ac{SNN} could be used with any sensor as stimulus.
The rest of the paper is structured as follows: section~\ref{Sec_Materials} introduces the materials used in this work, including the simulator and hardware used. The implemented methods are described in \ref{Sec_Methods}, together with the \ac{SNN} model. Then, the results obtained are presented and discussed in section~\ref{Sec_Results&Discussion}. This section is divided into two different subsections: first, the experiments run using the software simulator and then, the same experiments run on on the hardware platform. Finally, the conclussions are presented.
\section{Materials and Methods}
\subsection{Materials}
\label{Sec_Materials}
This section describes both the software and hardware used to perform the experiments.
\subsubsection{Brian~2}
\label{subsubsec_brian}
Brian~2 \cite{stimberg2019brian} is a neural simulator for \acp{SNN} written in Python programming language. Thus, it is a cross-platform which is available in different operating systems. In contrast to other \ac{SNN} simulators such as NEURON \cite{carnevale2006neuron} or PyNN \cite{davison2009pynn}, Brian~2 is highly flexible and it is easily adaptable with new non-standard neuron models and synapses. Brian~2 can be used to model and simulate complex problems faced by neuroscientists, as well as giving faster and more robust results before implementing the solution on a hardware platform.
\subsubsection{SpiNNaker}
\label{subsubsec_spinnaker}
SpiNNaker \cite{furber2012overview, furber2014spinnaker, furber2020spinnakerbook} is a massively parallel, multi-core computing system designed by the Advanced Processor Technologies (APT) Research Group from the University of Manchester. It was designed under the \ac{HBP} \cite{markram2012human} for simulating parts of the brain by using \acp{SNN}. SpiNNaker machines consist of SpiNNaker chips, which have eighteen 200-Hz ARM968 processor cores each \cite{painkras2013spinnaker}. This allows an asynchronous communication infrastructure for sending short packages (each of them representing a particular neuron firing) \cite{plana2007gals} identified using \ac{AER} \cite{mahowald1992vlsi}. Different SpiNNaker machines were built and commercialized, including SpiNN-3 and SpiNN-5, with 4 and 48 SpiNNaker chips each, respectively. They also include the spinnlinks \cite{plana2020spinnlink}, which allow real-time input/output interfacing with neuromorphic sensors and other neuromorphic platforms such as \acp{FPGA} \cite{yousefzadeh2017multiple, dominguez2016multilayer, schoepe2019neuromorphic}. A PyNN-based \cite{davison2009pynn} software package called sPyNNaker \cite{rhodes2018spynnaker} can be used to design and implement \acp{SNN} on these machines. The recently built million-core machine is at the School of Computer Science at the University of Manchester that can be used through the \ac{HBP} portal. In this work, a SpiNN-5 machine was used to run the simulations proposed.
\subsection{Methodology}
\label{Sec_Methods}
We simulated our \ac{sCPG} model on a standard computer using the Brian~2 Simulator to characterize the network dynamics, to analyse the number of neurons per population needed and to adjust the network parameters. The simulation results guided the subsequent neuromorphic implementation using the SpiNNaker platform.
\subsubsection{Neuron Model}
\label{subsubsec:neuron_model}
The \ac{LIF} model is used to implement the neuron on both the software simulator and the SpiNNaker hardware platform \cite{gerstner2002}. The model is defined within the equations (\ref{lif_eq_1}) and (\ref{lif_eq_2}).
\begin{equation}
\label{lif_eq_1}
\tau_{m} \frac{dV}{dt} = -(V-V_{r})+RI(t)
\end{equation}
\begin{equation}
\label{lif_eq_2}
if\: V(t) = V_{th}\quad then\quad \lim_{\delta \rightarrow 0; \delta > 0} V(t+\delta) = V_{r}
\end{equation}
where $V$ is the membrane potential of the neuron, $R$ represents the resistance of the membrane, $\tau_m$ the time constant of the neuron, $V_{r}$ the resting potential, $V_{th}$ the threshold and $I(t)$ is the stimulus.
\subsubsection{Network Model}
\label{subsubsec:network_model}
The \ac{SNN} model depicted in Figure~\ref{fig:SNN_architecture} was designed based on the neuron model presented in section~\ref{subsubsec:neuron_model}. The main objective of the proposed model is to generate a constant oscillation between the spikes produced in ensembles~A and~B, whose frequency varies depending on the value read from the \ac{FSR} sensor. Thus, the proposed \ac{CPG} is able to automatically adapt its behavior depending on the input stimulus.
The \ac{SNN} consists of different parts which are described next. It is important to note that each of the ensembles (also called populations) have the same number of neurons. The number of neurons in each population was set based on different experiments, which are presented in section \ref{Sec_Results&Discussion}.
\begin{figure}[h]
\centering\includegraphics[width=0.75\linewidth]{NN_arch.pdf}
\caption{Diagram of the proposed spiking neural network architecture.}
\label{fig:SNN_architecture}
\end{figure}
The main block of the architecture is the so-called $CPG_{AB}$, which consists of the populations~A and~B represented in Figure~\ref{fig:SNN_architecture}. These populations are self-excited and self-inhibited with a probability of 25\% and 75\% and weights of 4~nA and 1.5~nA, respectively. Moreover, a 75\% probability of having inhibitory synapses between neurons from the two aforementioned populations is also present. Thus, when one of the populations is producing spikes, the opposite is inhibited and, thus, generating the desired oscillation pattern. Populations~A and~B are injected with a constant external current in order to start generating the oscillation. Therefore, for these two populations equation~\ref{equation_CPG_AB} is used instead of equation~\ref{lif_eq_1}.
\begin{equation}
\label{equation_CPG_AB}
\frac{dV}{dt} = \frac{Vr-V+R(Iexc-Iinh+Ist)}{\tau_m}
\end{equation}
Where $I_{st}$ is the current injected to neurons in populations~A and~B. This value was set to 2.2~nA, which is sufficient for producing the desired rhythmic pattern.
Furthermore, populations~1 and~2 ($CPG_{12}$) both have the same number of neurons as those in $CPG_{AB}$, and are also interconnected in the same way. The projections between $CPG_{12}$ and $CPG_{AB}$ are depicted in Figure~\ref{fig:SNN_architecture}, and follow the same aforementioned probabilities (25\% for excitatory and 75\% for inhibitory projections). The weights between the different populations of the proposed model are specified in the same figure.
Finally, the reference population ($Ref$) was implemented as a Poisson distribution with variable frequency. In contrast to the populations from $CPG_{AB}$ and $CPG_{12}$, the number of neurons in $Ref$ was set to 50. These neurons are connected to populations~1 and~2 following the scheme presented in Figure ~\ref{fig:SNN_architecture}. This number of neurons was set to 50 since it was the optimum for producing biologically-plausible spiking rates in the population, with maximum and minimum frequencies close to the biological counterpart \cite{tripathy2014neuroelectro}.
The spiking rate of the Poisson distribution depends on the values obtained from the \ac{FSR} sensor used as input to population $Ref$. This sensor should be placed at the end of the leg of the robot. This sensor provides values between 0 and 5~V. Since the spinal cord ventral horn motor neuron alpha, which is the biological neuron taken as reference, has a spike rate between 10 and 171~Hz \cite{tripathy2014neuroelectro}, a linear regression was established in order to match the frequency of the Poisson distribution with the voltage value read from the sensor. Equation~\ref{eq_linearRegression}, where $V_s$ is the voltage value provided by the sensor, shows this relation to provide the desired rates.
\begin{equation}
\label{eq_linearRegression}
f_{Ref}=\frac{280V_s-950}{3}
\end{equation}
\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|}
\hline
\textbf{Parameter} &\textbf{Value} \\ \hline
\textbf{${u_{reset}}$} & -55.0 mV \\ \hline
\textbf{$ {u_{rest}}$} & -55.0 mV \\ \hline
\textbf{${u_{th}}$} & 15.0 mV \\ \hline
\textbf{$ {\tau_{m}}$} & 6.0 ms \\
\hline
\textbf{$ {\tau_{syn_e}}$} & 5.0 ms \\
\hline
\textbf{$ {\tau_{syn_i}}$} & 8.75 ms \\ \hline
\textbf{$ {c_{m}}$} & 0.1875 nF \\ \hline
\textbf{$ {\Delta_{t}}$} & 1.0 ms \\ \hline
\textbf{${I_{bias}}$} & 2.2 mA \\ \hline
\end{tabular}
\end{center}
\caption{\label{Table:NeuParams} Neuron parameters for the proposed \ac{CPG} in both the Brian~2 simulator and the SpiNNaker hardware platform.}
\end{table}
Based on these three blocks ($CPG_{AB}$, $CPG_{12}$ and $Ref$) and the connections between them, the proposed behavior explained at the begining of this section was achieved. Therefore, following Fig.~\ref{fig:SNN_architecture}, different scenarios can be analyzed. In the case where the spike rate of population $Ref$ is greater than the oscillation frequency of $CPG_{AB}$, population~1 will be inhibited and population~2 will be excited. Since population~1 is excited from A, but the number of spikes is lower than the ones that are inhibiting the same population from $Ref$, population 1 will have very low activity. The opposite occurs in population~2, which will be inhibited from B but excited from $Ref$ in a stronger way and, thus, having considerable more activity than population~1. The activity from population~2 will excite $CPG_{AB}$, increasing its oscillation frequency. Conversely, the opposite happens when the spike rate of $Ref$ is lower than the oscillation frequency of $CPG_{AB}$, where population~1 will have more activity than 2 and, therefore, inhibit $CPG_{AB}$ in order to reduce its frequency. As a result, the proposed network is able to adapt the frequency of the \ac{CPG} based on an input stimulus. This model was simulated in Brian~2 and emulated using SpiNNaker, and the results can be seen in section~\ref{Sec_Results&Discussion}.
\section{Results and Discussion}
\label{Sec_Results&Discussion}
\subsection{Brian~2 simulations}
The first experiment was performed to determine the number of neurons per population of the \ac{CPG} that was needed to achieve a stable rate value along the simulations. The parameters used for all the experiments are shown in Table~\ref{Table:NeuParams}. Figure~\ref{fig:IndexPopulations} shows the maximum, minimun and mean values obtained for the rate of the simulations performed. A thousand simulations per number of neurons were run. As the number of neurons increased, the rate achieved is more stable and the standard deviation becomes lower. Starting from 40 neurons per population in the $CPG_{AB}$, the standard deviation is less than 1.5 and the bahavior is more stable. A hundred neurons per population shows the most stable output rate with the least deviation.
\begin{figure}[t]
\centering
\includegraphics[width=.8\textwidth, keepaspectratio]{img/simulaciones.pdf}
\caption{Average, maximum and minimum rate values obtained for each number of neurons per population. The trace shows the mean, and, its shadow, the maximum and minimun rate of all the one thousand simulations performed.}
\label{fig:IndexPopulations}
\end{figure}
Once the number of neurons per population was fixed, to verify if the architecture presented in Section~\ref{Sec_Methods} behaved as expected, the operation of the $CPG_{AB}$ in isolation was analyzed. This experiment ensured that it was able to produce a constant oscillation. Then, the operation of the same \ac{CPG} was examined once interconnected with the $CPG_{12}$, performing tests with different stimuli to analyze the results obtained. Finally, the entire architecture was connected and analyzed in different scenarios based on the external input from the \ac{FSR} sensor.
\subsubsection{$CPG_{AB}$ analysis}
\label{subsubsec:CPGAB}
The topology of the $CPG_{AB}$ can be seen in Figure ~\ref{fig:SNN_architecture}, where green arrows denote excitatory connections and red arrows denote inhibitory connections. As mentioned in section~\ref{subsubsec:network_model}, $I_{St}$ is a constant current injected to all neurons in populations~A and~B, with a fixed value of 2.2~nA.
\begin{figure}[ht]
\centering
\includegraphics[width=\textwidth, keepaspectratio]{img/CPGAB10na.png}
\caption{Simulation of the $CPG_{AB}$ with a $I_{St}$ value of 10~nA. Increased oscillation frequency may be observed along with an increase in the amount of noise when compared to Figure \ref{fig:CPGAB22na}.}
\label{fig:CPGAB10na}
\end{figure}
\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth, keepaspectratio]{img/CPGAB22na.png}
\caption{Simulation of the $CPG_{AB}$ with a $I_{St}$ value of 2.2~nA. A lower oscillation frequency and almost total noise removal can be observed when compared to Figure \ref{fig:CPGAB10na}.}
\label{fig:CPGAB22na}
\end{figure}
This current is the minimum value required to produce the oscillatory pattern in the \ac{CPG}. While the proposed topology can work with higher values of $I_{St}$, this generates a higher frequency of oscillation and a noticeable increase in the noise introduced in the simulation (see figures~\ref{fig:CPGAB10na} and~\ref{fig:CPGAB22na}). Thus, this value was set to 2.2~nA in order to be able to more easily appreciate the effect of feedback on the \ac{CPG}. The results of the simulation performed are shown in Figure~\ref{fig:CPGAB22na}, where a frequency of, approximately, 5.8~Hz was obtained for each population, while the total frequency of the \ac{CPG} was 11.6~Hz.
\begin{figure}[t]
\centering
\includegraphics[width=\textwidth, keepaspectratio]{img/CPGS0-5V.png}
\caption{Results of the simulation of the proposed \ac{SNN} model when having a 5~V input from the \ac{FSR} sensor for 1000~ms between $t=1000 ms$ and $t=2000 ms$ and between $t=3000 ms$ and $t=4000 ms$ (generating a Poisson distribution of 171~Hz in $Ref$). For the rest of the simulation time, the sensor's output was set to 0~V.}
\label{fig:CPGS-0-5V}
\end{figure}
\begin{figure}[ht]
\centering
\includegraphics[width=\textwidth, keepaspectratio]{img/CPGSal1.png}
\caption{Results obtained when simulating random voltage readings from the \ac{FSR} sensor.}
\label{fig:CPGSal1}
\end{figure}
\begin{figure}[ht]
\centering
\includegraphics[width=\textwidth, keepaspectratio]{img/CPGSal2.png}
\caption{Results obtained when simulating a continuous increase in the frequency of $Ref$.}
\label{fig:CPGSal2}
\end{figure}
\subsubsection{Analysis of the effect of the sensor when used as input to the SNN}
In order to study the robustness of the network against sudden changes in the oscillation frequency, an experiment where the values read from the sensor were alternating between maximum and minimum voltage peaks was performed. Initially, a 5~V input was simulated in 1~s and 2~s, both with a duration of 1~s. This made neurons in population $Ref$ to fire at a frequency of, approximately, 171~Hz during this period. Before 1~s, between 2~s and 3~s, and after 4~s the sensor readings corresponded to 0~V. Figure \ref{fig:CPGS-0-5V} shows the results of this simulation. It can be observed that, at time zero, since no information was being received from the sensor, $Ref$ had no activity. Therefore, population 1 was excited by $CPG_{AB}$ and population~2 was inhibited. In turn, population 1 slightly inhibited $CPG_{AB}$. At 1~s, $Ref$ started firing at a frequency of approximately 171~Hz, exciting population~2 and inhibiting population~1. During this period, the former excited $CPG_{AB}$, increasing its oscillation frequency. After 2~s, population~1 started dominating population~2 again, slightly inhibiting $CPG_{AB}$ again. Exactly the same behavior can be seen again starting at 3~s. In this figure it can be observed how the frequency of $CPG_{AB}$ increased considerably between 1~s and 2~s and between 3~s and 4~s, obtaining minimum frequencies of 8~Hz and maximum frequencies of 15~Hz.
Finally, different simulations of more realistic cases were performed. Initially, 10 random voltage values were used in order to simulate different readings from the \ac{FSR} sensor. These values were updated every 500~ms. Specifically, the frequency values for Poisson distribution in $Ref$ were (171, 40, 80, 30, 5, 130, 50, 76, 20, 150)~Hz. In Figure~\ref{fig:CPGSal1} it can be seen how $CPG_{AB}$ adapts its oscillation frequency based on the inputs stimuli, obtaining maximum and minimum frequency peaks of 15~Hz and 8~Hz, respectively.
After this, a constant increase in the values of the readings from the sensor was simulated. In particular, increases in steps of 20~Hz per 500~ms were introduced in the frequency of $Ref$. To check the performance limits of the $CPG_{AB}$, the last injected frequency value exceeded up to 17\% of the maximum theoretical value of 171~Hz. Figure \ref{fig:CPGSal2} shows the results of this experiment.
As can be seen in the figure, although there is a significant increase in the amount of noise, the oscillation frequency of $CPG_{AB}$ does not increase, achieving a maximum frequency of 15~Hz.
\subsection{Running the model on SpiNNaker}
The proposed \ac{sCPG} model was tested in the SpiNNaker neuromorphic hardware. The neuronal model is defined in sPyNNaker \cite{rhodes2018spynnaker}, a PyNN-based software interface that allows a quick prototyping and implementation of spiking neural networks in the SpiNNaker platform.
The spiking neuron model is the \ac{LIF} with fixed threshold and decaying-exponential post-synaptic current, whose parameters are given in table \ref{Table:NeuParams}. These parameters were chosen so as to emulate the neuron dynamics of the simulations in Brian~2.
In order to show that the model achieves a good performance in SpiNNaker, we performed three tests: first, by verifying that the constant oscillations of the $CPG_{AB}$ were observed and matched the rates presented in Brian~2. Then, by implementing the whole \ac{sCPG} with increasing rates of the input sensor represented by the reference population. Finally, by testing the \ac{sCPG} under random stimuli.
\subsubsection{$CPG_{AB}$ implementation}
\begin{figure}[ht]
\centering
\includegraphics[width=0.95\textwidth, keepaspectratio]{img/CPG_AB_spinn.png}
\caption{SpiNNaker simulation of the $CPG_{AB}$.}
\label{fig:CPGAB_spinn}
\end{figure}
\begin{figure}[h!]
\centering
\includegraphics[width=0.95\textwidth, keepaspectratio]{img/CPG_barrido1_spinn.png}
\caption{SpiNNaker simulation of the $CPG$ for extreme values of the stimulus spiking rate (0.1~Hz and 171~Hz).}
\label{fig:CPGAB_barrido1}
\end{figure}
For the implementation of the CPG in Spinnaker (see Figure~\ref{fig:CPGAB_spinn}) 100 neurons were used, each with a constant current $I_{St}$ equal to 2.2~nA, like in the equivalent Brian experiment. The measured rate of the oscillatory pattern of populations~A and~B was 11.62~Hz, which matches the rate measured in the Brian simulation. Although some spikes were lost in the raster plot compared to Brian, which can be attributed to limited support of floating-point calculations in sPyNNaker, the pattern appears consistent and with little noise.
\begin{figure}[t]
\centering
\includegraphics[width=0.95\textwidth, keepaspectratio]{img/CPG_barrido2_spinn.png}
\caption{SpiNNaker simulation of the $CPG$ for ten increasing values of the stimulus rate (from 0~Hz to 50~Hz).}
\label{fig:CPGAB_barrido2}
\end{figure}
\subsubsection{$CPG$ under different stimuli}
The SpiNNaker implementation of the full \ac{CPG}, including the feedback network was tested under different conditions of the stimulus. First, we simulated a sudden change of the value of the sensor, represented by the rate of the Poisson generator in the $Ref$ population (see figure \ref{fig:CPGAB_barrido1}). This rate was set to 0.1~Hz for the first 2 seconds of the simulation and oscillated between 171~Hz and 0.1~Hz for the next four seconds, in order to appreciate both regimes of the \ac{CPG}. It can be seen how, with a low $Pref$ frequency, the first feedback population dominates and the rate of the output oscillatory is low, at around 12.5~Hz. With a high $Pref$ frequency, it is the second feedback population which dominates and the measured oscillatory pattern displays a peak frequency of 27.5~Hz.
\begin{figure}[t]
\centering
\includegraphics[width=0.95\textwidth, keepaspectratio]{img/CPG_random_spinn.png}
\caption{SpiNNaker simulation of the $CPG$ for ten random values of the stimulus rate (from 0~Hz to 50~Hz).}
\label{fig:CPGAB_random}
\end{figure}
Figures \ref{fig:CPGAB_barrido2} and \ref{fig:CPGAB_random} show the spiking response of the SpiNNker \ac{CPG} to increasing rates of $Ref$ and to random values of $Ref$, respectively. The two regimes can be clearly observed in the spiking response of populations~1 and~2 and in the measured oscillatory rates of Populations~A and~B, proving that the feedback mechanism works correctly.
\subsection{Comparison between the results obtained in Brian~2 and SpiNNaker}
Figure~\ref{fig:comparison} shows the comparison made between both approaches: the simulations on Brian~2 and the implementation on the SpiNNaker platform. In this experiment, the same input stimulus from the sensor was used for both approaches, which went from 0~Hz to 180~Hz. The rates generated by both \acp{sCPG} were very similar. In the case of the Brian~2, the operation frequency of the \ac{sCPG} ranged from 9.5~Hz to 14.9~Hz, and from 11.62~Hz to 26.66~Hz in the case of the SpiNNaker platform. The calculated Pearson correlation coefficient between both is 0.905.
\begin{figure}[h!]
\centering
\includegraphics[width=0.8\textwidth, keepaspectratio]{img/comparison.png}
\caption{Comparison of the results obtained in both Brian~2 simulation and SpiNNaker implementation. The plot shows the rate generated by the \ac{sCPG} when the input stimulus (population $Ref$) is changed from 0~Hz to 180~Hz. The blue trace shows Brian~2 results (left y-axis) and the red trace the SpiNNaker results (right y-axis).}
\label{fig:comparison}
\end{figure}
\section{Conclusions}
\label{Sec_Conclusions}
In this paper, we have presented what, to the best of our knowledge is, the first \Acl{sCPG} that incorporates a feedback in the loop to modify the locomotion frequencies of a legged robot through an adaptive learning mechanism. The feedback was provided by a \ac{FSR} (but any sensor might be used) to simulate the force exerted on each limb of a future robot. With the use of this sensor, we injected different stimuli to the \ac{sCPG}. Firstly, we performed some tests to find the optimal (minimum) input value, where the feedback effect could be easily observed. Then, some tests were performed to observe the effect in the oscillation frequencies under different stimuli. Finally, we carried out some experiments where the values read from the sensor were alternating between maximum and minimum voltage peaks in order to study the robustness of the \ac{sCPG} against sudden changes in the oscillation frequency. From these experiments, we conclude that our \ac{sCPG} presents a robust behavior in the adaptability of the oscillation frequencies. These frequencies can be used further in the generation of locomotion gaits for legged robots with the advantage that they can be modified depending on the terrain conditions.
The implementation of the \ac{sCPG} was firstly done by using the Brian~2 simulator and then, considering the same parameters, it was migrated to SpiNNaker. The results in both cases are highly the same ones as it is shown in Figure~\ref{fig:comparison}; this fact demonstrates the reproducibility of our architecture on any platform.
Compared to the biological locomotion mechanism, we considered that our approach is highly plausible in two senses, the first one is that the proposed network model is based on spiking neurons, which are considered the neuron models that mimic the best the behavior of biological neurons. The second aspect is that the implementation performed in SpiNNaker allowed us to improve it in terms of the power consumption, and the hardware by itself attempts to be an artificial representation of the brain.
As a future work, we propose to embed the SpiNNaker system into different legged robots (e.g. biped, quadruped and hexapod) to validate our approach on a real robotic platform. Also, it could directly process spatiotemporal patterns with the same \ac{sCPG} by incorporating a neuromorphic sensor.
\section*{Acknowledgements}
This work was partially supported by the Interreg Atlantic Area Programme through the European Regional Development Fund (TIDE - Atlantic network for developing historical maritime tourism, EAPA\_630/2018), by the Spanish grant (with support from the European Regional Development Fund) MIND-ROB (PID2019-105556GB-C33) and by the EU H2020 project CHIST-ERA SMALL (PCI2019-111841-2).
\bibliographystyle{model1-num-names}
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Gynoplistia (Gynoplistia) tergogibbosa is een tweevleugelige uit de familie steltmuggen (Limoniidae). De soort komt voor in het Neotropisch gebied.
Gynoplistia
Steltmug uit het Neotropisch gebied
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"We want 'BMW' standards' Government will be handing out 'Toilet of the year' award
News"We want 'BMW' standards' Government will be handing out 'Toilet of the...
Earlier this year, Local Government Development Minister, Nga Kor Ming made a surprise visit to Dataran Merdeka to check on the maintenance of public infrastructure and facilities in the city. Among the things he found in our public facilities, including toilets, are in need of repairs.
According to Nga, this is because the cleanliness of public toilets is closely related to the image of the country, especially in the main tourist destinations or gateways to our country.
Meanwhile, it seems that Nga is taking this matter seriously.
During an appearance on Astro Awani's Agenda Awani programme, Nga revealed that the government would be handing out the 'Toilet of the Year' award to the cleanest public toilet effective immediately.
He said this initiative is part of the government's efforts to improve the overall cleanliness of public toilets in the country, which had been our embarrassment for a long time.
Source: Skyscrapercity
"I don't care if people call me the toilet minister because what's important is for me to solve an issue that is close to the hearts of the people," he said.
"Public toilets should not be disregarded as those located in tourist spots and gateways into the country are what give tourists their first impression of Malaysia," he added.
Nga also shared that the award would be judged based on the dubbed 'BMW' concept, which were the Malay initials for bersih (clean), menawan (attractive) and wangi (pleasant smelling).
Tidak kisah label 'Menteri Tandas', janji khidmat berkualiti – Nga Kor Ming#AgendaAWANI pic.twitter.com/OV8crNEjnd
— 🇲🇾Astro AWANI🇲🇾 (@501Awani) January 17, 2023
Dirty toilets had been our embarrassment
Dirty toilets have been an issue for Malaysians for many years, with many locals and foreigners complaining about the lack of maintenance and poor hygiene.
In 2019, the then Prime Minister Tun Dr Mahathir Mohamad said he was very embarrassed when he inspects public toilets in Malaysia.
"Most of the time, they are filthy and stinking," he was quoted as saying by Free Malaysia Today.
Dr Mahathir also attributed issue to the state of civic-mindedness among the people and said that many could not be bothered to keep toilets clean.
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\section{Introduction}
\label{siosec:1}
\begin{quotation}
To many practitioners of quantum gravity the black hole plays the role of a
soliton, a non-perturbative field configuration that is added to the spectrum
of particle-like objects only after the basic equations of their theory have
been put down, much like what is done in gauge theories of elementary particles,
where Yang-Mills equations with small coupling constants determine the
small-distance structure, and solitons and instantons govern the large-distance
behavior.
Such an attitude however is probably not correct in quantum gravity. The coupling
constant increases with decreasing distance scale which implies that the
smaller the distance scale, the stronger the influences of ``solitons''.
At the Planck scale it may well be impossible to disentangle black holes from
elementary particles.
\rightline{-- G.~'t Hooft}
\end{quotation}
Quasi-normal modes (QNMs) describe small perturbations of a black hole which
is a thermodynamical system whose (Hawking) temperature and
entropy are given in terms of its global characteristics (total mass, charge
and angular momentum).
They are obtained by solving
a wave equation for small fluctuations subject to the conditions that the
flux be
ingoing at the horizon and
outgoing at asymptotic infinity.
These boundary conditions in general lead to a
discrete spectrum of complex frequencies whose
imaginary part determines the decay time of the small fluctuations
\begin{equation} \Im \omega = \frac{1}{\tau}\end{equation}
There is a vast literature on quasi-normal modes and we make no attempt to review it. Instead, we concentrate on obtaining analytic expressions for quasi-normal modes of various black hole perturbations of interest. One can rarely obtain analytic expressions in closed form. Instead, we discuss techniques which allow one to calculate the spectrum perturbatively starting with an asymptotic regime (e.g., high or low overtones). In asymptotically flat space, we discuss the cases of four-dimensional Schwarzschild and Kerr black holes. Generalization to higher-dimensional spacetimes does not present substantially new calculational challenges. However, we should point out that the case of a rotating black hole is considerably harder than the Schwarzschild case.
We also discuss asymptotically AdS spaces and obtain the spectrum as a perturbative expansion around high overtones. At leading order the frequencies are proportional to the radius of the horizon. When expanding around low overtones, one in general obtains an additional frequency which is inversely proportional to the horizon radius. Thus for large black holes there is a gap between the lowest frequency and the rest of the spectrum of quasi-normal modes.
We pay special attention to the lowest frequencies because they govern the behavior of the gauge theory fluid on the boundary per the AdS/CFT correspondence.
The latter may have experimental consequencies pertaining to the formation of the quark-gluon plasma in heavy ion collisions.
\section{Flat spacetime}
\label{siosec:2}
We start with a study of QNMs in asymptotically flat space-times.
We discuss scalar perturbations of Schwarzschild and Kerr black holes in four dimensions.
\subsection{Schwarzschild black holes}
The metric of a Schwarzschild black hole in four dimensions is
\begin{equation}
ds^2 = -f(r)\, dt^2 + \frac{dr^2}{ f(r)} +r^2 d \Omega^2
\ \ , \ \
f(r) = 1 - \frac{2G M}{r}\end{equation}
The Hawking temperature is
\begin{equation}
T_H = \frac{1}{8\pi GM} = \frac{1}{4\pi r_0}
\end{equation}
where $r_0 = 2GM$ is the radius of the horizon.
A spin-$j$ perturbation of frequency $\omega$ is governed by the radial equation
\begin{equation}
-f(r) \frac{d}{d r} \left( f(r)\frac{d\Psi}{d r}
\right) + V(r) \Psi =\omega^2 \Psi \end{equation}
where $V(r)$ is the ``Regge-Wheeler'' potential
\begin{equation} V(r) = f(r) \left( \frac{\ell (\ell+1)}{r^2} + \frac{(1-j^2)r_0}{r^3} \right)\end{equation}
The spin is $j=0,1,2$ for scalar, electromagnetic and gravitational perturbations, respectively.
It is advantageous to avoid integer values of $j$ throughout
the discussion and only take the limit
$j\to $ integer
at the end of the
calculation.
By defining the ``tortoise coordinate''
\begin{equation} r_* = \int \frac{dr}{f(r)} = r + r_0 \ln \left(\frac{r}{r_0} -1 \right) \end{equation}
the wave equation may be brought into a Schr\"odinger-like form,
\begin{equation}
-\frac{d^2\Psi}{d r_*^2} + V(r(r_*)) \Psi =\omega^2 \Psi \end{equation}
to be solved along the entire real $r_*$-axis.
At both ends the potential vanishes
($V\to 0$ as $r_*\to \pm\infty$)
therefore the solutions behave as
$\Psi\sim e^{\pm i\omega r_*}$.
For QNMs, we demand
\begin{equation} \Psi \sim e^{\mp i\omega r_*} \ \ , \ \ r_* \to \pm\infty\end{equation}
assuming $\Re \omega > 0$.
\subsubsection{Limit $\ell\to \infty$}
In this case it suffices to consider the potential near its maximum.
Expanding around the
maximum of the potential ($V_0' (r_{max}) = 0$) \cite{siob-ferrari-mashhoon},
\begin{equation} r_{max} = \frac{3}{2}\, r_0 +
\mathcal{O} (1/\ell) \,,\end{equation}
we obtain
\begin{equation} V_0 [ r(r_*)] \approx \alpha^2 - \beta^2
(r_*-r_*(r_{max}))^2 \,,\end{equation} where
\begin{equation} \alpha^2 =
\frac{4}{27} \left( \ell + \frac{1}{2} \right) r_0^2 + \mathcal{O} (1/\ell )
\ \ , \ \ \ \
\beta^2 = \frac{16}{729} \left( \ell + \frac{1}{2}
\right) + \mathcal{O} (1/\ell )\,.\end{equation}
The solutions to the wave equation are
\begin{equation} \Psi_n = H_n(\sqrt{i\beta} x)
e^{i\beta x^2/2} \ \ , \ \ n = 0,1,2,\dots\end{equation} where $H_n$ are
Hermite polynomials.
The
corresponding eigenvalues are
\begin{equation} \omega_n =\frac{2}{3\sqrt{3}\, r_0}
\left\{ \ell +\frac{1}{2} + i (n+\frac{1}{2}) \right\} + \mathcal{O} (1/\ell) \end{equation}
This result is in agreement with the standard WKB
approach~\cite{siob-konoplya}.
\subsubsection{Limit $n \to \infty$}
The asymptotic form of QNMs for large $n$ is
\begin{equation}\label{sioe-1} \frac{\omega_n}{T_H} = (2n+1)\pi i + \ln 3 \end{equation}
independent of the angular momentum quantum number $\ell$.
This form was first
derived numerically
\cite{siob-Chandra-Det,siob-Leaver,siob-Nollert,siob-Andersson,siob-Bachelot}
and subsequently confirmed analytically
\cite{siob-Motl-Nei}.
The large imaginary part of the frequency
($\Im\omega_n$)
makes the numerical analysis cumbersome
but is easy to understand because the spacing of frequencies is $2\pi i T_H$
which is the same as the spacing of poles of a thermal Green function on the
Schwarzschild black hole background.
On the other hand the real part ($\Re\omega_n$) is small.
Its
analytical value was first proposed by Hod \cite{siob-Hod}.
The analytical derivation of the asymptotic form (\ref{sioe-1}) of QNMs by Motl and Neitzke \cite{siob-Motl-Nei} offered a new surprise
because it heavily
relied on the black hole singularity.
It is intriguing that the unobservable
region beyond the horizon influences the behavior of physical quantities.
We shall
calculate the asymptotic formula for QNMs including first-order
corrections \cite{siob-MS}
by solving the wave equation
perturbatively for arbitrary spin of the wave.
We shall obtain agreement with results from
numerical analysis for gravitational and scalar
waves \cite{siob-Nollert,siob-Ber-Kok}
and WKB analysis for gravitational waves
\cite{siob-vdB}.
Let
\begin{equation} \Psi = e^{-i\omega r_*} f(r_*) ~. \end{equation}
We have
$f(r_*)\sim 1$ as $r_*\to +\infty$
and near the horizon,
$f(r_*)\sim e^{2i\omega r_*}$ (as $r_*\to -\infty$).
Let us continue $r$ analytically into
the complex plane and define the boundary condition at the horizon
in terms of the monodromy
of $f(r_*(r))$ around the singular point $r=r_0$,
\begin{equation} \mathcal{M} (r_0) = e^{-4\pi\omega r_0}\end{equation}
along a contour running counterclockwise.
We may deform the contour in the
complex $r$-plane so that it either lies
beyond the horizon ($\mathrm{Re} r
< r_0$) or
at infinity ($r\to \infty$).
The monodromy only gets a contribution from the segment lying beyond the
horizon.
It is convenient to change variables to
\begin{equation} z = \omega (r_* -i\pi r_0) = \omega (r + r_0 \ln (1-r/r_0))\end{equation}
(where we chose a branch such that~$z\to 0$ as $r\to 0$).
The potential can be written as a series in $\sqrt{z}$,
\begin{equation} V(z) = -\frac{\omega^2}{4z^2} \left( 1-j^2 + \frac{3\ell (\ell+1) +1- j^2
}{3}\, \sqrt{-\frac{2z}{\omega r_0}} + \dots \right)\end{equation}
which is a formal expansion in $1/\sqrt\omega$.
Now deform the
contour defining the monodromy so that it gets mapped onto the real axis in the $z$-plane.
Near the
singularity $z=0$,
\begin{equation} z \approx -\frac{\omega}{2r_0}\, r^2\end{equation}
Choose a contour in the $r$-plane so that near $r=0$,
the positive and negative real axes in the $z$-plane are
mapped onto
\begin{equation} \arg r = \pi - \frac{\arg\omega}{2} \ \ , \ \ \arg r = \frac{3\pi}{2}
- \frac{\arg\omega}{2} \end{equation}
in the $r$-plane, respectively.
These segments form a $\pi /2$ angle (independent of $\arg\omega$).
To avoid the $r=0$ singularity,
go around an arc of angle $3\pi /2$
which corresponds to an
angle of
$3\pi$ around $z=0$ in the $z$-plane.
Considering the black hole singularity ($r=0$), we note that there are two
solutions,
\begin{equation} f_\pm (r) = r^{1\pm j} Z_\pm (r) \end{equation}
where $Z_\pm$ are analytic functions of $r$.
Going around an arc of angle of $3\pi/2$, we obtain
\begin{equation} f_\pm (e^{3\pi i/2} r) = e^{3\pi (1\pm j) i/2} \, f_\pm (r)\end{equation}
which is an {\em exact} result.
To proceed further, we need to relate
the behavior of the wavefunction near the black hole singularity
to
its behavior at large $r$ in the complex $r$-plane.
To this end, we shall solve the wave equation perturbatively, thus writing
the wavefunction as a perturbation series in
$1/\sqrt\omega$.
At zeroth order, the wave equation reads
\begin{equation}
\frac{d^2\Psi^{(0)}}{d z^2} + \left( \frac{1-j^2}{4z^2} + 1 \right) \Psi^{(0)} = 0 \end{equation}
Two linearly independent solutions are
\begin{equation} f_\pm^{(0)} (z) = e^{iz}\, \Psi_\pm^{(0)} = e^{iz} \sqrt{\frac{\pi z}{2}} J_{\pm j/2} (z)\end{equation}
in terms of Bessel functions.
We deduce the behavior at infinity ($z\to\infty$)
\begin{equation} f_\pm^{(0)} (z) \sim e^{iz} \cos (z - \pi (1\pm j)/4)\end{equation}
The boundary conditions imply
$f(z)\sim$~const.~as $z\to\infty$
along the positive real axis in the $z$-plane.
Therefore, we ought to adopt the linear combination
\begin{equation} f^{(0)} = f_+^{(0)} - e^{-\pi ji/2}\, f_-^{(0)} \sim e^{iz} \sqrt z\,
H_{j/2}^{(1)} (z)\end{equation}
(in terms of a Hankel function).
As $z\to \infty$, we obtain
\begin{equation} f^{(0)}(z) \sim - e^{-\pi (1+j) i/4} \sin (\pi j/2) \end{equation}
a constant, as desired.
Going along the $3\pi $ arc around $z=0$ in the $z$-plane, we have
\begin{equation} f^{(0)}(e^{3\pi i} z) = e^{3\pi (1+j)i/2} \left( f_+^{(0)} (z) - e^{-7\pi ji/2} \, f_-^{(0)} (z)\right) \end{equation}
As $z\to\infty$,
\begin{equation} f^{(0)}(z) \sim e^{-\pi (1+j) i/4} \sin (3\pi j/2)
+ e^{\pi (1-j)i/4} \sin (2\pi j) e^{2iz} \end{equation}
The monodromy to zeroth order is
\begin{equation} \mathcal{M} (r_0) = -\frac{\sin (3\pi j/2)}{\sin (\pi j/2)}
= - (1+ 2\cos (\pi j)) \end{equation}
leading to a discrete set of complex frequencies (QNMs) \cite{siob-Motl-Nei}
\begin{equation}\label{sioe-2} \frac{\omega_n}{T_H} = (2n+1)\pi i + \ln (1+2\cos(\pi j) ) + \mathcal{O} (1/\sqrt n) \end{equation}
Next, we calculate the first-order correction to the above expression \cite{siob-MS}.
Expanding the wavefunction in $1/\sqrt\omega$,
\begin{equation} \Psi = \Psi^{(0)} + \frac{1}{\sqrt{-\omega r_0}}\, \Psi^{(1)} + \mathcal{O} (1/\omega)\end{equation}
the first-order correction obeys
\begin{equation}
\frac{d^2\Psi^{(1)}}{d z^2} + \left( \frac{1-j^2}{4z^2} + 1 \right) \Psi^{(1)} =\sqrt{-\omega r_0}\, \delta V \Psi^{(0)}\end{equation}
where
\begin{equation}
\delta V(z) = \frac{1-j^2}{4z^2} + \frac{1}{\omega^2}\, V[r(z)] \end{equation}
Two linearly independent solutions are
\begin{equation} \Psi_\pm^{(1)} (z) = \mathcal{C} \Psi_+^{(0)} (z)\int_0^z \Psi_-^{(0)}
\delta V \Psi_\pm^{(0)}
- \mathcal{C} \Psi_-^{(0)} (z)\int_0^z \Psi_+^{(0)}
\delta V \Psi_\pm^{(0)}\end{equation}
where
$\mathcal{C} = \frac{\sqrt{-\omega r_0}}{\sin (\pi j/2)}$
and the integral is along the positive real axis on the $z$-plane ($z>0$).
We obtain the large-$z$ behavior
\begin{equation} \Psi_\pm^{(1)} (z) \sim c_{-\pm} \cos (z-\pi (1+ j)/4)
- c_{+\pm} \cos (z-\pi (1-j)/4)\end{equation}
where
\begin{equation} c_{\pm\pm} = \mathcal{C} \int_0^\infty \Psi_\pm^{(0)} \delta V \Psi_\pm^{(0)}
\end{equation}
To obtain the small-$z$ behavior, expand
\begin{equation} \delta V(z) = -\frac{3\ell (\ell+1) + 1-j^2 }{6\sqrt{-2\omega r_0} }\, z^{-3/2} + \mathcal{O} (1/\omega) \end{equation}
It follows that
\begin{equation} \Psi_\pm^{(1)} = z^{1\pm j/2} G_\pm (z) + \mathcal{O} (1/\omega) \end{equation}
where $G_\pm$ are even analytic functions of $z$.
For the desired behavior as $z\to\infty$, define
\begin{equation} \Psi = \Psi_+^{(0)} + \frac{1}{\sqrt{-\omega r_0}}\, \left\{ \Psi_+^{(1)} - e^{-\pi ji/2} \Psi_-^{(1)}
+ e^{-\pi ji/2} \xi\Psi_-^{(0)}\right\}
+ \dots \end{equation}
where $\xi \sim \mathcal{O} (1)$
and dots represent terms of order higher than $\mathcal{O} (1/\sqrt\omega)$.
By demanding
$\Psi\sim e^{-iz}$ as $z\to +\infty$,
we fix
\begin{equation} \xi = \xi_+ + \xi_- \ \ , \ \
\xi_+ = c_{++} e^{\pi ji/2} - c_{+-}\ \ , \ \
\xi_- = c_{--} e^{-\pi ji/2} - c_{+-}\end{equation}
Then the requirement $f(z) = e^{iz} \Psi(z) \sim$ const.~as $z\to\infty$ yields
\begin{equation} f(z) \sim - e^{-\pi (1+j)i/4} \sin (\pi j/2) \left\{ 1 - \frac{\xi_-}{\sqrt{-\omega r_0}} \right\} \end{equation}
In the neighborhood of the black hole singularity
(around $z=0$), going around a $3\pi$ arc, we obtain
\begin{equation} \Psi_\pm^{(1)} (e^{3\pi i} z) = e^{3\pi (2\pm j) i/2 } \Psi_\pm^{(1)} (z) \end{equation}
therefore
\begin{eqnarray} \Psi (e^{3\pi i} z) &=& \Psi^{(0)} (e^{3\pi i} z)
\nonumber\\
& &- e^{3\pi ji/2}
\frac{1}{\sqrt{-\omega r_0}}\,
\left\{ \Psi_+^{(1)} (z)
- e^{-7\pi ji/2} (\Psi_-^{(1)} (z) - i\xi \Psi_-^{(0)}
(z)) \right\} \end{eqnarray}
As $z\to \infty$ along the real axis,
\begin{eqnarray} f (z) &\sim & e^{-\pi (1+j)i/4} \sin (3\pi j/2) \left\{ 1-\frac{1}{\sqrt{-\omega r_0}}\, A\right\} \nonumber\\
& & + e^{\pi (1-j)i/4}
\sin(2\pi j) \left\{ 1-\frac{1}{\sqrt{-\omega r_0}}\, B\right\} e^{2iz}\nonumber\end{eqnarray}
where
\begin{equation} A = \frac{i-1}{2}\ e^{\pi ji/2}\ \left( \xi_++i\xi_- - \xi \, \cot (3\pi j/2)\right)\end{equation}
and $B$ is not needed for our purposes.
The monodromy to this order reads
\begin{equation} \mathcal{M} (r_0) = - \frac{\sin (3\pi j/2)}{\sin (\pi j/2)}
\left\{ 1 + \frac{i-1}{2\sqrt{-\omega r_0}}\ e^{\pi ji/2}\ \left( \xi_- -\xi_+
+ \xi \cot(3\pi j/2) \right) \right\} \end{equation}
leading to the QNM frequencies \cite{siob-MS}
\begin{eqnarray} \frac{\omega_n}{T_H} &=& (2n+1)\pi i + \ln (1+2\cos(\pi j) )
+ \frac{e^{\pi ji/2}}{\sqrt{n+1/2}} \left( \xi_- -\xi_+
+ \xi \cot(3\pi j/2) \right) \nonumber\\
& & + \mathcal{O} (1/n) \end{eqnarray}
which
includes the $\mathcal{O} (1/\sqrt n)$ correction to the $\mathcal{O} (1)$ asymptotic expression (\ref{sioe-2}).
For an explicit expression, use
\begin{equation} \mathcal{J} (\nu,\mu) \equiv \int_0^\infty dz\, z^{-1/2} J_\nu (z) J_\mu (z) = \frac{\sqrt{\pi/2}
\, \Gamma (\frac{\nu+\mu + 1/2}{2})}{\Gamma (\frac{-\nu+\mu+3/2}{2})
\Gamma (\frac{\nu+\mu+3/2}{2}) \Gamma (\frac{\nu-\mu +3/2}{2} )}\end{equation}
We obtain
\begin{equation} c_{\pm\pm} = \pi\, \frac{3\ell (\ell + 1) +1-j^2}{12\sqrt 2\, \sin (\pi j/2)}
\, \mathcal{J} (\pm j/2, \pm j/2)\end{equation}
therefore
\begin{eqnarray} \xi_- -\xi_+
+ \xi \cot(3\pi j/2)
&=& (1-i) \ \frac{3\ell(\ell +1) +1-j^2}{24\sqrt 2 \pi^{3/2}}
\ \frac{\sin (2\pi j)}{\sin (3\pi j/2)}
\nonumber\\
& & \times \Gamma^2 (1/4)\ \Gamma(1/4 + j/2)
\ \Gamma (1/4 - j/2)\end{eqnarray}
where we also used the identity
$\Gamma (y) \Gamma (1-y) = \frac{\pi}{\sin (\pi y)}$.
This expression has a well-defined finite limit as $j\to$ integer.
For scalar waves, let
$j\to 0^+$. We obtain
\begin{equation} \frac{\omega_n}{T_H} = (2n+1)\pi i + \ln 3
+ \frac{1-i}{\sqrt{n+1/2}} \ \frac{\ell(\ell +1) +1/3}{6\sqrt 2 \pi^{3/2}}
\ \Gamma^4 (1/4) + \mathcal{O} (1/n) \end{equation}
which is in agreement with numerical results \cite{siob-Ber-Kok}.
For gravitational waves, we
let
$j\to 2$ and obtain
\begin{equation} \frac{\omega_n}{T_H} = (2n+1)\pi i + \ln 3
+ \frac{1-i}{\sqrt{n+1/2}} \ \frac{\ell(\ell +1) -1}{18\sqrt 2 \pi^{3/2}}
\ \Gamma^4 (1/4) + \mathcal{O} (1/n) \end{equation}
which is in agreement with the results from
a WKB analysis \cite{siob-vdB}
as well as numerical analysis \cite{siob-Nollert}.
\subsection{Kerr black holes}
Extending the above discussion to rotating (Kerr) black holes
is not straightforward.
Bohr's correspondence principle
\begin{equation} \delta M = \hbar\Re\omega\end{equation}
and the first law of black hole mechanics
\begin{equation} \delta M = T_H \delta S_{BH} + \Omega\delta J\end{equation}
imply the asymptotic expression\cite{siob-Hod}
\begin{equation}\label{sioe-1a} \Re\omega = T_H \ln 3 + m\Omega \end{equation}
where $m$ is the azimuthal eigenvalue of the wave and
$\Omega$ is the angular velocity of horizon.
In deriving the above, we identified $\delta S_{BH} \equiv \ln 3$ \cite{siob-BM}.
Even though the above result has the correct limit as $\Omega\to 0$ (in agreement with the Schwarzschild expression (\ref{sioe-1})), it is in conflict
with numerical results
\cite{siob-BCKO}
indicating $\Re\omega \approx m\Omega$.
To resolve the above contradiction, we shall obtain an analytic solution to the wave (Teukolsky \cite{siob-Teukolsky})
equation
which will be
valid for asymptotic modes bounded from above by $1/a$, where
\begin{equation} a= \frac{J}{M}\end{equation}
with $J$ being the angular momentum and $M$ the mass of the Kerr black hole.
The calculation will be valid for
$a\ll 1$ which
includes the Schwarzschild case ($a=0$) \cite{siob-MS2}.
Our results
will confirm Hod's
expression (\ref{sioe-1a})
and not necessarily contradict numerical results
(the latter may still be valid in the asymptotic regime $1/a \lesssim \omega$).
In the Schwarzschild limit ($a\to 0$)
the range of frequencies extends to infinity
and our expression
reduces to the expected form (\ref{sioe-1}).
The metric of a Kerr black hole is
\begin{eqnarray} ds^2 = &-& \left( 1- \frac{2Mr}{\Sigma} \right) dt^2 + \frac{4Mar\sin^2\theta}{\Sigma}\ dtd\phi + \frac{\Sigma}{\Delta}\ dr^2
\nonumber\\
&+& \Sigma d\theta^2 + \sin^2\theta \left( r^2+a^2 + \frac{2Ma^2 r\sin^2\theta}{\Sigma} \right)\
d\phi^2\end{eqnarray}
where
$ \Sigma = r^2 + a^2 \cos^2\theta$, $\Delta = r^2 -2Mr + a^2 =(r-r_-)(r-r_+)$
and we have set
Newton's constant $G=1$.
The angular velocity of the horizon and Hawking temperature, respectively, are
\begin{equation} \Omega = \frac{a}{2Mr_+}\ \ , \ \ \ \
T_H = \frac{1 - r_-/r_+}{8\pi M}
\end{equation}
\subsubsection{Massless perturbations}
Massless perturbations are governed by the Teukolsky wave equation \cite{siob-Teukolsky}
\begin{eqnarray}\left( \frac{(r^2+a^2)^2}{\Delta} - a^2 \sin^2\theta \right) \
\frac{\partial^2\Psi}{\partial t^2} + \frac{4Mar}{\Delta}\ \frac{\partial^2\Psi}{\partial t\partial\phi}
+ \left( \frac{a^2}{\Delta} - \frac{1}{\sin^2\theta}\right) \ \frac{\partial^2\Psi}{\partial\phi^2} & & \nonumber\\
- \frac{1}{\Delta^s} \frac{\partial}{\partial r} \left( \Delta^{s+1}
\frac{\partial\Psi}{\partial r} \right)
- 2s \left( \frac{M(r^2-a^2)}{\Delta} - r -ia\cos\theta \right)\ \frac{\partial\Psi}{\partial t}
& & \nonumber\\
- \frac{1}{\sin\theta} \frac{\partial}{\partial\theta}
\left( \sin\theta \frac{\partial\Psi}{\partial\theta} \right)
-2s \left( \frac{a(r-M)}{\Delta} + \frac{i\cos\theta}{\sin^2\theta} \right)\
\frac{\partial\Psi}{\partial\phi}
+ (s^2\cot^2\theta - s)\Psi &=& 0\nonumber\\ \end{eqnarray}
where $s=0,-1,-2$ for scalar, electromagnetic and gravitational perturbations, respectively.
a
Writing the wavefunction in the form
\begin{equation} \Psi = e^{-i\omega t} e^{im\phi} S(\theta) f(r) \end{equation}
we obtain the
angular equation
$$ \frac{1}{\sin\theta} (\sin\theta\ S')'
+
\left( a^2\omega^2 \cos^2\theta - \frac{m^2}{\sin^2\theta} -2a\omega s\cos\theta
- \frac{2ms\cos\theta}{\sin^2\theta}
- s^2 \cot^2\theta \right) S $$
\begin{equation} = -(A+s)S\end{equation}
where $A$ is the separation constant (eigenvalue) and the
radial equation
\begin{equation} \frac{1}{\Delta^s} (\Delta^{s+1} f')' + V(r) f = (A+a^2\omega^2) f\end{equation}
where the potential is given by
\begin{equation} V(r) = \frac{(r^2+a^2)^2\omega^2 - 4aMr\omega m + a^2m^2
+2ia(r-M) ms -2iM (r^2 - a^2) \omega s}{\Delta}
+ 2ir\omega s \end{equation}
Let us simplify the notation by placing the horizon at $r=1$,
i.e., by setting
\begin{equation} 2M = 1+a^2 \ \ , \ \ \ \
r_- = a^2 \ \ , \ \ r_+ = 1 \end{equation}
and solve the two wave equations by expanding in $a$.
We shall keep terms up to $\mathcal{O}(a)$
assuming $\omega$ is large but bounded from above by $1/a$,
($1\lesssim \omega \lesssim 1/a$).
Thus
$\omega$ is in an intermediate
range
which becomes asymptotic in the Schwarzschild limit $a\to 0$.
The solutions to the angular equation to lowest order are spin-weighted spherical
harmonics with eigenvalue
\begin{equation} A = \ell(\ell+1) - s(s+1) + \mathcal{O} (a\omega)\end{equation}
Near the horizon ($r\to 1$),
\begin{equation} f(r) \sim (r-1)^\lambda \ \ , \ \ \lambda = i(\omega - am) + \mathcal{O} (1/\omega)\end{equation}
At infinity ($r\to\infty$),
$f(r) \sim e^{i\omega r}$.
Introducing the ``tortoise coordinate''
\begin{equation} z = \omega r + (\omega - am) \ln (r-1) \end{equation}
the boundary conditions
read
\begin{equation} f(z) \sim e^{\pm iz} \ \ , \ \ z\to \pm\infty
\end{equation}
From the boundary condition at the horizon we deduce the monodromy for
the function
$\mathcal{F} (z) \equiv e^{iz} f(z)$ (notice that $\mathcal{F} \sim$ const.~as
$z\to +\infty$)
around the singular point
$r=1$,
\begin{equation} \mathcal{M} (1) = e^{4\pi (\omega - am)} + \mathcal{O} (a^2) \end{equation}
To express the radial equation in terms of the tortoise coordinate, define
\begin{equation} f(r) = \Delta_0^{-s/2}\ \frac{R(r)}{\sqrt{r(\omega r-am)}} \end{equation}
$\Delta_0 = r(r-1)$ (note $\Delta = \Delta_0 + \mathcal{O} (a^2)$).
Inverting $z=z(r)$,
\begin{equation} r = \sqrt{-\frac{2z}{\omega}} + \mathcal{O} (1/\omega) \end{equation}
the radial equation
to lowest order in $1/\sqrt\omega$ in terms of $R$ reads
\begin{equation} \frac{d^2R}{dz^2} + \left\{ 1 + \frac{3is}{2z} + \frac{4-s^2
- 4iams}{16z^2} \right\}\ R = 0\end{equation}
to be solved along the entire real axis.
This is Whittaker's equation. The
solutions may be written as
\begin{equation} M_{\kappa,\pm\mu}(x) = e^{-x/2} x^{\pm\mu + 1/2} M(\frac{1}{2} \pm \mu - \kappa, 1\pm 2\mu, x)\end{equation}
where $\kappa = \frac{3s}{4}$, $\mu^2 = \frac{s(s+4iam)}{16}$,
$M_{\kappa,\pm\mu}$ is Kummer's function (also called $\Phi$) and we set $x= 2iz$.
We need to introduce Whittaker's function
\begin{equation}
W_{\kappa,\mu}(x) =
\frac{\Gamma(-2\mu)}{\Gamma(\frac{1}{2} - \mu-\kappa)}\ M_{\kappa,\mu}(x)
+ \frac{\Gamma(2\mu)}{\Gamma(\frac{1}{2} +\mu-\kappa)}\ M_{\kappa,-\mu}(x)
\end{equation}
due to its clean asymptotic behavior,
\begin{equation} W_{\kappa,\mu}(x) \sim e^{-x/2}\ x^\kappa\ (1 + \mathcal{O} (1/x))
\ \ , \ \ \ \ |x|\to\infty~.\end{equation}
We may compute the monodromy by deforming
the contour as before.
Going around an arc of angle $3\pi$, we have
\begin{equation} M_{\kappa,\pm\mu}(e^{3\pi i} x)
= -i e^{\pm 3\pi i\mu} M_{-\kappa, \pm\mu} (x)\end{equation}
where we used
$M(a,b,-x) = e^{-x} M(b-a,b,x)$,
therefore
\begin{equation}
W_{\kappa,\mu}(e^{3\pi i} x) =
-i e^{3\pi i \mu}\ \frac{\Gamma(-2\mu)}{\Gamma(\frac{1}{2} - \mu-\kappa)}\ M_{-\kappa,\mu}(x)
-i e^{-3\pi i \mu}\ \frac{\Gamma(2\mu)}{\Gamma(\frac{1}{2} +\mu-\kappa)}\ M_{-\kappa,-\mu}(x)
\end{equation}
To find the asymptotic behavior, we need
\begin{equation} M_{-\kappa,\mu} (x) = \frac{\Gamma(1+2\mu)}{\Gamma(\frac{1}{2} +\mu +\kappa)}\
e^{-i\pi\kappa} W_{\kappa,\mu} (e^{i\pi} x) +
\frac{\Gamma(1+2\mu)}{\Gamma(\frac{1}{2} +\mu -\kappa)}\
e^{-i\pi(\frac{1}{2}+\mu +\kappa)} W_{-\kappa,\mu} (x)
\end{equation}
As $|x|\to\infty$, we obtain
\begin{equation} W_{\kappa,\mu}(e^{3\pi i} x) \sim A e^{x/2} x^\kappa
+ B e^{-x/2} x^{-\kappa} \end{equation}
where
\begin{equation} A =
-i e^{3\pi i \mu}\ \frac{\Gamma(-2\mu)}{\Gamma(\frac{1}{2} - \mu-\kappa)}\
\frac{\Gamma(1+2\mu)}{\Gamma(\frac{1}{2} +\mu +\kappa)}\ e^{-\pi i \kappa}
+ (\mu\to -\mu)
\end{equation}
and $B$ is not needed for our purposes.
After some algebra, we deduce
\begin{equation} A = - (1+2\cos \pi s) + \mathcal{O} (a^2)\end{equation}
where we used the identities
$\Gamma (1-x)\Gamma(x) = \frac{\pi}{\sin\pi x}$,
$\Gamma(\frac{1}{2}+x)\Gamma(\frac{1}{2} -x) = \frac{\pi}{\cos\pi x}$.
The monodromy around $r=1$ is
\begin{equation} \mathcal{M} (1) = e^{4\pi(\omega -ma)} = A
\end{equation}
therefore \cite{siob-MS2}
\begin{equation} \Re\omega = \frac{1}{4\pi}\ \ln (1+2\cos \pi s) + ma + \mathcal{O} (a^2) \end{equation}
in agreement with Hod's formula
for gravitational waves ($s=-2$)
in the
small-$a$ limit
(in which $\Omega \approx a$, $T_H \approx \frac{1}{4\pi}$).
However, it should be emphasized that these are not asymptotic values of
QNMs but bounded from above by $1/a$.
\subsubsection{Massive perturbations}
The case of massive perturbations is interesting because it reveals instabilities.
As is well-known, the Schwarzschild spacetime is stable against all kinds of
perturbations, massive or massless
which makes the
Schwarzschild geometry appropriate to study astrophysical
objects.
On the other hand, Kerr spacetime
is stable against massless perturbations
but not against massive bosonic fields \cite{siob-Det}. The
instability timescale is much larger than the age of
the Universe so the problem is not expected to have observable consequencies.
Nevertheless, the study of instabilities is an important subject and QNMs provide an indispensable tool.
For a massive scalar of mass $\mu$, the radial wave equation reads
\begin{equation}
\frac{d}{ d r}\left(\Delta\frac{dR}{ d r}\right)
+
\left\{
\frac{\omega^2(r^2+a^2)^2-4aMm\omega r+m^2a^2}{\Delta}
-\mu^2 r^2-a^2\omega^2-\ell(\ell+1)
\right\}R=0,
\end{equation}
We are interested in solving this equation for a small mass and low frequencies ($\mu, \omega \ll 1/M$) \cite{siob-Det}.
Away from the horizon ($r\gg M$), we may approximate by
\begin{equation} \frac{d^2}{dr^2} (rR) + \left[ -k^2 + \frac{2M\mu^2}{r} -
\frac{\ell(\ell+1)}{r^2} \right] rR = 0 \ \ , \ \ \ \ k^2 = \mu^2 - \omega^2 \end{equation}
The solution to this equation is given in terms of a confluent hypergeometric function,
\begin{equation} R(r) = (2kr)^\ell e^{-kr} U(\ell+1-M\mu^2/k,2(\ell+1),2kr) \end{equation}
Near the horizon ($r\ll \ell/|k|$), we may approximate by
\begin{equation} z(z+1) \frac{d}{dz} \left[ z(z+1) \frac{dR}{dz} \right] +
\left[ P^2 - \ell (\ell+1) z(z+1) \right] R =
0 \end{equation}
where $P = \frac{am-2Mr_+\omega}{r_+-r_-}$, $z = \frac{r-r_+}{r_+-r_-}$.
The solution to this equation is given in terms of a hypergeometric function,
\begin{equation} R(z) = \left( \frac{z}{z+1} \right)^{iP} F (-\ell, \ell+1; 1-2iP; z+1) \end{equation}
Matching the two expressions in the overlap region ($M\ll r\ll \ell/|k|$),
we obtain the frequencies
\begin{equation} \omega_n \approx \mu + i\gamma_n \ \ , \ \ \ \ n\in\mathbb{N} \end{equation}
where
\begin{equation} \gamma_n = \mathcal{C}_{\ell n} \mu (\mu M)^{4(\ell+1)} \frac{am}{M-2\mu r_+}
\prod_{j=1}^\ell \left[ j^2 \left( 1 - \frac{a^2}{M^2} \right)
+ \left( \frac{am}{M} - 2\mu r_+ \right)^2 \right] \end{equation}
and $\mathcal{C}_{\ell n} = \frac{2^{2(2\ell+1)}
(2\ell+1+n)!(\ell!)^2}{(\ell+1+n)^{2(\ell+2)} (2\ell+1)^2 n!
((2\ell)!)^4}$.
For $m>0$, we have $\gamma_n > 0$ yielding an instability.
For the fastest growing mode (with $\ell=1$, $m=1$, $n=2$ (2p state)) we have
\begin{equation} \tau = \frac{1}{\gamma} = \frac{24}{a\mu^2 (\mu M)^7} \end{equation}
which is generally large.
Notice that there is no instability
in the Schwarzschild limit ($a\to 0$)
and for massless perturbations ($\mu \to 0$);
in both cases, $\gamma\to 0$ and therefore the lifetime $\tau\to\infty$.
\subsection{Half-integer spin}
In the case of a perturbation of half-integer spin we need to solve the Teukolsky equation \cite{siob-Kh-Ru}
with potential
\begin{equation}\label{eqpot}
V(r) = f(r)\left( \frac{\ell(\ell+1)}{r^2} + \frac{1}{r^3} \right)
+\frac{2i\omega j}{r} - \frac{3i\omega j}{r^2} + \frac{j^2}{4r^4}
\end{equation}
where $j$ is the spin of the perturbing field (e.g., $j=1/2$ for Dirac fermion).
We shall set $r_0=1$, for simplicity, so $f(r) = 1 - \frac{1}{r}$.
Expanding around the black hole singularity $z=\omega r_* = 0$,
\begin{equation}\label{eqVexp}
\frac{1}{\omega^2}V(z) = \frac{3ij}{2z} - \frac{4-j^2}{16z^2} + \frac{\mathcal{A}}{\omega^{1/2} z^{3/2}} + \mathcal{O} (1/\omega) \ \ , \ \ \ \
\mathcal{A} = \frac{\ell(\ell+1)+ \frac{1-j^2}{3}}{2\sqrt 2 } \end{equation}
we obtain the zeroth-order wave equation
\begin{equation} \frac{d^2\Psi}{dz^2} + \left[ 1 - \frac{3ij}{2z} - \frac{4-j^2}{16z^2} \right] \Psi
=0 \end{equation}
whose solutions are the Whittaker functions
\begin{equation}\label{eqpsipm0} \Psi_\pm^{(0)} (z) = M_{\lambda,\pm\mu} (-2iz) \ \ , \ \ \ \
\lambda = \frac{3j}{4} \ \ , \ \ \mu = \frac{j}{4} \end{equation}
The calculation of the monodromy as before leads to the modes \cite{siob-Kh-Ru}
\begin{equation}\label{eqsp0} \frac{\omega_n}{T_H} = -(2n+1) \pi i + \ln (1+2\cos\pi j) + \mathcal{O} (1/\sqrt n) \end{equation}
in agreement with the result for integer spin ( which came from the Regge-Wheeler equation).
For a Dirac fermion, $j=1/2$, so
asymptotically, the real part vanishes.
The first-order correction may also be calculated as before \cite{siob-MS3}.
The result is
\begin{eqnarray}\label{eqsp1} \frac{\omega_n}{T_H} &=& -(2n+1) \pi i + \ln (1+2\cos\pi j) \nonumber\\
&& -\frac{2i}{\sqrt{-in/2}}\ \sin 4\pi\mu\ \frac{\bar b_+ A_- B_- + \bar b_- A_+ B_+}{e^{-4\pi i \mu}A_+ B_- - e^{4\pi i \mu}A_- B_+} + \mathcal{O} (1/n) \end{eqnarray}
where
\begin{equation} \bar b_\pm = \frac{\mathcal{A}}{4\mu} \int_0^\infty \frac{dz}{{z}^{3/2}}
M_{\lambda,\pm\mu} (-2iz) M_{\lambda,\pm\mu} (-2iz) \end{equation}
and $A_\pm = \frac{\Gamma (1\pm 2\mu)}{\Gamma(\frac{1}{2} \pm\mu+\lambda)}
e^{i\pi(\frac{1}{2} \pm\mu-\lambda)}$, $B_\pm = \frac{\Gamma (1\pm
2\mu)}{\Gamma(\frac{1}{2} \pm\mu-\lambda)} e^{-i\pi\lambda}$.
This result appears to be a complicated function of $j$, so let us look at specific cases.
For $j=1/2$ (Dirac fermions), we obtain
\begin{equation}\label{eqsp1aD} \frac{\omega_n}{T_H} = -(2n+1) \pi i +\frac{1+i}{2\sqrt{n}}\ \left( \ell + \frac{1}{2} \right)^2\ \Gamma^2\left( \frac{1}{4} \right)+ \mathcal{O} (1/n) \end{equation}
which is in good agreement with numerical data \cite{siob-MS3}.
For $j=3/2$, we find
\begin{equation} \frac{\omega_n}{T_H} = -(2n+1) \pi i + \mathcal{O} (1/n) \end{equation}
so there are no first-order corrections to the spectrum.
For $j=5/2$, we have
\begin{equation} \frac{\omega_n}{T_H} = -(2n+1) \pi i
+\frac{1+i}{\sqrt{2n}}\ \mathcal{A} \ \Gamma^2\left( \frac{1}{4} \right)+
\mathcal{O} (1/n) \end{equation}
etc.
All of the above spectra agree with the general expression we obtained for integer spin using the Regge-Wheeler equation.
The relation of the latter to the Teukolsky equation is worth exploring further.
\section{Anti-de Sitter spacetime}
\label{siosec:3}
According to the AdS/CFT correspondence,
QNMs of AdS black holes are expected to
correspond to perturbations of the dual Conformal Field Theory (CFT) on the boundary.
The
establishment of
such a correspondence is hindered by difficulties in solving the wave equation
governing the various types of perturbation.
In three dimensions one obtains a hypergeometric equation which leads to
explicit analytic expressions for the QNMs \cite{siob-CL,siob-BSS}.
In five dimensions one obtains a Heun equation and a derivation of analytic expressions for QNMs is no longer possible.
On the other hand, numerical results exist in four, five and seven dimensions
\cite{siob-HH,siob-Star,siob-Kono}.
\subsection{Scalar perturbations}
To find the asymptotic form of QNMs, we need to find an approximation to the wave equation valid in the
high frequency regime.
In three dimensions the resulting wave equation will be an exact equation (hypergeometric equation).
In five dimensions, we shall turn the Heun equation into a hypergeometric equation
which will lead to
an analytic expression for the asymptotic form of QNM frequencies
in agreement
with numerical results.
\subsubsection{AdS$_3$}
In three dimensions the wave equation for a massless scalar field is
\begin{equation}
\frac{1}{R^2\; r}\partial_r \left( r^3 \left( 1- \frac{r_0^2}{r^2}\right) \partial_r \Phi\right) -\frac{R^2}{r^2 - r_0^2 }\partial_t^2 \Phi + \frac{1}{r^2}\partial_x^2 \Phi =0
\end{equation}
Writing the wavefunction in the form
\begin{equation}
\Phi = e^{i(\omega t-px) }\Psi (y) ,\ \ \ \ \ y = \frac{r_0^2}{r^2}
\end{equation}
the wave function becomes
\begin{equation}
y^2 (y-1)\left( (y-1) \Psi' \right)'
+ \hat\omega^2\, y\Psi +\hat p^2\, y(y-1)\Psi
=0
\end{equation}
to be solved in the interval $0<y<1$, where
\begin{equation}
\hat\omega = \frac{\omega R^2}{2r_0} = \frac{\omega}{4\pi T_H},\ \ \ \hat p = \frac{pR}{2r_0} = \frac{p}{4\pi R T_H}\;.
\end{equation}
For QNMs, we are interested in the
solution
\begin{equation} \Psi (y) = y(1-y)^{i\hat\omega} {}_2F_1 (1+i(\hat\omega + \hat p), 1+i(\hat\omega - \hat p); 2; y)\end{equation}
which vanishes at the boundary ($y\to 0$).
Near the horizon ($y\to 1$), we obtain a mixture of ingoing and outgoing waves,
\begin{equation} \Psi \sim A_+ (1-y)^{-i\hat\omega} + A_-(1-y)^{+i\hat\omega}\ \ , \ \ \ \
A_\pm =
\frac{\Gamma(\pm 2i\hat\omega)}{\Gamma(1\pm i(\hat\omega + \hat p))\Gamma(1\pm i(\hat\omega - \hat p))}\nonumber\end{equation}
Setting $A_- =0$, we deduce the quasi-normal frequencies
\begin{equation} \hat\omega = \pm \hat p -in\quad,\quad n=1,2,\dots \end{equation}
which form a discrete spectrum of complex frequencies with $\Im\hat\omega < 0$.
\subsubsection{AdS$_5$}
Restricting attention to the case of a large black hole, the massless scalar wave equation reads
\begin{equation}
\frac{1}{r^3}\partial_r (r^5\, f(r)\, \partial_r \Phi) -\frac{R^4}{ r^2\, f(r) }\partial_{t}^2\Phi - \frac{R^2}{r^2}\; \vec\nabla^2\Phi = 0
\ \ , \ \ \ \ \ f(r) = 1- \frac{r_0^4}{r^4}
\end{equation}
Writing the solution in the form
\begin{equation}
\Phi = e^{i(\omega t - \vec p\cdot \vec x)} \Psi (y)
\ \ , \ \ \ \
y = \frac{r^2}{r_0^2}
\end{equation}
the radial wave equation becomes
\begin{equation}
(y^2-1)\left( y(y^2-1) \Psi' \right)' + \left(\frac{\hat\omega^2}{4}\, y^2 - \frac{\hat p^2}{4}\, (y^2-1)\right)\Psi = 0
\end{equation}
For QNMs, we are interested
in the analytic solution which vanishes at the boundary and behaves as an ingoing wave at the horizon.
The wave equation contains an additional
(unphysical) singularity at $y=-1$, at which the wavefunction behaves as
$\Psi \sim (y+1)^{\pm \hat\omega /4}$.
Isolating the behavior of the wavefunction near the singularities $y=\pm 1$,
\begin{equation}
\Psi (y) = (y-1)^{-i\hat\omega/4} (y+1)^{\pm\hat\omega/4} F_\pm (y)
\end{equation}
we shall obtain two sets of modes with the same $\Im\hat\omega$, but opposite
$\Re\hat\omega$.
$F_\pm (y)$ satisfies the Heun equation
\begin{eqnarray}
y(y^2-1) F\pm'' + \left\{ \left( 3- \frac{i\pm 1}{2}\, \hat\omega \right) y^2 - \frac{i \pm 1}{2}\, \hat\omega y -1 \right\} F_\pm' & & \nonumber\\
+ \left\{ \frac{\hat\omega}{2}\left( \pm \frac{i\hat\omega}{4} \mp 1-i\right) y - (i\mp 1)\frac{\hat\omega}{4} - \frac{\hat p^2}{4} \right\}\; F_\pm &=& 0
\end{eqnarray}
to be solved in a region in the complex $y$-plane
containing $|y|\ge 1$ which
includes the physical regime $r> r_h$.
For large $\hat\omega$, the constant terms in the polynomial coefficients of $F'$ and $F$ are small compared with the other terms,
therefore they may be dropped.
The wave equation may then be approximated by a hypergeometric equation
\begin{equation}
(y^2-1) F_\pm'' + \left\{ \left( 3- \frac{i\pm 1}{2}\, \hat\omega \right) y - \frac{i \pm 1}{2}\, \hat\omega \right\} F_\pm'
+ \frac{\hat\omega}{2}\left( \pm \frac{i\hat\omega}{4} \mp 1-i\right)\; F_\pm =0
\end{equation}
in the asymptotic limit of large frequencies $\hat\omega$.
The acceptable solution is
\begin{equation} F_0(x) = {}_2F_1 ( a_+, a_-; c; (y+1)/2)
\ \ , \ \ \ a_\pm = 1-{\textstyle{\frac{i \pm 1}{4}}}\,\hat\omega\pm 1
\quad,\quad c = {\textstyle{\frac{3}{2}}}\pm {\textstyle{\frac{1}{2}}}\,\hat\omega\end{equation}
For proper behavior at the boundary ($y\to\infty$), we demand that $F$ be a {\em polynomial},
which leads to the condition
\begin{equation} a_+ = -n \ \ , \ \ n = 1,2,\dots\end{equation}
Indeed, it implies that $F$ is a polynomial of order $n$, so as $y\to\infty$,
$F\sim y^n
\sim y^{-a_+}$
and $\Psi \sim y^{-i\hat\omega/4} y^{\pm\hat\omega/4} y^{-a_+} \sim y^{-2}$,
as expected.
We deduce the quasi-normal frequencies \cite{siob-MS4}
\begin{equation} \hat\omega = \frac{\omega}{4\pi T_H} = 2n(\pm 1-i) \end{equation}
in agreement with numerical results.
It is perhaps worth mentioning that these frequencies may also be deduced by a simple monodromy argument \cite{siob-MS4}.
Considering the monodromies around the singularities,
if the wavefunction has no singularities other than $y=\pm 1$,
the contour around $y=+1$ may be unobstructedly deformed into the contour
around $y=-1$, which yields
\begin{equation} \mathcal{M} (1) \mathcal{M} (-1) = 1\end{equation}
Since the respective monodromies are
$\mathcal{M} (1) = e^{\pi \hat\omega /2}$ and $\mathcal{M} (-1) = e^{\mp i\pi \hat\omega /2}$,
using $\Im\hat\omega < 0$, we deduce
$\hat\omega = 2n(\pm 1-i)$, in agreement with our result above.
\subsection{Gravitational perturbations}
Next we consider gravitational perturbations of AdS Schwarzschild black holes of arbitrary size in $d$ dimensions.
We shall derive analytic expressions for the asymptotic spectrum \cite{siob-NS} including first-order corrections \cite{siob-MNS}.
Our results will be in good agreement with numerical results.
The metric is
\begin{equation}\label{line}
ds^2 = -f(r)dt^2 +\frac{ dr^2 }{ f(r) } +r^2d \Omega_{d-2}^2\ \ ,\ \ \ f(r) = \frac{r^2}{R^2}+1-\frac{2\mu}{r^{d-3}} \;.
\end{equation}
The radial wave equation
can be cast into a Schr\"odinger-like form,
\begin{equation}\label{sch}
-\frac{d^2\Psi}{dr_*^2}+V[r(r_*)]\Psi =\omega^2\Psi \;,
\end{equation}
in terms of the tortoise coordinate defined by
\begin{equation}\label{tortoise}
\frac{dr_*}{dr} = \frac{1}{f(r)}\;.
\end{equation}
The potential $V$ for the various types of perturbation has been found by Ishibashi and Kodama \cite{siob-IK}.
For tensor, vector and scalar perturbations, we obtain, respectively,
\begin{equation}\label{eqVT} V_{\mathsf{T}} (r) = f(r) \left\{ \frac{\ell (\ell +d-3)}{r^2} + \frac{(d-2)(d-4) f(r)}{4r^2} + \frac{(d-2) f'(r)}{2r} \right\} \end{equation}
\begin{equation}\label{eqVV} V_{\mathsf{V}}(r) = f(r) \left\{ \frac{\ell (\ell +d-3)}{r^2} + \frac{(d-2)(d-4) f(r)}{4r^2} - \frac{r f'''(r)}{2(d-3)} \right\} \end{equation}
\begin{eqnarray}\label{eqVS} V_{\mathsf{S}}(r) &=& \frac{f(r)}{4r^2} \left[ \ell (\ell +d-3) - (d-2) + \frac{(d-1)(d-2)\mu}{r^{d-3}} \right]^{-2} \nonumber\\
&\times& \Bigg\{ \frac{d(d-1)^2(d-2)^3 \mu^2}{R^2r^{2d-8}}
- \frac{6(d-1)(d-2)^2(d-4)[\ell (\ell+d-3) - (d-2)] \mu}{R^2r^{d-5}}\nonumber\\
&& + \frac{(d-4)(d-6)[\ell (\ell+d-3) - (d-2)]^2 r^2}{R^2} +
\frac{2(d-1)^2(d-2)^4 \mu^3}{r^{3d-9}}\nonumber\\
&& + \frac{4(d-1)(d-2)(2d^2-11d+18)[\ell (\ell+d-3) - (d-2)]\mu^2}{r^{2d-6}}\nonumber\\
&& + \frac{(d-1)^2(d-2)^2(d-4)(d-6)\mu^2}{r^{2d-6}}
- \frac{6(d-2)(d-6)[\ell (\ell+d-3) - (d-2)]^2 \mu}{r^{d-3}}\nonumber\\
&& - \frac{6(d-1)(d-2)^2(d-4)[\ell (\ell+d-3) - (d-2)] \mu}{r^{d-3}}\nonumber\\
&& + 4 [\ell (\ell+d-3) - (d-2)]^3 + d(d-2) [\ell (\ell+d-3) - (d-2)]^2 \Bigg\} \nonumber\end{eqnarray}
Near the black hole singularity ($r\sim 0$),
\begin{equation}\label{eqVT0} V_{\mathsf{T}} = -\frac{1}{4r_*^2}+\frac{\mathcal{A}_{\mathsf{T}} }{[-2(d-2)\mu]^{\frac{1}{d-2}}} r_*^{-\frac{d-1}{d-2}} + \dots \, , \ \ \ \
\mathcal{A}_{\mathsf{T}} = \frac{(d-3)^2}{2(2d-5)}+\frac{\ell(\ell+d-3)}{d-2},
\end{equation}
\begin{equation}\label{eqVV0} V_{\mathsf{V}} = \frac{3}{4r_*^2}+\frac{\mathcal{A}_{\mathsf{V}} }{[-2(d-2)\mu]^{\frac{1}{d-2}}} r_*^{-\frac{d-1}{d-2}} + \dots \ \ , \ \ \ \
\mathcal{A}_{\mathsf{V}} = \frac{d^2-8d+13}{2(2d-15)} + \frac{\ell (\ell +d-3)}{d-2}\end{equation}
and
\begin{equation}\label{eqVS0}
V_{\mathsf{S}} = -\frac{1}{4r_*^2}+\frac{\mathcal{A}_{\mathsf{S}} }{[-2(d-2)\mu]^{\frac{1}{d-2}}} r_*^{-\frac{d-1}{d-2}} + \dots \, ,
\end{equation}
where
\begin{equation}\label{eqVS0a}
\mathcal{A}_{\mathsf{S}} = \frac{ (2d^3-24d^2+94d-116)}{4(2d-5)(d-2)}+\frac{ (d^2-7d+14)[ \ell(\ell+d-3)-(d-2)]}{(d-1)(d-2)^2}
\end{equation}
We have included only the terms which contribute to the order we are interested in.
We may summarize the behavior of the potential near the origin by
\begin{equation}\label{eqV0} V= \frac{j^2 -1}{4r_*^2}+\mathcal{A}\, r_*^{-\frac{d-1}{d-2}} + \dots \end{equation}
where $j=0$ ($2$) for scalar and tensor (vector) perturbations.
On the other hand, near the boundary (large $r$),
\begin{equation} V = \frac{j_\infty^2-1}{4(r_*-\bar r_*)^2} + \dots \ \ , \ \ \ \ \bar r_* = \int_0^\infty \frac{dr}{f(r)} \end{equation}
where $j_\infty = d-1$, $d-3$ and $d-5$ for tensor, vector and scalar perturbations,
respectively.
After rescaling the tortoise coordinate $(z=\omega r_*)$,
the wave equation to first order becomes
\begin{equation}\label{we-h}
\left( \mathcal{H}_0+\omega^{-\frac{d-3}{d-2}} \, \mathcal{H}_1 \right) \Psi =0,
\end{equation}
where
\begin{equation}\label{H0-H1}
\mathcal{H}_0= \frac{d^2}{dz^2}-\left[\frac{j^2-1}{4z^2}-1\right]\ \ ,\ \ \mathcal{H}_1=-\mathcal{A}
\; z^{-\frac{d-1}{d-2}}.
\end{equation}
By treating $\mathcal{H}_1$ as a perturbation, we may expand the wave function
\begin{equation}\label{expandwf}
\Psi(z)=\Psi_0(z)+\omega^{-\frac{d-3}{d-2}} \, \Psi_1(z)+\dots
\end{equation}
and solve the wave equation perturbatively.
The zeroth-order wave equation,
\begin{equation}\label{we-0}
\mathcal{H}_0\Psi_0(z)=0,
\end{equation}
may be solved in terms of Bessel functions,
\begin{equation}\label{soln_0}
\Psi_0(z)=A_1\sqrt{z}\, J_{\frac{j}{2}}(z)+A_2 \sqrt{z}\, N_{\frac{j}{2}}(z).
\end{equation}
For large $z$, it behaves as
\begin{eqnarray} \label{soln-0-0}
\Psi_0(z)&\sim& \sqrt{\frac{2}{\pi}}\left[A_1\cos(z-\alpha_+)+A_2\sin(z-\alpha_+)\right]\nonumber\\
&=&\frac{1}{\sqrt{2\pi}}(A_1-iA_2)e^{-i\alpha_+}e^{iz} + \frac{1}{\sqrt{2\pi}}(A_1+iA_2)e^{+i\alpha_+}e^{-iz}\nonumber
\end{eqnarray}
where $\alpha_\pm = \frac{\pi}{4}(1\pm j)$.
At the boundary ($r\to\infty$),
the wavefunction ought to vanish,
therefore the acceptable solution is
\begin{equation}\label{soln-0-infty}
\Psi_0(r_*) = B\sqrt{\omega(r_*-\bar r_*)}\; J_{\frac{j_\infty}{2}}(\omega (r_*-\bar r_*))
\end{equation}
Indeed, $\Psi \to 0$ as $r_*\to \bar r_*$, as desired.
Asymptotically (large $z$), it behaves as
\begin{equation}\label{eq54} \Psi(r_*) \sim \sqrt{\frac{2}{\pi}}\, B\cos\left[ \omega(r_*-\bar r_*)+\beta\right] \ , \ \ \ \
\beta =\frac{\pi}{4}(1+ j_\infty) \end{equation}
We ought to match this to the asymptotic form of the wavefunction in the vicinity of the black-hole singularity along the Stokes line $\Im z = \Im (\omega r_*) = 0$.
This leads to a
constraint on the coefficients $A_1,\ A_2$,
\begin{equation} \label{constraint_1}
A_1\tan(\omega \bar r_* -\beta -\alpha_+)-A_2=0.
\end{equation}
By imposing the boundary condition at the horizon
\begin{equation} \Psi(z) \sim e^{iz}\ \ , \ \ \ \ z\to -\infty\label{bc-0}\ ,
\end{equation}
we obtain a second constraint.
To find it,
we need to analytically continue the wavefunction near the
black hole singularity ($z=0$) to negative values of $z$.
A rotation of $z$ by $-\pi$ corresponds to a rotation by $-\frac{\pi}{d-2}$ near the origin in the complex $r$-plane.
Using the known behavior of Bessel functions
\begin{equation}\label{eqBrot} J_\nu (e^{-i\pi} z) = e^{-i\pi\nu} J_\nu (z) \ , \ \ \ \
N_\nu (e^{-i\pi} z) = e^{i\pi\nu} N_\nu (z) - 2i\cos \pi\nu\, J_\nu (z)\end{equation}
for $z<0$ the wavefunction changes to
\begin{equation}\label{soln_0r}
\Psi_0(z)= e^{-i\pi(j+1)/2} \sqrt{-z}\, \left\{ \left[ A_1 -i (1+e^{i\pi j}) A_2 \right]\, J_{\frac{j}{2}}(-z)+A_2 e^{i\pi j} \, N_{\frac{j}{2}}(-z) \right\}
\end{equation}
whose asymptotic behavior is given by
\begin{equation} \Psi \sim \frac{e^{-i\pi(j+1)/2}}{\sqrt{2\pi}} \left[ A_1-i(1+2e^{j\pi i}) A_2\right]\, e^{-iz}+\frac{e^{-i\pi(j+1)/2}}{\sqrt{2\pi}} \left[ A_1-iA_2\right]\, e^{iz} \end{equation}
Therefore we obtain a second constraint
\begin{equation}\label{constraint_2}
A_1 -i(1+2e^{j\pi i}) A_2 = 0\ \ .
\end{equation}
The two constraints are compatible provided
\begin{equation}\label{eqcomp}
\left| \begin{array}{cc} 1 & -i(1+2e^{j\pi i}) \\
\tan(\omega \bar r_*-\beta-\alpha_+) & -1 \end{array} \right| = 0
\end{equation}
which yields the quasi-normal frequencies \cite{siob-NS}
\begin{equation}
\omega \bar r_* =\frac{\pi}{4} (2+j+ j_\infty)-\tan^{-1} \frac{i}{1+2e^{j\pi i}} +n\pi
\end{equation}
The first-order correction to the above asymptotic expression may be found by standard perturbation theory \cite{siob-MNS}.
To first order, the wave equation becomes
\begin{equation}\label{1stwe1}
\mathcal{H}_0\Psi_1+\mathcal{H}_1\Psi_0=0
\end{equation}
The solution is
\begin{equation}\label{soln_1}
\Psi_1(z) = \sqrt{z}\, N_{\frac{j}{2}}(z)\int_0^z dz'\frac{\sqrt{z'}\, J_{\frac{j}{2}}(z')
\mathcal{H}_1\Psi_0(z') }{ \mathcal{W} } - \sqrt{z}\, J_{\frac{j}{2}}(z)\int_0^z dz'\frac{\sqrt{z'}\, N_{\frac{j}{2}}(z') \mathcal{H}_1\Psi_0(z') }{ \mathcal{W} }
\end{equation}
where $\mathcal{W} = 2/\pi$ is the Wronskian.
The wavefunction to first order reads
\begin{equation}\label{soln1st0}
\Psi(z)=\left\{A_1[1-b(z)] -A_2a_2(z)\right\}\sqrt{z} J_{\frac{j}{2}}(z) +\left\{A_2[1+b(z)]+A_1a_1(z)\right\}\sqrt{z} N_{\frac{j}{2}}(z)
\end{equation}
where
\begin{eqnarray}
a_1(z) &=& \frac{\pi\mathcal{A}}{2} \, \omega^{-\frac{d-3}{d-2}}\, \int_0^z dz'\;{z'}^{-\frac{1}{d-2}}J_{\frac{j}{2}}(z') J_{\frac{j}{2}}(z') \nonumber\\
a_2(z) &=& \frac{\pi\mathcal{A}}{2} \, \omega^{-\frac{d-3}{d-2}}\, \int_0^z dz'\;{z'}^{-\frac{1}{d-2}}N_{\frac{j}{2}}(z') N_{\frac{j}{2}}(z') \nonumber\\
b(z) &=& \frac{\pi\mathcal{A}}{2} \, \omega^{-\frac{d-3}{d-2}}\, \int_0^z dz'\;{z'}^{-\frac{1}{d-2}}J_{\frac{j}{2}}(z') N_{\frac{j}{2}}(z') \nonumber
\end{eqnarray}
and $\mathcal{A}$ depends on the type of perturbation.
Asymptotically, it behaves as
\begin{equation}\label{1stsoln}
\Psi(z)\sim \sqrt{\frac{2}{\pi}}\, [A_1' \cos(z-\alpha_+)+ A_2' \sin(z-\alpha_+)]\ ,
\end{equation}
where
\begin{equation}\label{eq91} A_1' = [1-\bar b]A_1-\bar a_2 A_2\ \ , \ \ \ \
A_2' = [1+\bar b]A_2+\bar a_1 A_1\end{equation}
and we introduced the notation
\begin{equation} \bar a_1 = a_1(\infty)\ \ , \ \ \ \ \bar a_2 = a_2(\infty)\ \ , \ \ \ \ \bar b = b(\infty) \ . \end{equation}
The first constraint is modified to
\begin{equation}\label{newconstr1} A_1' \tan (\omega \bar r_* -\beta -\alpha_+) - A_2' = 0\end{equation}
Explicitly,
\begin{equation}\label{newconstr1a} [ (1-\bar b)\tan (\omega \bar r_* -\beta -\alpha_+)- \bar a_1 ]A_1 -[1+\bar b +\bar a_2 \tan (\omega \bar r_* -\beta -\alpha_+)]A_2 = 0\end{equation}
To find the second constraint to first order,
we need to approach the horizon.
This entails a rotation by $-\pi$ in the $z$-plane.
Using
\begin{eqnarray} a_1 (e^{-i\pi} z) &=& e^{-i\pi \frac{d-3}{d-2}} e^{-i\pi j} a_1 (z)\ , \nonumber\\
a_2 (e^{-i\pi} z) &=& e^{-i\pi \frac{d-3}{d-2}} \left[ e^{i\pi j} a_2(z)
- 4 \cos^2 \frac{\pi j}{2} a_1(z) - 2i (1+e^{i\pi j} ) b (z) \right]\ , \nonumber\\
b (e^{-i\pi} z) &=& e^{-i\pi \frac{d-3}{d-2}} \left[ b(z) -i (1+e^{-i\pi j}) a_1(z) \right]\nonumber\end{eqnarray}
in the limit $z\to -\infty$ we obtain
\begin{equation}\label{soln1st0r}
\Psi(z) \sim -i e^{-ij\pi/2} B_1 \cos(-z-\alpha_+)
-i e^{ij\pi/2} B_2\sin(-z-\alpha_+)
\end{equation}
where
\begin{eqnarray}
B_1 &=&
A_1 -A_1e^{-i\pi\frac{d-3}{d-2}}[{\bar b}-i(1+e^{-i\pi j}){\bar a}_1]
\nonumber \\
& & -A_2e^{-i\pi\frac{d-3}{d-2}} \left[ e^{+i\pi j}{\bar a}_2-4\cos^2\frac{\pi j}{2}{\bar a}_1-2i(1+e^{+i\pi j}){\bar b} \right] \nonumber\\
& & -i (1+e^{i\pi j})\left[ A_2 +A_2e^{-i\pi\frac{d-3}{d-2}}[{\bar b}-i(1+e^{-i\pi j}){\bar a}_1]+A_1 e^{-i\pi\frac{d-3}{d-2}} e^{-i\pi j}{\bar a}_1 \right] \nonumber\\
B_2 &=& A_2+A_2e^{-i\pi\frac{d-3}{d-2}}[{\bar b}-i(1+e^{-i\pi j}){\bar a}_1]+A_1e^{-i\pi\frac{d-3}{d-2}}e^{-i\pi j}{\bar a}_1\nonumber
\end{eqnarray}
Therefore the second constraint to first order reads
\begin{equation}\label{newconstr2} [1-e^{-i\pi\frac{d-3}{d-2}}(i
\bar a_1 +\bar b)]A_1 -[i(1+2e^{i\pi j})+e^{-i\pi\frac{d-3}{d-2}}((1+e^{i\pi j})\bar a_1 +e^{i\pi j} \bar a_2-i\bar b)
]A_2 = 0 \end{equation}
Compatibility of the two first-order constraints yields
\begin{equation}\label{eq99}
\left| \begin{array}{cc} 1+\bar b+\bar a_2\tan (\omega \bar r_* -\beta -\alpha_+) & i(1+2e^{i\pi j})+e^{-i\pi\frac{d-3}{d-2}}((1+e^{i\pi j})\bar a_1 +e^{i\pi j} \bar a_2-i\bar b) \\
(1-\bar b)\tan (\omega \bar r_* -\beta -\alpha_+)- \bar a_1 & 1-e^{-i\pi\frac{d-3}{d-2}}(i
\bar a_1 +\bar b) \end{array} \right| = 0
\end{equation}
leading to the first-order expression for quasi-normal frequencies,
\begin{eqnarray}\label{eqo1st}
\omega {\bar r}_* &=& \frac{\pi}{4}(2+j+j_{\infty}) +\frac{1}{2i}\ln 2+n\pi \nonumber\\
& & -\frac{1}{8}\left\{ 6i\bar b -2i e^{-i\pi\frac{d-3}{d-2}} \bar b -9\bar a_1+e^{-i\pi\frac{d-3}{d-2}}{\bar a}_1 +{\bar a}_2 - e^{-i\pi\frac{d-3}{d-2}}{\bar a}_2 \right\}
\nonumber\end{eqnarray}
where
\begin{eqnarray}\label{eqab} \bar a_1 &=& \frac{\pi\mathcal{A}}{4} \left(\frac{n\pi}{2\bar r_*}\right)^{-\frac{d-3}{d-2}} \frac{\Gamma(\frac{1}{d-2})\Gamma(\frac{j}{2}+\frac{d-3}{2(d-2)})}{\Gamma^2(\frac{d-1}{2(d-2)})\Gamma(\frac{j}{2}+\frac{d-1}{2(d-2)})}\nonumber \\
\bar a_2 &=& \left[ 1+2\cot \frac{\pi (d-3)}{2(d-2)} \cot \frac{\pi}{2} \left( -j+\frac{d-3}{d-2}\right) \right]\bar a_1 \nonumber \\
\bar b &=& -\cot \frac{\pi (d-3)}{2(d-2)}\ \bar a_1 \nonumber\end{eqnarray}
Thus the first-order correction is $\sim \mathcal{O} (n^{-\frac{d-3}{d-2}})$.
The above analytic results are in good agreement with numerical results \cite{siob-CKL}
(see ref.~\cite{siob-MNS} for a detailed comparison).
\subsection{Electromagnetic perturbations}\label{sect3}
The
electromagnetic potential in four dimensions is
\begin{equation}\label{V-V}
V_{\mathsf{EM}} =\frac{\ell(\ell+1)}{r^2}f(r).
\end{equation}
Near the origin,
\begin{equation}\label{eqVEMr}
V_{\mathsf{EM}} =\frac{j^2-1}{4r_*^2}+\frac{\ell(\ell+1)r_*^{-3/2}}{2\sqrt{-4\mu}}+\dots \ ,
\end{equation}
where $j=1$. Therefore we have a vanishing potential to zeroth order.
To calculate the QNM spectrum we need to include first-order corrections from the outset.
Working as with gravitational perturbations, we obtain the
QNMs
\begin{equation}\label{eqEMo1}
\omega {\bar r}_* = n\pi -\frac{i}{4}\ln n+\frac{1}{2i}\ln\left( 2(1+i){\cal A}\sqrt{\bar r_*}\right) \ , \ \ \ \ \mathcal{A}
= \frac{\ell(\ell+1)}{2\sqrt{-4\mu}}
\end{equation}
Notice that the first-order correction behaves as $\ln n$, a fact which may be associated with gauge invariance.
As with gravitational perturbations, the above analytic results are in good agreement with numerical results \cite{siob-CKL}
(see ref.~\cite{siob-MNS} for a detailed comparison).
\section{AdS/CFT correspondence and hydrodynamics}
\label{siosec:6}
\begin{quotation}
A second unexpected connection comes from studies carried out using the Relativistic Heavy Ion Collider, a particle accelerator at Brookhaven National Laboratory. This machine smashes together nuclei at high energy to produce a hot, strongly interacting plasma. Physicists have found that some of the properties of this plasma are better modeled (via duality) as a tiny black hole in a space with extra dimensions than as the expected clump of elementary particles in the usual four dimensions of spacetime. The prediction here is again not a sharp one, as the string model works much better than expected. String-theory skeptics could take the point of view that it is just a mathematical spinoff. However, one of the repeated lessons of physics is unity - nature uses a small number of principles in diverse ways. And so the quantum gravity that is manifesting itself in dual form at Brookhaven is likely to be the same one that operates everywhere else in the universe.
\rightline{\small -- Joe Polchinski}
\end{quotation}
There is a correspondence between
$\mathcal{N}=4$ Super Yang-Mills (SYM) theory in the large $N$ limit
and type-IIB string theory in $\mathrm{AdS}_5\times \mathrm{S^5}$ (AdS/CFT correspondence).
In the low energy limit, string theory is
reduced to classical supergravity and the AdS/CFT correspondence allows one to calculate all
gauge field-theory correlation functions in the strong coupling limit leading to non-trivial predictions on the behavior of gauge theory fluids.
For example,
the entropy of $\mathcal{N}=4$ SYM
theory in the limit of large
't Hooft coupling is precisely 3/4 its value in the zero
coupling limit.
The long-distance (low-frequency) behavior of any
interacting theory at finite temperature must be described by fluid mechanics
(hydrodynamics).
This leads to a
universality in physical properties because
hydrodynamics implies very precise constraints on
correlation functions of conserved currents and
the stress-energy tensor.
Their correlators are
fixed once a few transport coefficients are
known.
\subsection{Hydrodynamics}
\label{sec:hydro}
To study hydrodynamics of the gauge theory fluid, suppose it possesses a conserved current
$j^\mu$.
For simplicity, let us set the
chemical potential $\mu = 0$, so that in thermal equilibrium
the charge density $\langle j^0\rangle =0$.
The retarded thermal Green
function is given by
\begin{equation}
G^R_{\mu\nu} (\omega, q) = -i\!\int\!d^4x\,e^{-iq\cdot x}\,
\theta(t) \langle [j_\mu(x),\, j_\nu(0)] \rangle \,,
\end{equation}
where $q=(\omega,\vec{q})$, $x=(t,\vec{x})$.
It
determines the response of the system to a small
external source coupled to the current.
For small $\omega$ and $|\vec{q}|$,
the external perturbation varies slowly in space and time.
Then a macroscopic hydrodynamic description for its evolution is possible \cite{siob-PSS}.
For a charged density obeying the diffusion equation
\begin{equation}
\partial_0 j^0 = D \nabla^2 j^0\,,
\end{equation}
where $D$ is the diffusion constant with dimension of length,
we obtain an overdamped mode with dispersion relation
\begin{equation}
\omega = - i D \vec{q}^2 \,,
\end{equation}
The corresponding retarded Green function has a pole at $\omega=-iD\vec{q}^2$
in the complex $\omega$-plane.
Another important conserved current is the stress-energy tensor
$T^{\mu\nu}$.
Its conservation law may be written as
\begin{equation}
\begin{split}
& \partial_0 \tilde T^{00} + \partial_i T^{0i} = 0\,,\\
& \partial_0 T^{0i} + \partial_j \tilde T^{ij} = 0\,,
\end{split}
\end{equation}
where
\begin{equation}
\begin{split}
\tilde T^{00} &= T^{00} - \rho, \qquad \rho =\langle T^{00}\rangle \,,\\
\tilde T^{ij} &= T^{ij} - p\delta^{ij}
=- \frac1{\rho + p}\Bigl[\eta \Bigl(\partial_i T^{0j} + \partial_j T^{0i}
-\frac23
\delta^{ij}\partial_k T^{0k}\Bigl)
+ \zeta \delta^{ij}\partial_k T^{0k}\Bigr],
\end{split}
\end{equation}
and $\rho$ ($p$) is the energy density (pressure) of the fluid,
$\eta$ ($\zeta$) is its shear (bulk) viscosity.
One obtains two types of eigenmodes,
the
shear modes which consist of transverse fluctuations of the momentum
density $T^{0i}$, with a purely imaginary eigenvalue
\begin{equation}
\omega = - i Dq^2 \ \ , \ \ \ \ D = \frac{\eta}{\rho+p} \,,
\end{equation}
and a sound wave due to simultaneous fluctuations of
the energy density $T^{00}$ and the longitudinal component of momentum
density $T^{0i}$, with dispersion relation
\begin{equation}
\omega = u_s q - \frac i2 \frac1{\rho+p}
\left(\zeta+\frac43\eta\right)q^2 \,,
\qquad u_s^2 = \frac{\partial p}{\partial\rho}\, .
\end{equation}
In a conformal field theory,
the stress-energy tensor is traceless, so
\begin{equation}\rho=3p\ \ , \ \ \ \ \zeta=0\ \ , \ \ \ \ u_s = \frac{1}{\sqrt 3}\end{equation}
\subsection{Branes}
\label{sec:grav}
To understand the gravitational side of the AdS/CFT correspondence, consider
a non-extremal 3-brane which is a solution of type-IIB low energy equations of motion.
In the near-horizon limit $r\ll R$ where $R$ is the AdS radius, the metric becomes
\begin{equation}
ds^2_{10} =
\frac{(\pi T R)^2}u
\left( -f(u) dt^2 + dx^2 + dy^2 +dz^2 \right)
+\frac{R^2}{ 4 u^2 f(u)} du^2 + R^2 d\Omega_5^2\,,
\end{equation}
where $T = \frac{r_0}{\pi R^2}$ is the Hawking temperature, and we have defined
$u = \frac{r_0^2}{r^2}$, $f(u)=1-u^2$.
The horizon corresponds to $u=1$ whereas spatial infinity is at $u=0$.
According to the gauge theory/gravity correspondence,
the above background metric with non-extremality parameter $r_0$
is dual to ${\cal N}=4$ $SU(N)$
SYM at finite temperature $T$
in the limit of $N\rightarrow \infty$, $g^2_{YM}N \rightarrow \infty$.
For the retarded Green function
\begin{equation}
G_{\mu\nu,\lambda\rho} (\omega, \vec{q})
= -i\!\int\!d^4x\,e^{-iq\cdot x}\,
\theta(t) \langle [T_{\mu\nu}(x),\, T_{\lambda\rho}(0)] \rangle\,.
\end{equation}
we deduce by considering an appropriate perturbation of the background metric \cite{siob-PSS},
\begin{equation}
G_{xy,xy}(\omega,\vec{q}) =
- \frac{ N^2 T^2 }{ 16 }\left( i\, 2 \pi T \omega + \vec{q}^2 \right) \,.
\end{equation}
leading to the shear viscosity of strongly coupled
${\cal N}=4$ SYM plasma (Kubo formula)
\begin{equation}
\eta = \lim_{\omega \rightarrow 0} \frac{1}{ 2\omega}
\int\!dt\,d\vec{x}\, e^{i\omega t}\,
\langle [ T_{xy}(x),\, T_{xy}(0)]\rangle =
\frac{\pi}8 N^2 T^3\,.
\end{equation}
Other correlators may also be found by different perturbations of the metric.
One obtains
\begin{subequations}\label{corr-T}
\begin{eqnarray}
G_{tx,tx}(\omega,\vec{q}) &=&
\frac{ N^2\pi T^3 \vec{q}^2 }{ 8 (i\omega - {\cal D} \vec{q}^2)}
+ \dots
\,,
\rule[-.2in]{0in}{.2in}\nonumber\\
G_{tx,xz}(\omega,\vec{q}) &=&
- \frac{ N^2\pi T^3 \omega |\vec{q}| }{ 8 (i\omega - {\cal D} \vec{q}^2)}
+ \dots
\,,\rule[-.2in]{0in}{.2in}\nonumber\\
G_{xz,xz}(\omega,\vec{q}) &=&
\frac{ N^2\pi T^3 \omega^2 }{ 8 (i\omega - {\cal D} \vec{q}^2)}
+ \dots
\,,
\end{eqnarray}
\end{subequations}
where
${\cal D} = \frac1{4\pi T}$.
From the above results, one may deduce the viscosity $\eta$.
Indeed,
recall from hydrodynamics
${\cal D}=\frac{\eta}{\rho+p}$.
Using the
entropy
\begin{equation}
s = \frac34 s_0 = \frac{\pi^2}2 N^2 T^3\,,
\end{equation}
where $s_0$ is the entropy at zero coupling,
and the thermodynamic equations
$s=\frac{\partial P}{\partial T}$,
$\rho=3p$, we deduce
$\rho+p=\frac{\pi^2}2N^2T^4$,
therefore
\begin{equation}\eta=\frac\pi8N^2T^3\ \ , \ \ \ \ \frac{\eta}{s} = \frac{1}{4\pi}\end{equation}
which agrees
with the Kubo formula.
It should be pointed out that there is no agreement unless $s= \frac{3}{4} s_0$, a fact which is still poorly understood.
The above result for the viscosity is based on the gravity dual of the gauge theory fluid and should correspond to its strong coupling regime.
At weak coupling, one obtains by a direct calculation
\begin{equation} \frac{\eta}{s} \gg \frac{1}{4\pi} \end{equation}
Thus the viscocity coefficient $\eta$ varies
as a function of the 't Hooft coupling,
\begin{equation}
\eta = f_\eta(g_{\mathrm{YM}}^2N) N^2T^3
\end{equation}
where $f_\eta(x)\sim \frac{1}{-x^2\ln x}$ for $x\ll1$ and
$f_\eta(x)=\frac\pi8$ for $x\gg1$.
\subsection{Schwarzschild black holes}
In the metric considered above, the horizon was flat. This corresponds to the limit of a large black hole.
For a black hole of finite size, the horizon is generally a sphere.
Then the boundary of spacetime is $S^3\times\mathbb{R}$.
This may be conformally mapped onto a flat Minkowski space.
Then by holographic renormalization,
the AdS$_5$-Schwarzschild black hole is dual to a spherical shell of plasma on the four-dimensional Minkowski space which first contracts and then expands (conformal soliton flow) \cite{siob-Princ}.
Quasi-normal modes govern the properties of this plasma with long-lived modes (i.e., of small $\Im\omega$) having the most influence.
For example, one obtains the ratio
\begin{equation} \frac{v_2}{\delta} = \frac{1}{6\pi} \Re \frac{\omega^4-40\omega^2+72}{\omega^3-4\omega} \sin \frac{\pi\omega}{2} \end{equation}
where
$v_2 = \langle \cos 2\phi \rangle$ evaluated at $\theta = \frac{\pi}{2}$ (mid-rapidity) and averaged with respect to the energy density at late times;
$\delta = \frac{\langle y^2 - x^2 \rangle}{\langle y^2 + x^2 \rangle}$ is the eccentricity at time $t=0$.
Numerically, $\frac{v_2}{\delta} = 0.37$, which compares well with the result from RHIC data, $\frac{v_2}{\delta} \approx 0.323$ \cite{siob-PHENIX}.
Another observable is the thermalization time which is found to be
\begin{equation} \tau = \frac{1}{2|\Im \omega|} \approx \frac{1}{8.6 T_{\mathrm{peak}}} \approx 0.08~\mathrm{fm/c}\ \ , \ \ \ \ T_{\mathrm{peak}} = 300~\mathrm{MeV} \end{equation}
not in agreement with the RHIC result $\tau \sim 0.6$~fm/c \cite{siob-RHIC}, but still encouragingly small.
For comparison, the corresponding result from perturbative QCD is $\tau \gtrsim 2.5$~fm/c \cite{siob-QCD,siob-QCD2}.
The above results motivate the calculation of low-lying QNMs. Earlier, we calculated analytically the asymptotic form of QNMs for large black holes.
We obtained frequencies which were proportional to the horizon radius $r_0$.
We found an infinite spectrum, however we missed the lowest frequencies which
are inversely proportional to $r_0$.
The latter are important in the understanding of the hydrodynamic behavior of the gauge theory fluid via the AdS/CFT correspondence.
\subsubsection{Vector perturbations}
We start with vector perturbations and work in a $d$-dimensional Schwarzschild background. It is convenient to introduce
the coordinate \cite{siob-ego}
\begin{equation}\label{eqru} u = \left( \frac{r_0}{r} \right)^{d-3} \end{equation}
The wave equation becomes
\begin{equation}\label{eq13} -(d-3)^2 u^{\frac{d-4}{d-3}}\hat f(u) \left( u^{\frac{d-4}{d-3}}\hat f(u) \Psi' \right)' +\hat V_{\mathsf{V}} (u)\Psi = \hat\omega^2 \Psi \ \ , \ \ \ \
\hat\omega = \frac{\omega}{r_0}\end{equation}
where prime denotes differentiation with respect to $u$ and we have defined
\begin{equation}\label{eq14} \hat f(u) \equiv \frac{f(r)}{r^2} = 1- u^{\frac{2}{d-3}} \left( u- \frac{1 - u}{r_0^2} \right) \end{equation}
\begin{equation}\label{eq15} \hat V_{\mathsf{V}} (u) \equiv \frac{V_{\mathsf{V}}}{r_0^2} = \hat f(u) \left\{ \hat L^2 + \frac{(d-2)(d-4)}{4} u^{-\frac{2}{d-3}}\hat f(u) - \frac{(d-1)(d-2)\left( 1+ \frac{1}{r_0^2} \right)}{2} u\right\} \end{equation}
where
$\hat L^2 = \frac{\ell (\ell +d-3)}{r_0^2} $.
First let us consider the large black hole limit $r_0 \to\infty$ keeping $\hat\omega$ and $\hat L$ fixed~(small).
Factoring out the behavior at the horizon ($u=1$)
\begin{equation} \Psi = (1-u)^{-i \frac{\hat\omega}{d-1}} F(u) \end{equation}
the wave equation simplifies to
\begin{equation}\label{sch2} \mathcal{A} F'' + \mathcal{B}_{\hat\omega} F' + \mathcal{C}_{\hat\omega , \hat L} F = 0 \end{equation}
where
\begin{eqnarray} \mathcal{A} &=& - (d-3)^2 u^{\frac{2d-8}{d-3}} (1-u^{\frac{d-1}{d-3}}) \nonumber\\
\mathcal{B}_{\hat\omega} &=& - (d-3) [ d-4-(2d-5)u^{\frac{d-1}{d-3}}]u^{\frac{d-5}{d-3}} - 2(d-3)^2 \frac{i\hat\omega}{d-1}\frac{u^{\frac{2d-8}{d-3}} (1-u^{\frac{d-1}{d-3}})}{1-u} \nonumber\\
\mathcal{C}_{\hat\omega , \hat L} &=& \hat L^2 + \frac{(d-2)[d-4-3(d-2)u^{\frac{d-1}{d-3}}]}{4}u^{-\frac{2}{d-3}} \nonumber\\
& & - \frac{\hat\omega^2}{1-u^{\frac{d-1}{d-3}}} + (d-3)^2 \frac{\hat\omega^2}{(d-1)^2}\frac{u^{\frac{2d-8}{d-3}} (1-u^{\frac{d-1}{d-3}})}{(1-u)^2}\nonumber\\
& &
- (d-3)\frac{i\hat\omega}{d-1} \frac{[ d-4-(2d-5)u^{\frac{d-1}{d-3}}]u^{\frac{d-5}{d-3}} }{1-u} - (d-3)^2 \frac{i\hat\omega}{d-1}\frac{u^{\frac{2d-8}{d-3}} (1-u^{\frac{d-1}{d-3}})}{(1-u)^2}\nonumber\end{eqnarray}
We may
solve this equation perturbatively by separating
\begin{equation} (\mathcal{H}_0 + \mathcal{H}_1) F = 0 \end{equation}
where
\begin{eqnarray}\label{eqH0} \mathcal{H}_0 F &\equiv& \mathcal{A} F'' + \mathcal{B}_0 F' + \mathcal{C}_{0 , 0} F \nonumber\\
\mathcal{H}_1 F &\equiv& (\mathcal{B}_{\hat\omega} - \mathcal{B}_0) F' + (\mathcal{C}_{\hat\omega , \hat L} - \mathcal{C}_{0 , 0}) F \nonumber\end{eqnarray}
Expanding the wavefunction perturbatively,
\begin{equation} F = F_0 + F_1 + \dots \end{equation}
at zeroth order the wave equation reads
\begin{equation}\label{eq22} \mathcal{H}_0 F_0 = 0 \end{equation}
whose acceptable solution is
\begin{equation}\label{eq23} F_0 = u^{\frac{d-2}{2(d-3)}} \end{equation}
being regular at both the horizon ($u=1$) and the boundary ($u=0$, or $\Psi \sim r^{-\frac{d-2}{2}}\to 0$ as $r\to\infty$).
The Wronskian is
\begin{equation} \mathcal{W} = \frac{1}{u^{\frac{d-4}{d-3}} (1-u^{\frac{d-1}{d-3}})} \end{equation}
and another linearly independent solution is
\begin{equation}\label{eqchF0} \check F_0 = F_0\int \frac{\mathcal{W}}{F_0^2} \end{equation}
which is unacceptable because it diverges at both the horizon ($\check F_0 \sim \ln (1-u)$ for $u\approx 1$) and the boundary ($\check F_0 \sim u^{-\frac{d-4}{2(d-3)}}$ for $u\approx 0$, or $\Psi \sim r^{\frac{d-4}{2}} \to\infty$ as $r\to\infty$).
At first order the wave equation reads
\begin{equation} \mathcal{H}_0 F_1 =- \mathcal{H}_1 F_0 \end{equation}
whose solution may be written as
\begin{equation}\label{eqF1} F_1 = F_0\int \frac{\mathcal{W}}{F_0^2} \int \frac{F_0\mathcal{H}_1 F_0}{\mathcal{A}\mathcal{W}} \end{equation}
The limits of the inner integral may be adjusted at will
because this amounts to adding an arbitrary amount of the unacceptable solution.
To ensure regularity at the horizon, choose one of the limits of integration at $u=1$
rendering the integrand regular at the horizon.
Then at the boundary ($u=0$),
\begin{equation} F_1 = \check F_0 \int_0^1 \frac{F_0\mathcal{H}_1 F_0}{\mathcal{A}\mathcal{W}} + \mathrm{regular~terms} \end{equation}
The coefficient of the singularity ought to vanish,
\begin{equation}\label{eq29} \int_0^1 \frac{F_0 \mathcal{H}_1 F_0}{\mathcal{A}\mathcal{W}} = 0 \end{equation}
which yields a constraint on the parameters (dispersion relation)
\begin{equation}\label{eqdisp} \mathbf{a}_0 \hat L^2 -i \mathbf{a}_1 \hat\omega - \mathbf{a}_2 \hat\omega^2 = 0 \end{equation}
After some algebra, we arrive at
\begin{equation}\label{eqcoef} \mathbf{a}_0 = \frac{d-3}{d-1} \ \ , \ \ \ \
\mathbf{a}_1 = d-3 \end{equation}
The coefficient $\mathbf{a}_2$
may also be found explicitly for each dimension $d$,
but it cannot be written as a function of $d$ in closed form.
It does not contribute to the dispersion relation at lowest order.
E.g., for $d=4,5$, we obtain, respectively
\begin{equation}\label{eqa2} \mathbf{a}_2 = \frac{65}{108} -\frac{1}{3}\ln 3 \ \ , \ \ \ \
\frac{5}{6}-\frac{1}{2}\ln 2 \end{equation}
Eq.~(\ref{eqdisp}) is quadratic in $\hat\omega$ and has two solutions,
\begin{equation} \hat\omega_0 \approx -i\frac{\hat L^2}{d-1} \ \ , \ \ \ \ \hat\omega_1 \approx -i \frac{d-3}{\mathbf{a}_2} + i\frac{\hat L^2}{d-1} \end{equation}
In terms of the frequency $\omega$ and the quantum number $\ell$,
\begin{equation}\label{eq34} \omega_0 \approx -i\frac{\ell(\ell+d-3)}{(d-1)r_0} \ \ , \ \ \ \ \frac{\omega_1}{r_0} \approx -i \frac{d-3}{\mathbf{a}_2} + i\frac{\ell(\ell+d-3)}{(d-1)r_0^2} \end{equation}
The smaller of the two, $\omega_0$,
is inversely proportional to the radius of the horizon
and is not included in the asymptotic spectrum.
The other solution, $\omega_1$,
is a crude estimate of the first overtone in the asymptotic spectrum, nevertheless
it shares two important features with the asymptotic spectrum:
it is proportional to $r_0$
and its dependence on $\ell$ is $\mathcal{O} (1/r_0^2)$.
The approximation may be improved by including higher-order terms.
This increases the degree of the polynomial in the dispersion relation (\ref{eqdisp}) whose roots then yield approximate values of more QNMs.
This method reproduces the asymptotic spectrum derived earlier albeit not in an efficient way.
To include finite size effects,
we shall use perturbation theory (assuming $1/r_0$ is small) and replace
$\mathcal{H}_1$ by
\begin{equation}\label{eqH1} \mathcal{H}_1' = \mathcal{H}_1 + \frac{1}{r_0^2} \mathcal{H}_H \end{equation}
where
\begin{equation} \mathcal{H}_H F \equiv \mathcal{A}_H F'' + \mathcal{B}_H F' + \mathcal{C}_H F \end{equation}
The coefficients may be easily deduced by collecting $\mathcal{O} (1/r_0^2)$ terms in the exact wave equation.
We obtain
\begin{eqnarray} \mathcal{A}_H &=& -2(d-3)^2 u^2(1-u) \nonumber\\
\mathcal{B}_H &=& -(d-3) u\left[ (d-3)(2-3u) - (d-1) \frac{1-u}{1-u^{\frac{d-1}{d-3}}} u^{\frac{d-1}{d-3}} \right] \nonumber\\
\mathcal{C}_H &=& \frac{d-2}{2} \left[ d-4-(2d-5)u - (d-1) \frac{1-u}{1-u^{\frac{d-1}{d-3}}} u^{\frac{d-1}{d-3}} \right] \nonumber\end{eqnarray}
Interestingly, the zeroth order wavefunction $F_0$ is an eigenfunction of $\mathcal{H}_H$,
\begin{equation} \mathcal{H}_H F_0 = -(d-2) F_0 \end{equation}
therefore the first-order finite-size effect is a simple shift of the angular momentum operator
\begin{equation} \hat L^2 \to \hat L^2 - \frac{d-2}{r_0^2} \end{equation}
The QNMs of lowest frequency are modified to
\begin{equation}\label{eqo0} \omega_0 = - i \frac{\ell(\ell+d-3)-(d-2)}{(d-1)r_0} + \mathcal{O} (1/r_0^2) \end{equation}
For $d=4, 5$, we have respectively,
\begin{equation} \omega_0 = - i \frac{(\ell-1)(\ell+2)}{3r_0} \ \ , \ \ \ \ - i \frac{(\ell+1)^2-4}{4r_0} \end{equation}
in agreement with numerical results \cite{siob-CKL,siob-Princ}.
According to the AdS/CFT correspondence,
dual to the AdS Schwarzschild black hole is a gauge theory fluid on the boundary of AdS ($S^{d-2} \times~\mathbb{R}$).
Consider the fluid dynamics ansatz
\begin{equation}\label{eqansv} u_i = \mathcal{K} e^{-i\Omega \tau} \mathbb{V}_i \end{equation}
where $u_i$ is the (small) velocity of a point in the fluid,
and $\mathbb{V}_i$ a vector harmonic on $S^{d-2}$.
Demanding that this ansatz satisfy the standard equations of linearized hydrodynamics,
one arrives at a constraint on the frequency of the perturbation $\Omega$ which yields \cite{siob-MP}
\begin{equation} \Omega = -i \frac{\ell(\ell+d-3)-(d-2)}{(d-1)r_0} + \mathcal{O} (1/r_0^2) \end{equation}
in perfect agreement with its dual counterpart.
\subsubsection{Scalar perturbations}
Next we consider scalar perturbations which are calculationally more involved but phenomenologically more important because theirspectrum contains the lowest frequencies.
For a scalar perturbation we ought to replace the potential $\hat V_{\mathsf{V}}$ by
\begin{eqnarray} \hat V_{\mathsf{S}}(u) &=& \frac{\hat f(u)}{4} \left[ \hat m + \left( 1 + \frac{1}{r_0^2} \right) u\right]^{-2} \nonumber\\
&\times& \Bigg\{ d(d-2) \left( 1+ \frac{1}{r_0^2} \right)^2 u^{\frac{2d-8}{d-3}}
- 6(d-2)(d-4)\hat m \left( 1+ \frac{1}{r_0^2} \right) u^{\frac{d-5}{d-3}}\nonumber\\
&& + (d-4)(d-6)\hat m^2u^{-\frac{2}{d-3}} +
(d-2)^2 \left( 1+ \frac{1}{r_0^2} \right)^3 u^3 \nonumber\\
&& + 2(2d^2-11d+18)\hat m \left( 1+ \frac{1}{r_0^2} \right)^2 u^2\nonumber\\
&& + \frac{(d-4)(d-6)\left( 1+\frac{1}{r_0^2} \right)^2}{r_0^2} u^2
- 3(d-2)(d-6)\hat m^2 \left( 1+\frac{1}{r_0^2} \right) u\nonumber\\
&& - \frac{6(d-2)(d-4)\hat m\left( 1+\frac{1}{r_0^2} \right)}{r_0^2} u + 2 (d-1)(d-2)\hat m^3 + d(d-2) \frac{\hat m^2}{r_0^2} \Bigg\} \nonumber\\ \end{eqnarray}
where
$\hat m = 2\frac{\ell (\ell+d-3) - (d-2)}{(d-1)(d-2)r_0^2} = \frac{2(\ell + d-2)(\ell -1)}{(d-1)(d-2)r_0^2} $.
In the large black hole limit $r_0\to \infty$ with $\hat m$ fixed (small), the potential simplifies to
\begin{eqnarray} \hat V_{\mathsf{S}}^{(0)}(u) &=& \frac{1-u^{\frac{d-1}{d-3}}}{4( \hat m + u)^2}
\Bigg\{ d(d-2) u^{\frac{2d-8}{d-3}}
- 6(d-2)(d-4)\hat m u^{\frac{d-5}{d-3}}\nonumber\\
&& + (d-4)(d-6)\hat m^2u^{-\frac{2}{d-3}} +
(d-2)^2 u^3\nonumber\\
&&
+ 2(2d^2-11d+18)\hat m u^2
- 3(d-2)(d-6)\hat m^2 u
+ 2 (d-1)(d-2)\hat m^3 \Bigg\} \nonumber\\ \end{eqnarray}
The wave equation has an additional singularity due to the double pole of the scalar potential
at $u = -\hat m$.
It is desirable to factor out the behavior not only at the horizon, but also at the boundary and the pole of the scalar potential,
\begin{equation}\label{eqPsiF} \Psi = (1-u)^{-i\frac{\hat\omega}{d-1}} \frac{u^{\frac{d-4}{2(d-3)}}}{\hat m + u} F(u) \end{equation}
Then the wave equation reads
\begin{equation}\label{eqwsc} \mathcal{A} F'' + \mathcal{B}_{\hat\omega} F' + \mathcal{C}_{\hat\omega} F = 0 \end{equation}
where
\begin{eqnarray} \mathcal{A} &=& - (d-3)^2 u^{\frac{2d-8}{d-3}} (1-u^{\frac{d-1}{d-3}}) \nonumber\\
\mathcal{B}_{\hat\omega} &=& - (d-3) u^{\frac{2d-8}{d-3}} (1-u^{\frac{d-1}{d-3}}) \left[ \frac{d-4}{u} -\frac{2(d-3)}{\hat m + u} \right] \nonumber\\
&& - (d-3) [ d-4-(2d-5)u^{\frac{d-1}{d-3}}]u^{\frac{d-5}{d-3}} - 2(d-3)^2 \frac{i\hat\omega}{d-1}\frac{u^{\frac{2d-8}{d-3}} (1-u^{\frac{d-1}{d-3}})}{1-u} \nonumber\\
\mathcal{C}_{\hat\omega} &=& - u^{\frac{2d-8}{d-3}} (1-u^{\frac{d-1}{d-3}}) \left[ -\frac{(d-2)(d-4)}{4 u^2} - \frac{(d-3)(d-4)}{u(\hat m + u)} + \frac{2(d-3)^2}{(\hat m + u)^2} \right] \nonumber\\
&& - \left[ \left\{ d-4-(2d-5)u^{\frac{d-1}{d-3}} \right\} u^{\frac{d-5}{d-3}} + 2(d-3) \frac{i\hat\omega}{d-1}\frac{u^{\frac{2d-8}{d-3}} (1-u^{\frac{d-1}{d-3}})}{1-u}\right]\left[ \frac{d-4}{2u} - \frac{d-3}{\hat m + u} \right] \nonumber\\
&& - (d-3)\frac{i\hat\omega}{d-1} \frac{[ d-4-(2d-5)u^{\frac{d-1}{d-3}}]u^{\frac{d-5}{d-3}} }{1-u} - (d-3)^2 \frac{i\hat\omega}{d-1}\frac{u^{\frac{2d-8}{d-3}} (1-u^{\frac{d-1}{d-3}})}{(1-u)^2}\nonumber\\
&& + \frac{\hat V_{\mathsf{S}}^{(0)}(u)-\hat\omega^2}{1-u^{\frac{d-1}{d-3}}} + (d-3)^2 \frac{\hat\omega^2}{(d-1)^2}\frac{u^{\frac{2d-8}{d-3}} (1-u^{\frac{d-1}{d-3}})}{(1-u)^2}\nonumber\end{eqnarray}
We shall define zeroth-order wave equation as $\mathcal{H}_0 F_0 = 0$, where
\begin{equation}\label{eq0sc} \mathcal{H}_0 F \equiv \mathcal{A} F'' + \mathcal{B}_0 F' \end{equation}
The acceptable zeroth-order solution is
\begin{equation}\label{eqF0sc} F_0(u) = 1 \end{equation}
which is plainly regular at all singular points ($u=0,1, -\hat m$).
It corresponds to a wavefunction vanishing at the boundary
($\Psi \sim r^{-\frac{d-4}{2}}$ as $r\to\infty$).
The Wronskian is
\begin{equation}\label{eqWsc} \mathcal{W} = \frac{\left( \hat m + u\right)^2 }{u^{\frac{2d-8}{d-3}} (1-u^{\frac{d-1}{d-3}})} \end{equation}
and an nacceptable solution is $ \check F_0 = \int \mathcal{W} $.
It can be written in terms of hypergeometric functions.
For $d\ge 6$, it has a singularity at the boundary, $\check F_0 \sim u^{-\frac{d-5}{d-3}}$ for $u\approx 0$,
or $\Psi \sim r^{\frac{d-6}{2}}\to\infty$ as $r\to\infty$.
For $d=5$, the acceptable wavefunction behaves as $r^{-1/2}$ whereas the unacceptable one behaves as $r^{-1/2} \ln r$.
For $d=4$, the roles of $F_0$ and $\check F_0$ are reversed, however the results still valid because the correct boundary condition at the boundary is a Robin boundary condition \cite{siob-ego,siob-MP}.
Finally, we note that $\check F_0$ is also singular (logarithmically) at the horizon ($u=1$).
Working as in the case of vector modes,
we arrive at the first-order constraint
\begin{equation}\label{eqcnssc} \int_0^1 \frac{\mathcal{C}_{\hat\omega}}{\mathcal{A}\mathcal{W}} = 0 \end{equation}
because $\mathcal{H}_1 F_0 \equiv (\mathcal{B}_{\hat\omega} - \mathcal{B}_0) F_0'
+ \mathcal{C}_{\hat\omega} F_0 = \mathcal{C}_{\hat\omega} $.
This leads to the
dispersion relation
\begin{equation}\label{eqcnssc2} \mathbf{a}_0 - \mathbf{a}_1 i\hat\omega - \mathbf{a}_2 \hat\omega^2 = 0 \end{equation}
After some algebra, we obtain
\begin{equation} \mathbf{a}_0 = \frac{d-1}{2} \ \frac{ 1+ (d-2)\hat m}{(1+ \hat m )^2} \ \ ,
\ \ \ \ \mathbf{a}_1 = \frac{d-3}{(1+ \hat m )^2} \ \ ,
\ \ \ \ \mathbf{a}_2 = \frac{1}{\hat m} \left\{ 1 + O(\hat m) \right\} \end{equation}
For small $\hat m$, the quadratic equation has solutions
\begin{equation}\label{eqosc1} \hat\omega_0^\pm \approx - i\frac{d-3}{2} \ \hat m \pm \sqrt{ \frac{d-1}{2} \ \hat m} \end{equation}
related to each other by $\hat\omega_0^+ = -\hat\omega_0^{-*}$, which is a
general symmetry of the spectrum.
Finite size effects
at first order amount to a shift of the coefficient $\mathbf{a}_0$ in the dispersion relation
\begin{equation} \mathbf{a}_0 \to \mathbf{a}_0 + \frac{1}{r_0^2} \mathbf{a}_H \end{equation}
After some tedious but straightforward algebra, we obtain
\begin{equation} \mathbf{a}_H = \frac{1}{\hat m} \left\{ 1 + O(\hat m) \right\} \end{equation}
The modified dispersion relation yields the modes
\begin{equation}\label{eqosc2} \hat\omega_0^\pm \approx - i\frac{d-3}{2} \ \hat m \pm \sqrt{ \frac{d-1}{2} \ \hat m +1} \end{equation}
In terms of the quantum number $\ell$,
\begin{equation}\label{eqosc2a} \omega_0^\pm \approx - i(d-3) \ \frac{\ell (\ell+d-3)-(d-2)}{(d-1)(d-2) r_0} \pm \sqrt{ \frac{\ell (\ell+d-3)}{d-2}} \end{equation}
in agreement with numerical results \cite{siob-Princ}.
Notice that the imaginary part is inversely proportional to $r_0$, as in vector case.
In the scalar case, we also obtained a
finite real part independent of $r_0$.
It yields the
speed of sound $v_s = \frac{1}{\sqrt{d-2}}$ which is the correct value in the presence of conformal invariance.
Turning to the implications of the above results for the AdS/CFT correspondence,
we may
perturb the gauge theory fluid on the boundary of AdS ($S^{d-2} \times \mathbb{R}$) using the ansatz
\begin{equation}\label{eqanss} u_i = \mathcal{K} e^{-i\Omega \tau} \nabla_i \mathbb{S} \ \ , \ \ \ \
\delta p = \mathcal{K}' e^{-i\Omega \tau} \mathbb{S} \end{equation}
where $u_i$ is the (small) velocity of a point in the fluid
and $\delta p$ is a pressure perturbation.
They are both given in terms of $\mathbb{S}$, a scalar harmonic on $S^{d-2}$.
Demanding that this ansatz satisfy the equations of linearized hydrodynamics,
one obtains a frequency of perturbation $\Omega$ in perfect agreement with our analytic result \cite{siob-ego,siob-MP}.
\subsubsection{Tensor perturbations}
Finally, for completeness we discuss the case of tensor perturbations.
Unlike the other two cases, the asymptotic spectrum of tensor perturbations is the entire spectrum.
To see this,
note that in the large black hole limit, the wave equation reads
\begin{eqnarray}\label{eqwavt} - (d-3)^2 (u^{\frac{2d-8}{d-3}} -u^3)\Psi'' - (d-3) [ (d-4)u^{\frac{d-5}{d-3}}-(2d-5)u^2]\Psi' && \nonumber\\
+ \left\{ \hat L^2 + \frac{d(d-2)}{4}u^{-\frac{2}{d-3}} + \frac{(d-2)^2}{4} u - \frac{\hat\omega^2}{1-u^{\frac{d-1}{d-3}}} \right\} \Psi &=& 0
\nonumber\end{eqnarray}
For the zeroth-order equation, we may set $\hat L = 0 = \hat\omega$.
The resulting equation may be solved exactly.
Two linaerly independent solutions are ($\Psi = F_0$ at zeroth order)
\begin{equation} F_0(u) = u^{\frac{d-2}{2(d-3)}} \ \ , \ \ \ \ \check F_0(u) = u^{-\frac{d-2}{2(d-3)}} \ln \left( 1-u^{\frac{d-1}{d-3}} \right) \end{equation}
Neither behaves nicely at both ends ($u=0,1$).
Therefore both are unacceptable which makes it
impossible to build a perturbation theory to calculate small frequencies which are inversely proportional to $r_0$.
This negative result is
in agreement with numerical results \cite{siob-CKL,siob-Princ} and in accordance with the
AdS/CFT correspondence.
Indeed,
there is no ansatz that can be built from tensor spherical harmonics $\mathbb{T}_{ij}$ satisfying the linearized hydrodynamic equations, because of the conservation and tracelessness properties of $\mathbb{T}_{ij}$.
\section{Conclusion}
\label{siosec:7}
We discussed the calculation of analytic asymptotic expressions for quasi-normal modes of various perturbations of black holes in asymptotically flat as well as anti-de Sitter spaces.
We also showed how perturbative corrections to the asymptotic expressions can be systematically calculated.
In view of the AdS/CFT correspondence, in AdS spaces we concentrated on low frequency modes because they govern the hydrodynamic behavior of the gauge theory fluid which is dual to the black hole.
Thus, these modes provide a powerful tool in understanding the hydrodynamics of a gauge theory at strong coupling.
They may lead to experimental consequences pertaining to the quark-gluon plasma produced in heavy ion collisions at RHIC and the LHC.
|
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| 6,559
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{"url":"https:\/\/discuss.codechef.com\/t\/whats-the-error-in-my-code-prime1\/50827","text":"# What's The error in my code? (PRIME1)\n\nI am a newbie to competitive programming . Can you guys please debug my code for the problem PRIME1 and tell me what\u2019s the issue ? It\u2019s giving correct ans for the custom inputs and default test cases\nhttps:\/\/codeshare.io\/mycode\n\nProblem -->https:\/\/www.codechef.com\/problems\/PRIME1\n\n1 Like\n\nHey @lordninja_1997, you can read this solution if you are stuck.\n\nHope you may get a little hint.\n\nConsider the test case\n1\n10 20\n\n@sagars21 You should really see the problem statement, it\u2019s not asking about printing the number which has prime number of set-bits rather it\u2019s asking for number of primes in the given range [L, R] with as constraint 1 \\leq (R - L) \\leq 10^{5}.\n\n@lordninja_1997 You need to use an updated version of Sieve of Eratosthenes known as Segemented Sieve.\nRefer to the links for understanding Segmented Sieve:\n\nMeanwhile I will update the post with my solution.","date":"2020-09-18 15:00:06","metadata":"{\"extraction_info\": {\"found_math\": false, \"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\": 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\": 0.8214107751846313, \"perplexity\": 1083.1985689164246}, \"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-2020-40\/segments\/1600400187899.11\/warc\/CC-MAIN-20200918124116-20200918154116-00199.warc.gz\"}"}
| null | null |
Senegalia polyphylla est une espèce d'arbres de la famille des Fabacées.
Description
Répartition
Liste des variétés
Selon :
variété Acacia polyphylla var. giganticarpa G.P. Lewis
Selon (Attention liste brute contenant possiblement des synonymes) :
variété Acacia polyphylla var. giganticarpa G.P. Lewis
variété Acacia polyphylla var. polyphylla
variété Acacia polyphylla var. rhytidocarpa L. Rico
Notes et références
Liens externes
Fabaceae
Espèce de Fabaceae (nom scientifique)
|
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"redpajama_set_name": "RedPajamaWikipedia"
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| 4,091
|
\section{Introduction}
In the present paper we consider the initial value (IV) problem for the so-called focusing nonlocal nonlinear Schr\"odinger (NNLS) equation (here and below $\bar{q}$ is the complex conjugate of $q$)
\begin{subequations}
\label{fsivp}
\begin{align}
\label{fsivp-a}
& iq_{t}(x,t)+q_{xx}(x,t)+2q^{2}(x,t)\bar{q}(-x,t)=0, & & x\in\mathbb{R},\,t>0, \\
\label{fsivp-b}
& q(x,0)=q_0(x), & & x\in\mathbb{R},
\end{align}
with symmetric nonzero boundary conditions:
\begin{equation}
\label{fsivp-c}
q(x,t) \to Ae^{2iA^2t}, \quad x\to\pm\infty,\quad t\geq 0,
\end{equation}
with some $A>0$ (throughout the paper we assume that $q(x,t)$ approaches the boundary values sufficiently fast).
\end{subequations}
The NNLS equation was introduced by Ablowitz and Musslimani in 2013 \cite{AMP} as a \textit{PT-}symmetric reduction ($r(x,t)=\bar{q}(-x,t)$)
of the well-known Ablowitz-Kaup-Newell-Segur (AKNS) system \cite{AKNS} (a.k.a. coupled Schr\"odinger equations):
\begin{subequations}
\label{fscs}
\begin{align}
\label{fscs-a}
iq_t(x,t)+q_{xx}(x,t)+2q^2(x,t)r(x,t)=0,\\
\label{fscs-b}
-ir_t(x,t)+r_{xx}(x,t)+2r^2(x,t)q(x,t)=0.
\end{align}
\end{subequations}
This reduction leads to (\ref{fsivp-a}) and is consistent with the \textit{PT-}symmetry condition \cite{BB}: if $q(x,t)$ is a solution of (\ref{fsivp-a}), then $\bar{q}(-x,-t)$ is a solution as well.
Therefore, the NNLS equation is related to the $PT$-symmetric theory, which is a state-of-the-art area in modern physics (see, e.g., \cite{B16, KYZ16, MA16} and references therein).
Also this equation is connected to the unconventional system
of coupled Landau-Lifshitz equations \cite{GA, R21} and it can be obtained as a small amplitude quasi-monochromatic reduction
of the nonlinear Klein-Gordon equation \cite{AM19}. Moreover, it can be viewed as a particular case of Alice-Bob nonlocal systems \cite{Lou18}.
The IV problem (\ref{fsivp-a}), (\ref{fsivp-b}) with
the boundary conditions $q(x,t)\to q_{\pm}(t)=Ae^{i\theta_\pm(t)}$ as $x\to\pm\infty$ was considered in \cite{ALM18}, where it was shown that the
admissible
boundary functions $q_{\pm}(t)$ are neither exponentially growing nor decaying only if $q_{\pm}(t)=Ae^{2iA^2t}$ or $q_{\pm}(t)=\pm Ae^{-2iA^2t}$.
Notice that the spectral pictures for these two cases are significantly different. For $q_{\pm}(t)=Ae^{2iA^2t}$, the continuous spectrum consists, as in the case of the classical focusing nonlinear Schr\"odinger (NLS) equation \cite{BK14,BM17}, of the real axis $\mathbb{R}$ and the segment $[-iA, iA]$, whereas when $q_{\pm}(t)=\pm Ae^{-2iA^2t}$ the continuous spectrum is purely real and has a gap $(-A, A)$ and thus the spectral picture is similar to that for the classical defocusing NLS equation \cite{ZS73, IU88} (see Sections 3 and 4 in \cite{ALM18} for details).
The choice of the (symmetric) boundary conditions (\ref{fsivp-c}) is inspired by considerable interest in nonlinear dynamics of modulation instability (MI)
in recent years (see, e.g., \cite{BM16, ET20, GS18, KHB16, KSER19, ZG13} and references therein).
The MI (a.k.a. the Benjamin-Feir instability \cite{BF67} in the context of
water waves) is related to numerous important physical phenomena, such as envelope solitons (``bright solitons''), envelope shocks, freak (rogue) waves, effects of hydrodynamic instability, to name but a few (see, e.g., \cite{BLS21-cimp, DR09, DDEG14, KPS09, ZO09} and references therein).
For the focusing NLS equation (which is a conventional model for studying the MI) the nonlinear stage of modulation instability was studied in \cite{BM17}, where the authors showed that in the solitonless case the large-time asymptotics of the modulus of the solution is formed solely by the boundary conditions of the problem
while only the phase parameters depend on the initial data.
Therefore, the solution exhibits the same large-time behavior for a large class of initial data and in this sense the asymptotic stage of MI is universal.
Later, this result was numerically established for other NLS-type models \cite{BLMT18}.
For both focusing NNLS and NLS equations, the stationary wave $Ae^{2iA^2t}$ is unstable under small perturbations.
In \cite{San18} Santini considered the periodic Cauchy problem for (\ref{fsivp-a}) and showed, using the perturbation approach, that Akhmediev-type rogue waves (see Section 2 in \cite{San18}; cf. \cite{YY} where the Peregrine-type rogue waves were obtained) are relevant for describing the evolution of the solution in an intermediate region, i.e., for $t$ such as $1\ll t\ll O(|\log\varepsilon|)$, where the perturbation of the stationary wave is $O(\varepsilon)$.
Particularly, it was rigorously demonstrated that
since Akhmediev-type soliton solutions of the NNLS equation blow up, in general, in finite time, the solution also blows up in the linear stage of MI.
In the present paper we study the nonlinear stage of MI for the nonlocal NLS equation. We do so by analyzing the solution $q(x,t)$ as $t\to\infty$, i.e., beyond the intermediate region considered in \cite{San18}. This can't be done by linearizing equation (\ref{fsivp-a}), so we utilize the full force of integrability of the IV problem (\ref{fsivp}).
Applying the inverse scattering transform (IST) method in the form of the matrix Riemann-Hilbert (RH) factorization problem \cite{FT, NMPZ84}, we adapt the nonlinear steepest-descent method (Deift and Zhou method, see \cite{DZ, DIZ} and \cite{DVZ94, DVZ97, MM, MM2} for its extensions) to the associated oscillatory RH problem.
We found that the asymptotic stage of MI in the case of the NNLS equation essentially depends on the initial data. Particularly, the modulus of the leading order asymptotic term depends explicitly on $q_0(x)$ (via the associated spectral functions) in all asymptotic regions (see Theorems \ref{fsth1pw} and \ref{fsth2} below).
In this sense, the nonlinear stage of MI is \textit{non-universal} in the case of the nonlocal equation (\ref{fsivp-a}), which is in a sharp contrast with the local NLS equation, where only the phase parameters depend on the initial data \cite{BLMT18, BM17}.
To be more specific, we present here rough results on the asymptotic behavior of $q(x,t)$
(see Theorems \ref{fsth1pw} and \ref{fsth2} below for the precise results).
\begin{customtheorem}{$\mathbf{1^\prime}$} (Plane wave region)
\\
Assuming that the initial data $q_0(x)$ is such that the solitons are absent (i.e., the associated spectral functions $a_j(k)$, $j=1,2$, see Section \ref{fssectspfunct}, have no zeros in the corresponding domains) and the winding of the argument of certain spectral function is less than $\pi$ (see Assumption (\ref{fsarg-ass})), the asymptotics of the solution $q(x,t)$
of problem (\ref{fsivp})
along the rays $\frac{x}{4t}=const$ with $|\frac{x}{4t}|>\sqrt{2}A$ has the form:
\begin{subequations}\label{fspl1}
\begin{align}
&q(x,t)=Ae^{-2\Im F_{\infty}(k_1)}
e^{2i(A^2t+\Re F_{\infty}(k_1))}
+o(1),&& t\to\infty,\quad \frac{x}{4t}>\sqrt{2}A,\\
&q(-x,t)=Ae^{2\Im F_{\infty}(k_1)}
e^{2i(A^2t+\Re F_{\infty}(k_1))}
+o(1),&& t\to\infty,\quad -\frac{x}{4t}<-\sqrt{2}A,
\end{align}
\end{subequations}
where $k_{1}=\frac{1}{2}\left(-\xi-\sqrt{\xi^2-2A^2}\right)$
with $\xi=\frac{x}{4t}$ for $x>0$
and the \textit{complex} constant $F_{\infty}(k_1)$ (which depends on $\xi$ through $k_1$) is given by (\ref{fsreimFinf}).
\end{customtheorem}
\begin{customtheorem}{$\mathbf{2^\prime}$} (Modulated elliptic wave region)\\
Under the same assumptions as in Theorem $1^{\prime}$ (with only difference that instead of Assumption (\ref{fsarg-ass}) we make Assumption (\ref{fsDelta-argew})),
the asymptotics of the solution $q(x,t)$
of problem (\ref{fsivp})
along the rays $\frac{x}{4t}=const$ with $0<|\frac{x}{4t}|<\sqrt{2}A$ has the form:
\begin{subequations}\label{fsasellw1}
\begin{align}
\nonumber
&q(x,t)=(A+\Im\alpha)
e^{-2\Im G_{\infty}(k_0,\alpha)}
\frac{\Theta(\frac{\Omega t}{2\pi}
+\frac{\omega}{2\pi}-\frac{1}{4}-v_{\infty}+c)
\Theta(v_{\infty}+c)}
{\Theta(\frac{\Omega t}{2\pi}
+\frac{\omega}{2\pi}-\frac{1}{4}+v_{\infty}+c)
\Theta(-v_{\infty}+c)}\\
&\qquad\qquad
\times e^{2i(tH_{\infty}+\Re G_{\infty}(k_0,\alpha))}
+o(1),\quad 0<\frac{x}{4t}<\sqrt{2}A,\\
\nonumber
&q(-x,t)=(A+\Im\alpha)
e^{2\Im G_{\infty}(k_0,\alpha)}
\frac{\Theta(\frac{\Omega t}{2\pi}
+\frac{\overline{\omega}}{2\pi}-\frac{1}{4}
+\overline{v_{\infty}}-\overline{c})
\Theta(-\overline{v_{\infty}}-\overline{c})}
{\Theta(\frac{\Omega t}{2\pi}
+\frac{\overline{\omega}}{2\pi}-\frac{1}{4}
-\overline{v_{\infty}}-\overline{c})
\Theta(\overline{v_{\infty}}-\overline{c})}\\
&\qquad\qquad
\times e^{2i(tH_{\infty}+\Re G_{\infty}(k_0,\alpha))}
+o(1),\quad 0>-\frac{x}{4t}>-\sqrt{2}A.
\end{align}
\end{subequations}
Here the genus-1 theta function $\Theta$ is given by (\ref{fsg1thf}) and the constants $\alpha$, $\Omega$, $v_{\infty}$ and $c$, which do not depend on the initial data $q_0(x)$, are given by (\ref{fsreaima}), (\ref{fsOmega}), (\ref{fsvinfty}) and (\ref{fsc}), respectively.
The complex constants $\omega$, $H_{\infty}$ and $G_{\infty}(k_0,\alpha)$, which depend on the initial data $q_0(x)$, are given by (\ref{fsomega}), (\ref{fsH0}) and (\ref{fsGinfty}), respectively.
Moreover, $G_{\infty}(k_0,\alpha)$ depends on the ray $\xi$ through $k_0$ and $\alpha$, where the former is defined as a unique solution of equation (\ref{fsintk0}).
\end{customtheorem}
\begin{remark}
Assumption (\ref{fsarg-ass}) is sufficient for establishing the asymptotics for the nonlocal NLS equation in the plane wave regions
(Theorem $1^\prime$).
Though the asymptotics in these regions has not been considered before
(to the best of our knowledge) for nonlocal equations, the analysis needed for obtaining this result is close to that used in the decaying
\cite{RS} and ``modulated constant'' zones \cite{RS20,RSs}.
Remarkably, a similar assumption (see Assumption (\ref{fsDelta-argew})) on the winding of the argument of the spectral function $(1+r_1(k)r_2(k))$ turns out to be sufficient for establishing the asymptotics in the modulated elliptic wave region as well (Theorem $2^\prime$).
Here the reasoning is more involving; particularly, we have to deal with a non-analytic phase function and unbounded entries of the jump matrix at a neighborhood of the stationary phase point (see Appendix C, item (ii)).
\end{remark}
\begin{remark}
In the case of the NNLS equation, the reflection coefficients $r_1(k)$ and $r_2(k)$ (see Section \ref{fssectspfunct}) are not connected (in contrast with the classical NLS equation); this ``lack of symmetry'' implies, in particular,
that $F_{\infty}(k_1)$ and $G_{\infty}(k_0,\alpha)$ in (\ref{fspl1}) and (\ref{fsasellw1}) can be
complex-valued and thus the modulus of the asymptotics depends on the initial data.
A similar lack of symmetry holds for other integrable nonlocal equations (see, e.g., \cite{AM17, ALM20, F16, HFX19, Y18}), which allows us to conjecture that
the modulation instability in other nonlocal models should also exhibit
a kind of non-universal behavior.
\end{remark}
\begin{remark}
It is known that the solution of the problem (\ref{fsivp}) can blow up in finite time.
Particularly, the ``breathing'' two-soliton solution \cite{ALM18}, Peregrine-type \cite{YY} and Akhmediev-type \cite{San18} solutions can blow up at a discrete set of points in the $(x,t)$ plane, even in the cases when the initial profile (i.e., $q(x,t=0)$) is smooth.
On the other hand, away from point singularities, a solution can be smooth and satisfying the boundary conditions for all $t\geq0$.
With this respect,
the Riemann-Hilbert problem provides a formalism for constructing global
solutions outside the domains where they may have irregular behavior.
Indeed, (i) the RH problem is intrinsically local and (ii) the jump matrix is usually analytic w.r.t. parameter(s) (say, $x$), which imply (in view of the analytic Fredholm alternative \cite{Zh89}) that the solution of the associated RH problem is meromorphic in $x$ (or, otherwise, the problem is solvable for no $x$; see, e.g., Chapter 3, Section 1 in \cite{FIKN}).
Particularly, in this paper we obtain the extension of the solution from a neighborhood of $t=\infty$ into the sectors $\frac{x}{4t}\in\mathbb{R}\setminus\{\pm\sqrt{2}A,0\}$.
\end{remark}
The article is organized as follows. In the Section 2 we develop the inverse scattering transform method in the form of the RH problem.
In Sections 3 and 4 we obtain the long-time asymptotics of the solution in the plane wave region and modulated elliptic wave region respectively, establishing the non-universality of the asymptotic stage of the modulation instability in these zones.
\section{Inverse scattering transform and the Riemann-Hilbert problem}\label{fsist}
In this section we reformulate the IST method for the IV problem (\ref{fsivp}) which was first developed in \cite{ALM18}, in the form suitable for asymptotic analysis, particularly, keeping the determinant of a matrix constructed from the Jost solutions to be equal to 1. We also point out that since the boundary conditions in (\ref{fsivp}) are symmetric, the implementation of the IST method is close to that in the case of the classical NLS equation \cite{BK14, BM17}; but the associated spectral functions satisfy different symmetry relations, which affects significantly the resulting asymptotic formulas.
\subsection{Direct scattering}
The NNLS equation (\ref{fsivp-a}) is a compatibility condition of the following system of linear equations \cite{AMP} (the so-called Lax pair)
\begin{align}
\label{fsLP}
&\Phi_{x}+ik\sigma_{3}\Phi=U\Phi,\\
&\Phi_{t}+2ik^{2}\sigma_{3}\Phi=V\Phi,
\end{align}
where $\sigma_3=\left(\begin{smallmatrix} 1& 0\\ 0 & -1\end{smallmatrix}\right)$ is the third Pauli matrix, $\Phi(x,t,k)$ is a $2\times2$ matrix-valued function, $k\in\mathbb{C}$ is a spectral parameter, and the $2\times2$ matrix coefficients $U(x,t)$ and $V(x,t,k)$ are given in terms of
$q(x,t)$ as follows:
\begin{equation}
U(x,t)=\begin{pmatrix}
0& q(x,t)\\
-\bar{q}(-x,t)& 0\\
\end{pmatrix},\qquad
V(x,t,k)=\begin{pmatrix}
V_{11}(x,t)& V_{12}(x,t,k)\\
V_{21}(x,t,k)& V_{22}(x,t)\\
\end{pmatrix},
\end{equation}
where $V_{11}=-V_{22}=iq(x,t)\bar{q}(-x,t)$, $V_{12}=2kq(x,t)+iq_{x}(x,t)$, and
$V_{21}=-2k\bar{q}(-x,t)+i(\bar{q}(-x,t))_{x}$.
Assuming that $\int_{\mathbb{R}}|q(x,t)-Ae^{2iA^2t}|\,dx<\infty$ for all $t\geq0$, introduce the $2\times2$ matrix valued functions $\Psi_j(x,t,k)$, $j=1,2$ as the solutions of the following linear Volterra integral equations
\begin{align}\label{fsPsi}
\nonumber
\Psi_j(x,t,k)=&e^{iA^2t\sigma_3}\mathcal{E}(k)\\
&+\int\limits_{(-1)^j\infty}^{x}G(x,y,t,k)(U(y,t)-U_0(t))\Psi_j(y,t,k)e^{i(x-y)f(k)\sigma_3}\,dy,j=1,2,
\end{align}
where $U_{0}(t)$ is the limits of $U(x,t)$ as $x\to\pm\infty$:
\begin{equation}
U(x,t)\to U_{0}(t),\quad x\to\pm\infty;\quad
U_0(t)=
\begin{pmatrix}
0& Ae^{2iA^2t}\\
-Ae^{-2iA^2t} & 0
\end{pmatrix}.
\end{equation}
The kernel $G(x,y,t,k)$ is defined as follows:
\begin{equation}
G(x,y,t,k)=e^{iA^2t\sigma_3}\mathcal{E}(k)
e^{-i(x-y)f(k)\sigma_3}\mathcal{E}^{-1}(k)
e^{-iA^2t\sigma_3},
\end{equation}
where
\begin{equation}\label{fsK}
\mathcal{E}(k)=\frac{1}{2}
\begin{pmatrix}
w(k)+\frac{1}{w(k)} & w(k)-\frac{1}{w(k)}\\
w(k)-\frac{1}{w(k)} & w(k)+\frac{1}{w(k)}
\end{pmatrix},\quad w(k)=\left(\frac{k-iA}{k+iA}\right)^{\frac{1}{4}},
\end{equation}
and
\begin{equation}\label{fsf}
f(k)=(k^2+A^2)^{\frac{1}{2}}.
\end{equation}
Here the functions $f(k)$ and $w(k)$ are fixed to be analytic
in $\in\mathbb{C}\setminus \overline{ B}$,
where
$$
B=(-iA,iA)\subset i\mathbb{R},
$$
and to have the
asymptotics
$$
f(k)=k+O(k^{-1}),\quad k\to\infty\quad\text{and}\quad
w(k)=1+O(k^{-1}),\quad k\to\infty.
$$
Particularly, we have $f(k)=\sqrt{k^2+A^2}$ for $k\in(0,\infty)$ and
$f(k)=-\sqrt{k^2+A^2}$ for $k\in(-\infty,0)$.
In what follows, $f_\pm(k)$ and $w_\pm(k)$ denote the limiting values
of the corresponding function
as $k$ approaches $B$ (oriented upward from $-iA$ to $iA$)
from the left/right (and similarly for $\mathcal{E}_\pm (k)$).
Notice that in spite of the jumps of $f$ and $\cal E$
across $B$, $G(x,y,t,k)$ is entire w.r.t. $k$ for all $x$, $y$, and $t$.
Since $f(k)$ is real for $k\in\mathbb{R}$
and $f_\pm(k)$ are real for $k\in B$, the integral equations (\ref{fsPsi})
are well-defined for $k\in\mathbb{R}\cup B$.
The columns of the matrices $\Psi_j(x,t,k)$, $j=1,2$ play a crucial role in the construction of the basic Riemann-Hilbert problem: a sectionally holomorphic matrix function can be defined in terms of the corresponding columns of $\Psi_j(x,t,k)$, $j=1,2$ (see (\ref{fsM}) below). In the next proposition we summarize the main properties of $\Psi_j(x,t,k)$, $j=1,2$ (we use the following notations: $Q^{[j]}$ stands for the $j$-th column of a matrix $Q$; $\mathbb{C}^{\pm}=\left\{k\in\mathbb{C}\,|\pm\Im k>0\right\}$;
$\overline{\mathbb{C}^{\pm}}=\left\{k\in\mathbb{C}\,|\pm\Im k\ge 0\right\}$):
\begin{proposition}
\label{fsproppsi1}
\begin{enumerate}[(i)]
\item The matrices $\Psi_{j\pm}(x,t,k)$, $j=1,2$ are well defined for $k\in B$
as the solutions of the integral equations (cf. (\ref{fsPsi}))
\[
\Psi_{j\pm}(x,t,k)=e^{iA^2t\sigma_3}\mathcal{E}_\pm(k)
+\int\limits_{(-1)^j\infty}^{x}G(x,y,t,k)(U(y,t)-U_0(t))\Psi_{j\pm}(y,t,k)
e^{i(x-y)f_\pm(k)\sigma_3}\,dy.
\]
\item The columns $\Psi_1^{[1]}(x,t,k)$ and $\Psi_2^{[2]}(x,t,k)$ are well-defined for $k\in\overline{\mathbb{C}^+}\setminus[0, iA]$, analytic for $k\in\mathbb{C}^+\setminus(0,iA]$ and continuous for $k\in\overline{\mathbb{C}^+}\setminus[0,iA]$; moreover,
\[
\Psi_1^{[1]}(x,t,k)=e^{iA^2t}
\begin{pmatrix}
1\\
0\end{pmatrix}
+O(k^{-1}),\quad \Psi_2^{[2]}(x,t,k)=
e^{-iA^2t}
\begin{pmatrix}
0\\
1\end{pmatrix}
+O(k^{-1}),\quad
k\rightarrow\infty, \quad k\in\mathbb{C}^+,
\]
and $\Psi_1^{[1]}(x,t,k),\Psi_2^{[2]}(x,t,k)=
O\left((k\pm iA)^{-\frac{1}{4}}\right)$ as $k\to\mp iA$.
\item The columns $\Psi_1^{[2]}(x,t,k)$ and $\Psi_2^{[1]}(x,t,k)$ are well-defined for $k\in\overline{\mathbb{C}^-}\setminus[-iA,0]$, analytic for $k\in\mathbb{C}^-\setminus[-iA,0)$ and continuous for $k\in\overline{\mathbb{C}^-}\setminus[-iA,0]$; moreover,
\[
\Psi_1^{[2]}(x,t,k)=
e^{-iA^2t}
\begin{pmatrix}
0\\
1\end{pmatrix}
+O(k^{-1}),\quad
\Psi_2^{[1]}(x,t,k)=
e^{iA^2t}
\begin{pmatrix}
1\\
0\end{pmatrix}
+O(k^{-1}),\quad k\rightarrow\infty,\quad k\in\mathbb{C}^-,
\]
and $\Psi_1^{[2]}(x,t,k),\Psi_2^{[1]}(x,t,k)=O\left((k\pm iA)^{-\frac{1}{4}}\right)$ as $k\to \mp iA$.
\item The functions $\Phi_j(x,t,k)$, $j=1,2$ defined by
\begin{subequations}\label{fsjost}
\begin{align}
&\Phi_j(x,t,k)=\Psi_j(x,t,k)e^{-(ix+2itk)f(k)\sigma_3},&& k\in\mathbb{R}\setminus\{0\},\quad j=1,2,\\
&\Phi_{j\pm}(x,t,k)=\Psi_{j\pm}(x,t,k)
e^{-(ix+2itk)f_\pm(k)\sigma_3},&&k\in B,\quad j=1,2,
\end{align}
\end{subequations}
are the (Jost) solutions of the Lax pair equations (\ref{fsLP}) satisfying
the boundary conditions
\begin{subequations}
\begin{align}
&\Phi_j(x,t,k)\rightarrow\Phi_0(x,t,k),&& x\rightarrow\pm\infty,\quad j=1,2,\quad
k\in\mathbb{R}\setminus\{0\},\\
&\Phi_{j\pm}(x,t,k)\rightarrow\Phi_{0\pm}(x,t,k),&& x\rightarrow\pm\infty,\quad j=1,2,\quad
k\in B,
\end{align}
\end{subequations}
where $\Phi_0(x,t,k)=e^{iA^2t\sigma_3}
\mathcal{E}(k)e^{-(ix+2itk)f(k)\sigma_3}$ and
$\Phi_{0\pm}(x,t,k)=e^{iA^2t\sigma_3}
\mathcal{E}_{\pm}(k)e^{-(ix+2itk)f_\pm(k)\sigma_3}$.
\item $\det\Psi_j(x,t,k)\equiv 1,\quad k\in\mathbb{R} \quad$ and $\quad\det\Psi_{j\pm}(x,t,k)\equiv 1,\quad k\in B, \quad j=1,2$.
\item The following symmetry relations hold:
\begin{subequations}\label{fssymmpsi}
\begin{equation}
\label{fssymmR}
\begin{aligned}
&\sigma_1\overline{\Psi_1^{[1]}(-x,t,-\bar{k})}=
\Psi_2^{[2]}(x,t,k),
\quad k\in\overline{\mathbb{C}^+}\setminus[0,iA],\\
&\sigma_1\overline{\Psi_1^{[2]}(-x,t,-\bar{k})}=
\Psi_2^{[1]}(x,t,k),
\quad k\in\overline{\mathbb{C}^-}\setminus[-iA,0],
\end{aligned}
\end{equation}
and
\begin{equation}
\label{fssymmseg}
\Psi_{j+}(x,t,k)=i\Psi_{j-}(x,t,k)\sigma_1,\quad k\in B,\quad j=1,2,
\end{equation}
\end{subequations}
where $\sigma_1=\bigl(\begin{smallmatrix}0& 1\\1 & 0\end{smallmatrix}\bigl)$ is the first Pauli matrix.
\end{enumerate}
\end{proposition}
\begin{proof}
Items (i)--(iv) follow directly from the integral representation (\ref{fsPsi}). Since the matrix $U(x,t)$ is traceless and
$\det \mathcal{E}(k)=1$, Item (v) follows.
Finally, (\ref{fssymmR}) in Item (vi) follows from the symmetries
\begin{equation}
\sigma_1 \overline{U}(-x,t)\sigma_1^{-1}=-U(x,t),\quad \text{and}\quad
\sigma_1 \overline{G(-x,-y,t,-\bar{k})}\sigma_1^{-1}=G(x,y,t,k),\, k\in\mathbb{C},
\end{equation}
whereas (\ref{fssymmseg}) is a consequence of the symmetry
\begin{equation}\label{fssymK}
\mathcal{E}_+(k)=i\mathcal{E}_-(k)\sigma_1,\quad k\in B.
\end{equation}
\end{proof}
\subsection{Spectral functions}\label{fssectspfunct}
The Jost solutions $\Phi_j(x,t,k)$, $j=1,2$ of the Lax pair (\ref{fsLP}) are related by a matrix independent of $x$ and $t$, which allows us to introduce
the scattering matrices $S(k)$ and $S_\pm(k)$ as follows:
\begin{equation}\label{fssr}
\Phi_1(x,t,k)=\Phi_2(x,t,k)S(k),\quad k\in\mathbb{R}\setminus\{0\};
\quad
\Phi_{1\pm}(x,t,k)=\Phi_{2\pm}(x,t,k)S_\pm(k),\quad k\in B.
\end{equation}
In terms of $\Psi_j(x,t,k)$, $j=1,2$,
the scattering relations (\ref{fssr}) read as follows (see (\ref{fsjost})):
\begin{subequations}\label{fssrpsi}
\begin{align}
\label{fssrpsia}
&\Psi_1(x,t,k)=\Psi_2(x,t,k)e^{-(ix+2itk)f(k)\sigma_3}S(k)
e^{(ix+2itk)f(k)\sigma_3},&& k\in\mathbb{R}\setminus\{0\},\\
&
\label{fssrpsib} \Psi_{1\pm}(x,t,k)=\Psi_{2\pm}(x,t,k)e^{-(ix+2itk)f_\pm(k)\sigma_3}S_\pm(k)
e^{(ix+2itk)f_\pm(k)\sigma_3},&& k\in B.
\end{align}
\end{subequations}
Let us denote the entries of $S(k)$ by
\begin{equation}\label{fsscatt}
S(k)=\begin{pmatrix}
a_1(k) & -b_2(k)\\
b_1(k) & a_2(k)
\end{pmatrix},\quad k\in\mathbb{R}\setminus\{0\};\quad
S_\pm(k)=\begin{pmatrix}
a_{1\pm}(k) & -b_{2\pm}(k)\\
b_{1\pm}(k) & a_{2\pm}(k)
\end{pmatrix},\quad k\in B.
\end{equation}
Taking into account the analytical properties of the columns of matrices $\Psi_j$, $j=1,2$ (see Items (ii), (iii) in Proposition \ref{fsproppsi1}), the function $a_1(k)$ is analytic in $\mathbb{C}^{+}\setminus(0, iA]$ and $a_2(k)$ is analytic in $\mathbb{C}^{-}\setminus[-iA, 0)$ whereas $b_j(k)$, $j=1,2$ are well-defined for $k\in\mathbb{R}\setminus\{0\}$. Indeed, (\ref{fssrpsia}) implies
\begin{subequations}
\begin{align}
&a_1(k)=\det\left(\Psi_1^{[1]}(0,0,k),\Psi_2^{[2]}(0,0,k)\right),\quad
k\in\overline{\mathbb{C}^{+}}\setminus[0, iA],\\
&a_2(k)=\det\left(\Psi_2^{[1]}(0,0,k),\Psi_1^{[2]}(0,0,k)\right),\quad
k\in\overline{\mathbb{C}^{-}}\setminus[-iA, 0],\\
&b_1(k)=\det\left(\Psi_2^{[1]}(0,0,k),\Psi_1^{[1]}(0,0,k)\right),\quad
k\in\mathbb{R}\setminus\{0\},\\
&b_2(k)=\det\left(\Psi_2^{[2]}(0,0,k),\Psi_1^{[2]}(0,0,k)\right),\quad
k\in\mathbb{R}\setminus\{0\}.
\end{align}
\end{subequations}
Moreover, $a_j(k)$, $b_j(k)$, $j=1,2$ have the following asymptotics as $k\to\infty$:
\begin{subequations}
\begin{align}
&a_1(k)=1+O(k^{-1}),&k&\to\infty,\quad k\in \overline{\mathbb{C}^{+}},\\
&a_2(k)=1+O(k^{-1}),&k&\to\infty,\quad k\in \overline{\mathbb{C}^{-}},\\
&b_j(k)=O(k^{-1}),&k&\to\infty,\quad k\in\mathbb{R}.
\end{align}
\end{subequations}
For $k\in B$, we define
$a_{j\pm}(k)$ and $b_{j\pm}(k)$, $j=1,2$ with the aid of the similar determinant representations:
\begin{subequations}
\begin{align}
&a_{1\pm}(k)=\det\left(\Psi_{1\pm}^{[1]}(0,0,k),\Psi_{2\pm}^{[2]}(0,0,k)\right),
\quad k\in B,\\
&a_{2\pm}(k)=\det\left(\Psi_{2\pm}^{[1]}(0,0,k),\Psi_{1\pm}^{[2]}(0,0,k)\right),
\quad k\in B,\\
&b_{1\pm}(k)=\det\left(\Psi_{2\pm}^{[1]}(0,0,k),\Psi_{1\pm}^{[1]}(0,0,k)\right),
\quad k\in B,\\
&b_{2\pm}(k)=\det\left(\Psi_{2\pm}^{[2]}(0,0,k),\Psi_{1\pm}^{[2]}(0,0,k)\right),
\quad k\in B.
\end{align}
\end{subequations}
In this way, $a_{1\pm}(k)$ turn to be the limiting values of $a_1(k)$
from the left/right for $k\in (0, iA)$ and
$a_{2\pm}(k)$ are the limiting values of $a_2(k)$
from the left/right for $k\in (-iA,0)$.
The symmetries (\ref{fssymmpsi}) imply the following symmetries of the spectral functions (cf. \cite{ALM18}):
\begin{subequations}\label{fsabsym}
\begin{align}
\label{fsajsym}
&\overline{a_1(-\bar{k})}=a_1(k),\quad k\in \overline{\mathbb{C}^{+}}\setminus[0, iA],\quad
\overline{a_2(-\bar{k})}=a_2(k),\quad k\in \overline{\mathbb{C}^{-}}\setminus[-iA, 0],\\
\label{fsbjsymm}
& b_2(k)=\overline{b_1(-k)},\quad k\in\mathbb{R}\setminus\{0\},
\end{align}
\end{subequations}
and
\begin{equation}
\label{fsajsymB}
a_{1\pm}(k)=a_{2\mp}(k),
\quad b_{1\pm}(k)=-b_{2\mp}(k),\quad k\in B.
\end{equation}
Notice that (\ref{fsajsym}) implies $\overline{a_{j+}(0)}=a_{j-}(0)$, $j=1,2$; combining this with (\ref{fsajsymB}) we arrive at the equality
$a_{1\pm}(0)=a_{2\pm}(0)$.
From Item (v) of Proposition \ref{fsproppsi1}, (\ref{fsjost}) and (\ref{fssr})
it follows that
$a_j(k)$ and $b_j(k)$, $j=1,2$
satisfy the determinant relations:
\begin{equation}
a_1(k)a_2(k)+b_1(k)b_2(k)=1,\ \ k\in\mathbb{R}\setminus\{0\};\quad
a_{1\pm}(k)a_{2\pm}(k)+b_{1\pm}(k)b_{2\pm}(k)=1,
\ \ k\in B.
\end{equation}
Notice that due to the Schwarz symmetry breaking for the solutions $\Psi_j(x,t,k)$, $j=1,2$, see (\ref{fssymmR}), the values of $a_1(k)$ for $k\in\mathbb{C}^+\setminus(0,iA]$ and $a_2(k)$ for $k\in\mathbb{C}^-\setminus(0,-iA]$ are, in general, \textit{not}
related.
Finally, we point out that $a_j(k),\,b_j(k)=O\left((k\pm iA)^{-\frac{1}{2}}\right)$ as $k\to\mp iA$.
\underline{\textbf{Notations}}
From now on we identify the values of $f(k)$, $w(k)$, $a_j(k)$ and $b_j(k)$, $j=1,2$ for $k\in B$ as the limiting values of the corresponding function from the right:
\begin{equation}\label{fsfj}
f(k):=f_-(k)=\sqrt{k^2+A^2},\quad k\in B,\quad
w(k):=w_-(k) ,\quad k\in B.
\end{equation}
and
\begin{equation}\label{fsajB}
a_j(k):=a_{j-}(k),\quad j=1,2,\quad k\in B,\quad
b_j(k):=b_{j-}(k),\quad j=1,2,\quad k\in B.
\end{equation}
\underline{\textbf{Assumption}}
\textit{(Zeros of the spectral functions $a_j(k), j=1,2$).}
We assume that $a_1(k)$ and $a_2(k)$ do not have zeros in $\overline{\mathbb{C}^+}$ and $\overline{\mathbb{C}^-}$ respectively (see, however, Remark \ref{remz} below).
Particularly, there are no spectral singularities (in other words, no zeros on $\mathbb{R}\cup \overline{B}$), particularly the virtual levels are absent (i.e., $a_1(iA)\neq0$ and $a_2(-iA)\neq0$).
\begin{remark}
Above Assumption is motivated by the fact that the pure background (i.e., $q(x,0)\equiv A$) gives rise to the spectral functions $a_j(k)\equiv 1$ and $b_j(k)\equiv0$, $j=1,2$.
Indeed, for such initial data $\Psi_j(0,0,k)=\mathcal{E}(k)$, $j=1,2$, therefore (\ref{fssrpsi}) implies that $S(k)=\mathcal{E}^{-1}(k)\mathcal{E}(k)=I$.
\end{remark}
\subsection{Riemann-Hilbert problem}
Now we are in a position to formulate the basic Riemann-Hilbert problem. Assuming that $a_j(k)$, $j=1,2$ have no zeros in the corresponding half-planes, define a $2\times 2$ matrix function $M(x,t,k)$ as follows:
\begin{equation}
\label{fsM}
M(x,t,k)=
\left\{
\begin{array}{lcl}
e^{-iA^2t\sigma_3}
\left(\frac{\Psi_1^{[1]}(x,t,k)}{a_{1}(k)},\Psi_2^{[2]}(x,t,k)\right),\quad k\in\mathbb{C}^+\setminus(0,iA],\\
e^{-iA^2t\sigma_3}
\left(\Psi_2^{[1]}(x,t,k),\frac{\Psi_1^{[2]}(x,t,k)}{a_{2}(k)}\right),\quad k\in\mathbb{C}^-\setminus[-iA, 0).\\
\end{array}
\right.
\end{equation}
Then the scattering relation (\ref{fssrpsi}) imply that $M(x,t,k)$ satisfies the multiplicative jump condition across the contour $\mathbb{R}\cup B$:
\begin{equation}\label{fsj}
M_+(x,t,k)=M_-(x,t,k)J(x,t,k),\quad k\in \mathbb{R}\cup B,
\end{equation}
where $M_{\pm}(\cdot,\cdot,k)$ denotes the nontangental limits of $M(\cdot,\cdot,k)$ as $k$ approaches the contour from the corresponding side (the real axis $\mathbb{R}$ is oriented from left to right and the segment $B$ is oriented upwards).
The jump matrix $J(x,t,k)$ has the form (follows from the scattering relations (\ref{fssrpsi}) and the symmetry condition (\ref{fssymmseg})):
\begin{equation}\label{fsjbrh}
J(x,t,k)=
\begin{cases}
\begin{pmatrix}
1+r_1(k)r_2(k) & r_2(k)e^{-(2ix+4itk)f(k)}\\
r_1(k)e^{(2ix+4itk)f(k)} & 1
\end{pmatrix}, &k\in\mathbb{R}\setminus\{0\},
\\
\begin{pmatrix}
-ir_2(k)e^{-(2ix+4itk)f(k)} & i\\
i(1+r_1(k)r_2(k)) & -ir_1(k)e^{(2ix+4itk)f(k)}
\end{pmatrix},& k\in(0,iA),
\\
\begin{pmatrix}
ir_2(k)e^{-(2ix+4itk)f(k)} & i(1+r_1(k)r_2(k))\\
i& ir_1(k)e^{(2ix+4itk)f(k)}
\end{pmatrix},& k\in(-iA,0),
\end{cases}
\end{equation}
with the reflection coefficients $r_j(k)=\frac{b_j(k)}{a_j(k)}$, $j=1,2$ (recall that the values of $r_j(k)$, $j=1,2$ and $f(k)$ are taken from the ``$-$'' (right) side of the segment $B$, see (\ref{fsfj}) and (\ref{fsajB})). Notice that $r_j(k)$, $j=1,2$ are bounded as $k$ approaches $\pm iA$:
\begin{equation}
r_j(k)=O(1),\quad k\to\pm iA.
\end{equation}
The matrix $M(x,t,k)$ satisfies the normalization condition
\begin{equation}\label{fsnorm}
M(x,t,k)=I+O(k^{-1}),\quad k\to\infty.
\end{equation}
Besides, since $k=\pm iA$ are not virtual levels (see Assumption in Section \ref{fssectspfunct} and Remark \ref{remz}), the possible singularities of
$M(x,t,k)$ at $k=\pm iA$ are square integrable:
\begin{equation}\label{fssing}
M(x,t,k)=O\left((k\pm iA)^{-\frac{1}{4}}\right),\quad k\to\mp iA.
\end{equation}
The basic Riemann-Hilbert problem consists in finding a sectionally holomorphic $2\times 2$ matrix $M(x,t,k)$, which satisfies (i) the multiplicative jump conditions (\ref{fsj}) given in terms of known reflection coefficients $r_j(k)$, $j=1,2$ and (ii) the normalization at infinity (\ref{fsnorm});
moreover, (iii) it is square integrable (satisfying (\ref{fssing})) at the endpoints $k=\pm iA$.
Assuming that the solution $M(x,t,k)$ of the basic Riemann-Hilbert problem (\ref{fsj}), (\ref{fsnorm}), (\ref{fssing}) exists, the solution $q(x,t)$ of the original initial value problem (\ref{fsivp}) can be found via the $(12)$ or $(21)$ entry of $M(x,t,k)$ as $k\to\infty$ (follows from the first equation in the Lax pair (\ref{fsLP})):
\begin{subequations}\label{fsasol}
\begin{equation}\label{fssol}
q(x,t)=2ie^{2iA^2t}
\lim_{k\to\infty}kM_{12}(x,t,k),
\end{equation}
and
\begin{equation}\label{fssol1}
q(-x,t)=-2ie^{2iA^2t}
\lim_{k\to\infty}k\overline{M_{21}(x,t,k)}.
\end{equation}
\end{subequations}
Notice that solution of the basic Riemann-Hilbert is unique, if it exists. Indeed, let $M$ and $\tilde M$ be
two solutions. Then, due to (\ref{fssing}), the possible singularities of
$M \tilde M^{-1}$ at the endpoints $k=\pm iA$ are weak, and $M \tilde M^{-1}$ has no jump in $\mathbb{C}$. Then, by the Liouville theorem, $M \tilde M^{-1}= I$
for all $k\in\mathbb{C}$.
\begin{remark}\label{fsxgz}
From (\ref{fsasol}) it follows that for obtaining the solution $q(x,t)$ of (\ref{fsivp}) for all $x\in \mathbb R$, it is enough to have the solution of the Riemann-Hilbert problem for $x\ge 0$ only.
\end{remark}
\begin{remark}
\label{remz}
Generically, $a_1(k)$ and $a_2(k)$ can have finite number of simple zeros in $\overline{\mathbb{C}^+}\setminus(0,iA]$ and $\overline{\mathbb{C}^-}\setminus(0,-iA]$ respectively (notice that since $a_1(k)$ and $a_2(k)$ are not related, their zeroes do not, in general, constitute pairs associated with solitons, as it takes place for the classical NLS equation \cite{BLM21}).
In this case the basic Riemann-Hilbert problem has to be supplemented by appropriate residue conditions defined in terms of the (known) zeros and norming constants.
On the other hand, spectral singularities may arise for non-generic initial data
(similarly to
the NLS equation with zero background \cite{Zh89-sing}); particularly, virtual levels (cf. Appendix B in \cite{BK14})
introduce non-square-integrable singularities
at the endpoints $k=\pm iA$
in the basic RH problem for $M(x,t,k)$.
To deal with singularities of all types in a systematic way, one can reformulate the basic RH problem in such a way that all singularities are replaced by additional jump conditions on an auxiliary part of the contour, which is a circle centered at $k=0$ with sufficiently large radius
$r=r(q_0(\cdot))$ (see \cite{BM19, BS04, Zh98}).
In this way, the original RH problem becomes regular;
however, its direct asymptotic analysis (without resorting to residue conditions) is problematic.
\end{remark}
\begin{remark}
Since $a_1(k)$ and $a_2(k)$ are not related, the spectral picture for the nonlocal problem is more rich and variegated comparing with the local case.
First, the number of zeros in the upper and in the lower half planes can be different (in view of the symmetry relations (\ref{fsajsym}), zeros are symmetric w.r.t. $i\mathbb{R}$, but not w.r.t. $\mathbb{R}$ as for the classical NLS equation).
Moreover, even if zeros of $a_1(k)$ and $a_2(k)$ constitute appropriate pairs, solitons associated to these zeros can blow up in finite time (see (4.62) in \cite{ALM18}).
Cases with equal number of purely imaginary zeros in $\mathbb{C}^{+}$ and $\mathbb{C}^{-}$ with the absolute values which are greater or equal to $A$ give rise to three different types of rogue waves
given in Theorems 1-3 in \cite{YY}.
Notice that apart from the case when the absolute values of these zeros are less than $A$, it is also possible
that, say, $a_1(k)$ has a (simple) zero at $k=ih$, $0<h<A$ and $a_2(k)$ has a zero at $k=-i\tilde{h}$, $\tilde{h}=A$ or $\tilde{h}>A$. Consequently, there can be
a ``mixture'' of spectral portraits, which in the local case correspond to the Kuznetsov-Ma (zeros at $k=\pm ih$, $h>A$), Peregrine (zeros at $k=\pm iA$) or Akhmediev (zeros at $k=\pm ih$, $0<h<A$) breathers.
\end{remark}
\section{Long-time asymptotics}
The implementation of the Deift--Zhou nonlinear steepest descent method is guided (by analogy with the classical steepest decent method) by the signature structure of the phase function in the jump matrix $J(x,t,k)$ given by (\ref{fsjbrh}), which is similar to that in the case of the NLS equation
with nonzero background \cite{BM17}.
Introduce the phase function $\theta(k,\xi)$ by (cf. (2.34) in \cite{BM17})
\begin{equation}\label{fstheta}
2ixf(k)+4itkf(k)=2it(4\xi+2k)f(k)\equiv 2it\theta(k,\xi),
\end{equation}
where $\xi=\frac{x}{4t}$.
The signature table of $\Im\theta(k,\xi)$ has qualitatively different form for $\xi>\sqrt{2}A$, $\xi=\sqrt{2}A$, $\sqrt{2}A>\xi>0$, and $\xi=0$, see Figure \ref{sign_pw} and Figure \ref{sign_ew} (cf. Figure 3.2 in \cite{BM17}).
For $\xi\ge\sqrt{2}A$, the stationary phase points (i.e., the points $k_s\in\mathbb{C}$ such that $\theta_k^\prime(k_s,\xi)=0$) are real and have the values
\begin{equation}
k_{1}=\frac{1}{2}\left(-\xi-\sqrt{\xi^2-2A^2}\right),\quad
k_{2}=\frac{1}{2}\left(-\xi+\sqrt{\xi^2-2A^2}\right),
\end{equation}
whereas for $\sqrt{2}A>\xi\ge 0$ the stationary phase points are complex conjugate:
\begin{equation}\label{fsstphc}
\tilde{k}_{1}=\frac{1}{2}\left(-\xi+i\sqrt{2A^2-\xi^2}\right),\quad
\tilde{k}_{2}=\frac{1}{2}\left(-\xi-i\sqrt{2A^2-\xi^2}\right).
\end{equation}
\begin{figure}[h]
\begin{minipage}[h]{0.49\linewidth}
\centering{\includegraphics[width=0.99\linewidth]{sign_table_pw.pdf}}
\caption{Signature table of the phase function $\theta(k,\xi)$ in the plane wave region: $\xi>\sqrt{2}A$.}
\label{sign_pw}
\end{minipage}
\hfill
\begin{minipage}[h]{0.49\linewidth}
\centering{\includegraphics[width=0.99\linewidth]{sign_table_ew.pdf}}
\caption{Signature table of the phase function $\theta(k,\xi)$ in the elliptic wave region: $\sqrt{2}A>\xi>0$.}
\label{sign_ew}
\end{minipage}
\end{figure}
In the present paper we consider the asymptotics of the solution $q(x,t)$ along the rays $\frac{x}{4t}=const$ for $|\frac{x}{4t}|>\sqrt{2}A$ (plane wave region) and for $0<|\frac{x}{4t}|<\sqrt{2}A$ (modulated elliptic wave region).
The transition zones (containing $x=0$ and $\frac{x}{4t}=\pm \sqrt{2}A$) will be addressed elsewhere.
\subsection{Plane wave regions: $|\frac{x}{4t}|>\sqrt{2}A$}
In the present Section we investigate the large-time behavior of the solution $q(x,t)$ along the rays $\frac{x}{4t}=const$ for $|\frac{x}{4t}|>\sqrt{2}A$. In view of (\ref{fsasol}) (see also Remark \ref{fsxgz}) it is enough to consider
$\xi=\frac{x}{4t}>\sqrt{2}A$ only.
According to the signature table of $\theta(k,\xi)$, see Figure \ref{sign_pw}, two different triangular factorizations of the jump matrix $J(x,t,k)$ needed for $k\in\mathbb{R}$ (cf. \cite{BM17, DIZ, RSs}):
\begin{subequations}\label{fstr}
\begin{equation}
\label{fstr1}
J(x,t,k)=
\begin{pmatrix}
1& 0\\
\frac{r_1(k)e^{2it\theta}}{1+ r_1(k)r_2(k)}& 1\\
\end{pmatrix}
\begin{pmatrix}
1+ r_1(k)r_2(k)& 0\\
0& \frac{1}{1+ r_1(k)r_2(k)}\\
\end{pmatrix}
\begin{pmatrix}
1& \frac{r_2(k)e^{-2it\theta}}{1+ r_1(k)r_2(k)}\\
0& 1\\
\end{pmatrix},\, k<k_1,
\end{equation}
and
\begin{equation}
\label{fstr2}
J(x,t,k)=
\begin{pmatrix}
1& r_2(k)e^{-2it\theta}\\
0& 1\\
\end{pmatrix}
\begin{pmatrix}
1& 0\\
r_1(k)e^{2it\theta}& 1\\
\end{pmatrix},\, k>k_1.
\end{equation}
\end{subequations}
In order to get rid of the diagonal factor in (\ref{fstr1}) we introduce the auxiliary function $\delta(k,k_1)$ as the solution of the following scalar Riemann-Hilbert problem:
\begin{equation}
\label{fsdrh}
\begin{aligned}
&\delta_+(k,k_1)=\delta_-(k,k_1)(1+r_1(k)r_2(k)),&& k\in(-\infty,k_1),\\
&\delta(k,k_1)\rightarrow 1, && k\rightarrow\infty.
\end{aligned}
\end{equation}
Though problem (\ref{fsdrh}) looks similar to that
in the case of the local NLS equation, it has an important distinction.
Namely, the jump $(1+r_1(k)r_2(k))$ is not, in general, real valued for $k\in(-\infty,k_1)$ (as it holds for the local NLS equation due to the inherent symmetries of the spectral functions, see \cite{BK14, BM17}).
The nonzero imaginary part gives rise to the singularity of $\delta$ (or $\delta^{-1}$, depending on the sign) at the endpoint $k=k_1$.
Indeed, by using the Plemelj-Sokhotski formula we obtain the following integral representation for $\delta(k,k_1)$:
\begin{equation}\label{fsdelta-int}
\delta(k,k_1)=\exp\left\{\frac{1}{2\pi i}\int_{-\infty}^{k_1}
\frac{\ln(1+r_1(\zeta)r_2(\zeta))}{\zeta-k}\,d\zeta
\right\}.
\end{equation}
Integrating by parts one concludes that
\begin{equation}\label{fsdelta-singular}
\delta(k,k_1)=
(k-k_1)^{i\nu(k_1)}e^{\chi(k,k_1)},
\end{equation}
where
\begin{equation}\label{fschi}
\chi(k,k_1)=-\frac{1}{2\pi i}\int_{-\infty}^{k_1}\ln(k-\zeta)d_{\zeta}\ln(1+ r_1(\zeta)r_2(\zeta)),
\end{equation}
and
\begin{equation}\label{fsnu}
\nu(k_1)=-\frac{1}{2\pi}\ln(1+r_1(k_1)r_2(k_1))
= -\frac{1}{2\pi}\ln|1+r_1(k_1)r_2(k_1)|-
\frac{i}{2\pi}\Delta(k_1),
\end{equation}
with
\begin{equation}\label{fsDelta-arg}
\Delta(k_1)=\int_{-\infty}^{k_1}d\arg(1+ r_1(\zeta)r_2(\zeta)).
\end{equation}
Since $\Delta(k_1)$ is not, in general, equal to zero, the matrix function $\delta^{\sigma_3}(k,k_1)$ is not bounded at $k=k_1$.
In order to justify the asymptotics in the plane wave region (see Theorem \ref{fsth1pw} below) we need the following additional
\underline{\textbf{Assumption}}
\textit{(Winding of the argument, plane wave region).}
We impose the following restriction on the winding of the argument of $(1+r_1(k)r_2(k))$ for $k<-\frac{A}{\sqrt{2}}$ in the plane wave region:
\begin{equation}\label{fsarg-ass}
\int_{-\infty}^{k}d\arg(1+ r_1(\zeta)r_2(\zeta))\in(-\pi,\pi),\quad \text{for all}\ \ k\in\left(-\infty,-\frac{A}{\sqrt{2}}\right).
\end{equation}
This implies that $|\Im \nu(k_1)|<\frac{1}{2}$ and, consequently, $\delta^{\sigma_3}(k,k_1)$ has a square integrable singularity at $k=k_1$:
$$
\delta(k,k_1)=O\left((k-k_1)^{-\frac{1}{2}+\varepsilon(k_1)}\right),\quad k\to k_1,\,\varepsilon(k_1)>0.
$$
Using the function $\delta(k,k_1)$ we make the first transformation of $M(x,t,k)$ as follows:
\begin{equation}\label{fsm1def}
M^{(1)}(x,t,k)=M(x,t,k)\delta^{-\sigma_3}(k,k_1),\quad k\in\mathbb{C}\setminus\left\{\mathbb{R}\cup \overline{B}\right\},
\end{equation}
where $\overline{B}=[-iA,iA]$. Then $M^{(1)}$ solves the following Riemann-Hilbert problem:
\begin{subequations}
\begin{align}
&M^{(1)}_+(x,t,k)=M^{(1)}_-(x,t,k)J^{(1)}(x,t,k),&& k\in\mathbb{R}\cup B,\\
&M^{(1)}(x,t,k)=I+O(k^{-1}), &&k\to\infty,\\
&M^{(1)}(x,t,k)=O\left((k\pm iA)^{-\frac{1}{4}}\right),&& k\to\mp iA,\\
\label{fsm1k1}
&M^{(1)}(x,t,k)=O\left((k-k_1)^{-\frac{1}{2}+\varepsilon(k_1)}\right),&& k\to k_1,\,\varepsilon(k_1)>0,
\end{align}
\end{subequations}
with the jump matrix $J^{(1)}(x,t,k)$ in the form
\begin{equation}
J^{(1)}=
\begin{cases}
\begin{pmatrix}
1& 0\\
\frac{r_1(k)\delta_-^{-2}(k,k_1)}{1+ r_1(k)r_2(k)}e^{2it\theta}& 1\\
\end{pmatrix}
\begin{pmatrix}
1& \frac{r_2(k)\delta_+^{2}(k,k_1)}{1+ r_1(k)r_2(k)}e^{-2it\theta}\\
0& 1\\
\end{pmatrix},& k<k_1,\\
\begin{pmatrix}
1& r_2(k)\delta^2(k,k_1)e^{-2it\theta}\\
0& 1\\
\end{pmatrix}
\begin{pmatrix}
1& 0\\
r_1(k)\delta^{-2}(k,k_1)e^{2it\theta}& 1\\
\end{pmatrix}, &k>k_1,\\
\begin{pmatrix}
-ir_2(k)e^{-2it\theta} & i\delta^{2}(k,k_1)\\
i(1+r_1(k)r_2(k))\delta^{-2}(k,k_1) & -ir_1(k)e^{2it\theta}
\end{pmatrix},& k\in(0,iA),\\
\begin{pmatrix}
ir_2(k)e^{-2it\theta} & i(1+r_1(k)r_2(k))\delta^{2}(k,k_1)\\
i\delta^{-2}(k,k_1)& ir_1(k)e^{2it\theta}
\end{pmatrix},& k\in(-iA,0).
\end{cases}
\end{equation}
Now we are in a position to start the so-called ``opening lenses'' procedure: the Riemann-Hilbert problem is transformed in such a way that
the jump matrix across the new contours significantly simplifies as
$t\to\infty$, and the original RH problem can be approximated by an exactly solvable one with well controlled errors.
For this purpose we need the spectral functions $r_j(k)$, $j=1,2$ to be analytically continued at least in a neighborhood of the contour $\mathbb{R}\cup B$.
This takes place, particularly, when the initial data $q_0(x)$ is a compact perturbation of the boundary values: for such $q_0(x)$, the reflection coefficients $r_j(k)$, $j=1,2$ can be continued to the whole complex plane.
Assuming that $r_j(k)$, $j=1,2$ can be continued at least in a
neighborhood of $\mathbb{R}\cup B$, we introduce $M^{(2)}(x,t,k)$ as follows (we drop the arguments of $M^{(j)}(x,t,k)$, $j=1,2$):
\begin{figure}[h]
\begin{minipage}[h]{0.99\linewidth}
\centering{\includegraphics[width=0.79\linewidth]{cont_1_pw.pdf}}
\caption{Contour $\hat\Gamma=\hat\gamma_1\cup\dots\cup\hat\gamma_4$ and domains $\Omega_j$, $j=0,\dots,4$ in the plane wave region.}
\label{cont_1_pw}
\end{minipage}
\end{figure}
$$
M^{(2)}=
\begin{cases}
M^{(1)},\, k\in\hat\Omega_0;\quad
M^{(1)}
\begin{pmatrix}
1& \frac{-r_2(k)\delta^{2}(k,k_1)}{1+r_1(k)r_2(k)}e^{-2it\theta}\\
0& 1\\
\end{pmatrix}
,\, k\in\hat\Omega_1;
\\
M^{(1)}
\begin{pmatrix}
1& 0\\
-r_1(k)\delta^{-2}(k,k_1)e^{2it\theta}& 1\\
\end{pmatrix}
,\, k\in\hat\Omega_2;\quad
M^{(1)}
\begin{pmatrix}
1& r_2(k)\delta^2(k,k_1)e^{-2it\theta}\\
0& 1\\
\end{pmatrix}
,\, k\in\hat\Omega_3;
\\
M^{(1)}
\begin{pmatrix}
1& 0\\
\frac{r_1(k)\delta^{-2}(k,k_1)}{1+r_1(k)r_2(k)}e^{2it\theta}& 1\\
\end{pmatrix}
,\, k\in\hat\Omega_4,
\end{cases}
$$
where $\Omega_j$, $j=1,\dots,4$ are depictured in Figure \ref{cont_1_pw}.
Then $M^{(2)}(x,t,k)$ solves the following Riemann-Hilbert problem on the contour $\hat\Gamma\cup B$,
$\hat\Gamma=\hat\gamma_1\cup\dots\cup\hat\gamma_4$ (see Figure \ref{cont_1_pw}):
\begin{subequations}
\begin{align}
&M^{(2)}_+(x,t,k)=M^{(2)}_-(x,t,k)J^{(2)}(x,t,k),&&k\in\hat\Gamma\cup B,\\
&M^{(2)}(x,t,k)=I+O(k^{-1}), &&k\to\infty,\\
&M^{(2)}(x,t,k)=O\left((k\pm iA)^{-\frac{1}{4}}\right),&& k\to\mp iA,\\
&M^{(2)}(x,t,k)=O\left((k-k_1)^{-\frac{1}{2}+\varepsilon(k_1)}\right),&& k\to k_1,\,\varepsilon(k_1)>0,
\end{align}
\end{subequations}
where
\begin{equation}
\label{fsJ2}
J^{(2)}=
\begin{cases}
\begin{pmatrix}
1& \frac{r_2(k)\delta^{2}(k,k_1)}{1+r_1(k)r_2(k)}e^{-2it\theta}\\
0& 1\\
\end{pmatrix}
,\, k\in\hat\gamma_1;\quad
\begin{pmatrix}
1& 0\\
r_1(k)\delta^{-2}(k,k_1)e^{2it\theta}& 1\\
\end{pmatrix}
,\ k\in\hat\gamma_2;
\\
\begin{pmatrix}
1& -r_2(k)\delta^2(k,k_1)e^{-2it\theta}\\
0& 1\\
\end{pmatrix}
,\, k\in\hat\gamma_3;\quad
\begin{pmatrix}
1& 0\\
\frac{-r_1(k)\delta^{-2}(k,k_1)}{1+r_1(k)r_2(k)}e^{2it\theta}& 1\\
\end{pmatrix}
,\, k\in\hat\gamma_4;\\
\begin{pmatrix}
0& i\delta^{2}(k,k_1)\\
i\delta^{-2}(k,k_1)&0
\end{pmatrix},\,k\in B.
\end{cases}
\end{equation}
Notice that according to the signature table of $\theta(k,\xi)$, the jump matrix $J^{(2)}(x,t,k)$ rapidly decays to the identity matrix for $k\in\hat\Gamma$ away from any vicinity of the stationary phase point $k=k_1$. In order to arrive to an exactly solvable (model) RH problem, we have to eliminate the dependence of $k$ in the jump across $k\in B$. This can be done by introducing the function $F(k,k_1)$ as a solution of the following scalar Riemann-Hilbert problem (cf. (4.10) in \cite{BKS11}):
\begin{subequations}\label{fsFRHab}
\begin{align}\label{fsFRH}
&F_+(k,k_1)F_-(k,k_1)=\delta^{2}(k,k_1),&& k\in B,\\
&F(k,k_1)=O(1),&&k\to\pm iA,\,k\to\infty.
\end{align}
\end{subequations}
Taking the logarithm of both sides in (\ref{fsFRH}) and dividing by $f(k)$ we obtain:
$$
\left(\frac{\ln F(k,k_1)}{f(k)}\right)_+ -
\left(\frac{\ln F(k,k_1)}{f(k)}\right)_-=
-\frac{2\ln\delta(k,k_1)}{f_-(k)},\quad k\in B.
$$
Then the Plemelj-Sokhotski formula gives the following integral representation for $F(k,k_1)$ (see (\ref{fsfj})):
\begin{equation}\label{fsF}
F(k,k_1)=\exp\left\{-\frac{f(k)}{\pi i}\int_{B}\frac{\ln\delta(\zeta,k_1)}{f(\zeta)(\zeta-k)}\,d\zeta\right\},\quad k\in\mathbb{C}\setminus\overline{B},
\end{equation}
which satisfies the RH problem (\ref{fsFRH}). In order to recover $q(x,t)$
from the solution of the RH problem, we will need the large-$k$ behavior of $F(k,k_1)$:
\begin{equation}
F(k,k_1)= e^{iF_{\infty}(k_1)}+O(k^{-1}),\quad
k\to\infty,
\end{equation}
where
\begin{equation}\label{fsFinf}
F_{\infty}(k_1)=-\frac{1}{\pi}
\int_{B}\frac{\ln\delta(\zeta,k_1)}{f(\zeta)}\,d\zeta.
\end{equation}
Taking into account (\ref{fsdelta-int}) and that the contour of integration in (\ref{fsFinf}) lies on the imaginary axis, the real and imaginary part of $F_{\infty}(k_1)$ can be written as follows (cf. purely real $g_{\infty}$ given by (4.25) in \cite{BM17} in the case of the local NLS equation):
\begin{subequations}\label{fsreimFinf}
\begin{align}
&\Re F_{\infty}(k_1)=-\frac{1}{2i\pi^2}\int_{B}\frac{1}{f(\zeta)}
\int_{-\infty}^{k_1}\frac{\ln|1+r_1(s)r_2(s)|}{s-\zeta}\,ds\,d\zeta,\\
&\Im F_{\infty}(k_1)=-\frac{1}{2i\pi^2}\int_{B}\frac{1}{f(\zeta)}
\int_{-\infty}^{k_1}\frac{\Delta(s)}{s-\zeta}\,ds\,d\zeta,
\end{align}
\end{subequations}
where $\Delta(s)$ is given by (\ref{fsDelta-arg}).
\begin{remark}
Due to the ``lack of symmetry'' for $r_1(k)$ and $r_2(k)$, the imaginary part of $F_\infty(k_1)$ is, in general, nonzero.
It is in a sharp contrast with the local case, where $\Im F_{\infty}$ (see $g_{\infty}$ given by (4.25) in \cite{BM17}) is always zero due to the symmetry $r_2(k)=\bar{r}_1(k)$ for $k\in\mathbb{R}$.
Consequently, the asymptotics of the modulus of $q(x,t)$
will depend on details of the initial data (cf. ``modulated constant'' region in the step-like problem for the NNLS equation \cite{RSs}). This is qualitatively different from the local case, where the asymptotics in the plane wave region depends on $q_0(x)$ through the phase shift only \cite{BM17}.
\end{remark}
\begin{remark}
\label{fsboundf}
Taking into account that (see Chapter I, Paragraph 8.3 in \cite{G66})
$$
\int_B\frac{d\zeta}{f(\zeta)(\zeta-k)}=i\pi
\left[(k+iA)^{-\frac{1}{2}}-(k-iA)^{-\frac{1}{2}}\right]+F_0(k),
$$
where $F_0(k)$ is an analytic function,
one concludes that $F(k,k_1)$ is bounded at the endpoints $k=\pm iA$.
\end{remark}
Now we define $M^{(3)}$ with the help of $F(k,k_1)$:
\begin{equation}
M^{(3)}(x,t,k)=e^{-iF_{\infty}(k_1)\sigma_3}
M^{(2)}(x,t,k)F^{\sigma_3}(k,k_1),
\quad k\in\mathbb{C}\setminus\left\{\mathbb{R}\cup\overline{B}\right\}.
\end{equation}
Then $M^{(3)}$ solves the RH problem with the constant jump across $B$:
\begin{subequations}\label{fsM3}
\begin{align}
&M^{(3)}_+(x,t,k)=M^{(3)}_-(x,t,k)J^{(3)}(x,t,k),&&
k\in\hat\Gamma\cup B,\\
&M^{(3)}(x,t,k)=I+O(k^{-1}), &&k\to\infty,\\
&M^{(3)}(x,t,k)=O\left((k\pm iA)^{-\frac{1}{4}}\right),&& k\to\mp iA,\\
&M^{(3)}(x,t,k)=O\left((k-k_1)^{-\frac{1}{2}+\varepsilon(k_1)}\right),&& k\to k_1,\,\varepsilon(k_1)>0,
\end{align}
\end{subequations}
with
\begin{equation}
\label{fsJ3}
J^{(3)}(x,t,k)=
\begin{cases}
i\sigma_1,&k\in B,\\
F^{-\sigma_3}(k,k_1)J^{(2)}(x,t,k)F^{\sigma_3}(k,k_1),&k\in\hat\Gamma.
\end{cases}
\end{equation}
The solution $q(x,t)$ of the Cauchy problem (\ref{fsivp}) can be found in terms of $M^{(3)}(x,t,k)$ as follows:
\begin{subequations}\label{fsasolM3}
\begin{align}\label{fssolM3}
&q(x,t)=2ie^{2iA^2t+2iF_\infty(k_1)}\lim_{k\to\infty}kM_{12}^{(3)}(x,t,k),&& x>0,\\
\label{fssol1M3}
&q(-x,t)=-2ie^{2iA^2t+2i\overline{F_\infty(k_1)}}\lim_{k\to\infty}k\overline{M_{21}^{(3)}(x,t,k)},&& x>0.
\end{align}
\end{subequations}
Now we can calculate the long-time asymptotics of the solution in the plane wave region.
\begin{theorem}\label{fsth1pw}
(Plane wave region).\\
Suppose that the initial data $q_0(x)$ is a compact perturbation of the background (\ref{fsivp-c}) and that the associated spectral functions $a_j(k)$ and $r_j(k)=\frac{b_j(k)}{a_j(k)}$, $j=1,2$ satisfy the following conditions:
\begin{enumerate}
\item $a_1(k)$ and $a_2(k)$ have no zeros in $\overline{\mathbb{C}^{+}}$ and $\overline{\mathbb{C}^{-}}$ respectively,
\item $\int_{-\infty}^{k}d\arg(1+ r_1(\zeta)r_2(\zeta))\in(-\pi,\pi)$, for all $k<-\frac{A}{\sqrt{2}}$.
\end{enumerate}
Then the solution $q(x,t)$
of problem (\ref{fsivp})
has the following long-time asymptotics along the rays $\frac{x}{4t}=const$ uniformly in any compact subset of $\{\frac{x}{4t}\in\mathbb{R}:|\frac{x}{4t}|>\sqrt{2}A\}$:
\begin{subequations}
\begin{align}
\label{fssolpw1}
&q(x,t)=Ae^{-2\Im F_{\infty}(k_1)}
e^{2i(A^2t+\Re F_{\infty}(k_1))}
+E_1(x,t),&& t\to\infty,\quad \frac{x}{4t}>\sqrt{2}A,\\
\label{fssolpw2}
&q(-x,t)=Ae^{2\Im F_{\infty}(k_1)}
e^{2i(A^2t+\Re F_{\infty}(k_1))}
+E_2(x,t),&& t\to\infty,\quad -\frac{x}{4t}<-\sqrt{2}A,
\end{align}
\end{subequations}
where $k_{1}=\frac{1}{2}\left(-\xi-\sqrt{\xi^2-2A^2}\right)$
with $\xi=\frac{x}{4t}>0$, $\Re F_{\infty}(k_1)$ and $\Im F_{\infty}(k_1)$ are given by (\ref{fsreimFinf}), and the decaying terms $E_j(x,t)$, $j=1,2$ have the following form depending on the value of $\Im\nu(k_1)$:
\begin{description}
\item[(a)] if $\Im\nu(k_1)\in\left(-\frac{1}{2},-\frac{1}{6}\right]$, then
\begin{align*}
&E_1(x,t)=t^{-\frac{1}{2}-\Im\nu(k_1)}c_1(k_1)
\exp\left\{2it(A^2+\theta(k_1,\xi))+i\Re\nu(k_1)\ln t\right\}
+R(x,t),\\
&E_2(x,t)=t^{-\frac{1}{2}-\Im\nu(k_1)}c_3(k_1)
\exp\left\{2it(A^2-\theta(k_1,\xi))-i\Re\nu(k_1)\ln t\right\}
+R(x,t).
\end{align*}
\item[(b)] if $\Im\nu(k_1)\in\left(-\frac{1}{6},\frac{1}{6}\right)$, then
\begin{align}
\label{fsE1b}
\nonumber
E_1(x,t)&=t^{-\frac{1}{2}+\Im\nu(k_1)}c_2(k_1)
\exp\left\{2it(A^2-\theta(k_1,\xi))-i\Re\nu(k_1)\ln t\right\}&\\
\nonumber
&\quad+
t^{-\frac{1}{2}-\Im\nu(k_1)}c_1(k_1)
\exp\left\{2it(A^2+\theta(k_1,\xi))+i\Re\nu(k_1)\ln t\right\}
+R(x,t),
\end{align}
\begin{align}
\nonumber
E_2(x,t)&=t^{-\frac{1}{2}+\Im\nu(k_1)}c_4(k_1)
\exp\left\{2it(A^2+\theta(k_1,\xi))+i\Re\nu(k_1)\ln t\right\}&\\
\nonumber
&\quad+
t^{-\frac{1}{2}-\Im\nu(k_1)}c_3(k_1)
\exp\left\{2it(A^2-\theta(k_1,\xi))-i\Re\nu(k_1)\ln t\right\}
+R(x,t).
\end{align}
\item[(c)] if $\Im\nu(k_1)\in\left[\frac{1}{6},\frac{1}{2}\right)$, then
\begin{align*}
&E_1(x,t)=t^{-\frac{1}{2}+\Im\nu(k_1)}c_2(k_1)
\exp\left\{2it(A^2-\theta(k_1,\xi))-i\Re\nu(k_1)\ln t\right\}+R(x,t),\\
&E_2(x,t)=t^{-\frac{1}{2}+\Im\nu(k_1)}c_4(k_1)
\exp\left\{2it(A^2+\theta(k_1,\xi))+i\Re\nu(k_1)\ln t\right\}+R(x,t).
\end{align*}
\end{description}
Here
\begin{align}
\nonumber
c_1(k_1)=&\frac{\sqrt{\pi}\left(w(k_1)-1/w(k_1)\right)^2F^2(k_1,k_1)}
{\sqrt{2}r_2(k_1)\Gamma(i\nu(k_1))}\\
\nonumber
&\times\exp\left\{
2iF_{\infty}(k_1)-\frac{\pi}{2}\nu(k_1)+\frac{3\pi i}{4}-2\chi(k_1,k_1)-
(1-2i\nu(k_1))\ln 2\sqrt{\frac{4k_1+2\xi}{f(k_1)}}
\right\},
\end{align}
\begin{align}
\nonumber
c_2(k_1)=&\frac{\sqrt{\pi}\left(w(k_1)+1/w(k_1)\right)^2}
{\sqrt{2}r_1(k_1)\Gamma(-i\nu(k_1))F^2(k_1,k_1)}\\
\nonumber
&\times\exp\left\{
2iF_{\infty}(k_1)-\frac{\pi}{2}\nu(k_1)+\frac{\pi i}{4}+2\chi(k_1,k_1)-
(1+2i\nu(k_1))\ln 2\sqrt{\frac{4k_1+2\xi}{f(k_1)}}
\right\},
\end{align}
\begin{align}
\nonumber
c_3(k_1)=&\frac{\sqrt{\pi}\left(w(k_1)+1/w(k_1)\right)^2
\overline{F^2(k_1,k_1)}}
{\sqrt{2}\,\overline{r_2}(k_1)\Gamma(-i\overline{\nu(k_1)})}\\
\nonumber
&\times\exp\left\{
2i\overline{F_{\infty}(k_1)}-\frac{\pi}{2}\overline{\nu(k_1)}+\frac{\pi i}{4}-2\overline{\chi}(k_1,k_1)-
(1+2i\overline{\nu(k_1)})\ln 2\sqrt{\frac{4k_1+2\xi}{f(k_1)}}
\right\},
\end{align}
\begin{align}
\nonumber
c_4(k_1)=&\frac{\sqrt{\pi}\left(w(k_1)-1/w(k_1)\right)^2}
{\sqrt{2}\,\overline{r_1}(k_1)\Gamma(i\overline{\nu(k_1)})
\overline{F^2(k_1,k_1)}}\\
\nonumber
&\times\exp\left\{
2i\overline{F_{\infty}(k_1)}-\frac{\pi}{2}\overline{\nu(k_1)}+\frac{3\pi i}{4}+2\overline{\chi}(k_1,k_1)-
(1-2i\overline{\nu(k_1)})\ln 2\sqrt{\frac{4k_1+2\xi}{f(k_1)}}
\right\},
\end{align}
where $\Gamma(\cdot)$ is the Euler Gamma-function and $w(k_1)$, $f(k_1)$, $\chi(k_1, k_1)$, $\nu(k_1)$, and $F(k_1,k_1)$ are given by (\ref{fsK}), (\ref{fsf}), (\ref{fschi}), (\ref{fsnu}) and (\ref{fsF}), respectively. The error term $R(x,t)$ has the form
\begin{equation}
\label{fsR3}
R(x,t)=
\begin{cases}
O\left(t^{-1+2|\Im\nu(k_1)|}\right),&\Im\nu(k_1)\not=0,\\
O\left(t^{-1}\ln t\right),&\Im\nu(k_1)=0.
\end{cases}
\end{equation}
\end{theorem}
\begin{proof}
See Appendix A.
\end{proof}
\subsection{The modulated elliptic wave regions: $0<|\frac{x}{4t}|<\sqrt{2}A$}\label{fsmewr}
The present Subsection is devoted to obtaining the large-time asymptotics of the solution in the modulated elliptic wave regions,
which are defined by $0<|\frac{x}{4t}|<\sqrt{2}A$.
The main difference of this case comparing with the plane wave regions is the absence of real stationary phase points (see (\ref{fsstphc})). Similarly to
\cite{BV07} (see also \cite{BM17, BKS11}), we set a change-of-factorization point $k=k_0$, $k_0<0$ (see Figure \ref{cont_1_ew}), and then deal with exponentially growing (as $t\to\infty$) jump matrices. This artificial ``stationary phase point'' will be found as the solution of a linear integral equation (see (\ref{fsintk0}) below).
The transformations from $M(x,t,k)$ to $M^{(2)}(x,t,k)$ are as in the plane wave case, with the only difference: instead of $\delta(k,k_1)$, in the modulated elliptic wave region we take $\delta(k,k_0)$.
As in the plane wave case, we make an assumption on the winding of the argument of $(1+r_1(k)r_2(k))$:
\underline{\textbf{Assumption}}
\textit{(Winding of the argument, elliptic wave region).}
We impose the following restriction on the winding of the argument of $(1+r_1(k)r_2(k))$ for $-\frac{A}{\sqrt{2}}<k<0$ in the modulated elliptic wave region (cf. (\ref{fsarg-ass})):
\begin{equation}\label{fsDelta-argew}
\int_{-\infty}^{k}d\arg(1+ r_1(\zeta)r_2(\zeta))
\in(-\pi,\pi),\quad \text{for all}\ \ k\in\left(-\frac{A}{\sqrt{2}},0\right),
\end{equation}
Then $\delta^{\sigma_3}(k,k_0)$ has square integrable singularity at $k=k_0$, and the Riemann-Hilbert problem for $M^{(2)}(x,t,k)$ has the form (see Figure \ref{cont_1_ew}):
\begin{figure}[h]
\begin{minipage}[h]{0.99\linewidth}
\centering{\includegraphics[width=0.79\linewidth]{cont_1_ew.pdf}}
\caption{Contour $\hat\Gamma=\hat\gamma_1\cup\dots\cup\hat\gamma_4$, where $\hat\gamma_j=\hat\gamma_{j0}\cup\hat\gamma_{j1}$, $j=2,3$, and domains $\Omega_j$, $j=0,\dots,4$ for the Riemann-Hilbert problem $M^{(2)}$ in the elliptic wave region.}
\label{cont_1_ew}
\end{minipage}
\end{figure}
\begin{subequations}
\begin{align}
&M^{(2)}_+(x,t,k)=M^{(2)}_-(x,t,k)J^{(2)}(x,t,k),&&k\in\hat\Gamma\cup B,\\
&M^{(2)}(x,t,k)=I+O(k^{-1}), &&k\to\infty,\\
&M^{(2)}(x,t,k)=O\left((k\pm iA)^{-\frac{1}{4}}\right),&& k\to\mp iA,\\
&M^{(2)}(x,t,k)=O\left((k-k_0)^{-\frac{1}{2}+\varepsilon(k_0)}\right),&& k\to k_0,\,\varepsilon(k_0)>0,
\end{align}
\end{subequations}
where the point $\alpha$ will be specified below (see (\ref{fsreaima})) and
\begin{equation}
\label{fsJ2ew}
J^{(2)}=
\begin{cases}
\begin{pmatrix}
1& \frac{r_2(k)\delta^{2}(k,k_0)}{1+r_1(k)r_2(k)}e^{-2it\theta}\\
0& 1\\
\end{pmatrix}
,\, k\in\hat\gamma_1;\quad
\begin{pmatrix}
1& 0\\
r_1(k)\delta^{-2}(k,k_0)e^{2it\theta}& 1\\
\end{pmatrix}
,\ k\in\hat\gamma_2;
\\
\begin{pmatrix}
1& -r_2(k)\delta^2(k,k_0)e^{-2it\theta}\\
0& 1\\
\end{pmatrix}
,\, k\in\hat\gamma_3;\quad
\begin{pmatrix}
1& 0\\
\frac{-r_1(k)\delta^{-2}(k,k_0)}{1+r_1(k)r_2(k)}e^{2it\theta}& 1\\
\end{pmatrix}
,\, k\in\hat\gamma_4;\\
\begin{pmatrix}
0& i\delta^{2}(k,k_0)\\
i\delta^{-2}(k,k_0)&0
\end{pmatrix},\,k\in B.
\end{cases}
\end{equation}
Notice that the jump matrix $J^{(2)}(x,t,k)$ is exponentially growing for $k\in\hat\gamma_{21}\cup\hat\gamma_{31}$.
To resolve the issue of this growth, we use the factorizations on this part of the contour, which are similar to
(4.2), (4.3) in \cite{BV07} (see also (5.3) in \cite{BM17}).
Namely, we define $M^{(3)}(x,t,k)$ as follows (see Figure \ref{cont_2_ew}):
$$
M^{(3)}=
\begin{cases}
M^{(2)}
\begin{pmatrix}
1& -\frac{\delta^{2}(k,k_0)}{r_1(k)}e^{-2it\theta}\\
0&1
\end{pmatrix},\, k\in\hat\Omega_{01};\quad
M^{(2)}
\begin{pmatrix}
1& \frac{\delta^{2}(k,k_0)}{r_1(k)}e^{-2it\theta}\\
0&1
\end{pmatrix},\, k\in\hat\Omega_{21};\\
M^{(2)}
\begin{pmatrix}
1& 0\\
\frac{e^{2it\theta}}{r_2(k)\delta^{2}(k,k_0)}&1
\end{pmatrix},\, k\in\hat\Omega_{02};\quad
M^{(2)}
\begin{pmatrix}
1& 0\\
-\frac{e^{2it\theta}}{r_2(k)\delta^{2}(k,k_0)}&1
\end{pmatrix},\, k\in\hat\Omega_{31};\\
M^{(2)},\text{ otherwise}.
\end{cases}
$$
\begin{figure}[h]
\begin{minipage}[h]{0.99\linewidth}
\centering{\includegraphics[width=0.79\linewidth]{cont_2_ew.pdf}}
\caption{Contour $\tilde{\Gamma}=\hat\Gamma\cup
\left(
\bigcup\limits_{i,j=2}^{3}
\hat\gamma_{ij}\right)
$
and domains in the Riemann-Hilbert problems for $M^{(j)}(x,t,k)$, $j=3,4,5$ in the elliptic wave region.}
\label{cont_2_ew}
\end{minipage}
\end{figure}
It is straightforward to show that jump matrix $J^{(3)}(x,t,k)$ associated with sectionally holomorphic matrix $M^{(3)}(x,t,k)$ grows as $t\to\infty$
for $k\in\hat\gamma_{21}\cup\hat\gamma_{31}$ only:
\begin{equation}
\label{fsJ3ew}
J^{(3)}=
\begin{cases}
\begin{pmatrix}
0& -\frac{\delta^{2}(k,k_0)}{r_1(k)}e^{-2it\theta}\\
\frac{r_1(k)}{\delta^{2}(k,k_0)}e^{2it\theta}&0
\end{pmatrix},\,k\in\hat\gamma_{21};\quad
\begin{pmatrix}
1& \frac{\delta^{2}(k,k_0)}{r_1(k)}e^{-2it\theta}\\
0&1
\end{pmatrix},\, k\in\hat\gamma_{22}\cup\hat\gamma_{23};
\\
\begin{pmatrix}
0& -r_2(k)\delta^{2}(k,k_0)e^{-2it\theta}\\
\frac{e^{2it\theta}}{r_2(k)\delta^{2}(k,k_0)}&0
\end{pmatrix},\,k\in\hat\gamma_{31};\quad
\begin{pmatrix}
1& 0\\
-\frac{e^{2it\theta}}{r_2(k)\delta^{2}(k,k_0)}&1
\end{pmatrix},\, k\in\hat\gamma_{32}\cup\hat\gamma_{33};
\\
J^{(2)}(x,t,k),\text{ otherwise}.
\end{cases}
\end{equation}
To circumvent the problem of exponentially growing anti-diagonal jump matrices across $\hat\gamma_{21}\cup\hat\gamma_{31}$, we employ the $g$-function mechanism, firstly introduced by Deift, Venakides and Zhou \cite{DVZ94, DVZ97}.
Namely, introduce a new phase function $h(k,\xi,k_0,\alpha)$ as a sectionally analytic function, which has a jump along $k\in
B\cup\hat\gamma_{21}\cup\hat\gamma_{31}$ and is bounded at the endpoints.
In order to deal with bounded at infinity sectionally analytic functions, $h(k)=h(k,\xi,k_0,\alpha)$ should have a behavior for large $k$ that is
similar to $\theta(k,\xi)$. Since (see (\ref{fstheta}))
\begin{equation}\label{fsthetakinf}
\theta(k,\xi)=2k^2+4\xi k+A^2+O(k^{-1}), \quad k\to\infty,
\end{equation}
we assume that
\begin{equation}\label{fshkinf}
h(k)=2k^2+4\xi k+H_\infty+O(k^{-1}), \quad k\to\infty,
\end{equation}
where $H_\infty$ will be found below (see (\ref{fsH0})).
Supposing that an appropriate $h(k)$ is known, we define $M^{(4)}(x,t,k)$ as follows:
\begin{equation}
M^{(4)}(x,t,k)=e^{-it(H_\infty-A^2)\sigma_3}M^{(3)}(x,t,k)
e^{-it(\theta(k,\xi)-h(k,\xi,k_0,\alpha))\sigma_3},\quad k\in\mathbb{C}\setminus
\left\{\tilde\Gamma\cup \overline{B}\right\}.
\end{equation}
Then $M^{(4)}(x,t,k)$ satisfies the following RH problem
\begin{subequations}
\begin{align}
&M^{(4)}_+(x,t,k)=M^{(4)}_-(x,t,k)J^{(4)}(x,t,k),&&k\in\tilde\Gamma\cup B,\\
&M^{(4)}(x,t,k)=I+O(k^{-1}), &&k\to\infty,\\
&M^{(4)}(x,t,k)=O\left((k\pm iA)^{-\frac{1}{4}}\right),&& k\to\mp iA,\\
&M^{(4)}(x,t,k)=O\left((k-k_0)^{-\frac{1}{2}+\varepsilon(k_0)}\right),&& k\to k_0,\,\varepsilon(k_0)>0,
\end{align}
\end{subequations}
where
\begin{equation}
\label{fsJ4ew}
J^{(4)}=
\begin{cases}
\begin{pmatrix}
0& -\frac{\delta^{2}(k,k_0)}{r_1(k)}e^{-it(h_++h_-)}\\
\frac{r_1(k)}{\delta^{2}(k,k_0)}e^{it(h_++h_-)}&0
\end{pmatrix},\,k\in\hat\gamma_{21};\quad
\begin{pmatrix}
1& \frac{\delta^{2}(k,k_0)}{r_1(k)}e^{-2ith}\\
0&1
\end{pmatrix},\, k\in\hat\gamma_{22}\cup\hat\gamma_{23};
\\
\begin{pmatrix}
0& -r_2(k)\delta^{2}(k,k_0)e^{-it(h_++h_-)}\\
\frac{e^{it(h_++h_-)}}{r_2(k)\delta^{2}(k,k_0)}&0
\end{pmatrix},\,k\in\hat\gamma_{31};\,
\begin{pmatrix}
1& 0\\
-\frac{e^{2ith}}{r_2(k)\delta^{2}(k,k_0)}&1
\end{pmatrix},\, k\in\hat\gamma_{32}\cup\hat\gamma_{33};\\
\begin{pmatrix}
1& \frac{r_2(k)\delta^{2}(k,k_0)}{1+r_1(k)r_2(k)}e^{-2ith}\\
0& 1\\
\end{pmatrix}
,\, k\in\hat\gamma_1;\quad
\begin{pmatrix}
1& 0\\
r_1(k)\delta^{-2}(k,k_0)e^{2ith}& 1\\
\end{pmatrix}
,\ k\in\hat\gamma_{20};
\\
\begin{pmatrix}
1& -r_2(k)\delta^2(k,k_0)e^{-2ith}\\
0& 1\\
\end{pmatrix}
,\, k\in\hat\gamma_{30};\quad
\begin{pmatrix}
1& 0\\
\frac{-r_1(k)\delta^{-2}(k,k_0)}{1+r_1(k)r_2(k)}e^{2ith}& 1\\
\end{pmatrix}
,\, k\in\hat\gamma_4;\\
\begin{pmatrix}
0& i\delta^{2}(k,k_0)e^{-it(h_++h_-)}\\
i\delta^{-2}(k,k_0)e^{it(h_++h_-)}&0
\end{pmatrix},\,k\in B.
\end{cases}
\end{equation}
The solution $q(x,t)$ can be found via $M^{(4)}(x,t,k)$ as follows:
\begin{subequations}\label{fsasolM4}
\begin{align}\label{fssolM4}
&q(x,t)=2ie^{2itH_\infty}\lim_{k\to\infty}kM_{12}^{(4)}(x,t,k),&& x>0,\\
\label{fssol1M4}
&q(-x,t)=-2ie^{2itH_\infty}\lim_{k\to\infty}k\overline{M_{21}^{(4)}(x,t,k)},&& x>0,
\end{align}
\end{subequations}
where the real constant $H_{\infty}$ is given by (\ref{fsH0}).
Now the task is to define
$h(k)\equiv h(k,\xi,k_0,\alpha)$ in a manner that the jump matrix $J^{(4)}(x,t,k)$ decays (exponentially fast) to $I$ except neighborhoods of stationary phase points and, possibly, some parts of the contour, where the jump matrix remains bounded as $t\to\infty$.
Similarly to \cite{BKS11}, Section 4.3.1, we define the differential $dh(k)$ which has three zeros at $k=\alpha$, $k=\overline{\alpha}$ and $k=k_0$:
\begin{equation}\label{fsdh}
dh(k)=4\frac{(k-k_0)(k-\alpha)(k-\overline{\alpha})}
{\sqrt{(k^2+A^2)(k-\alpha)(k-\overline{\alpha})}}dk.
\end{equation}
We consider $dh(k)$ as an Abelian differential of the second kind with poles at $\infty^{\pm}$
on the genus-1 Riemann surface $\Sigma$ of
\begin{equation}\label{fsgammaRS}
\gamma(k)=\sqrt{(k^2+A^2)(k-\alpha)(k-\overline{\alpha})},
\end{equation}
where the branch of the square root is specified by the asymptotics on the upper sheet $\Sigma_u$: $\gamma(k)\sim k^2$ as $k\to\infty^{+}$.
On the cuts $B$ and $(\overline{\alpha},\alpha)$ we set $\gamma(k)=\gamma_-(k)\equiv-\gamma_+(k)$.
The canonical basis $\{\mathfrak{a},\mathfrak{b}\}$ of cycles on this Riemann surface is defined as follows.
The $\mathfrak{b}$-cycle is a closed counterclockwise oriented simple loop around the branch cut $B$, which lies on the lower sheet $\Sigma_l$.
The $\mathfrak{a}$-cycle starts on the upper sheet from the point $\overline{\alpha}$, then approaches $-iA$ and returns to the starting point on the lower sheet (see Figure \ref{riemann_surf}).
\begin{figure}[h]
\begin{minipage}[h]{0.49\linewidth}
\centering{\includegraphics[width=0.99\linewidth]{riemann_surf.pdf}}
\caption{Canonical basis $\{\mathfrak{a},\mathfrak{b}\}$ of cycles on the Riemann surface $\Sigma$ of $\gamma(k)$. The solid lines lie on the upper sheet $\Sigma_u$, while the dashed lines lie on the lower sheet $\Sigma_l$.}
\label{riemann_surf}
\end{minipage}
\hfill
\begin{minipage}[h]{0.49\linewidth}
\centering{\includegraphics[width=0.99\linewidth]{fund_rect_2.pdf}}
\caption{The fundamental rectangle of the Riemann surface $\Sigma$, obtained by cutting it along the basis $\{\mathfrak{a},\mathfrak{b}\}$. $\Sigma_{u}$ and $\Sigma_{l}$ are the upper and the lower sheets of $\Sigma$ respectively; ``$+$'' and ``$-$'' denotes the left and the right sides of the corresponding branch cuts.}
\label{fund_rect}
\end{minipage}
\end{figure}
Define $h(k)$ as the sum of two Abelian integrals (cf. \cite{BKS11, BM17}):
\begin{equation}\label{fsh}
h(k)=\frac{1}{2}\left(\int_{iA}^{k}+\int_{-iA}^{k}\right)\,dh(z),
\end{equation}
where $dh(z)$ is given by (\ref{fsdh}).
In order to make the locally holomorphic multivalued function $h(k)$ single valued, we assume that all integrals along paths on the Riemann surface lie on the fundamental rectangle obtained by cutting this surface along the basis $\{\mathfrak{a},\mathfrak{b}\}$, see Figure \ref{fund_rect}.
The definition (\ref{fsh}) involves three real parameters: $k_0$, $\Re\alpha$ and $\Im\alpha$. We choose these parameters in such a way that the jump matrix $J^{(4)}(x,t,k)$ become bounded for $k\in B$ and $k\in\hat\gamma_{21}\cup\hat\gamma_{31}$ and decaying for the other parts of the contour:
\begin{enumerate}[(i)]
\item $h_+(k)+h_-(k)=0$, for $k\in B$,
\item $h_+(k)+h_-(k)\in\mathbb{R}$, for $k\in \hat\gamma_{21}\cup\hat\gamma_{31}$, is similar as that of $\Im\theta(k,\xi)$.
\end{enumerate}
These conditions are fulfilled for the parameters given in the following Proposition (cf. \cite{BM17, BKS11}).
\begin{proposition}\label{fsdefh}
The phase function $h(k)$ defined by (\ref{fsh}), satisfies conditions (i)--(iii) if the parameters $k_0$ and $\alpha$ have the following values:
\begin{equation}\label{fsreaima}
\Re\alpha=-k_0-\xi,\quad \Im\alpha=\sqrt{A^2+2k_0^2+2k_0\xi},
\end{equation}
and $k_0\in(-\xi/2,0)$ is the single solution of the integral equation:
\begin{equation}\label{fsintk0}
\int_B\sqrt{
\frac{(k+k_0+\xi)^2+2k_0^2+2\xi k_0+A^2}
{k^2+A^2}}
(k-k_0)\,dk =0.
\end{equation}
For such values of the parameters, $h(k)$ has the large $k$ asymptotics (\ref{fshkinf}), where
$H_\infty\in\mathbb{R}$ has the form
\begin{equation}\label{fsH0}
H_\infty=2\left(\int_{iA}^{\infty}+\int_{-iA}^{\infty}\right)\left[
\frac{(k-k_0)(k-\alpha)(k-\overline{\alpha})}{\gamma(k)}-
(k+\xi)\right]\,dk+2A^2.
\end{equation}
Moreover, for $k\in\hat\gamma_{21}\cup\hat\gamma_{31}$ the Abel integral $h(k)$ satisfies the following jump condition:
\begin{equation}\label{fshjumpa}
h_+(k)+h_-(k)=\Omega,
\quad k\in\hat\gamma_{21}\cup\hat\gamma_{31},
\end{equation}
where the real constant $\Omega$ is as follows:
\begin{equation}\label{fsOmega}
\Omega = \left(\int_{iA}^{\alpha}+\int_{-iA}^{\overline{\alpha}}\right)\,dh(k).
\end{equation}
\end{proposition}
\begin{proof}
See Appendix B.
\end{proof}
Having constructed the new phase function $h(k)$, which satisfies conditions (i)--(iii), we must eliminate the dependence of $k$ from the jump matrix $J^{(4)}(x,t,k)$ across $B$ and $\hat\gamma_{21}\cup\hat\gamma_{31}$.
To do this, we define the scalar function $G(k)=G(k,k_0,\alpha)$ as the solution of a scalar Riemann-Hilbert problem (cf. (\ref{fsFRHab})):
\begin{subequations}\label{fsGRHall}
\begin{align}\label{fsGRH}
&G_+(k,k_0,\alpha)G_-(k,k_0,\alpha)=\delta^{2}(k,k_0),&& k\in B,\\
&G_+(k,k_0,\alpha)G_-(k,k_0,\alpha)=
\frac{\delta^2(k,k_0)}{r_1(k)}e^{i\omega},
&&k\in\hat\gamma_{21},\\
&G_+(k,k_0,\alpha)G_-(k,k_0,\alpha)=
\delta^2(k,k_0)r_2(k)e^{i\omega},
&&k\in\hat\gamma_{31},\\
\label{fsGbound}
&G(k,k_0,\alpha)=O(1),&&k\to\pm iA,\,k\to\Re\alpha\pm i\Im\alpha,\,k\to\infty.
\end{align}
\end{subequations}
Using the arguments similar to those in the plane wave case for the auxiliary function $F(k,k_1)$, we arrive at the following integral representation for $G(k,k_0,\alpha)$:
\begin{align}
\nonumber
G(k,k_0,\alpha)=
\exp\left\{
-\frac{\gamma(k)}{2\pi i}\left(
\int_{B}\frac{2\ln\delta(\zeta,k_0)}{\gamma(\zeta)(\zeta-k)}\,d\zeta
+\int_{\hat\gamma_{21}}
\frac{\ln\frac{\delta^2(\zeta,k_0)}{r_1(\zeta)}+i\omega}
{\gamma(\zeta)(\zeta-k)}\,d\zeta\right.\right.\\
\label{fsintG}
\left.
\left.
+\int_{\hat\gamma_{31}}
\frac{\ln\left[\delta^2(\zeta,k_0)r_2(\zeta)\right]+i\omega}
{\gamma(\zeta)(\zeta-k)}\,d\zeta
\right)
\right\},
\end{align}
where $\omega\in\mathbb{C}$ is chosen to ensure that $G(k)$ is bounded as $k\to\infty$:
\begin{equation}\label{fsomega}
\omega=i\frac
{\int_{B}\frac{2\ln\delta(\zeta,k_0)}{\gamma(\zeta)}\,d\zeta
+\int_{\hat\gamma_{21}}
\ln\left[\frac{\delta^2(\zeta,k_0)}{r_1(\zeta)}\right]
\frac{d\zeta}{\gamma(\zeta)}
+\int_{\hat\gamma_{31}}
\ln[\delta^2(\zeta,k_0)r_2(\zeta)]
\frac{d\zeta}{\gamma(\zeta)}}
{\int_{\hat\gamma_{21}\cup\hat\gamma_{31}}\frac{d\zeta}{\gamma(\zeta)}}.
\end{equation}
This implies that $G(k)$ has the following behavior for the large $k$:
\begin{equation}
G(k,k_0,\alpha)=e^{iG_{\infty}(k_0,\alpha)}+O(k^{-1}),\quad k\to\infty,
\end{equation}
where the \textit{complex} constant $G_{\infty}(k_0,\alpha)$ has the form
\begin{align}
\nonumber
G_{\infty}(k_0,\alpha)=-\frac{1}{2\pi}\left(
\int_{B}\frac{2\ln\delta(\zeta,k_0)}{\gamma(\zeta)}\zeta\,d\zeta
+\int_{\hat\gamma_{21}}
\frac{\ln\frac{\delta^2(\zeta,k_0)}{r_1(\zeta)}+i\omega}
{\gamma(\zeta)}\zeta\,d\zeta\right.\\
\label{fsGinfty}
\left.+\int_{\hat\gamma_{31}}
\frac{\ln[\delta^2(\zeta,k_0)r_2(\zeta)]+i\omega}
{\gamma(\zeta)}\zeta\,d\zeta
\right).
\end{align}
Finally, arguing as in Remark \ref{fsboundf} we conclude that $G(k,k_0,\alpha)$ given by (\ref{fsintG}) satisfies (\ref{fsGbound}).
\begin{remark}
In the case of the classical (local) NLS equation, the reflection coefficients $r_1(k)$ and $r_2(k)$ have symmetries for $k\in\mathbb{R}$.
Since the symmetry axis of the contour of the RH problem (\ref{fsGRHall}) for $G(k,k_0,\alpha)$ is the real line, in the case of the local NLS equation the constants $\omega$ and $G_{\infty}(k_0,\alpha)$ are purely real (cf. $\omega$ and $g_{\infty}$ given by (5.44) and (5.47) respectively in \cite{BM17}).
In our case, however, the spectral data have symmetries with respect to the imaginary axis (see (\ref{fsabsym})), which leads to, in general, \textit{complex} valued constants $\omega$ and $G_{\infty}(k_0,\alpha)$.
Therefore, the large-time asymptotics of $q(x,t)$ depends on the initial data and, as in the plane wave region, the effect of modulation instability is non-universal in the modulated elliptic wave regions.
\end{remark}
\begin{remark}
In view of lack of symmetry between $r_1(k)$ and $r_2(k)$,
the function $G(k,k_0,\alpha)$ can have a singularity as $k$ approaches $k_0$,
which is in contrast with the case of the classical NLS equation.
Indeed, considering the behavior of contour integrals at the endpoints with logarithmic singularity (see Chapter I, Paragraph 8.5 in \cite{G66}) and using (\ref{fsdelta-singular}) with $k_0$ instead of $k_1$ we have that
\begin{subequations}
\begin{align}
\nonumber
&\frac{1}{2\pi i}
\int_{\hat\gamma_{21}}
\frac{\ln\frac{\delta^2(\zeta,k_0)}{r_1(\zeta)}}
{\gamma(\zeta)(\zeta-k)}\,d\zeta=
\frac{\ln r_1(k_0)-2\chi(k_0,k_0)-2\pi\nu(k_0)}{2\pi i\gamma_-(k_0)}
\ln(k-k_0)\\
& \qquad\qquad\qquad\qquad\qquad
-\frac{\nu(k_0)}{2\pi\gamma_-(k_0)}
\ln^2(k-k_0)+I_{k_0,1},\\
\nonumber
&\frac{1}{2\pi i}
\int_{\hat\gamma_{31}}
\frac{\ln[\delta^2(\zeta,k_0)r_2(\zeta)]}
{\gamma(\zeta)(\zeta-k)}\,d\zeta=
\frac{\ln r_2(k_0)+2\chi(k_0,k_0)+2\pi\nu(k_0)}{2\pi i\gamma_-(k_0)}
\ln(k-k_0)\\
& \qquad\qquad\qquad\qquad\qquad\qquad
+\frac{\nu(k_0)}{2\pi\gamma_-(k_0)}
\ln^2(k-k_0)+I_{k_0,2},
\end{align}
\end{subequations}
where $I_{k_0,j}$, $j=1,2$ are analytic in a neighborhood of $k=k_0$. Consequently we have that
\begin{equation}
G(k,k_0,\alpha)(k-k_0)^{\frac{\gamma(k)}{2\pi i\gamma_-(k_0)}
\ln r_1(k_0)r_2(k_0)}=O(1), \quad k\to k_0.
\end{equation}
Despite the possible strong singularity of $G(k,k_0,\alpha)$ (and, consequently, $M^{(5)}(x,t,k)$, see (\ref{fsM5}) and (\ref{fsM5RHd}) below) at $k=k_0$, we are able to construct the parametrix and make correct asymptotic estimates under the assumption (similar to the plane wave case) about smallness of $\arg(1+r_1(k)r_2(k))$, see Theorem \ref{fsth2} and Appendix C below.
\end{remark}
Now we are in a position to make the final transformation of the Riemann-Hilbert problem:
\begin{equation}\label{fsM5}
M^{(5)}(x,t,k)=e^{-iG_{\infty}(k_0,\alpha)\sigma_3}
M^{(4)}(x,t,k)G^{\sigma_3}(k,k_0,\alpha),\quad
k\in\mathbb{C}\setminus
\left\{\tilde\Gamma\cup \overline{B}\right\}.
\end{equation}
Then $M^{(5)}(x,t,k)$ solves the RH problem with a constant jump along the contours $B$, $\hat\gamma_{21}$ and $\hat\gamma_{31}$:
\begin{subequations}\label{fsM5RH}
\begin{align}
&M^{(5)}_+(x,t,k)=M^{(5)}_-(x,t,k)J^{(5)}(x,t,k),&&k\in\tilde\Gamma\cup B,\\
&M^{(5)}(x,t,k)=I+O(k^{-1}), &&k\to\infty,\\
&M^{(5)}(x,t,k)=O\left((k\pm iA)^{-\frac{1}{4}}\right),&& k\to\mp iA,\\
\label{fsM5RHd}
&M^{(5)}(x,t,k)
\begin{pmatrix}
(k-k_0)^{P(k)}& 0\\
0&
(k-k_0)^{-P(k)}
\end{pmatrix}
=O\left((k-k_0)^{-\frac{1}{2}+\varepsilon(k_0)}\right),&& k\to k_0,\,\varepsilon(k_0)>0,
\end{align}
\end{subequations}
where
$P(k)=\frac{\gamma(k)\arg(r_1(k_0)r_2(k_0))}
{2\pi\gamma_-(k_0)}$
and (recall that $\Omega\in\mathbb{R}$ is given by (\ref{fsOmega}))
\begin{equation}
\label{fsJ5ew}
J^{(5)}(x,t,k)=
\begin{cases}
\begin{pmatrix}
0& -e^{-it\Omega-i\omega}\\
e^{it\Omega+i\omega}&0
\end{pmatrix},&k\in\hat\gamma_{21}\cup\hat\gamma_{31},\\
i\sigma_1,&k\in B,\\
G^{-\sigma_3}(k,k_0,\alpha)J^{(4)}(x,t,k)G^{\sigma_3}(k,k_0,\alpha),&\text{othewise}.
\end{cases}
\end{equation}
The solution $q(x,t)$ can be found via $M^{(5)}(x,t,k)$ as follows:
\begin{subequations}\label{fsasolM5}
\begin{align}\label{fssolM5}
&q(x,t)=2ie^{2itH_\infty+2iG_{\infty}(k_0,\alpha)}
\lim_{k\to\infty}kM_{12}^{(5)}(x,t,k),&& x>0,\\
\label{fssol1M5}
&q(-x,t)=-2ie^{2itH_\infty+2i\overline{G_{\infty}(k_0,\alpha)}}
\lim_{k\to\infty}k\overline{M_{21}^{(5)}(x,t,k)},&& x>0.
\end{align}
\end{subequations}
\begin{theorem}(Elliptic wave region)
\label{fsth2}
Suppose that the initial data $q_0(x)$ is a compact perturbation of the background (\ref{fsivp-c}) and that the associated spectral functions $a_j(k)$ and $r_j(k)=\frac{b_j(k)}{a_j(k)}$, $j=1,2$ satisfy the following conditions:
\begin{enumerate}
\item $a_1(k)$ and $a_2(k)$ have no zeros in $\overline{\mathbb{C}^{+}}$ and $\overline{\mathbb{C}^{-}}$ respectively,
\item $\int_{-\infty}^{k}d\arg(1+ r_1(\zeta)r_2(\zeta))\in(-\pi,\pi)$, for all $k\in\left(-\frac{A}{\sqrt{2}},0\right)$.
\end{enumerate}
Then the solution $q(x,t)$
of problem (\ref{fsivp})
has the following large-time asymptotics along the rays $\frac{x}{4t}=const$ uniformly in any compact subset of $\{\frac{x}{4t}\in\mathbb{R}:\sqrt{2}A<|\frac{x}{4t}|<0\}$:
\begin{subequations}\label{fsasellw}
\begin{align}
\nonumber
&q(x,t)=(A+\Im\alpha)
e^{-2\Im G_{\infty}(k_0,\alpha)}
\frac{\Theta(\frac{\Omega t}{2\pi}
+\frac{\omega}{2\pi}-\frac{1}{4}-v_{\infty}+c)
\Theta(v_{\infty}+c)}
{\Theta(\frac{\Omega t}{2\pi}
+\frac{\omega}{2\pi}-\frac{1}{4}+v_{\infty}+c)
\Theta(-v_{\infty}+c)}\\
&\qquad\qquad
\times e^{2i(tH_{\infty}+\Re G_{\infty}(k_0,\alpha))}
+E_3(x,t),\quad 0<\frac{x}{4t}<\sqrt{2}A,\\
\nonumber
&q(-x,t)=(A+\Im\alpha)
e^{2\Im G_{\infty}(k_0,\alpha)}
\frac{\Theta(\frac{\Omega t}{2\pi}
+\frac{\overline{\omega}}{2\pi}-\frac{1}{4}
+\overline{v_{\infty}}-\overline{c})
\Theta(-\overline{v_{\infty}}-\overline{c})}
{\Theta(\frac{\Omega t}{2\pi}
+\frac{\overline{\omega}}{2\pi}-\frac{1}{4}
-\overline{v_{\infty}}-\overline{c})
\Theta(\overline{v_{\infty}}-\overline{c})}\\
&\qquad\qquad
\times e^{2i(tH_{\infty}+\Re G_{\infty}(k_0,\alpha))}
+E_4(x,t),\quad 0>-\frac{x}{4t}>-\sqrt{2}A.
\end{align}
\end{subequations}
Here the genus-1 theta function $\Theta$ is given by (\ref{fsg1thf}), the constants $\alpha$, $\Omega$, $v_{\infty}$ and $c$ which do not depend on the initial data $q_0(x)$ are given by (\ref{fsreaima}), (\ref{fsOmega}), (\ref{fsvinfty}) and (\ref{fsc}) respectively. Moreover, depended on the
associated to the initial value spectral data constants $\omega$ and $H_{\infty}$ and function $G_{\infty}(k_0,\alpha)$ are given by (\ref{fsomega}), (\ref{fsH0}) and (\ref{fsGinfty}) respectively.
Depending on the value of $\Im\nu(k_0)$, the decaying terms $E_3(x,t)$ and $E_4(x,t)$ are given by
\begin{description}
\item[(a)] if $\Im\nu(k_0)\in\left(-\frac{1}{2},-\frac{1}{6}\right]$, then
\begin{align*}
&E_3(x,t)=t^{-\frac{1}{2}-\Im\nu(k_0)}c_5(x,t)+R(x,t),\\
&E_4(x,t)=t^{-\frac{1}{2}-\Im\nu(k_0)}c_7(x,t)+R(x,t),
\end{align*}
\item[(b)] if $\Im\nu(k_0)\in\left(-\frac{1}{6},\frac{1}{6}\right)$, then
\begin{align*}
&E_3(x,t)=t^{-\frac{1}{2}+\Im\nu(k_0)}c_6(x,t)+
t^{-\frac{1}{2}-\Im\nu(k_0)}c_5(x,t)+R(x,t),\\
&E_4(x,t)=t^{-\frac{1}{2}+\Im\nu(k_0)}c_8(x,t)+
t^{-\frac{1}{2}-\Im\nu(k_0)}c_7(x,t)+R(x,t),
\end{align*}
\item[(c)] if $\Im\nu(k_0)\in\left[\frac{1}{6},\frac{1}{2}\right)$, then
\begin{align*}
&E_3(x,t)=t^{-\frac{1}{2}+\Im\nu(k_0)}c_6(x,t)+R(x,t),\\
&E_4(x,t)=t^{-\frac{1}{2}+\Im\nu(k_0)}c_8(x,t)+R(x,t).
\end{align*}
\end{description}
The oscillating terms $c_j(x,t)$, $j=\overline{5,8}$ have the following form
\begin{align}
&c_j(x,t)=2ie^{2itH_{\infty}+2iG_{\infty}(k_0,\alpha)}
\tilde{c}_j(x,t),\quad j=5,6,\\
&c_j(x,t)=-2ie^{2itH_{\infty}
+2i\overline{G_{\infty}(k_0,\alpha)}}
\overline{\tilde{c}_j(x,t)},\quad j=7,8,
\end{align}
where $\tilde{c}_j(x,t)$, $j=\overline{5,8}$ and the remainder $R(x,t)$ are given by (\ref{fstck0}) and (\ref{fsR3}) respectively.
\end{theorem}
\begin{proof}
See Appendix C.
\end{proof}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 8,805
|
Home | U.S. News
Trump Announces Tariffs on Steel, Aluminum Imports From Europe, Canada and Mexico
U.S. and European officials held last-ditch talks in Paris on Thursday, but now fears of a trade war are mounting
U.S. President Donald Trump swings a golf club during the White House Sports and Fitness Day event on the South Lawn of the White House in Washington, D.C., U.S., on Wednesday, May 30, 2018Credit: Al Drago/Bloomberg
The Trump administration announced Thursday it will impose tariffs on steel and aluminum imports from Europe, Mexico and Canada after failing to win concessions from the American allies. The decision could provoke retaliatory penalties and exacerbate trans-Atlantic and North American trade tensions.
The European Union responded immediately with a statement saying, "It's a bad day for world trade. US leaves us no choice but to proceed with a WTO dispute settlement case and the imposition of additional duties on a number of US imports."
Commerce Secretary Wilbur Ross said the tariffs would be 25 percent on steel and 10 percent on aluminum as the administration followed through on the penalties after earlier granting exemptions to buy time for negotiations.
Ross told reporters that talks with Canada and Mexico over revising the North American Free Trade Agreement were "taking longer than we had hoped." Talks with Europe had "made some progress" but not enough for additional exemptions, he said in a conference call from Paris.
"We continue to be quite willing and indeed eager to have further discussions," Ross said. He said he planned to travel to China on Friday for trade talks between the world's two biggest economies.
'Ethel at 100' – a poem by Ishmael Reed
Does the world really need more experts on racism and anti-Semitism?
European officials had braced for the tariffs and the EU has threatened to retaliate against U.S. orange juice, peanut butter and other goods in return. In terms of the NAFTA talks, the tariffs could hinder the negotiations among the North American neighbors.
Fears of a global trade war are already weighing on investor confidence and could hinder the global economic upturn. European officials argue that tit-for-tat tariffs will hurt growth on both sides of the Atlantic.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 2,392
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Get Involved / Events / Maria's Christmas Shop - Featuring Maria's Chocolate Bar!
Maria's Christmas Shop - Featuring Maria's Chocolate Bar!
Give gifts that give back this Holiday Season!
Maria's Christmas Shop is open for just 2 more days!
The shop has a variety of gifts, along with Maria's Chocolate Bar, which makes the perfect stocking stuffer! Maria's Chocolate Bar was created by our friends at Malley's who have teamed up with us in the fight against childhood cancer!
Maria's Christmas Shop will be open this weekend from 12-4pm on both Saturday and Sunday. Proceeds from your purchases in Maria's Shop will go towards funding childhood cancer research! The perfect gift!
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 2,020
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package javax.sip.header;
import java.text.ParseException;
/**
* The Call-ID header field uniquely identifies a particular invitation or all
* registrations of a particular client. A single multimedia conference can give rise to
* several calls with different Call-IDs, for example, if a user invites a
* single individual several times to the same (long-running) conference.
* Call-IDs are case-sensitive and are simply compared byte-by-byte.
* <p>
* Call-ID is generated by the combination of a random string and the
* softphone's host name or IP address. The combination of the To tag,
* From tag, and Call-ID completely defines a peer-to-peer SIP relationship
* between two users and is referred to as a dialog. It MUST be the same for
* all requests and responses sent by either User Agent in a dialog. It SHOULD be the
* same in each registration from a User Agent.
* <p>
* All SIP User Agents must have a means to guarantee that the Call-ID header fields
* they produce will not be inadvertently generated by any other User Agent. Note
* that when requests are retried after certain failure responses that solicit
* an amendment to a request (for example, a challenge for authentication),
* these retried requests are not considered new requests, and therefore do
* not need new Call-ID header fields.
* <p>
* Use of cryptographically random identifiers in the generation of Call-IDs is
* RECOMMENDED. Implementations MAY use the form "localid@host".
* <p>
* For Example:<br>
* <code>Call-ID: f81d4fae-7dec-11d0-a765-00a0c91e6bf6@jcp.org</code>
*
* @author BEA Systems, NIST
* @version 1.2
*
*/
public interface CallIdHeader extends Header {
/**
* Sets the Call-Id of the CallIdHeader. The CallId parameter uniquely
* identifies a serious of messages within a dialogue.
*
* @param callId - the string value of the Call-Id of this CallIdHeader.
* @throws ParseException which signals that an error has been reached
* unexpectedly while parsing the callId value.
*/
public void setCallId(String callId) throws ParseException;
/**
* Returns the Call-Id of CallIdHeader. The CallId parameter uniquely
* identifies a series of messages within a dialogue.
*
* @return the String value of the Call-Id of this CallIdHeader
*/
public String getCallId();
/**
* Compare this CallIdHeader for equality with another. This method
* overrides the equals method in javax.sip.Header. This method specifies
* object equality as outlined by
* <a href = "http://www.ietf.org/rfc/rfc3261.txt">RFC3261</a>.
* Call-IDs are case-sensitive and are simply compared byte-by-byte.
*
* @param obj the object to compare this CallIdHeader with.
* @return <code>true</code> if <code>obj</code> is an instance of this class
* representing the same CallIdHeader as this, <code>false</code> otherwise.
* @since v1.2
*/
public boolean equals(Object obj);
/**
* Name of CallIdHeader
*/
public final static String NAME = "Call-ID";
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,963
|
\section{Introduction}
Three-dimensional reconstruction of real-world objects and scenes of arbitrary reflectance is essential for many computer vision applications. In particular, a passive approach that can recover the 3D geometry for a view from a handful of images would be preferable. For downstream tasks such as scene navigation, object grasping, and augmented reality, explicit recovery of the reflectance properties in addition to the 3D geometry would be essential. As shown in \cref{fig:opening}(c), these requirements are hard to fulfill with neural view synthesis methods (\emph{e.g}\onedot} \def\Eg{\emph{E.g}\onedot, neural radiance field (NeRF)) as explicit geometry reconstruction is not their primary goal (\emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, volume density only provides coarse view-dependent surface geometry) and as they usually require dense view sampling. Classic stereopsis and multi-view stereo (MVS) approaches \cite{scharstein2002taxonomy}, especially with recent integration of learned features and filtering, still excel in their simplicity, accuracy, and passive setup for explicit 3D geometry reconstruction.
Reconstruction of a textureless non-Lambertian surface (\emph{e.g}\onedot} \def\Eg{\emph{E.g}\onedot, a porcelain vase), however, still remains elusive to stereo-based approaches as stereopsis is limited by its two fundamental requirements: correspondence matching and triangulation. Finding correspondences directly translates to making assumptions about the surface appearance, that they can be matched across views, \emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, they are view-independent and texture-rich. This has largely limited the application of stereo-based methods to textured and Lambertian surfaces. Geometry recovery by triangulation also limits the output to surface depth which is often insufficient for capturing details of surface geometry.
Surface geometry can instead be recovered as part of inverting the radiometric process of image formation. Various methods have been proposed for single-view geometry reconstruction of non-Lambertian surfaces by jointly estimating its reflectance. The geometry recovered in such inverse rendering approaches is, however, fundamentally limited to surface normals. Although surface normals can expose finer surface details, they do not directly represent the surface.
In this paper, we introduce a novel multi-view stereo method that enables the simultaneous recovery of surface normals and depth for textureless non-Lambertian surfaces. At the same time, the method explicitly recovers the complex reflectance of the target surface. Our method is purely image-based, requiring only 5 neighboring views for the reconstruction from a single view. Most important, our method can be applied to objects and scenes with complex reflectance captured under known but natural illumination. Our key idea is to integrate stereopsis with radiometric analysis so that radiometrically recovered geometric properties, namely surface normals, can serve as view-independent cues for multi-view stereopsis. We achieve this integration with an end-to-end learnable network which we refer to as nLMVS-Net.
Our nLMVS-Net consists of three key novel ideas. The first is a single-view shape-from-shading network that fully leverages radiometric likelihoods of surface normals. The network enables the estimation of per-pixel surface normal as a directional probability density which collectively serves as rich view-independent cues for subsequent multi-view stereo. The second key idea is a novel cost volume filtering network that leverages the recovered surface normal probability densities. The network integrates radiometric (\emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, surface normals) and geometric (\emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, correspondences) cues with a novel feature extraction layer and a consistency loss between the surface normal and depth estimates. The third is joint estimation of complex non-Lambertian reflectance by alternating with geometry estimation using a neural BRDF model \cite{chen2020ibrdf}.
\begin{table}[t]
\centering
\setlength{\tabcolsep}{2.3pt}
\scriptsize
\begin{tabular}{l|cccccc}
& Depth & Normal &
\begin{tabular}{c}
Non-\\Lambertian \\ Reflectance
\end{tabular} &
\begin{tabular}{c}
Sparse \\ View \\ Input
\end{tabular} &
\begin{tabular}{c}
Nat. \\ Illum.
\end{tabular} &
\begin{tabular}{c}
General \\ Object \\ Category
\end{tabular} \\ \hline
MVSNet \cite{yao2018mvsnet} & \checkmark & & & \checkmark & \checkmark & \checkmark \\
CVP-MVS \cite{yang2020cvpmvsnet} & \checkmark & & & \checkmark & \checkmark & \checkmark \\
NAS \cite{kusupati2020nas} & \checkmark & \checkmark & & \checkmark & \checkmark & \checkmark \\
\hline
Nam \emph{et al}\onedot \cite{nam2018svbrdf} & \checkmark & \checkmark & \checkmark & & & \checkmark \\
Cheng \emph{et al}\onedot \cite{cheng2021mv3d} & \checkmark & \checkmark & \checkmark & \checkmark & & \checkmark \\
Bi \emph{et al}\onedot \cite{bi2020deep3d} & \checkmark & \checkmark & \checkmark & \checkmark & & \checkmark \\
ON \cite{oxholm2015shape} & \checkmark & \checkmark & \checkmark & & \checkmark & \checkmark \\
\hline
NeRFactor \cite{zhang21nerfactor} & \checkmark & \checkmark & \checkmark & & \checkmark & \checkmark \\
PhySG \cite{zhanf2021physg} & \checkmark & \checkmark & \checkmark & & \checkmark & \checkmark \\
IDR \cite{yariv2020idr} & \checkmark & \checkmark & & & \checkmark & \checkmark \\
NeuS \cite{wang2021neus} & \checkmark & \checkmark & & & \checkmark & \checkmark \\
NeRS \cite{zhang2021ners} & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \\
MVSNeRF \cite{chen2021mvsnerf} & \checkmark & & & \checkmark & \checkmark & \checkmark \\
\hline
\rowcolor[rgb]{0.93,1.0,0.87} Ours & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark
\end{tabular}
\caption{Image-based 3D reconstruction methods that exploit multi-view observations. Our method can recover geometry and reflectance from sparse (5 views) observations captured under known but natural illumination without any category-specific shape prior, which remains challenging to existing methods.}
\label{tab:methods}
\end{table}
\begin{figure*}[t]
\centering
\includegraphics[width=\linewidth]{fig/overview.pdf}
\caption{Overview of our novel multi-view stereo method, nLMVS-Net. The shape-from-shading sub-network learns to recover per-pixel probability densities of surface normals for each view. The novel cost volume sub-network then learns to reconstruct per-pixel depth and surface normals from those and the input sparse multi-view images. By alternating with neural reflectance estimation, we jointly recover the complex surface reflectance of the object.
}
\label{fig:overview}
\end{figure*}
We also introduce two newly collected datasets, which we refer to as nLMVS-Synth and nLMVS-Real. The synthetic dataset (nLMVS-Synth) consists of 26850 rendered images of 2685 objects with 94 and 2685 different real-world reflectance and natural illumination, respectively. We use nLMVS-Synth to train nLMVS-Net and thoroughly evaluate its accuracy on unseen synthetic images. The new multi-view image dataset of real objects, namely nLMVS-Real, consists of 2569 multi-view images of 5 objects each with one of 4 different reflectances taken under 6 different natural illuminations. Each of the 5 different objects are replicated with a 3D printer so that accurate ground truth geometry is available for quantitative analysis. This dataset is unprecedented in size for an accurately radiometrically and geometrically calibrated multi-view image set for a variety of surfaces and would undoubtedly serve as a useful platform for a wide range of shape reconstruction and inverse rendering research.
Experimental results on these datasets and others, together with direct comparisons with existing methods, clearly demonstrate the effectiveness of our method.
We also show that the recovered depths and surface normals can be used to reconstruct a whole object from as few as 10 images.
Thanks to the passive setup and sparse inputs, nLMVS-Net may prove useful for many 3D sensing applications including mobile sensing, XR immersion, and robotic navigation. All the data and code will be publicly disseminated once the paper is accepted.
\section{Related Work}
\label{sec:related_work}
We review relevant works on imaged-based 3D geometry reconstruction, mainly those methods that exploit multi-view observations. \Cref{tab:methods} summarizes the differences of our method and others. Our method can recover geometry and reflectance of textureless, non-Lambertian surfaces from a sparse set (\emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, 5) of multi-view images captured under known but natural illumination without any category-specific shape prior, which remains challenging for existing methods.
\textbf{Multi-view stereo} relies on cross-view correspondence matching and triangulation. Traditional methods relied on manually designed distance metrics for correspondence detection and spatial aggregation \cite{rhemann2011fastcostvolume, galliani2015gipuma}. Recent works leverage deep neural networks to learn the metric directly from data. In particular, 3D convolutional neural networks are often used for cost volume filtering \cite{yao2018mvsnet, im2019dpsnet, yao2019rmvsnet, yang2020cvpmvsnet}. Kusupati \emph{et al}\onedot \cite{kusupati2020nas} trained a deep neural network with a consistency loss to jointly estimate per-pixel depth and surface normal. The architecture of the cost volume filtering network of nLMVS-Net is inspired by this work, but fundamentally differs in that it handles not only textureless surfaces, but also non-Lambertian reflectance and even explicitly estimates it. This expands the utility of MVS to objects that were conventionally out of reach.
\textbf{Inverse rendering} methods invert radiometric image formation to reconstruct object geometry \cite{horn1970sfs, johnson11sfs, barron2015sirfs, hertzmann2005examplebased, nam2018svbrdf}. Multi-view methods have exploited proxy geometry (\emph{e.g}\onedot} \def\Eg{\emph{E.g}\onedot, a 3D mesh model) to recover surface geometry by iterative, nonlinear optimization \cite{oxholm2015shape, xia2016xfm, nam2018svbrdf, zhanf2021physg}. Oxholm and Nishino \cite{oxholm2015shape} alternate between updating a 3D mesh and BRDF parameters so that they are consistent with the input multi-view images and a known illumination map. These approaches struggle to recover high-frequency details of surface geometry as nonlinear optimization of geometry is unstable due to the large number of free parameters, especially when the number of input images is small (\emph{e.g}\onedot} \def\Eg{\emph{E.g}\onedot, 20). A few methods handle sparse-view inputs \cite{bi2020deep3d, cheng2021mv3d}. They, however, require collocated point lighting. In contrast, our method works with sparse inputs (5 images and an illumination map) under complex natural illumination.
\textbf{Neural image synthesis} methods recover a volumetric representation of a scene from a large number (typically on the order of tens to 100) of multi-view images \cite{zhang21nerfactor, zhanf2021physg, boss2021neuralpil, yariv2020idr, wang2021neus}. Chen \emph{et al}\onedot \cite{chen2021mvsnerf} handles sparse (\emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, 3) views by conditioning the volume representation with input images. This method relies on volume rendering and the recovered volume density only provides view-dependent coarse depths. Zhang \emph{et al}\onedot \cite{zhang2021ners} achieves explicit reconstruction of surface geometry and reflectance from sparse (\emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, 7) views by leveraging category-specific shape templates. They also recovered 3D shapes for arbitrary object categories by exploiting cuboids as templates. As we show in the supplementary material, this method struggles to generalize to objects with complex geometry that cannot be approximated with cuboids.
\textbf{Multi-view stereo datasets} have been proposed for benchmarking \cite{aanaes2016dtumvs, schoeps2017eth3d, Knapitsch2017tanksandtemples, yao2020blendedmvs}. They, however, are not radiometrically calibrated as they focus on Lambertian or textured surfaces rather than non-Lambertian objects. For the evaluation of non-Lambertian MVS, linear high dynamic range images that accurately capture the appearance of non-Lambertian objects are essential. Although the Multiview Objects under Natural Illumination database \cite{oxholm2014mvshape} provides high dynamic range images along with ground truth geometry and illumination maps, the number of instances is limited (4 objects under 3 environments). We also found that the images of this dataset contain flaws (please see \cref{sec:results}). We introduce a novel real-world dataset that is accurate and extensive which can serve as a new platform for further studies on shape and reflectance recovery.
\section{Deep Non-Lambertian Multi-View Stereo}
\Cref{fig:overview} depicts the overall structure of our model nLMVS-Net. The inputs are five multi-view images of an object and an illumination map of the surrounding environment. We assume the latter can be captured with a light probe, or can be estimated with a separate method \cite{LeGendre2019deeplight, gardner2017indoor, Zhang2019outdoorlight}. Our nLMVS-Net consists of a single-view shape-from-shading network and a cost volume filtering network. Since the appearance of non-Lambertian objects (\emph{e.g}\onedot} \def\Eg{\emph{E.g}\onedot, gloss) changes according to the viewing direction, we cannot directly achieve correspondence matching on the input images, especially for textureless surfaces. Instead, we explicitly extract view-independent features, namely surface normals, but while canonically accounting for uncertainty by encoding them as directional distributions with the shape-from-shading network. The recovered per-pixel surface normal distributions add rich information in addition to the regular appearance for multi-view correspondence matching and shape reconstruction. We derive a novel cost-volume filtering network that achieves seamless integration of these rich geometric and visual cues. We also derive a joint estimation framework that explicitly estimates the surface reflectance expressed by an invertible network together with the normals and depth.
\subsection{Non-Lambertian Shape-from-Shading}
\label{sec:sfs}
The first step of nLMVS-Net is to recover the surface normals with associated uncertainties for each view. Surface normals naturally lie in a plausible range of directions for a given intensity as neither the illumination nor the reflectance is angularly unique \cite{oxholm2014mvshape}. As such, it is essential to model their uncertainties. For this, as depicted in \cref{fig:sfsnet_concept}, we derive a novel deep neural network that estimates the per-pixel probability density distribution of surface normals for each view of the multi-view input images.
\begin{figure}[t]
\centering
\subfloat[][Shape-from-Shading (SfS) Network]{
\includegraphics[keepaspectratio, width=0.96\linewidth]{fig/sfsnet_concept.pdf}
\label{fig:sfsnet_concept}
}
\\
\vspace{6pt}
\subfloat[][Coarse-to-Fine SfS]{
\includegraphics[keepaspectratio, width=0.96\linewidth]{fig/sampling_normals.pdf}
\label{fig:coarse-to-fine}
}
\caption{\subref{fig:sfsnet_concept} The shape-from-shading (SfS) network of nLMVS-Net learns to estimate pixel-wise probability densities of surface normals by aggregating local and global contextual information from the input view and observed pixel-wise likelihoods computed from the radiometric image formation model. \subref{fig:coarse-to-fine} We use the SfS network recursively to refine the observed likelihoods in a coarse-to-fine manner. The red circles on the probability densities are the sampled surface normal orientations, which are used as inputs to the network in subsequent iterations.}
\label{fig:sfsnet}
\end{figure}
We assume an opaque, homogeneous reflectance for the object whose BRDF can be expressed as $\rho(\bm{\omega_i}, \bm{\omega_o}, \bm{n})$, where $\bm{\omega_i}$ is the incident direction, $\bm{\omega_o}$ is the viewing direction, and $\bm{n}$ is the surface normal. We also assume that the cameras and the illumination environment are distant from the object, \emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, they can be approximated with an orthographic camera and an illumination map $L_i(\bm{\omega_o})$. Under these assumptions, the observed irradiance $E(\bm{\omega_o}, \bm{n})$ is
\begin{equation}
E(\bm{\omega_o}, \bm{n}) = \int L_i(\bm{\omega_i})\rho(\bm{\omega_i}, \bm{\omega_o}, \bm{n})\max(0, \bm{\omega_i}\cdot\bm{n})\mathrm{d}\bm{\omega_i}\,.
\label{eq:image-formation}
\end{equation}
We leave global light transport including shadows and interreflections for future work, and focus on object appearance by direct lighting which is dominant for single objects.
\begin{figure*}[t]
\centering
\includegraphics[width=\linewidth]{fig/cost_volume_filtering.pdf}
\caption{The architecture of the cost volume filtering network of nLMVS-Net. A latent cost volume is constructed from the multi-view surface normal densities and color appearance which is then filtered with 3D convolutional layers. The network outputs two 3D volumes: depth probability volume and surface normal volume that encode the per-pixel depth and surface normal estimates as probability densities.}
\label{fig:mvsnet}
\end{figure*}
Let us assume that we are given a current estimate of the reflectance. This reflectance will be updated later in an alternating outer loop. For a given hypothesized surface normal and known illumination, its likelihood can be defined as the discrepancy between the irradiance $E(\bm{\omega_o},\bm{n})$ computed from the given normal and the actual pixel value $I$:
\begin{equation}
p(I|\bm{n}) = \prod_k f(\log I^{(k)}; \log E^{(k)}(\bm{\omega_o},\bm{n}), b)\,,
\label{eq:normallikelihood}
\end{equation}
where $f(x; \mu, b)$ is the Laplace distribution and $k$ is index of color channels. We optimize the parameter $b$ with training data. The surface normal directions are discretized with a 2D hemispherical grid and the likelihoods are computed for each direction.
The observed surface normal likelihoods \cref{eq:normallikelihood} are too noisy and unreliable to use for cost volume filtering. We train the shape-from-shading network to refine and convert them into probability density distributions by aggregating local and global contextual information across the surface. As depicted in \cref{fig:coarse-to-fine}, for computational efficiency, we achieve this in a coarse-to-fine manner. We first divide the possible surface normal orientations into a 8$\times$8 grid and, for each grid, find the orientation that maximizes the observed likelihood $p\left(I| \bm{n} \right)$ with brute-force search. We use the set of sampled surface normals and their observed likelihoods as inputs for each pixel. In the subsequent iterations, we double the resolution of the grid and sample surface normals around those that have high probability in the previous iteration. We use the same network with the same weights for all stages.
Since the inputs of the network (\emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, sets of surface normals and their observed likelihoods) are unstructured, convolutions are not suitable for processing them. Instead, inspired by PointNet \cite{qi2016pointnet}, we extract a 64 dimensional feature vector for each sampled surface normal and then fuse the sample-wise features by using max-pooling. The fused features are concatenated with features extracted from the input image and filtered by 2D convolutional layers. We use the pixel-wise filtered feature $\bm{a}$, a decoder MLP $g(\bm{n}; \bm{a})$ that outputs a scalar value, and the observed likelihood distribution $p(I|\bm{n})$ to compute the output (unnormalized) probability density distribution $\hat{p}(\bm{n})$
\begin{equation}
\hat{p}(\bm{n}) = p(I|\bm{n}) g(\bm{n}; \bm{a})\,.
\end{equation}
We train the network with images of synthetic objects whose BRDF and surface normals are known. In training, we compute the observed surface normal likelihoods by using the ground-truth BRDF and evaluate the network output with cross entropy loss
\begin{equation}
L_\textrm{SfS} = -\sum_{i}M(\bm{n_i}) \log \left(\frac{\hat{p_i}(\bm{n_i})}{\sum_j \hat{p_j}(\bm{n_j})}\right),
\end{equation}
where $\{\bm{n_i}\}$ is the sampled (input) surface normal direction and $M$ is a binary mask (1 iff the ground-truth and the sampled surface normal are in the same grid). The loss is evaluated for every stage of the coarse-to-fine estimation.
As shown in \Cref{fig:sfsnet_concept}, the network significantly reduces the ambiguity of the observed likelihood distribution and extracts a well-defined probability density for each pixel.
\subsection{Cost Volume Filtering}
\label{sec:cost_volume_filtering}
From the recovered per-pixel surface normal probability densities for each view as well as the original input images, nLMVS-Net learns to filter a cost volume to recover the object 3D shape as depth and surface normals. \Cref{fig:mvsnet} shows the architecture of the cost-volume filtering network.
As depicted in \cref{fig:mvsnet}(a), the network takes in the multi-view input images as well as the outputs of the single-view shape-from-shading network, \emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, per-pixel surface normal probability densities for each view. The latter are represented as sets of surface normals and their probabilities, from which we extract pixel-wise features. Since the surface normals are estimated in the camera coordinate system of each view, we first consolidate the coordinate system by rotating them using the known camera extrinsic parameters. We apply a feature extraction layer similar to the one in the shape-from-shading network (see \cref{sec:sfs}) to convert the unstructured set of surface normals and their probabilities into a latent feature vector. The latent vector is concatenated with the input image and further filtered by a 2D UNet.
As illustrated in \cref{fig:mvsnet}(b), the surface normal and image features are then used to construct a 3D latent cost volume which is then filtered with 3D convolutional layers. The final outputs are per-pixel depths and surface normals in the reference view. The outputs of the 3D convolutional layers become a depth probability volume $\hat{p}(d;\bm{m})$ and a surface normal volume $\hat{\bm{n}}(d,\bm{m})$ where $d$ is a discretized hypothesis of depth. From these volumes, we compute the estimated depth $\hat{d}(\bm{m})$ and surface normal $\hat{\bm{n}}(\bm{m})$ as
\begin{equation}
\hat{d}(\bm{m}) = \sum_d \hat{p}(d;\bm{m}) d\,,
\end{equation}
\begin{equation}
\hat{\bm{n}}(\bm{m}) = \frac{\sum_d \hat{p}(d;\bm{m})\hat{\bm{n}}(d,\bm{m})}{\|\sum_d \hat{p}(d;\bm{m})\hat{\bm{n}}(d,\bm{m})\|}\,.
\end{equation}
\begin{figure}[t]
\centering
\includegraphics[keepaspectratio, width=\linewidth]{fig/result_ablation_wo_normal_volume.pdf}
\caption{Advantage of estimating surface normals and depth as separate quantities. Our surface normal estimates are mostly consistent with the true surface normals (GT) in both continuous regions and also at surface discontinuities. In contrast, if depth derivatives (differentiation) are used as surface normals (\emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, nLMVS-Net without normal volume--``w/o NV''), surface normals become erroneous at even continuous regions and high-frequency details of surface discontinuities are also lost or exaggerated. }
\label{fig:ablation_normal_volume}
\end{figure}
We ensure that the estimated depth and surface normals mostly agree with each other with a loss that aggregates the discrepancy in the directions of the surface normals and depth derivatives
\begin{equation}
L_\textrm{dn} = \sum_{\bm{m}}\arccos\left(\hat{\bm{n}}(\bm{m})\cdot\bar{\bm{n}}(\bm{m})\right),
\label{eq:loss_consistency}
\end{equation}
where $\bar{\bm{n}}(\bm{m})$ is the surface normal computed from the estimated depths $\hat{d}(\bm{m})$ with cross product of tangent vectors on the surface. As shown in \cref{fig:ablation_normal_volume}, this consistency holds only in C0 and C1 continuous regions and we do not use $\bar{\bm{n}}(\bm{m})$ as surface normal estimates. The summation in \cref{eq:loss_consistency} ensures that strict consistency is only mildly imposed and surface normals are allowed to deviate from the depth derivatives at surface discontinuities. This is possible as we recover depths and surface normals as separate quantities.
We also impose individual depth and surface normal supervisions
\begin{equation}
L_\textrm{d} = \sum_{\bm{m}} \|\hat{d}(\bm{m}) - d_\textrm{gt}(\bm{m})\|_1
\end{equation}
\begin{equation}
L_\textrm{n} = \sum_{\bm{m}} \arccos\left(\hat{\bm{n}}\left(\bm{m}\right) \cdot \bm{n_\textrm{gt}}(\bm{m}) \right)\,,
\end{equation}
where $d_\mathrm{gt}(\bm{m})$ and $\bm{n_\mathrm{gt}}(\bm{m})$ are the ground-truth depth and surface normal. The overall training loss is the weighted sum of these loss functions. We train this network separately from the shape-from-shading network.
\if 0
becomes
\begin{equation}
L\textrm{mvs} = \lambda_\mathrm{d}L_\mathrm{d} + \lambda_\mathrm{n}L_\mathrm{n} + \lambda_\mathrm{dn}L_\mathrm{dn},
\end{equation}
where we set the weights to $\lambda_\mathrm{d} = \lambda_\mathrm{n} = 1$, and $\lambda_\mathrm{dn} = 0.1$ in the experiments.
\fi
\subsection{Joint Shape and Reflectance Estimation}
\label{sec:shape_and_reflectance}
As \cref{fig:overview} depicts, we alternate between estimating the object geometry and estimating the reflectance (BRDF). We represent the surface BRDF with the conditional invertible neural BRDF model (conditional iBRDF model) \cite{chen2020ibrdf}. We update parameters of this model so that the difference between the input view images and the rendered images for each view is minimized. A challenge here is that pixel-wise intensity errors are too brittle as they suffer from geometry reconstruction errors. For this, we derive two loss functions that explicitly handle the reconstruction errors. The key ideas are that 1) we blur the images to evaluate the consistency in a coarse level, and that 2) we can find the ground truth surface normal around the estimated one that almost exactly satisfies the radiometric consistency and use it for rendering. Please see the supplementary material for further details.
\subsection{Whole 3D shape Recovery}
\label{sec:whole_shape_recovery}
Our nLMVS-Net can recover per-pixel surface normal and depth of a reference view image from 5 input view images. If we have a set of such multi-view images that collectively cover the entire object (typically 10 images) taken while moving around an object on a plane, we can recover the whole 3D object geometry by applying nLMVS-Net to 5 images each while each image becomes the reference view, after which we integrate all depth and surface normals. During the alternating estimation of geometry and reflectance, we can use all the images together to update a single reflectance estimate. In the geometry estimation, for each view, we select four neighboring views (2 to the left and 2 to the right for a typical 360$^\circ$ capture on a plane) as inputs to nLMVS-Net. In the reflectance estimation, we compute the loss function introduced in \cref{sec:shape_and_reflectance} for each view and minimize the sum of them. We then reconstruct a 3D mesh from the estimated depth and surface normals by converting them into oriented points and applying Poisson surface reconstruction \cite{kazhdan2006poisson}.
\section{Experimental Results}
\label{sec:results}
\begin{figure}[t]
\centering
\includegraphics[keepaspectratio, width=\linewidth]{fig/nlmvs-real.pdf}
\caption{Our new multi-view real object image dataset, nLMVS-Real, consists of radiometrically and geometrically accurately calibrated 2569 multi-view images of 120 combinations of 5 shapes, 4 materials, and 6 illumination environments.}
\label{fig:nlmvs_real}
\end{figure}
We evaluate the effectiveness of nLMVS-Net through extensive experiments using both synthetic and real images of objects of different shapes and reflectances taken in a variety of illumination environments. For this, we introduce novel large-scale synthetic and real datasets, which we refer to as nLMVS-Synth and nLMVS-Real, respectively.
\begin{figure*}[t]
\centering
\includegraphics[keepaspectratio, width=\linewidth]{fig/result_ablation_sfs.pdf}
\caption{Ablation study on our shape-from-shading sub-network (``w/o SfS'') which constructs a cost volume from multi-view image features without leveraging radiometric cues as per-pixel probabilistic surface normal likelihoods. For each result, we show the estimation errors as a color map. The results clearly show that the shape-from-shading sub-network is essential to handle textureless, non-Lambertian objects.}
\label{fig:result_ablation_sfs}
\end{figure*}
We first report that the Multiview Objects Under Natural Illumination Database \cite{oxholm2014mvshape} contains clear flaws in image capture including saturation, glare, and poor geometric calibration (please see the supplementary material for details). For this reason, numerical results on this dataset do not accurately reflect superiority of any method. This problem has been communicated with the authors of \cite{oxholm2014mvshape} and confirmed by them. In fact, one key contribution of our paper is the introduction of a new and a more extensive and accurate dataset that can replace this dataset. Radiometrically and geometrically accurate image capture for such dataset requires meticulous calibration and painstaking efforts in actual capture. Our new dataset (nLMVS-Real) would likely serve the community for a broad range of research on appearance modeling.
\begin{table}[t]
\centering
\footnotesize
\subfloat[][From 5 Views.]{
\setlength{\tabcolsep}{3pt}
\begin{tabular}{l|cc}
& Depth & Normal \\ \hline
MVSNeRF \cite{chen2021mvsnerf} & 5.59 \% & - \\
CVP-MVS \cite{yang2020cvpmvsnet} & 4.16 \% & - \\
IDR \cite{yariv2020idr} & 1.11\% & 11.0 deg \\
w/o SfS & 1.12\% & 11.2 deg \\
\rowcolor[rgb]{0.93,1.0,0.87} Ours & 0.92\% & 9.74 deg \\
\end{tabular}
\label{tab:comparison}
}
~~
\subfloat[][From 10 Views.]{
\vspace{4pt}
\setlength{\tabcolsep}{3pt}
\begin{tabular}{l|c}
& Mesh \\ \hline
NeRS \cite{zhang2021ners} & 0.63 \% \\
PhySG \cite{zhanf2021physg} & 0.61 \% \\
IDR \cite{yariv2020idr} & 0.25 \% \\
\rowcolor[rgb]{0.93,1.0,0.87} Ours + PSR \cite{kazhdan2006poisson} & 0.38 \%
\label{tab:result_mesh}
\end{tabular}
}
\caption{\subref{tab:comparison} Mean errors of the estimated depths and surface normals on the nLMVS-Synth dataset. The results clearly show the effectiveness of our method. \subref{tab:result_mesh} Mean error of 3D mesh models recovered from 10 view images. Even though we recover the mesh models by simply applying Poisson surface reconstruction (PSR) \cite{kazhdan2006poisson}, our results are quantitatively comparable to the state-of-the-art methods.}
\end{table}
\vspace{-12pt}
\paragraph{nLMVS-Synth Dataset}
We rendered a large number of training and test images of synthetic shapes \cite{xu2018relighting, stanford3dscan, suggestivecontour, plyfiles}, measured BRDFs \cite{matusik2003brdf}, and captured illumination maps \cite{hdrihaven, gardner2017indoor, lightprobe, hiresolightprobe}.
For training, we synthesized images of 2685 combinations of different shapes, materials, and illuminations. For each combination, we rendered images of randomly sampled 10 views. In total, the training set consists of 26,850 images. We also rendered a separate set of images for testing which consists of 4320 multi-view images of 216 different combinations of 6 shapes, 6 materials, and 6 illuminations. For each combination, we sampled 20 views on the horizontal line at equal intervals and added perturbations to them in the horizontal and vertical directions.
\vspace{-12pt}
\paragraph{nLMVS-Real Dataset}
\Cref{fig:nlmvs_real} shows example images from our new nLMVS-Real dataset. We captured approximately 20 HDR images at three different heights for each of all combinations of 5 shapes, 4 materials, and 6 illumination environments. We also captured illumination maps using RICOH THETA Z1. The objects are replicated using a 3D printer and painted with different materials. Ground-truth 3D mesh models are available for quantitative evaluations.
\begin{figure*}[t]
\centering
\subfloat[][]{
\includegraphics[keepaspectratio, height=131pt]{fig/result_comparison_on.pdf}
\label{fig:comparison_on}
}
\subfloat[][]{
\includegraphics[keepaspectratio, height=131pt]{fig/result_real.pdf}
\label{fig:result_real_shape}
}
\caption{\subref{fig:comparison_on} 3D mesh models and their appearance recovered from our estimation results on the Multiview Objects Under Natural Illumination Database \cite{oxholm2014mvshape}. Compared to the results of Oxholm and Nishino (ON) \cite{oxholm2015shape}, our results have fewer artifacts and surface details are successfully recovered. \subref{fig:result_real_shape} Recovered depths, surface normals, and whole 3D shape (mesh models) from our nLMVS-Real dataset. Please see supp. material for more results. Letters on the left denote different illumination environments. Our method successfully recovers accurate geometry for a wide variety of real-world objects.}
\end{figure*}
\vspace{-12pt}
\paragraph{Baseline Methods}
We compare our method with CVP-MVSNet \cite{yang2020cvpmvsnet} and MVSNeRF \cite{chen2021mvsnerf} which also handle sparse (\emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, 3 view) inputs. We could not directly compare our method with Kusupati \emph{et al}\onedot \cite{kusupati2020nas} as their network is trained to recover depths and normals for the entire scene rather than a single object. Instead, we compare our method with ours ``w/o SfS'' (without shape-from-shading) that constructs a cost volume only from multi-view image features similar to Kusupati \emph{et al}\onedot \cite{kusupati2020nas}. We also compare our method with IDR \cite{yariv2020idr}, a neural image synthesis method that recovers surface geometry from relatively sparse (\emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, typically 50 and 11 at minimum) view inputs.
\begin{figure}[t]
\centering
\includegraphics[keepaspectratio, width=\linewidth]{fig/result_brdf_shape-mat.pdf}
\caption{Estimated BRDFs under ``Court'' illumination. Please see supp. material for all results. The results are consistent across estimation from images of different shapes, which demonstrates the accuracy of our method.}
\label{fig:result_real_brdf}
\end{figure}
\vspace{-12pt}
\paragraph{Evaluation Metrics}
We measure the accuracy of the recovered depth and surface normals with mean absolute errors. For depth error, the scale of the object is normalized such that the diagonal length of its bounding box is 1.
\subsection{Results on Synthetic Data}
\paragraph{Accuracy of the Shape-from-Shading Network}
We first evaluate the accuracy of the proposed shape-from-shading network. Ground-truth BRDF was used to compute the input surface normal likelihood; \emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, we assume that the object's reflectance is known. The error between the ground-truth surface normals and those estimated to have the highest probability was lower than 10 deg for 83\% of all pixels. This is comparable to the accuracy of existing shape-from-shading methods such as Johnson and Adelson \cite{johnson11sfs} and the single-view method of Oxholm and Nishino \cite{oxholm2015shape}.
\vspace{-12pt}
\paragraph{Joint Shape and Reflectance Estimation Results}
\Cref{fig:opening,fig:result_ablation_sfs}, and \cref{tab:comparison} show qualitative and quantitative results. While existing methods and our method without the shape-from-shading cues (\emph{i.e}\onedot} \def\Ie{\emph{I.e}\onedot, ``w/o SfS'') fail on non-Lambertian and textureless objects, our method successfully recover both depths and surface normal these challenging objects. This clearly shows the effectiveness of our method, especially the importance of the shape-from-shading sub-network. Please see the supplementary material for more results and ablation studies.
\vspace{-12pt}
\paragraph{Accuracy of the Whole 3D Shape Recovery}
We can also recover 3D mesh models from our depth and surface normal estimates of 10 views (\cref{sec:whole_shape_recovery}) and compare the results with those of neural image synthesis methods \cite{zhang2021ners, zhanf2021physg, yariv2020idr}. For this experiment, we used 10 views uniformly sampled from the original 20 views of the nLMVS-Synth dataset. We evaluate the reconstruction accuracy with root-mean-square (RMS) of the distance from a point on the reconstructed mesh to the nearest point on the ground truth mesh. \Cref{tab:result_mesh} shows quantitative results. Even though we recover the mesh models by simply applying Poisson surface reconstruction \cite{kazhdan2006poisson}, our results are quantitatively comparable to the state-of-the-art methods. Please see the supplementary material for qualitative results.
\subsection{Results on Real Data}
\Cref{fig:comparison_on} shows whole 3D shape and appearance recovered from our estimation results on the Multiview Objects Under Natural Illumination Database \cite{oxholm2014mvshape}. We compare our results with those of of Oxholm and Nishino \cite{oxholm2015shape}. Our results have fewer artifacts and more surface details (\emph{e.g}\onedot} \def\Eg{\emph{E.g}\onedot, ears of the ``Horse'') are recovered.
\Cref{fig:result_real_shape} shows qualitative results of the recovered geometry on our nLMVS-Real Dataset. The results are of high quality even for complex shapes. \Cref{fig:result_real_brdf} shows several of the estimated BRDFs. The estimates are consistent across different shapes. Note that ground truth BRDF of the real materials cannot be easily acquired.
\section{Conclusion}
In this paper, we introduced nLMVS-Net, a neural multi-view stereo network that can recover both depth and surface normal at each pixel in the reference view for objects with complex reflectance taken under known but natural illumination. The method integrates radiometric cues in the form of view-independent surface normals recovered with a dedicated network into depth and surface normal cost volume filtering. By canonically modeling uncertainties of the surface normals, they provide rich cues for accurate geometry recovery. Experimental results clearly demonstrate the effectiveness of nLMVS-Net including its accuracy in recovering the complex reflectance of real-world objects. We believe nLMVS-Net can serve as a useful practical means for passive geometry recovery in the wild.
\section*{Acknowledgement}
This work was in part supported by
JSPS
20H05951,
21H04893,
JST
JPMJCR20G7,
JPMJSP2110,
and RIKEN GRP.
We also thank Shinsaku Hiura for his help in 3D printing.
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| 7,150
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{"url":"https:\/\/montoan.com\/toan-lop-8\/giai-bai-tap-bai-8-phan-tich-da-thuc-thanh-nhan-tu-bang-phuong-phap-nhom-hang-tu-dai-8.html","text":"# Gi\u1ea3i b\u00e0i t\u1eadp B\u00e0i 8: Ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p nh\u00f3m h\u1ea1ng t\u1eed \u2013 \u0110\u1ea1i s\u1ed1 8\n\n### B\u00e0i 47 trang 22 SGK \u0111\u1ea1i s\u1ed1 8 t\u1eadp 1\n\nPh\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed\na) \u00a0$x^2$ \u2013 xy + x \u2013 y = x(x \u2013 y) + (x \u2013 y) = (x \u2013 y)(x + 1)\nb) \u00a0xz + yz \u2013 5(x + y) = z (x + y) \u2013 5(x + y) = (x + y)(z \u2013 5)\nc) \u00a03$x^2$ \u2013 3xy \u2013 5x + 5y = 3x(x \u2013 y) \u2013 5(x \u2013 y) = (x \u2013 y)(3x \u2013 5)\n\n### B\u00e0i 48 trang 22 SGK \u0111\u1ea1i s\u1ed1 8 t\u1eadp 1\n\nPh\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed:\na) \u00a0$x^2$ + 4x \u2013 $y^2$ + 4 = ($x^2$ + 2.2.x + $2^2$) \u2013 $y^2$\n= $(x + 2)^2$ \u2013 $y^2$ = (x + 2 \u2013 y) (x + 2 + y)\n\n1. b) 3$x^2$ + 6xy + 3$y^2$ \u2013 3$z^2$\n\n= 3[($x^2$ + 2xy + $y^2$) \u2013 $z^2$]\n\n= 3[$(x + y)^2$ \u2013 $z^2$] = 3(x + y \u2013 z)(x + y + z)\n\n1. c) $x^2$ \u2013 2xy + $y^2$ \u2013 $z^2$ + 2zt \u2013 $t^2$\n\n= ($x^2$ \u2013 2xy + $y^2$) \u2013 ($z^2$ \u2013 2zt + $t^2$)\n\n= $(x \u2013 y)^2$ \u2013 $(z \u2013 t)^2$\n\n= [(x \u2013 y) \u2013 (z \u2013 t)] . [(x \u2013 y) + (z \u2013 t)]\n\n= (x \u2013 y \u2013 z + t)(x \u2013 y + z \u2013 t)\n\n### B\u00e0i 49 trang 22 SGK \u0111\u1ea1i s\u1ed1 8 t\u1eadp 1\n\nT\u00ednh nhanh:\na) 37,5.6,5 \u2013 7,5.3,4 \u2013 6,6.7,5 + 3,5.37,5\n= (37,5.6,5 + 3,5.37,5) \u2013 (7,5.3,4 + 6,6.7,5)\n= 37,5(6,5 + 3,5) \u2013 7,5(3,4 + 6,6)\n= 37,5.10 \u2013 7,5.10\n= 375 \u2013 75\n= 300\n\nb) \u00a0$45^2$ + $4^0$2 \u2013 $1^5$2 + 80.45\n= $45^2$ + 2.40.45+ $40^2$ \u2013 $15^2$\n= $(45+40)^2$ \u2013 $15^2$\n= $85^2$ \u2013 $15^2$\n= (85 + 15)(85 \u2013 15)\n= 100.70\n= 7000\n\n### B\u00e0i 50 trang 23 SGK \u0111\u1ea1i s\u1ed1 8 t\u1eadp 1\n\nT\u00ecm x bi\u1ebft:\na) \u00a0x(x \u2013 2) + x \u2013 2 = 0\n<=> (x \u2013 2) (x + 1) = 0\n<=> (x \u2013 2) = 0 ho\u1eb7c (x + 1) = 0\n<=> x = 2 ho\u1eb7c x = -1\n\nb) \u00a05x(x \u2013 3) \u2013 x + 3 = 0\n<=> 5x(x \u2013 3) \u2013 (x \u2013 3) = 0\n<=> (x \u2013 3) (5x \u2013 1) = 0\n<=> (x \u2013 3) = 0 ho\u1eb7c (5x \u2013 1) = 0\n<=> x = 3 ho\u1eb7c x = $\\frac{1}{5}$","date":"2018-08-17 01:30:45","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\": 0.817899763584137, \"perplexity\": 6659.060481678526}, \"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-2018-34\/segments\/1534221211403.34\/warc\/CC-MAIN-20180817010303-20180817030303-00357.warc.gz\"}"}
| null | null |
Q: Image Rectification for Shake Correction on OpenCV I've 2 pictures of the same scene from an uncalibrated camera. The pics are from a slightly different angle and scale(zoom) and I'd like to superpose them, rejecting any kind of shake. In other words, I should transform them so the shake becomes imperceptible, do a Motion Compensation.
I've already tried using a simple SURF (feature) detector along with Homography but sometimes the result isn't satisfactory. So I am thinking about trying Image Rectification to compensate the motion.
- Would it work with slight changes, such as user shake?
- Would it really work to reject shake for these 2 frames? And for a bigger buffer of pictures (10 maybe)?
- Anyone knows if it would fix scale disparity (different zoom in the images)?
- What the algorithm really do? Will it transform both pictures into a third orientation?
If there is a better solution, I would be glad to know =)
EDIT
I don't aim to compensate blur motion but the displacement itself. For example, in this file the author compensates the angle difference between two cameras by Image Rectification. How does it actually work? Does it always create an intermediate picture orientation or can I specify that one of the pictures shall remains still??
Also, would I be able to apply this to many frames or it would always find an intermediate orientation for each two frames I put in?
Cheers,
A: I'm not sure how well superimposing the images would work. Another way to remove blur (including motion blur which should dominate in handheld camera devices) from an image is by blind deconvolution. It is basically a method of finding the inverse of the blur filter that was physically applied (camera shaken) to the real image. There's plenty of techniques out on the web. I've specifically had good results using a modified version of the algorithm in this paper: http://www.cse.cuhk.edu.hk/~leojia/all_final_papers/motion_deblur_cvpr07.pdf
It also comes with an executable file somewhere around the web so you can see if it's fit for your purpose.
Good luck out there!
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 107
|
Q: Are variables static/extern by default in C? A simple question;
I know that function are extern by default in C. How about variables?
int a = 0;
int main(){
int b = 1;
return a+b;
}
Are a and b static/extern by default, or they don't have any storage specifiers if nothing is specified.
A: The variable a is defined outside the function. It is visible outside the current translation unit (TU) if the other TU contains extern int a;.
The variable b is defined inside the function. It is an automatic variable that is not visible outside the function.
See C11 §6.2.1 Scopes of identifiers for information about scopes. The variable a has file scope; the variable b has block scope.
See also §6.2.2 Linkages of identifiers for information about linkage. The variable a has external linkage. The variable b has no linkage.
See also §6.2.4 Storage durations of objects. The variable a has static storage duration. The variable b has automatic storage duration.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,068
|
from __future__ import absolute_import, division, print_function
from trakt import Trakt
from threading import Condition
import logging
import os
logging.basicConfig(level=logging.DEBUG)
class Application(object):
def __init__(self):
self.is_authenticating = Condition()
self.authorization = None
# Bind trakt events
Trakt.on('oauth.token_refreshed', self.on_token_refreshed)
def authenticate(self):
if not self.is_authenticating.acquire(blocking=False):
print('Authentication has already been started')
return False
# Request new device code
code = Trakt['oauth/device'].code()
print('Enter the code "%s" at %s to authenticate your account' % (
code.get('user_code'),
code.get('verification_url')
))
# Construct device authentication poller
poller = Trakt['oauth/device'].poll(**code)\
.on('aborted', self.on_aborted)\
.on('authenticated', self.on_authenticated)\
.on('expired', self.on_expired)\
.on('poll', self.on_poll)
# Start polling for authentication token
poller.start(daemon=False)
# Wait for authentication to complete
return self.is_authenticating.wait()
def run(self):
self.authenticate()
if not self.authorization:
print('ERROR: Authentication required')
exit(1)
# Simulate expired token
self.authorization['expires_in'] = 0
# Test authenticated calls
with Trakt.configuration.oauth.from_response(self.authorization):
# Expired token, requests will return `None`
print(Trakt['sync/collection'].movies())
with Trakt.configuration.oauth.from_response(self.authorization, refresh=True):
# Expired token will be refreshed automatically (as `refresh=True`)
print(Trakt['sync/collection'].movies())
with Trakt.configuration.oauth.from_response(self.authorization):
# Current token is still valid
print(Trakt['sync/collection'].movies())
def on_aborted(self):
"""Device authentication aborted.
Triggered when device authentication was aborted (either with `DeviceOAuthPoller.stop()`
or via the "poll" event)
"""
print('Authentication aborted')
# Authentication aborted
self.is_authenticating.acquire()
self.is_authenticating.notify_all()
self.is_authenticating.release()
def on_authenticated(self, authorization):
"""Device authenticated.
:param authorization: Authentication token details
:type authorization: dict
"""
# Acquire condition
self.is_authenticating.acquire()
# Store authorization for future calls
self.authorization = authorization
print('Authentication successful - authorization: %r' % self.authorization)
# Authentication complete
self.is_authenticating.notify_all()
self.is_authenticating.release()
def on_expired(self):
"""Device authentication expired."""
print('Authentication expired')
# Authentication expired
self.is_authenticating.acquire()
self.is_authenticating.notify_all()
self.is_authenticating.release()
def on_poll(self, callback):
"""Device authentication poll.
:param callback: Call with `True` to continue polling, or `False` to abort polling
:type callback: func
"""
# Continue polling
callback(True)
def on_token_refreshed(self, authorization):
# OAuth token refreshed, store authorization for future calls
self.authorization = authorization
print('Token refreshed - authorization: %r' % self.authorization)
if __name__ == '__main__':
# Configure
Trakt.base_url = 'http://api.staging.trakt.tv'
Trakt.configuration.defaults.client(
id=os.environ.get('CLIENT_ID'),
secret=os.environ.get('CLIENT_SECRET')
)
app = Application()
app.run()
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,512
|
HomeTop NewsCoronavirus: Care home deaths up as hospital cases fall
Coronavirus: Care home deaths up as hospital cases fall
A third of all coronavirus deaths in England and Wales are now happening in care homes, figures show.
Office for National Statistics data showed there were 2,000 coronavirus care home deaths in the week ending 17 April, double the previous week.
It brings the total number of deaths in care homes linked to the virus since the start of the pandemic to 3,096.
Projections for the following week - up to last Friday - suggested the numbers have since continued to rise.
It comes as coronavirus hospital deaths have started falling after peaking on 8 April.
The total number of hospital coronavirus deaths topped 20,000 at the weekend.
Mike Padgham, of the Independent Care Group, which represents care homes, said care homes were now the "true front line" in the fight against coronavirus.
He said it was taking a "terrible toll". "These are our loved ones - mothers, fathers, brothers, sisters, aunts, uncles and friends who have been taken from us early. They deserve better."
He said the sector needed more testing, protective equipment and money to tackle the outbreaks.Labour's Liz Kendall added the virus was having a "devastating impact" on care homes.
"Urgent action is needed to get a grip of this problem."
The government has recently expanded testing so all care home residents showing symptoms are now eligible for tests, while the Army is helping to distribute protective kit for staff.
Media captionUK holds a minutes silence for coronavirus key worker deaths
Meanwhile, a minute's silence has been held across the UK to commemorate the key workers who have died with coronavirus.
Prime Minister Boris Johnson, who returned to work on Monday, joined the tribute at 11:00 BST.
More than 100 NHS and care staff have died with the virus, as have many transport and other key workers.
Remembering 100 NHS workers who have died
'Living legend' doctor dies after contracting virus
Nurse, 84, 'gave her life to the NHS'
Why official virus care home deaths may be underestimate
The daily updates provided by government do not include care home deaths.
The ONS has been able to track these by looking at deaths certificates - but that means the data lags behind the hospital deaths provided by the government.
Up until 10 April just over 1,000 coronavirus-related deaths had been recorded in care homes so far.
A week later this had increased by another 2,000 to hit 3,096 in England and Wales.
Data provided by the Care Quality Commission, which receives reports from care homes in England, suggest the following week, up until last Friday, saw an even bigger rise.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 252
|
\subsection{\bf Renormalized spin-wave (RSW) theory}
The Hamiltonian of the system is
\begin{eqnarray} \label{rsw1}
H & = & - J_1\sum\limits_{\ll ij \gg _A } {{\bf S}_{1i}
\cdot {\bf S}_{1j}}\,-\,J_2\sum\limits_{\ll ij \gg _B } {{\bf S}_{2i}
\cdot {\bf S}_{2j}}\nonumber \\
& & +\,J \sum\limits_{\langle ij \rangle} {{\bf S}_{1i}
\cdot {\bf S}_{2j}}
\end{eqnarray} where the sums are over all sites of a three-dimensional cubic lattice:
$\langle i,j\rangle$ denotes the sum over the nearest neighbors, $\ll i,j \gg _A$ denotes the sum over the sites of the A sublattice, $\ll i,j \gg _B$ denotes the sum over the sites of the B sublattice.
The first two terms describe the ferromagnetic Heisenberg intra-sublattice
exchange $J_1>0, J_2>0$, while the third term describes the inter-sublattice exchange which is antiferromagnetic $J>0$.
To study a theory with the Hamiltonian Eq.(\ref{rsw1}) it is convenient to introduce Holstein-Primakoff representation for the spin
operators
\begin{eqnarray}\label{rsw2} & &
S_{1j}^+ = S^1_{1j} + i S^2_{1j}=\sqrt {2s_1-a^+_ja_j}\,\,\,\,a_j \nonumber \\
& & S_{1j}^- = S^1_{1j} - i S^2_{1j}=a^+_j\,\,\sqrt {2s_1-a^+_ja_j}
\\ & & S^3_{1j} = s_1 - a^+_ja_j \nonumber \end{eqnarray}
when the sites $j$ are from sublattice $A$ and
\begin{eqnarray}\label{rsw3} & &
S_{2j}^+ = S^1_{2j} + i S^2_{2j}=-b^+_j\,\,\sqrt {2s_2-b^+_jb_j}\nonumber \\
& & S_{2j}^- = S^1_{2j} - i S^2_{2j}=-\sqrt {2s_2-b^+_jb_j}\,\,\,\,b_j
\\ & & S^3_{2j} = -s_2 + b^+_jb_j \nonumber \end{eqnarray}
when the sites $j$ are from sublattice $B$. The operators $a^+_j,\,a_j$ and $b^+_j,\,b_j$ satisfy the Bose commutation relations.
In terms of the Bose operators and keeping only the quadratic and quartic terms, the effective Hamiltonian
Eq.(\ref{rsw1}) adopts the form
\begin{equation}\label{rsw4}H=H_2+H_4\end{equation} where
\begin{eqnarray}\label{rsw5}
H_2 & = & s_1 J_1\sum\limits_{\ll ij \gg _A }\left( a^+_i a_i\,+\,a^+_j a_j\,-\,a^+_j a_i\,-\,a^+_i a_j\right) \nonumber \\
& + & s_2 J_2\sum\limits_{\ll ij \gg _B }\left( b^+_i b_i\,+\,b^+_j b_j\,-\,b^+_j b_i\,-\,b^+_i b_j\right) \\
& + & J \sum\limits_{\langle ij \rangle}\left[s_1 b^+_j b_j + s_2 a^+_i a_i -
\sqrt{s_1 s_2}\left( a^+_i b^+_j+a_i b_j \right)\right] \nonumber
\end{eqnarray}
\begin{eqnarray}\label{rsw6}
H_4 & = & \frac 14 J_1 \sum\limits_{\ll ij \gg _A }\left[a^+_i a^+_j( a_i-a_j)^2 + (a^+_i- a^+_j)^2 a_i a_j\right] \nonumber \\
& + & \frac 14 J_2 \sum\limits_{\ll ij \gg _B }\left[b^+_i b^+_j( b_i-b_j)^2 + (b^+_i- b^+_j)^2 b_i b_j\right]\nonumber \\
& + & \frac 14 J \sum\limits_{\langle ij \rangle}\left[
\sqrt{\frac {s_1}{s_2}}\left( a_i b^+_j b_j b_j+a^+_i b^+_j b^+_j b_j \right)\right. \\
& + &\left. \sqrt{\frac {s_2}{s_1}}\left(a^+_i a_i a_i b_j+a^+_i a^+_i a_i b^+_j \right) - 4 a^+_i a_i b^+_j b_j \right] \nonumber
\end{eqnarray}
and the terms without operators are dropped.
The next step is to represent the Hamiltonian in the Hartree-Fock approximation
\begin{equation}\label{rsw7}H\approx H_{HF}=H_{cl}+H_q\end{equation} where
\begin{eqnarray}\label{rsw8} H_{cl} & = & 12 N J_1 s_1^2 (u_1-1)^2+ 12 N J_2 s_2^2 (u_2-1)^2 \nonumber \\
& + & 6 N J s_1 s_2 (u-1)^2,
\end{eqnarray}
\begin{eqnarray}\label{rsw9}
H_2 & = & s_1 J_1 u_1\sum\limits_{\ll ij \gg _A }\left( a^+_i a_i\,+\,a^+_j a_j\,-\,a^+_j a_i\,-\,a^+_i a_j\right) \nonumber \\
& + & s_2 J_2 u_2\sum\limits_{\ll ij \gg _B }\left( b^+_i b_i\,+\,b^+_j b_j\,-\,b^+_j b_i\,-\,b^+_i b_j\right) \\
& + & J u\sum\limits_{\langle ij \rangle}\left[s_1 b^+_j b_j + s_2 a^+_i a_i -
\sqrt{s_1 s_2}\left( a^+_i b^+_j+a_i b_j \right)\right] \nonumber
\end{eqnarray}
and $N=N_A=N_B$ is the number of sites on a sublattice. Equation (\ref{rsw9}) shows that the Hartree-Fock parameters $u_1,\,u_2$ and $u$ renormalize
the intra-exchange constants $J_1,\,J_2$ and the inter-exchange constant $J$, respectively.
It is convenient to rewrite the Hamiltonian in momentum space representation
\begin{equation}\label{rsw10}
H_q = \sum\limits_{k\in B_r}\left [\varepsilon^a_k\,a_k^+a_k\,+\,\varepsilon^b_k\,b_k^+b_k\,-
\,\gamma_k \left (a_k^+b_k^+ + b_k a_k \right )\,\right ],
\end{equation}
where the wave vector $k$ runs over the reduced first Brillouin zone $B_r$ of a
cubic lattice. The dispersions are given by equalities
\begin{eqnarray}\label{rsw11}
\varepsilon^a_k & = & 4s_1\,J_1\,u_1\varepsilon_k
\,+\,6s_2\,J u \nonumber\\
\varepsilon^b_k & = & 4s_2\,J_2\,u_2 \varepsilon_k \,+\,6s_1\,J\,u \\
\gamma_k & = & 2J\,u\,\sqrt{s_1\,s_2}\,\left(\cos k_x +\cos k_y + \cos k_z \right)\nonumber\end{eqnarray} with
\begin{eqnarray}\label{rsw12}\varepsilon_k & = & 6-\cos(k_x+k_y)-\cos(k_x-k_y) - \cos (k_x+k_z) \nonumber\\
& - & \cos(k_x-k_z)- \cos(k_y+k_z) - \cos(k_y-k_z).\end{eqnarray} To diagonalize the Hamiltonian one introduces new Bose fields
$\alpha_k,\,\alpha_k^+,\,\beta_k,\,\beta_k^+$ by means of the
transformation
\begin{eqnarray} \label{rsw12a} & &
a_k\,=u_k\,\alpha_k\,+\,v_k\,\beta^+_k\qquad
a_k^+\,=u_k\,\alpha_k^+\,+\,v_k\,\beta_k
\nonumber \\
\\
& & b_k\,=\,u_k\,\beta_k\,+\,v_k\,\alpha^+_k\qquad
b_k^+\,=\,u_k\,\beta_k^+\,+\,v_k\,\alpha_k
\nonumber \end{eqnarray} where the coefficients of the transformation $u_k$ and $v_k$ are real function of the wave vector $k$
\begin{eqnarray} \label{ferri11} &
&u_k\,=\,\sqrt{\frac 12\,\left (\frac
{\varepsilon^a_k+\varepsilon^b_k}{\sqrt{(\varepsilon^a_k+\varepsilon^b_k)^2-4\gamma^2_k}}\,+\,1\right
)}\nonumber \\
\\
& & v_k\,=\,sign (\gamma_k)\,\sqrt{\frac 12\,\left (\frac
{\varepsilon^a_k+\varepsilon^b_k}{\sqrt{(\varepsilon^a_k+\varepsilon^b_k)^2-4\gamma^2_k}}\,-\,1\right
)}\nonumber \end{eqnarray}
The transformed Hamiltonian adopts the form \begin{equation}
\label{ferri12} H_q = \sum\limits_{k\in B_r}\left
(E^{\alpha}_k\,\alpha_k^+\alpha_k\,+\,E^{\beta}_k\,\beta_k^+\beta_k\,+\,E^0_k\right),
\end{equation}
with new dispersions \begin{eqnarray} \label{ferri13} & & E^{\alpha}_k\,=\,\frac
12\,\left [
\sqrt{(\varepsilon^a_k\,+\,\varepsilon^b_k)^2\,-\,4\gamma^2_k}\,-\,\varepsilon^b_k\,+\,\varepsilon^a_k\right] \nonumber \\
\\
& & E^{\beta}_k\,=\,\frac
12\,\left [
\sqrt{(\varepsilon^a_k\,+\,\varepsilon^b_k)^2\,-\,4\gamma^2_k}\,+\,\varepsilon^b_k\,-\,\varepsilon^a_k\right]
\nonumber \end{eqnarray} and vacuum energy
\begin{equation}\label{ferri14}
E^{0}_k\,=\,\frac
12\,\left [
\sqrt{(\varepsilon^a_k\,+\,\varepsilon^b_k)^2\,-\,4\gamma^2_k}\,-\,\varepsilon^b_k\,-\,\varepsilon^a_k\right]\end{equation}
For positive values of the Hartree-Fock parameters and all values of $k\in B_r$,\,
the dispersions are nonnegative $ E^{\alpha}_k\geq 0,\, E^{\beta}_k \geq 0$. For definiteness I choose $s_1>s_2$.
With these parameters, the $\alpha_k$ boson is the long-range \textbf{(magnon)} excitation in the two-spin system with $E^{\alpha}_k\propto\rho k^2$, near the zero wavevector, while the $\beta_k$ boson is a gapped excitation.
To obtain the system of equations for the Hartree-Fock parameters we consider
the free energy of a system with Hamiltonian $H_{HF}$ equations (\ref{rsw8}) and (\ref{ferri12})
\begin{eqnarray}\label{rsw12}
\mathcal{F} & = & 12J_1 s_1^2 (u_1-1)^2+ 12J_2 s_2^2 (u_2-1)^2 \nonumber \\
& + & 6J s_1 s_2 (u-1)^2 + \frac 1N \sum\limits_{k\in B_r}E^{0}_k \\
& + & \frac {1}{\beta N} \sum\limits_{k\in B_r}\left[ \ln\left(1-e^{-\beta E^{\alpha}_k}\right)\,+\,\ln\left(1-e^{-\beta E^{\beta}_k}\right)\right].\nonumber\end{eqnarray}
where $\beta\,=\,1/T$\,\, is the inverse temperature. Then the three equations
\begin{equation}\label{rsw13}\partial\mathcal{F}/\partial u_1=0,\quad \partial\mathcal{F}/\partial u_2=0,\quad\partial\mathcal{F}/\partial u=0\end{equation} adopt the form
(see the appendix)
\begin{eqnarray}\label{rsw14} u_1 & = & 1-\frac {1}{6s_1} \frac 1N \sum\limits_{k\in B_r} \varepsilon_k \left[u_k^2 \,n_k^{\alpha}\, +\, v_k^2\, n_k^{\beta}\, +\, v_k^2\right]\nonumber \\
u_2 & = & 1-\frac {1}{6s_2} \frac 1N \sum\limits_{k\in B_r} \varepsilon_k \left[v_k^2 \,n_k^{\alpha}\, +\, u_k^2\, n_k^{\beta}\, +\, v_k^2\right]\nonumber \\
u & = & 1-\frac 1N \sum\limits_{k\in B_r} \left[\frac {1}{2s_1}\left(u_k^2 \,n_k^{\alpha}\, +\, v_k^2\, n_k^{\beta}\, +\, v_k^2\right)\right. \\
& + & \left. \frac {1}{2s_2} \left(v_k^2 \,n_k^{\alpha}\, +\, u_k^2\, n_k^{\beta}\, +\, v_k^2\right)\right. \nonumber \\
& - & \left.\frac 23 J u\left(1+n_k^{\alpha}+n_k^{\beta}\right) \frac {\left(\cos k_x +\cos k_y + \cos k_z \right)^2}{\sqrt{(\varepsilon^a_k\,+\,\varepsilon^b_k)^2\,-\,4\gamma^2_k}}
\right]\nonumber
\end{eqnarray}
where $n_k^{\alpha}$ and $n_k^{\beta}$ are the Bose functions of $\alpha$ and $\beta$ excitations. The Hartree-Fock parameters, the solution of the system of equations (\ref{rsw14}), are positive functions of $T/J$, $u_1(T/J)>0,\,u_2(T/J)>0$ and $u(T/J)>0$. Utilizing these functions, one can calculate the spontaneous magnetization of the system, which is a sum of the spontaneous magnetization on the two sublattices $M\,=\,M^A\,+\,M^B$, where
\begin{eqnarray} \label{rsw15}
M^A & = & <S^3_{1j}> \,\,\, j\,\, is\,\, from\,\, sublattice\,\, A \nonumber \\
\\
M^B & = & <S^3_{2j}> \,\,\, j\,\, is\,\, from\,\, sublattice\,\, B \nonumber \end{eqnarray}
In terms of the Bose functions of the $\alpha$ and $\beta$ excitations they adopt the form
\begin{eqnarray}\label{rsw16}
M^A & = & s_1\,-\,\frac 1N \sum\limits_{k\in B_r} \left[u_k^2 \,n_k^{\alpha}\, +\, v_k^2\, n_k^{\beta}\, +\, v_k^2\right] \\
M^B & = & - \,s_2\,+\,\frac 1N \sum\limits_{k\in B_r} \left[v_k^2 \,n_k^{\alpha}\, +\, u_k^2\, n_k^{\beta}\, +\, v_k^2\right]\nonumber \end{eqnarray}
The magnon excitation-$\alpha_k$ in the effective theory equation (\ref{ferri12})- is a complicated mixture of the transversal
fluctuations of the $A$ and $B$ spins. As a result the magnons' fluctuations suppress in a different way the magnetization on sublattices $A$ and $B$. Quantitatively this depends on the coefficients $u_k$ and $v_k$ in equations (\ref{rsw16}). At characteristic temperature $T^*$ spontaneous magnetization on sublattice $B$ becomes equal to zero, while spontaneous magnetization on sublattice $B$ is still nonzero. Above $T^*$ the system of equations (\ref{rsw14}) has no solution and one has to modify the spin-wave theory. The magnetization depends on the
dimensionless temperature $T/J$ and dimensionless parameters
$s_1,\,s_2,\,J_1/J$ and $J_2/J$. For parameters $s_1=1.5,\,s_2=1,\,J_1/J=0.94$ and $J_2/J=0.01$ the
functions $M^A(T/J)$ and $M^B(T/J)$ are depicted in
figure 1. The upper (blue) line is the sublattice $A$ magnetization, the bottom (red) line is the sublattice $B$ magnetization.
\begin{figure}[!ht]
\epsfxsize=8.cm
\epsfbox{rswt.Eps} \caption{(color online)\,The spontaneous
magnetization $M^A$-upper (blue) line and $M^B$-bottom (red) line as
a function of $T/J$ for parameters\,
$s_1\,=\,1.5,\,s_2\,=\,1,\,J_1/J\,=\,0.94$ and $J_2/J\,=\,0.01$.
$T^*$ is the temperature at which sublattice $B$ magnetization
becomes equal to zero}\label{fig1}
\end{figure}
\subsection{\bf Modified RSW theory}
Once suppressed, the sublattice $B$ magnetization cannot be restored increasing the temperature above T*. To formulate this mathematically
we modify the spin-wave theory using the idea of a description of the paramagnetic phase of 2D ferromagnets ($T>0$) by means of modified spin-wave
theory \cite{Takahashi1,Takahashi2} and its generalization \cite{Karchev08b}. We consider a two-sublattice system and, to enforce the magnetization on the two sublattices to be equal to zero in paramagnetic phase,
we introduce two parameters $\lambda_A$ and $\lambda_B$ \cite{Karchev08b}. The new Hamiltonian is obtained from the old one equation (\ref{rsw1}) by adding two new terms:
\begin{equation}
\label{ferri26} \hat{H}\,=\,H\,-\,\sum\limits_{i\in A}
\lambda_1 S^3_{1i}\,+\,\sum\limits_{i\in B} \lambda_2 S^3_{2i} \end{equation}
In momentum space
the new Hamiltonian adopts the form \begin{equation} \label{ferri27}
\hat{H} = \sum\limits_{k\in B_r}\left [\hat{\varepsilon}^a_k\,a_k^+a_k\,+\,\hat{\varepsilon}^b_k\,b_k^+b_k\,-
\,\gamma_k\,(b_k a_k+b_k^+ a_k^+)\right] \end{equation}
where the new dispersions are
\begin{equation} \label{ferri28}
\hat{\varepsilon}^a_k\,=\varepsilon^a_k\,+\,\lambda_1, \qquad
\hat{\varepsilon}^b_k\,=\varepsilon^b_k\,+\,\lambda_2.\end{equation}
Utilizing the same
transformation equations (\ref{rsw12a}) with parameters
\begin{eqnarray} \label{ferri29} &
&\hat{u}_k\,=\,\sqrt{\frac 12\,\left (\frac
{\hat{\varepsilon}^a_k+\hat{\varepsilon}^b_k}{\sqrt{(\hat{\varepsilon}^a_k+\hat{\varepsilon}^b_k)^2-4\gamma^2_k}}\,+\,1\right
)}\nonumber \\
\\
& &\hat{v}_k\,=\,sign (\gamma_k)\,\sqrt{\frac 12\,\left (\frac
{\hat{\varepsilon}^a_k+\hat{\varepsilon}^b_k}{\sqrt{(\hat{\varepsilon}^a_k+\hat{\varepsilon}^b_k)^2-4\gamma^2_k}}\,-\,1\right
)}\nonumber \end{eqnarray}
one obtains the Hamiltonian in diagonal forma
\begin{equation}
\label{ferri30} \hat{H} = \sum\limits_{k\in B_r}\left
(\hat{E}^{\alpha}_k\,\alpha_k^+\alpha_k\,+\,\hat{E}^{\beta}_k\,\beta_k^+\beta_k+\hat{E}^0_k\right),
\end{equation} where
\begin{eqnarray}\label{ferri31} & & \hat{E}^{\alpha}_k\,=\,\frac
12\,\left [
\sqrt{(\hat{\varepsilon}^a_k\,+\,\hat{\varepsilon}^b_k)^2\,-\,4\gamma^2_k}\,-\,\hat{\varepsilon}^b_k\,+\,\hat{\varepsilon}^a_k\right] \nonumber \\
& & \hat{E}^{\beta}_k\,=\,\frac
12\,\left [
\sqrt{(\hat{\varepsilon}^a_k\,+\,\hat{\varepsilon}^b_k)^2\,-\,4\gamma^2_k}\,+\,\hat{\varepsilon}^b_k\,-\,\hat{\varepsilon}^a_k\right]\\
& & \hat{E}^{0}_k\,=\,\frac
12\,\left [
\sqrt{(\hat{\varepsilon}^a_k\,+\,\hat{\varepsilon}^b_k)^2\,-\,4\gamma^2_k}\,-\,\hat{\varepsilon}^b_k\,-\,\hat{\varepsilon}^a_k\right]\nonumber\end{eqnarray}
It is convenient to represent the parameters
$\lambda_1$ and $\lambda_2$ in the form \begin{equation} \label{ferri32}
\lambda_1\,=\,6 J u s_2 (\mu_1\,-\,1),\quad
\lambda_2\,=\,6 J u s_1 (\mu_2\,-\,1). \end{equation} In terms of the new
parameters $\mu_1$ and $\mu_2$ the dispersions
$\hat{\varepsilon}^a_k$ and $\hat{\varepsilon}^b_k$ adopt the form
\begin{eqnarray} \label{ferri33} & & \hat{\varepsilon}^a_k\,=\,4 s_1
J_1\,u_1\,\varepsilon_k\,+\,6\,s_2\,J\,u\,\mu_1
\nonumber \\
\\
& &
\hat{\varepsilon}^b_k\,=\,4s_2\,J_2\,u_2\,\varepsilon_k\,+\,6\,s_1\,J\,u\,\mu_2
\nonumber \end{eqnarray}
They are positive ($\hat{\varepsilon}^a_k>0$, $\hat{\varepsilon}^b_k>0$) for all values of the wavevector $k$, if the parameters $\mu_1$ and $\mu_2$ are positive ($\mu_1>0,\,\mu_2>0$).
The dispersions Eq.(\ref{ferri31}) are well defined if square-roots in equations
(\ref{ferri31}) are well defined. This is true if \begin{equation}\label{ferri34} \mu_1
\mu_2\geq1.\end{equation} The $\beta_k$ excitation is gapped ($E^{\beta}_k>0 $)
for all values of parameters $\mu_1$ and $\mu_2$ which satisfy equation
(\ref{ferri34}). The $\alpha$ excitation is gapped if $\mu_1
\mu_2>1$, but in the particular case \begin{equation} \label{ferri35} \mu_1
\mu_2=1\end{equation} $\hat{E}^{\alpha}_0=0$, and near the zero wavevector
\begin{equation} \label{ferri35b}
\hat{E}^{\alpha}_k\approx \hat{\rho} k^2\end{equation} with
spin-stiffness constant
\begin{equation} \label{ferri35c} \hat{\rho}\,=\,\frac {8(s_2^2 J_2 u_2\mu_1
\,+\,s_1^2 J_1 u_1 \mu_2)\,+\,2s_1s_2J u}{(s_1 \mu_2-s_2\mu_1)}\end{equation} In
the particular case equation (\ref{ferri35}) $\alpha_k$ boson is the
long-range excitation (magnon) in the system.
We introduced the parameters $\lambda_1$ and $\lambda_2$ ($\mu_1, \mu_2$) to enforce the sublattice $A$ and $B$ spontaneous magnetizations
to be equal to zero in the paramagnetic phase. We find out the parameters $\mu_1$ and $\mu_2$, as well as the Hartree-Fock parameters, as functions of temperature, solving the system of five equations, equations (\ref{rsw14}) and the equations $M^A=M^B=0$, where the spontaneous magnetizations have the same representation as equations (\ref{rsw16}) but with coefficients $\hat{u}_k,\,\,
\hat{v}_k$, and dispersions $\hat{E}^{\alpha}_k,\,\, \hat{E}^{\beta}_k$ in the expressions for the Bose functions.
The numerical calculations show that for high enough temperature
$\mu_1\mu_2>1$. When the temperature decreases the product $\mu_1\mu_2$ decreases, remaining larger than one. The temperature at which the product becomes equal to one ($\mu_1\mu_2=1$) is the $N\acute{e}el$ temperature. Below $T_N$, the spectrum contains long-range (magnon) excitations, thereupon $\mu_1\mu_2=1$. It is convenient to represent the parameters in the following way:
\begin{equation}\label{MnV16}\mu_1=\mu, \quad\quad \mu_2=1/\mu.\end{equation}
In the ordered phase magnon excitations are the origin of the suppression of the magnetization. Near the zero temperature their contribution is
small and at zero temperature sublattice $A$ and $B$ spontaneous magnetization reach their saturation. On increasing the temperature magnon fluctuations suppress the sublattice $A$ magnetization and sublattice $B$ magnetization in different ways. At $T^*$ the sublattice $B$ spontaneous magnetization becomes equal to zero.
Increasing the temperature above $T^*$, the sublattice $B$ magnetization should be zero. This is why we impose the condition
$M^B(T)=0$ if $T>T^{*}$. For temperatures above $T^*$, the parameter $\mu$ and the Hartree-Fock parameters are solution of a system of four equations, equations (\ref{rsw14}) and the equation $M^B=0$. The Hartree-Fock parameters, as a functions of temperature $T/J$, are depicted in figure 2 for parameters $s_1=1.5,\,s_2=1,\,J_1/J=0.94$ and $J_2/J=0.01$. The vertical dotted (green) line corresponds to $T^*/J$.
\begin{figure}[!ht]
\epsfxsize=7.5cm \hskip -0.9cm \epsfbox{HFParameters.Eps}
\caption{(color online)\,Hartree-Fock parameters $u_1$,\,$u_2$ and
$u$ as a function of $T/J$ for
$s_1\,=\,1.5,\,s_2\,=\,1,\,J_1/J\,=\,0.94$ and $J_2/J\,=\,0.01$. The
vertical dotted (green) line corresponds to $T^*/J$ }\label{fig2}
\end{figure}
The function $\mu(T/J)$ is depicted in figure 3 for the same parameters.
\begin{figure}[!ht]
\epsfxsize=7.5cm \hskip -0.9cm \epsfbox{mu.Eps} \caption{(color
online)\,$\mu(T/J)$ for parameters
$s_1\,=\,1.5,\,s_2\,=\,1,\,J_1/J\,=\,0.94$ and $J_2/J\,=\,0.01$. The
vertical dotted (green) line corresponds to $T^*/J$, while (red)
dashed lines to $T_N/J$ and $\mu(T_N/J)$.}\label{fig2}
\end{figure}
We utilize the
obtained function $\mu(T)$, $u_1(T)$, $u_2(T)$, $u(T)$ to calculate the spontaneous magnetization as a function of the temperature. Above $T^*$, the magnetization of the system is equal to the sublattice $A$ magnetization. For the same parameters as above the
functions $M^A(T/J)$ and $M^B(T/J)$ are depicted in figure 4a.
The upper (blue) line is the sublattice $A$ magnetization, the bottom (red) line is the sublattice $B$ magnetization. The total magnetization $M\,=\,M^A\,+\,M^B$ is depicted in figure 4b.
\begin{figure}[!ht]
\epsfxsize=7.8cm \hskip -0.9cm \epsfbox{mrswt.Eps} \caption{(color
online)\,a) The sublattice $A$ spontaneous magnetization $M^A$-upper
(blue) line and sublattice $B$ spontaneous magnetization
$M^B$-bottom (red) line as a function of $T/J$ for parameters\,
$s_1\,=\,1.5,\,s_2\,=\,1,\,J_1/J\,=\,0.94$ and
$J_2/J\,=\,0.01$.\,\\b) The total spontaneous magnetization
$M^A\,+\,M^B$. $T^*/J$- vertical dotted (green) line}\label{fig4}
\end{figure}
\section{\bf $T_N$ and $T^*$ dependence on model's parameters}
The existence of two ferromagnetic phases $(0,T^*)$ and $(T^*,T_N)$ is a generic feature of two spin systems. The characteristic temperatures $T_N$ and $T^*$ strongly depend on the parameters of the model. Intuitively, it is clear that, if the inter-exchange is much stronger than intra-exchanges, the ferromagnetic order sets in simultaneously on both sublattices. This is not true, if inter-exchange is not so strong. To demonstrate this I study a system with sublattice $A$ spin $s_1=1.5$, and sublattice $B$ spin $s_2=1$. For parameters $J_1/J=0.5$ and $J_2/J=0.005$ the magnetization-temperature curve is depicted in FIG.5 curve "c". The ratio of the characteristic temperatures equals $T_N/T^*\,=\,1.722$. Increasing the inter-exchange coupling, $J_1/J=0.3$,\,$J_2/J=0.003$ (curve "b"), the ratio decreases $T_N/T^*\,=\,1.229$, and above some critical value of the inter-exchange constant $J_1/J=0.05$,\,$J_2/J=0.0005$ $N\acute{e}el$'s temperature becomes equal to $T^*$. There is only one ferromagnetic phase, and magnetization-temperature curve "a" is a typical Curie-Weiss curve. Despite this the system does not describe ferromagnet, because the spin wave excitations are superposition of the sublattice $A$ and $B$ spin excitations.
\begin{figure}[!ht]
\epsfxsize=9.5cm \hskip -0.8cm \epsfbox{Fig1.Eps} \caption{(color
online)\, The magnetization $2\,M^A\,+\,2\,M^B$ as a function of
$T/J$ for $s_1=1.5$ and $s_2\,=\,1$, curve
\textbf{a}:$J_1/J\,=\,0.05$,\,$J_2/J\,=\,0.0005$, curve
\textbf{b}:$J_1/J\,=\,0.3$,\,$J_2/J\,=\,0.003$, curve
\textbf{c}:$J_1/J\,=\,0.5$,\,$J_2/J\,=\,0.005$.}\label{fig5}
\end{figure}
Next, I consider a system with sublattice $A$ spin $s_1\,=\,1.5$, and sublattice $B$ spin $s_2\,=1\,$. The ratio of sublattice $B$ exchange constant $J_2$ and inter-exchange constant $J$ is fixed $j_2\,=\,J_2/J\,=\,0.01$, while the ratio $j_1\,=\,J_1/J$ varies. When the sublattice $A$ exchange constant $J_1$ increases $j_1=J_1/J\,=\,0.64,\,0.84,\,0.94$, the magnetization-temperature curve at temperatures below $T^*$ does not change. There is no visible difference between $T^*$ temperatures for the three values of the parameter $J_1/J$. The difference appears when the temperature is above $T^*$. Increasing sublattice $A$ exchange constat increases the $N\acute{e}el$ temperature. The three curves are depicted in figure 6.
\begin{figure}[!ht]
\epsfxsize=9.2cm \hskip -0.3cm \epsfbox{Fig2.Eps} \caption{(color
online)\, The magnetization $2\,M^A\,+\,2\,M^B$ as a function of
$T/J$ for $s_1=1.5$,\,\,$s_2\,=\,1$,\,\,$j_2\,=\,J_2/J\,=\,0.01$ and
three values of the parameter $j_1\,=\,J_1/J$; $j_1\,=\,0.94$
(black) squares,\, $j_1\,=\,0.84$ (red) circles,\, $j_1\,=\,0.64$
(blue) triangles}\label{fig6}
\end{figure}
\begin{figure}[!ht]
\epsfxsize=9.cm \hskip -0.3cm \epsfbox{Fig3.Eps} \caption{(color
online)\, The magnetization $2M^A+2M^B$ as function of $T/J$ for
$J_1/J=0.4$, $J_2/J\,=\,0.004$,\, $s_1=4$, and $s_2=0.5$-curve
\textbf{a}\,(green), $s_2=1.5$-curve \textbf{b}\,(red),
$s_2=2.5$-curve \textbf{c}\,(black)}\label{fig7}
\end{figure}
Finally, I consider three systems with equal exchange constants $J_1/J\,=\,0.4$, $J_2/J=0.004$ and sublattice $A$ spin $s_1=4$, but with three different sublattice $B$ spins (figure 7). The calculations show that decreasing the sublattice $B$ spin decreases $T^*$ temperature, increases the maximum of magnetization at $T^*$ and zero temperature magnetization.
\section{\bf Theory and experiment}
\subsection{\bf Sulpho-spinel $MnCr_2S_{4-x}Se_x$}
The sulpho-spinel $MnCr_2S_{4-x}Se_x$ has been investigated by measurements of the magnetization at $15.3kOe$ as a function of temperature (figure 94 in \cite{HBMM3}). The maximum in the magnetization versus temperature curve, which is typical of $MnCr_2S_4$ ($x=0$),
increases when $x$ increase, and disappears at $x=0.5$. The $N\acute{e}el$ temperature decreases from $74K$ at $x=0$ to $56K$ at $x=2$. The authors' conclusion is that the observed change of the magnetic properties is attributed to a decrease of the strength of the negative $Mn^{2+}-Cr^{3+}$ superexchange interaction with increasing $Se$ concentration.
We obtained, see figure 5, that the maximum of the magnetization is at $T^*$. Above $T^*$ the magnetization of the system is equal to the magnetization of sublattice $A$ spins. If we extrapolate this curve below $T^*$ down to zero temperature we will obtain a value close to $2s_1\mu_B$, where $s_1$ is the spin of the sublattice $A$ spin operators. The experimental figures \cite{HBMM3} show that extrapolations give one and the same result for all values of $x$. One can accept the fact that the $Se$ concentration do not influence over the value of sublattice $A$ spin and $s_1=1.5$.
Below $T^*$ the magnetization is a sum of sublattice $A$ and $B$ magnetization. Hence, the magnetization at zero temperature is equal to $2(s_1-s_2)\mu_B$. Therefore, one can determine the sublattice $B$ spin $s_2$. The results of the theoretical calculations of magnetization, in Bohr magnetons, are depicted in figure 8 for parameters $s_1=1.5,\,J_1/J=0.47,\,J_2/J=0.001$ and $s_2=1$-curve \textbf{a}(black); $s_2=0.7$-curve \textbf{b} (red), and $s_2=0.4$-curve \textbf{c} (blue).
\begin{figure}[!ht]
\epsfxsize=9.cm \hskip -0.3cm \epsfbox{SSPinel.Eps} \caption{(color
online)\, The magnetization $2M^A+2M^B$ as function of $T/J$ for
$J_1/J=0.47$, $J_2/J\,=\,0.001$,\, $s_1=1.5$, and $s_2=1$-curve
\textbf{a}\,(black), $s_2=0.7$-curve \textbf{b}\,(red),
$s_2=0.4$-curve \textbf{c}\,(blue)}\label{fig8}
\end{figure}
The temperature and magnetization axis are chosen in accordance with experimental figure.
Comparing figure 94 in \cite{HBMM3} and figure 7 in the present paper, one concludes that the effective sublattice $B$ spin $s_2$ decreases with increasing Se concentration, and this is the origin of the anomalous temperature variation of magnetization. The figure 8 shows that the present calculations capture the essential features of the system; increasing the $Se$ concentration (decreasing $s_2$) leads to a decrease of $N\acute{e}el$ temperature, $T^*$ temperature decreases too, and the maximum of the magnetization increases. Comparing the figure 8 in the present paper and figure 5 in \cite{Karchev08b} one realizes the importance of the present method of calculation for adequate reproducing the characteristic temperatures $T_N$, $T^*$, and the shape of the magnetization-temperature curves.
\subsection{\bf Vanadium spinel $MnV_2O_4$}
The spinel $MnV_2O_4$ is a two-sublattice ferrimagnet, with site $A$ occupied by the $Mn^{2+}$ ion, which is in the $3d^5$ high-spin configuration with quenched orbital angular momentum, which can be regarded as a simple $s=5/2$ spin. The B site is occupied by the $V^{3+}$ ion, which takes the $3d^{2}$ high-spin configuration in the triply degenerate $t_{2g}$ orbital and has orbital degrees of freedom. The measurements show that the setting in of the magnetic order is at $N\acute{e}el$ temperature $T_N=56.5K$ \cite{vanadium1} and that the magnetization has a maximum near $T^*=53.5K$. Below this temperature the magnetization sharply decreases and goes to zero when temperature approaches zero.
We consider a system which obtains its magnetic properties from $Mn$ and $V$ magnetic moments. Because of the strong spin-orbital interaction it is convenient to consider $jj$ coupling with $\textbf{J}^A=\textbf{S}^A$ and $\textbf{J}^B=\textbf{L}^B+\textbf{S}^B$. The sublattice $A$ total angular momentum is $j_A=s_A=5/2$, while the sublattice $B$ total angular momentum is $j_B=l_B+s_B$, with $l_B=3$, and $s_B=1$ \cite{vanadium1}.
Then the g-factor for the sublattice $A$ is $g_A=2$, and the atomic value of the $g_B$ is $g_B=\frac 54$. The sublattice $A$ magnetic order is antiparallel to the sublattice $B$ one and the saturated magnetization is $\sigma=2 \frac 52-\frac 54 4=0$, in agreement with the experimental finding that the magnetization goes to zero when the temperature approaches zero.
The Hamiltonian of the system is
\begin{eqnarray} \label{MnV1}
H & = & - \kappa_A\sum\limits_{\ll ij \gg _A } {{\bf J}^A_{i}
\cdot {\bf J}^A_{j}}\,-\,\kappa_B\sum\limits_{\ll ij \gg _B } {{\bf J}^B_{i}
\cdot {\bf J}^B_{j}}\nonumber \\
& & +\,\kappa \sum\limits_{\langle ij \rangle} {{\bf J}^A_{i}
\cdot {\bf J}^B_{j}}\end{eqnarray}
The first two terms describe the ferromagnetic Heisenberg intra-sublattice
exchange $\kappa_A>0, \kappa_B>0$, while the third term describes the inter-sublattice exchange which is antiferromagnetic $\kappa>0$.
To proceed we use the Holstein-Primakoff representation of the total angular momentum vectors ${\bf J}^A_{j}(a^+_j,a_j)$ and ${\bf J}^B_{j}(b^+_j,\,b_j)$, where $a^+_j,\,a_j$
and $b^+_j,\,b_j$ are Bose fields, and repeat the calculations from sections II and III. The magnetization of the system $g_A\,M^A\,+\,g_B\,M^B$ as a function of the temperature is depicted in figure 9 for parameters\, $\kappa_A/\kappa\,=\,0.45$\, and \,$\kappa_B/\kappa\,=\,0.001$. The parameters are chosen so that the calculations to reproduce the experimental value of the ratio $T_N/T^*$.
\begin{figure}[!ht]
\epsfxsize=8.5cm
\epsfbox{MnV2O4.Eps} \caption{(color online)\,The magnetization
$g_A\,M^A\,+\,g_B\,M^B$ as a function of $T/\kappa$ for parameters\,
$\kappa_A/\kappa\,=\,0.45$\, and \,$\kappa_B/\kappa\,=\,0.001$.
}\label{fig9}
\end{figure}
The profile of the magnetization-temperature curve is in a very good agrement with the experimental zero-field cooling (ZFC) magnetization curves \cite{vanadium2,vanadium3}. The anomalous temperature dependence of the magnetization is reproduced, but there is an
important difference between the interpretation of the experimental results in \cite{vanadium1,vanadium2,vanadium3,vanadium4,vanadium5}, and the present theoretical results. In the experimental papers $T_N$ is the temperature at which both the $Mn$ and $V$ magnetization become equal to zero. The present theory predicts two phases: at low temperatures $(0,T^*)$ sublattice $Mn$ magnetization and sublattice $V$ magnetization contribute to the magnetization of the system, while at high temperatures $(T^*,T_N)$ only $Mn$ ions have non-zero spontaneous magnetization.
The vanadium sublattice magnetization set in at $T^*$, and evidence for this is the abrupt decrease of magnetization below $T^*$, which also indicates that the magnetic order of vanadium electrons is anti-parallel to the order of $Mn$ electrons.
For samples cooled in a field (FC magnetization) the field leads to formation of a single domain and, in addition, increases the chaotic order of the spontaneous magnetization of the vanadium sublattice, which is antiparallel to it. As a result the average value of the vanadium magnetic order decreases and does not compensate the $Mn$ magnetic order. The magnetization curves depend on the applied field, and do not go to zero. For a larger field the (FC) curve increases when temperature decreases below $N\acute{e}el$ temperature . It has a maximum at the same temperature $T^*<T_N$ as the ZFC magnetization, and a minimum at $T_1^*<T^*$. Below $T_1^*$ the magnetization increases monotonically when temperature approaches zero.
The experiments with samples cooled in field (FC magnetization) provide a new opportunity to clarify the magnetism of the manganese vanadium oxide spinel. The applied field is antiparallel with vanadium magnetic moment and strongly effect it. On the other hand, the experiments show that there is no difference between ZFC and FC magnetization curves when the temperature runs over the interval ($T^*,T_N$) \cite{vanadium2,vanadium3}. They begin to diverge when the temperature is below $T^*$. This is in accordance with the theoretical prediction that the vanadium magnetic moment does not contribute the magnetization when $T>T^*$ and $T^*$ is the temperature at which the vanadium ions start to contribute the magnetization of the system.
Because of the strong field, the two vanadium bands are split and the magnetic moment of one of the $t_{2g}$ electrons is reoriented to be parallel with the field and magnetic order of the $Mn$ electrons. The description of this case is more complicate and requires three magnetic orders to be involved. When $T^*<T<T_N$ only $Mn$ ions have non zero spontaneous magnetization. At $T^*$ vanadium magnetic order antiparallel to the magnetic order of $Mn$ sets in and partially compensates it. Below $T_1^*$ the reoriented electron gives contribution, which explains the increasing of the magnetization of the system when the temperature approaches zero. A series of experiments with different applied field could be decisive for the confirmation or rejection of the $T^*$ transition. Increasing the applied field one expects increasing of $T^*_1$ and when the field is strong enough, so that all vanadium electrons are reoriented, an anomalous increasing of magnetization below $T^{*}$ would be obtained as within the ferromagnetic
phase of $UGe_2$ \cite{2fmp6}.
\section{\bf Summary}
In summary, I have worked out a renormalized spin-wave theory and its extension to describe the two phases $(0,T^*)$ and $(T^*,T_N)$ of a two sublattice ferrimagnet. Comparing the figure 4 in the present paper and figure 4 in \cite{Karchev08b} and figure 8 in the present paper and figure 5 in \cite{Karchev08b} one becomes aware of the relevance of the present calculations for the accurate reproduction of the basic features of the system near the characteristic temperatures $T_N$ and $T^*$.
The present theory of ferrimagnetism permits to consider more complicate systems such as $CeCrSb_3$ compound \cite{Jackson1} or the spinel $Fe_3O_4$ which are two sublattice ferrimagnets but with three spins.
\section{Acknowledgments}
This work was partly supported by a Grant-in-Aid DO02-264/18.12.08 from NSF-Bulgaria.
\begin{appendix}
\section{}
To make more transparent the derivation of the equations for the Hartree-Fock parameters Eq.(\ref{rsw14}) I consider the first term (the sublattice $A$ term) in the Hamiltonian of the magnon-magnon interaction Eq.(\ref{rsw6}). To write this term in the Hartree-Fock approximation one represents the product of two Bose operators in the form
\begin{equation}\label{App1}
a^+_i a_j\,=\,a^+_i a_j\,-\,<a^+_i a_j>\,+\,<a^+_i a_j> \end{equation} and neglects all terms $(a^+_i a_j\,-\,<a^+_i a_j>)^2$ in the four magnon interaction Hamiltonian. The result is
\begin{eqnarray}\label{App2}
\frac 12 a^+_i a_j a^+_i a_i&\approx&-<a^+_i a_{j}><a^+_i a_i> \nonumber \\& + & <a^+_i a_{j}> a^+_i a_i+a^+_ia_{j}<a^+_i a_i> \nonumber \\
\frac 12 a^+_{j} a_i a^+_{j} a_{j} &\approx & -<a^+_{j} a_i><a^+_{j} a_{j}> \nonumber \\ & + & <a^+_{j} a_i> a^+_{j} a_{j}+a^+_{j} a_i <a^+_{j} a_{j}> \nonumber \\
\frac 12 a^+_{j} a_j a^+_i a_{j} &\approx & -<a^+_{j} a_{j}><a^+_i a_{j}> \\ & + & <a^+_{j} a_{j}>a^+_i a_{j}+a^+_{j} a_{j}<a^+_r a_{j}> \nonumber\\
a^+_i a_i a^+_{j} a_{j} &\approx & -<a^+_i a_i>< a^+_{j} a_{j}> \nonumber \\ & + & <a^+_i a_i> a^+_{j} a_{j}+a^+_i a_i <a^+_{j} a_{j}> \nonumber \\
&-& <a^+_i a_{j}>< a^+_{j} a_i> \nonumber \\ & + & <a^+ _i a_{j}> a^+_{j} a_i+a^+_{j} a_i <a^+_i a_{j}> \nonumber
\end{eqnarray}
The Hartree-Fock approximation of the sublattice $A$ part of the Hamiltonian of magnon-magnon interaction reads
\begin{eqnarray}\label{App3}
& & \frac 14 J_1 \sum\limits_{\ll ij \gg _A }\left[a^+_i a^+_j( a_i-a_j)^2 + (a^+_i- a^+_j)^2 a_i a_j\right] \nonumber\\ & \approx & 12NJ_1 s_1^2 \left(u_1-1\right)^2 \\
& + & J_1 s_1 \left(u_1-1\right)\sum\limits_{\ll ij \gg _A }\left( a^+_i a_i\,+\,a^+_{j} a_{j}\,-\,a^+_{j} a_i\,-\,a^+_i a_{j}\right) \nonumber \end{eqnarray}
where the Hartree-Fock parameter $u_1$ is defined by the equation
\begin{equation}\label{App4}
u_1\,=\,1\,-\,\frac {1}{6 s_1}\frac 1 N \sum\limits_{k\in B_r}e_k <a^+_k a_k> \end{equation}
Combining the sublattice $A$ part of the Hamiltonian Eq.(\ref{rsw5}) (the first term) and Eq.(\ref{App3}) one obtaines the Hartree-Fock approximation for the sublattice $A$ part of the Hamiltonian
\begin{eqnarray}\label{App5}
H^A & \approx & 12NJ_1 s_1^2 \left(u_1-1\right)^2 \\
& + & J_1 s_1 u_1 \sum\limits_{\ll ij \gg _A }\left( a^+_i a_i\,+\,a^+_{j} a_{j}\,-\,a^+_{j} a_i\,-\,a^+_i a_{j}\right) \nonumber \end{eqnarray}
In the same way one obtains the Hartree-Fock approximation of the sublattice $B$ and inter sublattices parts of the Hamiltonian. The result is the $H_{HF}$ Hamiltonian Eqs.(\ref{rsw7},\ref{rsw8},\ref{rsw9}).
To calculate the thermal average $ <a^+_k a_k>$, in the Eq.(\ref{App4}), one utilizes the Hamiltonian $H_{HF}$. Therefor, the matrix element depends on the Hartree-Fock parameters, and equation (\ref{App4}) is one of the self consistent equations for these parameters.
The matrix element can be represented in terms of $\alpha_k (\alpha_k^+)$ and $\beta_k (\beta_k^+)$ Eq.(\ref{rsw12a})
\begin{equation}\label{App6}
<a^+_k a_k>\,=\,u_k^2 \,n_k^{\alpha}\, +\, v_k^2\, n_k^{\beta}\, +\, v_k^2 \end{equation}
where $n_k^{\alpha}=<\alpha_k^+\alpha_k>,\,n_k^{\beta}=<\beta_k^+\beta_k>$ are the Bose functions of $\alpha$ and $\beta$ excitations.
Substituting the thermal average in Eq.(\ref{App4}) with Eq.(\ref{App6}), one obtains that equation (\ref{App4}) is exactly the first equation of the system Eq.(\ref{rsw14}) which in turn is obtained from the first of the equations (\ref{rsw13}).
\end{appendix}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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\section{Introduction}\label{sec:introduction}
Traffic on the road networks of urban areas is continuously increasing.
Municipalities can act on the infrastructure to keep high mobility standards,
modifying it to avoid congestion and ensure reliability. Therefore, there is an
urge to provide decision-makers with tools to make informed decisions. For
this purpose, traffic simulation software has been developed to assess different
planning scenarios. To use these simulators, the \emph{network supply}, and the
\emph{travel demand} must be known with some certainty. The network supply is,
in general, defined as the maximum number of vehicles the network road
infrastructure can handle at a given time. In contrast, the demand can
generally be said to be the number of vehicles that would like to travel on the
network at a given time.
The network supply and travel demand interact dynamically, i.e., the users
travel in their vehicles from one location to another on the network and
interact with each other and with the road infrastructure. However, congestion
may occur, and users might change their decisions and re-distribute on the
network. If the demand and the network supply are known, it can be possible to
obtain accurate distributions of users on the given network by calculating an
equilibrium situation corresponding to solving a \emph{Dynamic Traffic
Assignment (DTA)} problem. Then, by varying the network supply, one can analyze
different scenarios to address a network design task. Consequently, if the
demand in a particular traffic network is unknown, it is desirable to estimate
it.
Travel demand can be modeled in many different ways but is commonly modeled
using \emph{dynamic Origin-Destination (OD) matrices}. These matrices describe
the aggregate demand pattern changing over time (dynamic) in a set of time
intervals of a much larger analysis period. Due to their simplicity and
conciseness, these dynamic OD matrices are usually the required input of many
traffic simulation software packages. Because of this, the problem of trying to
estimate dynamic OD matrices has gained a lot of attention from researchers in
recent years.
The problem of estimating dynamic OD matrices is usually referred to as the
\emph{Dynamic OD Estimation (DODE)} problem in the literature. Different
formulations exist, but it is commonly formulated as a bi-level optimization
problem consisting of an inner and an outer optimization problem. A proposed
dynamic OD matrix is given as input to the inner problem, and a DTA problem is
solved. The result is a routing of the users in the network between origins and
destinations at every time interval. In the outer optimization problem, the
dynamic OD matrices are adjusted to minimize the discrepancy between the routing
returned by the solution of the inner problem and the one observed in real-life,
i.e., the number of vehicles that transited in every time interval on every road
of the network as measured by sensors. The observed routing is usually expressed
in terms of the number of vehicles, average speeds, densities, etc., that have
been captured by sensors located along roads in the traffic network under
investigation. However, other kinds of traffic observations can also be included
(e.g., travel times, intersection turning ratios, etc.). This information is
assumed to be directly related to the unknown travel demand and can guide the
retrieval of such a demand. In other words, the DODE problem can be summarized
as the problem of finding the dynamic OD matrices that, when assigned to the
traffic network as vehicles traveling between origins and destinations,
reproduce the traffic measurements captured by sensors in the network. In
addition to this, the dynamic OD matrices should be close to some hypothesized
ones that can be determined, e.g., by the number of people living in the zones
that are considered as origins and destinations.
Solving bi-level optimization problems is quite challenging, as the inner
problem constrains the outer problem, i.e., only an optimal solution to the
inner problem is a feasible solution to the outer problem. To overcome this
challenge, it is crucial to design solution approaches that are efficient and
able to produce good and reliable solutions in a reasonable amount of time. As
such, much of the recent research on the DODE problem tries to include and
leverage additional input data or problem-specific knowledge to improve the
efficiency of the applied algorithms.
The DODE problem is solved frequently for a certain geographical area
of study and traffic network whenever a more up-to-date demand estimate
is needed. If the general structure of the traffic network and the possible OD
pairs within the area of study remain the same over a reasonable amount of time,
the input data in the form of recent traffic observations is the only component
of the DODE problem that changes from one optimization task to another. The
solution approaches that apply sequential optimization algorithms to solve the
DODE problem imply performing many DTAs in each separate optimization task,
essentially starting from scratch every time a new demand estimate is
needed. In a single optimization task, vast computational resources are spent on
performing the DTAs, and each DTA produces valuable information. This
information is usually discarded and not used in subsequent optimization tasks,
primarily due to the inherent sequential nature of some of the applied solution
approaches. In this context, an ML approach becomes appealing as it allows
leveraging data produced by many DTAs.
Therefore, we study an approach to bypass the computationally costly and
time-consuming computations performed in the solution of the inner optimization
problem by learning a model for the input-output relationship established by
solving this inner problem.
To benchmark the ML approaches, we compare them combined with classical
gradient-based approaches. In addition, we provide an analysis of the advantages
and disadvantages of these approaches.
Our work provides the following contributions: We design a possible way to use
ML in the solution of the DODE problem by learning a model for the inner problem
and reducing its computational cost. Further, we perform a fair computational
comparison under a controlled scenario, carefully designed and synthetically
generated, of two state-of-the-art methods and our new ML approach.
Finally, we provide an analysis of the advantages and disadvantages of the
different approaches and indications about the contexts in which they could be
performing the best.
All methods are here reimplemented and share the same subroutines. We use the
well-established, open-source traffic simulator SUMO \citep{sumo2018} to perform
the DTA in the inner optimization problem. As such, the DTA performed by SUMO
will be regarded as a black-box function that assigns to a given input dynamic
OD matrix a set of path flows in the network according to a certain equilibrium
criterion called a Stochastic User Equilibrium (SUE). This equilibrium criterion
is described in more detail in Section~\ref{sec:problem_statement}.
The rest of the chapter is outlined as follows. First,
Section~\ref{sec:literature_review} gives a general overview of the existing
literature on the DODE problem. Then, Section~\ref{sec:problem_statement}
introduces notation and the traditional (continuous) bi-level optimization
formulation of the DODE problem that we will use in the subsequent sections. In
Section~\ref{sec:solution_approaches}, we describe the approaches considered in
the study, and in Section~\ref{sec:experimental_setup}, the irregular grid
network and the synthetic problem data that we used for our experiments. Next,
the results are presented in Section~\ref{sec:results}. The best method turns
out to be a gradient-based approach with assignment matrix modeling, while the
ML approach shows inferior performance. Finally, we conclude with a discussion
of the results in Section~\ref{sec:conclusion}.
\section{Literature Review} \label{sec:literature_review}
In the classical static OD estimation problem, static OD trips are considered.
The problem is to estimate the demand in a single time interval (a single
OD matrix is estimated). On the other hand, time-dependent OD trips are
considered in the DODE problem, and the demand can vary in the different
time intervals (i.e., time-dependent OD matrices are estimated).
The static OD matrix estimation problem has a long history, and a large body of
literature on this problem is available. The ideas and insights that have been
gained through studying the static problem are also extended and applied to the
dynamic problem. For an overview of the different classical solution approaches
to the static problem, see \cite{abr1998, mar2009, ber2009}. On the other hand,
the most recent and extensive literature review on the dynamic problem is
provided in \cite{omr2012, dju2014}. In contrast, a literature review on much
earlier work is provided in \cite{bal2006}. For a more general overview of the
DODE problem and the different modeling components and decisions that have to be
considered when solving this problem, we refer the reader to \cite{lin2003,
ber2009}. Finally, an overview of related and relevant problems is provided in
\cite{ant2016}.
Most of the solution approaches to the DODE problem described in the literature
can be divided into two broad classes: DTA-based and non-DTA-based approaches. A
DTA-based approach is usually used in congested networks where the path choices
of the users of the network and the road-use patterns are of interest. DTA-based
approaches provide a sound way to consider behavioral factors that affect travel
decisions but are more computationally demanding than non-DTA-based approaches.
Contrary to this, in a non-DTA-based approach, vehicles are assumed to take the
shortest path, which is usually also the one that minimizes the travel time. In
this case, if the users of the traffic network are assumed to be able to take
the shortest path, then to solve the DODE problem, a non-DTA-based approach is
usually sufficient. Therefore, we focus on the literature concerned with
DTA-based solution approaches with this distinction in mind.
Usually, solution approaches to the outer problem of the bi-level formulation of
the DODE problem consider the problem of minimizing the discrepancy between the
quantities determined by a DTA solution and the corresponding observed
quantities given as input. The problem is treated as a continuous optimization
problem, and general-purpose optimization algorithms from local and global
optimization are used. The main advantage of general-purpose algorithms is that
they do not require exact knowledge of the functional relationship of the
variables to be estimated. The drawback is that these algorithms are usually
inefficient in their original form if the different algorithm components and
parameters are not adapted and tuned to the problem at hand. The general-purpose
algorithms applied to the DODE problem can be categorized as either
\emph{gradient-based} or \emph{derivative-free} optimization algorithms.
Gradient-based algorithms are iterative procedures that adjust estimates based
on the information provided by the gradient and possibly higher-order
derivatives. This is not the case for derivative-free algorithms (e.g.,
simulated annealing, evolutionary algorithms, and sampling-based algorithms,
such as the Nelder-Mead algorithm) that usually rely solely on Objective
Function (OF) evaluations.
We can further identify \emph{assignment matrix-based} or \emph{assignment
matrix-free} approaches within the class of gradient-based algorithms. The
distinction can be made based on whether an Assignment Matrix (AM) is used as a
part of the applied optimization algorithm or not. An AM summarizes the result
of a DTA and consists of elements that describe the utilization of the roads in
the traffic network with respect to the number of users that travel between
origins and destinations within a certain time period. This means that the AM
varies as a function of the travel demands. The solution approaches to the DODE
problem that uses gradients and AMs exploit that it can be possible to
analytically derive the exact gradient from a functional relationship between
the variables through the AM. On the other hand, a gradient-based but AM-free
approach primarily uses finite difference approximations of the gradient, which
are established through OF evaluations.
The most recent studies that adopt a gradient and AM-based approach are given in
\cite{ber2009, tol2013, fred2013, dju2017, sha2017, mas2018}. These studies
primarily focus on improving the efficiency of the applied algorithms by better
modeling the functional relationship between the variables that are to be
estimated. A common theme for the gradient and AM-based approaches is that count
observations are the only type of traffic observations usually given as input to
the optimization problem. The modeling of the relationship between the variables
to be estimated can be done through the AM. However, using this type of approach
limits the type of observations that can be accommodated in the optimization
problem. For example, the functional relationship between demands and
count observations can easily be established if a proportional relationship
between these variables is assumed (see Eq.\ref{eqn:assignmat_relation}).
However, for other types of observations, it can be harder and more cumbersome
to determine appropriate relationships between the variables to be estimated.
Gradient and AM-free approaches have also gained considerable attention in the
literature. Several researchers have especially been interested in studying and
applying different variations of the Stochastic Perturbation Simultaneous
Approximation (SPSA) algorithm by Spall \citep{spall1998}, tailoring it to the
DODE problem. This algorithm only relies on OF evaluations with no need for an
explicit characterization of the relationship between the variables to be
estimated. In each iteration of the SPSA algorithm, OF evaluations are used to
approximate the gradient. This approach makes it possible to include other types
of traffic observations besides count observations, and it has therefore been
the predominant approach in these cases \citep{vaz2009, cip2011, tym2015,
ant2015, lu2015, car2017}. Just like most gradient-based optimization
algorithms, the performance of the SPSA algorithm is sensitive to (i) the tuning
of algorithm parameters, (ii) the possibly very different magnitudes of the
variables to be estimated, and (iii) the OF shape. Different enhancements to the
SPSA algorithm in the mentioned references thus have also been focused on
components that address these points to improve the stability and robustness of
the algorithm when applied to the DODE problem.
A \emph{surrogate model} can be estimated based on empirical data if a model for
the OF is not available through theoretical argumentation. Gradient-based or
derivative-free methods can then be applied using the surrogate model.
In \cite{bal2006}, a model-based and derivative-free method is compared against
the SPSA algorithm. Response surface techniques are used to model the OF
by low order polynomials fitted locally to the values in correspondence of
sample points of the search space. The author applies a Stable Noisy
Optimization by Branch and Fit (SNOBFIT) algorithm that uses a derivative-free
Box-Complex algorithm. The Box-Complex algorithm is a direct search and
sampling-based method that extends the well-known Nelder-Mead algorithm. The
Box-Complex and SNOBFIT algorithm performed worse in efficacy and scalability
than the SPSA algorithm.
Generally, the derivative-free solution algorithms require a high number of OF
evaluations to obtain results comparable to the gradient-based solution
algorithms \citep{char2017}.
A promising line of research is provided in \cite{oso2019}, which describes a
surrogate model-based approach that relies on fitting simplified analytical
models to the underlying simulation and DTA model resulting in a system of
equations that can be solved efficiently by standard system of equations
solvers. The approach thus obtains good computational results under tight
computational budgets. The surrogate model-based approach is compared against
the SPSA and a derivative-free pattern search algorithm. The approach performs
well, while the pattern search algorithm and the SPSA algorithm perform poorly
in comparison.
Our work contributes to this thread of research by studying ML approaches to
determine surrogate models as an alternative to response surface techniques
\cite{bal2006} and the surrogate model-based approach proposed in
\cite{oso2019}.
Fewer studies can be found where model-free (and hence derivative-free)
algorithms have been applied to the DODE problem. These algorithms only rely on
OF evaluations and exhibit the advantage that they can be
distributed and parallelized, as they allow independent OF
evaluations. Evolutionary algorithms have been the most popular among
derivative-free optimization algorithms. Notably, in \cite{kat2006}, an
evolutionary algorithm was applied in a setting with distributed and parallel
computing. Other studies that apply evolutionary algorithms can be found in
\cite{vaz2009,omr2014}, while \cite{tse2007} also use an evolutionary algorithm,
but in a non-DTA based approach. However, in \cite{vaz2009}, the evolutionary
algorithm was shown to perform worse than the SPSA algorithm.
Two variants of DODE problems are usually addressed in the literature. Their
offline or online setting characterizes them. In an offline setting, historical
data is used to estimate the network-wide demand, such that long-term
predictions of future traffic conditions can be made. This is especially
beneficial to decision-makers. It enables them to evaluate different planning
scenarios and make informed decisions when proposed changes to infrastructure
and facilities are made. Offline demand estimation procedures are usually
applied in network-wide studies, so the computational cost can be considerably
high in this setting. In an online setting, real-time traffic data is used and
historical data to estimate the current level of demand such that short-term
predictions of future traffic conditions can be made. This primarily benefits
real-time traffic control and path-guidance systems. Online demand estimation
procedures are usually applied on smaller traffic networks or locally, e.g., at
intersections, where traffic patterns are identified, such that adaptive traffic
control strategies can be used. For references on work that studies the online
DODE problem, we refer the reader to \cite{ash2000, ant2009, omr2012}. In this
work, we focus on the offline, DTA-based, bi-level formulation of the DODE
problem.
\section{Notation and Problem Statement} \label{sec:problem_statement}
A traffic network can be defined as a directed graph $G = \left(N, A\right)$
consisting of a set of nodes $N$ and a set of arcs $A$. Each node in the network
represents a junction or an origin/destination point, while arcs represent
roads. The arcs are directed, which means that the traffic between two nodes can
be uni-directional and one-way roads are possible. The arcs in the network have
additional attributes that generally indicate how much and how well the roads in
the network can handle traffic. Some examples of essential arc attributes
are the number of lanes, the length $\left(\textnormal{kilometer}\right)$ and a
free-flow speed
$\left(\nicefrac{\textnormal{kilometer}}{\textnormal{hour}}\right)$ that is the
maximum allowed speed a vehicle can travel with on an uncongested road.
Additionally, geographical information can be added to the arcs and nodes to
indicate their physical location and shape.
A subset of the nodes $N$ in a traffic network can be identified as possible
origins and/or destinations. More precisely, we let $O \subseteq N$ be a set of
origins and $D \subseteq N$ a set of destinations, where it is usually the case
that $D \cap O \ne \emptyset$, i.e., it is possible for a node to be an origin
and a destination simultaneously. A \emph{trip} is the movement of a vehicle
from one location to another. More precisely, a trip departs from an origin $i
\in O$ and terminates at a destination $j \in D$. In this case, we associate the
trip with an OD $w = (i, j) \in W = O \times D$. Here $W$ is the set of
all OD pairs with size $\left|W\right| = m$, and it is assumed
that no trip departs and arrives in the same location, i.e., the OD pairs are
defined such that $i \neq j$ for all $w = (i, j) \in W$. Finally, a subset of
the arcs in the network $G$ is assumed to be equipped with sensors defined by
the set $Q = \left\{1, \hdots, n_Q\right\} \subseteq A$.
To define the quantities of interest in the DODE problem, we introduce an
analysis period $T = \left[0, t_{\textnormal{end}}\right)$ discretized into a
set of $n_S$ subintervals $\left\{[0, t_1), [t_1, t_2), \dots, [t_{n_S - 1},
t_{n_S} = t_{\textnormal{end}})\right\}$ of equal duration. For the sake of
convenience, we identify these intervals by the indices in the set $S =
\left\{1,\hdots, n_S\right\}$. These indices define the time intervals in which
we want to estimate the demands for each of the $m$ OD pairs. The estimation of
the demands is then based on the arc count observations made within these time
intervals.
The quantities of interest are usually referred to as being arranged in
matrices. Here, however, we will arrange these quantities in vectors. In other
words, we flatten or vectorize the matrices, i.e., given a matrix $\mathbf{A}
\in \mathbb{R}_{+}^{p_1 \times p_2}$, we concatenate consecutive rows of the
matrix in a column vector ($\mathbb{R}^{p_1 \times p_2} \rightarrow
\mathbb{R}^{p_1 \cdot p_2}$):
\begin{align}
\textnormal{vec}(\mathbf{A}) = \mathbf{a} = \left[a_{11},\dots, a_{p_11},\dots, a_{12}, \dots, a_{p_1 2}, \dots, a_{p_1 p_2}\right]^\top \in \mathbb{R}^{p_1 \cdot p_2 }.
\end{align}
The quantities of interest can then be described in terms of the following
vectors:
\begin{itemize}
\item $\mathbf{x}, \tilde{\mathbf{x}} \in \mathbb{R}_{+}^{m \cdot n_S}$ are
the vectors of \emph{estimated demands} and \emph{seed demands},
respectively. Each element of these vectors ${x}_{ws}$ or $\tilde{x}_{ws}$
is associated with an OD pair $w \in W$ and a time interval $s \in S$. The
vector $\mathbf{x}$ of estimated demands contains the estimate of the number
of trips made for each OD pair in each of the time intervals. The vector
$\tilde{\mathbf{x}}$ of seed demands defines the prior knowledge of the
number of trips made for each OD pair in each time interval. This prior
knowledge is usually assumed to have been obtained from a previous demand
study, e.g., from a population survey. Note that we model discrete values as
real numbers. We thus define the continuous relaxation of a discrete
optimization problem.
\item $\mathbf{x}^{\text{Lower}}, \mathbf{x}^{\text{Upper}} \in
\mathbb{R}_{+}^{m \cdot n_S}$ are the vectors of lower and upper bounds on
the estimated demands, respectively. These upper and lower bounds define the
\emph{search space}.
\item $\mathbf{c}, \hat{\mathbf{c}} \in \mathbb{Z}_{+}^{n_Q \cdot n_S}$ are
the vectors of estimated and observed arc counts, respectively. Each element
of these vectors $c_{qs}$ or $\hat{c}_{qs}$ is associated with a sensor $q
\in Q$ and a time interval $s \in S$.
\end{itemize}
The outer optimization problem of the bi-level formulation of the DODE problem
can now be defined as:
\begin{align}
\min\;\;& F(\mathbf{x}, \tilde{\mathbf{x}}, \mathbf{c}(\mathbf{x}), \hat{\mathbf{c}})
\label{eqn:1_estimation_problem} \\
\textrm{subject to } \;\; & \mathbf{x}^{\text{Lower}} \leq \mathbf{x} \leq \mathbf{x}^{\text{Upper}}
\label{eqn:2_estimation_problem}
\end{align}
The solution of this problem, $\mathbf{x}^*$, is the demand estimate that
results from minimizing the OF $F$, which we define as the
weighted sum of the measures of discrepancy between the estimated quantities and
their corresponding observed or a priori values:
\begin{align}
F(\mathbf{x}, \tilde{\mathbf{x}}, \mathbf{c}(\mathbf{x}), \hat{\mathbf{c}}) = \omega_1 \cdot f^{(1)}(\mathbf{x}, \tilde{\mathbf{x}}) + \omega_2 \cdot f^{(2)}(\mathbf{c}(\mathbf{x}), \hat{\mathbf{c}}), \quad \omega_1,\omega_2\in \mathbb{R}_+.
\label{eqn:objective_function}
\end{align}
In our specific case, the discrepancy $f^{(1)}$ is measured between the
estimated demands $\mathbf{x}$ and a priori known demands
$\tilde{\mathbf{x}}$ and the discrepancy $f^{(2)}$ between the estimated arc
counts $\mathbf{c}(\mathbf{x})$ and the observed arc counts $\hat{\mathbf{c}}$.
Note that in a more general setting, the OF may consist of
several additional terms $f^{(3)}, f^{(4)}, \dots$ with respective weights
$\omega_3, \omega_4, \dots$ that consider additional available information, such
as arc speed, density, travel times, turning ratios, etc., that can be included
to improve the guidance of the search process.
An inner optimization problem must be solved to evaluate the OF in
Eq.~\eqref{eqn:1_estimation_problem} for a proposed vector $\mathbf{x}$ of
demands to find a corresponding vector $\mathbf{c}(\mathbf{x})$ of arc counts.
The inner optimization problem takes the form of a DTA problem. The task is to
determine the routing of users between origins and destinations according to a
particular assignment principle. The users of the traffic network are assumed to
make decisions per the criterion specified by the assignment principle. Two
examples of assignment principles that are widely used and studied within the
area of transportation research are (i) the User Equilibrium (UE) principle
(Wardrop's first principle \citep{fri2016}), which states that each user makes
decisions that minimize their own individual travel time, and (ii) the System
Optimum (SO) principle (Wardrop's second principle \citep{fri2016}), which
states that users make joint decisions to minimize the total system travel time.
DTA models adopt an assignment principle and incorporate several different
travel choice components to reflect the travel choices a user of an actual
traffic network might face when wanting to travel between an origin and a
destination. Travel choices that are possible to model and include in a DTA
model are, among others: path choice, departure time choice, mode choice, and
destination choice, to name a few. However, in the context of the DODE problem,
a simple DTA model that only incorporates path and departure time choice
components is usually used, meaning path and departure time choices are
endogenous to the DTA model, while other travel choice components are exogenous
or fixed.
To obtain accurate travel times between origins and destinations, a DTA model
relies on an underlying traffic flow model, i.e., detailed traffic flow models
are used by DTA models to explicitly propagate vehicles from one arc to another
while considering space constraints. In other words, queuing and congestion are
modeled, and the effects of these phenomena are reflected in the travel time.
For a good introduction and a general overview of the DTA problem, we refer the
reader to \cite{peeta2001}, as we only give a brief description here.
Two traffic flow models are implemented in SUMO and can be used in conjunction
with a DTA: a \emph{mesoscopic} and a \emph{microscopic}. These two types of
traffic flow models differ in the level of detail in which they model traffic
flow dynamics. In the mesoscopic model, the arcs in a traffic network are
modeled as discrete queues through which vehicles are propagated. Further, a
coarser model for intersections and lane-changing is used \citep{sumo_meso}. On
the other hand, in the microscopic model, detailed quantities such as position,
speed, acceleration, and braking distance are considered in the propagation of
vehicles on an arc.
The mesoscopic model is computationally cheaper to solve and can provide the
necessary data to a sufficient degree of detail needed in the estimation
problem. Therefore, we choose that model.
A DTA can be obtained heuristically through an iterative simulation process
using the mesoscopic traffic flow model implemented in SUMO. At the end of the
iterative process, a stationary distribution of the path choice decisions of the
users of the traffic network respects an assignment principle. This assignment
principle is the Stochastic User Equilibrium (SUE) in SUMO. The SUE assignment
principle extends the UE assignment principle, where stochastic elements have
been incorporated into the DTA model. This form of UE assignment is regarded as
the more realistic, as uncertainty is incorporated in the assignment model to
take into account the uncertainty of the users' knowledge about network
conditions. Contrary to the UE assignment principle, which is defined in terms
of \emph{actual} travel times, the SUE assignment principle is instead defined
in terms of \emph{perceived} travel times.
The iterative method used by SUMO to determine a DTA that respects the SUE
assignment principle is described in \cite{gaw1998}. This method determines the
probabilities of choosing between path alternatives for each user who wants to
travel between an origin and destination at a certain time. In brief, the path
choice probabilities are determined based on (i) the arc travel times
experienced in the previous iteration, (ii) the sum of arc travel times along
different least-cost paths (these paths constitute a set of alternatives to a
user), and (iii) the previous probabilities of choosing the paths. These
quantities are used to obtain new estimates of the path choice probabilities at
each iteration. Finally, we note that the least-cost paths are computed
in parallel in SUMO by a time-dependent version of Dijkstra's algorithm,
while a single traffic simulation is single-threaded and sequential.
Note that we modeled demands $\mathbf{x}$ as continuous variables while
the mesoscopic simulator implemented by SUMO solves a discrete optimization
problem. When the demands are given to SUMO as input, they are rounded to
the nearest integer values. In all other cases, the demands are handled
as being continuous, which allows us to apply continuous optimization algorithms
in the outer-level problem.
For our purposes here, the DTA performed by SUMO can conveniently be defined by
the function:
\begin{align} \label{eqn:sumo_dta_map}
\Gamma: \mathbb{R}_{+}^{m \cdot n_S} \rightarrow \mathbb{Z}_{+}^{n_Q \cdot n_S}.
\end{align}
This function maps demands $\mathbf{x}$ to arc counts through a DTA, i.e.,
$\mathbf{x} \mapsto \Gamma(\mathbf{\mathbf{x}}) = \mathbf{c}(\mathbf{x})$. The
arc counts $\mathbf{c}(\mathbf{x})$, together with the corresponding input
demands $\mathbf{x}$, can then be used in the OF in
Eq.~\eqref{eqn:objective_function} to determine the quality of the current
demand estimate.
Eq.~\eqref{eqn:2_estimation_problem} defines upper and lower bounds on the
demands. These are usually supplied to avoid a situation where an unrealistic
high amount of demand is loaded on the traffic network, exceeding the network's
capacity. In a realistic setting, the bounds on the demands are usually
determined based on population survey data and experimental results from
previous studies.
In the remaining part of this work, we use the shorthand notation
$F(\mathbf{x})$ for the OF defined in Eq.~\eqref{eqn:objective_function}, as
$\tilde{\mathbf{x}}$ and $\hat{\mathbf{c}}$ are given and
$\mathbf{c}(\mathbf{x})$ is derived from $\mathbf{x}$.
\section{Solution Approaches} \label{sec:solution_approaches}
Different definitions of the discrepancy between observed and estimated
quantities in the OF $F$ are possible. Drawing on the knowledge obtained in
\cite{cip2011} and \cite{ant2016}, we use an OF that penalizes large errors
between observed and estimated quantities and that weights the different terms
evenly, i.e., we take into account that the different quantities $f^{(1)}$ and
$f^{(2)}$ that enter into the OF can have different magnitudes and hence
normalize their values. Thus, we define the terms $f^{(1)}$ and $f^{(2)}$ used
in the OF $F$ in the following functional form:
\begin{align}
f^{(1)}(\mathbf{x}, \tilde{\mathbf{x}}) =
\frac{
\sqrt{
\sum\limits_{ \substack{w \in W \\ s \in S} } \left(x_{ws} - \tilde{x}_{ws}\right)^2
}
}
{
\sqrt{\sum\limits_{ \substack{w \in W \\ s \in S} } \tilde{x}_{ws}^2}
}
\;\; \textnormal{and}\;\;
f^{(2)}(\mathbf{c}(\mathbf{x}), \hat{\mathbf{c}}) =
\frac{
\sqrt{
\sum\limits_{ \substack{q \in Q \\ s \in S} } \left(c_{qs} - \hat{c}_{qs}\right)^2
}
}
{
\sqrt{\sum\limits_{ \substack{q \in Q \\ s \in S} } \hat{c}_{qs}^2}
}.
\label{eqn:objective_function_terms}
\end{align}
To further limit the search space, we introduce generation constraints
\citep{ant2016} that set an upper bound on the number of outbound trips from an
origin. we let $o_i$ denote the maximum number of vehicles that can leave
origin $i \in O$ and enforce that:
\begin{align}
\sum_{\substack{j \in D, \; w = (i, j) \in W \\ s \in S}} x_{ws} \leq o_i \quad \forall i \in O.
\label{eqn:generation_constraints}
\end{align}
This type of constraint can easily be incorporated into the problem formulation
as it is typically the case that data for the values of $o_i$, $i\in O$ are
readily available and highly reliable, e.g., from survey data or population
density statistics. Other possible constraints are also mentioned in
\cite{ant2016}, such as trip distribution constraints or attraction constraints
that, contrary to the generation constraints, limit the number of trips that can
arrive at a certain destination. However, data pertaining to these constraints
might be harder to provide and will thus not be considered in this study.
The algorithms that follow are iterative algorithms. We define an iteration
index $\tau \in \left\{0, \hdots, \tau_{\textnormal{max}}\right\}$ where
$\tau_{\textnormal{max}}$ is the maximum number of iterations of an algorithm.
We thus let $\mathbf{x}_{\tau}$ define the estimate at iteration $\tau$.
\subsection{Gradient-based Approaches} \label{subsec:gradient_based_approach}
Gradient-based algorithms for continuous optimization problems
take the general form of an iterative procedure where an incumbent estimate at
iteration $\tau$ is adjusted in such a way that it is moved towards a minimum to
yield the new estimate at iteration $\tau + 1$:
\begin{align}
\mathbf{x}_{\tau+1} = \mathbf{x}_{\tau} + \eta_{\tau} \cdot \mathbf{d}_{\tau}.
\label{eq:adjustment_step}
\end{align}
Here $\eta_{\tau}$ is a scalar value that we will refer to as the
\emph{step rate}, and $\mathbf{d}_{\tau}$ is the \emph{descent
direction}. The descent direction is determined by the gradient
through $\mathbf{d}_{\tau}=-\mathbf{g}_{\tau}$. Different gradient-based
optimization algorithms differ in how the descent direction and the step
rate are chosen. For the DODE problem, it is possible to distinguish
two ways to derive the gradient: AM-based and AM-free.
\subsubsection{An Assignment Matrix-based Approach} \label{sec:assignmat_based_apporach}
Through the use of an AM the gradient of the OF
can be calculated analytically. The (vectorized) AM
$\mathbf{p}_{\tau} = \textnormal{vec}(\mathbf{P}_\tau(\mathbf{x}_{\tau}))$ at an
iteration $\tau$ consists of entries $p_{qrws} \in \left[0, 1\right]$ that
describe the proportion of trips $x_{ws}$ for OD pair $w \in W$ in time interval
$s \in S$ that go through arc $q \in Q$ in time interval $r \in S, \; r \geq s$.
In other words, depending on a number of factors such as the travel time between
origins and destinations and the length of the time intervals $s \in S$, the
traffic present on an arc $a \in A$ may originate from OD trips from several
different OD pairs from the current time interval or several previous time
intervals. Using this knowledge the OD trips can be related to the arc counts
through the linear relation:
\begin{align}
c_{qr} = \sum_{\substack{w \in W \\ s \in S \\ s \leq r}} p_{qrws} \cdot x_{ws}, \qquad \forall q \in Q, r \in S.
\label{eqn:assignmat_relation}
\end{align}
Through the use of the AM it is possible to derive an analytical
expression for the gradient of the OF $F$ at every iteration:
\begin{align}
\frac{\partial F}{\partial \mathbf{x}} &= \omega_1 \cdot \mathbf{g}^{(1)} + \omega_2 \cdot \mathbf{g}^{(2)},
\label{eqn:original_descent_direction}
\end{align}
where the vectors $\mathbf{g}^{(1)}$ and $\mathbf{g}^{(2)}$ are the gradients of
the two terms $f^{(1)}$ and $f^{(2)}$, respectively, whose elements can be
derived to be (see \ref{sec:grad_derivation}):
\begin{align}
g^{(1)}_{ws} = \frac{ \partial f^{(1)} }{ \partial x_{ws} }
=
\frac{
x_{ws} - \tilde{x}_{ws}
}
{
\sqrt{
\sum\limits_{ \substack{w' \in W \\ s' \in S } } \left(x_{w's'} - \tilde{x}_{w's'}\right)^2
} \cdot \sqrt{\sum\limits_{ \substack{w' \in W \\ s' \in S} } \tilde{x}_{w's'}^2}
}, \quad \forall w \in W, s \in S,
\label{eqn:first_grad}\\[2em]
g^{(2)}_{ws} = \frac{ \partial f^{(2)} }{ \partial x_{ws} }
= \frac{
\sum\limits_{ \substack{q' \in Q \\ r' \in S\\ r'\geq s} }
\left(
c_{q'r'}
- \hat{c}_{q'r'}
\right) \cdot p_{q'r'ws}
}
{
\sqrt{
\sum\limits_{ \substack{q' \in Q \\ r' \in S } } \left(c_{q'r'} - \hat{c}_{q'r'}\right)^2
} \cdot \sqrt{\sum\limits_{ \substack{q' \in Q \\ r' \in S} } \hat{c}_{q'r'}}
}, \quad \forall w \in W, s \in S.
\label{eqn:second_grad}
\end{align}
The descent direction in Eq.~\eqref{eq:adjustment_step} is then simply the
negative of the expression in Eq.~\eqref{eqn:original_descent_direction}:
\begin{align}
\mathbf{d}_{\tau} =
- \left(
\omega_1 \cdot \mathbf{g}^{(1)}_\tau + \omega_2 \cdot \mathbf{g}^{(2)}_\tau
\right).
\label{eqn:descent_direction_assignmat_based}
\end{align}
\subsubsection{An Assignment Matrix-free Approach}
\label{sec:assignment_matrix_free}
As mentioned in Section~\ref{sec:literature_review}, most of the studied
gradient-based and AM-free approaches for the DODE problem use the SPSA
algorithm. This algorithm uses the negative of the gradient as a way to obtain a
descent direction in a similar way as the previous approach. As no AM is needed
in the derivation of the gradient of the first OF term $f^{(1)}$, we can simply
use the exact gradient defined in Eq.~\eqref{eqn:first_grad}. However, the
gradient of the second OF term $f^{(2)}$ will have to be approximated because
now no AM is given and no functional relationship between the variables to be
estimated is assumed.
A one-sided finite difference approximation of the gradient is usually used:
\begin{align}
\tilde{\mathbf{g}}^{(2)}_{\tau} = \frac{f^{(2)}(\mathbf{c}(\mathbf{x}_\tau), \hat{\mathbf{c}}) - f^{(2)}(\mathbf{c}^{-}(\mathbf{x}_\tau), \hat{\mathbf{c}})}{b_\tau}
\cdot
\overline{\mathbf{\Delta}}_{\tau}
, \quad \tau \in \left\{0, \dots, \tau_{\textnormal{max}} \right\}.
\label{eqn:grad_approx_1}
\end{align}
Here, $\mathbf{c}(\mathbf{x}_\tau) = \Gamma(\mathbf{x}_{\tau})$, $
\mathbf{c}^{-}(\mathbf{x}_\tau) = \Gamma(\mathbf{x}_{\tau} - b_{\tau} \cdot
\mathbf{\Delta}_\tau)$ and $\mathbf{\Delta}_\tau \; \in \left\{-1, 1\right\}^{m
\cdot n_S}$ is a random perturbation vector, where the entries $\Delta_{ws}, w
\in W, s \in S$ are independent Bernoulli random variables taking the value $\pm
1$ with probability $\nicefrac{1}{2}$. Furthermore, the vector
$\overline{\mathbf{\Delta}}_\tau$ consists of entries
$\nicefrac{1}{\Delta_{ws}}$ and $b_\tau = \nicefrac{b}{\tau^\gamma}$ is defined
with respect to the parameters $b > 0$ and $\gamma > 0$. These parameters and
the Bernoulli distribution are usually chosen because they satisfy certain
conditions \citep{spall1992} that ensure the algorithm to be able to converge to
a minimum, asymptotically. To ensure compatibility with SUMO that only accepts
integer inputs, we keep the perturbation parameter fixed $b_\tau = 1$ throughout
all iterations, which is equivalent to perturbing each element in the demand
vector by $\pm 1$ trip.
\subsubsection{Determining Step Lengths} \label{sec:determine_step_length}
The step length in the descent direction can be chosen appropriately
by solving for $\eta_\tau$ a line search problem in each iteration $\tau$:
\begin{align}
\eta_\tau = \arg \min_{\alpha \geq 0} F\left(\mathbf{x}_{\tau} + \alpha \cdot \mathbf{d}_{\tau}\right).
\label{eqn:line_search}
\end{align}
The goal of the line search is to find the step rate $\alpha$ that minimizes the
OF in the descent direction given by $\mathbf{d}_\tau$. To solve this
sub-problem we use a multiple linear regression approach where a 2nd-degree
polynomial is fitted to sample points evaluated in the descent direction. More
specifically, we first define a single-variable function of the step rate
$\alpha$, as follows:
\begin{align}
y(\alpha) = F\left(\mathbf{x}_{\tau} + \alpha \cdot \mathbf{d}_\tau\right).
\label{eqn:uni_var}
\end{align}
Then, we determine:
\begin{enumerate}
\label{list:ub}
\item An upper bound $\ell$ on $\alpha$ imposed by the generation constraints in
Eq.~\eqref{eqn:generation_constraints}. An algorithmic sketch to
carry out this task is given in
Algorithm~\ref{alg:determine_max_step_length}.
\item A number of equally spaced points $\alpha_{1}, \hdots, \alpha_n, \; n
\geq 2$ to evaluate in the interval $\left[\nicefrac{\ell}{n}, \ell\right]$.
\end{enumerate}
Given these parameters we can obtain sample points with corresponding responses:
\[(\alpha_0, y(\alpha_0)), \hdots, (\alpha_n, y(\alpha_n)).\] The point
$\left(\alpha_0 = 0,\; y(\alpha_{0}) = F\left(\mathbf{x}_{\tau}\right)\right)$
is already known. In this case, by specifying two additional sample points we
are able to uniquely fit a 2nd-degree polynomial. More precisely, an estimator
for the function $y(\alpha)$ in Eq.~\eqref{eqn:uni_var} is:
\begin{align}
\hat{y}(\alpha) = \beta_0 + \beta_1 \cdot \alpha + \beta_2\cdot \alpha^2
\end{align}
where the coefficients $\beta_0, \hdots, \beta_2$ are determined by \emph{least
squares}, given the sample points and corresponding responses. The value
$\alpha_{\textnormal{min}}$ that minimizes this polynomial is given by
$\alpha_{\textnormal{min}} = \frac{-\beta_{1}}{2 \cdot \beta_{2}}$, if $\beta_2
> 0$. Otherwise, $\alpha_{\textnormal{min}}$ is taken to be the step rate that
produced the sample point with the smallest response.
\IncMargin{1em}
\begin{algorithm}[tb]
\small
\newcommand\mycommfont[1]{\ttfamily{#1}}
\SetCommentSty{mycommfont}
\SetAlgoLined\DontPrintSemicolon
\SetKwFunction{proc}{DetermineMaxStepRate}
\SetKwProg{myprocedure}{Procedure}{}{}
\myprocedure{\proc{$\mathbf{x}_{\tau}, \,\mathbf{x}_{l}, \,\mathbf{x}_{u},
\,\mathbf{d}_{\tau}, \,\ell_{\Delta} = 10^{8}, \,\epsilon_1 = 10^{-8}$}}{
$\ell \leftarrow 0$\; \While{\texttt{ true }}{ $\ell \leftarrow \ell +
\ell_{\Delta}$ \;
$\breve{\mathbf{x}} \leftarrow \mathbf{x}_{\tau} + \ell \cdot
\mathbf{d}_{\tau}$\;
\tcp{Apply upper and lower bounds }
$\breve{\mathbf{x}} \leftarrow \texttt{maximum(}\mathbf{x}_{l},
\,\,\breve{\mathbf{x}}\texttt{)}$\; $\breve{\mathbf{x}} \leftarrow
\texttt{minimum(}\mathbf{x}_{u}, \,\,\breve{\mathbf{x}}\texttt{)}$\;
\tcp{Check if generation constraints are violated or whether }
\tcp{all upper or lower bound constraints are binding}
\If{
$
\sum\limits_{\substack{j \in D,\,\, w = (i, j) \in W \\ s \in S}} \breve{x}_{ws} \texttt{ > } o_i \,\, \forall i \in O
\,\,
\vee
$
\mbox{}\phantom{\textbf{if}}
$
(\breve{x}_{ws} \texttt{ == } x^{\textnormal{Lower}}_{ws} \vee \breve{x}_{ws} \texttt{ == } x^{\textnormal{Upper}}_{ws}) \,\, \forall w \in W, s\in S
$
}{ \tcp{Backtrack and try again with a smaller step rate }
$\ell \leftarrow \ell - \ell_{\Delta}$\; $\ell_{\Delta}
\leftarrow \nicefrac{\ell_{\Delta}}{2}$\; \If{$\ell_{\Delta}
\texttt{ < } \epsilon_1$}{ \texttt{break}\; }
} } }
\tcp{Return the largest positive step rate that does not violate any constraints}
\KwRet $\ell$ \;
\caption{Procedure for determining the upper bound on the step rate.}
\label{alg:determine_max_step_length}
\end{algorithm}
\DecMargin{1em}
\subsubsection{Computational Complexity of the Gradient-based Approaches}
If we look at the computational cost associated with the AM-based approach, we
notice that two OF evaluations and thus DTA problems are solved in each
iteration. First, a single DTA is needed to obtain a (vectorized) AM
$\mathbf{p}_{\tau}$ such that the descent direction and two additional points
(using the relation in Eq.~\eqref{eqn:assignmat_relation}) in the descent
direction can be evaluated, and a 2nd-degree polynomial can be fitted. Using the
2nd-degree polynomial, the best step length in the descent direction can be
determined. Then, one additional DTA is solved to evaluate the new point that
has been found by using the best step length that minimizes the OF in the
descent direction.
On the other hand, the AM-free approach needs to solve up to four DTA problems
in each iteration, i.e., one DTA is required to estimate the gradient, and two
additional DTAs are needed for determining the best step length in the descent
direction. As with the AM-based approach, an additional DTA is then necessary to
evaluate a new estimate found.
\subsection{Machine Learning Approaches} \label{subsec:ml_approach}
The DTA performed by SUMO can be regarded as a black-box function that maps
input demands to network-specific quantities, such as arc counts, speeds,
densities, etc. As mentioned in Section~\ref{sec:problem_statement}, we will
focus on the arc counts. In this case, the black-box function representing the
DTA performed by SUMO can be described by Eq.~\eqref{eqn:sumo_dta_map}, a
vector-valued multivariate function that describes the input-output relationship
of the DTA performed by SUMO with respect to the output quantity we are
interested in modeling. The ML approach's main idea is to learn a model of this
input-output relationship.
A dataset is needed to learn a model of the input-output relationship. This
dataset can be obtained through a \emph{sampling strategy}, which is a technique
for deciding how many and which points should be included in a dataset provided
to a \emph{learning algorithm}. Using the dataset, the learning algorithm is
trained in a supervised fashion, which results in a model $\hat{\Gamma}$ for the
relationship in Eq.~\eqref{eqn:sumo_dta_map}. Subsequently, the DODE problem can
be solved using the obtained model as a surrogate for DTA in the OF.
\begin{figure*
\includegraphics[width=\textwidth,keepaspectratio]{Images/sampling_methods.pdf}
\caption{Example of a sampling strategy in the plane that uses a Sobol low-discrepancy sequence.}
\label{fig:sampling_methods}
\end{figure*}
Overall, the ML approach put forth here consists of three primary
components: a sampling strategy, the application of a ML algorithm
and a final application of an optimization algorithm to obtain an approximate
minimum of the DODE problem that is then to be evaluated and returned as a final
estimate. These steps are described in more detail in the following.
\subsubsection{Sampling Strategy}
The sampling strategy should preferably be chosen such that the amount of
information gained from a limited number of sample points is maximal. Sampling
more points than necessary implies additional computational resources and time.
In other words, for the dataset we want to obtain a set of points that are
sampled evenly in the search space. A way to accomplish this is by using
\emph{optimal experimental designs}, which among others include: Box-Behnken,
central composite, factorial designs, and latin hypercube sampling, to name a
few. These sampling strategies are specialized because they are tailored for
fitting specific parametric models (e.g., linear or multiple linear models).
Moreover, they dictate the exact number of samples needed to end up with a set
of sample points that covers the search space well. Consequently, these
strategies are well-suited for fitting models when prior knowledge of the
model's structure is available, and the sampling budget allows for the number of
samples required by the sampling strategy. If this is not the case, an
alternative is to use a strategy that samples points according to a
\emph{low-discrepancy sequence} (also referred to as a quasi-random sequence).
Examples of low-discrepancy sequences include Halton, Hammersley, Niederreiter,
and Sobol (see \cite{par2016} for more theoretical details on low-discrepancy
sequences).
An advantage of the strategies that generate sample points according to
low-discrepancy sequences is that they can evenly cover the search space,
regardless of the number of samples. It can also be possible to add additional
samples later to fill the search space progressively.
Ultimately, the chosen sampling strategy depends on (i) the dimensionality of
the problem and (ii) the simulation budget, which imposes an upper bound on the
number of points to evaluate, i.e., the number of DTAs to perform.
In our experiments (see Section~\ref{sec:results}), we will use a dataset with
points sampled according to the numbers in a Sobol sequence (an example is shown
in Figure~\ref{fig:sampling_methods})).
Formally, let $\mathcal{D}_\Gamma = \left\{(\mathbf{x}_{1}, \mathbf{y}_{1}),
\hdots, (\mathbf{x}_{n}, \mathbf{y}_{n}) \right\}$ denote the dataset
where $\mathbf{x}_{i} \in \mathbb{R}_+^{m \cdot n_S}$ is an element of a Sobol
sequence and $\mathbf{y}_{i}= \Gamma(\mathbf{x}_{i}) \in \mathbb{R}_+^{n_Q \cdot
n_S}$ for all $i \in \left\{1, \hdots, n\right\}$. Recall that $\Gamma$
represents the function applied by the SUMO simulator. The learning task is
to determine $\hat\Gamma$ such that it approximates well $\Gamma$ on new data
points.
\subsubsection{Machine Learning Algorithms}
A wide selection of off-the-shelf implementations of general-purpose ML
algorithms can be used to find $\hat\Gamma$.
The ML algorithms we are interested in studying can be categorized as
nonparametric models. In contrast to parametric models, nonparametric models are
more flexible as no prior assumptions are made on the structure of the model
that is to be trained.
It could be possible to learn the input-output relationship between the demand
and the scalar value of the second OF term in
Eq.~\eqref{eqn:objective_function}, that is:
\begin{align}
f^{(2)} : \mathbb{R}_+^{n_Q \cdot n_S} \rightarrow \mathbb{R}_+,
\label{eqn:objective_function_map}
\end{align}
This term of the OF measures the discrepancy between the observed arc counts and
the current estimate of arc counts, which depends indeed on the DTA. On the
contrary, the other term in Eq.~\eqref{eqn:objective_function}, $f^{(1)}$,
measures the discrepancy between the estimated demands and the seed demands and
does not require performing a DTA.
However, preliminary experiments showed that a better approach is trying to
learn the input-output relationship of a vector-valued multivariate function as
in Eq.~\eqref{eqn:sumo_dta_map} and predict the vector of arc counts. Note that
this approach has the advantage of being more robust to a change in the number
of sensors in the network (e.g., due to failure), since in that case the
corresponding predicted arc counts can be ignored in the calculation of
$f^{(2)}$. Learning a single model to predict $p$ target variables can be done
by inherently multi-target ML algorithms, which are able to exploit inter-target
correlations. The inherently multi-target ML algorithms that we will make use of
are \emph{Feed-Forward Networks (FNNs)} and $k$-Nearest Neighbors ($k$-NN). The
algorithms are briefly described in the following and in more detail in
Appendix~\ref{sec:ml_models}.
A \emph{Feed-Forward Network (FNN)} is a type of neural network consisting of
\emph{units} arranged in layers: An input layer, a number of hidden layers and
an output layer. A FNN architecture is thus mainly defined by the number of
layers (the depth of the network $m_d \in \mathbb{N}$ not counting the input
layer) and the number of units in each layer (the width of a layer $l_i \in
\mathbb{N}$, with $i \in \left\{1, \dots, m_d \right\}$), along with the
\emph{activation functions} used in the different layers. In the network
architectures that we consider a \emph{ReLU} ($\phi(\cdot) = \max(0, \cdot)$)
\emph{activation function} is used in the units situated in the hidden layers
and a linear activation function is used in the output layer, since the task of
learning $\Gamma$ is a regression task. Finally, to reduce overfitting and
improve the out-of-sample predictive performance a regularization parameter
$\lambda \in \mathbb{R}_+$ is also set. An appropriate value for this parameter
is usually chosen using out-of-sample \emph{Cross-Validation} (CV) techniques.
\emph{$k$-NN} is one of the simplest nonparametric models used for regression.
To predict the value $\hat{\mathbf{y}}$ of a new unseen point $\mathbf{x}$, $k$
needs to be specified. Its value specifies the number of points from a training
set $\mathcal{D}$ closest to $\mathbf{x}$ that should be used to calculate the
predicted value $\hat{\mathbf{y}}$. Unlike the FNN and most other ML algorithms,
no model must be determined, rather the training data are kept and continuously
used.
It is good and common practice for supervised learning tasks to perform
\emph{model selection and validation} to estimate the out-of-sample predictive
performance and obtain a model that ultimately has good \emph{prediction
accuracy} and generalizes well to unseen data. To perform model selection and
validation, we will use the MSE as a performance metric to evaluate the
performance of a trained model.
To select an appropriate FNN or $k$-NN model and estimate its performance on
unseen data, we will perform \emph{hyperparameter tuning} through an exhaustive
grid search and use $k$-fold CV (note that this $k$ is
different from $k$ in $k$-NN) on a dataset. For a hyperparameter
configuration, $k$-fold CV consists of the following steps: (i)
Divide the dataset into $k$ non-overlapping groups of approximately equal size,
then (ii) save a single fold as a validation dataset and use an ML algorithm to
train a model on the remaining $k - 1$ folds. Lastly, (iii) assess the
performance of the trained model by calculating the MSE on the held-out fold.
Steps (i) and (ii) are repeated $k$ times where a new fold is treated as the
validation dataset. Through this procedure, we obtain error estimates $MSE_1,
MSE_2, \dots, MSE_k$ that can be used to calculate the overall $k$-fold CV score:
\begin{align}
CV_{k} = \frac{1}{k} \sum_{i = 1}^{k} MSE_i
\end{align}
The $CV_k$ score estimates the error we can expect when using a trained model to
predict new values given unseen data. The model with the best score is chosen in
a model selection context. The value of $k$ is commonly set to 5 or 10, usually
due to computational considerations \citep{jam2013}.
\subsubsection{Optimization}
We can then solve the outer-level optimization problem in
Eq.~\eqref{eqn:1_estimation_problem} with $\hat{\Gamma}$ to model the
relationship in Eq.~\eqref{eqn:sumo_dta_map}. So instead of obtaining arc counts
by performing a time-consuming DTA with SUMO, we get arc counts by querying the
ML model $\hat{\Gamma}$. Since we use nonparametric ML algorithms, the OF is not
explicitly available. Hence, we need to resort to derivative-free methods.
However, now evaluating the OF has become fast, and we can use algorithms that
are less parsimonious in requiring this.
We can thus apply an off-the-shelf global optimization algorithm called the
\emph{basinhopping} algorithm, described in \cite{Dav1997} and implemented by
the SciPy Python library \citep{2020SciPy}. The basinhopping algorithm is
similar to the well-known \emph{simulated annealing} optimization algorithm in
the sense that it consists of two main components that are applied iteratively:
(i) A random perturbation of a current point and (ii) a criterion for accepting
or rejecting the perturbed point based on its OF value.
The basinhopping algorithm extends the idea of the simulated annealing algorithm
by applying a local optimization algorithm to the perturbed point to find a
local minimum of the OF before deciding to accept or reject the point that
resulted in the local minimum. This process is repeated until a maximum number
of iterations has been reached. The local optimization algorithm used in the
basinhopping algorithm as a subprocedure is, in this work, chosen to be a
Sequential Least-Squares Programming (SLSQP) algorithm also implemented by the
SciPy library. This choice is because this algorithm can handle not only the
upper and lower bound constraints in Eq.~\eqref{eqn:2_estimation_problem} but
also the inequality constraints in Eq.~\eqref{eqn:generation_constraints}.
Ultimately, the basinhopping algorithm is applied to find an approximate minimum
of the DODE problem. SUMO will then evaluate the final demand estimate as a
final result.
\section{Experimental Setup} \label{sec:experimental_setup}
We decided to test and compare the methods described in a controlled environment
by synthetically generating an artificial traffic network. To generate this test
data, three primary components are needed: (i) a traffic network where possible
OD pairs $W$ have been identified, (ii) a discretization of the analysis period
$T$, and (iii) a \emph{ground-truth} vector of demands based on (i) and (ii).
The specific parameters used in each of the experiments are described in
Section~\ref{sec:results}. Here, we focus on details of components (i)-(iii).
The network can be defined as an \emph{irregular grid network}. The network was
generated to contain features that can be encountered in a real traffic network.
More specifically, some paths in the network between origins and destinations
are shorter than others in terms of free-flow travel time. The network used is
depicted in Figure~\ref{fig:network_illustration} and described in more detail
in the following.
The network has $48$ directed arcs and $16$ nodes, either representing
intersections or origins and destinations. More precisely, $12$ of the nodes
represent origins and destinations, which means that $O = D$ and $|O| = |D| =
12$, resulting in $132$ OD pairs. Furthermore, the arcs in the network were
prescribed a speed limit of $50 \;
\nicefrac{\textnormal{kilometer}}{\textnormal{hour}}$ and assigned a default
length of $1250$ meters. The coordinates of the nodes in the network are then
perturbed by a uniform random number $\mathcal{U}(0, 1250)$, resulting in arcs
between nodes with different lengths, yielding the irregular grid.
We settled for a one-hour scenario with an analysis period $T = \left[0,
t_{\textnormal{end}}\right)$, where $t_{\textnormal{end}} = 3600 \textnormal{
seconds} = 60 \textnormal{ minutes} = 1 \textnormal{ hour}$. This one-hour time
period was discretized into $4$ time intervals of equal duration, i.e., we have
$S = \left\{1,...,n_S = 4\right\}$, where each of the indices in this set refers
to a time interval of $900 \textnormal{ seconds} = 15 \textnormal{ minutes}$
duration. Given this information and a network with OD pairs $W$, a ground-truth
vector of demands is constructed by sampling the number of trips defined for
each variable according to a continuous uniform distribution with lower bound
$a$ and upper bound $b$:
\begin{align}
x_{ws}^{\textnormal{True}} \sim U(a, b), \; \forall w \in W, s \in S.
\label{eqn:ground_truth}
\end{align}
From the ground-truth vector of demands, trip productions $o_i$ for $i =
1, \dots, |O|$ that enter into the generation constraints (in
Eq.~\eqref{eqn:generation_constraints}) were obtained in addition to upper and
lower bounds on the estimated demands:
\begin{align}
\mathbf{x}_{l} = \mathbf{0} \;\; \textnormal{and} \;\; \mathbf{x}_{u} = 1.5 \cdot \max\left(\mathbf{x}\right) \cdot \mathbf{1},
\end{align}
where $\mathbf{0}$ is an $m \cdot n_S$ vector of zeros and $\mathbf{1}$ is an $m
\cdot n_S$ vector of ones.
Finally, the ground-truth vector of demands was given to SUMO as input
and the iterative DTA procedure implemented by SUMO was run for $15$ iterations
yielding the vector $\hat{\mathbf{c}}$ of observed arc counts.
For the seed demand vector $\tilde{\mathbf{x}} \in \mathbb{R}^{m \cdot
n_S}$ we consider two scenarios:
\begin{description}
\item[Prior low-demand vector (LD):] This scenario simulates the case where
lower demand estimates are available from a previous study:
\begin{align}
\tilde{x}_{ws} = x_{ws}^{\textnormal{True}} \cdot \left(0.7 + 0.3 \cdot u_{ws}\right), \qquad u_{ws} \sim U(0, 1), \; \forall w \in W, \forall s \in S.
\end{align}{}
\item[Prior high-demand vector (HD):] This scenario simulates the case where
higher demands are available from a previous study:
\begin{align}
\tilde{x}_{ws} = x_{ws}^{\textnormal{True}} \cdot \left(0.9 + 0.3 \cdot u_{ws}\right), \qquad u_{ws} \sim U(0, 1), \; \forall w \in W, \forall s \in S.
\end{align}{}
\end{description}
These two scenarios were constructed based on the guidelines provided in
\cite{ant2016} and the computational experiments performed in \cite{cip2011,
mas2018}.
\begin{figure}[tb]
\centering
\subfigure[The network used in the case study. All the nodes on the perimeter of the network can be identified as origins and destinations.]{%
{
\raisebox{1.25cm}{\includegraphics[trim={2.5cm 2.5cm 2.5cm 2.5cm},clip,keepaspectratio,width=0.38\textwidth]{Images/network.pdf}}
\label{fig:network_illustration}
}
}
\hspace{1pt}
\subfigure[Characteristics of the synthetically generated test data using the artificial network.]{%
{
\includegraphics[trim={0.5cm 0.5cm 0.25cm 0.5cm},clip,keepaspectratio,width=0.543\textwidth]{Images/scen_od132_tripinfo.pdf}
\label{fig:network_1_characteristics}
}
}
\caption{The network used in the case study along with the characteristics of the synthetically generated test data.}
\end{figure}
The ground-truth vector of demands was generated according to
Eq.~\eqref{eqn:ground_truth}, using lower bound $a = 1$ and upper bound $b =
20$. The value for the upper bound $b$ depends on the number of OD pairs and the
size of the network, i.e., the network supply, which essentially determines how
much traffic the network can handle at a given point in time. In this case, the
appropriate upper bound was found experimentally by sampling different
ground-truth vectors of demand for increasing values of $b$. A DTA was
performed by SUMO for each of the generated ground-truth vectors, and the
resulting output from the DTA was assessed by checking the level of congestion
present in the network. Finally, the ground-truth vector of demands with
corresponding upper bound $b$ that generated a scenario with light congestion was
chosen as the basis for the case study using this network.
The scenario that was deemed the most appropriate was determined based on
assessing the characteristics of the three plots in
Figure~\ref{fig:network_1_characteristics}. In the first plot, we observe that
the average trip length is $4.6$ kilometers and, in the next plot, that the
average travel time for a trip is $338$ seconds. Finally, keeping these two
attributes in mind, we observe in the last plot that an average delay of $52$
seconds ($\nicefrac{52 \textnormal{ seconds}}{338 \textnormal{ seconds}} =
0.15\%$) of the total travel time is due to congestion and driving below the
possible free-flow speed. Furthermore, some unfortunate vehicles experience a
delay far more significant than the average of $52$ seconds, while on the other
hand, most vehicles experience only little to no travel time delays. Therefore,
based on these scenario attributes, we classify the scenario as a scenario with
light congestion.
For the results we present in the following sections, it is assumed that sensors
cover $100$\% of the network. A good overview of the problem of determining
appropriate locations to place sensors in a traffic network, along with some
recent developments on this problem, is given in \cite{vit2014, hu2014,
sal2019}. In addition to this, the arc counts obtained by the sensors are
assumed to be error-free. This is, of course, not the case in a real traffic
network, but it simplifies the analysis and comparison of the different solution
approaches. Lastly, we mention that all the experiments were executed using an
initial feasible solution consisting of all ones, i.e., $\mathbf{x}_{\tau = 0} =
\mathbf{1}$. This initial guess was chosen so to not confine the search for a
minimum to the vicinity of the seed demands.
To compare the performance of the different approaches, we report the Root Mean
Squared Error (RMSE). If we consider place-holders $\mathbf{y}, \hat{\mathbf{y}}
\in \mathbb{R}^{n}$, where $\mathbf{y}$ is a vector of observed values and
$\hat{\mathbf{y}}$ is a vector of estimated values, then the RMSE value is
defined as follows:
\begin{align}
\textnormal{RMSE}(\mathbf{y}, \hat{\mathbf{y}}) = \left(\frac{1}{n}\sum_{j = 1}^{n} (y_{i} - \hat{y}_{i})^2\right)^{\frac{1}{2}}.
\end{align}
This error measure is easily interpretable because the error is given in the
same units as the data. Furthermore, the RMSE is reported separately for each of
the different quantities entering the optimization problem, i.e., we report the
RMSE statistic for the arc counts and the demands. Finally, we remark
that for the demands, the RMSE is calculated based on the ground-truth
values and not on the seed demand vectors that enter the optimization
problem.
We note that the size of the network and the number of OD pairs, arcs
equipped with sensors and time intervals of the dataset described are
similar to those used in other algorithm comparison studies
\citep{cip2011, car2017, nig2018_1}, while larger sizes and numbers are
used in \cite{tol2013, ant2016, dju2017, mas2018}.
\section{Experimental Results} \label{sec:results}
We implemented all methods in Python with external calls to the SUMO simulator.
The primary Python libraries used include Pandas \citep{mck2010} for data
organization purposes, NumPy \citep{harris2020array} for its numerical methods
for fitting polynomials, along with SciPy \citep{2020SciPy} for its off-the-shelf
global optimization algorithms and scikit-learn's \citep{sklearn} implementation
of FNN and $k$-NN used in the ML approach. A snapshot
of the repository \citep{github_demand_estimation_data_available} containing the
codebase and the data supporting this study's findings are archived and openly
available in Zenodo \citep{zenodo_demand_estimation_data_available}. All
experiments described in this section were performed on a machine with an AMD
Ryzen 7 1800X eight-core processor and 32 GB of RAM, running Manjaro Linux.
\subsection{Computational Budget}
We studied the ability of the FNN and $k$-NN ML algorithms to learn the
input-output relationship using a different number of sample points and
hyperparameter configurations while the CV scores were monitored. The resulting
\emph{learning curves} are displayed in Figure~\ref{fig:learning_curve}. We
observe that by increasing the size of the training set, the CV scores improve
but only slightly.
As we want a model that performs as well as possible on unseen data (the test
scores) and is parsimonious in the usage of SUMO to perform DTAs, we settled to
use $200$ points for the dataset to train the ML approaches. This means
that we run SUMO for about $200$ DTAs, which took $3912.92 \textnormal{ sec} =
65.21\textnormal{ min}$ on our computational environment. We note that an
additional DTA (the $201$st DTA) will be needed by the ML approaches to evaluate
a final estimate. For the sake of fairness, we thus set a soft upper bound on
the number of allowed OF evaluations to $201$ for all other
approaches\footnote{Due to the inherent nature of some of the applied
approaches, a few more OF evaluations and thus DTAs might have
occurred in an iteration and the total number of OF evaluations
might not sum up to $201$ exactly.}.
\begin{figure}[tb]
\centering
\includegraphics[width = 0.75\textwidth]{Images/Learning_Curve.pdf}
\caption{
The learning curves and CV results associated with the training of the $k$-NN and FNN model.
The curves show the mean CV and training scores, while the shaded bands show the standard deviation.
The datapoints in the curves are related to the best mean CV score obtained for different sample sizes
and over all tested hyperparameter configurations.
}
\label{fig:learning_curve}
\end{figure}
\subsection{Parameter Tuning}
The gradient-based approaches, i.e., the AM-based and AM-free approach, do not
need parameter tuning before tackling the DODE problem. Indeed, the only
parameter, the step length, is determined automatically by the solution of the
line search in Eq.~\eqref{eqn:line_search}. Thus, these algorithms are
straightforward to apply, and no specific consideration has to be made
concerning their parameters.
For the ML approaches, the FNN and the $k$-NN model, the hyperparameters were
fine-tuned using a grid search coupled with $5$-fold CV using the $200$
generated sample points that act as re-usable historical simulation data.
The grid search was performed on the values reported in
Table~\ref{tab:hyperparameters}. The best performance was achieved by the
following settings:
\begin{itemize}
\item The FNN model with hidden layers containing
units $(0.75\cdot m \cdot n_S, 0.50\phantom{0} \cdot m \cdot n_S,
0.50\phantom{0} \cdot m \cdot n_S) = (l_1=396, l_2=264, l_3=264)$ along with
regularization parameter $\lambda=0.01$. This trained model is used in
method M3 in Table~\ref{tab:summary_table}. This model achieved a $5$-fold
CV score of $CV_5 = 579.1282$.
\item The $k$-NN model using $k = 43$ neighbours. This trained model is used in
method M4 in Table~\ref{tab:summary_table}. This model achieved a $5$-fold
CV score of $CV_5 = 621.2651$.
\end{itemize}
For the subsequent optimization step using a trained ML model (FNN or $k$-NN) as
a surrogate model for DTA, the basinhopping algorithm was used with default
parameters. Also, the local SLSQP minimizer was used with default parameters.
Preliminary experiments showed that $10$ iterations of the basinhopping
algorithm were enough to reach convergence and that improvements after that
stage become rare.
\subsection{Quality of Estimates}
In Table~\ref{tab:summary_table}, we present an overview of all
experiments conducted together with summary results, that we detail in the following.
\begin{table}
\footnotesize
\centering
\caption{
An overview and summary of the results obtained in the different
experiments E1-E12. Here, we define M1: AM-based approach,
M2: AM-free approach, M3: FNN predicting $\Gamma$,
M4: $k$-NN predicting $\Gamma$. For methods M3-M4 only the
running time of the optimization step is reported.
}
\input{Images/results_summary.tex}
\label{tab:summary_table}
\end{table}
\subsubsection{Gradient-based Approaches}
The final results obtained from the gradient-based approaches are plotted in
Figure~\ref{fig:assignmat_approach_estobs} and
Figure~\ref{fig:spsa_approach_estobs}. In these figures, the estimated
quantities $\mathbf{x}$ and $\mathbf{c}(\mathbf{x})$ have been plotted against
the ground-truth vector of demands $\mathbf{x}^{\textnormal{True}}$ and
the corresponding vector of observed arc counts $\mathbf{c}(\mathbf{x})$,
respectively. The corresponding plots that show the OF value history of the two
algorithms are shown in Figure~\ref{fig:assignmat_approach_iters} and
Figure~\ref{fig:spsa_approach_iters}.
If we compare the results in Figure~\ref{fig:assignmat_approach_estobs} and
Figure~\ref{fig:spsa_approach_estobs} between the two gradient-based approaches,
we observe that the AM-based approach outperforms the AM-free approach. In fact,
the AM-based approach is able to consistently overcome local minima and reach a
good demand estimate. This can be seen in
Figure~\ref{fig:assignmat_approach_estobs} where the estimated demands and the
ground-truth vector of demands align well, and so do also the estimated arc
counts and the observed arc counts.
If we look at the progress of the two algorithms in
Figure~\ref{fig:assignmat_approach_iters} and
Figure~\ref{fig:spsa_approach_iters}, we see that the AM-based
approach can find a good estimate within only a single OF
evaluation, while the AM-free approach uses a much larger number
of evaluations to arrive at good estimates.
If we return to Table~\ref{tab:summary_table} and the results relating to
methods M1 and M2's computational time, we observe that the AM-free (M2) appears
to be faster than the AM-based (M1) approach. This is the case, even though two
OF evaluations and thus DTA computations are needed in each iteration of M1,
while M2 needs up to four. The prolonged computational time can be attributed to
slow gradient calculations due to AM data organization, which takes time in
Python. As the network and scenario are scaled, we expect the case to be
inverted, i.e., data organization will take less time than performing DTA's.
\begin{figure}[tb]
\centering
\subfigure[The ground-truth values plotted against the estimated values.]{
\includegraphics[trim={0.225cm 0.1cm 1.25cm 0.0cm},clip,width=0.59\linewidth,keepaspectratio]{Images/estobs_E1-3.pdf}
\label{fig:assignmat_approach_estobs}
}
\hspace{1.0pt}
\subfigure[The OF value history. Utilizing output data directly from SUMO $\Gamma(\mathbf{x})$.]{
\includegraphics[trim={0.0cm 0.0cm 0.0cm 0.0cm},clip,width=0.35\linewidth]{Images/evals_E1-3.pdf}
\label{fig:assignmat_approach_iters}
}
\caption{The final results from experiments E1-E3, that used the gradient and AM-based approach.}
\label{fig:assignmat_approach}
\end{figure}
\begin{figure}[tb]
\centering
\subfigure[The ground-truth values plotted against the estimated values.]{
\includegraphics[trim={0.225cm 0.1cm 1.25cm 0.0cm},clip,width=0.59\linewidth,keepaspectratio]{Images/estobs_E4-6.pdf}
\label{fig:spsa_approach_estobs}
}
\hspace{1.0pt}
\subfigure[The OF value history. Utilizing output data directly from SUMO $\Gamma(\mathbf{x})$.]{
\includegraphics[trim={0.0cm 0.0cm 0.0cm 0.0cm},clip,width=0.35\linewidth]{Images/evals_E4-6.pdf}
\label{fig:spsa_approach_iters}
}
\caption{The final results from experiments E4-E6, that used the gradient and AM-free approach.}
\label{fig:spsa_approach}
\end{figure}
\subsubsection{ML Approaches}
\begin{table}[b]
\footnotesize
\centering
\caption{The ML model hyperparameters chosen for
hyperparameter tuning. Preliminary experiments were performed to narrow
down the domains of the hyperparameters. }
\begin{tabular}{c c c}
\toprule
\multicolumn{1}{c}{Machine learning alg.} & \multicolumn{1}{c}{Hyperparameter name} & \multicolumn{1}{c}{Domain} \\
\cmidrule(lr){1-1} \cmidrule(lr){2-2} \cmidrule(lr){3-3}
\multirow{4}{*}{FNN} &
\multirow{3}{*}{Architecture}
& \multirow{1}{*}{ $\{(0.75\cdot m \cdot n_S, 0.50\phantom{0} \cdot
m \cdot n_S, 0.50\phantom{0} \cdot m \cdot n_S),$ } \\
& & \multirow{1}{*}{ $\phantom{\{}(0.75\cdot m \cdot n_S,
0.25\phantom{0} \cdot m \cdot n_S, 0.25\phantom{0} \cdot m \cdot
n_S),$ } \\
& & \multirow{1}{*}{ $\phantom{\{}(0.75\cdot m \cdot n_S, 0.125
\cdot m \cdot n_S, 0.125 \cdot m \cdot n_S)\} $ } \\
& \multirow{1}{*}{Regularization $\lambda$} &
\multirow{1}{*}{$\{0.0001, 0.001, 0.01, 0.1\}$} \\
\midrule
\multirow{1}{*}{$k$-NN} & \multirow{1}{*}{Neighbours $k$} &
\multirow{1}{*}{$\{\lfloor 2^z \rfloor: z = 2 + i \cdot
\nicefrac{(6-2)}{14}, \forall i = 0, \dots, 14\}$} \\
\bottomrule
\end{tabular}
\label{tab:hyperparameters}
\end{table}
The final estimate reached by the $k$-NN approach is shown in
Figure~\ref{fig:knn_approach} and the one reached by the FNN approach in
Figure~\ref{fig:fnn_approach}. The figures also report the development of
solution quality over the $10$ iterations of the basinhopping algorithm which
typically yield around $6000$ OF evaluations using the surrogate
model $\hat{\Gamma}$.
Across the different experiments with the ML approaches, we observe that the two
ML models achieve very similar results. Under both models, the estimated and
observed arc counts align well but the ground-truth demands and the estimated
demands do not. In other terms, these approaches can find demand estimates that
reproduce the arc counts well but are in no way similar to the ground-truth
demands.
In the optimization step of the ML approaches, we observe a general lack of
progress. In fact, an examination of the quality of the data points against the
final point after the optimization step show that the ML approaches seem able to
improve only slightly the estimates already available initially.
Furthermore, if the OF values pertaining to the first and the second term of the
OF is inspected, then it appears that the first term (in
Eq.~\eqref{eqn:objective_function_terms}) relating to the demands is not worked
on as much as the second term that takes into account the arc counts. This
behavior helps explain why the ground-truth demands and the estimated demands do
not align well even when a seed vector is provided to guide the search. Another
reason for the overall poor performance can also be attributed to the
goodness-of-fit of the trained ML models. If the trained models do not
sufficiently capture the complex input-output relationship of a DTA performed by
SUMO, then we might only be able to explore or reach local minima of the DODE
problem in the subsequent optimization step that are not actual minima. A hint
that this might be the case is the high CV scores reported in
Figure~\ref{fig:learning_curve}.
\begin{figure}[tb]
\centering
\subfigure[The ground-truth values plotted against the estimated values.]{
\includegraphics[trim={0.225cm 0.1cm 1.25cm 0.0cm},clip,width=0.59\linewidth,keepaspectratio]{Images/estobs_E7-9.pdf}
\label{fig:knn_approach_estobs}
}
\hspace{1.0pt}
\subfigure[The OF value history. Utilizing output data from the surrogate $\hat{\Gamma}(\mathbf{x})$.]{
\includegraphics[trim={0.0cm 0.0cm 0.0cm 0.0cm},clip,width=0.35\linewidth]{Images/evals_E7-9.pdf}
\label{fig:knn_approach_iters}
}
\caption{The final results from experiments E7-E9, where the $k$-NN model predict $\Gamma$.}
\label{fig:knn_approach}
\end{figure}
\begin{figure}[tb]
\centering
\subfigure[The ground-truth values plotted against the estimated values.]{
\includegraphics[trim={0.225cm 0.1cm 1.25cm 0.0cm},clip,width=0.59\linewidth,keepaspectratio]{Images/estobs_E10-12.pdf}
\label{fig:fnn_approach_estobs}
}
\hspace{1.0pt}
\subfigure[The OF value history. Utilizing output data from the surrogate $\hat{\Gamma}(\mathbf{x})$.]{
\includegraphics[trim={0.0cm 0.0cm 0.0cm 0.0cm},clip,width=0.35\linewidth]{Images/evals_E10-12.pdf}
\label{fig:fnn_approach_iters}
}
\caption{The final results from experiments E10-E12, where the FNN model predict $\Gamma$.}
\label{fig:fnn_approach}
\end{figure}
\subsection{Scaling}
Under the assumption that the training set of data is available initially in the
form of historical data, then performing the optimization step on the ML models
took on average $108.47\textnormal{ sec}$ (average running time of M3-M4 in
Table~\ref{tab:summary_table}). In contrast, the average time for the
gradient-based approaches using SUMO directly for DTA was $2641.28\textnormal{
sec}$ (average running time of M1-M2 in Table~\ref{tab:summary_table}).
Further, depending on the network size, the ML approaches could scale better
than the gradient-based approaches. Compared to the gradient-based approaches
that perform many DTAs, starting from scratch in each new optimization task, the
ML approaches utilize existing DTA data, meaning that fewer DTAs overall might
be needed.
A factor affecting the running time of all approaches is the number of demand
variables to be estimated. Increasing the number of variables produces a more
complex estimation problem that results in many more DTAs having to be solved
for an approach to find improving estimates. To cope with this growth, it is
possible to manually adjust the number of variables, e.g., by merging OD pairs
by combining areas into larger zones or by adjusting the number of sub-intervals
of the analysis period in which the demand is estimated. Moreover, arcs equipped
with sensors can be prioritized, and arcs deemed less critical can be filtered
out, making it possible to scale to larger networks.
\section{Conclusions and Future Work} \label{sec:conclusion}
The results presented in Table~\ref{tab:summary_table} and the plots in
Figure~\ref{fig:assignmat_approach}, \ref{fig:spsa_approach},
\ref{fig:knn_approach}, and \ref{fig:fnn_approach} show that the AM-based
approach (method M1) outperforms, in terms of quality of the estimates produced,
the AM-free approach (method M2), as well as the ML approaches (methods M3-M4).
We also note that even if no seed vectors were supplied, the AM-based approach
could find a reasonable estimate for both the ground-truth demands and the
corresponding observed arc counts.
A further advantage of the AM-based approach is that it is easy to apply as no
parameters will have to be set or tuned before using the approach. Moreover,
only two new OF evaluations and thus DTA computations are needed
in each iteration, while in comparison, the AM-free approach needs up to four.
On the other hand, the disadvantage of the AM-based approach is that it might be
harder to include different, more complex types of data into the optimization
problem, as it can be harder to derive analytical expressions for the gradient
of function terms that take into account more complex data types such as road
queuing length, turning ratios, etc.
If we look at the results obtained with the ML approach in
Table~\ref{tab:summary_table} and Figures~\ref{fig:knn_approach} and
\ref{fig:fnn_approach}, we can conclude that the estimated and observed counts
align somewhat well, while the estimated demands and ground-truth demands do not
align at all. This result seems to remain the same independently of which ML
algorithm is used. Based on these results, the ML approach is not good if one
seeks a demand estimate that is sufficiently close to a given seed
vector. However, it can produce more diverse estimates than, e.g., the
AM-based approach and may be useful for other purposes.
Our conclusion is that the gradient-based approaches work the best. However, the
ML methodology does provide a way to utilize data generated through many DTAs,
and it might be a viable option if certain changes are made. In this case, we
suggest possible directions for future research to improve the ML approach:
\begin{itemize}
\item In the optimization step of the ML approach, investigate why only the
second OF term, relating to the arcs counts, appears to
have an effect. That is, determine why the first term pertaining to the
demands is not being optimized and able to guide the search even when
a seed vector is supplied.
\item Incorporate additional constraints into the optimization step of the
ML approach to further restrict the search space and possibly obtain better
estimates.
\item Use other types of information, e.g., about the complete paths used by
users in the network instead of just the arc counts.
\item Model a different part of the DODE problem and change the type of
prediction being made (i.e., Eq. \eqref{eqn:objective_function_map}) by
using more sophisticated ML models. For example, it can be conjectured that
by using Graph Neural Networks (GNN), it is possible to capture the cause
and effect better of the demand on the resulting arc counts as the
relationships and interdependencies that exists between the arcs and thus
arc counts in the traffic network are modeled more explicitly.
\end{itemize}
\clearpage
\bibliographystyle{tfcad}
|
{
"redpajama_set_name": "RedPajamaArXiv"
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| 360
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\section{Introduction}
\label{sec:intro}
Studying and monitoring of mammals and birds species can be performed using non-invasive sampling techniques. These techniques allow us to observe animal species for conservation purposes, e.g. to estimate population sizes of endangered species. Camera trapping is a method to digitally capture wildlife images. This method facilitates the register of terrestrial vertebral species, e.g. cryptic species. Consequently, camera traps can generate large volumes of information in short periods of time. Thus, the contributions in camera trapping are important for better species conservation decisions.
Camera traps are devices to capture animal images in the wild. These devices consist of a digital camera and a motion detector. They are triggered when the motion sensor detects movement and dependent on the temperature of the source in relation to the environment temperature. Biologist can monitor wildlife with camera traps for detecting rare species, delineating species distributions, monitoring animal behavior, and measuring other biological rates \cite{o2010camera}. Camera traps generate large volumes of information, for example a camera trapping study can generate until 200000 images, where 1\% of the information is valuable \cite{diaz2011densidad}. As a consequence, biologists have to analyze thousands of photographs in a manual way. Nowadays, software solutions cannot handle the increment of the number of images in camera trapping \cite{fegraus2011data}. Accordingly, it is important to develop algorithms to assist the post-processing of camera-trap images.
Background subtraction techniques could help to segment animals from camera-trap images. There is a significant body research of background subtraction focused in video surveillance \cite{brutzer2011evaluation}. Nevertheless, there are not enough methods that can handle the complexity of natural dynamic scenes \cite{mahadevan2010spatiotemporal}. Camera-trap images segmentation is important for animal detection and classification. Camera-traps images usually have ripping water, moving shadows, swaying trees and leaves, sun spots, scene changes, among others. Consequently, the models used to segment those types of images should have robust feature extractors. There are some segmentation methods in the literature applied to camera-trap images segmentation. Reddy and Aravind proposed a method to segment tigers on camera-trap images, using texture and color features with active contours \cite{reddy2012segmentation}. They do not make an objective evaluation of their method. Ren et al. developed a method to segment images from dynamic scenes, including camera-trap images; the method uses Bag of Words (BoW), Histogram of Oriented Gradients (HOG), and graph cut energy minimization \cite{ren2013ensemble}. They do not show the results on camera-trap images. Zhang et al. developed a method to segment animals from video sequences, using camera-trap images; the method uses BoW, HOG, and graph cut energy minimization \cite{zhang2015coupled}. They obtained 0.8695 of average f-measure on their own camera-trap data set.
Robust Principal Component Analysis (RPCA) is a method derived from Principal Component Analysis. RPCA assumes that a data matrix can be decomposed in a low-rank and a sparse matrix. RPCA has newly seen significant activity in many areas of computer sciences, particularly in background subtraction. As a result, there are some algorithms to solve the RPCA problem \cite{liu2012active,lin2010augmented,goldfarb2013fast,aybat2011fast,wang2012probabilistic}. In this work, we proposed a Multi-Layer RPCA approach in order to segment animals from camera-trap images. Our method combines color and texture descriptors as feature extractor, and solve the RPCA problem with some state-of-the-art algorithms. To our knowledge, this paper is the first work in proposing a Multi-Layer RPCA approach and using it for camera-trap images segmentation.
The paper is organized as follows. Section \ref{sec:mateAndMeth} shows material and methods. Section \ref{sec:expFram} describes the experimental framework. Section \ref{sec:results} presents the experimental results and the discussion. Finally, Section \ref{sec:conclusions} shows the conclusions.
\section{Materials and Methods}
\label{sec:mateAndMeth}
This section shows a brief explanation of the algorithms and metrics used in this paper.
\subsection{Robust Principal Component Analysis}
An image can be decomposed in a low-rank and sparse matrix. Equation \ref{eqn:decomposition} shows the RPCA problem, where $M$ is the data matrix, $L_0$ is the low-rank matrix, and $S_0$ is the sparse matrix. The low-rank matrix is the background and the sparse matrix is the foreground in background subtraction.
\begin{equation}
M=L_0+S_0
\label{eqn:decomposition}
\end{equation}
The RPCA problem can be solved with the convex program Principal Component Pursuit (PCP). This program computes $L$ and $S$, taking the objective function in the Equation \ref{eqn:objectFunction}, where $||L||_*$ denotes the nuclear norm of the low-rank matrix, $||S||_1$ denotes the $l_1$-norm of the sparse matrix, and $\lambda$ is a regularizing parameter. There are some algorithms to perform PCP such as Accelerated Proximal Gradient (APG), and Augmented Lagrange multiplier (ALM) \cite{candes2011robust}.
\begin{equation}
\begin{aligned}
& \text{minimize}
& & ||L||_* + \lambda ||S||_1 \\
& \text{subject to}
& & L+S=M
\end{aligned}
\label{eqn:objectFunction}
\end{equation}
\subsection{Multi-Layer Robust Principal Component Analysis}
Equation \ref{eqn:MMatrix} shows the data matrix $M$ in our Multi-Layer RPCA method, where $\beta \in [0,1]$ is a weight value indicating the contribution of the texture function to the overall data matrix. Function $f_t(x,y)$ denotes the texture descriptor extracted from each image, using the classic Local Binary Pattern (LBP) \cite{ojala2002multiresolution}. LBP describes the texture of an image using the neighborhood of each pixel. Function $f_c(x,y)$ denotes the color transformation for each image, converting to gray scale in this case. Our Multi-Layer RPCA computes the $L$ and $S$ matrices from the $M$ matrix in the Equation \ref{eqn:MMatrix}. Texture descriptors can work robustly into rich texture regions with light variation. However, they do not work in a efficient way on uniform regions such as water, the sky, and others. Color descriptors could overcome the texture descriptor limitation \cite{yao2007multi}. The Multi-Layer approach proposed in this paper was tested in camera traps for wildlife image segmentation.
\begin{equation}
M(x,y) = \beta f_t(x,y) + (1-\beta) f_c(x,y)
\label{eqn:MMatrix}
\end{equation}
\subsection{Evaluation Metrics}
\label{sec:evalMetrics}
The f-measure metric was chosen to evaluate the performance of the Multi-Layer RPCA. Equation \ref{eqn:fmeasure} shows the f-measure, where precision and recall are extracted from the confusion matrix. Precision is the proportion of predicted positives that are correctly real positives. In the same way, recall denotes the proportion of the real positives that are correctly predicted \cite{powers2011evaluation}. The confusion matrix is computed comparing the ground truth (GT) with the automatic segmented images.
\begin{equation}
\text{f-measure} = 2\frac{\text{precision}*\text{recall}}{\text{precision} + \text{recall}}
\label{eqn:fmeasure}
\end{equation}
\section{Experimental Framework}
\label{sec:expFram}
This section introduces the database used in this paper, the experiments executed, and the implementation details of our Multi-Layer RPCA.
\subsection{Database}
\label{subsec:database}
The Alexander von Humboldt Institute realizes samplings with camera traps in different regions of the Colombian forest. We select 25 cameras from 8 regions, where each camera has a relative unalterable environment. Each camera was placed in its site between 1 to 3 months. We extract 30 days and 30 nights of images from those cameras, in daytime color and nighttime infrared formats respectively. The database consists of 1065 GT images from the 30 days and 30 nights. The images have a spatial resolution of 3264x2448 pixels. The length of each day or night data set varies from 9 to 72 images, depending on the animal activity that day or night. Figure \ref{fig:GTImages} shows an example of the GT images.
\begin{figure}
\centering
\begin{subfigure}[b]{0.15\textwidth}
\includegraphics[width=\textwidth]{images/ground.JPG}
\caption{Original Image}
\label{fig:GroundImage}
\end{subfigure}
\begin{subfigure}[b]{0.15\textwidth}
\includegraphics[width=\textwidth]{images/truth.jpg}
\caption{Ground truth}
\label{fig:TruthImage}
\end{subfigure}
\caption{Ground truth example for the evaluation process, (a) original image, (b) ground truth or manual segmented image.}
\label{fig:GTImages}
\end{figure}
\subsection{Experiments}
The experiments computed the background models with different conditions and amount of images, observing the robustness of the Multi-Layer RPCA and the influence of pre-processing in the results. All experiments performed our method with $\beta=[0,0.05,0.1,0.15,\dots,1]$. Accordingly, Experiment 1 uses histogram equalization as pre-processing in the color transformed image, Figure \ref{fig:preprocess1} shows the pre-processing for each raw image. The background model is computed with entire days e.g. we take all images of day 1 and solve the RPCA problem in the Experiment 1. Experiment 2 computes the background model with entire nights; Figure \ref{fig:preprocess2} shows the pre-processing for each raw image. Experiment 3 takes entire days and nights e.g. we take all images of day 1 and night 1 to solve the RPCA problem. Experiment 3 uses two pre-processes, daytime images uses the pre-process in Figure \ref{fig:preprocess1} and nighttime images uses the pre-process in Figure \ref{fig:preprocess2}. Experiment 4 takes entire days and nights such as the Experiment 3, but it only uses the pre-processing in Figure \ref{fig:preprocess1} for all images.
We tested 9 algorithms to solve the RPCA problem in this paper. Active Subspace RPCA (AS-RPCA) \cite{liu2012active}; Exact ALM (EALM), Inexact ALM (IALM), Partial APG (APG-PARTIAL) and APG \cite{lin2010augmented}; Lagrangian Alternating Direction Method (LSADM) \cite{goldfarb2013fast}; Non-Smooth Augmented Lagrangian v1 (NSA1) and Non-Smooth Augmented Lagrangian v2 (NSA2) \cite{aybat2011fast}; Probabilistic Robust Matrix Factorization (PRMF) \cite{wang2012probabilistic}.
\begin{figure}
\centering
\includegraphics[width=0.38\textwidth]{images/preType1.pdf}
\caption{Block diagram of the pre-processing methods used in the Experiment 1, 3, and 4.}
\label{fig:preprocess1}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.38\textwidth]{images/preType2.pdf}
\caption{Block diagram of the pre-processing methods used in the Experiment 2 and 3.}
\label{fig:preprocess2}
\end{figure}
The foreground was obtained applying a post-process to the sparse matrix. The post-processing was the same for all experiments. This stage includes a hard threshold, morphological filters, and an active contours with a negative contraction bias \cite{caselles1997geodesic}. Figure \ref{fig:postprocess} shows the post-processing used. Finally, The f-measure was computed comparing each GT with each foreground. The average f-measure was computed as the mean of all f-measures. The results are displayed as a plot of the average f-measure vs $\beta$.
\begin{figure}
\centering
\includegraphics[width=0.22\textwidth]{images/postprocess.pdf}
\caption{Block diagram of the postprocessing.}
\label{fig:postprocess}
\end{figure}
\subsection{Implementation Details}
The RPCA algorithms were computed using the Sobral et al. library \cite{lrslibrary2015}. The rest of the source code was developed using the image processing toolbox of Matlab.
\section{Results}
\label{sec:results}
This section shows the results and discussions of the experiments introduced in the Section \ref{sec:expFram}. These results use the metrics explained in the Section \ref{sec:evalMetrics}.
Figures \ref{fig:ResultExperiment1} and \ref{fig:ResultExperiment2} show the average f-measure vs $\beta$ of the Experiments 1 and 2 for all RPCA algorithms chosen. Table \ref{tbl:summary} shows the summary of the best results for each experiment. APG-PARTIAL was the best algorithm in the Experiments 1 and 2. Daytime images have rich texture regions. In contrast, nighttime images have uniform color. Texture representations are more important on daytime images in the Experiment 1 due to $\beta=0.6$. On the contrary, color descriptors are more important on nighttime images in the Experiment 2 due to $\beta=0.3$. Those results show the importance of combining the color and texture descriptors. Figure \ref{fig:resultsExperiments} shows the performances of the RPCA normal algorithms when $\beta=0$. Thus, our Multi-Layer RPCA outperforms the RPCA normal methods.
Figures \ref{fig:ResultExperiment3} and \ref{fig:ResultExperiment4} show the average f-measure vs $\beta$ of the Experiments 3 and 4. Table \ref{tbl:summary} shows that dividing the pre-processing per daytime or nighttime in the Experiment 3 does not make a big difference in the results, but it increases the fine-tuning parameters. Table \ref{tbl:summary} shows that NSA2 was the best algorithm in the Experiments 3 and 4, contrary to the Experiments 1 and 2 where APG-PARTIAL was the best. NSA2 algorithm is a better choice than other RPCA algorithms, if we cannot differentiate between daytime and nighttime images, or if it is difficult to do so. On the other hand, APG-PARTIAL is better, if we have information about the infrared activation.
\begin{figure*}
\centering
\begin{subfigure}[b]{0.36\textwidth}
\includegraphics[width=\textwidth]{images/fmeasuresPerDay}
\caption{Average f-measure vs $\beta$ for the experiment 1}
\label{fig:ResultExperiment1}
\end{subfigure}
\begin{subfigure}[b]{0.36\textwidth}
\includegraphics[width=\textwidth]{images/fmeasuresPerNight}
\caption{Average f-measure vs $\beta$ for the experiment 2}
\label{fig:ResultExperiment2}
\end{subfigure}
\begin{subfigure}[b]{0.36\textwidth}
\includegraphics[width=\textwidth]{images/fmeasuresPerDayNightDiv}
\caption{Average f-measure vs $\beta$ for the experiment 3}
\label{fig:ResultExperiment3}
\end{subfigure}
\begin{subfigure}[b]{0.36\textwidth}
\includegraphics[width=\textwidth]{images/fmeasuresPerDayNight}
\caption{Average f-measure vs $\beta$ for the experiment 4}
\label{fig:ResultExperiment4}
\end{subfigure}
\caption{Results of the proposed experiments, (a) average f-measure vs $\beta$ per days, (b) average f-measure vs $\beta$ per nights, (c) average f-measure vs $\beta$ per days and nights with two different pre-processes, (d) average f-measure vs $\beta$ per days and nights with one pre-process.}
\label{fig:resultsExperiments}
\end{figure*}
Figure \ref{fig:visualResults} shows two visual results of the Multi-Layer RPCA. Figure \ref{fig:ground1} shows a daytime image without any pre-processing. Figure \ref{fig:ground2} shows an original nighttime image. Figures \ref{fig:sparse1} and \ref{fig:sparse2} show the sparse matrix after the hard threshold. Figures \ref{fig:foreground1} and \ref{fig:foreground2} show the foreground image. These color results are made with the GT images. Yellow-colored regions mean pixels that are on the GT and the automatic segmented images. Red and green regions are visual representations of the under and over segmentation.
\begin{figure}
\centering
\begin{subfigure}[b]{0.12\textwidth}
\includegraphics[width=\textwidth]{images/ground1.jpg}
\caption{Ground}
\label{fig:ground1}
\end{subfigure}
\begin{subfigure}[b]{0.12\textwidth}
\includegraphics[width=\textwidth]{images/sparse1.jpg}
\caption{Sparse}
\label{fig:sparse1}
\end{subfigure}
\begin{subfigure}[b]{0.12\textwidth}
\includegraphics[width=\textwidth]{images/foreground1.jpg}
\caption{Foreground}
\label{fig:foreground1}
\end{subfigure}
\begin{subfigure}[b]{0.12\textwidth}
\includegraphics[width=\textwidth]{images/ground2.jpg}
\caption{Ground}
\label{fig:ground2}
\end{subfigure}
\begin{subfigure}[b]{0.12\textwidth}
\includegraphics[width=\textwidth]{images/sparse2.jpg}
\caption{Sparse}
\label{fig:sparse2}
\end{subfigure}
\begin{subfigure}[b]{0.12\textwidth}
\includegraphics[width=\textwidth]{images/foreground2.jpg}
\caption{Foreground}
\label{fig:foreground2}
\end{subfigure}
\caption{Visual results of the Multi-Layer RPCA, (a) original daytime image, (b) sparse matrix after the hard threshold with APG-PARTIAL and $\beta=0.6$, (c) foreground, (d) original nighttime image, (e) sparse matrix after the hard threshold with APG-PARTIAL and $\beta=0.3$, (f) foreground.}
\label{fig:visualResults}
\end{figure}
\begin{table}
\centering
\caption{$\beta$ values and algorithms for the best performances of each experiment.}
\label{tbl:summary}
\begin{tabular}{cccc}
\hline
\textbf{Experiment} & \textbf{Algorithm} & $\boldsymbol{\beta}$ & \textbf{Avg f-measure} \\ \hline
Experiment 1 & APG-PARTIAL & 0.6 & 0.7539 \\
Experiment 2 & APG-PARTIAL & 0.3 & 0.7393 \\
Experiment 3 & NSA2 & 0.45 & 0.7259 \\
Experiment 4 & NSA2 & 0.55 & 0.7261 \\ \hline
\end{tabular}
\end{table}
\section{Conclusions}
\label{sec:conclusions}
We proposed a Multi-Layer RPCA for camera-trap image segmentation, using texture and color descriptors. The proposed algorithm is composed of pre-processing, RPCA algorithm, and post-processing. The pre-processing uses histogram equalization, Gaussian filtering, or a combination of both. The RPCA algorithm computes the sparse and low-rank matrices for background subtraction. The post-processing computes morphological filters and an active contours with a negative contraction bias. We proved the Multi-Layer RPCA algorithm in a camera-trap images database from the Colombian forest. The database was manually segmented to extract the f-measure of each automatic segmented image. We reach 0.7539 and 0.7393 of average f-measure in daytime and nighttime images respectively. The average f-measure was computed with all GT images. To our best knowledge, this paper is the first work in proposing Multi-Layer RPCA and using it for camera-trap images segmentation.\\
\\
\textbf{Acknowledgment.} This work was supported by the Colombian National Fund for Science, Technology and Innovation, Francisco Jos\'e de Caldas - COLCIENCIAS (Colombia). Project No. 111571451061.
\bibliographystyle{ieeetr}
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Welcome. I hope this Web page will be a helpful introduction to my surgical practice at Kaiser Permanente Downey Medical Offices and give you an opportunity to learn a little about me.
I was born and raised in Southern California, but I did most of my studies outside this region. My mother is a retired registered nurse who cared for patients preparing for surgery, and my father is a retired engineer. My three sisters and I were encouraged to excel in and enjoy the study of mathematics and science. This led me to study genetics at the University of California, Berkeley, and do basic science research in cancer biology.
My surgical practice at Kaiser Permanente reflects my interest in the diagnosis and treatment of cancer. I have a special interest in breast cancer, and I am involved in improving our screening and treatment of this disease. I realize that for most patients, a visit to a surgeon can be stressful. I feel it is my responsibility to make each patient feel comfortable with me and to help them understand their disease and their options for treatment.
I enjoy living and working in Southern California. I am close to my extended family and enjoy traveling with them, snowboarding, boating, scuba diving, and hiking. I find time to practice yoga, Crossfit, standup paddle boarding, and kayaking. I enjoy reading and cooking. I believe it is important to continually attempt new challenges. This year, I hope to lean to snow ski.
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Wallingford's Repair Café was the latest in a programme of such events held by community groups across Oxfordshire to encourage a "Fix-it" attitude and reduce electrical and other waste. Items repaired have included a sewing machine, vacuum cleaner, several toasters, a cuddly toy, a tent, and remote control car.
Tool sharpening and bike maintenance are among the services being offered which have been very popular. There were experts for electrical/electronic and textile repairs plus electrical safety testing and ad hoc repairs like glueing. Only minor repairs and maintenance can be undertaken due to time constraints but generally, the experts on hand will advise visitors how to complete the repairs or maintenance themselves where safe to do so. Sharing skills with visitors is one of the group's aims, to help more people consider repair or maintenance instead of the rubbish bin when an item breaks.
|
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| 1,691
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{"url":"https:\/\/socratic.org\/questions\/how-do-solve-the-following-linear-system-3x-4y-7-x-y-2","text":"# How do solve the following linear system?: 3x \u2013 4y = 7, x-y=2 ?\n\nMay 16, 2018\n\n$\\left(x , y\\right) = \\left(+ 1 , - 1\\right)$\n\n#### Explanation:\n\nGiven\n[1]$\\textcolor{w h i t e}{\\text{XXX}} 3 x - 4 y = 7$\n[2]$\\textcolor{w h i t e}{\\text{XXX}} x - y = 2$\n\nThere are several ways to solve this but since it was asked under \"Systems Using Substitution\", we will approach it that way:\n\nRearrange [2] into an equation in terms of $x$\n[3]$\\textcolor{w h i t e}{\\text{XXX}} x = y + 2$\n\nNow substitute $\\left(y + 2\\right)$ for $x$ in [1]\n[4]$\\textcolor{w h i t e}{\\text{XXX}} 3 \\left(y + 2\\right) - 4 y = 7$\n\nExpanding and simplifying [4]\n[5]$\\textcolor{w h i t e}{\\text{XXX}} - y + 6 = 7$\nor\n[6]$\\textcolor{w h i t e}{\\text{XXX}} y = - 1$\n\nNow substitute $\\left(- 1\\right)$ for $y$ back in [2] (or you could have used [1])\n[7]$\\textcolor{w h i t e}{\\text{XXX}} x - \\left(- 1\\right) = 2$\nSimplifying:\n[8]$\\textcolor{w h i t e}{\\text{XXX}} x = 1$","date":"2019-10-23 00:19:36","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 14, \"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\": 0.8647087216377258, \"perplexity\": 1382.4496586515936}, \"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-2019-43\/segments\/1570987826436.88\/warc\/CC-MAIN-20191022232751-20191023020251-00117.warc.gz\"}"}
| null | null |
All Categories > Optimization
Partner With a Google Ad Manager (DFP) Expert to Get Your Revenue Soaring!
Sovrn Publisher Advocate // July 9, 2018
If you've ever ridden in a small, 2-4 seater plane, you'll probably remember the experience for a lot of reasons. One thing you may have noticed with a smaller engine airplane is the instrument panel and other components around the pilot/co-pilot's chairs that manage the operations of the aircraft.
In larger aircraft, the same core components can also be found, but with significantly more features and functions by virtue of the performance and capacity requirements that come with transporting people and things at a much larger scale.
It's a similar situation when you compare Google Ad Manager (DFP) to most other ad servers. Many ad serving solutions for publishers offer the core features of inventory setup, ad delivery and some type of reporting; however, with Google Ad Manager, you get all of that and more in a comprehensive and feature-rich platform that sets the standard for small-to-enterprise level publishers.
One of the First!
In the mid-1990's, when internet advertising was in its infancy, a few small enterprises like Focalink/SmartBanner, AdConductor, and NetGravity launched their respective versions of the banner-ad delivery software. NetGravity's ad serving platform was acquired by DoubleClick when they bought NetGravity in 1999 and rebranded as the Dynamic Advertising Reporting & Targeting or "DART Enterprise" platform. DART Enterprise was then acquired by Google when Google bought DoubleClick in March of 2008. At the time, DoubleClick for Publishers (DFP) was already the standard-setting inventory management and ad delivery platform within the DART suite of solutions for digital marketers and web publishers.
Since Then
DFP has come a long way from its initial, basic banner ad delivery platform to the robust ad sales platform that it is today. In the premium and small business versions of DFP, its functionality and features include inventory management, ad delivery, reporting, forecasting, billing, audience data and sales operations. In addition to all of these features, larger publishers can seamlessly integrate the world's largest, real-time-bidding (RTB) ad exchange—Google AdX—with their DFP to add more Open and Private Marketplace (PMP) ad selling capabilities to their website monetization efforts.
More Value, More Expertise Needed
As with flying a 747 (compared to a two-seater airplane), the level of expertise a publisher will need when moving from a basic ad serving platform like Google's AdSense to DFP is significant. For this reason, it is in the publishers' best interest to invest in using DFP to its maximum potential. The more expertise you have managing DFP, the more you will be able to get the most revenue from advertising on your website. This is where partnering with experienced and qualified Google Ad Manager experts—such as Sovrn's Services team for training and/or management of your DFP network—can save you time and ensure that you're not leaving money on the table.
Getting the most out of your website monetization with Google Ad Manager requires effective management of your website's ad inventory, demand partnerships, and real-time selling strategies. To do these well, you need a responsive and thoughtful approach to the ever-changing dynamic of online advertising.
Whether it's training, set-up, clean-up, help with day-to-day ad operations or all of the above, Sovrn Services is here to help! Contact us to learn more about our flexible DFP consulting and training packages that are customized to your unique needs. Here's what Kevin Gentry, Product Manager at Ibotta, had to say about Ibotta's DFP consulting and training experience:
"With their expert knowledge in the space, it was super helpful to get training and an in-depth tutorial on AdTech best practices and DFP. As a company that is making an effort to be in front of new trends and technologies in ad tech, Sovrn's training efficiently brought the team up-to-speed and comfortable with using DFP. My team left Sovrn's training session with a better understanding of the ad tech space and best practices in programmatic."
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
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{-# LANGUAGE PolyKinds #-}
module Data.IxFunctor.Empty where
import Data.IxFunctor
class IxFunctor f => IxEmpty f where
iempty :: f i i a
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{"url":"https:\/\/www.physicsforums.com\/threads\/scalar-product-of-vectors.392139\/","text":"# Scalar product of vectors\n\n[PLAIN]http:\/\/img62.imageshack.us\/img62\/5319\/49966749.png [Broken]\n\nWhat is the scalar multiples of a vector actually?\nI was thinking L = c[2 1 2]T\nThen I looked for projection of v on L. But I got c in my answers which are not supposed to be...\n\nLast edited by a moderator:\n\nMark44\nMentor\n[PLAIN]http:\/\/img62.imageshack.us\/img62\/5319\/49966749.png [Broken]\n\nWhat is the scalar multiples of a vector actually?\nI was thinking L = c[2 1 2]T\nThen I looked for projection of v on L. But I got c in my answers which are not supposed to be...\nEvery vector in L is some scalar multiple of <2, 1, 2>. The line goes through the origin - the zero multiple of this vector is 0<2, 1, 2> = <0, 0, 0>, a vector that starts and ends at the origin. The line goes through the point (-4, -2, -4), which you can get by taking the -2 multiple of the vector.\n\nFor the reflection of v in the line, you want to find another vector w that is in the same plane as v and L, but is on the opposite side of L, and makes the same angle with L.\n\nLast edited by a moderator:\nSo I have to find angle theta between v and L, and then find vector w with negative theta?\nI also have to find the plane of v and L by cross product of v and L ....\n\nLast edited:","date":"2021-03-05 04:52:54","metadata":"{\"extraction_info\": {\"found_math\": false, \"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\": 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\": 0.9151437282562256, \"perplexity\": 435.1949135200191}, \"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-2021-10\/segments\/1614178369721.76\/warc\/CC-MAIN-20210305030131-20210305060131-00063.warc.gz\"}"}
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The newest part of the system is the conversational interface. What can it do? Client access to this interface is provided by a new chat dialog included in the smarthome server and is modeled to look like a typical instant messaging system, but instead of chatting with another user, you chat with smarthome. I also have a web based chat interface for access from the Internet. I can also send email to the system which upon authentication is passed to the conversational interface, processed and a return email sent with the responses.
The newest part of the system is the conversational interface. The ChatClient is the part of the SmarthomeServer which interacts with the ChatServer. As you can see it is meant to be familiar to anyone who is used to instant messaging.
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{
"redpajama_set_name": "RedPajamaC4"
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\section{Introduction}
Ever since the discovery of significant number of passive spiral galaxies without any apparent sign of ongoing star formation, the formation and evolution of these galaxies have received considerable attention observationally and theoretically (\citealt{Cou98}; \citealt{Dre99}; \citealt{Pog99}; \citealt{Bek02}; \citealt{Got03}; \citealt{Yam04}; \citealt{Mor06}; \citealt{Cor09}; \citealt{Hug09}; \citealt{Lee08}; \citealt{Mah09}; \citealt{Wol09}; \citealt{Mas10}; \citealt{Fra16}; \citealt{Fra18}). The first unusual spiral galaxies were identified by \citet{van76} in the Virgo cluster, so-called `anemic' spirals, and later, passive spirals were found in all environments and at low to high redshifts. Since early samples of red or passive spirals often show the evidence of mild star formation (SF) such as weak nebular emissions, ultraviolet (UV) light from young stellar populations, and infrared (IR) excess from warm dust by obscured SF, some of them may be in progress of star formation quenching rather than completely quiescent. On the other hand, some galaxies show little or no star formation activity despite their obvious spiral structure -- these are the genuine passive spirals. These unique galaxies are clear outliers from the well known color-morphology relations (\citealt{Hub38}; \citealt{Fio99}; \citealt{Ber00}; \citealt{Mig09}).
The existence of these galaxies leads to the following questions: (1) What is/are the origin(s) of passive spirals? (2) What physical processes have halted the star formation in passive spirals without destroying their spiral structures? (3) Are passive spirals eventually transformed into lenticular galaxies?
Recent studies suggest that the formation of passive spirals in the intermediate to high density environments is closely related with cluster environmental effects (\citealt{Got03}; \citealt{Mas10}; \citealt{Fra18}) such as thermal evaporation \citep{Cow77}, ram pressure stripping \citep{Gun72}, harassment \citep{Moo99}, starvation or strangulation (\citealt{Lar80}; \citealt{Bek02}), galaxy-galaxy interactions in high density regions including major \citep{Too72} and minor \citep{Wal96} mergers and tidal interactions. Moreover, a very recent study of \citet{Fra18} found that all low mass (M$_\star$ $< 1 \times 10^{10} M_{\odot}$) passive spirals in their sample are members of the Virgo cluster, and thus cluster-related environmental phenomena are most likely responsible for the quenching of those galaxies.
The existence of passive spirals is the strong evidence for the morphological transformation of spirals into S0s in rich clusters. \citet{Bek02} showed how cluster environmental quenching processes can transform spirals into S0s, passing through an intermediate passive spiral phase, using numerical simulations. After the gas is stripped, the spiral arm structures fade over several Gyrs. However, they claim that passive spirals are found anywhere from isolation to the centers of clusters and hence that no single mechanism can completely explain their origins.
In low density environments, secular evolution as a result of bars is a viable mechanism for quenching spirals (\citealt{Kor79}; \citealt{Kor04}; \citealt{Ath13}), which may convert them into S0s. Bars are commonly found structures in disk galaxies of the local universe. Recent work on the bar fraction of nearby disk galaxies suggests that the bar fraction is up to $\sim 50\%$ in optical studies (\citealt{Mar07}; \citealt{Ree07}; \citealt{Bar08}). The fraction rises to about 70\% in near-infrared studies (\citealt{Kna00}; \citealt{Men07}).
Bars play a significant role in the evolution of galaxy structure and morphology by transferring angular momentum and energy, and redistributing mass. They act on both baryonic and dark matter components of a galaxy (\citealt{Wei85}; \citealt{Deb98}, \citealt{Deb00}; \citealt{Ath03}). Bars funnel material towards the galaxy center, helping to grow bulge-like structures (\citealt{Kor04}), nuclear bars (\citealt{Erw04}) and feeding the central black hole (\citealt{Shl89}; \citealt{Shl90}; \citealt{Shl00}; \citealt{Jog06}). In particular, the role of driving gas inwards can trigger star formation in the center (e.g. \citealt{Haw86}; \citealt{Jog05}; \citealt{She05}), and lead to the more rapid consumption of the gas. \citet{Mas12} showed that a higher bar fraction in disk galaxies is associated with a lower HI gas content, and there are hints that at a fixed HI content barred galaxies are optically redder than unbarred galaxies. Since high-mass passive spirals (M$_\star$ $> 1 \times 10^{10} M_{\odot}$) are found not only in high density regions but in very low density regions (\citealt{Bam09}; \citealt{Mas10}; \citealt{Fra18}), it is suggested that internal processes such as bars are more important mechanisms to quench the star formation in high mass passive spirals.
While all these devoted studies have drawn attention to passive spirals, the origins and evolutionary pathways of passive spirals are still under debate. To confirm the origin of passive spirals, strong constraints can be provided by investigating the internal distribution of their stellar populations, which are poorly understood so far. That is, an important clue to their origin can be found in whether the quenching is inside-out or outside-in, as well as how old these systems are and how recently their star formation is quenched. Comparing the resolved stellar populations of passive spirals with S0s, their probable descendants, will be helpful to constrain the specific transformation mechanisms that are in action. In addition, the environmental dependence of passive spirals is also unclear. Thus, investigating the environments of individual galaxies may also provide constraints on the quenching mechanisms.
The purpose of this paper is to better understand the evolution of passive spiral galaxies by investigating their spatially resolved stellar populations, using the Calar Alto Legacy Integral Field Area (CALIFA; \citealt{San12}; \citealt{Hus13}) survey, which has been observing a wide range of galaxy morphologies with a wide field-of-view (FoV). In the last decade, the advent of integral field units (IFU) has allowed us to study the details of integrated and spatially resolved spectroscopic properties of galaxies, based on two-dimensional (2D) maps of kinematics and stellar populations. This is the first study of spatially resolved stellar populations for passive spirals. In this study, we ultimately aim to find evolutionary links between passive spirals and S0s.
This paper is organized as follows. Section 2 describes the galaxy samples adopted from the CALIFA survey. The analysis of data including line measurement is in Section 3. We present our results of stellar population properties for the passive spirals in Section 4. Finally, our discussion and conclusions on the evolution of passive spirals are given in Section 5.
\section{DATA and Sample Selection}
The CALIFA survey (\citealt{San12}; \citealt{Hus13}) was carried out using the 3.5m telescope of the Calar Alto observatory using the PMAS/PPAK spectrograph (\citealt{Rot05}; \citealt{Kel06}). The field of view of PPAK is $74\arcsec$ $\times$ 64$\arcsec$, which is filled with 382 fibers of 2.7$\arcsec$ diameter each \citep{Kel06}. The galaxies were observed with two spectroscopic setups, using the gratings V500 with a nominal resolution ($\lambda$/$\Delta \lambda$) of 850 at 5000 {\AA} (FWHM $\sim$ 6 {\AA}) and a wavelength range from 3745 to 7500 {\AA}, and V1200 with a better spectral resolution of 1650 at 4500 {\AA} (FWHM $\sim$ 2.7 {\AA}) and ranging from 3650 to 4840 {\AA}. More detailed information about the CALIFA sample, and the observational strategy, are available in the papers of CALIFA team (\citealt{Wal14}; \citealt{San12}; \citealt{Hus13}; \citealt{Gar15}; and \citealt{San16}). We here analyzed galaxies using only the V500 data cube for consistency.
The classification is based on the visual inspection by the authors using the SDSS g$-$, r$-$, and i$-$band composite color images and the spectra. We select spirals with red optical color and without nebular emissions. Among the visually selected red spirals, we limit the NUV$-$r colors of our sample to be larger than $5$ using the Galaxy Evolution Explorer (GALEX) in order to exclude actively star forming galaxies. In addition, edge-on galaxies, shell galaxies, and galaxies with ongoing mergers or strong tidal interactions with neighbors are excluded from our sample.
This process yields a final sample of $9$ passive spiral galaxies. The SDSS images of these galaxies are presented in Figure \ref{F1}. Six of them show well-developed spiral arms. The others have less prominent spiral arms but have subtle structures with discontinuous stellar distributions in their disks. We present about half of S0s in our sample to show that they are clearly different from passive spirals. S0s would have central star forming ring, inner bar and X-shaped structures but no spiral arms.
Passive spirals have stellar masses of $10.23 \lesssim$ log (M$_{\star}/$M$_{\odot}) \lesssim 10.8$, based on stellar masses from the NASA-Sloan Atlas (NSA, \citealt{Bla11}) catalog (Figure \ref{F2}). All passive spirals but one (NGC 3300) have $4.6 \micron -12 \micron < 2$ in the Wide-field Infrared Survey Explorer (WISE) IR color-color diagram (red stars in Figure \ref{F3}), which is the region where typical early-type galaxies are located (see Fig. 11 (b) of \citealt{Jar17}). Table \ref{Tbl1} summarizes the basic information of the 9 passive spirals.
From the CALIFA sample we select lenticular and star-forming spiral galaxies in the same stellar mass range as our passive spiral sample in order to more fairly compare their stellar populations. For our star forming spiral sample, we adopt the subtype of spirals from the NASA/IPAC Extragalactic Database (NED). Like the passive spiral sample, we excluded ongoing mergers or strong tidal interactions with neighbors. This results in a sample of $21$ S0s and $57$ spirals as a comparison sample. About half of S0s show embedded structures such as a nuclear star forming ring, inner bars/spirals, rings and X-shapes in disk, features that are typically observed in S0s (\citealt{But13}).
\begin{table*}
\caption{Basic information of 9 passive spirals}
\label{Tbl1}
\begin{tabular}{lccccccccrc}
\hline
Name & R.A. & DEC. & Redshift & log (M$_{\star}/$M$_\odot$) & M$_r$ & NUV$-$r & $[4.6]-[12]$ & $[3.4]-[4.6]$ & R$_e$ & n \\
& (deg.) & (deg.) & & & (mag) & & & & ($\arcsec$) & \\
(1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) & (11) \\
\hline
NGC 1666 & 072.1368 & -06.570053 & 0.001 & 10.23 & -20.16 & 5.44 & $1.42 \pm 0.049$ & $-0.02 \pm 0.009$ & 6.73 & 5.76 \\
NGC 5876 & 227.3816 & 54.506515 & 0.011 & 10.31 & -20.36 & 5.78 & $1.40 \pm 0.014$ & $-0.05 \pm 0.007$ & 10.51 & 5.14 \\
NGC 5794 & 223.9734 & 49.726063 & 0.014 & 10.31 & -20.37 & 5.74 & $0.50 \pm 0.044$ & $-0.04 \pm 0.008$ & 5.91 & 4.69 \\
NGC 495 & 020.7331 & 33.471387 & 0.014 & 10.38 & -20.54 & 5.99 & $0.51 \pm 0.069$ & $-0.05 \pm 0.009$ & 9.79 & 4.52 \\
NGC 3300 & 159.1601 & 14.171126 & 0.010 & 10.40 & -20.59 & 5.80 & - & - & 12.55 & 2.93 \\
NGC 2553 & 124.3958 & 20.903057 & 0.016 & 10.45 & -20.78 & 5.81 & $0.28 \pm 0.109$ & $-0.05 \pm 0.011$ & 8.30 & 4.51 \\
NGC 7563 & 348.9830 & 13.196131 & 0.014 & 10.55 & -20.87 & 5.81 & $0.64 \pm 0.039$ & $-0.07 \pm 0.009$ & 8.77 & 3.84 \\
UGC 1271 & 027.2502 & 13.211104 & 0.017 & 10.54 & -20.93 & 5.97 & $0.54 \pm 0.050$ & $-0.03 \pm 0.009$ & 8.20 & 4.20 \\
UGC 2018 & 038.1673 & 00.260080 & 0.021 & 10.73 & -21.47 & 5.74 & - & - & 8.70 & 5.18 \\
\hline
\end{tabular}
\\
\begin{flushleft}
Notes. Column 1 shows the name of the passive spiral, and Column 2 and 3 show the coordinates. Column 4 gives redshift, while Column 5 and 6 give the stellar mass and absolute magnitude in r$-$band, respectively. Column 7, 8 and 9 denote NUV$-$r and IR colors, respectively. Column 10 and 11 show the effective radius and S\'ersic index, respectively. Column 1 to 7, and Column 10 and 11 are from the NSA catalog. The NUV and r absolute magnitudes in the NSA are given for $h = 1$, where H$_0 = 100h$ km s$^{-1}$ Mpc$^{-1}$. IR colors in Column 8 and 9 are from the WISE catalog.
\end{flushleft}
\end{table*}
\begin{figure}
\includegraphics[width=8.5cm]{F1.pdf}
\caption{The SDSS g$-$, r$-$, and i$-$bands composite images of our 9 passive spirals and the example of S0 and spiral comparisons from the CALIFA archive. The galaxies are ordered from low to high stellar mass according to their NSA catalog stellar mass, for each morphology separately. All images are 120$\arcsec$ $\times$ 120$\arcsec$ in size. North is at the top and east is to the left. The white box in NGC1666 is CALIFA field of view.
\label{F1}}
\end{figure}
\begin{figure}
\includegraphics[width=8.5cm]{F2.pdf}
\caption{NUV$-$r vs. log (M$_{\star}/$M$_{\odot}$) for passive spirals and S0s. Red stars (and red in histogram) are 9 passive spirals and orange circles (and orange hatched in histogram) are 21 S0s. The green and blue squares indicate early- and late-type star-forming spiral galaxies. The distribution of galaxies from the NSA catalog is overlaid as contours.
\label{F2}}
\end{figure}
\begin{figure}
\includegraphics[width=8.5cm]{F3.png}
\caption{WISE color-color diagram for all CALIFA galaxies. The spheroidal (early-type), intermediate disk (disk), and star forming (SF) disk (late-type disk) galaxies are divided by dotted lines based on the schematic diagram from \citet{Jar17}. Symbols are the same as those in Figure \ref{F2}. We use the magnitudes in the WISE catalog extracted using elliptical aperture photometry. When the elliptical-aperture magnitude is not available, we use the instrumental profile-fit photometry magnitude (light red stars for passive spirals, orange open circles for S0s, green and blue open squares for early- and late-type spirals, respectively).
\label{F3}}
\end{figure}
\section{Analysis}
We spatially bin the CALIFA data by means of the centroidal Voronoi tessellation algorithm of \citet{Cap03} using the PINGSoft \citep{Ros12} software. The minimum S/N (per bin) for each galaxy is set to be between $15$ and $20$. To derive the stellar velocity ($v_{star}$) and velocity dispersion ($\sigma_{\star}$), emission lines are masked and the absorption line spectrum is fitted with the penalised pixel-fitting approach \citep[pPXF;][]{Cap03} using the stellar population model templates from the MILES stellar library \citep{Vaz10}. The process includes spatial masking of sky lines and bad pixels. The best fitting template combination is determined by $\chi^2$ minimization in pixel space. The best values of radial velocities and absorption line broadening ($\sigma$) for the stellar component are derived in each binned spectrum.
\subsection{Lick Indices}
The spectral range of the CALIFA data covers a number of absorption lines that can be used as tools to probe the stellar populations of a galaxy. We quantify the absorption features using line-strength indices such as H$\beta$, Mg$b$, Fe5270 and Fe5335, taken from the Lick/IDS system, using the code \textit{lick\_ew.pro} of \citet{Gra08}, part of their {\scriptsize EZ\_AGES} package, which is widely used to measure stellar populations of galaxies and star clusters from Lick indices.
Before calculating line-strength indices, we broadened the CALIFA spectra so that their spectral resolution after velocity dispersion correction in each bin agrees with the spectral resolution of each index in the Lick system (\citealt{Wor97}; \citealt{Tra98}) as implemented in the \textit{lick\_ew.pro} routine. We correct the intrinsic H$\beta$ emission to obtain the `genuine' H$\beta$ absorption line strength, because the observed H$\beta$ line is the combined result of intrinsic emission and intrinsic absorption. We regard the difference in H$\beta$ absorption line strength between the observation and best-fit template as the intrinsic H$\beta$ emission, and the genuine H$\beta$ absorption line-strength is recalculated by adding up this difference. The correction is applied only when the amplitude-to-noise (A/N) of H$\beta$ in each bin is greater than $3$. The estimated intrinsic emission values are similar to typical measurement errors at each radius. For passive spirals, the typical measurement error and intrinsic H$\beta$ emission are $0.17$ and $0.15$ {\AA} at the center and $0.25$ and $0.26$ {\AA} at 1 R$_e$.
\subsection{Lick Index Grid Method}
To derive luminosity-weighted simple stellar population (SSP)-equivalent parameters, we use the Lick index grid method, which derives the age, metallicity and abundance ratio by comparing Lick indices to SSP model grids, with iterations between different index-index planes \citep{Puz05}. Here, we adopt SSP models given by \citet{TMB} (hereafter, TMB model).
We use the indices plane of [MgFe]$^\prime$\footnote{[MgFe]$^\prime$ $=$ $\sqrt{\textrm{Mg}b \times (0.72 \times \textrm {Fe}5270 + 0.28 \times \textrm{Fe}5335)}$} versus H$\beta$ to estimate the metallicity and age. The [MgFe]$^\prime$ is insensitive to [$\alpha$/Fe], so it is a good tracer of metallicity. H$\beta$ is an age indicator, which is the least sensitive to [$\alpha$/Fe] among the Balmer lines \citep{Tho03}. We also use the Mg$b$-<Fe>\footnote{<Fe> $=$ (Fe5270 + Fe5335)$/2$} plane to estimate [$\alpha$/Fe]. The Mg$b$ is sensitive to [$\alpha$/Fe], and the <Fe> is a metallicity indicator.
To obtain fine accuracy in the estimation, we interpolate the TMB models to grids with $\sim 300,000$ individual models, spanning [Z/H] $= -0.33$ to $0.67$ (in the interval with $30$ steps), age $= 1$ to $15$ Gyr ($140$ steps) and [$\alpha$/Fe] $= -0.3$ to $0.5$ ($30$ steps). The majority of our measurements for the galaxies in this study are covered by these model parameter ranges. For seven points that lie outside the model grid space, we use the best fitting values at the boundary of the interpolated models.
\begin{figure*}
\centering
\includegraphics[width=18cm]{F41_n1666.pdf}
\caption{The SDSS optical images and maps of the derived parameters of the $9$ passive spirals in the CALIFA sample, ordered by increasing stellar mass from the NSA catalog. In the upper row, from left to right we show the SDSS r-band image, the SDSS r-band image with surface brightness contours (in yellow) and the one and two effective radius (ellipses), the stellar velocity map, and the velocity dispersion map. The velocity is normalized relative to the velocity of the brightest pixel. In the bottom row, we present the H$\beta$, Mg$b$, Fe5270 and Fe5335 maps. We mark the outermost of the surface brightness contour and the one and two effective radius (ellipses) on the parameter maps. In order to easily compare between galaxies, the range of the color bars is fixed for each parameter.
\label{F41}}
\end{figure*}
\addtocounter{figure}{-1}
\begin{figure*}
\centering
\includegraphics[width=18cm]{F42_n5876.pdf}
\caption{ {\it continued}
\label{F42}}
\end{figure*}
\addtocounter{figure}{-1}
\begin{figure*}
\centering
\includegraphics[width=18cm]{F43_n5794.pdf}
\caption{ {\it continued}
\label{F43}}
\end{figure*}
\addtocounter{figure}{-1}
\begin{figure*}
\centering
\includegraphics[width=18cm]{F44_n495.pdf}
\caption{ {\it continued}
\label{F44}}
\end{figure*}
\addtocounter{figure}{-1}
\begin{figure*}
\centering
\includegraphics[width=18cm]{F45_n3300.pdf}
\caption{ {\it continued}
\label{F45}}
\end{figure*}
\addtocounter{figure}{-1}
\begin{figure*}
\centering
\includegraphics[width=18cm]{F46_n2553.pdf}
\caption{ {\it continued}
\label{F46}}
\end{figure*}
\addtocounter{figure}{-1}
\begin{figure*}
\centering
\includegraphics[width=18cm]{F47_n7563.pdf}
\caption{ {\it continued}
\label{F47}}
\end{figure*}
\addtocounter{figure}{-1}
\begin{figure*}
\centering
\includegraphics[width=18cm]{F48_u1271.pdf}
\caption{ {\it continued}
\label{F48}}
\end{figure*}
\addtocounter{figure}{-1}
\begin{figure*}
\centering
\includegraphics[width=18cm]{F49_u2018.pdf}
\caption{ {\it continued}
\label{F49}}
\end{figure*}
\section{Results}
In Figure \ref{F41}, we present the SDSS r-band images, velocity ($v_\star$), velocity dispersion ($\sigma_\star$), and the absorption-line strength maps (e.g. H$\beta$, Mg$b$, Fe5270 and Fe5335) for our passive spiral sample. Our passive spirals have clear rotation and slightly higher velocity dispersion in the center, as also seen in the early type spiral galaxy, NGC 1167 from \citet{Fal17}. We do not find any asymmetry or distorted structures, as evidence for tidal interactions, within their kinematics. In general, H$\beta$ decreases toward the center of the galaxies and the other lines barely show any common trends. Mg$b$ and Fe lines are slightly enhanced along the bar in NGC 3300 and UGC 1271.
\subsection{Stellar populations of passive spiral galaxies}
Figure \ref{F5} presents index-index diagrams with isophotal radial profiles for our sample galaxies from the measurements of the absorption line strengths. For this, we first conduct isophotal photometry for the CALIFA r-band image of each target, using the IRAF/ELLIPSE task \citep{Jed87}. We then use these isophotes to estimate the radial profiles of the line indices.
In the top panels of Figure \ref{F5}, we present the median stellar population properties of each morphological type at each radius in comparison to the TMB model grids. The median line indices were estimated out to $2$ R$_e$, but we note that the signal-to-noise drops below $30$ at R $>$ R$_e$.
In Figure \ref{F5}, [$\alpha$/Fe] appears to be almost constant regardless of galaxy type or radius, whereas metallicity tends to decrease from early- to late-types and from the central to outer regions of galaxies. A common trend is also found for decreasing age and metallicity from early- to late-types, and also with radius. For comparison, we show the star-forming spirals within the same mass range as the other types out to $1.5$ R$_e$. Why the radial limit is $1.5$ R$_e$, and not $2$ R$_e$, is that most of these spirals have larger R$_e$ than passive spirals and S0s, and the FoV of CALIFA does not reach out to $2$ R$_e$ for more than $30 \%$ of our spirals. The star-forming spiral galaxies are clearly distinct from passive spirals and S0s in both index-index diagrams, which indicates that the stellar populations of passive spirals are closer to those of S0s rather than star-forming spirals. Hence, we focus on the comparison between passive spirals and S0s individually in the bottom panels of Figure \ref{F5}. Overall, we find that our passive spirals show a large variety of behavior among themselves. It is noticeable that S0s have even larger diversity in their stellar populations.
Figure \ref{F6} shows the stellar population maps for our passive spirals. The stellar populations are very diverse as well. NGC 1666 shows overall young ages but is slightly older in the vicinity of $1$ R$_e$. NGC 5876 tends to be older in the central bulge and along the bar. NGC 7563 show mostly old stellar populations. In the metallicity maps, the outer parts tend to be more metal-poor, although the fluctuations are large. [$\alpha$/Fe] tends to be slightly lower at the center, except in NGC 7563.
Figure \ref{F7} shows the distribution of stellar population parameters. Overall, S0s (orange hatched) span a wide range of stellar population parameters at all radii and the distributions of passive spirals (red filled) are encompassed by the ranges of S0 properties for all parameters The probability, P$_0$, of similarity in the cumulative distributions between the two galaxy types as returned by a Kolmogorov-Smirnov (KS) test is given in each panel. However, passive spirals seem to be slightly biased within the S0 distribution: towards higher [Z/H], lower [$\alpha$/Fe], and younger ages. Although such biases do not appear to be very obvious possibly due to the small sample size, some marginal differences are detected in the KS test: P$_0 = 0.13$ for age at $2$ R$_e$, P$_0 = 0.12$ for [Z/H] at $1$ R$_e$, and P$_0 = 0.03$ for [$\alpha$/Fe] at $1$ R$_e$.
One may suspect that this difference at outer region between passive spirals and S0s may be caused by the morphological difference between them, such as the difference in the fraction of bulge light at given radius. However, we confirmed that there is no systematic difference in the distribution of bulge fraction at any radius up to $2$ R$_e$ between our passive spirals and S0s. Both types of galaxies show consistent bulge fraction on average with large dispersion at given radius.
Although the stellar populations of the S0 galaxies are widely dispersed as already mentioned, their metallicities tend to be slightly richer in the center than in the outskirt, whereas their ages seem to be similar between the center and the outskirt. No radial gradient is found for [$\alpha$/Fe] on average. This trend is in good agreement with previous results (\citealt{Tab17}; \citealt{Fra18}).
\begin{figure*}
\includegraphics[width=18cm]{F5.png}
\caption{Top: Mg$b$ vs. <Fe> (left) and H$\beta$ vs. [MgFe]$^{\prime}$ (right) diagrams for passive spirals (red), spirals (green for Sa-Sb and blue for Sc-Sd spirals) and S0s (yellow) with TMB model grids for ages, metallicities, and abundance ratios. The line strengths are measured along annuli derived from isophotal photometry. The values at $1/8$ R$_e$ (center), $1/4$ R$_e$, $1/2$ R$_e$, $1$ R$_e$, $1.5$ R$_e$ and $2$ R$_e$ are the averages in each annulus with $1 \arcsec$ thickness at the given radius. In the Mg$b$ vs. <Fe> diagram, solid and dashed lines are the $10$ Gyr and $5$ Gyr models, respectively. The model lines of [Z/H] $= 0$ in the left diagram are emphasized as thick lines for each age. Each error bar indicates the median value of measurement uncertainties in each morphological type at the given radius. Bottom: the same index diagrams for passive spirals (colored) and S0s (pale brown) with TMB model grids. The center of each galaxy is marked with large symbols (stars for passive spirals and circles for S0s).
\label{F5}}
\end{figure*}
\begin{figure*}
\centering
\includegraphics[width=18cm]{F6_1.pdf}
\caption{SDSS r-band image, derived age, [Z/H], and [$\alpha$/Fe] maps for the passive spirals. The outermost surface brightness contour and the one and two effective radii ellipses are denoted by a yellow line and red ellipses respectively in each r-band image, and by a black line and red ellipses respectively in each stellar population map.
\label{F6}}
\end{figure*}
\addtocounter{figure}{-1}
\begin{figure*}[t]
\centering
\includegraphics[width=18cm]{F6_2.pdf}
\caption{ {\it continued}
\label{F62}}
\end{figure*}
\begin{figure}
\includegraphics[width=8.5cm]{F7.pdf}
\caption{Comparison of luminosity-weighted age (left column), metallicity (middle column) and $\alpha$-abundance (right column) at the center ($1/8$ R$_e$), $1/2$ R$_e$, $1$ R$_e$, and $2$ R$_e$ from top to bottom rows for passive spirals (red filled histogram) and S0s (orange hatched histogram). The median values of passive spirals and S0s are denoted in the top right corner of each panel.
\label{F7}}
\end{figure}
\subsection{Environments of passive spiral galaxies}
Next, we investigate how the stellar populations of passive spirals vary in each individual galaxy with their environment in Figure \ref{F8}. We adopt the number of group members (N$_m$) as an environmental indicator by using the group catalog of \citet{Tul15}. According to the information in this group catalog, our passive spiral sample exists over all environments from field to cluster. For instance, NGC 1666 is in isolation, while NGC 495 is a part of the Perseus-Pisces Supercluster.
The results show that the correlations are mostly unclear between the stellar populations and environment of the passive spirals in our sample. The $\Delta$age and $\Delta$[Z/H]] do not exhibit significant correlations with environments: Spearman's rank coefficient is $-0.29$ (the significance of deviation, P$_0 = 0.89$) for the age and $0.38$ (P$_0 = 0.38$) for the metallicity. On the other hand, even though there is the caveat of small-number statistics, we obtain a Spearman's rank coefficient for $\Delta$[$\alpha$/Fe] of $0.73$ (P$_0 = 0.03$). However, when we eliminate the single point in the upper-right corner (NGC 495) which makes the correlation look strong, the correlation coefficient becomes smaller ($0.59$ with P$_0 = 0.12$) but still is considerable. This means that, in denser environments, at 1 R$_e$ passive spirals have higher [$\alpha$/Fe] than in their centers, and this likely indicates they were quenched faster in their outskirt than in their centers, perhaps by physical mechanisms operating in the denser environment. Even though there is no correlation between [Z/H] and environment, the gradient mostly show negative values.
\begin{figure}[t]
\includegraphics[width=8.5cm]{F8.png}
\caption{Age, metallicity, and $\alpha$-abundance variations between the center (star symbol) and $1$ R$_e$ (dot symbol) in the left column and their differentials ($1$ R$_e$ $-$ center) in the right column for passive spirals with the number of group member. The measurement errors are shown. The Spearman's correlation coefficient and probability (P$_0$) are presented in the right panels. We adopt the membership information of each galaxy from the group catalog of \citet{Tul15}.
\label{F8}}
\end{figure}
\section{Discussion and Conclusions}
Now we discuss the evolutionary pathways for passive spirals. Today, one of the widely-believed origins of S0s is that they evolved from spiral galaxies. That is, S0s may be the end-product of the transformation of spiral galaxies that have had their gas content removed by means of external gravitational or non-gravitational forces, or by secular evolution. In this scenario, passive spirals could be objects caught in the transitional stage between normal star-forming spirals and S0s \citep{Bek02}. Previous studies argued that multiple quenching mechanisms are required (\citealt{Mas10}; \citealt{Fra18}). Our results are consistent with this suggestion to some extent.
There seem to exist evolutionary connections between passive spirals and S0s from the comparison of their stellar populations. The passive spirals may be the origin of at least a portion of S0s, with other evolutionary pathways contributing in parallel. By comparing stellar populations in Figs \ref{F5} and \ref{F7}, it is revealed that the S0s have a wider range of age, metallicity and $\alpha$-abundance at all radii out to $2$ R$_e$. The stellar populations of passive spirals are fully encompassed within the spread of S0 properties, although the distributions of passive spirals appear skewed toward slightly younger ages, higher metallicities, and lower $\alpha$-abundances.
For the origin of passive spirals, quenching by perturbation from a bar is one plausible scenario. As one can see in Fig. \ref{F1}, $7$ out of the $9$ passive spirals have clear bar features. This high bar fraction ($\sim 78 \%$) in passive spirals is consistent with previous results. \citet{Mas10} reported that red spirals have an optical bar fraction of at least $67 \pm 5\%$. On the other hand, \citet{Fra18} found that the bar fraction of passive spiral galaxies is significantly higher ($74 \pm 15\%$), compared to mass, redshift and T-type matched star-forming spiral galaxies ($36 \pm 5\%$). Therefore, we suspect that bars in galaxies, both in low and high density environments, may act to shut down the star formation, leaving behind spiral structures that may last for several Gyrs \citep{Bek02}. However, it is unclear if secular evolution by a bar is the only mechanism for quenching our passive spiral sample. Even though a large fraction of our passive spirals have bars in their disks, there still exist non-barred ones which could only be explained in this scenario if bars are transient phenomena \citep{Bou02}.
Quenching by environmental effects is also a possible scenario. As one can see in our results in Figure \ref{F8}, the $\Delta[\alpha$/Fe] of passive spirals are marginally related with their environments. It means that environmental effects may have influenced the quenching in outskirt of a galaxy. All our passive spirals, except NGC 1666 in isolation, have close neighbors ($\sim 47 - 274$ kpc), so there are opportunities for galaxies to be affected by their neighbors, even in sparse groups.
These passive spirals may have already depleted all their gas reservoirs, or they still have plenty of gas but it is not condensed enough to trigger star formation. Recently, \citet{Fre18} found a significant quantity of CO-traced low density gas in two (one is highly disturbed) post-starbursts (or `E+A') galaxies, which are currently quiescent galaxies. Similarly, \citep{Ell18} found there is still significant quantities of gas in some galaxy-galaxy mergers even after star formation was halted. Therefore, we check the gas contents of our passive spirals case by case. Table \ref{Tbl2} shows a summary of the information from literature about the intracluster medium (ICM) in their host groups, and HI and CO observations in each galaxy. We confirm that, except for NGC 5794 and NGC 495 (which were not observed in the HI Parkes All Sky Survey; HIPASS), our passive spirals were targeted but not detected. Therefore, based on the detection limit of the HIPASS ($10^{6} \times d_{Mpc}^{2}$; \citealt{Sta00}), we can place upper-limit on their HI masses of $\leq$ $ 10^{8.9} - 10^{9.6}$ M$_{\odot}$. This amount is obviously lower than the median HI masses of normal spiral galaxies in the HIPASS; log(M$_{HI}$/M$_{\odot}$) $= 9.59 \pm 0.43$ and $9.61 \pm 0.46$ in the stellar masses of log(M${_\star}$/M${_\odot}) = 10.25$ and $10.75$, respectively (\citealt{Par18}). Here, we describe some noticeable cases as follows. \\
\begin{table}
\caption{X-ray, HI and CO information of $9$ passive spirals}
\centering
\label{Tbl2}
\begin{tabular}{llrrcccccc}
\hline
Name & Group & N$_m$ & D$_{1st}$ & HI & CO & X-ray \\
& & & (kpc) & & & \\
(1) & (2) & (3) & (4) & (5) & (6) & (7) \\
\hline
NGC 1666 & NGC 1666 & 1 & - & $\times$ & - & $\times$ \\
NGC 5876 & NGC 5876 & 2 & 248 & - & $\times$ & - \\
NGC 5794 & NGC 5797 & 4 & 78 & - & - & - \\
NGC 495 & NGC 507 & 49 & 47 & - & - & $\circ$ \\
NGC 3300 & NGC 3300 & 3 & 274 & $\times$ & - & - \\
NGC 2553 & NGC 2563 & 21 & 229 & $\times$ & - & $\circ$ \\
NGC 7563 & NGC 7563 & 7 & 76 & $\times$ & - & - \\
UGC 1271 & NGC 677 & 10 & 132 & $\times$ & - & $\circ$ \\
UGC 2018 & UGC 2005 & 12 & 203 & $\times$ & - & - \\
\hline
\end{tabular}
\\
\begin{flushleft}
Notes. Column 1 gives the name of passive spirals, and Column 2 to 4 give the host galaxy of the group to which each passive spiral belongs, number of members (N$_m$), and the distance from the nearest neighbor adopted from \citet{Tul15}, respectively. Column 4 and 5 show the HI (HIPASS) and CO (EDGE-CALIFA Survey from \citealt{Bol17}) information of each galaxy. Column 6 describes if the group has an X-ray source): NGC 495 (\citealt{kim04}; \citealt{Sat09}), NGC 2553 (\citealt{Ras12}; \citealt{Mor17}) and UGC 1271 (\citealt{Osu17}). The symbols of `$\circ$' and `$\times$' denote if the source is `detected' or `non-detected', respectively. If the observation does not exist, we mark it with ` - '.
\end{flushleft}
\end{table}
\noindent \textit{NGC 5876.} NGC 5876 is listed in the recent CO observation of the EDGE-CALIFA Survey \citep{Bol17}, but no significant emission is detected (S$_{CO}$ $\Delta$v (Jy km s$^{−1}$) $<16.0$). This galaxy is in a pair with a normal spiral galaxy at a distance of $248$ kpc but there is no evidence for a direct interaction in the optical image. \\
\noindent \textit{NGC 2553.} Although NGC 2553 is quite far from the center of its group, no meaningful signal of HI is detected in this galaxy. The ICM is detected in this group (\citealt{Ras12}; \citealt{Mor17}). Therefore, this galaxy may be influenced by the environmental effects such as ram-pressure stripping or harassment. \\
\noindent \textit{NGC 1666.} The isolated galaxy NGC 1666 is notable. There is no meaningful HI signal in this galaxy, despite the fact that it may have rarely experienced environmental effects. In this case, secular evolution may be the main driver for star formation quenching. If there is no further inflow of fresh gas, the gas in the disk will run out in a few Gyrs (starvation or strangulation; \citealt{Lar80}). Especially, in the center of the galaxy, the age is the youngest and the metallicity is the richest among all of our passive spiral sample (see Fig. \ref{F8}). Hence, this galaxy may be quenched very recently. However, the question of how all its gas is used up by itself still remains. The enrichment of metallicity is also not easily understood but it may imply that the inflow of pristine gas has been cut off for some reason. \\
\noindent \textit{NGC 495.} NGC 495 is in the Perseus-Pisces Supercluster. This galaxy is close to the central galaxy of the cluster ($\sim200$ kpc) and has a close early-type neighbor at a distance of $\sim47$ kpc. In addition, there is ICM detected in this group (\citealt{kim04}; \citealt{Sat09}), so NGC 495 may have been influenced by ram-pressure stripping. Thus, we might expect that there is no or a very small amount of cold gas in this galaxy, but unfortunately NGC 495 is out of the coverage of the HIPASS. \\
We conclude that the similarity in stellar populations between passive spirals and S0s is in accordance with the idea that S0s may have formed through various evolutionary pathways, and passive spirals could be one of the channels transforming from spirals to S0s. (1) Passive spirals in isolation or low density regions might be just old spirals that have exhausted their fuel. Such gas consumption may have been accelerated by internal processes related with bar structure. (2) In denser environments, neighbor interactions or group/cluster mechanisms can help strip the gas away predominantly in the halo and outer disks, but still secular evolution by a bar could accelerate quenching. Both scenarios may explain the cessation of star forming activity without destroying the spiral structure.
The analysis of large public data sets such as those of the Sydney-AAO Multi-object Integral field Spectrograph galaxy survey (SAMI; \citealt{Cro12}) and the Mapping Nearby Galaxies at APO (MaNGA; \citealt{Bun15}) would overcome the small number statistics in this work, and provide deeper insights on their detailed evolutionary pathways.
\section*{Acknowledgments}
We gratefully thank the anonymous referee for constructive comments that have significantly improved this manuscript. This study uses data provided by the Calar Alto Legacy Integral Field Area (CALIFA) survey (http://califa.caha.es/). Based on observations collected at the Centro Astron\'omico Hispano Alem\'an (CAHA) at Calar Alto, operated jointly by the Max-Planck-Institut f\"ur Astronomie and the Instituto de Astrof\'isica de Andaluc\'ia (CSIC). H.J. acknowledges support from the Basic Science Research Program through the National Research Foundation (NRF) of Korea, funded by the Ministry of Education (NRF-2013R1A6A3A04064993).
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"redpajama_set_name": "RedPajamaArXiv"
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Three Things You Need to Know on February 8th
House and Senate negotiators are still working to reach a deal on border security and avoid another government shutdown. Democratic and Republican lawmakers have until one week from today to get a deal President Trump will sign so one-fourth of the government doesn't run out of money. Democrats and Republicans have been trading offers all week to provide funding for technology and fencing on the U.S. border with Mexico. Senate Appropriations Chairman Richard Shelby said he's hoping for a deal by Monday.
Apple is releasing an update to fix the FaceTime bug that allowed people to eavesdrop on conversations even if the other person didn't answer the call. Apple disabled its Group FaceTime feature last week when a 14-year-old in Arizona discovered the flaw. Apple is urging all users install the new software.
Denver Public Schools officials and the teachers union will get back to the bargaining table today as a potential strike looms. The Denver Classroom Teachers Association has a work stoppage set for Monday if there's no new deal in place. The new strike date was announced this week after state labor officials declined to intervene in the pay dispute. Teachers voted last month to walk off the job, but that had been put on hold until the state made a decision. Today's bargaining session gets underway at 5 p.m.
Denver Public Schools
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 457
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Baricella (Bolognese: , locally ) is a comune (municipality) in the Metropolitan City of Bologna in the Italian region Emilia-Romagna, located about northeast of Bologna.
Baricella borders the following municipalities: Argenta, Budrio, Ferrara, Malalbergo, Minerbio, Molinella, Poggio Renatico.
References
External links
Official website
Cities and towns in Emilia-Romagna
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 1,543
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Pala vald är en kommun i Estland. Den ligger i landskapet Jõgevamaa, i den centrala delen av landet, km sydost om huvudstaden Tallinn.
Följande samhällen finns i Pala vald:
Pala
Årsmedeltemperaturen i trakten är °C. Den varmaste månaden är juli, då medeltemperaturen är °C, och den kallaste är februari, med °C.
Referenser
Externa länkar
Historiska kommuner i Jõgevamaa
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
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"redpajama_set_name": "RedPajamaGithub"
}
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Kyle Lionhart Debut New Zealand Show Announced
Monday 4th February, 2019 2:02PM
Byron Bay surfer-songwriter Kyle Lionhart is bringing his reflective, folk-inflected tunes to Aotearoa for the very first time this March, to play a special headline show at Auckland's Anthology Lounge. The ex-busker turned neo-folk streaming superstar is hitting our shores ahead of 2019's release of Lionhart's keenly anticipated debut album, and has already won over a tonne of fans with appearances at such storied mega-festivals as Splendour in the Grass. Grip the details here...
Kyle Lionhart
Thursday 14th March – Anthology Lounge, Auckland
Tickets available HERE via UTR
Listen to Kyle Lionhart's streaming hit 'Sleep By Rivers'...
Watch the clip for Lionhart's 2017 single 'Call Back Home'...
Australian neo-folk singer-songwriter Kyle Lionhart has announced his first ever show in New Zealand this March.
Hailing from Byron Bay, Kyle Lionhart was a standout busker on the streets of the surf town, and quickly built his reputation from playing on the pathways to playing alongside some of the best at Bluesfest and Splendour in the Grass.
Although a relatively new name to some, Kyle has gained a legion of loyal fans since the release of his independently released debut EP Keep In Mind in mid-2015. He has since since sold over 6000 copies and seen over 3 million plays of lead single 'Sleep By Rivers' on Spotify alone.
2017 saw the release of mini album Eleven & Two. Produced by John Castle (Vance Joy, Washington, Cub Sport), this latest release of 7 tracks is filled with soaring indie-soul meets folk ballads about self-reflection. Of the record Kyle says:
"It's about avoiding that darker side of yourself, the side of ourselves that we consistently distract and sedate only for it to explode at the worst possible moments"
Ahead of the release of his debut album in late 2019, Kyle is holding his first NZ show in Auckland following a strong demand by local fans. An undeniable talent, Kyle Lionhart is destined to become your favourite new artist of 2019.
kylelionhartmusic.com/
2019-03-14 Thu 14th Mar
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Bring a friend or youth group to Camp Kintail for the weekend. For campers in grades 5-8. Play, sing, pray, and enjoy outdoor worship, swim, and be inspired! Climb our rockwall, try out the flying squirrel, paddle a kayak, try a low ropes adventure element, and meet new friends. This fun-filled weekend is a perfect chance to come to camp and learn about your faith. Our speaker is the Rev. Charmilla Ireland from Melville Brussels & St. Andrew's Molesworth Presbyterian Churches.
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{
"redpajama_set_name": "RedPajamaC4"
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Dedication
We would like to dedicate this book to our family and friends, who provided inspiration and support.
Acknowledgments
We would like to acknowledge Brenna Slabaugh for being our food stylist; Carl, Candice and Curtis Andre for their help with recipe testing and helpful suggestions; as well as our family, who gave us advice and support along the way.
Cover and book design by Lora Westberg
Photos by Erin Davis
Edited by Emily Beaumont
Copyright 2016 by Jon and Erin Davis
Published by Adventure Publications
820 Cleveland Street South
Cambridge, Minnesota 55008
adventurepublications.net
1-800-678-7006
All rights reserved
ISBN: 978-1-59193-565-0; eISBN: 978-1-59193-609-1
Introduction
Cabins and lake homes are meant for friends and family! We gather around decks, patios and boats for lazy conversation and needed relaxation. Pontoon boats in particular are part of the lake magic, as you cruise around sharing food and beverages, and they've long been associated with the lake-living tradition.
These recipes have been collected with a few things in mind. First, we wanted to create basic, honest food with as few processed ingredients as possible. Next, the recipes needed to be easy to prepare because you want to spend time with your guests, not in the kitchen. Some do take a bit more effort than others, but many can be prepared a day in advance. Other recipes are conducive to using more adventurous ingredients for more interest. These are indicated with the label "for a creative touch."
We also wanted to have a wide selection of recipes that are dairy free, gluten free or vegetarian for those cooks needing to accommodate certain dietary restrictions. These recipes are indicated by the following abbreviations: df=dairy free, gf=gluten free, gfo=gluten free option and v=vegetarian.
We hope you enjoy this collection of recipes and tips—and that this book might contribute to many memories of entertaining at your favorite summer retreat!
Table of Contents
Skewers
Antipasto Skewers
Bloody Mary Skewers
Caprese Salad Skewers
Charcuterie Skewers
Shrimp Cocktail Skewers
Marinated Shrimp Skewers
Chicken Satay Skewers
Kefta Skewers
Cantaloupe and Ham Skewers
Tropical Fruit Skewers
Dips
Chunky Salsa
Roasted Tomatillo Salsa
Guacamole
Roasted Tomatillo Guacamole
Yogurt-Feta Dip with Olives and Mint
Pimento Cheese
Hummus
Homemade Ranch
Tzatziki Dip
Caponata
Layered Greek Dip
Olive and Sun-Dried Tomato Tapenade
Finger Foods
Fresh Spring Rolls
Asparagus Wrapped in Prosciutto
Bacon-Wrapped Dates
Lox on Toasted Bagel Points
Grilled Caesar Salad
Falafel
Stuffed Mushrooms
Apple Wedges with Blue Cheese and Prosciutto
Twice-Baked Potato Skins
Stuffed Artichoke Bottoms
Spicy Tortilla Pinwheels
New Potatoes Stuffed with Roasted Garlic-Chipotle Aioli
Sandwiches & Wraps
Your Regular Ol' Pita
Egg Salad Pita
Chicken Salad Pita with Golden Raisins and Tarragon
Falafel Pita
Faux-Monsieur Wrap
Mediterranean Wrap
NOLA Wrap
Sweets
Puppy Chow
No-Bake Cookies
Peanut Butter Chocolate Chip Cookies
Brownie Cupcakes with Molten Caramel
Cracker Candy
Fresh Fruit Skewers
Cheesecake with Fresh Berry Compote
Buttermilk Panna Cotta with Candied Pistachios
Butterscotch Pudding
Drinks
White Sangria
Phyllis' Frozen Margaritas
Rhubarb Cooler with Ginger Ale
Waikiki "Mai Tai"
Sparkling Lemonade
Bloody Marys
Southern Sweet Tea
Spiced Apple Cider
About the Authors
Caprese Salad Skewers
Skewers
tips to make serving easy
We recommend using wooden skewers, as they are biodegradable and can even be used for campfire kindling.
For skewer recipes that are served cold, store prepared skewers in a large, flat, plastic container in a cooler until ready to eat.
For hot skewers, store them in a covered glass baking dish placed inside an insulated casserole carrier, or wrap the dish with a large bath towel to keep skewers warm until serving.
Where noted, skewers may be cut in half to make smaller portions. Use heavy kitchen shears to score the skewers in the middle first, and then you may snap them cleanly in two.
Each recipe in this chapter makes approximately 8-10 skewers.
Antipasto Skewers (gf) Makes 8–10 skewers
Italian for "before the meal," antipasto is traditionally a first course of cured meats and cheeses alongside pickled peppers and other vegetables. Here, classic Italian flavors are combined on a skewer for easy snacking.
Ingredients
8 ounces Monterey Jack cheese, cubed
6 ounces pepperoni slices
1 jar Italian-style mix of pickled vegetables, Giardiniera (cauliflower, carrots and peppers)
8-10 pepperoncini
1 pint cherry tomatoes
20 Kalamata olives, pitted
Directions
Alternate placing cheese, pepperoni slices (folded in quarters) and vegetables on skewers.
Note: Use high-quality pepperoni slices found in the deli section of your local grocery store (not the presliced frozen variety). If you cannot find high-quality pepperoni, you can substitute salami.
Bloody Mary Skewers (gf, v, df) Makes 8–10 skewers
These tasty snacks can be enjoyed alone or alongside Bloody Marys for happy hour.
Ingredients
8 ounces small pickles, such as gherkins or cornichons
6 ounces green olives stuffed with pimentos (or your favorite stuffed green olives)
16 ounces pickled okra
12 ounces pickled green beans, cut into bite-sized pieces
1 bunch baby radishes, thickly sliced
Directions
Use short skewers (skewers cut in half). Alternate placing pickles and other vegetables on skewers. Serve with Bloody Marys.
Caprese Salad Skewers (gf, v) Makes 8–10 skewers
Thought to have originated on the island of Capri, off Italy's Amalfi Coast, Caprese salad is a refreshing and satisfying snack. The green, white and red of the basil, mozzarella and tomato resemble the Italian flag.
Ingredients
Salt and pepper to taste
16 ounces fresh mozzarella balls (bocconcini), halved
1 pint cherry tomatoes
Handful fresh basil leaves, quartered
Directions
Use short skewers (skewers cut in half). Lightly salt and pepper halved mozzarella balls. Alternate placing cherry tomato, mozzarella halves and basil on skewers.
Charcuterie Skewers (gf) Makes 8–10 skewers
High in protein and low in carbs, these skewers are great snacks for active days on the lake.
Ingredients
1 pound assorted meats, sliced, such as turkey and roast beef
1/2 pound assorted cheeses, cubed, such as Swiss and Gouda
Directions
Use short skewers (skewers cut in half). Cut each slice of meat in half and fold into quarters. Alternate placing meats and cheeses on skewers.
For a creative touch:
Try salami, soppressata, capicola, manchego and Gruyère.
Shrimp Cocktail Skewers (gf, df) Makes 8–10 skewers
Always a crowd-pleaser! You can make the cocktail sauce mild or spicy to your preference.
Ingredients
3/4 cup ketchup
2 tablespoons prepared horseradish
1 tablespoon Dijon mustard
3-5 drops Worcestershire sauce
1 pound shrimp, headless, shelled, deveined, fully cooked and cooled
Directions
In a large bowl, combine ketchup, horseradish, mustard and Worcestershire. Toss shrimp in cocktail sauce and coat evenly. Place shrimp on skewers. Serve cold.
Marinated Shrimp Skewers (gf, df) Makes 8–10 skewers
Here's a fun way to enjoy shrimp: cool and tangy, with an Italian flair!
Ingredients
1/4 cup extra-virgin olive oil
1/2 red bell pepper
1/2 celery stalk, coarsely chopped
16 Kalamata olives, pitted
1 clove garlic
1 1/2 tablespoons lemon juice (about half a lemon)
Handful fresh parsley
Salt and pepper
1 pound shrimp, precooked
Directions
Combine olive oil, bell pepper, celery, olives, garlic, lemon juice, parsley, saltand pepper in a food processor; blend until smooth. Add shrimp to marinade and let sit in fridge for at least 30 minutes or up to 2 hours. Place shrimp on skewers. Serve cold.
Note: Do not prepare this the day ahead, as the shrimp will continue to cook in the lemon juice and will become tough.
Chicken Satay Skewers (gfo, df) Makes 8–10 skewers; entrėe serves 4–6
Satay is a wildly popular street food throughout Indonesia and Malaysia, where you can find numerous versions of grilled meat skewers, seasoned and served with a spicy sauce. Our version incorporates a typical variation—spicy peanut sauce—into a marinade that bakes right into the chicken. These are almost as tasty served cold as leftovers as they are right out of the oven.
Ingredients
6 boneless, skinless chicken thighs, cut into large thin sheets (about two pieces per thigh)
Marinade
2 cloves garlic, minced
1-2 hot chilies (such as Thai, serrano or jalapeños, depending on your preferred level of spiciness), minced
1 (1-inch) piece fresh ginger, peeled and minced
1/2 teaspoon dried turmeric
1 teaspoon ground coriander
1 teaspoon ground cumin
3 tablespoons soy sauce
3 tablespoons fish sauce
1/4 cup rice vinegar
A few drops sesame oil
1 tablespoon brown sugar
1/4 cup peanut butter
Directions
Combine marinade ingredients in a large bowl. Coat chicken in marinade; cover and refrigerate for 4 hours or overnight. The following day, soak skewers in water for 1 hour (weigh down with a plate to submerge). Preheat oven to 450 degrees. Place two pieces of chicken on each skewer. Place skewers on a baking sheet covered with aluminum foil and coated with canola oil. Bake chicken for 10 minutes, flip skewers and bake for an additional 20-25 minutes. Bake another 15 minutes, until chicken is brown and crisp on the edges. Serve hot or cold.
gfo: Use gluten-free varieties of soy sauce and fish sauce.
Serving suggestion: Serve with Fresh Spring Rolls.
Note: As an alternative to baking, grill skewers for 5 minutes on each side.
Kefta Skewers (gf, df) Makes 8–10 skewers; entrėe serves 4–6
Versions of this dish can be found from Bulgaria to Bangladesh. This one is probably closest to the Greek or Turkish style. Try spooning some Tzatziki Dip into a pita and then sliding the kefta off the skewer to make a tasty sandwich.
Ingredients
1/4 cup sesame seeds
1/2 cup onion, shredded and excess water removed using a paper towel
2 garlic cloves, minced
1/4 teaspoon paprika
1/4 teaspoon black pepper
1/4 teaspoon ground cumin
1/8 teaspoon ground cayenne pepper
Pinch cinnamon
1 tablespoon parsley, minced
1/2 pound ground beef
1/2 pound ground pork
1 egg, beaten
1 tablespoon salt
Directions
Soak skewers in water for at least 30 minutes before cooking to prevent the wood from burning. Toast sesame seeds briefly in a dry pan over medium heat until they just start to pop. Combine all ingredients, except for salt, in a large bowl; mix with your hands until the mixture just comes together. Allow seasoned meat to rest in the refrigerator for at least 30 minutes and up to 24 hours. Preheat oven to 400 degrees. Form the chilled meat mixture into 6-8 tube shapes or oblong balls (each is called a kefta) before sliding a skewer lengthwise through each. Sprinkle each kefta generously with salt. Bake on a rack placed in a foil-lined baking pan for 10-20 minutes until skewers reach an internal temperature of 170 degrees. Cooking time will vary, depending on the shape of the kefta.
Serving suggestion: Serve in pita pockets with Tzatziki Dip.
Cantaloupe and Ham Skewers (gf, df) Makes 8–10 skewers
Salty, savory ham and sweet, juicy melon make a surprisingly delicious combination!
Ingredients
1-2 thick slices precooked ham steak, cut into 1- to 2-inch cubes
1 ripe cantaloupe, cut into bite-sized cubes
Directions
In a sauté pan over medium-high heat, quickly sear the cubed ham steak until the edges start to turn golden brown. Remove from heat and let cool until warm to the touch. Alternate placing pieces of ham and cantaloupe on skewers. Serve immediately, or refrigerate for several hours before serving.
Tropical Fruit Skewers (gf, v, df) Makes 8–10 skewers
Try these for a refreshing snack that offers a taste of the tropics on a hot summer day.
Ingredients
2-3 mangoes, cut into bite-sized pieces
1 pineapple, peeled, cored and cut into bite-sized pieces
1 pint blueberries
Directions
Alternate placing pieces of fruit on skewers.
Pimento Cheese Dip
Dips
tips to make serving easy
Serve these dips with chips, crackers or fresh veggies.
Serve each recipe in a heavy glass bowl or a baking dish to keep the dip and chips, crackers or veggies in place.
Place each glass serving dish on top of a silicone trivet on the table of the pontoon to prevent the dish from sliding.
Use rectangular paper food trays (which can be purchased online) for serving individual portions.
Each recipe in this section serves 6-8.
Chunky Salsa (gf, v, df) Makes about 1 pint
Salsa is the Spanish word for "sauce," and there are as many different salsas out there as there are cooks. In this book we present two salsa recipes perfect for dipping tortilla chips. This one is chunky and fresh with a mild, peppery zing.
Ingredients
3-4 large tomatoes, cored, seeded and finely chopped
1 clove garlic, minced
4-5 sprigs cilantro, minced
1/2 cup white onion, finely chopped
1 serrano or small jalapeño pepper, minced (adjust to preferred level of spiciness)
Juice from 1 lime
Salt and pepper
Directions
In a large bowl, add tomatoes, garlic, cilantro, white onion, serrano chili and lime juice. Mix well. Add salt and pepper to taste. Serve with chips.
Note: Taste salsa after combining all ingredients and add more lime juice, if necessary. Some tomatoes are sweeter than others and will need a little bit more lime juice.
Roasted Tomatillo Salsa (gf, v, df) Makes about 1 pint
In contrast with the chunky salsa, this green salsa is smooth and tangy. Roasting the tomatillos gives it a slightly smoky flavor. Try it with frozen margaritas.
Ingredients
1/2 cup white onion, chopped
1 tablespoon canola or vegetable oil
5 medium tomatillos, husked and halved
2 cloves garlic, chopped
2 serrano chilies, chopped
1/3 cup fresh cilantro, chopped
Salt and white pepper
Directions
Place chopped onion into a small bowl. Cover with cold water and let sit for 15 minutes; drain. Add oil to a large shallow skillet over medium-high heat, and cook tomatillos, cut-side down, approximately 5 minutes. Turn tomatillos over and cook until soft (another 3-4 minutes). Remove tomatillos from pan and place in blender. Add garlic to pan over heat and cook for 30 seconds or until fragrant; remove from pan and add to blender along with tomatillos. Add onion, chilies and cilantro to blender; blend until smooth. Add salt and pepper to taste.
Guacamole (gf, v, df) Makes about 1 pint
This avocado-based dip has been popular since the time of the Aztecs, and for good reason! You will find that making your own guacamole from scratch is easy and a big improvement over store-bought varieties. Be sure to use ripe avocados: They should yield to the touch without being overly mushy. If you can't find any that are ripe yet, put a few into a paper bag and leave them on the kitchen counter. They should ripen in a day or two.
Ingredients
1/4 cup red or white onion, finely chopped
4 ripe avocados
Juice from 1 lime
8-10 sprigs fresh cilantro, minced
Salt and pepper
Directions
Place chopped onion into a small bowl. Cover with cold water and let sit for 15 minutes; drain. Cut each avocado in half; remove pit and scoop out flesh into a large bowl. Add onion, lime juice and cilantro. Mix well. Stir in salt and pepper to taste, adding more lime juice, if necessary. Serve with chips.
Roasted Tomatillo Guacamole (gf, v, df) Makes about 1 pint
A variation on classic guacamole, this version adds a smoky tang.
Ingredients
3 large avocados
1 recipe Roasted Tomatillo Salsa
Salt and pepper to taste
Directions
Cut each avocado in half; remove pit and scrape out flesh into a large bowl. Stir in salsa. Season with salt and pepper to taste.
Yogurt-Feta Dip with Olives and Mint (gf, v) Makes about 1 pint
This thick and tangy dip is great with cucumber slices or fresh veggies for dipping, but it also works well on crackers or French bread.
Ingredients
6 ounces feta
3/4 cup yogurt
1/4 cup fresh mint, chopped
1 tablespoon champagne vinegar
1 sprig oregano, chopped
1/8 teaspoon pepper
1 tablespoon olive oil
1/4 cup cream
Salt (optional)
10 Kalamata olives, finely chopped
Directions
Blend feta, yogurt, mint, vinegar, oregano, pepper and olive oil until well combined and mint is finely chopped. Stir in cream, adding more, if necessary, for blending. Stir in salt, if desired, and chopped olives. Serve cold.
Pimento Cheese (gf, v) Makes about 1 quart
A southern favorite, pimento cheese is becoming more and more popular across the rest of the U.S. Try this recipe and find out why! It's amazingly addictive on crackers or raw veggies.
Ingredients
3 cups cheddar cheese, shredded
8 ounces cream cheese, softened
1/2 cup mayonnaise
1/4 teaspoon garlic powder
1/4 teaspoon onion powder
1/4 teaspoon cayenne pepper
1 serrano or small jalapeño pepper, minced
1/4 teaspoon paprika
1 (4-ounce) jar diced pimentos, drained
Salt and pepper to taste
Directions
Combine all ingredients in a large bowl.
For a creative touch:
Add 1/8 teaspoon smoked paprika.
Note: For best results and a gluten-free option, shred your own cheese. Many brands of shredded cheese contain wheat gluten.
Hummus (gf, v, df) Makes about 1 1/2 quarts per pound of dried chickpeas
We first started making our own hummus a few years ago and swore we'd never go back to the store-bought kind. A little time invested, and you'll have much better-tasting hummus at a fraction of the cost. Hummus freezes well and will last for months. Tahini is a sesame paste (like peanut butter, but with sesame seeds) that can be found in the international aisle of most grocery stores. Don't take shortcuts with canned chickpeas! The secret to great hummus is freshly preparing it from dried beans. Three flavor variations are given below. You can experiment with adding different herbs or vegetables, as long as the ingredients are soft enough to puree in a food processor.
Ingredients
To Prepare Chickpeas
1 pound dried chickpeas
1 carrot, broken into large pieces
2 celery stalks, broken into large pieces
1/2 onion, halved
To Prepare Hummus
3 cups cooked chickpeas
3/4 cup tahini
1 1/2 tablespoons lemon juice (about half a lemon)
1 1/2 teaspoons salt
1 cup olive oil
1/4 cup fresh parsley
1 teaspoon onion powder
1/2 teaspoon garlic powder
Pepper to taste
Directions
Prepare Chickpeas: Soak chickpeas overnight in water. The following day, strain chickpeas; add to a slow cooker with carrot, celery and onion. Add water to cover by 1 inch. Cook on high for 4 hours. Let chickpeas cool to room temperature. Discard carrot, celery and onion; strain chickpeas to remove excess water.
Prepare Hummus: Blend 3 cups cooked chickpeas with remaining ingredients in a food processor. If the hummus is too thick, stir in additional olive oil and lemon juice. Add more salt to taste, if necessary.
Flavor Variations
Tomato-Infused Hummus
Add 4 ounces tomato paste before processing.
Roasted Garlic Hummus
Take a whole head of garlic and, with a serrated knife, chop the top of the head off so that most of the cloves are exposed. Sprinkle with salt and olive oil before wrapping loosely in foil and roasting at 500 degrees for about 15 minutes. The skin should start to blacken and the garlic cloves should be very soft. Allow the garlic to cool before squeezing out the roasted garlic into your hummus mixture.
Hummus with Fresh Herbs
Add 1/4 cup fresh basil and 2 tablespoons fresh oregano (or 1 teaspoon dry).
Roasted Red Pepper Hummus
Roast a whole red pepper at 500 degrees for 10-15 minutes until the skin blisters and blackens. Allow the pepper to cool before running it under tap water while rubbing the skin gently to remove the blackened parts. Remove the stems and seeds before blending into the hummus.
Note: A full pound of dry chickpeas will yield a quart and a half of hummus. If desired, split plain hummus into portions and make several different flavors. Or use some of the remaining chickpeas to make Falafel. Cooked chickpeas also store well in the freezer for future use.
Homemade Ranch (gf, v) Makes about 1 pint
Try this healthy homemade version and never go back to the store-bought kind!
Ingredients
1 cup mayonnaise
1/4 cup buttermilk
1/2 cup sour cream
1/4 teaspoon salt
1/3 cup fresh parsley, minced
1 tablespoon fresh dill, minced
1/4 cup fresh chives, minced
1/2 teaspoon black pepper
1/2 teaspoon lemon juice
1/4 teaspoon paprika
Directions
Combine all ingredients in a large bowl. For best results, let sit in the refrigerator for a few hours before serving. Serve cold.
Tzatziki Dip (gf, v) Makes about 3 cups
This popular Greek dish, somewhere between a condiment and a salad, goes with almost anything but is particularly tasty with Falafel or Kefta Skewers. For a nice thick consistency, it is important to use "Greek" strained yogurt. If that is unavailable in your area, put a quart of plain, unsweetened yogurt into a fine sieve and allow it to drain into a large bowl in the refrigerator overnight. You can discard the whey or use it in place of buttermilk when baking.
Ingredients
1 cucumber, peeled and chopped
2 cups plain Greek yogurt
1 teaspoon fresh mint, finely chopped
2 teaspoons fresh parsley, finely chopped
1 1/2 tablespoons lemon juice (about half a lemon)
1/4 teaspoon garlic powder
Salt and pepper to taste
Directions
Combine all ingredients in a large bowl. Serve cold.
Caponata (gf, df) Makes about 1 quart
Caponata is a traditional Sicilian dish that can be enjoyed as a side item or as a topping for pasta, sandwiches, burgers or almost anything you can think of. Don't be afraid of the anchovies! They cook down into the mixture and provide a deep savory flavor without overpowering the other ingredients.
Ingredients
1 medium eggplant (1/2 to 3/4 pound)
Salt and pepper
1/4 cup pine nuts
1/2 green bell pepper, chopped
1 medium-size yellow onion, chopped (about 1 cup)
1/2 cup olive oil
3 cloves garlic, minced
3 anchovy fillets, minced
1 tablespoon tomato paste
1/2 cup dry red wine
1 (14-ounce) can diced tomatoes or 1 large tomato, peeled and chopped
2 tablespoons capers, rinsed and drained
1/4 cup green olives, sliced
1/4 cup Kalamata olives, sliced
2 tablespoons fresh basil (or 1 tablespoon dried)
1/4 cup fresh parsley, chopped
Directions
Peel eggplant and cut into 1/2-inch cubes. Salt eggplant liberally and place in a colander or paper towel-lined bowl to drain. Meanwhile, toast pine nuts in a dry pan over medium-low heat, tossing frequently until fragrant and beginning to brown slightly, about 5 minutes. Set aside. Sauté bell pepper and onion in olive oil over medium-high heat in a large heavy skillet. (It will seem like a lot of olive oil at first, until all of the remaining ingredients are added.) Continue cooking until onion turns translucent and starts to brown slightly around the edges, about 10-15 minutes. Add garlic, anchovies, tomato paste and eggplant; continue to cook for an additional 10-15 minutes. Deglaze pan with wine, and add tomatoes along with their juices. Simmer for about 20 minutes to reduce, stirring occasionally. The final consistency should be quite thick and not at all runny. Remove from heat; add capers, olives, herbs and pine nuts. Season with salt and pepper to taste. Serve with crusty French bread or crackers.
Note: This recipe can easily be doubled. Just increase the time that the eggplant and tomato mixture simmers to about 30 minutes. Hot caponata packed into clean Mason jars and refrigerated will keep for up to a few weeks.
Layered Greek Dip (gf, v) Makes 8–10 servings
This is a cool Mediterranean twist on a traditional seven-layer dip.
Ingredients
2 cups hummus (tomato-infused version or store-bought)
2 cups plain Greek yogurt
2 tablespoons Greek seasoning herb blend
Juice from half a lemon (about 1 1/2 tablespoons)
Salt and pepper
1 cucumber, peeled, seeds removed and chopped
1 cup canned black olives, sliced
1/2 red bell pepper, chopped
1 bunch scallions, chopped
4 ounces feta, crumbled
Directions
Layer hummus evenly over bottom of a square 8- x 8-inch dish, spreading well into corners of dish. In a medium bowl, combine yogurt, Greek seasoning, lemon juice, salt and pepper. Add more seasoning to taste, if necessary. Layer yogurt mixture evenly over hummus layer. Sprinkle cucumber, black olives, red bell pepper, scallions and feta evenly over yogurt. Chill until ready to serve. Serve with tortilla chips or crackers.
Note: If you cannot find an herb blend of Greek seasoning, you can substitute 1/2 tablespoon each dried basil, oregano, parsley and onion powder.
Olive and Sun-Dried Tomato Tapenade (gf, v, df) Makes about 1 quart
Quick to make, this flavorful, Mediterranean-inspired topping is best enjoyed with crackers or on slices of toast or French bread. Try serving it alongside the Antipasto Skewers.
Ingredients
2 cloves garlic, cut in half
1/4 cup capers
2 cups canned black olives, sliced
1/2 cup green olives stuffed with pimentos, sliced
1/2 cup celery, sliced (about 1 stalk)
1/3 cup sun-dried tomatoes, sliced
1/2 tablespoon red wine vinegar
2 teaspoons dried oregano
1/3 cup high-quality olive oil
Directions
Blend all ingredients together in a food processor.
Asparagus Wrapped in Prosciutto
Finger Foods
tips to make serving easy
Serve finger foods in a portable shallow container, such as a heavy glass dish or a plastic container. Or arrange them on large serving trays, and then place the trays on silicone trivets to prevent sliding.
A spray bottle filled with water and a roll of paper towels make cleanup of sticky fingers a breeze and eliminate the worry of polluting the lake with soap.
Many of these recipes can be combined with recipes from other chapters to make complete meals.
Each recipe in this section serves 6-8.
Fresh Spring Rolls (gfo, v, df) Makes 10 spring rolls
Fresh spring rolls are a healthy snack and fun to make, once you get the hang of it. Cucumbers and mint make for a cooling treat on a hot day.
Ingredients
1 cup smooth peanut butter
2 tablespoons soy sauce
1 1/2 tablespoons Sriracha
2 tablespoons rice vinegar
1-2 tablespoons water
1 teaspoon fresh ginger, finely grated
1 small clove garlic, finely grated
1/2 teaspoon sesame oil
1/2 package vermicelli noodles (found in the international section of the grocery store)
8 spring roll wrappers (rice)
6 ounces baby spinach
1/2 cucumber, seeds scooped out and cut into thin strips
1 carrot, shredded
1/2 cup crushed roasted peanuts (optional)
1/2 cup scallions, sliced
1 bunch fresh cilantro
Small handful fresh mint
1 lime
Hoisin sauce for dipping (optional)
Directions
In a medium bowl, combine peanut butter, soy sauce, Sriracha, rice vinegar, water, ginger, garlic and sesame oil until well mixed. Set aside. Cook noodles for 3 minutes in boiling water. Strain, and rinse with cool water to prevent further cooking and to reduce stickiness. Set aside. Heat a gallon of water until hot to the touch (not boiling) to soften the spring roll wrappers.
To assemble spring rolls (see diagram), dip a spring roll wrapper into hot water until completely coated. Remove from water and place onto a large plate. The wrapper will begin to soften and become pliable and sticky. Place a small handful of spinach in the center of the wrap. Spread 2 tablespoons peanut butter mixture on top of spinach. On top of peanut butter mixture, layer roughly 1/4 cup noodles, a few cucumber strips, some shredded carrot, peanuts, scallions, a few sprigs cilantro (stems removed), two mint leaves and a small squeeze of lime juice. Wrap the spring roll by folding over one side of the wrapper to just cover the filling ingredients; fold each opposite side toward the middle over the filling about 2 inches. Then, holding the ends in, wrap the spring roll up. Serve immediately or chill for up to 2 hours before serving.
gfo: Use gluten-free spring roll wrappers, vermicelli noodles and soy sauce, and omit the hoisin sauce.
Serving suggestion: Serve alongside Chicken Satay Skewers.
Asparagus Wrapped in Prosciutto (gf, df) Makes 8–10 appetizer servings
Visually attractive, easy to make and even more fun to eat, this elegant dish is simply wonderful!
Ingredients
1 bunch asparagus, ends trimmed
1 1/2 tablespoons lemon juice (about 1/2 a lemon)
Salt and pepper to taste
4 ounces prosciutto, sliced into quarters (approximately 4- x 2-inch sheets)
Directions
Steam asparagus for about 1 minute or until stalks turn bright green and just begin to become tender. Remove from heat and rinse with cold water to prevent overcooking. Toss asparagus in lemon juice, salt and pepper. Wrap the bottom of each asparagus spear in a quarter of a prosciutto slice. Serve cold.
Bacon-Wrapped Dates (gf, df) Makes 24 bite-sized pieces
These are sometimes called "devils on horseback," though no one seems to know why. Maybe it's because the perfect combination of sweet dates and savory bacon sure feels a little sinful!
Ingredients
24 toothpicks
24 dates
1 pound bacon strips, cut into quarters
Directions
Soak toothpicks in water 15-20 minutes. Preheat oven to 425 degrees. Wrap each date with a piece of bacon, secure with a toothpick and place on a wire rack over a rimmed foil-lined baking sheet. Bake 10-12 minutes or until bacon is thoroughly cooked and crispy.
For a creative touch:
Try stuffing each date with a pistachio.
Note: Use thin strips of bacon. (Avoid using the thick-cut varieties.)
Lox on Toasted Bagel Points Makes 48 small bites
Smoky salmon and the smooth richness of cream cheese are perfectly complemented by tangy capers and the mild bite of chopped red onion. These are great for brunch with a cup of good coffee (or a glass of champagne!).
Ingredients
4 plain bagels
8 ounces cream cheese, softened
1/2 cup red onion, finely chopped
1/2 cup capers, coarsely chopped
6 ounces smoked salmon
Directions
Cut bagels in half and toast. Let bagels cool, and cut into sixths. Spread toasted bagel points evenly with cream cheese; sprinkle with red onion and capers, and layer with smoked salmon. Serve cold.
For a creative touch:
Try using different flavors of bagels, such as "everything" or "poppy seed."
Note: Be sure to keep these cold while on the boat until it's time to serve them. We find that soft, prepackaged bagels work best for this recipe.
Grilled Caesar Salad (gf) Makes 6 servings
You might not think a salad would make a great pontoon snack, but this preparation is both delicious and easy to eat. The romaine hearts are split lengthwise and brushed with a thick dressing, so they can be eaten with your fingers, mess free.
Ingredients
2 tablespoons olive oil
1 1/2 tablespoons balsamic vinegar
3 small romaine hearts, cut in half lengthwise, leaving the bottom stem intact
Dressing
1 clove garlic, minced
1 anchovy (or pickled herring) fillet
1 tablespoon lemon juice
1 teaspoon Dijon mustard
1 teaspoon Worcestershire
1 cup mayonnaise
1/2 cup Parmesan cheese, shredded
1/4 teaspoon salt
1/4 teaspoon pepper
Directions
In a large shallow skillet, add olive oil and balsamic vinegar, and heat over medium-high heat. Once skillet is hot, quickly sauté each romaine half, flat side down, for approximately 1 minute or until romaine starts to develop some color (but before romaine starts to wilt).
In a small food processor, blend garlic, anchovy, lemon juice, mustard and Worcestershire. In a small bowl, combine mayonnaise, Parmesan, salt and pepper; stir in anchovy mixture.
To serve, place grilled romaine hearts in a plastic container or on a serving platter, flat side up, and brush liberally with dressing. To eat, use the bottom stem portion of the dressed romaine heart as a handle.
Note: It is important to add the olive oil and balsamic vinegar to a cold pan and then increase the heat, to prevent the vinegar from spattering.
Falafel (gfo, v, df) Makes about 1 dozen
One of civilization's original street foods, falafel was popular among travelers along ancient spice-trading routes and incorporated faraway flavors, such as cumin, coriander and black pepper. Later, falafel became an important staple of early Christians as a meat substitute during Lent. Try it with Tzatziki Dip.
Ingredients
1 (15-ounce) can chickpeas, mashed
1 teaspoon sesame seeds
1 onion, coarsely chopped (about 2 cups)
1/2 cup fresh parsley, coarsely chopped
3 cloves garlic, coarsely chopped
1 tablespoon olive oil
1 egg
1 teaspoon ground cumin
1 teaspoon ground coriander
1 teaspoon salt
1/2 teaspoon pepper
1/4 teaspoon cayenne pepper
1 teaspoon lemon juice
1/4 teaspoon lemon zest
1 teaspoon baking powder
1 cup breadcrumbs
Vegetable or canola oil
Directions
Drain and rinse chickpeas. In a large bowl, mash chickpeas with a potato masher (do not blend). Briefly toast sesame seeds in a small pan over medium-high heat for about 30 seconds. Remove from heat and set aside. In a blender, combine onion, parsley and garlic; blend until smooth. In a large bowl, combine chickpeas, onion mixture and olive oil. In a small bowl, combine egg, cumin, coriander, salt, pepper, cayenne, lemon juice, lemon zest, baking powder and toasted sesame seeds; mix well. Add egg mixture to chickpea mixture until combined. Slowly add 3/4 cup breadcrumbs. If necessary, gradually add more breadcrumbs until mixture holds together enough to form into balls about the size of doughnut holes. Heat 1-2 inches of oil in a large shallow skillet until oil reaches 350 degrees. Fry balls, in batches, about 5-6 minutes or until brown and golden on all sides.
gfo: Use gluten-free breadcrumbs.
Stuffed Mushrooms (gfo, v) Makes about 20 stuffed pieces
Impress your guests with these fancy-looking bites that are actually pretty easy to make. They can be enjoyed cold, but they are best served warm.
Ingredients
16 ounces fresh mushrooms (white button or cremini)
1/2 cup onion, finely chopped
3 tablespoons olive oil
1 clove garlic, minced
1 1/2 tablespoons lemon juice (about half a lemon)
1/3 cup panko-style breadcrumbs
1/2 cup Romano cheese, freshly shredded or grated
1/4 cup fresh parsley, finely chopped
Salt and pepper to taste
Directions
Preheat oven to 425 degrees. Separate mushroom caps and stems, setting the caps aside. Dice the mushroom stems and reserve. Over medium-high heat, sauté onion in olive oil. When onion becomes soft and translucent (about 5 minutes), add chopped mushroom stems; sauté until stems expel juices, about 5-10 minutes. Add garlic and lemon juice, and cook a few more minutes until most of the liquid has evaporated. Remove mixture from heat and allow to cool slightly. Mix in breadcrumbs, cheese and parsley. Season with salt and pepper. Stuff mushroom caps with breadcrumb mixture. If stuffing is too dry, add more olive oil. Arrange stuffed mushrooms on a parchment paper-lined baking sheet and roast for 10 minutes or until mushroom caps are soft and stuffing begins to brown.
gfo: Use gluten-free breadcrumbs.
Note: Mushrooms can be stuffed up to a day or two ahead of time and stored in the refrigerator. Roast just before serving.
Apple Wedges with Blue Cheese and Prosciutto (gf) Makes about 20 bites
This is like a fancy cheese plate packaged into perfect little bites. Sweet-tart Granny Smith apples pair perfectly with salty cured ham and funky blue cheese. Try this treat as an appetizer or a dessert.
Ingredients
1 Granny Smith apple, sliced
Juice from half a lemon (about 2 tablespoons)
4 ounces blue cheese, sliced into bite-sized rectangles
4 ounces prosciutto, sliced into quarters (approximately 4- x 2-inch sheets)
Directions
Toss apple slices with lemon juice. Top each apple slice with a piece of blue cheese. Wrap each apple-and-blue cheese wedge with a quarter slice of prosciutto. Serve cold.
Twice-Baked Potato Skins (gf) Makes 8 appetizer servings
With this recipe, you can enjoy the classic flavors of fully loaded baked potatoes on the go. No forks or knives required!
Ingredients
4 Russet potatoes
2 cups cheddar cheese, shredded
1 bunch scallions, chopped
6 slices bacon, fried, cooled and crumbled
3/4 cup sour cream or plain Greek yogurt
1/2 cup milk
Salt and pepper to taste
Directions
Preheat oven to 425 degrees. Thoroughly rinse potatoes. Place potatoes on a baking sheet, and prick each potato with a knife to release steam during cooking. Bake potatoes until cooked completely through (about an hour to an hour and a half). Let potatoes cool enough to handle. Cut each potato in half lengthwise, and scoop out flesh of each half into a large bowl, reserving skins. Add 1 1/2 cups cheese, scallions, bacon, sour cream, milk, salt and pepper; mix thoroughly. Adjust potato mixture to desired thickness by adding more sour cream and/or milk. Taste potato mixture and adjust seasoning, if desired. Place empty skins onto a baking sheet, and fill skins with potato mixture. Bake potato skins at 375 degrees for 15 minutes; top with remaining cheese, and bake for an additional 5-10 minutes or until tops start to turn golden brown. To serve, cut each baked potato skin in half. Serve hot or cold.
gfo: Use gluten-free brands of shredded cheese, bacon and sour cream.
Stuffed Artichoke Bottoms (gf, v) Makes about 8–10 bites
Sometimes overlooked by cooks, tender artichoke bottoms pack a ton of flavor. Dressed with flavorful stuffing and fresh mozzarella, these tasty bites are best served warm.
Ingredients
1 (14-ounce) can artichoke bottoms
2 tablespoons shallot, minced
2 cloves garlic, minced
3-4 mushrooms (any kind), minced
1/4 cup red bell pepper, diced
Olive oil
Salt and pepper
2-3 basil leaves, minced
2 tablespoons parsley, minced
4 ounces fresh mozzarella, sliced into 8-10 rounds
Directions
Drain artichoke bottoms and place onto a parchment paper-lined baking sheet. In a large skillet, sauté shallot, garlic, mushrooms and red bell pepper in oil over medium heat until mushrooms become tender, about 10-15 minutes. Season with salt and pepper; stir in basil and parsley. Place large dollops of stuffing mixture on top of artichoke bottoms. Place one slice of mozzarella cheese over each stuffed artichoke bottom. Sprinkle with salt and pepper. Broil 5-7 minutes or until mozzarella becomes brown and bubbly.
Spicy Tortilla Pinwheels (v) Makes about 40 pinwheel bites
These tortilla bites can be made ahead and brought out for an afternoon snack or an appetizer at happy hour.
Ingredients
3-4 scallions, coarsely chopped
1 serrano or jalapeño pepper, seeds removed and coarsely chopped
1/4 red bell pepper, coarsely chopped
Handful of cilantro
8 ounces cream cheese, softened
4 ounces pimentos, diced
4 ounces black olives, diced
2 tablespoons hot sauce
Pinch of salt
6-8 large flour tortillas
Directions
Combine scallions, chili pepper, red bell pepper and cilantro in a food processor, and blend until ingredients are finely chopped; transfer to a large bowl. Stir in cream cheese, pimentos, black olives, hot sauce and salt; mix until thoroughly combined. Taste mixture and add more salt, if needed. Spread a large spoonful of cream cheese mixture onto a tortilla, and roll the tortilla up. Repeat with remaining tortillas. Refrigerate at least 1 hour before cutting. Once chilled, cut tortilla rolls into 1 1/2-inch pinwheels. Serve cold.
For a creative touch:
Try using different flavors of hot sauce or different varieties of peppers.
Note: These can turn out quite spicy, depending on the peppers that you use. To reduce spiciness, reduce hot sauce to 1 tablespoon and add an additional 1/8 teaspoon salt.
New Potatoes Stuffed with Roasted Garlic-Chipotle Aioli (gf, v) Makes 8–10 appetizer servings
These are perfect potato bites, creamy but with a hint of smoky chipotle.
Ingredients
2 pounds small new or red potatoes, about the size of golf balls
2 tablespoons olive oil
Salt and pepper
1 large sprig rosemary
6 large cloves garlic
1 cup sour cream
1 ounce cream cheese, softened
2 tablespoons sauce from a can of chipotles in adobo sauce
1 teaspoon paprika
Salt and pepper to taste
2 tablespoons fresh chives, finely chopped
Directions
Preheat oven to 425 degrees. Wash potatoes well and pat dry. Place potatoes in a large glass baking dish, and coat potatoes with olive oil, pepper and a generous amount of salt (about 1 tablespoon). Add rosemary and 6 cloves garlic, in their skins, to the dish; put dish in oven. After 20 minutes or until garlic cloves are soft beneath their papery skin, remove garlic from pan, and set aside. Continue roasting potatoes until completely cooked through (approximately 15 to 25 more minutes), stirring potatoes occasionally. Once potatoes are completely cooked, remove from oven and allow to cool to room temperature. In the meantime, prepare the aioli by combining sour cream, cream cheese, chipotle, paprika and 1/4 teaspoon salt. Peel roasted garlic, mince, and add to aioli mixture. Taste aioli, and add salt and pepper, if necessary. Once potatoes are cool, scoop out a tablespoon of flesh from the top of each potato using a melon baller or a small spoon. Sprinkle a generous amount of salt and a little bit of pepper over potatoes before filling. Using the melon baller, place about 1 tablespoon aioli into each potato. For a cleaner look, place aioli into a small plastic zip-top bag; cut off the tip of one corner, and use it as a piping bag. If potatoes are rolling around and not sitting flat, use a knife to cut the bottoms of potatoes to make a flat surface. Top potatoes with finely chopped fresh chives. Place potatoes in a large plastic container, and refrigerate until ready to eat.
Note: If you like a bit more kick, add a whole chipotle, minced (from the can of chipotles in adobo sauce), to the aioli mixture.
Faux-Monsieur Wrap
Sandwiches & Wraps
tips to make serving easy
For Sandwiches: The sandwich recipes in this chapter are designed for pita pockets, which are easier to pack and eat out on the water than sandwiches made with traditional breads. However, the recipes will work equally well on the bread of your choice. Take care not to split the bottom of the pita pocket when filling, to avoid any mess on the pontoon. For a gluten-free option, serve sandwich fillings in lettuce cups.
For Wraps: The wrap recipes yield about 4-6 rolled tortillas. Cut each rolled tortilla into 3- to 4-inch slices. You can use large rectangular tortillas for the most efficient use of surface area, but large round tortillas work just as well. For a creative touch, use spinach or other flavored tortillas.
These wraps are best made by layering the ingredients over 3/4 of the tortilla, leaving one edge of the tortilla free. When rolling, start with a side of the tortilla with ingredients, and roll toward the empty edge. This will help prevent some of the ingredients from sliding out of the finished wrap. These wraps can be made well in advance. Just be sure they are kept cold until time to serve.
Each recipe in this section serves 6-8.
Your Regular Ol' Pita Makes 6–8 servings
Sometimes classic is the only way to go. Ranch dressing adds a unique zing.
Ingredients
8 pita pockets (4 pitas cut in half)
8 slices sandwich meat of your choice, cut in half
8 slices cheese of your choice, cut in half
1/2 cup ranch dressing
Tomato slices
1/2 red onion, sliced
• 1/2 cucumber, peeled and cut into matchstick-sized pieces
2 cups baby spinach, coarsely chopped
Directions
In each pita pocket, add half of a slice of meat, top with half of a slice of cheese, drizzle with ranch and top with tomato, onion and cucumber slices. Add another half slice of meat and cheese, along with another drizzle of ranch and top with a few chopped spinach leaves.
Egg Salad Pita (v) Makes 6–8 servings
Cool, refreshing and hearty at the same time.
Ingredients
8 pita pockets (4 pitas cut in half)
8 eggs, hard-boiled
1/2 cup mayonnaise
1 tablespoon sharp mustard (such as Dijon or deli mustard)
1 teaspoon dried dill
1/4 teaspoon paprika
1/2 stalk celery, minced (optional)
Salt and pepper to taste
Directions
Peel eggs; coarsely chop and add to a large bowl with mayonnaise and next 5 ingredients. Mix well, and stuff into pita pockets.
Chicken Salad Pita with Golden Raisins Makes 6–8 servings
This is our absolute favorite way to make chicken salad. It's important to use roasted chicken, if you can. Pick up a rotisserie chicken from the grocery store, or roast a chicken for dinner and use the leftovers to make chicken salad for lunch the next day.
Ingredients
8 pita pockets (4 pitas cut in half)
3 cups roasted chicken (skin removed), cubed
1 large green apple, peeled and chopped
1/2 cup golden raisins
1/2 cup pecans, toasted and chopped
1 tablespoon fresh tarragon, minced
1 1/4 cups mayonnaise
2 tablespoons rice vinegar
1/4 teaspoon lemon zest
Salt and pepper to taste
Directions
In a large bowl, combine chicken, apples, raisins, pecans and tarragon. In a small bowl, combine mayonnaise, vinegar and lemon zest. Add salt and pepper to taste. Add mayonnaise mixture to chicken mixture, and toss to coat. Refrigerate for at least 1 hour before stuffing into pita pockets.
Falafel Pita (v) Makes 6–8 servings
Falafel is not only a great finger food, but it's also delicious in sandwiches. These pita sandwiches make a tasty and hearty vegetarian meal.
Ingredients
8 pita pockets (4 pitas cut in half)
Falafel
1 cup plain Greek yogurt or Tzatziki Dip
1/2 red onion, sliced
1 tomato, sliced
1 cucumber, peeled and sliced
Directions
Prepare Falafel as directed. In each pita pocket, place 2-3 Falafel balls. Top Falafel with yogurt, red onion, tomato and cucumber slices.
Faux-Monsieur Wrap Makes 6–8 servings
The croque-monsieur sandwich originated in French cafés around the turn of the twentieth century. On a cold and rainy day, a hot croque-monsieur covered in melted cheese is a wonderful thing. These wraps are a riff on the flavor profile of that hot sandwich, served cold for warm days by the water.
Ingredients
4 large tortillas
1/2 cup strawberry jam
1/2 pound ham deli meat, sliced
1/4 cup spicy mustard
1 cup Gruyère cheese, shredded
1 cup arugula
Directions
Spread jam on each tortilla. Layer with ham, mustard, shredded Gruyère and arugula. Roll each tortilla into a tight wrap, and cut into 3- to 4-inch slices. Serve cold.
For a creative touch:
Try substituting lingonberry jam for strawberry jam or adding sliced banana peppers to add a little more crunch.
Mediterranean Wrap (v) Makes 6–8 servings
Light and healthy, the hummus and feta cheese give this wrap enough weight to be really satisfying.
Ingredients
4 large tortillas
1 cup Tomato-Infused Hummus or a store-bought variety
1 cup Tzatziki Dip
2 carrots, grated
1/2 red onion, sliced
1/2 cup Kalamata olives, diced
2 ounces feta cheese, crumbled
2 cups baby spinach
Directions
On a large tortilla, spread evenly with a thin layer of hummus, followed by a thin layer of Tzatziki Dip. Top with grated carrots, red onion, Kalamata olives, feta cheese and a single layer of spinach leaves. Roll the tortilla into a tight wrap and cut into 3- to 4-inch slices. Serve cold.
NOLA Wrap Makes 6–8 servings
The muffuletta (pronounced muff-uh-lot-a) sandwich is one of the signature flavors of New Orleans. Invented in the French Quarter's Central Grocery, the muffuletta sandwich has gained fame worldwide. Enjoy these yummy wraps based on the flavors of the Big Easy classic.
Ingredients
4 large tortillas
8 ounces cream cheese, softened
1 cup Olive and Sun-dried Tomato Tapenade or store-bought
1/4 pound ham deli meat, sliced
1/4 pound Genoa salami, sliced
8 ounces provolone, sliced
8 pepperoncini, sliced
Directions
Spread cream cheese and olive tapenade evenly on each tortilla. Layer with ham, salami and provolone. Sprinkle with pepperoncini. Roll each tortilla into a tight wrap, and cut into 3- to 4-inch slices.
Brownie Cupcakes with Molten Caramel, Fresh Fruit Skewers, Peanut Butter Chocolate Chip Cookies
Sweets
tips to make serving easy
Be sure to pack along some napkins for these finger-licking-good desserts. Pack napkins in a large plastic bag with a heavy object inside—such as a large metal spoon—to prevent the napkins from blowing away.
Each of our half-pint sweets recipes—Cheesecake with Fresh Berry Compote, Buttermilk Panna Cotta and Butterscotch Pudding—yields approximately 8 half-pint jars.
Half-pint jelly jars are a convenient and fun way to take dessert with you. Alternatively, for the Panna Cotta and Butterscotch Pudding, you may use disposable cups and cover them with plastic wrap.
Each recipe in this section serves 8.
Puppy Chow (gf, v) Makes about a full gallon zip-top bag
The recipe name comes from its appearance, but there's no mistaking these perfect little bites of crispy, chocolate-and-peanut buttery goodness.
Ingredients
2 cups semisweet chocolate chips (1 [12-ounce] bag)
1/2 cup butter, melted
3/4 cup peanut butter, smooth
1 box rice cereal squares (12 ounces)
2 cups powdered sugar
Directions
In a medium saucepan over low heat, melt chocolate chips along with the already melted butter (this will prevent the chocolate from seizing up during melting). Add peanut butter and stir until well combined. In a very large bowl, combine rice cereal squares and melted chocolate mixture. Mix gently with a rubber spatula to avoid breaking the rice cereal squares. (This takes a little patience, but it will come together eventually.) Once cereal is completely coated, place about a quarter of the rice cereal mixture into a large plastic bag along with 1/2 cup powdered sugar. Seal the bag and shake gently until all of the rice cereal is evenly coated. Carefully remove coated rice cereal and place into a separate plastic container. Continue to add batches of chocolate-coated rice cereal and 1/2 cup powdered sugar until all cereal is coated. Serve at room temperature.
No-Bake Cookies (gfo, v) Makes about 2 dozen cookies
These are terrific on warm summer days when you'd rather not heat up the kitchen with a hot oven. This recipe doesn't require knives, so it's also a great way for young kids to join in the fun of cooking.
Ingredients
2 cups sugar
1/4 cup cocoa powder
1/2 cup butter (1 stick)
1/2 cup milk
1/2 cup peanut butter, smooth
2 cups rolled oats
1 cup peanuts
Directions
In a large saucepan, stir together sugar, cocoa, butter and milk. Bring to a boil and remove from heat. Stir in peanut butter, oats and peanuts. Allow to cool in pan for 5-10 minutes. Line a baking sheet with parchment paper, and drop spoonfuls of chocolate-oat mixture onto baking sheet. Refrigerate for at least 4 hours or until cookies are firm. Serve cold.
gfo: Use gluten-free oats.
Note: Keep cookies in the cooler until ready to eat.
Peanut Butter Chocolate Chip Cookies (gfo, v) Makes about 20 cookies
Erin has been perfecting this recipe for years; the best part is, you only have to get one bowl dirty to make these cookies! Be careful not to overcook them: They should not be fully set when you remove them from the oven.
Ingredients
1/2 cup smooth peanut butter
1/2 cup butter, softened
1 egg
1 1/4 cups flour
1/2 cup sugar
1/2 cup brown sugar
1/2 teaspoon baking powder
1/2 teaspoon baking soda
1/2 teaspoon vanilla
1 cup semisweet chocolate chips
Directions
Preheat oven to 375 degrees. In a large bowl, blend together peanut butter and butter. Add egg, 1/2 cup flour, sugars, baking powder, baking soda and vanilla. Mix until just combined. Slowly add remaining flour. Fold in chocolate chips. Roll into small balls and press slightly with a fork. Bake until just starting to brown (about 8 minutes). Remove cookies from oven but leave on baking sheet for another 4-5 minutes or until cookies firm up. Place cookies on cooling rack until completely cool.
gfo: Use a gluten-free all-purpose flour mixture.
Brownie Cupcakes with Molten Caramel (gfo, v) Makes 1 dozen cupcakes
These rich and chewy brownies contain a hidden surprise.
Ingredients
1 box chocolate brownie mix
12 cupcake liners
12 caramel squares (or other bite-sized candy pieces, such as peanut butter cups or caramel-filled chocolates), unwrapped
Directions
Preheat oven to 350 degrees. Follow package directions on brownie mix to make the batter. Place cupcake liners in a muffin tin; pour batter evenly into cupcake liners, filling about 2/3 of the way up. Bake cupcakes for 7-8 minutes or until about halfway cooked. Remove cupcakes from oven, and place a caramel (or candy piece) into the center of each cupcake. Place cupcakes back in the oven for another 10-12 minutes or until cupcakes are completely cooked through and caramel is melted. Serve warm.
gfo: Use a gluten-free brownie mix.
Note: These mixes typically call for additional ingredients, such as eggs, butter or oil, so read the directions of the mix that you are using and be sure to get the additional ingredients that it calls for.
Cracker Candy (gfo, v) Makes 8 servings
This recipe is super simple and uses only 5 ingredients, but it just might be the most delicious and addictive toffee candy you've ever tasted.
Ingredients
1/2 pound butter (2 sticks), plus more for greasing pan
1 (16-ounce) package saltine crackers
3/4 cup sugar
2 cups semisweet chocolate chips
3/4 cup chopped walnuts or pecans
Directions
Preheat oven to 425 degrees. Line a baking sheet with aluminum foil and grease liberally with butter. Arrange saltines in a single layer on foil-lined baking sheet. Melt butter in a saucepan over medium heat. When butter is melted, add sugar to pan and bring to a low boil. Boil for 3 minutes, stirring and scraping constantly with a wooden spoon to prevent burning. Carefully pour butter-sugar mixture over crackers, and bake for 5 minutes. Remove from oven, and sprinkle chocolate chips evenly over the top. As chips melt, use a rubber spatula to spread chocolate into an even layer. Sprinkle chopped nuts over top. Cool in the refrigerator until chocolate has fully hardened, at least 1 hour. Remove candy from foil and break into pieces. Store in refrigerator or cooler until ready to eat.
gfo: Use gluten-free matzo-style crackers instead of saltines.
Fresh Fruit Skewers (gf, v, df) Makes 8–10 skewers
Simple and straightforward, delicious fresh fruit is hard to beat as a healthy snack or a dessert.
Ingredients
1 pint blackberries, rinsed and drained
2 peaches, rinsed, peeled and cut into bite-sized pieces
1 pound fresh strawberries, rinsed and cut into bite-sized pieces
4 fresh kiwis, rinsed, peeled and cut into bite-sized pieces
Directions
Alternate placing fruit on skewers.
Cheesecake with Fresh Berry Compote (v) Makes 8 individual servings
Here is a real, made-from-scratch cheesecake with graham cracker crust and fresh berries, in individual portions.
Ingredients
3/4 cup graham cracker crumbs
1/3 cup pecans, toasted and finely chopped
2 tablespoons sugar
1/3 cup butter, melted
8 pint-size, ovenproof glass jars with lids
3 (8-ounce) packages cream cheese, softened
3/4 cup sugar
3 eggs
1 teaspoon vanilla extract
2 pints fresh berries (blueberries, raspberries, blackberries and/or strawberries), rinsed and drained
1/4 cup sugar
1/2 tablespoon orange liqueur, such as Cointreau (optional)
Directions
Preheat oven to 350 degrees. Combine graham cracker crumbs, pecans, sugar and melted butter in a large mixing bowl. Line the bottom of each jar with a half-inch layer of crust mixture, and pack down crust completely. (This is done easiest with a muddler.) Place jars onto a large rimmed baking sheet, and bake for 10-12 minutes or until crusts begin to brown slightly. Combine cream cheese and sugar using a mixer. Add eggs (one at a time) along with vanilla. Mix until well combined, but do not overmix. Pour batter equally into each jar, filling jars 3/4 full. Carefully wipe off any cream cheese mixture that may have spilled on sides of jars. Fill baking dish with 1-2 inches hot water; place jars in dish, and bake cheesecakes at 350 degrees for 25-30 minutes or until filling is set completely. Meanwhile, combine fresh berries, sugar and, if desired, Cointreau. When cheesecakes are completely cooked, remove from oven and let cool to room temperature. Cover jars with lids and store in the fridge for 4 hours (or overnight). Top with berry compote before serving. Replace lids and store in a cooler until ready to eat."
For a creative touch:
Substitute a quarter of a fresh vanilla bean for vanilla extract.
Buttermilk Panna Cotta with Candied Pistachios (gf) Makes 8 individual servings
Custardy and rich, the tartness of the buttermilk in this recipe is tempered with sugar and candied nuts.
Ingredients
4 cups buttermilk
3 1/2 teaspoons unflavored gelatin
2 cups heavy cream
1 cup sugar
2 teaspoons vanilla extract
Salt
8 pint-size, ovenproof glass jars with lids
1 cup pistachios, shelled
2 tablespoons honey
1 tablespoon sugar
Directions
In a large saucepan, add 2 cups buttermilk; sprinkle with gelatin. Let gelatin; rehydrate for 5 minutes before stirring to combine. In a medium saucepan, bring cream and 1 cup sugar to a gentle boil. Remove from heat; slowly stir into buttermilk-gelatin mixture. Whisk buttermilk-cream mixture over low heat until gelatin is completely dissolved (about 5-7 minutes). Remove from heat, and strain through a sieve into a large bowl to remove any undissolved gelatin particles. Add remaining buttermilk, vanilla and pinch of salt to bowl; stir to combine. Pour panna cotta mixture evenly into each jar until about 2/3 full. Cover each jar with a lid and very carefully move to the fridge to chill for at least 4 hours or overnight. Meanwhile, in a large bowl, combine pistachios, honey, 1 tablespoon sugar and pinch of salt; mix until nuts are evenly coated. Spread nuts in a thin layer on a parchment paper-lined baking sheet; bake at 350 degrees for 6-8 minutes. Remove nuts from oven; cool. When jars of panna cotta are set, top each jar with a layer of candied pistachios.
For a creative touch:
Substitute half of a fresh vanilla bean for vanilla extract, or add 1-2 drops of rose water to the buttermilk mixture before pouring into jars.
Note: Use high-quality, full-fat buttermilk, if available. It's also important to do the straining step to remove any undissolved gelatin; otherwise, the panna cotta will become grainy.
Butterscotch Pudding (gf, v) Makes 8 individual servings
A classic dessert that, sadly, isn't seen much these days, it's simple to make with common and affordable ingredients–in fact, you might have the ingredients in your pantry already. The "scotch" part of the name probably does not come from Scotch whisky, but it rather refers to the process of making butterscotch candy, either from the Middle English for "to cut or score the surface of" or as a derivative of the word "scorch." Nonetheless, Scotch whisky pairs beautifully with the caramel flavors of brown sugar and milk and adds a sophisticated, grown-up character.
Ingredients
2 cups milk
1 cup cream
1 tablespoon butter
1 cup brown sugar, unpacked
1/2 teaspoon kosher salt
1/4 cup cornstarch
4 egg yolks
1/4 teaspoon vanilla extract
1 tablespoon Scotch whisky (optional)
8 pint-size, ovenproof glass jars with lids
Directions
In a medium bowl, combine milk and cream. Measure about 1/2 cup of the milk-cream mixture and reserve in a separate bowl. Melt butter and brown sugar with salt in a medium saucepan and cook over medium heat for 2-3 minutes.
Pouring slowly and carefully, add the larger portion of the milk-cream mixture to the pan, whisking constantly until sugar dissolves. While the cream-sugar mixture in the pan is heating, combine reserved 1/2 cup milk-cream mixture with the cornstarch in a small bowl, and whisk to make a slurry with no remaining clumps of cornstarch.
Boil cream-sugar mixture for 2-3 minutes. It will get foamy, so be careful the pan doesn't overflow. Remove from heat and slowly add cornstarch slurry to the cream-sugar mixture while whisking. Return pan to heat, and boil for about 1 minute, stirring constantly until thick. Remove from heat.
In a small bowl, beat egg yolks. Slowly add about 1/4 cup of the hot pudding mixture to beaten egg yolks, whisking constantly to temper the yolks. Then add yolks to pan and whisk thoroughly. (The residual heat will cook the yolks.) Add vanilla and Scotch whisky, if using.
Pour into individual glass jars or let cool for a few minutes and pour into disposable cups. Allow the pudding to set in the refrigerator for at least 3 hours. On chilly evenings, Butterscotch Pudding can also be enjoyed slightly warm.
Note: If pint-size glass jars are not available, you can use large plastic cups.
White Sangria
Drinks
tips to make serving easy
Make all cold drinks in large sealable pitchers, and transport in coolers filled with ice.
Serve drinks in double-walled paper cups to help keep drinks cold or hot and to prevent plastic cups from accidentally being blown overboard.
Safety is always number one on the water. Please drink responsibly. For recipes that include alcohol, you may want to set aside a serving for the skipper to enjoy after the boat is safely ashore.
Each recipe in this section serves 6-8.
White Sangria (gf, v, df) Makes about 2 quarts
Startlingly, "sangria" is the Spanish word for bloodletting. This describes the deep red color of sangria as it is most commonly made: with red wine. This white sangria variation is a bit lighter and more refreshing. For an even lighter version, substitute sparkling water for the sparkling wine to make a delicious spritzer.
Ingredients
1/2 Bosc pear, peeled and sliced
1/2 Granny Smith apple, peeled and sliced
1/2 cantaloupe or honeydew melon, cut into 1-inch cubes
1 peach, chopped
2 plums, chopped
1 bottle white wine (Pinot Grigio or Sauvignon Blanc)
1 bottle Prosecco or sparkling white wine
Directions
Combine fruit and still wine in a large pitcher. Allow to rest in the refrigerator for several hours before serving or overnight. Just before serving, combine with equal parts sparkling wine or, if desired, sparkling water.
For a creative touch:
Experiment with different fruit combinations.
Phyllis' Frozen Margaritas (gf, v, df) Makes about 1 1/2 quarts
This recipe is named for Jon's Aunt Phyllis, who makes the best frozen margaritas. Frozen limeade makes a better, cleaner-tasting margarita than any commercial margarita mixes we have tried.
Ingredients
1 (12-ounce) can frozen limeade concentrate
6 ounces tequila (silver or reposado)
3 ounces orange liqueur, such as Triple Sec or Cointreau
Ice, crushed or cubed
Directions
Combine limeade concentrate with tequila and orange liqueur, using the limeade can to measure. Use the limeade can to measure 3 cans of ice cubes (about 36 ounces or 4 loose cups). Combine all ingredients into a blender; blend, working in batches, if necessary. More ice can be added for a thicker texture, if desired. Serve immediately.
Note: This can also be made ahead and kept in the freezer. If frozen, let soften at room temperature for about 20 minutes before serving.
Note: Silver tequila will have a stronger "bite", whereas reposado tequila will be somewhat smoother in flavor.
Rhubarb Cooler with Ginger Ale (gf, v, df) Makes about 3 quarts
A unique and refreshing nonalcoholic cooler, this drink is great for kids and adults of all ages.
Ingredients
4 cups water
4 cups rhubarb, coarsely sliced (about 2 stalks)
1/2 cup sugar
2/3 cup fresh squeezed orange juice (about 2 oranges)
2 liters ginger ale, chilled
Directions
In a medium saucepan, combine water, rhubarb and sugar. Bring to a boil, reduce heat and simmer until rhubarb is soft, approximately 15 minutes, stirring occasionally. Let rhubarb mixture cool slightly; strain liquid into a large pitcher using a colander. Add orange juice and ginger ale to pitcher, and mix well. Place pitcher in the refrigerator for 2 to 4 hours to cool before serving. Alternatively, combine all ingredients except the ginger ale. Chill rhubarb mixture in the refrigerator overnight. Add chilled ginger ale immediately before serving.
Waikiki "Mai Tai" (gf, v, df) Makes about 1 1/2 quarts
Inspired by the Mai Tais at the Barefoot Bar on Waikiki Beach, this is not the typical Mai Tai recipe. Always use fresh pineapple when possible. Blackstrap rum adds a touch of sweet molasses flavor that perfectly complements fresh pineapple.
Ingredients
2 cups fresh pineapple, chilled and cut into chunks
2 cups ice cubes
1/2 cup white rum
1/4 cup blackstrap rum
Water as needed
Directions
Combine pineapple, ice and rums in a blender; blend until smooth. Add water to reach desired consistency. Serve immediately, or make ahead and store in the freezer. To serve from frozen, remove from freezer and let soften at room temperature for about 20 minutes before serving.
For a creative touch:
Add 1 cup coconut milk before blending for a tropical piña colada.
Sparkling Lemonade (gf, v, df) Makes a little over 2 quarts
This is our version of the classic summer cooler. Try mixing equal amounts with Southern Sweet Tea to make an Arnold Palmer.
Ingredients
2/3 cup simple syrup
Juice from 6 lemons
64 ounces club soda, chilled
Directions
To make simple syrup, dissolve 2/3 cup sugar with 1 cup water in a small saucepan over medium heat. Bring to a boil; remove from heat, and cool to room temperature. Simple syrup can be stored in the refrigerator for up to a few weeks in advance. Combine all ingredients in a large pitcher, and mix well. Serve over ice.
Bloody Marys (gf, v, df) Makes about 2 quarts
These can be made without alcohol, if desired. Try them alongside Bloody Mary skewers.
Ingredients
64 ounces Spicy Hot V8 juice, chilled
Juice from 1 orange
1 tablespoon celery salt
1/4 teaspoon Worcestershire
1 cup vodka
Directions
Combine all ingredients in a large pitcher, and mix well. Serve over ice.
Southern Sweet Tea (gf, v, df) Makes a generous half-gallon
Our version is cold brewed and flavored with fresh orange and lemon.
Ingredients
1/2 gallon warm water
1/2 cup sugar
4 bags black tea
1/2 lemon, seeds removed and sliced
1/2 orange, quartered
Directions
Combine water and sugar in a large pitcher and stir to combine until sugar is dissolved. Add remaining ingredients into the pitcher, and mix well. Place pitcher in the refrigerator overnight to cool.
Spiced Apple Cider Makes a generous gallon
Warm apple cider and sweet spice are great for a brisk day on the water.
Ingredients
1 gallon apple cider
1 tablespoon whole cloves
1 tablespoon whole allspice
1 cinnamon stick
1 cup rum (optional)
Directions
Pour apple cider into a large saucepan. Place cloves and allspice inside a tea ball. Add tea ball and cinnamon stick to cider. Heat cider over medium heat until just simmering. Reduce heat to low; steep cider with spices for 20 minutes. Remove cinnam on stick and tea ball. Add rum, if desired, and stir to combine. Place cider in a large thermos or heatproof pitcher. Serve warm.
About the Authors
Erin grew up in Minnesota; with its 10,000 lakes, water was never far away. One of her favorite places is the family cabin, where pontoon rides and guests were always part of the scene. Jon grew up on the Carolina coast, where he loved the water and all the varying cuisines that his state had to offer. Both Erin and Jon are huge food enthusiasts with a passion for outdoor activity, travel, learning about different cuisines and trying new foods. As adventurous home cooks, they apply the same appreciation and discovery of good food to their own cooking.
|
{
"redpajama_set_name": "RedPajamaBook"
}
| 3,540
|
\section{Introduction}
\label{sec_introduction}
Galaxy mergers not only distort the morphology of the interacting galaxies, but as suggested by observations and predicted
by simulations, they can have strong influence on the physical properties of the galaxies, e.g. enhancement in star formation,
triggering of Active Galactic Nuclei (AGNs), and dilution of central metallicities \citep{kewley2006,dimatteo2007,cox2008,
ellison2008,ellison2019,scudder2012,torrey2012,satyapal2014,moreno2015,weston2017,bustamante2018}. However, untill recently,
how the merging process impacts the physical conditions of different gas phases in the galaxies was not well-explored. In a
recent study, \citet{ellison2018}, using \mbox{H\,{\sc i}}\ 21-cm\ emission, have found that the atomic gas fractions in post-mergers are
elevated compared to isolated galaxies, while \citet{pan2018} and \citet{violino2018} have found evidence for enhanced molecular
gas fractions in galaxy pairs using CO emission. On the other hand, recent high-resolution (parsec-scale) simulation of the
multi-phase interstellar medium in galaxy pairs shows that interactions elevate the cold-dense ($T<$300\,K; $n>$10\,cm$^{-3}$) gas
mass in galaxies by $\sim$18\% \citep{moreno2019}. This gas mass remains elevated during the galaxy-pair period, i.e. for
few Gyrs between the first and second pericentric passages. It is thus now the opportune time to investigate observationally
the cold gas properties in different merger stages and test predictions that are becoming available from statistical studies
using state-of-the-art simulations.
While the atomic and molecular gas has been mapped in some individual merging galaxies \citep[e.g.][]{hibbard1996,tacconi1999},
statistical studies of the cold gas in galaxy pairs and mergers have typically focused on the average gas properties (like gas
mass and fraction) derived using single dish radio observations \citep[e.g.][]{ellison2015,ellison2018}. Simulations of mergers,
however, predict concentration of stars and gas in centres of galaxies resulting from tidal torques \citep[e.g.][]{mihos1996,blumenthal2018}.
Observations of the gas in the inner regions of galaxy mergers are, hence, very relevant to understand gas kinematics and metallicity
in the nuclear regions and fueling of nuclear activity. High spatial resolution interferometric observations of absorption against
different radio emitting components in mergers provide an effective way of studying the cold gas within the central kilo-parsec
regions \citep[e.g.][]{srianand2015}. The \mbox{H\,{\sc i}}\ 21-cm\ absorption line has long been used to probe the neutral gas in radio-loud AGNs
\citep{vangorkom1989}. In particular, it has been used to trace gas infalling and feeding the central super-massive black hole,
as well as negative feedback in the form of outflows/winds driven by the central starbursts or AGNs \citep[e.g.][]{vermeulen2003,gupta2006,morganti2009,schulz2018}.
There have been \mbox{H\,{\sc i}}\ 21-cm\ absorption searches in local ($z\le0.1$) luminous infrared galaxies \citep[LIRGs;][]{mirabel1988}
and ultra-luminous infrared galaxies \citep[ULIRGs;][]{teng2013}, which are usually associated with gas-rich mergers \citep{sanders1996}.
However, these searches were conducted with single dish radio observations. Hence, the spatial resolution was not sufficient to
study the radio emission and \mbox{H\,{\sc i}}\ gas in the central kilo-parsec regions of these galaxies, and the absorption may be blended
with emission in these spectra as well. These studies were also not conducted on samples selected specifically as mergers with
strong radio-loud emission at their centres. Using radio interferometric observations of \mbox{H\,{\sc i}}\ 21-cm\ absorption, we have recently
conducted a pilot study of neutral gas in the central regions of a sample of galaxy mergers hosting radio-loud AGNs at $z\le0.2$
\citep[][hereafter D18]{dutta2018}. In this work, we expand our sample of radio-loud mergers with new \mbox{H\,{\sc i}}\ 21-cm\ absorption measurements.
Further, we connect the properties of the neutral gas in centres of mergers with their optical, infrared and radio properties,
and trace the evolution of neutral gas through different merger stages. We describe the sample and observations in Section~\ref{sec_observations}.
The results are presented and discussed in Section~\ref{sec_results}. We summarize our conclusions in Section~\ref{sec_summary}.
We adopt a flat $\Lambda$-cold dark matter cosmology with $H_{\rm 0}$ = 70\,km\,s$^{-1}$~Mpc$^{-1}$ and $\Omega_{\rm M}$ = 0.30 throughout
this work.
\section{Sample \& Observations}
\label{sec_observations}
\subsection{Sample}
\label{sec_sample}
We cross-matched visually-identified galaxy mergers \citep[see][]{darg2011,barcos2017,satyapal2017,weston2017,fu2018}
at spectroscopic $z\le$0.2 in the Sloan Digital Sky Survey \citep[SDSS;][]{york2000} with radio sources in the Faint Images
of the Radio Sky at Twenty-Centimeters \citep[FIRST; resolution$\sim$5$''$;][]{white1997} and the NRAO VLA Sky Survey \citep[NVSS;
resolution$\sim$45$''$;][]{condon1998}. We thus identified 45 mergers showing radio emission with flux density greater than
20\,mJy at 1.4\,GHz. The identification of mergers is carried out in the same way as explained in D18. We list here the selection
criteria for visually identifying mergers in the SDSS images $-$ (i) single galaxy with disturbed central morphology and/or tails;
(ii) single galaxy with double nuclei and/or tails; (iii) pair of interacting galaxies that show signatures of tidal disturbances.
In D18 we had studied a sub-sample of 10 mergers from the above sample, with flux density greater than 50~mJy at 1.4\,GHz.
Here we expand our sample with \mbox{H\,{\sc i}}\ 21-cm\ observations of 9 mergers with flux density $\sim$20-50~mJy at 1.4\,GHz. For 19
mergers from the above sample, \mbox{H\,{\sc i}}\ 21-cm\ observations are available in the literature (see table 5 of D18). Hence, the
sample used here for statistical analysis comprises 38 mergers, i.e. $\sim$84\% of the above mentioned sample of $z\le$0.2
radio-loud mergers.
From the available multi-wavelength data, we estimated various properties for the full sample (see Table~\ref{tab:fullsample}).
The stellar mass, $M_*$, is computed from SDSS photometry and the {\it kcorrect} algorithm (v\_4.2) by \citet{blanton2007}
\citep[see for details][]{dutta2017}. The total infrared luminosity, $L_{\rm IR}$, is obtained using either Infrared Astronomical Satellite
(IRAS) flux densities at 12, 25, 60 and 100\,$\micron$ \citep{moshir1990} following \citet{sanders1996}, or AKARI flux densities at
90 and 140\,$\micron$ \citep{kawada2007} following \citet{takeuchi2010}. The star formation rate (SFR) is taken from the MPA-JHU SDSS
DR7 spectroscopic catalog \citep{brinchmann2004,salim2007}. The spectral index ($\alpha_{0.15}^{1.4}$; $S_\nu \propto \nu^{\alpha}$)
is taken from the catalog of \citet{degasperin2018}, obtained from the 147\,MHz TIFR GMRT Sky Survey (TGSS) and 1.4\,GHz NVSS fluxes.
The median properties of the merger sample are: $z$ = 0.04, projected separation, $\rho$ = 6~kpc, radio power at 1.4\,GHz, $P_{1.4}$ =
$3\times10^{23}$~W~Hz$^{-1}$, $\alpha_{0.15}^{1.4}$ = $-$0.48, $M_*$ = $6\times10^{10}$~M$_\odot$, $L_{\rm IR}$\ = $6\times10^{11}$~L$_\odot$,
and SFR = 1~M$_\odot$~yr$^{-1}$. Note that we consider here only the parameters of the strong radio source whenever spatially resolved
data of multiple objects in a merger are available. In 85\% cases, the strong radio source has higher $M_*$. For the 20 pairs where $M_*$
estimation is possible for both the galaxies, 80\% are major-mergers with mass ratio $\le$1:4. The mass ratios are provided in Table~\ref{tab:fullsample}.
The galaxy pairs have typical line-of-sight velocity separation $\le500$\,km\,s$^{-1}$, with median of $\sim$100\,km\,s$^{-1}$. 72\% of the mergers are
LIRGs ($L_{\rm IR}$\ = $10^{11-12}$~L$_\odot$) and 25\% are ULIRGs ($L_{\rm IR}$\ $\ge10^{12}$~L$_\odot$). Based on BPT diagram \citep{baldwin1981} for
31 of the mergers with emission line measurements from SDSS spectra, 52\% of them can be classified as AGNs, 39\% as Composite and 9\%
as star-forming. However, based on the radio power, all the sources can be classified as radio-loud AGNs. Based on SDSS colour-magnitude
relation \citep{weinmann2006}, 58\% of the mergers are blue, 21\% are red, and 21\% are mixed (i.e. pair of blue and red galaxies).
To classify objects into different merger stages, we adapt from the six-stage merger classification scheme of the Great Observatories All-Sky
LIRG Survey \citep{haan2011}. We combine classes 1 and 2 of this scheme as the pre-merger stage (separate galaxies with symmetric disks or
asymmetric disks and/or tidal tails), classes 3 and 4 as the ongoing merger stage (two distinct nuclei in a common envelope or double nuclei
with tidal tails), and classes 5 and 6 as the post-merger stage (single/obscured nucleus with long prominent tails or disturbed central
morphology and short faint tails). There are 13, 12 and 13 mergers in the pre-merger, ongoing merger and post-merger stages, respectively.
The classification stage of each merger is also listed in Table~\ref{tab:fullsample}.
\subsection{Observations}
\label{sec_obs}
We obtained the redshifted \mbox{H\,{\sc i}}\ 21-cm\ line observations of the nine new mergers using the Giant Metrewave Radio Telescope (GMRT)
between October 2018 and March 2019. The observations were conducted using the L-band receivers and the GMRT Software Backend.
A spectral set-up of 16 MHz baseband bandwidth split into 512 channels was used, which resulted in a velocity resolution
of $\sim$7\,km\,s$^{-1}$\ and a coverage of $\sim$3600-3700\,km\,s$^{-1}$. Each source was observed for $\sim$2.5-3\,h. In addition, standard
calibrators were regularly observed for flux density, bandpass, and gain calibrations. The data were acquired in parallel hand
correlations. The data reduction was carried out in Astronomical Image Processing System ({\sc aips})\footnote{{\sc aips} is
produced and maintained by the National Radio Astronomy Observatory, a facility of the National Science Foundation operated under
cooperative agreement by Associated Universities, Inc.} following standard procedures \citep[][D18]{dutta2016}.
The GMRT 1.4\,GHz continuum images (resolution $\sim$2-3$''$) recover $\sim$80-100\% of the total flux of the radio sources
obtained in FIRST or NVSS. The 1.4\,GHz continuum contours are overlaid on SDSS images of the mergers in Fig.~\ref{fig:overlay}.
Four of the mergers show two radio continuum peaks. Absorption is detected from 8 out of 9 mergers. Properties of the \mbox{H\,{\sc i}}\
absorption spectra are listed in Table~\ref{tab:results}. The spectra along with the Gaussian fits to the absorption are shown
in Fig.~\ref{fig:21cmspectra}. The spectra are extracted towards the radio continuum peaks. The parameters from Gaussian fits
to the lines are given in Table~\ref{tab:gaussfit}.
\section{Results \& Discussion}
\label{sec_results}
\subsection{Incidence, $N$($\hi$)\ and kinematics of \mbox{H\,{\sc i}}\ gas}
\label{sec_results1}
Our new observations reveal 8 new \mbox{H\,{\sc i}}\ 21-cm\ absorption detections out of the 9 mergers observed. For the full sample of mergers,
the detection rate of \mbox{H\,{\sc i}}\ 21-cm\ absorption is $84\pm15$\% (i.e. 32/38). Note that we consider only absorption towards the strongest
radio continuum peak associated with the merger. We obtained a reference sample of 229 non-mergers (i.e. those that do not satisfy
the merger selection criteria listed in Section~\ref{sec_sample}) from the study of associated \mbox{H\,{\sc i}}\ absorption in $z\le0.2$ radio
galaxies presented in \citet{maccagni2017}. The detection rate in the non-merger sample is $23\pm3$\%, i.e. four times lower than
in the merger sample. Next, we estimate the detection rates in the merger and non-merger sample by imposing different $N$($\hi$)\ or
($\int\tau dv$) sensitivity limits (for spin temperature, T$_{s}$\ = 100~K, and covering factor, $C_{f}$\ = 1). As can be seen from Table~\ref{tab:rates},
the excess of incidence of \mbox{H\,{\sc i}}\ absorption in mergers compared to non-mergers increases by a factor of $\sim$4 to $\sim$38 as we
go for higher $N$($\hi$)\ sensitivity limits, implying that mergers show higher $N$($\hi$)\ on average.
This is confirmed by the fact that the $N$($\hi$)\ distribution of mergers and non-mergers are significantly different. A two-sided
Kolmogorov-Smirnov test shows maximum deviation between the two cumulative distributions of $D_{\rm KS}$ = 0.6, and probability
of finding the difference by chance is $P_{\rm KS}$ = $2\times10^{-8}$. Mergers give rise to stronger absorption on average and
have median $N$($\hi$)\ five times higher than non-mergers (see Fig.~\ref{fig:dist}). In addition, we find that the distribution of
the velocity shift ($v_{\rm shift}$) between the \mbox{H\,{\sc i}}\ absorption components and the systemic redshift of the galaxies hosting the
radio sources is different from that in non-mergers ($D_{\rm KS}$ = 0.3, $P_{\rm KS}$ = $3\times10^{-3}$). Mergers show three
times more redshifted (i.e. infalling) absorption than non-mergers (Fig.~\ref{fig:dist}). The fraction of components with $v_{\rm shift}$\
$\ge100$\,km\,s$^{-1}$\ is $30\pm7$\% in mergers compared to $9\pm4$\% in non-mergers. We do not find any significant difference in the
velocity widths (full width at half optical depth; FWHM) of the absorption in mergers and non-mergers ($D_{\rm KS}$ = 0.2,
$P_{\rm KS}$ = 0.3). Results from the comparison of \mbox{H\,{\sc i}}\ absorption properties between the samples of mergers and non-mergers
are given in Table~\ref{tab:kstest}.
Finally, to confirm the above differences, we create a mass- and redshift-matched reference sample of non-mergers from \citet{maccagni2017}.
In a sub-sample of 24 mergers, for each merger we randomly select a source from the non-merger sample with \mbox{H\,{\sc i}}\ 21-cm\ detection, that is within
$\pm$0.5~dex in $M_*$ and $\pm$0.1 in redshift, and repeat this 100 times. The resulting matched samples also have similar distributions of
$P_{1.4}$ (median $D_{\rm KS}$ = 0.3, $P_{\rm KS}$ = 0.1). We find that the $N$($\hi$)\ and $v_{\rm shift}$\ distributions in the matched samples are
significantly different as well (see Table~\ref{tab:kstest}). This indicates that the differences in \mbox{H\,{\sc i}}\ properties of the merger
sample from the non-merger sample are not driven by differences in stellar mass, but rather are likely to be driven by the merging process
feeding the central regions with large quantities of neutral hydrogen gas.
\begin{table}
\caption{Incidence of \mbox{H\,{\sc i}}\ absorption in mergers and non-mergers for different $N$($\hi$)\ sensitivity limits.}
\centering
\begin{tabular}{ccc}
\hline
$N$($\hi$)\ sensitivity & \multicolumn{2}{c}{Incidence of \mbox{H\,{\sc i}}\ absorption} \\
(T$_{s}$$/100$ K)($1/$$C_{f}$)(cm$^{-2}$) & Mergers & Non-mergers \\
\hline
All & 84 $\pm$ 15\% & 23 $\pm$ 3\% \\
$2\times10^{20}$ & 94 $\pm$ 17\% & 26 $\pm$ 6\% \\
$5\times10^{20}$ & 89 $\pm$ 16\% & 18 $\pm$ 3\% \\
$5\times10^{21}$ & 76 $\pm$ 17\% & 2 $\pm$ 1\% \\
\hline
\end{tabular}
\label{tab:rates}
\begin{flushleft}
\end{flushleft}
\end{table}
\begin{table}
\caption{Comparison of \mbox{H\,{\sc i}}\ absorption properties between the samples of mergers and non-mergers.}
\centering
\begin{tabular}{cccccc}
\hline
\mbox{H\,{\sc i}}\ property & \multicolumn{2}{c}{All} & \multicolumn{2}{c}{Mass-matched} \\
& $D_{\rm KS}$ & $P_{\rm KS}$ & $D_{\rm KS}$ & $P_{\rm KS}$ \\
(1) & (2) & (3) & (4) & (5) \\
\hline
$N$($\hi$)\ & 0.62 & $2\times10^{-8}$ & 0.70 & $3\times10^{-5}$ \\
FWHM & 0.19 & 0.32 & 0.32 & 0.13 \\
$v_{\rm shift}$\ & 0.33 & $3\times10^{-3}$ & 0.50 & $2\times10^{-3}$ \\
\hline
\end{tabular}
\label{tab:kstest}
\begin{flushleft}
{\it Notes.}
Column 1: \mbox{H\,{\sc i}}\ absorption property whose distributions in mergers and non-mergers are compared in a two-sided Kolmogorov-Smirnov (KS) test.
Columns 2 and 4: maximum deviation between the two cumulative distribution functions.
Columns 3 and 5: probability of finding the difference by chance.
\end{flushleft}
\end{table}
\begin{figure*}
\includegraphics[width=0.35\textwidth, angle=90]{nhi_dist.ps}
\includegraphics[width=0.35\textwidth, angle=90]{vshift_dist.ps}
\caption{Cumulative distributions of $N$($\hi$)\ {(\it left)} and $v_{\rm shift}$\ {(\it right)} in the sample of mergers (solid lines) and non-mergers
(dashed lines). The median values are demarcated by solid and dashed vertical ticks for mergers and non-mergers, respectively. The distributions
are significantly different for mergers and non-mergers, as indicated by results of two-sided KS tests.
}
\label{fig:dist}
\end{figure*}
\subsection{Implication of non-detections}
\label{sec_results2}
The only non-detection in the new sample presented here is towards the complex merger J0904$+$1435 consisting of three galaxies
(see Fig.~\ref{fig:overlay}). The radio emission is resolved in the GMRT map, with the strongest continuum peak having $\sim$14\%
of the total flux and not coinciding with any optical nuclei. Lack of absorption in this case could be related to the radio sightline
not probing the nuclear region and absence of \mbox{H\,{\sc i}}\ gas in the region probed between the merging galaxies. Among the mergers presented
here and in D18, there are four cases (J0915$+$4419, J1100$+$1002, J1315$+$6207 and J1518$+$4244), where the optical nuclei of both
the interacting galaxies (with $\rho\sim$6-20~kpc) are co-spatial with radio emission in GMRT maps (see Fig.~\ref{fig:overlay} and
figure 1 in D18). Absorption is detected towards only the stronger radio emission in three of them. From $3\sigma$ upper limit towards
the weaker radio source obtained by integrating over the velocity range of absorption detected towards the stronger source, we find
that the \mbox{H\,{\sc i}}\ optical depth towards the stronger source is higher by $\gtrsim2-4$ times. In case of the merger J1518$+$4244, absorption
is detected towards both the radio sources, but the stronger radio source shows two times higher integrated optical depth. Three of
these mergers also have higher SFR and dust depletion in the regions showing stronger radio emission, indicating a possible physical
connection between the presence of \mbox{H\,{\sc i}}\ gas, starburst and nuclear radio activity. However, we note that there is no clear connection
between the \mbox{H\,{\sc i}}\ gas and other properties like stellar mass for these four mergers, e.g. in two cases the stronger radio source showing
higher \mbox{H\,{\sc i}}\ optical depth has the higher stellar mass of the galaxy pair and it is vice-versa for the other two.
\subsection{\mbox{H\,{\sc i}}\ gas and merger properties}
\label{sec_results3}
We checked the dependence of the incidence of \mbox{H\,{\sc i}}\ absorption on various properties of the mergers as listed in Table~\ref{tab:fullsample}.
We find that the incidence of \mbox{H\,{\sc i}}\ is higher at smaller projected separations, i.e. $\sim$92\% at $\rho\le6$~kpc vis-\`{a}-vis $\sim$71\%
at higher $\rho$. Detections tend to be higher in the more advanced stages of merger. Further, the incidence is higher at smaller stellar
masses, i.e. $\sim$100\% at $M_*\le6\times10^{10}$~M$_\odot$ vis-\`{a}-vis $\sim$72\% at higher $M_*$. The non-detections in high stellar
mass-mergers are usually associated with red elliptical galaxies. In addition, we find that the incidence is higher at lower redshifts
($\sim$95\% at $z\le0.04$ compared to $\sim$72\% at $z>0.04$), and for flatter spectral index sources ($\sim$94\% at $\alpha_{0.15}^{1.4}>-0.48$
compared to $\sim$71\% at steeper $\alpha_{0.15}^{1.4}$). The dependence on spectral index could indicate higher incidence among sources
with more compact radio emission, that is better suited to detect gas in absorption \citep{gupta2006}.
We do not find any significant dependence of incidence on radio power, infrared luminosity, SFR and nebular emission line ratios.
Majority ($\sim$97\%) of the mergers in our sample are LIRGs or ULIRGs, which have been observed to show high incidence of \mbox{H\,{\sc i}}\
absorption. Using single dish observations, \citet{teng2013} have found 100\% incidence of \mbox{H\,{\sc i}}\ absorption in nine ULIRGs, while
\citet{mirabel1988} have found that the incidence increases with far-infrared luminosity, from 40\% for $L_{\rm FIR}$ $\ge10^{11}$~L$_\odot$
to 100\% for $L_{\rm FIR}$ $\ge10^{12}$~L$_\odot$ in a sample of eighty galaxies. Three and eight of the mergers in our full sample are
also present in the sample studied by \citet{teng2013} and \citet{mirabel1988}, respectively. Though as noted in Section~\ref{sec_introduction},
these samples were selected on the basis of infrared luminosity, without the constraints on morphology and radio continuum flux as in our
merger sample. We do not find a significant difference in the incidence between LIRGs ($\sim$83\%) and ULIRGs ($\sim$88\%) in our sample.
Though we note that our sample has three times less ULIRGs compared to LIRGs, and a larger sample is required to check if the incidence of
nuclear \mbox{H\,{\sc i}}\ gas increases with the infrared luminosity.
Next, we carry out correlation analysis between properties of the \mbox{H\,{\sc i}}\ gas ($N$($\hi$), FWHM and $v_{\rm shift}$) and those of the mergers using
non-parametric Kendall's $\tau$ test (see Table~\ref{tab:correl}). We do not find any significant correlation (i.e. $\ge3\sigma$) of
the properties of \mbox{H\,{\sc i}}\ with those of the mergers. This once again confirms that the merger-induced gas accretion is the main driver
behind the high detection rate of \mbox{H\,{\sc i}}\ 21-cm\ absorption. However, the fact that there is no strong relation between the galaxy
and absorption properties tells us that it is not straightforward to connect the central gas accumulation we infer based on \mbox{H\,{\sc i}}\ 21-cm\
absorption with the triggering or quenching of nuclear star formation.
We show in Fig.~\ref{fig:correl}, $N$($\hi$)\ measured for the mergers as a function of $z$, $M_*$ and $\rho$, i.e. the parameters
with which $N$($\hi$)\ shows tentative ($\sim2\sigma$) anti-correlation. Increase in $N$($\hi$)\ with decreasing redshift could indicate the
presence of more gas-rich mergers at lower redshifts. However, we note that the sample lacks low stellar mass systems at high
redshifts, likely due to selection bias. Hence, the dependence of $N$($\hi$)\ on redshift could be driven by its dependence on stellar
mass. We have checked that except redshift and stellar mass, no other galaxy properties are correlated with each other.
Here we focus on the tentative dependences of $N$($\hi$)\ on stellar mass and projected separation. Exploring the parameter space of merger properties
considered here, we find that majority of the large $N$($\hi$)\ absorption occur at smaller values of $M_*$ and $\rho$ (see Fig.~\ref{fig:ms_rho}).
We note that in the non-merger reference sample considered here, we do not find any trend of $N$($\hi$)\ or detection rate with $M_*$. Therefore,
the trend of higher incidence and higher $N$($\hi$)\ at lower $M_*$ in the merger sample could imply a physical connection between the merger type
and the \mbox{H\,{\sc i}}\ cross-section. Majority ($\sim$71\%) of the lower mass mergers (i.e. below the median $M_*$) are blue in colour, while only
$\sim$40\% of the higher mass mergers are blue. Hence, the dependence of $N$($\hi$)\ on $M_*$ could be due to higher concentration of \mbox{H\,{\sc i}}\ gas in
centres of wet or gas-rich mergers. However, this may also reflect the general trend of increasing detection rate of \mbox{H\,{\sc i}}\ emission and atomic
gas fraction with decreasing stellar mass observed in both isolated and post-merger galaxies \citep{catinella2018,ellison2018}.
We notice that most ($\sim$94\%) of the mergers with $\rho\le6$~kpc (that show higher detection rate) are in the ongoing or post-merger stages.
This motivated us to look at the evolution of \mbox{H\,{\sc i}}\ properties along the merger sequence. The properties of \mbox{H\,{\sc i}}\ gas in different merger stages
are listed in Fig.~\ref{fig:merger_stage}, which shows a typical example of a merger from our sample in each of the stages. The incidence, $N$($\hi$)\
and FWHM of \mbox{H\,{\sc i}}\ absorption increases from non-merger through post-merger stages, with 100\% detection in post-mergers. The fraction Red$/$(Red$+$Blue),
defined as the number of redshifted components ($v_{\rm shift}$\ $\ge$100\,km\,s$^{-1}$) divided by the total number of redshifted and blueshifted ($v_{\rm shift}$\ $\le-$100\,km\,s$^{-1}$)
components, is highest among ongoing mergers. All these are consistent with more gas flow to the central regions during different merger stages.
While the contrast between the non-merger and merger samples are statistically significant (as discussed in Section~\ref{sec_results1}), the
differences among the three merger stages themselves are not statistically significant based on two-sided KS-tests. However, these results do
point towards widespread presence of \mbox{H\,{\sc i}}\ gas with infall signatures throughout the merger process.
It is particularly interesting to note that large amount of cold \mbox{H\,{\sc i}}\ gas survives in centres of all post-mergers. This could result
out of combination of the circumnuclear gas in the progenitor galaxies as well as the merger channeling gas to the central regions.
This leads to the conclusion that the nuclear radio activity has not yet quenched or driven away the neutral gas in the circumnuclear
regions in the recently coalesced or post-merger stage \citep[i.e. within a $\sim$Gyr of coalescence, e.g.][]{lotz2008}. It is
possible that depletion of neutral gas due to either nuclear winds/radio jets as predicted by simulations \citep{dimatteo2005}
or condensation into molecular phase and consequently stars is yet to take place. On the other hand, nuclear accretion and/or
cooling of ionized gas into neutral gas are possibly still ongoing in the centres of these post-mergers.
The 100\% detection rate of \mbox{H\,{\sc i}}\ absorption and high values of $N$($\hi$)\ that we find in post-mergers is consistent with the results
of \citet{ellison2018}. They find higher (factor of $\sim$1.5) detection rate of \mbox{H\,{\sc i}}\ emission as well as atomic gas fraction (factor
of $\sim$3) in post-mergers compared to a control sample of isolated galaxies matched in stellar mass. Thus the merger process leads
to increase in both the concentration of nuclear \mbox{H\,{\sc i}}\ gas as well as the overall neutral gas fraction in post-mergers. Based on a revised
picture of the merger process, \citet{ellison2018} rule out a `blowout' phase in the merger-driven sequence of galaxy evolution \citep{hopkins2008}.
Our results support this and indicate that the circumnuclear \mbox{H\,{\sc i}}\ gas probably survives till the `quasar' phase in this evolutionary
picture. This is further corroborated by the results of \citet{teng2013}, who find 100\% incidence of \mbox{H\,{\sc i}}\ absorption in coalesced
ULIRGs compared to $\sim$60\% in far-infrared-weak quasars. In addition, while only $\sim$25\% of the post-mergers in \citet{ellison2018}
are classified as optical AGNs, all our post-mergers host radio-loud AGNs at their centres. This implies that the AGN activity in the
post-merger stage has not yet consumed or expelled the \mbox{H\,{\sc i}}\ gas fed to the nuclear regions by the merger, which could also have triggered
it in the first place.
\begin{table*}
\caption{Correlation analysis between \mbox{H\,{\sc i}}\ absorption and properties of the mergers.}
\centering
\begin{tabular}{ccccccccccccccc}
\hline
Parameter & \multicolumn{5}{c}{$N$($\hi$)} & \multicolumn{5}{c}{FWHM} & \multicolumn{4}{c}{$v_{\rm shift}$} \\
& $N$ & $r_k$ & $P(r_k)$ & $S(r_k)$ & & $N$ & $r_k$ & $P(r_k)$ & $S(r_k)$ & & $N$ & $r_k$ & $P(r_k)$ & $S(r_k)$ \\
(1) & (2) & (3) & (4) & (5) & & (6) & (7) & (8) & (9) & & (10) & (11) & (12) & (13) \\
\hline
$z$ & 38 & {\bf$-$0.19} & {\bf0.10} & {\bf1.7$\sigma$} & ~~ & 32 & $-$0.16 & 0.20 & 1.3$\sigma$ & ~~ & 32 & $-$0.03 & 0.82 & 0.2$\sigma$ \\
$\rho$ & 38 & {\bf$-$0.21} & {\bf0.06} & {\bf1.9$\sigma$} & ~~ & 32 & {\bf$-$0.20} & {\bf0.11} & {\bf1.6$\sigma$} & ~~ & 32 & 0.16 & 0.20 & 1.3$\sigma$ \\
$P_{1.4}$ & 38 & $-$0.11 & 0.36 & 0.9$\sigma$ & ~~ & 32 & $-$0.03 & 0.83 & 0.2$\sigma$ & ~~ & 32 & $-$0.13 & 0.30 & 1.0$\sigma$ \\
$\alpha_{0.15}^{1.4}$ & 33 & 0.04 & 0.76 & 0.3$\sigma$ & ~~ & 27 & 0.05 & 0.72 & 0.4$\sigma$ & ~~ & 27 & {\bf$-$0.26} & {\bf0.05} & {\bf1.9$\sigma$} \\
$M_*$ & 35 & {\bf$-$0.28} & {\bf0.02} & {\bf2.4$\sigma$} & ~~ & 30 & 0.02 & 0.86 & 0.2$\sigma$ & ~~ & 30 & $-$0.15 & 0.26 & 1.1$\sigma$ \\
$L_{\rm IR}$\ & 32 & 0.01 & 1.00 & 0.1$\sigma$ & ~~ & 27 & {\bf0.26} & {\bf0.05} & {\bf1.9$\sigma$} & ~~ & 27 & $-$0.06 & 0.68 & 0.4$\sigma$ \\
SFR & 31 & $-$0.12 & 0.37 & 0.9$\sigma$ & ~~ & 26 & 0.07 & 0.60 & 0.5$\sigma$ & ~~ & 26 & {\bf0.26} & {\bf0.06} & {\bf1.9$\sigma$} \\
\hline
\end{tabular}
\label{tab:correl}
\begin{flushleft}
Column 1: property of merger with which correlation of $N$($\hi$), FWHM and $v_{\rm shift}$\ of the absorption is tested.
Columns 2, 6, 10: number of measurements included in test.
Columns 3, 7, 11: Kendall rank correlation coefficient.
Columns 4, 8, 12: probability of correlation arising by chance.
Columns 5, 9, 13: significance of correlation assuming Gaussian statistics.
Upper limits of $N$($\hi$)\ are considered as censored data points during survival analysis with {\tt cenken} function in {\tt NADA} package in {\tt R}.
Tentative correlations are marked in bold.
\end{flushleft}
\end{table*}
\begin{figure*}
\includegraphics[width=0.25\textwidth, angle=90]{nhi_z.ps}
\includegraphics[width=0.25\textwidth, angle=90]{nhi_rho.ps}
\includegraphics[width=0.25\textwidth, angle=90]{nhi_ms.ps}
\caption{The $N$($\hi$)\ inferred for mergers as a function of redshift, projected separation and stellar mass, from left to right respectively.
Solid symbols correspond to detections while open symbols correspond to $3\sigma$ upper limits. Median values are marked by dotted lines.
$N$($\hi$)\ shows $\sim2\sigma$ anti-correlation with these parameters (see Table~\ref{tab:correl}).
}
\label{fig:correl}
\end{figure*}
\begin{figure}
\includegraphics[width=0.35\textwidth, angle=90]{ms_rho.ps}
\caption{Stellar mass versus projected separation of the mergers. Filled and open symbols represent detections (colour-coded in $N$($\hi$)\ as shown in the bar to the right)
and non-detections, respectively. The median $M_*$ and $\rho$ are marked by horizontal and vertical dashed lines, respectively. The detection rate and $N$($\hi$)\ are higher
for smaller values of $M_*$ and $\rho$.
}
\label{fig:ms_rho}
\end{figure}
\begin{figure*}
\includegraphics[width=1.0\textwidth]{merger_stage.ps}
\caption{SDSS colour composite image of a typical system in the non-merger, pre-merger, ongoing and post-merger stage, from left to right.
Below each example are listed, from top to bottom, the incidence of \mbox{H\,{\sc i}}\ absorption in that stage, and median $N$($\hi$), median FWHM and fraction
of redshifted components among all redshifted and blueshifted components for detections in that stage.
}
\label{fig:merger_stage}
\end{figure*}
\section{Conclusion}
\label{sec_summary}
We have presented a study of \mbox{H\,{\sc i}}\ 21-cm\ absorbing gas in central regions of 38 $z\le0.2$ radio-loud galaxy mergers.
We confirm that the merger sample, in comparison to a reference sample of non-merging radio galaxies, show higher:
(i) incidence of \mbox{H\,{\sc i}}\ 21-cm\ absorption by a factor of $\sim$4, (ii) $N$($\hi$)\ by a factor of $\sim$5, and (iii) infall signature,
in the form of redshifted absorption with respect to the systemic redshift, by a factor of $\sim$3. These differences
persist in the redshift- and stellar mass-matched samples of mergers and non-mergers as well.
We further analyze the dependence of the incidence, $N$($\hi$)\ and kinematics of the nuclear \mbox{H\,{\sc i}}\ gas in mergers on different
optical, infrared and radio properties of the mergers, as well as the evolution of the nuclear \mbox{H\,{\sc i}}\ gas along the merger
sequence. We do not find any significant ($\ge3\sigma$) correlation of the \mbox{H\,{\sc i}}\ absorption properties with the global
properties of the mergers. From comparison with stellar mass-matched reference sample of non-mergers and lack of strong
dependence of \mbox{H\,{\sc i}}\ gas on any properties of the galaxies, we conclude that the merging process is likely to be the dominant
factor behind the prevalence of high $N$($\hi$)\ absorption with signature of infall among mergers. We do find tentative trend
of increasing incidence and $N$($\hi$)\ with decreasing stellar mass and projected separation. This could be due to presence of
more \mbox{H\,{\sc i}}\ gas in central regions of blue gas-rich mergers and in later stages of mergers.
We find increasing trend of incidence, $N$($\hi$)\ and velocity width from the pre-merger to the post-merger stages, though the
differences in \mbox{H\,{\sc i}}\ gas properties between the merger stages are not statistically significant. The results presented here
could imply evolution in the \mbox{H\,{\sc i}}\ gas properties as the merger progresses, which is relevant to explore further with larger
samples of mergers. Higher spatial resolution resolved spectroscopy is also crucial to establish the connection of the \mbox{H\,{\sc i}}\
gas with nuclear starburst and radio activity. \\
\noindent \textbf{ACKNOWLEDGEMENTS} \newline \newline
\noindent
We thank the anonymous reviewer for their constructive comments.
RD acknowledges support from the Alexander von Humboldt Foundation.
We thank the staff at GMRT for their help during the observations.
GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research.
Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation,
and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/.
SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration
including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University,
University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica
de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory,
Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University,
Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group,
University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.
\def\aj{AJ}%
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\def\araa{ARA\&A}%
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\def\apjs{ApJS}%
\def\ao{Appl.~Opt.}%
\def\apss{Ap\&SS}%
\def\aap{A\&A}%
\def\aapr{A\&A~Rev.}%
\def\aaps{A\&AS}%
\def\azh{A$Z$h}%
\def\baas{BAAS}%
\def\bac{Bull. astr. Inst. Czechosl.}%
\def\caa{Chinese Astron. Astrophys.}%
\def\cjaa{Chinese J. Astron. Astrophys.}%
\def\icarus{Icarus}%
\def\jcap{J. Cosmology Astropart. Phys.}%
\def\jrasc{JRASC}%
\def\mnras{MNRAS}%
\def\memras{MmRAS}%
\def\na{New A}%
\def\nar{New A Rev.}%
\def\pasa{PASA}%
\def\pra{Phys.~Rev.~A}%
\def\prb{Phys.~Rev.~B}%
\def\prc{Phys.~Rev.~C}%
\def\prd{Phys.~Rev.~D}%
\def\pre{Phys.~Rev.~E}%
\def\prl{Phys.~Rev.~Lett.}%
\def\pasp{PASP}%
\def\pasj{PASJ}%
\def\qjras{QJRAS}%
\def\rmxaa{Rev. Mexicana Astron. Astrofis.}%
\def\skytel{S\&T}%
\def\solphys{Sol.~Phys.}%
\def\sovast{Soviet~Ast.}%
\def\ssr{Space~Sci.~Rev.}%
\def\zap{$Z$Ap}%
\def\nat{Nature}%
\def\iaucirc{IAU~Circ.}%
\def\aplett{Astrophys.~Lett.}%
\def\apspr{Astrophys.~Space~Phys.~Res.}%
\def\bain{Bull.~Astron.~Inst.~Netherlands}%
\def\fcp{Fund.~Cosmic~Phys.}%
\def\gca{Geochim.~Cosmochim.~Acta}%
\def\grl{Geophys.~Res.~Lett.}%
\def\jcp{J.~Chem.~Phys.}%
\def\jgr{J.~Geophys.~Res.}%
\def\jqsrt{J.~Quant.~Spec.~Radiat.~Transf.}%
\def\memsai{Mem.~Soc.~Astron.~Italiana}%
\def\nphysa{Nucl.~Phys.~A}%
\def\physrep{Phys.~Rep.}%
\def\physscr{Phys.~Scr}%
\def\planss{Planet.~Space~Sci.}%
\def\procspie{Proc.~SPIE}%
\let\astap=\aap
\let\apjlett=\apjl
\let\apjsupp=\apjs
\let\applopt=\ao
\bibliographystyle{mnras}
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| 8,426
|
Der Playa Yamana ist ein Strand am Ufer der Barclay Bay der Livingston-Insel im Archipel der Südlichen Shetlandinseln. Auf der Westseite des Kap Shirreff am nördlichen Ausläufer der Johannes-Paul-II.-Halbinsel liegt er zwischen dem Punta El Hallazgo im Norden und dem Punta Mazzei im Süden.
Wissenschaftler der 40. Chilenischen Antarktisexpedition (1985–1986) benannten ihn so, da sie am Punta El Hallazgo einen menschlichen Schädel der Yámana gefunden hatten.
Weblinks
Yamana, Playa im Composite Gazetteer of Antarctica (englisch und spanisch)
Strand Antarktikas
Livingston-Insel
|
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| 6,213
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{"url":"http:\/\/clay6.com\/qa\/27946\/mole-fraction-of-the-component-a-in-vapour-phase-is-x-and-mol-fraction-of-c","text":"Comment\nShare\nQ)\n\n# Mole fraction of the component 'A' in vapour phase is X and mol fraction of component 'A' in liquid mixture is Y $(P_A^0$=vapour pressure of pure A,$P_A^0$=vapour pressure of pure B) then total vapour of the liquid mixture is\n\n$\\begin{array}{1 1}(a)\\;\\large\\frac{P_B^0Y}{X}\\\\(b)\\;\\large\\frac{P_B^0X}{Y}\\\\(c)\\;\\large\\frac{P_A^0X}{Y}\\\\(d)\\;\\large\\frac{P_A^0Y}{X}\\end{array}$\n\nPartial pressure $=PX$-----(1)\nPartial pressure $=P_A^0Y$-----(2)\n$PX=P_A^0Y$\n$P=\\large\\frac{P_A^0Y}{X}$","date":"2020-01-27 15:11:32","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\": 0.6912746429443359, \"perplexity\": 9711.43005278728}, \"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-2020-05\/segments\/1579251700988.64\/warc\/CC-MAIN-20200127143516-20200127173516-00540.warc.gz\"}"}
| null | null |
Q: Gutenberg Plugin Creation Structure and Files I recently refereed few Gutenberg compatible plugins. Example : https://github.com/HardeepAsrani/gutenberg-boilerplate. I am not able to get how following file is created
https://github.com/HardeepAsrani/gutenberg-boilerplate/blob/master/dist/block.js
I did an npm install and it provided me following files
Files
Also not getting how webpack.config.js file is run.
Can anyone explain me ?
A: I've recently used that same boilerplate, and FYI, the package.json isn't well structured and has some old dependencies. I had to change some code in that file in order to get it to work. Here is my package.json:
{
"name": "gutenberg-boilerplate",
"scripts": {
"dev": "cross-env BABEL_ENV=default webpack --watch"
},
"description": "This plugin add meta boxes in gutenberg's sidebar",
"main": "src/index.js",
"devDependencies": {
"@babel/core": "^7.2.2",
"@babel/preset-env": "^7.2.0",
"babel-core": "^6.26.3",
"babel-loader": "^8.0.4",
"babel-plugin-add-module-exports": "^1.0.0",
"babel-plugin-transform-react-jsx": "^6.24.1",
"babel-preset-env": "^1.7.0",
"browser-sync": "^2.18.13",
"browser-sync-webpack-plugin": "^1.2.0",
"classnames": "^2.2.5",
"cross-env": "^5.1.1",
"css-loader": "^0.28.7",
"eslint": "^4.14.0",
"eslint-config-prettier": "^2.9.0",
"eslint-config-wordpress": "^2.0.0",
"eslint-plugin-prettier": "^2.7.0",
"extract-text-webpack-plugin": "^3.0.2",
"node-sass": "^4.7.2",
"postcss-loader": "^2.0.9",
"prettier": "^1.15.3",
"raw-loader": "^0.5.1",
"sass-loader": "^6.0.6",
"style-loader": "^0.19.1",
"webpack": "^3.10.0"
},
"version": "1.0.0",
"license": "MIT"
}
Also, you have to add a .babelrc file in your root directory with the following code:
{
"presets": ["@babel/preset-env"],
"plugins": [
["transform-react-jsx", {
"pragma": "wp.element.createElement"
}]
]
}
This ensures that the webpack config actually work.
And for answering your firs question. The file /dist/block.js is generated as result of the webpack.config.js output. Is is automatically created.
Here is my webpack.config.js file:
const path = require( 'path' );
const webpack = require( 'webpack' );
const ExtractTextPlugin = require( 'extract-text-webpack-plugin' );
// const BrowserSyncPlugin = require( 'browser-sync-webpack-plugin' );
// Set different CSS extraction for editor only and common block styles
const blockCSSPlugin = new ExtractTextPlugin( {
filename: './dist/block.css',
} );
// Configuration for the ExtractTextPlugin.
const extractConfig = {
use: [
{ loader: 'raw-loader' },
{
loader: 'postcss-loader',
options: {
plugins: [ require( 'autoprefixer' ) ],
},
},
{
loader: 'sass-loader',
query: {
outputStyle:
'production' === process.env.NODE_ENV ? 'compressed' : 'nested',
},
},
],
};
module.exports = {
entry: {
'./dist/block' : './src/index.js',
},
output: {
path: path.resolve( __dirname ),
filename: '[name].js',
},
watch: true,
devtool: 'cheap-eval-source-map',
module: {
rules: [
{
test: /\.js$/,
exclude: /(node_modules|bower_components)/,
use: {
loader: 'babel-loader',
},
},
{
test: /style\.s?css$/,
use: blockCSSPlugin.extract( extractConfig ),
},
]
},
plugins: [
blockCSSPlugin
],
};
In order to run the configuration you just have to type in your terminal npm run dev, since that's the script defined in the package.json here:
"scripts": {
"dev": "cross-env BABEL_ENV=default webpack --watch"
},
I hope this help you to get started ;)
|
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"redpajama_set_name": "RedPajamaStackExchange"
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| 8,089
|
Pilot 227 didn't have a name, only a number, but it liked to think of itself as "Jack". Or was it "Jill"? No matter. It flicked the only switch on the comm panel and said "Pilot 227 approaching target. All signs are good."
To say the "signs were good" really meant it hadn't crashed yet, but also hadn't reached the target. Through the ship's smoky canopy, nothing could be seen except for a reddish, murky gloom filled with oozing bubbles that made their way slowly up through the viscous slime. Jack and its squad-mates glided onward, following simple blinking lights on their piloting consoles.
It was just like the Committee to send them out with no instructions and poorly outfitted for combat. It was Jack's first Infection Raid, but it had heard horror stories of ships exploding mid-flight and of huge casualty rates. Jack didn't fancy being one of them.
All at once, an alarm sounded off to the right. An engine pod had flared out! Jack reached out one long tentacle and tried to give the pod's lever a turn, but it was too far away and stuck fast. The ship started to veer off course, threatening to crash into another pilot. It slithered a second tentacle out and pulled with all its might. Finally, the lever gave way, the engine spun back to life, and the ship righted itself. That was too close.
The Committee had outfitted their ships with a secret "Infection device" and ordered them delivered, but that would be for nothing if Jack crashed before it arrived at its target! Then, without warning, the target appeared. It loomed out of the void like a great, black eye. It was a sphere, covered in tiny bumps. The alarm sounded to fire the weapon and Jack grinned through both mouths and hit the launch button. They'd never know what hit them.
Neither did Jack. With a rush of hot fluid and a burst of pressure disks, his ship flew apart and Jack was launched bodily through the slime toward the target. What in the world was this? Jack looked to its left and right and saw ships exploding all around and other pilots flying toward the target. There were thousands of them, screaming through the ooze and dissolving away in the poisonous stuff.
They were the secret weapons? They were the Infection devices? No one was going to return from this mission! They'd hit the target and be absorbed, if they didn't disintegrate before impact. No wonder the Committee kept secrets from the pilots. They were on a suicide mission! Oh, the unfairness of it all! How could they do this to them? And why had no one ever warned the pilots of their fates? Come to think of it, where had all those horror stories come from anyway?
|
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| 1,623
|
{"url":"https:\/\/byjus.com\/question-answer\/which-one-of-the-following-is-the-correct-structure-of-an-oxy-acid-iiiiiiiv\/","text":"Question\n\n# Which one of the following is the correct structure of an oxy-acid?\n\nA\nI\nB\nII\nC\nIII\nD\nIV\n\nSolution\n\n## The correct option is B IIAn oxy-acid of phosphorus on complete neutralisation with sodium hydroxide solution gives an aqueous solution having sodium ions and oxy-acid anions in the ratio 2 : 1.\n\nSuggest corrections","date":"2021-12-08 09:31:07","metadata":"{\"extraction_info\": {\"found_math\": false, \"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\": 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\": 0.8592696189880371, \"perplexity\": 3370.4694099765093}, \"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\/1637964363465.47\/warc\/CC-MAIN-20211208083545-20211208113545-00291.warc.gz\"}"}
| null | null |
{"url":"https:\/\/too-meta.neocities.org\/anki\/computation\/1629613936285\/front\/","text":"Math and science::Theory of Computation\n\n# Context-free languages: closed operations\n\n### Context-free language closure\n\nIf $$L$$ and $$M$$ are context-free languages, then the following are also context-free languages:\n\n\u2022 $$L \\cup M$$\n\u2022 [operation 2]\n\u2022 [operation 3]\n\nIn other words, context-free languages are closed under union, [operation 2] and [operation 3].\n\nThere are important operations under which context free languages are not closed. Can you remember them?","date":"2023-02-06 04:01:48","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\": 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\": 0.8757430911064148, \"perplexity\": 4438.777362471434}, \"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-2023-06\/segments\/1674764500303.56\/warc\/CC-MAIN-20230206015710-20230206045710-00394.warc.gz\"}"}
| null | null |
\section{Introduction}
\label{sec:intro}
Recent theoretical progress on quantum criticality in two spatial dimensions ($d = 2$) has elucidated a number of critical phenomena beyond the Landau-Ginzburg-Wilson (LGW) paradigm, particularly in the context of $d=2$ magnetic insulators.\cite{rantner01, rantner02, senthil04a, senthil04b} In the LGW paradigm, one identifies one or more order parameters and uses them to construct an effective field theory based on symmetry alone, and studies criticality in this theory. The field theories that arise outside the LGW framework make up a much broader class than those arising within it, often involve fermions and/or gauge fields, and in general are less understood than those theories arising within the LGW framework.
Most analytical understanding of quantum criticality in $d=2$ is based on perturbative calculations in large-$n$ and $d = 3 - \epsilon$ expansions, and it would be extremely useful to obtain non-perturbative information that reduces our reliance on these formal limits. This is even true within the LGW framework, although, for example, the ${\rm O}(n)$ model is relatively well understood after extensive numerical and analytical studies.\cite{kleinertbook} The field theories that arise beyond the LGW paradigm have been much less studied, and non-perturbative information is more urgently needed. Toward this end, in this paper I argue that the O(4) model (with some anisotropy terms) is identical at low energies to an apparently quite different theory involving fermions and gauge fields, which is closely related to field theories describing one of the main classes of non-LGW criticality, namely critical spin liquids. This relation is a rare example of duality in $D = d+1 = 3$ space-time dimensions involving non-abelian global symmetries, non-abelian gauge fields, and fermions, without supersymmetry.
The proposed relation, which is the main result of this paper, is that the ${\rm O}(4)$ vector model is dual to a theory of $N_f = 2$ four-component Dirac fermions coupled to both ${\rm SU}(2)$ and ${\rm U}(1)$ gauge fields. We dub the latter theory QCED3, as it is in a sense a combination of $D=3$ quantum electrodynamics (QED3) and quantum chromodynamics (QCD3) with $N_c = 2$ colors. To obtain this relation, we begin with an XY antiferromagnet on the triangular lattice. This model can be treated directly by a Landau theory approach, and this leads to the O(4) field theory, with various anisotropy terms breaking the O(4) symmetry down to that of the original model. Alternatively, using abelian boson-vortex duality,\cite{peskin78, dasgupta81} the XY model is mapped onto a dual lattice model, from which we obtain QCED3 as a low-energy effective description. The non-abelian duality between the O(4) model and QCED3 thus emerges at low energy as a descendant of abelian boson-vortex duality on the lattice.
This result builds in a crucial way on work of Alicea \emph{et. al.}, where it was proposed, beginning with the same frustrated XY model, that the ${\rm O}(4)$ vector model is dual to $N_f = 2$ two-component Dirac fermions coupled to a ${\rm U}(1)$ Maxwell gauge field \emph{and} a ${\rm U}(1)$ Chern-Simons gauge field.\cite{alicea05a} Later, this result was obtained from a different point of view by Senthil and Fisher, who also argued that the ${\rm O}(4)$ model with a topological term ($\theta$-term at $\theta = \pi$) is dual to the same ${\rm U}(1)$ gauge theory but with no Chern-Simons term.\cite{senthil06} In these examples, either the original or dual theory involves a topological term, which prevents the development of a controlled large-$n$ or $d = 3 - \epsilon$ expansion. Because such expansions are possible for the dual partners without topological terms, these results are very useful for understanding their partners that do have topological terms. However, because only one dual partner can be directly analyzed, such dualities do not lead to much additional understanding of the critical behavior itself. The result presented here differs in the crucial respect that \emph{both} the original and dual theories lack topological terms, and thus both admit controlled expansions, potentially allowing greater insight into the critical properties.
In general, two field theories are dual when: (1) the two theories have identical low-energy physics, and (2) the variables in the two theories are \emph{mutually nonlocal}. That is, the fields representing one theory cannot be written as a local function of the fields in the other, and vice versa. The latter condition excludes trivial, local changes of variables. The classic example of such a duality for $D= 3$ is between the XY model and the abelian Higgs model.\cite{peskin78,dasgupta81} In general, it is known how to construct explicit duality relations for models with abelian global symmetries and abelian gauge fields -- without fermions -- in arbitrary space-time dimension.\cite{savit80} However, as in the field theories of interest here, many of the most interesting cases involve non-abelian global symmetries, non-abelian gauge fields and/or fermions, where no general techniques exist to construct useful duality relations. The primary exceptions are in $D = 2$, where bosonization\cite{gogolin-book} can be thought of as a duality, and in a number of supersymmetric field theories in higher dimensions.\cite{seiberg94a, seiberg94b, intriligator96, kapustin99} The results of this paper are a step toward understanding duality in a less restrictive context.
It is important at this stage to make a distinction between duality of field theories and duality of critical fixed points. By duality of field theories, we shall mean that as the parameters of the two theories are varied, they have the same phases and critical points, and all the same low-energy, long-wavelength behavior. Duality of fixed points, on the other hand, is a stronger statement, and is most easily defined by discussing its meaning in the context of the O(4)-QCED3 duality. The O(4) model has a Wilson-Fisher fixed point which can be accessed in a controlled fashion by a large-$n$ expansion, where one considers the ${\rm O}(n)$ model. Also, QCED3 has a critical fixed point that can be accessed in the large-$N_f$ expansion; we assume that this critical point survives down to the value $N_f = 2$ of interest here. By duality of fixed points, we would mean in this case that the O(4) Wilson-Fisher fixed point is identical to the QCED3 fixed point. However, it must be emphasized that this statement need not hold for the two \emph{field theories} to be dual. It could be the case that the O(4) and QCED3 fixed points are distinct, and, in each of the two field theories, both fixed points are present.
The O(4)-QCED3 duality as proposed is to be understood primarily as a duality between field theories. Whether it also leads to a duality between the O(4) and QCED3 fixed points is a more challenging question, and the available evidence does not allow us to reach a firm conclusion. However, it is plausible that the two fixed points are identical.
We now briefly outline the remainder of the paper. In Sec.~\ref{sec:prelims} we introduce the frustrated triangular lattice XY model, and review the treatment of Ref.~\onlinecite{alicea05a} up to the point where it deviates from our approach. In particular, we discuss a direct Landau theory approach, which leads to the O(4) field theory (Sec.~\ref{sec:directxy}), and the dual lattice model resulting from the boson-vortex duality transformation (Sec.~\ref{sec:dualmodel}). Next, we describe our route from the dual model to a continuum field theory (Sec.~\ref{sec:vortexfrac}), and proceed to give a more precise statement of the proposed duality (Sec.~\ref{sec:statement}). In the following two sections, we present the principal evidence for the duality: In Sec.~\ref{sec:evidence1} we set up a dictionary between operators in the O(4) and QCED3 field theories, and in Sec.~\ref{sec:evidence2} we demonstrate that the three stable phases of the original XY model can be realized in QCED3. We conclude in Sec.~\ref{sec:discussion} with a discussion of open issues and possible directions for future work. Three appendices contain various technical details.
\section{Preliminaries and Precursors}
\label{sec:prelims}
\subsection{Direct analysis of XY model}
\label{sec:directxy}
The initial steps needed to obtain the ${\rm O}(4)$-QCED3 duality have already been carried out by Alicea \emph{et. al.},\cite{alicea05a} so we review their results here and in Sec.~\ref{sec:dualmodel}, while introducing notation that will be important later on. At a certain point, which we identify in Sec.~\ref{sec:dualmodel}, our treatment deviates from theirs. As we shall very briefly outline, following their route leads instead to the duality between the ${\rm O}(4)$ model and Dirac fermions coupled to both Maxwell and Chern-Simons ${\rm U}(1)$ gauge fields. Our route to the ${\rm O}(4)$-QCED3 duality is described beginning in Sec.~\ref{sec:vortexfrac}.
The starting point, here and in Ref.~\onlinecite{alicea05a}, is an XY antiferromagnet on the triangular lattice, whose Hamiltonian is
\begin{equation}
\label{eqn:xymodel}
{\cal H} = U \sum_{\boldsymbol{r}} n_{\boldsymbol{r}}^2
+ J \sum_{\langle \boldsymbol{r} \boldsymbol{r}' \rangle} \cos (\phi_{\boldsymbol{r}} - \phi_{\boldsymbol{r}'} ) \text{.}
\end{equation}
Here, $J > 0$ and the second sum is over nearest-neighbor bonds. On every site of the triangular lattice $\boldsymbol{r}$ there is a ${\rm U}(1)$ quantum rotor, with angular position $e^{i \phi_{\boldsymbol{r}}}$ and integer-valued angular momentum $n_{\boldsymbol{r}}$, which satisfy the commutation relation $[n, e^{i \phi}] = e^{i \phi}$. This can be thought of as an effective theory for a $S = 1$ XY antiferromagnet. Alternatively, by the usual quantum-classical correspondence, its partition function describes a classical XY antiferromagnet of stacked triangular lattices, which has been extensively studied\cite{kawamura98, pelissetto02, delamotte04, calabrese04} (see also Ref.~\onlinecite{alicea05a} for a more detailed overview of the literature).
In this context, it is known that the model can realize three phases (provided next-neighbor ferromagnetic exchange is included), which are: (1) paramagnet (2) coplanar 120$^\circ$ magnetic order (Fig.~\ref{fig:orders}) and (3) two different collinear magnetic orders (Fig.~\ref{fig:orders} and Ref.~\onlinecite{alicea05a}). The paramagnet, coplanar state, and one of the two collinear states meet at a multicritical point (upon tuning both $J$ and the further-neighbor exchange), which is the Wilson-Fisher fixed point of the ${\rm O}(4)$ vector model. Either collinear state can arise adjacent to the multicritical point, depending on the sign of a dangerously irrelevant 6th-order term in the Landau theory (discussed below), and the distinction between the two collinear states will not play an important role in the present discussion.
\begin{figure}
\includegraphics[width=3in]{orders.eps}
\caption{Depiction of the coplanar $120^\circ$ ordered state (a), and one of the two collinear states (b). The filled circles represent sites with zero ordered moment. The other collinear state is depicted in Ref.~\onlinecite{alicea05a}.}
\label{fig:orders}
\end{figure}
The symmetries of Eq.~(\ref{eqn:xymodel}) will play a crucial role in our analysis, so we enumerate them here. The triangular lattice space group is generated by a translation by one lattice constant in the $x$-direction ($T_x$), a counterclockwise rotation by $\pi/3$ about a lattice site ($R_{\pi/3}$), and a reflection ${\cal R}_y : (x,y) \to (x, -y)$. The operators $n_{\boldsymbol{r}}$ and $\phi_{\boldsymbol{r}}$ transform as scalars under the space group. There is also a charge-conjugation (or spin flip) symmetry
\begin{eqnarray}
{\cal C} &:& n_{\boldsymbol{r}} \to - n_{\boldsymbol{r}} \\
{\cal C} &:& \phi_{\boldsymbol{r}} \to - \phi_{\boldsymbol{r}} \text{.}
\end{eqnarray}
And the antiunitary time-reversal operation
\begin{eqnarray}
{\cal T} &:& n_{\boldsymbol{r}} \to -n_{\boldsymbol{r}} \\
{\cal T} &:& \phi_{\boldsymbol{r}} \to \phi_{\boldsymbol{r}} + \pi \text{.}
\end{eqnarray}
Finally there is the ${\rm U}(1)$ phase rotation, which sends $\phi_{\boldsymbol{r}} \to \phi_{\boldsymbol{r}} + \alpha$. To distinguish it from other symmetry groups that will arise later on, we shall refer to this symmetry as ${\rm U}(1)_{XY}$.
To expose the ${\rm O}(4)$ structure, one goes to a path integral description of the partition function in terms of $\phi_{\boldsymbol{r}}(\tau)$, where $\tau$ is imaginary time, and focuses on those configurations of the phase field with lowest action. These are given by $e^{i \phi_{\boldsymbol{r}}} \sim e^{i \boldsymbol{Q} \cdot \boldsymbol{r}} z_1(\boldsymbol{r}, \tau) + e^{- i \boldsymbol{Q} \cdot \boldsymbol{r}} z_2(\boldsymbol{r}, \tau)$, where $\boldsymbol{Q} = (4\pi/3)\boldsymbol{x}$ (the lattice constant is set to unity), and $z_{1,2}$ are slowly varying functions of $\boldsymbol{r}$ and $\tau$. The vectors $\pm \boldsymbol{Q}$ lie at the corners of the hexagonal Brillouin zone and are the ordering wavevectors of the $120^\circ$ state. The action on $z_{1,2}$ of the microscopic symmetries is enumerated in Appendix~\ref{app:symms}.
Constrained by the microscopic symmetries, one then writes a continuum effective Lagrange density
\begin{equation}
\label{eqn:o4-lagrangian}
{\cal L} = | \partial_{\mu} Z |^2 + r Z^\dagger Z + u (Z^\dagger Z)^2 + v_4 |z_1|^2 |z_2|^2 \text{,}
\end{equation}
where terms of order $|z|^6$ and higher have been discarded, and $Z^T = (z_1 \, z_2)$. For $v_4 = 0$, the model's continuous symmetry is ${\rm SO}(4)$, which is broken down to ${\rm U}(1) \times {\rm U}(1)$ for $v_4 \neq 0$. The 6th order terms break the continuous symmetry down to ${\rm U}(1)_{XY}$. The $v_4$ and $r$ terms are relevant perturbations to the ${\rm O}(4)$ multicritical point, while the allowed 6th order (and higher) terms are irrelevant. At the mean-field level, the coplanar state arises when $r < 0$ and $v_4 > 0$, and has $\langle z_1 \rangle \neq 0$ and $\langle z_2 \rangle = 0$ (or vice-versa). The collinear state obtains for $v_4 < 0$ and has $| \langle z_1 \rangle| = |\langle z_2 \rangle| \neq 0$. Depending on the relative phase of $z_1$ and $z_2$ two different collinear ordering patterns are possible; this phase is determined by the sign of a dangerously irrelevant 6th order term.
Some of the properties of the ${\rm O}(4)$ critical point are known from numerical simulations and high-order perturbative calculations; see Ref.~\onlinecite{kleinertbook} for an extensive discussion (and tabulation) of critical properties of ${\rm O}(n)$ models. Approximately, the critical exponent $\nu \approx 0.75$, and $\eta \approx 0.027$. These exponents can be translated into scaling dimensions of fields by $\operatorname{dim} Z = (1 + \eta)/2 \approx 0.51$ and $\operatorname{dim} Z^\dagger Z = 3 - 1/\nu \approx 1.67$.
It will be convenient to use the fact that ${\rm SO}(4) \simeq [ {\rm SU}(2) \times {\rm SU}(2)]/ Z_2$. We thus introduce the matrix
\begin{equation}
{\cal Z} = \left( \begin{array}{cc}
z_1 & -z^*_2 \\
z_2 & z^*_1
\end{array} \right) \text{.}
\end{equation}
A general ${\rm SO}(4)$ rotation is realized by ${\cal Z} \to U_L {\cal Z} U_R$, where $U_{L,R} \in {\rm SU}(2)$. We shall thus refer to left and right ${\rm SU}(2)$ rotations, denoted by ${\rm SU}(2)_{L,R}$, with conserved currents $\boldsymbol{J}^{L,R}_{\mu}$. In terms of the fields,
\begin{eqnarray}
\boldsymbol{J}^L_{\mu} &=& \frac{1}{2} \operatorname{tr} \Big[ {\cal Z}^\dagger \boldsymbol{\sigma} (\partial_{\mu} {\cal Z}) \Big] \\
\boldsymbol{J}^R_{\mu} &=& \frac{1}{2} \operatorname{tr} \Big[ \boldsymbol{\sigma} {\cal Z}^\dagger (\partial_{\mu} {\cal Z}) \Big] \text{,}
\end{eqnarray}
where $\boldsymbol{\sigma} = (\sigma^1, \sigma^2, \sigma^3)$ is a vector of the $2\times 2$ Pauli matrices. The ${\rm U}(1)_{XY}$ symmetry is a subgroup of ${\rm SU}(2)_R$ and is generated by $2 (\boldsymbol{J}_0^R)^z$, while $\boldsymbol{J}^L_0$ generates rotations of the two slowly varying fields $z_1$ and $z_2$ into one another.
One of the major pieces of evidence for the ${\rm O}(4)$-QCED3 duality will be a dictionary identifying operators in the two field theories. To that end, we now enumerate some important operators in the ${\rm O}(4)$ model. Operators can be labeled by $(\ell_L , \ell_R)$, the total angular momentum quantum numbers of ${\rm SU}(2)_L \times {\rm SU}(2)_R$. It will sometimes be useful to also specify $(m_L, m_R)$, the projection quantum numbers of the angular momenta along the $z$-axis. Note that $2 m_R$ is the ${\rm U}(1)_{XY}$ charge. We have already discussed the boson field $Z$ itself, which transforms as $(1/2, 1/2)$, and the currents $\boldsymbol{J}^L_{\mu}$ and $\boldsymbol{J}^R_{\mu}$, which transform as $(1,0)$ and $(0,1)$, respectively, and are both vectors under Lorentz rotations (\emph{i.e.} space-time rotations). We shall also consider the following 9 Lorentz scalar bilinears in $Z$:
\begin{eqnarray}
\boldsymbol{N} &=& Z^\dagger \boldsymbol{\sigma} Z \\
\boldsymbol{I} &=& Z^T (i \sigma^2) \boldsymbol{\sigma} Z \\
\boldsymbol{I}^* &=& (\boldsymbol{I})^* \text{.}
\end{eqnarray}
Together these make up a $\ell_L = \ell_R = 1$ multiplet. We shall also consider the operators ${\cal O}_r = Z^\dagger Z$ and ${\cal O}_v = |z_1|^2 |z_2|^2 - (1/6) (Z^\dagger Z)^2$. ${\cal O}_r$ has $\ell_L = \ell_R = 0$, and ${\cal O}_v$ is a member of a $\ell_L = \ell_R = 2$ multiplet with $m_L = m_R = 0$. These play an important role as they are the terms in the Lagrangian that must be tuned to reach the ${\rm O}(4)$ critical point. Next, defining the ${\rm O}(4)$ vector $\phi_i$ ($i = 1,\dots,4$) by $z_1 = \phi_1 + i \phi_2$ and $z_2 = \phi_3 + i \phi_4$, we define the operator ${\mathfrak C} = i \epsilon_{i j k l} \epsilon_{\mu \nu \lambda} \phi_i \partial_{\mu} \phi_j \partial_{\nu} \phi_k \partial_{\lambda} \phi_l$, which is odd under ${\cal T}$ and ${\cal R}_y$. In a nonlinear sigma model version of the O(4) field theory, where the constraint $Z^\dagger Z = 1$ is imposed, if ${\mathfrak C}$ is integrated over space-time and added to the action it becomes the topological $\theta$-term.\cite{abanov00} While ${\mathfrak C}$ does not have any special topological significance as a local operator, we shall refer to it as the topological density.
\subsection{Dual model}
\label{sec:dualmodel}
In Ref.~\onlinecite{alicea05a}, boson-vortex duality was applied to the Hamiltonian Eq.~(\ref{eqn:xymodel}). This is a straightforward procedure for such a lattice XY model; here we review some crucial aspects, and more details are found in Ref.~\onlinecite{alicea05a}. The degrees of freedom of the dual model are vortices, which are bosons residing on the sites of the dual honeycomb lattice (Fig.~\ref{fig:duallattice}), and the vector potential and electric field of a non-compact ${\rm U}(1)$ gauge field, which reside on the nearest-neighbor bonds of the honeycomb lattice. Crucially, the vortices are at half-filling (an average of one-half vortex per honeycomb lattice site). This is a direct consequence of the frustration in the original XY model: the XY exchange term of Eq.~(\ref{eqn:xymodel}) can be rewritten as $- J \sum_{\langle \boldsymbol{r} \boldsymbol{r}' \rangle} \cos(\phi_{\boldsymbol{r}} - \phi_{\boldsymbol{r}'} + {\cal A}_{\boldsymbol{r} \boldsymbol{r}'} )$, where the flux associated with the non-fluctuating vector potential ${\cal A}_{\boldsymbol{r} \boldsymbol{r}'}$ is half a flux quantum, or $\pi$, for each triangular plaquette. This background flux has the consequence of forcing in half a vortex per site (on average) in the dual theory.
\begin{figure}
\includegraphics[width=3in]{duallattice.eps}
\caption{Relation between the dual honeycomb lattice (dashed lines) and the triangular lattice of the original XY model (solid lines). Honeycomb lattice sites correspond to triangular lattice plaquettes.}
\label{fig:duallattice}
\end{figure}
For technical convenience, we shall take the vortices to experience a hardcore repulsion, and only allow zero or one vortex on each honeycomb site. Such a modification of microscopic parameters will not affect the universal low-energy properties of phases and critical points in which we shall be interested.
The dual Hamiltonian is
\begin{eqnarray}
\label{eqn:dual-hamiltonian}
{\cal H}_{{\rm dual}}
&=& U' \sum_{\hexagon} \big[ (\nabla \times a)_{\hexagon} \big]^2 + J' \sum_{\langle \bar{r} \bar{r}' \rangle} e^2_{\bar{r} \bar{r}'} \nonumber \\
&-& t_v \sum_{\langle \bar{r} \bar{r}' \rangle} \big[ e^{i a_{\bar{r} \bar{r}'}} v^+_{\bar{r}} v^-_{\bar{r}'} + \text{H.c.} \big] \text{.}
\end{eqnarray}
Here, $\bar{r}$ labels the sites of the dual honeycomb lattice. $e_{\bar{r} \bar{r}'}$ and $a_{\bar{r} \bar{r}'}$ are, respectively, the electric field and vector potential residing on the honeycomb link joining $\bar{r}$ and $\bar{r}'$. On the same link these satisfy the canonical commutation relation $[e, a] = i$. The first term is a sum over all hexagonal plaquettes, and $(\nabla \times a)_{\hexagon}$ is the lattice curl, which is the discrete line integral of $a_{\bar{r} \bar{r}'}$ taken around the perimeter of a given hexagonal plaquette. The latter two terms are sums over nearest-neighbor honeycomb links. Because the vortices are hardcore bosons, their creation, destruction and number operators are represented using the $S = 1/2$ spin operators $(v^x_{\bar{r}}, v^y_{\bar{r}}, v^z_{\bar{r}})$, satisfying the usual commutation relation $[v^i_{{\bar r}}, v^j_{\bar{r}'} ] = i \delta_{\bar{r} \bar{r}'} \epsilon^{i j k} v^k_{\bar{r}}$. A vortex at site $\bar{r}$ is created by $v_{\bar{r}}^+ = v^x_{\bar{r}} + i v^y_{\bar{r}}$ and destroyed by $v^-_{\bar{r}} = (v^+_{\bar{r}})^\dagger$. The vortex number operator is $N_v(\bar{r}) = v^z_{\bar{r}} + 1/2$. The Hamiltonian is supplemented with the Gauss' law constraint
\begin{equation}
(\operatorname{div} e)_{\bar{r}} = v^z_{\bar{r}} \text{,}
\end{equation}
where $(\operatorname{div} e)_{\bar{r}} = \sum_{\bar{r}' \sim \bar{r}} e_{\bar{r} \bar{r}'}$ is the lattice divergence of $e_{\bar{r} \bar{r}'}$.
The parameters of the dual Hamiltonian are $U' \simeq U$, $J' \simeq J$, and the vortex hopping $t_v$. It should be emphasized that Eq.~(\ref{eqn:dual-hamiltonian}) is not an exact rewriting of the original XY model, and instead should be thought of as a low-energy effective theory. Conversely, the XY model of Eq.~(\ref{eqn:xymodel}) can \emph{also} be thought of as a low-energy effective theory for the dual model Eq.~(\ref{eqn:dual-hamiltonian}).
It is important to spell out the connection between the ${\rm U}(1)$ gauge field and the original XY model degrees of freedom. The magnetic flux represents the ${\rm U}(1)_{XY}$ charge density,
\begin{equation}
\label{eqn:flux-charge}
\frac{1}{2\pi} (\nabla \times a)_{\hexagon} \sim n_{\boldsymbol{r}},
\end{equation}
where $\hexagon$ is the honeycomb hexagon surrounding the triangular lattice site $\boldsymbol{r}$. Also, the electric field is related to the ${\rm U}(1)_{XY}$ current by
\begin{equation}
\sin (2 \pi e_{\bar{r} \bar{r}'} ) \sim \sin (\phi_{\boldsymbol{r}} - \phi_{\boldsymbol{r}'}) \text{,}
\end{equation}
where $(\boldsymbol{r}, \boldsymbol{r}')$ is the unique triangular lattice bond crossing the honeycomb link $(\bar{r}, \bar{r}')$. In the dual representation, ${\rm U}(1)_{XY}$ charge conservation is represented as the conservation of magnetic flux. Moreover, insertion of ${\rm U}(1)_{XY}$ charge (as by acting with $e^{i \phi_{\boldsymbol{r}}}$) is represented by the insertion of a quantized $2\pi$ magnetic flux. Such flux insertions are space-time magnetic monopole events, and will play a crucial role in our analysis.
Under the space group symmetry, $e_{\bar{r} \bar{r}'}$ and $a_{\bar{r} \bar{r}'}$ transform as pseudovectors, and $v^z_{\bar{r}}$ as a pseudoscalar. $v^{\pm}_{\bar{r}}$ transforms as a scalar under $T_x$ and $R_{\pi/3}$, and ${\cal R}_y : v^{\pm}_{\bar{r}} \to v^{\mp}_{\bar{r}'}$, where $\bar{r}'$ is the image of $\bar{r}$ under the reflection. Under charge-conjugation both $e$ and $a$ are odd, while
\begin{eqnarray}
{\cal C}: v^z_{\bar{r}} &\to& - v^z_{\bar{r}} \\
{\cal C}: v^{\pm}_{\bar{r}} &\to& v^{\mp}_{\bar{r}} \text{.}
\end{eqnarray}
Finally, under time-reversal $a$ is odd while $e$ is even, and
\begin{eqnarray}
{\cal T}: v^z_{\bar{r}} &\to& v^z_{\bar{r}} \\
{\cal T}: v^{\pm}_{\bar{r}} &\to& v^{\pm}_{\bar{r}} \text{.}
\end{eqnarray}
The challenge at this stage is to use the dual Hamiltonian to construct a continuum low-energy effective theory, which would then provide a dual description of the ${\rm O}(4)$ critical point. A natural approach would be to begin with Eq.~(\ref{eqn:dual-hamiltonian}) and construct a functional integral in terms of the phase field of the vortices $v^+ \sim e^{i \theta}$. However, as the vortices are at half-filling, the resulting functional integral is plagued with Berry phase terms, and does not directly lead to a useful continuum limit. Instead, it is necessary to choose some other set of variables that is amenable to a continuum description.
Alicea \emph{et. al.} chose to represent the vortices in terms of fermions using statistical transmutation, with the price of introducing a Chern-Simons gauge field $\alpha_{\bar{r} \bar{r}'}$.\cite{alicea05a} In a flux-smearing mean-field treatment, the vortices are fermions at half-filling on the honeycomb lattice (with zero background magnetic flux), and thus have a massless Dirac dispersion. To include fluctuations about the mean-field state, one re-couples the Dirac fermions to both the Chern-Simons gauge field and the Maxwell gauge field $a$ that arose in the boson-vortex duality. The resulting Euclidean Lagrangian is
\begin{eqnarray}
{\cal L} &=& \bar{\Psi} \gamma_{\mu} (\partial_{\mu} + i a_{\mu} + i \alpha_{\mu} ) \Psi +
\frac{1}{2 e^2} \sum_{\mu} (\epsilon_{\mu \nu \lambda} \partial_{\nu} a_{\lambda} )^2 \nonumber \\
&+& \frac{i}{4\pi} \alpha_{\mu} \epsilon_{\mu \nu \lambda} \partial_{\nu} \alpha_{\lambda} + \cdots \text{.}
\end{eqnarray}
The first term is the kinetic energy of the fermions and contains the coupling to the two gauge fields. The second term dictates that the $a_{\mu}$ gauge field obeys Maxwell dynamics, and the last term is the Chern-Simons term for $\alpha_{\mu}$. The coefficient of the Chern-Simons term is precisely that needed to attach $2\pi$ flux and transmute fermions into bosons (and vice versa). The ellipsis represents other (important) perturbations consistent with the underlying microscopic symmetries.
While this field theory is an intriguing dual representation of the ${\rm O}(4)$ model, the presence of the Chern-Simons term seriously hinders any direct analysis of it. It was conjectured in Ref.~\onlinecite{alicea05a} that the Chern-Simons term can simply be dropped without affecting the critical properties, but the arguments in favor of this conjecture are not conclusive, and are questionable given the later results of Ref.~\onlinecite{senthil06}. Motivated in part by a desire to avoid these issues, here we pursue a different approach that also leads to a fermionic gauge theory representation of the ${\rm O}(4)$ model, but without any topological terms.
\section{Duality between ${\rm O}(4)$ model and QCED3.}
\subsection{Vortex Fractionalization Route to Dual Effective Theory}
\label{sec:vortexfrac}
The present approach also begins with the dual Hamiltonian Eq.~(\ref{eqn:dual-hamiltonian}). The challenge is to construct a continuum effective theory that deals with the half-filling of the vortices, but also avoids the difficulties associated with statistical transmutation and the Chern-Simons term. To do this, we look to the theory of spin liquids in $S = 1/2$ Heisenberg models, which are after all also models of half-filled hardcore bosons. One route to describe spin liquids, in particular critical spin liquids that lack a spin gap, is to formally represent hardcore bosons (or spins) as bilinears of fermionic slave particles.\cite{wen02} Therefore it is reasonable to hope that a similar approach can describe criticality -- in particular, the ${\rm O}(4)$ critical point -- in the present model, and we shall argue that this is indeed the case. \footnote{It is natural to ask whether it is useful to instead split the vortices into \emph{bosonic} slave particles. A cursory investigation suggests that this route does not lead to an interesting dual description of the ${\rm O}(4)$ critical point.}
We represent the vortices using the fermionic operators $f_{\bar{r} \alpha}$, where $\alpha = 1,2$:
\begin{eqnarray}
v^+_{\bar{r}} &=& f^\dagger_{\bar{r}1} f^{\vphantom\dagger}_{\bar{r} 2} \\
v^z_{\bar{r}} &=& \frac{1}{2} ( f^\dagger_{\bar{r}1} f^{\vphantom\dagger}_{\bar{r}1} - f^\dagger_{\bar{r}2} f^{\vphantom\dagger}_{\bar{r}2} ) \text{.}
\end{eqnarray}
With the local constraint $f^\dagger_{\bar{r} \alpha} f^{\vphantom\dagger}_{\bar{r} \alpha} =1$ this change of variables provides an exact rewriting of the model. In these variables there is a local ${\rm SU}(2)$ gauge redundancy,\cite{affleck88a, dagotto88} which can be exposed by defining
\begin{equation}
\psi_{\bar{r}} = \left(
\begin{array}{c}
f^\dagger_{\bar{r} 1} \\
\epsilon_{\bar{r}} f_{\bar{r} 2}
\end{array} \right) \text{,}
\end{equation}
where $\epsilon_{\bar{r}} = 1$ ($-1$) for $\bar{r}$ in the A (B) sublattice. The fermions satisfy the local constraint equations $\psi^\dagger_{\bar{r}} \mu^i \psi_{\bar{r}} = 0$, where $\mu^i$ ($i = 1,2,3$) are the $2 \times 2$ Pauli matrices. This is simply the condition that the ${\rm SU}(2)$ gauge charge is zero at every lattice site. The vortex operators $v^{\pm}_{\bar{r}}$ and $v^z_{\bar{r}}$ can be written in manifestly ${\rm SU}(2)$ gauge-invariant forms, and so all physical operators are gauge invariant.
To proceed, we pass to a functional integral representation, where the action is $S = S_{{\rm U}(1)} + S_f$, where
\begin{eqnarray}
\label{eqn:u1-micropart}
S_{{\rm U}(1)} &=& \frac{1}{4 J'} \int d\tau \sum_{\langle \bar{r} \bar{r}' \rangle} \big[ \partial_{\tau} a_{\bar{r} \bar{r}'}
- ( \Delta a_0)_{\bar{r} \bar{r}'} \big]^2 \nonumber \\
&+& U' \int d\tau \sum_{\hexagon} (\nabla \times a)^2_{\hexagon} \text{.}
\end{eqnarray}
Here, we have introduced the notation $(\Delta f)_{\bar{r} \bar{r}'} = f(\bar{r}') - f(\bar{r})$ for a lattice derivative.
The fermionic part of the action is
\begin{eqnarray}
S_f &=& \int d\tau \sum_{\bar{r}} \psi^\dagger_{\bar{r}} \Big[ \partial_{\tau} + \frac{i}{2} a_0(\bar{r},\tau)
+ \frac{i \alpha_0^i(\bar{r}, \tau) \mu^i}{2} \Big] \psi^{\vphantom\dagger}_{\bar{r}} \nonumber \\
&-& \frac{i}{2} \int d\tau \sum_{\bar{r}} a_0(\bar{r}, \tau) \nonumber \\
&+& t_v \int d\tau \sum_{\langle \bar{r} \bar{r}' \rangle} \Big[ e^{i a_{\bar{r} \bar{r}'}} v^{+}_{\bar{r}} v^{-}_{\bar{r}'} + \text{H.c.} \Big] \text{.}
\label{eqn:f-micropart}
\end{eqnarray}
Note that we have made the gauge transformation $a_{\bar{r} \bar{r}'} \to a_{\bar{r} \bar{r}'} + \pi$ to change the sign of the last term. We have also introduced the Lagrange-multiplier field $\alpha^i_0$ ($i = 1,2,3$), which enforces the ${\rm SU}(2)$ gauge constraint and can be thought of as the time-component of the ${\rm SU}(2)$ gauge field.
The last term of Eq.~(\ref{eqn:f-micropart}) is quartic in the fermion operators, and to arrive at a candidate low-energy effective theory it can be decoupled using a Hubbard-Stratonovich field residing on the bonds of the lattice. One searches for mean-field saddle points of this field, and each such saddle point (upon including often important fluctuations) leads to a low-energy effective theory. Many distinct effective theories can be generated in this way,\cite{wen02} and one of the challenges of this approach is to decide which theory (if any) accurately captures the physics of the model at hand. In the present case we are guided by the requirement that the effective theory should be able to reproduce the phases and critical points that are known to be present from the analysis of the original XY model.
Rather than carry out the above mean-field procedure explicitly, we shall simply guess the form of the low-energy theory. To do this we write down an effective lattice gauge theory that reduces to the above model in a particular limit. This is equivalent to choosing a particular mean-field saddle point and then including the fluctuations about it. The effective lattice theory is obtained by replacing $S_f$ with
\begin{eqnarray}
S'_f &=& \int d\tau \sum_{\bar{r}} \psi^\dagger_{\bar{r}} \Big[ \partial_{\tau} + \frac{i}{2} a_0(\bar{r},\tau)
+ \frac{i \alpha_0^i(\bar{r}, \tau) \mu^i}{2} \Big] \psi^{\vphantom\dagger}_{\bar{r}} \nonumber \\
&-& \frac{i}{2} \int d\tau \sum_{\bar{r}} a_0(\bar{r}, \tau) \nonumber \\
&+& t \int d\tau \sum_{\langle \bar{r} \bar{r}' \rangle} \Big[ e^{- i a_{\bar{r} \bar{r}'} / 2} \psi^\dagger_{\bar{r}} U_{\bar{r} \bar{r}'} \psi^{\vphantom\dagger}_{\bar{r}'} + \text{H.c.} \Big] \text{.}
\label{eqn:f-effective}
\end{eqnarray}
Here $U_{\bar{r} \bar{r}'}$ is the spatial part of the ${\rm SU}(2)$ gauge field. It should be noted that, because the gauge field $a_{\bar{r} \bar{r}'}$ is noncompact, it is perfectly legitimate to have the object $e^{i a_{\bar{r} \bar{r}'}/2}$ appearing in the action.
We also include a Maxwell action $S_g$ for the ${\rm SU}(2)$ gauge field, with overall strength proportional to the coupling constant $1/g^2$. When $g \to \infty$ and $t$ is small, $U_{\bar{r} \bar{r}'}$ can be integrated out perturbatively in $t$. At leading order ($t^2$), one recovers the original dual Hamiltonian given by the action $S = S_{{\rm U}(1)} + S_f$, with an additional nearest-neighbor repulsive interaction between vortices. This interaction is not important for our purposes, as it does not change the symmetry of the model and is not expected to affect its universality class.
On the other hand, if we take $g$ small and $U'$ large, then the fluctuations of both gauge fields are suppressed, and in an appropriate gauge $U_{\bar{r} \bar{r}'} \approx 1$ and $\alpha^i_0 \approx a_{\bar{r} \bar{r}'} \approx a_0 \approx 0$. In this mean-field limit the fermions are described by the Hamiltonian
\begin{equation}
{\cal H}_{{\rm MFT}} = t \sum_{\langle \bar{r} \bar{r}' \rangle} \big[ \psi^\dagger_{\bar{r}} \psi_{\bar{r}'} + \text{H.c.} \big] \text{,}
\end{equation}
which is simply nearest-neighbor hopping of half-filled fermions on the honeycomb lattice. The corresponding low-energy theory is given by focusing on the excitations near the Dirac nodes and reintroducing the coupling to the gauge fields. The resulting Lagrangian density is
\begin{eqnarray}
{\cal L}_{{\rm QCED3}} &=& \bar{\Phi} \Big[ - i \gamma_{\mu} \big( \partial_{\mu} + \frac{i a_{\mu}}{2} + \frac{i \alpha^i_{\mu} \mu^i}{2} \big) \Big] \Phi \\
&+& \frac{1}{2 e^2} \sum_{\mu} (\epsilon_{\mu \nu \lambda} \partial_{\nu} a_{\lambda})^2
+ \frac{1}{2 g^2} f^i_{\mu \nu} f^i_{\mu \nu} \nonumber \text{.}
\end{eqnarray}
Here we have introduced the continuum Dirac field $\Phi$, which is related to $\psi_{\bar{r}}$ as discussed in Appendix~\ref{app:fermion-contlimit}. $\Phi$ is an eight-component object; these eight components arise from the two-component nature of $\psi_{\bar{r}}$, the two bands needed to represent each Dirac node, and the two-component flavor index corresponding to the two distinct nodes in the Brillouin zone. It is useful to define three different sets of Pauli matrices acting in this 8-component space; each set corresponds to its own type of ${\rm SU}(2)$ rotations. The $\mu^i$ Pauli matrices act in the ${\rm SU}(2)$ gauge space and generate gauge transformations. The $\tau^i$ Pauli matrices act in the band index, or Lorentz, space, and generate Lorentz transformations. Finally, the $\nu^i$ Pauli matrices act in the ${\rm SU}(2)$ flavor space and generate flavor rotations. $\Phi$ resides in the tensor product of these three ${\rm SU}(2)$ spaces, and products of different types of Pauli matrices (which commute) should be understood as matrix tensor products. The action of the various Pauli matrices on $\Phi$ is given explicitly in Appendix~\ref{app:fermion-contlimit}. It is convenient to think of $\Phi$ as composed of $N_f = 2$ flavors of four-component Dirac fermions, where each flavor transforms as a doublet under ${\rm SU}(2)$ gauge rotation and Lorentz transformations. Both flavors carry the same ${\rm U}(1)$ charge of $1/2$ under the dual gauge field $a_{\mu}$.
We have also introduced the field strength of the ${\rm SU}(2)$ gauge field,
\begin{equation}
f^i_{\mu \nu} = \partial_{\mu} \alpha^i_{\nu} - \partial_{\nu} \alpha^i_{\mu} + \epsilon_{i j k} \alpha^j_{\mu} \alpha^k_{\nu} \text{,}
\end{equation}
and the matrices $\gamma_{\mu}$ are defined in terms of the $\tau^i$ Pauli matrices as
\begin{equation}
\gamma_{\mu} = (\tau^3, \tau^2, -\tau^1) \text{.}
\end{equation}
Finally, we have defined
\begin{equation}
\bar{\Phi} = i \Phi^\dagger \tau^3 \text{.}
\end{equation}
A number of theories similar to ${\cal L}_{{\rm QCED3}}$, also involving Dirac fermions coupled to gauge fields, are interesting in the context of non-LGW criticality. This interest stems from the fact that the microscopic symmetries can (in some cases) be enough to forbid the addition of any relevant perturbations to the action, and the fixed point thus describes a stable critical phase.\cite{rantner01, rantner02, hermele04} Such critical phases have been discussed in a variety of physical settings.\cite{affleck88, marston89, franz01,vafek02, alicea05b, alicea06,ryu07, ran07,kaul08, cenkexu08a}
The global symmetries of ${\cal L}_{{\rm QCED3}}$ play a crucial role in our discussion. Aside from $D =3$ Poincar\'{e} invariance, the continuous global symmetry is ${\rm SU}(2) \times {\rm U}(1)$. The global ${\rm SU}(2)$ consists of rotations between the two flavors of Dirac fermions generated by the $\nu^i$ Pauli matrices. We thus dub it ${\rm SU}(2)_F$, and it has the conserved current
\begin{equation}
\boldsymbol{J}^F_{\mu} = \bar{\Phi} \gamma_{\mu} \boldsymbol{\nu} \Phi \text{.}
\end{equation}
The global ${\rm U}(1)$ is simply the ${\rm U}(1)_{XY}$ symmetry. Its realization in ${\cal L}_{{\rm QCED3}}$ follows directly from the boson-vortex duality transformation, and in particular the identification of $a_{\mu}$ magnetic flux and ${\rm U}(1)_{XY}$ charge density [Eq.~(\ref{eqn:flux-charge})]. The associated conserved current is thus
\begin{equation}
j^G_{\mu} = \frac{1}{2\pi} \epsilon_{\mu \nu \lambda} \partial_{\nu} a_{\lambda} \text{,}
\end{equation}
the flux of the $a_{\mu}$ gauge field.
The field theory ${\cal L}_{{\rm QCED3}}$, like other $D = 3$ theories of massless Dirac fermions coupled to gauge fields, is solvable in the large-$N_f$ limit.\cite{appelquist86, rantner01, rantner02, hermele04, hermele05, ran06} When $N_f \to \infty$ the fluctuations of the gauge fields are suppressed, and for most purposes the physics is identical to that of non-interacting fermions. Expanding about this limit, correlation functions can be calculated order-by-order in $1/N_f$, and it is found that various operators acquire anomalous dimensions. The principal result, then, is that the large-$N_f$ expansion describes an interacting critical fixed point,\cite{rantner01, rantner02} which we assume survives down to the case of interest, $N_f = 2$. Below, we shall refer to the $N_f = 2$ incarnation of the large-$N_f$ fixed point as the QCED3 fixed point, which should be distinguished, of course, from the QCED3 field theory.
\subsection{Statement of the proposed duality}
\label{sec:statement}
A brief statement of the proposed duality is that the O(4) model and QCED3 possess identical low-energy physics. Below, we shall elaborate on the meaning of this statement in order to give a more precise statement of the duality. We then outline the approach underlying the evidence for the duality, which is described in the following sections.
It is useful to remark that both the O(4) model and QCED3, provided arbitrary perturbations consistent with the underlying microscopic symmetries are added to each, are expected to be valid low-energy effective descriptions of the original model. This is expected simply because both were derived from the same microscopic starting point. This means, in particular, that any phase or critical point of either the direct or dual low-energy theory is a phase or critical point that presumably exists somewhere in the parameter space of the original XY model. It is not immediately obvious, however, that the O(4) model and QCED3 describe phases and critical points in the same part of parameter space. This is the crucial fact that needs to be established for the duality to hold.
With this remark in mind, the proposed duality can be precisely stated as follows: Beginning with ${\cal L}_{{\rm QCED3}}$, by adding operators consistent with the underlying microscopic symmetries one can tune the theory to an O(4) critical point identical to the Wilson-Fisher fixed point of the O(4) model. We shall call the resulting fine-tuned Lagrangian ${\cal L}^c_{{\rm QCED3}}$. Moreover, the effective Lagrangian
\begin{equation}
{\cal L}_{{\rm eff}} = {\cal L}^c_{{\rm QCED3}} + r \tilde{{\cal O}}_r + v \tilde{{\cal O}}_v \text{,}
\end{equation}
where $\tilde{{\cal O}}_r$ and $\tilde{{\cal O}}_v$ are QCED3 operators identified below in Sec.~\ref{sec:evidence1}, is identical at low energy to the O(4) model Lagrangian of Eq.~(\ref{eqn:o4-lagrangian}). These statements essentially amount to asserting that, indeed, the O(4) model and QCED3 describe the same region of the original model's parameter space.
Using the terminology introduced in Sec.~\ref{sec:intro}, this is a duality between field theories. It is natural to ask if there is \emph{also} a duality between the O(4) Wilson-Fisher fixed point and the QCED3 critical point. That is, are the O(4) and QCED3 fixed points identical or distinct?
We do not have a definitive answer to this question, but we will see it is plausible that the two fixed points are dual. This is discussed further in Sec.~\ref{sec:discussion}.
Most of the evidence presented in Secs.~\ref{sec:evidence1} and~\ref{sec:evidence2} pertains to the duality of field theories. However, we do present some information on scaling dimensions from the large-$N_f$ expansion for the QCED3 fixed point. These results are not relevant for establishing the duality between field theories, but they do provide some information about a potential duality of fixed points.
In Sec.~\ref{sec:evidence1} we set up a dictionary of operators between QCED3 and the O(4) model. In order to do this, it will be helpful to exploit the large-$N_f$ understanding of the QCED3 fixed point; this provides a controlled understanding of the field content of QCED3, which is our primary concern in establishing the duality between field theories. Next, in Sec.~\ref{sec:evidence2}, we describe how to access the stable phases of the original XY model in the QCED3 description.
\section{Evidence for the duality: operator dictionary}
\label{sec:evidence1}
To construct a dictionary between QCED3 and O(4) model operators, we begin by identifying the continuous global symmetries of the two field theories. We identify the ${\rm SU}(2)_F$ flavor symmetry of QCED3 with ${\rm SU}(2)_L$ of the O(4) model, which means that the currents $\boldsymbol{J}^F_{\mu}$ and $\boldsymbol{J}^L_{\mu}$ should also be identified.
Next, we identify $j^G_{\mu}$ with $2 (\boldsymbol{J}^R_{\mu})^z$, as these are the realizations of the ${\rm U}(1)_{XY}$ conserved current in QCED3 and the O(4) model, respectively.
As QCED3 does not have manifest ${\rm SU}(2) \times {\rm SU}(2)$ symmetry, it is less clear how to identify the remaining components of $\boldsymbol{J}^R_{\mu}$. An important part of the proposed duality is that, at the ${\rm O}(4)$ critical point, the ${\rm SU}(2)_L \times {\rm U}(1)_{XY}$ global symmetry of QCED3 is enlarged to ${\rm SU}(2)_L \times {\rm SU}(2)_R$. So, in particular, ${\rm U}(1)_{XY}$ is enlarged to ${\rm SU}(2)_R$, which happens quite explicitly in the O(4) model. Moreover, it should not be surprising that it is possible to enlarge ${\rm SU}(2) \times {\rm U}(1)$ to ${\rm SU}(2) \times {\rm SU}(2)$ by a suitable tuning of parameters, since both groups at least have the same Cartan subalgebra. We shall identify candidate QCED3 partners of the remaining components of $\boldsymbol{J}^R_{\mu}$ below.
To continue setting up our dictionary, it will be convenient to break QCED3 operators into two classes. The first class consists of all operators carrying zero ${\rm U}(1)_{XY}$ charge, or, equivalently, zero magnetic flux of the dual gauge field $a_{\mu}$. We refer to operators in the first class as non-monopole operators. The second class contains all monopole operators, which do carry an $a_{\mu}$ flux. The flux is quantized in multiples of $2\pi$, simply because the ${\rm U}(1)_{XY}$ charge is quantized in the original XY model. Non-monopole operators can be easily represented in terms of the fermion and gauge fields. On the other hand, as is typical for topological disorder operators, monopole operators are more difficult to represent in terms of the fields of the theory. However, they can be constructed using the state-operator correspondence of conformal field theory,\cite{borokhov02} and we shall take advantage of this approach here.
To be identified, two operators certainly must transform identically under Lorentz transformations, ${\rm SU}(2)_L$ (or, equivalently, ${\rm SU}(2)_F$), and ${\rm U}(1)_{XY}$. For non-monopole operators, in each case we have also verified, using the results enumerated in Appendix~\ref{app:symms}, that each pair of identified operators transforms identically under all the microscopic symmetries. For monopole operators, on the other hand, it is only known how to \emph{partially} determine the action of microscopic symmetries, up to a few unknown parameters.\cite{alicea05a, alicea08, hermele08} Here we shall do this, following the approach of Ref.~\onlinecite{hermele08}. In each case the transformations of the corresponding O(4) model operator can be determined completely using the results of Appendix~\ref{app:symms}, and are consistent with the partial results for the QCED3 counterpart.
We now proceed to identify some of the important O(4) model operators with QCED3 counterparts.
{\bf O(4) bilinear $\boldsymbol{N} = Z^\dagger \boldsymbol{\sigma} Z$.} This is perhaps the simplest operator to identify with a QCED3 partner. We identify $\boldsymbol{N}$ with
\begin{equation}
\tilde{\boldsymbol{N}} = -i \bar{\Phi} \boldsymbol{\nu} \Phi \text{.}
\end{equation}
Both $\boldsymbol{N}$ and $\tilde{\boldsymbol{N}}$ transform as a vector under ${\rm SU}(2)_L$, a scalar under Lorentz rotation, and carry zero ${\rm U}(1)_{XY}$ charge.
In the limit $N_f \to \infty$, the scaling dimension $\Delta_{\tilde{\boldsymbol{N}}}$ of $\tilde{\boldsymbol{N}}$ approaches 2. An inspection of the diagrams involved in the $1/N_f$ correction shows that the contributions from the ${\rm U}(1)$ and ${\rm SU}(2)$ gauge fields\cite{rantner02, ran06} simply add together, and
\begin{equation}
\Delta_{\tilde{\boldsymbol{N}}} = 2 - \frac{128}{3 \pi^2 N_f} + {\cal O}(1/N_f^2) \text{.}
\end{equation}
While this result is not to be trusted quantitatively, the qualitative trend that $\Delta_{\tilde{\boldsymbol{N}}} < 2$ is believed to be reliable.\cite{rantner02, hermele-erratum07} This should be compared to the fact that, in the large-$n$ expansion of the ${\rm O}(n)$ model, $\Delta_{\boldsymbol{N}} = 1 + {\cal O}(1/n)$. It is reasonable that these scaling dimensions become the same for the case of interest ($n = 4$ and $N_f = 2$).
{\bf O(4) field $Z$.} Since $Z$ carries ${\rm U}(1)_{XY}$ charge of unity, it is a monopole operator carrying $2\pi$ flux. To construct $2\pi$-monopoles in QCED3, we need to make use of the state-operator correspondence following Ref.~\onlinecite{borokhov02}. Accessible treatments of the state-operator correspondence can be found in Refs.~\onlinecite{polchinskibook} and~\onlinecite{metlitski08}. Briefly, for a $D=3$ Lorentz and scale invariant theory, such as the QCED3 fixed point, the state-operator correspondence states that local operators of the field theory are in one-to-one correspondence with quantum states of the same theory quantized on the two-dimensional unit sphere. Scaling operators (\emph{i.e.} eigenoperators of a renormalization group transformation) are mapped to eigenstates of the Hamiltonian on the 2-sphere, and the scaling dimension of the operator is equal to the energy of the corresponding state.
Here we are primarily concerned with using the state-operator correspondence to \emph{construct} monopole operators, by constructing the corresponding eigenstates of the Hamiltonian on the 2-sphere. This can be done for QCED3 in the large-$N_f$ limit, where the fluctuations of both gauge fields are suppressed and the $N_f \to \infty$ Hamiltonian is simply that of $N_f$ flavors of non-interacting 4-component fermions on the unit sphere. As $N_f$ is reduced from infinity down to the case of interest $N_f = 2$, gauge fluctuations will modify the states and change their energies (and hence their scaling dimensions).
However, even for $N_f = 2$, the states constructed with gauge fluctuations suppressed still correspond to local operators (although no longer to scaling operators), and we still use them to understand the field content of $N_f = 2$ monopole operators.
We shall see below that it will be useful to think in terms of $N_{f 2} = 2 N_f$ two-component fermions, each of which is a Lorentz doublet. A monopole operator with flux $2\pi q$ corresponds to a state of these fermions with a background $a_{\mu}$ flux of $2 \pi q$ on the sphere. Since the fermions carry $a_{\mu}$ charge of $1/2$, they feel only a flux of $\pi q$.
Let us now consider a $2\pi$-flux monopole operator, where the fermions feel a flux of $\pi$ from $a_{\mu}$; this violates the Dirac quantization condition and is thus apparently problematic. To illustrate the problem, recall that the
monopole's gauge field can be represented using a Dirac string carrying the $2\pi$-flux away from the center of the monopole in an infinitesimally thin solenoid. However, since the fermions feel only a $\pi$-flux from the solenoid, it is a physical object, and the resulting object is thus not a local operator. One might try to eliminate the Dirac string using the mathematical technology of sections and the monopole harmonics of Wu and Yang,\cite{wu76} but Dirac's quantization condition still enters there as a requirement that the transition function be single valued, and the problem is not avoided.
However, the Dirac quantization condition \emph{can} be repaired in the present case if flux in the ${\rm SU}(2)$ gauge field is also present, and so this must happen in order to get a local operator with unit ${\rm U}(1)_{XY}$ charge. In particular, we can consider putting a $2\pi$-flux monopole in $\alpha^3_{\mu}$ -- half of the 2-component fermions feel this as $\pi$ flux, and the other half feel it as $-\pi$ flux. (Other strengths of monopoles can also be considered, but these either lead to states that will have higher energy -- and thus higher scaling dimension -- or continue to violate the Dirac quantization condition.) Therefore, combined with the overall $\pi$-flux coming from $a_{\mu}$, there will be $N_f$ 2-component fermions moving in a background $2\pi$ flux, and $N_f$ fermions moving in zero flux. An issue that immediately arises is that the resulting state is not invariant even under global ${\rm SU}(2)$ gauge transformations. We return to this below, after discussing the structure of the state in the fixed gauge where there is a monopole in $\alpha^3_{\mu}$ and $\alpha^1_{\mu} = \alpha^2_{\mu} = 0$. It should be noted that this configuration of the ${\rm SU}(2)$ gauge field is not itself topologically stable, but is induced by the topologically stable monopole in the ${\rm U}(1)$ gauge field.
To understand the structure of the $2\pi$-monopole states and thus the corresponding operators, we shall need the spectrum of a single 2-component Dirac fermion on the 2-sphere, moving in a uniform background flux $2\pi f$. The energy levels for $|f| > 1$ are\cite{borokhov02}
\begin{equation}
E_p = \pm \sqrt{p^2 + p |f|} \text{,}
\end{equation}
where $p$ is a nonnegative integer. For $f = 0$ the form of the spectrum is the same, but $p$ is restricted to be positive and thus there are no $E_p = 0$ states. These levels are $(2 j_p + 1)$-fold degenerate, where $j_p = (1/2)(|f| -1) + p$, and transform in the $(2 j_p + 1)$-dimensional representation of the ${\rm SU}(2)$ Lorentz group (\emph{i.e.} rotation symmetry of the 2-sphere).
\begin{figure}
\includegraphics[width=3in]{zeromode.eps}
\caption{Illustration of the $2\pi$-monopole state whose corresponding operator is the QCED3 partner of the ${\rm O}(4)$ field $Z$. The spectrum of each 2-component fermion $\eta_{a \alpha}$ is shown. The fermions $\eta_{1 1}$ and $\eta_{21}$ both feel a net $2\pi$ flux through the sphere. The energy level spectrum for each of these fermions is symmetric about zero energy, where for each fermion there is a single zero energy state. The $\eta_{12}$ and $\eta_{22}$ fermions feel no flux, and also have a spectrum symmetric about zero energy, but with no zero energy state. All negative energy levels are filled, and one of the two zero mode states is filled to obtain a state with zero total charge under both the $a_{\mu}$ and $\alpha^3_{\mu}$ gauge fields.}
\label{fig:zeromode}
\end{figure}
We now specialize to $N_f = 2$, the case of interest. We represent $\Phi$ in terms of $N_{f 2} = 4$ two-component fermions $\eta_{a \alpha}$, where $a, \alpha = 1,2$ and $\Phi^T = (\eta^T_{1 1}, \eta^T_{1 2}, \eta^T_{2 1}, \eta^T_{2 2} )$. The $a$ index transforms as a doublet of ${\rm SU}(2)_L$, and the $\alpha$ index as a doublet of ${\rm SU}(2)$ gauge rotations. This means that the $\alpha = 1$ ($\alpha = 2$) fermions carry $\alpha^3_{\mu}$ charge of $1/2$ ($-1/2$). Then $\eta_{1 1}$ and $\eta_{2 1}$ feel flux $f = 1$, while $\eta_{1 2}$ and $\eta_{2 2}$ feel $f = 0$. The spectrum is as illustrated in Fig.~\ref{fig:zeromode}.
In order for the state to correspond to a gauge-invariant operator, it must carry zero $a_{\mu}$ charge. Moreover, we shall see below that it must also carry zero $\alpha^3_{\mu}$ charge. Now, both $a_{\mu}$ and $\alpha^3_{\mu}$, and hence the corresponding charges, change sign under the charge conjugation symmetry ${\cal C}$, which acts as a particle-hole transformation on the $\eta$-fermions. Crucially, ${\cal C}$ acts trivially on the $\alpha$ index of $\eta_{a \alpha}$ (see Appendix~\ref{app:symms}), so it does not exchange fermions feeling flux with those feeling no flux. Acting with ${\cal C}$ on the state illustrated in Fig.~\ref{fig:zeromode} results in another state of the same schematic form -- the only change is in the occupation of the zero mode states -- which must therefore have the same charges as the original state. The only consistent possibility is that both $a_{\mu}$ and $\alpha^3_{\mu}$ charges are zero, as needed. Other states with the correct charges, and higher energy, can be obtained from this state by moving fermions between levels.
Now we return to the question of gauge invariance of the $2\pi$-flux monopole state. To correspond to a gauge-invariant local operator, the state should be invariant under general ${\rm U}(1)$ and ${\rm SU}(2)$ gauge transformations. We can construct a gauge-invariant state starting with the gauge-fixed state discussed above, denoted by $| \psi_0 \rangle$. (Which of the two zero modes is filled is not important for this discussion, so we just focus on a single state.) The gauge-invariant state is constructed by integrating over all possible gauge transformations:
\begin{equation}
\label{eqn:ginvt-monopole}
|\psi\rangle = \int [d G_1] \int [d G_2] G_1 G_2 | \psi_0 \rangle \text{,}
\end{equation}
where $G_1$ and $G_2$ are unitary operators implementing ${\rm U}(1)$ and ${\rm SU}(2)$ gauge transformations, respectively, and the integrals are taken over all such unitary transformations. This state $| \psi \rangle$ is clearly gauge invariant, but we need to check that it does not vanish. This is done in Appendix~\ref{app:nonzero}, where it is shown that zero $a_{\mu}$ and $\alpha^3_{\mu}$ charge is a necessary and sufficient condition for $| \psi \rangle$ not to vanish.
We are now in a position to discuss the quantum numbers of the $2\pi$-flux monopole states depicted in Fig.~\ref{fig:zeromode}, and thus those of the corresponding operator. The negative energy single-particle levels, when fully occupied, are invariant under both Lorentz rotation and ${\rm SU}(2)_L$ flavor. However, the fermions feeling $f=1$ have $2$ zero-energy Lorentz-singlet levels, which are filled with a single fermion. This implies that the overall state transforms as a Lorentz singlet, but as a doublet under ${\rm SU}(2)_L$. We thus denote the corresponding monopole operator as the two-component object $\tilde{Z}$, where $\tilde{Z}^T = (\tilde{z}_1, \tilde{z}_2)$, and $\tilde{Z}$ transforms as a doublet under ${\rm SU}(2)_L$ and a singlet under Lorentz rotation. The complex conjugate $\tilde{Z}^*$ carries ${\rm U}(1)_{XY}$ charge $-1$ and corresponds to a state on the sphere with $-2\pi$ flux in $a_{\mu}$. These are the same quantum numbers carried by the ${\rm O}(4)$ field $Z$ (and its conjugate $Z^*$), and it is therefore reasonable to identify $\tilde{Z}$ and $Z$.
To work out the transformations of $\tilde{Z}$ under microscopic symmetries, we follow the procedure of Ref.~\onlinecite{hermele08} (which is based on that of Ref.~\onlinecite{alicea05a}), using the transformations for the fermion field $\Phi$ enumerated in Appendix~\ref{app:symms}. The basic idea is to use the facts that $\tilde{Z}$ is a ${\rm SU}(2)_L$ doublet and carries unit ${\rm U}(1)_{XY}$ charge to write down the most general transformation laws possible, which are
\begin{eqnarray}
T_x : \tilde{Z} &\to& e^{i \phi_T} \exp \Big( \frac{4 \pi i}{3} \sigma^3 \Big) \tilde{Z} \\
R_{\pi/3} : \tilde{Z} &\to& e^{i \phi_R} \sigma^1 \tilde{Z} \\
{\cal R}_y : \tilde{Z} &\to& e^{i \phi_{{\cal R}}} \tilde{Z} \\
{\cal C} : \tilde{Z} &\to& e^{i \phi_c} \sigma^1 \tilde{Z}^* \\
{\cal T} : \tilde{Z} &\to& c_{{\cal T}} \tilde{Z}^* \text{,}
\end{eqnarray}
where $\phi_T$, $\phi_R$, $\phi_{{\cal R}}$ and $\phi_c$ are arbitrary phases, and $c_{{\cal T}} = \pm 1$. We can partially determine these parameters by demanding that the action of the space group on $\tilde{Z}$ satisfy algebraic relations satisfied by its generators, and by making redefinitions of $\tilde{Z}$. The relations ${\cal R}_y^2 = R_{\pi/3}^6 = 1$ give the constraints $\phi_{{\cal R}} = 0, \pi$ and $\phi_R = \pi n_R / 3$, where $n_R = 0, 1, \dots, 5$. Also, $T_x R^2_{\pi/3} T_x R^{-2}_{\pi/3} = R_{\pi/3} T_x R^{-1}_{\pi/3}$ gives $\phi_T = 0$. Next, we redefine $\tilde{Z} \to \tilde{Z}' = e^{i \alpha} e^{i \beta \sigma^3} \tilde{Z}$, where $\alpha = - \phi_c / 2$, which has the effect of setting $\phi_c = 0$ in the above transformation laws. If $n_R < 3$, we choose $\beta = 0$, while for $n_R \geq 3$ we choose $\beta = \pi/2$, which has the effect of sending $n_R \to n_R - 3$ in the transformation laws above. To summarize, the most general transformation is then characterized by $\phi_T = \phi_c = 0$; $\phi_{{\cal R}} = 0, \pi$; $c_{{\cal T}} = \pm 1$; and $\phi_R = \pi n_R / 3$ where $n_R = 0,1,2$. If we choose $c_{{\cal T}} = -1$ and $\phi_{{\cal R}} = n_R = 0$, we obtain the same transformation laws as for the ${\rm O}(4)$ field $Z$, so it is indeed consistent with microscopic symmetries to identify $\tilde{Z}$ and $Z$.
{\bf Bilinears $\boldsymbol{I} = Z^T (i \sigma^2 \boldsymbol{\sigma}) Z$ and $\boldsymbol{I}^*$.} These objects have ${\rm U}(1)_{XY}$ charge of $\pm 2$. The QCED3 partners can thus be represented as states on the sphere where $a_{\mu}$ has $4\pi$ flux. In such a background gauge field, each $\eta_{a \alpha}$ fermion feels $2\pi$ flux, and no flux of the ${\rm SU}(2)$ gauge field is needed to satisfy the Dirac quantization condition. There are now four zero-energy single particle levels, and the lowest energy monopole state is obtained by filling all negative energy levels and filling the zero-energy levels with two fermions. We denote the vacuum state for $\pm 4\pi$ flux with no zero-energy levels filled by $| \pm \rangle$, and let $c^\dagger_{a \alpha}$ create a fermion in the zero-energy level corresponding to $\eta_{a \alpha}$. Focusing on $+ 4\pi$ flux, we consider the class of states $c^\dagger_{a \alpha} c^\dagger_{b \beta} | + \rangle$. There are a total of 6 such states. Three of these form a triplet under global ${\rm SU}(2)$ gauge transformations, and thus do not correspond to a local operator. The other 3 states are a singlet under global ${\rm SU}(2)$ gauge transformations, and a triplet under ${\rm SU}(2)_L$. These states can be labeled by $| I^i \rangle$ ($i = 1,2,3$) and written
\begin{equation}
|I^i \rangle = (i \sigma^2)_{\alpha \beta} [\sigma^i (i \sigma^2) ]_{a b} c^\dagger_{a \alpha} c^\dagger_{b \beta} | + \rangle \text{.}
\end{equation}
We denote the operator corresponding to these states by the vector $\tilde{\boldsymbol{I}}$, while its complex conjugate $\tilde{\boldsymbol{I}}^*$ is represented by the corresponding states for $a_{\mu}$ flux of $-4\pi$.
Just as for $\boldsymbol{I}$ ($\boldsymbol{I}^*$), $\tilde{\boldsymbol{I}}$ ($\tilde{\boldsymbol{I}}^*$) is a vector under ${\rm SU}(2)_L$, a Lorentz singlet, and carries ${\rm U}(1)_{XY}$ charge of $+2$ ($-2$). Transformations of $\tilde{\boldsymbol{I}}$ under microscopic symmetries can be worked out following the same procedure as above for $\tilde{Z}$, and can be chosen to agree with those of the ${\rm O}(4)$ model operator $\boldsymbol{I}$. Alternatively, if we think of $\tilde{\boldsymbol{I}}$ as the composite operator $\tilde{\boldsymbol{I}} \sim \tilde{Z}^T (i \sigma^2 \boldsymbol{\sigma}) \tilde{Z}$, then $\tilde{\boldsymbol{I}}$ and $\boldsymbol{I}$ transform identically, simply following from the identical transformations of $\tilde{Z}$ and $Z$.
{\bf Conserved current $\boldsymbol{J}^R_{\mu}$.} We have already identified $2 (\boldsymbol{J}_{\mu}^R)^z$ with the gauge flux $j^G_{\mu}$, but it remains to identify the other components $(\boldsymbol{J}^R_{\mu})^x , (\boldsymbol{J}^R_{\mu})^y$. We define linear combinations
\begin{equation}
(\boldsymbol{J}^R_{\mu})^{\pm} = (\boldsymbol{J}^R_{\mu})^x \pm i (\boldsymbol{J}^R_{\mu})^y \text{,}
\end{equation}
so that $(\boldsymbol{J}^R_{\mu})^{\pm}$ carries ${\rm U}(1)_{XY}$ charge $\pm 2$ and corresponds to a QCED3 monopole operator.
To construct the corresponding monopole operator using the state-operator correspondence, we let the operators $d^\dagger_{a \alpha \mu p}$ create a fermion in an energy $E_p$ level for $p = \pm 1$. Here the index $\mu$ transforms in the triplet representation of the Lorentz group. The states
$\epsilon_{\mu \nu \lambda} d^\dagger_{a \alpha \nu +} \sigma^i_{a b} d^{\vphantom\dagger}_{b \alpha \lambda -} | I^i \rangle$ have the correct quantum numbers to be identified with $(J^R_{\mu})^+$. However, there is another natural set of candidate states. Defining the gauge-triplet states
\begin{equation}
|G^i \rangle = (i \sigma^2)_{a b} [\sigma^i (i \sigma^2) ]_{\alpha \beta} c^\dagger_{a \alpha} c^\dagger_{b \beta} | + \rangle \text{,}
\end{equation}
we see that the states $\epsilon_{\mu \nu \lambda} d^\dagger_{a \alpha \nu +} \sigma^i_{\alpha \beta} d^{\vphantom\dagger}_{a \beta \lambda -} | G^i \rangle$ also have the correct quantum numbers to be identified with $(J^R_{\mu})^+$. While it is not clear which of these operators should be identified with $(J^R_{\mu})^+$, the more important point is that we have found at least one operator with the correct quantum numbers.
{\bf O(4) ``mass'' term ${\cal O}_r = Z^\dagger Z$.} This object must be identified with a QCED3 operator that is invariant under all symmetries of the field theory. Moreover, at the O(4) fixed point, it is the most relevant such operator. Using the QCED3 fixed point as a guide, the most relevant such operators in the large-$N_f$ limit (all with scaling dimension 4) are the Maxwell terms for the two gauge fields, and the following set of three quartic terms: $(\bar{\Phi} \Phi)^2$, $(\bar{\Phi} \boldsymbol{\nu} \Phi)^2$ and $(\bar{\Phi} \boldsymbol{\mu} \Phi)^2$. These quartic terms are independent, but to form a complete basis for all singlet quartic terms the additional operator $(\bar{\Phi} \gamma_{\mu} \Phi)^2$ must also be included. However, it can be shown that this operator actually has scaling dimension 6 in the $N_f \to \infty$ limit.\cite{hermele-unpub} As $N_f$ is reduced from infinity, some of the above dimension-4 operators are expected to become more relevant. Indeed, to identify the QCED3 and O(4) \emph{fixed points}, one of them must lower its dimension to about 1.67, the dimension of $Z^\dagger Z$ at the ${\rm O}(4)$ critical point, while the others must remain irrelevant (dimensions greater than 3). To have a clearer indication whether this is the case, it would be useful to calculate $1/N_f$ corrections to the dimensions of these operators. While similar calculations have appeared in the literature before,\cite{alicea05a, cenkexu08} $N_f = \infty$ shifts in scaling dimension [analogous to the fact that $(\bar{\Phi} \gamma_{\mu} \Phi)^2$ has dimension 6 here] are present but were not taken into account; this will modify the results. We hope that future work will resolve this issue, which would be useful in a variety of situations where similar field theories arise.
{\bf Anisotropy term ${\cal O}_v = |z_1|^2 |z_2|^2 - (1/6)Z^\dagger Z$.} This operator is a Lorentz singlet, carries zero ${\rm U}(1)_{XY}$ charge, and belongs to a $\ell_L = 2$ multiplet of ${\rm SU}(2)_L$ (with $m_L = 0$), so, as with ${\cal O}_r$ it is natural to identify it with a QCED3 operator quartic in the fermion fields. We have classified quartic terms according to their transformations under the Lorentz group and ${\rm SU}(2)_L$, and find that there are two independent terms with the correct quantum numbers:
\begin{eqnarray}
R_0 &=& (\bar{\Phi} \nu^3 \Phi)^2 - \frac{1}{3} (\bar{\Phi} \boldsymbol{\nu} \Phi)^2 \\
R_1 &=& (\bar{\Phi} \nu^3 \gamma_{\mu} \Phi)^2 - \frac{1}{3} (\bar{\Phi} \boldsymbol{\nu} \gamma_{\mu} \Phi)^2 \text{.}
\end{eqnarray}
The O(4) operator ${\cal O}_v$ should be identified with the more relevant of $R_0$ and $R_1$.
{\bf Topological density ${\mathfrak C}$.} We identify the O(4) operator ${\mathfrak C}$ with the QCED3 bilinear $\tilde{{\mathfrak C}} = -i \bar{\Phi} \Phi$, which is also odd under spatial reflections and time-reversal, but invariant under other symmetries.
It may seem that this identification spells trouble for a potential duality between O(4) and QCED3 \emph{fixed points}. ${\mathfrak C}$ is quartic in the ${\rm O}(4)$ field and has three derivatives, thus appearing strongly irrelevant, while $\tilde{{\mathfrak C}}$, as a fermion bilinear, na\"{\i}vely appears likely to be relevant. However, two points are in order. First, the O(4) model operator ${\mathfrak C}$ cannot be generalized in a natural way to the ${\rm O}(n)$ case (or to $d=3$), so the above intuition about its scaling dimension is suspect. Second, the scaling dimension of $\tilde{{\mathfrak C}}$ to leading order in the large-$N_f$ expansion is
\begin{equation}
\operatorname{dim} \tilde{\mathfrak C} = 2 + \frac{256}{3 \pi^2 N_f} + {\cal O}(1/N_f^2) \text{,}
\end{equation}
which, upon inspection of the diagrams involved, can be obtained by simply adding the corresponding anomalous dimensions for QED3\cite{hermele-erratum07} and QCD3.\cite{cenkexu08} Therefore, gauge fluctuations make $\tilde{{\mathfrak C}}$ substantially more irrelevant -- the coefficient of $1/N_f$ is quite large. The striking contrast from the behavior of the $\tilde{\boldsymbol{N}}$ bilinears, which become more relevant with decreasing $N_f$, is interpreted physically in Ref.~\onlinecite{hermele-erratum07}. It is then plausible that $\tilde{{\mathfrak C}}$ continues to be irrelevant, perhaps strongly so, down to $N_f = 2$.
\section{Evidence for the duality: stable phases}
\label{sec:evidence2}
We shall now show that the three stable phases of the O(4) model Eq.~(\ref{eqn:o4-lagrangian}) -- the paramagnet, and coplanar and collinear ordered states -- are realized simply in QCED3. While we do not have enough control over QCED3 at $N_f = 2$ to determine the phase diagram, the fact that all the known phases of the O(4) model can be realized is an important piece of evidence in support of the proposed duality.
We begin by considering the paramagnetic phase, which can be represented in the dual description by condensation of vortices.\cite{dasgupta81} We need to find a vortex condensate that does not break any microscopic symmetries, and to that end we consider
\begin{equation}
V = \Phi^T (i \mu^2) (i \nu^2) (i \tau^2) \Phi \text{,}
\end{equation}
which creates a single vortex. $V$ is invariant under $T_x$ and ${\cal T}$ and is a scalar under $R_{\pi/3}$. Under ${\cal R}_y$ and ${\cal C}$, $V \to V^\dagger$. Working in a fixed gauge, condensation of $V$ means that
$\langle V \rangle = e^{i \theta} | V | \neq 0$. If $\theta = 0$, then clearly the condensate preserves the microscopic symmetries. In fact, even if $\theta \neq 0$, the apparent breaking of ${\cal R}_y$ and ${\cal C}$ is a gauge artifact, as these symmetries can be restored by supplementing them with an appropriate gauge transformation. Alternatively, one can always choose a gauge such that $\theta = 0$.
We can understand the effect of this vortex condensation on the fermion spectrum, at the mean-field level, by adding the term $(\Delta/2) \int d^2 \boldsymbol{r} ( V + V^\dagger)$ to the mean-field Hamiltonian. It is easily seen that the dispersion relation becomes $E(\boldsymbol{k}) = \pm \sqrt{\boldsymbol{k}^2 + \Delta^2}$, and a gap of $2 \Delta$ is opened. In this gapped state, the ${\rm SU}(2)$ gauge field will become confining, thus removing single fermion excitations from the spectrum. Also, the ${\rm U}(1)$ gauge field will be in a Higgs phase, and its photon mode and excitations carrying nonzero ${\rm U}(1)_{XY}$ charge will acquire a gap. Therefore all excitations are gapped, no symmetries are broken, and we have a description of the paramagnet.
To access the magnetically ordered phases, we consider the Lagrangian ${\cal L} = {\cal L}_{{\rm QCED3}} + \boldsymbol{\alpha} \cdot \tilde{\boldsymbol{N}}$. At the mean-field level (and also at the QCED3 fixed point), the addition of $\boldsymbol{\alpha} \cdot \tilde{\boldsymbol{N}}$ will open a gap in the fermion spectrum. As a result the ${\rm SU}(2)$ gauge field will become confining, and monopole operators of the ${\rm U}(1)$ gauge field will acquire an expectation value -- the latter phenomenon corresponds to the spontaneous breaking of ${\rm U}(1)_{XY}$ symmetry and XY magnetic order. The photon of the ${\rm U}(1)$ gauge field remains gapless, and corresponds to the spin wave mode of the magnetically ordered state.
To determine the pattern of magnetic order, we note that because $\boldsymbol{\alpha} \cdot \tilde{\boldsymbol{N}}$ breaks various space group symmetries, it leads to a gapped ``vortex insulator,'' where the pattern of lattice symmetry breaking depends on $\boldsymbol{\alpha}$. The vortex insulators that result are the same as those arising in the discussion of Ref.~\onlinecite{alicea05a}, so we give only a brief summary of the results here. If $\boldsymbol{\alpha} = \alpha_z \boldsymbol{z}$, the resulting state is a vortex ``charge density wave,'' where vortices preferentially occupy one of the two honeycomb sublattices. This corresponds to the $120^\circ$ coplanar magnetically ordered state.\cite{alicea05a} On the other hand, if $\boldsymbol{\alpha} = \alpha_x \boldsymbol{x} + \alpha_y \boldsymbol{y}$, the resulting state is a vortex ``valence bond solid'' (VBS), where vortices hop back and forth preferentially on a subset of honeycomb lattice bonds. As detailed in Ref.~\onlinecite{alicea05a}, the vortex VBS states that arise here correspond to the collinear magnetically ordered states.
\section{Discussion}
\label{sec:discussion}
We have given evidence for a rare example of non-abelian duality (without supersymmetry) in $d=2$, between the O(4) model and QCED3 field theories. Both were derived as low-energy effective descriptions of the same triangular lattice frustrated XY model. The O(4) model arose from a standard Landau theory treatment. QCED3 was obtained by combining the abelian boson-vortex duality of the lattice model with a fermionic slave-particle treatment of the vortex degrees of freedom. By setting up an operator dictionary between the two field theories, and showing that both can realize the three stable phases of the original XY model, we argued that both field theories describe the same low-energy sector of the XY model and are thus dual.
As discussed in Sec.~\ref{sec:statement}, this result is to be understood primarily as a duality between field theories. It is natural to ask whether it is \emph{also} a duality between the O(4) and QCED3 fixed points, assuming that the QCED3 fixed point exists for $N_f = 2$. The two possibilities are that either the O(4) and QCED3 fixed points are identical, or they are distinct. The latter possibility would mean, for example, that the O(4) model realizes both fixed points somewhere in its parameter space. While we are not aware of any evidence for this, it is hard to rule out, especially if the $N_f = 2$ QCED3 fixed point is highly unstable and requires tuning of several parameters. However, given the available evidence on scaling dimensions of operators at the two fixed points, it is certainly plausible that they are identical.
Numerical simulations of QCED3 for various values of $N_f$ could potentially shed some light on this issue.
The O(4)-QCED3 duality suggests a number of directions to pursue a further understanding of $d=2$ non-abelian duality. One can certainly explore whether similar constructions, perhaps starting from other lattice models, lead to other duality relations. Another natural question is whether there are connections between the present results and $d=2$ dualities of supersymmetric field theories.\cite{intriligator96, kapustin99} Perhaps upon suitably breaking supersymmetry in a pair of dual theories, the O(4)-QCED3 duality -- or other, related dualities -- can be obtained.
Finally, it is interesting to remark that the O(4)-QCED3 duality can be viewed as a bosonization of QCED3, where the bosonized form is simply the O(4) model. If more examples of similar dualities are discovered, and better understood, they might eventually be useful as a kind of $d=2$ bosonization.
\acknowledgments{I am grateful to Jason Alicea and T. Senthil for useful comments, and especially to Jason Alicea, Matthew P. A. Fisher and Olexei Motrunich for a related prior collaboration.}
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{"url":"https:\/\/gigaom.com\/2007\/12\/17\/living-a-microsoft-office-free-lifestyle\/","text":"# Living a Microsoft Office Free Lifestyle\n\nAs part of my Leopard switch, I set one goal for myself: run nothing but Intel native applications. That meant finding a clear alternative for Microsoft Office.\n\n### Pages\n\nSticking with the iWork \u201808 trial, I began my migration quickly and easily. All my Word documents changed peacefully to Pages by default and all opened just fine. The only minor issue I ran into was not having Microsoft\u2019s font book, and therefor several obscure fonts were reset to Times New Roman. If anyone has a quick fix for this, I\u2019d be interested to hear. I imagine I could take the font book from a Mac with Office installed and simply replace my font book with it?\n\nOpening new documents was simple. Using the Blank template I was able to manage around Page\u2019s Inspector. However I quickly ran into problems re-saving edited documents. Pages by default saves in the Pages format. So even editing a .Doc requires you save it as Pages. That\u2019s a bit frustrating. You can export a file into Word for convenience, especially if you\u2019re planning on sharing those documents with others. But it would be much more convenient to be able to choose your format directly from the Save screen. So I began saving my documents in the Pages format and getting rid of the normal Word documents when done editing them. Fortunately for me, I didn\u2019t need to export documents as much as I thought I would. But again, it is frustrating after awhile. At least offer a keyboard command to quickly access the export feature so I don\u2019t have to rely on my mouse as frequently.\n\nThe one real benefit I found with Pages and iWork was how quickly it opened. I imagine since Office is currently not Intel native, it requires more time to open. We\u2019ll see how that remedies when Office \u201908 goes on sale. But it\u2019s nice not having to wait for a document to open. So far I\u2019ve been happy with Pages, until it comes to creating a new flyer, not based on any of their templates. When creating a new layout or design, I can get more done and faster through Photoshop.\n\n### Keynote & Numbers\n\nI\u2019m lumping Keynote and Numbers together because as a writer my main focus lies solely on document editing. So for a more precise comparison, I recommend trying them out yourselves.\n\nI think watching Steve Jobs\u2019 Keynotes has created a bias for me. Or if you\u2019re more familiar with An Inconvenient Truth, Al Gore relies on Keynote for his presentation. Feature wise, Keynote offers very similar features as PowerPoint, just in a more clean, streamlined fashion. Since it meshes directly with iPhoto and iTunes, it\u2019s a lot simpler to import music, photos, or even videos. One feature I truly love about Keynote is my ability to export it directly to iPod. When giving presentations I find it easier to carry around my iPod and A\/V chord instead of a laptop and chords. Much less fuss, and much more streamlined. You may not retain as many features, but for someone that needs something portable, it\u2019s a great idea. Over all I feel more satisfied with my Keynote presentations than I have with PowerPoint, so I\u2019m going to stick with it.\n\nNumbers was an interesting one for me. I could open my previous Excel files fine, but if they contained drop down menus, or set fields I began running into issues. Not a spreadsheet fiend, I think I\u2019d prefer Excel only because of its familiarity and the fact it seems a business staple.\n\n### Recommendation\n\nOne thing I appreciate overall with iWork and Mac is the attention to detail. For example iWork allows you to move a document currently being editing to another folder without any errors. The document will kindly ask whether too start saving there, or save in two locations. Between Pages and Keynote I feel satisfied for most of my current office needs.\n\nFor students, something to keep in mind, is universality. Obviously Office is the preferred choice for schools and teachers, so it might be best for you to stick with it. Especially for note taking, I remember enjoying Word\u2019s Notebook feature. Not only could I simultaneously record lecture from within Word, I could write clear outlined notes using its Notebook format. It was simple, efficient, and helped a lot.\n\nIf price is a factor for you, be sure and check out NeoOffice. It provides a classical approach and is completely free. iWork can be purchased for $79, and it looks like Office \u201908 will run you up$150 for the Student\/Teacher edition or \\$399 for Office Basic. If you\u2019re running low on hard drive space, try testing out Google Docs and Spreadsheets, ZoHo, or Adobe\u2019s new Buzzword. There are a variety of ways around office applications, so find what works most efficiently for you. If you have any recommendations or ideas, feel free to comment.","date":"2021-08-01 14:56:08","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\": 0.19685077667236328, \"perplexity\": 2107.859378859341}, \"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-2021-31\/segments\/1627046154214.36\/warc\/CC-MAIN-20210801123745-20210801153745-00518.warc.gz\"}"}
| null | null |
Q: What's the difference between tokio::select! A, B inside a loop and tokio::spawn two tasks each runs one of A, B? I'm new to asynchronous programming, therefore struggling with how different approach varies in behavior.
Consider the example given by tokio at github repo, chat.rs:
// snip
loop {
tokio::select! {
// A message was received from a peer. Send it to the current user.
Some(msg) = peer.rx.recv() => {
// do something
}
result = peer.lines.next() => match result {
// A message was received from the current user, we should
// broadcast this message to the other users.
Some(Ok(msg)) => {
// do something
}
Some(Err(e)) => {
// handle error
}
// The stream has been exhausted.
None => break,
},
}
}
// do something
What is the benefit of using loop select! over two tokio::spawn, like below:
let handle_1 = tokio::spawn(async move {
while let Some(msg) = peer.rx.recv() {
// do something
}
});
let handle_2 = tokio::spawn (async move {
loop {
let result = peer.lines.next();
match result {
Some(Ok(msg)) => {
// do something
},
Some(Err(e)) => {
// handle error
},
None => break,
};
}
});
handle_1.await;
handle_2.await;
// do something
A: In general, select! is more efficient because it doesn't need to spawn new tasks, which is very cheap but still more expensive than just polling futures. However, there are few caveats:
*
*If there are frequent messages, which makes the task more CPU-bound, it is recommend to spawn a new task, because select! run all futures on the same thread while spawn() may use a different thread in a multi-threaded runtime.
*The futures in select! should be cancellation-safe, meaning it is safe to drop them incompleted and this does not cause loss of any data. If this is not the case, there may be bugs. It makes it harder to program with select! than with tasks. See this post for example.
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\def\mathop{\rm rk\,}\nolimits{\mathop{\rm rk\,}\nolimits}
\def\mathop{\rm div\,}\nolimits{\mathop{\rm div\,}\nolimits}
\def\mathop{\rm Ad}\nolimits{\mathop{\rm Ad}\nolimits}
\def\mathop{\rm Res}\nolimits{\mathop{\rm Res}\nolimits}
\def\mathop{\rm codim}\nolimits{\mathop{\rm codim}\nolimits}
\def\mathop{\rm Sing}\nolimits{\mathop{\rm Sing}\nolimits}
\input amssym.def
\input amssym
\vsize = 25truecm
\hsize = 16truecm
\voffset = -.5truecm
\parindent=0cm
\baselineskip15pt
\overfullrule=0pt
\newlabel{def}{1.1
\vskip1cm
\centerline{\bf Symplectic singularities}
\smallskip
\centerline{Arnaud {\pc BEAUVILLE}}
\vskip1cm
{\bf Introduction}
\smallskip
\par\hskip 1truecm\relax We introduce in this paper a particular class of rational
singularities, which we call {\it symplectic}, and classify the simplest
ones. Our motivation comes from the analogy between rational
Gorenstein singularities and Calabi-Yau manifolds: a compact, K\"ahler
manifold of dimension $n$ is a Calabi-Yau manifold
if it admits a nowhere vanishing
$n$\kern-1.5pt - form, while a normal variety $V$ of dimension
$n$ has rational Gorenstein singularities\note{also called canonical
singularities of index $1$.} if its smooth part
$V_{\rm reg}$ carries a nowhere vanishing
$n$\kern-1.5pt - form, with the extra property that its pull-back in any resolution
$X\rightarrow V$ extends to a holomorphic form on $X$. Among Calabi-Yau
manifolds an important role is played by the symplectic (or hyperk\"ahler)
manifolds, which admit a
holomorphic, everywhere non-degenerate $2$\kern-1.5pt - form; by analogy we say that a
normal variety $V$ has {\it symplectic singularities} if $V_{\rm reg}$
carries a closed symplectic $2$\kern-1.5pt - form whose pull-back in any resolution
$X\rightarrow V$ extends to a holomorphic $2$\kern-1.5pt - form on $X$.
\par\hskip 1truecm\relax We will look for the simplest possible isolated symplectic
singularities ${\rm o}\in V$, namely those whose projective tangent cone is
smooth: this means that blowing up ${\rm o}$ in $V$ provides a resolution of
$V$ with a smooth exceptional divisor. Examples of such
singularities are obtained as
follows. Each simple complex Lie algebra has a smallest non-zero nilpotent
orbit
${\cal O}_{\rm min}$ for the adjoint action; its closure $\overline{\cal
O}_{\rm min}={\cal O}_{\rm min}\cup\{0\}$ has a symplectic singularity at $0$,
isomorphic to the cone over the smooth variety ${\bf P}{\cal
O}_{\rm min}:={\cal O}_{\rm min}/{\bf C^*}$. In
particular its projective tangent cone is smooth (it is isomorphic to
${\bf P}{\cal O}_{\rm min}$).
\par\hskip 1truecm\relax Our main result is the converse:\smallskip
{\bf Theorem}$.-$
{\it Let $(V,{\rm o})$ be an isolated symplectic singularity, whose
projective tangent cone is smooth. Then $(V,{\rm o})$ is analytically
isomorphic to
$(\overline{\cal O}_{\rm min},0)$ for some simple complex Lie algebra}.
\smallskip
\par\hskip 1truecm\relax The key point of the proof is the fact that the homogeneous space
${\bf P}{\cal O}_{\rm min}$ carries a holomorphic {\it contact structure}
(inherited from the symplectic structure of ${\cal O}_{\rm min}$). Given a
resolution $X\rightarrow V$ with a smooth exceptional divisor $E$, we show
that the extension to $X$ of the symplectic form has a
residue on $E$ which defines a contact structure. We then deduce from [B1]
that $E$ is isomorphic to some ${\bf P}{\cal O}_{\rm min}$,
and we conclude with a classical criterion of Grauert.
\par\hskip 1truecm\relax We discuss in \S 4 whether a classification of isolated symplectic
singularities makes sense. Each such singularity gives rise to many others by
considering its quotient by a finite group; to get rid of those we propose to
consider only isolated symplectic singularities with trivial local fundamental
group. The singularities $(\overline{\cal O}_{\rm min},0)$ have this property
when the Lie algebra is not of type $C_l$; it is certainly desirable to find
more examples.
\section{Definition and basic properties}
\par\hskip 1truecm\relax We consider algebraic varieties over ${\bf C}$ (our results extend
readily to the analytic category). We
will say that a holomorphic 2-form on a smooth variety is {\it
symplectic} if it is closed and non-degenerate at every point. A {\it
resolution} of an algebraic variety $V$ is a proper, birational morphism
$f:X\rightarrow V$ where $X$ is smooth.
\th Definition
\enonce A variety has a symplectic singularity at a point if this point
admits an open neighborhood $V$ such that:
\par\hskip 0.5truecm\relax {\rm a)} $V$ is normal;
\par\hskip 0.5truecm\relax {\rm b)} The smooth part $V_{\rm reg}$ of $V$ admits a symplectic $2$\kern-1.5pt -
form
$\varphi$;
\par\hskip 0.5truecm\relax {\rm c)} For any resolution $f:X\rightarrow V$, the pull back of
$\varphi$ to $f^{-1} (V_{\rm reg})$ extends to a holomorphic $2$\kern-1.5pt - form on
$X$.
\endth\label{def}
\par\hskip 1truecm\relax We will mostly consider a symplectic singularity as a germ $(V,{\rm o})$
-- in which case we will always assume that $V$ satisfies the conditions a)
to c).
\global\def\currenvir{subsection As for rational singularities it is enough to check c) for one
particular resolution: the point is that if $X\rightarrow Y$ is a proper
birational morphism of smooth varieties, a meromorphic form $\varphi$ on $Y$
is holomorphic if and only if $g^*\varphi$ is holomorphic.
\th Proposition
\enonce A symplectic singularity is rational Gorenstein.
\endth
\par\hskip 0.5truecm\relax{\it Proof}: We keep the notation of Definition \ref{def} and put $\dim
V=2r$. The form $\varphi^r$ generates the line bundle
$\omega^{}_{V_{\rm reg}}$, and for any resolution $X\rightarrow V$ extends to
a holomorphic form on $X$; this implies that $V$ has rational Gorenstein
singularities [R].\cqfd
\par\hskip 1truecm\relax The following remark shows that isolated symplectic singularities of
dimension $>2$ are {\it not} local complete intersections:
\th Proposition
\enonce Let $V$ be a variety with symplectic singularities which is locally
a complete intersection. Then the singular locus of $V$ has codimension
$\le 3$.
\endth
\par\hskip 0.5truecm\relax{\it Proof}: We can realize
locally
$V$ as a complete intersection in some smooth variety $S$.
The exact sequence
$$0\rightarrow N_{V/S}^* \longrightarrow
\Omega^1_S{}^{}_{|V}\longrightarrow
\Omega^1_V\rightarrow 0\ ,$$
provides a length $1$ locally free resolution of $\Omega^1_V$. We can assume
$\mathop{\rm codim}\nolimits \mathop{\rm Sing}\nolimits(V)\ge 3$; by the Auslander-Buchsbaum theorem and the fact that
$V$ is Cohen-Macaulay, the depth of $\Omega^1_V$ at every point of
$\mathop{\rm Sing}\nolimits(V)$ is $\ge 2$. It follows that $\Omega^1_V$ is a reflexive sheaf,
so the isomorphism
$\Omega^1_{V_{\rm reg}}\rightarrow T^{}_{V_{\rm reg}}$ defined by a symplectic
$2$\kern-1.5pt - form on $V_{\rm reg}$
extends to an isomorphism $\Omega^1_V\rightarrow T^{}_V$.
Combining the resolution of $\Omega^1_V$ and its dual we get an exact
sequence
$$0\rightarrow N_{V/S}^* \longrightarrow
\Omega^1_S{}^{}_{|V}\longrightarrow T_S{}^{}_{|V}\qfl{u} N_{V/S}\ ,$$
where the support of the cokernel $T^1$ of $u$ is exactly $\mathop{\rm Sing}\nolimits(V)$.
Using the Auslander-Buchsbaum theorem again we get
$\dim(T^1)=\dim\mathop{\rm Sing}\nolimits (V)\ge
\dim(V)-3$.\cqfd
\section{Examples}
\global\def\currenvir{subsection In dimension $2$, the symplectic singularities are the rational
double points (that is the A-D-E singularities).\par
\global\def\currenvir{subsection Any product of varieties with symplectic singularities has again
symplectic singularities.
\medskip
\global\def\currenvir{subsection {\it Quotient singularities}\label{qt}
\par\hskip 1truecm\relax The following result will provide us with a large list of symplectic
singularities:
\th Proposition
\enonce Let $V$ be a variety with symplectic singularities,
$G$ a finite group of automorphisms of $V$, preserving a symplectic $2$\kern-1.5pt -
form on $V_{\rm reg}$. Then $V/G$ has symplectic singularities.
\endth
\par\hskip 0.5truecm\relax{\it Proof}: We first observe that the fixed locus $F_g$ in $V_{\rm
reg}$ of any element $g\not=1$ in $G$ is a symplectic subvariety of
$V_{\rm reg}$, and therefore has codimension $\ge 2$. Let
$ V^{\rm o}:=V_{\rm reg}\mathrel{\hbox{\vrule height 3pt depth -2pt width 6pt}} \union_{g\not=1}F_g$. The symplectic
2-form on $V^{\rm o}$ descends to a symplectic 2-form on
$V^{\rm o}/G$, which extends to a symplectic 2-form $\varphi$ on
$(V/G)_{\rm reg}$. Let $g:Y\rightarrow V/G$ be a resolution of $V/G$; we
can find a commutative diagram
$$\diagram{X & \hfl{f}{} & V \cr
\vfl{}{} & & \vfl{}{} \cr
Y & \hfl{g}{} & V/G \cr
}$$where $f$ is a resolution of $V$.
Then $g^*\varphi$ is a meromorphic 2-form on $Y$, whose pull back to
$X$ is holomorphic. By an easy local computation, this implies that
$g^*\varphi$ is holomorphic.\cqfd
\medskip
\par\hskip 1truecm\relax This applies for instance when $V$ is a finite-dimensional
symplectic vector space, and $G$ a finite subgroup of ${\rm Sp}(V)$.
If we impose moreover that the non trivial elements of $G$ have all their
eigenvalues $\not=1$, then $V/G$ has an isolated symplectic
singularity. The case $\dim(V)=2$ gives the rational double points.
\par\hskip 1truecm\relax The Proposition also applies to the symmetric products
$V^{(p)}=V^p/{\goth S}_p$: if $V$ has symplectic singularities, so does
$V^{(p)}$.
\medskip
\global\def\currenvir{subsection {\it Nilpotent orbits}\label{nil}
\par\hskip 1truecm\relax Let ${\goth g}$ be a simple complex Lie
algebra
and ${\cal O}\i{\goth g}$ a nilpotent orbit (for the
adjoint action)\note{A general reference for nilpotent
orbits is [C-M].}. Then {\it the normalization of the closure
of ${\cal O}$ in ${\goth g}$ has symplectic singularities}. This is due to
Panyushev [P], who uses it to prove that this variety has rational Gorenstein
singularities. The point is that ${\cal O}$ can be identified with a
coadjoint orbit using the Killing form, and therefore carries the
Kostant-Kirillov symplectic
$2$\kern-1.5pt - form.
\par\hskip 1truecm\relax In particular, the Lie algebra ${\goth g}$ contains a unique
(non-zero) minimal nilpotent orbit ${\cal O}_{\rm min}$, which is contained
in the closure of all non-zero nilpotent orbits. The closure
$\overline{\cal O}_{\rm min}= {\cal O}_{\rm min}\cup\{0\}$ is normal, and has
an isolated symplectic singularity at
$0$.
\par\hskip 1truecm\relax This singularity can be described as follows. The orbit
${\cal O}_{\rm min}$ is stable by homotheties; the quotient
${\bf P}{\cal O}_{\rm min}:={\cal O}_{\rm min}/{\bf C}^*$ is a smooth,
closed subvariety of ${\bf P}({\goth g})$.
The variety $\overline{\cal O}_{\rm min}$ is the cone over ${\bf P}{\cal
O}_{\rm min}\i {\bf P}({\goth g})$. This means that we have a resolution
$f:L^{-1}
\rightarrow \overline{\cal O}_{\rm min}$, where $L$ is the restriction
of ${\cal O}_{{\bf P}({\goth g})}(1)$ to ${\bf P}{\cal O}_{\rm min}$,
and $f$ contracts to $0$ the zero section $E$ of $L^{-1} $. In this
situation $f$ is the blow up of
$0$ in $\overline{\cal O}_{\rm min}$, and the exceptional divisor $E$,
isomorphic to ${\bf P}{\cal O}_{\rm min}$, is the projective tangent cone
to $0$ in
$\overline{\cal O}_{\rm min}$.
\section{Characterization of minimal orbits singularities}
\global\def\currenvir{subsection This section is devoted to the proof of the theorem stated in the
introduction. So we let $(V, {\rm o})$ be an isolated symplectic singularity,
$f:X\rightarrow V$ the blow up of the
maximal ideal of ${\rm o}$ in $V$, and $E$ the exceptional
divisor. By construction $E$ is isomorphic to the projective tangent cone
to $V$ at ${\rm o}$; we assume that it is smooth. Since
$E$ is a Cartier divisor in $X$ it follows that $X$ is
smooth.
\par\hskip 1truecm\relax We denote by $i$ the embedding
of $E$ in $X$, and put $L:=i^*{\cal O}_X(-E)$.
By the standard properties of the blow up the line bundle $L$ on $E$ is
{\it very ample}.
\global\def\currenvir{subsection \label{loc} Let $\dim V=2r$. We can assume that $V\mathrel{\hbox{\vrule height 3pt depth -2pt width 6pt}}
\{{\rm o}\}$ carries a symplectic
$2$\kern-1.5pt - form which extends to a holomorphic $2$\kern-1.5pt - form $\varphi$ on $X$;
we have $\mathop{\rm div\,}\nolimits(\varphi^r)=kE$ for some integer $k\ge 0$. The adjunction
formula gives $K_E=L^{-k-1} $, so that $E$ is a Fano manifold. This implies
$H^0(E,\Omega^p_E)=0$ for each $p\ge 1$, and in particular $i^*\varphi=0$.
\par\hskip 1truecm\relax Let $e\in E$. Since $\varphi$ is closed, we can write $\varphi=d\alpha$
in a neighbourhood $U$ of $e$ in $X$, where $\alpha$ is a $1$\kern-1.5pt - form on
$U$ such that $i^*\alpha$ is closed. Shrinking $U$ if necessary we can
write $i^*\alpha=d(i^*g)$ for some function $g$ on $U$; replacing $\alpha$
by $\alpha-dg$ we may assume $i^*\alpha=0$. If $u=0$ is a local equation
of $E$ in $U$, this means that $\alpha$ is of the form $u\,\tilde
\theta+h\,du$, where $\tilde\theta$ is a $1$\kern-1.5pt - form and $h$ a function on
$U$; replacing $\alpha$ by $\alpha-d(hu)$ and $\tilde \theta$ by $\tilde
\theta-dh$ we arrive at
$\alpha=u\tilde\theta$ and
$$\varphi=du\wedge\tilde\theta + u\,d\tilde\theta\ .$$
\par\hskip 1truecm\relax This gives $\varphi^r=ru^{r-1}du\wedge
\tilde \theta\wedge (d\tilde \theta)^{r-1}+u^r(d\tilde
\theta)^r$. Thus the order of vanishing
$k$ of $\varphi^r$ along $E$ is
$\ge r-1$; the crucial point of the proof is the equality
$k=r-1$. We need an easy lemma:
\th Lemma
\enonce Let $X$ be a smooth closed
submanifold of a projective space ${\bf P}^N$, of degree
$\ge 2$. Then
$H^0(X,\hbox{\san \char3}^pT_X(-p))=0$ for
$0<p<\dim(X)$, and for $p=\dim(X)$ except if $X$ is a
hyperquadric.
\endth\label{W}
\par\hskip 0.5truecm\relax{\it Proof}: When $X$ is a hyperquadric our assertion is equivalent to
$H^0(X,\Omega^q_X(q))=0$ for $0<q<\dim(X)$, which can be checked by a
direct computation (see for instance [K], thm. 3). We assume
$\deg(X)\ge 3$.
\par\hskip 1truecm\relax The case $p=1$ follows from a more
general result of Wahl ([W], see remark below).
Then we use induction on the dimension of
$X$, the case of curves being clear. Let
$H$ be a smooth hyperplane section of $X$; the exact sequence
$$0\rightarrow T_H\longrightarrow T_X{}^{}_{|H}\longrightarrow
{\cal O}_H(1)\rightarrow 0$$
gives rise to exact sequences
$$0\rightarrow \hbox{\san \char3}^pT_H\,(-p)\longrightarrow
\hbox{\san \char3}^pT_X{}^{}_{|H}(-p)\longrightarrow \hbox{\san \char3}^{p-1}T_H(-(p-1))\rightarrow 0$$
By the induction hypothesis we conclude that $H^0(X,\hbox{\san \char3}^pT_X{}^{}_{|H}(-p))$
is zero for $ p\ge 2$, and therefore $H^0(X,\hbox{\san \char3}^pT_X{}^{}(-p))=0$
for $p\ge 2$.\cqfd
\rem{Remark} Wahl's result is rather
easy in our situation: using the exact sequence
$$0\rightarrow H^0(X,T_X(-1))\longrightarrow H^0(X,T_{{\bf
P}^N}(-1)^{}_{|X})\longrightarrow H^0(X,N_{X/{\bf P}^N}(-1))$$
and the
isomorphism ${\bf C}^{N+1}\mathrel{\mathop{\kern 0pt\longrightarrow }\limits^{\sim}} H^0(X,T_{{\bf
P}^N}(-1)^{}_{|X})$ deduced from the Euler exact sequence, we see that a
nonzero element of $H^0(X,T_X(-1))$ corresponds to a point $p\in{\bf
P}^N$ such that all projective tangent spaces
${\bf P}T_x(X)$, for $x$ in $X$, pass through $p$. This is easily seen
to be impossible, for instance by induction on $\dim(X)$.
\par\hskip 1truecm\relax It seems natural to conjecture that the statement of the lemma extends
to the more general situation considered in [W], namely that
$H^0(X,\hbox{\san \char3}^pT_X\otimes L^{-p})=0$ {\it for $p>0$ whenever $L$ is ample,
except if $(X,L)=({\bf P}^n,{\cal O}_{{\bf P}^n}(1))$, with $n\ge p$, or}
$(X,L)=(Q_p, {\cal O}_{Q_p}(1))$.
\smallskip
\global\def\currenvir{subsection We now prove the equality $k=r-1$. If
$E={\bf P}^{2r-1}$ and $L={\cal O}_{{\bf P}^{2r-1}}(1)$, $V$ is
smooth; if $E={\bf P}^{1}$ and $L={\cal O}_{{\bf P}^{1}}(2)$, $V$ is a
surface with an ordinary double point. We exclude these two cases. The perfect
pairing
$\Omega^1_X\otimes\Omega^{2r-1}_X\rightarrow K_X$ provides an isomorphism
$\Omega^{2r-1}_X\cong T_X\otimes K_X$; thus
exterior product with
$\varphi^{r-1}$ gives a linear map
$\Omega^1_X\rightarrow T_X(kE)$, which is an isomorphism
outside $E$ (it is the inverse of the isomorphism defined by $\varphi$).
This map may vanish on
$E$, say with order
$k-j$
$(j\le k)$, so that we get a map $\lambda:\Omega^1_X\rightarrow T_X(jE)$
whose restriction to $E$ is nonzero. Observe that $\mathop{\rm det}\nolimits \lambda$ is a
section of
${\cal O}_X(2(rj-k)E)$ which is nonzero outside $E$, hence $k\le rj$ and in
particular $j\ge 0$.
\def\ \longrightarrow \ {\ \longrightarrow \ }
\par\hskip 1truecm\relax We have a diagram of exact sequences
$$\diagram{& 0\ \longrightarrow \ L \ \longrightarrow \
\Omega^1_X{}^{}_{|E}
\ \longrightarrow \ \Omega^1_E\ \longrightarrow \ 0 &\cr
&\vfl{}{\lambda_{|E}}&\cr
&0\ \longrightarrow \ T _E\otimes
L^{-j} \ \longrightarrow \ T_X{}^{}_{|E}\otimes L^{-j}\ \longrightarrow \
L^{-j-1}\ \longrightarrow \ 0 &\ .}$$
Since $j\ge 0$ we have $\mathop{\rm Hom}\nolimits(L,L^{-j-1})=\mathop{\rm Hom}\nolimits(\Omega^1_E,L^{-j-1})=\mathop{\rm Hom}\nolimits(L,T
_E\otimes L^{-j})=0$ by lemma \ref{W}. Thus $\lambda^{}_{|E}$ factors through
a map $\mu: \Omega^1_E\rightarrow T _E\otimes L^{-j}$; since $\lambda$ is
antisymmetric $\mu$ is antisymmetric, that is comes from an element of
$H^0(E,\hbox{\san \char3}^{2}T_E\otimes L^{-j})$.
\par\hskip 1truecm\relax Since $\lambda^{}_{|E}$ is non-zero, lemma \ref{W} implies $j\le 1$,
hence
$k\le r$. Moreover if $k=rj$, $\mathop{\rm det}\nolimits\lambda$ does not vanish, hence $\lambda$
and therefore $\lambda^{}_{|E}$ are isomorphisms; but this is impossible
because
$\lambda^{}_{|E}$ vanishes on the sub-bundle $L\i\Omega^1_X{}^{}_{|E}$. Thus
we have $k<rj$, and therefore $j=1$ and $k=r-1$.
\global\def\currenvir{subsection Going back to the local computation of (\ref{loc}), we observe
that the form $\theta:=i^*\tilde\theta$ is defined globally as a section
of $\Omega^1_E\otimes L$: it is the image of $\varphi\in
H^0(X,\Omega^2_X(\log E)(-E))$ by the residue map $\Omega^2_X(\log
E)(-E)\rightarrow \Omega^1_E\otimes {\cal O}_X(-E)^{}_{|E}$.
We now know that the $(2r)$\kern-1.5pt - form
$du\wedge\tilde \theta\wedge (d\tilde \theta)^{r-1}$ on $U$ does not vanish,
so the twisted $(2r-1)$\kern-1.5pt - form $\theta\wedge (d\theta)^{r-1}\in
H^0(E,K_E\otimes L^r)$ does not vanish. This means, by definition, that
$\theta$ is a {\it contact structure} on the Fano manifold $E$. The
classification of Fano contact manifolds is an interesting problem, with
important applications to Riemannian geometry (see for instance [L] or [B2]).
Here we have one more information, namely that the line bundle $L$ is {\it
very} ample; this implies that $E$ is isomorphic to one of the homogeneous
contact manifolds
${\bf P}{\cal O}_{\rm min}$ ([B1], cor. 1.8).
\global\def\currenvir{subsection It remains to show that the embedding of $E$ in $X$
is isomorphic, in some open
neighbourhood of $E$, to the embedding of the zero section in the line bundle
$L^{-1}
\rightarrow E$. By a criterion of Grauert [G], it is sufficient to prove that
the spaces
$H^1(E,T_E\otimes L^k)$ and $H^1(E,L^k)$ are zero for $k\ge 1$. The second
assertion follows from the Kodaira vanishing theorem, since $E$ is a Fano
manifold. The first one can be deduced (with some work) from the Bott
vanishing theorem, but we found more convenient to use the following easy
lemma:
\th Lemma
\enonce Let $Z$ be a compact complex manifold, $E$ a vector bundle on $X$
spanned by its global sections, $L$ an ample line bundle on $X$. Then
$H^p(Z,K_Z\otimes E\otimes\mathop{\rm det}\nolimits E\otimes L)=0$ for $p\ge 1$.
\endth
\par\hskip 0.5truecm\relax{\it Proof}: Put $P={\bf P}_Z(E)$, and let $p:P\rightarrow Z$ be the
canonical fibration. Choose a surjective map ${\cal
O}_Z^{N+1}\rightarrow E$. It induces an embedding $P\lhook\joinrel\mathrel{\longrightarrow} Z\times {\bf
P}^N$. For each $j\ge 1$ the line bundle $p^*L\otimes {\cal O}_P(j)$ is the
restriction to $P$ of $L\boxtimes {\cal O}_{{\bf P}^N}(j)$, and therefore
is ample. We have $K_P\cong p^*(K_Z\otimes\mathop{\rm det}\nolimits E)\otimes {\cal
O}_P(-r)$, with $r={\rm rk}(E)$. By the Kodaira vanishing theorem
we have $H^p(P, p^*(K_Z\otimes\mathop{\rm det}\nolimits E\otimes L)\otimes {\cal O}_P(1))=0$
for $p\ge 1$. Since $Rp_*(p^*M\otimes {\cal O}_P(1)))\cong M\otimes E$ for
any line bundle $M$ on $Z$, our assertion follows.\cqfd
\section{Local fundamental group}
\global\def\currenvir{subsection In view of (\ref{qt}) it seems hopeless to classify all isolated
symplectic singularities: there are too many quotient singularities, already
in dimension $4$. One way to get around this problem is to consider only
singularities with {\it trivial local fundamental group}. We briefly recall
the definition: if
$(V,{\rm o})$ is an isolated singularity, we can find a fundamental system
$(V_n)_{n\ge 1}$ of neighbourhoods of
${\rm o}$ such that $V_q$ is a deformation retract of $V_p$ for $q\ge p$;
the group $\pi _1(V_n)$, which is independant of $n$ and of the particular
fundamental system, is called the local fundamental group of $V$ at ${\rm
o}$ and denoted $\pi _1^{\rm o}(V)$ (for a canonical definition one should be
more careful about base points, but this is irrelevant here).
\par\hskip 1truecm\relax If $(V,{\rm o})$ is a quotient of an isolated singularity $(W,\omega)$ by
a finite group $G$ acting on $W$ with $\omega$ as only fixed point, we have
an exact sequence
$$0\rightarrow \pi _1^{\omega}(W) \longrightarrow \pi _1^{\rm
o}(V)\longrightarrow G\rightarrow 0$$
(in particular $\pi _1^{\rm o}(V)=G$ if $W$ is smooth of dimension $\ge 2$).
Conversely, to each surjective homomorphism of $\pi _1^{\rm o}(V)$ onto a
finite group
$G$ corresponds an isolated singularity $(W,\omega)$ with an action of $G$
fixing only $\omega$ such that $W/G\cong V$; if $(V, {\rm o})$ is a
symplectic singularity, so is $(W,\omega)$. Therefore a first step in a
possible classification is to study isolated symplectic singularities
with trivial local fundamental group. It turns out that the singularities
$(\overline{\cal O}_{\rm min},0)$ are of this type (with one exception):
\th Proposition
\enonce Let ${\goth g}$ be a simple complex Lie algebra, and ${\cal O}_{\rm
min}\i {\goth g}$ its minimal nilpotent orbit. Then
$\pi _1^0(\overline{\cal O}_{\rm min})=0$ except if ${\goth g}$ is
of type $C_r$ $(r\ge 1)$; in that case $\pi _1^0(\overline{\cal O}_{\rm
min})={\bf Z}/(2)$, and the corresponding double covering
of $\overline{\cal O}_{\rm min}$ is smooth.
\endth
\par\hskip 0.5truecm\relax{\it Proof}: Consider the resolution $f:L^{-1}
\rightarrow\overline{\cal O}_{\rm min}$ (\ref{nil}); denote by
$E\i L^{-1} $ the zero section. Let $D$ be a tubular neighbourhood of $E$ in
$L^{-1} $, and $D^*=D\mathrel{\hbox{\vrule height 3pt depth -2pt width 6pt}} E$. Since the homogeneous space ${\bf P}{\cal
O}_{\rm min}$ is simply-connected, the homotopy exact sequence of the
fibration $f:D^*\rightarrow {\bf P}{\cal O}_{\rm min}$ reads
$$H_2({\bf P}{\cal O}_{\rm min},{\bf Z})\qfl{\partial}{\bf Z}\longrightarrow
\pi _1(D^*)\rightarrow 0\ ,$$where the map $\partial$ corresponds to the
Chern class $c_1(L^{-1} )\in H^2({\bf P}{\cal O}_{\rm min},{\bf Z})$.
\par\hskip 1truecm\relax Put $\dim {\bf P}{\cal O}_{\rm min}=2r-1$. Since $K_{{\bf P}{\cal
O}_{\rm min}}=L^{-r}$, the class
$c_1(L)$ is primitive unless ${\bf P}{\cal O}_{\rm min}={\bf P}^{2r-1}$,
that is ${\goth g}$ is of type $C_r$. Assume this is not the case. The
homotopy exact sequence gives
$\pi _1(D^*)=0$; since the pull back of any neighbourhood of $0$ in
$\overline{\cal O}_{\rm min}$ contains a tubular neighbourhood of $E$, this
implies $\pi _1^0(\overline{\cal O}_{\rm min})=0$.
\par\hskip 1truecm\relax If ${\goth g}$ is of type
$C_r$ the same argument gives $\pi _1^0(\overline{\cal O}_{\rm min})={\bf
Z}/(2)$; actually $\overline{\cal O}_{\rm min}$ is the cone over
${\bf P}^{2r-1}$ embedded into ${\bf
P}^{(r+1)(2r-1)}$ by the Veronese embedding, and this cone is isomorphic to the
quotient of ${\bf C}^{2r}$ by the involution $v\mapsto -v$.\cqfd
\global\def\currenvir{subsection It would be interesting to find more examples of isolated
symplectic singularities with trivial local fundamental group, and also
examples with {\it infinite} local fundamental group.
\vskip2cm
\centerline{ REFERENCES} \vglue15pt\baselineskip12.8pt
\def\num#1{\smallskip \item{\hbox to\parindent{\enskip [#1]\hfill}}}
\parindent=1.3cm
\num{B1} A.\ {\pc BEAUVILLE}: {\sl Fano contact manifolds and nilpotent
orbits}. Comment.\ Math.\ Helv.\ {\bf 73}, 566--583 (1998).
\num{B2} A.\ {\pc BEAUVILLE}: {\sl Riemannian Holonomy and Algebraic Geometry}.
Preprint math.AG/9902110.
\num{C-M} D.\ {\pc COLLINGWOOD}, W.\ {\pc MC}{\pc GOVERN}: {\sl Nilpotent
orbits in semi-simple Lie algebras}. Van Nostrand Reinhold Co., New York
(1993).
\num{G} H.\ {\pc GRAUERT}: {\sl \"Uber Modifikationen und exzeptionelle
analytische Mengen}. Math.\ Ann.\ {\bf 146}, 331--368 (1962).
\num{K} Y.\ {\pc KIMURA}: {\sl On the hypersurfaces of Hermitian
symmetric spaces of compact type}. Osaka J.\ Math.\ {\bf 16},
97--119 (1979).
\num{L} C.\ {\pc LE}{\pc BRUN}: {\sl Fano manifolds, contact
structures, and quaternionic geometry}. Int.\ J.\ of Math. {\bf 6},
419--437 (1995).
\num{P} D.I.\ {\pc PANYUSHEV}: {\sl Rationality of singularities and the
Gorenstein properties of nilpotent orbits}. Functional\ Anal.\ Appl.\
{\bf 25}, 225--226 (1991).
\num{R} M.\ {\pc REID}: {\sl Canonical $3$\kern-1.5pt - folds}. Journ\'ees de G\'eometrie
Alg\'ebrique d'Angers (1979), 273--310;
Sijthoff \& Noordhoff (1980).
\num{W} J.\ {\pc WAHL}: {\sl A cohomological characterization of}
${\bf P}^{n}$. Invent.\ Math.\ {\bf 72}, 315--322 (1983).
\vskip1cm
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\hfill\vtop{\eightrm\hbox to 5cm{\hfill Arnaud {\pq BEAUVILLE}\hfill}
\hbox to 5cm{\hfill DMI -- \'Ecole Normale
Sup\'erieure\hfill} \hbox to 5cm{\hfill (UMR 8553 du CNRS)\hfill}
\hbox to 5cm{\hfill 45 rue d'Ulm\hfill}
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Rotten Chestnuts
Because Life Is Not A Bumper Sticker
The Chestnut Tree
The Worst Argument in the World
Perestroika and Puppies – UPDATE
Watching the Sad/Rabid Puppies endgame should be interesting. At least, it should be more accessible than #GamerGate, which… how did that end, anyway? I sense much butthurt in SJW bastions like Cracked.com, but I don't really know, because I don't play video games and couldn't possibly muster up enough giveadamn to start. But even though I don't read Sci-Fi, it wouldn't be the special kind of hell "gaming" is to get up to speed… and I dig the Puppies' author blogs.
Anyway… for the record, here's my two cents: It'll end about as well for the SJWs as perestroika did for the USSR.
"Social Justice" is just Marxism-Leninism, comrades. We're all clear on that, right? They've just swapped out one set of question-begging bullshit jargon for another. And so, because it's Marxism-Leninism, it suffers from the same problem all Hegelian nonsense does — it's an all-or-nothing proposition. You can't be a little bit SJW, any more than you can have a kinda-synthesis or sorta-capitalism*. Gorbachev forgot that, so when he tried to loosen stuff up just a teeny bit in the old Soviet Union, the whole thing came crashing down around his head.
Admit one lie, you see, and you've tacitly admitted to all the other lies. And when your whole system is built on lies….
And that's the best case scenario, mind you. If the Hugo Award TrueFans (or whatever the acronym is) are smart, they'll go Gorbachev — grudgingly hold their noses while loudly proclaiming that they're voting for the """"""best"""""" of a very, very sorry lot…. and then the Puppies go away, because there's no more shit to be stirred — all the drama queen antics cease. That means there will forever be a year with a "wrong" Hugo, and the Hugo will never again be the Unsullied Pure SJW Award for Excellence in SJW Propaganda, but so what? There's always the Nebulas or the Galactic Vagina Trophy or whatever. (If there's one thing liberals are great at, it's singing their own praises; they'll come up with something).
But I'm betting they won't, because again, Gorbachev's the best case scenario. Ol' Mikhail himself would do it again in a heartbeat — he's still alive and kicking, not buried two feet under the Siberian permafrost — but many of his kommissars got what was coming to them…. and, of course, the shining beacon of world socialism guttered and went out. SJWs have no identity of their own; if they're not shrieking about something, they wink out of existence like quarks. So they'll burn it down, No Award everything, because at least that way they can play the martyr role for ever and ever and ever and ever and ever….
*In case you don't recall, "-Leninsm" got added to "Marxism" because Lenin's successful revolution proved Marx wrong. Marx said only advanced capitalist countries could ever progress to Revolution, because History. But Russia was a piss-poor, backwards place, and China was even worse (and North Korea's worst). So Comrade Vladimir had to talk very, very, very fast to show that Marx was right after all (and that's why every vile dictator who still calls himself a commie has penned six thousand volumes of "theory," to retcon Marx's theory into their present, shitty reality).
UPDATE: Thanks to File 770 for the linkage. They're on the anti-Puppy side, it seems, so if you want the view from over there, this seems like a good place to start.
This entry was posted in Uncategorized on April 30, 2015 by Severian.
← A Bad Attitude Towards the Classics Called It →
3 thoughts on "Perestroika and Puppies – UPDATE"
Gary May 3, 2015 at 8:45 pm
*In case you don't recall, "-Leninsm" got added to "Marxism" because Lenin's successful revolution proved Marx wrong.
A few years ago there was a gala celebration on the anniversary of one of Marx's great works. I thought it was the 150th anniversary, but the dates don't line up for the Communist Manifesto (1848, with US publication in 1872) or Das Kapital (1867). Anyway, I believe the hoopla was about one of these two.
At the time I heard someone on talk radio reviewing one of the more egregious accolades, a long, glowing article in the NY Times Book Review, I believe. He quoted the piece stating something along the lines of: "Although most of Marx's predictions failed to materialize, his theory is still an important intellectual achievement whose relevance continues to this day."* To which the commentator asked the obvious question: What good is a theory whose predictions are mostly incorrect, and why would it be "relevant"?
Good question. And the answer is the Communist Manifesto is no good, and is much, much worse than useless since it inspired a plague of totalitarianism that killed at least 90 million people in the 20th century (according to The Black Book of Communism). But it is still relevant because the lefties love this stuff, not for its predictive value, but because it confirms their distorted worldview and allows them to think of their tantrum-like envy as righteous anger at injustice.
* See the section titled "Influence" in Wikipedia's article on the Communist Manifesto. It begins, "A number of 21st-century writers have commented on the Communist Manifesto's continuing relevance." and quotes "the English Marxist Chris Harman" as saying "There is still a compulsive quality to its prose as it provides insight after insight into the society in which we live, where it comes from and where its going to. …"
Severian May 4, 2015 at 1:27 pm
"There is still a compulsive quality to its prose as it provides insight after insight into the society in which we live, where it comes from and where its going to. …"
Well, there is that, I suppose. Much like witchcraft trial transcripts tell us a lot about the society in which they lived. They tell us nothing about witchcraft — because, you know, there's no such thing — but quite a bit about the anxieties of the witchfinders. So, too, with Marx — the world doesn't really work like that, comrades, but it's fascinating to see that you think it does.
And that's the fundamental problem with immanentizing the eschaton. The Social Justice Warriors fail to convince on so many grounds, but they all come back to: What's the point? What end state is to be achieved if everyone plays Depression Quest instead of World of Warcraft, and all sci-fi novels are about disabled transgender were-seals of color being inclusive?
Is that world better than this one? In what specific ways? And what will you yourself do, O fearsome Social Justice Warrior, when the Revolution comes and your whole reason for existence is gone?
Marx tried to describe the classless society a few times, if I recall. A very few, because they were always hilarious. Something about how the New Soviet Man would tend his garden in the morning, work in the factory in the afternoon, and critique opera at night. But whatever — Come the Revolution, those kids who were mean to me in high school are gonna get it…..
Pingback: A Fistful of Puppies 5/3 | File 770
The Stakeholder State
Arguing with God
The Pleasures of Ketman
Pickle Rick on The Stakeholder State
Pickle Rick on Arguing with God
Publius on Arguing with God
MBlanc46 on Arguing with God
WOPR on Arguing with God
"H8"
39.2% of Statistics Are Made Up
Basic Life Lessons
Caesarism
Chestnut of the Week
D3: The Dim Devil's Dictionary
Deeper Thoughts / Think Pieces
Explaining Academia
Gleichschaltung Watch
Golden Chestnuts
Know Your History
Know Your Leftist
Latest Wikipedia Talk Page Mess
Leftist Unreality
Life is Not a Bumper Sticker
Non-Intersectional
Quinn's First Law
Settled Science Update
Stink Bomb
Stop an Echo
The Fundamental Paradox of Internet Liberalism
The Grasshopper Lies Heavy
Things Dead White Guys Said
Things I Wish Conservatives Understood
Things I Wish Liberals Understood
Thinking like a Liberal
This Post is "Racist"
Weimar America
Blog of the Nightfly
Kirk Forlatt
Liberae Sunt Nostrae Cogitatiores
Yard Sale of the Mind
Email (Severian)
Should We do a Rotten Chestnuts Friday Book Club?
Yes 105 ( 93.75 % )
No 7 ( 6.25 % )
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{"url":"https:\/\/physics.stackexchange.com\/questions\/177867\/is-sound-a-nambu-goldstone-mode","text":"# Is sound a Nambu-Goldstone mode?\n\nThe usual sound exists in solids, liquids, and gases, as a long-wavelength excitation with linear dispersion. Can its presence be attributed to the spontaneous breaking of some symmetry? In other words, is it a Goldstone mode of some symmetry?\n\n\u2022 You can view a massless klein gordon field as a goldstone boson for a spontaneously broken shift symmetry (since the vev is not invariant under shifts of the value of phi). I'm guessing it's the same for sound waves, the background density breaks the shift symmetry andsoundwaves could be viewed as the associated goldstone mode \u2013\u00a0Andrew Apr 22 '15 at 22:10\n\nYes sound is a goldstone mode. Consider, for example, an ideal gas with particles at positions $\\mathbf{x}_i$. There is a symmetry where we can displace each particle by some displacement $\\mathbf{u}$. Of course this symmetry breaks spontaneously. By definition, we only observe $\\mathbf{u}=\\mathbf{0}$.\n\nThe goldstone modes corresponding to this symmetry are modes where $\\mathbf{u}$ is nonzero and varies spatially with some wavevector $\\mathbf{k}$. That is, each particle gets displaced according to $\\mathbf{x}_i \\to \\mathbf{x}_i + \\mathbf{u} \\cos(\\mathbf{k} \\cdot \\mathbf{x}_i)$. This displacment will cause a sinusoidal variation in density, and therefore sinusoidal varation in pressure, which is what sound is.\n\nNotice that the energy of the mode goes to zero as $\\mathbf{k}$ goes to zero, since the $\\mathbf{k}=\\mathbf{0}$ limit is just a uniform shift, which requires zero energy. That is the idea behind goldstone modes. This same logic applies in liquids and solids as well.\n\n\u2022 Thanks to Andrew and NowIGetToLearnWhatAHeadIs but I still am not convinced (read: do not understand). Both a liquid and a gas have a continuous shift symmetry, while a solid has a discrete shift symmetry. In particular, this translational symmetry is not broken in an ideal gas, contrary to what seems to be implied in the answer. It is obvious that the translation of all particles in the system, as explained in the answer is a zero-energy excitation. But it is not obvious how the system looks without this symmetry, or how this symmetry is spontaneously broken. \u2013\u00a0jarm Apr 23 '15 at 8:01\n\u2022 I think you are saying that you do see how sound in solids is a goldstone mode, because there is a continuous symmetry that breaks and gives you a discrete symmetry. Now when I was talking about liquids and gases, I was referring to a particle based model. This model has a continuous symmetry that is broken, and the state with a broken symmetry has no remaining symmetry because particles in a liquid and gas are disordered. \u2013\u00a0Brian Moths Apr 23 '15 at 19:28\n\u2022 Now you were probably looking at it from a field-theoretic point of view, where the fluid is represented by density, pressure, and velocity fields. In that case the ground state does have translational symmetry (zero velocity, uniform density and pressure), so there does not seem to be a broken symmetry, and so you would be led to say that sound is not a goldstone mode. That is an interesting point and I didn't think about that. \u2013\u00a0Brian Moths Apr 23 '15 at 19:31\n\nIt depends on what sound you are talking about. Yes, in crystalline solids, sound is nothing but propagating phonons, in which case it is the Goldstone modes corresponding to broken translational symmetry.\n\nIn fluids, sound is a pressure-density wave and there it is not a Goldstone mode. It instead arises because of conservation laws governing the conservation of momentum and of mass (non-relativistically and in the absence of reactions) along with the presence of inertia.","date":"2021-05-06 07:36:21","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\": 0.810151219367981, \"perplexity\": 282.4336680300202}, \"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-2021-21\/segments\/1620243988741.20\/warc\/CC-MAIN-20210506053729-20210506083729-00251.warc.gz\"}"}
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Q: XSLT differing column style global I have the following problem:
I have a xml file and created a xslt to display the contents nicely. The data is a table with three column. Currently I define the style globally:
<style> table td {text-align:right; padding-right:10px; }</style>
Now for styleguide reasons I need to have a different style for each row. E.g. text-align left for column 1 and text-align right for column2. I could add the style to each td but this would make maintenance cumbersome and prone for bugs.
I found the colgroup but I am not sure how to define the alignment etc. So far I understood that I need to add colgroup{} to <style></style> and inside the {} have several col{} "children"; one for each column.
<style> table colgroup{col{align:right}col{align:right }col{align:left }} </style>
I get no errors but there is no effect on my displayed xml file in the browser.
Is it even possible / allowed?:
link
Quite old so I am not sure if it still applies.
PS: I am really new to xml and xslt. So there might be an easy solution but I have not found it so far.
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De Sierra de Baoruco (ook gespeld als Sierra de Bahoruco) is een bergketen in het zuiden van de Dominicaanse Republiek. De keten is vooral bekend als vindplaats van het zeldzame mineraal larimar en is ook een beschermd natuurgebied UICN-categorie II, nationaal park, 1092 km² groot.
Ligging
De Sierra de Baoruco ligt voor een deel in de gelijknamige provincie Baoruco. Vanaf de grens is de keten 70 kilometer lang, tot aan de Caraïbische Zee. In Haïti gaat ze over in het Massif de la Selle. De bergketen is 40 kilometer breed.
Geologie
De Sierra de Baoruco bestaat uit een kalksteenplateau dat door geologische krachten naar het noorden omvergeduwd is. Daarom heeft het gebergte in het noorden scherpe randen, die boven de Hoya de Enriquillo uitsteken. Op veel plaatsen zijn er afzettingen van zout en gips. Deze plaatsen heten Salinas Barahona. In het zuiden zijn er glooiende hellingen die afdalen naar het schiereiland Barahona. Er zijn drie bergen hoger die hoger zijn dan 2000 meter.
In het gebergte bevindt zich een zoutmeer, Laguna de Oviedo. In een van de hoogste delen bevindt zich de Hoyo de Aceitillar, een overblijfsel van een oud meer.
Larimar
Het gebied is een van de weinige vindplaatsen van het zeldzame mineraal larimar. Dit mineraal ontstaat uit het fluviale sediment van de rivier Baoruco.
Het voorkomen van het mineraal in het gebied was in 1916 al bekend aan de priester Miguel Domingo Fuertes Lorén van Barahona. Op 22 november van dat jaar vroeg hij een concessie aan het Ministerie van Mijnbouw om een blauwachtig gesteente te delven, dat hij daar gevonden had. Hij kreeg echter geen gehoor.
In 1974 werd het mineraal opnieuw ontdekt door Norman Rilling, een vrijwilliger van het Vredeskorps. Hij gaf het de naam "Larimar". Dit is een combinatie van de voornaam van zijn dochter (Larissa) en het Spaanse woord voor de zee (mar), vanwege de blauwe kleur.
Verder stroomopwaarts van de rivier Baoruco vond men nog meer van dit blauwe gesteente op een plaats die Los Chupaderos wordt genoemd. Dit is nog steeds de belangrijkste vindplaats van het mineraal.
Natuur
De regenval bedraagt meer dan 600 millimeter per jaar. De hellingen zijn begroeid met pijnbomen. In het oostelijke gedeelte bevinden zich wat kleine stukken nevelwoud.
Toppen
Er zijn drie toppen die hoger zijn dan 2000 meter. De hoogste is de Loma del Toro (2367 meter). Verder zijn er twee naamloze bergen, van 2275 en 2085 meter hoog.
Gebergte in de Dominicaanse Republiek
Nationaal park van de Dominicaanse Republiek
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Q: Can an EAGLLayer have 'selective' retained backing? I'm making a painting program for iOS using openGL ES 2.0. In my program, there's an EAGLLayer with a retained backing. Each drawing operation 'sticks to' the layer, thus building up the user's painting.
Now, however, I need some graphics to appear on the screen without getting added to the painting--like a cursor that can be positioned by touches and effects the style of drawing but shouldn't actually become part of the drawing.
Can I do this by adding a second renderbuffer for the cursor in the same EAGLLayer or would it be better to have another UIView on top of the painting UIVIew?
A: For my purposes, there was very little down-side to having a UIView (cursor) floating on top of my EAGLLayer. Added the UIView as a sub-view of my main view controller's view, not of the EAGLLayer and made sure that it was on top of the EAGLLayer. Not sure why I thought this would be tricky, in retrospect!
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'Immigration Nation' Filmmakers: 'The System Chews Up People'
By Dave Davies
Published August 17, 2020 at 12:46 PM CDT
This is FRESH AIR. I'm Dave Davies in today for Terry Gross.
(SOUNDBITE OF DOCUMENTARY, "IMMIGRATION NATION")
BRIAN: Policia. We're not going to yell out in the hallway through a closed door, ma'am. That's not how we do business. Please open the door so I can talk to you.
DAVIES: That's the sound of an immigration raid getting underway in the new six-part documentary series "Immigration Nation" now streaming on Netflix. Our guests today are the series' co-directors and co-executive producers, Christina Clusiau and Shaul Schwarz. They spent three years filming immigration enforcement actions and their effects after President Trump took office, and they had remarkable access to agents of Immigration and Customs Enforcement, or ICE. As you'll hear, the filmmakers' relationship with ICE deteriorated sharply after the agency saw rough drafts of the planned episodes.
The series follows ICE agents, their supervisors and spokesmen, activists, immigrants and their families and even a smuggler who guides migrants across the U.S. border for hefty fees. The stories are compelling, and they raise questions about the impact of the Trump administration's crackdown on immigration. Shaul Schwarz and Cristina Clusiau have collaborated on several previous documentaries, including the Emmy award-winning films "A Year In Space" and "Trophy." Schwarz spent time around the U.S.-Mexican border for his 2013 film "Narco Cultura," which premiered at the Sundance Festival in 2013. Schwarz and Clusiau joined me via Skype from Brooklyn.
Well, welcome to FRESH AIR, both of you. And congratulations on the documentary. So let's begin with the immigration arrest that we just heard a bit of that opens the series. Do you want to just explain what's happening here a bit, and then we'll listen and talk a bit more about how they get in?
SHAUL SCHWARZ: Well, we are in New York City with Fugitive Operations. That's a part of ICE that basically gets what they refer to as targets, an alien - I'm using their terminology - an alien that's committed a crime. And they are looking to, basically, make an arrest to that individual. In doing so, ICE usually does some pre-work and some kind of detective work to know where the individual's at or what's the best way to approach it. And, usually, the individuals on these task force start very early in the morning, and the scene you are seeing is when they're knocking on a door, I'd say, just after 6:00 a.m. in the Bronx.
DAVIES: Right. And we'll just note that there are quite a number of ICE officers sort of lined up in the hallway. So let's hear what happens. This is briefly edited for length. Let's listen.
(SOUNDBITE OF DOCUMENTARY "IMMIGRATION NATION")
(SOUNDBITE OF DOOR OPENING)
BRIAN: How are you doing? Sorry to bother you. We need to come in and talk to you. We don't all have to come in, just a couple of us, but I want to show you some pictures. Somebody we're looking for has been using this address.
ANNA: Oh, OK.
BRIAN: All right.
ANNA: You want to come in?
BRIAN: Yeah, if you don't mind. What's your name, ma'am?
ANNA: Anna (ph).
BRIAN: Anna, OK, do you mind if I come in? How many people are in here?
ANNA: Three adults and one baby.
UNIDENTIFIED AGENT #1: She's in the bathroom.
ANNA: No, no, they're not telling me nothing.
BRIAN: If you don't mind, can you just go in the living room? I'll tell everything that's going on.
ANNA: (Speaking Spanish).
BRIAN: Dave (ph), I'm going to explain to the daughter what's going on.
He has a criminal warrant. He was deported before. It's actually a federal offense to come back in the country, so I have a warrant for his arrest.
ANNA: Can I see the warrant?
BRIAN: I'm not obligated to show it to anybody. I have a warrant, trust me. I'm not in here without it, all right? I have a warrant for his arrest. I've got to take him to the Southern District of New York. He's going to be remanded today.
ANNA: OK, but I need - can I see any paperwork?
BRIAN: Yeah, I'll give you a card.
ANNA: No, I mean, like, paperwork saying that you guys have...
BRIAN: Sure.
ANNA: ...Permission to come in here or something.
BRIAN: Oh, no, I have a warrant for him, and I know he lives here. So that's why I'm in here. Plus, you opened the door and let me in.
DAVIES: And that's from the documentary "Immigration Nation," which is co-directed by our guests Christina Clusiau and Shaul Schwarz. You know, I've heard immigration attorneys advise people who lack legal status that if ICE officers show up at your door, you're not obliged to open the door; you're not obliged to let them in, which some might find a little strange, given that they're federal officials. Talk a little bit about what we're hearing here and how ICE officers manage the rules to get into an apartment in a circumstance like this.
CHRISTINA CLUSIAU: That is correct. Usually, if it's an administrative warrant - which a number of these warrants are with fugitive ops teams - they are not allowed to just enter a property unless they are given permission. So what generally happens is they knock on the door - they call it a knock-and-talk - and they convince the individual inside - if they believe that the target that they're going after is in the apartment or is using the address, they use all sorts of tactics, as you hear, to get access to the apartment. And then, at that point, they can make an arrest and detain the individual that they were targeting. And so in this situation, because they only have an administrative warrant, they need the individual to open the door, and if not, they usually have to leave.
DAVIES: Right. So what begins as, open the door ma'am so we can talk, ends with, I don't have to show you the warrant.
SCHWARZ: Correct. It's a cat and mouse, if you will. For the ICE agents who work in fugitive operations, there's a lot of prep work that goes in. They want to get in that door. They're there. They've woken up early. They're keen to get their arrests.
This is also during an operation - you know, when Trump came into power, there was this push to install fear, if you will, to know that there is activities. New York City ICE was upset. They didn't see cooperation from the local police, and they wanted to make a point that if you're not going to play along, we're going to get out there and we're going to take people, you know - specifically they go after what's called targets. Those are the people who both have an immigration offense and some kind of other criminal act that could be small or big.
But there's also what's called a collateral arrest, when you encounter people that are at that address that are simply here with an immigration offense. So this was part of an operation that was called Keep Safe, and it was kind of a pushback to the city to show that they will be aggressive and they will get out there.
DAVIES: You know, they begin when they knock on the door by saying policia - police. Are they police?
SCHWARZ: They are police. But that is a tactic they are literally taught. The idea is, like, if they say ICE, the door is not opening, as far as they're concerned.
CLUSIAU: And just to add to that, you know, I think what we started to see during this period of time is that there was much more awareness of ICE officers coming to doors early in the morning, and so there was also a pushback from immigration advocates and immigration lawyers to know your rights, to state to individuals that you're not obliged to open the door if somebody comes to your door and says that they're immigration.
And so ICE had to get creative with their tactics. And so they're trained to say police. They're trained to convince them to open the door, just as Shaul said, to say that, you know, this is - we're looking for somebody that's using this address. And, generally, we saw most people comply with that, but others don't. And so there was always a pushback - is that they would go to a number of doors in the morning, and, you know, they would maybe be able to enter into 1 out of 5 apartments or 1 out of 6. And as time went on, through this period of time, we saw that getting increasingly more difficult for them.
DAVIES: And you noted that there would be a target person for the arrest. But then, if there are other people there who don't have legal status, they would arrest them, too, typically call them collaterals, and they'd like to get the numbers up. There's a moment here where we hear the officer involved in the raid that we heard - I think his name is Brian (ph) - talking about how this whole collateral thing didn't sit so well with him. Let's listen.
BRIAN: I don't really - I don't do collaterals. I just don't think it's right. Like, if I get somebody that's not cooperative, it's a different story. But if you let me into your house and talk to me, I'm not going to roll your fingerprints and arrest you just because you're here illegally. I know it's my job, but I've - you know, I've got guys that are aggravated felons that I'd like to catch. I don't care about the guy that's minding his own business and cooperating with me. Just for the sake of numbers, anyway.
DAVIES: Interesting, isn't it? In "Immigration Nation," I think one of the most fascinating things about the six-part documentary is how many ICE agents you get in candid moments, expressing opinions. I want to play a couple of them here, besides those. One is a couple of officers - and this is in Charlotte, N.C. - where ICE has gone on an aggressive enforcement campaign after a new local sheriff was elected who terminated a program in which people arrested locally would be routinely turned over to immigration authorities. So ICE decided to react to that by going out and arresting people into the community, which created quite a reaction. And what we're going to hear here is a couple of ICE agents returning from one of these actions where they've arrested several immigrants.
UNIDENTIFIED AGENT #2: My last stop, one of the guys, like - he goes, what are you doing? I said, you're under arrest. What am I under arrest for? I said, you're here illegally. He goes, you can't arrest us for being here illegally anymore.
UNIDENTIFIED AGENT #3: (Laughter).
UNIDENTIFIED AGENT #2: I said, really? Watch this.
UNIDENTIFIED AGENT #3: You can't arrest us for being here illegally anymore. They told me at a press conference that this is a sanctuary place, and you're not allowed to arrest me anymore. They did? They lied to you. (Laughter).
DAVIES: I want to play one more clip. Then we'll talk. This is another officer, Mike (ph), who is working along the U.S.-Mexican border, driving along in a pickup and sharing his view of this job. Let's listen.
MIKE: I can't tell you how exhausting it is day in and day out to be putting cuffs on people that - you honestly can't blame one iota for what they did. They didn't kill their wife. They didn't set off a bomb somewhere. They didn't rob a bank. Doing exactly what I would do in their situation, which is to try to come here. I don't like that about my career, but I still think it's important to do it. And I put my personal feelings aside, which - yeah, maybe that's what every Nazi said, right? That I put my feelings aside. But I actually believe in the cause of trying to enforce some sort of sovereignty over our borders. And no one's figured out a better way to do it yet.
DAVIES: And that's from the documentary "Immigration Nation," a six-part documentary series now streaming on Netflix, co-directed by our guests, Shaul Schwartz, and Christina Clusiau.
This is a remarkable look inside of ICE. Did most officers have some ambivalence about arresting and deporting these people, who - many of whom they had to see as pretty desperate about seeking to better their lives?
SCHWARZ: I'd say some. I think some did. I think perhaps the majority did not or didn't show it quite - but, you know, ICE is a big agency. And there's definitely all kind of shades of officers. There was definitely overall an emboldment (ph) during the Trump era that kind of went from the top down of this proud to do the job and to push back and to show. So I think we show that in the show of the number game and the people kind of really feeling - you know, I remember when we started. They said, you know, now we're supported. The gloves are off. And there was - a lot of people felt excited about - that they get to do their job in their language. But, you know, there are certainly officers that were different and questioned it. I remember we spent a lot of officer - a lot of time with an officer called Judy (ph) in New York. And I think she questioned it from the beginning. Her tactics and her showing discretion to how to do her job was a less offensive way and really trying to minimize this situation. So I think we saw all shades of reactions.
DAVIES: Let me reintroduce you. We're going to take a little break here. Shaul Schwarz and Cristina Clusiau are co-directors of the six-part documentary series "Immigration Nation," now available for streaming on Netflix. We'll be right back after this break. This is FRESH AIR.
(SOUNDBITE OF SLOWBERN'S "WHEN WAR WAS KING")
DAVIES: This is FRESH AIR. And my guests are Shaul Schwarz and Cristina Clusiau, co-directors and co-producers of the new six-part documentary series "Immigration Nation," now available for streaming on Netflix.
You know, I have to ask you how you got this incredible access to ICE, which is not known for opening its doors to media.
SCHWARZ: Yeah. We had a relationship with ICE from prior work on working the Mexican-American drug war. And I had worked with Homeland Security investigation, which is a part of ICE, back almost a decade ago on some of the drug work they do. And during that, I met a ICE spokesman which I stayed an acquaintance or became, really, a friend of. And through the years, I would ask him during the Obama times once or twice, if - in very uncasual ways - but if we could also do an immigration story. And the general feel I got at that time is, you know, no one's really complaining. Let's - no need for this.
And, you know, immigration was - has always been a hot issue, but it wasn't what it became under the Trump era. And as Trump was campaigning and shortly after he had won the election, me and Christina thought, we wonder if ICE position would change? We certainly expected them to come under a lot of heat during this administration. And we thought this might be a time where they would want to trust someone to go in there. And we pitched them with the idea. We said, listen. You're going to come under a lot of heat. Most people don't understand the complexity of the issue and what ICE actually does as a whole. And we would love to do a portrait of the agency under this administration and see what - the position your officers are in and see how that whole immigration system looks in this time. And that's kind of how it started.
DAVIES: So you had a contract with them - right? - which guaranteed you independence. But it gave them the right to review the material once you were prepared to air it and object on certain limited, specific grounds. What could they object to?
CLUSIAU: Correct. So we had what was called a multimedia agreement. And it's not - it's something that all production companies have if you are working with a government agency such as DHS. And so within that contract, it said that ICE had the right to review the cuts for factual inaccuracies, law enforcement sensitive information - so tactics that they use that are not publicly available or publicly known - and any sort of privacy Fourth Amendment rights.
DAVIES: And when you showed them some early drafts of the episodes, what happened?
CLUSIAU: So that's when, really, the tone changed. We had a really good relationship for 2 1/2 years. We had the ability to work within the system all over the country. And when we started to show them cuts, they clearly determined that this is not favorable to them and that this is not something that they liked. And so they started to push back on other things, not only the three things that we mentioned that were in the contract, but also they tried to editorialize some of the content.
SCHWARZ: Yeah. They - eventually, for months, we would be back and forth with the spokesman. They would come up with, to say the least, bizarre legal ideas of why certain things should be deleted. And they were very - the pattern was very clear when it was unfavorable. And when they had anything, they would just go at the opportunity. They claimed, really, at times, quite ridiculous claims. You know, to give a quick example, there was a machine that takes your fingerprints when officers are out in the field. They saw a scene that officers do it and take a couple of collateral arrests and told us that we should take out the scene because that is law enforcement sensitive. Well, we Googled it. And we saw that it was all over the place.
DAVIES: All over the place as in, like, on their own website, right?
SCHWARZ: Yeah. So then, at first, we were like, this picture is all over media. Then we saw that the picture was actually distributed by ICE spokesmen, who are the ones telling us that this is law enforcement sensitive. It's really unfortunate. I think we are grateful to the boots on the ground kind of men and women of ICE for being super real, for letting us be flies on the wall, for being open, for being honest, for being complex. And that's the show we wanted to put forward. And I think if, you know - the requests that they made that did make sense, some of them were not in the contract. They said, you know, please take the last names of our officers and delete those. And we are like, of course. That seems like a request that is very fair. But we just wish it didn't kind of become what it had. But it was also very telling about this administration.
DAVIES: You know, the Trump administration's policy of separating families at the border - or zero tolerance - is portrayed in the film. There's one case, a man named Bernardo (ph), who came from Guatemala with his son, Emilio (ph). And they were separated. And you filmed him at a detention center, I believe, in El Paso, while his son was allowed to go and live with Bernardo's sister-in-law. Was that in Houston? I'm trying to remember.
SCHWARZ: Yes.
DAVIES: Right. So I want to hear a moment here where Bernardo was talking to you at the detention center utterly distraught, in tears. We'll listen to just a bit because it's in Spanish. But I thought we - I just wanted to get a sense of the emotional impact of some of these scenes. Let's listen to this man who's been separated from his son.
BERNADO: (Speaking Spanish).
DAVIES: Essentially, he's saying there, I haven't seen my son in three months. And we don't know what's going to happen. You know, it gradually dawned on the media and the public what was happening with this child separation, but not immediately because it was implemented before it was publicly announced. You were following, you know, immigration enforcement through this period. Did you see this unfold in real time?
SCHWARZ: Yeah. Pretty much. We - when the story broke, we were inside the El Paso detention center. So as we kind of tiptoed to get this story - and I remember being there one day and asking one of the deportation officers if he knows if there's any separated family of - fathers. We were in a male cell here. And he went into the cell. Sam (ph) is his name. And he kind of really nonchalantly asked, hey, is there - you know, how many of you have been separated from your kids? And out of 20 in that room, 18 raised their hand. And I do remember me and Christina kind of being like, ho. And that's where we met Bernardo and some of the other fathers we portray in the show.
DAVIES: All right. Let me reintroduce you. And we'll take another break here. Christina Clusiau and Shaul Schwarz are co-directors and co-producers of the six-part documentary series "Immigration Nation" - now available for streaming on Netflix. They'll talk more about what they observed of immigration enforcement after we take a break. I'm Dave Davies. And this is FRESH AIR.
(SOUNDBITE SERGIO AND ODAIR ASSAD'S "SAGA DOS MIGRANTES: SAUDADES")
DAVIES: This is FRESH AIR. I'm Dave Davies, in for Terry Gross, who's off this week. My guests are Shaul Schwarz and Christina Clusiau, co-directors and co-producers of the six-part documentary series "Immigration Nation," which is now available for streaming on Netflix. They spent three years filming immigration enforcement and its effects with remarkable inside access to immigration officers as they arrested and detained undocumented immigrants. When we left off, we'd heard about a man named Bernardo who'd come to the U.S. from Guatemala and was arrested and detained and separated from his teenage son.
What's really remarkable about this, I think, is that you not only show Bernardo, who's at the detention center in El Paso, but you find Emilio, his son, who is at his aunt's house in Houston, and you really cover both ends of the story. There are times when Emilio and his father Bernardo are talking. We hear both ends of the conversation. We hear Emilio, the son, talking to his mother in Guatemala. And this is pretty remarkable stuff. How did you track this down and manage to cover both sides of this drama?
CLUSIAU: Yeah, because we met Bernardo initially, and he, you know, wanted to tell his story, wanted to share what he was going through. He also told us that it was very important for us to not just tell his story from in detention but to tell the story of his son, of his sister-in-law and his wife back in Guatemala.
And so we kind of felt that we started to understand that when you detain an individual within ICE detention, you're not just detaining that person, that there is a circular effect that happens to all members of their family. So whether it be Rebecca, who is in Guatemala, who is waiting for Bernardo to make sure that he is safe, whether there is Emilio, who felt at the time that he was the reason that they were separated, you know, this, like, trauma and blame, and you start to see the effect of the whole cycle, that it's just not the person in detention, but it's everybody else, the entire family.
And so we started to go to - we went to Houston. We talked to Emilio. We talked to Irene (ph), his - the sister-in-law. And then we also went - we felt it was really important to show the life in Guatemala and what was happening there. And so we went to see Rebecca and the other two kids to understand what they were going through because of this separation and this detention of Bernardo.
DAVIES: You know, we should also note that Bernardo was seeking asylum, right? And he was presented with a choice, right? You can go back to Guatemala, be deported, you - we'll send you and Emilio back to Guatemala if you will give up your asylum claim, right? So there was an out for him if he just gave up his case, right?
CLUSIAU: Correct. And I think the trick was - is that a lot of the tactics that we saw and that we talked about earlier is this idea to make life so unbearable that you will just give up. And so we saw it, for example, with Bernardo. We saw it with another character, Berta. We saw it with another character, Deborah, that - you put the paperwork in administrative processing. You make it terrible for them to stay here, that they just want to give up, even though they are trying to respect the laws and trying to do everything in their power to do it the right way, to file for asylum, to ask for protection, that our laws allow us to do. But this administration wants to make you give up.
DAVIES: You know, the case of Berta is interesting. She came with her granddaughter - right? - who a local gang wanted to take her for, quote-unquote, "marriage." And so they left, came and applied for asylum. And then Berta, while - you know, presented herself as the law provides and, while waiting for a resolution of the case, is held in a detention center for 17 months. You know, the Trump administration has said - we've heard the president say, look; this request for asylum has become a gambit that, you know, economic migrants play. They all come with a script - oh, you know, in my village, I face danger if I go back, and therefore I'm seeking asylum.
In your experience talking to the many, many immigrants that you spoke to, did you get any sense that anyone was trying to kind of game the system and misrepresent the dangers that they faced?
SCHWARZ: Yes, there were some. I think there are some people who use that as a loophole. With that said, there's many who don't, who you get a sense that their case is super real. There's many who had fear that didn't exactly qualify, wasn't documented well enough. But what we would see overwhelmingly, especially as time kind of pushed forward and the remain in Mexico policy, so to speak, came is that there wasn't a real attempt to weed out those who are gaming the system and those who are real; there was an attempt to send a message that you are not wanted.
In Berta's case, like we said, she did everything correctly. Her case was very, very strong. There was great documentation of past issues. Here's a lady that could qualify from a bond from ICE. They get all - but they choose to hold her for 17 months, and the reason was sending a message. If you come here, this is what - this is pre- (ph) making immigrants wait in Mexico.
So, yes, I do think there was a loophole in asylum that was sometimes there, and some people took advantage, but I think the correction, so to speak, was not a real attempt to correct. And we've seen other reports of people whose job it is in USCIS to interview these people and - saying that the system was constantly putting pressure on them to find anything to toss them. So, you know, we have to kind of be careful about the lines here.
DAVIES: You know, the last episode of this series takes us to the border where Customs and Border Protection, you know, seeks to stop people who are coming across the border, and there are also officials of ICE and its - what? - I guess the investigation and security division. Is that what it's called?
SCHWARZ: Homeland...
CLUSIAU: Homeland Security Investigations.
DAVIES: Right. You have a little anecdote of one agent, who is also a paramedic, who assists people who are dying, starving and dehydrating in the desert. He gets a call on the radio that there's a guy out on a road who's in pretty bad shape. He finds him. And he's a young Guatemalan man who is lost. And the agent could see from the truck that he has little spines and thorns and barbs in his lips, which tells him he was so desperate he was eating the cactus.
CLUSIAU: Yeah. I mean, this unit is an elite Border Patrol unit called BORSTAR - border, trauma...
SCHWARZ: Search and rescue.
CLUSIAU: ...Search and rescue. And their role is complex because they're tasked with, one, helping those that they find lost in the desert and, two, then detaining them. And so there's this complexity that happens. And I think when the officer approaches him on the side of the road, he had already - he had seen this before. This wasn't the first time that he found a migrant that had crossed and spent 15 days in the desert and had to eat cactuses and had no water. And so their job is to help them. But then at the same time, the flip side of that is because they are still a law enforcement agency, that individual is detained.
DAVIES: He literally picks the barbs out of his lips and tongue before he arrests him.
CLUSIAU: Exactly.
SCHWARZ: It's an amazing moment where, again, if you look at it in the cat and mouse, the cat gets a mouse, helps him for a second. But everybody - and the immigrant is thankful, but it's just the sheer information that we saw kind of unfold of the immigrant saying that he was left to die and someone else has died and that he's walked 15 days and how dehydrated he is. And even - I mean, this was near Tulsa, and he asks him if he's next to LA. Just the confusion, and it was - to us and to our camera person - Erik's filming there - it was so haunting to see. But I think for the agents on the ground, this is the reality. This is something that happens day to day. And there is this kind of feeling we got there and elsewhere filming the show that they're almost desensitized in a way to that.
And even as he helps him - right after the young Guatemalan man is taken by the ambulance, he talks to one of his colleagues and say how fun this area is and how they kind of chase people. And there's a duality of this chase that leads people deeper into the desert where they might die - and at the same time, seeing this agent being able to change his hat on and be very kind and picking out the thorns and helping and perhaps saving lives.
DAVIES: We're going to take another break here, so let me reintroduce you. Shaul Shwarz and Christina Clusiau are co-directors of the six-part documentary series "Immigration Nation," now available for streaming on Netflix. We'll be right back after a break. This is FRESH AIR.
DAVIES: This is FRESH AIR, and my guests are Christina Clusiau and Shaul Schwarz, co-directors and co-producers of the new six-part documentary series "Immigration Nation," now available for streaming on Netflix.
We meet a guy named Caesar (ph) - or Cesar, I guess, who's an interesting example of an undocumented immigrant. You want to just explain his situation?
SCHWARZ: Yeah. He is - well, he was brought here when he was 2 years old. He eventually becomes legal, has a green card, and he joins the U.S. Marines. Well, Cesar commits a crime after being in the Marines of possession of marijuana - a large quantity, by the way - but signs a plea deal, does not spend a day in jail and continues his life. Twelve years later, he takes a vacation to Costa Rica. And on the way back, he is arrested, turned over to ICE and deported. Cesar is one of hundreds, possibly thousands, of deported veterans - people who have served in our armed forces and have been deported after for committing a certain crime. And unlike most of these veterans, Cesar chose to come back home and live as a fugitive. He believes that he's an American. He did not want to stay in Mexico. And we met him after he had been in hiding for over six years.
DAVIES: Right. And we'll listen to a moment from the documentary. And this is where - he has gone to try and visit the newly elected Governor of Arizona, Michelle Lujan Grisham, who, as a congressperson, had expressed support for veterans in this position, who had been deported. And he's going to see the governor because she could grant a pardon to him for the marijuana conviction that led to him being deported, which presumably would allow him to regain status and live legally in the United States. And what we'll hear here is where an assistant to the governor has come out, a young woman, and explained that the governor is too busy to meet with him now. And so Cesar is standing in this reception area, there are a lot of people around, and he pleads with this young assistant to help him.
CESAR LOPEZ: I'm tired. And I'm tired of the politicians not listening to us. How can they do this to us? We were willing to give our lives. I would have given my life for you right now. I would stand in front of a bullet for anyone here. All I ask is for her to say - you know what? - you guys are worth it. You guys are our Marines, our Army. You should have never been deported. This should have never happened. This is a tear in the American fabric of our society, and we need to mend it. And we need to mend it with actions, not words. We need to do it now. Save me, please. I want to come home legally.
DAVIES: It's quite a moment. He's wearing his Marine uniform there as he is in the governor's reception area. Do you know if he ever got to meet with the governor? Was it ever resolved?
SCHWARZ: He did not meet with the governor. But I am happy to say that a few weeks ago, Cesar actually received the pardon from the governor. So he is in the process of getting - trying to fix his status. Even though he was pardoned, he's still currently undocumented and is trying to work with his immigration lawyers to change that.
DAVIES: So it's not clear that that will happen. He still has to make his case.
CLUSIAU: Correct.
SCHWARZ: Correct. It's unclear. We have seen other veterans that were pardoned that were able to do it. But since Cesar did choose to come back, it's hard to say. And he's trying to make his, case even though the governor did pardon him. Cesar is one of many veterans who are really activists trying to change this. And I think this is something that really hit us hard. And it says something about the system in large - this debate is so heated, and we're so quick to disagree and scream at each other as a country about it. And the strange thing is I think we saw a lot of things that we think we could agree on. And this is a great example. I mean, how many Americans really think we should be deporting our veterans? I doubt many. Yet this has been active since the Clinton days.
DAVIES: How is it that undocumented people can join the military and then be deported for? It. How does this happen?
CLUSIAU: Yes, so you have to be a legal permanent resident or a green card holder in order to join the military. And so it's not undocumented individuals. You have to have some sort of status in the country in order to join the military. And so Cesar - at that period of time, he had a legal permanent residence and a green card holder. So he was able to join the military.
SCHWARZ: But during President Clinton, there was a reform, which was really a very restrictive - that's our last time we have overhauled the immigration system. And it was really a very restrictive reform. And as part of that, it said that legal residents, including green card holders which commit a crime - first it was felonies. It's been dropped to nonviolent crimes, as well, later - could be deported. It didn't specifically target veterans, but it included them. And so ever since then, we've seen these people basically turn into deportable. And just as a reference, immigrants widely serve our country. There's been over half a million immigrants - legal residents - that decided to join the armed forces in this country.
SCHWARZ: Did you need to get specific permission from everyone that you filmed? I'm wondering what kind of legal and ethical issues come into play when you're, you know filming, you know, an arrest or some other operation. Sure.
CLUSIAU: We did get specific permission from anybody that we filmed and any of the characters that we profiled throughout the series. It became tricky, especially when we are embedding with ICE because, for example, when you go to a door with ICE at 6 a.m. and knock on the door, we needed to make it very clear from the outset that we were not with ICE, that we were independent journalists and that we were requesting to come in and document. A lot of times, people would say no. You know, I'm not interested. And we would back off and wait outside. And others would say, yes, you can come in and document. I think people wanted to record what was happening. And so after that, we would follow up with them again and say, you know, we need you to sign releases. You know, we would like to tell your story. We'd like to continue on. And so those were the processes we'd take. And even when we were in detention centers, we had a protocol that we would need individuals that we spoke to sign releases.
SCHWARZ: And just to add, when we met Cesar, the deported veteran, he told us about his story and that he was a fugitive in his own country. And I remember the first question was, like, are you sure you want to do this? You would basically be calling (ph) yourself. And he said, a Marine never hides, kind of almost like a gimmick. And I remember that when we got closer to Cesar, maybe a month into shooting, we looked at him and when his wife was there, too. And we said, Cesar, when we asked you, you kind of said that. Are you sure? Do you want to do this? It's better - if you don't, it's better that we back up now. And I remember that at that time, we, like - him, like, actually sitting with his wife and digesting that and coming back and saying, yes, let's do this.
But a lot of these, it's an example of these relationships that you would have to manage over a course of a time to make sure that those who are telling their stories really understand what they're doing. And, you know, now that it's come out, we've had great response from a lot of the immigrants and from some of the ICE agents but predominately from the immigrants coming back and kind of saying, you know, oh, my God. This has come to life. And just seeing what they went through. And we're grateful for those who took the leap of faith and gave us the trust to tell their story.
DAVIES: Well, Shaul Schwarz, Christina Clusiau, thank you so much for speaking with us.
SCHWARZ: Thank you.
CLUSIAU: Thank you.
DAVIES: Christina Clusiau and Shaul Schwarz are co-directors and co-producers of the six-part documentary series "Immigration Nation," now available for streaming on Netflix. Coming up, Kevin Whitehead reviews jazz pianist and composer James Carney's new album, "Pure Heart." This is FRESH AIR.
(SOUNDBITE OF ALFREDO RODRIGUEZ'S "VEINTE ANOS")
DAVIES: This is FRESH AIR. Jazz pianist and composer James Carney has worked as a music editor in the film industry, produced a Brooklyn concert series and led a few varied bands of his own. Along the way, he's met a diverse set of musicians. He collected a handful for a new sextet record. Jazz critic Kevin Whitehead has more.
[POST-BROADCAST CORRECTION: Aug. 17, 2020. This report incorrectly identified Michelle Lujan Grisham as the governor of Arizona. Lujan Grisham is the governor of New Mexico.]
(SOUNDBITE OF JAMES CARNEY SEXTET'S "MAYOR OF MARCELLUS") Transcript provided by NPR, Copyright NPR.
This report incorrectly identified Michelle Lujan Grisham as the governor of Arizona. Lujan Grisham is the governor of New Mexico.
Dave Davies is a guest host for NPR's Fresh Air with Terry Gross.
See stories by Dave Davies
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 7,719
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Q: Spring Boot UserDetailsService getting all users with same username Im going trough project https://github.com/royclarkson/spring-rest-service-oauth#spring-rest-service-oauth and inside is class:
public class CustomUserDetailsService implements UserDetailsService
and inside I override method
@Override
public UserDetails loadUserByUsername(String username) throws UsernameNotFoundException {
List<User> user = userRepository.findUserByLogin(username);
if (user == null) {
throw new UsernameNotFoundException(String.format("User %s does not exist!", username));
}
my question is can I get all Users with identical username?
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,213
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package org.omg.spec.dd._20100524.di;
import javax.xml.bind.annotation.XmlAccessType;
import javax.xml.bind.annotation.XmlAccessorType;
import javax.xml.bind.annotation.XmlAttribute;
import javax.xml.bind.annotation.XmlID;
import javax.xml.bind.annotation.XmlSchemaType;
import javax.xml.bind.annotation.XmlSeeAlso;
import javax.xml.bind.annotation.XmlType;
import javax.xml.bind.annotation.adapters.CollapsedStringAdapter;
import javax.xml.bind.annotation.adapters.XmlJavaTypeAdapter;
import org.omg.spec.bpmn._20100524.di.BPMNLabelStyle;
/**
* <p>Java class for Style complex type.
*
* <p>The following schema fragment specifies the expected content contained within this class.
*
* <pre>
* <complexType name="Style">
* <complexContent>
* <restriction base="{http://www.w3.org/2001/XMLSchema}anyType">
* <attribute name="id" type="{http://www.w3.org/2001/XMLSchema}ID" />
* </restriction>
* </complexContent>
* </complexType>
* </pre>
*
*
*/
@XmlAccessorType(XmlAccessType.FIELD)
@XmlType(name = "Style")
@XmlSeeAlso({
BPMNLabelStyle.class
})
public abstract class Style {
@XmlAttribute(name = "id")
@XmlJavaTypeAdapter(CollapsedStringAdapter.class)
@XmlID
@XmlSchemaType(name = "ID")
protected String id;
/**
* Gets the value of the id property.
*
* @return
* possible object is
* {@link String }
*
*/
public String getId() {
return id;
}
/**
* Sets the value of the id property.
*
* @param value
* allowed object is
* {@link String }
*
*/
public void setId(String value) {
this.id = value;
}
}
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{
"redpajama_set_name": "RedPajamaGithub"
}
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The Portable Kristeva
EUROPEAN PERSPECTIVES
European Perspectives
_A Series in Social Thought and Cultural Criticism_
Lawrence D. Kritzman, Editor
_European Perspectives_ presents outstanding books by leading European thinkers. With both classic and contemporary works, the series aims to shape the major intellectual controversies of our day and to facilitate the tasks of historical understanding.
For a complete list of books in the series, see European Perspectives.
The Portable Kristeva
UPDATED EDITION
Kelly Oliver, Editor
Columbia University Press
_New York_
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E-ISBN 978-0-231-51806-2
Library of Congress Cataloging-in-Publication Data
Kristeva, Julia, 1941–
The portable Kristeva / Kelly Oliver, editor. — Updated ed.
p. cm. — (European perspectives)
Includes bibliographical references and index.
ISBN 0–231–12628–X. (cl : alk. paper) — ISBN 0–231–12629–8 (ppr : alk. paper)
1. Semiotics. 2. Language and languages—Philosophy. 3. Psychoanalysis. 4. Identity (Psychology) 5. Women. I. Oliver, Kelly.
II. Title. III. Series.
P99.K694 2002
808′.00141—dc21
2002018722
Columbia University Press gratefully acknowledges permission to reprint from the following:
"My Memory's Hyperbole" by Julia Kristeva. Copyright © _New York Literary Forum_ , 1984. Reprinted with permission of the publisher.
Excerpts from _Revolution in Poetic Language_ by Julia Kristeva. Copyright © Columbia University Press, 1984. Reprinted with permission of the publisher.
Excerpt from _Desire in Language_ by Julia Kristeva. Copyright © Columbia University Press, 1980. Reprinted with permission of the publisher.
Excerpts from _Time and Sense_ by Julia Kristeva. Copyright © Columbia University Press, 1996. Reprinted with permission of the publisher.
Excerpts from _Tales of Love_ by Julia Kristeva. Copyright © Columbia University Press, 1987. Reprinted with permission of the publisher.
Excerpt from _Black Sun_ by Julia Kristeva. Copyright © Columbia University Press, 1989. Reprinted with permission of the publisher.
Excerpts from _New Maladies of the Soul_ by Julia Kristeva. Copyright © Columbia University Press, 1995. Reprinted with permission of the publisher.
Excerpts from _Powers of Horror_ by Julia Kristeva. Copyright © Columbia University Press, 1982. Reprinted with permission of the publisher.
Excerpts from _Strangers to Ourselves_ by Julia Kristeva. Copyright © Columbia University Press, 1991. Reprinted with permission of Columbia University Press and Pearson Education Limited..
"Interview with Elaine Hoffman Baruch" originally published under the title "Julia Kristeva" in _Women Analyze Women: In France, England, and the United States_ , edited by Baruch and Lucienne J. Serrano. Copyright © New York University Press, 1988. Reprinted with permission of the publisher.
Excerpt from _Hannah Arendt_ by Julia Kristeva. Copyright © Columbia University Press, 2001. Reprinted with permission of the publisher.
Excerpt from _The Sense and Non-Sense of Revolt_ by Julia Kristeva. Copyright © Columbia University Press, 2000. Reprinted with permission of the publisher.
Excerpts from _Intimate Revolt_ by Julia Kristeva. Copyright © Columbia University Press, 2002. Reprinted with permission of the publisher.
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Contents
_Preface: About This Collection_
_Introduction: Kristeva's Revolutions_
PART 1 _Kristeva's Trajectory: In Her Own Words_
"My Memory's Hyperbole" (1984), from _New York Literary Forum_
PART 2 _The Subject in Signifying Practice_
_Revolution in Poetic Language_ (1974)
Prolegomenon
The Semiotic and the Symbolic
Negativity: Rejection
_Desire in Language_ (1980)
From One Identity to an Other (1975)
_Time and Sense_ (1994)
Is Sensation a Form of Language? (abridged)
Freudian Time
PART 3 _Psychoanalysis of Love: A Counterdepressant_
_Tales of Love_ (1987)
Freud and Love: Treatment and Its Discontents (abridged)
Throes of Love: The Field of the Metaphor (abridged)
Extraterrestrials Suffering for Want of Love
_Black Sun_ (1989)
Psychoanalysis—A Counterdepressant
_New Maladies of the Soul_ (1993)
The Clinic: The Soul and the Image (abridged)
In Times Like These, Who Needs Psychoanalysts?
PART 4 _Individual and National Identity_
_Powers of Horror_ (1980)
Approaching Abjection (abridged)
From Filth to Defilement (abridged)
_Strangers to Ourselves_ (1989)
Toccata and Fugue for the Foreigner
Might Not Universality Be... Our Own Foreignness? (abridged)
In Practice...
PART 5 _Maternity, Feminism, and Female Sexuality_
_Desire in Language_ (1980)
The Maternal Body (1975), from "Motherhood According to Bellini"
_Tales of Love_ (1987)
Stabat Mater (1976)
_Julia Kristeva in Conversation with Rosalind Coward_ (1984)
_New Maladies of the Soul_
Women's Time (1977)
Interview with Elaine Hoffman Baruch on Feminism in the United States and France (1980)
_Black Sun_ (1989)
Illustrations of Feminine Depression
_Hannah Arendt_ (1999)
Female Genius: General Introduction
PART 6 _Revolt and Imagination_
_The Sense and Non-sense of Revolt_ (1996)
What Revolt Today?
_Intimate Revolt_ (1998)
The Future of Revolt
Revolt Today
Elements for Research
_Bibliography_
_Index_
Preface: About This Collection
This collection of Julia Kristeva's writings is designed to give the reader a representative selection from all her major works over the last two decades. The selections were chosen to reflect Kristeva's most significant contributions to the human sciences, including philosophy, literary theory, linguistics, cultural studies, psychoanalytic theory, and feminist theory. In these selections, Kristeva introduces the terminology and conceptual framework with which she goes on to analyze texts, music, visual arts, language, and culture. These selections, then, include her most important theoretical innovations, but they do not include her fiction or detailed applications of her techniques to art and literature. Still, this volume will introduce the reader to the methodology and terminology that inform all Kristeva's writings.
The selections are ordered topically but the original publication dates are included in the table of contents for readers who prefer to read chronologically. I have divided the texts under six topics: (1) Kristeva's Trajectory; (2) The Subject in Signifying Practice; (3) Psychoanalysis of Love: A Counterdepressant; (4) Individual and National Identity; (5) Maternity, Feminism, and Female Sexuality; and (6) Revolt and Imagination. Much of Kristeva's writing, however, touches on several issues at once, so many of these selections could have been placed under different topics. For example, the discussion of the semiotic chora from _Revolution in Poetic Language_ , in part 2, focuses on the relationship between poetic language and the maternal body. And one of the selections from _Powers of Horror_ , in part 4, includes an important discussion of abjection and the maternal body, which informs Kristeva's later writings on female sexuality. In addition, the selections from _Tales of Love_ , in part 3, and the selections from _Powers of Horror_ , in part 4, include Kristeva's ongoing formulations of subjectivity and signification. The reader may want to refer to the introduction before each part to get a sense of some of the issues addressed in each selection.
In addition to the six introductions, I have included a general introduction in which I discuss one of Kristeva's most revolutionary contributions to the human sciences as it evolves throughout her writings, her attempt to bring the speaking body back into theoretical discourse. _The Portable Kristeva_ begins with Kristeva's autobiographical essay "My Memory's Hyperbole," originally published as "Mémoires" in 1983. In this provocative essay, Kristeva describes her intellectual trajectory since her arrival in Paris in December 1965. The introduction before each part also gives more information about Kristeva's intellectual trajectory.
Julia Kristeva was born in Bulgaria in 1941. Although her education in Eastern Europe familiarized her with Marxism and Russian, she was introduced to Western thought and French in her early education by French nuns. Before leaving Bulgaria to continue her education in Paris, Kristeva worked as a journalist for a communist newspaper. She went to Paris in December 1965 on a doctoral research fellowship to work with Lucien Goldmann in Hautes Etudes at the Sorbonne, where she also worked with Roland Barthes and Claude Lévi-Strauss. Within one year Kristeva's articles were being published in _Critique_ , _Langages_ , and _Tel Quel_. She became involved with the _Tel Quel_ group and later married the head of the group, novelist Philippe Sollers. They had a son in 1976. In 1970 she was appointed to the editorial board of _Tel Quel_ , where she served until the journal was disbanded in 1983 and became the journal _Infini_.
Since her first book, _Sémiotikè: Recherches pour une sémanalyse_ , was published in 1969, Julia Kristeva has become one of the most prolific theorists in France. The importance of her writing over the past two decades has been felt across the human sciences. The impact of her doctoral dissertation, published as _La Révolution du langage poétique_ in 1974, is still being felt. Although the influence of psychoanalysis is manifest in her earliest work, which includes _Sémiotikè_ (1969), _Le Texte du roman_ (1970), _Révolution_ (1974), and _Polylogue_ (1977), this work is centered around linguistic analysis, including empirical studies. Her interest in psychoanalytic theory led her to complete training in psychoanalysis in 1979. While interest in language still motivates her work, her writings of the 1980s and 1990s reflect her training and practice as a psychoanalyst. She still maintains her psychoanalytic practice.
After Kristeva defended her dissertation, she was appointed to the faculty of the Department of Science of Texts and Documents at the University of Paris VII, where she continues to teach in the Department of Literature and Humanities. She also holds a regular visiting appointment at Columbia University in the French Department and at the University of Toronto.
Recently, Kristeva became a novelist with the publication of her first novel, _Les Samouraïs_ , in 1990, her second, _Le vieil homme et les loups_ , in 1991, and her third, _Possessions_ , in 1996. Her writing is unique in that it skillfully brings together psychoanalytic theory and clinical practice, literature, linguistics, and philosophy.
_Kelly Oliver_
Introduction: Kristeva's Revolutions
Meaning has become the central problem of philosophy and the human sciences. I am thinking of two general senses in which this is true. Contemporary theorists ask, "What does our language mean, to what does it refer?" And this question stands upon another, larger, question that has been the subject of philosophy since its inception—"What is the meaning of life?" Meaning operates on various interconnected levels simultaneously. For example, the ordinary language philosopher determines precisely what we mean when we use a particular word by looking at how the word is used. The philologist traces the etymological history of a particular word, whereas the philosopher of language or linguist determines how words have meaning at all; how does language work so that individual words, phrases, and sentences have meaning? Linguists and psychologists might also be concerned with what kinds of meaning language has for the addresser and for the addressed. This kind of analysis leads to general questions about the meaning of human experience and perception and the relation of language to life. The multivalent meaning of _meaning_ is reflected in the various ways in which the problem of meaning is presented in the human sciences.
Traditionally, philosophers have tried to describe human experience by abstracting from their own experience and articulating the essential characteristics of that experience. As philosophy has become more aware of itself and its methodologies, it has become concerned with the relation between experience itself and its articulation of experience. This kind of philosophical reflection leads to the question "What might get lost in the translation from experience as it is lived to the philosopher's articulation of it?" With the so-called linguistic turn in philosophy, and poststructuralism's attention to language and metaphor, the connection between lived experience and the language in which we articulate that experience has become complicated. The relation between experience and language is no longer seen as the relation between the original and its vessel, mirror image, or inferior copy. Yet what do we mean when we describe the essential characteristics of experience? What do we mean when we make philosophical or theoretical statements? What is the relationship between the theory and what it purports to describe? Can we mean what we say and say what we mean? What is the relationship between language and meaning?
The linguistic turn in philosophy might be said to begin with Hegel, who maintains that, through the dialectical movement of consciousness, the meaning of the world is realized in its philosophical articulation. For Hegel there is a necessary relationship between conceptualization, which he insists is necessary to self-consciousness and articulation. In _Phenomenology of Spirit_ , the highest level of consciousness is reached when we can describe our experience—when we mean what we say and say what we mean—when there is no gap between language and our experience. Reality is what is rational, and what is rational can be articulated.
Nietzsche seems to assert that if there is no gap between language and our experience, it is not because the real is rational and therefore articulable. Rather, language and grammar produce a rational reality. In _On the Genealogy of Morals_ he maintains that grammar divides sentences into nouns, verbs, and objects, and is therefore responsible for our belief in subjects and substance that transcend activities. In "On Truth and Lies in the Ultramoral Sense," he describes the meaning of words as the result of an arbitrary process of sedimentation and coagulation over time, a history which we forget when we use words.
Influenced by Nietzsche, especially in his later work, Heidegger insists that language is not a mere instrument for the communication of information. Rather, language is the unfolding of meaning itself, including the meaning of human experience. We do not speak language; rather, language speaks us. Heir to both Nietzsche and Heidegger, Jacques Derrida also expands Ferdinand de Saussure's notion that words have meaning only in their differential relation to other words. Saussure proposed that reference is not a necessary relationship between a word and a thing, but an arbitrary relationship between a word and a concept; the signifier (sound pattern of a word) and the signified (concept) have an arbitrary relationship. Meaning is the result of a system of differences without any positive terms. Derrida goes one step further to assert that the signified itself is also the product of differential relationships between signifiers; meaning is produced through an endless chain of signifiers. He introduces the term _différance_ to refer to the difference through which meaning is produced, a difference that can never be articulated or conceptualized. The operations of difference and differentiation that make meaning and thought possible can never themselves be thought; the difference of difference itself must always be deferred in our attempts to articulate it or think it.
In spite of the pessimism about the possibility of articulating our experience, and the professionalization of the disciplines, in some sense, philosophy is still held accountable for the meaning of life. Philosophers try to coordinate not only words and their meanings but also the meaning of this activity for life. This larger question of meaning moves us from the questions "What is our experience?" or "How do we articulate it?" to "Why... why bother?" "Why do we do what we do?" "Why should we?" These questions return us to a more specific sense of meaning with Nietzsche's question in _On the Genealogy of Morals_ , "Why ask why?" Why do we need to ask these questions? What is the experience that gives rise to such questions, and how does this experience become articulated in these questions? What is the relationship between life and meaning?
The advent of psychoanalysis further complicates these questions. Like the Nietzchean genealogist, the psychoanalyst is concerned to diagnose displaced meanings that lurk behind the apparent meaning of our articulation of experience. The concern is no longer whether language can adequately capture, reflect, or copy experience but how we can interpret the meaning of this language as it points to that which necessarily escapes it. Now we are concerned with the hidden, veiled, or unconscious meanings of our language use; we are concerned precisely with the way in which our language does _not_ re-present our conscious experience.
Bringing linguistics to Freudian psychoanalytic theory, Jacques Lacan claims that the unconscious is structured like a language. Like language, we need to interpret unconscious processes in terms of syntax and semantics. More than this, the effects of the unconscious are seen as breaks in language—slips of the tongue, jokes, misreadings—and the unconscious is formed in relation to language. Language and signification become signs that point to, rather than represent, our unconscious motivations. Language provides clues to discovering the key to the mystery of all our questions of "why?"—especially the question "Why do we speak?"
I rehearse these questions of meaning here because I think that Julia Kristeva addresses them in a unique way. Where others have seen an impasse, Kristeva has imagined an adventurous journey, though certainly not without its dangers and pitfalls. In an age of theoretical pessimism on all sides, Kristeva brings together the two questions of meaning, the meaning of language and the meaning of life, to provide hopeful answers that are more than mere theoretical exercises. Taking up the question "Why do we speak?" in all its ambiguities, Kristeva addresses the issues of the relationship of meaning to language, the relationship of meaning to life, and the relationship of language to life. In fact, Kristeva's most famous contribution to language theory, the distinction between the symbolic and the semiotic elements of signification, speaks to these questions in a revolutionary way, opening pathways rather than resigning us to an impasse.
Kristeva maintains that all signification is composed of two elements, the symbolic and the semiotic. The symbolic element is what philosophers might think of as meaning proper. That is, the symbolic is the element of signification that sets up the structures by which symbols operate. The symbolic is the structure or grammar that governs the ways in which symbols can refer. The semiotic element, on the other hand, is the organization of drives in language. It is associated with rhythms and tones that are meaningful parts of language and yet do not represent or signify something. In _Revolution in Poetic Language_ (1974), Kristeva maintains that rhythms and tones do not _represent_ bodily drives; rather bodily drives are _discharged_ through rhythms and tones. In _New Maladies of the Soul_ (1993), she discusses different ways of representing that are not linguistic in a traditional sense. There, Kristeva says that the meaning of the semiotic element of language is "translinguistic" or "nonlinguistic" (pp. 32–33, 31); she explains this by describing these semiotic elements as irreducible to language because they "turn toward language even though they are irreducible to its grammatical and logical structures" (p. 35). This is to say that they are irreducible to the _symbolic element_ of language. The symbolic element of language is the domain of position and judgment. It is associated with the grammar or structure of language that enables it to signify something.
The symbolic element of language should not, however, be confused with Lacan's notion of the Symbolic, which includes the entire realm of signification whereas Kristeva's symbolic is one element of that realm. While Lacan's Symbolic refers to signification in the broadest possible sense, including culture in general, Kristeva's symbolic is a technical term that delimits one element of language associated with syntax. In addition, Kristeva's semiotic element ( _le sémiotique_ ) should not be confused with semiotics ( _la sémiotique_ ), the science of signs.
The dialectical oscillation between the semiotic and the symbolic is what makes signification possible. Without the symbolic element of signification, we have only sounds or delirious babble. But without the semiotic element of signification, signification would be empty and we would not speak; for the semiotic provides the motivation for engaging in signifying processes. We have a bodily need to communicate. The symbolic provides the structure necessary to communicate. Both elements are essential to signification. And it is the tension between them that makes signification dynamic. The semiotic both motivates signification and threatens the symbolic element. The semiotic provides the movement or negativity, and the symbolic provides the stasis or stability that keeps signification both dynamic and structured.
Kristeva compares her dialectic between semiotic and symbolic, or negativity and stasis, to Hegel's dialectic; but for her, unlike Hegel, there is no synthesis of the two elements, no _Aufhebung_ (sublation or cancellation with preservation). In _Revolution_ , she maintains that negativity is not merely the operator of the dialectic but the fourth term of the dialectic. There, she replaces the Hegelian term _negativity_ with the psychoanalytic term _rejection_ , which adds the connotation of connection to bodily drives. Because they indicate the drive force in excess of conscious thought, Kristeva prefers the terms _expenditure_ and _rejection_ "for the movement of material contradictions that generate the semiotic function" (p. 119). For Kristeva, unlike Hegel, negativity is never canceled and the contradiction between the semiotic and the symbolic is never overcome.
While the symbolic element gives signification its meaning in the strict sense of reference, the semiotic element gives signification meaning in a broader sense. That is, the semiotic element makes symbols matter; by discharging drives in symbols, it makes them significant. Even though the semiotic challenges meaning in the strict sense, meaning in the terms of the symbolic, it gives symbols their meaning for our lives. Signification makes our lives meaningful, in both senses of meaning—signifying something and having significance—through its symbolic and semiotic elements. The interdependence of the symbolic and semiotic elements of signification guarantees a relationship between language and life, signification and experience; the interdependence between the symbolic and semiotic guarantees a relationship between body ( _soma_ ) and soul ( _psyche_ ).
One of Kristeva's most important contributions to contemporary theory is her attempt to bring the speaking body back into the discourses of the human sciences. Her writing challenges theories that rely on unified, fixed, stagnant theories of subjectivity; she insists on semiotic negativity, which produces a dynamic subjectivity. Yet she challenges theories that would reduce subjectivity to chaotic flux; she also insists on symbolic stasis and identity. Her writing stages the oscillation between the semiotic and the symbolic elements in signification. In order to bring the body back into theories of language, she develops a science that she calls "semanalysis," which is a combination of semiotics, taken from Charles Pierce and Ferdinand de Saussure, and psychoanalysis, taken from Sigmund Freud, Jacques Lacan, and Melanie Klein.
Following Lacan, Kristeva maintains that subjectivity is formed in conjunction with language acquisition and use. All of Kristeva's writing has addressed the relationship between language and subjectivity. Kristeva is concerned with the places where self-identity is threatened, the limits of language. As a result, her work is focused between the two poles of language acquisition and psychotic babble. She is interested both in how the subject is constituted through language acquisition and in how the subject is demolished with the psychotic breakdown of language. These limits of language point to the delicate balance between semiotic and symbolic, between affects and words. The motility of the subject and the subject's ability to change are the result of the interplay of semiotic drive force and symbolic stasis. Because of the relationship between language and subjectivity, the psychoanalyst can work backward from language in order to diagnose the analysand's problems with self-image. Freud called psychoanalysis the "talking cure" because the analysand's articulation of his or her malaise is the fulcrum of clinical practice.
Kristeva attempts to bring the speaking body back into discourse by arguing both that the logic of language is already operating at the material level of bodily processes and that bodily drives make their way into language. She postulates that signifying practices are the result of material bodily processes. Drives make their way into language through the semiotic element of signification, which does not _represent_ bodily drives but _discharges_ them. In this way, all signification has material motivation. All signification discharges bodily drives. Drives move between _soma_ and _psyche_ , and the evidence of this movement is manifest in signification.
Kristeva takes up Freud's theory of drives as instinctual energies that operate between biology and culture. Drives have their source in organic tissue and aim at psychological satisfaction. Drives are heterogeneous; that is, there are several different drives that can conflict with each other. In _Revolution_ , Kristeva describes drives as "material, but they are not solely biological since they both connect and differentiate the biological and symbolic within the dialectic of the signifying body invested in practice" (p. 167). Nearly two decades later, Kristeva emphasizes the same dialectical relationship between the two spheres—biological and social—across which the drives operate. In _New Maladies of the Soul_ , she describes the drives as "a pivot between 'soma' and psyche,' between biology and representation" (p. 30). Drives can be reduced neither to the biological nor to the social; they operate in between these two realms and bring one realm into the other. Drives are energies or forces that move between the body and representation. This notion of drives challenges the traditional dualism between the biological and the social, the body and the mind. Kristeva's attempts to bring the body back to theory also challenge traditional notions of the body; for her, the body is more than material.
By insisting that language expresses bodily drives through its semiotic element, Kristeva's articulation of the relationship between language and the body circumvents the traditional problems of representation. The tones and rhythms of language, the materiality of language, is bodily. Traditional theories, which postulate that language represents bodily experience, fall into an impossible situation by presupposing that the body and language are distinct, even opposites. Some traditional theories postulate that language is an instrument that captures, mirrors, or copies bodily experience. The problem, then, becomes how to explain the connection between these two distinct realms of language, on the one hand, and material, on the other.
Since traditional theories have not been able to explain adequately how language is related to the material world, some contemporary theorists have proposed that language does not refer to some extralinguistic material world; rather, language refers only to itself. Words have their meaning in relation to other words and not in relation to things in the world. We can discern the meaning of words by analyzing the structures within which words operate rather than examining the correspondence between words and things. Whereas Husserlian phenomenology describes words as windows onto the meaning constituted by the transcendental subject, structuralism describes words as elements operating within systems that constitute their meanings, and poststructuralism describes words as traces of the processes of difference and deferral that constitute the illusion of their stable meaning and determinant references, Kristeva describes the meaning of words as combinations of dynamic bodily drive force or affect and stable symbolic grammar.
Kristeva criticizes Husserlian phenomenology for taking one stage of the process of subjectivity and fetishizing it. The stasis and stability of the transcendental ego is but one element of subjectivity. In addition, for Kristeva meaning is not the unified product of a unified subject; rather, meaning is Other and as such makes the subject other to itself. Meaning is not constituted by a transcendental ego; meaning is constituted within a biosocial situation. Infants are born into a world where words already have meanings. Meaning is constituted through an embodied relation with another person. In this sense, meaning is Other; it is constituted in relation to an other and it is beyond any individual subjectivity. Insofar as meaning is constituted in relationships—relationships with others, relationships with signification, relationships with our own bodies and desires—it is fluid. And the subject for whom there is meaning is also fluid and relational.
Kristeva maintains that any theory of language is also a theory of the subject. In "From One Identity to an Other" and _Revolution_ , against Husserl's transcendental ego Kristeva postulates her notion of a subject-in-process/on trial ( _le sujet en procès_ ). Taking poetic language as emblematic, Kristeva argues, in _Desire in Language_ , that signification is "an undecidable process between sense and nonsense, between _language_ and _rhythm_ " (p. 135). The Husserlian transcendental ego cannot account for nonsense or rhythm within signification; it cannot account for the unconscious. But heterogeneity within signification points to heterogeneity within the speaking subject; if language is a dynamic process then the subject is a dynamic process. Like signification, the subject is always in a constant process of oscillation between instability and stability or negativity and stasis. The subject is continually being constituted within this oscillation between conscious and unconscious as an open system, subject to infinite analysis. The Cartesian _cogito_ and the Husserlian transcendental ego, then, are only moments in this process; they are neither chronologically nor logically primary.
Although structuralism does not posit a Husserlian transcendental ego, it does silence the speaking body in favor of bloodless structures. Kristeva describes these theories as necrophiliac. She begins _Revolution in Poetic Language:_
Our philosophies of language, embodiments of the Idea, are nothing more than the thoughts of archivists, archaeologists, and necrophiliacs. Fascinated by the remains of a process which is partly discursive, they substitute this fetish for what actually produced it.... These static thoughts, products of a leisurely cognition removed from historical turmoil, persist in seeking the truth of language by formalizing utterances that hang in midair, and the truth of the subject by listening to the narrative of a sleeping body—a body in repose, withdrawn from its socio-historical imbrication, removed from direct experience.
(p. 13)
Feminism has levied similar criticisms against ahistorical theories that ignore or silence the body, particularly women's bodies. Some feminists have been concerned to articulate a feminine sexuality and subjectivity. Luce Irigaray maintains that feminine sexuality and women's bodies have been defined as the Other of masculine sexuality and men's bodies, that women are not subjects but the Other against which men become subjects. Many feminists argue that women's experiences have been silenced by cultures whose governments and intellectual lives have been controlled by men. Conceptions of subjectivity that once were thought to apply universally—the Cartesian _cogito_ , the Kantian autonomous subject, the Husserlian trancendental ego—have been challenged as genderspecific conceptions of man. Feminists have rejected ahistorical notions of subjectivity, which privilege characteristics historically associated with men and masculinity.
While poststructuralist theories generally do not propose formalizing utterances or subjectivity in terms of ahistorical structures or concepts, few of them suggest ways to articulate the body. Kristeva's best-known poststructuralist colleague, Jacques Derrida, struggles with the relationship between language and the living, speaking body. In the most reductionistic and hostile readings, Derrida's critics take a phrase from _Of Grammatology_ , "there is nothing outside of the text," out of context to claim that Derrida is a linguistic monist or a nominalist who does not believe in the reality of anything other than language itself (p. 158). A careful reading of Derrida makes this position difficult to defend. As Derrida says in an interview with Richard Kearney: "It is totally false to suggest that deconstruction is a suspension of reference. Deconstruction is always deeply concerned with the 'other' of language. I never cease to be surprised by critics who see my work as a declaration that there is nothing beyond language, that we are imprisoned in language; it is, in fact, saying the exact opposite" ( _Dialogues_ , p. 123).
Derrida's work is a continual struggle to articulate the "Other" of language, which, as he reminds us, is impossible (see "Psyche," p. 60). The Other of language is antithetical to language even if it is the call from this Other that gives language its meaning. Still, language always only points to that which is absent; it is this absence that makes signification possible. Words can do no more than point to, or conjure, the absence of that about which they speak. That about which they speak—life, love, the material world, even language itself—is other to words.
In Derrida's account in _Of Grammatology_ , language does violence to this otherness (p. 135). At best, language gives us traces of something beyond language, homicidal traces that turn life into death. Although in "Circumfessions" Derrida dreams of a writing that could directly express the living body without violence, for him, language is always the dead remains of a living body: "If I compare the pen to a syringe, and I always dream of a pen that would be a syringe, a suction point rather than that very hard weapon with which one must inscribe, incise, choose, calculate, take ink before filtering the inscribable, playing the keyboard on the screen, whereas here, once the right vein has been found, no more toil, no responsibility, no risk of bad taste nor of violence, the blood delivers itself all alone, the inside gives itself up" (p. 12). Even as Derrida imagines writing that is like a transfusion of the living body into language, he resigns himself to the violence of trying to inscribe the uninscribable. The living body is this uninscribable. Kristeva's theory more optimistically addresses the problem of the relationship between language and bodily experience by postulating that, through the semiotic element, bodily drives manifest themselves in language. Instead of lamenting what is lost, absent, or impossible in language, Kristeva marvels at this other realm that makes its way into language. The force of language is living drive force transferred into language. Signification is like a transfusion of the living body into language. This is why psychoanalysis can be effective; the analyst can diagnose the active drive force as it is manifest in the analysand's language. Language is not cut off from the body. And while for Kristeva bodily drives involve a type of violence, negation, or force, this process does not merely necessitate sacrifice and loss. The drives are not sacrificed to signification; rather, bodily drives are an essential semiotic element of signification.
In addition to proposing that bodily drives make their way into language, Kristeva maintains that the logic of signification is already present in the material of the body. Once again combining psychoanalytic theory and linguistics, Kristeva relies on both Lacan's account of the infant's entrance into language and Saussure's account of the play of signifiers. Lacan points out that the entrance into language requires separation, particularly from the maternal body. Saussure maintains that signifiers signify in relation to one another through their differences. Combining these two theses, it seems that language operates according to principles of separation and difference, as well as identification and incorporation. Kristeva argues that the principles or structures of separation and difference are operating in the body even before the infant begins to use language.
In _Revolution in Poetic Language_ , Kristeva proposes that the processes of identification or incorporation and differentiation or rejection that make language use possible are operating within the material of the body. She maintains that before the infant passes through what Freud calls the oedipal phase, or what Lacan calls the mirror stage, the patterns and logic of language are already operating in a preoedipal situation. In _Revolution_ she focuses on differentiation or rejection and the oscillation between identification and differentiation. She identifies material rejection (for example, the expulsion of waste from the body) as part of the process that sets up the possibility of signification.
She calls the bodily structures of separation the "logic of rejection." For Kristeva the body, like signification, operates according to an oscillation between instability and stability, or negativity and stases. For example, the process of metabolization is a process that oscillates between instability and stability: food is taken into the body and metabolized and expelled from the body. Because the structure of separation is bodily, these bodily operations prepare us for our entrance into language. From the time of birth, the infant's body is engaging in processes of separation; anality is the prime example. Birth itself is also an experience of separation, one body separated from another.
Part of Kristeva's motivation for emphasizing these bodily separations and privations is to provide an alternative to the Lacanian model of language acquisition. Lacan's account of signification and self-consciousness begins with the mirror stage and the paternal metaphor's substitution of the law of the father for the desire of the mother. In the traditional psychoanalytic model of both Freud and Lacan, the child enters the social realm and language out of fear of castration. The child experiences its separation from the maternal body as a tragic loss and consoles itself with words instead. Paternal threats make words the only, if inadequate, alternative to psychosis. Kristeva insists, however, that separation begins prior to the mirror or oedipal stage and that this separation is not only painful but also pleasurable. She insists that the child enters the social realm and language not just because of paternal threats but also because of paternal love.
At bottom, Kristeva criticizes the traditional account because it cannot adequately explain the child's move to signification. If what motivates the move to signification are threats and the pain of separation, then why would anyone make this move? Why not remain in the safe haven of the maternal body and refuse the social realm and signification with its threats? Kristeva suggests that if the accounts of Freud and Lacan were correct, then more people would be psychotic (see _Revolution_ , p. 132; _Tales_ , pp. 30, 31, 125). The logic of signification is already operating in the body, and therefore the transition to language is not as dramatic and mysterious as traditional psychoanalytic theory makes it out to be.
Reconnecting bodily drives to language is the project not only of her theoretical work but also of her clinical psychoanalytic practice and one aspect of her fiction. Since _Tales of Love_ (1983), Kristeva has been including notes from analytic sessions in her theory and fiction. In her theory she uses these notes to further substantiate her diagnosis of literary texts and culture. She often diagnoses a gap between her analysand's words and his or her affects. Affects are physical and psychic manifestations of drive energy; recall that drive energy has its source in bodily organs and its aim in satisfaction of desires. Kristeva describes a phenomenon whereby it seems that words become detached from their affects and the corresponding drive energy, and the job of the analyst is to try to help the analysand put them back together again.
A fragile connection between words and affects is set up during a child's acquisition of language and simultaneous acquisition of a sense of self or subjectivity. If this connection between words and affects is broken or never established, borderline psychosis can be the result. Kristeva suggests that in contemporary culture more slippage, or a different kind of slippage, seems to occur than in the past between words and affects, between who we say we are and our experience of ourselves. Perhaps the abyss between our fragmented language and our fragmented sense of ourselves is the empty soul or psyche of the postmodern world. Kristeva's writing attempts to negotiate this impasse by bringing the body back into language and bringing language back into the body, by reconnecting bodily drives to language.
Her discussion of the need to reconnect words and affects, language and the body, is punctuated with quotations from her analysands' speech. Not only does this strategy address the absence of the speaking body from traditional theoretical discourse but also the transcripts stand as examples of the practical consequences of traditional dualistic theoretical positions on the relationship between language and life, symbols and experience, mind and body. Her strategy of including her notes from analytic sessions, peppered with the words of her analysands, brings the speaking body into theoretical discourse. These speaking bodies are articulating the pain of living in worlds where symbols have been detached from affect, where the meaning of words has been detached from the meaning of life, from what matters.
The affective or semiotic element of language matters in the double sense of giving language its raison d'être and its material element. In _New Maladies of the Soul_ Kristeva suggests that the loss of meaning and the emptiness of contemporary life are related to an uncoupling of affect and language that is encouraged by the very remedies contemporary society proposes for dealing with the problem. Contemporary society offers two primary ways of addressing the malaise caused by the disconnection of affect and language: drugs (narcotics, psychotropic drugs, and antidepressants) and media images. Kristeva suggests that both drugs and media images do nothing to treat the cause of our malaise; rather, they can be seen as symptoms of the problem itself. The problem, as she articulates it in _New Maladies of the Soul_ , is that contemporary culture has left behind the psyche or soul. The soul is empty or nonexistent, and without it our lives, our words, have no meaning.
With the scientific revolution in the seventeenth and eighteenth centuries, religion lost its power to provide language and life with meaning. In the nineteenth and twentieth centuries, we have become suspicious of science and technology to the extent that they no longer provide language and life with meaning. After Nietzsche's proclamations that God is dead and that scientific and philosophical Truth have been clinging to His stinking corpse, where can we find meaning? At one extreme, contemporary theories that propose dogmatic and fixed notions of meaning seem artificial and desperate. At the other, theories that propose that ultimately there is no meaning and anything goes seem equally artificial and frustrating. Neither extreme can provide an anchor for meaning. Neither extreme can reconnect meaning to our language and lives. In fact, these extremes might be symptoms of the separation of meaning from our language and our lives. Theories that propose the meaninglessness of life or the impossibility of connecting language and life can been seen as symptoms of a general malaise caused by a feeling of emptiness.
Working between what she identifies as the extremes of totalitarianism and delirium, Kristeva diagnoses this emptiness as a lack of psyche or soul. In _New Maladies of the Soul_ , she suggests that our souls ( _psyche_ ) have been flattened and emptied by the rhythms and images of our culture, which are two-dimensional. Life takes place on the screen—movie screens, TV screens, computer screens. Yet these media images merely cover over the surface of the emptiness that we feel facing the loss of meaning. Psychotropic drugs and antidepressants flatten the psyche. They relieve the feeling of crisis caused by a loss of meaning but leave a feeling of emptiness; they flatten or empty the patient's affects. Both drugs and media images provide false or artificial selves, which only temporarily smooth over the surface of an otherwise empty psyche. By substituting surface images for psychic depth, drugs and media images close psychic space.
Psychic space is the space between the human organism and its aims; it is the space between the biological and the social. It is the space through which drives move energy between these two interconnected spheres. It is within this psychic space that affects materialize between bodily organs and social customs. Our emotional lives depend on this space. Meaning is constituted in this space between the body and culture. Our words and our lives have meaning by virtue of their connection to affect. The meaning of words (in the narrow sense of the symbolic element of language) is charged with affective meaning (in the broader sense of the semiotic element of language) through the movement of drive energy within psychic space.
As Kristeva says in _Tales of Love_ , we are extraterrestrials wandering and lost without meaning because of this abolition of psychic space: "What analysands are henceforth suffering from is _the abolition of psychic space_. Narcissus in want of light as much as of a spring allowing him to capture his true image, Narcissus drowning in a cascade of false images (from social roles to the _media_ ), hence deprived of substance or place" (p. 373). We experience somatic symptoms cut off from their psychic or affective meaning. The goal of the analyst, then, is to reconnect _soma_ and _psyche_ , body and soul. The "talking cure" involves giving meaning to language by reconnecting words and affects and thereby giving meaning to life. Psychoanalysis is unique in that it tries to open up psychic space and provide various interpretations with which to give meaning to both language and life.
In _Tales of Love_ , Kristeva identifies meaning—both the meaning of life and the meaning of language—with love. "Today Narcissus is an exile, deprived of his psychic space, an extraterrestrial with a prehistory bearing, wanting for love. An uneasy child, all scratched up, somewhat disgusting, an alien in a world of desire and power, he longs only to reinvent love" (pp. 382–83). The analysand is a child with no adequate images of a loving mother or a loving father. Kristeva suggests that in the West Christianity has traditionally provided images of a loving mother and a loving father, as problematic as those images might be. But with contemporary suspicions of religion, she seems to ask, where can we find images of loving mothers and fathers? And without images of loving mothers and fathers, how can we love ourselves?
For Kristeva, love provides the support for fragmented meanings and fragmented subjectivities. Love provides the support to reconnect words and affects. She says that "love is something spoken, and it is only that" (p. 277). Our lives have meaning for us, we have a sense of ourselves, through the narratives we prepare to tell others about our experience. Even if we do not tell our stories, we live our experience through the stories that we construct in order to "tell ourselves" to another, a loved one. As we wander through our days, an event takes on its significance in the narrative that we construct for an imaginary conversation with a loved one as we are living it. The living body is a loving body, and the loving body is a speaking body. Without love we are nothing but walking corpses. Love is essential to the living body, and it is essential in bringing the living body to life in language.
Psychoanalysis is a love relationship that builds spoken spaces through transferential love, "that summons the ability to idealize at the very core of desire and hatred" (p. 382). Psychoanalysis addresses this ability to idealize and, through the power of transference and the articulation or elaboration of that transference, calls forth the analysand's imaginary or idealized relations. The way in which relations are structured in the imaginary determines how the analysand relates to others. The transference love of the analytic session provides a space within which those structures can safely be examined and altered. Insofar as the psychoanalytic relationship operates according to transference love, the ethics of psychoanalysis is an ethics of love. Transference and countertransference provide the safety net that supports the redirection and reconnection of affective drive force and signification. Transference and countertransference are love relations that can spark the imagination and open up the possibility of re-imaging and thus re-signifying affects. In _Time and Sense_ (1994), Kristeva suggests that transference in the psychoanalytic session inscribes flesh in words. Psychoanalysts "transform the patient's flesh, which [they] have shared with [their] own, into word-presentations." In this way psychoanalysis can treat somatic symptoms by transforming the body through words. The connection between flesh and words conjured and refigured in analytic transference opens up the space for idealization that Kristeva associates with love and psychic space. And this space for idealization gives the analysand a renewed image of self.
In _Black Sun_ (1987), Kristeva claims that while religious rituals and literature are cathartic, psychoanalysis goes further as an _elaboration_ of the drive processes and their relation to the signifying process. This elaboration is crucial in treating the causes and not just the symptoms of neurosis. While the semiotic drive force is powerful when discharged in signifying practices, the position of judgment made possible by the symbolic element of signification is necessary not only to direct but also redirect that discharge. While there are various discourses that engage theories of subjectivity and many types of cathartic practices that can rejuvenate meaning, for Kristeva psychoanalysis is the only place where _theories_ of subjectivity and the dynamic _practice_ of the subject-in-process come together so dramatically. The psychoanalytic session is an attempt to come to terms with the dynamic nature of the subject while opening onto its fluidity.
Some of Kristeva's critics have argued that psychoanalysis does not provide an adequate ethics or politics. One concern is that Kristeva seems to suggest that individual psychoanalytic treatment is necessary to counteract everything from melancholy and depression to xenophobia and ethnic violence. The idea that we all need to seek the professional services of psychoanalysts is not only impractical but also politically suspect: psychoanalysis is expensive and time-consuming and can be elitist. Psychoanalysis is also a relationship between two individuals, one in the employ of the other. As such, a politics that privileges psychoanalysis seems to foreclose the importance and possibility of social movements and group initiatives. All social problems are analyzed in terms of individual psychological problems rather than social and institutional problems. This recalls some feminists' criticisms of Freudian psychoanalysis for reducing women's oppression and silence to individual neurosis and hysteria.
Although Kristeva does maintain that psychoanalysis brings together theory and practice in a unique way and that it can elaborate psychic dynamics that other forms of signification manifest, she does not restrict these operations to psychoanalysis. Rather, she justifies the continued use of psychoanalysis. More than this, her elaboration of psychoanalysis works to emphasize the role of the imagination or imaginary realm in the construction of our sense of ourselves and others. Kristeva suggests that we cannot change our practice until we change the way that we imagine ourselves and others. Significant political change and policy reform can result only from changes in our individual and cultural imaginary.
In _Strangers to Ourselves_ (1991) and _Nations Without Nationalism_ (1993), Kristeva uses psychoanalysis as a model for analyzing relations between peoples of different nations and ethnic backgrounds. Just as she brings the speaking body back into language by putting language into the body, she brings the subject into the place of the other by putting the other into the subject. Just as the pattern or logic of language is already found within the body, the pattern or logic of alterity is already found within the subject. In a Hegelian move, Kristeva makes the social relation interior to the psyche. This is why the subject is never stable but always in process/on trial. Kristeva suggests that if we can learn to live with the return of the repressed other within our own psyches, then we can learn to live with others. With her notions of the subject-in-process, and the other within, she attempts to articulate an ethical relationship between conscious and unconscious, self and other, citizen and foreigner, identity and difference, that rather than relying solely on sacrifice and violence, is built on acceptance and love.
TEXTS CITED IN INTRODUCTION
Derrida, Jacques. Interview with Richard Kearney. In _Dialogues with Contemporary Continental Thinkers_. Richard Kearney, ed. Manchester: Manchester University Press, 1984.
_Of Grammatology_. Gayatri Spivak, tr. Baltimore: Johns Hopkins University Press, 1976.
"Psyche: Inventions of the Other." In _Reading DeMan Reading_. Catherine Porter, tr., L. Waters and W. Godzich, eds. Minneapolis: University of Minnesota Press, 1989, pp. 25–65.
"Circumfession." In _Jacques Derrida_. Geoffrey Bennington, tr. Chicago: University of Chicago Press, 1993.
NOTES
Thanks to Tamsin Lorraine, Noëlle McAfee, Benigno Trigo, and Ewa Ziarek for helpful comments on earlier versions of this introduction.
. The three terms of the Hegelian dialectic are commonly referred to as thesis, antithesis, and synthesis, which correspond to Universal, Particular, Individual.
. In the history of philosophy, the distinction between body and soul has also been discussed as a distinction between body and mind, or the mind-body problem.
. For a more developed account of Kristeva's theory of drives, see my _Womanizing Nietzsche: Philosophy's Relation to the "Feminine,"_ ch. 6, "Save the Mother" (New York: Routledge, 1995).
. Kristeva's theory also challenges the narrow conception of material as it is opposed to social or linguistic.
. Traditional theories have tried to address these problems in various ways. Referential theories of meaning have held that the meaning of a word is its reference to something extralinguistic, something in the world. The meaning of a word is either what it refers to (some thing) or the relationship between the word and its referent. But as Frege pointed out, meaning and reference are not the same since there are many different ways of referring to the same thing; and not all these linguistic expressions necessarily have the same meaning even if they have the same referent. The most famous example is the reference to Venus as both the morning star and the evening star. Some theorists (e.g., Locke, Husserl, Saussure) have tried to avoid some of the problems of referential theories by supposing that the meaning of a word is determined by the thought that corresponds to that word. The referent in this case becomes an idea or concept and not a material thing in the world. These theories, however, merely displace the problems of reference from the material world to the world of ideas. All the problems of correspondence still obtain. Some contemporary theorists (Austin, Wittgenstein, Searle) propose that meaning is determined by the use of words and that the use of words must be analyzed as a type of activity with certain rules and regulations. The way in which words are used, however, varies as much as the thoughts or ideas associated with them and their possible material referents.
. For a feminist criticism of Descartes, see Susan Bordo, _The Flight to Objectivity_ (Albany, N.Y.: suny Press, 1987). For a feminist criticim of Kant, see Robin Schott's _Cognition and Eros: A Critique of the Kantian Paradigm_ (Boston: Beacon Press, 1988). Kristeva's relationship to feminism is complex. For a discussion of these issues, see Kelly Oliver, _Reading Kristeva: Unraveling the Doublebind_ (Bloomington: Indiana University Press, 1993).
. For a detailed analysis of the relationship between language and the living body in Derrida's "Circumfessions," see my article "The Maternal Operation" in Mary Rawlinson et al., eds., _Derrida and Feminism_ (New York: Routledge, 1996).
. Kristeva's writings themselves can be read as an oscillation between an emphasis on separation and rejection and an emphasis on identification and incorporation. In _Revolution_ (1974) and _Powers of Horror_ (1980) she focuses on separation and rejection; in _Tales of Love_ (1983) and _Black Sun_ (1987) she focuses on identification and incorporation. In _Strangers to Ourselves_ (1989) she again analyzes separation and rejection. And in _New Maladies of the Soul_ (1993) she returns to identification and incorporation. In an interview with Rosalind Coward in 1984 at the Institute of Contemporary Arts, Kristeva claims that for this reason _Powers of Horror_ and _Tales of Love_ should be read together; alone each provides only half of the story.
. Starting with _Tales of Love_ and continuing through _New Maladies of the Soul_ , Kristeva begins to insert what appear as her notes from analytic sessions into her texts.
. See some of the essays in _Ethics, Politics, and Difference in Julia Kristeva's Writing_ , ed. Kelly Oliver (New York: Routledge, 1993), especially Graybeal, Rose, McAfee, Moruzzi, Lowe, Butler, and Edelstein.
PART 1
_Kristeva's Trajectory: In Her Own Words_
My Memory's Hyperbole
"My Memory's Hyperbole," translated by Athena Viscusi, was published in a special issue of the _New York Literary Forum_ on "The Female Autograph" in 1984. This autobiographical essay first appeared as 'Mémoires' in 1983 in the journal that replaced _Tel Quel_ , _Infini_. In this essay Kristeva situates her own work in relation to existential philosophy, linguistics, literature, structuralism, and deconstruction. She describes the most important influences on her thinking and writing, including her involvement with the _Tel Quel_ group and her friendship with Emile Benveniste. She traces _Tel Quel_ 's association with the French Communist Party (PCF). And she describes her movement away from politics and feminism after her trip to China in 1974. In addition, she anticipates some of her latest writing on nationalism.
My Memory's Hyperbole
_Hyperbole! from my memory..._
— _Mallarmé_ , " _Prose pour des esseintes_ "
When the _New York Literary Forum_ asked me to contribute an autobiographical text for this special issue, I had just finished reading _La Cérémonie des adieux_ by Simone de Beauvoir. One must surely be endowed with the naive cruelty of this exceptional woman to create such a myth or, at the very least, to make it exist by giving it a narrative thread. In spite of the legend that surrounds the author of _Mandarins_ , I am convinced that she has still not been properly evaluated as a chronicler who knew how to construct an entire cultural phenomenon. And isn't it the same austere and cutting pen of this feminist in search of rationalism that gave _Les Temps modernes_ its true erotic consistency? Before Marxian rationalizing turned this journal into an idol for the international Left, from the postwar period to today, Beauvoir's cold account of a sexuality more contained than unveiled gave the publication its well-known aura.
My own history and, perhaps most of all, the disturbing abyss that the psychoanalytic experience shapes between "what is said" and undecidable "truth" prevent me from being a good witness. Moreover, _making history_ now appears to me, as I will try to show in the course of this essay, a task that, if it has not become impossible, has now been displaced. Rather than compiling "archives" or "annals," other questions make us stretch meaning into fiction. I say "us" because it seems to me that a profound turmoil has occurred in the last few years, still barely visible but operating in all spheres of culture.
What follows, then, will be an autobiography in the first person plural, a "we" of complicity, friendship, love. This "we" is the setting commonly recommended by the social contract for illusions, idealizations, errors, constructions. To write the autobiography of this "we" is surely a paradox that combines the passion for truth of the "I" with the absolute logical necessity of being able to share this truth only in part. To share it, first of all, between "us," so that this "we" survives. To share it also with you, so that an account, a report, a scheme remains (autobiography is a narration), rather than have speech fall into the fervor of dreams or poetry. Being hyperbolic, this "we" will retain from the problem-ridden paths of "I"s only the densest image, the most schematic, the one closest to a cliché. Should I shy away from it? I think of Canto III of Dante's _Paradiso_ where the writer, having had visions, hurries to push them aside for fear of becoming a new Narcissus. But Beatrice herself shows him that such a denial would be precisely a mistake comparable to the narcissistic error. For if an immediate vision is possible and must be sought, then it is necessarily accompanied by visionary constructions that are imperfect... fragmentary, schematic.... Truth can only be partially spoken. And it is enough to begin.... Common sense notwithstanding, this hyperbolic "we" is, in effect, only a part of "me." It is merely a temporary stability in which projections and identifications are settled among some and allow the history of a perpetually changing whole to be written. A "we" is alive only if it is never the same. As the chief locus of the image, it thrives only on the change of images. What the "I" loses in delegating itself to the group is partially regained in the metamorphoses of the "we." It is by transforming itself, by changing itself totally that the collective image, the group portrait, proves it is a momentarily fixed passion. To speak of "us" is not an analysis; it is a history that analyzes itself. But isn't any autobiography, even if it doesn't involve "us," a desire to make a collective public image exist, for "you," for "us"?
If you watch newsreels from World War II through the Algerian War on French television, you will find the same rhetoric of the image (technical improvements don't really affect the televised aesthetic of this period). The same verbal rhetoric lasts until 1962–1963: romanticism, bombast, bathos doled out by the slightly nasal voice of an anchorman adept at intoning war bulletins. In the shadow of political events, a fundamental change of outlook was necessary for us to regard this verbal edema as obsolete, to realize it belonged to another era. I see the written trace of this change in the austere paring down of the _nouveau roman_ , in its obsession with precision and details, for example, as well as the whole intellectual trend centered on the study of forms. This formalism was the purging of that subjective or rhetorical edema that our parents had set up to protect themselves against the devastating suffering of wars, or that they had used to construct their martyrdom. Fundamentally, May '68, despite its romantic airs, functioned like the fever of this process—an _analytic_ process (in the etymological sense of the term, that is, dissolving, abrasive, lucid) that leads us to a modernity that is, of course, mobile, eccentric, and unpredictable, but that breaks with the preceding years and that, or so it seems, must leave its mark on the end of our century.
In short, an account of the intellectual path of this period should primarily be an account of change—and for some it was an explosion—of bodies, of discourses, of ways of being. A sexuality freed from moral constraints, an image of the body no longer merely captured in a fine narcissistic surface but vaporized and sonorized with the help of drugs or rock or pop music if need be.... These mutations, these revolutions, contained as many delights as dramas, which had to be confronted, displaced and sublimated at each bend. Women with the pill, free love in broad daylight, assaults on the family, but also, the quest for complicity, tenderness, the security of a childhood always begun a new.... The adventure of ideas should be read against the background of a revolution in the reproduction of the species that attacks the classic conception of the sexual difference, makes women emerge aggressively, and finally leads to erotic ties around a new calm and civilizing secular cult of the child.... Political demands, of course! But also something beyond demands, with their explosiveness integrated into the fabric of time, of ethics.
The _Tel Quel_ Experience As It Was
During Christmas '65, in a bleak and rainy Paris, I would have been completely disappointed with the "city of lights" had I not attended midnight mass at Notre Dame, the ultimate meeting place for tourists. When I arrived in the French capital, I met people who were rather poor, whereas the elegant little restaurants and the chic little boutiques seemed to me to belong to a prewar movie. Between the technical brilliance of America and the leveling radicalisms of East European societies (which embodied, for me, two aspects of "modernity"), France seemed stuck in a pleasant archaicness, attractive and unreal. However, the social discontent that was brewing reached me through newspapers and conversations I overheard—even among people who seemed to be well off. I then realized that this country of shopkeepers wished to become the most developed of East European countries, as if its occult, unspoken goal was transforming itself into a society such as the one I had just left, a society that was criticized in Paris, only in fascinated, hushed tones.
My scholarship, in the framework of Franco-Bulgarian cultural agreements, encouraged my meeting writers and academics. I was, therefore, immediately immersed in an intellectual universe that both partook of this climate (by its interest in critical Marxism, in détente, in what was to become "socialism with a human face," etc.) and, at the same time, was wholly outside of it. I saw intellectuals as forming a real citadel within the state, without, however, burning their bridges to politics. They seemed to be engaged in a unique task: a subtle (even esoteric) and generous task, which not only was specifically French in its refinement and predisposition to formulas but also had universal aims and stakes. Having come to France under the auspices of the Gaullist dream of a "Europe from the Atlantic to the Urals," I felt I had found in this territory that stretched from the publishing house of Le Seuil to the EHESS (then EPHE) a cosmopolitanism that transcended the socialist and the European domains and that constituted a continent of thought, speculation, and writing corresponding to the high points of the universalistic legend of Paris.
I had received a francophile and francophone education. Since I had been trained as an intellectual in the French sense of the word, the _Marseillaise_ , and Voltaire, Victor Hugo, Anatole France—authors in no way incompatible, so it was said, with Marxist-Leninism—had been my language but also my moral textbooks. I was then in no way out of my element in the intellectual climate of Paris. I even had the impression, when I wasn't viewed as a more or less monstrous anomaly, that people saw in me, aside from my Stalinism, a perfect product of the French system projected into the future. Moreover, the Hautes Etudes was the ideal place for me: a structure of meeting and greeting similar to the one that served wandering scholastics in the best periods of the Middle Ages.
As soon as I arrived, I found in this environment a hospitality that, though cold and suspicious, was nonetheless functional and reliable; besides, it never contradicted itself. Despite the xenophobia, antifeminism, or anti-Semitism of one person or another, I maintain that French cultural life, as I have known it, has always been marked by a curiosity, discreet but generous, reticent but essentially receptive to nomadisms, oddities, to graftings and exogamies of all kinds. The great tolerance of the English or the enormous capacity for assimilation among Americans surely provides more existential opportunities. But they are, finally, because of their lesser _resistance_ , less conducive to the production of new thoughts.
The particular climate of France at that time can be understood in sociological terms. The chasm between social archaism and intellectual advances gave the latter an autonomy that helped them grow. Furthermore, the independence of Gaullist nationalism gave freedom of thought a power unequalled elsewhere: outside of France, there was nowhere else in the world where one could, in the heart of the most official institutions and in the spotlight of the media, draw simultaneously on Marx, Saint Augustine, Hegel, Saussure, and Freud. Finally, the genius of French institutions knew how to accommodate safety valves or precarious loop-holes alongside bureaucratic or bureaucratized bastions: the Ecole des Hautes Etudes counterbalancing the Sorbonne, _Tel Quel_ developing despite the NRF or _Temps Modernes_. It is banal to say that this universalistic cosmopolitan climate belongs to a tradition, one that probably dates back to the eminence of clerks and that established intellectuals of the eighteenth century as an autonomous force, beyond but not outside the city-state. However, this tradition also has an intrapsychic, sexual basis.
When thought admits its indebtedness to language—which was the case of the French "essayist" tradition long before structuralism—the speaking being is thrown into the infinite conceived as the power and cunning of the verb. From this locus, the intellectual acquires a transpolitical and transmoral function. Without belonging to any particular group or sect, yet giving the appearance of belonging to one, he thus reaches, by the very range of his search, the key zones, the most sensitive areas of social understanding. Modern art, madness, subjective experience, various marginal phenomena then became not mere objects of observation but actual fields of _study_ , as well as of _implication_ , which allow for an oblique grappling with "the social." In this way, the dilemma of "engagement" was reworked and displaced for us. It had become an implication, wholly comprised within the intellectual adventure that we lived as a _practice_ , subverting the distinctions between the individual/society, subject/group, form/content, style/meaning. With Michel Foucault and Jacques Lacan we didn't have to attack Jean-Paul Sartre's walls. The labyrinths of the _speaking subject_ —the microcosm of a complex logic whose effects had only partially surfaced in society—led us directly toward regions that were obscure but crucial, specific but universal, particular but transhistorical, far from society's policed scenarios.
In any event, at the end of '65, I landed at Lucien Goldmann's and Roland Barthes's doors at the Hautes Etudes. Lucien Goldmann welcomed me to his seminar on the "sociology of the novel" with fraternal distraction, convinced that I was a congenital Marxist, since I came from Eastern Europe. At the time, he was settling scores with existentialism, which was of little interest to me (I had arrived in Paris with two modern authors, Maurice Blanchot and Ferdinand Céline, in my suitcase), but the immeasurable practical help he gave me ensured my survival in France in the beginning. It was a kind of help that only those exiled from any country know how to give. With much liberalism and understanding, he directed my thesis on the origins of novelistic discourse, a thesis I defended, not without insolence, amid the generalized commotion of May '68. The atmosphere of a Goldmann seminar was very cosmopolitan: Marxism had already become a Third World matter, but it was also a refuge for young Germans and Italians rebelling against the legacy of families that had been more or less accomplices of the nazi or fascist regimes.... In addition, the Vietnam War was raging, and it simply seemed natural for us to side with the victims, that is, with the Marxists. Invoking this war, I thus refused René Girard's invitation to work in an American university. I found Goldmann's objection to my decision candid at the very least: "one has to go there in order to defeat capitalism from the inside," he said to me.
At the same time, at the Hautes Etudes, located in the same C section of the Sorbonne, the teaching of Roland Barthes attracted me because of its capacity to make formalism, which I had found reductive, extremely appealing. His audience, which was more exclusively French in those days (except for a few, Todorov among them who had come to France before), was astounded by the suicide of Lucien Sebag, which remained a mystery beyond all words, all comments. On my arrival, the only topic of conversation was the presentation on Stéphane Mallarmé that Philippe Sollers had just given. I thus read a few issues of _Tel Quel_ , and I met Sollers in May '66 through Gérard Genette, who was then attending the same seminar though he was an established literary critic.
Our first conversations with Sollers, in the office at 27 rue Jacob, at the Deux Magots, later at the Coupole, and at the Rose-Bud (Montparnasse soon became our neighborhood) were full of intellectual passion. I can still see us discussing _L'Expérience intérieure_ of Georges Bataille, a still vilified author whom Sollers had helped me discover. We also spoke of nationalism, for a quarrel divided East European intellectuals: should Sovietization be resisted with cosmopolitanism or nationalism? Lastly, there was feminism: "We women, like the proletariat, have nothing to lose but our chains," I used to say, with a simplicity that could only have been disarming. Soon after, our friend Sarah George-Picot, who was later in the Psychépo group with me, filmed an interview on this theme—a precocious feminist document that I believe is lost....
These details would have a personal meaning only if they did not reveal an important aspect of a period soon labeled "structuralist."
For us, structuralism (insofar as one can make generalizations about studies that range from Roman Jakobson's to Claude Lévi-Strauss's, or to certain works of Emile Benveniste, as well as of Barthes or Algirdas J. Greimas) was already accepted knowledge. To simplify, this meant that one should no longer lose sight of the real constraints, "material," as we used to say, of what had previously and trivially been viewed as "form." For us, the logic of this formal reality constituted the very meaning of phenomena or events that then became structures (from kinship to literary texts) and thus achieved intelligibility without necessarily relying on "external factors." From the outset, however, our task was to take this acquired knowledge and immediately do something else.
For some, the important task was to "deconstruct" phenomenology and structuralism as a minor form of a hidden metaphysics. Among these was Jacques Derrida, whose Introduction to Husserl's _Origins of Geometry_ had been discovered by Sollers, and who was involved in _Tel Quel_ for a time, when he already considered literature the privileged object of desire and analysis. For others, among whom I place myself, it was essential to "dynamize" the structure by taking into consideration the speaking subject and its unconscious experience on the one hand and, on the other, the pressures of other social structures. I seized upon Saussure's _Anagrammes_ , parts of which Jakobson and Starobinski had published. From this starting point, I tried to establish a "paragrammatical" conception of the literary text as a distortion of signs and their structures that produces an infinitesimal overdetermination of meaning in literature. From the same perspective, I reinterpreted a writer just republished in the U.S.S.R., whom we often read in Eastern Europe, seeing in his work a synthesis of formalism and history: Mikhail Bakhtin. A postformalist, he had introduced, through the carnival, Rabelais, Dostoyevsky, and the polyphonics of the modern novel, the notion of _alterity and dialogism_ into the arsenal of studies inspired by formalism. My conception of dialogism, of ambivalence, or what I call "intertextuality"—notions heavily indebted to Bakhtin and Freud—were to become gadgets that the American university is now in the process of discovering.
This compelling interest in the outer limits of a structure or subjective identity was stimulated by contact with modern literary texts: Bataille first, Mallarmé, Lautréamont, Artaud, Joyce, as well as the publications of my friends at _Tel Quel_. In their writings they aimed at reworking and enriching the technique of the _nouveau roman_ , to make it incorporate a painful, dramatic, or ecstatic internal experience, which its somewhat protestant austerity had rejected. Bataille, Joyce, and Artaud were the initiators of this writing technique, which we often reread and discussed. Sollers's _Requiem_ , with its traces of the military hospital and the Algerian War, is a good indication of the change of direction imposed on the formalist legacy.
Concern with style as experience or as subjective symptomatology was to lead me to an increasingly _clinical_ way of viewing language: acquisition of language by children, on the one hand, dissolution and pathology of discourse, on the other. Little by little, my "semiolotic" mode of thinking (which I already called "semanalysis") expanded to include a truly psychoanalytic approach.
Psychoanalysis—as the locus of extreme abjection, the refuge of private horror that can be lifted only by an infinite-indefinite displacement in speech and its effects—represents for me today the logical consequence of my initial questioning, which it still allows me to pursue. Leaving aside the uncertainties or the perversities of analytic institutions, I see psychoanalysis as the lay version, the only one, of the speaking being's quest for truth that religion symbolizes for certain of my contemporaries and friends. My own prejudice would lead me to think that God is analyzable. Infinitely....
My friendship with Emile Benveniste holds an important place in this period dominated by my participation in _Tel Quel_. This austere scholar, who used to read to me from the _Rigveda_ directly from Sanskrit into French and whose name appears below a _Surrealist Manifesto_ , borrowed the "Rodez Letters" from me so he could read them during the constitutional congress of the International Semiology Association, held in Warsaw in 1968. He secretly confided in me his belief that there were only two great French linguists: Mallarmé and Artaud. I can see him, some time later, at the hospital in Saint-Cloud, then later in Créteil, stricken with aphasia but surprisingly warm toward me, tracing with a trembling hand on a white sheet of paper the enigmatic letters T-H-E-O.
... _Tel Quel_ became, I think, the privileged link where the structuralist advance turned into an analysis of subjectivity. For the first time in modern history, except for the very brief futurist-formalist alliance shattered by the Stalinist regime in the U.S.S.R., a kind of thought was emerging that had as its foundation—as its object of analysis but especially its primary stimulant—the practice of writing in the process of production. A devaluated or simply ornamental zone, also far removed from the large art market that benefits painting, film, theater, and music— _l'écriture limite_ became the symptom around which a new theoretical discourse on language as subjective experience was constituted. This was not a mere "theory of literature" that remains, by its imaginary uncertainties, the weak link in the social sciences, but a testing point for psychoanalysis, one that is called upon to measure itself against a social creation, the text, rather than a private delirium. Finally, this writing is a site where the "sacred" is subverted, insofar as it is the discourse of a crisis in identity.
As I see it, this latter point, fundamental because of the breadth of the tradition it touches on (in France, largely Catholicism) and because of the interest it holds for the post-May '68 generation, is often misunderstood. It is interpreted as a manifestation of distress, the fad of a generation bereft of revolutionary ideas, even a joke. If it is true that Maurice Clavel ostensibly waived the post-'68 banner of this movement, then _Tel Quel_ bears the responsibility for its nocturnal emergence, like that of an old mole gnawing through the basements of mechanistic rationalism. Without the flair of the "nouveaux philosophes"—who are, all in all, fellow travelers closer to the media than to our research—our own thoughts on writing and the various mythemes of the sacred (from the sacrificial rite that institutes the symbolic to the Virgin, and the topos of the incarnation) have had a swift and artful dissemination whose toughness and corrosiveness have not always been appreciated. In short, these thoughts, as various articles and works of fiction published in _Tel Quel_ demonstrate, have nothing to do with a religious psychology or ideology but rather with certain phantasmic and linguistic knots on which the power of the sacred is built.
I remember the visit to the offices of _Tel Quel_ of an editor from the Soviet journal _Voprossi Filosoffi_. A specialist, I think, in aesthetics and modern literature, she was shocked by the formalism of the novels published in the series and by critics who left no room for the "soul," for the _doucha_ , as she said. This provoked great hilarity on Sollers's part, who was astonished to hear a "dialectical materialist" express herself in such a way. I am convinced that this laughter lives on in the author of _Paradis_ and _Eloge à Jean Paul II_.
The plurality, the diversity of these orientations—literature, psychoanalysis, history of religions—is disconcerting. Some readers have exhibited a tendency to see decided reversals in this phenomenon. It is true that the dominant concerns have not always been the same. "Semantic materialism" may have been overtaken by the "subject on trial," but it was never eclipsed. The names of Bataille, Sade, Artaud, and Joyce have remained fixed references, attesting not only that our aim has not been principally, even exclusively, literary, but that an experiment was involved even though personal or circumstantial limitations led to highlighting only one aspect of a palette of possibilities.
Obviously, each person who has worked, or who does work, with, for, or against _Tel Quel_ has his or her own profile, his or her own limit. From Barthes, Todorov, Genette, Derrida, from Deguy, Hallier, Faye, Ricardou, Baudry, Henric, etc., to those—such as Sollers, Pleynet, Risset, Devade, Houdebine, and Scarpetta, who continue to be involved or, more indirectly, B.-H. Levy first of all but also Benoist, Muray, and Jambet—the epistemological, ideological, stylistical options clearly vary (even diverge) among the writers. Is public opinion wrong to associate these irreducible diversities, somehow and in spite of everything, to the myth of a poststructuralism or to _Tel Quel_? It seems to me that the common denominator among these divergences, which perhaps hinge on a question of generation or "the spirit of the times," nevertheless lies in a postphenomenological or postanalytical vigilance. We set forth as pioneers—some of us cautiously, others recklessly—against what must be termed the phobic discretion of phenomenology and analysis before the contemporary aesthetic experience and what we have called the modern religion, that is, politics. One day, we will have to accept, or dare to think, that we are responsible for a certain position in language from which the meaning of the human adventure, bordering on the insane, is deciphered with an involvement that is decidedly risky (this has nothing to do with neutral "scientific" description).
In fact, a future historian of ideas will be able to discern the harbinger of the present insurrection against political reductionism in a specific lecture at a Milan colloquium when we criticized "politics as common measure." That historian will be able to decipher in our readings of Hegel, during our memorable "theoretical groups" at 44 rue de Rennes not simply "the only initiation to speculative philosophy appealing to today's youth" (as a journalist recently said) but also, and above all, the never abandoned effort to take transcendence seriously and to track down its premises in the innermost recesses of language. We will also be able to see, for instance, how certain brilliant students from my courses on Céline became journalists expert in the subtleties of right-wing aesthetics, or in the diffuse spirituality of our times.
I am not trying to have laurels bestowed upon us as precursors of the movement of vulgarization peculiar to contemporary cultural life. I would rather reestablish differences. Whether we came from a Catholic education or a frankly atheist one, or from an exquisite blend of the two, familiarity with Freud and with style in modern art and literature modified for us the enigma of Faith as well as the omnipotence of universal reason. Without rejecting their appeal, their economy was transformed into an inquiry on the dynamics of the speaking Subject and of Meaning. More than the convivial embroidery of Heidegger on the canvas of Logos, it was _Lacan's_ insolence in daring to introduce the "great Other" into the very heart of the speaking structure that propelled us on this course. We were attempting, in our own fashion, to circumscribe the unavoidable necessity of this Other and to analyze its crises, which determine the transformations, the life, and the history of discourses. That there is meaning, which is "One" and polyphonic nevertheless; that it exists but only in the irreducible multiplicities, that it follows the whims of desires and games of languages—these are surely views common to artists and analysts. In holding to these views, we necessarily felt far removed from both the antioedipals and the "deconstructionists." In a margin, irreducible and constructive, such as it is: _tel quel_.
What's the Use of Politics in Times of Distress?
_Clarté_ , the journal of communist students, had published, at the end of 1965, I think, a large picture of Sollers along with a text in which he explained, in essence, that only the socialist Revolution could provide a social setting propitious to avant-garde writing. This was, before the mediation of Genette, my first encounter with _Tel Quel_. And the first seduction. The theme Sollers elaborated had struck me. Not that the romantics or the surrealists hadn't proclaimed it before him. But it seemed to me completely unrealistic from the standpoint of the socialism I had experienced. I knew to what extent a regime born of a Marxist social mutation rejected not merely all aesthetic formalism deemed individualistic or antisocial, but also all individual stylistic experience that could question or explore the common code and its stereotypes in which ideology must seek shelter in order to dominate. Nevertheless, the logical firmness and the existential assurance of this young star in a _nouveau roman_ , rewritten by the painful adventure of the Algerian War and the Bataillian mystique, led me, as well as those who were to become my friends at _Tel Quel_ , to think that "in France, it would be different." In addition, hadn't Louis Althusser, whom we met soon after, taken the toughest (for me, the most "Stalinist") points of Marxism in order to instill new hope in the French Communist Party and all of French society, the harbinger of a worldwide Marxist spring? I remained, then, less sensitive to the arguments of the director of studies of the rue d'Ulm than to the revolutionary aestheticism of _Tel Quel_ , which seemed, after all, to bode well for the success of the futurist utopia.
Our attitude, which many termed scandalous at the time and which I now regard as illusory, still constitutes the national wager in France today. Were we, then, in the avant-garde on this level as well?
An important point must be emphasized to understand our boarding the Communist Party vessel. The French Communist Party (PFC) was, and still remains to a large extent, the only French party to have a cultural politics. The fact that today this party has lost its intellectuals of national and international renown does little to change its impact upon the cultural workers at the base. Even more—and in my mind this is essential—the PFC is the only party in France to have drawn a lesson (often machiavellically subtle thought for the most part clumsily and dogmatically applied) from having closely witnessed the great adventures of twentieth-century thought and art. The Socialist Party has only followed this course somewhat belatedly. Scorched by Stalinist social realism and shaken by détente, the Kremlin, with Aragon (like the Vatican with Mauriac), had already hailed the work of the young Sollers. But starting in 1966, the entire machine of the PFC awakened to the experiments of the avant-garde. Let's not forget that in France, institutional recognition of Russian formalism, futurism, and, by analogy, contemporary writing, with literary theory as one of its facets, first came with the publications of the PFC, _Les Lettres Françaises_ and the _Nouvelle Critique_ , and the colloquia it organized (Cluny I and Cluny II). In fact, I recently saw Japanese academics in Kyoto initiated into semiology through the published acts of these colloquia.
It is clear that without the fomentation of the militant base (schoolteachers and professors), the "social sciences" in their structuralist hue, and this includes Lacanian psychoanalysis, would not have invaded the university. Although the Edgar Faure reform provided a helping hand in this assault, these disciplines and methodologies nevertheless get their clientele from the audience of the PFC—notwithstanding the protests of leftists declaring "war unto death against the Communist Party." This may seem paradoxical on the part of a party devoted—if one is to believe its programs—to Marxist-Leninism. Those were times for "revisionism," however, and I'll always remember the words of comrade Juquin, during a luncheon of the _Nouvelle Critique_ colloquium, explaining to my companions, young bourgeois recently interested in the doctrine, that "Leninism is obsolete." The PFC was trying to take a social-democrat turn which, as we know, failed. The Socialist Party profited from this failure and gained ground, thus pushing the Communist Party toward its present decline.
But to remain on the cultural level, the narrow-minded battle of Mme Saunié-Seite against all forms of noninstitutionalized thought was nevertheless correct on this point: the Communist Party certainly appropriated, on behalf of the establishment, those currents of thought and aesthetic creation that would have remained marginal without it. From the moment of institutionalization, however, we ceased to believe in the permanent subversiveness of the Communist Party and ceased to see ourselves in what we had briefly believed was fated to mark the explosive beginnings of a revolutionary party.
Before coming to this moment of divorce, though, I cannot help but emphasize the scandal that our attitude caused in the moderate intelligentsia. I will pass over the first greeting I received from French public opinion: an insulting article in the magazine _Minute_ , claiming to unmask me, on the basis of an article on Bakhtin I had published in _Critique_ , as a Soviet spy. It was brought to me at Cochin hospital, where I was suffering from viral hepatitis in the spring of 1967, and I think it aided my recovery.
More spectacular in my view were articles in the _Nouvel Observateur_ , in which, after publication in the _Tel Quel_ series of a book by Pierre Daix, then still a member of the French Communist Party, we were labeled "Jdanovians" and "catatonics." I admit that I still find the connection between the rigidity of Jdanov and our baroque readings of Sade, Bataille, Freud, or the materialism of Lucretius to be rather tenuous. What I think I understand, however, is the feeling of betrayal, of a truly narcissistic injury, that an essentially Trotskyist—as it should be in the West—left must have felt in seeing our rapprochement to the Communist Party.
What, in fact, were we doing on this galley? Can one discern a general reason, a common denominator in this provisional attraction to the PFC beyond our very diverse psychological motivations, linked to each of our personal histories?
The generation of our elders, which should reproach itself for its dogmatic words and deeds and the more or less tragic consequences that occurred during its stint in the Communist Party, typically explains or, better yet, stigmatizes our behavior as "religious." As if religion were unanalyzable, the fascinating and indescribable enigma before which reason must lay down its arms.
For us, on the contrary, religion, I repeat, was not an enemy to flee, a target for reinvestment beneath the facade of a lay institution. It had already become a discourse for analysis. Since we were neither guilty of terrorist words and deeds, nor even secretly religious, what were we looking for in the PCF? My hypothesis, I think, far from exempting us, casts a less violent but more cruel light on the cynicism that binds the individual to politics, on the perversion that lies at the heart of the political institution, regardless of its nature.
As a state within the state, having considerable powers of dissemination and propaganda distinct from the traditional circuits saturated with more conventional products, the PCF was the best mouthpiece for experimental literary or theoretical work. To make this work public, in order to continue it, seemed to us imperative in an era of mass media. Indeed, an interview with Jean Paulhan, published at the time, compared the surrealists to _Tel Quel_ , emphasizing that we were a "mass movement." It was true, and to a large extent thanks to the Communist Party; but, on the whole, the idea was to use the Communist Party, not to be used by it.
To be sure, we did not deliberately exploit this misunderstanding. If there was any cynicism on our part, it can be derived from what must rightly be called our exaggerated regard for theory. Dialectical materialism, which, in our view, represented Hegel overturned by Lucretius, Mallarmé, and Freud (to cite only three parameters of a nonmechanistic materialism), gave us some hope, if not of modifying the bureaucratic defects of an oppressive machine—we didn't have the pragmatic soul of law-enforcers or founders of morally pure communities—at least of bracketing them.
I identify as political perversion a coherent structure determined by an ideal (this ideal was _theoretical_ for us; perhaps it has been _moral_ for others), which nevertheless uses the abjections of a reality, one that is neglected or even foreclosed, on behalf of libidinal or sublimated gratifications. (Our own gratification was essentially the development and appreciation of our work.) During the anarchic eruptions of May '68 (in which we participated around the clock), we kept from the beginning a foot on the barricades (that romantic intoxication corresponded to our erotic rhythms and our thoughts, which had broken with convention) and an eye in search of something that could ensure cultural transmission, something in the party that could be useful (to us).
Does this mean that I consider the intellectual essentially ambivalent, torn, treacherous? Not at all. Not only because others were, at the time, greater anarchists or conformists, depending on the logic of their own history. Not only because the principal result of May '68 was to accelerate the revisionism of the PCF, leading to a general social-democratization of French society—a process during which communist sensibility swerved to the center left, while Gaullist sensibility engendered a powerful center right, creating a bipartyism in the face of which any revolutionary stance was, ipso facto, transformed into an archaically oedipal attitude. But most of all, because this shift to the outskirts of the PCF gave us a clear view of the reality of a machine, of a group of human beings constituting itself to serve as the conveyor between, on the one hand, the ideal (be it murderous) and, on the other, the individual (whatever that person's value).
Rejected by both the perverted and the "political" animal, this machine is the killer mechanism of individual difference. "Society is a crime committed in common": in congresses and articles, in courses and theses, we have never ceased observing the truth of Freud's famous statement.
Because I brushed against this perverse experience in its cultural manifestation, I still cannot discard the idea that it is the central problem of modern social life, one we still need to analyze. My _Essai sur l'abjection_ is probably indirectly linked to this notion. One thing is certain: it is because we saw what was perverse in our relation to the Communist Party that we kept aloof, from then on, from any other political perversion, even a left-wing one. Our Maoism was an antiorganizational, antipartisan antidote, a utopia in pure form, which had nothing to do with the sects of the left (which were wary of us, and rightly so), proletarian or not, all of whom were rejects fascinated by or love-hating the Communist Party. In this light, the PCF itself does not appear an oddity. More radically, more somberly, it is the essence of the political tie: popular common sense, radical rationalization, the banal hideout, the orthodox lining of perversion.
What about the schisms, anathemas, persecutions, exclusions that checkered our game with these intrinsically perverse institutions? When they did not grow out of individual psychoanalysis, they were based on the wounds that our child's play with the (red) fire of politics reopened in the flesh of phobic adults. At times, reading articles in which some Parisian writer labeled me a Bogdanov, enemy of the wise Lenin, along with metaphors unleashed from the cellars of Bolshevism, I felt immersed in the universe of _The Possessed_. The sleepwalking fascination exerted by the clichés of the October Revolution on intellectuals weaned on the French Revolution seemed to illustrate a demonic and inevitable eternal return, in which it is impossible to distinguish between cause and effect, living spark and apocalyptic debacle.
As this period was ending, at least for me personally, my Czech friend Antonin Liehm arrived in Paris. An editor of the journal _Literarni Listi_ , Liehm was at the center of the "Prague spring" and had been expelled from his country after the arrival of Soviet tanks. He and I resumed our conversations on "liberty and Marxism" in jest, with an irony that only the phoenix people of Central and Eastern Europe can keep alive. About the same time, Louis Althusser, a leader with a great following, was proclaiming the necessity of maintaining the "dictatorship of the proletariat" but in a state of tension that seemed on the verge of breaking down. For the liberal press, however, the myth of the "Stalinist dogmatism" of _Tel Quel_ was in full swing. It was time to flee.
Peking-Shanghai-Louoyang-Nanking-Xian-Peking... New York
When we left, in the spring of 1974, for the first great voyage of Western intellectuals to China after the Cultural Revolution, many considered the trip a pilgrimage to the Mecca of dogmatism. It was impossible for me to make French intellectuals and my friends from Eastern Europe recognize that the China of the Cultural Revolution represented hope for national and libertarian socialism. For some of us, this gesture of friendship and adherence to the Chinese revolution was a way of associating with a left-wing political movement devoid of the Communist Party legacy. For others such as myself, who were not interested in political discourse, it was a means of finding another set of social and historical roots for "internal experience."
What we were looking for in the spasms of Chinese antibureaucratism at a moment when the party machinery had exploded and women, after the young, were suddenly pushed to the front line was Taoist culture, Chinese writing, and poetry, like jade, bland but subtle.
Joseph Needham, whom I had met in the chapel of Caius College, in Cambridge, and to whom we owe the monumental _Science and Civilisation in China_ , had no trouble convincing me that Mao, poet and writer, was the most faithful modern version of ancestral Taoism. I loved—I still love—to lose myself, as in a dream, in the characters of Chinese texts that my professor at Jussieu had rudimentarily taught me. In short, it was classical China, dressed in the worker's blue suit of socialism, that we had gone to find, more interested in Ming tombs or Buddhist steles than in the stories ("bricks, as information theory uses the term," said Roland Barthes) of the friendly Chinese activist comrades. I myself was alarmed by the profound, unflagging, sly presence of the Soviet model, the only sign of the twentieth century in this land of peasants, and all the more evident because it was violently resisted. This led me to write an awkward book, _Des Chinoises_ [1974], in which I tried to convey the strangeness of China and to explain the fascination we Occidentals feel for it, a fascination unquestionably involved with our own strange, foreign, feminine, psychotic aspects.
Politically, I saw nothing that might possibly prevent the Cultural Revolution from becoming a national and socialist variation, whose basic reference point remains the province of the Soviets. It marked my farewell to politics, including feminism.
The eruptions, encounters, loves, passions, as well as the more or less liberated or controlled eroticism that have shaped each person's biography constitute, I am convinced, the deepest influences on an individual path. In this essay, I simply present visible surface effects. Only a diary, a novel, could perhaps one day restore the wild indecency of it.
I can say, however, that for most of the Paris-Peking-Paris travelers (Roland Barthes, Philippe Sollers, Marcelin Playnet, François Wahl, and myself), this arduous journey, one that from the outset was more cultural than political, definitively inaugurated a return to the only continent we had never left: internal experience.
The psychoanalytic adventure on which my inquiries into infantile language, psychotic discourse, and style had started me finally led me to the Institute of Psychoanalysis. Lacan, whose seminar I attended until 1974 and whose baroque genius sometimes upset me as much as an actual session with an analyst, had not managed to free himself of the constraints his entourage imposed on him to follow us to China, as he wished to do. Even then, I thought I could discern signs of age in him—and signs of imposture in his school. I therefore avoided following him to his painful end.
The psychoanalytic experience struck me as the only one in which the wildness of the speaking being, and of language, can be heard. Political adventures, against the background of desire and hate that analysis openly unveils, appeared to me the way distance changes them: like a power of horror, like abjection. The sublime and horribly compromised work of Céline gave me the opportunity to speak of this.
_Tel Quel_ —never a whole, but rather a provisional association of individuals as they were, _tel quels_ —continued to develop, more than ever emphasizing the irreducible nature of writing, style, passion. Barthes's _Fragments d'un discours amoureux_ became the best-seller of a formalism altered in its very core: the pleasure of the text. Sollers, after _Nombres_ and _Lois_ and _H_ , which explore oneiric and vocal writing, published the first part of _Paradis_ , a saga in which the impact of sexual and political reality is bound to an apocalyptic lyricism that he was able, like a bard, to voice and stage in an excessive, magical performance that traveled from Beaubourg to Greenwich Village.
An unavoidable stage of our journey was our discovery of America. Pleynet, who sought out all forms of modern painting, had for some time been a frequent visitor. Since the early 1970s, I had been, in turn, warmly welcomed by a generous American university, free and encouraging in its curiosity and intellectual naiveté. The Alexandrine, cosmopolitan, decadent climate of New York City always gives me (this despite the archaisms of the American left) the impression of a latter-day Rome; I find nothing more stimulating to my work than those sojourns across the Atlantic. It seems to me that the Western individual, whose "hecceite" we, with Duns Scotus, unearthed in the last few issues of _Tel Quel_ , simultaneously enjoys, in the United States, a barbaric youth and an exquisite exhaustion.
To view my skeptical appreciation for this state of mind—of which the United States is clearly only an emblem—merely as a fad would be to ignore the individualist and universalist, desperate and jubilant aloofness, with its solitary atomism and its neutralized polyglotism, which substitutes for a community in this country of immigrants. They are traits specific to this _fin de siècle_ culture; jazz and rock are their popular manifestations. The United States is a culture in which you write a novel as though you were playing jazz or rock, where you can hear or think discourses, beginning with the convulsive excesses of individuals in the modern megalopolis, whose words seem to be mere provisional and inessential masks. It could be that they represent inordinate ambitions that often disturb editors, analysts, and academics alike. What is clear is that in this inordinacy there is no adherence to a culture, be it local, regional, French, Latin, or Mediterranean. It is perhaps a quest, in form and meaning, for these limits, which have become the reality, the _tel quel_ , of our time.
While the Latin American or Arab Marxist revolution is brewing on the doorstep of the United States, I feel closer to truth and liberty when I work within the space of this challenged giant, which may, in fact, be on the point of becoming a David before the growing Goliath of the Third World.
I dream that our children will prefer to join this David, with his errors and impasses, armed with our erring and circling about the Idea, the Logos, the Form: in short, the old Judeo-Christian Europe.
If it is only an illusion, I like to think it may have a future.
PART 2
_The Subject in Signifying Practice_
Revolution in Poetic Language
_Revolution in Poetic Language_ is probably Julia Kristeva's best-known text, for the central themes of her work over the last two decades have their beginnings here. Kristeva presented _La Révolution du langage poétique_ , 646 pages, for her State Doctorate in July 1973 in Paris. It was originally published in 1974 by Editions du Seuil. Columbia University Press published Margaret Waller's translation of just one-third of the original text in 1984. The following selection is part of that translation. The portions of _Révolution_ that have not been translated contain detailed analyses of texts by Lautréamont and Mallarmé. Those translated into English form the theoretical framework that Kristeva uses to analyze these texts. Here I have included the Prolegomenon and the following chapters from part 1, "The Semiotic and the Symbolic"—
1. The Phenomenological Subject of Enunciation
2. The Semiotic Chora Ordering the Drives
5. The Thetic: Rupture and/or Boundary
6. The Mirror and Castration
8. Breaching the Thetic: Mimesis
9. The Unstable Symbolic
10. The Signifying Process
12. Genotext and Phenotext
And from part 2, "Negativity: Rejection"—
1. The Fourth "Term" of the Dialectic
7. Freud's Notion of Expulsion: Rejection.
Kristeva's thesis is that nineteenth-century post-Symbolist avant-garde literature performs a revolution in language that transforms the structure of literary representation—a revolution in poetic language is analogous to a political revolution. The writings of Lautréamont and Mallarmé are examples of the revolution in language staged by the disruption of what Kristeva calls the "semiotic chora" in language. In the first part of _Revolution_ , "The Semiotic and the Symbolic," Kristeva describes what she means by semiotic chora and how this semiotic element of language differs from the symbolic element of language. Kristeva takes the term _chora_ from _Timeaus_ , where Plato used it to refer to a receptacle. For the ancient Greeks chora meant space, area, or land. Kristeva uses it to mean the space in which drives enter language. The semiotic chora is associated with the maternal body because the infant's drives are structured around the mother's body. Following Lacan, Kristeva describes the infant's movements through the mirror stage and castration to signification. Yet she insists that the semiotic chora, with its regulation and motility, prefigures the specular realm of the mirror stage. The semiotic chora is associated with sounds and rhythms that set up the possibility of signification before the infant (mis)recognizes itself in the mirror image.
Poetic language can reactivate the semiotic drive force in language through its sounds and rhythms. Poetic language performs what Kristeva calls a _reversed reactivation_ of the contradiction between semiotic and symbolic. Recall from the introduction to this collection, "Kristeva's Revolutions," that the semiotic is the element of signification associated with drives and affects, while the symbolic is the element of signification associated with position and judgment. The tension or contradiction between the semiotic and the symbolic elements is what makes language signify and significant. Poetic language does not represent the semiotic chora or drives in language; rather, poetic language reactivates the contradiction between the semiotic and the symbolic. By reactivating the drives in language, poetic language displays the process through which all signification is possible: all signification is possible through the dialectical movement between semiotic and symbolic, negativity and stases. Kristeva calls the founding moment of stasis in this dialectical process "the thetic" or a "thetic break."
Poetic language plays between what Kristeva calls the "genotext" and the "phenotext." The genotext is the underlying drive force in language. The phenotext is structured and grammatical; it makes communication possible. The genotext is a space that can be mapped in a topology but is not calculable. The phenotext, on the other hand, is a structure that can be calculated in an algebra. Whereas the genotext is a process, the phenotext is static. The distinction between genotext and phenotext corresponds to the distinction between semiotic and symbolic. The distinctions set up in _Revolution_ inform all Kristeva's writing.
In the second part of _Revolution_ , "Negativity: Rejection," Kristeva argues that poetic language is unique in that it displays the process through which signification is possible. Like poetic language, all signification is the result of a dialectical movement between semiotic and symbolic elements. In poetry, however, this dialectical tension is on display because of the poet's attention to the rhythms of words. The contradiction between semiotic and symbolic elements in language is never overcome through some kind of Hegelian dialectical synthesis. Rather, in Kristeva's description of the dialectical oscillation between these two elements, the contradiction itself is reactivated. In this way, negativity, or what, following Freud, she calls "rejection," makes its way into signification. Negativity is not sublimated into a higher level of stasis in the signifying process; rather, semiotic negativity is a necessary element of the signifying process that cannot be incorporated into symbolic stasis.
Desire in Language
"D'une identité l'autre" was originally read at a seminar organized by Jean-Marie Benoist and directed by Claude Lévi-Strauss at the Collège de France, January 27, 1975. It first appeared in print in _Tel Quel_ in the summer of 1975. It was reprinted in _Polylogue_ in 1977. "D'une identité l'autre" was translated as "From One Identity to an Other" by Thomas Gora, Alice Jardine, and Leon Roudiez in _Desire in Language: A Semiotic Approach to Literature and Art_ , edited by Roudiez and published by Columbia University Press in 1980.
In this essay, Kristeva takes up some of the themes from _Revolution in Poetic Language_ (1974). She further elaborates the revolutionary aspect of poetic language, especially the relationship between poetic language and the speaking subject. Poetic language puts the speaking subject in crisis. Here she proposes that the rhythms of poetic language not only violate the grammar of language but also render syntax indeterminate. Syntactical elisions in recent literature make it impossible to determine or distinguish basic syntactical categories like object or verb. The rhythms of language allow phonemes to function apart from the symbolic register of meaning and reference. Poetic language operates between sense and nonsense, meaning and nonmeaning. Moreover, poetic language shows how all signification operates between these two realms. All signification is undeterminable in this way.
Poetic language makes it clear that signification is a process that is not completely controlled by a unified subject. The two registers, semiotic and symbolic, of poetic language suggest a split subject, the split subject of psychoanalysis who always operates between unconscious and conscious realms. The semiotic and the symbolic elements of language become associated with the unconscious and consciousness. Kristeva challenges the Husserlian notion of a transcendental ego and postulates a subject-in-process or on trial ( _le sujet en procès_ ). The speaking subject is never fully developed or unified; rather the subject is a precarious process. In "From One Identity to an Other," as in _Powers of Horror_ (1980), Kristeva applies her analysis of the questionable subject-inprocess of poetic language to the writing of Louis-Ferdinand Céline.
Time and Sense
_Le temps sensible: Proust et l'expérience littéraire_ was originally published in Paris by Gallimard in 1994. Ross Guberman's translation, _Time and Sense: Proust and Literary Experience_ was published by Columbia University Press in 1996. Part of chapter 6, "Is Sensation a Form of Language?" and one section, "Freudian Time," of chapter 10, "Losing Impatience," are reprinted here. _Time and Sense_ is a lengthy, in-depth study of Proust's writings. For the first time, Kristeva devotes an entire book to the work of one writer. She analyzes everything from Proust's philosophy of time to the sentence structure and phonemes in his writings.
In "Is Sensation a Form of Language?" Kristeva analyzes the relationship between sensation and thought and sensation and language in the history of philosophy and psychoanalysis from Plato to Melanie Klein. She suggests that the practice of psychoanalysis, through transference and countertransference, attempts to reconnect sensation and language. She maintains that writing is also a process that moves back and forth between signs and flesh. In the section from chapter 10, Kristeva describes the time of transference as the time in which the unconscious (which operates outside of time) is inscribed.
_Revolution in Poetic Language_
Prolegomenon
Our philosophies of language, embodiments of the Idea, are nothing more than the thoughts of archivists, archaeologists, and necrophiliacs. Fascinated by the remains of a process that is partly discursive, they substitute this fetish for what actually produced it. Egypt, Babylon, Mycenae: we see their pyramids, their carved tablets, and fragmented codes in the discourse of our contemporaries and think that by codifying them we can possess them.
These static thoughts, products of a leisurely cogitation removed from historical turmoil, persist in seeking the truth of language by formalizing utterances that hang in midair and the truth of the subject by listening to the narrative of a sleeping body—a body in repose, withdrawn from its sociohistorical imbrication, removed from direct experience: "To be or not to be... To die, to sleep... To sleep—perchance to dream."
And yet, this thinking points to a truth, namely, that the kind of activity encouraged and privileged by (capitalist) society represses the _process_ pervading the body and the subject, and that we must therefore break out of our interpersonal and intersocial experience if we are to gain access to what is repressed in the social mechanism: the generating of significance.
The archivistic, archaeological, and necrophilic methods on which the scientific imperative was founded—the building of arguments on the basis of empirical evidence, a systematizable given, and an observable object—in this case, language—are an embarrassment when applied to modern or contemporary phenomena. These methods show that the capitalist mode of production has stratified language into idiolects and divided it into self-contained, isolated islands—heteroclite spaces existing in different temporal modes (as relics or projections), and oblivious of one another.
These random discursive instances have yet to be assigned a typology corresponding to the subjective and socioeconomic typologies in society as a whole. Instead, as agents of totality, in positions of control, science and theory intervene to make such discursive instances intelligible, each within its separate domain, even though they may lose them and have to start unifying them over and over again, if only provisionally—for that is their Long March. Linguistics, semiotics, anthropology, and psychoanalysis reveal that the thinking subject, the Cartesian subject who defines his being through thought or language, subsumes within that being and the operations which supposedly structure it, all translinguistic practice—a practice in which language and the subject are merely moments. From this perspective, the philosophy of language and the "human sciences" that stem from it emerge as reflections on moments. Whether they are viewed as simply linguistic, subjective, or more largely socioeconomic—depending on the "discipline"—such moments are nevertheless fragments, remains; their individual articulation is often examined, but rarely their interdependence or inception.
The critical question is not whether one can do otherwise. One clearly cannot if the object chosen is a human universe of full subjects who simply make systematic combinations in language and are themselves implicated in communication. Nor is it a question of calculating the pyramid's base and slant height and miming traces on Babylonian tablets or letters in Cretan linear writing. Such refinements in economics, phenomenology, and psychoanalysis de-structure finite systems and show that they are produced by a random albeit necessary causality. But one must still posit an "outside" that is in fact internal to each closed set, since otherwise the set would remain enclosed, even if internal differentiation could be extended indefinitely. One must, then, decenter the closed set and elaborate the dialectic of a process within plural and heterogeneous universes.
We will make constant use of notions and concepts borrowed from Freudian psychoanalytic theory and its various recent developments in order to give the advances of _dialectical logic_ a _materialist foundation_ —a theory of signification based on the subject, his formation, and his corporeal, linguistic, and social dialectic. Our purpose is not to adhere to the orthodoxy of any particular school, but rather to select those aspects of analytic theory capable of rationalizing the signifying process as it is practiced within texts. Does this dialectic itself avoid archivism? At least it indicates its own position, and renounces both the totalizing fragmentation characteristic of positivist discourse, which reduces all signifying practices to a formalism, and a reductive identification with other (discursive, ideological, economic) islands of the social aggregate.
From this position, it seems possible to perceive a signifying practice which, although produced in language, is only intelligible _through_ it. By exploding the phonetic, lexical, and syntactic object of linguistics, this practice not only escapes the attempted hold of all anthropomorphic sciences, it also refuses to identify with the recumbent body subjected to transference onto the analyzer. Ultimately, it exhausts the ever tenacious ideological institutions and apparatuses, thereby demonstrating the limits of formalist and psychoanalytic devices. This signifying practice—a particular type of modern literature—attests to a "crisis" of social structures and their ideological, coercive, and necrophilic manifestations. To be sure, such crises have occurred at the dawn and decline of every mode of production: the Pindaric obscurity that followed Homeric clarity and community is one of many examples. However, with Lautréamont, Mallarmé, Joyce, and Artaud, to name only a few, this crisis represents a new phenomenon. For the capitalist mode of production produces and marginalizes, but simultaneously exploits for its own regeneration, one of the most spectacular shatterings of discourse. By exploding the subject and its ideological limits, this phenomenon has a triple effect and raises three sets of questions:
1. Because of its specific isolation within the discursive totality of our time, this shattering of discourse reveals that linguistic changes constitute changes in the _status of the subject_ —his relation to the body, to others, and to objects; it also reveals that normalized language is just one of the ways of articulating the signifying process that encompasses the body, the material referent, and language itself. How are these strata linked? What is their interrelation within signifying practice?
2. The shattering further reveals that the capitalist mode of production, having attained a highly developed means of production through science and technology, no longer need remain strictly within linguistic and ideological _norms_ , but can also integrate their _process qua process_. As art, this shattering can display the productive basis of subjective and ideological signifying formations—a foundation that primitive societies call "sacred" and modernity has rejected as "schizophrenia." What is the extent of this integration? Under what conditions does it become indispensable, censured, repressed, or marginal?
3. Finally, in the history of signifying systems and notably that of the arts, religion, and rites, there emerge, in retrospect, fragmentary phenomena that have been kept in the background or rapidly integrated into more communal signifying systems but point to the very process of significance. Magic, shamanism, esoterism, the carnival, and "incomprehensible" poetry all underscore the limits of socially useful discourse and attest to what it represses: the _process_ that exceeds the subject and his communicative structures. But at what historical moment does social exchange tolerate or necessitate the manifestation of the signifying process in its "poetic" or "esoteric" form? Under what conditions does this "esoterism," in displacing the boundaries of socially established signifying practices, correspond to socioeconomic change, and, ultimately, even to revolution? And under what conditions does it remain a blind alley, a harmless bonus offered by a social order that uses this "esoterism" to expand, become flexible, and thrive?
If there exists a "discourse" that is not a mere depository of thin linguistic layers, an archive of structures, or the testimony of a withdrawn body, and is, instead, the essential element of a practice involving the sum of unconscious, subjective, and social relations in gestures of confrontation and appropriation, destruction and construction—productive violence, in short—it is "literature," or, more specifically, the _text_. Although simply sketched out, this notion of the text (to which we shall return) already takes us far from the realm of "discourse" and "art." The text is a practice that could be compared to political revolution: the one brings about in the subject what the other introduces into society. The history and political experience of the twentieth century have demonstrated that one cannot be transformed without the other—but could there be any doubt after the overturning [ _renversement_ ] of the Hegelian dialectic and especially after the Freudian revolution? Hence, the questions we will ask about literary practice will be aimed at the political horizon from which this practice is inseparable, despite the efforts of aestheticizing esoterism and repressive sociologizing or formalist dogmatics to keep them apart. We shall call this heterogeneous practice _signifiance_ to indicate, on the one hand, that biological urges are socially controlled, directed, and organized, producing an excess with regard to social apparatuses; and, on the other, that this instinctual operation becomes a _practice_ —a transformation of natural and social resistances, limitations, and stagnations—if and only if it enters into the code of linguistic and social communication. Laing and Cooper, like Deleuze and Guattari, are right to stress the destructuring and a-signifying machine of the unconscious. Compared with the ideologies of communication and normativeness, which largely inspire anthropology and psychoanalysis, their approach is liberating. What is readily apparent, however, is that their examples of "schizophrenic flow" are usually drawn from modern literature, in which the "flow" itself exists only through language, appropriating and displacing the signifier to practice _within it_ the heterogeneous generating of the "desiring machine."
What we call _signifiance_ , then, is precisely this unlimited and unbounded generating process, this unceasing operation of the drives toward, in, and through language; toward, in, and through the exchange system and its protagonists—the subject and his institutions. This heterogeneous process, neither anarchic, fragmented foundation nor schizophrenic blockage, is a structuring and de-structuring _practice_ , a passage to the outer _boundaries_ of the subject and society. Then—and only then—can it be jouissance and revolution.
NOTES
. "Device" is Kristeva's own choice for the translation of _dispositif_ : "dispositif," something devised or constructed for a particular purpose.—Trans.
. The expression _le renversement de Hegel_ refers to a complex series of visions and revisions of the materialist debt to Hegel's dialectic. Kristeva's use of the term would seem to be informed by Althusser's "symptomatic reading" of Marx. In "Contradiction and Overdetermination," Althusser questions Marx's ambiguous and metaphorical statement that the Hegelian dialectic is "standing on its head" and "must be turned right side up again," and he argues that the materialist "inversion" of Hegel is no inversion at all. _For Marx_ , Ben Brewster (New York: Random House, 1969), pp. 89–116. I have therefore translated _renversement_ as "overturning" to convey the notion of a radical transformation that may or may not consist in a "reversal" of Hegel's dialectic.—Trans.
. Gilles Deleuze and Félix Guattari, _Anti-Oedipus: Capitalism and Schizophrenia_ , Robert Hurley et al., tr. (New York: Viking Press, 1977).
The Semiotic and the Symbolic
_Further determine [the] object for itself, [a] logic behind consciousness_
— _Hegel, Autumn 1831_
1. The Phenomenological Subject of Enunciation
We must specify, first and foremost, what we mean by the _signifying process_ vis-à-vis general theories of meaning, theories of language, and theories of the subject.
Despite their variations, all modern linguistic theories consider language a strictly "formal" object—one that involves syntax or mathematicization. Within this perspective, such theories generally accept the following notion of language. For Zellig Harris, language is defined by: (1) the arbitrary relation between signifier and signified, (2) the acceptance of the sign as a substitute for the extralinguistic, (3) its discrete elements, and (4) its denumerable, or even finite, nature. But with the development of Chomskyan generative grammar and the logico-semantic research that was articulated around and in response to it, problems arose that were generally believed to fall within the province of "semantics" or even "pragmatics," and raised the awkward question of the _extralinguistic_. But language [ _langage_ ]—modern linguistics' self-assigned object—lacks a subject or tolerates one only as a _transcendental ego_ (in Husserl's sense or in Benveniste's more specifically linguistic sense), and defers any interrogation of its (always already dialectical because translinguistic) "externality."
Two trends in current linguistic research do attend to this "externality" in the belief that failure to elucidate it will hinder the development of linguistic theory itself. Although such a lacuna poses problems (which we will later specify) for "formal" linguistics, it has always been a particular problem for semiotics, which is concerned with specifying the functioning of signifying practices such as art, poetry, and myth that are irreducible to the "language" object.
1. The first of these two trends addresses the question of the so-called arbitrary relation between signifier and signified by examining signifying systems in which this relation is presented as "motivated." It seeks the principle of this motivation in the Freudian notion of the unconscious insofar as the theories of drives [ _pulsions_ ] and primary processes (displacement and condensation) can connect "empty signifiers" to psychosomatic functionings, or can at least link them in a sequence of metaphors and metonymies; though undecidable, such a sequence replaces "arbitrariness" with "articulation." The discourse of analysands, language "pathologies," and artistic, particularly poetic, systems are especially suited to such an exploration. Formal linguistic relations are thus connected to an "externality" in the psychosomatic realm, which is ultimately reduced to a fragmented substance [ _substance morcelée_ ] (the body divided into erogenous zones) and articulated by the developing ego's connections to the three points of the family triangle. Such a linguistic theory, clearly indebted to the positions of the psychoanalytic school of London and Melanie Klein in particular, restores to formal linguistic relations the dimensions (instinctual drives) and operations (displacement, condensation, vocalic and intonational differentiation) that formalistic theory excludes. Yet for want of a dialectical notion of the _signifying process_ as a whole, in which significance puts the subject in process/on trial [ _en procès_ ], such considerations, no matter how astute, fail to take into account the syntactico-semantic functioning of language. Although they rehabilitate the notion of the fragmented body—pre-Oedipal but always already invested with semiosis—these linguistic theories fail to articulate its transitional link to the post-Oedipal subject and his always symbolic and/or syntactic language. (We shall return to this point.)
2. The second trend, more recent and widespread, introduces within theory's own formalism a "layer" of _semiosis_ , which had been strictly relegated to pragmatics and semantics. By positing a _subject of enunciation_ (in the sense of Benveniste, Culioli, and others), this theory places logical modal relations, relations of presupposition, and other relations between interlocutors within the speech act, in a very deep "deep structure." This _subject of enunciation_ , which comes directly from Husserl and Benveniste (see n. 3), introduces, through categorical intuition, both _semantic fields_ and _logical_ —but also _intersubjective_ — _relations_ , which prove to be both intra- and translinguistic.
To the extent it is assumed by a subject who "means" ( _bedeuten_ ), language has "deep structures" that articulate _categories_. These categories are semantic (as in the semantic fields introduced by recent developments in generative grammar), logical (modality relations, etc.), and intercommunicational (those that Searle called "speech acts" seen as bestowers of meaning). But they may also be related to historical linguistic changes, thereby joining diachrony with synchrony. In this way, through the subject who "means," linguistics is opened up to all possible categories and thus to philosophy, which linguistics had thought it would be able to escape.
In a similar perspective, certain linguists, interested in explaining semantic constraints, distinguish between different types of _styles_ depending on the speaking subject's position vis-à-vis the utterance. Even when such research thereby introduces stylistics into semantics, its aim is to study the workings of signification, taking into account the subject of enunciation, which always proves to be the phenomenological subject.
Some linguistic research goes even further: starting from the subject of enunciation/transcendental ego and prompted by the opening of linguistics onto semantics and logic, it views signification as an ideological and therefore historical production.
We shall not be able to discuss the various advantages and drawbacks of this second trend in modern linguistics except to say that it is still evolving and that, although its conclusions are only tentative, its epistemological bases lead us to the heart of the debate on phenomenology which we can only touch on here—and only insofar as the specific research we are at present undertaking allows.
To summarize briefly what we shall elucidate later, the two trends just mentioned designate _two modalities_ of what is, for us, the same signifying process. We shall call the first _the semiotic_ and the second _the symbolic_. These two modalities are inseparable within the _signifying process_ that constitutes language, and the dialectic between them determines the type of discourse (narrative, metalanguage, theory, poetry, etc.) involved; in other words, so-called natural language allows for different modes of articulation of the semiotic and the symbolic. On the other hand, there are nonverbal signifying systems that are constructed exclusively on the basis of the semiotic (music, for example). But, as we shall see, this exclusivity is relative, precisely because of the necessary dialectic between the two modalities of the signifying process, which is constitutive of the subject. Because the subject is always _both_ semiotic _and_ symbolic, no signifying system he produces can be either "exclusively" semiotic or "exclusively" symbolic, and is instead necessarily marked by an indebtedness to both.
2. The Semiotic _Chora_ : Ordering the Drives
We understand the term "semiotic" in its Greek sense: σημεĩον = distinctive mark, trace, index, precursory sign, proof, engraved or written sign, imprint, trace, figuration. This etymological reminder would be a mere archaeological embellishment (and an unconvincing one at that, since the term ultimately encompasses such disparate meanings), were it not for the fact that the preponderant etymological use of the word, the one that implies a _distinctiveness_ , allows us to connect it to a precise modality in the signifying process. This modality is the one Freudian psychoanalysis points to in postulating not only the _facilitation_ and the structuring _disposition_ of drives, but also the so-called _primary processes_ , which displace and condense both energies and their inscription. Discrete quantities of energy move through the body of the subject who is not yet constituted as such and, in the course of his development, they are arranged according to the various constraints imposed on this body—always already involved in a semiotic process—by family and social structures. In this way the drives, which are "energy" charges as well as "psychical" marks, articulate what we call a _chora_ : a nonexpressive totality formed by the drives and their stases in a motility that is as full of movement as it is regulated.
We borrow the term _chora_ 11 from Plato's _Timaeus_ to denote an essentially mobile and extremely provisional articulation constituted by movements and their ephemeral stases. We differentiate this uncertain and indeterminate _articulation_ from a _disposition_ that already depends on representation, lends itself to phenomenological, spatial intuition, and gives rise to a geometry. Although our theoretical description of the _chora_ is itself part of the discourse of representation that offers it as evidence, the _chora_ , as rupture and articulations (rhythm), precedes evidence, verisimilitude, spatiality, and temporality. Our discourse—all discourse—moves with and against the _chora_ in the sense that it simultaneously depends upon and refuses it. Although the _chora_ can be designated and regulated, it can never be definitively posited: as a result, one can situate the _chora_ and, if necessary, lend it a topology, but one can never give it axiomatic form.
The _chora_ is not yet a position that represents something for someone (i.e., it is not a sign); nor is it a _position_ that represents someone for another position (i.e., it is not yet a signifier either); it is, however, generated in order to attain to this signifying position. Neither model nor copy, the _chora_ precedes and underlies figuration and thus specularization, and is analogous only to vocal or kinetic rhythm. We must restore this motility's gestural and vocal play (to mention only the aspect relevant to language) on the level of the socialized body in order to remove motility from ontology and amorphousness where Plato confines it in an apparent attempt to conceal it from Democritean rhythm. The theory of the subject proposed by the theory of the unconscious will allow us to read in this rhythmic space, which has no thesis and no position, the process by which signifiance is constituted. Plato himself leads us to such a process when he calls this receptacle or _chora_ nourishing and maternal, not yet unified in an ordered whole because deity is absent from it. Though deprived of unity, identity, or deity, the _chora_ is nevertheless subject to a regulating process [ _réglementation_ ], which is different from that of symbolic law but nevertheless effectuates discontinuities by temporarily articulating them and then starting over, again and again.
The _chora_ is a modality of signifiance in which the linguistic sign is not yet articulated as the absence of an object and as the distinction between real and symbolic. We emphasize the regulated aspect of the _chora_ : its vocal and gestural organization is subject to what we shall call an objective _ordering_ [ _ordonnancement_ ], which is dictated by natural or sociohistorical constraints such as the biological difference between the sexes or family structure. We may therefore posit that social organization, always already symbolic, imprints its constraint in a mediated form that organizes the _chora_ not according to a _law_ (a term we reserve for the symbolic) but through an _ordering_. What is this mediation?
According to a number of psycholinguists, "concrete operations" precede the acquisition of language, and organize preverbal semiotic space according to logical categories, which are thereby shown to precede or transcend language. From their research we shall retain not the principle of an operational state but that of a preverbal functional state that governs the connections between the body (in the process of constituting itself as a body proper), objects, and the protagonists of family structure. But we shall distinguish this functioning from symbolic operations that depend on language as a sign system—whether the language _langue_ ] is vocalized or gestural (as with deaf-mutes). The kinetic functional stage of the _semiotic_ precedes the establishment of the sign; it is not, therefore, cognitive in the sense of being assumed by a knowing, already constituted subject. The genesis of the _functions_[ 18 organizing the semiotic process can be accurately elucidated only within a theory of the subject that does not reduce the subject to one of understanding, but instead opens up within the subject this other scene of presymbolic functions. The Kleinian theory expanding upon Freud's positions on the drives will momentarily serve as a guide.
Drives involve pre-Oedipal semiotic functions and energy discharges that connect and orient the body to the mother. We must emphasize that "drives" are always already ambiguous, simultaneously assimilating and destructive; this dualism, which has been represented as a tetrad or as a double helix, as in the configuration of the DNA and RNA molecule, makes the semiotized body a place of permanent scission. The oral and anal drives, both of which are oriented and structured around the mother's body, dominate this sensorimotor organization. The mother's body is therefore what mediates the symbolic law organizing social relations and becomes the ordering principle of the semiotic _chora_ , which is on the path of destruction, aggressivity, and death. For although drives have been described as disunited or contradictory structures, simultaneously "positive" and "negative," this doubling is said to generate a dominant "destructive wave" that is drive's most characteristic trait: Freud notes that the most instinctual drive is the death drive. In this way, the term "drive" denotes waves of attack against stases, which are themselves constituted by the repetition of these charges; together, charges and stases lead to no identity (not even that of the "body proper") that could be seen as a result of their functioning. This is to say that the semiotic _chora_ is no more than the place where the subject is both generated and negated, the place where his unity succumbs before the process of charges and stases that produce him. We shall call this process of charges and stases a _negativity_ to distinguish it from negation, which is the act of a judging subject.
Checked by the constraints of biological and social structures, the drive charge thus undergoes stases. Drive facilitation, temporarily arrested, marks _discontinuities_ in what may be called the various material supports [ _matériaux_ ] susceptible to semiotization: voice, gesture, colors. Phonic (later phonemic), kinetic, or chromatic units and differences are the marks of these stases in the drives. Connections or _functions_ are thereby established between these discrete marks, which are based on drives and articulated according to their resemblance or opposition, either by slippage or by condensation. Here we find the principles of metonymy and metaphor indissociable from the drive economy underlying them.
Although we recognize the vital role played by the processes of displacement and condensation in the organization of the semiotic, we must also add to these processes the relations (eventually representable as topological spaces) that connect the zones of the fragmented body to each other and also to "external" "objects" and "subjects," which are not yet constituted as such. This type of relation makes it possible to specify the _semiotic_ as a psychosomatic modality of the signifying process; in other words, not a symbolic modality but one articulating (in the largest sense of the word) a continuum: the connections between the (glottal and anal) sphincters in (rhythmic and intonational) vocal modulations, or those between the sphincters and family protagonists, for example.
All these various processes and relations, anterior to sign and syntax, have just been identified from a genetic perspective as previous and necessary to the acquisition of language, but not identical to language. Theory can "situate" such processes and relations diachronically within the process of the constitution of the subject precisely because _they function synchronically within the signifying process of the subject himself_ , that is, the subject of _cogitatio_. Only in _dream_ logic, however, have they attracted attention, and only in certain signifying practices, such as the _text_ , do they dominate the signifying process.
It may be hypothesized that certain semiotic articulations are transmitted through the biological code or physiological "memory" and thus form the inborn bases of the symbolic function. Indeed, one branch of generative linguistics asserts the principle of innate language universals. As it will become apparent in what follows, however, the _symbolic_ —and therefore syntax and all linguistic categories—is a social effect of the relation to the other, established through the objective constraints of biological (including sexual) differences and concrete, historical family structures. Genetic programmings are necessarily semiotic: they include the primary processes such as displacement and condensation, absorption and repulsion, rejection and stasis, all of which function as innate preconditions, "memorizable" by the species, for language acquisition.
Mallarmé calls attention to the semiotic rhythm within language when he speaks of "The Mystery in Literature" ["Le Mystére dans les lettres"]. Indifferent to language, enigmatic and feminine, this space underlying the written is rhythmic, unfettered, irreducible to its intelligible verbal translation; it is musical, anterior to judgment, but restrained by a single guarantee: syntax. As evidence, we could cite "The Mystery in Literature" in its entirety. For now, however, we shall quote only those passages that ally the functioning of that "air or song beneath the text" with woman:
And the instrument of Darkness, whom they have designated, will not set down a word from then on except to deny that she must have been the enigma; lest she settle matters with a wisk of her skirts: "I don't get it!"
—They [the critics] play their parts disinterestedly or for a minor gain: leaving our Lady and Patroness exposed to show her dehiscence or lacuna, with respect to certain dreams, as though this were the standard to which everything is reduced.
To these passages we add others that point to the "mysterious" functioning of literature as a rhythm made intelligible by syntax: "Following the instinct for rhythms that has chosen him, the poet does not deny seeing a lack of proportion between the means let loose and the result." "I know that there are those who would restrict Mystery to Music's domain; when writing aspires to it."
What pivot is there, I mean within these contrasts, for intelligibility? a guarantee is needed—
Syntax—
... an extraordinary appropriation of structure, limpid, to the primitive lightning bolts of logic. A stammering, what the sentence seems, here repressed [... ]
The debate—whether necessary average clarity deviates in a detail—remains one for grammarians.
Our positing of the semiotic is obviously inseparable from a theory of the subject that takes into account the Freudian positing of the unconscious. We view the subject in language as decentering the transcendental ego, cutting through it, and opening it up to a dialectic in which its syntactic and categorical understanding is merely the liminary moment of the process, which is itself always acted upon by the relation to the other dominanted by the death drive and its productive reiteration of the "signifier." We will be attempting to formulate the distinction between _semiotic_ and _symbolic_ within this perspective, which was introduced by Lacanian analysis, but also within the constraints of a practice—the _text_ —which is only of secondary interest to psychoanalysis.
5. The Thetic: Rupture and/or Boundary
We shall distinguish the semiotic (drives and their articulations) from the realm of signification, which is always that of a proposition or judgment, in other words, a realm of _positions_. This positionality, which Husserlian phenomenology orchestrates through the concepts of _doxa_ , _position_ , and _thesis_ , is structured as a break in the signifying process, establishing the _identification_ of the subject and its object as preconditions of propositionality. We shall call this break, which produces the positing of signification, a _thetic_ phase. All enunciation, whether of a word or of a sentence, is thetic. It requires an identification; in other words, the subject must separate from and through his image, from and through his objects. This image and objects must first be posited in a space that becomes symbolic because it connects the two separated positions, recording them or redistributing them in an open combinatorial system.
The child's first so-called holophrastic enunciations include gesture, the object, and vocal emission. Because they are perhaps not yet sentences (NP-VP), generative grammar is not readily equipped to account for them. Nevertheless, they are already thetic in the sense that they separate an object from the subject and attribute to it a semiotic fragment, which thereby becomes a signifier. That this attribution is either metaphoric or metonymic ("woof-woof" says the dog, and all animals become "woof-woof") is logically secondary to the fact that it constitutes an _attribution_ , which is to say, a positing of identity or difference, and that it represents the nucleus of judgment or proposition.
We shall say that the thetic phase of the signifying process is the "deepest structure" of the possibility of enunciation, in other words, of signification and the proposition. Husserl theologizes this deep logic of signification by making it a productive _origin_ of the "free spontaneity" of the Ego:
Its _free spontaneity and activity_ consists in positing, positing on the strength of this or that, positing as an antecedent or a consequent, and so forth; it does not live within the theses as a passive indweller; the theses radiate from it as from a primary source of generation [ _Erzeugungen_ ]. Every thesis begins with a _point of insertion_ [ _Einsatzpunkt_ ] with a point at which _the positing has its origin_ [ _Ursprungssetzung_ ]; so it is with the first thesis and with each further one in the synthetic nexus. This "inserting" even belongs to the thesis as such, as a remarkable modus of original actuality. It somewhat resembles the _fiat_ , the point of insertion of will and action.
In this sense, _there exists only one signification_ , that of the thetic phase, which contains the object as well as the proposition, and the complicity between them. There is no sign that is not thetic and every sign is already the germ of a "sentence," attributing a signifier to an object through a "copula" that will function as a signified. Stoic semiology, which was the first to formulate the matrix of the sign, had already established _this complicity between sign and sentence_ , making them proofs of each other.
Modern philosophy recognizes that the right to represent the founding _thesis_ of signification (sign and/or proposition) devolves upon the transcendental ego. But only since Freud have we been able to raise the question not of the origin of this thesis but rather of the process of its production. To brand the thetic as the foundation of metaphysics is to risk serving as an antechamber for metaphysics—unless, that is, we specify the way the thetic is produced. In our view, the Freudian theory of the unconscious and its Lacanian development show, precisely, that thetic signification is a stage attained under certain precise conditions during the signifying process and that it constitutes the subject without being reduced to his process precisely because it is the threshold of language. Such a standpoint constitutes neither a reduction of the subject to the transcendental ego, nor a denial [ _dénégation_ ] of the thetic phase that establishes signification.
6. The Mirror and Castration: Positing the Subject as Absent from the Signifier
In the development of the subject, such as it has been reconstituted by the theory of the unconscious, we find the thetic phase of the signifying process, around which signification is organized, at two points: the mirror stage and the "discovery" of castration.
The first, the mirror stage, produces the "spatial intuition" which is found at the heart of the functioning of signification—in signs and in sentences. From that point on, in order to capture his image unified in a mirror, the child must remain separate from it, his body agitated by the semiotic motility we discussed above, which fragments him more than it unifies him in a representation. According to Lacan, human physiological immaturity, which is due to premature birth, is thus what permits any permanent positing whatsoever and, first and foremost, that of the image itself, as separate, heterogeneous, dehiscent. Captation of the image and the drive investment in this image, which institute primary narcissism, permit the constitution of objects detached from the semiotic _chora_. Lacan maintains, moreover, that the specular image is the "prototype" for the "world of objects." Positing the imaged ego leads to the positing of the object, which is, likewise, separate and signifiable.
Thus the two separations that prepare the way for the sign are set in place. The sign can be conceived as the voice that is projected from the agitated body (from the semiotic _chora_ ) onto the facing _imago_ or onto the object, which simultaneously detach from the surrounding continuity. Indeed, a child's first holophrastic utterances occur at this time, within what are considered the boundaries of the mirror stage (six to eighteen months). On the basis of this positing, which constitutes a _break_ , signification becomes established as a digital system with a double articulation combining discrete elements. Language learning can therefore be thought of as an acute and dramatic confrontation between positing-separating-identifying and the motility of the semiotic _chora_. Separation from the mother's body, the _fort-da_ game, anality and orality, all act as a permanent negativity that destroys the image and the isolated object even as it facilitates the articulation of the semiotic network, which will afterwards be necessary in the system of language where it will be more or less integrated as a _signifier_.
Castration puts the finishing touches on the process of separation that posits the subject as signifiable, which is to say, separate, always confronted by an other: _imago_ in the mirror (signified) and semiotic process (signifier). As the addressee of every demand, the mother occupies the place of alterity. Her replete body, the receptacle and guarantor of demands, takes the place of all narcissistic, hence imaginary, effects and gratifications; she is, in other words, the phallus. The discovery of castration, however, detaches the subject from his dependence on the mother, and the perception of this lack [ _manqué_ ] makes the phallic function a symbolic function— _the_ symbolic function. This is a decisive moment fraught with consequences: the subject, finding his identity in the symbolic, _separates_ from his fusion with the mother, _confines_ his jouissance to the genital, and transfers semiotic motility onto the symbolic order. Thus ends the formation of the thetic phase, which posits the gap between the signifier and the signified as an opening up toward every desire but also every act, including the very jouissance that exceeds them.
At this point we would like to emphasize, without going into the details of Lacan's argument, that the phallus totalizes the effects of signifieds as having been produced by the signifier: the phallus is itself a signifier. In other words, the phallus is not given in the utterance but instead refers outside itself to a precondition that makes enunciation possible. For there to be enunciation, the _ego_ must be posited in the signified, but it must do so as a function of the _subject_ lacking in the signifier; a system of finite positions (signification) can only function when it is supported by a subject and on the condition that this subject is a want-to-be [ _manque à être_ ]. Signification exists precisely because there is no subject in signification. The gap between the imaged ego and drive motility, between the mother and the demand made on her, is precisely the break that establishes what Lacan calls the place of the Other as the place of the "signifier." The subject is hidden "by an ever purer signifier"; this want-to-be confers on an _other_ the role of containing the possibility of signification; and this other, who is no longer the mother (from whom the child ultimately separates through the mirror stage and castration), presents itself as the place of the signifier that Lacan will call "the Other."
Is this to say, then, that such a theoretical undertaking transcendentalizes semiotic motility, setting it up as a transcendental Signifier? In our view, this transformation of semiotic motility serves to remove it from its autoerotic and maternal enclosure and, by introducing the signifier/signified break, allows it to produce signification. By the same token, signification itself appears as a stage of the signifying process—not so much its base as its boundary. Signification is placed "under the sign of the preconscious." Ultimately, this signifier/signified transformation, constitutive of language, is seen as being indebted to, induced, and imposed by the social realm. Dependence on the mother is severed, and transformed into a symbolic relation to an other; the constitution of the Other is indispensable for communicating with an other. In this way, the signifier/signified break is synonymous with social sanction: "the first social censorship."
Thus we view the thetic phase—the positing of the _imago_ , castration, and the positing of semiotic motility—as the place of the Other, as the precondition for signification, that is, the precondition for the positing of language. The thetic phase marks a threshold between two heterogeneous realms: the semiotic and the symbolic. The second includes part of the first and their scission is thereafter marked by the break between signifier and signified. _Symbolic_ would seem an appropriate term for this always split unification that is produced by a rupture and is impossible without it. Its etymology makes it particularly pertinent. The σύμβολον is a sign of recognition: an "object" split in two and the parts separated, but, as eyelids do, σύμβολον brings together the two edges of that fissure. As a result, the "symbol" is any joining, any bringing together that is a contract—one that either follows hostilities or presupposes them—and, finally, any exchange, including an exchange of hostility.
Not only is symbolic, thetic unity divided (into signifier and signified), but this division is itself the result of a break that put a heterogeneous functioning in the position of signifier. This functioning is the instinctual semiotic, preceding meaning and signification, mobile, amorphous, but already regulated, which we have attempted to represent through references to child psychoanalysis (particularly at the pre-Oedipal stage) and the theory of drives. In the speaking subject, fantasies articulate this irruption of drives within the realm of the signifier; they disrupt the signifier and shift the metonymy of desire, which acts within the place of the Other, onto a jouissance that divests the object and turns back toward the autoerotic body. That language is a defensive construction reveals its ambiguity—the death drive underlying it. If language, constituted as symbolic through narcissistic, specular, imaginary investment, protects the body from the attack of drives by making it a place—the place of the signifier—in which the body can signify itself through positions; and if, therefore, language, in the service of the death drive, is a pocket of narcissism toward which this drive may be directed, then fantasies remind us, if we had ever forgotten, of the insistent presence of drive heterogeneity.
All poetic "distortions" of the signifying chain and the structure of signification may be considered in this light: they yield under the attack of the "residues of first symbolizations" (Lacan), in other words, those drives that the thetic phase was not able to sublate [ _relever_ , _aufheben_ ] by linking them into signifier and signified. As a consequence, any disturbance of the "social censorship"—that of the signifier/signified break—attests, perhaps first and foremost, to an influx of the death drive, which no signifier, no mirror, no other, and no mother could ever contain. In "artistic" practices the semiotic—the precondition of the symbolic—is revealed as that which also destroys the symbolic, and this revelation allows us to presume something about its functioning.
Psychoanalysts acknowledge that the pre-Oedipal stages Melanie Klein discusses are "analytically unthinkable" but not inoperative; and, furthermore, that the relation of the subject to the signifier is established and language learning is completed only in the pregenital stages that are set in place by the retroaction of the Oedipus complex (which itself brings about initial genital maturation). Thereafter, the supposedly characteristic functioning of the pre-Oedipal stages appears only in the complete, postgenital handling of language, which presupposes, as we have seen, a decisive imposition of the phallic. In other words, the subject must be firmly posited by castration so that drive attacks against the thetic will not give way to fantasy or to psychosis but will instead lead to a "second-degree thetic," that is, a resumption of the functioning characteristic of the semiotic _chora_ within the signifying device of language. This is precisely what artistic practices, and notably poetic language, demonstrate.
Starting from and (logically and chronologically) after the phallic position and the castration that underlies it—in other words, after the Oedipus complex and especially after the regulation of genitality by the retroactive effect of the Oedipus complex in puberty—the semiotic _chora_ can be read not as a failure of the thetic but instead as its very precondition. Neurotics and psychotics are defined as such by their relationship to what we are calling the thetic. We now see why, in treating them, psychoanalysis can only conceive of semiotic motility as a disturbance of language and/or of the order of the signifier. Conversely, the refusal of the thetic phase and an attempt to hypostasize semiotic motility as autonomous from the thetic—capable of doing without it or unaware of it—can be seen as a resistance to psychoanalysis. Some therefore even contend that one can find in poetry the unfolding of this refusal of the thetic, something like a direct transcription of the genetic code—as if practice were possible without the thetic and as if a text, in order to hold together as a text, did not require a completion [ _finition_ ], a structuration, a kind of totalization of semiotic motility. This completion constitutes a synthesis that requires the thesis of language in order to come about, and the semiotic pulverizes it only to make it a new device—for us, this is precisely what distinguishes a text as _signifying practice_ from the "driftinginto-non-sense" [ _dérive_ ] that characterizes neurotic discourse. The distinction cannot be erased unless one puts oneself outside "monumental history" in a transcendence which often proves to be one of the reactionary forces combining that history's discrete blocks.
In this way, only the subject, for whom the thetic is not a repression of the semiotic _chora_ but instead a position either taken on or undergone, can call into question the thetic so that a new disposition may be articulated. Castration must have been a problem, a trauma, a drama, so that the semiotic can return through the symbolic position it brings about. This is the crux of the matter: both the completion of the Oedipus complex and its reactivation in puberty are needed for the _Aufhebung_ of the semiotic in the symbolic to give rise to a signifying _practice_ that has a sociohistorical function (and is not just a self-analytical discourse, a substitute for the analyst's couch). At the same time, however, this completion of the Oedipal stage and the genitality it gives rise to should not repress the semiotic, for such a repression is what sets up metalanguage and the "pure signifier." No pure signifier can effect the _Aufhebung_ (in the Hegelian sense) of the semiotic without leaving a remainder, and anyone who would believe this myth need only question his fascination or boredom with a given poem, painting, or piece of music. As a traversable boundary, the thetic is completely different from an imaginary castration that must be evaded in order to return to the maternal _chora_. It is clearly distinct as well from a castration imposed once and for all, perpetuating the well-ordered signifier and positing it as sacred and unalterable within the enclosure of the Other.
8. Breaching the Thetic: Mimesis
Signification in literature implies the possibility of denotation. But instead of following denotative sequences, which would lead, from one judgment to another, to the knowledge of a real object, literary signification tends toward the exploration of grammaticality and/or toward enunciation. _Mimesis_ is, precisely, the construction of an object, not according to truth but to _verisimilitude_ , to the extent that the object is posited as such (hence separate, noted but not denoted); it is, however, internally dependent on a subject of enunciation who is unlike the transcendental ego in that he does not suppress the semiotic _chora_ but instead raises the _chora_ to the status of a signifier, which may or may not obey the norms of grammatical locution. Such is the _connoted_ mimetic object.
Although mimesis partakes of the symbolic order, it does so only to reproduce some of its constitutive rules, in other words, grammaticality. By the same token, it must posit an object, but this "object" is merely a result of the drive economy of enunciation; its true position is inconsequential. What is more, when poetic language—especially modern poetic language—transgresses grammatical rules, the _positing_ of the symbolic (which mimesis has always explored) finds itself subverted, not only in its possibilities of _Bedeutung_ or denotation (which mimesis has always contested), but also as a possessor of _meaning_ (which is always grammatical, indeed more precisely, syntactic). In imitating the constitution of the symbolic as _meaning_ , poetic mimesis is led to dissolve not only the denotative function but also the specifically thetic function of _positing_ the subject. In this respect, modern poetic language goes further than any classical mimesis—whether theatrical or novelistic—because it attacks not only denotation (the positing of the object) but meaning (the positing of the enunciating subject) as well.
In thus eroding the verisimilitude that inevitably underlay classical mimesis and, more important, the very position of enunciation (i.e., the positing of the subject as absent from the signifier), poetic language puts the subject in process/on trial through a network of marks and semiotic facilitations. But the moment it stops being mere instinctual glossolalia and becomes part of the linguistic order, poetry meets up with denotation and enunciation—verisimilitude and the subject—and, through them, the social.
We now understand how the thetic conditions the possibilities of truth specific to language: all transgressions of the thetic are a crossing of the boundary between true and false—maintained, inevitably, whenever signification is maintained, and shaken, irremediably, by the flow of the semiotic into the symbolic. Mimesis, in our view, is a transgression of the thetic when truth is no longer a reference to an object that is identifiable outside of language; it refers instead to an object that can be constructed through the semiotic network but is nevertheless posited in the symbolic and is, from then on, always verisimilar.
Mimetic verisimilitude does not, therefore, eliminate the unique break Frege saw presiding over signification. Instead it maintains that break because it preserves meaning and, with it, a certain object. But neither true nor false, the very status of this verisimilar object throws into question the absoluteness of the break that establishes truth. Mimesis does not actually call into question the unicity of the thetic; indeed it could not, since mimetic discourse takes on the structure of language and, through narrative sentences, posits a signified and signifying object. Mimesis and the poetic language inseparable from it tend, rather, to prevent the thetic from becoming theological; in other words, they prevent the imposition of the thetic from hiding the semiotic process that produces it, and they bar it from inducing the subject, reified as a transcendental ego, to function solely within the systems of science and monotheistic religion.
To note that there can be no language without a thetic phase that establishes the possibility of truth, and to draw consequences from this discovery, is quite a different matter from insisting that every signifying practice operate uniquely out of the thetic phase. For this would mean that the thetic, as origin and transcendence, could only produce (in the Husserlian sense) a tautological discourse, which, having originated in a thesis, can only be a synthesis of theses. We maintain therefore that science and theological dogma are doxic. By repressing the _production_ of doxy, they make the thetic a belief from which the quest for truth departs; but the path thus programmed is circular and merely returns to its thetic point of departure. If mimesis, by contrast, pluralizes denotation, and if poetic language undermines meaning, by what specific operations are these corruptions of the symbolic carried out?
As we know, Freud specifies two fundamental "processes" in the work of the unconscious: _displacement_ and _condensation_. Kruszewski and Jakobson introduced them, in a different way, during the early stages of structural linguistics, through the concepts of _metonymy_ and _metaphor_ , which have since been interpreted in light of psychoanalysis.
To these we must add a third "process"—the _passage from one sign system to another_. To be sure, this process comes about through a combination of displacement and condensation, but this does not account for its total operation. It also involves an altering of the thetic _position_ —the destruction of the old position and the formation of a new one. The new signifying system may be produced with the same signifying material; in language, for example, the passage may be made from narrative to text. Or it may be borrowed from different signifying materials: the transposition from a carnival scene to the written text, for instance. In this connection we examined the formation of a specific signifying system—the novel—as the result of a redistribution of several different sign systems: carnival, courtly poetry, scholastic discourse. The term _intertextuality_ denotes this transposition of one (or several) sign system(s) into another; but since this term has often been understood in the banal sense of "study of sources," we prefer the term _transposition_ because it specifies that the passage from one signifying system to another demands a new articulation of the thetic—of enunciative and denotative positionality. If one grants that every signifying practice is a field of transpositions of various signifying systems (an intertextuality), one then understands that its "place" of enunciation and its denoted "object" are never single, complete, and identical to themselves, but always plural, shattered, capable of being tabulated. In this way polysemy can also be seen as the result of a semiotic polyvalence—an adherence to different sign systems.
Along with condensation ( _Verdichtung_ ) and displacement ( _Verschiebung_ ), Freud also speaks of _considerations of representability_ ( _die Rücksicht auf Darstellbarkeit_ ), which are essential to dream work ( _die Traumarbeit_ ). Representability comes about through a process, closely related to displacement but appreciably different from it, that Freud calls "ein Vertauschung des sprachlichen Ausdruckes." We shall call _transposition_ the signifying process' ability to pass from one sign system to another, to exchange and permutate them; and _representability_ the specific articulation of the semiotic and the thetic for a sign system. Transposition plays an essential role here inasmuch as it implies the abandonment of a former sign system, the passage to a second via an instinctual intermediary common to the two systems, and the articulation of the new system with its new representability.
Poetic mimesis maintains and transgresses thetic unicity by making it undergo a kind of anamnesis, by introducing into the thetic position the stream of semiotic drives and making it signify. This telescoping of the symbolic and the semiotic pluralizes signification or denotation: it pluralizes the thetic doxy. Mimesis and poetic language do not therefore disavow the thetic; instead they go through its truth (signification, denotation) to tell the "truth" about it. To be sure, the latter use of the term "truth" is inappropriate, since it no longer refers to denotative truth in Frege's sense. This "second truth" reproduces the path which was cleared by the first truth (that of _Bedeutung_ ) in order to posit itself. Both mimesis and poetic language with its connotations assume the right to enter into the social debate, which is an ideological debate, on the strength of their confrontation with _Bedeutung_ (signification and denotation) but also with all meaning, and hence all enunciation produced by a posited subject.
But mimesis and poetic language do more than engage in an intraideological debate; they question the very principle of the ideological because they unfold the _unicity_ of the thetic (the precondition for meaning and signification) and prevent its theologization. As the place of production for a subject who transgresses the thetic by using it as a necessary boundary—but not as an absolute or as an origin—poetic language and the mimesis from which it is inseparable, are profoundly a-theological. They are not critics of theology but rather the enemy within and without, recognizing both its necessity and its pretensions. In other words, poetic language and mimesis may appear as an argument complicitous with dogma—we are familiar with religion's use of them—but they may also set in motion what dogma represses. In so doing, they no longer act as instinctual floodgates within the enclosure of the sacred and become instead protestors against its posturing. And thus, its complexity unfolded by its practices, the signifying process joins social revolution.
9. The Unstable Symbolic: Substitutions in the Symbolic—Fetishism
The thetic permits the constitution of the symbolic with its vertical stratification (referent, signified, signifier) and all the subsequent modalities of logico-semantic articulation. The thetic originates in the "mirror stage" and is completed, through the phallic stage, by the reactivation of the Oedipus complex in puberty; no signifying practice can be without it. Though absolutely necessary, the thetic is not exclusive: the semiotic, which also precedes it, constantly tears it open, and this transgression brings about all the various transformations of the signifying practice that are called "creation." Whether in the realm of metalanguage (mathematics, for example) or literature, what remodels the symbolic order is always the influx of the semiotic. This is particularly evident in poetic language since, for there to be a transgression of the symbolic, there must be an irruption of the drives in the universal signifying order, that of "natural" language which binds together the social unit. That the subject does not vanish into psychosis when this transgression takes place poses a problem for metaphysics, both the kind that sets up the signifier as an untransgressable law and the kind for which there exists no thetic and therefore no subject.
The semiotic's breach of the symbolic in so-called poetic practice can probably be ascribed to the very unstable yet forceful positing of the thetic. In our view, the analysis of texts shows that thetic lability is ultimately a problem with imaginary captation (disorders in the mirror stage that become marked scopophilia, the need for a mirror or an identifying addressee, etc.) and a resistance to the discovery of castration (thereby maintaining the phallic mother who usurps the place of the Other). These problems and resistances obstruct the thetic phase of the signifying process. When they fail to prevent the constitution of the symbolic (which would result in psychosis), they return in and through its position. In so doing, they give rise to "fantasies"; more importantly, they attempt to dissolve the first social censorship—the bar between signifier and signified—and, simultaneously, the first guarantee of the subject's position—signification, then meaning (the sentence and its syntax). Language thus tends to be drawn out of its symbolic function (sign-syntax) and is opened out within a semiotic articulation; with a material support such as the voice, this semiotic network gives "music" to literature.
But the irruption of the semiotic within the symbolic is only relative. Though permeable, the thetic continues to ensure the position of the subject put in process/on trial. As a consequence, musicality is not without signification; indeed it is deployed within it. Logical syntheses and all ideologies are present, but they are pulverized within their own logic before being displaced toward something that is no longer within the realm of the idea, sign, syntax, and thus Logos, but is instead simply semiotic functioning. The precondition for such a heterogeneity that alone posits and removes historical meaning is the thetic phase: we cannot overemphasize this point.
Without the completion of the thetic phase, we repeat, no signifying practice is possible; the negation/denial [ _dénégation_ ] of this phase leads the subject to shift the thetic, even though he is determined by it, onto one of the places that the signifying process must cross on its way to fulfillment. Negating or denying the symbolic, without which he would be incapable of doing anything, the subject may imagine the thetic at the place of an object or a partner. This is a fetishist mechanism, which consists in denying the mother's castration, but perhaps goes back even further to a problem in separating an image of the ego in the mirror from the bodily organs invested with semiotic motility. Negation-as-denial ( _Verneinung_ ) or disavowal ( _Verleugung_ ) in perversion, which may go so far as the foreclosure ( _Verwerfung_ ) of the thetic phase, represent different modalities capable of obscuring castration and the sexual difference underlying it as well as genital sexuality. Further on we shall see how a marked investment in anal eroticism leads to this rejection of the thetic because it allows a questioning of the symbolic order; but by this very process it shifts the _thesis_ onto _objects_. The prototype of such objects is excrement since it is midway between an autoerotic body, which is not yet autonomous from its eroticized sphincters, and the pleasure the mother's body or her supposed phallus would procure—a belief that is disclaimed but maintained, behind, as a compromise.
Since there can be no signifying practice without a thetic phase, the thetic that does not manage to posit itself in the symbolic order necessarily places itself in the objects surrounding the body and instinctually linked to it. Fetishism is a compromise with the thetic; although erased from the symbolic and displaced onto the drives, a "thesis" is nevertheless maintained so that signifying practice can take place. Therefore we shall contend that it is the thetic, and not fetishism, that is inherent in every cultural production, because fetishism is a displacement of the thetic onto the realm of drives. The instinctual _chora_ articulates facilitations and stases, but fetishism is a telescoping of the symbolic's characteristic thetic moment and of one of those instinctually invested stases (bodies, parts of bodies, orifices, containing objects, and so forth). This stasis thus becomes the ersatz of the sign. Fetishism is a stasis that acts as a thesis.
We might then wonder whether the semiotic's dismantling of the symbolic in poetry necessarily implies that the thetic phase is shifted toward the stases of the semiotic _chora_. Doesn't poetry lead to the establishment of an object as a substitute for the symbolic order under attack, an object that is never clearly _posited_ but always "in perspective." The object may be either the body proper or the apparatuses erotized during vocal utterance (the glottis, the lungs), objects that are either linked to the addressee of desire or to the very material of language as the predominant object of pleasure. Moreover, since the symbolic is corrupted so that an object—the book, the work—will result, isn't this object a substitute for the thetic phase? Doesn't it take the thetic's place by making its symbolicity opaque, by filling the thetic with its presence whose pretension to universality is matched only by its very finite limits? In short, isn't art the fetish par excellence, one that badly camouflages its archaeology? At its base, isn't there a belief, ultimately maintained, that the mother is phallic, that the ego—never precisely identified—will never separate from her, and that no symbol is strong enough to sever this dependence? In this symbiosis with the supposedly phallic mother, what can the subject do but occupy her place, thus navigating the path from fetishism to autoeroticism? That indeed is the question.
In order to keep the process signifying, to avoid foundering in an "unsayable" without limits, and thus posit the subject of a practice, the subject of poetic language clings to the help fetishism offers. And so, according to psychoanalysis, poets as individuals fall under the category of fetishism; the very practice of art necessitates reinvesting the maternal _chora_ so that it transgresses the symbolic order; and, as a result, this practice easily lends itself to so-called perverse subjective structures. For all these reasons, the poetic function therefore converges with fetishism; it is not, however, identical to it. What distinguishes the poetic function from the fetishist mechanism is that it maintains a "signification" ( _Bedeutung_ ). All its paths into, indeed valorizations of, presymbolic semiotic stases, not only require the ensured maintenance of this signification but also serve signification, even when they dislocate it. No text, no matter how "musicalized," is devoid of meaning or signification; on the contrary, musicalization pluralizes meanings. We may say therefore that the text is not a fetish. It is, moreover, just like "natural" language in this regard, if the abstract word is thought of as a correlate for the fetish in primitive societies. The text is completely different from a fetish because it _signifies_ ; in other words, it is not a _substitute_ but a _sign_ (signifier/signified), and its semantics is unfurled in sentences. The text signifies the un-signifying: it assumes [ _relève_ ] within a signifying practice this functioning (the semiotic), which ignores meaning and operates before meaning or despite it. Therefore it cannot be said that everything signifies, nor that everything is "mechanistic." In opposition to such dichotomies, whether "materialist" or "metaphysical," the text offers itself as the dialectic of two heterogeneous operations that are, reciprocally and inseparably, preconditions for each other.
We understand, then, that this heterogeneity between the semiotic and the symbolic cannot be reduced to computer theory's well-known distinction between "analog" and "digital." An analog computer is defined as any device that 'computes' by means of an analog between real, physical, _continuous_ quantities and some other set of variables," whereas the digital computer presupposes " _discrete_ elements and discontinuous scales."
Certain linguists have wanted to transpose this distinction—which arose with the development of computers and perhaps applies to "natural" codes (nerve cell codes or animal communication, for example)—onto the functioning of language. But in making this transposition, one quickly forgets not only that language is simultaneously "analog" and "digital" but that it is, above all, a doubly articulated system (signifier and signified), which is precisely what distinguishes it from _codes_. We therefore maintain that what we call the semiotic can be described as both analog and digital: the functioning of the semiotic _chora_ is made up of continuities that are segmented in order to organize a digital system as the _chora_ 's guarantee of survival (just as digitality is the means of survival both for the living cell and society); the stases marked by the facilitation of the drives are the discrete elements in this digital system, indispensable for maintaining the semiotic _chora_.
Yet this description (which itself is possible only on the basis of a highly developed symbolic system) does not account for what produces the _qualitative leap_ between a code and a double articulation. But this essential phase is precisely what we are examining when we distinguish between the semiotic and the symbolic, and when we assign the thetic phase the role of boundary between the two heterogeneous domains. Because of the human being's prematurity, his semiotic "code" is cut off from any possible identification unless it is assumed by the other (first the mother, then the symbolic and/or the social group). Making the analog digital is thus not enough to ensure our bodily survival because it cannot check the drives' endless facilitations. An _alteration_ must be made, making the _other_ the regulator between the semiotic _chora_ and the totality called the _ecosystem_. This alteration makes it possible to gather together the analog and digital "code" and, through a break prepared by the mirror stage, posit it as unified, mastered, dominated, and in another space—imaginary, representational, symbolic. Through this alteration, the "code" leaves the place of the body and the ecosystem and, freed from their constraints, acquires the variability characteristic of a system of "arbitrary" signs—human language—the later development of which forms the immense edifice of signifying practices.
The _semiotic_ (analog and digital) thereby assumes the role of a linguistic signifier signifying an _object_ for an _ego_ , thus constituting them both as thetic. Through its thetic, altering aspect, the signifier _represents_ the subject—not the thetic ego but the very process by which it is posited. A signifier indebted in this manner to semiotic functioning tends to return to it. In all its various vacillations, the thetic is displaced toward the stages previous to its positing or within the very stases of the semiotic—in a particular element of the digital code or in a particular continuous portion of the analog code. These movements, which can be designated as fetishism, show (human) language's characteristic tendency to return to the (animal) code, thereby breaching what Freud calls a "primal repression." The thetic—that crucial place on the basis of which the human being constitutes himself as signifying and/or social—is the very place textual experience aims toward. In this sense, textual experience represents one of the most daring explorations the subject can allow himself, one that delves into his constitutive process. But at the same time and as a result, textual experience reaches the very foundation of the social—that which is exploited by sociality but which elaborates and can go beyond it, either destroying or transforming it.
10. The Signifying Process
Once the break instituting the symbolic has been established, what we have called the semiotic _chora_ acquires a more precise status. Although originally a precondition of the symbolic, the semiotic functions within signifying practices as the result of a transgression of the symbolic. Therefore the semiotic that "precedes" symbolization is only a _theoretical supposition_ justified by the need for description. It exists in practice only within the symbolic and requires the symbolic break to obtain the complex articulation we associate with it in musical and poetic practices. In other words, symbolization makes possible the complexity of this semiotic combinatorial system, which only theory can isolate as "preliminary" in order to specify its functioning. Nevertheless, the semiotic is not solely an abstract object produced for the needs of theory.
As a precondition of the symbolic, semiotic functioning is a fairly rudimentary combinatorial system, which will become more complex only after the break in the symbolic. It is, however, already put in place by a biological setup and is always already social and therefore historical. This semiotic functioning is discernible before the mirror stage, before the first suggestion of the thetic. But the semiotic we find in signifying practices always comes to us after the symbolic thesis, after the symbolic break, and can be analyzed in psychoanalytic discourse as well as in so-called artistic practice. One could not, then, limit oneself to representing this semiotic functioning as simply "analog" or "digital" or as a mere scattering of traces. The thetic gathers up these facilitations and instinctual semiotic stases within the positing of signifiers, then opens them out in the three-part cluster of referent, signified, and signifier, which alone makes the enunciation of a truth possible. In taking the thetic into account, we shall have to represent the semiotic (which is produced recursively on the basis of that break) as a "second" return of instinctual functioning within the symbolic, as a negativity introduced into the symbolic order, and as the transgression of that order.
This transgression appears as a breach [ _effraction_ ] subsequent to the thetic phase, which makes that phase negative and tends to fuse the layers of signifier/signified/referent into a network of traces, following the facilitation of the drives. Such a breach does not constitute a positing. It is not at all thetic, nor is it an _Aufhebung_ of "original doxy" through a synthesizing spiral movement and within the pursuit of the exhaustion of truth undertaken by Hegelian absolute knowledge. On the contrary, the transgression breaks up the thetic, splits it, fills it with empty spaces, and uses its device only to remove the "residues of first symbolizations" and make them "reason" [ _raisonner_ ] within the symbolic chain. This explosion of the semiotic in the symbolic is far from a negation of negation, an _Aufhebung_ that would suppress the contradiction generated by the thetic and establish in its place an ideal positivity, the restorer of presymbolic immediacy. It is, instead, a _transgression_ of position, a reversed reactivation of the contradiction that instituted this very position.
The proof is that this negativity has a tendency to suppress the thetic phase, to de-syn-thesize it. In the extreme, negativity aims to foreclose the thetic phase, which, after a period of explosive semiotic motility, may result in the loss of the symbolic function, as seen in schizophrenia.
"Art," on the other hand, by definition, does not relinquish the thetic even while pulverizing it through the negativity of transgression. Indeed, this is the only means of transgressing the thetic, and the difficulty of maintaining the symbolic function under the assault of negativity indicates the risk that textual practice represents for the subject. What had seemed to be a process of fetishizing inherent in the way the text functions now seems a structurally necessary protection, one that serves to check negativity, confine it within stases, and prevent it from sweeping away the symbolic position.
The regulation of the semiotic in the symbolic through the thetic break, which is inherent in the operation of language, is also found on the various levels of a society's signifying edifice. In all known archaic societies, this founding break of the symbolic order is represented by murder—the killing of a man, a slave, a prisoner, an animal. Freud reveals this founding break and generalizes from it when he emphasizes that society is founded on a complicity in the common crime. We indicated earlier how language, already as a semiotic _chora_ but above all as a symbolic system, is at the service of the death drive, diverts it, and confines it as if within an isolated pocket of narcissism. The social order, for its part, reveals this confinement of the death drive, whose endless course conditions and moves through every stasis and thus every structure, in an act of murder. Religions, as we know, have set themselves up as specialists on the discourse concerning this radical, unique, thetic event.
Opposite religion or alongside it, "art" takes on murder and moves through it. It assumes murder insofar as artistic practice considers death the inner boundary of the signifying process. Crossing that boundary is precisely what constitutes "art." In other words, it is as if death becomes interiorized by the subject of such a practice; in order to function, he must make himself the bearer of death. In this sense, the artist is comparable to all other figures of the "scapegoat." But he is not just a scapegoat; in fact, what makes him an artist radically distinguishes him from all other sacrificial murderers and victims.
In returning, through the event of death, toward that which produces its break; in exporting semiotic motility across the border on which the symbolic is established, the artist sketches out a kind of second birth. Subject to death but also to rebirth, his function becomes harnessed, immobilized, represented, and idealized by religious systems (most explicitly by Christianity), which shelter him in their temples, pagodas, mosques, and churches. Through themes, ideologies, and social meanings, the artist introduces into the symbolic order an asocial drive, one not yet harnessed by the thetic. When this practice, challenging any stoppage, comes up, in its turn, against the produced object, it sets itself up as a substitute for the initially contested thetic, thus giving rise to the aesthetic fetishism and narcissism supplanting theology.
12. Genotext and Phenotext
In light of the distinction we have made between the semiotic _chora_ and the symbolic, we may now examine the way texts function. What we shall call a _genotext_ will include semiotic processes but also the advent of the symbolic. The former includes drives, their disposition, and their division of the body, plus the ecological and social system surrounding the body, such as objects and pre-Oedipal relations with parents. The latter encompasses the emergence of object and subject, and the constitution of nuclei of meaning involving categories: semantic and categorial fields. Designating the genotext in a text requires pointing out the transfers of drive energy that can be detected in phonematic devices (such as the accumulation and repetition of phonemes or rhyme) and melodic devices (such as intonation or rhythm), in the way semantic and categorial fields are set out in syntactic and logical features, or in the economy of mimesis (fantasy, the deferment of denotation, narrative, etc.). The genotext is thus the only transfer of drive energies that organizes a space in which the subject is not _yet_ a split unity that will become blurred, giving rise to the symbolic. Instead, the space it organizes is one in which the subject will be _generated_ as such by a process of facilitations and marks within the constraints of the biological and social structure.
In other words, even though it can be seen in language, the genotext is not linguistic (in the sense understood by structural or generative linguistics). It is, rather, a _process_ , which tends to articulate structures that are ephemeral (unstable, threatened by drive charges, "quanta" rather than "marks") and nonsignifying (devices that do not have a double articulation). It forms these structures out of: (a) instinctual dyads, (b) the corporeal and ecological continuum, (c) the social organism and family structures, which convey the constraints imposed by the mode of production, and (d) matrices of enunciation, which give rise to discursive "genres" (according to literary history), "psychic structures" (according to psychiatry and psychoanalysis), or various arrangements of "the participants in the speech event" (in Jakobson's notion of the linguistics of discourse). We may posit that the matrices of enunciation are the result of the repetition of drive charges (a) within biological, ecological, and sociofamilial constraints (b and c), and the stabilization of their facilitation into stases whose surrounding structure accommodates and leaves its mark on symbolization.
The genotext can thus be seen as language's underlying foundation. We shall use the term _phenotext_ to denote language that serves to communicate, which linguistics describes in terms of "competence" and "performance." The phenotext is constantly split up and divided, and is irreducible to the semiotic process that works through the genotext. The phenotext is a structure (which can be generated, in generative grammar's sense); it obeys rules of communication and presupposes a subject of enunciation and an addressee. The genotext, on the other hand, is a process; it moves through zones that have relative and transitory borders and constitutes a _path_ that is not restricted to the two poles of univocal information between two full-fledged subjects. If these two terms—genotext and phenotext—could be translated into a metalanguage that would convey the difference between them, one might say that the genotext is a matter of topology, whereas the phenotext is one of algebra. This distinction may be illustrated by a particular signifying system: written and spoken Chinese, particularly classical Chinese. Writing represents/articulates the signifying process into specific networks or spaces; _speech_ (which may correspond to that writing) restores the diacritical elements necessary for an exchange of meaning between two subjects (temporality, aspect, specification of the protagonists, morpho-semantic identifiers, and so forth).
The signifying process therefore includes both the genotext and the phenotext; indeed it could not do otherwise. For it is in language that all signifying operations are realized (even when linguistic material is not used), and it is on the basis of language that a theoretical approach may attempt to perceive that operation.
In our view, the process we have just described accounts for the way all signifying practices are generated. But every signifying practice does not encompass the infinite totality of that process. Multiple constraints—which are ultimately sociopolitical—stop the signifying process at one or another of the theses that it traverses; they knot it and lock it into a given surface or structure; they discard _practice_ under fixed, fragmentary, symbolic _matrices_ , the tracings of various social constraints that obliterate the infinity of the process: the phenotext is what conveys these obliterations. Among the capitalist mode of production's numerous signifying practices, only certain literary texts of the avant garde (Mallarmé, Joyce) manage to cover the infinity of the process, that is, reach the semiotic _chora_ , which modifies linguistic structures. It must be emphasized, however, that this total exploration of the signifying process generally leaves in abeyance the theses that are characteristic of the social organism, its structures, and their political transformation: the text has a tendency to dispense with political and social signifieds.
It has only been in very recent years or in revolutionary periods that signifying practice has inscribed within the phenotext the plural, heterogeneous, and contradictory process of signification encompassing the flow of drives, material discontinuity, political struggle, and the pulverization of language.
Lacan has delineated four types of discourse in our society: that of the hysteric, the academic, the master, and the analyst. Within the perspective just set forth, we shall posit a different classification, which, in certain respects, intersects these four Lacanian categories and, in others, adds to them. We shall distinguish between the following signifying practices: narrative, metalanguage, contemplation, and text-practice.
Let us state from the outset that this distinction is only provisional and schematic, and that although it corresponds to actual practices, it interests us primarily as a didactic implement [ _outil_ ]—one that will allow us to specify some of the modalities of signifying dispositions. The latter interest us to the extent that they give rise to different practices and are, as a consequence, more or less coded in modes of production. Of course narrative and contemplation could also be seen as devices stemming from (hysterical and obsessional) transference neurosis; and metalanguage and the text as practices allied with psychotic (paranoid and schizoid) economies.
NOTES
. See Zellig Harris, _Mathematical Structures of Language_ (New York: Interscience Publishers, 1968). See also Maurice Gross and André Lentin, _Introduction to Formal Grammars_ , M. Salkoff, tr. (Berlin: Springer-Verlag, 1970); M.-C. Barbault and J.-P. Desclés, _Transformations formelles et théories linguistiques_ , Documents de linguistique quantitative, no. 11 (Paris: Dunod, 1972).
. On this "object" see _Langages_ 24 (December 1971), and, for a didactic, popularized account, see Julia Kristeva, _Le Langage, cet inconnu_ (Paris: Seuil, 1981).
. Edmund Husserl, in _Ideas: General Introduction to Pure Phenomenology_ , W. R. Boyce Gibson, tr. (London: Allen & Unwin, 1969), posits this subject as a subject of intuition, sure of this universally valid unity (of consciousness), a unity that is provided in _categories_ itself, since transcendence is precisely the immanence of this "Ego," which is an expansion of the Cartesian _cogito_. "We shall consider conscious experiences," Husserl writes, " _in the concrete fullness and entirety_ with which they figure in their concrete context—the _stream of experience_ —and to which they are closely attached through their own proper essence. It then becomes evident that every experience in the stream which our reflexion can lay hold on has _its own essence open to intuition_ , a 'content' which can be considered in its _singularity in and for itself_. We shall be concerned to grasp this individual content of the _cogitatio_ in its _pure_ singularity, and to describe it in its general features, excluding everything which is not to be found in the _cogitatio_ as it is in itself. We must likewise describe the _unity of consciousness_ which is demanded _by the intrinsic nature of the cogitationes_ , and so necessarily demanded that they could not be without this unity" (p. 116). From a similar perspective, Benveniste emphasizes language's dialogical character, as well as its role in Freud's discovery. Discussing the I/you polarity, he writes: "This polarity does not mean either equality or symmetry: 'ego' always has a position of transcendence with regard to _you_." In Benveniste, "Subjectivity in Language," _Problems in General Linguistics_ , Miami Linguistics Series, no. 8, Mary Elizabeth Meek, tr. (Coral Gables, Fla.: University of Miami Press, 1971), p. 225. In Chomsky, the subject-bearer of syntactic synthesis is clearly shown to stem from the Cartesian _cogito_. See his _Cartesian Linguistics: A Chapter in the History of Rationalist Thought_ (New York: Harper & Row, 1966). Despite the difference between this Cartesian-Chomskyan subject and the transcendental ego outlined by Benveniste and others in a more clearly phenomenological sense, both these notions of the act of understanding (or the linguistic act) rest on a common metaphysical foundation: consciousness as a synthesizing unity and the sole guarantee of Being. Moreover, several scholars—without renouncing the Cartesian principles that governed the first syntactic descriptions—have recently pointed out that Husserlian phenomenology is a more explicit and more rigorously detailed basis for such description than the Cartesian method. See Roman Jakobson, who recalls Husserl's role in the establishment of modern linguistics, "Linguistics in Relation to Other Sciences," in _Selected Writings_ , 2 vols. (The Hague: Mouton, 1971), 2:655–96; and S.-Y. Kuroda, "The Categorical and the Thetic Judgment: Evidence from Japanese Syntax," _Foundations of Language_ 9 (November 1972): 153–85.
. See the work of Ivan Fónagy, particularly "Bases pulsionnelles de la phonation," _Revue Française de Psychanalyse_ 34 (January 1970): 101–36, and 35 (July 1971): 543–91.
. On the "subject of enunciation," see Tzvetan Todorov, spec. ed., _Langages_ 17 (March 1970). Formulated in linguistics by Benveniste ("The Correlations of Tense in the French Verb" and "Subjectivity in Language," in _Problems_ , pp. 205–16 and 223–30), the notion is used by many linguists, notably Antoine Culioli, "A propos d'opérations intervenant dans le traitement formel des langues naturelles," _Mathématiques et Sciences Humaines_ 9 (Summer 1971): 7–15; and Oswald Ducrot, "Les Indéfinis et l'énonciation," _Langages_ 5 (March 1970): 91–111. Chomsky's "extended standard theory" makes use of categorial intuition but does not refer to the subject of enunciation, even though the latter has been implicit in his theory ever since _Cartesian Linguistics_ (1966); see his _Studies on Semantics in Generative Grammar_ , Janua Linguarum, series minor, no. 107 (The Hague: Mouton, 1972).
. See John R. Searle, _Speech Acts: An Essay on the Philosophy of Language_ (London: Cambridge University Press, 1969).
. See Robert D. King, _Historical Linguistics and Generative Grammar_ (Englewood Cliffs, N.J.: Prentice-Hall, 1969); Paul Kiparsky, "Linguistic Universals and Linguistic Change," in _Universals of Linguistic Theory_ , Emmon Bach and Robert T. Harms, eds. (New York: Holt, Rinehart & Winston, 1968), pp. 170–202; and Kiparsky, "How Abstract Is Phonology?" mimeograph reproduced by Indiana University Linguistics Club, October 1968.
. S.-Y. Kuroda distinguishes between two styles, "reportive" and "nonreportive." "Reportive" includes first-person narratives as well as those in the second and third person in which the narrator is "effaced"; "non-reportive" involves an omniscient narrator or "multi-consciousness." This distinction explains certain anomalies in the distribution of the adjective and verb of sensation in Japanese. (Common usage requires that the adjective be used with the first person but it can also refer to the third person. When it does, this agrammaticality signals another "grammatical style": an omniscient narrator is speaking in the name of a character, or the utterance expresses a character's point of view.) No matter what its subject of enunciation, the utterance, Kuroda writes, is described as representing that subject's _Erlebnis_ ("experience"), in the sense Husserl uses the term in _Ideas_. See Kuroda, "Where Epistemology, Style, and Grammar Meet," mimeographed, University of California, San Diego, 1971.
. Even the categories of dialectical materialism introduced to designate a discourse's conditions of production as essential bestowers of its signification are based on a "subject-bearer" whose logical positing is no different from that found in Husserl (see above, n. 3). For example, Cl. Haroche, P. Henry, and Michel Pêcheux stress "the importance of linguistic studies on the relation between utterance and enunciation, by which the 'speaking subject' situates himself with respect to the representations he _bears_ —representations that are put together by means of the linguistically analyzable 'preconstructed."' They conclude that "it is undoubtedly on this point—together with that of the syntagmatization of the characteristic substitutions of a discursive formation—that the contribution of the theory of discourse to the study of ideological formation (and the theory of ideologies) can now be most fruitfully developed." "La Sémantique et la coupure saussurienne: Langue, langage, discours," _Langages_ 24 (December 1971): 106. This notion of the subject as always already there on the basis of a "preconstructed" language (but how is it constructed? and what about the subject _who constructs_ before _bearing_ what has been constructed?) has even been preserved under a Freudian cover. As a case in point, Michel Tort questions the relation between psychoanalysis and historical materialism by placing a subject-bearer between "ideological agency" and "unconscious formations." He defines this subject-bearer as "the biological specificity of individuals (individuality as a biological concept), inasmuch as it is the material basis upon which individuals are called to function by social relations." "La Psychanalyse dans le matérialisme historique," _Nouvelle Revue de Psychanalyse_ 1 (Spring 1970): 154. But this theory provides only a hazy view of how this subject-bearer is produced through the unconscious and within the "ideological" signifier, and does not allow us to see this production's investment in ideological representations themselves. From this perspective, the only thing one can say about "arts" or "religions," for example, is that they are "relics." On language and history, see also Jean-Claude Chevalier, "Langage et histoire," Langue Française 15 (September 1972): 3–17.
. On the phenomenological bases of modern linguistics, see Kristeva, "Les Epistémologies de la linguistique," _Langages_ 24 (December 1971): 11; and especially Jacques Derrida, "The Supplement of Copula: Philosophy before Linguistics," Josué V. Harari, tr., _Textual Strategies_ , Josué V. Harari, ed. (Ithaca, N.Y.: Cornell University Press, 1979), pp. 82–120; _Of Grammatology_ , Gayatri Chakravorty Spivak, tr. (Baltimore: Johns Hopkins University Press, 1976), pp. 27–73; and _Speech and Phenomena, and Other Essays on Husserl's Theory of Signs_ , David B. Allison, introd. and tr. (Evanston, Ill.: Northwestern University Press, 1973).
. The term _chora_ has recently been criticized for its ontological essence by Jacques Derrida, _Positions_ , Alan Bass, annotator and tr. (Chicago: University of Chicago Press, 1981), pp. 75 and 106, n. 39.
. Plato emphasizes that the receptacle (ύποδοχεĩον), which is also called space (χώρα) vis-à-vis reason, is necessary—but not divine since it is unstable, uncertain, ever changing, and becoming; it is even unnameable, improbable, bastard: "Space, which is everlasting, not admitting destruction; providing a situation for all things that come into being, but itself apprehended without the senses by a sort of bastard reasoning, and hardly an object of belief. This, indeed, is that which we look upon as in a dream and say that anything that is must needs be in some place and occupy some room." ( _Timaeus_ , Francis M. Cornford, tr., 52a–52b). Is the receptacle a "thing" or a mode of language? Plato's hesitation between the two gives the receptacle an even more uncertain status. It is one of the elements that antedate not only the _universe_ but also _names_ and even _syllables_ : "We speak... positing them as original principles, elements (as it were, letters) of the universe; whereas one who has ever so little intelligence should not rank them in this analogy even so low as syllables" (ibid., 48b). "It is hard to say, with respect to any one of these, which we ought to call really water rather than fire, or indeed which we should call by any given name rather than by all the names together or by each severally, so as to use language in a sound and trustworthy way.... Since, then, in this way no one of these things ever makes its appearance as the same thing, which of them can we steadfastly affirm to be _this_ —whatever it may be—and not something else, without blushing for ourselves? It cannot be done" (ibid., 49b–d).
. There is a fundamental ambiguity: on the one hand, the receptacle is mobile and even contradictory, without unity, separable and divisible: presyllable, preword. Yet, on the other hand, because this separability and divisibility antecede numbers and forms, the space or receptacle is called _amorphous_ ; thus its suggested rhythmicity will in a certain sense be erased, for how can one think an articulation of what is not yet singular but is nevertheless necessary? All we may say of it, then, to make it intelligible, is that it is amorphous but that it "is of such and such a quality," not even an index or something in particular ("this" or "that"). Once named, it immediately becomes a container that takes the place of infinitely repeatable separability. This amounts to saying that this repeated separability is "ontologized" the moment a _name_ or a _word_ replaces it, making it intelligible: "Are we talking idly whenever we say that there is such a thing as an intelligible Form of anything? Is this nothing more than a word?" (ibid., 51c). Is the Platonic _chora_ the "nominability" of rhythm (of repeated separation)?
Why then borrow an ontologized term in order to designate an articulation that antecedes positing? First, the Platonic term makes explicit an insurmountable problem for discourse: once it has been named, that functioning, even if it is presymbolic, is brought back into a symbolic position. All discourse can do is differentiate, by means of a "bastard reasoning," the receptacle from the motility, which, by contrast, is not posited as being "a _certain_ something" [ _une telle_ ]. Second, this motility is the precondition for symbolicity, heterogeneous to it, yet indispensable. Therefore what needs to be done is to try to differentiate, always through a "bastard reasoning," the specific arrangements of this motility, without seeing them as recipients of accidental singularities, or a _Being_ always posited in itself, or a projection of the _One_. Moreover, Plato invites us to differentiate in this fashion when he describes this motility, while gathering it into the receiving membrane: "But because it was filled with powers that were neither alike nor evenly balanced, there was no equipoise in any region of it; but it was everywhere swayed unevenly and shaken by these things, and by its motion shook them in turn. And they, being thus moved, were perpetually being separated and carried in different directions; just as when things are shaken and winnowed by means of winnowing baskets and other instruments for cleaning corn... it separated the most unlike kinds farthest apart from one another, and thrust the most alike closest together; whereby the different kinds came to have different regions, even before the ordered whole consisting of them came to be... but were altogether in such a condition as we should expect for anything when deity is absent from it" (ibid., 52d–53b). Indefinite "conjunctions" and "disjunctions" (functioning, devoid of Meaning), the _chora_ is governed by a necessity that is not God's law.
. The Platonic space or receptacle is a mother and wet nurse: "Indeed we may fittingly compare the Recipient to a mother, the model to a father, and the nature that arises between them to their offspring" (ibid., 50d); "Now the wet nurse of Becoming was made watery and fiery, received the characters of earth and air, and was qualified by all the other affections that go with these..."; ibid., 52d; translation modified.
. "Law," which derives etymologically from _lex_ , necessarily implies the act of judgment whose role in safeguarding society was first developed by the Roman law courts. "Ordering," on the other hand, is closer to the series "rule," "norm" (from the Greek γνώμων, meaning "discerning" [adj.], "carpenter's square" [noun]), etc., which implies a numerical or geometrical necessity. On normativity in linguistics, see Alain Rey, "Usages, jugements et prescriptions linguistiques," _Langue Française_ 16 (December 1972): 5. But the temporary ordering of the _chora_ is not yet even a _rule_ : the arsenal of geometry is posterior to the _chora_ 's motility; it fixes the _chora_ in place and reduces it.
. Operations are, rather, an act of the subject of understanding.
Hans G. Furth, in _Piaget and Knowledge: Theoretical Foundations_ (Englewood Cliffs, N.J.: Prentice-Hall, 1969), offers the following definition of "concrete operations": "Characteristic of the first stage of operational intelligence. A concrete operation implies underlying general systems or 'groupings' such as classification, seriation, number. Its applicability is limited to objects considered as real (concrete)" (p. 260).—Trans.
. Piaget stresses that the roots of sensorimotor operations precede language and that the acquisition of thought is due to the symbolic function, which, for him, is a notion separate from that of language per se. See Jean Piaget, "Language and Symbolic Operations," in _Piaget and Knowledge_ , pp. 121–30.
. By "function" we mean a dependent variable determined each time the independent variables with which it is associated are determined. For our purposes, a function is what links stases within the process of semiotic facilitation.
. Such a position has been formulated by Lipot Szondi, _Experimental Diagnostic of Drives_ , Gertrude Aull, tr. (New York: Grune & Stratton, 1952).
. See James D. Watson, _The Double Helix: A Personal Account of the Discovery of the Structure of DNA_ (London: Weidenfeld & Nicholson, 1968).
. Throughout her writings, Melanie Klein emphasizes the "pre-Oedipal" phase, i.e., a period of the subject's development that precedes the "discovery" of castration and the positing of the superego, which itself is subject to (paternal) Law. The processes she describes for this phase correspond, _but on a genetic level_ , to what we call the semiotic, as opposed to the symbolic, which underlies and conditions the semiotic. Significantly, these pre-Oedipal processes are organized through projection onto the mother's body, for girls as well as for boys: "at this stage of development children of both sexes believe that it is the body of their mother which contains all that is desirable, especially their father's penis." _The Psycho-analysis of Children_ , Alix Strachey, tr. (London: Hogarth Press, 1932), p. 269. Our own view of this stage is as follows: Without "believing" or "desiring" any "object" whatsoever, the subject is in the process of constituting himself vis-à-vis a nonobject. He is in the process of separating from this nonobject so as to make that nonobject "one" and posit himself as "other": the mother's body is the not-yet-one that the believing and desiring subject will imagine as a "receptacle."
. As for what situates the mother in symbolic space, we find the phallus again (see Jacques Lacan, "La Relation d'objet et les structures freudiennes," _Bulletin de Psychologie_ , April 1957, pp. 426–30), represented by the mother's father, i.e., the subject's maternal grandfather (see Marie-Claire Boons, "Le Meurtre du Père chez Freud," _L'Inconscient_ 5 [January–March 1968]: 101–29).
. Though disputed and inconsistent, the Freudian theory of drives is of interest here because of the predominance Freud gives to the death drive in both "living matter" and the "human being." The death drive is transversal to identity and tends to disperse "narcissisms" whose constitution ensures the link between structures and, by extension, life. But at the same time and conversely, narcissism and pleasure are only temporary positions from which the death drive blazes new paths [ _se fraye de nouveaux passages_ ]. Narcissism and pleasure are therefore inveiglings and realizations of the death drive. The semiotic _chora_ , converting drive discharges into stases, can be thought of both as a delaying of the death drive and as a possible realization of this drive, which tends to return to a homeostatic state. This hypothesis is consistent with the following remark: "at the beginning of mental life," writes Freud, "the struggle for pleasure was far more intense than later but not so unrestricted: it had to submit to frequent interruptions." _Beyond the Pleasure Principle_ , in _The Standard Edition of the Works of Sigmund Freud_ , James Strachey, ed. (London: Hogarth Press and the Institute of Psychoanalysis, 1953), 18:63.
. Mallarmé, _Oeuvres complètes_ (Paris: Gallimard, 1945), pp. 382–87.
. Ibid., p. 383.
. Ibid., pp. 383 and 385.
. Ibid., pp. 385–86.
. Husserl, _Ideas_ , p. 342.
. In _Ideas_ , posited meaning is "the unity of meaning and thetic character." "The concept of proposition ( _Satz_ )," Husserl writes, "is certainly extended thereby in an exceptional way that may alienate sympathy, yet it remains within the limits of an important unity of essence. We must constantly bear in mind that for us the concepts of meaning ( _Sinn_ ) and posited meaning (or position) ( _Satz_ ) contain nothing of the nature of expression and conceptual meaning, but on the other hand include all explicit propositions and all propositional meanings" ( _Ideas_ , p. 369). Further on, the inseparability of posited meaning, meaning, and the object is even more clearly indicated: "According to our analyses these concepts indicate an abstract stratum belonging to the _full tissue of all noemata_ [emphasis added]. To grasp this stratum in its all-enveloping generality, and thus to realize that it is represented in _all act-spheres_ , has a wide bearing on our way of knowledge. Even in the plain and simple _intuitions_ the concepts meaning ( _Sinn_ ) and posited meaning ( _Satz_ ) which belong inseparably to the concept of object ( _Gegenstand_ ) have their necessary application." (pp. 369–70).
. On the matrix of the sign as the structure of a logical proof, see Emile Bréhier, _La Théorie des incorporels dans l'ancien stoicisme_ (Paris: J. Vrin, 1970).
. "The fact is that the total form of the body by which the subject anticipates in a mirage the maturation of his power is given to him only as _Gestalt_ , that is to say, in an exteriority in which this form is certainly more constituent than constituted, but in which it appears to him above all in a contrasting size ( _un relief de stature_ ) that fixes it and in a symmetry that inverts it, in contrast with the turbulent movements that the subject feels are animating him." Lacan, "The Mirror Stage as Formative of the Function of the I," in _Ecrits/A Selection_ , Alan Sheridan, tr. (New York: Norton, 1977), p. 2.
. "The Subversion of the Subject and the Dialectic of Desire in the Freudian Unconscious," _Ecrits/A Selection_ , p. 319.
. In Lacan's terminology, castration and the phallus are defined as "position," "localization," and "presence": "We know that the unconscious castration complex has the function of a knot:... (2) in a regulation of the development that gives its _ratio_ to this first role: namely, the _installation_ in the subject of an unconscious _position_ without which he would be unable to identify himself with the ideal type of his sex..." ("The Signification of the Phallus," _Ecrits/A Selection_ , p. 281; emphasis added). "We know that in this term Freud specifies the first genital maturation: on the one hand, it would seem to be characterized by the imaginary dominance of the phallic attribute and by masturbatory _jouissance_ and, on the other, it _localizes_ this _jouissance_ for the woman in the clitoris, which is thus raised to the function of the phallus" (p. 282; emphasis added). "[The phallus] is the signifier intended to _designate_ as a whole the effects of the signified, in that the signifier conditions them by its _presence_ as a signifier" (p. 285; emphasis added).
. Lacan himself has suggested the term "want-to-be" for his neologism ( _manque à être_ ). Other proposed translations include "want-of-being" (Leon S. Roudiez, personal communication) and "constitutive lack" (Jeffrey Mehlman, "The 'Floating Signifier': From Lévi-Strauss to Lacan," _Yale French Studies_ 48 (1972): 37).—Trans.
. _Ecrits/A Selection_ , p. 299.
. Ibid.
. Our definition of language as deriving from the death drive finds confirmation in Lacan: "From the approach that we have indicated, the reader should recognize in the metaphor of the return to the inanimate (which Freud attaches to every living body) that margin beyond life that language gives to the human being by virtue of the fact that he speaks, and which is precisely that in which such a being places in the position of a signifier, not only those parts of his body that are exchangeable, but this body itself" ("The Subversion of the Subject and the Dialectic of Desire in the Freudian Unconscious," _Ecrits/A Selection_ , p. 301). We would add that the symbolism of magic is based on language's capacity to store up the death drive by taking it out of the body. Lévi-Strauss suggests this when he writes that "the relationship between monster and disease is internal to [the patient's] mind, whether conscious or unconscious: It is a relationship between symbol and thing symbolized, or, to use the terminology of linguists, between signifier and signified. The shaman provides the sick woman with a _language_ , by means of which unexpressed and otherwise unexpressible psychic states can be immediately expressed. And it is the transition to this verbal expression—at the same time making it possible to undergo in an ordered and intelligible form a real experience that would otherwise be chaotic and inexpressible—which induces the release of the physiological process, that is, the reorganization, in a favorable direction, of the process to which the sick woman is subjected." Claude Lévi-Strauss, "The Effectiveness of Symbols," in _Structural Anthropology_ , 2 vols., Claire Jacobson and Brooke Grundfest Schoepf, trs. (New York: Basic Books, 1963), 1:197–98; translation modified.
. See Lacan, "On a Question Preliminary to Any Possible Treatment of Psychosis," in _Ecrits/A Selection_ , p. 197.
. "The theory of textual writing's history may be termed 'monumental history' insofar as it serves as a 'ground' [ _fait fond_ ] in a literal way, in relation to a 'cursive,' figural (teleological) history which has served at once to constitute and dissimulate a written/exterior space.... Writing 'that recognizes the rupture' is therefore irreducible to the classical (representational) concept of 'written text': what it writes is never more than one part of itself. It makes the rupture the intersection of two sets (two irreconcilable states of language)," Philippe Sollers writes, "Program," in _Writing and the Experience of Limits_ , David Hayman, ed., Philip Barnard and David Hayman, trs. (New York: Columbia University Press, 1983), p. 7. Our reading of Lautréamont and Mallarmé will attempt to follow these principles; see _La Révolution du langage poétique_ (Paris: Seuil, 1974), pp. 361–609.
. Indeed, even Lacanian theory, although it establishes the signifier as absolute master, makes a distinction between two modalities of the signifier represented by the two levels of the "completed graph" ( _Ecrits/A Selection_ , p. 314). On the one hand, the _signifier_ as "signifier's treasure," as distinct from the _code_ , "for it is not that the univocal correspondence of a sign with something is preserved in it, but that the signifier is constituted only from a synchronic and enumerable collection of elements in which each is sustained only by the principle of its opposition to each of the others" (p. 304). Drives function within this "treasure of the signifiers" (p. 314), which is also called a signifying "battery." But from that level on, and even beforehand, the subject submits to the signifier, which is shown as a "punctuation in which the signification is constituted as finished product" (p. 304). In this way the path from the treasure to punctuation forms a "previous site of the pure subject of the signifier," which is not yet, however, the true place [ _lieu_ ] of the Other. On that level, the psychotic "dance" unfolds, the "pretense" [ _feinte_ ] that "is satisfied with that previous Other," accounted for by game theory. The fact remains that this _previous site_ does not exhaust the question of signification because the subject is not constituted from the code that lies in the Other, but rather from the message emitted by the Other. Only when the Other is distinguished from all other partners, unfolding as signifier and signified—and, as a result, articulating himself within an always already sentential signification and thus transmitting messages—only then are the preconditions for language ("speech") present.
At this second stage, the signifier is not just a "treasure" or a "battery" but a _place_ [ _lieu_ ]: "But it is clear that Speech begins only with the passage from 'pretense' to the order of the signifier, and that the signifier requires another locus—the locus of the Other, the Other witness, the witness Other than any of the partners—for the Speech that it supports to be capable of lying, that is to say, of presenting itself as Truth" (p. 305). Only from this point will the ego start to take on various configurations. What seems problematic about this arrangement, or in any case what we believe needs further development, is the way in which the "battery," the "treasure" of the signifier, functions. In our opinion, game theory cannot completely account for this functioning, nor can a signification be articulated until an alterity is _distinctly posited_ as such. One cannot speak of the "signifier" before the positing or the thesis of the Other, the articulation of which begins only with the mirror stage. But what of the previous processes that are not yet "a site," but a _functioning_? The thetic phase will establish this functioning as a signifying _order_ (though it will not stop it) and will return in this order.
. _Effraction_ , in French, is the juridical term for "breaking and entering"; in Kristeva's sense it also means a "breaking into" or "breaking through." I have translated it as "breach": the act or result of breaking and, more significantly, an infraction or violation as of a law.—Trans.
. It has recently been emphasized that _mimesis_ is not an imitation of an object but a reproduction of the trajectory of enunciation; in other words, _mimesis_ departs from denotation (in Frege's sense) and confines itself to meaning. Roland Barthes makes this explicit: "The function of narrative is not to 'represent,' it is to constitute a spectacle still very enigmatic for us... Logic has here an emancipatory value—and with it the entire narrative. It may be that men ceaselessly re-inject into narrative what they have known, what they have experienced; but if they do, at least it is in a form which has vanquished repetition and instituted the model of a process of becoming. Narrative does not show, does not imitate; the passion which may excite us in reading a novel is not that of a 'vision' (in actual fact, we do not 'see' anything). Rather it is that of meaning... ; 'what happens' is language alone, the adventure of language, the unceasing celebration of its coming." Barthes, "Introduction to the Structuralist Analysis of Narratives," in _Image, Music, Text_ , Stephen Heath, tr. (New York: Hill & Wang, 1977), pp. 123–24. This is also what Goethe means when he writes: "In your own mode of rhyme my feet I'll find, / The repetitions of pleasures shall incite: / At first the sense and then the words I'll find [Erst werd ich Sinn, sodann auch Worte finden], / No sound a second time will I indite / Unless thereby the meaning is refined / As you, with peerless gifts, have shown aright!" But this analysis of meaning through sounds must result in a new device that is not just a new meaning but also a new "form": "Measured rhythms are indeed delightful, / And therein a pleasing talent basks; / But how quickly they can taste so frightful, / There's no blood nor sense in hollow masks [Hohle Masken ohne Blut und Sinn]. / Even wit must shudder at such tasks / If it can't, with new form occupied, / Put an end at last to form that's died." "Imitation" [ _Nachbildung_ ], _West-Eastern Divan/West-Oestlicher Divan_ , J. Whaley, tr. (London: Oswald Wolff, 1974), pp. 34–37.
. This is why Lacan stated in his spring 1972 seminar that the expression _Die Bedeutung des Phallus_ is a tautology.
. See Jakobson, "L'importanza di Kruszewski per lo sviluppo della linguistica generale," _Ricerche Slavistiche_ 14 (1967): 1–20.
. See Lacan, _Ecrits/A Selection_ , pp. 156–57, et passim.
. See Kristeva, _Le Texte du roman: Approche sémiologique d'une structure discursive transformationnelle_ (The Hague: Mouton, 1970).
. "We have not yet referred to any other sort of displacement [ _Verschiebung_ ]. Analyses show us, however, that another sort exists and that it reveals itself in a change in the _verbal expression_ of the thoughts concerned... One element is replaced by another [ein Element seine Wortfassung gegen eine andere vertauscht].... Any one thought, whose form of expression may happen to be fixed for other reasons, will operate in a determinant and selective manner on the possible forms of expression allotted to the other thoughts, and it may do so, perhaps, from the very start—as is the case in writing a poem [Der eine Gedanke, dessen Ausdruck etwa aus anderen Gründen feststeht, wird dabei verteilend und auswählend auf die Ausdrucksmöglichkeiten des anderen einwirken, und dies vielleicht von vorneherein, ähnlich wie bei der Arbeit des Dichters]." _The Interpretation of Dreams_ , _Standard Edition_ , 5:339–40; _Gesammelte Werke_ (London: Imago, 1942), 2–3:344–45. See "La Transposition, le déplacement, la condensation," _La Révolution du langage poétique_ , pp. 230–39.
. Goethe speaks of this when, describing the Arabic tradition, he calls to mind the poet whose role is to express "Undeniable truth indelibly: / But there are some small points here and there / Which exceed the limits of the law [Ausgemachte Wahreit unauslöschlich: / Aber hie und da auch Kleinigkeiten / Ausserhalb der Grenze des Gesetzes]." "Fetwa," _West-Eastern Divan_ , pp. 30–33.
. "Yet this 'object of perspective,' may be handled in different ways. In fetishism (and, in my view, in art works), it pushes itself into the great ambiguous realm of disavowal, and materializes... As a result, we see... that all scientific or esthetic observation or activity has a part to play in the fate reserved for the 'perspective object,"' writes Guy Rosolato, "Le Fétishisme dont se 'dérobe' l'objet," _Nouvelle Revue de Psychanalyse_ 2 (Autumn 1970): 39.
For a more complete account of this concept in English, see Rosolato, "Symbol Formation," _International Journal of Psychoanalysis_ 59 (1978): 303–13.—Trans.
. As Jean Pouillon remarks, "if words were merely fetishes, semantics would be reduced to phonology." "Fétiches sans fétichisme," _Nouvelle Revue de Psychanalyse_ 2 (Autumn 1970): 147.
. By contrast, discourse in Molière's "Femmes savantes" is an exemplary case of the fetishizing process since it focuses exclusively on the signifier. "It is indeed the sign that becomes an erotic object and not the 'erotic' signified of discourse, as is usual in simple cases of repression (obscene talk or graffiti). It is not obsession but perversion." Josette Rey-Debove, "L'Orgie langagière," _Poétique_ 12 (1972): 579.
. See John von Neumann, _The Computer and the Brain_ (New Haven: Yale University Press, 1958).
. Anthony Wilden, "Analog and Digital Communication," _Semiotica_ 6, no. 1 (1972): 50–51.
Kristeva gives a loose translation of these passages in French. I have restored the original English quotation. Wilden, it should be noted, uses "computer" in the broad sense, whether the device actually computes in the strict sense or not.—Trans.
. Ibid., p. 55.
. Benveniste has taught us not to confuse these two operations, but rather to call something a language only when it has a double articulation; the distinction between phonemes devoid of meaning and morphemes as elements—for which no code is pertinent—is a _social_ , specifically human occurrence. See "Animal Communication and Human Language," _Problems_ , pp. 49–54.
. This is what Hegel believes. At the end of the "Larger Logic," describing negativity as that which constructs absolute knowledge, he writes: "This negativity, as self-transcending contradiction, is the _reconstitution of the first immediacy_ , of simple universality; for, immediately, the Other of the Other and the negative of the negative is the _positive_ , _identical_ , and _universal_." _Hegel's Science of Logic_ , W. H. Johnston and L. G. Struthers, trs., 2 vols. (London: Allen & Unwin, 1929; 1966), 2:478; emphasis added.
. _Moses and Monotheism_ , _Standard Edition_ , 23:7–137.
. The two roles have often merged, as Georges Dumézil reminds us in _Mitra-Varuna_ (Paris: Gallimard, 1948). See "Deux conceptions de la souveraineté," _La Révolution du langage poétique_ , pp. 545–52.
. See "Shifters, Verbal Categories, and the Russian Verb," in Jakobson, _Selected Writings_ , 2:130–47.
. See Joseph Needham, _Science and Civilisation in China_ , 4 vols. (Cambridge: Cambridge University Press, 1960), vol. 1.
. From a similar perspective, Edgar Morin writes: "We can think of magic, mythologies, and ideologies both as mixed systems, making affectivity rational and rationality affective, and as outcomes of combining: a) fundamental drives, b) the chancy play of fantasy, and c) logico-constructive systems. (To our mind, the theory of myth must be based on triunic syncretism rather than unilateral logic.)" He adds, in a note, that "myth does not have a single logic but a synthesis of three kinds of logic." "Le Paradigme perdu: La Nature humaine," paper presented at the "Invariants biologiques et universaux culturels" Colloquium, Royaumont, September 6–9, 1972.
. Lacan presented this typology of discourse at his 1969 and 1970 seminars.
Negativity: Rejection
_The negative having been in all probability greatly strengthened by the "struggle," a decision between insanity and security is imminent_.
— _Kafka, Diaries, February 2, 1922_
1. The Fourth "Term" of the Dialectic
The notion of _negativity_ ( _Negativität_ ), which may be thought of as both the cause and the organizing principle of the _process_ , comes from Hegel. The concept of negativity, distinct from that of nothingness ( _Nichts_ ) and negation ( _Negation_ ), figures as the indissoluble relation between an "ineffable" mobility and its "particular determination." Negativity is the mediation, the supersession of the "pure abstractions" of being and nothingness in the concrete where they are both only moments. Although _negativity_ is a concept and therefore belongs to a contemplative (theoretical) system, it reformulates the static _terms_ of pure abstraction as a process, dissolving and binding them within a mobile law. Thus, while still maintaining their dualism, negativity recasts not only the theses of _being_ and _nothingness_ , but all categories used in the contemplative system: universal and particular, indeterminate and determinate, quality and quantity, negation and affirmation, and the like. Negativity constitutes the logical impetus beneath the thesis of negation and that of the negation of negation, but is identical to neither since it is, instead, the logical functioning of the movement that produces the theses.
Lenin noted Hegel's statement that the "triplicity" of the dialectic is its "external, superficial side." By contrast, negativity is the liquefying and dissolving agent that does not destroy but rather reactivates new organizations and, in that sense, affirms. As transition ( _Übergang_ ), negativity constitutes an _enchaînement in the choreographical sense, "the necessary connection" and "the immanent emergence of distinctions." Here Lenin writes:_
Very important!! This is what it means, in my opinion:
1) _Necessary_ connection, the objective connection of all the aspects, forces, tendencies, etc., of the given sphere of phenomena;
2) The "immanent _emergence_ of distinctions"—the inner objective logic of evolution and of the struggle of the differences, polarity.
Lenin underscores and accepts the notion of "inherent negativity" as an _objective_ principle—the principle of all physical and spiritual life—and not as a simple "subjective craving to shake and break down what is fixed and true." In the final analysis, dialectical materialism will inherit from Hegel's dialectic this and only this founding principle; it will reinstate materialist dualism and see negativity at work in and through two differentiated and heterogeneous orders.
Before returning to this heteronomy, we would like to stress that the Hegelian conception of negativity already prepared the way for the very possibility of thinking a materialist _process_. While remaining an intraspeculative notion, Hegelian negativity bursts, as it were, from within its conceptual unity since it links [ _enchaîne_ ]—unleashes [ _déchaîne_ ]—the "real" and the "conceptual," the objective and the subjective, and, if one wished to find its representation, culminates in the ethical order: although it is _objectivity_ itself, negativity is at the same time and for that very reason the "free subject." The _ethics_ that develops in the process of negativity's unfolding is not the kind of "ethics" that consists in obedience to laws. It amounts instead to the corruption and absorption of laws by what Hegel calls the aesthetic. The subject of that Hegelian aesthetic—the free subject par excellence—reveals the diremption [ _épuisement_ ] of the ethical subject and effects its _Aufhebung_ in order to reintroduce him into a process of transformation of community relations and discursive strata. The logical definition given to this negativity is freedom "for itself": "The highest form of nothingness [taken] for itself is _freedom_ , but it is negativity to the extent that it goes as deep into itself as possible, and is itself affirmation."
As the logical expression of the objective process, negativity can only produce a subject in process/on trial. In other words, the subject, constituted by the law of negativity and thus by the law of an objective reality, is necessarily suffused by negativity—opened onto and by objectivity, he is mobile, nonsubjected, free. A subject submerged in negativity is no longer "outside" objective negativity as a transcendent unity or a specifically regulated monad; instead he positions himself as the " _innermost_ and _most objective_ moment of Life and Spirit." This Hegelian principle is the ferment of dialectical materialism, where it becomes both the concept of _human activity_ as revolutionary activity and that of the _social and natural laws_ this activity shows to be objective. Hegel writes:
The negativity which has just been considered is the _turning-point_ of the Notion. It is the simple point of negative self-relation, the internal source of all activity, vital and spiritual self-movement, the dialectic soul which all truth has in it and through which it alone is truth; for the transcendence of the opposition between the Notion and Reality, and that unity which is the truth, rest upon this subjectivity alone.—The second negative, the negative of the negative, which we have reached, is this transcendence of the contradiction but is no more the _activity_ of _an_ external reflection than the contradiction is; it is the _innermost_ and _most objective_ moment of Life and Spirit, by virtue of which a subject, the person, the free, has being.
Lenin notes in the margins of this passage: "the kernel of dialectics," "the criterion of truth (the unity of the concept and reality)."
But the materialist dialectic will retain only one element of the subject's negativation: his subordination, as a unit, to the social and natural process. Inheriting the weak points of dialectical materialist logic, dogmatico-revisionism will either dismiss the very problem of the subject and retain only the process of substance in a Spinozistic sense or the process of modes of production (as in dogmatism); or else it will hypostasize a psychological "subject" that has no process and only an external negativity (as in revisionism).
Let us take a closer look at the vicissitudes and dead ends of Hegelian negativity. If "the truth is, not either Being or Nothing, but that Being—not passes—but _has passed over_ into Nothing, and Nothing into Being" (emphasis added), and if "their truth is therefore this _movement_ , this immediate disappearance of the one into the other, in a word, _Becoming_ ; a movement wherein both are distinct, but in virtue of a distinction which has equally immediately dissolved itself," then we see that this supersession amounts to the erasing of heterogeneity within the Hegelian dialectic. Nothing, posited as such or active as a _relation_ in negativity, can only be a _Becoming_ or an _abstract negation_ : the "absolute void" in Oriental systems. When negativity is considered a logical operation, it becomes reified as a void, as an absolute zero—the zero used in logic and serving at its base—or else as a connective in the logical Becoming. Yet what the dialectic represents as negativity, indeed Nothing, is precisely that which remains outside logic (as the signifier of a subject), what remains heterogeneous to logic even while producing it through a movement of separation or rejection, something that has the necessary objectivity of a law and can be seen as the logic of matter. This notion is possible because of and in spite of Hegel because he maintains, in opposition to Spinoza, the inseparability, the interpenetration, indeed the contradiction of "Being" and "Nothing" even if only within the sphere of the Idea:
Those who assert the proposition that Nothing is just Nothing, and even grow heated in its defence, do not know that in so doing they are subscribing to the abstract Pantheism of the Eleatics and, in essentials, of Spinoza. That view in philosophy which takes for principle that Being is merely Being, and Nothing merely Nothing, deserves the name of system of identity: this abstract identity is the essence of Pantheism.
To those surprised by this thesis of the inseparability of Being and Nothing, Hegel objected that such "wonderment... forgets that in this Science [philosophy] there occur determinations quite different from those of ordinary consciousness and so-called common-sense,—which is not exactly sound understanding, but understanding educated up to abstractions and the faith, or rather superstition, of abstractions."
A _negativity_ inseparable from the Hegelian notion of _Being_ is thus precisely what splits and prevents the closing up of Being within an abstract and superstitious understanding. It points to an outside that Hegel could only think of as something inherent in belief, and which his phenomenological descendants would posit as a negative theology. We nevertheless maintain that Hegelian negativity prevents the immobilization of the thetic, unsettles doxy, and lets in all the semiotic motility that prepares and exceeds it. Hegel, moreover, defines this negativity as the _fourth term_ of the true dialectic: triplicity is only an appearance in the realm of the Understanding.
The logic exposed above will become materialist when, with the help of Freud's discovery, one dares think negativity as the _very movement of heterogeneous matter_ , inseparable from its differentiation's symbolic function. Although in Kant this material movement of scission, of rejection (to which we shall return), remains a "negative" term for the understanding, it is conceived dialectically, _because it is considered inseparable from Being_ , as a fundamental _positivity_ : "In this respect therefore mere Unseparateness or Inseparability would be a good substitute for Unity; but these would not express the affirmative nature of the relation of the whole."
Thus, even while maintaining Kantian oppositions, the Hegelian dialectic moves toward a fundamental reorganization of these oppositions—one that will establish an _affirmative negativity_ , a _productive dissolution_ in place of "Being" and "Nothing." The theology inherent in this reorganization will, however, leave its mark in an implicit teleology: namely, the _Becoming_ that subordinates, indeed erases, the moment of rupture.
7. Freud's Notion of Expulsion: Rejection
Rejection, or expenditure, constitutes the key moment shattering unity, yet it is unthinkable outside unity, for rejection presupposes thetic unity as its precondition and horizon, one to be always superseded and exceeded. Rejection serves to bind only to the extent that it is the _precondition_ of the binding that takes place on another scene. To posit rejection as fundamental and inherent in every thesis does not mean that we posit it as origin. Rejection rejects origin since it is always already the repetition of an impulse that is itself a rejection. Its law is one of returning, as opposed to one of becoming; it returns only to separate again immediately and thus appear as an impossible forward movement.
Of the terms "rejection," "scission," and "separation," _rejection_ is the one that best designates, archaeologically, the instinctual, repetitive, and transsignifying aspect of the dynamics of signifiance. It implies a preverbal "function," one that is prelogical and a-logical in the sense that the _logos_ signifies a "relation," a "connection." _Scission_ and _separation_ are more appropriate terms for that rupture when it is considered from the point of view of the subject and already constituted meaning, which is to say, within a perspective that takes into account language and the unity of the subject—a signifying sociality dependent on norms. We shall stress the first term ( _rejection_ ) because it suggests the heterogeneity of signifiance we are attempting to demonstrate, and because, within the text, it opens up an a-signifying, indeed prelinguistic, crucible. But we shall use the other terms ( _scission_ and _separation_ ) as well because they emphasize the underlying unity which withdraws and is reconstituted in the return of rejection. They also signal the permanent logical constraint of an insurmountable _consciousness_ , which ensures the reactivation of rejection in a process, thus saving it from foundering in inarticulable instinctuality, where signifying production would be impossible. Our conception of rejection will oscillate between the two poles of drives and consciousness, and this ambiguity will reveal the ambiguity of process itself, which is both divided and unitary. But to the extent that these two threads (drives and consciousness) intersect and interweave, the _unity of reason_ which consciousness sketches out will always be shattered by the _rhythm_ suggested by drives: repetitive rejection seeps in through "prosody," and so forth, preventing the stasis of One meaning, One myth, One logic.
In Freud's article on _Verneinung_ [negation], expulsion ( _Ausstossung_ ) is what constitutes the real object as such; it also constitutes it as lost, thus setting up the symbolic function. For the pleasure-ego, the oral ego of incorporation and unification ( _Einbeziehung_ ), the outside does not matter. Expulsion ( _Ausstossung_ ) establishes an outside that is never definitively separate—one that is always in the process of being posited. But in doing so, it already runs counter to the unifying pleasure principle and sets up the most radical exteriority: the struggle with the latter will represent the recipient _topos_ , the mobile _chora_ of the subject in process/on trial. The pleasure principle, which unifies and identifies, seems to have been conceived by Freud as an aid to repression. Expulsion (and its symbolic representation in the sign of negation), acting against the pleasure principle, acts against the consequences of repression. "The performance of the function of judgement is not made possible," writes Freud, "until the creation of the symbol of negation has endowed thinking with a first measure of freedom from the consequences of repression and, with it, from the compulsion of the pleasure principle."
Significantly, in thinking the establishment of the symbolic function through the symbol of negation, Freud remarks that the symbolic function is instituted on the basis of _expulsion_ ( _Ausstossung_ , referred to as _Verwerfung_ [foreclosure] in "Wolf Man"), but says nothing about the "drive bases" of this "act," or about the drive that activates this "kineme": in other words, he says nothing about rejection. As a result of this omission, Freud sets up an opposition, via expulsion, between the symbolic function and _Einbeziehung_ —unification, incorporation—which refers to orality and pleasure. The symbolic function is thereby dissociated from all pleasure, made to oppose it, and is set up as the paternal place, the place of the superego. According to this view, the only way to react against the consequences of repression imposed by the compulsion of the pleasure principle is to renounce pleasure through symbolization by setting up the sign through the absence of the object, which is expelled and forever lost.
What this interpretation seems to rule out is the pleasure underlying the symbolic function of expulsion, a pleasure which this function represses but that can return to it and, when combined with oral pleasure, disturb, indeed dismantle, the symbolic function. In any case, it can transform ideation into an "artistic game," corrupt the symbolic through the return of drives, and make it a semiotic device, a mobile _chora_. This pleasure derives from the anal drive—anal rejection, anality—in which Freud sees the sadistic component of the sexual instinct and which he identifies with the death drive. We would like to stress the importance of anal rejection or anality, which precedes the establishment of the symbolic and is both its precondition and its repressed element. Because the process of the subject involves the process of his language and/or of the symbolic function itself, this implies—within the economy of the body bearing it—a reactivation of anality. The texts of Lautréamont, Jarry, and Artaud—among others—explicitly point to the anal drive that agitates the subject's body in his subversion of the symbolic function.
Freud's silence, both on the subject of anality and in front of Signorelli's frescoes, is not just the symptom of a certain blindness toward homosexuality, which, to his credit, he nevertheless sees at the basis of social institutions. His silence is also bound up with psychoanalysis' silence about the way the literary function subverts the symbolic function and puts the subject in process/on trial. Although psychoanalysis may speak of fantasies in literature, it never mentions the economy of the subject bound up with those fantasies that dissolves the symbolic and language. If the return of rejection, by corrupting both the symbolic and sublimation in modern texts, attests to the presence of the death drive—a destruction of both the living being and the subject—how can we neglect the jouissance harbored by this "aggressivity," this "sadistic component"? The jouissance of destruction (or, if you will, of the "death drive"), which the text manifests through language, passes through an unburying of repressed, sublimated anality. In other words, before arranging itself in a new semiotic network, before forming the new structure which will be the "literary work," the not yet symbolized drive and the "residues of first symbolizations" attack, through unburied anality and fully cognizant of homosexuality, all the stases of the signifying process: sign, language, identifying family structure.
It will now be helpful to recall in more detail the role that rejection and jouissance play in the symbolic function and in putting that function in process/on trial. Although the sadistic component of the sexual instinct makes a veiled appearance in both the oral and genital phase, it dominates the anal phase and is so essential to libidinal economy that Freud recognizes that there might be such a thing as a primary sadism, one "that has been turned round upon the subject's own ego" before any object has been isolated, and would hence constitute primary masochism. What we mean by _rejection_ is precisely the semiotic mode of this permanent aggressivity and the possibility of its being _posited_ , and thus _renewed_. Although it is destructive—a "death drive"—rejection is the very mechanism of reactivation, tension, life; aiming toward the equalization of tension, toward a state of inertia and death, it _perpetuates_ tension and life.
The anal phase designated by psychoanalysis comes before the Oedipus conflict and the separation of the ego from the id in Freudian topography. This phase concludes a more extensive and more fundamental period for the infantile libido: the period called _sadistic_ , which predominates before the Oedipus complex begins and constitutes an oral, muscular, urethral, and anal sadism. In all these forms, of which the anal is the last to be repressed and hence the most important, energy surges and discharges erotize the glottic, urethral, and anal sphincters as well as the kinetic system. These drives move through the sphincters and arouse pleasure at the very moment substances belonging to the body are separated and rejected from the body. This acute pleasure therefore coincides with a loss, a separation from the body, and the isolating of objects outside it. Before the body itself is posited as a detached alterity, and hence the real object, this expulsion of objects is the subject's fundamental experience of separation—a separation which is not a lack, but a discharge, and which, although privative, arouses pleasure. The psychoanalyst assumes that this jubilant loss is simultaneously felt as an attack against the expelled object, all exterior objects (including father and mother), and the body itself.
The problem then becomes how to hold this "aggressivity" in check. In other words, how does one curb the pleasure of separation caused by rejection, the ambivalence of which (the body's jouissance plus the loss of body parts) constitutes a nexus of the pleasure and threat that characterizes drives. The "normal," Oedipal way of curbing this pleasure consists in identifying the body proper with one of the parents during the Oedipal stage. At the same time, the rejected object definitively separates and is not simply rejected but suppressed as a material object; it is the "opposite other" [ _l'autre en face_ ] with whom only one relation is possible—that of the sign, symbolic relation _in absentia_. Rejection is thus a step on the way to the object's becoming-sign, at which the object will be detached from the body and isolated as a real object. In other words, rejection is a step on the way to the imposition of the _superego_.
However, as cases of child schizophrenia prove, the violence of rejection and of the anal pleasure it produces is sometimes so powerful that Oedipal identification cannot absorb and symbolize them by setting up a signifiable, real object. In such instances, the body is unable to "defend" itself against rejection through suppression or repression and the pleasure aroused by the return of rejection immobilizes the body there. Rejection and sadism, which is its psychological side, return and disturb the symbolic chains put in place by the Oedipal complex. Melanie Klein interprets the behavior "disturbances" that result as the organism's "defenses" against the danger of aggressivity. But she recognizes that "this defense... is of a _violent_ character and differs fundamentally from the later mechanism of repression," which symbolism establishes. These "defenses" are resistances, _thetic substitutes_ for the "violent" drive process, which, far from having a psychological value of prevention, _arrange_ the "sadistic" drive charge, _articulate_ rejection in such a way that it is not subsumed by the construction of a _superego_ (as is the case in the Oedipus complex). The distortion of words, the repetition of words and syntagms, and hyperkinesia or stereotypy reveal that a _semiotic network_ —the _chora_ —has been established, one that simultaneously defies both verbal symbolization and the formation of a superego patterned after paternal law and sealed by language acquisition.
Indeed, the acquisition of language and notably syntactic structure, which constitutes its normativeness, is parallel to the mirror stage. Language acquisition implies the suppression of anality; in other words, it represents the acquisition of a capacity for symbolization through the definitive detachment of the rejected object, through its repression under the sign. Every return of rejection and of the erotic pleasure it produces in the sphincters disturbs this symbolic capacity and the acquisition of language that fulfills it. By inserting itself into the signifying system of language, rejection either delays its acquisition or, in the case of the schizoid child, prevents it altogether. In the adult, this return to nonsublimated, nonsymbolized anality breaks up the linearity of the signifying chain, and suffuses it with paragrams and glossolalia. In this sense, interjections—those semiotic devices that run through modern phenotexts and become rhythmic expectorations in Artaud—convey the struggle of a nonsublimated anality against the superego. Ideologically, this transformation of the signifying chain attacks, provokes, and unveils repressed sadism—the anality underlying social apparatuses.
There exist two signifying modalities that seem to permit the survival of rejection to the extent that they harmonize the shattering brought about by rejection, affirm it, and make it positive without suppressing it under paranoid paternal unity. The first of these modalities is _oralization_ : a reunion with the mother's body, which is no longer viewed as an engendering, hollow, and vaginated, expelling and rejecting body, but rather as a vocalic one—throat, voice, and breasts: music, rhythm, prosody, paragrams, and the matrix of the prophetic parabola; the Oedipus complex of a far-off incest, "signifying," the real if not reality. The second modality, always inseparable from the first, appears in the reunion with brothers' bodies, in the reconstitution of a _homosexual phratry_ that will forever pursue, tirelessly and interminably, the murder of the One, the Father, in order to impose _one_ logic, _one_ ethics, _one_ signified: _one_ , but _other_ , critical, combatant, revolutionary—the brothers in Freud's primal horde, for example, or Michelangelo's "Battle of the Centaurs" in Florence.
These two modalities—oralization and the homosexual phratry—point to the two sides—"poetic" and "mastering"—of texts, situated on the path of rejection, which carry out the signifying process by making it a production for community use. The "poetic" side of the text can be seen in the supposedly pianistic scansion of sentences in _Maldoror_ , Mallarméan rhythmics, the iciness of "Hérodiade," or in the opulent chic of Méry Laurent, coveted by the Parisian poetic inner circle. Examples vary: from preciosity and snobbery (a token of the forbidden, idealized, and oralized mother) to the glottal spasm in Malarmé; or, in Lautréamont, a mother who is oceanic and submissive though she is also the overpossessive lover of the hanged man. The Hegelian philosophy in Mallarmé's _A Throw of the Dice_ and _Igitur_ , the monastic, sacramental, and ritual call of his _Le "Livre"_ , and the broken and then restored logic of Lautréamont's _Poems_ show that the second, "mastering" modality is a lining of the first, "poetic" modality.
Oralization can be a mediator between the fundamental sadism of rejection and its signifying sublimation. Melody, harmony, rhythm, the "sweet," "pleasant" sounds and poetic musicality found in "symbolist" poetry and in Mallarmé, for example, may be interpreted as oralization. This oralization restrains the aggressivity of rejection through an attempted fusion with the mother's body, a devouring fusion: Mallarmé's biography documents this attempt. A return to oral and glottal pleasure combats the superego and its linear language, which is characterized by the subject/predicate sequences of its syntagms. Suction or expulsion, fusion with or rejection of the mother's breast seem to be at the root of this erotization of the vocal apparatus and, through it, the introduction into the linguistic order of an excess of pleasure marked by a redistribution of the phonematic order, morphological structure, and even syntax: portmanteau words in Joyce and syntax in Mallarmé, for example.
The oral cavity is the first organ of perception to develop and maintains the nursing infant's first contact with the outside but also with the _other_. His initial "burrowing" movement, which is meant to establish contact—indeed biologically indispensable fusion—with the mother's body, takes on a _negative_ value by the age of six months. The rotating movement of the head at that age indicates refusal even before the "semantic," abstract word "no" appears at fifteen months. Fusing orality and devouring, refusing, negative orality are thus closely intermingled, as they are in the anal stage that follows. During this stage aggressivity is accentuated, ensuring the body's separation from and always already negative relation to the outside and the other. In addition, even if it is recognized as more archaic than rejection, fusing orality and the libidinal drive it supports are _borne_ by rejection and, in the genesis of the subject's symbolic functioning, _determined_ by it.
If, through a defusion of the drives or for some other reason, _rejection_ as the bearer of drives or, more precisely, their negative discharge, is accentuated, this discharge uses the muscular apparatus as a passageway for discharging energy in brief spurts: pictorial or dancing gesturality may be ascribed to this mechanism. But rejection may pass through the vocal apparatus as well. The oral cavity and the glottis are the only internal organs that do not have the characteristic capacity of muscular apparatuses to restrain bound energy. Instead they free discharges through a finite system of phonemes specific to each language, by increasing their frequency, by accumulating or repeating them, and thus determining the choice of morphemes. They may even condense several "borrowed" morphemes into a single lexeme. In so doing, the rejection that invests the oral cavity awakens in and through it the "libidinal," "unifying," "positive" drive which characterizes, at the earliest stages, this same cavity in its initial "burrowing" movement. Through the new phonematic and rhythmic network it produces, rejection becomes a source of "aesthetic" pleasure. Thus, without leaving the line of meaning, it cuts up and reorganizes that line by imprinting on it the path of drives through the body: from the anus to the mouth.
Rejection therefore constitutes the return of expulsion— _Ausstossung_ or _Verwerfung_ —within the domain of the constituted subject: rejection _re_ constitutes real objects, "creates" new ones, reinvents the real, and resymbolizes it. Although in so doing rejection recalls a schizoid regressive process, it is more important to note that rejection positivizes that process, affirming it by introducing the process into the signifying sphere: the latter thus finds itself separate, divided, put in process/on trial. This symbolization of rejection is the place of an untenable contradiction which only a limited number of subjects can reach. Although rejection includes the moment of "excorporation," ("expectoration" in Artaud's terms, or "excretion" in Bataille's), this motorial discharge and corporeal spasm are invested in the sign—in language—which is itself already divided, reintroducing and unfolding within it the very mechanics by which the separation between words and things is produced. Rejection thus unfolds, dismantles, and readjusts both the _vocal_ register (as in Mallarmé's texts or Lautréamont's _Maldoror_ ) and the _logical_ register (as in Ducasse's _Poems_ ). Rejection is reintroduced and reiterated in a divided language.
Characteristically, the formalist theory of symbolism simplifies the signifying process by seeing it only as a _text_ (in the sense of a coded or deviant distribution of marks), without perceiving the drive rejection that produces it, straddling the corporeal and natural on the one hand, the symbolic and social on the other, and found in each of them specifically. By contrast, recognizing the dialectical heterogeneity of these "orders" means indicating, above all, that rejection—anal, sadistic, aggressive—posits the "object" and the "sign," and that it constitutes the _real_ where phantasmatic or objective reality is found. From this standpoint, the subject seems to have two possibilities.
Either he goes elsewhere, which is to say, beyond rejection into reality, forever surpassing the trajectory of separation and scission, living it only as the spin-off or side aspect of a "commitment" to the real where all the logic of _meta_ \- is reified: _meta_ subject, _meta_ language, _meta_ physics. In this case, he places himself under the law of the father and takes on both this paranoia and the homosexuality connoting paranoia, the sublimation of which is all too fragile: here we see Orestes who murders his mother in the name of the laws of the city-state.
Or else the subject constantly returns to rejection and thus reaches what lies beneath the paranoid homosexuality laid bare by signifying production: the schizoid moment of scission. Mallarmé's suffering body and, later, the shattered and mummified body of Artaud attest to this loss of unity.
The representation of the "character" who becomes the place of this process is one that normative consciousness finds intolerable. For this "character"'s polymorphism is one that knows every perversion and adheres to none, one that moves through every vice without taking up any of them. Unidentical and inauthentic, his is the wisdom of artifice which has no interiority and is constant rejection. He is familiar with the social organism and its paranoid reality but makes light of it and, for them, he is an unbearable monstrosity. This has always been his traditional representation, from Heraclitus' "misanthropy" to the maliciousness of [Diderot's] _Le Neveu de Rameau_ and his _Paradoxe du comédien_.
Within the Greek tradition, the extant fragments of Heraclitus seem to have come closest to grasping the process of a simultaneous "hypertrophy of a self" and its separation within maintained reason. Thus, without leaving the domain of reason, Heraclitus makes of reason not a logical unity, as Plato and the Stoics have accustomed us to understanding it, but rather a divided speech, a counterspeech, sanctioning [ _homologuant_ ] what stands separate: words and things, but also things among things and words among words—the word as rejection of both the thing that it utters and another word, said or unsaid. Only the "clever" one who has mastered the technique of saying can achieve this "poetic" wisdom, τò σοφóυ, "art." This does not mean that "art," which maintains words within rejection, is a discourse on discourse: the discursive is only one of the phenomenal and linguistic manifestations of the process. Although metalanguage can apprehend this process only through language, by pursuing stylistic, logical, and etymological figures, the separation that discourse replays refers to presymbolic and intrasymbolic rejection, where logos and its sanction disappear. It refers to the a-symbolized and a-symbolizable scission, to the nothing that is neither one nor multiple, but rather the "infinite nothingness" spoken of by speculative philosophy, which we shall posit as matter that is always already split; from it, repeated rejections will generate not only the thetic logos but its shattering.
Heraclitean art is the practice that takes up, through the _logos_ , this _separation_ without beginning or end, which certain Freudian formulations assign to the unconscious. "Of all the discourses I have heard," states one of the Heraclitean fragments, "not one manages to distinguish the distinct element that makes art what it is." No discourse can identify the distinct element—instinctual matter—that characterizes art. Although it contradicts the One and discourse, instinctual matter is inscribed in them in order to reject them and reject itself from them. Iamblichus echoes Heraclitus, suggesting that the singular and rare man who is able to achieve rejection in reason does so on the basis of matter. Though this man is more than matter, matter is his precondition; it produces him by rejecting itself and rejecting him: "Hence I posit two kinds of sacrifice. On the one hand, those of completely purified men, which, as Heraclitus says, even a singular man can only rarely carry out, or only a numbered few; and on the other hand, those that remain material [ _restent dans la matière_ ]."
Now that we have followed the notion of expulsion [ _repoussement_ ] in Freud, let us pick it up again in Hegel, who opened the way for the notion of _negativity_ outlined at the beginning of this chapter. In Hegel, the term _Repulsion_ designates a movement within negativity that comes close to what we have called _rejection_ yet does not coincide with it. _Repulsion_ is the negative relation of the One with itself, as opposed to _Becoming_ , which is "a transition of Being into Nothing." Since it is the fundamental determination of the One and its fragmentation, Repulsion both ensures the preservation of the One and produces the plurality of Ones by the Attraction it presupposes. Thus we see that Hegelian Repulsion is always subordinate to Unicity and that, in beginning to act within it, Repulsion calls Unicity into question only _from the outside_ , by adding multiple external meanings. There is no doubt, and Hegel himself stresses, that Repulsion fundamentally interiorizes negativity, in opposition to Kantian analytics where the "two basic forces remain, within matter, opposed to one another, external and independent," and where "Kant determines... repulsive force... as a _superficial force_ , by means of which parts of matter can act upon one another only at the common surface of contact." But in internalizing Repulsion within the One itself and in making Repulsion what specifies, determines, and, in sum, identifies the One, Hegel subordinates Repulsion to what we have called the "symbolic function"; whereas Freud, on the other hand, joins dialectical logic by making _expulsion_ the essential moment in the constitution of the symbolic function. The difference is that, in Freud, what activates expulsion is "another scene" based on the drives. Since he does not have this heteronomy in view, Hegel can only supercede the exteriority of Repulsion that Freud has sketched out. This comes about because separation in Hegel becomes the explanation of what the One is in itself; it gets exported outside this One, which is always already constructed, becomes exteriorized, and, as a result of the dialectic, ends up in an exteriority:
The self-repulsion of the One is the explication of that which the One is in itself; but infinity, as split-up, is here infinity which has _passed beyond itself_ : and this it has done through the immediacy of the infinite entity, the One. It is a simple relation of One to One, and equally, or rather, the absolute unrelatedness of the One; it is the former according to the simple affirmative self-relation of One, and the latter according to the same as negative. In other words, the plurality of the One is its self-positing; the One is its own negative self-relation and nothing else, and this relation (the One itself) is many Ones. But equally, plurality is merely external to the One; for the _One also is the transcending of Otherness, Repulsion is its self-relation and simple self-identity. The plurality of Ones is infinity, as contradiction which unconcernedly produces itself_.
What Hegel does not envisage is the moment the One is _shattered_ in a return of Repulsion onto itself, which is to say, a turning against its own potential power for positing and multiplying the One. Nor does Hegelian logic see the heterogeneous parcelling of the symbolic, which underlies the symbolic's very constitution and constantly undermines it even while maintaining it in process; the simultaneous existence of the _boundary_ (which is the One) and the a-reasonable, a-relative, a-mediating _crossing_ of that boundary; or the possibility of the constitution-unconstitution of One meaning-nonmeaning, passing through categorial boundaries ("inside," "one," "multiple," etc.), which is precisely what _rejection_ brings about in the "schizoid" process of the text.
The ideational closure of the Hegelian dialectic seems to consist in its inability to posit negativity as anything but a repetition of ideational unity in itself. The exteriority to which it is condemned _in fact_ is thus bound up with the ideational enclosure, in which, despite many detours, its trajectory ends. Repeated rejection, far from purely and simply restoring the series of many Ones, instead opens up in and through Unity—we are tempted to say beyond "signifying unity" and "subjective unity"— _the material process of repeated_ (a-signifying and instinctual) _scissions_ ; these repeated scissions act with the regularity of objective laws and recall, through the rifts or new arrangements they produce, the pulsation of that process through symbolic unification. These are the conclusions we may draw from a materialist interpretation, opened up by the Freudian position on repetition compulsion.
Indeed, although for Freud _Ausstossung_ or _Verwerfung_ posits the sign, it already functions beforehand, "objectively" so to speak, in the movement of living matter subject to natural and social constraints. "In order to understand this step forward [the constitution of the real as separate], we must recollect that all presentations originate from perceptions and are repetitions of them."
While establishing the sign, subject, and judgment, _Verwefung_ points _at the same time_ toward the repeated scissions of a-symbolized living matter and toward the inorganic. The drive that thus takes shape operates in a transsymbolic realm that sends the signifying body back to biological a-signifiance and finally to death. Moreover what is _represented_ as a "death" is probably—as a great many "literary" texts show—nothing but the verbalization of this rejection, this multiplied rupture of all unity, including that of the body: "Now we shall have to call it the decorporealization of reality, the kind of rupture intent, it would seem, on multiplying; a rupture between things and the feeling they produce in our mind, the place they must take."
Freud reveals the obstinate and constraining return of rejection, its "repetition compulsion," as one of the "ultimate" mechanisms of psychic functioning—more essential than the "pleasure principle"—and characterizes it as "demonic," as "an urge inherent in organic life" to stop the galloping evolution of organic forms and their symbolizing capacity in order to return to a state of inertia and constancy. Through these formulations and beyond Freud's speculations on death (avowed as such by Freud himself), from observations about "schizophrenia," but, for our purposes, even more so from modern texts, there emerges the confirmation of an objective law. _Rejection_ , the specific movement of matter, produces its various forms, including their symbolic manifestations, at the same time that it ensures, by its repetition, a _threshold of constancy_ : a _boundary_ , a restraint around which difference will be set up—the path toward symbolization. But even as it posits the symbolic and its differentiation, this expenditure of _drives_ returns—notably in the text—to shatter difference and introduce, through its play, what silently acts on it: the scissions of matter. Because these scissions—which Freud situates in the _id_ or in the _unconscious_ —irrupt within the differentiation of symbolic play, we maintain that the signifying process practiced in its infinite totality has no unconscious; in other words, the text has no unconscious. Repeated and returned rejection opposes repression and, in Freudian terms, reintroduces "free energy" into "bound energy."
We have now reached a crucial point in the notion of _signifying process_. Rejection, which is the signifying process' powerful mechanism, is heterogeneous, since it is, from a Freudian standpoint, _instinctual_ , which means that it constitutes an articulation [ _charnière_ ] between the "psychical" and the "somatic." So much so that although the dichotomy between these two "orders" is upheld, it is also dialecticized, and the "signifier" appears only as a _thesis_ —a positing—of infinite repetitions of material rejections when "free energy," always already splitting, doubling, and rejecting, collides against the walls of natural and social _structures_ , which Freud terms "external disturbing forces," crystallizing "unities." Freud notes that "the manifestations of a compulsion to repeat... exhibit to a high degree an instinctual character and, when they act in opposition to the pleasure principle, give the appearance of some 'daemonic' force at work." Further on, he continues:
But how is the predicate of being "instinctual" related to the compulsion to repeat? At this point we cannot escape a suspicion that we may have come upon the track of a universal attribute of drives and perhaps of organic life in general which has not hitherto been clearly recognized or at least not explicitly stressed. _It seems, then, that a drive is an urge inherent in organic life to restore an earlier state of things_ which the living entity has been obliged to abandon under the pressure of external disturbing forces; that is, it is a kind of organic elasticity, or, to put it another way, the expression of the inertia inherent in organic life.
Conformist psychoanalysis after Freud has embarked on an attempt to "break down the id's resistances" by interpreting them and thereby suppressing drive rejection within the domain of so-called action in order to "signify" or "nuance" it. When established as a principle, this normalization of rejection contributes to the destruction of the "spearhead" of the signifying process. On the other hand, when rejection is brought back to its essential motor functions, when it necessarily becomes, whether unconsciously or voluntarily, the maintained and reinforced agent of the signifying process, it produces new cultural and social formations which are innovative and—under specific conditions which we shall discuss further on—subversive.
How is this return of rejection—this _surplus of rejection_ that puts in process/on trial the symbolic already instituted by _Verwerfung_ —represented in discourse? What is the negativity of the text, which is different from symbolic negation in judgment and is sustained by the threatened subject? What is its libidinal organization and discursive economy?
According to Freud in his article "Negation," symbolization implies a repression of pleasure and erotic drives. But this repression is not absolute. Freud implies that complete repression (if it were possible) would stop the symbolic function. Repression, Lacan explains, is a " _kind of discordance_ between the signified and the signifier that is determined by any censorship originating in society." Setting up the symbolic function requires this repression and prevents the removed truth of the real from slipping in anywhere except "between the lines," that is, in the linguistic structure, as "negation" for instance.
"The performance of the function of judgment," Freud continues, "is not made possible until the creation of the symbol of negation has endowed thinking with a first measure of freedom from the consequences of repression." Let us now return to an earlier point in the text on negation. For Freud, "negation is a lifting of the repression [ _Aufhebung der Verdrängung_ ]," which means an "intellectual acceptance of the repressed," but not its discharge or its "consumption." As a consequence, the "intellectual function" is separated from the "affective process," which results in "a kind of intellectual acceptance of the repressed, while at the same time what is essential to the repression persists."
The appearance of the symbol of negation in the signifier thus partially liberates repression and introduces into the signifier a part of what remains outside the symbolic order: what was repressed and what Freud calls "affective." These are instinctual, corporeal foundations stemming from the concrete history of the concrete (biological, familial, social) subject. Although it is true that the "affective" can be grasped only through discursive structuration, it would be semantic empiricism to believe that it does not in some fashion exist outside it. Clearly, negation as a _symbolic function_ inherent in judgment (inherent in symbolization) constitutes an intellectual sublimation ( _Aufhebung_ ) of only one part of foreclosure ( _Verwerfung_ ).
_Negation-as-denial_ [ _dénégation_ ] in cases of "obsessive ideas," writes Freud, allows "the ideational content of what is repressed... [to] reach consciousness." In analysis, through transference, "we succeed in conquering the negation as well, and in bringing about a full intellectual acceptance of the repressed; but the repressive process itself is not yet removed by this."
By contrast, in aesthetic productions, which do not involve transference, negation is not "conquered." Rejection operates in them and does not produce an "intellectual acceptance of the repressed" (in other words, it does not effect the passage of the repressed element into the signified, into the symbolic function). Instead it _marks signifying material_ with the repressed. This observation implies, on the one hand, that setting up the symbolic function (founded on judgment) requires a transference situation. It implies, on the other hand, that the symbolic function already carries out the distinction not only between "objective" and "subjective," but also between "signifier" and "signified." The reintroduction of the symbol of negation into poetic language (as opposed to the reintroduction of negation as "denial" [ _dénégation_ ] into analysis), _arranges the repressed element in a different way_ , one that does not represent an "intellectual acceptance of the repressed," an _Aufhebung_ , but instead constitutes a postsymbolic (and in this sense antisymbolic) hallmarking of the material that remained intact during first symbolization. This "material," expelled by the sign and judgment from first symbolizations, is then withdrawn from the unconscious into language, but is not accepted there in the form of "metalanguage" or any kind of intellection. The repeated death drive (negativity, destruction) withdraws from the unconscious and _takes up a position as already positivized and erotized in a language_ that, through drive investment, is organized into prosody or rhythmic timbres. If, as Freud writes in the same article, "in analysis we never discover a 'no' in the unconscious and [if] that recognition of the unconscious on the part of the ego is expressed in a negative formula," then the semiotic device constructed by poetic language through the positing of language as a symbolic system constitutes third-degree negativity. It is neither the lack of a "no" (as in the unconscious), nor a negative formula (a sign of the instituted symbolic function), nor negation-as-denial (symptoms of the neurotic ego idealizing the repressed), but instead a _modification of linguistic and logical linearity and ideality_ , which cannot be located in any ego. Poetic rhythm does not constitute the acknowledgment of the unconscious but is instead its expenditure and implementation.
For psychoanalysis, "the true subject is the subject of the unconscious" who appears only in the phenomenon of transference. Clearly, this is not the poetic subject. Although psychoanalysis and, hence, transference have allowed the (plural) topographies of the subject to emerge for science, the topography of poetic language appears as one that draws out, within a signifying device (which has been called "prosody," "art," and so forth), not the "ideational content" of what remains outside first symbolization, but rather its _economy_ : the _movement_ of rejection. This rejection may be implied in affirmative judgment ( _Bejahung_ ) (as in Lautréamont), or in linguistic morphology and syntax (as in Mallarmé); in other words, it may appear in the symbol of negation or in morphosyntactic destruction. Poetic negativity is third-degree rejection. As the rejection of symbolic and neurotic negation, it recalls, spatially and musically, the dialectical moment of the generating of signifiance.
In so doing, the text _momentarily_ sets right the conflict between signifier and signified established by the symbol of negation and which determines all censorship originating in society—repositing it, of course, but redistributing it as well. The text makes rejection work on and in the very place of symbolic and social censorship, which establishes language as a symbolic system with a double articulation: signifier and signified.
NOTES
. Hegel's terminology poses a problem. Whereas the French translations Kristeva cites are generally consistent in their rendering of key terms, no such "standards" inform the various English translations of either _Phenomenology of Spirit_ —even the title is a point of contention—or _Science of Logic_. Both texts, for example, refer to _Nichts_ , commonly translated as _néant_ in French but as "Nothing" in Johnston and Struthers's _Hegel's Science of Logic_ or as "nothingness" in A. V. Miller's _Phenomenology_. The same problem arises with _le devenir_ ("Becoming" or "process of Becoming"), _extériorisation_ ("exteriorization" or "expression"), and other such terms. I have not standardized these two different translations. When the discussion of Hegel does not refer to a specific work, I have generally selected French cognates.—Trans.
. Lenin, "Conspectus of Hegel's Book on _The Science of Logic_ ," Clemens Dutt, tr., _Collected Works_ , Stewart Smith, ed. (Moscow: Foreign Languages Publishing House, 1961), 38:230.
. Ibid., p. 97.
. See "Religion in the Form of Art," in Hegel, _Phenomenology of Spirit_ , A. V. Miller, tr. (Oxford: Oxford University Press, 1977), pp. 424–53.
. Hegel, _Encyclopédie des sciences philosophiques_ , vol. 1, _Science de la logique_ (1817), B. Bourgeois, tr. (Paris: Vrin, 1970), p. 203.
. Lenin, "Conspectus," _Collected Works_ 38:229.
. _Hegel's Science of Logic_ , W. H. Johnston and L. G. Struthers, trs. (London: Allen & Unwin, 1929; 1966), 1:95; emphasis added.
. Ibid., p. 96.
. Ibid., p. 97.
. Ibid., 2:478–79.
. Ibid., 1:104.
. Freud, "Negation," _Standard Edition_ , 19:239.
. "Foreclosure," write J. Laplanche and J.-B. Pontalis, is a "term introduced by Jacques Lacan denoting a specific mechanism held to lie at the origin of the psychotic phenomenon and to consist in a primordial _expulsion_ of a fundamental 'signifier' (e.g., the phallus as signifier of the castration complex) from the subject's symbolic universe." _The Language of Psychoanalysis_ , Daniel Lagache, introd., Donald Nicholson-Smith, tr. (London: Hogarth Press, 1973), p. 166; emphasis added.—Trans.
. See _Beyond the Pleasure Principle_ , _Standard Edition_ , 18:54–55.
. Melanie Klein, "The Importance of Symbol-Formation in the Development of the Ego," in _Contributions to Psychoanalysis_ (London: Hogarth Press, 1948), p. 237.
. Psychoanalysis places the mirror stage between the ages of 6 and 18 months, after which the so-called phallic stage begins. Observations have shown that around the latter period (age 2), language acquisition is inhibited despite the accelerated maturation of the brain and its lateralization. After this period of inhibition until the end of the Oedipus complex, and thus the decline of the phallic stage (between the ages of 4 and 5), the major elements of linguistic competence are acquired at an accelerated rate. After this, in the latency period, the curve of language acquisition becomes less steep, rising only slightly. See Eric H. Lenneberg, _Biological Foundations of Language_ (New York: Wiley, 1967), pp. 168, 376.
. A text is paragrammatic, writes Leon S. Roudiez, "in the sense that its organization of words (and their denotations), grammar, and syntax is challenged by the infinite possibilities provided by letters or phonemes combining to form networks of significations not accessible through conventional reading habits...," "Twelve Points from Tel Quel," _L'Esprit Créateur_ 14 (Winter 1974): 300. See Kristeva's essay, "Pour une sémiologie des paragrammes," in Σημειωτιχή, pp. 174–207.—Trans.
. See "Le Dispositif sémiotique du texte," _La Révolution du langage poétique_ , pp. 209–358.
. On Mallarmé, Hegel, and the "wife-concept," see _La Révolution du langage poétique_ , pp. 534–40.
. See René Spitz, _The First Year of Life: A Psychoanalytical Study of Normal and Deviant Development of Object Relations_ (New York: International Universities Press, 1965), p. 193.
. "In my opinion, in the normal state of fusion of the two drives, aggression plays a role which is comparable to that of a carrier wave. In this way the impetus of aggression makes it possible to direct both drives toward the surround. But if the aggressive and libidinal drives do not achieve fusion or, alternately, if a defusion has taken place, then aggression is returned against the own person; and in this case libido also can no longer be directed toward the outside" (ibid., p. 288).
. See Freud, "The Economic Problem of Masochism," _Standard Edition_ , 19:159–70.
. Alliteration, assonance, etc. See _La Révolution du langage poétique_ , pp. 210–19.
. Portmanteau words, see ibid.
. Freud on the "Wolf Man" in "Inhibitions, Symptoms and Anxiety," _Standard Edition_ , 20:104ff.
. See André Green, "La Projection."
. Isidore Ducasse's _Maldoror_ , first published in its entirety in 1869, was signed: comte de Lautréamont. The following year, under his own name, Ducasse published _Poems_.—Trans.
. Jean Bollack and Heinz Wismann, _Héraclite ou la séparation_ (Paris: Minuit, 1972), p. 14.
. The theory of drives, for example.
. Bollack and Wismann, _Héraclite_ , p. 30.
Bollack and Wismann interpret σοφóυ as "ingeniousness and savoir-faire." "Art" therefore refers to "a way of fashioning discourse and the disposition of its material" (p. 306). Compare the English translation by G. S. Kirk: "Of all whose accounts I have heard no one reaches the point of recognizing that wise is separated from all." _Heraclitus: The Cosmic Fragments_ (Cambridge: Cambridge University Press, 1954), p. 398.—Trans.
. Bollack and Wismann, _Héraclite_ , p. 226. See also p. 69.
. Although the French translators use the term _repoussement_ for both Freud's _Ausstossung_ and Hegel's _Repulsion_ , I maintain the standard English translation of these terms, "expulsion," and "Repulsion," respectively.—Trans.
. See _Hegel's Science of Logic_ 1:180–83. Hegel uses the terms _abstossen_ (to repulse), _repellieren_ (to repel) and _Repulsion_ (repulsion). In French, both verbs are translated as _repousser_ and the noun as _repoussement_.—Trans. See Hegel, _Science de la logique_ , Pierre-Jean Labarrière and Gwendoline Jarczyk, trs. (Paris: Aubier-Montaigne, 1972), vol. 1, Book 1 (1812), pp. 138 f.
. _Hegel's Science of Logic_ , 1:195; emphasis added.
. Ibid., 182; emphasis added.
. "Negation," _Standard Edition_ , 19:237.
. Artaud, "Description d'un état physique," _Oeuvres complètes_ (Paris: Gallimard, 1956), 1:75. In Part C of _La Révolution du langage poétique_ ("L'Etat et le mystère"), we stress the a-theological function of this shattering of the One (notably pp. 579 ff.). We recall the statement noted by Gisela Pankow in the "dream of the 'non-existent God"': "Schizophrenia is synonymous with atheism," in _L'Homme et sa psychose_ (Paris: Aubier-Montaigne, 1969), p. 220.
. "In the works of my later years ( _Beyond the Pleasure Principle_ [1920], _Group Psychology and the Analysis of the Ego_ [1921], and _The Ego and the Id_ [1923]), I have given free reign to the inclination, which I have kept down for so long, to speculation." "An Autobiographical Study," _Standard Edition_ , 20:57.
. _Beyond the Pleasure Principle_ , _Standard Edition_ , 18:35 and 36; translation modified.
. _Standard Edition_ , 19:235–39.
. Lacan, "Introduction au commentaire de Jean Hyppolite," in _Ecrits_ , p. 372.
. See "Rhythmes phoniques et sémantiques," _La Révolution du langage poétique_ , pp. 209–63.
_Desire in Language_
From One Identity to an Other
I shall attempt, within the ritual limits of a one-hour seminar, to posit (if not to demonstrate) that every language theory is predicated upon a conception of the subject that it explicitly posits, implies, or tries to deny. Far from being an "epistemological perversion," a definite subject is present as soon as there is consciousness of signification. Consequently, I shall need to outline an epistemological itinerary: taking three stages in the recent history of linguistic theory, I shall indicate the variable position these may have required of the speaking subject-support within their object language. This—on the whole, technical—foray into the epistemology of linguistic science will lead us to broach and, I hope, elucidate a problem whose ideological stakes are considerable but whose banality is often ignored. Meaning, identified either within the unity or the multiplicity of subject, structure, or theory, necessarily guarantees a certain transcendence, if not a theology; this is precisely why all human knowledge, whether it be that of an individual subject or of a meaning structure, retains religion as its blind boundaries, or at least, as an internal limit, and at best, can just barely "explain and validate religious sentiment" (as Lévi-Strauss observed, in connection with structuralism).
Second, I shall deal with a particular signifying practice, which, like the Russian Formalists, I call "poetic language," in order to demonstrate that this kind of language, through the particularity of its signifying operations, is an unsettling process—when not an outright destruction—of the identity of meaning and speaking subject, and consequently, of transcendence or, by derivation, of "religious sensibility." On that account, it accompanies crises within social structures and institutions—the moments of their mutation, evolution, revolution, or disarray. For if mutation within language and institutions finds its code through this signifying practice and its questionable subject in process that constitutes poetic language, then that practice and subject are walking a precarious tightrope. Poetic language, the only language that uses up transcendence and theology to sustain itself; poetic language, knowingly the enemy of religion, by its very economy borders on psychosis (as for its subject) and totalitarianism or fascism (as for the institutions it implies or evokes). I could have spoken of Vladimir Mayakovsky or Antonin Artaud; I shall speak of Louis-Ferdinand Céline.
Finally, I shall try to draw a few conclusions concerning the possibility of a _theory_ in the sense of an _analytical discourse_ on signifying systems, which would take into account these crises of meaning, subject, and structure. This for two reasons: first, such crises, far from being accidents, are inherent in the signifying function and, consequently, in sociality; second, situated at the forefront of twentieth-century politics, these phenomena (which I consider within poetic language, but which may assume other forms in the West as well as in other civilizations) could not remain outside the so-called human sciences without casting suspicion on their ethic. I shall therefore and in conclusion argue in favor of an analytical theory of signifying systems and practices that would search within the signifying phenomenon for the _crisis_ or the _unsettling process_ of meaning and subject rather than for the coherence or identity of either _one_ or a _multiplicity_ of structures.
Without referring back to the stoic sage, who guaranteed both the sign's triad and the inductive conditional clause, let us return to the congruence between conceptions of language and of subject where Ernest Renan left them. We are all aware of the scandal he caused among nineteenth-century minds when he changed a theological discourse (the Gospels) not into a _myth_ but into the _history_ of a man and a people. This conversion of _theological_ discourse into _historical_ discourse was possible thanks to a tool (for him, scientific) whose omnipotence he never ceased praising—philology. As used by Renan or Eugene Burnouf in Avestic Studies, for example, philology incorporates the _comparativism_ of philologists Franz Bopp or August Schleicher. Whatever the difference between comparativists seeking those _laws_ unique to _families_ of languages and philologists deciphering the _meaning_ of _one_ language, a common conception of language as an _organic identity_ unites them. Little does it matter that, as comparativists believed, this organic identity articulates itself thanks to _a law_ that crosses national and historical language borders making of them one family (cf. Jacob Grimm's phonetic laws); or that, as philologists believed, this organic identity articulates itself thanks to _one meaning_ —singular and unique—inscribed into a text still undeciphered or whose decipherability is debatable. In both cases this _organic identity_ of law or meaning implies that language is the possession of a _homo loquens_ within history. As Renan writes in _Averoés et l'Averroïsme_ , "for the philologist, a text has only one meaning" even if it is through "a kind of necessary misinterpretation" that "the philosophical and religious development of humanity" proceeds. Closer to the objectivity of the Hegelian "consciousness of self" for the comparativists, embodied in a singularity that, be it concrete, individual, or national, still owes something to Hegel for the philologists; language is always _one_ system, perhaps even one "structure," always _one meaning_ , and, therefore, it necessarily implies a subject (collective or individual) to bear witness to its history. If one has difficulty following Renan when he affirms that "rationalism is based on philology"—for it is obvious that the two are interdependent—it is no less obvious that philological reasoning is maintained through the identity of a historical subject: a subject in becoming. Why? Because, far from dissecting the internal logic of sign, predication (sentence grammar), or syllogism (logic), as did the universal grammar of Port Royal, the comparativist and philological reason that Renan exemplifies considers the signifying unit in itself (sign, sentence, syllogism) as an unanalyzable given. This signifying unit remains implicit within each description of law or text that philologists and comparativists undertake: linear, unidimensional descriptions—with no analysis of the sign's density, the logical problematic of meaning, etc.—but which, once technically completed, restore structural identity (for the comparativists) or meaning (for the philologists); in so doing they reveal the initial presupposition of the specifically linguistic undertaking as an ideology that posits either the people or an exceptional individual as appropriating this structure or this meaning. Because it is in itself unanalyzable (like the sign, sentence, and syllogism, it has no density, no economy), this subject-support of comparativist laws or of philological analysis does not lend itself to change, that is to say, to shifting from one law to another, from one structure to another, or from one meaning to another, except by postulating the movement of becoming, that is, of history. In the analysis of a signifying function (language or any "human," social phenomenon), what is censured at the level of semantic complexity reemerges in the form of a becoming: that obliteration of the density that constitutes sign, sentence, and syllogism (and consequently, the speaking subject), is compensated for by historical reasoning; the reduction of the complex signifying economy of the speaking subject (though obliquely perceived by Port Royal) produces without fail an opaque "I" that makes history. Thus, philological reasoning, while founding history, becomes a deadlock for language sciences, even though there actually is in Renan, beyond countless contradictions, an appreciation of universal grammar, a call for the constitution of a linguistics for an isolated language (in the manner of the ancient Indian grammarian Pānini), and even surprisingly modern proposals that advocate the study of crisis rather than normality, and in his Semitic studies the remarks on "that delirious vision transcribed in a barbaric and undecipherable style" as he calls the Christian gnostic texts, or on the texts of John the Apostle.
Linguistic reasoning, which, through Saussure, succeeded philological reasoning, works its revolution precisely by affecting the constitutive unity of a particular language; a language is not a system, it is a system of signs, and this vertically opens up the famous gap between signifier and signified, thus allowing linguistics to claim a logical, mathematical formalization on the one hand, but on the other, it definitely prevents reducing a language or text to one law or one meaning. Structural linguistics and the ensuing structural movement seem to explore this epistemological space by eliminating the speaking subject. But, on a closer look, we see that the subject they legitimately do without is nothing but the subject (individual or collective) of historico-philological discourse I just discussed, in which the Hegelian consciousness of self became stranded as it was concretized, embodied in philology and history; this subject, which linguistics and the corollary human sciences do without, is the "personal identity, miserable treasure." Nevertheless, a subject of enunciation takes shape within the gap opened up between signifier and signified that admits both structure and interplay within; and structural linguistics ignores such a subject. Moreover, because it left its place vacant, structural linguistics could not become a linguistics of speech or discourse; it lacked a grammar, for in order to move from sign to sentence the place of the subject had to be acknowledged and no longer kept vacant. Of course, generative grammar does reinstate it by rescuing universal grammar and the Cartesian subject from oblivion, using that subject to justify the generative, recursive functions of syntactic trees. But in fact, generative grammar is evidence of what structural linguistics omitted, rather than a new beginning; whether structural or generative, linguistics since Saussure adheres to the same presuppositions, implicit within the structuralist current, explicit in the generative tendency that can be found summed up in the philosophy of Husserl.
I refer modern linguistics and the modes of thought which it oversees within the so-called human sciences back to this founding father from another field, but not for conjunctural reasons, though they are not lacking. Indeed, Husserl was invited to and discussed by the Circle of Prague; indeed, Jakobson explicitly recognized in him a philosophical mentor for post-Saussurian linguists; indeed, several American epistemologists of generative grammar recognize in Husserlian phenomenology, rather than in Descartes, the foundations of the generative undertaking. But it is possible to detect in Husserl the basis of linguistic reasoning (structural or generative) to the extent that, after the reduction of the Hegelian consciousness of self into philological or historical identity, Husserl masterfully understood and posited that any signifying act, insofar as it remains capable of elucidation by knowledge, does not maintain itself by a "me, miserable treasure" but by the " _transcendental ego_."
If it is true that the division of the Saussurian sign (signifier/signified), unknown to Husserl, also introduces the heretofore unrecognized possibility of envisioning language as a free play, forever without closure, it is also true that this possibility was not developed by Saussure except in the very problematic _Anagrammes_. Moreover, this investigation has no linguistic followers, but rather, philosophical (Heideggerian discourse) and psychoanalytic (Lacan's signifier) contemporaries or successors, who today effectively enable us to appreciate and circumscribe the contribution of phenomenological linguistics from a Husserlian perspective. For post-Saussurian structural linguistics still encloses the signifier, even if nonmotivated, within patterns of a signification originally destined for faultless communication, either coinciding with the explicit signified or set off a short distance from it, but still fastened to the unalterable presence of meaning and, similarly, tributary to phenomenological reason.
It is therefore impossible to take up the congruence between conceptions of language and of subject where Renan left off without recalling how Husserl shifted ground by raising it above empiricism, psychologism, and incarnation theories typical of Renan. Let us examine for a moment the signifying act and the Husserlian transcendental ego, keeping in mind that linguistic reason (structural or generative) is to Husserl what philological reason was to Hegel: reduction perhaps, but also concrete realization, that is, failure made manifest.
As early as _Logical Investigations_ of 1901, Husserl situates the sign (of which one could have naively thought that it had no subject) within the act of expressing meaning, constituted by a judgment on something: "The articulate sound-complex, the written sign, etc., first becomes a spoken word or communicative bit of speech, when a speaker produces it with the intention of 'expressing himself about something' through its means."
Consequently, the thin sheath of the sign (signifier/signified) opens onto a complex architecture where intentional life-experience captures material (hylic) multiplicities, endowing them first with noetic meaning, then with noematic meaning, so that finally the result for the judging consciousness is the formation of an _object_ once and for all signified as real. The important point here is that this real _object_ , first signified by means of hylic data, through noesis and noemis, if it exists, can only be transcendental in the sense that it is elaborated in its identity by the judging consciousness of transcendental ego. The signified is transcendent as it is posited by means of certain concatenations within an experience that is always confined to judgment; for if the phenomenologist distinguishes between intuiting and endowing with meaning, then perception is already _cogitation_ and the _cogitation_ is transcendent to perception. So much so that if the world were annihilated, the signified _res_ would remain because they are transcendental: they "refer entirely to a consciousness" insofar as they are signified _res_. The _predicative_ (syntactic) operation constitutes this judging consciousness, positing at the same time the signified _Being_ (and therefore, the object of meaning and signification) and the _operating consciousness_ itself. The ego as support of the predicative act therefore does not operate as the ego-cogito, that is, as the ego of a logically conceived consciousness and "fragment of the world"; rather, the transcendental ego belongs to the constituting operating consciousness, which means that it takes shape within the predicative operation. This operation is _thetic_ because it simultaneously posits the thesis (position) of both Being _and_ ego. Thus, for every signified transcendental object, there is a transcendental ego, both of which are givens by virtue of thetic operation—predication of judgment.
"Transcendental egology" thus reformulates the question of the signifying act's subject: (1) the operating consciousness, through predication simultaneously constitutes Being, the (transcendent) signified real object, and the ego (in so far as it is transcendental); the problematic of the sign is also bound up in this question; (2) even if intentionality, and with it, the judging consciousness, is already a given in material data and perceptions, as it "resembles" them (which allows us to say that the transcendental ego is always already in a way given), _in fact_ , the ego constitutes itself only through the operating consciousness at the time of predication; the subject is merely the subject of predication, of judgment, of the sentence; (3) "belief" and "judgment" are closely interdependent though not identical: "The syntheses of belief ( _Glaubenssynthesen_ ) find their 'expression' in the forms of stated meaning."
Neither a historical individual nor a logically conceived consciousness, the subject is henceforth the operating thetic consciousness positing correlatively the transcendental Being and ego. Thus, Husserl makes clear that any linguistic act, insofar as it sets up a signified that can be communicated in a sentence (and there is no sign or signifying structure that is not already part of a sentence), is sustained by the transcendental ego.
It is perhaps not unimportant that the rigor of Judaism and the persecution it has been subjected to in our time underlie Husserl's extraordinarily firm elucidation of the transcendental ego, just as they are the foundation of the human sciences.
For the purposes of our discussion, we can draw two conclusions from this brief review:
1. It is impossible to treat problems of signification seriously, in linguistics or semiology, without including in these considerations _the subject thus formulated as operating consciousness_. This phenomenological conception of the speaking subject is made possible in modern linguistics by the introduction of logic into generative grammar and, in a much more lucid manner, through a linguistics (developing in France after Benveniste) that is attuned to the _subject of enunciation_ and includes in the latter's operating consciousness not only logical modalities, but also interlocutory relationships.
2. If it is true, consequently, that the question of signification and therefore of modern linguistics is dominated by Husserl, the attempts to criticize or "deconstruct" phenomenology bear concurrently on Husserl, meaning, the still transcendental subject of enunciation, and linguistic methodology. These criticisms circumscribe the metaphysics inherent in the sciences of signification and therefore in the human sciences—an important epistemological task in itself. But they reveal their own shortcomings not so much, as some believe, in that they prevent serious theoretical or scientific research, but in that such "deconstructions" refuse (through discrediting the signified and with it the transcendental ego) what constitutes one function of language though not the only one: to express meaning in a communicable sentence between speakers. This function harbors coherence (which is indeed transcendental) or, in other words, social identity. Let us first acknowledge, with Husserl, this thetic character of the signifying act, which establishes the transcendent object and the transcendental ego of communication (and consequently of sociability), before going beyond the Husserlian problematic to search for that which produces, shapes, and exceeds the operating consciousness (this will be our purpose when confronting poetic language). Without that acknowledgment, which is also that of the episteme underlying structuralism, any reflection on significance, by refusing its thetic character, will continually ignore its constraining, legislative, and socializing elements: under the impression that it is breaking down the metaphysics of the signified or the transcendental ego, such a reflection will become lodged in a negative theology that denies their limitations.
Finally, even when the researcher in the field, beginning with what is now a descriptive if not scientific perspective, thinks he has discovered givens that may escape the _unity_ of the transcendental ego (because each identity would be as if flaked into a multiplicity of qualities or appurtenances), the discourse of knowledge that delivers this multiplied identity to us remains a prisoner of phenomenological reason for which the multiplicities, inasmuch as they signify, are givens of consciousness, predicates within the same eidetic unity: the unity of an object signified by and for a transcendental ego. In an interpretive undertaking for which there is no domain heterogeneous to meaning, all material diversities, as multiple attributes, revert to a real (transcendental) object. Even apparently psychoanalytic interpretations (relationship to parents, etc.), from the moment they are posited by the structuring learning as particularities of the transcendental real object, are false multiplicities; deprived of what is heterogeneous to meaning, these multiplicities can only produce a plural identity—but an identity all the same, since it is eidetic, transcendental. Husserl therefore stands on the threshold not only of modern linguistics concerned with a subject of enunciation, but of any science of man as signified phenomenon, whose objecthood, even if multiple, is to be restored.
To the extent that poetic language operates with and communicates meaning, it also shares particularities of the signifying operations elucidated by Husserl (correlation between signified object and the transcendental ego, operating consciousness, which constitutes itself by predication—by syntax—as thetic: thesis of Being, thesis of the object, thesis of the ego). Meaning and signification, however, do not exhaust the poetic function. Therefore, the thetic predicative operation and its correlatives (signified object and transcendental ego), though valid for the signifying economy of poetic language, are only one of its _limits_ : certainly constitutive, but not all-encompassing. While poetic language can indeed be studied through its meaning and signification (by revealing, depending on the method, either structures or process), such a study would, in the final analysis, amount to reducing it to the phenomenological perspective and, hence, failing to see what in the poetic function departs from the signified and the transcendental ego and makes of what is known as "literature" something other than knowledge: the very place where social code is destroyed and renewed, thus providing, as Artaud writes, "A release for the anguish of its time" by "animating, attracting, lowering onto its shoulders the wandering anger of a particular time for the discharge of its psychological evil-being."
Consequently, one should begin by positing that there is within poetic language (and therefore, although in a less pronounced manner, within any language) a _heterogeneousness_ to meaning and signification. This _heterogeneousness_ , detected genetically in the first echolalias of infants as rhythms and intonations anterior to the first phonemes, morphemes, lexemes, and sentences; this heterogeneousness, which is later reactivated as rhythms, intonations, glossalalias in psychotic discourse, serving as ultimate support of the speaking subject threatened by the collapse of the signifying function; this heterogeneousness to signification operates through, despite, and in excess of it and produces in poetic language "musical" but also nonsense effects that destroy not only accepted beliefs and significations, but, in radical experiments, syntax itself, that guarantee of thetic consciousness (of the signified object and ego)—for example, carnivalesque discourse, Artaud, a number of texts by Mallarmé, certain Dadaist and Surrealist experiments. The notion of _heterogeneity_ is indispensable, for though articulate, precise, organized, and complying with constraints and rules (especially, like the rule of _repetition_ , which articulates the units of a particular rhythm or intonation), this signifying disposition is not that of meaning or signification: no sign, no predication, no signified object and therefore no operating consciousness of a transcendental ego. We shall call this disposition _semiotic_ ( _le sémiotique_ ), meaning, according to the etymology of the Greek _sémeion_ (σημεϮον), a distinctive mark, trace, index, the premonitory sign, the proof, engraved mark, imprint—in short, a _distinctiveness_ admitting of an uncertain and indeterminate articulation because it does not yet refer (for young children) or no longer refers (in psychotic discourse) to a signified object for a thetic consciousness (this side of, or through, both object and consciousness). Plato's _Timaeus_ speaks of a _chora_ (χώρα), receptacle (ύποδοχεϮον), unnameable, improbable, hybrid, anterior to naming, to the One, to the father, and consequently, maternally connoted to such an extent that it merits "not even the rank of syllable." One can describe more precisely than did philosophical intuition the particularities of this signifying disposition that I have just named semiotic—a term which quite clearly designates that we are dealing with a disposition that is definitely heterogeneous to meaning but always in sight of it or in either a negative or surplus relationship to it. Research I have recently undertaken on child language acquisition in the prephonological, one could say prepredicative stages, or anterior to the "mirror stage," as well as another concomitant study on particularities of psychotic discourse aim notably at describing as precisely as possible—with the help of, for example, modern phono-acoustics—these semiotic operations (rhythm, intonation) and their dependence vis-à-vis the body's drives observable through muscular constractions and the libidinal or sublimated cathexis that accompany vocalizations. It goes without saying that, concerning a _signifying practice_ , that is, a socially communicable discourse like poetic language, this semiotic heterogeneity posited by theory is inseparable from what I shall call, to distinguish it from the latter, the _symbolic_ function of significance. The symbolic ( _le symbolique_ ), as opposed to the semiotic, is this inevitable attribute of meaning, sign, and the signified object for the consciousness of Husserl's transcendental ego. Language as social practice necessarily presupposes these two dispositions, though combined in different ways to constitute _types of discourse_ , types of signifying practices. Scientific discourse, for example, aspiring to the status of metalanguage, tends to reduce as much as possible the semiotic component. On the contrary, the signifying economy of poetic language is specific in that the semiotic is not only a constraint as is the symbolic, but it tends to gain the upper hand at the expense of the thetic and predicative constraints of the ego's judging consciousness. Thus in any poetic language, not only do the rhythmic constraints, for example, perform an organizing function that could go so far as to violate certain grammatical rules of a national language and often neglect the importance of an ideatory message, but in recent texts, these semiotic constraints (rhythm, phonic, vocalic timbres in Symbolist work, but also graphic disposition on the page) are accompanied by nonrecoverable syntactic elisions; it is impossible to reconstitute the particular elided syntactic category (object or verb), which makes the meaning of the utterance undecidable (for example, the nonrecoverable elisions in _Un Coup de Dés_ ). However elided, attacked, or corrupted the symbolic function might be in poetic language, due to the impact of semiotic processes, the symbolic function nonetheless maintains its presence. It is for this reason that it is a language. First, it persists as an internal limit of this bipolar economy, since a multiple and sometimes even incomprehensible signified is nevertheless communicated; second, it persists also because the semiotic processes themselves, far from being set adrift (as they would be in insane discourse), set up a new formal construct: a so-called new formal or ideological "writer's universe," the never-finished, undefined production of a new space of significance. Husserl's "thetic function" of the signifying act is thus reassumed, but in different form: though poetic language unsettled the position of the signified and the transcendental ego, it nonetheless posits a thesis, not of a particular being or meaning, but of a signifying apparatus; it posits its own process as an undecidable process between sense and nonsense, between _language_ and _rhythm_ (in the sense of linkage that the word "rhythm" had for Aeschylus's _Prometheus_ according to Heidegger's reading), between the symbolic and semiotic.
For a theory attuned to this kind of functioning, the language object itself appears quite differently than it would from a phenomenological perspective. Thus, a phoneme, as distinctive element of meaning, belongs to language as symbolic. But this same phoneme is involved in rhythmic, intonational repetitions; it thereby tends toward autonomy from meaning so as to maintain itself in a semiotic disposition near the instinctual drives' body; it is a sonorous distinctiveness, which therefore is no longer either a phoneme or a part of the symbolic system—one might say that its belonging to the set of the language is indefinite, between zero and one. Nevertheless, the set to which it thus belongs exists with this indefinition, with this fuzziness.
It is poetic language that awakens our attention to this undecidable character of any so-called natural language, a feature that univocal, rational, scientific discourse tends to hide—and this implies considerable consequences for its subject. The support of this signifying economy could not be the transcendental ego alone. If it is true that there would unavoidably be a speaking _subject_ since the signifying set exists, it is nonetheless evident that this subject, in order to tally with its heterogeneity, must be, let us say, a questionable _subject-in-process_. It is of course Freud's theory of the unconscious that allows the apprehension of such a subject; for through the surgery it practiced in the operating consciousness of the transcendental ego, Freudian and Lacanian psychoanalysis did allow, not for (as certain simplifications would have it) a few typologies or structures that might accommodate the same phenomenological reason, but rather for heterogeneity, which, known as the unconscious, shapes the signifying function. In light of these statements, I shall now make a few remarks on the questionable subject-in-process of poetic language.
1. The semiotic activity, which introduces wandering or fuzziness into language and, a fortiori, into poetic language is, from a synchronic point of view, a mark of the workings of drives (appropriation/rejection, orality/anality, love/hate, life/death) and, from a diachronic point of view, stems from the archaisms of the semiotic body. Before recognizing itself as identical in a mirror and, consequently, as signifying, this body is dependent vis-à-vis the mother. At the same time instinctual and maternal, semiotic processes prepare the future speaker for entrance into meaning and signification (the symbolic). But the symbolic (i.e., language as nomination, sign, and syntax) constitutes itself only by breaking with this anteriority, which is retrieved as "signifier," "primary processes," displacement and condensation, metaphor and metonomy, rhetorical figures—but which always remains subordinate—subjacent to the principal function of naming-predicating. Language as symbolic function constitutes itself at the cost of repressing instinctual drive and continuous relation to the mother. On the contrary, the unsettled and questionable subject of poetic language (for whom the word is never uniquely sign) maintains itself at the cost of reactivating this repressed instinctual, maternal element. If it is true that the prohibition of incest constitutes, at the same time, language as communicative code and women as exchange objects in order for a society to be established, _poetic language would be_ for its questionable subject-in-process the _equivalent of incest_ : it is within the economy of signification itself that the questionable subject-in-process appropriates to itself this archaic, instinctual, and maternal territory; thus it simultaneously prevents the word from becoming mere sign and the mother from becoming an object like any other—forbidden. This passage into and through the forbidden, which constitutes the sign and is correlative to the prohibition of incest, is often explicit as such (Sade "Unless he becomes his mother's lover from the day she has brought him into the world, let him not bother to write, for we shall not read him,"— _Idée sur les romans_ ; Artaud, identifying with his "daughters"; Joyce and his daughter at the end of _Finnegans Wake_ ; Céline, who takes as pseudonym his grandmother's first name; and innumerable identifications with women, or dancers, that waver between fetishization and homosexuality). I stress this point for three reasons:
( _a_ ) To emphasize that the dominance of semiotic constraint in poetic language cannot be solely interpreted, as formalist poetics would have it, as a preoccupation with the "sign," or with the "signifier" at the expense of the "message"; rather, it is more deeply indicative of the instinctual drives' activity relative to the first structurations (constitution of the body as self) and identifications (with the mother).
( _b_ ) To elucidate the intrinsic connection between literature and breaking up social concord: because it utters incest, poetic language is linked with "evil"; "literature and evil" (I refer to a title by Georges Bataille) should be understood, beyond the resonances of Christian ethics, as the social body's self-defense against the discourse of incest as destroyer and generator of any language and sociality. This applies all the more as "great literature," which has mobilized unconsciousnesses for centuries, has nothing to do with the hypostasis of incest (a petty game of fetishists at the end of an era, priesthood of a would-be enigma—the forbidden mother); on the contrary, this incestuous relation, exploding in language, embracing it from top to bottom in such a _singular_ fashion that it defies _generalizations_ , still has this common feature in all outstanding cases: it presents itself as demystified, even disappointed, deprived of its hallowed function as support of the law, in order to become the cause of a permanent trial of the speaking subject, a cause of that agility, of that analytic "competency" that legend attributes to Ulysses.
( _c_ ) It is of course possible, as Lévi-Strauss pointed out to Dr. André Green, to ignore the mother-child relationship within a given anthropological vision of society; now, given not only the thematization of this relationship, but especially the mutations in the very economy of discourse attributable to it, one must, in discussing poetic language, consider what this presymbolic and transsymbolic relationship to the mother introduces as aimless wandering within the identity of the speaker and the economy of its very discourse. Moreover, this relationship of the speaker to the mother is probably one of the most important factors producing interplay within the structure of meaning as well as a questioning process of subject and history.
2. And yet, this reinstatement of maternal territory into the very economy of language does not lead its questioned subject-in-process to repudiate its symbolic disposition. Formulator—logothete, as Roland Barthes would say—the subject of poetic language continually but never definitively assumes the thetic function of naming, establishing meaning and signification, which the paternal function represents within reproductive relation. Son permanently at war with father, not in order to take his place, nor even to endure it, erased from reality, as a symbolic, divine menace and salvation in the manner of Senatspräsident Schreber. But rather, to signify what is untenable in the symbolic, nominal, paternal function. If symbolic and social cohesion are maintained by virtue of a sacrifice (which makes of a _soma_ a sign toward an unnameable transcendence, so that only thus are signifying and social structures clinched even though they are ignorant of this sacrifice) and if the paternal function represents this sacrificial function, then it is not up to the poet to adjust to it. Fearing its rule but sufficiently aware of the legislation of language not to be able to turn away from this sacrificial-paternal function, he takes it by storm and from the flank. In _Maldoror_ , Lautréamont struggles against the Omnipotent. After the death of his son Anatole, Mallarmé writes a _Tombeau_ , thanks to which a book replaces not only the dead son, his own father, mother, and fiancée at the same time, but also hallowed humanism and the "instinct of heaven" itself. The most analytical of them all, the Marquis de Sade, gives up this battle with, or for, the symbolic legislation represented by the father, in order to attack the power represented by a woman, Madame de Montreuil, visible figurehead of a dynasty of matrons toward whom he usurps, through writing, the role of father and incestuous son; here, the transgression is carried out and the transsymbolic, transpaternal function of poetic language reaches its thematic end by staging a simultaneously impossible, sacrificial, and orgastic society—never one without the other.
Here we must clearly distinguish two positions: that of the rhetorician and that of the writer in the strongest sense of the word; that is, as Céline puts it, one who has "style." The rhetorician does not invent a language; fascinated by the symbolic function of paternal discourse, he _seduces_ it in the Latin sense of the verb—he "leads it astray," inflicts it with a few anomalies generally taken from writers of the past, thus miming a father who remembers having been a son and even a daughter of his father, but not to the point of leaving cover. This is indeed what is happening to the discourse of contemporary philosophers, in France particularly, when, hemmed in by the breakthroughs in social sciences on the one hand, and social upheavals on the other, the philosopher begins performing literary tricks, thus arrogating to himself a power over imaginations: a power which, though minor in appearance, is more fetching than that of the transcendental consciousness. The stylist's adventure is totally different; he no longer needs to seduce the father by rhetorical affectations. As winner of the battle, he may even drop the name of the father to take a pseudonym (Céline signs with his grandmother's first name), and thus, in the place of the father, assume a different discourse; neither imaginary discourse of the self, nor discourse of transcendental knowledge, but a permanent go-between from one to the other, a pulsation of sign and rhythm, of consciousness and instinctual drive. "I am the father of my imaginative creations," writes Mallarmé at the birth of Geneviève. "I am my father, my mother, my son, and me," Artaud claims. Stylists all, they sound a dissonance within the thetic, paternal function of language.
3. Psychosis and fetishism represent the two abysses that threaten the unstable subject of poetic language, as twentieth-century literature has only too clearly demonstrated. As to _psychosis_ , symbolic legality is wiped out in favor of arbitrariness of an instinctual drive without meaning and communication; panicking at the loss of all reference, the subject goes through fantasies of omnipotence or identification with a totalitarian leader. On the other hand, where _fetishism_ is concerned, constantly dodging the paternal, sacrificial function produces an objectification of the pure signifier, more and more emptied of meaning—an insipid formalism. Nevertheless, far from thus becoming an unpleasant or negligible accident within the firm progress of symbolic process (which, in the footsteps of science, would eventually find signified elements for all signifiers, as rationalists believe), these borderline experiences, which contemporary poetic language has undergone, perhaps more dramatically than before or elsewhere, show not only that the Saussurian cleavage (signifier/signified) is forever unbridgeable, but also that it is reinforced by another, even more radical one between an instinctual, semioticizing body, heterogeneous to signification, and this very signification based on prohibition (of incest), sign, and thetic signification establishing signified object and transcendental ego. Through the permanent contradiction between these two dispositions (semiotic/symbolic), of which the internal setting off of the sign (signifier/signified) is merely a witness, poetic language, in its most disruptive form (unreadable for meaning, dangerous for the subject), shows the constraints of a civilization dominated by transcendental rationality. Consequently, it is a means of overriding this constraint. And if in so doing it sometimes falls in with deeds brought about by the same rationality, as is, for example, the instinctual determination of fascism—demonstrated as such by Wilhelm Reich—poetic language is also there to forestall such translations into action.
This means that if poetic economy has always borne witness to crises and impossibilities of transcendental symbolics, in our time it is coupled with crises of social institutions (state, family, religion), and, more profoundly, a turning point in the relationship of man to meaning. Transcendental mastery over discourse is possible, but repressive; such a position is necessary, but only as a limit open to constant challenge; this relief with respect to repression—establishing meaning—is no longer possible under the incarnate appearance of a providential, historical, or even rationalist, humanist ego (in the manner of Renan), but through a _discordance_ in the symbolic function and consequently within the identity of the transcendental ego itself: this is what the literary experience of our century intimates to theoretical reason, thereby taking its place with other phenomena of symbolic and social unrest (youth, drugs, women).
Without entering into a technical analysis of the economy specific to poetic language (an analysis too subtle and specious, considering the purpose of this specific paper), I shall extract from Céline, first, several procedures and, second, several themes, which illustrate the position of the unsettled, questionable subject-in-process of poetic language. I shall not do this without firmly underlining that these themes are not only inseparable from "style," but that they are produced by it; in other words, it is not necessary "to know" them, one could have heard them by simply listening to Céline's staccato, rhythmic discourse, stuffed with jargon and obscenity.
Thus, going beyond semantic themes and their distributions, one ought to examine the functioning of poetic language and its questionable subject-in-process, beginning with constitutive linguistic operations: syntax and semantics. Two phenomena, among others, will become the focus of our attention in Céline's writing: _sentential rhythms_ and _obscene words_. These are of interest not only because they seem to constitute a particularity of his discourse, but also because, though they function differently, both of them involve constitutive operations of the judging consciousness (therefore of identity) by simultaneously perturbing its clarity and the designation of an object (objecthood). Moreover, if they constitute a network of constraints that is added to denotative signification, such a network has nothing to do with classic poeticness (rhythm, meter, conventional rhetorical figures) because it is drawn from the drives' register of a desiring body, both identifying with and rejecting a community (familial or folk). Therefore, even if the so-called poetic codes are not recognizable within poetic language, a constraint that I have termed semiotic functions in addition to the judging consciousness, provokes its lapses, or compensates for them; in so doing, it refers neither to a literary convention (like our poetic canons, contemporary with the major national epics and the constitution of nations themselves) nor even to the body _itself_ , but rather, to a signifying disposition, pre- or transsymbolic, which fashions any judging consciousness so that any ego recognizes its crisis within it. It is a jubilant recognition that, in "modern" literature, replaces petty aesthetic pleasure.
_Sentential rhythms_. Beginning with _Death on the Installment Plan_ , the sentence is condensed: not only does Céline avoid coordination and embeddings, but when different "object-phrases" are, for example, numerous and juxtaposed with a verb, they are separated by the characteristic "three dots." This procedure divides the sentence into its constitutive phrases; they thus tend to become independent of the central verb, to detach themselves from the sentence's own signification, and to acquire a meaning initially incomplete and consequently capable of taking on multiple connotations that no longer depend on the framework of the sentence, but on a free context (the entire book, but also, all the addenda of which the reader is capable). Here, there are no syntactic anomalies (as in the _Coup de Dés_ or the glossalalias of Artaud). The predicative thesis, constitutive of the judging consciousness, is maintained. By using three dots to space the phrases making up a sentence, thus giving them rhythm, he causes connotation to rush through a predication that has been striated in that manner; the denotated object of the utterance, the transcendental object, loses its clear contours. The elided object in the sentence relates to a hesitation (if not an erasure) of the _real object_ for the speaking subject. That literature is witness to this kind of deception involving the object (object of love or transcendental object), that the existence of the object is more than fleeting and indeed impossible: this is what Céline's rhythms and syntactic elisions have recently evidenced within the stern humor of an experiment and with all its implications for the subject. This is also true of Beckett, whose recent play, _Not I_ , spoken by a dying woman, sets forth in elided sentences and floating phrases the impossibility of God's existence for a speaking subject lacking any object of signification and/or love. Moreover, beyond and with connotation, with the blurred or erased object, there flows through meaning this "emotion" of which Céline speaks—the nonsemanticized instinctual drive that precedes and exceeds meaning.
The exclamation marks alternating with three dots even more categorically point to this surge of instinctual drive: a panting, a breathlessness, an acceleration of verbal utterance, concerned not so much with finally reaching a global summing up of the world's meaning, as, to the contrary, with revealing, within the interstices of predication, the rhythm of a drive that remains forever unsatisfied—in the vacancy of judging consciousness and sign—because it could not find an other (an addressee) so as to obtain meaning in this exchange. We must also listen to Céline, Artaud, or Joyce, and read their texts in order to understand that the aim of this practice, which reaches us as a language, is, through the signification of the nevertheless transmitted message, not only to impose a music, a rhythm—that is, a polyphony—but also to wipe out sense through nonsense and laughter. This is a difficult operation that obliges the reader not so much to combine significations as to shatter his own judging consciousness in order to grant passage through it to this rhythmic drive constituted by repression and, once filtered by language and its meaning, experienced as jouissance. Could the resistance against modern literature be evidence of an obsession with meaning, of an unfitness for such jouissance?
_Obscene words_. Semantically speaking, these pivotal words in the Célinian lexicon exercise a _desemanticization_ function analogous to the fragmentation of syntax by rhythm. Far from referring, as do all signs, to an object exterior to discourse and identifiable as such by consciousness, the obscene word is the minimal mark of a situation of desire where the identity of the signifying subject, if not destroyed, is exceeded by a conflict of instinctual drives linking one subject to another. There is nothing better than an obscene word for perceiving the limits of a phenomenological linguistics faced with the heterogeneous and complex architectonics of significance. The obscene word, lacking an objective referent, is also the contrary of an autonym—which involves the function of a word or utterance as sign; the obscene word mobilizes the signifying resources of the subject, permitting it to cross through the membrane of meaning where consciousness holds it, connecting it to gesturality, kinesthesia, the drives' body, the movement of rejection and appropriation of the other. Then, it is neither object, transcendental signified, nor signifier available to a neutralized consciousness: around the object denoted by the obscene word, and that object provides a scanty delineation, more than a simple context asserts itself—the drama of a questioning process heterogeneous to the meaning that precedes and exceeds it. Childrens' counting-out rhymes, or what one calls the "obscene folklore of children," utilize the same rhythmic and semantic resources; they maintain the subject close to these jubilatory dramas that run athwart the repression that a univocal, increasingly pure signifier vainly attempts to impose upon the subject. By reconstituting them, and this on the very level of language, literature achieves its cathartic effects.
Several themes in Céline bring to light the relationships of force, at first within the family triangle, and then in contemporary society, that produce, promote, and accompany the particularities of poetic language to which I have just referred.
In _Death on the Installment Plan_ , the most "familial" of Céline's writings, we find a paternal figure, Auguste: a man "of instruction," "a mind," sullen, a prohibitor, prone to scandal, full of obsessional habits like, for example, cleaning the flagstones in front of his shop. His anger explodes spectacularly once, when he shuts himself up in the basement and shoots his pistol for hours, not without explaining in the face of general disapproval, "I have my conscience on my side," just before falling ill. "My mother wrapped the weapon in several layers of newspaper and then in a cashmere shawl... 'Come, child... come!' she said when we were alone [... ] We threw the package in the drink."
Here is an imposing and menacing father, strongly emphasizing the enviable necessity of his position, but spoiling it by his derisive fury: undermined power whose weapon one could only take away in order to engulf it at the end of a journey between mother and son.
In an interview, Céline compares himself to a "society woman" who braves the nevertheless maintained family prohibition, and who has the right to her own desire, "a choice in a drawing room": "the whore's trade doesn't interest me"; before defining himself, at the end: "I am the son of a woman who restored old lace... [I am] one of those rare men who knows how to distinguish batiste from valencienne... I do not need to be taught. I know it."
This fragile delicacy, heritage of the mother, supports the language—or if you wish, the identity—of him who unseated what Céline calls the "heaviness" of men, of fathers, in order to flee it. The threads of instinctual drive, exceeding the law of the paternal word's own mastery, are nonetheless woven with scrupulous precision. One must therefore conceive of another disposition of the law, through signified and signifying identity and confronting the semiotic network: a disposition closer to the Greek _gnomon_ ("one that knows," "carpenter's square") than to the Latin _lex_ , which necessarily implies the act of logical and legal judgment. A device, then, a regulated discrimination, weaves the semiotic network of instinctual drives; if it thus fails to conform to signifying identity, it nevertheless constitutes another identity closer to repressed and gnomic archaisms, susceptible of a psychosis-inducing explosion, where we decipher the relationship of the speaker to a desiring and desired mother.
In another interview, this maternal reference to old lacework is explicitly thought of as an archeology of the word: "No! In the beginning was emotion. The Word came next to replace emotion as the trot replaces the gallop [... ] They pulled man out of emotive poetry in order to plunge him into dialectics, that is, into gibberish, right?" Anyway, what is _Rigodon_ if not a popular dance which obliges language to bow to the rhythm of its emotion.
A speech thus slatted by instinctual drive—Diderot would have said "musicated"—could not describe, narrate, or theatricalize "objects": by its composition and signification it also goes beyond the accepted categories of lyric, epic, dramatic, or tragic. The last writings of Céline, plugged in live to an era of war, death, and genocide, are what he calls in _North_ , "the vivisection of the wounded," "the circus," "the three hundred years before Christ."
While members of the Resistance sing in alexandrine verse, it is Céline's language that records not only the institutional but also the profoundly symbolic jolt involving meaning and the identity of transcendental reason; fascism inflicted this jolt on our universe and the human sciences have hardly begun to figure out its consequences. I am saying that this literary discourse enunciates through its formal decentering, more apparent in Artaud's glossalalias, but also through the rhythms and themes of violence in Céline, better than anything else, the faltering of transcendental consciousness: this does not mean that such a discourse is aware of such a faltering or interprets it. As proof, writing that pretends to agree with "circus" and "vivisection" will nonetheless find its idols, even if only provisional; though dissolved in laughter and dominant nonsense, they are nevertheless posited as idols in Hitlerian ideology. A reading of any one of Céline's anti-Semitic tracts is sufficient to show the crudely exhibited phantasms of an analysand struggling against a desired and frustrating, castrating, and sodomizing father; sufficient also to understand that it is not enough to allow what is repressed by the symbolic structure to emerge in a "musicated" language to avoid its traps. Rather, we must in addition dissolve its sexual determinations. Unless poetic work can be linked to analytical interpretation, the discourse that undermines the judging consciousness and releases its repressed instinctual drive as rhythm always turns out to be at fault from the viewpoint of an ethic that remains with the transcendental ego—whatever joys or negations might exist in Spinoza's or Hegel's.
Since at least Hölderlin, poetic language has deserted beauty and meaning to become a laboratory where, facing philosophy, knowledge, and the transcendental ego of all signification, the impossibility of a signified or signifying identity is being sustained. If we took this venture seriously—if we could hear the burst of black laughter it hurls at all attempts to master the human situation, to master language by language—we would be forced to reexamine "literary history," to rediscover beneath rhetoric and poetics its unchanging but always different polemic with the symbolic function. We could not avoid wondering about the possibility, or simultaneously, the legitimacy of a theoretical discourse on this practice of language whose stakes are precisely to render impossible the transcendental bounding that supports the discourse of knowledge.
Faced with this poetic language that defies knowledge, many of us are rather tempted to leave our shelter to deal with literature only by miming its meanderings, rather than by positing it as an object of knowledge. We let ourselves be taken in by this mimeticism: fictional, paraphilosophical, parascientific writings. It is probably necessary to be a woman (ultimate guarantee of sociality beyond the wreckage of the paternal symbolic function, as well as the inexhaustible generator of its renewal, of its expansion) not to renounce theoretical reason but to compel it to increase its power by giving it an object beyond its limits. Such a position, it seems to me, provides a possible basis for a theory of signification, which, confronted with poetic language, could not in any way account for it, but would rather use it as an indication of what is heterogeneous to meaning (to sign and predication): instinctual economies, always and at the same time open to biophysiological sociohistorical constraints.
This kind of heterogeneous economy and its questionable subject-inprocess thus calls for a linguistics other than the one descended from the phenomenological heavens—a linguistics capable, within its language object, of accounting for a nonetheless articulated _instinctual drive_ , across and through the constitutive and insurmountable frontier of _meaning_. This instinctual drive, however, located in the matrix of the sign, refers back to an instinctual body (to which psychoanalysis has turned its attention), which ciphers the language with rhythmic, intonational, and other arrangements, nonreducible to the position of the transcendental ego even though always within sight of its thesis.
The development of this theory of signification is in itself regulated by Husserlian precepts, because it inevitably makes an _object_ even of that which departs from meaning. But, even though abetting the law of signifying structure as well as of all sociality, this expanded theory of signification cannot give itself new objects except by positing itself as nonuniversal: that is, by presupposing that a questionable subject-in-process exists in an economy of discourse other than that of thetic consciousness. And this requires that subjects of the theory must be themselves subjects in infinite analysis; this is what Husserl could not imagine, what Céline could not know, but what a woman, among others, can finally admit, aware as she is of the inanity of Being.
When it avoids the risks that lie in wait for it, literary experience remains nevertheless something other than this analytical theory, which it never stops challenging. Against knowing thought, poetic language pursues an effect of _singular truth_ , and thus accomplishes, perhaps, for the modern community, this solitary practice that the materialists of antiquity unsuccessfully championed against the ascendance of theoretical reason.
NOTES
"D'une identité l'autre," the original title of Kristeva's essay reflects and makes use of the title of Céline's novel _D'un château l'autre_. Although this has been translated as _Castle to Castle_ , the more literal "From One Identity to an Other" has been chosen in order to keep the ambiguous feeling of the French as well as the word "other," an important one in philosophy since Hegel and also in Kristeva's work.—Trans.
. Claude Lévi-Strauss, _L'Homme nu_ (Paris: Plon, 1971), p. 615.
. Kristeva's French phrase is _mise en procès_ , which, like _le sujet en procès_ , refers to an important, recurring concept—that of a constantly changing subject whose identity is open to question.
. Ernest Renan, _Oeuvres complètes_ , (Paris: Calmann-Lévy, 1947–58) 3:322.
. Ernest Renan, _The Future of Science_ (Boston: Roberts Bros., 1891), p. 402.
. Lévi-Strauss, _L'Homme nu_ , p. 614.
. See Jean Starobinski, _Les Mots sous les mots_ (Paris: Gallimard, 1971).—Ed.
. Edmund Husserl, _Logical Investigations_ , J. N. Findlay, tr. (London: Routledge & Kegan Paul, 1970), pp. 276–77.
. Edmund Husserl, _Ideas: General Introduction to Pure Phenomenology_ , W. R. Boyce Gibson, tr. (London: Collier-Macmillan, 1962), pp. 93–94 and 101.
. Edmund Husserl, _Erste Philosophie_ , VIII, in _Husserliana_ (The Hague: Hrsg. von R. Boehm, 1956).
. Husserl, _Ideas_ , p. 313.
. Antonin Artaud, "L'Anarchie sociale de l'art," in _Oeuvres complètes_
(Paris: Gallimard, 1956), 8:287.
. See Kristeva, _La Révolution du language poétique_ (Paris: Seuil, 1974), pp. 274ff.—Ed.
. Louis-Ferdinand Céline, _Death on the Installment Plan_ , Ralph Manheim, tr. (New York: New Directions, 1966), p. 78.
_Time and Sense_
Is Sensation a Form of Language?
Freud's View of Perception and Consciousness: Questions of Identity and Difference
We know that the notion of sensation is not central in Freud's writings. Even so, he addresses the concept in his letters to Fliess (1887–1902), in his _Project for a Scientific Psychology_ (1895), in his _Interpretation of Dreams_ (1900), and finally in his much-discussed _Note upon the "Mystic Writing-Pad"_ (1925). Although Freud adapts his notion of sensation to suit his continually developing work, certain points remain consistent throughout these four texts.
First of all, perception is connected to the Perceptual-Conscious system, which lacks memory because it retains no trace of what has occurred.
Yet in the beginning were perceptions. What is a perception? "[It consists of] neurons in which perceptions originate, to which consciousness attaches, but which in themselves retain no trace of what has happened. For _consciousness and memory are mutually exclusive_."
This is followed by the "indication of perception," which is "the _first registration_ of the perceptions; _it is quite incapable of consciousness_ , and arranged according to associations by simultaneity."
_Unconsciousness_ "is the second registration, arranged according to other (perhaps causal) relations."
It is important to note here that perception "registers" "simultaneity" and the unconscious registers "causal relations."
Unconscious traces "would perhaps correspond to _conceptual memories_ ; equally inaccessible to consciousness."
The _preconscious_ is "the third transcription, attached to word-presentations and corresponding to our official ego.... This _secondary thought-consciousness_ is subsequent in time, and is probably linked to the hallucinatory activation of word-presentations, so that the neurons of consciousness would once again be perceptual neurons and in themselves without memory."
Freud adds: "I explain the peculiarities of the psychoneuroses by supposing that _the translation has not taken place_ in the case of some of the material."
These passages are still worthy of note, not because of the neurological notions they offer (notions that have been challenged by more recent advances in neurological research) but because they propose a _multilayered model_ (Perception, Unconsciousness, Consciousness). Each layer is defined by the presence (or absence) of language, memory, or both language and memory. According to Freud's early model, the three layers must be subjected to a sort of "translation" of the subject to function in a psychologically sound manner.
We must not misinterpret the term _perceptual-conscious_. Although Freud may seem to be positing an _identity_ between Perception and Consciousness, he also emphasizes their _difference_ by stressing that word-presentations in the preconscious and the "secondary thought-consciousness" he associates with the hallucinatory activation of word-presentations are _subsequent_.
What Freud calls the _Wahrnehmung_ (ω) system—"perception"—is set into motion by quantities minute enough for quantity to become quality. This third system of neurons (ω-neurons) consists of "neurons of perception." It functions alongside the exogenous ψ-neurons and the endogenous ψ-neurons. The ω-system transmits neither quantity nor quality to the ψ-system, for it can only excite ψ: "In the case of every external perception a qualitative excitation occurs in system ω, which in the first instance, however, has no significance for system ψ. It must be added that the system ω excitation leads to system ω discharge, and information of this... reaches system ψ. _The information of this discharge from system_ ω _is thus the indication of quality or of reality for system_ ψ."
In a second logical and chronological stage, during which judgment comes into play, "the perceptions, on account of their possible connection with the wished-for object, [arouse] interest, and their complexes are dissected into an unassimilable component (the thing) and one known to the ego from its own experience (attribute, activity)—what we call _understanding_." Note that the _wished-for_ (and unassimilable) object appears at the same time as _understanding_ , both of which are placed in sharp contrast to the preceding instance of sensation-perception founded on "information" and "indications."
The implications of this are clear: perception ( _Wahrnehmung_ ) "excites" understanding, which makes understanding a _secondary effect_. This process is contingent on _two sorts_ of contact with verbal expression. It is important to note that these are two distinct experiences—and their dissimilarity is what facilitates the passage from perception to expression.
On the one hand, painful objects make us cry out, and these cries endow the object with its character by making it an object of suffering that is capable of leaving us with a conscious memory, whereas perception that is not inscribed through a verbal expression (such as a simple scream) cannot be remembered. Freud associates the objects that make us cry out with pain with a second class of sonorous objects: complex, perceptual objects for which sound plays a pivotal role.
On the other hand, a supplementary process comes into play. "In virtue of the trend towards _imitation_ , which emerges during judging, it is possible to find the information of movement attaching to this soundimage." The series of movements can thus become conscious, and one can voluntarily emit sounds that are associated with particular perceptions. By observing these auditory signs of discharge, the subject discovers memories in himself that become conscious perceptions and can be invested by the ψ-system.
"Thus we have found that it is characteristic of the process of _cognitive_ thought that during it attention is from the first directed to the _indications_ of thought-discharge, to the indications of speech."
Here Freud takes a logical shortcut that is important to note: information of discharged thought _sets into motion_ the process of _cognitive thinking_ , yet it is not the same as cognitive thinking. Similarly, auditory _imitation_ or cries are not the same as _linguistic signs_ , as Freud would lead us to believe. Freud forgets, however, that he used the word _index_ to describe the perception and its expression. The link between a given sensation (of a pain or of a sound) and a given vocal utterance (expressing distress or imitation and object) places the subject in what Freud calls _thing-presentations_ , and not in _word-presentations_. It places them in what Melanie Klein and Hanna Segal call "symbolic equivalencies" (cries, imitation) and in a domain of _signifiance_ that is not one of verbal representation or the linguistic signifier. Instead, it is the register of the memory trace, of "representability," of the "container" or the "fetish"—a register that does not separate the thing represented from the representing self. It can grow into or merge with a sign-judgment, or it can remain at its own level without ever reaching that of the representation or of the signifier.
In reality, the _Unconscious_ is what enables Freud's model of the psychic apparatus to function as a cognitive apparatus. We see the unconscious at work in the metaphor of the mystic writing-pad.
The psychic apparatus contains two layers: the upper layer (the stimulus-screen) and the lower layer (the surface that receives the stimulus), which is known as the Perceptual-Conscious system. The piece of celluloid is compared to the Perceptual-Conscious system with its stimulus-screen, while the waxed paper on which the trace is engraved is compared to the Unconscious: the Unconscious is a protected receptacle of endogenous or exogenous perceptual excitations, and its traces can be registered such that they imitate motor activity and eventually turn into judgments. Such a model requires several conditions:
• an accumulation and a reactivation of preconscious verbal representations;
• a lessening of the quantity of perceptual excitation through the possible intervention of a psychopharmacological drug; and
• the intervention of a third factor operating within the space between the other two and serving as both a screen for the excitation and a liaison with the world of signs. This third factor would play a pre-Oedipal, paternal role and would be a source of support for primary identification. Freud does not address this third element (which is a precondition for signs and thought) until he addresses the neurological model of perception as he pursues later developments in his discovery of psychoanalysis.
Taken as a whole, Freudian theory offers us a concept of sensation-perception that is _separate_ from the strictly psychoanalytic view that identification and the Oedipal complex are essential for mental functioning.
What is more, after Freud isolates the _Wahrnehmung_ (ω) system from the φ-exogenous and ψ-endogenous systems, he identifies Perception and Consciousness by relying on a paradox or an impatient logic (that Lacan cultivated) seeking to identify prelanguage and language (cries and imitation = judgment). Freud's notion presents us with two possibilities: either we take into account logical impatience (or confusion?), which would imply the eradication of the internal hierarchy of the psychic apparatus described in the _Note upon the "Mystic Writing-Pad,"_ or we revive the "multilayered" function of the psychic apparatus by trying to return to the logical order of judgment that cloaks the anterior or inferior stages made up of _quasi-signs_. In such stages, we find what I call the "semiotic" and what Freud calls "cries," "imitations," and "perceptions-excitations," which can reach consciousness only if they are linked with language and with unconscious desires (even though they come from a different register).
If we accept the second hypothesis, we understand that the speaking subject's access to sensations requires an expanded and nuanced rhetoric. This rhetoric could name unnameable experiences without becoming reduced to a "pure signifier" but by relying on perceptive and sensory regression. Whether you are a therapist or a writer, if you seek to offer signs and style to this sensory cave, which is for the most part unnameable, you will encounter a true experience ( _Erlebnis_ and _Erfahrung_ ). After you identify yourself with what is perceived and who is perceiving, you become not a "decoder" but an "encoder," a "nomothet," as Plato says in the _Cratylus_ , a legislator, a creator of a language able to describe a singular experience.
Before returning to this _poiesis_ of sensory nomination, let us take a brief detour through the cognitivist approach to sensation-perception.
The Cognitivists' Appropriation of Sensation
Cognitivists are the only contemporary theoreticians who study the sequence of sensation, perception, and emotion. Most of them believe that sensations are either _complementary judgments_ (such as statements where the sensation of redness is the same as the clause "I sense redness" and where _red_ is an _object_ , a _logical complement_ ) or _adverbial judgments_ (such as "I feel as if it were red" when _red_ is being used as an adverb). Such judgments may or may not be accompanied by emotions that are themselves evaluating _judgments_. According to the cognitivists, whether _cognitive awareness_ is central to perception or simply a precondition for perception, it is intrinsic to the process of sensation.
Some researchers have challenged these claims, basing their criticisms on recorded observations of phylogenetic and ontogenetic phenomena. When animals perceive certain conditions in their environment and react with fear, for example, their fear stems not from an evaluative _judgment_ but from their initial _impulse_. Similarly, when children are affected by a color or a sound they have perceived, they show their reaction on their face _before_ they have acquired the tools of evaluative logic. In the field of psychology, R. B. Zajonc (in a 1980 article published in _American Psychologist_ ) has proposed that olfactory and gustatory stimuli (like aural stimuli for infants) prompt immediate emotional responses that do not necessarily entail judgment. We know that certain emotional and sensory states can be induced by various drugs and hormones (valium, for instance, alters the state of the subject's perceptions and emotions without regard for his evaluation of the information he takes in). We also know that in human beings as well as in animals, emotions can be stimulated without implicating the part of the brain used in judgment.
In many species, moreover, a direct line can be traced between the retina and the hypothalamus, and this connection enables the organism to generate an emotional reaction to respond to sensory input. Although we do not know for certain that this line exists in human beings, such a connection might explain why certain tests have revealed our "noncognitive preference" for tones and polygons that we perceive spontaneously even when they are so blurred that they can no longer be distinguished from one another.
For these reasons, several scholars have concluded that although sensations-emotions _can_ stem from rational evaluation, the ability to create propositions _is not_ a precondition for sensations-emotions.
In response to these findings, scholars such as S. G. Clarke have suggested that we consider both feeling and emotion ("emotion as feeling," as Clarke puts it) to be unities of information that are _not complex enough_ to adopt the form of a proposition or to be judgments (of threat, danger, misfortune, and so forth). Although varying degrees of "cognitive (evaluative) penetration" can have a bearing on sensation, the cognitive process itself is not necessarily a precondition for sensation.
In fact, some sensations are "cognitively impenetrable," such as _akrasia_ (the term used to describe the phenomenon by which sensations tend either to be delayed or to linger even after our affective judgment has changed). In other words, the rational control of sensations is not enough to change them. Even so, Clarke concludes that the constraints of normalization and signification affect perceptions and emotions before they can be controlled directly. We must remember, however, that these constraints are of another order. They are different from propositional processes such as "belief" or "evaluation" and should not be described in syntactic, semantic, or rhetorical terms.
Plato's Cave and the Sensory Cave
Let us turn briefly to the philosophical debate that asks whether a sensation is a thought. This debate has important ramifications for contemporary philosophical inquiry, but its origins date back to antiquity. The polemics of this debate inform two diametrically opposed conceptions of psychic life.
The trace (or perhaps the scar) of this debate dates back to the well-known episode in book seven of the _Republic_ , in which Plato describes a _cave_ at the rear of which dance shadows of chained prisoners and people carrying various objects. These "shadow" are "the _symbols of sensory experience_ ," which are by the same token intelligible realities. There are two kinds of shadows, one primary and the other secondary. Both are cast by the Fire placed behind the prisoners. Fire being a symbol for the Sun or for Good and Evil. The prisoners see nothing but shadows of the outside world, yet if they leave the cave, they will be blinded by the sun. Thus they must access an intermediate reality that is neither a sensory illusion nor an invisible secret but a mathematical construction of forms providing a path toward true knowledge. Ever since Plato posited this notion, we have found ourselves in an _aporia of sensation_. Sensation, which cannot be reduced to ideas even though it is intrinsically dependent on them, can never be equivalent to Intelligence (because Intelligence is, after all, paramount). Nevertheless, sensation can only exist if it makes itself intelligible. The cave of Plato's "shadows" considers emotion to be a rudimentary stage along the path to representation. Tricked as it is by illusions, sensation is inevitably false, for it is always contingent upon the Intelligible.
The difficulty of defining sensation prompts us to shift our discussion to a disorder that has attracted the attention of psychotherapists, psychiatrists, neurologists, and contemporary psychoanalysts: autism. It has recently been suggested that autistic symptoms are caused by an inability to acquire language despite the existence of a complex sensory life. I refer to this ailment because its specialists have offered a useful theoretical understanding of sensation and of the relationship between sensation and language.
The psychic and technical complexity of autism impels us to expand our philosophical paradigm and to posit what must be called _another cave_ , one even more profound and inexpressible than Plato's. Indeed, since this cave is deprived of the intelligible and evaluative Fire-Sun, it is _a sensory cave without any symbols_ (without "shadows," as Plato would say). In this sensory cave, a lived Experience ( _Erlebnis_ ) that has not yet been given form by cognitive experience ( _Erfahrung_ ), and that often resists it, can nevertheless encounter thing-presentations that endow its inner workings with form and signification. Sensory experience, which is incited by thing-presentations, plays an important role in the psychic experience of the speaking subject. _Word-presentations_ do not necessarily convey this experience. Although everyone has a sensory cave, some of us experience it as a psychic catastrophe (those afflicted with autism being the most extreme example), some attain jouissance from it (hysterics complain that what is felt and what is said are in constant conflict), and some attempt to turn it into a normative discourse generating the coalescence between sensations and linguistic signs that we call literary style.
By hypothesizing that the sensory cavern is ubiquitous and for the most part irreducible to language, am I subscribing to the notion that autism is _universal_ , endogenous, occurring before what Melanie Klein calls the "depressive position," and at the fringe of psychic life? Not exactly. If we borrow the terms of what Freud calls an "economic" conception (as opposed to a model that relies on chronological or developmental stages), we may consider the sensory cavern to be an essential part of the psychic apparatus, which is heterogeneous. The psychic apparatus is a stratified _significance_ that excessively rigid linguistic and cognitive discourses sometimes conceal or restrict to the dimension of language modeled on the Idea.
The autistic child withdraws into his sensory cave, which he effectively fossilizes and renders inexpressible. F. Tustin has broadened our notion of autism by showing that the neurotic personality contains an element of autism. The neurotic personality is a manifestation of a defeated autism, which may in itself prove to be a sign of its universal and fundamental permanence in the psyche.
Let us examine the problem in another way. Even if sensation-perception, which is an essential and archaic part of psychic experience, cannot be absorbed by—or reduced to—language, the sensory domain's resistance to being reduced to the cognitive domain is not necessarily experienced through the painful form of autism, for it can also be expressed through perversion, art, or psychoanalysis.
Interpretation between Word-Signs and Word-Fetishes: A Source of Beauty
The dynamics of writing in Proust's work are not all that different from the dynamics of listening that characterize psychoanalytic interpretation. Writing is memory regained from signs to flesh and from flesh to signs through an intense identification (and a dramatic separation from) an other who is loved, desired, hated, and rendered indifferent. Interpretation shares these same qualities, at least during those rare moments of grace when countertransference responds to the logic of transference and reshapes the psychic map of the analyst and the analysand. Yet what exactly occurs when we provide a name for our patients' often inexpressible sensations?
The process of naming sensations requires an _identification_ with the analysand that mobilizes my entire psychic apparatus. I identify with his biography, his presumed and even transgenerational memory, and his presumed sensation. The resulting display of countertransference is an imaginary operation, yet it is also a real one. It is a sort of _transubstantiation_ (Joyce, another extremely sensitive author, used this Catholic liturgical term to describe the subjective economy of writing as the advent of new signs and a new body). Whether this identification is of the primary, secondary, projective, or any other variety, we should consider it in its paroxysmal intensity, a need that has not been sufficiently addressed by classic psychoanalytic theory (which is too preoccupied with neurosis) but which depressive, psychotic, and especially autistic symptoms have made apparent.
To reach this paroxysmal intensity of identification, which is absolutely essential for certain treatments, a psychoanalyst would do well to consider what Merleau-Ponty says about the way our own bodies affect the outside world as well as the bodies of other people. Merleau-Ponty sees this relationship as _reversible_ and _chiasmic_ , for touch is always tangible, sight is always visible, substance is body, and the same is other. He wants to challenge the metaphysical dichotomies of philosophy and psychology. Our instincts (which are borne out by science) tell us that an _X_ perceives a _Y_ from whom it is presumed to be always already separated. In the spirit of his radicalization of Husserl, however, Merleau-Ponty challenges the very existence of this separation. I believe it would be legitimate to transpose this _interpenetration_ and _reversibility_ —which operate between who or what perceives and what is perceived and between who or what feels and what is felt—not only onto psychoanalysis but onto the reading of literary texts. Merleau-Ponty uses the loaded term _flesh_ to refer to this process:
It is said that the colors, the tactile reliefs given to the other, are for me an absolute mystery, forever inaccessible. This is not completely true; for me to have not an idea, an image, nor a representation, but as it were the imminent experience of them, it suffices that I look at a landscape, that I speak of it with someone. Then, through the concordant operation of his body and my own, what I see passes into him, this individual green of the meadow under my eyes invades his vision without quitting my own, I recognize in my green his green, as the customs officer recognizes suddenly in a traveler the man whose description he had been given. There is here no problem of the _alter ego_ because it is not I who sees, not he who sees, because an anonymous visibility inhabits both of us, a vision in general, in virtue of that primordial property that belongs to the flesh, being here and now, of radiating everywhere and forever, being an individual, of being an individual, of being also a dimension and a universal.
"Once again, the flesh we are speaking of is not matter. It is the coiling over of the visible upon the seeing body, of the tangible upon the touching body... this pact between them and me according to which I lend them my body, in order that they inscribe upon it and give me their resemblance, this fold, this central cavity of the visible which is my vision.... We must not think the flesh starting from substances, from body and spirit—for then it would be the union of contradictories—but we must think it, as we said, as an element, as the concrete emblem of a general manner of being."
"We touch here the most difficult point, that is, the bond between the flesh and the idea, between the visible and the interior armature which it manifests and which it conceals. No one has gone further than Proust in fixing the relations between the visible and the invisible."
Merleau-Ponty's remarks, which are problematic and mystically significant, are useful for a reader of Proust: they free up the representability of what is felt, which is torn between world and thought. This two-sided sensoriality is a "way of being" that characterizes the experience of writing in the sense of a "time regained." The philosopher tries to make this sensation surge forth into the world, whereas the psychoanalyst experiences it through transference and countertransference. A _state of flesh_ appears to underlie the therapeutic act, but it can become a true _therapeutic act_ only if language is led to the reversible and chiasmic sensation that supports it.
Becoming flesh is one element in the analytic process that must be restored, although not at the expense of all the others. Indeed, granting a sign to what is sensed presupposes a distance, and perhaps a split—a distance that explains the professional perversion displayed by psychoanalysts. The act of naming consists of abandoning the pleasure and pain of carnal identification, of carnal texture, in order to dissociate thing-presentations and word-presentations. Interpretation arranges word-presentations in an arbitrary autonomy stemming from their status as signs that are distinct from perception-sensations. Interpretation goes on to constitute these word-presentations as fetishes, to prompt the patient to play with these words-signs-fetishes, and then gives them back to him, like a mother to her child, in the initial form of play-objects. We transform the patient's flesh, which we have shared with our own, into word-presentations. By placing, repeating, and punctuating these word-presentations, however, we give words the consistency of reified symbols and link them to thing-presentations in the same way that the writer repeats, loves, and organizes his text. Thus the analyst uses sensorial _fixations_ as a starting point for sensory _play_ and then for _words_ , but words that are _word-pleasures_ , _word-things_ , and _word-fetishes_. We could describe the analyst's naming process as the art of making the flesh of signs into transitional objects, an art that is more essential for the treatment of narcissistic disorders than for any other treatment. The reification, or fetishization, of the word plays an important role in the passage from sensation to the idea and to the relaxation of the logical order in which the idea is expected to expand itself into a thought.
Those who have treated autistic children have observed that such children experience a sort of aesthetic pleasure the first time they use words, which are charged with sensations more than ideas. Beauty, then, is needed for psychic growth and the expansion of thought, but it can exist only if the analyst who carries out this process is capable of creating this same beauty and jouissance for himself and the other. For this reason, studying Proustian pleasures permits one not only to share my questionable interest in the excitation that supported the art of the famous writer known as "little Marcel" until his death but to consider the sadomasochistic element of aesthetic performance hidden in _psychoanalytic interpretation_ in general, especially when analysts are faced with psychosis or autism. We do experience unconscious sadomasochistic pleasure when we identify with a chained-up soul, with the palpitating and mute sensation that does not know me as an _other_ even though it includes me in its touch, its saliva, its breathing, and its blank, fleeing, or persecuting gaze. There is also a violent pleasure stemming from the word that I neither hear nor see but produce. Through a hole in my consciousness, which is temporarily opened as flesh, I see a shackled psyche. I cultivate it with my fusion, yet I know that it needs for me to take some distance from it. In that way, this other flesh, responding to my named pleasure, can perhaps become someone else, a _subject_.
Freud became aware of the commonplace, innocuous way that the protective violence of naming evolves by observing the famous _Fort-Da_ game his grandson played with a wooden reel and a piece of string. He emphasized the game's violent side in his analysis of _Die Verneinung_ , the well-known and ambiguous "negativity" that rejects eroticism while positing a primary symbolism that operates through a dialectic relying on an incessant rejection of the drives. Parents witness negativity when their children have temper tantrums while acquiring language and/or an Oedipal positioning. Violence is intrinsic to the process of naming the senses, and it is especially useful for ushering along the inner workings of treatment. Indeed, how could we create a discontinuity, how could we break up a _sign_ for an _object_ that can only be constituted by becoming an object of desire, if we do not disturb the patient's continuous and analogical sensoriality or if we fail to impose on him our own desire for a name, for an object? Desire, which takes things away from us, can only hurt and wound us. What is more essential, then, are kindness and tact, especially in treatments that go beyond aesthetic pleasure and depend on the analyst's distance as well as on his own latent sadomasochism.
Psychoanalysts have a long way to go toward perfecting their own art of rhetoric. Reading Proust makes us think of figures who can shape the flesh of our intense identifications with people who neither talk nor think about their sensations. Even so, we should not allow ourselves to be overcome with phenomenological beatitude. Instead, we should strive to remain attentive to the sadomasochistic logic of both sensory _identification_ and _nomination_. And why? So that we might use these sensory processes not as the threshold of our jouissance but as a way to care for the other when the specificity of the human being as a speaking being seems to be lost. Indeed, if we look beyond the autistic symptom of the sensory cave, we shall discover a borderline region in our psyche that is restored by aesthetic experience and that nourishes psychoanalytic interpretation without being reduced to it.
NOTES
. Letter to Fliess, December 6, 1896, in Freud, _Standard Edition_ , 1:234.
. Ibid., pp. 234–35. Italics mine.
. On several occasions, Freud compared the system, or consciousness, to perception.—Trans.
. _Project for a Scientific Psychology_ , in _Standard Edition_ , 1:325.
. Ibid., p. 366.
. Ibid., p. 367.
. Ibid. Italics mine.
. See the metapsychology papers in appendix C of _Standard Edition_ , 14:109–215.
. See Segal, "Notes on Symbol Formation," _International Journal of Psychoanalysis_ 37 (1957).
. See Kristeva, _Revolution in Poetic Language_ , Margaret Waller, tr. (New York: Columbia University Press, 1984).
. See "Imaginary Experience," in ch. 4. "The Experience of Time Embodied," in Kristeva, _Time and Sense_ , Ross Guberman, tr. (New York: Columbia University Press, 1996).
. W. Sellars subscribes to the adverbial theory, whereas Searle believes that the contents of a perception is a clause. E. Wright claims that sensory processes have a passive component and that they are not of an epistemic or intentional character, contrary to what A. Ben-Zeev has proposed. At the same time, while C. S. Peirce notes that the sensation process, like other phenomena of the mind, relies on an "inference," he prefigured later thinkers who believe that sensation possesses a particularly "irreducible vagueness." See also R. C. Solomon, _The Passions_ (New York: Doubleday, 1976) and W. Lyons, _Emotions_ (Cambridge: Cambridge University Press, 1980) as well as works by Lazarus and Greenspan.
. R. B. Zajonc, "Feeling and Thinking Preferences Need No Inferences," _American Psychology_ 35 (1980).
. Clarke, "Emotions: Rationality Without Cognitivism," _Dialogue: The Canadian Philosophical Review_ 25, no. 4 (1986): 663–74.
. See, for instance, Tustin, _Autistic Barriers in Neurotic Patients_ (London: Carnac Books, 1986).
. See Kristeva, _Time and Sense_ , p. 376, n. 87.—Trans.
. Tustin, _Autistic Barriers_.
. See my "Joyce: The Gracehoper or Orpheus' Return." in _New Maladies of the Soul_ , Ross Guberman, tr. (New York: Columbia University Press, 1995), pp. 172–88.
. M. Merleau-Ponty, _The Visible and the Invisible_ , Alphonso Lingis, tr. (Evanston, Ill.: Northwestern University Press, 1968), p. 142.
. Ibid., pp. 146–47.
. Ibid., p. 149.
. See D. Meltzer and M. H. Williams, _The Apprehension of Beauty: The Role of Aesthetic Conflict in Development, Art, and Violence_ (N.p.: Clunie Press, Roland Harris, 1988).
. Freud, _Beyond the Pleasure Principle_ , in _Standard Edition_ , 1813–64.
. Freud, "Negation," in _Standard Edition_ , 19:233–39.
Freudian Time
According to Freud, the unconscious does not know negatives or contrasts, and it also does not know time. Unbeknownst to us, this provides for a scene consisting of our desires as well as our drives, of which the most "instinctual" is the death drive. Freud offers an unexpected gift to those who subscribe to his beliefs. By relieving us of our anxieties about enduring, the Freudian unconscious throws us into the pure time of what is unbearable, which proves to be a logical space. It is up to us to discover the key to this logic, to write a novel about the interpretation of dreams.
The neurotic seeks to repress the outside-time of the unconscious. The psychotic attempts to tear a hole in it; a specialist of ellipses, he always loses at least one of his logical links, which nonetheless reappears in an act of madness. The pervert plays with outside-time, reifying it in the part-objects that he ritualistically uses to respond to his sexual needs. Yet he becomes exhausted by these needs, primarily because he cannot access their meaning—which is reflected in the poor quality of his discourse and his fantasies. To put it briefly, each psychic structure has its own way of placing the unconscious "outside-time" within temporal duration. What is more, each time the subject fails to absorb this transposition, the different versions of the failure are embodied in the various structures.
When Freud claims, not incorrectly, that he succeeds where the paranoid person fails, he most likely means that psychoanalytic interpretation takes into account the subject's inability to represent his _other_. He hopes, however, that by delineating various levels of representation (primary and secondary processes, fantasies as well as drives, and the entire conceptual framework of psychoanalytic theory), he will be able to inscribe _the outside-time_ of the subject and his other's fight to the finish inside _the time of transference_. Although Freud makes this laudable revelation, which leads him to compare the psychoanalytic experience with the psychotic's experience (psychoanalysis obviously overcomes psychosis even though psychosis is present in interpretative countertransference), he says nothing about what perversion has taught him. He also says little about neurosis (the negative of perversion), especially obsessional neurosis.
The fantasy makes the unconscious into a narrative. As a result, when the outside-time of the unconscious is named and recounted, it acquires meaning, a goal, and a value. The fantasy, along with the dream narrative, becomes a narration torn between the atemporality of the unconscious and the forward-moving flight of the story. The fantasy is the novel that Freud asked his patients to bring him. As opposed to the neurotic, who is afraid and ashamed of his fantasies, and the pervert, who acts them out meticulously without being disturbed by what they mean, the analysand is invited to do with words what the pervert does with things (and with people who are reduced to mere things). He is invited to _stage_ his unconscious. When the pervert's staging occurs in the form of a metaphor placed in the world of an unmistakably temporal discourse, a _story_ is set into motion. Still, the reason that the fantasy is not just any narrative but a novel in miniature is that it is structured like a "catastrophe" in the mathematical sense of the word. The fantasy is at the boundary between the outside-time space of the unconscious (which threatens to consume it by depriving it of words in order to direct it toward drives and acts) and the haste of the narration (which is the hero's seduction of his victim and the narrator's seduction of his addressee).
Because of this "catastrophic" dynamic, the narrative-fantasy is always augmented with interpolations, retracings, signs of childishness or divisions of jouissances that do not necessarily find a style of their own but place the analysand in an amphibious temporality. This two-sided temporality is a source of _jouissance_ when the fantasy enacts unconscious desire and of _logic_ when the action projected onto the axis of past-present-future takes into account interaction with other people. This sort of double temporality is favorable to analysis, and the speaking being's division works within it. Hence it is entirely prepared to project itself in the sublimations of the imaginary-novel. We read novels with our fantasies, yet novelists transpose their own fantasies onto the supple structure of a genre that seeks only to submit to the fantasies of a given reader. Art begins when a transposition comes into play that consists of rhetorical figures, syntactic structures, and superimposed characters. Still, _sublimation_ takes place when the fantasy is put into words. If the analysand is not ever so slightly like a narrator, he is silenced. He occasionally causes gripping or commonplace signs to emanate from the nameless border of his unconscious, but he never tells _his_ story. The analyst yields to this scenario by becoming bored or by playfully offering his own fantasies to the analysand. In other words, if transference and countertransference fail to make the analysand a narrator, the analysis breaks down and dies. Did Freud wish for his patients to become budding narrators? Did he transform the subjects of civilization and its discontents into novelists lacking an aesthetic religion?
NOTES
. See André Green, "Temps et mémoire," _Nouvelle Revue de Psychanalyse_ 41 (1990): 176–260, and _Revue française de psychanalyse_ 43 (1979), devoted to memory and recollection in psychoanalytic practice.
. See Julia Kristeva, "Psychoanalysis and the Polis," _Critical Inquiry_ 9, no. 1 (September 1982): 77–92.
. See Thom, _Modèles mathématiques de la morphogenèse. Recueil de textes sur théorie des catastrophes et applications_ (Paris: uge, 1974).
PART 3
_Psychoanalysis of Love: A Counterdepressant_
Tales of Love
_Histoires d'amour_ was originally published in Paris by Denoël in 1983. It was translated as _Tales of Love_ by Leon Roudiez for Columbia University Press in 1987. In _Tales of Love_ Kristeva develops a theory and history of love wherein it operates between need and desire. She substantiates her theory with analyses of love from Plato's eros, through biblical love, Christian Agape, Molière's _Dom Juan_ , Shakespeare's _Romeo and Juliet_ , Jeanne Guyon the mystic's eroticism, Baudelaire's passion, Stendhal's politics of passion, to Bataille's erotics.
She begins _Tales of Love_ with an analysis of Freud's theory of eros. An earlier version of the first chapter "Freud and Love," a portion of which is reprinted here, was published as "L'abjet d'amour" in _Tel Quel_ in spring, 1982. In "Freud and Love," against Lacan, Kristeva suggests that the paternal function does not just include castration threats and law. The father is not merely the stern father of the law. Rather, she proposes a loving father, what she calls "the imaginary father." The imaginary father provides the loving support that enables the child to abject, or separate from, its mother and enter the social (see part 4 on abjection in _Powers of Horror_ ). Following Freud's notion of the father of preindividual history, Kristeva describes the imaginary father as a mother-father conglomerate. In her scenario, the imaginary father performs the function of love. It is the child's feeling that it is loved that allows the child to separate from the safe haven of the maternal body. Threats and laws alone do not provide this necessary support.
On the traditional psychoanalytic model of both Freud and Lacan, the child enters the social or language out of fear of castration. The child experiences its separation from the maternal body as a tragic loss and consoles itself with words. Paternal threats make words the only, if inadequate, alternative to psychosis. Kristeva insists, however, that separation begins prior to the mirror stage or Oedipal situation and that this separation is not only painful but also pleasurable. She insists that the child enters the social and language not only because of paternal threats but also owing to paternal love. She describes the infant's identification with paternal love or the imaginary father as a metaphor of love. In "Throes of Love," she associates the operations of metaphor with the psychoanalytic notion of transference. She suggests that the infant's identification with the imaginary father is actually a type of transference to the place of love. The infant's separation from the maternal body is dependent upon a transference to this supportive love. This transference operation prefigures and sets up the possibility of metaphor and language. And, conversely, as Kristeva says, love is always spoken. She proposes her notion of love and metaphorical transference identification as an alternative to Lacan's notion of desire and metonymical displacement.
Kristeva criticizes the Lacanian scenario because it cannot adequately explain the child's move to signification. If the motivation for the move to signification is threats and the pain of separation, then why would anyone make this move? Why not remain in the safe haven of the maternal body and refuse the social and language with its threats? Why aren't more people psychotic? Kristeva suggests that just as the separations inherent in the material of the body are pleasurable, even if they are also sometimes painful, so too the separations that make signification possible are pleasurable. The logic of signification is already operating in the body, and therefore the transition to language is not as dramatic and mysterious as traditional psychoanalytic theory makes it out to be.
In the last chapter of _Tales of Love_ , "Extraterrestrials Suffering for Want of Love," Kristeva prefigures the issues that she takes up again in _New Maladies of the Soul_ (1993). Here she diagnoses contemporary analysands' sufferings as the result of the abolition of psychic space. With the break up of Christianity, Kristeva describes a culture caught at a stage in the process of subjectivity between identification and differentiation. No cultural image of a mother is available to offset the horrifying abject mother, and as a result women are denigrated and motherhood disdained. And on the other hand, no cultural image of a loving father who might ease the move away from the abject maternal body is present. Contemporary analysands are extraterrestrials suffering from the want of love from either mother or father. They are caught in the not-yet of subjectivity that leaves them empty and unsatisfied.
Black Sun
_Soleil Noir: Dépression et Mélancolie_ was originally published in Paris by Gallimard Press in 1987. It was translated by Leon Roudiez as _Black Sun: Depression and Melancholy_ for Columbia University Press in 1989. This selection is the first chapter of that translation. In _Black Sun_ , Kristeva diagnoses the common structure of depression and melancholy as a structure of mourning for the lost maternal "object" (which she calls a "Thing" since it is not fully an object), and the failure of language to compensate for the loss. It is the inability of signifiers to compensate for the loss of the maternal Thing that leads to a sense of emptiness and meaninglessness; words are meaningless to express the pain of depression and melancholy. Here Kristeva develops and uses her notion of the abject mother from _Powers of Horror_ (1980) and her notion of the imaginary father from _Tales of Love_ (1983).
Kristeva suggests that whereas antidepressants treat only the symptoms of depression, psychoanalysis can treat the causes and provide a needed counterdepressant. Psychoanalysis can provide the loving support needed to leave the maternal body and to accept the consolation of words and an interpretative framework. The interpretative framework of psychoanalysis provides the psychic meaning necessary to fill the emptiness of psychic space. Psychoanalytic interpretation can help the analysand construct an eroticized maternal body that is as desirable as it is abject (the case of female heterosexuality is more complex; see part 5) and a loving imaginary father who supports the movement from the maternal body into language. This love allows affects to connect with words, drives to connect to language, and re-creates meaning.
New Maladies of the Soul
_New Maladies of the Soul_ was translated by Ross Guberman for Columbia University Press in 1994 from the original published as _Les Nouvelles Maladies de l'âme_ in Paris by Fayard in 1993. In _New Maladies of the Soul_ , Kristeva powerfully diagnoses the loss of meaning and emptiness of contemporary life. In the first chapter, "The Soul and the Image," she asks whether "in the wake of psychiatric medicines, aerobics, and media zapping, does the soul still exist?" (p. 3). Continuing to challenge the distinction between nature and culture, she situates the contemporary soul between biology and sociology. The soul or psyche mediates between the body, others, and our representations of ourselves. Without an adequate language to express the body or our relation to others, we turn to drugs (antidepressants, tranquilizers, narcotics) and/or media images to fill the void. But drugs and television only postpone the feelings of emptiness and lack of satisfaction. Kristeva maintains that we need new ways to reattach language to affect.
In the second chapter, "In Times Like These, Who Needs Psychoanalysts?" she discusses the relation between drives, affects, and language. She situates Freudian drives between biology and culture and delineates the special role of psychoanalysis in addressing this psychic life that operates between the two realms. She articulates "new maladies of the soul" and psychic emptiness, which she maintains are unique in each analysand. She maps a new terrain for psychoanalysis and suggests new routes to meaning. She extends her thesis from _Black Sun_ that perhaps psychoanalysis can provide a counterdepressant that treats the cause of our depression and not just an antidepressant that treats the symptoms.
Tales of Love
Freud and Love: Treatment and Its Discontents
In his journey through the land of love Freud reaches Narcissus only after having traveled over the dissociated space of hysteria. The latter leads him to establish the "psychic space" that he will explode, first through Narcissus and finally through the death drive, into the impossible spaces of "lovehate," that is, infinite transference.
Narcissism—a Screen for Emptiness
The hypothesis of Narcissus is crucial to this Freudian course. Before calling itself "death," the libido undergoes a first threat to its omnipotence—one that makes the existence of an _other_ for the _self_ appear problematic. Freud seems to suggest that it is not Eros but narcissistic primacy that sparks and perhaps dominates psychic life; he thus sets up self-deception as the basis of one's relationship to reality. Such a perpetuation of illusion, however, finds itself rehabilitated, neutralized, normalized, at the bosom of my loving reality. For Freud, as we know, binds the state of loving to narcissism; the choice of the love object, be it "narcissistic" or "anaclitic," proves satisfying in any case if and only if that object relates to the subject's narcissism in one of two ways: either through personal narcissistic reward (where Narcissus is the subject), or narcissistic delegation (Narcissus is the other; for Freud, the woman). A narcissistic destiny would in some way underlie all our object choices, but this is a destiny that society, on the one hand, and the moral rigor of Freud, on the other, tend to thrust aside in favor of a "true" object choice. And yet on closer examination even the Ego Ideal, which insures the transference of our claims and desires toward a true object laden with all the pomp of good and beauty as defined by parental and social codes, is a revival of narcissism, its abeyance, its conciliation, its consolation. Freud's text, one might say, imposes an omnipresence of narcissism which permeates the other realms to the point that one finds it again in the _object_ (where it is reflected)—if we assume that an object can be designated, in other words symbolized and loved as such, outside of chaos, rejection, and destruction.
Moreover, the ubiquity of the notion of "narcissism" goes hand in hand with its being far from originary. It is a supplement, and Freud points out that it is the product of a "new action," which we should understand as that of a third realm supplementing the autoeroticism of the mother-child dyad: "The autoerotic drives, however, are there from the very first; so there must be something added to autoeroticism—a new psychical action—in order to bring about narcissism."
That observation endows narcissism with an intrasymbolic status, dependent upon a third party but within a disposition that chronologically and logically precedes that of the Oedipal Ego. It prompts one to conceive of an archaic disposition of the paternal function, preceding the Name, the Symbolic, but also preceding the "mirror stage," whose logical potentiality it would harbor—a disposition that one might call that of the Imaginary Father (a point I shall return to). Lacan takes up Freud's observation only briefly to emphasize the need to stipulate the "mirror stage." He specifies that "The human ego establishes itself on the basis of the imaginary relation."
The questions prompted by the Freudian notion of narcissism would then be the following: What is this narcissistic "identity"? How stable are its borders, its relation to the other? Does the "mirror stage" emerge out of nowhere? What are the conditions of its emergence? A whole _complex structuration_ can seemingly be conceived through what is after all a psychiatric term, "narcissism"; it is an already ternary structuration with a different articulation from the Ego-object-Other triangle that is put together in the shadow of the Oedipus complex.
Furthermore, the ubiquity of Freudian narcissism has caused some to suggest that narcissism is no more than a Freudian fantasy—and that nothing else exists but originary mimetism. Such a thesis is probably a paranoid version of what would lie at the basis of social and symbolic relations: it finds its mechanism in the "scapegoat" theory, where Melanie Klein's "projective relationship" unwittingly serves as a cornerstone for society and the sacred. Nevertheless, it is still a fact that narcissism, caught in a play of rebounds within the Freudian text, in a first stage seems to be a mimetic play that would establish psychic identities (Ego/object), until that play finally, and in the dizziness of rebounds, reveals itself as a screen over _emptiness_. That notion has been developed in psychoanalysis by André Green, whose reflections I draw upon for this particular point.
Consequently I shall emphasize this notion of emptiness, which is at the root of the human psyche. It does not reveal itself merely because "psychotic states" have broken forth on psychoanalytic couches or have shown through the low points of many neuroses. One is compelled to note that the aims of psychoanalysis have changed. After psychiatric _semeiology_ , Freud had discovered the _symptom_ as metaphor, that is, condensation, of fantasy. Now, and thanks to Lacan, one analyzes the symptom as a screen through which one detects the workings of _significance_ (the process of formation and de-formation of meaning and the subject); these coextend with the speaking being as such and, consequently, they cut through not only "normal" and "pathological" states but also psychoanalytic symptomatology. In this respect, the arbitrariness of the Saussurian sign has placed us in front of a _bar_ , or even an _emptiness_ , that constitutes the referent/signified/signifier relationship, of which Lacan has merely taken up the "visible" aspect in the _gaping hole_ of the mirror stage. Saussure's _arbitrariness_ of the sign and Lacan's _gaping hole_ both readily point to what might be understood from the standpoint of representation—given the uneasy uncertainty, ubiquity, and inconsistency of "narcissism" in Freud...
Thus, against the background of linguistic theory and language learning, the _emptiness_ that is intrinsic to the beginnings of the symbolic function appears as the first separation between what is not yet an _Ego_ and what is not yet an _object_. Might narcissism be a means for protecting that emptiness? But against what?—a protection of emptiness (of "arbitrariness," of the "gaping hole") through the display of a decidedly narcissistic parry, so that emptiness can be maintained, lest chaos prevail and borders dissolve. Narcissism protects emptiness, causes it to exist, and thus, as lining of that emptiness, insures an elementary separation. Without that solidarity between emptiness and narcissism, chaos would sweep away any possibility of distinction, trace, and symbolization, which would in turn confuse the limits of the body, words, the real, and the symbolic. The child, with all due respect to Lacan, not only _needs_ the real and the symbolic—it signifies itself as child, in other words as the subject that it is, and neither as a psychotic nor as an adult, precisely in that zone where _emptiness and narcissism_ , the one upholding the other, constitute the zero degree of imagination.
We have, however, reached the threshold of another question: What is it that preserves this emptiness—a cause for complaint but also an absolute necessity of the so-called narcissistic structures, a fleeting effect of enigmatic as well as creative non-sense—at the heart of childhood narcissism? This is where we need to return to the notion of "identification."
Einfühlung—an Identification with a Metaphorical "Object"
Amatory identification, _Einfühlung_ (the assimilation of other people's feelings), appears to be madness when seen in the light of Freud's caustic lucidity: the ferment of collective hysteria in which crowds abdicate their own judgment, a hypnosis that causes us to lose perception of reality since we hand it over to the _Ego ideal_. The object in hypnosis devours or absorbs the ego, the voice of consciousness becomes blurred, "in loving blindness one becomes a criminal without remorse"— _the object has taken the place of what was the ego ideal_.
The identification that provides the support for the hypnotic state known as loving madness rests upon a strange object. This archaic identification, which is characteristic of the oral phase of the libido's organization where what I incorporate is what I become, where _having_ amounts to _being_ , is not, truly speaking, objectal. I identify, not with an object, but with what offers itself to me as a _model_. That enigmatic apprehending of a _pattern_ to be imitated, one that is not yet an object to be libidinally cathected, leads us to wonder whether the loving state is a state without object and reminds us of an archaic _reduplication_ (rather than imitation), "possible before any choice of object." This enigmatic, nonobjectal identification might be related to the internal, recursive, redundant logic of discourse, which is accessible within the "afterspeech"; it is an identification that sets up love, the sign, and repetition at the heart of the psyche. For the sake of an object to come, later or never?... It does not matter, since I am already in the throes of _Einfühlung_.... Later I shall examine the conditions that allow the advent of that uni-fication, that identification, on the basis of autoeroticism and within the pre-Oedipal triad...
For the moment let me simply note that becoming _as_ the One is imagined by Freud as an oral assimilation; indeed he links the possibility of archaic identification to the "oral phase of the libido's organization," and he then cites Robertson Smith who, in his _Kinship and Marriage_ (1885), describes the communal bonds set up through participation in a common meal as resting upon "the acknowledgment of the possession of a common substance." Ferenczi and his followers would later develop the notions of _introjection_ and _incorporation_.
Nevertheless, one might well wonder about the notional slippage that takes place between the "incorporation" of an object, or even its "introjection," and an _Identifizierung_ that is not on the level of "having" but locates itself at once on that of "being like." On what ground, within what material does _having_ switch over to _being?_ While seeking an answer to that question it appeared to me that incorporating and introjecting orality's function is the essential substratum of what constitutes man's being, namely, _language_. When the object that I incorporate is the speech of the other—precisely a nonobject, a pattern, a model—I bind myself to him in a primary fusion, communion, unification. An identification. For me to have been capable of such a process, my libido had to be restrained; my thirst to devour had to be deferred and displaced to a level one may well call "psychic," provided one adds that if there is repression it is quite primal, and that it lets one hold on to the joys of chewing, swallowing, nourishing oneself... with words. In being able to receive the other's words, to assimilate, repeat, and reproduce them, I become like him: One. A subject of enunciation. Through psychic osmosis/identification. Through love.
Freud has described the One with whom I fulfill the identification (this "most primitive aspect of affective binding to an object") as a Father. Although he did not elaborate what he meant by "primary identification," he made it clear that this father is a "father in individual prehistory."
An "Immediate" and Objectless Identification
A strange father if there ever was one, since for Freud, because there is no awareness of sexual difference during that period (more accurately: within that disposition), such a "father" is the same as "both parents." Identification with that "father in prehistory," that Imaginary Father, is called "immediate," "direct," and Freud emphasizes again, "previous to any concentration on any object whatsoever": Only with secondary identification does the "libidinal covetousness that is part of the first sexual period and is directed toward the father and the mother appear, in normal instances, to be resolved in a secondary, mediate identification that would come and reinforce the primary, direct identification."
The whole symbolic matrix sheltering emptiness is thus set in place in an elaboration that precedes the Oedipus complex. Indeed, if the primary identification constitutive of the Ego Ideal does not involve libidinal cathexis, drives are dissociated from the psychic realm. Simultaneously, what one can only call the _absolute_ existence of _transference_ is established, a transference laden with libido. It is a transference rather than an "identification," a transference in the sense of _Verschiebung_ , a displacement, as in the _Interpretation of Dreams_ , but also and at the same time in the sense of _Übertragung_ , as it will show up during treatment and be directed toward the person of the analyst. Finally, such a transference is called _immediate (unmittelbare)_ and works in the direction of a complex, composite, and, in short, imaginary realm ("the father in individual prehistory").
We know that, _empirically_ , the first affections, the first imitations, and the first vocalizations as well are directed toward the mother; it is thus hardly necessary to stress that one's pointing to the Father as the magnet for primary love, primary identification, is tenable only if one conceives of _identification_ as being always already within the symbolic orbit, under the sway of language. Such appears to be, implicitly, the Freudian position, which owes its acuity as much to Freud's sensitivity concerning the dominant place of language in the constitution of _being_ as it does to the resurgence of monotheism in his thought. But is there really a difference?
On the contrary, there is Melanie Klein's well-known position, which must be called inexpressible and closer to ordinary common sense. The bold theoretician of the death drive is also a theoretician of gratitude seen as "an important offshoot of the capacity for love," "necessary for the acknowledgment of what is 'good' in others and in oneself." Where does this capacity come from? It is innate and leads to the experience of a "good breast" that sates the child's hunger; it is also apt to convey the feeling of a plenitude that would be the prototype of all subsequent experience of jouissance and happiness. Melanie Klein's gratitude is nevertheless and at the same time directed toward the maternal object in its entirety: "I am not saying that for the child the breast simply represents a physical object."
Yet, along with such innateness, Melanie Klein maintains that the capacity for love is not an activity of the organism (as it would seem to be for Freud, according to Klein) but rather that it is a "primordial activity of the ego." Gratitude would stem from a necessity to confront the forces of death and consist in a "progressive integration born out of the life drive." Without being identical with the "good object," the idealized object reinforces it. "Idealization stems from persecution anguish and constitutes a defense against it," "the ideal breast is a complement of the devouring breast." It is as if those who are unable to set up a "good breast" for themselves naturally manage it by idealizing; now idealization often collapses and reveals its cause, which is the persecution against which it had established itself. But how does one succeed in idealizing? By what miracle is that possible in a Kleinian life where two live without a third party other than a persecuting or fascinating penis?
The problem is not to find an answer to the enigma: Who might be the object of primary identification, daddy or mummy? Such an attempt would only open up the impossible quest for the absolute origin of the capacity for love as a psychic and symbolic capacity. The question is rather: Of what value would the question be when it actually bears on states existing on the border between the psychic and the somatic, idealization and eroticism, within analytic treatment itself? To emphasize transference, the love that founds the analytic process, implies that one hears the discourse that is performed there starting with that limit of advent-and-loss of the subject—which is _Einfühlung_.
Provided one does not forget that in analysis any discourse complies with the dynamics of identification, with and beyond resistances, this entails at least two consequences for interpretation. First, the analyst situates himself on a ridge where, on the one hand, the "maternal" position—gratifying needs, "holding" (Winnicott)—and on the other the "paternal" position—the differentiation, distance, and prohibition that produces both meaning and absurdity—are intermingled and severed, infinitely and without end. Analytic tactfulness—ultimate refuge of an interpretation's relevance—is perhaps no more than the capacity to make use of identification and along with it the imaginal resources of the analyst, in order to accompany the patient as far as the limits and accidents of his object relations. This ability is even more important precisely when the patient has difficulty in establishing, or fails to establish, an object relation.
Metonymic Object and Metaphorical Object
Second, the _Einfühlung_ gives the language signifier exchanged during treatment a heterogeneous, drive-affected dimension. It loads it with something preverbal, or even nonrepresentable that needs to be deciphered while taking into account the more precise articulations of discourse (style, grammar, phonetics), and at the same time while cutting through language, in the direction of the unspeakable, indicated by fantasies and "insight" narratives as well as by symptomatic misspeech (slips of the tongue, illogical statements, etc.).
Such analytic attentiveness to _Einfühlung_ through transference speech imposes another status of the psychic _object_ on the analyst's attention, one that is different from the metonymic object of desire called "object 'a"' by Lacan.
We are dealing less with a partial object than with a nonobject. As magnet of identification constitutive of identity and condition for that unification, which insures the advent of a subject for an object, the "object" of _Einfühlung_ is a _metaphorical_ object. Carrying autoerotic motility to the unifying image of One Agency that already sets me up _as_ an opposite One is the zero degree of subjectivity. _Metaphor_ should be understood as movement toward the discernible, a journey toward the visible. _Anaphora_ , _gesture_ , _indication_ , would probably be more adequate terms for this sundered unity, in the process of being set up, which I am at present conjuring. Aristotle refers to an _epiphora_ : a generic term for the metaphorical motility previous to any objectivation of _a_ figurative meaning.... The object of love is a metaphor for the subject—its constitutive metaphor, its "unary feature," which, by having it choose an adored part of the loved one, already locates it within the symbolic code of which this feature is a part. Nevertheless, situating this unifying guideline within an objectality in the process of being established rather than in the absolute of the reference to the Phallus as such has several advantages. It makes the transference relation dynamic, involves to the utmost the interpretative intervention of the analyst, and calls attention to countertransference as identification, this time of the analyst with the patient, along with the entire aura of imaginary formations germane to the analyst that all this entails. Without those conditions, doesn't analysis run the risk of becoming set within the tyranny of idealization, precisely? Of the Phallus or of the superego? A word to wise Lacanians should be enough!
Metonymic object of desire. Metaphorical object of love. The former controls the phantasmatic _narrative_. The latter outlines the _crystallization_ of fantasy and rules the poeticalness of the discourse of love...
During treatment, the analyst interprets his desire and his love, and that sets him apart from the perverse position of the seducer and from that of a virtuous Werther as well. But he must display himself sometimes as desiring, other times as loving. By ensuring a loving Other to the patient, the analyst (temporarily) allows the Ego in the throes of drive to take shelter in the following fantasy: the analyst is not a dead Father but a living Father; this nondesiring but loving father reconciles the ideal Ego with the Ego Ideal and elaborates the psychic space where, possibly and subsequently, an analysis can take place.
Henceforth, the analyst must in addition let it be known—since he is an analyst and neither a good shepherd nor a father-confessor—that he is a fleeting, failing, or even abject subject of desire. He will then trigger within the psychic space his love has allowed to exist the tragicomedy of life drives and death drives, knowing in his nescience that if Eros opposes Thanatos they are not evenly matched in their struggle. For Thanatos is pure while Eros has, since the beginning, been permeated with Thanatos, the most deep-seated drive being the death drive (Freud).
To say that the analyst handles _love_ as a discourse allowing idealizing distance as a condition for the very existence of psychic space is not to assimilate the analytic attitude to that of a _primary love_ object, the archaic prototype of the _genital_ love, as Balint's work suggests with seductive munificence. Concentrating, _for a while_ , one's thoughts on love within analysis actually leads one to scrutinize, in the treatment, not a narcissistic merger with the maternal container but the emergence of a _metaphorical object_ —in other words, the very splitting that establishes the psyche and, let us call this splitting "primal repression," bends the drive toward the symbolic of an other. Only the metaphorical dynamics (in the sense of a _heterogeneous_ displacement shattering the isotopy of organic needs) justifies that this other be a Great Other. The analyst thus temporarily stands in the place of the Great Other inasmuch as he is a metaphorical object of idealizing identification. It is in knowing this and doing it that he creates the space of transference. If he represses it, on the other hand, the analyst becomes the _Führer_ that Freud already loathed in _Group Psychology_ —a loathing that showed to what extent analytic practice was not exempt from such hysterical phenomena.
Hate Identification, Love Identification
"It is easy," Freud believed,
to translate into a phrase the difference between identification with the father and affection for the father as sexual object ( _der Unterschied einer solchen Vateridentifizierung von einer Vaterobjektwahl_ ): in the first instance the father is what one would want to _be_ ( _das, was man sein möchte_ ), in the second he is what one would want to _have (das, was man haben möchte_ ). In the first instance, it is the subject of the _ego_ that is concerned, in the second it is its object. That is why identification is possible before any choice of object is made ( _Es ist also der Unterschied, ob die Bindung am Subjekt oder am Objekt des Ichs angreift. Die erstere ist darum bereits vor jeder sexuellen Objektwahl möglich_ ).
It will be noted that the first identification Freud points to in this study is a morbid identification with the mother (for instance, the little girl takes up her mother's cough on account of "a hostile desire to take the mother's place— _ein feindseliges Ersetzenwollen der Mutter_ —in which case the symptom expresses the erotic fondness for the father"). Though conceived within the system of the Oedipus complex ( _Entweder ist die Identifizierung dieselbe aus dem Ödipuskomplex_ ), such an identification nevertheless reminds one of Melanie Klein's projective identification, which is sustained by the "hostile" as well as guilt-ridden desire to take the place of a persecuting mother out of envy. Object identification because of hatred for one part of the object and fear of persecution. The second type of identification is revealed by a symptom that apes that of the loved one (the daughter, Dora, catches the father's cough). Here, "identification has taken the place of erotic propensity, and the latter has been changed, through regression, into identification" ( _die Identifizierung sei an Stelle der Objektwahl getreten, die Objektwahl sei zur Identifizierung regrediert_ ). Without hostility in this case, identification coincides with the object of desire through "a kind of insertion of the object into the ego" ( _gleichsam durch Introjektion des Objekts ins Ich_ ). Love, contrary to the morbid identification mentioned above, would be the merging of the identifying ideal with the object of desire. In the third place, libidinal desires can be completely lacking when identification with another person is made on the basis of some common traits.
One is thus led to conceive of at least two identifications, a primal one, resulting from a sentimental ( _Gefühlsbindung an ein Objekt_ ), archaic, and ambivalent affection for the maternal object, more frequently produced by the impetus of guilt-producing hostility, and the other, which underlies the introjection into the ego of an object itself already libidinal ( _libidinöse Objektbindung_ ), providing the dynamics of the pure loving relationship. The first is closer to depersonalization, phobia, and psychosis; the second is closer to hysterical lovehate, taking to itself the phallic ideal that it pursues.
Between Hysteria and Inability to Love
The lover is a narcissist with an _object_. Love involves a sizable _aufhebung_ of narcissism; consequently, the relationship established by Freud between love and narcissism must not cause us to forget their essential difference. Is it not true that the narcissist, as such, is precisely someone incapable of love?
The lover, in fact, reconciles narcissism and hysteria. As far as he is concerned, there is an idealizable other who returns his own ideal image (that is the narcissistic moment), but he is nevertheless an other. It is essential for the lover to maintain the existence of that ideal other and to be able to imagine himself similar, merging with him, and even indistinguishable from him. In amorous hysteria the ideal Other is a reality, not a metaphor. The archeology of such an identifying possibility with an _other_ is provided by the huge place taken up within narcissistic structure by the vortex of _primary identification_ with what Freud called a "father of individual prehistory." Endowed with the sexual attributes of both parents, and by that very token a totalizing, phallic figure, it provides satisfactions that are already psychic and not simply immediate, existential requests; that archaic vortex of idealization is immediately an _other_ who gives rise to a powerful, already psychic transference of the previous semiotic body in the process of becoming a narcissistic Ego. Its very existence and my being able to take myself for it—that is what already moves us away from the primal maternal satisfaction and situates us within the hysterical universe of loving idealization.
It is obvious from the behavior of young children that the first love object of boys and girls is the mother. Then where does one fit in this "father of individual prehistory"? Freud's bent perhaps causes him to speak as a Jew, but he speaks primarily as a psychoanalyst. He in fact dissociates idealization (and with it the amatory relationship) from the bodily exchange between mother and child, and he introduces the Third Party as a condition of psychic life, to the extent that it is a loving life. If love stems from narcissistic idealization, it has nothing to do with the protective wrapping over skin and sphincters that maternal care provides for the baby. Worse yet, if that protection continues, if the mother "clings" to her offspring, laying on it the request that originates in her own request as confused neoteinic and hysteric in want of love, the chances are that neither love nor psychic life will ever hatch from such an egg. The loving mother, different from the caring and clinging mother, is someone who has an object of desire; beyond that, she has an Other with relation to whom the child will serve as go-between. She will love her child with respect to that Other, and it is through a discourse aimed at that Third Party that the child will be set up as "loved" for the mother. "Isn't he beautiful," or "I am proud of you," and so forth, are statements of maternal love because they involve a Third Party; it is in the eyes of a Third Party that the baby the mother speaks to becomes a _he_ , it is with respect to others that "I am proud of you," and so forth. Against this verbal backdrop or in the silence that presupposes it the bodily exchange of maternal fondness may take on the imaginary burden of representing love in its most characteristic form. Nevertheless, without the maternal "diversion" toward a Third Party, the bodily exchange is abjection or devouring; the eventual schizophrene, whether phobic or borderline, will keep its hot-iron brand against which his only recourse will be hatred. Any borderline person ends up finding a mother who is "loving" for her own sake, but he cannot accept her as loving himself, for she did not love any _other_ one. The Oedipal negation of the father is here linked with a complaint against an adhesive maternal wrapping, and it leads the subject toward psychic pain dominated by the inability to love.
If one grants the ternary structure of narcissism and its already harboring the hysterical beginning of an idealizable object (the object of love germane to primary identification), how can one, to the contrary, understand the inability to love? The cold, set, and somewhat false complaint of the borderline person that he is unable to love needs perhaps to be related not to narcissism but to autoeroticism. Previous to the "new psychic action" that includes a third party within narcissism, the autoerotic set-up has neither an other nor an image. All of its figures, all figures disappoint it as much as they fascinate it. The autoerotic person cannot allow himself to be "loved" (no more than he can let himself be lovable), except by a maternal substitute who would cling to his body like a poultice—reassuring balm, asthmogenic perhaps, but nevertheless a permanent wrapping. Such a false mother is the only "farthering" [ _pèremanence_ ] tolerated by one who, henceforth, will indolently be able to enjoy his own organs in polymorphous perversity. He is undifferentiated, set within the shattered territories of his parceled body, coiled up about his erogenous zones. He is indifferent to love, withdrawn in the pleasure that a provisionally reassuring diving-suit gives him. The autoerotic person is not, however, autistic: he discovers objects, but they are objects of hatred. Nevertheless, during those moments that have no saving grace and when the subject is deprived of durability, the hatred that an opposite object projects before him works indeed more strongly upon himself, threatening him with decomposition or petrifaction. The autoerotic person who complains or boasts of being unable to love is afraid of going mad—schizophrenia or catatonia...
Dynamics of the Ideal
The subject exists only inasmuch as it identifies with an ideal other who is the speaking other, the other insofar as he speaks. A ghost, a symbolic formation beyond the mirror, this Other who is indeed the size of a Master, is a magnet for identification because he is neither an object of need nor one of desire. The Ego ideal includes the Ego on account of the love that this Ego has for it and thus unifies it, restrains its drives, turns it into a _Subject_. An Ego is a body to be put to death, or at least to be deferred, for the love of the Other and so that Myself can be. Love is a death sentence that causes me to be. When death, which is intrinsic to amorous passion, takes place in reality and carries away the body of one of the lovers, it is at its most unbearable; the surviving lover then realizes the abyss that separates the imaginary death that he experienced in his passion from the relentless reality from which love had forever set him apart: saved...
The subject's identification with the symbolic Other, with its Ego Ideal, goes through a narcissistic absorption of the mother as object of need, an absorption that sets up the Ideal Ego. The lover is cognizant of the regression that leads him from adoring an ideal ghost to the ecstatic or painful inflating of his own image, his own body.
Such a logic of idealizing identification leads one to posit, as lining of the visual, specular structure of the fantasy ($ ◊a) in search of the ever inadequate image of a desired other, the existence of a preliminary condition. If the object of fantasy is receding, metonymical, it is because it does not correspond to the preliminary ideal that the identification process, $ ε A, has constructed. The subject exists because it belongs to the Other, and it is in proceeding from that symbolic belonging that causes him to be subject to love and death that he will be able to set up for himself imaginary objects of desire. Transferred to the Other ($ ε A) as to the very place from which he is seen and heard, the loving subject does not have access to that Other as to an object, but as to the very possibility of the perception, distinction, and differentiation that allows one to see. That Ideal is nevertheless a blinding, nonrepresentable power—sun or ghost. Romeo says, "Juliet is the sun," and that loving metaphor transfers onto Juliet the glare Romeo experiences in the state of love, dedicating his body to death in order to become immortal within the symbolic community of others restored by his love, precisely.
The ideal identification with the Symbolic upheld by the Other thus activates speech more than image. Doesn't the signifying voice, in the final analysis, shape the visible, hence fantasy? Whenever we observe how young children learn forms, we are led to understand to what extent "sensorimotor spontaneity" is of little avail without the help of language. Poets have known from time immemorial that music is the language of love, and it has led them to suggest that the yearning captured by the loved beauty is nevertheless transcended—preceded and guided—by the ideal signifier: a sound on the fringe of my being, which transfers me to the place of the Other, astray, beyond meaning, out of sight. In short, identification causes the subject to exist within the signifier of the Other. Archaically, primitively, it is not object-oriented but carried out as transference to the place of a captivating and unifying feature, a "unary feature." The analyst is an object (necessarily a partial one) but he also exerts the drawing power of a "unary feature," of a nonobject: the actual drifting of a possible metaphoricity.
Here the term metaphor should not bring to mind the classic rhetorical trope ( _figurative_ vs. _plain_ ), but instead, on the one hand, the modern theories of metaphor that decipher within it an indefinite jamming of semantic features one into the other, a meaning being acted out; and, on the other, the drifting of heterogeneity within a heterogeneous psychic apparatus, going from drives and sensations to signifier and conversely.
Since it is not object-oriented, identification reveals how the subject that ventures there can finally find himself a hypnotized slave of his master; how he can turn out to be a nonsubject, the shadow of a nonobject. Nevertheless, it is because identification is not object-oriented that the signifier's nonobject-oriented underlying layer of drives becomes activated during the treatment that is carried out without the _Einfühlung_ being repressed. In such a case, therefore, it is possible for transference to gain a hold on nonobject-oriented psychic states such as "false selves," borderline cases, and even psychosomatic symptoms. It is indeed true that one is ill when not loved; this means that a psychic structure that lacks an identifying metaphor or idealization tends to realize it in that embodied nonobject called somatic symptom—illness. Somatic persons are not those who do not verbalize; they are subjects who lack or miscarry the dynamics of metaphoricity, which constitute idealization as a complex process.
Finally, being the magnet for loving identification causes the _Other_ to be understood not as a "pure signifier" but as the very space of metaphorical shifting: a condensation of semantic features as well as nonrepresentable drive heterogeneity that subtends them, goes beyond them, and slips away. Actually, by stressing the partiality of the "unary feature" during idealizing identification, Lacan located idealization solely within the field of the signifier and of desire; he clearly if not drastically separated it from narcissism as well as from drive heterogeneity and its archaic hold on the maternal vessel. To the contrary, by emphasizing the _metaphoricity_ of the identifying idealization movement, we can attempt to restore to the analytic bond located there (transference and countertransference) its complex dynamic, which includes the narcissistic, drive-animated preobject-orientation and allows it to be tied down to signifying ideals. From this standpoint, there would be no analytical idealization that did not rest upon sublimation. In other words, psychoanalysis skirts religious faith in order to expend it in the form of literary discourse.
Immediate and Absolute
Freud's definition of "primary identification" as "direct and immediate" ( _direkte und unmittelbare_ ) has not, as far as I know, aroused the attention of analysts. In light of that phrase, let us reflect for a moment on the value that speculative philosophy, particularly that of Hegel, assigns to such _immediacy_.
The immanent presence of the Absolute in Knowing is _immediately_ revealed to the Subject as the recognition of that which never left him. More specifically, the Hegelian _immediate_ ( _Unmittelbare_ ) is the ultimate disengagement of consistency for the sake of form, the internal overthrow of reflection-in-itself, matter being removed from the self, without yet being for itself and hence for the other. Hegel notes in his _Science of Logic_ , "Immediacy, which, as reflection-in-itself, is _consistency_ ( _Bestehen_ ) as well as form, reflection on something else, reflection _doing away with itself_." Heidegger, in his text on Hegel's Introduction to the _Phenomenology of the Spirit_ entitled "Hegel and His Concept of Experience," wished to investigate that immediate presence of the Absolute in order to show the a priori or arbitrariness of the "immediate" and reveal, on both its far and near sides, the "blossoming of the Logos," dear to Heideggerian discourse. Within the scope of these reflections, one might maintain that the _immediate_ , being the autoseverance of certainty in the self, is at the same time that which severs it from object-relation and bestows on it its power of acquittance ( _Absolvenz_ ) without mediation, without object, but keeping and containing both; hence the immediate is the very logic of _parousia_ , that is, the presence of the subject for the object. "It behooves him to keep any relation that merely pertains to the object...," is Heidegger's comment. As the most basic indication of parousia, the immediate also presents itself as the logic of _Absolvenz_ , as severance outside of relationship, and constitutes the absoluteness of the absolute. "It is there, in auto-representation, that the parousia of the absolute is displayed."
In other words, the presence of the Absolute in Knowing is _immediately_ revealed to the subject; consequently, any other "means" of knowledge is no more than a recognition. "The absolute is from the outset in and for itself beside us and wants to be beside us," Hegel states in his Introduction to the _Phenomenology_. Such a _being-beside-us_ would be "the manner in which the light of the truth of the absolute itself enlightens us," as Heidegger says in his commentary. We are immediately within parousia, "always-already," before producing a "relationship" to it.
Let us put aside the visual aspect, be it imagined or imaginary, of that immediacy of the Absolute, which Heidegger enabled us to hear when he unfolded the word for knowledge ( _Wissenschaft_ ) in its sonorousness ( _novisse_ , to have a knowledge of, _viso_ , to look at), and which Lacan emphasized when he placed the _mirror_ at the core of the Ego's formation. Let me first stress that specular fascination is a belated phenomenon in the genesis of the Ego. And let us try to think through the philosophical investigation against the backdrop of what the analyst might see in the appearance of the term "immediate" at the heart of primary identification.
With Freud, the arbitrariness of paternal emergence seems undeniable, at any rate absolutely necessary to the interpretative analytic construction. Nevertheless, clinical experience has led us to ascertain that the advent of the _Vater der persönlichen Vorzeit_ takes place thanks to the assistance of the so-called pre-Oedipal mother, to the extent that she can indicate to her child that her desire is not limited to responding to her offspring's request (or simply turning it down). This assistance is none other than maternal desire for the Father's Phallus.
Which one? The child's father or her own? For "primary identification" the question is not relevant. If there is an _immediacy_ of the child's identification with _that desire_ (of the Father's Phallus), it probably comes from the child's not having to elaborate it; rather, he receives it, mimics it, or even sustains it through the mother who offers it to him (or refuses it) as a gift. In a way, such an identification with the father-mother conglomerate, as Freud would have it, or with what we have just called the maternal desire for the Phallus, comes as a godsend. And for a very good reason, since without that disposition of the psyche, the child and the mother do not yet constitute "two"...
As for the image making up this "imagination," it should not be conceived as simply visual but as a representation activating various facilitations corresponding to the entire gamut of perceptions, especially the _sonorous_ ones; this because of their precocious appearance in the domain of neuropsychological maturation, but also because of their dominant function in speech.
Nevertheless, let us not be mistaken about the ease of such an _immediacy_. It entails an important consequence: within that logic, the word "object," just like the word "identification," becomes _improper_. A notyet-identity (of the child) is transferred or rather displaced to the site of an Other who is not libidinally cathected as an object but remains an Ego Ideal.
Not I
Let me now point out that the most archaic unity that we thus retrieve—an identity so autonomous that it calls forth displacements—is that of the Phallus desired by the mother. It is the unity of the imaginary father, a coagulation of the mother and her desire. The imaginary father would thus be the indication that the mother is not complete but that she wants... Who? What? The question has no answer other than the one that uncovers narcissistic emptiness; "At any rate, not I." Freud's famous "What does a woman want" is perhaps only the echo of the more fundamental "What does a mother want?" It runs up against the same impossibility, bordered on one side by the imaginary father, on the other by a "not I." And it is out of this "not I" (see Beckett's play with that title) that an Ego painfully attempts to come into being...
In order to maintain himself in that place, to assume the _leap_ that will definitely anchor him in the imaginary father and in language or even in art, the speaking being must engage in a struggle with the imaginary mother, for whom it will eventually constitute an object separated from the Ego. But we are not at that stage yet. The immediate transference toward the imaginary father, who is such a godsend that you have the impression that it is he who is transferred into you, withstands a process of rejection involving what may have been chaos and is about to become an _abject_. The maternal space can come into being as such, before becoming an object correlative to the Ego's desire, only as an _abject_.
In short, primary identification appears to be a transference to (from) the imaginary father, correlative to the establishment of the mother as "ab-jetted." Narcissism would be that correlation (with the imaginary father and the "ab-jetted" mother) enacted around the central emptiness of that transference. This emptiness, which is apparently the primer of the symbolic function, is precisely encompassed in linguistics by the bar separating signifier from signified and by the "arbitrariness" of the sign, or in psychoanalysis by the "gaping" of the mirror.
If narcissism is a defense against the emptiness of separation, then the whole contrivance of imagery, representations, identifications, and projections that accompany it on the way toward strengthening the Ego and the Subject is a means of exorcising that emptiness. Separation is our opportunity to become narcists or narcissistic, at any rate subjects of representation. The emptiness it opens up is nevertheless also the barely covered abyss where our identities, images, and words run the risk of being engulfed.
The mythical Narcissus would heroically lean over that emptiness to seek in the maternal watery element the possibility of representing the self or the other—someone to love. Beginning with Plotinus at least, theoretical thought has forgotten that it rumbled along over emptiness before lovingly springing toward the solar source of representation, the light that enables us to see and with which we aspire to become equal, idealization following upon idealization, perfecting upon perfecting: _In lumine tuo videbimus lumen_. Psychotic persons, however, remind us, in case we had forgotten, that the representational contrivances that cause us to speak, elaborate, or believe rest upon emptiness. Possibly the most radical atheists are those who, not knowing what the ability to represent owes to a Third Party, remain prisoners of the archaic mother, for whom they mourn in the suffering of emptiness.
Within sight of that Third Party I elaborate the narcissistic parry that allows me to block up that emptiness, to calm it and turn it into a producer of signs, representations, and meanings, I elaborate it within sight of the Third Party. I seduce this "father of individual prehistory" because he has already caught me, for he is simple virtuality, a potential presence, a form to be cathected. Always already there, the forming presence that nonetheless satisfies none of my autoerotic needs draws me into the imaginary exchange, the specular seduction. He or I—who is the agent? Or even, is it he or is it she? The immanence of its transcendence, as well as the instability of our borders before the setting of my image as "my own," turn the murky source ( _eine neue psychische Aktion_ ) from which narcissism will flow into a dynamics of confusion and delight. Secrets of our loves.
The Ideal Ego sated with the Ego Ideal will take over from that alchemy and strengthen the defenses of the narcissistic Ego. Consciousness, along with moral conscience (that stern and precious paternal inheritance), will not truly lead us, under the tyrannical protection of the Superego, to forget the narcissistic emptiness and its surface composed of imaginary recognitions and cathexes. At least it will help us block them up; they always remain as more or less painful wounds at the heart of our functions, successes, or failures. Beneath homosexual libido, which our social objectives catch and maintain captive, the chasms of narcissistic emptiness spread out; although the latter can be a powerful motive for ideal or superegotic cathexis, it is also the primary source of inhibition.
In being narcissistic one has already throttled the suffering of emptiness. The fragility, however, of the narcissistic elaboration, underpinning the ego image as well as ideal cathexes, is such that its cracks immediately reveal the negative of our image films to those that others consider to be "narcissistic." More than insane, empty, that lining of our projection and representation devices is yet another defense of the living being. When he succeeds in eroticizing it, when he allows the nonobject-oriented, prenarcissistic violence of the drive directed toward an abject to run wild, then death triumphs in that strange path. The death drive and its psychological equivalent, hatred, is what Freud discovers after stopping off at Narcissus. Narcissism and its lining, emptiness, are in short our most intimate, brittle, and archaic elaborations of the death drive. The most advanced, courageous, and threatened sentries of primal repression.
In contrast with Melanie Klein's "projective identification," the proposition I am offering here has the advantage of pointing to, even before the Oedipal triangle and within a specific disposition, the place of the Third Party; without the latter, the phase Melanie Klein calls "schizo-paranoid" could not become a "depressive" phase and thus could not carry the "symbolic equivalences" to the level of linguistic "signs." The archaic inscription of the father seems to me a way of modifying the fantasy of a phallic mother playing at the phallus game all by herself, alone and complete, in the back room of Kleinism and post-Kleinism.
As for language, the notion outlined here differs, furthermore, from innatist theories concerning linguistic competence (Chomsky) as well as from Lacanian notions of an always-already-there of language that would be revealed as such in the subject of the unconscious. I of course assume, with respect to the _infans_ , that the symbolic function preexists, but also maintain an evolutionary postulate that leads me to seek to elaborate _various dispositions_ giving access to that function, and this corresponds as well to various psychic structures.
In the light of the above, what I have called a "narcissistic structuration" appears to be the earliest juncture (chronologically and logically) whose spoors we might detect in the unconscious. Conversely, understanding narcissism as origin or as undecomposable, unanalyzable screen leads the analyst (no matter what theoretical warnings might be given in other respects) to present his interpretative discourse as a haven, either comforting or confrontingly aggressive, for a narcissism that thus finds itself recognized and renewed. Whether comforting or authenticating (by rational criticism, for instance, in interpretations of the "mental process" sort), such a welcome falls into the trap of narcissism and seldom succeeds in leading it through the Oedipal procession on to the topology of a complex subject.
In fact, clinical practicians like Winnicot protected themselves against such a danger, if only by always advocating a mixture of "narcissistic" and "Oedipal" interpretations in so-called psychotic states. Nevertheless, if the dead end that has just been noted can be encountered by others, the reason for it must probably be located in a basic omission—that of the agency of the imaginary father from the start of primary identification, an agency of which "projective identification" is a more belated consequence (logically and chronologically). One may still reach that dead end, by the same token, if one ignores the very concrete and specific structuration required by psychicism within that very elementary disposition, which the term "narcissism" threatens to reduce to a fascination for what is nothing but the mother's phallus.
Persian or Christian
The dynamics of primary identification, which structures _emptiness_ and _object_ as what may have appeared as a "narcissistic screen," will allow us to examine another enigmatic juncture on the Freudian path.
Freud's uneasiness concerning Christianity is well known, and his rationality would not let him put it into words with respect to revealed religion, but, dazzled and prudent, he did express it when faced with Persian religion. "The sun-drenched face of the young Persian god has remained incomprehensible to us." It is indeed possible to interpret that refulgent jouissance as "direct and immediate" primary identification with the Phallus desired by the mother; this amounts neither to being the mother's Phallus nor entering the Oedipal drama. A certain phantasmatic incestuous potentiality is thus set aside; it works from the place of the imaginary father and constitutes the basis of imagination itself. Moreover, the subsequent naming of that relationship perhaps represents the conditions of sublimation.
In Freud's text, the "refulgent and incomprehensible" face lacking an Oedipal feeling of fault or guilt would be that of the leader of the horde of brothers who kills the father and boasts of his feat (as Ernest Jones suggests). One might, on the other hand, consider a pre- or non-Oedipal disposition of that jouissance; a position of symbolicity that stems from primary identification, coupled with what the latter infers in regard to sexual nondifferentiation (father-and-mother, man-and-woman) and immediate transference to the site of _maternal desire_. That would constitute a fragile inscription of subjecthood, one which, under the subsequent Oedipal sway, would retain no more than a phantasmatic status. In addition, such a warm but dazzling, domesticated paternity includes imaginary exultation as well as a risk of dissolving identities that the Freudian Oedipal process alone ends up strengthening, in the ideal hypothesis of course.
Maintaining against the winds and high tides of our modern civilization the requirement of a stern father who, through his Name, brings about separation, judgment, and identity, constitutes a necessity, a more or less pious wish. But we can only note that jarring such sternness, far from leaving us orphaned or inexorably psychotic, reveals multiple and varied destinies for paternity—notably archaic, imaginary paternity. Those destinies could or can be manifested by the clan as a whole, by the priest, or by the therapist. In all cases, however, we are dealing with a function that guarantees the subject's entry into a disposition, a fragile one to be sure, of an ulterior, unavoidable Oedipal destiny, but one that can also be playful and sublimational.
Seducer or Ideal Father
The tragic dynamic of the Father's idealization is taken up again in _Moses and Monotheism_ through the theme of the election of the Jewish people by its God and through the story of Moses. There is nothing to make one conceive this election as a revival of the old idea, subsequently abandoned by Freud, of the father as the hysterical person's first seducer. The father who brings a people into being through his love is perhaps indeed closer to the "father of individual prehistory," and, at any rate, to the idealizing agency that drains early identifications, not as object but as "unary feature." One might nevertheless interpret Freudian thought with respect to this loving father in the following fashion. The hysterical structure of the horde of brothers construes him as a seducer, an agent of the libido, of Eros, and puts him to death; this is Moses' murdered body. Yet there is also a structural necessity for his unique love as symbolic choice; it appears later on as a pressing need to lay down moral rules or a right to the tribe. The father will then be recognized not as seducer but as Law, as an abstract agency of the One that selects our identifying and idealizing power. The Christian trinity, for its part, reconciles the seducer and the legislator by inventing another form of love— _agape_ , symbolic (nominal, spiritual) from the very start _and_ corporeal, absorbing the acknowledged murder of the erotic body into the universalist profusion of the symbolist distinction for everyone (brother or stranger, faithful or sinner).
What is opposed to the recognition of the imaginary father? What is it that produces its repression, or even its burial? Freud drops the word "character," with its well-known anal connotations. "Whatever resistance character might later be able to bring to bear against the influence of abandoned sexual objects, the effects of earlier identifications, carried out in the most precocious stages of life, will always keep their general, lasting features."
Character is one of the limits to what is analyzable, and that is confirmed by the difficulties encountered in the region we are now investigating. Furthermore, because of the anal character's resistance against primary identification, the advent of the abject during treatment can clearly be seen as the first breach in resistance.... Nevertheless and above all it is Oedipal rivalry, which creates mediations, that tragically darkens the dazzlement of primary identification. Within the Oedipus complex, the question is no longer "Who _is_ it?" but "Who _has_ it?"; the narcissistic question "Am I?" becomes a possessive or attributive question, "Have I?" It is nonetheless true that by starting from Oedipal dramas and their failures—backwards, in other words—one will be able to detect the particulars of primary identification. It is to be noted, however, that "boundary states" lead us there directly, locating the Oedipal conflict as ulterior or secondary.
A boy will have difficulty tearing himself away from the petrifying situation of being his mother's phallus; or if he succeeds, through the maternal grandfather (among others) who has come in between, he will never cease waging war against his brothers in the shadow of an inaccessible father. Only in poetic enunciation will it be possible for him to be son-and-father within the immediate and direct disposition of primary identification, and bypassing sexual difference—witness the troubadours and Joyce. As for the girl, she will retain the traces of that primary transference only if assisted by a father having a maternal character, who nevertheless will not be of much help in her breaking away from the mother and finding a heterosexual object. She will thus tend to bury that primary identification under the disappointed feverishness of the homosexual, or else in abstraction, which, as it flies away from the body, fully constitutes itself as "soul" or fuses with an Idea, a Love, a Self-sacrifice.... If ever a jouissance remains, it still seems to partake of that archaic differentiation that Freud so delicately and elliptically touched on under the heading of "primary identification."
"Narcissistic structure" thus remains a permanent fixture in the love grievances that beckon to us...
NOTES
. This corresponds to, although it does not fully render, Kristeva's coinage, _hainamoration_. It was suggested by Margaret Waller (who translated _Revolution in Poetic Language_ ) to replace one of my own less fortunate neologisms—and I am indebted to her for many other suggestions and corrections as well.—Trans.
. See _On Narcissism: An Introduction_ (1914), in vol. 14 of the _Standard Edition of the Complete Psychological Works of Sigmund Freud_ , 24 vols., James Strachey, tr. and ed. (London: Hogarth Press, 1953–1974). This text is doubtless very bound up with the war, Freud's insecurity, and Jung.
Nevertheless, from the time of his earliest works, Freud insisted on a _resistance_ that would have been imbedded in the very structure of neurons, as well as on _inhibition_ as master faculty of the Ego ( _Project for a Scientific Psychology_ [895], _Standard Edition_ 1). "We must reckon with the possibility that something in the nature of the sexual drive itself is unfavorable to the realization of complete satisfaction," he notes in "The Tendency to Debasement in Love," in _The Psychology of Love_ , _Standard Edition_ 11:188–89, before discovering narcissism at the same time as the illusion present at the outset of psychicism, as it is at the heart of amatory experience. Next comes what Freud himself called the "strange" postulate of death drive, posited toward the end of an exposition on the impossible in love, on loving hatred, and primary masochism ("Beyond the Pleasure Principle," _Standard Edition_ 18:51–61).
. "Die autoerotischen Triebe sind aber uhrfänglich; es muss also irgend etwas zum Autoerotismus hinzukommen, eine neue psychische Aktion, um den Narzissmus zu gestalten." _Standard Edition_ 14:77.
. Jacques Lacan, _Les Ecrits techniques de Freud_ , in _Le Séminaire_ (Paris: Seuil, 1975), 1:133.
. André Green, _Narcissisme de vie, narcissisme de mort_ (Paris: Minuit, 1983).
. See "Being in Love and Hypnosis," in _Group Psychology and the Analysis of the Ego_ (1921), _Standard Edition_ 18:111ff.
. Ibid., p. 112.
. "Identification," in _Group Psychology and the Analysis of the Ego_ , _Standard Edition_ 18:105.
. Ibid., p. 105.
. Ibid., p. 110.
. Ibid., p. 107.
. "Diese scheint zunächst nicht Erfolg oder Ausgang einer Objektbesetzung zu sein, sie ist eine _direkte_ und _unmittelbare_ und frühzeitiger als jede Objektbesetzung." _The Ego and the Id_ (1923), _Standard Edition_ 19:31. One of the main ideas of Freud's breviary of love amounts to positing that the Oedipus complex's decline (which he calls "natural" but is in fact enigmatic) during the latency period favors the inhibition of partial drives and strengthens ideals—thus making the erotico-ideal cathexis of the love object possible during puberty. "I am in love" is a fact of adolescence when the teenager is capable of partial repression because of difficulties in realizing Oedipal fantasies and can project his idealizing capabilities onto a person toward whom erotic desire can be deferred. See Christian David, _L'Etat amoureux_ (Paris: Payot, 1971). Nevertheless, the premises for such a state of love go back to _primary identification_ and, before they constitute a lover, they shape psychic space itself.
. Melanie Klein, _Envy and Gratitude_ (London: Hogarth Press, 1957), p. 187. See also Melanie Klein and Jean Rivière, _Love, Hate, and Reparation_ (London: Hogarth Press, 1967). On Melanie Klein see Jean-Michel Petot, _Melanie Klein, le moi et le bon object (1932–1960)_ (Paris: Dunot, 1982).
. Melanie Klein, _Envy and Gratitude_ , p. 180.
. Ibid., p. 191.
. Ibid., p. 193.
. Recalling that in analytical literature the object is in most instances a partial object (mammilla, scybalum, phallus, urine), Lacan specifies: "This feature, this partial feature, rightly emphasized in objects, is applicable not because these objects are part of a total object, the body, but because they represent only partially the function that produces them." Being a function of separation and of want that found the signifying relationship, these objects, designated by a lower case "a," will be called "objects of want": "These objects have one common feature in my elaboration of them—they have no specular image, or, in other words, alterity. It is what enables them to be the 'stuff,' or rather the lining, though not in any sense the reverse, of the very subject that one takes to be the subject of consciousness.... It is to this object that cannot be grasped in the mirror that the specular image lends its clothes." "Subversion of the Subject and Dialectic of Desire," in _Ecrits/A Selection_ , Alan Sheridan, tr. (New York: Norton, 1977), pp. 315–16.
Lacan discovered in _fantasy_ the exemplary efficacy of the object "a" since in his view the structure of fantasy is linked "to the condition of an object,... the moment of a 'fading' or eclipse of the subject that is closely bound up with the _Spaltung_ or splitting that it suffers from its subordination to the signifier" (p. 313). That is what is symbolized by the formula, ($ ◊ a) where ◊ indicates desire. Finally, the _metonymical_ structure defines the Lacanian object relation to the extent that "it is the connection between signifier and signifier that permits the elision in which the signifier installs the want-of-being in the object relation, using the value of 'reference back' possessed by signification in order to invest it with the desire aimed at the very want it supports." "The Agency of the Letter in the Unconscious" (p. 164).
. "Take just one signifier as an emblem of this omnipotence [of the other's authority], that is to say of this wholly potential power ( _ce pouvoir tout en puissance_ ), this birth of possibility, and you have the unary feature ( _trait unaire_ ), which, by filling in the invisible mark that the subject derives from the signifier, alienates this subject in the primary identification that forms the ego ideal." "Subversion of the Subject and Dialectic of Desire," in _Ecrits/A Selection_ , p. 306.
The unary feature of Lacan goes back to the "unique feature" ( _einziger Zug_ ), to which would be limited the identification that is only partial, according to Freud in _Identification_ (das beide Male die Identifizierung eine partielle, höchst beschränkte ist). See the _Seminars on Transference_ (1960–1961) and on _Identification_ (1961–1962). Lacan takes advantage of that partial status, on the whole rather imprecise with Freud, in order to insist upon the _unique feature_ ( _einziger Zug_ ) that establishes identification as intrinsically symbolic, hence subjected to the distinctiveness of signifying traits, and finally ruled by the benchmark of One feature, of the Unique—foundation of my very own unicity.... This unary feature is not "in the first field of narcissistic identification" where we have witnessed the emergence of the imaginary Father; Lacan sees it straight off "in the field of desire... in the reign of the signifier." _The Four Fundamental Concepts of Psychoanalysis_ (New York: Norton, 1978), p. 256.
. See Michael Balint, _Amour primaire et technique psychanalytique_ (Paris: Payot, 1972).
. See "Identification," in _Group Psychology and the Analysis of the Ego_ , _Standard Edition_ 18:105.
. "Therefore the subject becomes conscious of his desire in the other, by means of the other's image, which presents him with the specter of his own mastery." Lacan, _Les Ecrits techniques de Freud_ , in _Le Séminaire_ , 1:178.
. "[The imaginary position of desire] is conceivable only to the extent that a guide may be found beyond the imaginary, at the level of the symbolic plane, the legal exchange that can be embodied only on the basis of verbal exchange among human beings. The guide that rules the subject is the ego ideal" (ibid., p. 162). And this is true even if "love is a phenomenon taking place on the level of the imaginary and provoking a real subduction of the symbolic, a kind of annulment or perturbation of the ego ideal" (ibid.).
. _The Ego and the Id_ , _Standard Edition_ 19:31.
. G. W. F. Hegel, _Science de la logique_ (Paris: Vrin, 1970), pp. 385–86.
. Ibid.
. _Totem and Taboo_ , _Standard Edition_ 13:153.
. See _Moses and Monotheism_ , _Standard Edition_ 23:110.
. _The Ego and the Id_ , _Standard Edition_ 19:31.
Throes of Love: The Field of the Metaphor
Through the Looking Glass
It may seem paradoxical to be seeking the discourse of amatory relationships in borderline aesthetics. It may seem strange that, instead of bringing to the fore the straightforward language of simple idealization of the love object, one analyzes the painful or ecstatic states where the object slips away. Such a choice is not imposed simply because the staging of amatory capture in a narrative has been more fully investigated. It has been determined essentially by two observations.
The first, psychoanalytic in nature, amounts to asserting that the amatory experience rests on _narcissism_ and its aura of emptiness, seeming, and impossibility, which underlies any _idealization_ equally and essentially inherent in love. Even more so, when the social consensus gives _little_ or _no_ support to such an idealizing possibility, as may be observed at the present time (a phenomenon of which the religious and moral crisis is only one aspect), the derealization that underlies amatory idealism shows up with its full power.
In the second place, when one transposes into language the idealization on the edge of primal repression that amatory experience amounts to, this assumes that scription and writer invest in language in the first place precisely because it is a favorite object—a place for excess and absurdity, ecstasy and death. Putting love into words, and this stresses the utterance more than the propositional act ("I must _utter_ as close as possible to what I am experiencing with the other"), necessarily summons up not the narcissistic _parry_ but what appears to me as narcissistic _economy_. Such and such loving speech that we view as being in a state of uncertainty and metaphorical condensation reveals the continuity of the narcissistic economy, and this includes the "insignificant" love experience that does not dare express itself differently from what is on the surface, does not venture to seek its logic beyond the looking glass where lovers bewitch each other. Because it thus speaks love's painful but also constituent truth, that scription attracts us. We become its readers during the intervals of our own loves when we are able to withstand looking at them beyond the surface, in more fundamental fashion. It is a view that we cannot necessarily share with our partners but to which our dreams, our anguish, and our jouissance bear witness.
On the Referent and Subject of the Metaphor
Let us call metaphor, in the general sense of a _conveyance of meaning_ , the economy that modifies language when subject and object of the utterance act muddle their borders. One already senses that one of the purposes of this study is to base a theory of metaphor on a given number of specific states of the subject of the utterance act. My reading of metaphoricalness constitutes neither a philosophical challenge against the metaphor, nor an expansion (conversely symmetrical) of its impact on any language act; it assumes a theoretical distance that is not one of speculative philosophy either. It finds its justification in the ambiguous, loving distance, germane to psychoanalytic transference, and is based on contemporary analyses (semantic, syntactic, discursive) of the metaphorical act. I shall, however, try to understand such broadened metaphoricalness within the amatory economy of the subject of the utterance act, who demonstrates by means of metaphors the complex process of identification (narcissism _and_ idealization).
"The metaphorical exists only within the bounds of metaphysics," Heidegger propounds. The assertion is incontrovertible as far as the field of metaphysics itself is concerned, and it suits the metaphoricalness particular to philosophical discourse, which was able to survive because of the very banishment of the metaphor. I shall, nevertheless, in this discussion, go over some points that are essential to my purpose.
We know that, ever since Plato (see _Gorgias_ , but also _Phaedrus_ ), philosophical discourse has been obsessed with setting up the boundary between philosophy and rhetoric, which is the real requirement for its existence.
Eidos, Omoiosis, Analogia
The problematics of _ressemblance_ , of the "striking image," worries, as we know, the whole of Platonic thought. It has often been shown, since Heidegger, how light, the "visible," and the "image" conceal themselves in the "idea" and establish thought itself as a lexicalized metaphor, _eidos_. Let us, however, remove from that constituent imagery of the _idea_ the portion of resemblance that, for its part, sustains the metaphor. "It is the east, and Juliet is the sun," Romeo tells Juliet, for Juliet and the sun are equally dazzling to him, they are alike in that both are a dazzling light. _Omoioma_ , _atos:_ Plato uses those words when discussing love in _Phaedrus_ , and he posits that the amorous soul notices an _omoioma_ , an _imitation_ of celestial things in the things of this world that _resemble_ them and for that very reason causes it to fall in love, puts it beside itself. One is in love with what resembles an ideal that is out of sight but present in the memory. The entire motion of metaphorical conveyance is already present in the _omoiosis_ relation, which has the advantage, at the very dawn of Greek thought, of placing love in concert with image-making, resemblance, homologation. Greek ontology buried that movement, but we find it again, with the same Platonistic terminology, in the Gospels, where _omoioma_ is used to think out the relations between God and his creatures (Romans 6:5). Nevertheless, medieval theology, moving away from the amatory metaphoricalness of the Gospels, became interested in the Aristotelian notion of _analogia_ , intent as it was to make the state of shock inherent in amatory _omoiosis_ and metaphor thinkable. Aristotle's place is thus fundamental in the "ontologizing of the metaphor" constituted by creating the philosophical category of _analogy_. Torn between ontology and theology, Aristotle's thought keeps aiming for their reconciliation, which, as it is impossible, finally wrecks his ontological design. One of the tokens of this conflict is the effort to elaborate a univocal philosophical language untainted by any poeticalness and yet attentive to some of the signifying effects of the latter.
Having thus expelled metaphorical ambiguity from the field of philosophy, Aristotle kept trying to gain, within that very field, "a scrap of equivocalness." He succeeded in doing so, on the one hand, by gradually blunting the predicative function's preciseness (the predicative copula may be understood as a _being said of_ —"Socrates is [said to be] a man"—and as a _being in_ —"Socrates is a musician," where "musician" is an accident of the substance). But on the other hand and above all, Aristotle is led to speak of _analogy_ (in a different sense from the one he ascribes to this word when he considers it as an instance of metaphor) when discussing aporia in "the multiple meanings of being." There is a being, but this may be said in various ways. How can we reconcile these two assertions if not by _analogy_? Indeed, having inherited from outside his own philosophy a Platonic theology of the being-as-One, Aristotle is forced to reconcile his discourse on the physical world in the diversity of its categorial meanings with the _pros hen, ad unum_. The divine _ousia_ constantly underlies the categorial oneness of being. That is precisely what is written in the _Metaphysics_ when the word analogy is introduced: "the causes of all are the same. They are the same or analogous," and further on, "the causes of substances may be treated as the causes of all things." The thinkable, the ontological, is based on the theological unthinkable, which, although unthinkable, but perhaps for that very reason, sets the structure of the investigation. The analogy thus introduced was first proportional, hence mathematical, before it was set forth as _attributive_ analogy. By breaking with the _Poetics_ , Aristotle salvages _some_ metaphoricalness for the sake of another no longer metaphorical but transcendental discourse: analogy is witness to this _pros hen, ad unum_ in his investigation. And one will have to wait for the whole post-Kantian expansion of positivist logic before Carnap and Russell would define predication as the assignment of something to a class and thus extricate the problem of _attribution_ from the sphere of _analogy_. What is nevertheless lost along the way are the other meanings of the predicative copula, notably the function it has to designate the acting being, thereby giving rise in particular to a question concerning the very act of uttering. The philosophical salvaging of analogy by Aristotle had the advantage of opening up the question of _being_ as act, and at the same time of raising the problem, if only implicitly, of the _act of naming_. Certain Aristotelian expressions, moreover, state this rather clearly: "The metaphor signifies things in action" ( _Rhetoric_ III, II, 1411b, 24–25); "the imitators may represent the whole story dramatically, as though they were actually doing the things described" ( _Poetics_ 1448a, 24); "Now the action is represented in the play by the Fable or Plot" ( _Poetics_ 1450a, 3).
Let us not forget that advantage, let us not bury it in the simple logical motion of predication or predication as motion. For such a dynamic will enlighten us concerning the significance of the other metaphor, the real one, the poetic one. Let me simply stress here that analogy, even when philosophical, is necessary for thought in order to organize an investigation (not a science) that would be ontotheological (Heidegger's phrase) and dependent on being as _One_ and on the _act_.
Furthermore, medieval theology, splitting off in its turn from the poetical metaphoricalness of biblical discourse, postulated with Thomas Aquinas an _analogia entis_. It distinguished first between an analogy of _proportio_ (comprising a definite distance and a strict relationship, _determinata habitudo_ , between the terms) and an analogy of _proportionalitas_ , which is a simple similarity of ratios (for instance, six is to three as four is to two). But in order to imagine the relationship between infinite God and finite creatures Thomas Aquinas posited _causality_ itself as _analogy_. What had been a relationship of significance (of creatures by analogy with God) becomes an _efficiency_ : one may name God according to creatures only on account of the relationship between creatures and God, their principle and their cause, in whom all the perfections of existing beings preexist excellently. Such an analogy, which has been raised to the level of cause, indeed excludes the strictly poetical metaphor; but, as Paul Ricoeur notes, it also integrates it surreptitiously; this happens when, examining two analogous meanings (for instance, using "wise" in speaking of man and of God), Thomas sees that the _nominis significatio_ (germane to the "wise man" and attributed to God by analogy) is exceeded in the _res significata_ (God) by a surplus of meaning impossible to circumscribe... The surplus of meaning (the _res significata_ is richer than the _nominis significatio_ ) that results from the _new predicative motion_ is, properly speaking, the metaphorical effect specific to poetry, which Thomas's logicality wished to contain by means of _analogia entis_.
A final observation concerning the philosophical history of the metaphor as outlined by Paul Ricoeur will bring us closer to my purpose. It is true that a certain conception of the metaphor, itself stemming from a reductive metaphysical interpretation, which moreover is no longer in favor, lends itself to restricting that image to the field of metaphysics. I refer to the interpretation that sees in it a simple shift from _literal_ to _figurative_ , _primary_ to _secondary_ , _animate_ to _inanimate_ , and so on: all such distinctions are indeed metaphysical, they can be upheld only within a naive theory of metaphor dominated by the _word_ and insensitive to its syntactical and narrative dissemination. The work done I. A. Richards, Max Black, and, on a different level, by Emile Benveniste, Roman Jakobson, and contemporary semanticists who, in their wake, locate the metaphor in _sentence_ and _discourse_ bring out a certain potentiality that is specific to the Aristotelian interpretation of the metaphor. The _kurion_ ("common" name) or the _idion_ (translated as "proper") simply refer to the _starting term_ of metaphorical motion and seem not to have had for the Greek philosopher the meaning of a primal, primitive ( _etumon_ ) own. Present day theory of metaphor brings to the fore the interference between two _nonhierarchized semantic fields_ and two reference areas also nonhierarchized; it does so by giving greater importance in its analysis to the sentence or discourse context of metaphorical motion as well as to the utterance act as referential and intersubjective act.
"Being Like" or the "Unbeing"
Metaphoricalness consequently appears to me as the utterance not only of a being-as-One and acting, but rather, or even on the contrary, as the indication of uncertainty concerning the reference. _Being like_ is not only _being_ and _nonbeing_ , it is also a longing for _unbeing_ in order to assert as only possible "being," not an ontology, that is, something outside of discourse, but the constraint of discourse itself. The "like" of metaphorical conveyance both assumes and upsets that constraint, and to the extent that it probabilizes the identity of signs, it questions the very probability of the reference. Being?— _Unbeing_.
Paul Ricoeur, in his fine study, speaks of an "ontological vehemence" specific to the semantic aim of the metaphor as act, which harbors in itself the premonition of the unknown that the concept is about to take hold of. This is where I part company with him. His interpretation permanently ontologizes the metaphor, which he had yet so strongly reinstated in its possible but not absolute ontotheological scope. By saying that the metaphor signals a new reference to be named, Ricoeur encloses metaphorical dynamics within a speculative philosophy whose plan he explicitly acknowledges, a philosophy subservient to being-as-One, comparable to the process that, besides, we both detected in Aristotle and Thomas Aquinas.
Is there, however, another possibility for thinking out metaphoricalness, without simplifying it in order to reduce it to a metaphysics itself simplified, and without limiting its impact as "premonition of a concept" within the framework of speculative philosophy? It seems so to me. I shall interpret metaphorical dynamics as established not by the designation of a reference inevitably reducible to being, but by the relationship the speaking subject has with the Other during the utterance act. The utterance is precisely what seems to me, from the position of an analyst, the only basis for meaning and significance in discourse.
What I am calling for is not a simple reversal in perspective: setting up an inner foundation, a "mood," a basis for discourse—in place of an outer one, the referent. The _subject_ is not simply an inside facing the referential outside. The subjective structure, understood as a specific articulation of the relationship between speaking subject and Other, determines the very situation of reality, its existence or nonexistence, its overturning or hypostasis. In such a perspective, ontology becomes subordinate to the signifying structure that sustains a given subject in its transference upon the Other.
I have observed that the ultimate support of Aristotelian metaphor is a being who acts. The poetic as well as the categorial metaphor merely conveys "motion and life"; yet Aristotle stresses that "act is motion." Nevertheless, in the face of the difficulties that ontology encounters in its attempt to define "strength" and "act," I shall venture the following proposition. The "being who acts" could exist only for a subject in symbolic _contact_ , that is to say in motion, in _transference_ with another. The being who acts gives its all in subjective experience, and this is even truer in the love between two subjects—that climax of destabilizing-stabilizing identification. There is no act, just as there is no sexual act, outside of love, for it is in the constituent violence of its field that the subject's signifying structure is shaken, drives and ideals included. There, on account of the subject's modification—the questioning of the subject in amatory experience—a modification of its being and of being is carried out; they are opened out, if you will, unfurled. No longer physics but speaking subjectivity will henceforth ask the key epistemological question; what is mobility, what is innovation? "What is" means, in this context, how does one express them? The amatory experience as dynamics of the crisis and of subjective and discursive renewal, along with its linguistic correlative, metaphoricalness, appears to be, from that standpoint, at the core of an essential debate.
The univocity of signs undergoes equivocality and is resolved in a more or less undecidable connotation when the subject of the utterance, in a state of transference (of love) toward the other transposes the same process of identification, of transference, to the units of language—the signs. The undeniable referential effect of this process, which stems from the referent having been made ambiguous, should not conceal its subjective basis. The signifying unit (the "sign") opens up and reveals its components: drives and sensory elements (as in a synesthetic metaphor)—while the subject itself, in a state of loving transference, flares up from sensation to idealization.
If one agrees with that interpretation, one understands why philosophical thought on metaphor is rooted, with Plato, in a reflection on love and on the direction philosophical discourse must take in relation to that reflection: Plato aims at a mastery of _love_ and at the same time of _metaphor_ , through ontotheology. One also understands why theological discourse alone, concerned with the One and the relationship of the speaking being to that One—hence with faith—was forced to proceed edge-to-edge along the metaphor, which produced a determination of the theory of _analogy_ starting from the poetic field but outside of it. Finally, when theology is emptied of its essence and, with Descartes, holds the other in a position of a _causa sive rationem_ and seeks the true basis of reason only in the articulation of judgment and no longer in analogy, which, even when preserved, loses its function—we then witness a double banishment. Nascent rationalism brushes aside in the same stroke _analogy_ , the scar of metaphoricalness in the specific domain of ontotheology, and its correlative, the _Ego affectus est_ : the loving subject. To make possible the advent of _judgment_ and the _Ego cogito_.
Psychoanalysis: Poetry and History
The psychoanalytic stance allows one to record a true transformation of Western discourse, in which the metaphor is at stake, accomplished at the expense of the loving subject; it thus determines a position that can only be termed outrageous within the history and typology of interpretative discourse. Functioning under the same amatory conditions that rule the production of metaphoricalness in poetic discourse, psychoanalysis nevertheless keeps a certain distance from it since it produces, with respect to that discourse, a knowledge effect. Does this mean that it produces its concept? If that were true, it would not be distinguishable from speculative philosophy and ontotheology. It might be better to say that it analyzes in precise fashion such a proximity to speculative philosophy. Not in disseminating each concept by way of metaphor or asserting that every sign is necessarily a forgotten metaphor that must be brought to the fore in order to dissolve its idealizing conceptual seizing. Rather, it does so by preserving a _typology of discourses_ (for instance, the "poetical" is not the "philosophical" discourse, which is not the "analytical"), and setting for itself the regular task of being, on the one hand, a scene of metaphor production (as in the amatory state or in poetry) and, on the other, a scene of _provisional_ interpretation. It is the _provisional_ (this means such-andsuch, for the _moment_ ) that inserts _duration_ instead of the _absolute_ in psychoanalytic interpretation. _Psychoanalysis is the most internalized moment of Western historicality_. The provisional also inserts the _chance_ of subjective encounter in the dynamics of transference. If it is the amatory impact that makes me say, and if such saying can have a history, this means there is no absolute that is external to our love, our discourse. Neither your actual history nor anyone else's holds the reference to our discourse's signification. Being in love conveys a throbbing, passionate, unique meaning, but only here and now, and which might, in another juncture, be absurd. For the first time love, and with it metaphoricalness, are removed from the authoritarian domination of a _Res externa_ , necessarily divine or deifiable. Love and metaphoricalness, thus deontologized or, in the extreme, dehumanized, henceforth constitute a determination of language with all its resources spread out. The subject himself/herself is merely a subject: a provisional accident, differently renewed within the only _infinite_ space where we might unfurl our loves, that is, the infinity of the signifier. _Love is something spoken, and it is only that_ : poets have always known it.
From now on amatory styles will be spread out before us like different historical embodiments of the metaphoricalness that is essential to loving states: like stylistic variants of the _cure_ , another name for _life_ , which the Western subject has experienced for two thousand years through his amorous attitudes, which have been inserted in amatory codes now made official.
NOTES
. I. A. Richards, _The Philosophy of Rhetoric_ , 1936 (London: Oxford University Press, 1965); Max Black, _Models and Metaphors_ (Ithaca: Cornell University Press, 1962); Roman Jakobson and Morris Halle, _Fundamentals of Language_ , 1956 (The Hague: Mouton, 1962); Jakobson, "La Métaphore," in _Languages_ 54 (1979).
. _Der Satz vom Grund_ (Pfullingen: Neske, 1957), pp. 77–90.
. Paul Ricoeur has lucidly discussed this problem, as well as the ensuing metaphysico-metaphorical deconstruction in the work of Jacques Derrida. See _La Métaphore vive_ (Paris: Seuil, 1975), pp. 356ff.
. As J. Vuillemin has shown in _De la logique à la théologie_ (Paris: Flammarion, 1967).
. Ricoeur, _La Métaphore vive_ , p. 344.
. _Metaphysics_ , book XII, ch. 5, 1071a, 33–35.
. Vuillemin, _De la logique à la théologie_ , p. 22.
. _Summa_ , Ia, question 13, art. 5.
. Ricoeur, _La Métaphore vive_ , p. 356.
Extraterrestrials Suffering for Want of Love
The Crisis
The analyst is by definition tuned in to the crisis: the analytical contract issues from an inevitable discontent. The existence of psychoanalysis thus reveals the permanency, the inescapable nature of crisis. The speaking being is a wounded being, his speech wells up out of an aching for love, and the "death drive" (Freud) or the "unbeing" (Lacan) that are coextensive with human nature determine, if they do not justify them, the discontents of civilizations.
Such a view is not necessarily a product of pessimism ("one can do nothing in the face of crisis, that is the way it is") or a disparagement of the present moment ("there is nothing new, things have always been like that"). Psychoanalytic fundamentalism nonetheless shifts the question's viewpoint. On the one hand, periods and societies that believe they are outside the crisis appear, in the psychoanalyst's eyes, symptomatic: through what miracle of repression, idealization, or sublimation has the discontent with "splitting" been stabilized, or even harmonized, within a code of believable, sound, permanent values? On the other hand, in the Jewish and Christian West, the analyst is able to identify a _perpetuum mobile_ that, nurturing the crisis basic to the speaking condition and sustained by it, creates the problems the West alone can resolve, although it never succeeds in doing so; and yet, it symbolizes them indefinitely in defilement and by passion, both henceforth universalized. In that case, where is the crisis? What makes up its painful image? Surely not a consciousness shattered by the unconscious, for the former can only recognize itself there, coil up, and speak of it, thus producing a new discourse, baroque or Joycean, witness to an "internal experiment" or to the shaping of a "theater of cruelty." If art may resemble a crisis, it is above all a resurrection. The crisis exists only for mirrors that are enamored of stable images; for calculators that are panic-stricken by swirling markets and currencies, for stabilizing consciences that believe in the contemporary divinity known as a "balance sheet." The analyst is neither an artist nor an accountant. Between the two, he is one of the last images of the fullness of passion.
What are analysands complaining of, dwellers in giant cities who have lost their bearings? Can we isolate _the_ contemporary sickness, the one that colors the end of the twentieth century and slips it into the third millennium?
The Abolition of Psychic Space
To say that _hatred_ or _death drive_ prevails in the complaint more than inhibited desire or a mistreated eros is right but insufficient. Freud already knew it, from _Beyond the Pleasure Principle_ (1920) up to _Civilization and Its Discontents_ (1929) and _Analysis Terminable and Interminable_ (1937). After him, and independently of him, it is remarkable that women analysts, from Melanie Klein to Sabine Spielrein, have not ceased emphasizing that morbid component of the psyche. Resistant to the notion of castration, a woman perhaps accepts it only when confronted with a dying body (her child's in the worst of cases). Moreover, the dramas of individuation demand of her such a violent rejection of the mother, and by the mother, that in the hatred of the loved object a woman immediately finds herself in a known and intolerable country.
What analysands are henceforth suffering from is _the abolition of psychic space_. Narcissus in want of light as much as of a spring allowing him to capture his true image, Narcissus drowning in a cascade of false images (from social roles to the media), hence deprived of substance or place: these contemporary characters are witnesses to our being unable today to elaborate primary narcissism.
Neither screen nor state, primary narcissism is already a structure, previous to the Oedipus complex, which operates on the basis of three terms. The central node of connection and disconnection, fullness and emptiness, positions and losses represents the instability of the _narcissistic subject_. He remains there, attracted on the one hand by the magnet of _primary identification_ , which is a father imagined to be loving, "father of individual prehistory," the seed of the Ego ideal; and on the other, by a magnet of desire and hatred, fascination and disgust, constituted by the archaic mother who has ceased to be a container of needs but not yet made up into a taboo object of desire: neither subject nor object, an _"abject"-mother_ , a place of warding off and differentiation, an infection. The breaking up of Christianity has left those three agencies in suspense.
The image of the Virgin—the woman whose entire body is an emptiness through which the paternal word is conveyed—had remarkably subsumed the maternal "abject," which is so necessarily intrapsychic. Lacking that safety lock, feminine abjection imposed itself upon social representation, causing an actual denigration of women; this in turn gave rise to increased antifeminism but even more so to a strong reaction on the part of women who were unwilling to bear, in narcissistic fashion, the representation of their own rejection of the maternal, which no available secular code could now guarantee. The first feminist generation rejected, through the "women-as-object," the narcissistic wound constituted by maternal sexuality and countered it with the image of the virile activist who was less a libertine than a monitor; the second advocated a centripetal, mitigated, soothed feminine sexuality, before unearthing, quite recently, under the guise of romances among women, sadomasochistic havoc.
In similar fashion, the lack of a secular variant of the loving father makes contemporary discourse incapable of assuming primary identification—the substratum for our idealizing constructions. Thus orphaned, the homosexuality of a man seeking a feminine stance facing the other man encounters only its immediate erotic fulfillment. As to the woman, she lacks a go-between in order to assimilate the supposedly paternal Law and finds herself thrown into paranoia.
Between those two absences in contemporary discourse, Narcissus does not have his own territory. Without a paternal value, he is the negative version of a homosexual, potential but empty of desire. Handed over to an abject mother, he can have no recourse to the holy virgin to liberate himself of her. Worse yet, as an emancipated modern, he does not dare give himself the right to fight her. Like John, he walls himself in, is inhibited, distraught, hermetic, wracked by nightmares, ready to plunge into drugs if he could allow himself to be a happy Narcissus. His thought escapes him, his speech appears to him as empty as his body. "There are blank spaces between each word," he says in sibylline fashion. He specifies that his words do not hold together, for there is a void that breaks them into syllables, purloins them, and blows them up before they settle down between himself and those he speaks with.
As for Juliet, she throws herself into orgies that leave her cold, humiliated, full of rage, and always ready to become ill in order finally to put a stop to the merry-go-round of a life controlled by a perverse father. The latter, a left-wing activist, gave his daughter to understand that stealing was part of the class struggle—until she got caught, thus punished for the father's greatest pleasure (secret, of course) and the mother's greatest shame. "I am trying to write," says Juliet, "but that isn't possible, for I have no place to settle down for that."
It is the paroxysmal consequence of a death drive that no object succeeds in hemming in, no idealization in displacing; the closeness to a psychosis that is more and more perceptible under the appearances of obsessions and hysteria—granted. But the frequency of psychotic symptoms in the area surrounding neuroses and perversions points to a deep challenge to _psychic space_ , of which psychoanalysis, its revolutionary explorer, has inherited the whole Western, speculative history.
Narcissus: My Fellow Being, My Brother
At the risk of simplifying, let us consider that this now destroyed _Psychic space_ was constituted at the waning of the Ancient world with the advent of the Christian era. The myth of Narcissus and its neo-Platonistic elaborations on the one hand, Christly passion on the other, mark out the outline of that space. Ovid's _Metamorphoses_ gave us the first complete version of that myth. Narcissus, that perverse child, appears in it as the first modern antihero, the nongod par excellence. His murky, swampy, invisible drama must have summed up the anguish of a drifting mankind, deprived of stable markers. The imposing body of Greek sculpture becomes scattered at the time of the other crisis constituted by the waning of the Ancient world, which gives rise to the unhealthy and hardly tragic story of an ordinary being who knows neither what he wants nor what he loves. A _novitas furoris_ is what we read in Ovid, a new madness. But who is the model for that?
The one in love with his fleeting reflection is in fact someone deprived of his own proper space. He loves nothing because he is nothing. When he realizes that the other, in the spring, is merely an image of himself, Narcissus, unable to withstand such represented property, commits suicide. He is resuscitated, however, and not only as the flower bearing the same name, which takes his body's place. Narcissus is compensated for by the genius of speculative thought, starting with Plotinus and up to the Fathers of the Church who rehabilitate the narcissian concern for one's own proper space, beyond the condemnation of the narcissistic error. Torn away from the Ancient city-state ( _polis_ ) now falling apart, thrown into the civilized world ( _oikoumene_ )—for which the present-day equivalent would be advanced mass-mediatization—man, seized by an unnamable solitude, was called upon to withdraw into himself and discover himself as a psychic being.
We have seen what efforts were made by Plotinus to build up the dignity inherited from ascetic solitude. His autarkic divinity proceeds by way of _reflections_ , it explicitly follows the narcissian dynamic of inessential and yet necessary reverberations and rebounds, for they stem not from Narcissus but from the One. These thoughts then bind together in its unity, through the immanence of transcendence, the very motion of reflection, thus erecting a new psyche. The Western soul is no longer that of a Platonistic "Eros pteros," obsessed with the supralunar world, but that of a thinking space fastened on the same through the intermediary of the One, both origin and light of thought. Western innerness thus asserts itself, _monos pros monon_ , establishing the space of psychic solitude. The dismal encounter between Narcissus and his death-bearing because fleeting image has been replaced by hands clasped in prayer—by being _alone-with-oneself_. Mythic tragedy has been changed into meditation and introspection. Henceforth there is an _inside_ , an internal life, to be contrasted with the _outside_. Plotinus is on the ridge of that separation, the solar outside of the One making up the contemplative inside of the Wise man, without any otherness.
To Love or to Think
Christly passion, by bringing in the _impossible_ , has jolted and opened up narcissism's calm contemplation, neutralized by the autarkic divinity's thought. Sin and passion indicate to Narcissus, who gazes at himself in the Beyond, that everything is not heavenly in this hell, and the son of God himself may be abandoned by his Father. The One is an Other in the agape of the Cross. Theological guile, however, did not forget that salvation, eventually, took over from narcissism. Not only must one love the other as one loves oneself, but God himself is amenable to our love only to the extent that we love our "own and proper" good. In connection with _Amor sui_ we have reread Thomas Aquinas, who, in the wake of Augustine, already preaches that the right way to love is "to love oneself," "for and because of God." We have thus noted that without any selfishness, which is indeed a very secondary phenomenon, the Angelic Doctor advocates recognizing one's "own proper good" as the only possible access to the _being good_ , which is God. Such an appropriation of God and, conversely, the deification of one's own proper good, is an awesome dialectic, through which, thanks to a creating, donating Third Party, the Church promises salvation to narcissism, which is henceforth entitled, thanks to God, to withdraw into itself.
As long as the Western Self could think of itself as an _Ego affectus est_ , with Bernard of Clairvaux for instance, its psychic space—introspective container of primary narcissism—remained safe and was constantly able to integrate crises. The heroism of an _Ego cogito_ , which Descartes brought in along Aquinas's whitewashed (i.e., more philosophical than theological) tracks, led to the conquest of the _outside_ , neglected in the narcissian salvation device. The outside of nature, to be subjugated by science; the outside of the pleasurable object, to be dominated through the sadomasochistic dynamics of libertine erotics. Galileo and Sade are the heroes of that conquering epic, whose ruin was heralded by Senatspräsident Schreber. In the eyes of this jurist, as interpreted by Freud, a person who, in the wake of humanism and the bourgeois revolution, experienced the impossibility of a stabilized psychic space (his own was shattered by rays and fundamental language), the unbeliever's world is established only through mystical delirium—thus always in a recourse to God, but a recourse that is henceforth devoid of meaning, insane. We have not escaped from the dilemma: Galileo and the revolutionary Sade on one side, the mad legislator Schreber on the other. The discontent always arises out of a repudiation of love—of the _Ego affectus est_.
There has been too much stress on the crisis in paternity as cause of psychotic discontent. Beyond the often fierce but artificial and incredible tyranny of the Law and the Superego, the crisis in the paternal function that led to a deficiency of psychic space is in fact an erosion of the loving father. It is for want of paternal love that Narcissi, burdened with emptiness, are suffering; eager to be others, or women, they want to be loved.
One has wrongly picked a quarrel with Freud in matters of sexuality: he supposedly did not understand women, he repressed his homosexuality, remained a Jewish, "uxorious" bourgeois.... Freud's discovery, which opened the royal road of sexuality, actually bears on the unbearable aspect of psychic space—an unbearable psychic space, hence laden with illusions, hallucinations, lies.... Let us think once more about all his outlines, sketches, topographies, and territories that he does not cease proposing and renewing, from the _Project for a Scientific Psychology_ (1895) to _Moses and Monotheism_ (1939). Lacan picked it up again, precisely in that place, to suggest, with the help of Borromean knot and topology, the vistas and infinitudes pertaining to the signifier's experience, which he no longer believes to be internal but wants to maintain amenable to spatialization, totalization, as well as controllable, mathematizeable. Is that possible?
On Eccentric Seeming: Imagination as Process
The stakes of psychoanalysis—but also its crisis—are there. Are we to build a psychic space, a certain mastery of the One, at the very heart of the psychic founderings of anguished, suicidal, and impotent people? Or on the contrary are we to follow, impel, favor breakaways, driftings? Are we concerned with rebuilding their own proper space, a "home," for contemporary Narcissi: repair the father, soothe the mother, allow them to build a solid, introspective inside, master of its losses and wanderings, assuming that such a goal is attainable? Or does not the abundance of sufferers who find their fulfillment, their relaxation, and their satisfaction only in intoxication (from drugs to sacred music, which do away with individuality and sex for the sake of infinity) indicate that a psychic era has come to an end?
I see psychoanalysis rather as the instrument of a departure from that enclosure, not as its warden. Does the old psychic space, the machinery of projections and identifications that relied more or less on neuroses for reinforcement, no longer hold together? Well, it may be because another mode of being, of unbeing, is attempting to take its place. We should not attempt to give it the outlines of the "own proper self" while assuring it of our authority as psychoanalysts and filling it with the psychological meaning of our interpretations. Let it remain floating, empty at times, inauthentic, obviously lying. Let it pretend, let the seeming take itself seriously, let sex be as unessential because as important as a mask or a written sign—dazzling outside, nothing inside.
Am I seeing the European psychic space toppling over into the Japanese? And asking the analyst to be the agent of a new reign of the inauthentic, the promoter of a socialist empire of "false selves"? Has not the art of all periods already blazed that trail?
To the extent that the analyst not only causes truths to emerge but also tries to alleviate the pains of John or Juliet, he is duty bound to help them in building their own proper space. Help them not to suffer from being mere extras in their lives or splinters of parceled out bodies carried along by the spate of their pleasure. Help them, then, to speak and write themselves in unstable, open, undecidable spaces. The free associations of analytic discourse paves the way for the polylogic of such a nomination and such eccentric writing. It is not a matter of filling John's "crisis"—his emptiness—with meaning, or of assigning a sure place to Juliet's erotic wanderings, but to trigger a discourse where his own "emptiness" and her own "out-of-placeness" become essential elements, indispensable "characters" if you will, of a _work in progress_. What is at stake is turning the crisis into a _work in progress_.
Speaking, writing? Is that not again building "one's own," be it polyvalent? While waiting for social institutions to integrate such extraterrestrials, those survivors of primary narcissism, it is still in the imagination and symbolic realizations that their faltering identity will best find a way to construct itself as necessarily false—imaginary. When behaviors and institutions will have integrated the failure of representation not as a misfire on the part of the machine or a suffering of the individual, but as an illusion among others, a new adjustment of narcissism will have been effected. It will remove guilt from the stable image and divest the transcendental Unity that insures its authenticity. It will actualize the seeming, the imagination. For such an open, undecidable psychic space, the crisis will not be a suffering but a sign within a framework whose truth lies in its ability to absorb seemings. I speak in favor of imagination as antidote for the crisis. Not in favor of "power to the imagination," which is the rallying cry of perverts longing for the law. But in favor of saturating powers and counterpowers with imaginary constructions—phantasmatic, daring, violent, critical, demanding, shy... Let them speak, the ET's shall live. Imagination succeeds where the narcissist becomes hollowed out and the paranoid fails.
Amatory Discourses and Transferences
Now imagination is a discourse of transference—of love. Through and beyond desire that longs for immediate consummation, love is edged with emptiness and supported by taboos. The fact that today we have no love discourse reveals our inability to respond to narcissism. Indeed, amatory relationship is based on narcissistic satisfaction on the one hand, on idealization on the other. If the "crisis" of psychic space sinks its roots into the "death of God," let us remember that for the West, "God is love." Paul's agape of the cross, John's "God is love," doubtless leave us cold, but empty, too. Freud, the post-Romanticist, was the first to turn love into a cure; he did this, not to allow one to grasp a truth, but to provoke a rebirth—like an amorous relationship that makes us good as new, temporarily and eternally. For transference, like love, is a true process of self-organization, comparable to what contemporary logical and biological theories call "open systems."
Psychoanalysis thus does not inaugurate a new amatory code, following on courtliness, libertine thought, romanticism, and pornography. It asserts the end of codes but also the permanence of love as builder of spoken spaces. If it shows that the transferential or amatory principle is indispensable for a body to be living rather than being a corpse under care, it paradoxically undramatizes the amorous relationship yet cathected in transference. The analytical pact, like Faust's pact with the devil, insures your renewal, your rebirth, your youth; against that background, your necessarily amorous crises might be temporary and unessential contracts. Freud had considered suggesting, among the powerful antidotes against the discontents of civilization, the amatory relationship; nevertheless he gave that up very quickly, for, in his view, if love furnishes an overwhelming feeling of fulfilled narcissism, nothing is more hurtful than a breakup. He forgot, however, in that text, to mention that the psychoanalytic cure continues to feed on a love that transcends the hazards of loves. A transference love that summons that ability to idealize at the very core of desire and hatred—hollowing out and relieving perversion.
John and Juliet precisely come looking for that ability at the analyst's, who is perhaps the only one to allow them to glimpse an abeyance of their narcissistic wounds. Without ideological, moral, or biased suggestions, but through a simple listening, lovingly absent-minded...
From Cherubino to ET
Thanks to Christian elaborations, Narcissus was able to rally, give himself musical and pictural dignity, and move generations on account of his metamorphoses. Into Cherubino, for instance. The one who, in Mozart's opera, knowing nothing about love, experiences a tenderness full of desire but does not know what it is.
Today Narcissus is an exile, deprived of his psychic space, an extraterrestrial with a prehistory bearing, wanting for love. An uneasy child, all scratched up, somewhat disgusting, without a precise body or image, having lost his specificity, an alien in a world of desire and power, he longs only to reinvent love. The ET's are more and more numerous. We are all ET's.
The only common ground between the contemporary symptom and Cherubino is that the language that tames and makes us love this being uprooted from psychic space remains always imaginary. Music, film, novel. Polyvalent, undecidable, infinite. A permanent crisis.
NOTES
1. On the topic of narcissism one might read Heinz Kohut, _The Analysis of the Self_ (New York: International University Press, 1971) and _The Restoration of the Self_ (New York: International University Press, 1977); Otto F. Kernberg, _Borderline Conditions and Pathological Narcissism_ (New York: Aronson, 1975); and works by André Green, especially _Narcissisme de vie, narcissisme de mort_ (Paris: Minuit, 1983), as well as _La Nouvelle Revue de Psychanalyse_ 13 (1976), for an overview and a fuller bibliography.
. For a psychoanalytic approach to the Japanese world, see Doi Takeo, _The Anatomy of Dependence_ (New York: Kodansha International, 1973).
. Sigmund Freud, _Civilization and Its Discontents_ (1930), in _Standard Edition_ , vol. 21.
Black Sun
Psychoanalysis—A Counterdepressant
For those who are racked by melancholia, writing about it would have meaning only if writing sprang out of that very melancholia. I am trying to address an abyss of sorrow, a noncommunicable grief that at times, and often on a long-term basis, lays claims upon us to the extent of having us lose all interest in words, actions, and even life itself. Such despair is not a revulsion that would imply my being capable of desire and creativity, negative indeed but present. Within depression, if my existence is on the verge of collapsing, its lack of meaning is not tragic—it appears obvious to me, glaring and inescapable.
Where does this black sun come from? Out of what eerie galaxy do its invisible, lethargic rays reach me, pinning me down to the ground, to my bed, compelling me to silence, to renunciation?
The wound I have just suffered, some setback or other in my love life or my profession, some sorrow or bereavement affecting my relationship with close relatives—such are often the easily spotted triggers of my despair. A betrayal, a fatal illness, some accident or handicap that abruptly wrests me away from what seemed to me the normal category of normal people or else falls on a loved one with the same radical effect, or yet... What more could I mention? An infinite number of misfortunes weigh us down every day... All this suddenly gives me another life. A life that is unlivable, heavy with daily sorrows, tears held back or shed, a total despair, scorching at times, then wan and empty. In short, a devitalized existence that, although occasionally fired by the effort I make to prolong it, is ready at any moment for a plunge into death. An avenging death or a liberating death, it is henceforth the inner threshold of my despondency, the impossible meaning of a life whose burden constantly seems unbearable, save for those moments when I pull myself together and face up to the disaster. I live a living death, my flesh is wounded, bleeding, cadaverized, my rhythm slowed down or interrupted, time has been erased or bloated, absorbed into sorrow... Absent from other people's meaning, alien, accidental with respect to naive happiness, I owe a supreme, metaphysical lucidity to my depression. On the frontiers of life and death, occasionally I have the arrogant feeling of being witness to the meaninglessness of Being, of revealing the absurdity of bonds and beings.
My pain is the hidden side of my philosophy, its mute sister. In the same way, Montaigne's statement "To philosophize is to learn how to die" is inconceivable without the melancholy combination of sorrow and hatred—which came to a head in Heidegger's _care_ and the disclosure of our "being-for-death." Without a bent for melancholia there is no psyche, only a transition to action or play.
Nevertheless, the power of the events that create my depression is often out of proportion to the disaster that suddenly overwhelms me. What is more, the disenchantment that I experience here and now, cruel as it may be, appears, under scrutiny, to awaken echoes of old traumas, to which I realize I have never been able to resign myself. I can thus discover antecedents to my current breakdown in a loss, death, or grief over someone or something that I once loved. The disappearance of that essential being continues to deprive me of what is most worthwhile in me; I live it as a wound or deprivation, discovering just the same that my grief is but the deferment of the hatred or desire for ascendency that I nurture with respect to the one who betrayed or abandoned me. My depression points to my not knowing how to lose—I have perhaps been unable to find a valid compensation for the loss? It follows that any loss entails the loss of my being—and of Being itself. The depressed person is a radical, sullen atheist.
Melancholia—Somber Lining of Amatory Passion
A sad voluptuousness, a despondent intoxication make up the humdrum backdrop against which our ideals and euphorias often stand out, unless they be that fleeting clearmindedness shredding the amorous hypnosis that joins two persons together. Conscious of our being doomed to lose our loves, we grieve perhaps even more when we glimpse in our lover the shadow of a long lost former loved one. Depression is the hidden face of Narcissus, the face that is to bear him away into death, but of which he is unaware while he admires himself in a mirage. Talking about depression will again lead us into the marshy land of the Narcissus myth. This time, however, we shall not encounter the bright and fragile amatory idealization; on the contrary, we shall see the shadow cast on the fragile self, hardly dissociated from the other, precisely by the _loss_ of that essential other. The shadow of despair.
Rather than seek the meaning of despair (it is either obvious or metaphysical), let us acknowledge that there is meaning only in despair. The child king becomes irredeemably sad before uttering his first words; this is because he has been irrevocably, desperately separated from the mother, a loss that causes him to try to find her again, along with other objects of love, first in the imagination, then in words. Semiology, concerned as it is with the zero degree of symbolism, is unavoidably led to ponder over not only the amatory state but its corollary as well, melancholia; at the same time it observes that if there is no writing other than the amorous, there is no imagination that is not, overtly or secretly, melancholy.
Thought—Crisis—Melancholia
Nevertheless, melancholia is not French. The rigor of Protestantism or the matriarchal weight of Christian orthodoxy admits more readily to a complicity with the grieving person when it does not beckon him or her into _delectatio morosa_. While it is true that the French Middle Ages rendered sadness by means of delicate tropes, the Gallic, renascent, enlightened tone tended toward levity, eroticism, and rhetoric rather than nihilism. Pascal, Rousseau, and Nerval cut a sorry figure—and they stand as exceptions.
For the speaking being life is a meaningful life; life is even the apogee of meaning. Hence if the meaning of life is lost, life can easily be lost: when meaning shatters, life no longer matters. In his doubtful moments the depressed person is a philosopher, and we owe to Heraclitus, Socrates, and more recently Kierkegaard the most disturbing pages on the meaning or lack of meaning of Being. One must, however, go back to Aristotle to find a thorough reflection on the relationship philosophers have maintained with melancholia. According to the _Problemata_ (30, I), attributed to Aristotle, black bile ( _melaina kole_ ) saps great men. The (pseudo-)Aristotelian reflection focuses on the _ethos-peritton_ , the exceptional personality, whose distinctive characteristic would be melancholia. While relying on the Hippocratic notions of four humors and temperaments, Aristotle breaks new ground by removing melancholia from pathology and locating it in nature but also and mainly by having it ensue from _heat_ , considered to be the regulating principle of the organism, and _mesotes_ , the controlled interaction of opposite energies. This Greek notion of melancholia remains alien to us today; it assumes a "properly balanced diversity" ( _eukratos anomalia_ ) that is metaphorically rendered by froth ( _aphros_ ), the euphoric counterpoint to black bile. Such a white mixture of air ( _pneuma_ ) and liquid brings out froth in the sea, wine, as well as in the sperm of man. Indeed, Aristotle combines scientific statement with mythical allusions as he links melancholia to spermatic froth and eroti, with explicit references to Dionysus and Aphrodite (953b, 31–32). The melancholia he evokes is not a philosopher's disease but his very nature, his _ethos_. It is not what strikes the first Greek melancholy hero, Bellerophon, who is thus portrayed in the _Iliad_ (VI, 200–203): "Bellerophon gave offense to the gods and became a lonely wanderer on the Aleian plain, eating out his heart and shunning the paths of men." Self-devouring because forsaken by the gods, exiled by divine decree, this desperate man was condemned not to mania but to banishment, absence, void... With Aristotle, melancholia, counterbalanced by genius, is coextensive with man's anxiety in Being. It could be seen as the forerunner of Heidegger's anguish as the _Stimmung_ of thought. Schelling found in it, in similar fashion, the "essence of human freedom," an indication of "man's affinity with nature." The philosopher would thus be "melancholy on account of a surfeit of humanity."
This perception of melancholia as an extreme state and as an exceptionality that reveals the true nature of Being undergoes a profound transformation during the Middle Ages. On the one hand, medieval thought returned to the cosmologies of late antiquity and bound melancholia to Saturn, the planet of spirit and thought. Dürer's _Melancholia_ (1514) was a masterful transposition into graphic art of theoretical speculations that found their highest expression with Marsilio Ficino. Christian theology, on the other hand, considered sadness a sin. Dante set "the woeful people who have lost the good of the intellect" in "the city of grief" ( _Inferno_ , III). They are "wretched souls" because they have lost God, and these melancholy shadows constitute "the sect of the wicked displeasing both to God and to His enemies"; their punishment is to have "no hope of death." Those whom despair has caused to turn violent against themselves, suicides and squanderers, are not spared either; they are condemned to turn into trees ( _Inferno_ , XIII). Nevertheless, medieval monks did promote sadness: as mystical ascesis ( _acedia_ ) it became essential as a means toward paradoxical knowledge of divine truth and constituted the major touchstone for faith.
Changing in accordance with the religious climate, melancholia asserted itself, if I may say so, in religious doubt. There is nothing more dismal than a dead God, and Dostoyevsky himself was disturbed by the distressing sight of the dead Christ in Holbein's painting, contrasted with the "truth of resurrection." The periods that witness the downfall of political and religious idols, periods of crisis, are particularly favorable to black moods. While it is true that an unemployed worker is less suicidal than a deserted lover, melancholia does assert itself in times of crisis; it is spoken of, establishes its archeology, generates its representations and its knowledge. A written melancholia surely has little in common with the institutionalized stupor that bears the same name. Beyond the confusion in terminology that I have kept alive up to now (What is melancholia? What is depression?), we are confronted with an enigmatic paradox that will not cease questioning us: if loss, bereavement, and absence trigger the work of the imagination and nourish it permanently as much as they threaten it and spoil it, it is also noteworthy that the work of art as fetish emerges when the activating sorrow has been repudiated. The artist consumed by melancholia is at the same time the most relentless in his struggle against the symbolic abdication that blankets him... Until death strikes or suicide becomes imperative for those who view it as final triumph over the void of the lost object...
Melancholia/Depression
I shall call _melancholia_ the institutional symptomatology of inhibition and asymbolia that becomes established now and then or chronically in a person, alternating more often than not with the so-called manic phase of exaltation. When the two phenomena, despondency and exhilaration, are of lesser intensity and frequency, it is then possible to speak of neurotic depression. While acknowledging the difference between melancholia and depression, Freudian theory detects everywhere the same _impossible mourning for the maternal object_. Question: impossible on account of what paternal weakness? Or what biological frailty? Melancholia—we again encounter the generic term after having demarcated psychotic and neurotic symptomatologies—admits of the fearsome privilege of situating the analyst's question at the intersection of the biological and the symbolical. Parallel series? Consecutive sequences? A dangerous crossing that needs to be clarified, another relationship that needs to be thought up?
The terms melancholia and depression refer to a composite that might be called melancholy/depressive, whose borders are in fact blurred, and within which psychiatrists ascribe the concept of "melancholia" to the illness that is irreversible on its own (that responds only to the administration of antidepressants). Without going into details about various types of depression ("psychotic" or "neurotic," or, according to another classification, "anxious," "agitated," "retarded," or "hostile"), or concerning myself with the promising but still imprecise field in which one studies the exact effects of antidepressants (monoamine oxidase inhibitors, tricyclics, and heterocyclics) or thymic stabilizers (lithium carbonates), I shall examine matters from a _Freudian point of view_. On that basis, I shall try to bring out, from the core of the melancholy/depressive composite, blurred as its borders may be, what pertains to a common experience of _object loss_ and of a _modification of signifying bonds_. These bonds, language in particular, prove to be unable to insure, within the melancholy/depressive composite, the autostimulation that is required in order to initiate given responses. Instead of functioning as a "rewards system," language, on the contrary, hyperactivates the "anxiety-punishment" pair, and thus inserts itself in the slowing down of thinking and decrease in psychomotor activity characteristic of depression. If temporary sadness or mourning on the one hand, and melancholy stupor on the other are clinically and nosologically different, they are nevertheless supported by _intolerance for object loss_ and _the signifier's failure_ to insure a compensating way out of the states of withdrawal in which the subject takes refuge to the point of inaction (pretending to be dead) or even suicide. Thus I shall speak of depression and melancholia without always distinguishing the particularities of the two ailments but keeping in mind their common structure.
The Depressive Person: Full of Hatred or Wounded, Mourned "Object" and Mourned "Thing"
According to classic psychoanalytic theory (Abraham, Freud, and Melanie Klein), depression, like mourning, conceals an aggressiveness toward the lost object, thus revealing the ambivalence of the depressed person with respect to the object of mourning. "I love that object," is what that person seems to say about the lost object, "but even more so I hate it; because I love it, and in order not to lose it, I imbed it in myself; but because I hate it, that other within myself is a bad self, I am bad, I am nonexistent, I shall kill myself." The complaint against oneself would therefore be a complaint against another, and putting oneself to death but a tragic disguise for massacring an other. Such logic presupposes, as one can imagine, a stern superego and a whole complex dialectic of idealization and devalorization of self and other, the aggregate of these activities being based on the mechanism of _identification_. For my identification with the loved-hated other, through incorporation-introjectionprojection, leads me to imbed in myself its sublime component, which becomes my necessary, tyrannical judge, as well as its subject component, which demeans me and of which I desire to rid myself. Consequently, the analysis of depression involves bringing to the fore the realization that the complaint against oneself is a hatred for the other, which is without doubt the substratum of an unsuspected sexual desire. Clearly such an advent of hatred within transference entails risks for the analysand as well as the analyst, and the therapy of depression (even the one called neurotic) verges on schizoid fragmentation.
Melancholy cannibalism, which was emphasized by Freud and Abraham and appears in many dreams and fantasies of depressed persons accounts for this passion for holding within the mouth (but vagina and anus also lend themselves to this control) the intolerable other that I crave to destroy so as to better possess it alive. Better fragmented, torn, cut up, swallowed, digested... than lost. The melancholy cannibalistic imagination is a repudiation of the loss's reality and of death as well. It manifests the anguish of losing the other through the survival of self, surely a deserted self but not separated from what still and ever nourishes it and becomes transformed into the self—which also resuscitates—through such a devouring.
Nevertheless, the treatment of narcissistic individuals has led modern analysts to understand another form of depression. Far from being a hidden attack on an other who is thought to be hostile because he is frustrating, sadness would point to a primitive self—wounded, incomplete, empty. Persons thus affected do not consider themselves wronged but afflicted with a fundamental flaw, a congenital deficiency. Their sorrow doesn't conceal the guilt or the sin felt because of having secretly plotted revenge on the ambivalent object. Their sadness would be rather the most archaic expression of an unsymbolizable, unnameable narcissistic wound, so precocious that no outside agent (subject or agent) can be used as referent. For such narcissistic depressed persons, sadness is really the sole object; more precisely it is a substitute object they become attached to, an object they tame and cherish for lack of another. In such a case, suicide is not a disguised act of war but a merging with sadness and, beyond it, with that impossible love, never reached, always elsewhere, such as the promises of nothingness, of death.
Thing and Object
The depressed narcissist mourns not an Object but the Thing. Let me posit the "Thing" as the real that does not lend itself to signification, the center of attraction and repulsion, seat of the sexuality from which the object of desire will become separated.
Of this Nerval provides a dazzling metaphor that suggests an insistence without presence, a light without representation: the Thing is an imagined sun, bright and black at the same time. "It is a well-known fact that one never sees the sun in a dream, although one is often aware of some far brighter light."
Ever since that archaic attachment the depressed person has the impression of having been deprived of an unnameable, supreme good, of something unrepresentable, that perhaps only devouring might represent, or an _invocation_ might point out, but no word could signify. Consequently, for such a person, no erotic object could replace the irreplaceable perception of a place or preobject confining the libido or severing the bonds of desire. Knowingly disinherited of the Thing, the depressed person wanders in pursuit of continuously disappointing adventures and loves; or else retreats, disconsolate and aphasic, alone with the unnamed Thing. The "primary identification" with the "father in individual prehistory" would be the means, the link that might enable one to become reconciled with the loss of the Thing. Primary identification initiates a compensation for the Thing and at the same time secures the subject to another dimension, that of imaginary adherence, reminding one of the bond of faith, which is just what disintegrates in the depressed person.
With those affected by melancholia, primary identification proves to be fragile, insufficient to secure other identifications, which are symbolic this time, on the basis of which the _erotic Thing_ might become a captivating _Object of desire_ insuring continuity in a metonymy of pleasure. The melancholy Thing interrupts desiring metonymy, just as it prevents working out the loss within the psyche. How can one approach the place I have referred to? Sublimation is an attempt to do so: through melody, rhythm, semantic polyvalency, the so-called poetic form, which decomposes and recomposes signs, is the sole "container" seemingly able to secure an uncertain but adequate hold over the Thing.
I have assumed depressed persons to be atheistic—deprived of meaning, deprived of values. For them, to fear or to ignore the Beyond would be self-deprecating. Nevertheless, and although atheistic, those in despair are mystics—adhering to the preobject, not believing in Thou, but mute and steadfast devotees of their own inexpressible container. It is to this fringe of strangeness that they devote their tears and jouissance. In the tension of their affects, muscles, mucous membranes, and skin, they experience both their belonging to and distance from an archaic other that still eludes representation and naming, but of whose corporeal emissions, along with their automatism, they still bear the imprint. Unbelieving in language, the depressive persons are affectionate, wounded to be sure, but prisoners of affect. The affect is their thing.
The Thing is inscribed within us without memory, the buried accomplice of our unspeakable anguishes. One can imagine the delights of reunion that a regressive daydream promises itself through the nuptials of suicide.
The looming of the Thing summons up the subject's life force as that subject is in the process of being set up; the premature being that we all are can survive only if it clings to an other, perceived as supplement, artificial extension, protective wrapping. Nevertheless, such a life drive is fully the one that, _at the same time_ , rejects me, isolates me, rejects him (or her). Never is the ambivalence of drive more fearsome than in this beginning of otherness where, lacking the filter of language, I cannot inscribe my violence in "no," nor in any other sign. I can expel it only by means of gestures, spasms, or shouts. I impel it, I project it. My necessary Thing is also and absolutely my enemy, my foil, the delightful focus of my hatred. The Thing falls from me along the outposts of significance where the Word is not yet my Being. A mere nothing, which is a cause, but at the same time a fall, before being an Other, the Thing is the recipient that contains my dejecta and everything that results from _cadere_ ("to fall")—it is a waste with which, in my sadness, I merge. It is Job's ashpit in the Bible.
Anality is summoned during the process of setting up this Thing, one that is our own and proper Thing as much as it is improper, unclean. The melancholy person who extols that boundary where the self emerges, but also collapses in deprecation, fails to summon the anality that could establish separations and frontiers as it does normally or as a bonus with obsessive persons. On the contrary, the entire ego of those who are depressed sinks into a diseroticized and yet jubilatory anality, as the latter becomes the bearer of a jouissance fused with the archaic Thing, perceived not as a significant object but as the self's borderline element. For those who are depressed, the Thing like the self is a downfall that carries them along into the invisible and unnameable. _Cadere_. Waste and cadavers all.
The Death Drive as Primary Inscription of Discontinuity (Trauma or Loss)
Freud's postulate of a _primary masochism_ is consonant with aspects of narcissistic melancholia in which the dying out of all libidinal bonds appears not to be a simple matter of turning aggressiveness toward the object back into animosity against the self but is asserted as previous to any possibility of object positioning.
Brought up by Freud in 1915, the notion of "primary masochism" became established in his work after the "death drive" turned up, particularly in "The Economic Problem of Masochism" (1924). Having observed that living beings appeared later than the nonliving, Freud thought that a specific drive must reside in them, which tended toward "a return to an earlier state." After _Beyond the Pleasure Principle_ (1920), which established the notion of the death drive as a tendency to return to the inorganic state and homeostasis, in opposition to the erotic principle of discharge and union, Freud postulated that one part of the death or destructive drive is directed toward the outside world, notably through the muscular system, and is changed into a purely destructive drive, one of ascendency or strong willpower. In the attendance of sexuality it constitutes sadism. Freud points out nevertheless that " _Another portion does not share in this transposition_ outwards: it remains inside... and becomes libidinally bound there. It is in this portion that we have to recognize the original, erotogenic masochism." Since hatred of the other was already considered "older than love," would such a masochistic withdrawal of hatred point to the existence of a yet more archaic hatred? Freud seems to imply that: indeed, he considers the death drive as an intrapsychic manifestation of a phylogenetic inheritance going back to inorganic matter. Nevertheless, aside from those conjectures that most analysts since Freud do not endorse, it is possible to note if not the anteriority at least the strength of the disintegration of bonds within several psychic structures and manifestations. Furthermore, the frequency of masochism, the presence of negative therapeutic reaction, and also various pathologies of early childhood that seem to precede the object relation (infantile anorexia, merycism, some forms of autism) prompt one to accept the idea of a death drive that, appearing as a biological and logical inability to transmit psychic energies and inscriptions, would destroy movements and bonds. Freud refers to it thus:
If we take into consideration the total picture made up of the phenomena of masochism immanent in so many people, the negative therapeutic reaction and the sense of guilt found in so many neurotics we shall no longer be able to adhere to the belief that mental events are exclusively governed by the desire for pleasure. These phenomena are unmistakable evidence of the presence of a power in mental life which we shall call the aggression or destruction drive, and which we trace back to the original death drive of living matter.
Narcissistic melancholia would display such a drive in its state of disunity with the life drive. The melancholy person's superego appears to Freud as "a cultivation of death drive." And yet the problem remains: is this melancholy diserotization opposed to the pleasure principle? Or is it, on the contrary, implicitly erotic? This would mean that the melancholy withdrawal would always be an overturning of the object relation, a metamorphosis of the hatred against the other. The work of Melanie Klein, who attached the greatest importance to the death drive, seems to have it depend, for the most part, on object relation, masochism and melancholia appearing then as imagos of the internalized bad object. Nevertheless, the Kleinian argument acknowledges situations in which erotic bonds are severed, without clearly stating whether they have never existed or have been broken off (in the latter case it would be the projection's introjection that would lead to such a withdrawal of erotic cathexis).
We shall take note particularly of the Kleinian definition of splitting introduced in 1946. On the one hand it moves backward from the depressive position toward a more archaic, paranoid, schizoid position. On the other, it distinguishes a binary splitting (the distinction between "good" and "bad" object insuring the unity of the self) and a parcellary splitting—the latter affecting not only the object but, in return, the very self, which literally "falls into pieces."
Integration/Nonintegration/Disintegration
For our purpose it is absolutely essential to note that such falling into pieces may be caused either by a drive-related _nonintegration_ impeding the cohesion of the self or by a disintegration accompanied by anxieties and provoking the schizoid splitting. In the first hypothesis, which seems to have been borrowed from Winnicott, nonintegration results from biological immaturity; if it is possible to speak of Thanatos in this situation, the death drive appears as a biological unfitness for sequentiality and integration (no memory). In the second hypothesis, that of a disintegration of the self consequent to reversing the death drive, we observe "a Thanatic reaction to a threat that is in itself Thanatic." Rather close to Ferenczi's concept, this one emphasizes the human being's tendency toward fragmentation and disintegration as an expression of the death drive. "The early ego largely lacks cohesion, and a tendency towards integration alternates with a tendency towards disintegration, a falling into bits... the anxiety of being destroyed from within remains active. It seems to me in keeping with the lack of cohesiveness that under the pressure of this threat the ego tends to fall into pieces." If schizoid fragmentation is a radical, paroxysmal manifestation of parceling, melancholy inhibition (psychomotor retardation, deficiency in sequentiality) can be considered another manifestation of the disintegration of bonds. How so?
Following upon the deflection of the death drive, the _depressive affect_ can be interpreted as a defense against parceling. Indeed, sadness reconstitutes an affective cohesion of the self, which restores its unity within the framework of the affect. The depressive mood constitutes itself as a narcissistic support, negative to be sure, but nevertheless presenting the self with an integrity, nonverbal though it might be. Because of that, the depressive affect makes up for symbolic invalidation and interruption (the depressive's "that's meaningless") and at the same time protects it against proceeding to the suicidal act. That protection, however, is a flimsy one. The depressive denial that destroys the meaning of the symbolic also destroys the act's meaning and leads the subject to commit suicide without anguish of disintegration, as a reuniting with archaic non-integration, as lethal as it is jubilatory, "oceanic."
Hence, schizoid parceling is a defense against death—against somatization or suicide. Depression, on the other hand, does without the schizoid anguish of fragmentation. But if depression is not fortunate enough to rely on a certain _erotization of suffering_ , it cannot act as a defense against the death drive. The relief that precedes some suicides perhaps translates the archaic regression by means of which the act of a denied or numbed consciousness turns Thanatos back on the self and reclaims the nonintegrated self's lost paradise, one without others or limits, a fantasy of untouchable fullness.
The speaking subject can thus react to trouble not only through defensive parceling but also through slowing down—inhibition, denial of sequentiality, neutralization of the signifier. Some immaturization or other neurobiological features tending toward nonintegration may condition such behavior. Is it a defensive one? Depressed persons do not defend themselves against death but against the anguish prompted by the erotic object. Depressive persons cannot endure Eros; they prefer to be with the Thing up to the limit of negative narcissism leading them to Thanatos. They are defended against Eros by sorrow but without defense against Thanatos because they are wholeheartedly tied to the Thing. Messengers of Thanatos, melancholy people are witness/accomplices of the signifier's flimsiness, the living being's precariousness.
Less skillful than Melanie Klein in presenting a new repertory of drives, the death drive in particular, Freud nevertheless seems drastic. As he sees it, the speaking being, beyond power, desires death. At this logical extreme, desire no longer exists. Desire becomes dissolved in a disintegration of transmission and a disintegration of bonds. Be it biologically predetermined, following upon preobject narcissistic traumas, or quite simply caused by inversion of aggressiveness, the phenomenon that might be described as a _breakdown of biological and logical sequentiality_ finds its radical manifestation in melancholia. Would the death drive be the primary (logically and chronologically) inscription of that breakdown?
Actually, if the death drive remains a theoretical speculation, the experience of depression confronts the observer as much as the patient with the enigma of mood.
Is Mood a Language?
Sadness is the fundamental mood of depression, and even if manic euphoria alternates with it in the bipolar forms of that ailment, sorrow is the major outward sign that gives away the desperate person. Sadness leads us into the enigmatic realm of _affects_ —anguish, fear, or joy. Irreducible to its verbal or semiological expressions, sadness (like all affect) is the _psychic representation of energy displacements_ caused by external or internal traumas. The exact status of such psychic representations of energy displacements remains, in the present state of psychoanalytic and semiological theories, very vague. No conceptual framework in the relevant sciences (particularly linguistics) has proven adequate to account for this apparently very rudimentary representation, presign and prelanguage. The "sadness" mood triggered by a stimulation, tension, or energy conflict within a psychosomatic organism is not a _specific_ answer to a release mechanism (I am not sad as a response to or sign for _X_ and only _X_ ). Mood is a "generalized transference" (E. Jacobson) that stamps the _entire_ behavior and all the sign systems (from motor functions to speech production and idealization) without either identifying with them or disorganizing them. We are justified in believing that an archaic _energy signal_ is involved, a phylogenetic inheritance, which, within the psychic space of the human being, is _immediately_ assumed by verbal representation and consciousness. Nevertheless, such an "assumption" is not related to what occurs when the energies that Freud calls "bonded" lend themselves to verbalization, association, and judgment. Let us say that representations germane to affects, notably sadness, are _fluctuating_ energy cathexes: insufficiently stabilized to coalesce as verbal or other signs, acted upon by primary processes of displacement and condensation, dependent just the same on the agency of the ego, they record through its intermediary the threats, orders, and injunctions of the superego. Thus moods are _inscriptions_ , energy disruptions, and not simply raw energies. They lead us toward a modality of significance that, on the threshold of bioenergetic stability, insures the preconditions for (or manifests the disintegration of) the imaginary and the symbolic. On the frontier between animality and symbol formation, moods—and particularly sadness—are the ultimate reactions to our traumas, they are our basic homeostatic recourses. For if it is true that those who are slaves to their moods, beings drowned in their sorrows, reveal a number of psychic or cognitive frailties, it is equally true that a diversification of moods, variety in sadness, refinement in sorrow or mourning are the imprint of a humankind that is surely not triumphant but subtle, ready to fight, and creative...
Literary creation is that adventure of the body and signs that bears witness to the affect—to sadness as imprint of separation and beginning of the symbol's sway; to joy as imprint of the triumph that settles me in the universe of artifice and symbol, which I try to harmonize in the best possible way with my experience of reality. But that testimony is produced by literary creation in a material that is totally different from what constitutes mood. It transposes affect into rhythms, signs, forms. The "semiotic" and the "symbolic" become the communicable imprints of an affective reality, perceptible to the reader (I like this book because it conveys sadness, anguish, or joy) and yet dominated, set aside, vanquished.
Symbolic Equivalents/Symbols
Assuming that affect is the most archaic inscription of inner and outer events, how does one reach the realm of signs? I shall accept Hanna Segal's hypothesis, according to which, beginning with separation (let us note that a "lack" is necessary for the _sign_ to emerge), the child produces or uses objects or vocalizations that are the _symbolic_ equivalents of what is lacking. Later, and beginning with the so-called depressive position, it attempts to signify the sadness that overwhelms it by producing within its own self elements alien to the outer world, which it causes to correspond to such a lost or shifted outerness; we are then faced with _symbols_ properly speaking, no longer with equivalencies.
Let me add the following to Hanna Segal's position: what makes such a triumph over sadness possible is the ability of the self to identify no longer with the lost object but with a third party—father, form, schema. A requirement for a denying or manic position ("no, I haven't lost; I evoke, I signify through the artifice of signs and for myself what has been parted from me"), such an identification, which may be called phallic or symbolic, insures the subject's entrance into the universe of signs and creation. The supporting father of such a symbolic triumph is not the oedipal father but truly that "imaginary father," "father in individual prehistory" according to Freud, who guarantees primary identification. Nevertheless, it is imperative that this father in individual prehistory be capable of playing his part as oedipal father in symbolic Law, for it is on the basis of that harmonious blending of the two facets of fatherhood that the abstract and arbitrary signs of communication may be fortunate enough to be tied to the affective meaning of prehistorical identifications and the dead language of the potentially depressive person can arrive at a live meaning in the bond with others.
Under the totally different circumstances of literary creation, for instance, the manic position as sheathing of depression—an essential moment in the formation of the symbol—can be manifested through the establishment of a symbolic lineage. We may thus find a recourse to proper names linked to a subject's real or imaginary history, with that subject declaring itself their heir or equal; what they truly memorialize, beyond paternal weakness, is nostalgic dedication to the lost mother.
At the outset we have objectal depression (implicitly aggressive) and narcissistic depression (logically previous to the libidinal object relation)—an affectivity struggling with signs, going beyond, threatening, or modifying them. Starting from such a setting, the line of questioning that I shall pursue could be summed up as follows: aesthetic and particularly literary creation, and also religious discourse in its imaginary, fictional essence, set forth a device whose prosodic economy, interaction of characters, and implicit symbolism constitute a very faithful semiological representation of the subject's battle with symbolic collapse. Such a literary representation is not an _elaboration_ in the sense of "becoming aware" of the inter- and intrapsychic causes of moral suffering; that is where it diverges from the psychoanalytic course, which aims at dissolving this symptom. Nevertheless, the literary (and religious) representation possesses a real and imaginary effectiveness that comes closer to catharsis than to elaboration; it is a therapeutic device used in all societies throughout the ages. If psychoanalysts think they are more efficacious, notably through strengthening the subject's cognitive possibilities, they also owe it to themselves to enrich their practice by paying greater attention to these sublimatory solutions to our crises, in order to be lucid counterdepressants rather than neutralizing antidepressants.
Is Death Nonrepresentable?
Having posited that the unconscious is ruled by the pleasure principle, Freud very logically postulated that there is no representation of death in the unconscious. Just as it is unaware of negation, the unconscious is unaware of death. Synonymous with absence of jouissance, imaginary equivalent of phallic dispossession, death could not possibly be seen. It is, perhaps, for that very reason that it opens the way to speculation.
And yet, as clinical experience led Freud to the notion of narcissism, ending in the discovery of the death drive and the second topography, he compelled us to recognize a vision of the psychic apparatus in which Eros is threatened with domination by Thanatos and where, consequently, the possibility of representing death should be examined from a different standpoint.
_Castration fear_ , glimpsed until then as underlying the conscious death anguish, does not disappear but is overshadowed by the _fear of losing the object_ or _losing oneself as object_ (etiology of melancholia and narcissistic psychoses).
Such an evolution in Freudian thought leaves us with two problems that have been emphasized by André Green.
First, what about the _representation_ of the death drive? Unknown to the unconscious, it is, with the "second Freud," a "cultivation of the superego," as one might put it in turning Freud's phrase around. The death drive splits the very ego into one component that is unaware of such drive while being affected by it (that is, its unconscious component) and another component that struggles against it (that is, the megalomaniac ego that negates castration and death and fantasizes immortality).
More basically, however, does not such a splitting cut across all discourse? The symbol is established through a negation ( _Verneinung_ ) of the loss, but a disavowal ( _Verleugnung_ ) of the symbol produces a physic inscription as close as one can get to hatred and a hold over the lost object. That is what one deciphers in the blanks of discourse, vocalizations, rhythms, syllables of words that have been devitalized and need to be restored by the analyst on the basis of an apprehended depression.
Thus, if the death drive is not represented in the unconscious, must one invent another level in the psychic apparatus where—simultaneously with jouissance—the being of its nonbeing would be recorded? It is indeed a production of the split ego, made up of fantasy and fiction—in short, the level of the imagination, the level of writing—which bears witness to the hiatus, blank, or spacing that constitutes death for the unconscious.
Dissociations of Forms
Imaginary constructions change the death drive into eroticized aggression against the father or terrified loathing of the mother's body. We know that at the same time as he discovered the power of the death drive Freud shifted his interest not only from the theoretical model of the first topography (conscious/preconscious/unsconscious) toward that of the second topography, but especially, and thanks to the shift, turned toward the analysis of imaginary productions (religions, arts, literature). He found in them a kind of representation of death anxiety. Does this mean that dread of dying—which henceforth is not summed up in castration fear but includes it and adds to it the wounding and perhaps even the loss of integrity of the body and the self—finds its representations in formations that are called "transconscious" in the imaginary constructions of the split subject, according to Lacan? Doubtless so.
The fact remains that another reading of the unconscious itself might locate within its own fabric, such as certain dreams disclose it for us, that nonrepresentative spacing of representation that is not the _sign_ but the _index_ of death drive. Dreams of borderline patients, schizoid personalities, or those undergoing psychedelic experiments are often "abstract paintings" or cascades of sounds, intricacies of lines and fabrics, in which the analyst deciphers the dissociation—or a nonintegration—of psychic and somatic unity. Such indices could be interpreted as the ultimate imprint of the death drive. Aside from the images of the death drive, necessarily displaced on account of being eroticized, the work of death as such, at the zero degree of psychicism, can be spotted precisely in the _dissociation of form_ itself, when form is distorted, abstracted, disfigured, hollowed out: ultimate thresholds of inscribable dislocation and jouissance...
Furthermore, the unrepresentable nature of death was linked with that other unrepresentable—original abode but also last resting place for dead souls, in the beyond—which, for mythical thought, is constituted by the female body. The horror of castration underlying the anguish of death undoubtedly accounts in large part for the universal partnership with death of the penis-lacking feminine. Nevertheless, the death drive hypothesis compels a different reasoning.
Death-Bearing Woman
For man and for woman the loss of the mother is a biological and psychic necessity, the first step on the way to becoming autonomous. Matricide is our vital necessity, the sine-qua-non condition of our individuation, provided that it takes place under optimal circumstances and can be eroticized—whether the lost object is recovered as erotic object (as is the case for male heterosexuality or female homosexuality), or it is transposed by means of an unbelievable symbolic effort, the advent of which one can only admire, which eroticizes the _other_ (the other sex, in the case of the heterosexual woman) or transforms cultural constructs into a "sublime" erotic object (one thinks of the cathexes, by men and women, in social bonds, intellectual and aesthetic productions, etc.). The lesser or greater violence of matricidal drive, depending on individuals and the milieu's tolerance, entails, when it is hindered, its inversion on the self; the maternal object having been introjected, the depressive or melancholic putting to death of the self is what follows, instead of matricide. In order to protect mother I kill myself while knowing—phantasmatic and protective knowledge—that it comes from her, the death-bearing she-Gehenna... Thus my hatred is safe and my matricidal guilt erased. I make of Her an image of Death so as not to be shattered through the hatred I bear against myself when I identify with Her, for that aversion is in principle meant for her as it is an individuating dam against confusional love. Thus the feminine as image of death is not only a screen for my fear of castration, but also an imaginary safety catch for the matricidal drive that, without such a representation, would pulverize me into melancholia if it did not drive me to crime. No, it is She who is death-bearing, therefore I do not kill myself in order to kill her but I attack her, harass her, represent her...
For a woman, whose specular identification with the mother as well as the introjection of the maternal body and self are more immediate, such an inversion of matricidal drive into a death-bearing maternal image is more difficult, if not impossible. Indeed, how can She be that bloodthirsty Fury, since I am She (sexually and narcissistically), She is I? Consequently, the hatred I bear her is not oriented toward the outside but is locked up within myself. There is no hatred, only an implosive mood that walls itself in and kills me secretly, very slowly, through permanent bitterness, bouts of sadness, or even lethal sleeping pills that I take in smaller or greater quantities in the dark hope of meeting... no one, unless it be my imaginary wholeness, increased with my death that accomplishes me. The homosexual shares the same depressive economy: he is a delightful melancholy person when he does not indulge in sadistic passion with another man.
The fantasy of feminine immortality perhaps has its basis in the feminine germinal transmission, capable of parthenogenesis. Furthermore, the new techniques of artificial reproduction endow the female body with unsuspected reproductive possibilities. If that feminine "allmightiness" in the survival of the species can be undermined through other technical possibilities that, or so it seems, might make man pregnant as well, it is likely that this latter eventuality could attract only a small minority, even though it fulfills the androgynous fantasies of the majority. Nevertheless, the essential component of the feminine conviction of being immortal in and beyond death (which the Virgin Mary so perfectly embodies) is rooted less in those biological possibilities, where it is hard to discern the "bridge" to the psyche, than in "negative narcissism."
In its climax, the latter weakens the aggressive (matricidal) affect toward the other as well as the despondent affect within oneself and substitutes what one might call an "oceanic void." It is a feeling and fantasy of pain, but anestheticized, of jouissance, but in suspense, of an expectation and a silence as empty as they are fulfilled. In the midst of its lethal ocean, the melancholy woman is the dead one that has always been abandoned within herself and can never kill outside herself. Modest, silent, without verbal or desiring bonds with others, she wastes away by striking moral and physic blows against herself, which, nevertheless, do not give her sufficient pleasures. Until the fatal blow—the definitive nuptials of the Dead Woman with the Same, whom she did not kill.
One cannot overemphasize the tremendous psychic, intellectual, and affective effort a woman must make in order to find the other sex as erotic object. In his philogenetic musings, Freud often admires the intellectual accomplishment of the man who has been (or when he is) deprived of women (through glaciation or tyranny on the part of the father of the primal horde, etc.). If the discovery of her invisible vagina already imposes upon woman a tremendous sensory, speculative, and intellectual effort, shifting to the symbolic order _at the same time_ as to a sexual object of a sex other than that of the primary maternal object represents a gigantic elaboration in which a woman cathexes a psychic potential greater than what is demanded of the male sex. When this process is favorably carried out, it is evidenced by the precocious awakening of girls, their intellectual performances often more brilliant during the school years, and their continuing female maturity. Nevertheless, it has its price in the constant tendency to extol the problematic mourning for the lost object... not so fully lost, and it remains, throbbing, in the "crypt" of feminine ease and maturity. Unless a massive introjection of the ideal succeeds, at the same time, in satisfying narcissism with its negative side _and_ the longing to be present in the arena where the world's power is at stake.
NOTES
_Note_ : All biblical references follow the text of The _Jerusalem Bible_ , Reader's Edition (Garden City, N.Y.: Doubleday, 1968)—Trans.
. See my _Tales of Love_ (New York: Columbia University Press, 1987).
. See _La Melanconia dell'uomo di genio_ (Genoa: Enrica Salavaneschi, 1981).
. On melancholia in the history of art and ideas see the basic work by Raymond Klibanski, Erwin Panofski, and Fritz Saxl, _Saturn and Melancholy_ (London: T. Nelson, 1964).
. See Karl Abraham, "Préliminaires à l'investigation et au traitement psychanalytique de la folie maniaco-depressive et des états voisins" (1912), in _Oeuvres complètes_ (Paris: Payot, 1965), 1:99–113; Sigmund Freud, "Mourning and Melancholia" (1917), in _Standard Edition_ , 14:237–58; Melanie Klein, "A Contribution to the Psychogenesis of Manic-Depressive States" and "Mourning and Its Relation to Manic-Depressive States," in _Contributions to Psychoanalysis, 1921–1945_ (London: Hogarth Press, 1948), pp. 282–338. Klein's "A Contribution" is reprinted in Peter Buckley, ed., _Essential Papers on Object Relations_ (New York: New York University Press, 1986).
. As was stressed in Pierre Fédida's "Le Cannibalisme mélancolique," in _L'Absence_ (Paris: Gallimard, 1978), p. 65.
. See Edith Jacobson, _Depression: Comparative Studies of Normal, Neurotic, and Psychotic Conditions_ (New York: International University Press, 1977); B. Grunberger, "Etude sur la dépression" and "Le Suicide du mélancolique," in _Le Narcissisme_ (Paris: Payot, 1975); G. Rosolato, "L'Axe narcissique des dépressions," in _Essais sur le symbolique_ (Paris: Gallimard, 1979).
. Having noted that, from the very dawn of Greek philosophy, holding on to the _thing_ is bound up with the utterance of a statement and the assertion of its truth, Heidegger nevertheless throws open the matter of the "historied" aspect of the _thing:_ "The question of the thing again comes into motion from its beginning" ( _What Is a Thing?_ W. B. Barton, Jr., and Vera Deutsch, trs. [Chicago: Henry Regnery, 1967], p. 48). Without going into the history of that conception of the thing but opening it up in the between that extends from the thing to man, Heidegger notes, through a reading of Kant, "that this _between_ as an anticipation _(Vorgriff)_ reaches beyond the thing and similarly back behind us" ( _ibid_., p. 243).
Through the opening created by Heidegger's question, but also following upon Freud's shaking up rational certainties, I shall speak of the _Thing_ as being the "something" that, seen by the already constituted subject looking back, appears as the unspecified, the unseparated, the elusive, even in its determination of actual sexual matter. I shall restrict the term _Object_ to the space-time constant that is verified by a statement uttered by a subject in control of that statement.
. Gérard de Nerval, _Aurelia_ , in _Selected Writings_ , Geoffrey Wagner, tr. (Ann Arbor: University of Michigan Press, 1957), p. 130.
. See Sigmund Freud, _The Ego and the Id_ , _Standard Edition_ , 19:31.
. One should differentiate my statement from that of Lacan, who discusses the notion of _das Ding_ starting from Freud's _Entwurf_ : " _Das Ding_ is not involved with what, in a manner somewhat reflexive to the extent that it can be made explicit, leads man to challenge his words as referring to the things they have nevertheless created. There is something else in _das Ding_. What there is is the true secret.... Something that wants. _The_ need and not just needs, pressure, emergency. The state of _Not des Lebens_ is life's state of emergency..., the amount of energy preserved by the body considering the response and what is necessary for the preservation of life" ( _L'Ethique de la psychanalyse_ , seminar of December 9, 1959 [Paris: Seuil, 1986], pp. 58ff.).
This would involve psychic inscriptions ( _Niederschrift_ ) earlier than the fourth year of life, always "secondary" for Lacan but close to "quality," to "effort," to the "endopsychic structure." "The _Ding_ as _Fremde_ , as an alien and even sometimes hostile place, at any rate as the first outside space... is that object, _das Ding_ , as the subject's absolute Other that must be recovered. It is recovered, at the most, as regret.... It is in the state of hoping and waiting for it that such optimal tension, on this side of which there is no more perception or effort, will be sought after in the name of the pleasure principle" (p. 65). And even more clearly: " _Das Ding_ is originally what we therefore call the beyond-the-signified. It is in relation to _that beyond-the-signified and a pathetic link to it that the subject maintains its distance and constitutes itself in such a world of relationships, of primary affect previous to any repression_. The entire first articulation of _Entwurf_ is built around that" (pp. 67–68). Nevertheless, while Freud emphasizes that the _Thing_ shows up only as a "cry," Lacan translates this as _word_ , playing on the ambivalent meaning of the word _mot_ in French (" _mot_ is that which is silent"). "The things we are dealing with... are things insofar as they are silent. And silent things are not quite the same as things that have no connection with words" (pp. 68–69; translation mine.—Trans.).
. "Significance" refers to semantic operations that are both fluid and archaic—with the latter word restricted to its Freudian sense. It refers to the work performed in language that enables a text to signify what representative and communicative speech does not say.—Trans.
. See Sigmund Freud, _Papers on Metapsychology_ , _Standard Edition_ 14:139.
. See Sigmund Freud, "The Economic Problem of Masochism," _Standard Edition_ 19:159–70.
. See Sigmund Freud, _An Outline of Psychoanalysis_ , _Standard Edition_ 23:139–207.
. "The Economic Problem of Masochism," _Standard Edition_ 19:163.
. _Papers on Metapsychology_ , _Standard Edition_ 14:139.
. See Sigmund Freud, "Analysis Terminable and Interminable," _Standard Edition_ 23:243.
. _The Ego and the Id_ , _Standard Edition_ 19:53.
. See Melanie Klein, _Developments in Psychoanalysis_ (London: Hogarth Press, 1952).
. See Jean-Michel Petot, _Melanie Klein, le moi et le bon objet_ (Paris: Dunod, 1932).
. Melanie Klein, _Developments in Psychoanalysis_ , p. 296.
. André Green, in _Narcissisme de vie, narcissisme de mort_ (Paris: Minuit, 1983), defines the notion of "negative narcissism" thus: "Beyond the parceling that fragments the self and brings it back to autoeroticism, _absolute_ primary narcissism demands the mimetic quietness of death. It seeks the non-desire of the other, nonexistence, which is another way of reaching immortality" (p. 278; translation mine.—Trans.).
. Concerning affect, see Jacobson, _Depression_ , and André Green, _Le Discours vivant_ (Paris: Presses Universitaires de France, 1971).
. See my _Revolution in Poetic Language_ , Margaret Waller, tr. (New York: Columbia University Press, 1984), ch. 1, secs. 2 and 5: "We understand the term 'semiotic' in its Greek sense: σημεων = distinctive mark, trace, index, precursory sign, imprint, trace, figuration.... This modality is the one Freudian psychoanalysis points to in postulating not only the _facilitation_ and the structuring _disposition_ of drives, but also the so-called primary processes which displace and condense both energies and their inscription. Discrete quantities of energy move through the body of the subject who is not yet constituted as such and, in the course of his development, they are arranged according to the various constraints imposed upon this body—always already involved in a semiotic process—by family and social structures. In this way the drives, which are 'energy' charges as well as 'psychical' marks, articulate what we call a _chora_ : a nonexpressive totality formed by the drives and their stases in a motility that is as full of movement as it is regulated" (p. 25). On the other hand, the _symbolic_ is identified with judgment and the grammatical sentence: "We shall distinguish the semiotic (drives and their articulation) from the realm of signification, which is always that of a proposition or judgment, in other words, a realm of _positions_. This positionality, which Husserlian phenomenology orchestrates through the concepts of _doxa_ , _position_ , and _thesis_ , is structured as a break in the signifying process, establishing the _identification_ of the subject and its object as preconditions of propositionality. We shall call this break, which produces the positing signification, a _thetic_ phase. All enunciation, whether of a word or of a sentence, is thetic. It requires an identification; in other words, the subject must separate from and through his image, from and through his objects. This image and objects must first be posited in a space that becomes symbolic because it connects the two separated positions, recording them or redistributing them in an open combinatorial system" (p. 43).
. See Hanna Segal, "Notes on Symbol Formation," _International Journal of Psychoanalysis_ 38 (1957): 391–97.
. See _On Narcissism_ (1914), _Standard Edition_ 14:73ff.; _Beyond the Pleasure Principle_ (1920), _Standard Edition_ 18:3ff.; and _The Ego and the Id_ (1923), _Standard Edition_ 19:3ff.
. Green, _Narcissisme de vie, narcissisme de mort_ , pp. 255ff.
. Thus the murder of the father in _Totem and Taboo_ (1913) or the deadly threatening vagina in _The Uncanny_ (1919).
_New Maladies of the Soul_
The Clinic: The Soul and the Image
_It is more important that men create the logos of the soul than of the body._
_—Democritus_
Do you have a soul? This question, which may be philosophical, theological, or simply misguided in nature, has a particular relevance for our time. In the wake of psychiatric medicines, aerobics, and media zapping, does the soul still exist?
Medicine or Philosophy?
Fruitful debates between ancient Greek doctors and philosophers caused the "psyche" to undergo some delicate variations before becoming the "anima" of the Latin Stoics. Doctors of antiquity returned to the metaphysical distinction between the body and the soul and came up with a viable analogy that prefigured modern psychiatry: they spoke of "maladies of the soul" that were comparable to maladies of the body. These maladies of the soul included the passions, from sadness to joy and even delirium. Although some doctors used this parallelism to support a "monistic" conception of human beings, for most of them, the radical difference between the psychic and somatic realms was confirmed by their mutual presence, if not their isomorphy.
Dualisms have prevailed since antiquity, some thought to consist of complementary dynamics of flux and others of troublesome contradictions. Despite scientific efforts that have attempted to reduce it to soma, the psyche, which we have failed to locate (is it in the heart? the humors? the brain?), has remained an implacable enigma. As a structure of meaning, the psyche represents the bond between the speaking being and the other, a bond that endows it with a therapeutic and moral value. Furthermore, by rendering us responsible to our bodies, the psyche shields us from biological fatalism and constitutes us as speaking entities.
Christ's incarnation, that is, the body-and-soul Passion of Man-God, gave momentum to the psychic dynamic that has been nurturing the inner life of Christian humanity for two thousand years. Passionate excesses directed toward the absolute subject—God or Jesus—ceased to be pathological. Instead, they were thought to map out the mystic itinerary of a soul aiming for the Ultimate. Before mental illness could be rethought, however, the dialectic of the Trinity had to be broken, anatomy had to adapt to the body, and the paroxysmal humors had to become objects of observation and surveillance. At that point, mental illness entrenched itself in the sacred space of the insane asylum. Michel Foucault has written a brilliant history of this clinic, which acknowledged the soul, but only as a sign of a sick body. Let us recall, however, that this gesture began well before the Age of Reason, for its roots can be traced to Greek philosophy and medicine, which introduced the distinction and analogy between maladies of the body and maladies of the soul. Like the ancient Greeks, modern psychiatrists—notably Philippe Pinel—have subscribed to physical and moral theories of the origins of mental illness.
Freud can be placed in this tradition, for he explicitly promoted a philosophical dualism that he developed through his conception of the "psychic apparatus"—a theoretical construction that is irreducible to the body, subject to biological influences, yet primarily observable in linguistic structures. Fixed firmly in biology by the drives yet contingent upon an autonomous logic, the soul, as a "psychic apparatus," gives rise to psychological and somatic symptoms and is modified during transference.
By giving priority to the psyche, however, the inventions of the unconscious and of transference do more than resurrect the ancient Greek debate about the soul and the body. What is more important, the Freudian notion of the psyche challenges this formerly presumed dualism and goes beyond the hypertrophy of the psychological that many see as the defining feature of psychoanalysis. In this vein, several aspects of psychoanalysis cross the boundary between body and soul and explore various elements that transcend this dichotomy: for instance, the energy component of drives, the determination of meaning through sexual desire, and the inscription of the treatment within transference, which is understood to be a repetition of prior psychosensory traumas. Nevertheless, the linguistic mechanism remains at the core of treatment: as a signifying construct, the speech of both the analysand and the analyst incorporates different _series of representations_. We recognize the diversity of these series, yet we can rightfully claim that they are primarily "psychic" in origin, irreducible as they are to the biological substrata that contemporary science has more or less categorized for us.
By proposing _different_ models of the soul, psychoanalysis expands our notion of the "psyche," acknowledges the peculiarities of our means of signification, and absorbs pathology into specific logical systems. Although the notion of psychological illness does not lose its specific validity, psychoanalysis tends to associate it with one of the logical possibilities inherent in any Freudian "psychic apparatus" or Lacanian "speakbeing" [ _parlêtre_ ]. Although the notions of "norm" and "anomaly" are also challenged, the impact of psychoanalysis is not confined to the ensuing subversion—one that has attracted libertarian spirits for almost a century. The emphasis on _meaning_ and the use of _eroticized speech_ in transference remain the most important features of the singular adventure of Freud's discovery.
Loyal to the ethics of the person that the West has developed within the folds of its philosophy, religion, and science, psychoanalysis appeals to the life of speaking beings by reinforcing and exploring their _psychic life_. You are alive if and only if you have a psychic life. However distressing, unbearable, deadly, or exhilarating it may be, this psychic life—which combines different systems of representation that involve language—allows you access to your body and to other people. Because of the soul, you are capable of action. Your psychic life is a discourse that acts. Whether it harms you or saves you, you are its subject. Our purpose here is to analyze psychic life, that is, to break it down and to start over. The substantial effects of meaningful representations have never been recognized and put to use with so much precision and force. With Freud, the _psyche_ is reborn. Enriched by the Judaic pluralism of its interpretations, the soul has evolved into a multifaceted and polyphonic psyche that is better equipped to serve the "transubstantiation" of the living body. Hence, we can appreciate the powerful synthesis Freud made of the traditions preceding his own, for by assigning a new value to the soul, Freud was able to elaborate a course of action that is at once therapeutic and moral.
Progress in the natural sciences, notably in biology and neurobiology, has enabled us to envision the death of the soul. Since we are continually decoding the secrets of neurons, their tendencies and their electrical dynamics, do we still have a need for this age-old chimera? Have we not come up with cognitive constructs that can account for cellular as well as human behavior?
However that may be, one cannot help noticing that the subject, whose soul was considered banished from the "pure" sciences, is making a triumphant comeback in the most sophisticated biological theories that make up cognitive science. "The image is present in the brain before the object," claim biologists. "Cognitive architecture is not limited by the nervous system; on the contrary, the nervous system is penetrated by the cognitive architecture that takes place there." "We cannot dispense with a teleonomy here." "I cannot see how we might conceive of mental functioning that did not include a representation of the goal, that is, that did not imply a subject that attempts to represent both itself and its expected goal."
Image before object, subject, teleonomy, representation: where is the soul to be found? If cognitive science is not to lead biology toward a spiritualist rebirth, we must ask how a soul is made. What kinds of representations and which logical varieties constitute the soul? Psychoanalysis does not necessarily have the answers to these questions, but it is the one discipline that is searching for them.
Can We Speak of New Patients?
At the same time, everyday experience points to a spectacular reduction of private life. These days, who still has a soul? We are all too familiar with the sort of emotional blackmail that reminds us of television serials, but this coercion is merely a by-product of the hysterical failure of psychic life that romantic dissatisfaction and middle-class domestic comedy have already depicted for us. As for the renewed interest in religion, we have reason to wonder if it stems from a legitimate quest, or from a psychological poverty that requests that faith give it an artificial soul that might replace an amputated subjectivity. For an affirmation emerges: today's men and women—who are stress-ridden and eager to achieve, to spend money, have fun, and die—dispense with the representation of their experience that we call psychic life. Actions and their imminent abandonment have replaced the interpretation of meaning.
We have neither the time nor the space needed to create a soul for ourselves, and the mere hint of such activity seems frivolous and ill-advised. Held back by his aloofness, modern man is a narcissist—a narcissist who may suffer, but who feels no remorse. He manifests his suffering in his body and he is afflicted with somatic symptoms. His problems serve to justify his refuge in the very problems that his own desire paradoxically solicits. When he is not depressed, he becomes swept away by insignificant and valueless objects that offer a perverse pleasure, but no satisfaction. Living in a piecemeal and accelerated space and time, he often has trouble acknowledging his own physiognomy; left without a sexual, subjective, or moral identity, this amphibian is a being of boundaries, a borderline, or a "false self"—a body that acts, often without even the joys of such performative drunkenness. Modern man is losing his soul, but he does not know it, for the psychic apparatus is what registers representations and their meaningful values for the subject. Unfortunately, that darkroom needs repair.
Of course, the society that shapes modern individuals does not leave them stranded. They can find one possibly effective solution for their problems in neurochemistry, whose methods can often treat insomnia, anxieties, certain psychotic states, and some forms of depression. And who could find fault with that? The body conquers the invisible territory of the soul. Let it stand for the record. There is nothing you can do about it. You are overwhelmed with images. They carry you away, they replace you, you are dreaming. The rapture of the hallucination originates in the absence of boundaries between pleasure and reality, between truth and falsehood. The spectacle is life as a dream—we all want this. Do this "you" and this "we" exist? Your expression is standardized, your discourse becomes normalized. For that matter, do you really have a discourse of your own?
If drugs do not take over your life, your wounds are "healed" with images, and before you can speak about your states of the soul, you drown them in the world of mass media. The image has an extraordinary power to harness your anxieties and desires, to take on their intensity and to suspend their meaning. It works by itself. As a result, the psychic life of modern individuals wavers between somatic symptoms (getting sick and going to the hospital) and the visual depiction of their desires (daydreaming in front of the TV). In such a situation, psychic life is blocked, inhibited, and destroyed.
We see all too easily, however, that this mutation may be beneficial. More than just a commodity or a new variant of the "opium of the people," the current transformation of psychic life may foreshadow a new humanity, one whose psychological conveniences will be able to overcome metaphysical anxiety and the need for meaning. Wouldn't it be great to be satisfied with just a pill and a television screen?
The problem is that the path of such a superman is strewn with traps. A wide variety of troubles can bring new patients to the analyst's couch: sexual and relationship difficulties, somatic symptoms, a difficulty in expressing oneself, and a general malaise caused by a language experienced as "artificial," "empty," or "mechanical." These patients often resemble "traditional" analysands, but "maladies of the soul" soon break through their hysterical and obsessional allure—"maladies of the soul" that are not necessarily psychoses, but that evoke the psychotic patient's inability to symbolize his unbearable traumas.
As a result, analysts must come up with new classification systems that take into account wounded "narcissisms," "false personalities," "borderline states," and "psychosomatic conditions." Whatever their differences, all these symptomatologies share a common denominator—the inability to represent. Whether it takes the form of psychic mutism or adopts various signs experienced as "empty" or "artificial," such a deficiency of psychic representation hinders sensory, sexual, and intellectual life. Moreover, it may strike a blow to biological functioning itself. In a roundabout manner, the psychoanalyst is then asked to restore psychic life and to enable the speaking entity to live life to its fullest.
Are these new patients a product of contemporary life, which exacerbates our familial situations and infantile difficulties and makes them into symptoms of a particular era? If not, are dependence on medicines and refuge in the image merely modern renditions of the narcissistic inadequacies common to all times? Finally, have patients changed or has analytic practice changed, such that analysts have sharpened their interpretations of previously neglected symptomatologies? These questions as well as others will be asked by the readers of this book, just as they are asked by its author. The fact remains, however, that analysts who do not discover a _new malady of the soul_ in each of their patients do not fully appreciate the uniqueness of each individual. Similarly, we can place ourselves at the heart of the analytic project by realizing that these new maladies of the soul go beyond traditional classification systems and their inevitable overhaul. What is more important, they embody difficulties or obstacles in psychic representation, difficulties that end up destroying psychic life. Revitalizing grammar and rhetoric, and enriching the style of those who wish to speak with us because they can no longer remain silent and brushed aside: do such projects not mirror the new life and new psyche that psychoanalysis wishes to unearth?
NOTES
. Jackie Pigeaud's excellent book _La Maladie de l'âme: Etude sur la relation de l'âme et du corps dans la tradition medico-philosophique antique_ (Paris: Les Belles Lettres, 1989) retraces the history of these issues and draws some epistemological and moral conclusions that are relevant to the contemporary human sciences. This book has greatly influenced my own thoughts on the subject.
. See Michel Foucault, _The Birth of the Clinic: An Archaeology of Medical Perception_ , A. M. Sheridan Smith, tr. (New York: Pantheon Books, 1973); and his _Madness and Civilization: A History of Insanity in the Age of Reason_ , Richard Howard, tr. (New York: Pantheon Books, 1965).
. See Philippe Pinel, _Treatise on Insanity_ , D. D. Davis, tr. (Birmingham, Ala.: Classics of Medicine, 1983); and his _Nosographie philosophique_ (Paris, 1813).
. See Pigeaud, _La Maladie de l'âme_ , p. 534.
. The dualist point of view is sustained throughout Freud's writings. It is most clearly exemplified by his opposition of the life drive and the death drive. "Our views have from the very first been dualistic and today more than ever more definitely dualistic than before—now that we describe the opposition as being not between ego instincts and sexual instincts, but between life instincts and death instincts." _Beyond the Pleasure Principle_ (1920), in _The Standard Edition of the Complete Psychological Works of Sigmund Freud_ , James Strachey, ed. (London: Hogarth Press, 1953–1974), 18:53.
. From _Project for a Scientific Psychology_ (1895) to _The Interpretation of Dreams_ (1900) and _Metapsychology_ (1915), this "psychic apparatus" adopts the form of two well-known topographical models (Conscious, Preconscious, Unconscious; and Superego, Ego, and Id). Freud's notion has not ceased to influence the work of his followers (Lacan and Bion have proposed their own variants of the psychic apparatus).
. Jacques Hochmann and Marc Jeannerot, _Esprit où es-tu? Psychanalyse et neuroscience_ (Paris: Odile Jacob, 1991), p. 71.
. Z. Pylyszyn, "Computation and Cognition: Issues in the Foundation of Cognitive Science," _Behavioural Brain Sciences_ , 1980, pp. 111–69. Cited by Hochmann and Jeannerot, _Esprit où es-tu?_ p. 81.
. Hochmann and Jeannerot, _Esprit où es-tu?_ p. 129.
. Hochmann and Jeannerot, _Esprit où es-tu?_ p. 53.
In Times Like These, Who Needs Psychoanalysts?
I am picturing a sprawling metropolis with glass and steel buildings that reach to the sky, reflect it, reflect each other, and reflect you—a city filled with people steeped in their own image who rush about with overdone makeup on and who are cloaked in gold, pearls, and fine leather, while in the next street over, heaps of filth abound and drugs accompany the sleep or the fury of the social outcasts.
This city could be New York; it could be any future metropolis, even your own.
What might one do in such a city? Nothing but buy and sell goods and images, which amounts to the same thing, since they both are dull, shallow symbols. Those who can or wish to preserve a lifestyle that down-plays opulence as well as misery will need to create a space for an "inner zone"—a secret garden, an intimate quarter, or more simply and ambitiously, a psychic life.
Yet that is where the story gets complicated. The West has been crafting this inner life since the beginning of the Christian era, when Plotinus transformed a Janus-faced Narcissus into two hands joined in prayer. Inner life has been reinforced by the spiritual path and carnival of the Middle Ages, and it has been shaped by Montaigne's fragile ego, Diderot's passions, and the meditations of Hegel and Kant. It has since become a psychic drama, a psychodrama.
Plotinus has degenerated into... Dallas. Indeed, the residents of this steel city are not in want of inner drama—in fact, they are as anxious, depressed, neurotic, and psychotic as the Freudian unconscious would wish them to be. If we believe, however, that we can escape from the surface value of our actions, we fall into the trap of psychology. Therefore, psychoanalysis has some work ahead of it, since Freud's doctrine seeks precisely to free us from this suppressed space of psychological ill-being.
The city that I chose as an image of contemporary life encourages us to include _social history_ as one of the elements of organization and permanency that constitute psychic life. Using the terminology of our industrial society, one could say that psychoanalysis turns money into time and joins painful affect with language—language that may be listless or indecipherable, but that is always directed toward other people. Such an extraordinary metamorphosis, which goes against the tide of the market economy as well as the neurosis that it patterns, may also shed light on psychosis. Two thousand years of inner experience have built this prison of the soul, a prison that offers psychoanalysis an innocent vulnerability in which it can pierce a hole that will serve to resound the polyphony of our motives.
Proust has accorded us the finest summary of what is becoming (or will soon become) the Freudian psyche: "Those who suffer feel closer to their soul." Or perhaps:
For even if we have the sensation of being always enveloped in, surrounded by our own soul, still it does not seem a fixed and immovable prison; rather do we seem to be borne away with it, and perpetually struggling to transcend it, to break out into the world, with a perpetual discouragement as we hear endlessly all around us that unvarying sound which is not an echo from without, but the resonance of a vibration from within.
Here, Proust evokes the permanency of the psyche and offers a glimpse of its limits. Freud has provided us with a preliminary method for achieving this sort of listening, but we still need to elaborate our approach. Our empathy and familiarity with the malady of the soul will enable us to transcend the psyche—forever.
The psychic realm may be the place where somatic symptoms and delirious fantasies can be worked through and thus eliminated: as long as we avoid becoming trapped inside it, the psychic realm protects us. Yet we must transform it through _linguistic activity_ into a form of sublimation or into an intellectual, interpretive, or transformational activity. At the same time, we must conceive of the "psychic realm" as a _speech act_ , that is, neither an acting-out nor a psychological rumination within an imaginary crypt, but the link between this inevitable and necessary rumination and its potential for verbal expression.
For this reason, the current onslaught of psychological illness, which takes the form of "soap operas" that inevitably cater to the other side of the society of performance and stress, seems to call out to psychoanalysis. "Tell us the meaning of our inner turmoil, show us a way out of it"—such is the cry of psychological helplessness, of the alter ego of the society, of the spectacle. As a result, psychoanalysis wagers to modify the prison of the soul that the West has made into a means of survival and protection, although this prison has recently been revealing our failings. This wager is therapeutic as well as ethical, and incidentally, political. Yet although we may seek the acceptance and even expansion of psychoanalysis, our wish is coming up against some substantial barriers.
I am not referring to the ever-present danger of transforming psychoanalysis into a normalization that would guide patients toward social success. Such a deterioration of psychoanalytic treatment, traditionally American, is widely known and denounced, and even if it remains a threat, resisting it was primarily a matter for the past that we still must keep in mind.
In my view, psychoanalysis will soon be confronted with two major issues that concern the problem of the organization and permanency of the psyche. The first issue pertains to its competition with the neurosciences. From now on, "take a pill or talk" may replace "to be or not to be." The second issue regards the challenge to which psychoanalysis is subject as a result of our desire to _remain in ignorance_ , a desire that is in harmony with the apparent simplicity that pharmacology offers, and that also reflects the negative narcissism of modern man.
Biology and Language: Freudian Drives and the Imaginary
The analytic position could be briefly outlined as follows: an unconscious psychic life is governed by determinants and restrictions that can be described and modified through an interpretation of the transference relation.
Some of these determinants and restrictions are _biological_ in nature: recent advances in neurobiology and pharmacology have had an impact on our _behavior_ and have enabled us to modify certain _fragments_ of psychic life. The connection between analytic treatment and these interventions is more topical than ever, and this link is attracting the attention of analysts—who consider each concrete situation to be a singular experience.
The "attack" of the neurosciences is not making psychoanalysis defunct, but it is encouraging us to reconsider the Freudian concept of the _drive_. The drive is a pivot between "soma" and "psyche," between biology and representation—the highest level of organization and permanency to which Freudian listening and theory can aspire—that is, to which analytic construction (or imagination) can aspire. For what we understand by biology is—drives and energy, if you wish, but always already a "carrier of meaning" and a "relation" to another person, even though this person may be yourself.
Owing to its dual nature (biological and energetic/semiotic), the drive is also a structure. Within the space between its source (an organ) and its aim (satisfaction), its strength or weakness governs the restrictions placed on each subject. These restrictions circumscribe relationships that are among the most stubborn, because they are the most archaic (ontoand phylogenetically speaking), and the most discordant in terms of linguistic expression. In addition, the ego and its object relation are shaped within this drive framework.
The structure of the subject bases itself upon the different positions of the ego with respect to the different modalities of the object, and we must underscore that egos as well as the types of objects formed within the space between drives and language are _diverse in nature_. Nevertheless, any Freudian analyst would know that these subjective structures are charged with both the fate of drives and their dual nature (one that stems from biology and _non_ linguistic representation).
For example, the fantasy, which could be considered a result of the eruption of the drive into the dispassionate logic of judgment—a logic that consequently finds itself transformed into a hallucination or a fit of delirium, reminds us that drives (and by implication, affects) form not only a myth, but also an element of organization and permanency that incites changes in the activity of thinking (as well as of judging and speaking). We also need to analyze the intermingling of drives and language with respect to the dulling of affects, to the disavowal of the object, and to the lifeless speech that characterizes those who suffer from depression.
That depression denies the meaning of discourse—which is to escort eros to the object—implies that the aggressive (or death) drive prevents a separation between the ego and the object. In its place, the death drive ushers in a melancholic subject—a negative Narcissus, an absolute master not of an object, but of a deadly _Thing_ that must never be lost.
In short, if we take the "myth" of the drive seriously, we must realize that an _imaginary deployment_ reconstructs the logic of the drive in order to free up the linguistic restrictions that ultimately govern our capacities as speaking beings. It does so to show that this element of organization and permanency (discourse) consists not only of myriad significations and logical implications or presuppositions, but also of an interruption of the ability to produce speech (which can be schizophrenic or depressive—the figures vary). This imaginary deployment thereby reveals itself as a privileged witness to the _meaning_ of the drive that joins the _signification_ of speech.
Once fascinated by linguistics, contemporary psychoanalysis has a growing interest in drives, an interest that stems from Freud's legacy as well as from the daunting impact of the neurosciences. As a result, contemporary psychoanalysis has been attempting to decode the drama of drives while going beyond the _signification of language_ that conceals the _meaning of drives_.
Traces of the meaning of drives can be translinguistic. Let us take the example of the voice: vocal stresses and rhythms often harbor the secret eroticism of depressed people who have severed the bond between language and the other, but who have nevertheless buried their affects in the hidden code of their vocalizations—in which the analyst may discover a desire that is not as dead as it may seem.
This brings me to the elements of organization and permanency that are the immediate object of analytic interpretation, insofar as they stem from our relation with others and are manifested through language. In light of what I have said concerning the primacy of drive destiny, these restrictions on signification would appear to constitute a complex, _heterogeneous_ structure that is formed from the first years of our lives, grows and develops alongside us, and ultimately determines our symbolic destiny.
As a result of the growth of linguistics and of the other "human sciences" during the 1960s, the notion of _structure_ in psychoanalysis (for which we are primarily indebted to Jacques Lacan) has enabled us to surmise more accurately than ever the organization of this _symbolic destiny_ , this "being of language" that governs psychic life. Freudian analysts will agree that a discourse or symptom with which someone entrusts us can be taken as a whole, whose parts can only acquire meaning through the relationship between speaking subjects and their addressee, notably their analyst.
What is more, Freudian analyses have already noted that while this network of signifying relations that characterize symptoms, discourses, transference, and subjects is a _theoretical construction_ , it is nevertheless the only _reality_ in which psychic life can be manifested and developed. A fortiori, it constitutes the sole reality that offers the analyst—to whom someone has made a direct request—the possibility of intervening and modifying it. This aspect of analysis brings up three pressing questions:
1. Can we reduce the fate of speaking beings to _language_ and _speech_ , or do other _systems of representation_ have a bearing on their logical features and on the actual psychic level that encompasses meaning for the subject?
2. Which characteristics of _interpretive language_ are able to echo the symbolic fate of subjects, and thus affect and modify their biological substratum?
3. If analytic treatment is capable of such modifications, how might we define its boundaries and its _ethics_?
• The growth of semiology, which has encouraged us to contemplate various signifying systems (the iconic code, the musical code, and so forth) that are irreducible to language (whether language is considered as a specific language or a discourse, a structure or a grammar, an utterance or an enunciation), has shattered "linguistic imperialism." In like manner, the return to Freud, and more specifically to his conception of _representation_ , has acknowledged the diversity of psychic representatives: thing-presentation, word-presentation, drive representative, affect representation. This has resulted in a "multilayered" model of psychic _signifiance_ , one that incorporates heterogeneous _marks_ and _signs_. Analysts must be aware of this polyphony if they wish to approach the discourse that is addressed to them from different linguistic and translinguistic levels (the voice, movement, and so forth) as well as to identify the levels that reveal the significance that discourse has for transference.
• In an ideal situation, interpretive silence would make these different structures of meaning, which shelter the subject's symptom, reverberate into his conscious. More directly and more frequently, however, analytic _interpretation_ is what reveals the diverse linguistic and translinguistic expressions of ill-being and restores them to the subject. How does it do this? By giving a name to the familial determinants that have tainted sexual development with a given symptom or structure. What is more important, though, is that interpretation offers an _appropriate formulation_ that is expressed in elliptical, metaphorical, or condensed terms and has a bearing on both the analyst's affects and its own series of psychic representatives (of words, things, and drives).
• A veritable poiesis comes into play here, one that includes the musical qualities of the voice as well as tropes and the rhetorical analysis of mental functioning. As the ultimate reality of transference and countertransference, this poiesis has an effect on conscious listening and exerts an influence on the patient's unconscious psychic representatives, which can be assumed to be closely related to the flux of the neurons that make up subcortical, "electrical," or "humoral" systems. Perhaps there is nothing that would form links between unconscious psychic representatives or separate them from the realm of neurobiology. Yet, while theoreticians and scientists are pondering the relationship between psychoanalysis and neurobiology, interpretive language is producing its own psychosomatic effects.
• If we take this to be true, we cannot help being struck by the violence of analytic interpretation. The mere fact that patients ask us to fulfill their request does not seem to justify such violence. Does their request not constitute an integral part of the symptom as well as the onset of its excess? Consequently, the ethics of psychoanalysis might base itself on two requirements that are characteristic of the Western rationalism from which it stems:
• On the one hand, there is a need to uphold a _single_ meaning, a _single_ truth that is valid and demonstrable in a given situation. This is the "normative" side of psychoanalysis. Indeed, the norm is dictated by the state of psychoanalytic theory and by any given analyst's position within it.
• On the other hand, there is a need to preserve respect (by way of freedom) for the patient's desire and jouissance, which are what determine his ability to accept our interpretation (since the structure of the patient emerges out of his particular resistance to our interpretation). At the same time, the validity of interpretation itself is challenged, for the analyst's jouissance is revealed, although it is clouded by the "truth" of his interpretive construction.
No other discourse in the history of Western rationalism has wagered to counterbalance truth and jouissance, authority and transgression. The ensuing equilibrium preserves the vitality of this discourse, a vitality that grows out of the immanence of death (the discourse of knowledge) and resurrection (the discourse of desire). As a result, psychoanalysis upsets the social contract, which is founded, according to Freud, on an act of murder. Analysts do not shy away from being dead fathers of knowledge, but they are also subjects of affect, desire, and jouissance. Consequently, they are distanced from schools and institutions and concentrate instead on restructuring other people's psyches.
Each Treatment Is Unique
Two phenomena prompt us to consider each analytic situation to be a specific microcosm: first, the various forms of psychic representation that turn toward language even though they are irreducible to its grammatical and logical structures, and second, the bipolarity of transference and countertransference that cloaks interpretive discourse.
To put it another way, although the psychiatric notions of "structure" (hysterical, obsessional, schizophrenic, paranoid, etc.) can offer an initial and rudimentary outline that the analyst may find useful, these notions are unable to withstand a microanalysis that is attentive to the diversity and polyvalence of psychic representatives. We have a growing interest in structural interferences as well as "borderline states" that go beyond their status as new clinical occurrences indicating the growth of subjectivity and psychic states, for they also have the advantage of challenging the foundation of traditional classification systems.
Hence, although the interest that psychoanalysts have in the linguistic and translinguistic expression of psychic determinants can sometimes make analysis appear abstract, this abstraction ends up personalizing each treatment as much as possible. Each treatment becomes an ideolect, a work of art, as well as a temporary installation of a new theoretical creation within the Freudian world. As a result, we would like to know which features of this discourse can be identified with Freudian thought, as well as where we can draw the line between loyalty, innovation, and dissension.
The history of the analytic movement combined with the current ecumenism of its tenets (Freudian, Kleinian, Winnicottian, Lacanian, and so forth) shows that despite various misunderstandings and impasses, Freud has staked out a path that all innovators must respect if they lay claims to psychoanalysis. It is admittedly a narrow path, one in which sexual experience resists language. This leads to repression and to the related necessity that we use language in order to interpret hidden unconscious signs. But it is also the path through which the eroticization of language within transference allows us to convey sexual experience and to relieve symptoms, which in turn endows us with a greater capacity for signification. Need I emphasize that in proposing that this be the goal of analysis, I am in no way advocating the normalization of the patient?
Two Obstacles to Analytic Speech
I shall briefly outline two examples of analytic treatment, examples that will serve to underscore my remarks and to point out two often-met obstacles to analytic speech.
_Depression_. Florence, a thirty-year-old woman who suffered from intense bouts of manic-depression, came to see me. She had previously attempted analysis with one of my colleagues, but she stopped going because she felt it was aggravating the intensity and frequency of her cycles. Florence had consulted a psychiatrist before coming to me. He put her on imipramine, but her previous analyst was unwilling to pursue treatment under such conditions.
At first we engaged in psychotherapy. After a while, though, Florence chose to lie down on the couch. She was still taking imipramine at the time. A few months later, she went off antidepressants and continued her analysis without taking any medication. Florence believed that imipramine had diminished her excessive anxiety and had allowed her to speak about the tragic events of her childhood and her life without falling back into the states of serious depression that she had often experienced. Her anxiety threshold seemed rather low, and its stabilization during treatment encouraged drives and their representatives to bond with verbal representations.
It seemed to me, however, that a certain distancing resulted from these chemical interventions—which seemed necessary though provisional. Nevertheless, I believed that in addition to the bonds they supported between drives and words, they offered another advantage. The introduction of a third party (medication, psychiatry) tempered Florence's manic elation—for she was not omnipotent and neither was I; a third party and an alternate reality were involved.
This also enabled us to tackle her narcissism, on the one hand, and its projection onto the exaggerated idealization with which she adorned me, on the other. Hence, a modified anxiety threshold made it possible to confront the manic-depressive devices that Florence had put into place in order to deal with loss and separation. A new object relation was established between us, one that was less catastrophic and less threatened by the unbearable danger of the annihilation she feared might follow a real or imaginary separation. Once this new object relation—which was also a new subjective structure—became stronger, Florence stopped taking imipramine. From that point on, she tried to rely solely on the symbolic and imaginary network that we had built up through the "regional" help of imipramine. She did so without resorting to chemical products, but to the psychic representatives we had restructured and whose disorganization was much less threatening to her than before.
During the portion of the analysis in which she was taking imipramine, I had the impression that the intensity of her drives was in check, but that her discourse was "numbed." My feeling arose primarily from the fact that while taking imipramine, Florence was able to have dreams pertaining to anxiety states that she had previously been unable to represent—the anxiety of being swallowed up and devoured by her mother, and inversely, the anxiety of swallowing up and devouring her mother. Yet even though Florence was able to have and report these dreams (which already was a substantial psychic development as compared to the depressive silence and "blank death" of the depressed signifier that had once characterized her), she approached her dreams with a sense of distance and a defensive lack of understanding. Then, in the second phase of the analysis, we were able to return to these dreams and analyze them.
First dream: A dream about a cannibalistic wedding. The wedding resembles her parents' wedding photo. In this dream, the guests eat each other's body parts and heads. The scene takes place in the staircase of my building.
Second dream: Florence vomits after the sex act, and her mother's head falls into the basin. She has this dream just before becoming pregnant.
In what way were we able to return to these dreams? Florence, who became a mother during her analysis and who continued treatment without the use of medication, had nevertheless developed another symptom. She had become very frightened by her relentless and exhausting fantasies of assassinating her daughter, and she never tired of telling me how preoccupied she was with these obsessions. Florence specified that she did not really feel capable of acting out her fantasies, although she was quite worn out by her phantasmatic ruminations.
I said, "assassin—basin—assimilate." By way of this interpretation—which was highly condensed and which bore witness to a tragic, grotesque poetics—Florence was able to ascertain the meaning of her drives as well as the symbolic signification of her two previous dreams. Then, she could relate them to her current anxieties. Her desire to assassinate her daughter was a by-product of her desire to assimilate (devour) imipramine, and more important, to absorb the head and body parts (breast, basin [ _sein_ , _bassin_ ] of her mother (the cannibal dream) that she chose to spit up into a basin (the vomiting dream) in order to make a place for her own child (to become pregnant, to occupy her own basin).
The meaning of drives in her dreams had already taken effect in her psyche by pushing aside her depressive symptoms, if only because her effort to report her dreams came to replace a melancholic silence. Nevertheless, the meaning of her drives failed to attain the signification of speech, and my interpretations spurred no associations. Eventually, however, the meaning of her drives was able to attain a symbolic signification, a working-out.
_Assassin—basin—assimilate_. I considered my interpretation to be a "vibration from within" (as Proust would say) that resounded between inexpressible, anxiety-ridden, or depressive drive representatives and an explanation that the patient, with the help of certain aspects of my interpretation, came up with herself—an explanation of her depressive side as well as her manic one. Florence did not wish to assassinate her daughter. She merely wished to reject the image of the daughter that she herself was, the assassin-cannibal daughter that constituted her self-image, a daughter who assimilated, devoured, and "vomited" her mother in order to avenge her infantile paralysis (her immobility from the basin) that had seriously handicapped her when she was very young and had separated her from her mother (orality is often overinvested in order to encompass an object that has eluded a failing motivity).
Like the explanatory, rhetorical work we subsequently engaged in, my transferential word-play resulted from my empathy with my patient's drive economy. I identified with her narcissistic wound and her oral voracity, as well as with her manic attempts to use devouring and evacuation to avenge the depressive _Thing_ for which there were no linguistic signs, but only echolalia that bore the intensities of her drives. My interpretation reintroduced this drive economy into the assassin's divested language (Florence wanted to kill, but she felt detached and distanced from her otherwise obsessive desire). What may have appeared to be "word-play" served to revitalize language and transference, on the one hand, and the analysand, on the other. My interpretation accomplished this by recalling infantile time and the history of the archaic fantasy, and by compensating for a narcissistic wound.
I would like to emphasize a few aspects of this analytic fragment that I consider to be of paramount importance for psychoanalysis today and, why not, tomorrow.
• The role that pharmacology played in this treatment leads me to believe that the dialogue between neuroscience and psychoanalysis will follow two basic trends. First, there will be an increasing number of patients who undergo joint treatments (pharmacological and psychoanalytic), and this alliance will require an accurate assessment of the effects of medication as well as of their interaction with transference. Second, the public will need to be made aware of the vast array of psychological illnesses that are not targeted by pharmacology—illnesses that reaffirm the need for traditional psychoanalytic treatment. We require a more precise analysis of the relationship between the psychic apparatus and transference. In other words, our analyses will have to be attentive to the "translatability" of drives into words.
• The "signifier of death" is readily apparent to analysts who are aware of the depressive speech that results from the patient's _disavowal of the signifier_ ("lifeless" speech that is painstaking, void, monotonous, accelerated yet self-effacing, "nonexistent"), and from the devalorization of language as an aspect of transference.
• Desire and the determinants of the symptom that are not signified within speech, however, seem to have deposited or coded their meaning in the preverbal register (of voice and intonation) or in a homophony that leads to the play of signifiers, or to an echolalia.
• Analytic interpretation may become a temporary party to regression and stagnation by making itself an echo of such meaning while serving as a bridge to intellectualization and to conscious formations not only of trauma but also of desire that works within a language directed toward the other.
• Depression appears to stem from a relation to the other that is not separated from depressed subjects, but that remains under their grasp in the form of their _Thing_ , which is unnameable and deadly (we discovered this symbiotic reunion in the "paradise not lost" of the "suicide wedding"). This particular object relation is clearly embedded in the "form" as well as the "content" of depressive discourse: both object relations and the structure of discourse function at the same level as the determinants of depression. Consequently, the intervention of analysis depends, or should depend (by way of its form and signification), on these two permanent factors of the subject's psyche—the _object_ and _discourse_.
_Perversion_. The following factors have led to my interest in perversion, a disorder that is quite widespread these days and particularly resistant to analysis:
• Narcissistic satisfaction by a part object is supplemented by a fetishist and exhibitionist discourse of someone who is all-knowing and has no desire to learn.
• The overestimation of speech becomes a resistance to analysis: _affects_ are split from the _discourse_ that recounts the perverse fantasy. This sort of isolation persists even when a fantasy is reported to the analyst with the unconscious intention of including him in the patient's sadomasochistic economy.
• As a result, it may prove necessary to verify that _the image_ and _the representations of the perverse act_ are _possible_ within transference. This sort of actualization of the perverse _scenario_ within the treatment mobilizes the intensities of the preverbal affect or drive representatives, and constitutes a precondition for their "translation" into interpretive speech.
Didier entered into analysis with the complaint that he was unable to have any satisfying sexual relations. It soon become apparent that his sexuality was voyeuristic and exhibitionist, masturbatory, and one in which sadomasochistic scenarios gave him the most pleasure. Didier was an amateur painter, though he never showed his paintings to anyone except his mother, while she was still living. Ever since his "audience" had died, his mother's apartment was closed off, and Didier dared not lay a finger on it or sell it.
Didier's discourse remained very fluent throughout his analysis. He knew everything and needed nothing from me. By way of his masturbatory speech, which bore witness to an exorbitant infantile power, Didier described his rituals as if he were reading a film script, coldly exposing the actions of actors whom he directed from afar. I had a feeling—or a countertransferential conviction—that Didier's secret resided in his mother's apartment, as well as in a _secret discourse_ that entombed his drives and affects and prevented them from coming forth in his speech. This patient's speech was cut off from his affects; his affects were not to be found in his speech.
As a result, I agreed to look at Didier's artwork, which consisted of collages made of cut-up posters drenched or daubed with colors, of blank pages, and so forth. Didier's voice became increasingly animated. He would explain his paintings to me from the couch, or he would show me a photograph that allowed me to follow his remarks. Nevertheless, his discourse remained neutral, technical, and aesthetic. It was I who had to come up with the perverse signification of his exposition—of the cut-up organs, of the fecal substances. During the treatment, I allotted Didier a certain perverse acting-out—that is, the display of his paintings—and I transplanted onto this demonstration the discourse of the antiperversion that he lacked.
He accepted this perverse fantasy—his or mine?—and his phantasmatic potential was thereby unleashed. Fantasies grew to replace his periods of acting-out without completely eliminating them. Nevertheless, since Didier was able to integrate them and to work them out by way of his discourse, he lost his relentless need to act out. Thus, he was able to create a new and more complex psychic structure.
In the pervert's case, the other is reduced to being the agent of the subject's sadomasochistic pleasure—which also ensures the subject's omnipotence. Although the ensuing discourse displays the logical and grammatical features of normative speech, it holds no heuristic or commutative value. Indeed, the unconscious meaning that it actually conveys resides in the neutralization of the other (the analyst) and in the reduction of a perverse megalomania into an object-fetish. If we wish to be privy to the workings of this unconscious determination, the speech-fetish must be dismantled. The analyst can use words to enrich the scenario- _image_ , as well as the _act_ that is in fact the pervert's "real language." And it will then become possible to endow speech with the multifaceted, heuristic, and commutative dimension it once had—the dimension in which the subject's complexity will be played out, and not the pervert's repudiation.
Insofar as the onset of transference is contingent upon the desire to know, to know _oneself_ , and to transform _oneself_ and grow, we have reason to wonder if this subjective pose is not historically determined. This subjective desire can appear in various guises, ranging from the ethical demands of a Jewish God to the Trinitarian mystery of Christian subjectivity and even to the "what do I know?" put forth by Montaigne, whose split ego prefigures in many ways the one that Freud has described. These different forms can be seen as foundations of Western history as well as of psychoanalysis (in the sense of an infinite appropriation of memory into a new history of subjects made ill by their symptoms). On the other hand, satisfying the narcissistic discontent that accompanies the modern crisis of values seems to be at odds with this sort of psychic inquiry, an inquiry that seems necessary for any transformation of subjectivity.
Psychoanalysis goes against the grain of the modern convenience that calls attention not to the end of the Story of Civilization but to end of the possibility of _telling a story_. Nevertheless, this end and this convenience are beginning to overwhelm us, and we have been led to criticize and to reject them.
Be that as it may, psychoanalytic technique cannot ignore this narcissistic withdrawal and decline of desire. Psychoanalysis will need to acknowledge and assimilate these conditions before it can attempt to go further and to strive for a new form of self-knowledge, one that Freud has already outlined by placing the "malady" at the very essence of the psyche and by making psychic life into an interminable construction-destruction. The psychoanalytic approach to depression and perversion, among other "modern" symptoms, shows that the analytic field is reaching out to the very boundaries that offer it the most resistance.
In my view, contemporary psychoanalysis, and especially that of the future, is an art—I admit, an artifice—that may allow the men and women of our modern, sleek, lofty, costly, and profit-bearing cities to preserve a life for themselves. Why? Because the speaking being's life begins and ends with psychic life, a life for which speech is one axis of a heterogeneous dynamic. Freudian psychoanalysis has more to offer than a simple refuge for a society of spectacle and consumption. While acknowledging and assimilating the logic of monetary exchange, it also overthrows our alienating metropolises and incites real change. If it fails to do this, what else will inspire change, faced as we are with the glow of our silver high-rises, the implacable banality of banks, and the fact that destiny is being programmed into the genetic code itself?
Therefore, I suggest that in the future, psychoanalysis may be one of the few remaining endeavors that will allow change and surprise, that is, that will allow life. It will remain cognizant of the elements of psychic permanency (from biology to drives and language), but it will also provide support for those who wish to alter these elements. For by remaining loyal to Freud's skepticism while recognizing the resiliency of psychic discourse, we contend that such a modification is possible.
NOTES
. Marcel Proust, "Les Plaisirs et les jours," _Jean Santeuil_ (Paris: Bibliothèque de La Plèiade, 1971), p. 6.
. Marcel Proust, _Swann's Way_ , in _Remembrance of Things Past_ , vol. 1, C. K. Scott Moncrieff and Terence Kilmartin, trs. (New York: Random House, 1981), p. 93.
. André Green, _Narcissisme de vie, narcissisme de mort_ (Paris: Minuit, 1983).
. Julia Kristeva, _Black Sun: Depression and Melancholia_ , Leon S. Roudiez, tr. (New York: Columbia University Press, 1989).
PART 4
_Individual and National Identity_
Powers of Horror
_Pouvoirs de l'horreur_ was originally published in Paris by Editions du Seuil in 1980. It was translated as _Powers of Horror_ , by Leon Roudiez for Columbia University Press in 1982. Part of that translation appears here. In _Powers of Horror_ , Kristeva analyzes the separations necessary to set up identity. She applies her analysis of perversion and phobia to the work of Louis-Ferdinand Céline.
In _Powers of Horror_ , relying on the work of Mary Douglas in _Purity and Danger_ (1969), Kristeva defines a notion of abjection with which she diagnoses separation and identification in both individuals and nations or societies. In the first chapter, "Approaching Abjection," Kristeva suggests that the abject is not, as we might ordinarily think, what is grotesque or unclean; rather it is what calls into question borders and threatens identity. The abject is on the borderline, and as such it is both fascinating and terrifying. Ultimately, the abject is identified with the maternal body since the uncertain boundary between maternal body and infant provides the primary experience of both horror and fascination.
As Kristeva describes the process of separation in _Powers of Horror_ , the infant must go through a stage of abjection in which it "abjects," or finds abject, its mother's body. In order to be weaned the infant must find its mother's body both fascinating and horrifying. The (male) infant experiences a horror at its dependence on the maternal body that allows the weaning process; but the (male) infant also experiences a fascination with the maternal body that allows an eroticization of the female body. In a 1980 interview in _Women Analyze Women_ , Kristeva suggests that her description of the process of abjection as a splitting of the mother into sublime and terrifying in _Powers of Horror_ applies only to males (see part 5 in this volume). Females do not split the mother, but merely try (unsuccessfully) to rid themselves of her. She diagnoses female sexuality as a melancholy sexuality in _Black Sun_.
With her theory of abjection Kristeva challenges Lacan's account of the acquisition of language and onset of self-consciousness through the mirror stage and castration threats. Before the mother or the maternal body becomes an object for the infant, it is an abject. It is neither object nor nonobject, but something in between. Kristeva resists both Freud's and Lacan's identification of the maternal body as the infant's first object. She insists that there is a process of identification and separation that complicates the infant's relation with the maternal body. The maternal body is not simply an object, or the first object, or even a partial object, for the infant. Subjectivity is a process that is set in motion long before Lacan's mirror stage.
In "From Filth to Defilement," Kristeva also challenges Freud's analysis in _Moses and Monotheism_ where he maintains that the social is set up against the murder of the father. Here, Kristeva claims that the social is set up against the feminine, specifically the maternal. The social is defined by repressing maternal authority. She emphasizes the shift from matriarchy to patriarchy that accompanies the shift from polytheism to monotheism. Here she extends her analysis of the way in which an individual identity is constructed against the exclusion of the abject maternal body to the way in which a cultural or national identity is constructed against the exclusion of maternity and the feminine.
Strangers to Ourselves
_Étrangers à nous-mêmes_ was originally published in Paris by Fayard in 1988. Leon Roudiez translated _Étrangers à nous-mêmes_ as _Strangers to Ourselves_ for Columbia University Press in 1991. Part of that translation appears here. In "Toccata and Fugue for the Foreigner," Kristeva describes the experience of the foreigner estranged from his or her homeland. The foreigner experiences a loss of his or her mother, motherland, mother-tongue. Caught between two languages, the foreigner can be reduced to silence. In this text, the foreigner becomes an outward manifestation of the estranged psychic relation between conscious and unconscious. The body of _Strangers to Ourselves_ traces the notion of foreigner or stranger from the Ancient Greeks, through the Talmud, the New Testament, the Renaissance, the Enlightenment, to present-day France and the issue of nationalism. She analyzes the rights of citizenship as a paradox that excludes the foreigner in order to protect "the rights of man."
In _Strangers to Ourselves_ Kristeva associates the individual struggle to face the return of the repressed unconscious stranger or foreigner that inhabits our psyche with the social struggle to live with foreigners. There she takes up the question "how can I live with others, with otherness, without ostracism but also without leveling difference?" She maintains that encounters with foreigners can help to reacquaint us with the otherness within our own psyches. And, conversely, accepting our unconscious drives, the other within, can help us to accept others within our society. In "Might Not Universality Be... Our Own Foreignness?" and "In Practice...," Kristeva maintains that psychoanalysis, with its attempts to embrace the otherness within, becomes a model for an ethics that will embrace difference: "The ethics of psychoanalysis implies a politics: it would involve a cosmopolitanism of a new sort that, cutting across governments, economies, and markets, might work for a mankind whose solidarity is founded on the consciousness of its unconscious—desiring, destructive, fearful, empty, impossible" ( _Stranger to Ourselves_ , p. 192). Following Montesquieu's notion of cosmopolitanism, Kristeva concludes that we need a new cosmopolitan community that is based on radical strangeness or difference and born out of the individualism of contemporary culture.
Powers of Horror
Approaching Abjection
_No Beast is there without glimmer of infinity, No eye so vile nor abject that brushes not Against lightning from on high, now tender, now fierce_.
_—Victor Hugo_ , La Légende des siècles
Neither Subject nor Object
There looms, within abjection, one of those violent, dark revolts of being, directed against a threat that seems to emanate from an exorbitant outside or inside, ejected beyond the scope of the possible, the tolerable, the thinkable. It lies there, quite close, but it cannot be assimilated. It beseeches, worries, and fascinates desire, which, nevertheless, does not let itself be seduced. Apprehensive, desire turns aside; sickened, it rejects. A certainty protects it from the shameful—a certainty of which it is proud holds on to it. But simultaneously, just the same, that impetus, that spasm, that leap is drawn toward an elsewhere as tempting as it is condemned. Unflaggingly, like an inescapable boomerang, a vortex of summons and repulsion places the one haunted by it literally beside himself.
When I am beset by abjection, the twisted braid of affects and thoughts I call by such a name does not have, properly speaking, a definable _object_.
The abject is not an ob-ject facing me, which I name or imagine. Nor is it an ob-jest, an otherness ceaselessly fleeing in a systematic quest of desire. What is abject is not my correlative, which, providing me with someone or something else as support, would allow me to be more or less detached and autonomous. The abject has only one quality of the object—that of being opposed to _I_. If the object, however, through its opposition, settles me within the fragile texture of a desire for meaning, which, as a matter of fact, makes me ceaselessly and infinitely homologous to it, what is _abject_ , on the contrary, the jettisoned object, is radically excluded and draws me toward the place where meaning collapses. A certain "ego" that merged with its master, a superego, has flatly driven it away. It lies outside, beyond the set, and does not seem to agree to the latter's rules of the game. And yet, from its place of banishment, the abject does not cease challenging its master. Without a sign (for him), it beseeches a discharge, a convulsion, a crying out. To each ego its object, to each superego its abject. It is not the white expanse or slack boredom of repression, not the translations and transformations of desire that wrench bodies, nights, and discourse; rather it is a brutish suffering that "I" puts up with, sublime and devastated, for "I" deposits it to the father's account ( _verse au père—père-version_ ): I endure it, for I imagine that such is the desire of the other. A massive and sudden emergence of uncanniness, which, familiar as it might have been in an opaque and forgotten life, now harries me as radically separate, loathsome. Not me. Not that. But not nothing, either. A "something" that I do not recognize as a thing. A weight of meaninglessness, about which there is nothing insignificant, which crushes me. On the edge of nonexistence and hallucination, of a reality that, if I acknowledge it, annihilates me. There, abject and abjection are my safeguards. The primers of my culture.
The Improper/Unclean
Loathing an item of food, a piece of filth, waste, or dung. The spasms and vomiting that protect me. The repugnance, the retching that thrusts me to the side and turns me away from defilement, sewage, and muck. The shame of compromise, of being in the middle of treachery. The fascinated start that leads me toward and separates me from them.
Food loathing is perhaps the most elementary and most archaic form of abjection. When the eyes see or the lips touch that skin on the surface of milk—harmless, thin as a sheet of cigarette paper, pitiful as a nail paring—I experience a gagging sensation and, still farther down, spasms in the stomach, the belly; and all the organs shrivel up the body, provoke tears and bile, increase heartbeat, cause forehead and hands to perspire. Along with sight-clouding dizziness, _nausea_ makes me balk at that milk cream, separates me from the mother and father who proffer it. "I" want none of that element, sign of their desire; "I" do not want to listen, "I" do not assimilate it, "I" expel it. But since the food is not an "other" for "me," who am only in their desire, I expel _myself_ , I spit _myself_ out, I abject _myself_ within the same motion through which "I" claim to establish _myself_. That detail, perhaps an insignificant one, but one that they ferret out, emphasize, evaluate, that trifle turns me inside out, guts sprawling; it is thus that _they_ see that "I" am in the process of becoming an other at the expense of my own death. During that course in which "I" become, I give birth to myself amid the violence of sobs, of vomit. Mute protest of the symptom, shattering violence of a convulsion that, to be sure, is inscribed in a symbolic system, but in which, without either wanting or being able to become integrated in order to answer to it, it reacts, it abreacts. It abjects.
The corpse (or cadaver: _cadere_ , to fall), that which has irremediably come a cropper, is cesspool, and death; it upsets even more violently the one who confronts it as fragile and fallacious chance. A wound with blood and pus, or the sickly, acrid smell of sweat, of decay, does not _signify_ death. In the presence of signified death—a flat encephalograph, for instance—I would understand, react, or accept. No, as in true theater, without makeup or masks, refuse and corpses _show me_ what I permanently thrust aside in order to live. These body fluids, this defilement, this shit are what life withstands, hardly and with difficulty, on the part of death. There, I am at the border of my condition as a living being. My body extricates itself, as being alive, from that border. Such wastes drop so that I might live, until, from loss to loss, nothing remains in me and my entire body falls beyond the limit— _cadere_ , cadaver. If dung signifies the other side of the border, the place where I am not and which permits me to be, the corpse, the most sickening of wastes, is a border that has encroached upon everything. It is no longer I who expel, "I" is expelled. The border has become an object. How can I be without border? That elsewhere that I imagine beyond the present, or that I hallucinate so that I might, in a present time, speak to you, conceive of you—it is now here, jetted, abjected, into "my" world. Deprived of world, therefore, I _fall in a faint_. In that compelling, raw, insolent thing in the morgue's full sunlight, in that thing that no longer matches and therefore no longer signifies anything, I behold the breaking down of a world that has erased its borders: fainting away. The corpse, seen without God and outside of science, is the utmost of abjection. It is death infecting life. Abject. It is something rejected from which one does not part, from which one does not protect oneself as from an object. Imaginary uncanniness and real threat, it beckons to us and ends up engulfing us.
It is thus not lack of cleanliness or health that causes abjection but what disturbs identity, system, order. What does not respect borders, positions, rules. The in-between, the ambiguous, the composite. The traitor, the liar, the criminal with a good conscience, the shameless rapist, the killer who claims he is a savior.... Any crime, because it draws attention to the fragility of the law, is abject, but premeditated crime, cunning murder, hypocritical revenge are even more so because they heighten the display of such fragility. He who denies morality is not abject; there can be grandeur in amorality and even in crime that flaunts its disrespect for the law—rebellious, liberating, and suicidal crime. Abjection, on the other hand, is immoral, sinister, scheming, and shady: a terror that dissembles, a hatred that smiles, a passion that uses the body for barter instead of inflaming it, a debtor who sells you up, a friend who stabs you....
In the dark halls of the museum that is now what remains of Auschwitz, I see a heap of children's shoes, or something like that, something I have already seen elsewhere, under a Christmas tree, for instance, dolls I believe. The abjection of Nazi crime reaches its apex when death, which, in any case, kills me, interferes with what, in my living universe, is supposed to save me from death: childhood, science, among other things.
The Abjection of Self
If it be true that the abject simultaneously beseeches and pulverizes the subject, one can understand that it is experienced at the peak of its strength when that subject, weary of fruitless attempts to identify with something on the outside, finds the impossible within; when it finds that the impossible constitutes its very _being_ , that it _is_ none other than abject. The abjection of self would be the culminating form of that experience of the subject to which it is revealed that all its objects are based merely on the inaugural _loss_ that laid the foundations of its own being. There is nothing like the abjection of self to show that all abjection is in fact recognition of the _want_ on which any being, meaning, language, or desire is founded. One always passes too quickly over this word, "want," and today psychoanalysts are finally taking into account only its more or less fetishized product, the "object of want." But if one imagines (and imagine one must, for it is the working of imagination whose foundations are being laid here) the experience of _want_ itself as logically preliminary to being and object—to the being of the object—then one understands that abjection, and even more so abjection of self, is its only signified. Its signifier, then, is none but literature. Mystical Christendom turned this abjection of self into the ultimate proof of humility before God, witness Elizabeth of Hungary who "though a great princess, delighted in nothing so much as in abasing herself."
The question remains as to the ordeal, a secular one this time, that abjection can constitute for someone who, in what is termed knowledge of castration, turning away from perverse dodges, presents himself with his own body and ego as the most precious nonobjects; they are no longer seen in their own right but forfeited, abject. The termination of analysis can lead us there, as we shall see. Such are the pangs and delights of masochism.
Essentially different from "uncanniness," more violent, too, abjection is elaborated through a failure to recognize its kin; nothing is familiar, not even the shadow of a memory. I imagine a child who has swallowed up his parents too soon, who frightens himself on that account, "all by himself," and, to save himself, rejects and throws up everything that is given to him—all gifts, all objects. He has, he could have, a sense of the abject. Even before things for him _are_ —hence before they are signifiable—he drives them out, dominated by drive as he is, and constitutes his own territory, edged by the abject. A sacred configuration. Fear cements his compound, conjoined to another world, thrown up, driven out, forfeited. What he has swallowed up instead of maternal love is an emptiness, or rather a maternal hatred without a word for the words of the father; that is what he tries to cleanse himself of, tirelessly. What solace does he come upon within such loathing? Perhaps a father, existing but unsettled, loving but unsteady, merely an apparition but an apparition that remains. Without him the holy brat would probably have no sense of the sacred; a blank subject, he would remain, discomfited, at the dump for nonobjects that are always forfeited, from which, on the contrary, fortified by abjection, he tries to extricate himself. For he is not mad, he through whom the abject exists. Out of the daze that has petrified him before the untouchable, impossible, absent body of the mother, a daze that has cut off his impulses from their objects, that is, from their representations, out of such daze he causes, along with loathing, one word to crop up—fear. The phobic has no other object than the abject. But that word, "fear"—a fluid haze, an elusive clamminess—no sooner has it cropped up than it shades off like a mirage and permeates all words of the language with nonexistence, with a hallucinatory, ghostly glimmer. Thus, fear having been bracketed, discourse will seem tenable only if it ceaselessly confronts that otherness, a burden both repellent and repelled, a deep well of memory that is unapproachable and intimate: the abject.
Beyond the Unconscious
Put another way, it means that there are lives not sustained by _desire_ , as desire is always for objects. Such lives are based on _exclusion_. They are clearly distinguishable from those understood as neurotic or psychotic, articulated by _negation_ and its modalities, _transgression, denial_ , and _repudiation_. Their dynamics challenges the theory of the unconscious, seeing that the latter is dependent upon a dialectic of negativity.
The theory of the unconscious, as is well known, presupposes a repression of contents (affects and presentations) that, thereby, do not have access to consciousness but effect within the subject modifications, either of speech (parapraxes, etc.), or of the body (symptoms), or both (hallucinations, etc.). As correlative to the notion of _repression_ , Freud put forward that of _denial_ as a means of figuring out neurosis, that of _rejection_ ( _repudiation_ ) as a means of situating psychosis. The asymmetry of the two repressions becomes more marked owing to denial's bearing on the object whereas repudiation affects desire itself (Lacan, in perfect keeping with Freud's thought, interprets that as "repudiation of the Name of the Father").
Yet, facing the ab-ject and more specifically phobia and the splitting of the ego, one might ask if those articulations of negativity germane to the unconscious (inherited by Freud from philosophy and psychology) have not become inoperative. The "unconscious" contents remain here _excluded_ but in strange fashion: not radically enough to allow for a secure differentiation between subject and object, and yet clearly enough for a defensive _position_ to be established—one that implies a refusal but also a sublimating elaboration. As if the fundamental opposition were between I and Other or, in more archaic fashion, between Inside and Outside. As if such an opposition subsumed the one between Conscious and Unconscious, elaborated on the basis of neuroses.
Owing to the ambiguous opposition I/Other, Inside/Outside—an opposition that is vigorous but pervious, violent but uncertain—there are contents, "normally" unconscious in neurotics, that become explicit if not conscious in "borderline" patients' speeches and behavior. Such contents are often openly manifested through symbolic practices, without by the same token being integrated into the judging consciousness of those particular subjects. Since they make the conscious/unconscious distinction irrelevant, borderline subjects and their speech constitute propitious ground for a sublimating discourse ("aesthetic" or "mystical," etc.), rather than a scientific or rationalist one.
An Exile Who Asks, "Where?"
The one by whom the abject exists is thus a _deject_ who places (himself), _separates_ (himself), situates (himself), and therefore _strays_ instead of getting his bearings, desiring, belonging, or refusing. Situationist in a sense, and not without laughter—since laughing is a way of placing or displacing abjection. Necessarily dichotomous, somewhat Manichaean, he divides, excludes, and without, properly speaking, wishing to know his abjections is not at all unaware of them. Often, moreover, he includes himself among them, thus casting within himself the scalpel that carries out his separations.
Instead of sounding himself as to his "being," he does so concerning his place: " _Where_ am I?" instead of " _Who_ am I?" For the space that engrosses the deject, the excluded, is never _one_ , nor _homogeneous_ , nor _totalizable_ , but essentially divisible, foldable, and catastrophic. A deviser of territories, languages, works, the _deject_ never stops demarcating his universe whose fluid confines—for they are constituted of a nonobject, the abject—constantly question his solidity and impel him to start afresh. A tireless builder, the deject is in short a _stray_. He is on a journey, during the night, the end of which keeps receding. He has a sense of the danger, of the loss that the pseudo-object attracting him represents for him, but he cannot help taking the risk at the very moment he sets himself apart. And the more he strays, the more he is saved.
Time: Forgetfulness and Thunder
For it is out of such straying on excluded ground that he draws his jouissance. The abject from which he does not cease separating is for him, in short, a _land of oblivion_ that is constantly remembered. Once upon blotted-out time, the abject must have been a magnetized pole of covetousness. But the ashes of oblivion now serve as a screen and reflect aversion, repugnance. The clean and proper (in the sense of incorporated and incorporable) becomes filthy, the sought-after turns into the banished, fascination into shame. Then, forgotten time crops up suddenly and condenses into a flash of lightning an operation that, if it were thought out, would involve bringing together the two opposite terms but, on account of that flash, is discharged like thunder. The time of abjection is double: a time of oblivion and thunder, of veiled infinity and the moment when revelation bursts forth.
Jouissance and Affect
Jouissance, in short. For the stray considers himself as equivalent to a Third Party. He secures the latter's judgment, he acts on the strength of its power in order to condemn, he grounds himself on its law to tear the veil of oblivion but also to set up its object as inoperative. As jettisoned. Parachuted by the Other. A ternary structure, if you wish, held in keystone position by the Other, but a "structure" that is skewed, a topology of catastrophe. For, having provided itself with an alter ego, the Other no longer has a grip on the three apices of the triangle where subjective homogeneity resides; and so, it jettisons the object into an abominable real, inaccessible except through jouissance. It follows that jouissance alone causes the abject to exist as such. One does not know it, one does not desire it, one joys in it ( _on en jouit_ ). Violently and painfully. A passion. And, as in jouissance where the object of desire, known as object _a_ (in Lacan's terminology), bursts with the shattered mirror where the ego gives up its image in order to contemplate itself in the Other, there is nothing either objective or objectal to the abject. It is simply a frontier, a repulsive gift that the Other, having become alter ego, drops so that "I" does not disappear in it but finds, in that sublime alienation, a forfeited existence. Hence a jouissance in which the subject is swallowed up but in which the Other, in return, keeps the subject from foundering by making it repugnant. One thus understands why so many victims of the abject are its fascinated victims—if not its submissive and willing ones.
We may call it a border; abjection is above all ambiguity. Because, while releasing a hold, it does not radically cut off the subject from what threatens it—on the contrary, abjection acknowledges it to be in perpetual danger. But also because abjection itself is a composite of judgment and affect, of condemnation and yearning, of signs and drives. Abjection preserves what existed in the archaism of preobjectal relationship, in the immemorial violence with which a body becomes separated from another body in order to be—maintaining that night in which the outline of the signified thing vanishes and where only the imponderable affect is carried out. To be sure, if I am affected by what does not yet appear to me as a thing, it is because laws, connections, and even structures of meaning govern and condition me. That order, that glance, that voice, that gesture, which enact the law for my frightened body, constitute and bring about an effect and not yet a sign. I speak to it in vain in order to exclude it from what will no longer be, for myself, a world that can be assimilated. Obviously, _I am_ only _like_ someone else: mimetic logic of the advent of the ego, objects, and signs. But when I _seek_ (myself), _lose_ (myself), or experience _jouissance_ —then "I" is _heterogeneous_. Discomfort, unease, dizziness stemming from an ambiguity that, through the violence of a revolt _against_ , demarcates a space out of which signs and objects arise. Thus braided, woven, ambivalent, a heterogeneous flux marks out a territory that I can call my own because the Other, having dwelt in me as alter ego, points it out to me through loathing.
This means once more that the heterogeneous flow, which portions the abject and sends back abjection, already dwells in a human animal that has been highly altered. I experience abjection only if an Other has settled in place and stead of what will be "me." Not at all an other with whom I identify and incorporate, but an Other who precedes and possesses me, and through such possession causes me to be. A possession previous to my advent: a being-there of the symbolic that a father might or might not embody. Significance is indeed inherent in the human body.
At the Limit of Primal Repression
If, on account of that Other, a space becomes demarcated, separating the abject from what will be a subject and its objects, it is because a repression that one might call "primal" has been effected prior to the springing forth of the ego, of its objects and representations. The latter, in turn, as they depend on another repression, the "secondary" one, arrive only a posteriori on an enigmatic foundation that has already been marked off; its return, in a phobic, obsessional, psychotic guise, or more generally and in more imaginary fashion in the shape of _abjection_ , notifies us of the limits of the human universe.
On such limits and at the limit one could say that there is no unconscious, which is elaborated when representations and affects (whether or not tied to representations) shape a logic. Here, on the contrary, consciousness has not assumed its rights and transformed into signifiers those fluid demarcations of yet unstable territories where an "I" that is taking shape is ceaselessly straying. We are no longer within the sphere of the unconscious but at the limit of primal repression that, nevertheless, has discovered an intrinsically corporeal and already signifying brand, symptom, and sign: repugnance, disgust, abjection. There is an effervescence of object and sign—not of desire but of intolerable significance; they tumble over into non-sense or the impossible real, but they appear even so in spite of "myself" (which is not) as abjection.
Premises of the Sign, Linings of the Sublime
Let us pause a while at this juncture. If the abject is already a wellspring of sign for a nonobject, on the edges of primal repression, one can understand its skirting the somatic symptom on the one hand and sublimation on the other. The _symptom_ : a language that gives up, a structure within the body, a nonassimilable alien, a monster, a tumor, a cancer that the listening devices of the unconscious do not hear, for its strayed subject is huddled outside the paths of desire. _Sublimation_ , on the contrary, is nothing else than the possibility of naming the prenominal, the preobjectal, which are in fact only a transnominal, a transobjectal. In the symptom, the abject permeates me, I become abject. Through sublimation, I keep it under control. The abject is edged with the sublime. It is not the same moment on the journey, but the same subject and speech bring them into being.
For the sublime has no object either. When the starry sky, a vista of open seas or a stained glass window shedding purple beams fascinate me, there is a cluster of meaning, of colors, of words, of caresses, there are light touches, scents, sighs, cadences that arise, shroud me, carry me away, and sweep me beyond the things that I see, hear, or think. The "sublime" object dissolves in the raptures of a bottomless memory. It is such a memory, which, from stopping point to stopping point, remembrance to remembrance, love to love, transfers that object to the refulgent point of the dazzlement in which I stray in order to be. As soon as I perceive it, as soon as I name it, the sublime triggers—it has always already triggered—a spree of perceptions and words that expands memory boundlessly. I then forget the point of departure and find myself removed to a secondary universe, set off from the one where "I" am—delight and loss. Not at all short of but always with and through perception and words, the sublime is a _something added_ that expands us, overstrains us, and causes us to be both _here_ , as dejects, and _there_ , as others and sparkling. A divergence, an impossible bounding. Everything missed, joy—fascination.
Before the Beginning: Separation
The abject might then appear as the most _fragile_ (from a synchronic point of view), the most _archaic_ (from a diachronic one) sublimation of an "object" still inseparable from drives. The abject is that pseudo-object that is made up _before_ but appears only _within_ the gaps of secondary repression. _The abject would thus be the "object" of primal repression_.
But what is primal repression? Let us call it the ability of the speaking being, always already haunted by the Other, to divide, reject, repeat. Without _one_ division, _one_ separation, _one_ subject/object having been constituted (not yet, or no longer yet). Why? Perhaps because of maternal anguish, unable to be satiated within the encompassing symbolic.
The abject confronts us, on the one hand, with those fragile states where man strays on the territories of _animal_. Thus, by way of abjection, primitive societies have marked out a precise area of their culture in order to remove it from the threatening world of animals or animalism, which were imagined as representatives of sex and murder.
The abject confronts us, on the other hand, and this time within our personal archeology, with our earliest attempts to release the hold of _maternal_ entity even before ex-isting outside of her, thanks to the autonomy of language. It is a violent, clumsy breaking away, with the constant risk of falling back under the sway of a power as securing as it is stifling. The difficulty a mother has in acknowledging (or being acknowledged by) the symbolic realm—in other words, the problem she has with the phallus that her father or her husband stands for—is not such as to help the future subject leave the natural mansion. The child can serve its mother as token of her own authentication; there is, however, hardly any reason for her to serve as go-between for it to become autonomous and authentic in its turn. In such close combat, the symbolic light that a third party, eventually the father, can contribute helps the future subject, the more so if it happens to be endowed with a robust supply of drive energy, in pursuing a reluctant struggle against what, having been the mother, will turn into an abject. Repelling, rejecting; repelling itself, rejecting itself. Ab-jecting.
In this struggle, which fashions the human being, the _mimesis_ , by means of which he becomes homologous to another in order to become himself, is in short logically and chronologically secondary. Even before being _like_ , "I" am not but do _separate, reject, ab-ject_. Abjection, with a meaning broadened to take in subjective diachrony, _is a precondition of narcissism_. It is coexistent with it and causes it to be permanently brittle. The more or less beautiful image in which I behold or recognize myself rests upon an abjection that sunders it as soon as repression, the constant watchman, is relaxed.
The "Chora," Receptacle of Narcissism
Let us enter, for a moment, into that Freudian _aporia_ called primal repression. Curious primacy, where what is repressed cannot really be held down, and where what represses always already borrows its strength and authority from what is apparently very secondary: language. Let us therefore not speak of primacy but of the instability of the symbolic function in its most significant aspect—the prohibition placed on the maternal body (as a defense against autoeroticism and incest taboo). Here, drives hold sway and constitute a strange space that I shall name, after Plato ( _Timaeus_ 48–53), a _chora_ , a receptacle.
For the benefit of the ego or its detriment, drives, whether life drives or death drives, serve to correlate that "not yet" ego with an "object" in order to establish both of them. Such a process, while dichotomous (inside/outside, ego/not ego) and repetitive, has nevertheless something centripetal about it: it aims to settle the ego as center of a solar system of objects. If, by dint of coming back toward the center, the drive's motion should eventually become centrifugal, hence fasten on the Other and come into being as sign so as to produce meaning—that is, literally speaking, exorbitant.
But from that moment on, while I recognize my image as sign and change in order to signify, another economy is instituted. The sign represses the _chora_ and its eternal return. Desire alone will henceforth be witness to that "primal" pulsation. But desire ex-patriates the _ego_ toward an _other_ subject and accepts the exactness of the ego only as narcissistic. Narcissism then appears as a regression to a position set back from the other, a return to a self-contemplative, conservative, self-sufficient haven. Actually, such narcissism never is the wrinkleless image of the Greek youth in a quiet fountain. The conflicts of drives muddle its bed, cloud its water, and bring forth everything that, by not becoming integrated with a given system of signs, is abjection for it.
Abjection is therefore a kind of _narcissistic crisis_ : it is witness to the ephemeral aspect of the state called "narcissism" with reproachful jealousy, heaven knows why; what is more, abjection gives narcissism (the thing and the concept) its classification as "seeming."
Nevertheless, it is enough that a prohibition, which can be a superego, block the desire craving an other—or that this other, as its role demands, not fulfill it—for desire and its signifiers to turn back toward the "same," thus clouding the waters of Narcissus. It is precisely at the moment of narcissistic perturbation (all things considered, the permanent state of the speaking being, if he would only hear himself speak) that secondary repression, with its reserve of symbolic means, attempts to transfer to its own account, which has thus been overdrawn, the resources of primal repression. The archaic economy is brought into full light of day, signified, verbalized. Its strategies (rejecting, separating, repeating/abjecting) hence find a symbolic existence, and the very logic of the symbolic—arguments, demonstrations, proofs, etc.—must conform to it. It is then that the object ceases to be circumscribed, reasoned with, thrust aside: it appears as abject.
Two seemingly contradictory causes bring about the narcissistic crisis that provides, along with its truth, a view of the abject. _Too much strictness on the part of the Other_ , confused with the One and the Law. The _lapse of the Other_ , which shows through the breakdown of objects of desire. In both instances, the abject appears in order to uphold "I" within the Other. The abject is the violence of mourning for an "object" that has always already been lost. The abject shatters the wall of repression and its judgments. It takes the ego back to its source on the abominable limits from which, in order to be, the ego has broken away—it assigns it a source in the non-ego, drive, and death. Abjection is a resurrection that has gone through death (of the ego). It is an alchemy that transforms death drive into a start of life, of new significance.
Perverse or Artistic
The abject is related to perversion. The sense of abjection that I experience is anchored in the superego. The abject is perverse because it neither gives up nor assumes a prohibition, a rule, or a law, but turns them aside, misleads, corrupts, uses them, takes advantage of them, the better to deny them. It kills in the name of life—a progressive despot; it lives at the behest of death—an operator in genetic experimentations; it curbs the other's suffering for its own profit—a cynic (and a psychoanalyst); it establishes narcissistic power while pretending to reveal the abyss—an artist who practices his art as a "business." Corruption is its most common, most obvious appearance. That is the socialized appearance of the abject.
An unshakable adherence to Prohibition and Law is necessary if that perverse interspace of abjection is to be hemmed in and thrust aside.
Religion, Morality, Law. Obviously always arbitrary, more or less; unfailingly oppressive, rather more than less; laboriously prevailing, more and more so.
Contemporary literature does not take their place. Rather, it seems to be written out of the untenable aspects of perverse or superego positions. It acknowledges the impossibility of Religion, Morality, and Law—their power play, their necessary and absurd seeming. Like perversion, it takes advantage of them, gets round them, and makes sport of them. Nevertheless, it maintains a distance where the abject is concerned. The writer, fascinated by the abject, imagines its logic, projects himself into it, introjects it, and as a consequence perverts language—style and content. But on the other hand, as the sense of abjection is both the abject's judge and accomplice, this is also true of the literature that confronts it. One might thus say that with such a literature there takes place a crossing over of the dichotomous categories of Pure and Impure, Prohibition and Sin, Morality and Immorality.
For the subject firmly settled in its superego, a writing of this sort is necessarily implicated in the interspace that characterizes perversion; and for that reason, it gives rise in turn to abjection. And yet, such texts call for a softening of the superego. Writing them implies an ability to imagine the abject, that is, to see oneself in its place and to thrust it aside only by means of the displacements of verbal play. It is only after his death, eventually, that the writer of abjection will escape his condition of waste, reject, abject. Then, he will either sink into oblivion or attain the rank of incommensurate ideal. Death would thus be the chief curator of our imaginary museum; it would protect us in the last resort from the abjection that contemporary literature claims to expend while uttering it. Such a protection, which gives its quietus to abjection, but also perhaps to the bothersome, incandescent stake of the literary phenomenon itself, which, raised to the status of the sacred, is severed from its specificity. Death thus keeps house in our contemporary universe. By purifying (us from) literature, it establishes our secular religion.
As Abjection—So the Sacred
Abjection accompanies all religious structurings and reappears, to be worked out in a new guise, at the time of their collapse. Several structurations of abjection should be distinguished, each one determining a specific form of the sacred.
Abjection appears as a rite of defilement and pollution in the paganism that accompanies societies with a dominant or surviving matrilineal character. It takes on the form of the _exclusion_ of a substance (nutritive or linked to sexuality), the execution of which coincides with the sacred since it sets it up.
Abjection persists as _exclusion_ or taboo (dietary or other) in monotheistic religions, Judaism in particular, but drifts over to more "secondary" forms such as _transgression_ (of the Law) within the same monotheistic economy. It finally encounters, with Christian sin, a dialectic elaboration, as it becomes integrated in the Christian Word as a threatening otherness—but always nameable, always totalizable.
The various means of _purifying_ the abject—the various catharses—make up the history of religions, and end up with that catharsis par excellence called art, both on the far and near side of religion. Seen from that standpoint, the artistic experience, which is rooted in the abject it utters and by the same token purifies, appears as the essential component of religiosity. That is perhaps why it is destined to survive the collapse of the historical forms of religions.
Outside of the Sacred, the Abject Is Written
In the contemporary practice of the West and owing to the crisis in Christianity, abjection elicits more archaic resonances that are culturally prior to sin; through them it again assumes its biblical status, and beyond it that of defilement in primitive societies. In a world in which the Other has collapsed, the aesthetic task—a descent into the foundations of the symbolic construct—amounts to retracing the fragile limits of the speaking being, closest to its dawn, to the bottomless "primacy" constituted by primal repression. Through that experience, which is nevertheless managed by the Other, "subject" and "object" push each other away, confront each other, collapse, and start again—inseparable, contaminated, condemned, at the boundary of what is assimilable, thinkable: abject. Great modern literature unfolds over that terrain: Dostoyevsky, Lautréamont, Proust, Artaud, Kafka, Céline.
Catharsis and Analysis
That _abjection_ , which modernity has learned to repress, dodge, or fake, appears fundamental once the analytic point of view is assumed. Lacan says so when he links that word to the _saintliness_ of the analyst, a linkage in which the only aspect of humor that remains is blackness.
One must keep open the wound where he or she who enters into the analytic adventure is located—a wound that the professional establishment, along with the cynicism of the times and of institutions, will soon manage to close up. There is nothing initiatory in that rite, if one understands by "initiation" the accession to a purity that the posture of _death_ guaranteed (as in Plato's _Phaedo_ ) or the unadulterated treasure of the "pure signifier" (as is the gold of truth in _The Republic_ , or the pure separatism of the statesman in the _Statesman_ ). It is rather a heterogeneous, corporeal, and verbal ordeal of fundamental incompleteness: a "gaping," "less One." For the unstabilized subject who comes out of that—like a crucified person opening up the stigmata of its desiring body to a speech that structures only on condition that it let go—any signifying or human phenomenon, insofar as it _is_ , appears in its being as abjection. For what impossible _catharsis_? Freud, early in his career, used the same word to refer to a therapeutics, the rigor of which was to come out later.
With Plato and Aristotle
The analyst is thus and forever sent back to the question that already haunted Plato when he wanted to take over where Apollonian or Dionysiac religion left off. Purification is something only the Logos is capable. But is that to be done in the manner of the _Phaedo_ , stoically separating oneself from a body whose substance and passions are sources of impurity? Or rather, as in the _Sophist_ , after having sorted out the worst from the best; or after the fashion of the _Philebus_ by leaving the doors wide open to impurity, provided the eyes of the mind remain focused on truth? In such a case, pleasure, having become pure and true through the harmony of color and form as in the case of accurate and beautiful geometric form, has nothing in common, as the philosopher says, with "the pleasure of scratching" ( _Philebus_ 51).
Catharsis seems to be a concern that is intrinsic to philosophy, insofar as the latter is an ethics and unable to forget Plato. Even if the _mixture_ seems inevitable toward the end of the Platonic course, it is the mind alone, as harmonious wisdom, that insures purity: catharsis has been transformed, where transcendental idealism is concerned, into philosophy. Of the cathartic incantation peculiar to mysteries, Plato has kept only, as we all know, the very uncertain role of poets whose frenzy would be useful to the state only after having been evaluated, sorted out, and purified in its turn by wise men.
Aristotelian catharsis is closer to sacred incantation. It is the one that has bequeathed its name to the common, aesthetic concept of catharsis. Through the mimesis of passions—ranging from enthusiasm to suffering—in "language with pleasurable accessories," the most important of which being _rhythm_ and _song_ (see the _Poetics_ ), the soul reaches _orgy_ and _purity_ at the same time. What is involved is a purification of body and soul by means of a heterogeneous and complex circuit, going from "bile" to "fire," from "manly warmth" to the "enthusiasm" of the "mind." Rhythm and song hence arouse the impure, the other of mind, the passionate-corporeal-sexual-virile, but they harmonize it, arrange it differently from the wise man's knowledge. They thus soothe frenzied outbursts (Plato, in the _Laws_ , allowed such use of rhythm and meter only to the mother rocking her child), by contributing an _external_ rule, a poetic one, which fills the gap, inherited from Plato, between body and soul. To Platonic _death_ , which owned, so to speak, the state of purity, Aristotle opposed the act of _poetic purification_ —in itself an impure process that protects from the abject only by dint of being immersed in it. The abject, mimed through sound and meaning, is _repeated_. Getting rid of it is out of the question—the final Platonic lesson has been understood: one does not get rid of the impure; one can, however, bring it into being a second time, and differently from the original impurity. It is a repetition through rhythm and song, therefore through what is not yet, or no longer is "meaning," but arranges, defers, differentiates and organizes, harmonizes pathos, bile, warmth, and enthusiasm. Benveniste translates "rhythm" by "trace" and "concatenation" ( _enchaînement_ ). Prometheus is "rhythmical," and we call him "bound" ( _enchaîné_ ). An attachment on the near and far side of language. Aristotle seems to say that there is a discourse of sex and that is not the discourse of knowledge—it is the only possible catharsis. That discourse is audible, and through the speech that it mimics it repeats on another register what the latter does not say.
Philosophical Sadness and the Spoken Disaster of the Analyst
Poetic catharsis, which for more than two thousand years behaved as an underage sister of philosophy, face to face and incompatible with it, takes us away from purity, hence from Kantian ethics, which has long governed modern codes and remains more faithful to a certain Platonic stoicism. By means of the "universalizing of maxims," as is well known, the Kant of the _Foundations of the Metaphysics of Ethics_ or of the _Metaphysical Principles of Virtue_ advocated an "ethical gymnastics" in order to give us, by means of consciousness, control over our defilements and, through that very consciousness, making us free and joyous.
More skeptical and, from a certain point of view, more Aristotelian, Hegel, on the contrary, rejects a "calculation" that claims to eliminate defilement, for the latter seems _fundamental_ to him. Probably echoing the Greek polis, he conceives of no other ethics than that of the _act_. Also distrustful, however, of those fine aestheticizing souls who find purity in the elaboration of empty forms, he obviously does not hold to the mimetic and orgiastic catharsis of Aristotle. It is in the _historical_ act that Hegel sees fundamental impurity being expended; as a matter of fact, the latter is a sexual impurity whose historical achievement consists in marriage. But—and this is where transcendental idealism, too, sadly comes to an end—here it is that desire ( _Lust_ ), thus normalized in order to escape abject concupiscence ( _Begierde_ ), sinks into a banality that is sadness and silence. How come? Hegel does not condemn impurity because it is exterior to ideal consciousness; more profoundly—but also more craftily—he thinks that it can and should get rid of itself through the historico-social act. If he thereby differs from Kant, he nevertheless shares his condemnation of (sexual) impurity. He agrees with his aim to keep consciousness apart from defilement, which, nevertheless, dialectically constitutes it. Reabsorbed into the trajectory of the Idea, what can defilement become if not the negative side of consciousness—that is, lack of communication and speech? In other words, defilement as reabsorbed in marriage becomes sadness. In so doing, it has not strayed too far from its logic, according to which it is a border of discourse—a silence.
It is obvious that the analyst, from the abyss of his silence, brushes against the ghost of the sadness Hegel saw in sexual normalization. Such sadness is the more obvious to him as his ethics is rigorous—founded, as it must be in the West, on the remains of transcendental idealism. But one can also argue that the Freudian stance, which is dualistic and dissolving, unsettles those foundations. In that sense, it causes the sad, analytic silence to hover above a strange, foreign discourse, which, strictly speaking, shatters verbal communication (made up of a knowledge and a truth that are nevertheless heard) by means of a device that mimics terror, enthusiasm, or orgy, and is more closely related to rhythm and song than it is to the World. There is mimesis (some say identification) in the analytic passage through castration. And yet it is necessary that the analyst's interpretative speech (and not only his literary or theoretical bilingualism) be affected by it in order to be analytical. As counterpoise to a purity that found its bearings in disillusioned sadness, it is the "poetic" unsettlement of analytic utterance that testifies to its closeness to, cohabitation with, and "knowledge" of abjection.
I am thinking, in short, of the completely mimetic _identification_ (transference and countertransference) of the analyst with respect to analysands. That identification allows for securing in their place what, when parcelled out, makes them suffering and barren. It allows one to regress back to the affects that can be heard in the breaks in discourse, to provide rhythm, too, to concatenate (is that what "to become conscious" means?) the gaps of a speech saddened because it turned its back on its abject meaning. If there is analytic jouissance it is there, in the thoroughly poetic mimesis that runs through the architecture of speech and extends from coenesthetic image to logical and phantasmatic articulations. Without, for that matter, biologizing language and while breaking away from identification by means of interpretation, analytic speech is one that becomes "incarnate" in the full sense of the term. On that condition only, it is "cathartic"—meaning thereby that it is the equivalent, for the analyst as well as for the analysand, not of purification but of rebirth with and against abjection.
NOTES
. Francis de Sales, _Introduction to a Devout Life_ , Thomas S. Kepler, tr. (New York: World, 1952), p. 125.
Modified to conform to the French text, which reads, "l'abjection de soymesme."—Trans.
. Jacques Lacan, _Télévision_ (Paris: Seuil, 1974), p. 28.
. In connection with catharsis in the Greek world, see Louis Molinier, _Le Pur et l'impur dans la pensée des Grecs_ (Paris: Klincksieck, 1952).
. See A. Philonenko, "Note sur les concepts de souillure et de pureté dans l'idéalisme allemand," _Les Etudes Philosophiques_ 4 (1972): 481–93.
From Filth to Defilement
_Abjection [...] is merely the inability to assume with sufficient strength the imperative act of excluding abject things (and that act establishes the foundations of collective existence)_.
_[...] The act of exclusion has the same meaning as social or divine sovereignty, but it is not located on the same level; it is precisely located in the domain of things and not, like sovereignty, in the domain of persons. It differs from the latter in the same way that anal eroticism differs from sadism_.
_—Georges Bataille_ , Essais de sociologie
Mother-Phobia and the Murder of the Father
In psychoanalysis as in anthropology one commonly links the sacred and the establishment of the religious bond that it presupposes with _sacrifice_. Freud tied the sacred to taboo and totemism, and concluded that, "we consider ourselves justified in substituting the father for the totem animal in the male's formula of totemism." We are all familiar with that Freudian thesis as to the murder of the father and, more specifically, with the one he develops in _Moses and Monotheism_ : in connection with Judaic religion the archaic father and master of the primeval horde is killed by the conspiring sons who, later seized with a sense of guilt for an act that was upon the whole inspired by ambivalent feelings, end up restoring paternal authority, no longer as an arbitrary power but as a right; thus renouncing the possession of all women in their turn, they establish at one stroke the sacred, exogamy, and society.
There is nevertheless a strange slippage in the Freudian argument, one that has not been sufficiently noticed. Relying on numerous readings in ethnology and the history of religions, more specifically on Frazer and Robertson Smith, Freud notes that the morality of man starts with "the two taboos of totemism"— _murder_ and _incest_. _Totem and Taboo_ begins with an evocation of the "dread of incest," and Freud discusses it at length in connection with taboo, totemism, and more specifically with food and sex prohibitions. The woman- or mother-image haunts a large part of that book and keeps shaping its background even when, relying on the testimony of obsessional neurotics, Freud slips from dread (p. 23: "His incest dread"; p. 24: "the incest dread of savages"; p. 161: "The interpretation of incest dread," "This dread of incest") to the inclusion of dread symptom in obsessional neurosis. At the same time he leaves off speculating on incest ("we do not know the origin of incest dread and do not even know how to guess at it," p. 162) in order to center his conclusion in the second taboo, the one against murder, which he reveals to be the murder of the father.
That such a murderous event could be as much mythical as endowed with founding properties, that it should be both the keystone to the desire henceforth known as Oedipal and a severance that sets up a signifier admitting of logical concatenation, analytic attention now knows only too well. Divergences from and even contradictions of this Freudian thesis are finally no more than variants and confirmations. What will concern me here is not that aspect of the Freudian position, which I shall consider to have been logically established. I shall attempt to question the other side of the religious phenomenon, the one that Freud points to when he brings up dread, incest, and the mother; one that, even though it is presented as the second taboo founding religion, nevertheless disappears during the final elucidation of the problem.
The Two-sided Sacred
Could the sacred be, whatever its variants, a two-sided formation? One aspect founded by murder and the social bond made up of murder's guilt-ridden atonement, with all the projective mechanisms and obsessive rituals that accompany it; and another aspect, like a lining, more secret still and invisible, nonrepresentable, oriented toward those uncertain spaces of unstable identity, toward the fragility—both threatening and fusional—of the archaic dyad, toward the nonseparation of subject/object, on which language has no hold but one woven of fright and repulsion? One aspect is defensive and socializing, the other shows fear and undifferentiation. The similarities that Freud delineates between religion and obsessional neurosis would then involve the defensive side of the sacred. Now, to throw light on the subjective economy of its other side, it is phobia as such, and its drifting toward psychosis, that one would need to tackle head on.
That, at any rate, will be my point of departure. For we shall see, in a large number of rituals and discourses involved in making up the sacred—notably those dealing with _defilement_ and its derivations in different religions—an attempt at _coding_ the other taboo that the earliest ethnologists and psychoanalysts viewed as presiding over social formations: beside death, _incest_. Lévi-Strauss's structural anthropology has shown how all systems of knowledge in so-called primitive societies, and myths in particular, are a later elaboration, within stages of symbolicity, of the prohibition that weighs on incest and founds the signifying function as well as the social aggregate. What will concern me here is not the socially productive value of the son-mother incest _prohibition_ but the alterations, within subjectivity and within the very symbolic competence, implied by the _confrontation with the feminine_ and the way in which societies code themselves in order to accompany as far as possible the speaking subject on that journey. Abjection, or the journey to the end of the night.
Prohibited Incest vs. Coming Face to Face with the Unnameable
What we designate as "feminine," far from being a primeval essence, will be seen as an "other" without a name, which subjective experience confronts when it does not stop at the appearance of its identity. Assuming that any Other is appended to the triangulating function of the paternal prohibition, what will be dealt with here, beyond and through the paternal function, is a coming face to face with an unnamable otherness—the solid rock of jouissance and writing as well.
I shall set aside in this essay a different version of the confrontation with the feminine, one that, going beyond abjection and fright, is enunciated as ecstatic. "The light-suffused face of the young Persian god" Freud refers to, and similarly, in a more secular fashion, Mallarmé's claim to be that "startled hero," "merry" for having overcome the "dishevelled tuft"—both point to another manner of coming to terms with the unnamable. That kind of confrontation appears, where our civilization is concerned, only in a few rare flashes of writing. Céline's laughter, beyond horror, also comes close to it, perhaps.
Narcissus and Murky Waters
Freud had strongly emphasized, at the outset of _Totem and Taboo_ , "man's deep aversion to his former incest wishes" (p. 24). He had reminded us of the properties of the taboo: it is "sacred, consecrated; but on the other hand it means uncanny, dangerous, forbidden and unclean" (p. 26); as to the object of taboos, "The prohibition mostly concerns matters that are capable of enjoyment" ( _Genussgefähig_ ) (p. 31), they include the "unclean" (p. 32). The contact avoidance that he observes in it nevertheless makes him think only of compulsion and its rituals, while the ambivalent hostility it harbors suggests to him paranoid projection. The two structures cause the threat that would be hovering over the subject to converge on the paternal apex—the one that prohibits, separates, prevents contact (between son and mother?). This hypothesis would suggest an idyllic dual relationship (mother-child), which, to the extent that the father prevents it, changes into an ulterior aversion to incest. The idea of such a soothing dual relationship crops up again when Freud draws up the hypothesis of a transition between the primeval horde and civilized society, transition in which the sons, out of "maternal love," and/or supported by "homosexual feelings and activities" (p. 186), would renounce mothers and sisters and set up an organization based at first on matriarchal law, and ultimately on patriarchal law.
Nevertheless there are other thoughts of Freud, from which he will not draw any conclusions, that allow one to progress in another direction. He first appears to refer states of fear and impurity to primary narcissism, a narcissism laden with hostility that does not yet know its limits. For we are dealing with imprecise boundaries in that place, at that moment, where pain is born out of an excess of fondness and a hate that, refusing to admit the satisfaction it also provides, is projected toward an other. Inside and outside are not precisely differentiated here, nor is language an active practice or the subject separated from the other. Melanie Klein will make of this area her privileged field of observation; it is well known that Winnicot found in it a fruitful terrain for the etiology of psychoses and "false selves" as well as for creation and play. But it is Freud indeed who blazes the trail. Let us read more carefully the following passages, which can be understood in another way than as preludes to the obsessional or paranoid structure.
Under conditions whose nature has not yet been sufficiently established, internal perceptions of emotional and thought processes can be projected outwards in the same way as sense perceptions; they are thus employed for building up the external world, though they should by rights remain part of the internal world. This may have some genetic connection with the fact that the function of attention was originally directed not towards the internal world but towards the stimuli that stream in from the external world, and that that function's only information upon endopsychic processes was received from feelings of pleasure and unpleasure. It was not until a language of abstract thought had been developed, that is to say, not until the sensory residues of verbal presentations had been linked to the internal processes, that the latter themselves gradually became capable of being perceived. Before that, owing to the projection outwards of internal perceptions, primitive men arrived at a picture of the external world which we, with our intensified conscious perception, have now to translate back into psychology.
And further along, in a footnote:
The projected creations of primitive men resemble the personifications constructed by creative writers; for the latter externalize in the form of separate individuals the opposing instinctual impulses struggling within them.
Incest and the Preverbal
Let me sum up. There would be a "beginning" preceding the word. Freud, echoing Goethe, says so at the end of _Totem and Taboo_ : "In the beginning was the deed." In that anteriority to language, the outside is elaborated by means of a projection from within, of which the only experience we have is one of pleasure and pain. An outside in the image of the inside, made of pleasure and pain. The nondistinctiveness of inside and outside would thus be unnamable, a border passable in both directions by pleasure and pain. Naming the latter, hence differentiating them, amounts to introducing language, which, just as it distinguishes pleasure from pain as it does all other oppositions, founds the separation inside/outside. And yet, there would be witnesses to the perviousness of the limit, artisans after a fashion who would try to tap that preverbal "beginning" within a word that is flush with pleasure and pain. They are _primitive man_ through his ambivalences and the _poet_ through the personification of his opposing states of feeling—but also perhaps through the rhetorical recasting of language that he effects and over which Freud, who says he is heedful and fascinated, never tarries. If the _murder_ of the father is that historical event constituting the social code as such, that is, symbolic exchange and the exchange of women, its equivalent on the level of the subjective history of each individual is therefore the _advent of language_ , which breaks with perviousness if not with the chaos that precedes it and sets up denomination as an exchange of linguistic signs. Poetic language would then be, contrary to murder and the univocity of verbal message, a reconciliation with what murder as well as names were separated from. It would be an attempt to symbolize the "beginning," an attempt to name the other facet of taboo: pleasure, pain. Are we finally dealing with incest?
Not quite, or not directly. When Freud again speaks, still in _Totem and Taboo_ , "of the first beginnings in childhood" of libidinal trends, he asserts that "from the very first" "they are not yet directed toward any external object." As he did in _Three Essays on the Theory of Sexuality_ , he calls autoeroticism the phase which gives way to object-choice. Nevertheless he inserts between the two stages a third one that will hold our attention.
In this intermediary stage [...] the sexual impulses which formerly were separate have already formed into a unit and have also found an object; but this object is not external and foreign to the individual, but is his own ego, which is formed at this period.
Fixation at this stage will be called _narcissism_. Let me try to point out the latent meanings of the definition. Narcissism is predicated on the existence of the _ego_ but not of an _external object_ ; we are faced with the strange correlation between an entity (the ego) and its converse (the object), which is nevertheless not yet constituted; with an "ego" in relation to a nonobject.
Two consequences seem necessarily to follow from such a structure. On the one hand, the nonconstitution of the (outside) object as such renders unstable the ego's identity, which could not be precisely established without having been differentiated from an other, from its object. The ego of primary narcissism is thus uncertain, fragile, threatened, subjected just as much as its nonobject to spatial ambivalence (inside/outside uncertainty) and to ambiguity of perception (pleasure/pain). On the other hand, one has to admit that such a narcissistic topology has no other underpinning in psychosomatic reality than the mother-child dyad. Now, though that relation has always been immersed in language, it allows the latter's inscription in the future subject only when biophysiological preconditions and the conditions of the Oedipus complex permit the setting up of a triadic relationship. The subject's _active_ use of the signifier truly dates only from this moment. By stressing the inherence of language in the human state, by overestimating the subject's having been the slave of language since before his birth, one avoids noting the two moods, active and passive, according to which the subject is constituted in the signifier; by the same token one neglects the economy of narcissism in the elaboration and practice of the symbolic function.
That having been said, the archaic relation to the mother, narcissistic though it may be, is from my point of view of no solace to the protagonists and even less so to Narcissus. For the subject will always be marked by the uncertainty of his borders and of his affective valency as well; these are all the more determining as the paternal function was weak or even nonexistent, opening the door to perversion or psychosis. The edenic image of primary narcissism is perhaps a defensive negation elaborated by the neurotic subject when he sets himself under the aegis of the father. On the other hand, patients who have recently come to the couch (borderline cases, false selves, etc.) reveal the horror of that dual war, its terror, and the ensuing fear of being rotten, drained, or blocked.
Defilement as Ritual Rescue from Phobia and Psychosis
This abjection, which threatens the ego and results from the dual confrontation in which the uncertainties of primary narcissism reside—is it such as to motivate, if not explain, the incest dread of which Freud speaks? I believe so. If it be true, as Claude Lévi-Strauss has demonstrated, that the prohibition of incest has the logical import of founding, by means of that very prohibition, the discreteness of interchangeable units, thus establishing social order and the symbolic, I shall maintain that such a logical operation is carried out owing to a subjective benefit derived from it on the level of libidinal economy. Incest prohibition throws a veil over primary narcissism and the always ambivalent threats with which it menaces subjective identity. It cuts short the temptation to return, with abjection and jouissance, to that passivity status within the symbolic function, where the subject, fluctuating between inside and outside, pleasure and pain, word and deed, would find death, along with nirvana. Phobia alone, crossroad of neurosis and psychosis, and of course conditions verging on psychosis, testify to the appeal of such a risk; as if, with regard to it, the taboo barring contact with the mother and/or primary narcissism suddenly disintegrated.
A whole facet of the sacred, true lining of the sacrificial, compulsive, and paranoid side of religions, assumes the task of warding off that danger. This is precisely where we encounter the rituals of defilement and their derivatives, which, based on the feeling of abjection and all converging on the maternal, attempt to symbolize the other threat to the subject: that of being swamped by the dual relationship, thereby risking the loss not of a part (castration) but of the totality of his living being. The function of these religious rituals is to ward off the subject's fear of his very own identity sinking irretrievably into the mother.
The Poverty of Prohibition: Georges Bataille
The logic of prohibition, which founds the abject, has been outlined and made explicit by a number of anthropologists concerned with defilement and its sacred function in so-called primitive societies. And yet Georges Bataille remains the only one, to my knowledge, who has linked the production of the abject to _the weakness of that prohibition_ , which, in other respects, necessarily constitutes each social order. He links abjection to "the inability to assume with sufficient strength the imperative act of excluding." Bataille is also the first to have specified that the plane of abjection is that of the _subject/object relationship_ (and not subject/other subject) and that this archaism is rooted in anal eroticism rather than sadism.
In the following, my point will be to suggest that such an archaic relationship to the _object_ interprets, as it were, the relationship to the _mother_. Her being coded as "abject" points to the considerable importance some societies attribute to women (matrilineal or related filiation, endogamy, decisive role of procreation for the survival of the social group, etc.). The symbolic "exclusory prohibition" that, as a matter of fact, constitutes collective existence does not seem to have, in such cases, sufficient strength to dam up the abject or demoniacal potential of the feminine. The latter, precisely on account of its power, does not succeed in differentiating itself as _other_ but threatens one's _own and clean self_ , which is the underpinning of any organization constituted by exclusions and hierarchies.
But before outlining the _weakness of prohibition_ and finally the _matrilineal order_ that can be perceived in those communities, let us return to the anthropological delineation of the logic of _exclusion_ that causes the abject to exist.
The Fundamental Work of Mary Douglas
Anthropologists, since Sir James George Frazer, W. Robertson Smith, Arnold van Gennep, and Alfred Reginald Radcliff-Brown, or Rudolf Steiner, have noted that secular "filth," which has become sacred "defilement," is the _excluded_ on the basis of which religious prohibition is made up. In a number of primitive societies religious rites are purification rites whose function is to separate this or that social, sexual, or age group from another one, by means of prohibiting a filthy, defiling element. It is as if dividing lines were built up between society and a certain nature, as well as within the social aggregate, on the basis of the simple logic of _excluding filth_ , which, promoted to the ritual level of _defilement_ , founded the "self and clean" of each social group if not of each subject.
The purification rite appears then as that essential ridge, which, prohibiting the filthy object, extracts it from the secular order and lines it at once with a sacred facet. Because it is excluded as a possible object, asserted to be a nonobject of desire, abominated as ab-ject, as abjection, filth becomes defilement and founds on the henceforth released side of the "self and clean" the order that is thus only (and therefore, always already) sacred.
Defilement is what is jettisoned from the _symbolic system_. It is what escapes that social rationality, that logical order on which a social aggregate is based, which then becomes differentiated from a temporary agglomeration of individuals and, in short, constitutes a _classification system_ or a _structure_.
The British anthropologist Mary Douglas begins by construing the "symbolic system" of religious prohibitions as a reflection of social divisions or even contradictions. As if the social being, coextensive with a "symbolic system," were always present to itself through its religious structures, which transfer its contradictions to the level of rituals. And yet, at a second stage of her thinking, Mary Douglas seems to find in the human body the prototype of that translucid being constituted by society as symbolic system. As a matter of fact, the explanation she gives of defilement assigns in turn different statuses to the human body: as ultimate cause of the socioeconomic causality, or simply as metaphor of that sociosymbolic being constituted by the human universe always present to itself. In so doing, however, Mary Douglas introduces willy-nilly the possibility of a subjective dimension within anthropological thought on religions. Where then lies the subjective value of those demarcations, exclusions, and prohibitions that establish the social organism as a "symbolic system"? The anthropological analysis of these phenomena was for Mary Douglas essentially _syntactic_ at first: defilement is an element connected with the boundary, the margin, and the like, of an order. Henceforth she finds herself led to _semantic_ problems: what is the _meaning_ that such a border element assumes in other psychological, economic, and other, systems? At this moment of her thinking there emerges a concern to integrate Freudian data as semantic values connected with the psychosomatic functioning of the speaking subject. But a hasty assimilation of such data leads Mary Douglas naively to _reject_ Freudian premises.
Finally, such a conception disregards both _subjective dynamics_ (if one wishes to consider the social set in its utmost particularization) and _language as common and universal code_ (if one wishes to consider the aggregate and the social aggregates in their greatest generality). Lévi-Strauss's structural anthropology had one advantage among others; it linked a classification system, that is, a symbolic system, within a given society, to the order of language in its universality (binary aspects of phonology, signifier-signified dependencies and autonomies, etc.). In thus attaining universal truth, it nevertheless neglected the subjective dimension and/or the diachronic and synchronic implication of the speaking subject in the universal order of language.
Consequently, when I speak of _symbolic order_ , I shall imply the dependence and articulation of the speaking subject in the order of language, such as they appear diachronically in the advent of each speaking being and as analytic listening discovers them synchronically in the speech of analysands. I shall consider as an established fact the analytic finding that different subjective structures are possible within that symbolic order, even if the different types recorded here seem subject to discussion and refinement, if not reevaluation.
One might advance the hypothesis that a (social) symbolic system _corresponds_ to a specific structuration of the speaking subject in the _symbolic order_. To say that it "corresponds" leaves out questions of cause and effect; is the social determined by the subjective, or is it the other way around? The subjective-symbolic dimension that I am introducing does not therefore reinstate some deep or primary causality in the social _symbolic system_. It merely presents the _effects_ and especially the _benefits_ that accrue to the speaking subject from a precise symbolic organization; perhaps it explains what desiring motives are required in order to maintain a given social symbolics. Furthermore, it seems to me that such a statement of the problem has the advantage of not turning the "symbolic system" into a secular replica of the "preestablished harmony" or the "divine order"; rather, it roots it, as a _possible variant_ , within the only concrete universality that defines the speaking being—the signifying process.
In the Same Fashion as Incest Prohibition
We are now in a position to recall what was suggested earlier concerning that border of subjectivity where the object no longer has, or does not yet have, a correlative function bonding the subject. On that location, to the contrary, the vacillating, fascinating, threatening, and dangerous object is silhouetted as nonbeing—as the abjection into which the speaking being is permanently engulfed.
Defilement, by means of the rituals that consecrate it, is perhaps, for a social aggregate, only one of the possible foundings of abjection bordering the frail identity of the speaking being. In this sense, abjection is coextensive with social and symbolic order, on the individual as well as on the collective level. By virtue of this, abjection, just like _prohibition of incest_ , is a universal phenomenon; one encounters it as soon as the symbolic and/or social dimension of man is constituted, and this throughout the course of civilization. But abjection assumes specific shapes and different codings according to the various "symbolic systems." I shall attempt to examine some of its variants: _defilement, food taboo_ , and _sin_.
Sociohistorical considerations can be brought in at a second stage. They will allow us to understand why that demarcating imperative, which is subjectively experienced as abjection, varies according to time and space, even though it is universal. I shall nevertheless stick to a typological argument. Prohibitions and conflicts that are specific to a given subject and ritualized by religion for a given type of body will appear as isomorphic with the prohibitions and conflicts of the social group within which they happen. Leaving aside the question of the priority of one over the other (the social does not represent the subjective any more than the subjective represents the social), I shall posit that they both follow the same logic, with no other goal than the survival of both group and subject.
My reflections will make their way through anthropological domains and analyses in order to aim at a deep psychosymbolic economy: the general, logical determination that underlies anthropological variants (social structures, marriage rules, religious rites) and evinces a specific economy of the speaking subject, no matter what its historical manifestations may be. In short, an economy that analytic listening and semanalytic deciphering discover in our contemporaries. Such a procedure seems to me to be directly in keeping with Freudian utilization of anthropological data. It inevitably entails a share of _disappointment_ for the empirical-minded ethnologist. It does not unfold without a share of _fiction_ , the nucleus of which, drawn from actuality and the subjective experience of the one who writes, is projected upon data collected from the life of other cultures, less to justify itself than to throw light on them by means of an interpretation to which they obviously offer resistance.
The Margin of a Floating Structure
Taking a closer look at defilement, as Mary Douglas has done, one ascertains the following. In the first place, filth is not a quality in itself, but it applies only to what relates to a _boundary_ and, more particularly, represents the object jettisoned out of that boundary, its other side, a margin.
Matter issuing from them [the orifices of the body] is marginal stuff of the most obvious kind. Spittle, blood, milk, urine, faeces or tears by simply issuing forth have traversed the boundary of the body. [...] The mistake is to treat bodily margins in isolation from all other margins.
The potency of pollution is therefore not an inherent one; it is proportional to the potency of the prohibition that founds it.
It follows from this that pollution is a type of danger which is not likely to occur except where the lines of structure, cosmic or social, are clearly defined.
Finally, even if human beings are involved with it, the dangers entailed by defilement are not within their power to deal with but depend on a power "inhering in the structure of ideas." Let us posit that defilement is an objective evil undergone by the subject. Or, to put it another way, the danger of filth represents for the subject the risk to which the very symbolic order is permanently exposed, to the extent that it is a device of discriminations, of differences. But from where and from what does the threat issue? From nothing else but an equally objective reason, even if individuals can contribute to it, and which would be, in a way, the frailty of the symbolic order itself. A threat issued from the prohibitions that found the inner and outer borders in which and through which the speaking subject is constituted—borders also determined by the phonological and semantic differences that articulate the syntax of language.
And yet, in the light of this structural-functional X-ray of defilement, which draws on the major anthropological works of modern times, from W. Robertson Smith to Marcel Mauss, from Emile Durkheim to Claude Lévi-Strauss, one question remains unanswered. Why does _corporeal waste_ , menstrual blood and excrement, or everything that is assimilated to them, from nail-parings to decay, represent—like a metaphor that would have become incarnate—the objective frailty of symbolic order?
One might be tempted at first to seek the answer in a type of society where defilement takes the place of supreme danger or absolute evil.
Between Two Powers
Nevertheless, no matter what differences there may be among societies where religious prohibitions, which are above all behavior prohibitions, are supposed to afford protection from defilement, one sees everywhere the importance, both social and symbolic, of women and particularly the mother. In societies where it occurs, ritualization of defilement is accompanied by a strong concern for separating the sexes, and this means giving men rights over women. The latter, apparently put in the position of passive objects, are, nonetheless, felt to be wily powers, "baleful schemers" from whom rightful beneficiaries must protect themselves. It is as if, lacking a central authoritarian power that would settle the definitive supremacy of one sex—or lacking a legal establishment that would balance the prerogatives of both sexes—two powers attempted to share out society. One of them, the masculine, apparently victorious, confesses through its very relentlessness against the other, the feminine, that it is threatened by an asymmetrical, irrational, wily, uncontrollable power. Is this a survival of a matrilineal society or the specific particularity of a structure (without the incidence of diachrony)? The question of the origins of such a handling of sexual difference remains moot. But whether it be within the highly hierarchical society of India or the Lele in Africa it is always to be noticed that the attempt to establish a male, phallic power is vigorously threatened by the no less virulent power of the other sex, which is oppressed (recently? or not sufficiently for the survival needs of society?). That other sex, the feminine, becomes synonymous with a radical evil that is to be suppressed.
Let us keep that fact in mind; I shall return to it later on for the interpretation of defilement and its rites. In the meantime I turn to the particulars—the prohibited objects and the symbolic devices that accompany those prohibitions.
Excrements and Menstrual Blood
While they always relate to corporeal orifices as to so many landmarks parceling-constituting the body's territory, polluting objects fall, schematically, into two types: excremental and menstrual. Neither tears nor sperm, for instance, although they belong to borders of the body, have any polluting value.
Excrement and its equivalents (decay, infection, disease, corpse, etc.) stand for the danger to identity that comes from without: the ego threatened by the non-ego, society threatened by its outside, life by death. Menstrual blood, on the contrary, stands for the danger issuing from within the identity (social or sexual); it threatens the relationship between the sexes within a social aggregate and, through internalization, the identity of each sex in the face of sexual difference.
Maternal Authority as Trustee of the Self's Clean and Proper Body
What can the two types of defilement have in common? Without having recourse to anal eroticism or the fear of castration—one cannot help _hearing_ the reticence of anthropologists when confronted with that explanation—it might be suggested, by means of another psychoanalytic approach, that those _two_ defilements stem from the _maternal_ and/or the feminine, of which the maternal is the real support. That goes without saying where menstrual blood signifies sexual difference. But what about excrement? It will be remembered that the anal penis is also the phallus with which infantile imagination provides the feminine sex and that, on the other hand, maternal authority is experienced first and above all, after the first essentially oral frustrations, as sphincteral training. It is as if, while having been forever immersed in the symbolics of language, the human being experienced, in addition, an _authority_ that was a—chronologically and logically immediate—repetition of the _laws_ of language. Through frustrations and prohibitions, this authority shapes the body into a _territory_ having areas, orifices, points and lines, surfaces and hollows, where the archaic power of mastery and neglect, of the differentiation of proper-clean and improper-dirty, possible and impossible, is impressed and exerted. It is a "binary logic," a primal mapping of the body that I call semiotic to say that, while being the precondition of language, it is dependent upon meaning, but in a way that is not that of _linguistic_ signs nor of the _symbolic_ order they found. Maternal authority is the trustee of that mapping of the self's clean and proper body; it is distinguished from paternal laws within which, with the phallic phase and acquisition of language, the destiny of man will take shape.
If language, like culture, sets up a separation and, starting with discrete elements, concatenates an order, it does so precisely by repressing maternal authority and the corporeal mapping that abuts against them. It is then appropriate to ask what happens to such a repressed item when the legal, phallic, linguistic symbolic establishment does not carry out the separation in radical fashion—or else, more basically, when the speaking being attempts to think through its advent in order better to establish its effectiveness.
Defilement Rite—a Social Elaboration of the Borderline Patient?
The structuralist hypothesis is well known. Basic symbolic institutions, such as _sacrifice_ or _myths_ , expand on logical processes inherent in the economy of language itself; in doing so they realize for the community what makes up in depth, historically and logically, the speaking being as such. Thus _myth_ projects on contents that are vitally important for a given community those binary oppositions discovered at the level of phonematic concatenation of language. As for _sacrifice_ , it solemnizes the vertical dimension of the sign: the one that leads from the thing that is left behind, or killed, to the meaning of the word and transcendence.
Following that line, one could suggest that the rites surrounding defilement, particularly those involving excremential and menstrual variants, shift the _border_ (in the psychoanalytic meaning relating to borderline patients) that separates the body's territory from the signifying chain; they illustrate the boundary between semiotic authority and symbolic law. Through language and within highly hierarchical religious institutions, man hallucinates partial "objects"—witnesses to an archaic differentiation of the body on its way toward ego identity, which is also sexual identity. The _defilement_ from which ritual protects us is neither sign nor matter. Within the rite that extracts it from repression and depraved desire, defilement is the translinguistic spoor of the most archaic boundaries of the self's clean and proper body. In that sense, if it is a jettisoned object, it is so from the mother. It absorbs within itself all the experiences of the nonobjectal that accompany the differentiation mother-speaking being, hence all ab-jects (from those the phobic shuns to those that hem in split subjects). As if purification rites, through a language that is already there, looked back toward an archaic experience and obtained from it a partial object, not as such but only as a _spoor_ of a preobject, an archaic parceling. By means of the symbolic institution of ritual, that is to say, by means of a system of ritual exclusions, the partial object consequently becomes _scription_ —an inscription of limits, an emphasis placed not on the (paternal) Law but on (maternal) Authority through the very signifying order.
NOTES
. In _Totem and Taboo_ (1913), in vol. 13 of _Complete Works_. References will be to the Vintage Book edition published by Random House.
. Ibid., p. 170.
. Ibid., p. 185.
. See René Girard, _Des Choses cachées depuis la fondation du monde_ (Paris: Grasset, 1978).
. Freud quoted from T. W. Atkinson's _Primal Law, Totem and Taboo_ (London, 1903); see p. 184n.
. _Totem and Taboo_ , pp. 85–86, although the translation used is that of the _Complete Works_ , 13:64.
. _Totem and Taboo_ , p. 86n; quoted from the _Complete Works_ , 13:65.
. _Totem and Taboo_ , p. 207.
. _Totem and Taboo_ , pp. 115–16.
. See Georges Bataille, "L'Abjection et les formes misérables," in _Essais de sociologie, Oeuvres complètes_ (Paris: Gallimard, 1970), 2:217ff.
. Mary Douglas, _Purity and Danger_ (London: Routledge & Kegan Paul, 1969), p. 121.
. Ibid., p. 113.
. Ibid.
. See ibid., pp. 149ff.
. "For the Lele evil is not to be included in the total system of the world, but to be expunged without compromise"; ibid., p. 171.
Strangers to Ourselves
Toccata and Fugue for the Foreigner
Foreigner: a choked up rage deep down in my throat, a black angel clouding transparency, opaque, unfathomable spur. The image of hatred and of the other, a foreigner is neither the romantic victim of our clannish indolence nor the intruder responsible for all the ills of the polis. Neither the apocalypse on the move nor the instant adversary to be eliminated for the sake of appeasing the group. Strangely, the foreigner lives within us: he is the hidden face of our identity, the space that wrecks our abode, the time in which understanding and affinity founder. By recognizing him within ourselves, we are spared detesting him in himself. A symptom that precisely turns "we" into a problem, perhaps makes it impossible, The foreigner comes in when the consciousness of my difference arises, and he disappears when we all acknowledge ourselves as foreigners, unamenable to bonds and communities.
Can the "foreigner," who was the "enemy" in primitive societies, disappear from modern societies? Let us recall a few moments in Western history when foreigners were conceived, welcomed, or rejected, but when the possibility of a society without foreigners could also have been imagined on the horizon of a religion or an ethics. As a still and perhaps ever utopic matter, the question is again before us today as we confront an economic and political integration on the scale of the planet: shall we be, intimately and subjectively, able to live with the others, to live _as others_ , without ostracism but also without leveling? The modification in the status of foreigners that is imperative today leads one to reflect on our ability to accept new modalities of otherness. No "Nationality Code" would be practicable without having that question slowly mature within each of us and for each of us.
While in the most savage human groups the foreigner was an enemy to be destroyed, he has become, within the scope of religious and ethical constructs, a different human being who, provided he espouses them, may be assimilated into the fraternities of the "wise," the "just," or the "native." In Stoicism, Judaism, Christianity, and even in the humanism of the Enlightenment, the patterns of such acceptance varied, but in spite of its limitations and shortcomings, it remained a genuine rampart against xenophobia. The violence of the problem set by the foreigner today is probably due to the crises undergone by religious and ethical constructs. This is especially so as the absorption of otherness proposed by our societies turns out to be unacceptable by the contemporary individual, jealous of his difference—one that is not only national and ethical but essentially subjective, insurmountable. Stemming from the bourgeois revolution, nationalism has become a symptom—romantic at first, then totalitarian—of the nineteenth and twentieth centuries. Now, while it does go against universalist tendencies (be they religious or rationalist) and tends to isolate or even hunt down the foreigner, nationalism nevertheless ends up, on the other hand, with the particularistic, demanding individualism of contemporary man. But it is perhaps on the basis of that contemporary individualism's subversion, beginning with the moment when the citizen-individual ceases to consider himself as unitary and glorious but discovers his incoherences and abysses, in short his "strangenesses"—that the question arises again: no longer that of welcoming the foreigner within a system that obliterates him but of promoting the togetherness of those foreigners that we all recognize ourselves to be.
Let us not seek to solidify, to turn the otherness of the foreigner into a thing. Let us merely touch it, brush by it, without giving it a permanent structure. Simply sketching out its perpetual motion through some of its variegated aspects spread out before our eyes today, through some of its former, changing representations scattered throughout history. Let us also lighten that otherness by constantly coming back to it—but more and more swiftly. Let us escape its hatred, its burden, fleeing them not through leveling and forgetting, but through the _harmonious_ repetition of the differences it implies and spreads. _Toccatas and Fugues_ : Bach's compositions evoke to my ears the meaning of an acknowledged and harrowing otherness that I should like to be contemporary, _because_ it has been brought up, relieved, disseminated, inscribed in an original play being developed, without goal, without boundary, without end. An otherness barely touched upon and that already moves away.
Scorched Happiness
Are there any happy foreigners?
The foreigner's face burns with happiness.
At first, one is struck by his peculiarity—those eyes, those lips, those cheekbones, that skin unlike others, all that distinguishes him and reminds one that there is _someone_ there. The difference in that face reveals in paroxystic fashion what any face should reveal to a careful glance: the nonexistence of banality in human beings. Nevertheless, it is precisely the commonplace that constitutes a commonality for our daily habits. But this grasping the foreigner's features, one that captivates us, beckons and rejects at the same time. "I am at least as remarkable, and therefore I love him," the observer thinks; "now I prefer my own peculiarity, and therefore I kill him," he might conclude. From heart pangs to first jabs, the foreigner's face forces us to display the secret manner in which we face the world, stare into all our faces, even in the most familial, the most tightly knit communities.
Furthermore, the face that is so _other_ bears the mark of a crossed threshold that irremediably imprints itself as peacefulness or anxiety. Whether perturbed or joyful, the foreigner's appearance signals that he is "in addition." The presence of such a border, internal to all that is displayed, awakens our most archaic senses through a burning sensation. Vivid concern or delight, set there in these other features, without forgetfulness, without ostentation, like a standing invitation to some inaccessible, irritating journey, whose code the foreigner does not have but whose mute, physical, visible memory he keeps. This does not mean the foreigner necessarily appears absent, absentminded, or distraught. But the insistent presence of a lining—good or evil, pleasing or death-bearing—disrupts the never regular image of his face and imprints upon it the ambiguous mark of a scar—his very own well-being.
For, curiously, beyond unease, such a doubling imposes upon the other, the observer, the feeling that there is a special, somewhat insolent happiness in the foreigner. Happiness seems to prevail, _in spite of everything_ , because something has definitely been exceeded: it is the happiness of tearing away, of racing, the space of a promised infinite. Such happiness is, however, constrained, apprehensively discreet, in spite of its piercing intrusion, since the foreigner keeps feeling threatened by his former territory, caught up in the memory of a happiness or a disaster—both always excessive.
Can one be a foreigner and happy? The foreigner calls forth a new idea of happiness. Between the fugue and the origin: a fragile limit, a temporary homeostasis. Posited, present, sometimes certain, that happiness knows nevertheless that it is passing by, like fire that shines only because it consumes. The strange happiness of the foreigner consists in maintaining that fleeing eternity or that perpetual transience.
The Loss and the Challenge
A secret wound, often unknown to himself, drives the foreigner to wandering. Poorly loved, however, he does not acknowledge it: with him, the challenge silences the complaint. It is a rare person who, like some Greeks (such as Aeschylus' _Suppliants_ ), the Jews (the faithful at the wall of lamentations), or psychoanalysts, leads the foreigner to avow a humbled entreaty. He is dauntless: "You have caused me no harm," he disclaims, fiercely, "It is I who chose to leave"; always further along, always inaccessible to all. As far back as his memory can reach, it is delightfully bruised: misunderstood by a loved and yet absentminded, discreet, or worried mother, the exile is a stranger to his mother. He does not call her, he asks nothing of her. Arrogant, he proudly holds on to what he lacks, to absence, to some symbol or other. The foreigner would be the son of a father whose existence is subject to no doubt whatsoever, but whose presence does not detain him. Rejection on the one hand, inaccessibility on the other: if one has the strength not to give in, there remains a path to be discovered. Riveted to an elsewhere as certain as it is inaccessible, the foreigner is ready to flee. No obstacle stops him, and all suffering, all insults, all rejections are indifferent to him as he seeks that invisible and promised territory, that country that does not exist but that he bears in his dreams, and that must indeed be called a beyond.
The foreigner, thus, has lost his mother. Camus understood it well: his Stranger reveals himself at the time of his mother's death. One has not much noticed that this cold orphan, whose indifference can become criminal, is a fanatic of absence. He is a devotee of solitude, even in the midst of a crowd, because he is faithful to a shadow: bewitching secret, paternal ideal, inaccessible ambition. Meursault is dead unto himself but keyed up with an insipid intoxication that takes the place of passion. Likewise, his father, who started vomiting while watching an execution, understood that being sentenced to death is the only thing a man might truly consider worth bothering with.
Suffering, Ebullience, and Mask
The difficulties the foreigner will necessarily encounter—one mouth too many, incomprehensible speech, inappropriate behavior—wound him severely, but by flashes. They make him turn gray, imperceptibly, he becomes smooth and hard as a pebble, always ready to resume his infinite journey, farther, elsewhere. The (professional, intellectual, affective) aim that some set for themselves in such an unrestrained fugue is already a betrayal of strangeness, for as he chooses a program he allows himself a respite or a residence. On the contrary, according to the utmost logic of exile, all aims should waste away and self-destruct in the wanderer's insane stride toward an elsewhere that is always pushed back, unfulfilled, out of reach. The pleasure of suffering is a necessary lot in such a demented whirl, and amateur _proxeni_ know it unconsciously as they choose foreign partners on whom to inflict the torture of their own contempt, their condescension, or, more deceitfully, their heavy-handed charity.
The foreigner is hypersensitive beneath his armor as activist or tireless "immigrant worker." He bleeds body and soul, humiliated in a position where, even with the better couples, he or she assumes the part of a domestic, of the one who is a bother when he or she becomes ill, who embodies the enemy, the traitor, the victim. Masochistic pleasure accounts for his or her submissiveness only in part. The latter, in fact, strengthens the foreigner's mask—a second, impassive personality, an anesthetized skin he wraps himself in, providing a hiding place where he enjoys scorning his tyrant's hysterical weaknesses. Is this the dialectic of master and slave?
The animosity, or at least the annoyance aroused by the foreigner ("What are you doing here, Mac, this is not where you belong!"), hardly surprises him. He readily bears a kind of admiration for those who have welcomed him, for he rates them more often than not above himself, be it financially, politically, or socially. At the same time he is quite ready to consider them somewhat narrow-minded, blind. For his scornful hosts lack the _perspective_ he himself has in order to see himself and to see them. The foreigner feels strengthened by the distance that detaches him from the others as it does from himself and gives him the lofty sense not so much of holding the truth but of making it and himself relative while others fall victim to the ruts of monovalency. For they are perhaps owners of things, but the foreigner tends to think he is the only one to have a biography, that is, a life made up of ordeals—neither catastrophes nor adventures (although these might equally happen), but simply a life in which acts constitute events because they imply choice, surprises, breaks, adaptations, or cunning, but neither routine nor rest. In the eyes of the foreigner those who are not foreign have no life at all: barely do they exist, haughty or mediocre, but out of the running and thus almost already cadaverized.
Aloofness
Indifference is the foreigner's shield. Insensitive, aloof, he seems, deep down, beyond the reach of attacks and rejections that he nevertheless experiences with the vulnerability of a medusa. This is because his being kept apart corresponds to his remaining aloof, as he pulls back into the painless core of what is called a soul the humbleness that, when all is said and done, amounts to plain brutality. There, soured of mawkishness, but of sensitivity as well, he takes pride in holding a truth that is perhaps simply a certainty—the ability to reveal the crudest aspects of human relationships when seduction fades out and proprieties give way before the results of confrontations: a clash of bodies and tempers. For the foreigner, from the height of an autonomy that he is the only one to have chosen when the others prudently remain "between themselves," paradoxically confronts everyone with an asymbolia that rejects civility and returns to a violence laid bare. The brutes' encounter.
Not belonging to any place, any time, any love. A lost origin, the impossibility to take root, a rummaging memory, the present in abeyance. The space of the foreigner is a moving train, a plane in flight, the very transition that precludes stopping. As to landmarks, there are none. His time? The time of a resurrection that remembers death and what happened before, but misses the glory of being beyond: merely the feeling of a reprieve, of having gotten away.
Confidence
There remains, however, the self-confidence of being, of being able to settle within the self with a smooth, opaque certainty—an oyster shut under the flooding tide or the expressionless joy of warm stones. Between the two pathetic shores of courage and humiliation, against which he is tossed by the clashes of others, the foreigner persists, anchored in himself, strengthened by such a secret working-out, his neutral wisdom, a pleasure that has been numbed by an unattainable solitude.
Deep-seated narcissism? Blank psychosis beneath the swirl of existential conflicts? In crossing a border (... or two) the foreigner has changed his discomforts into a base of resistance, a citadel of life. Moreover, had he stayed home, he might perhaps have become a dropout, an invalid, an outlaw... Without a home, he disseminates on the contrary the actor's paradox: multiplying masks and "false selves" he is never completely true nor completely false, as he is able to tune in to loves and aversions the superficial antennae of a basaltic heart. A headstrong will, but unaware of itself, unconscious, distraught. The breed of the tough guys who know how to be weak.
This means that, settled within himself, the foreigner has no self. Barely an empty confidence, valueless, which focuses his possibilities of being constantly other, according to others' wishes and to circumstances. I do what _they_ want _me_ to, but it is not "me"—"me" is elsewhere, "me" belongs to no one, "me" does not belong to "me,"... does "me" exist?
Parceling
Nevertheless, such hardness in a state of weightlessness is an absolute that does not last. The traitor betrays himself. Whether a Maghrebian street sweeper riveted to his broom or an Asiatic princess writing her memoirs in a borrowed tongue, as soon as foreigners have an action or a passion, they take root. Temporarily, to be sure, but intensely. For the foreigner's aloofness is only the resistance with which he succeeds in fighting his matricidal anguish. His hardness appears as the metamorphosis of an archaic or potential parceling that runs the risk of bringing his thought and speech down to chaos. Thus does he value that aloofness, his hardness—let us leave it alone.
The flame that betrays his latent fanaticism shows only when he becomes attached—to a cause, to a job, to a person. What he finds there is more than a country; it is a fusion, in which there are not two beings, there is but a single one who is consumed, complete, annihilated.
Social standing or personal talent obviously stamps such a vocation with appreciable variations. Whatever their differences, however, all foreigners who have made a _choice_ add to their passion for indifference a fervent extremism that reveals the origin of their exile. For it is on account of having _no one_ at home against whom to vent their fury, their conflagration of love and hatred, and of finding the strength not to give in to it, that they wander about the world, neutral but solaced for having developed an interior distance from the fire and ice that had seared them in the past.
A Melancholia
Hard-hearted indifference is perhaps no more than the respectable aspect of nostalgia. We all know the foreigner who survives with a tearful face turned toward the lost homeland. Melancholy lover of a vanished space, he cannot, in fact, get over his having abandoned a period of time. The lost paradise is a mirage of the past that he will never be able to recover. He knows it with a distressed knowledge that turns his rage involving others (for there is always an other, miserable cause of my exile) against himself: "How could I have abandoned them? I have abandoned myself." And even he who, seemingly, flees the slimy poison of depression, does not hold back, as he lies in bed, during those glaucus moments between waking and sleeping. For in the intervening period of nostalgia, saturated with fragrances and sounds to which he no longer belongs and which, because of that, wound him less than those of the here and now, the foreigner is a dreamer making love with absence, one exquisitely depressed. Happy?
Ironists and Believers
Yet, he is never simply torn between here and elsewhere, now and before. Those who believe they are crucified in such a fashion forget that nothing ties them there anymore, and, so far, nothing binds them here. Always elsewhere, the foreigner belongs nowhere. But let there be no mistake about it: there are, in the way one lives this attachment to a lost space, two kinds of foreigners, and this separates uprooted people of all countries, occupations, social standing, sexes... into two irreconcilable categories. On the one hand, there are those who waste away in an agonizing struggle between what no longer is and what will never be—the followers of neutrality, the advocates of emptiness; they are not necessarily defeatists, they often become the best of ironists. On the other hand, there are those who transcend: living neither before nor now but beyond, they are bent with a passion that, although tenacious, will remain forever unsatisfied. It is a passion for another land, always a promised one, that of an occupation, a love, a child, a glory. They are believers, and they sometimes ripen into skeptics.
Meeting
Meeting balances wandering. A crossroad of two othernesses, it welcomes the foreigner without tying him down, opening the host to his visitor without committing him. A mutual recognition, the meeting owes its success to its temporary nature, and it would be torn by conflicts if it were to be extended. The foreign believer is incorrigibly curious, eager for meetings: he is nourished by them, makes his way through them, forever unsatisfied, forever the party-goer, too. Always going toward others, always going farther. Invited, he is able to invite himself, and his life is a succession of desired parties, but short-lived, the brilliance of which he learns to tarnish immediately, for he knows that they are of no consequence. "They welcome me, but that does not matter.... Next... It was only an expenditure that guarantees a clear conscience..." A clear conscience for the host as well as the foreigner. The cynic is even more suited for a meeting: he does not even seek it, he expects nothing from it, but he slips in nevertheless, convinced that even though everything melts away, it is better to be with "it." He does not long for meetings, they draw him in. He experiences them as in a fit of dizziness when, distraught, he no longer knows whom he has seen nor who he is.
The meeting often begins with a food fest: bread, salt, and wine. A meal, a nutritive communion. The one confesses he is a famished baby, the other welcomes the greedy child; for an instant, they merge within the hospitality ritual. But this table corner, where they gulp with such pleasure, is covered with the paths of memory: one remembers, makes plans, recites, sings. The nourishing and initially somewhat animal banquet rises to the vaporous levels of dreams and ideas: the hospitality merrymakers also become united for a while through the spirit. A miracle of flesh and thought, the banquet of hospitality is the foreigners' utopia—the cosmopolitanism of a moment, the brotherhood of guests who soothe and forget their differences, the banquet is outside of time. It imagines itself eternal in the intoxication of those who are nevertheless aware of its temporary frailty.
Sole Liberty
Free of ties with his own people, the foreigner feels "completely free." Nevertheless, the consummate name of such a freedom is solitude. Useless or limitless, it amounts to boredom or supreme availability. Deprived of others, free solitude, like the astronauts' weightless state, dilapidates muscles, bones, and blood. Available, freed of everything, the foreigner has nothing, he is nothing. But he is ready for the absolute, if an absolute could choose him. "Solitude" is perhaps the only word that has no meaning. Without other, without guidepost, it cannot bear the difference that, alone, discriminates and makes sense. No one better than the foreigner knows the passion for solitude. He believes he has chosen it for its enjoyment, or been subjected to it to suffer on account of it, and there he is languishing in a passion for indifference that, although occasionally intoxicating, is irreparably without an accomplice. The paradox is that the foreigner wishes to be alone but with partners, and yet none is willing to join him in the torrid space of his uniqueness. The only possible companions would be the members of an affiliation whose uniformity and readiness discourage him, whereas, on the contrary, the lack of accordance on the part of distinguished persons helplessly sends him back to his own distress. Accordance is the foreigner's mirage. More grueling when lacking, it is his only connection—utopic or abortive as it may be. If it appears under the self-satisfying guise of charity or any other right-thinking humanism, he accepts it of course, but in a hard-hearted, unbelieving, indifferent manner. The foreigner longs for affiliation, the better to experience, through a refusal, its untouchability.
A Hatred
"Experiencing hatred": that is the way the foreigner often expresses his life, but the double meaning of the phrase escapes him. Constantly feeling the hatred of others, knowing no other environment than that hatred. Like a woman who, accommodating and conniving, abides by her husband's rebuff as soon as she makes the merest suggestion of a word, gesture, or intention. Like a child that hides, fearful and guilty, convinced beforehand that it deserves its parents' anger. In the world of dodges and shams that make up his pseudo-relationships with pseudo-others, hatred provides the foreigner with consistency. Against that wall, painful but certain, and in that sense familiar, he knocks himself in order to assert, to others and to himself, that he is here. Hatred makes him real, authentic so to speak, solid, or simply existing. Even more so, it causes to resound on the _outside_ that other hatred, secret and shameful, apologetic to the point of abating, that the foreigner bears _within himself_ against everyone, against no one, and which, in the case of flooding, would cause a serious depression. But there, on the border between himself and others, hatred does not threaten him. He lies in wait, reassured each time to discover that it never misses an appointment, bruised on account of always missing love, but almost pleased with the persistence—real or imaginary?—of detestation.
Living with the other, with the foreigner, confronts us with the possibility or not of _being an other_. It is not simply—humanistically—a matter of our being able to accept the other, but of _being in his place_ , and this means to imagine and make oneself other for oneself. Rimbaud's _Je est un autre_ ("I is an other") was not only the acknowledgment of the psychotic ghost that haunts poetry. The word foreshadowed the exile, the possibility or necessity to be foreign and to live in a foreign country, thus heralding the art of living of a modern era, the cosmopolitanism of those who have been flayed. Being alienated from myself, as painful as that may be, provides me with that exquisite distance within which perverse pleasure begins as well as the possibility of my imagining and thinking, the impetus of my culture. Split identity, kaleidoscope of identities: can we be a saga for ourselves without being considered mad or fake? Without dying of the foreigner's hatred or of hatred for the foreigner?
Detestation tells you that you are an intruder, that you are irritating, and that this will be shown to you frankly and without caution. No one in this country can either defend or avenge you. You do not count for anyone; you should be grateful for being tolerated among us. Civilized people need not be gentle with foreigners. "That's it, and if you don't like it why don't you go back where you came from!" The humiliation that disparages the foreigner endows his master with who knows what petty grandeur. I wonder if Wanda's husband would have dared to act as brazenly like a Don Juan, to discover libertine bents in himself, to flaunt the girlfriends she, alas, did not have the sense of humor to appreciate—if his wife had not come from Poland, that is from nowhere, without the family or friends that constitute, in spite of what people say, a shelter against narcissism and a rampart against paranoid persecutions. I wonder if his in-laws would have so brutally taken his child away from Kwang, at the time of his separation from Jacqueline, if he did not have such an incomprehensible way of pronouncing words and forgetting verbs, what was called an obsequious way of conducting himself and which was just his own way of being polite, and that inability to strike up a friendship with colleagues at a bar, on the occasion of a fishing trip... But perhaps Wanda and Kwang are suffering from something more than being foreign, and Marie or Paul might have the same problems if they were a bit different, a bit special, if they did not play the game, if they were like foreigners from within. Or should one recognize that one becomes a foreigner in another country because one is already a foreigner from within?
The Silence of Polyglots
Not speaking one's mother tongue. Living with resonances and reasoning that are cut off from the body's nocturnal memory, from the bittersweet slumber of childhood. Bearing within oneself like a secret vault, or like a handicapped child—cherished and useless—that language of the past that withers without ever leaving you. You improve your ability with another instrument, as one expresses oneself with algebra or the violin. You can become a virtuoso with this new device that moreover gives you a new body, just as artificial and sublimated—some say sublime. You have a feeling that the new language is a resurrection: new skin, new sex. But the illusion bursts when you hear, upon listening to a recording, for instance, that the melody of your voice comes back to you as a peculiar sound, out of nowhere, closer to the old spluttering than to today's code. Your awkwardness has its charm, they say, it is even erotic, according to womanizers, not to be outdone. No one points out your mistakes, so as not to hurt your feelings, and then there are so many, and after all they don't give a damn. One nevertheless lets you know that it is irritating just the same. Occasionally, raising the eyebrows or saying "I beg your pardon?" in quick succession lead you to understand that you will "never be a part of it," that it "is not worth it," that there, at least, one is "not taken in." Being fooled is not what happens to you either. At the most, you are willing to go along, ready for all apprenticeships, at all ages, in order to reach—within that speech of others, imagined as being perfectly assimilated, _someday_ —who knows what ideal, beyond the implicit acknowledgment of a disappointment caused by the origin that did not keep its promise.
Thus, between two languages, your realm is silence. By dint of saying things in various ways, one just as trite as the other, just as approximate, one ends up no longer saying them. An internationally known scholar was ironical about his famous polyglotism, saying that he spoke Russian in fifteen languages. As for me I had the feeling that he rejected speech and his slack silence led him, at times, to sing and give rhythm to chanted poems, just in order to say something.
When Hölderlin became absorbed by Greek (before going back to the sources of German), he dramatically expressed the anesthesia of the person that is snatched up by a foreign language: "A sign, such are we, and of no meaning / Dead to all suffering, and we have almost / Lost our language in a foreign land" ( _Mnemosyne_ ).
Stuck within that polymorphic mutism, the foreigner can, instead of saying, attempt doing—housecleaning, playing tennis, soccer, sailing, sewing, horseback riding, jogging, getting pregnant, what have you. It remains an expenditure, it expends, and it propagates silence even more. Who listens to you? At the most, you are being tolerated. Anyway, do you really want to speak?
Why then did you cut off the maternal source of words? What did you dream up concerning those new people you spoke to in an artificial language, a prosthesis? From your standpoint, were they idealized or scorned? Come, now! Silence has not only been forced upon you, it is within you: a refusal to speak, a fitful sleep riven to an anguish that wants to remain mute, the private property of your proud and mortified discretion, that silence is a harsh light. Nothing to say, nothingness, no one on the horizon. An impervious fullness: cold diamond, secret treasury, carefully protected, out of reach. Saying nothing, nothing needs to be said, nothing can be said. At first, it was a cold war with those of the new idiom, desired and rejecting; then the new language covered you as might a slow tide, a neap tide. It is not the silence of anger that jostles words at the edge of the idea and the mouth; rather, it is the silence that empties the mind and fills the brain with despondency, like the gaze of sorrowful women coiled up in some nonexistent eternity.
"The Former Separations from the Body" (Mallarmé, "Cantique de Saint Jean")
To disagree. Constantly, about nothing, with no one. Coping with that with astonishment and curiosity, like an explorer, an ethnologist. Becoming weary of it and walled up in one's tarnished, neutralized disagreement, through lack of having the right to state it. No longer knowing what one truly thinks, except that "this is not it": that the words, the smiles, the manias, the judgments, the tastes of the native are excessive, faltering, or simply unjust and false, and he cannot imagine—proud as he is of being on his own ground—that one might speak, think, or act differently. In that case, why not tell him so, "argue"? But what right do we have? Perhaps we should ourselves assume that right, challenging the natives' assurance?
No. Those who have never lost the slightest root seem to you unable to understand any word liable to temper their point of view. So, when one is oneself uprooted, what is the point of talking to those who think they have their own feet on their own soil? The ear is receptive to conflicts only if the body looses its footing. A certain imbalance is necessary, a swaying over some abyss, for a conflict to be heard. Yet when the foreigner—the speech-denying strategist—does not utter his conflict, he in turn takes root in his own world of a rejected person whom no one is supposed to hear. The rooted one who is deaf to the conflict and the wanderer walled in by his conflict thus stand firmly, facing each other. It is a seemingly peaceful coexistence that hides the abyss: an abysmal world, the end of the world.
Immigrants, Hence Workers
The foreigner is the one who works. While natives of the civilized world, of developed countries, think that work is vulgar and display the aristocratic manners of offhandedness and whim (when they can...), you will recognize the foreigner in that he _still_ considers work as a value. A vital necessity, to be sure, his sole means of survival, on which he does not necessarily place a halo of glory but simply claims as a primary right, the zero degree of dignity. Even though some, once their minimal needs are satisfied, also experience an acute pleasure in asserting themselves in and through work: as if _it_ were the chosen soil, the only source of possible success, and above all the personal, steadfast, nontransferable quality, but fit to be moved beyond borders and properties. That the foreigner is a worker would seem like a cheap paradox, inferred from the quite controversial existence of "immigrant workers." I have nevertheless come across, in a French village, ambitious farmers who had come from a different region, more hard-working than others and wanting to "make a niche" for themselves by the sweat of their brows, hated as much for being intruders as for being relentless, and who (the worst of insults during demonstrations) heard themselves called Portuguese and Spaniards. Indeed, as they confided, the others (in this case they meant the Frenchmen who were sure of themselves) are never as persistent in their work; you really have to be without anything and thus, basically, to come from somewhere else, to be attached to it to that extent. Now, were they doing the unpleasant work in that village? No, they were simply always doing something, those "foreigners" who had come from another province.
With the second generation, it is true, it happens that these demons for work slacken. As a defiance of industrious parents, or an inevitably excessive aping of native behavior, the children of foreigners are often and from the very start within the code of _dolce vita_ , slovenliness, and even delinquency. Many "reasons" are given for that, of course.
But as far as the immigrant is concerned, he has not come here just to waste his time away. Possessed with driving ambition, a pusher, or merely crafty, he takes on all jobs and tries to be tops in those that are scarcest. In those that nobody wants but also in those that nobody has thought of. Man or woman for odd jobs, but also a pioneer in the most up-to-date disciplines, off-the-cuff specialist in unusual or leading occupations, the foreigner devotes himself and exerts himself. If it be true that, in the process, like everyone else he aims at profits and savings for later and for his family, his planning supposes (in order to achieve that aim, and more than with others) an extravagant expenditure of energy and means. Since he has nothing, since he is nothing, he can sacrifice everything. And sacrifice begins with work: the only property that can be exported duty free, a universally tried and tested stock for the wanderer's use. What bitterness then, what disaster it is when one does not obtain one's green card.
Slaves and Master
Dialectics of master and slave? The amount of strength changes the very balance of power. The weight of foreigners is measured not only in terms of greater numbers (from that standpoint did not slaves always constitute an overwhelming majority?) but is also determined by the consciousness of being somewhat foreign as well. On the one hand, because everyone is, in a world that is more open than ever, liable to become a foreigner for a while as tourist or employee of a multinational concern. On the other hand, because the once solid barrier between "master" and "slave" has today been abolished, if not in people's unconscious at least in our ideologies and aspirations. Every native feels himself to be more or less a "foreigner" in his "own and proper" place, and that metaphorical value of the word "foreigner" first leads the citizen to a feeling of discomfort as to his sexual, national, political, professional identity. Next it impels him to identify—sporadically, to be sure, but nonetheless intensely—with the other. Within this motion guilt obviously has its part but it also fades away to the advantage of a kind of underhanded glory of being a little like those other "gooks" ( _métèques_ ), concerning which we now know that, disadvantaged as they may be, they are running before the wind. A wind that jostles and ruffles but bears us toward our own unknown and who knows what future. There is thus set up between the new "masters" and the new "slaves" a secret collusion, which does not necessarily entail practical consequences in politics or the courts (even if they, too, feel its effects progressively, slowly) but, especially with the native, arouses a feeling of suspicion: Am I really at home? Am I myself? Are _they_ not masters of the "future"?
Such a habit for suspicion prompts some to reflect, rarely causes humbleness, and even more rarely generosity. But it also provokes regressive and protectionist rage in others: must we not stick together, remain among ourselves, expel the intruder, or at least, keep him in "his" place? The "master" then changes into a slave hounding his conqueror. For the foreigner perceived as an invader reveals a buried passion within those who are entrenched: the passion to kill the _other_ , who had first been feared or despised, then promoted from the ranks of dregs to the status of powerful persecutor against whom a "we" solidifies in order to take revenge.
Void or Baroque Speech
To be of no account to others. No one listens to you, you never have the floor, or else, when you have the courage to seize it, your speech is quickly erased by the more garrulous and fully relaxed talk of the community. Your speech has no past and will have no power over the future of the group: why should one listen to it? You do not have enough status—"no social standing"—to make your speech useful. It may be desirable, to be sure, surprising, too, bizarre or attractive, if you wish. But such lures are of little consequence when set against the _interest_ —which is precisely lacking—of those you are speaking to. Interest is self-seeking, it wants to be able to use your words, counting on your influence, which, like any influence, is anchored in social connections. Now, to be precise, you have none. Your speech, fascinating as it might be on account of its very strangeness, will be of no consequence, will have no effect, will cause no improvement in the image or reputation of those you are conversing with. One will listen to you only in absentminded, amused fashion, and one will forget you in order to go on with serious matters. The foreigner's speech can bank only on its bare rhetorical strength, and the inherent desires he or she has invested in it. But it is deprived of any support in outside reality, since the foreigner is precisely kept out of it. Under such conditions, if it does not founder into silence, it becomes absolute in its formalism, excessive in its sophistication—rhetoric is dominant, the foreigner is a baroque person. Baltasar Graciàn and James Joyce had to be foreigners.
Orphans
To be deprived of parents—is that where freedom starts? Certainly foreigners become intoxicated with that independence, and undoubtedly their very exile is at first no more than a challenge to parental overbearance. Those who have not experienced the near-hallucinatory daring of imagining themselves without parents—free of debt and duties—cannot understand the foreigners' folly, what it provides in the way of pleasure ("I am my sole master"), what it comprises in the way of angry homicide ("Neither father nor mother, neither God nor master...").
Eventually, though, the time of orphanhood comes about. Like any bitter consciousness, this one has its source in others. When others convey to you that you are of no account because your parents are of no account, that, as they are invisible, they do not exist, you are suddenly aware that you are an orphan, and, sometimes, accountable for being so. A strange light then shines on that obscurity that was in you, both joyful and guilty, the darkness of the original dependency, and transforms it into a solidarity with close relatives of earlier days, henceforth forfeited. How could it possibly not have been understood that you were always with them, dependent on a past that only parents know, on the precious, exquisite pain that you will share with no one else? How is it that they, the others, do not know that your parents are still at your side, unseen witnesses to your problems with the natives? Well, no! They do not, they do not want to know it. They thus reveal your own rejection far from those you have abandoned without really doing so—"I know, but just the same..." They thus also reveal your own underhanded perversion. You then experience as murderous those natives who never speak of your close relatives—sure, they were close in the past and elsewhere, unmentionable, buried in another language. Or else they allude to them in such absentminded way, with such offhanded scorn that you end up wondering if those parents truly exist, and in what ghostly world of an underground hell. The pain you feel facing those empty eyes that have never seen _them_. Loss of self in the presence of those distant mouths that do not weigh the artifice of the speech that evokes _them_.
But, by the way, who is the murderer? The one who does not know my relatives, or myself, as I erect my new life like a fragile mausoleum where their shadowy figure is integrated, like a corpse, at the source of my wandering? The indifference of others with respect to my kin makes them at once mine again. The community of my own—translucent, slackened by thousands of kilometers and a near-permanent daytime forgetfulness—is thus created by the scornful absentmindedness of others. In the face of that injustice of which I am both source and victim, a "we" emerges. Certainly not, I do not idealize them! I do not use the indifference of others in order to enhance their merit. I know only too well their insignificancy, and my own... And yet there is a fondness that binds to the grave what is beyond the grave, the survivor that I am to my forebears. I hear the sound of bells, a fragrance of warm milk fills my throat: they, the parents from abroad, are those who come to life again in my senses, under the blind stare of scornful paternalism.
And nevertheless, no, I have nothing to say to them, to my parents. Nothing. Nothing and everything, as always. If I tried—out of boldness, through luck, or in distress—to share with them some of the violence that causes me to be so totally on my own, they would not know where I am, who I am, what it is, in others, that rubs me the wrong way. I am henceforth foreign to them. They are my children who do not follow me, sometimes admiring, sometimes fearful, but already bruised, reconciled to being alone in their turn, and doomed not to understand. I must come to terms with it and, with that unassuaged sense of hunger in the body, after having spoken to them, must accept the idea that our "we" is a stirring mirage to be maintained at the heart of disarray, although illusive and lacking real strength. Unless it be precisely the strength of illusion that, perhaps, all communities depend on, and of which the foreigner constantly experiences the necessary, aberrant unreality.
Do You Have Any Friends?
The foreigner's friends, aside from bleeding hearts who feel obliged to do good, could only be those who feel foreign to themselves. Other than that, there are of course paternalists, paranoid and perverse people, who each have the foreigner of their choice, to the extent that they would invent him if he did not exist.
Paternalists: how they understand us, how they commiserate, how they appreciate our talents, provided they can show that they have "more"—more pain, more knowledge, more power, including that of helping us to survive...
Paranoid persons: no one is more excluded than they are and, in order to demonstrate that fact, they choose as backdrop to their delirium a basic outcast, the ordinary foreigner, who will be the chosen confidant of the persecutions they themselves suffer even more than he does—until they "discover" in this foreigner in the proper sense of the term a usurper and one of the causes of their misfortune, for if the world does not understand them it is precisely because "foreigners now monopolize public opinion's concern." ..
Perverse people: their jouissance is secret and shameful and, hidden in their shell, they would gladly put up a foreigner within it, who presumably would be happy thus to have a home, even though it might be at the cost of sexual or moral slavery, which is proffered lecherously, innocently...
In that case, all that would be left for foreigners would be to join together? Foreigners of the world, unite? Things are not so simple. For one must take into consideration the domination/exclusion fantasy characteristic of everyone: just because one is a foreigner does not mean one is without one's own foreigner, and the faith that abated at the source is suddenly rekindled at the journey's end in order to make up from whole cloth an identity the more exclusive as it had once been lost. In France, Italians call the Spaniards foreigners, the Spaniards take it out on the Portuguese, the Portuguese on the Arabs or the Jews, the Arabs on the blacks, and so forth and vice versa.... And even if there are links between one another (are they not on the same side as opposed to the natives?), these unfailingly snap when fanatical bonds fuse together again communities cemented by pure, hard fantasies. Here, on foreign soil, the religion of the abandoned forebears is set up in its essential purity and one imagines that one preserves it better than do the parents who have stayed "back home." As enclave of the other within the other, otherness becomes crystallized as pure ostracism: the foreigner excludes before being excluded, even more than he is being excluded. Fundamentalists are more fundamental when they have lost all material ties, inventing for themselves a "we" that is purely symbolic; lacking a soil it becomes rooted in ritual until it reaches its essence, which is sacrifice.
Might Not Universality Be... Our Own Foreignness?
Freud: "Heimlich/Unheimlich"—the Uncanny Strangeness
Explicitly given limited scope, as it was at first connected with aesthetic problems and emphasized texts by E. T. A. Hoffmann, Freud's _Das Unheimliche_ (1919) surreptitiously goes beyond that framework and the psychological phenomenon of "uncanny strangeness" as well, in order to acknowledge itself as an investigation into _anguish_ generally speaking and, in a fashion that is even more universal, into the _dynamics of the unconscious_. Indeed, Freud wanted to demonstrate at the outset, on the basis of a semantic study of the German adjective _heimlich_ and its antonym _unheimlich_ that a negative meaning close to that of the antonym is already tied to the positive term _heimlich_ , "friendlily comfortable," which would also signify "concealed, kept from sight," "deceitful and malicious," "behind someone's back." Thus, in the very word _heimlich_ , the familiar and intimate are reversed into their opposites, brought together with the contrary meaning of "uncanny strangeness" harbored in _unheimlich_. Such an immanence of the strange within the familiar is considered as an etymological proof of the psychoanalytic hypothesis according to which "the uncanny is that class of the frightening which leads back to what is known of old and long familiar," which, as far as Freud was concerned, was confirmed by Schelling, who said that "everything is _unheimlich_ that ought to have remained secret and hidden but has come to light" (p. 225).
Consequently therefore, that which _is_ strangely uncanny would be that which _was_ (the past tense is important) familiar and, under certain conditions (which ones?), emerges. A first step was taken that removed the uncanny strangeness from the outside, where fright had anchored it, to locate it inside, not inside the familiar considered as one's own and proper, but the familiar potentially tainted with strangeness and referred (beyond its imaginative origin) to an improper past. The other is my ("own and proper") unconscious.
What "familiar"? What "past"? In order to answer such questions, Freud's thought played a strange trick on the aesthetic and psychological notion of "uncanny strangeness," which had been initially posited, and rediscovered the analytical notions of _anxiety_ , _double_ , _repetition_ , and _unconscious_. The uncanny strangeness that is aroused in Nathaniel (in Hoffmann's tale, _The Sandman_ ) by the paternal figure and its substitutes, as well as references to the eyes, is related to the castration anxiety experienced by the child, which was repressed but surfaced again on the occasion of a state of love.
The Other Is My (Own and Proper) Unconscious
Furthermore, Freud noted that the archaic, narcissistic self, not yet demarcated by the outside world, projects out of itself what it experiences as dangerous or unpleasant in itself, making of it an alien _double_ , uncanny and demoniacal. In this instance the strange appears as a defense put up by a distraught self: it protects itself by substituting for the image of a benevolent double that used to be enough to shelter it the image of a malevolent double into which it expels the share of destruction it cannot contain.
The repetition that often accompanies the feeling of uncanny strangeness relates it to the "compulsion to repeat" that is peculiar to the unconscious and emanating out of "drive impulses"—a compulsion "proceeding from the drive impulses and probably inherent in the very nature of the drives—a compulsion powerful enough to overrule the pleasure principle" (p. 238).
The reader is henceforth ready to accept the feeling of uncanny strangeness as an instance of anxiety in which "the frightening element can be shown to be something repressed which _recurs_ " (p. 241). To the extent, however, that psychic situations evidencing an absolute repression are rare, such a return of the repressed in the guise of anxiety, and more specifically of uncanny strangeness, appears as a paroxystic metaphor of the psychic functioning itself. The latter is indeed elaborated by repression and one's necessarily going through it, with the result that the builder of the _other_ and, in the final analysis, of the _strange_ is indeed repression itself and its perviousness. "We can understand why linguistic usage has extended _das Heimliche_ into its opposite, _das Unheimliche_ ; for this uncanny is in reality nothing new or alien, but something which is familiar and old-established in the mind and which has become alienated from it only through the process of repression" (p. 241).
Let us say that the psychic apparatus represses representative processes and contents that are no longer necessary for pleasure, self-preservation, and the adaptive growth of the speaking subject and the living organism. Under certain conditions, however, the repressed "that ought to have remained secret" shows up again and produces a feeling of uncanny strangeness.
While saying that he would henceforth tackle "one or two more examples of the uncanny," Freud in his text actually continues, by means of a subtle, secret endeavor, to reveal the circumstances that are favorable to going through repression and generating the uncanny strangeness. The confrontation with _death_ and its representation is initially imperative, for our unconscious refuses the fatality of death: "Our unconscious has as little use now as it ever had for the idea of its own mortality." The fear of death dictates an ambivalent attitude: we imagine ourselves surviving (religions promise immortality), but death just the same remains the survivor's enemy, and it accompanies him in his new existence. Apparitions and ghosts represent that ambiguity and fill with uncanny strangeness our confrontations with the image of death.
The fantasy of being buried alive induces the feeling of uncanny strangeness, accompanied by "a certain lasciviousness—the phantasy, I mean, of intra-uterine existence" (p. 244). We are confronted with a second source of the strange: "It often happens that neurotic men declare that they feel there is something uncanny about the female genital organs. This _unheimlish_ place, however, is the entrance to the former _Heim_ of all human beings, to the place where each one of us lived once upon a time and in the beginning." "There is a joking saying that 'Love is homesickness"' (p. 245).
The _death_ and the _feminine_ , the end and the beginning that engross and compose us only to frighten us when they break through, one must add "the living person [... ] when we ascribe evil intentions to him [... ] that are going to be carried out with the help of special powers" (p. 243). Such malevolent _powers_ would amount to a weaving together of the symbolic and the organic—perhaps _drive_ itself, on the border of the psyche and biology, overriding the breaking imposed by organic homeostasis. A disturbing symptom of this may be found in epilepsy and madness, and their presence in our fellow beings worries us the more as we dimly sense them in ourselves.
A Semiology of Uncanny Strangeness
Are death, the feminine, and drives always a pretext for the uncanny strangeness? After having broadened the scope of his meditation, which might have led to seeing in uncanniness the description of the working of the unconscious, which is itself dependant on repression, Freud marked its required limits by stressing a few particularities of the semiology within which it emerges. Magical practices, animism, or, in more down-to-earth fashion, "intellectual uncertainty" and "disconcerted" logic (according to E. Jentsch) are all propitious to uncanniness. Now, what brings together these symbolic processes, quite different for all that, lies in a weakening of the value of signs as such and of their specific logic. The symbol ceases to be a symbol and "takes over the full functions of the thing it symbolizes" (p. 244). In other words, the sign is not experienced as arbitrary but assumes a real importance. As a consequence, the material reality that the sign was commonly supposed to point to crumbles away to the benefit of imagination, which is no more than "the over-accentuation of psychical reality in comparison with material reality" (p. 244). We are here confronted with "the omnipotence of thought," which, in order to constitute itself invalidates the arbitrariness of signs and the autonomy of reality as well and places them both under the sway of fantasies expressing infantile desires or fears.
Obsessional neuroses, but also and differently psychoses, have the distinctive feature of "reifying" signs—of slipping from the domain of "speaking" to the domain of "doing." Such a particularity _also_ evinces the fragility of repression and, without actually explaining it, allows the return of the repressed to be inscribed in the reification under the guise of the uncanny affect. While, in another semiological device, one might think that the return of the repressed would assume the shape of the somatic symptom or of the acting out, here the breakdown of the arbitrary signifier and its tendency to become reified as psychic contents that take the place of material reality would favor the experience of uncanniness. Conversely, our fleeting or more or less threatening encounter with uncanny strangeness would be a clue to our psychotic latencies and the fragility of our repression—at the same time as it is an indication of the weakness of language as a symbolic barrier that, in the final analysis, structures the repressed.
Strange indeed is the encounter with the other—whom we perceive by means of sight, hearing, smell, but do not "frame" within our consciousness. The other leaves us separate, incoherent; even more so, he can make us feel that we are not in touch with our own feelings, that we reject them or, on the contrary, that we refuse to judge them—we feel "stupid," we have "been had."
Also strange is the experience of the abyss separating me from the other who shocks me—I do not even perceive him, perhaps he crushes me because I negate him. Confronting the foreigner whom I reject and with whom at the same time I identify, I lose my boundaries, I no longer have a container, the memory of experiences when I had been abandoned overwhelm me, I lose my composure. I feel "lost," "indistinct," "hazy." The uncanny strangeness allows for many variations: they all repeat the difficulty I have in situating myself with respect to the other and keep going over the course of identification-projection that lies at the foundation of my reaching autonomy.
At this stage of the journey, one understands that Freud took pains to separate the uncanniness provoked by aesthetic experience from that which is sustained in reality; he most particularly stressed those works in which the uncanny effect is abolished because of the very fact that the entire world of the narrative is fictitious. Such are fairy tales, in which the generalized artifice spares us any possible comparison between sign, imagination, and material reality. As a consequence, artifice neutralizes uncanniness and makes all returns of the repressed plausible, acceptable, and pleasurable. As if absolute enchantment—absolute sublimation—just as, on the other hand, absolute rationality—absolute repression—were our only defenses against uncanny strangeness... Unless, depriving us of the dangers as well as the pleasures of strangeness, they be the instruments of their liquidation.
Subjects, Artists, and... a King
Linked to anguish, as we have seen, the uncanny strangeness does not, however, merge with it. Initially it is a shock, something unusual, astonishment; and even if anguish comes close, uncanniness maintains that share of unease that leads the self, beyond anguish, toward depersonalization. "The sense of strangeness belongs in the same category as depersonalization," Freud noted, and many analysts have stressed the frequency of the _Unheimliche_ affect in phobia, especially when the contours of the self are overtaxed by the clash with something "too good" or "too bad." In short, if anguish revolves around an _object_ , uncanniness, on the other hand, is a _destructuration of the self_ that may either remain as a psychotic _symptom_ or fit in as an _opening_ toward the new, as an attempt to tally with the incongruous. While it surely manifests the return of a familiar repressed, the _Unheimliche_ requires just the same the impetus of a new encounter with an unexpected outside element: arousing images of death, automatons, doubles, or the female sex (the list is probably not complete, as Freud's text leaves such an impression of a rather distant reserve—because it is passionate), uncanniness occurs when the boundaries between _imagination_ and _reality_ are erased. This observation reinforces the concept—which arises out of Freud's text—of the _Unheimliche_ as a crumbling of conscious defenses, resulting from the conflicts the self experiences with an other—the "strange"—with whom it maintains a conflictual bond, at the same time "a need for identification and a fear of it" (Maurice Bouvet). The clash with the other, the identification of the self with that good or bad other that transgresses the fragile boundaries of the uncertain self, would thus be at the source of an uncanny strangeness whose excessive features, as represented in literature, cannot hide its permanent presence in "normal" psychical dynamics.
A child confides in his analyst that the finest day in his life is that of his birth: "Because that day it was me—I like being me, I don't like being an other." Now he feels other when he has poor grades—when he is bad, alien to the parents' and teachers' desire. Likewise, the unnatural, "foreign" languages, such as writing or mathematics, arouse an uncanny feeling in the child.
This is where we leave the extraordinary realm of literary uncanniness to find its immanence (a necessary hence commonplace one) in psychism as the experience of otherness. It is possible, as Yvon Brès said, that Freud's recourse to aesthetic works in order to set up the notion of uncanny strangeness was an admission that psychoanalysis could not possibly deal with it. Man would be facing a kind of "existential apriorism," in the presence of which Freudian thought merges with Heidegger's phenomenology. Without going so far as to assume such a link, let us note, however, that Freud picks up the phrase again in _The Future of an Illusion_ (1927): civilization humanizes nature by endowing it with beings that look like us—it is such an animistic process that enables us "to breathe freely [and] feel at home in the uncanny [so that we] can deal by psychical means with our [previously] senseless anxiety." Here uncanny strangeness is no longer an artistic or pathological product but a psychic law allowing us to confront the unknown and work it out in the process of _Kulturarbeit_ , the task of civilization. Freud, who "must himself plead guilty to a special obtuseness in the matter" of the uncanny, thus opens up two other prospects when confronting the strange, which is related to anguish. On the one hand, the sense of strangeness is a mainspring for identification with the other, by working out its depersonalizing impact by means of astonishment. On the other hand, analysis can throw light on such an affect but, far from insisting on breaking it down, it should make way for esthetics (some might add philosophy), with which to saturate its phantasmal progression and insure its cathartic eternal return, for instance with readers of disturbing tales.
The violent, catastrophic aspect the encounter with the _foreigner_ may assume is to be included in the generalizing consequences that seem to stem out of Freud's observations on the activating of the uncanny. As test of our astonishment, source of depersonalization, we cannot suppress the symptom that the foreigner provokes; but we simply must come back to it, clear it up, give it the resources our own essential depersonalizations provide, and only thus soothe it.
And yet, the uncanny strangeness can also be evacuated: "No, that does not bother me; I laugh or take action—I go away, I shut my eyes, I strike, I command..." Such an elimination of the strange could lead to an elimination of the psyche, leaving, at the cost of mental impoverishment, the way open to acting out, including paranoia and murder. From another point of view, there is no uncanny strangeness for the person enjoying an acknowledged power and a resplendent image. Uncanniness, for that person, is changed into management and authorized expenditure: strangeness is for the "subjects," the sovereign ignores it, knowing how to have it administered. An anecdote related by Saint-Simon provides a good illustration of that situation. The Sun-King (French psychoanalysts strangely avoid questioning major political and artistic figures of national history, even though the latter is so weighed down with discourse and psychological enigmas as well) erases the uncanny and his fear in order to display the whole of his being exclusively within the law and the pleasure of Versailles' pomp. Disturbed innerness is the courtiers' lot; they were the compost of the psychic subtlety that the brilliant writer of memoirs has handed down to us, often remarkably anticipating Freud's speculations.
Finally, some might change the weird into irony. One imagines Saint-Simon, a shrewd smile on his lips, as far removed from regal censorship as he was from the courtiers' embarrassment: the humorist goes right through uncanny strangeness and—starting from a self-confidence that is his own or is based on his belonging to an untouchable universe that is not at all threatened by the war between same and others, ghosts and doubles—seeing in it nothing more than smoke, imaginary structures, signs. To worry or to smile, such is the choice when we are assailed by the strange; our decision depends on how familiar we are with our own ghosts.
The Strange Within Us
The uncanny would thus be the royal way (but in the sense of the court, not of the king) by means of which Freud introduced the fascinated rejection of the other at the heart of that "our self," so poised and dense, which precisely no longer exists ever since Freud and shows itself to be a strange land of borders and othernesses ceaselessly constructed and deconstructed. Strangely enough, there is no mention of _foreigners_ in the _Unheimliche_.
Actually, a foreigner seldom arouses the terrifying anguish provoked by death, the female sex, or the "baleful" unbridled drive. Are we nevertheless so sure that the "political" feelings of xenophobia do not include, often unconsciously, that agony of frightened joyfulness that has been called _unheimlich_ , that in English is _uncanny_ , and the Greeks quite simply call _xenos_ , "foreign"? In the fascinated rejection that the foreigner arouses in us, there is a share of uncanny strangeness in the sense of the depersonalization that Freud discovered in it, which takes up again our infantile desires and fears of the other—the other of death, the other of woman, the other of uncontrollable drive. The foreigner is within us. And when we flee from or struggle against the foreigner, we are fighting our unconscious—that "improper" facet of our impossible "own and proper." Delicately, analytically, Freud does not speak of foreigners: he teaches us how to detect foreignness in ourselves. That is perhaps the only way not to hound it outside of us. After Stoic cosmopolitanism, after religious universalist integration, Freud brings us the courage to call ourselves disintegrated in order not to integrate foreigners and even less so to hunt them down, but rather to welcome them to that uncanny strangeness, which is as much theirs as it is ours.
In fact, such a Freudian distraction or discretion concerning the "problem of foreigners"—which appears only as an eclipse or, if one prefers, as a symptom, through the recall of the Greek word _xenoi_ 7—might be interpreted as an invitation (a utopic or very modern one?) not to reify the foreigner, not to petrify him as such, not to petrify _us_ as such. But to analyze it by analyzing us. To discover our disturbing otherness, for that indeed is what bursts in to confront that "demon," that threat, that apprehension generated by the projective apparition of the other at the heart of what we persist in maintaining as a proper, solid "us." By recognizing _our_ uncanny strangeness we shall neither suffer from it nor enjoy it from the outside. The foreigner is within me, hence we are all foreigners. If I am a foreigner, there are no foreigners. Therefore Freud does not talk about them. The ethics of psychoanalysis implies a politics: it would involve a cosmopolitanism of a new sort that, cutting across governments, economies, and markets, might work for a mankind whose solidarity is founded on the consciousness of its unconscious—desiring, destructive, fearful, empty, impossible. Here we are far removed from a call to brotherhood, about which one has already ironically pointed out its debt to paternal and divine authority—"In order to have brothers there must be a father," as Louis-François Veuillot did not fail to say when he sharply addressed humanists. On the basis of an erotic, death-bearing unconscious, the uncanny strangeness—a projection as well as a first working out of death drive—which adumbrates the work of the "second" Freud, the one of _Beyond the Pleasure Principle_ , sets the difference within us in its most bewildering shape and presents it as the ultimate condition of our being _with_ others.
NOTES
. Sigmund Freud, _The Uncanny_ , in _The Standard Edition of the Complete Psychological Works of Sigmund Freud_ , 17:220. Page numbers given parenthetically in text refer to this volume.
There are, as usual, discrepancies between the French and English translations of Freud. Here it is especially bothersome because _Das Unheimliche_ comes out in French as _l'inquiétante étrangeté_ , a phrase that matches Kristeva's vocabulary very neatly but is at a linguistic remove from our "uncanny." While following Strachey's translation, thus letting "the uncanny" stand in all the quotations from Freud's text, I have tried to bridge the gap between French and English words by occasionally rendering the French phrase, _inquiétante étrangeté_ , in Kristeva's text, as "uncanny strangeness"—Trans.
. See Paul Denis, "L'Inquiétante Etrangeté chez l'enfant," _Revue de Psychanalyse_ 3 (1981): 503.
. See Yvon Brès, "Modestie des philosophes: modestie des psychanalystes," _Psychanalyse à l'Université_ 11 (October 1986): 585–86. Beyond the frequency of the word _Unheimliche_ in German, which removes a bit of spice from the encounter, Brès notes a certain thematic convergence in its use between Freud and Heidegger. With the latter, anguish, which resides in the being-in-the world, is uncanniness ("In der Angst ist einem 'unheimlich"'— _Sein und Zeit_ , section 40): "But this distressing aspect, this strangeness, signifies at the same time the not-being-at-home." Later, _What Is Metaphysics_ (1929) clarifies existential anguish as experienced when facing the impossibility of any determination, and it is again described as _Unheimlichkeit_.
. Freud, _The Future of an Illusion_ , _Standard Edition_ , 21:17.
. Freud, _The Uncanny_ , _Standard Edition_ , 17:220.
. "Five or six days later I was at the King's supper [... ]. As sweets were being served, I noticed something or other, rather large, seemingly black, in the air over the table, which I was unable either to make out or point to, so rapidly did this large thing fall at the end of the table [... ] The noise it made when falling and the weight of the thing nearly caused it to give way and caused the dishes to jump, but without upsetting any [... ] The King, after the impact, half turned his head and, without being disturbed in any way, I believe, he said, those are my fringes. It was indeed a bundle, larger than the hat of a priest... It had been thrown from far behind me [... ] and a small bit that had come loose in the air had fallen on top of the King's wig; Livry, who was seated to his left, saw it and removed it. He came near the end of the table and saw that they were indeed fringes twisted into a bundle [... ] Livry, wanting to remove the bundle, found a note attached to it; he took it and left the bundle [... ]. It contained, in a misshapen, extended writing, like that of a woman, these very words: Take your fringes back, Bontemps; they are more trouble than pleasure. I kiss the King's hands. It was rolled but not sealed. The King again wanted to take it from D'Aquin's hands who stepped back, sniffed it, rubbed it, turned it every which way, and showed it to the King without letting him touch it. The King asked him to read it aloud, even though he himself read it at the same time. That, said the King, is rather insolent!—but in an even, somewhat statesmanlike tone of voice. After that he asked that the bundle be removed [... ] Afterwards the King no longer mentioned it and no one dared speak about it, not aloud at any rate; and the remainder of the supper was served as if nothing had happened." Saint-Simon, _Mémoires_ , "Bibliothèque de la Pléiade" (Paris: Gallimard, 1983), pp. 632–33. Christian David accompanies this excerpt with a keen commentary in "Irréductible étrangeté," _Revue de Psychanalyse_ 3 (1981): 463–71.
. Freud, _The Uncanny_ , _Standard Edition_ , 17:221.
In Practice...
Should nationality be obtained automatically or, on the contrary, should it be chosen by means of a responsible, deliberate act? Is _jus solis_ sufficient to erase _jus sanguinis_ (when children of immigrants born on French soil are involved), or is it necessary to have an expression of desire from the parties concerned? May foreigners obtain political rights? Subsequent to the right to join labor unions and professional associations, should the very right to vote be granted them within local communities and, eventually, on the national level?
Questions do keep piling up; and the Committee of Wise Men (as it was dubbed by the media) who pondered over the "Nationality Code" has drawn up reasonable suggestions. Having noted that "France has, in both relative and absolute terms, the largest foreign population in its modern history," and that "it is not in the interest of any country to allow excessively large foreign minorities to develop on its soil, minorities that would call attention to themselves through insisting on their difference or through being excluded from social and national life," the Committee on Nationality chaired by Marceau Long advocated "granting French nationality to those foreigners who have settled in France on a long-term basis" and improving the "modalities of acquiring [French nationality] as a result of a conscious choice, which would be advantageous to the individual's integration." It posited "integration as a necessity." Those suggestions will most obviously be discussed, questioned, at least partly adopted, and are necessarily evolutive in nature.
In the kaleidoscope that France is becoming—kaleidoscope first of the Mediterranean and progressively of the third world—the differences between natives and immigrants will never be as clear-cut as before. The homogenizing power of French civilization, which has been able to take in and unify over the course of centuries various influences and ethnic groups, has been tried and tested. Now France today is in the process of welcoming newcomers who do not give up their particularities. The situation is quite different from the one that presided over the beginnings of the United States of America, which offered a new religious and economic faith to uprooted people who all found themselves in the same boat. In France, at the end of the twentieth century, each is fated to remain the same _and_ the other—without forgetting his original culture but putting it in perspective to the extent of having it not only exist side by side but also alternate with others' culture. A new homogeneity is not very likely, perhaps hardly desirable. We are called upon, through the pressures of the economy, the media, and history to live together in a single country, France, itself in the process of being integrated into Europe. We already have so many difficulties—but also so many advantages—coexisting in this new multinational (and not supranational) country that Europe has become—even though it is made up of nations whose cultures have been close, religions similar, and economies interdependent for centuries! Consequently one can assess the difficulty presented, in the bosom of the same political entity (even though it might be in the process of being integrated with others), by the cohabitation of people whose considerable ethnic, religious, and economic diversity clashes with the present tradition and mentality of those welcoming them. Are we headed for a jigsaw-puzzle nation made up of various particularities, whose predominant numbers remain French for the time being—but for how long?
A changed attitude of mind is necessary in order to favor the best harmony in such a versatility. What might be involved, in the final analysis, is extending to the notion of _foreigner_ the right of respecting our own foreignness and, in short, of the "privacy" that insures freedom in democracies. The access of foreigners to political rights will follow on the heels of that evolution and, necessarily, with adequate legal guarantees. One might imagine, for instance, a "double nationality" statute that would give those "foreigners" who want it a number of rights—but also the political duties specific to natives, with a reciprocity clause giving the latter rights and duties in the countries of origin of those same foreigners. Such a rule, easily applicable within the European Economic Community, could be tempered and adjusted for other countries.
Nevertheless, the fundamental question that slows down such arrangements, which lawyers and politicians are at present working out under the changing constraints of national economic needs, belongs to a more psychological or even metaphysical realm. In the absence of a new community bond—a saving religion that would integrate the bulk of wanderers and different people within a new consensus, other than "more money and goods for everyone"—we are, for the first time in history, confronted with the following situation: we must live with different people while relying on our personal moral codes, without the assistance of a set that would include our particularities while transcending them. A paradoxical community is emerging, made up of foreigners who are reconciled with themselves to the extent that they recognize themselves as foreigners. The multinational society would thus be the consequence of an extreme individualism, but conscious of its discontents and limits, knowing only indomitable people ready to help themselves in their weakness, a weakness whose other name is our radical strangeness.
NOTES
. See _Etre français aujourd'hui et demain_ (Paris: 10/18, 1988), 2:235–36.
PART 5
_Maternity, Feminism, and Female Sexuality_
Desire in Language
"Motherhood According to Giovanni Bellini"
"Motherhood According to Giovanni Bellini" was first published in _Peinture_ in December 1975 (when Kristeva was pregnant with her son who was born in 1976) and was reprinted in _Polylogue_ (Paris: Editions de Seuil) in 1977. The first section, "The Maternal Body," first appeared in translation by Claire Pajaczkowska in the journal _m/f_ in 1979. It was translated by Thomas Gora, Alice Jardine, and Leon Roudiez in _Desire in Language_ , edited by Leon Roudiez (New York: Columbia University Press) in 1980. "The Maternal Body," from _Desire in Language_ is reprinted here. In this section, Kristeva sets up a theory of maternity with which she goes on to analyze some of Bellini's paintings of the Madonna and Child.
Kristeva argues that the two discourses of maternity that are currently available, science and Christianity, are inadequate to explain maternity. Science explains maternity as a natural, and therefore presocial, biological process. Yet, where is the mother in this process? Is she the subject of this process or merely subject to it? If the mother is seen as merely subject to this process over which she has no control, then her identity (and subsequently the identity of the infant who identifies with her) as a speaking subject is threatened. If, on the other hand, the mother is seen as the master of this process, then she is the master of something presocial and biological and her identity (and subsequently the identity of the infant) as a speaking subject is once again threatened. Science cannot account for the splitting of subjectivity in the maternal body.
Although Christianity does address the move from nature to culture in the maternal body with the image of the Virgin Mary, in "Stabat Mater" Kristeva suggests that the image of the Virgin does not provide an adequate model of maternity; with the Virgin, the maternal body is reduced to silence. In both "Stabat Mater" and "Motherhood According to Bellini" Kristeva claims that pregnancy and childbirth can be experienced as a reunion with one's own mother. "By giving birth, the woman enters into contact with her mother; she becomes, she is her own mother; they are the same continuity differentiating itself. She thus actualizes the homosexual facet of motherhood." (p. 239). Kristeva's thesis that pregnancy and childbirth reunite a woman and her mother and bring back primal homosexual bonds is radically opposed to Freud's theory that childbirth is motivated by penis envy. Kristeva suggests a notion of the maternal body that locates its _jouissance_ in femininity and maternity itself rather than the Freudian notion of the maternal body, which is always defined in relation to masculine sexuality and a phallic economy of desire.
Tales of Love
In _Tales of Love_ , Kristeva complicates not only the paternal function but also the maternal function (see part 3 above). Unlike Freud and Lacan, who attribute language acquisition and socialization to the paternal function and ignore the function of the mother as anything other than the primary object or partial object, Kristeva elaborates and complicates the maternal function. She insists that there is regulation and structure in the maternal body and the child's relationship to that body. Before the paternal law is in place, the infant is subject to maternal regulations, what Kristeva calls "the law before the law." While in the womb, the fetus is engaged in processes of exchange with the maternal body that are regulated by that body. After birth, there are further exchanges between the maternal body and the infant. The mother monitors and regulates what goes into, and what comes out of, the infant's body. Language acquisition and socialization, insofar as they develop out of regulations and law, have their foundations in the maternal function prior to the law of the father of traditional psychoanalysis.
In "Stabat Mater," Kristeva suggests that Freud's account of motherhood as either an attempt to satisfy penis envy (baby = penis) or a reactivated anal drive (baby = feces) is merely a masculine fantasy. With regard to the complexities of maternal experience, claims Kristeva, "Freud offers only a massive nothing, which, for those who might care to analyze it, is punctuated with this or that remark on the part of Freud's mother, proving to him in the kitchen that his own body is anything but immortal and will crumble away like dough; or the sour photograph of Marthe Freud, the wife, a whole mute story." (p. 255)
Originally titled "Héréthique de l'amour," "Stabat Mater" was published in _Tel Quel_ (Winter 1977) and reprinted in _Histoires d'amour_ (1983). "Stabat Mater" was translated by Leon Roudiez as part of _Tales of Love_ (New York: Columbia University Press, 1987). "Stabat Mater" is a Latin hymn that begins with the words "Stabat mater dolorosa," "Stood the Mother, full of grief." "Stabat Mater" is written in two columns. In one column Kristeva poetically describes her own experience of motherhood and the birth of her son (1976), and in the other she argues that we need to reconceive maternity. In her interview with Rosalind Coward, Kristeva says that with the split columns she was trying to represent the wound or scar as the place from which the theoretician writes. The theoretician writes a knowing discourse about something, in this case maternity, in which she is deeply and painfully involved. Kristeva uses the scarred text to conjure that pain.
In the theoretical half of the text, Kristeva suggests that we need an image of maternity that can found, rather than threaten, the social relationship. Western images of maternity, especially what she calls the "cult of the Virgin Mary," do not allow for an image of the mother as a speaking social being. "Stabat Mater" is a manifesto of sorts that ends with a call for a reconceived notion of maternity and an heretical ethics, "herethics," based on a reconceived maternity. Insofar as this ethics of maternity would replace the Catholic image of the Virgin bearing her sorrow and baring her breast, it would be a heretical ethics, an ethics that does not reduce women to "milk and tears."
In "Stabat Mater" and "Women's Time" (1979) Kristeva suggests that currently the only way available for women to reestablish their identities with the maternal body is through becoming mothers themselves. Pregnancy allows for an identification with an other: "Pregnancy is a dramatic ordeal: a splitting of the body, the division and coexistence of self and other, of nature and awareness, of physiology and speech" (p. 219). Pregnancy not only identifies a woman with her own mother, but also requires a new notion of identity. As Kristeva argues in "Stabat Mater," neither the mother nor the fetus controls pregnancy. The maternal body operates between nature and culture, between biology and sociology. Neither the mother nor fetus is a unified subject. Rather, the maternal body is the most obvious example of a subject-in-process. Kristeva developed her notion of a subject-in-process in "From One Identity to an Other" and in _Revolution_ , where she maintains that we are all subjects-in-process.
Kristeva further delineates the maternal and paternal functions in her interview with Rosalind Coward. There, Kristeva suggests that the distinction between these two necessary functions is breaking down. In this interview, Kristeva makes it clear that maternal and paternal functions can be performed by various people in an infant's development. She also discusses her relationship to feminism. This interview took place at the Institute of Contemporary Arts in London at a conference on Desire in which Kristeva participated. It was published in the _Institute of Contemporary Arts Documents_ in 1984 in a special issue on desire.
New Maladies of the Soul
"Women's Time"
"Le Temps des femmes," originally published in _34/44: Cahiers de recherche de sciences des textes et documents_ , no. 5, was originally translated by Alice Jardine and Harry Blake as "Women's Time," in _Signs_ (Autumn 1981) and reprinted in _Feminist Theory: A Critique of Ideology_ , edited by N. Keohane, M. Z. Rosaldo, and B. C. Gelpi (Brighton: Harvester Press, 1982). This translation was also reprinted in _The Kristeva Reader_ in 1986, edited by Toril Moi. A slightly updated version of "Le Temps des femmes" was reprinted in _Nouvelles maladies de l'âme_ (Paris: Fayard, 1993) and newly translated as "Women's Time" by Ross Guberman in _New Maladies of the Soul_ (New York: Columbia University Press, 1994). The new translation by Ross Guberman appears here.
"Women's Time" has had a mixed response from feminists in the United States. In this essay, Kristeva analyzes different tendencies in the women's movement and feminist theory, primarily in Western Europe and also in the United States and Eastern Europe. She identifies what she calls three generations of feminism, which she complicates throughout her analysis. The first (prior to 1968) feminism is the feminism of suffragettes and existentialists. It is a struggle over the identity of woman as rational citizen, deserving of the "rights of man." These feminists maintain that the ideal "woman" contains the same characteristics of the ideal "man" and the struggle is to insert her in man's linear history. The second (after 1968) feminism is the feminism of psychoanalysts and artists. It is a struggle against reducing the identity of woman to the identity of man by inserting her into his linear time. These feminists assert a unique essence of woman or the feminine which falls outside of phallic time and phallic discourse. Kristeva delineates the advantages, advances, and limitations of both of these feminist strategies. Ultimately, she rejects them both for their tendencies to reify and idealize a notion of woman that is homogeneous and does not allow for individual differences. Kristeva identifies herself with a third generation of feminists who challenge notions of seamless identity in general, and notions of man and woman in particular. The last paragraph of "Women's Time," recently added to the essay, points to a post-feminist future.
Interview with Elaine Hoffman Baruch on Feminism in the United States and France
In her interview with Elaine Hoffman Baruch, Kristeva discusses the notion of abjection developed in _Powers of Horror_. She indicates that the abjection of the maternal body that she described in _Powers of Horror_ applies only to the experience of the male infant. The female infant has a different relationship to the maternal body. In addition, she discusses her views on feminism in the United States; she is asked to compare her views with those of Dinnerstein, Chodorow, Millett, and Firestone. Also, she addresses issues raised by advances in reproductive technology. This interview took place in Paris in 1980. A translation of the interview by Brom Anderson was first published in _Partisan Review_ in 1984. An expanded version of that interview was reprinted in _Women Analyze Women_ , edited by Elaine Baruch and Lucienne Serrano, published by New York University Press in 1988. That expanded version is reprinted here.
Black Sun
In her earlier work, _Revolution in Poetic Language_ , Kristeva follows Lacan in identifying sexual difference with differing relations to the phallus, in her later work, _Black Sun_ (1987), she suggests that sexual difference is a result of differing relations to the maternal body. Although even traditional Freudian theory identifies the phallus and the maternal body in the figure of the phallic mother, in _Black Sun_ Kristeva explores a melancholy element of feminine sexuality that cannot be completely explained in terms of either the notion of a phallic mother or the notion of a castrated mother.
In _Black Sun_ , Kristeva describes feminine sexuality as a melancholy sexuality because the female infant cannot abject the maternal body without abjecting herself. "Matricide," says Kristeva "is our vital necessity"; the infant must be weaned from the maternal body (p. 27). Weaning requires that the infant abject the maternal body, not as the desiring body of a woman, but as the container that meets its needs. Within a patriarchal and heterosexist culture, however, while males can abject and eroticize the maternal body in order to develop a heterosexual sexuality, females can neither abject nor eroticize the maternal body in order to develop a heterosexual sexuality: "in order to separate from their mother's bodies females must separate from themselves as women; and in order to maintain some identification with their mothers as the bodies of women females carry around the 'corpse' of their mother's bodies locked in the crypt of their psyches" (p. 28–29). Because the girl's first love object is her mother, in a heterosexist culture, this primary homosexual feminine sexuality remains repressed and we lack ways of describing loving relations between women, homosexual or otherwise. Feminine sexuality is melancholic because to identify as women, females must identify with an abject maternal body.
Hannah Arendt
Kristeva's _Female Genius: Life, Madness, Words_ is a trilogy. Volume one is on Hannah Arendt ( _Le génie féminin_ , tome I. _La Vie: Hannah Arendt—ou l'action comme naissance et comme étrangeté_ [Fayard, 1999]; translated by Ross Guberman as _Life: Hannah Arendt—or Action as Birth and Estrangement_ [Columbia University Press, 2000]). Volume two is on Melanie Klein ( _Le génie féminin_ , tome II. _La Folie: Melanie Klein—ou le matricide comme douleur et comme créativité_ [Fayard, 2000]; translated by Ross Guberman as _Madness: Melanie Klein—or Matricide as Pain and Creativity_ [Columbia University Press, 2001]). Volume three, _Les Mots_ , is on Colette.
In her introduction to _Female Genius_ , which appears in volume one, _Hannah Arendt_ , Kristeva proposes that the genius is an antidote to massification. Although the genius represents originality that stands out against an assembly-line world, she becomes what she is through an interaction with her environment and with others. The genius is a subject who finds herself at a historical intersection and crystallizes its possibilities. In a sense her genius belongs to all of us. It is the therapeutic invention by which we too create and live. We are fascinated by the ordinary lives of geniuses because this ordinariness also infuses our own with their genius. Kristeva says that our very existence is indefinitely renewable through the extraordinary within the ordinary. Geniuses allow us to believe that we too can "be someone."
Ultimately, the genius of everyday life is women's genius, particularly a mother's genius. In creating new human beings, mothers are each singular innovators, reinventing the child anew every time. Kristeva suggests that mothers might represent the "only safeguard against the wholesale automation of human beings." Each mother, and each mother-child relation, is unique. She sees her project in _Female Genius_ as a call to "the singularity of every woman."
Desire in Language
Motherhood According to Giovanni Bellini
The Maternal Body
Cells fuse, split, and proliferate; volumes grow, tissues stretch, and body fluids change rhythm, speeding up or slowing down. Within the body, growing as a graft, indomitable, there is an other. And no one is present, within that simultaneously dual and alien space, to signify what is going on. "It happens, but I'm not there." "I cannot realize it, but it goes on." Motherhood's impossible syllogism.
This becoming-a-mother, this gestation, can possibly be accounted for by means of only two discourses. There is _science_ ; but as an objective discourse, science is not concerned with the subject, the mother as site of her proceedings. There is _Christian theology_ (especially canonical theology); but theology defines maternity only as an impossible elsewhere, a sacred beyond, a vessel of divinity, a spiritual tie with the ineffable godhead, and transcendence's ultimate support—necessarily virginal and committed to assumption. Such are the wiles of Christian reason (Christianity's still matchless rationalism, or at least its rationalizing power, finally become clear); through the maternal body (in a state of virginity and "dormition" before Assumption), it thus establishes a sort of subject at the point where the subject and its speech split apart, fragment, and vanish. Lay humanism took over the configuration of that subject through the cult of the mother; tenderness, love, and seat of social conservation.
And yet, if we presume that _someone_ exists throughout the process of cells, molecules, and atoms accumulating, dividing, and multiplying without any _identity_ (biological or socio-symbolical) having been formed so far, are we not positing an animism that reflects the inherent psychosis of the speaking Being? So, if we suppose that a _mother_ is the subject of gestation, in other words the _master_ of a process that science, despite its effective devices, acknowledges it cannot now and perhaps never will be able to take away from her; if we suppose her to be _master_ of a process that is prior to the social-symbolic-linguistic contract of the group, then we acknowledge the risk of losing identity at the same time as we ward it off. We recognize on the one hand that biology jolts us by means of unsymbolized instinctual drives and that this phenomenon eludes social intercourse, the representation of preexisting objects, and the contract of desire. On the other hand, we immediately deny it; we say there can be no escape, for mamma is there, she embodies this phenomenon; she warrants that _everything is_ , and that it is representable. In a double-barreled move, psychotic tendencies are acknowledged, but at the same time they are settled, quieted, and bestowed upon the mother in order to maintain the ultimate guarantee: symbolic coherence.
This move, however, also reveals, better than any mother ever could, that the maternal body is the place of a splitting, which, even though hypostatized by Christianity, nonetheless remains a constant factor of social reality. Through a body, destined to insure reproduction of the species, the woman-subject, although under the sway of the paternal function (as symbolizing, speaking subject and like all others), more of a _filter_ than anyone else—a thoroughfare, a threshold where "nature" confronts "culture." To imagine that there is _someone_ in that filter—such is the source of religious mystifications, the font that nourishes them: the fantasy of the so-called "Phallic" Mother. Because if, on the contrary, there were no one on this threshold, if the mother were not, that is, if she were not phallic, then every speaker would be led to conceive of its Being in relation to some void, a nothingness asymetrically opposed to this Being, a permanent threat against, first, its mastery, and ultimately, its stability.
The discourse of analysis proves that the _desire_ for motherhood is without fail a desire to bear a child of the father (a child of her own father) who, as a result, is often assimilated to the baby itself and thus returned to its place as _devalorized man_ , summoned only to accomplish his function, which is to originate and justify reproductive desire. Only through these phantasmatic nuptials can the father-daughter incest be carried out and the baby come to exist. At that, the incest is too far removed, bringing peace only to those who firmly adhere to the paternal symbolic axis. Otherwise, once the object is produced, once the fruit is detached, the ceremony loses its effect unless it be repeated forever.
And yet, through and with this desire, motherhood seems to be impelled _also_ by a nonsymbolic, nonpaternal causality. Only Ferenczi, Freud, and, later, Marie Bonaparte, have spoken about this, evoking the biological destiny of each differentiated sex. Material compulsion, spasm of a memory belonging to the species that either binds together or splits apart to perpetuate itself, series of markers with no other significance than the eternal return of the life-death biological cycle. How can we verbalize this prelinguistic, unrepresentable memory? Heraclitus' flux, Epicurus' atoms, the whirling dust of cabalic, Arab, and Indian mystics, and the stippled drawings of psychedelics—all seem better metaphors than the theories of Being, the logos, and its laws.
Such an excursion to the limits of primal regression can be phantasmatically experienced as the reunion of a woman-mother with the body of _her_ mother. The body of her mother is always the same Master-Mother of instinctual drive, a ruler over psychosis, a subject of biology, but also, one toward which women aspire all the more passionately simply because it lacks a penis: that body cannot penetrate her as can a man when possessing his wife. By giving birth, the woman enters into contact with her mother; she becomes, she is her own mother; they are the same continuity differentiating itself. She thus actualizes the homosexual facet of motherhood, through which a woman is simultaneously closer to her instinctual memory, more open to her own psychosis, and consequently, more negatory of the social, symbolic bond.
_The symbolic paternal facet_ relieves feminine aphasia present within the desire to bear the father's child. It is an appeasement that turns into melancholy as soon as the child becomes an object, a gift to others, neither self nor part of the self, an object destined to be a subject, an other. Melancholy readjusts the paranoia that drives to action (often violent) and to discourse (essentially parental, object-oriented, and pragmatic discourse) the feminine, verbal scarcity so prevalent in our culture.
_The homosexual-maternal facet_ is a whirl of words, a complete absence of meaning and seeing; it is feeling, displacement, rhythm, sound, flashes, and fantasied clinging to the maternal body as a screen against the plunge. Perversion slows down the schizophrenia that collapsing identities and the delights of the well-known and oft-solicited (by some women) pantheist fusion both brush up against.
Those afflicted or affected by psychosis have put up in its place the image of the Mother: for women, a paradise lost but seemingly close at hand; for men, a hidden god but constantly present through occult fantasy. And even psychoanalysts believe in it.
Yet, swaying between these two positions can only mean, for the woman involved, that she is within an _enceinte_ separating her from the world of everyone else. Enclosed in this "elsewhere," an _enceinte_ woman loses communital meaning, which suddenly appears to her as worthless, absurd, or at best, comic—a surface agitation severed from its impossible foundations. Oriental nothingness probably better sums up what, in the eyes of a Westerner, can only be regression. And yet it is jouissance, but like a negative of the one, tied to an object, that is borne by the unfailingly masculine libido. Here, alterity becomes nuance, contradiction becomes a variant, tension becomes passage, and discharge becomes peace. This tendency toward equalization, which is seen as a regressive extinction of symbolic capabilities, does not, however, reduce differences; it resides within the smallest, most archaic, and most uncertain of differences. It is powerful sublimation and indwelling of the symbolic within instinctual drives. It affects this series of "little differences-resemblances" (as the Chinese logicians of antiquity would say). Before founding society in the same stroke as signs and communication, they are the precondition of the latter's existence, as they constitute the living entity within its species, with its needs, its elementary apperceptions and communication, distinguishing between the instinctual drives of life and death. It affects primal repression. An ultimate danger for identity, but also supreme power of symbolic instance thus returning to matters of its concern. Sublimation here is both eroticizing without residue and a disappearance of eroticism as it returns to its source.
The speaker reaches this limit, this requisite of sociality, only by virtue of a particular, discursive practice called "art." A woman also attains it (and in our society, _especially_ ) through the strange form of split symbolization (threshold of language and instinctual drive, of the "symbolic" and the "semiotic") of which the act of giving birth consists. As the archaic process of socialization, one might even say civilization, it causes the childbearing woman to cathect, immediately and unwittingly, the physiological operations and instinctual drives dividing and multiplying her, first, in a biological, and finally, a social teleology. The maternal body slips away from the discursive hold and immediately conceals a cipher that must be taken into account biologically and socially. This ciphering of the species, however, this pre- and transsymbolic memory, makes the mother mistress of neither begetting nor instinctual drive (such a fantasy underlies the cult of any ultimately feminine deity); it does make of the maternal body the stakes of a natural and "objective" control, independent of any individual consciousness; it inscribes both biological operations and their instinctual echoes into this necessary and hazardous _program_ constituting every species. The maternal body is the module of a biosocial program. Its jouissance, which is mute, is nothing more than a recording, on the screen of the preconscious, of both the messages that consciousness, in its analytical course, picks up from this ciphering process and their classifications as empty foundation, as a-subjective lining of our rational exchanges as social beings. If it is true that every national language has its own dream language and unconscious, then each of the sexes—a division so much more archaic and fundamental than the one into languages—would have its own unconscious wherein the biological and social program of the species would be ciphered in confrontation with language, exposed to its influence, but independent of it. The symbolic destiny of the speaking animal, which is essential although it comes second, being superimposed upon the biological—this destiny _seals off_ (and in women, in order to preserve the homology of the group, it _censures_ ) that archaic basis and the special jouissance it procures in being transferred to the symbolic. Privileged, "psychotic" moments, or whatever induces them naturally, thus become necessary. Among such "natural" inducements, maternity is needed for this sexual modality to surface, this fragile, secretly guarded and incommunicable modality, quickly stifled by standard palliatives (by virile and "rational" censorship, or by the sentimentality of "maternal" tenderness toward a substitute-object for everything). This process is quite rightly understood as the demand for a penis. Fantasy indeed has no other sign, no other way to imagine that the speaker is capable of reaching the Mother, and thus, of unsettling its own limits. And, as long as there is language-symbolism-paternity, there will never be any other way to represent, to objectify, and to explain this unsettling of the symbolic stratum, this nature/culture threshold, this instilling the subjectless biological program into the very body of a symbolizing subject, this event called motherhood.
In other words, from the point of view of social coherence, which is where legislators, grammarians, and even psychoanalysts have their seat; which is where every body is made homologous to a male speaking body, motherhood would be nothing more than a phallic attempt to reach the Mother who is presumed to exist at the very place where (social and biological) identity recedes. If it is true that idealist ideologies develop along these lines, urging women to satisfy this presumed demand and to maintain the ensuing order, then, on the other hand, any negation of this utilitarian, social, and symbolic aspect of motherhood plunges into regression—but a particular regression whose currently recognized manifestations lead to the hypostasis of blind substance, to the negation of symbolic position, and to a justification of this regression under the aegis of the same Phallic Mother-screen.
The language of art, too, follows (but differently and more closely) the other aspect of maternal jouissance, the sublimation taking place at the very moment of primal repression within the mother's body, arising perhaps unwittingly out of her marginal position. At the intersection of sign and rhythm, of representation and light, of the symbolic and the semiotic, the artist speaks from a place where she is not, where she knows not. He delineates what, in her, is a body rejoicing [ _jouissant_ ]. The very existence of aesthetic practice makes clear that the Mother as subject is a delusion, just as the negation of the so-called poetic dimension of language leads one to believe in the existence of the Mother, and consequently, of transcendence. Because, through a symbiosis of meaning and nonmeaning, of representation and interplay of differences, the artist lodges into language, and through his identification with the mother (fetishism or incest), his own specific jouissance, thus traversing both sign and object. Thus, before all other speakers, he bears witness to what the unconscious (through the screen of the mother) records of those clashes that occur between the biological and social programs of the species. This means that through and across secondary repression (founding of signs), aesthetic practice touches upon primal repression (founding biological series and the laws of the species). At the place where it obscurely succeeds within the maternal body, every artist tries his hand, but rarely with equal success.
Nevertheless, craftsmen of Western art reveal better than anyone else the artist's debt to the maternal body and/or motherhood's entry into symbolic existence—that is, translibidinal jouissance, eroticism taken over by the language of art. Not only is a considerable portion of pictorial art devoted to motherhood, but within this representation itself, from Byzantine iconography to Renaissance humanism and the worship of the body that it initiates, two attitudes toward the maternal body emerge, prefiguring two destinies within the very economy of Western representation. Leonardo Da Vinci and Giovanni Bellini seem to exemplify in the best fashion the opposition between these two attitudes. On the one hand, there is a tilting toward the body as fetish. On the other, a predominance of luminous, chromatic differences beyond and despite corporeal representation. Florence and Venice. Worship of the figurable, representable man; or integration of the image accomplished in its truth-likeness within the luminous serenity of the unrepresentable.
A unique biographical experience and an uncommon, historical intersection of pagan-matriarchal Orientalism with sacred Christianity and incipient humanism were perhaps needed for Bellini's brush to retain the traces of a marginal experience, through and across which a maternal body might recognize its own, otherwise inexpressible in our culture.
NOTES
. "Dormition" refers to the period of the Virgin Mary's death, which is viewed merely as a period of sleep, before she was carried to heaven (Assumption). The word originated in the _Transitus Maria_ , a fifth-century Byzantine apocrypha.—Trans.
. The French word _enceinte_ has been kept as the only way to preserve the pun: _enciente_ is a protective wall around a town; _femme enceinte_ is a pregnant woman.—Trans.
Tales of Love
Stabat Mater
The Paradox: Mother or Primary Narcissism
If it is not possible to say of a _woman_ what she _is_ (without running the risk of abolishing her difference), would it perhaps be different concerning the _mother_ , since that is the only function of the "other sex" to which we can definitely attribute existence? And yet, there, too, we are caught in a paradox. First, we live in a civilization where the _consecrated_ (religious or secular) representation of femininity is absorbed by motherhood. If, however, one looks at it more closely, this motherhood is the _fantasy_ that is nurtured by the adult, man or woman, of a lost territory; what is more, it involves less an idealized archaic mother than the idealization of the _relationship_ that binds us to her, one that cannot be localized—an idealization of primary narcissism. Now, when feminism demands a new representation of femininity, it seems to identify motherhood with that idealized misconception and, because it rejects the image and its misuse, feminism circumvents the real experience that fantasy overshadows. The result?—a negation or rejection of motherhood by some avant-garde feminist groups. Or else an acceptance—conscious or not—of its traditional representations by the great mass of people, women and men.
I
FLASH—instant of time or of dream without time; inordinately swollen atoms of a bond, a vision, a shiver, a yet formless, unnameable embryo. Epiphanies. Photos of what is not yet visible and that language necessarily skims over from afar, allusively. Words that are always too distant, too abstract for this underground swarming of seconds, folding in unimaginable spaces. Writing them down is an ordeal of discourse, like love. What is loving, for a woman, the same thing as writing. Laugh. Impossible. Flash on the unnameable, weavings of abstractions to be torn. Let a body venture at last out of its shelter, take a chance with meaning under a veil of words. WORD FLESH. From one to the other, eternally, broken up visions, metaphors of the invisible.
II
Christianity is doubtless the most refined symbolic construct in which femininity, to the extent that it transpires through it—and it does so incessantly—is focused on _Maternality_. Let us call "maternal" the ambivalent principle that is bound to the species, on the one hand, and on the other stems from an identity catastrophe that causes the Name to topple over into the unnameable that one imagines as femininity, nonlanguage, or body. Thus Christ, the Son of man, when all is said and done, is "human" only through his mother—as if Christly or Christian humanism could only be a maternalism (this is, besides, what some secularizing trends within its orbit do not cease claiming in their esotericism). And yet, the humanity of the Virgin mother is not always obvious, and we shall see how, in her being cleared of sin, for instance, Mary distinguishes herself from mankind. But at the same time the most intense revelation of God, which occurs in mysticism, is given only to a person who assumes himself as "maternal." Augustine, Bernard of Clairvaux, Meister Eckhart, to mention but a few, played the part of the Father's virgin spouses, or even, like Bernard, received drops of virginal milk directly on their lips. Freedom with respect to the maternal territory then becomes the pedestal upon which love of God is erected. As a consequence, mystics, those "happy Schrebers" (Sollers) throw a bizarre light on the psychotic sore of modernity: it appears as the incapability of contemporary codes to tame the maternal, that is, primary narcissism. Uncommon and "literary," their present-day counterparts are always somewhat oriental, if not tragical—Henry Miller, who says he is pregnant; Artaud, who sees himself as "his daughters" or "his mother"... It is the orthodox constituent of Christianity, through John Chrysostom's golden mouth, among others, that sanctioned the transitional function of the Maternal by calling the Virgin a "bond," a "medium," or an "interval," thus opening the door to more or less heretical identifications with the Holy Ghost.
This resorption of femininity within the Maternal is specific to many civilizations, but Christianity, in its own fashion, brings it to its peak. Could it be that such a reduction represents no more than a masculine appropriation of the Maternal, which, in line with our hypothesis, is only a fantasy masking primary narcissism? Or else, might one detect in it, in other respects, the workings of enigmatic sublimation? These are perhaps the workings of masculine sublimation, a sublimation just the same, if it be true that for Freud picturing Da Vinci, and even for Da Vinci himself, the taming of that economy (of the Maternal or of primary narcissism) is a requirement for artistic, literary, or painterly accomplishment?
Within that perspective, however, there are two questions, among others, that remain unanswered. What is there, in the portrayal of the Maternal in general and particularly in its Christian, virginal, one, that reduces social anguish and gratifies a male being; what is there that also satisfies a woman so that a commonality of the sexes is set up, beyond and in spite of their glaring incompatibility and permanent warfare? Moreover, is there something in that Maternal notion that ignores what a woman might say or want—as a result, when women speak out today it is in matters of conception and motherhood that their annoyance is basically centered. Beyond social and political demands, this takes the well-known "discontents" of our civilization to a level where Freud would not follow—the discontents of the species.
A Triumph of the Unconscious in Monotheism
It would seem that the "virgin" attribute for Mary is a translation error, the translator having substituted for the Semitic term that indicates the sociolegal status of a young unmarried woman the Greek word _parthenos_ , which on the other hand specifies a physiological and psychological condition: virginity. One might read into this the Indo-European fascination (which Dumézil analyzed) with the virgin daughter as guardian of paternal power; one might also detect an ambivalent conspiracy, through excessive spiritualization, of the mother-goddess and the underlying matriarchy with which Greek culture and Jewish monotheism kept struggling. The fact remains that western Christianity has organized that "translation error," projected its own fantasies into it, and produced one of the most powerful imaginary constructs known in the history of civilizations.
The story of the virginal cult in Christianity amounts in fact to the imposition of pagan-rooted beliefs in, and often against, dogmas of the official Church. It is true that the Gospels already posit Mary's existence. But they suggest only very discreetly the immaculate conception of Christ's mother, they say nothing concerning Mary's own background and speak of her only seldom at the side of her son or during crucifixion. Thus Matthew 1:20 ("... the angel of the Lord appeared to him in a dream and said, 'Joseph, son of David, do not be afraid to take Mary home as your wife, because she has conceived what is in her by the Holy Spirit"'), and Luke 1:34 ("Mary said to the angel, 'But how can this come about since I do not know man?"') open a door, a narrow opening for all that, but one that would soon widen thanks to apocryphal additions, on impregnation without sexuality; according to this notion a woman, preserved from masculine intervention, conceives alone with a "third party," a nonperson, the Spirit. In the rare instances when the Mother of Jesus appears in the Gospels, she is informed that filial relationship rests not with the flesh but with the name or, in other words, that any possible matrilinearism is to be repudiated and the symbolic link alone is to last. We thus have Luke 2:48–49 ("... his mother said to him, 'My child, why have you done this to us? See how worried your father and I have been, looking for you.' 'Why were you looking for me?' he replied. 'Did you not know that I must be busy with my father's affairs?"'), and also John 2:3–5 ("... the mother of Jesus said to him, 'They have no wine.' Jesus said, 'Woman, why turn to me? My hour has not come yet."') and 19:26–27 ("Seeing his mother and the disciple he loved standing near her, Jesus said to his mother, 'Woman, this is your son.' Then to the disciple he said, 'This is your mother.' And from that moment the disciple made a place for her in his home.")
Starting from this programmatic material, rather skimpy nevertheless, a compelling imaginary construct proliferated in essentially three directions. In the first place, there was the matter of drawing a parallel between Mother and Son by expanding the theme of the immaculate conception, inventing a biography of Mary similar to that of Jesus, and, by depriving her of sin to deprive her of death. Mary leaves by way of Dormition or Assumption. Next, she needed letters patent of nobility, a power that, even though exercised in the beyond, is nonetheless political, since Mary was to be proclaimed queen, given the attributes and paraphernalia of royalty and, in parallel fashion, declared Mother of the divine institution on earth, the Church. Finally, the relationship with Mary and from Mary was to be revealed as the prototype of a love relationship and followed two fundamental aspects of western love: courtly love and child love, thus fitting the entire range that goes from sublimation to asceticism and masochism.
Neither Sex nor Death
Mary's life, devised on the model of the life of Jesus, seems to be the fruit of apocryphal literature. The story of her own miraculous conception, called "immaculate conception," by Ann and Joachim, after a long, barren marriage, together with her biography as a pious maiden, show up in apocryphal sources as early as the end of the first century. Their entirety may be found in the _Secret Book of James_ and also in one of the pseudepigrapha, the Gospel according to the Hebrews (which inspired Giotto's frescoes, for instance). Those "facts" were quoted by Clement of Alexandria and Origen but not officially accepted; even though the Eastern Church tolerated them readily, they were translated into Latin only in the sixteenth century. Yet the West was not long before glorifying the life of Mary on its own but always under orthodox guidance. The first Latin poem, "Maria," on the birth of Mary was written by the nun Hrotswith von Gandersheim (who died before 1002), a playwright and poet.
Fourth-century asceticism, developed by the Fathers of the Church, was grafted on that apocryphal shoot in order to bring out and rationalize the immaculate conception postulate. The demonstration was based on a simple logical relation: the intertwining of sexuality and death. Since they are mutually implicated with each other, one cannot avoid the one without fleeing the other. This asceticism, applicable to both sexes, was vigorously expressed by John Chrysostom ( _On Virginity_ : "For where there is death there is also sexual copulation, and where there is no death there is no sexual copulation either"); even though he was attacked by Augustine and Aquinas, he nonetheless fueled Christian doctrine. Thus, Augustine condemned "concupiscence" ( _epithumia_ ) and posited that Mary's virginity is in fact only a logical precondition of Christ's chastity. The Orthodox Church, heir no doubt to a matriarchy that was more intense in eastern European societies, emphasized Mary's virginity more boldly. Mary was contrasted with Eve, life with death (Jerome, _Letter 22_ , "Death came through Eve but life came through Mary"; Irenaeus, "Through Mary the snake becomes a dove and we are freed from the chains of death"). People even got involved in tortuous arguments in order to demonstrate that Mary remained a virgin after childbirth (thus the second Constantinople council, in 381, under Arianistic influence, emphasized the Virgin's role in comparison to official dogma and asserted Mary's perpetual virginity; the 451 council called her _Aeiparthenos_ —ever virgin). Once this was established, Mary, instead of being referred to as Mother of man or Mother of Christ, would be proclaimed Mother of God: _Theotokos_. Nestorius, patriarch of Constantinople, refused to go along; Nestorianism, however, for all practical purposes died with the patriarch's own death in 451, and the path that would lead to Mary's deification was then clear.
I
Head reclining, nape finally relaxed, skin, blood, nerves warmed up, luminous flow: stream of hair made of ebony, of nectar, smooth darkness through her fingers, gleaming honey under the wings of bees, sparkling strands burning bright... silk, mercury, ductile copper: frozen light warmed under fingers. Mane of beast—squirrel, horse, and the happiness of a faceless head, Narcissuslike touching without eyes, sight dissolving in muscles, hair, deep, smooth, peaceful colors. Mamma: anamnesis.
Taut eardrum, tearing sound out of muted silence. Wind among grasses, a seagull's faraway call, echoes of waves, auto horns, voices, or nothing? Or his own tears, my newborn, spasm of syncopated void. I no longer hear anything, but the eardrum keeps transmitting this resonant vertigo to my skull, the hair. My body is no longer mine, it doubles up, suffers, bleeds, catches cold, puts its teeth in, slobbers, coughs, is covered with pimples, and it laughs. And yet, when its own joy, my child's, returns, its smile washes only my eyes. But the pain, its pain—it comes from inside, never remains apart, other, it inflames me at once, without a second's respite. As if that was what I had given birth to and, not willing to part from me, insisted on coming back, dwelled in me permanently. One does not give birth in pain, one gives birth to pain: the child represents it and henceforth it settles in, it is continuous. Obviously you may close your eyes, cover up your ears, teach courses, run errands, tidy up the house, think about objects, subjects. But a mother is always branded by pain, she yields to it. "And a sword will pierce your own soul too..."
Dream without glow, without sound, dream of brawn. Dark twisting, pain in the back, the arms, the thighs—pincers turned into fibers, infernos bursting veins, stones breaking bones: grinders of volumes, expanses, spaces, lines, points. All those words, now, ever visible things to register the roar of a silence that hurts all over. As if a geometry ghost could suffer when collapsing in a noiseless tumult... Yet the eye picked up nothing, the ear remained deaf. But everything swarmed, and crumbled, and twisted, and broke—the grinding continued... Then, slowly, a shadowy shape gathered, became detached, darkened, stood out: seen from what must be the true place of my head, it was the right side of my pelvis. Just bony, sleek, yellow, misshapen, a piece of my body jutting out unnaturally, asymmetrically, but slit: severed scaly surface, revealing under this disproportionate pointed limb the fibers of a marrow... Frozen placenta, live limb of a skeleton, monstrous graft of life on myself, a living dead. Life... death... undecidable. During delivery it went to the left with the afterbirth... My removed marrow, which nevertheless acts as a graft, which wounds but increases me. Paradox: deprivation and benefit of childbirth. But calm finally hovers over pain, over the terror of this dried branch that comes back to life, cut off, wounded, deprived of its sparkling bark. The calm of another life, the life of that other who wends his way while I remain henceforth like a framework. Still life. There is him, however, his own flesh, which was mine yesterday. Death, then, how could I yield to it?
II
Very soon, within the complex relationship between Christ and his Mother where relations of God to mankind, man to woman, son to mother, and the like, are hatched, the problematics of _time_ similar to that of cause loomed up. If Mary preceded Christ and he originated in her if only from the standpoint of his humanity, should not the conception of Mary herself have been immaculate? For, if that were not the case, how could a being conceived in sin and harboring it in herself produce a God? Some apocryphal writers had not hesitated, without too much caution, to suggest such an absence of sin in Mary's conception, but the Fathers of the Church were more careful. Bernard of Clairvaux is reluctant to extol the conception of Mary by Anne, and thus he tries to check the homologation of Mary with Christ. But it fell upon Duns Scotus to change the hesitation over the promotion of a mother goddess within Christianity into a logical problem, thus saving them both, the Great Mother as well as logic. He viewed Mary's birth as a _praeredemptio_ , as a matter of congruency: if it be true that Christ alone saves us through his redemption on the cross, the Virgin who bore him can but be preserved from sin in "recursive" fashion, from the time of her own conception up to that redemption.
For or against, with dogma or logical shrewdness, the battle around the Virgin intensified between Jesuits and Dominicans, but the Counter-Reformation, as is well known, finally ended the resistance: henceforth, Catholics venerated Mary in herself. The Society of Jesus succeeded in completing a process of popular pressure distilled by patristic asceticism, and in reducing, with neither explicit hostility nor brutal rejection, the share of the Maternal (in the sense given above) useful to a certain balance between the two sexes. Curiously and necessarily, when that balance began to be seriously threatened in the nineteenth century, the Catholic Church—more dialectical and subtle here than the Protestants who were already spawning the first suffragettes—raised the Immaculate Conception to dogma status in 1854. It is often suggested that the blossoming of feminism in Protestant countries is due, among other things, to the greater initiative allowed women on the social and ritual plane. One might wonder if, in addition, such a flowering is not the result of a _lack_ in the Protestant religious structure with respect to the Maternal, which, on the contrary, was elaborated within Catholicism with a refinement to which the Jesuits gave the final touch, and which still makes Catholicism very difficult to analyze.
The fulfillment, under the name of Mary, of a totality made of woman and God is finally accomplished through the avoidance of death. The Virgin Mary experiences a fate more radiant than her son's: she undergoes no calvary, she has no tomb, she doesn't die and hence has no need to rise from the dead. Mary doesn't die but, as if to echo oriental beliefs, Taoists' among others, according to which human bodies pass from one place to another in an eternal flow that constitutes a carbon copy of the maternal receptacle—she is transported.
Her transition is more passive in the Eastern Church: it is a Dormition ( _Koimesis_ ) during which, according to a number of iconographic representations, Mary can be seen changed into a little girl in the arms of her son who henceforth becomes her father; she thus reverses her role as Mother into a Daughter's role for the greater pleasure of those who enjoy Freud's "Theme of the Three Caskets."
Indeed, _mother_ of her son and his _daughter_ as well, Mary is also, and besides, his _wife_ : she therefore actualizes the threefold metamorphosis of a woman in the tightest parenthood structure. From 1135 on, transposing the Song of Songs, Bernard of Clairvaux glorifies Mary in her role of beloved and wife. But Catherine of Alexandria (said to have been martyred in 307) already pictured herself as receiving the wedding ring from Christ, with the Virgin's help, while Catherine of Siena (1347–80) goes through a mystical wedding with him. Is it the impact of Mary's function as Christ's beloved and wife that is responsible for the blossoming out of the Marian cult in the West after Bernard and thanks to the Cistercians? _Vergine Madre, figlia del tuo Figlio_ , Dante exclaims, thus probably best condensing the gathering of the three feminine functions (daughter-wifemother) within a totality where they vanish as specific corporealities while retaining their psychological functions. Their bond makes up the basis of unchanging and timeless spirituality; "the set time limit of an eternal design," _Termine fisso d'eterno consiglio_ , as Dante masterfully points out in his _Divine Comedy_.
The transition is more active in the West, with Mary rising body and soul toward the other world in an _Assumption_. That feast, honored in Byzantium as early as the fourth century, reaches Gaul in the seventh under the influence of the Eastern Church; but the earliest Western visions of the Virgin's assumption, women's visions (particularly that of Elizabeth von Schönau, who died in 1164) date only from the twelfth century. For the Vatican, the Assumption became dogma only in 1950. What death anguish was it intended to soothe after the conclusion of the deadliest of wars?
Image of Power
On the side of "power," _Maria Regina_ appears in imagery as early as the sixth century in the church of Santa Maria Antiqua in Rome. Interestingly enough, it is she, woman and mother, who is called upon to represent supreme earthly power. Christ is king but neither he nor his father are pictured wearing crowns, diadems, costly paraphernalia, and other external signs of abundant material goods. That opulent infringement to Christian idealism is centered on the Virgin Mother. Later, when she assumed the title of _Our Lady_ , this would also be an analogy to the earthly power of the noble feudal lady of medieval courts. Mary's function as guardian of power, later checked when the Church became wary of it, nevertheless persisted in popular and pictorial representation, witness Piero della Francesca's impressive painting, _Madonna della Misericordia_ , which was disavowed by Catholic authorities at the time. And yet, not only did the papacy revere more and more the Christly mother as the Vatican's power over cities and municipalities was strengthened, it also openly identified its own institution with the Virgin: Mary was officially proclaimed Queen by Pius XII in 1954 and _Mater Ecclesiae_ in 1964.
Eia Mater, Fons Amoris!
Fundamental aspects of Western love finally converged on Mary. In a first step, it indeed appears that the Marian cult homologizing Mary with Jesus and carrying asceticism to the extreme was opposed to courtly love for the noble lady, which, while representing social transgression, was not at all a physical or moral sin. And yet, at the very dawn of a "courtliness" that was still very carnal, Mary and the Lady shared one common trait: they are the focal point of men's desires and aspirations. Moreover, because they were unique and thus excluded all other women, both the Lady and the Virgin embodied an absolute authority the more attractive as it appeared removed from paternal sternness. This feminine power must have been experienced as denied power, more pleasant to seize because it was both archaic and secondary, a kind of substitute for effective power in the family and the city but no less authoritarian, the underhand double of explicit phallic power. As early as the thirteenth century, thanks to the implantation of ascetic Christianity and especially, as early as 1328, to the promulgation of Salic laws, which excluded daughters from the inheritance and thus made the loved one very vulnerable and colored one's love for her with all the hues of the impossible, the Marian and courtly streams came together. Around the time of Blanche of Castile, (who died in 1252), the Virgin explicitly became the focus of courtly love, thus gathering the attributes of the desired woman and of the holy mother in a totality as accomplished as it was inaccessible. Enough to make any woman suffer, any man dream. One finds indeed in a _Miracle de Notre Dame_ the story of a young man who abandons his fiancee for the Virgin: the latter came to him in a dream and reproached him for having left her for an "earthly woman."
Nevertheless, besides that ideal totality that no individual woman could possibly embody, the Virgin also became the
I
Scent of milk, dewed greenery, acid and clear, recall of wind, air, seaweed (as if a body lived without waste): it slides under the skin, does not remain in the mouth or nose but fondles the veins, detaches skin from bones, inflates me like an ozone balloon, and I hover with feet firmly planted on the ground in order to carry him, sure, stable, ineradicable, while he dances in my neck, flutters with my hair, seeks a smooth shoulder on the right, on the left, slips on the breast, swingles, silver vivid blossom of my belly, and finally flies away on my navel in his dream carried by my hands. My son.
Nights of wakefulness, scattered sleep, sweetness of the child, warm mercury in my arms, cajolery, affection, defenseless body, his or mine, sheltered, protected. A wave swells again, when he goes to sleep, under my skin—tummy, thighs, legs: sleep of the muscles, not of the brain, sleep of the flesh. The wakeful tongue quietly remembers another withdrawal, mine: a blossoming heaviness in the middle of the bed, of a hollow, of the sea... Recovered childhood, dreamed peace restored, in sparks, flash of cells, instants of laughter, smiles in the blackness of dreams, at night, opaque joy that roots me in her bed, my mother's, and projects him, a son, a butterfly soaking up dew from her hand, there, nearby, in the night. Alone: she, I, and he.
He returns from the depths of the nose, the vocal chords, the lungs, the ears, pierces their smothering stopping sickness swab, and awakens in his eyes. Gentleness of the sleeping face, contours of pinkish jade—forehead, eyebrows, nostrils, cheeks, parted features of the mouth, delicate, hard, pointed chin. Without fold or shadow, neither being nor unborn, neither present nor absent, but real, real inaccessible innocence, engaging weight and seraphic lightness. A child?—An angel, a glow on an Italian painting, impassive, peaceful dream—dragnet of Mediterranean fishermen. And then, the mother-of-pearl bead awakens: quicksilver. Shiver of the eyelashes, imperceptible twitch of the eyebrows, quivering skin, anxious reflections, seeking, knowing, casting their knowledge aside in the face of my nonknowledge: fleeting irony of childhood gentleness that awakens to meaning, surpasses it, goes past it, causes me to soar in music, in dance. Impossible refinement, subtle rape of inherited genes: before what has been learned comes to pelt him, harden him, ripen him. Hard, mischievous gentleness of the first ailment overcome, innocent wisdom of the first ordeal undergone, yet hopeful blame on account of the suffering I put you through, by calling for you, desiring, creating... Gentleness, wisdom, blame: your face is already human, sickness has caused you to join our species, you speak without words but your throat no longer gurgles—it harkens with me to the silence of your born meaning that draws my tears toward a smile.
The lover gone, forgetfulness comes, but the pleasure of the sexes remains, and there is nothing lacking. No representation, sensation, or recall. Inferno of vice. Later, forgetfulness returns but this time as a fall—leaden—grey, dull, opaque. Forgetfulness: blinding, smothering foam, but on the quiet. Like the fog that devours the park, wolfs down the branches, erases the green, rusty ground, and mists up my eyes.
Absence, inferno, forgetfulness. Rhythm of our loves.
A hunger remains, in place of the heart. A spasm that spreads, runs through the blood vessels to the tips of the breasts, to the tips of the fingers. It throbs, pierces the void, erases it, and gradually settles in. My heart: a tremendous pounding wound. A thirst.
Anguished, guilty. Freud's _Vaterkomplex_ on the Acropolis? The impossibility of being without repeated legitimation (without books, man, family). Impossibility—depressing possibility—of "transgression."
Either repression in which _I_ hands the Other what I want from others.
Or this squalling of the void, open wound in my heart, which allows me to be only in purgatory.
I yearn for the Law. And since it is not made for me alone, I venture to desire outside the law. Then, narcissism thus awakened—the narcissism that wants to be sex—roams, astonished. In sensual rapture I am distraught. Nothing reassures, for only the law sets anything down. Who calls such a suffering jouissance? It is the pleasure of the damned.
II
fulcrum of the humanization of the West in general and of love in particular. It is again about the thirteenth century, with Francis of Assisi, that this tendency takes shape with the representation of Mary as poor, modest, and humble—madonna of humility at the same time as a devoted, fond mother. The famous nativity of Piero della Francesca in London, in which Simone de Beauvoir too hastily saw a feminine defeat because the mother kneeled before her barely born son, in fact consolidates the new cult of humanistic sensitivity. It replaces the high spirituality that assimilated the Virgin to Christ with an earthly conception of a wholly human mother. As a source for the most popularized pious images, such maternal humility comes closer to "lived" feminine experience than the earlier representations did. Beyond this, however, it is true that it integrates a certain feminine masochism but also displays its counterpart in gratification and jouissance. The truth of it is that the lowered head of the mother before her son is accompanied by the immeasurable pride of the one who knows she is also his wife and daughter. She knows she is destined to that eternity (of the spirit or of the species), of which every mother is unconsciously aware, and with regard to which maternal devotion or even sacrifice is but an insignificant price to pay. A price that is borne all the more easily since, contrasted with the love that binds a mother to her son, all other "human relationships" burst like blatant shams. The Franciscan representation of the Mother conveys many essential aspects of maternal psychology, thus leading up to an influx of common people to the churches and also a tremendous increase in the Marian cult—witness the building of many churches dedicated to her ("Notre Dame"). Such a humanization of Christianity through the cult of the mother also led to an interest in the humanity of the father-man: the celebration of "family life" showed Joseph to advantage as early as the fifteenth century.
What Body?
We are entitled only to the ear of the virginal body, the tears, and the breast. With the female sexual organ changed into an innocent shell, holder of sound, there arises a possible tendency to eroticize hearing, voice, or even understanding. By the same token, however, sexuality is brought down to the level of innuendo. Feminine sexual experience is thus rooted in the universality of sound, since wit is distributed _equally_ among all men, all women. A woman will only have the choice to live her life either _hyperabstractly_ ("immediately universal," Hegel said) in order thus to earn divine grace and homologation with symbolic order; or merely _different_ , other, fallen ("immediately particular," Hegel said). But she will not be able to accede to the complexity of being divided, of heterogeneity, of the catastrophic fold-of-"being" ("never singular," Hegel said).
Under a full, blue gown, the maternal, virginal body allowed only the breast to show, while the face, with the stiffness of Byzantine icons gradually softened, was covered with tears. Milk and tears became the privileged signs of the _Mater Dolorosa_ who invaded the West beginning with the eleventh century, reaching the peak of its influx in the fourteenth. But it never ceased to fill the Marian visions of those, men or women (often children), who were racked by the anguish of a maternal frustration. Even though orality—threshold of infantile regression—is displayed in the area of the breast, while the spasm at the slipping away of eroticism is translated into tears, this should not conceal what milk and tears have in common: they are the metaphors of nonspeech, of a "semiotics" that linguistic communication does not account for. The Mother and her attributes, evoking sorrowful humanity, thus become representatives of a "return of the repressed" in monotheism. They reestablish what is nonverbal and show up as the receptacle of a signifying disposition that is closer to so-called primary processes. Without them the complexity of the Holy Ghost would have been mutilated. On the other hand, as they return by way of the Virgin Mother, they find their outlet in the arts—painting and music—of which the Virgin necessarily becomes both patron saint and privileged object.
The function of this "Virginal Maternal" may thus be seen taking shape in the Western symbolic economy. Starting with the high Christly sublimation for which it yearns and occasionally exceeds, and extending to the extralinguistic regions of the unnameable, the Virgin Mother occupied the tremendous territory on this and that side of the parenthesis of language. She adds to the Christian trinity and to the World that delineates their coherence the heterogeneity they salvage.
The ordering of the maternal libido reached its apotheosis when centered in the theme of death. The _Mater Dolorosa_ knows no masculine body save that of her dead son, and her only pathos (which contrasts with the somewhat vacant, gentle serenity of the nursing Madonnas) is her shedding tears over a corpse. Since resurrection there is, and, as Mother of God, she must know this, nothing justifies Mary's outburst of pain at the foot of the cross, unless it be the desire to experience within her own body the death of a human being, which her feminine fate of being the source of life spares her. Could it be that the love, as puzzling as it is ancient, of mourners for corpses relates to the same longing of a woman whom nothing fulfills—the longing to experience the wholly masculine pain of a man who expires at every moment on account of jouissance due to obsession with his own death? And yet, Marian pain is in no way connected with tragic outburst: joy and even a kind of triumph follow upon tears, as if the conviction that death does not exist were an irrational but unshakeable maternal certainty, on which the principle of resurrection had to rest. The brilliant illustration of the wrenching between desire for the masculine corpse and negation of death, a wrenching whose paranoid logic cannot be overlooked, is masterfully presented by the famous _Stabat Mater_. It is likely that all beliefs in resurrections are rooted in mythologies marked by the strong
I
Belief in the mother is rooted in fear, fascinated with a weakness—the weakness of language. If language is powerless to locate myself for and state myself to the other, I assume—I want to believe—that there is someone who makes up for that weakness. Someone, of either sex, _before_ the id speaks, before language, who might make me be by means of borders, separations, vertigos. In asserting that "in the beginning was the Word," Christians must have found such a postulate sufficiently hard to believe and, for whatever it was worth, they added its compensation, its permanent lining: the maternal receptacle, purified as it might be by the virginal fantasy. Archaic maternal love would be an incorporation of my suffering that is unfailing, unlike what often happens with the lacunary network of signs. In that sense, any belief, anguished by definition, is upheld by the fascinated fear of language's impotence. Every God, even including the God of the Word, relies on a mother Goddess. Christianity is perhaps also the last of the religions to have displayed in broad daylight the bipolar structure of belief: on the one hand, the difficult experience of the Word—a passion; on the other, the reassuring wrapping in the proverbial mirage of the mother—a love. For that reason, it seems to me that there is only one way to go through the religion of the Word, or its counterpart, the more or less discreet cult of the Mother; it is the "artists"' way, those who make up for the vertigo of language weakness with the oversaturation of sign systems. By this token, all art is a kind of counter reformation, an accepted baroqueness. For is it not true that if the Jesuits finally did persuade the official Church to accept the cult of the Virgin, following the puritanical wave of the Reformation, that dogma was in fact no more than a pretext, and its efficacy lay elsewhere. It did not become the opposite of the cult of the mother but its inversion through expenditure in the wealth of signs that constitutes the baroque. The latter renders belief in the Mother useless by overwhelming the symbolic weakness where she takes refuge, withdrawn from history, with an overabundance of discourse.
The immeasurable, unconfinable maternal body.
First there is the separation, previous to pregnancy, but which pregnancy brings to light and imposes without remedy.
On the one hand—the pelvis: center of gravity, unchanging ground, solid pedestal, heaviness and weight to which the thighs adhere, with no promise of agility on that score. On the other—the torso, arms, neck, head, face, calves, feet: unbounded liveliness, rhythm and mask, which furiously attempt to compensate for the immutability of the central tree. We live on that border, crossroads beings, crucified beings. A woman is neither nomadic nor a male body that considers itself earthly only in erotic passion. A mother is a continuous separation, a division of the very flesh. And consequently a division of language—and it has always been so.
Then there is this other abyss that opens up between the body and what had been its inside: there is the abyss between the mother and the child. What connection is there between myself, or even more unassumingly between my body and this internal graft and fold, which, once the umbilical cord has been severed, is an inaccessible other? My body and... him. No connection. Nothing to do with it. And this, as early as the first gestures, cries, steps, long before _its_ personality has become my opponent. The child, whether _he_ or _she_ , is irremediably an other. To say that there are no sexual relationships constitutes a skimpy assertion when confronting the flash that bedazzles me when I confront the abyss between what was mine and is henceforth but irreparably alien. Trying to think through that abyss: staggering vertigo. No identity holds up. A mother's identity is maintained only through the well-known closure of consciousness within the indolence of habit, when a woman protects herself from the borderline that severs her body and expatriates it from her child. Lucidity, on the contrary, would restore her as cut in half, alien to its other—and a ground favorable to delirium. But also and for that very reason, motherhood destines us to a demented jouissance that is answered, by chance, by the nursling's laughter in the sunny waters of the ocean. What connection is there between it and myself? No connection, except for that overflowing laughter where one senses the collapse of some ringing, subtle, fluid identity or other, softly buoyed by the waves.
Concerning that stage of my childhood, scented, warm, and soft to the touch, I have only a spatial memory. No time at all. Fragrance of honey, roundness of forms, silk and velvet under my fingers, on my cheeks. Mummy. Almost no sight—a shadow that darkens, soaks me up, or vanishes amid flashes. Almost no voice in her placid presence. Except, perhaps, and more belatedly, the echo of quarrels: her exasperation, her being fed up, her hatred. Never straightforward, always held back, as if, although the unmanageable child deserved it, the daughter could not accept the mother's hatred—it was not meant for her. A hatred without recipient or rather whose recipient was no "I" and which, perturbed by such a lack of recipience, was toned down into irony or collapsed into remorse before reaching its destination. With others, this maternal aversion may be worked up to a spasm that is held like a delayed orgasm. Women doubtless reproduce among themselves the strange gamut of forgotten body relationships with their mothers. Complicity in the unspoken, connivance of the inexpressible, of a wink, a tone of voice, a gesture, a tinge, a scent. We are in it, set free of our identification papers and names, on an ocean of preciseness, a computerization of the unnameable. No communication between individuals but connections between atoms, molecules, wisps of words, droplets of sentences. The community of women is a community of dolphins. Conversely, when the other woman posits herself as such, that is, as singular and inevitably in opposition, "I" am startled, so much that "I" no longer know what is going on. There are then two paths left open to the rejection that bespeaks the recognition of the other woman as such. Either, not wanting to experience her, I ignore her and, "alone of my sex," I turn my back on her in friendly fashion. It is a hatred that, lacking a recipient worthy enough of its power, changes to unconcerned complacency. Or else, outraged by her own stubbornness, by that other's belief that she is singular, I unrelentingly let go at her claim to address me and find respite only in the eternal return of power strokes, bursts of hatred—blind and dull but obstinate. I do not see her as herself but beyond her I aim at the claim to singularity, the unacceptable ambition to be something other than a child or a fold in the plasma that constitutes us, an echo of the cosmos that unifies us. What an inconceivable ambition it is to aspire to singularity, it is not natural, hence it is inhuman; the mania smitten with Oneness ("There is only One woman") can only impugn it by condemning it as "masculine"... Within this strange feminine see-saw that makes "me" swing from the unnameable community of women over to the war of individual singularities, it is unsettling to say "I." The languages of the great formerly matriarchal civilizations must avoid, do avoid, personal pronouns: they leave to the context the burden of distinguishing protagonists and take refuge in tones to recover an underwater, transverbal communication between bodies. It is a music from which so-called oriental civility tears away suddenly through violence, murder, blood baths. A woman's discourse, would that be it? Did not Christianity attempt, among other things, to freeze that see-saw? To stop it, tear women away from its rhythm, settle them permanently in the spirit? Too permanently...
II
dominance of a mother goddess. Christianity, it is true, finds its calling in the displacement of that biomaternal determinism through the postulate that immortality is mainly that of the name of the Father. But it does not succeed in imposing _its_ symbolic revolution without relying on the feminine representation of an immortal biology. Mary defying death is the theme that has been conveyed to us by the numerous variations of the _Stabat Mater_ , which, in the text attributed to Jacopone da Todi, enthralls us today through the music of Palestrina, Pergolesi, Haydn, and Rossini.
Let us listen to the baroque style of the young Pergolesi (1710–36), who was dying of tuberculosis when he wrote his immortal _Stabat Mater_. His musical inventiveness, which, through Haydn, later reverberated in the work of Mozart, probably constitutes his one and only claim to immortality. But when this cry burst forth, referring to Mary facing her son's death, _Eia Mater, fons amoris!_ ("Hail mother, source of love!")—was it merely a remnant of the period? Man overcomes the unthinkable of death by postulating maternal love in its place—in the place and stead of death and thought. This love, of which divine love is merely a not always convincing derivation, psychologically is perhaps a recall, on the near side of early identifications, of the primal shelter that insured the survival of the newborn. Such a love is in fact, logically speaking, a surge of anguish at the very moment when the identity of thought and living body collapses. The possibilities of communication having been swept away, only the subtle gamut of sound, touch, and visual traces, older than language and newly worked out, are preserved as an ultimate shield against death. It is only "normal" for a maternal representation to set itself up at the place of this subdued anguish called love. No one escapes it. Except perhaps the saint, the mystic, or the writer who, through the power of language, nevertheless succeeds in doing no better than to take apart the fiction of the mother as mainstay of love, and to identify with love itself and what he is in fact— _a fire of tongues_ , an exit from representation. Might not modern art then be, for the few who are attached to it, the implementation of that maternal love—a veil over death, in death's very site and with full knowledge of the facts? A sublimated celebration of incest...
**Alone of Her Sex**
Freud collected, among other objects of art and archeology, countless statuettes representing mother goddess. And yet his interest in them comes to light only in discreet fashion in his work. It shows up when Freud examines artistic creation and homosexuality in connection with Leonardo da Vinci and deciphers there the ascendancy of an archaic mother, seen therefore from the standpoint of her effects on man and particularly on this strange function of his sometimes to change languages. Moreover, when Freud analyzes the advent and transformations of monotheism, he emphasizes that Christianity comes closer to pagan myths by integrating, through and against Judaic rigor, a preconscious acknowledgment of a maternal feminine. And yet, among the patients analyzed by Freud, one seeks in vain for mothers and their problems. One might be led to think that motherhood was a solution to neurosis and, by its very nature, ruled out psychoanalysis as a possible other solution. Or might psychoanalysis, at this point, make way for religion? In simplified fashion, the only thing Freud tells us concerning motherhood is that the desire for a child is a transformation of either penis envy or anal drive, and this allows her to discover the neurotic equation child-penis-feces. We are thus enlightened concerning an essential aspect of male phantasmatics with respect to childbirth, and female phantasmatics as well, to the extent that it embraces, in large part and in its hysterical labyrinths, the male one. The fact remains, as far as the complexities and pitfalls of maternal experience are involved, that Freud offers only a massive _nothing_ , which, for those who might care to analyze it, is punctuated with this or that remark on the part of Freud's mother, proving to him in the kitchen that his own body is anything but immortal and will crumble away like dough; or the sour photograph of Marthe Freud, the wife, a whole mute story... There thus remained for his followers an entire continent to explore, a black one indeed, where Jung was the first to rush in, getting all his esoteric fingers burnt, but not without calling attention to some sore points of the imagination with regard to motherhood, points that are still resisting analytical rationality.
There might doubtless be a way to approach the dark area that motherhood constitutes for a woman; one needs to listen, more carefully than ever, to what mothers are saying today, through their economic difficulties and, beyond the guilt that a too existentialist feminism handed down, through their discomforts, insomnias, joys, angers, desires, pains, and pleasures... One might, in similar fashion, try better to understand the incredible construct of the Maternal that the West elaborated by means of the Virgin, and of which I have just mentioned a few episodes in a never-ending history.
What is it then in this maternal representation that, alone of her sex, goes against both of the two sexes, and was able to attract women's wishes for identification as well as the very precise interposition of those who assumed to keep watch over the symbolic and social order?
Let me suggest, by way of hypothesis, that the virginal maternal is a way (not among the less effective ones) of dealing with feminine paranoia.
—The Virgin assumes her feminine denial of the other sex (of man) but overcomes him by setting up a third person: _I_ do not conceive with _you_ but with _Him_. The result is an immaculate conception (therefore with neither man nor sex), conception of a God with whose existence a woman has indeed something to do, on condition that she acknowledge being subjected to it.
—The Virgin assumes the paranoid lust for power by changing a woman into a Queen in heaven and a Mother of the earthly institutions (of the Church). But she succeeds in stifling that megalomania by putting it on its knees before the child-god.
—The Virgin obstructs the desire for murder or devouring by means of a strong oral cathexis (the breast), valorization of pain (the sob), and incitement to replace the sexed body with the ear of understanding.
—The Virgin assumes the paranoid fantasy of being excluded from time and death through the very flattering representation of Dormition and Assumption.
—The Virgin especially agrees with the repudiation of the other woman (which doubtless amounts basically to a repudiation of the woman's mother) by suggesting the image of A woman as Unique: alone among women, alone among mothers, alone among humans since she is without sin. But the acknowledgment of a longing for uniqueness is immediately checked by the postulate according to which uniqueness is attained only through an exacerbated masochism: a concrete woman, worthy of the feminine ideal embodied by the Virgin as an inaccessible goal, could only be a nun, a martyr, or, if she is married, one who leads a life that would remove her from that "earthly" condition and dedicate her to the highest sublimation alien to her body. A bonus, however: the promised jouissance.
A skillful balance of concessions and constraints involving feminine paranoia, the representation of virgin motherhood appears to crown the efforts of a society to reconcile the social remnants of matrilinearism and the unconscious needs of primary narcissism on the one hand, and on the other the requirements of a new society based on exchange and before long on increased production, which require the contribution of the superego and rely on the symbolic paternal agency.
While that clever balanced architecture today appears to be crumbling, one is led to ask the following: what are the aspects of the feminine psyche for which that representation of motherhood does not provide a solution or else provides one that is felt as too coercive by twentieth-century women?
The unspoken doubtless weighs first on the maternal body: as no signifier can uplift it without leaving a remainder, for the signifier is always meaning, communication, or structure, whereas a woman as mother would be, instead, a strange fold that changes culture into nature, the speaking into biology. Although it concerns every woman's body, the heterogeneity that cannot be subsumed in the signifier nevertheless explodes violently with pregnancy (the threshold of culture and nature) and the child's arrival (which extracts woman out of her oneness and gives her the possibility—but not the certainty—of reaching out to the other, the ethical). Those particularities of the maternal body compose woman into a being of folds, a catastrophe of being that the dialectics of the trinity and its supplements would be unable to subsume.
Silence weighs heavily nonetheless on the corporeal and psychological suffering of childbirth and especially the self-sacrifice involved in becoming anonymous in order to pass on the social norm, which one might repudiate for one's own sake but within which _one must_ include the child in order to educate it along the chain of generations. A suffering lined with jubilation—ambivalence of masochism—on account of which a woman, rather refractory to perversion, in fact allows herself a coded, fundamental, perverse behavior, ultimate guarantee of society, without which society will not reproduce and will not maintain a constancy of standardized household. Feminine perversion does not reside in the parceling or the Don Juan–like multiplying of objects of desire; it is at once legalized, if not rendered paranoid, through the agency of masochism: all sexual "dissoluteness" will be accepted and hence become insignificant, provided a child seals up such outpourings. Feminine perversion [ _père-version_ ] is coiled up in the desire for law as desire for reproduction and continuity, it promotes feminine masochism to the rank of structure stabilizer (against its deviations); by assuring the mother that she may thus enter into an order that is above humans' will it gives her her reward of pleasure. Such coded perversion, such close combat between maternal masochism and the law have been utilized by totalitarian powers of all times to bring women to their side, and, of course, they succeed easily. And yet, it is not enough to "declaim against" the reactionary role of mothers in the service of "male dominating power." One would need to examine to what extent that role corresponds to the biosymbolic latencies of motherhood and, on that basis, to try to understand, since the myth of the Virgin does not subsume them, or no longer does, how their surge lays women open to the most fearsome manipulations, not to mention blinding, or pure and simple rejection by progressive activists who refuse to take a close look.
Among things left out of the virginal myth there is the war between mother and daughter, a war masterfully but too quickly settled by promoting Mary as universal and particular, but never singular—as "alone of her sex." The relation to the other woman has presented our culture, in massive fashion during the past century, with the necessity to reformulate its representations of love and hatred—inherited from Plato's _Symposium_ , the troubadours, or Our Lady. On that level, too, motherhood opens out a vista: a woman seldom (although not necessarily) experiences her passion (love and hatred) for another woman without having taken her own mother's place—without having herself become a mother, and especially without slowly learning to differentiate between same beings—as being face to face with her daughter forces her to do.
Finally, repudiation of the other sex (the masculine) no longer seems possible under the aegis of the third person, hypostatized in the child as go-between: "neither me, nor you, but him, the child, the third person, the nonperson, God, which I still am in the final analysis..." Since there is repudiation, and if the feminine being that struggles within it is to remain there, it henceforth calls for, not the deification of the third party, but countercathexes in strong values, in strong _equivalents of power_. Feminine psychosis today is sustained and absorbed through passion for politics, science, art... The variant that accompanies motherhood might be analyzed perhaps more readily than the others from the standpoint of the rejection of the other sex
I
The love of God and for God resides in a gap: the broken space made explicit by sin on the one side, the beyond on the other. Discontinuity, lack, and arbitrariness: topography of the sign, of the symbolic relation that posits my otherness as impossible. Love, here, is only for the impossible.
For a mother, on the other hand, strangely so, the other as arbitrary (the child) is taken for granted. As far as she is concerned—impossible, that is just the way it is: it is reduced to the implacable. The other is inevitable, she seems to say, turn it into a God if you wish, it is nevertheless natural, for such an other has come out of myself, which is yet not myself but a flow of unending germinations, an eternal cosmos. The other goes much without saying and without my saying that, at the limit, it does not exist for itself. The "just the same" of motherly peace of mind, more persistent than philosophical doubt, gnaws, on account of its basic disbelief, at the symbolic's allmightiness. It bypasses perverse negation ("I know, but just the same") and constitutes the basis of the social bond in its generality, in the sense of "resembling others and eventually the species." Such an attitude is frightening when one imagines that it can crush everything the other (the child) has that is specifically irreducible: rooted in that disposition of motherly love, besides, we find the leaden strap it can become, smothering any different individuality. But it is there, too, that the speaking being finds a refuge when his/her symbolic shell cracks and a crest emerges where speech causes biology to show through: I am thinking of the time of illness, of sexual-intellectualphysical passion, of death...
II
that it comprises. To allow what? Surely not some understanding or other on the part of "sexual partners" within the preestablished harmony of primal androgyny. Rather, to lead to an acknowledgment of what is irreducible, of the irreconcilable interest of both sexes in asserting their differences, in the quest of each one—and of women, after all—for an appropriate fulfillment.
These, then, are a few questions among others concerning a motherhood that today remains, after the Virgin, without a discourse. They suggest, all in all, the need of an ethics for this "second" sex, which, as one asserts it, is reawakening.
Nothing, however, suggests that a feminine ethics is possible, and Spinoza excluded women from his (along with children and the insane). Now, if a contemporary ethics is no longer seen as being the same as morality,; if ethics amounts to not avoiding the embarrassing and inevitable problematics of the law but giving it flesh, language, and jouissance—in that case its reformulation demands the contribution of women: Of women who harbor the desire to reproduce (to have stability). Of women who are available so that our speaking species, which knows it is mortal, might withstand death. Of mothers. For an heretical ethics separated from morality, an _herethics_ , is perhaps no more than that which in life makes bonds, thoughts, and therefore the thought of death, bearable: herethics is undeath ( _amort_ ), love... _Eia mater, fons amoris..._ So let us again listen to the _Stabat Mater_ , and the music, all the music... it swallows up the goddesses and removes their necessity.
NOTES
. Between the lines of this section one should be able to detect the presence of Marina Warner, _Alone of All Her Sex: The Myth and Cult of the Virgin Mary_ (New York: Knopf, 1976) and Ilse Barande, _Le Maternel singulier_ (Paris: Aubier-Montaigne, 1977), which underlay my reflections.
. Georges Dumézil, _La Religion romaine archaïque_ (Paris: Payot, 1974).
. The French version quoted by Kristeva ("Woman, what is there in common between you and me?") is even stronger than the King James translation, "Woman, what have I to do with thee?"—Trans.
. Jung thus noted the "hierogamous" relationship between Mary and Christ as well as the overprotection given the Virgin with respect to original sin, which places her on the margin of mankind; finally, he insisted very much on the Vatican's adoption of the Assumption as dogma, seeing it as one of the considerable merits of Catholicism as opposed to Protestantism. C. G. Jung, _Answer to Job_ (Princeton: Princeton University Press, 1969).
. As Caelius Sedulius wrote, "She... had no peer / Either in our first mother or in all women / Who were to come. But alone of all her sex / She pleased the Lord" ("Paschalis Carminis," Book II, lines 68ff. of _Opera Omnia_ [Vienna, 1885]). Epigraph to Marina Warner, _Alone of All Her Sex_.
Julia Kristeva in Conversation with Rosalind Coward
ROSALIND COWARD: Could you say something more about your notion of transference in the book [ _Tales of Love_ ]. At one point you say that almost all of human history and human philosophy around the subject of love could be described as a transference. Could you explain that a bit more?
KRISTEVA: The word transference is a technical word, it comes from psychoanalysis. I think it was a great discovery by Freud to consider that what happens between the patient and the analyst is a sort of love which is a displacement of love-traumatism or love-disappointments from the past reality through the actual cure. And from that point on it was possible to remember what happened in the personal history. But also Freud tried to extrapolate this notion of transference from the cure itself to the whole field of human creativity: art, history, and the like. This extrapolation was not done very explicitly: when he analyzes religion, for instance, or some works of art by Michelangelo, he doesn't speak about transference, but I think it's implicit in his vision. There is something very romantic in Freud's vision of human relationships. His device, which is psychoanalysis, has always been analyzed in comparison with the development of scientific thought, and in comparison with religion. Maybe it will be necessary to compare it with the development of romanticism as well. His romantic death instinct. Eros and so on are a constant from romantic literature. He always said that the great artists preceded him in this way, by analyzing the human psyche. So transference is a therapeutic device but also something that has always operated in creation. And the Freudian view of symbolic creations allows us now to view it in a different way perhaps.
COWARD: Correct me if I'm wrong but my understanding of what you mean by transference is that the analytic process, in going back to the earliest stages of the child's life, reactivates the first form of love the child achieved or failed to achieve.
KRISTEVA: Yes, and he places this onto the analyst. It is a very dangerous moment because in a special article about identification Freud speaks about love and compares it with hypnosis. And he says that in this situation the person is really submitted to the beloved who can be a tyrant which is very often noticeable not only in relations but also in mass history—the Führer and so on. So there can be a submission from the person to the beloved and it can also happen in the psychoanalytic cure. And unfortunately there are psychoanalysts in psychoanalytic movements who use this kind of submission. And people are right to be afraid of this.
For the psychoanalyst the problem is he knows what kind of dangerous weapon he has... to make this person go through this danger and to give to the person the whole range of his symbolic and imaginary capacity in order not to be submitted in other experiences but instead of this to be alive and perfectly present.
COWARD: You seem to be saying that in analysis that relationship of love that the analyst has with the analysand is one that to some extent goes back over the primary construction of identification. In the book you do relate to that and this is where you draw on the myth of Narcissus: you feel that psychoanalysis has shown us how the subject is actually constituted in its first identifications. And that the whole history of love has been one or other form of demonstrating that process of primary identification. Is that right?
KRISTEVA: What happens in psychoanalysis is the discovery of some substantial points in the human development, psychic development. The first essential point that Freud made was narcissism. We know that when he began psychoanalysis he found a hysterical desire which was masculine as well as feminine. And then he was aware of the fact that this desire is limited and the transference which we spoke about is not endless and there are cases in which transference doesn't work. And then he discovered that there was an organization of the psychic space that he called narcissism. It was a word already used by psychiatrists, but Freud used it in a different way in order to stress the organization which is universal for every person, which is not symptomatic, in the sense that a symptom may be considered as an illness or something which is pejorative, but which is universal in the organization of every psychic space. This means that at some point of his life the human being is fascinated by his image. But it is possible only if this human being is capable of some separation from his mother and is capable of grasping some imaginary forms, which is the zero degree of the third between the infant and the mother. And this zero degree is not a word used by Freud; I use the word, Freud speaks about the father of pre-individual history, which is not grasped as a real person by the infant but like a sort of symbolic instance; something that is here that cannot be here—the possibility of absence, the possibility of love, the possibility of interdiction but also a gift. And this is something different from the overwhelming presence of the mother which is loving but which is also too much desiring, too much in close proximity with the child, and in this way she perhaps cannot give enough space for this symbolic elaboration. That's why he stressed the necessity, even for the narcissistic organization which is the primary one, the necessity for the existence of this third position.
COWARD: How do those ideas about narcissism relate to Lacan's notion of the mirror phase, because it seems to me that you talk of this first experience of love as almost being the first experience of the self, or the first grasp of the self—it's an identification built on a void where before there was only fragmentation and drives, and that the child identifies with an imaginary Other who is the speaking subject and who introjects the words of the speaking subject and has an imaginary sense of its own unity. I wanted to know how that relates to Lacan's notion of the mirror phase, where he seems to be talking about the same thing. Is yours an extension of that, or a kind of criticism of that?
KRISTEVA: Lacan is a very important figure, everyone agrees with that, though he may be a very controversial one. The point of the mirror stage in his work was very important, because he drew back the consideration of the psychic space precisely to the archaic stages which were not well observed or analyzed by analysts of his time. Afterwards different works have been written in this field and about this stage. And I think some parts of Winnicott's work, even though he doesn't mention the mirror stage, do deal with this stage or the very early stages of infant play.
What I wanted to do was two things. First, to make more detailed the archaic stages preceding the mirror stage because I think that the grasping of the image by the child is a result of a whole process. And this process can be called _imaginary_ , but not in the specular sense of the word, because it passes through voice, taste, skin and so on, all the senses yet doesn't necessarily mobilize sight. That's why I think it is an attempt to elaborate the early development in a more precise and a nonspecular way.
And this is important with regard to art. Because I think in modern art there is this so-called crisis of representation which is a crisis generally, and more commonly of visual representation—the breaking of the image, abstract art, and so on. From this point of view you could say that modern art is a sort of elaboration of this narcissistic and prenarcissistic dynamic, where the figure is not yet constituted as one, as a coherent figure, where hearing, skin, taste, and so on enter into account. That's why it is important for me to stress the previous-to-the-mirror-stage development, that I called in different elaborations that are not in this book but other books, the _semiotic_ variety of meaning in order to differentiate it from the _symbolic_ variety of meaning which will be more connected to a coherent and full image, and to the verbal sign which always refers to objects which are total and not split.
The second point, which is perhaps different from Winnicott's, is the accent put on the third position, the so-called father of the prehistory. Because if I have read Winnicott well, he always talks about the child and the good-enough mother, which is an enigma, nobody knows what the good-enough mother is. I wouldn't try to explain what that is, but I would try to suggest that maybe the good-enough mother is the mother who has something else to love besides her child; it could be her work, her husband, her lovers, etc. If for a mother the child is the meaning of her life, it's too heavy. She has to have another meaning in her life. And this other meaning in her life is the father of prehistory. And it's the guarantee of a love relationship between the mother and the child. If it doesn't exist it produces a clash which produces all sorts of inhibitions, and also difficulty to even acceed to language.
COWARD: I understand that you use the term 'the imaginary father' or the 'father of the individual prehistory' as the third term, but before the actual symbolic triangle.
KRISTEVA: Yes, exactly, some sort of archaic occurrence of the symbolic.
COWARD: You say in your book and you've just repeated that you're not referring to a real father or a real man. You're actually referring to the mother's desire being elsewhere as a necessary precondition for that kind of primary separation to take place. At the same time I did find it slightly worrying reading the book that it seemed to repeat some of those classic Freudian divisions of father and mother, even in maintaining those terms, even in maintaining the paternal metaphor which is something that very much comes from Freud and Lacan. And there were for me very strong echoes of nineteenth-century philosophy, twentieth-century philosophy, the division between the maternal too-close, too-natural bond that's undifferentiated, and the paternal, which is the intellectual, the altruistic love... it's very like Bachofen. And in your instance, the paternal metaphor stands for the sense of positions of speaking. But I wondered what you felt about the kinds of criticisms that we have now become familiar with from feminism. And someone like Irigary, say, with that criticism that the paternal metaphor is itself a problem because it reproduces ideologies about women and men, even in attempts to talk symbolically.
KRISTEVA: I think I understand your preoccupation. It's true that feminism has been very much against these sharp distinctions. I have two things to say. First, for me it is not absolutely necessary to call them mother or father—what is necessary is to have three terms, if you prefer call them X and Y, why not? But I'm not sure that changes much. What is necessary for what I call the psychic space to acceed to language is the existence of this distance and I cannot imagine another organization but the one of the three terms.
The second thing is that this is only a basic condition which I think is a kernel one in every civilization, which is a universal one for the symbolic acquisition. But there are ideological changes and historical differences and I think maybe the time we're going through now is more perverse, or if you like more baroque, a play with the psychic space, which supposes that these distinctions between X and Y are not so sharp, and which supposes that there are contaminations between them. This gives to the modern psychic space something that resembles the medieval, the fact that people don't have fixed identities but have the impression to bring masks, to have looks and not essential authenticities. This is due to the crisis of the paternal function and the rendering of my 'X' and 'Y' ambiguous. This is a contemporary fact.
For me the feminist movement has several positive points, particularly on the liberation of women. But maybe one of its most unexpected achievements at the moment will be to contribute to the creation of this baroque space, which is not now perceived in this way. What is perceived by the feminist movement now is mainly the rigor or the constraints: for instance in France, the aspect the feminist movement gives is the interdiction on sexist publicity and so on. Public opinion recently has a very problematic idea of the feminist movement as a movement more capable of interdiction than invention. But I think it is a momentary phenomenon. What will be retained from this contribution, and particularly in the field of ideas, will be this ambiguization of identities that goes in the sense of a new baroquism. Maybe we have lived too long in a postwar climate which was the climate of militancy and it was necessary for several reasons: political and economic, as well as sexual. I am under the impression, from my patients and also from my students that there is a desire for a "belle époque," for a new turn of the century, which doesn't mean that demands of militants should be put aside. But we have to add to them something more subtle, and more linked with desire, love, and so on. I think the success of different discourses particularly on desire and love is due to this need, which is a modern one, which maybe characterizes the end of the twentieth century.
COWARD: I'm not sure that I share your view of feminism as being something that is mainly about prohibitions at this stage. This relates to one of the points I wanted to make. For me one of the transforming aspects of feminism has been precisely its recasting of notions of love from the couple toward the friendship, from the sexual, erotic, idealizing love—I'm not saying that feminism is not erotic and not sexual—but for me that's been one of the positive recastings, almost in the way that you talk of psychoanalysis actually, as being an investigation of love as well as a cure for it. I think a lot of feminists would be critical of the notion of love that you talk about. You start the book by saying you think there is something, an _absolute_ state of love, that can be described. And I think that a lot of feminists would say this is a particular historical state which contains as many problems as pleasures.
KRISTEVA: It is very difficult when we want to describe something essentially, not to generalize. If you want to generalize you might appear to be schematic although that is not the intention. For instance, if you take the configuration of love, it's true that there are different historically based amorous forms—that's what I try to examine from some point of view. But it's true also that there is a situation which is differently organized in different historical spaces, but which nevertheless has some essential points that last in every time, in every space. For me this is essential. And this allows for scientific investigation. There are some universals and that's why we can investigate them. Otherwise everything is different and nothing can be investigated scientifically or theoretically. Then everything could only be described poetically or literarily or in an individual manner.
What is universal in the love situation is, on the one hand, for me, the narcissistic investment which is a necessity for the living being to last, to stay alive, to preserve itself. And on the other hand, the idealization. The possibility for this living being to project himself through an ideal instance and to identify with it. And this can be found in different kinds of friendship, sympathy, love, homosexual, erotic—differently orchestrated. The emphasis may be put in this situation more on violence, or more on narcissism, or more on idealization, or more or the erotic, and so on. But the two components: narcissism and idealization will last, will endure.
COWARD: So would you say that those universal aspects are more significant, than the particular forms as expressed over history on the one hand, and on the other, the particular object choices. For example, about homosexuality and heterosexuality—are you more interested in the similarities or in the differences. You make some fairly tantalizing remarks about homosexuality throughout the book. I'd be interested to know whether you do actually see there being significant differences and if so what would they be for you?
KRISTEVA: I think that every difference is significant. But what I would like to consider is the very particularity of the love experience of every person. I would say even that what interests me when I listen to someone in a psychoanalytic session is not to know that Jean is homosexual and Marie is not, but what kind of particular homosexuality he is living, not to put an etiquette on it, homosexual or heterosexual. Because there are sometimes more resemblances between one homosexual and one heterosexual than the people considered to belong to the same group. I'm not interested in groups. I am interested in individuals. And it's true that homosexual particularities can be apparent in the amorous behavior of a person who claims to be in this group. But it's not this main purpose that interests me.
I think that one of the negative points of the feminist movement, of all movements, is to consider that we can exhaustively understand a human being by classifying him somehow. First we had different economic classes; now in a more subtle way we have different sexual classes, which is perhaps a step forward because it's more deeply interested in the developments of the psychic experience. But it's not enough. I have the deep conviction that every person has a very particular sexuality. This sexuality and this kind of love organization is what interests me and not the group of _the_ homosexuals, _the_ heterosexuals, and so on.
COWARD: It seems to me that you're maintaining a kind of dual position by saying that on the one hand it's the individual, the particularities of the individual that gives significance, meaning to that individual. On the other hand, there are generalities in the process of love if not the object choices of love. I wonder how you would classify the more historical approach that would err toward the former I suppose, that meaning is given to sexuality by different situations and different histories. I'm thinking of Foucault's _History of Sexuality_ , which had a big impact here. This book would absolutely refuse your generalities.
KRISTEVA: And the reverse is true also! It's a field I'm not investigating, you can't do everything.
It's very legitimate to put some historical questions about why and for what historical reasons, for instance a Plotinian discourse has been organized, or a narcissist's discourse has been organized, but it is not the question I have analyzed.
If I understand your question correctly, it's about the legitimacy of this separation, of the psychoanalytical investigation from the historical one. I think it's possible to support this separation when we want to go as deeply as possible into the psychic particularity of sexual and love organization. If you stress the social conditions of these amorous discourses, for instance, you can very quickly disregard the particularity of what happens in the inner life. Your other question was about how to put together the tendency to generalize on the one hand and the tendency to individualize on the other. This is a problem for every human scientist. For instance, if you take linguistics, we try to describe what is the deep structure and then to individualize, if you can say that, the surface structure. You put some universal components on the basis and try to see developments of the universal components on the surface structure. You always have a subject and a predicate but you have different phrases on the surface.
In this type of investigation, which I would say is more difficult than linguistics, the problem is even more complicated because the neutrality of the theoretician is put into question. I cannot have a neutral position when I speak about love. And this is one of the reasons why I cannot involve myself in a so-called neutral historical discourse.
I think when a theoretician speaks about love, he or she is too much involved, and honestly he or she has to take account and tell people why he or she, in what way they are involved and not to block this involvement by a neutral historical discourse about classes, the economy, and the like. It can be done but it doesn't interest me.
I wanted to give an image of this contradiction which is, on the one hand, a description of the universal and the individual and, on the other hand, the involvement of the author. I tried to give an image of this in the chapter of _Histoires d'amour_ , which is about maternal love and is presented in two kinds of typeface: on the left you have a sort of literary poetic text and on the right, a more theoretical or academic discourse. And for me it's not a coherent text. I didn't want to give an impression of coherence, on the contrary I wanted to give an impression of a sort of wound, a scar. In the field of social sciences, human sciences, particularly psychoanalysis, the theoretician is posited precisely on this place of the scar, because we are holding a knowing discourse, a discourse that pretends to some objectivity and at the same time we elaborate this discourse through what is often painful involvement in the observation. We have to exhibit this contradiction, this pain. Maybe it's a point which may appear too literary and not scientific, but I think this is the point that many human sciences and philosophy particularly (which is not a human science but is a discourse on meaning and psychic space) have reached. It is more and more difficult to have a sort of mastered academic neutral discourse. It is possible for academic or deductive purposes and so on. But the very point human sciences have achieved is this one—because we are aware of the transference that links the author and his object.
COWARD: I think we in England have been very attracted to French thought. For left-wing intellectuals, our "other" has been France and we've had an idealizing relationship to France. So for many of us some of your more recent statements about politics have been bewildering.
I wondered, particularly, given what you've just said about not being able to take a neutral position—that you are involved yourself in any utterance you make—whether you'd accept a comment that perhaps some of the political metaphors you use seem very much like the subject of this book, in that they seem to be about an idealized love, this time a political love. I'll explain what I mean. Like many people in England you passed through a phase of seeing in China the embodiment of the kind of ideal socialist society. Recently you made a statement in a piece called _Mémoires_ that it was your disillusionment with China that ended your involvement with socialism, and feminism. And now you've published a number of things which make it clear, for example, that you see a lot more freedom within America than in China, and perhaps more than anywhere else. Don't these extremes of idealized love and disillusionment show the dangers of not being critical of love?
KRISTEVA: It's a point of personal history, I suppose from different people here in this room, having different histories, the appreciation of political actuality would be different. I will speak briefly about my history through politics. I come from a socialist country and my natural way would be, as most dissidents have done, to move to the Right, as has been said in a schematic way. But nevertheless these two realities exist. What I did was something else—I went to the Left because I was under the impression, and I still am, that socialist ideas and Marxist ideas understood in particular ways, are the more generous ideas of our time; and that different, positive social transformations, can be done with this, besides the despotism and totalitarianism of Eastern countries. This is one point.
Second, I had the impression that because of the Western tradition—which is more democratic than the East European tradition—the communist movements could be more liberal and could allow a richer development of individuals' art and creativity without dogmatism.
I have never been a member of a Communist Party but we tried with _Tel Quel_ and others to organize meetings and discussions with Communist intellectuals. My experience didn't confirm my initial impression. The French Communist Party, particularly, is very strongly dependent on the Soviet one and it gives a different problematic, different colorations of the ideological development of Marxism within the research institutes of the French Communist Party. In the meantime we went to China and for me it was more a cultural interest than a political one. There were both interests. But I wanted to see what can be done when Marxism is developed in a country that possessed a different cultural background, that doesn't have a monolithic religion, that thinks in a particular way, that speaks in a particular way because I think the Chinese character and language indicate not a particular mentality, which would be a racist position, but a different logic of organization. I wanted to see what could be the difference of a society organized on the basis of the meeting of these two components. And what I saw was very problematic, particularly in the situation of women. Several positive things have been done and said, but I couldn't discover any liberation of women in the sense of the Western movements, and of course in different fields, as well. So this was for me a point of a reevaluation of the whole problematic of political involvement. And personally from the point of view of my own development I thought that it would be more honest for me not to engage politically but to try to be helpful or useful in a narrow field, where the individual life is concerned, where the individual way of expression is concerned, and where I can do something more objective and maybe more sharp, and more independent of different political pressures.
I also have the impression that in our modern society, and it's a sort of heritage from the eighteenth-century French Revolution I suppose, we have a new religion which is not only sex—which may be important but also very pleasant and not dangerous—we have a religion which is politics. We think that everything is political. When we say political we say something which cannot be analyzed, it's the final act. This is political... stop. It's tremendously important, this final enigma, which is politics. We can say that different social sciences try to analyze it, but nevertheless it's there, it's present even in the questions, even in the objections when people say why don't you consider political events. Because it's considered as the most important. And what is interesting now in the new French government is that they try to develop some ideological fields, cultural fields, and so on, and this puts the stress, the dominance on the fact that politics is not the only, the dominant important phenomenon, that there are other expressions within human society that can be taken into consideration. And it's done by a political regime—that's what is happening now and the future will show the consequences. The political regime shows that politics is not the only thing that's important. That's what interests me.
When I spoke about love and stressed Christianity, for me that's not nostalgia. It's more a questioning about the discourse that can take the place of this religious discourse which is cracking now. And I don't think political discourse can take its place. The political discourse, the political causality which is dominant even in human sciences in universities and everywhere is too narrow and too feeble in comparison with St. Bernard and St. Thomas. If we stay with only a political explanation of human phenomena we will be overwhelmed by the so-called mystical crisis, or spiritual crisis—that happens, it's a reality. Every bourgeois family has a son or daughter who has a mystical crisis—it's understandable because of this very schematic explanation of such phenomenon as love or desire simply by politics. So my problem is: how, through psychoanalysis or something else like art, through such discourses can we try to develop a more complicated elaboration, discourse, sublimation of these critical points of the human experience, which cannot be reduced to a political causality.
COWARD: If you love yourself through another, what kind of love is that? Is that agape or eros?
KRISTEVA: The differentiation between agape and eros has been done by a scholar called Nigren in the thirties—he wrote a book about it, and I used this a lot, this research. The difference between the two is that eros is a sort of ascendant movement, it tries to achieve something that is placed above, it tries to go beyond the possibilities of the person he loves; it aspires to power and it's compared to an erection in an organic sense of the word. Agape is something else, it's a sort of gift, it comes to you from outside, you don't need to merit it, it's a sort of profusion, it's the love of parents for their children, for instance, when it happens which is not very often.
Both phenomenon happen in analysis. We can observe also erotic movements but in this sense they will be more connected with desire and violence and sado-masochistic dynamics. While in agape the phenomenon is more sublimated, for me, it is more related to an ideal instance and in this case the analyst is considered as a sort of ideal, an ideal I.
AUDIENCE: It is somewhat strange that the inability to love or be loved makes somebody a patient. If that's the area where trouble lies and if love is the remedy... you seem to describe the love that takes place in an analytic situation as simply a reactivated early infantile love.
KRISTEVA: Partly.
AUDIENCE: But surely there's something that happens, a step further than that that is necessary for a successful cure, that is entirely new, that is specific to that situation and it is actually taking place in the reality of that relationship.
KRISTEVA: You are right. Maybe I expressed myself in a very inexact way, if I said that what is actualized in transference is only the infantile love. I think it's one of the aspects of the human experience that is actualized but it's not the only one. Also, we can bring in the cure, in the transference different events that happen in your actual life, not only the past one but the current one. That's why it's a laboratory of different events, past or present.
What I wanted to say is that through this reactualization you can render your love affairs more vivid in the cure, reelaborate them and be able to displace them and to pass through the suffering, for instance all different amorous pains.
AUDIENCE: But isn't it a different kind of love, neither a reenactment of either past or present other love affairs, but one that goes on between therapist and patient, analyst and patient, which has its own specific character that is not a repetition.
KRISTEVA: I would call it a reelaboration. There is a part of repetition and there is a new part which is added and which makes this transference a sort of innovation. That's why it's not a mere repetition. If it were only a repetition it would be something morbid. It's a point which is very important for me because you know generally people imagine a psychoanalyst as a sort of obsessional person, very rigid who doesn't say anything, is dark and silent and so on. That's important perhaps because it's a way that Freud and psychoanalysts invented to resist the seduction of the patient. But it's of no use with narcissistic patients and I think modern patients are more and more narcissistic for different, perhaps sociological, reasons, because of the family, different difficulties of child-mother relationship, different causes. The fact is that, here, with more and more narcissistically suffering people, the psychoanalyst should not behave as if he were an obsessional or morbid person. I think that we have to construct something, not only to analyze, but to give something new. From this point of view the simple repetition which never occurs because in every transference there is something new that happens, it's particularly true with a narcissistic person—to give them something new, something that they have never experienced. That's why the imaginary and the symbolic possibilities of the analyst are very important. People come to you because they know that you can give them something that they have never had. This is important and this is dangerous because of the sort of victim position that can be developed in such situations. And if the analyst doesn't know this, if he can't get rid of this overwhelming domination it's very dangerous. But I think it's an important point with the new kind of patients we have now.
BARBARA TAYLOR: I may have misunderstood you but there appears to be an elision between love and desire in the way you're describing transference love. Would it not be correct to say that, for Freud, in fact, transference love is profoundly defensive in character, and one of the things it defends the analyst against is desire, that is the fantasy which is in the gap between need and demand, which is often extremely hostile in character, as you say violent, sadistic. So that the feeling of being in love and being loved is a way of delegitimizing the hostile character of desire itself.
KRISTEVA: I think Freud was right to first of all stress the hostile component of desire and also the erotic one. He speaks of Eros and Thanatos, but this is an essential part of erotic ways and that's what happens with neurotic patients. What I wanted to stress is something else which is not elaborated by Freud very much because he didn't work with psychotics, he didn't like them and he was right, it is very difficult. But it is a problem which is more and more an actual problem. You have the impression that the patient who is coming is a neurotic and very quickly it appears that he has some psychotic margins. From this point of view you have to construct something and to stress the idealizing part of the transference, which can be a resistance and you are right that Freud described it like this. But it is not only a resistance. You have to work with this as far as the cure is concerned. On the other hand, as far as the social field is concerned, and I persist in thinking that the social field is concerned through psychoanalysis, art as well as politics—the idealization is a very essential part of creation, of the possibility of innovation, as well as style movements and desire.
In this book I stressed more idealization and love and it can appear that I have in mind only this part of the cure. But I have already written another book called _The Powers of Horror_ where the problem of negativity, rejection, hostility has been the dominant problem. So in order to have a complete image of what happens in the cure we have to read the two books.
I want to stress again that this book was purposely partial. I had the impression that in modern human sciences literature there were few elaborations of what is faith, what is idealization, what is positive, what is value, on what grounds are they based? I wanted in a sort of polemical way to stress this part of the human psyche, the idealization, love, the positive. My previous book was concerned with rejection and hate, particularly in different phobias but also in the psychotic stages and psychotic situations where the rejection of the other and the hate for the other become predominant, in desire, but also in murder. The problematic of this book was to describe how in different religions and literary elaborations people tried to defend against these negative impulses, negative drives, through different rituals, for instance, of catharsis, purification, and so on.
My last point has to do with a French writer very much compromised during Nazism, Céline, who was a violent anti-Semite. I am not sure the book answered all the questions about hatred and values but I think it shed some light on them. So then it was necessary for me, and again I think it is a lack in human sciences, to try to show what happens in other kinds of cultural elaborations which are not elaborations about evil, about the negative but that are preoccupied with the sublime.
COWARD: Do you draw a distinction between love and desire?
KRISTEVA: Yes. For me desire doesn't involve idealization. Idealization is a level which concerns the symbolic elaboration, while desire is deeply involved in passion and depends on the symbolic imaginary. For me desire is more dominated by passion, by drives, instinct.
COWARD: One of the points that puzzle me is your assertion about the crisis of idealization in love. Is psychoanalysis really the only code that is investigating that process, because it seems to me that to some extent we're swamped with it rather than there being an absence of it.
KRISTEVA: I would ask what other codes are there that elaborate idealization.
COWARD: I know they're not art or religion but in popular culture for example there is a massive representation of narcissistic love.
KRISTEVA: Yes there are works, there are productions... It is unimaginable that a society could exist without different fields where such kinds of idealization exist. And popular art, different kinds of art, go in this direction. But what I wanted to say is that in the psychoanalytical field you have at the same time the practice and the attempt to think about it, to elaborate a discourse about not the surface of idealization, not of the external aspects of what _is_ idealized but of what are the dynamic causes of the idealization. For me the psychoanalytic field has the advantage of being at the same time the practice and the attempt to think about it, to elaborate a coherent discourse about not the surface of idealization, not of the external aspects of what is idealized but of what are the dynamic causes of idealization. For me the psychoanalytic field has the advantage of being at the same time the practice and the metalanguage of idealization, the metalanguage which is not only description but which gives, not the final because I hope there will be other propositions, but some causes of this idealization and the ideal state. I don't think it happens in theology—it doesn't exist anymore—or in philosophy. In art criticism, classical art describes different forms of idealization but it doesn't say what happens in the subjectivity of the artist when he does this.
JACQUELINE ROSE: At the risk of fulfilling a stereotype I want to say that I think that everything you've said is very political and what you're saying is political. And that's what's at stake in the discussion that has just taken place. The way I would like to pose the question is to bring it back to what I see as a very significant change in your work. It came out a bit earlier when you talked about the carnivalesque in relation to feminism and your earlier work on what you used to call, and perhaps still call, the semiotic moment, the moment of the before, of the presymbolic. In your earlier work it seemed very much as if the celebration was of the possibility of that presymbolic expression and of the necessity of it, whereas now it seems that in relation to psychoanalysis you're talking about the necessity of the symbolic and the need to move out of those fragmented forms of expression and experience. And I think that's the point at which a political problem emerges for many people, especially for feminists, because the discourse of love and idealization, of which you're talking this evening, and the discourse of relations in what is after all still a family unit between father, mother, and child, may well be seen by feminists as discourses of which they have been victims in some sense. Now in your work there seems to be a move toward a celebration of that and a loss of that earlier emphasis on what can't be spoken with them. I know that's a very serious psychoanalytic problem because I know what it means to construct _another_ idealization of those presymbolic moments, it also has its dangers. But nonetheless there seems to be a move across from one side of your division to another, and in a sense that seems to lead to almost what you concluded with, which would I know pose a problem for many people here, which is that only in love and art are we living beings. And your account of the political, which seems to be a consequence of what you are doing, is a relegation of the political to a marginal and inadequate arena of work. And in a sense your personal history, which I'm sure we've all responded to, has a classical ring about it. It's the story of somebody who became disillusioned with politics and those very big desires for change—which I would want to argue are also based on love, for example, love of the victim of exploitation—leads to a move into a more personal, more individualized sphere because of a kind of giving-up of those larger questions in which I'd want to say the question of love is at least as important, and perhaps more importantly important.
KRISTEVA: I agree with you that this interest for the love discourse and for psychoanalysis and art even can be considered as political in the deeper and larger sense of the word, social and the like. What I wanted to say is that it seems to me that if artists or psychoanalysts act politically they act politically through an intervention on an individual level. And it can be a main political concern to give value to the individual. My reproach to some political discourses with which I am disillusioned is that they don't consider the individual as a value.
ROSE: That's what is special about feminism... it brings subjectivity... kristeva: Well I am involved in different feminist movements and I dare say from time to time it does, and from time to time it does not, because there are dangers.... We are not preserved from what happened to different political groups, the sort of dogmatism and also violence and the annihilation of some personal particularities. It has happened also to feminist movements and to feminist groups—I have seen that. I suppose that honestly women will recognize that it can also happen in feminist groups. That's why I say that, of course, political struggles for people that are exploited will continue, they have to continue, but they will continue perhaps better if the main concern remains the individuality and the particularity of the person.
ROSE: I agree with a lot of what you've just said. But what I wanted to say about feminism was that for many people in England, the reason many feminists have such a hard time in relationship to certain dogmatisms of say the Marxist Left is precisely because of their insistence on bringing into the political arena the questions of subjectivity and sexuality.
KRISTEVA: It is true. That's why feminist movements have had so much difficulty with leftist movements for some time. Now it seems to be accepted but I think it's only a very surface acceptance. It's a question also to be put to feminists themselves. I think we now have sufficient strength to be able to criticize ourselves; we have passed the point when everything that was done by feminists was fine and we have to applaud. We can now, without fearing a collapse of the movement, criticize the movement. I remember that we elaborated some time ago in France an article about the feminist movement, a sort of _compte rendu_ of what has been done before, and we put this as _unes femmes_ (instead of _une femme_ ) in order to stress that there is a group, a plurality, but that this plurality is composed of different individuals, unities. And if the feminist movement is a movement of individuals I think it's a good political answer to what I called the political religion which can erase the individual.
AUDIENCE: I would just like to say that perhaps you need a third book which combines the issues of hate with the issues of love. I am not very familiar with the works of the early Church Fathers. Their discussions of evil involve a sort of transcendence of that to the good, whereas I think psychoanalysis has introduced a kind of wicked, witty, mischievous mix of the way to understand that love and hate are always tangled up together.
KRISTEVA: This is true. It happens that in my presentation, I stressed the love situation and I still think that I was right. Because it's very disturbing to speak about love. People think that either you are a little bit ethereal or that you are not aware that there are struggles and hate and violence in the world and so on. Or that you are a little bit religious or something like that. Love has become the modern obscenity, it's more obscene than sex, you can talk about sex and violence and that's OK; everybody knows that exists, but love is too strange. So I just tried to stress this in my presentation. But if you read the book, you will find that I begin by speaking of love and end up by speaking of hate. I can't finish the paragraph without speaking about hate because they are so mingled.
New Maladies of the Soul
Women's Time
National and European Women
The nation, which was the dream and the reality of the nineteenth century, seems to have reached both its peak and its limit with the 1929 crash and the National Socialist apocalypse. We have witnessed the destruction of its very foundation—economic homogeneity, historical tradition, and linguistic unity. World War II, which was fought in the name of national values, brought an end to the reality of the nation, which it turned into a mere illusion that has been preserved for ideological or strictly political purposes ever since. Even if the resurgence of nations and nationalists may warrant hope or fear, the social and philosophical coherence of the nation has already reached its limit.
The search for economic _homogeneity_ has given way to _interdependence_ when it has not yielded to the economic superpowers of the world. In like manner, _historical_ tradition and _linguistic_ unity have been molded into a broader and deeper denominator that we might call a _symbolic denominator_ : a cultural and religious memory shaped by a combination of historical and geographical influences. This memory generates national territories determined by the ever diminishing but still widespread conflicts between political parties. At the same time, this common "symbolic denominator" is a means not only to globalization and economic standardization but also to entities that are greater than any one nation and that _sometimes_ embrace the boundaries of an entire continent.
In this way, a "common symbolic denominator" can lead to a new social grouping that is greater than the nation, though it enables the nation to retain and build upon its characteristics instead of losing them. This transformation occurs, however, within a paradoxical temporal structure, a sort of "future perfect" in which the most deeply repressed and transnational past gives a distinctive character to programmed uniformity. For the memory in question (the common symbolic denominator) is linked to the solution that spatially and temporally united human groupings have offered less for the problems of the _production_ of material goods (which is the domain of economics, human relations, and politics) than of _reproduction_ —the survival of the species, life and death, the body, sex, and the symbol. If it is true, for instance, that Europe represents this sort of sociocultural grouping, its existence stems more from its "symbolic denominator" of art, philosophy, and religion than from its economic profile. Of course, economics is a function of collective memory, but its characteristics are easily modified by pressures from one's partners in the world.
Therefore, we see that this sort of social grouping is endowed with a _solidity_ rooted in the various modes of reproduction and its representations by which the biological species is placed within a temporally determined humanity. Yet, it is also tainted with a certain _fragility_ , for the symbolic denominator can no longer aspire to universality and endure the influences and assaults inflicted by other sociocultural memories. Hence, Europe, which is still fairly inconstant, is obliged to identify with the cultural, artistic, philosophical, and religious manifestations of other supranational groupings. Such identifications are of no surprise when the entities in question share a historical connection, like Europe and North America, or Europe and Latin America. They also occur, however, when the universality of this symbolic denominator juxtaposes two modes of production and reproduction that may seem incongruous, like those of Europe and the Arab world, Europe and India, Europe and China, and so forth.
In short, when dealing with the sociocultural groupings of the "European" type, we are forever faced with two major issues: first, that of _identity_ , which is brought about by historical sedimentation, and second, the _loss of identity_ , which is caused by memory links that bypass history in favor of anthropology. In other words, we are confronted with two temporal dimensions: the time of linear, _cursive_ history, and the time of another history, that is, another time, a _monumental_ time (the nomenclature comes from Nietzsche) that incorporates these supranational sociocultural groupings within even larger entities.
I would like to draw attention to certain formations that seem to embody the dynamics of this sort of sociocultural organism. I am speaking of groups we call "sociocultural" because they are defined by their role in production, but also (and especially) because of their role in the mode of reproduction and its representations. Although these groups share all the traits of the sociocultural formation in question, they _transcend_ it and link it to other sociocultural formations. I am thinking specifically of sociocultural groups that we summarily define according to age categories (for instance, "European youth"), or gender divisions (for instance, "European women"), and so forth. Clearly, European youth and European women have a particularity of their own, and it is no less obvious that what defines them as "youth" or "women" is concomitant with their "European" origin and shared by their counterparts in North America and China, among others. Insofar as they participate in "monumental history," they are not merely European "youth" or "women." In a most specific way, they will mirror the universal features of their structural position with regard to reproduction and its representations.
In the pages that follow, I would like to place the problematics of European women in the context of an inquiry into time, that is, the time that the feminist movement has not only inherited but altered. Then, I shall delimit two phases or two generations of women, whose respective demands cause them to be directly universalist or cosmopolitan, though they still can be distinguished from each other. The first generation is particularly linked to national concerns, and the second, which tends to be determined by the "symbolic denominator," is European and trans-European. Finally, I shall attempt to use the problems I am addressing and the type of analysis I am proposing to show that against the backdrop of what has become a global generality, a European stance (or at least a stance taken by a European woman) has emerged.
Which Time?
Joyce said "Father's time, mother's species," and it seems indeed that the evocation of women's name and fate privileges the _space_ that _generates_ the human species more than it does _time_ , destiny, or history. Modern studies of subjectivity—of its genealogy or its accidents—have reaffirmed this separation, which may result from sociohistorical circumstances. After listening to his patients' dreams and fantasies, Freud grew to believe that "hysteria was linked to place." Subsequent studies on children's acquisition of the symbolic function have shown that the permanency and quality of maternal love pave the way for the earliest spatial references, which give rise to childhood laughter and then prepare the whole array of symbolic manifestations that permit sign and syntax.
Before endowing the patient with a capacity for transference and communication, do not both anti-psychiatry and applied psychoanalysis (when applied to the treatment of psychoses) purport to mark out new places that serve as gratifying and healing substitutes for long-standing deficiencies of maternal space? The examples of this are many, but they all converge upon the problematics of space, which so many religions with a matriarchal bent attribute to "the woman" and which Plato, who echoed the atomists of antiquity within his own system, referred to as the aporia of the _chora_ , a matrixlike space that is nourishing, unnameable, prior to the One and to God, and that thus defies metaphysics.
As for time, female subjectivity seems to offer it a specific concept of measurement that essentially retains _repetition_ and _eternity_ out of the many modalities that appear throughout the history of civilization. On the one hand, this measure preserves cycles, gestation, and the eternal return of biological rhythm that is similar to the rhythm of nature. Its predictability can be shocking, but its simultaneity with what is experienced as extra-subjective and cosmic time is a source of resplendent visions and unnameable jouissance. On the other hand, it preserves a solid temporality that is faultless and impenetrable, one that has so little to do with linear time that the very term "temporality" seems inappropriate. All-encompassing and infinite, like imaginary space, it reminds us of Hesiod's Kronos, the incestuous son who smothered Gaea with his entire being in order to take her away from Ouranos the father. It also recalls the myths of resurrection in the various traditions that have perpetuated the trace of a maternal cult through its most recent manifestation within Christianity. In Christianity, the body of the Virgin Mother does not die, but travels from one space to another within the same time frame, whether by dormition (according to the Orthodox faith) or assumption (according to Catholicism).
These two types of temporality—cyclical and monumental—are traditionally associated with female subjectivity, when female subjectivity is considered to be innately maternal. We must not forget, however, that repetition and eternity serve as fundamental conceptions of time in numerous experiences, notably mystical ones. That the modern feminist movement has identified with these experiences suggests that it is not intrinsically incompatible with "masculine" values.
On the other hand, female subjectivity poses a problem only with respect to a certain conception of time, that of time as planning, as teleology, as linear and prospective development—the time of departure, of transport and arrival, that is, the time of history. It has been amply demonstrated that this sort of temporality is inherent in the logical and ontological values of any given civilization. We can assume that it explains a rupture, a waiting period, or an anxiety that other temporalities hide from our view. This sort of time is that of language, of the enunciation of sentences (noun phrase and verb phrase, linguistic topic and comment, beginning and end), and it is maintained through its outer limit—death. A psychoanalyst would call it obsessional time, for the very structure of the slave can be found within the mastery of this time. A male or female hysteric (who suffers from reminiscences, according to Freud) would identify, rather, with prior temporal modalities—the cyclical, the monumental.
Within the bounds of a given civilization, however, this antinomy of psychic structures becomes an antinomy among social groups and ideologies. Indeed, the radical viewpoints of certain feminists are akin to the discourse of marginal spiritual or mystic groups, as well as, interestingly enough, to the concerns of modern science. Is it not true that the problematics of a time indissociable from space—of a space-time placed in an infinite expansion or articulated by accidents and catastrophes—are of great interest to space science as well as genetics? And in a different way, is it not true that the media revolution that has manifested itself as the information age suggests that time is frozen or exploded according to the fortuity of demand? Is it a time that returns to its source but cannot be mastered, that inexorably overwhelms its subject and restricts those who assimilate it to only two concerns: who will wield power over the origin (its programming) and the end (its use)?
The reader may be struck by these fluctuating points of reference—mother, woman, hysteric. Although the seemingly coherent use of the word "woman" in current ideology may have a "popular" or "shock" effect, it eradicates the differences among the various functions and structures that operate beneath this word. The time may have come, in fact, to celebrate the _multiplicity_ of female perspectives and preoccupations. In a more accurate, honest, and less self-serving way, we must guarantee that the _fundamental difference_ between the sexes arises out of the network of these differences. Feminism has accomplished a formidable task by making this difference a _painful_ one, which means it is able to generate contingency and symbolic life in a civilization that has nothing to do besides playing the stock market and waging war.
We cannot speak about Europe or about "women in Europe" without defining the history that encompasses this sociocultural reality. It is true that a feminine sensibility has been in existence for more than a century now, but it is likely that by introducing its notion of time, it clashes with the idea of an "Eternal Europe," or perhaps even a "Modern Europe." Feminine sensibility, rather, would look for its own trans-European temporality by way of the European past and present as well as the European "ensemble," defined as the storehouse of memory. We can contend, however, that European feminist movements have displayed three attitudes toward this conception of linear temporality—a temporality that we readily deem to be masculine, and that is as "civilizational" as it is obsessional.
Two Generations
When the women's movement began as the struggle of suffragists and existential feminists, it sought to stake out its place in the linear time of planning and history. As a result, although the movement was universalist from the start, it was deeply rooted in the sociopolitical life of nations. The political demands of women, their struggles for equal pay for equal work and for the right to the same opportunities that men have, as well as the rejection of feminine or maternal traits considered incompatible with participation in such a history all stem from the _logic of identification_ with values that are not ideological (such values have been rightly criticized as too reactionary) but logical and ontological with regard to the dominant rationality of the nation and the state.
It is unnecessary to enumerate all the benefits that this logic of identification and spirited protest have offered and still offer to women (abortion rights, contraception, equal pay, professional recognition, and more). These benefits have had or will soon prove to have even more significant effects than those of the Industrial Revolution. This current of feminism, which is universalist in scope, _globalizes_ the problems of women of various social categories, ages, civilizations, or simply psychic structures under the banner of Universal Woman. In this world, a reflection about _generations_ of women could only be conceived of as a succession, a progression that sought to implement the program set out by its founding members.
A second phase is associated with women who have come to feminism since May 1968 and who have brought their aesthetic or psychoanalytic experiences with them. This phase is characterized by a quasi-universal rejection of linear temporality and by a highly pronounced mistrust of political life. Although it is true that this current of feminism still has an allegiance to its founding members and still focuses (by necessity) on the struggle for the sociocultural recognition of women, in a _qualitative_ sense, it sees itself in a different light from the prior generation of feminists.
The "second phase" women, who are primarily interested in the specificity of feminine psychology and its symbolic manifestations, seek a language for their corporeal and intersubjective experiences, which have been silenced by the cultures of the past. As artists or writers, they have undertaken a veritable exploration of the _dynamics of signs_. At least on the level of its intentions, their exploration is comparable to the most ambitious projects for religious and artistic upheaval. Attributing this experience to a new generation does not merely imply that new concerns have been added to the earlier demands of sociopolitical identity, for it also means that by requiring that we recognize an irreducible and self-sufficient singularity that is multifaceted, flowing, and in some ways nonidentical, feminism is currently situated outside the linear time of identities that communicate through projections and demands. Today, feminism is returning to an archaic (mythic) memory as well as to the cyclical or monumental temporality of marginal movements. It is clearly not by chance that the European and trans-European problem has manifested itself at the same time as this new phase of feminism.
What sociopolitical processes or events have led to this mutation? What are its problems, its contributions, its limits?
Socialism and Freudianism
It could be maintained that this new generation of women has a more pronounced presence in Western Europe than in the United States, which may be attributed to the _rupture_ in social relations and attitudes that has been caused by socialism and Freudianism. Although _socialism_ as an egalitarian doctrine is now experiencing a profound crisis, it still requires that governments and political parties of all persuasions expand solidarity by redistributing wealth and allowing free access to culture. _Freudianism_ , which serves as an internal mechanism of the social realm, challenges egalitarianism by exploring sexual difference as well as the singularity of subjects who preserve their individuality.
Western socialism, shaken from its beginnings by the egalitarian or differential demands made by its women (Flora Tristan, for instance), has not hesitated to rid itself of those women who want us to recognize the specificity of the female role in culture and society. In the spirit of the egalitarian and universalist context of Enlightenment humanism, the only idea that socialism has held to is the notion that identity between the sexes is the only way to liberate the "second sex." For the moment, I shall refrain from pursuing the fact that this "ideal of equality" has not really been adopted by the actual movements and political parties that lay claims to socialism, and that since May 1968, the new generation of Western European women has been inspired, to some extent, by a revolt against the reality of the situation. Let me simply note that in theory (and in practice, in the case of Eastern Europe), socialist ideology, which is founded on the idea that human beings are determined by their relation to _production_ , has ignored the role of the human being in _reproduction_ and the _symbolic order_. As a result, socialist ideology has been compelled, in its totalizing, if not totalitarian, spirit, to believe that the specific nature of women is unimportant, if not nonexistent. We have begun to realize, moreover, that Enlightenment humanism and even socialism have imposed this same egalitarian and censuring treatment onto individual religious groups, especially Jewish ones.
Nevertheless, the effects of this attitude are of paramount importance for women. Let us take the example of the evolution of women's destiny in the socialist countries of Eastern Europe. It would only be a slight exaggeration to say that in these countries, the demands of the suffragists and existential feminists have been met, at least to a large degree. What is more, in Eastern Europe, various blunders and vacillations have not prevented three of the most important demands of the early feminist movement from being answered to: the demands of economic, political, and professional equality. The fourth demand, sexual equality, which would require permissiveness in sexual relationships as well as abortion and contraceptive rights, remains inhibited by a certain Marxist ethics as well as by the reason of state. Thus, it is the fourth equal right that poses a problem and seems _vital_ to the struggle of the new generation. This may be true, but because of the successful socialist agenda (which has been quite disappointing, in reality), this struggle will no longer aim specifically for equality. At this point in its journey, the new generation is coming up against what I have called the _symbolic_ question.
Sexual, biological, physiological, and reproductive difference reflects a difference in the relation between subjects and the symbolic contract—that is, the social contract. It is a matter of clarifying the difference between men and women as concerns their respective relationships to power, language, and meaning. The most subtle aspects of the new generation's feminist subversion will be directed toward this issue in the future. This focus will combine the sexual with the symbolic in order to discover first the specificity of the feminine ( _le féminin_ ) and then the specificity of each woman.
The saturation of socialist ideology and the exhaustion of its plan in favor of a new social contract has made way for Freudianism. I am not unaware, however, that militant women have seen Freud as an annoying male chauvinist from a Vienna that was at once puritanical and decadent, as someone who believed women were submen, castrated men.
Castrated or Subject to Language
Before we bypass Freud in order to propose a more accurate vision of women, let us first attempt to understand his notion of castration. The founder of psychoanalysis posited a castration _anxiety_ or _fear_ and a correlative penis _envy_ , both of which are _imaginary_ constructs peculiar to the _discourse_ of neurotic _men as well as women_. A close reading of Freud that goes beyond the biological and mechanical models of his day enables us to delve into these issues more deeply.
First, the castration fantasy and its correlative penis envy are like the "primal scene" in that they are all _hypotheses, a priori_ judgments intrinsic to psychoanalytic theory itself. These notions represent logical necessities that are relegated to the "origin" in order to explain that which never fails to function in neurotic discourse. In other words, neurotic discourse (in men as well as women) can only be understood in terms of its own logic if we acknowledge its fundamental sources—the primal scene and castration fantasy—even if these are never present in reality itself. The reality of castration is as real as the supposed "big bang" at the origin of the universe, yet we are much less shocked when this sort of intellectual process concerns inanimate matter than when it is applied to our own subjectivity and to the fundamental mechanism of our epistemic thought.
Furthermore, certain Freudian texts (like _The Interpretation of Dreams_ , but especially those of the second topology, in particular the _Metapsychology_ ) as well as their recent elaborations (notably by Jacques Lacan), suggest that castration is an imaginary construction stemming from a psychic mechanism that constitutes the symbolic field as well as anyone who enters it. Castration, then, would be the advent of sign and of syntax, that is, of language as a _separation_ from a fusion state of pleasure. In this way, the institution of an _articulated network_ of _differences_ , which refers to objects separated from a subject, forms _meaning_. This logical operation of separation, which has been described by child psychology and psycholinguistics, anticipates the syntactic links of language for boys as well as girls. Freud offers a new approach to this notion by postulating that certain biological or familial conditions prompt some women (notably hysterics) to deny this logical operation of separation and the language that ensues, whereas some men (notably obsessional neurotics) glorify this separation and language while trying, petrified as they are, to master them.
Analytic practice has shown that in fantasies, the penis becomes the primary referent of this operation of separation and gives full meaning to the _lack_ or _desire_ that constitutes subjects when they join the order of language. In order for this operation, which constitutes the symbolic and social orders, to reveal its truth and be accepted by both sexes, it would be wise to add to it the entire series of deprivations and exclusion that accompany the fear of losing one's penis and impose the loss of wholeness and completeness. Castration, then, would be the ensemble of "cuts" that are indispensable to the advent of the symbolic.
Living the Sacrifice
Whether or not women are aware of the mutations that have generated or accompanied their awakening, the question they are asking themselves today could be formulated as follows: _what is our place in the social contract?_ If this contract, whose terms do not treat everyone in an equal fashion, bases itself upon an ultimately sacrificial relationship of separation and articulation of differences that serves to create a meaning that can be communicated, what is our place in the order of sacrifice and/or language? Since we no longer wish to be excluded from this order, and we are no longer satisfied with our perpetually assigned role of maintaining, developing, and preserving this sociosymbolic contract as mothers, wives, nurses, doctors, teachers, and so forth, how might we appropriate our own space, a space that is passed down through tradition and that we would like to modify?
It is difficult to enumerate with certainty the aspects of the current relationship between women and the symbolic that stem from sociohistorical circumstances (including patriarchal, Christian, humanist, and socialist ideologies, among others), or from a structure. We can only speak of a structure observed in a sociohistorical context, that of Western Christian civilization and its secular ramifications. At the interior of this psychosymbolic structure, women feel rejected from language and the social bond, in which they discover neither the affects nor the meanings of the relationships they enjoy with nature, their bodies, their children's bodies, another woman, or a man. The accompanying frustration, which is also experienced by some men, is the quintessence of the new feminist ideology. Consequently, it is difficult, if not impossible, for women to adhere to the sacrificial logic of separation and syntactic links upon which language and the social code are based, and this can eventually lead to a rejection of the symbolic that is experienced as a rejection of the paternal function and may result in psychosis.
Faced with this situation, some women have sought to develop a new perspective—through new objects and new analyses—for anthropology, psychoanalysis, linguistics, and other disciplines that explore the symbolic dimension. Other, more subjective women, who have come forth in the wake of contemporary art, have attempted to modify language and other codes of expression through a style that remains closer to the body and to emotion. I am not referring here to "female language," whose existence as a particular syntactic style is problematic, and whose apparent lexical specificity may be less a product of sexual difference than of social marginality. I am also not speaking of the aesthetic value of creations by women, most of which mirror a more or less euphoric and depressed romanticism, on the one hand, and stage an explosion of an ego that lacks narcissistic gratification, on the other. This leads me to believe that the primary focus of the new generation of women has become the sociosymbolic contract as a sacrificial contract.
For more than a century, anthropologists and sociologists have attracted our attention to the society-sacrifice that works behind "savage thought," wars, dream discourse, or great writers. In so doing, these scholars have reformulated and analyzed the metaphysical question of evil. If society is truly founded on a communal murder, the realization that castration provides the basis for the sociosymbolic is what will enable human beings to postpone murder. We symbolize murder (and ourselves) and thus have an opportunity to transform baleful chaos into an optimal sociosymbolic order.
Today's women have proclaimed that this sacrificial contract imposes itself against their will, which has compelled them to attempt a revolt that they perceive to be a resurrection. Society as a whole, however, considers this revolt to be a refusal and it can result in violence between the sexes (a murderous hatred, the breakup of the couple and the family) or in cultural innovation. In fact, it probably leads to them both. In any event, that is where the stakes are, and they are of enormous consequence. By fighting against evil, we reproduce it, this time at the core of the social bond—the bond between men and women.
The Terror of Power or the Power of Terrorism
First in the former socialist countries (such as the former Soviet Union and China) and later, increasingly, in Western democracies, feminist movements have enabled women to attain positions of leadership in the worlds of business, industry, and culture. Even if various forms of unfair discrimination and persecution continue to hold sway, the struggle against these is a struggle against the ways of the past. Even if the cause has been made known and the principles accepted, there still are obstacles that need to be overcome. Thus, although the ensuing struggle remains one of the major _preoccupations_ of the new generation, in a strict sense of the word, it is no longer its primary _problem_. With respect to _power_ , however, its problem could be stated as follows: What occurs when women attain power and identify with it? What occurs when they reject power but create an analogous society, a counterpower that ranges from a coterie of ideas to terrorist commandos?
That women have assumed commercial, industrial, and cultural power has not changed the nature of this power, which can be clearly seen in the case of Eastern Europe. The women who have been promoted to positions of leadership and who have suddenly obtained economic (as well as narcissistic) advantages that had been refused to them for thousands of years are the same women who become the strongest supporters of the current regimes, the guardians of the status quo, and the most fervent protectors of the established order. This identification between women and a power that they once found frustrating, oppressive, or unattainable has often been used to the advantage of such totalitarian regimes as the German National Socialists or the Chilean junta. One possible explanation of this troubling phenomenon might be that it results from a paranoid counterinvestment (in the psychoanalytic sense) of an initially denied symbolic order. Even so, this does not prevent its massive propagation around the world, sometimes in more subtle forms than the totalitarian ones I have mentioned. In any event, all these forms share an interest in equalization, stability, and conformity, though this comes at a cost: the eradication of each individual's uniqueness, of personal experiences, and of the vagaries of life.
Some may regret that the rise of a libertarian movement such as feminism may wind up reinforcing conformity, and others will celebrate this consequence and use it to their advantage. Electoral campaigns and political life never fail to bet on the latter alternative. Experience has shown that even the antiestablishment or innovative initiatives led by women dragged in by power (when they do not readily submit to it) are quickly attributed to "the system." The self-proclaimed democratization of institutions that pride themselves on accepting women most often means that they simply add a few female "bosses" to their ranks.
The various feminist currents, which tend to be more radical in approach, reject the powers that be and make the second sex into a _countersociety_ , a sort of alter ego of official society that harbors hopes for pleasure. This female society can be opposed to the sacrificial and frustrating sociosymbolic contract: a countersociety imagined to be harmonious, permissive, free, and blissful. In our modern societies, which do not acknowledge an afterlife, the countersociety is the only refuge for jouissance, for it is precisely an anti-utopia, a place outside the law, yet a path to utopia.
Like all societies, the countersociety bases itself upon the expulsion of an already excluded element. The scapegoat deemed responsible for evil thus keeps it away from the established community, which is thereby exonerated of any responsibility for it. Modern protest movements have often reproduced this model by designating a guilty party that shields them from criticism, whether it be the foreigner, money, another religion, or the other sex. If we take this logic at face value, does feminism not become a sort of reverse sexism?
In our world, the various marginal groups of sex, age, religion, ethnic origin, and ideology represent a refuge of hope, that is, a secular transcendence. All the same, insofar as the number of women affected by these problems has increased (albeit in a less dramatic way than was the case a few years ago), the problem of the countersociety is becoming an enormous one, no more and no less important than "half the sky."
It is not the case that protest movements, including feminism, are "libertarian at first" and then dogmatic only later. They do not fall into the abyss of defeated models through the fault of some internal deviation or external maneuver. The particular structure of the logic of counterpower and countersociety is what lies behind its essence as an image of defeated society or power. In such a perspective, which is most likely too Hegelian, modern feminism would be a single moment in an ongoing process—the process of becoming aware of the implacable violence (of separation and castration) that underlies _any_ symbolic contract.
The large number of women participating in terrorist groups like the Palestinian commandos, the Baader-Meinhoff Gang, and the Red Brigades, has been noted. Exploitation of women is still far too frequent, and the traditional prejudices against women are so fierce that we cannot evaluate this phenomenon in an objective manner, though we may rightfully claim that it stems from a negation of the sociosymbolic contract as well as its counterinvestment. This paranoid mechanism is at the base of all forms of political commitment and it can generate various humanizing attitudes. Yet when a woman feels ruthlessly isolated and becomes aware of her affective experience as a woman or her status as a social being who remains unknown to the discourse and the powers that be (everything from her own family to the social institutions of the world), she can make herself into a "possessed" agent through the counterinvestment of the violence she encounters. She fights against her frustration, then, with weapons that may appear extreme at first glance, but that are justifiable and understandable once the narcissistic suffering that elicits their use is recognized.
This terrorist violence, which is inevitably directed against the regimes of current bourgeois democracies, assigns itself a program of liberation that consists of an order even more repressive and sacrificial than the one it is fighting. Indeed, the object of female terrorists groups' aggression is not the various totalitarian regimes, but the liberal regimes that are becoming increasingly democratic. Their mobilization comes about in the name of a nation, an oppressed group, or what is believed to be a good and sound human essence, that is, the fantasy of an archaic fulfillment that would be disturbed by an arbitrary, abstract, and thus undesirable order. Although this order has been accused of being oppressive, is our primary criticism not that it is weak? That it does not stand up to a substance believed to be pure and good but that is lost forever, a substance that the marginalized woman hopes to recover?
Anthropologists have affirmed that the social order is a sacrificial one, yet sacrifice stops violence and develops into its own order (through prayer or social well-being). If we reject it, we subject ourselves to the explosion of the so-called good substance that uncontrollably erupts outside the bounds of law and rights, like an absolute arbitrariness.
As a result of the crisis of monotheism, two centuries of revolutions (most recently materialized as Fascism and Stalinism) have staged the tragedy of the logic of oppressed goodwill that winds up as a massacre. Are women more able than other social groups to invest in the implacable terrorist mechanism? Perhaps one might merely note that ever since the dawn of feminism (and even before), women who fall outside the norm have often gained power through murder, conspiracy, or assassination. Eternal debt toward the mother has made her more vulnerable to the symbolic order, more fragile when she suffers from it, and more virulent when she protects herself. If the archetypal belief in a good and sound chimerical substance is essentially a belief in the omnipotence of an archaic, fulfilled, complete, all-encompassing mother who is not frustrated, not separated, and who lacks the "cut" that permits symbolism (that is, who lacks castration), the ensuing violence would be impossible to defuse without challenging the very myth of the archaic mother. It has been noted that feminist movements have been invaded by paranoia, and we may remember Lacan's scandalous pronouncement that "There is no such thing as Woman." Indeed, she does not exist with a capital "W," as a holder of a mythical plenitude, a supreme power upon which the terror of power as well as terrorism as the desire for power base themselves. All the same, talk about a forceful subversion! Talk about playing with fire!
Creators: Male and Female
The desire to be a mother, which the previous generation of feminists held to be alienating or reactionary, has not become a standard for the current generation. Nevertheless, there is a growing number of women who find maternity to be compatible with their professional careers (this is also due to such improvements in living conditions as the increase of daycare centers and nursery schools, the more active participation of men in domestic life, and so forth). Furthermore, women are finding that maternity is vital to the richness of female experience, with its many joys and sorrows. This trend is illustrated to its fullest extent in lesbian mothers or in certain single mothers who reject the paternal function. The latter cases exemplify one of the most dramatic examples of the rejection of the symbolic order to which I referred earlier on, and they also exhibit an ardent deification of maternal power.
Hegel distinguishes between female right (familial and religious) and male law (civil and political). Although our societies are very well acquainted with the uses and abuses of this male law, we must admit that for the moment, female right appears to be a void. If these practices of fatherless maternity were to become the norm, it would become absolutely necessary to develop appropriate laws that could diminish the violence that might be inflicted on the child and the father. Are women equipped for this psychological and legal responsibility? That is one of the most profound questions that the members of this new generation of women are coming up against, especially when they refuse to confront such questions because they are gripped with a rage against the order and its law that victimizes them.
Faced with this situation, feminist groups are becoming increasingly aware (especially when they try to broaden their audience) that refusing maternity cannot be their primary political approach. The majority of women today feel that they have a mission to put a child into the world. This brings up a question for the new generation that the preceding one repudiated: what lies behind this desire to be a mother? Unable to answer this question, feminist ideology opens the door to a return of religion, which may serve to pacify anxiety, suffering, and maternal expectations. Although we can only offer a partial adherence to Freud's belief that the desire to have a child is the desire to have a penis, and is thus a replacement for phallic and symbolic power, we still must pay close attention to what today's women have to say about this experience. Pregnancy is a dramatic ordeal: a splitting of the body, the division and coexistence of self and other, of nature and awareness, of physiology and speech. This fundamental challenge to identity is accompanied by a fantasy of wholeness of narcissistic self-containment. Pregnancy is a sort of institutionalized, socialized, and natural psychosis. The arrival of the child, on the other hand, guides the mother through a labyrinth of a rare experience: the love for another person, as opposed to love for herself, for a mirror image, or especially for another person with which the "I" becomes merged (through amorous or sexual passion). It is rather a slow, difficult, and delightful process of becoming attentive, tender, and self-effacing. If maternity is to be guilt-free, this journey needs to be undertaken without masochism and without annihilating one's affective, intellectual, and professional personality, either. In this way, maternity becomes a true _creative act_ , something that we have not yet been able to imagine.
At the same time, women's desire for affirmation has emerged as a longing for artistic and especially literary creation. Why the emphasis on literature? Is it because when literature is in conflict with social norms, it diffuses knowledge and occasionally the truth about a repressed, secret, and unconscious universe? Is it because literature intensifies the social contract by exposing the uncanny nature of that which remains unsaid? Is it because it plays with the abstract and frustrating order of social signs, of the words of everyday communication, and thus creates a place for fantasy and pleasure?
Flaubert said, "Madame Bovary, c'est moi." These days, some women think, "Flaubert, c'est moi." This claim points not only to an identification with the power of the imaginary, but also to women's desire to lift the sacrificial weight of the social contract and to furnish our societies with a freer and more flexible discourse that is able to give a name to that which has not yet been an object of widespread circulation: the mysteries of the body, secret joys, shames, hate displayed toward the second sex.
For this reason, women's writing has recently attracted a great deal of attention from "specialists" as well as the media. Nevertheless, the stumbling blocks that it must overcome are not inconsequential. Does women's writing not consist of a morose rejection of the very "male literature" that serves as a model for so much of women's writing? Thanks to the stamp of feminism, do we not sell many books whose naïve whining or commercialized romanticism would normally be scoffed at? Do female writers not make phantasmatic attacks against Language and the Sign, which are accused of being the ultimate mainstays of male chauvinist power, in the name of a body deprived of meaning and whose truth would only be "gestural" or "musical"?
Nevertheless, however questionable the results of women's artistic productions may be, the symptom has been made clear: women _are_ writing. And we are eagerly waiting to find out what _new material_ they will offer us.
In the Name of the Father, the Son—and the Woman?
These few characteristic features of the new generation of women in Europe show that these women are placed within the same framework as the religious crisis of contemporary civilization. In my view, religion is our phantasmatic necessity to procure a _representation_ (which could be animal, feminine, masculine, or parental, among others) that replaces the element that makes us what we are—our capacity to form symbols. Feminism today seems to constitute exactly this sort of _representation_ , one that complements the frustration that women feel when faced with the Christian tradition and its variation—secular humanism. That this new ideology has some affinities with so-called matriarchal beliefs does not obliterate its radical innovation, for it participates in the antisacrificial trend that drives our culture. Although this ideology contests these constraints, it still remains vulnerable to the hazards of violence and terrorism. When radicalism goes this far, it challenges the very notion of social exchange.
Some contemporary thinkers maintain that modernity is the first era in human history in which human beings have attempted to live without religion. As it stands today, is feminism not about to become a sort of religion? Or will it manage to rid itself of its belief in Woman, Her power, and Her writing and support instead the singularity of each woman, her complexities, her many languages, at the cost of a single horizon, of a single perspective, of faith?
Is it a matter of ultimate solidarity, or a matter of analysis?
Is it an imaginary support in a technocratic era that frustrates narcissistic personalities, or a measurement of the time in which the cosmos, atoms, and cells—our true contemporaries—call for the formation of a free and flowing subjectivity?
Another Generation Is Another Space
It is now becoming possible to have a more objective perspective on the two preceding generations of women. I am suggesting, then, that a _third one_ is taking shape, at least in Europe. I am thinking neither of a new age group (although its importance is far from negligible) nor of a new "mass feminist movement" that would follow in the footsteps of the second generation. The meaning I am attributing to the word "generation" suggests less a chronology than a _signifying_ space, a mental space that is at once corporeal and desirous.
For this third generation, which I strongly support (which I am imagining?), the dichotomy between man and women as an opposition of two rival entities is _a problem for metaphysics_. What does "identity" and even "sexual identity" mean in a theoretical and scientific space in which the notion of "identity" itself is challenged? I am not simply alluding to bisexuality, which most often reveals a desire for totality, a desire for the eradication of difference. I am thinking more specifically of subduing the "fight to the finish" between rival groups, not in hopes of reconciliation—since at the very least, feminism can be lauded for bringing to light that which is irreducible and even lethal in the social contract—but in the hopes that the violence occurs with the utmost mobility within individual and sexual identity, and not through a rejection of the other.
As a result, both individual equilibrium and social equilibrium (which emerges through the homeostasis of aggressive forces typical of social, national, and religious groups) are made vulnerable. All the same, does not the unbearable tension that underlies this "equilibrium" lead those who suffer from it to avoid it, to seek another way of regulating _difference?_
Despite the apparent indifference that has been shown toward the militancy of the first and second generations of women, I have generally found sexism to be less pronounced than before.
With the exception of the proclaimed rights of male and female homosexuals, sex has an ever shrinking hold on subjective interest. This "desexualization" goes as far as challenging not only humanism, but also the anthropomorphism that serves as a basis for our society. For this reason, "the man and the woman" are less of a fulcrum for social interest than they once were. The paroxysmal narcissism and egoism of our contemporaries only seem to contradict the retreat from anthropomorphism, for when anthropomorphism does not fall into technological supremacy or a general state of automation, it is forced to look to spirituality. Could the sexual revolution and feminism have merely been transitions into spiritualism?
That spiritualism turns to evasion or to conformist repression should not obscure the radical nature of the process, which comes forth as an _interiorization of the fundamental separation of the sociosymbolic contract_. From that point on, the other is neither an evil being foreign to me nor a scapegoat from the outside, that is, of another sex, class, race, or nation. I am _at once the attacker and the victim_ , the same _and_ the other, identical _and_ foreign. I simply have to analyze incessantly the fundamental separation of my own untenable identity.
Religion is willing to accept this European awareness of _intrinsic evil_ , which emerges from the ideological accomplishments and impasses of the feminist experience. Is any other discourse able to support it? Along with psychoanalysis, the role of aesthetic practices needs to be augmented, not only to counterbalance the mass production and uniformity of the information age, but also to demystify the idea that the community of language is a universal, all-inclusive, and equalizing tool. Each artistic experience can also highlight the diversity of our identifications and the relativity of our symbolic and biological existence.
Understood as such, aesthetics takes on the question of morality. The imaginary helps to outline an ethics that remains invisible, as the outbreak of the imposture and of hatred wreaks havoc on societies freed from dogmas and laws. As restriction and as play, the imaginary enables us to envision an ethics aware of its own sacrificial order and that thus retains part of the burden for each of its adherents, whom the imaginary pronounces guilty and responsible, though it offers them the direct possibility of jouissance, of various aesthetic productions, of having a life filled with trials and differences. This would be a utopian ethics, but is any other kind possible?
In this sense, we might return to Spinoza's question: are women subject to ethics? Women are probably not subject to the ethics laid out by classical philosophy, with which generations of feminists have had a dangerously precarious relationship. Nevertheless, do women not participate in the upheaval that our society is experiencing on several levels (war, drugs, artificial insemination), an upheaval that will require a new ethics? If we consider feminism to be a _moment_ in the thought pertaining to the anthropomorphic identity that has diminished the freedom of our species, we will only be able to answer this question in the affirmative once this moment has come to a close. And what is the meaning of the current "politically correct" movement that has swept across the United States? European consciousness has surpassed such concerns, thanks, in some respects, to the dissatisfaction and creativity of its women.
NOTES
. See _The Freud/Jung Letters_ , Ralph Manheim and R. F. C. Hull, tr. (Princeton, N.J.: Princeton University Press, 1974).
. See René Spitz, _The First Year of Life: A Psychoanalytic Study of Normal and Deviant Development of Object Relations_ (New York: International Universities Press, 1966); D. W. Winnicott, _Playing and Reality_ (New York: Basic Books, 1971); Julia Kristeva, "Place Names," _Desire in Language: A Semiotic Approach to Literature and Art_ , Thomas Gora, Alice Jardine, Leon S. Roudiez, tr. (New York: Columbia University Press, 1980), pp. 271–95.
. See Plato, _Timaeus_ , Francis M. Cornford, tr. (New York: Harcourt, Brace, 1937): "Space, which is everlasting, not admitting destruction; providing a situation for all things that come into being but itself apprehended without the senses by a sort of bastard reasoning, and hardly an object of belief. This, indeed, is that which we look upon as in a dream and say that anything that is must needs be in some place and occupy some room" (52a–52b). See my remarks on the _chora_ in _Revolution in Poetic Language_ , Margaret Waller, tr. (New York: Columbia University Press, 1984).
. See Julia Kristeva, "Stabat Mater," in _Tales of Love_ , Léon S. Roudiez, tr. (New York: Columbia University Press, 1983).
. See H. C. Puech, _La Gnose et le temps_ (Paris: Gallimard, 1977).
. See D. Desanti, "L'autre sexe des bolcheviks," _Tel Quel_ 76 (1978); and Julia Kristeva, _About Chinese Women_ , Anita Barrows, tr. (London: Marion Boyars, 1977).
. See Arthur Hertzberg, _The French Enlightenment and the Jews_ (New York: Columbia University Press, 1968); and _Les Juifs et la révolution française_ , B. Blumenkranz and A. Soboul, ed. (Paris: Editions Privat, 1976).
. From time to time, this work is published in various academic women's journals, one of the most prestigious being _Signs: Journal of Women in Culture and Society_ , University of Chicago Press. Also of note are the special issue of the _Revue des sciences humaines_ 4 (1977) entitled "Ecriture, féminité, féminisme" and "Les femmes et la philosophie" in _Le Doctrinal de sapience_ 3 (1977).
. See the various linguistic studies on "female language," such as Robin Lakoff, _Language and Women's Place_ (New York: Harper & Row, 1974); Mary R. Key, _Male/Female Language_ (Metuchen, N.J.: Scarecrow Press, 1973); and A. M. Houdebine, "Les femmes et la langue," _Tel Quel_ 74 (1977): 84–95.
. See Julia Kristeva, _About Chinese Women_.
. See M. A. Macciocchi, _Eléments pour une analyse du fascisme_ (Paris: 10/18, 1976); Michèle Mattelart, "Le Coup d'état au féminin," _Les Temps modernes_ (January 1975).
. The principles of a "sacrificial anthropology" have been laid out by René Girard in _Violence and the Sacred_ , Patrick Gregory, tr. (Baltimore: Johns Hopkins University Press, 1977); and especially in _Things Hidden Since the Foundation of the World_ , Stephen Bann and Michael Metteer, tr. (Palo Alto: Stanford University Press, 1987).
. See Micheline Enriquez, "Fantasmes paranoïaques: Différences de sexes, homosexualité, loi du père," _Topiques_ 13 (1974).
. See Claude Lévi-Strauss et al., _L'Identité: séminaire interdisciplinaire_ (Paris: Grasset & Fasquelle, 1977).
Interview with Elaine Hoffman Baruch on Feminism in the United States and France
BARUCH: In an interview that you had done once for _Psych et Po_ , which was translated in an anthology edited by Elaine Marks and Isabelle de Courtivron called _New French Feminisms_ , you said, and here is the translation: "There can be no sociopolitical transformation without a transformation of subjects, in other words, in our relation to social constraints, to pleasure and, more deeply, to language." Elsewhere you have spoken about the importance of language for structuring experience, and so have other French theorists. American feminists speak about the importance of language also, but they are talking about something quite different from what you are talking about. How could we go about changing our relation, particularly women's relation, to social constraints, to pleasure, and, especially, to language?
KRISTEVA: When I spoke the sentence you have quoted, it had to do with the following: very often, in France, a certain sort of feminism had posed itself solely as a movement of sociological protest, which consisted in making of women a sort of social force or motor which would ultimately take on the role played in Marxist theory by the proletariat. Here is a class or social group which is oppressed, which is not paid well enough, which does not have its proper place in production and in political representation, and this oppressed class, this oppressed social stratum, should fight, essentially, to obtain this recognition—economic, political, and ideological. I, on the other hand—and I am not alone in this; a large part of the French feminist movement, I think, is aware of this problematic—think that women's protest is situated at an altogether different level. It is not first of all a social protest, although it is also that. It is a protest which consists in demanding that attention be paid to the subjective particularity which an individual represents, in the social order, of course, but also and above all in relation to what essentially differentiates that individual, which is the individual's sexual difference. Well then: how can one define this sexual difference? It is not solely biological; it is, above all, given in the representations which we make ourselves of this difference, and we have no other means of constructing this representation than through language, through tools for symbolizing. Now these tools for symbolizing are common to the two sexes. Everyone speaks English if you're English; everyone speaks French if you're French, whether we are men or women. So how do we situate ourselves in relation to these universal tools in order to try to mark our difference?
Here the position of some feminists has seemed to me rather strange and regressive. Certain feminists, in France, particularly, say that whatever is in language is of the order of strict designation, of understanding, of logic, and is male. Ultimately, theory, science, is phallic, is male. On the other hand, that which in language, according to the same feminists, is feminine, is whatever has to do with the imprecise, with the whisper, with impulses, perhaps with primary processes, with rhetoric—in other words, speaking roughly, the domain of literary expression, the region of the tacit, the vague, and where one would escape from the too-tight tailoring of the linguistic sign and of logic. I think that this is, so to speak, a Manichean position which consists in designating as feminine a phase or a modality in the functioning of language. And if one assigns to women that phase alone, this in fact amounts to maintaining women in a position of inferiority, and in any case of marginality, to reserving them the place of the childish, of the unsayable, or of the hysteric.
That the valorization of this modality of expression can have a critical, if not a subversive function, is obvious; but I think that it is not sufficient either. On the other hand, other women say that we must equip ourselves with or appropriate the logical, mastering, scientific, theoretical apparatus. They consider it as an extremely gratifying promotion that there are women physicists, theorists, and philosophers. In saying this, they preserve for women an extremely important place in the domain of culture. But these attitudes can be accompanied by a denial of two things; on the one hand, of the question of power and, on the other, of the particularity of women. One can be a theoretician and a woman, or only a theoretician and not a woman. In other words one can fit oneself to the dominant discourse—theoretical discourse, scientific discourse—and on the basis of that find an extremely gratifying slot in society, but this to the detriment of the expression of the particularity belonging to the individual as a woman.
On the basis of this fact, it seems to me that what one must try to do is not to deny these two aspects of linguistic communication, the mastering aspect and the aspect which is more of the body and of the impulses, but to try, in every situation and for every woman, to find a proper articulation of these two elements. What does "proper" mean? That which best fits the specific history of each woman, which expresses her better. So you see that I would be just as much against the slogan, "All women should master the dominant discourse." I am also against the position which asserts that all that is part of the game of power and that women must express themselves in literature. I think that the time has come when we must no longer speak of "all women." We have to talk in terms of individual women and that each should try to find her place inside these two poles. I gave a talk on this some time ago which appeared in _Les Cahiers du Grif_ , which is the Belgian women's paper, and it was called "Unes Femmes," spelled "unes" with an "s" on the end and "femmes" with an "s." What I meant by that is that there is a community of women, but what seemed to me important is that this community should be made up of particularities and that it not be a uniform mass. And one of the gravest dangers that now presents itself in feminism is the impulse to practice feminism in a herd. I think that at first this was perhaps something important because people cried out, "We demand abortion," "We demand the social advantages we have been denied," but now this "we" is becoming troublesome. There have to be "I's" and women have to become authors, actors, not to hypostasize or overvalue those particular kinds of work, but I say this so that this perspective will push each one of us to find her own individual language.
BARUCH: Would you say something about your concept of "abjection" in your book _Powers of Horror_?
KRISTEVA: The term in French has a much more violent sense than in English. It means something disgusting.
BARUCH: _Abasement_ perhaps? _Degradation?_ It doesn't quite cover it but are these terms closer?
KRISTEVA: Yes, there is all that; there is also the aspect of nausea, of wanting to vomit. _L'abjection_ is something that disgusts you. For example, you see something rotting and you want to vomit. It's "abject" on the level of matter. It can also be a notion that concerns moral matters—an _abjection_ in the face of crime, for example. But it is an extremely strong feeling which is at once somatic and symbolic, and which is above all a revolt of the person against an external menace from which one wants to keep oneself at a distance, but of which one has the impression that it is not only an external menace but that it may menace us from the inside. So it is a desire for separation, for becoming autonomous and also the feeling of an impossibility of doing so—whence the element of crisis which the notion of abjection carries within it. Taken to its logical consequences, it is an impossible assemblage of elements, with a connotation of a "fragile limit."
BARUCH: Would you say that women's experience of abjection, to use the English word for a moment, is the same as men's, or is it different? Is there a sexual differentiation?
KRISTEVA: To tell the truth, I did that work without asking myself that question. I wanted first of all to scan the notion in a more general way. But obviously I did it also on the basis of my own experience, because it is mainly a psychoanalytical book, but which like all psychoanalytical books is somewhat self-analytical, like—I am going to make a pretentious comparison—Freud's _Interpretation of Dreams_ , which was based essentially on his dreams—and so this book is in great measure based on my own experience. I would say that abjection is a category which cuts across the two sexes, as one can be phobic whether one is a man or a woman or as one can be schizophrenic whether one is a man or a woman. On the other hand I have asked myself whether men and women behave in the same way when abjection becomes a source of pleasure. When, in other words, there are eroticizations of abjection, as for example one finds in the case of perversions: sexual pleasure in the face of disgusting things or in the face of disgusting actions. And in fact I think that here I can say that there is a difference in the relations of man and woman in this regard. I think that a woman does not eroticize abjection or the abject by herself. She does it if she is in a relationship with a man. In other words, if she does it, it is to carry out the desire of a man.
I do not think that there is a propensity to perversion in women. Cases of feminine perversion are very rare, and are above all perversions which are meant to satisfy the perversion of a man. Why? Because this relation to abjection is finally rooted in the combat which every human being carries on with one's mother. In order that we become autonomous it is necessary that one cut the instinctual dyad of the mother and the child and that one become something other.
Now a woman gets rid of her mother in a much more complex way than a man. Either we don't succeed in doing so, and we carry with us this living corpse—but in that case we women (and, once again, it's very difficult to generalize) close our eyes: that is to say, we don't want to know, we don't eroticize this relationship. There is, as it were, a veil, like the hysterical veil which one sees in the gaze, very often, of the hysterical woman, which is extremely brilliant but sees nothing—a veiled gaze at a region of forgetfulness, which is the archaic relationship with the mother. Or one recognizes this relationship with the archaic mother, but in this case there are different forms of defense, of which feminism can be one, or again, if one enters the combat, this gives rise to fairly serious forms of psychosis. And this retreat, the eroticization of the mother, which produces abjection as a source of pleasure, does not seem to me something built in.
BARUCH: Is what you have said about the eroticization of abjection connected with Freud's theory of the splitting of the sexual object into the degraded and the exalted?
KRISTEVA: Yes. Exactly.
BARUCH: And would you agree that women do not split the sexual object in the same way that men do?
KRISTEVA: Exactly. They don't have to divide the object—the feminine sexual object has only to be abandoned: one abandons the mother for the father. And therefore the cleavage happens differently.
BARUCH: That's the cleavage.
KRISTEVA: Right. The question of the eroticization of abjection—it's interesting, what you asked—can present itself in another form as well, not only that of the desire which a woman can have for a man but also in the case of female homosexuality. That is, when one has not made the move to a male object but chooses as an erotic object an object of the same sex. Thus, inside a certain sort of female homosexuality one can find an eroticization of "abjection." This is not the case for all female homosexuality, for here we have a rather interesting range of variations.
BARUCH: There are two rather well-known books in the United States: one by Dorothy Dinnerstein, called _The Mermaid and the Minotaur_ , and the other by Nancy Chodorow called _The Reproduction of Mothering_ , whose thesis is that the exaltation and the degradation of the woman stem from the fact that it is mothers who rear children, and that if fathers or men were to have equal responsibility for the rearing of infants, this would eliminate all of our sexual malaise and end all of the problems having to do with women's inaccessibility to culture.
KRISTEVA: I don't think so. Because if there is a sort of rage against mothers it is not only because they take care of the child, it's because they carry it in their bodies. And that is something which men, even if they handle the diapers, can't do. I think that there is rooted a negative desire, a certain rejection of the maternal function—a fascinated rejection. Moreover the fact that men do the same work as women with regard to the education of children or their early upbringing will certainly change things in the psychic functioning of children. But I don't know if it will do so in the way foreseen by these feminists. In fact it will first displace and then decimate the paternal function. It will render ambiguous the paternal role. Up to the present, in the division of sexual roles, the mother takes care of the child, the father is farther away. The father represents the symbolic moment of separation.
BARUCH: And you feel that that should be retained?
KRISTEVA: If we do what they call for, that is, if the fathers are always present, if fathers become mothers, one may well ask, who will play the role of separators?
BARUCH: Couldn't they both be? Couldn't both sexes be nurturers and differentiators somehow?
KRISTEVA: I would like to think so. But it would be very difficult. What seems more likely is just that there will be many borderline children produced, and it will become necessary to find a third party, for example, the child psychotherapist, the school, all those medical sectors of the different "psy's": psychoanalysts, psychiatrists, psychotherapists, et cetera, who will play the paternal role. The number of helping institutions for early childhood, for school children, that are forming now in our society, is extraordinary, and one may well ask oneself what their function is. Well, every time I have looked closely at what these people do, it is, of course, to replace a failed mother, as is remarked only too often. But it is above all to replace a nonexistent father: to play the role of the separator, to play the role of someone who comforts the mother in order to permit her to take her role in hand, but at the same time the role is one of a third party. The question I think one ought to ask is not so much what must be done in order that women be happy, it is: what is to be done in order that children have a development—not a normal development—but let us say a development which permits them to accede to the various elements of human culture? And I think that what interferes with that access is the underestimation of the paternal function.
BARUCH: Nancy Chodorow would say that the function of the father has nothing to do with his sex, and that someone female could play the same role of separator.
KRISTEVA: Yes, certainly; that's why I say "a third party"—who could be the woman psychotherapist of the hospital where one can go with the child. In the family, the mother can be this third party, in relation to the father, or further, to a symbolic institution (religion, morality, social and professional goal). But how can a mother gain access to this third or symbolic function? That is the problem.
BARUCH: To return to that problem of not being able to overcome the biological fact of the mother carrying the child, never mind rearing it. How would you feel if the biological revolution were to go so far that the reproduction of the infant would take place outside the womb? Would you welcome that possibility, which is no longer quite so much of a fantasy as we had considered it even five years ago?
KRISTEVA: It's a very grave question and in fact I think about it often. We are all caught up in moral scruples, and we tell ourselves that in the near future such a prospect is to be avoided for ontological and ethical reasons, for the various experiments which could be done in this area should have guarantees. People have the impression that they are exposing themselves to kinds of arbitrariness which are not very far from the experiments of the Nazis, which hover on the horizon. This is a defensive attitude, which I cannot keep myself from having. But I think that nothing will stop "progress" and that, as you say, this will be the case some day. Assuming that, the question to ask ourselves is, how will sexual roles be distributed? What will fathers do and what will mothers do, when the child is no longer carried in the uterus?
Here we are in the face of a humanity whose character is completely unforeseeable. In the present state of things, there are two attitudes one might have. One, a defensive one, would consist in saying: there must be preserved, along a straight Freudian line, the distribution of the paternal function on the one side and the maternal function on the other, so that the speaking subjects who are constructed, psychically and not just biologically, can have the "normality" which we think of as theirs; and what is this normality? It is that which succeeds in getting along, surviving, in the Oedipal triangle, that is, the defensive position. It seems to be more and more untenable. Hence the interest that I have in the cases of "borderlines." For I think that we will not be able to hold on for very long to this position—the fathers on one side, the mothers on the other. There will be mixtures of these two functions, which will give rise to a very different psychic map of humanity. One will no longer see, or very rarely—we are daydreaming, but perhaps it is not altogether a mere daydream, that hypothesis of which you spoke—if the production of children outside the uterus were to be realized, the good neurotic caught between Daddy and Mommy. One will have a psychic structure much closer to what is now seen as borderline, I suppose. Which does not necessarily mean that it will be outside the social order.
For a modern individual, who has had to manage the array of information of our times, which is scientific information, which is the mixture of the media—along with television, there are ten thousand sorts of information which bombard us constantly—if an individual wants to be, not someone who lives in the middle of the seventeenth, eighteenth, or nineteenth century, but contemporary with that information, one should be an individual who is not individual, but an explosion of either polyvalence or polymorphism. Well, that is someone of whom one cannot yet have the map, the precise representation. But I think that what some are trying to address today starting from these cases of borderlines, or indeed what a certain sort of modern art today displays as subjectivity, will approach that sort of individual. So what I can say is that the interest which the psychoanalyst can bring at the present moment to subjectivities which are not neurotic, but which have something to do with what is called psychosis, well, that interest will permit us to address with more assurance the psychic problems that will pose themselves in the face of this new, artificially manufactured humanity. For the moment, this is, again, a dream.
BARUCH: Or a nightmare.
KRISTEVA: Or a nightmare. It is fairly terrifying. But perhaps one must not close one's eyes to it. There is going to be a great battle around this; the opposite attitude will be taken by the moral authorities: the Church, a certain part of the psychoanalytic profession, which will fight for the classic Oedipus, and initially this will be a safety belt—perhaps a saving one—which will permit us to push away this experiment or at least to protect humanity from a certain number of moral risks which this experiment implies. But I think that if one calculates over the long term, if science were capable of what you say, the moral authorities would not be able to resist very long. And at that moment it would be necessary to have a knowledge of the human psychic structure in order to have a response or a way of acting toward those individuals. And for the moment I don't know what means we can have for knowing what problems these people can pose, except for these cases of borderlines and even psychosis.
BARUCH: Do you feel that desire between the sexes depends on difference, on differentiation? Could it possibly be founded on something else?
KRISTEVA: I don't think that it's founded only on difference; it's also founded on sameness. Anyway, one must know what one means by "desire." If you mean a desire as Freud defined it or as it functions in Western literature, for example, or when one takes the texts of Hegel, desire is founded on the notion of negativity, of lack, and therefore always on difference. But if you mean by desire, the attraction of the sexes to each other or of individuals to each other, which makes it possible for the sexual act to take place, that, I think, in great part, functions on the basis of identification. For example, all homosexuality (but not only homosexuality, also the attraction of many men to women) has arisen on the basis of the similarity or identification which one may feel with another. This is not necessarily desire in the Hegelian sense of the term, but it is an attraction in the sense of the Freudian eros.
BARUCH: What do you see as the place of love in the new conservatism of the family?
KRISTEVA: It's the only thing which can save us. My seminar, this year, at Paris VII University, is on the "Love object." One would have to try, in this situation, to save some territories of freedom. What is a territory of freedom? It is, in what concerns affective work, let us say, a place where people could explore the limits of their discourse, of their thought, of their manipulation of colors and sounds, of words, whatever you like. But the space of freedom for the individual is love—it is the only place, the only moment in life, where the various precautions, defenses, conservatism break down and one tries to go to the limit of one's being, so it's fundamental. The love relation is a situation where the limits between the _Ego_ and the _Other_ are constantly abolished and established.
BARUCH: Well, that is an assumption that many women today would not accept at all.
KRISTEVA: Yes. An assumption, yes.
BARUCH: People like Kate Millett in _Sexual Politics_ , or Shulamith Firestone in the _Dialectic of Sex_ say that love is a myth propagated by men for the control of women, that, in effect, what it has done is to perpetuate the hierarchy of the sexes and make women accept their oppressive place within the family. Firestone has said that men don't really know how to love at all—it's only women who know how to love. So this would seem totally opposed to your point of view, which is that love can be a species of freedom, the only means of defense against an oppressive state.
KRISTEVA: There are many things to be said about that. First of all, love is not something fixed; there is a history of love. When one takes the evolution of this concept in the West, one realizes that love for the Greeks was not the same thing as medieval love—courtly love—Romantic love, and existentialist love. So there is an evolution which is not necessarily progress. I would call it a recreation, but in any case a movement in what is called love, and it is obvious that in certain situations and some of the time, it has been possible that it is a means of blackmail by one sex of the other—and essentially by the male in the history of humanity as we have experienced it in relation to the female. But that is a vision, perhaps, through the wrong end of the telescope, which doesn't interest me very much because if you look at things that way, the whole of culture oppresses women—a madrigal or Shakespeare is antiwoman. Fine, if one wants to put it that way, but, on that basis, long live genetic manipulation or whatever. What is one supposed to do about it? What does one suggest as an alternative? It doesn't seem to me a very exalted view of things. On the contrary, I am not in favor of decimating men or of believing that patriarchy is a horror. I think that culture—in particular Occidental culture, which is founded on patriarchy and expressed in the great religions which were—which still are—Judaism and Christianity—has produced profoundly true visions of the human being as the symbolical being, as the being who lives in language and who is not reduced just to the womb and to reproduction. Now love is a moment in the life of a speaking being who, all the while caught in the body, opens oneself to the symbolic dimension. I love the other, who is not necessarily me, and who gives me the possibility of opening myself to something other than myself. This can take place through an imaginary fusion with this outer body, but if it is experienced not in a merely narcissistic way but as the governing principle of my whole subsequent existence, what I call love is openness to the other, and it is what gives me my human dimension, my symbolic dimension, my cultural and historical dimension. So if one says that it's patriarchy which produces that, long live patriarchy.
I for my part say that the love relation is the only chance to go through narcissism toward the recognition of the symbolic moment. And I would look with horror on a humanity that would decapitate or wipe out this symbolic moment. If that's what some feminists propose, I don't want any of it.
BARUCH: Well, I guess that some of them, at least, would say that what they propose is a different form of love from what has existed in the past. As you point out there is a history of love, there are changes, and no doubt there will be transformations.
KRISTEVA: As you say, they will probably say that there are forms of love, but I don't know if they would recognize that love is a relation not merely to another self ( _moi_ ) as we come together in order to get ourselves narcissistic gratifications, but it is also, by means of that, an _opening of my self_ toward a symbolic dimension. Love is not simply when you give pleasure to each other, it can even be very different; it's above all when I am able to listen to Gesualdo, or to see a Rothko painting. Those can be moments of love. I am not capable of seeing them or of hearing those objects if I am caught in an essentially biological dimension or the dimension of protest. And I think that the feminists now, after a phase which was essentially critical or protesting, are trying to find a way of talking to people—to women—about that opening, the symbolic dimension where women ought to place themselves, and not to shut themselves up in wombs, or in machines which make children outside wombs. Can you imagine a humanity having as an objective or as sole horizon the reproduction of the species? The symbolic is a matter for speaking beings, and we women are first of all speaking beings. That must not be left to the patriarchy alone.
Black Sun
Illustrations of Feminine Depression
The following fragments do not open up the universe of clinical melancholia; rather, they lead us into neurotic regions of the melancholy/depressive set. What one notices there is the alternation between depression and anxiety, depression and perverse action, loss of object and meaning of speech and sadomasochistic domination over them. Being caught in woman's speech is not merely a matter of chance that could be explained by the greater frequency of feminine depressions—a sociologically proven fact. This may also reveal an aspect of feminine sexuality: its addiction to the maternal Thing and its lesser aptitude for restorative perversion.
Cannibalistic Solitude
_The Body as Tomb or the Omnipotent Devouring_. From the time of her birth Helen suffered from serious motor problems that had required several surgical operations and confined her to bed until she was three. The little girl's brilliant intellectual development, however, enabled her to have an equally brilliant professional career, all the more so since nothing remains of her earlier motor deficiencies or of the family context that, quite obviously, fostered them.
Nothing, that is, aside from frequent instances of serious depression that did not seem triggered by the current reality, a rather prosperous one, of Helen's life. A number of situations (speaking with more than one person, being in a public place, defending a position shared by none of the people present) produced in her a state of stupor. "I find myself glued to the spot, as if paralyzed, I lose the ability to speak, my mouth fills with chalk, my mind is completely empty." She was overcome with a sense of total incapacity, quickly followed by utter dejection that separated Helen from the world, caused her to withdraw into her room, dissolve into tears, and remain speechless, thoughtless for days on end. "As if I were dead but I do not even think of killing myself, nor do I desire to do so, it is as if it had already been done."
In such circumstances, "being dead" meant a physical experience for Helen, an unspeakable one at first. When she later tried to find words to describe it, she spoke of states of artificial weightiness, of swept-out dryness, of absence against a backdrop of dizziness, of emptiness cut out into black lightning... But those words still seemed to her too imprecise for what she experienced as a total paralysis of psyche and body, an irremediable dissociation between herself and everything else, and also within what should have been "she." An absence of sensations, a loss of pain or hollowing out of sorrow—an absolute, mineral, astral numbness, which was nevertheless accompanied by the impression, also an almost physical one, that this "being dead," physical and sensory as it might be, was also a thought nebula, an amorphous imagination, a muddled representation of some implacable helplessness. The reality and fiction of death's being. Cadaverization and artifice. An absolute impotence that was, nevertheless, secretly all powerful. The artifice of maintaining herself alive, but... "beyond it all." Beyond castration and disintegration; being _as if_ she were dead, _playing_ dead seemed for Helen when she could talk about it, therefore after the event, like a "poetics" of survival, an inverted life, coiled around imaginary and real disintegration to the extent of embodying death _as if_ it were real. In that worldview, swallowing a vial of barbiturates is not a choice but a gesture that is imperative on the basis of an elsewhere—a non-act, or rather a sign of completion, a near-aesthetic harmonization of its fictitious fullness, "beyond."
A total oceanic death would engulf the world and Helen's being in a prostrate, mindless, motionless passivity. Such a lethal flood could settle down for days and weeks on end, allowing neither interest in nor access to any exteriority. When an object's image or a person's face managed to crystallize in it, they were at once perceived as precipitates of hatred, as hurtful or hostile elements, both disintegrating and agonizing, which she could face in no other way except by killing them. Putting those aliens to death was then a substitute for being dead, and the lethal flood changed into torrents of anguish. Nevertheless, it was anguish that kept Helen alive. It was her vital dance, following and in addition to morbid stupor. Certainly painful and insufferable, anguish just the same gave her access to an extent of reality. The faces to be killed were mainly the faces of children. That unbearable temptation horrified her and gave her the impression of being monstrous, and yet _being_ —emerging out of nothingness.
Faces of the disabled child that she was and henceforth wanted to be finished with? It would seem, rather, that the desire to kill was triggered only when the world of others, previously taken over by the lethal self in its almighty helplessness, succeeded in becoming free from the confinement where dreamlike melancholia had trapped her. Then confronted with others without seeing them as such, the depressed Helen continued to project onto them: "I am not killing my frustraters or my tyrants, I am killing _their_ baby, which they have dropped."
Like an Alice in distressland, the depressed woman cannot put up with mirrors. Her image and that of others arouse within her wounded narcissism, violence, and the desire to kill—from which she protects herself by going through the looking glass and settling down in that other world where, by limitlessly spreading her constrained sorrow, she regains a hallucinated completeness. Beyond the grave, Proserpina survives as a blind shade. Her body is already elsewhere, absent, a living corpse. It often happens that she does not feed it or else, on the contrary, she stuffs it the better to get rid of it. Through her fuzzy, tear-misted gaze that sees neither you nor herself, she savors the bitter sweetness of being forsaken by so many absent ones. Concerned with brooding, within her body and her psyche, over a physical and moral distress, Helen nevertheless strolls among the others—when she leaves her graveyard bed—like an extraterrestrial, the inaccessible citizen of the magnificent land of Death, of which no one could ever deprive her.
At the start of her analysis Helen was warring with her mother—inhuman, artificial, nymphomaniac, incapable of any feeling, and having thoughts only, so said the patient, for money or for seduction. Helen remembered her mother's "bursting into" her room as "a desecration, a forcible entry, a rape," or her overly intimate, overly explicit remarks—"in fact, I thought them obscence"—made in the presence of friends, which made her blush with shame... and pleasure.
Behind that veil of erotic aggressiveness, however, we uncovered another relationship between the handicapped child and her mother. "As much as I try to imagine her face, now or at the time of my childhood, I don't see it. I am sitting on someone who holds me, perhaps on her lap, but actually it isn't anybody. A person would have a face, a voice, a glance, a head. The fact is that I perceive nothing of the sort, merely a support, that's all, nothing else." I venture an interpretation: "As to the other, you have perhaps assimilated her into yourself, you wanted her support, her legs, but as for everything else, _she_ was perhaps _you._ " "I had a dream," Helen went on, "I was climbing your stairs, they were covered with bodies that looked like the people on my parents' wedding photo. I myself had been invited to that wedding, it was a cannibalistic meal, I was supposed to eat those bodies, those scraps of bodies, those heads, my mother's head also. It was ghastly."
Orally assimilating the mother who gets married, who has a man, who flees. Possessing her, holding her within oneself so as never to be separated from her. Helen's almightiness shows through the mask of aggressiveness and shores up the other's nonexistence in her daydream as well as the difficulty she experiences in deciding who she is when facing a person different from herself, separated from herself, in actual life.
The thought of a minor surgical operation distresses Helen so much that she is willing to run the risk of aggravating her condition rather than confronting anesthesia. "It's too dismal, being put to sleep, I don't think I could stand it. They are going to go through me, of course, but that isn't what frightens me. It's strange, I have the feeling that I'm going to end up being frightfully alone. Even so, that's preposterous, because in fact, people will never have taken care of me so much." She perhaps feels that the surgical "operation" (I refer to my own interpretational "operations") will take away someone close, some indispensable person, whom she imagines she has locked up within herself and constantly keeps her company? "I don't see who that might be. I've already told you, I think of no one, for me there is no other one, I see no one by my side as far back as I can remember... I forgot to tell you, I've had sex and I was nauseated. I vomited and I saw, as if I were in between sleep and wakefulness, something like the head of a child falling into the washbasin while a voice called me from a distance, but mistakenly calling me by my mother's name." Helen thus confirmed my interpretation—she had locked up a fantasy, the representation of her mother, within her body. And she reeled as she spoke of it, as if she were disconcerted by having to relinquish, if only by words, the object that was imprisoned within herself, and which, if she happened to miss it, would plunge her into a bottomless grief. Punctual and remarkably regular, she forgot, for the first time during her analysis, the time of her ensuing appointment. At the next meeting, she confessed that she remembered nothing about the meeting previous to the one she missed: everything was void, blank, she felt drained and frightfully sad, nothing meant anything, she was once more back in those states of stupor that are so painful... Had she tried to lock me within herself instead of the mother we had flushed out? To confine me in her body so that, the one blended with the other, we could no longer meet, since she had for a time incorporated, ingested, buried me in her imaginary tomb-like body, as she had done with her mother?
_Perverse and Frigid_. Helen often complained that her words, with which she hoped to "touch" me, were actually hollow and dry, "far removed from true feeling": "It is possible to say anything, it may be a piece of information, but it has no meaning, at any rate not for me." That description of her speech reminded her of what she called her "orgies." Beginning with her teens and up to the start of her analysis she alternated between states of prostration and "erotic feasts": "I did everything and anything, I was man, woman, beast, whatever was called for, it created a sensation, and me, it made me come, I think, but it wasn't really me. It was pleasant, but it was someone else."
Omnipotence and disavowal of loss led Helen on a feverish quest for gratification: she could do everything, she was almightiness. A narcissistic and phallic triumph, such a maniacal attitude finally turned out to be exhausting, since it blocked all possibility of symbolization for the negative affects—fear, sorrow, pain...
Nonetheless, when the analysis of omnipotence gave those affects access to speech, Helen went through a period of frigidity. The maternal object, necessarily erotic, which had first been captured in order to be annihilated in Helen, once it was recovered and named during the course of analysis did probably, and for a time, fulfill the patient. "I have her within me," the frigid woman seemed to say, "she doesn't leave me, but no one else can take her place, I am impenetrable, my vagina is dead." Frigidity, which is essentially vaginal and can be partly compensated for with clitoral orgasm, betrays an imaginary capture by the frigid woman of a maternal figure anally imprisoned and transferred to the cloaca-vagina. Many women know that in their dreams their mothers stand for lovers or husbands and vice versa, and they keep settling with them, without satisfaction, accounts of anal possession. Such a mother, who is imagined as indispensable, fulfilling, intrusive, is for that very reason death-bearing: she devitalizes her daughter and leaves her no way out. What is more, since she has been imagined as monopolizing the jouissance her daughter had given her, but without returning anything in its stead (without getting her pregnant), such a mother cloisters the frigid woman in an imaginary solitude that is affective as well as sensory. The partner would need to be imagined, in turn, as "more-than-a-mother," in order to act the part of both "Thing" and "Object," in order not to fall short of the narcissistic request, but also and foremost in order to dislodge that request and lead the woman to cathex her autoeroticism in a jouissance of the other (separate, symbolic, phallic).
Two forms of jouissance thus seem possible for a woman. On the one hand there is phallic jouissance—competing or identifying with the partner's symbolic power—which mobilizes the clitoris. On the other hand, there is an _other jouissance_ that fantasy imagines and carries out by aiming more deeply at psychic space, and the space of the body as well. That other jouissance requires that the melancholy object blocking the psychic and bodily interior literally be liquefied. Who is capable of doing it? An imagined partner able to dissolve the mother imprisoned within myself by giving me what she could and above all what she could not give me, while remaining in a different place—no longer the mother's but that of the person who can obtain for me the major gift she was never able to offer: a new life. A partner who acts neither the father's part, ideally rewarding his daughter, nor the symbolic stallion's that one is supposed to obtain through a manly competition.
The feminine interior (meaning the psychic space and, at the level of bodily experience, the vagina-anus combination) can then cease being the crypt that encloses the dead woman and conditions frigidity. Putting to death the death-bearing mother within me endows the partner with the appeal of a life-giver, precisely of one who is "more-than-a-mother." He is not a phallic mother but rather a restoration of the mother by means of a phallic violence that destroys the bad but also bestows and honors. The so-called vaginal jouissance that follows is symbolically dependent, as can be seen, on a relation to the Other no longer imagined as part of a phallic outbidding, but as an invigorator of the narcissistic object and able to insure its _outward_ displacement—by giving a child, by himself becoming the link between the mother-child bond and phallic power, or else by furthering the beloved woman's symbolic life.
There is no evidence that the other jouissance is absolutely necessary for a woman's psychic fulfillment. Very often, either phallic, professional, or maternal compensation, or else clitoral pleasure are frigidity's hermetic veil. Just the same, if men and women endow the _other jouissance_ with nearly sacred value, it is perhaps because it is the language of the female body that has temporarily triumphed over depression. It is a triumph over death, surely not as the individual's ultimate fate, but over the imaginary death where the premature human being is permanently at stake if abandoned, neglected, or misunderstood by the mother. Within feminine fantasy such a jouissance assumes a triumph over the death-bearing mother, in order for the interior to become a source of rewards while eventually becoming a source of biological life, childbearing, and motherhood.
To Kill or to Kill Oneself: The Enacted Wrongdoing
_The Act Would Be Merely Reprehensible_. Feminine depression is occasionally concealed by a feverish activity that gives the depressed person the appearance of a practical woman, at ease with herself, who thinks only of being useful. To such a mask, which many women wear either deceitfully or unwittingly, Marie-Ange adds a cold urge for revenge, a true death-bearing plot, of which she herself is surprised to be the brain and the weapon, and which brings her suffering because she experiences it as a serious wrongdoing. Having discovered that her husband deceived her, Marie-Ange succeeds in identifying her rival and indulges in a series of more or less childish or diabolical schemings in order simply to eliminate the intruder, who happens to be a friend and colleague. It mainly amounts to pouring sleeping drugs and other harmful products into coffee, tea, and other drinks that Marie-Ange offers her freely. But it also goes as far as slashing her car's tires, disabling the brakes, and so forth.
A kind of rapture seizes Marie-Ange when she undertakes such retaliations. She forgets her jealousy and her wound and, even though ashamed of what she is doing, she comes close to feeling gratified. To be at fault causes her to suffer because being at fault gives her joy, and vice versa. Hurting her rival, disorienting her, or even killing her, does that not also amount to inserting herself into the other woman's life, giving her jouissance unto death? Marie-Ange's violence endows her with a phallic power that makes up for humiliation and, even more so, gives her the feeling of being more powerful than her husband—more authoritative, so to speak, over his mistress' body. The complaint against the husband's adultery is but a trivial coating. While wounded by her spouse's "wrongdoing," what rouses Marie-Ange's suffering and avenging mood is neither moral castigation nor the complaint about the narcissistic wound inflicted by her guilty husband.
In more primary fashion, _any possibility for action_ would appear to be seen by her fundamentally as a transgression, as a wrongdoing. Acting would amount to compromising herself, and when the depressive retardation underlying inhibition hampers any other possibility of realization, the only act that is possible for such a woman becomes the major wrongdoing—to kill or to kill oneself. One may imagine an intense oedipal jealousy with respect to the parents' "primal act," doubtless perceived and thought of always as reprehensible; or a precocious harshness on the part of the superego, a fierce hold on the Thing-Object of archaic homosexual desire... "I do not act, or if I do it is abominable, it must be reprehensible."
In the manic phase, the paralysis of action takes on the appearance of insignificant activity (and for that very reason hardly culpable), hence possible, or else it aspires to the major wrongdoing.
_A Blank Perversion_. Loss of the erotic object (unfaithfulness or desertion by the lover or husband, divorce, etc.) is felt by the woman as an assault on her genitality and, from that point of view, amounts to castration. At once, such a castration starts resonating with the threat of destruction of the body's integrity, the body image, and the entire psychic system as well. As a result, feminine castration, rather than being diseroticized, is concealed by narcissistic anguish, which masters and protects eroticism as a _shameful secret._ Even though a woman has no penis to lose, it is her entire being—body and especially soul—that she feels is threatened by castration. _As if her phallus were her psyche_ , the loss of the erotic object breaks up and threatens to empty her whole psychic life. The outer loss is immediately and depressively experienced as an inner void.
This means that the psychic void and the painful affect that constitutes its minute yet intense expression settle in place instead of the shameful loss. Depressive behavior develops on the basis of and within such a void. Blank activity, lacking meaning, may just as well follow a death-bearing course (killing the rival who steals the partner) or an innocuous one (wearing herself out doing housework or checking the children's homework). She remains constantly restrained by an aching psychic wrapping, anesthetized, as if "dead."
In the early stages of analysis for depressive women their emptiness as living dead is honored and respected. Only through friendly collusion, free from superego tyranny, does analysis allow shame to be spoken out and death to find its orbit as the death wish. Marie-Ange's desire to cause (the other's) death so as not to pretend to be dead (herself) can then be narrated as a sexual desire to joy in her rival or to give her jouissance.
For that reason, depression appears as the veil of a _blank perversion_ —one that is dreamed of, desired, even thought through, but unmentionable and forever impossible. The depressive course precisely avoids carrying out the perverse act: it hollows out the painful psyche and stands in the way of experienced sex as shameful. Melancholia's unbounded activity, which is somewhat hypnoidal, secretely cathexes perversion in the most inflexible feature of the law—constraint, duty, destiny, and even the fatality of death.
By revealing the sexual (homosexual) secret of the depressive course of action that causes the melancholy person to _live with death_ , analysis gives back its place to desire within the patient's psychic territory (the death drive is not the death wish). It thus marks off a psychic territory that becomes able to integrate _loss_ as signifiable as well as erogenetic. The separation henceforth appears no longer as a threat of disintegration but as a _stepping stone_ toward some other—conflictive, bearing Eros and Thanatos, open to both meaning and nonmeaning.
_Don Juan's Wife—Sorrowful or Terrorist_. Marie-Ange has an elder sister and several younger brothers. She has always been jealous of that elder sister, the father's favorite, but she retains from her childhood the certainty that she was abandoned by her mother, whose many successive pregnancies claimed all her attention. No hatred toward her sister or her mother seems to have been shown in the past, any more than at present. Marie-Ange, on the contrary, comported herself like a well-behaved child, sad, always withdrawn. She was afraid of going out, and when her mother went shopping she would wait for her by the window, worried. "I stayed in the house as if I were there in her stead, I preserved her fragrance, I imagined her presence, I kept her with me." Her mother deemed that such sadness was not normal. "That nun's expression is deceitful, she is hiding something," the matriarch would say disapprovingly, and those words would discourage the little girl even more as she withdrew to her inner hiding place.
It took Marie-Ange a long time to talk of her present depressive states. Under the surface of the always punctual, busy, and faultless teacher, a woman showed up who sometimes took extended sick leaves because she did not want to, could not, leave her house; in order to imprison what fleeing presence?
Nevertheless, she managed to control her states of total dereliction and paralysis by identifying with the maternal figure: either with the superactive housewife, or even—and this is how she came to take action against her rival—with a desired phallic mother whose homosexual passive partner she would like to be or, conversely, whose body she herself would like to arouse by putting her to death. So, Marie-Ange told me a dream that enabled her to glimpse the kind of passion that nourished her hatred for her rival. She manages to open the door of her husband's mistress' car to hide an explosive in it. But in fact it is not a car, it is her mother's bed; Marie-Ange is huddled against her, and she suddenly notices that this mother, who so generously breast-fed the swarm of little boys who came after Marie-Ange, owned a penis.
The heterosexual partner of a woman, when the relationship is satisfying from her point of view, often bears the attributes of her mother. The depressive woman goes against this rule only indirectly. Her favorite partner or her husband is a fulfilling although unfaithful mother. The desperate woman can then be dramatically, painfully, attached to her Don Juan. For, beyond the fact that he gives her the possibility of enjoying an unfaithful mother, Don Juan satisfies her eager thirst for other women. His own mistresses are her own mistresses. His exploits satisfy her own erotomania and provide her with an antidepressive, a feverish excitement beyond pain. If the sexual desire underlying that passion were repressed, murder might take the place of embrace and the depressed woman might change into a terrorist.
Taming sorrow, not fleeing sadness at once but allowing it to settle for a while, even to blossom, and in this way to wear itself out: that is what one of the temporary and yet indispensable phases of analysis might be. Could the wealth of my sadness be my way of protecting myself against death—the death of the desired/rejected other, the death of myself?
Marie-Ange had muffled within herself the distress and devalorization where the real or imaginary maternal neglect had left her. The idea of her being ugly, useless, and insignificant did not leave her, but it was more of an ambiance than an idea, nothing obvious, just the glum coloring of a dull day. On the other hand, the desire for death, for her own death (for want of avenging herself on the mother) filtered into her phobias: fear of falling out the window, from the elevator, off a rock, or off the slope of a mountain. Fear of finding herself in a void, of dying of the void. A permanent vertigo. Marie-Ange protected herself from it for the time being by displacing it onto her rival, who was supposed to be drowned in poison or vanish in a car going at breakneck speed. Her life was unharmed at the price of the other's sacrificed life.
The terrorism of such depressive hysteria is often expressed by aiming for the mouth. Many stories involving harems and other feminine jealousies have established the image of the poisoner as a privileged image of feminine Satanism. Poisoning drink or food nevertheless reveals, beyond the raging sorceress, a little girl deprived of the breast. And if it is true that little boys are also deprived, everyone knows that man recovers his lost paradise in the heterosexual relationship, but also and mainly through various roundabout means that lavish oral satisfactions on him or do so by means of orality.
Acting out, where a woman is concerned, is more inhibited, less developed, and consequently it can be, when it takes place, more violent. For the loss of the object seems beyond remedy for a woman and its mourning more difficult, if not impossible. So, substitutive objects, perverse objects that should lead her to the father, seem derisory to her. She often reaches heterosexual desire by repressing archaic pleasures, even pleasure itself—she yields to heterosexuality in frigidity. Marie-Ange wants to keep her husband to herself, for herself but not for sexual pleasure. Access to jouissance is then effected only through man's perverse object: Marie-Ange's pleasure comes from the mistress, and when her husband does not have one he no longer interests her. The depressive woman's perversion is deceitful, it needs the go-between and screen of man's object-woman in order to seek the other sex. But once settled on that path, the tired-out desire of the melancholy woman knows no bounds: it wants everything, to the end, until death.
The sharing of that death-bearing secret with analysts is not merely a test of their reliability or of the difference between their discourse and the domain of law, condemnation, or repression. Such a trust ("I am having you share in my crime") is an attempt to win over the analyst into a common jouissance—the one that the mother declined, that the mistress steals. By pointing out that the trust is an attempt to gain ascendency over the analyst as erotic object, the interpretation maintains the patient in the truth of her desire and her attempts at manipulation. But in abiding by an ethics that does not merge with that of punitive legislation the analyst recognizes the reality of the depressive stance, and asserting the symbolic legitimacy of its distress, allows the patient to seek out other means, symbolic or imaginary, of working out her suffering.
A Virgin Mother
_"Black Hole"_. To her it seemed as if conflicts with, desertions by, separations from her lovers did not affect her, she experienced no grief. No more than when her mother died... This did not imply an indifference that would be based on self-control and mastery of the situation or else (and this is most frequently the case) on hysterical repression of sadness and desire. When Isabel, during sessions, attempted to piece together such states, she would speak of "anesthetized wounds," "numbed sorrow," or "a blotting out that holds everything in check." I had the impression that she had fitted in her psychic space one of those "crypts" Maria Torok and Nicolas Abraham talk about, in which there was nothing, but the whole depressive identity was organized around this nothingness. Such nothingness was an absolute. Grief, humiliating by dint of having been kept secret, unnameable, and unspeakable, had turned into a _psychic silence_ that did not repress the wound but took its place and, what is more, by condensing it, gave it back an exorbitant intensity, imperceptible by sensations and representations.
Melancholy mood, with her, amounted only to mental blanks, evasiveness, distraught and seemingly hallucinated gazings on what may have been grief, but which Isabel's superego dignity at once transformed into inaccessible hypertrophy. A nothingness that is neither repression nor simply the mark of the affect but condenses into a _black hole_ —like invisible, crushing, cosmic antimatter—the sensory, sexual, fantasy-provoking ill-being of abandonments and disappointments. Narcissistic wounds and castration, sexual dissatisfaction and fantasy-laden dead-ends become telescoped into a simultaneously killing and irretrievable burden that organizes her subjectivity; within, she is nothing but bruises and paralysis; outside, all that was left to her was acting out or sham activism.
Isabel needed that "black hole" of her melancholia in order to construct her living motherhood and activities outside it, just as others organize themselves around repression or splitting. It was her own thing, her home, the narcissistic center where she foundered as much as she replenished herself.
Isabel decided to have a child at the darkest moment of one of her depressive periods. Disappointed by her husband, distrustful of what appeared to be her lover's "childish inconsistency," she wanted to have her child "for herself." Knowing who fathered it mattered little to her. "I want the child, not the father," the "virgin mother" reflected. She had to have a "reliable companion," "Someone who would need me, we would be accomplices, we would never leave each other, well, almost never..."
The child conceived as antidote against depression is destined to bear a heavy burden. The indeed virginal calmness of the pregnant Isabel—no period in her life had ever seemed so euphoric to her as her pregnancy—concealed a bodily tension that any heedful observer would have detected at the beginning of this analysis. Isabel did not manage to relax on the couch but, her neck muscles tensed and her feet on the ground ("so as not to damage your belongings," she said), she seemed ready to leap forward and confront some threat or other. That of being made pregnant by the analyst? Some unweaned babies' hyperkinesia no doubt conveys their mothers' unnamed, unconscious, utmost physical and psychic tension.
_Living for the Sake of Dying_. Anxiety over deformity in the fetus, common in most pregnant women, reached a suicidal peak with Isabel. She imagined that her baby would die during delivery or be born with a serious congenital defect. She would then kill it, before killing herself, mother and child becoming united again, inseparable in death as in pregnancy. The much hoped for birth changed into a burial, and the vision of the funeral exalted the patient, as if she had desired her child for death alone. She would give birth for death's sake. The brutal stopping of the life she was preparing to give, and of her own as well, was destined to spare her all worry, to relieve her of the troubles of life. Birth destroyed the future and the project.
Desire for a child was revealed as narcissistic desire for lethal fusion—it was a death of desire. Thanks to her child Isabel would elude the risks of erotic ordeals, the surprises of pleasure, the uncertainties of the other's discourse. Once she had become a mother she would be able to remain a virgin. Deserting the child's father in order to live as a single woman (or else as an imaginary couple with her analyst?), alone with her daydreams, needing no one and threatened by none, she entered motherhood as one enters a convent. Isabel was getting ready to gaze upon herself complacently in that living being destined for death that her child was to be, like a painful shadow of herself that she would at last be able to care for and bury, whereas no one would be capable of doing it "properly" for herself. The depressive mother's selflessness is not without a modicum of paranoid smugness.
When little Alice was born, Isabel felt as if she were bombarded by reality. The baby's neonatal jaundice and the first childhood illnesses that were inordinately serious threatened to change the death fantasy into an unbearable fact. Undoubtedly with the help of analysis, Isabel was not swallowed up by postpartum blues. Her depressive inclination was transformed into a fierce struggle to save the life of her daughter, whose development she henceforth followed with great tenderness, albeit with the temptation to be overprotective.
_Smug Abnegation_. The initial melancholia was devoured by "Alice's problems." Nevertheless, without disappearing, it acquired another aspect. It was transformed into total ascendancy, both oral and anal, over the girl's body, and her development was thus set back. Feeding Alice, controlling her meals, weighing her, weighing her again, supplementing the diet prescribed by some doctor or other by drawing from the advice found in such-and-such a book... Checking Alice's stools until she started school and afterward, her constipations, her diarrheas, giving her enemas... Watching over her sleep—what is the normal length of sleep for a two-year-old? And a three-year-old? A four-year-old? And is not this babble rather an abnormal cry? The obsessive anxiety of the "typical" worried mother was multiplied by Isabel. As an unwed mother wasn't she responsible for everything? Wasn't she all that this "poor Alice" had in the world? Her mother, father, aunt, grandfather, grandmother? The grandparents, having deemed that this birth was not very orthodox, had stood aloof from the "virgin mother" and unwittingly given Isabel an additional excuse in her need to be all-powerful.
A depressive person's pride is immeasurable, and this is something one must take into account. Isabel is ready to take on any labor, worry, duty, trouble, even defect (if someone chanced to find any), rather than to admit her suffering. Alice has become a new speech inhibitor in the already not-so-talkative world of her mother. For the sake of the daughter's well-being, the mother had to "hold out": facing up to things, not appearing to be an inadequate person or a loser.
How long can this last, this delightful, smug imprisonment by the sadness of being alone, the sorrow _of not being?_ With some women, it lasts until the child no longer needs her, has sufficiently grown up, and leaves her. They then find themselves abandoned once more, downcast, this time without being able to resort to another childbirth. Pregnancy and motherhood turned out to be a parenthesis within the depression, a new negation of that impossible loss.
Isabel, for her part, did not wait that long. She had the verbal and erotic recourse of transference. She could cry and break down before her analyst, trying to come to life again not beyond but this time _through_ the mourning of the analysis, ready to hear a wounded speech. Once solitude has been named, we are less alone if words succeed in infiltrating the spasm of tears—provided they can find an addressee for an overflow of sorrow that had up to then shied away from words.
_Aroused Father and Ideal Father_. Isabel's dreams and fantasies might suggest that she had been the victim of a precocious seduction on the part of her father or some other adult among their acquaintances. No precise memory clearly surfaced from Isabel's discourse, either to confirm or deny it; the hypothesis was suggested by an oneiric, repetitive sequence where Isabel is alone in a closed room with an older man who is irrationally pushing her against the wall; or one in her father's office where again the two of them are alone, with her shaking less from fear than from emotion, blushing and perspiring, such an incomprehensible state filling her with shame. Was this true seduction or a desire to be seduced? Isabel's father appears to have been an uncommon character. A poor farmer who became the manager of a firm, he aroused the admiration of his employees, friends, and children, and particularly that of Isabel. And yet this man, aiming at success, had frightful, sudden changes of mood, especially under the influence of alcohol, which he indulged in more and more as he grew older. Isabel's mother would conceal that emotional instability; at the same time she compensated for it and held it in contempt. As far as the child was concerned, such contempt meant that mother disapproved of the father's sexuality, his excessive fire, his lack of composure. A father, in short, who was both desired and condemned. He might have been, to a certain extent, an identifying solution for his daughter, a support in her rivalry with and disappointment in the mother, the genitor who was always distracted by another baby. But beyond an intellectual and social attraction, that father was also a disappointing figure. "From my point of view he was immediately demystified, I could not believe in him as outsiders did, he was my mother's creation, her biggest baby...."
Her father's symbolic existence doubtless helped Isabel in erecting her professional armor, but the erotic man, the imaginary father, the loving, giving, and gratifying one had become unbelievable. He displayed emotions, passions, and pleasures from the angle of crisis and anger—fascinating, but how dangerous and destructive. The link between pleasure and symbolic dignity that is insured by an imaginary father, as he leads his child from primary to secondary identification, no longer existed for Isabel.
She then had a choice between a paroxysmal sexual life and... "virginity"—between perversion and abnegation. The experience of the former had filled her years as a teenager and a young woman. Such excesses, or "overflows" as she called them, punctuated the end of her depressive episodes. "It was as if I were drunk, and afterwards I ended up vacuous. Perhaps I am like my father. But his constant fluctuation between high and low—that, I don't want. I prefer serenity, stability, sacrifice if you wish. The sacrifice for my daughter, however, is it really a sacrifice? It is a moderate joy, a permanent joy.... Well, a well-tempered joy, like the clavier."
Isabel gave a child to her ideal father—not the father who displayed a drunken body but the father with the absent body, therefore a dignified father, a master, a leader. The masculine body, the aroused and drunken body, that is the mother's object: Isabel leaves it to that deserting rival, for in the competition with her mother's presumed perversion, the daughter at once admitted she was a minor, a loser. As for her, she chose the prestigious name, and it is precisely as a celibate, unwed mother that she will succeed in preserving it in its untouchable perfection, dissociating it from the "overly" aroused masculine body, which is manipulated by the other woman.
If it be true that such a paternity largely conditions Isabel's depression, forcing her back toward the mother from whom she could not be separated without risks (of stimulation, of imbalance), it is also true that, through his ideal aspect, his symbolic success, such a father also provides his daughter with a few means, admittedly ambiguous, to pull herself through. In becoming the mother _and_ the father Isabel has finally reached an absolute. But does the ideal father exist anywhere other than in the abnegation of his own daughter as celibate, unwed mother?
When all is said and done, however, and even if it is only with one child, Isabel manages much better than her mother. For is it not true that if she does not produce many children, she does everything for a single one? Nevertheless, that overtaking the mother in the imagination is only a temporary solution to depression. Mourning still remains impossible under the guise of a masochistic triumph. The real work remains to be done, through separation from the child and, finally, through separation from the analyst, so that a woman might try to face the void within the meaning that is produced and destroyed in all its connections and all its objects...
NOTES
. One is particularly indebted to the works of André Green for having developed the notion of "psychic void." See, among others, "L'Analyste, la symbolisation et l'absence dans la cure analytique," at the Twenty-ninth International Psychoanalytic Congress, 1975, and _Narcissisme de vie, narcissisme de mort_ (Paris: Minuit, 1983).
Hannah Arendt
Female Genius: General Introduction
_One of the most fervent passions is the genius's love of truth_.
— _LaPlace_
"What a genius!" Our recent claims of discovering "genius" within ourselves—whether in the form of a talent, a natural gift, or a prolonged search for truth—have put an end to the ancient deification of personality. At first, the divine spirit charged with watching over the birth of the future hero was transformed into a viable means of innovation. As Voltaire put it, "this invention in particular appeared to be a gift from the gods; this _ingenium quasi ingenitum_ was a sort of divine inspiration." Whether by simple metonymy or by analogy, "a genius" later became someone who "displayed genius," if not someone who simply happened to influence someone else.
Hannah Arendt, one of the protagonists of this three-part work, made light of "the genius," whom she considered to be a product of the Renaissance. Tired of being reduced to the fruits of their labors, the men of the Renaissance became increasingly munificent, and as they lost touch with God, they grafted His transcendence onto the very best among their ranks. Since that time, the _divine_ , disguised as a genius, has made up for this loss by producing a mystery play that has transformed the creator into something unique. Does this mean that the absolute has descended upon us? Or that we should consider this loss to be a challenge to humanity? Is it a demand from a superman? Or is it a refusal to lower ourselves to the level of "products" or "appearances" in a society plagued by "consumption" and the "spectacle"? Suffice it to say that "genius" is a therapeutic invention that keeps us from dying from equality in a world without a hereafter.
Even so, do we dare speak about "genius" without ignoring the "evil genius" who devoted all his resources to deluding Descartes himself? In our day, it would appear, the word "genius" stands for paradoxical occurrences, unique experiences, and remarkable excesses that manage to pierce through an increasingly automated world. The troubling, even formidable, emergence of such phenomena helps us understand the meaning of human existence. Does this mean that genius helps substantiate the meaning of life? The protagonists of this work believe that it does not: as we shall see, my geniuses consider life to be substantiated through more modest means indeed. They do suggest, however, that our existence can be perpetually revived by that which is extraordinary. Significantly, however, this brand of extraordinariness is not achieved by gaining entry into the hallowed halls that record the rigorous ordeals of history. Like the ancient Greek heroes, my geniuses displayed qualities that, while no doubt exceptional, can be found in most of us. And they (the geniuses, which in this case are three _female_ geniuses) did not hesitate to make mistakes and to let us know their limitations. What distinguishes these geniuses from us is simply that they have left us to judge a body of work rooted in the biography of their experience. The work of a genius culminates in the birth of a subject.
Each of us leads some sort of existence, and many of us have lived through adventures, often interesting ones, that can provide fodder for family legend and sometimes for the local newspaper or even the nightly news. Yet such experiences are not the stuff of a noteworthy biography. Let us agree here to use the term "genius" to describe those who force us to discuss their story because it is so closely bound up with their creations, in the innovations that support the development of thought and beings, and in the onslaught of questions, discoveries, and pleasures that their creations have inspired. In fact, these contributions touch us so intimately that we have no choice but to moor them in the lives of their authors.
Some works of art have an impact that is greater than the sum of their parts. The way these works affect us depends ultimately on the historical disturbances they bring about and on the way they influence other people and their followers—in sum, their effect depends on the way _we_ respond to them. When someone finds himself at this juncture and capitalizes upon it, he becomes a genius—even if all he ever did was be born into the world, work, and then die. We endow him with a biography that fails to explain the excess, the indulgences, or the invasiveness of his life. Still, the reason we afford such a biography to geniuses, and not to just anyone, is to sound an alarm: regardless of whatever creation, work of art, or deed has come about, someone has lived. Are we someone? Are you someone? Try to be someone!
A Mozart concerto, a funny Charlie Chaplin scene, and Madame Curie's discovery of radium were all events as unusual as they were inevitable, and as unforeseen as they were indispensable. Since "it" took place, we cannot imagine a world without "it," as if "it" has always been with us. The temporary shock caused by such acts and works makes us want to explain "it" away by conjuring up the superhuman and by contemplating the destiny or the genetics that preside over the birth of individuals. That is, when we do not make "it" into an everyday occurrence by proclaiming, as did Buffon, that "genius is endless patience" or, for the more romantic among us, by repeating Valery's words: "Genius! O endless impatience!" At the same time, when geniuses demand that we endow them with a life that amounts to less than their "genius" itself, they play another trick on us: they make us look at ourselves in a way that is just as ingenious as the way they locate their extraordinary character between their own pleas and the unpredictable opinion of the human beings who respond to them and who ordain them. At heart, they are geniuses for us—and for eternity, so much so that we become geniuses ourselves, the sort of geniuses that accompany "our own" geniuses.
And what role do women play in all this? Is it true, as La Bruyère and others have written, that women have "talent and genius... only for handiwork"? Of course, it has long been asserted that women's only genius is the genius of their patience, whereas style is the exclusive province of men.
The twentieth century has put an end to the notion that women are the birthing half of a species of mammals. The growth of industry, which demanded a female workforce, and then the growth of science, which has slowly increased our knowledge of procreation, have effectively freed women from the constraints of the life cycle. Although these trends have been underway for thousands of years, only privileged minorities and a few exceptional personalities have been able to take advantage of them thus far. The twentieth century has made this emancipation accessible to the majority of women, particularly in the industrialized world, and we have every reason to believe that women in Asia, Africa, and Latin America are prepared to follow a similar path. For better or for worse, the next century will be a female one—and female genius, as described in this work, gives us hope that it might be for the better.
The feminist movement is the third stage in the progress of women (the first being the suffragist movement in the late nineteenth century and the second being the militant struggle for equal rights in all aspects of life, as described in Simone de Beauvoir's manifesto _The Second Sex_ ). The feminist movement, beginning with the unrest in the late 1960s, focused with a heartfelt violence on this newfound freedom and on the unforeseen differences that such freedom laid bare: the existence of another sexuality, another language, and another politics. But this rejection of tradition did not avoid falling prey to excess, the most troubling example of which was to see motherhood as the ultimate proof that women have been exploited by every imaginable form of patriarchy since time immemorial. In the manner of libertarian "movements," the feminists have assembled "all women" into an emancipating force, or even a revolutionary force, as is the case with the majority of proletariat groups and developing countries. These downward drifts, far from being a thing of the past, have become tainted with a reactionary conformity that manages to discredit any notion of feminine specificity or freedom that is not based on seduction—which means not based on reproduction and consumption. Putting that aside, and putting aside the balancing act that characterizes all manner of social mores, much evidence points to a revival of women's emancipation.
One example may be found in the prominent (and growing) role that women play in the political life of democracies. We can safely assume that this display of political and economic competence will only become broader and more widely accepted, not only in the Western world but also in developing countries.
Motherhood, which has benefitted from scientific progress and which was demeaned at one time in certain quarters, has since emerged as the most essential of the female vocations. In the future, motherhood will be desired, accepted, and carried out with the greatest blessings for the mother, the father, and the child. Will mothers become our only safeguard against the wholesale automation of human beings?
In the end, the particular accomplishments of each woman and her personality, which cannot be reduced to the common denominator of a group or a sexual entity, have become not only possible but also proclaimed with great pride. It is because I am myself, and specifically myself, that I am able to introduce the contributions of women to a large segment of the world.
This particularity is where we shall find the sparkle of female genius. Recognizing the substantial contribution made by a few extraordinary women whose life and work have left their mark on the history of this century is one way to call attention to the singularity of every woman. Is it not true that going beyond your own limits presents a more appealing antidote to the various forms of "groupthink," whether they be generously libertarian or sensibly conformist?
We still must acknowledge that, no matter how far science may progress, women will continue to be the mothers of humanity. Through their love of men, too, women will continue to give birth to children. That fate, though tempered by various techniques and by a sense of solidarity, will remain an all-consuming and irreplaceable vocation. Everyone knows that women, through an osmosis with the species that makes them radically different from men, inherit substantial obstacles to realizing their genius and to contributing another specific, if not ingenious, talent to the culture of humanity that they shelter in their wombs. Many people have thumbed their noses at these insurmountable natural conditions that appear to banish female geniuses for good—and such caricaturists have not always been wretched misogynists. Think of the marvelous Mlle de Merteuil, who thought that certain women, such as the Présidente de Tourvel, would never amount to "more than a type of species." Joyce, that unsurpassed wordsmith who knew his Molly from personal experience, believed he was in the right when he accorded time to men while reserving space and the species for women: "Father's time, mother's species." And Baudelaire, the most disdainful of them all, scoffed at "the childish side of motherhood."
These views are not wrong, but they fail to tell the whole story. Mothers can be geniuses, not only of love, tact, self-denial, suffering, and even evil spells and witchcraft but also of a certain approach to living the life of the mind. That approach to being a mother and a woman, at times warmly accepted and at times outright refused or wrought with conflict, bestows upon mothers a genius all their own. Women, greater in number and in confidence than ever before, have proved this beyond cavil: though curled up like children in space and in the species, women are also able to work toward unique, innovative creations and to remake the human condition. The three women who are the subject of this work are by no means the only women to have left their mark on the increasingly diverse pursuits of our time. My personal affinities are what led me to read, enjoy, and choose Hannah Arendt (1906–1975), Melanie Klein (1882–1960), and Colette (1873–1954). I hope that by the end of this work, the reader will be persuaded that my personal choices are worthy of a more objective selection.
The twentieth century was one in which the accelerated progress of technology revealed, more forcefully than before, both the excellence of humankind and the risks of self-destruction that lurk within it. The Holocaust alone proves this to be the case, and it is hardly necessary to add the atomic bomb and the dangers of globalization to the list.
With value systems fallen by the wayside, we now deem life to be the ultimate good. It is both a threatened life and a desirable life—but in the end, what sort of life is it? Hannah Arendt was consumed with such thoughts when she responded to the death camps of two totalitarian regimes by setting her hopes on a respectable political activity that would lay bare the "miracle of natality."
But Arendt did not wish to believe that language could turn mad and that the "good sense" of humanity could conceal the threat of lunacy. It would be up to Melanie Klein to investigate these chasms of the human psyche and to devote herself to studying the death drive that gives life to the speaking being from the onset, although melancholia and paranoid schizophrenia question the primacy of that operation.
The sensualists and seductresses who become intoxicated with the flesh of an apricot, with the arum of their lover's member, or with a schoolteacher's lilac-scented breasts have not, for all that, abandoned the atomic age. If the twentieth century turns out to be more than just a terrible memory, it will be in part because of the pleasure and immodesty of the liberated women that Colette described with the impertinent grace of the insurgent that she was. A zest for words, when grafted onto the robots that we have become, may be the most wonderful gift that female writing can offer the mother tongue.
I include here two German-speaking Jewish women who explored, in the English language and in London and New York, the weightiness of politics and the limits of human nature. I also include a French countrywoman who rekindled the fire of the materialists and a sophisticated debauchery. The genius of these three women has restored, with a complexity that complements the truths they tell, the many faces of modern Time.
These three women lived, thought, loved, and worked with men—with their men, sometimes by tolerating the authority of a master or by depending on his love, and sometimes by running the risks inherent in rebellious acts that are tinged with an unimpeachable innocence. In each case, however, these women were able to maintain more or less respectable independence.
It may come as a surprise that this book discusses, among Arendt's other writings, the political works on anti-Semitism and totalitarianism that made her famous. Tracing the development of her work seemed to be the most fruitful avenue, tracing the portrait of the woman-thinker whose substantial contributions to political thought have been either praised or criticized by others before me. I also consider how Arendt gave voice to Heidegger's concept of _Dasein_ [Being] and yet replaced the solitude of the "being-thrown-in-the-world" with the virtuosity of the "appearance." Heidegger's concept of errancy, when cast against the anonymity of the "they," becomes suddenly unrecognizable once Arendt focuses on the miraculous "birth of each person" into the "frailty of human affairs," that is, into political life. Though she always remained attentive to the great philosopher's work, Arendt, that lover of pure thought, was able to move beyond it and to become a political theorist in a class by herself—one who has been discussed at length and yet who remains just as topical today. Not only was Arendt the first person to link the two totalitarian regimes because they both destroyed human life but also she made it known that the "appearance" is a condition intrinsic to humanity: she reveals the irreducible singularity of each person, provided that he finds the courage to partake in the common sense of those around him. After all, the media frenzy that has shaken up the world since Arendt's death amounts perhaps to more than just a curse, particularly if we examine it through the lens of the genius of this woman who revalued political meaning as a "taste" for showing, observing, remembering, and recounting.
Freud had just discovered the unconscious as well as the relationship between mental illness and sexuality. He was surveying the pitfalls of pleasure while settling scores with the social conformists who did not want—and who still do not want—to admit that the human body is a being of desire. To this concern for Eros and Thanatos, the founder of psychoanalysis added far more strident battles with his disciples that were primarily Oedipal in nature. It was at that time that Melanie Klein devoted herself to studying decompensation. Caring for children had taught her that in the beginning is the urge to destroy, an urge that eventually is transformed into madness but that always remains a conduit of desire. Freud had already said as much, but it was Klein who fully developed the notion. A more radical pioneer of child psychoanalysis than was Anna Freud, Klein created the real possibility of a psychoanalysis of psychosis, one that could circumvent the spiritualism of Jung that had wandered, against Freud's teachings, into that very domain.
Despite the dogmatism of the ferocious explorer that she is accused of being, Klein's work lends itself to a popular readership. Her work has been carried forward by original and fruitful developments that proved her right all along: W. R. Bion and David W. Winnicott were not her disciples but her followers. Without them, and without the modern psychoanalysis of psychosis and autism that dominate her work, we still would not understand the distinguishing mark of modern culture that is the ever-present risk of madness and the wide range of treatments we can use to stave it off.
The idea that pleasure is not only organic but also emerges in words, as long as those words become sensory, has never been articulated more effectively than by the French geniuses after Rabelais, particularly by the eighteenth-century sensualists and libertines. And yet it is Colette who can claim the privilege of saturating the French language with the pagan tastes that make up the charm of our civilization, all the while telling us how this sort of sensuality is rooted in the sexual antics of the well-bred or in the poignant pleasures of the common folk. To realize her genius, Colette, unlike Arendt and Klein, did not first have to overcome a master: she saw her husbands, Willy, and then Jouvenel, as primarily a source of assistance and protection, and in the end, an annoyance. Rather, Colette had to face the authority of the mother tongue, which forced her to confront both reason and femininity, to love both of them equally, and to transmute one into the other. Colette's only real rival would prove to be Proust, whose narrative search has a social and metaphysical complexity that goes well beyond the adventures of Claudine and her counterparts. And yet Colette far surpasses Proust in the art of capturing pleasures that have never been lost.
These three experiences, these three truth-telling works were produced at both the heart of this century and at its margins. Though Arendt, Klein, and Colette were not truly excluded or marginalized, they nevertheless lay outside the norm. These women manifested their freedom to explore without heeding the dominant trends, institutions, parties, or schools of thought. Arendt's work is interdisciplinary (is it philosophy? political science? sociology?), and it delves into religions and into ethnic and political groupings; her work avoids the mainstream views of the "Right" as well as the "Left." Klein, for her part, challenged the conformity of the Freudians, and without fearing the consequences of being disloyal to the prevailing psychoanalytic orthodoxy of the day, she broke entirely new ground in the study of the Oedipus complex, fantasy, language, and prelanguage. At first provincial and outrageous, and then worldly while remaining a woman of the people, Colette was never fully part of the literary establishment until she developed her insight into social mores and her sensual rebellion.
Though innovative in its refusal to conform, the genius of these women came at a price: rebels glean their stimulation from their genius, and they pay for it by being ostracized, misunderstood, and disdained. That fate is common to all geniuses. Is it also common to women in general?
_Life, madness_ , and _words_ : the three women relied on them to become lucid and passionate investigators while drawing on their existence as much as on their thinking and while sharing their unique perspective on the most important issues of our time. I attempt to study these women without limiting myself to the well-known themes always linked to their names. Hannah Arendt is more than just "the banality of evil" and the Eichmann trial, and more than just the linking of Nazism and Stalinism. Melanie Klein went further than the "precocious paranoid projection," the "want and gratitude" commanded by the "part object" that is the mother's breast and the "multiple splitting" that culminates in endogenous psychosis. And the provocation of the little urchin who acted outrageously in order to prevail at the Académie Goncourt does not fully account for the magic of Colette. These themes are no more than a few trees obscuring forests that are far more appealing but that are also dangerously more complex.
Of course, the zeal of the experts has already put to rest these commonplace associations: our three protagonists, often misunderstood or even persecuted during their lives, have since acquired their own set of commentators and fanatic adherents. I do not devote a great deal of time here to the work of the many specialists who have already spent much energy, with scrupulous attention to detail, on reconstructing various controversies and on clearing up the inevitable misunderstandings that shaped the paths of these three women.
Instead, I limit myself to studying these three women carefully and faithfully so as to reconstruct their individuality while putting each in her proper perspective—not to liken what cannot be likened, but to portray, amid the resonance that will sound among these three compositions, the complexity of twentieth-century culture as well as the major role played by women in its most vulnerable arenas: life, madness, and words.
Do we owe these uncommon forms of genius and these unforgettable innovations to these women's femininity, so unusual in itself? It is a question worth asking, and the title of this work implies that we do. At this early stage, however, I would rather not respond to the question. I began this study with the hypothesis that I knew nothing, that "woman" is an unknown, or at least that I preferred not to "define" what a woman is so that an answer might emerge out of a careful accumulation of examples. So perhaps, after accompanying each woman into her own genius, we will strike a chord that appears to bring them all together. We may hear some music composed of singularities, dissonant keys, and counterpoints that go beyond the fundamental tonalities. Perhaps that is what female genius is—that is, if female genius even exists. For now, I suggest that we reserve judgment until the end of our journey.
NOTES
. The Greek _daimōn_ , and then the Latin _genius_ , watched over the birth of men and their works. Women, for their part, were granted a _juno_ , a profoundly protective double of the self.
. The _Robert_ dictionary traces the latter evolution to 1689.
PART 6
_Revolt and Imagination_
The Sense and Non-sense of Revolt
_The Sense and Non-sense of Revolt_ , translated by Jeanine Herman and published by Columbia University Press in 2000, is the first volume of _The Powers and Limits of Psychoanalysis_ , which presents a two-year lecture course given by Kristeva at the University of Paris VII. Her 1994–1995 seminar was transcribed and edited by her students and published in 1996 by Fayard as _Sens et non-sens de la révolte_. Here Kristeva revisits the theme of revolution so prominent in her earlier work. In _Revolution in Poetic Language_ Kristeva identifies the possibility of revolution in language—a revolution she deems analogous to social revolution—with (maternal) semiotic forces in avant-garde literature. In _Powers of Horror_ this semiotic force of drives is associated not only with the maternal but more particularly with the abject or revolting aspects of the maternal; the revolting becomes revolutionary through the return of the repressed (maternal) within (paternal) symbolic systems. Two decades later, in _The Sense and Non-sense of Revolt_ , Kristeva asks if revolt is possible today. She claims that within post-industrial and post-Communist democracies we are confronted with a new political and social economy governed by the spectacle within which it becomes increasingly difficult to think of the possibility of revolt. The two main reasons are that within media culture the status of power and the status of the individual have changed.
Kristeva argues that there is a power vacuum in contemporary culture that results in the inability to locate the agent or agency of power and authority or to assign responsibility. We live in a no-fault society in which crime has become a media-friendly spectacle and government and social institutions normalize rather than prohibit. There is no authority against which to revolt, so whom or what can we revolt against? In addition, the human being as a person with rights is becoming nothing more than an ensemble of organs that can be bought and sold or otherwise exchanged, what Kristeva calls the "patrimonial individual." How can an ensemble of organs revolt? Not only is there no one or nothing to revolt against; there isn't anyone to revolt.
Entering the social order requires assimilating its authority through a revolt by which the individual makes meaning his or her own. Revolt, then, is not a transgression against law or order but a displacement of its authority within the psychic economy of the individual. Psychoanalysis and literature become the primary domains of this revolutionary displacement. This displacement gives the individual a sense of inclusion in meaning making and in the social that supports creative activities and the sublimation of drives. Without this displacement and the resulting feeling of inclusion, the individual cannot own the meanings of culture and therefore cannot find meaning in anything. Revolt is necessary for happiness and for freedom.
Intimate Revolt
The psychic revolt that makes creativity and meaning possible is what Kristeva calls "intimate revolt" in volume two of _The Powers and Limits of Psychoanalysis_ , published by Columbia University Press in 2001 as _Intimate Revolt_ , translated by Jeanine Herman from the French _La révolte intime_ , published in 1997 by Fayard. In the second year of her lecture course, 1995–1996, Kristeva continues to develop the relationship among psychic revolt, creativity, imagination, and politics. As in the first volume she devotes part of the course to analyzing the notion of revolt in the works of Aragon, Sartre, and Barthes. The first selections included here are the preface to a short book, _L'avenir d'une révolte_ (Calmann-Lévy, 1998), which makes up part 2, "The Future of Revolt," of _Intimate Revolt_ , followed by chapter 1 of _Intimate Revolt_ , entitled "What Revolt Today?"(which begins both the Fayard and Lévy editions). Kristeva maintains that intimate revolt is necessary for psychic life and that it is necessarily unceasing. Sensory intimacy and sensory experience, identified with the "universe of women," become the fertile ground of self-reflection and self-questioning that opens psychic life to "infinite re-creation." Facilitated by negative drive force, this intimate psychic revolt makes possible both autonomy and connection with others.
"Elements for Research," the third selection from _Intimate Revolt_ included here, was also originally published as part of _L'avenir d'une révolte_ in a chapter entitled "Europhilie-Europhobie," translated as "Europhilia-Europhobia" in _Intimate Revolt_. In this chapter, Kristeva discusses her relation to the United States and the reception of her work in North America. After describing the intellectual "hospitality" of North America, she continues with these "Elements for Research," with which she attempts to clarify some of her concepts that have been most influential in the North American context: intertextuality, the semiotic-symbolic distinction, abjection, and foreignness.
The Sense and Non-sense of Revolt
What Revolt Today?
The title of this book is meant to evoke the current political state and the lack of revolt that characterizes it. I promise not to elude this aspect of the problem, but I will approach things from a bit of a distance: from the roots of memory, which is nothing other than language and the unconscious. There are two facets to the reflections presented here: the first concerns psychoanalysis, its history, and its present state; the second takes into consideration different literary texts.
I will explain first what I mean by "revolt" and why the problematic of the sense and non-sense of revolt is inscribed in a psychoanalytical perspective. A number of major texts of our time can be approached from this angle, and I have selected the works of three well-known authors, each linked, though differently, to rebellion in the twentieth century: namely, Aragon, Sartre, and Barthes.
Some psychoanalytical questions will allow us a more profound approach to these three authors. To begin quite naturally—some might say provocatively—I think it would be useful to look into the etymology of the word "revolt," a word that is widely used, if not banal, but that holds a few surprises. As a linguist by training, I sought out what linguists had to say about it. Two semantic shifts mark the evolution of the word: the first implies the notion of movement, the second, that of space and time.
Movement
The Latin verb _volvere_ , which is at the origin of "revolt," was initially far removed from politics. It produced derivatives with meanings—semes—such as "curve," "entourage," "turn," "return." In Old French, it can mean "to envelop," "curvature," "vault," and even "omelet," "to roll," and "to roll oneself in"; the extensions go as far as "to loaf about" ( _galvauder_ ), "to repair," and "vaudeville" ( _vaudevire_ , "refrain"). If this surprises you, so much the better: surprise is never extraneous to revolt. Under Italian influence in the fifteenth and sixteenth centuries, _volutus_ , _voluta_ —in French _volute_ , an architectural term—as well as _volta_ and _voltare_ suggest the idea of circular movement and, by extension, temporal return. _Volta_ also means "time"—as in "one time" or "once"—hence, "turning back." Another direct derivative from Latin belongs in this lineage, the adjective _volubilis_ , "that which turns with ease," as in _volubilitas linguae_ ; the French equivalent is _volubile_ (voluble). And _volumen_ , sheets of paper scrolled around a stick, with the spatial meaning of "wrapping" or "covering," results in "volume," which comes to mean "book" in the thirteenth century. (In a second usage the word acquired the more abstract meaning of "mass" and "thickness.") That the book has kinship with revolt might not be self-evident at first, but I will try to remedy this obfuscation.
The linguist Alain Rey stresses the cohesion of these diverse etymological evolutions, which start with a matrix and driving idea: "to twist, roll, wrap" (going back to the Sanskrit _varutram_ , the Greek _elutron_ , _eiluma_ ) and "covering," an object that serves as a wrapping. The idea of twisting or enveloping, a topological and technical concept, is dominant; it can even be found in the name of the Swedish car company, Volvo, "I roll." The old Indo-European forms * _wel_ and * _welu_ evoke a voluntary, artisanal act, resulting in the denomination of technical objects that protect and envelop. Today we are barely aware of the intrinsic links between "revolution" and "helix," "to rebel" ( _se révolter_ ), and "to wallow" ( _se vautrer_ ). But while I encourage readers to use etymology as a deciphering tool, do not rely solely on the appearance (or image) of a word and its meaning. Go further, go elsewhere, interpret. Interpretation, as I understand it, is itself a revolt.
"Evolution," in its first attested appearance in 1536, inherits the semes I have just mentioned but concerns only the movement of troops being deployed and redeployed. More interesting as far as the modern meaning of the word is that "to revolt" and "revolt," which come from Italian words that maintained the Latin meanings of "to return" and "to exchange," imply a diversion at the outset that will soon be assimilated to a rejection of authority. In sixteenth-century French, "to revolt" is a pure Italianism and signifies "to turn," "to avert" (to revolt the face elsewhere), or "to roll up" (thus hair was revolted). In 1501 the sense of a reversal of allegiance—siding with the enemy or religious abjuration—is attested, close to the Italianism "volte-face" (about-face). Thus in Calvin ("If a city or a country revolted from its prince...") or in Théodore de Bèze ("Those who revolt from Jesus Christ...") the idea of abjuration is linked to that of cycle and return, sometimes indicating only a change of party. In the psychological sense, the word contains an idea of violence and excess in relation to a norm and corresponds to _émouvoir_ (to move), hence _émeute_ (riot) for "revolt."
In the sixteenth century, the word does not involve the notion of force but strictly indicates opposition: to leave (a party), to abjure (a belief), to turn away (from a dependency). Until the eighteenth century, the word "revolt" is not used for war, as is the series "rebel," "rebellion," but is used in the political and psychological domain: "It's always been allowed by right of war to fire revolt between one's enemies," Laodice says to Arsinoë, in Corneille's _Nicomedes_. There is also reference to "feelings in revolt."
The historical and political sense of the word prevails until the end of the seventeenth century and beginning of the eighteenth: in _The Age of Louis XIV_ , Voltaire uses "revolt" to mean civil war, unrest, cabal, insurrection, war, and revolution when speaking of Mazarin's time. The relationship between "revolt" and "revolution" is not yet clearly established, revolution maintaining its celestial origins until 1700.
Time and Space
Turning to the semantic line of time and space, the Latin verb _revolvere_ engenders intellectual meanings: "to consult" or "reread" (Horace) and "to tell" (Virgil). "Revolution" appears later, entering the French language in scholarly astronomical and chronological vocabularies. In the Middle Ages, the word "revolution" is used to mark the end of a period of time that has "evolved"; it signifies completion, an occurrence, or a completed duration (the seven days of the week). In the fourteenth century, the notion of space is added: mirrors, interlocking objects, the projection of images. The revolution of human affairs is a stopping point in a preexisting curve. Gradually, the term comes to signify change, mutation. In 1550, and for a century afterward, it is applied to another semantic field, that of politics: thus the revolution of time leads to the revolution of State. In the second half of the seventeenth century, in the context of the Fronde and the period that followed, from Gondi to Retz and Bossuet, the word's political sense of conflict or social upheaval is confirmed. In the eighteenth century, "revolution" becomes more specific and widespread, with parallels frequently drawn between planetary and political mutations.
That's all I have to say about the evolution of the term "revolt," but I hope I have given you an idea of the richness of its polyvalence; I wanted to wrest it, etymologically, from the overly narrow political sense it has taken in our time. From these various etymological uses, I would like you to remember what I will call the "plasticity" of the term throughout its history, as well as its dependence on historical context. I have made passing reference to its links with astronomy but also with Protestantism, the Fronde, and the Revolution to show how rooted this plasticity is in scientific and political history. This preoccupation will guide the following reflections.
In the series of rather disparate semes I proposed, a number of them ought to be thought of in relation to this book's title, which emphasizes the impact, as much as the impasses, of revolt ("the sense and nonsense"): the non-sense suggested by words such as _galvaudage_ (sullying, idling about) and _vaudeville_ but also the uncertainties and randomness implicit in "reversal," "abjuration," "change," "detour," which repeat and transform, as well as the semes "curve," "quarrel," and "book"; "cycle," "stalling," and "upheaval"; and finally, "recovery," "unfolding," and the somewhat bland "reassessment." Also worth noting are the classic, though very different, uses of this notion by clans, tradesmen, and diverse social groups (artisans, astronomers, meteorologists), as well as its uses in psychology and politics.
In short, revolt twists and turns—indeed, veers off—depending on history. It is up to us to complete it. But why now? Why, given the plasticity I have briefly described, grapple with revolt now? What do I mean to convey in the present context, if it is true that historical context must be taken into account in order to renew the sense of the word? In response, allow me to make a point to which I will not return but which I would like to place on the implicit horizon of this book. This political observation supports a reflection I have expressed and pursued on various occasions that concerns the moment we are traversing and, to my mind, particularly justifies the necessity of reexamining the notion of revolt.
A Normalizing and Pervertible Order
The postindustrial and post-Communist democracies we live in, with their affairs and scandals, share characteristics that humanity has never confronted. Two of these accompany the society of the image, or of the spectacle, and justify the attempt to rethink the notion of revolt even while they seem to exclude the possibility of it: the status of _power_ and that of the _individual_.
_The Power Vacuum_
As watchers and readers of the media, we all know what the power vacuum means: the absence of plans, disorder, all the things we speak of and that political parties show the effects of, that we as citizens show the effects of. Yet in spite of this anarchy (who governs? who is going where?), signs of a new world order do exist, and if examined closely this order appears to be both normalizing and falsifiable, normalizing _but_ falsifiable. This is what grounds my inquiry into the possibility of revolt.
Consider the status of the legal system, of law: we no longer speak of culpability but of public menace; we no longer speak of fault (in an automobile accident, for example) but of damages. Instead of responsibility, there is liability; the idea of responsibility-without-fault is becoming acceptable; the right to punish is fading before administrative repression; the theatricality of the trial is disappearing in favor of the proliferation of delaying techniques. Crime cannot be found at the same time as prohibition; as a result, people are increasingly excited when they think they have unearthed a guilty party, a scapegoat. Look at the scandals judges, politicians, journalists, businesspeople are involved in. Crime has become theatrically media-friendly. I do not contest the benefits of this situation for democracy: perhaps we have in fact arrived at a so-called liberal society in which there is no surveillance and no punishment except in these theatrically mediatized cases that become a sort of catharsis of the citizen's nonexistent guilt. Though we are not punished, we are, in effect, normalized: in place of the prohibition or power that cannot be found, disciplinary and administrative punishments multiply, repressing or, rather, normalizing everyone.
This regulation—invisible power, nonpunitive legislation, delaying tactics, on the one hand, and media theatricalization, the fear of getting caught up, of being theatricalized in turn, on the other—supposes and engenders the breaches and transgressions that accompany business, speculation, and Mafia activity. The causes for this are multiple, but on the legal level, it is possible to describe what allows for them in terms of normalization, on the one hand, and perversification, on the other. There are no longer laws but measures. (What progress! How reassuring for democracy!) Measures are susceptible to appeals and delays, to interpretations and falsifications. This means that, in the end, the new world order normalizes and corrupts; it is at once normalizing and pervertible. Examples of this abound in all countries. Note, for example, the importance of stock market speculation on industrial production; bookkeeping leads to the accumulation of capital, on the right as on the left, and to the falsification of true wealth, which even recently was still measured in terms of production and industrial capacities. This example may clarify my idea of the new world order as a normalizing and falsifiable order. It is neither totalitarianism nor fascism (as is said in Italy particularly), though we have a tendency to resuscitate these terms in order to continue thinking according to old schemas. Still, the current normalizing and falsifiable order is formidable in another way: indirect and redirectable repression. Faced with these impasses, shouldn't we try to determine how a new regulation of power and transgression has come to replace the totalitarianisms of yesteryear and stop letting old terms like "fascism" and "totalitarianism" distract us?
_The Patrimonial Individual_
Because literature reveals the singularity of experience, it is worth looking at what is becoming of the individual, the singular subject, in this new normalizing and pervertible economic order. Consider the status of the individual in the face of biological technologies. The human being tends to disappear as a person with rights, since he/she is negotiated as possessing organs that are convertible into cash. We are exiting the era of the subject and entering that of the patrimonial individual: "I" am not a subject, as psychoanalysis continues to assert, attempting the rescue—indeed, the salvation—of subjectivity; "I" am not a transcendental subject either, as classical philosophy would have it. Instead, "I" am, quite simply, the owner of my genetic or organo-physiological patrimony; "I" possess my organs, and that only in the best-case scenario, for there are countries where organs are stolen in order to be sold. The whole question is whether my patrimony should be remunerated or free: whether "I" can enrich myself or, as an altruist, forgo payment in the name of humanity or whether "I," as a victim, am dispossessed of it. Some provisions set forth by the European Economic Community concerning the dynamics of the sale of bodies have even found that, thanks to biotechnological advances, the patrimonial individual may favor European economic development. Happily, speculations such as these incite resistance and are challenged by many jurists. Nevertheless, the primacy of the market economy over the body is certainly something to worry about, perhaps even to get dramatic about, to protest before things are firmly established, before it is definitely too late. Again, I am not discussing the democratic advantages that this new world order may entail; they are no doubt considerable. Still, I would underscore that an essential aspect of the European culture of revolt and art is in peril, that the very notion of culture as revolt and of art as revolt is in peril, submerged as we are in the culture of entertainment, the culture of performance, the culture of the show.
The Culture of Revolt
The European tradition, where this phenomenon is most manifest, has an experience of culture that is at once inherent in the social fact and active as its critical conscience. Europeans are cultured in the sense that culture is their critical conscience; it suffices to think of Cartesian doubt, the freethinking of the Enlightenment, Hegelian negativity, Marx's thought, Freud's unconscious, not to mention Zola's _J'accuse_ and formal revolts such as Bauhaus and surrealism, Artaud and Stockhausen, Picasso, Pollock, and Francis Bacon. The great moments of twentieth-century art and culture are moments of formal and metaphysical revolt. Stalinism no doubt marked the strangling of the culture of revolt, its deviation into terror and bureaucracy. Can one recapture the spirit itself and extricate new forms from it beyond the two impasses where we are caught today: the failure of rebellious ideologies, on the one hand, and the surge of consumer culture, on the other? The very possibility of culture depends on our response.
Just under the surface of this question is another we could legitimately ask: what is the necessity of this culture of revolt? Why relentlessly attempt to resuscitate forms of cultures whose antecedents lie in Cartesian doubt and Hegelian negativity, the Freudian unconscious and the avant-garde? Aren't they simply lost forever? Why should we want to find modern responses to these past experiences? After the death of ideologies, shouldn't we just be content with entertainment culture, show culture, and complacent commentary?
We shouldn't! I will try to demonstrate why through a discussion of Freud, for in listening to human experience, psychoanalysis ultimately communicates this: happiness exists only at the price of a revolt. None of us has pleasure without confronting an obstacle, prohibition, authority, or law that allows us to realize ourselves as autonomous and free. The revolt revealed to accompany the private experience of happiness is an integral part of the pleasure principle. Furthermore, on the social level, the normalizing order is far from perfect and fails to support the excluded: jobless youth, the poor in the projects, the homeless, the unemployed, and foreigners, among many others. When the excluded have no culture of revolt and must content themselves with regressive ideologies, with shows and entertainments that far from satisfy the demand of pleasure, they become rioters.
The question I would like to examine—from the somewhat narrow though not socially irrelevant perspectives of private life, psychological life, art, and literature—is the necessity of a culture of revolt in a society that is alive and developing, not stagnating. In fact, if such a culture did not exist, life would become a life of death, that is, a life of physical and moral violence, barbarity. This is a matter of the survival of our civilizations and their freest and most enlightened components. There is an urgent need to develop the culture of revolt starting with our aesthetic heritage and to find new variants of it. Heidegger thought only religion could save us; faced with the religious and political impasses of our time, an experience of revolt may be the only thing that can save us from the automation of humanity that is threatening us. This revolt is under way, but it has not yet found its voice, any more than it has found the harmony likely to give it the dignity of Beauty. And it might not.
That's where we are, and I see no other role for literary criticism and theory than to illuminate the experiences of formal and philosophical revolt that might keep our inner lives alive, this psychological space we call a soul and that is no doubt the hidden side, the invisible and indispensable source of what is Beautiful. Starting here, I will try to integrate the notion of the culture of revolt in the realms of art and literature, understood as experiences, and to raise the stakes. This means going beyond the notion of text—the elaboration of which I have contributed to, along with so many others—which has become a form of dogma in the best universities in France, as well as in the United States and other, more exotic places. In its stead, I will try to introduce the notion of experience, which includes the pleasure principle as well as the rebirth of meaning for the other, which can only be understood in view of the experience of revolt.
My writing a book and your reading it might seem evidence that culture is still possible, that it goes without saying, and that there can be only one version of it. Allow me to express my concern about this notion. Our modern world has reached a point in its development where a certain type of culture and art, if not all culture and all art, is threatened, indeed, impossible. Not, as I have said, the art or culture of the show, or the art or culture of consensual information favored by the media, but specifically the art and culture of revolt. Even when examples of this culture are produced, they take on such strange and stark forms that their meanings are lost on the audience. At that point, it is our responsibility to be interpreters, givers of meaning. For this reason, I am including critical work in the contemporary aesthetic experience: more than ever, we are faced with the necessary and inevitable osmosis between production and interpretation, a process that also implies a redefinition of the distinction between the critic, on the one hand, and the writer or artist, on the other.
It is not at all certain that a culture and art of revolt can see the light of day when prohibition and power have taken the forms of falsifiable normalization that I have described or when the individual has become a patrimonial ensemble of accessories with market value. If this is the case, who can revolt, and against what? Can a patrimony of organs revolt against a normalizing order? How? Through remote-controlled images? If we want to talk about art and culture in this context, clarification is necessary: what culture are we talking about?
I do not have the answer, but I propose a reflection. I submit that past experience, the memory of it, and particularly the memory of the Second World War, the Holocaust, and the fall of Communism, should make us attentive to our cultural tradition, which has advanced a thought and an artistic experience of the human subject. This subjectivity is coextensive to time—an individual's time, history's time, being's time—more clearly and more explicitly than anywhere else. _We are subjects, and there is time_. From Bergson to Heidegger, from Proust to Artaud, Aragon, Sartre, Barthes, different figures of subjectivity have been thought out and put into words or given form in our contemporary culture. Likewise, various modalities of time lead us not to imagine an end of history (as some have been able to do in the United States or Japan) but to try to bring new figures of temporality to the fore.
Let us, then, contemplate and highlight the experiences of writers attentive to the dramas of subjectivity and to different approaches to time. They will allow us to consider the historical moment as well as the multiple, ruptured temporality that men and women experience today, that shuttles them from fundamentalism or nationalism to biotechnology. Let us not be afraid to examine meticulously these explorations of subjective space, these complexities, these impasses; let us not be afraid to raise the debate concerning the experience of time. People today are eager for introspection and prayer: art and culture respond to this need, particularly the unusual, even ugly forms that artists are now proposing. Often, they are aware of their place as rebels in the new normalizing and pervertible order. But they also sometimes revel in a rudimentary—or, on the contrary, refined—minimalism. The role of the art critic then becomes essential to clarifying the subjective and historical experience of the writer or painter. Rather than falling asleep in the new normalizing order, let us try to rekindle the flame (easily extinguishable) of the culture of revolt.
The Lost Foundation
The question I would like to ask at the outset can be formulated this way: Is the Beautiful still possible? Does Beauty still exist? If the answer is yes, as I think it is (for what other antidote to the collapse of fantastic ideologies, what other antidote to death, than Beauty?), then what Beauty does one observe in contemporary works of art? I will draw on a few examples from the 1993 Venice Biennale to guide this brief inquiry. When I attended this event, I had—and still have—the impression that the examples of modern art being presented were not situated within the same history of the Beautiful offered by museums, including museums of modern art of the last twenty or thirty years. Certainly present were the perfection and technical mastery of the American artist Louise Bourgeois, who transforms trauma into fetish, and the skulls of the French sculptor Reynaud, who in a graceful and Cartesian way alleviates an obsession with death. But there was also something different that appeared to be the emblem of this biennale and perhaps even of contemporary art. Two works particularly struck me, for they seemed to bear a symbolic meaning of which the artists who made them may not have been aware. These two installations, or, if you prefer, sculptures, one by the German artist Hans Haacke, the other by the American artist Robert Wilson, in different ways represented the collapse of a foundation. Haacke's unusual installation had visitors walk on ground that shifted, crumbled; Wilson's ground did not erode but caved in, sank. A field of ruins, on the one hand; sinking ground, on the other. Viewers were fascinated, overwhelmed by volume, as if a troubling question had physically seized them in these two spaces. Loss of certainty, loss of memory. Political, moral, aesthetic loss?
To me, these artistic expressions resonate—in the furthest reaches of our culture's memory—with the Bible, particularly, Psalm 118, which talks of builders rejecting a stone that then becomes a cornerstone. This is done through God, and it is marvelous in our eyes. A song of glory and joy follows: _Exultate, Jubilate_ , a hymn found in Catholic ritual, other rituals celebrating foundations, and Mozart.
We are a long way from that. We can no longer exult or be jubilant about our foundations. Artists no longer have pedestals. Art is no longer certain it can be this cornerstone. The ground is sinking; the foundation no longer exists. A great artist, the writer Marcel Proust, was able to celebrate the cornerstone in the image of the cobblestones of Saint Mark's in Venice, to extract from it a metaphor for art made from the vestiges of these traditions. This cornerstone may return at some point, but today it is crumbling. And we are anxious and unsettled. We don't know where to go. Are we still capable of going anywhere? We are confronted with the destruction of our foundation. Part of our pedestal is falling into ruin.
Yet there is an exquisite ambiguity to this moment, harrowing though it is, for it is not solely negative. The simple fact that an installation has been created in a place where the foundations are disintegrating gives rise to a question as well as to anxiety. This is the sense of Haacke's and Wilson's constructions: a question, a sub-version, a re-volt in the etymological sense of the word (a return toward the invisible, a refusal and displacement). And this question is a sign of life—certainly a modest, humble, minimal one but already a detour, a revelation, a shifting of the collapse—and it is deeply affecting. Of course, it isn't quite jubilation or exultation, as the response being formulated is minute, but it is a sign of life nevertheless, a timid promise, anguished and yet existent.
Many young artists make installations rather than simple art objects. Are these merely signs of an incapacity to produce a distinct and intense object? An inability to concentrate metaphysical and aesthetic energy within a frame, on a piece of wood, in bronze or marble? Perhaps. But I think something else is at stake. In an installation, the entire body is called on to participate through its senses—sight, of course, but also hearing, touch, sometimes smell. As if instead of creating an object, these artists seek to situate us in a space at the borders of the sacred and ask us not to contemplate images but to commune with beings, an unquestionably tentative and sometimes unvarnished communion but a call nonetheless. And seeing these young artists' installations, tangles, bundles, pipes, fragments, and various mechanical objects, I got the impression that beyond the malaise of a lost foundation, they were communicating this: the ultimate goal of art is perhaps what was once celebrated as incarnation. I mean by that the desire to make one feel—through abstraction, form, color, volume, sensation—a real experience.
Contemporary art installations aspire to incarnation but also to narration. These installations have a history: the history of Germany, the history of prehistoric man, the history of Russia, as well as more modest personal histories. An installation invites us to tell our story, to participate, through it and our sensation, in a communion with being. It also produces an unsettling complicity with our regressions, for when faced with these fragments, these flashes of sensations, these disseminated objects, you no longer know who you are. You are on the verge of vertigo, a black hole, a fragmentation of psychical life that some call psychosis or autism. Is it not the fearsome privilege of contemporary art to accompany us in these new maladies of the soul?
And yet I think we are experiencing a low period. I tried to compare the current situation with the end of the Roman Empire in my novel _The Old Man and the Wolves_. Back then, however, a new religion was emerging, one that was already astonishing, though its arts and splendors had yet to come. Today, I am not certain that a new religion is arriving or that this would even be desirable. But I think we all need an experience, by which I mean something unknown, surprise, pain, or delight, and then comprehension of this impact. Is it still possible? Perhaps not. Perhaps charlatanism is today's currency, and everything is both spectacle and merchandise, while those we call marginal have definitively become excluded. In this context, obviously, one has to be very demanding, that is, disappointed. Personally, once over the disappointment, I prefer to welcome these experiences: I keep my curiosity on call, expectant.
Freud Again: Rebellion and Sacrifice
Parallel to the etymological and semiological references I have given for the term "revolt" (recalling its plasticity, its social, political, ethical motivations), two occurrences of "revolt" in Freud show the rigor and deeprootedness of the word in both the history of psychoanalysis and its current state. At issue here are oedipal revolt, on the one hand, and, on the other, the return of the archaic, in the sense of the repressed but also the timelessness ( _zeitlos_ ) of the drive.
I will return to the Oedipus complex at length in a later chapter, but in order to anchor the notion of revolt firmly in Freudian thought, I would like to remind you here that, according to Freud, the oedipal is a component of the human psyche composed of two evolutions: on the one hand, from a structural point of view, the Oedipus complex and the incest taboo organize the psyche of the speaking being; on the other, according to a speculation that is less historical than historic, Freud attributes the origin of civilization to nothing less than the murder of the father, which means that the transmission and permanence of the oedipal over generations can be understood in light of a phylogenetic hypothesis.
Why is the oedipal permanent in all humans? Why must the subject live through the oedipal as a child and then see it repeated in various metamorphoses throughout his/her life? Freud responds to these questions in _Totem and Taboo_ , telling a story that is not as subjective as one might like to think and that should not necessarily be filed away as part of Freud's private "novel" or Freud's "folly."
To summarize, at the origin, primitive men lived in hordes dominated by a fearsome male who demanded total submission from his sons and prohibited access to women, the sexual enjoyment of whom he reserved for himself. One day, the sons plotted a conspiracy and revolted (there we are!) against the father: they killed him and ate him. After this totemic meal, they identified with him, and after this primary ceremony of humanity, which saw the concomitance of revolt and feast (remember this concomitance!), they replaced the dead father with the image of the father, with the totem symbol of power, the figure of the ancestor. From then on, guilt and repentance cemented the bond, the social pact, among the sons, among the brothers; they felt guilty and banded together as a result of this guilt, and "the dead father became stronger than the living one had been" (p. 143). The dead man elicited such guilt in the brothers that he became all-powerful, forcing them to keep themselves in check, to curb their desires through a sense of wrongdoing. The impulse of affection—which existed simultaneously with the impulse of hatred—was transformed into repentance and sealed the social link that first appeared as a religious link.
It is important to know that, for Freud, the social order is fundamentally religious. Which leads us to a first question: if the rebellious man is a religious man, what happens when the man is no longer religious? Is he still rebellious? How so? It is no doubt unnecessary to remind you that religion can make man docile and has no qualms about doing so. Read Nietzsche's indignations against Christianity; these are more pertinent than facile secularisms. Furthermore, the social and/or religious link is also (though not only, keeping Nietzsche in mind) where revolt finds its conditions of possibility, hence its openings and traps, which are where I am headed. If art and literature are in fact a continuation of the sacred by other means (and not unaware of desacralization but, on the contrary, quite aware of it), this could not be more topical.
But let us return to our Freudian fable: the social link is founded as a religious link, the brothers deny themselves the women, rules of exogamic exchange are elaborated. The brothers, who have become social beings, resorb the feminine, renounce it. This feminine is the feminine of women, as objects of desire, but also the brothers' feminine, in the sense of their passive desire for the father, their love for and fascination with the father. Freud asserts that it is this repressed homosexuality that provides the basis for the social contract: guilt and repressed homosexuality; one synthesizes that which keeps one in check in the name of the father. _Homo religiosis_ is born, shaped by feelings of guilt and obedience. It is in this context that Freud speaks of an "uprising": "The _tumultuous mob_ of brothers were filled with the same contradictory feelings which we can see at work in the ambivalent father-complexes of our children and of our neurotic patients" (p. 143; emphasis mine). And Freud emphasizes the necessity to mimic this revolt: not to reproduce it exactly but to represent it in the form of a festive or sacrificial commemoration, composed of the joy of the initial crime subjacent to the religious sentiment, to guilt, to repentance, or to propitiation. After emphasizing the need for "remembrance of the triumph over the father," Freud goes on:
Satisfaction over that triumph led to the institution of the memorial festival of the totem meal, in which the _restrictions_ of deferred obedience no longer held. Thus it became a duty to _repeat_ the crime of parricide again and again in the _sacrifice_ of the totem animal, whenever, as a result of the changing conditions of life, the cherished fruit of the crime—appropriation of the paternal attributes—threatened to disappear. We shall not be surprised to find that _the element of filial rebelliousness_ also emerges, in the later products of religions, often in the strangest disguises and transformations.
(p. 145; emphasis mine)
I will let you appreciate the richness of Freud's text, and I point out that the "fruit" of this rebellion is the appropriation of the father's qualities; the "fruit" is subjacent to the "guilt." Like the religious experience, Freud's text emphasizes the guilt following the rebellion, but he is also the first to underscore the "fruit" of this rebellion and to invite us to think of situations where it "threatens to disappear," because it is then, and only then, that guilty obedience yields to the necessity to repeat the rebellion, particularly in the form of ritual sacrifice. When pleasure is no longer found in bonds, we start the revolt all over again. Religion allows us to do this by means of ritual sacrifice, a coded revolt.
One might ask how the rebellion can be repeated in other forms. Let us say, to anticipate, that when the sacred-social bond founded on guilt weakens, the logical—psychological—demand reappears to restart the rebellion (this is a function of the sacred as symbolic commemoration of the crime). But in certain situations wherein the bond and/or guilt is weakened, it is impossible or at least very difficult to recapture the festive "fruit" procured through the imaginary or symbolic reiteration of the rebellious act that is the sacred celebration.
Why does one sacrifice? Why does one enter into a religious pact and embrace fundamentalism, of whatever sort? Because, Freud tells us, the benefits we extract from the social contract threaten to disappear "as a result of the changing conditions of life": unemployment, exclusion, lack of money, failure in work, dissatisfactions of every kind. From then on, assimilation to the social link disintegrates; the profit "I" find in my integration in the _socius_ collapses. What does this profit consist of? It is nothing other than the "appropriation of the paternal attributes." In other words, "I" felt flattered to be promoted to the level of someone who could, if not be the father, at least acquire his qualities, identify with his power; "I" was associated with this power; "I" was not excluded; "I" was one of those who obeyed him and were satisfied with that. But sometimes this identification with power no longer works; "I" feel excluded; "I" can no longer locate power, which has become normalizing and falsifiable. What happens then?
"We shall not be surprised to find that the element of filial rebelliousness also emerges," Freud remarks, and this is when revolt is set in motion, "in the _later_ products of religions, often in the strangest disguises and transformations." What Freud calls a reappearance of defiance are cathartic experiences, rituals that have one or several (religious) meanings expended in an ordered profusion of signs (chants, dances, invocations, prayers, etc.). Thus we see the development of new attempts at rebellion, different from the primary revolt that was the murder of the father, in the form of religious worship and its pageantry, which today we consider aesthetic or artistic. A sacrificial situation is reproduced through which an imaginary power (which is not immediately political but has this latent vocation) is established and activated. Each participant hopes to satisfy the need to confront an authority in his/her imagination; it becomes possible not only to protest indefinitely (the rite is repeated) but also to renew the rite, in a way, with the dazzling expenditures that accompany religious celebrations: dances, trances, and other festivities inseparable from the scene of the sacrifice.
The problematic Freud broadly outlines here—condensed from a problematic of authority, of transgression as murder, of mimesis or representation, and of art as expenditure—is that there is a need for sacrifice in the sense of a remembrance and representation of the initial murder. As a speaking animal (capable of psychological representation, the results of which are thought and language), the human being needs to recall the qualities of the father (which Lacan will call the "paternal function") if and only if he mimics the transgression of his authority or the revolt against this identity. This reprise of the primary rebellion can take different forms: either a simple representation of the murder (these are the variants of sacrifices that all religions perform), or an acting out (where religious members of one community sacrifice religious members of another community), or in a _sublimated_ form (as in the expenditure of festivities such as dances, incantations, rites, a crucible of what will become art).
The question I would like to ask (and whose gravity surely is obvious) is, hasn't this logic, which Freud brought to the fore and which characterizes the religious, social, and artistic man, reached a saturation point? Perhaps this is where we are: neither guilty nor responsible but consequently incapable of revolt.
The second occurrence of the theme of revolt in Freud is found in an October 8, 1936, letter to the philosopher and psychoanalyst Ludwig Binswanger. Objecting to Binswanger's philosophical flights and metaphysical speculations, which he finds far removed from both the clinic and the scientific thought he considers to be his own, Freud writes: "I have always dwelt only in the ground floor and basement of the building.... In that you are the conservative, I am the revolutionary. Had I only another life of work before me I should dare to offer even those highly born people a home in my lowly dwelling." (Translation: you are highly placed; I would like to offer people like you who deign to accord me some attention a place in this basement where I am trying to develop a revolutionary spirit.) It is easy to establish the juncture between this image of the "lowly," "revolutionary" house and the series of archaeological metaphors in Freud whereby the unconscious is presented as invisible, hidden away, low. The comparison I am suggesting shows that the word "revolutionary" used by Freud has nothing to do with moral, much less political, revolt; it simply signifies the possibility that psychoanalysis has to access the archaic, to overturn conscious meaning. However—and this is where Freud's apparent modesty is revealed to be extreme ambition—someone who accesses the archaic and the impossible temporality that is timelessness (the unconscious has been unaware of time since _The Interpretation of Dreams_ ) is not only benevolent and indulgent but "revolutionary," in all the malleable senses of the word I presented at the start of this chapter. In short, Freud is a revolutionary in search of lost time.
This is the second direction I will try to explore: rebellion as access to the archaic, to what I will call an impossible temporalizing, which, as I said, will be the topic of a later chapter devoted to a discussion of time according to Freud. I take the term "temporalizing" from Heidegger, which he uses to demonstrate that even in ecstasy, even in an ecstatic state where time seems suspended, time, supposed time, is always already there. On the other hand, Freud was perhaps the only one to posit what he called "non-time," the "timeless" ( _zeitlos_ in German), time undone.
The return, or access, to the archaic as access to a timeless temporality: this is the experience whose analysis I propose here and that the great literary texts, particularly _Remembrance of Things Past_ , allow us to approach. The access to the archaic, to timelessness, to "pure embodied time," to use Proust's expression, also prepares us for benevolence. Isn't a good analyst one who welcomes us with benevolence, with indulgence, without scores to settle, calmly, in a lowly dwelling, as Freud says, and in this sense, a revolutionary one, giving us access to our own "lowly dwelling"?
This image brings me back to the lost foundation and the installations of destroyed habitats I spoke of while describing the Venice Biennale. Robert Wilson's installation was called _Memory/Loss_. I found in it the access to the archaic that Proust symbolizes magnificently in _Remembrance_. You entered a great hall, took off your shoes, and walked on cracked clay that gave beneath you and made you feel as though you were losing your footing. A projector illuminated a bust of a man with a shaved head. A text was handed out, and a story was told of a strange people: it was their custom to shave the heads of future slaves and then expose them to the sun. This caused their hair to grow inside as opposed to outside their skulls, which in turn led them to lose their memories. By telling us this fable with the aid of light, texture, and sound, Wilson invited us to experience the threat of the loss of memory that the normalizing order imposes on us.
For me, the analytical revolt, in the sense of the oedipal revolt and the return to the archaic, is an antidote to the threat of lost memory that certain contemporary artists seem to perceive. I propose three figures of revolt based on the Freudian experience:
• revolt as the transgression of a prohibition;
• revolt as repetition, working-through, working-out; and
• revolt as displacement, combinatives, games.
Logically independent—in social behaviors, for example—these figures are nevertheless interdependent in the psychological experience, where they are imbricated in the psychical apparatus as well as in artistic or literary works.
Why Aragon, Sartre, and Barthes? Or, More Analytically, Who's Afraid of Aragon, Sartre, and Barthes?
Besides the chance encounters and historical influences that have shaped my own course, I consider Aragon, Sartre, and Barthes representative of three essential challenges that have marked the century. Even today we have trouble assessing the upheaval their experiences have brought to mindsets, ideas, literature, and language.
In the wake of surrealism and having succumbed to Stalin's attraction, Aragon's poetic writing links sexual jouissance to the jouissance of language. This approach has inspired French poets from the troubadours to Rimbaud. Georges Bataille proposed a meditation on it, inspired by mystics, Hegel, and Freud. Antonin Artaud burned with the sonorous intensities of a body whose fibers, set ablaze, challenged the facilities of sex and psychological identity: a refusal that toppled into psychosis. Aragon conducts this deidentification of sex and language to two unsustainable points: the pleasure of power and the intoxication of lying. Neither true nor false, literary revolt is plausible, as Aristotle's _Poetics_ already asserted. With Aragon, the plausible is pushed to the extremes of identity games—the extremes of sexual roles, the extremes of ideological opinions, the extreme virtuosity of words—and confronts revolt with the risks of compromise and cynicism.
Sartre meanwhile anchors this debate on the other and being in the literary experience (read _Nausea_ and _Being and Nothingness_ at the same time), a debate that Hegel and Heidegger's philosophy deployed on academic terrain and that French thought has in large part tried to dispel. But having transfused being into the other and vice versa, Sartre applies this vision of being-as-other to politics and to all human words as long as they are in a political context. One might regret the resulting politicization of the being-as-other that leads to certain engagements that curiously forget to question their own bad consciences. But one cannot forget the simultaneous elevation of the political to the level of being-asother and the virtually mystical implications that Sartre achieves in the literary context (reread his plays, _Nausea_ , and _The Words_ ) and subsequently in politics. In his incisive book, Francis Jeanson rightly questions the beliefs of Sartre the atheist: Sartre's atheism is not a rationalism but a complete engagement in the being-as-other of human existence. We must continue this questioning if we want to find the possible or impossible meaning of modern atheism.
Finally, Barthes caused a scandal in the sixties, when ideologies were far from dead, by declaring in substance that everything ideological was semiological and by pulverizing the polished surface of ideas, beliefs, myths, fashions, texts in a polyphony of logics, semantic networks, and intertexts. The new priests that govern the media of France today are still upset with this musician of meaning for revealing—and for teaching us to reveal—all that is left unsaid under the appearance of messages, phenomena, and images.
For different reasons, each justifiable, these three experiences provoke fascination and, especially today, rejection. I will come back to the psychological and political reasons for such an attitude. Yet it seems important to underscore right away the common impetus that incites and characterizes the specific resistance toward these authors' works. The innovation of their texts, which has yet to be fully appreciated, resides in the revolt against identity: the identity of sex and meaning, of ideas and politics, of being and the other.
The demands of identity do not stem solely from a rationalist or Cartesian ideology that these three writers, in their specific manners, disturb. These demands are rooted in the speaking being's need to defend identity, which is a biological and psychological necessity and which monotheistic religion perfects and sanctifies. Loosening the strictures concerning "one's own" and the "identical," "true" and "false," "good" and "bad" becomes necessary for survival, because symbolic organizations, like organisms, endure on the condition of renewal and joy. Destroying them in a movement of revolt, however, leads to the risk of new defenses, false and deadly in other ways. In any case, the revolt against the One, which stands out in the experiences of Aragon, Sartre, and Barthes, raises the question of another structuring of subjectivity. Another humanity, we might say peremptorily, can be heard not only in their thought but also—and this is essential, for it signals the depth of the phenomenon—in their language: a humanity that takes the risk of confronting religion and the metaphysics that nourishes it, confronting the meaning of language.
This challenge is sizable and laden with compromises, mistakes, failures. Something new took place in Europe, the irruption of which Freud theorized with the discovery of the unconscious and which is manifested in the radical movements marking the shared thought-language destiny at the heart of what is still called literature and, indeed, philosophy. The unity of the speaking being, sealed by consciousness, is influenced by a network of biology and meaning, so that series of heterogeneous representations constitute our psychical apparatus. "We," "me," "I" are formed of multiple facets, and this polyphony—which depresses us or allows us pleasure, which nullifies or glorifies us—resonates in the polysemy of our verbal exchanges, extracts thought from the yoke of the rational, and reconciles an eccentric subject to the pulse of being. To write and/or to think can become, in this perspective, a constant calling into question of the psyche as well as the world.
It is no longer a matter of conforming to the universal (in the best of cases, everyone aspiring to the same values, human rights, for example) or asserting one's difference (ethnic, religious, sexual) as untouchable and sacred; still less of fighting one of these tendencies with the other or simply and skillfully combining them. It is a matter of pushing the need for the universal _and_ the need for singularity to the limit in each individual, making this simultaneous movement the source of both thought and language. "There is meaning": this will be my universal. And "I" use the words of the tribe to inscribe my singularity. _Je est un autre_ ("I is another"): this will be my difference, and "I" will express my specificity by distorting the nevertheless necessary clichés of the codes of communication and by constantly deconstructing ideas/concepts/ideologies/philosophies that "I" have inherited. The borders of philosophy and literature break down in favor of a _process_ of meaning and the speaking being, meanings emitted and values received.
Other eras have had this experience. Its radicalness, however, is unique in our century, one of education and information. The intensity of the avant-garde movements, their impact on political debates as well as on the desires of youth, has lent it the value of a mass movement. Those devoted to old ways of thinking are keeping watch: they do not understand, or understand too well, and oppose when they do not censure. Repressive returns to systems foregrounding the needs of identity are resurfacing: nationalism, traditionalism, conservatism, fundamentalism, and so on. Thought is content to build archives: we take stock and kneel down before the relics of the past in a museumlike culture or, in the case of popular variants, in a culture of distraction. We could spend years doing this. But revolt has taken place, it has not been erased, it can be read, and it offers itself to a rootless humanity now governed by the relativism of images as well as monetary and humanitarian indifference. Nonetheless the capacity for enthusiasm, doubt, and the pleasure of inquiry has perhaps not been entirely lost. This is at the heart of the ultimate defense of human life: the meaning of language and the architecture of the idea in the human mind. This at least is the presupposition of this book, or, if you like, this is my belief.
NOTES
. For those interested in the subject, I recommend Alain Rey, _Révolution: Histoire d'un mot_ (Paris: Gallimard, 1989), particularly pp. 21–32, which I refer to here.
. Corneille, _Selections; or, Polyeuctus/The Liar/Nicomedes_ , trans. John Cairncross (Harmondsworth: Penguin, 1980), act 5, scene 6, p. 309.
. Corneille, _Polyeuct_ , trans. Noel Clark (Bath, U.K.: Absolute, 1993), act 1, scene 4, p. 157.
. Voltaire, _The Age of Louis XIV_ , chapter 4.
. Rey, _Révolution_ , p. 34.
. In 1636, in Father Monet's _Dictionnaire français-latin_ ; see Rey, _Révolution_ , p. 36.
. The word is used in the sense of "conflict" in Bossuet ("Fatales révolutions des monarchies," _Oraisons funèbres_ , sermon 71). Montesquieu uses it to mean "social upheaval" ("upheavals which plunge rich men into destitution and swiftly raise the poor, as if on wings, to the height of opulence" [ _Persian Letters_ , trans. C. J. Betters (Harmondsworth, U.K.: Penguin, 1973), letter 98, p. 182]), and La Rochefoucauld uses it to describe changes in taste ("Une révolution générale qui change le goût des esprits aussi bien que les fortunes du monde," maxim 259, quoted in Rey, _Révolution_ , p. 53). [The Fronde was an insurrectionary French political party during the minority of Louis XIV and the ministry of Cardinal Mazarin. Members were called _frondeurs_ , from the French for "slingshot."—Trans.]
. Rey, _Révolution_ , p. 54. See also p. 56, where Rey quotes Voltaire: "Il se peut que notre monde ait subi autant de changements que les états ont éprouvé de révolutions" (from _Essai sur les moeurs_ ).
. I will not probe these legal matters any further, but those interested in the topic can do so in a very good book by jurist and University of Paris I professor Mireille Delmas-Marty: _Pour un droit commun_ (Paris: Seuil, 1994). In it, she details the status of law in the contemporary world, its banality, its theatricality, and the invisibility of power, along with the punitive proceedings that have resulted.
. Julia Kristeva, _The Old Man and the Wolves_ , trans. Barbara Bray (New York: Columbia University Press, 1994).
. I will examine the timelessness of the unconscious in volume 2, _Intimate Revolt_.
. Sigmund Freud, _Totem and Taboo: Some Points of Agreement Between the Mental Lives of Savages and Neurotics_ , trans. James Strachey (New York: Norton, 1950). The German text dates from 1912–1913.
. Quoted in Ernest Jones, _The Life and Work of Sigmund Freud_ (New York: Basic, 1957), 3:204. At the end of his life, Ludwig Binswanger drew closer to the phenomenologists, particularly Heidegger (from whom he is nevertheless very different) and maintained his ambition to combine psychoanalysis and phenomenology.
. One can—and I have done so elsewhere—call on other texts to highlight the radical evolution that is related to this new stage of what Nietzsche called "monumental history": not the linear, cursory history of sociopolitical events but fixed psychological attitudes, beliefs, and religions. And I could have—should have—spoken of Albert Camus; _The Rebel_ is essential, and _The Stranger_ , with its blank writing, incites an unsettling strangeness that goes well beyond humanistic testament. The current return to Camus has revived the moralist and the metaphysical importance of his writing.
. Francis Jeanson, _Sartre: Les Ecrivains devant Dieu_ (Paris: Desclée de Brouwer, 1966).
Intimate Revolt
The Future of Revolt
_What is essential in the revolutionary is not that he overturns as such; it is rather that in overturning he brings to light what is decisive and essential._
_—Heidegger, Nietzsche (1961)_
Preface
While we celebrate the events of May 1968, some people writing novels about it, others denouncing its imposture, analysts have facilitated its eternal return in well-worn words. The enraged have taken up the path of intimate revolt. It is the same one: that of realists who want the impossible.
Poetry has always been able to utter the will of free will, coming back to the memory of words and extracting its sense and time. In periods that we vaguely sense to be in decline or at least in suspension, questioning remains the only possible thought: an indication of life that is simply alive.
Intimacy is not the new prison. The need for connection might establish another politics, some day. Today, psychical life knows that it will only be saved if it gives itself the time and space of revolt: to break off, remember, refashion. From prayer to dialogue, through art and analysis, the capital event is always the great infinitesimal emancipation: to be restarted unceasingly. Without it, all that globalization can do is calculate the growth rate and genetic probabilities.
Truths, including scientific ones, are perhaps illusions, but they have the future ahead of them. In counterpoint to certainties and beliefs, permanent revolt is this putting into question of the self, of everything and nothingness, which clearly no longer has a place.
Nevertheless, if there is still time, we should wager on the future of revolt. As Albert Camus said, "I revolt, therefore we are." Or rather: I revolt, therefore we are _to come_.
A luminous and painstaking experience.
Revolt Today
In this volume of _The Powers and Limits of Psychoanalysis_ I will discuss intimate revolt, and I will explore new texts among the works of the three major authors examined in volume 1, each an integral part of the revolt of the twentieth century: Aragon, Sartre, and Barthes. I would first like to emphasize the paradoxical logic by which this experience of revolt is accomplished. The first part of this volume will be devoted to studying the crises and advances of modern man, realized through the paradoxes of forgiveness, time, intimacy, and image. But for now I will start by situating how the problematic of revolt corresponds more and more precisely to what is at stake today, both in terms of the intimacy on which our notion of happiness depends and the social link that determines what we call the political.
The Dignity of Revolt (the Novel)
With the French Revolution, the word "revolt," with its rich and complex etymology, acquired its current, distinctly political meaning. Thus when we speak of revolt today we first understand a protest against already established norms, values, and powers. For more than two centuries, political revolt has represented the secular version of this negativity that characterizes the life of consciousness when the latter attempts to remain faithful to its profound logic. A synonym of dignity, revolt is our mysticism.
Now it has become apparent that the new world order—whose democratic advantages no longer need to be praised in spite of its risks and even its impasses in the East and the West—is not favorable to this revolt.
Against whom does one revolt if power and values are vacant or corrupt? Or, to put it even more gravely, who can revolt if man has become a simple conglomerate of organs, no longer a subject but a patrimonial person, a person belonging to the patrimony, financially, genetically, and physiologically, a person barely free enough to use a remote control to choose his channel. I am oversimplifying and darkening this depiction of our current state in order to highlight what we all sense: not only that political revolt is being mired in compromises between parties whose differences are less and less obvious to us but especially that an essential component of European culture—a culture fashioned by doubt and critique—is losing its moral and aesthetic impact. This moral and aesthetic dimension finds itself marginalized and exists only as a decorative alibi tolerated by the society of the spectacle, when it is not simply submerged, made impossible by entertainment culture, performance culture, show culture.
At the risk of aggravating my image as someone who enjoys dramatizing the present state of things, I would like to discuss my novel, _Possessions_. It is a detective story that takes place in an imaginary town called Santa Varvara, which is emblematic of the global village, and begins with the discovery of a decapitated woman, Gloria Harrison, a translator and mother of a difficult child. The reader discovers that the murderers, the authors of this decapitation, are many. In this image of female and maternal suffering that sums up the difficulty of being a woman I have put much of my personal experience: the decapitated woman is me. I am also another woman in the novel, Stéphanie Delacour, a Parisian journalist who conducts the inquiry into the murder alongside the principal investigator, Northrop Rilksy. In the criminal and virtual universe of Santa Varvara a police investigation is still possible: the detective novel, a popular genre that keeps the possibility of questioning alive, basically tells the reader, "You can know."
Is that why when people stop reading, they still read detective novels: the degree zero of this aptitude for judgment that is the interrogation, our only remaining defense against the "banality of evil"? I consider my book, among so many others, as a low form of revolt. But are other, higher forms really more convincing?
The universe of women moreover allows me to suggest an alternative to the robotizing and spectacular society that is damaging the culture of revolt: this alternative is, quite simply, sensory intimacy. Though possessed by their sensibilities and passions, certain human beings nevertheless continue to ask themselves questions. I am convinced that after all the more or less reasonable and promising projects and slogans the feminist movement has promulgated over the past decades, the arrival of women at the forefront of the social and ethical scene has had the result of revalorizing the sensory experience, the antidote to technical hairsplitting. The immense responsibility of women in regard to the survival of the species—how to preserve the freedom of our bodies while at the same time ensuring the conditions for better lives for our children?—goes hand in hand with this rehabilitation of the sensory.
The novel is privileged terrain for such an exploration and its communication to the greatest number. Alongside and in addition to the culture of the image—its seduction, its swiftness, its brutality, and its frivolity—the culture of words, the narrative and the place it reserves for meditation, seems to me to offer a minimal variant of revolt. It is not much, but we may have reached a point of no return, from which we will have to re-turn to the little things, tiny revolts, in order to preserve the life of the mind and of the species.
Revolt, then, as return/turning back/displacement/change, constitutes the profound logic of a certain culture that I would like to revive here and whose acuity seems quite threatened these days. What makes sense today is not the future (as communism and providential religions claimed) but revolt: that is, the questioning and displacement of the past. The future, if it exists, depends on it.
But let me return to the meaning of this revolt, which seems to me to indicate what is most alive and promising about our culture.
Man in Revolt (Retrospective Return)
Since Socrates and Plato and more explicitly with Christian theology, man has been invited to a "return." Some of you still maintain the traces of this, if not the practice. This is notably the goal of Saint Augustine's repetition, founded on the retrospective link to the already-there of the Creator: the possibility of questioning one's own being, searching for oneself ( _se quaerere_ : "quaesto mihi factus sum"), is offered by this aptitude for return, which is simultaneously recollection, interrogation, and thought.
Yet technological development has favored the knowledge of stable values to the detriment of thought as return, as search (as repetition or as _se quaerere_ , "going in quest of oneself"). Moreover, the desacralization of Christianity, as well as its own intrinsic tendencies toward stabilization and reconciliation in the immutability of being, have discredited—when they have not rendered impossible—this battle with the world and with oneself that also characterizes Christian eschatology. Henceforth, the interrogation of values was transformed into nihilism, by which I mean the rejection of old values in favor of a cult of new values, interrogation of which is suspended. What has been taken for revolt or revolution for two centuries, particularly in politics and its attendant ideologies, has more often been this abandonment of retrospective questioning in favor of a rejection, pure and simple, of the old, destined to be replaced by new dogmas.
Generally, when the media employ the word "revolt," we understand nothing other than this nihilistic suspension of questioning in favor of so-called new values, which as values, precisely, have forgotten to question themselves and have thereby fundamentally betrayed the meaning of revolt that I am trying to emphasize here. The nihilist is not a man in revolt in the sense that I investigated in volume 1. The pseudorebellious nihilist is in fact a man reconciled with the stability of new values. And this stability, which is illusory, is revealed to be deadly, totalitarian. I can never sufficiently emphasize the fact that totalitarianism is the result of a certain fixation of revolt in what is precisely its betrayal, namely, the suspension of retrospective return, which amounts to a suspension of thought. Hannah Arendt has brilliantly developed this elsewhere.
In this book, as in my lectures and my novels, I am seeking experiences in which this work of revolt, which opens psychical life to infinite re-creation, continues and recurs, even at the price of errors and impasses. Because we can't fool ourselves: it is not enough to revive the permanence of revolt, which technology may have blocked, in order to recapture happiness or some sort of serene stability of being. Revolt exposes the speaking being to an untenable conflict, whose necessary jouissance and morbid impasses our century has assumed the formidable privilege of manifesting. But this occurs in a manner very different from that of the nihilist, who is fixed in the celebration of his rejection of the old or in the unquestioned positivity of the new.
This is where we are: we can either renounce revolt by withdrawing into old values or indeed new ones that do not look back on themselves and do not question themselves or, on the contrary, relentlessly repeat retrospective return so as to lead it to the limits of the representable/thinkable/tenable (to the point of possession), limits made evident by certain advances of the culture of the twentieth century.
Take note: the revolt of modern man is not a simple reprise of the retrospective link that founds the innermost recesses of the Christian man, serene in his quest, which is completed by a return to the _summum esse_. While following the path of retroactive questioning, modern man comes to an irreconcilable conflict. Although it may have been produced in the margins of art or the mysticism of previous eras, this conflict has never attained the paroxysm or vastness one can observe in it in modernity.
Just as the concept of process distinguishes modern history from that of antiquity, based on the destiny and brilliance of great men, the concept of self-organization is specific to contemporary history, which in the twentieth century occurred in bouts of crisis. I likewise submit that the concept of man in revolt distinguishes the modern man from both the Christian man, reconciled with God ("coram Deo"), and the nihilist, his enraged but symmetrical opposite.
Revolt as Jouissance and Dispersion (Psychoanalysis)
In what sense is revolt as we understand it—along with Freud, who invites us to recapture the diabolical unconscious, and certain contemporary writers who explore the border states of the mind—the retrospective relationship of _tendere esse_ with the "not yet" and "already no longer"?
I will venture one answer: revolt is distinguished from this notably by the fact that the tension toward unity, being, or the authority of the law (although always at work in modern revolt) is accompanied by centrifugal forces of dissolution and dispersion.
What's more, this conflict gives rise to a jouissance that is not simply the narcissistic or egoistic caprice of man spoiled by consumer society or the society of the spectacle. The jouissance at issue here—and this is where Freud's contribution is radical—proves indispensable to keeping the psyche alive, indispensable to the faculty of representation and questioning that specifies the human being. In this sense, Freud's discovery of the unconscious was the new Archimedean point that—for the psyche, always already dependent on the Other and the other—would constitute the favored place for life to find its meaning. This is only possible if, the psyche is capable of revolt. On this point Freud founded psychoanalysis as an invitation to anamnesis in the goal of a rebirth, that is, a psychical restructuring.
Through a narrative of free association and in the regenerative revolt against the old law (familial taboos, superego, ideals, oedipal or narcissistic limits, etc.) comes the singular autonomy of each, as well as a renewed link with the other. But this other Freudian palace of memory that psychoanalysis revisits and transforms was not recognized by Hannah Arendt, who lauded Saint Augustine's palace of memory but questioned psychology and psychoanalysis, which in her eyes were general sciences of "monotonous sameness."
Negativity in Revolt (Philosophy and... Freud)
The modern age, which I will date for convenience's sake from the French Revolution, highlights the negative share of this retrospective return. Personal or collective experience became an experience of conflict, of contradiction.
Being itself is wrought by nothingness, philosophy essentially says, emphatically since Hegel and differently with Heidegger and Sartre. This copresence of nothingness in being takes the dialectical form in Hegel. Starting with his text _What Is Metaphysics?_ (1929), Heidegger makes a distinction between the negation internal to judgment and a Nothingness that annihilates differently from how thought does: it is in feeling and anxiety that the philosopher will seek the nuclear forms of what he calls a repulsion, which is man's characteristic feature as a reject, an outcast, of being. _Dasein_ is a repulsion; "ecstasy" is another word for "abjection." Have we sufficiently considered this similarity?
In _Being and Nothingness_ (1943), Sartre relies on this difference between negation proper to thought and a primordial annihilation/nothingness. But more than repulsion he emphasizes freedom and definitively asserts himself as more Hegelian than Heideggerian, in the field of philosophy as well as in his political anarchism.
If I am rereading these texts, it is because they are a testimony of an extraordinary moment in Western thought, the moment when retrospective return—that is, the knowing subject's questioning of himself and his truth—leads him to nothing less than a familiarity with psychosis. Because the annihilating force ( _Kraft_ ) behind the concept, the disquieting eruption of which the concept must absorb (Hegel), as well as the sentiment of dissociation or repulsion in Heidegger and even "the prejudicative nothingness" of Sartre (who sustained his notion of freedom as radical violence, as a questioning of all identity, all faith, all law), all these advances, when confronted with human realities to make their logic accessible, come up against a psychical reality that endangers consciousness and exposes itself to the pulse of being. Erasure of subject/object borders, assault of the drive: language making itself tonality ( _Stimmung_ ), memory of being, music of the body and of matter. Heidegger seeks to capture this near psychosis in being, by respectfully visiting the work of Hölderlin. Sartre flees it by holding on to a totalizing and translucid consciousness, for which Flaubert, "the family idiot," and Genet, "actor and martyr," in melancholy and perversion, through style and play, offer more reason and humanism than the radical destruction of Artaud.
It may be surprising to maintain that the psychoanalytic movement inaugurated by Freud belongs to this interrogation into Nothingness and negativity. I am not talking about American psychoanalysis, dominated by ego psychology, but the radical interrogation into the psyche that Freud leads to the borders of biology and being, of which we find testimony in a still enigmatic text of 1925, _Die Verneinung_ (Negation). For the first time, a few years before _What Is Metaphysics?_ Freud links the fate of two types of negations: rejection, proper to the drive ( _Ausstossung_ or _Verwerfung_ ), and negativity, internal to judgment. In sum, he maintains that the symbol and/or thought are a sort of negativity, which itself is but a transformation under certain conditions of rejection or of an unbinding proper to the drive, which he calls the death drive.
We must now ask ourselves this question: under what conditions does the rejecting drive become symbolizing negativity? All psychoanalytical research on the "paternal function" (Lacan) or the "good-enough mother" (Winnicott), to name just a couple, is devoted to answering this question. Melanie Klein bases her most original work on the importance of this dissociating, rejecting drive, well before the appearance of the unity of the ego; this is the so-called schizoparanoid phase, which precedes the depressive phase that generates symbolism and language. The work on narcissism, borderline personalities, and so on attempts to deepen this modality of the psyche dependent on the archaic, the instinctual, the maternal, and, beyond that, the extrapsychical to the point of biology or being (depending on the school).
These different currents of theoretical thought in philosophy and psychoanalysis have had this particularity in modernity: they have attained, through retrospective questioning—that is, through inquiry or analysis—this border region of the speaking being that is psychosis.
Parallel to philosophy and psychoanalysis, in ways not theoretical but proper to language itself, the practice of writing attains non-sense too by unfolding meaning to the point of sensations and drives, finding its pulse in a realm that is no longer symbolic but semiotic. I am thinking of the desemanticization of style through ellipses in Mallarmé or through polyphony and portmanteau words in Joyce. Through language, and a linguistic overcompetence, an apparent regression is obtained, a childlike state of language. The semiotic _chora_ , this infralinguistic musicality that all poetic language aims for, becomes the main objective of modern poetry, an experimental psychosis. By this I mean that psychosis is the work of a subject, but a subject in process. It is through the archaeology of his unity, conducted in the material of language and thought itself, that the subject reaches the hazardous regions where this unity is annihilated.
Paradoxical Logic (Resistances to Psychoanalysis)
Thought or writing in revolt—which I will investigate in Sartre, Aragon, and Barthes—attempt to find a representation (a language, a thought, a style) for this confrontation with the unity of law, being, and the self to which man accedes in jouissance. As you know, jouissance is perceived by the old norm as an evil. Yet insofar as jouissance is thought/written/represented, it traverses evil, and thereby it is perhaps the most profound manner of avoiding the radical evil that would be the stopping of representation and questioning. The permanence of contradiction, the temporariness of reconciliation, the bringing to the fore of everything that puts the very possibility of unitary meaning to the test (such as the drive, the unnamable feminine, destructivity, psychosis, etc.): these are what the culture of revolt explores.
That is, it announces a veritable transformation of man issued from the Christian eschatology of retrospection as the path of truth and intimacy. The Freudian discovery is not a rejection of this tradition but a deepening of it to the limits of conscious unity; starting here, the Freudian path announces a possible transformation of our culture, inasmuch as it initiates another relationship to meaning and the One.
As you might have gathered, it is not exclusively in the world of action that this revolt is realized but in that of psychical life and its social manifestations (writing, thought, art), a revolt that seems to me to manifest the crises of modern man as much as the advances. Yet as a transformation of man's relationship to meaning this cultural revolt intrinsically concerns public life and consequently has profoundly political implications. In fact, it poses the question of another politics, that of permanent conflictuality.
You are no doubt familiar with the attack, denigration, and marginalization that psychoanalysis has undergone recently. While analysis has been the object of resistance since its inception (inevitably, insofar as it basically collides with the human being's desire not to know, the human being preferring sexual mystification to confronting truths that may place him in revolt), it seems the shunting aside of psychoanalysis today can be explained by other causes. The conditions of modern lives—with the primacy of technology, image, speed, and so forth, inducing stress and depression—have a tendency to reduce psychical space and to abolish the faculty of representation. Psychical curiosity yields before the exigencies of so-called efficiency; the unquestionable advances of the neurosciences are then ideologically valorized and advocated as antidotes to psychical maladies. Gradually, these maladies are denied as such and reduced to their biological substrata, a neurological deficiency.
A schematic materialism claims to do without the Freudian dualism that reserved a place for initiative, autonomy, the desire of the subject; a hard-line cognitivism subsumes within the same logic both the neuronal economy and the heteronomy of psychical representations dependent on the other. Ideological protests of a politically correct sort extol ethnic and sexual difference while refusing the rational approaches (psychoanalysis among them) that allow a better grasp of this singularity. By denigrating what they call an analytical universalism, these currents swing from militancy to a sectlike logic. Finally, psychoanalytical societies themselves contribute to discrediting psychoanalysis, with their delicate politics and concern for safeguarding their clinical purity or, on the contrary, an overly aggressive ideological, if not spiritual, orientation, and thereby undermine the Copernican revolution that Freud introduced in the twentieth century and that we increasingly perceive to be the only one that does not turn away from either malady or the revolts of modernity.
Perhaps it is necessary to recall some of the paradoxical logics of the analytical cure to highlight the type of intimacy the analytical experience has brought into being, as modern art has, though by completely different means.
Freud underscored the unprecedented timeless ( _Zeitlos_ ), which no philosophy had isolated before him and which characterizes the unconscious: while human existence is intrinsically linked to time, the analytical experience reconciles us with this timelessness, which is that of the drive, and more particularly the death drive. Unlike any other translation or deciphering of signs, analytical interpretation emerges as a secular version of forgiveness, in which I see not just a suspension of judgment but a giving of meaning, beyond judgment, within transference/countertransference.
Timelessness, a modification of judgment: the analytical experience leads us to the borders of thought, and venturing into these regions is of interest to the philosopher as well as to the moralist, since the examination of thought (what is a thought, without time, without judgment?) implies an examination of judgment, morality, and, ultimately, the social link.
Of particular interest are the aesthetic or literary variants of timelessness and forgiveness such as the analytical experience reveals them. In short, with timelessness and forgiveness we revisit nothing less than our intimate depths, which appear to us as an experience in suffering. [ _en souffrance_ = lost, as a package; awaiting delivery; in pain.—Trans.] Isn't it true that the various forms of the possession of our intimacy, including the most demonic and most tragic, remain our refuge and our resistance in the face of a so-called virtual world where judgments are blurred or assume an archaic and barbarous form? It is precisely in the imaginary experience, particularly in literature, that this intimacy is deployed, with its timelessness and its strange forgiveness.
Intimacy in Revolt (the Imaginary)
Am I essentially pleading the case of intimate revolt as the only possible revolt? I am not unaware of the commercial impasses and spectacular miasmas of all the imaginary productions in which our rebellious intimacy manifests itself. There are periods when even the mystical path—this acceleration of liberating transformations—is confined within treatments aimed at pathology or else within spiritualist or decorative ghettos. This is one of those periods.
Faced with the invasion of the spectacle, we can still contemplate the rebellious potentialities that the imaginary might resuscitate in our innermost depths. It is not a time of great works, or perhaps, for us, contemporaries, they remain invisible. Nevertheless, by keeping our intimacy in revolt we can preserve the possibility of their appearance.
NOTES
. The ancient forms * _wel_ and * _welu_ , referring to a voluntary, artisanal act, lead to the appellation of technical objects that protect and encase and evolve toward the sense of "return," "discovery," "circular movement of the planets," " _volte-face_ " in Italian [about face], " _vaudeville_ " in French, "volume" ( _volumen_ )—which results in "book"—and the Swedish car company Volvo ("I roll"). For a more precise etymology, see _The Powers and Limits of Psychoanalysis_ , vol. 1: _The Sense and Non-Sense of Revolt_ , trans. Jeanine Herman (New York: Columbia University Press, 2000), chap. 1.
. See Hannah Arendt, especially _Eichmann in Jerusalem: A Report on the Banality of Evil_ , _The Human Condition_ , and _The Life of the Mind_.
. Hannah Arendt, _The Life of the Mind_ , vol. 1, _Thinking_ (New York: Harcourt, 1971), p. 35.
. See Julia Kristeva, _Revolution in Poetic Language_ , trans. Margaret Waller (New York: Columbia University Press, 1984), pp. 25–30.
Elements for Research
I would like to discuss a few themes of my work that seem to have been most commented on in the United States and to make a few clarifications.
1. Intertexuality has always had a lot of success: international star or fluff, depending on the source. This notion, issued from my reading of Bakhtine, encourages one to read the literary text as an intersection of other texts. It has often been understood in a formalist or structuralist perspective, as an appeal to citations or a variant of the old criticism of sources. For me, it has always been about introducing history into structuralism: the texts that Mallarmé or Proust read and that flowed through _Coup de dés_ or _Remembrance of Things Past_ , for example, allow us to introduce into the laboratory of writing itself Mallarmé's interest in anarchy or Proust's interest in the Jewish mysticism of Zohar or the Dreyfus Affair. At the same time, by showing how much the inside of the text is indebted to its outside, interpretation reveals the inauthenticity of the writing subject: the writer is a subject in process, a carnival, a polyphony without possible reconciliation, a permanent revolt. The apparently post-structuralist theme of intertexuality introduced what I have dealt with in my most recent books regarding the intrinsic link between culture and revolt, which in my eyes is indissoluble.
2. The distinction that I established between the semiotic and the symbolic is not freighted with any political or feminist intention. It is an attempt to think of meaning not as structure but as process or procedure, by distinguishing between signs and their syntactic and logical concatenation, on the one hand, and things having to do with the transverbal, on the other. I say transverbal, for to say preverbal leads to confusion: the semiotic is not independent of language; it interferes with language and, under its domination, articulates other arrangements of meaning, which are not significations, but rhythmic, melodic articulations.
Under the influence of the Freudian distinctions between thing-presentation and word-presentation, I try to take into account the dualism that defines the human mind and, more particularly, the instinctual and ultimately biological constraints subjacent to meaning and signification. For "in the beginning was the Word," but it is a repressed of the beginning. I am convinced that the future of psychoanalysis is headed in this direction: the advancement of translinguistic unconscious logics toward biological and neurobiological constraints. At the Centre du Vivant at the University of Paris–VII Denis-Diderot, we will try to work on bringing together the concerns of biologists and psychoanalysts. This aspect of the implications of the semiotic is not taken into consideration in American research.
This gives me occasion to point out that collaboration with American psychoanalysts is, for the moment, not very fruitful. Aside from a few recitations of Lacanian discourse, more frequently encountered in literature departments than in clinical circles, psychoanalysts in the United States are scarcely interested in Freudian psychoanalytical research in France. Our two concerns—to open psychoanalysis to biology but also to extract it from its isolation and make it intervene in social policy, concerns that are likely to revitalize contemporary psychoanalysis—do not seem to touch our American colleagues. They tend to succumb to a sort of anti-Freudian revisionism, when not to a prickly retreat to Freudian tradition, understood moreover and paradoxically as a prescriptive psychology more than as a careful reading of Freudian texts. It is to be hoped, however, that, as the new head of the IPA, Otto Kernberg, who is very familiar with French psychoanalytical research, will be able to change this state of things.
Moreover, this transverbal semiotic refers to the archaic mother-child relationship and allows me to inscribe in certain modalities of language this feminine-maternal that Freud called a "dark continent" or even "a Minoan-Mycenean civilization" (from the name of the Greek civilization before that of classical Greece). This other logic of a feminine-maternal that defies normative representation and is situated at the antipodes of phallic representation, as well as at the antipodes of the phallic feminine, is my contribution to conceptualizing the feminine, certainly in relation to the political but through the intermediary of the sacred.
I am convinced that this new millennium, which seems so eager for religion, is in reality eager for the sacred. By this I mean the human desire to think (not in the sense of calculating but of questioning) that distinguishes human beings from other species and thus, _a contrario_ , brings them closer to them. This human distinction, which has been called the sense of the divine or the sacred, is contained for me—as a writer, psychoanalyst, and semiotician—in the emergence of language itself. The semiotic, with its maternal dependencies, seems to me to be the distant horizon to which thought gains access when it tries to think of itself at the borders of physis and being immersed in it. Seen in this way, as the emergence of meaning, the semiotic seems to me to stir up the metaphysical dichotomies (body/soul, physical/psychical). Which is to say, my preoccupation with the sacred is ultimately an antimetaphysical preoccupation and only by derivation a feminist one. If I am in fact passionately attached to the recognition of women in social, political, and intellectual life, it is only insofar as we can bring a different attitude to power and meaning. An attitude that takes the needs of the survival of our species seriously, as well as its desires for the sacred; women are situated at the crossroads of these two exigencies.
3. The abject and abjection are notions that I first developed based on my clinical experience and the symptoms that I later called new maladies of the soul, where the separation between subject and object is not yet clear but where these two quasi entities are exhausted in fascination and repulsion. Borderline personalities and certain aspects of depression may be described based on this psychical economy, which also refers to the archaic relationship of nonseparation with the maternal container: the mother being the primary ab-ject. Artists such as Picasso and De Kooning know something about this.
At the same time, with the notion of abject-abjection, I tried to tackle the complex universe of an author like Céline. Céline, a master of popular fiction, with a style at once slangy and singsong, and the bearer of extraordinary emotion, but also the Céline who, far from taking the cathartic path of abjection taken by religions (I support the idea that all religion is a purification of the abject), relentlessly tracked down imaginary abjections that he transformed into political realities. His anti-Semitism and his abject compromises with Nazi ideology were expressed in his sorry pamphlets, which I was one of the first to try to read fearlessly, as an analyst.
This venture into the (admittedly) dangerous terrain of abjection earned me much support: a number of American as well as international artists saw themselves in the experience of abjection, which in effect is similar to the psychotic states confronted by art. It also earned me the wrath of _The Nation_ , which decreed that my analysis of Céline sought to exonerate him (as if to try to understand necessarily meant to pardon). I came up against one of the most dogmatic misinterpretations of my research, which I took as a sort of excommunication for supporting the very attempt to think. This excommunication seemed to me a tragic version of a recent event, itself rather comic, where a prankster from New York University claimed to unmask "French impostors" by refuting formulas where there were only metaphors.
4. Foreignness, finally, is a theme, as you can see, that I hold dear to my heart. _Strangers to Ourselves_ , which won the Académie de Paris Hertz prize, gave me the chance to explore the history of foreigners, their current fate, and the way they have been thought of in the West. But in it I also developed a position that is still difficult to get across: namely that, faced with the national depression that France is experiencing (as are other countries) as a result of globalization and the influx of immigrants and against the fanatical reactions to this depression (such as the National Front, for example), it is important first to restore national confidence, just as one restores the narcissism or ego ideal of a depressed patient before undertaking the actual analysis (i.e., dissolution) of his resistances and defenses.
I am convinced that, at least in the coming century, the cosmopolitan society of which we have dreamt since the Stoics and particularly during the Age of Enlightenment will not be realized in the utopic form of the universalist melting pot, made uniform by the market, the media, or the Internet. It will instead take the form of a more or less conflictual coexistence of nations or groups of nations, brought to live with and against others. A mixture of respect for national identity and of encouragement in the general interest must henceforth replace the abuses of the current globalization.
NOTES
. Julia Kristeva, _New Maladies of the Soul_ , trans. Ross Guberman (New York: Columbia University Press, 1995).
. _Strangers to Ourselves_ , trans. Leon S. Roudiez (New York: Columbia University Press, 1991).
Bibliography
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1977. _Polylogue._ Paris: Editions du Seuil.
1980. _Desire in Language._ Translated by Thomas Gora, Alice Jardine, and Leon
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1980. _Pouvoirs de l'horreur._ Paris: Editions du Seuil, 1980. Translated by Leon
Roudiez as _Powers of Horror._ New York: Columbia University Press, 1982.
1981. _Le langage, cet inconnu._ Paris: Editions du Seuil. Translated by Anne Menke as _Language, the Unkown._ New York: Columbia University Press, 1989.
1983. _Histoires d'amour._ Paris: Editions Denoël. Translated by Leon Roudiez as _Tales of Love_. New York: Columbia University Press, 1987.
1985. _Au commencement etait l'amour._ Paris: Hachette. Translated by Author Goldhammer as _In the Beginning Was Love: Psychoanalysis and Faith._ New York: Columbia Press, 1988.
1986. _The Kristeva Reader._ Edited by Toril Moi. New York: Columbia Press, 1986.
1987.
_Soleil noir: Depression et mélancolie._ Paris: Gallimard. Translated by Leon Roudiez as _Black Sun._ New York: Columbia University Press, 1989.
1989. _Étrangers à nous-mêmes._ Paris: Fayard. Translated by Leon Roudiez as _Strangers to Ourselves_. New York: Columbia University Press, 1991.
1990. _Lettre ouverte à Harlem Désir._ Paris: Editions Rivages.
1990. _Les Samouraïs._ Paris: Fayard. Translated by Barbara Bray as _The Samurai._ New York: Columbia University Press, 1992.
1991. _Le vieil homme et les loups._ Paris: Fayard. Translated by Barbara Bray as _The Old Man and the Wolves_. New York: Columbia University Press, 1994.
1993. _Proust and the Sense of Time._ Translated by Stephen Bann. New York: Columbia University Press.
1993. _Les Nouvelles maladies de l'âme._ Paris: Fayard. Translated by Ross Guberman as _New Maladies of the Soul._ Columbia University Press, 1995.
1993. _Nations Without Nationalism._ Partly translated from _Lettre ouverte à Harlem Désir_ (1990) by Leon Roudiez. New York: Columbia University Press.
1994. _Le temps sensible: Proust et l'expérience littéraire._ Paris: Gallimard. Translated as by Ross Guberman _Time and Sense: Proust and the Experience of Literature._ New York: Columbia University Press, 1996.
——. 1996. _Possessions_. Paris: Fayard. Translated by Barbara Bray as _Possessions_. New York: Columbia University Press, 1998.
——. 1996. _Sens et non-sens de la révolte_. Vol. 1 of _Pouvoirs et limites de la psychanalyse_. Paris: Fayard. Translated by Jeanine Herman as _The Sense and Nonsense of Revolt_ , vol. 1 of _The Powers and Limits of Psychoanalysis_. New York: Columbia University Press, 2000.
——. 1997. _La révolte intime_. Vol. 2 of _Pouvoirs et limites de la psychanalyse_. Paris: Fayard, 2001. Translated by Jeanine Herman as "Intimate Revolt," part 1 of _Intimate Revolt_ , vol. 2 of _The Powers and Limits of Psychoanalysis_. New York: Columbia University Press, 2001.
——. 1998. _L'avenir d'une révolte_. Paris: Calmann-Lévy. Translated by Jeanine Herman as "The Future of Revolt," part 2 of _Intimate Revolt_ , vol. 2 of _The Powers and Limits of Psychoanalysis_. New York: Columbia University Press, 2001.
——. 1998. _Contre la dépression nationale: Entretien avec Philippe Petit_. Paris: Textuel.
——. 1998. _Le féminin et le sacré_ (with Catherine Clément). Paris: Stock. Translated by Jane Marie Todd as _The Feminine and the Sacred_. New York: Columbia University Press, 2001.
——. 1999. _Le génie féminin_ , tome I. _La Vie: Hannah Arendt—ou l'action comme naissance et comme étrangeté_. Paris: Fayard, 1999. Translated by Ross Guberman as _Life: Hannah Arendt—or Action as Birth and Estrangement_ , vol. 1 of _Female Genius_. New York: Columbia University Press, 2000.
——. 2000. _The Crisis of the European Subject_. Translated by Susan Fairfield.
New York: The Other Press.
——. 2000. _Le génie féminin_ , tome II. _La Folie: Melanie Klein—ou le matricide comme douleur et comme créativité_. Paris: Fayard. Translated by Ross Guberman as _Madness: Melanie Klein; or, Matricide as Pain and Creativity_ , vol. 2 of _Female Genius_. Columbia University Press, 2001.
Books on Kristeva in English
Cooper, Sarah. _Relating to Queer Theory: Rereading Sexual Self-Defition with Irigaray, Kristeva, Wittig, and Cixous_. New York: Peter Lang, 2000.
Crownfield, David, ed. _Body/Text in Julia Kristeva: Religion, Women, and Psychoanalysis_. Albany: SUNY Press, 1992.
Fletcher, John, and Andrew Benjamin, eds. _Abjection, Melancholia and Love._ New York: Routledge Press, 1990.
Grosz, Elizabeth. _Sexual Subversions._ Boston: Allen & Unwin, 1989.
Huntington, Patricia. _Ecstatic Subjects, Utopia, and Recognition: Kristeva, Heidegger, Irigaray_. Albany: SUNY Press, 1998.
Lechte, John. _Julia Kristeva._ New York: Routledge Press, 1990.
Lechte, John, and Mary Zournazi, eds. _After the Revolution: On Kristeva_. Syndey: Artspace, 1998.
McAfee, Noelle. _Habermas, Kristeva, and Citizenship_. Ithaca, N.Y.: Cornell University Press, 2000.
Oliver, Kelly. _Reading Kristeva: Unraveling the Doublebind._ Bloomington: Indiana University Press, 1993.
-—, ed. _Ethics, Politics and Difference in Kristeva's Writing._ New York: Rout- ledge Press, 1993.
-—. _Subjectivity Without Subjects_. Lanham, MD: Rowman and Littlefield, 1998.
Payne, Michael. _Reading Theory: An Introduction to Lacan, Derrida, and Kristeva_. New York: Blackwell, 1993.
Rienke, Martha. _Sacrificed Lives: Kristeva on Women and Violence_. Bloomington: Indiana University Press, 1997.
Smith, Anna. _Julia Kristeva: Readings of Exile and Estrangement_. New York: St. Martin's, 1996.
Smith, Anne-Marie. _Julia Kristeva: Speaking the Unspeakable_. Sterling, VA: Pluto Press, 1998.
Wardi, Eynel. _Once Below a Time: Dylan Thomas, Julia Kristeva, and Other Speaking Subjects_. Albany: SUNY Press, 2000.
Index
Abject, the; and new maladies of the soul; and revolution
Abjection; as ecstasy; eroticization of; feminine; of the maternal body; of the mother; and new maladies of the soul; as source of pleasure; time of
_About Chinese Women_ (Kristeva)
Abraham, Nicholas
Activity; linguistic; and metaphor; of thinking; transformational
Aesthetics; borderline; and creation; of European culture; and experience; and the French Communist Party; practice of; revolutionary; right-wing; and task; and timelessness; and works
_The Age of Louis XIV_ (Voltaire)
Aggressivity; in analytic discourse; in _chora_ ; erotic; in melancholia; toward object
Alterity; in Bakhtin; body as; mother as place of; in signification; in subject
Althusser, Louis
Ambiguity; and abjection; of drives; of language; metaphorical; in transference
Ambivalence
Anality; and character; and drives; and eroticism; oral stage of; and pleasure; and possession
_Analysis Terminable and Interminable_ (Freud)
Anti-Semitism
Aquinas, Thomas
Aragon, Louis; and revolt; on subjectivity
Archaic, the
Arendt, Hannah; on psychoanalysis
Aristotle; on melancholia; on metaphor
Art; and abjection; Beauty in; and conflict; and crisis; and death; as expenditure; and experience; as fetish; and genius; Heraclitean; and idealization; language of; and melancholia; modern; as religion; and revolt; threat to
Artaud, Antonin; body of; and European culture; and negativity; on sex and language; on subjectivity
Atheism
_Aufhebung_
St. Augustine
Authority; maternal; paternal; semiotic
Autism
Autoeroticism; of mother-child dyad
Automation of humanity
Autonomy
Bacon, Francis
Bakhtin, Mikhail
Barande, Ilse
Barthes, Roland; and revolt; on subjectivity
Baruch, Elaine Hoffman
Bataille, Georges
Baudelaire, Charles
Bauhaus
Beauty. _See also_ Aesthetics
Beckett, Samuel
_Bedeuting_
Being; feminine; and nothingness; and Other; as repulsion; and revolt. _See also_ Speaking being
_Being and Nothingness_ (Sartre)
Being-as-other
Bellerophon
Bellini, Giovanni
Benveniste, Emile
Bergson, Henri
Bernard of Clairvaux
_Beyond the Pleasure Principle_ (Freud)
Bèze, Théodore de
Bible, the
Binswanger, Ludwig
Biography
Biology
Bion, W. R.
Bisexuality. _See also_ Homosexuality
Black, Max
_Black Sun_
Body; absent; autoerotic; brother's; clean and proper; desiring; drunken; dying; erotic; female; as fetish; fragmented; human; infant's; instinctual; limits of; living; masculine; maternal; and Merleau-Ponty; mother's; music of; paralysis of the; sale of; semiotic; semiotic processes and; separation and; sexed; signification inscribed in; signifying; sleeping; social; space of the; speaking; and technology; virginal
Bonaparte, Marie
Bossuet, Jacques-Bénigne
Boundary; of assimilability; and filth; of semiotic authority and symbolic law; set up by rejection; states; of subject and society; thetic as; between true and false; where self emerges
Bourgeois, Louise
Brès, Yvon
Brown, Alfred Reginald Radcliffe
Buffon, Georges
Calvin, John
Camus, Albert
Carnivalism; circus
Cartesianism
Castration; anxiety; fantasy; fear of; knowledge of; of mother; threats
Catharsis; in literature; of religious rituals
Catherine of Alexandria
Catherine of Siena
Cathexis; oral
Céline, L. F.; and abject-abjection
Cherubino
Childbirth; male phantasmatics of
China
Chodorow, Nancy
Chomsky, Noam
_Chora_ ; and psychosis
Christianity; ascetic; and maternity; and melancholia; Nietzsche on; and retrospective return; virgin cult in
Chrysostom, John
_Civilization and Its Discontents_ (Freud)
Cogito
Colette
Communism; French
Consciousness. _See also_ Unconscious
Consumerism
Cooper
Corneille, Pierre
Corpse; of God; living; of the mother's body
Cosmopolitanism; Stoic
_Coup de dés_ (Mallarmé)
Coward, Rosalind
Crisis; of ego; in identity; of meaning; and melancholia; of Other; in paternity; permanency of; in psyche; religious and moral; in signification; of social institutions; of social structures; of subject; of symbolic; as work in progress
Criticism, art
Culture: as conscience; consumer; of distraction; European; of the image; of performance; of revolt; threat to; of words
_daimōn_ ( _genius_ )
Dante
_Dasein. See_ Being
Da Vinci, Leonardo
Death; and art; and Beauty; deification of; fear of; image of; and love; and melancholia; time of. _See also under_ Drive
De Beauvoir, Simone
Deconstruction
Defilement
De Kooning, Willem
Deleuze, Gilles
Delirium
Della Francesca, Piero
De Merteuil
Democracy
Derrida, Jacques; on language and meaning
Descartes, René. _See also_ Cartesianism
Desire; of analyst; archaic homosexual; to be another; and difference; and drives; heterosexual; hysterical; infantile; to kill; Lacanian; for the masculine corpse; of the mother; for motherhood; object of; Oedipal; of the other; for power; sexual; unveiled by analysis
_Desire in Language_ (Kristeva)
Dialectic: of biological and social spheres; fourth term of Hegelian; in Freudian negativity; of master and slave; materialist foundation for; of negativity; between psychic and somatic realms; of semiotic and symbolic; within the subject; of the Trinity
Dialogism
Diderot, Denis
_Différance_
Difference; and bisexuality; in body; establishment of; and the foreigner; individual; in meaning; meaning as function of; positing of; sexual; and solitude
Dinnerstein, Dorothy
Dogma; of the Assumption; of the Church; of the Immaculate Conception; poetic language and; theological
Dogmatism; formalist; specialist
Don Juan
Dostoevsky, Fyodor
Douglas, Mary
Dreams; of depressed persons
Dreamwork
Drive: assault of; autoerotic; death; erotic; and negativity; and psychoanalysis; and revolt
Drugs
Dumézil, G.
Dürer, Albrecht
Durkheim, Emile
Echolalia
Economy: and new world order; and normalization
Ego; death of the; of depressed persons; disintegration of; establishment of; Ideal; narcissistic; neurotic; Oedipal; split; transcendental; unity of
Elaboration: _vs_. catharsis
_Enceinte_
Eroticism; anal; and Colette; and madness
Erotic man
Erotic rhythms
Erotic Thing
Errancy
Ethics; Christian; and the foreigner; Kantian; of love; Marxist; of motherhood; of the person; of psychoanalysis; Utopian
European Economic Community
Evil: banality of; radical
Evolution: etymology of
Exclusion; logic of
Excrement
Falsifiability
Fantasies
Fascism. _See also_ Totalitarianism
Father, archaic; castrating and sodomizing; _chora_ anterior to; erosion of loving; and foreigner; ideal; imaginary; law of; loving; murder of; name of; Oedipal; of pre-history; qualities of; and sacrifice; as seducer; seduction of
Faust
_Female Genius: Life, Madness, Words_ (Kristeva)
Feminine: aspect, the; being; and defilement; depression; ease; ethics; fantasy; interior; jealousies; masochism; perversion; psyche; renunciation of; representation; sensibility; sexual experience; space underlying language; unnamable
Feminism; anti-; French; modern; and Protestantism; as religion; and the sacred; and semiotic-symbolic distinction; since May '; in the U.S.
Feminist movement; French; and sensory intimacy; stages of
Feminists; American; criticisms of Freud; existential
Ferenczi, Sándor
Fetish; aesthetic; body as; and poetic language
Firestone, Shulamith
Flaubert, Gustave
Flesh; inscribed in words; and signs; wounded in melancholia
Foreigner; and France; and integration; in self
Foreignness
Foucault, Michel
Foundation: for dialectic; of language; lost
Frazer, Sir James George
Freedom
Free will
Frege, Gottlieb; and truth
French Revolution
Freud, Anna
Freud, Sigmund; and desire; and drives; and European culture; and the father; and identification; and identity; and love; on maternity; and melancholia; and modernity; and narcissism; and negativity; on rebellion; and retrospective return; and revolt; and semiotic-symbolic distinction; on sex and language; theory of unconscious; and time; and the _unheimlich_
Fronde, the
Fundamentalism
Future, the
_The Future of an Illusion_ (Freud)
Galileo
Genet, Jean
Genius; and the Divine; of women
Gennep, Arnold van
Genotext
Globalization
Glossolalia; in Artaud
Goethe, Johann Wolfgang von
Gondi, Jean de (Cardinal de Retz)
_Gorgias_ (Plato)
Graciàn, Baltasar
Green, André
Guattari, Félix
Guberman, Ross
Guilt: in new world order; and revolt; and ritual sacrifice
Haacke, Hans
Hegel, G.W.F.; and the aesthetic; and desire; and dialectic; and dialectical materialism; inversion of dialectic; and negativity; and repulsion; and Sartre; and self-consciousness; on sex and language
Heidegger, Martin; and Arendt; and Binswanger; and negativity; on religion; on revolution; and Sartre; on subjectivity; on temporalizing
_(H)eimlich(e)_
Heraclitus
Herethics
Herman, Jeanine
Heroes
Hippocrates
History; and artistic installations; end of; and female genius; and formalism in Bakhtin; and genius; and language; literary; modern; monumental; of psychoanalysis; and revolt; and "revolution,"; and signification; social; and structuralism; of the subject; time of; Western and psychoanalysis
Hoffmann, E.T.A.
Holbein, Hans
Hölderlin, Friedrich
Holocaust
Holophrastic utterance
Homosexuality; female; feminine; and Freud; male; paranoid; repressed
Husserl, Edmund
Hysteria; depressive
Identity: and the death drive; dissolving; of the ego; imaginary; lack of in the _chora_ ; loss of; moral; of the mother; multiplied; narcissistic; plural; positing of; and pregnancy; revolt against; sexual; signified and signifying; social; sociopolitical; split; subjective
Ideology; end of; feminist; Hitlerian; and semiotics; signification as; socialist
Imaginary, the; of analyst; construction; deployment; identity; object of desire; paternity; power of the; structures; symbolic
Imagination; and revolution
Incest taboo
Incorporation
Individual: patrimonial, the; and revolution
Installations, artistic
Intellectuals
Interpretation; analytic; of incest dread; provisional
_The Interpretation of Dreams_ (Freud)
Intertextuality
Intimacy: and psychoanalysis; and revolt; sensory; and time
Irigaray, Luce
_J'accuse_ (Zola)
Jakobson, Roman
Jeanson, Francis
Job
Jones, Ernst
_Jouissance_ ; absence of; feminine; maternal; of the mother; other; patient's/analyst's; of the perverse; phallic; and revolt; and _signifiance_ ; translibidinal; unto death; vaginal
Joyce, James; language of; on women
Judgment
Jung, C. G.
Kafka, Franz
Kant, Immanuel
Kernberg, Otto
Kierkegaard, SÌren
Klein, Melanie; genius of; on rejecting drive
La Bruyère, Jean de
Lacan, Jacques; and mirror-stage/phase; on paternal function; and paternal metaphor
Laing, R. D.
Language: acquisition of; dead; as double articulation; female; Klein on; as male; meaning of; and memory; necrophilic theories of; and negativity; as open/undecidable; preconditions for; and retrospective return; revolution in; and the sacred; and semiotic-symbolic distinction; and sexuality. _See also_ Poetic language
LaPlace, Pierre de
La Rochefoucauld, François de
Lautréamont, le Comte de (Isidore-Lucien Ducasse)
Law; desire for; and ethics; of the father; of God; and invisibility of power; in language; male; matriarchal; and normalization; patriarchal; questioning of; and revolt; as semiotic ordering; signifier as; symbolic; and the uncanny
_L'écriture limite_
Lenin, V. I.
Lévi-Strauss, Claude
Libidinal economy
Libido; homosexual; maternal
_Life: Hannah Arendt--or Action as Birth and Estrangement_ (Kristeva)
Literature; avantgarde; and identity; and intimacy; as religion; and revolt; and revolution; romantic; and subjectivity
Love; in analysis; is spoken; maternal; necessary for life; paternal
Madness. _See also_ Psychosis
_Madness: Melanie Klein--or Matricide as Pain and Creativity_ (Kristeva)
Mallarmé, Stéphane; body of; and intertexuality; language of
Marginalization; of morality; of psychoanalysis
Marx, Karl
Masculine, the. _See also_ Father; Men
Massification
Materialism
Materiality; of body; and compulsion; of drives; and language; and rejection; and support of language
Maternal: anguish of, the; authority of; aversion to; cult of; as entity; as figure; frustration of; function of; and _Jouissance_ ; and libido; and love; and negativity; neglect by; and new maladies of the soul; position of; psychology of; as receptacle/container; representation of; and revolution; and semiotic-symbolic distinction; as source of words; space of; substitute for; as _Thing_ ; Virginal; wrapping of. _See also_ Body: maternal; Mother
Maternity; fatherless
Matriarchy
Mauss, Marcel
May 1968 events
Meaning; abject; and Barthes; and Freud; and identity; of language; loss of; and metaphor; and mimesis; plural/overdetermined; process of; and revolt; and the sacred; and semiotic/poetic language; and semiotic-symbolic distinction; and sexuality; unconscious; unitary
Media; and revolt
Melancholia; and cannibalism; people with; philosopher with; stupor of; woman with
Memory; body's; instinctual; loss of
_Memory/Loss_ (installation; Wilson)
Men: and female genius; and women. _See also_ the Masculine
Merleau-Ponty, Maurice
_The Mermaid and the Minotaur_ (Dinnerstein)
Metaphor: archaeological; and collective analogy; and condensation; of metaphysical interpretation; mystic writing pad; paternal; poetic; political
Metonymy; of desire; and displacement; in Lacan; of pleasure
Millett, Kate
Mimesis; of passions; poetic; and sacrifice
Mimeticism
Mirror stage; preconditions for
Modernity; in art; and psychoanalysis
Moi, Toril
Montaigne, Michel de
Montesquieu, Baron de (Charles-Louis de Secondat)
Morpheme
_Moses and Monotheism_ (Freud)
Mother: and abjection; archaic; body of the; castrated; depressive; desire of the; desiring and desired; forbidden; and foreigner; and genius; good-enough; image of the; incomplete; loss of the; lost; loving; oceanic; phallic; phobia; and semiotic-symbolic distinction; and speaking subject; as subject of gestation; Virgin; watery. _See also_ the Maternal
Mourning; of analysis; for the lost object; violence of
Movement
Mozart, Wolfgang Amadeus
Murder; communal
Music; and foundations; as language of love
Myth; of dogmatism of _Tel Quel_ ; of Narcissus; virginal
Name of the Father
Narcissism; economy of, and emptiness; and the foreigner; and love; and melancholia; negative; primary
Narcissus; myth of
_The Nation_
Nationalism
_Nausea_ (Sartre)
Necrophilia
Negation; as denial; as fourth term of dialectic; Freudian; and Hegelian repulsion; of the negation
_Negation_ ( _Die Verneinung_ ; Freud)
Negativity: and dialectic; and Hegel; and narcissism; in revolt
Nerval, Gérard de
Neurosis; obsessional
_New French Feminisms_
_New Maladies of the Soul_ (Kristeva)
_Nicomedes_ (Corneille)
Nietzsche, Friedrich; on Christianity; and meaning; on monumental history; on revolution
Nihilism
Normalization; and memory loss; and power; and revolt
Nothingness
Novel: detective; and sensory experience
Oedipal triangle
Oedipus complex; and jealousy; and revolt
_The Old Man and the Wolves_ (Kristeva)
(O)ther: within; absolute; and being; child as; of death; death of the; eroticization of the; fear of the; as foreigner; Freud on; ideal; identification with the; of language; loss of the; meaning as; in melancholia; rejection of the; and revolt; speaking
Ovid
Paranoia; female; of feminist movements
Parthanogenesis
Pascal
Paternal: apex of; authority of; figure of; position of; role of; threats of
Paternal function
Patriarchy
Personality
Perversion; and abjection; blank; epistemological; feminine; political; of psychoanalysts
_Phaedrus_ (Plato)
Phallic; dispossession; function; ideal; stage
Phallus; of mother; as signifier
Phenomenology
Phoneme
Picasso, Pablo
Pinel, Philippe
Plato; and the _chora_ ; and metaphor; and "return,"
Pleasure
Pleasure principle
Plotinus
Poetic language; and psychosis
_Poetics_ (Aristotle)
Political correctness
Politics: and abjection; and Arendt; and intimacy; and new world order; and retrospective questioning; and revolution; and the sacred; Sartre on; and semiotic-symbolic distinction; women in
Pollock, Jackson
_Polylogue_
_Possessions_ (Kristeva)
Power: agency of; invisibility of; and normalization; pleasure of; and revolt; totem symbol of; vacuum of; and women
_The Powers and Limits of Psychoanalysis_ (Kristeva)
_Powers of Horror_ (Kristeva)
Practice; _signifiance_ as; signifying; of subject-in-process; subject of a; text as
Pregnancy
Pre-Oedipal
Presymbolic
Preverbal
_Project for a Scientific Psychology_ (Freud)
Protestantism
Proust, Marcel; and foundations; and intertexuality; on subjectivity; on time
Psyche; and artists; Freudian; painful; paralysis of; polyphonic
Psychoanalysis; American; and the archaic; and Binswanger; history of; and rebirth; resistances to; and revolt; and revolution; and subjectivity
Psychosis, feminine; pregnancy as; and retrospective return
Punishment
_Purity and Danger_ (Douglas)
Rabelais, François
_The Rebel_ (Camus)
Regression; infantile, and motherhood; primal
Rejection; logic of; of mother by woman; and negativity; normalization of; subversiveness of; of the symbolic
Religion: and abjection; and Arendt; art as; and the future; Heidegger on; and identity; new; Protestant; and ritual sacrifice; and the sacred; and social order. _See also_ Christianity
_Remembrance of Things Past_ (Proust)
Renaissance, the
Repression; of crisis; of homosexuality; and identity; of imaginary father; and meaning; opposed by rejection; primal; secondary; of semiotic; and symbolic function
Reproduction
_The Reproduction of Mothering_ (Chodorow)
Repulsion
Responsibility
Retrospective return
Revolt: and artistic installations; culture of; dignity of; etymology of; and feast; and Freud; future of; against identity; intimate; literary; man in; of modernity; negativity in; oedipal; political; three figures of
Revolution; bourgeois; etymology of; and French Communist Party; intimate; and motherhood; poetic language and; political _vs_. textual; and revolt; sexual; _signifiance_ as; symbolic
_Revolution in Poetic Language_ (Kristeva)
Rey, Alain
Reynaud
Rhythm; in _chora_ ; of drives; of emotion; in literature; in poetry; sentential
Richards, I. A.
Ricoeur, Paul
Rousseau, Jean-Jacques
Sacred, the; and religion
Sacrifice
Sade, Marquis de; sadism; sadomasochism
Saint-Simon, Comte de (Claude-Henri de Rouvroy)
Sartre, Jean-Paul; and revolt
Saussure, Ferdinand de
Schelling, Friedrich
Schizophrenia; of children; schizoid splitting
Schreber, Senatspräsident
Science: biological; and emancipation of women; and the future; and motherhood
_The Second Sex_ (de Beauvoir)
Segal, Hanna
Self, the; and consciousness
Semanalysis
Semiology
Semiotics; already social; authority; as feminine; and ideology; and language; moment
Semiotic-symbolic distinction
_The Sense and Non-sense of Revolt_ (Kristeva)
Separation; and abjection; between ego and object; from mother; necessary for signification
_se quaerere_ (going in quest of oneself)
Sexuality; bi-; and difference 61; feminine; and identity; and language; and meaning; revolution in. _See also_ Eroticism; Homosexuality
Signification; collapse of; of language; perverse; preconditions for; of speech; symbolic
Silence; depressive; of the foreigner; interpretive; of the maternal body; melancholic; of the polyglot; psychic
Smith, W. Robertson
Social contract
Socrates
Sollers, Phillipe
Soul; in Aristotle; chained-up; depth of the; in Plato; prison of the; Western. _See also_ Psyche
Space; and revolt
Speak-being
Speaking being; and revolt
Spectacle, the; and jouissance; and lost foundations; and revolt; and revolution
Spielrein, Sabine
Spinoza, Baruch "Stabat Mater" (Kristeva)
Stalinism. _See also_ Totalitarianism
Stockhausen, Karlheinz
_The Stranger_ (Camus)
_Strangers to Ourselves_ (Kristeva)
Structuralism
Subject-in-process/on trial
Subjectivity; advent of; amputated; border of; Christian; female; fragmented; free flowing; Freud on; and genius; and identity; and literature; and the political; relation to language; and retrospective return; and revolt; speaking
Suffragist movement
Superego
Surrealism
Symbolic, the; construct; destiny; dissolving of; exchange; function; necessary for semiotic; and negativity; order; play; power; preconditions for
_Tales of Love_ (Kristeva)
Technology; and return
_Tel Quel_
Text; as practice
"Theme of the Three Caskets,"
Thetic; necessary for language; and semiotic, poetic language
_Thing_ ; depressive; maternal
_Three Essays on the Theory of Sexuality_ (Freud)
Time; and intimacy; and men; and psychoanalysis; and revolt; and "revolution,"; and space; and subjectivity; and unconscious
Timelessness ( _zeitlos_ )
Torok, Maria
Totalitarianism; Arendt on; and normalization; and retrospective questioning
_Totem and Taboo_ (Freud)
Transference; counter-; generalized; is dynamic; as love relation; and meaning; and metaphor
Transgression
Unconscious; and identity; relation to semiotic; and retrospective return; and revolt; and time; and timelessness
"Unes Femmes,"
_(U)nheimlich(e)_
Unnamable; _chora_
Unsayable
Valéry, Paul
Venice; Biennale (1993) in
Veuillot, Louis-Francois
Violence; of analytic interpretation; in Céline; of drives; of love; of naming; phallic; of rejection; between the sexes; of the symbolic contract; terrorist
Virgin, the; body of; cult of; as feminine ideal; myth of
Voltaire
Warner, Marina
_What Is Metaphysics?_ (Heidegger)
Wilson, Robert
Winnicott, David W.
Woman; dead; defined; and mother; as object of exchange; as other; the other of; and poetic language; and psychic space; as song beneath the text 39; universal
Women; in China; community of; and defilement; denigration of; emancipation of; European; genius of; and power; protective double of; and sensory intimacy; and species; as subject of ethics; and terrorism; universe of. _See also_ the Feminine; the Maternal
_Women Analyze Women_
"Women's Time" (Kristeva)
_The Words_ (Sartre)
World order, new
World War II
Wound; melancholic; narcissistic
Writing; and analytic discourse; is amorous; literary; and melancholia; and speech; women's
Zola, Émile
European Perspectives
_A Series in Social Thought and Cultural Criticism_
Lawrence D. Kritzman, Editor
Julia Kristeva | _Strangers to Ourselves_
---|---
Theodor W. Adorno | _Notes to Literature_ , vols. 1 and 2
Richard Wolin, editor | _The Heidegger Controversy_
Antonio Gramsci | _Prison Notebooks_ , vols. 1 and 2
Jacques LeGoff | _History and Memory_
Alain Finkielkraut | _Remembering in Vain: The Klaus Barbie Trial and Crimes Against Humanity_
Julia Kristeva | _Nations Without Nationalism_
Pierre Bourdieu | _The Field of Cultural Production_
Pierre Vidal-Naquet | _Assassins of Memory: Essays on the Denial of the Holocaust_
Hugo Ball | _Critique of the German Intelligentsia_
Gilles Deleuze and Félix Guattari | _What Is Philosophy?_
Karl Heinz Bohrer | _Suddenness: On the Moment of Aesthetic Appearance_
Julia Kristeva | _Time and Sense_
Alain Finkielkraut | _The Defeat of the Mind_
Julia Kristeva | _New Maladies of the Soul_
Elisabeth Badinter | _XY: On Masculine Identity_
Karl Löwith | _Martin Heidegger and European Nihilism_
Gilles Deleuze | _Negotiations, 1972–1990_
Pierre Vidal-Naquet | _The Jews: History, Memory, and the Present_
Norbert Elias | _The Germans_
Louis Althusser | _Writings on Psychoanalysis: Freud and Lacan_
Elisabeth Roudinesco | _Jacques Lacan: His Life and Work_
Ross Guberman | _Julia Kristeva Interviews_
Kelly Oliver | The Portable Kristeva
Pierra Nora | _Realms of Memory: The Construction of the French Past_
|
vol. 1: _Conflicts and Divisions_
|
vol. 2: _Traditions_
|
vol. 3: _Symbols_
Claudine Fabre-Vassas | _The Singular Beast: Jews, Christians, and the Pig_
Paul Ricoeur | _Critique and Conviction: Conversations with François Azouvi and Marc de Launay_
Theodor W. Adorno | _Critical Models: Interventions and Catchwords_
Alain Corbin | _Village Bells: Sound and Meaning in the Nineteenth-Century French Countryside_
Zygmunt Bauman | _Globalization: The Human Consequences_
Emmanuel Levinas | _Entre Nous_
Jean-Louis Flandrin and Massimo Montanari | _Food: A Culinary History_
Alain Finkielkraut | _In the Name of Humanity: Reflections on the Twentieth Century_
Julia Kristeva | _The Sense and Non-Sense of Revolt: The Powers and Limits of Psychoanalysis_
Régis Debray | _Transmitting Culture_
Sylviane Agacinski | _The Politics of the Sexes_
Alain Corbin | _The Life of an Unknown: The Rediscovered World of a Clog Maker in Nineteenth-Century France_
Michel Pastoureau | _The Devil's Cloth: A History of Stripes and Striped Fabric_
Julia Kristeva | _Hannah Arendt_
Carlo Ginzburg | _Wooden Eyes: Nine Reflections on Distance_
Elisabeth Roudinesco | _Why Psychoanalysis?_
Alain Cabantous | _Blasphemy: Impious Speech in the West from the Seventeenth to the Nineteenth Century_
Julia Kristeva | _Melanie Klein_
Julia Kristeva | _Intimate Revolt and The Future of Revolt: The Powers and Limits of Psychoanalysis_ , vol. 2
|
{
"redpajama_set_name": "RedPajamaBook"
}
| 6,599
|
package kubernetes
import (
"context"
"crypto/md5"
"encoding/base64"
"encoding/json"
"fmt"
"reflect"
"testing"
"github.com/google/go-cmp/cmp"
"github.com/google/go-containerregistry/pkg/authn"
"github.com/google/go-containerregistry/pkg/name"
corev1 "k8s.io/api/core/v1"
metav1 "k8s.io/apimachinery/pkg/apis/meta/v1"
fakeclient "k8s.io/client-go/kubernetes/fake"
)
var dockerSecretTypes = []secretType{
dockerConfigJSONSecretType,
dockerCfgSecretType,
}
type secretType struct {
name corev1.SecretType
key string
marshal func(t *testing.T, registry string, auth authn.AuthConfig) []byte
}
func (s *secretType) Create(t *testing.T, namespace, name string, registry string, auth authn.AuthConfig) *corev1.Secret {
return &corev1.Secret{
ObjectMeta: metav1.ObjectMeta{
Name: name,
Namespace: namespace,
},
Type: s.name,
Data: map[string][]byte{
s.key: s.marshal(t, registry, auth),
},
}
}
var dockerConfigJSONSecretType = secretType{
name: corev1.SecretTypeDockerConfigJson,
key: corev1.DockerConfigJsonKey,
marshal: func(t *testing.T, target string, auth authn.AuthConfig) []byte {
return toJSON(t, dockerConfigJSON{
Auths: map[string]authn.AuthConfig{target: auth},
})
},
}
var dockerCfgSecretType = secretType{
name: corev1.SecretTypeDockercfg,
key: corev1.DockerConfigKey,
marshal: func(t *testing.T, target string, auth authn.AuthConfig) []byte {
return toJSON(t, map[string]authn.AuthConfig{target: auth})
},
}
func TestAnonymousFallback(t *testing.T) {
client := fakeclient.NewSimpleClientset(&corev1.ServiceAccount{
ObjectMeta: metav1.ObjectMeta{
Name: "default",
Namespace: "default",
},
})
kc, err := New(context.Background(), client, Options{})
if err != nil {
t.Errorf("New() = %v", err)
}
testResolve(t, kc, registry(t, "fake.registry.io"), authn.Anonymous)
}
func TestAnonymousFallbackNoServiceAccount(t *testing.T) {
kc, err := New(context.Background(), nil, Options{
ServiceAccountName: NoServiceAccount,
})
if err != nil {
t.Errorf("New() = %v", err)
}
testResolve(t, kc, registry(t, "fake.registry.io"), authn.Anonymous)
}
func TestSecretNotFound(t *testing.T) {
client := fakeclient.NewSimpleClientset()
kc, err := New(context.Background(), client, Options{
ServiceAccountName: NoServiceAccount,
ImagePullSecrets: []string{"not-found"},
})
if err != nil {
t.Errorf("New() = %v", err)
}
testResolve(t, kc, registry(t, "fake.registry.io"), authn.Anonymous)
}
func TestServiceAccountNotFound(t *testing.T) {
client := fakeclient.NewSimpleClientset(&corev1.ServiceAccount{
ObjectMeta: metav1.ObjectMeta{
Name: "default",
Namespace: "default",
},
})
kc, err := New(context.Background(), client, Options{
ServiceAccountName: "not-found",
})
if err != nil {
t.Errorf("New() = %v", err)
}
testResolve(t, kc, registry(t, "fake.registry.io"), authn.Anonymous)
}
func TestAttachedServiceAccount(t *testing.T) {
username, password := "foo", "bar"
client := fakeclient.NewSimpleClientset(&corev1.ServiceAccount{
ObjectMeta: metav1.ObjectMeta{
Name: "svcacct",
Namespace: "ns",
},
ImagePullSecrets: []corev1.LocalObjectReference{{
Name: "secret",
}},
},
dockerCfgSecretType.Create(t, "ns", "secret", "fake.registry.io", authn.AuthConfig{
Username: username,
Password: password,
}),
)
kc, err := New(context.Background(), client, Options{
Namespace: "ns",
ServiceAccountName: "svcacct",
})
if err != nil {
t.Fatalf("New() = %v", err)
}
testResolve(t, kc, registry(t, "fake.registry.io"),
&authn.Basic{Username: username, Password: password})
}
// Prioritze picking the first secret
func TestSecretPriority(t *testing.T) {
secrets := []corev1.Secret{
*dockerCfgSecretType.Create(t, "ns", "secret", "fake.registry.io", authn.AuthConfig{
Username: "user", Password: "pass",
}),
*dockerCfgSecretType.Create(t, "ns", "secret-2", "fake.registry.io", authn.AuthConfig{
Username: "anotherUser", Password: "anotherPass",
}),
}
kc, err := NewFromPullSecrets(context.Background(), secrets)
if err != nil {
t.Fatalf("NewFromPullSecrets() = %v", err)
}
expectedAuth := &authn.Basic{Username: "user", Password: "pass"}
testResolve(t, kc, registry(t, "fake.registry.io"), expectedAuth)
}
func TestResolveTargets(t *testing.T) {
// Iterate over target types
targetTypes := []authn.Resource{
registry(t, "fake.registry.io"),
repo(t, "fake.registry.io/repo"),
}
for _, secretType := range dockerSecretTypes {
for _, target := range targetTypes {
// Drop the .
testName := secretType.key[1:] + "_" + target.String()
t.Run(testName, func(t *testing.T) {
auth := authn.AuthConfig{
Password: fmt.Sprintf("%x", md5.Sum([]byte(t.Name()))),
Username: "user" + fmt.Sprintf("%x", md5.Sum([]byte(t.Name()))),
}
kc, err := NewFromPullSecrets(context.Background(), []corev1.Secret{
*secretType.Create(t, "ns", "secret", target.String(), auth),
})
if err != nil {
t.Fatalf("New() = %v", err)
}
authenticator := &authn.Basic{Username: auth.Username, Password: auth.Password}
testResolve(t, kc, target, authenticator)
})
}
}
}
func TestAuthWithScheme(t *testing.T) {
auth := authn.AuthConfig{
Password: "password",
Username: "username",
}
kc, err := NewFromPullSecrets(context.Background(), []corev1.Secret{
*dockerConfigJSONSecretType.Create(t, "ns", "secret", "https://fake.registry.io", auth),
})
if err != nil {
t.Fatalf("New() = %v", err)
}
authenticator := &authn.Basic{Username: auth.Username, Password: auth.Password}
testResolve(t, kc, registry(t, "fake.registry.io"), authenticator)
testResolve(t, kc, repo(t, "fake.registry.io/repo"), authenticator)
}
func TestAuthWithPorts(t *testing.T) {
auth := authn.AuthConfig{
Password: "password",
Username: "username",
}
kc, err := NewFromPullSecrets(context.Background(), []corev1.Secret{
*dockerConfigJSONSecretType.Create(t, "ns", "secret", "fake.registry.io:5000", auth),
})
if err != nil {
t.Fatalf("New() = %v", err)
}
authenticator := &authn.Basic{Username: auth.Username, Password: auth.Password}
testResolve(t, kc, registry(t, "fake.registry.io:5000"), authenticator)
testResolve(t, kc, repo(t, "fake.registry.io:5000/repo"), authenticator)
// Non-matching ports should return Anonymous
testResolve(t, kc, registry(t, "fake.registry.io:1000"), authn.Anonymous)
testResolve(t, kc, repo(t, "fake.registry.io:1000/repo"), authn.Anonymous)
}
func TestAuthPathMatching(t *testing.T) {
rootAuth := authn.AuthConfig{Username: "root", Password: "root"}
nestedAuth := authn.AuthConfig{Username: "nested", Password: "nested"}
leafAuth := authn.AuthConfig{Username: "leaf", Password: "leaf"}
partialAuth := authn.AuthConfig{Username: "partial", Password: "partial"}
kc, err := NewFromPullSecrets(context.Background(), []corev1.Secret{
*dockerConfigJSONSecretType.Create(t, "ns", "secret-1", "fake.registry.io", rootAuth),
*dockerConfigJSONSecretType.Create(t, "ns", "secret-2", "fake.registry.io/nested", nestedAuth),
*dockerConfigJSONSecretType.Create(t, "ns", "secret-3", "fake.registry.io/nested/repo", leafAuth),
*dockerConfigJSONSecretType.Create(t, "ns", "secret-4", "fake.registry.io/par", partialAuth),
})
if err != nil {
t.Fatalf("New() = %v", err)
}
testResolve(t, kc, registry(t, "fake.registry.io"), authn.FromConfig(rootAuth))
testResolve(t, kc, repo(t, "fake.registry.io/nested"), authn.FromConfig(nestedAuth))
testResolve(t, kc, repo(t, "fake.registry.io/nested/repo"), authn.FromConfig(leafAuth))
testResolve(t, kc, repo(t, "fake.registry.io/nested/repo/dirt"), authn.FromConfig(leafAuth))
testResolve(t, kc, repo(t, "fake.registry.io/partial"), authn.FromConfig(partialAuth))
}
func TestAuthHostNameVariations(t *testing.T) {
rootAuth := authn.AuthConfig{Username: "root", Password: "root"}
subdomainAuth := authn.AuthConfig{Username: "sub", Password: "sub"}
kc, err := NewFromPullSecrets(context.Background(), []corev1.Secret{
*dockerConfigJSONSecretType.Create(t, "ns", "secret-1", "fake.registry.io", rootAuth),
*dockerConfigJSONSecretType.Create(t, "ns", "secret-2", "1.fake.registry.io", subdomainAuth),
})
if err != nil {
t.Fatalf("New() = %v", err)
}
testResolve(t, kc, registry(t, "fake.registry.io"), authn.FromConfig(rootAuth))
testResolve(t, kc, registry(t, "1.fake.registry.io"), authn.FromConfig(subdomainAuth))
// Unrecognized subdomain uses Anonymous
testResolve(t, kc, registry(t, "2.fake.registry.io"), authn.Anonymous)
}
func TestAuthSpecialPathsIgnored(t *testing.T) {
auth := authn.AuthConfig{Username: "root", Password: "root"}
auth2 := authn.AuthConfig{Username: "root2", Password: "root2"}
kc, err := NewFromPullSecrets(context.Background(), []corev1.Secret{
// Note the paths need a trailing '/'
*dockerConfigJSONSecretType.Create(t, "ns", "secret-1", "https://fake.registry.io/v1/", auth),
*dockerConfigJSONSecretType.Create(t, "ns", "secret-2", "https://fake2.registry.io/v2/", auth2),
})
if err != nil {
t.Fatalf("New() = %v", err)
}
testResolve(t, kc, registry(t, "fake.registry.io"), authn.FromConfig(auth))
testResolve(t, kc, repo(t, "fake.registry.io/repo"), authn.FromConfig(auth))
testResolve(t, kc, registry(t, "fake2.registry.io"), authn.FromConfig(auth2))
testResolve(t, kc, repo(t, "fake2.registry.io/repo"), authn.FromConfig(auth2))
}
func TestAuthDockerRegistry(t *testing.T) {
auth := authn.AuthConfig{Username: "root", Password: "root"}
kc, err := NewFromPullSecrets(context.Background(), []corev1.Secret{
*dockerConfigJSONSecretType.Create(t, "ns", "secret", "index.docker.io", auth),
})
if err != nil {
t.Fatalf("New() = %v", err)
}
testResolve(t, kc, repo(t, "ubuntu"), authn.FromConfig(auth))
testResolve(t, kc, repo(t, "knative/serving"), authn.FromConfig(auth))
}
func TestAuthWithGlobs(t *testing.T) {
auth := authn.AuthConfig{Username: "root", Password: "root"}
kc, err := NewFromPullSecrets(context.Background(), []corev1.Secret{
*dockerConfigJSONSecretType.Create(t, "ns", "secret", "*.registry.io", auth),
})
if err != nil {
t.Fatalf("New() = %v", err)
}
testResolve(t, kc, registry(t, "fake.registry.io"), authn.FromConfig(auth))
testResolve(t, kc, repo(t, "fake.registry.io/repo"), authn.FromConfig(auth))
testResolve(t, kc, registry(t, "blah.registry.io"), authn.FromConfig(auth))
testResolve(t, kc, repo(t, "blah.registry.io/repo"), authn.FromConfig(auth))
}
func testResolve(t *testing.T, kc authn.Keychain, target authn.Resource, expectedAuth authn.Authenticator) {
t.Helper()
auth, err := kc.Resolve(target)
if err != nil {
t.Errorf("Resolve(%v) = %v", target, err)
}
got, err := auth.Authorization()
if err != nil {
t.Errorf("Authorization() = %v", err)
}
want, err := expectedAuth.Authorization()
if err != nil {
t.Errorf("Authorization() = %v", err)
}
if diff := cmp.Diff(want, got); diff != "" {
t.Error("Resolve() diff (-want, +got)\n", diff)
}
}
func toJSON(t *testing.T, obj interface{}) []byte {
t.Helper()
bites, err := json.Marshal(obj)
if err != nil {
t.Fatal("unable to json marshal", err)
}
return bites
}
func registry(t *testing.T, registry string) authn.Resource {
t.Helper()
reg, err := name.NewRegistry(registry, name.WeakValidation)
if err != nil {
t.Fatal("failed to create registry", err)
}
return reg
}
func repo(t *testing.T, repository string) authn.Resource {
t.Helper()
repo, err := name.NewRepository(repository, name.WeakValidation)
if err != nil {
t.Fatal("failed to create repo", err)
}
return repo
}
// TestDockerConfigJSON tests using secrets using the .dockerconfigjson form,
// like you might get from running:
// kubectl create secret docker-registry secret -n ns --docker-server="fake.registry.io" --docker-username="foo" --docker-password="bar"
func TestDockerConfigJSON(t *testing.T) {
username, password := "foo", "bar"
kc, err := NewFromPullSecrets(context.Background(), []corev1.Secret{{
ObjectMeta: metav1.ObjectMeta{
Name: "secret",
Namespace: "ns",
},
Type: corev1.SecretTypeDockerConfigJson,
Data: map[string][]byte{
corev1.DockerConfigJsonKey: []byte(
fmt.Sprintf(`{"auths":{"fake.registry.io":{"username":%q,"password":%q,"auth":%q}}}`,
username, password,
base64.StdEncoding.EncodeToString([]byte(username+":"+password))),
),
},
}})
if err != nil {
t.Fatalf("NewFromPullSecrets() = %v", err)
}
reg, err := name.NewRegistry("fake.registry.io", name.WeakValidation)
if err != nil {
t.Errorf("NewRegistry() = %v", err)
}
auth, err := kc.Resolve(reg)
if err != nil {
t.Errorf("Resolve(%v) = %v", reg, err)
}
got, err := auth.Authorization()
if err != nil {
t.Errorf("Authorization() = %v", err)
}
want, err := (&authn.Basic{Username: username, Password: password}).Authorization()
if err != nil {
t.Errorf("Authorization() = %v", err)
}
if !reflect.DeepEqual(got, want) {
t.Errorf("Resolve() = %v, want %v", got, want)
}
}
func TestKubernetesAuth(t *testing.T) {
// From https://github.com/knative/serving/issues/12761#issuecomment-1097441770
// All of these should work with K8s' docker auth parsing.
for k, ss := range map[string][]string{
"registry.gitlab.com/dprotaso/test/nginx": []string{
"registry.gitlab.com",
"http://registry.gitlab.com",
"https://registry.gitlab.com",
"registry.gitlab.com/dprotaso",
"http://registry.gitlab.com/dprotaso",
"https://registry.gitlab.com/dprotaso",
"registry.gitlab.com/dprotaso/test",
"http://registry.gitlab.com/dprotaso/test",
"https://registry.gitlab.com/dprotaso/test",
"registry.gitlab.com/dprotaso/test/nginx",
"http://registry.gitlab.com/dprotaso/test/nginx",
"https://registry.gitlab.com/dprotaso/test/nginx",
},
"dtestcontainer.azurecr.io/dave/nginx": []string{
"dtestcontainer.azurecr.io",
"http://dtestcontainer.azurecr.io",
"https://dtestcontainer.azurecr.io",
"dtestcontainer.azurecr.io/dave",
"http://dtestcontainer.azurecr.io/dave",
"https://dtestcontainer.azurecr.io/dave",
"dtestcontainer.azurecr.io/dave/nginx",
"http://dtestcontainer.azurecr.io/dave/nginx",
"https://dtestcontainer.azurecr.io/dave/nginx",
}} {
repo, err := name.NewRepository(k)
if err != nil {
t.Errorf("parsing %q: %v", k, err)
continue
}
for _, s := range ss {
t.Run(fmt.Sprintf("%s - %s", k, s), func(t *testing.T) {
username, password := "foo", "bar"
kc, err := NewFromPullSecrets(context.Background(), []corev1.Secret{{
ObjectMeta: metav1.ObjectMeta{
Name: "secret",
Namespace: "ns",
},
Type: corev1.SecretTypeDockerConfigJson,
Data: map[string][]byte{
corev1.DockerConfigJsonKey: []byte(
fmt.Sprintf(`{"auths":{%q:{"username":%q,"password":%q,"auth":%q}}}`,
s,
username, password,
base64.StdEncoding.EncodeToString([]byte(username+":"+password))),
),
},
}})
if err != nil {
t.Fatalf("NewFromPullSecrets() = %v", err)
}
auth, err := kc.Resolve(repo)
if err != nil {
t.Errorf("Resolve(%v) = %v", repo, err)
}
got, err := auth.Authorization()
if err != nil {
t.Errorf("Authorization() = %v", err)
}
want, err := (&authn.Basic{Username: username, Password: password}).Authorization()
if err != nil {
t.Errorf("Authorization() = %v", err)
}
if !reflect.DeepEqual(got, want) {
t.Errorf("Resolve() = %v, want %v", got, want)
}
})
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,279
|
Q: Windows 10 home updates fail with error 0x80070057 I am a regular computer user and i am using lenovo Z51-70 laptop which runs on windows 10 home. Recently i saw i stopped getting new updates for my OS and i am getting an error message like the one shown below
Update error - There are some problem installing updates, But we will try again later..........
This may help(0x80070057)
I am totally fed up seeing this for a long time. May I know what problem it is? Also how to get rid of it?
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,662
|
Q: Make show/hide element inside li on mouseenter/mouseleave in Angular 5 So I have a basic <ul> in Angular 5 containing an *ngFor that populates its <li> children based on an array. Nothing fancy. Now, I want that on hover over each li, a pencil and a trash icon become visible. So far, I managed to make all pencil and trash icons visible at the same time, but this is not the behavior I am looking for. I want the user to be able to see that there is an edit/delete option on each particular li.
This is my code, adapted after this Plunk: https://embed.plnkr.co/xgI5jOPI9HDUJb71RfmT/.
<ul class="list-group">
<li class="list-group-item" (dblclick)="editTodo(todo)" *ngFor="let todo of todosList">
<span (mouseenter)="mouseOvered=true" (mouseleave)="mouseOvered=false">
{{todo.text}}
<i [className]="mouseOvered ? 'fa fa-pencil' : 'hidden'" (click)="editTodo(todo)"></i>
<i [className]="mouseOvered ? 'fa fa-trash' : 'hidden'" (click)="deleteTodo(todo)"></i>
</span>
</li>
</ul>
Edit based on Saksham's suggestion:
I added 2 methods, mouseEnter(todo) and mouseLeave(todo) and inside them I assigned the mouseOvered property to the particular hovered-over todo. So now, my code looks like this:
app.component.html
...
<span (mouseenter)="mouseEnter(todo)" (mouseleave)="mouseLeave(todo)">
{{todo.text}}
<i [className]="todo.mouseOvered ? 'fa fa-pencil' : 'hidden'" (click)="editTodo(todo)"></i>
<i [className]="todo.mouseOvered ? 'fa fa-trash' : 'hidden'" (click)="deleteTodo(todo)"></i>
</span>
app.component.ts
mouseEnter(todo) {
todo.mouseOvered = true;
}
mouseLeave(todo) {
todo.mouseOvered = false;
}
A: What you can do is add a new property mouseOvered to each object in todosList and initialize it with false.
Then, all you have to do is this:
<ul class="list-group">
<li class="list-group-item" (dblclick)="editTodo(todo)" *ngFor="let todo of todosList">
<span (mouseenter)="todo.mouseOvered=true" (mouseleave)="todo.mouseOvered=false">
{{todo.text}}
<i [className]="todo.mouseOvered ? 'fa fa-pencil' : 'hidden'" (click)="editTodo(todo)"></i>
<i [className]="todo.mouseOvered ? 'fa fa-trash' : 'hidden'" (click)="deleteTodo(todo)"></i>
</span>
</li>
</ul>
Not sure if this is the best approach out there but it will work.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,375
|
#include "inneractiveplugin.h"
#include "adinterface.h"
#include <QtDeclarative/qdeclarative.h>
#include <QDeclarativeEngine>
#include <QDeclarativeContext>
#include <QDebug>
void inneractivePlugin::initializeEngine(QDeclarativeEngine *engine)
{
if (!engine->rootContext()->contextProperty("adInterface").isValid()) {
AdInterface *adI = new AdInterface(engine);
engine->rootContext()->setContextProperty("adInterface", adI);
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Сіжі́-ле-Шате́ль () — муніципалітет у Франції, у регіоні Бургундія-Франш-Конте, департамент Сона і Луара. Населення — осіб (2011).
Муніципалітет розташований на відстані близько 310 км на південний схід від Парижа, 95 км на південний захід від Діжона, 34 км на північний захід від Макона.
Демографія
Розподіл населення за віком та статтю (2006):
Економіка
Посилання
Сіжі-ле-Шатель на сайті французького Національного інституту географії
Сіжі-ле-Шатель на сайті французького Національного інституту статистики й економічних досліджень
Сіжі-ле-Шатель на сайті Quid (загальні відомості, історія, пам'ятки, фото, адреси)
[ Розташування муніципалітету Сіжі-ле-Шатель на мапі Франції та сусідні муніципалітети]
Мапа муніципалітету Сіжі-ле-Шатель на сайті Mapquest
Див. також
Список муніципалітетів департаменту Сона і Луара
Примітки
Муніципалітети департаменту Сона і Луара
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{"url":"http:\/\/lptms.u-psud.fr\/maurizio-fagotti\/publications\/","text":"# Publications\n\n###### Theses:\n\nEntanglement & Correlations in exactly solvable models\n\nPhD, University of Pisa (Italy)\nMarch 2012\nsupervisor: Pasquale Calabrese\n[pdf]\n\nDinamica di non-equilibrio dell\u2019entanglement e delle correlazioni in una catena di spin\n\nMaster, University of Pisa (Italy)\nMarch 2009\nsupervisor: Pasquale Calabrese\n[pdf]\n\nLa fase di Berry \u2013 la fase geometrica in meccanica quantistica\n\nBachelor, University of Pisa (Italy)\nDecember 2005\nsupervisor:\u00a0Mihail Mintchev\n[pdf]\n\nPapers\n\narXiv\n\nBibliometrics\n\n###### List of papers:\n\n[the articles highlighted in orange are highly cited in the field (according to the database Web of Science on 26\/05\/2020)]\n\n\u2022 L. Zadnik, S. Bocini, K. Bidzhiev, and M. Fagotti\nMeasurement catastrophe and ballistic spread of charge density with vanishing current\n[cited by]\n\n One of the features of many-body quantum systems with Hilbert-space fragmentation is the existence of stationary states manifesting quantum jamming. It was recently shown that these are \u201cstates with memory\u201d, in which, e.g., measuring a localised observable has everlasting macroscopic effects. We study such a measurement catastrophe with an example that stands out for its clarity. We show in particular that at late times the expectation value of a charge density becomes a nontrivial function of the ratio between distance and time notwithstanding the corresponding current approaching zero.\n\u2022 M. Fagotti\nGlobal Quenches after Localised Perturbations\n\n We investigate the effect of a single spin flip preceding a global quench between translationally invariant local Hamiltonians in spin-1\/2 chains. The effect of the localised perturbation does not fade away however large the distance from the perturbation is. In particular, translational invariance is not restored and the infinite time limit depends on whether the spin was flipped or not. We argue that this phenomenon is more general than the particular example considered and we conjecture that it is triggered by topological properties, specifically, the existence of \u201csemilocal charges\u201d.\n\u2022 K. Bidzhiev, M. Fagotti, and L. Zadnik\nMacroscopic effects of localised measurements in jammed states of quantum spin chains\n\n A quantum jammed state can be seen as a state where the phase space available to particles shrinks to zero, an interpretation quite accurate in integrable systems, where stable quasiparticles scatter elastically. We consider the integrable dual folded XXZ model, which is equivalent to the XXZ model in the limit of large anisotropy. We perform a jamming-breaking localised measurement in a jammed state. We find that jamming is locally restored, but local observables exhibit nontrivial time evolution on macroscopic, ballistic scales, without ever relaxing back to their initial values.\n\u2022 V. Alba, B. Bertini, M. Fagotti, L. Piroli, and P. Ruggiero\nGeneralized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects\n\n We give a pedagogical introduction to the Generalized Hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of the theory. Finally, we present some open questions and suggest perspectives on possible future directions.\n\u2022 L. Zadnik, K. Bidzhiev, and M. Fagotti\nThe Folded Spin-1\/2 XXZ Model:\nII. Thermodynamics and Hydrodynamics with a Minimal Set of Charges\n\n We study the (dual) folded spin-1\/2 XXZ model in the thermodynamic limit. We focus, in particular, on a class of \u201clocal\u201d macrostates that includes Gibbs ensembles. We develop a thermodynamic Bethe Ansatz description and work out generalised hydrodynamics at the leading order. Remarkably, in the ballistic scaling limit the junction of two local macrostates results in a discontinuity in the profile of essentially any local observable.\n\u2022 L. Zadnik and M. Fagotti\nThe Folded Spin-1\/2 XXZ Model:\nI. Diagonalisation, Jamming, and Ground State Properties\n\n We study an effective Hamiltonian generating time evolution of states on inter- mediate time scales in the strong-coupling limit of the spin-1\/2 XXZ model. To leading order, it describes an integrable model with local interactions. We solve it completely by means of a coordinate Bethe Ansatz that manifestly breaks the translational symmetry. We demonstrate the existence of exponentially many jammed states and estimate their stability under the leading correction to the effective Hamiltonian. Some ground state properties of the model are discussed.\n\u2022 E. Granet, M. Fagotti, and \u00a0F. H. L Essler\nFinite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions\n\n We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models.\n\u2022 Maurizio Fagotti\nLocally quasi-stationary states in noninteracting spin chains\n\n Locally quasi-stationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By solving the dynamics in inhomogeneous noninteracting spin chains, we identify the set of LQSSs as a subspace that is invariant under time evolution, and we explicitly construct the latter in a generalised XY model. As a by-product, we exhibit an exact generalised hydrodynamic theory (including \u201cquantum corrections\u201d).\n\u2022 Vincenzo Alba, Bruno Bertini, and Maurizio Fagotti\nEntanglement evolution and generalised hydrodynamics: interacting integrable systems\n\n We investigate the dynamics of bipartite entanglement after the sudden junction of two leads in interacting integrable models. By combining the quasiparticle picture for the entanglement spreading with Generalised Hydrodynamics we derive an analytical prediction for the dynamics of the entanglement entropy between a finite subsystem and the rest. We find that the entanglement rate between the two leads depends only on the physics at the interface and differs from the rate of exchange of thermodynamic entropy. This contrasts with the behaviour in free or homogeneous interacting integrable systems, where the two rates coincide.\n\u2022 Maurizio Fagotti\nOn the size of the space spanned by a nonequilibrium state in a quantum spin lattice system\n\n We consider the time evolution of a state in an isolated quantum spin lattice system with energy cumulants proportional to the number of the sites $$L^d$$. We compute the distribution of the eigenvalues of the time averaged state over a time window $$[t_0,t_0+t]$$ in the limit of large $$L$$. This allows us to infer the size of a subspace that captures time evolution in $$[t_0,t_0+t]$$ with an accuracy $$1-\\epsilon$$. We estimate the size to be $$\\frac{\\sqrt{2\\mathfrak{e}_2}}{\\pi}\\mathrm{erf}^{-1}(1-\\epsilon) L^{\\frac{d}{2}}t$$, where $$\\mathfrak{e}_2$$ is the energy variance per site, and $$\\mathrm{erf}^{-1}$$ is the inverse error function.\n\u2022 Bruno Bertini, Maurizio Fagotti, Lorenzo Piroli, and Pasquale Calabrese\nEntanglement evolution and generalised hydrodynamics: noninteracting systems\n\n The large-scale properties of homogeneous states after quantum quenches in integrable systems have been successfully described by a semiclassical picture of moving quasiparticles. Here we consider the generalisation for the entanglement evolution after an inhomogeneous quench in noninteracting systems in the framework of generalised hydrodynamics. We focus on the protocol where two semi-infinite halves are initially prepared in different states and then joined together, showing that a proper generalisation of the quasiparticle picture leads to exact quantitative predictions. If the system is initially prepared in a quasistationary state, we find that the entanglement entropy is additive and it can be computed by means of generalised hydrodynamics. Conversely, additivity is lost when the initial state is not quasistationary; yet the entanglement entropy in the large-scale limit can be exactly predicted in the quasiparticle picture, provided that the initial state is low entangled.\n\u2022 Maurizio Fagotti\nHigher-order generalized hydrodynamics in one dimension: The noninteracting test\nPhys. Rev. B 96, 220302(R) (2017)\u00a0[cited by]\n\n We derive a dynamical equation that describes the exact time evolution in generic (inhomogeneous) noninteracting spin-chain models. Assuming quasistationarity, we develop a (generalized) hydrodynamic theory. The question at hand is whether some large-time corrections are captured by higher-order hydrodynamics. We consider in particular the dynamics after two chains, prepared in different conditions, are joined together. In these situations, a light cone, separating regions with macroscopically different properties, emerges from the junction. In free fermionic systems some observables close to the light cone follow a universal behavior, known as Tracy-Widom scaling. Universality means a weak dependence on the system\u2019s details, so this is the perfect setting where hydrodynamics could emerge. For the transverse-field Ising chain and the XX\u00a0model, we show that hydrodynamics captures the scaling behavior close to the light cone. On the other hand, our numerical analysis suggests that hydrodynamics fails in more general models, whenever a condition is not satisfied.\n\u2022 Lorenzo Piroli, Jacopo De Nardis, Mario Collura, Bruno Bertini, and Maurizio Fagotti\nTransport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions\nPhys. Rev. B 96, 115124 (2017)\u00a0[cited by]\n\n We consider\u00a0the nonequilibrium protocol where two semi-infinite gapped XXZ chains, initially prepared in different equilibrium states, are suddenly joined together. At large times, a generalized hydrodynamic description applies, according to which the system can locally be represented by space- and time-dependent stationary states. The magnetization displays an unusual behavior: depending on the initial state, its profile may exhibit abrupt jumps that can not be predicted directly from the standard hydrodynamic equations and which signal nonballistic spin transport. We ascribe this phenomenon to the structure of the local conservation laws and make a prediction for the exact location of the jumps. We find that the jumps propagate at the velocities of the heaviest quasiparticles. By means of time-dependent density matrix renormalization group simulations we show that our theory yields a complete description of the long-time steady profiles of conserved charges, currents, and local correlations.\n\u2022 Vincenzo Alba and Maurizio Fagotti\nPrethermalization at Low Temperature: The Scent of Long-Range Order\nPhys. Rev. Lett. 119, 010601 (2017)\u00a0[cited by]\n\n Nonequilibrium time evolution in isolated many-body quantum systems generally results in thermalization. However, the relaxation process can be very slow, and quasistationary nonthermal plateaux are often observed at intermediate times. The paradigmatic example is a quantum quench in an integrable model with weak integrability breaking; for a long time, the state cannot escape the constraints imposed by the approximate integrability. We unveil a new mechanism of prethermalization, based on the presence of a symmetry of the prequench Hamiltonian, which is spontaneously broken at zero temperature and is explicitly broken by the postquench Hamiltonian. The typical time scale of the phenomenon is proportional to the thermal correlation length of the initial state, which diverges as the temperature is lowered. We show that the prethermal quasistationary state can be approximated by a mixed state that violates cluster decomposition property. We consider two examples: the transverse-field Ising chain, where the full-time evolution is computed analytically, and the (nonintegrable) anisotropic next-nearest-neighbor Ising model, which is investigated numerically.\n\u2022 Maurizio Fagotti\nCharges and currents in quantum spin chains: late-time dynamics and spontaneous currents\n2017 J. Phys. A: Math. Theor. 50 034005\u00a0[cited by]\n\n We review the structure of the conservation laws in noninteracting spin chains and unveil a formal expression for the corresponding currents. We briefly discuss how interactions affect the picture. In the second part, we explore the effects of a localized defect. We show that the emergence of spontaneous currents near the defect undermines any description of the late-time dynamics by means of a stationary state in a finite chain. In particular, the diagonal ensemble does not work. Finally, we provide numerical evidence that simple generic localized defects are not sufficient to induce thermalization.\n\u2022 Bruno Bertini, Mario Collura, Jacopo De Nardis, and Maurizio Fagotti\nTransport in Out-of-Equilibrium XXZ\u00a0Chains: Exact Profiles of Charges and Currents\nPhys. Rev. Lett. 117, 207201 (2016)\u00a0[cited by]\n\n We consider the nonequilibrium time evolution of piecewise homogeneous states in the XXZ\u00a0spin-1\/2\u00a0chain, a paradigmatic example of an interacting integrable model. The initial state can be thought of as the result of joining chains with different global properties. Through dephasing, at late times, the state becomes locally equivalent to a stationary state which explicitly depends on position and time. We propose a kinetic theory of elementary excitations and derive a continuity equation which fully characterizes the thermodynamics of the model. We restrict ourselves to the gapless phase and consider cases where the chains are prepared: (1) at different temperatures, (2) in the ground state of two different models, and (3) in the \u201cdomain wall\u201d state. We find excellent agreement (any discrepancy is within the numerical error) between theoretical predictions and numerical simulations of time evolution based on time-evolving block decimation algorithms. As a corollary, we unveil an exact expression for the expectation values of the charge currents in a generic stationary state.\n\u2022 Bruno Bertini and Maurizio Fagotti\nDetermination of the Nonequilibrium Steady State Emerging from a Defect\nPhys. Rev. Lett. 117, 130402 (2016)\u00a0[cited by]\n\n We consider the nonequilibrium time evolution of a translationally invariant state under a Hamiltonian with a localized defect. We discern the situations where a light cone spreads out from the defect and separates the system into regions with macroscopically different properties. We identify the light cone and propose a procedure to obtain a (quasi)stationary state describing the late time dynamics of local observables. As an explicit example, we study the time evolution generated by the Hamiltonian of the transverse-field Ising chain with a local defect that cuts the interaction between two sites (a quench of the boundary conditions alongside a global quench). We solve the dynamics exactly and show that the late time properties can be obtained with the general method proposed.\n\u2022 Fabian H L Essler and Maurizio Fagotti\n\n We review the dynamics after quantum quenches in integrable quantum spin chains. We give a pedagogical introduction to relaxation in isolated quantum systems, and discuss the description of the steady state by (generalized) Gibbs ensembles. We then turn to general features in the time evolution of local observables after the quench, using a simple model of free fermions as an example. In the second part we present an overview of recent progress in describing quench dynamics in two key paradigms for quantum integrable models, the transverse field Ising chain and the anisotropic spin-$$\\frac{1}{2}$$ Heisenberg chain.\n\u2022 Anton S. Buyskikh, Maurizio Fagotti, Johannes Schachenmayer, Fabian Essler, and Andrew J. Daley\nEntanglement growth and correlation spreading with variable-range interactions in spin and fermionic tunneling models\nPhys. Rev. A 93, 053620 (2016)\n\n We investigate the dynamics following a global parameter quench for two one-dimensional models with variable-range power-law interactions: a long-range transverse Ising model, which has recently been realized in chains of trapped ions, and a long-range lattice model for spinless fermions with long-range tunneling. For the transverse Ising model, the spreading of correlations and growth of entanglement are computed using numerical matrix product state techniques, and are compared with exact solutions for the fermionic tunneling model. We identify transitions between regimes with and without an apparent linear light cone for correlations, which correspond closely between the two models. For long-range interactions (in terms of separation distance r, decaying slower than $$1\/r$$), we find that despite the lack of a light cone, correlations grow slowly as a power law at short times, and that\u2014depending on the structure of the initial state\u2014the growth of entanglement can also be sublinear. These results are understood through analytical calculations, and should be measurable in experiments with trapped ions.\n\u2022 Maurizio Fagotti\nLocal conservation laws in spin-1\/2 XY chains with open boundary conditions\nJ. Stat. Mech. (2016) 063105\n\n We revisit the conserved quantities of the spin-$$\\frac{1}{2}$$ XY model with open boundary conditions. In the absence of a transverse field, we find new families of local charges and show that half of the seeming conservation laws are conserved only if the number of sites is odd. In even chains the set of noninteracting charges is abelian, like in the periodic case when the number of sites is odd. In odd chains the set is doubled and becomes non-abelian, like in even periodic chains. The dependence of the charges on the parity of the chain\u2019s size undermines the common belief that the thermodynamic limit of diagonal ensembles exists. We consider also the transverse-field Ising chain, where the situation is more ordinary. The generalization to the XY model in a transverse field is not straightforward and we propose a general framework to carry out similar calculations. We conjecture the form of the bulk part of the local charges and discuss the emergence of quasilocal conserved quantities. We provide evidence that in a region of the parameter space there is a reduction of the number of quasilocal conservation laws invariant under chain inversion. As a by-product, we study a class of block-Toeplitz-plus-Hankel operators and identify the conditions that their symbols satisfy in order to commute with a given block-Toeplitz.\n\u2022 Maurizio Fagotti\nControl of global properties in a closed many-body quantum system by means of a local switch\n\n We consider non-equilibrium time evolution after a quench of a global Hamiltonian parameter in systems described by Hamiltonians with local interactions. Within this background, we propose a protocol that allows to change global properties of the state by flipping a switch that modifies a local term of the Hamiltonian (creating a defect). A light-cone that separates two globally different regions originates from the switch. The expectation values of macroscopic observables, that is to say local observables that are spatially averaged within a subsystem, slowly approach new asymptotic values determined by the defect. The process is almost reversible: flipping again the switch produces a new light-cone with the two regions inverted. Finally, we test the protocol under repeated projective measurements. As explicit example we study the dynamics in a simple exactly solvable model but analogues descriptions apply also to generic models.\n\u2022 Maurizio Fagotti and Mario Collura\nUniversal prethermalization dynamics of entanglement entropies after a global quench\n\n We consider the quantum XY model and study the effects of interacting perturbations on the time evolution of the von Neumann and R\\\u2019enyi entropies of spin blocks after global quenches. We show that the entropies are sensitive to perturbations that break hidden symmetries behind the integrability of the model. At times much larger than the characteristic time of the well-known linear increase of the entropies, we identify a time window characterized by a novel linear growth followed by saturation. The typical time of the phenomenon is inversely proportional to the perturbation strength and the behavior is trigger off by the extinction of an infinite number of local conservation laws following a non-abelian algebra. The universality of the crossover is revealed by a semi-classical picture that captures the leading behavior of the entropies. We check our theoretical predictions against iTEBD simulations. The good agreement between theory and numerics substantiates the method developed in [Bertini and Fagotti, J. Stat. Mech. (2015) P07012] for investigating a pre-relaxation limit in weakly interacting models.\n\u2022 Bruno Bertini and Maurizio Fagotti\nPre-relaxation in weakly interacting models\nJ. Stat. Mech. (2015) P07012\n\n We consider time evolution in models close to integrable points with hidden symmetries that generate infinitely many local conservation laws that do not commute with one another. The system is expected to (locally) relax to a thermal ensemble if integrability is broken, or to a so-called generalised Gibbs ensemble if unbroken. In some circumstances expectation values exhibit quasi-stationary behaviour long before their typical relaxation time. For integrability-breaking perturbations, these are also called pre-thermalisation plateaux, and emerge e.g. in the strong coupling limit of the Bose\u2013Hubbard model. As a result of the hidden symmetries, quasi-stationarity appears also in integrable models, for example in the Ising limit of the XXZ model. We investigate a weak coupling limit, identify a time window in which the effects of the perturbations become significant and solve the time evolution through a mean-field mapping. As an explicit example we study the XYZ spin-$$\\frac{1}{2}$$ chain with additional perturbations that break integrability. One of the most intriguing results of the analysis is the appearance of persistent oscillatory behaviour. To unravel its origin, we study in detail a toy model: the transverse-field Ising chain with an additional nonlocal interaction proportional to the square of the transverse spin per unit length (2013 Phys. Rev. Lett. 111 197203). Despite being nonlocal, this belongs to a class of models that emerge as intermediate steps of the mean-field mapping and shares many dynamical properties with the weakly interacting models under consideration.\n\u2022 Maurizio Fagotti\nConservation laws for a class of generic Hamiltonians\n\n Within a strong coupling expansion, we construct local quasi-conserved operators for a class of Hamiltonians that includes both integrable and non-integrable models. We explicitly show that at the lowest orders of perturbation theory the structure of the operators is independent of the system details. Higher order contributions are investigated numerically by means of an ab initio method for computing the time evolution of local operators in the Heisenberg picture. The numerical analysis suggests that the quasi-conserved operators could be approximations of a quasi-local conservation law, even if the model is non-integrable.\n\u2022 Demetrio Logoteta, Paolo Marconcini, Claudio Bonati, Maurizio Fagotti, Massimo Macucci\nHigh-performance solution of the transport problem in a graphene armchair structure with a generic potential\nPhys. Rev. E 89, 063309 (2014)\n\n We propose an efficient numerical method to study the transport properties of armchair graphene ribbons in the presence of a generic external potential. The method is based on a continuum envelope-function description with physical boundary conditions. The envelope functions are computed in the reciprocal space, and the transmission is then obtained with a recursive scattering matrix approach. This allows a significant reduction of the computational time with respect to finite difference simulations.\n\u2022 Maurizio Fagotti\nOn Conservation Laws, Relaxation and Pre-relaxation after a Quantum Quench\nJ. Stat. Mech. (2014) P03016\n\n We consider the time evolution following a quantum quench in spin-$$\\frac{1}{2}$$ chains. It is well known that local conservation laws constrain the dynamics and, eventually, the stationary behavior of local observables. We show that some widely studied models, such as the quantum XY model, possess extra families of local conservation laws in addition to the translation invariant ones. As a consequence, the additional charges must be included in the generalized Gibbs ensemble that describes the stationary properties. The effects go well beyond a simple redefinition of the stationary state. The time evolution of a non-translation-invariant state under a (translation-invariant) Hamiltonian with a perturbation that weakly breaks the hidden symmetries underlying the extra conservation laws exhibits pre-relaxation. In addition, in the limit of small perturbation, the time evolution following pre-relaxation can be described by means of a time-dependent generalized Gibbs ensemble.\n\u2022 Maurizio Fagotti, Mario Collura, Fabian H L Essler, and Pasquale Calabrese\nRelaxation after quantum quenches in the spin-1\/2\u00a0Heisenberg XXZ chain\nPhys. Rev. B 89, 125101 (2014)\n\n We consider the time evolution after quantum quenches in the spin-$$\\frac{1}{2}$$\u00a0Heisenberg XXZ quantum spin chain with Ising-type anisotropy. The time evolution of short-distance spin-spin correlation functions is studied by numerical tensor network techniques for a variety of initial states, including N\u00e9el and Majumdar-Ghosh states and the ground state of the XXZ chain at large values of the anisotropy. The various correlators appear to approach stationary values, which are found to be in good agreement with the results of exact calculations of stationary expectation values in appropriate generalized Gibbs ensembles. In particular, our analysis shows how symmetries of the post-quench Hamiltonian that are broken by particular initial states are restored at late times.\n\u2022 Maurizio Fagotti\nDynamical Phase Transitions as Properties of the Stationary State: Analytic Results after Quantum Quenches in the Spin-1\/2 XXZ Chain\n\n The (Loschmidt) overlap between the state at different times after a quantum quench is attracting increasing interest, as it was recently shown that in the thermodynamic limit its logarithm per unit of length has a non-analytic behavior if a Hamiltonian parameter is quenched across a critical point. This phenomenon was called a \u201cdynamical phase transition\u201d in analogy with the behavior of the canonical partition function at an equilibrium phase transition. We distinguish between local and nonlocal contributions to the aforementioned quantity and derive an analytic expression for the time evolution of the local part after quantum quenches in the XXZ spin-$$\\frac{1}{2}$$ chain. The state that describes the stationary properties of (local) observables can be represented by a Gibbs ensemble of a generalized Hamiltonian; we reveal a deep connection between the appearance of singularities and the excitation energies of the generalized Hamiltonian.\n\u2022 Maurizio Fagotti and Fabian H L Essler\nStationary behaviour of observables after a quantum quench in the spin-1\/2 Heisenberg XXZ chain\nJ. Stat. Mech. (2013) P07012\n\n We consider a quantum quench in the spin-$$\\frac{1}{2}$$ Heisenberg XXZ chain. At late times after the quench it is believed that the expectation values of local operators approach time-independent values that are described by a generalized Gibbs ensemble. Employing a quantum transfer matrix approach we show how to determine short-range correlation functions in such generalized Gibbs ensembles for a class of initial states.\n\u2022 Maurizio Fagotti and Fabian H L Essler\nReduced density matrix after a quantum quench\nPhys. Rev. B 87, 245107 (2013)\n\n We consider the reduced density matrix (RDM) $$\\rho_A(t)$$\u00a0for a finite subsystem A\u00a0after a global quantum quench in the infinite transverse-field Ising chain. It has been recently shown that the infinite time limit of $$\\rho_A(t)$$\u00a0is described by the RDM $$\\rho_{{\\rm GGE}, A}$$\u00a0of a generalized Gibbs ensemble. Here, we present some details on how to construct this ensemble in terms of local integrals of motion, and show its equivalence to the expression in terms of mode occupation numbers widely used in the literature. We then address the question of how $$\\rho_A(t)$$\u00a0approaches $$\\rho_{{\\rm GGE}, A}$$\u00a0as a function of time. To that end, we introduce a distance on the space of density matrices and show that it approaches zero as a universal power law $$t^{-3\/2}$$\u00a0in time. As the RDM completely determines all local observables within A, this provides information on the relaxation of correlation functions of local operators. We then address the issue of how well a truncated generalized Gibbs ensemble with a finite number of local higher conservation laws describes a given subsystem at late times. We find that taking into account only local conservation laws with a range at most comparable to the subsystem size provides a good description. However, excluding even a single one of the most local conservation laws in general completely spoils this agreement.\n\u2022 Maurizio Fagotti\nFinite-size corrections versus relaxation after a sudden quench\nPhys. Rev. B 87, 165106 (2013)\n\n We consider the time evolution after sudden quenches of global parameters in translational invariant Hamiltonians and study the time average expectation values and entanglement entropies in finite chains. We show that in noninteracting models the time average of spin correlation functions is asymptotically equal to the infinite time limit in the infinite chain, which is known to be described by a generalized Gibbs ensemble. The equivalence breaks down considering nonlocal operators, and we establish that this can be traced back to the existence of conservation laws common to the Hamiltonian before and after the quench. We develop a method to compute the leading finite-size corrections. We find that the finite-size corrections are generally large in observables with large relaxation timescales.\n\u2022 Fabian H L Essler, Stefano Evangelisti, and Maurizio Fagotti\nDynamical Correlations After a Quantum Quench\nPhys. Rev. Lett. 109, 247206 (2012)\n\n We consider dynamic (non-equal-time) correlation functions of local observables after a quantum quench. We show that, in the absence of long-range interactions in the final Hamiltonian, the dynamics is determined by the same ensemble that describes static (equal-time) correlations. For many integrable models, static correlation functions of local observables after a quantum quench relax to stationary values, which are described by a generalized Gibbs ensemble. The same generalized Gibbs ensemble then determines dynamic correlation functions, and the basic form of the fluctuation dissipation theorem holds, although the absorption and emission spectra are not simply related as in the thermal case. For quenches in the transverse field Ising chain, we derive explicit expressions for the time evolution of dynamic order parameter correlators after a quench.\n\u2022 Pasquale Calabrese, Fabian H L Essler, and Maurizio Fagotti\n\n We consider the stationary state properties of the reduced density matrix as well as spin\u2013spin correlation functions after a sudden quantum quench of the magnetic field in the transverse field Ising chain. We demonstrate that stationary state properties are described by a generalized Gibbs ensemble. We discuss the approach to the stationary state at late times.\n\u2022 Pasquale Calabrese, Fabian H L Essler, and Maurizio Fagotti\n\n We consider the time evolution of order parameter correlation functions after a sudden quantum quench of the magnetic field in the transverse field Ising chain. Using two novel methods based on determinants and form factor sums respectively, we derive analytic expressions for the asymptotic behaviour of one- and two-point correlators. We discuss quenches within the ordered and disordered phases as well as quenches between the phases and to the quantum critical point. We give detailed accounts of both methods.\n\u2022 Maurizio Fagotti\nNew insights into the entanglement of disjoint blocks\n2012 EPL 97 17007\n\n We study the entanglement of two disjoint blocks in spin-1\/2 chains obtained by merging solvable models, such as XX and quantum Ising models. We focus on the universal quantities that can be extracted from the R\u00e9nyi entropies $$S_\\alpha$$. The most important information is encoded in some functions denoted by $$F_\\alpha$$. We compute $$F_2$$\u00a0and we show that $$F_\\alpha-1$$\u00a0and $$F_{\\rm v. N.}$$, corresponding to the von Neumann entropy, can be negative, in contrast to what observed in all models examined so far. An exact relation between the entanglement of disjoint subsystems in the XX model and that in a chain embodying two quantum Ising models is a by-product of our investigations.\n\u2022 Pasquale Calabrese, Fabian H L Essler, and Maurizio Fagotti\n\n We consider the time evolution of observables in the transverse-field Ising chain after a sudden quench of the magnetic field. We provide exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter. We employ two complementary approaches based on asymptotic evaluations of determinants and form-factor sums. We prove that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can also be understood in terms of a GGE. We present a conjecture on how these results generalize to particular quenches in other integrable models.\n\u2022 Maurizio Fagotti, Claudio Bonati, Demetrio Logoteta, Paolo Marconcini, and Massimo Macucci\nArmchair graphene nanoribbons: PT-symmetry breaking and exceptional points without dissipation\nPhys. Rev. B 83, 241406(R) (2011)\n\n We consider a single-layer graphene nanoribbon with armchair edges and with a longitudinally constant external potential, pointing out that it can be described by means of an effective non-Hermitian Hamiltonian. We show that this system has some features typical of dissipative systems, namely, the presence of exceptional points and of PT-symmetry breaking, although it is not dissipative.\n\u2022 Maurizio Fagotti and Pasquale Calabrese\nUniversal parity effects in the entanglement entropy of XX chains with open boundary conditions\nJ. Stat. Mech. (2011) P01017\n\n We consider the R\u00e9nyi entanglement entropies in the one-dimensional XX spin-chains with open boundary conditions in the presence of a magnetic field. In the case of a semi-infinite system and a block starting from the boundary, we derive rigorously the asymptotic behavior for large block sizes on the basis of a recent mathematical theorem for the determinant of Toeplitz plus Hankel matrices. We conjecture a generalized Fisher\u2013Hartwig form for the corrections to the asymptotic behavior of this determinant that allows the exact characterization of the corrections to the scaling at order $$o(\\ell^{-1})$$\u00a0for any n. By combining these results with conformal field theory arguments, we derive exact expressions also in finite chains with open boundary conditions and in the case when the block is detached from the boundary.\n\u2022 \u00a0Maurizio Fagotti, Pasquale Calabrese, and Joel E Moore\nEntanglement spectrum of random-singlet quantum critical points\nPhys. Rev. B 83, 045110 (2011)\n\n The entanglement spectrum (i.e., the full distribution of Schmidt eigenvalues of the reduced density matrix) contains more information than the conventional entanglement entropy and has been studied recently in several many-particle systems. We compute the disorder-averaged entanglement spectrum in the form of the disorder-averaged moments $$\\mathrm{Tr}[\\rho_A^{\\alpha}]$$\u00a0of the reduced density matrix $$\\rho_A$$\u00a0for a contiguous block of many spins at the random-singlet quantum critical point in one dimension. The result compares well in the scaling limit with numerical studies on the random XX\u00a0model and is also expected to describe the (interacting) random Heisenberg model. Our numerical studies on the XX\u00a0case reveal that the dependence of the entanglement entropy and spectrum on the geometry of the Hilbert space partition is quite different than for conformally invariant critical points.\n\u2022 Maurizio Fagotti and Pasquale Calabrese\nEntanglement entropy of two disjoint blocks in XY chains\nJ. Stat. Mech. (2010) P04016\u00a0[cited by]\n\n We study the R\u00e9nyi entanglement entropies of two disjoint intervals in XY chains. We exploit the exact solution of the model in terms of free Majorana fermions and we show how to construct the reduced density matrix in the spin variables by taking the Jordan\u2013Wigner string between the two blocks properly into account. From this we can evaluate any R\u00e9nyi entropy of finite integer order. We study in detail critical XX and Ising chains and we show that the asymptotic results for large blocks agree with recent conformal field theory predictions if corrections to the scaling are included in the analysis correctly. We also report results for the gapped phase and after a quantum quench.\n\u2022 Vincenzo Alba, Maurizio Fagotti, and Pasquale Calabrese\nEntanglement entropy of excited states\nJ. Stat. Mech. (2009) P10020\n\n We study the entanglement entropy of a block of contiguous spins in excited states of spin chains. We consider the XY model in a transverse field and the XXZ Heisenberg spin chain. For the latter, we developed a numerical application of the algebraic Bethe ansatz. We find two main classes of states with logarithmic and extensive behavior in the dimension of the block, characterized by the properties of excitations of the state. This behavior can be related to the locality properties of the Hamiltonian having a given state as the ground state. We also provide several details of the finite size scaling.\n\u2022 Maurizio Fagotti and Pasquale Calabrese\nEvolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field\nPhys. Rev. A 78, 010306(R) (2008)\n\n The nonequilibrium evolution of the block entanglement entropy is investigated in the XY\u00a0chain in a transverse magnetic field after the Hamiltonian parameters are suddenly changed from and to arbitrary values. Using Toeplitz matrix representation and multidimensional phase methods, we provide analytic results for large blocks and for all times, showing explicitly the linear growth in time followed by saturation. The consequences of these analytic results are discussed and the effects of a finite block length is taken into account numerically.","date":"2021-12-06 08:33:09","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\": 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\": 0.7083727121353149, \"perplexity\": 639.2963525675643}, \"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-2021-49\/segments\/1637964363290.59\/warc\/CC-MAIN-20211206072825-20211206102825-00450.warc.gz\"}"}
| null | null |
Jurjan Koenen (Bussum, 18 november 1970) is een Nederlands honkballer.
Club
Koenen begon met honkbal op achtjarige leeftijd. In 1987 debuteerde hij in het eerste team van HCAW in de Hoofdklasse. Hij speelde als derde honkman en catcher. In 2005 besloot hij te stoppen in het eerste team. Hij ging spelen in Heren 3 van HCAW. In 2006 keerde hij voor zes wedstrijden terug als catcher omdat de vereniging te kampen had met een tekort aan spelers. Ook in 2008 maakte de routinier, inmiddels tevens coach van het eerste team, een rentree. Hij kwam uit op 1 juni 2008 en 2 juni 2008 in de wedstrijden tegen de landskampioen Kinheim. Op 37-jarige leeftijd kon hij op 2 juni ervoor zorgen door het beslissende punt te scoren dat HCAW de wedstrijd won met 2-1. In totaal speelde Koenen tot op heden 691 wedstrijden op het hoogste niveau. Hij had het record in Nederland met het hoogste aantal gespeelde wedstrijden in de hoofdklasse bij 1 vereniging. Op 12 mei 2013 werd Dè Flanegin van Hoofddorp Pioniers recordhouder voor meeste gespeelde wedstrijden in de Hoofdklasse bij één club.
Meest Waardevolle Speler
In 2003 werd Koenen door de KNBSB uitgeroepen tot Meest Waardevolle Speler in de Hoofdklasse van dat jaar. Hij behaalde toen een slaggemiddelde van .327, scoorde 23 punten en zorgde voor 16 binnengeslagen punten. Ook had hij als derde honkman het laagste foutpercentage met drie fouten. Koenen behaalde met HCAW tweemaal de landstitel, in 1996 en 1998. Ook won hij in het jaar 2000 met de club de Cup Winners Cup. Tijdens dit Europese toernooi werd hij ook gekozen tot Meest Waardevolle Speler.
International
Koenen kwam ook uit voor het nationale team. Op 10 juni 1991 was zijn eerste wedstrijd tegen Taipei, een oefeninterland. Hij behaalde als international tweemaal met het Nederlands team het Europese Kampioenschap, in 1993 en in 2001.
Trainer en andere werkzaamheden
In 2008 was Koenen samen met Roy Berrevoets coach van Heren 1 van HCAW. In het seizoen 2009 deed hij dat samen met Ronald Jaarsma. Op 12 april 2007 werd hij benoemd tot erelid van de vereniging en werd besloten zijn rugnummer uit de roulatie te nemen als eerbetoon. Koenen studeerde bedrijfskunde aan de Hogeschool van Amsterdam van 1991 tot 1995 en is werkzaam als cluster manager bij Capgemini. Op 25 augustus 2009 besloot hij te stoppen met zijn werk voor HCAW als hoofdcoach omdat hij meer tijd met zijn gezin wilde doorbrengen. Hij werd opgevolgd door de Amerikaan Bill Froberg.
Nederlands honkballer
Nederlands honkbalcoach
|
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Arthur Kampela
Website: http://www.kampela.com/
Composer and virtuoso guitar player Kampela is the winner of the 1995 International Guitar Composition Competition (Caracas, Venezuela) and winner of the 1998 Lamarque-Pons Guitar Composition Competition (Montevideo, Uruguay). He has received commissions and awards from the Collegium Novum Zurich 2013, DAAD (Artist-in-Residence Berliner Künstlerprogramm 2012–2013), New York Philharmonic (2009), Koussevitzky Foundation (2007), Fromm Music Foundation (1998), ISCM/World Music Days Stuttgart 2006, Germany, Rio-Arte Foundation, Brazil (1999) and fellowships from the Brazilian Government (CNPq) and Columbia University (1990–1998), among many others. Kampela has broken new ground in two particular ways: first, in his native country he has fused popular and vernacular styles with contemporary textural techniques. His 1988 CD Epopeia e Graça uses popular music forms deconstructing samba, jazz, and musical theater, with new music's resources, creating a true hybrid genre. Second, working with new extended-techniques for acoustic instruments, for instance in his series of Percussion Studies for solo guitar (1989 to the present), Kampela has created an entirely new playing technique extending it to many acoustic instruments. Several doctorate thesis across the globe have been written about Kampela's music and extended-techniques for diverse instruments, principally the ones focusing on his Percussion Studies for guitar (for example, the theses of Graziela Brotz [2003], Paulino de Oliveria Neto [2010], Marlon Titre [2013], Fernando Cury [2006 master's thesis/2014 dissertation], among many other authors.) Some recent compositional commissions/projects are Migro for guitarist and five mobile ensembles, commissioned by the Collegium Novum Zurich for the Tage Für Neue Music Festival, Zurich, Switzerland, with soloist Arthur Kampela and conducted by Jonathan Stockhammer conductor, 14 November 2013; Das Tripas Coração ('From the Guts, heart') for two pianos and two percussion, for the Berlin Piano-Percussion Ensemble, commissioned by the DAAD and the MaerzMusik Festival Berlin, which premiered on 19 March 2014; Ultraschall Festival Berlin with a three-concert retrospective presenting some of his large chamber works (i.e., Antropofagia and "…B…") and the premiere of Máquina do Mundo ('The Machine of the World'), for solo contrabass clarinet played by Theo Nabicht, 18 and 19 January 2013; "...B..." for ten instrumental soloists, video, and electronics, which premiered on 19 July at the Darmstadt Ferienkurse 2012 and was performed by the Linea Ensemble of Strasbourg, Jean-Philippe Wurtz, conductor (Koussevitzky commission); Uma Faca Só Lâmina ('A Knife All Blade'), for string quartet, which premiered in May 2013 with a performance by the Momenta String Quartet at the Americas Society in New York City; As If, trio for guitar accordion and clarinet, commissioned by the Warsaw Autumn Festival 2013 and guitarist Klara Tomljanović; Motets for two guitars, premiered at the Église Saint-Maurice (Cathedral) Reims, France, by the Newman and Oltman Guitar Duo, 2011; Not I for horn solo, horn player's voice, and light, premiered in November 2011 in Freiburg as well as at the Konzerthaus Berlin (May 2012) by Delphine Gauthier-Guiche; MACUNAÍMA, premiered by the New York Philharmonic conducted by Magnus Lindberg in 2009; Elastics II for flutes, guitar and electro-acoustic sounds, and Percussion Study V for viola alla chitarra and electroacoustic sounds, performed at the Museum of Modern Art of Strasbourg, France, by the Linea Ensemble, with Pablo Marquez, guitar/viola, and Mario Carolli, flute(s) (2007); Antropofagia, premiered at the ISCM 2006 (World Music Days) at the Theaterhaus Stuttgart by the Kammerensemble Neue Musik Berlin and Wiek Hijmans, on electric guitar (Fromm Commission). Kampela's works have been performed in South America, Europe, Asia, and the United States. He holds a doctorate in music composition from Columbia University where he studied with Mario Davidowsky and Fred Lerdahl. Previously, he studied with Ursula Mamlok at Manhattan School of Music (1992). He has also received private lessons from British composer Brian Ferneyhough (1993). In Brazil (1986–1988) he studied with the German composer Hans-Joachim Koellreutter. Kampela's writings about his theoretical ideas on Micro-Metric Modulation and on extended-techniques include his 1998 doctoral dissertation Micro-Metric Modulation: New Directions in the Theory of Complex Rhythms, and, more recently, his article "Micro-Metric Rhythms and Noises Emanations from the Stochastic Cloud," which was included in a new book on Xenakis published in November 2012 by Pendragon Press. As a doctoral candidate at the City University of New York, Graziela Bortz based her dissertation ("Rhythm in the Music of Brian Ferneyhough, Michael Finissy and Arthur Kampela: A Guide for Performers," 2003) on Kampela's theory of Micro-Metric Modulation, using it to analyze the rhythmic strata of her subjects' compositions. "Uma Faca Só Lâmina" ('A knife All Blade'), for String Quartet Arthur Kampela on YouTube Arthur Kampela's sound files on Myspace
Description: Played live by the Momenta String Quartet on May 30th 2013 at the Americas Society NYC
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\section{Introduction}
Flavor compounds form the physical basis for a wide range of gustatory and olfactory sensations experienced by humans \cite{fisher2007food}. By interacting with the biological machinery, these compounds evoke a complex perception of taste and odor. Flavor perception is an emergent property of the complex biological system, the complete understanding of which still eludes us \cite{fisher2007food,shepherd2015neuroenology,malnic1999combinatorial,mouritsen2015science,newcomb2013genetics}. While simple associations between molecular properties and perception indicate the chemical basis of flavor \cite{fisher2007food}, such knowledge is mainly heuristics-based and remains unstructured.
\\
Creating a detailed catalog of various aspects of flavor compounds offers an approach leading to a systemic interpretation of flavor sensation. Such a repository, on one side, would have the molecular descriptors enumerating physico-chemical properties of the flavor compounds. On the other side, it would have natural sources (in which these compounds are found), sensory features (such as flavor percepts), mechanisms of synthesis, regulatory status, and applications (such as foods categories in which the compound is utilized), among others. Such a compilation opens up space for asking a variety of data-driven questions. FlavorDB was created to incorporate multidimensional aspects of flavor molecules and represent their molecular features, flavor profiles, and details of natural sources \cite{garg2018flavordb}.
\\
Despite being the most comprehensive repository of flavor compounds, FlavorDB missed out some of the critical details of flavor compounds available in the literature. FlavorDB2 expands the flavor space, thereby providing a significant advancement from FlavorDB. FlavorDB2 is a combination of 'entity space' and 'molecular space' (fig. \ref{flavordb2}) where former provides the entities utilized in food from natural sources and latter shows the molecular and flavor profiles. One of the databases with closely aligned objectives, FooDB(http://foodb.ca), collates molecules from food ingredients. Some of the resources that have attempted to create a data compilation on specific aspects of flavor include Flavornet (Arn and Acree, 1998), BitterDB \cite{wiener2012bitterdb}, SuperSweet \cite{ahmed2010supersweet}, SuperScent \cite{dunkel2009superscent}. Among the other efforts of data compilation are those targeted at nutritional factors (NutriChem), polyphenols (Phenol-Explorer), and the medicinal value of food \cite{scalbert2011databases, rothwell2013phenol, jensen2015nutrichem, neveu2010phenol}. The uniqueness of FlavorDB lies in its extensive coverage of flavor compounds and nutritional information to more accurately convey ingredient's flavor profile.
\\
FlavorDB2 collates information from various sources, including FooDB, Flavornet, SuperSweet, BitterDB, and Fenaroli's Handbook of Flavor Compounds to build a comprehensive and structured repository of flavor molecules. While the number of compounds (25,595), ingredients (936), and ingredient categories (34) remain the same as that in FlavorDB, FlavorDB2 adds depth by adding a wide range of molecular features.
\begin{figure}[!htb]
\includegraphics[width=0.5\textwidth]{fig1_flavordb2.jpg}
\caption{FlavorDB2 provides significantly advanced attributes of flavor compounds and search mechanisms. It presents a comprehensive repository of flavor compounds through a user-friendly interface and interlinked search engines for exploring the flavor universe.}
\label{flavordb2}
\end{figure}
\section{database overview}
The details of expanded content to enrich the characterization of flavor molecules are provided below. We have exhaustively accounted for an array of features of flavor compounds making it as comprehensive as possible through this expansion.
\subsection{Collection and Compilation of New Data}
We sought to compile a detailed profile of each of the naturally occurring synthetic compound comprising of a wide variety of molecular attributes: (i) variety of nomenclatures/IDs, (ii) flavor description, (iii) regulatory status, (iv) taste/aroma threshold values, (v) natural occurrence, (vi) composition, (vii) consumption statistics, (viii) specifications, (ix) reported uses in food categories, and (x) synthesis (see fig. \ref{schema}). These features represent vital attributes of flavor compounds that bring value to the users of the database. Please refer the Figures S1, S2, S3, S4, S5, and S6 in Supplementary data for the statistics of flavor consumption, food category, regulatory status, and their chemical properties.
\begin{figure*}[!htb]
\includegraphics[width=\textwidth]{fig_2.jpg}
\caption{Schematic view of FlavorDB2 highlighting the search and molecular properties of the data. (1) Flavor Molecules Search (A. Common name, B. FEMA Number, C. CAS Number, D. Functional Group, E. Flavor Profile, F. FEMA Flavor Profile, G. Description of the Molecule, H. Regulatory Status, I. Trade Association Guidelines, J. Natural Occurrence, K. Aroma Threshold Values, L. Taste Threshold Values, M. Synthesized by, N. Food Category, O. Range of Molecular Weight, P. Hydrogen bond donors and acceptors, Q. Type of molecules, R. JSME Molecular Editor), (2) Entities/Ingredients Search, (3) Natural Sources Search, (4) Flavor Pairing Search, (5) Advanced Search, (6) Molecular Profile and Chemical Properties (A. Molecular and Flavor Profile, B. Physicochemical Properties, C. Nomenclature, D. Description, E. Regulatory Status, F. Aroma/Taste Threshold values, G. Natural Occurrence, H. Composition, I. ADMET Properties, J. 2D/3D Properties, K. Consumption, L. Specifications, M. Reported Uses, N. Synthesis, O. Physical-Chemical Characteristics), (7) Molecule of the Day.}
\label{schema}
\end{figure*}
\subsection{Molecular Nomenclature/IDs}
One of the issues in dealing with flavor compounds is variation in their nomenclature. A flavor compound could be identified with any of the following nomenclatures/IDs: common name, IUPAC (International Union of Pure and Applied Chemistry), SMILES (Simplified Molecular-Input Line-Entry System), Empirical Formula, CAS (Chemical Abstracts Service) Number, FEMA (Flavor Extract Manufacturers Association) Number, FL (FLAVIS) Number, NAS (National Academy of Sciences) Number, COE (Council of Europe) Number, EINECS (European Inventory of Existing Commercial Substances) Number, or JFCFA (Joint FAO/WHO Expert Committee on Food Additives) Number. Given this redundancy in naming, one of the challenges in the flavor molecular space is to arrive at the right compound given one of its diverse IDs. Hence, we have implemented search for all major molecular IDs used for flavor compounds (in basic and/or advanced search). The nomenclature field also provides a list of synonyms helping further in reducing the ambiguity in the identification of the desired compound.
\subsection{Description}
Beyond a list of flavor descriptors previously made available in FlavorDB, the 'Description' field provides a brief nuanced description of the flavor. For example, for compound allyl hexanoate, reported to be found in pineapple among other ingredients, the description field reads as – 'A colorless liquid with sweet, pineapple-like taste, and fruit-like aroma'.
\subsection{Regulatory Status}
This field provides regulatory/safety details about compounds as per the regulatory bodies such as COE, JECFA, FDA (Food and Drug Administration), IOFI (International Organization of the Flavor Industry), and Trade Association Guidelines. The information includes acceptable quantity/concentration of the compound (in parts per million (ppm), parts per billion (ppb), or mg) and nature identical status, etc. For allyl hexanoate, apart from providing the acceptable level of usage (COE-5ppm; FDA-21; CFR-172.515; JECFA-0-0.13 mg/kg; Trade Association Guidelines-10.749 mg), the field mentions that the compound is of natural origin.
\subsection{Aroma/Taste Threshold Values}
This field provides the information of aroma/taste threshold values at specific concentrations with nuanced details of the taste/aroma. For allyl hexanoate, this field reads as 'Taste attributes at 10 ppm; sweet, juicy, fresh, pineapple, and fruity'.
\subsection{Natural Occurrence}
The natural occurrences field provides details of the natural ingredients/sources in which the compound is reported to be found. For allyl hexanoate, this field reads as 'Developed in a baked potato, mushroom, and pineapple'.
\subsection{Consumption}
This field provides the compound's consumption details in terms of annual (in pounds) and individual consumption (mg/kg/day). The reported annual consumption is 16033.3 lb for allyl hexanoate, whereas the individual consumption is 0.01358 mg/kg/day.
\subsection{Specifications}
This field provides details of the compound such as appearance, solubility, acid value, specific gravity, refractive index, assay, boiling, and melting points. For allyl hexanoate, this field suggests that its appearance is 'colorless to light-yellow'; it is soluble in ethanol; its specific gravity is 0.884-0.890 (25°C), and boiling point is 185°C.
\subsection{Reported Uses}
A compound is used in various food categories (such as Alcoholic Beverages, Hard Candy, Chewing gum, etc.) as a flavoring agent. This field provides the compound's various usage as per FEMA. Allyl hexanoate is reported to be used in alcoholic beverages, gravies, baked goods, hard candy, chewing gum, meat products, frozen dairy, non-alcoholic beverages, gelatins puddings, and soft candy.
\subsection{Synthesis}
A compound is synthesized through a chemical process, either from a natural source or via synthetic mechanisms. This field provides details of the source compound and the process used for its synthesis. Allyl hexanoate is reported to be synthesized by esterification of \textit{n}-caproic acid with allyl alcohol in the presence of concentrated \ce{H2SO4} or naphthalene-$\beta$-sulfonic acid in benzene under a nitrogen blanket.
\section{use cases}
\subsection{Searching Flavor Compounds by Alternative IDs}
FlavorDB2 can be searched for flavor compounds using a wide variety of molecular IDs/nomenclatures namely common name, IUPAC, SMILES, CAS Number, FEMA Number, FL Number, NAS Number, EINECS Number, and JFCFA Number. In the presence of using diverse molecular numbering systems, this enables reaching the desired flavor compounds in the repository.
\subsection{Flavor Compounds Used in Food Category}
One may search the 'food category' to know all compounds associated to a category. For a compound against each category, the usual and maximum concentration at which it is used is also listed. Users can create a compounded query to get the flavor compounds by adding multiple food categories using @ (AND) or ! (OR) operator.
\subsection{Flavor Compounds based on Regulatory Status}
Flavor compounds can be searched based on their IOFI values namely natural, artificial, nature identical, not nature identical, artificial and identical. One can also search based on COE values namely approved, approved in some quantity, used provisionally, unknown. FlavorDB2 will generate the list of flavor molecules based on the input query.
\subsection{Flavor Compound Synthesis}
To identify a flavor compound that involves a given chemical in its synthesis process, one could search by the name(s) of the chemical(s). For example, searching by 'acetic acid' opens a list of flavor compounds involving acetic acid in their synthesis. One can create a compounded query to add more compounds with the help of @ (AND) or ! (OR) operator. The query can be performed not only on compounds but also on chemical processes (such as 'esterification', 'distillation') or similar terms used in the synthesis field.
\section{implementation}
Consistent with FlavorDB, FlavorDB2 database has been designed using MySQL (https://www.mysql.com). Django (https://www.djangoproject.com), a Python web development framework, has been used for webserver development \cite{holovaty2009definitive}. To enhance the functionality of FlavorDB2, jQuery, Bootstrap, D3.js, and Google Charts libraries along with HTML, CSS and Javascript were used. Apache HTTP Server route requests to Django and helps to enable data compression for faster page load times. FlavorDB2 can be viewed in the latest versions of Google Chrome, Firefox, Opera, Internet Explorer, and Microsoft Edge.
\section{conclusion}
Investigation of molecules and components associated with flavor sensation is of keen interest for food pairing \cite{blumenthal2008big} and aroma blending \cite{chambers2013associations}. FlavorDB2 provides the detailed information of flavor molecules using 'entity space' and 'molecular space' which will help in molecular gastronomy, predicting odor from chemical properties, and food pairing applications \cite{keller2017predicting, spence2013touch, this2002molecular}.
In spite of our earnest attempts, FlavorDB2 is an updated and advanced repository of flavor molecules in which several new attributes are added to analyze the flavor compounds from various perspectives. The data of flavor molecules of an ingredient is limited due to the unavailability of the information. These advanced properties simplify the search for flavor molecules.
\section{availability}
The FlavorDB2 database is freely accessible at \url{https://cosylab.iiitd.edu.in/flavordb2/}. Users are not required to register or log in to access any feature available in the database.
\section*{Acknowledgment}
G.B. thanks Indraprastha Institute of Information Technology (IIIT-Delhi) for providing computational facilities and support. G.B. thanks Technology Innovation Hub (TiH) Anubhuti for the research grant. N.G., D.B., N.G., R.T. and A.S. were Summer Research Interns and M.G. is a Research Scholar in Dr. Bagler's lab (Complex Systems Laboratory) at Center for Computational Biology. All research interns are thankful to IIIT-Delhi for the support. M.G. thanks IIIT-Delhi for the fellowship. This research was partially supported by the Infosys Centre for Artificial Intelligence.
\bibliographystyle{IEEEtran}
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- more granular profiling
- added `ApiInfo.getModDirectory` and `LibShapeDraw.debugDump`
## 1.3.1
- added compatibility layer to support other mods that proxy
`Minecraft.mcProfiler`, such as LiteLoader
- implement FML coremod interface to make installation more flexible
- added `AnimatedValue` convenience class
- added methods to make wireframe `GLUShape`s with arbitrary line widths
- primitive types are now serializable
## 1.3
- updated for Minecraft 1.4.5
- improved Trident animation library integration: added animation convenience
methods to `Vector3` and defined the `Animates` interface
- primitive types are now directly comparable: added `equals`, `hashCode`, and
`Vector3.equalsExact` methods
- added `Axis` enum and associated convenience methods to `Vector3` and
`ShapeRotate`
- defined `XrayShape` interface
- added `Shape.onAdd`, `onRemove`, `onPreRender`, and `onPostRender` methods
- `LibShapeDraw.getShapes`, `getEventListeners`, and `Shape.getTransforms` now
return read-only views. All modifications must use `addShape`, `removeShape`,
`clearShapes`, etc.
- many documentation improvements
## 1.2.2
- updated for Minecraft 1.4.4
- improved Trident animation library integration: added animation convenience
methods to `Color` and `ShapeTransform`
## 1.2.1
- updated for Minecraft 1.4.2
- added a section to the profiler so users can see the performance impact of
LibShapeDraw on the shift-F3 debug screen; accessible under
`root.gameRenderer.level.LibShapeDraw`
- a few minor internal changes to better support deobfuscation
- added `Timeline.playLoop(boolean reverse)` convenience method
## 1.2
- updated for Minecraft 1.4
- added update check
- added a few more convenience methods for primitive types
- fixed minor bug with `isVisibleWhenHidingGui` logic
## 1.1
- use a new rendering hook, eliminating graphical glitches near water
- improved Trident animation library integration: built-in interpolators for
types in `libshapedraw.primitive`
- added `getPartialTick` method to `LSDPreRenderEvent` and `MinecraftAccess`
- added many other convenience methods, especially for `Vector3`
- added `mcmod.info` files and a logo for improved ForgeModLoader integration
(Forge is still supported but *not* required)
## 1.0
- initial release for Minecraft 1.3.2
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,968
|
{"url":"http:\/\/www.chegg.com\/homework-help\/questions-and-answers\/if-a-commercial-solar-cell-with-a-maximum-output-of-2-amps-at-05-v-cost-30-what-will-be-th-q3409498","text":"## physics\n\nIf a commercial solar cell with a maximum output of 2 amps at 0.5 V cost $30, what will be the cost of a PV plant per peak kilowatt? ## Answers (3) \u2022 ## You need a Homework Help subscription to view this answer! ### Chegg Homework Help subscribers get: \u2022 Full access to our library of 2 million Q&A posts \u2022 24\/7 help from our community of subject experts \u2022 Fast answers from experts, around the clock Start Free Trial... Your free trial lasts for 7 days. Your subscription will continue for$14.95\/month unless you cancel.\n\nGet homework help","date":"2013-05-25 20:24:42","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\": 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\": 0.5506613254547119, \"perplexity\": 8826.162564637569}, \"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-2013-20\/segments\/1368706298270\/warc\/CC-MAIN-20130516121138-00086-ip-10-60-113-184.ec2.internal.warc.gz\"}"}
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<dt><span class="strong"><a href="../com/asmita/movieTicket/entity/Auditorium.html#addMovieSchedule(com.asmita.movieTicket.entity.impl.ShowInfoImpl)">addMovieSchedule(ShowInfoImpl)</a></span> - Method in interface com.asmita.movieTicket.entity.<a href="../com/asmita/movieTicket/entity/Auditorium.html" title="interface in com.asmita.movieTicket.entity">Auditorium</a></dt>
<dd> </dd>
<dt><span class="strong"><a href="../com/asmita/movieTicket/entity/impl/AuditoriumImpl.html#addMovieSchedule(com.asmita.movieTicket.entity.impl.ShowInfoImpl)">addMovieSchedule(ShowInfoImpl)</a></span> - Method in class com.asmita.movieTicket.entity.impl.<a href="../com/asmita/movieTicket/entity/impl/AuditoriumImpl.html" title="class in com.asmita.movieTicket.entity.impl">AuditoriumImpl</a></dt>
<dd> </dd>
<dt><a href="../com/asmita/movieTicket/entity/Address.html" title="interface in com.asmita.movieTicket.entity"><span class="strong">Address</span></a> - Interface in <a href="../com/asmita/movieTicket/entity/package-summary.html">com.asmita.movieTicket.entity</a></dt>
<dd> </dd>
<dt><a href="../com/asmita/movieTicket/service/AddressService.html" title="interface in com.asmita.movieTicket.service"><span class="strong">AddressService</span></a> - Interface in <a href="../com/asmita/movieTicket/service/package-summary.html">com.asmita.movieTicket.service</a></dt>
<dd> </dd>
<dt><a href="../com/asmita/movieTicket/entity/Auditorium.html" title="interface in com.asmita.movieTicket.entity"><span class="strong">Auditorium</span></a> - Interface in <a href="../com/asmita/movieTicket/entity/package-summary.html">com.asmita.movieTicket.entity</a></dt>
<dd> </dd>
<dt><a href="../com/asmita/movieTicket/entity/impl/AuditoriumImpl.html" title="class in com.asmita.movieTicket.entity.impl"><span class="strong">AuditoriumImpl</span></a> - Class in <a href="../com/asmita/movieTicket/entity/impl/package-summary.html">com.asmita.movieTicket.entity.impl</a></dt>
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<dt><span class="strong"><a href="../com/asmita/movieTicket/entity/impl/AuditoriumImpl.html#AuditoriumImpl()">AuditoriumImpl()</a></span> - Constructor for class com.asmita.movieTicket.entity.impl.<a href="../com/asmita/movieTicket/entity/impl/AuditoriumImpl.html" title="class in com.asmita.movieTicket.entity.impl">AuditoriumImpl</a></dt>
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<dt><a href="../com/asmita/movieTicket/service/AuditoriumService.html" title="interface in com.asmita.movieTicket.service"><span class="strong">AuditoriumService</span></a> - Interface in <a href="../com/asmita/movieTicket/service/package-summary.html">com.asmita.movieTicket.service</a></dt>
<dd> </dd>
<dt><a href="../com/asmita/movieTicket/service/impl/AuditoriumServiceImpl.html" title="class in com.asmita.movieTicket.service.impl"><span class="strong">AuditoriumServiceImpl</span></a> - Class in <a href="../com/asmita/movieTicket/service/impl/package-summary.html">com.asmita.movieTicket.service.impl</a></dt>
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<dt><span class="strong"><a href="../com/asmita/movieTicket/service/impl/AuditoriumServiceImpl.html#AuditoriumServiceImpl(int)">AuditoriumServiceImpl(int)</a></span> - Constructor for class com.asmita.movieTicket.service.impl.<a href="../com/asmita/movieTicket/service/impl/AuditoriumServiceImpl.html" title="class in com.asmita.movieTicket.service.impl">AuditoriumServiceImpl</a></dt>
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{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,767
|
Q: How to determine the version of libc6 to be used with Tensorflow? I am trying to install Tensorflow on a machine that I do not have root access. I have followed all the steps and the installation has been successful. However, when I try to import Tensorflow in Python, I get an error that an old version of libc6 is installed.
I have tried the solution suggested here, but I could only get it to work once and I am not able to use the same solution now.
It looks like there are two versions of libc6 installed on the machine: the first one is /lib64/libc6.so and the other one is /usr/lib/libstdc++-libc6.2-2.so.3. Apparently, TF uses the first one which has an older version of libc6 and returns an error ImportError: /lib64/libc.so.6: version 'GLIBC_2.14' not found.
How can I force TF to use the second library, which is a more recent version of libc6, in order to solve this problem?
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 8,730
|
Q: Launching UWP application as system prior to Windows Login Use Case
Currently I am developing a Windows Login Provider which uses a Windows Universal App (UWP) to be able to capture a selfie using a webcam of the workstation. This use-case consist of two components:
*
*Windows Login Provider:
This component is a COM object that talks with the Windows
ICredentialProvider. This component gives me unlimited
possibilities to interact with an user before logging in. The main
goal is to require additional identification details about the user.
*Webcam UWP:
This is a Windows Universal Application (UWP) which displays a
Live View of the Webcam feed on a laptop, and is able to take picture controlled
by the user. I configured the UWP to start with a Declaritive URI. With this we can start the application using Windows Run.
Goal
The goal of this use-case is to launch the Webcam UWP application the Windows login phase. So when a user is booting its laptop and is prompted for his credentials using my Credential Provider, an additional webcam application is launched to take a portrait photo.
Problem
The main issue where I am running into is that I am not able to start the webcam application during Windows Login screen. During development I can test my Credential Provider with CredUI (The CredUIPromptForWindowsCredentials function creates and displays a configurable dialog box that allows users to supply credential information by using any credential provider installed on the local computer), with this I can test my Credential Provider and also launching the Webcam UWP application. This is working successfully and I want to achieve the same result during Windows Login, but unfortunately it doesn't. I think there are two possibilities that result in a negative outcome:
1. Insufficient Permissions to launch the UWP application during Windows Login
Note: In my CredentialProvider launch my programs with the Process Class:
Process.Start("<application name>");
Windows UWP application code signing consists out of multiple categories. I signed with Visual Studio my UWP application with a self signed certificate. The outcome of this code signing is that my UWP app is signed with SignatureKind: Developer. You can see in below screenshot Powershell GetAppPackage:
Details Custom UWP application
During my testing I found that during Windows Login the UWP is unable to launch. I receive a popup with the following error: "You'll need a new app to open this *** link. My thought process was that maybe my UWP application is not configured correctly. So I tried using the Windows Calculator which has a different SignatureKind: Store, since it is an application you can download from the Windows Store. With Calculator I received the same error.
Digging a bit deeper into this problem I found out about the different Signaturekinds. According to Microsoft only the SignatureKind System has additional capabilities but they are no where to be found. The description of SignatureKind System is:
The package is signed by a certificate that's also used to sign the Windows Operating System. These packages can have additional capabilities not granted to normal apps. For example, the built-in Settings app.
To test this I used Windows Narrator application (which has a SignatureKind with System) to be launched from my Credential Provider. The outcome is my desired goal. Successfully the Windows Narrator Application launched and was reading out loud information during my Windows login session.
2. URI activation not working during Login Session
When looking in Windows Event Viewer I can see the following error.
The description for Event ID 0 from source VSTTExecution cannot be found. Either the component that raises this event is not installed on your local computer or the installation is corrupted. You can install or repair the component on the local computer.
If the event originated on another computer, the display information had to be saved with the event.
The following information was included with the event:
(devenv.exe, PID 16724, Thread 1) IdleProcessorManager.DoWork - Job threw:
Invalid URI: The format of the URI could not be determined. at
at System.Uri.CreateThis(String uri, Boolean dontEscape, UriKind uriKind)
at System.Uri..ctor(String uriString)
at Microsoft.VisualStudio.TestTools.TestCaseManagement.SolutionIntegrationManager.IsRunConfig(String filename)
at Microsoft.VisualStudio.TestTools.TestCaseManagement.SolutionIntegrationManager.<AddSolutionFilesRunConfigsToTmi>d__351.MoveNext()
at Microsoft.VisualStudio.TestTools.TestCaseManagement.IdleProcessorManager.DoWork()
I am ware that UWP application uses OnLaunched & OnActivated functions to start etc. For instance the ActivationKind. I am not familiar with this, so maybe this can be a solution?
Given the above information I hope anyone has experience in solving my problem. The outcome is that I want to be able to launch my custom webcam UWP application during login screen on Windows, just like Windows Narrator. Any help is appreciated!
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,308
|
title: "Other Resources"
linktitle: "Other Resources Overview"
description: "Other resources for Community Pharmacy"
date: 2018-09-01
publishdate: 2018-09-01
lastmod: 2018-09-01
categories: ["support"]
tags: ["resources"]
menu:
docs:
parent: "other-resources"
weight: 1
weight: 70
draft: false
aliases: [/other-resources/]
toc: false
---
# Other Resources
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,886
|
\subsection*{An inversion formula}
{$~~~~~$}For the situation where we have no massless poles, or where we subtract them out, the crossing symmetric amplitude has an expansion
\begin{equation}}\def\ee{\end{equation}
\label{eq:cpqdef}
\mathcal{M}_{0}(s_1,s_2)=\sum_{p, q=0}^{\infty} {\mathcal W}_{p q} x^{p} y^{q}\,,
\ee
with $x=-\left(s_1 s_2 + s_2 s_3+s_3 s_1\right)$, $y=-s_1 s_2 s_3$. Note that $H\left(s_1^{\prime} ; s_1, s_2,s_3\right)=\frac{ x \left(2 s_1'-3a\right)}{x a -x s_1'+s_1^{'3}}\,,$ which can be seen by writing $s_k$'s in terms of $(z,a)$ and identifying $\frac{z^{3}}{\left(z^{3}-1\right)^{2}}=\frac{-x}{27a^2}$. We can now expand \eqref{eq:disper00} in powers of $x, a$
using the s-channel discontinuity which has a partial wave expansion in terms of Gegenbauer polynomials involving {\it even} spins
{\begin{small}
\begin{equation}}\def\ee{\end{equation}\nonumber
\begin{split}
&\mathcal{A}\left(s_1,s_2^{(+)}(s_1,a)\right)=\Phi(s_1)\sum_{\ell=0}^{\infty}\left(2\ell+2\alpha\right)a_\ell(s_1)C^{(\alpha)}_{\ell}\left(\sqrt{\xi(s_1,a)}\right)\,,\\
&\xi(s_1,a)=\xi_0+4\xi_0\left(\frac{a}{s_1-a} \right),~\xi_0=\frac{s_1^2}{(s_1-2\mu/3)^2}
\end{split}
\ee
\end{small}}\\
where $\alpha=\frac{d-3}{2}$, $\Phi(s_1)=\Psi(\alpha)\frac{\sqrt{s_1+\frac{\mu}{3}}}{\left(s_1-\frac{2\mu}{3}\right)^{\alpha}}$ and $\Psi(\alpha)$ is real positive number. Expanding the Gegenbauer polynomials around $\xi=\xi_{0}$,
with $p_{\ell}^{(j)}\left(\xi_{0}\right)=\partial^j C^{(\alpha)}_{\ell}\left(\sqrt{\xi}\right)/{\partial{\xi^j}}{ |}_{\xi=\xi_0},
$ we find the coefficient of $a^m$ leading to an inversion formula
\begin{equation}}\def\ee{\end{equation}
\begin{split}\label{eq:cpqallform}
&{\mathcal{W}}_{n-m,m}=\int_{\frac{2\mu}{3}}^{\infty}\frac{d s_1}{s_1}\Phi(s_1)\sum_{\ell=0}^{\infty}\left(2\ell+2\alpha\right)a_\ell(s_1)\mathcal{B}_{n,m}^{(\ell)}(s_1)\,,\\
&\mathcal{B}_{n,m}^{(\ell)}(s_1)=\sum_{j=0}^{m}\frac{p_{\ell}^{(j)}\left(\xi_{0}\right) \left(4 \xi_{0}\right)^{j}(3 j-m-2n)(-n)_m}{\pi s_1^{2 n+m} j!(m-j)!(-n)_{j+1}}\,,
\end{split}
\ee
for $~n\geq 1$. Note that ${\mathcal{W}}_{0,0}=\alpha_0$.
Eq.\eqref{eq:cpqallform} allows two lines of investigation. {\bf (a)} For $n\geq m$ with $n\geq 1$, we get the coefficients in terms of $a_\ell(s_1)$. Since partial wave unitarity implies $0\leq a_\ell(s_1)\leq 1$, we can find positivity constraints on ${\mathcal{W}}_{n-m,m}$. {\bf (b)} For $n<m$ with $n\geq 1$, the coefficients should vanish, as needed by eq.\eqref{eq:cpqdef}, which give rise to non-trivial constraints on $a_\ell(s_1)$. Notice that since $\ell$ is even, we will need $\ell\geq 2n$. These sum rules or ``null constraints" are instrumental in getting the lower bounds on ${\mathcal{W}}_{n-m,m}$ in EFTs. We will use these sum rules to put a bound on the total cross section at any $s_1$, generalizing the famous Froissart bound. \\
{\bf Constraining QFTs}:
Now from eq \eqref{eq:cpqallform}, we can derive inequalities involving ${\mathcal{W}}_{p,q}$.
We use the unitarity constraints $0\leq a_{\ell}(s_1)\leq 1$ as well as
$C_{\ell-k }^{(\alpha+k)}\left(\frac{2 \mu }{3 \delta }+1\right)\geq 0,$ for $\delta=s_1-\frac{2\mu}{3}\geq 0, ~\alpha\geq 0,~\mu\geq0 \,$. Since the range of $s_1$ in eq.(\ref{eq:cpqallform}) starts at $2\mu/3$, we have introduced $\delta$ as a convenient variable. We have $\sqrt{\xi_0}=\frac{2 \mu }{3 \delta }+1$.
Note that $p_\ell^{(j)}$'s involve derivatives of Gegenbauer. Specifically we find the useful expression
\begin{small}
\begin{equation}}\def\ee{\end{equation}\nonumber
\mathcal{B}^{(\ell)}_{n,m}(s_1)=\sum_{k=0}^{m}\mathfrak{U}^{(\alpha)}_{n,m,k} (-1)^{k+m}C_{\ell-k }^{(\alpha+k)}\left(\frac{2 \mu }{3 \delta }+1\right)\,,
\ee
\end{small}
where \cite{foot3}
\begin{small}
\begin{equation}}\def\ee{\end{equation}\nonumber
\label{eq:Bellnmk}
\mathfrak{U}^{(\alpha)}_{n,m,k}=\sum _{j=k}^m \frac{\sqrt{16 \xi _0}^k (\alpha )_k (m+2 n-3j) \Gamma (n-j) \Gamma (2 j-k)}{s_1^{m+2 n}\Gamma (k) j! (m-j)!(j-k)!(n-m)!}\,,
\ee
\end{small}
is positive for $n\geq m$. Note that in the sum, $(-1)^{k+m}$ spoils the definite sign of $\mathcal{B}^{(\ell)}_{n,m}(s_1)$. We can search for $\chi _n ^{(r,m)}(\mu,\delta)$, such that
\begin{equation}}\def\ee{\end{equation}\nonumber
\label{eq:Bellnmall}
\begin{split}
&\sum_{r=0}^{m}\chi _n ^{(r,m)}(\mu,\delta)\mathcal{B}^{(\ell)}_{n,r}(s_1)=\mathfrak{U}^{(\alpha)}_{n,m,m} C_{\ell-m }^{(\alpha+m)}\left(\frac{2 \mu }{3 \delta }+1\right)\geq 0,
\end{split}
\ee
for $m\leq n$.
A solution is easily found using the following recursion relation:
\begin{equation}}\def\ee{\end{equation}\label{rec}
\begin{split}
&\chi_n^{(r,m)}(\mu,\delta)=\sum_{j=r+1}^m (-1)^{j+r+1}\chi_n^{(j,m)} \frac{\mathfrak{U}^{(\alpha)}_{n,j,r}(\frac{2\mu}{3}+\delta)}{\mathfrak{U}^{(\alpha)}_{n,r,r}(\frac{2\mu}{3}+\delta)}\,, \nonumber
\end{split}
\ee
with $\chi _n ^{(m,m)}(\mu,\delta)=1$. Using the recursion relation, one can check that \cite{exp1} $\chi_n^{(r,m)}>0$, for $n\geq m$. Then eq.(\ref{eq:cpqallform}) leads to \cite{comm1}
\begin{equation}}\def\ee{\end{equation}\label{eq:nonpcpq1}
\begin{split}
\sum_{r=0}^{m}\chi _n ^{(r,m)}(\mu,\delta=0){\mathcal{W}}_{n-r,r}\geq 0,
\end{split}
\ee
which we will refer to as non-perturbative constraints to differentiate from the EFT constraints to be derived next.
In order to derive EFT bounds, we start with eq.\eqref{eq:cpqallform} and write
\begin{small}
\begin{equation}}\def\ee{\end{equation}\label{Weff}
{\mathcal{W}}^{(\delta_0)}_{n-m,m}\equiv\int_{\delta_0+\frac{2\mu}{3}}^{\infty} \frac{d s_1}{s_1}\Phi(s_1)\sum_{\ell=0}^{\infty}\left(2\ell+2\alpha\right)a_\ell(s_1)\mathcal{B}_{n,m}^{(\ell)}(s_1)\,,
\ee
\end{small}
for $~n\geq 1$, which defines for us the Wilson coefficients and are the ${\mathcal{W}}$'s in eq.\eqref{eq:cpqallform} when $\delta_0=0$.
In such cases, we can show that
\begin{equation}}\def\ee{\end{equation}\label{eq:Bellnmall2}
\begin{split}
\sum_{r=0}^{m}\chi _n ^{(r,m)}(\mu,\delta_0)\mathcal{B}^{(\ell)}_{n,r}\left(\delta+\frac{2\mu}{3}\right)\geq 0,
\end{split}
\ee
for $\delta\geq\delta_0$.
This leads to positivity constraints
\begin{equation}}\def\ee{\end{equation}\label{eq:nonpcpq}
\begin{split}
\sum_{r=0}^{m}\chi _n ^{(r,m)}\left(\mu,\delta=\delta_0\right){\mathcal{W}}^{(\delta_0)}_{n-r,r}\geq 0,
\end{split}
\ee
for $~\mu\geq0,~\delta_0\geq 0, ~m\leq n$.
{Since $\mathcal{B}^{(\ell)}_{n,0}\left(\delta+\frac{2\mu}{3}\right)=\frac{2 C_{\ell }^{(\alpha )}\left(\frac{2 \mu }{3 \delta }+1\right)}{\pi \left(\delta +\frac{2 \mu }{3}\right)^{2 n} }$, we have
\begin{equation}}\def\ee{\end{equation}\label{eq:Wn0only}
{\mathcal{W}}_{n,0}^{(\delta_0)}\leq \frac{1}{\left(\delta_0+\frac{2\mu}{3}\right)^2}{\mathcal{W}}_{n-1,0}^{(\delta_0)}\,.
\ee
Our expressions are in agreement with the limited number of cases known in the literature \cite{RMTZ, TWZ,Caron-Huot:2020cmc} except that our derivation is manifestly crossing symmetric from the start and admit a straightforward generalization \cite{known}.
An immediate application of our general formulae is the examination of the $n\gg m$ limit. We find simply
\begin{equation}}\def\ee{\end{equation}
\sum _{r=0}^m ~\frac{n^{m-r}}{ (m-r)!~ \left(\delta _0+\frac{2 \mu }{3}\right)^{m-r}}~\frac{{\mathcal{W}}^{(\delta_0)}_{n-r,r}}{{\mathcal{W}}^{(\delta_0)}_{n,0}}\geq 0\,,
\ee
for $n\gg m$. We have checked that tree level type II string theory, to be discussed below, respects this.\\
{\bf Null constraints: }
To derive lower bounds, we make use of the $n<m$ vanishing conditions arising from eq.(\ref{eq:cpqallform}). In the large $\delta$ limit, we have \cite{foot4}
\begin{equation}}\def\ee{\end{equation}\nonumber
\begin{split}
&\mathcal{B}_{n,m}^{(\ell)}(\delta)=\frac{C_{\ell }^{(\alpha )}(1)}{\pi}~\frac{D^{(n,m)}_{\ell,\alpha}}{\delta^{2n+m}}+\oforder{\frac{\mu}{\delta^{2n+m+1}}}\,,\\
&D^{(n,m)}_{\ell,\alpha}=\sum_{j=0}^{m}\frac{(-4)^j \left(-\frac{\ell }{2}\right)_j \left(\alpha+\frac{\ell }{2}\right)_j}{\left(\alpha +\frac{1}{2}\right)_j} \frac{(3j-m-2n) \Gamma(m-n)}{j! (m-j)! (j-n)!}\,.
\end{split}
\ee
Then in the limit when $\delta_0\gg \mu$ we have \cite{foot5}
\begin{small}
\begin{equation}}\def\ee{\end{equation}\label{eq:largesDell}
\int_{\delta_0}^{\infty} \frac{d s_1}{s_1^{\alpha+1/2}} ~\sum_{\ell=2}^{\infty}\left(2\ell+2\alpha\right)~a_\ell(s_1)~\frac{C_{\ell }^{(\alpha )}(1)}{\pi}~\frac{D^{(n,m)}_{\ell,\alpha}}{s_1^{2n+m}}=0\,.
\ee
\end{small}
{for $m>n,~n\geq 1$.}
For example $m=2,n=1$ gives
$
D^{(1,2)}_{\ell,\alpha}=\frac{2 \ell (\ell+2 \alpha ) (-11-10 \alpha +2 \ell (\ell+2 \alpha ))}{ (2 \alpha +1) (2 \alpha +3) }\,,
$
which was first derived in \cite{TWZ} from fixed-$t$ dispersion relations \cite{foot6}.
Once these null constraints are in place, a judicious use of Cauchy-Schwarz inequality as used in \cite{TWZ}, or a more constraining numerical argument used in \cite{Caron-Huot:2020cmc} can be pursued to derive lower bounds. The existence of such bounds was originally emphasized in \cite{nimayutin}. Our approach gives completely general expressions for the independent null constraints.\\
{\bf Applications: }
We will now consider two applications. The first application will make use of the $n\geq m$ constraints while the second will use the $n<m$ constraints arising from eq.(\ref{eq:cpqallform}).
{\it Tree level type II superstring theory:}
The four dilaton type II superstring tree amplitude is given by \cite{green}
$$
\mathcal{M}(s_1,s_2)=-\frac{\Gamma \left(-s_1\right) \Gamma \left(-s_2\right) \Gamma \left(s_1+s_2\right)}{\Gamma \left(s_1+1\right) \Gamma \left(-s_1-s_2+1\right) \Gamma \left(s_2+1\right)}\,.
$$
We consider the amplitude $\mathcal{M}^{(cl)}$ obtained after subtracting out the massless pole $-\frac{1}{s_1 s_2 (s_1+s_2)}$.
We can easily compute the ${\mathcal{W}}_{p,q}$, for example \cite{green},
$
{\mathcal{W}}_{0,0}= 2 \zeta (3),~{\mathcal{W}}_{0,1}= -2 \zeta (3)^2,~{\mathcal{W}}_{0,2}= \frac{2}{3} \left(2 \zeta (3)^3+\zeta (9)\right)\,,
$
${\mathcal{W}}_{1,0}= 2 \zeta (5),~{\mathcal{W}}_{1,1}= -4 \zeta (3) \zeta (5)$. Suppose we are given the first few terms in the derivative expansion. Then, can we say where the first massive string pole would occur? More precisely in eq.(\ref{Weff}), what is the maximum $\delta_0$ we can use? Using the methods in this paper, we can address this question.
From $m=1,n=1$ (6 derivatives) condition \eqref{eq:nonpcpq} ($\mu=0$) gives us $ \frac{3 \zeta (5)}{\delta _0}-2 \zeta (3)^2>0$, which implies $\delta_0<1.07644$. Similarly from other conditions, we can show that $\delta_0<\delta_0^{(\max)}$.
\begin{figure}[hbt!]
\centering\includegraphics[width=0.42\textwidth]{type2stringm12345}
\caption{$\delta_0^{(\max)}$ vs $2(2n+m)$, the derivative order, for $m=1,2,3,4,5$. }
\label{fig:type2string}
\end{figure}
In figure \eqref{fig:type2string}, we have shown that for higher constraints \cite{foot7}, the $\delta_0^{(\max)}$ converges towards $1$, which is exactly the location of the first massive pole!
{\it Bound on total scattering cross-section:}
Now, we will exploit the null constraints arising from $m>n$ in \eqref{eq:cpqallform} to bound total scattering cross-sections. We will be in $d=4$ or $\alpha=1/2$ and we will use the standard notation $s=s_1+4/3$ with $\mu=4$. The null constraints read
\begin{equation}}\def\ee{\end{equation}\label{sum00}
\int_{4}^{\infty}\frac{ds}{s-\frac{4}{3}} \Phi(s) \sum_{\ell=2 n}^{\infty}(2 \ell+1) a_{\ell}(s) {\mathcal B}_{m,n}^{(\ell)}(s-\frac{4}{3})=0,
\ee
where $\Phi(s)=\sqrt{\frac{s}{s-4}}$.
for $m>n ,~ n \geq 1$.
For $m+n\leq \ell,~m>n,~n\geq 1$ we can verify that ${\mathcal B}_{m,n}^{(\ell)}(s-\frac{4}{3})\geq 0$. Then we can write \eqref{sum00} as
\begin{equation}}\def\ee{\end{equation}\label{sum01}
\begin{split}
\int_{4}^{\infty}\frac{ds}{s-\frac{4}{3}} \Phi(s)\sum_{\ell=2 n}^{L_{max}} (2\ell+1)a_{\ell}(s) {\mathcal B}_{m,n}^{(\ell)}(s-\frac{4}{3})\leq 0 \,,
\end{split}
\ee
for $ m+n \leq L_
{max},~ m>n,~n\geq 1$.
We have placed the contributions arising from $\ell\geq L_{max}+2$ on the right which gives the inequality.
From unitarity, we know that $0 \leq a_{\ell}(s)\leq 1$. The inequalities \eqref{sum01} impose further conditions on the $a_{\ell}(s)$. We convert the integral over $s$ in \eqref{sum01} as a sum by defining $s(k)=4+k \frac{(s_{max}-4)}{N_{max}}$.
Using the constraints \eqref{sum01}, we want to bound the total scattering cross section $\sigma(s)$ \cite{foot8}
\begin{equation}}\def\ee{\end{equation}
\sigma(s)=\frac{16 \pi}{s-4}\sum_{\ell=0}^{\infty}(2\ell+1)a_{\ell}(s)\approx \frac{16 \pi}{s-4}\sum_{\ell=0}^{L_{max}}(2\ell+1)a_{\ell}(s) \,.
\ee
We maximize the value of
$
\frac{s-4}{16\pi} \times \sigma(s)=\bar{\sigma}= \sum_{\ell=0}^{L_{max}}(2\ell+1)a_{\ell}(s)
$.
\begin{figure}[hbt!]
\centering\includegraphics[width=0.4\textwidth]{Lmax364660}
\caption{The bound on $\bar{\sigma}(s)$ using constraints \eqref{sum01} with $L_{max}=36, 46,60$. The black dashed line is the Froissart bound on $\bar{\sigma}$. The red line is maximum $\bar{\sigma}$ obtained using the pion bootstrap in \cite{ABPHAS}. }
\label{fig:Lmax36smax90Nmax480}
\end{figure}
The bound is shown in figure \eqref{fig:Lmax36smax90Nmax480} for various \cite{foot9} $L_{\max}=36,46,60$. A fit with $\bar{\sigma}_0 \times s \log^2\left(\frac{s}{s_0}\right)$ can be found. The $L_{\max}=36$ gives fit values $\bar{\sigma}_0=0.29,s_0=0.128$, similarly $L_{\max}=60$ gives fit values $\bar{\sigma}_0=0.22,s_0=0.066$. The convergence with the spin sum is suggested by the figure but appears to be slow for higher values of $s$.
Also it is clear that the $\bar{\sigma}$ found using a typical S-matrix living on the boundary of the so-called river arising from the S-matrix bootstrap \cite{ABPHAS} or even the lake boundary in \cite{andrea}, is far below the numerical bound presented.
Note that Froissart bound \cite{foot10} \textit{i.e.,} $\bar{\sigma}\lesssim \frac{s}{16}~\log^2(s/s_0)$ (which is not valid for lower value of $s$ we are considering) is below the numerical bound. The main utility of our numerical bound is that it is valid for {\it any} $s\geq 4$ unlike the Froissart bound which is valid for $s\gg 4$. It will be fascinating to derive analytic bounds using the present method and see if a stronger than Froissart bound is possible at higher energies. In existing derivations of the Froissart bound, the role of crossing symmetry has not been explored. We derive a simple analytic bound in the supplementary material. \\
{\bf Feynman Block expansion of amplitude: }
We will now address how the structure of the Feynman diagram expansion emerges from our analysis.
Given the partial wave expansion of the s-channel discontinuity, we can write the amplitude as
\begin{small}
\begin{equation}}\def\ee{\end{equation}
\label{eq:Dyson2}
\begin{split}
&\mathcal{M}(s_1, s_2)=\alpha_{0}+\frac{1}{\pi} \int_{\frac{2\mu}{3}}^{\infty}\sum_{\ell=0}^{\infty} \frac{d \sigma}{\sigma}H\left(\sigma ;s_1, s_2, s_3\right)\\
&\left( \Phi(\sigma;\alpha)\left(2\ell+2\alpha\right)~\frac{a_\ell(\sigma)}{\left(\sigma-\frac{2\mu}{3}\right)^\ell}~Q_\ell(\sigma;s_2^{(+)}(\sigma,a))\right)\,,
\end{split}
\ee
\end{small}
where $
Q_{\ell}(s_1,s_2)=\left(s_1-\frac{2\mu}{3}\right)^\ell C^{(\alpha)}_{\ell}\left(1+2\frac{s_2+\frac{\mu}{3}}{s_1-\frac{2\mu}{3}}\right)\,.$ Let us refer to $H Q_\ell$ as the Dyson block--note that this block has non-local negative powers of $x$ which should cancel on using the null constraints. A natural way to proceed would be to use a basis which has these spurious negative powers of $x$ removed at the onset. This leads us to define the Feynman block:
\begin{equation}}\def\ee{\end{equation}
M^F_{\ell}(\sigma;s_1, s_2)=\sum_{i=1}^{3}M_{\ell}^{(i)}(\sigma;s_1, s_2)+M_\ell^{(c)}(\sigma;s_1,s_2)\,,\nonumber
\ee
where, s-channel part of the Feynman block is
\begin{equation}}\def\ee{\end{equation}\nonumber
M_{\ell}^{(1)}(\sigma;s_1, s_2)=Q_{\ell}(s_1, s_2)\left(\frac{1}{{\sigma-s_1}}-\frac{1}{\sigma}
\right)\, .
\ee
The $t,u$-channel are given by
$M_{\ell}^{(2)}(\sigma;s_1, s_2)=M_{ \ell}^{(1)}(\sigma;s_2, s_3)$,
$M_{\ell}^{(3)}(\sigma;s_1, s_2)=M_{ \ell}^{(1)}(\sigma;s_3, s_1)$. $M_{\ell}^{(c)}(\sigma;s_1, s_2)$ are contact terms involving polynomials of $s_i$'s. To find this write
\begin{equation}}\def\ee{\end{equation}\nonumber
\mathcal{D}_{\ell}(\sigma)=\frac{1}{\sigma}Q_{\ell}(\sigma,s_2^{(+)})H(\sigma;s_1,s_2,s_3)-\sum_{i=1}^{3}M_{\ell}^{(i)}(\sigma;s_1, s_2)\,.
\ee
For example
$
\mathcal{D}_{\ell=2}(\sigma)=\frac{x~ b_{0,2}^{(2)}}{a-\sigma}+\frac{x~ (b_{0,2}^{(2)}+2 b_{2,0}^{(2)})}{\sigma}
=\frac{2 x~ b_{2,0}^{(2)}}{\sigma}-\frac{y~ b_{0,2}^{(2)}}{ (\sigma)^2}-\left(x~b_{0,2}^{(2)}\right)\sum_{n=2}^{\infty}a^n (\sigma)^{-n-1}\,,$
where $b_{n,m}^{(\ell)}=\frac{1}{n!m!}\partial_{s_1}^{n}\partial_{s_2}^{m}\left[Q_{\ell}(s_1,s_2)\right]$. We throw away negative powers in $x$ (non-local terms), which gives
\begin{equation}}\def\ee{\end{equation}
M_{\ell=2}^{(c)}(\sigma;s_1, s_2)=\frac{2 x~ b_{2,0}^{(2)}}{\sigma}-\frac{y~ b_{0,2}^{(2)}}{ \sigma^2}\,,
\ee
which is the polynomial form of the contact term.
This can be repeated for any $\ell$. In general, we can write the Feynman block expansion of an amplitude
\begin{equation}}\def\ee{\end{equation}
\label{eq:Feynman}
\begin{split}
&\mathcal{M}(s_1, s_2)=\alpha_{0}+\frac{1}{\pi} \sum_{\ell=0}^{\infty}\int_{\frac{2\mu}{3}}^{\infty} \frac{d \sigma}{\left(\sigma-\frac{2\mu}{3}\right)^\ell}\\&\times \Big( \Phi(\sigma;\alpha)\left(2\ell+2\alpha\right)~a_\ell(\sigma)~M^F_\ell(\sigma;s_1,s_2)\Big)\,,
\end{split}
\ee
{This demonstrates how the structure of the Feynman diagram expansion, involving exchanges and contact diagrams, emerges from the dispersion relation. Eq. \eqref{eq:Dyson2} converges for $-6.71\mu<a<2\mu/3$ \cite{AK}. Thus, expanding \eqref{eq:Dyson2} around $a=0$ gives a convergent representation in $a^n x^m$ powers. The difference between \eqref{eq:Feynman} and \eqref{eq:Dyson2} are the terms $m<n$ in the latter. Removing these will leave us with a convergent representation \eqref{eq:Feynman} around $a=0$--see supplementary material for further checks.}
\\
{\bf Discussion: }
The crossing symmetric dispersion relation approach, presented in this paper, promises to open up a new and efficient way to study field theories. We saw how the picture of Feynman diagrams emerges from the crossing symmetric approach; seeing this using the fixed-$t$ dispersion relation is impossible as crossing symmetry is imposed as a constraint. It will be very interesting to connect the ideas and techniques in this paper with the ``EFT-hedron'' picture in \cite{huang}. Another place where we expect these crossing symmetric dispersion relations to play an important role \cite{dualus} is the formulation of the dual S-matrix bootstrap in higher dimensions. So far, an explicit attempt has only been made in 2 dimensions \cite{dual}.
On the CFT side, we have shown in \cite{GSZ} how the manifestly crossing symmetric method extended to CFT Mellin amplitudes leads to the sum rule constraints arising from the two-channel dispersion relation presented in \cite{joaopaper},\cite{joaopaper2}. Furthermore, the CFT generalized null constraints admit a straightforward derivation and are needed to show the equivalence. This suggests that the manifestly crossing symmetric dispersion relation will not only be more systematic but will have more constraints than what is easily derivable in the two-channel symmetric approach.
\section*{Acknowledgments}
We thank Parijat Dey, Kausik Ghosh, Parthiv Haldar and Apratim Kaviraj for useful discussions. Special thanks to Andrew Tolley for comments on the draft and to Yu-tin Huang for comments on the draft and sharing \cite{huang}. We especially thank Rajesh Gopakumar for numerous discussions and encouragement for this work, comments on the draft, as well as for ongoing collaboration in \cite{GSZ}.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 1,688
|
using Foundation;
using System;
using System.CodeDom.Compiler;
using UIKit;
namespace MyHealth.Client.iOS
{
[Register ("UserView")]
partial class UserView
{
[Outlet]
UIKit.UILabel ageBirth { get; set; }
[Outlet]
UIKit.UILabel bloodGroupLabel { get; set; }
[Outlet]
UIKit.UIView contentView { get; set; }
[Outlet]
UIKit.UILabel genreLabel { get; set; }
[Outlet]
UIKit.UILabel heightLabel { get; set; }
[Outlet]
UIKit.UILabel idLabel { get; set; }
[Outlet]
UIKit.UILabel nameLabel { get; set; }
[Outlet]
UIKit.UIView userFrameView { get; set; }
[Outlet]
UIKit.UIImageView userImageView { get; set; }
[Outlet]
UIKit.UILabel weightLabel { get; set; }
[Outlet]
UIButton btnUserLogin { get; set; }
void ReleaseDesignerOutlets ()
{
if (ageBirth != null) {
ageBirth.Dispose ();
ageBirth = null;
}
if (bloodGroupLabel != null) {
bloodGroupLabel.Dispose ();
bloodGroupLabel = null;
}
if (contentView != null) {
contentView.Dispose ();
contentView = null;
}
if (genreLabel != null) {
genreLabel.Dispose ();
genreLabel = null;
}
if (heightLabel != null) {
heightLabel.Dispose ();
heightLabel = null;
}
if (idLabel != null) {
idLabel.Dispose ();
idLabel = null;
}
if (nameLabel != null) {
nameLabel.Dispose ();
nameLabel = null;
}
if (userFrameView != null) {
userFrameView.Dispose ();
userFrameView = null;
}
if (userImageView != null) {
userImageView.Dispose ();
userImageView = null;
}
if (weightLabel != null) {
weightLabel.Dispose ();
weightLabel = null;
}
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,712
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Franck Fabry Named Vice President of U.S. Sales at Williams Sound
Eden Prairie, Minn. – Williams Sound, global designer and manufacturer of wireless communication technology, is pleased to announce the appointment of Franck Fabry to the new position of Vice President of U.S. Sales.
Fabry brings 20-plus years of sales and sales management experience in multiple industries, including the audio-visual marketplace. He brings extensive expertise developing and managing cross-functional and multinational sales teams, including direct sales staffs, manufacturers' representative networks, distribution channels and technical support personnel.
Prior to joining Williams Sound, Fabry served as Vice President, Central Region Sales for Bosch Security Systems Inc. (previously Telex Communications Inc.), a manufacturer of audio, video, intrusion and access systems headquartered in Fairport, NY. Prior to that, he held the positions of Director, Americas Export Sales, and Manager, Middle East and Africa Sales, for Telex Communications.
"Williams Sound is pleased and excited to add Franck to our Management Team," said Paul Ingebrigtsen, President and CEO of Williams Sound. "His depth of industry knowledge and experience will help drive our future sales success."
Adds Fabry, "I'm fortunate and excited to be associated with Williams Sound, one of the most reputable manufacturers of professional communication technology. I'm really looking forward to this new opportunity and feel Williams Sound is well positioned for unprecedented growth. My goal is to bring passion, leadership and hard work to further expand Williams Sound's presence in the U.S. market."
Williams Sound is a global designer and manufacturer of wireless communication technology, serving personal and professional listening needs worldwide for more than 35 years. Williams Sound offers products and service for such commercial markets as hearing assistance, language interpretation, tour, corporate, education, government and house of worship. These products include the Digi-Wave™ Digital Communication Systems, Personal PA® FM Listening Systems, Portable Hearing Assistance Tour Guide Systems, SoundPlus® Infrared Systems and Hearing Helper® FM Listening Systems.
Williams AV Launches WAV Pro Wi-Fi Receiver as Dedicated Assistive Listening Device
Norhisham (Nori) Iskhandar Named as International Technical Sales Manager
Williams AV Announces Pro AV Training Sessions for Fall 2022
WaveCAST and FM+ Products Now Integrates with Third-Party Room Controllers
Per Danzl Named New Vice President of Engineering at Williams AV
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 5,763
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Söll is a well-known ski resort 10km south of Kufstein. Once a favourite of boozy, raucous visitors in the 1980s, the resort has successfully reinvented itself and is now a family-oriented place with myriad outdoor activities.
The highest skiing area overlooking the resort is Hohe Salve at 1828m.
Ready to go? Get to the heart of Söll with one of Lonely Planet's in-depth, award-winning guidebooks.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,668
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{"url":"https:\/\/control.com\/forums\/threads\/24vac-to-24vdc.3695\/","text":"# 24vac to 24vdc\n\nA\n\n#### Aaron\n\nI need to power a 24vdc fan that draws 80ma and 2W. I have a 24vac supply. What is the best way to rectify it?\n\nL\n\n#### Larry Decker\n\nUse a bridge rectifier. They are cheap and available at any electronics store, even Radio Shack.\n\nC\n\n#### Claus Moos\n\nYoy need a bridge rectifier, 1000\u00b5F cap. and a LM317 regulator.\n\nTry http:\/\/www.national.com\/ds\/LM\/LM117.pdf\n\nIf you dont use the LM317, you will get app 30V (24 * sqrt(2)).\n\nKind regards Claus Moos\n\nS\n\n#### Steven Shepard\n\nYou need to solarize the power system for this DC device and take it off the electric grid completely. Solar would be a more economical and reliable means of powering any DC electrical load.\n\nFor your application all you need are:\n2 each 12VDC, 500mA solar modules (to acheive 24VDC operation $94.95 each. 1 each 6 Amp\/hour battery$30.00\n1 each 24VDC charge controller $183.00 Add some wire and misc. hardware and your done. The solar modules will last about twenty years or more. So will the electronics. The battery will have to be replaced every three to five years. It really is too simple not to do. You install this power system and you can almost forget about it. Most certainly it is a one time electric bill to power your DC device instead of paying to power it every month for the rest of your life. SBT Designs 25840 IH-10 West #1 Boerne, Texas 78006 210-698-7109 FAX: 210-698-7147 www.sbtdesigns.com Please note we are moving our email address to [email protected]. Please update our information in your records. R #### Ramer-1, Carl I, too, am a solar enthusiast, but this particular application (at least with so little information provided) hardly sounds like a candidate for solarization. The initial dollar budget doesn't include proper brackets for the modules and a reasonable cost for the labor involved. Assuming the omitted items to be worth about$100, the initial cost would be about $500. Depending on whether you use the 2 watt or the 80 milliamp figure, the load for the fan would be 2 watts x 24 hours=48 watt-hours per day running continuously. That's less than 1.5 kilowatt hours per month. Even if grid power was 25 cents per kilowatt hour, the break even point for the initial cost would be somewhere near 2000 months. It's safe to assume that during the first 166 years of operation the system would need repairs so the payback period would be extended. A simple full wave rectifier, bought or made with a few dollars worth of diodes from Radio Shack will convert the 24 VAC to clean enough and close enough DC for the fan. Even assuming a very inefficient conversion process, the return is short order. Don't forget the K.I.S.S. principle. Carl Ramer Controls & Protective Systems Design Space Gateway Support, Inc. Kennedy Space Center K #### Kelly, Rick Hello... Please tell me you are joking here... Aaron stated, in his message, that he wanted to run a 24 Vdc 2 watt fan. That sure sounds like a small PC case fan to me. You suggested a solar option to save money... lets look at the dollars involved here. SS> For your application all you need are: SS> 2 each 12VDC, 500mA solar modules (to acheive 24VDC operation$94.95 each.\nSS> 1 each 6 Amp\/hour battery $30.00 SS> 1 each 24VDC charge controller$183.00\n\nYour proposed solution has a cost of (94.95 x 2) = 189.90 + 30.00 + 183.00 = \\$ 402.90.\n\nThe fan in question pulls a whopping 2 watts from the power supply. Lets assume that it is the worst power supply in the world and it actually pulls 2.5 watts from the wall due to losses. So... at 2.5 watts it would take us 400 hours of run time to consume 1 KWh.\n\nWhere I live... we pay, on average, 8 cents per each KWh consumed. So... we can pay for (402.90 \/ .08 = 5036) 5036 KWh with our money.\n\nAs we saw before... it takes us 400 hours to consume 1 KWh so we can pay for 2014400 (400 x 5036) run time hours. 2014400 hours is (2014400 \/ 24) 83933 days or (83933 \/ 365) 229 years. I bet the fan in question won't last any longer then 5 years.\n\nSomeone please check my math... So does the solar solution make sense... not to me.\n\nBest Regards...\n\nRick Kelly\n\nChief Electrical Technician\nNatural Cuts, Cheese Operations\n\n[email\u00a0protected]\n(613) 537-8069 (V)\n(613) 537-8044 (F)\n\nJ\n\n#### johan bengtsson\n\nWell, 4 diodes and a capacitor. Since you need much less than 1A you can take almost any diode you find since most of them is 1A or bigger (I usually use 1N4002, but it doesn't really\nmatter) The capacitor could be any with enough capacitance and voltage, I would suggest at least some 220uF (80mA discharges this approx 3V in 1\/2\nperiod at 50Hz, very much rounded value) bigger capacitor is ok, more than 2200uF would never be needed in this application.\n\nThis gives you a voltage somewhat higher than you might want to. I think the fan will accept this quite happily (it will go a little bit faster than\nexpected). If you really want to give it more exacly 24V put in a 7824 or similar circuit. If you select this way you should have the capacitor to be around 1000uF - 2200uF otherwise the IC might not work good enough. Preferably a capacitor at approx 1uF at the output from the IC too.\n\n\/Johan Bengtsson\n\n----------------------------------------\nP&L, Innovation in training\nBox 252, S-281 23 H{ssleholm SWEDEN\nTel: +46 451 49 460, Fax: +46 451 89 833\nE-mail: [email\u00a0protected]\nInternet: http:\/\/www.pol.se\/\n----------------------------------------\n\nS\n\n#### Steven Shepard\n\nNo, it is not a joke.\n\nYou guys are not even considering the savings that a power system like this would provide your companies. The application discussed is a place to start solarizing the operation of any facility. And I am referring to long term\noperation that is truly more reliable than what you are receiving from the utility at this time.\n\nI am referring to 99.9% reliable power. You have no power system at this time with that kind of capability. Your utility cannot make that claim.\nUtility power goes out all the time for maintenance and repairs due to storms. I am referring to long term operation. In order of twenty years or more of capability and performance. I am referring to energy independence that no utility would bother to offer you. With solar you become your own\npower producer. I am referring to clean power that does not pollute, does not make noise, does not endanger your working environment at all.\n\nSo justify converting utility AC power to DC power and then paying for that power over and over and over again every month, every year. Your not buying power, you are just borrowing it. Justify all the hardware required to make\nthat conversion. Justify the wasted power in the effort. Justify the dirty AC power received. Then justify subsidizing a energy source and utility energy provider whose only purpose in life is to take your money. Your claim makes no sense.\n\nThe simple justification for solar is, after you pay for your hardware the power source is free today, free tomorrow, free next year and you can\nabsolutely bank that the Sun is going to rise. It is clean. It is the right thing to do once you start thinking long term and cease being a short sighted consumer.\n\nSBT Designs\n25840 IH-10 West #1\nBoerne, Texas 78006\n210-698-7109\nFAX: 210-698-7147\nwww.sbtdesigns.com\n\nM\n\n#### Michael Griffin\n\nYou can get full bridge rectifiers in a single 4 pin package which will mount to a panel quite nicely. This is much easier to mount than 4\nindividual diodes would be. We've used them to supply DC to large contactor coils (this is sometimes referred to as an \"economy DC circuit\"). I don't have a part number handy, but you should be able to find what you need in\nwhatever your local equivalent of an Electrosonic catalogue is.\n\nI might also be inclined to dispense with the capacitor suggested by Mr. Bengtsson. Filtering is always nice, but I doubt that the motor will mind the ripple. The core losses would be slightly higher, but this is probably not significant compared to the existing losses in a such a small motor. Of course if Mr. Bengtsson had a particular reason to suggest the capacitor, you would be better off listening to him, rather than me on this matter.\n\n**********************\nMichael Griffin\n[email\u00a0protected]\n**********************\n\nD\n\n#### Dean Reimer\n\nHi Steven,\n\nI think we all appreciate that your heart is in the right place, but for most industrial users I think solar power on a small, local scale, is impractical.\n\nSure, you can use solar to cleanly and perpetually power all the 24VDC fans on your desktop computers, but at my plant it is not the desktop computers that are critical to plant operation. We have thousands of horsepower worth of AC motors operating at 600VAC. How am I going to run all these on solar power, especially in Vancouver, BC where it is overcast 8 months of the year? Who cares if all my computers work in a power outage when the plant is down and we aren't producing our product?\n\nI think solar power has great potential in residential or office type environments, but Rick Kelly's argument was right on - from a pure cost\nperspective there is absolutely no payback. You would have to justify the expense based on environmental considerations and the uninterruptible nature of the power source (especially valid for a computer data centre for example).\n\nCheers,\n\nDean Reimer\nBPB Westroc Inc.\n\nR\n\n#### Rick Kelly\n\nSteven...\n\nThis is shaping up to be an interesting discussion. However as it is not directly tied to the interests of the list, I will respond to your last message via e-mail instead of through the list.\n\nOhh... if anyone else wants to partake in this thread... send me a message and I will CC you on my response to Steven.\n\nBest Regards...\n\nRick Kelly\n\nChief Electrical Technician\nNatural Cuts, Cheese Operations\n\n[email\u00a0protected]\n(613) 537-8069 (V)\n(613) 537-8044 (F)\n\nA\n\nHi Aaron:\nFirstable I think the power for your surge of 24 Vac is appropiate. (You don't ask about it).\nThen your Surge is not appropriated for 24 Vdc under a light calculation, it is for 33 Vdc when You use a full wave rectifier with capacitor. For 24 Vdc, better 25 Vdc (over the nominal requirement in this case), we need a source of 17,7 Vac with the following calculation: Vef=0,707 Vmax for a senoidal wave rectifier where in our Case the measured V is Vef.(17,7 Vac)\nand Vmax is 25 V. For this reason You must down your source Voltage of 24 Vac to 17,7 Vac with accoupling a trafo or use at the output of the DC (after a 4 diodes Bridge and a Capacitor, under suggest of Mr .Bengtsson and Mr. Carl Ramer ) a, Voltage Regulator chip to 24-25 Vdc.\n\nI hope it helps You.\n\nE-Mail:[email\u00a0protected]\n\nJ\n\n#### Johan Bengtsson\n\nWell, whatever...\n\n\/Johan Bengtsson\n\n----------------------------------------\nP&L, Innovation in training\nBox 252, S-281 23 H{ssleholm SWEDEN\nTel: +46 451 49 460, Fax: +46 451 89 833\nE-mail: [email\u00a0protected]\nInternet: http:\/\/www.pol.se\/\n----------------------------------------\n\nS\n\n#### Steven Shepard\n\nTroll this.\n\nWith a thanks and a nod to Steve Spence, this is contributing material from the book I am working on. Hope for publication by the end of this year.\n\nTop twenty reason for using solar:\n\nReason #1 - Solar is the \"IDEAL\" source of energy simple because it is delivered free to your home, business, plant, work place, etc. each and every day. It comes in many varieties that seem to suit your particular local in the form of wind, sun, water, bio gas, wood, etc. and of course you can mix and match systems to again suit your particular energy needs.\n\nReason # 2 : There are NO costs associated with \"delivery \" of solar energy to your site, unlike fossil fuels which require transmission lines, open mining, blasting, digging, strip mining, laying power lines, transport, and\nfinally conversion all of which cause BILLIONS of tons of pollution worldwide in doing all this busy work. Solar energy is delivered RIGHT to\nyour \"front door\" and causes NO pollution in the delivery of the energy course.\n\nReason # 3: Solar energy is generated from the most awesome nuclear power plant in the universe - our star called the SUN. Fortunately the Sun\nrequires NO maintenance at this time and is not schedule for any blackouts for the next few billion years.. Sorry engineers, we cannot touch it or tweak it!\n\nReason # 4: Once installed PROPERLY and CORRECTLY, solar energy collectors virtually require NO upkeep and VERY LITTLE maintenance compared to a system that uses fossil fuels to generate electricity or produce hot water. I can\nunderstand installation ignorance being a challenge for some users of this group.\n\nReason # 5: Solar requires ABSOLUTELY NO FUEL TO BUY FROM ANYONE to produce the energy (electricity or thermal energy) on site once a suitable collector is installed on site.\n\nReason #6: Once the collector is purchased and up and operating the collectors product ABSOLUTELY NO EMISSIONS as do ALL fossil fuel sources and\nnuclear reactors, breeders or otherwise.\n\nReason #7: Solar energy gives you piece of mind NO fossil fuel source can ever give you. That is an intangible , but none the less - VERY valuable. It is controlled by NO one. It is mostly free of politics and cartels at this point in time. Even better, management and marketing cannot get their hands on the source and artificially limit and control the supply.\n\nReason #8: IT requires NO military presence and thus we could be using the money spent on \"protecting or vital interests\" for other more important things on this planet. Like making the automation industry much more substantial in this country.\n\nReason #9: Once the solar energy device is turned on it GIVES YOU BACK YOUR INVESTMENT day in and day out over its lifetime. That can NEVER be said for ANY fossil fuel generating system. The cost to decommission a nuclear power plant alone is in the BILLIONS of dollars. Guess what? The cost to\nremove a solar hot water heater is minimal and all the glass, copper and aluminum can be recycled very easy.\n\nReason #10: Solar energy once paid for is virtually FREE!\n\nReason #11: As the price of fossil fuels increase the \"payback\" of a solar energy system decreases.\n\nReason #12: The saving you get from a solar energy system by displacement of fossil fuel energy are TAX free.\n\nReason #13: You can bank the energy savings (caused by NOT buying fossil fuel energy) and let it compound and at the end of its useful life one can more than purchase another system or take a well deserved vacation! One CANNOT do this with a fossil fuel generating system as it COST you money to :feed\" it day in and day out!\n\nReason #14: Solar energy systems can be deployed in the field RAPIDLY, unlike fossil fuel plans or nuclear plants which take YEARS from start to\nfinish simply because of their complexity.\n\nReason #15: Solar energy is ideal because the technology is not overly complicated and can be installed and deployed by most people with minimal\neducation. (Excluding skeptical engineers and technicians.)\n\nReason #16: Solar energy DISPLACES a fossil fuel energy source, so when and if a blackout comes to your area guess what? YOU will have hot water or\nelectricity when your neighbors may not!\n\nReason #17: Solar thermal energy is a great match for DHW and radiant floor heating and cooling. With fossil fuel energy sources such as baseboard heat, steam heat, or electric resistance heat one uses WAY more energy than needed when a lower grade of heat will do the same thing!\n\nReason #18: In combination with energy efficient building practices the cost of a solar electric or solar thermal system one can drastically reduce the initial cost of a system, so that it is simply more affordable.\n\nReason #19: It is \"decentralized power\" and collectively it has the power to transform our world quicker than we may realize.\n\nAND, the top twenty reason for using solar: Promoting the purchase, installation and use of solar technology upsets and disturbs a lot of stupid people.\n\nThe whole idea is to use solar energy devices FIRST and fossil fuel as an energy BACK UP. If anyone wants to add to this list of reason why solar energy is the ideal energy source, please do so!\n\nSBT Designs\n25840 IH-10 West #1\nBoerne, Texas 78006\n210-698-7109\nFAX: 210-698-7147\nwww.sbtdesigns.com\n\nR\n\n#### Rick Kelly\n\nSteven\n\nYour tone is both insulting and inappropriate there are no IGNORANT or STUPID readers of this list. If you do not wish to discuss this in an\nprofessional manner then there is nothing further to discuss. I have neither the time or the patience for a discussion that offers no intelligent discourse. I consider this thread closed.\n\nBest Regards...\n\nRick Kelly\n\nChief Electrical Technician\nNatural Cuts, Cheese Operations\n\n[email\u00a0protected]\n(613) 537-8069 (V)\n(613) 537-8044 (F)\n\nJ\n\n#### Jacek Dobrowolski\n\nSteven Shepard wrote:\nNo, it is not a joke.\n.......\n\nI am referring to 99.9% reliable power.......\n\nTry to achieve that somewhere near the North or South Pole - something like lasting for half a year, long night - sorry I couldn't\nresist saying that.\n\nI'm working in rather small machinery company and we need about 50 kVA of power, so tell me how much would cost us a solar system of that capacity - overkill.\n\nRegards,\n\nJacek Dobrowolski\nSoftware Eng.\n\nAutomation Department\nSecondary Division\nITM Poland Ltd.\nul. Warsztatowa 19a\nPOLAND\ndirect line: +48(48)3686341\nfax: +48(48)3686101\n\nM\n\n#### Mark Genovese\n\nAs this is a small DC motor the 'Quality' of the DC should not be an issue. Therefore consider a Half-wave rectifier.\n\nThis is simply a single diode placed between the AC supplay and the DC motor. A diode acts as a one way valve allowing the flow of electric current in only one direction.\n\nThe diode wired in series with the fan will block half of the AC. It should be sized large enough to handle the current draw of the motor. You may place more than one diode in paralle to acheive the necessary current rating. Beware that diode are polarized the negative end is marked with a band. So if you gang several together make sure the bands are all on the same connection side.","date":"2021-04-21 21:11:36","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\": 0.3568393290042877, \"perplexity\": 2505.743119501054}, \"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-2021-17\/segments\/1618039550330.88\/warc\/CC-MAIN-20210421191857-20210421221857-00142.warc.gz\"}"}
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