text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
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gaycen.me 9 out of 10 based on 400 ratings. 900 user reviews.
GEM EQUINOX SERVICE MANUAL Pdf Download.
View and Download GEM Equinox service manual online. Equinox Electronic Keyboard pdf manual download.
The schematics try to reflect the wiring approach I took. Each stage including the power supply has its own ground bus or ground star point. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,337 |
At NE Flower Boutique we specialize in providing excellent service, preparing exquisite designs and delivering freshness every time!
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We have been started out from our NE Philadelphia location in 2010 and have grown ever since!
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Call or text or place your order online for Same Day Flower Delivery in Philadelphia! | {
"redpajama_set_name": "RedPajamaC4"
} | 1,488 |
Eurydera sublaevis is een keversoort uit de familie van de loopkevers (Carabidae). De wetenschappelijke naam van de soort is voor het eerst geldig gepubliceerd in 1835 door Castelnau.
sublaevis | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,587 |
https://www.ncadvertiser.com/news/article/Cause-of-Dan-s-Highway-inferno-in-New-Canaan-14848962.php
Cause of Dan's Highway inferno in New Canaan still unknown
By Michael Mayko, Justin Stock and Grace Duffield
Published 10:07 am EST, Wednesday, November 20, 2019
Fire destroyed a house at 322 Dan's Highway in New Canaan on Saturday, Nov. 16, 2019.
Photo: Grace Duffield / Hearst Connecticut Media
Investigators still don't know the cause of a fire that caused heavy damage to a house on Dan's Highway Saturday afternoon.
Fire Marshal Fred Baker said Tuesday investigators still did not know what started the fire.
Fueled by gusty winds Saturday afternoon, flames could be seen above the roof of the three-story house.
"We saw heavy fire on our arrival," Fire Chief Jack Hennessey said late Saturday. "The house is located in a non-hydrant area which made it difficult to fight. We had to call for mutual aid."
Hennessey said fire crews from Norwalk, Wilton, Pound Ridge, N.Y. and South Salem, N.Y. were among the municipalities that sent help. The Vista, N.Y. department also responded as well as New Canaan Emergency Medical Services crews.
"We laid 4,700 feet of five-inch supply line into a pond on Dan's Highway to get the water we needed," he said. "We had at least seven tankers on the scene."
Hennessey said the second and third floors of the home were heavily damaged, making it uninhabitable.
"The family was able to get out safely," he said. "There were no injuries."
He said the family found a place to stay.
"It took us about an hour and a half to bring the fire under control," Hennessey said. "But we're keeping crews there all night."
At a late hour, firefighters were still extinguishing hot spots in the home.
The family called 911 shortly before 2:30 p.m. while the fire already had reached the roof.
Police Officer Owen Ochs was one of the first to arrive and placed a call for mutual help.
At one point, nearby neighbors at the intersection of Dan's Highway and Ponus Ridge left their home for safety reasons. They returned just before 5 p.m.
Hennessey said the New Canaan Fire Marshal's office along with the State Fire Marshal have begun an investigation into the cause of the fire.
On Sunday afternoon, a moving truck, and a repair van were seen in the driveway of the home. A man on a lawnmower, and another man with a leafblower were seen cleaning up debris on the property. Dry sand was also up, and down the sides of Dan's Highway and Ponus Ridge.
The man on the lawnmower was seen in front of the home, and on Dan's Highway while also going down the home's driveway, and throughout the whole property. The man with the leafblower was seen in the backyard, and neighboring yard where debris also blew to.
The roads, and sand were covered in water Monday after 7 a.m. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,333 |
3rd-strike.com | Dragon Ball Z: Extreme Butoden – Review
Follow Genre: Fighting
Developer: Arc System Works
Publisher: Bandai Namco Games
Platform: 3DS
Tested on: 3DS
Dragon Ball Z: Extreme Butoden – Review
November 25, 2015 - ThaMofo - No Comments
Good: Graphical style, Simple
Bad: No online, Perhaps a bit 'too simple' at times
After truckloads of iterations of Dragon Ball Z games, another one appears exclusively for the Nintendo 3DS. What makes this one quite interesting is the fact that the genre went back to its roots by making a 2D fighting game, with tag team mechanics. We were curious to see how Goku faired in his transition from modern to retro but we also hoped to see some original content, which is something many of the previous games lack, as you're always plowing through the same incoherent storyline (which in a way is understandable as the anime is around 500 episodes), next to a flimsy made up plot in order to offer a bit more than the events that occur in the anime.
Unsurprisingly we are once again treated to the original story of the anime, that starts off from when the Saiyans first come to earth, trying to gain contact with Goku, as he was originally sent down to Earth as a child, to take over the planet. The good-natured Goku of course forgot all about his quest and lives a peaceful life as the protector of Earth. The story hits off when his long forgotten brother comes to the planet to wreak havoc. After this portion all the story arcs are told in a few phrases, with a battle in-between, providing hardly any information for those who are not yet familiar with the franchise, or simply haven't watched the anime or read the manga. Nonetheless, a fighting game such as this one does not necessarily need a thick plot to be decent.
Other than the original story, the creators tried to insert some new content with 'another' new story, that situates itself after the anime. Due to an extra power at work, all of Goku's enemies that he has ever defeated are alive once again to exact their revenge. While Goku is more powerful than ever, and he could defeat them separately, seeing they are all together, it will become hard not to succumb to their reign of terror.
All story portions of the game are brought by small visual novel-like cutscenes, with a few text windows, often not even properly showing what is actually going on. Whilst the limited animations are done properly, it would have been nice to get a little more action, rather than motionless faces.
Appearance wise the game grabs back to the days of yore, with a pixilated style, albeit a very detailed one. Every character is portrayed in a detailed fashion, every move is fluent and there are enough fighters, as well as supporting characters to choose from. The backgrounds have a more 3D visual appearance but you can't interact with it.
Story portions are presented with still pictures and text windows, which is enough for the overall presentation of the story but less is not always more. It would have been nice to see a few scenes from the anime or other moving cutscenes implemented.
Upbeat battle themes are mixed with the original Japanese voice cast, creating a very authentic Dragon Ball Z experience. This portion of the game is well taken care of, especially the voice acting adds another layer to the experience. It's only sad that the English cast was not implemented, because many have grown up with the English voices. Even though these voices were not always that consistent, it would have been a very nice touch.
Dragon Ball Z: Extreme Butoden is a fighting game, with tag team mechanics to ensure hectic and action packed battles, albeit with simplified controls and skills. All in all, this game might resemble a portable Marvel vs. Capcom, yet with a less flashy appeal to it. Nonetheless, it's all about fighting, however you look at the game.
You'll be able to choose several different modes such as the story, adventure, extreme world tournament, battle and versus and a 'guild card' function that doesn't truly do that much. You'll have to start off playing the story mode, if you wish to unlock adventure or the extreme world tournament. The other modes are already available from the start. While all modes are pretty much the same, you'll be able to unlock supporting characters when completing challenges in the adventure mode. It was only sad to see that the game does not support Download Play, forcing players to each buy their own copy of the game.
Normally you'll be able to choose three different fighters, or two fighters and two support characters or one fighter and four support characters, when doing normal battles. In the story mode you'll only be able to play with one character, as all the different branches of the story mode revolve around specific hero characters. During combat you'll be able to switch fighters or summon support characters by tapping the touch screen.
In battle it's a simple matter of linking different sets of punches and charging up your KI in order to perform stronger attacks. To be honest, this game feels a bit more like a button basher, instead of a very tactical fighting game. This might also be because both characters always stay relatively close to one another, making sure action is always nearby.
Those who wish to brush up on some things they forgot about Dragon Ball Z will have some fun browsing through the gallery in the extras but in the end it's only a simple gimmick. You can also register a team setup here, making you load your favorite combination rather than always having to compose it over and over again.
Dragon Ball Z: Extreme Butoden is a fun, simple fighting game, especially with the rather low difficulty settings. Nonetheless, even when playing solo, this game proves to have enjoyable tag team mechanics, even though it tends to feel like a button basher. There is a bit of content to unlock motivating you to play through the adventure mode, which makes it a tad more appealing. This game will never truly wow you, but it's certainly worth it if you're looking for a simple brawler.
Dragon Ball Z: Extreme Butoden - Review, 7.0 out of 10 based on 1 rating
ThaMofo
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Killer Queen Black on Xbox Game Pass in the new year | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,094 |
package org.appcelerator.titanium.util;
import java.util.Collections;
import java.util.HashMap;
import java.util.Map;
import org.appcelerator.titanium.TiApplication;
/*
* A Class which allows us to pull resource integers
* off of the various R class structures using
* strings at runtime.
*/
public class TiRHelper {
private static final String LCAT = "TiRHelper";
private static final boolean DBG = TiConfig.LOGD;
private static Map<String, Class<?>> clsCache = Collections.synchronizedMap(new HashMap<String, Class<?>>());
private static Map<String, Integer> valCache = Collections.synchronizedMap(new HashMap<String, Integer>());
private static String clsPrefixAndroid = "android.R$";
private static String clsPrefixApplication = null;
public static final class ResourceNotFoundException extends ClassNotFoundException {
private static final long serialVersionUID = 119234857198273641L;
public ResourceNotFoundException(String resource) {
super("Resource not found: " + resource);
}
}
private static Class<?> getClass(String classname) throws ClassNotFoundException {
Class<?> cls = clsCache.get(classname);
if (cls != null) return cls;
cls = Class.forName(classname);
clsCache.put(classname, cls);
return cls;
}
protected static String[] getClassAndFieldNames(String path) {
int lastDot = path.lastIndexOf('.');
String className = lastDot < 0 ? "" : path.substring(0, lastDot < 0 ? 1 : lastDot).replace('.', '$');
String fieldName = lastDot < 0 ? path : path.substring(lastDot + 1);
return new String[] { className, fieldName };
}
protected static int getResource(String prefix, String path) throws ResourceNotFoundException {
Integer i = valCache.get(path);
if (i != null) return i;
return lookupResource(prefix, path, getClassAndFieldNames(path));
}
protected static int lookupResource(String prefix, String path, String[] classAndFieldNames) throws ResourceNotFoundException {
// Get the clsPrefixApplication if this is the first time
if (clsPrefixApplication == null)
clsPrefixApplication = TiApplication.getInstance().getApplicationInfo().packageName + ".R$";
if (prefix == null) {
prefix = clsPrefixApplication;
}
Integer i = null;
// Load the field
try {
i = getClass(prefix + classAndFieldNames[0]).getDeclaredField(classAndFieldNames[1]).getInt(null);
} catch (Exception e) {
if (DBG) {
Log.e(LCAT, "Error looking up resource: " + e.getMessage(), e);
}
valCache.put(path, 0);
throw new ResourceNotFoundException(path);
}
valCache.put(path, i);
return i;
}
public static int getResource(String path, boolean includeSystemResources) throws ResourceNotFoundException {
Integer i = valCache.get(path);
if (i != null) return i;
String[] classAndFieldNames = getClassAndFieldNames(path);
try {
int resid = lookupResource(clsPrefixApplication, path, classAndFieldNames);
return resid;
} catch (ResourceNotFoundException e) {
if (!includeSystemResources) {
throw e;
}
return lookupResource(clsPrefixAndroid, path, classAndFieldNames);
}
}
public static int getResource(String path) throws ResourceNotFoundException
{
return getResource(path, true);
}
public static int getApplicationResource(String path) throws ResourceNotFoundException {
return getResource(clsPrefixApplication, path);
}
public static int getAndroidResource(String path) throws ResourceNotFoundException {
return getResource(clsPrefixAndroid, path);
}
/*
* Clears the cache. Should only be used in low memory situations
* as clearing the cache will adversely affect performance.
*/
public static void clearCache() {
valCache.clear();
clsCache.clear();
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,751 |
\section{INTRODUCTION}
\label{sec:Introduction}
Measurements of \ensuremath{C\!P}\xspace-violating asymmetries in the \ensuremath{\Bz {\kern -0.16em \Bzb}}\xspace system provide
tests of the Standard Model by over-constraining the
Cabibbo-Kobayashi-Maskawa (CKM)
quark-mixing matrix~\cite{CabibboKobayashi}
through the measurement of the unitarity angles.
Measuring the time-dependent \ensuremath{C\!P}\xspace asymmetry in a neutral-$B$-meson
decay to a \ensuremath{C\!P}\xspace eigenstate dominated by the tree-level amplitude
$\ensuremath{b}\xspace \to \ensuremath{u}\xspace{\bar\ensuremath{u}\xspace}\ensuremath{d}\xspace$
gives an approximation $\alpha_{\rm eff}$ to the CKM unitarity angle
$\alpha\equiv \arg\left[-V_{td}^{}V_{tb}^{*}/V_{ud}^{}V_{ub}^{*}\right]$.
The correction $\Delta\alpha= \alpha-\alpha_{\rm eff}$
accounts for the additional contributions from loop (penguin)
amplitudes. The value of $\Delta\alpha$ can be extracted from an
analysis of the
branching fractions of the $B$ decays into the full set of
isospin-related channels~\cite{gronau90}.
Measurements of branching fractions and time-dependent \ensuremath{C\!P}\xspace
asymmetries in $B\to\pi\pi$, $\rho\pi$, and $\rho\rho$
have already provided information on $\alpha$.
Because the branching
fraction\footnote{Charge conjugate $B$ decay modes are implied in this paper.}
for $B^0\to\pi^0\pi^0$ is comparable to that for
$B^+\to\pi^+\pi^0$ and $B^0\to\pi^+\pi^-$,
the limit on the correction is weak:
$|\Delta\alpha_{\pi\pi}|<41^\circ$ at 90$\%$ confidence level
(C.L.)~\cite{pi0pi0}.
On the contrary,
the $\ensuremath{B^0}\xspace\to\rho^0\rho^0$ decay has a much
smaller branching fraction than
$\ensuremath{B^0}\xspace\to\rho^{+}\rho^{-}$ and $B^{+}\to\rho^{+}\rho^0$
channels~[\ref{ref:vvbabar}$-$\ref{ref:rho0rhop2}].
As a consequence, it is possible to set a tighter limit on
$\Delta\alpha_{\rho\rho}$~\cite{gronau90, rhoprhom, falketal}.
This makes the $\rho\rho$ system particularly effective for
measuring~$\alpha$.
In $B\to\rho\rho$ decays the final state is
a superposition of \ensuremath{C\!P}\xspace-odd and \ensuremath{C\!P}\xspace-even states.
An isospin-triangle relation~\cite{gronau90} holds for each
of the three helicity amplitudes, which can be separated through
an angular analysis. The measured polarizations in
\ensuremath{\ensuremath{\Bu}\xspace \to \rho^+ \rho^0 }\xspace~\cite{vvbabar,rho0rhopbelle,rho0rhop2}
and \ensuremath{\,\ensuremath{B^0}\xspace \to \rho^+\rho^-}\xspace~[\ref{ref:rhoprhom}$-$\ref{ref:rhoprhom4}] modes
indicate that the $\rho$'s are nearly entirely
longitudinally polarized.
In this paper we present evidence for the \ensuremath{\ensuremath{B^0}\xspace \to \rho^0 \rho^0 }\xspace decay, the first
measurement of the longitudinal polarization fraction in this decay,
and updated constraints on the penguin contribution to the
measurement of the unitarity angle $\alpha$. These results supersede
our previous limits on this decay~\cite{vvbabar, rho0rho02}.
\section{THE \babar\ DETECTOR AND DATASET}
\label{sec:babar}
These results are based on data collected
with the \babar\ detector~\cite{babar} at the PEP-II asymmetric-energy
$e^+e^-$ collider~\cite{pep2} located at the Stanford Linear Accelerator
Center. A sample of $347.5\pm 1.9$ million $\ensuremath{B\Bbar}\xspace$ pairs,
corresponding to an integrated luminosity of approximately 316~\ensuremath{\mbox{\,fb}^{-1}}\xspace,
was recorded at the $\Y4S$ resonance with the center-of-mass (c.m.) energy
$\sqrt{s} = 10.58$ GeV.
We use a sample of 28~\ensuremath{\mbox{\,fb}^{-1}}\xspace taken 40~\ensuremath{\mathrm{\,Me\kern -0.1em V}}\xspace below the $\Y4S$
resonance to study background contributions from
$e^+e^-\rightarrow q\bar{q}~( q = u, d, s, \mathrm{or}~c)$
continuum events.
Charged-particle momenta and trajectories are measured in a tracking system
consisting of a five-layer double-sided silicon vertex tracker
and a 40-layer drift chamber,
both within a 1.5-T solenoidal magnetic field.
Charged-particle identification is provided by
measurements of the energy loss
in the tracking devices and by a ring-imaging Cherenkov detector.
\section{ANALYSIS METHOD}
\label{sec:Analysis}
We select $\ensuremath{\,\ensuremath{B^0}\xspace \to \rho^0\rho^0}\xspace\to(\pi^+\pi^-)(\pi^+\pi^-)$
candidates from combinations of
four charged tracks that
are consistent with originating from a single vertex near
the $e^+e^-$ interaction point.
The identification of signal $B$ candidates is based
on several kinematic variables.
The beam-energy-substituted mass,
$\mbox{$m_{\rm ES}$}\xspace = [(s/2 + {\mathbf {p}}_i\cdot {\mathbf{p}}_B)^2/E_i^2-
{\mathbf {p}}_B^2]^{1/2}$,
where the initial total $e^+e^-$
four-momentum $(E_i, {\mathbf {p_i}})$ and the \ensuremath{B}\xspace
momentum ${\mathbf {p_B}}$ are defined in the laboratory frame, is
centered near \ensuremath{B}\xspace mass with a resolution of $2.6~\ensuremath{\mathrm{\,Me\kern -0.1em V}}\xspace$ for signal
candidates.
The difference between the reconstructed \ensuremath{B}\xspace energy in the
c.m. frame and its known value
$\mbox{$\Delta E$}\xspace = E_B^{\rm cm} - \sqrt{s}/2$ has a maximum near zero with a
resolution of $20~\ensuremath{\mathrm{\,Me\kern -0.1em V}}\xspace$ for signal events. Four other kinematic
variables describe two possible
$\pi^+\pi^-$ pairs: they are invariant masses $m_1(\pi\pi)\equiv
m_{1}$ and $m_2(\pi\pi)\equiv m_{2}$,
and helicity angles $\theta_1,\ \theta_2$.
The angular distribution of the $\ensuremath{\,\ensuremath{B^0}\xspace \to \rho^0\rho^0}\xspace$ decay products
can be expressed as a function of the helicity angles
$\theta_1$ and $\theta_2$, which are defined
as the angles between the direction of $\pi^+$ and the direction
of the \ensuremath{B}\xspace in the rest system of each $\rho^0$.
The resulting angular distribution
${d^2\Gamma / (\Gamma\,d\!\cos \theta_1\,d\!\cos \theta_2)}$ is
\begin{eqnarray}
{9 \over 4} \left \{ {1 \over 4} (1 - f_L)
\sin^2 \theta_1 \sin^2 \theta_2 + f_L \cos^2 \theta_1 \cos^2 \theta_2 \right\},
\label{eq:helicityshort}
\end{eqnarray}
\noindent where $f_L=|A_0|^2/(\Sigma|A_\lambda|^2)$ is the
longitudinal polarization fraction and
$A_{\lambda=-1,0,+1}$ are the helicity amplitudes.
The selection requirements for signal candidates are the following:
$5.240 < \mbox{$m_{\rm ES}$}\xspace < 5.290~\ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c^2}}\xspace$,
$|\mbox{$\Delta E$}\xspace|<$ 85~\ensuremath{\mathrm{\,Me\kern -0.1em V}}\xspace,
$550< m_{1,2} < 1050~\ensuremath{\mathrm{\,Me\kern -0.1em V}}\xspace$,
and $|\cos\theta_{1,2}|<0.98$.
The latter requirement removes a region with low reconstruction
efficiency. In addition, we veto the copious decays
$\ensuremath{B^0}\xspace\to D^{(*)-}\ensuremath{\pi^+}\xspace\to(h^+\ensuremath{\pi^-}\xspace\pim)\ensuremath{\pi^+}\xspace$,
where $h^+$ refers to a pion or kaon, by requiring the
invariant mass of the three-particle combination
to differ from the $D$-meson mass by more
than $13.2~\ensuremath{\mathrm{\,Me\kern -0.1em V}}\xspace$, or $40~\ensuremath{\mathrm{\,Me\kern -0.1em V}}\xspace$ if the kaon is positively identified.
We reject the dominant continuum
background by requiring $|\cos\theta_T| < 0.8$, where $\theta_T$
is the angle between the $B$-candidate thrust axis
and that of the remaining tracks and neutral clusters in
the event, calculated in the c.m. frame.
We suppress continuum background further using the polar
angles of the $B$ momentum vector and the $B$-candidate thrust
axis with respect to the beam axis in the c.m. frame.
Other discriminating variables calculated in the c.m. frame
include the two Legendre moments $L_0$ and $L_2$ of the energy
flow around the $B$-candidate thrust axis~\cite{bigPRD}
and the sum of the transverse momenta of all particles in the rest
of the event,
calculated with respect to the $B$ direction.
These variables are combined in a neural network, whose output is
transformed into the approximately Gaussian-distributed variable
$\mathcal{E}$.
After application of all selection criteria,
$N_{\rm cand}=65180$ events are retained,
most of which are background events,
well separated in the kinematic observables
from $\ensuremath{\ensuremath{B^0}\xspace \to \rho^0 \rho^0 }\xspace$, $B^0\to \rho^0f_0(980)$, and
$B^0\to f_0(980)f_0(980)$ signal candidates.
On average, each selected background event has $1.05$ candidates,
while in Monte Carlo (MC) samples we find
$1.15$ and $1.03$ candidates
for longitudinally and transversely polarized
$B^0\to\rho^0\rho^0$ decays, respectively.
When more than one candidate is present in the same event,
the candidate having the best $\chi^2$ consistency
with a single four-pion vertex is selected.
The signal selection efficiency determined
from Monte Carlo~\cite{GEANT} simulation
is 23.5\% or 28.9\% for longitudinally or transversely
polarized events, respectively.
MC simulation shows that 18\% of longitudinally
and 4\% of transversely polarized signal
events are misreconstructed with one or more tracks
not originating from the $B^0\to\rho^0\rho^0$ decay.
These are mostly due to combinatorial background from
low-momentum tracks from the other \ensuremath{B}\xspace meson in the event.
Further background separation is achieved by
the use of multivariate $B$-flavor-tagging
algorithms trained to identify primary leptons, kaons, soft pions,
and high-momentum charged particles
from the other $B$~\cite{babarsin2beta}.
The discrimination power arises from the difference between
the tagging efficiencies for signal and background in seven
tagging categories ($c_{\rm tag}=1-7$).
\clearpage
\section{MAXIMUM LIKELIHOOD FIT}
\label{sec:fit}
We use an unbinned extended maximum likelihood fit to extract
the $B^0\to\rho^0\rho^0$ event yield and fraction of longitudinal
polarization $f_L$. We also fit for the event yield of $B^0\to\rho^0f_0$
and $B^0\to f_0f_0$ decays, as well as several background categories.
The likelihood function is
\begin{equation}
{\cal L} = \exp\left(-\sum_{k}^{} n_{k}\right)\,
\prod_{i=1}^{N_{\rm cand}}
\left(\sum_{j}~n_{j}\,
{\cal P}_{j}(\vec{x}_{i})\right),
\label{eq:likel}
\end{equation}
where $n_j$ is the number of events for each hypothesis $j$
(signal $B^0\to\rho^0\rho^0$ , five other $B$-decay classes,
and continuum), and
${\cal P}_{j}(\vec{x}_{i})$ is the corresponding
probability density function (PDF), evaluated with
the variables
$\vec{x}_{i}=\{m_{\rm{ES}}, \Delta E, {\cal E},
m_1, m_2, \cos\theta_1, \cos\theta_2, c_{\rm tag}\}$
of the $i$th event.
We use MC-simulated events to parameterize contributions from
other $B$ decays. The charmless modes are grouped into several
classes with similar kinematic and topological properties:
$B^0\to \rho^0f_0(990)$;
$B^0\to f_0(980)f_0(980)$;
$B^0\to a_1^{\pm}\pi^{\mp}$;
and a combination of other charmless modes, including
$B^0\to \rho^0K^{*0}$, $B^+\to\rho^+\rho^0$, $B\to\rho\pi$,
and $B^0\to\rho^+\rho^-$.
One additional class accounts for the remaining neutral and
charged $B$ decays to charm modes. The number of events in each
class $n_{j}$ is left free in the fit.
We ignore any other four-pion final states in our invariant mass
window whose contributions are expected to be small.
Since the statistical correlations among the variables are found to be small,
we take each ${\cal P}_j$ as the product of the PDFs for the
separate variables. Exceptions are the kinematic correlation between the two
helicity angles in signal, and mass-helicity correlations in
other $B$-decay classes and misreconstructed signal.
They are taken into account as discussed below.
We use double-Gaussian functions to parameterize the
$m_{\rm{ES}}$ and $\Delta E$ PDFs for signal,
and a relativistic Breit-Wigner (BW)
for the resonance masses of $\rho^0$~\cite{pdg2006}
and $f_0(980)$~\cite{f0mass}.
The angular distribution at production for
$B^0\to\rho^0\rho^0$, $B^0\to \rho^0f_0$, and $B^0\to f_0f_0$
modes (expressed as a function of the longitudinal
polarization in Eq.~(\ref{eq:helicityshort}) for
\ensuremath{\ensuremath{B^0}\xspace \to \rho^0 \rho^0 }\xspace) is multiplied by a detector acceptance function
${\cal G}(\cos\theta_1, \cos\theta_2)$,
determined from MC.
The distributions of misreconstructed signal events
are parameterized with empirical shapes in a way similar
to that used for $B$ background, as described below.
The ${\cal E}$ variable is described by three asymmetric
Gaussian functions with different parameters for signal
and background distributions.
The PDFs for exclusive non-signal \ensuremath{B}\xspace decay modes are
generally modeled with empirical analytical distributions.
Several variables have distributions
identical to those for signal, such as $m_{\rm{ES}}$
when all four tracks come from the same $B$, or $\pi^+\pi^-$
invariant mass $m_{1,2}$ when both tracks come from
a $\rho^0$ meson.
In certain exclusive modes the two $\rho^0$ candidates
can have very different mass and helicity distributions,
{\em e.g.}\ when only one of the two $\rho^0$ candidates
is a genuine $\rho^0$ meson
or when one of the two $\rho^0$ candidates contains a
high-momentum pion (as in $B\to a_1\pi$). In such cases,
we use a four-variable correlated mass-helicity PDF.
The signal and $B$-background PDF parameters are extracted from
MC simulation. The initial continuum background PDF parameters
are obtained from data in $m_{\rm{ES}}$ and $\Delta E$ sidebands
and are then left free in the fit. The MC parameters for
$m_{\rm{ES}}$, $\Delta E$, and ${\cal E}$ PDFs are adjusted by
comparing data and MC in control channels with similar
kinematics and topology,
such as $B^0\to D^-\pi^+$ with $D^-\to K^+\pi^-\pi^-$.
Finally, the $B$-flavor tagging PDFs for all decay modes are
the normalized discrete $c_{\rm tag}$ distributions of tagging
categories.
Large samples of fully reconstructed $B$-meson decays are
used to obtain the $B$-tagging efficiencies for signal $B$ decays
and to study systematic uncertainties in the MC values
of $B$-tagging efficiencies for the $B$ backgrounds.
\section{RESULTS}
\label{sec:results}
Table~\ref{tab:results} shows the results of the fit.
The $\ensuremath{\,\ensuremath{B^0}\xspace \to \rho^0\rho^0}\xspace$ decay is observed with a significance of $3.0\sigma$,
as determined by
the quantity $\sqrt{-2\log(\mathcal{L}_0/\mathcal{L}_{\max})}$, where
$\mathcal{L}_{\max}$ is the maximum likelihood value, and
$\mathcal{L}_0$ is the likelihood for a fit with the signal
contribution set to zero. It corresponds to a probability of
background fluctuation
to the observed signal yield of 0.1$\%$, including systematic
uncertainties, which are assumed to be Gaussian-distributed. We do not
observe significant event yields for $\ensuremath{\,\Bz \to \rho^0 f_0(980)}\xspace$ and $\ensuremath{\,\Bz \to f_0(980) f_0(980)}\xspace$
decays. Background yields are found to be consistent with
expectations.
In Fig.~\ref{fig:projections} we show the projections of the fit results
onto $m_{\rm ES}$ and $\mbox{$\Delta E$}\xspace$.
\begin{table}[ht]
\centering
\caption{
Summary of results: signal yield ($n_{\rm sig}$, events),
fraction of longitudinal polarization ($f_L$),
selection efficiency (Eff), branching fraction (${\cal B}_{\rm sig}$),
branching fraction upper limit (UL) at 90\% CL,
and significance (including systematic uncertainties).
The systematic errors are quoted last. We also show
the background yields for $a_1\pi$, $\ensuremath{B\Bbar}\xspace$, and
$\ensuremath{q\overline q}\xspace$ components (events, with only statistical uncertainties
quoted).
}
\vspace{0.2cm}
\begin{tabular}{lcc}
\hline\hline
& ~~~~~~~~~ & \vspace*{-0.3cm} \\
Quantity & & Value \\
& & \vspace*{-0.3cm} \\
\hline
& & \vspace*{-0.3cm} \\
$n_{\rm sig}$ ($B^0\to\rho^0\rho^0$)
& & $98^{+32}_{-31}\pm 22$ \\
& & \vspace*{-0.3cm} \\
$f_L$
& & $0.86^{+0.11}_{-0.13}\pm 0.05$ \\
& & \vspace*{-0.3cm} \\
Eff (\%) & & $24.2\pm 1.0$ \\
& & \vspace*{-0.3cm} \\
${\cal B}_{\rm sig}$ $(\times 10^{-6})$ & & $1.16^{+0.37}_{-0.36}\pm0.27$ \\
& & \vspace*{-0.3cm} \\
Significance ($\sigma$) & & $3.0$ (3.4 statistics only) \\
& & \vspace*{-0.4cm} \\
& & \vspace*{-0.3cm} \\
\hline
& & \vspace*{-0.3cm} \\
$n_{\rm sig}$ ($B^0\to \rho^0f_0$)
& & $12^{+18}_{-17}\pm 13$ \\
& & \vspace*{-0.3cm} \\
Eff (\%) & & $20.7\pm 0.8$ \\
& & \vspace*{-0.3cm} \\
${\cal B}_{\rm sig}\times{\cal B}(f_0\to\pi^+\pi^-)$ $(\times 10^{-6})$
& & $0.17^{+0.25}_{-0.23}\pm 0.18$ \\
& & \vspace*{-0.3cm} \\
UL$\times{\cal B}(f_0\to\pi^+\pi^-)~(\times 10^{-6})$ & & $0.68$ \\
& & \vspace*{-0.3cm} \\
\hline
& & \vspace*{-0.3cm} \\
$n_{\rm sig}$ ($B^0\to\ f_0 f_0$)
& & $-5^{+7}_{-6}\pm 12$ \\
& & \vspace*{-0.3cm} \\
Eff (\%) & & $23.5\pm 0.9$ \\
& & \vspace*{-0.3cm} \\
${\cal B}_{\rm sig}\times{\cal B}^2(f_0\to\pi^+\pi^-)$ $(\times 10^{-6})$
& & $-0.06^{+0.08}_{-0.07} \pm 0.15$ \\
& & \vspace*{-0.3cm} \\
UL$\times{\cal B}^2(f_0\to\pi^+\pi^-)~(\times 10^{-6})$ & & $0.33$ \\
& & \vspace*{-0.3cm} \\
\hline
& & \vspace*{-0.3cm} \\
$n_{a_1\pi}$ & & $90^{+26}_{-25}$ \\
& & \vspace*{-0.3cm} \\
$n_{\rm charmless}$ & & $-17^{+113}_{-99}$ \\
& & \vspace*{-0.3cm} \\
$n_{\ensuremath{B\Bbar}\xspace}$ & & $3280^{+187}_{-194}$ \\
& & \vspace*{-0.3cm} \\
$n_{\ensuremath{q\overline q}\xspace}$ & & $61719^{+286}_{-289}$ \\
& & \vspace*{-0.3cm} \\
\hline\hline
\end{tabular}
\label{tab:results}
\end{table}
\begin{figure}[ht]
\centerline{
\setlength{\epsfxsize}{0.5\linewidth}\leavevmode\epsfbox{fig01.eps}
\setlength{\epsfxsize}{0.5\linewidth}\leavevmode\epsfbox{fig02.eps}
}
\caption{
Projections of the multidimensional fit onto
$m_{\rm ES}$ and $\Delta E$ after a requirement on the
signal-to-background probability ratio
with the plotted variable excluded.
This requirement maximizes the fraction of
signal events in the sample.
The data points are overlaid by the solid (dashed) line,
which shows the full (background only) PDF projection.
The individual PDF components are shown for the
$B^0\to\rho^0\rho^0$ (solid red) and $B^0\to\rho^0f_0$ modes (dotted green).
}
\label{fig:projections}
\end{figure}
\section{SYSTEMATIC STUDIES}
\label{sec:Systematics}
Dominant systematic errors in the fit originate from statistical uncertainties
in the PDF parameterizations, due to the limited
number of events in the control samples.
The PDF parameters are varied by their respective uncertainties
to derive the corresponding systematic errors
(15, 11, 12 events for $\rho^0\rho^0$, $\rho^0f_0$, and $f_0f_0$
respectively, and 0.05 for $f_L$).
We also assign a systematic error of 2 events for $\rho^0\rho^0$ and
$f_0f_0$ and 7 events for $\rho^0f_0$ (0.02 for $f_L$)
to account for a possible fit bias, evaluated with MC experiments.
The above systematic uncertainties do not scale with event yield
and are included in the calculation of the significance of the result.
We also assign 8\%, 5\%, 10\% multiplicative systematic error due to
possible fit bias for $\rho^0\rho^0$, $\rho^0f_0$, and $f_0f_0$ modes,
respectively.
We estimate the systematic uncertainty due to
the interference between $\rho^0\rho^0$ and $a_1^{\pm}\pi^{\mp}$ final
states using
simulated samples in which the decay amplitudes for $B^0\to\rho^0\rho^0$
are generated according to this measurement
and those for $B^0\to a_1^{\pm}\pi^{\mp}$ correspond
to a branching fraction of $(39.7\pm3.7)\times 10^{-6}$~\cite{a1pi}.
Their amplitudes are modeled with a Breit-Wigner function
for all $\rho\to\pi\pi$ and $a_1\to\rho\pi$ combinations
and their relative phase is assumed to be constant across the phase space.
The strong phases and \ensuremath{C\!P}\xspace\ content of the interfering state
$a_1^{\pm}\pi^{\mp}$
are varied between zero and a maximum using uniform prior distributions.
We take the RMS variation of the average signal yield
(14 events for the $\rho^0\rho^0$ yield, or $0.03$ for $f_L$)
as a systematic uncertainty.
Uncertainties in the reconstruction efficiency
arise from track finding (2\%),
particle identification (2\%),
and other selection requirements,
such as vertex probability (2\%),
track multiplicity (1\%),
and thrust angle (1\%).
\section{IMPLICATIONS FOR THE CKM ANGLE $\alpha$}
\label{sec:alpha}
Since the tree contribution to the $B^0\to\rho^0\rho^0$
decay is color-suppressed,
the decay rate is sensitive to the penguin amplitude.
Thus, this mode
has important implications for constraining
the uncertainty
in the measurement of the CKM unitarity angle $\alpha$
due to penguin contributions to
$B\to\rho\rho$ decays.
In the isospin analysis~\cite{gronau90},
we minimize a $\chi^2$ that includes the measured quantities
expressed as the lengths of the sides of the isospin triangles.
We use the measured branching fractions and
fractions of longitudinal polarization of the
$\ensuremath{\ensuremath{\Bu}\xspace \to \rho^+ \rho^0 }\xspace$~\cite{rho0rhopbelle,rho0rhop2}
and $\ensuremath{\,\ensuremath{B^0}\xspace \to \rho^+\rho^-}\xspace$~\cite{rhoprhombelle, rhoprhom4}
decays, the \ensuremath{C\!P}\xspace-violating parameters $S^{+-}_{L}$ and $C^{+-}_{L}$
obtained from the time evolution of the longitudinally
polarized $\ensuremath{\,\ensuremath{B^0}\xspace \to \rho^+\rho^-}\xspace$ decay~\cite{rhoprhombelle, rhoprhom4},
and the branching fraction of $\ensuremath{\,\ensuremath{B^0}\xspace \to \rho^0\rho^0}\xspace$ from this analysis.
We assume Gaussian behavior of the distributions.
We neglect $I=1$ isospin contributions,
non-resonant and isospin-breaking effects.
With the \ensuremath{\,\ensuremath{B^0}\xspace \to \rho^0\rho^0}\xspace measurement we obtain the
constraint on $\alpha$ due to the penguin contribution
and obtain a 68\% (90\%) CL limit on
$\Delta\alpha_{\rho\rho}=\alpha-\alpha_{\rm eff}$
of $\pm 18^{\mathrm o}$ ($\pm 21^{\mathrm o}$).
Fig.~\ref{fig:alphascan} shows the
$\Delta\chi^2$ on $\Delta\alpha_{\rho\rho}$.
The central value of $\alpha$ obtained from the isospin
analysis is the same as $\alpha_{\rm eff}$,
which is constrained by the relation
$\sin(2\alpha_{\rm eff})= S^{+-}_{L}/({1-C^{+-2}_{L}})^{1/2}$
and is measured with the $B^0\to\rho^+\rho^-$
decay~\cite{rhoprhombelle,rhoprhom4}.
The error due to the penguin contribution becomes
the dominant uncertainty in the measurement of $\alpha$ using
$B\to\rho\rho$ decays. However, once the sample
of $B^0\to\rho^0\rho^0$ decays becomes more significant,
time-dependent angular analysis will allow us
to measure the \ensuremath{C\!P}\xspace\ parameters $S^{00}_{L}$ and $C^{00}_{L}$,
analogous to $S^{+-}_{L}$ and $C^{+-}_{L}$,
resolving ambiguities inherent to isospin triangle orientations.
\begin{figure}[t]
\begin{center}
\setlength{\epsfxsize}{1.0\linewidth}\leavevmode\epsfbox{fig03.eps}
\caption{$\Delta\chi^2$ on $\Delta\alpha_{\rho\rho}$
obtained from the isospin analysis discussed in the text.
The dashed lines at $\Delta\chi^2 = 1$ and $\Delta\chi^2 = 2.7$
are taken for the $1\sigma$ (68\%) and $1.64\sigma$ (90\%)
interval estimates.}
\label{fig:alphascan}
\end{center}
\end{figure}
\section{SUMMARY}
\label{sec:Summary}
In summary, we have found evidence for \ensuremath{\ensuremath{B^0}\xspace \to \rho^0 \rho^0 }\xspace\ decay with $3.0\sigma$
significance. We measure
\begin{displaymath}
{\ensuremath{\cal B}\xspace}(\ensuremath{\ensuremath{B^0}\xspace \to \rho^0 \rho^0 }\xspace) = 1.16^{+0.37}_{-0.36}\ (\mathrm{stat.})\pm0.27\ (\mathrm{syst.})
\end{displaymath}
and we determine the longitudinal polarization fraction for these
decays of
\begin{displaymath}
f_L = 0.86^{+0.11}_{-0.13}\ (\mathrm{stat.})\pm 0.05\ (\mathrm{syst.})
\end{displaymath}
The measurement of this branching fraction combined with that for
$B^+\to\rho^0\rho^+$ and $B^0\to\rho^+\rho^-$ decays provides
a constraint on the penguin uncertainty
in the determination of the CKM unitarity angle $\alpha$.
We find no significant evidence for the decays $B^0\to \rho^0f_0$
and $B^0\to f_0f_0$. These results are preliminary, and they supersede
our previous measurements~\cite{vvbabar, rho0rho02}.
\section{ACKNOWLEDGMENTS}
\label{sec:Acknowledgments}
We are grateful for the
extraordinary contributions of our PEP-II\ colleagues in
achieving the excellent luminosity and machine conditions
that have made this work possible.
The success of this project also relies critically on the
expertise and dedication of the computing organizations that
support \babar.
The collaborating institutions wish to thank
SLAC for its support and the kind hospitality extended to them.
This work is supported by the
US Department of Energy
and National Science Foundation, the
Natural Sciences and Engineering Research Council (Canada),
Institute of High Energy Physics (China), the
Commissariat \`a l'Energie Atomique and
Institut National de Physique Nucl\'eaire et de Physique des Particules
(France), the
Bundesministerium f\"ur Bildung und Forschung and
Deutsche Forschungsgemeinschaft
(Germany), the
Istituto Nazionale di Fisica Nucleare (Italy),
the Foundation for Fundamental Research on Matter (The Netherlands),
the Research Council of Norway, the
Ministry of Science and Technology of the Russian Federation, and the
Particle Physics and Astronomy Research Council (United Kingdom).
Individuals have received support from
the Marie-Curie IEF program (European Union) and
the A. P. Sloan Foundation.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,793 |
To make up for a lack of keys, early laptops came with a special function key, the Fn key. This was used in combination with other keys like a Shift key, giving those keys multiple purposes.
On the old Compaq SLT the Fn (function) key is located in the lower-left corner, enclosed in a rectangle. Other keys with rectangles are activated when they're pressed with the Fn key. So the arrow keys (in the lower-right corner) double as other cursor-movement keys. Notice how the embedded numeric keypad also becomes an embedded cursor-movement pad as well. What a nightmare!
Most modern laptops retain the Fn key, but it's used primarily to activate special laptop functions. These functions share other keys on the keyboard, typically the Function keys. They're marked by special icons and are color coded to match the Fn key.
Some Fn keys can be rather fun. For example, on the IBM laptop, Fn+PgUp is used to turn on a tiny keyboard light in the laptop's lid. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,785 |
\section{Introduction} \label{intro}
Protoplanetary disk observations provide snapshots of the planetary formation processes that help us understand the physical characteristics of such disks. However, understanding planetary formation requires modeling the evolution and composition of protoplanetary disks. Considering the different physical states of the various components of a protoplanetary disk is therefore necessary to constrain favorable scenarios for planetary formation, growth, and migration, and solve the apparent inconsistency between the formation and migration timescales.
Since the discovery of the first exoplanet \citep{mayor95}, planetary formation scenarios have frequently been revisited. Even before \citet{charbonneau00} showed the gaseous giant nature of the observed exoplanets, \citet{pollack96} described how gaseous planets could form by accretion of gas on previously accumulated solid cores of a few times the mass of the Earth and estimated a typical planetary formation timescale around $10^{6-7}$ years (compatible with the typical disk lifetime of a few million years as inferred from observations by \citet{beckwith96} and \citet{hartmann98}). \citet{papaloizou99} also noted that hot Jupiters were unlikely to have formed in situ, therefore requiring some sort of planetary migration. Type I inward migration due to Lindblad resonances with the planet are well known from \citet{goldreich79}, \citet{arty93}, and \citet{ward97}, who estimated a migration timescale of about $10^{5}$ years for a typical Earth-mass planet in a minimum mass solar nebula \citep{weiden77, hayashi81}. \citet{kory93} noted that planets should therefore be lost by spiraling into their host star before they could actually grow. Early on, \citet{ward91} detailed the analytical expression of the corotation torque, before \citet{tanaka02} added a 3D analytical expression of the vortensity gradient horseshoe drag torque (tested numerically by \citet{bate03} and \citet{dangelo03}), and \citet{baruteau08} later completed this with the entropy gradient horseshoe drag torque. In the meantime, \citet{alibert05} and \citet{ida08} investigated the inconsistency between the timescales of planet formation and migration and noted that the mass-distance distribution of the exoplanets is inconsistent with the rapid inward migration of planetary cores. They noted that the type I inward migration should be slowed down by at least an order of magnitude to allow planets to form and avoid falling into the star. Part of the solution, investigated by \citet{hellary12}, would consist in accelerating the planet formation by considering a proper temperature treatment and a 3D disk model. However, this is not sufficient, and most of the efforts have been concentrated on slowing down the inward migration. Various models have been tested to achieve that goal. One of them is the model reported by \citet{terquem03},
who studied the effects of a regular magnetic field, while \citet{nelson04} focused on turbulent magnetism. \citet{kuchner02}, on the other hand, studied the consequences of an inner cavity and determined that such a hole could halt inward migration. \citet{jc05} found that self-shadowing in the disk can slightly decrease the migration rate. \citet{masset06b} described that a sharp positive surface mass density gradient could have similar consequences for the creation of planetary traps at the zero-torque radii. Subsequent efforts from \citet{paarm06,paarm08}, \citet{paarp08}, \citet{baruteau08}, \citet{kley08}, \citet{kley09}, and \citet{ayliffe10} investigated the possibility of slowing down and reversing the inward migration by considering more complete models involving proper radiative transfer and thermal consideration: this appeared to be possible for sufficiently low mass planets ($M_{P} \, <\, 40\, M_{\oplus}$). \citet{menou04} studied the effects of opacity transitions on the migration rate and showed that if some specific conditions are met, the migration could be stopped in a steady-state $\alpha$ disk. \citet{paarp09a} estimated that almost any positive surface mass density gradient could act as a protoplanet trap. Zero-torque radii were later analyzed by \citet{lyra10}, \citet{bitsch11}, and \citet{hasegawa112}: they appear to be very important in preventing the fall of the planets into their star, but also in creating a favorable zone for the interactions between planetesimals where they are able to combine. \citet{horn12} estimated that giant planet cores could form at convergent zero-torque radius for sub-$M_{\oplus}$ planets in 2-3 Myr.
There appears to be a strong correlation between the migration rate and the surface mass density and mid-plane temperature gradients that also strongly depend on the disk composition (gas-to-dust ratio, chemical abundances). Although the influence of the dust composition is not commonly used in recent numerical simulations of evolving protoplanetary disks, \citet{helling00} and \citet{semenov03} studied how opacities are affected by temperature. It therefore appears to be necessary to consider how the dust main component phases change in order to estimate the temperature more accurately. From reliable evolved disk radial profiles, we skip the planetary core formation stage and consider how a formed core dynamically interacts with the disk. The resonant torques that a planet exerts on a disk can be calculated from \citet{goldreich79}, \citet{ward88}, and \citet{arty93}, and we considered the refinements from \citet{paar11} to more accurately calculate the various contributions of the corotation torques. In their simulations, \citet{bitsch11} found a possible equilibrium radius of a planet with 20 Earth masses around 12.5 AU. \citet{hasegawa112} also analyzed the influence of the heat transition barrier on the migration torques. Whereas most of the previous work has applied the torque formulae to simplified semi-analytical density and temperature profiles \citep{hasegawa111,paar11}, to simple density prescriptions with a self-consistent 2D-temperature structure \citep{bitsch11,bitsch13}, or to steady-state accretion disk models \citep{bitsch14}, we intend to apply similar reasoning to more realistic disks obtained from numerically simulated viscous evolution rather than analytical steady state disks.
\citet{baillie14} (referred to hereafter as \citetalias{baillie14}) have shown that some of the features of viscous $\alpha$-model protoplanetary disks that are observed around forming stars can be retrieved numerically using a viscous evolution hydrodynamical code. These simulations confirmed the importance of jointly considering the dynamics, thermodynamics, and geometry of the disk. However, as the temperature affects the gas-to-dust ratio of the main components of the disk, the opacity of the disk is affected as well. Therefore, it is important to take into account a consistent composition of the disk when calculating its temperature. We here improve the numerical model of BC14 to consider these changes in the phases of the disk components. The thermal model includes both viscous heating and irradiation heating. We follow the evolution of an initial minimum mass solar nebula. The geometry (including the delimitations of shadowed regions) is calculated self-consistently, with the thermal structure obtained by semi-analytical radiative transfer calculations. The obtained density and temperature radial profiles show discontinuities compared to previous results from \citetalias{baillie14}. Density bumps mainly result in temperature irregularities such as bumps, troughs, and plateaux. The snow or sublimation lines are also enlarged. Using our density and temperature profiles, we compute the torque that the disk would exert on a planet embedded in the disk. The total torques (resulting from the Lindblad and corotation resonances) provide the direction of migration of the planetary core within the disk, allowing us to identify convergence and divergence regions, which are also called planetary traps and deserts
Section \ref{methods} details how the hydrodynamical code of \citet{baillie14} is upgraded to consider variations of the dust composition with temperature. The density radial profiles resulting from the viscous evolution and the calculated thermodynamical and geometrical profiles of the disk are shown in Sect. \ref{res}. These radial profiles, and especially the mid-plane temperature, are analyzed in Sect. \ref{disc}, where we also discuss the influence of the composition of the disk and reconsider the definitions of snowline and sublimation line. Finally, Sect. \ref{torque} calculates the resonant torques of potential planetary embryos in the disk and follows their migration, defining planetary traps and deserts.
\section{Methods} \label{methods}
\subsection{Disk model}
We consider the same model of a viscous $\alpha$ disk \citep{shakura73} as was used in \citetalias{baillie14} and use the same terminology as in that paper. The turbulent viscosity is set to $\alpha_{\mathrm{visc}}= 10^{-2}$ as is commonly accepted for T Tauri star protoplanetary disks without deadzones \citep{fromang06}. The time evolution of the surface mass density is given by Eq. \ref{lb74} from \citet{lyndenbellpringle74},
\begin{equation}
\frac{\partial \Sigma(r,t)}{\partial t} = \frac{3}{r} \, \frac{\partial}{\partial r}\left(\sqrt{r} \, \frac{\partial}{\partial r} \left( \nu(r,t) \, \Sigma(r,t) \, \sqrt{r}\right) \right)
\label{lb74}
.\end{equation}
Similarly to BC14, we applied Eq. \ref{lb74} to a one-dimensional grid of masses that are logarithmically distributed in radius between $R_{*}$ and 1000 AU: each of these masses represents an annulus in the disk. We imposed that the flux at the inner edge cannot be directed outward. The inner mass flux gives the mass accretion rate of the disk. The temperature in the mid-plane, $T_{m}(r)$, results from the combination of viscous heating, stellar irradiation heating, and radiative cooling in the mid-plane.
The grazing angle $\alpha_{gr}(r)$ defines the angle at which the star sees the photosphere at a given radial location $r$. Comparisons between an imposed geometry following that prescription and a free geometry calculated along with a consistent temperature are shown in \citetalias{baillie14}, along with a discussion of the necessity of these geometric refinements. The grazing angle, which controls the amount of energy that the star provides to the disk photosphere, is related to the photosphere height $H_{ph}(r)$ through Eq. \ref{alphagr}:
\begin{equation}
\alpha_{gr}(r) = \arctan\left(\frac{dH_{ph}}{dr}(r)\right) - \arctan\left(\frac{H_{ph}(r)-0.4 R_{*}}{r}\right)
\label{alphagr}
.\end{equation}
A positive grazing angle at a given radius results in an irradiated photosphere at that location, while regions that are not irradiated are shadowed by inner regions. Using Eq. 18 from \citet{calvet91}, we calculated the temperature in the mid-plane, accounting for viscous heating, stellar irradiation, and radiative cooling. The viscous contribution depends on both the surface mass density obtained after temporal evolution and on the mid-plane temperature itself (through the viscosity):
\begin{equation}
F_{v}(r) = \frac{1}{2} \Sigma(r) \nu(r) \left( R \frac{\mathrm{d}\Omega}{\mathrm{d}r} \right)^{2} = \frac{9}{4} \Sigma(r) \nu(r) \Omega^{2}(r)
.\end{equation}
Therefore, we solved Eq. 18 from \citet{calvet91} numerically as an implicit equation on the mid-plane temperature. Considering a hydrostatic equilibrium, the vertical density distribution follows a Gaussian, and we can use Eq. A9 from \citet{dullemond01} to calculate the ratio $\chi$ of the photosphere height to the pressure scale height. The disk vertical density profile is therefore assumed to be the same as an isothermal vertical structure at the mid-plane temperature. This approximation is reasonable below a few pressure scale heights, where most of the disk mass is located. The opacities are also functions of the temperature, as detailed in Sect. \ref{realopa}. We can then estimate the corresponding presumed photosphere height $H_{ph}$ at each radial location and therefore access $\frac{dH_{ph}}{dr}$. Applying Eq. \ref{alphagr}, we can verify whether the presumed grazing angle has the required precision or if we should iterate on it. The impossibility of solving that problem for any positive value of the grazing angle results in a disk column that is not directly irradiated by the star, and therefore we removed the irradiation heating term from the mid-plane temperature equation.
Thus, the geometrical structure (photosphere and pressure heights) was determined jointly with the temperature by iterating numerically on the grazing angle value: the algorithm is thoroughly described in \citetalias{baillie14}.
\subsection{Realistic opacities}
\label{realopa}
While \citetalias{baillie14} did take into account both sources of heating, they only partially considered the thermal variations of the physical composition of the disk. Indeed, \citetalias{baillie14} considered that the dust grains invariably have the same opacity for any temperature below 1500 Kelvin (considered here to be the sublimation temperature of the silicate dust); and another constant opacity (a hundred times lower) for temperatures above 1500 K. In the present paper, we refine the model by considering a more elaborate model of opacities based on optical constants measured in laboratory experiments, accounting for the variations of dust composition as a function of the local temperature. The computation of the Rosseland mean opacities follows the procedure described by \citet{helling00} and \citet{semenov03}. We assumed that the dust grains are composed of a mixture of different elements: olivine silicate, iron, pyroxene, troilite, refractory and volatile organics, and water ice, with initial abundances (before volatiles sublimation) given in Table \ref{tempchgt}. The relative abundances of the opacity model are updated depending on the temperature of the medium and the sublimation temperatures (Table \ref{tempchgt}). We assumed for the dust grains a modified MRN size distribution \citep{pollack85, helling00,semenov03}, that is, grain sizes varying from 0.005 to 5 $\mu$m with a $-3.5$ power-law exponent size distribution. The absorption coefficients of the composite dust grains were computed using the Maxwell-Garnett mixing rule followed by the Mie theory. The tabulated values of the gas opacity computation are taken from \citet{helling00}.
Figure \ref{opa} presents the Rosseland ($\chi_{R}$) and Planck ($\kappa_{P}$) opacity variations with temperature. The Planck mean opacities at stellar effective temperature $T_{*} = 4000$ K in extinction ($\chi_{P}^{*}$) and absorption ($\kappa_{P}^{*}$) are also shown. These opacities are necessary in particular for calculating the irradiation heating as described in \citet{calvet91}, \citet{jc04}, and \citet{jc08}.
It appears that these opacities vary by several orders of magnitude over the concerned temperature range and that these variations are particularly steep near the sublimation temperature of the major disk gas components. These elements and their sublimation temperatures are presented in Table \ref{tempchgt}; sublimation temperatures are given by \citet{pollack94}, corresponding to gas densities of about $10^{-10} \, \mathrm{g.cm^{-3}}$.
\begin{figure}[htbp!]
\center
\includegraphics[width=\hsize]{opacity_table.eps}
\caption{Mean-opacity variations with local temperature. Black: Rosseland mean opacity in extinction. Red: Planck mean opacity in absorption. Yellow: Planck mean opacity in extinction at stellar irradiation temperature. Blue: Planck mean opacity in absorption at stellar irradiation temperature.}
\label{opa}
\end{figure}
\begin{table}
\begin{center}
$\begin{array}{c|c|c}
\mathrm{Elements} & \mathrm{Sublimation} & \mathrm{Relative}\\
& \mathrm{Temperature} & \mathrm{Abundances}\\
\hline
\mathrm{Water\, ice} & \mathrm{160\, K} & 59.46 \, \% \\
\mathrm{Volatile\, Organics} & \mathrm{275\, K} & 5.93 \, \% \\
\mathrm{Refractory\, Organics} & \mathrm{425\, K} & 23.20 \, \% \\
\mathrm{Troilite\, (FeS)} & \mathrm{680\, K} & 1.57 \, \% \\
\mathrm{Olivine} & \mathrm{1500\, K} & 7.46 \, \% \\
\mathrm{Pyroxene} & \mathrm{1500\, K} & 2.23 \, \% \\
\mathrm{Iron} & \mathrm{1500\, K} & 0.16 \, \% \\
\end{array}$
\end{center}
\caption{Sublimation temperatures and relative abundances that affect the disk gas opacity.}
\label{tempchgt}
\end{table}
\subsection{Testing the radial resolution}
Our evolution code requires a double check both on the temporal and on the spatial resolution that the structure of our code (density time evolution precedes geometry and temperature calculation and so on for each iteration) allows us to treat sequentially. First, the timestep is adjusted to limit the mass transfers to 1\% of the available mass in each bin of the simulation, and then the radial resolution can be controlled by ensuring that the surface mass density profiles are consistent over 1 million years for different radial resolutions. Figure \ref{rescomp} shows the radial density profiles between 1 and 100 AU after 100,000 years and 1 million years for a range of radial resolutions extending from 5 points per decade to 50 points per decade. Stronger differences around 1 AU are due to the boundary conditions of the test numerical simulations for which the inner edge of the disk was considered to be at 1 AU for the purpose of the comparison: as the computation time increases exponentially, simulations using the highest number of points per decade could only be run over a few decades. We note that the surface mass density profiles are very similar until 100,000 years, after which the differences are more obvious. However, the density profiles remain quite close and the only consequence of the difference seems to be a delay in the viscous evolution for the simulations with 30 and more points per decade.
\begin{figure}
\begin{center} $
\begin{array}{c}
\includegraphics[width=8cm, clip=true]{yr_100000.eps}\\
\includegraphics[width=8cm, clip=true]{yr_1000000.eps}\\
\end{array} $
\end{center}
\caption{Compared evolution of the surface-mass density after 100,000 years (upper panel) and 1 million years of evolution (lower panel) of an initial MMSN for various resolutions from 5 to 50 points per decade.}
\label{rescomp}
\end{figure}
Therefore, we estimate that a disk evolution with a good radial resolution (e.g., 40 points per decade as in the rest of the paper) can be approximated from interpolating the density radial profile of a disk generated by a less radially resolved simulation (5 points per decade) for an accessible computation time. The thermal and geometric structure can then be calculated based on the resampled density structure of the disk.
Assuming a temperature profile following a power law in $T \propto r^{-0.5}$ and a temperature resolution of 0.01 K, we can analytically estimate the highest possible radial resolution for two consecutive bins to have temperatures that differ by at least that temperature precision: this optimal resolution is around 100 points per decade. To keep a safety margin (in particular to allow for the temperature fluctuations due to the opacities), we chose to resample our disks with 40 points per decade, which provides a good radial precision and allows a good thermal and geometrical precision.
\section{Results} \label{res}
We followed the evolution of an initial minimum mass solar nebula \citep{weiden77} with the scaling from \citet{hayashi81}:
\begin{equation}
\label{eqmmsn}
\Sigma (r) = 17,000 \left(\frac{r}{1 \, \mathrm{AU}}\right)^{-3/2} \mathrm{kg\cdot m^{-2}}
.\end{equation}
The central star was a classical T Tauri type young star with constant $M_{*} = 1 \, M_{\odot}$, $R_{*} = 3 \, R_{\odot}$, $T_{*} = 4000 \, \mathrm{K}$ and $\mathcal{L}_{*} = 4 \pi \, R_{*}^{2} \, \sigma_{B} \, T_{*}^{4}$ throughout the simulation.
The choice of the minimum mass solar nebula (MMSN) is motivated by several arguments. First, \citetalias{baillie14} investigated a diversity of initial disk conditions (total disk mass and radial distribution of the initial angular momentum) and found that these numerical simulations converged to similar steady states (characterized by a uniform mass flux and an asymptotic surface mass density distribution in $r^{-1}$), although in slightly different timescales. In addition, \citet{vorobyov07} showed that the MMSN density profile (following a power-law in $r^{-1.5}$) was consistent with an intermediate stage of an evolving protoplanetary disk under self-regulated gravitational accretion. Therefore, the MMSN profile makes an initial profile as reasonable as any other snapshot that could have been taken in the disk evolution. Finally, this fiducial case makes sense because we can better compare our results with previous studies.
\subsection{Time evolution}
\label{evol}
Figure \ref{sigma} presents the evolution of such a disk over 10 million years. Although the protoplanetary disk gas is believed to photo-evaporate in a few million years \citep{font04, alexander07, alexander09, owen10}, we let our numerical simulations extend over longer times to reach a stationary steady-state, which is
characterized by a uniform mass flux (within one order of magnitude maximum), as seen in Fig. \ref{fluxb}.
\begin{figure}[htbp!]
\center
\includegraphics[width=\hsize]{sigmam_MMSNmultit_1000.eps}
\caption{Surface mass density radial profile evolution for an initial minimum mass solar nebula in the case of a self-consistently calculated geometry with a full continuous model of opacities. Simulations are resampled to 40 points per decade.}
\label{sigma}
\end{figure}
As \citetalias{baillie14} detailed, the disk starts to spread viscously outward before beginning to accrete onto the central star after a few thousand years. Figure \ref{sigma} shows that the surface mass density radial profile can be modeled as a power
law by segments. While two segments seem to be sufficient until 10,000 years, longer evolution times require at least one more segment. In the early times, the single connexion point between the two power-laws connects an inner region that has already evolved toward a steady-state power-law radial profile for this region, and an outer region that is much closer to the initial state. We therefore call that radial location the relaxation radius. After 10,000 years, the (inner) relaxation radius is located between 7 and 10 AU. After 1 million years, a secondary "knee" appears around 250 AU. In the intermediate region (10-250 AU), the viscous evolution appears weaker than in the simulations
of \citetalias{baillie14} with a simpler opacity model. At 1 Myr, the surface mass density profile can be modeled as a power
law between 10 and 250 AU with $\Sigma(r) \propto r^{-1.2}$, and at 10 Myr, we can approximate the density profile by $\Sigma(r) \propto r^{-1.1}$. In this region, and evolved disks, the power-law indices are comparable with those from \citetalias{baillie14} and with those observed by \citet{isella09} in the Taurus region and \citet{andrews09} and \citet{andrews10} in the Ophiuchus region.
Figure \ref{fluxb} shows the time evolution of the mass flux as a function of the radial distance. We note that these radial profiles present bumps that were not visible in \citetalias{baillie14}. Although the directions and amplitudes remain globally identical, some irregularities appear; for example, in the 7-10 AU region where the 1 Myr flux profile is briefly inverted and the 10 Myr profile is no longer uniform over that range (the flux varies by almost a factor 10).
\begin{figure}[htbp!]
\center
\includegraphics[width=\hsize]{fluxb_MMSNmultit_1000.eps}
\caption{Mass flux radial profile evolution for an initial minimum mass solar nebula in the case of a self-consistently calculated geometry with a full continuous model of opacities.}
\label{fluxb}
\end{figure}
\subsection{Thermal evolution}
\label{Tevol}
The thermal evolution of the disk is presented in Fig. \ref{Tm}. The mid-plane temperature is calculated in a similar way to \citetalias{baillie14}. However, the calculation of the mid-plane temperature takes into account a composition of the dust that is consistent with the temperature (i.e., where sublimated species have been removed from the opacity calculation according to Table \ref{tempchgt}) while iterating over the possible grazing angles and mid-plane temperatures: the temperature obtained after the algorithm converged therefore validates the consistent composition. As described in Sect. \ref{methods}, the geometric and thermal structure are recalculated over 40 points per decade.
As in \citetalias{baillie14}, the mid-plane temperature presents irregular features that did not appear in the radial profiles obtained with the simpler opacity model of \citetalias{baillie14}. In particular, we note the temperature plateaux at the change of phase temperatures of the dust components (see Table \ref{tempchgt}). As the disk evolves, the sublimation plateaux drift inward: the silicate sublimation plateau is inside 0.2 AU after 1 Myr while it was originally between 0.3 and 1.3 AU. In addition to these plateaux, we note the troughs around 10 AU and 250 AU, which drift inward as the disk evolves. These features are analyzed more thoroughly in Sect. \ref{tempprofile}. However, it appears that the temperature in the region between these features can be modeled as a power law, with $T(r) \propto r^{-0.47}$ beyond 1 Myr, which recalls the usual approximation of \citet{chiang97} or \citet{dullemond01}, according to which $T(r) \propto r^{-1/2}$.
\begin{figure}[htbp!]
\center
\includegraphics[width=\hsize]{Tm_MMSNmultit_1000.eps}
\caption{Evolution of the mid-plane temperature as a function of the radial distance for an initial minimum mass solar nebula in the case of a self-consistently calculated geometry with a full continuous model of opacities.}
\label{Tm}
\end{figure}
\subsection{Geometry evolution}
\label{geoevol}
As the geometry of the disk is calculated jointly and self-consistently with the thermodynamical structure, irregular features can also be expected in the height radial profiles, as shown in Fig. \ref{hcgm}: the pressure scale height shows radial gradient discontinuities similar to those observed in Fig. \ref{Tm}. Similarly, it is possible to approximate the pressure scale height by an almost constant power law between 20 AU and 250 AU: $h_{\mathrm{pressure}} = r^{1.26}$ after 1 Myr and $h_{\mathrm{pressure}} = r^{1.28}$ at 10 Myr. These index values are very close to the $9/7$ index suggested by \citet{chiang97} in the case of a passive disk for which the photosphere height (height at which the line-of-sight optical depth equals 1) would be directly proportional to the pressure scale height. It appears then that the approximation
of $h_{\mathrm{pressure}} \propto r^{9/7}$ can only be valid in the region between 10 and 250 AU, where the disk photosphere is irradiated and the opacity varies smoothly with the temperature (i.e., where the temperature is lower than the sublimation temperature of the main components, as listed in Table \ref{tempchgt}).
\begin{figure}[htbp!]
\center
\includegraphics[width=\hsize]{hcgm_MMSNmultit_1000.eps}
\caption{Evolution of the pressure scale height as a function of the radial distance for an initial minimum mass solar nebula in the case of a self-consistently calculated geometry with a full continuous model of opacities.}
\label{hcgm}
\end{figure}
The radial profile of the photosphere height (Fig. \ref{Hm}) reveals a zone inside of 10 AU where the disk photosphere is irregularly irradiated, while it is entirely irradiated in the outer regions. Between 20 and 250 AU, the pressure scale height can be approximated by a power law: $H_{\mathrm{photo}} \propto r^{1.11}$ after 100,000 yr and $h_{\mathrm{pressure}} \propto r^{1.14}$ at 1 Myr and 10 Myr. These index values are reminiscent of those expected by \citet{kenyon87} around $9/8$ and obtained by the numerical simulations of \citetalias{baillie14}.
\begin{figure}[htbp!]
\center
\includegraphics[width=\hsize]{Hm_MMSNmultit_1000.eps}
\caption{Evolution of the photosphere height as a function of the radial distance for an initial minimum mass solar nebula in the case of a self-consistently calculated geometry with a full continuous model of opacities.}
\label{Hm}
\end{figure}
The evolution of the photosphere height over pressure scale height ratio $\chi$ is displayed in Fig. \ref{khim}. As predicted by \citet{dullemond01}, the values are in the range from 1.5 to 6. However, unlike the usual approximation ($\chi = 4$) suggested by \citet{chiang97}, this ratio is neither constant nor uniform. This $\chi$ profile, like the grazing angle $\alpha$ profile (Fig. \ref{alphagrm}) show similar gradient discontinuities as in the surface mass density or temperature radial profiles. The non-irradiated zones also appear quite obvious in these figures because they correspond to locations where $\chi$ and the grazing angle are not defined.
\begin{figure}[htbp!]
\center
\includegraphics[width=\hsize]{khim_MMSNmultit_1000.eps}
\caption{Evolution of the pressure scale height to photosphere height ratio as a function of the radial distance for an initial minimum mass solar nebula in the case of a self-consistently calculated geometry with a full continuous model of opacities. Missing points are due to the regions of the disk that are not directly in the stellar line of sight at a given location and evolution time.}
\label{khim}
\end{figure}
\begin{figure}[htbp!]
\center
\includegraphics[width=\hsize]{alphagrm_MMSNmultit_1000.eps}
\caption{Evolution of the grazing angle as a function of the radial distance for an initial minimum mass solar nebula in the case of a self-consistently calculated geometry with a full continuous model of opacities. Missing points are due to the regions of the disk that are not directly in the stellar line of sight at a given location and evolution time.}
\label{alphagrm}
\end{figure}
\section{Discussion} \label{disc}
\subsection{Influence of the disk composition on density and temperature local gradients}
By comparing these results with the simulations of \citetalias{baillie14}, we note how important it is to take the physical composition of the dust into account by using a complete model of opacities that varies with temperature. The main difference in the surface mass density radial profiles resides in the secondary knee that appears at 1 Myr around 250 AU. Earlier conclusions from \citetalias{baillie14} remain valid: the surface-mass density profile evolves toward a shallower profile, first in the inner regions and then increasingly farther away from the star. However, when the relaxation radius reaches 250 AU, the profile is then fragmented into three power-law segments. This creates a discontinuity in the density gradient that may strongly influence the exchange of angular momentum with possible planetary cores within the disk (see Sect. \ref{torque}). In addition to that, we note that the mass flux may reverse in the middle of the disk until as late as 1 Myr. These density bumps obviously have consequences for the thermodynamical and geometrical structures. The mid-plane temperature and grazing angle radial profiles do in fact present new features, particularly at the radii of these discontinuities, when the physical composition of the disk is properly treated. Temperature plateaux are other important consequences as they may affect, for instance, the snowline position (see Sect. \ref{snowline}).
\subsection{Temperature radial profile analysis}
\label{tempprofile}
Figure \ref{profilT} details the temperature structure in the mid-plane of the protoplanetary disk after 1 Myr of evolution. As well as the mid-plane temperature, Fig. \ref{profilT} also displays the grazing angle and optical depth radial profiles, and the distribution of the heating sources.
\begin{figure}[htbp!]
\center
\includegraphics[width=\hsize]{disk_1000000sav_tau.eps}
\caption{Mid-plane temperature radial profile (black) after 1 million years of evolution of a minimum mass solar nebula with a self-consistently calculated geometry and a full continuous model of opacities. Disk shadowed regions are displayed in gray. The ratio of the viscous heating contribution over the total heating (viscous heating rate) is presented in red, the grazing angle radial profile in yellow, and the optical depth radial profile in blue.}
\label{profilT}
\end{figure}
We first note is that the black curve shows temperature plateaux that coincide with the sublimation temperatures listed in Table \ref{tempchgt}. These plateaux are not flat, but present variations of a few Kelvin over radial regions that may be up to 1 AU wide. As Fig. \ref{opa} showed, opacities may vary quite strongly with temperature around these changes of phases. Thus, the temperature drop induced by a local surface mass density variation can be compensated for by an opacity variation over a few Kelvin to provide the equivalent heat and maintain a quasi-constant temperature. In these regions, the irradiation heating effectively has a more important contribution than outside, where it tends to become negligible compared to the viscous heating. This is confirmed by the red curve, which represents the ratio of the viscous contribution over the total heating received by the disk (viscous heating rate): the troughs at 0.1, 0.4, 0.7, 1.2, and 2 AU coincide with the temperature plateaux. This transition is called heat transition barrier by \citet{hasegawa112}. In addition, we note that the silicate sublimation plateau migrates inward as the disk evolves, and after 1 Myr, it is located at the disk inner edge. We interpret the inner disk physical structure as follows:
\begin{itemize}
\item The surface mass density is generally a decreasing function of the radial distance.
\item When a phase-transition temperature is reached, the opacity suddenly increases because of new condensed species, even though the temperature remains stable over a few fractions of an AU.
\item The viscosity $\nu = \alpha_{\mathrm{visc}} \, c_{s} \, h_{\mathrm{pressure}}$ therefore follows the temperature stability. As the density and the angular velocity decrease outward, the quantity of viscous heating decreases as well.
\item To maintain the temperature, the irradiation heating tries to compensate for the viscous heating loss, looking for an optimal grazing angle that can maximize the irradiation heating from the star.
\item At some radii, the disk photosphere geometry is such that the irradiation heating can no longer compensate for the loss in viscous heating. The grazing angle then drops until the disk photosphere is not irradiated anymore. The viscous heating remains the only source of heating, resulting in a shadowed region.
\item The temperature decreases again because of the lack of irradiation heating. However, the opacity variation is smoother now that we are no longer at the phase transition temperature. The viscosity now decreases, reinforcing the decrease in viscous heating. In the meantime, the opacity is now much higher than it was before the change of phase.
\end{itemize}
In addition to these plateaux, the mid-plane temperature radial profile shows two important troughs with an amplitude drop of about 10 Kelvin. The first one, located around 10 AU, coincides with the limit where the dominating source of heating changes: viscous heating is clearly stronger below 10 AU, while stellar irradiation heating dominates outside that limit (red curve from Fig. \ref{profilT}). The second trough, around 250 AU, generates a drop in temperature from 20 to 8 Kelvin. At these temperatures, the opacity varies by two orders of magnitude over a temperature range of 20 Kelvin (Fig. \ref{opa}): the grazing angle drops and the geometry tends to shadowing. The temperature bump disappears in simpler opacity models \citepalias{baillie14}. In addition, it remains present (although less pronounced) in earlier evolution ages.
Furthermore, we note that in the irradiation-dominated region, the disk is permanently irradiated, which is not the case in the inner regions (see gray bands in Fig. \ref{profilT}). These shadowed regions coincide with a drop in the grazing angle (see yellow curve in Fig. \ref{profilT}). Moreover, all the temperature plateaux (all are located below 10 AU) correspond to irradiated zones, while the outer edges of the plateaux (where the temperature starts dropping again) trigger shadowed regions, as detailed above. The region between 20 and 250 AU matches the two-layer model of \citet{chiang97} well because the temperature is clearly below the dust sublimation temperatures, and therefore in a temperature domain where the opacity varies so smoothly that it can approximated by a constant, allowing the retrieval of the simulation results from \citetalias{baillie14}.
Finally, the stellar line-of-sight optical depth radial profile (blue curve in Fig. \ref{profilT}) shows that the disk becomes optically thin beyond 20 AU. However, the optical thickness drops again at the heat transition barrier (around 10 AU at 1 Myr)
\subsection{Snow region}
\label{snowline}
While the snowline is defined as the radius at which the temperature is equal to the water ice condensation temperature (160 K), the fact that we now observe a plateau around that temperature shows that we should rather talk about a snow region than a snowline. Figure \ref{snowzone} presents the evolution of the inner and outer edges of the plateau around the water ice condensation temperature. Given the precision on the temperature, and in the opacity model, we chose to define the plateau temperature range as $160 \, \mathrm{K} \, \pm \, 2 \, \mathrm{K}$. The snow region can be as wide as 1 AU at early ages and migrates inward until it stabilizes below 2 AU in a few Myr
\begin{figure}[htbp!]
\center
\includegraphics[width=\hsize]{snowzone2.eps}
\caption{Time evolution of the snow region (mid-plane radial location for which the temperature coincides with the water-ice condensation temperature $\pm$ 2 K).}
\label{snowzone}
\end{figure}
Similarly, we define the silicate sublimation region in place of the silicate sublimation line at $1500 \, \mathrm{K} \, \pm \, 20 \, \mathrm{K,}$ and we present the evolution of its edges in Fig. \ref{sublzone}. The sublimation region initially spreads from 0.3 to 1.3 AU. It also migrates inward and seems to reach the inner edge of the disk in a few Myr.
\begin{figure}[htbp!]
\center
\includegraphics[width=\hsize]{subzone2.eps}
\caption{Time evolution of the silicates sublimation zone (mid-plane radial location for which the temperature coincides with the silicate sublimation temperature $\pm$ 20 K).}
\label{sublzone}
\end{figure}
It appears that the zone of the mid-plane in which the sublimation of an element can occur is AU-wide instead of the expected sharp frontier usually called snow or sublimation line. At this temperature, the corresponding element is sublimated, which affects the medium opacity and therefore the heating received by the disk at this location. This heating variation is compensated for by a grazing angle variation that maintains a smoother continuity of the temperature and gas-to-dust ratio. The origin of the plateau is therefore related to the partial and gradual sublimation of the element that is sublimated at this temperature: the gas-to-dust ratio of that element is close to 0 at the outer edge of the plateau while it increases inward up to 1 at the inner edge. The other elements gas-to-dust ratios are mostly unaffected at this temperature. Partial sublimation could occur layer by layer on dust particles or on a vertical scale (the column height of the sublimated material increasing inward).
The changes of phase can now occur in much wider regions than the previous snowlines. This may favor smooth variations in physical compositions across the disk as the planetary embryo migrates inward across the snow or sublimation region. This may influence the chemical models, for example, those that try to explain the abundance of carbon in the so-called carbon-rich planets: \citet{fortney10} and \citet{madhu11} suggested that, at equilibrium, all the available O should go into organics, whereas \citet{venot12} described a non-equilibrium chemistry to model the C/O ratio. Therefore, the shallow variations of the temperature profile may favor equilibrium chemistry.
\section{Consequences on planet traps and deserts}
\label{torque}
The results reported above clearly show that rapid variations of temperature and density occur in the disk in the transition region. It is thought that such a transition may potentially create planets traps and deserts. This has been explored previously in static-disk models, but never in dynamically evolving disks. Thus in the following we compute the torque that the disk would exert on a putative planet. In particular we explore how planet traps appear, move, and disappear in the disk.
Assuming that it has already formed, a planetary embryo exchanges angular momentum with the disk \citep{goldreich79,ward88,arty93,jc05}. These exchanges are due to the resonances excited by the planetary embryo in the disk (Lindblad resonances caused by the action of the induced spiral arms, and corotation resonances). Thus, the planet exerts a torque on the disk and therefore the disk exerts an opposite torque on the planet. We calculate these torques in the case of the evolved disk described in the previous section. We then study their effects on potential planetary embryos. We assume here that the disk structure is not modified by the planet.
\subsection{Lindblad torques}
A given perturber, such as the planet in our disk, excites Lindblad resonances of multiple orders \citep{goldreich79,goldreich80}. Using a two-dimensional approximation, considering laminar disks, a planet on a circular orbit, ignoring the disk self-gravity and assuming thermal equilibrium, \citet{paarp08} were able to derive the following formula for the total Lindblad torque exerted by the disk over the planet:
\begin{equation}
\label{gammalin}
\Gamma_{\mathrm{Lindblad}} = - \frac{\Gamma_{0}(r_{P})}{\gamma} \left(2.5 \, - 1.7 \frac{\partial \ln T}{\partial \ln r}(r_{P}) + 0.1 \frac{\partial \ln \Sigma}{\partial \ln r}(r_{P}) \right)
,\end{equation}
with $\gamma = 1.4$, the adiabatic index,\\
$\Gamma_{0}(r_{P}) = \left(\frac{q}{h}\right)^{2} \, \Sigma(r_{P}) \, r_{P}^{4} \, \left(\Omega(r_{P})\right)^{2}$,\\
$h=\frac{h_{\mathrm{press}}(r_{P})}{r_{P}}$,\\
and $\Omega(r_{P})$ the Keplerian angular velocity at the planet position in the disk.
Although we just showed in the previous sections that the disk can present radial variation in density and temperature gradients, the torque expressions are still evaluated at the planet radial location. \citet{ward97}, \citet{hasegawa111,hasegawa112}, and \citet{masset11} (Appendix B) developed fully analytic torque expressions that could account for the local gradients at each resonance location rather than just considering the gradients at the planet radius. However, these formulas could not retrieve the amplitude of the expression derived in \citet{paarp08}, which was benchmarked against numerical simulations. In addition, more subtle expressions involving the second derivative of the temperature derived by \citet{masset11} (Eq. 79) were only tested in an isothermal disk. To be consistent with the corotation torque expressions from \citet{paar11}, we therefore estimated the total Lindblad torque using the expression of \citet{paarp08} (our Eq. \ref{gammalin}).
We note that the Lindblad torque presents a stronger dependence on the temperature gradient than on the density gradient, which reflects the effect of the pressure buffer described in \citet{ward97}. Following a similar process as in \citet{bitsch11} and \citet{bitsch13,bitsch14}, we can use here the results of Sect. \ref{res}, which provide the density and temperature of an evolved disk at a given date, therefore gaining in consistency as the temperature is not set to a power law and is calculated jointly with the geometry of the disk from the density resulting of the viscous evolution.
\subsection{Corotation torques}
Corotation resonances are known to exert complicated torques that include linear and nonlinear parts. \citet{paarp09b} showed that the corotation torques are generally nonlinear in the usual range of viscosity ($\alpha_{\mathrm{visc}} < 0.1$). The nonlinear contribution, due to the horseshoe drag \citep{ward91} caused by the interaction between the planet and the fluid element moving in its vicinity, is also known for having two possible origins: barotropic, intially formalized by \citet{tanaka02}, and entropic, detailed by \citet{baruteau08}.
Concerning the horseshoe drag, \citet{paar11} described the density perturbation generated by the corotation resonances and provided expressions for both the entropy and vortensity (or barotropic) contributions. Assuming a gravitational softening $b=0.4 h_{\mathrm{press}}$, \citet{bitsch11} and \citet{bitsch14} summarized these expressions to obtain the following contributing torques:
\begin{eqnarray}
\label{gammahsentro} \Gamma_{\mathrm{hs,entro}} &=& - \frac{\Gamma_{0}(r_{P})}{\gamma^{2}} \, 7.9 \, \left(-\frac{\partial \ln T}{\partial \ln r}(r_{P}) + (\gamma-1) \frac{\partial \ln \Sigma}{\partial \ln r}(r_{P}) \right)\\
\label{gammahsbaro} \Gamma_{\mathrm{hs,baro}} &=& - \frac{\Gamma_{0}(r_{P})}{\gamma} 1.1 \left(\frac{\partial \ln \Sigma}{\partial \ln r}(r_{P}) + \frac{3}{2}\right)
.\end{eqnarray}
\citet{paar11} showed that in the absence of saturation of the linear contributions, the total corotation torque can be defined as
\begin{equation}
\label{gammacor}
\Gamma_{\mathrm{corotation}} = \Gamma_{\mathrm{hs,baro}} + \Gamma_{\mathrm{hs,entro}}
.\end{equation}
It appears that this unsaturated corotation torque strongly depends on the temperature and surface mass density gradients. It also
scales with $M_{\mathrm{P}}^2$, as does the Lindblad torque. However, \citet{paarp09a} showed that given the viscous, diffusive, and libration timescales, the linear effects of the corotation torques can be saturated for some viscosities and some planet masses. For our disk that evolved for 1 Myr, the viscosity range compared to Fig. 14 from \citet{paarp09a} suggests that saturation cannot be neglected for planetary masses higher than $6 M_{\mathrm{\oplus}}$. \citet{paar11} defined weight functions for the partial saturation of the corotation torque. These functions vary with the half-width of the horseshoe, which depends on the mass of the planet. Appendix A of \citet{bitsch11} summarized this method and added correcting factors. We used a similar torque calculation, which is necessary to take into account the variations with the planet mass.
\subsection{Planetary core migration}
\subsubsection{Migration direction}
In the present exercise, we set the planet mass to a typical giant planet core mass $M_{P} = 10 \, M_{\mathrm{\oplus}}$ and varied $r_{P}$, the initial planet location. The total torque exerted by the disk over the planet is given by
\begin{equation}
\label{gammatot}
\Gamma_{\mathrm{tot}} = \Gamma_{\mathrm{Lindblad}} + \Gamma_{\mathrm{corotation}}
.\end{equation}
A positive torque exerted by the disk on the planet means that the disk gives angular momentum to the planet and therefore that the planet migrates outward. In contrast, a negative total torque results in the disk gaining angular moment from the planet, and the planet migrating inward. Thus, at the locations where the total torque sign changes, we can define two physical radii:
\begin{itemize}
\item If the total torque is negative inside and positive outside that line, the potential planets are driven away from that location, therefore defining a depleted region in planetary cores, corresponding to the planet deserts of \citet{hasegawa12}.
\item If the total torque is positive inside and negative outside, the potential planets converge toward this location, which we thus call a planetary trap. Such a zero-torque radius was called by \citet{lyra10} the equilibrium radius. \citet{hasegawa111} studied the vertical effects of the planet mass, but only considered fixed surface mass density radial profiles, while \citet{hasegawa112} estimated planet trap locations due to Lindblad torques alone.
\end{itemize}
\subsubsection{Density and temperature features at the origins of the traps and deserts}
Figure \ref{multitorque1M} presents the radial profiles of the Lindblad, corotation and total torques after 1 million years of evolution, when the planetary cores can already exist but the gas disk is not yet completely photo-evaporated. We chose to focus on the planetary formation region and therefore to limit the radial extent of our migration investigation up to 20 AU. The torques are normalized by $\Gamma_{0}$. A left-pointing arrow shows a negative torque and therefore an inward migration, while a right-pointing arrow shows a positive torque or outward migration.
\begin{figure}[htbp!]
\center
\includegraphics[width=\hsize]{resample1000000_xlog.eps}
\caption{Radial radial profile of the migration torques (black arrows showing the direction of migration: outward for positive torques and inward for negative torques) after 1 Myr of evolution. Lindblad torques (blue), corotation torques (red), and shadowed regions (gray) are also represented.}
\label{multitorque1M}
\end{figure}
The Lindblad torque is mostly negative except around 10 AU, where the temperature gradient is reversed. The corotation torque is mainly positive, but it can become negative in the temperature plateaux regions where the temperature gradient is shallower (Fig. \ref{tottorque1M}). The orders of magnitude of the two contributions are comparable, and the resulting total torque alternates between positive (outward) regions and negative (inward) regions. After 1 million years of evolution, outward migration could occur below 0.33 AU, between 0.41 and 0.60 AU, between 0.85 and 1.7 AU, and between 2.2 and 8.0 AU. As a consequence, planets could accumulate at the traps located around 0.33, 0.60, 1.7, and 8.0 AU and the regions around 0.41, 0.85, and 2.2 AU should be strongly depleted in planets. The snowline (dotted line at 1.8 AU in Fig. \ref{multitorque1M}) seems to be closely related to the nearby trap at 1.7 AU: the inner edge of the 160 K-plateau coincides with a trap, while there is a planetary desert at the outer edge of the plateau, as shown in Fig. \ref{tottorque1M},
which presents the total torque together with the surface mass density and temperature radial profiles. As a comparison, \citet{bitsch11} found a possible equilibrium radius around 12.5 AU for a 20 Earth-masses planet, which could be consistent with our 8 AU-trap.
As the total torque strongly depends on the surface mass density and temperature gradients (see Eqs. \ref{gammalin}-\ref{gammatot}), we can here relate the torque radial profile with the bumps in surface mass density and troughs in temperature. We note here that the density bump around 6 AU seems to result in a stronger positive torque gradient, in agreement with the estimate of \citet{masset06b} that sharp surface mass density gradients are required to slow-down type I migration. On the other hand, the temperature irregularity located between 9 and 10 AU seems to be at the origin of the torque inversion in this region. The density profile there does not seem to affect the total torque trend. This sharp temperature gradient appears to be correlated with an inner shadowed region, as expected by \citet{kretke12}, who described a model in which the absence of stellar irradiation could lead to an outward migration, and therefore estimated that sustaining an outward migration in an irradiated and active disk would be difficult without any shadowing effects. This correlation confirms the importance of properly taking into account the geometry and photosphere irradiation. \citet{kretke12} found traps inside 1 AU for the most massive embryos and estimated that a mass accretion rate $\dot{M}\, > \, 10^{-8}\, M_{\odot}.\mathrm{yr}^{-1}$ was required to trap planetary cores at radii compatible with known gas giant planet radii. This is compatible with our present study and the mass accretion rates obtained by \citetalias{baillie14} for evolution ages younger than 1 Myr.
\begin{figure}[htbp!]
\center
\includegraphics[width=\hsize]{resample1000000_lincor_TSxlog.eps}
\caption{Radial profile of the total torque (black arrows showing the direction of migration) after 1 Myr of evolution. Temperature radial profile (blue curve), surface mass density radial profile (red curve), and shadowed regions (gray regions) are also represented.}
\label{tottorque1M}
\end{figure}
\subsubsection{Earlier time evolution}
To follow the evolution of the trap and desert locations, Fig. \ref{torquemultit} presents the total torque profiles as functions of the radial distance for different ages. After 1000 years, we can only find two traps around 0.22 and 11 AU and one desert located at 7 AU. The trap is correlated with the shadow region just outside the temperature plateau at the water ice sublimation temperature (160 K).
After 10,000 years, we now have two traps (4 and 13 AU) and three deserts (3.5 and 6 AU), while the water ice sublimation plateau appears to be located around the 5 AU. The outer trap may be due to the temperature gradient inversion there.
After 100,000 years of evolution, we now have four traps (0.45, 0.75, 2, and 10 AU) and four deserts (0.23, 0.6, 1, and 3 AU). The traps appear to be located in the outer parts of the shadowed regions, while three of the deserts are at the inner edges of the shadowed zones. In addition, the water ice line coincides with the trap at 2 AU.
Traps and deserts seem to relate better to the variation in the temperature gradient than to the surface mass density gradient trends, as expected from the coefficients in Eq. \ref{gammalin}.
\begin{figure}[htbp!]
\begin{center} $
\begin{array}{cc}
\includegraphics[width=\hsize, clip=true]{resample1000_lincor_TSxlog.eps}\\
\includegraphics[width=\hsize, clip=true]{resample10000_lincor_TSxlog.eps}\\
\includegraphics[width=\hsize, clip=true]{resample100000_lincor_TSxlog.eps}\\
\end{array} $
\end{center}
\caption{Radial profiles of the total torque (black arrows showing the direction of migration) after 1000 years (upper panel), 10,000 years (middle panel), and 100,000 years (lower panel) of evolution. Temperature radial profiles (blue curve), surface mass density radial profiles (red curve), and shadowed regions (gray regions) are also represented.
\label{torquemultit}
\end{figure}
\subsubsection{Trap and desert migration}
To better follow the evolution of the traps and deserts, Fig. \ref{traptime} presents the variations in number and position of these traps and deserts.
\begin{figure}[htbp!]
\center
\includegraphics[width=\hsize]{rmulti_1000_lc_log.eps}
\caption{Time evolution of the migration traps (blue "+") and deserts (red "x"). The snowline position (dotted line) and the heat transition radius (dashed line) are also represented.}
\label{traptime}
\end{figure}
Figure \ref{traptime} shows the evolution of the traps and deserts. We first note that in the early evolution of the disk, it seems to be possible to create traps and deserts below 0.3 AU. However, as these traps disappear in a few thousand years (much before a steady-state is reached), they probably only exist as long as the disk "remembers" the initial condition of the simulation. Second, it appears that there is a permanent trap correlated with the heat transition barrier (dashed line): this trap is systematically slightly (less than 1 AU) inward of that viscous-irradiation transition (consistent with the planetary trap position of a 20 Earth-masses planet estimated by \citet{bitsch11}), recalling
the estimate of \citet{hasegawa112} that the heat transition barrier was at the origin of trapping regions. Between 10,000 and 100,000 years, the heat transition barrier moves slightly outward, which may coincide with the outward drift of the relaxation radius that crosses the planetary formation region at this age (see Sect. \ref{sigma}). That trapping location is the outer boundary of an outward-migrating region that initially spreads from around 6.5 AU (about 1 AU outer to the water ice sublimation line) up to $\sim$ 13 AU. After 10,000 years of evolution, that outward-migrating region is divided into two (sometimes three) sequences of (outward-migrating + inward-migrating) regions. A depleted zone in planets can be found $\sim$ 1 AU outside of the water ice sublimation line at any time.
After 10,000 years, we also note traps and deserts following the main dust component sublimation lines:
\begin{itemize}
\item the water ice sublimation line coincides with a systematic trap,
\item the volatile organics sublimation line is closely accompanied by an inner trap and an outer desert,
\item the refractory organics and troilite sublimation lines are similarly bordered, if not as closely as the volatile organics line,
\item the silicate sublimation line is closely followed by an outer desert region.
\end{itemize}
From Fig. \ref{tottorque1M}, we can infer that the space between two sublimation regions is a zone of outward migration: therefore the chances of a planet to become trapped or significantly slowed down in the inner disk are not negligible. Once trapped, the forming planet is very likely to follow the trap migration. In addition, most of the planet traps (those that are correlated with the heat-transition barrier or the ice lines) seem quite sustainable: these traps and deserts slowly migrate inward with the sublimation lines as the disk ages and cools down. Only a few isolated transient traps and deserts appear between the water-ice line and the heat-transition barrier. However, it is very likely that a planet in such a disappearing trap would be trapped again in the next outer trap.
\citet{kley09} suggested that a possible scenario to address the inconsistency between the formation and migration timescales could be the retention of the icy cores at the snowline. We extend
this: it is possible to trap planets at any main dust component sublimation line. Dust sublimation is a physical mechanism sufficiently efficient to trap planets along the ice lines. In addition, as suggested by the correlation of the trap or desert locations with respect to the shadowed regions (Fig. \ref{tottorque1M}), the heating sources play an important role in trapping planets. This is reinforced by the presence of traps along the heat-transition barrier.
\subsubsection{Perspectives}
Although multiple planet-systems seem to be the most common configuration, we here only studied the interaction of a single planet with the disk. \citet{cossou13} showed that multiple planetary cores tend to be trapped in chains of mean motion resonances. Therefore, a proper treatment of multiple planet interaction with the disk requires considering the dynamics of these planets in addition to the disk dynamics. Coupling our hydrodynamical approach with an N-body code requires a more thorough study and will be the object of a future paper. In addition, as we have detailed, our current model does not take into account the feedback of the planet on the disk, which is currently not affected by the planet. This might also be necessary for future studies.
We leave the consideration of dead zones for
a future paper because they probably generate density and temperature irregularities that have been shown to be favorable for creating planetary traps and deserts. Although the torque expressions detailed above show a limited dependency on the planet mass ($\propto M_{\mathrm{P}}^{2})$), this is kept for a subsequent review, along with the dependency on the disk mass and the mass accretion rate.
\section{Conclusions}
We have studied the viscous evolution of a protoplanetary disk, using an $\alpha$ prescription for its viscosity. Starting with an initial minimum mass solar nebula, we self-consistently calculated the geometry, thermodynamics, and density distribution evolution of such a disk, taking into account the various sources of heating (viscous and irradiation), the shadowing effects, and the physical composition. The physical phases of the various dust components have a dramatic influence on the opacity of the disk and therefore reflect on the mid-plane temperature. The evolved density radial profiles present a few irregularities compared to the previous
results of \citetalias{baillie14}. These density bumps mainly result in temperature features (bumps, troughs, plateaux) and also widen the snowline and sublimation line regions. Our main result is that snowlines may better be called snow regions, AU-wide smooth variations, rather than sharp frontiers in the disk. Close to the sublimation temperature of the main dust elements, the disk mid-plane temperature becomes constant. This could result in a less sudden and strong change of phase than initially thought, involving partial sublimation. Given an element in Table \ref{tempchgt}, and if we focus on the disk mid-plane region for which the temperature corresponds to that element sublimation temperature within a few Kelvin, the gas-to-dust ratio of that element would vary from $\sim 0$ at the outer edge of the temperature plateau to $\sim 1$ at the inner edge (the rest of the material is unaffected at these temperatures). A planetesimal crossing such a region inward might then be able to melt layer by layer, with possible consequences on its mineral petrology in the case of a future recondensation. Another way to model the partial sublimation would be to consider a vertical gradient of gas-to-dust ratio for the element in question: the element would be sublimated from the mid-plane up to a given altitude that would vary with the radial distance in the plateau. The farther into the plateau, the higher that limit, and the greater the proportion of the material of the column that is sublimated. Such a refinement would affect the dust vertical transport as studied by \citet{ciesla10b}, for example. Possible combinations of vertical and radial gradients of gas-to-dust ratio could also reflect the physics of the temperature plateaux.
From these density and temperature radial profiles, we estimated the resonant torques that potential planetary cores would exert on the disk. From the total torque sign (resulting from the Lindblad and corotation resonances), we derived the locations of planetary traps and deserts and followed their own migration as the disk ages: after 1 Myr, four planetary traps were identified around 0.33, 0.60, 1.7, and 8.0 AU, with three planetary deserts around 0.41, 0.85, and 2.2 AU.
As stated by \citet{masset06b}, density and temperature discontinuities appear to be the key characteristics leading to the generation of planetary traps: temperature troughs, density bumps, changes of phases, and heat transitions clearly affect the potential planet migration. Previous works indicated that density and temperature irregularities can slow down type I migration to allow planets to grow in a reasonable time. Our evolution code shows that such structures naturally arise during the disk evolution when the coupling between the disk dynamics, thermodynamics, and geometry is taken into account: planets can be trapped at the main dust component sublimation lines. Additional simulations are still required to estimate by how much planetary embryos can be slowed down by being trapped, and whether they can actually migrate along with the planetary traps. It appears necessary to synchronize the planet and trap migration rates, and this study requires a more thorough calculation of the planet feedback on the disk. Other sources of discontinuities, such as deadzones, may affect these migration torques and create more planetary traps or deserts. This will be treated in a separate paper.
\begin{acknowledgements}
We thank Esther Taillifet for enlightening discussions. We are also indebted to Bertram Bitsch and Dominic Macdonald for valuable suggestions that improved the quality of the manuscript significantly. We also thank the referee for detailed and constructive comments that improved the quality of the paper. This work was supported by IDEX Sorbonne Paris Cit\'e. We acknowledge the financial support from the UnivEarthS Labex program of Sorbonne Paris Cit\'e (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02).
\end{acknowledgements}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,363 |
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{"url":"https:\/\/goodresearch.dev\/zipf.html","text":"# A sample project: Zipf\u2019s law\u00b6\n\nLet\u2019s look at how we can use the suggested organization in a real project. We use the example of calculating Zipf\u2019s law for a series of English texts, which was suggested in the book Research Software Engineering in Python, and was released under a CC-BY license. You can see the completed project on Github.\n\n## What is Zipf\u2019s law, anyway?\u00b6\n\nZipf\u2019s law comes from quantitative linguistics. It states the most used word in a language is used twice as much as the second most used word, three times as much of the third, etc. It\u2019s an empirical law that holds in different languages and texts. There\u2019s a lot of interesting theories about why it should hold - have a look at the Wikipedia article if you\u2019re curious. A generalized form of Zipf\u2019s law states that:\n\n$p(r) = \\frac{1}{Cr^\\alpha}$\n\nThat is, the frequency of $$r^{th}$$ most frequent word in a language is a power law with exponent $$\\alpha$$; the canonical Zipf\u2019s law is obtained when $$\\alpha=1$$. $$C$$ is a constant that makes the distribution add up to 1.\n\n## Our project\u00b6\n\nThe goal of the project is to measure that Zipf\u2019s law holds in three freely available texts. We\u2019ll proceed as follows:\n\n2. compute the distribution of words\n\n3. fit Zipf\u2019s law to each of them\n\n4. output metrics\n\n5. plot some diagnostics\n\nLet\u2019s consider different ways to organize the different subcomponents and define how they should interact with each other. It\u2019s clear that the processing has the nice structure of a (linear) directed acyclic graph (DAG).\n\nFig. 13 The Zipf project can be described as a linear directed acyclic graph (DAG)\n\nApproach 1. We could make each box a separate script with command line arguments. Each script would be backed with module code that would help in a common library. Then, we would glue these scripts together with a bash file, or perhaps with make. This approach has a lot of merit, and in fact was the one that was originally suggested by the book: it\u2019s clean and it\u2019s standardized. One inconvenience is that it involves writing a lot of repetitive code in order to define command line interfaces. There\u2019s also a bit of overhead in writing both a script and module code for each subcomponent.\n\nApproach 2. We could make each box a separate function, held in a module. Then, we would glue these functions together with a Python script. This Python script would have its own command line arguments, which we could set in a bash script. One merit of the approach is that it has less overhead - fewer files and cruft - than the first approach.\n\nThe tradeoff between these two approaches lies in the balance between generality and complexity. The first is a bit more flexible than the second. We can\u2019t run a single component of our analysis separately from the command line - we\u2019ll need to implement tests instead, which feel a little less intuitive. If we wanted to run an analysis of tens of thousands of books, parallelizing would also be easier with the first approach (e.g. with make).\n\nFor this example, however, I have a slight preference for the second approach, so that\u2019s the one we will implement. Keeping the number of command line tools to create to one means we\u2019ll worry less about cruft and more about the computations. Let\u2019s take a look at the DAG again to see how we\u2019ll split the job:\n\nFig. 14 The Zipf project split into different sub-components.\n\nWe\u2019ll create one module to compute the distribution of words, and another to fit Zipf\u2019s law. We will create tests for each of those two modules. We\u2019ll wrap the two modules as well as glue code inside a command line tool. Plotting will take place in jupyter notebook, which makes it easy to change plots interactively.\n\nI encourage you to also have a look at the Python RSE github repo for an alternative implementation to examine the tradeoffs in different implementations.\n\nNote\n\nMost of the code is taken verbatim from the Py-RSE repo. Our emphasis here is on organizing project files.\n\n## Setup\u00b6\n\nLet\u2019s proceed with setting up the project. zipf is a reasonable project name, so let\u2019s go ahead and create a new project with that name:\n\n(base) ~\/Documents $cookiecutter gh:patrickmineault\/true-neutral-cookiecutter Use zipf, zipf, and zipf as the answers to the first 3 questions, and \u201cZipf\u2019s law project\u201d as the description. Then proceed to create an environment and save it: cd zipf conda create --name zipf python=3.8 conda activate zipf conda env export > environment.yml Then we can sync to a Github remote. My favorite way of doing this is to use the GUI in vscode, which saves me from going to Github to create the remote and then type on the command line to sync locally. We can fire up vscode using: code . Then, in the git panel, we hit \u201cPublish to Github\u201d to locally set up git and create the Github remote in one shot. Now we have a good looking project skeleton! We can set up black in vscode so that whenever a file is saved, it is formatted in a standard way. Time to add some code to it. Note If you prefer, you can instead go through github.com to create a new repo and follow the command line instructions there. ## Download the texts\u00b6 We want to download three texts and put them in the data folder. Ideally, we\u2019d do this automatically, for example with a bash file with calls to wget. However, the terms and conditions from Project Gutenberg state: The website is intended for human users only. Any perceived use of automated tools to access the Project Gutenberg website will result in a temporary or permanent block of your IP address.The website is intended for human users only. Any perceived use of automated tools to access the Project Gutenberg website will result in a temporary or permanent block of your IP address. \u2013Project Gutenberg Caution Document manual steps in README.md! Not a big deal! We can download the files manually and document the source in the README.md file. Let\u2019s download the following files manually and put them in the data folder: \u2022 Draculadata\/dracula.txt \u2022 Frankensteindata\/frankenstein.txt \u2022 Jane Eyredata\/jane_eyre.txt ## Count the words\u00b6 The next step is to calculate word counts for each text. We will create a module called parse_text in the zipf folder. It will contain a function count_words that takes in a text string and outputs a set of counts. This function will itself call a helper function _clean_gutenberg_text. Note that the function starts with an underscore to indicate that it is meant to be a private function used internally by the module. _clean_gutenberg_text will explicitly filter out boilerplate from project Gutenberg texts. There\u2019s a significant amount of boilerplate at the start of e-books and license information at the end, which might skew the word count distribution. Thankfully, there are phrases in the e-books which delimit the main text, which we can detect: \u2022 START OF THE PROJECT GUTENBERG EBOOK \u2022 END OF THE PROJECT GUTENBERG EBOOK Because we only have three books in our collection, we can manually test that each book is processed correctly. However, if we ever process a fourth, unusually formatted text, and our detection didn\u2019t work, we want our pipeline to fail in a graceful way. Thus, we add in-line assert statements to make sure our filter finds the two delimiters in reasonable locations in the text. def _clean_gutenberg_text(text): \"\"\" Find fences in a Gutenberg text and select the text between them. \"\"\" start_fence = \"start of the project gutenberg ebook\" end_fence = \"end of the project gutenberg ebook\" text = text.lower() start_pos = text.find(start_fence) + len(start_fence) + 1 end_pos = text.find(end_fence) # Check that the fences are at reasonable positions within the text. assert 0.000001 < start_pos \/ len(text) <= 0.1 assert 0.9 < end_pos \/ len(text) <= 1.0 return text[start_pos:end_pos] Now we can use call this function in another wrapper function that counts words ike so: import string import collections def count_words(f, clean_text=False): \"\"\" Count words in a file. Arguments: f: an open file handle clean_text (optional): a Boolean, if true, filters out boilerplate typical of a Gutenberg book. Returns: A dict keyed by word, with word counts \"\"\" text = f.read() if clean_text: text = _clean_gutenberg_text(text) chunks = text.split() npunc = [word.strip(string.punctuation) for word in chunks] word_list = [word.lower() for word in npunc if word] word_counts = collections.Counter(word_list) return dict(word_counts) To test that the count_words function works as intended, we make a sample txt file in the tests folder which contains dummy data: The *** START OF THE PROJECT GUTENBERG EBOOK *** OF TO to I i i and and and and THE The THE the thE [...] *** END OF THE PROJECT GUTENBERG EBOOK *** OF If our function works correctly, it should ignore all the text outside of the start and end fences. It should return: {'the': 5, 'and': 4, 'i': 3, 'to': 2, 'of': 1} We set up a test function in test_parse_text.py that loads this test text and verifies that the word counts are correctly measured. The test can be run with: $ pytest tests\/test_parse_text.py\n\n\nThe resulting module and test can be viewed on Github.\n\n## Calculate Zipf\u2019s law\u00b6\n\nOnce we have word counts, we can calculate Zipf\u2019s law based on word counts. We use the method proposed in Moreno-Sanchez et al. (2016), which is implemented in the book Research Software Engineering with Python. The method calculates the maximum likelihood $$\\alpha$$ parameter for the empirical distribution of ranks. It starts with $$\\alpha = 1$$ and refines the estimate through gradient descent. We implement this method in fit_distribution.py.\n\nIt\u2019s quite easy to make a mistake in calculating the exponent by incorrectly implementing the error function. To protect ourselves against this, in our test suite, we generate data from a known distribution with $$\\alpha = 1$$ and verify that the correct exponent is estimated. We put this test, test_fit_distribution.py under the tests folder.\n\n## Write the command line interface\u00b6\n\nWe are now ready to write glue code to run our pipeline from the command line. We create a script, run_analysis.py, under the scripts folder. Our script takes in two different command line arguments, or flags:\n\n\u2022 in_folder: the input folder containing txt files.\n\n\u2022 out_folder: where we will output the results\n\nWe create this command line interface using argparse. This looks like this:\n\nif __name__ == \"__main__\":\nparser = argparse.ArgumentParser(description=\"Compute zipf distribution\")\nargs = parser.parse_args()\n\nmain(args)\n\n\nThe main function first verifies that there are files to be processed and creates the output folder if necessary. To manipulate paths, it uses the pathlib module. The function then runs each of the stages of the pipeline in turn until completion. We don\u2019t write tests this part of the code, as we\u2019ve lifted the error-prone aspects of the code elsewhere. Again, the goal is rarely to get 100% coverage, but rather to have good coverage where it counts.\n\nThe code uses a for loop to construct a table of results, which is then loaded into pandas, and then dumped to disk as csv. Pandas is not strictly necessary to write a csv file, but it\u2019s the default choice to work with tabular data in Python, so it is used here. Have a look at the script here.\n\n## Make summary figures\u00b6\n\nFinally, to generate figures, we prefer the jupyter notebook environment. Polishing figures takes some trial and error, and the jupyter notebook environment makes it easy to iterate on figures. The notebook, in scripts\/visualize_results.ipynb, takes in results files as csvs, and generates figures and summary tables from them.\n\nFig. 15 A plot generated by our pipeline. Zipf distribution estimated on the movel Frankenstein by Mary Shelley.\n\nWe used the standard choice of matplotlib for the figures, although with the stylesheet from seaborn, which is more aesthetically pleasing. Note, however, that there are a number of excellent libraries for interactive graphics, so if this was critical, we could certainly apply this here. There is no computation in the notebook, only figure and summary table generation, which keeps the code in the notebook to a minimum.\n\n## What did we learn?\u00b6\n\nWe saw how to organize an analysis according to the organization proposed in this handbook. We created a new project folder and module with the true neutral cookiecutter. If this analysis were part of a larger project - a paper or book chapter - we would re-use the same project folder, and add new pipelines and analyses to the project.\n\nWhen I started this project, I was surprised by how many macro- and micro-decisions were needed to be made about how a pipeline works and how it\u2019s organized. A little bit of thinking ahead can avoid days of headaches later on. In this case, we chose a lightweight structure with one entry script calling module functions. These module functions are short and most of them are pure functions. Pure functions are easier to test. Indeed, we wrote unit tests to check that these functions worked as intended. That way, once the code was written and tests passed, it was crystal clear that the code worked as intended. We separated module code from glue code and plotting code. The resulting code is decoupled and easily maintainable.\n\nWriting code in this organized way is effortful. Over the long term, this methodical approach is more efficient, and more importantly, it\u2019s less stressful.\n\n5-minute exercise\n\nHow would you change this pipeline so that it computes error bars for the parameters of the Zipf distribution through bootstrapping? Would you need to change existing functions? What function would you need to add? If you\u2019re feeling adventurous, go ahead and implement it! It\u2019s definitely more than a 5-minute project!","date":"2022-01-27 07:32:02","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 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\": 0.48976826667785645, \"perplexity\": 884.3334796610777}, \"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-2022-05\/segments\/1642320305242.48\/warc\/CC-MAIN-20220127072916-20220127102916-00388.warc.gz\"}"} | null | null |
Q: Xamarin Forms w/ Mobile Blazor Bindings - How to specify dependency injection in Blazor app for class defined in Android / iOS projects Within my Blazor app, I am trying to determine the amount of available storage of the Android or iOS device.
I have found an answer here that is relevant:
Can I check available storage in the Device on Xamarin Forms?
As per the accepted answer, I have implemented the following:
Defined the Interface in the Blazor project
public interface IStorage
{
double GetRemainingStorage();
}
Created a class in the Android project
[assembly: Xamarin.Forms.Dependency(typeof(AndroidStorageManager))]
namespace MyApp.Android
{
public class AndroidStorageManager : IStorage
{
public double GetRemainingStorage()
{
var freeSpace = Android.OS.Environment.ExternalStorageDirectory.UsableSpace;
return freeSpace;
}
}
}
Created a class in the iOS project
[assembly: Xamarin.Forms.Dependency(typeof(iOSStorageManager))]
namespace MyApp.iOS
{
public class iOSStorageManager : IStorage
{
public double GetRemainingStorage()
{
var freeSpace = NSFileManager.DefaultManager.GetFileSystemAttributes(Environment.GetFolderPath(Environment.SpecialFolder.Personal)).FreeSize;
return freeSpace;
}
}
}
The Issue
Despite the definition of the dependencies with the [assembly: attribute, when my Blazor app tries to inject an instance of IStorage, it throws an exception:
Unable to resolve service for type 'IStorage' ...
Of course, I'm not able to define the dependency injection for IService in the Blazor app on startup, since the AndroidStorageManager and iOSStorageManager are defined in the device-specific projects which are already referencing the Blazor app.
I suspect I need some other way of defining the DI for IService in the Android and iOS apps, but can't see how to do it.
Can anyone offer any advice?
A: I seem to have found a workaround for my immediate issue, but I'm sure there must be a more elegant solution.
The exception was being generated when trying to inject an instance of the class associated with the IStorage interface.
public class MyManager {
private IStorage _storage;
public MyManager(IStorage storage) {
_storage = storage;
}
...
}
Rather then relying on the Blazor DI to resolve this dependency, I was able to use Xamarin.Forms DI to inject an instance manually, as follows:
public class MyManager {
private IStorage _storage;
public MyManager() {
_storage = DependencyService.Get<IStorage>();
}
...
}
I'm assuming that my original code wasn't working because Xamarin.Forms and Blazor are not sharing the same DI container. I'm not sure.
I'd be interested in anyone that can suggest a more elegant solution.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,655 |
Q: Не могу разобраться ObservableCollection с ListBox Проблема скорее всего в привязке. В ListBox не прибавляются элементы.
<Window x:Class="WpfApplication2.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
xmlns:local="clr-namespace:WpfApplication2"
mc:Ignorable="d"
Title="MainWindow" Height="350" Width="525">
<Window.Resources>
<local:MyList x:Key="MyData"/>
<DataTemplate x:Key="temp">
<Border Margin="5" BorderThickness="1" BorderBrush="SteelBlue" CornerRadius="4" Width="370">
<Grid Margin="3">
<Grid.ColumnDefinitions>
<ColumnDefinition Width="Auto"/>
<ColumnDefinition/>
</Grid.ColumnDefinitions>
<Image Grid.RowSpan="2" Width="100" Height="75" Margin="6"
Source="{Binding Path=Img}"/>
<StackPanel Grid.Column="1" Margin="2,6">
<TextBlock Text="{Binding Path=Name}"/>
<TextBlock Text="{Binding Path=Surname}"/>
<TextBlock Text="{Binding Path= Country}"/>
</StackPanel>
</Grid>
</Border>
</DataTemplate>
</Window.Resources>
<Grid>
<ListBox ItemTemplate="{StaticResource temp}" ItemsSource="{Binding Source={StaticResource MyData}}" x:Name="listBox" HorizontalAlignment="Left" Height="258" Margin="10,10,0,0" VerticalAlignment="Top" Width="358"/>
<Button x:Name="Add" Content="Add" HorizontalAlignment="Left" Margin="388,85,0,0" VerticalAlignment="Top" Width="75" Click="Add_Click"/>
<Button x:Name="Edit" Content="Edit" HorizontalAlignment="Left" Margin="388,110,0,0" VerticalAlignment="Top" Width="75" Click="Edit_Click"/>
<Button x:Name="Remove" Content="Remove" HorizontalAlignment="Left" Margin="387,135,0,0" VerticalAlignment="Top" Width="75" Click="Remove_Click"/>
</Grid>
Вот сам клас:
public partial class MainWindow : Window
{
private Window1 wd;
private MyList MyData;
public MainWindow()
{
InitializeComponent();
MyData = new MyList();
MyData.Add(new Person("1", "2", "3", null));
MyData.Add(new Person("1", "2", "3", null));
}
}
class MyList : ObservableCollection<Person>
{
public ObservableCollection<Person> MyData;
public MyList() : base()
{
MyData = new ObservableCollection<Person>();
MyData.Add(new Person("1", "2", "3", null));
MyData.Add(new Person("1", "2", "3", null));
}
}
class Person
{
public string Name { get; set; }
public string Surname { get; set; }
public string Country { get; set; }
public Image Img { get; set; }
public Person(string name, string surname, string country, Image img)
{
Name = name;
Surname = surname;
Country = country;
Img = img;
}
public Person() { }
}
A: Где вы находите такие способы создания коллекций?)
Ну, исправим то что есть:
<local:MyList x:Key="MyData"/>
Объект создается в ресурсе окна, соответственно добавление элементов в коллекцию должно происходить в конструкторе этого объекта. То что вы добавляете элементы в *.cs файле, это не совсем то, так как это не тот объект к которому вы привязываетесь.(привязка идет к объекту созданному в ресурсе).
Идем дальше. Раз уж вы решили создать коллекцию унаследовавшись от нее самой, то добавляйте элементы унаследованным методом:
public class MyList : ObservableCollection<Person>
{
public MyList() : base()
{
Add(new Person("1", "2", "3", null));
Add(new Person("1", "2", "3", null));
}
}
В принципе все, должно работать.
Пару замечаний по вашему коду:
public ObservableCollection<Person> MyData;
Если вы будете привязываться к MyData то привязка не пройдет. Привязка работает только со свойствами, т.е. должно выглядеть так:
public ObservableCollection<Person> MyData { get; set; }
Как это делается обычно:
В проекте должен быть класс VM, реализующий интерфейс INotifyPropertyChanged. Этот класс будет являться DataContext-oм для вашего окна(как задать DataContext). В этом классе и объявить список:
public class MainVM : INotifyPropertyChanged
{
public ObservableCollection<Person> MyList { get; set; }
public MainVM()
{
MyList = new ObservableCollection<Person>();
MyList.Add(new Person("1", "2", "3", null));
MyList.Add(new Person("1", "2", "3", null));
}
//---------------------
//реализация интерфейса
} //---------------------
После таких манипуляций, использовать привязку одно удовольствие:
<ListBox ItemsSource="{Binding MyList}"/>
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,623 |
Wine and a light appetizer included in the ticket price.
BAY SHORE LYRIC OPERA will present two performances of Giacomo Puccini's opera La Bohème, May 19 & 20, 2018 as part of their 2018 season at the beautiful Veterans Memorial Hall of Santa Cruz, 846 Front St, Santa Cruz, CA 95060. This production is fully-staged, sung in Italian with English supertitles and will feature BSLO's artists accompanied by the members of the Winchester Orchestra under the baton of Michael DiGiacinto. Wine and a light appetizer will be included in the ticket price as well.
La Bohème had its world premiere at the Teatro Regio, Turin, 1896. The opera was based on the famous French novelist and poet Henri Muger's Scènes de la Vie de Bohème. La Bohème, the passionate, timeless and indelible story of love among young artists in Paris can stake its claim as one of the world's most popular operas. Our production is family friendly and we welcome children 12 and under free. Produced in an intimate venue, this opera has the ability to make a powerful first impression and to reveal unsuspected treasures after dozens of hearings. At first glance, La Bohème is the definitive depiction of the joys and sorrows of love and loss. In the intimate setting of the beautiful Veterans Memorial Building located in downtown Santa Cruz, a closer inspection of this opera reveals the deep emotional significance hidden in seemingly trivial things like a hand muff or a bonnet, an old overcoat or a chance meeting with a neighbor.
Bay Shore Lyric Opera's artists perform with West Bay Opera, Opera San Jose and other Bay Area companies. Cast members include: Delmar McComb, Julio Ferrari, Jennifer Der Torossian-Studley and Kristin Genis-Lund, among others. The production will include English supertitles, with wine and a light appetizer included in the ticket price.
When: May 19, 2018 (opening) at 7:30p, and May 20th (matinee) at 2:00p.
Where: Veterans Memorial Hall of Santa Cruz, 846 Front St, Santa Cruz, CA 95060.
Why: To provide fully staged professional opera productions of the highest artistic quality by the community and for the community. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,619 |
Server.com was a software as a service (SaaS) provider that offered a suite of services from 1996 until 2007. It was the first SaaS site to offer a variety of services and the first to use the term WebApp to describe its services.
It was selected as an Incredibly Useful Site by Yahoo! Internet Life magazine.
net magazine listed Server.com among the 100 most influential websites of all time.
Server.com launched in 1996 offering the first online personal information manager.
In 1997, they rolled out the first threaded message board service;
the first web based mailing list manager;
one of the first online calendar services; and one of the first online form builders.
In 2000, Server.com partnered with NBCi and became server.snap.com until 2001.
In 2001, Server.com was serving 100 million monthly pageviews. Media Life declared it one of the 20 biggest ad domains on the Web.
In 2002, Server.com developed one of the first web-based RSS aggregators.
In 2007, all services were moved to YourWebApps.com.
The domain name Server.com was sold in 2009 for $770,000.
References
External Links
YourWebApps.com - Hosts one last forum as of July, 2022.
NE Disc App - A working recreation of the DiscussionApp service.
sean.brunnock.com - Founder's personal account of Server.com.
Web applications
Internet forum hosting
Electronic mailing lists
Calendaring software
News aggregators
Personal information managers
Internet_properties_established_in_1996
Internet properties disestablished in 2007
Defunct websites | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,009 |
\section{Introduction}
Fermions, constrained by the Pauli exclusion principle, behave very
differently from bosons, to which such a principle does not apply. \ In a many
particle system, the former tend to stay away from each other, while, on the
contrary, the latter tend to be gregarious. \ In the most fundamental level,
fermions (leptons and quarks) are the building block for all the matter with
mass, while bosons serve as the mediator for all the fundamental forces in
nature. \ In spite of this vast difference, when mixed together at
temperatures so low that the de Broglie wavelength of the particles becomes
comparable to or even longer than the interparticle spacing, fermions and
bosons can conspire to create fascinating quantum effects at the macroscopic
scale that are of fundamental interest across a broad spectrum of physics,
especially within the disciplines of condensed matter and nuclear\ physics.
\ As most substances in nature solidify before the temperature could reach the
regime where the macroscopic quantum nature of liquid (or gas) can be
manifested, the combination of liquid isotopes between $^{3}$He and $^{4}$He
\cite{bardeen66} has remained the only laboratory accessible system until
recently when the rapid technological advancement in cooling and trapping of
neutral atoms has completely turned the situation around. \ Not only has it
resulted\ in a dramatic proliferation of such systems, including $^{6}$Li -
$^{7}$Li \cite{hulet01,schrek01}, $^{6}$Li - $^{23}$Na \cite{hadzibabic02},
$^{87}$Rb -$^{40}$K\cite{ferrari02,inguscio02,jin04,simoni06}, $^{6}$Li -
$^{87}$Rb \cite{courteille08}, but more significantly, with ultracold atomic
gases, important parameters, including the interaction between particles of
same or different species, can be tuned precisely
\cite{ketterle04,jin04,simoni06,courteille08}, allowing the physics of
Fermi-Bose mixture to be investigated in a well controlled manner, in regimes
possibly well beyond the reach by traditional solid state systems. \ \
Recently, by changing the Feshbach detuning across a certain critical point at
which all the minority atoms pair up with the majority ones to form a
molecular Bose condensate, the group at MIT \cite{ketterle08} has successfully
created, from a two-component Fermi mixture with population imbalance, a
quantum gas where Bose molecules are mixed with spin-polarized (unpaired
majority) fermions. \ In addition to confirming an earlier theoretical
prediction of the existence of a transition from full miscibility to phase
separation \cite{viverit00,molmer98}, using the same system, they were able to
determine the effective dimer-fermion scattering length within a reasonable
agreement with the prediction made more than 50 years ago \cite{skorniakov56}
but never verified experimentally, once again demonstrating that the ultracold
atom system provides an excellent experimental platform for testing theories.
Inspired by this work, instead of one Fermi state as in a single-component
Fermi-Bose mixture in Ref. \cite{ketterle08}, we consider a two-component
Fermi-Bose mixture involving a hyperfine state $\left\vert b\right\rangle $ of
a bosonic atom with mass $m_{B}$ and \ two equally populated hyperfine states:
spin up $\left\vert \uparrow\right\rangle $ and spin down $\left\vert
\downarrow\right\rangle $ of a fermionic atom with mass $m_{F}$. \ The latter
Fermi system when equipped with Feshbach resonance has been the main source of
inspiration for much recent excitement in the forefront of ultracold atomic
physics, due chiefly to the vital role it plays in the study of crossover from
Bose-Einstein condensation (BEC) of tightly bound atom pairs to\ nonlocal
Bardeen-Cooper-Schrieffer (BCS) atom pairs. \ Thus, mixtures of bosons with
such Fermi systems shall be widely accessible to experiments.
The low temperature physics of the two-component model under consideration is
dominated by s-wave collisions, which, given that the Pauli exclusion
principle prohibits s-wave scattering between identical fermions, are
parameterized with three scattering lengths:\ $a_{BB}$, $a_{FF}$, and $a_{BF
$, describing, respectively, s-wave scattering between two bosons, between two
fermions of opposite spins, and between a boson and a fermion of either spin,
assuming that scattering a boson off a spin-up fermion has the same amplitude
as that off a spin-down fermion. \ In principle, $a_{BB}$\ must be positive
necessitated by the Bose stability in the mixture, while $a_{BF}$ and $a_{FF}$
can take both positive and negative values as they are not subject to similar
constraints. \ Thus, in spite of the restriction on $a_{BB}$, such a model can
still represent drastically different regimes of physics as far as pairings
and instabilities are concerned. \ In the present work, we aim to extend the
physics of phase and phase separation at finite temperature from single- to
two-component systems where fermions have the opportunity to form correlated
BCS pairs. \ As a result, we limit our study to systems with repulsive
($a_{BF}>0$) Bose-Fermi and attractive ($a_{FF}<0$) Fermi-Fermi interaction. \
\ In Sec. \ref{sec:thermodynamical potential}, we review, within the framework
of mean-field theory, the path integration formulation of the
finite-temperature thermodynamic potential and derive from it the
Landau-Ginzburg expansion. In contrast to the existing works for the
two-component model \cite{Viverit00,Stoof00,pu10}, which have various
purposes, we focus on producing phase diagrams in the space made up of
chemical potentials, which are intensive statistical variables that must
remain invariant among the separated phases and hence uniquely define a phase
separation \cite{radzihovsky08}. This is to be contrasted to spaces where
coordinates are served, for example, by particle number densities, of which
separated phases in a phase separation have different values
\cite{Viverit00,Salasnich07}. \ In Sec. III, we apply the analytical
intuitions derived from the Landau-Ginzburg theory to identify as well as to
clarify the features that are generic to the finite-temperature phase diagrams
within the validity of our model.\ The utility of such phase diagrams can be
most easily appreciated when one wants to map out the particle number
densities for a trapped model where the local density approximation holds.
\ An example will be shown in Sec. \ref{sec:an application}, which illustrates
how the surrounding large BEC affects the physics of pairing among fermions in
a tightly confined trap. \ Finally, we provide a short conclusion and
discussion in Sec. \ref{sec:conclusion}. \
\section{Mean-Field Thermodynamic Potential and Landau-Ginzburg Expansion}
\label{sec:thermodynamical potential}
The thermodynamic properties of our model can be described by the partition
function $Z$, which is a functional integral over both the complex fields for
bosons: $\psi_{\mathbf{k},B}\left( \tau\right) $ and $\psi_{\mathbf{k
,B}^{\ast}\left( \tau\right) $ and the Grassman fields for fermions:
$\psi_{\mathbf{k,}\sigma}\left( \tau\right) $ and $\bar{\psi}_{\mathbf{k
,\sigma}\left( \tau\right) $ in the momentum $\left( \hbar\mathbf{k
\right) $ and imaginary time $\left( \tau\right) $ space \cite{negele98}.
\ In this work, we limit our study to the regime of temperature far below
$T_{B}$ $=2\pi\hbar^{2}\left[ n_{B}/\zeta\left( 3/2\right) \right]
^{2/3}/(m_{B}\,k_{B})$, where $n_{B}$ is the Bose atom number density, $k_{B}$
the Boltzman constant, and $\zeta\left( x\right) $ the Riemann-Zeta
function. \ In this limit, bosons are virtually all condensed to the zero
momentum mode, and the standard symmetry breaking ansatz, $\psi_{\mathbf{k
,B}\left( \tau\right) =\psi_{\mathbf{0},B}+\phi_{\mathbf{k}\neq0,B}\left(
\tau\right) $, is therefore applicable, where $\psi_{\mathbf{0},B}$ is a
classical field (not part of the path integration variable) for condensed
particles, and $\phi_{\mathbf{k},B}\left( \tau\right) $ is a bosonic field
for condensate excitations or simply phonons for a dilute gas where the usual
Bogoliubov approximation holds \cite{Stoof00}. \ Further, for pedagogical
reason, we opt to first ignore all the phonon degrees of freedom, justifying,
however, in the end of the paper, that the ensuing formalism, when
appropriately modified, can be applied for a large class of Fermi-Bose
mixtures where the effects of phonons are included. \
The grand partition function $Z$, at temperature $T\left( \equiv1/k_{B
\beta\right) $, boson chemical potential $\mu_{B}$, and fermion chemical
potential $\mu_{F}$, then reads $Z=\int D\left[ \bar{\psi},\psi\right]
\exp\left( -S[n_{B},\bar{\psi},\psi]/\hbar\right) $, where $n_{B}=\left\vert
\psi_{\mathbf{0},B}\right\vert ^{2}/V$ $\ $is the boson number density, $V$
the total volume, $S$ the action given b
\begin{align}
S & =\hbar\beta V\left( \frac{g_{BB}}{2}n_{B}^{2}-\mu_{B}n_{B}\right)
+\nonumber\label{S}\\
& \int_{0}^{\hbar\beta}d\tau\left[ \sum_{\mathbf{k},\sigma}\bar{\psi
}_{\mathbf{k},\sigma}\left( \hbar\frac{\partial}{\partial\tau}+\xi
_{\mathbf{k}}\right) \psi_{\mathbf{k},\sigma}\right. \nonumber\\
& \left. +\frac{U}{V}\sum_{\mathbf{k},\mathbf{k}^{\prime},\mathbf{q}
\bar{\psi}_{\mathbf{k},\uparrow}\bar{\psi}_{\mathbf{q}-\mathbf{k},\downarrow
}\psi_{\mathbf{k}^{\prime},\downarrow}\psi_{\mathbf{q}-\mathbf{k}^{\prime
},\uparrow}\right]
\end{align}
In arriving at Eq. (\ref{S}), we have incorporated the interaction between
fermions and bosons into Eq. (\ref{S}) via $\xi_{\mathbf{k}}=\epsilon
_{\mathbf{k}}-\mu$ in terms of the effective fermion chemical potential
$\mu=\mu_{F}-g_{BF}n_{B}$, where $\epsilon_{\mathbf{k}}=\left( \hbar
k\right) ^{2}/2m_{F}$ is the kinetic energy of a fermion with a momentum
$\hbar\mathbf{k}$,\ and $g_{BB}=4\pi\hbar^{2}a_{BB}/m_{B}$ and $g_{BF
=4\pi\hbar^{2}a_{BF}/m_{BF}$ measure the strengths of respective s-wave
scatterings with $m_{BF}=2m_{B}m_{F}/(m_{B}+m_{F})$, and we have also modeled
the interaction between fermions of opposite spins with the parameter $U$,
which, in the actual calculation, will be replaced in favor of the physical
parameter $U_{0}\left( =4\pi\hbar^{2}a_{FF}/m_{F}\right) $ via the standard
renormalization relation $U^{-1}=U_{0}^{-1}-\sum_{\mathbf{k}}\epsilon
_{\mathbf{k}}^{-1}/(2V)$. \
\ In anticipation of the BCS pairing as a result of an attractive
fermion-fermion interaction, we follow the standard procedure in which we
first introduce the auxiliary bosonic fields $\Delta$ and $\Delta^{\ast}$
(assuming they are uniform and static) and then apply the Hubbard-Stratonovic
decomposition to change the partition function into $Z=\int D\left[ \bar
{\psi},\psi,\Delta^{\ast},\Delta\right] \exp\left( -S^{\prime}[n_{B
,\bar{\psi},\psi,\Delta^{\ast},\Delta]/\hbar\right) $, where the action
\begin{align}
S^{\prime} & =\hbar\beta\left[ V\left( \frac{g_{BB}}{2}n_{B}^{2}-\mu
_{B}n_{B}\right) -V\frac{\left\vert \Delta\right\vert ^{2}}{U}+\sum
_{\mathbf{k}}\xi_{\mathbf{k}}\right] \nonumber\\
+ & \sum_{\mathbf{k},i\omega_{n}}\mathbf{\psi}_{\mathbf{k},i\omega_{n
}^{\dag}\left(
\begin{array}
[c]{cc
-i\hbar\omega_{n}+\xi_{\mathbf{k}}, & \Delta\\
\Delta^{\ast}, & -i\hbar\omega_{n}-\xi_{\mathbf{k}
\end{array}
\right) \mathbf{\psi}_{\mathbf{k},i\omega_{n}},
\end{align}
is expressed in terms of Nambu spinor $\mathbf{\psi}_{\mathbf{k},i\omega_{n
}=(\psi_{\mathbf{k,}i\omega_{n},\uparrow},\bar{\psi}_{-\mathbf{k,-}i\omega
_{n},\downarrow})^{T}$, with $\psi_{\mathbf{k,}i\omega_{n},\uparrow\text{ or
}\downarrow}$ being the field components in the imaginary (Matsubara)
frequency $i\omega_{n}$ space.
Finally, by integrating out fermionic fields and carrying out a summation over
the Matsubara frequency, we arrive, within the saddle point approximation, at
the grand thermodynamic potential (density) [$\Omega=-\ln Z/(\beta V)]$
\begin{align}
\Omega & =\frac{1}{2}g_{BB}n_{B}^{2}-\mu_{B}n_{B}+\Omega_{F}\left\{
=-\frac{\Delta^{2}}{U}\right. \nonumber\\
& \left. +\frac{1}{V}\sum_{\mathbf{k}}\left[ \xi_{\mathbf{k}
-E_{\mathbf{k}}+2\beta^{-1}\ln f\left( -E_{\mathbf{k}}\right) \right]
\right\} \label{Omega
\end{align}
for a mixture with Bose particle number density $n_{B}$ and Fermi particle
number density
\begin{equation}
n_{F}=\frac{1}{V}\sum_{\mathbf{k}}\left[ 1-\frac{\xi_{\mathbf{k}
}{E_{\mathbf{k}}}\tanh\frac{\beta E_{\mathbf{k}}}{2}\right]
,\label{fermi number density
\end{equation}
where $E_{\mathbf{k}}=\sqrt{\xi_{\mathbf{k}}^{2}+\Delta^{2}}$ is the
quasiparticle energy, and $f\left( \varepsilon\right) =1/(e^{\varepsilon
/k_{B}T}+1)$ is the standard Fermi-Dirac distribution. \ Alternatively, we can
write $\Omega_{F}$ defined in Eq. (\ref{Omega}) as a Landau-Ginzburg expansion
in terms of the order parameter $\Delta$ according to
\begin{equation}
\Omega_{F}=\alpha_{0}+\alpha_{2}\Delta^{2}+\frac{\alpha_{4}}{2}\Delta
^{4}\cdots\label{Omega_F
\end{equation}
where
\begin{subequations}
\label{a024
\begin{align}
\alpha_{0} & =\frac{2}{V\beta}\sum_{\mathbf{k}}\ln f\left( -\xi_{\mathbf{k
}\right) ,\\
\alpha_{2} & =-\frac{1}{U}-\frac{1}{2V}\sum_{\mathbf{k}}\frac{1-2f\left(
\xi_{\mathbf{k}}\right) }{\xi_{\mathbf{k}}},\\
\alpha_{4} & =\frac{1}{V}\sum_{\mathbf{k}}\frac{1}{4\xi_{\mathbf{k}}^{2
}\times\nonumber\\
& \left\{ \frac{1-2f\left( \xi_{\mathbf{k}}\right) }{\xi_{\mathbf{k}
}-2\beta f\left( \xi_{\mathbf{k}}\right) \left[ 1-f\left( \xi_{\mathbf{k
}\right) \right] \right\} .
\end{align}
Equations (\ref{Omega}) and (\ref{Omega_F}) serve as the foundations for our
studies below.
\section{Phase Diagrams in Chemical Potential Space}
In this section, we aim to gain a systematic understanding of the phase
diagrams at finite temperature. An immediate obstacle to our goal is the
existence of a large number of free parameters in our model. \ In order to
alleviate this difficulty, we introduce a parameter $A=\hbar^{2}\left(
3\pi^{2}\right) ^{2/3}/2m_{F}$ which has the physical meaning that
$An_{F}^{2/3}$ equals the Fermi energy $\epsilon_{F}$, and adopt a unit system
generalized from Ref. \cite{viverit00}, in which several key parameters are
scaled according to
\end{subequations}
\begin{align*}
\bar{\Omega} & =\frac{g_{BF}^{10}\Omega}{g_{BB}^{5}A^{6}},\bar{\mu}_{B
=\frac{g_{BF}^{5}\mu_{B}}{g_{BB}^{3}A^{3}},\bar{\mu}_{F}=\frac{g_{BF}^{4
\mu_{F}}{g_{BB}^{2}A^{3}},\\
\bar{n}_{B} & =\frac{g_{BF}^{5}n_{B}}{g_{BB}^{2}A^{3}},\bar{n}_{F
=\frac{g_{BF}^{6}n_{F}}{g_{BB}^{3}A^{3}},\bar{k}=\frac{g_{BF}^{2}k}{g_{BB}A}.
\end{align*}
Additionally, $\Delta$, $\mu$, $k_{B}T$, and $\epsilon_{\mathbf{k}}$ are
scaled same as $\mu_{F}$, and the interaction between fermions of opposite
spins [$\bar{U}_{0}=U_{0}/(g_{BF}^{2}/g_{BB})$] is measured relative to
$g_{BF}^{2}/g_{BB}$ - the magnitude of induced fermion-fermion interaction due
to the density fluctuation of Bose condensate \cite{viverit00}. \ As can be
seen, the three original free parameters $\left( g_{BF},g_{BB},U_{0}\right)
$ are now reduced into a single scaled parameter $\bar{U}_{0}$, making this
unit system particularly suitable for studies aimed at identifying features
generic to all the phase diagrams. \ To gain a qualitative understanding of
this unit system, we note that for a mixture of $^{87}$Rb and $^{84}$Rb with
$a_{BB}=100a_{0}$ and $a_{BF}=550a_{0}$ where $a_{0}$ is the Bohr radius
\cite{bohn99}, the unit is 1.61$\times10^{-49}$ J m$^{3}$ for $U_{0}$,
(2.15$\times10^{-30}$ J, 3.84$\times10^{-31}$ J) for $\left( \mu_{F},\text{
}\mu_{B}\right) $, (1.34$\times10^{19}$ m$^{-3}$, 7.49$\times10^{19}$
m$^{-3}$) for $\left( n_{F}\text{, }n_{B}\right) $, and 156~$n$K for $T$.
\ (However, for notational simplicity, same symbols will be used to stand for
the scaled variables throughout the rest of the paper.)
Figures \ref{Fig:Zero}(b) and \ref{Fig:Finite} showcase the features that are
characteristic of both the zero- and the finite-temperature phase diagrams for
a typical system within the validity of our model. They are constructed
numerically by minimizing the potential in Eq. (\ref{Omega}) with respect to
$n_{B}$ and $\Delta$, which amounts to analyzing the saddle point equations
and the relevant Hessian matrix \cite{Stoof00,pu10}, as well as comparing, in
the coexistence regions, the thermodynamic potentials of the possible phases
listed below:
(V) for an empty phase where both $n_{B}=0$ and $n_{F}=0$,
(B) for a pure boson phase where $n_{B}\neq0$ and $n_{F}=0$,
(N) for\ a normal state of Fermi gas where $n_{B}=0$, $\Delta=0$, and
$n_{F}\neq0$,
(S) for a superfluid Fermi gas where $n_{B}=0$, $\Delta\neq0$, and $n_{F
\neq0$,
(BN) for a normal Fermi-Bose mixture where $n_{B}\neq0$, $\Delta=0$, and
$n_{F}\neq0$, and finally
(BS) for a superfluid Fermi-Bose mixture where $n_{B}\neq0$, $\Delta\neq0$,
and $n_{F}\neq0$
\begin{figure}
[ptb]
\begin{center}
\includegraphics[
height=3.7749in,
width=3.4212in
{figs1ab.eps
\caption{(a) is the illustration designed to aid the understanding of the
zero-temperature phase diagram in (b) where $U_{0}=$-1.126. Units are defined
in the text.
\label{Fig:Zero
\end{center}
\end{figure}
\ \ \ \
In order to capture the physics, making the study of phase diagrams more
illuminating, we complement our numerical study with an analysis founded on
the Landau-Ginzburg theory in the low temperature limit $T<<\mu$. \ In this
limit, $\alpha_{4}$ [Eq. (\ref{alpha4}) below] is always positive, and we only
need to consider the Landau-Ginzburg expansion up to the fourth order in
$\Delta$, \
\begin{align}
\Omega & =\frac{1}{2}n_{B}^{2}-\mu_{B}n_{B}+\alpha_{0}\left( \mu,T\right)
\nonumber\\
& +\alpha_{2}\left( \mu,T\right) \Delta^{2}+\frac{\alpha_{4}\left(
\mu,T\right) }{2}\Delta^{4}, \label{Omega_simple
\end{align}
where the integrals for the Landau coefficients in Eqs. (\ref{a024}) can be
evaluated explicitly with the results \cite{lifshitz80}
\begin{subequations}
\label{a024-1
\begin{align}
\alpha_{0} & =-\mu^{5/2}\left[ \frac{2}{5}+\frac{\pi^{2}}{4}\left(
\frac{T}{\mu}\right) ^{2}\right] ,\\
\alpha_{2} & =-\frac{1}{U_{0}}+\frac{3}{4}\mu^{1/2}\ln\frac{\pi T}{8\mu
e^{\gamma-2}},\\
\alpha_{4} & =\frac{21}{32}\mu^{1/2}\frac{\zeta\left( 3\right) }{T^{2}},
\label{alpha4
\end{align}
with $\gamma\approx0.577$ being the Euler's constant. \ Further, in the same
limit, we can ignore the thermal population in comparison with the population
inside the Fermi sphere so that the Fermi density can be approximated a
\end{subequations}
\begin{equation}
n_{F}=-\frac{\partial\Omega}{\partial\mu_{F}}=\mu^{3/2}\left[ 1+\frac{\pi
^{2}}{8}\left( \frac{T}{\mu}\right) ^{2}\right] \simeq\mu^{3/2}, \label{nF
\end{equation}
Equations (\ref{a024-1}) and (\ref{nF}) form the backbone of the analytical
discussions that we carry out below. \
Consider first the mixed phase where both $n_{B}$ and $n_{F}$ have finite
values. \ We begin with the saddle-point equation for $n_{B}
\begin{equation}
n_{B}-\mu_{B}+\mu^{3/2}=0,
\end{equation}
which, when the use of $\mu=\mu_{F}-n_{B}$ is made, leads to a cubic equation
for$\sqrt{\mu}
\begin{equation}
\left( \sqrt{\mu}\right) ^{3}-\left( \sqrt{\mu}\right) ^{2}+\left(
\mu_{F}-\mu_{B}\right) =0. \label{cubic
\end{equation}
The positive root to Eq. (\ref{cubic}) that lies below 2/3 (or$\sqrt{\mu}$
$<2/3$) represents a local stable mixed phase, where the inequality is derived
by subjecting Eq. (\ref{Omega_simple}) to the local stability criteria that
$\partial^{2}\Omega/\partial n_{B}^{2}$ be positive. \ A simple analysis then
shows that Eq. (\ref{cubic}) supports the local stable mixed phase in the
chemical potential space between the line [labeled as 1 in Fig. \ref{Fig:Zero
(a)]:
\begin{equation}
\mu_{B}=\mu_{F}, \label{line 1
\end{equation}
and the parallel line [labeled as 2 in Fig. \ref{Fig:Zero}(a)] shifted with
respect to Eq. (\ref{line 1}) by $4/27$:
\begin{equation}
\text{ }\mu_{B}=\mu_{F}-4/27. \label{line 2
\end{equation}
Next, consider the pure Bose phase described by the bosonic potential
$\Omega_{B}=n_{B}^{2}/2-\mu_{B}n_{B}$ and the pure Fermi phase described by
the fermionic potential $\Omega_{F}=-\frac{2}{5}\mu_{F}^{5/2}$. \ In the
region that supports the pure Fermi (Bose) phase, the effective chemical
potential for fermions $\mu_{F}-n_{B}$ (bosons $\mu_{B}-n_{F}$) must be
negative. \ As a result, the pure Bose phase exists above the line in Eq.
(\ref{line 1}), and the pure Fermi phase exists below the curve [labeled as 3
in Fig. \ref{Fig:Zero}(a)]
\begin{equation}
\mu_{B}=\mu_{F}^{3/2}. \label{line 3
\end{equation}
It is then clear that the pure Fermi phase coexists with the mixed phase in
the region below curve 3 but between lines 1 and 2, and it also overlaps with
the pure Bose phase in the upper right region below curve 3 and above line 1.
So far, nothing has been said regarding the nature of the Fermi gas component.
To answer this question, we go to the saddle point equation for $\Delta^{2}$
\begin{equation}
\Delta^{2}=-\frac{\alpha_{2}\left( \mu,T\right) }{\alpha_{4}\left(
\mu,T\right) }.
\end{equation}
Evidently, because $\alpha_{4}\left( \mu,T\right) $ is always positive, only
when $\alpha_{2}\left( \mu,T\right) <0$ does BCS order or superfluidity
occur. \ Let $\mu_{F}^{\#}$ be the root to the threshold conditio
\begin{equation}
\alpha_{2}\left( \mu_{F}^{\#},T\right) =-\frac{1}{U_{0}}+\frac{3}{4
\sqrt{\mu_{F}^{\#}}\left( \ln\frac{\pi T}{8\mu_{F}^{\#}e^{\gamma-2}}\right)
=0. \label{alpha 2
\end{equation}
In the limit where $T$ goes to zero, $\mu_{F}^{\#}$ also goes to zero, and
hence as expected under the attractive Fermi-Fermi interaction, fermions at
$T=0$ either exist as a pure S state or mix with\ bosons to form a mixed BS state.
Finally, by comparing the energies of the phases in each coexistent region, we
change Fig. \ref{Fig:Zero}(a) into the phase diagram in Fig. \ref{Fig:Zero
(b), which features a tricritical point (labeled as $\ast$) at which the
transition between BS and S changes from the second- to first-order type, and
a critical point (labeled as $\times$) at which the second-order transition
line between B and BS and the two first-order transition lines between S and,
respectively, BS and B meet. \ The explanations are provided as follows. The
first-order transition line (dotted) between B and S is given by
\begin{equation}
\mu_{B}=\sqrt{4/5}\mu_{F}^{5/4}, \label{first-order 1
\end{equation}
which is obtained by setting $\Omega_{B}=\Omega_{F}$. \ The interception
between Eq. (\ref{line 1}) and Eq. (\ref{first-order 1}) defines the critical
point ($\mu_{F}^{\times}=\,\mu_{B}^{\times}=25/16$). The comparison between
$\Omega$ and $\Omega_{F}$ determines the first-order transition between BS and
S, which starts from the critical point $\times$ and ends at the tricritical
point $\ast$ with $\left( \mu_{F}^{\ast}=4/9,\mu_{B}^{\ast}=8/27\right) $ at
which $n_{B}=\partial\Omega/\partial n_{B}=\partial^{2}\Omega/\partial
n_{B}^{2}=0$. \
Note that for a single-component model with the repulsive Bose-Fermi
interaction, the phase diagram at $T=0$ has the same structure as
Fig.\ref{Fig:Zero}(b) except that S and BS are replaced, respectively, with N
and BN, owing to the absence of pairing mechanism for fermions
\cite{ketterle08}. \ As stressed in the introduction,\ an advantage of the
phase diagram in the chemical potential space is that each phase separation
manifests itself as a unique coexistence curve, making its identification
particularly transparent. \ For example, Fig. \ref{Fig:Zero} (b) automatically
rules out phase separations other than those between a pure Fermi and a pure
Bose phase and between a pure Fermi and a mixed phase. \ Thus, there is no
need to hypothesize and analyze the existence of, for example, a phase
separation between a pure bosonic and a mixed phase or that between two
different mixed phases, as did in works where phase analysis was performed in
space made up of particle number densities \cite{Viverit00,Salasnich07}
\begin{figure}
[ptb]
\begin{center}
\includegraphics[
height=3.5544in,
width=3.4757in
{figs2ab.eps
\caption{The phase diagram (a) at $T=0.001$ and (b) at $T=0.25$. $U_{0}$ is
same as in Fig. \ref{Fig:Zero}, and units are defined in the text.
\label{Fig:Finite
\end{center}
\end{figure}
\
At (low) finite temperature [Fig. \ref{Fig:Finite}(a)], the pure Fermi phase
is divided into N and S by the vertical (second-order transition) line
$\mu_{F}=\mu_{F}^{\#}$, where $\mu_{F}^{\#}$ increases with temperature
according to Eq. (\ref{alpha 2}), and the mixed phase is split into BN and BS
by the (second-order transition) line, $\mu_{B}=\mu_{F}+n_{F}^{\#}-\mu
_{F}^{\#},$ which begins at point \# and ends at point $\times$, with
$n_{F}^{\#}$ being the Fermi number density [Eq. (\ref{fermi number density})]
at $\Delta=0$ and $\mu=\mu_{F}^{\#}$. \ As the temperature increases, both the
$N$ and $BN$ region expand while $S$ and $BS$ contracts. \ A further increase
in the temperature so that $\mu_{F}^{\#}$ lies beyond $\mu_{F}^{\ast}$ at the
tricritical point results in a complete elimination of the phase space for the
superfluid Fermi-Bose (BS) mixture as shown in Fig. \ref{Fig:Finite}(b), where
the normal state Fermi-Bose mixture remains as the only mixed phase.
At this point, we recall that our analysis rests upon an assumption that the
term $\pi^{2}T^{2}/8\mu^{2}$ in Eq. (\ref{nF}) be much less than 1, which is
therefore applicable only to situations where the Fermi surface is well
defined (relative to the temperature of interest). At zero temperature, the
Fermi surface is fixed by $\mu=4/9$ for line 2 (and the tricritical point),
but is not defined for line 1 where $\mu=0$; line 1 holds only for $T=0$. \ As
a result, the line dividing BN and BS in Fig. \ref{Fig:Finite}(a) (which
corresponds to line 1 at zero temperature in Fig. \ref{Fig:Zero}) is far more
sensitive to the temperature increase than the first-order transition line
(and the tricritical point). \
The line between B and BN requires a special explanation. \ At zero
temperature, due to the Fermi-Dirac distribution, the chemical potential for a
normal state of Fermi gas must be positive, and under such a circumstance, the
pure Bose phase (B) is well-defined - the space above line 1, where the
chemical potential is negative $\mu<0$, is defined as the phase B. \ As
temperature increases, the Fermi surface becomes less sharply defined, and so
does the distinction between B and BN. In fact, at finite temperature there is
nothing to prevent the chemical potential for fermions from becoming negative,
just as for distinguishable particles that follow the Maxwell's distribution.
\ In our study here, the line between B and BN is defined in such a way that
the Fermi density along this line is 10$^{-12}$, a small threshold
artificially introduced to indicate that the region in B is virtually free of
fermions. \ But, we stress that in contrast to the line between BN and BS
across which there is a second-order phase transition due to the emergence of
the order parameter $\Delta$ which breaks the symmetry, there is no real phase
transition for fermions across the line between B and BN. \
\section{An Application: Tightly trapped Fermions Embedded in a Large BEC}
\label{sec:an application}
In practice, phase diagrams come in different forms, depending on the
application at hands. \ A complete mapping of the phase diagram including all
the critical points in the chemical potential space as we have done in the
previous section is significant, not only because it provides a roadmap for
constructing phase diagrams in other spaces, but also because it can greatly
facilitate both the identification and the interpretation of the important
features emerging from these diagrams. \ As an application, we consider, in
this section, a double species experiment in which spherically symmetric
harmonic trap potentials, $V_{B,F}\left( r\right) $, are tuned to differ in
such a manner that fermions are tightly confined inside a much larger BEC, and
use it as a model to explore how the surrounding bosons affect the physics of
Fermi pairing. \ This model is the two-component analog of the
single-component system experimentally realized by the MIT group in 2002
\cite{hadzibabic02}. It also represents an example in which the traps are
oppositely arranged compared to those adopted to implement the idea of using a
small\ trapped BEC to probe the properties of a large Fermi gas\ component
\cite{pu10,bhongale08}.
In our study below, we assume that the Fermi component, although small
compared to the BEC, is still sufficiently large so that the local-density
approximation is directly applicable. Thus, for fermions, we introduce a local
chemical potential $\mu_{F}\left( r\right) =\mu_{F}-V_{F}\left( r\right)
$, in addition to a global chemical potential $\mu_{F}$, which is fixed by
the\ total particle number. \ In contrast, for bosons, owing to its large
size, to a good approximation, we\ can regard its chemical potential, within
the distance\ scale in the order of the size of the Fermi gas, to be a
constant, $\mu_{B}$, independent of the variation of the radial distance $r$. \
Figure \ref{Fig: Tight} (a) displays the phase diagram for a homogeneous
system in the $T-\mu_{F}$ space for $\mu_{B}=0.35$ [slightly smaller than
$\mu_{B}^{\ast}$ in Fig. \ref{Fig:Finite}(a)]. \ \ At a given temperature and
within the local-density approximation, a potential profile $V_{F}\left(
r\right) $ along the radially outward direction in the real space induces an
image $\mu_{F}\left( r\right) $ in the form of a vertical line moving down
an arrow as indicated in Fig. \ref{Fig: Tight}. \ Then, by traversing from the
tail to the head of the arrow and translating each point [$\mu_{F}\left(
r\right) $] on the vertical line into the density via the mapping $\rho
_{F}^{h}\left( \mu_{F}\left( r\right) \right) $, we can construct, from
the center to the edge of the trap, the density distribution $\rho_{F}\left(
r\right) \equiv\rho_{F}^{h}\left( \mu_{F}\left( r\right) \right) $, where
$\rho_{F}^{h}\left( x\right) $ calculates the Fermi density for a
homogeneous phase at the chemical potential $x$. \ Using the rules just
outlined and given the locations and the sizes of the vertical lines indicated
in Fig. \ref{Fig: Tight}(a), we can easily arrive at the following qualitative conclusions.
(a) At sufficiently high temperature (the arrow on the right), the density
profile consists of a normal phase (N) core surrounded by a (spherical) shell
of a BN mixture.
(b) As temperature is lowered (the arrow in the middle), superfluidity (S)
emerges from the core with N being sandwiched between S and BN.
(c) As temperature is further reduced (the arrow on the left), $N$ disappears
and substituted in its place is the Bose-superfluidity mixture (BS).
(d) A further reduction in the temperature completely eliminates $BN$,
creating a density profile, reminiscent of the high temperature case in (a),
except that $N$ and $BN$ in (a) are now replaced with $S$ and $BS$, respectively.
An intriguing aspect of such a mixture is that both critical temperatures and
Fermi profiles depend strongly on $\mu_{B}$ - the chemical potential of the
surrounding BEC. As $\mu_{B}$\ can be independently tuned in experiments, we
have at our disposal a convenient tool to selectively access the parts of
phase diagrams, that are physically interesting. \ Suppose that we want to
access the first-order phase transition. \ We can do so simply by increasing
$\mu_{B}$ beyond a certain threshold value. \ An example is given in Fig.
\ref{Fig: Tight}(b) where $\mu_{B}$ is fixed to $0.45$, a value slightly
higher than $\mu_{B}^{\ast}$ in Fig. \ref{Fig:Finite}(a). \ As can be seen,
part of the transition line dividing pure and mixed states changes its nature
from second order in Fig. \ref{Fig: Tight}(a) to first order in Fig.
\ref{Fig: Tight}(b). \ Thus, although the system can undergo a similar set of
phase transitions as in Fig. \ref{Fig: Tight}(a) [at the expense of a higher
Fermi chemical potential (or density) and a smaller BS region], a density
discontinuity is expected to emerge from Fermi profiles on a sphere that
divides the two phases sharing the same first-order transition line
\begin{figure}
[ptb]
\begin{center}
\includegraphics[
height=3.5016in,
width=3.4238in
{figs3ab.eps
\caption{The phase diagram in the $T-\mu_{F}$ space when the chemical
potential for the bosons is fixed to (a) $\mu_{B}=0.35$ and (b) $\mu_{B
=0.45$. The features in (a) and (b) can be easily deduced from the phase
diagrams in the previous section. $U_{0}$ is same as in Fig. \ref{Fig:Zero},
and units are defined in the text.
\label{Fig: Tight
\end{center}
\end{figure}
\section{Conclusion}
\label{sec:conclusion}
A unique advantage of a cold atom system is that its system parameters can be
precisely tuned, allowing it to access a larger regime of phase diagrams.
Further, availability of detection techniques, such as absorption laser
imaging of densities and radio-frequency (RF) spectroscopy \cite{chin04},
makes the experimental determination of such phase diagrams in fine detail
possible. \ In this work, we have performed a systematic study of the
finite-temperature phase diagram in the chemical potential space for a
two-component Fermi-Bose mixture with attractive Fermi-Fermi and repulsive
Fermi-Bose interaction. Using a combination of scaling and Landau-Ginzburg
theory, we have identified, within the framework of mean-field theory, a set
of features generic to the phase diagrams for such mixtures.\ Further, we have
applied the theory to explore the physics of pairing among fermions in a
tightly confined trap surrounded by a large BEC gas.
Finally, we comment that so far, our analysis is based on the thermodynamic
potential in Eq. (\ref{Omega}) derived when all the phonon fields,
$\phi_{\mathbf{k},B}\left( \tau\right) $, are ignored. \ In more realistic
situations, we need to retain the phonon fields, $\phi_{\mathbf{k},B}\left(
\tau\right) $, which, after being explicitly integrated out under the
Bogoliubov approximation, is shown to induce an attractive interaction,
$U^{ind}\left( \mathbf{q}\right) =-g_{BF}^{2}/g_{BB}/\left[ 1+\left(
\hbar\mathbf{q}/\sqrt{4m_{B}g_{BB}n_{B}}\right) ^{2}\right] $, between
fermions when the retardation effect is ignored \cite{Stoof00,wang06}. \ \ The
net effect of $\phi_{\mathbf{k},B}\left( \tau\right) $ is then to change
$U_{0}$ to $U^{eff}\equiv U_{0}-g_{BF}^{2}/g_{BB}$, for the s-wave scattering,
which is expected to dominate all the other partial-wave scatterings. Thus,
the phase-diagram features presented in this work shall remain qualitatively
true not only for two-component Fermi-Bose mixtures with direct Fermi-Fermi
attraction ($U_{0}<0$), but also for those with direct Fermi-Fermi repulsion
$\left( U_{0}>0\right) $ but attractive effective Fermi-Fermi interaction
($U^{eff}<0$) \cite{viverit02}; the latter case turns out to cover several
important systems of current experimental interest, including $^{40}$K-$^{87
$Rb and $^{6}$Li-$^{7}$Li \cite{illuminati04}.
\section{Acknowledgement}
This work is supported by the US National Science Foundation and US Army
Research Office.
\bigski
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 304 |
\section{Introduction}
A Morse function on a smooth manifold is called perfect if the number of critical points equals the sum of Betti numbers.
Not every manifold possesses a perfect Morse function. Homological spheres (that are not spheres) do not possess it;
manifolds with torsions in homologies do not possess it, etc. On the other hand, the celebrated Millnor-Smale cancelation technique for critical points with neighbor indices (or, equivalently, cancelation of handles)
provides a series of existence-type theorems \cite{Fomenko,Milnor} which are the key tool in Smale's proof of generalized Poincare conjecture \cite{Smale}.
In the paper we focus on one particular example of a perfect Morse function and discuss some related problems.
Namely, we bound ourselves by the space of configuration of the equilateral polygonal linkage with odd number $n=2k+1$ of edges. As the ambient space it makes sense to take either $\mathbb{R}^2$ or $\mathbb{R}^3$,
which gives us the spaces $M_2(n)$ and $M_3(n)$.
In bigger dimension the configuration space is not a manifold. The number $n$ is chosen to be odd by the same reason: for even $n$, the configuration space of the equilateral polygonal linkage has singular points.
We are interested in finding a "natural" perfect Morse function, that is, a function that has a transparent physical or geometrical meaning.
The first candidate of a "natural" Morse function on $M_2(n)$ was the oriented area function $A$. Indeed, it a Morse function with
an easy description of its critical points as cyclic polygons (that is, polygons with a superscribed circle), and a simple formula for
the Morse index of a critical point \cite{khipan}. However, for $M_2(n)$
$A$ is not perfect. In particular, for the
equilateral pentagonal linkage it has one extra local maximum
(except for the global maximum) and one extra local minimum, see
Example \ref{Expentagon}.
For the equilateral heptagonal linkage the number
of Morse points greatly exceeds the sum of Betti numbers of the
configuration space.
To build up a perfect Morse function, we take the space $M_3(n)$ and \textit{decorate} it.
The decorated space $\widetilde{M}_3(n)$ is well adjusted for
an appropriate
generalization $S$ of the area function $A$.
Its critical points (loosely speaking) are again cyclic polygons.
Surprisingly, the function $S$ is a perfect Morse function.
As a
direct corollary we interpret cyclic equilateral polygons as
independent generators of the homology groups of the configuration
space $\widetilde{M}_3(n)$.
\section{Preliminaries and notation}\label{section_preliminaries}
For an odd $n=2k+1$
an equilateral \textit{polygonal $n$-linkage} should be interpreted as a collection of rigid
bars of lengths $1$ joined consecutively by revolving joints in a
chain.
\textit{A configuration} of the polygonal $n$-linkage in the
Euclidean space $ \mathbb{R}^d$, $d=2, \ 3$ is a sequence of points
$R=(p_1,\dots,p_{n+1}), \ p_i \in \mathbb{R}^d$ with
$1=|p_i,p_{i+1}|$ and $1=|p_n,p_{1}|$ modulo the action of
orientation preserving isometries of the space $\mathbb{R}^d$.
We also call $P$ \ a \textit{polygon}. A configuration carries
a natural orientation which we indicate in figures by an arrow.
The set $M_d(n)$ of all configurations up to an orientation-preserving isometry of the ambient space is \textit{the moduli
space, or the configuration space of the polygonal linkage }$L$.
For $d=2,3$ the space $M_d(n)$ is a smooth manifold.
We explain below in this paragraph what is known about planar
configurations and the signed area function as the Morse function on
the configuration space.
\begin{definition} \label{Dfn_area} The \textit{signed area} of a polygon $P\in M_2(n)$ with the vertices \newline $p_i = (x_i,
y_i)$ is defined by
$$2A(P) = (x_1y_2 - x_2y_1) + \ldots + (x_ny_1 - x_1y_n).$$
\end{definition}
\begin{definition}
A
polygon $P$ is \textit{cyclic} if all its vertices $p_i$
lie on a circle.
\end{definition}
Cyclic polygons arise here as critical points of the signed area:
a polygon $P$ is a critical point of the
signed area function $A$ iff $P$ is a cyclic configuration.
Their Morse indices are known \cite{khipan,zhu}.
\medskip
\begin{example} \label{Expentagon} \cite{panzh} The equilateral pentagonal linkage has 14 cyclic
configurations indicated in Fig. 4.
(1). The convex regular pentagon and its mirror image are the global maximum and
minimum of the signed area $A$. Their Morse indices are $2$ and $0$
respectively.
(2). The starlike configurations are a local maximum and a local
minimum of $A$.
(3). There are ten configurations that have three consecutive
edges aligned. Their Morse indices equal $1$.
\end{example}
\begin{figure}[h]\label{pentagon}
\centering
\includegraphics[width=5 cm]{pentagon.eps}
\caption{Cyclic configurations of the equilateral pentagonal linkage
}
\end{figure}
\section{The decorated configuration space $\widetilde{\mathcal{M}}_3(n)$ and the area function $S$}\label{Section_decorated}
\begin{definition}
The \textit{decorated configuration space} is defined as the set of pairs
$$\widetilde{M}_3(n)=\{(P,\xi)| P \ \hbox {is a polygon in $\mathbb{R}^3$
with the sidelengths}\ 1; \ \xi \in S^2,
\}$$ factorized by the diagonal action of the orientation
preserving isometries of $\mathbb{R}^3$.
Here $S^2 \in \mathbb{R}^3$ is the unit sphere centered at the
origin $O$.
\end{definition}
\begin{lemma}\begin{enumerate}
\item The space $\widetilde{M}_3(n)$ is an orientable fibration over $M_3(n)$ whose
fiber is $S^2$.
\item The Euler class of the fibration equals zero.
\end{enumerate}
\end{lemma}
Proof. (1) The set of all polygons with fixed sidelengths (before
factorization by isometries) is known to be orientable. Therefore the set of the
pairs (a polygon, a vector) is also orientable as a trivial
fibration. Since we take a factor by the action
of orientation preserving isometries, the result is also orientable.
(2) $s(P):=\frac{\overrightarrow{p_1p_2}}{|p_1p_2|}$ defines a non-zero section. \qed
The Gysin sequence implies:
\begin{corollary}\label{Cor_Gisin}
\begin{enumerate}
\item We have the following short exact sequence:
$$0\rightarrow H^m(M(n)) \rightarrow H^m(\widetilde{M}(n)) \rightarrow H^{m-2}(M(n)) \rightarrow 0.$$
\item The homology groups $H_m(\widetilde{M}(n))$ are free abelian. For the Betti numbers we have:
$$\beta^m(\widetilde{M}(n))= \beta^m({M}(n))+\beta^{m-2}({M}(n)).\qed$$
\end{enumerate}
\end{corollary}
\begin{definition} \label{Dfn_areaR3} Let $(P,\xi) \in \widetilde{M}_3(n)$, let $ (x_i,
y_i)$ be the vertices of $P$. The \textit{ area} of the pair $(P,\xi)$ is defined as
the scalar product:
$$2S(P,\xi)=( p_1 \times p_2 + p_2 \times p_3+ \dots + p_n\times p_1,\xi).$$
An alternative equivalent definition is:
$$S(P,\xi)=A(pr_{\xi^\perp}(P)),$$
where $pr_{\xi^\perp}$ is the plane orthogonal to $\xi$ and
cooriented by $\xi$.
\end{definition}
\medskip
\begin{proposition}\label{Thm_crirical_3D}
For an equilateral polygon with odd number of edges, critical points $(P, \xi)$ of the function $S$ are
pairs $(P, \xi)$ such that $P$ is a planar cyclic
polygon, and $\xi$ is orthogonal to the affine hull of $P$.
If $(P, \xi)$ is a critical point, then $(P, -\xi)$ is critical as well.
\end{proposition}
Proof.
The paper \cite{KhristofPanina} contains a characterization of all critical points for a generic polygonal linkage (which is not necessarily equilateral). In
our particular case it implies that
critical points $(P, \xi)$ of the function $S$ fall into two classes:
\begin{enumerate}
\item \textbf{Planar cyclic configurations.}
These are pairs $(P, \xi)$ such that $P$ is a planar cyclic
polygon, and $\xi$ is orthogonal to the affine hull of $P$.
\item \textbf{Non-planar configurations.} They are characterized
by the three following conditions:
\begin{enumerate}
\item The vectors $\xi$ and $\overrightarrow{S}=p_1 \times p_2 + p_2 \times p_3+ \dots + p_n\times p_1$
are parallel (but they can have opposite directions).
\item The orthogonal projection of $P$ onto the plane $\overrightarrow{S(P)}^\perp$ is a
cyclic polygon.
\item For every $i$, the vectors $\overrightarrow{T_i}$, $\overrightarrow{S}$, and $\overrightarrow{d_i}$ are
coplanar.
\end{enumerate}
Here $\overrightarrow{d_i}$ is the $i$-th short diagonal,
$\overrightarrow{T_i}$ is the vector area of the triangle
$p_{i-1}p_ip_{i+1}$.
\end{enumerate}
Let us show that the second class (non-planar configurations) is empty.
Indeed, given a non-planar critical configuration, introduce a Cartezian system with the $z$-axes parallel to $\xi$. The three conditions (a), (b), and (c) implie that the absolute value of the slope
of an edge with respect to the plane $(x,y)= \xi^\perp$ does not depend
on the edge. This implies a contradiction with the closing condition: $\sum_{i=o}^n (z(p_i)-z(p_{i-1}))=0,$ where the indices are modulo $n$.\qed
\bigskip
\begin{theorem}\label{Cor_perfectMorse}
\begin{enumerate}
\item The function $S$ is a perfect Morse function on the decorated configuration space $\widetilde{M}_3(L)$ for an equilateral linkage with odd number of edges.
\item Each critical point of the function $S$ is a pair $(P,\xi)$, where
$P$ is a planar cyclic configuration, $\xi$ is a unit vector orthogonal to $P$.
Each planar cyclic configuration $P$ gives two critical points of the function $S$ (with two different choices of the normal vector $\xi$).
\item The Morse index of a critical point $(P,\xi)$ is
$$m(P,\xi)=2e-2\omega -2,$$
where $\omega$ is the winding number $P$ around the center of the circumscribed circle,$e$ is the number of edges that go counterclockwise.\footnote{ The vector $\xi$ sets an orientation on the plane of the polygon,
so it makes sense to speak of "edges going clockwise" and "edges going counterclockwise". }
\end{enumerate}
\end{theorem}
Proof. (\textit{i})
The second statement is already proven. Let us show that the number of critical points equals the sum of Betti numbers.
The latter
are already known due to A. Klyachko \cite{klya}:
$$\beta^{2p}(M_3(n)) = \sum _{0\leq i\leq
p}\left(\!\! \begin{array}{c}2k\\ i
\end{array}\!\!\right),\;\;p<k.$$
By Corollary \ref{Cor_Gisin}
we
have
$$\beta^{2p}(\widetilde{M}_3(n))=\sum _{0\leq i\leq p}\left(\!\!
\begin{array}{c}n\\ i
\end{array}\!\!\right),\;\;p<k.$$
Each equilateral cyclic $n$-gon with an orthogonal vector $\xi$ is defined by its winding number $\omega$ and by the set of edges that go clockwise.
Assume that the winding number is positive (negative values are treated by symmetry).
If the number of edges that go clockwise is $e$, then the winding number ranges from $ 1$ to $ (k-e)$.
For $p=0,1,..., k$ denote by $N^p_n$ the number of such cyclic
equilateral polygons for which
$e-\omega-1=p.$
Then
$\widetilde{\beta}^{2p}_n=N^p_n.$
(\textit{iii}) Straightforward analysis of the Hesian matrix is very complicated (probably impossible), so we use derive a combinatorial approach. We prove the formula for Morse index by induction by $n$. The base is given by equilateral pentagon.
By symmetry, we assume in whatfollows that we have a critical point $(P,\xi)$ such that $S(P,\xi)>0$, or, equivalently, with winding number $\omega >0$.
Proof is based on two observations:
(1) There is a natural embedding of a neighborhood of $P$ in space $M_2(n)$ to $\widetilde{M}_3(n)$. It sends a configuration $P$ to $(P,\xi)$ with the same $P$ and $\xi$ orthogonal to the affine hull of $P$. The direction of $\xi$ we choose in the way such that $S$ is positive. Let us choose a basis of the tangent space $T_{(P,\xi)}\widetilde{M}_3(n)$ which starts by the pushforward of a basis of $T_PM_2(n)$ and ends by coordinates of $\xi$. The Hessian matrix related to this basis is a block matrix:
$$HESS(P,\xi)=\left(
\begin{array}{ccc}
H_1 & 0 & 0\\
0 & H_2 & 0 \\
0 & 0 & -E\\
\end{array}
\right),
$$
where $H_1$ is the $(n-3)\times (n-3)$ Hessian matrix of the planar polygon $P$ related to the area function $A$ and the space $M_2(n)$; $E$ is the the $2\times 2$ unit matrix.
(2) For an $(n+2)$-gon and a number $1 \leq i \leq n$, consider the embedding $\varphi_i:\widetilde{M}_3(n)\rightarrow \widetilde{M}_3(n+2)$ which keeps $\xi$ and replaces the edge number $i$ by a fold of three edges (see Fig. 1, (3) for an equilateral triangle with an edge by a three-fold). Each critical point $(P,\xi)\in {\widetilde{M}_3}(n)$ induces a critical point $\varphi_i(P,\xi) \in \widetilde{M}_3(n+2)$. Since the embedding has codimension two, and all Morse indices can only be even, we have either
$m(\varphi_i(P,\xi)) = m(P,\xi)$, $m(\varphi_i(P,\xi)) = 2+ m(P,\xi)$, or $m(\varphi_i(P,\xi)) = 4+ m(P,\xi)$.
More precisely, replacement of an edge replaced by a three-fold adds two extra columns to $H_1$ and two extra columns to $H_2$.
We know from \cite{khipan} that the Morse index of $P$ related to $M_2(n)$ and the oriented area $A$ (that is, the number of negative eigenvalues of $H_1$) equals $e-2\omega-1$. It increases by one after replacement of an edge by a three-fold. This only leaves the case $m(\varphi_i(P,\xi)) = 2+ m(P,\xi)$.
These arguments allows to make an induction step $n \rightarrow n+2$ and thus proves (\textit{iii}) for all cyclic configurations with triple edges.
It remains to prove the formula for configurations without triple edges, that is, with all the edges going counterclockwise. We keep assuming that $S(P,\xi)>0$, so there are exactly $k$ such polygons: with $\omega =1,2,3,...,k$.
Their Morse indices should be $2n-4$, $2n-6$, $2n-8$, etc. The only question is which configuration has one or the other index.
We know that $H_1$ contributes $n-3$, $n-5$, $n-7$, etc. to each of the Morse indices. The block $H_2$ contributes not more than $n-3$, and $-E$ contributes exactly two. The statement follows.
\qed
As an illustration, we list below
all cyclic equilateral pentagons and heptagons. The first column depicts a combinatorial type, the third one
tells the number of configurations of this type, and the last one tells the Morse index.
\begin{figure}[h]
\centering
\subfigure[Critical equilateral pentagons]{
\includegraphics[width=6 cm]{Critpents.eps}}
\subfigure[Critical equilateral heptagons]{
\includegraphics[width=6 cm]{Crit7gons.eps}}
\label{Figure_7gon}
\end{figure}
\section*{Concluding remarks}
Decorated configuration space and the ares $S$ can be defined for a polygonal linkage that is not necessarily equilateral.
However, generically, the function $S$ is not a perfect Morse function.
In the paper we omit the discussion about non-degenericity of critical points, since it appears to be somewhat technical. However the following arguments work:
We may replace the equilateral linkage $(1,1,...,1)$ by its perturbation $(1+\epsilon_1,1+\epsilon_2,...,1+\epsilon_n)$ has non-degenerate critical configurations that are close to above described equilateral ones.
\section*{Acknowledgements} This work is
supported by the Russian Science Foundation under grant 16-11-10039.
| {
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} | 5,716 |
Q: Setup fails to give DLL access rights for local user When I install my application using the setup executable (generated using NSIS) on certain computers a particular DLL does not get the ACL for the the local Users group in its security permissions. The result is that loading the DLL in question only works for administrators.
It is always the same DLL that is affected. All the other DLLs install perfectly. The DLL is properly signed.
The DACL for a DLL usually contains these entries:
*
*SYSTEM
*John Doh (john@doe.local)
*Administrators
(PC-NAME\Administrators)
*User (PC-NAME\Users) --- this one is missing on the affected DLL
What could cause this, and how can I fix it?
A: I think I found it.
The local user installs the program using the administrator account, but some dll is locked.
After a reboot, the dll is getting overwritten, but now the rights for the local user(s) are missing!
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 647 |
Чуфу́т-Кале́ (, «Юдейська Фортеця»), раніше Кирк-Ор (, «Сорок замків»), Джевхер-Кермен (, «Фортеця коштовностей») — середньовічне місто-фортеця у південно-західному Криму. Одне з найвідоміших і найбільших кримських «печерних міст», розташоване на внутрішній гряді Кримських гір за 3 км на схід від Бахчисараю. Пам'ятка культурної спадщини України національного значення. Із 2014 року, перебуває під російською окупацією.
Варіанти назв
Кирк-Єр, Кирк-Ор () — тюркська назва фортеці у ХІІІ–XVII століттях. У ХІХ ст. А. Гаркаві висунув гіпотезу про іраномовне (аланське) походження цього топоніму (від слова «кер-кері» — «фортеця для захисту тилу»), який міг бути переосмислений тюрками у дусі народної етимології;
Кале (, фортеця) — використовувалося в тарханних ярликах кримських ханів і караїмами, зокрема, у книгах надрукованих у чуфуткальській друкарні (заснована 1731 року);
Чуфут-Кале, Джуфут-Кале, Чіфут-Калесі — в перекладі з кримськотатарської мови «єврейська фортеця» (Cufut — єврей, Qale — фортеця). Назва відома з кінця XVII століття і використовується до сьогодні, у тому числі науковцями;
Джевхер/Гевхер-Кермен (Gevher Kermen — в перекладі з кримськотатарської «фортеця коштовностей») — імовірно, назва дана через те, що в'їзди до фортеці могли бути прикрашеними напівдорогоцінним чи дорогоцінним камінням;
Села Єгудім (Давньоєвр. סלע יהודים — скеля іудеїв (караїмською вимовою) та Села ха-Карай (у іврит. סלע הקראים — скеля караїмів) — назви, які вживалися виключно в караїмській літературі з другої половини XIX століття; перша запроваджена караїмським газзаном, дослідником і колекціонером А. С. Фірковичем;
Чуфт-Кале, Джуфт-Кале (у перекладі з тюркського «подвійна (парна) фортеця», Чӱфт / Джӱфт — пара, Qale — фортеця) — найпізніша назва, яка з'являється на початку XX століття і використовується окремими караїмськими інтелектуалами пострадянської епохи.
Окремі науковці ототожнювали Чуфут-Кале з середньовічним містом Фулли, яке відоме з раннього середньовіччя як центр православної єпархії, а у VIII—IX століттях ще й як хозарська фортеця. Більшість дослідників цю версію не поділяє.
Історія
За результатами археологічних досліджень та аналізу писемних джерел можна виділити такі етапи історії городища:
VI–Х століття (частина дослідників вважає, що поселення виникло у Х–ХІ століттях). Засновано у місцевості, де основну частину населення становили алани, масове проникнення яких у Крим почалося в серед. ІІІ століття. На початку цього періоду створено оборонну систему, головною ланкою якої став Середній мур. Він перетинає плато в найвужчому місці та має браму (Орта-Капу, Середня брама). Перед стіною влаштовано рів, вирубаний у скелі, а перед північним флангом муру — ще два коротких рови, які захищали хвіртку, призначену для вилазок. Ущелини в урвищах перегородили короткими стінами. Біля них створили перші печерні приміщення для укриття вартових. Імовірно, у фортеці була християнська базиліка, на що вказують фрагменти ранньовізантійських мармурових архітектурних деталей у муруванні пізньосередньовічних споруд. На схилах плато відомо 3 ранньосередньовічних могильники. На плато матеріалів цього періоду мало. Це, імовірно, пов'язано з тим, що фортецю використовували як прихисток на випадок воєнної загрози і постійно тут перебувала лише невелика залога. Письмові згадки відсутні.
ХІ — сер. XIV століття. З'являються писемні джерела про фортецю. Припускають, що перша згадка про фортецю (1253) міститься у творі посланця французького короля Гійома де Рубрука, який повідомляв про «40 замків» між Судаком і Херсоном. У цьому разі це переклад тюркомовної назви «Кирк-Єр/Ор», під яким поселення відоме до XVII століття. Після утворення Кримського улуса Золотої орди Кирк-Єр став ставкою окремого тумену (тьми). Арабський літописець Рукнеддін Бейбарс згадує про пограбування Кирк-Єра 1299 військом золотоординського еміра Ногая. Арабський географ Абу-ль-Фіда (1321) повідомляє, що місцеве населення — аси (алани) — знаходять там прихисток під час воєнної загрози. Гіпотетично в районі брами Кічик-Капу на цьому етапі сформувався християнський печерний монастир — попередник Бахчисарайського Свято-Успенського монастиря;
Сер. XIV — XV століття. На початку цього періоду фортецю захопили татари, 1346 споруджено мечеть. У XIV столітті в місті поселилися караїми і створили тут свій торговельно-ремісничий осередок (нове місто). У 1420-х рр. кілька років фортецею володів Девлет-Берди, син Таш-Тимура і дядя майбутнього першого кримського хана. Особливого значення Кирк-Єр набув на початку існування незалежного Кримського ханату. У 2-й пол. 1430-х рр. чи на поч. 1440-х рр. засновник ханату Хаджі Ґерай переніс сюди із Солхата (нині м. Старий Крим) свою головну ставку — місто на кілька десятиліть стає столицею нової держави. Із цього часу на плато з'являється масовий археологічний матеріал. Забудовано територію Старого міста, реконструйовано оборонну систему, перебудовано мечеть (1455), споруджено мавзолей Джаніке Ханим (1437) — доньки хана Тохтамиша і сестри еміра Едигея. Перед Середнім муром з'явився торговельно-ремісничий посад, утворений іудейською (скоріш за все, караїмською) громадою. Із XV століття ханські ярлики згадують про 3 громади в місті: мусульманську, іудейську (більшість — караїми) та християнську. У 1459 року Хаджі Ґерай надав тарханну грамоту всім трьом громадам, тобто звільнив їх від виплат податків і зборів. У тарханній грамоті 1468 року хана Нур Девлет Ґерая мешканцям Кирк-Єра згадані вірмени. Є версія, що у правління першого кримського хана алани, греки та готи були витіснені із Кирк-Єра і фортеця була передана караїмам, проте імовірно тоді розпочався процес залишення міста православними. Хаджі Ґерай та його наступники у 1455—1551 рр. карбували в Кирк-Єрі монети. У 2-й пол. XV ст. у фортеці почали утримувати знатних полонених і послів ворожих держав, так, наприклад, у 1493 році там був ув'язнений посол Великого князівства Литовського і Руського Леж.
XVI — 2-га пол. ХІХ століття. На поч. XVI століття хан переїхав у палац — Девлет-Сарай — в урочищі Салачик біля підніжжя скелі, на якій стоїть Чуфут-Кале. Коли в 1-й пол. XVI століття в долині р. Чурук-Су (притока Качі) заснували новий ханський палац, навколо якого виросло м. Бахчисарай, татари почали залишати фортецю. Більшість населення в ній тепер становили іудеї, переважно караїми (яким було заборонено мешкати в Бахчисараї). Близько 1500 року до Криму з Персії переїхав караїмський просвітник Сінан Бей-Ходжа, який до смерті у 1551 році займався навчанням караїмів, іноді насильницькими методами. Його нащадки до сер. XVIII століття служили Ґераям, керували кінським і монетним дворами, мали почесний титул «ага» та очолювали караїмську громаду фортеці. У ханський період караїми користувалися внутрішньою судовою автономією. У середині XVII століття почали вживати нову назву міста — Чуфут-Кале, буквально «Іудейська/Єврейська фортеця» (у російських джерелах — «Жидовский городок»). У цей період споруджено Східний мур із брамою Біюк-Капу (Велика брама). Ще О. Бертьє-Делагард на основі фортифікаційних особливостей муру відносив його створення до XVI століття, що узгоджується з даними новітніх розкопок. Із цього часу бурхливо розвивалася житлова забудова як старої, так і нової, частин. Фортеця зберігала своє воєнне значення: так, 1628 тут під час міжусобної війни витримали облогу хан Мегмед Ґерай III та його брат калга-султан Шагін Ґерай. У XVII столітті кримські хани продовжували тримати в Чуфут-Кале важливих бранців, серед них польського гетьмана Миколая Потоцького (сер. століття), московських боярина Василя Бутурліна та князя Андрія Ромадановського (друга пол. століття). У другій пол. XVII століття, за повідомленням турецького мандрівника Евлія Челебі, вся адміністрація міста була караїмською («іудейською»). На той момент його, ймовірно, вже залишила не лише більшість татар, а й вірменів. Чуфут-Кале перетворився на духовний і культурний центр кримських караїмів. У 1731 році вони у його стінах відкрили першу в Криму типографію, яка з 1734 року почала друкувати книжки переважно на івриті. На сер. ХІХ століття у фортеці було 300 будинків та близькь 1600 жителів. У другій пол. ХІХ століття мешканці цілком залишили поселення, оскільки після анексії Криму (1783) було скасовано заборону караїмам жити в Бахчисараї. У 1844—1867 роках у Чуфут-Кале діяла караїмська школа, яка мала сприяти утриманню жителів у місті. Одним з останніх його мешканців був газзан, дослідник та колекціонер А. С. Фіркович (1786/87–1874), який переїхав туди з Луцька. Він висував плани переселення у місто караїмів із Литви чи суботників із Персії, але реалізувати їх не вдалося. Релігійний центр караїмів у ХІХ ст. було перенесено з Чуфут-Кале до Євпаторії.
Опис
Городище займає скелясте мисоподібне плато і складається із 3-х частин: 1) Бурунчак — великий пустир (близько 26 га), що його використовували як вигон для худоби, а у XVIII столітті навіть як ханський звіринець; 2) Старе місто (понад 7 га) у найвужчій частині плато, було обмежене із заходу невисокою огорожею, яка відокремлювала його від Бурунчаку, а зі сходу — Середнім оборонним муром, який має типові ранньовізантійські риси; 3) Нове місто (більше 3 га) — забудована територія між Середнім та Східним мурами. Останній збудований у дусі пізньосередньовічної фортифікації з урахуванням можливостей використання вогнепальної зброї.
У Старому місті (західній давнішій частині) збереглися численні печери, руїни мечеті, мавзолей дочки золотоординського хана Тохтамиша Джаніке (1437 року), два караїмські храми (кенаси). У Новому місті був ханський монетний двір, і чимало житлових будинків.
Мавзолей Джаніке Ханим — прекрасний зразок монументальної сельджуцької архітектури XV ст. З ім'ям Джаніке пов'язано кілька легенд. Одна з них свідчить, що Ханим жила у палаці на Чуфут-Кале поруч із казармами на тисячу воїнів і була ватажком цього гарнізону. Вона загинула, відважно захищаючи місто під час облоги, після чого хан наказав спорудити на місці її загибелі мавзолей восьмигранної форми, прикрашений різьбленими колонами, з покритим різьбленням високим порталом. У його глибині, на ступінчастому підвищенні, лежить надгробок з написом витонченою арабською в'яззю: «Це гробниця славетної царівни Джаніке Ханим, дочки Тохтамиш хана, що померла місяця рамазану 841 року».
Серед архітектурних пам'ятників, що збереглися, слід відзначити оборонну стіну Х століття, яка будувалася з трьох шарів (бокові стіни — з добре оброблених вапнякових блоків, а простір між ними був заповнений грубим ламаним каменем, скріпленим вапняним розчином). Загальна товщина стіни сягала 5 м.
До нашого часу з пам'яток караїмської громади у Старому місті найкраще збереглися будівлі двох кенас. Велику кенасу традиційно датують XIV ст., але за архітектурними ознаками та сучасними уявленнями про історію поселення можна припустити, що вона виникла не раніше XVII ст. Друга, мала кенаса, постала наприкінці XVIII століття, коли в Чуфут-Кале переселилася частина караїмів з покинутого ними Мангупа. У Новому місті вцілів комплекс садиби А.Фірковича. Із приблизно 200 печерних споруд більшість з'явилася у XVII–XVIII століттях, вони були господарських приміщеннями на садибах. У печерах у районі брами Кічик-Капу (Південних Малих воріт), за свідченням Евлії Челебі (1666), жили найбідніші мешканці.
Водопостачання фортеці в період раннього середньовіччя забезпечувала масштабна гідротехнічна споруда — колодязь Тік-Кую (із кримськотатарською «Вертикальний колодязь»), який поєднує похилу галерею (120 м) і вертикальну шахту (глибина понад 30 м), на дні якої два басейни. Над входом у галерею в давнину була башта, яка розташовувалася перед Кічик-Капу. Припускають, що ця система служила не лише для прихованого підходу до води, а, за потреби, могла слугувати укриттям для значної кількості людей чи використовуватися з культовою метою.
У Новому місті, біля садиби Фірковича, розташований шахтний колодязь Копка-Кую. У XVII столітті в колодязях води вже не було, її транспортували до міста на в'ючних тваринах від джерел Газі-Мансур (біля мусульманського некрополя в Йосафатовій долині) та Юсуф-Чокрак (3,5 км на південь, біля гори Бешик-Тау).
За 300 м на південний схід від Біюк-Капу у верхів'ї Йосафатової долини (названа за схожістю і призначенням з однойменною долиною в Єрусалимі) починається територія великого караїмського некрополя Балта-Тіймез (із караїмської «Сокира не торкнеться»), на якому століттями ховали караїмів Криму, а також із Західної України, Литви та інших регіонів світу. Тут зосереджено близько 7 тисяч надгробків, близько 3,4 тисяч, із яких мають епітафії (найраніші з них належать до середини 14 ст.). Поховання вихідців із чуфуткальської громади продовжували здійснювати аж до початку ХХ століття.
Археологічні дослідження на городищі проводили У.Боданінський і О.Акчокракли (1925—28), експедиція Інституту археології АН УРСР (керівник — Є.Веймарн, 1950-ті рр.), спільна експедиція Сімферопольського університету та Бахчисарайського історико-архітектурного музею (керівники — О.Герцен і Ю.Могаричев, 1983, 1987—88), експедиція Бахчисарайського заповідника (керівник — С.Карлов, 2000). Ранньосередньовічний могильник у долині Маріам-Дере досліджували П.Бабенчиков (1946—47), Є.Веймарн (1947), В.Кропоткін (1950—61); усього тут розкопано 109 склепів, 24 підбійні та 2 ґрунтові могили. Некрополь Балта-Тіймез вивчали Д.Хвольсон (1878, 1881), О.Мещерська і О.Хосроєв (1980-ті рр.). У 1997—2014 роках гебраїсти України, Росії та Ізраїлю проводили тут епіграфічні дослідження.
Чуфут-Кале у ХІХ–ХХ ст. відвідували відомі діячі мистецтва та культури різних народів, зокрема, О. Грибоєдов, А. Міцкевич, Л. Українка, М. Коцюбинський, І. Крамськой, І. Рєпін.
Фотогалерея
Сучасний правовий статус Чуфут-Кале
Чуфут-Кале є пам'яткою архітектури національного значення згідно з Постановою КМУ № 518 від 25 червня 2020 р. (охоронний номер 010082). До складу пам'ятки національного значення входять такі елементи:
Мури фортеці з брамою та баштою, V—VI століття, охор. № 010082/1
Східний мур фортеці з великою брамою, XIII-XIV століття, охор. № 010082/2
Мур фортеці з малою брамою, XIII-XIV століття, охор. № 010082/3
Гробниця «Дюрбе Джаніке Ханим», 1437 рік, охор. № 010082/4;
Караїмська кенаса (велика), XIV століття, охор. № 010082/5;
Караїмська кенаса (мала), XVIII століття, охор. № 010082/6;
Жилий будинок XVIII століття, охор. № 010082/7
Також згідно з іншими нормативними актами, зокрема,
постановою Ради Міністрів УРСР від 21.06.1965 р. № 711, діл. № 66;
рішенням Кримського облвиконкому від 05.09.1969 р. № 595, діл. № 692;
рішенням Кримського облвиконкому від 22.05.1979 р. № 284;
рішенням Кримського облвиконкому від 15.01.1980 р. № 16;
рішенням Кримського облвиконкому від 20.02.1990 р. № 48;
охороняються державою:
комплекс архітектурно-археологічний мис Бурунчак:
а) споруди наземні оборонні;
б) споруди печерні;
в) басейн водозбірний;
г) огорожі по краю обриву (руїни);
д) стіна, що відокремлює Бурунчак від Старого міста (руїни);
Комплекс «Старого міста»:
а) споруди оборонні у щілинах по краю обриву;
б) палац (руїни);
в) забудова житлова (руїни);
г) мечеть (руїни);
д) споруди печерні в районі південних воріт;
е) споруди печерні оборонні та господарські;
Комплекс «Нового міста»:
а) палац (руїни);
б) будинок гостьовий (руїни);
в) будинок житловий (будинок доглядача);
г) забудова житлова;
д) колодязь «Коплі-Кую»;
е) споруди печерні у малому рову перед середньою стіною;
є) споруди печерні «В'язниця»;
ж) споруди печерні оборонні;
Комплекс пам'яток, розташованих за межами городища:
а) басейн водозбірний перед воротами «Біюк-Капу»;
б) кладовище в Іософатовій долині;
в) споруди печерні на південному схилі балки Мар'ям-Дере;
г) притулок прискельний у південному обриві мису Бурунчак;
д) стіна оборонна середня з воротами Орта-Капу та системою ровів на території міста
Рішенням Кримського облвиконкому від 22.05.1979 р. № 284, встановлена охоронна зона, межі котрої проходять на відстані 70 м на північний захід від «бурунчацької» стіни (точки 1-4), по лінії на північний схід від обриву плато на відстані 50 м від «східної» стіни (точки 5-7) і далі по лінії на південний захід від обриву (точки 7-1); Рішенням Кримського облвиконкому від 15.01.1980 р. № 16, встановлена охоронна зона площею 113 га, що охоплює плато, на якому розташоване городище, і смугу вздовж південного обриву шириною з півночі на південь 250 м і довжиною із заходу на схід 1300 м, з ранньосередньовічним та караїмським кладовищами.
Чуфут-Кале — входить до складу Бахчисарайського історико-культурного заповідника і є одним із найбільш відвідуваних туристами його об'єктів. У 2012 Україна включила до Попереднього списку Всесвітньої спадщини ЮНЕСКО об'єкт «Культурний ландшафт печерних міст Кримської Готії», до складу якого входить Чуфут-Кале. Легальні органи влади не можуть здійснювати ефективний контроль за цією пам'яткою через протидію Росії, яка незаконно окупувала у 2014 році АР Крим і м. Севастополь, тому Україна звернулася з проханням до ЮНЕСКО здійснити моніторинг ситуації на тимчасово окупованих територіях, зокрема, щодо збереження об'єктів культурного спадку України.
Примітки
Література
Акчокраклы О.[-Н. А.] Новое из истории Чуфут-Кале // Известия Таврического общества истории, археологии и этнографии (ИТОИАЭ). Т. 2(59). / Отв. ред. Н. Л. Эрнст. Симферополь, 1928. С. 159—172.
Вус О. В. Оборонна доктрина Візантії у Північному Причорномор'ї: інженерний захист Таврики та Боспора в кінці IV –– на початку VII ст. –– Львів: Тріада Плюс, 2010. –– 304 с.
Вус О. В. Опорна фортеця Кирк-Ор у контексті військово-інженерних заходів Візантії на Кримському півострові в VI ст. –– Київ, 2016. –– URL: https://byzantina.wordpress.com/2016/09/15/vus-6/.
О. Г. Герцен. Чуфут-Кале //
Гайко Г. , Білецький В. , Мікось Т., Хмура Я. Гірництво й підземні споруди в Україні та Польщі (нариси з історії). — Донецьк: УКЦентр, Донецьке відділення НТШ, «Редакція гірничої енциклопедії», 2009. — 296 с.
Герцен А. Г., Могаричев Ю. М. Мусульманский период в истории Чуфут-Кале (середина XIV — начало XVI в.) // Материалы Конгресса исламской археологии России и стран СНГ / Под ред. Х. М. Абдуллина, А. Г. Ситдикова. Казань: Институт археологии АН РТ, 2016б. С. 95–102.
Герцен О. Г. Чуфут-Кале // Енциклопедія історії України: у 10 т. / редкол.: В. А. Смолій (голова) та ін. ; Інститут історії України НАН України. — К. : Наук. думка, 2013. — Т. 10 : Т — Я. — С. 584. — 784 с. : іл. — ISBN 978-966-00-1359-9.
В. Гулевич. Казимир Яґайлович і Менґлі Ґірей: від друзів до ворогів // Український історичний журнал. — К., № 1 (508) за січень-лютий 2013.— С. 40-66. ISSN 0130-5247.
Горный Крым. Атлас туриста / ГНПП «Картографія», Укргеодезкартографія ; ред.: Д. И. Тихомиров, Д. В. Исаев, геоинформ. подгот. Е. А. Стахова. — К. : ДНВП «Картографія», 2010. — 112 с.
Чернышева Е. В. О формах культурной интеграции караимов и иудеев-раббанитов в крымское общество XV– XVII столетий // Вопросы крымскотатарской филологии, истории и культуры. –2016, — -Вып. 3. — С. 183—196.
Фортеці України
Замки та палаци Криму
Середньовічні міста
Столиці Кримського ханату
Середньовічний Крим
Археологія Бахчисарайського району
Печерні міста Криму
Аланські поселення
Половецькі поселення
Пам'ятки архітектури України національного значення в Криму | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 304 |
Q: Merge multiple lists of dictionaries and rename the key What is the most pythonic way to merge two list dictionaries please? Say I have two list of dictionaries as:
sold=[
{'dept': '001', 'sku': 'foo', 'qty': 100},
{'dept': '002', 'sku': 'bar', 'qty': 200},
{'dept': '003', 'sku': 'baz', 'qty': 300}
]
returns=[
{'dept': '001', 'sku': 'foo', 'qty': 10},
{'dept': '002', 'sku': 'bar', 'qty': 20}
]
desired_output=[
{'dept': '001', 'sku': 'foo', 'sold': 100, 'return': 10},
{'dept': '002', 'sku': 'bar', 'sold': 200, 'return': 20},
{'dept': '003', 'sku': 'baz', 'sold': 300, 'return': 0}
]
The code below worked, but is there a more elegant/pythonic way to do this please
merge = []
for s in sold:
found = False
for r in returns:
if (s.get('sku') == r.get('sku') and s.get('dept') == r.get('dept')):
merge.append({'sku': r.get('sku'), 'dept': r.get('dept'), 'sold': s.get('qty'), 'return': r.get('qty')})
found = True
break
if not found:
merge.append({'sku': s.get('sku'), 'dept': s.get('dept'), 'sold': s.get('qty'), 'return': 0})
I have checked this post: How to merge lists of dictionaries, it doesn't give me exactly what I want:
*
*I need to merge by multiple keys, i.e. sku and dept
*I have to rename the qty to sold and return respectively from 2 lists of dictionaries.
I tried something like below but couldn't get it work:
result = [
s['return'] = r['qty']
for s in sold
for r in return
if s['sku'] == r['sku'] and s['dept'] == r['dept']]
Thanks
A: This mutates the sold dictionary.
temp = {(cd["dept"], cd["sku"]):cd["qty"] for cd in returned}
for cd in sold:
cd["sold"] = cd["qty"]
del cd["qty"]
cd["return"] = temp.get((cd["dept"], cd["sku"]), 0)
print sold
If you don't want to mutate it, you can use this
temp, result = {(cd["dept"], cd["sku"]):cd["qty"] for cd in returned}, []
for cd in sold:
temp_dict = {}
for k, v in cd.items():
if k == "sold":
temp_dict["sold"] = cd["qty"]
else:
temp_dict[k] = cd[k]
temp_dict["return"] = temp.get((cd["dept"], cd["sku"]), 0)
result.append(temp_dict)
print result
Output
[{'sku': 'foo', 'dept': '001', 'sold': 100, 'return': 10},
{'sku': 'baz', 'dept': '002', 'sold': 200, 'return': 20},
{'sku': 'foo', 'dept': '003', 'sold': 300, 'return': 0}]
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,651 |
\section{Introduction}
Proving termination of programs is a challenging and important problem
whose solutions can significantly improve software reliability and
programmer productivity. Termination analysis also plays a role in
the analysis of reactive systems, non-terminating systems that engage
in ongoing interaction with their environments. In this case,
a termination argument is used to prove liveness properties such as the
absence of deadlock or livelock, by establishing that some desired
behaviour is not postponed forever. While the problem of proving
termination has now been extensively studied
\cite{Tiwari04,Podelski2004,Braverman06,Berdine2007,Gupta2008,Chawdhary2008,Gulwani09,Gulwani09speed,Kroening2010,Harris2010,TsitovichSWK11,Ben-Amram2012,LeikeH15},
search for efficient methods for proving non-termination that can cover a broad range of programs
remains open.
A huge body of work has been done on proving termination of programs
that is based on a number of techniques such as abstract
interpretation \cite{Berdine2007,Chawdhary2008,TsitovichSWK11}, bounds
analysis \cite{Gulwani09,Gulwani09speed}, ranking functions
\cite{Bradley2005,Cousot05}, recurrence sets
\cite{Gupta2008,Harris2010} and transition invariants
\cite{Kroening2010,Podelski2004}. The most popular technique to prove
termination is through the synthesis of a ranking function, a mapping
from the state space to a well-founded domain, whose value
monotonically decreases as
the computation progresses.
However, it is known that the linear ranking approach cannot completely resolve the
problem \cite{PodelskiR04,Braverman06}, since there are terminating
programs that have no such ranking function \cite{Ben-Amram2012}. Moreover,
linear ranking functions do not suffice for all loops, and, in
particular for multipath loops \cite{Ben-Amram2014}. Thus, the
problem of decidability of termination for linear loops stays open, in
its different variants.
Monotonicity is a useful property that is often
encountered in computer programs \cite{Gupta1990,Spezialetti1995}. Indeed, a very
high percentage of variables of programs are monotonic in nature and
therefore the analysis of such programs can be significantly improved
by exploiting monotonicity. The complexity of the termination problem
together with the observation that most loops in practice have
(relatively) simple termination argument and are monotone in nature
suggest the use of light-weight static analysis for this purpose.
The termination problem is a hard problem, and one can expect it to be decidable only in the simplest cases \cite{Braverman06}. In this work we study the termination problem of a simple class of loops with multiple paths and linear monotone assignments. The loop is specified by some initial condition, a loop guard, and a ``loop body'' of some restricted form.
We allow the loop guard to be either a conjunction of diagonal-free constraints (i.e. where the only allowed comparisons are between a loop variable and a constant) or diagonal constraints (where difference between two variables can be also compared with constants). The analysis takes advantage of properties of monotone expressions \cite{Gupta1990,Spezialetti1995}, where we use recurrence relations to model the loop iteration update of each loop variable over a single variable $n \in \mathbb{N}$ denoting the loop counter. We consider a wide variety of loop forms with different syntactic structure (i.e. different forms of loop guard and update expressions). For each of these forms we identify exactly the concrete conditions under which the loop can be said to be non-terminating. These conditions turn out to have a surprising level of complexity. In particular, we find that these conditions can differ, depending on the assumptions that we make about the syntactic structure of the loop.
An advantage of the proposed approach is that it works on programs as they are, without imposing any extra annotation effort or invoking a safety checker as other methods typically do.
To demonstrate the efficiency of the proposed approach we compare our
implementation against the (strongest) tools that participate in
SV-COMP\footnote{\url{http://sv-comp.sosy-lab.org/2016/}} using two
benchmarks: the SNU real-time benchmark (\path{www.cprover.org/goto-cc/examples/snu.html}) and the Power-Stone benchmark
\cite{Ku2007}. Namely, we compare the implementation against the tools
AProVE \cite{AProveIJCAR14} and 2ls \cite{cdksw2015}. Our implementation
outperforms both AProVE and 2ls in two aspects. First, it can handle a larger
class of monotone programs than both AProVE and 2ls. Second,
for the programs that all tools can handle our tool can decide
termination much faster.
\paragraph*{Related Work.}
Termination is a fundamental decision problem in program verification. In particular, termination of programs with linear assignments and guards has been extensively studied over the last decade. This has led to the development of powerful semi-algorithms to prove termination via synthesis of ranking functions, several of which have been implemented in software-verification tools such T2 \cite{Cook2006} and ARMC \cite{Podelski07armc}. The work in \cite{Colon2001,ColonS02,Bradley2005} use algorithms with sub-procedure for ranking individual paths; which is focused on the iterative construction of a termination argument for a full program. See the surveys by Ben-Amram and Genaim \cite{Ben-Amram2014}, and by Gasarch \cite{Gasarch15a} describing semi-algorithmic approaches to termination based on ranking functions.
In \cite{Tiwari04} Tiwari proves that the termination of a class of single-path loops with linear guards and assignment is decidable when the domain of the variables is $\mathbb{R}$. Braverman proved that this holds for $\mathbb{Q}$ as well \cite{Braverman06}. However, both have considered universal termination of single-path loops, the termination of single/multi-path loops for a given input left open.
Biere, Artho, and Schuppan propose an encoding of liveness properties into
an assertion \cite{Biere02livenesschecking}. This approach allows proving termination of programs without a ranking sub-procedure. It has been reported to prove termination of programs that require non-linear ranking functions.
Prior experimental results on some benchmarks indicate this encoding results in difficult safety checks \cite{Cook2010}.
Berdine et al. present an algorithm for proving termination that is based on
abstract interpretation \cite{Berdine2007}. Using an invariance analysis they construct a variance analysis,
and they use the fact that the transitive closure of a well-founded
relation is also well-founded to show that the fixed-point obtained by their analysis is correct.
\section{Preliminaries}
In this section we introduce some definitions that we use throughout the paper.
\begin{definition}
A linear loop $\mathcal{L}$ with integer variables $x_1,..,x_n$ is a while loop of the form
$$
\textbf{while} ~ (\phi_1 \land ... \land \phi_{m}) ~ \textbf{do} ~\{s_1;...; s_n \}
$$
where each condition $\phi_i$ is one of the following form $(x_i \sim c)$ or $( (x_i - x_j) \sim c)$
such that $c \in \mathbb{Z}$ and $\sim \in \{<, \leq, >, \geq\}$. We call the constraints of the form $(x_i \sim c)$ as diagonal-free constraints and the constraints of the form $( (x_i - x_j) \sim c)$ as diagonal constraints.
Each instruction $s_i$ is one of the following form
$$
s_i : = Assignment \mid \textbf{if} ~ \phi~ \textbf{then} ~ Assignment ~ \textbf{else} ~ Assignment
$$
where $\phi$ is a condition and $Assignment$ can be of the following form
$$
x_i := u \mid x_i := u * x_i \mid x_i := x_i + v \mid x_i := u * x_i + v
$$
such that $u, v \in \mathbb{Z}$.
\end{definition}
Intuitively, the semantics of a while loop can be interpreted as follows: starting from initial values for the variables $x_1,..., x_n$ (the input), the instructions $s_1,...,s_n$ are executed either sequentially or conditionally as far as the condition $(\phi_1 \land ... \land \phi_{m})$ holds. We say that the loop terminates for a given input if the condition $(\phi_1 \land ... \land \phi_{m})$ eventually evaluates to \textit{false}.
In this paper we are interested in studying termination of linear
monotone loops. The property of monotonicity of a statement is
defined with respect to a specific loop surrounding the statement.
Consider a while loop $\mathcal{L}$ and a statement $\verb+s+: x :=
e;$ inside the loop. Further consider a single execution of the loop
which involves $n$ iterations through the loop. Let $\ell_1,
\ell_2,...,\ell_n$ denote the $n$ consecutive iterations of the loop
and $x_1, x_2,.., x_m$, denote the values assigned to $x$ during these
iterations, where $m \leq n$ because statement $\verb+s+$ may not be
executed during every iteration if there are conditional branches
inside the loop.
\begin{definition}[Monotonic statements \cite{Spezialetti1995}]
A statement $\verb+s+$ is considered to be loop monotonic w.r.t. loop
$\mathcal{L}$ if the sequence of values assigned to variable $x$
during successive executions of $\verb+s+$ forms an increasing or
decreasing sequence of values (i.e. $x_i < x_{i+1}$ or $x_i >
x_{i+1}$).
The monotonic statement $\verb+s+$ is considered to be regular
monotonic if the sequence $x_1, x_2,.., x_m$ is an arithmetic
progression or geometric progression. Otherwise, the monotonic
statement is considered to be irregular monotonic.
\end{definition}
The class of monotonicity of a statement $\verb+s+: x := e;$
surrounded by a loop $\mathcal{L}$ can be determined using a set of
static techniques. In \cite{Spezialetti1995} a sophisticated static
analysis is employed in order to determine loop monotonic
variables. For space reasons we omit discussion of these techniques
and we refer the reader to \cite{Spezialetti1995}. Throughout this
paper we use the following notations: $\uparrow$ to denote a
monotonically increasing update expression, $\downarrow$ to denote a
monotonically decreasing update expression, and $\rightarrow$ to denote a
constant expression.
\section{Single-path Linear Monotone Loops}
In this section we consider termination of single-path linear monotone loops. We consider first
termination of single-path loops with diagonal-free constraints and then single-path loops with diagonal constraints.
The structure of single-path loops with diagonal-free constraints that we consider has the following form
\begin{equation} \label{cyclesWithoutCond}
\begin{array}[t] {l}
\textbf{while} (x \sim c)~ \textbf{ do} ~
\{ x := \verb+f+(x);
\}
\end{array}
\end{equation}
where $\sim \in \{<, \leq, >, \geq \}$, $c \in \mathbb{Z}$,
and the statement $\verb+s+: x := \verb+f+(x);$ is a monotonic statement. Termination of a program of the form (\ref{cyclesWithoutCond}) is very straightforward and can be decided using Lemma \ref{BoundeAboveBelow}.
\begin{lemma} \label{BoundeAboveBelow}
Let $\mathcal{L}$ be a program of the form (\ref{cyclesWithoutCond}). Then $\mathcal{L}$ is terminating if $\sim \in \{<, \leq \}$ and $\verb+s+ \uparrow$ or $\sim \in \{>, \geq \}$ and $\verb+s+ \downarrow$. On the other hand, $\mathcal{L}$ is non-terminating if $\sim \in \{<, \leq \}$ and $\verb+s+ \downarrow$ or $\sim \in \{>, \geq \}$ and $\verb+s+ \uparrow$, given that the initial value of $x$ (let us call it $x_0$) satisfies the loop guard.
\end{lemma}
\subsection{Single-path Loops with Diagonal Constraints} \label{sec: GapConst}
In this section we consider single-path loops with diagonal constraints of the form
\begin{equation} \label{cyclesWithGapConstraints}
\begin{array}[t] {l}
\textbf{while} ~ ( (x - y) \sim c)~ \textbf{ do} ~
\{ x := \verb+f+_1(x); ~ y := \verb+f+_2(y);
\}
\end{array}
\end{equation}
where $\sim \in \{<, \leq, >, \geq \}$, $c \in \mathbb{Z}$, and the statements $\verb+s+_1: x := \verb+f+_1(x);$ and $\verb+s+_2: y := \verb+f+_2(y);$ are monotonic statements.
In Table \ref{table:classification} we classify linear monotone expressions into regular and irregular expressions, where regular expressions are classified further into regular expressions with arithmetic progression and regular expressions with geometric progression. We model the loop iteration update of each loop variable as a recurrence equation over a new variable $n \in \mathbb{N}$ denoting the loop counter.
\begin{table}
\centering
\adjustbox{max width=\textwidth}{
\begin{tabular}{|c|c|c|c|}
\hline
Update expression & Regularity class & Recurrence equation & Notation \\
\hline
$x:= x + v, v \neq 0 $ & Regular with arithmetic progression & $x_n = x_0 + v * n$ & $R_{a}$ \\
\hline
$x:= u * x, u > 1 $ & Regular with geometric progression & $x_n = x_0 * u^{n}$ & $R_{g}$ \\
\hline
$x:= u* x + v, u > 1, v \neq 0 $ & Irregular & $x_n = u^{n} * x_0 + \sum_{n = 0}^{n-1} (u ^{n} * v) $ & $I$ \\
\hline
\end{tabular} }
\caption{A summary of classification of linear monotone expressions} \label{table:classification}
\end{table}
Recurrence equations are fundamental models used for the definition of relations between consecutive elements of a sequence. In this work, we show that for linear monotone programs, it is more natural to represent the behaviour of loop variables and to reason about termination using recurrence equations instead of using conventional approaches such as linear ranking approach. Using such formalization, the analysis can take advantage of fundamental mathematical properties of various types of recurrence relations which arise during the analysis. As shown in Table \ref{table:classification} there are two types of recurrence equations that arise during the analysis of monotone programs: linear and exponential equations.
We now discuss different procedures to analyse termination of a program of the form (\ref{cyclesWithGapConstraints}) depending on the various types of recurrence relations which arise during the analysis.
We consider the case where $\sim \in \{>, \geq \}$ since the analysis of the case where $\sim \in \{<, \leq \}$ is very similar. Note that if the variables move in opposite directions (i.e. one increases and the other decreases) then the analysis is trivial (i.e. if $x$ moves up and $y$ moves down then the program is non-terminating, while if $x$ moves down and $y$ moves up then the program is terminating, given that the initial values $(x_0, y_0)$ satisfy the loop guard). However, if the variables move in the same direction then the analysis can be non-trivial.
\subsubsection{When both variables grow/decay linearly of the form $R_a$.} \label{sec: Ra}
Let $\verb+s+_1$ and $\verb+s+_2$ be monotonic statements of the form $R_{a}$. Termination of a program of the form (\ref{cyclesWithGapConstraints}) can be then decided using the following rules.
\begin{enumerate}
\item If $(\verb+s+_1 \uparrow \land ~ \verb+s+_2 \uparrow \land ~ (v_1 \geq v_2)) $ then the program is non-terminating. If $(\verb+s+_1 \uparrow \land ~ \verb+s+_2 \uparrow \land ~ (v_1 < v_2)) $ then the program is terminating.
\item If ($\verb+s+_1 \downarrow \land ~ \verb+s+_2 \downarrow \land ~ (|v_1| \leq |v_2|)) $ then the program is non-terminating. If $(\verb+s+_1 \downarrow \land ~ \verb+s+_2 \downarrow \land ~ (|v_1| > |v_2|)) $ then the program is terminating.
\end{enumerate}
\subsubsection{When both variables grow/decay exponentially of the form $R_{g}$.} \label{sec: Rg}
Let $\verb+s+_1$ and $\verb+s+_2$ be monotonic statements of the form $R_{g}$. Termination of a program of the form (\ref{cyclesWithGapConstraints}) can be then decided using the following rules.
\begin{enumerate}
\item If $(\verb+s+_1 \uparrow \land ~ \verb+s+_2 \uparrow \land ~ (u_1 \geq u_2)) $ then the program is non-terminating. If $(\verb+s+_1 \uparrow \land ~\verb+s+_2 \uparrow \land ~ (u_1 < u_2)) $ then the program is terminating.
\item If ($\verb+s+_1 \downarrow \land ~ \verb+s+_2 \downarrow \land ~ (|u_1| \leq |u_2|)) $ then the program is non-terminating. If $(\verb+s+_1 \downarrow \land ~ \verb+s+_2 \downarrow \land ~ (|u_1| > |u_2|)) $ then the program is terminating.
\end{enumerate}
\subsubsection{When one variable grows/decays linearly and the other exponentially.} \label{sec: RaANDRg}
Let $\verb+s+_1$ be a monotonic statement of the form $R_{a}$ and $\verb+s+_2$ be a monotonic statement of the form $R_g$ or $I$. Then termination can be decided using the following rules.
\begin{enumerate}
\item If $(\verb+s+_1 \uparrow \land ~ \verb+s+_2 \uparrow)$ then the program is terminating since for any exponential function and any linear function with positive growth, the exponential function will eventually outstrip the linear function.
\item If ($\verb+s+_1 \downarrow \land ~ \verb+s+_2 \downarrow ) $. This case requires a special decision procedure (see Algorithm \ref{alg:specialProcedureCase4}) since it is not obvious whether there will be an iteration at which the guard $(x_n - y_n \sim c)$ can be violated.
\end{enumerate}
\begin{algorithm}
\caption{Special decision procedure for case 2}
\label{alg:specialProcedureCase4}
\textbf{Input}: $(x_0, y_0, v_1, v_2, u, c, \sim)$ \\
\textbf{output}: \{\textit{terminating, non-terminating}\}\\
\textbf{int} $n := 1$; \\
\textbf{while} (\textit{true}) \\
\hspace*{10 pt}\{ \\
\hspace*{15 pt} $x_n = (x_0 + v_1 * n)$; \hspace*{5 pt} $y_n = u^{n} * y_0 + \sum_{n = 0}^{n-1} (u ^{n} * v_2)$; \\
\hspace*{15 pt} \textbf{if} ( ($\sim= ` > $' $\land$ $y_n \geq (x_n - c)$) $\lor$ ($\sim= ` \geq $' $\land$ $y_n > (x_n - c)$) ) \textbf{return} \textit{terminating}; \\
\hspace*{15 pt} \textbf{if} $(y_n < (x_n - c) \land x_n < 0 \land y_n <0)$ \textbf{return} \textit{non-terminating};\\
\hspace*{15 pt} $n:= n+1$; \\
\hspace*{10 pt} \}
\end{algorithm}
Note that when algorithm \ref{alg:specialProcedureCase4} terminates with `terminating' then the search has reached an iteration where the loop guard is violated. On the other hand, when the algorithm terminates with `non-terminating' then the search has reached an iteration where $(y_n < (x_n - c) \land x_n < 0 \land y_n <0)$. This condition is sufficient to guarantee non-termination of this form of loops since $x$ is decreasing linearly while $y$ is decreasing exponentially.
We now turn to discuss the case where $x$ grows/decays exponentially and $y$ grows/decays linearly. In this case termination can be decided as follows.
\begin{enumerate}
\item If $(\verb+s+_1 \downarrow \land ~ \verb+s+_2\downarrow)$ then the program is terminating since there will be an iteration where $x$ can be smaller than $y$. This is due to the assumption that $x$ is decreasing exponentially while $y$ is decreasing linearly.
\item If ($\verb+s+_1 \uparrow \land ~ \verb+s+_2 \uparrow ) $. This case requires a special decision procedure (similar to Algorithm \ref{alg:specialProcedureCase4} above) but it differs at the condition at which it returns `non-terminating' which will be of the form $(x_n > (y_n + c)) $. This is due to the observation that once the exponential function outstrips the linear function at some iteration it continues to outstrip it at all future iterations.
\end{enumerate}
\subsubsection{When both variables grow/decay exponentially.} \label{sec: RgANDI}
In this case a decision procedure similar to Algorithm \ref{alg:specialProcedureCase4} can be used to decide termination. The procedure differs from Algorithm \ref{alg:specialProcedureCase4} at the condition at which it terminates with `non-terminating'. That is, if both variables are moving up then the procedure terminates with `non-terminating' when the search reaches an iteration at which ($(x_n > y_n + c) \land u_1 \geq u_2$) since both $x$ and $y$ grow exponentially as the loop proceeds. On the other hand, if both variables are moving down then the condition at which the algorithm terminates with `non-terminating' will be of the form $(y_n < (x_n -c) \land x_n <0 \land y_n < 0 \land u_1 \leq u_2)$ since both variables decay exponentially as the loop proceeds.
\paragraph*{}
In Table \ref{table:classificationStoppingCond} we summarise the stopping condition at which a decision procedure of the form \ref{alg:specialProcedureCase4} returns `non-terminating' when the variables $x$ and $y$ move in the same direction but with different mathematical behaviour. Note that the procedures return `terminating' when the loop guard $(x - y \sim c)$, where $\sim \in \{>, \geq\}$, is violated but they differ at the stopping condition at which they return `non-terminating' since this depends on the characteristics of the recurrence update equations of $x$ and $y$ (i.e. whether they grow/decay linearly or exponentially). The +, -- signs used as a superscript of notations $R_a$, $R_g$, and $I$ to indicate whether the variable is moving up (+) or moving down (--).
\begin{table}
\centering
\small
\begin{tabular}{|c|c|}
\hline
Update statements & Stopping condition (non-termination) \\
\hline
$(1) ~ \verb+s+_1 = R_a^{-} \land \verb+s+_2 = R_g^{-}$ & \multirow{ 2}{*} {$(y_n < (x_n - c) \land x_n < 0 \land y_n <0)$} \\ (2) $\verb+s+_1 = R_a^{-} \land \verb+s+_2 = I^{-}$& \\
\hline
$(3) ~ \verb+s+_1 = R_g^{+} \land \verb+s+_2 = R_a^{+}$ & \multirow{ 2}{*} {$(x_n > (y_n + c)) $} \\ (4) $\verb+s+_1 = I^{+} \land \verb+s+_2 = R_a^{+}$ & \\
\hline
$(5) ~\verb+s+_1 = R_g^{+} \land \verb+s+_2 = I^{+}$ & \multirow{ 2}{*} {$( (x_n > y_n + c) \land u_1 \geq u_2)$} \\ (6) $\verb+s+_1 = I^{+} \land \verb+s+_2 = R_g^{+}$ & \\
\hline
$(7)~ \verb+s+_1 = R_g^{-} \land \verb+s+_2 = I^{-}$ & \multirow{ 2}{*} {$(y_n < (x_n -c) \land x_n <0 \land y_n < 0 \land u_1 \leq u_2)$} \\ (8) $\verb+s+_1 = I^{-} \land \verb+s+_2 = R_g^{-}$ & \\
\hline
\end{tabular}
\caption{Stopping condition at which the procedure returns non-terminating} \label{table:classificationStoppingCond}
\end{table}
\vspace*{-2em}
\section{Multi-path Loops with Diagonal-free Constraints}
Paths of multi-path loops can interleave in a non-trivial manner. Reasoning about termination of multi-path loops is therefore a challenging task. The class of multi-path loops that we consider has the following form
\begin{equation} \label{cyclesWithCond1}
\textbf{while} ~ (x \sim c) ~ \textbf{ do} ~ \{ \textbf{if} ~ (x \sim^{'} c_1) ~ \textbf{then} ~ x := \verb+f+_1(x); ~ \textbf{else } ~ x := \verb+f+_2(x); \}
\end{equation}
\paragraph*{•} where the statements $\verb+s+_1:x := \verb+f+_1(x);$ and $\verb+s+_2:x := \verb+f+_2(x);$ are monotonic statements, $\sim, \sim^{'} \in \{<, \leq, >, \geq \}$, and $c, c_1 \in \mathbb{Z}$. We refer to the assignment $x := \verb+f+_1(x)$ as a conditional assignment, as its execution depends on the truth value of the condition $(x \sim^{'} c_1)$. As we shall see in this section the complexity of termination analysis of a program of the form (\ref{cyclesWithCond1}) varies depending on the class of monotonicity of the statements $\verb+s+_1$ and $\verb+s+_2$ and whether the conditional branches of the program interleave between iterations. During the analysis of the different cases of a program of the form (\ref{cyclesWithCond1}) we use $\phi$ to refer to the loop guard $(x \sim c)$ and $\verb+B+$ to refer to the condition $(x \sim^{'} c_1)$. We write $\sim_{\phi}$ to refer to the relation operator used in the loop guard, $\sim_{\verb+B+}$ to refer to the relation operator used in the if-branch, and $\sim_{\neg \verb+B+}$ to refer to the relation operator used in the else-branch.
\begin{observation} \label{Obs1}
If the statements $\verb+s+_1$ and $\verb+s+_2$ in program (\ref{cyclesWithCond1}) have the same monotonicity behaviour (i.e. both are monotonically increasing or monotonically decreasing) then we can safely ignore \verb+B+ and use Lemma \ref{BoundeAboveBelow} to verify termination.
\end{observation}
\subsection{When One Statement is Monotone and the other is Constant} \label{sec:f1Monotonef2Constant}
In this section we analyse termination of a program of the form (\ref{cyclesWithCond1}) under the assumption that one of the update statements is strictly monotone and the other is constant. In this case there are several sub-cases to consider depending on the operators $\sim$, $\sim^{'}$ and the class of monotonicity of the statements $\verb+s+_1$ and $\verb+s+_2$.
\begin{enumerate}
\item When $\sim_{\phi} \in \{ >, \geq\}$ (i.e. $x$ is bounded from below in loop guard $\phi$) and $\sim_{\verb+B+} \in \{<, \leq\}$ (i.e. $x$ is bounded from above in $\verb+B+$) and $\verb+s+_1$ $\uparrow$ and $\verb+s+_2$ $\rightarrow_{b}$ (i.e. $\verb+f+_2(x) : = b$, where $b$ is a constant). From the syntactic structure of the given loop form and by observing the way the loop variable $x$ is changed w.r.t to the loop condition it is easy to see that for this form of loops there is only one condition of non-termination. This happens when $(b \sim_{\phi} c)$, where $\sim_{\phi}$ is the relational operator used in the guard $\phi$. Note that the if-branch can not contribute towards the termination of the loop since $\verb+s+_1$ is monotonically increasing and $x$ is bounded from below in $\phi$. However, from the given loop form we note that when the if-branch is triggered then the else-branch will be triggered at some later iteration. Hence, the formula of non-termination for this form of loops can be described as follows
\begin{equation} \label{caseOne}
NT = (x_0 \models \phi \land (b \sim_{\phi} c) )
\end{equation}
where $x_0$ denotes the initial value of $x$ and $x_0 \models \phi$ means that the guard $\phi$ is evaluated to \textit{true} when $x = x_0$. If formula NT is satisfiable then we say the loop is non-terminating. Note that formula (\ref{caseOne}) can be used also to verify termination of loops in which $\sim_{\phi} \in \{<, \leq\}$, $\sim_{\verb+B+} \in \{ >, \geq\}$, $\verb+s+_1$ $\downarrow$, and $\verb+s+_2$ $\rightarrow_{b}$ for the same reasoning given above.
\item When $\sim_{\phi} \in \{ >, \geq\}$ and $\sim_{\verb+B+} \in \{ <, \leq\}$ and $\verb+s+_1 \downarrow$ and $\verb+s+_2 \rightarrow_{b}$. For this form of loops there is only one case of non-termination. This case happens when the else-branch is triggered during the execution of the loop and that $(b \sim_{\phi} c)$ and $(b \sim_{\neg \verb+B+} c_1)$. Note that if the if-branch is triggered during the execution of the loop then the loop will eventually terminate since $x$ is bounded from below in $\phi$ and from above in $\verb+B+$ and $\verb+s+_1$ is monotonically decreasing.
\begin{equation} \label{caseTwo}
NT = (x_0 \models \phi \land x_0 \not\models \verb+B+ \land (b \sim_{\phi} c) \land (b \sim_{\neg \verb+B+} c_1) )
\end{equation}
Formula (\ref{caseTwo}) can be used also to verify termination of loops in which $\sim_{\phi} \in \{<, \leq\}$, $\sim_{\verb+B+} \in \{>, \geq \}$, $\verb+s+_1 \uparrow$, and $\verb+s+_2 \rightarrow_{b}$ for the same reasoning given above.
\item When $\sim_{\phi} \in \{ <, \leq\}$ and $\sim_{\verb+B+} \in \{ <, \leq\}$ and $\verb+s+_1 \uparrow$ and $\verb+s+_2 \rightarrow_{b}$.
Analysing termination of this form of loops is non-trivial since the conditional branches of the loop can interleave between iterations. However, before discussing the conditions of non-termination of this form of loops we need to observe the following. From the syntactic structure of the given loop form we note that when the loop is non-terminating and the if-branch is triggered then the else-branch will be triggered at some later iteration since $x$ is bounded from above in \verb+B+ and $\verb+s+_1$ is monotonically increasing. On the other hand, when the else-branch is triggered then the if-branch may or may not be triggered at future iterations depending on the value of the constant $b$. Hence, finding the conditions of non-termination of this form of loops requires some numerical analysis.
Since $x$ is bounded from above in $\verb+B+$ and $\verb+s+_1$ is monotonically increasing then we need to compute the smallest value of $x$ that falsifies the condition \verb+B+ when the if-branch is triggered with $x = d$, where $d \in \{x_0, b\}$. That value can be computed using some special numerical procedures depending on the class of monotonicity of the statement $\verb+s+_1$. That is, if $\verb+s+_1$ is $R_{a}$ (i.e. has the form $x:= x + v$) then one can use formula (\ref{maxequation}). On the other hand, if $\verb+s+_1$ is $R_{g}$ or $I$ then one needs to use Algorithm \ref{alg:specialProcedureCasePsiGAndI}, where the bound $c_1$ that appears in the algorithm is the bound that $x$ is compared to in the condition \verb+B+.
\begin{equation} \label{maxequation}
\psi_{a}(d) =
\begin{cases}
((c_1 + v) - ( (c_1 - d) ~ \% ~ v)) & \textrm{if $ \sim_{\textsc{B}} =`\leq$' } \\
( ( (c_1 - 1) + v) - ( (c_1 - 1) - d) ~ \% ~ v) )) & \textrm{if $ \sim_{\textsc{B}} =`<$' }
\end{cases}
\end{equation}
Let us explain the intuition behind formula (\ref{maxequation}). Note that at each iteration the if-branch is triggered the variable $x$ is incremented by $v$. Hence, the maximum value that $x$ can reach from the consecutive execution of
the if-branch is either $(c_1+ v)$ or $((c_1 - 1) + v)$ depending on $\sim_{\verb+B+}$. Therefore, if $(c_1 - d)$ is a multiple of $v$ then the smallest value of $x$ that falsifies \verb+B+ will be either $(c_1+ v)$ or $(c_1 - 1) + v)$. On the other hand, if $(c_1 - d)$ is not a multiple of $v$ then the remainder needs to be subtracted from the maximum value $(c_1+ v)$ or $((c_1 - 1) + v)$ depending on $\sim_{\verb+B+}$.
\begin{algorithm}
\caption{Special procedure $\psi_{g}, \psi_{I}$}
\label{alg:specialProcedureCasePsiGAndI}
\textbf{Input}: $(d, c_1, u, v, \sim_{\verb+B+})$ \\
\textbf{int} $n := 1$; $x_{n-1} := d$; \\
\textbf{while} (\textit{true}) \\
\hspace*{10 pt}\{ \\
\hspace*{20 pt} $x_n = (u * x_{n-1} + v)$; \hspace*{5 pt} $n++$;\\
\hspace*{20 pt} \textbf{if} ( ($\sim_{\verb+B+}= ` < $' $\land$ $x_n \geq c_1$) $\lor$ ($\sim_{\verb+B+}= ` \leq $' $\land$ $x_n > c_1$) ) \textbf{return} $x_n$; \\
\hspace*{10 pt} \}
\end{algorithm}
By analysing the conditional branches of the loop and their possible interleaving one can see that there are four conditions of non-terminating for this form of loops, which can be formalised as follows
\begin{equation} \label{caseFive}
NT = \begin{array}[t]{l}
( (x_0 \models \phi \land x_0 \not \models \verb+B+ \land b \sim_{\phi} c \land b \sim_{\neg \verb+B+} c_1) ~\lor \\ ~ (x_0 \models \phi \land x_0 \models \verb+B+ \land \psi(x_0) \sim_{\phi} c \land b \sim_{\phi} c \land b \sim_{\neg \verb+B+} c_1) ~\lor \\
~(x_0 \models \phi \land x_0 \models \verb+B+ \land \psi(x_0) \sim_{\phi} c \land b \sim_{\phi} c \land b \sim_{\verb+B+} c_1 \land \psi(b) \sim_{\phi} c) ~\lor \\
~ (x_0 \models \phi \land x_0 \not \models \verb+B+ \land b \sim_{\phi} c \land b \sim_{\verb+B+} c_1 \land \psi(b) \sim_{\phi} c) )
\end{array}
\end{equation}
where $\psi(x_0)$ returns the smallest value of $x$ at which the if-branch becomes disabled after being triggered using the value $x_0$, and $\psi(b)$ returns the smallest value of $x$ at which the if-branch becomes disabled after being triggered using the value $b$. Note that we write $\psi(x)$ in the formula which can be either $\psi_a$ or $\psi_g$ or $\psi_I$ depending on the class of monotonicity of the statement $\verb+s+_1$.
\item When $\sim_{\phi} \in \{ <, \leq\}$ and $\sim_{\verb+B+} \in \{ <, \leq\}$ and $\verb+s+_1 \downarrow$ and $\verb+s+_2 \rightarrow_{b}$. For this form of loops there are two cases of non-termination. The first case is when the if-branch is triggered during the execution of the loop. In this case the loop will not terminate since $x$ is bounded from above in both $\phi$ and $\verb+B+$ and $\verb+s+_1$ is monotonically decreasing. The second case is when the else-branch is triggered and that $(b \sim_{\phi} c)$. In this case the loop will not terminate regardless of which branch is triggered between iterations.
\begin{equation} \label{caseSix}
NT = ( (x_0 \models \phi \land x_0 \models \verb+B+) \lor (x_0 \models \phi \land x_0 \not \models \verb+B+ \land b \sim_{\phi} c) )
\end{equation}
Formula (\ref{caseSix}) can be used also to verify termination of loops in which $\sim_{\phi} \in \{ >, \geq \}$ and $\sim_{\verb+B+} \in \{ >, \geq \}$ and $\verb+s+_1 \uparrow$ and $\verb+s+_2 \rightarrow_{b}$.
\item When $\sim_{\phi} \in \{ >, \geq\}$ and $\sim_{\verb+B+} \in \{ >, \geq \}$ and $\verb+s+_1 \downarrow$ and $\verb+s+_2 \rightarrow_{b}$. Termination analysis of this form of loops is similar to case 3 above in the sense that deriving the conditions of non-termination requires performing some numerical analysis. The only difference here is the formula that is used to compute the smallest value of $x$ that falsifies the condition \verb+B+ when the if-branch is triggered at some prior iteration with $x =d$, where $d \in \{x_0, b\}$, since $\verb+s+_1$ in this case is monotonically decreasing.
This value can be computed using formula (\ref{minequation}) in case $\verb+s+_1$ is $R_{a}$ (i.e. has the form $x:= x + v$) or using a special procedure similar to Algorithm \ref{alg:specialProcedureCasePsiGAndI} in case $\verb+s+_1$ is $R_{g}$ or $I$.
\begin{equation} \label{minequation}
\psi^{'}_{a} (d) =
\begin{cases}
( (c_1 - v) + ( (d - c_1) ~ \% ~ v)) & \textrm{if $ \sim_{\textsc{B}} = `\geq$'} \\
( ((c_1 +1) - v) + ( (d - (c_1 + 1)) ~ \% ~ v))) & \textrm{if $ \sim_{\textsc{B}} =`>$'}
\end{cases}
\end{equation}
Similar to case 3 above there are four conditions of non-termination of this form of loops which can be formalized as given in formula (\ref{caseSeven}).
\begin{equation} \label{caseSeven}
NT = \begin{array}[t]{l}
( (x_0 \models \phi \land x_0 \not \models \verb+B+ \land b \sim_{\phi} c \land b \sim_{\neg \verb+B+} c_1) ~\lor \\ ~ (x_0 \models \phi \land x_0 \models \verb+B+ \land \psi^{'}(x_0) \sim c \land b \sim_{\phi} c \land b \sim_{\neg \verb+B+} c_1 ) ~\lor \\
~ (x_0 \models \phi \land x_0 \models \verb+B+ \land \psi^{'}(x_0) \sim_{\phi} c \land b \sim c \land b \sim_{\phi} c_1 \land \psi^{'}(b) \sim_{\phi} c) ~ \lor \\
~ (x_0 \models \phi \land x_0 \not \models \verb+B+ \land b \sim_{\phi} c \land b \sim_{\verb+B+} c_1 \land \psi^{'}(b) \sim_{\phi} c) )
\end{array}
\end{equation}
\end{enumerate}
\subsection{When Both Update Statements are Strictly Monotone} \label{sec:ConditioalBothMonotone}
This is the most challenging form of loops to consider since at some iteration of the loop the variable $x$ may be updated using the arbitrary monotone statement $\verb+s+_1$ while in some later iteration it may be updated using the arbitrary monotone statement $\verb+s+_2$. Hence, to analyse termination of this form of loops we need to consider several sub-cases depending on the class of monotonicity of the statements $\verb+s+_1$ and $\verb+s+_2$ and the operators $\sim$ and $\sim^{'}$.
\begin{enumerate}
\item When $\sim_{\phi} \in \{ >, \geq\}$ and $\sim_{\verb+B+} \in \{ >, \geq \}$ and $\verb+s+_1 \uparrow$ and $\verb+s+_2 \downarrow$. Surprisingly, this case is trivial since there is only one condition under which the loop can be non-terminating as described in formula (\ref{caseOneMonotone}).
\begin{equation} \label{caseOneMonotone}
NT = (x_0 \models \phi \land x_0 \models \verb+B+)
\end{equation}
That is, if the if-branch is triggered in the first iteration of the loop then the loop is non-terminating since $\verb+s+_1$ is monotonically increasing and $x$ is bounded from below in both $\phi$ and $\verb+B+$. Note that the else-branch cannot contribute towards the non-termination of the loop since $\verb+s+_2$ is monotonically decreasing and $x$ is bounded from below in $\phi$ and from above in $\neg \verb+B+$.
Formula (\ref{caseOneMonotone}) can be used also to verify termination of loops in which $\sim_{\phi} \in \{ <, \leq\}$, $\sim_{\verb+B+} \in \{ <, \leq \}$, $\verb+s+_1 \downarrow$, and $\verb+s+_2 \uparrow$ for the same reasoning given above.
\item When $\sim_{\phi} \in \{ <, \leq\}$ and $\sim_{\verb+B+} \in \{ <, \leq \}$ and $\verb+s+_1 \uparrow$ and $\verb+s+_2 \downarrow$. For this form of loops it is not possible to derive a concrete formula for verifying termination as we have done for the previous cases since in case of non-termination the two branches will activate each other in alternation and hence the loop variable will be updated using any of the two arbitrary statements. We therefore use a special procedure to analyse termination of this form of loops. The procedure (see Algorithm \ref{alg:specialProcedure4.3.2}) is guaranteed to return with a correct answer. The procedure uses the auxiliary formulas $\psi(x)$ and $\psi^{'}(x)$ to compute the precise value of $x$ between iterations.
The procedure maintains a list called PASSED to store the values of $x$ that are already examined. Note that if at some iteration of the loop the guard $\phi$ is violated then the loop is terminating. On the other hand, if the search reaches a fixed point (i.e. the same value of $x$ is encountered again during the search) then the loop is non-terminating. Reaching a fixed point in case of non-termination is guaranteed since the domain of $x$ at both branches is finite. Note also that for this form of loops the if-branch is the only branch that can contribute towards the termination of the loop as $x$ is bounded from above in $\phi$ and $\verb+s+_1$ is monotonically increasing. This is the reason why we check for termination only at the if-branch.
\begin{algorithm} [h!]
\caption{Special decision procedure for case 2 at Section \ref{sec:ConditioalBothMonotone}}
\label{alg:specialProcedure4.3.2}
\textbf{Input}: $(x_0, \phi, \verb+B+)$ \\
\textbf{output}: \{\textit{terminating, non-terminating}\}\\
PASSED := $\emptyset$; \textbf{int} VAL = $x_0$; \\
\textbf{while} (\textit{true}) \\
\hspace*{10 pt} \textbf{if} (VAL $\not \models \verb+B+$) \textbf{then} \textbf{if} ($\psi^{'}$(VAL) = $x_i$) for any $x_i \in $ PASSED \textbf{then} \\ \hspace*{20 pt} \textbf{return} \textit{`non-terminating'} \textbf{else} \{add VAL to PASSED; VAL:= $\psi{'}$(VAL)\} \\
\hspace*{10 pt} \textbf{if} (VAL $\models \verb+B+$) \textbf{then} \textbf{if} ($\psi$(VAL) = $x_i$) for any $x_i \in $ PASSED \textbf{then} \\ \hspace*{20 pt} \textbf{return} \textit{`non-terminating'} \textbf{else if} ($\psi$(VAL) $\not \models \phi$) \textbf{then} \\ \hspace*{20 pt} \textbf{return} \textit{`terminating'} \textbf{else} \{add VAL to PASSED; VAL:= $\psi$(VAL)\}
\end{algorithm}
\item When $\sim_{\phi} \in \{ <, \leq\}$ and $\sim_{\verb+B+} \in \{>, \geq\}$ and $\verb+s+_1 \uparrow$ and $\verb+s+_2 \downarrow$. For this form of loops there is only one case of non-termination. This case happens when the else-branch is triggered at the first iteration of the loop. Since $x$ is bounded from above in $\phi$ and from above in $\neg \verb+B+$ and $\verb+s+_2$ is monotonically decreasing then the loop will not terminate in this case. Note that the if-branch cannot contribute towards the non-termination of the loop since $x$ is bounded from below in \verb+B+ and from above in $\phi$ and $\verb+s+_1$ is monotonically increasing.
\begin{equation} \label{caseThreeMonotone}
NT = (x_0 \models \phi \land x_0 \not\models \verb+B+)
\end{equation}
Note that formula (\ref{caseThreeMonotone}) can be used also to verify termination of loops in which $\sim_{\phi} \in \{>, \geq\}$ and $\sim_{\verb+B+} \in \{ <, \leq\}$ and $\verb+s+_1 \downarrow$ and $\verb+s+_2 \uparrow$.
\item When $\sim_{\phi} \in \{>, \geq\}$ and $\sim_{\verb+B+} \in \{ <, \leq\}$ and $\verb+s+_1 \uparrow$ and $\verb+s+_2 \downarrow$. This case is similar to case 2 above since in case of non-termination the conditional branches will interleave between iterations in a non-trivial manner. The only difference here is that the if-branch in this case cannot contribute towards the termination of the loop while the else-branch can do so.
\begin{algorithm} [h!]
\caption{Special decision procedure for case 4 at Section \ref{sec:ConditioalBothMonotone}}
\label{alg:specialProcedure4.3.4}
\textbf{Input}: $(x_0, \phi, \verb+B+)$ \\
\textbf{output}: \{\textit{terminating, non-terminating}\}\\
PASSED := $\emptyset$; \textbf{int} VAL = $x_0$; \\
\textbf{while} (\textit{true}) \\
\hspace*{10 pt} \textbf{if} (VAL $ \models \verb+B+$) \textbf{then} \textbf{if} ($\psi$(VAL) = $x_i$) for any $x_i \in $ PASSED \textbf{then} \\ \hspace*{20 pt} \textbf{return} \textit{`non-terminating'} \textbf{else} \{add VAL to PASSED; VAL := $\psi$(VAL) \} \\
\hspace*{10 pt} \textbf{if} (VAL $ \not\models \verb+B+$) \textbf{then} \textbf{if} ($\psi{'}$(VAL) = $x_i$) for any $x_i \in $ PASSED \textbf{then} \\ \hspace*{20 pt} \textbf{return} \textit{`non-terminating'} \textbf{else if} ($\psi{'}$(VAL) $\not \models \phi$) \textbf{then} \\ \hspace*{20 pt} \textbf{return} \textit{`terminating'} \textbf{else} \{add VAL to PASSED; VAL := $\psi{'}$(VAL);\}
\end{algorithm}
\vspace*{-1em}
\end{enumerate}
In Table \ref{table:verification} we summarize the termination rules of all possible cases of multi-path loops with diagonal-free constraints of the form (\ref{cyclesWithCond1}), where $c$ represents the bound that the loop variable is compared to in $\phi$, and $c_1$ is the bound that the variable is compared to in the condition \verb+B+. Since the relational operator used in the guard $\phi$ and in the condition $\verb+B+$ can be either bounded from below $\{>, \geq\}$ or bounded from above $\{<, \leq\}$ and that the update statements $\verb+s+_1$ and $\verb+s+_2$ can be either $\uparrow$ or $\downarrow$ or $\rightarrow_{b}$, then we have a total of 36 cases to consider as shown in the table. We now discus some simple examples of loop programs to demonstrate how the termination rules described in Table \ref{table:verification} can be used to decide termination.
\begin{table} [h!]
\centering
\adjustbox{max width=\textwidth}{
\begin{tabular}{|c|c|}
\hline
Loop form & Termination rule \\
\hline
(1) $(\sim_{\phi} \in \{>, \geq\} \land \sim_{\verb+B+} \in \{<, \leq\} \land \verb+s+_1 \uparrow \land \verb+s+_2 \rightarrow_{b}) $ & \multirow{2}{*}{$(x_0 \models \phi \land (b \sim_{\phi} c) ) $} \\ (2) $(\sim_{\phi} \in \{<, \leq\} \land \sim_{\verb+B+} \in \{ >, \geq\} \land \verb+s+_1 \downarrow \land \verb+s+_2 \rightarrow_{b})$ &\\ (3) $(\sim_{\phi} \in \{>, \geq\} \land \sim_{\verb+B+} \in \{ >, \geq\} \land \verb+s+_1 \rightarrow_{b} \land \verb+s+_2 \uparrow)$ &\\ (4) $(\sim_{\phi} \in \{<, \leq\} \land \sim_{\verb+B+} \in \{ <, \leq\} \land \verb+s+_1 \rightarrow_{b} \land \verb+s+_2 \downarrow)$ & \\
\hline
(5) $(\sim_{\phi} \in \{ >, \geq\} \land \sim_{\verb+B+} \in \{ <, \leq\} \land \verb+s+_1 \downarrow \land \verb+s+_2 \rightarrow_{b})$ & \multirow{ 2}{*}{$ (x_0 \models \phi \land x_0 \not\models \textsc{B} \land (b \sim_{\phi} c) \land (b \sim_{\neg \textsc{B}} c_1) ) $} \\ (6) $(\sim_{\phi} \in \{<, \leq\} \land \sim_{\verb+B+} \in \{>, \geq \} \land \verb+s+_1 \uparrow \land \verb+s+_2 \rightarrow_{b})$ & \\
\hline
(7) $(\sim_{\phi} \in \{ >, \geq\} \land \sim_{\verb+B+} \in \{ >, \geq\} \land \verb+s+_1 \rightarrow_{b} \land \verb+s+_2 \downarrow )$ & \multirow{ 2}{*}{$ (x_0 \models \phi \land x_0 \models \textsc{B} \land (b \sim_{\phi} c) \land (b \sim_{\textsc{B}} c_1) ) $} \\ (8) $(\sim_{\phi} \in \{<, \leq\} \land \sim_{\verb+B+} \in \{<, \leq \} \land \verb+s+_1 \rightarrow_{b} \land \verb+s+_2 \uparrow )$ & \\
\hline
(9) $(\sim_{\phi} \in \{ >, \geq\} \land \sim_{\verb+B+} \in \{ <, \leq\} \land \verb+s+_1 \rightarrow_{b} \land \verb+s+_2 \uparrow)$ & \multirow{ 2}{*}{$ \begin{array}[t]{l} ( (x_0 \models \phi \land x_0 \not\models \textsc{B}) ~ \lor ~(x_0 \models \phi \land x_0 \models \textsc{B} \land b \sim_{\phi} c) ) \end{array} $} \\ (10) $(\sim_{\phi} \in \{ <, \leq\} \land \sim_{\verb+B+} \in \{ >, \geq\} \land \verb+s+_1 \rightarrow_{b} \land \verb+s+_2 \downarrow)$ & \\
\hline
(11) $(\sim_{\phi} \in \{ <, \leq\} \land \sim_{\verb+B+} \in \{ <, \leq\} \land \verb+s+_1 \downarrow \land \verb+s+_2 \rightarrow_{b})$
& \multirow{ 2}{*}{$ \begin{array}[t]{l} ( (x_0 \models \phi \land x_0 \models \textsc{B}) ~ \lor ~(x_0 \models \phi \land x_0 \not \models \textsc{B} \land b \sim_{\phi} c) ) \end{array}$} \\ (12) $(\sim_{\phi} \in \{ >, \geq \} \land \sim_{\verb+B+} \in \{ >, \geq \} \land \verb+s+_1 \uparrow \land \verb+s+_2 \rightarrow_{b})$ & \\
\hline
(13) $(\sim_{\phi} \in \{ <, \leq\} \land \sim_{\verb+B+} \in \{ <, \leq\} \land \verb+s+_1 \uparrow \land \verb+s+_2 \rightarrow_{b})$ & $\begin{array}[t]{l}
( (x_0 \models \phi \land x_0 \not \models \textsc{B} \land b \sim_{\phi} c \land b \sim_{\neg \textsc{B}} c_1) ~\lor \\ ~ (x_0 \models \phi \land x_0 \models \textsc{B} \land \psi(x_0) \sim_{\phi} c \land b \sim_{\phi} c \land b \sim_{\neg\textsc{B}} c_1) ~\lor \\
~(x_0 \models \phi \land x_0 \models \textsc{B} \land \psi(x_0) \sim c \land b \sim_{\phi} c \land b \sim_{\textsc{B}} c_1 \land \psi(b) \sim_{\phi} c) ~\lor \\
~ (x_0 \models \phi \land x_0 \not \models \textsc{B} \land b \sim_{\phi} c \land b \sim_{\textsc{B}} c_1 \land \psi(b) \sim_{\phi} c) )
\end{array}$ \\
\hline
(14) $ (\sim_{\phi} \in \{ <, \leq\} \land \sim_{\verb+B+} \in \{ >, \geq\} \land \verb+s+_1 \rightarrow_{b} \land \verb+s+_2 \downarrow)$ & $\begin{array}[t]{l}
( (x_0 \models \phi \land x_0 \models \textsc{B} \land b \sim_{\phi} c \land b \sim_{ \textsc{B}} c_1) ~\lor \\ ~ (x_0 \models \phi \land x_0 \not \models \textsc{B} \land \psi(x_0) \sim_{\phi} c \land b \sim_{\phi} c \land b \sim_{\textsc{B}} c_1) ~\lor \\
~(x_0 \models \phi \land x_0 \not \models \textsc{B} \land \psi(x_0) \sim c \land b \sim_{\phi} c \land b \sim_{\neg \textsc{B}} c_1 \land \psi(b) \sim_{\phi} c) ~\lor \\
~ (x_0 \models \phi \land x_0 \models \textsc{B} \land b \sim_{\phi} c \land b \sim_{\neg \textsc{B}} c_1 \land \psi(b) \sim_{\phi} c) )
\end{array}$ \\
\hline
(15) $ (\sim_{\phi} \in \{ >, \geq\} \land \sim_{\verb+B+} \in \{ >, \geq \} \land \verb+s+_1 \downarrow \land \verb+s+_2 \rightarrow_{b})$ & $\begin{array}[t]{l}
( (x_0 \models \phi \land x_0 \not \models \textsc{B} \land b \sim_{\phi} c \land b \sim_{\neg \textsc{B}} c_1) ~\lor \\ ~ (x_0 \models \phi \land x_0 \models \textsc{B} \land \psi^{'}(x_0) \sim_{\phi} c \land b \sim_{\phi} c \land b \sim_{\neg \textsc{B}} c_1 ) ~\lor \\
~ (x_0 \models \phi \land x_0 \models \textsc{B} \land \psi^{'}(x_0) \sim_{\phi} c \land b \sim_{\phi} c \land b \sim_{\phi} c_1 \land \psi^{'}(b) \sim_{\phi} c) \lor \\
~ (x_0 \models \phi \land x_0 \not \models \textsc{B} \land b \sim_{\phi} c \land b \sim_{\textsc{B}} c_1 \land \psi^{'}(b) \sim_{\phi} c) )
\end{array}$ \\
\hline
(16) $ (\sim_{\phi} \in \{ >, \geq\} \land \sim_{\verb+B+} \in \{<, \leq\} \land \verb+s+_1 \rightarrow_{b} \land \verb+s+_2 \downarrow)$ & $\begin{array}[t]{l}
( (x_0 \models \phi \land x_0 \models \textsc{B} \land b \sim_{\phi} c \land b \sim_{ \textsc{B}} c_1) ~\lor \\ ~ (x_0 \models \phi \land x_0 \not \models \textsc{B} \land \psi^{'}(x_0) \sim_{\phi} c \land b \sim_{\phi} c \land b \sim_{\textsc{B}} c_1) ~\lor \\
~(x_0 \models \phi \land x_0 \not \models \textsc{B} \land \psi^{'}(x_0) \sim c \land b \sim_{\phi} c \land b \sim_{\neg \textsc{B}} c_1 \land \psi^{'}(b) \sim_{\phi} c) ~\lor \\
~ (x_0 \models \phi \land x_0 \models \textsc{B} \land b \sim_{\phi} c \land b \sim_{\neg \textsc{B}} c_1 \land \psi^{'}(b) \sim_{\phi} c) )
\end{array}$ \\
\hline
(17) $(\sim_{\phi} \in \{ >, \geq\} \land \sim_{\verb+B+} \in \{ >, \geq \} \land \verb+s+_1 \uparrow \land \verb+s+_2 \downarrow)~~$ & \multirow{ 2}{*}{$(x_0 \models \phi \land x_0 \models \textsc{B}) $} \\ (18) $(\sim_{\phi} \in \{ <, \leq\} \land \sim_{\verb+B+} \in \{ <, \leq \} \land \verb+s+_1 \downarrow \land \verb+s+_2 \uparrow)~~$ & \\
\hline
(19) $(\sim_{\phi} \in \{ <, \leq\} \land \sim_{\verb+B+} \in \{>, \geq\} \land \verb+s+_1 \uparrow \land \verb+s+_2 \downarrow)~~$ & \multirow{ 2}{*} {$(x_0 \models \phi \land x_0 \not\models \textsc{B}$)} \\ (20) $(\sim_{\phi} \in \{>, \geq\} \land \sim_{\verb+B+} \in \{ <, \leq\} \land \verb+s+_1 \downarrow \land \verb+s+_2 \uparrow)~~$ & \\
\hline
(21) $(\sim_{\phi} \in \{ <, \leq\} \land \sim_{\verb+B+} \in \{ <, \leq \} \land \verb+s+_1 \uparrow \land \verb+s+_2 \downarrow)~~$
& \multirow{ 2}{*} {Special decision procedure (see Algorithm \ref{alg:specialProcedure4.3.2})} \\ (22) $(\sim_{\phi} \in \{ <, \leq\} \land \sim_{\verb+B+} \in \{>, \geq\} \land \verb+s+_1 \downarrow \land \verb+s+_2 \uparrow)~~$ & \\
\hline
(23) $(\sim_{\phi} \in \{>, \geq\} \land \sim_{\verb+B+} \in \{ <, \leq\} \land \verb+s+_1 \uparrow \land \verb+s+_2 \downarrow$) ~~
& \multirow{ 2}{*} {Special decision procedure (see Algorithm \ref{alg:specialProcedure4.3.4})} \\ (24) $(\sim_{\phi} \in \{ >, \geq\} \land \sim_{\verb+B+} \in \{ >, \geq \} \land \verb+s+_1 \downarrow \land \verb+s+_2$ $\uparrow)$ ~~ & \\
\hline
~~(25-28) $( \sim_{\phi}, \sim_{\verb+B+} \in \{<, \leq, >, \geq \} \land \verb+s+_1 \rightarrow_{b_1} \land~ \verb+s+_2 \rightarrow_{b_2})~$ & $\begin{array}[t]{l}
( (x_0 \models \verb+B+ \land b_1 \sim_{\phi} c \land b_1 \sim_{\textsc{B}} c_1) ~ \lor
(x_0 \not\models \verb+B+ \land b_2 \sim_{\phi} c \land b_2 \sim_{\neg \textsc{B}} c_1) ~ \lor \\
~ (b_1 \sim_{\phi} c \land b_2 \sim_{\phi} c)) \end{array}$ \\
\hline
(29-32) $(\sim_{\phi}, \sim_{\verb+B+} \in \{<, \leq, >, \geq \} \land \verb+s+_1 \uparrow \land~ \verb+s+_2 \uparrow) ~~~~~$ & See Observation \ref{Obs1} \\
(33-36) $(\sim_{\phi}, \sim_{\verb+B+} \in \{<, \leq, >, \geq \} \land \verb+s+_1 \downarrow \land~ \verb+s+_2 \downarrow) ~~~~~$ & \\
\hline
\end{tabular} }
\caption{The termination rules of all possible cases for loop programs of the form (\ref{cyclesWithCond1}) \label{table:verification}}
\end{table}
\begin{example}
Consider the program:
$$
\textbf{while} (x \geq 5) ~ \{ \textbf{if}~ (x \geq 10)~ \textbf{then}~ x:= x+1; \textbf{else} ~ x:= x-1; \}
$$
with $x_0 = 15$. Note that the syntactic structure of the given program matches with case 17 in Table \ref{table:verification} and hence we need to use the rule $(x_0 \models \phi \land x_0 \models \textsc{B}) $ to verify termination. As one can see the rule holds for the given program and hence the loop is non-terminating.
\end{example}
\begin{example}
Consider the program:
$$
\textbf{while} (x \leq 10) ~ \{ \textbf{if}~ (x \leq 5)~ \textbf{then}~ x:= x+2; \textbf{else} ~ x:= x-3; \}
$$
with $x_0 = 3$. For this program we will use Algorithm \ref{alg:specialProcedure4.3.2} to verify termination. Note that after five iterations (i.e. $x =3, 5, 7, 4, 6, 3$) the search will reach a fixed point with $x =3$ and hence the program is non-terminating.
\end{example}
\section{Experimental Results} \label{sec:experimentalResults}
In this section, we give a brief description about the implementation of the approach, the tools used in the comparisons, and the conclusions drawn from the evaluation results obtained from the selected termination tools.
\subsection{The implementation of the proposed approach}
As mentioned earlier, the paper takes a different strategy to deal with common case of loop programs (monotone programs): rather than using ranking function based approach to decide termination, we apply check static analysis types of pattern matching. Therefore, the termination problem for such class of programs is reduced to the satisfiability of a math-formula, i.e., a boolean combination of loop variables and linear mathematical relations over these variables. The implementation of the approach consists of the following three phases.
\begin{itemize}
\item First, a simple program slicing technique is used to prune all statements in the analysed program that are not related to termination, leaving only those which can affect termination of the program.
\item Second, a static analysis types of pattern matching based on the techniques proposed in \cite{Spezialetti1995} is used to determine the class of loop monotonic variables (i.e. whether the loop counter is updated according to a monotonically increasing expression, monotonically decreasing expression, or a constant expression).
\item Then by a case distinction on the shape and the direction of the monotonic loop counter updates, termination is decided for given initial values using the termination rules derived in this paper (see Table \ref{table:verification}).
\end{itemize}
\subsection{Brief description about the tools used in the comparison}
We compare our tool with two state-of-the-art tools: (1) AProVE \cite{AProveIJCAR14} which is a system for automated termination and complexity proofs of term rewrite systems (TRSs), and (2) 2LS \cite{cdksw2015} a CPROVER-based framework, which reduces program analysis problems expressed in second order logic such as invariant or ranking function inference to synthesis problems over templates. In the 5th Competition on Software Verification (SV-COMP'16), AProVE was the strongest tool for the termination category, while 2LS has been shown to be a powerful tool for proving termination for larger programs with thousands of lines of code \cite{cdksw2015}. We evaluate the tools using a large number of ANSI-C programs including:
\begin{itemize}
\item The SNU real-time benchmark suite that contains small C programs used for worst-case execution time analysis which are available at \path{www.cprover.org/goto-cc/examples/snu.html};
\item The Power-Stone benchmark suite as an example set of C programs for embedded systems \cite{Ku2007}.
\end{itemize}
During the evaluation we make the following manual simplifications: (1) we move the loops in the programs to the main function, (2) we simplify the complex statements and functions that do not affect the termination of the loop (e.g., make the function only contains one return statement), and (3) we add some variables declaration and initialization to ensure the correctness of the program. Our simplifications do not affect the outcome of termination of programs.
\subsection{The evaluation results}
All experiments were run on Ubuntu 14.10, 3.2 GHZ Intel Core 4 duo CPU with 8GB RAM. The results for SNU and Power-Stone are presented in Tables \ref{table:SNU} and \ref{table:PowerStone}. Each table reports the number of loops that were proven as terminating (T), non-terminating (NT), time-out (TO), or Maybe (M).
Note that we set the timeout value to 300s. In most cases, the tools decide within a few seconds.
As we observe in almost every program the proposed approach requires cheaper computational effort to verify termination. The verification time is reported in millisecond for our tool while it is reported in seconds for the other tools.
It is interesting to mention that for the analysed programs of the SNU benchmark suite, AProVE could handle only 23 programs while 2LS could handle 45 programs. On the other hand, for the Power-Stone benchmark suite, AProVE could handle only 30 programs while 2LS could handle 53 programs. More detailed information on the results and performance of the tools is available at \path{ https://sites.google.com/site/termresult}.
Our implementation outperforms both AProVE and 2ls in two aspects. First, it can handle a larger
class of monotone programs than both AProVE and 2ls. Second, for the programs that all tools can handle our tool can decide termination much faster. The key advantage of the proposed approach is that it uses a light-weight static analysis technique based on recurrence equations to reason about termination, while the other tools use synthesis approaches based on ranking techniques. Finding a ranking function of a loop program and proving its correctness is often expensive. The tools need to infer ranking functions and invariants on demand by iterating the loops.
The analysis shows that tools based on ranking techniques may fail to find a ranking function even for simple monotone loop programs as shown in Tables \ref{table:SNU} and \ref{table:PowerStone}.
During the analysis, we note also that the tool AProVE does not handle very well programs with complex statements (i.e. those which contain pointers, arrays, and other data structures) even that the update statements that affect termination are simple monotone statements. For such cases the tool generates ``Maybe'' as an output.
Finally, it is interesting to mention that the proposed static technique can be easily integrated into existing tools to handle common cases (monotone programs) in a much faster way.
\begin{table} [h!]
\tiny
\adjustbox{max width=\textwidth}{
\begin{minipage}{0.60 \textwidth}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
\textbf{Programs$\backslash$Tools} & \multicolumn{2}{c|}{Our tool} & \multicolumn{2}{c|}{AProVE} &\multicolumn{2}{c|}{2ls} \\
\hline
& result & time(\textbf{ms}) & result & time(s) & result & time(s) \\
\hline
adpcm\_loop12.c & T & 1.173 & T & 6.18 & T & 0.76 \\
\hline
fft1\_loop6.c & T & 1.186 & M & 1.12 & T & 0.40 \\
\hline
minver\_loop2.c & T & 1.601 & M & 1.10 & T & 0.17 \\
\hline
crc\_loop3.c & T & 1.765 & T & 54.27 & M & 0.42 \\
\hline
minver\_loop6.c & T & 2.209 & M & 1.10 & T & 0.23 \\
\hline
fft1\_loop1.c & T & 0.904 & M & 1.18 & T & 0.18 \\
\hline
fft1\_loop4.c & T & 0.915 & T & 2.41 & T & 0.18 \\
\hline
minver\_loop7.c & T & 1.795 & M & 1.16 & T & 0.20 \\
\hline
fft1\_loop5.c & T & 1.493 & M & 1.14 & TO & 300.06 \\
\hline
adpcm\_loop11.c & T & 0.955 & T & 2.69 & T & 0.48 \\
\hline
adpcm\_loop9.c & T & 1.306 & T & 2.19 & T & 0.17 \\
\hline
fft1\_loop2.c & T & 0.848 & M & 1.34 & T & 0.19 \\
\hline
fft1\_loop3.c & T & 1.121 & M & 1.07 & M & 0.77 \\
\hline
matmul\_loop1.c & T & 1.375 & M & 2.89 & T & 0.22 \\
\hline
crc\_loop1.c & T & 1.318 & T & 10.28 & T & 0.16 \\
\hline
adpcm\_loop5.c & T & 1.091 & T & 9.17 & T & 0.56 \\
\hline
minver\_loop1.c & T & 1.666 & M & 1.18 & T & 0.15 \\
\hline
fft1k\_loop4.c & T & 1.807 & M & 1.04 & M & 9.01 \\
\hline
adpcm\_loop17.c & T & 1.342 & M & 1.17 & T & 1.27 \\
\hline
minver\_loop9.c & T & 2.118 & M & 1.19 & T & 0.53 \\
\hline
lms\_loop6.c & T & 1.137 & M & 1.12 & M & 0.36 \\
\hline
adpcm\_loop16.c & T & 1.286 & M & 1.23 & T & 1.15 \\
\hline
ludcmp\_loop4.c & T & 8.527 & M & 1.32 & T & 0.41 \\
\hline
lms\_loop7.c & T & 1.093 & M & 1.24 & T & 0.18 \\
\hline
ludcmp\_loop5.c & T & 1.178 & M & 1.10 & TO & 300.06 \\
\hline
fft1k\_loop2.c & T & 0.848 & T & 1.98 & T & 0.18 \\
\hline
adpcm\_loop4.c & T & 0.978 & M & 2.01 & T & 0.12 \\
\hline
adpcm\_loop1.c & T & 1.003 & T & 2.07 & T & 0.11 \\
\hline
ludcmp\_loop1.c & T & 1.568 & M & 1.29 & TO & 300.02 \\
\hline
fir\_loop1.c & T & 0.928 & T & 1.97 & T & 0.13 \\
\hline
minver\_loop3.c & T & 2.326 & M & 1.10 & T & 0.43 \\
\hline
adpcm\_loop10.c & T & 1.630 & T & 2.80 & T & 0.14 \\
\hline
adpcm\_loop15.c & T & 1.364 & M & 1.23 & M & 3.44 \\
\hline
adpcm\_loop2.c & T & 1.209 & T & 1.98 & T & 0.14 \\
\hline
adpcm\_loop14.c & T & 1.229 & T & 22.24 & T & 0.24 \\
\hline
adpcm\_loop3.c & T & 1.241 & T & 8.87 & T & 0.63 \\
\hline
qsort-exam\_loop1.c & T & 1.882 & M & 1.13 & M & 0.28 \\
\hline
minver\_loop4.c & T & 2.138 & M & 1.14 & T & 0.23 \\
\hline
adpcm\_loop13.c & T & 1.032 & T & 2.51 & T & 0.16 \\
\hline
minver\_loop5.c & T & 1.169 & M & 2.27 & T & 0.39 \\
\hline
minver\_loop8.c & T & 1.781 & M & 1.11 & T & 0.27 \\
\hline
adpcm\_loop7.c & T & 1.133 & T & 5.29 & T & 0.13 \\
\hline
fir\_loop5.c & T & 1.195 & M & 1.06 & M & 0.82 \\
\hline
matmul\_loop2.c & T & 1.412 & M & 8.78 & T & 0.30 \\
\hline
fir\_loop2.c & T & 0.899 & T & 2.13 & T & 0.18 \\
\hline
lms\_loop4.c & T & 1.330 & M & 1.14 & TO & 300.22 \\
\hline
lms\_loop5.c & T & 1.146 & M & 1.15 & TO & 300.22 \\
\hline
adpcm\_loop8.c & T & 1.374 & T & 6.31 & T & 0.13 \\
\hline
fft1k\_loop1.c & T & 0.916 & T & 1.95 & T & 0.21 \\
\hline
jfdctint\_loop1.c & T & 0.981& T & 2.47 & T & 0.39 \\
\hline
adpcm\_loop6.c & T & 1.024 & M & 2.41 & T & 0.17 \\
\hline
fft1k\_loop3.c & T & 2.066 & M & 1.21 & TO & 300.02 \\
\hline
fir\_loop4.c & T & 1.355 & M & 1.15 & M & 1.08 \\
\hline
ludcmp\_loop2.c & T & 1.194 & M & 1.28 & T & 3.73 \\
\hline
fir\_loop3.c & T & 1.046 & M & 1.17 & TO & 300.22 \\
\hline
ludcmp\_loop3.c & T & 1.177 & M & 1.15 & TO & 300.04 \\
\hline
jfdctint\_loop2.c & T & 1.919 & TO & 300.06 & T & 0.83 \\
\hline
jfdctint\_loop3.c & T & 9.560 & TO & 300.05 & T & 0.74 \\
\hline
lms\_loop2.c & T & 0.898 & T & 2.14 & T & 0.17 \\
\hline
lms\_loop1.c & T & 1.074 & T & 1.98 & T & 0.13 \\
\hline
fibcall\_loop1.c & T & 0.995 & T & 44.49 & M & 6.24 \\
\hline
lms\_loop3.c & T & 1.261 & M & 1.10 & M & 0.85 \\
\hline
crc\_loop2.c & T & 1.612 & TO & 300.05 & T & 0.33 \\
\hline
Total & 63 & 99.102 & 23 & 1154.1 & 45 & 2442.33 \\
\hline
\end{tabular}
\captionsetup{font=tiny}
\caption{SNU real-time benchmark suite}
\label{table:SNU}
\end{minipage}
\begin{minipage}{0.55 \textwidth}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
\textbf{Programs$\backslash$Tools} & \multicolumn{2}{c|}{Our tool} & \multicolumn{2}{c|}{AProVE} &\multicolumn{2}{c|}{2ls} \\
\hline
& result & time(\textbf{ms}) & result & time(s) & result & time(s) \\
\hline
adpcm\_loop12.c & T & 2.494 & M & 13.64 & T & 0.29 \\
\hline
blit\_loop3.c & T & 1.244 & M & 2.01 & T & 0.14 \\
\hline
compress\_loop6.c & T & 1.312 & TO & 319.34 & T & 0.22 \\
\hline
huff\_loop1.c & T & 1.221 & T & 4.85 & T & 0.19 \\
\hline
compress\_loop7.c & T & 1.569 & M & 8.84 & T & 26.41 \\
\hline
compress\_loop8.c & T & 1.117 & M & 1.68 & T & 18.54 \\
\hline
pocsag\_loop2.c & T & 2.110 & M & 1.13 & T & 0.66 \\
\hline
adpcm\_loop11.c & T & 1.787 & TO & 306.37 & T & 0.93 \\
\hline
huff\_loop2.c & T & 1.500 & T & 16.92 & T & 1.46 \\
\hline
blit\_loop1.c & T & 1.188 & M & 1.25 & T & 0.49 \\
\hline
adpcm\_loop9.c & T & 1.695 & T & 2.57 & T & 0.48 \\
\hline
huff\_loop3.c & T & 1.375 & M & 4.36 & T & 6.30 \\
\hline
g3fax\_loop1.c & T & 1.108 & T & 6.53 & T & 1.50 \\
\hline
compress\_loop4.c & T & 1.120 & T & 2.89 & T & 22.48 \\
\hline
compress\_loop1.c & T & 1.149 & T & 2.38 & T & 1.04 \\
\hline
jpeg\_loop10.c & T & 1.056 & T & 2.47 & T & 0.18 \\
\hline
crc\_loop1.c & T & 1.352 & T & 9.84 & T & 0.17 \\
\hline
compress\_loop5.c & T & 1.101 & T & 2.02 & T & 12.30 \\
\hline
huff\_loop4.c & T & 1.718 & T & 4.51 & T & 2.77 \\
\hline
compress\_loop2.c & T & 1.034 & M & 2.93 & T & 0.58 \\
\hline
compress\_loop3.c & T & 1.045 & M & 6.07 & T & 0.88 \\
\hline
ucbqsort\_loop4.c & T & 0.960 & M & 1.43 & M & 0.13 \\
\hline
adpcm\_loop4.c & T & 1.938 & M & 2.18 & T & 0.13 \\
\hline
adpcm\_loop1.c & T & 1.622 & T & 10.14 & T & 0.25 \\
\hline
adpcm\_loop10.c & T & 1.873 & M & 1.14 & T & 2.15 \\
\hline
adpcm\_loop5.c & T & 1.593 & T & 5.50 & T & 0.15 \\
\hline
ucbqsort\_loop3.c & T & 0.981 & M & 1.24 & M & 0.15 \\
\hline
adpcm\_loop2.c & T & 1.480 & M & 1.82 & T & 0.18 \\
\hline
ucbqsort\_loop2.c & T & 1.056 & M & 1.39 & M & 0.13 \\
\hline
adpcm\_loop3.c & T & 1.468 & T & 22.39 & T & 0.29 \\
\hline
v42\_loop5.c & T & 1.515 & M & 1.06 & TO & 300.71 \\
\hline
ucbqsort\_loop1.c & T & 1.420 & T & 6.51 & T & 0.56 \\
\hline
v42\_loop3.c & T & 0.941 & T & 1.98 & T & 0.19 \\
\hline
jpeg\_loop3.c & T & 1.343 & M & 2.20 & T & 0.12 \\
\hline
pocsag\_loop1.c & T & 1.075 & T & 1.83 & T & 0.15 \\
\hline
pocsag\_loop4.c & T & 1.479 & T & 2.43 & T & 0.57 \\
\hline
jpeg\_loop2.c & T & 1.265 & T & 9.07 & T & 0.21 \\
\hline
jpeg\_loop7.c & T & 1.277 & M & 2.23 & T & 0.13 \\
\hline
pocsag\_loop5.c & T & 1.788 & T & 1.49 & T & 0.23 \\
\hline
jpeg\_loop6.c & T & 1.110 & T & 2.08 & T & 0.19 \\
\hline
v42\_loop2.c & T & 0.952 & T & 1.75 & T & 0.17 \\
\hline
fir\_loop2.c & T & 1.758 & M & 1.24 & M & 1.68 \\
\hline
adpcm\_loop7.c & T & 1.404 & T & 2.21 & T & 0.17 \\
\hline
jpeg\_loop1.c & T & 1.163 & T & 2.60 & T & 0.24 \\
\hline
adpcm\_loop8.c & T & 1.439 & T & 2.85 & T & 0.12 \\
\hline
v42\_loop4.c & T & 1.518 & M & 1.20 & TO & 300.35 \\
\hline
adpcm\_loop6.c & T & 1.518 & T & 4.96 & T & 0.15 \\
\hline
fir\_loop1.c & T & 1.148 & M & 1.24 & TO & 300.31 \\
\hline
pocsag\_loop3.c & T & 0.974 & T & 1.81 & T & 0.11 \\
\hline
jpeg\_loop11.c & T & 1.033 & T & 7.39 & T & 10.35 \\
\hline
fir\_loop3.c & T & 1.191 & M & 1.15 & M & 1.38 \\
\hline
blit\_loop2.c & T & 1.450 & M & 1.26 & T & 0.37 \\
\hline
jpeg\_loop8.c & T & 2.366 & T & 11.33 & T & 21.05 \\
\hline
huff\_loop5.c & T & 1.836 & M & 9.61 & T & 1.86 \\
\hline
pocsag\_loop6.c & T & 1.535 & M & 5.07 & T & 0.41 \\
\hline
v42\_loop6.c & T & 1.440 & M & 1.94 & M & 1.39 \\
\hline
pocsag\_loop8.c & T & 2.197 & M & 1.17 & T & 0.45 \\
\hline
v42\_loop1.c & T & 1.328 & T & 18.66 & T & 0.15 \\
\hline
jpeg\_loop5.c & T & 1.148 & T & 6.28 & T & 0.14 \\
\hline
jpeg\_loop4.c & T & 1.363 & M & 2.66 & T & 0.20 \\
\hline
jpeg\_loop9.c & T & 1.182 & T & 2.57 & T & 5.45 \\
\hline
pocsag\_loop7.c & T & 1.246 & M & 7.05 & T & 0.27 \\
\hline
crc\_loop2.c & T & 1.576 & T & 61.93 & M & 0.58 \\
\hline
Total & 63 & 88.244 & 30 & 958.64 & 53 & 1051.98 \\
\hline
\end{tabular}
\captionsetup{font=tiny}
\caption{PowerStone benchmark suite}
\label{table:PowerStone}
\end{minipage}
}
\end{table}
\section{Conclusion and Future Work}
We presented an efficient approach to prove termination of monotone programs, a class of loops
that is often encountered in computer programs. The approach uses a light-weight static analysis technique based on recurrence equations and takes advantage of properties of monotone functions.
The proposed approach leads to significant performance improvement against previous tools where they are applicable.
In future work, we aim to extend the tool to support a richer class of monotone programs, in particular we aim to study termination of multi-path programs that are more general than the ones considered in this paper, but for which termination is still decidable. Furthermore, since the termination problem is obviously related to the worst-case execution time problem (WCET): a loop program that does not terminate has an unbounded WCET, we aim also to extend the tool to reason about WCET of monotone loops while taking advantage of the termination rules derived in the paper.
\bibliographystyle{plain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,785 |
Welcome to our blog, the digital brainyard to fine tune "Digital Master," innovate leadership, and reimagine the future of IT.
The magic "I" of CIO sparks many imaginations: Chief information officer, chief infrastructure officer , Chief Integration Officer, chief International officer, Chief Inspiration Officer, Chief Innovation Officer, Chief Influence Office etc. The future of CIO is entrepreneur driven, situation oriented, value-added,she or he will take many paradoxical roles: both as business strategist and technology visionary,talent master and effective communicator,savvy business enabler and relentless cost cutter, and transform the business into "Digital Master"!
The future of CIO is digital strategist, global thought leader, and talent master: leading IT to enlighten the customers; enable business success via influence.
Seeing is Believing: From Big Data to Big Picture
9:33 PM Pearl Zhu 5 comments
Seeing is believing, one picture is worth a thousand words, all being said, Big Data need be painted into Big Picture, to capture big insight.
In order to create an effective visualization, business need to understand the meaning of data, after taking 5W+1H navigation, and using five senses to make sense of data, now, are you ready to move Big Data to the next level, from science to art, from common sense to unconventional wisdom, from black & white to full color spectrum?
And the right set of tools will make work more enjoyable, according to 2012 InformationWeek Business Intelligence, Analytics and Information Management Survey. Nearly half (45%) of the 414 respondents to the poll, which was conducted late last year, cited "ease-of-use challenges with complex software/less-technically savvy employees" as the second-biggest barrier to adopting BI/analytics products. That was just behind the biggest barrier, "data quality problems," cited by 46% or respondents.
From data visualization to advanced data visualization, it's not only about more advanced, easy-to-use visualized tools, but also about advanced data talent, they are artist, story teller, poet, anthropologist, historian, philosopher, and they happen to be data scientist too -the data analyst who lives in California or beyond, with open mindset in designing, building, and using interactive, fluid, dynamic, and even three-dimensional visualization.
Like artist, they master the visual design elements, such as line, form, shape, and color, with principles like balance and variety, to make a visualization more vivid and customized for trends and comparisons. A piece of fine art does have both deep meaning and elegant style.
Seeing is believing! Advanced Data visualization will provide better features such as:
A Single Screen Shot: one can fit tens of thousands (an order of-magnitude difference) of data points onto a single screen.
Visual Querying : relatively easily visualize and identify a pattern or click on a portion of graph or chart, then quickly zoom in to research the details;
Multi-dimensional linking & Chart: you can select one chart, via dynamic link, you can navigate into other charts . An extra axis in space, alongside an existing one or in a new direction (for a 3D chart), can also be useful for showing new variables
Personalization. The visualization tool is easy to use with personalized design, also addressing privacy and risk issues. You can give power users more in-depth view, and the view depend on one's position, job requirement and role-base access privileges.
Humanization: To get value from big data. Especially those "deep and broad data sets", you must add contextual information and place analytical capability in the hands of those who need it, taken from the world of bits and bytes and converted into real insight & foresight for real businesspeople.
It takes sense and sensitivity to transform Big Data into Big picture, it's not illusion, but illustration, to capture big insight from our big busyness world and small mankind world, always keep customers in mind, keep business purpose in mind, keep long term perspective in mind; but also open mind to be bold, creative and colorful.
Enterprise Weather Forecast: From Social Wind to Social Rain
Just like this Summer, people pray for rain worldwide, same as at many organizations, culture is a bit drought, and morale is a little low, after getting enough social technology insight, they look forward to have some social wind blow up, and social rain is coming soon:
1. From Social Organization to Social Economy
Social Computing grows with speed and scale, a just-published McKinsey study, "The social economy: Unlocking value and productivity through social technologies," indicated, about 1.5 billion number of social networking users globally; 70% proportion of companies using social technologies, 90% proportion of companies using social technologies that report some business benefit from them; 20-25% potential improvement possible in knowledge worker productivity. Overall, it is estimated that between $900 billion and $1.3trillion in value can be unlocked through the use of social technologies.
Social technologies enable social behaviors to take place online, endowing these interactions with scale, speed and disruptive economics of the internet;
Provide platforms for content creation, distribution, and consuming. Co-creation and transformation of personal and group communication into content.
The real power of social technology also comes from the innate appeal of interacting socially and pleasure and intellectual stimulation that people derive from sharing what they know, expressing opinions and learning what others know and think.
2. Social Rain Strengthen Social Architecture & Culture of Innovation
Social organization need solid foundation and well designing, social architecture will help such works. The Wikipedia definition "Social architecture" is the conscious design of an environment that encourages a desired range of social behaviors leading towards some goal or set of goals" applies to organizational culture, social psychology, and community psychology.
Encourage Innovation: Using boundary spanning to fill out structural holes: Social Architecture is the fundamental structure of how we connect. One of the barriers to creativity and innovation is structural holes (connections that need to exist to make further connections). Boundary spanners (those that walk between groups) close the structural holes so that innovation can pass along in an organization. Using compensation, positive reinforcement, and providing organizational incentives for these boundary spanners to exist the organization becomes more innovative. However, boundary spanners tend to control the lines that connect the groups. Too many can cause problems in the organization. So the structures need to be set to encourage these behaviors, but only to the extent that it has positive impact.
Culture Trumps leadership & strategy to be key business success factor: culture is about attitudes and behaviors, there isn't just one corporate culture. There's an overall corporate culture, lots of sub-cultures, and sub-sub-cultures within those: Seen in isolation, the interactions between various groups within an organization, provide little insight into the culture of the organization as a whole. Which of course means that have understand "what the culture of the organization is" via series of cultural analysis such as: social interaction analysis, sociograms, sociomapping and sociometrics;
Enforce Culture of Innovation at Agile Business: There're three different types of groups: Organization structure (formal hierarchy); Work structures (tend to be horizontal interactions); and Social structures (tend to be any which way). The reason for identifying and using these three sets of groupings is to discover the degree of 'cultural coherence' within an organization, which may help recognize those positive cultural or sub-cultural traits, then using social technologies to amplify and enforce them to cultivate seven habit of the culture of innovation, as culture is a self-reinforcing loop. It also reflects business's core values & beliefs', which is correlated with business strategy/execution and talent management for long term.
3. Social Rain Nurtures Big Data Oasis
Data from social media sites, videos, audio files, images, emails, text messages, mobile transactions, and more have put us on pace to see a total of 35 zettabytes of data by 2020, that being said, social rain is nurturing Big Data oasis:
Business Foresight: Big Data created by social technology can help forecast and monitor operations and distributions, and optimize demand-supply value chain via improving intra-or inter-organizational collaboration and communication.
Customer Insight: Big Data also derives customer insights, helps real-time, multi-channel customer interaction & communication, to improve customer care and gain insight about what customer need next before they know themselves.
Deliver ROI for Social Business: Big Data analytics is about getting a working feedback loop from the social world back to us, let business quickly processes the vast data streams, analyze them, and deliver ROI for social business.
From social business to social economy, from social wind to social rain, social echnology brings up the scale and speed of influence, to inspire enterprise creativity and amplify collective human capability.
Five Principles in Enterprise Principles
Principles are general rules and guidelines, intended to be enduring and seldom amended.
Principles are general rules and guidelines, intended to be enduring and seldom amended, that inform and support the way in which an organization sets about fulfilling its mission. The style of the principle should be short and recognizable. Its definition describes "what" the principle means in the language understood by stakeholders. The motivation describes "why" the principle is important to achieving the organizational mission. The implications describe "how" the principle changes behavior.
1. Principles in Overall Business
First, principles are statements of belief that reflect the values, culture and real-world concerns of the organization. They normally have a longer shelf life than objectives, strategies, etc. Principles are certainly there to guide the organization, not just for the professional, they are not the same as ethics; but also for decision making, governance., etc.
Principle - a general guideline that requires judgment and informs decisions
Policy – clear governable rules. Not following these kills a project (or worse).
Standard – specific requirements that projects/artifacts/roadmaps shall meet.
Procedure – standardized activities and deliverables to reduce risk and minimize errors.
Guideline – best practices and reference models that we collectively agree will improve delivery, quality, and reduce cost.
2. The principle in Decision Making
Enterprise principles provide a basis for decision-making throughout an enterprise and inform how the organization sets about fulfilling its mission. Principles are those core decisions values (not value as in benefit, but values as in beliefs) that shape behavior and define culture.
Principles allow many people to individually make their own decisions to run in the same direction to meet the same objectives in a rapid manner. Not everyone will follow. But many will. As principles provide a guideline of harmonizing decision-making across a distributed organization. In particular, they are a key element in a successful architecture governance strategy.
3. The principle in Talent Management
Principles are used to guide professionals along with ethics and values. Normally the common bond between departments, business units, divisions, and branches are strategic goals and objectives. Principles are also used to help people identify choices and make appropriate decisions.
Cultural values shape behaviors and principles help to articulate these values. Principles power individual and group dynamics, as it defines expected behavior
4. The principle in Enterprise Architecture
Principles can be used to reduce the set of options that a solution architect may choose from, and may be used to guide teams to address key challenges that plague an organization and which are often overlooked.
They can drive behavior or architectural decision, architecture is largely about coordinating action across heterogeneous communities. Principles help these communities agree on what they will do in concert and equally important, what they won't do.
5. The Principle in Governance
Governance: Don't step out of line, and the line is drawn sharply. :-(
Principles: Please step into line, and the line is drawn with broader strokes. :-)
The standards can change without changing the principle. Principles underpin the governance, and governance follows principles. Principles provide a more robust foundation that makes it possible to straightforwardly derive solution-level governance from enterprise-level governance.
There is often a difference between what organizations say and what organizations do, corporate governance has a responsibility to set and develop enterprise culture. So, it will certainly articulate the highest level of values/principles.
The principle is philosophy, based on your business value and strategy, 3P: Principle, Purpose, and Progress are inter-related with each other, as the principle is a positive guideline, helps the business make progress and fulfill the purpose.
"Purpose and principle clearly understood and articulated, and commonly shared, are the genetic code of any healthy organization. To the degree that you hold purpose and principles in common among you, you can dispense with command and control. People will know how to behave in accordance with them, and they'll do it in thousands of unimaginable, creative ways. The organization will become a vital, living set of beliefs."
Dee Hock, Founder of VISA, quoted by Alan Hirsch in The Forgotten Ways
Three Inspiring Quotes to learn about Neil Armstrong's Legacy
Neil Armstrong, the first man landed on the Moon about 43 years ago, passed away yesterday, what can we learn from his legacy? Here are three inspiring quotes from him:
1. "That's one small step for [a] man, one giant leap for mankind." --Neil Armstrong
When he set foot on the moon, he made a giant leap for all human kind on the earth and climaxed a monumental achievement in human history.
Such "One giant leap for mankind" reminds one generation to the other, human can make impossible possible, the spirit of life is to explore unknown, the big earth is a only small blue dot in universe, one need be confident and humbled at the same time;
Armstrong's footprint on moon represented progresses made by human spirit, the power of imagination and wisdom from above.
"I think we're going to the moon because it's in the nature of the human being to face challenges. It's by the nature of his deep inner soul... we're required to do these things just as salmon swim upstream." --Neil Armstrong
What are the natures of human being? The curiosity--the raw intelligence to dig through wonders; the creativity: the innate ability to create noble ideas; the intelligence: understand and master the discipline to overcome obstacles and make improvement; the humanism: the nature of deep inner spirit to pursuit of liberty, equality, and happiness.
Going to the Moon was such a dream work, to fulfill mankind's imagination, with technology becomes more advanced today, going to Mars, pioneered by robots: Spirit, Opportunity and Curiosity, continue to carry on such space mission, to discover universe, and touch human's deep heart.
"Mystery creates wonder and wonder is the basis of man's desire to understand." -- Neil Armstrong
Nature is full of mystery, it's just a tip of iceberg for what human know, compared to unknown. One need admire nature first. When human spirit is harmonizing with nature wonder, human kind may debunk one mystery by the other.
Such wonders take wisdom, wisdom speaks of nature, wisdom is multi-dimensional pursuit; and wisdom is nature power.
May Neil Armstrong's legacy inspire the new chapter of space adventures.
15 Classic EA Elevator Pitches in 15 Words
1. EA is to deliver business vision- "You can't change what you can't see"
2. EA influences the HOW by asking the WHY.
3. EA helps to optimize all aspects of the enterprise to increase profitability.
4. EA increases company profitably by better optimizing resources
5. EA works on Decision support for business capability improvement & investment decisions.
6. EA is a continuous improvement exercise that "promises" to bring some value - eventually
7. EA communicates the CEO vision to the entire organization.
8. EA is 90% WHY and 10% HOW
9. EA is coherent, coordinate capacity to develop capability
10. EA is an actionable, risk-reducing method for modeling organization change by communicating impact
11. EA is a bridge to connect & encompasses business transformation from A to B
12. EA: WHY" = Justifies "HOW" initiatives.
13. EA should give the business end-to-end visibility.
14.EA arranges enterprise muscles, bones, nerves and brain for cheetah-like agility
15. If movie is a condensed view of life, EA is a condensed view of business
Bonus Reminding:
EA IS NOT ALL ABOUT IT!
EA IS ALL ABOUT TRANSFORMATION
TRANSFORMATION IS NOT ALL ABOUT IT
EA is a business best practice on "Simplicity is optimum of sophistication"
A Tale of Two Processes
BPM becomes more critical than ever in most of organizations today, some call it as technology's third wave, some may think it takes fifth discipline, because BPM underpins business's capability, and capability will decide business's strategy and affect business execution.
There are also different process terms coined out: lean process, or intelligent process, here, we brainstorm a tale of two processes: robust process and dark process.
1. Robust Process
Robust process means the higher level of process effectiveness and efficiency. It goes beyond process automation, or even process improvement, it also means process optimization and process maturity.
The 20 characteristics of robust process:
- Availability
- Accountability
-Clarity
-Collaboration
-Flexibility
-Durability
- Reliability
- Maintainability
- Usability
- Repeat-ability
- Detect-ability
-Holism
- Data and Process Integrity
-Consistent high-level performance
- Self-recovery & Self-repair
- Anticipated vs unanticipated
- Scalability
--Transparency
Robust process also means more broader concept:
(1) A set of connected things or parts forming a complex whole,
(2) A set of things working together as parts of a mechanism or an interconnecting network
Robust Process takes more than a single 'process owner', but everyone who has a vested interest, which usually means the whole organization and not some silo or functional entity either.
Robust process may take out of box thinking, one may need step outside the process domain to think about robustness.
The robust process means there's risk management well embedded into process, to make process and business as a whole more resilient.
The robustness of process also means: there're robustness of loyal users, usually enable innovation, empower employees, and deliver measurable business result.
2. Dark Process
Some may call dark process as "unofficial process", which means that these are not identified, recognized, sanctioned or supported. We know they exist, but they are not "visible to management".
Some also observe: creative people and innovative organizations will be empowered to solve ever changing problems around them ... and those believing in the fiction of uniformity, will call that work "dark processes".
That being said, It doesn't make dark process right or wrong. they are problems, also opportunities, and probably bigger than we think. Most of what we do in a social setting & work settings are not explicitly known. Even the people who perform as part of a dark process don't necessarily know why they are doing so. Like riding a bike, the exact movements necessary to keep your balance
It is perhaps the next good practice. Instead of reducing these processes, business should expose and understand why they exist in the first place. If they exist because so called 'best practice' or innovative initiative, then removing them erodes business success. Perhaps Dark Processes are the cool things we can find, and rebels are responsible for their existence, they are the processes that are not designed in the ivory process tower
What is called dark processes is simply what keeps a company running against its organizational restraints. Process reflects more the increasing power of process technology to support processes, and the desire to reach beyond the old fictions of what an organization does, and attempt to fill in all the details
Still, like "shadow IT" or architecture debt, there's opportunity and risk, the effort can be put to shine some light on these dark processes, if it's process innovation, the governance may help amplify and share the best practice, if it causes security or compliance issues, it need be eliminated.
Either robust process or dark process, today's BPM need touch enterprise's body and heart, make business more agile and flexible than ever.
Middle Seat Pondering: Aviation's Three Progresses & Three Dilemmas
Airline may not be the industry with most of news, surely it's an industry full of paradox: there are both excitement and frustration; regulation & chaos; the higher operational cost & razor thin profit, the golden old days & lost decade; the higher into the sky and lower as underdog, both as economy's barometer and milk cow for federal tax; it's a technology business in the cloud, and the retailers with wings; though, the industry has been running for more than half century, it still takes energy, and inspiration to find its mojo.
In last couple of years, Airline do make some modest profit and recover back to the right track, most importantly, the industry continue to make impressive progress in a few key areas matter for customers, matter for nations and matter for economy:
1. Significant Operational Improvement
According to the Department of Transportation (DOT) Air Travel Consumer Report released recently, 80.7 percent of flights arrived within 15 minutes of scheduled arrival time in June 2012 – a nearly 4 percentage point improvement from the same month last year. The industry has posted year-over-year gains in each of the past nine months. Also 99.67 percent of all U.S. airline passengers had their bags properly delivered, an all-time record for any June since the government began keeping records in 1988; the previous record was set in June 2011. The May baggage-handling performance represented the 13th consecutive month of year-over-year improvement. The two areas of improvement are related: When flights are late, bags often miss their connection. If the current pace continues, the airlines will beat their best full-year performance, recorded in 1991, when nearly 83 percent of flights arrived on time. Airline also set the highest safety record in aviation history recently.
Why do these operational improvements so matter for airlines? When flights are on time, it isn't just good for passengers – it also helps the airlines' bottom lines; statistically, it costs an average of $75 a minute to operate a plane. Last year, domestic delays cost airlines an estimated $5.2 billion. U.S. airlines made a combined $577 million in profit last year. Moreover, it cost industry 74million/year due to bad experiences from delays, cancellations and poor communication of changes; 58% customers' bad experiences are caused by similar reasons, and 70% of delays and cancellations are due to factors within the control of airline
"Our member airlines are delivering levels of customer service that no other industry, given its complexity, matches and are working to make air travel even more efficient for passengers and shippers," said A4A President and CEO Nicholas E. Calio. "Thanks to ongoing operational improvements throughout the system, airlines are delivering a strong on-time performance."
2. Make Some Profit
The last decade is the lost decade for Airlines, due to economy tsunami, human calamity, nature disaster and flying fuel cost., etc, this is the industry faces more uncertainty, competition and complexity than any other industry, for years U.S. airlines have operated under a tax, regulatory and infrastructure environment that has made it increasingly difficult to be sustainably profitable and compete globally.
Airline took innovative approach to shape up the ancillary revenue model, go beyond the one size fitting all-take anyone from anywhere to everywhere, the change in model last two years enabled airlines to achieve razor-thin profits. For all of 2011, U.S. airlines earned less than $600 million or 81 cents per enplaned passenger. When the airlines are able to be sustainably profitable, everybody wins. A profitable airline industry can support more jobs, enable airlines to reinvest in their product with new planes and provide greater choices for customers, it enables the benevolent business life cycle for transportation and tourism industry overall.
Furthermore, Airline is barometer of national economy, an unprofitable industry will be forced to cuts routes and flights, leading to fewer consumer choices, frustration and fewer jobs, become the burden for community & society, and directly or indirectly affect customers' happiness index, or business's optimism indicator.
3. Invest in Future
NestGen: Besides grasping current opportunity to run Airline as more healthy business, Airline also ally to advocate & invest NexGen air traffic system, According to the Federal Aviation Administration, NextGen promises to make air travel more convenient and dependable while flights remain safe, secure and hassle-free. Delays are estimated to be reduced by 38 percent by 2020, providing approximately $24 billion in cumulative benefits while saving 1.4 billion gallons of fuel and related emissions.
BioFuel: fuel becomes key factor to make and break an Airline these days. Forward-looking, global leading Airlines also pioneer to experiment on biofuel, it takes cross-industrial collaboration and global collective value chain on shared quest to advance sustainable biofuels. Airlines also promises to look at advancing biofuels that will support sustainability standards, collaborate as part of the group with top organizations to create biofuels certification criteria, and advance making aviation biofuels more attractive in the market. It will significantly benefit industry if the solutions can be found to make alternative fuel available at commercial scale and secure a sustainable future for aviation, it's also one of many recent initiatives it has engaged in to promote more environmentally friendly air travel.
Regardless such impressive progresses made by Airlines, it still faces more dilemmas to achieve true operational excellence, customer satisfaction and high-performance result.
Below are some dilemmas facing Aviation:
1. From "Leg Room" Pitch to Elevator Pitch
Airline has its own unique pitch which is widely accepted as the standard. Airlines front-to-rear space is measured by "pitch," defined as the distance between any given point on a seat to the identical point on the seat in the next row forward or to the rear. Airline can adjust pitch in one-inch increments, regardless of airplane model, so the legroom you get is strictly up to each individual airline . Pitch is a totally accurate way to measure how much front-to-rear space you have, for your legs and at reading-working level.
However, the dilemma is: Airline should both be good at leg room pitch in the plane and elevator pitch in board room, not only should Airlines be masters at changing cattle into sardines, but also they need be the change agent to deeply discover the business purpose, industry mission and service value, Airline is not only in the transportation business to send passenger from A to B, but also in the information business to understand the whole business picture and economic dynamic.
2. Delight Customer & Make Profit at same Time
That-FEE—keeps business survive, even with chance to thrive, it has also repeatedly top the list of passenger complaints, as the industry still suffers from low customer satisfaction,
Therefore, aviation faces another dilemma: how to delight customers and make profit at the same time?
Optimize Overall Customer Life Cycle Experience: Services that consumers pay for should be better than services they get for free. Via the progresses made by Airline we discussion earlier, It's consistent with consumer result: "Ever since baggage fees were introduced, baggage service has improved considerably," the report said. "By charging fees, once neglected baggage service departments have become star revenue performers for airlines" that generates millions in revenue.", on the other hand: baggage service may have improved, but the boarding process has not, as everyone now tries to carry on their bags and jams the boarding area to get on early enough to get room for them, airline may just need continue to improve and optimize business processes, to make customers feel the service worthy of fees. . Don't damage your brand by nickel-and-diming, focus on overall experience.
Enhance Customer Loyalty: You must first know who your customers are — not those who pay, but those who get others to pay. Then you must instill loyalty in these people, which is a tricky business when you have just destroyed your brand with a code-shared flight: Book on you, fly on them; Be generous with the little thing, pay attention to details which matter, be proactive to create upsides from negative; be creative to enchant customer; be sensitive about social influence and be open for customers' opinions and feedback.
Make better choice with Reasonable Cost: The report, "Shocking News: A la Carte Shopping is Good for Consumers," calls add-on fees "the ultimate compliment for the consumer" because they give passengers the right to choose how they want to fly; and provide freedom of choices for customers who are able to pay for the services they value most.
Educate Travelers: The truth of the matter, air travel is the most efficient, safest and most affordable that it's ever been, to gain customers heart & pocket, Airline also need continue to educate travelers either via real life experience or social influence, to amplify good effort and behavior, and cultivate more advocates or travel influencers to inspire Aviation's growth, this is not just a legacy industry, it's an exciting travel partner to lift up human's body and spirit.
3. NexGen Mindset, Culture, Process with NextGen Technology
The Airlines need continue their journey in operational excellence by taking advantage of better technology: Airlines are flying newer planes with fewer maintenance problems. New tools track the boarding of passengers and loading of baggage onto individual flights, make more realistic schedules, the analytics tools to make fly smart, and social tools to engage customers and employees.
The dilemma here is: Airline can not just sit to wait for the NextGen technology ready, they need well prepare the convergence of nextGen mindset, culture, process and nextGen technology.
Airline should cultivate the open mindset, the culture of innovation, the fresh talent pipeline, and more optimized business processes to differentiate competitive uniqueness; Invest in tomorrow, and focus on today, well balance the long term perspective with short term win, continue to modernize legacy infrastructure, realize higher levels of satisfaction & loyalty, and deliver high performance result.
Five Senses to Make Sense of Big Data
Big Data will sharpen business's sense and sensitivity; and the five senses can also help make sense of Big Data.
Big Data opens up a new chapter for predictive analytics, however, Big Data is so new, a little bit messy, and the tools are also at developing stage to present the complete picture customers need. There seems to be some uncertainty about the value proposition, the ROI of big data, and about the tools that would let people take advantage of it.
So the company should do some further preparation & experiementing before jumping in the new Big Data technologies such as: Hadoop, MapReduce, NoSQL, and NewSQL. In order to prepare for the Big Data journey, besides 5W+1H navigation roadmap brainstormed earlier, we may also take advantage of Five Big Senses to make sense of Big Data. Five senses are human's natural capabilities to adapt to living environment, connect to nature, and experience the life, Five senses may also bring some new perspectives & imagination in Big Data, find new angles to manage it and new lenses to look at it.
1. Smell Data
Big Data like running river, continues to grow, merge into data Sea, with volume, velocity and variety. Where is data coming from? Operation data such as financial data, logistic data and HR data come from organizational supply chain, customer data from CRM/marketing, and big data from social/mobile/cloud/RFID, the deeper the data sea, the more hidden treasure is undiscovered, and more danger when navigate it.
If Big Data is like big sea, then it may just smell like ocean, one time it is fresh, the other time, it smells salty, can you smell the big fish--the distinctive opportunities such as revenue growth or cost optimization or the big threatening risks as shark approaching, or do you smell the sea grass or coral , the delightful chances to serve customers better,
Data is more like water, fresher is better, but if too little or too shallow, there's no fish in it, being able to process and analyze your data as soon as possible is critical to gain competitive business advantage, however, the effective data management including data collection, data storage, data cleansing and data quality., are all necessary steps for treasure hunt.
2. Listen to Data:
Big Data may also like a piece of music palyed remotely, inundated with many voices and noises, it takes effort and focus to capture & amplify it.
Big Data such as customers' feedback, and employee's opinions, one voice maybe a noise, but collective data is chorus, and statistic analytics such as sentiment analysis (Discover the positive and negative opinions about a product or brand), gap analysis (helps companies compare actual performance with potential performance) will directly drive such as pricing strategy, customer insight, supply chain optimization and strategic workforce planning.
Big Data can make contribution to pricing strategy. Pricing is one of the most powerful levers for improving profitability. Clear feedback loops so pricing teams can assess effectiveness and adjust as needed. Research shows that price management initiatives can increase a company's margins by 2 to 7 percent in 12 months—yielding an ROI between 200 and 350 percent.
By listening Big Data, business can answer fundamental business questions—such as "Who is my most profitable customer?" and "What is my most profitable product or region?"
3. Feel Data
Feeling is through heart, not always from mind, feeling the pulse of business heartbeat means deeply customers' participation and employees' engagement.
Feeing the data to diagnose the business illness at the key arena via pondering the right questions:
What's the management's decision point in key strategic issues?
What's the touch point to engage employees and improve productivity
What's customers' pain point and how to optimize customer life cycle management
What's the leverage point when bridging strategy and execution
What's the tipping point to inspire the culture of innovation & change management
What's the inflection point to take advantage of the new process and technology
The first step in making the most of your analytic DNA is to assess your current capabilities. Feel the data is to diagnose and determine the company's current maturity and where the gap is, it also helps executives more clearly understand both the internal and external factors affecting profitability at a granular level and strategic level.
4. See Through Data
Almost all organizations are aware of the potential of Big Data & Predictive Analysis, but very few have defined and articulated an enterprise vision and strategy for using it.
When we look at the Big Data Sea, what do we see, how to perceive it?
Do we see the data ocean like blue diamond under the sun, or the gray limestone through the shadow? Do we see the ebbs and flows, beauty of sea life, or the danger of whirling tides? Do we capture the color theme, the myth of pattern and the symbol of life in Big Data sea.
We should look for those enchanting pictures of data, also the missing pieces of data, Big Data can envision the mega-trends of business and its ecosystem, data insight and foresight provide the scientific scenario analytics via asking what are the trends, what is going to happen, and what are the best could be happened., etc.
See & Perceive Data: It's all about business perception via better visualized tool...to perceive the future of business Such big data insight will help leaders use a multi-faceted approach to business, integrating strategy, execution, governance, analytics, technology, and compliance. All are essential for capturing the full picture of high performance business.
5. Taste Data
Crunching data, not for swallowing, which may cause indigestion; small taste first will help find sweet spot, or learning some bitter lessons and hot, spicy trends.
· Tasting Data is like to have salad, need add some dressing, messy but creamy, made of the organic fruit and vegetables, have it to keep enterprise body fit;
· Tasting Data is like to eat ice cream, to cool down irrational decisions or energize your business mood, it should be a delightful experience.
· Tasting Data is like to try spicy food, stimulate business's appetite, keep employees' morale on;
· Tasting Data is like to drink juice, the juice is made of fresh fruit, and insight and wisdom is extracted from data, essential matters;
· Tasting Data is also like to have a cup of coffee or tea, bitter, but energize you thinking….
Using five senses to make sense of Big Data, Big Data will sharpen business's sense and sensitivity; to capture the full picture of future of business, so organization can well understand the challenges and better evaluate Big Data Life Cycle Management solutions, such as how to deploy it, secure it, govern it, persist it, make sense of it, to achieve the expected business results and goals.
Seven Cultural Habits to Harness Effective Business Innovation
"We must look at the lens through we see the world, as well as the world we see, and that the lens itself shapes how we interpret the world." ― Stephen R. Covey
From an innovation report released by Booz earlier this year, culture is key to innovation, as they surveyed almost 600 innovation leaders in companies around the world, large and small, in every major industry sector, Culture matters, enormously, Studies have shown again and again that there may be no more critical source of business success or failure than a company's culture --it trumps strategy and leadership. Companies whose strategic goals are clear, and whose cultures strongly support those goals, possess a huge advantage, especially for the areas such as innovation.
What is culture? Culture is how groups of people think and do things at organization. Culture is habit, culture is attitude, and culture is brand. The author of "Seven Habits of Highly Effective People", Stephen R. Covey passed away last month, his book has been sold more than 25 millions of copies in different languages, though the book is more about individual self-improvement, the concept and philosophy and seven habits of essential can also help business improve organizational habit, to experience more successful innovation journey.
1. Be Proactive
"Two people can see the same thing, disagree, and yet both be right. It's not logical; it's psychological." - Stephen R. Covey
Being proactive means people in the organization appreciate creativity, not just be compliant for survival; they are encouraged to be proactively questioning, connecting, collaborating and solving problems creatively. Because at some lagging businesses with conservative or negative culture encourage employees to be steadfast to the point that they'd become risk-averse, tolerant of mediocrity, and suspicious of outside or new ideas.
For business leaders, it means they may push the new ideas proactively on how to leverage culture to drive innovation and increase business flexibility and agility, on the other side, they also cultivate the culture of "Pull": proactively seek team feedback, deeply understand the potential business success factor and obstacles, and shape the culture which can harvest innovation.
2. Begin with the End in Mind
Innovation takes vision, vision may also help overcome culture inertia, as when everyone in the organization is collaborating to work towards the same goal; status quo, egos and silos no longer act as roadblocks, Knowledge and creativity are unleashed to produce outcomes.
Begin with end in mind also means: innovation is the means to the end, not the end, the end is how to delight customers or improve employee satisfaction, with such noble goals in mind, the culture can become more resilient to adapt to changes, employees are easier to get buy in, and vision may also convey the good story telling to inspire culture of innovation.
3. Put First Things First
"We see the world, not as it is, but as we are or, as we are conditioned to see it." ― Stephen R. Covey
Culture is also about how to focus, focus on a few things matter for the business, and the business also has capabilities to do better than competitors, Isn't that what innovation is all about: do it better, differentiate yourself from your competition, run, grow and transform the business. The other thing to consider is it's not just about technology, it's about people, the partnerships, the process, and capability.
Put First Things First also means prioritizing, prioritizing the business goals which are most critical to your strategy; prioritizing the project investments which can help improve your key capabilities; prioritizing also means to follow 80/20 rule: to put 80% of resources into 20% activities which can produce the best business results; from change management perspective: emphasizing just a few will allow you to move the needle on culture change much more easily: such as selecting a few key behaviors to change, rather than trying to create a completely different culture overnight.
4. Think Win-Win
"When the trust account is high, communication is easy, instant, and effective." ― Stephen R. Covey
Culture is also about attitude, mutual trust is a good attitude to shape culture of innovation, to build up win-win relationship between employees and organization, business and customers; More specifically, it's about building up the culture of "Reward success AND failure" - the logic here is that you reward people for trying new actions, and doubly reward them for successes. If you punish failure, you shut down innovation immediately.
Well, innovation is more about a process than a disruptive, enchanting new product these days. We need to tolerate the failure, also make the effort on a "lessons learned" exercise to share. And, this entire innovation process area needs some oversight to make it not be a major business disruption. There are systematic ways to manage these actions effectively and to benefit business for long term.
5. Empathy-Seek First to Understand, then to be Understood
"Treat them all the same by treating them differently." ― Stephen R. Covey,
Business leaders may think ideally that employees are paid to make a difference, the reality is that in many organizations, employees are trained to be compliance on the work being told to do, never to ask "why" or think independently, as employees' creativity is not evaluated fairly in business's talent agenda.
Empathy means business leaders and talent managers need deeply understand the value, the motivation and the habits of employees, and take customized talent solution to encourage innovative behaviors: as most of creative ideas or solutions will usually come from the collective knowledge and experiences of the employees and the customers, not from the most powerful person or the smartest guy/gal in the room. And culture will be shaped by the majority of people in the organization.
6. Synergize
"Habit is the intersection of knowledge (what to do), skill (how to do), and desire (want to do)."
-- Stephen R. Covey
The creative team is usually composed of all sorts of talents, with heterogeneous cognizance, strength and skills, especially those roadrunner people who want to understand the whole game, the whole business — not just their job; people who think like business people and owners, people who shows curiosity to ask why — not like narrowly focused employees who follow rules and crave order only.
The culture as habit here will harness the intersection of collective knowledge, wisdom, and aspiration, synergize creative disruption, enhance interdependent, collaborative and even codependent culture, and channel such energy, enthusiasm, and ideas.
7. Sharpen the Saw
"Sow a thought, reap an action; sow an action, reap a habit; sow a habit, reap a character; sow a character, reap a destiny." ― Stephen R. Cove
The culture is a habit, the good habit is also an attitude, one may need to take most of the time to sharpen the saws, such as prepare the team, understand the problem, get the right tool ready before jumping in approaching solutions or drawing conclusions.
However, sharpening the saw is means to the end, not the end. Some businesses misunderstand the innovation purpose, may think innovation is implementing the latest and greatest technology, rather than using advances in technology or existing technology differently to provide innovative solutions for business now and in the future.
Like individual's habit, cultural habit is hard to change, but it's changeable, business leaders can approach changing an organization's culture evolutionarily or disruptively, below are ten contemporary business cultures to catalyze innovation and drive business transformation.
1) Customer-Centric Culture
2) Analytics-Based Culture
3) Design Thinking Culture
4) Diversity-Enhanced Culture
5) Learning-Enabled Culture
6) Crowd-Sourcing Culture
7) Self-Managed Culture
8) Innovation-Amplified Culture
(9) Risk-Awareness & Tolerance Culture
(10) Cross-functional Collaborative Culture
Reusability is Both Art & Science
We should not be talking about the reusability of masks or other devices until we know whether they actually work to begin with. ~ Jeffrey Levi
Reuse is good, however, the dogmatic insistence on reuse at all costs has cost far more than people realize. To avoid misuse of reuse, one needs look at the issue with the full depth it deserves.
1. Reuse Takes Strategic Thinking
Re-use is to balance paradox of Simplicity vs. Complexity
Re-usability and Simplicity compliment each other to certain level of granularity within the organization. Re-usability will bring in required simplicity at an Enterprise level. When it comes to systems level, it becomes more tactical and at this level, it could become overkill. It's never a question about operational advantages we get from re-usability like savings in costs (development and Maintenance), rapid deployments.. etc. But many times re-usability brings in additional complexity to support re-usable aspect. Many of times this happens because of overkill of re-usability and same is the case with too much of generalization at systems level. Reducing complexity is a key goal, but not necessarily the most important, for example, consistency and validity can be extremely important. That said, reuse is to balance the paradox of simplicity and complexity.
The art of strategy in reusability
Good reusability strategy need diagnose current problems, then, set up guideline, and take cohesive action to execute it:
(1) How does re-use be managed and validated for fit-to-purpose.
(2) The value derives from understanding the requirements and what is driving them
(3) Understand the 'big picture' from who is sponsoring the endeavor and keep in touch with them on a regular basis
(4) Knows when to reuse and when not to reuse: where it may be bad, where there may be risks, but also where, if appropriately mitigated the reuse could be good
(5) How to handle reuse at both strategic and tactical level
2. The Art of Reuse in Architectural Design
Re-use spans all the levels of EA abstraction all the way through realization:
Needs of reuse is very simple, applied is difficult: Enterprise economic rationalization is both in project and wide enterprise. The business context is mandatory to inform level of reuse of value. It takes consideration of Enterprise Architecture Design.
EA is both art and science: The EA abstract layers include such as Generalization (Reuse)/Specialization (Customization), Classification (portfolio Management). Software Architecture is an art and Governance sometimes may not serve the goal of creating good art, but deploying services or components to the enterprise without governance is an invitation to a nightmare. Whether from ignorance or negligence, omitting a versioning strategy will cost more than any potential benefit from reuse. , In organizations where the culture promotes strong governance, you may be more likely to achieve the return on the investment from reuse that you are looking for.
Simplicity is the most important design principle. Reuse is about creating simple building blocks that can be applied over and over to minimize design cost and maximize value over the Lifecycle. Standards and Architecture framework attempt to improve this value by focusing us on functional boundaries. If we want to build reusable component, we must define all the reuse cases at the design level and build this component based on it, focused on real reusable cases instead of building something in a generic way and hoping that it could be reused later.
That said, architecture need play significant role in orchestrating reusability, agility and flexibility, to craft more cohesive business capabilities, value/cost/risk analysis need be done more coherently, organism & holism are the characteristics of effective business.
3. The Science of Reuse
Reuse of existing people, processes, locations, systems, services, data, applications and technology will always be considered first in the provision of any service to the Business Rationale. Re-use at the implementation levels (OO, POJO and EJB) and the related advantages are well known, but this is where the re-use could become overkill for various reasons like tactical solutions, performance, demand, etc. It should well clarify via scientific analysis and calculation:
(1) What is necessary and what is optional
(2) How reuse can be achieved
(3) Associated ROI.
(4)Where is it deployed (multiple sites, outsourced cloud infrastructure, etc.)?
(5) Which modules are used by which people in which processes?
(6)What are the integration points (people, process, technology) for these modules?
(7) Are there technical standards issues with the product?
(8) Are there SLA issues?
Shared components make economic sense, but that is conditional to business need and must be planned from that respect. One should have little faith in either accidental (emergent) or speculative reuse ("build it and they will come"). Throwing up services because "everyone's doing it" is only going to waste time and money. Reuse is science in this regard.
Moreover, reuse is useful, but it must be done intelligently. To be effectively used, one must also learn from the past. Not only should we question the applicability of a component for re-use, but we need to capture and analyze the lessons learned from the previous applications of the component. This needs to be done as part of the adoption process. Blind reuse results in the cut/paste issues that can come from adoption of inefficient generic or inappropriate components being forced into new roles. Where components are a good fit, we should reuse, or at least modify the component rather than starting from scratch.
In conclusion, re-sue is necessity, but it should be a natural reflex, and find the right "tipping point," the art of reusability is about architectural design thinking and strategic planning; the science of reusability is related to governance and in-depth analysis & calculation, to achieve business results such as cost effectiveness & productivity, and good for business' long term development.
Ten Excepts From Business Architecture Brainstorming
Enterprise architecture related to corporate business, and the documents and diagrams that describe that architectural structure of the business. People who build business architecture are known as Business Architects. Business architecture bridges between the enterprise business model and enterprise strategy on one side and the business functionality of the enterprise on another side.
rom Wikipedia, A business architecture is a part of an
Below are ten additional insights about BA:
Business architecture seeks to represent the architecture of an organization in terms of performance, process, information, and capability - either as it exists or as it is intended to be, thereby facilitating the planning and communicating of business change initiatives.
Business Architecture is the requirement set for the Business; IT architecture may be one of those requirements. Other requirements might include Capabilities, Processes, changes in organizational structure, changes in value chains and systems.
Business Architecture is a series of methods and industry standard practices to describe what you do, why, how, where and who derives or contributes the value of such interactions. It's about 90% of Why & What and 10% of How. This is captured at a high level in a current state ("as is"), an idealized future view ("to be") and a roadmap to take us there.
Business Architecture input can be used into organizational structure, and scope of responsibilities in an alliance type venture; BA input can also be used into where to direct resources and attention to strengthening business capabilities;
BA helps orchestrate the interrelationship between people and process, enterprise as a whole is more about people, process and technology. And EA = EBA + EITA, BA may focus on strategy maps, organizational structure, business capability analysis, BA can also be taken as an effective communication tool with well-visualized deliverables.
Business architecture needs to define the following components:
1) A framework for Business Architecture
2) A Method (Cookbook)
3) A set of deliverables
4) A Meta model
BA's Purpose: As an effective communication & governance tool to blueprint future of business, BA is not just for knowledge collection, more about capturing business insight/foresight.
BA's Main Components: Business Value System, Organizational Structure, Business Processes, Business Capability, Business Culture…..
BA's Hierarchy: A significant component of EA, 95% of votes agree EA = EBA + EITA
BA's Users/Customers: Besides enterprise architects and business analysts, management teams from top-down, use BA to help in decision making.
The Future of BA Brainstorm:
Is there such thing as Agile BA or Social BA—the Blueprint for Social Enterprise or Agile Business.
Should Business Culture be included into BA?
How to make BA deliverable more visualized to delight users?
Enterprise Weather Forecast: From Social Wind to S...
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Ten Excepts From Business Architecture Brainstormi...
Three DIYs at Future of Enterprise
Five Criteria How CIOs Evaluate Vendors
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Three Big Insights from Information Abundance | {
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69 Articles 69 Articles
Nov 2, 2012 Video
Global RallyCross comes to Vegas with SEMA [UPDATE]
Global RallyCross is an interesting motorsport. Beginning in 2010 at the X Games, the series races on short tracks made partly of asphalt and partly of dirt, along with a signature variation called the Joker Lap, in which drivers are required to take an alternate, slightly longer route that generally incorporates a 70-foot gap jump.
Jeremy Korzeniewski
Nov 1, 2012 SEMA
We obsessively covered the 2012 SEMA Show
Party's over, folks. Despite the fact that the city of Las Vegas is a-hustlin' and a-bustlin' 24/7, the lights are officially being turned off here at the 2012 SEMA Show. Thus, our bags are packed and we're getting the heck out of here.
Steven J. Ewing
Pics Aplenty: Scion FR-S and Subaru BRZ show up en masse at SEMA
Scion made a huge investment in the 2012 SEMA show, and its spanking new FR-S coupe, by putting hundreds of cars in the hands of tuners. The result on the floor of the Las Vegas Convention Center is unmissable, as just about everywhere we turn we find another FR-S peeking out at us.
Seyth Miersma
Pure Vision Design imagines what could have been with Martini Racing 1966 Ford Mustang T-5R [w/video]
Imagine, for a moment, this scene taking place way back in the 1960s:
Tekked-Out Prius, Rowdy Camry round out Toyota's SEMA offerings
Jeffrey N. Ross
RK Concepts custom motorcycles look ready for Rod Serling
You unlock this door with the key of imagination. Beyond it is another dimension – a dimension of sound, a dimension of sight, a dimension of mind. You're moving into a land of both shadow and substance, of things and ideas. You've just crossed over into... the SEMA Zone.
Chevy cooks up custom Camaro, Corvette for "Smoke," Fieri
NASCAR driver Tony Stewart is known as "Smoke" to many, and the custom Camaro ZL1 he helped create for SEMA reflects his sometimes mysterious personality. Chevy design manager Dave Ross worked with Stewart to come up with not only the flat red and silver tribal theme, but the custom gray-metallic paint and the red-haloed
Chris Tutor
Toyota Shows three tuner Avalons in Sin City
Who knew the Toyota Avalon could be so... sporty? SEMA isn't just about tuning no-brainers like the Ford Mustang and Scion FR-S, it's about showing what's possible for a wide variety of cars, even seemingly geriatric machines like the big Avalon.
2013 Lexus GS 350 F Sport Supercharged adds what we've been missing
If there's one legitimate complaint that can be hurled at the 2013 Lexus GS 350 F Sport, it's that it has no more power than its less-sporty siblings. It's not that 306 horsepower and 277 pound-feet of torque isn't enough for good performance – as the GS 350's 5.7-second sprint to 60 can attest – it's that a separate model that's billed as a performance version could use a few bonus ponies to keep enthusiasts buyers from feeling snubbe
Holman & Moody 50th Anniversary TdF Mustang is a blast from the past
It's easy to forget it was Holman & Moody that helped first put a Ford Mustang on track in competition. Well before Carroll Shelby ever spun a wrench on one of the pony cars, H&M served up a set of race engines for Alan Mann Racing. That team took four specially prepared 1964 notchback Mustang models to the 4,000-mile Tour de France Automobile and brought home first place in the T
Zach Bowman
Underground Racing creates 1,000-hp Audi R8 GT
It is unlikely that anybody has ever accused the Audi R8 GT of being a slow car, but like everything else on display at the SEMA Show – where the unofficial motto should be "if there's a will, there's a way" – Underground Racing has proven that fast can also get faster. Starting life as a 560-horsepower Jeffrey N. Ross
Scion FR-S SCCA World Challenge racecar, ready for the track
Of all the many Scion FR-S models here on the SEMA floor in Las Vegas – and there are a great many of them, have no doubt – the very purpose-built car from Stout Racing is one that we may hear about again in the future.
Mopar launches Jeep Performance Parts with Wrangler Sand Trooper
Chevrolet builds Sonic B-Spec racer concept
Chevrolet Performance worked over the Chevrolet Sonic just for this year's SEMA show to create this B-Spec racecar concept. Built to conform to all of rules and regulations of the B-Spec subcompact classes in both the SCCA and the Grand-Am series, the five-door features new coilovers on all four
Ford Mustang Build Powered by Women proves the XXs can compete [w/video]
What's so special about the customized Mustang you see above? Well, first of all, it's very well done – nicely designed and assembled with care – but that's not its main claim to fame. In an industry dominated by persons born with both X and Y chromosomes, the XXs don't want to be overlooked, and so this Ford Mustang Powered by Women came into existence.
Jeep JK Six Pak Concept is the three-row family off-roader you've been hankering for
Quality Metalcraft's CEO Michael Chetcuti has got big plans for the Jeep Wrangler – big enough to seat six, in fact. This QMC J
Scion FR-S Tuner Challenge declares a winner
We're all still a little taken aback at the sheer number of Scion FR-S mods we've seen at SEMA this year. Not only did the FR-S win the Best of Show award for the Sport Compact class, but based on gross tonnage the rear-drive Scion has got to be one of the most popular models in the tune
Fisker Karma and 3M at SEMA, that's a wrap
Electric carmaker Fisker has partnered with car-wrapping specialists 3M for an interesting demonstration of what could be at this year's SEMA festivities. As we reported in greater detail earlier, the folks from 3M are wrapping up the Karma in a few fa
HRE carbon fiber wheels for all your customizing desires
HRE has brought some pretty excellent wheels to market in the past, such as the retro-tastic Vintage Series, bridging old and new in fantastic fashion. The wheel-maker's latest offering is the Carbon Series CF2 Concept, now on display at SEMA.
Acura preps ILX for endurance racing challenge
Acura has used the occasion of this year's SEMA show to unveil a 2013 ILX that is remarkably different from the road-going car that we are familiar with. A far distance from the rather mildly performing street car, this ILX Endurance Racer is actually prepped to race at the grueling 25 Hours of Seyth Miersma | {
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before long; in the near future; at an early date: Let's leave soon.
Obsolete. immediately; at once; forthwith.
SoonerRead more in this article about some frequently asked questions and fun facts related to our definitions.
sooner or later, eventually: Sooner or later his luck will run out.
would sooner, to prefer to: I would sooner not go to their party.Compare rather(def 9).
Why, some might be asking, am I being so harsh on their work so soon after they died?
As soon as this attack [happened], Paris citizens came together to show were are not afraid, we are Charlie Hebdo.
"I think it is important to say it is too soon to judge success or failure," said Col. Steven Warren, a Pentagon spokesman.
But the jokes flow at such a torrential pace that duds are soon forgotten; the best are even Spamalot-worthy.
"We would just as soon stay away from a group that will create controversy," the Cubs general manager Sam Bernabe told the paper.
Anyhow, Jasper Jay began to sulk as soon as he heard the news.
If you are determined to expel all comfort from your house, be a Drunkard; and you will soon do it effectually.
But soon my mind began to employ the interval more profitably.
The natives of this part of the island became very friendly, as soon as they had recovered from their first suspicions.
Old English sona "at once, immediately, directly, forthwith," from West Germanic *sæno (cf. Old Frisian son, Old Saxon sana, Old High German san, Gothic suns "soon"). Sense softened early Middle English to "within a short time" (cf. anon). American English. Sooner for "Oklahoma native" is 1930 (earlier "one who acts prematurely," 1889), from the 1889 opening to whites of what was then part of Indian Territory, when many would-be settlers sneaked onto public land and staked their claims "sooner" than the legal date and time.
see as soon as; fool and his money are soon parted; had rather (sooner); just as soon; no sooner said than done; speak too soon. | {
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} | 9,601 |
{"url":"https:\/\/birch-lang.org\/getting-started\/macos\/","text":"# macOS\n\nThe recommended package manager is Homebrew. To install dependencies, use:\n\nbrew install autoconf automake libtool flex bison boost eigen libyaml libomp\n\n\nOnce these dependencies are installed, follow the usual instructions to install Birch itself.\n\nError\n\nBirch requires a newer version of Bison than that provided by macOS. The above command installs an appropriate version. If, however, you get a syntax error in parser.ypp when trying to install the Birch compiler, it is likely that the system version is still being used. In that case, try:\n\nbrew link --force bison","date":"2019-08-18 04:29:58","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\": 0.44601714611053467, \"perplexity\": 9806.311879268904}, \"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-2019-35\/segments\/1566027313617.6\/warc\/CC-MAIN-20190818042813-20190818064813-00065.warc.gz\"}"} | null | null |
(1) "Qualified opportunity fund" has the same meaning as defined in subsection (d) of Section 1400Z-2 of Title 26 of the United States Code.
(2) "Skilled and trained workforce" has the same meaning as provided in Chapter 2.9 (commencing with Section 2600) of Part 1 of Division 2 of the Public Contract Code.
(1) Is financed by a qualified opportunity fund.
(2) At least 50 percent of the project is affordable housing and at least two-thirds of the development's square footage is designated residential.
(3) Is not located on a site requiring demolition of affordable housing or conversion of rental units to for-sale units, or a site with mobilehomes or other special occupancies.
(4) Is consistent with the general plan and the housing element that is adopted within 10 years of the date of the project application for which an environmental impact report has been certified.
(5) Complies with previously approved applicable mitigation measures and standards.
(6) Has available existing utilities and schools to serve the project.
(A) The site of the project shall be subject to a phase I environmental assessment conducted in a manner that meets the most current requirements adopted by ASTM International for Standard Practice for Environmental Site Assessments: Phase I Environmental Site Assessment Process.
(B) If the results of a phase I environmental assessment conducted pursuant to subparagraph (A) conclude that further investigation is required, the site of the project shall be subject to a phase II environmental assessment conducted in a manner that meets the most current requirements adopted by ASTM International for Standard Practice for Environmental Site Assessments: Phase II Environmental Site Assessment Process.
(C) (i) If the results of a phase II environmental assessment conducted pursuant to subparagraph (B) conclude that further investigation is required, the site of the project shall be subject to a preliminary endangerment assessment prepared by an environmental assessor to determine the existence of any release of a hazardous substance on the site and to determine the potential for exposure of future occupants to significant health hazards from any nearby property or activity.
(ii) If a release of a hazardous substance is found to exist on the site, the release shall be removed, or any significant effects of the release shall be mitigated to a level of insignificance in compliance with state and federal requirements, as determined by the Department of Toxic Substances Control.
(iii) If a potential for exposure to significant health hazards from surrounding properties or activities is found to exist, the effects of the potential exposure shall be mitigated to a level of insignificance in compliance with state and federal requirements, as determined by the Department of Toxic Substances Control.
(8) Is not located on a site that has culture or historic resources.
(D) A site that is included on any list of facilities or sites compiled pursuant to Section 65962.5 of the Government Code.
(E) Land subject to ground failure or designated for protection of natural resources.
(F) Land under a conservation easement.
(10) Does not have any significant impacts that have not been publicly disclosed, analyzed, and mitigated.
(i) The project proponent shall ensure that the prevailing wage requirement is included in all contracts for the performance of the work.
(iii) Except as provided in clause (v), all contractors and subcontractors shall maintain and verify payroll records pursuant to Section 1776 of the Labor Code and make those records available for inspection and copying as provided in therein.
(iv) Except as provided in clause (v), the obligation of the contractors and subcontractors to pay prevailing wages may be enforced by the Labor Commissioner through the issuance of a civil wage and penalty assessment pursuant to Section 1741 of the Labor Code, which may be reviewed pursuant to Section 1742 of the Labor Code within 18 months after the completion of the project by an underpaid worker through an administrative complaint or civil action, or by a joint labor-management committee though a civil action under Section 1771.2 of the Labor Code. If a civil wage and penalty assessment is issued, the contractor, subcontractor, and surety on a bond or bonds issued to secure the payment of wages covered by the assessment shall be liable for liquidated damages pursuant to Section 1742.1 of the Labor Code.
(2) (A) Certify to the local agency that a skilled and trained workforce will be used to complete the project.
(i) The project proponent shall require in all contracts for the performance of work that every contractor and subcontractor at every tier will individually use a skilled and trained workforce to complete the project.
(ii) Every contractor and subcontractor shall use a skilled and trained workforce to complete the project.
(iii) Except as provided in clause (iv), the project proponent shall provide to the local agency, on a monthly basis while the project or contract is being performed, a report demonstrating compliance with Chapter 2.9 (commencing with Section 2600) of Part 1 of Division 2 of the Public Contract Code. A monthly report provided to the local agency pursuant to this clause shall be a public record under the California Public Records Act (Chapter 3.5 (commencing with Section 6250) of Division 7 of Title 1 of the Government Code) and shall be open to public inspection. A project proponent that fails to provide a monthly report demonstrating compliance with Chapter 2.9 (commencing with Section 2600) of Part 1 of Division 2 of the Public Contract Code shall be subject to a civil penalty of ten thousand dollars ($10,000) per month for each month for which the report has not been provided. Any contractor or subcontractor that fails to use a skilled and trained workforce shall be subject to a civil penalty of two hundred dollars ($200) per day for each worker employed in contravention of the skilled and trained workforce requirement. Penalties may be assessed by the Labor Commissioner within 18 months of completion of the project using the procedures for issuance of civil wage and penalty assessments set forth in Section 1741 of the Labor Code, and may be reviewed pursuant to the procedures set forth in Section 1742 of the Labor Code. Penalties shall be paid to the State Public Works Enforcement Fund.
(iv) Clause (iii) shall not apply if all contractors and subcontractors performing work on the project are subject to a project labor agreement that requires compliance with the skilled and trained workforce requirement and provides for enforcement of that obligation through an arbitration procedure. For purposes of this clause, "project labor agreement" has the same meaning as set forth in paragraph (1) of subdivision (b) of Section 2500 of the Public Contract Code.
(1) Ensure that the project proponent has met the requirements of subdivision (c).
(2) Issue and publish a draft determination that the project is exempt pursuant to this section.
(3) (A) Hold a noticed public hearing no earlier than 30 days following the publication of the draft determination and at least 30 days prior to the issuance of a final determination in areas affected by the project to hear and respond to public comments.
(B) Publication of the notice shall be no fewer times than required by Section 6061 of the Government Code, by the lead agency in a newspaper of general circulation in the area affected by the proposed project. If more than one area will be affected, the notice shall be published in the newspaper with the largest circulation from among the newspapers of general circulation in those areas.
(e) If the lead agency determines that a project is not subject to this division pursuant to this section and it determines to approve or carry out the project, the lead agency shall file a notice with the Office of Planning and Research in the manner specified in subdivisions (b) and (c) of Section 21152 at least 30 days following the noticed public hearing. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,008 |
\section{Introduction}\label{sec:intro}
The Universe provides a remarkable laboratory where matter reaches temperatures and densities inaccessible on Earth.
Consequently, phenomena observed by astrophysicists have been the first source of precision measurements of fundamental properties of atoms and molecules~\cite{Hoyle:1954zz, refId0}, and have uncovered new particle physics~\cite{doi:10.1146/annurev.aa.27.090189.003213}.
But as rich as the study of light-emitting astrophysical objects is, it reaches only $15\%$ of the matter in the Universe.
The rest of the matter is dark, and its particle nature is unknown.
While experiments have slowly expanded their reach into the enormous parameter space of possible dark matter particle interaction channels and strengths~\cite{Penning_2018,Dainese:2019rgk,PhysRevD.101.052002,PhysRevLett.118.221803,Diamond:2019luc,Roszkowski_2018,Conrad:2017pms}, they have yet to produce a detection.
However, gravitational-wave observatories like LIGO~\cite{TheLIGOScientific:2014jea} and Virgo~\cite{TheVirgo:2014hva} provide a new way of detecting astrophysical objects where dark matter is on the same footing as visible matter.
Gravitational-wave detections do not require any coupling between dark and visible matter; they only require that dark matter gravitates.
The connection between dark matter and gravitational-wave sources has been explored previously, perhaps most notably with the first detection of a binary black-hole (BBH), GW150914~\cite{Abbott:2016blz}, by the LIGO and Virgo collaborations (LVC).
Primordial black-holes(PBHs)~\cite{Carr2016}, long theorized to be a component of dark matter, were invoked as a possible progenitor~\cite{Bird:2016dcv, Sasaki:2016jop} due to the previously unobserved high mass of GW150914's constituents.
Other gravitational-wave studies~\cite{Clesse:2020ghq, Abbott:2005pf,PhysRevLett.121.231103,PhysRevLett.123.161102,PhysRevD.101.104041} have explored the PBH paradigm for dark matter and set upper limits on the fraction of dark matter in PBHs.
While PBHs do not invoke the existence of new particles in the universe today, their presence requires yet undiscovered inflationary-era physics.
Here we present a new paradigm which connects gravitational-wave observations to dark matter through dissipative dark matter.
In contrast to PBHs, dissipative dark matter works within the standard cosmological history, and introduces dark particle physics with a complexity resembling that of the Standard Model.
Dissipative dark matter models allow for the formation of compact objects through the cooling and eventual gravitational collapse of dark matter.
Therefore, gravitational-wave observations of BBH mergers could either confirm or severely constrain dissipative dark matter models.
We note that this paradigm is in contrast with the weakly-interacting massive particle (WIMP) paradigm that includes a single cosmologically relevant dark matter particle whose primary interaction is with the Standard Model.
The WIMP paradigm is appealing in its simplicity, but it is increasingly under pressure from both the lack of results in direct detection experiments~\cite{Bertone:2018krk} and from astrophysical data that may prefer self-interacting dark matter~\cite{Bullock:2017xww,Essig:2018pzq,Choquette:2018lvq,Latif:2018kqv,DAmico:2017lqj,2020Univ....6..107D}.
In this article, we argue that gravitational-wave observations may already be probing the properties of dark matter.
Of particular interest to our work is GW190425~\cite{Abbott:2020uma}, which was a $5\sigma$ deviation in total mass from all other observed Galactic binary neutron stars (BNS) prompting speculation that the signal could be from a BBH, a neutron star - black hole (NSBH), or a PBH~\cite{Clesse:2020ghq} merger.
Here, we show that if GW190425 is caused by compact objects made of atomic dark matter, it constrains the dark proton mass directly through the Chandrasekhar Limit, and implies cooling properties of dark matter which could provide a possible parameter space for dark matter particle interactions.
\section{\label{sec:DBHform}Black Hole Formation from dissipative dark matter}
Black holes are simple objects in general relativity, carrying only three parameters: mass, spin, and electric charge~\cite{Kerr:1963ud}.
The Chandrasekhar limit~\cite{Chandrasekhar:1931ih} provides a fundamental upper mass limit for degenerate stars where Fermi degeneracy pressure balances the gravitational force toward collapse. In the absence of nuclear forces, any compact object heavier than the Chandrasekhar limit must be a black hole. While the Chandrasekhar limit gives the lowest possible mass for a black hole from gravitational collapse, it makes no further prediction about the actual black hole mass spectrum, which depends on the formation process of black holes.
In scenarios where black holes made of dark matter form via astrophysical processes, the spectrum of black holes may be used to constrain the properties of dark matter, if a dark analogue to the Chandrasekhar limit exists.
We consider here a dark matter model with simple chemistry, forming only a single atom analogous to hydrogen.
All dark black holes (DBHs) are then formed by direct collapse.
In a model of dark matter with an abundant spin-1/2 particle of mass $m_x$, analogous to the standard model proton (mass $m_p$), the dark matter Chandrasekhar mass limit ($M_{\textrm{DC}}$) is $\SI{1.4}{\sol} (m_p/m_x)^2$.
While dark matter may well have more complex chemistry, including nuclear forces only yields marginal changes to the model given that both the Chandrasekhar limit and the maximum neutron star mass are of the order $(\hbar c / G)^{3/2}/m_p^2 = \SI{1.9}{\sol}$.
Atomic dark matter~\cite{Feng_2009} consists of two spin-1/2 particles oppositely charged under a new force.
The dark fermion masses are $m_x$ and $m_c$, with $m_x > m_c$. The particles interact through a force analogous to electromagnetism, mediated by a massless dark photon, with interaction strength determined by the dark fine structure constant $\alpha_D$ (where $\alpha = 1/137$ is the fine structure constant in the Standard Model).
The oppositely charged particles can form bound states similar to atomic and molecular hydrogen, $H_D$ and $H_{D,2}$, with the lighter dark particle analogous to the standard model electron.
In regions of sufficient density~\cite{PhysRevLett.120.051102}, the dark matter gas may cool by standard radiative cooling processes including recombination, Bremsstrahlung, and collisional excitation of the atoms or molecules~\cite{PhysRevD.96.123001}.
In lower-density regions, cooling is inefficient, which is consistent with the observed dark matter halos.
Even if dark matter is dissipative, only a fraction of the gas will cool, and of that, only a fraction will end up in compact objects.
We call the fraction of dark matter that ultimately ends up in DBHs, $f$.
We use gravitational-wave observations to constrain $f$, by modeling the population of binary DBHs after Population-III stars.
Briefly, Population-III stars form from midsize halos dominated by atomic hydrogen. Radiative processes cool the gas, allowing it to collapse inwards. Hydrogen molecules are formed as the gas contracts, enabling additional cooling. At sufficient density, the primary cooling processes become inefficient and the gas begins reheating, with some of the gas eventually fragmenting into small protostars\cite{Glover2012}. Assuming the same general process can occur for dissipative dark matter halos, some of the dark matter will collapse into a pseudo-protostar, but, lacking pressure from nuclear fusion-induced radiation, will collapse further into a black hole. The mass spectrum of dark matter compact objects formed this way is obtainable, to a first approximation, by rescaling results from Population-III star formation literature~\cite{1976MNRAS.176..483R,1976MNRAS.176..367L,Abel:2001pr,doi:10.1146/annurev.astro.42.053102.134034}. The minimum Jeans mass in the dark matter gas can be computed analytically and depends on microphysical parameters. Simulations of Pop III star formation follow the hydrodynamical evolution of the gas and find that the smallest proto-stars formed are significantly larger than the analytic minimum. Combining the minimum Jeans mass calculation for atomic dark matter with a rescaling from simulation results gives the minimum mass of dark black holes~\cite{Shandera:2018xkn},
\begin{align}
\label{eq:Mdj}
M_{\textrm{DJ}} \approx \SI{800}{\sol} \left(\frac{m_p}{m_x}\right)^{5/2} \left(\frac{m_c}{m_e}\right)^{1/2} \left(\frac{\alpha_D}{\alpha}\right)^{1/2}.
\end{align}
\linebreak
This minimum mass depends on the coldest temperature the gas can reach, proportional to the energy gap of the lowest rotational modes of the $H_{2}$ molecule for Population-III stars and $H_{D,2}$ for the dark compact objects.
LVC data directly constrains the dark Chandrasekhar limit, since any black holes observed must be larger than $M_{DC}$. However, if the black holes are formed by direct collapse in a cooling gas, then $M_{\textrm{DJ}}$ can also be constrained. While simulations of dissipative dark matter are required to provide the precise numerical coefficient in Eq.(\ref{eq:Mdj}), this interpretation is a powerful one as it allows the molecular energy gap to be inferred. We present both constraints below in order to demonstrate how the spectrum of compact objects can provide new constraints on the particle physics and chemistry of the dark sector.
We use Population-III star formation studies~\cite{doi:10.1146/annurev.astro.42.053102.134034} to set several parameters or parameter ranges of the dark black holes that should be determined by hydrodynamics and gravity rather than by particle physics. We take the initial mass function to be given by $\mathcal{P}(m) \propto m^{-b}$, ranging from $M_{\textrm{min}}$ up to $M_\textrm{max} = r M_{\textrm{min}}$ for some $m_x$, $m_c$ and $\alpha_D$. The range of $r$ extends from 2 to 1000 distributed log-uniformly, while $b$ ranges from -1 to 2 uniformly in our study. We denote the DBH population parameters $\{M_{\textrm{min}}, r , b\}$ as a vector $\overline{\theta}$. The merger time for binaries is given by the Peters formula~\cite{PhysRev.131.435}, which depends on the initial distribution of the eccentricities and the semi-major axis of the binary. Again based on Population-III star populations~\cite{doi:10.1146/annurev.astro.42.053102.134034, Hartwig:2016nde}, we draw the eccentricities of the binaries, $e$, from $\mathcal{P}(e) \propto e^{m}$ with $0.1 < e < 1$ and $m = 1$. The semi-major axis, $a$, follows the distribution $\mathcal{P}(x) \propto x^k$ where $x = \log_{10}(a/a*)$, $k = -1/2$ with the range of $a$ proportional to $M^{1/3}$, and we rescale $a*$. The mass ratio, $q = m_\textrm{light} / m_\textrm{heavy}$ follows the distribution $\mathcal{P}(q) \propto q^n$ with $n = -0.55$. The merger time is taken to be \SI{10}{\giga\year}, appropriate for binaries formed at high redshifts ($z > 1$). We use LVC data to constrain $f$, assuming the fraction of DBHs in binaries is $f_\textrm{binary} = 0.26$~\cite{doi:10.1146/annurev.astro.42.053102.134034}.
\section{Constraining properties of dark black hole populations}\label{sec:paramConstraints}
Gravitational-wave observations from the LVC~\cite{LIGOScientific:2018mvr} infer the component masses $m_1$ and $m_2$ of merging black holes. Specifically the binary chirp mass $\mathcal{M} = (m_1 m_2)^{0.6}/ (m_1 + m_2)^{0.2}$ is measured very accurately. Given LVC observations as a function of chirp mass, we constrain $f$ and $M_{\textrm{min}}$ by calculating the posterior probability of $f$ and $M_{\textrm{min}}$ conditioned on the predicted DBH merger event rate $R$, and the sensitivity of the LIGO and Virgo detectors~\cite{Abadie:2010cg}. We use a Bayesian approach to infer $f$ and $\overline{\theta} = \{M_{\textrm{min}}, r , b\}$, $P(f, \overline{\theta} | \overline{\mu}) \propto P(\overline{\mu} | f, \overline{\theta}) P(f, \overline{\theta})$, where $\overline{\mu}$ is a vector corresponding to the expected number of DBH detections from the LVC in pre-defined chirp mass bins over $\mathcal{M}\in$ [\SI{0.2}, \SI{200}{\sol}], such that $\mu_i$ is the mean event count in the $i^{th}$ chirp mass interval. $P(f, \overline{\theta})$ denotes the prior probabilities of $f, M_{\textrm{min}}, r$ and $b$ assumed to be independent of each other. We use uniform priors for $f$, $M_{\textrm{min}}$ and $b$, and a logarithmic prior for $r$. In order to obtain the posterior probability distribution of $f$ and $\overline{\theta}$, we must predict the probability of obtaining event counts, $n_i$ in a bin with $\mu_i = R_i(f, \overline{\theta}) V_i(\overline{\theta})T$, where $R_i$ is the predicted rate of mergers for DBH binaries, $V_i$ is the spatial volume surveyed by a gravitational-wave detector, and $T$ is the observation time.
The DBH merger rates are modeled as a function of chirp mass, $\mathcal{M}$ and $f$ following ~\cite{Shandera:2018xkn}, and computed in the $i^{th}$ chirp mass interval using
\begin{align}
\begin{split}\label{eq:rate}
R_i (\mathcal{M} = m_i | f, \overline{\theta}) =
P_i (m_i | t_{\textrm{m}}, \overline{\theta})
\times
\left(\frac{dP(t_{\textrm {m}} = \SI{10}{\giga\year} | \overline{\theta})}{dt}\right) \\
\times
\left(\frac{\rho_{\textrm{DM}} \times f \times f_{\textrm{binary}}}
{\langle M \rangle}\right),
\end{split}
\end{align}
where $\rho_{\textrm{DM}}$ = \SI{3.3e19}{\sol\per\giga\parsec\cubed} is the density of dark matter in the universe, $f_{\textrm{binary}} = 0.26$, and $P(\mathcal{M} | t_m, \overline{\theta})$ is the chirp mass distribution of binary systems that would merge at a given merger time $t_{\textrm{m}}$, $P(t_{\textrm{m}}=\SI{10}{\giga\year} | \overline{\theta})$ is the probability that the merger time of the binary is \SI{10}{\giga\year}, roughly the age of the universe, and $\langle M \rangle$ is the mean component mass of DBH given the initial mass distribution, computed for some $\overline{\theta}$.
The LVC has detected several binary black hole mergers during the first, second and third advanced LIGO-Virgo observing runs. We include all published events from these observing runs~\cite{LIGOScientific:2018mvr,Abbott:2020niy} excluding the known BNS detection, GW170817~\cite{TheLIGOScientific:2017qsa}, as definitely not a DBH detection. We assume that the event count $n_i$ observed by the LVC in a given chirp mass interval $i$ follows a Poisson distribution~\cite{Biswas:2007ni}, $\mathcal{P}(\mu_i | f, \overline{\theta}) = \mu_i^{n_i}e^{-\mu_i}/n_i !$, with independent $\mu_i$.
To approximate $V_iT$ in our predetermined chirp mass bins, we use the horizon distance which depends on the chirp mass as $\mathcal{M}^{5/6}$~\cite{Abadie:2010cg}. For a given chirp mass, we use the predicted distribution of mass ratios for DBH binaries to compute a weighted average over all possible binaries allowed for that chirp mass. Equation~\ref{eq:VT1} was used to compute the $VT$ for a compact binary uniquely described by its mass ratio, $q$ and chirp mass, $m_i$. We then use equation~\ref{eq:VT2} to calculate the weighted average of the $VT$s for a given chirp mass over mass ranges representative of the search parameter spaces used for compact binary coalescences conducted in data from the second and third observing runs of LVC~\cite{Mukherjee:2018yra}. The posterior distribution for $f$ and $M_{\textrm{min}}$ is finally obtained by marginalizing the four dimensional posterior distribution over the undetermined parameters, $r$ and $b$. More information on methods is provided in appendices~\ref{appendix:posteriors} and \ref{appendix:VT}.
\begin{figure*}
\includegraphics[width=\textwidth]{VT_Rates.png}
\caption{Sensitive volume (\textit{left}) and rate of DBH mergers (\textit{right}) evaluated over pre-defined chirp mass bins for different values of $M_{\textrm{min}}$. The slope of the initial mass distribution, $b = 2$ and ratio, $r = 100$ for both figures, while the fraction of dark matter in DBHs, $f$ is set to be $10^{-4}$. }
\label{fig:VT_R}
\end{figure*}
\begin{figure}[ht]
\includegraphics[width=\columnwidth]{constraints_f_Mmin_gwtc1_2.png}
\caption{Constraint on the fraction of dark matter $f$ in DBHs against the minimum allowed mass of DBH $M_{\textrm{min}}$ for the dissipative dark matter model of~\cite{Shandera:2018xkn} if (a) none of LVC's binary black holes are DBHs (\textit{dashed}), (b) all LVC detections are either from astrophysical or DBH binaries with equal probability (agnostic about origin) (\textit{dotted}), (c) GW190425 is a DBH binary detection (\textit{blue}), and (d) GW190425 and GW190814 are from DBH binaries (\textit{pink}). Constraints for (c) and (d) are computed under an agnostic assumption about the origins of other LVC events. The Chandrasekhar limit for conventional black holes (\SI{1.4}{\sol}) is plotted for reference. The contours mark 90\% confidence regions.}
\label{fig:constraints}
\end{figure}
Assuming GW190425~\cite{Abbott:2020uma}, is a binary DBH signal and that the other LVC detected events from the first, second and the first half of the third observing runs~\cite{LIGOScientific:2018mvr,Abbott:2020niy} are either conventional BBH or DBH binaries with equal probabilities, we report the constraints on the parameters $f (10^{-10} - 1)$, and $M_{\textrm{min}}(10^{-3} - \SI{3}{\sol})$ in figure \ref{fig:constraints}.
The chirp mass $1.4^{-0.02}_{+0.02} \si{\sol}$ and total mass $(M = m_1+ m_2)$ $3.4^{-0.2}_{+0.3} \si{\sol}$ of this system are five standard deviations greater than those observed for known Galactic BNS systems, implying that GW190425 could possibly be from a BBH or an NSBH merger.
However, if one of the components is a black-hole, it would be the smallest known black hole by a significant margin, and such small black holes have not been observed prior to LIGO~\cite{2011ApJ...741..103F}, though they have been proposed to form through various channels~\cite{Faber:2012rw, Gupta:2019nwj, Bramante:2017ulk, Belczynski_2012}.
Another detection, GW190814~\cite{Abbott:2020khf} with chirp mass $6.1^{+0.06}_{-0.05}\si{\sol}$, has prompted speculation about possible dark matter origins for the binary~\cite{Clesse:2020ghq}.
Figure \ref{fig:constraints} shows that the addition of GW190814 as a DBH detection widens the constraint on $M_{\textrm{min}}$ while constraining $f$ to a narrower range of lower values.
The lighter mass event dominates the constraints on $M_{\textrm min}$ when we have a wide range of allowed masses.
It is evident from equation~\ref{eq:rate} is that we have more DBHs at lower masses than higher masses. This factor later cancels with the sensitive volume, where the horizon distance scales as $\mathcal{M}^{5/6}$, such that $f$ is lowered when we include the heavier binary.
\begin{table}
\begin{tabularx}{\columnwidth}[t]{p{1.35in}p{.6in}p{.7in}p{.65in}}
\footnotesize{\textbf{Observed DBH binary}} & \footnotesize{$\mathbf{\mathcal{M}}$\textbf{/ \si{\sol}}} & \footnotesize{$\mathbf{M_{\textrm{min}}}$\textbf{/ \si{\sol}}} & \footnotesize{$\mathbf{m_x}$\textbf{/GeV}}\\
\hline
GW190425 & 1.44 & 0.062--1.34 & 0.95--4.44 \\
GW190425, GW190814 & 1.44, 6.1 &0.054--1.50 & 0.91--4.76 \\
\end{tabularx}
\caption{Probable minimum masses of dark black-holes, $M_{\textrm{min}}$, and the corresponding heavy fermion masses, $m_x$ for the two cases of observed dark black-hole binaries. Heavy fermion masses are computed using the dark matter Chandrasekhar mass limit, by setting $M_{DC}=M_{\textrm min}$ determined from the data.}
\label{table:masses}
\end{table}
If GW190425 is a DBH binary, $M_{\textrm{min}}$ lies below \SI{1.4}{\sol}, the Chandrasekhar limit for astrophysical black holes, to greater than $99.9\%$ confidence. Using the Chandrasekhar limit equation, we get dark heavy fermion masses ($m_x$) ranging from 0.95 -- \SI{4.44}{\giga\electronvolt} for the possible values of $M_{\textrm{min}}$ between 0.062 -- 1.34 \si{\sol}, which is greater than the mass of the proton $(m_p)$, \SI{0.938 }{\giga\electronvolt}. We report the possible heavy fermion masses from the Chandrasekhar mass limit for the considered DBH detections in table~\ref{table:masses}.
Alternatively, using Population-III star formation as a guide to black hole formation in the atomic dark matter scenario~\cite{Shandera:2018xkn}, we find that dark-hydrogen molecular cooling dissipates the average kinetic energy to \SI{2.2}{\milli\electronvolt} for $M_{\textrm{DJ}} = \SI{0.92}{\sol}$ ( roughly the most probable value assuming only GW190425 is a DBH), assuming $m_x = \SI{14}{\giga\electronvolt}$, $m_c = \SI{325}{\kilo\electronvolt}$, and $\alpha_D = 0.01$. The Chandrasekhar mass for $m_x = \SI{14}{\giga\electronvolt}$ is much lower, at \SI{6e-3}{\sol}.
If none of the compact binary coalescences observed by the LVC are DBH binaries, we get upper limits on $f$ for a range of possible $M_{\textrm{min}}$, also shown in figure \ref{fig:constraints}. For $M_{\textrm{min}}$ lower than \SI{0.2e-2}{\sol}, $f$ is completely unconstrained. This is due to the inconclusive limits on $f$ for low mass compact object binaries from searches for sub-solar mass binaries in gravitational-wave data~\cite{PhysRevLett.121.231103, PhysRevLett.123.161102, PhysRevD.101.104041}, and partly due to the assumed priors for our parameters, specifically on $r=M_{\textrm{max}}/M_{\textrm{min}}$.
\section{Constraints on cooling rates}
Besides the lower bound of the dark-matter particle mass from the Chandrasekhar limit, the existence of DBHs also provides a novel way to limit the energy dissipation rate of dark matter.
Forming a DBH requires the originating dark matter halo to lose order one of its kinetic energy density $\mathcal{E}_{\rm k}$, on a time-scale shorter than its free-fall time $t_{\rm ff}$, which is the time for the halo to collapse under its own gravity. The cooling rate $\Lambda$ in the birthplace halos of DBHs must satisfy \cite{PhysRevLett.120.051102},
\begin{align}
\begin{split}
\Lambda \geq \left(\frac{\mathcal{E}_{\rm k}}{t_{\rm ff}}\right) \left(\frac{1}{n_{\rm D}}\right)^2,
\end{split}\label{eq:lambda_ff}
\end{align}
where the normalizing factor $n_{\rm D}$ is the number density of the dominant mass component of dissipative dark matter, analogous to the number density of hydrogen, $n_{\rm H}$ (as opposed to the total number density, $n$) in the Standard Model. Note that, while the free-fall time only depends on $n_{\rm D}$, the kinetic energy density represents all dark-matter particles. That difference introduces a non-trivial temperature dependence to equation (\ref{eq:lambda_ff}) as the ionization fraction varies with temperature.
To illustrate the constraint we chose $m_x = \SI{14}{\giga\electronvolt}$, consistent with the scenario that GW190425 is a binary DBH. In figure \ref{fig:coolingrates} we plot the above constraint on cooling rate $\Lambda$, across a range of temperatures corresponding to halo masses of $10^5 - \SI{e9}{\sol}$ at redshifts $z = 5$ and $z = 10$. For reference, free-fall times are $\mathcal{O}(\SI{0.1}{\giga\year})$ for these redshifts. \cite{PhysRevLett.120.051102}. The black line shows an atomic dark matter cooling curve for reference~\cite{PhysRevD.96.123001}.
To obtain an upper limit on cooling at high temperatures, we use observations of galaxy cluster collisions that indicate dark matter experiences minimal energy loss due to dark particle interactions~\cite{Markevitch:2003at}. For a cluster with dark matter surface density $\Sigma_{\rm s}$, colliding at velocity $v_{\rm coll}$ with another cluster, the cooling rate can be bounded by the maximum fraction of energy lost by the dark matter $f_{\rm lost}$, as,
\begin{align}
\begin{split}
\Lambda \leq \left(\frac{f_{\rm lost} \mathcal{E}_{\rm k} v_{\rm coll}}{\Sigma_{\rm s}}\right)\left(\frac{m_x}{n_{\rm D}}\right)
\end{split}
\end{align}
Figure \ref{fig:coolingrates} shows how this constraint applies to cluster-scale temperatures if observational data bounds $f_{\rm lost} = 0.01, 0.1, 0.3$ (darkest to lightest). We use $v_{\rm coll}=\SI{1000}{\kilo\meter\per\second}$, $\Sigma_s = \SI{0.25}{\gram\per\centi\meter\squared}$ appropriate for the Bullet Cluster~\cite{Markevitch:2003at}.
The lack of observed dwarf galaxies in contrast to the result from cosmological simulations - called ``the missing-satellite problem" - may suggest that dwarf galaxies are fragile under galaxy cluster collisions~\cite{Bullock:2017xww}. Interestingly, our analysis shows that some dwarf galaxies are likely to be disrupted by such collisions if dark matter is sufficiently dissipative to have formed the constituent DBHs of GW190425. Figure \ref{fig:coolingrates} shows a range of temperatures appropriate for dwarf galaxies with $\Sigma_{\rm s} =\SI{e-3}{\gram\per\centi\meter\squared}$, where collisions with $v_{\rm coll} = \SI{100}{\kilo\meter\per\second}$~\cite{Herrmann_2016,McConnachie_2012}, likely lead to disruption ($f_{\rm lost} \geq 0.5$). We show how the interactions that lead to cooling will also lead to the disruption of low temperature structures (dwarf galaxies) in collisions, without affecting large scale structure.
\begin{figure}
\includegraphics[width=\columnwidth]{cooling_rates.png}
\caption{\label{fig:coolingrates}Cooling rate constraints from dark black hole detections combined with large scale structure collisions. Shaded regions correspond to the allowed parameter space in which (\textit{blue}) small halos at $z = 5, 10$ where DBHs form, (\textit{red}) energy loss fraction $f_{\rm lost} = 0.01, 0.1, 0.3$ (solid to dashed), for galaxy cluster collisions, and (\textit{brown}) $f_{\rm lost} = 0.5$ for dwarf galaxy collisions. We also include the cooling function (solid black line) for an example atomic dark matter model consistent with the interpretation that GW190425 is a binary DBH $(m_x = \SI{14}{\giga\electronvolt}, m_c = \SI{325}{\kilo\electronvolt}, \alpha_D = 0.01)$.
}
\end{figure}
\section{Comparison with alternate dark matter compact object constraints}
Compact objects have long been considered as a possible component of the dark matter~\cite{Hawking1971, Chapline1975}, and by the 1990s interest in this candidate class peaked. Microlensing experiments that sought to measure signatures of compact objects in the galactic halo had promising early results that suggested a population of dark objects~\cite{Alcock:1993eu}. As LIGO and Virgo secured funding and broke ground, there was similar interest in the prospect of observing these objects via independent methods~\cite{Nakamura:1997sm}. Interest waned as microlensing surveys~\cite{Allsman:2000kg,Tisserand:2006zx}, gravitational-wave searches~\cite{Abbott:2005pf,PhysRevLett.121.231103,PhysRevLett.123.161102,Abbott:2007xi,wade2015}, and dwarf galaxy dynamics calculations~\cite{Brandt:2016aco,Koushiappas:2017chw} determined that compact objects are unlikely to make up all of the dark matter.
\begin{figure}
\includegraphics[width=\columnwidth]{constraints_DMcompactObj.png}
\caption{\label{fig:CODM}Constraints on the fraction of dark matter in compact objects $f$ with our constraint on DBH overlaid. The DBH constraints are plotted for the mean of the mass distributions that extend over $M_{\textrm{min}} - M_{max}$. The O2 LVC constraints are specific to the PBH scenario of ~\cite{Nakamura:1997sm}. The microlensing constraints are derived from~\cite{Allsman:2000kg,Tisserand:2006zx,ogle}, and dwarf galaxy dynamics from~\cite{Brandt:2016aco,Koushiappas:2017chw}. The x-axis denotes the mass in solar masses of the dark matter object. PBH constraints are derived from~\cite{PhysRevLett.123.161102,Gaggero:2016dpq,Raidal:2017mfl,Raidal:2018bbj,Ali-Haimoud:2017rtz}. \textit{SB} stands for stochastic background.
}
\end{figure}
In the model we present, only a small fraction of the total dark matter cools and collapses to form DBH binaries. Indeed, the fraction of dark matter contained in DBHs is far below existing constraints on compact object dark matter. Figure \ref{fig:CODM} shows that if GW190425 and GW190814 are not DBH binaries, the resulting constraints on our model are $O(10^2 - 10^5)$ times stricter than limits from microlensing and dwarf galaxy dynamics. Conversely, if GW190425 is a DBH, then it exists in a region unconstrained by these observations. In figure \ref{fig:CODM}, we also show limits on $f_{\textrm{PBH}}$ from the non-observation of a stochastic background in the first and second observing runs of LIGO-Virgo reported in \cite{Raidal:2017mfl, Raidal:2018bbj}. \cite{Ali-Haimoud:2017rtz} reports potential upper limits on $f_{\rm PBH}$ for equal mass binaries with $M_{\rm PBH} \in [10, 300 \si{\sol}]$, also shown in figure \ref{fig:CODM}.
In interpreting figure \ref{fig:CODM}, note that the PBH constraints assume a delta function for initial black hole masses, except the O2 stochastic background constraint of \cite{Raidal:2018bbj} which assumes a lognormal mass function for PBHs, while in the DBH case the mass on the x-axis is the average mass over all initial mass distributions we considered for a given $M_{\textrm{min}}$ (see Fig. 1).
\section{Conclusion}
Gravitational-wave astronomy can play a key role in understanding the properties of dissipative dark matter that can cool to form compact objects like DBHs. We illustrate how only a single gravitational-wave detection of a DBH binary opens up a novel framework for studying the properties of dissipative dark matter from gravitational wave astronomy. Interpreting GW190425 as a DBH binary not only constrains $f$ and $M_{\textrm{min}}$ for a DBH binary population predicted for atomic dark matter
in~\cite{Shandera:2018xkn}, but the constraints on $M_{\textrm{min}}$ also provide a direct upper limit on the heavy dark fermion mass $m_x$ through the Chandrasekhar limit (using $M_{\textrm DC}=M_{\textrm min}$. From the fact that the minimum of the dark-matter BH mass distribution is smaller than the usual Chandrasekhar limit of $1.4\,M_{\odot}$, we find that $m_x>0.95\,{\textrm GeV}$ with $99.9\%$ confidence. We also illustrate how an additional heavier DBH detection, GW190814, has little effect on the predicted $M_{\textrm{min}}$ but constrains $f$ to a higher extent. In this case, the Chandrasekhar limit allows for heavy dark fermion masses to be smaller than the proton mass.
Assuming a simple dark matter model forming bound states analogous to those of hydrogen, for which we adopt Population-III star formation and binary parameters for our DBH population, we also estimate atomic-physics parameters for dark matter. For example, if $M_{\textrm{DJ}} = \SI{0.92}{\sol}$ (the most probable value of $M_{\textrm min}$ if only GW190425 is a DBH), and assuming $m_x = \SI{14}{\giga\electronvolt}$, $m_c = \SI{325}{\kilo\electronvolt}$, and $\alpha_D = 0.01$, we estimate the molecular energy gap for these dark atoms to be \SI{2.2}{\milli\electronvolt}. If GW190425 is a DBH merger from a scenario similar to those we have studied here, additional small black holes would likely be observed by gravitational-wave detectors in the near future. In the future, the presence of an electromagnetic counterpart or the measurement of tidal deformability could each rule out the binary black hole scenario for events like GW190425. However, the observation of a population of sub-solar mass black holes would be clear evidence of a population of black holes that are distinct from standard formation mechanisms. This would need to be further studied and put into context of broader cosmological observables to determine the support for different scenarios such as the collapse of atomic dark matter that we discuss here, and others like primordial black holes, dark matter induced collapse of neutron stars, etc.
Assuming none of the LVC-detected events originate from dissipative dark matter allows a strong constraint on the fraction of dark matter in compact objects. We present the two scenarios of a DBH detection and the DBH null result mutually exclusively to illustrate concisely the information we can infer. This is a novel approach to constrain dark matter self-interactions, complimentary to studies of structure on the scale of galaxies and above. Especially if future gravitational-wave searches in the sub-solar mass regime do not find any compact object mergers, gravitational-wave data could be a means to rule out a significant range of dissipative dark matter models.
| {
"redpajama_set_name": "RedPajamaArXiv"
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{"url":"https:\/\/deepai.org\/publication\/pomset-logic-a-logical-and-grammatical-alternative-to-the-lambek-calculus","text":"# Pomset logic: a logical and grammatical alternative to the Lambek calculus\n\nThirty years ago, I introduced a non commutative variant of classical linear logic, called POMSET LOGIC, issued from a particular denotational semantics or categorical interpretation of linear logic known as coherence spaces. In addition to the multiplicative connectives of linear logic, pomset logic includes a non-commutative connective, \"<\" called BEFORE, which is associative and self-dual: (A<B)^=A^ < B^ (observe that there is no swapping), and pomset logic handles Partially Ordered MultiSETs of formulas. This classical calculus enjoys a proof net calculus, cut-elimination, denotational semantics, but had no sequent calculus, despite my many attempts and the study of closely related deductive systems like the calculus of structures. At the same period, Alain Lecomte introduced me to Lambek calculus and grammars. We defined a grammatical formalism based on pomset logic, with partial proof nets as the deductive systems for parsing-as-deduction, with a lexicon mapping words to partial proof nets. The study of pomset logic and of its grammatical applications has been out of the limelight for several years, in part because computational linguists were not too keen on proof nets. However, recently Sergey Slavnov found a sequent calculus for pomset logic, and reopened the study of pomset logic. In this paper we shall present pomset logic including both published and unpublished material. Just as for Lambek calculus, Pomset logic also is a non commutative variant of linear logic \u2014 although Lambek calculus appeared 30 years before linear logic ! \u2014 and as in Lambek calculus it may be used as a grammar. Apart from this the two calculi are quite different, but perhaps the algebraic presentation we give here, with terms and the semantic correctness criterion, is closer to Lambek's view.\n\n## Authors\n\n\u2022 4 publications\n\u2022 ### Proof nets for the Displacement calculus\n\nWe present a proof net calculus for the Displacement calculus and show i...\n06\/06\/2016 \u2219 by Richard Moot, et al. \u2219 0\n\n\u2022 ### The Logic for a Mildly Context-Sensitive Fragment of the Lambek-Grishin Calculus\n\nWhile context-free grammars are characterized by a simple proof-theoreti...\n01\/10\/2021 \u2219 by Hiroyoshi Komatsu, et al. \u2219 0\n\n\u2022 ### Sequentialization for full N-Graphs via sub-N-Graphs\n\nSince proof-nets for MLL- were introduced by Girard (1987), several stud...\n03\/01\/2018 \u2219 by Ruan V. B. Carvalho, et al. \u2219 0\n\n\u2022 ### Provability in BI's Sequent Calculus is Decidable\n\nThe logic of Bunched Implications (BI) combines both additive and multip...\n03\/03\/2021 \u2219 by Alexander Gheorghiu, et al. \u2219 0\n\n\u2022 ### On the Unity of Logic: a Sequential, Unpolarized Approach\n\nThe present work aims to give a unity of logic via standard sequential, ...\n12\/16\/2019 \u2219 by Norihiro Yamada, et al. \u2219 0\n\n\u2022 ### Computational Aspects of the Calculus of Structure\n\nLogic is the science of correct inferences and a logical system is a too...\n01\/21\/2013 \u2219 by M\u00e1rio S. Alvim, et al. \u2219 0\n\n\u2022 ### A theory of linear typings as flows on 3-valent graphs\n\nBuilding on recently established enumerative connections between lambda ...\n04\/27\/2018 \u2219 by Noam Zeilberger, et al. \u2219 0\n\n##### This week in AI\n\nGet the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.\n\n## 1 Presentation\n\nLambek\u2019s syntactic calculus as Lambek [16] used to call his logic, was in keeping with his preference for algebra (confirmed with his move from categorial grammars to pregroup grammars, which are not a logical system.) Up to the invention of linear logic in the late 80s, Lambek calculus was a rather isolated logical system, despite some study of frame semantics, which are typical of substructural logics.\n\nLinear logic [7] arose from the study of the denotational semantics of system F, itself arising from the study of ordinals. [6] For interpreting systems F (second order lambda calculus) with variable types, one needed to refine the categorical interpretation of simply typed lambda calculus with Cartesian Closed Categories. In order to quantify over types Girard considered the category of coherence spaces (first called qualitative domains) with stable maps (which preserve directed joins and pullbacks). A finer study of coherence spaces led Girard to discompose the arrow type construction in to two steps: one is to contract several object of type into one (modality\/exponential !) and the other one being linear implication (noted ) which rather corresponds to a change of state than to a consequence relation.\n\nLinear logic was first viewed as a proof system (sequent calculus or proof nets) which is well interpreted by coherence spaces. The initial article [7] also included the definition of phase semantics, that resembles frame semantics developed for the Lambek calculus. It was not long before the connection between linear logic and Lambek calculus was found: after some early remarks by Girard, Yetter [50] observed the connection at the semantic level, while Abrusci [1] explored the syntactic, proof theoretical connection, while [34] explored proof nets and completed the insight of [46]. Basically Lambek calculus is non commutative intuitionistic multiplicative logic, the order between the two restrictions, intuitionistic and non commutative, being independent. An important remark, that I discussed with Lamarche in [15], says that non commutativity requires linearity in order to get a proper logical calculus.\n\nAround 1988, my PhD advisor Jean-Yves Girard pointed to my attention a binary non commutative connective in coherence spaces. In coherence spaces, this connective has intriguing properties:\n\n\u2022 is self dual , without swapping the two components \u2014 by we mean that there is a pair of canonical invertible linear maps between and .\n\n\u2022 is non commutative\n\n\u2022 is associative ;\n\n\u2022 it lies in between the commutative conjunction and disjunction there is a canonical linear map from to an one from to 111Coherence spaces validate the mix rule ;\n\nI designed a proof net calculus with this connective, in which a sequent, that is the conclusion of a proof, is a partially ordered multiset of formulas. This proof net calculus enjoys cut-elimination and a sound and faithful (coherence) semantics 222In the sense that having an interpretation is the same as being syntactically correct cf. theorem 8 preserved under cut elimination. I proposed a version of sequent calculus that easily translates into those proof nets and enjoys cut-elimination as well. [32] However despite many attempts by me and others (Sylvain Pogodalla, Lutz Stra\u00dfburger) over many years we did not find a sequent calculus that would be complete w.r.t. the proof nets. Later on, Alessio Guglielmi, soon joined by Lutz Stra\u00dfburger, designed the calculus of structures, a term calculus more flexible than sequent calculus (deep inference) with the before connective [9, 10, 11], a system that is quite close to dicograph rewriting [40, 41], described in section 3.2. They tried to prove that one of their systems called BV was equivalent to pomset logic and they did not succeed. As a reviewer of my habilitation [42] Lambek wrote:\n\nHe constructs a model of linear logic using graphs, which is new to me. His most original contribution is probably the new binary connective which he has added to his non commutative version of linear logic, although I did not find where it is treated in the sequent calculus. (J. Lambek, Dec. 3, 2001)\n\nI deliberately omitted my work on sequent calculus in my habilitation manuscript, because none of the sequent calculi I experimented with was complete w.r.t. pomset proof nets which are \u201dperfect\u201d, i.e. enjoy all the expected proof theoretical properties. In addition, by that time, I did not yet have a counter example to my proposal of a sequent calculus, the one in picture 5 of section 6 was found ten years later with Lutz Stra\u00dfburger.\n\nHowever, very recently, Sergey Slavnov found a sequent calculus that is complete w.r.t. pomset proof nets. [48] The structure of the decorated sequents that Slavnov uses is rather complex 333A decorated sequent according to Slavnov is a multiset of pomset formulas with binary relations between sequences of length of formulas from ; those relations are such that whenever the two sequences and have no common elements and entails for any permutation of \u2013 those relations correspond top the existence of disjoint paths in the proof nets from to . and the connective is viewed as the identification of two dual connectives one being more like a and the other more like a . As this work is not mine I shall not say much about it, but Slavnov\u2019s work really sheds new light on pomset logic. Given the complexity of this sequent calculus it is pleasant to have some simple sequent calculus and a rewriting system for describing most useful proof nets e.g. the one used for grammatical purposes.\n\nPomset logic and the Lambek calculus systems share some properties:\n\n\u2022 They both are linear calculi;\n\n\u2022 They both handle non commutative connective(s) and structured sequents;\n\n\u2022 They both have a sequent calculus;\n\n\u2022 They both enjoy cut-elimination;\n\n\u2022 They both have a complete sequent calculus (regarding pomset logic the complete sequent calculus is quite new);\n\n\u2022 They both can be used as a grammatical system.\n\nHowever Lambek calculus and pomset logic are quite different in many respects:\n\n\u2022 Lambek calculus is naturally an intuitionistic calculus while pomset logic is naturally a classical calculus \u2014 although in both cases variants of the other kind can be defined.\n\n\u2022 Lambek calculus is a restriction of the usual multiplicative linear logic according to which the connectives are no longer commutative, while pomset logic is an extension of usual commutative multiplicative linear logic with a non commutative connective.\n\n\u2022 Lambek calculus deals with totally ordered multisets of hypotheses while pomset logic deals with partially ordered multisets of formulas. As grammatical systems, pomset logic allows relatively free word order, while Lambek calculus only deals with linear word orders.\n\n\u2022 Lambek calculus has an elegant truth-value interpretation within the subsets of a monoid (frame semantics, phase semantics), while there is not such a notion for pomset logic.\n\n\u2022 Lambek calculus has no simple concrete interpretation of proofs up to cut elimination (denotational semantics) while coherence semantics faithfully interprets the proofs of pomset logic.\n\nThis list shows that those two comparable systems also have many differences. However, the presentation of Pomset logic provided by the present article make Lambek calculus and pomset logic rather close on an abstract level. As he told many of us, Lambek did not like standard graphical or geometrical presentation of linear logic like proof nets. He told me several times that moving from geometry to algebra has been a great progress in mathematics and solved many issues, notably in geometry, and that proof net study was going the other way round. I guess this is related to what he said about theorem 8.\n\nIt seems that this ingenious argument avoids the complicated long trip condition of Girard. It constitutes a significant original contribution to the subject. (J. Lambek,Dec 3 2001)\n\nThis paper is a mix (!) of easy to access published work, [5, 34, 4, 37, 38, 35, 43] research reports and more confidential publications [32, 31, 5, 18, 34, 31, 33, 18, 19, 15, 20, 40, 41, 39, 42, 30] unpublished material between 1990 and 2020, that are all presented in the same and rather new unified perspective; the presented material can be divided into three topics:\n\nproof nets\n\nhandsome proof nets both for MLL Lambek calculus and pomset logic, and other work on proof nets [5, 15, 34],\n\ncombinatorics\n\n(di)cographs and sp\u00a0orders [31, 32, 35, 4, 40, 41, 39, 42, 43, 42, 43, 30],\n\ncoherence semantics\n\n[32, 33, 38, 42],\n\ngrammatical applications\n\nof pomset logic to computational linguistics [18, 19, 20, 40, 41, 42].\n\nThe contents of the present article is divided into six sections as follows:\n\n1. We first present results on series parallel partial orders, cographs and dicographs that subsumes those two notions and present dicograph either as sp\u00a0pomset of formulas or as dicographs of atoms, and explain the guidelines for finding a sequent calculus. This combinatorial part is a prerequisite for the subsequent sections.\n\n2. We then present proofs in an algebraic manner, with deduction rules as term rewriting.\n\n3. Proof nets without links, the so called handsome proof nets, are presented as well as the cut elimination for them.\n\n4. The semantics of proof nets, preserved under cut elimination and equivalent to their syntactic correctness is then presented.\n\n5. Then the sequentialisation \u201dthe quest\u201d of a complete sequent calculus is discussed and we provide an example of a proof net that does not derive from any simple sequent calculus.\n\n6. Finally we explain how one can design grammars by associating words with partial proof nets of pomset logic.\n\n## 2 Structured sequents as dicographs of formulas\n\n### 2.1 Looking for structured sequents\n\nThe formulas we consider are defined from atoms (propositional variables or their negation) by means of the usual commutative multiplicative connectives and together with the new non commutative connective (before)\u2014 the three of them are associative.\n\nIt is assumed that formulas are always in negative normal form: negation only apply to propositional variables; this is possible and standard when negation is involutive and satisfies the De Morgan laws:\n\n (A\u22a5)\u22a5=A(AB)\u22a5=(A\u22a5\u2297B\u22a5)(A\n\nWe want to deal with series parallel partial orders of formulas: corresponds to parallel composition of partial orders (disjoint union) and corresponds to the series composition of partial orders (every formula in the first partial order is lesser than every formula in the second partial order ). Thus, a formula written with and corresponds to a partial order between its atoms. Unsurprisingly, we firstly need to study a bit partial orders defined with series and parallel composition.\n\nHowever, what about the multiplciative, conjunction namely the connecitve? It is commutative, but it is distinct from . In order to include in this view, where formulas are binary relations on their atoms, we consider, the more general class of irreflexive binary relations that are obtained by parallel composition, series composition and symmetric series compositions, which basically consists in adding the relations of and the ones of . The relations that are defined using , , are called directed cographs or dicographs for short.\n\nIf only and are used the relations obtained are cographs. They have already been quite useful for studying MLL, see e.g. theorem 4 thereafter.\n\nBefore defining pomset logic, we need a presentation of directed cographs.\n\n### 2.2 Directed cographs or dicographs\n\nAn irreflexive relation may be viewed as a graph with vertices and with both directed edges and undirected edges but without loops. Given an irreflexive relation let us call its directed part (its arcs) and its symmetric part (its edges) . It is convenient to note for the edge or pair of arcs in and to denote for in when is not in .\n\nWe consider the class of dicographs, dicographs for short, which is the smallest class of binary irreflexive relations containing the empty relation on the singleton sets and closed under the following operations defined on two cographs with disjoint domains and yielding a binary relation on\n\n\u2022 symmetric series composition\n\n\u2022 directed series composition\n\n\u2022 parallel composition\n\nWhenever there are no directed edges (a.k.a. arcs) the dicograph is a cograph ( is not used). Cographs are characterised by the absence of as many people (re)discovered including us [35], see e.g. [14].\n\nWhenever there are only directed edges (a.k.a. arcs) the dicograph is an sp\u00a0order ( is not used) \u2014 as rediscovered in [32], see e.g. [24]\n\nLet us call this class the class of dicographs.\n\nWe characterised the class of directed dicographs as follows [4, 40, 41]:\n\n###### Theorem 1\n\nAn irreflexive binary relation is a dicographs if and only if:\n\n\u2022 is N-free ( is an sp\u00a0order).\n\n\u2022 is -free ( is a cograph).\n\n\u2022 Weak transitivity:\nforall in the domain of\nif and then and\nif and then\n\nA dicograph can be described with a term in which each element of the domain appears exactly once. This term is written with the three binary operators , and and for a given dicograph this term is unique up to the associativity of the three operators, and to the commutativity of the first two, namely and .\n\nThe dual of a dicograph on is defined as follows: points are given a superscript, and or , , , , .\n\nTwo points and of are said to be equivalent w.r.t. a relation whenever for all with one as and . There are three kinds of equivalent points:\n\n\u2022 Two points and in a dicograph are said to be freely equivalent in a dicograph (notation ) whenever the term can be written (using associativity of and and the commutativity of ) . In other words, , , .\n\n\u2022 Two points and in a dicograph are said to be arc equivalent in a dicograph (notation ) whenever the term can be written (using associativity of , and and the commutativity of and ) . In other words, , , .\n\n\u2022 Two points and in a dicograph are said to be edge equivalent in a dicograph (notation ) whenever the term can be written (using associativity of and and the commutativity of ) . In other words, , , .\n\n### 2.3 Dicograph inclusion and (un)folding\n\nThe order on a multiset of formulas, can be viewed as a set of contraints. Hence, when a sequent is derivable with an sp\u00a0order it is also derivable with a sub sp\u00a0order \u2014 we named this structural rule entropy [32]. Most of the transformations of a dicograph into a smaller (w.r.t. inclusion) dicograph preserve provability. Hence we need to characterise the inclusion of a dicograph into another and possibly to view the inclusion as a computational process that can be performed step by step. Fortunately,in [4] we characterised the inclusion of a dicograph in another dicograph by a rewriting relation:\n\n###### Theorem 2\n\nA dicograph is included into a dicograph if and only if the term rewrites to the term using the rules of figure 1 \u2014 up to the associativity of , and , and to the commutativity of and .\n\n### 2.4 Folding and unfolding pomset logic sequents\n\nA structured sequent of pomset logic (resp. of MLL) is a multiset of formulas of pomset logic (resp. of MLL) with the connectives endowed with a dicograph.\n\nOn such sequents one may define \u201cfolding\u201d and \u201cunfolding\u201d which transform a dicograph of formulas into another dicograph of formulas by combining two equivalent formulas and of the dicograph into one formula (folding) or by splitting one compound formula into its two immediate subformulas and with and equivalent in the dicograph. More formally:\n\nFolding\n\nGiven a multiset of formulas endowed with a dicograph ,\n\nif in rewrite into \u2014 in the multiset, the two formulas and have been replaced with a single .\n\nif in rewrite into \u2014 in the multiset, the two formulas and have been replaced with a single formula .\n\nif in rewrite into \u2014 in the multiset, the two formulas and have been replaced with a single formula .\n\nUnfolding\n\nis the opposite:\n\nturn into \u2014 in the multiset, the formula has been replaced with two formulas and with\n\nturn into \u2014 in the multiset, the formula has been replaced with two formulas and with\n\nturn into \u2014 in the multiset, the formula has been replaced with two formulas and with\n\n### 2.5 A sequent calculus attempt with sp\u00a0pomset of formulas\n\nIf we want to extend multiplicative linear logic with a non commutative multiplicative self dual connective (rather than to restrict existing connective to be non commutative), and want to handle partially ordered multisets of formulas, with corresponding to \u201dthe subformula is smaller than the subformula \u201d.\n\nThat way one may think of an order on computations: a cut between and reduces to two smaller cuts and with the cut on being prior to the cut on , while a cut between and reduces to two smaller cuts and with the cut on being in parallel with the cut on . This makes sense when linear logic proofs are viewed as programs and cut-elimination as computation.\n\nDoing so one may obtain a sequent calculus using partially ordered multisets of formulas as in [32] but if one wants a sequent with several conclusions that are partially ordered to be equivalent to a sequent with a unique conclusion, one has to only consider sp\u00a0partial orders of formulas, as defined in subsection 2.2 with parallel composition noted and series composition noted .\n\nIf we want all formulas in the sequent to be ordered the calculus should handle right handed sequents i.e. be classical.444Lambek calculus is intuitionistic and when it is turned into a classical systems, formulas are endowed with a cyclic order,[50, 1, 15], i.e. a ternary relation which is not an order and which is quite complicated when partial \u2014 see the \u201dseaweeds\u201d in [3].\n\nAs seen above, we can represent this sp\u00a0partially ordered multiset of formulas endowed with an sp\u00a0order by an sp\u00a0term whose points are the formulas and such a term is unique up to the commutativity of and the associativity of and .\n\nWe know how the tensor rule and the cut rule behave w.r.t. formulas. The only aspect that deserves some tuning, is the order on the formulas after applying those binary rules. Our choice is guided by two independent criteria:\n\n1. The resulting partial order should be an sp\u00a0order.\n\n2. This sequent calculus should enjoy cut elimination:\n\n\u2022 If there is a cut between and with coming immediately from a rule from and and coming immediately from a rule from one should be able to locally turn those rules into two consecutive cuts, one between and and then one with .\n\n\u2022 If there is a cut between and with coming immediately from a rule from and coming immediately from a rule from one should be able to locally turn those rules into two consecutive cuts, one between and and then one with .\n\nA simple sequent calculus is provided in figure 2. 555An alternative solution to have on sp\u00a0orders is to have rule between two minimum in their order component, and to have cut between two formulas one of which is isolated in its ordered sequent. This alternative is trickier and up to our recent investigation does not enjoy better properties than the version given above in figure 2\n\nA property of this calculus is that cuts can be part of the order on conclusions. Indeed, one may define a cut as a formula that never is used as a premise of a logical rules. That way, the order can be viewed as an order on computation. A cut reduces into two cuts that are : , while cut reduces into two cuts that are : \u2014 beware that is a cut and that a operation on dicographs is different from the connective, which combines formulas. When one of the two premises of the cut is an axiom, this axiom and the cut are simply removed from the proof as usual, and this is possible because cut only applies when the two premises are isolated in the sp\u00a0order. An alternative proof of cut elimination can be obtained from the cut elimination theorem for proof nets with links or without to be defined in sections 3.2 or 7.1, as established in [32, 37, 41] \u2014 because the reduction of a proof net coming from a sequent calculus proof also comes from a sequent calculus proof. Thus one has:\n\n###### Theorem 3\n\nSequent calculus of figure 2 enjoys cut-elimination.\n\n## 3 Pomset logic and MLL as (di)cograph rewriting:\n\nBefore we define a deductive system for pomset logic, let us revisit (as we did in [39, 43]) the deductive system of Multiplicative Linear Logic (MLL). Those results are highly inspired from proof nets, but once they are established they can be presented before proof nets are defined.\n\nIn this section a sequent is simply a dicograph of atoms which as explained above can be viewed using folding of section 2.4 as a dicograph of formulas or as an sp\u00a0order between formulas depending on how many folding transformations and which one are performed.\n\nRegarding, multiplicative linear logic (MLL), observe that is the largest cograph or even the largest dicograph w.r.t. inclusion that could be derived in MLL \u2014 indeed there cannot be any tensor link nor any before connection between the two dual occurrences of atoms issued from the same axiom link, for two reasons: first in sequent calculus they cannot lie in different sequents and therefore they cannot be conjoined by or ; second, as explained in subsection 3.2, in the proof net this would result in a prohibited (ae) cycle. Observe that , the largest derivable cograph in MLL is acutally derivable in MLL, hence in any extension of MLL:\n\n \\prooftree\\prooftree\\prooftree\\prooftree\\prooftree\u22a2a1,a1\u22a5\\justifies\u22a2AX1:a1a1\u22a5\\using\\prooftree\u22a2a2,a2\u22a5\\justifies\u22a2a2a2\u22a5\\using\\justifies\u22a2AX2:\u22971\u2264i\u22642(aiai\u22a5)\\using\u2297\\prooftree\u22a2a3,a3\u22a5\\justifies\u22a2a3a3\u22a5\\using\\justifies\u22a2AX3:\u22971\u2264i\u22643(aiai\u22a5)\\using\u2297\\prooftree\u22a2a4,a4\u22a5\\justifies\u22a2a4a4\u22a5\\using\\justifies\u22a2AX4:\u22971\u2264i\u22644(aiai\u22a5)\u22ef\\using\u2297\\justifies\u22a2AX5:\u22ef\\using\u2297\n\n### 3.1 Standard multiplicative linear logic as cograph rewriting\n\nIn [39] we considered an alternative way to derive theorems of usual multiplicative linear logic MLL, by considering a formula as a binary relation, and more precisely as a cograph over its atoms, by viewing as and as . As there is no connective in linear logic the series composition is not used, and there is no sp\u00a0order on conclusions.\n\nBecause of the chapeau of the present section 3 any sequent of MLL can be viewed is a cograph on atoms that is included into . Because of theorem 1, rewrites to using the rules of figure 1 that concern and i.e. , and . Observe that when viewed as a linear implication (considering the rules involving those two connectives), the first line is an incorrect linear implication, while is derivable in MLL and in MLL+MIX where the rule MIX is the one studied in [5], which also is derivable with :\n\n \\prooftree\u22a2\u0393\u22a2\u0394\\justifies\u22a2\u0393,\u0394\\usingMIX\n\nActually all tautologies of multiplicative linear logic MLL can be derived using from an axiom , and all tautologies of linear logic enriched with the MIX rule, MLL+MIX, can be derived by and (MIX).\n\nThus, we can define a proof system gMLL for MLL working with sequents as cographs of atoms as follows. Axioms are : (the two dual atoms are connected by an edge in a different relation called for axioms). There is just one deduction rule presented as a rewrite rule (up to commutativity and associativity): .\n\nLet us call this deductive system gMLL (g for graph), then [39, 43] established that cograph rewriting is an alternative proof systems to MLL and MLL+MIX.\n\n###### Theorem 4\n\nMLL proves a sequent with atoms if and only if gMLL proves the unfolding of (the cograph of atoms corresponding to , that is the of the unforging of each formula in ), i.e. rewrites to using .\n\nMLL+MIX proves a sequent with atoms if and only if gMLL+mix proves the unfolding of , i.e. rewrites to using and .\n\nProof.\u2003 Easy induction on sequent calculus proofs see e.g. [39, 43]. A direct proof by Stra\u00dfbruger can be found in [49].\n\nThe interesting thing is that all proofs can be transformed that way. Unfortunately it if much easier with an inductive definition of proofs like sequent calculus, and, unfortunately for pomset logic, it is hard to prove it directly on a non inductive notion of proof like proof nets.\n\n###### Proposition 1\n\nThe calculi gMLL and gMLL+mix can safely be extended to structured sequents of formulas of MLL (not just atoms), i.e. cographs of MLL formulas with the rules of folding and unfolding with the same results.\n\nProof.\u2003 This is just an easy remark, based on proof nets, which can be viewed as a consequence subsection 7.1.\n\n### 3.2 Pomset logic as a calculus of dicographs: dicog-RS\n\nUsing the above results for MLL suggests defining a deductive system for pomset logic in the same manner. All rewriting rules are correct but : they correspond to proof nets or to sequent calculus derivations (with the sp-pomset sequent calculus of figure 2) and to canonical linear maps in coherence spaces. So it suggest that a rewriting system defined as gMLL+mix in the previous section (but with dicographs instead of cographs) might yield all the proofs we want e.g. all correct proof nets.\n\nAxioms\n\nis a tautology.\n\nRules\n\nWhenever a dicograph of atoms which is a tautology rewrites to a dicograph (hence with the sames atoms) by any of the 10 rules , , , , , , , , , of figure 1 \u2014 i.e. all rules of figure 1 but .\n\nUnfortunately, proving that all proof nets are derivable by rewriting is not simpler than proving that they can be obtained from the sequent calculus. This would entail the equivalence of pomset logic with BV calculus as discussed in [12].\n\n### 3.3 Cuts\n\nWhat about the cut rule? For such logical systems based on rewriting systems like gMLL(+MIX), of the dicog-RS\u00a0view of pomset logic, which does not work with \u201dlogical rules\u201d in the standard sense, there are no binary rules that would combine a and a . So the only view of a cut is simply a tensor which never is inserted inside a formula. A dicograph may be written . Observe that contains the duals of the atoms in , because it is a cut, and that there is one for each , because they are the atoms of minus the well balanced atoms of and , one cannot say that the pair corresponds to some from \u2014 necessarily for some pair one is among the and and one is among the and .\n\nHowever one cannot say that a proof of dicog-RS, i.e. a sequence of derivations yielding a dicograph with cuts (i.e. with a sub dicograph term ) may be turned into a dicog-RS\u00a0derivation whose final dicographs is restricted to the atoms that are neither in not in . Indeed the atoms in and vanish during the process and none of the rewrite rules is able to do so \u2014 furthermore if one looks at step by step cut elimination, it precisely uses the prohibited rewriting rule !\n\nWe shall see later that in fact cut elimination holds for proof nets that are dicographs of atoms but without any inductive notion of derivation.\n\n## 4 Proof nets\n\nThis section presents proof structures and nets (the correct proof structures), in an abstract and algebraic manner, without links nor trip conditions: such proof strctures and nets are called handsome proof structures and nets. Basically proof nets consists in a dicograph of atoms representing the conclusion formula, and axioms that are disjoint pairs of dual atoms constituting a partition of the atoms of . The proof net can be viewed as an edge bi-coloured graph: the dicograph is represented by arcs and edges (Red and Regular in the pictures), while the axioms (Blue and Bold in the picture). In such a setting, the correctness criterion expresses some kind of orthogonality between and . A proof net can also be viewed as a term, axioms being denoted by indices used exactly twice on dual atoms.\n\n### 4.1 Handsome pomset proof nets\n\nIn fact, proof nets have (almost) been defined above!\n\nA pomset logic handsome proof structure or dicog-PN\u00a0is a dicograph over a (multi)set of atoms, , i.e. propositional letters and their duals. it is fairly possible that two atoms have the same name, i.e. it is a multiset of atoms. Let us call the binary relation or simply using the notations of the previous section 2.2; observe that no two edges are incident, and that each point is incident to exactly one edge in : the edges constitute a perfect matching of the whole graph with both edges and edges and arcs.\n\nGiven two proof structures and whose atoms and axioms are the same, and whose conclusion formulas and only differ because of the associativity of and the commutativity of , the proof structures and are equal \u2014 while in proof structures with links they would be different.\n\n###### Correctness criterion 1\n\nA handsome proof structure is said to be a proof net whenever every elementary circuit (directed cycle) of alternating edges in and in contains a chord \u2014 an edge or arc connecting two points of the circuit but not itself nor its reverse in the circuit. In short, every ae\u00a0circuit contains a chord. Observe that this chord cannot be in , hence it is in , and it can either be an arc or an edge.\n\n###### Theorem 5 (Nguy\u00ean)\n\nRecently it was established that checking whether a proof structure satisfies the above correctness criterion is coNP complete [25].\n\n###### Theorem 6\n\nGiven a proof net if (so ) using rewriting rules of Figure 1 except then is a proof net as well, i.e. all the rewrite rule preserve the correctness criterion on page 1.\n\nProof.\u2003 See [40, 41].\n\nIt is easily seen that in general does not preserve correctness:\n\n. Using , rewrites to\n, and the proof net contains the chordless \u00e6\u00a0circuit .\n\nObserve that it does not mean that every correct proof net with axioms can be obtained from by the allowed rewrite rules (all but ) where is . Indeed, since it is known that but one cannot tell that is not used. Indeed, as shown above does not preserve correctness but it may happen:\n\nAs indicated in section 2.2 we write for the edge or par of opposite arcs\n\nis correct, and using it rewrites to which is correct as well.\n\n### 4.2 Cut and cut-elimination\n\nWhat about the cut rule? This calculus has no rules in the standard sense, in particular no binary rules that would combine a and a . A cut is a tensor which never is inserted inside a formula.\n\nSo a cut in this setting simply is a symmetric series composition in a dicograph whose form is . Assume the atoms of are so atoms of are . Cut-elimination consist in suppressing all edges and arcs between two atoms of , all edges and arcs between two atoms of , and all edges with \u2014 so the only edges incident to are (call those edges atomic cuts) and with neither in not in . If, in this graph, an atom is in the relation with an in , then the result of cut elimination is the closest point not in nor in reached by an alternating sequence of -edges and elementary cuts starting from \u2013 observed that this point is necessarily named , that we call its cut neighbour. To obtain the proof resulting from cut-elimination suppress all the atoms of and as well as the incident arcs and edges and connect every atom to its cut neighbour with a edge.\n\n###### Theorem 7\n\nCut elimination preserves the correctness criterion of dicog-PN\u00a0proof nets and consequently the f dicog-PN\u00a0proof nets enjoy cut-elimination.\n\nProof.\u2003 The preservation of the absence of chordless \u00e6\u00a0circuit during cut elimination is proved in [40, 41].\n\n### 4.3 From sequent calculus and rewrite proofs to dicog-PN\n\nProofs of the sequent calculus given in figure 2 are easy turn into a dicog-PN\u00a0proof net inductively. Such a derivation starts with axioms as it is well known, and in any kind of multiplicative linear logic the atoms and that can be traced from the axiom that introduced them to the conclusion sequent, which, after some unfolding can be viewed as a dicograph of atoms . The dicog-PN\u00a0proof structure corresponding to the sequent calculus proof simply is , and fortunately is a correct proof net.\n\n###### Proposition 2\n\nA proof of sequent calculus corresponds to a dicog-PN\u00a0i.e. to a handsome proof structure without chordless alternate elementary path, i.e. into a handsome proof net.\n\nProof.\u2003 By induction on the proof, we showed in shown in [40, 41] that the neither the rules nor the the unfolding can introduce a chordless ae\u00a0cycle.\n\nThe above result also yield cut elimination for the sequent calculus. Indeed, proof nets obtained by cut-elimination from a proof net issued from the sequent calculus also are issued from the sequent calculus.\n\nThe derivation by dicograph rewriting dicog-RS\u00a0also only yield correct proof structures.\n\n###### Proposition 3\n\nAny proof obtained by rewriting from yields a handsome proof structure without chordless alternate elementary path, i.e. into a dicog-PN.\n\nProof.\u2003 Observe that satisfies the criterion, so because of theorem 6, the result is clear.\n\n## 5 Denotational semantics of pomset logic within coherence spaces\n\nDenotational semantics or categorical interpretation of a logic is the interpretation of a logic in such a way that a proof of is interpreted as a morphism from an object to an object in such a way that whenever reduces to by (the transitive closure) of -reduction or cut-elimination. A proof of (when there is no ) is simply interpreted as a morphism from the terminal object to . More details can be found in [17, 8].\n\nOnce the interpretation of propositional variables is defined, the interpretation of complex formulas is defined by induction on the complexity of the formula. The set of morphisms from to is in bijective correspondence with an object written . Morphisms are defined by induction on the proofs and one has to check that the interpretations of a proof before and after one step of cut elimination is unchanged.\n\nFor intuitionistic logic, the category is cartesian closed, and for classical logic, at least simply, it is impossible666The fact that cartesian closed categories with involutive negation have at most one morphim between any two object is known as Joyal argument (see e.g. [17]); however there are complicated solutions like Selinger\u2019s control categories [47] for classical deductive systems that \u201dcontrol\u201d the non determinism of classical cut elimination,like Parigot\u2019s calculus, [26].. Regarding linear logic, a categorical interpetation takes place in a monoidal closed category (with monads for the exponentials of linear logic).\n\n### 5.1 Coherence spaces\n\nThe category of coherence spaces is a concrete category: objects are (countable) sets endowed with a binary relation, and morphimms are linear maps. It interprets the proofs up to cut-elimination or reduction initially propositional intuitionistic logic and propositional linear logic (possibly quantified). Actually, coherence spaces are tightly related to linear logic: indeed, linear logic arose from this particular semantics, invented to model second order lambda calculus i.e. quantified propositional intuitionistic logic [6]. Coherence spaces are themselves inspired from the categorical work on ordinals by Jean-Yves Girard; they are the binary qualitative domains.\n\nA coherence space is a set (possibly infinite) called the web of whose elements are called tokens, endowed with a binary reflexive and symmetric relation called coherence on noted or simply when is clear.\n\nThe following notations are common and useful:\n\niff and\niff or\niff and\n\nA proof of is to be interpreted by a clique of the corresponding coherence spaces , a cliques being a set of pairwise coherent tokens in \u2014 we write for and for all . Observe that forall , if then . A linear morphism from to is a morphism mapping cliques of to cliques of such that:\n\n\u2022 Let be a family of pairwise compatible cliques that is to say then .777The morphism is said to be stable when holds more generally for the union of a directed family of cliques of , i.e. .\n\n\u2022 if then .\n\nDue to the removal of structural rules, linear logic has two kinds of conjunction:\n\n \\prooftree\u22a2\u0393,A\u22a2\u0394,B\\justifies\u0393,\u0394,A\u2297B\\using\u2297\\prooftree\u22a2\u0393,A\u22a2\u0393,B\\justifies\u0393,A&B\\using&\n\nThose two rules are equivalent when contraction and weakening are allowed. The multiplicatives (contexts are split, above) and the additives (contexts are duplicated, above). Regarding denotational semantics, the web of the coherence space associated with a formula with a multiplicative connective is the Cartesian product of the webs of and \u2014 while it is the disjoint union of the webs of and when is additive.\n\nNegation is a unary connective which is both multiplicative and additive: and iff\n\nOne may wonder how many binary multiplicatives there are, i.e. how many different coherence relations one may define on from the coherence relations on and on .\n\nWe can limit ourselves to the ones that are covariant functors in both and \u2014 indeed there is a negation, hence a contravariant connective in is a covariant connective in . Hence when both components are so are the two couples, and when they are both coherent, so are the two couples.\n\nTo define a multiplicative connective, is to define when in function of and , so to fill a nine cell table \u2014 however if is assumed to be covariant in both its argument, seven out of the nine cells are filled.\n\n A\u2217B\\sincoh=\\scoh\\sincoh\\sincoh\\sincohNE?=\\sincoh=\\scoh\\scohSW?\\scoh\\scoh\n\nIf one wants to be commutative, there are only two possibilities, namely () and ().\n\nHowever if we don\u2019t ask for the connective to be commutative we have a third connective (and actually a fourth connective which is )\n\n AB\\sincoh=\\scoh\\sincoh\\sincoh\\sincoh\\scoh=\\sincoh=\\scoh\\scoh\\sincoh\\scoh\\scoh\n\nThis connective generalises to partial orders. Assume we have an sp\u00a0order on the formulas can be defined with and \u2014 two tuples and of the web are strictly coherent whenever .\n\nLinear implication, which can be defined as is :","date":"2021-11-28 06:38:22","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\": 0.8947288990020752, \"perplexity\": 1003.162074646045}, \"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\/1637964358469.34\/warc\/CC-MAIN-20211128043743-20211128073743-00046.warc.gz\"}"} | null | null |
Q: Error while using Toast.makeToast in non activity class using kotlin I am building a chatting application in android using Kotlin. I want to long press on a message to copy it on the clipboard. This function is working fine but I am unable to show a toast due to some error. Here is my code.
class ChatFromItem(val text: String, val user: User): Item<ViewHolder>() {
override fun bind(viewHolder: ViewHolder, position: Int) {
viewHolder.itemView.textView_from_row.text = text
viewHolder.itemView.textView_from_row.setOnLongClickListener {
Toast.makeText(this, "Message copied", Toast.LENGTH_LONG).show()
val clipboard = it.context.getSystemService(Context.CLIPBOARD_SERVICE) as ClipboardManager
val myClip = ClipData.newPlainText("label", text)
clipboard.primaryClip = myClip
true
}
val uri = user.profileImageUrl
val target = viewHolder.itemView.imageView_chat_from_row
Picasso.get().load(uri).into(target)
}
override fun getLayout(): Int {
return R.layout.chat_from_row
}
}
Some people might get confused as of why there is a 'true' written at the very bottom of .setOnLongClickListener. Without the toast statement the rest of the code is working fine. I have tested it many times.
I am including an image containing the error message that android studio is showing me.
Thank you in advance.
A: You need to pass context or get it from a view, like itemView.context.
A: When you are using setOnLongClickListener { /* your code here */ } in kotlin it is the equivlent to:
setOnLongClickListener(new OnLongClickListener() {public boolean onLongClick(View v){ /* your code here */ }}); in java
Therefore when you do this:
viewHolder.itemView.textView_from_row.setOnLongClickListener {
Toast.makeText(this, "Message copied", Toast.LENGTH_LONG).show()
....
}
It's the equivalent to this:
setOnLongClickListener(new OnLongClickListener() {
@Override
public boolean onLongClick(View v) {
Toast.makeText(this, "Message copied", Toast.LENGTH_LONG).show()
}
});
As you can see the this in the code above is not of the type Context it's of the type OnLongClickListener!
You can find a context using the view that you have:
Toast.makeText(viewHolder.itemView.context, "Message copied", Toast.LENGTH_LONG).show()
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,689 |
SUMMER PROCESS ART: Marshmallow Painting!
Marshmallows and summer -- they just go together, right? The promise of s'mores is one of the main reasons my kiddo wants to go camping this month! And ever since our Carnival Corral party, miss R has been requesting marshmallows every time she spies our leftover bags in the depths of the pantry. Even baby… Continue reading SUMMER PROCESS ART: Marshmallow Painting! | {
"redpajama_set_name": "RedPajamaC4"
} | 7,532 |
Q: maya python iterate each obj in a list IHello everyone I need help to understand how to access to each single object in list, if you have time...
I have a list 'objects' made by getting the user selection, I loop it to randomise position but even if seems that I properly select all the single objects, the random value is applied like they are just 1 object, everything moves together ...I'd like to random the single obj separately.
Thanks in advance
F
for j in objects:
mc.select(j)
print(j)
for i in j:
x = random.uniform(-1,15)
y = random.uniform(0, 12)
z = random.uniform(-5, 15)
mc.move(x, y, z)
A: Not sure what you need the second loop for, but it seems to work fine. I simplified it a little bit like this:
import random
import maya.cmds as cmds
objects = cmds.ls(sl=True)
for j in objects:
x = random.uniform(-1,15)
y = random.uniform(0, 12)
z = random.uniform(-5, 15)
cmds.move(x, y, z, j)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,914 |
passodelvivione » Rock / Pop » Polvo - Today's Active Lifestyles
Polvo - Today's Active Lifestyles flac mp3
Polvo Alternative Pop/Rock Alternative/Indie Rock Indie Rock Math Rock
Today's Active Lifestyles
Alternative Pop/Rock,Alternative/Indie Rock,Indie Rock,Math Rock
Recording location:
VOX ASF APE ADX MPC AIFF
Today's Active Lifestyles (Cass, Album, Promo). Today's Active Lifestyles (Cass, Album, cle).
Today's Active Lifestyles is Polvo's second studio album. It was produced by Bob Weston and released on Merge Records in 1993. Early versions of the cover art featured red tigers in the yellow color field, but these were soon removed due to a lawsuit from its painter Andy Freeburn. The album was released on Merge Records. Tilebreaker" was released as a 7" single with the song "Chameleon" and the instrumental "Tiara Fetish" on the B-side.
Today's Active Lifestyles goes from the raucous "Thermal Treasure," with its tangled guitars, into the meandering "Lazy Comet," with its singsong, rhyming lyrics, to the spare, melancholy "My Kimono," which features a solo by guitarist Ash Bowie. And that's just the album's first three songs! The band experiments with several ideas throughout the album, and each concept is successful.
And it seems like they've spoken. I mean, when was the last time you heard anyone talk about Polvo" And I don't mean your immigrant maid. Regardless, Today's Active Lifestyles is a great release from a band whose sound is exciting, even after so many years. The mathy dissonance, twisting melodies and ear-piercing harmonics that get coupled with such sweet vocals might remind of Yo La Tengo covering Slint, but 'Sure Shot' has much more clear contemporaries.
Today's Active Lifestyles. By: Polvo (1993, Rock). Wrong audio? Try another! More albums from Polvo
Today's Active Lifestyles is woven with the thread that ties together skaters, metal fans, and indie rockers. Today's Active Lifestyles Polvo. Even when they were at their most restless and esoteric - the constantly changing tempos, the vocals fully buried under a mass of amplified guitar - Polvo were headbanging hard rock music. Today's Active Lifestyles is woven with the thread that ties together skaters, metal fans, and indie rockers.
Today's Active Lifestyles. Album Name Today's Active Lifestyles. Labels Merge Records. Music StyleNoise Rock. Members owning this album0. 1993 studio album by Polvo. Today's Active Lifestyles. Never a band to follow formulaic musical styles," she writes, "Polvo once again shakes things up with its twisted song structures of multiple tempos and intricate, distorted guitars. In the sense that it is sprawling, falling, tipping all over the place
1 Thermal Treasure Polvo 4:32
2 Lazy Comet Polvo 3:49
3 My Kimono Polvo 2:21
4 Sure Shot Polvo 3:24
5 Stinger (Five Wigs) Polvo 7:23
6 Tilebreaker Polvo 4:09
7 Shiska Polvo 1:30
8 Time Isn't on My Side Polvo 3:06
9 Action Vs. Vibe Polvo 3:43
10 Gemini Cusp Polvo 7:05
Polvo - Primary Artist
Bob Weston - Engineer
felt boot
One of the best albums of the '90s. This is right up there with Loveless, Slanted and Enchanted, and Soundtracks for the Blind as a piece of work which perfected the sound of it's creator. How this album differs from those is that Polvo had no greater influence on bands that followed. No blind imitators. Nor ravenous fandom. What they had instead was some of the most unusually metered guitar rock to ever be recorded (Slint not withstanding.) Highly recommended for any fans of noisy guitar rock, spacious composition, and appreciators of unusual time signatures.
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Chapel Hill - Young Rock download | {
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} | 7,322 |
Q: Cassandra data directory does not get updated with deletion Currently, I am bench marking Cassandra database using YCSB framework. During this time I have performed (batch) insertion and deletion of the data quite regularly.
I am using Truncate command to delete keyspace rows. However, I am noticing that my Cassandra data directory swells up as the experiments.
I have checked and can confirm that even there is no data in the keystore when I checked the size of data directory. Is there a way to initialize a process so that Cassandra automatically release the stored space, or does it happen over time.
A: When you use Truncate cassandra will create snapshots of your data.
To disable it you will have to set auto_snapshot: false in cassandra.yaml file.
If you are using Delete, then cassandra use tombstone,i.e your data will not get deleted immediately. Data will get deleted once compaction is ran.
To remove previous snapshots one can use nodetool snapshot command.
| {
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} | 7,600 |
7.5 liter instant boiling water units are designed to provide the best solution for your needs, whether it's in the boardroom, office, home or commercial kitchen.
Perfect kitchen utility for offices, factory canteens, sporting clubs and hospitals.
Clean, effecient, easy to operate, economical to use and built to last. | {
"redpajama_set_name": "RedPajamaC4"
} | 131 |
At 8 feet wide and 25 feet deep, de Medici Ming Fine Paper in Seattle might not seem the kind of store where a person could spend hours browsing. But paper seems to have a mysterious ability to captivate.
recalling a woman years ago who spent the better part of a day going through the shop's colorful supplies of paper and related products, imported from places such as Thailand, Italy and the Philippines.
During its nearly two decades in business, the small store at 1222 First Ave., near the Seattle Art Museum, has developed a loyal following. The store first opened in 1983 on First Avenue and University Street. Inspired by Marie Papier in Paris, the store was originally dedicated to the art of letter writing. It quickly grew into providing papers from around the world in all forms for all sorts of projects.
The name comes from two of the cultures who historically have had the most to do with development of paper: The Chinese who invented it, and the Italians who made an everyday style of it. The de Medici Family and the Ming Dynasty governed their respective cultures from the 1200's-1600's, and, still today in Seattle, in this Renaissance paper bouquet. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,864 |
Q: Kong :: Client IP missing in X-FORWARDED-FOR Using Kong ingress controller (v2.1) in Kubernetes. Running in Digital Ocean.
The problem is that client IP is missing in X-FORWARDED-FOR header for HTTPS request, yet present on the HTTP request. I need to be able to see the IP on the HTTPS requests as well.
The value received in X-FORWARDED-FOR header on HTTP request is "<the-client-ip>, <the-k8s-node-ip>".
Yet in case of HTTPS request the value is "<the-k8s-node-ip>". The client-ip is lost.
Kong installed using Help. The most relevant part of config is:
proxy:
enabled: true
http:
enabled: true
annotations:
service.beta.kubernetes.io/do-loadbalancer-protocol: "http"
service.beta.kubernetes.io/do-loadbalancer-algorithm: "round_robin"
service.beta.kubernetes.io/do-loadbalancer-tls-ports: "443"
service.beta.kubernetes.io/do-loadbalancer-tls-passthrough: "true"
A: The problem is with the SLL Passthrough. You can't modify headers when using this configuration. You should rather use SSL termination, unless you have some specific compliance requirements.
Checkout the doc for more:
https://www.digitalocean.com/docs/networking/load-balancers/how-to/ssl-passthrough/
| {
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package ru.aoleynikov.service;
import java.awt.List;
import java.util.ArrayList;
import ru.aoleynikov.model.AnonUser;
import ru.aoleynikov.model.BaseUser;
import ru.aoleynikov.dao.ConnectionWithDataBaseDao;
import ru.aoleynikov.model.User;
/**
* Service class.
* @author Anton Oleynikov
* created on 30.11.2017
*/
public class Service {
/**
* Service for get user.
* @param user user
* @return
*/
public BaseUser get(BaseUser user) {
return new ConnectionWithDataBaseDao().getUser(user);
}
/**
* Service for get all users.
* @return list
*/
public ArrayList<BaseUser> getAll() {
return new ConnectionWithDataBaseDao().getAll();
}
/**
* Service for add user.
* @param user user
*/
public void addUser(BaseUser user) {
new ConnectionWithDataBaseDao().createUser(user);
}
/**
* Service for authentication user.
* @param user user
* @return boolean
*/
public boolean authUser(AnonUser user) {
return new ConnectionWithDataBaseDao().authUser(user);
}
/**
* Service for deletes user.
* @param user user
*/
public void deleteUser(BaseUser user) {
new ConnectionWithDataBaseDao().deleteUser(user);
}
/**
* Service for edit user.
* @param editUser
*/
public void editUser(BaseUser editUser) {
new ConnectionWithDataBaseDao().editUser(editUser);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
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Q: How to tell if someone came to my website from facebook using mobile app I have the following php code on my server that allows me to tell if user cam to my webpage from facebook:
if ($_SERVER[HTTP_REFERER] == "https://www.facebook.com/") { do stuff }
So, the problem here is that people are also using facebook on mobile using facebook app, so I don't get the referral link this way.
Is there any way I can tell if someone came to my webpage clicking on a link using facebook app?
A: I would suggest to use a regex for matching.
http://php.net/manual/en/function.preg-match.php
For example
if (preg_match("/.*\.(facebook|fbdcn)\.com/i", $_SERVER[HTTP_REFERER])) {
echo "A match was found.";
} else {
echo "A match was not found.";
}
You can use this site to find a good regex.
https://regex101.com/
| {
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{"url":"https:\/\/www.physicsforums.com\/threads\/odd-determinant.257763\/","text":"Odd determinant\n\n1. Sep 20, 2008\n\nTTob\n\nI don't understand this :\n\nlet A is n x n matrix whose entries are precisely the numbers 1, 2, . . . , n^2.\nPut odd numbers into the diagonal of A, only even numbers above the diagonal and arrange the entries under the diagonal arbitrarily. Then det(A) is odd.\n\nWhat is the explanation ?\n\n2. Sep 20, 2008\n\nHallsofIvy\n\nStaff Emeritus\nWhat have you tried? In particular, have you tried seeing what happens for n= 2 and 3?\n\n3. Sep 22, 2008\n\nTTob\n\nfor n=2 we have det(A) = -5. so what ?","date":"2016-10-23 20:28:15","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\": 0.9416816830635071, \"perplexity\": 787.7822570854748}, \"config\": {\"markdown_headings\": false, \"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-2016-44\/segments\/1476988719416.57\/warc\/CC-MAIN-20161020183839-00312-ip-10-171-6-4.ec2.internal.warc.gz\"}"} | null | null |
An Initiative to Create New Journal Metrics
We've written before (here, here, and here) about the problems with using the Clarivate Analytics journal impact factor to judge the quality of a paper or an author and about international efforts to decrease the emphasis on impact factor as a criterion for rewards, including cash, recognition, promotion, and tenure.
A representative of Clarivate Analytics is on record as stating that the journal impact factor should not be used in these ways. Jonathan Adams, director of the Institute for Scientific Information at the Web of Science (the citation indexing service owned by Clarivate Analytics) is quoted in the article "Impact Factors: Payment by Results," "…we worry about misuse of the journal impact factor as the JIF is not, and has never been an indicator of research performance."
We know. And so do others. But the impact factor still dominates the evaluation of academic performance.
The discussion just got amped up via an article in Nature, The International Journal of Science. An international group of academics has announced an initiative "to create a constructive role for jou rnal metrics in scholarly publishing and to displace the dominance of impact factors in the assessment of research."
The authors describe the initiative and its challenges in this way: "…a group of bibliometric and evaluation specialists, scientists, publishers, scientific societies and research-analytics providers are working to hammer out a broader suite of journal indicators, and other ways to judge a journal's qualities. It is a challenging task: our interests vary and often conflict, and change requires a concerted effort across publishing, academia, funding agencies, policymakers and providers of bibliometric data."
Some of their suggested indicators include curating (expertise and diversity of the editorial board, acceptance rate, and transparency of acceptance criteria), data (citations or reporting standards), and evaluating research (transparency of the process and the number and diversity of peer reviewers and their timeliness).
The authors expose the inadequacy of the journal impact factor as a measure of academic excellence. The journal impact factor, they write, "…was specifically intended to support librarians who wanted to evaluate their collections and researchers who wished to choose appropriate publication venues, as well as to provide insights for scholars, policymakers and research evaluators. Its inventors never expected the broad use and rampant misuse that developed."
The authors propose four criteria to prevent abuse of the system they are seeking to develop and suggest the creation of a governing organization that would focus on journal indicators.
They're recruiting: "We invite all interested stakeholders to contact us to join this initiative. On the basis of these responses, we aim to launch the governing body at a second workshop in 2020."
← Preprint Servers' Function and Expansion
Ochsner Journal Summer Issue Available Now → | {
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\section{Introduction}\label{sec:sec1}
Droplet impact on liquid surfaces occurs in many natural and industrial processes, such as precipitation \cite{Raes2000CyclingAerosol}, spray coating \cite{Guo2016CrownFormation}, fuel atomization \cite{Moreira2010DropletImpactICE}, and spray cooling \cite{Horacek2005NozzleSpray, Kim2004CoolingPlain, Shedd2005SprayCooling, Xie2012FilmFlow}. The outcomes of the impact mainly include bouncing \cite{Tang2019InterfacialGas, Wang2008LowVelocity, Beesabathuni2015ImmiscibleInterface}, coalescence \cite{Blanchette2009, Geri2017DelayCoalescence, Kulkarni2021CoalescenceSpreading}, jet breakup \cite{Agbaglah2015VortexJet, Liu2018WindDropJet, Pan2010SurfaceProperties, Blanco2021JetBurstingBubbles, Das2022EvolutionJetPool}, and splashing \cite{Lee2015VortexSplashing, Leng2001SplashSphere, Motzkus2011AirborneParticle}. In addition, the impact can result in the entrapment of air bubbles \cite{Deng2007ViscositySurface, Oguz1990BubbleEntrainment, Haldar2018ChemicallyGelation}, which is often accompanied by high-speed jets \cite{Rein1996TransitionalRegime}. The bubble entrapment is known to be important for the generation of noise, the production of aerosols, and the transport of gases across the ocean surface \cite{Deane2002ScaleBubble, Franz1959SplashSound, Pumphrey1990EntraimentBubble}.
The pinch-off of bubbles after the droplet impact on liquid pools has been considered in many studies \cite{Franz1959SplashSound, Pumphrey1988SoundEmittedWater, Chen2014ViscosityEffect, Ray2012BubbleScaling, Morton2000FlowRegime, Ray2015RegimesCoalescence, Oguz1990BubbleEntrainment, Pumphrey1990EntraimentBubble, Deng2009BubblePhenomenon, Deng2007ViscositySurface}. The impact creates a cavity at the impact point, and then a single bubble is pinched off at the cavity bottom as the cavity contracts, and this bubble was named a \emph{regular bubble}. The Weber number $\text{We}\equiv \rho U_{0}^{2}{{D}_{0}}/\sigma $ can be used to indicate the ratio between inertial and capillary forces, where $\rho $ and $\sigma $ are the density and surface tension coefficient of the fluid, ${{U}_{0}}$ and ${{D}_{0}}$ are the speed and diameter of the droplet, respectively. Bay et al. \cite{Ray2015RegimesCoalescence} studied the effect of the inertial force on the crater shape just before collapse, and found that the crater width and wave swell angle (i.e., the angle of the crater cusp just before the crater collapses) increase as the We increases and the regular bubble pinch-off occurs for wave swell angles ranging from 100${}^\circ $ to 120${}^\circ $. Capillary waves were found to travel along the interface and merge at the cavity bottom to produce a regular bubble \cite{Deng2009BubblePhenomenon, Leng2001SplashSphere, Rein1996TransitionalRegime}. The capillary number $\text{Ca}\equiv \mu {{U}_{0}}/\sigma $ can be used to indicate the ratio between viscous and capillary forces, where $\mu $ is the fluid dynamic viscosity. The viscosity and the surface tension could affect the regular bubble pinch-off, and the regular bubble pinch-off cannot be found when the capillary number is larger than 0.6 \cite{Deng2007ViscositySurface}. The regular bubble pinch-off was also studied numerically using the volume of fluid (VOF) method \cite{Berberovic2011InertiaFlow, Morton2000FlowRegime, Oguz1990BubbleEntrainment, Ray2012BubbleScaling}. Oguz et al. \cite{Oguz1990BubbleEntrainment} found that whether a bubble is entrapped or not is determined by the competition between the timescale for the cavity to achieve its maximum depth and the timescale of the capillary wave. Morton et al. \cite{Morton2000FlowRegime} described the importance of the capillary wave propagation to the bubble pinch-off, and vortex rings were found in the process of the bubble pinch-off. The entrapped bubble was found to depend on the cavity shape and its maximum depth \cite{Ray2012BubbleScaling}. Chen et al. found \cite{Chen2014ViscosityEffect} that both the lower and upper limits of the regular bubble entrapment region increased with the liquid viscosity, and scaling models for the lower and upper limits of regular bubble entrapment were proposed.
A \emph{large bubble} can be entrapped after the closure of the crown during the droplet impact on a pool at large Weber numbers \cite{Xu2018TemperatureBubble, Bisighini2010CraterEvolution}. The size of the entrapped large bubble can be several times larger than the initial droplet \cite{Zou2012LargeBubble}. Numerical and experimental studies on the cavity dynamics \cite{Dake2017BubbleVortex} found that large bubbles were entrapped during the impact of prolate-shaped droplets. Large bubble entrapment was also found to be a vortex-driven phenomenon after the impact of an oscillating droplet \cite{Thoraval2016VortexRing}.
The deformation of the cavity and the entrapment of bubbles result from the interplay of inertia, viscous force, surface tension, and gravity. Most existing studies focus on the effects of inertial force, viscous force, and surface tension force \cite{Deng2007ViscositySurface, Deng2009BubblePhenomenon, Ray2015RegimesCoalescence, Zeff2000SingularityDynamic}. However, there are few studies on the effect of gravity, even though the gravitational force can significantly alter the evolution of the interface and affect bubble entrapment. The impact of droplets at high environmental pressure is crucial to many relevant applications, such as fuel atomization in internal combustion engines \cite{Panao2005SprayInjectionSystem, Singh2007EngineCombustionModel} and the droplet impact in nuclear power plants \cite{Zhang2020DropletNuclearInstallation, Kanazawa1995CoolantDropletBehavior, Okawa2007DropletsAnnularFlow}. In addition, the impact of droplets at low gravity is also important to many relevant applications, such as spray cooling in moving systems and fire extinguishing in spacecraft \cite{Tao2013DropletSolidMicrogravity, Han2014WaterMistMicrogravity}. The effect of the environmental pressure has been proved to be very important during the impact of droplets on solid surfaces \cite{Xu2007SplashInterplay, Xu2005Splashing}. In addition, the effect of the environmental pressure was also important in the droplet impact on a liquid pool \cite{Klyuzhin2010PersistingDropletsSurfaces, Marcotte2019EjectaCorollaSplashes}. Klyuzhin et al. \cite{Klyuzhin2010PersistingDropletsSurfaces} studied the effect of the environmental pressure on the droplet floating time when droplets impact a liquid pool at a low impact speed, and they found that the floating time decreases linearly with decreasing the environmental pressure. In addition, Marcotte et al. \cite{Marcotte2019EjectaCorollaSplashes} studied the effect of the environmental pressure on splashing when ethanol droplets impact liquid pools of different viscosities, and they found that decreasing the environmental pressure could suppress splashing for high-viscosity liquid pools but could not suppress splashing for low-viscosity liquid pools. In our study, the effect of the environmental pressure on bubble entrapment during droplet impact on liquid pools is studied.
In this paper, we focus on the cavity deformation and bubble entrapment after droplets impact a liquid pool. We aim to reveal the role of gravity and environmental pressure on regular bubble pinch-off and large bubble entrapment. The cavity shape and its depth are studied at different gravities in our simulations since the cavity shape and the timescale for the cavity to achieve its maximum depth are important to the bubble pinch-off. The regimes of bubble pinch-off and the theoretical threshold at different gravities are studied here, while previous studies \cite{Deng2007ViscositySurface, Oguz1990BubbleEntrainment, Pumphrey1990EntraimentBubble, Deng2009BubblePhenomenon, Morton2000FlowRegime, Ray2012BubbleScaling, Chen2014ViscosityEffect, Ray2015RegimesCoalescence} mainly considered earth's gravity. Inspired by previous research showing that the environmental pressure is important to the droplet impact on liquid pools \cite{Klyuzhin2010PersistingDropletsSurfaces, Marcotte2019EjectaCorollaSplashes}, we study the effect of the environmental pressure on the bubble entrapment during the impact process. The regimes of bubble entrapment at different environmental pressures are studied, and the regular bubble pinch-off is found to transform into large bubble entrapment as the environmental pressure increases, whereas the large bubble entrapment was previously observed mainly at large Weber numbers at standard environmental pressure \cite{Xu2018TemperatureBubble, Bisighini2010CraterEvolution}. The experimental setup is introduced in Sec.\ \ref{sec:sec2}. The numerical methodology is presented in Sec.\ \ref{sec:sec3}. Results are discussed and analyzed in Sec.\ \ref{sec:sec4}, including the model validation, the effects of gravity and environmental pressure on the cavity deformation and bubble entrapment. Conclusions are summarized in Sec.\ \ref{sec:sec5}.
\section{Experimental setup}\label{sec:sec2}
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{figure01}\\
\caption{(a) Schematic diagram of the experimental setup. (b) Droplet at the instant of impact. (c) Bubble pinch-off and Worthington jet after the impact.}\label{fig:fig01}
\end{figure}
The setup for the impact experiment is schematically shown in Fig.\ \ref{fig:fig01}. By pushing a syringe to produce a droplet at a syringe tip, the droplet fell and impacted the target liquid pool. The liquid pool is in an open acrylic container with a size of $40\times 40\times 30$ mm$^3$. The width of the container is more than $10 D_0$, and the depth of the container is more than 6 times the maximum depth of the cavity. The influence of the container's wall on the impact process can be neglected. A high-speed camera (Photron Fastcam SA1.1) was used to film the impact process from the side. The resolution is $1024\times 896$ pixels, corresponding to a spatial resolution of 15.9 $\mu \text{m/pixel}$. The frame rate is 6000 frames per second (fps), and the exposure time is 1/30000 seconds. An LED light was used as the light source, combined with a frosted screen to diffuse the light. A typical image at the impact instant is shown in Fig.\ \ref{fig:fig01}b, and a typical regular bubble after the impact is shown in Fig.\ \ref{fig:fig01}c. Using a customized image-processing program of Matlab, we measured the droplet size, the impact speed, and the cavity deformation from the images.
The droplet and the pool were prepared using the same liquid, a mixture of glycerin and water with a mass fraction of glycerin of 62\%. The physical properties of the mixture were measured experimentally. We measured the density of the mixture by an electronic liquid densitometer (WLD-MD01, XIONGFA), measured the surface tension of the mixture by a platinum ring tensiometer (MC-1021, MINCE), and measured the dynamic viscosity of the mixture by a digital viscometer (NDJ-8S, SHANGPU). The room temperature is 26.5 ${}^\circ $C. The density of the mixture is 1156 kg/m$^3$, the surface tension is 68 mN/m, and the dynamic viscosity is 9.5 mPa$\cdot$s.
\section{Numerical methodology}\label{sec:sec3}
The system of droplet impact consists of two immiscible and incompressible phases, i.e., the liquid and air phases. The VOF method in OpenFOAM is employed for the simulation. The OpenFOAM version used in this study is OpenFOAM-2.1.x. The continuity equation and momentum equation are respectively
\begin{equation}\label{eq:eq01}
\nabla \cdot (\rho \mathbf{u})=0,
\end{equation}
\begin{equation}\label{eq:eq02}
\frac{\partial (\rho \mathbf{u})}{\partial t}+\nabla \cdot (\rho \mathbf{uu})=-\nabla p+\nabla \cdot \mu [\nabla \mathbf{u}+{{(\nabla \mathbf{u})}^{\text{T}}}]+\rho \mathbf{g}+\sigma \kappa \nabla \alpha,
\end{equation}
where $\mathbf{u}$ is velocity vector, $\mu$ is dynamic viscosity, $\mathbf{g}$ is gravitational acceleration, $p$ is pressure, $\alpha $ is volume fraction, and $\kappa$ is interfacial curvature, which can be calculated as
\begin{equation}\label{eq:eq03}
\kappa =-\nabla \cdot \left( \frac{\nabla \alpha }{\left| \nabla \alpha \right|} \right).
\end{equation}
The interface is blurred due to numerical diffusion and the discretization of the convective term is important. To keep the sharp resolution of the interface, Weller \cite{Waller2008} add an artificial convective term into the phase fraction equation
\begin{equation}\label{eq:eq04}
\frac{\partial \alpha }{\partial t}+\nabla \cdot (\mathbf{u}\alpha )+\nabla \cdot \left[ \alpha (1-\alpha ){{c}_{\alpha}} \left| \mathbf{u} \right| \frac{\nabla \alpha }{\left| \nabla \alpha \right|} \right]=0.
\end{equation}
The third term on the left-hand side of Eq.\ (\ref{eq:eq04}) is an extra artificial convective term, where ${c}_{\alpha}$ is the compression coefficient and ${{c}_{\alpha }}=1$ in our study.
The physical properties can be obtained from the volume fraction
\begin{equation}\label{eq:eq05}
\rho =\alpha {{\rho }_{l}}+(1-\alpha ){{\rho }_{g}},
\end{equation}
\begin{equation}\label{eq:eq06}
\mu =\alpha {{\mu }_{l}}+(1-\alpha ){{\mu }_{g}},
\end{equation}
where the subscripts $l$ and $g$ refer to the properties for liquid and gas, respectively. The interFoam solver, which has been used in many previous studies \cite{Chen2014ViscosityEffect, Gupta2020SplashingMovingInterface, Hoang2013DynamicsBreakupJunction} to simulate incompressible multiphase flows, is employed in this study. Governing equations (1)-(3) are discretized using the finite volume method. Discretized linear matrices for the mass and momentum equations are solved using the Preconditioned BiConjugate Gradient (PBiCG) method and the Preconditioned Conjugate Gradient (PCG) method, respectively. A critical work for the volume fraction equation is to ensure the boundedness of the volume fraction. The multi-dimensional universal limiter with explicit solution (MULES) \cite{Damian2013ModelSimultaneousInterfaces} developed from the flux correct transport (FCT) algorithm \cite{Boris1973FluxCorrectedTransport} is used to ensure the boundedness of the volume fraction.
Since the process of cavity deformation and bubble entrapment is symmetric, axisymmetric simulations are performed by setting a wedge domain in cylindrical coordinate. The axial section of the computational domain is rectangular (20 mm $\times $ 15 mm), and the depth of the pool is 10 mm. The droplet is initialized above the pool surface with a separation of $0.1D_0$. We set the bottom of the domain as a wall with a no-slip boundary, and the side and top as open boundaries. The initial speed of the droplet is $U_0$. In the simulations of environmental pressure variation, the gas density is varied as the influence of pressure on the liquid density, liquid viscosity, and air viscosity is negligible. The properties of the air at different environmental pressures are obtained from NIST REFPROP, and the properties of the liquid are the same as that in experiments at 26.5 ${}^\circ $C. The Weber number, as a ratio between the inertia and surface tension force, is varied by varying the droplet speed ${{U}_{0}}$ from 2.1 to 4 m/s. The Bond number $\text{Bo}\equiv {\rho gD_{0}^{2}}/{\sigma }$, as a ratio between the gravitational and surface tension forces, is varied by varying the gravitational acceleration \emph{g} from 0 to 10 $\text{m}/{{\text{s}}^{2}}$. The Weber number is in a range of $157.4<\text{We}<571.2$ and the Bond number is in a range of $0<\text{Bo}<0.8$, and the corresponding Froude number $\text{Fr}\equiv {{{U}_{0}}}/{\sqrt{g{{D}_{0}}}}$, a ratio between the inertia and gravitational force, is in a range of $0<\text{Fr}<4500$.
\begin{figure*}
\centering
\includegraphics[width=1.4\columnwidth]{figure02}\\
\caption{Grid-independence study for the droplet impact process. The mesh size was progressively refined from ${{D}_{0}}/\Delta x=21$ to 168. ${{D}_{0}}=2.07$ mm. (a) Cavity depth and the distance from the pool surface to the bottom of the regular bubble at $\text{We}=227$ and $P^*=1$, (b) Gas-liquid interface profiles at 20.5 ms at $\text{We}=227$ and $P^*=1$, (c) Cavity depth at $\text{We}=571$ and $P^*=1$, (d) Cavity depth during the large bubble entrapment at $\text{We}=279.9$ and $P^*=30$.}\label{fig:fig02}
\end{figure*}
A grid-independence study for the impact process was performed, as shown in Fig.\ \ref{fig:fig02}. Before the bubble pinch-off, the depth of the cavity $H$ was measured from the initial surface of the liquid pool to the bottom of the cavity, and after the bubble pinch-off, $H$ was measured from the initial surface of the liquid pool to the bottom of the regular bubble, as illustrated in Fig.\ \ref{fig:fig02}a. The comparison of $H$ with different grid resolutions at $\text{We}=227$ is shown in Fig.\ \ref{fig:fig02}a. We can see that when the grid resolution ${{D}_{0}}/\Delta x$ increases from 42 to 84, the maximum difference in $H$ after the droplet pinch-off is about 9.1$\%$ at 23.7 ms. However, when ${{D}_{0}}/\Delta x$ increases from 84 to 168, $H$ is very close, with a maximum difference of 2.2$\%$ at 23.7 ms, and thus the grid resolution of ${{D}_{0}}/\Delta x=84$ is sufficient for further simulations of the cavity deformation and the bubble pinch-off. Fig.\ \ref{fig:fig02}b shows the gas-liquid interface profiles at 20.5 ms. The bubble pinch-off could not be captured using the coarse grid (${{D}_{0}}/\Delta x=21$) at $\text{We}=227$. If the grid resolution is higher than ${{D}_{0}}/\Delta x=84$, the interface profiles were almost the same, and the bubble pinch-off could be captured well. Therefore, the grid resolution of ${{D}_{0}}/\Delta x=84$ is sufficient for further simulations of the cavity deformation and the bubble pinch-off. In addition, a grid independence study was also performed when the droplets impact at a higher We of 571 (the maximum Weber number considered in this study), and the results (Fig.\ \ref{fig:fig02}c) show that if the grid resolution is higher than ${{D}_{0}}/\Delta x=84$, the cavity depth $H$ is also independent of the grid resolution before 27 ms. After that is the formation of the Worthington jet, which is very fast, and there is still a slight deviation between the grids of ${{D}_{0}}/\Delta x=84$ and ${{D}_{0}}/\Delta x=168$. The Worthington jet is not our main concern in this study because if the phenomenon of the regular bubble does not occur, we only consider the time evolution of the cavity before the cavity achieves its maximum depth. Therefore, the grid resolution of ${{D}_{0}}/\Delta x=84$ is sufficient for the simulations at a higher Weber number. To check the grid independence at higher environmental pressure, a grid-independence study was also performed when the droplet impacts at $P^*=30$ (the maximum environmental pressure considered in this study), as shown in Fig.\ \ref{fig:fig02}d. In this scenario, the entrainment of a large bubble occurs soon (at about 3 ms) after the droplets impact at $\text{We}=279.9$. The results show that the cavity depth when the droplet impacts at a higher environmental pressure is very close in different grid resolutions. Therefore, a grid resolution of ${{D}_{0}}/\Delta x=84$ was used for further simulations of the cavity deformation and the bubble entrainment.
\section{Results and discussions}\label{sec:sec4}
\subsection{Model validation}\label{sec:sec41}
\begin{figure*}
\centering
\includegraphics[width=1.8\columnwidth]{figure03}\\
\caption{Comparisons between the numerical and experimental results after a droplet impacting a liquid pool. (a) Morphological variations (see Videos 1 and 2 in Supplementary Material \cite{SM}). (b) Cavity depth and the distance from the pool surface to the bottom of the regular bubble. $D_0=2.07$ mm and $\text{We}=227$. }\label{fig:fig03}
\end{figure*}
The accuracy of numerical simulation is validated against the droplet impact experimental data. The instant of the droplet impact is set as $t = 0$. The comparison of surface profiles between numerical simulation and experimental images is shown in Fig.\ \ref{fig:fig03}a. The cavity develops into a hemisphere and then retracts, and a regular bubble is pinched off in the end. At the very beginning stages of the impact in the experiment, a very small bubble is seen at the base of the cavity. The small bubble is from the rupture of the air film between the bottom of the droplet and the pool surface \cite{Tang2019InterfacialGas, Jian2020SplitAirDisk, Qi2020AirHeatedSubstrates, Tran2013AirEntrainmentLiquid, Lo2017AtomicallySmoothSubstrate, Langley2017UltraViscousDrops}. Since it is very small and happens at the very early stage of the impact process, its effect on the cavity deformation and the subsequent bubble entrapment is negligible. Since this study mainly focuses on the evolution of the air cavity and the subsequent bubble entrapment, we do not attempt to resolve the formation of the small bubble in the numerical simulation, which requires a grid resolution of sub-micrometer and is very computational demanding. The comparison shows good agreement between the simulation and the experiment in the time evolution of the free surface profile. There is a slight mismatch in time between the numerical and experimental results in the last three frames. One reason is that the error in time accumulates during the simulation of the cavity evolution which is much longer than the pinch-off of the regular bubble, and another reason is the one-frame uncertainty in determining the exact time of drop impact ($t = 0$) in the experimental sequences.
The cavity depth (before the bubble pinch-off) and the distance from the pool surface to the bottom of the regular bubble (after the bubble pinch-off) are used for the quantitative assessment of the numerical simulation. The comparisons between numerical and experimental results are shown in Fig.\ \ref{fig:fig03}b. The cavity depth increases as it expands and then decreases as it retracts. After 20 ms, \emph{H} increases further as the bubble moves downward in the liquid pool. The comparison shows good agreement between the simulation and the experiment, and indicates that the simulation can predict the cavity deformation and the bubble pinch-off.
\subsection{Effects of gravity}\label{sec:sec42}
\begin{figure*}
\centering
\includegraphics[width=1.2\columnwidth]{figure04}\\
\caption{Cavity evolution after droplet impact at different gravities (see Videos 3 and 4 in Supplementary Material \cite{SM}). $D_0=2.1$ mm and $\text{We}=223.1$. The front of the capillary wave is highlighted by white arrows. The cylindrical air pocket is also highlighted by the magnified image at 19.9 ms in (a). }\label{fig:fig04}
\end{figure*}
\begin{figure*}
\centering
\includegraphics[width=1.25\columnwidth]{figure05}\\
\caption{Pressure fields during the propagation of capillary wave. (a) $t = 6$ ms, (b) $t = 13$ ms. $\text{Bo}=0.75$, $D_0=2.1$ mm and $\text{We}=223.1$.}\label{fig:fig05}
\end{figure*}
To analyze the effect of the gravitational force on the cavity deformation and bubble pinch-off, we study the cavity behaviors by varying the gravity from 0 to 10 m/s$^2$ while fixing the other parameters. The evolution of the cavity at different Bond numbers is shown in Fig.\ \ref{fig:fig04}. A regular bubble is pinched off at earth's gravity ($\text{Bo}=0.75$, see Fig.\ \ref{fig:fig04}a). In contrast, at low gravity ($\text{Bo}=0.15$), the phenomenon of regular bubble pinch-off disappears (see Fig.\ \ref{fig:fig04}b).
The front of the capillary wave can be seen from the sharp shape on the surface of the cavity, which is highlighted by white arrows in Fig.\ \ref{fig:fig04}, and the origin of the capillary wave is due to the strong surface disturbance immediately after the initial contact of the impacting drop with the undisturbed liquid surface \cite{Morton2000FlowRegime, Berberovic2009LiuidLayer, Oguz1991CalculationUnderwaterNoise, Kassim2004DropCoalescenceInterface}. When a capillary wave is created, the sharp curvature of the interface at the front of the capillary wave induces a strong variation of the local pressure \cite{Berberovic2009LiuidLayer}. The pressure distribution (see Fig.\ \ref{fig:fig05}) shows that the front of the capillary wave separates the high-pressure region and the relatively low-pressure region. Therefore, the front of the capillary wave can be identified by the sharp curvature on the surface of the cavity. At earth's gravity, the capillary wave propagates downward along the cavity surface, as shown at 13 ms in Fig.\ \ref{fig:fig04}a. The capillary wave reaches the lowest point at the cavity bottom at 19.9 ms, producing a cylindrical air pocket (like a U shape) at the cavity bottom, as highlighted by the magnified image at 19.9 ms in Fig.\ \ref{fig:fig04}a. Then the mouth of the cylindrical air pocket closes, and a regular bubble is pinched off. In contrast, at low gravity ($\text{Bo}=0.15$), the interface at the cavity bottom alters its moving direction to the upward at 28.9 ms (see the magnified interface shape), and a jet is produced finally without regular bubble pinch-off.
To further clarify the difference between the two scenarios, the velocity fields are compared in Fig.\ \ref{fig:fig06}. At normal gravity ($\text{Bo}=0.75$), the cavity surface moves inward, and the speed of the cavity surface is largest at the mouth of the air cylinder, and the speed of the interface at the bottom of the air cylinder is almost zero, as shown in Fig.\ \ref{fig:fig06}a. Thus, the mouth of the cylinder closes at high speed to pinch off a regular bubble. In contrast, at low gravity ($\text{Bo}=0.15$), the interface at the bottom of the cavity moves upward at high speed, which results in a high-speed jet and prevents the bubble pinch-off, as shown in Fig.\ \ref{fig:fig06}b.
\begin{figure*}
\centering
\includegraphics[scale=0.55]{figure06}\\
\caption{Comparison of the velocity fields at different gravities. (a) $\text{Bo}=0.75$, $t=19.9$ ms, with regular bubble pinch-off, (b) $\text{Bo}=0.15$, $t=28.9$ ms, no bubble pinch-off. $D_0=2.1$ mm and $\text{We}=223.1$.}\label{fig:fig06}
\end{figure*}
The evolution of the cavity depth before the formation of the Worthington jet is shown in Fig.\ \ref{fig:fig07}a. Initially, the cavity depth $H$ increases rapidly due to the large inertia of the droplet fluid. As the droplet fluid sinks and the cavity expands, the growth of the cavity slows down, and the growth rate of the cavity depth decreases. After reaching a maximum cavity size, the cavity retracts due to the gravitational force. Therefore, the cavity depth decreases.
\begin{figure*}
\centering
\includegraphics[scale=0.55]{figure07}\\
\caption{Effects of gravity on cavity deformation. (a) Time evolution of the cavity depth before the formation of the Worthington jet at different gravities. $D_0=2.1$ mm and $\text{We}=223.1$. (b) Maximum depth of the cavity $H_m^*$ at different gravities. The symbols are the results of numerical simulation, and the solid lines are theoretical results predicted by Eq.\ (\ref{eq:eq12}).}\label{fig:fig07}
\end{figure*}
The maximum depth of the cavity ${{H}_{m}}$ is defined as the maximum depth measured from the initial pool surface to the bottom of the cavity along the axis of symmetry ($r=0$) before the formation of the Worthington jet. The time variation of the cavity depth in Fig.\ \ref{fig:fig07}a also shows that the maximum cavity depth is affected by gravitational force. With increasing the gravity, the maximum cavity depth decreases, and the time to reach the maximum cavity depth decreases. This can be explained by the conversion and conservation of energy. The droplet's initial energy ${{E}_{0}}$ includes kinetic and surface energy. The kinetic energy can be expressed as
\begin{equation}\label{eq:eq07}
{{E}_{k0}}=\frac{1}{12}\pi \rho D_{0}^{3}U_{0}^{2}.
\end{equation}
The initial surface energy of the droplet is
\begin{equation}\label{eq:eq08}
{{E}_{s0}}=\pi \sigma D_{0}^{2}.
\end{equation}
The droplet's initial kinetic energy and the surface energy are converted to the gravitational potential energy of the liquid crown and the surface energy of the cavity liquid. The increment in the gravitational potential energy is due to the liquid originally in the cavity position (before the droplet impact) moving to a higher position and forming the liquid crown (after the droplet impact). Therefore, the increment in the gravitational potential energy as the cavity expands to its maximum depth ${{H}_{m}}$ can be approximated as ${{E}_{p}}=mg{{H}_{m}}$, where \emph{m} is the mass of the elevated liquid and the elevated height of the liquid can be estimated by ${{H}_{m}}$. Since the cavity can be approximated by a hemisphere when it expands to the maximum depth \cite{Berberovic2009LiuidLayer, Bisighini2010CraterEvolution, Engel1966CraterDepth, Leng2001SplashSphere}, the mass of the elevated liquid can be expressed as $m=\rho V=2\pi \rho H_{m}^{3}/3$. Therefore, the increment in the gravitational potential energy of the liquid crown as the cavity expands to its maximum depth can be expressed as
\begin{equation}\label{eq:eq09}
{{E}_{p}}=\frac{2}{3}\pi \rho gH_{m}^{4}.
\end{equation}
We ignore the kinetic energy of the liquid crown because the cavity can be assumed as quasi-stationary when it achieves its maximum depth. A precise calculation of the surface energy should consider the change in the surface area from the initial flat surface of the pool to the cavity and the crown, which is complex geometry and difficult to calculate directly. Since the cavity is almost hemispherical, we can simply estimate the scale of the variation of the surface area as $2\pi H_{m}^{2}$. Hence, the variation in the surface energy can be estimated as
\begin{equation}\label{eq:eq10}
{{E}_{s}}=2\pi \sigma H_{m}^{2}.
\end{equation}
The droplet's initial energy is approximately the sum of the increment of the surface energy of the cavity and the gravitational potential energy of the liquid crown,
\begin{equation}\label{eq:eq11}
{{E}_{k0}}+{{E}_{s}}_{0}={{E}_{p}}+{{E}_{s}}.
\end{equation}
By substituting Eqs.\ (\ref{eq:eq07})-(\ref{eq:eq10}) into Eq.\ (\ref{eq:eq11}), we can get
\begin{equation}\label{eq:eq12}
\text{We} = 8\text{Bo}{{(H_{m}^{*})}^{4}}+24{{(H_{m}^{*})}^{2}}-12,
\end{equation}
where $H_{m}^{*}$ is the maximum dimensionless depth of the cavity and is defined as $H_{m}^{*}\equiv {{H}_{m}}/{{D}_{0}}$.
The maximum depth of the cavity at different gravities is shown in Fig.\ \ref{fig:fig07}b. The symbols are the results of the numerical simulation, and the lines are the theoretical results predicted by Eq.\ (\ref{eq:eq12}). The comparison shows reasonable agreement between the simulation and the theoretical prediction. The maximum depth of the cavity decreases with increasing $\text{Bo}$, and increases with increasing $\text{We}$. The reason is that the droplet with a larger $\text{We}$ has more inertia, which can be converted to more surface energy of the cavity, and thus produces a deeper cavity.
To determine the condition of regular bubble pinch-off, we produce a map of impact outcomes by varying the droplet speed $U_0$ and the gravitational acceleration $g$, as shown in Fig.\ \ref{fig:fig08}. Regular bubbles are produced when the inertia effect is strong (i.e., large We) and the gravitational force is large (i.e., large Bo). After the impact, capillary waves are formed near the impact point, and propagates inward and downward along the cavity surface. The pinch-off of a regular bubble occurs if the timescale for the cavity to achieve its maximum depth $t_m$ is smaller than the timescale of the capillary wave $t_w$ \cite{Morton2000FlowRegime, Oguz1990BubbleEntrainment}. The timescale for the cavity to achieve its maximum depth \cite{Oguz1990BubbleEntrainment} can be expressed as
\begin{equation}\label{eq:eq13}
{{t}_{m}}\sim c_{{m}}^{-4/3}U_{0}^{1/3}{{D}_{0}},
\end{equation}
where ${{c}_{m}}\sim {{(g\sigma /\rho )}^{1/4}}$ is the minimum speed of the capillary-gravity surface wave. The timescale of capillary wave is
\begin{equation}\label{eq:eq14}
{{t}_{w}}\sim {{\left[ (\sigma /\rho ){{k}^{3}} \right]}^{-1/2}},
\end{equation}
where $k$ is the wavenumber, $k\sim {{({{D}_{0}}\text{We})}^{-1}}$ \cite{Oguz1990BubbleEntrainment}. Therefore, the threshold of regular bubble pinch-off can be expressed as
\begin{equation}\label{eq:eq15}
\text{We}\sim {{\text{Bo}}^{-1/4}}.
\end{equation}
\begin{figure}
\centering
\includegraphics[scale=0.38]{figure08}\\
\caption{Regime map of regular bubble pinch-off after droplet impact at different gravities. The solid line is the theoretical threshold of the bubble pinch-off predicted by Eq.\ (\ref{eq:eq15}) with a fitting coefficient of 170. $D_0=2.1$ mm. }\label{fig:fig08}
\end{figure}
The line in Fig.\ \ref{fig:fig08} is the theoretical threshold of the bubble pinch-off predicted by Eq.\ (\ref{eq:eq15}). The threshold from the numerical results agrees well with scaling model predicted by Eq.\ (\ref{eq:eq15}), confirming the accuracy of the above theoretical analysis. The analysis also shows that the main role of the gravitational force in the pinch-off of regular bubbles is to induce capillary-gravity surface waves. If the gravitation force is strong, the capillary-gravity waves propagate quickly to create a cavity of a hemispherical shape. Then the capillary wave propagates to the lowest point of the cavity, producing a cylinder of air. Finally, the cylindrical air pocket pinches off to produce a regular bubble. If the gravitational force increases (i.e., Bo increases), the capillary-gravity waves propagate faster, and the pinch-off of regular bubbles becomes easier. Therefore, the threshold Weber number of bubble pinch-off decreases as the Bond number increases.
\subsection{Effects of the environmental pressure}\label{sec:sec43}
\begin{figure*}
\centering
\includegraphics[width=1.6\columnwidth]{figure09}\\
\caption{Cavity behaviors after the impact at different environmental pressures. (a) Pinch-off of a regular bubble at $P^*=1$; (b) Entrapment of a large bubble at $P^*=28$ (see Video 5 in Supplementary Material \cite{SM}). $D_0=2.1$ mm and $\text{We}=279.9$.}\label{fig:fig09}
\end{figure*}
Environmental pressure plays an essential role in the impact of droplets on a liquid pool \cite{Klyuzhin2010PersistingDropletsSurfaces, Marcotte2019EjectaCorollaSplashes}, and its effect on bubble entrapment is discussed in this section. The evolution of the cavity at different environmental pressures is compared in Fig.\ \ref{fig:fig09}. The relative pressure is used $P^*\equiv P/{{P}_{0}}$, where $P$ is the environmental pressure, and ${{P}_{0}}$ is the standard pressure, 1 bar. At standard environmental pressure $P^*=1$, the crown moves upward and also outward, as shown at 1.7 ms in Fig.\ \ref{fig:fig09}a. The capillary wave propagates inward along the cavity interface, and a cylindrical air pocket is produced at the bottom of the cavity at 21.8 ms, and the mouth of the cylindrical air pocket contracts to pinch off a regular bubble at 23.6 ms. In contrast, when the environmental pressure is high, the liquid crown moves upward and also inward, as shown at 1.4 ms in Fig.\ \ref{fig:fig09}b for $P^*=28$. The liquid crown becomes thicker as it moves inward. Then, the rim of the liquid crown collides, sealing a large bubble below the surface of the pool. Meanwhile, an upward jet and a downward jet are produced because of the inertia of the collision of the crown rim. Then, the downward jet punctures into the large bubble, which finally converges at the center. Meanwhile, the upward jet breaks up into secondary droplets owing to the jet's capillary instability.
To analyze the mechanism of large bubble entrapment, we consider the vorticity field and the pressure field. Upon the impact, strong vorticity is induced at the interface. Then the vorticity detaches from the interface and forms a vortex ring. The pressure, vorticity, and velocity fields are shown in Figs.\ \ref{fig:fig10}a and \ref{fig:fig10}b. A pressure difference is found in the air phase between the two sides of the liquid crown, and the vorticity detaches from the crown surface to form a vortex ring, as shown at 1.4 ms in Fig.\ \ref{fig:fig10}a. The variation of the vorticity and the pressure along the surface of the crown at a typical instant are plotted in Figs.\ \ref{fig:fig10}c and \ref{fig:fig10}d, respectively. As the environmental pressure increase, the vorticity becomes stronger, and the pressure difference between the two sides of the crown rim becomes larger. The stronger vortex and the larger pressure difference push the rim to bend inward and downward (see the velocity field in Fig.\ \ref{fig:fig10}b and the shape of the crown rim in Fig.\ \ref{fig:fig10}e). The crown rims finally contact and entrap a large bubble.
\begin{figure*}
\centering
\includegraphics[width=1.65\columnwidth]{figure10}\\
\caption{(a) Pressure fields (left) and vorticity fields (right) of large bubble entrapment. (b) Velocity fields of large bubble entrapment. The relative pressure is $P^*=28$. (c) Vorticity along the surface of liquid crown. The surface of the crown is highlighted by a red line in the inset. (d) Pressure along the surface of liquid crown. (e) Shape of the liquid crown rim. $t=3$ ms. $D_0=2.1$ mm and $\text{We}=279.9$. }\label{fig:fig10}
\end{figure*}
To characterize the entrapped large bubbles, we plot the volumes of large bubbles at different environmental pressures in Fig.\ \ref{fig:fig11}. The bubble can be much larger than the initial droplet size. For example, at $P^*=10$ and $\text{We}=437.3$, the volume of the large bubble is almost 27.5 times the initial droplet volume. The volume of the large bubble decreases with increasing environmental pressure. As environmental pressure increases, vorticity becomes stronger, and the pressure difference between the two sides of the crown rim becomes larger. The stronger vortex and the larger pressure difference push the crown to bend inward and downward. The bending degree of the crown increases with the environmental pressure (see Fig.\ \ref{fig:fig10}e). Thus, the volume of the entrapped large bubble decreases as we increase the environmental pressure. The maximum volume of the large bubble occurs at the left end of each curve for a fixed $\text{We}$, as shown in Fig.\ \ref{fig:fig11}. If the environmental pressure decreases further, the transition from large bubble to regular bubble occurs. The threshold for the transition will be discussed later in this section.
At high environmental pressure, it is also possible to entrap two bubbles after the impact. The evolution of the cavity for two-bubble entrapment in a typical case is compared with that for single bubble entrapment in Fig.\ \ref{fig:fig12}. At the standard environmental pressure, a regular bubble is pinched off at 20 ms, as shown in Fig.\ \ref{fig:fig12}a. In contrast, when the relative pressure is 20, two bubbles were pinched off as shown at 20 ms in Fig.\ \ref{fig:fig12}b. As the capillary wave propagates inward along the interface of the cavity, a cylinder of air is formed at 18 ms. By comparing with the air cylinder at $P^*=1$, we can see that the air cylinder at $P^*=20$ is much longer than that at $P^*=1$ (see the size of the air cylinder at 18 ms in Fig.\ \ref{fig:fig12}a and \ref{fig:fig12}b). Therefore, when the mouth of the air cylinder closes, the air bubble produced from the cylinder is very long. Consequently, the long bubble further pinches off into two bubbles by collapsing at the waist, as shown at 18.6 ms and 20 ms in Fig.\ \ref{fig:fig12}b.
\begin{figure}
\centering
\includegraphics[scale=0.35]{figure11}\\
\caption{The normalized volumes of large bubbles entrapped after droplet impact at different environmental pressures. $V_0$ is the volume of the droplet. $D_0=2.1$ mm.}\label{fig:fig11}
\end{figure}
\begin{figure*}
\centering
\includegraphics[width=1.5\columnwidth]{figure12}\\
\caption{Evolution of the cavity after droplet impact: (a) Entrapment of a single bubble at $P^*=1$. (b) Entrapment of two bubbles at $P^*=20$ (see Video 6 in Supplementary Material \cite{SM}). $D_0=2.1$ mm, and $\text{We}= 188.9$.}\label{fig:fig12}
\end{figure*}
To determine the conditions of different regimes of bubble entrapment, we produce a regime map of the impact outcomes by varying the droplet speed and the environmental pressure. Large bubble entrapment occurs under a wide range of environmental pressure, as shown in Fig.\ \ref{fig:fig13}. A threshold for the transition from regular bubble pinch-off to large bubble entrapment is found, which is indicated by the red dashed line. Pan et al. \cite{Pan2010SurfaceProperties} studied the effect of the liquid viscosity on droplet impact and found that the threshold for the large bubble occurrence was almost not affected by the liquid viscosity. Therefore, the pressure threshold \emph{P} for the large bubbles occurrence at different environmental pressures can be expressed as a function of the liquid density $\rho$, the droplet diameter $D_0$, and the droplet speed $U_0$, i.e., $P=f(\rho ,\sigma ,{{D}_{0}},{{U}_{0}})$. Xu et al. \cite{Xu2017BurningEthanolSurface} studied the threshold for the large bubble occurrence based on dimensional analysis and suggested a power function of $f(\text{We})$, i.e., $f({\rm{We}}) \sim {\rm{W}}{{\rm{e}}^a}$, where \emph{a} is constant. Substituting it into $P=\rho U_{0}^{2}f(\text{We})$, the threshold for large bubble occurrence at different environmental pressures can be expressed as
\begin{equation}\label{eq:eq16}
\text{We}\sim {(\sigma /{D_0}{P_0})^{ - b}}{P^*}^b,
\end{equation}
where $b\equiv 1/(a+1)$ is constant for this study, which can be obtained by fitting. As shown in Fig.\ \ref{fig:fig13}, the scaling agrees well with the numerical simulation.
Figure 13 also shows the transition threshold from no bubble to the regular bubble pinch-off.
At $\text{We}>320$, there is only a narrow range of pressure for regular bubble pinch-off. As mentioned above, the pinch-off of a regular bubble occurs if the timescale for the cavity to achieve its maximum depth $t_m$ is smaller than the timescale of the capillary wave $t_w$. Chen et al. \cite{Chen2006PartialCoalescenceInterface} found that the density of the ambient fluid played an important role in capillary wave propagation when droplets impact a liquid surface. In our previous study \cite{Xu2022CrownRupturePressure}, we found that the environmental pressure mainly affected the density of the ambient gas during the droplet impact. We introduce the effect of the environmental pressure on the capillary wave propagation, and the minimum speed of the capillary-gravity surface wave can be expressed as ${{c}_{m}}\sim {{(g\sigma /\rho ')}^{1/4}}$, where $\rho '$ is the effective density $\rho '=\rho -m{{\rho }_{g}}$ with ${{\rho }_{g}}$ is the density of the ambient gas and \emph{m} is a constant coefficient. From Eq.\ (\ref{eq:eq14}), the timescale of the capillary wave is ${{t}_{w}}\sim {{[(\sigma /\rho '){{k}^{3}}]}^{-1/2}}$. Therefore, the threshold of regular bubble pinch-off can be obtained when the timescale for the cavity to achieve its maximum depth is equal to the timescale of the capillary wave: $\text{We}\sim \text{B}{{\text{o}}^{-1/4}}{{\left[ {{(\rho -m{{\rho }_{g}})}^{5}}/{{\rho }^{5}} \right]}^{-1/4}}$. Since the air density is proportional to the environmental pressure, ${{P}^{\text{*}}}=P/{{P}_{0}}={{\rho }_{g}}/{{\rho }_{0}}$, after rearrangement, the threshold for the transition from no bubble to the regular bubble pinch-off can be expressed in dimensionless form as
\begin{equation}\label{eq:eq17}
\text{We}\sim \text{B}{{\text{o}}^{-1/4}}{{(1-n{{P}^{\text{*}}})}^{-5/4}},
\end{equation}
where $n\equiv m{{\rho }_{0}}/\rho $ is a constant coefficient, which can be obtained by fitting. As shown in Fig.\ \ref{fig:fig13}, the scaling agrees well with the numerical simulation.
However, at $220<\text{We}<320$, as the environmental pressure increases, the process changes from regular bubble pinch-off to large bubble entrapment. When the Weber number is less than 320 at low environmental pressure, the timescale for the cavity to achieve its maximum depth is all smaller than the timescale of the capillary wave, ${{t}_{m}}<{{t}_{w}}$, so the regular bubble pinch-off occurs. For example, when $\text{We}=279.9$ at the standard environmental pressure (see Fig.\ \ref{fig:fig09}a), the time for the cavity to reach its maximum depth ${{t}_{m}}$ is about 15.1 ms, and the time of the capillary wave ${{t}_{w}}$ is about 21.8 ms (${{t}_{m}}<{{t}_{w}}$), thus the regular bubble pinch-off occurs. The phenomenon of two-bubble pinch-off occurs at low Weber number and moderate environmental pressure, as shown in Fig.\ \ref{fig:fig13}. When the environmental pressure is moderate, the liquid crown moves upward, and then sinks into the pool owing to the gravity and the surface tension force because the vorticity and the pressure difference are not enough to push the crowns to move inward to contact. As the capillary wave propagates inward along the cavity interface, a long cylinder of air is formed. Finally, two bubbles are produced when the mouth of the long cylinder of air closes and the waist pinches off.
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{figure13}\\
\caption{Regime map of bubble entrapment after droplets impact a liquid pool at different environmental pressures. The red dashed line is the threshold for the transition from regular bubble to large bubble entrapment predicted by Eq.\ (\ref{eq:eq16}) with a fitting coefficient of 1280 and $b = -0.5$. The black dash-dotted line is the threshold for the transition from no bubble to regular bubble pinch-off predicted by Eq.\ (\ref{eq:eq17}) with a fitting coefficient of 1180 and $n = -0.1$. The solid lines are just guides to the eye.}\label{fig:fig13}
\end{figure}
\section{Conclusions}\label{sec:sec5}
In this study, the cavity deformation and bubble entrapment after the impact of droplets on a liquid pool are studied by combined experimental measurements and numerical simulations. The numerical simulations are validated against experimental results by comparing the evolution of the cavity. The regular bubble pinch-off is the result of the capillary wave propagating downward along the surface of the cavity and merging at the bottom of the cavity. The large bubble entrapment is the result of the liquid crowns merging at the mouth of the cavity. Gravity and environmental pressure play important roles in cavity deformation and bubble entrapment. The maximum depth of the cavity decreases as the gravitational effect becomes stronger. A regime map of bubble entrapment is obtained at different gravities. The phenomenon of regular bubble pinch-off may disappear as the gravity decreases. As the environmental pressure is increased, the regular bubble pinch-off is transformed into the large bubble entrapment. The process of the large bubble entrapment is controlled by the vortex ring at the gas-liquid interface and the pressure difference between the two sides of the liquid crown. The volume of the large bubble entrapped decreases with increasing the environmental pressure. A regime map of bubble entrapment is obtained at different environmental pressures. When the environmental pressure is high and the Weber number is large, the strong vorticity at the gas-liquid interface and the large pressure difference between the two sides of the rim make the crown rim collide to entrap a large bubble. When the environmental pressure is low, a regular bubble is pinched off at the bottom of the cavity due to the propagation of the capillary waves. Finally, the thresholds for the transitions from no bubble to regular bubble and to large bubble regimes are analyzed.
This paper reports an experimental and numerical study of a droplet impacting a liquid pool. There are still many open questions for the impact process, such as the subsequent dynamics of the entrapped bubble and the dynamics of the liquid jet produced after bubble entrapment. This study of the impact of droplets on a liquid pool will not only deepen our understanding of the impact dynamics but also will be useful for the optimization of the relevant applications.
\section*{Acknowledgements}
This work is supported by the National Natural Science Foundation of China (Grant Nos.\ 51676137, 51921004).
\section*{Conflict of interest}
The authors have no conflicts to disclose.
\section*{Data Availability Statement}
The data that support the findings of this study are available from the corresponding author upon reasonable request.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,225 |
Q: Getting uninitialized constant error in rails app, but can pull data fine from rails console I'm trying to use the twitter gem, in my home#controller I have
@tweets = Twitter.user_timeline("pantsstore").limit(2)
and
<%= @tweets %> in homeController#index
but I'm getting an
uninitialized constant Spree::HomeController::Twitter
error. Where should I put 'require 'twitter''? Or how do I initialize the variable Twitter? I can pull tweets fine from the rails console with
Twitter.user_timeline("pantsstore").limit(2)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,925 |
Similar to janitorial work, porters ensure that communities are tidy and free from clutter. Porters maintain the environment that residents and visitors enjoy. They provide value and quality by assessing the needs of the complex and providing solutions. All experience levels encouraged to apply - from seasoned journeymen to entry level. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,966 |
Q: Why do I need to include https in externals for my rollup.config.js import typescript from 'rollup-plugin-typescript2'
import commonjs from 'rollup-plugin-commonjs'
import json from '@rollup/plugin-json'
import resolve from 'rollup-plugin-node-resolve'
import builtins from 'rollup-plugin-node-builtins'
export default {
input: "./index.ts",
output: {
file: "./dist/main.compiled.js",
format: "cjs",
sourcemap: true
},
external: ['https'], //Why???
plugins: [
typescript(),
commonjs(),
json(),
builtins(),
resolve()
]
}
If I don't include 'https' in my externals I get this error:
xhr = new global.XMLHttpRequest();
^
TypeError: global.XMLHttpRequest is not a constructor
when I import this package and use services which creates httpAgent for my axios client
import { Agent } from 'https'
httpAgent: new Agent({ keepAlive: true })
I thought builtins() solves this.
I am using yarn run rollup -c to build my project
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,265 |
Q: Buttons (and other clips) getting pixeled or distorsioned when scaling down in flash Our images in buttons and other components are getting pixeled or distorsionated, when scaling down or up the whole movie.
Left without scaling, right with scaling down
We have this properties over each image of the movie:
Any idea what could it be?
Thanks.
A: If your bitmaps are set to smooth, it could be your stage's quality is set too low.
stage.quality = StageQuality.MEDIUM;
Is usually a good setting for bitmap smoothing.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,741 |
using System;
using System.Collections.Generic;
using System.Linq;
using System.Threading.Tasks;
using Abc.Zebus.Directory.Configuration;
using Abc.Zebus.Directory.DeadPeerDetection;
using Abc.Zebus.Directory.Storage;
using Abc.Zebus.Testing;
using Abc.Zebus.Testing.Extensions;
using Abc.Zebus.Util;
using Moq;
using NUnit.Framework;
namespace Abc.Zebus.Directory.Tests.DeadPeerDetection
{
[TestFixture]
public class DeadPeerDetectorTests
{
private const int _transientPeerTimeout = 60 * 10;
private const int _persistentPeerTimeout = 60 * 30;
private const int _debugPeerTimeout = 60 * 60;
private readonly TimeSpan _pingInterval = 5.Minutes();
private PeerDescriptor _transientAlivePeer0;
private PeerDescriptor _transientAlivePeer1;
private PeerDescriptor _transientDeadPeer;
private PeerDescriptor _persistentAlivePeer;
private PeerDescriptor _persistentDeadPeer;
private PeerDescriptor _debugPersistentAlivePeer;
private PeerDescriptor _debugTransientAlivePeer;
private Mock<IPeerRepository> _peerRepositoryMock;
private TestBus _bus;
private DeadPeerDetector _detector;
private Mock<IDirectoryConfiguration> _configurationMock;
private PeerDescriptor _persistencePeer;
private PeerDescriptor _directoryPeer;
private string[] _peersNotToDecommission;
[SetUp]
public void Setup()
{
_transientAlivePeer0 = CreatePeerDescriptor("Abc.TransientAlive.0", isUp: true, isPersistent: false, hasDebuggerAttached:false);
_transientAlivePeer1 = CreatePeerDescriptor("Abc.TransientAlive.1", isUp: true, isPersistent: false, hasDebuggerAttached: false);
_transientDeadPeer = CreatePeerDescriptor("Abc.TransientDead.0", isUp: false, isPersistent: false, hasDebuggerAttached: false);
_persistentAlivePeer = CreatePeerDescriptor("Abc.PersistentAlive.0", isUp: true, isPersistent: true, hasDebuggerAttached: false);
_persistentDeadPeer = CreatePeerDescriptor("Abc.PersistentDead.0", isUp: false, isPersistent: true, hasDebuggerAttached: false);
_debugPersistentAlivePeer = CreatePeerDescriptor("Abc.DebugPersistentAlive.0", isUp: true, isPersistent: true, hasDebuggerAttached: true);
_debugTransientAlivePeer = CreatePeerDescriptor("Abc.DebugTransientAlive.0", isUp: true, isPersistent: false, hasDebuggerAttached: true);
_persistencePeer = CreatePeerDescriptor("Abc.Zebus.PersistenceService.0", isUp: true, isPersistent: false, hasDebuggerAttached: false);
_directoryPeer = CreatePeerDescriptor("NonStandardDirectoryName", isUp: true, isPersistent: false, hasDebuggerAttached: false);
_directoryPeer.Subscriptions = new[] { new Subscription(new MessageTypeId(typeof(RegisterPeerCommand))) };
_peersNotToDecommission = new string[0];
_peerRepositoryMock = new Mock<IPeerRepository>();
var peerDescriptors = new List<PeerDescriptor>
{
_transientAlivePeer0,
_transientAlivePeer1,
_transientDeadPeer,
_persistentAlivePeer,
_persistentDeadPeer,
_debugPersistentAlivePeer,
_debugTransientAlivePeer,
_persistencePeer
};
_peerRepositoryMock.Setup(repo => repo.GetPeers(It.IsAny<bool>())).Returns(peerDescriptors);
_peerRepositoryMock.Setup(repo => repo.Get(It.IsAny<PeerId>())).Returns<PeerId>(peerId => peerDescriptors.FirstOrDefault(x => x.Peer.Id == peerId));
_bus = new TestBus();
_configurationMock = new Mock<IDirectoryConfiguration>();
_configurationMock.As<IDirectoryConfiguration>().SetupGet(conf => conf.TransientPeerPingTimeout).Returns(_transientPeerTimeout.Seconds());
_configurationMock.As<IDirectoryConfiguration>().SetupGet(conf => conf.PersistentPeerPingTimeout).Returns(_persistentPeerTimeout.Seconds());
_configurationMock.As<IDirectoryConfiguration>().SetupGet(conf => conf.DebugPeerPingTimeout).Returns(_debugPeerTimeout.Seconds());
_configurationMock.As<IDirectoryConfiguration>().SetupGet(conf => conf.PeerPingInterval).Returns(_pingInterval);
_configurationMock.As<IDirectoryConfiguration>().SetupGet(conf => conf.WildcardsForPeersNotToDecommissionOnTimeout).Returns(() => _peersNotToDecommission);
_detector = new DeadPeerDetector(_bus, _peerRepositoryMock.Object, _configurationMock.Object);
_detector.TaskScheduler = new CurrentThreadTaskScheduler();
_bus.HandlerExecutor = new HangOnThrowHandlerExecutor();
}
[Test]
public void should_ping_peers()
{
_detector.DetectDeadPeers();
_bus.ExpectExactly(_transientAlivePeer0.PeerId, new PingPeerCommand());
_bus.ExpectExactly(_transientAlivePeer1.PeerId, new PingPeerCommand());
_bus.ExpectExactly(_persistentAlivePeer.PeerId, new PingPeerCommand());
_bus.ExpectExactly(_debugPersistentAlivePeer.PeerId, new PingPeerCommand());
_bus.ExpectExactly(_debugTransientAlivePeer.PeerId, new PingPeerCommand());
}
[Test]
public void forget_decommissioned_peers()
{
_detector.DetectDeadPeers();
SetupPeerRepository(_persistentAlivePeer);
_detector.DetectDeadPeers();
_detector.KnownPeerIds.ShouldBeEquivalentTo(new[] { _persistentAlivePeer.PeerId });
}
[Test]
public void should_not_ping_until_the_ping_interval_elapsed()
{
var startTime = SystemDateTime.UtcNow;
using (SystemDateTime.PauseTime(startTime))
{
_detector.DetectDeadPeers();
}
using (SystemDateTime.PauseTime(startTime + _pingInterval - 1.Second()))
{
_detector.DetectDeadPeers();
}
_bus.ExpectExactly(_transientAlivePeer0.PeerId, new PingPeerCommand());
_bus.ExpectExactly(_transientAlivePeer1.PeerId, new PingPeerCommand());
_bus.ExpectExactly(_persistentAlivePeer.PeerId, new PingPeerCommand());
_bus.ExpectExactly(_debugPersistentAlivePeer.PeerId, new PingPeerCommand());
_bus.ExpectExactly(_debugTransientAlivePeer.PeerId, new PingPeerCommand());
}
[Test]
public void should_not_timeout_if_a_transient_service_responds_to_the_second_ping()
{
SetupPeerRepository(_transientAlivePeer0);
SetupPeerResponse(_transientAlivePeer0.PeerId, false, true);
using (SystemDateTime.PauseTime())
{
var startTime = SystemDateTime.UtcNow;
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand());
SystemDateTime.PauseTime(startTime.AddSeconds(_transientPeerTimeout - 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
SystemDateTime.PauseTime(startTime.AddSeconds(_transientPeerTimeout + 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
}
}
[Test]
public void should_not_timeout_if_a_persistent_service_responds_to_the_second_ping()
{
SetupPeerRepository(_persistentAlivePeer, _transientAlivePeer0);
SetupPeerResponse(_transientAlivePeer0.PeerId, true, true);
SetupPeerResponse(_persistentAlivePeer.PeerId, false, true);
using (SystemDateTime.PauseTime())
{
var startTime = SystemDateTime.UtcNow;
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_transientPeerTimeout - 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_persistentPeerTimeout - 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_persistentPeerTimeout + 1));
_detector.DetectDeadPeers();
_bus.ExpectNothing();;
}
}
[Test]
public void should_not_timeout_if_a_debug_service_responds_to_the_second_ping()
{
SetupPeerRepository(_debugPersistentAlivePeer, _debugTransientAlivePeer);
SetupPeerResponse(_debugPersistentAlivePeer.PeerId, false, true);
SetupPeerResponse(_debugTransientAlivePeer.PeerId, false, true);
using (SystemDateTime.PauseTime())
{
var startTime = SystemDateTime.UtcNow;
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_debugPeerTimeout - 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_debugPeerTimeout + 1));
_detector.DetectDeadPeers();
_bus.ExpectNothing();
}
}
[Test]
public void should_timeout_if_a_transient_service_does_not_respond_in_time()
{
SetupPeerRepository(_transientAlivePeer0);
SetupPeerResponse(_transientAlivePeer0.PeerId, false, false);
using (SystemDateTime.PauseTime())
{
var startTime = SystemDateTime.UtcNow;
var firstPingTimestampUtc = startTime;
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand());
SystemDateTime.PauseTime(startTime.AddSeconds(_transientPeerTimeout - 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
SystemDateTime.PauseTime(startTime.AddSeconds(_transientPeerTimeout + 1));
_detector.DetectDeadPeers();
_bus.Expect(new UnregisterPeerCommand(_transientAlivePeer0.Peer, firstPingTimestampUtc));
}
}
private static readonly string[] _peersNotToDecommissionExamples =
{
"Abc.TransientAlive.0",
"Abc.TransientAlive.*",
"*Abc.TransientA*",
"Abc.TransientAlive.?",
};
[Test]
[TestCaseSource(nameof(_peersNotToDecommissionExamples))]
public void should_mark_as_not_responding_if_a_transient_peer_in_the_whitelist_does_not_respond_in_time(string peerNotToDecommission)
{
_peersNotToDecommission = new[] { peerNotToDecommission };
SetupPeerRepository(_transientAlivePeer0);
SetupPeerResponse(_transientAlivePeer0.PeerId, false, false);
using (SystemDateTime.PauseTime())
{
var startTime = SystemDateTime.UtcNow;
var firstPingTimestampUtc = startTime;
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_transientPeerTimeout - 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_transientPeerTimeout + 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new MarkPeerAsNotRespondingCommand(_transientAlivePeer0.Peer.Id, firstPingTimestampUtc));
}
}
[Test]
public void should_timeout_if_a_persistent_service_does_not_respond_in_time()
{
SetupPeerRepository(_persistentAlivePeer, _transientAlivePeer0);
SetupPeerResponse(_transientAlivePeer0.PeerId, true, true);
SetupPeerResponse(_persistentAlivePeer.PeerId, false, false);
using (SystemDateTime.PauseTime())
{
var startTime = SystemDateTime.UtcNow;
var firstPingTimestampUtc = startTime;
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_transientPeerTimeout - 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
_bus.ClearMessages();
var retryTimestamp = startTime.AddSeconds(_persistentPeerTimeout - 1);
SystemDateTime.PauseTime(retryTimestamp);
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_persistentPeerTimeout + 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new MarkPeerAsNotRespondingCommand(_persistentAlivePeer.Peer.Id, firstPingTimestampUtc));
}
}
[Test]
public void should_not_decommission_directory_peer()
{
SetupPeerRepository(_directoryPeer, _transientAlivePeer0);
SetupPeerResponse(_transientAlivePeer0.PeerId, false, false);
SetupPeerResponse(_directoryPeer.PeerId, false, false);
using (SystemDateTime.PauseTime())
{
var startTime = SystemDateTime.UtcNow;
var firstPingTimestampUtc = startTime;
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_transientPeerTimeout - 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_transientPeerTimeout + 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new UnregisterPeerCommand(_transientAlivePeer0.Peer, firstPingTimestampUtc));
}
}
[Test]
public void should_not_decommission_the_persistence()
{
SetupPeerRepository(_persistencePeer);
SetupPeerResponse(_persistencePeer.PeerId, false, false);
using (SystemDateTime.PauseTime())
{
var startTime = SystemDateTime.UtcNow;
var persistenceDownDetectedCount = 0;
_detector.PersistenceDownDetected += () => persistenceDownDetectedCount++;
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand());
SystemDateTime.PauseTime(startTime.AddSeconds(_transientPeerTimeout - 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
SystemDateTime.PauseTime(startTime.AddSeconds(_transientPeerTimeout + 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
persistenceDownDetectedCount.ShouldEqual(1);
}
}
private class PeerEvent
{
public PeerId PeerId { get; private set; }
public DateTime Timestamp { get; private set; }
public PeerEvent(PeerId peerId, DateTime timestamp)
{
PeerId = peerId;
Timestamp = timestamp;
}
}
[Test]
public void should_raise_PingMissed_before_a_peer_is_marked_as_timed_out()
{
SetupPeerRepository(_persistentAlivePeer, _transientAlivePeer0);
SetupPeerResponse(_transientAlivePeer0.PeerId, true, true);
SetupPeerResponse(_persistentAlivePeer.PeerId, false, false);
using (SystemDateTime.PauseTime())
{
var missedPings = new List<PeerEvent>();
_detector.PingTimeout += (peer, timestamp) => missedPings.Add(new PeerEvent(peer, timestamp));
var startTime = SystemDateTime.UtcNow;
_detector.DetectDeadPeers();
SystemDateTime.PauseTime(startTime.Add(_pingInterval - 1.Second()));
_detector.DetectDeadPeers();
missedPings.Count.ShouldEqual(0);
SystemDateTime.PauseTime(startTime.Add(_pingInterval + 1.Second()));
_detector.DetectDeadPeers();
missedPings.Count.ShouldEqual(1);
missedPings.First().PeerId.ShouldEqual(_persistentAlivePeer.PeerId);
SystemDateTime.PauseTime(startTime.Add(_pingInterval + _pingInterval + 1.Second()));
_detector.DetectDeadPeers();
missedPings.Count.ShouldEqual(2);
missedPings.All(evt => evt.PeerId == _persistentAlivePeer.PeerId).ShouldBeTrue();
}
}
[Test]
public void should_raise_PeerResponding_when_peer_starts_replying_again_to_ping()
{
SetupPeerRepository(_persistentAlivePeer);
SetupPeerResponse(_persistentAlivePeer.PeerId, false, false, false, true);
using (SystemDateTime.PauseTime())
{
var startTime = SystemDateTime.UtcNow;
var firstPingTimestampUtc = startTime;
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_persistentPeerTimeout - 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_persistentPeerTimeout + 1));
_detector.DetectDeadPeers();
_bus.Expect(new MarkPeerAsNotRespondingCommand(_persistentAlivePeer.Peer.Id, firstPingTimestampUtc));
_bus.ClearMessages();
// simulate MarkPeerAsNotRespondingCommand handler
_persistentAlivePeer.Peer.IsResponding = false;
SystemDateTime.PauseTime(SystemDateTime.UtcNow.Add(_pingInterval));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(SystemDateTime.UtcNow.Add(_pingInterval));
_detector.DetectDeadPeers();
_bus.Expect(new MarkPeerAsRespondingCommand(_persistentAlivePeer.Peer.Id, SystemDateTime.UtcNow));
}
}
[Test]
public void should_timeout_if_any_debug_service_does_not_respond_in_time()
{
SetupPeerRepository(_debugPersistentAlivePeer, _debugTransientAlivePeer);
SetupPeerResponse(_debugPersistentAlivePeer.PeerId, false, false);
SetupPeerResponse(_debugTransientAlivePeer.PeerId, false, false);
using (SystemDateTime.PauseTime())
{
var startTime = SystemDateTime.UtcNow;
var firstPingTimestampUtc = startTime;
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_debugPeerTimeout - 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(new PingPeerCommand(), new PingPeerCommand());
_bus.ClearMessages();
SystemDateTime.PauseTime(startTime.AddSeconds(_debugPeerTimeout + 1));
_detector.DetectDeadPeers();
_bus.ExpectExactly(
new UnregisterPeerCommand(_debugTransientAlivePeer.Peer, firstPingTimestampUtc),
new UnregisterPeerCommand(_debugPersistentAlivePeer.Peer, firstPingTimestampUtc)
);
}
}
private void SetupPeerRepository(params PeerDescriptor[] peer)
{
_peerRepositoryMock.Setup(repo => repo.GetPeers(It.IsAny<bool>())).Returns(new List<PeerDescriptor>(peer));
}
private void SetupPeerResponse(PeerId peerId, params bool[] respondToPing)
{
var invocationCount = 0;
_bus.AddHandlerForPeer<PingPeerCommand>(peerId, cmd =>
{
var shouldRespond = invocationCount < respondToPing.Length && respondToPing[invocationCount];
++invocationCount;
if(shouldRespond)
return true;
throw new InvalidOperationException();
});
}
private static PeerDescriptor CreatePeerDescriptor(string peerId, bool isPersistent, bool isUp, bool hasDebuggerAttached)
{
var descriptor = new Peer(new PeerId(peerId), "tcp://abcdell348:58920", isUp).ToPeerDescriptor(isPersistent);
descriptor.HasDebuggerAttached = hasDebuggerAttached;
return descriptor;
}
/// <summary>
/// Executes handler synchronously but hangs on exceptions
/// </summary>
public class HangOnThrowHandlerExecutor : TestBus.IHandlerExecutor
{
public Task<CommandResult> Execute(ICommand command, Func<IMessage, object> handler)
{
var taskCompletionSource = new TaskCompletionSource<CommandResult>();
try
{
var result = handler != null ? handler(command) : null;
taskCompletionSource.SetResult(new CommandResult(0, string.Empty, result));
}
catch (Exception)
{
return new TaskCompletionSource<CommandResult>().Task;
}
return taskCompletionSource.Task;
}
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,764 |
<?php // explore.php :: Handles all map exploring, chances to fight, etc.
function move() {
global $userrow, $controlrow;
if ($userrow["currentaction"] == "Fighting") { header("Localização: index.php?do=fight"); die(); }
$latitude = $userrow["latitude"];
$longitude = $userrow["longitude"];
if (isset($_POST["north"])) { $latitude++; if ($latitude > $controlrow["gamesize"]) { $latitude = $controlrow["gamesize"]; } }
if (isset($_POST["south"])) { $latitude--; if ($latitude < ($controlrow["gamesize"]*-1)) { $latitude = ($controlrow["gamesize"]*-1); } }
if (isset($_POST["east"])) { $longitude++; if ($longitude > $controlrow["gamesize"]) { $longitude = $controlrow["gamesize"]; } }
if (isset($_POST["west"])) { $longitude--; if ($longitude < ($controlrow["gamesize"]*-1)) { $longitude = ($controlrow["gamesize"]*-1); } }
$townquery = doquery("SELECT id FROM {{table}} WHERE latitude='$latitude' AND longitude='$longitude' LIMIT 1", "towns");
if (mysql_num_rows($townquery) > 0) {
$townrow = mysql_fetch_array($townquery);
include('towns.php');
travelto($townrow["id"], false);
die();
}
$chancetofight = rand(1,5);
if ($chancetofight == 1) {
$action = "currentaction='Fighting', currentfight='1',";
} else {
$action = "currentaction='Exploring',";
}
$updatequery = doquery("UPDATE {{table}} SET $action latitude='$latitude', longitude='$longitude', dropcode='0' WHERE id='".$userrow["id"]."' LIMIT 1", "users");
header("Location: index.php");
}
?> | {
"redpajama_set_name": "RedPajamaGithub"
} | 3,948 |
{"url":"http:\/\/mathhelpforum.com\/advanced-math-topics\/115634-any-help-appreciated-y-sin-x-sketch-print.html","text":"# Any help appreciated with y\u00b2=sin x sketch\n\nPrintable View\n\n\u2022 November 19th 2009, 01:39 PM\nshadz\nplease help-problem now solved\nsolved with books\n\u2022 November 19th 2009, 02:35 PM\nbigwave\nare you graphing $y^2 = sin x$ as $y = \\sqrt{sin x}$\n\u2022 November 20th 2009, 12:04 PM\nshadz\nnow solved\n\u2022 November 20th 2009, 12:31 PM\nshadz\nI have now done this,using books\n\u2022 November 20th 2009, 01:02 PM\ne^(i*pi)\nQuote:\n\nOriginally Posted by shadz\nAny help appreciated with a tricky question of the form - using your knowledge of the graph of y=sin x, sketch, with reasons, the graph of y\u00b2=sin x for 0 is larger than or equal to x is larger than or equal to 3 pie.\n(Rofl)\n\n$\\sqrt{sin(x)}$ is imaginary for $\\pi < x < 2\\pi$\n\u2022 November 20th 2009, 01:38 PM\nshadz\nI have now done this,using books","date":"2014-10-25 21:22:35","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\": 0, \"img_math\": 0, \"codecogs_latex\": 4, \"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\": 0.6745482683181763, \"perplexity\": 5655.812692738564}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"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-2014-42\/segments\/1414119650516.39\/warc\/CC-MAIN-20141024030050-00160-ip-10-16-133-185.ec2.internal.warc.gz\"}"} | null | null |
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Rose Lane… because your family is like our family. | {
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Washington, DC – The Commodity Futures Trading Commission (CFTC) today issued an order filing and settling charges against Glencore Agriculture B.V., f/k/a Glencore Grain B.V. (Glencore B.V.), located in Rotterdam, the Netherlands, and Glencore Ltd., located in Stamford, Connecticut, finding that on multiple trading days during May 2013, June 2013, May 2014, and June 2014, Glencore B.V. and Glencore Ltd. held net positions in the ICE Futures Cotton No. 2 contracts (cotton futures) that, on an aggregated basis, exceeded the speculative position limits established by the CFTC. In addition, the CFTC Order finds that on twenty-four occasions between January 2013 and November 2015, Glencore B.V. and Glencore Ltd. executed exchange of futures for physical transactions (EFPs) opposite each other's cotton futures trading accounts, even though their accounts were not independently controlled as required for such transactions not to constitute illegal wash trades. And, on at least two occasions in 2013 and 2014, Glencore B.V. submitted to the CFTC a Form 304 that failed to represent accurately all required information, including its short cash sales commitments, according to the CFTC Order.
The CFTC Order requires Glencore B.V. and Glencore Ltd., jointly and severally, to pay a $2 million civil monetary penalty and to cease and desist from further violations of the Commodity Exchange Act (CEA) and CFTC Regulations, as charged.
According to the CFTC Order, at all times relevant to the Order, Glencore centralized the management of its global cotton business under the direction of a single trading manager (referred to in the Order as Head of Cotton), who oversaw cotton operations across all Glencore entities. The Head of Cotton directly supervised cotton traders at Glencore B.V. and was also the direct supervisor of Glencore Ltd.'s head cotton trader.
The CEA and CFTC Regulations set limits on the net long or net short position that any person may hold or control for certain commodities, including a limit of 5,000 cotton futures for a single month, other than the spot month, exclusive of bona fide hedging transactions. The CFTC Order finds that because Glencore B.V. and Glencore Ltd. operated their cotton trading under the common control of Glencore's Head of Cotton, their cotton futures positions should have been aggregated for purposes of complying with the Commission's position limits. When aggregated, the cotton futures positions of Glencore B.V. and Glencore Ltd. exceeded 5,000 net contracts, exclusive of bona fide hedging transactions, on multiple days during May 2013, June 2013, May 2014, and June 2014.
The CEA and CFTC Regulations permit noncompetitive trading, such as EFPs, only if such transactions are conducted in accordance with rules of an exchange, such as the Intercontinental Exchange (ICE), that are approved by the CFTC. At all times relevant to this Order, ICE rules permitted the transaction of EFPs between independently controlled accounts. However, the CFTC Order finds that Glencore B.V.'s and Glencore Ltd.'s cotton futures trading accounts were both ultimately controlled by Glencore's Head of Cotton. As a result they were not independently controlled. Nevertheless, between January 2013 and November 2015, Glencore B.V. and Glencore Ltd. executed twenty-four EFPs opposite one another's accounts, according to the CFTC Order.
The Order further states that CFTC Regulations require cotton merchants and dealers holding or controlling reportable futures positions to file a monthly Statement of Cash Positions in Cotton (Form 304), as of the close of business on the last Friday of the month. On the Form 304, entities report the composition of their fixed price cash position in cotton and cotton products, including the quantity of open fixed price purchase and fixed price sale commitments. The CFTC Order finds that Glencore B.V. filed two erroneous Form 304 reports with the CFTC—one on May 31, 2013 and a second on May 30, 2014—that overstated the quantities of its fixed price cotton cash positions.
The CFTC thanks and acknowledges the Dutch Authority for the Financial Markets for its assistance in this matter.
CFTC Division of Enforcement staff members responsible for this action are James Deacon, Ilana Waxman, Laura Brookover, Kara Mucha, John Buffington, James H. Holl, III, and Rick Glaser. The Division of Enforcement would like to recognize the assistance of other CFTC staff: Janet Briner, Kelly Beck, Harry Hild, and Matthew Hunter. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,181 |
\section{Introduction}
QCD is a four-dimensional gauge theory describing strong interaction of quarks and gluons. There is a growing amount of evidence that QCD (and Yang-Mills theories in general) possess a hidden symmetry. This symmetry has a dynamical origin in the sense that it is not seen at the level of classical Lagrangian and manifests itself at quantum level through remarkable integrability properties of effective dynamics.
The simplest example which allows us to explain integrability phenomenon is a process of deeply inelastic scattering (DIS) of an energetic hadron off virtual photon, $\gamma^*(q) + h(p) \to \text{everything}$. This process played a distinguished r\^ole in early days of QCD development and it led, in particular, to
important discoveries such as QCD factorization and formulation of parton model for hard processes (see e.g. \cite{book}).
The total cross-section of of DIS process is related by the optical theorem to imaginary part of the forward scatteting amplitude $\gamma^*(q)+h(p)\to\gamma^*(q)+h(p)$ (see Fig.~\ref{dis}). It is parameterized by the so-called structure functions $F(x,q^2)$ depending on the photon virtuality $q^2<0$ and dimensionless Bjorken variable $0<x<1$. The latter is related to the total center-of-mass energy of the process as $s=(p+q)^2=-q^2(1-x)/x$.
\begin{figure}[ht]
\ifarxiv
\centerline{\includegraphics[height=3cm]{DIS1cm}}
\else
\centerline{\includegraphics[height=3cm]{DIS1times}}
\fi
\caption[]{\small The total cross-section of deep inelastic scattering $\gamma^*(q)+h(p)\to {\rm everything}$ is related by the optical theorem to imaginary part of the forward scatteting amplitude. Solid and wavy lines denote quarks and gluons, respectively. }
\label{dis}
\end{figure}
The integrability has been first discovered in Refs.~\cite{Lipatov94,FK95,Korchemsky95} in the study of high-energy, $s\gg -q^2$ (or equivalently $x\to 0$) asymptotics of $F(x,q^2)$.
Experimental data indicate that the structure functions increase in this limit as a power of the energy, $F(x,q^2)\sim (1/x)^{\omega}$, in a quantitative agreement with the Regge theory prediction. At weak coupling, the same behavior can be obtained through resummation of perturbative corrections to the structure functions enhanced by logarithm of the energy~\cite{BFKL}. The structure functions obtained in this way satisfy nontrivial multi-particle Bethe-Salpeter like evolution equations~\cite{Bartels80,KP80}.
These equations have resisted analytical solution but a breakthrough occurred after it was found \cite{Lipatov94,FK95,Korchemsky95} that, in multi-color limit, these equations can be mapped into a Sch\"odinger equation for a completely integrable quantum (noncompact) Heisenberg $SL (2, \mathbb{C})$ spin chain. This opened up the possibility of applying the quantum inverse scattering methods for the construction of the exact solution to the evolution equation in planar QCD.
Later, similar integrable structures have been found in Refs.~\cite{BDM98,Belitsky99,BDKM99} in the study of dependence of the structure functions $F(x,q^2)$ on the momentum transfered $q^2$. At large $Q^2=-q^2$, the operator product expansion can be applied to expand the moments of the structure functions
in powers of a hard scale $1/Q$
\begin{align}\label{OPE}
\int_0^1 dx\, x^{N-1} F(x,q^2) =\sum_{L\ge 2} \frac{c_{N,L}(\alpha_s(Q^2))}{Q^L} \vev{p|O_{N,L}|p}_{\mu^2=Q^2} \,.
\end{align}
Here the expansion runs over local composite gauge invariant operators ({\it Wilson operators}) of Lorentz spin $N$ and twist $L$. The corresponding coefficient functions $c_{N,L}(\alpha_s(Q^2))$ can be computed at
weak coupling as a series in the QCD coupling constant $\alpha_s(\mu^2)=g^2/(4\pi)$ normalized at
$\mu^2=Q^2$. At the same time, the matrix element of the Wilson operator with respect to
hadron state $\vev{p|O_{N,L}|p}_{\mu^2=Q^2}$ is a nonperturbative quantity. Its absolute value can not be computed perturbatively whereas its dependence on the hard scale $Q^2$ is governed by
the renormalization group (Callan-Symanzik) equations
\begin{align}\label{CS}
\mu^2\frac{d}{d\mu^2} \vev{p|O^{(\alpha)}_{N,L}|p} = - \gamma^{(\alpha)}_{N,L}(\alpha_s) \vev{p|O^{(\alpha)}_{N,L}|p} \,.
\end{align}
Here we introduced the superscript $(\alpha)$ to indicate that for given $N$ and $L$ there are a few Wilson operators parameterized by the index $\alpha$. The Callan-Symanzik equation \re{CS} has the meaning of a conformal Ward identity for the Wilson operators with the anomalous dimension $ \gamma^{(\alpha)}_{N,L}(\alpha_s) $ being the eigenvalue of the QCD dilatation operator (see e.g. review \cite{BKM03}).
The Wilson operators are built in QCD from elementary quark and gluon fields and from an arbitrary number of covariant derivatives. In general, such operators mix under renormalization with other operators carrying the same Lorentz spin and twist. Diagonalizing
the corresponding mixing matrix we can find the spectrum of the anomalous dimensions $\gamma^{(\alpha)}_{N,L}(\alpha_s)$. For the Wilson operators of the lowest twist, $L=2$, the anomalous dimensions can be obtained in the closed form \cite{GW73}, whereas for higher twist operators the problem becomes extremely nontrivial already at one loop
due to a complicated form of the mixing matrix \cite{BFLK85}. Quite remarkably, the spectrum of
the anomalous dimensions can be found exactly in QCD in the sector of the so-called maximal-helicity Wilson operators. The reason for this is that the one-loop mixing matrix in QCD in this sector can be mapped in the multi-color limit into a Hamiltonian of the Heisenberg $SL(2 ,\mathbb{R})$ spin chain~\cite{BDM98,Belitsky99,BDKM99}. The twist of the Wilson operator $L$ determines the length of the spin chain while the spin operators in the each site are defined by the generators of the `collinear' $SL(2 ,\mathbb{R})$ subgroup of the full conformal group~\cite{Makeenko:bh,Ohrndorf82}. As a result, the exact spectrum of one-loop anomalous dimensions can be computed with a help of Bethe Ansatz~\cite{QISM}.
Let us now examine the relation \re{OPE} for large Lorentz spin, $N\gg 1$. This limit has important phenomenological applications in QCD~\cite{Simula:2000ka,Gardi:2002xm}. It is known \cite{GW73} that the anomalous dimensions of Wilson operators grow as their Lorentz spin increases. As a consequence, the dominant contribution to \re{OPE} only comes from the operators with the minimal anomalous dimension $\gamma^{(0}_{N,L} = \min_{\alpha} \gamma^{(\alpha)}_{N,L}$.
Quite remarkably, this anomalous dimension has a universal (twist $L$ independent) logarithmic scaling behavior at large $N$ to all loops~\cite{Korchemsky88,bgk}
\begin{align}\label{min}
\gamma^{(0)}_{N,L} = 2 \Gamma_{\rm cusp}(\alpha_s) \ln N + O(N^0)\,,
\end{align}
where $\Gamma_{\rm cusp}(\alpha_s)$ is the \textit{cusp anomalous dimension} \cite{Korchemsky:1987wg}.
By definition, $\Gamma_{\rm cusp}(\alpha_s)$ governs the scale dependence
of Wilson lines with light-like cusps \cite{polyakov2,Korchemskaya:1992je} and its relation to anomalous dimensions of large
spin Wilson operators is by no means obvious.
It can be understood \cite{Korchemsky88} by invoking the physical picture of deep inelastic scattering at large $N$. In terms of the moments \re{OPE}, large $N$ corresponds to the region of $x\to 1$.
For $x\to 1$ the final state in the deep inelastic scattering has a small invariant mass, $s=Q^2(1-x)/x \ll Q^2$, and it consists of a collimated jet of energetic particles accompanying by soft gluon radiation.
Interacting with soft gluons, the particles inside the jet acquire the eikonal phases given by
Wilson line operators $P\exp(i\int_0^\infty dt\, p\cdot A(pt))$ evaluated along semi-infinite line in the direction of the particle momenta. In this way, for $x\to 1$, complicated QCD
dynamics in deep inelastic scattering admits an effective description in terms
of Wilson lines~\cite{Ivanov:1985np}. The relation \re{min} between anomalous dimensions and cusp singularities
of light-like Wilson lines is just one of the application of this formalism. Another examples
include the relation between light-like Wilson loops with on-shell scattering amplitudes,
Sudakov form factors, gluon Regge trajectories etc (see Ref.~\cite{Drummond:2007aua} and references
therein).
At present, integrability of the dilatation operator in planar QCD has been verified to two loops in the $SL(2;\mathbb{R})$ sector of maximal helicity operators~\cite{Belitsky:2006av}. In other sectors, the dilatation operator receives additional contribution that breaks integrability already to one loop. This contribution vanishes however for large values of the Lorentz spin $N\gg 1$ thus suggesting that integrability in planar QCD gets restored to all loops in the leading large $N$ limit~\cite{GKK02}. Indeed, as was shown in Ref.~\cite{bgk}, the all-loop dilatation operator in QCD in the $SL(2;\mathbb{R})$ sector can be mapped in the large $N$ limit into a Hamiltonian of a {\em classical} Heisenberg $SL(2;\mathbb{R})$ spin chain. In this manner, the Wilson operators
with large $N$ are described by the so-called finite-gap solutions and the spectrum of anomalous dimension can be found through their semiclassical quantization. In
particular, the relation \re{min} naturally appears as describing the ground state energy
of the classical $SL(2;\mathbb{R})$ spin chain of an arbitrary length $L$ and total
spin $N$.
The above mentioned integrability structures (those of the scattering amplitudes in the Regge limit
and of the dilatation operator) are not specific to QCD. They are
also present in generic four-dimensional gauge theories including supersymmetric Yang-Mills
models with $\mathcal{N}=1,2,4$ supercharges. Supersymmetry enhances the
phenomenon by extending integrability to a larger class of observables.
In this context, the maximally supersymmetric $\mathcal{N}=4$ Yang-Mills
theory is of a special interest with regards to the AdS/CFT correspondence
\cite{maldacena}. The gauge/string
duality hints that these structures should manifest themselves through hidden
symmetries of the scattering amplitudes and of anomalous dimensions in dual
gauge theories to all loops.
\section{Integrability of dilatation operator in QCD}
In this section, we review a hidden integrability of the dilatation operator in a generic
four-dimensional Yang-Mills theory describing the coupling of gauge fields
to fermi\-ons and scalars. Depending on the representation in which the latter
fields are defined, we can distinguish two different types of the gauge
theories: QCD and supersymmetric extensions of Yang-Mills theory (SYM).
In QCD, the gauge fields are coupled to quarks in the fundamental
representation of the $SU(N_c)$ gauge group.
The quarks are described by four-component Dirac fermions $\psi$ and the gauge field strength
$F_{\mu\nu}=\frac{i}{g}[D_\mu,D_\nu]$ is determined in terms of the covariant
derivatives $D_\mu = \partial_\mu - i g A_\mu^a t^a$ with generators
$t^a$ in the fundamental representation of the $SU(N_c)$ normalized
conventionally as ${\rm tr} \, (t^a t^b) = \frac12 \delta^{ab}$.
In SYM theory, the gauge fields are coupled to fermions (gauginos) and scalars belonging to the adjoint representation of the $SU(N_c)$ group.
The supersymmetric Yang-Mills theories with $\mathcal{N}=1,2$ and $4$ supercharges are obtained from the Lagrangian of generic Yang-Mills theory by adjusting the number of gaugino and scalar species.
The gauginos are described by the Weyl fermion $\lambda^A$ which belongs to
the fundamental representation of an internal $SU(\mathcal{N})$ symmetry group
with its complex conjugate $\bar \lambda_A=(\lambda^A)^*$. The scalars are
assembled into the antisymmetric tensor $\phi^{AB} = - \phi^{BA}$, with its
complex conjugate $( \phi^{AB} )^\ast = \bar\phi_{AB}$. As we explain below,
integrability is not tied to supersymmetry and the phenomenon persists in the
generic Yang-Mills theory for arbitrary $\mathcal{N}$, to two loop order at least.
\subsection{Light-ray operators}
Let us first consider renormalization of local gauge invariant operators in QCD. As the simplest example, we examine the following twist-two operator contributing to the moments of DIS structure function \re{OPE}
\begin{align}\label{qq}
\vev{p|O_{N,L=2}(0)|p} = \vev{p|\bar\psi\, \gamma_+ D_+^{N-1} \psi(0)|p}\,.
\end{align}
It is built from two quark fields and $(N-1)$ covariant derivatives $D_+=(n\cdot D)$ projected onto light-like vector $n_\mu=q_\mu-p_\mu q^2/(2 pq)$ and $\gamma_+=(n\cdot \gamma)$ being the projected Dirac matrix. Discussing renormalization properties
of Wilson operators like \re{qq} it is convenient to switch from infinite set
of local operators \re{qq} parameterized by positive integer $N$ to a single
nonlocal {\it light-ray operator}
\begin{align}\label{O-def}
\mathbb{O}(z_1,z_2) = \bar \psi(z_1 n) \gamma_+ [n z_1, n z_2] \psi(z_2 n)
= \sum_{N\ge 1}\left[ \bar\psi\, \gamma_+ D_+^{N-1} \psi\right] \frac{(z_1-z_2)^{N-1}}{(N-1)!}+\ldots
\end{align}
Here $z_1$ and $z_2$ are scalar variables defining the position of quark fields
on the light-cone and the gauge link $[n z_1, n z_2]\equiv P\exp(ig\int_{z_1}^{z_2} dt \,A_+(nt))$ is inserted to ensure gauge invariance of $\mathbb{O}(z_1,z_2)$. Also,
ellipses in the right-hand side of \re{O-def} stand for terms involving total derivatives
of the twist-two operators and, therefore, providing vanishing contribution to
the forward matrix element $\vev{p|\mathbb{O}(z_1,z_2)|p}$.
We recall that local gauge invariant operators
satisfy the evolution equation \re{CS}. The same is true for the
light-ray operators \re{O-def} although the explicit form of the evolution equation is different due to nonlocal form of the light-ray operators. In particular, for the operators
\re{O-def} the evolution equation takes the following form
\cite{AZ78,BFLK85,BB89,MRGDH94}
\begin{equation}
\left(
\mu \frac{\partial}{\partial \mu} + \beta(g^2) \frac{\partial}{\partial g^2}
\right) \mathbb{O} (z_1, z_2)
=
- [ \mathbb{H}_2(g^2) \cdot \mathbb{O}] (z_1, z_2)
\, ,
\label{RG}
\end{equation}
with the evolution kernel $\mathbb{H}_2$ to be specified below.
The evolution equation \re{RG} expresses the conformal Ward identity in QCD and the beta-function term takes into account conformal symmetry breaking contribution.
The evolution operator $\mathbb{H}_2$ in the right-hand side of \re{RG} defines a representation of the dilatation operator on the space spanned by nonlocal light-ray operators \re{O-def}. In general,
$\mathbb{H}_2$ has a matrix form as the light-ray operators with different
partonic content could mix with each other.
The evolution kernel $\mathbb{H}_2$ has a perturbative expansion in powers of the coupling constant and
admits a representation in the form of an integral operator acting on light-cone coordinates $z_1$ and $z_2$ of $\mathbb{O}(z_1, z_2)$.
To the lowest order in the coupling, its explicit form
has been found in QCD in Ref.~\cite{BB89} and its generalization to
Yang-Mills theories with an arbitrary number of supercharges has been derived in Ref.~\cite{BDKM04}. The corresponding expressions for $\mathbb{H}_2$ are given below in Eq.~\re{H-tw-2} .
The main advantage of \re{RG} compared with the conventional approach based on
explicit diagonalization of the mixing matrix for local Wilson operators is that the
problem of finding the spectrum of anomalous dimensions can be mapped into
spectral problem for one-dimensional quantum mechanical Hamiltonian $\mathbb{H}_2$. As we will see in a moment, the same happens in QCD
for Wilson operators of high twist $L\ge 3$, in which case the corresponding evolution operator $\mathbb{H}_L$ in the sector of maximal helicity operators
turns out to be equivalent for a Hamiltonian of Heisenberg $SL(2;\mathbb{R})$ spin chain of length $L$.
\subsection{Light-cone formalism}
Discussing integrability of the dilatation operator in QCD and in SYM theories, it
is convenient to employ the ``light-cone formalism'' \cite{KogSop,BLN83,Mandelstam83}. In this
formalism one integrates out non-propagating components of fields and formulates
the (super) Yang-Mills action in terms of ``physical'' degrees of freedom.
Although the resulting action is not manifestly covariant under the Poincar\'e
transformations, the main advantage of the light-cone formalism for SYM theories
is that the $\mathcal{N}-$extended supersymmetric algebra is closed off-shell for
the propagating fields and there is no need to introduce auxiliary fields. This
allows us to design a unifying light-cone superspace formulation of various
$\mathcal{N}-$extended SYM, including the ${\cal N} = 4$ theory for which a
covariant superspace formulation does not exist.
In the light-cone formalism, one quantizes the Yang-Mills theory in a noncovariant,
light-cone gauge $(n\cdot A) \equiv A_+(x) = 0$. Introducing an auxiliary
complimentary light-like vector $\bar n_\mu$,
such that $\bar n^2=0$ and $(n\cdot \bar n)=1$, we split three remaining components of the gauge field into longitudinal, $A_- (x)$, and two
transverse holomorphic and antiholomorphic components, $A(x)$ and $\bar A(x)$,
respectively,
\begin{equation}
A_- \equiv (\bar n \cdot A)\,,\qquad A \equiv \ft1{\sqrt{2}}(A_1 +
i A_2) \, , \qquad
\bar A \equiv A^* = \ft1{\sqrt{2}}(A_1 - i A_2)
\, .
\label{gauge-perp}
\end{equation}
In the similar manner, the
fermion field ${\psi}(x)$ can be decomposed
with a help of projectors $ \Pi_\pm = \ft12 \gamma_\pm
\gamma_\mp$ as
\begin{equation}
{\psi} = {\Pi}_+ {\psi} + {\Pi}_- {\psi} \equiv {\psi}_+ + {\psi}_-\,,
\label{good-bad}
\end{equation}
where the fermion field ${\psi}_+$ has two nonzero components
\begin{equation}
q_{ \uparrow}
= \frac12 ( 1 - \gamma_5 ) \psi_+
\, , \qquad q_{\downarrow} = \frac12 ( 1 + \gamma_5 )
\psi_+ \,.
\label{1/2-QCD}
\end{equation}
Then, one finds that the fields ${\psi}_-(x)$ and $A_-(x)$ can be integrated out
and the resulting action of the Yang-Mills theory is expressed in terms of
``physical'' fields: complex gauge field, $A(x)$ and $\bar A(x)$, two components of fermion fields, $q_{ \uparrow}(x)$ and $q_{ \downarrow}(x)$, and, in the case of supersymmetric gauge theory, complex scalar fields $\phi(x)$. When applied to the vacuum states, the fields $(A,\,q_{ \downarrow},\, \phi,\, q_{ \uparrow},\,\bar A)$
create massless particles of helicity $(-1,-\ft12,0,\ft12,1)$, respectively.
Taking the product of `physical' fields and light-cone derivatives $D_+=\partial_+$,
we can construct the set of local gauge invariant operators. Such operators define
the representation of the so-called collinear $SL(2;\mathbb{R})$ subgroup of the conformal group and they are known in QCD literature as \textit{quasipartonic operators}.
A distinguished feature of these operators is that their twist equals the number of constituent physical fields~\cite{BFLK85}. In analogy with \re{O-def}, we can
replace an infinite number of Wilson operators of a given twist $L$ with a few
nonlocal light-ray operators $\mathbb{O}(z_1,\dots , z_L)$. The latter can be thought of
as generating functions for the former. Due to different
$SU(N_c)$ representation of fermions (fundamental in QCD and adjoint in SYM), the definition of such operators
is slightly different in the two theories.
In QCD, in the simplest
case of twist two, we can distinguish four different light-ray operators
(plus complex conjugated operators)
\begin{align}\notag
& \mathbb{O}_{qq}^{(0)}(z_1, z_2) = \bar q_{\uparrow}(n z_1) q_{ \uparrow}(n z_2) \,,\quad
\mathbb{O}_{gg}^{(0)}(z_1, z_2) = \mathop{\rm tr}\nolimits\left[ \partial_+ \bar A(n z_1) \partial_+ A(n z_2)\right]\,,
\\[2mm]
& \label{tw-2}
\mathbb{O}_{qq}^{(1)}(z_1, z_2) = \bar q_{\downarrow}(n z_1) q_{ \uparrow}(n z_2) \,, \quad
\mathbb{O}_{gg}^{(2)}(z_1, z_2) = \mathop{\rm tr}\nolimits\left[ \partial_+ A(n z_1) \partial_+ A(n z_2)\right] \,,
\end{align}
where the subscript ($qq$ and $gg$) indicates particle content of the operator
and the superscript defines the total helicity. In this basis, the operator
\re{O-def} is given by a linear combination of $ \mathbb{O}_{qq}^{(0)}(z_1, z_2)$ and complex conjugated operator.
The operators $\mathbb{O}_{qq}^{(0)}$ and $\mathbb{O}_{gg}^{(0)}$ have the same quantum numbers and mix under
renormalization. At the same time, the operators $\mathbb{O}_{qq}^{(1)}$ and $\mathbb{O}_{gg}^{(2)}$ carry different helicity and have an autonomous
scale dependence. In what follows we shall refer to them as maximal helicity
operators. The reason why we distinguish such operators is that the one-loop dilatation operator in QCD is integrable in the sector of maximal helicity
operators only.
For higher twist $L\ge 3$ we can define three different types of maximal
helicity operators in QCD:
\begin{align}
& \mathbb{O}_{qqq}^{(3/2)} (z_1, z_2, z_3)
=
\varepsilon_{ijk} \, q_{\uparrow}^i (z_1 n) q_{\uparrow}^j (z_2 n) q_{\uparrow}^k (z_3 n)
\, , \label{O3-QCD}
\\\label{O-mixed}
& \mathbb{O}_{qg \ldots g q}^{(L-1)} (z_1, \ldots, z_L)
= \bar q_{\downarrow}(n z_1) \partial_+ A(nz_2)\ldots \partial_+ A(nz_{L-1})
q_{ \uparrow}(n z_L) \, ,
\\\label{ggg}
& \mathbb{O}_{g \ldots g }^{(L)} (z_1, \ldots, z_L)
= \mathop{\rm tr}\nolimits\left[ \partial_+ A(nz_1)\ldots \partial_+ A(nz_{L})\right]\, ,
\end{align}
to which we shall refer as baryonic $(L=3)$ operators, mixed quark-gluon operators and
gluon operators, respectively.
We remind that since quark fields belong to the fundamental representation of the $SU(N_c)$ group, the length of the operator \re{O3-QCD} ought to be $N_c=3$. At the same time, gluon fields are in the adjoint representation and the single trace
operator \re{ggg} is well-defined for arbitrary $N_c$ and twist $L$. The same applies to the mixed quark-gluon operators \re{O-mixed}.
The operators \re{O3-QCD} and \re{O-mixed} have a direct phenomenological significance: their matrix elements determine the
distribution amplitude of the delta-isobar~\cite{BroLep79} and higher twist contribution to spin structure functions, respectively.
\subsection{Evolution kernels}
The light-ray operators \re{tw-2} -- \re{ggg} satisfy the evolution equation \re{RG}. Let us first examine twist-two quark operators $\mathbb{O}_{qq}^{(0)}$ and $\mathbb{O}_{qq}^{(1)}$ defined in \re{tw-2}. The operator $\mathbb{O}_{qq}^{(0)}$ can mix with the gluon operator $\mathbb{O}_{gg}^{(0)}$. To simplify the situation,
we can suppress the mixing by choosing the two quark fields inside $\mathbb{O}_{qq}^{(0)}$ to have different flavor. To one-loop order, the evolution kernel receives
the contribution from one-gluon exchange between two quark fields and from self-energy corrections. The latter one is the same for the two operators while the former one is different
\begin{align} \notag
\mathbb{H}^{(1)}_{qq} &=\frac{g^2 C_F}{8\pi^2}\left[H_{12} + 2 \gamma_q \right]\,,
\\[2mm] \label{H-tw-2}
\mathbb{H}^{(0)}_{qq}&=\frac{g^2 C_F}{8\pi^2}\left[H_{12} + V_{12} + 2 \gamma_q \right]\,.
\end{align}
Here $C_F=t^at^a=(N_c^2-1)/(2N_c)$ is the quadratic Casimir of the $SU(N_c)$ in the fundamental representation, $\gamma_q=1$ is one-loop anomalous dimension
of quark field in the axial gauge $A_+=0$ and $H_{12}$ and $V_{12}$ are integral operators
\begin{align}\notag
[ {H}_{12} \cdot
\mathbb{O} ] (z_1, z_2) &= \int_0^1 \frac{d \alpha}{\alpha} \bar\alpha
\Big[ 2 \mathbb{O} (z_1, z_2) - \mathbb{O} (\bar\alpha z_1 + \alpha
z_2, z_2) - \mathbb{O} (z_1, \alpha z_1 + \bar\alpha z_2) {}\Big],
\\\label{LightConeKernel}
[ {V}_{12} \cdot
\mathbb{O} ] (z_1, z_2) &= \int_0^1 d\alpha_1\int_0^{\bar\alpha_1}d\alpha_2\,
\mathbb{O}(\alpha_1 z_1 + \bar\alpha_1 z_2,\alpha_2 z_2 + \bar\alpha_2 z_1)\,,
\end{align}
where $\bar\alpha_i \equiv 1 - \alpha_i$. These operators have a transparent
physical interpretation: they displace two particles along the light-cone in the direction of each other.
To find the spectrum of anomalous dimensions of twist-two quark operators
generated by light-ray operators \re{tw-2}, we have to diagonalize
the operators $\mathbb{H}^{(1)}_{qq}$ and $\mathbb{H}^{(0)}_{qq}$. This can be
done with a help of conformal symmetry. We recall that the conformal symmetry
is broken in QCD at loop level. However the dilatation operator receives
conformal symmetry breaking contribution only starting from two loops and, as a consequence, the one-loop evolution kernels in QCD have to respect conformal symmetry of QCD Lagrangian. For nonlocal light-ray operators built from fields $X(n z)$,
the full $SO(2,4)$ conformal symmetry reduces to its collinear $SL(2;\mathbb{R})$
subgroup acting on one-dimensional light-cone coordinates of fields~\cite{Makeenko:bh,Ohrndorf82}
\begin{align}
z \to \frac{az+b}{cz+d}\,,\qquad X(z n ) \to (cz+d)^{-2j} X\left(\frac{az+b}{cz+d}n \right)
\end{align}
with $ad-bc=1$. The generators of these transformations are
\begin{align}\label{l-col}
L^-=-\partial_z\,,\qquad L^+=2j z+ z^2\partial_z\,,\qquad L^0=j+z\partial_z\,.
\end{align}
Here $j$ is the conformal weight of the field. For `physical' components of fermions, $\psi_+$, it equals $j_q=1$, for transverse components
of gauge field, $\partial_+ A$ and $\partial_+\bar A$, it is $j_g=3/2$ and for scalars
$j_s=1/2$.
In application to light-ray quark operators, $\mathbb{O}_{qq}^{(0)}(z_1, z_2)$ and $\mathbb{O}_{qq}^{(1)}(z_1, z_2)$, the conformal symmetry dictates that the one-loop evolution kernels \re{H-tw-2} have to commute with the two particle conformal spin
$ L_1^\alpha+L_2^\alpha$ (with $\alpha=-,+,0$).
As a consequence, $\mathbb{H}_{qq}^{(h=0,1)}$ is a function of the corresponding two-particle Casimir operator
\begin{align}
L_{12}^2=\sum_{\alpha=+,-,0} (L_1^\alpha+L_2^\alpha)^2 = J_{12}(J_{12}-1)\,.
\end{align}
To find the explicit form of this dependence, it suffices to examine the action of the two
operators, $\mathbb{H}_{qq}^{(h)}$ and $L_{12}^2$, on the same test function $(z_1-z_2)^{n}$, which is just the lowest weight in the tensor product of two $SL(2;\mathbb{R})$ representations carrying the spin $J_{12}=n+2$. Replacing $\mathbb{O}(z_1,z_2)\to (z_1-z_2)^{J_{12}-2}$ in \re{LightConeKernel} we
find
\begin{align}\label{h12}
H_{12} = 2\left[\psi(J_{12})-\psi(2)\right]\,,\qquad V_{12} = 1/(J_{12}(J_{12}-1))\,,
\end{align}
where $\psi(x)=d\ln\Gamma(x)/dx$ is Euler psi-function. Together with \re{H-tw-2} these relations determine the spectrum of anomalous dimensions of twist-two quark operators.
\subsection{Relation to Heisenberg \texorpdfstring{$SL(2;\mathbb{R})$}{SL(2;R)} spin chain}
As the first sign of integrability, we notice that $H_{12}$ coincides
with the known expression for two-particle Hamiltonian of Heisenberg spin chain~\cite{KRS81,TTF83}
\begin{align}\label{closed}
H_L=H_{12}+\ldots+H_{L1}\,,\qquad H_{i,i+1} = \psi(J_{i,i+1})-\psi(2j)\,,
\end{align}
where the spin operators are identified as $SL(2;\mathbb{R})$ conformal generators \re{l-col}. As follows from \re{H-tw-2}, the one-loop dilatation operator $\mathbb{H}_{qq}^{(1)}$
depends on $H_{12}$ and, therefore, it is mapped into Heisenberg $SL(2;\mathbb{R})$ spin chain of length 2. At the same time, the dilatation operator $\mathbb{H}_{qq}^{(0)}$ receives the additional contribution $V_{12}$. It preserves the conformal symmetry but breaks
integrability. Notice that $V_{12}$ vanishes for large values of the conformal spin $J_{12}\gg 1$ so that the two evolution kernels, $\mathbb{H}_{qq}^{(0)}$ and $\mathbb{H}_{qq}^{(1)}$, have the same asymptotic behavior at
large $J_{12}$. This suggests that for the operator $\mathbb{H}_{qq}^{(0)}$ integrability is restored in the limit of large conformal spin only.
For twist-two operators, the anomalous dimensions are uniquely determined by their conformal spin. To appreciate the power of integrabilty, we have to consider
Wilson operators of high twist $L\ge 3$. For example, for the maximal helicity baryonic operators \re{O3-QCD} the one-loop dilatation operator has the form \cite{BDKM99}
\begin{align}
\mathbb{H}_{qqq}^{(3/2)} = \frac{\alpha_s}{2\pi}\left[ (1+1/N_c) (H_{12}+H_{23}+H_{31})+\frac32 C_F\right]
\end{align}
with $N_c=3$ and $H_{12}$ given by \re{h12}. Comparing this relation with \re{closed} we recognize that $\mathbb{H}_{qqq}^{(3/2)}$ can be mapped into
Heisenberg spin chain of length $L=3$. The spin at each site $j=1$ is determined
by the conformal spin of quark field.
For gluon operators of the maximal helicity \re{ggg} the dilatation operator receives
contribution from self-energy corrections to gluon fields and from one-gluon exchange between any pair of gluons. The latter produces both planar and nonplanar corrections (for $L>3$). In the planar limit, the one-loop dilatation operator has the following form~\cite{Belitsky00}
\begin{align}
\mathbb{H}_{g \ldots g }^{(L)} = \frac{g^2 N_c}{8\pi^2} (H_{12}+\ldots+H_{L1})\,,
\end{align}
where two-particle kernel $H_{i,i+1}$ acts locally on light-cone coordinates of
gluons with indices $i$ and $i+1$. The conformal symmetry implies that $H_{i,i+1}$
is a function of the conformal spin of two gluons $J_{i,i+1}$. Quite remarkably, the
dependence of $H_{i,i+1}$ on $J_{i,i+1}$ has the same form as in \re{closed}. As a consequence, the one-loop planar dilatation operator
for maximal helicity gluon operator \re{ggg} coincides with the Hamiltonian of the
Heisenberg $SL(2;\mathbb{R})$ spin chain. The length of the spin chain equals
the twist of the operator $L$ and the spin in each site $j=3/2$ coincides with the
conformal spin of the gluon field.
For mixed quark-gluon operators of the maximal helicity \re{O-mixed}, the quark fields can
interact in the planar limit with the adjacent gluon fields only while quark-quark
interaction is suppressed in this limit. As a consequence, the one-loop dilatation
operator has the following form in the planar limit
\begin{align} \label{open}
\mathbb{H}_{qg \ldots gq}^{(L-1)} = \frac{g^2 N_c}{8\pi^2} (U_{12} + H_{23}+\ldots+H_{L-1,L}+U_{L-1,L})\,.
\end{align}
Here $H_{i,i+1}$ describes the interaction of two gluons with aligned helicities and
it is the same as in \re{closed}. The kernels $U_{12}$ and $U_{L-1,L}$ describes quark-gluon interaction
and their explicit form can be found in Ref.~\cite{DKM00,Belitsky:1999bf}. Notice that the operator $\mathbb{H}_{qg \ldots gq}^{(L-1)}$ has the form of a Hamiltonian of {\it open spin chain} of length
$L$. The spin in sites $1$ and $L$ coincides with the conformal spin of
quark $j_q=1$ and the spin in all remaining sites is given by gluon conformal spin
$j_g=3/2$. As was shown in Ref.~\cite{DKM00,Belitsky:1999bf}, the open spin chain \re{open} is integrable.
\subsection{Exact solution}
Integrability of the one-loop dilatation operator allows us to find
the exact spectrum of anomalous dimensions with a help of the Bethe Ansatz
\cite{BDM98,Belitsky99,BDKM99}
\begin{align} \notag
& \gamma_{N,L} = \frac{g^2 N_c}{8\pi^2} {\mathcal E}_{N,L} + O(g^4)\,,
\\
& {\mathcal E}_{N,L}
= \sum_{k=1}^N \frac{2j}{u_k^2 + j^2}= i \frac{d}{d u}\ln \frac{Q(u + ij)}{Q(u - ij)}\bigg|_{u=0}\, .
\label{E-Q}
\end{align}
Here $j$ is the conformal spin in each site ($j=1$ for quark operators and $j=3/2$ for gluon operators),
$u_k$ are Bethe roots and $Q(u)$ is a polynomial of degree $N$ of the form
\begin{equation}
Q(u)=\prod_{j=1}^N (u-u_j)\, .
\label{Bethe}
\end{equation}
The function $Q(u)$ defined in this way has the meaning of the eigenvalue of the Baxter operator for the
$SL(2,\mathbb{R})$ magnet~\cite{Korchemsky95,Derkachov99}. It satisfies the finite-difference
Baxter equation
\begin{equation}
t_L(u) Q(u) = (u+ij)^L Q(u+i) + (u-ij)^L Q(u-i)\,,
\label{Baxter-eq}
\end{equation}
where $t_L(u)$ is the transfer matrix of the spin chain
\begin{equation}
t_L(u) = 2u^L+q_2 u^{L-2} +\ldots+ q_L
\label{transfer}
\end{equation}
and $q_2,\ldots,q_L$ are the conserved charges.
The Baxter equation \re{Baxter-eq} alone does not specify $Q(u)$ uniquely and it has to be supplemented
by additional condition for analytical properties of $Q(u)$. For the $SL(2;\mathbb{R})$ spin
chains describing the anomalous dimensions, $Q(u)$ has to be a polynomial in the spectral parameter.
Being combined with the Baxter equation \re{Baxter-eq},
this condition determines $Q(u)$ up to an overall normalization and, as a consequence, allows us to establish the quantization conditions for the $q-$charges and to compute the
exact energy ${\mathcal E}_{N,L}$.
Solving the Baxter equation \re{Baxter-eq} for $N=0,1,\ldots$ one finds the eigenspectrum of the Hamiltonian $\mathbb{H}_{L}$ and, as
a consequence, determines the exact spectrum of the anomalous dimensions
of the maximal helicity baryon operators (for $j=1$ and $L=3$) and of
maximal helicity gluon operators (for $j=3/2$ and $L\ge 2$).
The spectrum obtained in this way exhibits remarkable regularity: almost all eigenvalues are double degenerate and for large $N$ they
belong to the set of trajectories~\cite{Korchemsky95,Korchemsky:1995be}. Both properties are ultimately related to integrability
of the dilatation operators and can be served to test integrability at high loops.
For the $SL(2;\mathbb{R})$ spin chains under consideration, the Baxter equation approach and conventional Bethe Ansatz are equivalent. Indeed, substituting \re{Bethe} into the Baxter equation \re{Baxter-eq}, one finds that the roots $u_j$ satisfy the conventional $SU(2)$ Bethe equations for spin $(-j)$. The fact that the spin is negative leads to a number of important differences as compared to ``compact''
$SU(2)$ magnets. In particular, the Bethe roots take real values only and the
number of solutions is infinite~\cite{Korchemsky95,Korchemsky:1995be}.
\subsection{Semiclassical limit}
The Baxter operator approach
becomes advantageous when one studies the properties of anomalous dimensions
at large spin $N$ and/or twist $L$. The reason for this is that the Baxter equation
\re{Baxter-eq} takes the form of discretized Schr\"odinger equation. After rescaling
of the spectral parameter, $u\to (N+Lj) x$, we can seek for solution to \re{Baxter-eq} in the WKB form~\cite{PG92,Sklyanin,Korchemsky:1995be}
\begin{align}\label{WKB}
Q(Nx) = \exp\left(\frac{i}{\hbar} S(x)\right)\,,\qquad \hbar =1/(N+Lj)\,,
\end{align}
where the action function $S(x)$ admits an expansion in powers of $\hbar$. Substitution of \re{WKB} into the Baxter equation \re{Baxter-eq} yields the equation for $S(x)$ which can be solved as a series in $\hbar$. To leading order we have
\begin{align}
S(x) = \int_{x_0}^x dx\, p(x) + O(\hbar)\,,
\end{align}
where the momentum $p(x)$ is defined on the spectral curve (``equal energy'' condition) of the classical $SL(2;\mathbb{R})$ magnet $y(x)=2x^L\sinh p(x)$ with
\cite{Korchemsky:1996kh}
\begin{equation}
\Gamma_L: \qquad y^2=(t_L(x))^2 - 4x^{2L}\,.
\label{curve}
\end{equation}
The classical dynamics on this spectral curve has been studied in detail in Refs.~\cite{Korchemsky:1997yy,GKK02}.
Using \re{WKB} we can compute the asymptotic behavior of the energy as~\cite{Korchemsky:1995be,Belitsky:2006en}
\begin{align}\label{E-as}
\mathcal{E}_{N,L}^{\rm (as)} = 2\ln 2 + \sum_{n=1}^L \left[ \psi(j+i\delta_n)+ \psi(j-i\delta_n)
-\psi(2j)\right] +\ldots\,,
\end{align}
where ellipses denote terms subleading at large $(N+jL)$. Here $\delta_n$ are roots
of the transfer matrix defined in \re{transfer}, $t_L(\delta_n)=0$. They depend on the conserved charges $q_2,\ldots,q_L$ whose values satisfy the WKB quantization
conditions
\begin{align}\label{q-as}
\oint_{\alpha_k} dx \, p(x) = 2\pi\hbar (\ell_k+\ft12)\,,\qquad (\text{for $k=1,\ldots,L-1$})\,.
\end{align}
Here integration goes over the cycles $\alpha_k$ on the complex curve \re{curve} encircling intervals on the real axis satisfying $y^2(x)>0$ and integers $\ell_k$ enumerate the
quantized values of the charges $q_2,\ldots,q_L$ and the energy $\mathcal{E}_{N,L}=\mathcal{E}_{N,L}(\ell_1,\ldots,\ell_{L-2})$.
For large spin $N$ and twist $L$, the minimal
energy $\mathcal{E}_{N,L}^{(0)}=\min_{\ell_k} \mathcal{E}_{N,L} $ has the following scaling behavior~\cite{Belitsky:2006en}
\begin{align}
\mathcal{E}_{N,L}^{(0)} = f(\rho)\ln N + O(N^0) \,,\qquad \rho=\frac{L}{\ln N}=\text{fixed}\,,\quad N,L\gg 1
\end{align}
where $f(\rho)$ is the so-called generalized scaling function. Detailed analysis of the relations \re{E-as} and \re{q-as} can be found in Refs.~\cite{Korchemsky:1995be,BDKM99,Belitsky00,GKK02,Belitsky:2006en}. For recent development
in the generalized scaling function in $\mathcal{N}=4$ SYM see review Ref.~\cite{chapter3}.
So far we have discussed the exact solution for the one-loop anomalous dimensions of
quark and gluon maximal helicity operators. For the anomalous dimensions of mixed quark-gluon operators \re{O-mixed}, similar analysis of the spin chain
\re{open}
can be carried out using Bethe Ansatz for open $SL(2;\mathbb{R})$ spin chains~\cite{Belitsky00,DKM00}.
\subsection{Integrability of dilatation operators in SYM theories}
In this subsection, we extend consideration to supersymmetric Yang-Mills theories.
Discussing integrability of dilatation operator in these theories, it is convenient to employ supersymmetric version of light-cone
formalism due to Mandelstam~\cite{Mandelstam83} and
Brink~{\it et al.}~\cite{BLN83}. In this formalism, all symmetries of SYM theory become manifest and
calculations can be performed in a unified manner for different
numbers of supercharges $\mathcal{N}=0,1,2,4$.
The maximally-supersymmetric $\mathcal{N}=4$ SYM theory is a finite,
four-dimensional conformal field theory~\cite{Mandelstam83,BLN83,SW81,HST84},
while the $\mathcal{N}=0$ theory corresponds to pure gluodynamics.
Defining a SYM theory on the light-cone, one starts with the
component form of the action, fixes the light-cone gauge $A_+(x) = 0$, decompose all propagating, ``physical'' fields
into definite helicity components. In the case of $\mathcal{N}=4$ SYM,
they include helicity $(\pm 1)$ fields, $A(x)$
and $\bar A(x)$, built from two-dimensional transverse
components of the gauge field, complex scalar fields
$\phi^{AB}$ of helicity $0$ and helicity $\pm 1/2$ components of Majorana--Weyl
fermions, $\lambda^A$ and $\bar\lambda_A$, all in the adjoint representation of the
$SU(N_c)$ gauge group. An important
property of the light-cone formalism, which makes it advantageous over the
covariant one, is that the latter fields have only one non-vanishing component. As a consequence, one can describe helicity $(\pm
1/2)$ fermions by Grassmann-valued complex fields without any Lorentz index.
Introducing four fermionic coordinates $\theta^A$ (with $A=1,\ldots,4$) possessing the helicity $(-\ft12)$ and their conjugates $\bar\theta_A$ with helicity $\ft12$, we can assemble the above fields into a single, complex chiral $\mathcal{N}=4$ superfield~\cite{BLN83}
\begin{eqnarray}
\hspace{-3mm}\Phi (x, \theta^A) &=&
\partial_+^{-1}A(x)
+ \theta^A \partial_+^{-1}\bar\lambda_A (x) + \frac{i}{2!} \theta^A \theta^B \bar
\phi_{AB} (x)
\nonumber\\
\hspace{-3mm}&-&\!\frac{1}{3!} \varepsilon_{ABCD} \theta^A \theta^B \theta^C \lambda^D
(x)\! - \frac{1}{4!} \varepsilon_{ABCD} \theta^A \theta^B \theta^C \theta^D
\partial_+ \bar{A} (x) . \quad \ \label{N=4-field}
\end{eqnarray}
It embraces all particle helicities, from $-1$ to $1$ with half-integer step,
and, therefore, $\Phi (x, \theta^A)$ describes a CPT self-conjugate
supermultiplet.
Gauge theories on the light-cone with less or no supersymmetry can be deduced
from the maximally supersymmetric $\mathcal{N}=4$ theory by removing ``unwanted''
physical fields. In the superfield formulation this amounts to a truncation of
the $\mathcal{N}=4$ superfield, or equivalently, reduction of the number of
fermionic directions in the superspace~\cite{BT83}. For instance,
to get the ${\mathcal N} = 1$ superfields one removes three odd
coordinates $\theta^2=\theta^3 = \theta^4 = 0$, whereas for ${\mathcal N} =
0$ all $\theta$'s in \re{N=4-field} have to be set to zero. Notice that under
this procedure the truncated $\mathcal{N}=2$, $\mathcal{N}=1$ and $\mathcal{N}=0$ theories involve only half of the fields described by the $\mathcal{N}-$extended
SYM theory and the other half of the needed particle content arises from the
complex conjugated superfields $\bar\Phi \equiv \Phi^\ast$.
Explicit expressions for the action of the SYM theory in terms of
the light-cone superfields can be found in Ref.~\cite{BDKM04}.
In a close analogy with \re{ggg},
we can introduce multiparticle single-trace operators built
from light-cone superfields
\begin{equation}
\label{WilsonOperators}
\mathbb{O}(Z_1,\ldots,Z_L) = {\rm tr} \, \{ \Phi (Z_1) \Phi (Z_2) \cdots \Phi
(Z_L) \} \,,
\end{equation}
where $\Phi(Z) \equiv \Phi^a(Z) t^a$ is a matrix ($SU(N_c)$) valued superfield and $Z=(x,\theta^A)$ denotes its position in
the superspace with four even coordinates, $x_\mu$, and $\mathcal{N}$ odd
coordinates, $\theta^A$ with $A=1,\ldots, \mathcal{N}$. In
addition, we choose all superfields to be located along the light-cone
direction in the four-dimensional Minkowski space defined by the light-like
vector $n_\mu$ (with $n^2=0$), so that
$n \cdot A = A_+ =0$. Similarly to the QCD case, the positions
of the superfields on the light-cone are parameterized by real numbers
$x_\mu = z n_\mu$,
$
\Phi(Z_k) \equiv \Phi(z_k n,\theta_k^A)\, .
$
The single-trace operators \re{WilsonOperators} represent a natural
generalization of nonlocal light-ray operators in QCD, cf. Eq.~\re{ggg}. To
obtain the latter it is sufficient to expand $\mathbb{O}(Z_1,\ldots,Z_L)$ in
powers of odd variables $\theta^{A_1}_1\ldots \theta^{A_L}_L$. As in QCD,
nonlocal operators \re{WilsonOperators} serve as generating functions for Wilson
operators with the maximal Lorentz spin and minimal twist equal to the number of
constituent fields $L$. Such operators define a representation of the
$SL(2|\mathcal{N})$ subgroup of the full superconformal group.
Examining light-ray operators \re{WilsonOperators} in SYM theories with different number of supercharges, we find that $\mathcal{N}=4$ case is special. In $\mathcal{N}=4$ SYM theory there is only one independent chiral
superfield $\Phi(Z)$ and, as a consequence, the operators \re{WilsonOperators}
generate \textsl{all} Wilson operators of twist$-L$ built from $L$
fundamental fields. For $\mathcal{N}\le 2$, the superfield $\Phi(Z)$ and its conjugate
$\bar\Phi(Z)$ are independent of each other and, in addition to the operators in
\re{WilsonOperators}, one can introduce ``mixed'' operators built from both
superfields. This means that in the $\mathcal{N}=0,1$ and $2$ SYM theories, the
operators \re{WilsonOperators} only generate a certain subset of the existing
Wilson operators in the $SL(2|\mathcal{N})$ subsector.
The light-ray operators \re{WilsonOperators} play a special role
as far as integrability is concerned. Namely, as was shown in Refs.~\cite{BDKM04}, the one-loop dilatation operator acting on the space of single-trace operators
\re{WilsonOperators} can be mapped in the multicolor limit into a Hamiltonian of
a completely integrable Heisenberg $SL(2|\mathcal{N})$ spin chain. As before,
the length of the spin chain coincides with the number of superfields in \re{WilsonOperators} and spin operators are generators
of a collinear $SL(2|\mathcal{N})$ subgroup of the full superconformal
group~\cite{BDKM04}.
We recall that in SYM theories with $\mathcal{N} \le 2$ supercharges the operators \re{WilsonOperators} only generate a subsector of Wilson operators
of twist $L$. To describe the remaining
operators, one has to consider single-trace operators built from both superfields, like $ {\rm tr} \, \{ \Phi (Z_1) \bar\Phi (Z_2) \cdots \Phi
(Z_L) \}$.
For such operators, the one-loop dilatation operator involves
the additional term describing the exchange interaction between superfields on the light-cone $\Phi\bar\Phi\to\bar\Phi\Phi$. It breaks integrability symmetry and generates a mass gap in the spectrum of the anomalous dimensions~\cite{BDKM99}. At the same time, for large values of the superconformal spin the exchange interaction vanishes
and integrability gets restored in the leading large spin asymptotics of the anomalous dimensions.
\subsection{Integrability in QCD and SYM beyond one loop}
It is well-known that the conformal symmetry is broken in QCD and SYM theories
with $\mathcal{N} < 4$ supercharges while in the maximally supersymmetric
$\mathcal{N}=4$ model it survives on the quantum level. However the conformal
anomaly modifies anomalous dimensions starting from two loops only and,
therefore, the one-loop dilatation operator inherits the conformal symmetry of
the classical theory~\cite{BKM03,Belitsky:2004cz}.
Starting from two-loop order, the dilatation operator in
the $SL(2)$ sector acquires several new features. First, it receives conformal
symmetry breaking corrections arising both due to a nonzero beta-function and
a subtle symmetry-violating effect induced by the regularization procedure~\cite{Muller:1993hg}. Second, the form of the
dilatation operator starts to depend on the representation of the fermion fields,
i.e., fundamental $SU(3)$ in QCD and adjoint $SU(N_c)$ in SYM theories. The
difference between the two is that it is only in the latter case that one can
select planar diagrams by going over to the multi-color limit, while in the
former case the large-$N_c$ counting is inapplicable and the two-loop dilatation
operator receives equally important contributions from both planar and nonplanar
Feynman graphs. Thus, by studying the two-loop dilatation operator in the $SL(2)$
sector we can identify what intrinsic properties of gauge theories (conformal symmetry, supersymmetry and/or planar limit) are responsible for the existence of the integrability phenomenon per se.
For an all-loop dilatation operator $\mathbb{H}
(\lambda)$, depending on 't Hooft coupling constant $\lambda=g^2 N_c/(8\pi^2)$ and acting on a
Wilson operator built from $L$ constituent fields and an arbitrary number of
covariant derivatives, integrability would require, in general, the existence of
$L$ conserved charges. Two of the charges---the light-cone component of the
total momentum of $L$ fields and the scaling dimension of the operator---follow
immediately from Lorentz covariance of the gauge theory. However, the identification of the remaining charges $q_k(\lambda)$ with
$k=3,\ldots,L$ is an extremely nontrivial task. The eigenvalues of the charges
$q_k$ define the complete set of quantum numbers parameterizing the eigenspectrum
of the dilatation operator. Integrability imposes a nontrivial analytical
structure of anomalous dimensions of Wilson operators and implies the double
degeneracy of eigenvalues with the opposite parity
\cite{Korchemsky95,GraMat95,BDKM99}. At the same time, breaking of integrability leads to lifting of the degeneracy
in the eigenspectrum of the one-loop dilatation operator.
Explicit two-loop calculation of the anomalous dimensions of the aforementioned
aligned-helicity fermionic operators in all SYM theories showed that
the same relation between integrability and degeneracy of the eigenstates holds true to two loops. Namely, as was found in Refs.~\cite{Belitsky:2006av}, the desired pairing of eigenvalues occurs for three-gaugino operators in SYM
theories with $\mathcal{N}=1,2$ supercharges and the $SU(N_c)$ gauge group.
The two-loops dilatation operator in SYM theories receives conformal
symmetry breaking contribution and, in addition, it depends on the
number of supercharges $\mathcal{N}$. The latter dependence comes about through the contribution of $2(\mathcal{N}-1)$ real scalars and $\mathcal{N}$ gaugino fields propagating inside loops. Both contributions to two-loop dilatation operator can be factored out (modulo an additive normalization factor) into a multiplicative c-number. This property makes the
eigenspectrum of the two-loop dilatation operator alike in all gauge theories
including the $\mathcal{N}=4$ SYM in which case the dilatation operator is believed to be integrable to all loops \cite{review}. Summarizing the results of two-loop calculations of the anomalous dimension in QCD and in SYM theories, integrability of the dilatation operator only requires the planar limit but it is sensitive neither to conformal symmetry, nor to supersymmetry~\cite{Belitsky:2006av}. For recent
discussion of integrability in relation to non-planar corrections to the anomalous dimensions in $\mathcal{N}=4$ SYM see review Ref.~\cite{chapter4}.
In this section, discussing the properties of anomalous dimensions
we restricted ourselves to the $SL(2)$ sector.
There have been several developments that we cannot address
here in detail. In particular,
an important observation was made in Ref.~\cite{Ferretti:2004ba}, where it was shown that the diagonal part of one-loop QCD evolution kernels governing the scale dependence of Wilson operators of arbitrary twist, can be written in a Hamiltonian form in terms of quadratic Casimir operators of the full conformal $SO(2,4)$ group. This observation was used in Ref.~\cite{Braun:2009vc} to
work out the non-diagonal parts of the evolution kernels for generic
twist-four operators.
\section{Integrability in high energy scattering}
In the previous section, we described how integrability emerges in the problem
of finding the dependence of the structure functions $F(x,Q^2)$ on the hard scale $Q^2$. In this section, we explain that yet another integrability symmetry arises in the high-energy limit.
In application to the structure function $F(x,Q^2)$ this limit corresponds to $x\to 0$ for fixed $Q^2$.
At small $x$, the invariant energy $s=Q^2(1-x)/x$ of colliding virtual photon and hadron becomes large and the structure function is expected to have Regge-like
scaling behavior $F(x,Q^2)\sim (1/x)^{\omega}$. In terms of moments \re{OPE},
this corresponds to appearance of the Regge pole at $N=\omega$
\begin{align}\label{lambda1}
\tilde F_N(q^2) = \int_0^1 dx\,x^{N-1} F(x,q^2) \sim \frac{1}{N-\omega}\,.
\end{align}
It is well-known \cite{BFKL} that perturbative corrections to $F(x,q^2)$ are enhanced at small $x$ by large logarithms $\sim (\alpha_s \ln(1/x))^p$. This raised
the hope that the Regge behavior \re{lambda1} can be derived in QCD from
resummation of such corrections to all loops. Going to moments, the expansion over $(\alpha_s\ln s)^p$ is traded for the expansion of $\tilde F_N(q^2)$ over $(\alpha_s/N)^p$.
\subsection{Evolution equation}
Careful study of asymptotic behavior of Feynman diagrams
describing interaction between virtual photon and hadron
shows that the dominant contribution to $F(x,q^2)$ only comes $t-$channel exchange of particles of maximal spin, i.e. gluons (see Fig.~2). Moreover, in the center-of-mass
frame of $\gamma^*(q)$ and $h(p)$, due to hierarchy of the scales, $s\gg Q^2$, interaction takes place in the two-dimensional plane orthogonal to the plane defined by the momenta of scattered particles, $p_\mu$ and $q_\mu$. This implies that in generic Yang-Mills theory the leading high-energy asymptotic behavior of the scattering amplitudes is driven by $t-$channel exchange of an arbitrary number of gluons. In the so-called generalized leading logarithmic approximation,
their contribution to the moments \re{lambda1} takes the form
\begin{align}\label{F-T}
\tilde F_N(q^2) = \sum_{L\ge 2} \int [d^2k]\int [d^2k'] \ \Phi_{\gamma^*}(\{k\}) \,T_L(\{k\},\{k'\};N)\, \Phi_{h}(\{k'\})\,,
\end{align}
where integration goes over two-dimensional momenta of $L$ gluons propagating
in the $t-$channel, $[d^2k]=\prod_1^L d^2k_i$ and similarly for $[d^2 k']$. Here, the wave functions $\Phi_{\gamma^*}(\{k\})$ and $\Phi_{h}(\{k'\})$ describe the coupling of $L$ gluons to virtual photon and hadron, respectively. Also, $T_L(\{k\},\{k'\};N)$ describes
elastic scattering of $L$ gluons in the $t-$chan\-nel (see Fig.~\ref{diag}) and is the main object of
our consideration.
\begin{figure}[ht]
\ifarxiv
\centerline{\includegraphics[height=4cm]{BKPcm}}
\else
\centerline{\includegraphics[height=4cm]{BKPtimes}}
\fi
\caption[]{\small The Feynman diagrams contributing to the deep inelastic scattering in the generalized leading logarithmic approximation. Wavy lines denote (reggeized) gluons.
They couple to virtual photons through a quark loop.}
\label{diag}
\end{figure}
It is convenient to rewrite \re{F-T} as the following matrix element
\begin{align}\label{F-vev}
\tilde F_N(q^2) = \sum_{L\ge 2} \vev{\Phi_{\gamma^*}|T_L(N)|\Phi_{h}}\,,
\end{align}
where the minimum number of two gluons, $L=2$, is required in order to get a colorless exchange. The transition operator $T_L(N)$ describes the elastic
scattering of $L$ gluons. In the generalized leading logarithmic approximation,
the Feynman diagrams contribution to $T_L(N)$ have ladder structure as shown in Fig~\ref{diag}. They can be
resummed leading to the following Bethe-Salpeter equation~\cite{Bartels80,KP80}
\begin{align}\label{BS}
N T_L(N) = T_L^{(0)} + \frac{\alpha_s}{2\pi} \mathbb{H}_L\,T_L(N)\,,
\end{align}
where $ T_L^{(0)}$ corresponds to the free propagation of $L$ gluons in the $t-$channel and the evolution operator $\mathbb{H}_L$ describes their pair-wise interaction. The operator $\mathbb{H}_L$ acts both on two-dimensional momenta
and on colors of $L$ gluons and has the following two-particle form
\begin{align}
\mathbb{H}_L = \sum_{1\le i<j\le L} H_{ij}\, t_i^a t_j^a\,.
\end{align}
Each term in this sum is given by the product of the color factor involving color
charges of two gluons and two-particle kernel $H_{ij}$ acting locally on the tranverse momenta of gluons with indices $i$ and $j$. The kernel $H_{ij}$ is known as BFKL
operator \cite{BFKL} and it is defined below in \re{H-oper}.
Combining together \re{BS} and \re{F-vev} we obtain the following expression for $\tilde F_N(q^2)$
\begin{align}
\tilde F_N(q^2) = \sum_{L\ge 2} \vev{\Phi_{\gamma^*}|\lr{N- \frac{\alpha_s}{2\pi} \mathbb{H}_L}^{-1} T_L^{(0)}|\Phi_{h}}\,.
\end{align}
We observe that $\tilde F_N(q^2)$ has (Regge) singularities in $N$ which are determined by the eigenspectrum of the operator $\mathbb{H}_n$, the so-called
BKP equation \cite{Bartels80,KP80},
\begin{equation}
{\mathbb H}_L \Psi_{L,\{q\}}(k_1,\ldots,k_L) = E_{L,\{q\}}
\Psi_{L,\{q\}}(k_1,\ldots,k_L) \,.
\label{BKP}
\end{equation}
The solutions to \re{BKP} define color singlet compound states
of $L$ gluons and we introduced $\{q\}$ to denote the set of quantum numbers parameterizing all solutions. Having solved Schr\"odinger like equation \re{BKP},
we can compute the moments of the structure function as~\cite{Korchemsky95}
\begin{align}\label{sol}
\tilde F_N(q^2) = \sum_{L\ge 2} \sum_{\{q\}} \lr{N- \frac{\alpha_s}{2\pi} E_{L,\{q\}}}^{-1} \beta_{L,\{q\}}\,.
\end{align}
Here the impact factor $\beta_{L,\{q\}}= \vev{\Phi_{\gamma^*}|\Psi_{L,\{q\}}}\vev{\Psi_{L,\{q\}}|T_L^{(0)}|\Phi_{h}}$ measures the projection of the eigenstates onto the wave functions
of scattered particles. The double sum in \re{sol} runs over the possible number of gluons $L\ge 2$ and
over all eigenstates of the BKP Hamiltonian \re{BKP} parameterized by the conserved
charges $q$.
We observe that this relation has an expected Regge form \re{lambda1}.
Moreover, the leading Regge behavior of the structure function is controlled
by right-most singularity of $\tilde F_N(q^2)$ in complex $N$ plane. According to \re{sol}, it corresponds to the {\it maximal} value of the `energy' $E_{L,\{q\}}$.
\subsection{Conformal \texorpdfstring{$SL(2;\mathbb{C})$}{SL(2;C)} symmetry}
We recall that $k_i$ in the BKP equation \re{BKP} describe two-dimensional transverse momenta of $i$th gluon and the relation \re{BKP} can be interpreted as
two-dimensional Schr\"o\-din\-ger equation for $n$ particles carrying $SU(N_c)$ color charges.
As was found in \cite{Lipatov90,Lipatov94,FK95}, the BKP equation \re{BKP} becomes integrable in the multi-color limit. In this limit, the relevant ladder Feynman diagrams contributing to $\tilde F_N(q^2)$ have the topology of a cylinder and, as a consequence, the evolution operator ${\mathbb H}_L$ reduces to the sum of terms corresponding to
pairwise nearest-neighbor BFKL interactions:
\begin{equation}
{\mathbb H}_L = \frac12 \sum_{k=1}^L { H}_{k,k+1} + O(1/N_c^2)
\label{H-multi}
\end{equation}
with periodic boundary conditions ${H}_{L,L+1}={H}_{L,1}$. Notice that this
relation is exact for $L=2$.
The BFKL operator ${H}_{k,k+1}$ has a number of remarkable properties
which allow us to solve the Schr\"odinger equation (\ref{BKP})
exactly~\cite{Lipatov85,Lipatov90}. To elucidate these properties it is convenient
to switch from two-dimensional momenta $k_i$ to two-dimensional coordinates $b_i$ via Fourier transform and, then, introduce complex holomorphic and the
antiholomorphic coordinates
\begin{equation}
\vec{k}_i\quad \mapsto\quad \vec{b}_i=\{x_i,y_i\} \quad \mapsto \quad (z_{i} = x_{i}+i
y_{i}\,,\quad \bar{z}_{i} = x_{i}-i y_{i})\,.
\end{equation}
Quite remarkably, ${H}_{12}$ is invariant under the conformal $SL(2;\mathbb{C})$ transformations of the gluon coordinates on the plane~\cite{Lipatov85,Lipatov90}
\begin{equation}
z_k \to \frac{a z_k + b }{c z_k + d}\,,\qquad (ad-bc=1)\,,
\end{equation}
and similarly for antiholomorphic coordinates $\bar z_k$.
The generators of these transformations are
\begin{equation}\label{c-gen}
L_{k,-}=-\partial_{z_k}\,,\qquad L_{k,0}=z_k\partial_{z_k}\,,\qquad
L_{k,+}=z_k^2\partial_{z_k}\,,
\end{equation}
and the corresponding antiholomorphic generators $\bar L_{k,-}$, $\bar
L_{k,0}$ and $\bar L_{k,+}$ are given by similar expressions with $z_k$ replaced
by $\bar z_k$, with $k=1,2$ enumerating particles. Then, ${H}_{12}$ commutes with all two-particle generators
\begin{equation}\label{?-1}
[ {H}_{12},L_{1,a}+L_{2,a}] =
[ {H}_{12},\bar L_{1,a}+\bar L_{2,a}] = 0\,
\end{equation}
with $a=+,-,0$. This implies that, firstly, ${H}_{12}$ only depends on the
two-particle Casimir operators of the $SL(2,\mathbb{C})$ group
\begin{equation}\label{SL2C-Casimir}
{L}_{12}^2=-(z_1-z_2)^2\partial_{z_1}\partial_{z_2}\,,\qquad
\bar{{L}}_{12}^2=-(\bar z_1-\bar z_2)^2\partial_{\bar z_1}
\partial_{\bar z_2}\,,
\end{equation}
and, secondly, the eigenstates of ${H}_{12}$ have
to diagonalize the Casimir
operators
\begin{equation}\label{eig-SL2C}
{L}_{12}^2\Psi_{n,\nu}=h(h-1) \Psi_{n,\nu}\,,\qquad
\bar {L}_{12}^2\Psi_{n,\nu}=\bar h(\bar h-1) \Psi_{n,\nu}\, .
\end{equation}
Here a pair of complex conformal spins is introduced
\begin{equation}\label{h}
h=\frac{1+n}2+i\nu\,, \qquad \quad
\bar h=\frac{1-n}2+i\nu\,
\end{equation}
with a non-negative integer $n$ and real $\nu$ that specify the irreducible
(principal series) representation of the $SL(2,\mathbb{C})$ group to which
$\Psi_{n,\nu}$ belongs. The solutions to Eqs.\ (\ref{eig-SL2C}) are \cite{Lipatov85}
\begin{equation}\label{wf-2}
\Psi_{n,\nu}(b_1,b_2) =\left(\frac{z_{12}}{z_{10}z_{20}}\right)^{(1+n)/2+i\nu}
\left(\frac{\bar z_{12}}{\bar z_{10}\bar z_{20}}\right)^{(1-n)/2+i\nu}\,,
\end{equation}
where $z_{jk}=z_j-z_k$ and $b_0=(z_0,\bar z_0)$ is the collective
coordinate, reflecting the invariance of $ {H}_{12}$ under
translations. The corresponding eigenvalue of $H_{12}$ reads~\cite{BFKL,Lipatov85}
\begin{equation}\label{2-en}
E_{n,\nu}=2\psi(1)-\psi\left(\frac{n+1}2+i\nu\right)
-\psi\left(\frac{n+1}2-i\nu\right)\,.
\end{equation}
Its maximal value, $\textrm{max}\,E_{n,\nu}=4\ln 2$, corresponds to $n=\nu=0$,
or equivalently $h=\bar h=1/2$. It defines the position of the right-most
singularity $\omega=4\ln 2 \,{\alpha_s N_c}/{\pi} $ in \re{lambda1}
known as the BFKL pomeron~\cite{BFKL}.
The relations \re{wf-2} and \re{2-en} define the exact solution to the
Schr\"odinger equation \re{BKP} for $n=2$, that is for the color-singlet compound state built from two reggeized gluons.
\subsection{Heisenberg \texorpdfstring{$SL(2;\mathbb{C})$}{SL(2;C)} spin chain}
Using (\ref{2-en}) one can reconstruct the operator form of the BFKL kernel
${H}_{12}$ on the representation space of the principal series of
the $SL(2,\mathbb{C})$ group
\begin{equation}\label{H-oper}
{H}_{12}=\frac12\left[H(J_{12}) + H(\bar J_{12})\right] \,,\qquad
H(J)=2\psi(1)-\psi(J)-\psi(1-J)\,,
\end{equation}
where, as before, the two-particle spins are defined as ${L}_{12}^2 = J_{12}
(J_{12}-1)$ and $\bar{L}_{12}^2=\bar J_{12}(\bar J_{12}-1)$. Notice that we
already encountered the similar Hamiltonian in Sect.~2 (see Eq.~\re{closed}) and found that it gives rise to integrability for the dilatation operator.
Most remarkably, the Hamiltonian \re{H-multi} has the same hidden integrability as
the dilatation operator \re{closed} and it coincides in fact with the Hamiltonian of
the $SL(2,\mathbb{C})$ Heisenberg magnet~\cite{Lipatov94,FK95}.
The important difference
between the two operators is that they are defined on the different space
of functions: the operator \re{closed} acts on the nonlocal light-ray operators \re{O-def} which are polynomials in the light-cone coordinates while the eigenfunctions of the operator
\re{H-oper} are single-valued functions on the two-dimensional plane, Eq.~\re{wf-2}.
This leads to a dramatic change in the properties of the two evolution kernels.
The number of sites in the Heisenberg $SL(2,\mathbb{C})$ spin chain \re{H-multi}
equals the number of particles and the corresponding spin operators are
identified as six generators, $L_k^\pm, L_k^0$ and $\bar L_k^\pm,\bar L_k^0$,
of the $SL(2,\mathbb{C})$ group. It possesses a large-enough set
of mutually commuting conserved charges $q_n$ and $\bar q_n$ $(n=2,...,L)$ such
that $\bar q_n= q_n^\dagger$ and $[\mathbb{H}_L,q_n]=[\mathbb{H}_L,\bar
q_n]=0$. The charges $q_n$ are polynomials of degree $n$ in the holomorphic
spin operators.
They have the following form~\cite{Lipatov94,FK95}
\begin{equation}
q_n= \sum_{1\le j_1 < j_2 < ... < j_n \le L} z_{j_1j_2}z_{j_2j_3}... z_{j_nj_1}
p_{j_1}p_{j_2}...p_{j_n}
\label{q_n}
\end{equation}
with $z_{jk}=z_j-z_k$ and $p_j=i\partial_{z_j}$. The ``lowest'' charge $q_2$ is
related to the total spin of the system $h$. For the principal series of the
$SL(2,\mathbb{C})$ it takes the following values
\begin{equation}
q_2=-h(h-1)\,,\qquad h=\frac{1+n_h}2+i\nu_h\,,
\label{h1}
\end{equation}
with $n_h$ integer and $\nu_h$ real. The eigenvalues of the integrals of motion,
$q_2,...,q_L$, form the complete set of quantum numbers parameterizing the
$L-$gluon states \re{BKP}.
Identification of \re{H-multi} as the Hamiltonian of the $SL(2,\mathbb{C})$
Heisenberg magnet allows us to map the $L-$gluon states into the eigenstates
of this lattice model. In spite of the fact that the Heisenberg $SL(2,\mathbb{C})$ magnet represents a generalization of the $SL(2,\mathbb{R})$ spin chain, finding its exact solution
is a much more complicated task. The principal
difficulty is that, in distinction with $SL(2,\mathbb{R})$ magnet, the quantum space of
the $SL(2,\mathbb{C})$ magnet does not possess a highest weight -- the so-called
``pseudo-vacuum state'' -- and, as a consequence, conventional methods like
the Algebraic Bethe Ansatz method~\cite{QISM} are not applicable. The eigenproblem
\re{H-multi} has been solved exactly in Refs.~\cite{DKM01,KKM02,DKKM02} using the
method of the Baxter ${Q}-$operator~\cite{Baxter,Sklyanin,Bazhanov:1989nc,PG92} which does not rely on
the existence of a highest weight. In this approach, it becomes possible to
establish the quantization conditions for the integrals of motion $q_3,...,q_L$ and
to obtain an explicit form for the dependence of the energy $E_L$ on the integrals
of motion.
In this manner, the spectrum of the $L-$gluon state has been calculated for $L\ge 3$ particles: For $L=3$ few low-lying states have been found in
\cite{JW99,BLV99} and the complete spectrum of states for $3 \le L \le 8$ was
determined in \cite{KKM02,DKKM02} (see also \cite{VL01}). The obtained eigenspectrum
has a very rich structure. The quantized values of the conserved $q-$charges and the energy $E_L$ depend on the integer $n_h$ and the real number $\nu_h$ defining the total $SL(2,\mathbb{C})$ spin of the state, Eq.~\re{h}. In addition, they also depend on the ``hidden'' set of integers
$\Mybf{\ell}=(\ell_1,\ell_2,...,\ell_{2(L-2)})$. As a function of $\nu_h$, the charges form a
family of trajectories in the moduli space $\Mybf{q}=(q_2,q_3,...,q_L)$ labelled
by integers $n_h$ and $\Mybf{\ell}$. Each trajectory in the $q-$space induces
a corresponding trajectory for the energy $E_L=E_L(\nu_h;n_h,\Mybf{\ell})$.
The origin of these trajectories and the physical interpretation of the integers
$\Mybf{\ell}$ can be understood by solving the Schr\"odinger
equation \re{BKP} within the semiclassical approach described in the next subsection.
\subsection{Semiclassical limit}
In the semiclassical approach \cite{DKM03}, we assume that the $SL(2;\mathbb{C})$ spins $h$ and $\bar h$
are large and apply the WKB methods to construct the asymptotic solution to \re{BKP}.
One might expect a priori that this approach could be applicable only for
highly-excited states. Nevertheless, as was demonstrated in \cite{DKM03}, the
semi-classical formulae work with good accuracy throughout the whole spectrum.
{}From the viewpoint of classical dynamics, the multi-gluon states \re{BKP} are describe
by a chain of interacting particles `living' on the two-dimensional $\vec b-$plane
\cite{Korchemsky:1997yy,GKK02}. The classical model inherits the complete
integrability of the quantum noncompact spin magnet. Its Hamiltonian and the
integrals of motion are obtained from \re{H-multi}, \re{H-oper} and \re{q_n}
by replacing the momentum operators by the corresponding classical functions.
Since the Hamiltonian \re{H-multi} is given by the sum of holomorphic and
antiholomorphic functions, from point of view of classical dynamics the model
describes two copies of one-dimensional systems defined on the complex $z-$
and $\bar z-$lines. The solutions to the classical equations of motion have a
rich structure and turn out to be intrinsically related to the finite-gap
solutions to the nonlinear equations \cite{NMPZ84,Krichever77}; namely, the
classical trajectories have the form of plane waves propagating in the chain
of $L$ particles. Their explicit form in terms of the Riemann $\theta-$functions
was established in \cite{Korchemsky:1997yy} by the methods of finite-gap theory
\cite{NMPZ84,Krichever77}.
In the semiclassical approach, the eigenfunctions in
\re{H-multi} have the standard WKB form, $\Psi_{\rm WKB}(\vec z_1, \ldots,
\vec z_L)\sim \exp(iS_0/\hbar)$ where the Planck constant $\hbar = |q_2|^{-1/2}$ is related to the lowest charge \re{h1} and the action function $S_0$ satisfies the Hamilton-Jacobi
equations in the classical $SL(2;\mathbb{C})$ spin chain. It turns out that the solutions to
these equations are determined by the same spectral curve \re{curve}
as for the $SL(2;\mathbb{R})$ spin chain. The charges $\Mybf{q}$ define the moduli of this curve and take arbitrary complex values in the classical model.
Going over to the quantum model, we find that charges $\Mybf{q}$ are quantized.
The quantization
conditions for the charges $\Mybf{q}$ follow from the requirement that
$\Psi_{\rm WKB}(\vec z_1, \ldots,\vec z_L)$ has to be a single-valued function of $\vec z_i$. As was shown in
Refs.~\cite{GKK02,DKM03}, these conditions can be expressed in terms of the
periods of the ``action'' differential over the canonical set of the $\alpha-$
and $\beta-$cycles on the Riemann surface corresponding to the complex curve
\re{curve}
\begin{equation}
\mathop{\rm Re}\nolimits \oint_{\alpha_k}dx\,p(x) =\pi\,\ell_{2k-1}
\, , \qquad
\mathop{\rm Re}\nolimits \oint_{\beta_k}dx\,p(x) =\pi \, \ell_{2k}
\, ,
\label{WKB-intro}
\end{equation}
with $k=1,\ldots,L-2$ and $\Mybf{\ell}=(\ell_1,\ldots,\ell_{2L-4})$ being the set
of integers. The relations \re{WKB-intro} define the system of $2(L-2)$ real
equations for $(L-2)$ complex charges $q_3,...,q_L$ (we recall that the
eigenvalues of the ``lowest'' charge $q_2$ are given by \re{h1}). Their
solution leads to the semiclassical expression for the eigenvalues of the
conserved charges. In turn, the energy of the $L-$gluon states $E_{L,q}$
can be expressed as a function of $q_3,...,q_L$. In the semiclassical approach,
the corresponding expression is
\begin{eqnarray}\label{E-specc}
E_L^{\rm (as)}
&=& 4 \ln 2
\\
&+& 2 \mathop{\rm Re}\nolimits \sum_{k=0}^L
\bigg[
\psi(1 + i \mathop{\rm Re}\nolimits \delta_k + | \mathop{\rm Im}\nolimits \delta_k|)
+
\psi(i \mathop{\rm Re}\nolimits \delta_k + |\mathop{\rm Im}\nolimits \delta_k|) - 2 \psi(1)
\bigg]
\, , \nonumber
\end{eqnarray}
where $\delta_k$ are roots of the polynomial $t_L(u)$ defined in \re{transfer}.
{The expression in Eq.~\re{E-specc} is similar to the energy of
the $SL(2,\mathbb{R})$ magnet in Eq.~\re{E-as} although the properties
of the two models are different.} As was demonstrated in
\cite{DKM03}, the resulting semiclassical expressions for $q_3,...,q_L$ and
$E_L$ are in good agreement with exact results~\cite{KKM02,DKKM02}.
A novel feature of the quantization conditions \re{WKB-intro} is that they
involve \textsl{both} the $\alpha-$ and $\beta-$periods on the Riemann surface.
This should be compared with the situation in the Heisenberg $SL(2,\mathbb{R})$
magnet discussed in Section~2.6. There, the WKB quantization conditions involve
only the $\alpha-$cycles, Eq.~\re{q-as}, since the $\beta-$cycles correspond to
classically forbidden zones. For the $SL(2,\mathbb{C})$ magnet, the classical
trajectories wrap over an arbitrary closed contour on the spectral curve
\re{curve} leading to \re{WKB-intro}. This fact allows us to explore the full
modular group~\cite{Dubrovin81} of the complex curve \re{curve} and explain
the fine structure of the exact eigenspectrum of the $SL(2;\mathbb{C})$ magnet.
More details can be found in Ref.~\cite{DKM03}.
\section{Concluding remarks}
In this review, we have described integrability symmetry in application to the deeply inelastic scattering in QCD. Due to space limitations, we did not review various important topics
and we refer the interested reader to Ref.~\cite{Belitsky:2004cz} for a comprehensive review on the subject.
We would like to emphasize that integrability is not of a mere academic interest in QCD as it offers a powerful technique for solving important phenomenological problems such as finding the scale dependence of hadronic structure functions of higher twist and describing their high-energy (Regge) asymptotic behaviour. On theory side, the very fact that QCD
evolution equations exhibit integrability property provides yet another indication that QCD
possesses some hidden (integrable) structures waiting to be uncovered.
\section*{Acknowledgements}
It is a pleasure to thank A.~Belitsky, V.~Braun, S.~Derkachov, A.~Gorsky, A.~Manashov
and D.~M\"uller for an enjoyable collaboration on the topics reviewed above.
\phantomsection
\addcontentsline{toc}{section}{\refname}
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"redpajama_set_name": "RedPajamaArXiv"
} | 8,789 |
Già sindaco di Valdidentro, suo comune natale, dal 1956 al 1964 e dal 1965 al 1970, è stato deputato della Democrazia Cristiana dal 1972 al 1976.
Collegamenti esterni
Politici della Democrazia Cristiana
Deputati della VI legislatura della Repubblica Italiana
Sindaci in Italia | {
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domestic violence, sexual assault, human trafficking and other crimes.
Select and purchase your favorite week of the year for $100 and receive a 1-in-52 chance to win an extraordinary one-week stay in a delightful one-bedroom apartment in Le Marais, a trendy and historic district in Paris, France alive with restaurants, fashion boutiques, quaint shops, art galleries and museums. Your getaway includes roundtrip airfare for two.
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Q: Intellij IDEA locking changeset How do you lock certain files or changesets in Intellij IDEA VCS (git) to prevent them from being accidentally commited?
I need it for certain property files which should have prod-settings in git, but dev-settings at local PC.
A: I think you can list files which you don't want to commit in .gitignore.
https://help.github.com/articles/ignoring-files
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Q: Obtain Contents In Ajax I want to validate a file being uploaded via Ajax before the user can submit it. I make sure it is a .txt or .csv in javascript, then I want to call my controller to verify it matches our CSV standard.
I have :
<input type="file" name="csvFile" id="csvFile" onchange="validateFile()"/>
and
function validateFile() {
var file = document.getElementById("csvFile");
var extension = file.value.split('.').pop();
if (extension != "csv" && extension != "txt") {
alert("A .csv or .txt file is required for upload");
return false;
}
$.ajax({
url: '@Url.Action( "ValidateCSV","UploadCSV")',
type: "POST",
data: { file: document.getElementById("csvFile") }, //unclear here
success: function () {
alert("success");
},
error: function (error) {
alert("failed:" + error);
}
});
}
for the ajax data, how do i go about getting the HttpPostedFileBase that the controller wants from the file? I was wanting to do all the validation before the user is allowed to submit it. I'm not 100% that I'm 'allowed' to do this
Thankyou for any guidance
A: Have you tried to put the input in a form?
<form action="" method="post" enctype="multipart/form-data">
<input type="file" name="csvFile" id="csvFile" class="file" onchange="changeFile();validFile();" />
<div class="fakefile">
<input id="csvFileFakeId" />
<button onclick="return false;" class="blue">Browse</button>
</div>
<button type="submit">Upload</button>
</form>
Validate the file type, if invalid, clear the input and alert the user.
<script type="text/javascript">
var fileId = "csvFile";
var fakeFileId = "csvFileFakeId";
function changeFile() {
var value = $("#" + fileId).val().split('\\').pop();
$("#" + fakeFileId).val(value);
};
function validateFile() {
var file = document.getElementById("csvFile");
var extension = file.value.split('.').pop();
if (extension != "csv" && extension != "txt") {
alert("A .csv or .txt file is required for upload");
$('#csvFile').val('');
$('#csvFileFakeId').val('');
return false;
}
};
</script>
And when the post the form (this assumes the MVC endpoint is Upload or you have mapped that path
[HttpPost]
public ActionResult Upload(HttpPostedFileBase file)
{
....
}
A: I have an answer here using HTML5 file api. Upload photo with jQuery Dialog in ASP.NET MVC site
it was down voted but I always use it for uploading and it works.
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\section{Introduction}
\label{sec:intro}
The success of clean energy sources is predicated on improvements in
energy storage technologies. State-of-the-art Li-ion batteries,
although instrumental in considerable advances in portable electronics,
cannot cope with the minimum
storage\cite{VanNoorden2014,Yoo2013,Muldoon2014,Shterenberg2014} and
safety\cite{Cohen2000} requirements dictated by grid and transport
applications.
A viable strategy for post-Li-ion technology is to replace Li with
safer and earth-abundant Mg. Magnesium has the advantage of doubling
the total charge per ion, which results in larger theoretical volumetric
capacity compared to typical Li-ion
batteries.\cite{Aurbach2002,Muldoon2012,Yoo2013,VanNoorden2014,Muldoon2014,Shterenberg2014}
Most importantly, in Mg-ion batteries the intercalation architecture of
the graphitic-anode for Li-ions is replaced by a high-energy density
metal anode ($\sim$~700~Ah~l$^{-1}$ and $\sim$~3830 Ah~l$^{-1}$,
respectively).\cite{Aurbach2002,Muldoon2012,VanNoorden2014,Muldoon2014,Shterenberg2014,Liu2015}
Notwithstanding the tantalizing advantages of Mg-ion technology, its
distinct electrochemistry imposes serious limitations on the kind of
electrolyte that can reversibly plate and strip Mg, and at the same time
sustain high-voltage cathode materials. For example, Mg-ion electrolytes
that are analogous to their Li-ion counterparts (e.g.\ PF$_6^-$ Li$^+$)
and solvents (e.g.\ propylene carbonate/dimethyl carbonate) irreversibly
decompose at the Mg anode, producing passivating layers that are
impermeable to Mg-ions, and inhibit further electrochemical
activity.\cite{Brow1985,Aurbach2011}
To circumvent this issue, efforts by Gregory \emph{et
al.}\cite{Gregory1990,Muldoon2014} demonstrated \emph{quasi}-reversible
Mg-plating from Grignard's reagents. Greater coulombic efficiencies and
anodic stabilities were achieved by Aurbach and collaborators after many
years of meticulous tuning of the organic magnesium aluminum chloride
salts (organo-magnesium-chloride complexes) dissolved in ethereal
solutions, namely the dichloro complex (DCC) and the ``all phenyl
complex''
(APC).\cite{Aurbach2001,Aurbach2002a,Gizbar2004,Mizrahi2008,Aurbach2011,Pour2011,Yoo2013,Doe2013,Doe2014,Barile2014a,Barile2014}
Similarly, Shao \emph{et al.}\cite{Shao2013} achieved Mg deposition by
combining Mg(BH$_4$)$_2$ and LiBH$_4$ in diglyme. The air-sensitivity
and low anodic stability of previous Mg-ion electrolytes led Kim
\emph{et al.}\cite{Kim2011} to propose a non-nucleophilic salt
comprising AlCl$_3$ and hexamethyldisilazide magnesium chloride
(HMDSMgCl). Recently, Mohtadi, Arthur and co-workers at Toyota developed a series of halogen--free electrolyte based on Mg borohydride, boron-clusters and carboranes, which are not corrosive and with relatively high anodic-stability $\sim$~3.8--4.0~V.\cite{Tutusaus2015,Carter2014,Mohtadi2012} Subsequently, Doe~\emph{et al.}\cite{Doe2013,Doe2014}
developed an inexpensive electrolyte termed Magnesium Aluminum Chloride
Complex (MACC) which is formed by mixing two common inorganic salts,
namely AlCl$_3$ with MgCl$_2$ in ethereal solutions. MACC possesses a
relatively large anodic stability ($\sim$~3.1~V) and good reversible Mg
deposition/stripping. The MACC electrolyte is the focus of the current
paper.
The good performance of an electrolyte is dictated by few but important
parameters such as high coulombic efficiency, high anodic and cathodic
stabilities, and high diffusivity of the ion carriers, which depend
ultimately on the structural composition of the electrolyte at rest and
during electrochemical cycling. In the present study we interrogate the
MACC electrolyte composition with the goal of elucidating: \emph{i}) the
functional species of the electrolyte, and \emph{ii}) the complex
equilibria regulating the MACC speciation after prolonged
electrochemical cycling, a process termed as
conditioning\cite{Shterenberg2014}, and after inactivity, termed as
aging\cite{Barile2014}. Aiming to describe important macroscopic effects
observed in electrochemical experiments from the ground-up, and provide
an atomistic picture of the processes regulating the speciation in the
MACC electrolyte at different electrochemical conditions, we explore the
complex chemical space of Mg-Cl-Al-THF (with THF as
tetrahydrofuran) combining Density Functional Theory (DFT) with
Classical Molecular Dynamics (CMD) simulations. The computational
strategy is general and suitable to other electrolytes, ionic liquids
and a variety of liquid media.
On the basis of previous experimental XRD, Raman and NMR
observations\cite{Pour2011} on the APC electrolyte, similar to MACC but
with organic moieties on the Al$^{3+}$ ion, it is speculated that ${\rm
Mg}_m{\rm Al}_n{\rm Cl}_{[(2m)+(3n)]}$ comprises the magnesium chloride
monomer, $[\mu-$MgCl$\cdot$5THF$]^+$, the dimer
$[\mu-$Mg$_2$Cl$_3\cdot$6THF$]^+$ and AlCl$_4^-$ as counterion. While
monomer and dimer ions are yet to be observed during electrochemical
cycling in both MACC and APC, they are thought to be the active
Mg$^{2+}$ carriers during electrochemical cycling. Barile \emph{et
al.}\cite{Barile2014} also speculated that higher order magnesium-chloro
structures such as trimer and multimeric units may exist, and they are
included in this study.
With the aid of density functional theory calculations and molecular
dynamics we are able to show that the MACC electrolyte bears a simple
chemical structure with very few species present. By knowing the stable
species of the electrolyte, we elucidate the equilibria taking place in
the electrolyte, showing that the Mg$^{2+}$ carriers, MgCl$^+$ are
continuously exchanged with MgCl$_2$ (and AlCl$_4^-$ with AlCl$_3$), and
changes of these equilibria alter the observed electrochemical
performance of the electrolyte. Finally, our results suggest some
explanation for the phenomena of electrolyte aging and conditioning.
These findings are instrumental for progressing the development of the
next generation of Mg-ion batteries. Particularly, we demonstrate the
working of the MACC electrolyte, and also provide clear directions for
the improvement of the electrolyte performance.
\section{Methodology}
\label{sec:method}
\subsection{\emph{Ab initio} molecular solvation and periodic bulk calculations}
\label{subsec:QM}
Due to the importance of strong interactions between solvent molecules
and the species in the MACC electrolyte, we model, using Density
Functional Theory (DFT), each magnesium-aluminum-chloride complex with
an explicit solvent of THF molecules in the first solvation shell and an
implicit model in the outer shells to describe long-range
solvent-solvent interactions. The methodology is shown in
Fig.~\ref{fig:solvation}, where 3 THFs are included in the first
solvation shell of MgCl$^+$, while the domain indicated by the cyan halo
depicts outer shells, which are modeled as a dielectric medium by the
Polarizable Continuum Model (PCM).\cite{Tomasi2005}
\begin{figure}[ht]
\centering
\includegraphics[width=1.0\columnwidth]{figure1.pdf}
\caption{\label{fig:solvation} Diagram showing the approximation used to
capture the solvation structure of magnesium-aluminum-chloride
complexes (see Equations~\ref{eq:foamtionenergy}). Inner circle MACC
cluster with a 1$^{st}$ shell of explicit solvent of THFs, outer circle
(cyan halo) for longer range solvation shells.}
\end{figure}
According to Figure~\ref{fig:solvation} $G_{\rm PCM}$, the Gibbs free
energy of the fully solvated Mg-Cl-Al-THF clusters are set by
Equation~\ref{eq:foamtionenergy}.
\begin{equation}
\label{eq:foamtionenergy}
G_{\rm PCM} = E_{\rm PCM} + {\rm ZPE}_{\rm expl} + q_{\rm expl} -
TS_{\rm expl}
\end{equation}
where $G_{\rm PCM}$ and $E_{\rm PCM}$ represent the Gibbs free energy
and total energy of the fully solvated complex (explicit solvent and
implicit solvent, see Figure~\ref{fig:solvation}), while ZPE$_{\rm
expl}$, $q_{\rm expl}$, and $TS_{\rm expl}$ are the zero point energy
correction, the thermal contribution, and the entropic term
respectively, approximated by the MACC clusters comprising only the
explicit solvent. To obtain the explicit part of $E_{\rm PCM}$ (see
Fig.~\ref{fig:solvation}), we first relax the geometries of the
magnesium-aluminum-chloro clusters (comprising an explicit 1$^{st}$
solvation shell of THFs) within the DFT approximation with B3LYP and a
6-31+G(d) basis-set implemented in Gaussian09.\cite{g09} Previous
battery studies have demonstrated that B3LYP can accurately reproduce
experimental results.\cite{Rajput2015,Ong2011,Zhang2014,Okoshi2013}
More details on the methodology are provided in the Supplementary
information. Finally, $E_{\rm PCM}$ of Eq.~\ref{eq:foamtionenergy} is
obtained from a single point energy calculation on the relaxed
structures using the PCM model.\cite{Tomasi2005} Frequency analysis is
performed to ensure that the relaxed structures are real minima as well
as to compute the free energy corrections (i.e.\ ZPE$_{\rm expl}$,
$q_{\rm expl}$, and $TS_{\rm expl}$).
To evaluate some important reactions involving solid phases, we employ
the B3LYP functional available in VASP.\cite{Kresse93,Kresse96} The
total energy is sampled on a well-converged
4$\times$4$\times$4~\emph{k}-point grid (and a
16$\times$16$\times$16~\emph{k}-point grid for Al and Mg metals)
together with projector augmented-wave theory\cite{Kresse99} and a 520
eV plane-wave cutoff. Forces on atoms are converged to less than
1$\times$10$^{-2}$ eV/{\AA}. In order to compare the liquid species
participating to chemical reactions containing solid phases (see
Table~\ref{tb:equil_reactions}) we simulated the relaxed structures
obtained from molecular PCM calculations with periodic boundary
conditions employing a box of size 20$\times$20$\times$20~\AA$^3$ and
the VASP setup indicated above. Thus, the chemical potential of
molecules and ions coordinated by THF (see
Table~\ref{tb:equil_reactions}) are referenced to the liquid THF via the
experimental enthalpy of vaporization $\Delta$H~$\sim$~0.331
eV.\cite{Scott1970}
For relevant clusters, $^{35}$Cl and $^{25}$Mg NMR shielding tensors
(only the isotropic shielding part is discussed) are provided as useful
fingerprints to guide experiments. NMR parameters are obtained with
Gauge-Independent Atomic Orbital theory\cite{Wolinski1990} on the
relaxed structures at the 6-31+G(d) level of accuracy, but increasing
the basis-set quality to 6-311+G(d,p). Basis-set convergence on the NMR
isotropic shielding for these molecules are discussed in the
Supplementary Information.
\subsection{Debye-H{\"{u}}ckel correction}
To account for the electrostatic interactions of ions in the
electrolytic solution, we apply a potential energy correction to the
reactions energies (see Table~{\ref{tb:equil_reactions}}) based on
Debye-H\"{u}ckel theory.{\cite{Debye1923,Robinson1968}} Therefore the
$\Delta$E corrected by the Debye-H{\"{u}}ckel model $\Delta$E$_{D-H}$
becomes:
\begin{equation}
\Delta E_{D-H} = \Delta E + \sum^m_{i = 0} u_i
\end{equation}
where $\Delta$E obtained from DFT calculations at infinite
dilution, $m$ is the total number of ion $i$, and $u_i$ the
electrostatic potential energy given by
Equation~{\ref{eq:debye_huckel}},
\begin{equation}
\label{eq:debye_huckel}
u_i = -\frac{z_i^2 e^2 \kappa}{8 \pi \epsilon_r \epsilon_0} \frac{1}{1 +
\kappa a_0}
\end{equation}
\begin{equation}
\label{eq:screening_length}
\kappa^2 = \sum_{i} \frac{z_i^2 e^2 c_i^0}{\epsilon_r \epsilon_0 k_B T}
\end{equation}
where $z_i$ is the charge number and $c_i^0$ the number
concentration of ion $i$, $\epsilon_r$ the relative dielectric constant
($\sim$7.5 for THF), $\epsilon_0$ the vacuum permittivity, $k_B$ the
Boltzmann constant, $T$ the temperature, $e$ the electron charge, $a_0$
the minimum separation of ions, and $\kappa^{-1}$ the Debye screening
length. We set $a_0$ to be $\sim$~7.1~{\AA} that is the minimum
separation of the van der Waals spheres of MgCl$^+$(3THF) and
AlCl$_4^-$. Since the $\Delta$E$_{D-H }$ of
Equation~{\ref{eq:debye_huckel}} depends on the ionic activity $c_i^0$,
which in turn depends on the magnitude of the Debye-H\"uckel correction,
the $\Delta$E$_{D-H }$ has to be evaluated numerically through an
iterative self-consistent procedure. Self-consistency of $u_i$ is
achieved when the concentration (of the charged species, i.e. MgCl$^+$)
equals the input concentration.
In general, the Debye-H\"{u}ckel theory is not appropriate for the description of concentrated
solutions; for this reason we use the extended Debye-H\"{u}ckel approximation (which holds for concentrations $<$ 10$^{-1}$~M), see Eq.{~\ref{eq:debye_huckel}} which is compatible with the concentrations of the charged species in solution ($\sim$ 92 mM for MgCl$^+$ and AlCl$_4^-$).
\subsection{Classical molecular dynamics simulations of bulk electrolytes}
All classical molecular dynamics (CMD) simulations to study the dynamic
structure of the MACC electrolyte are computed using
LAMMPS\cite{LAMMPSref} and treat the effect of the THF solvent
explicitly. The THF-THF, and THF-ion interactions are modeled using the
Generalized Amber Force Field~\cite{Wang2004,Wang2006} (GAFF), whereas
Mg and Cl partial charges presented in Table~\ref{tb:charges} are
computed with the RESP procedure by fitting the electrostatic potential
surface of the optimized geometries using
Antechamber.\cite{Bayly1993,Wang2004,Wang2006}
\begin{table}[th]
\caption{\label{tb:charges} Computed RESP charges and van der Waals
parameters ($\epsilon$~in~kcal~mol$^{-1}$ and $\sigma$~in~\AA) for Mg
and Cl used in the classical CMD simulations of MACC electrolyte.}
\begin{tabular*}{\columnwidth}{@{\extracolsep{\fill}}lcc@{}}
\hline\hline
Species & Mg & Cl \\
\hline
MgCl$_2$ & 0.9380 & --0.4690 \\
MgCl$^+$, Monomer & 1.4021 & --0.4021$^*$ \\
Mg$_2$Cl$_3^+$, Dimer & 1.2621 & --0.5081$^*$ \\
Mg$_3$Cl$_5^+$, Trimer & 1.1264 & --0.4758$^*$ \\
\hline
Atom & $\epsilon$ & $\sigma$ \\
\hline
Mg & 0.88 & 1.64 \\
Cl & 0.71 & 4.02 \\
\hline\hline
\end{tabular*}
{\small$^*$Compensating Cl$^-$ counterions were assigned a charge of --1
to maintain charge neutrality.}
\end{table}
\noindent The GAFF force field parameters for THF were benchmarked
against the experimental properties and found to reproduce the
experimental values adequately; for example the experimental density of
THF ($\sim$ 0.889~g/cm$^3$) is well reproduced by CMD simulations
($\sim$ 0.882~g/cm$^3$),\cite{Rajput2015} similarly the experimental
diffusion coefficient ($\sim$ 300.00$\times$10$^{-11}$~m$^{2}$/s) is in
good agreement with the calculated value ($\sim$
211.34$\times$10$^{-11}$~m$^{2}$/s).\cite{Rajput2015}
The MACC electrolyte structures initially optimized with Gaussian09
(see above) are inserted into a periodic box of size
48$\times$48$\times$48~\AA$^3$ containing 800 THF molecules at the
experimental THF density (0.889 g/cm$^3$). The infinite dilution limit
is simulated for each complex, i.e.\ only one molecule was inserted in
the CMD box. Then, each configuration is equilibrated for 1~ns in the
isothermal-isobaric ensemble (NPT) which is sufficient to converge the
density, with minimal variation ($\sim$ 1\% ) from the THF experimental
value. Subsequently, a 1~ns simulation is performed in the canonical
ensemble (NVT) at 300~K, of which the first 200~ps is utilized for
equilibration, within which convergence of each simulation is achieved,
followed by a production time of 800~ps. A time step of 1~fs is used.
To identify how THF coordinates to the Mg$_x$Cl$_y$ (i.e.\ monomer,
dimer and trimer) ionic species, it is not necessary to consider changes
of the ion structures during coordination by THF. Therefore, in the CMD
simulations the ions are held rigid (in the electrolyte solvent) at the
fully relaxed geometries as obtained by Gaussian09, thus removing the
necessity of parameterizing bonded interactions of each ion.
\section{Results}
\label{sec:results}
To isolate the electro-active species comprising the MACC electrolyte,
we first study the structures and composition of various magnesium
chloride complexes hypothesized to be present in the electrolyte. The
Mg-Al-Cl-THF chemical space is further enlarged by additional structures
that are guessed by chemical intuition or results of CMD simulations.
Consequently, we study the salt solvation by altering the first
solvation shell of the magnesium-chloro complexes considered. The
Supplementary Information reports the atomic positions of the
thermodynamic stable structures.
\subsection{Magnesium-chloride complexes}
\label{sec:method}
Previous experimental efforts have attempted to understand the complex
structure of the magnesium-chloride complexes of the MACC electrolyte.
The combined X-ray diffraction, Raman, and NMR spectroscopies by Aurbach
and co-workers established that Mg$^{2+}$ in THF exists always as a six
coordinated ion in the form of monomer MgCl$^+$(5THF) or dimer
Mg$_2$Cl$_3^+$(6THF).\cite{Gizbar2004,Pour2011} In contrast to these
results, a more recent theoretical investigation\cite{Wan2014}
elucidated the first solvation shell of the MgCl$^+$ and Mg$_2$Cl$_3^+$
magnesium organo-chloro species in the bulk electrolyte using \emph{ab
inito} molecular dynamics calculations, and suggested that the MgCl$^+$
monomer is always coordinated by three THFs, leading to a total Mg
coordination of four. Similar findings were supported by the
experimental NMR and XANES work of Nakayama \emph{et
al}.\cite{Nakayama2008}
We benchmark our modelling strategy on previous experimental and
theoretical results by simulating several magnesium-chloride complexes
in different THF environments combining DFT and CMD calculations, as
outlined above.
To measure the stability of magnesium-chloride clusters in THF we
compute (with DFT) the formation free energy $\Delta F$ at fixed THF
chemical potential $\mu _{\rm THF}$:
\begin{equation}
\label{eq:formationgibbs}
\Delta F = G(n_{\rm Mg}, n_{\rm Cl}, n_{\rm THF}) - G(n_{\rm Mg}, n_{\rm Cl}) -n_{\rm THF}\mu_{\rm THF}
\end{equation}
where $G(n_{\rm Mg}, n_{\rm Cl})$ and $G(n_{\rm Mg}, n_{\rm Cl}, n_{\rm
THF})$ of Eq.~\ref{eq:formationgibbs} are the Gibbs free energy of each
Mg$_x$Cl$_y$ cluster isolated and coordinated by $n_{THF}$ molecules.
Throughout the paper all references to ``formation~energy'' refer to the
formation free energy $\Delta F$.
Figure~\ref{fig:complex_hulls} depicts the free energies of formation
$\Delta F$ for the magnesium-chloride complexes as a function of THF
coordination (bottom $x$-axis) and total Mg coordination (top $x$-axis)
obtained from B3LYP calculations.
\begin{figure}[!t]
\centering
\includegraphics[width=1.0\columnwidth]{figure2.pdf}
\caption{\label{fig:complex_hulls} Formation free energy (in eV) of
magnesium-chloride complexes as a function of THF coordination for a)
MgCl$^+$ (monomer), b) Mg$_2$Cl$_3^+$ (dimer), c) Mg$_3$Cl$_5^+$
(trimer), and d) MgCl$_2$. Arrows indicates the most stable THF
coordination environment for each complex. Snapshots of the most stable
magnesium-chloride complexes are also depicted.}
\end{figure}
Each minimum in Fig.~\ref{fig:complex_hulls} represents the most stable
structure for a particular Mg-Cl complex, hence its most stable Mg
coordination. Figure~\ref{fig:complex_hulls} shows that the preferred
magnesium coordination is 4-fold for both MgCl$^+$(3THF) and
MgCl$_2$(2THF), 5-fold for the dimer Mg$_2$Cl$_3^+$(4THF), and 6-fold
for the trimer Mg$_3$Cl$_5^+$(6THF). Interestingly, the total Mg
coordination number increases with the size of the magnesium-chloride
cluster. The stable structures show a coordination of 3 THFs for the
monomer MgCl$^+$ and 2 THFs for each Mg atom in dimer Mg$_2$Cl$_3^+$
(4THFs in total). These results are consistent with theoretical findings
by Wan \emph{et al.}~\cite{Wan2014} and XANES spectroscopy
data.\cite{Nakayama2008}
Classical molecular dynamic simulations are used to clarify the dynamics
of the ion complexes in MACC in THF solvent. Figure~\ref{fig:md_rdf}
plots the radial distribution functions (RDF, black lines), and the
corresponding coordination numbers for the 4 complexes (red and blue
dashed and dotted lines, respectively) obtained from CMD calculations.
More RDF plots of different atom pairs are available in the
Supplementary Information.
\begin{figure}[h]
\centering
\includegraphics[width=1.0\columnwidth]{figure3.pdf}
\caption{\label{fig:md_rdf}Mg-O(THF) radial distribution function (black
curves), and coordination numbers (red dashed lines) as function of the
Mg-O separation (in \AA) for the magnesium chloride-complexes. a)
MgCl$_2$, b) MgCl$^+$ monomer, c) Mg$_2$Cl$_3^+$ dimer, and d)
Mg$_3$Cl$_5^+$ trimer. The THF coordination numbers for the first
coordination shell are indicated by the blue dotted lines.}
\end{figure}
The peaks located between 2.0-2.5 \AA{} in each RDF indicate the first
coordination shell of Mg experienced by THF, and its integration (see
blue dotted lines) the number of THF molecules coordinated by Mg atoms.
For dimer and trimer of Fig.~\ref{fig:md_rdf}~c)~and~d) the peaks from
4.5 to 5.0~\AA{} are the oxygen atoms of the THFs coordinating the
nearest neighbors Mg atoms. Figure~\ref{fig:md_rdf} obtained from
classical molecular dynamic simulations, shows that the overall Mg
coordination number for each Mg-Cl complex is consistent with the
prediction from the DFT formation energies (see above). Our preliminary
CMD simulations demonstrated that the coordination of MgCl$^+$ is
wrongly predicted to be 6, if Mg$^{2+}$ and Cl$^-$ ionic charges are
assigned to +2 and --1 for Mg and Cl ions,
respectively.\cite{Wan2014,Nakayama2008} This is because charge
transfer processes occurring within each complex reduce the nominal
charges on both Cl and Mg (as seen in Table~\ref{tb:charges}), hence
lowering the overall Mg coordination number to 4. Moreover, we find two
kinds of Mg-THF coordinations observed for the charged ions-- THF
molecules are either strongly coordinated to the complex, or weakly
coordinated, thereby setting up a free exchange of THF molecules with
the bulk solution and the first solvation shell. For Mg$_2$Cl$_3^+$, two
THF molecules are strongly coordinated to each Mg atom, while a third
THF molecule is constantly exchanged between the bulk region and the Mg
atoms in an alternating manner, leading to an effective coordination
number of 2.5 THFs per Mg atom. For instance, this exchange occurs after
900 ps for Mg$_2$Cl$_3^+$. For the MgCl$^+$ monomer, the coordination
number is predicted to be 3.7 THFs, and slightly larger than in previous
\emph{ab initio} MD simulations (3 THFs for MgCl$^+$).\cite{Wan2014}
Overall, the coordination numbers computed from both DFT and CMD are
consistent with previous XANES,\cite{Nakayama2008} with sub-ambient
pressure ionization with nano-electrospray mass
spectroscopy,{\cite{Liu2015a}} and accurate \emph{ab initio} MD studies
consolidating the idea that THF steric hindrances and Mg-Cl charge
transfer lead to THF not being able to fulfill the typical sixfold
coordination of Mg in solids.\cite{Wan2014} To conclude, DFT coupled
with computationally inexpensive CMD simulations provides a robust
strategy to interrogate the structural characteristic of the species in
the MACC electrolyte.
To study the effect of electrolyte composition on the stability of the
MACC complexes, we analyze the stable phases of the Mg-Cl-Al-THF
chemical space using the the total energies of more than hundred
Mg$_x$Cl$_y$ and Al$_x$Cl$_y$ molecules with variable THF coordination
numbers.
Figure~\ref{fig:mg_cl_thf_grandphasediag} shows the grand-potential
phase diagram\cite{Ong2008} for the Mg-Cl-THF system at the bulk THF
chemical potential, where black lines set the boundaries of the stable
regions, and red-dots indicate the stable phases. To the best of our
knowledge this is the first instance of grand-potential phase diagrams
together with DFT calculations being used to analyze the structure of a
liquid electrolyte.
\begin{figure}[h!]
\centering
\includegraphics[width=1.0\columnwidth]{figure4.pdf}
\caption{\label{fig:mg_cl_thf_grandphasediag} a) Mg-Cl-THF
grand-potential phase diagram as function of Cl concentration at the
bulk THF chemical potential. Red dots connected by black lines indicate
the stable magnesium-chloride complexes, and unstable species by yellow
squares. b) shows a region close to the stability lines. Coordinating
THF molecules indicated by T. Dashed lines for the dimer and trimer
concentrations. }
\end{figure}
The THF chemical potential is calculated using the same procedure
exposed in Sec.~\ref{sec:method} from a cluster of 7 THF molecules
extracted from an well equilibrated \emph{ab initio} MD, see more
details in Ref.~\cite{Canepa2015} The grand potential formation free
energy of each complex is calculated with respect to Mg$^{2+}$ in THF
and Cl$^-$ in THF as these are the relevant reference states for the
complexes in THF. At Cl compositions of 0.0 (equivalent to 0 \% Cl and
100 \% Mg, or Mg$^{2+}$) and 1.0 (equivalent to 100 \% Cl and 0 \% Mg,
or Cl$^-$), Mg$^{2+}$ and Cl$^-$ species are coordinated by 6 and 0
THFs, respectively. The formation free energies of Fig.{~\ref{fig:mg_cl_thf_grandphasediag}} and successive grand-potential phase diagrams contain the vibrational entropy as indicated by Eq.~{\ref{eq:foamtionenergy}} and Eq.~{\ref{eq:formationgibbs}. Our calculations do not capture the configurational entropy that would tend to stabilize low coordination number.}
At first glance
Fig.~\ref{fig:mg_cl_thf_grandphasediag}a and b show that solutions
containing Mg and Cl in THF form stable magnesium-chloride complexes,
and only MgCl$^+$(3T) (with T for THF) and MgCl$_2$(2T) are observed to
be the stable phases (see red dots) through the entire Cl composition.
We find that neither the dimer, nor the trimer are stable in bulk THF
(see yellow squares marked as Mg$_2$Cl$_3^+$(4T) and Mg$_3$Cl$_5^+$(6T)
for the dimer, trimer, respectively in
Fig.~\ref{fig:mg_cl_thf_grandphasediag}b). Notably, the stable phases
identified by the grand-potential phase diagram of
Fig.~\ref{fig:mg_cl_thf_grandphasediag} correspond to the lowest
formation energies of the magnesium-chloride complexes as presented in
Fig.~\ref{fig:complex_hulls}. As already mentioned, the dimer
Mg$_2$Cl$_3^+$ was isolated with X-ray on mono-crystals as one of the
products of crystallization of the APC electrolyte,\cite{Pour2011} while
trimer and higher order structures were speculated to exist by
Barile~\emph{et al}.\cite{Barile2014} as a byproduct of polymerization
of the principal MACC components MgCl$_2$, monomer and dimer.
By isolating the most stable Mg$_x$Cl$_y$ components from the
grand-potential phase diagram of Fig.~\ref{fig:mg_cl_thf_grandphasediag}
we can estimate the reaction energies to form dimer and trimer complexes
from the MgCl$^+$ as seen in Fig.~\ref{fig:reaction}.
\begin{figure}[h!]
\centering
\includegraphics[width=1.0\columnwidth]{figure5.pdf}
\caption{\label{fig:reaction} Chemical reaction for monomer converting
into dimer and trimer, with relative free energy (in meV). }
\end{figure}
Figure~\ref{fig:reaction} clearly shows that both dimer and trimer are
not accessible in normal thermodynamic conditions (with almost 1~eV to
create the trimer from the monomer). Hence our results argue against
the existence of such magnesium-chloride agglomerates in the actual
solution.\cite{Pour2011,Benzmayza2013,Doe2014,Barile2014}
To explore the morphology of the MACC electrolyte further and analyze
possible changes that might occur to its structure, we investigate the
stability of the electrolyte with varying THF chemical potential, and
therefore look for possible conditions under which unstable structures
from Fig.~\ref{fig:mg_cl_thf_grandphasediag} can be stabilized (e.g.\
dimer and trimer).
Figure~\ref{fig:mg_cl_thf_grand_drying} shows the grand-potential phase
diagram\cite{Ong2008} for the Mg-Cl-THF system at the chemical potential
corresponding to a THF activity of $10^{-6}$ (which means lowering the
THF chemical potential by $\sim$~--34.25~kJ~mol$^{-1}$).
\begin{figure}[!ht]
\centering
\includegraphics[width=1.0\columnwidth]{figure6.pdf}
\caption{\label{fig:mg_cl_thf_grand_drying} a) Mg-Cl-THF grand-potential
phase diagram as function of Cl concentration at the THF chemical
potential under drying conditions (with activity of THF $=$ 10$^{-6}$).
Red dots connected by black lines indicate the stable magnesium chloride
complexes, and unstable species are indicated by yellow squares. b)
shows a region close to the stability lines. Coordinating THF molecules
indicated by T. Dashed lines as guide for dimer and trimer
concentrations. }
\end{figure}
Changing the THF chemical potential affects directly the relative
stability of the THF coordination environment experienced by the MACC
complexes, and low-coordination situations are preferred at low THF
chemical potentials. For example, the THF coordination of MgCl$_2$
decreases from 2THF to 1THF, but the relative stability order between
MgCl$_2$ and MgCl$^+$ is maintained. Lowering the chemical potential of
THF in the bulk solution emulates the process of drying, where the
solvent evaporates, and thereby only the strongly-bound THF molecules
remain coordinated to the complexes.
Interestingly, from Fig.~\ref{fig:mg_cl_thf_grand_drying} we notice that
the free energy of the dimer complex now approaches the ground state
line (see black line), meaning that this structure might become
accessible under conditions of evaporating/drying solvent. The dimer is
only $\sim$~0.02 eV above the stability line that is enough to be
accessible by thermal fluctuations, and may explain why the dimer was
successfully crystallized.\cite{Pour2011} In summary our results show
that in pure Mg-Cl-Al-THF solutions neither the dimer nor the trimer
exist at equilibrium, but a reduction of the THF chemical potential, as
experienced in drying, may lead to the formation of dimers.
\subsection{Aluminum complexes in THF and Al-Cl-Mg Phase Diagram}
To complete the thermodynamic analysis of the possible species in the
MACC electrolyte we perform a similar study of Al-Cl in THF.
Figure~\ref{fig:Al_Cl_THF_grandphasediag} shows the Al-Cl-THF
grand-potential phase-diagram, where at Cl compositions of 0.0 and 1.0
are located the isolated species of Al$^{3+}$ and Cl$^-$ coordinated by
5 and by 0 THFs, respectively.
\begin{figure}[t]
\centering
\includegraphics[width=1.0\columnwidth]{figure7.pdf}
\caption{\label{fig:Al_Cl_THF_grandphasediag} Al-Cl-THF grand-potential
phase diagram as function of Cl concentration at the THF chemical
potential. Red dots connected by black lines indicate the stable
magnesium-chloride complexes, and unstable species are indicated by
yellow squares. Coordinating THF molecules are indicated by T.}
\end{figure}
Figure~{\ref{fig:Al_Cl_THF_grandphasediag}} suggests that the stable
species in the electrolyte are: AlCl$_2^{2+}$(2THF), AlCl$_2^+$(2THF),
AlCl$_3$(THF) and AlCl$_4^-$, with no Al$_x$Cl$_y$ polymeric species
found to be stable in THF. Figure~\ref{fig:Al_Cl_THF_grandphasediag}
also captures the coordination of the aluminum chloride species by THF,
with fourfold coordination for AlCl$_3$(THF); AlCl$_4^-$ being already
fourfold coordinated does not have strongly bonded THF molecules.
Figure~{\ref{fig:Al_Cl_Mg-THF_pd}} shows the ternary Al-Cl-Mg
grand-potential phase-diagram at the THF chemical potential and black
lines indicate tie-lines (more detail in the Supplementary Information). Although the ternary Al-Cl-Mg grand-potential phase-diagram shows
tie-lines such as Mg$^{2+}$ -- AlCl$_2^+$(2THF), MgCl$^+$(3THF) -- AlCl$_2^+$(2THF), and MgCl$^+$(3THF) -- AlCl$^{2+}$(2THF) these species cannot
co-exist as they do not respect the charge neutrality of the MACC
electrolyte. The orange part of the PD in
Fig.~{\ref{fig:Al_Cl_Mg-THF_pd}} represents the zone where ionic
species can co-exist and respect charge neutrality. Therefore, from the
Al-Cl-THF grand-potential PD we deduce that the important equlibria will
only occur among MgCl$^+$, AlCl$_4^-$ and MgCl$_2$ and AlCl$_3$ species
and the dashed tie-line indicate their interaction. In the orange area, the only plausible equilibria that respect charge neutrality are either MgCl$^+$(3THF) with AlCl$_4^-$ or MgCl$_2$(2THF) with AlCl$_3$(THF). We use a dashed line
for the interaction between MgCl$^+$(3THF) and AlCl$_4^-$ to indicate
the small driving force of this reaction (see $\Delta$E$_{D-H}$ of
reaction (c) in Table~{\ref{tb:equil_reactions}}), which will be
discussed in more detail later. The stable composition of the MACC electrolyte is the MgCl$^+$(3THF) and AlCl$_4^-$ tie-line.
\begin{figure}[t]
\centering
\includegraphics[width=0.9\columnwidth]{figure8.pdf}
\caption{\label{fig:Al_Cl_Mg-THF_pd} Liquid Al-Cl-Mg-THF
grand-potential phase diagram at the THF chemical potential. Red dots
connected by black lines indicate the stable magnesium- and
aluminum-chloride complexes. Coordinating THF molecules are indicated by
T. Orange area and dashed line indicate the exchange reaction (c) (see
Table~{\ref{tb:equil_reactions}} and text for more details). Tie-lines do not necessary respect charge neutrality (see text and Supplementary Information).}
\end{figure}
Despite the small dielectric constant of THF ($\sim$~7.58 at 298~K),
from the phase diagram of Figure~{\ref{fig:Al_Cl_Mg-THF_pd}} we do not
find stable ionic couples (e.g.\ MgCl$^+$AlCl$_4^-$) that would hinder
the electrochemical function of the electrolyte. For example, the
formation free energy of the monomer and the dimer ionic couples
[MgCl$\cdot$(3THF)]$^+$AlCl$_4^-$ and
[Mg$_2$Cl$_3$$\cdot$(4THF)]$^+$AlCl$_4^-$ require $\sim$~0.064~eV and
$\sim$~0.088~eV, respectively.
\subsection{MACC under equilibrium and conditioning}
We use the knowledge of the stable species gained from grand-potential
phase diagrams to explain the phenomenological effects observed in the
MACC electrolyte under electrochemical cycling.
MACC electrolytes exhibit high coulombic efficiency, but only after
extensive electrochemical cycling, a process termed
conditioning.\cite{Shterenberg2014} Barile \emph{et
al.}\cite{Barile2014} demonstrated that when a conditioned MACC
electrolyte is left to rest for a prolonged period of time it shows
lower coulombic efficiencies than when conditioned, and referred as
``aging'' of the electrolyte. The changes in the electrolyte species
caused by aging and conditioning can be rationalized by evaluating
possible reaction equilibria occurring in bulk and at the electrodes
summarized in Table~{\ref{tb:equil_reactions}}. The grand-potential
phase diagrams in Fig.~\ref{fig:mg_cl_thf_grandphasediag},
Fig.~\ref{fig:mg_cl_thf_grand_drying},
Fig.~\ref{fig:Al_Cl_THF_grandphasediag} and
Fig.~\ref{fig:Al_Cl_Mg-THF_pd} attest to the presence of only four
stable magnesium/aluminum chloride species, MgCl$_2$, MgCl$^+$,
AlCl$_3$ and AlCl$_4 ^-$ limiting the total number of species in the
reactions of Table~\ref{tb:equil_reactions}. Here, we do not consider
the ionic dissociation of MgCl$_2$ (ALCl$_3$) in Mg$^{2+}$ (Al$^{3+}$)
and Cl$^-$ because of their high-energy in our simulations. In
addition, DFT calculations and \emph{ab initio} MD dynamics confirm that
Cl$^-$ is poorly coordinated by THF.
\begin{table*}[!ht]
\caption{\label{tb:equil_reactions}Possible reaction equilibria of the
Al-Cl-Mg-THF system, $\Delta$E and corrected by Debye-H\"{u}ckel
$\Delta$E$_{D-H}$ (in eV). $\Delta$E are computed from the total energy ($E_{\rm PCM}$ for liquid molecules) of each species.
}
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}lcccr@{}}
\hline \hline
\multicolumn{2}{c}{Reaction} & $\Delta$E & $\Delta$E$_{D-H}$ \\
\hline
(a) & MgCl$_2$(s) + 2THF(l) $\leftrightarrow$ MgCl$_2$(2THF)(l) & 0.251 & -- \\
(b) & AlCl$_3$(s) + THF(l) $\rightarrow$ AlCl$_3$(THF)(l) & --1.138 & -- \\
(c) & MgCl$^+$(3THF)(l) + AlCl$_4^-$(l) $\leftrightarrow$ MgCl$_2$(2THF)(l) + AlCl$_3$(THF)(l) & --0.106 & 0.085 \\
\hline
\multicolumn{2}{c}{Mg displacement of Al} &$\Delta$E & $\Delta E_{D-H} $\\
\hline
(d) & 2AlCl$_3$(THF)(l) + 3Mg(s) + 4THF(l) $\rightarrow$ 3MgCl$_2$(2THF)(l) + 2Al(s) & --2.186 & -- \\
(e) & AlCl$_4^-$(l) + MgCl$^+$(3THF)(l) + 1.5Mg(s) + 2THF(l) $\rightarrow$ 2.5MgCl$_2$(2THF)(l) + Al(s) & --1.199 & --1.033 \\
\hline \hline
\end{tabular*}
\end{table*}
The reaction energy ($\Delta$E) at the dilute limit, and with the
Debye-H\"{u}ckel correction ($\Delta$E$_{D-H}$) are included in
Table~{\ref{tb:equil_reactions}}. The Debye-H\"{u}ckel correction
captures the electrostatic interaction of charged species in solution at
dilute activities, and stabilizes the ions in the electrolyte, thus
affecting some reaction energies of Table~{\ref{tb:equil_reactions}}. By
fixing the MACC concentrations at the typical experimental value of
0.5~M,{\cite{Doe2014}} the computed $\Delta$E$_{D-H}$ correction for
reactions (c) and (e) is substantial and $\sim$~0.1914 eV.
Reaction (a) of Table~\ref{tb:equil_reactions} dictates the equilibrium
of MgCl$_2$ between its liquid and solid state, a reaction which is
predicted as endothermic. The magnitude of the $\Delta E$ shows that
MgCl$_2$ is sparingly ``dissolved'' in ethereal organic solvents such
as THF or glymes and is supported by previous experimental
evidences.\cite{Doe2014,Liao2015} Reaction (b) that sets the
``dissolution'' of AlCl$_3$ in THF, is highly exothermic suggesting that
AlCl$_3$ occurs in liquid THF.
In order to maintain charge neutrality, the activities of the charged
species in solution, namely MgCl$^+$(3THF)(l) and AlCl$_4^-$(l), must
remain equal, and this condition is regulated by reaction (c) of
Table~\ref{tb:equil_reactions}. Reaction (c) is slightly exothermic,
favoring the formation of neutral molecules (MgCl$_2$ and AlCl$_3$) in
the electrolyte. Nevertheless, when the Debye-H{\"{u}}ckel
correction is applied to reaction (c), the formation of ions is favored
guaranteeing the operability of the MACC electrolyte. This stresses the
importance to include the effect of the ion activities to compute
properly reaction energies in liquids. Moreover, for the ionic strengths
in the MACC electrolyte, the Debye-H{\"{u}}ckel correction is
sufficient, and no higher order corrections are necessary. The
conductivity of the MACC electrolyte is related directly to the
concentration of the charged ionic species MgCl$^+$, and AlCl$_4^-$. The
slightly endothermic nature of reactions (c) $\Delta$E$_{D-H}$ shows
that under thermodynamic equilibrium the charged species MgCl$^+$ and
AlCl$_4^-$ are present in the electrolyte. At the solubility limit
of MgCl$_2$ $\sim 7.8\times10^{-4}$ M in THF (set by reaction (a)) and for a 0.5~M of AlCl$_3$ in
THF, the MgCl$^+$ activity is approximately 92~mM, which is high
enough to guarantee good ionic conductivity (see discussion later). Note that the Debye-H{\"{u}}ckel correction on the $\Delta$E of reaction (c) is concentration dependent (see Eq.{~\ref{eq:screening_length}}) and is calculated for a 0.5 M solution of MACC electrolyte.
The processes of non-electrochemical Mg and Al deposition are regulated
by reactions (d) and (e) in Table~\ref{tb:equil_reactions}. Reaction (d)
depicts the equilibrium between magnesium aluminum chloride neutral
species and Mg and Al metals. The highly exothermic character of
reaction (d) explains that Al deposition is preferred at the cost of Mg
dissolution. A similar trend is observed for reaction (e) that
establishes the equilibrium of charged and neutral magnesium aluminum
chloride species and the respective metals. The reduction potential of
Al ($\sim$~--1.67~V vs.\ NHE) is more positive than for Mg
($\sim$~--2.35~V vs.\ NHE) and ensures immediate Al deposition during
initial electrochemical cycles. Spontaneous Al deposition sets a
thermodynamic driving force for the process of aging, in absence of an
applied potential at the electrode.
According to reactions (d) and (e) of Table~\ref{tb:equil_reactions}
when a conditioned electrolyte is allowed to rest (i.e.\ not undergoing
electrochemical cycling) the concentration of the electroactive species
available in solution, MgCl$^+$ and AlCl$_4^-$, decrease by several
orders of magnitude as Al ions in solutions are deposited on the
electrode. Though the contribution of Debye-H\"{u}ckel correction is
substantial on the $\Delta$E of reaction (e), it is not sufficient to
stop Al deposition. We speculate that the spontaneous nature of
reactions (d) and (e), along with concomitant parasitic polymerization
reactions of the solvent at the Mg surface,\cite{Barile2014} dictate
the process of electrolyte aging.
On the basis of reactions (d) and (e) of
Table~\ref{tb:equil_reactions}, we suggest that during the first few
electrochemical cycles of Mg deposition of a freshly prepared MACC
electrolyte, Al ions in solution (AlCl$_4^-$) are easily displaced,
thereby decreasing the initial coulombic efficiency of the electrolyte
as observed by Barile \emph{et al}\cite{Barile2014} ---this process is
called conditioning of the electrolyte (see discussion later). However,
during conditioning the presence of a chemical or electrical potential
promotes reaction (c) furhter towards the formation of
MgCl$^+$(AlCl$_4^-$) species, hence favoring Mg deposition over Al. The
concepts of electrolyte aging and conditioning will be clarified further
in the discussion section.
\subsection{$^{25}$Mg and $^{35}$Cl NMR properties of selected Mg$_x$Cl$_y$ structures}
To aid the interpretation of future NMR experiments on the MACC
electrolyte we computed the NMR isotropic shielding fingerprints of
$^{25}$Mg and $^{35}$Cl of selected MACC complexes. In general, changes
in charge density localization on different MACC complexes directly
alter the screening effects experienced by each NMR nucleus giving rise
to different NMR responses.
While Mg posses an NMR active nucleus, due to its low abundance
$^{25}$Mg requires expensive high field NMR instruments. Therefore, in
this analysis $^{25}$Mg data will be complemented by data on the more
abundant $^{35}$Cl nucleus.
Figure~\ref{fig:mr_shifts} shows the $^{25}$Mg and $^{35}$Cl NMR
isotropic shifts in THF for some relevant Mg$_x$Cl$_y$ clusters isolated
from the grand-potential phase diagrams of
Figs.~\ref{fig:mg_cl_thf_grandphasediag}
and~\ref{fig:mg_cl_thf_grand_drying}.
\begin{figure}[t]
\centering
\includegraphics[width=1.0\columnwidth]{figure9.pdf}
\caption{\label{fig:mr_shifts} a) $^{25}$Mg and b) $^{35}$Cl NMR
isotropic shifts (in ppm) of relevant species magnesium-chloride complex
ions in the MACC electrolytes. Colors for different magnesium-chloride
complexes. Coordinating THF molecules indicated by T. Note that NMR data
are not shifted to $^{25}$Mg or $^{35}$Cl standard reference compounds.
Range of isotropic shifts for compounds with more than one Mg or Cl
atoms is indicated by error bars.}
\end{figure}
The $^{35}$Mg and $^{35}$Cl isotropic shielding (of
Fig.~\ref{fig:mg_cl_thf_grandphasediag}) fall at very different absolute
values. Note that NMR data of Fig.~\ref{fig:mr_shifts}a and
Fig.~\ref{fig:mr_shifts}b are not shifted to $^{25}$Mg and $^{35}$Cl
standard reference compounds. Our results indicate that $^{25}$Mg NMR
should be able to distinguish very well between charged Mg$_x$Cl$_y$
complexes (i.e.\ MgCl$^+$($n$T) and Mg$_2$Cl$_3^+$($n$T)) and neutral
species (MgCl$_2$($n$T)) in the MACC electrolyte. In addition we predict
that $^{35}$Cl NMR can discriminate between monomer and dimer species
(MgCl$^+$($n$T) and Mg$_2$Cl$^+_3$($n$T)), complementing $^{25}$Mg NMR
data. Though the combination of $^{25}$Mg and $^{35}$Cl NMRs can
clearly differentiate between the stoichiometry of magnesium-chloride
complexes, our calculations suggest that it will be more difficult to
make conclusive claims on the effect played by the solvent (THF) with
NMR. Furthermore, while the analysis of the Mg-Cl grand-potential PD
suggests that agglomeration of MgCl$^+\cdots$MgCl$_2$ is significantly
more likely to occur than the distinct dimer (Mg$_2$Cl$_3^+$, see
discussion later), the spectroscopic differences between the two species
may be subtle. For $^{25}$Mg data an increase of the isotropic shift is
observed for increasing THF coordination, see for example the trend for
MgCl$^+$($2$T) to MgCl$^+$($5$T). Less pronounced is the $^{35}$Cl NMR
shift decrease as a response to an increase of the THF coordination
number (see Fig.~\ref{fig:mr_shifts}b).
\section{Discussion}
\label{sec:discussion}
In this work, the stable species present in the MACC electrolyte are
predicted using CMD and \emph{ab initio} calculations.
Although this investigation provides an important understanding of the
composition of the MACC electrolyte, it deals with bulk MACC solution
and does not explicitly account for: \emph{i}) the effect of the anode
and cathode surfaces, \emph{ii}) the existence of parasitic chemical
reactions that might alter the electrolyte composition, and \emph{iii})
the presence of impurities.
From the formation energies and grand-potential phase diagrams of
magnesium-chloride complexes we demonstrated that only two major Mg(Al)
species are present at equilibrium conditions in MACC, namely the
neutral MgCl$_2$(AlCl$_3$) and electro-active MgCl$^+$(AlCl$_4^-$). We
demonstrate that larger Mg$_x$Cl$_y$ units such as dimer and trimer are
not stable, though they might become accessible at room temperature by
changing the solvent conditions (drying/crystallization).
Polymerization of THF by AlCl$_3$ is also possible\cite{Barile2014,
Canepa2015}, and has the effect of decreasing the solvating capabilities
of THF towards the species in solution (MgCl$^+$ and MgCl$_2$).
Therefore THF-polymerization represents an alternative mechanism to
emulate drying conditions in solution and stabilize the dimer species.
In drying conditions achieved with crystallization procedures, the dimer
Mg$_2$Cl$_3^+$ has been successfully isolated,\cite{Pour2011} but
results in a electrochemically inert solution when redissolved in THF.
Benzmayza \emph{et al.},{\cite{Benzmayza2013}} speculated that the lack
of solvent in certain electrochemical conditions, for example when
MgCl$^+$ and MgCl$_2$ approach the anode surface, is responsible for the
formation of the dimer species. These experimental observations are
consistent with our theoretical findings suggesting that the operation
of the MACC electrolyte is ascribed to its simple chemical
structure/composition, and regulated by uncomplicated equilibria.
Interestingly, previous theoretical investigations of the monomer and
dimer coordination in THF,\cite{Wan2014} have demonstrated that the
symmetry of the dimer is largely perturbed by the THF solvent, forming
an open structure that resembles an isolated magnesium chloride molecule
interacting with a dangling monomer, i.e.\ MgCl$_2\cdots$MgCl$^+$.
Combining these observations, we speculate that the dimer Mg$_2$Cl$^+_3$
originates from the agglomeration of MgCl$_2$ available in solution and
MgCl$^+$. Under conditions of drying/crystallization, similar
agglomeration mechanisms can explain the formation of larger order
magnesium-chloride structures (e.g.\ trimer and polymeric units), which
have been speculated to exist.\cite{Barile2014} To this end, we have
computed useful $^{25}$Mg and $^{35}$Cl NMR fingerprints of the stable
and unstable MACC species.
Our findings also shed light on the coordination of inorganic aluminum
magnesium-chloride complexes. In line with preliminary experimental and
theoretical work,\cite{Nakayama2008,Wan2014,Liu2015a} we demonstrate
that magnesium-chloride salts in THF solutions cannot fulfill the
typical 6-fold coordination of Mg$^{2+}$ in solids, but always prefer
lower coordination numbers (e.g.\ 4-fold for the monomer
MgCl$^+$(3THF)). According to the vast organic
literature,{\cite{Guggenberger1968,Garsta2004,Pirinen2013}} Grignard
reagents' MgXR$_2$ (with X = Cl, Br) and halides salts (MgCl$_2$ and
MgBr$_2$) in THF are typically found 4-fold coordinated, and confirm our
findings. Compared to multi-dentate linear glymes (e.g. diglyme and
tetraglyme) the ability for THF to coordinate ions is limited by the
bulkier structure of the ring, and this has been also demonstrated
experimentally and computationally by Seo \emph{et al.}{\cite{Seo2014}}
Moreover, the coordination environment in the crystalline state does not
necessarily reflect the coordination in the liquid
phase.{\cite{Ansell1997,Wernet2004}}
A closer analysis of our data shows that the stable Mg coordination
number increases as a function of the Mg-Cl complex size from monomer to
trimer. In a recent study, some of us attested that lower Mg$^{2+}$
coordination numbers decreases the desolvation energy required to shed
the solvent during plating and stripping.\cite{Canepa2015} We speculate
that the larger Mg$^{2+}$ desolvation energy for bigger Mg-Cl complexes
(e.g.\ dimer and trimer) can inhibit the delivery of fresh Mg$^{2+}$ at
the Mg-anode during plating.
By identifying the principal species of the MACC electrolyte at
equilibrium, MgCl$^+$(3THF), MgCl$_2$(2THF), AlCl$_4^-$, and
AlCl$_3$(THF), we can explain the phenomenological effects observed in
the MACC electrolyte under electrochemical cycling. A thermodynamic
analysis of the bulk electrolyte properties suggests that the
equilibrium between MgCl$^+$ and MgCl$_2$ (and AlCl$_4^-$ and AlCl$_3$)
in THF tends towards a solution dominated by charged MgCl$^+$ (and
AlCl$_4^-$) species, (see reaction (c)
Table{~\ref{tb:equil_reactions}} corrected by the Debye-H\"{u}ckel
model), which provides the appropriate conditions for ion conductivity.
The $\Delta E$s calculated for each equilibria dictate the activity
ratio between MgCl$^+$ and MgCl$_2$ that impacts the number of charge
carriers (MgCl$^+$) available in solution, and ultimately impacts the
ionic conductivity of the MACC electrolyte. In MACC AlCl$_4^-$
functions as a shuttle replenishing Cl$^-$ ions (at the anode surface)
during Mg stripping (at the anode);\cite{Canepa2015} reaction (c) of Table~\ref{tb:equil_reactions} suggest that the ratio between
AlCl$_4^-$ and AlCl$_3$ is large, hence allowing the complex
dynamics of Mg stripping and dissolutions.
The availability of MgCl$^+$ in solution is not only controlled by
reaction (c) but also depends on the low solubility of MgCl$_2$ in THF
(see reaction (a)). Liao \emph{et al.}{\cite{Liao2015}} demonstrated
that the solubility of MgCl$_2$ can increase dramatically provided the
presence of Cl$^-$ acceptors in solution. While AlCl$_3$ seems
appropriate (as demonstrated by reaction (c)), other Cl$^-$ ions
acceptors can be introduced as ``additives`` (e.g. Mg(HMDS)$_2$)
promoting large quantities of MgCl$^+$ in solution.
However, by using the Debye-H\"{u}ckel corrected $\Delta$E of
reaction (c) we find that a significant concentration of charge
carriers is still available in solution. For example using a typical
concentration of 0.5~M for AlCl$_3$, and assuming that the maximum
activity of soluble MgCl$_2$ in THF is~7.8$\times$10$^{-4}$~M (set by
reaction (a)), we expect a concentration of MgCl$^+$(3THF) in solution
to be $\sim$~0.092~M. Notably, for this concentration we could derive,
using the Kohlrausch's law for weak electrolytes, an ionic
conductivity of $\sim$~1.96~mS~cm$^{-1}$, which is in very good
agreement with the experimental value measured by Doe \emph{et al.}
($\sim$~2~mS~cm$^{-1}$) for a fully conditioned
electrolyte.{\cite{Doe2014}} See Supplementary Information for the full
derivation of the ionic conductivity.
The Al-Cl-Mg-THF phase diagram does not indicate the formation of stable
${\rm AlCl}_4^-\cdots {\rm Mg}_x{\rm Cl}_y$ ionic couples, though some
of these clusters might be accessible within small energy windows
(0.064~$-$~0.088~eV) with further repercussions on electrolyte
conductivity. In general, the small dielectric constant of THF
($\sim$~7.58) and glymes favor the formation of ionic couples, an
indication that the next generation of solvents for Mg-ion batteries
requires solvent with better screening properties.
\begin{figure*}[!ht]
\centering
\includegraphics[scale=0.85]{figure10.pdf}
\caption{\label{fig:agingcond_schematic} Schematic of the processes of
aging (a) and conditioning (b) of the MACC electrolyte in a battery
setup. Panel (a) Al deposition at the Mg-anode electrode is depicted by
orange stripes and supported by reaction (d) and (e) of
Table~{\ref{tb:equil_reactions}}. Panel (b) shows the activity gradients
of MgCl$^+$ and AlCl$_4^-$ arising from the Mg plating process as well
as continuous regeneration of these species in the bulk solution.
During aging the species (i.e.\ MgCl$^+$, MgCl$_2$, AlCl$_4^-$, and
AlCl$_3$) in solution are distributed homogeneously in the electrolyte.
}
\end{figure*}
Although we do not explicitly consider the Mg-electrode, from the
reaction energy discussed in Table~\ref{tb:equil_reactions} we provide
important considerations on the process of aging of the electrolyte.
Figure~\ref{fig:agingcond_schematic} summarizes the processes of aging
(a) and conditioning (b) of the MACC electrolyte. From the equilibrium
between Mg-Cl-Al species in solutions and Mg/Al bulk metals, we
demonstrate that AlCl$_4^-$ ions in solutions are easily displaced
during the initial stages of Mg deposition. In fact, Al deposition at
the anode is ensured by a small Al reduction potential ($\sim$~--1.67~V
vs.\ NHE) compared to Mg ($\sim$~--2.35~V vs.\ NHE) setting a
thermodynamic driving force for the process of aging. Finally, further
aluminum depletion from the solution upon electrolyte resting which
impacts the amount of MgCl$^+$ in solution, could be one of the causes
of aging of the MACC electrolyte. Additionally, parasitic
polymerization reactions of the solvent have also been
speculated\cite{Barile2014} to be the source of electrolyte aging.
Under open circuit conditions (battery at rest), the reaction at the
anode/electrolyte interface is largely controlled by the activity of
MgCl$^+$ species available since reaction (c) dominates the
composition of the electrolyte (see Table~{\ref{tb:equil_reactions}}).
Reactions (d) and (e) favor the formation of Al deposition under open
circuit, leading to AlCl$_4^-$ (and MgCl$^+$) depletion form the
solution, resulting in the aging of the electrolyte. However, when an
aged electrolyte is subjected to charging, the presence of an applied
potential drives Mg deposition on the anode, resulting in not only
setting a concentration gradient of MgCl$^+$ (AlCl$_4^-$) from the bulk
towards the anode (cathode) but also a continuous regeneration of
MgCl$^+$ in the solution. After aging, the electrolyte will require a
few charge-discharge cycles before the composition in the solution is
stabilized and the charged species (MgCl$^+$ and AlCl$_4^-$) are
abundantly present leading to smooth Mg deposition/stripping.
Therefore, the state of conditioning in the electrolyte represents a
transition between the Al-deposition regime (aging) and the Mg
deposition/stripping regime during regular battery operation. Barile
\emph{et al.}\cite{Barile2014} have estimated that about 100
electrochemical cycles are needed to condition the MACC electrolyte.
This explains why low coulombic efficiencies of fresh MACC solutions
have been attributed to Al deposition during the initial electrochemical
cycles. SEM-EDS measurements of a Pt electrode that underwent Mg
deposition during electrolyte conditioning showed large quantities of
permanently deposited Al,\cite{Barile2014} corroborating our modeling
results.
Barile~\emph{et al.}{\cite{Barile2014}} suggested that the MACC
electrolyte is conditioned when the Mg/Al molar ratio in solution is
$\sim$~2.6:1, from which they concluded that dimer species must be
present in the electrolyte. However, our grand-potential phase diagrams
(see Fig.~{\ref{fig:mg_cl_thf_grandphasediag}} and
Fig.~{\ref{fig:mg_cl_thf_grand_drying}}) indicate that dimer species are
unlikely to be present in the electrolyte at equilibrium, but only
become accessible when drying or crystallizing the electrolyte. The
Mg/Al ratio observed experimentally ($\sim$~2.6:1) for conditioned
electrolytes can alternatively stem from the presence of agglomerates
MgCl$^+\cdots$MgCl$_2$ (the only stable species in solution) instead of
distinct dimer ions ---MgCl$^+\cdots$MgCl$_2$ clusters have been
isolated previously using \emph{ab initio} MD on a similar
electrolyte.{\cite{Wan2014}}
\section{Conclusions}
\label{sec:conclusions}
With the intention of elucidating the structural composition of the MACC
electrolyte, we carried out \emph{ab initio} calculations and
classical molecular dynamics simulations on more than a hundred
molecules and ions that could be structurally and functionally relevant
for this electrolyte. We find that only MgCl$^+$, MgCl$_2$, AlCl$_4^-$
and AlCl$_3$ are stable constituents of the electrolyte. The
thermodynamic analysis of the MACC composition excludes the presence of
multimeric Mg$_x$Cl$_y^+$ units such as dimer and trimer under
equilibrium conditions. These species can be stabilized under
conditions of solvent drying.
Equilibrium between the MACC species (i.e\ MgCl$^+$ MgCl$_2$, AlCl$_4^-$
and AlCl$_3$) in liquid THF and Mg and Al metals suggests that Al is
easily displaced from the solution during early Mg deposition cycles.
This effect reduces the electrolyte coulobmic efficiency providing an
explanation for the process of aging. In general, Al deposition on
Mg-metal is always favored and leads to the more complex issue of
electrolyte aging. We explain conditioning as the process which promotes
the stabilization of charged species (MgCl$^+$ and AlCl$_4^-$) in
solution due to a potential (chemical or applied), enabling Mg smooth
deposition/stripping.
Computation of the NMR shifts of the relevant MACC species shows
distinct $^{25}$Mg and $^{35}$Cl NMR signatures for monomer, dimer and
MgCl$_2$, concluding that \emph{in-situ} NMR can clarify the composition
of the MACC electrolyte as well as transformation of the MACC solution
occurring during aging and conditioning of the electrolyte. Our
analysis indicates that MgCl$_2$ is sparingly soluble in THF, but its
solubility can be increased by introducing Cl$^-$ acceptors.
Finally, the computational strategy adopted in this investigation is
readily applicable in a high-throughput fashion to study other liquid
media, specifically to progress the understanding of liquid
electrolytes, and to screen for new electrolytes for the next
generation of rechargeable batteries.
\begin{acknowledgements}
This work was fully supported as part of the Joint Center for Energy
Storage Research (JCESR), an Energy Innovation Hub funded by the U.S.
Department of Energy, Office of Science, and Basic Energy Sciences. This
study was supported by Subcontract 3F-31144. We also thank the National
Energy Research Scientific Computing Center (NERSC), a DOE Office of
Science User Facility supported by the Office of Science of the U.S.
Department of Energy under Contract No. DE-AC02-05CH11231, for providing
computing resources. PC and SJ are thankful to Dr.\ Xiaohui Qu at the Lawrence
Berkeley National Laboratory for numerous suggestions. All authors are
also indebted to Dr.\ Kevin R. Zavadil at Sandia National Lab, Dr.\
Christopher Barile and Prof.\ Andrew Gewirth at University of Illinois
Urbana-Champaign for stimulating discussions.
\end{acknowledgements}
| {
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Freshman: I love this campus! If you're looking for a small, friendly, lively school, come here! The campus is very diverse and over 20 nations are represented in the student body. The staff are all wonderful and really want to see you succeed! The students on and off campus are friendly and helpful. There are over 30 clubs, free tutoring, therapy services, and trips available to just students. Penn State Harrisburg is a great campus!
Freshman: Hello! I will be a Freshman at Penn State Abington this year. This campus is beautiful and the people working there are all extremely nice and helpful. They have plenty of diversity as people from all over the world are attending this school with their program for international students. The housing is very nice, as you have a full kitchen, living room, wifi, heating, and other amenities at your disposal. However, you must by your own groceries and cook for yourself because they do not offer meal plans at this campus. This would be my only complaint. Hope I helped! | {
"redpajama_set_name": "RedPajamaC4"
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{"url":"https:\/\/www.physicsforums.com\/threads\/greens-theorem-in-3-dimensions-problem.313638\/","text":"# Green's Theorem in 3 dimensions problem\n\n1. May 12, 2009\n\n### duki\n\n1. The problem statement, all variables and given\/known data\n\nEvaluate: $$\\int _C{xydx - yzdy + xzdz}$$\nC: $$\\vec{r}(t) = t\\vec{i} + t^2\\vec{j} + t^4\\vec{k}$$\no <= t <= 1\n\n2. Relevant equations\n\n3. The attempt at a solution\n\nI understand that you cannot use Green's Theorem in 3 dimensions. How else can I go about solving this?\n\nLast edited by a moderator: May 12, 2009\n2. May 12, 2009\n\n### HallsofIvy\n\nStaff Emeritus\nRe: Curve\n\nJust use the standard definition of a \"line integral\".\n\nOn C, x= t, y= t2, and z= t4\ndx= dt, dy= 2tdt, and dz= 4t3.\n\nxydx- yzdy+ xzdz= (t)(t2)dt- (t2)(t4)(2tdt)+ (t)(t4)(4t3dt.\n\nIntegrate that from t= 0 to t= 1.\n\n3. May 12, 2009\n\n### duki\n\nRe: Curve\n\nOhhh snap. I remember talking about the fundamental theorem of line integrals now. Thanks!\n\n4. May 12, 2009\n\n### gabbagabbahey\n\nRe: Curve\n\n$x$, $y$ and $z$ will all be functions of $t$ along the curve....You should be able to simply look at the parametric equation for your curve $\\vec{r}(t) = t\\hat{i} + t^2\\hat{j} + t^4\\hat{k}$ and read off what those functions are.....Then you can easily express $dx$, $dy$ and $dz$ in terms of $dt$ and you integral will simply be a single variable integration...\n\nEDIT: Halls beat me to it.\n\n5. May 12, 2009\n\n### duki\n\nRe: Curve\n\nOk so I got:\n\nEDIT:\n$$\\int _0^1{4t^4 dt} = \\frac{4t^5}{5} => \\frac{4}{5}$$ ?\n\nLast edited: May 12, 2009","date":"2017-12-17 14:46:25","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.47041991353034973, \"perplexity\": 3020.561451251896}, \"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-2017-51\/segments\/1512948596051.82\/warc\/CC-MAIN-20171217132751-20171217154751-00478.warc.gz\"}"} | null | null |
Q: (mySQL) Database Structure Advice Please I am building a site that is a database of spare parts for cars. The information in the database is essentially:
1) Manufacturer
2) Model
3) Parts Main Category
4) Parts Sub Category
5) Image Diagram
6) Label of Part in Diagram
7) Part Number
8) Part Name
I was going to build it in a multi-table structure, something along these lines:
MARQUES
=======
marque_id, marque_name
MODELS
======
model_id, marque_id, model_name
CATEGORIES
==========
cat_id, model_id, cat_name
SUBCATEGORIES
=============
subcat_id, subcat_name, subcat_diagram, cat_id, subcat_parts
PARTS
=======
part_id, part_name, part_description
The reason for doing it this way would be because there are lots of overlap between fields (e.g. there are only a handful of manufacturers, and many parts share the same image diagram etc), so it seems to me it would be more efficient this way (te remove redundant data).
However, I am now wondering whether indexing everything properly and the development overhead required to acheive a multi-table structure ahead is worth it. Running searches will also be a lot easier if it is all in one table.
Could I just stick it all into one massive table? And if the advice is to build it into multi-tables, is there software available that will help me "split it up" and do the necesary indexing?
The site will feature a multi-page browsing interface. You select your marque, then model, then category, then subcategory, then choose your part.
There will be about 700,000 records at first, and probably will grow over time.
Thanks for any advice.
A: For searching my suggestion is to use the Sphinx Search or other similar tool.
A: This page here as a very detailed answer. Basically your problem is the same as anyone designing a product catalog with a search feature - One item may fall under many categories.
I recommend checking this out first, and if it doesn't answer your question then let us know how it is different from what you want to achieve and we will do what we can.
Database Structure Advice Needed
| {
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Rain Taxi is a Minneapolis-based book review and literary organization. In addition to publishing its quarterly print edition, Rain Taxi maintains an online edition with distinct content, sponsors the Twin Cities Book Festival, hosts readings, and publishes chapbooks through its Brainstorm Series. Rain Taxis mission is "to advance independent literary culture through publications and programs that foster awareness and appreciation of innovative writing." , the magazine distributes 18,000 copies through 250 bookstores as well as to subscribers. The magazine is free on the newsstand. It is also available through paid subscription. Structurally, Rain Taxi is a 501(c)(3) non-profit. It sells advertising at below market rates, much of it to literary presses.
History
The magazine was founded in 1996 by Carolyn Kuebler, Randall Heath, and David Caligiuri (who resigned with issue one). Current editor Eric Lorberer joined the staff after issue one. The magazine is art-directed and business-managed by Kelly Everding.
Rain Taxi has been relatively free of controversy and widely lauded for its role in bringing to light books which might not otherwise be reviewed. It has been awarded the 2000 Utne Reader Alternative Press Award for Best Arts and Literature Coverage and Best Literary Journal in City Pages (Minneapolis). Editor Eric Lorberer was named to the Publishers Weekly "The Twin Cities Top 10."
An exception to the lack of controversy was David Foster Wallace's Summer 2001 review of The Best of the Prose Poem: An International Journal (White Pine Press). The review, which took the form of a bullet-pointed index that "broke down the anthology into numerical components," inflamed many of the book's contributors. See responses in Fall 2001 print edition of the magazine.
The magazine publishes relatively few dismissive reviews. Lorberer explained that "the reason the majority of the reviews are positive is that the process of selection itself is an aspect of reviewing–we're trying to select the best of the best." And former Board Member and Twin Cities journalist Josie Rawson notes, "There are so few avenues in the reviewing press for praise for books from small presses, independent presses, it's hardly worth wasting space on books nobody should be reading anyway."
Rain Taxi Review of Books (Print)
Rain Taxi focuses on literary fiction, poetry, and non-fiction with an emphasis on small press and offbeat books. The review features interviews with prominent writers such as Lydia Davis and Tao Lin; reviewers include Sharon Mesmer, Jacob Appel, Spencer Dew, Noah Eli Gordon and Mark Terrill.
Raintaxi.com
The site includes distinct content not found in the print edition, as well as information about events publications. , it receives approximately 15,000 hits a day.
Brainstorm Series Chapbooks
Rain Taxi publishes limited edition chapbooks, each limited to 300 copies or less. Authors have included Kees 't Hart, Alice Notley, Donald Revell, Dara Wier, Nathaniel Tarn, Paul Auster, Russell Edson, Anne Waldman and Rikki Ducornet (collaboration), Kai Nieminen, James Tate, Stephen Dixon, Paul Metcalf, and Clayton Eshleman.
Twin Cities Book Festival
Rain Taxi launched the Twin Cities Book Festival in 2001. The festival includes readings, talks, book signings, panel discussions, children's activities, book arts demonstrations, a used book sale, and a Literary Magazine Fair.
Rain Taxi Readings
The Rain Taxi Reading Series began in 1998 and has hosted more than 200 writers.
References
External links
Official website
Book review magazines
Rain Taxi
Magazines established in 1996
Magazines published in Minnesota
Quarterly magazines published in the United States
Mass media in Minneapolis–Saint Paul | {
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<resources>
<string name="app_name">Sunshine Reloaded</string>
<string name="api_url" translatable="false">http://api.openweathermap.org/data/2.5/</string>
<string name="error_while_loading">Error while loading data</string>
<string name="retry">Retry</string>
<string name="today">Today</string>
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\section{Introduction}
The cellular automaton (CA) approach to traffic flow theory
\cite{NaSch} has attracted much interest in recent years (see e.g.\
\cite{juelbook}). Compared to the earlier attempts in modeling
traffic flow (see e.g.\ \cite{juelbook,Light,Kern,helbing} and references
therein) CA models can be used very
efficiently for computer simulations. This makes it possible to perform
real time simulations even for very large networks \cite{network,city}.
Due to the relevance of these models for applications it is important to
understand the underlying physics thoroughly.
The cellular automaton model of Nagel and Schreckenberg (NaSch model)
\cite{NaSch} provides a simple but quite realistic description of traffic flow.
The road is divided into $L$ cells so that the model is discrete in space
and time. Each cell can either be empty or occupied by one of
$N$ cars $j=1,\ldots, N$ with velocities $v_j=0,...,v_{max}$. $v_{max}$
is assumed to be the same for all the cars.
The update is divided into four steps which are applied {\em in parallel} to
all cars. The first step (R1) is an acceleration step. The velocities $v_j$
of each car $j$ not already propagating with the maximum velocity $v_{max}$
are increased by one. The second step (R2) is designed to avoid accidents.
If a car has $d_j$ empty cells in front of it and its velocity (after
step (R1)) exceeds $d_j$ the velocity is reduced to $d_j$. Up to now
the dynamics is completely deterministic. Noise is
introduced via the randomisation step (R3). Here the velocities of moving cars
$(v_j\geq 1)$ are decreased by one with probability $p$.
The steps (R1)--(R3) give the new velocity $v_j$ for each car $j$.
In the last step of the update procedure the positions $x_j$ of the
cars are shifted by $v_j$ cells (R4) to $x_j+v_j$.
We consider here only periodic boundary conditions. Thus the model
contains three parameters: the maximum velocity $v_{max}$, the
probability for braking $p$, and the average density $\rho =N/L$.
A basic feature of traffic models is the relation between
density $\rho$ and the average flow $J=\rho \bar v$ (fundamental diagram)
where $\bar v=\frac{1}{N}\sum_{j=1}^Nv_j$ is the average velocity.
Fig.\ \ref{fig1} shows the fundamental diagram
for different values of $p$. One observes two effects as the noise $p$
is increased, namely a decrease of the flow and a shift of the maximum
towards smaller densities. In the low-density limit $\rho \ll 1$ one
always finds free flow behavior with $J(\rho) \simeq (v_{max}-p)\rho$
whereas for high densities $1-\rho \ll 1$ one has $J(\rho)
\simeq (1-p)(1-\rho)$.
Although the model cannot be solved exactly for arbitrary parameter values,
two limits of the model can be treated analytically. Firstly the
case $v_{max} = 1$ which is solved excactly with improved mean field
methods \cite{Cluster,Comf}. Here the fundamental diagram is
symmetric due to particle-hole symmetry. Considering larger maximum
velocities $v_{max}\geq 2$ one can obtain solutions only in the
deterministic limit $p=0$ where the flow is given by
\begin{equation}
\label{flow_det}
J(\rho) = \min ( \rho~v_{max} , 1-\rho ).
\end{equation}
In the free flow regime where $J(\rho)=\rho v_{max}$ all cars propagate with
maximum velocity whereas in the jammed phase the flow is limited by the
number of empty cells. These limits will be discussed further in the
later sections.
Such a transition from a free flow regime at low densities to a congested
flow regime where start and stop waves dominate the dynamics are quite
typically for traffic flow. Several attempts have been made to
explain the nature of this transition in the CA model
\cite{Vilar}-\cite{Luebeck}.
It seems, however, that no consensus has been reached yet.
Here we present results of an extensive numerical investigation of the
parameter dependence of the transition in the NaSch model.
We examine several quantities which give information about the location
$\rho_c$ and the nature of the phase transition.
The outline of the paper is as follows: In the next section we discuss
the relaxation into the steady state. Section 3 is devoted to
measurements of an order-parameter. Section 4 shows the behavior of
the spatial correlation function. Our results are
discussed in the final section.
\section{Relaxation}
A characteristic feature of a second order phase transition is the
divergence of the relaxation time at the transition point. For
technical reasons Cs\'anyi and Kert\'{e}sz \cite{Csanyi}
made no direct
measurements of the relaxation time, but used the following approach:
Starting from a random configuration of cars with velocity $v_j=0$ the
average velocity $\bar v(t)$ is measured at each time step $t$.
For $t\rightarrow\infty$ the system reaches a stationary state
with average velocity $\left < \bar v_{\infty} \right >$. The
relaxation time is characterised by the parameter \cite{Csanyi}
\begin{equation}
\label{eq:relax}
\tau= \int\limits_{0}^{\infty}\biggl[ {\rm min}\{v^{\ast}(t),\
\langle \bar{v}_{\infty}\rangle\} - \langle \bar{v}(t)\rangle\biggr]\
dt \ .
\end{equation}
$v^{\ast}(t)$ denotes the average velocity in the acceleration phase
$t\rightarrow 0$ for low vehicle density $\rho\rightarrow
0$. Because the vehicles do not interact with each other,
$v^{\ast}(t) = (1-p)t$ holds in this regime.
Thus the relaxation time is obtained by summing up the deviations of the
average velocity $\langle \bar{v}(t)\rangle $
from the values of a system with one single vehicle which can move
without interactions with other cars ($\rho\rightarrow 0$).
One finds a maximum of the relaxation parameter near, but {\em below}, the
density of maximum flow for $p=0.25$ and ${v_{\mathit{max}}}=5$
(see \cite{Csanyi}).
Within this investigation we extended the set of braking parameters
($p = 0 \dots 0.75$) in order to study the parameter dependence of the
maximum of $\tau$. We took into account system sizes up to $L=30000$
where the position $\rho_c$ of the maximum of $\tau$ becomes size
independent. The transition density is given by $\rho_c$ of the
largest system we took into account.
The results for $p=0$ and $p=0.25$ are shown in Figs.\ \ref{fig2}
and \ref{fig3}. A comparison of $\rho_c$ with the density of maximum flow
$\rho({q_{\mathit{max}}})$ shows smaller values of the transition
densities for all values of $p$ taken into account.
Taking the magnitude of $\tau$ as a characteristic value for the
relaxation time one can estimate the dynamical exponent. Furthermore
the scaling behavior of the width $\sigma(L)$ and height $\tau_m(L)$
of the peak has been taken into account,
\begin{equation}
\label{eq:defz}
\tau_m(L)\propto L^z,
\qquad
\label{eq:defnu}
\sigma(L)\propto L^{-1/\nu}.
\end{equation}
We find $z=0.28$ and $\nu =5.7$ for $p=0.5$ and $z=0.36$ and $\nu
=6.8$ for $p=0.25$.
Note that the peak is not symmetric so that it is difficult to
determine its width.
Comparing our data with \cite{Csanyi} two facts have to be mentioned.
First, our results for $p=0.25$ are completely different from the exponents
obtained in \cite{Csanyi}. The second remarkable point is the
occurance of negative values for the relaxation times (see Fig.\
\ref{fig3}).
This effect is not shown in \cite{Csanyi}. One can think that it emerges from
inaccurate measurements or finite size effects, but
the negative values are a consequence of the definition (\ref{eq:relax}).
If we look at the time evolution of
$ \left < \bar{v}(t)\right >/ \left <\bar v_{\infty} \right >$
we see the reason for this unpleasent feature (Fig.\ \ref{fig4}):
For $\rho>\rho_{c}$ the system gets temporarily into states which have
a higher average velocity than the stationary state such that
$\left < \bar{v}(t)\right > > \left < \bar v_{\infty} \right>$ holds
within this time interval.
This over-reaction is a consequence of the relaxation mechanism which can
be divided into two phases for $p>0$. Within the first few time steps
small clusters which occur in the initial configuration vanish.
The second phase is characterized by the growth of surviving
jams. More and more cars get trapped into large jams and therefore the
average flow decreases to its stationary value. This decrease causes
negative values of $\tau$ at large densities.
Finally one should note that (\ref{eq:relax}) can only be interpreted
as a relaxation time for a purely exponential decay,
$\langle \bar{v}_{\infty}\rangle - \langle \bar{v}(t)\rangle
\propto e^{-t/\tau}$. Figure \ref{fig4} shows, however, that this is
not the case for $\rho>\rho_c$, where one even finds a non-monotonic
relaxational behavior. In order to get a clear picture of the nature
of the transition one should therefore examine various quantities.
\section{Order Parameter}
For a proper description of the transition one should introduce an
order parameter which has a qualitative different behavior within
the two phases. A first candidate would be the analogue of the magnetisation
in the Ising model, i.e.\ the number of cars. However, since this quantity is
conserved in the NaSch model it can not serve as an order parameter.
Therefore the density of nearest neighbour pairs
\begin{equation}
\label{opdef}
m = \frac{1}{L}\sum_{i=1}^{L} n_in_{i+1},
\end{equation}
with $n_i=0$ for an empty cell and $n_i=1$ for a cell occupied by a
car (irrespective of its velocity), is the simplest choice of a local
quantity with a nontrivial behavior at the transition density. Taking into
account the braking rule (R2) $m$ gives the density of those cars with
velocity $0$ which had to brake due to the next car ahead.
Although the order parameter introduced in \cite{Vilar}
is defined as a time average it shows a quite similar behavior. For large
time periods it measures the densities of cars with velocity 0 \cite{eisi}.
Vilar et al.\ \cite{Vilar} only investigated the deterministic
case $p=0$ for which their order parameter is identical to ours, but
also in the presence of noise the values differ only slightly.
First we will discuss the behavior of the order parameter in the case
$p=0$. Below the transition density,
\begin{equation}
\label{rhocdet}
\rho_c = \frac {1}{v_{max}+1},
\end{equation}
the order parameter vanishes because every car has at least $v_{max}$
empty sites in front and propagates with $v_{max}$. Within the jammed
phase the flow is
limited by the number of empty cells and also stopped cars occur.
In the presence of noise the behavior of the order
parameter qualitativly changes in the vicinity of the transition
density. Within this region $m$ decays exponentially. Assuming $m$ is
a possible choice for the order parameter this implies the absence of
criticality in the nondeterministic case.
Figure \ref{fig6} shows that the order parameter does not exhibit
a sharp transition. Although it becomes rather small for small
densities it is still different from zero. The situation is quite similar
to the behavior of the order parameter in finite systems \cite{finite}.
The transition is smeared out by the noise and the transition density
is shifted towards smaller values.
In order to have a suitable criterion for the determination of the transition
density, we analysed the scaling behavior of the order parameter near the
transition density $\rho_c$. Fig.~\ref{fig7} shows that one gets a quite
reasonable data collaps using the scaling form
\begin{equation}
\label{rhoscale}
\overline m(\rho) = \Pi(p) m(\rho + \Delta \rho_c).
\end{equation}
$\Pi(p)$ is a scaling factor and $\Delta \rho_c$ is the shift of
the transition density compared to the deterministic value (\ref{rhocdet}).
The values of the transition densities are shown in Fig.\ \ref{fig8}.
This results are in good agreement with the results
obtained from the measurement of $\tau$.
\section{Spatial Correlations}
A striking feature of second order phase transitions is the
occurence of a diverging length scale at criticality and a corresponding
algebraic decay of the correlation function.
Using lattice gas variables the density-density correlation function
is defined by
\begin{equation}
\label{korrdef}
G(r) = \frac{1}{L}\sum_{i=1}^{L} n_in_{i+r}- \rho^2 .
\end{equation}
Again it is very instructive to consider the deterministic case
($p=0$) first. In the vicinity of the transition density one oberves a
decay of the amplitude of $G(r)$ for larger values of the distance
between the sites. Precisely at $\rho_c$, however, the correlation
function is given by
\begin{equation}
\label{korrdet}
G(r) = \cases{\rho_c-\rho_c^2 & for\ $r \equiv 0$ mod$(v_{max}+1)$ \cr
-\rho_c^2 & else \cr}
\end{equation}
because there are exactly $v_{max}$ empty sites in front of each car.
Considering small, but finite, values of $p$ the correlation function
has the same structure as in the deterministic case, but the amplitude
decays exponentially for all values of $\rho$.
The decay of the amplitude determines the correlation length for a
given pair of $(p, \rho)$, which is finite for all densities in the
presence of noise.
The maximal value of the correlation length $\xi_{max}$
determines the transition density for small values of $p$.
Numerically we find
\begin{equation}
\label{ximaxasym}
\xi_{max} \sim p^{-\frac{1}{2}}.
\end{equation}
In fact, this picture can be confirmed analytically for $v_{max}=1$
\cite{unp}. Using the results of \cite{Cluster} one obtains $\xi_{max}^{-1}
=\ln\left(\frac{1-p}{1-p-\sqrt{p}}\right)$ for the correlation length
$\xi_{max}$ at $\rho=1/2$. Therefore $\xi_{max}\propto 1/\sqrt{p}$ for
small $p$.
This exponent seems to be independent of $v_{max}$ although the
particle-hole symmetry is broken for $v_{max}>1$.
If one considers larger values of $p$ the correlation length gives not
the relevant length scale which is then determined by the size distribution
of jams. A numerical analysis of this limit is
quite difficult and has to be referred to future work.
\section{Discussion and Summary}
Our results suggest a consistent picture of the jamming transition in the
NaSch CA. Measurements of the order parameter and the
correlation function show that critical behavior only occurs in the
deterministic limit where the transition density is given by
$\rho_c = (v_{max}+1)^{-1}$ (see also \cite{Vilar,NaHerr}). The presence of
any noise destroys long-range correlations. The behavior is
analogous to a second order phase transition in finite systems \cite{finite}.
We have, however, checked carefully that our results are not affected by
finite-size effects and are solely due to the presence of noise.
Analogous behavior is also found in the Ising chain in a transverse field
\cite{ferenc}. The transverse field $\Gamma$ is the control parameter
and corresponds to the density $\rho$ in the NaSch model whereas the
temperature $T$ corresponds to the noise parameter $p$. This correspondance
can be used to predict scaling laws. These predictions are currently under
investigation and results will be published elsewhere.
We found qualitatively the same behavior of the relaxation parameter
as shown in \cite{Csanyi}, but some
important new features have been observed. An important result is the
occurance of negative values of $\tau$ which is a consequence of the
relaxation mechanism beyond the transition density: Within
the first few time steps small jams which are present in the initial
condition die out. The second phase is dominated by the formation of
large jams. Thus at a certain time intervall the average flow is
systematically larger than the stationary value, which causes negative
contributions at that time. Consequently one has to question
whether $\tau$ gives meaningful results concerning the relaxation time or
not.
The order parameter does not vanish exactly, but the transition density
could be determined from the scaling behavior. This suggests that the
system is not critical in a strict sense.
Measurements of the density-density correlation function and the
correlation length confirm this picture. We find a finite
correlation length in the presence of noise ($p>0$). The maximum
correlation length diverges in the deterministic
limit like $\frac{1}{\sqrt p} $ for all values of $v_{max}$ we investigated
($v_{max}=2,3,5$). For the case $v_{max}=1$ this result
can also be confirmed by analytical calculations.
Our conclusions have to be compared with those of other investigations where
signals of a second order transition also in nondeterministic cases
have been found. From our point of view these results are
either a consequence of a special limit considered or the
methods chosen. Nagel and Paczuski \cite{Pac} showed the existence
of self-organized critical behavior for the outflow region of a
large jam in the cruise-control limit. They found a scale-invariant size
distribution of jams from measurements far downstream of the megajam.
In this region most of the cars propagate without any fluctuations
such that this limit is also an example for scale-invariance in
deterministic flow. Very recently an investigation of the probabilistic
version of the NaSch model has been performed \cite{Luebeck} and it has
been argued, that at the jamming transition critical behavior occurs also
for the nondeterministic cases.
However, the order parameter introduced in \cite{Luebeck} does also not
vanish exactly below the transition density. All the data presented in
\cite{Luebeck} are consistent with our interpretation of the nature
of the transition. In contrast to the view of \cite{Luebeck} we expect
true phase separation only in the limit $p\to 1$.
Another indication for the absence of critical behavior is the
well-established fact (see e.g.\ \cite{Csanyi} and Fig.\ \ref{fig8})
that the density of maximum flow $\rho(q_{max})$ and the transition
density $\rho_c$ are different.
It would be rather surprising if the system exhibits a genuine
second order phase transition with diverging correlation length.
Correlations obviously favor states with higher flow (see e.g.\ Figs.\
\ref{fig9} and \ref{fig10}, which show that occupancies of cells in front
of a car are surpressed which is the generalization of the particle-hole
attraction observed in \cite{Cluster} for $v_{max}=1$). Therefore
one should expect that the state with the strongest correlations is also
the state with the highest flow, as in the deterministic case.
In conclusion, we found the absence of criticality in the NaSch model
in the presence of noise. For finite $p$ the second order transition
of the deterministic case is smeared out, similar to the situation of
a second order transition in a finite system. Here this effect
is caused by the presence of noise, $p>0$.
For small values of $p$ one finds an
ordering transition close to $\rho_c=1/(v_{max}+1)$. Larger values of
the noise favour the formation of jams and a tendency to phase
separation occurs (see also \cite{ZPR,Luebeck,Chowd}). We therefore
are currently investigating the limit $p \rightarrow 1$ more carefully.
The results will be presented in a future publication.\\[0.3cm]
\noindent{\bf Acknowledgments:}\\
Part of this work has been performed within the research program of
the SFB 341 (K\"oln--Aachen--J\"ulich). We like to thank D.\ Chowdhury,
F.\ Igl\'oi, and J.\ Kert\'esz for valuable discussions and the
the HLRZ at the Forschungszentrum J\"ulich for generous allocation
of computing time on the Intel Paragon XP/S~10.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,318 |
iFi iTube
Pandora's box of hi-fi tricks?
Product name: iFi iTube pre amp
Manufacturer: iFi
Cost: 275 UK pounds.
(Currency conversion)
(YMMV)
Reviewer: Nick Whetstone - TNT UK
Reviewed: October, 2013
A little while back I reviewed a remarkable USB DAC from iFi, remarkable in that it was such a step forward in sound quality from previous USB DACs. It turns out that the iDAC is just part of a range of products that look very similar, and are designed to work together. In this review I'll take a look at the iTube, a valve pre amp that is so much more than just another amplification stage, and the Gemini D-H, iFi's replacement for a standard USB cable.
I'll start with the iTube that came to me in the same very classy packaging as the iDAC had, and looks very similar to its stable mate. It's dimensions are (H x W x D): 28mm x 68mm x 158mm). On the front panel is a volume control knob and two switches. On the rear panel are two pairs of RCA (phono) sockets for analogue input and output. With very little space on the these end panels, the power input socket is moved to a side panel, with the power supplied from a wallwart PSU.
iFi liken the iTube to a Swiss Army pen knife, ie a collection of tools in a small package, and that's a good analogy. It's more than a simple pre amplifier or buffer, although it will perform that function very well using a ( General Electric 5670 based) valve circuit almost miraculously hidden inside it's small case. If you require the gain of a preamp, the iTube can be configured to give gain but if you don't need any then it will also function as a buffer, ie zero gain. You choose how it acts by setting DIP switches on the underside of the case. In buffer mode the input impedance is 1 M ohm, and in preamp mode 100K, both high enough to ensure that there is never an impedance mismatch with whatever is plugged into it. That's a pretty versatile piece of kit but there's more!
The iTube contains two additional switchable circuits. One, called the Digital Antidote Plus® is claimed to "re-equalise harsh, "ringing" digital sources which causes listening fatigue". The second, called the The 3D HolographicSound® system is claimed to provide a more three dimensional effect to the music, and is based on an idea put forward by Alan Blumlein way back in the 1930's. It's difficult not to notice the irony of a piece of equipment designed to work in 21st century digital systems that returns to valves and 1930's theory for much of its design, but in hi-fi, we know that much of the so-called older technology still works perfectly well. Anyway, it is claimed that the 3D HolographicSound® system will compensate for how we actually hear sound, and in doing so improve how we perceive the sound stage, and the various components, ie instruments in it.
The iTube also has an an analogue volume control for those that prefer to use one instead of the digital volume control in a computer source. However, if it isn't required, that volume control can be left out of circuit (by selecting buffer mode). Clearly a great deal of thought has gone into the design of the iTube to offer as much as possible but without putting too much unnecessary 'clutter' in the signal path. I hope that I have covered everything with this rather clever box of tricks, and you can read a fuller description of all this on iFi's site.
Of course, it's one thing to look clever, and another to be clever. As the old saying goes: 'he's a clever old cock but he can't lay eggs'. So how does the iTube actually perform? It made sense to team it up with the iFi iDAC for this review, although I also tried it with the Miniwatt n4, and an old CD player. I used a few different amplifiers, and both my own familiar MS Pageants and a pair of Alacrity Audio Caterthun 8's.
Where do I start with something like this? Well, overall, the iTube is a very transparent piece of hi-fi. Whether I was using it in pre amp mode, or buffer, or even when using the 'effects', the music remained clear, and for want of a better word, untainted. Having the volume control in circuit may have been very slightly noticeable but you would have to listen very hard. So don't worry that it may somehow do unpleasant things to the music, it doesn't in any way. I say that because when we go to such lengths to produce bit-perfect sound from the source, it may seem odd to place something in the audio chain that 'messes' with that signal. I can say that in none of the configurations that I tried did I feel that anything was awry.
iFi talk of the philosophy of adding 'valve sound' to a system, and I personally go along with what they say. Adding valves generally makes music 'nicer' to listen to, and in some systems, eg using classT/class-D amplification I would say that a preceding valve stage is mandatory. I hadn't been using a valve stage between the iFi iDAC and Gainclone monoblocks and was undecided if the iTube made much difference. But with a Virtue Audio Sensation class-D amplifier, I clearly preferred the sound with the iTube acting as a valve buffer. I didn't really find the need for more gain but changed to the 6 db setting simply to hear if there was any difference apart from how loud the system would play. Apart from my comment about the volume control, there was no audible difference in sound quality between the pre amp with gain, and buffer without.
Moving to the 3D settings, I started off with the selector switch in its middle position, ie the circuit is switched out. Moving the switch to the down position didn't result in any immediately noticeable change but after a while (and several instances of switching the circuit in and out) I did perceive what was going on. The sound stage is less compressed, particularly sounds from the lower end of the frequency range are better spread out. There were three effects resulting from this. First off I felt that the perceived 3D effect was increased. By that I don't mean that the sound stage was deeper, but each element within in was more 'rounded' than flat. Secondly, the instruments in the sound stage were spaced more widely apart. Thirdly, and this was more noticeable as I listened to more material, the drum kit in particular the bass drum became much more prominent, not in an imposing way but just so that it added more to the overall enjoyment of whatever I was listening too, and did give a more 'live' feel to the music too. It should also be said that the effect of the 3D circuit is more discernible as you turn up the volume.
I do have desktop speakers on my main computer system but they are the cheapo active type, so I set up an alternative system of a Bantam Audio class-T amp, and some small Pioneer speakers that I have had sitting around on my test bench for years. The sound quality from these speakers isn't great but the system, with the iTube of course, did enable me to experience what the 3d circuit does with near field listening. In this case, the 3D switch is set to the up position. Perhaps due to listening much closer to the speakers, the effect this time was immediately apparent. The sound stage got wider, the imaging was clearer, and the lower end was firmer, and slightly fuller. Again, all this benefit was not at the expense of transparency, or something sounding 'not quite right'.
Moving on to try the Digital Antidote Plus circuit (DAPC), I found that to be a lot harder to perceive any difference, and before I go further, I should state that it is designed to work primarily with SACD players, although it will work with any digital system. Said to remove digital harshness, this circuit is probably invaluable on lesser digital systems but I am finding these days that there is almost no harshness from a good system. The system (computer and hi-fi) that I was using at the time of testing this circuit ran off the excellent James Audio mains conditioner that itself removes a lot of glare from the sound. Reluctantly I swapped out the conditioner for a simple trailing mains lead with 6 sockets and powered up the same system again. Now I felt that the DAPC was making more of an improvement, although it's something that you probably wouldn't notice unless it was pointed out to you. In the hope of giving the DAPC a real test, I got out my old Philips CD723 CD player and connected that to the iTube. WOW - I hadn't listened to the CD723 for a long time but it made me realise how far digital playback has come in the last 15 years or so! Suffice to say that I wasn't tempted to get out a lot of my old CD's but it did show the DAPC to be working more effectively than it had done with a better digital source. In short, how much benefit the DAPC will provide will depend much on the source that it is used with, and the quality of your mains supply. But again, it did nothing negative so going back to the analogy of a Swiss Army penknife, it's a tool that you may not require but it is at least there if you need it in difference circumstances. However, as with the 3D circuit, the effect of the DAPC is much clearer as you increase the volume. I found it possible to turn the volume up (much) higher without that slightly edgy feeling. In other words, I could play much louder without it sounding uncomfortable (and for that reason I left the DAPC switched on all the time).
For me, the iTube 'does what it says on the tin'. The valve stage adds enjoyment to the listening experience, the music is simply more natural and relaxing to listen to. The 3D feature is something that I found myself leaving switched in because I liked the sound stage, and particularly the fuller bottom end, and more realism that it provided. The versatility is also welcome if like me you get to use a wide range of amplification and speakers, or you simply want to use the iTube in different systems. It worked faultlessly all through a very long auditioning process, and despite it's long list of features, was easy to set up and use, although it is one item where you should certainly read the instructions. I'm sure that there will be some purists scoffing at the idea of (and claims for) the Digital Antidote Plus® and the 3D HolographicSound® but the fact is they do work, and in my opinion improve the listening experience, the latter more so. All this makes the iTube fairly unique (at least at the time of writing this review) so I would say to anybody looking for an upgrade to their system, give the iTube a try, I am sure that you will be very pleasantly surprised, and at the price it's a lot of features for the outlay. One last point that shouldn't really need making but I will anyway: the iTube is very unlikely to make a poor hi-fi system sound good so if you have a problem with yours, remedy that first and then try it.
iFi Gemini D-H USB cable
Another USB cable?
Product name: Gemini USB cable. Manufacturer: iFi
Cost: 0.7 metre version 165 UK pounds; 1.5 metre version 235 UK pounds.
Yes (or is that no?) I hear you saying - another USB cable? It seems that boutique USB cables will become the norm from companies producing upmarket USB DACs, so let's take a look, and listen to the one from iFi. (Lucio doesn't like cable reviews on TNT so I hope that I don't get into trouble with this one)
It's natural to compare the Gemini with the U-Craft USB cable from KingRex. Apart from the colours, they look much the same right down to the aluminium connectors. They both come beautifully packaged, and they both do the same job, ie separate the signal and power lines, deal with radio frequency interference (RFI), and facilitate the supply of power from another source such as a battery pack or separate power supply. One nice little bonus with the Gemini is that it comes with an adaptor so that the cable can not only be used with their own USB DAC (and others that use a type-B socket) but also those with a type-A plug, ie the "hiFace DAC or USB converter, Devilsound DAC, etc.
Comparing the Gemini to the U-Craft, the first real difference that I noticed was that the two separate conductors stay separate until the last RFI blocker that is adjacent to the USB connector that plugs into the DAC. The last metre of the U-Craft has both the separate conductors combined (back) into the same cable, something that I still don't understand. Again comparing the Gemini to the U-Craft, the cables are round in section, and quite flexible, making it much easier to place them where you want them, and less likely to dislodge what ever they are attached to. The machined aluminium alloy connectors are very similar to those on the U-Craft, and again are claimed to provide shielding as well as rigidity. In addition to the shielded connectors, the Gemini boasts not one but three "Custom designed adjustable triple RF silencers, providing the widest possible filter range without affecting the USB signal". Finally, "the Gemini cable adheres to the 90 ohm specification of the USB transmission protocol exhibiting just a 1% deviation from the 90 ohm impedance end to end (ie. connector + cable together)". As regards appearance, the Gemini looks a bit more 'grown up' compared to the rather glitzy look of the U-Craft but of course which looks more appealing is down to personal taste.
In use the Gemini is certainly noticeably better than a bog standard USB cable, but as with the U-Craft, I couldn't honestly say that I found it significantly better than the Elijah Audio cable that I auditioned in this review of the hiFace converter. Of course it is a much better constructed cable with the RFI shielding, and perhaps if RFI was more of a problem in my home I may have heard a difference but I can only report honestly what I did hear. Another factor that may affect trials of this sort of equipment could be the excellent James Audio mains conditioner that I use in my auditions. Obviously the better a system is, and if it has better mains, it will sound better, the harder it is to get further improvement. So I went to some trouble and removed the mains conditioner from the system, and plugged everything into a standard mains distribution block, the sort that you can buy for a few pounds in a local hardware store. The glare that the conditioner removes was back, and now when I used the Gemini or Elijah Audio cables with a separate power supply, the improvement was more discernible. However, if I am totally honest, I still couldn't detect a difference between the Gemini and the Elijah Audio cable.
I'm not going to dismiss the Gemini. I felt that it is better designed than the U-Craft (in terms of the power and signal cables being kept separate almost until the end of the cable that goes into the DAC), and the cables are more flexible, and therefore user-friendly, and it's only 255 pounds here in the UK for the longer, 1.5 metre version that is comparable to the U-Craft that costs over 500 pounds, ie twice as much. The shorter, 0.7 metre version of the Gemini cost 165 pounds against the 66 pounds for the Elijah Audio cable (that is a bit shorter again) but the build quality is clearly superior, and it boasts the RFI shielding that the latter doesn't have. With respect to Elijah Audio, and I have been using their cable for many months now without a problem, it doesn't look as if it would survive as much handling as the Gemini. Certainly at the price of the shorter version (and why not just place your DAC nearer your computer source?) I am happy to recommend it. I see it like this: I have here a cheap watch that was given away as a bonus in a mail order sale. It keeps almost perfect time. A friend has his Rolex watch costing thousands of pounds, also keeping perfect time. Should we dismiss the Rolex simply on the grounds of its extra cost? No because a lot more has gone into the Rolex in terms of time and materials, and that's how I see the Gemini (much of which I understand is assembled by hand). Had it been the price of the U-Craft, I would not be recommending it, but considering the work that goes into making it, I felt that the price is fair.
I should just add that while using the Gemini, in conjunction with the Paul Hynes SR3-05 power supply, the iFi iDAC and iTube, and the Caterthun 8 speakers, I heard what I considered to be the best sounding hi-fi that I have heard to date in terms of detail, tone, and clarity. So the Gemini certainly wasn't letting the side down, and is probably one of those components of a hi-fi system that is more appreciated in a better system.
© Copyright 2013 Nick Whetstone - nick@tnt-audio.com - www.tnt-audio.com | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,620 |
Toxicogenomic Responses of the Model Legume Medicago truncatula to Aged Biosolids Containing a Mixture of Nanomaterials (TiO2, Ag, and ZnO) from a Pilot Wastewater Treatment Plant
Title Toxicogenomic Responses of the Model Legume Medicago truncatula to Aged Biosolids Containing a Mixture of Nanomaterials (TiO2, Ag, and ZnO) from a Pilot Wastewater Treatment Plant
Authors Chen, C, Unrine, JM, Judy, JD, Lewis, RW, Guo, J, McNear, DH, Tsyusko, OV
Journal Environmental Science & Technology
Pagination 8759 - 8768
Toxicogenomic responses in Medicago truncatula A17 were monitored following exposure to biosolids-amended soils. Treatments included biosolids produced using a pilot wastewater treatment plant with either no metal introduced into the influent (control); bulk/ionic TiO2, ZnO, and AgNO3 added to influent (bulk/dissolved treatment); or Ag, ZnO, and TiO2 engineered nanomaterials added to influent (ENM treatment) and then added to soil, which was aged in the field for 6 months. In our companion study, we found inhibition of nodulation in the ENM but not in the bulk/dissolved treatment. Gene expression profiling revealed highly distinct profiles with more than 10-fold down-regulation in 239 genes in M. truncatula roots from the ENM treatment, while gene expression patterns were similar between bulk/dissolved and control treatments. In response to ENM exposure, many of the identified biological pathways, gene ontologies, and individual genes are associated with nitrogen metabolism, nodulation, metal homeostasis, and stress responses. Expression levels of nine genes were independently confirmed with qRT-PCR. Exposure to ENMs induced unique shifts in expression profiles and biological pathways compared with bulk/dissolved treatment, despite the lack of difference in bioavailable metal fractions, metal oxidation state, and coordination environment between ENM and bulk/dissolved biosolids. As populations of Sinorhizobium meliloti Rm2011 were similar in bulk/dissolved and ENM treatments, our results suggest that inhibition of nodulation in the ENM treatment was primarily due to phytotoxicity, likely caused by enhanced bioavailability of Zn ions.
URL http://pubs.acs.org/doi/abs/10.1021/acs.est.5b01211http://pubs.acs.org/doi/pdf/10.1021/acs.est.5b01211
DOI 10.1021/acs.est.5b01211
Short Title Environ. Sci. Technol. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,981 |
\section{INTRODUCTION}
Networked dynamic systems arise in many synthetic and natural systems in science and engineering~\cite{Mesbahi2010}; in particular multi-agent systems offer an interesting control paradigm.
Each agent augments the system with an additional (local) computational resource, motivating the concept of \emph{distributed controllers \& estimators}~\cite{Acikmese2014,HudobadebadynFillt2017,Li2017}, leading to a notion of \emph{local} control versus \emph{global} control.
The latter seeks to design control laws to guide groups of agents to a desired objective, and the former seeks to design on-board controllers for each agent to facilitate their role in the global control law.
A class of the more widely used local control laws is called \emph{consensus}, where each agent averages data from their neighbours to compute a parameter related to their objective -- for example, heading, position or a formation center~\cite{Mesbahi2010,Hudobadebadyn2016,Olfati-Saber2004}.
The attractive feature of consensus is how the interconnections between agents -- the so-called \emph{network} or \emph{graph topology} -- affect the performance and agreement characteristics of the algorithm~\cite{Kim2006,Krishnan2017a}.
Graph-theoretic characteristics, such as symmetry, structural balance and graph spectra provide additional insights into the control-theoretic behaviour of consensus ~\cite{Rahmani2009a,Alemzadeh2017,Hudobadebadyn2017,Altafini2013,HudobaDeBadyn2015a}.
Global controllers for multi-agent systems take many forms~\cite{harrison2018optimal}, eg.,
potential field approaches~\cite{Chaimowicz2005},
smoothed particle hydrodynamics~\cite{Pimenta2013} and {density control}~\cite{Eren2017}.
In~\cite{Krishnan2017,Krishnan2016}, density control with only relative measurements of position between agents is considered, and
mean-field control is used to tackle multi-agent interactions by considering a mass flow in the large-$N$ limit~\cite{Albi2016,caines2013mean,Fornasier2013}.
The main interest area of the current paper is networked dynamic systems in which the underlying network is time-varying.
Examples of such systems are switching and proximity-based consensus~\cite{Mesbahi2010,Olfati-Saber2004,Nabi-Abdolyousefi2011} and the Vicsek flocking model~\cite{Tahbaz-Salehi2007}.
State-dependency refers to networks in which the underlying graph varies based on the state of the nodes.
State-dependent networks have been considered in~\cite{Kim2006,Albi2016,Fornasier2013,Mesbahi2002,Mesbahi2005,Awad2015,Awad2018}, but few underlying principles for designing controllers to account for this difficult nonlinearity has been proposed.
A wide range of real-life networked systems are state-dependent.
To tackle this problem, we propose a twofold extension of the work in~\cite{Eren2017}.
First, we consider state-dependent networked dynamic systems, instead of single-integrator dynamics.
Second, we propose a control method for these systems by using a feedback-based density control law that utilizes \emph{optimal mass transport} (OMT).
OMT was considered for linear systems in~\cite{Chen2017}, non-linear systems in~\cite{elamvazhuthi2016optimal} and for density tracking of non-interacting agents in~\cite{Chen2018}.
Our contribution considers OMT for multi-agent systems, in particular ones with state-dependent dynamics.
In the OMT problem, the initial and final densities $\rho_0$ \& $\rho_1$ of the agents are specified.
The solution to the problem yields a time-dependent density profile with boundary conditions imposed by $\rho_0,\rho_1$, and a velocity field that together satisfy the continuity equation.
We aim to use this velocity field as a feedforward control input to the state-dependent multi-agent system, coupled with a density control feedback law.
Using a modified form of kernel density estimation (KDE) that takes into account the state-dependent dynamics, we will show that the combination of the two control techniques will allow us to propose a physically realizable control strategy for state-dependent networked dynamic systems.
This paper is organized as follows.
The mathematical preliminaries, including notation, optimal mass transport, and density control with the KDE procedure are reviewed in \S\ref{sec:math-prel}.
The problem statement and paper contributions are outlined in \S\ref{sec:probl-stat-contr}.
We present the feedforward controller based on OMT in \S\ref{sec:feedb-contr-state}, and the state-dependent KDE in \S\ref{sec:dens-estim-kern}.
Examples are provided in \S\ref{sec:examples}, and the paper is concluded in \S\ref{sec:conclusion}.
\section{MATHEMATICAL PRELIMINARIES AND BACKGROUND}
\label{sec:math-prel}
\subsection{Mathematical Notation}
We follow the standard graph theory notation listed in~\cite{Mesbahi2010}.
A measure space $(\Sigma,\mathcal{A},\mu)$ is a triple containing a \emph{sample space} $\Sigma\subset \mathbb{R}^n$, a $\sigma$-algebra of subsets of $\Sigma$, and a \emph{measure} $\mu$ that assigns the `size' $\mu(A) \in \mathbb{R}_+$ to a set $A \in \mathcal{A}$.
The \emph{Borel $\sigma$-algebra} $\mathcal{B}$ is generated from the countable unions, intersections and complements of open subsets of $\mathbb{R}^n$.
The \emph{Lebesgue measure} $\lambda$ assigns to a closed interval $[a,b]\subset\mathbb{R}$ the `size' $b-a$; this can be extended to $\mathbb{R}^n$ by considering products of measures.
A measure $\mu$ is called \emph{absolutely continuous} with respect to a measure $\nu$ if $\nu(A) = 0$ $ \implies$ $ \mu(A)=0$ for $A\in\mathcal{A}$; $\mu$ is called \emph{Lebesgue absolutely continuous} if $\nu = \lambda$.
This is denoted $\mu \ll \nu$.
If $\mu \ll \nu$, there exists a function $f:\mathbb{R}\to\mathbb{R}_+$ called a \emph{Radon-Nikodym derivative}, or \emph{density}, of $\mu$ with respect to $\nu$.
It is denoted $f := \frac{d\mu}{d\nu}$, and satisfies the property that for all $A\in\mathcal{A}$, $\mu(A) = \int_A fd\nu$.
Let $\pi(x,y)$ be a joint measure on $\mathcal{X}\times\mathcal{Y}$.
We denote the set of such joint measures $\pi$ by $P(\mathcal{X},\mathcal{Y})$.
The \emph{marginal} $\pi_{x}$ of $\pi$ on $\mathcal{X}$ is defined as the push-forward under the projection map $X$ on $\mathcal{X}$:
$
\pi_x = X_\# \pi,
$
where $X(x,y) = x$.
Similarly, the marginal $\pi_y$ of $\pi$ on $\mathcal{Y}$ is given by
$
\pi_y = Y_\# \pi,
$
where $Y(x,y) = y$.
We denote the convolution of two functions $f,g$ as $f\star g$, or the convolution of a function $f$ and measure $\mu$ as $f \star \mu$.
\subsection{Optimal Mass Transport}
Informally speaking, the \emph{optimal mass transport} problem is to find a mapping between two densities that minimizes some cost.
Formally speaking, we consider two measures\footnote{If the measures are Lebesgue absolutely continuous, one can equivalently consider densities $\rho_0,\rho_1$.} $\mu_0,\mu_1$ on $\mathbb{R}^n$ with equal mass: $\int_{\mathbb{R}^n} d\mu_0 = \int_{\mathbb{R}^n}d\mu_1.$
The \emph{optimal mass transport} problem~\cite{Villani2003,Villani2009} is to find a measurable map $ T:\mathbb{R}^n \to \mathbb{R}^n$ taking $\mu_0$ to $\mu_1$ via the following optimization problem:
\begin{align}
\arraycolsep=1.5pt\def1.2{1.2}
\begin{array}{ll}
\mathrm{minimize} & \int_{\mathbb{R}^n} c\left(x,T(x) \right) d\mu_0(x)\\
\mathrm{subject~to} & \int_{x\in A} d\mu_1(x) = \int_{T(x)\in A} d\mu_0(x),
\forall A \subset \mathbb{R}^n,
\end{array}\label{eq:16}
\end{align}
where $c$ is a cost function depending on the initial and transported masses.
The constraint in Problem~\eqref{eq:16} means that $\mu_1$ is the \emph{push-forward} measure of $\mu_0$ under the map $T$, in that for each Borel set $B\in \mathcal{B}:= \sigma(\mathbb{R}^n)$, we have that $\mu_1(B) = \mu_0 \left( T^{-1}(B) \right)$.
This is denoted as $ T_{\#} \mu_0 = \mu_1$.
A generalization of Problem~\eqref{eq:16} by Kantorovich is able to pick out the optimal map $T$, if it exists, for a certain class of costs $c$ under the assumption of absolute continuity of the measures~\cite{Kantorovich1948}.
Here, we consider a joint distribution $\pi(x,y)$ on $\mathbb{R}^n\times\mathbb{R}^n$ and solve for the optimal admissible measure $\pi$ given some cost $c(x,y)$.
The set of admissible measures $\pi$ are those whose marginals are $\mu_0$ and $\mu_1$:
$
X_\# \pi = \mu_0,~ Y_\# \pi = \mu_1.
$
This is equivalent to requiring
\begin{align}
\pi(A \times \mathbb{R}^n) = \mu_0 (A),~\pi(\mathbb{R}^n \times B) = \mu_1(B)\label{eq:17}
\end{align}
for all measurable $A\subset\mathbb{R}^n$ and $B\subset\mathbb{R}^n$.
The \emph{Kantorovich relaxed optimal mass transport problem}~\cite{Kantorovich1948} is given by
\begin{align}
\begin{array}{ll}
\mathrm{minimize} & \int_{\mathbb{R}^n\times \mathbb{R}^n} c(x,y) d\pi(x,y)\\
\mathrm{subject~to} & \pi \in \left\{ \pi \in P(\mathbb{R}^n,\mathbb{R}^n)~ \mathrm{s.t.}~\eqref{eq:17}~\text{holds} \right\}.
\end{array}\label{eq:18}
\end{align}
\begin{proposition}[\cite{Villani2003,Villani2009}]
For quadratic costs $c(x,y) = \|x-y\|^2$, the support of the optimal joint measure $\pi^*(x,y)$ of Problem~\eqref{eq:18} is exactly the graph of the optimal map $T^*(x)$ minimizing Problem~\eqref{eq:16}.
\end{proposition}
For quadratic costs, Benamou and Brenier formulated an equivalent problem in terms of a constrained fluid mechanics model.
\begin{proposition}[\cite{Benamou2000}]
\label{prop:bb}
Given Lebesgue absolutely continuous $\mu_0,\mu_1$ with Radon-Nikodym densities $\rho_0,\rho_1$ respectively, Problem \eqref{eq:18} with quadratic costs is equivalent to
\begin{align}
\arraycolsep=1.6pt\def1.2{1.2}
\begin{array}{ll}
\inf_{\rho,v} &\int_{\mathbb{R}^n} \int_0^1 \frac{1}{2} \|v(t,x)\|^2\rho(t,x)dtdx\\
\mathrm{subject~to} & \frac{\partial \rho}{\partial t} + \nabla \cdot (v \rho) = 0\\
&\rho(0,x) = \rho_0(x),~\rho(1,y) = \rho_1(y).
\end{array}\label{eq:23}
\end{align}
Furthermore, the solution to Problem~\eqref{eq:23} is of the form
$
v(t,x) = \nabla \varphi(t,x),
$
where $\varphi(t,x)$ is the Lagrange multiplier of the constraints
and the solution to the Hamilton-Jacobi equation $\partial_t \phi + \frac{1}{2}|\nabla \phi|^2 = 0$.
\end{proposition}
\begin{remark}
The optimal map $T^*$ of Problem~\eqref{eq:18} in the case of quadratic costs can be reconstructed from the variable $v(t,x)$ from the solution of Problem~\eqref{eq:23}.
This formally establishes the equivalence stated in Proposition~\ref{prop:bb}~\cite{Benamou2000}.
\end{remark}
\subsection{Density Control and Kernel Density Estimation}
In~\cite{Eren2017}, a feedback control law to drive a group of single-integrator agents to a desired density profile $\rho_1(x,t)$ was analyzed.
The following feedback law is proposed to compute the velocity field as a function of the error in density $\Phi(x,t):=\rho(x,t) - \rho_1(x)$ as
\begin{equation}
v(x,t) = - \hspace{0.5mm} \alpha \hspace{0.5mm} \frac{\nabla\Phi(x,t)}{\rho(x,t)} \hspace{1mm}.
\label{eqn: controlLaw}
\end{equation}
Density control of multi-agent systems is impacted by the ability of individual agents to discern the local density profile from measurements of their neighbours.
Since the number of agents is finite, the local density profile must be approximated from finitely many samples $r_i(t)$.
This can be accomplished using \emph{kernel density estimation}~\cite{wand1994kernel,Parzen1962}.
The kernel density estimate $\hat \rho(t,x)$ at any point $x\in\mathbb{R}^n$ and time $t\in\mathbb{R}_+$ is given by
\begin{align}
\hat \rho(t,x) = \int_{\mathbb{R}^n} \left[ \prod_{k=1}^d \dfrac{1}{h_k} K \left( \dfrac{x^{[k]} - \xi^{[k]}}{h_k} \right) \right] dP_N(t,\xi). \label{eq:29}
\end{align}
Here, $K:\mathbb{R}\to \mathbb{R}$ is called the \emph{smoothing kernel}, $h_k$ is called the \emph{smoothing parameter}, and $dP_N(t,\xi)$ is a sum of Dirac measures at sample points:
\begin{align}
dP_N(t,\xi) = \dfrac{1}{N} \sum_{r(t) \in S(t)} \delta\left(\xi - r(t) \right) d\xi.
\end{align}
Since $\delta(\cdot)$ is the Dirac delta functional, Equation~\eqref{eq:29} can be written as
\begin{align}
\hat \rho(t,x) = \dfrac{1}{N} \sum_{i=1}^N \left[ \prod_{k=1}^d \dfrac{1}{h_k} K \left(\dfrac{x^{[k]} - r_i^{[k]}}{h_k} \right) \right].
\end{align}
The control law~\eqref{eqn: controlLaw} then uses the estimate $\hat\rho(x,t)$ in place of knowledge of the true density $\rho(x,t)$, where the sample points $r(t)$ are taken to be the agent states:
\begin{align}
v(x,t) = - \alpha \dfrac{\nabla( \hat \rho(x,t) - \rho_1(x) )}{\hat \rho (x,t) }.
\end{align}
In~\cite{Eren2017}, Gaussian kernels were used -- this induces an all-to-all communication; every agent is able to sample the position every other agent.
The control law~\eqref{eqn: controlLaw} has a convergence guarantee listed in Theorem~6 of \cite{Eren2017}.
\section{PROBLEM STATEMENT AND CONTRIBUTIONS}
\label{sec:probl-stat-contr}
In this paper, we consider state-dependent networked dynamic systems with $N$ agents on a bounded region $\mathcal{R}\subset \mathbb{R}^n$, where the $i$th agent's state evolves according to the dynamics
\begin{align}
\dot x_i = f(\mathcal{G}(\textbf{x}),\textbf{x}) + B u_i(\textbf{x},t),~\textbf{x}:=(x_1,\dots,x_n).
\end{align}
A prototypical example of such a system is \emph{state-dependent consensus}
\begin{align}
\dot x_i =\sum_{j\neq i} A(x_i,x_j)\cdot(x_i - x_j) + u_i,\label{eq:2}
\end{align}
where the edge weight $w_{ij}:=A(x_i,x_j) $ changes depending on the state of the agent $i$ and its neighbour $j$.
In general, one can consider an \emph{interaction kernel} $H(x)$ that generates a consensus-like dynamics by convolution with the Dirac measure supported at agent states~\cite{Albi2016,Fornasier2013}:
\begin{align}
\mu_N(x) = \frac{1}{N}\sum_{j=1}^N \mathbf{1}_{\{x_j\}}(x) = \frac{1}{N} \sum_{j=1}^N \delta(x-x_j).\label{eq:1}
\end{align}
Using Equation~\eqref{eq:1}, we can write a general multi-agent system as
\begin{align}
\dot x_i = \left(H \star \mu_N\right)(x_i) + u_i.
\end{align}
A simple example motivated by robotics is proximity-based edge switching, where $A(x_i,x_j) = 1$ if $\|x_i - x_j \| \leq r$ and 0 otherwise, where $r$ is some communication radius.
This corresponds to an interaction kernel
$
H(x) = x \mathbf{1}_{\|x\|\leq r} (x).
$
As the number of agents $N$ grows sufficiently large, one can consider the time-dependent \emph{density} of agents $\rho(x,t)$ over a region of the state space.
In the context of mean-field control, the formal large-$N$ limit of the dynamics~\eqref{eq:2} produces the \emph{mean field dynamics} \cite{Albi2016,Fornasier2013},
\begin{align}
\arraycolsep=0.5pt\def1.2{1.5}
\begin{array}{ll}
& \dfrac{\partial \rho }{\partial t} + \nabla_x\cdot \left[ \left( \mathcal{P}(\rho(x,t),t) + u\right) \rho \right] = 0\\
& \mathcal{P}(\rho(x,t),x) = \int A(x,y)(y-x) \rho(y,t)dy.
\end{array}\label{eq:3}
\end{align}
We now state the contributions of this paper, namely the feedforward OMT scheme with kernel density estimation shown in Figure~\ref{fig:blkdiag}.
\tikzstyle{block} = [draw, fill=blue!20, rectangle,
minimum height=2em, minimum width=4em]
\tikzstyle{sum} = [draw, fill=blue!20, circle, node distance=0.75cm]
\tikzstyle{input} = [coordinate]
\tikzstyle{output} = [coordinate]
\tikzstyle{pinstyle} = [pin edge={to-,thin,black}]
\begin{figure}
\centering
\begin{tikzpicture}[auto, node distance=2cm,>=latex']
\node [input, name=input] {};
\node [block, right of=input] (omt) {OMT};
\node [sum, right of=omt,node distance=2cm] (sum) {};
\node [block, right of=sum] (swarm) {Swarm};
\draw [->] (omt) -- node[name=u] {$\rho(x,t)$} (sum);
\node [output, right of=swarm] (output) {};
\node [block, below of=swarm,node distance=1cm] (measurements) {KDE};
\draw [->] (sum) -- node {$v(x,t)$} (swarm);
\draw [->] (swarm) -- node [name=y] {$\bf{x}$}(output);
\draw [->] (y) |- (measurements);
\draw [->] (measurements) -| node[pos=0.4] {} node [pos=0.25, above] {$\hat{\rho}(x,t)$} (sum);
\end{tikzpicture}
\caption{Block diagram of density control scheme}
\label{fig:blkdiag}
\end{figure}
\textit{Contribution 1: Feed-Forward Density Control With Optimal Mass Transport.}
We consider a generalization of the Brenier-Benamou OMT problem \eqref{eq:23} with the continuity equation constraint replaced by the mean-field dynamics~\eqref{eq:3}:
\begin{align}
\arraycolsep=1.6pt\def1.2{1.2}
\begin{array}{ll}
\inf_{\rho,v} &\int \int_0^1 \frac{1}{2} \|v(t,x)\|^2\rho(t,x)dtdx\\
\mathrm{subject~to} & {\partial_t \rho } + \nabla_x \cdot \left[ \left( \mathcal{P}(\rho(x, t),x) + v\right) \rho \right] = 0\\
& \mathcal{P}(\rho(x,t),x) = \int A(x,y)(y-x) \rho(y,t)dy\\
&\rho(0,x) = \rho_0(x),~\rho(1,y) = \rho_1(y).
\end{array}\label{eq:4}
\end{align}
The solution to Problem~\eqref{eq:4} yields two variables with important physical interpretations.
The time-varying density $\rho(t,x)$ represents the mass of agents with dynamics \eqref{eq:2} with inputs $u_i(x,t):= v(x_i,t)$; the velocity field $v(x,t)$ is precisely the input $u_i$ given to agent $i$ at position $x$ at time $t$.
Problem~\eqref{eq:4} assumes that the initial and final masses of agents are distributed in the mean-field limit according to densities $\rho_0$ and $\rho_1$, respectively.
When considering finitely many agents, any initial density will take the form of Equation~\eqref{eq:1} - namely, it will be a Dirac measure supported at the agent states, also called the \emph{empirical density}.
Hence, in general, the boundary conditions on the density in Problem~\eqref{eq:4} can be either \emph{deterministic} (in the case of Dirac measures supported at the agent states), or \emph{probabalistic} (in the sense that the initial/final agent states $x_i(0)$ and $x_i(1)$ are randomly distributed according to the densities $\rho_0$ and $\rho_1$).
In the latter case, as $N\to\infty$, the Dirac measure supported at the agent states at time $t$ converges in a formal sense to the density $\rho(\cdot,t)$~\cite{Albi2016,Fornasier2013}.
In either case, we consider the velocity field $v(x,t)$ as a feed-forward input to the dynamics~\eqref{eq:2}.
Since the number of agents is finite, the empirical density at time $t$ will only approximate the density $\rho(x,t)$ from the solution of Problem~\eqref{eq:4}.
\textit{Contribution 2: Feedback Density Control with Kernel Density Estimation and State-Dependent Constraints.}
In a state-dependent networked dynamic system, eg., Equation~\eqref{eq:2}, the existence of an edge indicates some notion of information transfer between agents.
Hence, a physical estimation scheme and density control law can only allow $i$ to sample those agents $j$ such that $A(x_i,x_j) \neq 0$.
The second contribution of this paper is to extend the KDE procedure in~\cite{Eren2017} by solving a quadratic program for an optimal kernel that takes into account the state-dependent communication constraints.
\section{FEEDBACK CONTROL OF STATE-DEPENDENT NETWORKED DYNAMIC SYSTEMS}
\label{sec:feedb-contr-state}
Consider the state-dependent consensus dynamics \eqref{eq:2}.
Let $v_1(x,t)$ denote the velocity field from the solution to Problem~\eqref{eq:4}, and let $v_2(x,t)$ denote the velocity field from the control law~\eqref{eqn: controlLaw}.
Our proposed control law is then given by the velocity field (with $\alpha > 0$),
\begin{align}
&u(x,t) =
\begin{cases}
v_1(x,t) - \alpha \dfrac{\nabla\left( \rho(x,t) - \rho_1(x) \right)}{\rho(x,t)} & 0 \leq t \leq 1\vspace{1mm}\\
v_2(x,t) - \mathcal{P}(\mu(x,t),x) & t \geq 1
\end{cases}\label{eq:5}\\
&\mathcal{P}(\mu(x,t),x) = \int A(x,y)(y-x) \mu(y,t)dy.
\end{align}
Of course, the switch at $t=1$ is completely arbitrary, and can be altered by changing the time horizon of Problem~\eqref{eq:4}.
The main result of this section is the following theorem, an extension of Theorem 6 in~\cite{Eren2017}.
Informally, it states that as the number of agents in the system tends as $N\to\infty$, the velocities of the agents performing the state-dependent control law~\eqref{eq:5} will vanish asymptotically.
\begin{theorem}
\label{thr:1}
\textit{
Consider a system of $N$ agents $\mathcal{S}(t)$ on a bounded region $\mathcal{R}\subset\mathbb{R}^n$ with individual dynamics given by \eqref{eq:2} and with control law~\eqref{eq:5}.
Further suppose that the initial swarm density $\rho(x,t)$ and target density $\rho_1(x)$ satisfy the boundary condition $\nabla \Phi(x,t) = 0$ on $\partial \mathcal{R}$.
As $t\to\infty$, for sufficiently large $N$ the error density $\Phi(x,t)$ converges to zero:
$ \lim_{t\to\infty} \Phi(x,t) = 0,~\text{for }x \in \mathcal{R}$
and so $\hat\rho(x,t) \to \rho_1(x)$.
Furthermore, the velocities of all agents vanish asymptotically:
$
\lim_{t\to\infty} \dot x(t) = 0, ~\text{for }x\in \mathcal{R}.
$
}
\end{theorem}
The proof is discussed in the Appendix.
\section{DENSITY ESTIMATION FOR KERNELS\\ WITH COMPACT SUPPORT}
\label{sec:dens-estim-kern}
Consider a state-dependent consensus dynamics as in Equation~\eqref{eq:2}
where $A(x_i,x_j)$ is a state-dependent edge weight.
In order to implement the density control law, each agent must be able to estimate the density of nearby agents to generate the correct velocity field.
In this section, we discuss optimal kernels designed to achieve this task that are subject to the state-dependent constraints imposed by $A(x_i,x_j)$.
The state-dependent constraints in some (informal) sense denote `information transfer' between agents $i$ and $j$.
If $A_{ij}=0$, then agents $i$ and $j$ cannot detect each other, and the KDE procedure should reflect this.
To illustrate this notion, consider Figure~\ref{fig:sub1}.
In 1D kernel density estimation, there are two parameters selected \emph{a priori} that influence the quality of the estimated probability density function, namely the kernel $K$ and the smoothing parameter $h$.
We consider an optimal selection of $K$ subject to the state-dependent constraints; we leave the task of selecting $h$ for future work.
For now, we just need the following assumption on $h$ as a function of the number of samples:
$
\lim_{N\to\infty} Nh(N) = \infty.
$
The standard metric for measuring the quality of the estimated probability density function is given by the \emph{mean integrated square error}
$
E_{\text{MISE}}:= \mathbb{E} \left[ \int \left( \hat \rho(x) - \rho(x) \right)dx \right].
$
By extracting out the dependence on the number of samples $N$, and the choice of smoothing parameter $h$, one can obtain the \emph{asymptotic mean integrated square error} (AMISE) \cite{wand1994kernel}:
$
E_{\text{MISE}} := E_{\text{AMISE}} + o \left( (hn)^{-1} + h^4 \right).
$
One can factor the AMISE into a product of two terms, one depending on $h$ and one depending on $K$: $ E_{\text{AMISE}} = C_1(K)C_2(h)$, where
\begin{align}
C_1(K) &:= \left[ \left(\int K(x)^2 dx \right)^4 \left( \int x^2 K(x) dx \right) ^2\right]^{1/5}.
\end{align}
\begin{figure}
\centering
\includegraphics[scale = 0.5]{kernelconstraint}
\caption{Illustration of (proximity-based) state-dependent constraints on the KDE procedure. Dotted lines indicate samples the center agent cannot measure.}
\label{fig:sub1}
\end{figure}
Hence, by fixing $a:= \int x^2 K(x)dx$ depending on the length of the boundary of our estimation horizon, the only parameter left to optimize is the \emph{roughness} of $K(x)$: $\int K(x)^2dx$.
We can write an optimization problem as follows:
\begin{align}
\begin{array}{ll}
\mathrm{minimize} & \int K(x)^2 dx \\
\mathrm{subject~to} & \int K(x) = 1,~ \int xK(x) = 0\\
& \int x^2 K(x) = a^2 < \infty,~ K(x) \geq 0.
\end{array}\label{eq:37}
\end{align}
In one dimension, the solution to Problem~\eqref{eq:37} is given by \cite{wand1994kernel},
\begin{align}
K^a(x) = \dfrac{3}{4} \dfrac{1}{a\sqrt{5}} \left[ 1- \left( \dfrac{x}{a\sqrt{5}} \right)^2 \right] \mathbf{1}_{\{|x| \leq a\sqrt{5}\}}.\label{eq:39}
\end{align}
We wish to find the solution to a modified version of this problem where we enforce a compact support constraint of the form $\{K(x) = 0,~x\in \mathcal{A},~\mathcal{A}^c~\text{compact}\}$.
To this end, notice that Problem~\eqref{eq:37} can be numerically solved by discretizing it as follows.
Denote the region of the problem as $X= \{ x ~:~ |x| \leq B\}$.
Discretize $X$ into $N$ points spaced $dx$ apart.
Let the vector $x:=\{x_i\}_{i=1}^N \in [-B,B]^N$ consist of these points, and let $k:=\{k_i\}_{i=1}^N$ be the vector of the kernel $K$ evaluated at these points, i.e. $k_i = K(x_i)$.
Discretizing the integrals yields a quadratic program of the form:
\begin{align}
\begin{array}{ll}
\mathrm{minimize} & k^Tk\\
\mathrm{subject~to} & \sum_{i=1}^N k_i dx = 1,~ \sum_{i=1}^N x_i k_i = 0\\
& \sum_{i=1}^N x_i^2 k_i dx = a^2,~ k_i \geq 0 ,~1\leq i \leq N.
\end{array}\label{eq:38}
\end{align}
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{qpSolnSupportTest}
\caption{Optimal kernels with unconstrained support, and support constrained to $[-2,2]\setminus{[1/4,3/4]}$, with second moment $a=5^{-1/2}$. The unconstrained kernel solution is exactly given by Equation~\eqref{eq:39}.}
\label{fig:kernel}
\end{figure}
As discussed before, an agent's state-dependent density estimate will depend on sampling points from agents that have an edge between them.
Hence, in the density estimate for agent $i$, the kernel $K$ will only depend upon the state of agent $i$ and its neighbours $\mathcal{N}_i$.
The density estimate of agent $i$ is written as
\begin{align}
\hat{\rho}_i(t,x(t)) = \dfrac{1}{Nh^d} \sum_{j \in\mathcal{N}_i} \left [ \prod_{k=1}^d K_i\left( \dfrac{x_i(t) - x_j(t)}{h}, x_j\right) \right]
\end{align}
where the support of the kernel is restricted to the support of the state-dependent edge weight $A(x_i,x_j)$:
\begin{align}
A(x_i,x_j) = 0 \implies K(h^{-1}(x_i-x_j), x_j) = 0.
\end{align}
To extend Problem~\eqref{eq:38} to multi-dimensional systems, we consider \emph{multiplicative kernels} for $x_i \in \mathbb{R}^n$, where each dimension is estimated independently:
$
K({\bf x}) = \prod_{k=1}^N K_k(x_k).
$
This yields the final optimal kernel problem with compact support constraint.
For brevity, we show the explicit form for the 2D problem, as it is clear (yet notationally cumbersome) how to write the general $N$D problem:
\begin{align}
\begin{array}{ll}
\mathrm{minimize} & \sum_i^{N_x} \sum _j^{N_y} k_{ij}^2\\
\mathrm{subject~to} & \sum_{i=1}^{N_x}\sum_{j=1}^{N_y} k_{ij} dxdy = 1,~k_{ij} \geq 0 ,~\forall i,j\\
& \sum_{i=1}^{N_x} x_i k_{ij} = 0,~\sum_{i=1}^{N_x} x_i^2 k_{ij} dx = a^2,~\forall j\\
& \sum_{j=1}^{N_y} y_j k_{ij} = 0,~\sum_{j=1}^{N_y} y_j^2 k_{ij} dx = a^2,~\forall i\\
&k_{ij} = 0 \text{ if } (x_i,y_j) \in \mathcal{A},~\mathcal{A}^c\text{ compact} .
\end{array}\label{eq:7}
\end{align}
It is important to note that removing a compact interval from the kernel may bias the density estimate - this is unavoidable.
The compact support constraint defines a \emph{selection-biased distribution (SBD)}; each agent samples the distribution $g(x) = w(x) \rho(x)/\mu$, with $ w(x) = \mathbf{1}_{\mathcal{A}^c}(x), \mu =\int w(x) \rho(x) dx $.
The standard \emph{unbiased} kernel density estimate of a SBD involves multiplying the kernel by a factor of $\mu/w(x)$~\cite{Gill1988,Wu1996}, which is unbounded for our choice of $w(x)$.
Techniques for unbiasing $\hat\rho(x)$ will be left for future work.
\section{EXAMPLES}
\label{sec:examples}
We numerically simulate $N=200$ agents with interaction kernel $H(x) = x \mathbf{1}_{\|x\|\leq 0.01} (x)$.
The velocity field $\mathcal{P}[\mu](x)$ is evaluated with the Dirac measure \eqref{eq:1}, effectively yielding $N$ single-integrator agents that are able to only sample agents a short distance away from each other.
The optimal mass transport problem was solved using open-source code, utilizing a primal-dual algorithm~\cite{Papadakis2014,Peyre2011}.
The density profile and velocity field was calculated over a $100\times100\times100$ grid in $x,y$ and $t$ space.
The initial density $\rho_0(x)$ was a 2D Gaussian at the center of a $[0,1]^2$ grid, and the target density was a ring of 2D Gaussians, as shown in Figure~\ref{fig:dens}.
The superimposed optimal density profile over time, and the states of the agents over time integrating the feedback and feedforward control law are shown in Figure~\ref{fig:results}.
As one can see, the agents are more organized around the final density distributions when using the feedback law as opposed to just integrating the feedforward law, as shown in Figure~\ref{fig:results2}.
\begin{figure}
\centering
\includegraphics[width=0.6\columnwidth]{dens}
\caption{Left: Initial density $\rho_0$. Right: Target density $\rho_1$.}
\label{fig:dens}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.65\columnwidth]{results.png}
\caption{Optimal density profiles over time, and superimposed agent states using the feedback density control law.}
\label{fig:results}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.65\columnwidth]{resultsnoFB.png}
\caption{Optimal density profiles over time, and superimposed agent states with only the feedforward control.}
\label{fig:results2}
\end{figure}
\section{CONCLUSION}
\label{sec:conclusion}
In this paper, we examined density control of state-dependent networked dynamic systems.
We utilized the optimal mass transport problem to design a feed-forward velocity field propelling agents with initial conditions sampled from a density profile $\rho_0$ to some target density $\rho_1$.
We then tackled the problem of using a density feedback control law with sparse measurements dictated by the state-dependent edge switching constraints of the agents.
We utilized kernel density estimation to convert measurements of neighboring agents into a local estimate of the swarm density, which was then used to calculate a feedback density control law.
In particular, a quadratic program was designed to find the optimal kernel subject to the state-dependent edge switching.
There are many open problems remaining, here we discuss several.
First, the selection of an optimal interaction distance $r = h$ for proximity-based edge switching.
This will depend on, for example, $\rho_0,~\rho_1$ and $N$.
If $h$ is large, this will require more on-board computation and sensing capability; if $h$ is small, agents will be isolated.
Second, one can consider the task of determining a state-dependent kernel yielding an unbiased estimate of $\rho$.
\section*{APPENDIX}
We now state the proof of Theorem~\ref{thr:1}.
\begin{proof}
First, recall the following theorem about consistency of the estimate $\hat \rho(x,t)$.
\begin{theorem}[\cite{Wied2012}]
\label{thr:2}
\textit{
Consider a kernel density estimation scheme for the target density $\rho(x)$.
Suppose the smoothing parameter $h$ is chosen as a function of the number of samples $N$:
$
\lim_{N\to\infty} Nh(N) = \infty.
$
Then, at each point of continuity $x$ of $\rho$, the estimator $\hat \rho_N(x)$ is weakly consistent in that for all $\epsilon>0$,
$
\lim_{N\to\infty} \mathbb{P} \left(|\rho_N(x) - \rho(x) | > \epsilon \right) = 0.
$
}
\end{theorem}
By Theorem~\ref{thr:2}, under the assumption on the smoothing parameter $h$, we have that as $N\to\infty$, $\hat\rho(t,x) \to \rho(t,x)$ with probability 1 for any finite $t$.
Consider the following Lyapunov function:
\begin{align}
V(t) = \int_{\mathcal{R}} \left( \dfrac{\rho(x,t)}{\alpha} \right)^2 \dot x ^T \dot x~ dx.\label{eq:6}
\end{align}
As $N\to\infty$, the velocity field $\dot x$ approaches the mean-field limit \cite{Albi2016}:
$
\dot x = \mathcal{P}(\mu,t) + u(x,t),
$
where
$
\mathcal{P}(\mu,x) = \int A(x,y)(y-x)\mu(y,t)dy,
$
and $\mu:=\mu(y,t)$ is the measure satisfying
$
{\partial t} + \nabla \cdot \left( \left( \mathcal{P}(\mu,t) + u(x,t) \right) \mu \right) = 0.
$
Under the control law~\eqref{eq:5}, it follows that for sufficiently large $t$, the Lyapunov function \eqref{eq:6} can be written as
\begin{align}
V(t) = \int_{\mathcal{R}} \nabla \Phi(x,t)^T \nabla \Phi(x,t) dx.
\end{align}
The time derivative of $V(t)$ is then given by
\begin{align}
\dot V(t)
&= \alpha \int_{\mathcal{R}} \xi(x,t)^T \Delta \xi(x,t) dx,
\end{align}
where $\xi(x,t) := \nabla \Phi(x,t)$.
Since $\nabla\Phi(x,t) = 0$ on $\partial\mathcal{R}$, we have that $\xi(x,t) = 0 $ on $\partial \mathcal{R}$ which is a Dirichlet boundary condition.
It follows that $\dot V(t) < 0$ since the Dirichlet problem for the Laplace operator has strictly negative eigenvalues~\cite{Li1983}.
Therefore, by LaSalle's Invariance Principle, we can conclude that $\lim_{t\to\infty} \nabla \Phi(x,t)=0$, and so $\lim_{t\to\infty} \Phi(x,t) = \text{constant}$.
However, since $\nabla\Phi(x,t)=0$ on $\partial\mathcal{R}$, the mass $\int_{\mathcal{R}} \Phi(x,t) dx$ is conserved for all $t>0$ (in that $\int_{\mathcal{R}} \Phi(x,t) dx = 0$) and so we have that
$
\int_{\mathcal{R}} \hat \rho(x,t) dx = \int_{\mathcal{R}} \rho(x,t) dx.
$
Consequently, it follows that $\lim_{t\to\infty} \Phi(x,t) = 0$, and hence $\lim_{t\to\infty} \rho(x,t) = \lim_{t\to\infty} \hat \rho(x,t)$ which completes the proof.
\end{proof}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,286 |
Q: HTML cache history back If I use history.back() for button press then what will happen?
Will the HTML content be displayed from the local history of the browser or the cache and without the browser requesting to the server? Or will the browser request to the server based on the URL that resides in history of browser?
A: Calling "history.back()" in JavaScript is the same as hitting the back button in the browser's user interface (however, there can be slight differences if the currently viewed location contains frames and those have been navigated, if you're pedantic).
As for if the result comes from the server or "cache": it's up to the user agent (browser). The specification (RFC 2616 section 13.13, http://256stuff.com/gray/docs/rfc2616/13.html#13.13) says:
History mechanisms and caches are
different. In particular history
mechanisms SHOULD NOT try to show a
semantically transparent view of the
current state of a resource. Rather, a
history mechanism is meant to show
exactly what the user saw at the time
when the resource was retrieved.
However, the user agent implementation quality differs. For example, the relevant meta bug for Mozilla/Firefox can be found at https://bugzilla.mozilla.org/show_bug.cgi?id=288462
If the page you're trying to "back" to has suitable caching headers, it will be fetched from a cache instead of from the server.
A: This is browser dependent.
The behavior of the history.back() button is up to the browser manufacturer.
A: history.go(-1) does the very same thing and is the same across all browsers...
if (!defined('MODULE_FILE'))
{
$back = "<script>history.go(-1);</script>";
print_r($back);
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,923 |
Q: Mass and frequency of photons Light is affected by gravity which means light has got mass. Quantum theory tells us that light consists of discrete quanta of energy, which we call photons. These photons have a rest mass of zero (as a consequence of special relativity), but a "moving photon" (I don't know whether that notion is stupid) has got some mass.
According to Planck, a photon travelling with a frequency ϑ will be associated with an energy
$$
E=hϑ.
$$
Since the same photon is travelling at the speed of light, it should hold valid for relativity also. In relativistic theory, the energy of a photon is given by
$$
E=pc
$$
for a photon $p=mc$ where $m$ is the relativistic mass of the photon.
Hence $E=mc^2$
Comparing both equations,
$$
hϑ=mc^2$$
or
$$m=hϑ/c^2$$
which means the mass of a photon is dependent on its frequency. This is the cause of redshift of light in a gravitational field. But how frequency account for mass? Is it a direct evidence that light and matter are not distinct entities of the universe, but matter is nothing but condensed energy?
A: There is a great misunderstanding here. The photon is an elementary particle (the gamma in the table is the photon) of spin one and mass zero. This has been validated innumerable times in nuclear physics, atomic physics and particle experiments. There is no question about it.
Special relativity treats the four-vector of a particle. In this framework the masses of all particles are the four vector dot product, called the invariant mass and does not change, hence the name.
In General Relativity the total four vector follows the geodesics of the four dimensional space time , it is the total four-vector that bends in space time , whether a massive particle or a massless one.
All the rest is misuse of formulas , due to fundamental misunderstanding of special relativity.
A: I think the answer could be just as simple as that mass of any body i just a projection of that system vibrating. Consider a particle vibrating about a fixed position which starts gaining speed but first when it had zero speed or small vibration frequency its body vibrations were restricted to small particle area but when it start vibrating its projection disperses to a relatively bigger area and when it approaches "c" it completely vanishes. So i think you get the idea that what i am saying.
A: Light is a gravitational wave of bent space, it travels at the velocity of C, where time slows down. At that velocity (with time dilation) it makes a gravity wave into the photon. Mass is nothing more than the potential energy of a gravity wave of relativistic bent space. because it is traveling relativistic-ally it is slowing time and bending space. So when the time dilation of a photon or a "micro-gravity wave" travels through a gravitational part of space, like the side of the planet, the planet's time dilation adds to the sin wave of the light's frequency of time dilation causing it to bend along the planet's time dilation gravity gradient. Where ever mass is, there shall you Always find slower time. I like this question it gets to the real facts fast!
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,080 |
What is next for the Warriors if DeMarcus Cousins cannot suit up?
Those who know him best -- and they can fit inside a shot glass -- insist Cousins just doesn't trust very many, that's all.
But what happens when the flesh and blood that's closest to him -- his own body -- winds up being the most untrustworthy of all?
DeMarcus Cousins suffered his left quadriceps injury in Game 2 on Monday.
There's nothing else that can explain why, for the second time in 14 months, the 6-foot-11, 270-pound center dropped to the floor without being pushed and immediately grabbed a body part in pain.
The extent of the left quad injury he suffered in Monday's Game 2 came down Tuesday as a reported tear, which will more than likely sideline him for the rest of the playoffs.
When Cousins hustled for a stolen pass in the first quarter and fell right in front of the Warriors' bench, players and coaches jumped and knew something was wrong. The Oracle Arena crowd instantly hushed. This was no ordinary plop.
Charles Barkley is hoping for the best for DeMarcus Cousins.
Since it is a tear, his season is pretty much over. Had it been a strain, depending on severity, it would have cost him a chunk of the postseason -- if not all of it.
Cousins is in a Warriors' uniform only because the Achilles he tore two Februarys ago with the New Orleans Pelicans led him to Oakland in a search to restore his All-Star status, win a championship and mainly to cash in as a free agent this summer. It appeared a worthwhile gamble, to play for peanuts (relatively speaking) on what amounts to a stopover while mending peacefully and gradually without any sense of urgency on the team's behalf.
Cousins put in the work, returned earlier than expected in January, was heartily welcomed by his new teammates and gradually regained his timing and conditioning. The Warriors carefully rationed his minutes and touches and yet, he averaged 25.7 minutes per game this season and looked frisky at times. His 16.3 points and 8.2 rebounds per game were impressive on a team that was loaded without him.
The Clippers took down the Warriors with a monumental rally in Game 2.
He's a big man with a gentle touch, capable of posting up or shooting 3-pointers. Yet he's someone who languished nonetheless for six turbulent seasons in Sacramento before a flash of brilliance and refreshing serenity in his brief stay in New Orleans.
To the two-time defending champion Warriors, who have four other All-Stars in the rotation, Cousins' worth is negotiable. More talent on the floor is always better. Still, Cousins amounts to a bonus and insurance in case something goes really wrong on this three-peat chase. Their vaunted "Hamptons Five" lineup, with smaller and quicker players, was used in Game 1 vs. the Clippers while Cousins had six turnovers and fouled out.
If Cousins is out, the Warriors have few options at center (and none who can match his skill set). Andrew Bogut was signed a month ago, but is fit and knows the system. Kevon Looney is more athletic and has played well as of late. And that's about it.
There are longer-term implications as well, depending on what the MRI says. Cousins wanted to make a splash in free agency and because of a salary cap that's very limiting to what the Warriors can offer. That splash would be elsewhere and the Warriors are fine with that.
"This is a one-year deal with us … we'd like to help him win a championship and sign a great contract somewhere else," Kerr said.
Instead, Cousins must deal with betrayal, from the person closest to him: Himself. | {
"redpajama_set_name": "RedPajamaC4"
} | 5,288 |
\section{Introduction and Background} \label{intro}
\noindent The use of idempotents in the construction of cyclic error
correcting codes is well established and the resulting literature
is extensive (for example, see
\cite{McW},\,\cite{Rmn},\,\cite{vanL1}). The basic building blocks
for this theory are the primitive idempotents. Any cyclic code may
be described by a unique idempotent and this idempotent is a sum
of primitive idempotents. For binary cyclic codes, efficient
algorithms exist for the calculation of these primitive
idempotents.
Another way of constructing idempotents in the binary case is by
using cyclotomic cosets and it was this property which was
exploited by Shibuya and Sakaniwa in \cite{Shi}.
Their goal was to use idempotents to construct parity check matrices for LDPC
codes which have
no cycles of length 4 in their factor graphs. At the heart of their technique is a
lemma which is a variation of a result used by Weldon
\cite{We}, for the construction of difference set cyclic codes.
Using this lemma and a subsequent theorem, they were able to
simplify the problem of determining which of the idempotents
that are constructed, using a single cyclotomic coset, do not have cycles of length 4. They then
extended this theory to more general idempotents.
This approach to the construction of LDPC codes has the great
advantage of simplicity, the parity check matrices depend only
upon the correct choice of cyclotomic cosets and these are very
easily calculated. However, we believe that this advantage is
offset by some fundamental weaknesses.
Whilst the absence of 4 cycles is a desirable objective in the
construction of LDPC codes it is not mandatory \cite{Tian}, since
there are some good codes which do not have this property. An
example of such a code is included in this paper. The code rate is
also an important property of codes but, as Shibuya and Sakaniwa
admit in their conclusion, the codes which they construct in this
way are \lq\lq \textit{expected} to have a large minimum distance
\emph{at the expense of rate}\rq\rq (our italics). The minimum
distance of a code is a crucial property but there is no
indication in \cite{Shi} of how either a single cyclotomic coset,
or combinations of more than one cyclotomic cosets, should be
chosen to guarantee that the code constructed has a large minimum
distance.
In order to address the question of how to choose
idempotents which will produce good LDPC codes we propose an
entirely different route. As in \cite{Shi}, we shall deal
exclusively with binary cyclic codes. Making effective use of the
Mattson-Solomon polynomial, we produce an algorithm which not only
allows us to choose, in a systematic way, idempotents with low
weight, and therefore a correspondingly sparse parity check
matrix, but also with the desirable features that the
corresponding codes have a high code rate and a large minimum
distance.
This paper is organised as follows. In \mbox{section\
\ref{theory}} we shall review the necessary theory
and explain how
it will be used to provide an algorithm for the determination of
idempotents which may be used to construct good codes. In
\mbox{section\ \ref{imp}} the design and implementation of this
algorithm is given and then, in \mbox{section\ \ref{exs}}, some of
the results are displayed. Finally, in \mbox{section\ \ref{con}},
we draw our conclusions on this approach.
\section{Binary Idempotents}\label{theory}
Let $F=GF(2)$, $n$ be a positive integer and $\mathcal{F}$ be the
splitting field for $x^n-1$ over $F$. Let $\alpha\in\mathcal{F}$
be a primitive $n$th root of unity and let $T(x)$ be the
polynomials in $\mathcal{F}[x]$ of degree $\leq n-1$. If $a(x)\in
T(x)$ then the map $\Phi\, :T\rightarrow T $ is defined by
\begin{equation}\label{MS}
[\Phi(a)](z)=\sum_{j=1}^na(\alpha^j)z^{n-j}
\end{equation}and $\Phi(a)$ is the
Mattson-Solomon polynomial of $a$ (see \cite{McW}). (We use $x$
and $z$ for the polynomial variables to distinguish between the
polynomials in the domain and codomain of $\Phi$.) If $\circ$ is
multiplication of polynomials$\mod (x^n-1)$ and $\ast$ is defined
on $T(z)$ by the rule $(\sum a_iz^i)\ast(\sum b_iz^i)=\sum
a_ib_iz^i$ then it is well known \cite{McW},\cite{vanL1}, that
$$\Phi\, :(T,+,\circ )\rightarrow (T,+,\ast )
$$ is an isomorphism of rings, in particular it is an isomorphism
of the additive groups.
If $S(x)$ is the subset of $T(x)$ consisting of polynomials with
coefficients
in $GF(2)$ (binary polynomials) and $E(x)$ is the subset of $T(x)$ consisting of idempotents,
both of these subsets are \textit{additive subgroups} of $T(x)$.
It is easy to show (see \cite{McW}) that
\begin{eqnarray}\label{isos}
\Phi\,:(S(x),+) &\rightarrow & (E(z),+) \\
\Phi\,:(E(x),+) &\rightarrow & (S(z),+)
\end{eqnarray}are both isomorphisms and
from this it is obvious that
\begin{equation}
\label{main_iso}\Phi\,:(S(x)\cap E(x),+)\rightarrow (E(z)\cap
S(z),+)
\end{equation}is also an isomorphism.
\medskip Suppose that $u(x)$ is a binary idempotent which is used to
construct a parity check matrix for a cyclic code. The parity
check matrix is constructed from the $n$-cyclic shifts of $u(x)$
\cite{Pl}, and so for the resulting code to be a LDPC code, $u(x)$
must have low weight.
If $h(x)=\mathrm{gcd}(x^n-1,u(x))$ and $g(x)=(x^n-1)/h(x)$, then
$g(x)$ is the generator of the cyclic code. If the generator,
$g(x)$, has degree $n-k$, the dimension of the code is $k$ and
the larger the value of $k$, the better the code rate. Since
$g(x)$ is a divisor of $x^n-1$, all of the zeros of $g(x)$ are
$n$th roots of unity, and there are $n-k$ of these. Further,
gcd$(g(x),h(x))$=1 and $x^n-1=h(x)g(x)$, so that the number of
distinct $n$th roots of unity which are also roots of $u(x)$ is
$k$. The dimension of the code is therefore the number of $n$th
roots of unity which are also roots of $u(x)$.
The BCH bound of the code is determined by the number of
consecutive powers of $\alpha$, taken cyclically (mod\,$ n$),
which are also roots of $g(x)$. For the reasons outlined in the
previous paragraph, this is precisely the same as the number of
consecutive powers of $\alpha$, taken cyclically (mod\,$ n$),
which are \textit{not} roots of $u(x)$.
The important features of the code are therefore determined by:
\medskip
\begin{tabular}{cl}
(a) & the weight of the idempotent $u(x)$, \\
(b) & the number of $n$th roots of unity which are roots of $u(x)$, \\
(c) & the number of consecutive
powers of $\alpha$ which are \textit{not} roots of $u(x)$.
\end{tabular}
\medskip Take $u(x)\in S(x)\cap E(x)$ and let $\Phi(u)=\theta$ be
its MS polynomial. The inverse mapping
\begin{equation}
\label{inv_iso}\Phi^{-1}\,:(S(z)\cap E(z),+)\rightarrow (E(z)\cap
S(x),+)
\end{equation}is defined as follows:
If $A(z)=[\Phi(a)](z)$ is the Mattson-Solomon polynomial of the
polynomial $a(x)=a_0+a_1x+\dots+a_nx^{n-1}$ then, for $i=0,\ldots
,n-1,$
\begin{equation}\label{inverse}
a_i=\frac{1}{n}A(\alpha^i)
\end{equation}
(see \cite{McW}). Let $h(z)=\mathrm{gcd}(\theta(z),z^n-1)$ and let
$f(z)=(z^n-1)/h(z)$.
The three key properties relating to the idempotent $u(x)$, listed
above, are easily gleaned from its Mattson-Solomon polynomial
$\theta (z)$, and $f(z)$, as follows:
\subsection{The weight of $\mathbf{ u(x)}$}\label{wt-of-u}
The weight of $u(x)$ is the number of $n$th roots of unity which
are zeros of $f(z)$. To see this note that $f(\alpha^i)=0$ if and
only if $\theta(\alpha^i)=1$, since idempotents take only the
values $0$ and $1$ in $ \mathcal{F}$. Now $u=\Phi^{-1}\theta$ and
the coefficients of $u(x)=u_0+u_1x+\ldots+u_{n-1}x^{n-1}$ are
given by
\begin{equation}\label{coeffs}
u_i=\theta(\alpha^i) \mod 2\quad \mathrm{for}\ i=0,\ldots
n-1\,
\end{equation} (\textit{cf } equation (\ref{inverse})). Thus
$ u_i=1$ precisely
when $f(\alpha^i)=0$, giving the weight of $u(x)$ as the degree of
the polynomial $f(z)$.
\subsection{The zeros of $\mathbf{ u(x)}$.}\label{zeros-of-u}
From the definition of the MS polynomial,
(\ref{MS}),
\begin{equation}\label{theta}
\theta(z)=\sum_{j=1}^nu(\alpha^j)z^{n-j}
\end{equation}
and
the number of zeros of $u(x)$ which are roots of unity is clearly $n-\mathrm{wt}(\theta(z))$.
\subsection{The BCH bound of the code.}\label{bch-bound}
The BCH bound of the code is the largest number of consecutive
powers of $\alpha$ which are \textit{not} roots of $u(x)$, i.e.
the number of consecutive $i$, taken (mod\,$ n$), such that
$u(\alpha^i)=1$. From (\ref{theta}), this is the largest number of
consecutive non-zero coefficients in $\theta$, taken cyclically
(mod $n$).
\bigskip\noindent Using this information, a systematic search for
idempotents can now be made in increasing order of weight, with
accompanying knowledge of the number of roots which are $n$th
roots of unity and the corresponding BCH bound. This algorithm is
constructed in the Mattson-Solomon domain.
Let the decomposition of $z^n-1$ into
irreducible (over $F=GF(2)$) polynomials be $z^n-1=f_1(z)f_2(z)\ldots
f_t(z)$.
For $i=1,\ldots,t,$ let $k_i(z)=(z^n-1)/f_i(z)$ and let $\theta_i(z)$ be the associated
primitive idempotent (see \cite{McW} or \cite{vanL1}).
These are displayed below in an array, together with other
idempotents:
\bigskip
\begin{equation}\label{array1}
\left.
\begin{array}{cccc
u_1(x) & \null \qquad\null & \theta_1(z) & f_1(z) \\
u_2(x) & & \theta_2(z) & f_2(z) \\
\vdots & & \vdots & \vdots \\
u_t(x) & & \theta_t(z) & f_t(z)\\
\end{array}
\right\}
\end{equation}
\bigskip
\noindent Here $u_1(x),u_2(x),\ldots,u_t(x)$ are the idempotents whose
Mattson-Solomon polynomials are $\theta_1(z),\theta_2(z),\ldots
,\theta_t(z)$, respectively. Let $I\subseteq \{1,2,\ldots,t\}$ and
let $u,\theta$ and $f$ be defined as $u=\sum_{i\in I}u_i$,
$\theta=\sum_{i\in I}\theta_i$ and $f(z)=\prod_{i\in I}f_i(z)$.
From the properties of primitive idempotents, if
$h(z)=\mathrm{gcd}(\theta(z),z^n-1)$ then it follows that
gcd$(f(z),h(z))=1$ and $z^n-1=f(z)h(z).$ The idempotent $u$ will
now have the following properties.
\begin{eqnarray}
\mathrm{wt}(u) &=& \sum_{i\in I}\mathrm{deg}(f_i)\label{eqn:wt-of-u}\,,\\
\mathrm{number\ of\ zeros\ of\ u}&=& n-\mathrm{wt}(\theta)\label{eqn:zeros-of-u}\,.
\end{eqnarray}
The BCH bound is determined from $\theta(z)$ as explained in
\ref{bch-bound}.
Since methods for finding the $\theta_i$ and $f_i$ are well
documented (see e.g.
\cite{vanL2})
a search algorithm can be built
around this observation to find a suitable weight idempotent with a known number of zeros and a known BCH bound.
The rows of the array (\ref{array1}), are ordered by the degree of the polynomials, i.e.
$\mathrm{deg}(f_i)\leq\mathrm{deg}(f_{i+1})$ for all $i$, and a search can be made in increasing order of weight.
When a successful outcome has been obtained, \textit{only at this
stage}
is the \textit{inverse Fourier transform} (MS$^{-1}$) evaluated
to find the corresponding idempotent. All of the information which
is required will already be known.
\section{Design and Implementation}\label{imp}
If $t$ denotes the number of cyclotomic cosets modulo $n$, the
complexity of an exhaustive search algorithm is
$\mathcal{O}(2^t)$. We reduce this search complexity by targeting
the search on the three key parameters:
\subsection{Sparseness of the parity-check
matrix}\label{sparseness}
In \cite{We}, Weldon introduced
difference-set cyclic codes. These codes have the desirable
property that the parity check equations are orthogonal on all
bits and have no cycles of length 4 in their factor graphs. A
necessary condition for this is that if $v(x)$ is the polynomial
which generates the parity check matrix then the weight of $v(x)$
must satisfy the inequality
\begin{equation}\label{eqn:diff-set}
\mathrm{wt}(v(x))(\mathrm{wt}(v(x))-1)\leq n\,,
\end{equation}where $n$ is the code length. Since the weights of the idempotents
$u(x)$ are related to the
degrees of the $f_i$ by (\ref{eqn:wt-of-u}), a reasonable bound is
\begin{align}
\sum_{i\subseteq I}\text{deg}(f_i) \leq
\sqrt{n}\,.\label{eqn:wt-bound}
\end{align}In practice we have gone a little beyond this limit
and this has enabled us to find some good codes which do have
cycles of length 4 in their factor graph.
\subsection{Code-rate}\label{code-rate}
The code-rate is directly proportional to the number of roots of
$u(x)$. If we let $R_{min}$ represent our minimum desired
code-rate then, following equation~(\ref{eqn:zeros-of-u}), we can
refine our search bound to
\begin{align}
\text{wt}(\theta) \le (1-R_{min})n\,.\label{eqn:theta-bound}
\end{align}
\subsection{Minimum distance}\label{min-dist}
Let $d$ be the lowest desired minimum distance and let
$r_{\theta}$ be the largest number of consecutive non-zero
coefficients, taken cyclically $\mod n$, of $\theta$. Then,
following the discussion of \ref{bch-bound}, we restrict our
search algorithm to those $\theta$ for which
\begin{align}
r_{\theta} > d\label{eqn:dmin-bound}
\end{align}
\noindent We develop an efficient, but exhaustive recursive
tree-search based on the above bounds. The developed search
algorithm, Algorithm~\ref{alg:search}, is initialised by setting
$\mathbf{V}$ and $index$ to $\emptyset$ and $-1$ respectively.
\renewcommand{\algorithmicrequire}{\textbf{Input:}}
\renewcommand{\algorithmicensure}{\textbf{Output:}}
\begin{algorithm}
\caption{CodeSearch($\mathbf{V}$, $index$, $\mathbf{F}(x)$, $\mathbf{Q}(z)$)}\label{alg:search}
\begin{algorithmic}[1]
\REQUIRE $R_{min} \Leftarrow$ minimum code-rate of interest\\
$d \Leftarrow$ lowest expected minimum distance\\
$\delta \Leftarrow$ small positive integer\\
$\mathbf{F}(x) \Leftarrow \{f_i(x)\}$ $\forall i \in I$ sorted in ascending order of the
degree\\$\mathbf{Q}(z) \Leftarrow \{\theta_i(z)\}$ $\forall i \in I$
\ENSURE $\mathbf{CodesList}$ contains set of codes
\STATE $\mathbf{T} \Leftarrow \mathbf{V}$
\FOR {\big($i$=$index$+1; $i \le \text{Size}\left(I\right)$; $i$++\big)}
\STATE $\mathbf{T}_\text{prev} \Leftarrow \mathbf{T}$
\IF {\big($\sum_{\forall j \in\mathbf{T}}\text{deg}(f_j(x))+\text{deg}(f_i(x)) \le \sqrt{n}+\delta$\big)}
\STATE Append $i$ to $\mathbf{T}$
\STATE $\theta(z) \Leftarrow \sum_{\forall j \in \mathbf{T}} \theta_j(z)$
\IF {\big($\text{wt}(\theta(z)) \le (1-R_{min})n$ \textbf{and} $r_{\theta} > d\big)$}
\STATE $u(x) \Leftarrow \text{MS}^{-1}\left(\theta(z)\right)$
\IF {$u(x)$ is non-degenerate}
\STATE $\mathcal{C} \Leftarrow$ a cyclic code defined by $u(x)$
\IF {\big($\mathcal{C} \notin \mathbf{CodeList}$\big)}
\STATE Add $\mathbf{C}$ to $\mathbf{CodeList}$
\ENDIF
\ENDIF
\ENDIF
\STATE CodeSearch($\mathbf{T}$, $index$, $\mathbf{F}(x)$, $\mathbf{Q}(z)$)
\ENDIF
\STATE $\mathbf{T} \Leftarrow \mathbf{T}_\text{prev}$
\ENDFOR
\end{algorithmic}
\end{algorithm}
\section{Code Example and Performance}\label{exs}
Since the algorithm is an exhaustive search, the code construction
method presented in this paper is able to produce, in addition to
new codes, many well-know cyclic codes, for example the
Difference-Set Cyclic codes and the Euclidean and Projective
Geometry codes. Some of the new codes which we have found using
this technique are presented in Table~\ref{tbl:code-examples}. All
codes in Table~\ref{tbl:code-examples}, except those labelled with
$^*$, have orthogonal parity-check equations.
\begin{center}
\bottomcaption{\label{tbl:code-examples}Examples of the constructed codes}
\tablefirsthead{\hline\hline
\multicolumn{1}{|c|}{($n$, $k$)} &
\multicolumn{1}{|c|}{$u(x)$} &
\multicolumn{1}{|c|}{$d_{min}$}\\
\hline\hline}
\tablehead{\hline
\multicolumn{3}{|l|}{\small \tablename\ \thetable{} $-$ \sl continued from previous page}\\\hline
\multicolumn{1}{|c|}{($n$, $k$)} &
\multicolumn{1}{|c|}{$u(x)$} &
\multicolumn{1}{|c|}{$d_{min}$}\\
\hline}
\tabletail{\hline
\multicolumn{3}{|r|}{\small \sl continue on next page}\\
\hline}
\tablelasttail{\hline\hline}
\begin{supertabular}{|l@{\hspace{0.1in}}|p{3.5in}|r@{\hspace{0.2in}}|}
(51,26)$^*$ & $1+x^3+x^6+x^{12}+x^{17}+x^{24}+x^{27}+x^{34}+x^{39}+x^{45}+x^{48}$ & $10$\\\hline
(63,44)$^*$ & $1+x^7+x^9+x^{14}+x^{18}+x^{27}+x^{28}+x^{35}+x^{36}+x^{45}+x^{49}+x^{54}+x^{56}$ & $8$\\\hline
(93,47) & $1+x^2+x^8+x^{31}+x^{32}+x^{35}+x^{47}$ & $8$\\\hline
(105,53) & $ 1+x^4+x^{30}+x^{32}+x^{45}+x^{46}+x^{53}$ & $8$\\\hline
(117,72)$^*$ & $1+x+x^2+x^4+x^8+x^{11}+x^{16}+x^{22}+x^{32}+x^{44}+x^{59}+x^{64}+x^{88}$ & $12$\\\hline
(127,84)$^*$ & $1+x+x^2+x^4+x^8+x^{16}+x^{32}+x^{55}+x^{59}+x^{64}+x^{91}+x^{93}+x^{109}+x^{110}+x^{118}$ &
$10$\\\hline
(219,101) & $1+x^2+x^8+x^{32}+x^{73}+x^{74}+x^{77}+x^{89}+x^{110}+x^{128}+x^{137}$ & $12$\\\hline
(255,135) & $1+x^4+x^{13}+x^{21}+x^{39}+x^{54}+x^{55}+x^{91}+x^{121}+x^{123}+x^{148}+x^{195}$ & $13$\\\hline
(255,175) & $1+x+x^3+x^7+x^{15}+x^{26}+x^{31}+x^{53}+x^{63}+x^{98}+x^{107}+x^{127}+x^{140}+x^{176}+x^{197}+
x^{215}$ & $17$\\\hline
(341,205) & $1+x^{29}+x^{87}+x^{92}+x^{94}+x^{114}+x^{122}+x^{156}+x^{202}+x^{203}+x^{213}+x^{217}+x^{234}+
x^{257}+x^{273}$ & $16$\\\hline
(511,199) & $1+x+x^3+x^7+x^{15}+x^{31}+x^{63}+x^{82}+x^{100}+x^{127}+x^{152}+x^{165}+x^{201}+x^{255}+x^{296}+
x^{305}+x^{331}+x^{403}$ & $19$\\\hline
(511,259) & $1+x^{31}+x^{42}+x^{93}+x^{115}+x^{217}+x^{240}+x^{261}+x^{360}+x^{420}+x^{450}+x^{465}$ &
$13$\\\hline
(819,435) & $1+x+x^3+x^7+x^{15}+x^{31}+x^{63}+x^{127}+x^{204}+x^{255}+x^{409}+x^{511}$ & $13$\\\hline
(819,447) & $1+x+x^3+x^7+x^{15}+x^{31}+x^{63}+x^{127}+x^{204}+x^{255}+x^{350}+x^{409}+x^{511}+x^{584}+x^{701}$
& $16$\\\hline\hline
\end{supertabular}
\end{center}
\begin{figure}[hbt]
\centering\includegraphics[angle=270,width=4in]{fer-gf2-127-84.eps}
\caption{\label{fig:fer-gf2-127-84}Frame error performance of the
$(127,84)$ cyclic code}
\end{figure}
\noindent Throughout the paper, it is assume that the codewords are
transmitted across a noisy communication channel with BPSK
modulation and at the receiving end is the modified
Belief-Propagation decoder which approximates the
Maximum-Likelihood decoder~\cite{Patent}.
Figure~\ref{fig:fer-gf2-127-84} shows the frame-error-rate (FER)
performance of the $(127,84)$ cyclic code, which is a code which
does have cycles of length 4. Neverthless, the performance of
this code is outstanding and, at $10^{-3}$ FER, it is within
$0.2$dB of the sphere-packing-bound constraint for binary
transmission.
\begin{figure}[hbt]
\centering\includegraphics[angle=270,width=4in]{fer_255_175.eps}
\caption{\label{fig:fer-gf2-255-175}Frame error performance of the
$(255,175)$ codes}
\end{figure}
Figure~\ref{fig:fer-gf2-255-175} shows the performance of two
$(255,175)$ codes, one constructed using our method and one an
irregular computer generated code. We can see that our code, which
achieves a coding gain of around $0.4$dB compared to the
equivalent irregular code, performs approximately withinr $0.15$dB
of the sphere-packing-bound constraint for binary transmission.
\begin{figure}[hbt]
\centering\includegraphics[angle=270,width=4in]{fer_341_205.eps}
\caption{\label{fig:fer-gf2-341-205}Frame error performance of the
$(341,205)$ codes}
\end{figure}
Our construction method can produce LDPC codes with high minimum
distance and therefore they do not suffer from error-floor.
Figure~\ref{fig:fer-gf2-341-205} demonstrates the performance of
our $(341,205)$ code, which is inferior to the equivalent
irregular code in the low signal-to-ratio region, but the
irregular code exhibits early error-floor due to its low minimum
distance.
\section{Conclusions}\label{con}
A method of constructing binary cyclic codes from the finite-field
transform (Mattson-Solomon) domain is able to produce a large
number of codes which have high minimum-distance and code-rate.
These codes have sparse parity-check matrix and thus are
applicable as LDPC codes. Due to their cyclic property these LDPC
codes have $n$ parity-check equations instead of $n-k$ equations
as in the case of random LDPC codes. With these extra parity-check
equations to iterate with, the performance of the iterative
decoder is improved.
In designing cyclic LDPC codes of length $n$, our new method
allows one to increase the $d_{min}$ of the code by combining
additional irreducible factors of $1+z^n$ which, in turn, reduces
the sparseness of the parity-check matrix. The ability to control
the sparseness of the parity-check matrix is a trade-off against
the minimum distance of the code.
Simulation results have shown that the our cyclic codes have
outstanding performance which are superior to the equivalent
irregular LDPC codes. The high $d_{min}$ of these codes ensures
the absence of an early error-floor in their performance.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,224 |
\section{Introduction}
\label{sec:intro}
The last decade of observations by untargeted optical time-domain surveys has unveiled a population of exceptionally bright optical transients, with peak magnitudes of M~$\lesssim-21$, labeled ``superluminous supernovae" \citep[SLSNe;][]{qu11,gy12}. There are two broad classes: SLSNe~II, which exhibit signatures of hydrogen in their optical spectra, and SLSNe~I (or SLSNe~Ic), which do not. SLSNe~II are heterogeneous in both luminosity and host environment \citep[][]{gy09,le15,sc16}, and the bulk of the population consists of events displaying signatures of interaction similar to classical SNe IIn \citep[e.g., SN2006gy;][]{smi07}, with a smaller contribution from intrinsically bright events reminiscent of classical SNe II \citep[e.g., SNe 2008es, 2013hx;][]{mi09,ge09,in16}.
Hydrogen-poor SLSNe \citep[][]{qu11,gy12,in13} are the most common type of SLSN, although they are still intrinsically rare compared to other SN types \citep[91$^{+76}_{-36}$ SNe yr$^{-1}$ Gpc$^{-3}$,][]{pr17}, and spectroscopically linked to normal or broad-lined type Ic SNe \citep{pasto10}. Their characteristic spectroscopic evolution and connection with massive star explosions have been a distinctive trait of SLSNe~I, together with their typical explosion location in dwarf, metal-poor and star-forming galaxies \citep[e.g.][]{lu14,le15,an16,pe16,ch17}.
This relatively simple description and overall SLSN~I paradigm is now becoming more complex. The original definition of SLSNe~I has been loosened in terms of the magnitude threshold \citep[e.g.,][]{in13,lu16,pr17},
and the existence of two subclasses of SLSNe~I, with a difference in the speed of their light-curve evolution (slow- versus fast-evolving), is debated. The concept that all SLSNe~I originate from the same progenitor scenario and/or explosion mechanism, with differences principally driven by variations in ejecta mass \citep{ni15}, has been challenged by their spectroscopic evolution \citep{in17}.
This complexity is increasing with new data releases from the Palomar Transient Factory \citep{2017arXiv170801623D} and the Pan-STARRS1 Medium Deep Survey \citep{lu17}, and with future data releases from the Dark Energy Survey (DES) Supernova Program \citep[DES-SN;][]{dessn}. Moreover, the next generation of telescopes will likely bring an order of magnitude increase in sample sizes: \citet{sco16} predicted 10,000 SLSNe~I will be discovered by the Large Synoptic Survey Telescope (LSST), and \citet{in17b} calculate a discovery rate of $\sim$200 SLSNe~I during the five-year deep field survey of the European Space Agency {\it Euclid} satellite, with the potential for further discoveries up to $z\sim6$ \citep[e.g.][]{yan17,smi17} with the \textit{Wide-Field InfraRed Survey Telescope} (\textit{WFIRST}). Mapping the spectroscopic evolution of such a large number of targets will be challenging to achieve.
In this paper, we introduce a new statistical approach to defining and classifying SLSNe that could be used in current (e.g., DES, PTF, and Pan-STARRS1) and forthcoming large samples of SLSN~I candidates. The technique neither assumes an arbitrary magnitude limit, nor relies on a detailed spectroscopic evolution, and is developed using the published data set of SLSNe~I. We also present an analysis, based on statistical tools, showing the existence of two subclasses from their spectrophotometric evolution. These two methodologies, combined together, will characterize and classify a homogeneous sample of SLSNe~I, as well as select those events that can be used as cosmological standardizable candles \citep[see][]{in14}.
\section{Sample and methodology}\label{sec:sgp}
\subsection{Sample selection}\label{ss:sample}
\label{sec:sample}
We begin by constructing our SLSN~I sample from published events in the literature. We require a well-observed sample, with at least six epochs of photometric data between phases of $-15$\,d to $+30$\,d, of which at least one must lie between $-15$\,d and $0$\,d, sampling a synthetic box filter at rest-frame 4000\,\AA.
This synthetic filter was introduced in \citet{in14}, together with a second box filter at 5200\,\AA, which are designed to sample two regions of SLSN~I spectra that are dominated by continuum, with few absorption features. In this paper, all phases are given in rest-frame days relative to peak brightness in our synthetic 400\,nm filter.
We further select our SLSN~I sample to only contain events with a single main peak in the light curve, as otherwise there can be ambiguity in identifying the main peak and measuring phases.
We therefore exclude those events with a \lq secondary peak\rq\/ \citep[e.g. iPTF13dcc, iPTF15esb;][around 5\% of the literature SLSNe~I]{vr17,yan17b}, where a \lq secondary peak\rq\/ is defined as a peak, before or after the brightest (main) peak, showing an absolute magnitude difference of $\lesssim 1$ mag with respect to the main peak. We also remove events with H$\alpha$ in their spectra \citep[e.g., iPTF13ehe;][]{yan15}, another 5\% of SLSNe~I in the literature. Note we do not exclude {\it a priori} SLSNe~I with early-time \lq bumps\rq\/ (see Table~\ref{table:datano}).
Around 50\% of the published SLSN~I events in the literature pass our requirements, and these can be found in Table~\ref{table:data}, while those rejected are reported in Table~\ref{table:datano} together with the criterion by which they are removed from the sample.
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{filters2.pdf}
\caption{The synthetic box filters at 4000\,\AA\ and 5200\,\AA\ (solid lines), together with the closest Johnson bands ($B$ and $V$ respectively; dashed lines), and the closest SDSS filters ($u$ and $g$; dash-dot lines). The box filters have widths of 800\,\AA\ and 1000\,\AA\ respectively.}
\label{fig:bands}
\end{figure}
We $k$-correct all published photometry for each object to our two synthetic filters (400\,nm and 520\,nm), calculated with the \textsc{snake}\footnote{https://github.com/cinserra/S3} software package \citep{in16}, which also estimates the uncertainties on the $k$-corrections. The synthetic filters, together with the standard Bessell $B$/$V$ filters and Sloan Digital Sky Survey (SDSS) $u$/$g$ filters, are shown in Figure~\ref{fig:bands}.
Applying $k$-corrections from arbitrary observed filters over $0.1<z<4.0$ to $B$ and $V$ instead of the two box filters would result in a difference of $-0.03$\,mag at peak epoch (both $400-B$ and $520-V$), and $0.01$\,mag ($400-B$) and $0.05$\,mag ($520-V$) around 30 days after rest-frame maximum. When observed spectra for a specific SLSN are not available, we use an average SLSN~I time-series spectral energy distribution (SED), based on the methodology of \citet{pr17}. We correct all our observed photometry for Milky Way extinction prior to $k$-correction using the prescriptions of \citet{sf11}, but make no corrections for extinction in the SN host galaxies, which is believed to be small \citep[e.g.][]{ni15,le15}. Finally, we convert the rest-frame apparent magnitudes into absolute magnitudes using a flat $\Lambda$CDM cosmology, with $H_{0}=72$\,km\,s$^{-1}$\,Mpc$^{-1}$, $\Omega_\mathrm{matter}=0.27$, and $\Omega_{\Lambda}=0.73$.
\begin{deluxetable*}{l|c}
\tablecaption{SLSNe~I that did not pass our selection criteria.\label{table:datano}}
\tablehead{
\colhead{Selection criterion} & \colhead{SLSNe~I}}
\startdata
Light-curve sampling & SN2006oz (1), SN2007bi (2), SNLS06D4eu (3), SNLS07D2bv (3), PTF09cwl (4), PTF09atu (4),\\
& PTF10hgi (5), PS1-10awh (6), DES14X3taz (7), DES15E2mlf (8), SSS120810:231802-560926 (9),\\
& LSQ14bdq (10), LSQ14an (11), SN2017egm (12) \\
Double peak & iPTF13dcc (13), iPTF15esb (14)\\
Late time H{$\alpha$} & iPTF13ehe$^\dagger$ (15), iPTF16bad (14)\\
Chauvenet's criterion & DES13S2cmm (16), PS1-14bj (17)\\
\enddata
\tablecomments{References: 1. - \citet{le12} - 2. \citet{gy09} - 3. \citet{ho13} - 4. \citet{qu11} - 5. \citet{in13} - 6. \citet{cho11} - 7. \citet{smi16} - 8. \citet{pan17} - 9. \citet{ni14} - 10. \citet{ni15a} - 11. \citet{in17} - 12. \citet{bose17} - 13. \citet{vr17} - 14. \citet{yan17} - 15. \citet{yan15} - 16. \citet{papa15} - 17. \citet{lu16} \\
$\dagger$ Used as a test in the four observables parameter space (4OPS)}
\end{deluxetable*}
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{GP_paper_v3.pdf}
\caption{Upper panel: Gaussian process (GP) fitting of SN2015bn, with the \textsc{george} machine learning library compared to a 3rd-order polynomial (dotted line). Center and lower panels: two other example GP fits. The center panel is SN2010gx, a well-sampled event, and the lower panel is PTF12dam, a sparsely-sampled event. In all panels, the data are shown as filled circles, the GP fits are solid lines, and the uncertainty in the fit is the shaded area.}
\label{fig:GP}
\end{figure}
\subsection{Gaussian processes regression}\label{ss:gp}
\label{sec:GP}
To estimate the SLSN~I brightness around peak epoch ($-15\leq\mathrm{phase}\leq30$), where literature SLSNe~I have the most coverage, we investigate several techniques to fit the available data set, including polynomial fitting \citep[as in][]{in14}, and interpolation using Gaussian processes (GPs) regression \citep{bishop,gps}. GPs are already successfully used in several areas of astronomy \citep[e.g.][]{maha08,way09,gibson12} and in the context of supernovae \citep[e.g.][]{kim13,scalzo14,2017arXiv170901513D}. In supernova analyses, GPs can be used for Bayesian regression and mean function fitting with a non-parametric approach, e.g. broad-band light-curves, bolometric light-curve, temperature and radius evolution, as well as line profiles in spectra.
A GP assumes that our variable $y$ is randomly drawn from a Gaussian distribution with a certain mean and covariance ($y\sim f(\mu,\sigma^2)$), and then considers $N$ such variables drawn from a multivariate Gaussian distribution computing their joint probability density. This is $Y\sim f(m,K)$, where $Y = (y_1, ...,y_N)^T$, $m = (\mu_1, ...,\mu_N)^T$ is the mean vector (transposed) and $K$ is the covariance matrix, called the \lq kernel\rq\/, having a $N\times N$ dimension of the form
\begin{center}
\[
K=
\begin{bmatrix}
\sigma_1^2 & \dots & cov(y_1,y_N) \\
\vdots & \ddots & \vdots \\
cov(y_1,y_N)& \dots & \sigma_N^2\\
\end{bmatrix}.
\]
\end{center}
In the case of uncorrelated variables $cov(y_i,y_j)=0$, this becomes a diagonal matrix. This approach provides for a probability distribution over functions and it allows us to compute a confidence region for the underlying model of our variable. A GP is hence specified by its mean function and kernel.
To reach convergence of the distribution, the kernel hyper-parameters are optimized using the maximum likelihood method. We test several kernels to find the most suitable covariance function for the objects in our SLSN sample. The kernels we consider are an exponential sine squared kernel (suited for periodic functions), a linear kernel, a polynomial kernel and a squared exponential kernel. As a basic metric for quality of fit we compute the $\chi^2$, comparing the mean of the GP posterior distribution to our data. We find that the \lq Matern-3/2\rq\ kernel gives the best fit. The kernel can be written in terms of radius, $r = | a_i - a_j |$, as:
\begin{equation}
f(r)= c^{2} \, \left( 1 + \frac{\sqrt{3}\,r}{t} \right) exp\left( - \frac{\sqrt{3}\,r}{t} \right),
\end{equation}
where $c$ and $t$ are the best fit hyper-parameters.
We use the Python package {\sc george} \citep{george} to perform our GP regression. Figure~\ref{fig:GP} (top) shows a comparison between the Matern-3/2 kernel and a third-order polynomial fit. The GP fit is a better representation of the data with respect to the polynomial, meaning a lower $\chi^2$.
Figure~\ref{fig:GP} also shows examples of the GP fits to 400\,nm data, while all the fits are reported in Appendix~\ref{sec:GPfits}. As expected, when the data are sparse the fit uncertainties are larger (bottom panel). A key advantage of the GP fitting is that the fit uncertainties, as a function of phase, are naturally produced by the GP fitting. Accurate uncertainties will be important for the analysis in this paper. We further refer to \citet{sdm2014} for a more in-depth analysis of advantages and drawbacks of GPs in astronomy.
We fit our entire SLSN sample
from -15\,d (in the 400\,nm band) to +55\,d. Whenever the data or GP uncertainties on the magnitude are smaller than those reported by the survey that discovered the SLSN, we replace them with the typical survey photometric uncertainties at the redshift of the SN (e.g., for the 400\,nm band, PS1 averaged uncertainties at $z <0.25$ and $0.25<z<0.60$ are 0.02 and 0.06\,mag, while the DES uncertainties at $z<0.60$ and $0.60<z<0.90$ are 0.04 and 0.05\,mag)\footnote{Derived from SLSN PS1 and DES papers listed in Tables~\ref{table:data}~\&~\ref{table:datano} and from DES private communications.}. The resulting fit magnitudes are reported in Table~\ref{table:data}, together with their uncertainties.
\begin{deluxetable*}{lcccccccccc}
\tabletypesize{\scriptsize}
\tablewidth{0pt}
\tablecaption{Sample of SLSNe~I. Associated errors in parentheses.\label{table:data}}
\tablehead{
\colhead{SN} & \colhead{$z$} &\colhead{Ref.$^a$} & \colhead{Type } & \colhead{$M$(400)$_{\rm 0}$} & \colhead{$M$(400)$_{\rm 0}$-$M$(520)$_{\rm 0}$}
& \colhead{$\Delta M_{20}$(400)} & \colhead{$\Delta M_{30}$(400)} & \colhead{$M$(400)$_{\rm 30}$-$M$(520)$_{\rm 30}$} & \colhead{$v_{\rm 10}$\,\,$^b$} & \colhead{ $\dot{v}$\,\,$^c$}
}
\startdata
Gaia16apd &0.102&1&fast & -21.87 (0.04)&-0.18 (0.07) &0.69 (0.06)&1.30 (0.08)&0.28 (0.07)&13200 (2000)&50 (70)\\
PTF12dam&0.107&2& slow &-21.70 (0.07) &-0.23 (0.06) &0.31 (0.09)&0.40 (0.18)&-0.09 (0.12)&9500 (1000)&5 (50)\\
SN2015bn &0.114&3& slow &-21.92 (0.02) &-0.15 (0.04) &0.36 (0.05)&0.66 (0.06)&0.04 (0.07)&9000 (1000)&25 (45)\\
SN2011ke& 0.143&2&fast & -21.23 (0.09) & 0.04 (0.13) &0.89 (0.09)&1.63 (0.09)&0.59 (0.03)&17800 (2000)&280 (75)\\
SN2012il & 0.175&2&fast & -21.54 (0.10)& -0.02 (0.11) &1.39 (0.17)&1.65 (0.17)&0.48 (0.13)&17500 (2000)&242.5 (100)\\
PTF11rks & 0.190&2&fast & -20.61 (0.05) &0.20 (0.06)&0.87 (0.07)&2.11 (0.11)&1.16 (0.15)&17200 (2000)&110 (100)\\
SN2010gx& 0.230&2&fast & -21.73 (0.02)& -0.11 (0.02) &0.76 (0.03)&1.55 (0.04)&0.53 (0.03)&18500 (2000)&260 (100)\\
SN2011kf& 0.245&2&fast &-21.74 (0.15) &- &0.52 (0.18)&1.03 (0.21)&-&-&-\\
LSQ12dlf& 0.255&2& fast &-21.52 (0.03) &0.05 (0.03)&0.76 (0.04)&1.27 (0.11)&0.57 (0.10)&15600 (1000)&145 (32.5)\\
LSQ14mo &0.256&4,5&fast &-21.04 (0.05) &-0.08 (0.04) &1.30 (0.14)&2.23 (0.14)&0.61 (0.02)&14000 (1800)&130 (82.5)\\
PTF09cnd& 0.258&2&fast &-22.16 (0.08) &- &0.71 (0.14)&1.04 (0.12)&-&-&-\\
SN2013dg& 0.265&2&fast &-21.35 (0.05) &-0.26 (0.08)&1.03 (0.06)&1.90 (0.08)&0.56 (0.10)&15700 (1000)&265 (55)\\
SN2005ap& 0.283&2&fast &-21.90 (0.04) &- &0.85 (0.09)&-&-&-&-\\
PS1-11ap &0.524&2& slow &-21.78 (0.03) &-0.25 (0.03) &0.35 (0.04)&0.67 (0.05)&-0.06 (0.05)&8800 (2500)&15 (87.5)\\
PS1-10bzj& 0.650&2&fast &-21.03 (0.06) &0.15 (0.11)&1.23 (0.32)&1.82 (0.26)&0.94 (0.25)&-&-\\
iPTF13ajg &0.740&6&fast &-22.42 (0.07) &-0.29 (0.09) &0.19 (0.10)&0.45 (0.10)&-0.11 (0.09)&15500 (2000)&100 (100)\\
PS1-10ky & 0.956&2&fast &-22.05 (0.06) &-0.06 (0.07)&0.61 (0.07)&1.20 (0.07)&0.25 (0.06)&-&-\\
SCP-06F6& 1.189&2&fast &-22.19 (0.03) &- &0.57 (0.15)&0.96 (0.30)&-&-&-\\
PS1-11bam & 1.565 & 7,8& - &-22.45 (0.10) & - & 0.36 (0.14)&0.60 (0.14)&-&-&-\\
\cutinhead{Test}
iPTF13ehe &0.343&9&slow &-21.58 (0.04) & -0.29 (0.05) &0.08 (0.06)&0.22 (0.06)&-0.10 (0.05)&10600 (2300)&-\\
\cutinhead{Outliers}
PS1-14bj &0.521&10& - &-20.44 (0.05) & 0.22 (0.06) &0.03 (0.07)&0.07 (0.07)&-0.01 (0.07)&-&-\\
DES13S2cmm &0.663&11& - &-20.41 (0.05) & -0.24 (0.06) &0.83 (0.09)&0.96 (0.13)&0.23 (0.14)&-&-\\
\enddata
\tablecomments{$^a$ References for observed light curves and spectra: 1. \citet{kan17} -- 2. \citet{in14} and references therein -- 3. \citet{ni16} -- 4. \citet{ch17a} -- 5.\citet{le15b} -- 6. \citet{vr14}
-- 7. \citet{berger12} -- 8. \citet{lu17}
-- 9. \citet{yan15} -- 10. \citet{lu16} -- 11. \citet{papa15} .\\
$^b$ km\,s$^{-1}$, measured from \ion{Fe}{2} $\lambda$5169.\\
$^c$ km\,s$^{-1}$\/ day$^{-1}$, $\Delta v/\Delta t$, where $\Delta t$ is measured from +10 to +30\,d using \ion{Fe}{2} $\lambda$5169.}
\end{deluxetable*}
\subsection{Line velocity measurements}\label{ss:lv}
\label{sec:velocities}
Our final measurements concern the SLSN spectra, and in particular the estimation of the photospheric velocities. In core collapse SNe, \ion{Sc}{2} $\lambda$6246, and subsequently \ion{Fe}{2} $\lambda$5169, are the best available proxies to trace the photospheric evolution due to their small optical depth \citep{branch02}. In SLSN~I spectra, \ion{Sc}{2} is not visible, but \ion{Fe}{2} has been measured using several different approaches \citep[e.g.][]{in13,ni15,liu17}.
We measure the line velocities in all spectra from +10 to +30\,d. Before +10\,d, the ionic component is weak \citep{in13} and contaminated by \ion{Fe}{3} \citep{liu17}. When spectra around $10\pm2$\,d and $30\pm2$\,d are not available for a given SLSN, we estimate the velocity from a least-squares fit of the measurements from nearby epochs and account for an additional uncertainty in the estimate using $\sigma_{\rm final} = \Delta t / \sigma_{\rm measure}$,
where $\Delta t$ is the phase difference (in seconds) between the estimated and measured epochs. Only 12 out of the 19 SLSNe have spectra covering the wavelength region and the time-frame of interest (see Table~\ref{table:data}).
We measure the velocity from fits to the absorption minima. We experiment with three different profiles for the fits (Gaussian, skewed Gaussian, and Voight), finding an overall agreement among the three profiles. We repeat the measurements several times for each feature, changing the continuum levels to better estimate the uncertainties. We then use the mean of the measurements as the final value, and the standard deviations as the uncertainty estimate; the values are tabulated in Table~\ref{table:data}. This approach has been widely used in measuring the line velocities of SLSNe~I, with consistent results \citep[e.g.][]{pasto10,cho11,in13,smi17}.
We have also cross-checked our velocity measurements using a GP approach (Section~\ref{sec:GP}), fitting the wavelength region from 4800\,\AA\ to 5200\,\AA, and finding the local minimum. We use the same Matern-3/2 kernel as with the light curve fitting. As would be expected, given the greater flexibility, the GP fits usually return a $\chi^2$ comparable to or lower than the standard fitting procedure, with the advantage of improving fitting/deblending multi-component profiles without a biased prior knowledge of the feature types and numbers (e.g., absorptions/emissions with P-Cygni profiles, Lorentzian or Voight wings, etc.). However, to properly evaluate the uncertainties we need a kernel function based on the uncertainties in the flux of the spectra. This information is missing for $\sim$40\% of our data set, and hence we use the profile fitting to allow for consistency in the approach.
Our measurements and line evolutions are broadly in agreement with those of \citet{liu17}, those reported in the papers listed in Table~\ref{table:data}, and the photospheric velocities reported by the modeling of \citet{maz16}. The only noticeable difference is in the velocity of Gaia16apd, where we found a decrease of $\sim$1000\,km\,s$^{-1}$\ over the phase range analyzed. This is due to the presence of galaxy lines that make the fit more complicated and biased by the choice of the number of components to analyze.
The \ion{Fe}{2} $\lambda$5169\,\AA\ velocity measurement is reported as that at +10\,d, or $v_\mathrm{10}$ (km\,s$^{-1}$), while the velocity evolution over the phase range from 10\,d to 30\,d post-peak is $\dot{v}= -\Delta v/ \Delta t$ (km\,s$^{-1}$\,day$^{-1}$), in a similar fashion to that used in SNe Ia \citep{be05}.
\section{The Four Observables Parameter Space (4OPS)}\label{sec:4ops}
\begin{figure*}
\center
\includegraphics[width=0.9\textwidth]{SLSNe_4OPS_final_GP_bw4.pdf}
\caption{The Four Observables Parameter Space (4OPS) plot. Top left: peak luminosity of our literature SLSN~I sample in the 400\,nm band (\bluemag{0}) versus the decline in magnitude over 30 days $\Delta\bluemag{30}$. Top right: \bluemag{0} versus color at $+30$\,d (\ensuremath{\bluemag{30}-\redmag{30}}). Bottom left: peak color (\ensuremath{\bluemag{0}-\redmag{0}}) versus $\Delta\bluemag{30}$. Bottom right: \ensuremath{\bluemag{0}-\redmag{0}}\ versus \ensuremath{\bluemag{30}-\redmag{30}}. 99.72\% confidence bands from the Bayesian linear regression are also shown for each panel. The four plots allow the definition of a main population of SLSN I regardless of the peak luminosity. A SLSN~I will belong to the main population if it falls in the confidence interval for the blue areas in the A and D panels or, alternatively, in the orange areas of the B and C panels. 4OPS can also be used to predict missing observables for a SLSN.}
\label{fig:4OPS}
\end{figure*}
\begin{deluxetable*}{ccccccccc}
\tablewidth{0pt}
\tablecaption{Fit parameters and statistical results of the four observables parameter space relations\label{table:fit}.}
\tablehead{4OPS Panel &$x$ & $y$ &\colhead{N (objects)}& \colhead{$\beta$} & \colhead{$\alpha$} & \colhead{$\sigma$} & \colhead{Variance} & \colhead{Pearson}}
\startdata
A & $\Delta M$(400)$_{\rm 30}$ & $M$(400)$_{\rm 0}$ & 18 & $-22.62\pm0.21$& $0.75\pm0.15$ & $0.32\pm0.23$ & $0.10\pm0.05$ & $0.82\pm0.11$ \\
B & $M$(400)$_{\rm 30}$ - $M$(520)$_{\rm 30}$ & $M$(400)$_{\rm 0}$ & 14 & $-22.02\pm0.13$& $1.14\pm0.26$ & $0.29\pm0.24$ & $0.08\pm0.05$ & $0.87\pm0.11$ \\
C & $\Delta M$(400)$_{\rm 30}$ & $M$(400)$_{\rm 0}$ - $M$(520)$_{\rm 0}$ & 14 & $-0.30\pm0.11$& $0.16\pm0.07$ & $0.14\pm0.12$ & $0.02\pm0.01$ & $0.62\pm0.24$ \\
D & $M$(400)$_{\rm 30}$ - $M$(520)$_{\rm 30}$ & $M$(400)$_{\rm 0}$ - $M$(520)$_{\rm 0}$ & 14 & $-0.22\pm0.04$& $0.03\pm0.09$ & $0.08\pm0.08$ & $0.01\pm0.01$ & $0.84\pm0.13$ \\
\enddata
\tablecomments{Least squares fits for a Bayesian weighted linear regression with weighted errors both in $x$ and $y$ of the form $\eta$ = $\beta$ + $\alpha\times x'$ + $\epsilon$, where $x = x' + x_{\rm err}$ and $y = \eta + y_{\rm err}$. The $\sigma$ is the standard deviation (in $y$) of this fit. The last column gives the Pearson correlation coefficient $r$.}
\end{deluxetable*}
Having assembled our SLSN~I data sample in Section~\ref{sec:sample}, we now investigate methods for classifying the events based mainly on photometric data. Our light curve fitting has provided smooth time-dependent light curves in the 400\,nm and 520\,nm filters, together with realistic estimates of the uncertainties at interpolated epochs. We select various observational quantities for which we can explore the classification potential, based on the inferred decline rates (cf. the $\Delta M_{15}$ quantities used in studies of SNe Ia), peak magnitudes, and colors. Specifically, we use
\begin{enumerate}
\item The peak luminosity in the 400\,nm filter, \bluemag{0};
\item The decline in magnitudes in the 400\,nm filter over the 30 days following peak brightness, $\Delta\bluemag{30}$;
\item The $400-520$ color at peak, \ensuremath{\bluemag{0}-\redmag{0}};
\item The $400-520$ color at $+30$ days, \ensuremath{\bluemag{30}-\redmag{30}}.
\end{enumerate}
These four observational quantities are tabulated in Table~\ref{table:data}, and we visualize the relationships between them in Figure~\ref{fig:4OPS}, which we term the \lq four observables parameter space\rq\ (or 4OPS).
\begin{figure*}
\center
\includegraphics[width=0.31\textwidth]{SLSNe_4OPS_test1c.pdf}
\includegraphics[width=0.31\textwidth]{SLSNe_4OPS_test2c.pdf}
\includegraphics[width=0.31\textwidth]{SLSNe_4OPS_test3c.pdf}
\caption{The Four Observables Parameter Space (4OPS) plot predictions. Left: if information is available only for panel A, the prediction in panel D is the black shaded area of. Middle: if information for panels A and B is available, the predictions in panels C and D is shown (solid black line). Right: for panels A and C, the prediction in B and D is shown (solid black line).}
\label{fig:4OPSprediction}
\end{figure*}
We use a Bayesian approach to evaluate a linear regression of these parameters, allowing for the uncertainties in both the $x$ and $y$ variables (see Section~\ref{ss:gp}) and any intrinsic scatter \citep[see][for further details]{ke07}. This process uses Bayesian inference that returns random draws from the posterior. Convergence to the posterior is performed using a Markov chain Monte Carlo with $10^5$ iterations. We note that the probability of retrieving a slope $\alpha=0$ from the random draws in our fits is 0\%, i.e., the correlations are highly significant.
As a final quality check before the definition of a likelihood area we use Chauvenet's criterion, which is a statistical procedure that provides an objective and quantitative method for data rejection based on the standard deviation of a distribution. It compares the absolute value of the difference between the suspected outliers and the mean of the sample divided by the sample standard deviation.
We apply that in the light-curve and color evolution space, and identify two such outliers, DES13S2cmm and PS1-14bj, which for example have a $\delta y_{\rm (theory - measure)} / \sigma$ of $\sim$5 (DES13S2cmm) and $\sim$7 (PS1-14bj) for the peak-decline relation (see Panel A of Figure~\ref{fig:4OPS}), and hence greater than the Chauvenet threshold of 2.20, valid for a sample of 18 objects (cf. Table~\ref{table:data}).
Using the weighted linear regression fits on our final sample (see Table~\ref{table:data}) and their standard deviation ($\sigma$), we define a 3$\sigma$ region as the likelihood area in which our sample of SLSNe~I lie (see Table~\ref{table:fit} for the fit parameters). We use this area to define the photometric properties of a SLSN~I events -- by construction, it includes all SLSNe~I in our sample with sufficient photometric sampling and that do not exhibit peculiarities such as clear interaction or double-peaked light curves.
In Figure~\ref{fig:4OPS}, the two sets of diagonal panels (i.e., panels A/D and panels B/C) each display information from all four variables, and thus contain complementary information; the adjacent panels (both horizontally and vertically) contain ancillary information. The adjacent panels can also be used to predict the values (with a 3$\sigma$ uncertainty) of the other two missing variables. For example, if the peak luminosity (\bluemag{0}) and luminosity decline ($\Delta\bluemag{30}$) are measured, the SLSN colors at peak and at $+30$ days can be reliably estimated (left of Figure~\ref{fig:4OPSprediction}). If we have information on three out of four observables, we can predict the fourth one with a higher precision, namely 3$\sigma$ of the strongest among the two correlations using the missing observables (middle and right in Figure~\ref{fig:4OPSprediction}). This could be useful in current and future surveys when a band, or measurement, is not sampled due to redshift, cadence or adverse weather.
A SLSN~I belonging to the main population has to be in both the blue regions in Figure~\ref{fig:4OPS} (A and D panels) or, alternatively, in both the two orange regions perpendiculars to the blue (B and C panels). This allows us to define the bulk
of the SLSNe~I without any arbitrary magnitude limit. As a consequence, the hypersurfaces can be used to identify/classify objects as SLSNe~I in future and current surveys \citep[e.g. PS1, PTF and DES SN sample][Angus et al. in prep.]{lu17,2017arXiv170801623D} when a spectroscopic evolution is not available. However, other peculiar objects can populate the same parameter space (see next two paragraphs) and hence at least a spectrum might be warranted (see Section~\ref{sec:vel}).
We note that the outliers represent 5\% of the full literature SLSN~I sample and 9\% of those passing the selection criteria in Section~\ref{ss:sample}. This implies that the definition of a SLSN~I is achieved with a confidence level of at least 90\% which, according to Dixon's Q test, is statistically significant.
To test this approach, we measured the same quantities for a literature SLSN~I showing an H{$\alpha$}\ profile and slower light curve after 150 days, namely iPTF13ehe \citep[][]{yan15}.
We find iPTF13ehe lies in all the areas and close to three slow-evolving SLSNe~I (see Figure~\ref{fig:4OPStest} and Table~\ref{table:data}). In this case we infer that iPTF13ehe, despite its late-time behavior, is consistent with a main population SLSN I.
Figure~\ref{fig:4OPStest} also shows a SLSN~I outlier (PS1-14bj) together with other literature SNe of all types, corrected for Galactic and host extinction. Only SLSNe IIn, such as SN2006gy, and potentially some super-Chandrasekhar (SC) type Ia SNe (e.g., SN2009dc) populate the same part of the parameter space as SLSNe I. However, the spectra of these classes appear quite different from SLSNe~I. Normal H-poor SNe, such as type Ia, Ic and broad-line Ic fall below the likelihood area in panel A, as they are fainter and do not evolve as fast as the relationship would predict. Moreover, type Ic and broad-line Ic SNe have redder colors than SLSNe~I at peak and 30 days (Panel D of Figure~\ref{fig:4OPStest}), as expected from the spectroscopic evolution of SLSNe~I that at 30 days resembles a type Ic SN at peak \citep{pasto10,in13}. Furthermore, a superluminous tidal disruption event \citep[e.g. ASASSN-15lh,][]{le16}, which has also been suggested to be a SLSN~I \citep[e.g.][]{dong16}, falls outside the likelihood area since it is brighter and bluer than the main population of SLSNe I.
\begin{figure}
\center
\includegraphics[width=\columnwidth]{SLSNe_4OPS_testSN2.pdf}
\caption{Our SLSNe I test object (iPTF13ehe), the outliers PS1-14bj and DES13S2cmm, and various other SN types in the parameter space of Figure~\ref{fig:4OPS}. The only type of SN that could appear in the same region as SLSNe~I are the very bright type IIn (SLSNe~IIn) and possibly superchandra type Ia (Ia SC). Data references: type Ia SN2011fe \citep{brown14,pereira13}; type Ic SN1994I \citep{richmond96}; type broad-line (BL) Ic SN1998bw \citep{pat01}; tidal disruption event (TDE) ASASSN-15lh \citep{dong16,le16}; hydrogen-rich interacting SLSN IIn S2006gy \citep{smi07}, type Ia-CSM/IIn SN2005gj \citep{aldering06,prieto07}, superchandra (SC) type Ia SN2009dc \citep{tauben11}}.
\label{fig:4OPStest}
\end{figure}
\begin{figure*}
\center
\includegraphics[width=18cm]{SLSNe_vel_vs_phot4.pdf}
\caption{Fe~{\sc ii} $\lambda$5169 velocities at $+10$\,d versus various photometric observables. A partitional cluster analysis using K-means methodology finds the same two classes of SLSNe~I in each plot. BIC curves are reported for each cluster in the first and fourth row. In the fourth column we show the histogram of the velocities. The bin dimension has been chosen accordingly with Sturges' formula, which accounts only for data size and it is optimal for smaller data sets.}
\label{fig:velobs}
\end{figure*}
\section{Photospheric velocity versus photometric observables}\label{sec:vel}
As discussed in the introduction, it is unclear if both fast- and slow-evolving
SLSNe~I are two different manifestations of the same explosion mechanism, or intrinsically different transients \citep[in terms of combination of powering mechanisms and/or progenitor scenario, e.g.][]{gy12,ni15,in17}. Combining photometric and spectroscopic measurements of a SN class can in principle reveal important physical information, or the existence of classes and/or subclasses of transients \citep[e.g.][]{hamuy03,be05,claudia17b}. To investigate we employ a similar method to that used for SNe Ia \citep{be05}, using our photospheric velocity measurements from Section~\ref{sec:velocities} (Table~\ref{table:data}).
We initially compare the \ion{Fe}{2} velocity at +10\,d with our photometric observables in Figure~\ref{fig:velobs}, using the 4OPS variables and the decline rate over 20 days in the 400\,nm filter ($\Delta\bluemag{20}$), easier to measure for high-redshift and/or fast-evolving objects. We then perform a partitional cluster analysis, for each combination shown in Figures~\ref{fig:velobs}, using the K-means methodology.
Such a cluster analysis separates samples in groups of equal variance, minimizing the within-cluster sum of squared criterion to find the centroids of the groups \citep{kmeans}. To choose the ideal number of clusters, we initially applied a Gaussian Mixture Model using an expectation-maximization algorithm \citep{fraley2002}, and subsequently we searched for the ideal number of clusters (the K in K-means and ranging from 1 to 9) through the Bayesian Information Criterion \citep[BIC,][]{bic}, which has a probabilistic interpretation \citep{kass1995}. That creates a function ($f({\rm K})$) dependent on the number of clusters. The highest absolute value of the second derivative of the function returns the ideal number of clusters. We show the results of this test in Figure~\ref{fig:velobs}.
This statistical approach reveals the presence of two well-separated clusters in all of the spectroscopic/photometric observable parameter spaces (see Figure~\ref{fig:velobs}), allowing a natural grouping of SLSNe that can be investigated using other relationships. We also run a Monte Carlo Markov Chain with $10^5$ iterations, allowing the data to vary inside the uncertainties. We retrieve similar clusters between 95\% and 97\% of the cases, with the only exception in the peak luminosity versus the \ion{Fe}{2} velocity at +10\,d, in which we retrieved similar clusters in $\sim$90\% of the cases.
On the basis of the results of the cluster analysis, we then further investigate the spectroscopic evolution of the two clusters comparing their initial photospheric velocity with their photospheric evolution. The comparison shown in Figure~\ref{fig:vdot} suggests that the higher the photospheric velocity, the larger the gradient and hence the faster the velocity decreases. We also perform a partitional cluster analysis on the measurements of Figure~\ref{fig:vdot} finding again the same two clusters of the above analysis. Therefore, combining the information of the cluster analysis together with those of Figures~\ref{fig:velobs} and \ref{fig:vdot}, we outline the following SLSN~I subclasses:
\begin{enumerate}
\item A first group (\lq Fast\rq), consisting of SLSNe~I with fast-evolving light curves, a broad range of peak colors ($-0.3\lesssim\ensuremath{\bluemag{0}-\redmag{0}}\lesssim0.2$), and a broad color evolution with red objects becoming redder faster (Panel D of Figure~\ref{fig:4OPS}). They have higher expansion velocities ($v_{10}\gtrsim12000$\,km\,s$^{-1}$) and large velocity gradients.
\item A second group (\lq Slow\rq), consisting of SLSNe~I with slow-evolving light curves, a narrow range of peak colors, and a color evolution of only 0.2\,mag in 30 days following peak brightness (panels in Figure~\ref{fig:4OPS}). They have lower expansion velocities compared to the fast group ($v_{10}\lesssim10000$\,km\,s$^{-1}$), and a low velocity gradient.
\end{enumerate}
We can distinguish between these two subgroups of SLSNe~I by combining almost any photometric observable with a spectrum taken around +10\,d. We applied this to iPTF13ehe, our test SLSN~I that passed the cut in the 4OPS (see Figure~\ref{fig:4OPS}) and hence defined as a main population SLSN, and found that to be clustered with the Slow group.
\begin{figure}
\center
\includegraphics[width=\columnwidth]{SLSNe_vdot.pdf}
\caption{Left panel: \ion{Fe}{2} $\lambda$5169 velocity evolution from +10 to +30 days ($\dot{v}$) versus \ion{Fe}{2} $\lambda$5169 velocities at $+10$\,d. Right panel: histogram of the velocity evolution, with the bin dimension chosen using Sturges' formula, which accounts only for data size and it is optimal for smaller data sets.}
\label{fig:vdot}
\end{figure}
\section{Implications for SLSNe~I}\label{sec:dis}
\label{sec:discussion}
In this paper we have used various photometric measurements of SLSNe~I to identify a main population of SLSN events, which remains the primary purpose of our work. In this section, we discuss the implications of our results.
\subsection{Consequences of the four observables parameter space}
The parameter space of Figure~\ref{fig:4OPS} may in principle be used to help physically understand the explosion mechanisms of these transients. Relationships between the change in luminosity in one band (panel A) and the color evolution (panel B), and the broad band behavior of a SN at a given epoch (panels C \& D) are broad reflections of the physical properties of the SN ejecta (i.e. diffusion time, opacity and temperature). The correlation shown within panel A is likely a reflection of the diffusion time of the ejecta -- similar to that seen within SNe Ia \citep{phillips93}. However, as we do not consider the light curves of SLSNe~I to be radioactively driven \citep[e.g.][]{ni13,in17}, for SLSNe~I this correlation is unlikely to be solely related to the mass of the ejecta produced.
On the other hand, the tight relation presented in panel D of the 4OPS (see Figure~\ref{fig:4OPS} and Table~\ref{table:fit}) between the color observed at peak and at +30\,d suggests that these two are correlated by one physical parameter only, which could be the temperature or the radius.
A wide range of possibilities have been postulated to explain SLSN~I luminosities, such as the rapid spin-down of a magnetar \citep[e.g.][]{kb10,wo10,de12}, the interaction between the SN ejecta and the surrounding CSM previously ejected from the massive central star \citep[e.g.][]{ch12,woosley17}, and a pair instability explosion \citep[e.g.][]{kozyreva17}.
For all three models there are multiple parameters at play in the production of the overall luminosity and color evolution of the transient. As such, the linking of an observed behavior to a dominant physical parameter becomes complex. For example, a magnetar magnetic field strength, spin-period and explosion ejecta mass are all factors in the luminosity evolution \citep{kb10}, whilst within the interaction model, the mass of the ejecta, its density profile and distribution coupled with the mass, distance and volume of the CSM shell must be considered \citep[e.g.][]{ch13,woosley17}.
At present there are no model predictions that aptly describe the broad-band behavior shown in Figure~\ref{fig:4OPS}. This could be due to the fact that the diffusion time not only depends upon the ejected mass, but also on the ejecta velocity and its opacity to optical-wavelength photons. Opacities, in particular, are determined by the temperature and composition of the ejecta and therefore may vary with time during the SLSN~I evolution \citep{maz16}. Thus, explaining the relation observed within any of panels A, B and C of the 4OPS with any of the above suggested scenarios is not trivial. Nonetheless, the presence of the relations hints that a pure radiative transfer in the SN ejecta should be at play and any model that aims to explain such SNe should take these observational properties into account.
The primary purpose of our work is to define a main population of SLSNe~I. Within the context of a magnetar powered event, favored by several observational studies \citep[e.g.][]{ch15,ni15,smi16,in16a},
the behavior observed could be explained by the magnetar energy injection always occurring at a certain time (e.g., shortly after the explosion). Such a scenario would allow the diffusion time of the ejecta to be comparable to the time needed for the SN to reach peak luminosity (i.e., panel A). An injection this early would also provide the rotational energy needed to overwhelm the initial thermal energy of the SN explosion, and hence provide the energy source which drives the main peak of the light curve \citep{kb10}. Such a population of engine driven SLSNe~I would be composed of brighter objects that are overall bluer and more slowly evolving than dimmer events. Moreover, redder objects in this main population would evolve faster in both luminosity and color as inferred from Figure~\ref{fig:4OPS}, panel D, and previously shown by \citet{in14}.
Objects outside the main population of SLSNe~I, but with a luminosity evolution that could be explained by an inner engine, have already been found \citep[e.g.][ and the Dark Energy Survey collaboration, private communications]{gr15,ka16}, but their spectrophotometric evolution is different to SLSNe~I, and this is reflected in Figure~\ref{fig:4OPStest}. These objects could belong to a similar engine-driven transient family, only here the injected energy and/or the timescale over which it is injected would be somewhat different.
\subsection{Consequences of the cluster analysis and photopsheric velocity evolution}
The analysis of Section~\ref{sec:vel} returns two subclasses, which are outlined in terms of spectrophotometric evolution during the first 30 days from peak, as well as a distinct photospheric velocity behavior. In the context of the magnetar scenario,
the almost flat velocity evolution exhibited by the slow subclass, and their overall slower velocity, suggests that the photosphere reaches the internal shell created by the magnetar bubble \citep[see eq. 7 in][]{kb10} earlier than in the fast subclass. Fast SLSNe~I with a high photospheric velocity also have a larger velocity gradient. This could be related to additional energy deposited by the magnetar into the ejecta \citep{de12}. Such energy is a function of the spin period \citep[see eq. 1 in][]{kb10}, and faster rotation would imply more energy and hence faster ejecta.
The almost frozen spectral evolution exhibited after peak by slow SLSNe~I \citep{ni16,in17} supports our findings and the idea that the photosphere reaches the inner shell earlier than in the fast events. In addition, the slow events show forbidden lines earlier, suggesting they become optically thin earlier. This could be explained by a high amount of oxygen \citep[$\sim10$M$_{\odot}$,][]{je17}, whose recombination could hasten the process.
Generally, differences in properties in SN subclasses, and hence between the slow and the fast, could be due to different degrees of mixing or geometry \citep{le15b,in16a,le17}, which is true regardless of the source of additional luminosity. The photospheric velocity depends on the the optical depth, for which the heavy elements with higher line opacities are the prime contributor.
A more efficient mixing of heavy elements in the outer ejecta might result in an initial higher photospheric velocity, whereas a less efficient one could lead to slow velocity and constant temperature. The gradient evolution may also be explained in terms of the ejecta density structure or of the photosphere moving to non-mixed layers of the ejecta.
\subsection{Consequences for standardization}
Figure~\ref{fig:4OPS} can be used to define a homogeneous population of events, with 90\% of previously classified SLSNe I meeting our definition, for further study in a cosmological context. This can be used for current (e.g,. DES, Pan-STARRS) and new generation (e.g., LSST, {\it Euclid} and \textit{WFIRST}) surveys to identify/classify (also in real time) SLSNe~I. This would allow identification even without a spectroscopic evolution, important given relatively limited spectroscopic resources. Moreover, with only a spectrum at +10 days, the identification can be confirmed as well as distinguishing between the fast and slow subgroups. This, together with Figure~\ref{fig:4OPS}, strengthens further the possibility to use them as standardizable candles at high-redshift. The next logical step is to discern the two subclasses only with photometry and/or to move this analysis to shorter wavelengths (e.g., the rest-frame ultraviolet) allowing higher redshifts to be studied.
\software{snake \citep{in16}, george \citep{george}}
\acknowledgments{We acknowledge support from EU/FP7-ERC grant 615929. We thank two anonymous referees, a statistician and an astronomer, for their suggestions that have improved the paper. CI thanks Stuart Sim for stimulating discussions, as well as the organisers and participants of the Munich Institute for Astro- and Particle Physics (MIAPP) workshop ``Superluminous supernovae in the next decade". }
\bibliographystyle{apj}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,147 |
package com.svbio.cloudkeeper.testkit;
import java.util.concurrent.ConcurrentLinkedQueue;
import java.util.concurrent.Executor;
/**
* {@link Executor} implementation that runs all tasks in the current thread upon invocation of {@link #executeNext()}
* or {@link #executeAll()}.
*/
public final class CallingThreadExecutor implements Executor {
private final ConcurrentLinkedQueue<Task> pendingTasks = new ConcurrentLinkedQueue<>();
private static final class Task {
private final long submissionTimeMillis;
private final StackTraceElement[] stackTrace;
private final Runnable runnable;
private Task(Runnable runnable) {
submissionTimeMillis = System.currentTimeMillis();
stackTrace = Thread.currentThread().getStackTrace();
this.runnable = runnable;
}
@Override
public String toString() {
StringBuilder builder = new StringBuilder(256);
builder.append("Task submitted at time ").append(submissionTimeMillis);
if (stackTrace.length > 0) {
for (StackTraceElement element: stackTrace) {
builder.append("\n\tat ").append(element);
}
}
return builder.toString();
}
}
@Override
public void execute(Runnable command) {
pendingTasks.add(new Task(command));
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public boolean hasPendingTasks() {
return !pendingTasks.isEmpty();
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/**
* Runs the next task, in the current thread.
*
* @throws java.util.NoSuchElementException if there are no more pending tasks
*/
public void executeNext() {
Task task = pendingTasks.remove();
task.runnable.run();
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/**
* Runs all pending tasks in the current thread, until the queue of pending tasks is empty.
*/
public void executeAll() {
while (hasPendingTasks()) {
executeNext();
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{"url":"https:\/\/hackaday.io\/project\/9077-trs-80-model-1-on-a-pic32","text":"0%\n0%\n\n# TRS-80 Model 1 on a PIC32\n\nTRS-80 Model I emulated on a PIC32MX processor; VGA, PS\/2, and SD for tape and disk images. Oh, and glourious cassette sound.\n\nSimilar projects worth following\n12.4k views\nTRS-80 Model I emulated on a PIC32MX processor. It provides VGA video and PS\/2 keyboard so as to be usable with commonly available hardware to-date (well, PS\/2 keyboards are becoming rare, but it works with a USB-to-PS\/2 adapter as well).\n\nI did this project to keep myself occupied while recovering from some surgery in 2015, for which I would have limited mobility for about a month. I didn't think I'd be up to doing bench work, so I used some existing PCBs to allow me to focus on the firmware, which I could do lying down (both literally and figuratively). I used a UBW32 (from Schmalzhaus) as a CPU 'breakout board' and also a UBW32-MCC (from Dontronics) to provide the VGA, PS\/2 keyboard, SD card, and power connectors.\u00a0 Later, I\u00a0supported another board:\u00a0 the Olimex Duinomite-mini (and reportedly the Duinomite with the IO board).\u00a0 The Olimex boards are much easier to come by, inexpensive, and ready to use out-of-box.\u00a0 But no color :(.\u00a0 But, hey, the TRS-80 Model I was a monochrome, anyway!\u00a0 (I just like the green screen effect.)\n\nQ.v. a little demo from early on running the famous dancing demon:\n\n\"If I have seen farther than others, it is because I have stood on the shoulders of giants.\" -- Newt.\n\nThere was a lot of existing code that I relentlessly twisted to my own twisted porpoises, so it's appropriate for me to give a shout-out to those who wittingly or unwittingly helped in some way.\n\nProps to Geoff Graham, who allowed me to pilfer his Maximite code for the video and keyboard 'drivers'. And also indirectly to Lucio Di Jasio, for describing the clever 'SPI and DMA as a video generator' technique, which was used in Geoff's project (and by extension, mine). I am very jealous that I can't claim to have invented that myself! Brilliant!\n\nProps also to Tim Mann, a developer of software for the TRS-80 (actual) back in the day, and also creator of the 'xtrs' emulator for unixian systems. I used the Z80 CPU emulation code (which I modified a bit for my purposes). (It, in turn, is derived from another source which I cannot name, or else I'd cite it as well. Clarendon Hill? Either way, the license seems functionally public domain.)\n\nProps also to Matthew Reed, author of TRS32, an excellent (albeit non-open-source) emulator for Win32 systems. I use it sometimes for comparison, and also the TRSTools are quite useful for extracting files from floppy images.\n\nProps also to all those others who helped kept the memory of the TRS-80 alive; otherwise I would have had scratch to work with when starting this out.\u00a0 In particular those who have supplied rare software and manuals, so that I could realize exotic things like the 'high-resolution' graphics HRG1B modification, and the Orchestra 80 sound.\n\nThanks also to those who have helped by indulging me in testing builds on boards that I do not have in my possession to get those working.\u00a0 Debugging by text messaging is even less efficient than printf() style debugging.\n\nAnyway, I've derived a lot of entertainment from it.\u00a0 I can't believe I'm still hacking on this 3 years and augmenting it 3 years hence.\u00a0 It's kind of remarkable what we thought was cool in those days looking back from the present.\n\n### trs80sd-20180727a.zip\n\n****added hrg syscalls feature**** SD card filesystem contents; unzip into the root of a microSD (up to 32 Gb), to have requisite files in place for the emulator to be useful. Firmware images and the boot loader exe in 'doc'. These are not required for the emulator of course (the image has to be burned onto the chip!), but I put them in here for convenience to causally interested parties, to avoid downloading the source, setting up the toolchain, and building. Operation of the bootloader exe (Windows) is intuitively obvious. It's HID-based, so no drivers are needed. It does not appear to be usable on XP alas, so you'll need win 7 and up. There is also a 'README.txt' in the 'doc' folder which explains things in more detail.\n\nx-zip-compressed - 29.41 MB - 07\/27\/2018 at 19:12\n\n### trs80sd-20180526a.zip\n\n****added bitmap screen cap feature**** SD card filesystem contents; unzip into the root of a microSD (up to 32 Gb), to have requisite files in place for the emulator to be useful. Firmware images and the boot loader exe in 'doc'. These are not required for the emulator of course (the image has to be burned onto the chip!), but I put them in here for convenience to causally interested parties, to avoid downloading the source, setting up the toolchain, and building. Operation of the bootloader exe (Windows) is intuitively obvious. It's HID-based, so no drivers are needed. It does not appear to be usable on XP alas, so you'll need win 7 and up. There is also a 'README.txt' in the 'doc' folder which explains things in more detail.\n\nx-zip-compressed - 29.40 MB - 05\/26\/2018 at 17:20\n\n### trs80sd-20180515a.zip\n\n****adds screen cap capability**** SD card filesystem contents; unzip into the root of a microSD (up to 32 Gb), to have requisite files in place for the emulator to be useful. Firmware images and the boot loader exe in 'doc'. These are not required for the emulator of course (the image has to be burned onto the chip!), but I put them in here for convenience to causally interested parties, to avoid downloading the source, setting up the toolchain, and building. Operation of the bootloader exe (Windows) is intuitively obvious. It's HID-based, so no drivers are needed. It does not appear to be usable on XP alas, so you'll need win 7 and up. There is also a 'README.txt' in the 'doc' folder which explains things in more detail.\n\nx-zip-compressed - 29.40 MB - 05\/16\/2018 at 02:09\n\n### trs80sd-20180510a.zip\n\n****adds traps for Level I, and sundry config enhancements**** SD card filesystem contents; unzip into the root of a microSD (up to 32 Gb), to have requisite files in place for the emulator to be useful. Firmware images and the boot loader exe in 'doc'. These are not required for the emulator of course (the image has to be burned onto the chip!), but I put them in here for convenience to causally interested parties, to avoid downloading the source, setting up the toolchain, and building. Operation of the bootloader exe (Windows) is intuitively obvious. It's HID-based, so no drivers are needed. It does not appear to be usable on XP alas, so you'll need win 7 and up. There is also a 'README.txt' in the 'doc' folder which explains things in more detail.\n\nx-zip-compressed - 29.36 MB - 05\/11\/2018 at 03:32\n\n\u2022 1 \u00d7 Olimex Duinomite-MINI Alternative board; no soldering. If you go this route, you only need the SD card, and optionally the audio amplifier.\n\u2022 1 \u00d7 2 GB microSD card this project is barely useable without cassette and floppy disk images. I think 2 GB is the max that the MicroChip firmware can support. EDIT: no, I have used it successfully with 8 and 32GB cards.\n\u2022 1 \u00d7 Audio amplifier; e.g. LM386 and speaker for convenience, if you want sound. Commodity board via eBay.\n\u2022 1 \u00d7 UBW32 If you're gong to do it my original way, you'll need this and all subseqently listed parts. CPU breakout board; Schmalzhaus, various retailers\n\u2022 1 \u00d7 UBW32-MCC connectors board; dontronics UBW32-MCC-PCB-Letter\n\n# Summary\n\nOK, so I implemented bitmap screen capture.\u00a0 (I also fixed some bugs since last post regarding the Help screen)\n\n# Deets\n\nI had recently implemented a Screen Capture feature that captured the TRS-80 screen in text mode.\u00a0 It was a bit of work to get that implemented -- mostly because of infrastructure needs (e.g. generating file names, etc.) -- so I decided to make my life easier then by just doing a text-mode capture.\u00a0 That was easy, since the TRS-80 is a character device, but that mode doesn't capture hypervisor screens, color, or HRG graphics.\u00a0 So doing a bitmap capture was left for a separate activity.\u00a0 Well, I guess now was the time for that.\u00a0 (Oh, along the way I fixed some Help screen bug reported by a user Mikael \u2609. Bonnier -- thanks so much for the detailed info; that really makes it easier to fix.)\n\nThe TRS-80 is principally a monochrome device, but I support some color boards, and so I did want to be able to have color output.\u00a0 There's a boatload of image formats, but I chose to 'be conservative in what I send', and settled quickly on Windows DIB format as an easy-to-generate-and-widely-accepted format for output.\n\nDIB itself supports many forms of data representation, from monochrome 1-bit-per-pixel to 32-bits-per-pixel.\u00a0 The TRS-80 was natively monochrome, so 1bpp was natural, but I did want to capture my glorious colour extensions, so I wanted a color form.\u00a0 4bpp made a lot of sense, but then I'd have to fiddle with a color look-up table ('CLUT'\/palette) and I just didn't want to fiddle with that, so I decided to unconditionally emit a 24bpp image.\u00a0 This simplified coding, though it made file size much bigger than it strictly needed to be.\u00a0 But who cares?!\u00a0 You've got huge SD to store it!\u00a0 So I carried on with 24bpp in all cases for now.\n\nSo I started coding.\u00a0 At first I got some images that were plausible, but nonsensical:\n\nexamining these I could tell that I had flubbed up byte offsets into the screen buffers and some other bugs.\u00a0 Hacking a little further, I got:\n\nThis looks sensible, but I know it's not right because the colors are wrong.\u00a0 Red and Blue were switched, so I fixed that:\n\nNow,! we're there!\u00a0 I also added in support for the HRG mod, which is technically a separate overlay frame buffer:\n\nwho can forget sinus?\n\nBut one thing to note is that these bitmaps are in the native resolution of the TRS-80 -- i.e. 384x192 -- and does not consider that those pixels are not square.\u00a0 For most anticipated uses (e.g. documentation), this is probably fine, but strictly it is not aspect-ratio-correct.\u00a0 I leave it as an exercise for the user to translate in their own programs to do that correction.\u00a0 E.g. here is a native cap:\n\nbut here is how it looks on a real screen, as fixed up in Photoshop:\n\nThe needed transformation is simple:\u00a0 2x horizontal and 3x vertical.\u00a0 I could have done this in the emulator code, but it would have made the file size even bigger, and incurred more CPU, so I left that as a post-production exercise when needed.\n\nThe file writing activity seems to take a lot of time.\u00a0 On my UBW32 device, a screen cap takes about 3 sec(?!?!!).\u00a0 So understand that the entire system will be non-responsive during that time.\n\nThe default key binding for screen cap is aF8, but it can be altered in the config file, as with the others:\n\ntextcap= F8 #capture text screen buffer (ansi)\ntextcapu= sF8 #capture text screen buffer (unicode)\nbmpcap= aF8 #capture bitmap screen buffer\n\n# Future\n\nMaybe I'll implement 4-bit indexed color, and 1-bit monochrome formats.\u00a0 This should conserve the I\/O bandwidth, making of snappier snaps.\u00a0 The images currently are 200k, but a monochrome would be 9k, and a 4bbp color would be 36k, so there's a real savings.\u00a0\u00a0If it turns out to save execution time, then...\n\n\u2022 ### Screen Capture 001\n\nFor a while I've wanted to be able to capture various outputs of the emulator to files for offline use.\u00a0 My prior filesystem corruption problem took precedence over any features that involved writing to the filesystem, but since that got resolved, I feel more free to implement some of these other things.\n\nMost of these capture features are imagined to dump to an automatically named file based on a prefix and sequence number so as to avoid overwriting existing stuff, and keep it ordered.\u00a0 This would require some machinery to be created find the highest sequence number to use within the context of a prefix and for a given directory.\u00a0 Since directory enumeration is rather slow, I wanted to keep a persistent 'index' to give a hint as to where to start the numbering.\u00a0 When a new file names is to be generated, it can start at the value in the 'index', and then bump the number.\u00a0 The index is not required, but it speeds up the generation process by giving a start point that is likely to work, thereby avoiding a bunch of directory traversal.\u00a0 Since I had just finished implementing a config file reader, and which has writing capability, I decided to simply reuse that format for the 'index' file.\n\nSince the TRS-80 display is a character array (as opposed to a pixel array), it is very straightforward to dump the video buffer to a text file.\u00a0 However, there are a couple quirks:\n\n1. the TRS-80 (allegedly due to a bug) oftentimes puts chars 0x00-0x1f instead of 0x40-0x5f in the video buffer.\u00a0 Visually, this is not confusing, because they render the same, but from a binary standpoint of course this looks like gibberish.\u00a0 I fixup those character ranges so they read sensibly in a text editor.\n2. the character array implicitly word-wraps at col 64, so I add linefeeds at the end-of-line so again it looks sane in a text editor.\n3. the character set of the TRS-80 contains a few unusual characters (e.g. arrows), and then of course all the semi-graphics characters.\u00a0 These aren't going to render at all without some help.\n\nThe first two quirks were easily coded around, but for the third I found a font which contains the TRS-80 Model I semi-graphics characters (actually they have the full TRS-80 Model I character set).\u00a0 This is the AnotherMansTreasureMIB64C2X3Y.ttf TrueType font, to be had at:\nhttp:\/\/www.kreativekorp.com\/software\/fonts\/trs80.shtml\n(along with many others).\n\nTo pull this off, I have another screen capture mode which emits a UCS-2 LE file, and which translates the semi-graphics and special characters into the Unicode range e000-e0ff.\u00a0 So, for those screen captures, you can open them in some editor that allows you to choose the font, and you can now see the TRS-80 screen in it's normal state.\u00a0 Also, since this is text, instead of a bitmap, you can cut-paste the text for your cut-and-pasting pleasure.\u00a0 If your editor has the ability to 'embed fonts' (e.g. Word, LibreOffice), then they can be viewed correctly on other machines even if they don't have the particular font installed.\n\nHere's a few sample captures:\n\nI have to post these as png because I can't embed the fonts on the web such that plaintext would make sense, but as you can see, I highlighted some of the text (the blue stuff) so that you can more easily see where the character boundaries are located in the textual screen capture.\u00a0 (The green and black obviously is just my specifying the text foreground and background colors, for visual effect).\n\nAnyway, I imagine this will be helpful for when I get around to producing some sexy documentation.\u00a0 If nothing else, I can stop using my phone cam to take pics of the screen for these logs!\n\nHere are a few others for your retrocomputing viewing pleasure.\u00a0 This is how we did it in the 1970's:\n\nThe screen cap function is bound by default to F8 for plaintext, and shift-F8 for unicode translation (for use with the special font).\u00a0 Like the other bindings,...\n\n\u2022 ### Config File and Features Controlled Thereby\n\nI've long wanted a config file for this project, but never got around to actually implementing one.\u00a0 I decided to give it a go.\u00a0 I found a useful opensource (apache 2) INI file reader project: \"minIni\", which is designed for embedded (and moreover already had IO bindings to the MDD filesystem library I am using), so this made support much easier with not having to write the parser myself.\n\nMy main motivation for the config file was to specify some useful parameters such as:\n\n\u2022 auto load a floppy so I don't have to go through the hypervisor every boot\n\u2022 specify an alternative ROM to use, instead of always Level II BASIC\n\nOther less critical but nifty parameters are:\n\n\u2022 control how long the splash screen art is displayed\n\u2022 support alternative splash screens with ease\n\u2022 change foreground\/background colors on the color board\n\u2022 alternative key bindings for various hypervisor functions\n\nThere is been a placeholder file in the root of the distribution SD card image for some years now, named 'trs80.cfg'.\u00a0 Up to now, it was zero length, but now it has various entries coincidentally set to the baked-in defaults.\u00a0 It should be self-evident how it works, but there are some caveats:\n\nThe file contents should be treated as case-sensitive.\u00a0 'Splash' is not the same as 'splash', and changing it will not result in the desired setting having effect.\n\nRelated in particular, is specifying key bindings.\u00a0 This is a limited feature, but you can assign the 'F' keys to various functions listed in the file.\u00a0 They must be named like 'F10', not\u00a0'f10'.\u00a0 The keys may be preceded by any of three modifier characters: 's' for shift, 'c' for control, and 'a' for alt.\u00a0 So, 'sF10' means 'shift-F10' and 'scaF9' means 'shift-control-alt-F9'.\u00a0 There are also a couple special keys named:\u00a0 'Pause', 'SysRq', 'PrtScn'.\u00a0 I don't really anticipate using the keybinding feature that much myself, but I've always been concerned about the 'Pause', 'SysRq', 'PrtScn' buttons, because keyboard manufacturers have a tendency to move those and sometimes make them hard to get to (sometimes requiring yet another 'shift' key).\u00a0 Also, if you have a habit of accidentally hitting the reset button, maybe you want to make that harder by also requiring 'alt' or something on it.\n\nThe ROM feature is for loading a custom ROM.\u00a0 There are two baked-in ROM images, referenced by the well-known (and case-sensitive!) name of 'level1' and 'level2'.\u00a0 Otherwise, it is assumed to be a filename of a file in the 'rom' directory of the SD card.\u00a0 Also, a custom ROM cannot easily have cassette traps of the same sorts as I have implemented for 'level2', and plan for 'level1', but if you know your ROM is derived from either the level1 or level2 rom (e.g. System80, or maybe something you hacked yourself), and that the cassette routines are in exactly\u00a0the same place, then you can 'force=level2' to make those traps be applied, anyway.\u00a0 (Later, I plan to implement some 'syscall'-esque mechanism for truly custom ROMs; e.g. perhaps supporting a CP\/M build).\n\nThere will be other features added over time that will likely extend the file's content beyond what I have described here.\u00a0 E.g. 'media' only preloads the first disk drive at present, but I'll probably extend that for all four, and also the two tape decks.\n\n\u2022 ### Minor Cassette Enhancement\n\nThe cassette I\/O functionality has, since the beginning, been realized with traps in the ROM routines that are serviced on the host side of the emulator.\u00a0 This saved me the trouble of trying to emulate the pulses with the correct timing for the Z-80 code, and had the side benefit of being some 160x faster than native cassette.\n\nA user had reported that EDTASM did not seem to do anything useful when trying to save and load programs from the cassette, and it was hypothesized that it might be doing it's own I\/O directly, without using the ROM routines (and thereby my traps did no good).\u00a0 A quick disassembly verified that this was the case.\u00a0 In fact, it also has it's own copies of the keyboard, video, and printer device drivers, and it doesn't use any ROM routines!\n\nUpon closer inspection of the disassembly, I noticed that the routines were very similar to the same ones in ROM.\u00a0 At a source level, they were identical except for a very few omissions that were pertinent to the BASIC environment.\u00a0 One would think this is wasteful, since they are right there in the ROM, but it occurred to me that EDTASM may have been produced \/before\/ the ROM was created, and that the device drivers may have been platform-specific code given to Microsoft to integrate into their BASIC codebase to result in what became \"Level II BASIC\".\n\nIn any event, because the code was so similar, it occurred to me that it might be possible to simply patch EDTASM to forward the key parts of the cassette implementation to the ROM, and then it would benefit from the existing traps.\n\nThis plan was underway until I noticed a snag:\u00a0 while at a source level, the code is identical, the machine code is not.\u00a0 In particular, there is a state variable stored in RAM that is placed differently between the EDTASM and the ROM.\u00a0 (a software copy of port 0xff).\u00a0 For most of the cassette implementation, this doesn't matter, but it did for the cassette on\/off, and for the video functions which are also on port 0xff.\n\nI could have said 'Hail, Mary', and just hoped for the best -- I suspect it would have been OK -- but then again it might not have.\u00a0 After a while, it dawned on me that I could patch most of the code -- the data I\/O, and leave the cassette on\/off code unmodified, and avoid there being changed assumptions about the location of the state variable (in ROM, at 4028, in EDTASM, at 403d).\n\nIn the emulator, I had already virtualized the cassette relay bit, and also the drive select latch at 37e4, but I had never provided implementation.\u00a0 So, this update provides implementation for those two things, allowing me to make my patched EDTASM.\n\nI tested it out by entering a small program (the example from the manual), saving the source to tape, clearing memory, loading the source back in, assembling and saving the binary to another tape.\u00a0 The resulting tape images looked fine, so I conclude that works as-expected.\n\nI placed my modified EDTASM in the SD image under the name 'edtasm-p.cas' ('p' for 'patched').\u00a0 You load it just as you would the original.\u00a0 It is derived from version 1.2.\n\n\u2022 ### Orchestra 80\/85 Support\n\nThe PWM has been in-place for quite some time (and is used for the 'cassette sound' feature that many games use), but I had never gotten around to implementing the Orchestra 80 support, even though it should be simple.\u00a0 Part of the reason was that I didn't have any software or files for it, and part was just that I had forgotten about it.\n\nSince I had a little time today, I decided to do a little research on the web, and found a copy of the ORCH85\/CMD and a few music files.\u00a0 Also, I found a copy of the manual for Orch 80.\n\nI have no idea how to run this program, and it seems I would need a minor in musicology to understand a lot of the stuff in the transcription setting, but I think I can manage loading a file and playing it.\u00a0 It turns out there is a command, 'GET', which loads, 'scores', and plays the music files, so that is good enough for my testing, I think.\n\nThe hardware was trivially simple:\u00a0 two I\/O ports (0xb9 and 0xb5 -- seems unusual) write an 8-bit sample to a DAC for left and right channels.\u00a0 The rest is all done in software.\u00a0 So I coded a connection from those I\/O ports to the existing PWM.\n\nFor the Olimex board, it required a little thinking:\u00a0 that board only has one PWM channel.\u00a0 I decided to simply average the two channels' values in that case.\u00a0 Since the channels are written one at a time, I needed to store the last written value for each channel, and average those to create the effective setting for the PWM.\n\nThe initial sound output sounded pretty bad, but was recognizable.\u00a0 Could it have really been this bad back in the day?\u00a0 Or was it my crappy amp and speaker (a couple bucks on ebay based on an LM386, and an equally cheap speaker element probably intended for a toy)?\u00a0 Or was it the output filter on the boards?\u00a0 Maybe a combination of all these things?\n\nI figured it would be best to start, if possible, with just one note.\u00a0 Ideally generating a sine wave, but I couldn't figure out how to get that fancy.\u00a0 But I did figure out that I could enter the music of 'W0' which meant 'a whole note of middle C'.\u00a0 Then I captured that signal.\u00a0 It looked like crap (sorry, I should have captured the scope trace, but I didn't), so there definitely was a weird signal going into the audio amp.\n\nI added a little testing code to write all the values sent to a file, so I could analyse the data stream.\u00a0 The data at first glance did seem to look like it probably would have generated that waveform, so I started to guess that it is a signed\/unsigned problem.\n\nI loaded the file into a waveform editor as a 'raw' file, and started with 'unsigned' (since that is the way I was interpreting it), and visually the waveform did look like the scope trace.\u00a0 I re-imported it as 'signed' and then it looked much more sane (with an apparent fundamental, and some lower amplitude harmonics riding on top of that).\n\nSo, changing to unsigned is just a simple matter of an offset of 128, and that seemed to do the trick.\u00a0 The scope trace looked sane, and the output was improved.\u00a0 I wouldn't go so far as to say it sounds great, but it was not as bad as it was.\u00a0 Maybe it would sound even better with a better amp, speaker, and filter than I am using.\n\nThe copy of the orch85 software I have on-hand is for disk, so I created a floppy image 'orch85.dmk' which has that, and some music files.\u00a0 If you want to try the software, know that you need to specify some parameters on startup:\n\n'speedup' indicates that a speedup modification was installed on the TRS-80.\u00a0 Answer 'no' to this.\u00a0 (much as I would like to speedup, the 80 MHz PIC32MX doesn't have enough free cycles to do it).\n\nThen it asks for number of voices 3\/4\/5.\u00a0 I suggest picking '4' since that is the default and seems to be what most files are configured for.\n\nLastly, it asks if you want to 'save program'.\u00a0 This creates a copy of orch85\/cmd that has the above options...\n\n\u2022 ### Bugthzs 002\n\nThere has been a known issue for quite a while that cassette writes can cause filesystem corruption on the SD card.\u00a0 Usually, I approach bugs from a 'surely it's something I did' standpoint (and in truth, I prefer if it's something I did, because then I'm in a position to fix it), but sometimes it's not, and you have to be prepared that you might have to prove it one way or the other.\n\nLong story short:\u00a0 there appears to be a bug in the Microchip MDD library specifically when opening a file in the \"r+\" mode, and when the file length is 0.\u00a0 If you do, you will incur file system corruption upon subsequent writing.\u00a0 If the file is of non-zero length, then \"r+\" works as expected (and thank goodness for that).\n\nI am using the latest libraries, to wit 1.4.4, which interestingly contains a fix to \"r+\" mode (though apparently unrelated to this issue).\n\nAnyway, because of the nature of the problem (only with 0 length files), what I do is translate \"r+\" to \"w+\" when the file length is zero.\u00a0 This incurs some otherwise unnecessary file operations on opening, and has some consequences regarding position in the filesystem and timestamps (because in \"w+\" mode the file is deleted and then re-created), but I think this is minor enough to disregard - especially relative to alternative:\u00a0 filesystem corruption.\n\nSo hopefully this is the end of this issue.\u00a0 It was a long and painful journey.\n\n\u2022 ### HRG1B Support\n\nThere were a very few 'high-resolution' modifications available for the TRS-80 Model I.\u00a0 Some were downright weird, such as the 80-GRAPHIX board, which worked though the character generator.\u00a0 One of the more sane ones was the HRG1B, which was produced in The Netherlands .\u00a0 It worked by or'ing in video dots from a parallel memory buffer, and this buffer was sized at the TRS-80's native resolution of 384x192.\n\nThis was on my 'to-do- list of things to implement, but [harald-w-fischer], actually had one of these on-hand from time long past.\u00a0 He also had manuals, some of the stock software, and some extensions he his self wrote!\u00a0 This was needed to be able to faithfully reproduce the behaviour, and some of my initial assumptions were proven false by it.\n\nSince my emulator already has framebuffer(s) at the native resolution, my thinking was that this would be easy to implement.\u00a0 However, I was mistaken.\u00a0 It was mostly\u00a0easy to implement, but there were several challenges.\n\n\u2022 merging\nAt first I planned to directly set bits into the 'master' frame buffer(s) when writes to the HRG1B happened, but after disassembling the 'driver', it was clear this wouldn't work.\u00a0 For one, there needs to be supported reads from the HRG buffer that don't reflect merging, so a separate backing buffer would be needed to do this.\u00a0 Second, the HRG supports a distinct on\/off capability, so again the separate buffer would be needed, but also the case of when to merge the buffers arises.\u00a0 Lastly, the computational overhead of doing the merging on-demand caused overload and required some legerdemain.\n\u2022 memory\nWhereas the Olimex Duinomite-Mini board (which Harald is using) can easily accommodate the 9K frame buffer required, my color UBW32-based board is just too memory constrained.\u00a0 The color boards already have 3 frame buffers, and this makes a fourth.\u00a0 Initial experiments were done on the Olimex, where the memory was not a problem, but I really wanted it to work on color, too.\n\nThe first experiment I tried was to just see if there would be enough time to merge the image during the vertical blanking interval.\u00a0 Since I am upscaling the TRS-80 native 384x192 to 768x576, and then padding with blanking around to get to 800x600, there is a bunch of vertical retrace time where I could do the buffer merging.\u00a0 Maybe the processor is fast enough to do it on-the-fly?\n\nWell, no, it's not.\u00a0 The buffers are small (9K), and the operation is simple (or'ing on the hi-res buffer onto the main buffer), and the operation is done on a word basis on word-aligned quantities, but it's not enough.\u00a0 The major problem is that the vertical blanking interval is driven in software by a state machine that is in turn driven by an Interrupt Service Routine (ISR) at the horizontal line frequency.\u00a0 The vertical state machine is mostly line counters for the vertical 'front porch', sync period, and 'back porch'.\u00a0 So, although the vertical blanking period is a long time in toto, it is comprised of a bunch of short times.\u00a0 The naive implementation requires all the work to be done actually during a horizontal line period.\u00a0 In my first iteration, I wound up dividing the work into chunklettes, spreading out between several horizontal line intervals.\u00a0 I generated a test pattern, and this scheme appeared to work.\n\nHaving received the HRG1B driver and sample apps from Harald, I naturally had to immediately disassemble them.\u00a0 I have to say, the driver is a little piece of art.\u00a0 The goal is to extend the existing BASIC with some new keywords, and what they chose to do was hook a routine that is sometimes used during the basic execution process (it is rst10h, used to skip whitespace to the next token).\u00a0 The hook observes if it is coming from the interesting places, and either leaves if not, or carries on with it's shenanigans.\u00a0 The shenanigans consist of...\n\n\u2022 ### Bugthzs 001\n\nOK, after quite some time of quiescence on this project, some bugs were brought to my attention.\n\nFirst, rather embarrassingly, a character generator bug resulted in to graphics characters being incorrectly rendered.\u00a0 [harald-w-fischer] had pointed this out over a year ago, but due to ever-present-and-multitudinous weirdness in this platform, I did not receive notification of his posting until recently, when [Mikael ?. Bonnier] observed similar consequences.\u00a0 Thank you guys, and apologies for not having corrected it until now.\u00a0 (And extra special thanks to Harald for digging into the code to effect the fix himself!)\u00a0 I also reflected this fix into the 'wide character' font, and along the way noticed that character 0x7f didn't look quite right, and fixed that too.\n\nSecond, and perhaps more embarrassingly, Mikael discovered that saving to cassette tapes did not function.\u00a0 I guess I have never actually tried to save to a cassette, because Lo! and Behold! it is true it did not work.\u00a0 This ultimately was due to a trivial logic error of inversion:\u00a0 the cassette write routine is meant to verify that a cassette is selected, before writing data.\u00a0 In fact, the opposite was done, and if a cassette was selected, it would abort writing.\u00a0 Heaven's knows what would have happened if you tried to save with no cassette selected (Heavens does know:\u00a0 crashy-crashy).\u00a0 Anyway, that logic error is corrected.\n\nSo those two bugs are fixed, and I have updated the 'files' section with images I have tested.\u00a0 I left previous image in place just in case this for some reason doesn't work, but I'm quite confident of the fixes.\n\nLastly, Harald has a rare-ish piece of hardware:\u00a0 a modded Model I with the HRG1B board.\u00a0 There were a very few 'high resolution' boards for the Model I back in the day, but most were farcically unusable.\u00a0 The HRG1B seems to me to be the only sensible implementation, which is a dot addressable pixel array (of the impressive 384x192 resolution!) that overlays the native resolution.\u00a0 I can only guess as to how much such a thing cost back then.\u00a0 Anyway, I've never found any documentation on such, much less software, but Harald has a vintage copy of the graphics kernel driver and some sample programs, so I'm now eager to implement that support.\u00a0 I haven't spent much time on the software, but a cursory disassembly of the kernel and a glance at the BASIC source looks like might be some interesting things are in there!\n\n\u2022 ### USB to PS\/2 keyboard adapter improvement\n\nPS\/2 keyboards are getting rarer, and I knew I had successfully used one of the USB to PS\/2 adapters before, but for some reason it no longer worked. So, out came the oscilloscope again.\n\nWhat I found was that the keyboard (or probably it was the adapter) was continually sending the 0xaa value every 600 ms. That value, 0xaa, is the 'Basic Assurance Test' (BAT), meaning that the keyboard passed the power-on self-test. But why was it sending it repeatedly, and not sending any key codes?\n\nI hazarded a guess that it want some interaction from the host, so I sent the 'set LEDs' code upon reception of the BAT. Doing so seemed to take the adapter out of whatever state it was in, and restored relaying of keycodes from the USB keyboard.\n\nWhile I had my probe wires soldered to the board, I tried a USB wireless keyboard through the adapter. This did not work. Unlike as with the wired USB keyboard, in this case the adapter simply remained silent.\n\nSo, I've checked all that in, and you should now be OK to use one of those adapters with the emulator, with a more modern USB (wired) keyboard if you don't have a native PS\/2 one on-hand.\n\n\u2022 ### 2nd Platform Support -- Olimex board\n\n\"...O frabjous day! Callooh! Callay!' He chortled in his joy.\"\n\nToday I finished porting the code to the Olimex Duinomite Mini board, so now you can have your emulator for about $25 USD (for what we paid upwards of a couple grand in the day), and soooo much more reliable. (and no soldering for the Olimex board). I have tested video, keyboard, SD card (cassette\/floppy), and sound. I believe the porting task to be complete. I have updated the project-related file to now contain both firmware images, one for the UBW32 (based) board, and also the aforementioned Olimex board. The Olimex board does imply some limitations: \u2022 it is a monochrome only VGA board. Since the original TRS-80 was monochrome, this isn't the end of the world, but you won't be able to simulate the green screen filter. Also, pay a little closer attention to the controls states in the 'hypervisor' since you won't have color cues to guide you. But I think the reverse video does an adequate job of letting you know what control has the focus. \u2022 this board does not have a battery-backed RTC, alas. I haven't really been using that feature yet, anyway, since OSs needed to be patched to use the aftermarket RTC's of those days. I guess it would affect the file modification date on the SD card, but who cares? \u2022 this board only has one PWM channel, so you won't get Orchestra-85 stereo. I arbitrarily selected 'right' as the available channel. The cassette-based sound is directed there, so you can play all the games just fine. Do note that the PWM channel on this board is not capacitively coupled. \u2022 this board can be run from USB power, or from adapter by selecting a jumper near the jack. YOU MUST USE ONLY 5V REGULATED ADAPTER with the Olimex board. Not even 7v. Get a cheap 5V switcher wall wart off ebay or something. There is a zener on the board to help a little with booboos, but mr zener gets pretty hot and cranky when he's made to work. I guess what I have left is serial emulation, maybe hard disk, maybe some sort of printer, and maybe a 3D printed case might be nifty. \u2022 1 Get a Supported Board Either 1. get a UBW32 for the CPU. plenty of online retailers for this. proceed to step 2, or 2. get an Olimex Duinomite-mini (which I use), or Duinomite with the IO adapater (which I do not have, but reportedly it also works). If you use these boards, you won't have to solder anything, but you will be limited to monochrome (small loss, as the TRS80 was monochrome, but I do like my green screen). If you do this, you can skip ahead to step 3 \u2022 2 Add Required Support Hardware for UBW32 (if you are using that board) get a UBW32-MCC for the jacks. assemble it. It's a fairly simple board. I do highly recommend buying a CR1616 solder tab (search 'gameboy' on ebay) battery that you can wrap in electrical tape and stuff underneath the mounted UBW32. Anyway, you'll need the connectors. The parts list enumerates the peculiar ones; the rest are commodity parts, so I didn't list them. Alternatively, you can make your own PCB, of course. Mostly, it just provides mounting for the connectors. \u2022 3 Get an LCD monitor capable of 800x600 with VGA (db25) Adapter get a monitor. I am running just fine on a modern LCD flat panel ## Enjoy this project? Share ## Discussions 7FFFH wrote 07\/23\/2022 at 04:38 point Still checking back into this project every so often to read the discussion notes and hope that there is enough interest to explore\/develop more features perhaps including perhaps a serial port in some way...? Wondering how many of these emulators have actually been built by people around the world? If the postings of people on this forum are just a fraction, then I would say quite a few... I am still impressed and my Olimex duinomite-mini is still working amazingly rock solid with this project. Are you sure? yes | no ziggurat29 wrote 07\/23\/2022 at 16:43 point I'm pleased that you are pleased! I'm interested in your thoughts about what you would like having serial be able to do. wrt expanding it with hard serial, I'm currently working a job and so don't have the cycles just now, but maybe towards the end of the season, I can carve out some time. Are you sure? yes | no Jim Bailey wrote 05\/20\/2022 at 05:18 point Thank you for a great emulator, it only took about five minutes to set it up and going back to 1980... now I only need a 110 baud modem and Compuserv! Are you sure? yes | no ziggurat29 wrote 05\/21\/2022 at 15:23 point Sweet! Yes, a Compuserv simulation was something I had hoped to produce as a companion project, but life gets in the way, and anyway I can't find enough historical records to even start to design something that would look alike. I do remember that 'CB Simulator' was more-or-less their killer app. My hope was to go Emulator->USB->DesktopApp->Internet->Cloud-hosted CompuServe Simulation. Then you should be able to 'log in' with a terminal app on the emulator and chat with other people live (a count of which I expect to realistically be zero at any given moment, so I'd probably also have an Eliza-esque chatbot there so folks aren't completely lonely), and then also bridge to some RSS feeds for actual up-to-date real news stories to view. Are you sure? yes | no Jim Bailey wrote 06\/02\/2022 at 05:53 point The funny thing is, one has to wonder just how much disk space did their content really take up. By today's standards... would it fit an SD card, it just might! :-) Are you sure? yes | no Frank N. Stein wrote 08\/23\/2020 at 20:47 point Thank you very much for this fantastic emulator! It is really great! It was one of the first computers I programmed on in the early 80s. Can you tell me how to activate Orchestra Sound? Or is there a demo at the cassettes? HRG Graphics worked out very well after a bit of trial and error! :-) I have your emulator running on a DUINOMITE-eMEGA and it works really great! It would be great if the BluePill SPO256 would work with it! Are you sure? yes | no ziggurat29 wrote 05\/21\/2022 at 15:31 point Orchestra Sound should be ready to go immediately. It comes out on the same pins as the cassette port, and is 8bit PWM. I don't remember if the demo disks have an app that drives the Orch85, but those are readily discoverable in the various existing software archives; e.g. http:\/\/cpmarchives.classiccmp.org\/trs80.php Back in the actual day I did make SP0256 synthesizers for folks and I attached them via the printer parallel port. I didn't get around to physically realizing the parallel port on this project despite its being relatively easy to do so. Food for thought. Then again, I might could merge that project into this one. The thing is, though, that the SP0256 synth was never an official peripheral, so it would be a highly bespoke application. But it might give me an excuse to write some Level II BASIC apps! lol! Are you sure? yes | no 7FFFH wrote 04\/23\/2020 at 09:42 point Hi there, Is anybody still interested in this project,... or who has built one recently or interested in further developing the software, printer port, RTC etc? I found that it works amazingly well. Let us know your experiences? Are you sure? yes | no ziggurat29 wrote 04\/24\/2020 at 03:36 point the RTC \/should\/ be functional right now, at least for newclock80, etc. To wit the various *DOS have to be patched to make actual use of it, though. As for printer, I had contemplated it. One approach is hardware -- to use the GPIO of the host board. This should be easy to do, but it would almost certainly be board-specific in the details of the pin assignments. The other was to simply printer capture to a file that is saved to the SD. Both seem to have merits. Serial support was what I had planned to do next -- both physical UART (board-specific, like printer), but especially USB emulation. With the serial support I had hoped to enable dialup capability to a companion project that would provide things like simulated services of old, e.g. Compuserve, BBS, etc. The USB serial has a challenge in that the project is really strapped for CPU cycles, and the MicroChip library code really eats them up. The big challenge I perceive at the moment is board support. When I originally did the project, I used a 'UBW32 MCC' which was a labor of love from some guys in AUS who have since retired, and either way those PCBs are not sold anymore. It was a somewhat costly option, and assembly was required. I then ported to the Olimex DuinoMite to have a new platform option, but very shortly thereafter those became difficult to find, too; sigh, lol. One other user found a board that looked very suitable, though I thought the USD$60 price tag to be a bit steep.\u00a0 I stumbled across another board about a year ago that was in the \\$20 range which looked really good.\u00a0 Alas, I lost my notes, and cannot remember the part numbers\/vendors for either of those boards.\n\nI could lay out my own bespoke board, but that's probably more $$& time that I want to sink into it right now. If I did, I'd probably go with the MZ series or maybe even an STM32. The 80 MHz PIC32MX can juuusst barely pull off a timing-accurate 1.77 MHz Z80 with a little overhead for the peripherals, and even then it cheats a bit here and there (especially disk IO; the emulator plays catch-up when it gets behind -- mostly you don't notice but I guess some low-level utility software might detect there being a glitch in the matrix). The MZ chip was quite buggy when it first came out, though I think this project would not be affected. The STM32 are so very cheap, though I don't know if the DMA\/SPI shenanigans used for the VGA skulduggery are possible on those parts. Anyway, the project is still alive, though I'm not actively working on this one at the moment. I'm please to hear it is working for you, and it would be my pleasure to support more boards to continue to give life to this important piece of computing history - klunky though it was, it by far outsold PET and APPLE II in its day! Are you sure? yes | no amacuser1 wrote 12\/23\/2018 at 10:45 point Hi - To all the forum members. I've had a go at the TRS-80 on a PIC32 over the weekend and have a slight issue. I'm using the Olimex Mini which has flashed ok with the hex file provided. I notice when using Newdos 3.0 in Hypervisor and loading drives 0 through 3 with virtual dmks, that when i try to list the files on disks 1 through 3 with Newdos - that Newdos does not respond with files on those disks however - if i type FREE from Newdos, all drives are displayed and if I have a single file on either virtual disks 1 to 3 and the disks are named the same as the files on them, then the programs will run ok. I've tried TRSDOS but the same is happening. I've think Dir,1 is the correct syntax to load and list Drive 1 in Newdos but all I get is a listing of Drive 0. Is this a timing issue or just my bad syntax. Cheers and thanks - KingKappa Are you sure? yes | no amacuser1 wrote 12\/29\/2018 at 01:32 point Hi all - I've gone to Dosplus3.1 and all is good. Sorry for the previous post. Cheers KingKappa Are you sure? yes | no m.kabbedijk wrote 12\/11\/2018 at 11:58 point Looking for a 3D case for your Duinomite-mini? https:\/\/www.thingiverse.com\/thing:928034 Are you sure? yes | no ziggurat29 wrote 12\/11\/2018 at 15:39 point oh, nice; thanks for the link! Are you sure? yes | no Jim Bailey wrote 05\/20\/2022 at 05:30 point Thank you I ordered two of these to be printed... Are you sure? yes | no Jim Bailey wrote 06\/02\/2022 at 05:59 point I had PCBWAY print two of them and both of them fit the boards perfectly. The tops and bottom half of the cases mate very well. Thanks for the tip! Are you sure? yes | no george bright wrote 12\/06\/2018 at 19:41 point did you ever release the source or does anyone know if it will run on the Olimex Duinomite eMega? Are you sure? yes | no ziggurat29 wrote 12\/08\/2018 at 04:30 point the repository link is on the left side near the top. It has a star next to it (might be easier to search the page for 'Repository' to locate it quicker). Are you sure? yes | no 7FFFH wrote 11\/28\/2018 at 12:21 point Thanks you so much to all the contributors of this project. I have been following for quite a while and eventually acquired a DuinoMite-Mini and joined in the fun... but alas there is no case readily available for this board leaving it a little exposed on the desk ? ... Using recycled sheet metal from an old Pentium PC tower case, I made my own, cut, folded, soldered in the cornes, with slots and holes cut and filed for the various ports, + hammertone grey\/silver spray, I allowed enough internal room for the Olimex RTC extension (maybe a later contribution is to acquire the tool chain and develop an option to support this RTC). For a dev board the DuinoMite-Mini with this software is amazingly stable, possible more so than I remember the original model I hardware to be. Photos are here: Are you sure? yes | no ziggurat29 wrote 12\/01\/2018 at 15:06 point Oh, that's neat. Nice metalwork. And I wasn't aware of the RTC extension, perhaps I should support it in the firmware as I do with the UBW32 version. (At the same time, I don't have any TRS-80 software that actually uses the RTC, so I guess it's not so much a priority relative to some other things). But if you want to try your hand at it, I'll give you some pointers where to look. This project source is rather kludgy; I wouldn't want you to go blind reading it cold. I myself had considered doing a 3D printed case, but never got around to learning how. (I did notice there is silver-grey filament available for those that might want the 'authentic' look.) It certainly is more stable than the original. My 'actual' eventually would not stay running for more than a couple minutes before crashing (damned that card edge to the EI), so I tossed the lot of it into the dumpster back in 1990, I think. In some ways I regret that, but in most others I do not. I had been lugging it around already for 10 years at that point, and I got 'out' of computers in 1984. Lol; \"Just when I thought I was out, they pull me back in.\" Are you sure? yes | no Mikael \u2609. Bonnier wrote 05\/24\/2018 at 06:47 point It would be good if one could use the GPIO and UEXT pins and LEDs on DuinoMite and DuinoMite-Mini using Z80 ports, because then it would work from all programming languages e.g. MMSFORTH v2.0. Perhaps one could also use the serial ports, including the one connected to USB. Are you sure? yes | no ziggurat29 wrote 05\/24\/2018 at 15:03 point serial, both hardware and usb, have long since been planned. The USB currently takes a bit more processing away from the emulator than I would like, though I am hopeful that with some effort I can improve that to usefulness. Time is, alas, the elusive commodity to both man and machine. Controlling gpio pins via port I\/O seems a bit application-specific (and board-specific), so it's unlikely that I would do that any time soon since it doesn't reflect the actual TRS-80 hardware, and this is an emulator that hardware, after all. I do intend to support one hardware serial port, which will use some external pins, and have contemplated a physical presentation of the printer port, though that's been low on my list. Serial will come before printer, and printer will probably start as file capture to disk. Similar with the LEDs. The DuinoMite (mini, at least) seems to only have one useable LED (the green one), whereas the UBW32 has 4. I currently use them for debugging, since I've never been able to get the JTAG working on these boards (I suspect the bootloader is doing something that interferes with that, but I don't know for certain). However, redirecting some of the IO space for new functionality definitely doable, and all the source is there to hack on. There's a well-defined 'ports' module where 'in' and 'out' are handled, so you can make those calls do whatever you like. I have also implemented 'traps' which use some unimplemented Z80 instructions. Some traps are used for the existing ROM patches, but other traps are used for 'syscalls' which are intended for custom ROMs or OSs. One day I hoped to make a CP\/M, which to wit never existed for the Model I for a bunch of technical reasons. At the same time, that aspiration is a bit off the beaten path of the scope of this project, and probably is best suited for an entirely new project from ground up, though you lose the charm of the perversity in running a CP\/M on the Model I. I suspect that similar arguments could be made regarding creating hardware extensions for the Model I (e.g. the GPIO functions): it doesn't represent the reality of the Model I being emulated, so does that make more sense for a separate project altogether? But maybe it does. Anyway, all the source is there, and the changes needed should be surgical enough that you could easily merge them into any ongolng changes and bugfixes that are released in the upstream codebase (except maybe if serial or printer happened, which risk colliding with pin assignments). Are you sure? yes | no Mikael \u2609. Bonnier wrote 05\/24\/2018 at 21:56 point I cannot compile it myself, because I can't get the right compiler. I asked this before: \"I could not find MPLAB IDE v8.22 on http:\/\/www.microchip.com\/development-tools\/pic-and-dspic-downloads-archive . The closest are v8.20a and v8.30. Why are you using this version and not the latest?\" About GPIO and LEDs one might say this is a partial emulation of \"Expansion Interface\" for TRS-80 Model I: http:\/\/www.trs-80.org\/radio-shack-expansion-interface\/ . That had a parallel port that might have had a Z80 PIO and I believe those have pins you can set to be in- or outputs: http:\/\/www.z80.info\/z80pio.htm . Maybe one can find GPIO-pins that are common to Maximite and DuinoMite. Are you sure? yes | no yeti wrote 05\/25\/2018 at 09:04 point Are you sure? yes | no Mikael \u2609. Bonnier wrote 05\/25\/2018 at 09:45 point It's possible to run CP\/M on TRS-80 Model I using a modification, see http:\/\/www.vcfed.org\/forum\/showthread.php?51162-CP-M-mapper-for-the-TRS-80-Model-I-its-here! Are you sure? yes | no yeti wrote 05\/25\/2018 at 11:58 point CP\/M with less then 64k RAM is no fun and every serious CP\/M program expects an 80 chars per line display. I had CP\/M on a TRS-80 clone with 64k RAM in the early 80s and the 64x16 screen was a major pain! If patching in 64k RAM support and an 80x24 or 80x25 video mode could be done, it would be a nice system. I'd even be happy about it if it were a CP\/M only emulator dropping the TRS-80 features. ;-) Are you sure? yes | no Mikael \u2609. Bonnier wrote 05\/25\/2018 at 13:39 point There is already CP\/M for DuinoMite and DuinoMite-Mini (PIC32). I made a video about it in 2013, but the video description is probably more interesting than the video: 'COMAL-80 in CP\/M-80 2.2 (Z80-SIM) on DuinoMite-Mini (PIC32\/MIPS)' https:\/\/youtu.be\/p_MXmeJkYmg I don't use that CP\/M much because its terminal emulation (VT52?) doesn't work with COMAL-80. I think the character set and sound of the TRS-80 are funny and the hypervisor also makes it easy to switch diskettes. About the TRS-80 parallel port: At least it gives 4 input and 9 output pins even though they are not bidirectional. Are you sure? yes | no ziggurat29 wrote 05\/25\/2018 at 14:42 point Lol; a bit more response than I expected! re: printer\/expansion interface - yes, the plan was to find a (common, if possible, but if not it's not the end of the world) 8 bit out port and 8 bit in port to emulate the printer. But it just hasn't been a priority for me up to this point, figuring people probably are less interested. But that might satisfy your (Mikael) I\/O needs, while keeping faithful to the 'TRS-80 emulation' intent. And Yeti is right, of course, it was just a simple latch on the actual device. The TRS-80 didn't use the various Z-80 family support chips. The Model II, did, and I wouldn't mind making an emulator for such, but it seems that is a machine lost to time as far as documentation and software go. Anyway, if and when I get around to implementing the hardware printer port, I think it would be fine to make the 8-bit printer port bi-di as a undocumented non-feature, because that shouldn't break any TRS-80 software assumptions. re: compiler. I believe I am using the latest tools for MPLab - 8.92 to wit. The real caveat is 'not MPLabX', though you're welcome to try. This caveat arises from two sources: a) I originally used code from Geoff Graham's Maximite, which had that caveat. But very nearly all that code has over the years been removed through natural evolutionary processes. b) Microchip has a delightfully 90's-era retro-business sensibility in charging$$ for their toolchains, and I'm simply not going to pay.\u00a0 I'll go to STM first (even with the horrible java based IDE and rather poor library code.\u00a0 But hey, at least I have the source there, and could debug into, say, strtol(), which is quite buggy on C32 incidentally; grrr.)\u00a0 But this project arose on a lark, and I happened to have a UBW32 PIC32MX board on-hand at the time, and that's how it came about the way it is.\u00a0 I have from time-to-time thought about making a custom board with a chip of my own choosing, which will give me much more speed and storage and video (and hence a wider range of emulation targets), but somehow I feel that might be a fool's errand.\n\nre:\u00a0 CP\/M.\u00a0 My motivation for even contemplating it was simply because as a child I couldn't afford a CP\/M machine, so I thought it might be a fun perversity to put one on this TRS-80 platform.\u00a0 But as Yeti points out:\u00a0 CP\/M really expects an 80 col display (and probably 25 or so lines), which the TRS-80 definitely didn't have.\u00a0 There is also the problem of the memory holes where the devices go.\u00a0 In the real world the ROM would be a problem, but it's not here because the ROM is implemented in RAM, anyway.\u00a0 I just needed to implement the 'syscall' to switch it out.\u00a0 But anyway, trying to implement the CP\/M then becomes such a customization that really is it a TRS-80 emulator anymore, and is it just better to make a new project.\u00a0 I could totally make one for this physical platform, but as Mikael has pointed out, hasn't that already been done?\u00a0 But maybe I should take a peek at the other project, and if there is something that can be improved upon, I might take a swag at it.\u00a0 Creating as it's own project, loooots could be improved (e.g. video, keyboard, disk -- pretty much everything!) over trying to wedge it into the TRS-80 hardware assumptions.\u00a0 Coincidentally, about a year ago I helped with another project which involved my disassembling the OS, which was CPM 2.2 based, so I have fairly recent carnal knowledge of it's innards.\n\nBut it will not be a particularly fast machine.\u00a0 The 80MHz PIC2MX can just keep up to make a 1.7 MHz Z-80 (and even that is only possible thanks to it's 70's era CISC design - 4-23 T for an instruction!).\u00a0 There is an undocumented debug feature in that the green led (on the Duinomite-mini; white on my UBW32) is turned on when the emulator is wasting time to throttle back to the 1.7 MHz speed.\u00a0 As such, it is effectively a PWM LED showing computational load in the emulator.\u00a0 E.g. when disk I\/O happens, that sucks up time from the emulator and the LED goes dark because there's no time to waste.\u00a0 And when the hypervisor dialogs are up, it goes dim, because of the extra processing incurred by the message loop of the dialog manager.\n\nAre you sure? yes | no\n\nMikael \u2609. Bonnier wrote 05\/25\/2018 at 17:18 point\n\nYou wrote you used MPLAB C32 v2.02a, but on\u00a0https:\/\/www.microchip.com\/development-tools\/pic-and-dspic-downloads-archive I can only find \"v2.02a upgrade\". Is this enough or do you need an original \"MPLAB C Compiler for PIC32\" to upgrade from?\n\nAre you sure? yes | no\n\nziggurat29 wrote 05\/26\/2018 at 00:24 point\n\nit might be fine to use that as-is, but it might have been an upgrade from whatever before.\u00a0 It was many years ago that I set up my build machine; but regardless, I think the main point is 'use the latest stuff relevant to the MPLab 8 product line (and \/not\/ MPLabX'), which includes the MPLab IDE and various compilers.\u00a0 In this case, we only care about the PIC32 compiler.\u00a0 You'll be fine.\u00a0 Jump into the pool.\n\nAre you sure? yes | no\n\nyeti wrote 05\/26\/2018 at 01:57 point\n\nI tried https:\/\/github.com\/TheCodeman\/z80pack-1.17-ksd-pic32 but I did not get far with it. And when it finally ran, I did not get the applications configured to the needed terminal sequences.\nAnd having only some fixed disk image files, file handling really is ugly.\n\nhttp:\/\/www.mathematik.uni-ulm.de\/users\/ag\/yaze-ag adds finer control over keyboard mappings, a commandline editor and commandline history at the emulator level. That makes using it really nice!\n\nhttps:\/\/schorn.ch\/altair.html emulates 8080, Z80, 8086 (and the beta version adds 68000). So CP\/M archaeology on different CPUs is easy with it.\n\nhttps:\/\/github.com\/MockbaTheBorg\/RunCPM runs on several microcontrollers, DOS, Windows and Posix and maps file access to the host's filesystem. That might break some really picky software, but so far I do not have problems with it on Linux. RunCPM optionally adds Lua\u00a0 and accessing GPIOs of e.g. the ArduinoDUE is supported too. This project is alive and problems typically get fixed really fast.\n\nAre you sure? yes | no\n\nziggurat29 wrote 05\/26\/2018 at 17:19 point\n\nhmm; the more we write about it, the more it makes be believe that really any notional CP\/M should just be a separate project, instead of my perversely trying to get it to run in the emulated TRS-80 Model I environment.\u00a0 I just don't know if I should do it, since as you pointed out there are already so many existing ones in the wild.\u00a0 Is it worthwhile for me to bother?\u00a0\u00a0Plus, all my other other non-profitable babies are crying and starved for attention.\u00a0 When will I ever get back to my cryptographic calculator; lol?\n\nAre you sure? yes | no\n\nMikael \u2609. Bonnier wrote 03\/17\/2018 at 21:36 point\n\nThis works on DuinoMite-Mini, but I could not get it to work on DuinoMite. It then complains about there being no file system on the SD-card even though the same SD-card works well in DuinoMite-Mini. Other systems work with SD-card in DuinoMite e.g. MMBASIC 4.5. There must be some small patch you could apply to the TRS-80 emulator so that it works on DuinoMite too.\n\nAre you sure? yes | no\n\nziggurat29 wrote 03\/18\/2018 at 00:00 point\n\nThanks so much for playing with the emulator!\u00a0 I apologize for not having responded to any of your prior questions -- for some reason this site never gave me notifications of such until just today.\nGive me a moment to study them all, and I'll reply forthwith....\n\nAre you sure? yes | no\n\nziggurat29 wrote 03\/18\/2018 at 00:52 point\n\nIssue with semi-graphics\n\nI noticed another poster (who I also neglected, a year ago!) found what he reports as a bug in the font images for characters 0x86 and 0x97, which are in the graphics range.\u00a0 I still need to study those.\u00a0 But being off in the font would definitely create visual issues like you saw.\u00a0 Since this is an emulator, and is running the original code, it is more likely something I did (font) than something the author did (Bill Gates, haha).\n\nSaving to Cassette\n\nThis really should work fine.\u00a0 I am pretty sure I have tested writing -- especially because testing is pretty boring when you can't save your programs!\u00a0 I will need to fire up my board (it's been a while!) and verify, but I'm pretty sure that works.\u00a0 I also think floppy works.\u00a0 Floppy was the last thing I implemented.\u00a0 Admittedly, most of what I tested was reading, to run programs, but there are no special restrictions that I remember regarding writing, so it should just work.\u00a0 But I really need to do some hands-on testing before I can assure you of that.\n\nBasic Level 3\n\nWhy not?\u00a0 I do have a copy of the cassette version of Level III, and it mostly just hooks vectors like DOS does, which works, so I would \/think\/ it would be fine.\u00a0 But I'll have to test, and I admit I've never tried to run it.\u00a0 Though it would be interesting if it doesn't work.\n\nDuinoMite-Mini vs DuinoMite\n\nThis is an interesting question.\u00a0 I have a DuinoMite-Mini in-hand, but not a DuinoMite.\u00a0 There is possibly a hardware difference that would need to be taken into consideration.\u00a0 I need to look at the schematics.\u00a0 It's possible that the firmwares that you mention detect the platform and switch, say, gpio lines to accommodate.\u00a0 SD is pretty easy:\u00a0 it's just SPI with a few control lines.\u00a0 So it should be accommodable with a some mods to init code.\n\nI have to admit some disappointment that the various off-the-shelf boards have incrementally become unavailable.\u00a0 The UBW32 version I developed on is now unobtainium, and the DuinoMite-mini that I ported to provide an alternative cheap platform went off-the-market about a month after I completed the port! lol!\u00a0 Sometimes I think I should just make my own board.\u00a0 After all, that was the point of the Maximite to begin with:\u00a0 just a demo of the then-new PIC32MX to make an 80's style machine with minimal support components.\u00a0 But it's a labor of love, and not of money, so it's hard to justify dumping in the costs.\u00a0 On the other hand, the retrocomputing really is a lot of fun.\u00a0 This was it!\u00a0 This is how we did things once-upon-a-time!\n\nAre you sure? yes | no\n\nMikael \u2609. Bonnier wrote 03\/18\/2018 at 05:17 point\n\nI noticed the sine-plotting program works in a TRS-80 emulator for Linux that's included in e.g. Ubuntu 16.04: xtrs.\n\nI can save to diskette using LBASIC called BASIC in\u00a0ld531.dmk. If it is possible to save to cassette it would be good if you could make a video about how, or write it down in detail, because I think I've tried every way.\n\nThe last GPL-version of MMBASIC i.e. DMBASIC can also use the microSD-card in both DuinoMite-Mini and DuinoMite with DuinoMite-IO:\nhttps:\/\/github.com\/OLIMEX\/DuinoMite\/tree\/master\/SOFTWARE\/DMBasic\/src\n\nVGA already works with the TRS-80 emulator in both.\n\nYou can still buy DuinoMite-Mini and DuinoMite with DuinoMite-IO from Olimex and also here where I live:\n\nhttps:\/\/www.olimex.com\/Products\/Duino\/Duinomite\/DUINOMITE-MINI\/\n\nhttps:\/\/www.olimex.com\/Products\/Duino\/Duinomite\/DUINOMITE\/\n\nhttps:\/\/www.olimex.com\/Products\/Duino\/Duinomite\/DUINOMITE-IO\/\n\nhttps:\/\/www.electrokit.com\/duinomitemini.49379\n\nhttps:\/\/www.electrokit.com\/duinomite.49405\n\nhttps:\/\/www.electrokit.com\/duinomiteio.49381\n\nIf some local reseller sells other Olimex boards one could probably ask them to import a DuinoMite-Mini.\n\nAre you sure? yes | no\n\nyeti wrote 05\/07\/2018 at 06:53 point\n\nhttps:\/\/www.olimex.com\/Products\/Duino\/Duinomite\/_resources\/DuinoMite-UM-1-03.pdf on page 13: \"\"\"As DuinoMite, and DuinoMite-Mega are designed to be low power boards there is provision for the SD-card power supply to be shut down, this is done with FET2 connected to STB_E on RB13 port of PIC32.\"\"\"\n\nAre you sure? yes | no\n\nziggurat29 wrote 05\/07\/2018 at 12:53 point\n\nThat's a great observation. Knowing that's there, I can see it in the schematic. You might have cracked the case.\u00a0 I'll see about making a modification, and then hopefully Mikael can kindly validate, since I don't have a board to test with myself.\n\nAre you sure? yes | no\n\nziggurat29 wrote 05\/07\/2018 at 19:04 point\n\nFYI, it does look like that was it, so 1000 thanks for knowing of that passage in the manual.\u00a0 Mikael validated it on his board, so there will be an update forthcoming...\n\nAre you sure? yes | no\n\nyeti wrote 05\/07\/2018 at 19:20 point\n\nI remembered that RetroBSD toggles a port on Duinomites to access the SD card and then it was easy to find in the manual.\n\nAre you sure? yes | no\n\nziggurat29 wrote 05\/09\/2018 at 16:47 point\n\nOh, I've long been meaning to give RetroBSD a whirl; thanks for reminding me of it!\n\nAre you sure? yes | no\n\nMikael \u2609. Bonnier wrote 02\/23\/2018 at 17:28 point\n\nWould it be possible to get BASIC Level 3 (III) in the emulator?\n\nAre you sure? yes | no\n\nziggurat29 wrote 03\/31\/2018 at 03:05 point\n\nseems to work as is.\u00a0 I have loaded it, and it hooks in correctly.\u00a0 I haven't actually run a Level3 program, but I have no reason to think it will not work perfectly as-is.\u00a0 Maybe I'll fiddle with this a bit later.\u00a0 Just load it as any other system cassette program.\u00a0 Don't forget the filename 'system' requires is case-sensitive!\u00a0 It also only requires the first letter, so I just use 'L'.\n\nAre you sure? yes | no\n\nMikael \u2609. Bonnier wrote 02\/23\/2018 at 17:27 point\n\nHow do you save a BASIC program on a virtual cassette? I tried to load test.cas and then enter a program and csave \"hello\" and also csave hello but nothing seems to save on the cassette. Is it not possible to save on cassette using this emulator? How do you save a BASIC-program on floppy disk using this emulator?\n\nAre you sure? yes | no\n\nziggurat29 wrote 03\/31\/2018 at 03:12 point\n\nThere was an embarrassing bug on cassette saving that I have fixed in the firmware image I just posted.\u00a0 Short story:\u00a0 I had a logic inversion testing that a cassette was selected.\u00a0 I meant to bail if no cassette was selected, but in fact I bailed if a cassette \/was\/ selected.\u00a0 Whoops!\nNote:\u00a0 the 'new' feature does not work, so you currently need to have a blank tape file already on the disk.\u00a0 I don't know why I didn't implement 'new' but I can see I didn't and I need to look into that.\u00a0 In the updated file, I included 10 blank tape images for your saving convenience.\u00a0 Big picture:\u00a0 they're simply empty files, so you can make as many as you like as needed.\nSome things:\n*\u00a0 don't forget you need to put the cassette into 'record' mode!\u00a0 In the hypervisor, you'll see the word 'play'.\u00a0 This is actually a button, and if you 'click' on it with the spacebar, it will toggle to 'rec' for record.\u00a0 This reopens the file for writing, and you can save programs.\n*\u00a0 I saved your 'sine.cas' using the feature.\u00a0 Now you can plot a beautiful sinusoid in glourious 128 x 48 resolution!\n*\u00a0 The Microchip provided FAT source code seems to be bad.\u00a0 I might look into replacing it with a 3rd party (4th party?) implementation that is more reliable.\n\nAre you sure? yes | no\n\nMikael \u2609. Bonnier wrote 03\/31\/2018 at 13:02 point\n\nI can save to cassette now using e.g. CSAVE \"SINE.BAS\" on TEST008.CAS in REC mode, and I can use NEW and CLOAD it again after changing TEST008.CAS to Play mode. The first time I tested this the whole microSD-card was blanked and even the volume name was blanked. Then I saved it using csave \"mobluse\" to TEST008.CAS i.e. lower case and without extension. I had to reformat and copy all files to the SD-card again. When I reformatted it I used FAT32, before it was probably just FAT. I did have a backup of all files on SD-card. This is just a small SD-card of 128MB. I don't know if it was lower case, lack of extension, or non FAT32 that caused the SD-card to be erased.\n\nAre you sure? yes | no\n\nMikael \u2609. Bonnier wrote 03\/31\/2018 at 13:06 point\n\nA feature request would be to see if the CAS-file is binary or BASIC-programs in the list, because now one doesn't know if a file should be loaded with SYSTEM or CLOAD. E.g. I tried to load MUSIC.CAS with both methods, but without getting anything to run.\n\nAre you sure? yes | no\n\nMikael \u2609. Bonnier wrote 03\/31\/2018 at 19:41 point\n\nIt would be good if there where a command-line program for e.g. Linux that could export and import BASIC-programs (both Level 2 and 3) as text-files in UTF-8 to and from CAS-files. The TRS-80 graphics characters are not part of UTF-8, but there are UTF-8 fonts that have them, e.g. teletext2 and teletext4, see\u00a0https:\/\/github.com\/mobluse\/semigraphics .\n\nThe CAS-format of this emulator seems to be the same as the CAS-format of \"xtrs\" emulator for Linux, and that has a program \"cassette\" to handle CAS-files and CPT-files. Unfortunately the \"cassette\" program in Linux can't export and import text-files from the cassette-files. (Both \"xtrs\" and \"cassette\" are in Ubuntu in e.g. Microsoft Store.)\n\nHowever, one can load the CAS-files using \"cassette\" and then use CLOAD and LLIST in \"xtrs\" to list the program on stdout.\n\nIn order to input programs into the emulator one can use a system\u00a0https:\/\/pyautogui.readthedocs.io\/ that reads files and simulates keypresses in the emulator, and then one use CSAVE \"FILENAME.BAS\". Then one can use the resulting CAS-file in this emulator for PIC32.\n\nAre you sure? yes | no\n\nziggurat29 wrote 04\/01\/2018 at 00:05 point\n\n(hopefully this reply will show up correctly; this site only will nest replies so deeply)\nLol!\u00a0 Coincidentlly I had just written a utility to dump a 'cas' file to a text dump for BASIC a few hours ago.\u00a0 It was pretty trivial to do, though I hadn't considered retokenizing plaintext text back to cas form.\u00a0 Generating binaries for the myriad systems out there is probably impractical for me, but the good news it's it's just a single C++ file, so compiling from the source should be really easy to do on an as needed basis.\u00a0 I should test that it still compiles clean on gcc, since I myself am using Dev Studio.\n\nI have long planned a feature to direct line printer to a text file on the SD, and also to read a text file into keyboard.\u00a0 The former should be straightforward, and the latter a little tricky with character pacing to keep the reading reliable.\u00a0 Maybe you've motivated me to finally implement those!\n\nRegarding your filesystem issues, I am beginning to think there may be some issues with the FSfs library that I am using that does the FAT I\/O to the SD card, or perhaps I am failing to do something to cause it to write the modified directory structures out.\u00a0 I don't know what that would be, but I did notice there is no 'flush' capability on files, and I emulated that by closing, then re-opening, the cassette file when the writing is finished.\u00a0 I need to spend some time on this, and perhaps just switch to a different library that I have had better luck with in other projects (FATfs), so stay tuned for that.\n\nI have to go back to work just now, so it will be a few days before I can dig into these things (alas), but hey, you're plotting sine waves now, lol!\n\nAre you sure? yes | no\n\nMikael \u2609. Bonnier wrote 04\/01\/2018 at 09:55 point\n\nPrinting to and reading keypresses from files is a good idea. There is also the USB-serial port that one could LPRINT and LLIST to and receive keypresses from using e.g. Tera Term because that has configurable delays for characters and lines when pasting code. I saw BASIC Level III has support for output to serial port, so one might use the serial port for that instead. The DuinoMite-Mini and other PIC32-boards also have other serial ports that use pins.\n\nI just want to remind you that the new version still doesn't work on DuinoMite with DuinoMite-IO. Actually it works a bit worse now since in the old version from 2016 you got a screen with text that the SD-card didn't work, but now you only get a blank screen. I think you should be able to get a free DuinoMite with DuinoMite-IO from Olimex to test with, because this project could increase their sales. One advantage with DuinoMite-IO is that it has connectors for speaker sound -- the DuinoMite-Mini only has pins for sound, but I have connected them to a speaker.\n\nAre you sure? yes | no\n\nziggurat29 wrote 04\/01\/2018 at 14:43 point\n\nYes! on serial.\u00a0 That is a long standing planned enhancement.\u00a0 Actually, the boards do enumerate as USB serial even now, I just haven't hooked the stream up to anything yet. (I wanted to get floppy working first, and that was a \/lot\/ of work.\u00a0 Then I had to go back to work!)\u00a0 It's still on my to-do.\u00a0 One potential challenge is that device code (from Microchip's libraries) mostly works in a polling scheme, which I suspect might be too much for the main emulation loop to deal with, so I need to study the source and profile the execution.\n\nJust now,\u00a0I am trying to understand the filesystem corruption issue, which seems to be a critical issue.\u00a0 I have re-read the Microchip application notes, and don't seem to be missing anything, but I have to thoroughly review.\u00a0 Slightly related to that is the issue with the other board.\u00a0 I studied the schematics, so there doesn't seem an electrical reason it shouldn't work, but clearly something is awry.\u00a0 I wish I had one on-hand.\u00a0 Maybe I am just clocking SD too fast, though I\u00a0don't think so.\u00a0 But maybe.\n\nAre you sure? yes | no\n\nMikael \u2609. Bonnier wrote 04\/06\/2018 at 20:30 point\n\nThe reason it works with DuinoMite-Mini and not with DuinoMite might have to do with an old library for SD-cards, see this post on Olimex forum:\n\nhttps:\/\/www.olimex.com\/forum\/index.php?topic=6098.msg25177#msg25177\n\nAre you sure? yes | no\n\nziggurat29 wrote 04\/07\/2018 at 14:58 point\n\nThanks for the feedback regarding the SD code.\u00a0 I'm already using a later version of the filesystem library code than the official maximite codebase (well, at least the copy that I have); maybe I should revert?\u00a0 I'm reticent to do so except experimentally, because there are clearly bug fixes that were introduced in the later version that I have integrated.\n\nAlso, being as the Duinomite and the Mini are electrically the same (for SD at least), my mind is still blown as to why there is a difference.\u00a0 But there it is, your problems indicate that there is \/some\/ difference.\u00a0 My thoughts then started to wander to SPI clock speed.\u00a0 However, I am using the same configuration as the MM-BASIC, so this feels like a shot in the dark.\n\nSome other interesting things are your notice that not having a card inserted no longer presents the 'please insert a card' message.\u00a0 There haven't been any changes to that code (that tests and presents the message), however the way it works is:\n\n1) test for SD card presence\n2) init the SD card\n3) test for various required directories\n4) create them if needed\n5) purge the 'temp' directory\n\nIf any of those fail, they have their own distinct error message.\u00a0 Since you have no error message, that almost certainly means the board is 'hung' in the SD card library, though it could be any of those steps, since there is no output message prior to those steps.\u00a0 I'm guessing #1 or #2, but not with certainty.\n\nPerhaps I need to implement some boot time messages.\u00a0 Currently there is a 'splash' screen for artistic purposes, which would need to go away, but science must take precedence over art, alas....\n\nAre you sure? yes | no\n\nziggurat29 wrote 04\/07\/2018 at 15:10 point\n\ncoincidentally, I did the other day implement a basic-to-cas translation program, and it seems to work correctly.\u00a0 Next time I release a package, I'll include that.\u00a0 As mentioned, it will be in source code form, rather than compiled, because it will be too much for me to attempt to maintain binaries for all the platforms out there.\u00a0 On the other hand, it is a trivial program -- just one source file, and only standard library dependencies -- so it should be trivial to compile on an as-needed basis.\u00a0 I'll do a trial compilation on gcc beforehand, since gcc and MSVC have different interpretations of the language and cautionary warnings, and I like clean builds.\n\nAre you sure? yes | no\n\nMikael \u2609. Bonnier wrote 04\/07\/2018 at 20:12 point\n\nI just want to clarify: I have a microSD-card (FAT32 128MB) that works in the DuinoMite-Mini in the DuinoMite and now the screen is just black. With the old version you got a message: \"No Filesystem on SD Card!\". You still get this message on the DuinoMite-Mini, if you boot without SD-card. Maybe you could send some message on the USB serial port during boot, so that one knows it works a little. The same DuinoMite works well with e.g. MMBASIC 4.5.\n\nAre you sure? yes | no\n\nMikael \u2609. Bonnier wrote 04\/10\/2018 at 12:12 point\n\nI have problems with the CAS-files I saved to. I tried to copy them from microSD-card to HDD, but xcopy complained and stopped copying, and recommended chkdsk on the SD-card. I did that, but then the files that I had saved to were 0 bytes long.\n\nThe type of the file system is FAT32.\nVolume DUINOMITE created 2018-03-31 14:30\nVolume Serial Number is F814-531B\nWindows is verifying files and folders...\nThe size of the \\cass\\test001.cas entry is not valid.\nThe size of the \\cass\\test008.cas entry is not valid.\nFile and folder verification is complete.\n\nWindows has made corrections to the file system.\nNo further action is required.\n\n121 715 712 bytes total disk space.\n1 024 bytes in 1 hidden files.\n8 192 bytes in 5 folders.\n23 476 224 bytes in 76 files.\n98 229 248 bytes available on disk.\n\n1 024 bytes in each allocation unit.\n118 863 total allocation units on disk.\n95 927 allocation units available on disk.\n\nAre you sure? yes | no\n\nziggurat29 wrote 04\/10\/2018 at 18:27 point\n\nYes, that is the filesystem corruption I had mentioned before.\u00a0 For some reason, the FAT is not being flushed when the file is closed.\u00a0 I need to dig into this some more.\u00a0 In a way I hope it's simply my bug, because I can fix that.\u00a0 Debugging can be a bit slow-going since I don't have JTAG on these boards, though.\u00a0 But obviously this really needs fixing.\n\nAre you sure? yes | no\n\nziggurat29 wrote 04\/27\/2018 at 17:09 point\n\nnote for posterity on this thread:\u00a0 I did work around the filesystem corruption issue, which seems to be a bug in the MDD library specifically when opening zero-length files in \"r+\" mode.\u00a0 There is a separate log post on that issue, and the firmware image has been updated to include the workaround.\nThe workaround has the side effect of moving the filename in the directory listing and changing the case (because of the way MDD implements the \"w+\" mode, which I am using in the special case of zero-length files).\nThese side effects do not occur with non-zero length files, so an alternative workaround is simply to put a single byte in any zero-length files.\u00a0 That byte will get overwritten when you save, and it avoids the MDD bug.\n\nAre you sure? yes | no\n\nMikael \u2609. Bonnier wrote 02\/23\/2018 at 17:25 point\n\nI have tested this TRS-80 emulator on DuinoMite-Mini and it works well, but there are some issues with semigraphics characters, see my video on https:\/\/youtu.be\/_GjVNnPW9Zs .\n\nAre you sure? yes | no\n\nziggurat29 wrote 03\/31\/2018 at 03:13 point\n\nThank you so much for your meticulous work.\u00a0 Harald Fischer discovered the same problem (unfortunately, I did not see his post until a year later), and I have corrected this in the current image.\u00a0 Now your sines look...\u00a0 Sinusoidal!\n\nAre you sure? yes | no\n\nharald-w-fischer wrote 03\/05\/2017 at 11:48 point\n\nI like this project and are about to add support for the HRG1B graphics extension. In the meanwhile I would like to note that there is an error in the graphics character font for characters 0x86 and 0x97 in file trs80font_alt.c as follows:\n\n\/\/{ 0x0007, 0x0007, 0x0007, 0x0007, 0x0007, 0x0007, 0x0007, 0x0007, 0x0007, 0x0007, 0x0007, 0x0007 },\u00a0\u00a0 \u00a0\/\/0x86 wrong HF\n{ 0x0007, 0x0007, 0x0007, 0x0007, 0x0038, 0x0038, 0x0038, 0x0038, 0x0000, 0x0000, 0x0000, 0x0000 },\u00a0\u00a0 \u00a0\/\/0x86 correct HF\n\n\/\/{ 0x003f, 0x003f, 0x003f, 0x003f, 0x0007, 0x0007, 0x0007, 0x0007, 0x003f, 0x003f, 0x003f, 0x003f },\u00a0\u00a0 \u00a0\/\/0x97 wrong HF\n{ 0x003f, 0x003f, 0x003f, 0x003f, 0x0038, 0x0038, 0x0038, 0x0038, 0x0038, 0x0038, 0x0038, 0x0038 },\u00a0\u00a0 \u00a0\/\/0x97\u00a0 correct HF\n\nI will post again when have made some progress with HRG1B extnsion.\n\nRegards\n\nAre you sure? yes | no\n\nziggurat29 wrote 03\/18\/2018 at 00:09 point\n\nThanks so much for the feedback!\u00a0 I apologize for not having responded for now over a year, but this site has never given me notifications until just today (despite my having been on here several times over the past year).\u00a0 I will take a gander at your bug fix and integrate.\n\nI am interested in the HRG1B extension, and had considered implementing it myself since you've got the framebuffer right there, but I never found any software that used it, so I never got around to it.\u00a0 I'd love to see some software run that uses it.\u00a0 (similar with the Orchestra80 emulation, and hard disk)\n\nCheers!\n\nAre you sure? yes | no\n\nziggurat29 wrote 09\/09\/2016 at 14:58 point\n\n@Hacker404: \u00a0re descenders, yes, for the most part\u00a0you should be able to simply move them up a pix and have them look correct. \u00a0'p' is the exception because it has two lines of descender in the image I have sent, so you need also clear the last line (making it look like a reversed 'q')\n\nI have sent you the data (too long to post here), but as an example, here is image of the\u00a0the lowercase 'p' with 'descender':\n\n{ 0x0000, 0x0000, 0x002c, 0x0032, 0x0032, 0x002c, 0x0020, 0x0020, 0x0020, 0x0000, 0x0000, 0x0000 }, \/\/p\n\nto convert it to 'no descender' you would remove the top row\u00a0(the first 0x0000) and stick a\u00a0blank row\u00a0at the bottom\u00a0(the last entry); i.e.\n\n{\u00a00x0000,\u00a00x002c, 0x0032, 0x0032, 0x002c, 0x0020, 0x0020, 0x0020, 0x0000, 0x0000, 0x0000,\u00a00x0000\u00a0}, \/\/p\n\nand in the special case of 'p' clear row 7 to zero. \u00a0(the others don't require this, they only have one descender row)\n\n{\u00a00x0000,\u00a00x002c, 0x0032, 0x0032, 0x002c, 0x0020, 0x0020, 0x0000, 0x0000, 0x0000, 0x0000,\u00a00x0000\u00a0}, \/\/p\n\nThe characters affected are:\n\n'g', 'j', 'p', 'q', 'y'\n\nNotes:\n\n1)\u00a0I explained separately why these are 16-bit quantities -- a technical need for my emulator. \u00a0Only the lower 6 bits are significant, so disregard the 10 leading bits.\n\n2)\u00a0Similarly, this bit image is for the full 6x12 character cell (I do graphics through the char gen as well). \u00a0If you are generating the signals via hardware, and only need the character images with no descenders, you probably\u00a0want to drop the last 5 entries (raster lines) since they are always blank in that case.\n\n3) Lastly, these image include the inter-character spacing in bit 0 (hence why all the even numbers). \u00a0If you generate that part of timing electronically, then shift all values down one, and there will only be 5 significant digits, so less logic (maybe;\u00a0I guess the compiler will figure out that bit 0 is always 0 and there's not a lot of logic needed to generate for that case!)\n\n4) Oh yes, 'lastly' lastly, as mentioned separately, if you are generating your video signals in hardware, you probably don't need the images for the\u00a0graphics characters (0x80-0xff) and the first 32 which alias the uppercase characters (0x00-0x1f -> 0x40-0x5f). \u00a0Maybe that saves some logic for you.\n\nDoing the things above will yield a 5x7 char gen array that should be accurate for the TRS-80 Model I second versions chargen (no-descenders, corrected bug for 'flying 'a'').\n\nCheers!\n\nAre you sure? yes | no\n\nHacker404 wrote 09\/07\/2016 at 23:40 point\n\nHi, I love the project.\n\nI would like to ask a favor. I am making a hardware clone, It's here -\n\nI had a system crash and i lost the pixel data used by the character ROM (generator).\n\nCan you send a link to where you found it or a copy of your data? I would save me so much time. I am especially wanting the very simplified model I character set that hasn't been modified because I want to fit into the computational logic of a CPLD if possible so I don't have to include an expensive fast FLASH chip just for this function.\n\nThank, Rob.\n\nAre you sure? yes | no\n\nziggurat29 wrote 09\/08\/2016 at 14:56 point\n\nAbsolutely. \u00a0Send me a PM with where I can send it (email or whatever).\n\nSystem crash sucks! \u00a0I myself\u00a0have a little stack of harddrives with long lost projects. \u00a0One day I may become bold enough to take the soldering iron to them....\n\nWhere I got it: \u00a0I found a TrueType font for the characters. \u00a0I then wrote a Windows program to emit text with the font, followed by code to pluck the pixels from the resulting screen image\u00a0and assemble the binary image for the character generator. \u00a0This was straightforward, if boring code. \u00a0Also, the TrueType font was not absolutely correct, so there was an intermediate correction step (minor;\u00a0characters 00-1f alias 40-5f, and c0-ff alias 80-bf).\n\nThe output I generate is (now) a simplified format; an array\n\nconst unsigned short g_abyFontData_00[256][12]\n\nof binary pixel data. \u00a0Each of the second subscript\u00a00-11 is successive rows, and each of the first is obviously characters. \u00a0The values are row data, msb = first pixel, with the value right justified, i.e. there are leading zeros for unused pixels; the trs80 character cell is 6x12 pix. \u00a0So why did I use unsigned short instead of unsigned char? \u00a0For my software generator, I generated two fonts, one for normal and one for the wide characters, hence I needed more bits for the latter. \u00a0I'm sure you wont need that for your hardware-based system, but I wanted to explain why\u00a0the extra bits are there.\n\nAs simple as that array definition is, I suspect you can use it as-is, perhaps with some textual massaging for getting it into the form you need for your CPLD. \u00a0If it's more handy for you to have it in a different form, let me know; I could tweak the fontmaker\u00a0program output for you to save you\u00a0some time in the text editor.\n\nFinal note: \u00a0this image represents the last character generator rom -- i.e. the one with the glourious one-pix descenders. \u00a0There were two prior: \u00a0the second had no descenders, which made some chars look goofy, and the first had a bug where the @ was raised one row. \u00a0If you wanted to have those for historical accuracy, you could tweak the font generator (or really just\u00a0hand edit the binary since the change is trivial) to create them.\n\nAnyway, let me know where you what me to send whatever and I'll do so.\n\nCheers and good luck! \u00a0I think your hardware replica is very cool, too!\n\n-dave\n\nAre you sure? yes | no\n\nHacker404 wrote 09\/09\/2016 at 05:30 point\n\nHi,\n\nI tried a version with descender and that was too complex to fit into the small CPLD that I am using so I am really after a version with no descender. Can I just lift the descender characters up a couple of pix or are they different in other ways?\n\nThanks.\n\nAre you sure? yes | no\n\nmauroxavierneto wrote 01\/18\/2016 at 22:02 point\n\nI tried to write\u00a0your hex in my\u00a0\u00a0Colour Maximite from Altronics (K9555), but it\u00a0doesn\u00b4t work (black screen). Can you give me any tip to compile from the source to run in my board?\n\nAre you sure? yes | no\n\nziggurat29 wrote 01\/18\/2016 at 22:33 point\n\nHmm, I would \/think\/ that it would work as-is with the colour maximite, but I did toss out a lot of maximite model-specific stuff, so maybe I rendered it more bound to the UBW32 version. \u00a0(e.g.\u00a0I'm pretty\u00a0sure the original monochrome model is not supported).\n\nOn second thought, I believe the major difference between the 'classic' colour maximite and the UBW32 version has to do with the linker script, to accomodate a different boot loader. \u00a0If that's true, then the prebuilt hex file for the UBW32 version could easily be expected to not work for different hardware (well, different\u00a0memory layout).\n\nAs an initial sanity check, I would flash back your original firmware to prove the board is good, and not bricked, then we can look at what needs to be done here.\n\nSo, are you able to compile at all now? \u00a0The project should be self contained, (I think). \u00a0It is created for the older Microchip stuff (i.e. pre-MPLABX). \u00a0Coincidentally I had just set up a new build VM, so I can see I installed:\n* \u00a0MPLAB IDE v8.92\n* \u00a0MPLAB C32 v2.02a\n\nI'm pretty sure that \u00a0is all you need insofaras toolchain. \u00a0You may want to do this in a virtual machine (as I do) because you really want to compile with -Os, which you only get for 60 days. \u00a0It will work at -O1 (supported by the 'Lite' version), but the extra optimization really\u00a0helps having more free CPU overhead for the emulation.\n\nOK, also let me know if you can get the code from the repository (linked on the project page). \u00a0That's a Fossil-SCM repository; if you log in as 'anonymous', then you will be able to download a zip file of the current source snapshot. \u00a0On the other hand, if you have trouble or just don't want to bother, then PM me with, say, and email, and I'll zip up my project workspace and send it to you. \u00a0At least then you'll have a chance at futzing with it to see what's up. \u00a0Actually, I'd like to know, too, since it really should run on the 'classic' colour maximite just fine, but I don't have one in my possession to test with. \u00a0I'll do a little googling on the model you mention to see if there is anything obvious about it's implementation.\n\nYour English is surely better than my Portuguese.\n\nAre you sure? yes | no\n\nmauroxavierneto wrote 01\/18\/2016 at 22:46 point\n\nMy board are working ok, I reversed to original firmware and it\u00b4s fine. I\u00b4m curious about the fact that in the Geoff\u00b4s Projects site are saying that the UBW32 and Colour Maximite share exactly the same firmware...\n\nhttp:\/\/geoffg.net\/ubw32.html\n\nWhen I saw\u00a0your site in 2015, I tried to compile the firmware\u00a0without success (has generated a .elf and have the same black screen). In any case,\u00a0I\u00b4m glad that you answered me so fast.\n\nI will gonna try to compile it again...\n\nAre you sure? yes | no\n\nMikael \u2609. Bonnier wrote 05\/07\/2018 at 16:21 point\n\nI could not find\u00a0MPLAB IDE v8.22 on http:\/\/www.microchip.com\/development-tools\/pic-and-dspic-downloads-archive . The closest are v8.20a\u00a0and v8.30. Why are you using this version and not the latest?\n\nAre you sure? yes | no\n\nziggurat29 wrote 01\/18\/2016 at 23:25 point\n\n(I don't know why I can't reply to your last post, so I am replying to your first; this may make messages out of order).\n\nYes, hasty words about the bootloader. \u00a0I concur that is not it. \u00a0I did notice one thing looking at the code, in Main.c::18-21, I have commented-out an include that originally have a bunch of #pragma config items for doing all manner of things like setting up clocks, etc. \u00a0I took that out, because the UBW32 bootloader does that beforehand, but maybe it is still necessary for 'classic' colour maximite. \u00a0I don't think I have that file in the repo (\"Configuration Bits.h\"), but I can send it to you if you want to try that.\n\nSome other things:\n* \u00a0black screen. \u00a0Hmm. \u00a0Is CPU halted, or is it just unable to generate video? \u00a0As a quicky, you can plug your [black screen] maximite into USB, and you should still get CDC enumeration (I have that in the firmware, though I'm not using it yet. \u00a0But it will enumerate as a COM port).\n* \u00a0When I was bringing the board up, I relied upon twinkling the various LEDs to know how far it got in the code. \u00a0(I don't know why, I cannot use JTAG to debug this board and firmware). \u00a0Things like\n\nLATECLR = 1<<0; \/\/led 3 (yellow) on\n\nLATECLR = 1<<1; \u00a0\/\/put on the red light\n\nLATECLR = 1<<2; \/\/led 1 (white) on\n\nLATECLR = 1<<3; \/\/led 4 (green) on\n\nwill turn on the various LEDs, and you can move that code incrementally down to see where things start to croak. \u00a0I would start an Main.c:1978 (after setting vectored interrupts) \u00a0with the yellow LED, and do a kind of manual binary search up until about 2001, at which point all the hardware should have been initialized successfully, and the video machine cranked up. \u00a0If you need to go further, at line 2019, you should definitely have something on the screen, because that's a decorative simulation of the random screen data on boot up that the original machine had.\n\nI do appreciate your trying out the project, and I'm sure we can make it work.\n\nAre you sure? yes | no\n\nmauroxavierneto wrote 01\/18\/2016 at 23:42 point\n\nWhen I flashed with your actual hex, I think the CPU was freezed because when I turn on the Colour Maximite,\u00a0the keyboard led flashed one time in the boot, and then turn off one second after. I tried some keyboard commands to control de TRS80emu but nothing has happened, no sound, no image, no lights.\n\nCan you send me a new .hex file compiled\u00a0with the original\u00a0\"Configuration Bits.h\"?\n\nAre you sure? yes | no\n\ngreenaum wrote 01\/06\/2016 at 19:35 point\n\nIf a disk program doesn't load in extra data once running, then a snapshot would be fine anyway. Indeed many of the games for the Spectrum (an example I'm most familiar with) are snapshotted after the copy-protection check has been done.\n\nThe Multiface, btw, was an add-on for 8-bit computers, those that exposed the CPU bus to a connector on the back, at least. Usually paged in it's own ROM, and contained 8K RAM (or early versions used the screen RAM for workspace, messing the screen up til the game re-drew it). Pressing a button tripped the NMI line and paged in it's ROM, from there you could snapshot to any medium it supported.\n\nThere was also some nice support software that you could load into the 8K RAM. Stuff that would search for values in the machine's main RAM, for things like life counters, spaceship shield levels, etc. It could alter the code from there, letting you make\u00a0 up your own cheats. Magazines were full of POKEs back then, Multiface or otherwise, you could always type your own in, after the machine code has loaded but before it runs.\n\nAh, the good old days! I can see why you're doing this!\n\nOn the issue of disk drives, the common controller chips have been emulated somewhere or other, there might be code you can plug in, perhaps if you contacted a friendly emulator author. Sure you know, programmers are usually keen to share code with someone who appreciates it and can put it to use, even if the source isn't publicly released.\n\nAre you sure? yes | no\n\nziggurat29 wrote 01\/08\/2016 at 02:20 point\n\nI can see the Multiface via wikipedia. \u00a0I don't think we had one for the TRS-80, but probably could have, at least for the Model I, which had the whole bus pants-down on the card edge (a lot of it's electrical undoing, and part of the reason for the unibody Model III and IV. \u00a0Well that and FCC part 15...).\n\nYes, the existing desktop emulators have plenty of \u00a0existing\u00a0code to use; I would probably use xtrs's at least for reference, if not as-is. \u00a0Still, the idea of making a BogoDOS interests me because I'm making new Z80 code for an old machine (and because it might give a better user experience, sort of like with the cassette emulation, which now makes 'cassettes' a delight to work with). \u00a0But you never know what I'll do -- I certainly don't -- and I'm eager to get back to my cryptographic calculator project, so I want to close this one up for a while....\n\nAre you sure? yes | no\n\ngreenaum wrote 01\/06\/2016 at 02:08 point\n\nAs far as disk loading goes, you could do what the early ZX Spectrum emulators did, with (originally) .SNA and then .Z80 files. Just take a snapshot (from a PC emulator, perhaps) of the machine's RAM and registers (including hardware ones) while a program is running. Then have a simple menu system, outside the TRS-80 emulation, that loads the snapshot into RAM.\n\nAnother way might be to add some pseudo-instructions of your own to the Z80, that load in snapshots. Then patch the DOS \/ BASIC etc to use them, at which time the hardware takes over and loads a snapshot in.\n\nOr if not pseudo-instructions, have your hardware keep an eye on a certain I\/O address, and again, load in a snapshot when it's called. Patch your routines accordingly.\n\nYes, it's cheating, but easier than emulating a disk drive, and it gets the job done!\n\nActually snapshotting was done back in the day, the Multiface interface would dump a memory \/ register snapshot to disk \/ microdrive \/ etc, as a way of supporting hardware that the Spectrum's own ROM didn't.\n\nFor bigger games that rely on disk access, this won't work, but are there any?\n\nAre you sure? yes | no\n\nziggurat29 wrote 01\/06\/2016 at 03:40 point\n\nYou make valid points; I do currently use some unimplemented instructions to facilitate\u00a0a 'trap' mechanism, and I currently\u00a0use that to patch the ROM cassette routines to directly read from SD rather than bit-bang in at realtime speed. \u00a0Now cassette is some 160x faster -- it's more pleasant than floppy disk, haha. \u00a0But I'm hosed if I want to run a program that has it's own low-level cassette loader. \u00a0And yes there many that do their own disk IO -- it was commonly done\u00a0as a copy protection scheme (e.g. non-standard formatted track that BACKUP can't copy). \u00a0But, also as you point out, 'who cares'? because this is more of a toy than a saleable product.\n\nAs for snapshotting running state, that should be child's play, especially because the entire address space is only 64K, and I've got a 2GB SD card, haha, so room for\u00a0some 32000 snapshots, haha. \u00a0Maybe I'll add that....\n\nAre you sure? yes | no\n\n## Similar Projects\n\nProject Owner Contributor\n\n### Fixing 37-year-old software: Three Mile Island\n\nJorj Bauer\n\nProject Owner Contributor\n\n### The PCW Project\n\nJames Ots\n\nProject Owner Contributor","date":"2022-12-04 22:28:32","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\": 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\": 0.4590916335582733, \"perplexity\": 3316.6153123179533}, \"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\/1669446710980.82\/warc\/CC-MAIN-20221204204504-20221204234504-00083.warc.gz\"}"} | null | null |
Sitra Ahra is the fourteenth full-length musical album by Therion released on 17 September 2010 in Europe, and 26 October 2010 in North America. It is the first studio release since Gothic Kabbalah in 2007. The album title was announced on 4 February 2010. It refers to the Qliphoth of Qabalistic lore.
Track listing
Charts
Personnel
Christofer Johnsson – guitar, keyboards
Christian Vidal - guitar
Nalle "Grizzly" Påhlsson – bass guitar
Johan Koleberg – drums
Thomas Vikström – vocals
Snowy Shaw – vocals
Lori Lewis – vocals
Linnéa Vikström – vocals on "Sitra Ahra", "Kings of Edom", "Land of Canaan" and "Hellequin"
Mika "Belfagor" Hakola (Ofermod, Nefandus) - harsh vocals on "Din"
Petter Karlsson - vocals on "2012", writer of "Hellequin"
Marcus Jupither - vocals on "Hellequin"
Thomas Karlsson – lyrics
Thomas Ewerhard – cover artwork
References
Therion (band) albums
Nuclear Blast albums
2010 albums | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,521 |
How to Get the Most Out of Playing the Lottery Online
Home » How to Get the Most Out of Playing the Lottery Online
Purchasing a ticket in a lottery game is a fun way to spend time. The opportunity to win big prize money is a big draw for lottery fans, and the best way to get the most out of your ticket purchase is to check your odds before buying. This will help you buy the best possible ticket, and will also help you increase your odds of winning.
Lotteries have been around for many centuries. They were first organized by governments to fund important projects, such as the Great Wall of China. They were also used to improve fortifications and prepare for wars during the Middle Ages. Governments also used lotteries to help the poor, which is still a popular practice today.
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Another common game is Keno. It uses a wheel system to draw the numbers, and uses an approved random number generator. The odds of winning are close to 50%. Several states also offer online scratch cards. The top prize in keno is usually $100,000.
The New York state lottery has had the highest sales values in the US for more than 20 years. They offer a wide range of games, including Lotto, Mega Millions, and Powerball. In addition to these, New York offers local state games.
Many people think that the past draws have an impact on the future draws. This is known as the gambler's fallacy. Although it is a commonly held belief, the truth is that the randomness of events does not influence the results. In most lotteries, the house edge is close to 50 percent.
The odds of winning a jackpot are virtually impossible for any individual, but if you are lucky enough to win, your prize will be split between you and another lottery participant. A popular tip for maximizing your odds of winning is to wait for the big jackpots. The smaller jackpots still have significant prizes.
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\section{S1 Extraction of parameters from fit to power spectral density (PSD)}
Here we describe how to extract nanoparticle parameters, such as mass $m$ and radius $r$, and parameters about the motion of the nanoparticle in the trap, such as damping of the particle motion $\Gamma_0$, from fitting to the measured power spectral density. Experimental data is directly recorded from the photodiode signal, which means the particle position is recorded in volts as function of time.
{\it Equation of Motion:}
The time trace signal contains generally the motion of the particle in
\emph{x}, \emph{y} and \emph{z} degrees of motion of the particle, which we simplify to one dimension \emph{x}:
\begin{equation}
\label{eq:equationofmotion}
\ddot{x}(t)+\Gamma_{0} \dot{x}(t) +\frac{k_{0} +k_{fb}(t)}{m}x(t)= \frac{F_{\rm th}(t)}{m}
\end{equation}
{\it Power spectral density (PSD) with gamma factor $\gamma$:}
We can write the PSD of the trapped nanosphere from
the above equation of motion. However, to be able to fit to the
experimental data it should be noted that the above is measured in
nm$^{\text{2}}$/Hz. Whereas experimental PSD of the recorded time trace is in
V$^{\text{2}}$/Hz, therefore the experimental PSD should look like as
\begin{equation}
\label{eq:fullpsd}
S_{x}(\omega) = \gamma^2\frac{k_B T_0}{\pi m}\frac{\Gamma_0}{([\omega_0 + \delta \omega]^2 - \omega^2)^2 + \omega^2[\Gamma_0 + \delta \Gamma_0]} ,
\end{equation}
where $\gamma$ is the conversion factor from volts to nanometers
in units of V/m.
{\it Fitting gives A, B, C parameters in the PSD model:}
We can simplify Eq.~(\ref{eq:fullpsd}) as
\begin{equation}
\label{eq:psdfit}
S_{x}^{exp} = \frac{A}{(B^2-\omega^2)^2+\omega^2 C^2} .
\end{equation}
We fit the experimental PSD with the simplified
Lorentzian according to Eq.~(\ref{eq:psdfit}), where $A:=\frac{\gamma^2 k_B T_0\Gamma_0}{\pi m}$,
$B:= \omega_0 + \delta \omega$ and $C:= \Gamma_0 + \delta \Gamma$ are free fit parameters. To obtain the particles mass $m$ we fit to the PSD of
a particle ($\delta\omega=0$, $\delta\Gamma=0$) at thermal equilibrium at $T_0=$300K.
{\it Obtaining radius $r$:}
Based on the fluctuation-dissipation theorem the damping of the
particle is $\Gamma_0$ and thus can be described as~\cite{beresnev1990motion}
\begin{equation}
\label{eq:fullGamma0}
\Gamma_0 = \frac{6 \pi \xi r}{m} \frac{0.619}{0.619+Kn}(1 +c_k),
\end{equation}
where $r$ is the radius of the trapped particle, $\xi=18.6\mu$Pa s is the viscosity of air, $c_k=(0.31Kn)/(0.785+1.152Kn+Kn^2)$ is a function of the Knudsen number
\begin{equation}
Kn = \overline{l}/p,
\end{equation}
where $\overline{l}$ is the mean free path of the gas particles at the given pressure $p$. We Taylor expand Eq.~(\ref{eq:fullGamma0}) for small Kn$^{\text{-1}}$ to first
order and rewrite for radius $r$,
\begin{equation}
\label{eq:radius}
r = 0.619 \frac{9 \pi \xi d_m^2}{\sqrt{2} \rho k_B T_0}\frac{p}{\Gamma_0} ,
\end{equation}
where $d_m$ is the diameter of air molecules and $\rho$ is the density of the nanoparticle.
{\it Calculating the maximal possible position resolution of the detection method used:} Note that $p$ and $\Gamma_0$ are quantities measured and extracted from parameter $C$ of the Lorentzian fit,
respectively, thus are directly from experimental data. From \emph{r} it is
easily enough possible to obtain the mass of the trapped particle.
From having obtained the mass of the particle we can go back to the
PSD fitting Eq.(\ref{eq:psdfit}), and rearrange to give the conversion
factor,
\begin{equation}
\label{eq:conversationfactor}
\gamma = \sqrt{\frac{A}{C}\frac{\pi m}{k_B T_0}}
\end{equation}
The noise equivalent power (NEP) of a detector characterises the resolution of a detector. For the balanced photodiode detectors used the $NEP_{det} = 70nV/\sqrt{Hz}$. Equivalently, we can work out the position resolution of our setup
\begin{equation}
\label{eq:positionsensitivity}
S_{x,min} = \frac{NEP_{det}}{\gamma} .
\end{equation}
A typical value for $S_{x,min} $ is 17fm$/\sqrt{Hz}$, which is the minimum achievable in our system.
The current experimental position resolution, $S_{x,exp} = 0.53 pm/\sqrt{Hz}$, is limited by
the noise floor which currently is at $NEP_{exp} = 2\mu V/\sqrt{Hz}$ as analysed from experimental data as in Fig.1a). Parameters as extracted from the fit to the PSD shown in Fig.1 are summarised in Tab.\ref{tab:fittingtable}.
\begin{table}[htb]
\centering
\begin{tabular}{l|r|l|l}
Quantity & Typical & Units & Error\\
& Value & & ($\pm \%$)\\
\hline
Pressure, $p$ & $7 \times 10^{-2}$ & mbar & 15\\
Collisional Damping Rate, $\Gamma_0$ & 400 & Hz & 3\\
Radius, $r$ & 75 & nm & 18\\
Mass, $m$ & $3 \times 10^{-18}$ & kg & 21\\
Conversion Factor, $\gamma$ & $4 \times 10^{6}$ & V/m & 34\\
C.o.M Temperature, $T_0$ & $\sim$ 300 & K & \\
Q factor, & $2 \times 10^{3}$ & & 4\\
S$_{\text{x,min}}$ & $17 \times 10^{-15}$ & m$/\sqrt{Hz}$ & 34\\
S$_{\text{x,exp}}$ & $53 \times 10^{-11}$ & m$/\sqrt{Hz}$ & 34\\
\hline
& & & \\
\end{tabular}
\caption{\label{tab:fittingtable}Table shows the parameters obtained via fitting to a PSD of an uncooled 75nm radius nanosphere trapped at 7$\times$10$^{-2}$mbar. The values given here correspond to the frequency domain trace shown in Fig.1.}
\end{table}
{\it Evaluation of mechanical quality factor $Q_m$:} The PSD is fitted by the Lorentzian according to Eq.(\ref{eq:fullpsd}) and the full width at half maximum $\Delta\omega$ is compared to the mean frequency $\omega_0$ of the motion in the respective direction: $Q_m=\omega_0/\Delta\omega$. $Q_m$ for the 300K peak in Fig.\ref{fig:temperature} is given in Tab.\ref{tab:fittingtable}. Assuming the motion of the particle is dominated by gas collisions, then the width of the PSD is determined by the collisional damping rate $\Gamma_0$ and we can write: $Q_m=\omega_0 / \Gamma_0$. We apply this analysis to the lower graph in Fig.\ref{fig:temperature} and find $Q_m=$5$\times$10$^{7}$.
{\it Evaluation of the temperature of the motion from Lorentzian fits:} We assume that the particle without feedback is at thermal equilibrium with the surrounding gas at $T_0 = 300$K, which is confirmed by our experimental study for various trapping laser powers. Fitting the Lorentzian according to Eq.(\ref{eq:fullpsd}) to a PSD of the particles motion for a particle at thermal equilibrium with the back ground gas we are able to extract $\gamma^2k_B T_0/ \pi m$. Using this we are able to extract the damping parameters $\Gamma_0$ and $\delta\Gamma$ from a fit to a PSD of particle motion for a cooled nanoparticle as shown in Fig.(\ref{fig:temperature}). Finally we can obtain $T_{cm}$ by using
\begin{equation}
\label{eq:tempcal}
T_{cm}=T_{0} \frac{\Gamma_0}{\Gamma_0 + \delta\Gamma}.
\end{equation}
\begin{figure
\centering
\includegraphics[width=0.9\textwidth]{forpaper_uncoolcool-1.pdf}
\caption{ \textbf{Temperature evaluation from fits to PSD.} The hollow points show the PSD for the z-motion with no feedback applied. The temperature is therefore assumed to be 300K. The solid points show the PSD for the z-motion with feedback turned on. The temperature of the z-motion is evaluated by fitting a Lorentzian to the experimental data points and has been evaluated to be 222mK. It can be seen that the peak approaches the noise floor, and a fit is still possible.The laser power used for this figure is higher than that in the main text and Fig.3, hence the Z frequency peak occurs at a higher frequency.}
\label{fig:temperature}
\end{figure}
\section{S2 Evaluation of resolution of position detection from wavelength scan of trapping light:} Here we describe the detection of the particle position by analysing the optical interference pattern of the field which is Rayleigh scattered by the particle $E_{scat}$, which is re-collimated by the parabolic mirror and the diverging reference field $E_{div}$, which is diverging and therefore loosing intensity radiating away from the mirror.
{\it Determining the particle position resolution:} In our case the trapped nanoparticle modulates the trapping laser
field as the back-scattered laser light from the particle acquires a position-dependent phase shift. Although in reality stochastically driven, here for simplicity we model the movement of the particle in the trap as $z(t)=z_0 sin(\omega t + \alpha)$, with $\alpha$ is the phase and $z_0$ is the amplitude of the motion of the particle in the $z$-direction.
{\it The scattered field:} The oscillating particle then Rayleigh scatters the trapping light in all directions, half of which is then collected and collimated in the opposite direction of the trapping laser by the
paraboloidal mirror. The modulation of the scattered light depending the movement of the particle can be written as
\begin{equation}
\label{eq:scatteringfield}
E_{scat} = E_{scat,0} e^{i \beta \sin(\omega_{0} t)},
\end{equation}
where we can write $\beta = z_0\partial_z\alpha$. We work out the phase of the motion of the
particle to be $\alpha = kz - arctan(z/z_R)$, with $k$ is the spring constant and $z_R$ the Rayleigh distance of the optics. Therefore $\partial\alpha
= k-1/z_R$, assuming $z/z_R$ is small, which results in
\begin{equation}
\label{eq:betafactor}
\beta = kz_0 - \frac{z_0}{z_R}.
\end{equation}
{\it The diverging reference field:} We represent the reference field as the
diverging field produced by the focussing of the trapping laser by the
paraboloidal mirror, represented as
\begin{equation}
\label{eq:referencefield}
E_{div} = E_{div,0} e^{i\theta},
\end{equation}
where $\theta = 2fk + \pi$, where \emph{f} is the focal length of the
mirror, and $\pi$-term is introduced due to the Gouy phase shift.
{\it Interference of both fields, homodyne detection:} The combination of both the scattering field and the reference field
forms part of our homodyne detection scheme, which can be written as
\begin{equation}
\label{eq:intensity}
\begin{split}
I(t) & \approx |E_{scat} + E_{div}|^2 \\
& \approx E_{div,0}^2 + E_{scat,0}^2 + \\
& 2 E_{div,0}E_{scat,0}[\sin(\theta)\sin(\beta \sin(\omega_{0} t)) + \cos(\theta)\cos(\beta \sin(\omega_{0} t))] .
\end{split}
\end{equation}
Using the Jacobi-Anger identity we can expand the Bessel functions to leading order
\begin{equation}
\label{eq:intensityexpanded}
\begin{split}
I(t) & \approx E_{div,0}^2 + E_{scat,0}^2 \\
& + 2 E_{div,0}E_{scat,0}[\sin{(\theta)} \times J_0(\beta) + \sin{(\theta)} \times 2J_1(\beta)\sin{(\omega_{0} t)} \\
& + \cos{(\theta)} \times 2J_2(\beta)\sin{(2\omega_{0} t)}],
\end{split}
\end{equation}
where J$_{\text{n}}$($\beta$) is a Bessel function of the first kind, with
\emph{n}=(0,1,2\ldots{}). For the leading order in $\beta$, we can write $J_0(\beta)\approx$1, and $J_1(\beta)$ and
$J_2(\beta)$ refer to the amplitude of the first and second harmonic of the particle motion along a given axis. The ratio of these two
amplitudes gives us the a means by which we can extract $z_0$. By
expanding the Bessel functions to their first order we have
\begin{equation}
\label{eq:rfactor}
\begin{split}
\varrho & = \frac{J_2(\beta)}{J_1(\beta)} = \frac{\beta^2/8}{\beta/2},\\
& = \frac{1}{4}\beta.
\end{split}
\end{equation}
The ratio of these amplitudes we obtain experimentally. We also know that the amplitudes of these terms depend on the wavenumber
\emph{k}. By changing the wavelength we can make the amplitude of one harmonic
more prominent than the other, while the sum of the square of the two amplitudes should stay constant. Since we also know z$_{\text{0}}$ in terms of volts through our recorded signal we can then produce an alternative means to obtain $\gamma$, the conversion factor from Eq.(\ref{eq:conversationfactor}). We can then obtain mass $m$ and radius $r$ of the particle without any knowledge of
the pressure $p$ and damping factor $\Gamma_0$. The method is also transcend any assumption about the theoretical kinetic model being used.
\begin{figure
\centering
\includegraphics[width=0.8\textwidth]{Scan.pdf}
\caption{ {\bf Wavelength scan to measure relative amplitude change in the first and second harmonic of the trap frequency for the z-peak.} The relative amplitude change depending on the wavelength of the trapping laser is used to evaluate the resolution for the detection of the particle position. For a 60nm diameter silica particle, trapped at $1\times 10^{-2}$mbar we can observe how the amplitude of the first order peak (top panel, fitted with $\sin{(\theta)} 2J_1(\beta)\sin(\omega_{0} t)$) and second order peak (lower panel, fitted with $\cos{(\theta)} 2J_2(\beta)\sin{(2\omega_{0} t)}$), changes as the wavelength of the laser if varied to extract a parameter independent position resolution. }
\label{fig:wavescan}
\end{figure}
{\it Experimental implementation of wavelength scan:} The parabolic mirror used has a focal distance of $f=3.1$ mm. By varying the trapping laser wavelength in the range 1545nm to 1555nm in steps of 5pm, with this we are able to vary the phase $\theta$ by $5.2\pi$ in steps of $0.03\pi$.
{\it Results:} Fig.3c) by comparing the change in amplitude of the first and second order $z$ motion peaks we calculate the value for $\beta$ in Eq.(\ref{eq:betafactor}). From this we extract the maximum position of particle motion in the $z$ direction, $z_{0}=119\pm10$nm. From equipartition theorem: $m= k_{b}T_{cm}/\omega_{0}^{2}z_{0}^{2} $, with $T_{cm} = 300$K we can obtain a pressure independent measure of the particles mass m$=3\pm0.5\times10^{-19}$kg. Assuming a spherical particle the particle has a radius r$=30$nm$(\pm2)$nm. Finally using $\gamma = V/z_{0}$ where V is the voltage detected on our photodiode, and equation 12 it is possible to calculate the the position resolution of our set up to be $S_{x,exp}=200\pm20 fm/\sqrt{Hz}$.
This wavelength scan method to evaluate the position resolution is more accurate than the method used in supplement S1. Applying the methodology in S1 results in larger errors originating from large uncertainty in the measurement of the pressure in the vacuum chamber, by circumventing pressure readings and exclusivity using the measurements of the of the optical intensity measured by our detector.In Principle this method can be used to measure any spherical particle without knowing its density.
\section{S3 Particle preparation and trapping}
{\it Nanoparticle preparation and trap loading:} Nanoparticles loaded into the optical trap at atmospheric pressure via the use of an Omron micro-Air nebuliser. The nebuliser disperses droplets containing individual nanoparticles. The trapping region was evacuated by a turbo-molecular pump (Pfeiffer, 70l/s) to as low as 1$\times$10$^{-6}$mbar with the particle in the trap. The nebuliser is loaded with a suspension of aqueous liquid containing the nano-particles. The suspension used is prepared by diluting a suspension of 26nm -160nm (diameter) silicon dioxide nano-particles in deionized water using micro pipettes. The suspension is then sonicated for 15 minutes (37kHz, 300K in an ultrasound bath) before being loaded into the nebuliser. A concentration of 76,000 particles per ml was found to work well experimentally when the particles where dispersed into the vacuum chamber. Once a particle is trapped we begin to evacuate the chamber. We tried particles from many different suppliers and manufacturers, but had best trapping and pumping results with particles from the companies micro-particles GmbH and Corpuscular. The trapping success was increased significantly by turning the feedback stabilisation on with previously known feedback parameters.
{\it Experimental setup of trap:} The optical trap is generated with light from a stabilised fibre laser ($\lambda=1550$nm, NKT Koheras Basik CI5, 40mW). The output of the laser is intensity modulated by a AOM (PhotonLines, 80MHz) according to a feedback signal (see supplement S6 for details). The light then seeds an erbium doped fibre amplifier (EDFA, NuPhoton) to a maximum power of 1W. The light is focused by a high numerical aperture (NA=0.995) parabolic aluminium mirror which is mounted in a vacuum chamber. We trap silica (SiO$_2$) nanoparticles at vacuum as low as 1$\times$10$^{-6}$mbar and at trap frequency $\omega_0$. This trap frequency can be controlled by varying the laser power and hence the optical spring constant to achieve a $\omega_0$ in the range 10kHz to 300kHz. The particle is a driven dipole and hence radiates a field, a backwards propagating fraction of which is collected and collimated by the same parabolic mirror. Interference between this back scattered field $E_{scat}$, and the highly divergent field which passes without interacting with the particle through the focus $E_{div}$ (the local oscillator reference field), provides interferometric position resolution (see Fig.~1d) in the main paper). By allowing the reference field to diverge, we make the reference field amplitude comparable with that scattered by the particle, giving a large modulation visibility at the detector. This results in a high particle position resolution.
\section{S4 The parabolic mirror and calculating its NA}
The mirror has been precision machined directly from aluminium by the company Symonds Mirror Technology with a surface tolerance of 15nm. There is no optical or protective coating attached to the aluminium surface. The parabolic mirror as a reflective high NA optic is a cheap alternative to lens optics. The mirror is easy to implement and to us at ultra-high vacuum, which is more difficult for high NA objective lenses. Another advantage, the mirror does not have chromatic effects, which make the position of the focal point independent of the wavelength used. The latter might be interesting for multi-wavelength spectroscopy and manipulation techniques.
{\it Evaluation of the numerical aperture:} The geometry of the mirror trap is illustrated in Fig.(\ref{fig:MirrorDiagram}). The numerical aperture (NA) is defined as the light acceptance cone of the parabolic mirror. As the scattered light from a trapped particle diverges from the focus, we consider the solid angle at the distance $z_{0}$ as a fraction of the maximum angle of acceptance $2\pi$. Thus allowing us to write~\cite{varga2000focusingnumerical}:
\begin{equation}
\rm NA=\int_0^\theta\sin\theta'd\theta'=1-\cos\theta.
\end{equation}
\begin{figure
\centering
\includegraphics[width=0.3\textwidth]{MirrorDiagram.pdf}
\caption{ \textbf{Geometry of the parabolic mirror.} The polarisable particle is trapped in the diffraction limited focal point of the parabolic mirror. We have used a number of different mirror designs though out the experiment, which differ in the working distance, the focal point with respect to the plane surface of the mirror and the numerical aperture NA. The more of the paraboloid used for the mirror, the higher the NA. The NA can also be varied/reduced for a given mirror by modification of the waist of the laser light incident on the mirror: If the light spot is smaller than the machined paraboloid, the the NA is less than the maximum. Typical mirrors, as used here, have a NA$\approx$1.}
\label{fig:MirrorDiagram}
\end{figure}
The general paraboloid function is $z=r^2/(4f)$, where $z$ is the height above the bottom of the mirror, $r$ is the radius of the paraboloid at $z$, and $f$ is the focal length. For the paraboloid as shown in Fig.\ref{fig:MirrorDiagram} at the maximum radius $r_0$ and at the corresponding height $z_0$, with $z_0\leq f$, the angle $\theta$ between the optical axis and the edge of the paraboloid is given by
\begin{equation}
\tan(\theta)=\frac{r_0}{(f-z_0)}=\frac{r_0}{f-r_0^2/(4f)}.
\end{equation}
We can thus define the NA of the parabolic mirror to be
\begin{equation}
\rm NA = 1-\cos \bigg( \arctan \bigg[ \frac{r_0}{f-r_0^2/(4f)} \bigg] \bigg).
\end{equation}
The mirror used for the majority of experiments in this study, had a focal length of $f$=3.1mm and $r_0$=12.7mm, which gives a NA of 0.995.
\section{S5 Evaluation of noises in the experiment by Allan deviation}
We analyse the noise in the experiment using Allan variance evaluation of the frequency dependent noise in the signal of the mechanical harmonic oscillator. The noise analysed contains information about fluctuation of amplitude, frequency and phase of the harmonically oscillating motion of the trapped particle.
Allan variance $\sigma_j^2$ can be depicted in the following steps.: 1) Take a long sequence of time domain data, $z(t)$. We choose z-direction of motion as this is the most sensitive in the experiment.
2) Chop signal in sequences according to time parameter $\tau$ and average the signal within $\tau$. 3) Repeat for various values of $\tau$ and plot according to:
\begin{equation}
\label{eq:allanvariance}
\sigma_j^2 = \frac{1}{2(n-1)} \sum_{i} \left(z_{i+1}(\tau_j) - z_{i}(\tau_j)\right)^2 .
\end{equation}
We will use Allan deviation which is given by $\sigma_j$. We repeat the procedure for variation of accessible experimental parameters: background pressure, feedback modulation depth $\eta$, and feedback phase. We find [in agreement with modelling] that the harmonic motion of the trapped particle is dominated by noise from collisions with background gas. Laser noise amplitudes are small compared to the collisional noise.
{\bf Allan Deviation: Pressure Variation.}
Having created a means by which we can produce the Allan variance/deviation; we can start to compare at different parameter
variations. We are concerned specifically in our trapping frequency range, namely 10 kHz to 300 kHz, indicated as grey area in the Allan deviation figures.
\begin{figure}[htb]
\centering
\includegraphics[width=0.75\textwidth]{avar_pressure.pdf}
\caption{\label{fig:avar_pressure}
{\bf Noise from pressure variation:}Allan variance of 150nm particle as it is cooled with constant feedback parameters but at different background pressure in the vacuum chamber. The different colour lines indicated Alan deviation at different pressures. The grey are indicated the frequency range of the mechanical oscillation of the trapped particle where the noise couples directly to the motion. Noise at the frequencies of $x,y,z$-motion, at along the vertical dashed lines, will need to be reduced as much as possible to realise a extreme high Q oscillator.}
\end{figure}
It is apparent from Fig.\ref{fig:avar_pressure} that by decreasing pressure the Allan deviation is decreasing and approaching the noise floor of the experiment. The noise floor was taken with no particle in the trap, but with the laser system, detectors and detection electronics in usual operation mode. It represents the minimum noise level possible at the given configuration of the experiment. The clear trend in pressure dependency toward the noise floor indicates that random gas collisions are the dominating noise source for the motion of the trapped particle. This is in agreement with the theoretical modelling described in the main text.
Each data string used for this Allan deviation noise analysis was taken for the duration of one second, which is a comparably short time. Therefore we do not expect to cancel [average out] any random noises in this measurements.
Data has not been taken at conditions and durations to perform a specifically low noise measurement. The Allan noise plots are meant to illustrate the usual noise level in a typical experiment, where there is clearly a lot of room for noise reduction procedures.
{\bf Allan Deviation: Feedback Modulation Depth Variation.}
Here we vary the feedback modulation depth $\eta$ while keeping all other parameters constant.
\begin{figure}[htb]
\centering
\includegraphics[width=0.75\textwidth]{avar_gain.pdf}
\caption{\label{fig:avar_gain}{\bf Noise from feedback gain variation:} Allan deviation of the time-domain signal of the trapped particle motion in z-direction as it is cooled with increased modulation depth $\eta$ of the parametric feedback at constant pressure 5$\times10^{-6}$mbar and feedback phase $\phi$=70 degrees.}
\end{figure}
We can see that there is no clear $\eta$-dependency from the noise levels (see Fig.\ref{fig:avar_gain}) and the magnitude of the variation within the data set is much less compared to the observed variation for the pressure dependence.
To further cool the particle a naive attempt could be to increase $\eta$ further. However we experimentally observe that after a certain gain factor threshold at a relative modulation depth of a few percent, we are unable to cool the motion of the trapped particle instead heating of the motion was observed.
One could speculate that this is due to noise being introduced by the feedback while increasing the modulation depth. Instead this analysis, using Allan
deviation, indicates that this is not the case, as there is no obvious trend in the noise depending on $\eta$. Our analysis suggests that the reason for the non-trivial relation between $\eta$ and cooling temperature is within the parametric dynamics of the feedback itself.
{\bf Allan Deviation: Feedback Phase.}
As shown in Fig.3) (in the main text) modulation of the feedback phase $\phi$ affects the temperature of the particle's centre of mass motion in the trap. Once again the question we explore here is if this effect is related to noise introduced by the feedback. We plot Allan deviation as we change phase in Fig.\ref{fig:avar_phase}
\begin{figure}[htb]
\centering
\includegraphics[width=0.75\textwidth]{avar_phase.pdf}
\caption{\label{fig:avar_phase}{\bf Noise from feeddback phase variation:} Allan deviation for the backscattered light off a trapped 150nm particle. Pressure is constant at 5$\times 10^{-6}$mbar and the modulation depth is constant at $\eta$=0.39$\%$ . The phase of the feedback loop $\phi$ is varied as indicated in the legend of the plot.}
\end{figure}
and find no clear relation between the feedback phase and the noise. In the main body of the paper we explain the observed heating and cooling effect as depending on the phase by an optical spring effect rather than related to noise.
In summary, from Allan deviation of feedback modulation depth and of phase variation we conclude that no systematic noise effects are introduced to the motion of the particle by feedback.
\section{S6 Feedback implementation}
While the first linear feedback scheme demonstrated in optomechanics for a cavity mirror setup~\cite{PhysRevLettCohadon}. the feedback was a phase shifted proportional feedback that applies a direct force via radiation pressure. The method here used is one of a parametric feedback and based on the modulation of the optical spring constant of the trap. Parametric feedback cooling takes advantage of parametric excitation, that is to say when a parametric oscillator is driven at twice the natural frequency the particles oscillation locks to the modulation phase resulting in amplification. By adjusting the phase of the driving at twice the frequency damping of the particles motion occurs. This means that to damp the motion of an optically trapped particle we need to modulate our laser intensity at twice the trap frequency and with a phase shift relative to that of the particle motion. The method used to achieve this experimentally can be seen in Fig.\ref{fig:ExperimentalDiagram}.
\begin{figure}[h]
\centering
\includegraphics[width=0.7\textwidth]{Feedback.pdf}
\caption{ \textbf{Feedback cooling scheme. }The scattered light from the particle is collected by a single photodiode. The detected signal can be considered a carrier wave containing three signals of differing frequency's corresponding to the trap frequency's of each spatial degree of freedom plus noise. This signal is then sent to three different lock in amplifiers (ZI HF2LI Lock-in Amplifier), where the signals are extracted for each spatial degree of freedom. In each of the lock in amplifiers the frequency $\omega $ and phase $\theta$ of the particle motion in one spatial degree of freedom is extracted. This information is then used to create a sine wave with amplitude $A$, twice the frequency of the trap frequency and a phase shift $\delta\theta $ relative to its measured phase, resulting in a feedback signal equivalent to $x\dot{x}$. These frequency doubled and phase shifted signals for each spatial degree of freedom are added together before being sent to a AOM, to modulate the intensity of the laser beam.
}
\label{fig:ExperimentalDiagram}
\end{figure}
To quantify the strength of the applied feedback we define the modulation depth $\eta$ of the optical feedback signal as $\eta = I_{fb}/I_{0}$where $I_{0}$ is the laser intensity without feedback and $I_{fb}$ is the amplitude of the feedback modulation. By adjusting the size of the modulation depth we can control the amount of damping we induce via feedback cooling and thus raise or lower the temperature of our trapped nanoparticle as desired (See Fig.2d in the main text). This controlled heating and cooling of an optically trapped particle is a useful tool for the manipulation and the preparation of mechanical states of trapped nanoparticles.
\section{S7 Derivation for connection of feedback modulation depth to underlying dynamics of the trapped particle}
Eq.(1) in the main text can be written in the following form
\begin{equation}
\label{eq:2}
\ddot{x}(t) + \Gamma_0 \dot{x}(t) + \omega_0^2
x(t) = \frac{1}{m} (F_{th}(t) + F_{fb}(t)),
\end{equation}
where $F_{fb}(t) = - k_{fb}(t)x(t)$, considering the particles motion as $x(t)=A\sin(\omega_{0} t)$, we can write $F_{fb}$ in terms of the particles motion
\begin{equation}
\label{eq:FP}
F_{fb}(t) = - \frac{2 \Delta k }{A^2 \omega_0} x(t)^2 \dot{x}(t).
\end{equation}
The modulation depth is defined as $\eta = \Delta k/k_{0}=\Delta k/m \omega_{0}^{2}$ allowing us to write the equation of motion in terms of our modulation depth
\begin{equation}
\label{eq:2}
\ddot{x}(t) + \Gamma_0 \dot{x}(t) + \omega_0^2
x(t) = \frac{F_{th}(t)}{m} - \frac{2 \eta \omega_0}{A^2 } x^2(t) \dot{x}(t).
\end{equation}
Making the slow-varying approximation $(x(t) = \bar{x} + \delta x(t) )$, which means that the mean of the position $\bar{x}$ is varying much slower with time as the position fluctuations $\delta x(t)$, we can write,
\begin{equation}
\label{eq:6}
\begin{split}
\dot{x}(t)^2x(t) & = (\bar{x}(t) + \delta x(t))^2(\dot{\bar{x}}(t) + \delta \dot{x}(t))\\
& = (\bar{x}^2(t) + \delta x^2(t) +2\delta x(t)\bar{x}(t))(\dot{\bar{x}}(t) + \delta \dot{x}(t))\\
& = \bar{x}^2(t)\dot{\bar{x}}(t) + \delta x^2(t)\dot{\bar{x}}(t) + 2\bar{x}(t) \dot{\bar{x}}(t) \delta x(t) \\
& + \bar{x}^2(t) \delta \dot{x}(t) + \delta x^2(t) \delta \dot{x}(t) + 2 \bar{x}(t) \delta x(t) \delta\dot{{x}}(t)
\end{split}
\end{equation}
and retaining only the linear terms in $\delta x $, we write our feedback force Eq.(\ref{eq:FP}) as
\begin{equation}
\label{eq:6}
F_{fb}(t) = - \frac{2 \Delta k }{A^2 \omega_0} ( \overline{x}^{2}x(t) + \overline{x}^{2} \dot{x}(t)) ,
\end{equation}
noting $\overline{x} = A/2$, we can write the equation of motion in the following form
\begin{equation}
\label{eq:3}
\ddot{x}(t) + \Gamma_0 \left\{1 +\frac{\eta \omega_0}{2 } \right\}\dot{x}(t) + [\omega_0+\delta \omega]^2 x(t) = \frac{1}{m} F_{\rm th}(t).
\end{equation}
Taking the Fourier transform of the function and rearranging yields the following Power Spectral Density, $S_{x}(\omega)$,
\begin{equation}
\label{eq:4}
S_{x}(\omega) = \frac{2 k_b T_{0}}{\pi m}\frac{\Gamma_0}{([\omega_0+\delta \omega]^2 +
\omega^2)^2 + \omega^2(\Gamma_0 + \eta \omega_0/2 )^2}
\end{equation}
\\
Knowing that the integral of a power spectral density can be written
as
\begin{equation}
\label{eq:5}
\begin{split}
\langle x^2 \rangle & = \int_{0}^{\infty} S_{x}(\omega) d\omega \\
& = \frac{\Gamma_0 k_b T_{0}}{2 \pi m}
\int_{-\infty}^{\infty}
\frac{1}{([\omega_0+\delta \omega]^2+\omega^2)^2+\omega^2(\Gamma_0 +
\eta \omega_0/2 )^2} d\omega \\
& = \frac{\Gamma_0 k_b T_{cm}}{m}
\frac{1}{\omega_0^2 (\Gamma_0 + \eta \omega_0/2 ) }
\end{split}
\end{equation}
Using the equipartition theroem we note,
\begin{equation}
\label{eq:6}
\begin{split}
\frac{1}{2}k_bT_{cm} & = \frac{1}{2} m \omega_{0}^2 \langle x^2
\rangle \\
& = \frac{1}{2} m \omega_{0}^2
\frac{\Gamma_0 k_b T_{0}}{ m}
\frac{1}{\omega_0^2 (\Gamma_0 +
\eta \omega_0/2 )}, \\
\implies T_{cm} & = T_0 \frac{\Gamma_0}{\Gamma_0 + \eta \omega_0/2 }.
\end{split}
\end{equation}
This shows an inverse relation to the modulation depth $\eta$ of the
feedback introduced to the system, in agreement with Eq.(9). From this we can see that if
$\eta \to \infty$ then $T_{cm} \to 0$. This of course is something we
do not observe experimentally. We find that as $\eta$ increases there
is plateau of the particles temperature and sometimes an increase in the temperature such that the particle can be lost from the trap. This we infer to be due to the particle experiencing a greater impulse at higher modulation depths and therefore, resulting in nonlinear response.
\section{S8 System Limitations}
In this section we discuss what causes limitations to cool towards the ground state in our system. The ability to cool a particle depends upon the resolution of which its position can be resolved. There are several sources of noise in the system which need to be minimized to produce the highest possible position resolution including measurement uncertainty due to the random arrival of photons at the particle's location and measurement backaction due to momentum transfer from photons to the particle.
\subsection{S8.1 Detection resolution limits}
To examine whether the particle motion is resolvable in the ground state we consider the motion of the particle in the ground state given by
\begin{equation}
\label{eq:4}
\langle x_{ground} \rangle = \sqrt{\frac{\hbar}{m\omega_{0}}}.
\end{equation}
The size of the ground state for a 66nm silica particle with $\omega_{0}=2 \pi \times 100$kHz is $\langle x_{ground} \rangle = 6.5$pm. The detection resolution of our system has been evaluated in supplement S2 to be $S_{x,exp}=200\pm20 fm/\sqrt{Hz}$. For an integration time of 1 second we arrive at a resolution of $200\pm20 fm$. This resolution is sufficient to resolve 32 points per oscillation satisfying the Nyquist theorem. To cool a mechanical mode to near its ground state it is needed to resolve a zero-point motion $\Delta x$ at least within the (thermal) decoherence time. The mean thermal occupancy for an optically levitated nanoparticle is:
\begin{equation}
\label{eq:4}
\langle n \rangle = \frac{k_{b} T_{n}}{\hbar \omega_{0}},
\end{equation}
where $T_{n}=k_{0}\langle x \rangle^{2}/k_{b}$, allowing us to write an expression for the zero-point motion,
\begin{equation}
\label{eq:4}
\Delta x = \sqrt{\frac{k_{b}}{k_{0}}}(\sqrt{T_{n+1}}-\sqrt{T_{n}}).
\end{equation}
The zero-point motion $\Delta x = 2.6$pm and at $10^{-9}$mbar the thermal decoherence time is on the order of $10^{6} s$. Therefore for an integration time of one second a zero-point motion can be resolved and at the predicted ultra-high vacuum (and therefore low $\Gamma_0$) condition the detection resolution of our system should even allow for the spatial resolution of the ground state.
\subsection{S8.2 Detection efficiency limits}
Maximum detection efficiency occurs when $100\% $ of information carrying photons are collected by the detector in the system. To examine the detection efficiency in our system we must consider the fraction of light the particle sees of the laser light passing through the focus. The size of the laser focus is given by w$_{waist}= 2 \pi $w$_{0}$, where w$_{0}$ is the beam waist. While the particle will explore an area of w$_{particle} = \pi x_{0}y_{0}$. The fraction of light at the laser focus the particle sees is $\eta_{Area} = $w$_{particle}/$w$_{waist}$. The amount of light scattered by the particle is given by the Rayleigh scattering cross-section is given by,
\begin{equation}
\label{eq:4}
\sigma_{s} = \frac{2 \pi^{5}}{3}\frac{(2r)^{6}}{\lambda^4}\bigg(\frac{n^{2}-1}{n^2 +2}\bigg)^{2}.
\end{equation}
For a given laser power $P_{0}$ and radius of particle $r$, the power scattered by a nanoparticle within the trap is given by,
\begin{equation}
\label{eq:4}
P_{scat} = \frac{\sigma_{s}}{2 \pi r^{2}} P_{0} \eta_{Area}.
\end{equation}
Therefore we can find the number of photons scattered in a given in a second is,
\begin{equation}
\label{eq:4}
N_{scat} = P_{scatt}/h \omega_{0}.
\end{equation}
The percentage of photons collected $\eta_{trans}$ can be calculated by accounting for the number of photons lost by absorption in the optical components and the amount of photons collected by the parabolic mirror, which collects $50\%$ of the scattered photons (a significant improvement on lens based traps). Combining this with the quantum efficiency of the detector $\eta_{Q}$ we can write an expression for the power detected as
\begin{equation}
\label{eq:4}
P_{det}=\eta_{Q}\eta_{trans}P_{scat}.
\end{equation}
The signal amplitude measured on the detector in volts is given by $I_{det}=P_{det} \times 1.0A/W \times G$. Where the transimpedance gain is given by $G \sim 10^{5}$V/A. Thus for the particle in the ground state with $\langle x_{ground}\rangle= 6.5$pm we expect about 30pV of electrical signal from the detector according to the estimated fraction of the Rayleigh scattered photons incident on the detector. The sensitivity of the balanced photo detector is $70nV/\sqrt{Hz}$ and the Zurich Instruments UHFLI lock-in amplifier has a sensitivity of 1nV. For the signal to therefore be detectable in the ground state an amplification/gain of about 2500 and an integration time of one second will be needed. We conclude that the detection efficiency is not putting a too strong constraint on the approach of the ground state.
\subsection{S8.3 Measurement noise in the system}
As the modulation depth of the feedback signal is increased an increase in the cooling rate is increased. However as the modulation depth exceeds $1\%$ the cooling rate starts to reduce and the particle temperature increases (as shown in Fig.(\ref{fig:moddepth})). This is suggestive of classical measurement noise, such as detection noise, electronic noise imparted by the FPGA system, amplifiers and the lock-in amplifiers in the system. Any such noises, if picked up by the measurement system, will be amplified by the feedback loop, which is the suspected reason for the observed effect of $\eta$ in Fig.(\ref{fig:moddepth}) and thus places a serious limit on the cooling rate that can be achieved in the system. However it is expected that the cooling rate achieved for modulation depths of $\eta\leq 1\%$ will be sufficient to cool to smaller $\bar n$ (ultimately only limited by the photon recoil rate, see below S8.4), if the background pressure and therefore also $\Gamma_0$ are reduced.
\subsection{S8.4 Photon Recoil Limit}
The laser light used to trap scattering off the particle imparts a momentum kick to the trapped particle, acting as an additional heating source. In our system the collisional damping from background gases is much larger than this effect. However as the particle is cooled and the temperature reduced a point will be reached where photon recoil will become an observable effect~\cite{Jain2016}. The photon recoil rate is given by,
\begin{equation}
\label{eq:4}
\Gamma_{recoil}= \frac{1}{5}\frac{P_{scatt}}{m c^{2}}\frac{2 \pi c}{\lambda \omega_{0}}.
\end{equation}
For our system $\Gamma_{recoil}= 31.8$kHz, thus considering the phonon number at the steady state $n\delta\Gamma = 7000 \times 2\pi \times 500$Hz= 21MHz, we predict that at 24 phonons $\Gamma_{recoil}$ photon recoil will become a limiting factor in our system and will therefore prevent ground state cooling.
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,918 |
Q: Default A record for custom nameserver I have quite a few domains parked that are currently not in use, so I am looking into a dead simple way to maintain them and display a custom parking-page. I do not want to update every single one the DNS-records on all of the domains separately – instead I want the ability to just have default nameservers / NS-records for all the domains and to have "the rest handle itself".
What I am looking for is setting up a custom nameserver (ie. ns.example.com) which I can apply for each domains; what I want to happen then is that all domains with that nameserver automatically gets an A-record which I can point to the server of my liking.
On that "target"-server I can then just check the URL and display an appropriate parking-page (if needed, or just serve a default one).
I've begun reading up on BIND setting up a custom nameserver – is this the way to go? If so, anything special I should look into to speed up the time to deployment?
Or even better, are there any "ready to use"-solutions that would fit my needs? (Preferably free, but I'm more than willing to pay for good systems).
A: This should be moved to unix.se ... but to do this is fairly easy. I run my own DNS servers so I buy a domain, set its DNS servers to ns1.mydomain and ns2.mydomain, and run a few shell scripts on my primary and secondary servers to set up zone files, an apache vhost, and mail service.
If you don't feel like duct taping your own solution together like I did, there are service management consoles that you can use that would do all of this, and allow creation of sub-management, etc for resellers and so on. If this is of interest to you, I'd recommend looking at ISPConfig - https://www.ispconfig.org
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,143 |
Peugeot Revs Up Launch of 70 MPG Diesel Hybrid
The Peugeot diesel hybrid promises to average better than 70mpg and have the lowest carbon-dioxide emissions of any car other than a pure electric.
Published: 10-Jun-2007
PEUGEOT plans to be the first manufacturer to offer a small family car with a diesel-electric hybrid power unit. It will be a version of the new 308, revealed last week, and will be on sale before the end of the decade.
EU carmakers have watched the success of petrol-electric hybrids from Toyota and Honda but claim their diesel-engined cars deliver better fuel consumption and produce less carbon dioxide. But diesel cars are unpopular in some countries, notably America. In Britain, hybrids qualify as alternative-fuel vehicles for low car tax and exemption from the London congestion charge, while diesels do not.
Peugeot does not sell in America, but sees an increasing trend for hybrids in Europe and elsewhere. Toyota sold more than 22,000 Prius cars in Europe last year, 5,000 of them in the UK.
Toyota Redesigns Estima Hybrid Minivan
The new Estima Hybrid features the THS II, optimized for use on a minivan, though there is still no decision on whether or not it will be available in North America.
A Closer Look at Peugeot 307 CC Hybride HDi
A mixed-cycle fuel consumption of nearly 70 mpg (UK) means a gain of some 30 percent compared to the standard HDi model.
All Aboard Manchester's Hybrid-electric Bus
Shuttle service operator, First has been testing the latest electro-diesel hybrid engine on services linking Manchester's rail stations, shopping and business areas. First shuttle bus photo courtesy of British Bus Models. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,631 |
'use strict';
var React = require('react');
var Reflux = require('reflux');
var VideoItem = require('../video-item/video-item.component');
var MovieActions = require('../../actions/movie/movie-actions');
var MovieStore = require('../../store/movie/movie-store');
var Movie = React.createClass({
mixins: [Reflux.connect(MovieStore)],
getInitialState: function () {
//movieList : [{
// screenshotsPath: String, //视频截图的文件
// title: String, //视频标题
// description: String, //视频描述
// }]
return {
movieList: []
}
},
componentWillMount: function () {
MovieActions.getMovies();
},
render: function () {
var movieList = this.state.movieList.length === 0 ? '' : (<VideoItem videoItems={this.state.movieList}/>);
return (
<div id="movie-div" className="container-fluid">
<div className="movie-header">
<p>电影 </p>
<a href="moviesmore.html">更多>></a>
</div>
<div className="movie-line"></div>
{movieList}
</div>
);
}
});
module.exports = Movie;
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,944 |
Babette Beaullieu has worked as a sculptor and art educator for 20 years. She works primarily in wood and organic materials which she collects. She has exhibited her wood and mixed media sculptures in galleries and museums through Louisiana and Texas including the New Orleans Museum of Art, Contemporary Art Center in New Orleans, Brunner Gallery of Baton Rouge, D.o.c.s Gallery in New Orleans, Galeria de Suenos in Lafayette, and Sculpture Symposium at the Museum of Fine Arts in Houston.
She has also been commissioned to produce outdoor sculpture works for private collectors in California, Colorado, and Louisiana. In July 2008, Private Spaces, an exhibit of Beaullieu's new work opened at Shaw Center for the Arts in Baton Rouge, Louisiana. Her installation, Secret Gardeners, was part of a city-wide project in New Orleans that opened in November 2008 through AORTA Project's "Community art in the post-disaster landscapes of today".
Beaullieu lives and works north of New Orleans where she teaches Advanced Sculpture in secondary education in the St. Tammany Talented Arts Program. She holds a BFA from the University of California in Santa Barbara in Sculpture. Her art profession began after years in the marine industry where she came to regard her boatbuilding and sail making as the beginning of her interest in sculpture. She has studied art in Europe and recently traveled throughout Bali to study textiles and wood carving.
Private Spaces (2008) Shaw Center for the Arts, Baton Rouge | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,033 |
Q: If you apply the Distributive Property to a Rational and an Irrational number, which will your solution be? Say that "A" and "B" are Rational, and C is irrational, would the solution to "A(B+C)" be Rational or Irrational? An example for clarification would be wonderful.
A: Remember how to add, subtract, multiply, and divide fractions:
$$
\frac p q \pm \frac r s = \frac{ps \pm qr}{qs}, \qquad
\frac p q \cdot \frac r s = \frac{pr}{qs}, \qquad \frac{p/q}{r/s} = \frac{ps}{qr}.
$$
You have $B+C$ and $B$ is rational and $C$ is irrational. Say $B = \dfrac p q$ and $p,q$ are integers. If $B+C$ is rational, then $B+C = \dfrac r s$ for some integers $r,s$, and then
$$
\frac pq + C = \frac r s, \text{ and therefore } C = \frac r s - \frac p q =\cdots \quad\text{(So $C$ would be rational.)}
$$
Hence $B+C$ must be irrational.
Next we ask whether $A(B+C)$ might be rational. Since $A$ is rational, there are integers $k,\ell$ such that $A=k/\ell$. If $A(B+C)$ is rational then there are integers $m,n$ such that
$$
\frac k \ell (B+C) = A(B+C) = \frac m n, \text{ and so } B+C = \frac{m/n}{k/\ell} = \frac{m\ell}{kn}, \text{ so } B+C \text{ would be rational}.
$$
A: HINT:
Sum of a rational and an irrational number is always irrational
$$\text{AND}$$ Product of a rational and an irrational number is a non-zero rational.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 563 |
The 2001 Music City Bowl was the fourth edition of the bowl game held. It was played on December 28, 2001, at LP Field in Nashville, Tennessee, and featured the Boston College Eagles and the Georgia Bulldogs.
Game Recap
Georgia scored first on a 15-yard touchdown pass from quarterback David Greene to wide receiver Fred Gibson, giving the Bulldogs an early 7-0 lead. Boston College kicker Sandro Sciortino kicked a 25-yard field goal near the end of the quarter, to cut the lead to 7-3. In the second quarter, quarterback Brian St. Pierre threw a 10-yard touchdown pass to wide receiver Dedrick Dewalt, as Boston College took a 10-7 lead.
Sandro Sciortino added another 26 yard field goal to take a 13-7 lead. Georgia kicker Billy Bennett kicked a 24-yard field goal before halftime, and BC led 13-10 at halftime. In the third quarter, Georgia's Verron Haynes scored on a 1-yard touchdown run. The ensuing extra point attempt failed, and Georgia clung to a 16-13 lead. With less than 5 minutes left in the game, William Green rushed for a 7-yard touchdown, giving Boston College a 20-16 lead. BC's defense held on for the win. Green was named the game's Most Valuable Player.
References
External links
USA Today game summary
Music City Bowl
Music City Bowl
Boston College Eagles football bowl games
Georgia Bulldogs football bowl games
Music City Bowl
December 2001 sports events in the United States | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,601 |
Parkview House Care Limited is a Private Limited Company. Company number assigned by Companies House is 05233630. The company was incorporated on Thursday 16th September 2004, so the company age is 11 years 9 months 9 days. The company registration status is Active. The company Standard Industrial Classification is 87300, so Parkview House Care Limited is engaged in Residential care activities for the elderly and disabled. Parkview House Care Limited register address is EIGHTH FLOOR, 167 FLEET STREET, London (area code: EC4A 2EA). The company changed its name 2 times. On Monday 23rd November 2009 the name changed to Carebase (Parkview) Limited. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,738 |
Top Medical Anthropology Bachelors degree Programs - 2021
Students who are passionate about Medical Anthropology can study up to a Doctors degree research scholarship. Currently, 74 students earn a some level of degree in Medical Anthropology around the United States each year. More students graduate with a degree in Medical Anthropology in the state of Missouri than any other state. The average annual income for an undergraduate degree in Medical Anthropology is $39,900.
All Award of less than 1 academic year Bachelors degree Postbaccalaureate certificate Masters degree Doctors degree research scholarship
AllFloridaMissouriNebraskaPennsylvania
See where Medical Anthropology is the most popular major in the U.S.
This heat map represents the states that have the highest percent of Medical Anthropology degrees compared to all other degrees awarded in that state.
Top Colleges for Medical Anthropology
Thinking about majoring in Medical Anthropology? You should check out Washington University in St Louis or the University of Miami! These institutions are some of the best campuses to study Medical Anthropology. Currently, Washington University in St Louis has 52 graduates earning their Bachelors degree in Medical Anthropology, while the University of Miami has 2 students earning a Bachelors degree in Medical Anthropology. Learn more about college options in the table below.
Careers for Medical Anthropology Majors
The highest paying career for Medical Anthropology majors is Anthropology and Archeology Teachers, Postsecondary. But, something else to consider is how many job openings there currently is. A job that is in high need that a degree in Medical Anthropology can prepare you for is Anthropology and Archeology Teachers, Postsecondary.
Top Paying Careers for Medical Anthropology
Most in Demand Careers for Medical Anthropology | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 483 |
> # Freud
>
> # en su tiempo
>
> # y en el nuestro
## ELISABETH ROUDINESCO
**Traducción de**
Horacio Pons
www.megustaleerebooks.com
El secreto de un hombre no es su complejo de Edipo [...], es el límite mismo de su libertad, su poder de resistencia a los suplicios y la muerte.
JEAN-PAUL SARTRE
###
Introducción
Un hombre solo está verdaderamente muerto, decía Jorge Luis Borges, cuando muere a su vez el último hombre que lo ha conocido. Es lo que hoy sucede en el caso de Freud, aunque vivan todavía unas pocas personas que tuvieron algún contacto con él en su infancia. Freud dedicó la vida a escribir, y si bien alguna que otra vez destruyó documentos de trabajo y cartas para complicar la tarea de sus biógrafos futuros, se entregó con tamaña pasión a la huella, la arqueología y la memoria, que lo perdido no es nada en comparación con lo conservado. Tratándose de un destino semejante, el historiador se enfrenta a un exceso de archivos y, en consecuencia, a una pluralidad infinita de interpretaciones.
Además de unos veinte volúmenes y más de trescientos artículos, Freud dejó una cantidad considerable de notas, borradores, agendas, dedicatorias y anotaciones en las obras de su inmensa biblioteca instalada en el Freud Museum de Londres. Escribió, al parecer, alrededor de veinte mil cartas, de las que solo se conserva la mitad. Estas, en su mayor parte, se han publicado en francés o, cuando no es así, están en proceso de fijación del texto en alemán. A ello se suman intervenciones y entrevistas de gran riqueza realizadas en la década de 1950 por Kurt Eissler, psicoanalista emigrado de Viena a Nueva York, así como textos acerca de unos ciento sesenta pacientes ahora identificados, pero en su mayoría poco conocidos.
Traducidas a una cincuentena de lenguas, las obras de Freud son de dominio público desde 2010, y ya se puede acceder a una parte esencial de sus archivos en el Departamento de Manuscritos de la Library of Congress (LoC, Biblioteca del Congreso) de Washington, después de treinta años de polémicas y terribles batallas. También pueden consultarse diversos documentos en el Freud Museum de Viena.
Sobre Freud se han escrito varias decenas de biografías, desde la primera aparecida mientras aún vivía, en 1924, obra de su discípulo Fritz Wittels, norteamericano naturalizado, hasta la de Peter Gay publicada en 1988, pasando por el monumental edificio en tres volúmenes de Ernest Jones, puesto en entredicho a partir de 1970 por Henri F. Ellenberger y los trabajos de la historiografía científica, a la que me adhiero. Eso sin contar el trabajo historiográfico realizado por Emilio Rodrigué, primer biógrafo latinoamericano, que en 1996 tuvo la audacia de inventar un Freud de la sinrazón más cercano a un personaje de García Márquez que a un científico originario de la vieja Europa. Cada escuela psicoanalítica tiene su Freud —freudianos, posfreudianos, kleinianos, lacanianos, culturalistas, independientes— y cada país ha creado el suyo. Cada momento de la vida de Freud ha sido objeto de decenas de comentarios y cada línea de su obra se ha interpretado de numerosas maneras, a tal punto que, al modo de Georges Perec, podemos trazar una lista de todos los ensayos aparecidos sobre el tema de un «Freud acompañado»: Freud y el judaísmo, Freud y la religión, Freud y las mujeres, Freud clínico, Freud en familia con sus cigarros, Freud y las neuronas, Freud y los perros, Freud y los francmasones, etc. Pero también, destinados a los muchos adeptos de un antifreudismo (o _Freud bashing_ ): Freud rapaz, Freud organizador de un gulag clínico, demoníaco, incestuoso, mentiroso, falsario, fascista. Freud está presente en todas las formas de expresión y de relatos: caricaturas, cómics, libros de arte, retratos, dibujos, fotografías, novelas clásicas, pornográficas o policiales, filmes de ficción, documentales, series de televisión.
Tras decenios de hagiografías, aborrecimientos, trabajos científicos, interpretaciones innovadoras y declaraciones abusivas, y luego de los múltiples retornos a sus textos que han salpicado la historia de la segunda mitad del siglo XX, nos cuesta mucho saber quién era verdaderamente Freud: a tal punto el exceso de comentarios, fantasías, leyendas y rumores ha terminado por distorsionar lo que fue el destino paradójico de ese pensador en su tiempo y en el nuestro.
Por eso, y dado que yo misma frecuenté durante mucho tiempo los textos y los lugares de la memoria freudiana, en el marco de mi enseñanza o con motivo de mis viajes y mis investigaciones, me he propuesto exponer de manera crítica la vida de Freud, la génesis de sus escritos, la revolución simbólica que lo tuvo por iniciador en los albores de la Belle Époque, los tormentos pesimistas de los años locos y los momentos dolorosos de la destrucción de sus iniciativas por los regímenes dictatoriales. La apertura de los archivos y el acceso a un conjunto de documentos todavía no analizados me brindaron la posibilidad de adoptar un enfoque de esas características, y la empresa se vio facilitada por el hecho de que ningún historiador francés se había aventurado todavía en este terreno dominado desde hace lustros por investigaciones en inglés de gran calidad.
En este aspecto, quiero dar las gracias a título póstumo a Jacques Le Goff, quien, durante una prolongada conversación y frente a mis vacilaciones, me alentó vivamente a lanzarme a esta empresa y me dio valiosas indicaciones acerca de la manera como convenía observar a Freud en la construcción de su época, a la vez que esta lo construía.
Así pues, se encontrará en este libro, dividido en cuatro partes, el relato de la existencia de un hombre ambicioso perteneciente a un extenso linaje de comerciantes judíos de Galitzia oriental que se dio el lujo, a lo largo de una época turbulenta —el derrumbe de los Imperios Centrales, la Gran Guerra, la crisis económica, el triunfo del nazismo—, de ser a la vez un conservador ilustrado en busca de liberar el sexo a fin de controlarlo mejor, un descifrador de enigmas, un observador atento de la especie animal, un amigo de las mujeres, un estoico aficionado a las antigüedades, un «desilusionador» de lo imaginario, un heredero del romanticismo alemán y un dinamitero de las certezas de la conciencia, pero también, y acaso sobre todo, un judío vienés, deconstructor del judaísmo y de las identidades comunitarias, tan apegado a la tradición de los trágicos griegos (Edipo) como a la herencia del teatro shakespeariano (Hamlet).
A la vez que se volcaba en la ciencia más rigurosa de su tiempo —la fisiología—, consumió cocaína y, en 1884, creyó descubrir sus virtudes digestivas. Se aventuró en el mundo de lo irracional y del sueño, identificándose con el combate de Fausto y Mefistófeles, de Jacob y el ángel, y después fundó un cenáculo según el modelo de la república platónica, al que arrastró a discípulos fascinados por la búsqueda de una revolución de las conciencias. Con la pretensión de aplicar sus tesis a todos los dominios del saber, se equivocó en lo concerniente a las innovaciones literarias de sus contemporáneos —que tomaron sin embargo sus modelos—, desconoció el arte y la pintura de su tiempo y adoptó posiciones ideológicas y políticas bastante conservadoras, pero impuso a la subjetividad moderna una pasmosa mitología de los orígenes cuyo poderío parece más vivo que nunca cuando más se intenta erradicarlo. Al margen de la historia del «hombre ilustre», abordé, como contrapunto, la de algunos de sus pacientes que llevaron una «vida paralela» sin relación con la exposición de su «caso». Otros reconstruyeron su cura como una ficción y, por último, aun otros, más anónimos, salieron de las sombras gracias a la apertura de sus archivos.
Freud siempre pensó que lo que él descubría en el inconsciente anticipaba lo que sucedía a los hombres en la realidad. Por mi parte he decidido invertir esa proposición y mostrar que lo que Freud creyó descubrir no era, en el fondo, sino el fruto de una sociedad, de un entorno familiar y de una situación política cuya significación él interpretaba magistralmente para presentarla como una producción del inconsciente.
He aquí al hombre y la obra inmersos en el tiempo de la historia, la larga duración de una narración donde se mezclan pequeños y grandes acontecimientos, vida privada y vida pública, locura, amor y amistades, diálogos de largo aliento, agotamiento y melancolía, tragedias de la muerte y la guerra y, para terminar, exilio hacia el reino de un futuro siempre incierto y siempre por reinventar.
## PRIMERA PARTE
# VIDA DE FREUD
### 1
Los comienzos
A mediados del siglo XIX, la aspiración de los pueblos europeos a disponer de sí mismos inflamaba los espíritus. Por doquier, de este a oeste, tanto en el corazón de las naciones ya democráticas como en el seno de las comunidades todavía arcaicas o de las minorías integradas en los Imperios Centrales, un nuevo ideal de emancipación surgía en las conciencias, ilustrando la gran profecía enunciada por Saint-Just en 1794: «Sepa Europa que ya no queréis un solo desdichado ni un solo opresor en territorio francés; fructifique este ejemplo sobre la tierra [...]. La felicidad es una idea nueva en Europa».
El año de 1848 puso en marcha un viraje. Primavera de los pueblos y de las revoluciones, primavera del liberalismo y del socialismo, aurora del comunismo. Tras años de guerras, masacres, sojuzgamientos y rebeliones, hombres de lenguas y costumbres diferentes reclamaban la abolición de los antiguos regímenes monárquicos restaurados en los países donde la epopeya napoleónica había contribuido, no mucho tiempo atrás, a difundir los ideales de 1789: «Un fantasma recorre Europa: el fantasma del comunismo», escribían Marx y Engels en 1848, y proseguían: «Todas las fuerzas de la vieja Europa se han unido en santa cruzada para acosar a ese fantasma».
Si esas revoluciones fueron reprimidas en toda Europa, las ideas que expresaban siguieron propagándose de manera contradictoria, según se refirieran a la Ilustración francesa, caracterizada por la búsqueda de un ideal de civilización universal fundada en una práctica política, o, al contrario, en la _Aufklärung_ alemana, cuya vocación filosófica tenía sus orígenes en la religión protestante.
Sin embargo, a mediados del siglo XIX esas dos concepciones de la Ilustración (civilización y _Kultur_ ) —la primera universalista, y la segunda más identitaria— entraron en contradicción con los regímenes políticos deseosos de restaurar, bajo nuevas formas, el antiguo orden del mundo, gravemente quebrantado por la primavera de las revoluciones. Así apareció el nacionalismo.
Para responder a la aspiración de los pueblos y luchar contra la universalización de los ideales de la Ilustración, la burguesía industrial en plena expansión hizo suya la idea de nación para transformarla en su contrario. Procuró entonces unificar, no a los hombres entre sí, sino naciones jerarquizadas concebidas como entidades distintas las unas de las otras, cada una de ellas asimilada a la suma de sus particularismos. El principio afirmado por la Ilustración francesa, conforme al cual el hombre debía definirse como un sujeto libre, y el ideal alemán de la cultura identitaria fueron sucedidos por una doctrina fundada en la obligación en que se veían todos los seres humanos de pertenecer a una comunidad o una raza: el hombre en sí no existe, se decía; solo hay hombres sujetos a un territorio, a un Estado nación. Cada uno tenía el deber de ser francés, italiano, alemán, antes de ser un sujeto de derecho, al margen de toda pertenencia.
En ese mundo europeo en plena mutación, también los judíos aspiraban a un ideal de emancipación. Convertidos en ciudadanos con todas las de la ley desde 1791, los judíos franceses habían ganado los mismos derechos que los demás ciudadanos, pero a condición de renunciar a la carga de la doble identidad. Para ellos solo debía contar el acceso al estatus de sujeto de derecho, liberado de las servidumbres de la religión y del influjo comunitario. En virtud de ello se les había autorizado, en privado, a practicar el culto de su preferencia. Al mismo tiempo el judaísmo se convirtió, para el Estado laico, en una religión como cualquier otra; dejaba de ser la religión madre, la religión odiada desde la Edad Media, la religión del pueblo elegido que había dado origen al cristianismo. La idea de que uno pudiera definirse como judío en el sentido de tener la identidad judía era contraria al ideal universalista del laicismo francés.
En Alemania, tierra de la Reforma luterana, el proceso de emancipación ambicionado por la Haskalá —el movimiento de la Ilustración judía fundado por Moses Mendelssohn— apuntaba, no a integrar a los judíos como ciudadanos con todas las de la ley, sino a permitirles ser a la vez «judíos _y_ alemanes». Opuestos al jasidismo, otro componente de la Ilustración que intentaba revalorizar la espiritualidad judía —sobre todo en Europa oriental—, los partidarios de la Haskalá afirmaban que los judíos modernos podrían vivir de acuerdo con dos pertenencias positivas: una dependiente de la fe, otra, del territorio. Con la condición, de todos modos, de que se deshicieran de los lastres de una tradición religiosa demasiado apremiante.
En la generalidad del mundo germanoparlante en vías de industrialización —de Europa del Norte a la _Mitteleuropa_ —, los judíos asquenazíes no habían conquistado los mismos derechos que en Francia. Repartidos en las cuatro grandes provincias antaño situadas en el corazón del Santo Imperio Romano Germánico —Galitzia, Moravia, Bohemia y Silesia— e incorporadas luego al Imperio austrohúngaro, ocupaban en realidad un territorio más amplio de fronteras indeterminadas —la famosa _Yiddishland_ — donde se agrupaban en comunidades de una misma lengua y circulaban por una zona inestable entre Polonia, Lituania, Bielorrusia, Ucrania, Rumanía y Hungría.
Al no tener acceso a todas las profesiones, esos judíos estaban condenados, para escapar a la humillación de serlo, ya fuera a la conversión, ya fuera a la práctica del autoodio judío, ya fuera al éxito intelectual, a menudo vivido a la manera de una revancha: «Si los judíos se destacaron en la universidad», escribe William Johnston, «es porque sus familias los exhortaron a trabajar con más empeño para vencer los prejuicios».
Los judíos emancipados del siglo XIX creían, así, ser capaces de escapar a la persecución ancestral mediante la integración en la sociedad burguesa industrial e intelectual de diferentes maneras, según el país donde habitaran: como ciudadanos con todas las de la ley en Francia, como individuos pertenecientes a una comunidad en Inglaterra y más adelante en Estados Unidos, como súbditos judeoalemanes en el mundo germánico y como minorías en los Imperios Centrales. Muchos de ellos transformaron su apellido con motivo de las distintas migraciones que los afectaron: de ahí el movimiento de germanización o afrancesamiento de los nombres polacos, rusos o rumanos en esa época. Y muchos renunciaron a la circuncisión o se convirtieron.
Pero a medida que el nacionalismo se apartaba de los antiguos ideales de la primavera de los pueblos, comenzaron a ser rechazados, ya no por su religión sino por su «raza», es decir, debido a una pertenencia identitaria invisible que parecía resistirse a las conversiones y que, al mismo tiempo, los forzaba a definirse, también a ellos, como originarios de una nación. Tal fue la paradoja del nacimiento del antisemitismo, que reemplazó al viejo antijudaísmo. El judío dejó de ser condenado al ostracismo por su práctica de la _otra_ religión —el primer monoteísmo—; ahora se lo miraba como miembro de una raza en busca de una nación.
Si durante siglos los europeos solo habían tenido que vérselas con judíos _dispersos_ , es decir, con un pueblo de parias consciente del rechazo que provocaba, y que entendía su unidad o su universalidad sin referencia a frontera alguna, pronto iban a tener que enfrentarse con un pueblo que, como ellos, estaba obligado a definirse como una nación: la nación judía. Pero ¿qué es una nación sin fronteras? ¿Qué es un pueblo sin territorio? ¿Qué son una nación y un pueblo compuestos de sujetos o individuos que, a fuerza de tener su origen en diferentes naciones, no son ciudadanos de ninguna parte?
Fue en ese mundo en plena efervescencia, marcado por una urbanización y una germanización graduales de los judíos del reino de los Habsburgo, donde nació Jacob Kallamon (Kalman) Freud, en Tysmenitz, aldea ( _shtetl_ ) de Galitzia oriental, el 18 de diciembre de 1815, seis meses después de la derrota de las tropas napoleónicas en Waterloo. Como muchos judíos establecidos en esa zona de Europa oriental, ahora incorporada al imperio de los Habsburgo, su padre, Schlomo Freud, originario de Buczacz, ejercía la profesión de comerciante. Tras el nacimiento de su hijo mayor, la mujer de Schlomo, Peppi Hofmann-Freud, hija de Abraham Siskind Hofmann, negociante en tejidos y otros artículos de primera necesidad, trajo al mundo otros dos varones —Abae y Josef— y una niña. El apellido Freud derivaba sin duda del nombre de pila Freide que llevaba la bisabuela de Schlomo.
Comerciante de lanas en Breslau, Abae tuvo muy poca suerte con sus hijos: un varón hidrocefálico y débil mental, otro que se volvió loco. Al pensar en sus tíos y sus primos durante su viaje a París en 1886, Freud, por entonces ferviente admirador de Jean-Martin Charcot y convencido del origen hereditario de las neurosis, no vacilaba en afirmar que una tara neuropatológica afectaba a su familia: «En mi calidad de neurólogo me preocupan tanto estas cosas como a un marinero el mar». Y agregaba: «Estas cosas son muy corrientes en las familias judías».
Hacia mediados de 1832, cuando tenía apenas diecisiete años, Jacob se casó en Tysmenitz con la joven Sally Kanner, hija de un comerciante. Según la costumbre todavía vigente en la época, las dos familias habían concertado el matrimonio. En un primer momento la pareja se alojó en casa de la familia Kanner, donde Sally trajo al mundo dos varones: Emanuel en 1833 y Philipp un año después. Tuvo a continuación otros dos hijos que murieron de pequeños.
Siskind Hofmann y Schlomo Freud se entendían a las maravillas. Como solía suceder en las familias extensas del _shtetl_ , regidas por la ley del padre y los matrimonios consanguíneos, tres generaciones vivían bajo el mismo techo o en el mismo barrio. Las mujeres permanecían en el hogar para criar a los hijos en compañía de sus madres, hermanas, suegras, criadas o ayas, mientras que los hombres, padres, yernos e hijos, se encargaban de los negocios fuera de la casa: por un lado el poderío femenino reducido al territorio de lo íntimo y de las tareas domésticas, por otro el poder masculino en perpetuo exilio. Dentro de ese orden familiar, donde cada cual ocupaba un lugar bien definido desde el nacimiento hasta la muerte, las relaciones entre suegro y yerno revelaban ser tan importantes como las existentes entre padre e hijo, abuelo y nieto o tío y sobrino. Casado en la adolescencia y ya padre de dos hijos a los diecinueve años, Jacob perpetuó esa tradición. Como su padre, se habituó a acompañar a su abuelo materno (Siskind) en sus viajes de negocios a Moravia, donde la política austríaca de asimilación era más rigurosa que en Galitzia y, por lo tanto, más orientada no solo a la germanización de los judíos sino también a su integración en un modo de vida más urbano.
Los dos hombres dormían en posadas judías, respetaban los ritos ancestrales y, al hacerlo, chocaban con las leyes discriminatorias, a la vez que descubrían maneras de vivir más modernas que la suya en el _shtetl_. Uno seguía apegado a la herencia del jasidismo, en tanto que Jacob, si bien piadoso y perfecto conocedor de la lengua sagrada, comenzaba a interesarse en los ideales de la Haskalá. A los veinte años Jacob se convirtió en socio de su abuelo.
En julio de 1844 ambos iniciaron juntos un trámite administrativo con el fin de que los inscribieran en la lista de los judíos «tolerados» en Freiberg. Tras recordar a las autoridades que compraba paños en Moravia, que los llevaba a Galitzia para teñirlos y que sobresalía en el comercio de cáñamo, miel y sebo, Siskind reclamó además la prórroga de su pasaporte y el de su nieto. Luego de muchas y farragosas gestiones se les concedió la «tolerancia».
Cuatro años después la revolución de los pueblos, que estremeció Europa, permitió a los judíos del Imperio austrohúngaro obtener derechos civiles y políticos. La urbanización progresaba a medida que, bajo el efecto de la explosión demográfica, las poblaciones judías de Galitzia emigraban al oeste y el sur. Jacob aprovechó esa situación para solicitar autorización a fin de fijar domicilio en Freiberg. Con el paso de los años deshizo lentamente los lazos que todavía lo ataban a la tradición jasídica de su padre, para romper mejor con la mentalidad del _shtetl_ e integrarse en la nueva sociedad burguesa.
Y como una manera de señalar su evolución, compró un ejemplar de la Biblia de Ludwig Philippson, primer traductor al alemán del texto hebreo. Publicada entre 1838 y 1854 y destinada al uso de los judíos reformados, la obra respetaba la integridad de las Sagradas Escrituras, pero acompañaba el texto de una lujosa iconografía tomada del antiguo Egipto. En la página de guarda Jacob dejó anotada la fecha del 1 de noviembre de 1848, como una manera de celebrar la primavera de los pueblos.
Convertido en liberal sin dejar por eso de salpicar sus conversaciones con numerosas anécdotas tomadas de la larga tradición del humor judío, Jacob terminó por ignorar las ceremonias religiosas. Pero tenía el cuidado de celebrar Purim y Pésaj como fiestas familiares. La primera conmemoraba la liberación de los judíos del Imperio persa, y la segunda, la salida de Egipto y el fin del sojuzgamiento del hombre por el hombre: dos fiestas de la libertad en las cuales se arraigaba su adhesión a los ideales de la rebelión de los pueblos.
Entre 1848 y 1852 Jacob prosiguió con su vida itinerante. Tras la muerte de Sally se casó con una tal Rebekka, hija de un comerciante, con la que no tuvo descendencia, al mismo tiempo que su hijo mayor desposaba a los diecinueve años a una joven judía, Maria Rokach, cuya familia procedía de Rusia. En 1855 Maria trajo al mundo a su primer hijo, Johann (John) Freud, futuro compañero de juegos de su tío Sigmund, nacido un año después de él. Vino a continuación Pauline, nacida el 20 de noviembre de 1856.
Emanuel, el primer hijo de Jacob, se convirtió a su turno en socio de su padre como este lo había sido del suyo y de su abuelo. En cuanto a Philipp, el menor, se mantuvo soltero y solo fundó una familia una vez instalado en Manchester, a donde había emigrado con su hermano alrededor de 1859, cuando su padre se marchó de Freiberg. Los dos hicieron fortuna en el comercio de telas y joyería. Jacob no mencionó nunca su segundo matrimonio, cuyas huellas fueron descubiertas por historiadores. ¿Había repudiado a Rebekka? No hay ninguna prueba. Algunos comentaristas inventaron toda una novela con referencia a esa segunda esposa, de la que no se sabe casi nada y cuya existencia Freud desconocía.
Lo cierto es que el 29 de julio de 1855 contrajo un nuevo matrimonio con una muchacha, Amalia Nathansohn, hija de Jacob Nathansohn, agente comercial procedente de Odesa y radicado en Viena. Nacida en Brody en 1835 y única mujer en una fratría de cuatro varones, Amalia pertenecía a la generación de los dos hijos de su esposo. La unión fue bendecida conforme al rito reformado por Isaac Noah Mannheimer. El oficiante recitó las siete bendiciones nupciales y el recién casado rompió un vaso bajo sus pies en recuerdo de la destrucción del Templo de Jerusalén.
Imperiosa, autoritaria y sin duda mucho más afligida que su madre y su abuela por la falta de libertad individual que aún forzaba a las mujeres de la época a ser exclusivamente madres, Amalia se negó a dejarse encerrar en la cárcel de un modelo familiar condenado a la extinción. Pero carecía, sin embargo, de los medios para rebelarse contra su condición de esposa en el hogar. Delgada, elegante, bella, jovial, capaz de una enorme resistencia física, psíquica y moral, supo conservar su autonomía en un mundo en plena mutación. Dio a ese marido que habría podido ser su padre ocho hijos en diez años, tres varones y cinco niñas: Sigmund, Julius, Anna, Regine Debora (apodada Rosa), Maria (apodada Mitzi), Esther Adolfine (apodada Dolfi), Pauline Regine (apodada Paula) y Alexander. La enumeración hace notar que nunca dejó de estar embarazada entre la fecha de su casamiento y la del nacimiento de su último hijo, en 1866. Por lo demás, no se sabe por qué, si era tan fértil, no tuvo más hijos luego de esa fecha.
El 6 de mayo de 1856, entonces, Amalia dio a luz a su primer hijo, Sigmund (Sigismund), llamado Schlomo-Shelomoh en homenaje al patriarca de Tysmenitz. Jacob, que había anotado en hebreo en su famosa Biblia la fecha de la muerte de su padre, ocurrida el 21 de febrero, agregó la del nacimiento de este nuevo Schlomo, «admitido en la Alianza» (circuncidado) una semana después. En 1891 daría a su hijo esa obra como regalo de cumpleaños, luego de haberla hecho reencuadernar: «Hijo que es querido para mí, Shelomoh [...]. Te lo obsequié como recuerdo y signo de amor de tu padre, que te ama con amor eterno. En la ciudad capital, Viena, 29 de nisán de [5]651, 6 de mayo de 1891».
Desde su nacimiento Sigmund fue para Amalia un motivo de orgullo y altivez. Ella lo llamaba «mi Sigi de oro», le hablaba naturalmente en yiddish y siempre lo prefirió al resto de sus hijos, convencida de que llegaría a ser un gran hombre. Un día, en una pastelería, se encontró con una anciana, que le anunció que su hijo era un genio. Se sintió con ello ratificada en su certeza, que Freud siempre juzgó ridícula: «Harto frecuentes han de ser tales profecías; ¡hay tantas madres esperanzadas y tantas viejas campesinas u otras viejas mujeres que han perdido su poder en la tierra y por eso se han vuelto al futuro!».
Amalia transmitió su convicción a Jacob, que comenzó entonces a admirar a su hijo, en la creencia de que algún día sería superior a él. En tanto que los hombres de la familia, ayudados por sus yernos o sostenidos por sus suegros, siempre se habían visto como honrados comerciantes de lana y artículos surtidos, Jacob, que ahora se adhería plenamente a la Ilustración judía, pensó muy pronto que su hijo podría acceder a un destino distinto del de sus antepasados: ya no el negocio sino el saber. Lo inició, pues, en el relato bíblico como en una novela familiar genealógica, lo que le procuró un intenso placer. A lo largo de toda su escolaridad el joven Freud seguiría empapándose de la lengua bíblica, en contacto sobre todo con Samuel Hammerschlag, su profesor de hebreo, que lo ayudaría además a financiar sus estudios: «En su alma», escribiría Freud en 1904, a la muerte de aquel, «ardía una chispa del mismo fuego que animó a los grandes sabios y profetas judíos».
Dijera lo que dijese al respecto, Freud tomó así muy tempranamente conocimiento del texto sagrado. En la infancia nada lo atraía más que la saga egipcia de Moisés, las aventuras de José y sus hermanos o los múltiples matrimonios de los patriarcas centenarios que engendraban una numerosa descendencia con sus mujeres, sus concubinas o sus criadas. Adoraba a Sansón, Saúl, David, Jacob. En los textos del judaísmo reencontraba algunos rasgos estructurales de su propia familia, y más adelante deduciría de ellos que una gran familia es siempre una bendición al mismo tiempo que un motivo de inquietud. Aficionado a deleitarse en sus fantasías y sus ensoñaciones, le gustaba imaginar que su medio hermano Philipp, que vivía bajo el mismo techo que él, era el verdadero esposo de su madre y que su padre era su abuelo. Por eso tenía celos de ese soltero, en tanto que se entendía de maravilla con su otro medio hermano, Emanuel, que se había casado con una mujer de su misma generación. Algunos historiadores imaginaron, sin aportar la más mínima prueba de ello, que Philipp había sido realmente amante de Amalia.
Apegado a su joven y seductora madre, a quien amaba de manera egoísta, Freud la miraba en su infancia como una mujer a la vez viril y sexualmente deseable. Durante un viaje en tren, entre Freiberg y Leipzig, quedó deslumbrado con su desnudez, y más adelante contó un célebre sueño de angustia en el cual la veía dormida y transportada a su cama por personajes con pico de pájaro que le recordaban las divinidades egipcias reproducidas en la Biblia paterna. A continuación consideró que los niños que habían sido preferidos por su madre acarreaban consigo, una vez llegados a la edad adulta, un optimismo inquebrantable. Más aún, deduciría de esta convicción la idea de que las relaciones de amor entre las madres y los hijos varones son las más perfectas y despojadas de ambivalencia. En realidad, jamás pudo dilucidar la índole del vínculo que lo unía a su madre. Para él, el amor maternal —y más aún el amor de la madre por el hijo varón— era algo que estaba en la naturaleza de las cosas.
Con su _nanny_ descubrió otro aspecto del amor maternal. Contratada como niñera, Resi Wittek (o Monika Zajic) era vieja, fea y poco deseable: todo lo contrario de Amalia. Pero brindó a Freud afecto y sensualidad. En síntesis, algo carnal que le faltaba en la relación con su madre: «Ella fue», diría más adelante, «mi maestra en cosas sexuales. [...] [M]e ha lavado con agua enrojecida, en la que se había lavado antes». Ardiente católica, Monika le hablaba en checo, le contaba historias de diablos y santos y lo llevaba a iglesias en las que se celebraba el culto de María. Freud descubrió así la segunda religión monoteísta, religión de la carne, del pecado, de la confesión y de la culpa, con sus imágenes piadosas, sus rosarios, su iconografía barroca, sus representaciones del infierno. Cuando volvía a su casa, Sigmund predicaba y glorificaba el nombre del Dios de los cristianos. Pero al nacer Anna, Philipp, el «mal hermano», hizo encarcelar a Monika por robo. Privado de su madre, confinada en su habitación tras el reciente parto, y despojado de su nodriza, Sigmund comenzó a proferir alaridos. Creía a pies juntillas que habían encerrado a Amalia en un baúl.
En 1905, en los _Tres ensayos de teoría sexual_ , Freud afirmó que las nodrizas poco concienzudas acariciaban los órganos genitales de los niños para adormecerlos. Al tomar conocimiento de esta observación, varios comentaristas imaginaron a posteriori que Monika había sobado el pene del pequeño Sigmund y que ese era, a no dudar, el origen de la pasión de este por el estudio de la sexualidad humana. Así se abrió paso la idea de un Freud que había sufrido abusos de su nodriza, como tantos otros rumores en torno de la vida privada del fundador del psicoanálisis.
En su infancia Sigmund tuvo como compañeros de juegos a Pauline y John, con quienes formaba un trío. Treinta años después, en un artículo sobre los «recuerdos encubridores», contó que un hombre de treinta y ocho años, a quien él había curado de una fobia, había evocado un recuerdo infantil que enmascaraba otro mucho más reprimido.
De hecho, en ese texto Freud ponía en juego sus propios recuerdos para ilustrar su teoría, y el hombre cuya historia daba a conocer no era otro que él mismo. Dos primos y una prima juegan en un prado, decía, y cada uno de ellos recoge un ramo. Como la niña junta la mayor cantidad de flores, los dos varones, celosos, le arrebatan el ramo. Cuando ella se queja a una campesina, que la consuela y le da una rebanada de pan, los varones tiran las flores para ganarse también su parte de la hogaza: «Este pan me sabe exquisito en el recuerdo; y con esto se interrumpe la escena». Y unas páginas más adelante Freud señalaba «el punto de contacto [entre] el desflorar [y] el arrebatar las flores».
No hacía falta nada más para que algunos comentaristas, confundiendo realidad y fantasia inconsciente, aprovecharan para afirmar que, en su infancia, Freud había desflorado efectivamente a su sobrina con la complicidad de su sobrino.
La leyenda de un Freud víctima de abusos de su nodriza y violador de su sobrina encuentra su fuente, por lo tanto —como todas las otras leyendas—, en la propia obra freudiana, reinterpretada sin cesar al capricho de especulaciones o construcciones infundadas. En cambio, lo que está establecido con certeza es que Freud mantenía relaciones de complicidad y rivalidad con su sobrino mayor que él. Como todos los varones enfrentados a niñas de su edad, John y Sigmund «a veces [se] porta[ban] cruelmente» con Pauline. Eran inseparables, se querían, se acusaban o se peleaban. Al comparar esta amistad infantil con la de Bruto y César, Freud hizo de ella la matriz de lo que más adelante serían sus relaciones con los hombres de su entorno, maestros, discípulos, amigos, adversarios, enemigos: «Un amigo íntimo y un enemigo odiado fueron siempre los requerimientos necesarios de mi vida afectiva; siempre supe crearme a ambos de nuevo, y no rara vez ese ideal infantil se impuso hasta el punto de que amigo y enemigo coincidieron en la misma persona».
En 1860 la familia Freud se instaló en Leopoldstadt, un suburbio popular de Viena poblado de judíos pobres que residían a veces en viviendas insalubres. Otra vez embarazada, Amalia enfermó de tuberculosis y tuvo que pasar varios períodos en los Cárpatos para restablecerse. En esa época Jacob seguía autocalificándose de comerciante de lanas. Sin embargo, víctima de la mecanización de la producción de textiles, nunca logró llegar a ser un comerciante próspero. Con la ayuda de sus hijos del primer matrimonio, no obstante, pudo asegurar una vida decente a su numerosa prole.
Después de haber sido la encarnación de una fuerte autoridad paterna, Jacob daba de sí mismo la imagen de un hombre débil y humillado. Por eso acariciaba, con más intensidad que nunca, el sueño de que su hijo disfrutara de un destino más glorioso que el suyo, pero sin olvidar, empero, honrar lo que él había sido antaño: «Mi Sigismund tiene más inteligencia en el dedo pequeño del pie que yo en la cabeza, pero jamás se atrevería a contradecirme». Schlomo-Sigismund fue el primero en el extenso linaje de los Freud, procedentes de los _shtetl_ de Europa oriental, en acceder a otra carrera que la de comerciante.
De esa época procede su identificación con figuras de conquistadores, vencedores luego vencidos, pero siempre dispuestos a vengar al padre o a superarlo: Aníbal, Alejandro, Napoleón. Lo testimonia el recuerdo que conservó de una escena de la infancia: el relato hecho por su padre de una vieja anécdota destinada a demostrarle que el presente era mejor que el pasado. Una vez, le había dicho Jacob, «vino [...] un cristiano y de un golpe me quitó el gorro y lo arrojó al barro exclamando: "¡Judío, bájate de la acera!"». Y a la pregunta de su hijo sobre su reacción, había respondido: «Me bajé a la calle y recogí el gorro».
A esta escena que le disgustaba, Sigmund había opuesto otra, más ajustada a sus aspiraciones: el episodio histórico en que Amílcar había hecho jurar a su hijo Aníbal que se vengaría de los romanos y defendería Cartago hasta la muerte.
De ese modo se afirmó en el imaginario del joven la preocupación por restablecer el recuerdo de un poder patriarcal que no dejaba de deshacerse ante su vista. La anécdota del gorro de piel, en efecto, contaba no solo la historia de una claudicación paterna frente al antisemitismo, sino también el itinerario de un hijo que desde muy temprano se había asignado la misión de revalorizar simbólicamente la ley del padre por un acto de rebelión a la altura de Aníbal. No solo había que superar al padre, sino que además era preciso cambiar de cultura sin traicionar jamás la identidad judía de los ancestros. Al trazar así su destino, Freud se asociaba a la historia de los hijos de la burguesía comercial judía del Imperio austrohúngaro, obligados a despojarse de su judaísmo para ser intelectuales o científicos. Para vivir como judíos, habían tenido que adoptar la cultura griega, latina y alemana.
Ernst Simon, un filósofo israelí de origen berlinés, afirmó en 1980 que Freud se había preparado para el bar-mitzvá y había realizado la ceremonia a los trece años. Y como prueba de lo que sostenía, traía a colación una confidencia del propio Freud. Este contó un día, en efecto, que a los catorce años le habían regalado las obras del escritor judío alemán Ludwig Börne, admirador de la Revolución francesa y heredero de la _Aufklärung_. Freud las conservó piadosamente como los únicos libros procedentes de su juventud. Y Simon deducía de ello que, en realidad, se los habían regalado al cumplir trece años y que, en consecuencia, se trataba de un obsequio recibido con motivo de su bar-mitzvá. Esta interpretación es seductora, sin duda, pero nada prueba que la ceremonia tuviera efectivamente lugar. En cambio, es indudable que Freud admiraba a ese escritor, de quien recordaba estas palabras: «Una vituperable cobardía para pensar nos refrena a todos. Más oprimente que la censura de los gobiernos es la censura que la opinión pública ejerce sobre nuestra labor espiritual».
Durante el verano de 1865 Josef Freud, hermano de Jacob, fue detenido por posesión de billetes falsos. Algunos meses después lo condenaron a diez años de cárcel: «Mi padre, que a causa del disgusto encaneció en pocos días, solía decir siempre que el tío Josef no era un mal hombre, pero sí un idiota». Nada permite decir, como lo han hecho algunos comentaristas, que este asunto se habría ocultado al joven Sigmund, con la consecuencia de provocar en su subjetividad de adulto una gran «catástrofe» existencial. En realidad, Freud fue sensible a esa nueva humillación del padre y recordó en esa oportunidad que la relación de tío con sobrino había sido, en su propia infancia, un motivo de odio y amistad.
A los trece años intimó con Eduard Silberstein, hijo de un banquero judío rumano establecido en Jassy y luego en Braila, una ciudad a orillas del Danubio. Criado por un padre medio loco y sometido a la ortodoxia religiosa, Eduard aspiraba a ser un librepensador. Así, se hizo amigo y fue condiscípulo del hijo de Jacob en el Realgymnasium de Viena y después en el Obergymnasium.
Se tejieron entonces lazos entre las familias de los dos adolescentes. Anna Silberstein y Amalia Freud se reunían en la estación termal de Roznau para tomar las aguas y charlar sobre sus problemas domésticos, mientras los dos muchachos, apasionados por la literatura, se imaginaban que eran héroes de una novela. Para alimentar mejor sus ensoñaciones, fundaron una «Academia Castellana» en homenaje a su escritor predilecto: Cervantes. En ese cenáculo, que los tenía por únicos miembros, sus placeres intelectuales procedían de una libre práctica de la palabra iniciática. Intercambiaban sus misivas en alemán y castellano a la vez que aderezaban ambas lenguas con palabras que funcionaban como un lenguaje codificado. Y para mostrar su veneración por la novela picaresca, se asignaron nombres tomados del célebre «Coloquio de los perros» de las _Novelas ejemplares_.
En ese relato Cervantes presenta al perro Berganza, narrador inveterado, y al perro Cipión, filósofo cínico y amargo, ambos hijos de la bruja Montiela, a quien deben su asombrosa facultad de disertar sobre los vagabundeos del alma humana. A través de ese coloquio el autor se entrega a una crítica feroz de las perversiones humanas y de las injusticias de su época.
No nos sorprenderemos de que Freud escogiera llamarse Cipión, como una autoafirmación de su fe en la incapacidad del ser humano para dominar sus pasiones. Y pese a ello, decía, «el hombre que piensa» es el único capaz de decidir al respecto: «Es su propio legislador, su confesor y su juez».
Fascinado desde temprana edad por esa concepción de la libertad humana, Freud, llegado a la adolescencia, tuvo con respecto a su propia sexualidad una actitud ambivalente. Por un lado sufría las frustraciones impuestas por la sociedad en que vivía, al punto de considerarlas como la causa de los tormentos subjetivos más sombríos; por otro, consideraba la exhibición pulsional como una fuente de destrucción. De ahí un culto marcado por el control de los desórdenes del yo. Prefiriendo el deseo no saciado al goce de los cuerpos, no vacilaba en rememorar una escena infantil durante la cual había orinado en el dormitorio de sus padres en presencia de estos: «Este chico nunca llegará a nada», había dicho Jacob. Desafiado por esa frase paterna, Freud no dejó de contabilizar, a lo largo de muchos años, todos sus éxitos intelectuales a fin de demostrarse que nunca sería un inútil. Judío sin Dios, puritano emancipado capaz de dominar sus pulsiones y criticar los perjuicios del puritanismo, presentó de sí mismo la imagen de un rebelde bien ordenado, apasionado desde su infancia por los misterios y las extravagancias de la sexualidad humana. Siempre se definiría como un «liberal a la antigua usanza», alimentado por la _Neue Freie Presse_ , principal diario del Imperio austrohúngaro, fundado en 1864, y en el cual colaboraban eminentes intelectuales vieneses: Hugo von Hofmannsthal, Stefan Zweig, Arthur Schnitzler, Theodor Herzl.
Durante el verano de 1871, acompañado por Eduard, Freud se alojó en Freiberg en la casa de la familia de Ignaz Fluss, comerciante textil y un viejo amigo de Jacob Freud. Turbado por la hija de Ignaz, Gisela, una niña de doce años que también era hermana de su camarada Emil Fluss, le dio el nombre de _Ichthyosaura_ y se autodesignó como «príncipe del Liásico y señor del Cretácico», en referencia a un poema de Viktor von Scheffel sobre el fin de la era de los saurios, esos animales rebeldes al orden del mundo pero impotentes para impedir la catástrofe final.
Un año después Freud volvió a ver a Gisela. Con aparente indiferencia, la dejó regresar a su internado y luego comenzó a vagabundear por los bosques de su infancia, pensando en lo que podría haber sido su vida si sus padres no se hubiesen marchado de Freiberg y, en vez de hacer suyo el nuevo destino vienés, él hubiera aceptado tomar a su cargo el negocio de Jacob y casarse, a la misma edad que este, con una joven procedente de su medio.
Para poner mejor fin a la era prehistórica de los amores imposibles entre saurios —señor del Cretácico e _Ichthyosaura_ —, explicó a Eduard que el verdadero objeto de su deseo no era Gisela sino Eleonora, la madre de esta:
Me parece que transferí a la hija, bajo la forma de amistad, el respeto que me inspira la madre. Soy un observador perspicaz o me tengo por tal: mi vida dentro de una familia numerosa, donde se desarrollan tantos caracteres, ha aguzado mi mirada y estoy lleno de admiración por esa mujer a quien no iguala del todo ninguno de sus hijos.
Eleonora Fluss tenía cualidades de las que carecía Amalia. Moderna, liberal, culta, se había deshecho del espíritu del gueto. En cuanto a su marido, al contrario de Jacob Freud, se había mostrado capaz de superar la crisis que había vivido la industria textil. Al haber conservado su fortuna, no se había mudado de Freiberg a Viena, ciudad detestada por Sigmund, que amaba la naturaleza, las flores, las setas, los bosques, los animales y la vida al aire libre. Con motivo de ese retorno a la comarca natal, el joven se fabricó pues una doble «novela familiar». Mientras imaginaba lo que habría podido ser su vida si hubiera hecho carrera en el comercio textil, aspiraba también a otra parentalidad: tener un padre idéntico a Ignaz Fluss y una madre semejante a Eleonora. Esto le permitía, claro está, sublimar su atracción carnal por Gisela. Una manera entre otras de tomar distancia con respecto a su propio padre, que, a la misma edad que él, no se había visto obligado a refrenar su sexualidad.
Una anécdota muestra hasta qué punto el joven Freud era capaz de inventar una novela familiar conforme a sus deseos y, a la vez, juzgar con gran severidad a las familias que violaban las reglas de la compostura burguesa. Y, desde luego, consideraba que en el corazón de ese sistema las familias judías tenían el deber de ser más ejemplares que las demás. Por eso se horrorizó, en septiembre de 1872, al descubrir la banal grosería de un padre y una madre en el tren que lo llevaba de Freiberg a Viena:
Él era de la madera con que el destino, llegado el momento, hace malandrines: astuto, mentiroso, mantenido por su querida familia en la convicción de ser un hombre de talento, y todo eso acompañado de una ausencia de principios y de concepción del mundo. Una cocinera de Bohemia, dueña del más perfecto rostro de bulldog que yo haya visto en mi vida, completaba el panorama. Me harté de esa canalla. Durante la conversación me enteré de que la dama judía y toda su familia eran originarios de Meseritsch; justamente el montón de mierda que conviene a este tipo de producto.
Y algunas líneas más adelante, sensible al sufrimiento de las madres neuróticas, contaba a Emil Fluss su encuentro, en el mismo tren, con «una mujer nerviosa, excitada, trémula, acompañada por una niña de doce años con rostro de ángel», a quien él no había dejado de mirar a lo largo de todo el viaje: «Llegaba así a Viena. Vi una vez más a la mujer nerviosa y la hija rubia, y me juré apuntar el lugar donde, en la multitud vienesa, volviera a encontrarlas. De ese modo termina mi pequeña novela».
Educado de manera liberal, en el seno de un sistema familiar endogámico y todavía marcado por la tradición de los matrimonios concertados, Freud tuvo una infancia feliz entre un padre que habría podido ser su abuelo, una madre que habría podido casarse con su medio hermano y sobrinos que tenían la misma edad que él. Si bien sus cinco hermanas lo veneraban, también lo consideraban tiránico. Él vigilaba sus lecturas, no soportaba el ruido del piano —que lo perturbaba en sus preciosos estudios— y le parecía normal que quedaran relegadas en una sola habitación iluminada con bujías, cuando por su parte él tenía un cuarto para su exclusivo disfrute y contaba con el beneficio de una lámpara de aceite.
Como la mayoría de las mujeres de su generación, las hermanas de Freud no tuvieron otro destino que el de convertirse en esposas, madres o sirvientas, y no recibieron ninguna formación intelectual que les permitiera escapar a su condición. Anna fue la única que estudió para ser maestra. Hacia los dieciséis años comenzó a cortejarla un viejo tío de la familia Nathansohn que se había lanzado a la búsqueda de una nueva esposa y pretendía llevarla a Odesa. Horrorizado ante la idea de una unión consanguínea entre una adolescente y un viejo, Freud se opuso con la mayor firmeza. Anna tuvo luego la fortuna de contraer un buen matrimonio con Eli Bernays, hermano de Martha, y de emigrar a Estados Unidos, donde sus cinco hijos disfrutaron de una vida próspera.
Rosa, la preferida de Freud, tan neurasténica como él, se casó con un jurista, Heinrich Graf, que murió al cabo de poco tiempo. Su hijo Hermann perdió la vida en la Gran Guerra, y su hija Cäcilie (Mausi) se suicidó en 1922 después de que, embarazada, su amante la abandonara. Maria se casó con un primo lejano de Bucarest, Moritz Freud, con quien tuvo cinco hijos: entre ellos un mortinato y otras dos víctimas de muerte violenta (suicidio y accidente). Casada con Valentin Winternitz, Paula, viuda tras esta unión, tuvo una única hija. En cuanto a Adolfine, permaneció soltera y ejerció de ama de llaves de su madre, que le infligió numerosas humillaciones.
En el corazón de esta organización del parentesco, en la que las mujeres aún estaban privadas de todo acceso a un oficio y los primos y los parientes cercanos se casaban unos con otros, a veces con diferencias de edad que transformaban a jóvenes esposas en viudas, Freud se convirtió muy pronto en un perspicaz espectador de la evolución de la familia burguesa y del paso de un modelo antiguo —el encarnado por su padre y su abuelo— a uno nuevo: el de los matrimonios por amor, fundado en la libre elección de los futuros cónyuges.
Al observar diversas familias cercanas a la suya, Freud se complacía en inventar relaciones entre madres, padres e hijos que, en realidad, no eran sino el espejo de las transformaciones del orden familiar a las que él mismo se enfrentaba. Y por eso fue tan sensible a la idea de que el padre estaba perdiendo su omnipotencia original y debía ahora compartir el poder con la madre.
El orden familiar que había impregnado a Freud en su infancia y durante su adolescencia descansaba sobre tres fundamentos: la autoridad del marido, la subordinación de las mujeres y la dependencia de los hijos. Al otorgar a la madre un lugar central, al precio de hacer mella en la autoridad paterna, el nuevo orden buscaba asimismo la manera de poner bajo control aquello que, en el imaginario de la sociedad de la segunda mitad del siglo XIX, amenazaba dar libre curso a una peligrosa irrupción de lo femenino, es decir, a la sexualidad calificada de «histérica» o «nerviosa», que se juzgaba mucho más devastadora por no estar ya sometida a la función materna.
Para evitar ese «desastre antropológico» tan temido, y que tenía además como telón de fondo un descenso real de la natalidad y la fertilidad en Occidente, médicos y demógrafos afirmaban que la mujer debía ser ante todo una madre a fin de que el cuerpo social estuviera en condiciones de resistir a la presunta tiranía de un goce femenino liberado de sus ataduras y capaz, decían, de aniquilar la sociedad.
Si el joven Freud, embargado por un deseo carnal, prefería ver en cada muchacha la sombra tendida de su madre, al extremo de enamorarse de ellas, era sin duda porque lo fascinaba la irrupción del deseo femenino. Lejos de rechazarlo o juzgarlo amenazante para la sociedad, quería aprehender su significación, explorarlo, verbalizarlo. Y al mismo tiempo adoptaba dos actitudes en apariencia contradictorias: una apuntaba a erotizar todas las relaciones intrafamiliares e incluso a imaginar transgresiones e ignominias que solo existían en sus fantasías, y otra, al contrario, tendía a racionalizar la peligrosidad presunta de la pulsión sexual y a sofocarla, condición de una real emancipación de la sexualidad humana. Esta dialéctica siempre recurrente entre una afirmación del valor creador de la erotización y la necesidad de ponerla bajo control sería una constante en su vida y su obra.
Freud sintió muy pronto atracción por los mitos de la antigua Grecia, lo cual le permitiría más adelante trasladar a la clínica de las neurosis y las neurastenias de fines del siglo XIX un gran relato de los orígenes fundado en diversas formas de dualidad: dualidad entre los Titanes, divinidades primordiales, y los dioses del Olimpo, vencedores de las antiguas fuerzas telúricas; dualidad entre un principio de placer y un principio de realidad, entre lo irracional y lo racional, e incluso entre una pulsión de destrucción (Tánatos) y una pulsión de vida (Eros), etc.
La adhesión a una dialéctica de esas características ya daba testimonio de la política de la amistad propia del universo psíquico freudiano: el amigo indispensable está condenado a ser el indispensable enemigo. Siempre inclinado a las formulaciones tajantes y excluyentes, Freud se definiría sin cesar, frente a su entorno, como un contradictor audaz, dispuesto en todo momento a defender una posición extrema y asumir los costes correspondientes. Y atribuía ese ardor no solo a una construcción originada en sus relaciones infantiles con su sobrino John, sino también a una herencia ancestral: se sentía capaz, decía, de sacrificar su vida con el mismo júbilo de que habían dado pruebas los hebreos en la defensa de su Templo.
Durante los años pasados en la escuela secundaria Freud tuvo buenos profesores y fue un excelente alumno: el primero de su clase. De todas maneras, no vacilaba en erigirse en portavoz de sus compañeros para protestar contra un docente impopular o considerado ignorante. En junio de 1869 varios alumnos fueron sancionados por haber ido a lugares de mala fama. Freud no estaba entre ellos porque solo parecía interesarse en el saber y la cultura. No se le conoce ninguna relación amorosa significativa antes del matrimonio, y cuando Marie Bonaparte, siempre curiosa por los asuntos de la sexualidad, le preguntó si había tenido relaciones carnales en su juventud y, como los jóvenes de su generación, frecuentado los burdeles de Viena, él hizo oídos sordos a su pregunta. Freud nunca habló de su vida sexual anterior al matrimonio, actitud que dio lugar a una multitud de rumores y juicios apresurados.
En el momento en que se preparaba para entrar en la universidad, el liberalismo parecía en plena expansión en el Imperio austrohúngaro. Sin embargo, al cabo de algunos meses se anunció una crisis financiera de extrema gravedad, que terminó por estallar en mayo de 1873, al mismo tiempo que una epidemia de cólera. Como consecuencia se produjo una serie de bancarrotas y quiebras que se extendieron a toda Europa. Arruinados por un sistema económico al que se habían adherido con entusiasmo, los liberales perdieron poco a poco sus ilusiones, en tanto que las minorías nacionales ponían en entredicho, con sus reivindicaciones, la relativa estabilidad de la monarquía bicéfala. Se acusó entonces a los judíos vieneses urbanizados de ser los responsables de la desestabilización de los mercados. Los periodistas estigmatizaron sus presuntas «maniobras» y los caricaturistas disfrutaron de lo lindo propagando su veneno en la prensa. Aquí y allá florecían dibujos que representaban a agentes de cambio y bolsa de nariz ganchuda y pelo crespo.
Una vez más, en ese contexto, se tuvo a los judíos por responsables de la puesta en marcha de un proceso de transformación social que iba a culminar en una evolución de las costumbres fundada en una nueva organización de la familia. El pueblo judío, se decía, ¿no es desde siempre un pueblo errante sin patria ni fronteras, un pueblo maldito, movido por el afán de lucro y siempre dispuesto a propiciar comercios sexuales perversos? ¿No es incestuoso y sodomita por naturaleza? ¿No es el judío tan peligroso como el homosexual, el travesti o la histérica? ¿No es culpable, por su «femineidad» supuesta, de la destrucción de la familia patriarcal?
En esa época Viena se había convertido en el refugio de todos los judíos de Europa oriental, originarios de Galitzia, Hungría, Rusia, Moldavia. Al contrario de Jacob Freud, en su mayoría habían logrado integrarse en la nueva sociedad liberal, en un principio como comerciantes o banqueros —en el caso de la primera generación— y luego como editores, periodistas, mecenas, abogados, escritores, poetas, científicos, filósofos, historiadores. Pero con la ampliación gradual de la crisis, esta integración exitosa, de tipo comunitario, se tornó sospechosa a los ojos de la opinión pública y suscitó odios y discriminaciones.
El adjetivo «antisemita» lo había utilizado por primera vez en Alemania, en 1860, un eminente orientalista judío de Bohemia, que había calificado con ese término la expresión de un prejuicio hostil a quienes se llamaba entonces, con una palabra culta, ya no judíos sino semitas. Frente a esta nueva forma de odio, el gran movimiento de emancipación de la Haskalá, nacido en la Ilustración, corría el riesgo de aparecer en lo sucesivo como una suerte de interludio. Hasta entonces denunciados por su pertenencia a una religión, los judíos eran estigmatizados como originarios de una «mala raza», la de los semitas. En 1879 la palabra dejó la esfera de los debates científicos entre filólogos para constituir, en la pluma del mediocre publicista Wilhelm Marr, el núcleo de una nueva visión del mundo: el antisemitismo.
Reivindicado por ligas de reciente formación, el antisemitismo terminó por dar cuerpo a un movimiento que promovía la expulsión de los judíos de Alemania con destino a Palestina, y su estigmatización como una «clase peligrosa» para la pureza de la raza germánica, llamada «aria». En pocos años, y hasta la Primera Guerra Mundial, el antisemitismo se difundió por toda Europa en numerosas variantes: biológica, higienista, racialista, nacionalista.
Enfrentado durante sus años de universidad a esa mutación del antijudaísmo en antisemitismo, Freud se identificó cada vez más con el héroe de su juventud, Aníbal, general semita. A lo largo de sus estudios despreció a quienes lo trataban de «sucio judío» o esperaban que admitiera su «inferioridad racial». En varias ocasiones no vaciló, bastón en ristre, en poner en desbandada a diversos canallas que lo habían colmado de insultos. Como contrapunto, cultivó la idea de que al estar excluido, en cuanto judío, de la «mayoría compacta», podría conservar una independencia de criterio que después le permitiría defenderse mejor de los prejuicios. Le gustaban muy poco «las liturgias del cuerpo social, los coros de protesta, las consignas anónimas entonadas al tuntún».
Hambriento de saber, soñador de gloria y conquista, consideró en un primer momento la posibilidad de emprender una carrera política, para decidir luego que sería filósofo, después jurista y por último naturalista... Pensó varias veces en embarcarse en una nave y recorrer los océanos, a la manera de un Charles Darwin, el héroe de la ciencia moderna a quien más admiraba porque su doctrina, decía, «prometía un extraordinario avance en la comprensión del universo». Pero también se comparaba con Cristóbal Colón, el aventurero de los mares, el descubridor del Nuevo Mundo. Deseoso de otra identidad y siempre preocupado por superar a su padre y acceder, por la gracia de maestros excepcionales, a una cultura científica, se inició entonces en los debates filosóficos de su tiempo de la mano de Franz Brentano, cuya enseñanza seguía.
Sobrino de Clemens Brentano e influido por la escuela romántica alemana, ese filósofo, que sería ulteriormente maestro de Husserl, exponía en su cátedra de Viena, entre 1874 y 1894, los principios de una psicología empírica centrada en un análisis de las modalidades de la conciencia del que estaba excluida toda forma de subjetividad. En ese aspecto Franz Brentano se presentaba como un renovador de las tesis del filósofo alemán Johann Friedrich Herbart, quien, en el linaje de Kant y Fichte, había sido uno de los fundadores de la ciencia psicológica moderna. Por eso tenía muchos discípulos en el mundo académico germanoparlante y sobre todo en Austria, donde médicos y pedagogos laicos reivindicaban su doctrina.
Con un enfoque basado en una concepción del yo que suponía la relación con una alteridad —un «no yo»—, Herbart había contribuido al estallido de la noción clásica de identidad subjetiva. Profesaba la idea de que el sujeto humano está dividido en una serie de átomos reprimidos en el umbral de la conciencia y que luchan unos contra otros para invadir esta última. En otras palabras, había planteado, durante la primera mitad del siglo XIX, los principios de una llamada teoría «dinámica» del inconsciente, en la que entraban en juego tres polos: la representación, la pulsión y la represión.
Partidario del orden y el conservadurismo político, Herbart había sido en Alemania el iniciador de una pedagogía que valoraba el saber de los «expertos» en detrimento del espíritu inventivo. Muy apreciada por el medio académico vienés, su obra se había granjeado adeptos entre quienes a continuación intentaron reformar la enseñanza de las ciencias naturales y la medicina. Sin dejar de ser teísta y de preconizar los valores de un catolicismo reformado, Brentano se consideraba seguidor de la doctrina herbartiana y apelaba a la noción de intencionalidad, que unía a la de representación para designar el acto mediante el cual la conciencia se orienta hacia un objeto. También distinguía dos categorías de actos mentales: los juicios de afirmación y negación y las actitudes conjugadas de odio y amor.
Freud recordaría esa enseñanza en el momento de elaborar su doctrina. Pero en esa época todavía soñaba con ir a la búsqueda de un doctorado de filosofía. Con la ayuda de su amigo y condiscípulo Josef Paneth, se propuso pues impugnar el teísmo de Brentano y adherirse al materialismo de Ludwig Feuerbach, un filósofo alemán que acababa de morir y cuya enseñanza estaba muy presente en la cultura vienesa de la década de 1870. Crítico del pensamiento hegeliano, Feuerbach había sostenido que la afirmación de una trascendencia llevaba a una alienación y que, para salir de esta, había que efectuar un retorno al hombre concreto. Sensualismo y crítica de la religión: esas eran las tesis que inspiraron precozmente a Freud y que, de hecho, contribuyeron en esa época a apartarlo de la especulación filosófica juzgada demasiado abstracta y, sobre todo, demasiado teológica. A través del sensualismo de Feuerbach, Freud llegó a tomar en consideración la diferencia de los sexos y el reconocimiento de una alteridad —un yo [ _je_ ] y un tú—, y por la crítica de la alienación hizo suya la idea de que la religión era siempre un obstáculo al progreso del conocimiento humano. Así, el joven Freud se entregó a una admiración sin límites por ese filósofo materialista cuya vida y pensamiento había descubierto al leer la biografía dedicada a él por Karl Grün.
Después de librar batalla contra Brentano —su respetado profesor, que pese a ello aceptó dirigir su tesis—, Freud renunció a emprender una carrera de filosofía sin traicionar, empero, su adhesión al materialismo de Feuerbach. En 1873, a los diecisiete años, entró en la Universidad de Viena para realizar estudios científicos: anatomía, biología, zoología, fisiología, medicina. Pero como le gustaba prohibirse placeres a fin de acceder mejor a lo que juzgaba esencial para sí mismo, siguió dejándose seducir por el pensamiento especulativo. Por lo demás, este nunca estaría ausente de su proceder y, después de 1923, terminaría por impregnar el conjunto de su obra: «En mi juventud», dirá a Jones, «me sentí muy atraído por la especulación [filosófica], pero me aparté valerosamente de ella».
Dotada de una organización excepcional, la gigantesca Universidad de Viena vivía por entonces un período de plena expansión pese a la existencia de graves dificultades financieras. En el ámbito de las ciencias naturales era una de las mejores de Europa por su capacidad de reunir a brillantes científicos del mundo germanoparlante, a menudo liberales en política y, en todo caso, duchos en las justas oratorias y las más famosas controversias. Entre ellos, Carl Claus, profesor de anatomía comparada y zoología, que había introducido el pensamiento darwiniano en Austria, y Ernst Wilhelm von Brücke, médico y fisiólogo de origen berlinés, perteneciente a la gran corriente positivista y antivitalista representada por Hermann von Helmholtz y Emil Du Bois-Reymond.
Para comprender el papel desempeñado por esa enseñanza en la trayectoria de Freud, y sobre todo en su elaboración de una nueva dinámica materialista de la psique, hay que recordar que a fines del siglo XIX la fisiología dominaba los estudios médicos. Sobre la base del método anatomoclínico, conforme al cual la enfermedad es la expresión de una lesión orgánica, el enfoque fisiológico concebía esta como la consecuencia de una modificación funcional de un órgano. Pero también se apoyaba en la doctrina darwiniana, de la cual tomaba los instrumentos para interrogarse sobre el origen y la evolución de los organismos vivos, así como sobre las fuerzas instintivas que subyacen a la actividad humana. Sus representantes estaban, además, animados por un verdadero espíritu de cruzada, cuyo objetivo apuntaba a hacer valer, contra la vieja medicina romántica, la idea de que el organismo humano se componía exclusivamente de fuerzas físicas y químicas.
En treinta años, y sin crear escuela, los fisiólogos terminaron por imponerse como los representantes de una especie de vanguardia de la medicina de lengua alemana. Y aplicaron su modelo a la neurología y la psicología para unirlas y separarlas de la filosofía especulativa. Al mismo tiempo, renunciaron a toda consideración de la subjetividad —en el sentido filosófico—, centrando sus trabajos en la primacía de la observación. En esa perspectiva, los problemas del alma y la psique solo podían resolverse mediante un enfoque monista capaz de incorporar el fenómeno de la conciencia al campo de la fisiología y, por ende, de la ciencia experimental. Para el joven Freud ese compromiso con la fisiología y el evolucionismo perpetuaba una adhesión ya antigua a la filosofía materialista.
En el verano de 1875 realizó por fin su sueño de viajar a Manchester para pasar un tiempo con su medio hermano. Preparó su viaje con minucia, recitó versos, escribió cartas, se sumergió en la historia inglesa y se afirmó fanáticamente «anglómano». Soñaba ya con llegar a ser ciudadano inglés: « _To become an Englishman»_. A despecho de «la niebla, la lluvia, el conservadurismo y la embriaguez», sentía una profunda atracción por Inglaterra, por su sistema económico y político, por su literatura y por su culto de una ciencia experimental que le parecía muy alejada de la tradición metafísica alemana. En una carta a Eduard Silberstein escribía:
Si quisiera actuar sobre una gran masa de individuos, en vez de una pequeña cohorte de lectores o pares, Inglaterra sería el país indicado para esa ambición. Un hombre considerado, sostenido por la prensa y los ricos, podría hacer milagros para aliviar los padecimientos físicos si fuera lo bastante investigador para internarse en nuevos caminos terapéuticos.
Entretanto, fue en Trieste, donde Carl Claus había fundado un instituto de investigaciones sobre los animales marinos, donde efectuó sus primeros trabajos de zoología, a la vez que descubría el mundo mediterráneo. Apasionado por el hermafroditismo, Claus le había encargado someter a prueba la reciente afirmación del investigador polaco Szymon Syrski, que pretendía haber descubierto testículos en las anguilas. Al cabo de dos períodos de trabajo y el examen de cuatrocientos especímenes, Freud intentó efectivamente confirmar la hipótesis del «órgano de Syrski», pero aprendió sobre todo, a disgusto, a plegarse a las exigencias de la ciencia experimental. Y aprovechó su estancia para interesarse en la sensualidad de las mujeres italianas, a quienes comparaba con divinidades.
Gran maestro de la escuela austríaca de fisiología, Brücke había logrado unir en una misma enseñanza la tradición alemana de la medicina de laboratorio y la mirada clínica formada en la práctica hospitalaria vienesa. Personaje pintoresco, de melena pelirroja y sonrisa diabólica, este especialista berlinés en la fisiología de los ojos, la digestión y la voz era asimismo un enamorado de la poesía y la pintura, que no vaciló en inventar una «escritura universal» —la pasigrafía—, a la que adjudicaba el potencial de transcribir, algún día, todas las lenguas del planeta. Ejercía sobre sus alumnos un verdadero poder de seducción, tanto por sus capacidades para transmitir los principios de la ciencia de los organismos como por su concepción elitista y hasta tiránica de la jerarquía universitaria. Apreciaba el talento y propiciaba en sus discípulos la eclosión de la inteligencia, a la vez que los ayudaba a progresar y liberarse de toda mentalidad arribista. Ninguno de ellos le sería infiel. No bien conquistado, Freud lo vio como un maestro, en el que admiraba la mirada azul y penetrante y sobre todo una autoridad patriarcal que le parecía inmune a la claudicación: todo lo contrario de Jacob Freud.
En el laboratorio de Brücke conoció a tres fisiólogos brillantes: Sigmund Exner, Ernst von Fleischl-Marxow y Josef Breuer. Este último se interesaba ya en las medicinas del alma y por lo tanto en las enfermedades mentales, tratadas por la psiquiatría, y las enfermedades nerviosas, que estaban en la órbita de la neurología.
Los tres formaban parte de una comunidad científica de aspecto nobiliario, donde se mezclaban relaciones intrafamiliares, intercambios clínicos, amistades, inclinaciones amorosas, ambiciones sociales, gustos estéticos y un deseo de cambiar la vida, sobre la base de la ciencia anatomoclínica más refinada del mundo europeo. La mayoría de los miembros de ese cenáculo, fuesen ricos o pobres, pertenecían a la burguesía liberal progresista. Visitantes asiduos de los salones literarios y los cafés, mantenían vínculos con artistas, escritores, filólogos, universitarios, periodistas. Unos eran judíos, otros no; los había librepensadores e incluso protestantes o católicos, pero todos se habían apartado del influjo de un ideal religioso juzgado anticientífico y oscurantista.
Tras el estudio de la sexualidad de las anguilas Freud se propuso ir a Berlín, ciudad admirada, para asistir a los cursos de Helmholtz y Du Bois-Reymond. Al cabo de un tiempo renunció al proyecto y prosiguió con sus trabajos zoológicos. Bajo la batuta de Brücke e impregnado de evolucionismo, se consagró, gracias a la magia del microscopio, al estudio de las neuronas del cangrejo y luego a la médula espinal de uno de los peces más primitivos ( _Ammocoetes petromyzon_ ), lo cual le permitió elevarse hasta el sistema nervioso central del hombre. A continuación trabajó en la elaboración de una teoría del funcionamiento de las células y las fibrillas nerviosas, a la vez que hacía una carrera médica clásica, completada con una formación de dos semestres en el laboratorio de química del profesor Carl Ludwig. En síntesis, Freud estaba por entonces en vías de convertirse en uno de los mejores investigadores de su generación en anatomía, biología y fisiología.
En marzo de 1881 finalizó sus estudios, defendió su tesis doctoral y se lo designó en el cargo de preparador (asistente) en el Instituto de Fisiología de su venerado maestro. Entretanto había cumplido su año de servicio militar obligatorio y, para escapar al tedio, había traducido el duodécimo volumen de las obras completas de John Stuart Mill, dedicado a la emancipación de las mujeres, a Platón, a la cuestión obrera y al socialismo. La invitación a hacer ese trabajo procedía de Theodor Gomperz, que se había dirigido a Brentano, quien, a su vez, le había hablado de las cualidades excepcionales de su ex alumno. Miembro de una familia de banqueros e industriales judíos de Moravia, Gomperz, políglota y helenista distinguido, padecía crisis de melancolía y exaltación. Solo concebía la cultura ( _Bildung_ ) y el progreso bajo la forma de un refinamiento creciente en el uso de las lenguas. Más adelante Freud mantendría excelentes relaciones con este intelectual vienés que le había hecho descubrir el método filológico, y que sería incluso el médico de su esposa.
A pesar de sus cualidades como investigador, Freud, por consejo de Brücke, decidió en el verano de 1882 inclinarse por una carrera de médico y, por lo tanto, proseguir su formación en el Hospital General de Viena. Habida cuenta de su juventud, no tenía posibilidad alguna de suceder a su maestro en la dirección del instituto, toda vez que dos asistentes de este —Exner y Fleischl— tenían prioridad sobre él. Además, como no disponía de ninguna fortuna personal, no podía contemplar la posibilidad de ser titular de un cargo muy mal remunerado. En esa fecha, por otra parte, ya pensaba en un futuro muy distinto.
Así, después de mostrar una curiosidad insaciable por las ciencias naturales más avanzadas de su tiempo, aprendió a reconocer la verdad de la amonestación de Mefistófeles en el _Fausto_ de Goethe: «En vano rondará usted de ciencia en ciencia, / cada quien solo aprende lo que puede aprender».
### 2
Amores, tempestades y ambiciones
Ya lo he dicho: Freud afirmó a menudo que toda su existencia había estado marcada por la necesidad de encontrar un amigo indispensable que fuera igualmente un indispensable enemigo. En 1899, con referencia a _Fausto_ , destacó a ese respecto que todas sus amistades masculinas habían sido las encarnaciones de una figura de su infancia —su sobrino John— «que "antaño se mostró a mis opacos ojos"; son _resucitados_ ».
Con sus numerosas citas de los textos de Goethe, Freud se atribuyó desde época muy temprana un estatus análogo al del príncipe de las letras alemanas, su escritor predilecto. Admiraba tanto como este la _Weltliteratur_ , la literatura universal, la civilización grecolatina, Oriente y la sensualidad de los pueblos primordiales. Le encantaba contar la historia del orfebre Demetrio que, en Éfeso, en el año 54, se había opuesto a los judíos, los cristianos y el apóstol Pablo porque la nueva religión monoteísta atacaba a las antiguas divinidades y el comercio de estatuillas de la diosa Artemis: «¡Grande es Diana Efesia!», gritaban los amotinados. Y Freud, como Goethe, hacía del orfebre el símbolo de la resistencia del artista frente a la militancia religiosa, sin dejar de recordar que las figuraciones de la diosa madre ( _Ur Mutter_ ) existían en todos los cultos, desde la primitiva Oupis hasta la Virgen María.
Freud se sentía el heredero de Goethe. Como él, había sido el favorito de su madre, nacido «negro» y prometido a un destino heroico. Al identificarse tanto con Fausto como con Mefistófeles, se asignó muy pronto la misión de dar existencia a lo que el discurso de la razón procuraba enmascarar: la parte oscura de la humanidad, lo que hay de diabólico en ella; en resumen, lo reprimido, lo desconocido, el sexo prohibido, la extrañeza, lo irracional, la farmacopea. Además, Freud compartía con Goethe un mismo culto de la naturaleza, una aversión al dogmatismo, un amor loco por la arqueología e Italia, un rechazo de la metafísica y una capacidad inaudita de mantener amistades duraderas para luego deshacerlas.
Y fue en la más pura tradición del _Sturm und Drang_ (tempestad y pasión) —encarnado por Goethe y _Las cuitas del joven Werther_ — que Freud, científico positivista, darwiniano y racional, en busca de gloria y adversidad, especializado en la observación de los animales marinos, se enamoró, a los veintiséis años, de Martha Bernays. Tras la conmoción que había suscitado en él Gisela Fluss diez años antes, se había mostrado muy poco interesado en las muchachas. Afectado de inhibición, angustia y neurastenia, caía periódicamente presa de enfermedades somáticas: malestares, desmayos, trastornos cardíacos y digestivos, migrañas, neuralgias de origen inflamatorio, colitis. Su cuerpo, al que llamaba «nuestro pobre Konrad», jamás lo dejaba tranquilo. Una vez contrajo incluso una fiebre tifoidea leve, y después una forma atenuada de viruela. Víctima —él, el trabajador incansable— de dolores físicos, muy pronto se aficionó a la nicotina, primero en cigarrillos y luego en puros: una veintena por día. Solo el hombre que sufre puede realizar algo, pensaba, y cuando el bienestar lo invadía no lograba ni crear ni pensar. En 1897 declaró que las adicciones no eran otra cosa que sustitutos de la práctica de la masturbación: necesidad propia de la especie humana salida del mundo animal. ¿Cómo no evocar aquí las célebres palabras de Darwin, que tan bien convienen a la génesis y el devenir de la obra freudiana: «El diablo con forma de babuino es nuestro abuelo»?
Una vez más, se trató de una historia de familias y encuentros cruzados. Nacida en Hamburgo el 26 de julio de 1861, Martha era hija de Berman Bernays, comerciante de paños y bordados, que había conocido la bancarrota y la cárcel a raíz de malos negocios, tras lo cual se instaló en Viena en 1869. Aunque de escasa fortuna, los Bernays eran de una condición social e intelectual superior a los Freud. Célebre filólogo alemán apegado al judaísmo ortodoxo, Jacob Bernays (1821-1881), hermano de Berman y tío de Martha, se había negado a convertirse y prefirió renunciar a un puesto de profesor en una universidad prusiana antes que renegar de su fe. Comentarista de la obra de Aristóteles, había puesto de relieve, contra la interpretación clásica, el carácter médico de la catarsis, que veía menos como una purgación del alma que como una terapia ancestral, originada en el corpus hipocrático y apta para reducir las violencias colectivas. Los trágicos griegos, entonces, la habían heredado. Aunque nunca lo conoció, Freud admiraba a ese sabio riguroso y ascético, enamorado de los hombres, y que había sido amante de uno de sus ex alumnos, el poeta Paul Heyse.
Quinta integrante de una fratría de seis, dos de los cuales habían muerto de pequeños y un tercero en la adolescencia, Martha estaba muy apegada a su hermano Eli, convertido en cabeza de familia después de la muerte de Berman, y a su hermana menor Minna, que no se le parecía en nada. Los tres vivían con su madre, Emmeline, hija de comerciantes, judía practicante, arrogante, egoísta, imbuida de prejuicios religiosos y que, según el rito ortodoxo, había sacrificado su cabellera al día siguiente de sus nupcias, para usar a partir de entonces peluca.
Novio de Anna, hermana de Freud, Eli visitaba con frecuencia a la familia en compañía de su madre y sus dos hermanas. Una noche de abril de 1882 Martha conoció a quien iba a ser su esposo. Al ver a esa joven elegante, de rasgos delicados y pelo oscuro, que llevaba un vestido de cuello ajustado y calzaba finas botas con cordones, Freud experimentó un sentimiento extraño, convencido al instante de que ella, una mujer que era lo contrario de su madre, sería para él la mujer de su vida. Por eso se dejó desbordar por ese estado amoroso, cuyos efectos devastadores siempre temía. Durante sus largos años de estudio no había soñado más que con la ciencia y la celebridad, a costa de reprimir sus afectos.
Pese a su timidez enfermiza, se apresuró a conquistar a esa mujer, cortejada por otros y de la que deseaba adueñarse. Todos los días le enviaba una rosa acompañada de un verso latino. El 27 de junio de 1882 se comprometieron en secreto y decidieron de común acuerdo respetar las convenciones victorianas de su tiempo, que obligaban a los futuros cónyuges a someterse a un largo período de castidad prenupcial. Freud no había terminado su formación médica y, en consecuencia, no podía pensar en fundar rápidamente una familia.
En ese final del siglo XIX las jóvenes de la buena sociedad, sometidas a noviazgos interminables y consumidas por la frustración, se sumían a menudo en una neurosis histérica que las llevaba a consultar a especialistas en enfermedades nerviosas. En cuanto a los varones, frecuentaban los burdeles o tenían amoríos con mujeres casadas, hartas por su parte de una vida conyugal muchas veces monótona. Freud escogió la abstinencia, las drogas, la exaltación romántica y la sublimación, lo cual lo llevó a ser un excelente epistológrafo.
Durante años intercambió con Martha, que vivía en Wandsbek, cerca de Hamburgo, una voluminosa correspondencia amorosa en la cual se mostraba alternativamente tiránico, impetuoso, celoso, melancólico, prolífico y capaz de elaborar, hasta en sus más mínimos detalles, proyectos de vida cotidiana, en los que llegaba al extremo de describir por anticipado cómo veía la organización de la casa. Martha debía ser su dulce princesa, afirmaba Freud, aquella a quien se hacen mil regalos y se dan mil vestidos elegantes. Pero también tendría el deber de ceñirse a la organización de la pareja y el hogar, así como a la educación de los hijos, y apartarse de todo proyecto de emancipación. En cada página de cada carta Freud contradecía las tesis de Stuart Mill, a pesar de que había traducido su obra dedicada a la libertad de las mujeres.
Y de igual modo, pensaba contra sí mismo al adoptar en su vida privada prejuicios y comportamientos dominantes que, sin embargo, reprobaba en sus manifestaciones públicas. Martha le respondía siempre con cierta firmeza que no aceptaría que la tiranizara, pero nunca conseguía impedir que su prometido se refiriera a sus celos y su rivalidad con quienes la frecuentaban, en especial Fritz Wahle, un seductor artista que había osado darle un beso. Freud también prohibía a su querida y tierna princesa tratar con familiaridad a sus admiradores, e incluso agarrarse del brazo de un hombre cuando se daba el gusto de acudir a una pista de patinaje. Un día se ofuscó porque ella había visitado a una amiga de la infancia que había tenido una relación carnal con su prometido antes de la boda. Freud velaba por su buena salud y se preocupaba por su peso y su palidez. En una palabra, el enamoramiento y la abstinencia lo tornaban insoportable, despótico e irracional.
Persuadido de que su amor por Martha era más fuerte que el de ella por él, llegó a reprocharle que le hubiera dado su consentimiento sin sentir por él un verdadero afecto. Se quejaba además de los sufrimientos que padecía cuando creía darse cuenta de que ella se esforzaba en vano por amarlo. En junio de 1884 trazó el balance de sus relaciones:
Quiero decir que yo me impuse a ti y que tú me aceptaste sin gran afecto. Sé que todo esto ha cambiado por fin, y este éxito, que yo deseaba más que cualquier otra cosa, y cuya prolongada ausencia ha constituido mi mayor tristeza, me presta alientos, ayudándome a encararme con los otros éxitos que aún anhelo. [...] ¿Te acuerdas de cómo nos peleábamos y de que nunca te rendías? Éramos dos personas que pensábamos de manera distinta en todas las facetas de la existencia; dos personas decididas a quererse por encima de todo y que, de hecho, ya se amaban. Y luego, cuando sobrevino una época prolongada en que no surgieron diferencias entre nosotros, tuve que admitir, confrontado conmigo mismo, que antes, a pesar de ser mi amada, te mostrabas tan pocas veces de acuerdo conmigo, que nadie hubiera podido deducir de tu conducta que te estabas preparando para compartir mi vida.
Buscando una vez más al indispensable enemigo, comenzó a detestar a Emmeline, la madre de Martha, quien por otra parte le pagaba con la misma moneda y, al contrario de su hija, no consideraba a su futuro yerno como un ser excepcional. Le reconocía empero algunas cualidades: constancia, tenacidad, temeridad. Si mucho tiempo atrás Freud se había enamorado de una muchacha porque admiraba en ella la sombra de su madre, esta vez se empeñó en separar a la madre de la hija. Le reprochaba a la primera asemejarse a un hombre y haberlo privado de la segunda al mudarse de Viena a Wandsbek. Por añadidura, se mofaba abiertamente de las prácticas religiosas de la familia Bernays. Calificaba de camelos oscurantistas los ritos alimentarios y la observancia del sabbat, y conminaba a Martha a apartarse de ellos si no quería reprimendas. El destino de las muchachas, también decía, es dejar a padre y madre para someterse a la autoridad del marido.
Como Martha había puesto en manos de su hermano Eli la administración de una parte de la dote que ella había heredado de su tío Jacob, Freud encontró la manera de rivalizar con su futuro cuñado, al extremo de acusarlo de hacer transacciones dudosas y exigir a su prometida una ruptura inmediata. En realidad, Eli era víctima de un chantaje que le hacía una mujer, sin duda una antigua amante, que le reclamaba dinero para criar al hijo que habría tenido con él. Y usó entonces la dote destinada a su hermana. Indignada, Martha apoyó a Eli, a quien Freud trató de bellaco. Fue preciso que se produjera el casamiento entre Eli y Anna, en 1883, para que cesaran las hostilidades.
Así como Freud había necesitado a un enemigo para arrancar de su entorno a la mujer deseada, para hacerse amar por ella recurrió en su combate a una indispensable amiga: Minna Bernays, la hermana menor de Martha. A lo largo de ese interminable noviazgo Minna se convirtió en su cómplice y su aliada intelectual, capaz de oponerse a Emmeline, sobre todo en el terreno de la religión: «No quieres mucho a tu madre», le diría Freud un día a Martha, «pero estás llena de miramientos con ella. Minna, por su parte, la adora y no la trata con consideración». Esta situación convenía además a su concepción de un orden familiar ampliado. Ya en 1882 se decía mucho más atraído por Minna debido al hecho de que era la novia de su amigo vienés Ignaz Schönberg. La inteligencia y el espíritu cáustico de su futura cuñada le parecían en extremo encantadores. Por eso le escribía cartas de una infinita ternura en las cuales le hacía numerosas confidencias y la llamaba «querida mía, mi hermana». Como Emmeline no había autorizado a Minna a comprometerse con Schönberg, Freud le enviaba clandestinamente las cartas de este. En parte a causa de este juego sutil entre Martha, Minna y los dos amigos, algunos comentaristas supusieron la existencia de un amorío, inhallable en los archivos, entre Sigmund y su cuñada.
Freud se había forjado la certeza de que Minna se le asemejaba y era tan salvajemente apasionada como él, aun cuando en lo físico pareciera la melliza de su hermana. En consecuencia, consideraba a Ignaz —un hombre prudente y ponderado— como un doble de Martha que prefería a una mujer fuerte y autoritaria antes que a una dulce y delicada princesa. Y deducía de ello que las dos parejas formarían en el porvenir un valeroso cuarteto en el que, con armonía, se mezclarían temperamentos opuestos. Así creía poder reconstruir en su vida futura el ideal de fraternidad conflictiva al que estaba tan apegado desde su infancia. Pero en 1885 Schönberg, ya afectado por la tuberculosis, se vio con Minna por última vez antes de reunirse en Baden con Freud, que juzgó desesperado su estado. Su muerte provocó en este una gran conmoción, agravada por el hecho de que, poco tiempo antes, su camarada Nathan Weiss, ante quien se abría la perspectiva de una brillante carrera de neurólogo, se había ahorcado en un establecimiento de baños al volver de su viaje de bodas.
Redactadas en un estilo a menudo caótico, las cartas escritas por Freud durante ese período dan testimonio de un verdadero talento literario. Escribía a vuela pluma y sabía, en pocas líneas, expresar sus afectos, explorar su inconsciente y sus pulsiones y manifestar con palabras simples pero sabiamente elegidas sus estados de ánimo, sus perturbaciones, sus vacilaciones, su ambivalencia. Siempre dispuesto a cuestionarse y manejar el humor en pleno torrente de furia, tenía aptitud para dar de sí mismo y de los otros una imagen picaresca y lúcida, esbozando aquí y allá retratos de una infinita sutileza. Bosquejaba situaciones, mencionaba anécdotas o contaba sus sueños sin caer jamás ni en la jerga cientificista —a pesar del uso de términos latinos— ni en el relato sentimentaloide. Una verdadera lección de anatomía novelesca.
Pero la exaltación amorosa de la que dio muestras en diversas ocasiones también tenía por origen un consumo excesivo de drogas. Entre 1884 y 1887, mientras era asistente en el Hospital General, Freud manifestó un entusiasmo considerable por las múltiples propiedades de la planta llamada coca ( _Erythroxylum coca_ ) y del alcaloide extraído de sus hojas, la cocaína. Conocida desde mediados del siglo XIX por sus efectos tónicos y euforizantes, esta sustancia había constituido el tema de numerosas publicaciones. Descontento por haberse visto obligado a abandonar la investigación científica para dedicarse a la práctica médica, Freud esperaba hacer un gran descubrimiento que lo elevara a la celebridad. Y, de tal modo, se lanzó a un estudio histórico clínico de las virtudes de la cocaína en el tratamiento de las afecciones cardíacas, la depresión y los estados provocados por la abstinencia de morfina.
De resultas de ello, experimentó con la droga en sí mismo como un remedio milagroso que supuestamente le permitiría luchar contra su neurastenia y los efectos devastadores de su abstinencia sexual. «Cuídate, princesa mía», le escribía a Martha en junio de 1884, «cuando vuelva te besaré hasta hacerte enrojecer toda [...]. Y si te muestras indócil, verás quién es el más fuerte de los dos: la dulce muchachita que no come lo suficiente o el fogoso hombretón que tiene cocaína en el cuerpo.» Con la intención de ayudar a su amigo Ernst von Fleischl-Marxow, que había sufrido una grave herida durante una experiencia de patología anatómica y había sido víctima de una amputación fallida del pulgar, le administró cocaína. De ese modo creía poder deshabituarlo a la morfina, que le resultaba indispensable para aliviar sus dolores. Freud ignoraba entonces que ese tratamiento llevaría a Fleischl a sustituir una toxicomanía por otra. Como el propio Freud no era dependiente de aquella droga, se negaba a admitir la existencia de varios casos de adicción, señalados, empero, en la literatura médica de su tiempo.
En su entusiasmo llegó además a sugerir a dos de sus colegas oftalmólogos, Carl Koller y Leopold Königstein, que utilizaran las propiedades analgésicas de la coca en las operaciones oculares. Y fue así como Koller se convirtió en el inventor de la anestesia local.
El episodio de la cocaína, que suscitó interpretaciones delirantes en no pocos comentaristas, debe comprenderse como una etapa importante en la trayectoria del joven Freud. Un día este contó que el estudio de la coca había constituido para él un _allotrion_ que había intentado en vano alejar de sí: un momento marginal pero profundo y esencial. En otras palabras, es preciso admitir que, con el uso de esa droga, Freud se enfrentó a su «demonio», su _hybris_ , su desmesura, la parte irracional de sí mismo que siempre lo llevaría a desafiar el orden de la razón, ya fuera en el interés prestado a los fenómenos ocultos y la telepatía o en su atracción por las especulaciones más extravagantes. Durante ese episodio comprobó hasta qué punto la droga podía ser a la vez el mal y el remedio del mal, la herramienta diabólica capaz de producir estados mentales patológicos para tratar a continuación de erradicarlos. Ese paso por la droga, que duró varios años, fue para él, por lo tanto, una manera de hacer el duelo del enfoque fisiológico en beneficio del estudio de los fenómenos psíquicos.
La práctica hospitalaria permitió a Freud conocer a varias eminencias de la ciencia médica e iniciarse en todas las especialidades: la cirugía con Theodor Billroth, la dermatología con Hermann von Zeissl, la oftalmología, la clínica de enfermedades nerviosas, la psiquiatría en el servicio de Theodor Meynert y, para terminar, la medicina interna bajo la batuta de Hermann Nothnagel, a quien comparó con un gigante teutón salido de los bosques germánicos: «Este hombre no es de nuestra raza. Cabellos rubios y rostro cubierto de pelos con dos enormes verrugas en la mejilla y la base de la nariz».
En esa época la creciente influencia de la medicina hospitalaria vienesa, ligada a la profusión de pacientes llegados de todos los ámbitos del mundo germanoparlante, iba a la par con una actitud específica de algunos miembros del gremio que se interesaban mucho más en la investigación, las autopsias y la patología anatómica que en la relación terapéutica. En ellos la fascinación por la muerte se imponía al deseo de curar o prestar asistencia a los cuerpos sufrientes. El arte clínico más consumado consistía entonces en señalar en el cuerpo de un agonizante los signos de una enfermedad que solo se revelaría gracias a la autopsia. El joven Freud afrontó esa prueba pasando una noche entera a la cabecera de un enfermo afectado de escorbuto que, según su sospecha, había tenido una hemorragia cerebral. Anotó hora por hora la progresión de los síntomas y asistió al deceso observando cómo efectúa el ser humano el gran tránsito.
Dentro del hospital los mandarines mostraban despreocupación y hasta una bella arrogancia con los pacientes. Se expandía así ese «nihilismo terapéutico» tan característico del espíritu vienés de la segunda mitad del siglo XIX. Convencidos —con razón, por otra parte— de que las enfermedades formaban parte de la vida, sus adeptos procuraban comprenderlas y describirlas más que curarlas.
Procedente en línea directa de esta tradición de la patología anatómica, encarnada sobre todo por Carl von Rokitansky, Theodor Meynert, gran maestro de la psiquiatría vienesa, era un pintoresco personaje, colérico y ambivalente, dotado de un «exterior bastante llamativo, una enorme cabeza encaramada sobre un pequeño cuerpo y una cabellera desmelenada que tenía la molesta costumbre de caerle sobre la frente, y que él debía echar sin cesar hacia atrás». Esta manera de ser no era, sin duda, ajena al interés que él prestaba a la confusión mental ( _amentia_ ). Inspirado en el modelo herbartiano, Meynert distinguía el córtex superior, del que hacía una instancia de socialización, y el córtex inferior, terreno privilegiado de lo arcaico. En esa perspectiva, asimilaba el yo primario a la parte genéticamente primordial del inconsciente, y el yo secundario al instrumento de un control de la percepción. Freud retomaría en parte sus tesis en el _Proyecto de psicología_.
Meynert dejó su marca en la escuela vienesa de psiquiatría al pretender acentuar aún más la idea de que todos los fenómenos psicológicos se reducían a un sustrato orgánico. Con la elaboración de una verdadera «mitología cerebral» adoptaba, en ese ámbito, el punto de vista del nihilismo terapéutico. Apenas se ocupaba de los alienados que tenía a su cargo y prefería consagrar su tiempo a estudiar la anatomía del cerebro, con el objeto de proponer una clasificación «natural» de los trastornos mentales.
En 1883 Freud fue durante cinco meses alumno de ese científico, que suscitó en él una fuerte impresión. Y gracias a él tuvo la oportunidad, por única vez en su vida, de observar a varias decenas de enfermos mentales a quienes los médicos infligían diversos tratamientos corporales sin prestar atención a su palabra. Es evidente que Freud no sentía atracción alguna por el enfoque de la locura (las psicosis) y no compartía ni la mitología cerebral de Meynert ni su nihilismo. Como había abandonado la investigación en fisiología para dedicarse al ejercicio de la medicina, era preciso además que tomara en consideración la relación terapéutica. Y por eso decidió orientarse en primer lugar hacia la neurología y luego hacia el estudio de las enfermedades de los nervios, esas famosas neurosis observadas con tanta frecuencia en la sociedad occidental, y que ocasionaban trastornos de la personalidad: angustia, histeria, obsesión, neurastenia. Él mismo era un producto puro de ellas. En 1885, gracias a Meynert, Nothnagel y Brücke, obtuvo el título de _Privatdozent_ , que lo habilitaba para enseñar en la Universidad de Viena.
Hijo de un rabino, pero perteneciente a la generación de judíos vieneses ansiosos por asimilarse, Josef Breuer, nacido en 1842, también se veía destinado a la fisiología. Y fue en el laboratorio de Ewald Hering, rival de Brücke, donde comenzó a trabajar en el problema de la respiración, antes de llegar a ser asistente de Johann von Oppolzer, un notable internista, y de elegir la carrera médica para interesarse a continuación en la neurología y luego en la psicología, y por ende en las enfermedades nerviosas. Profesional humanista, muy alejado del nihilismo terapéutico de las figuras más influyentes del cuerpo médico, Breuer había sabido tejer una red de relaciones personales en el seno de la burguesía acomodada, a tal punto que era médico de sus colegas y de numerosos intelectuales vieneses. Entre ellos Brentano, Billroth, Rudolf Chrobak —célebre obstetra— y, por último, Marie von Ebner-Eschenbach, con la cual mantuvo una vasta correspondencia: «En Breuer», escribe Hirschmüller, «los pacientes encontraban, además de un médico competente, un interlocutor estimulante y un amigo personal. Era la representación misma del médico de familia de comienzos del siglo XIX, que, con la especialización creciente, se había hecho cada vez menos habitual».
Freud lo había conocido hacia 1877 —quizá un poco antes— y había asistido a sus cursos sobre las afecciones renales, a la vez que, como él, se vinculaba con Fleischl y Exner. Gradualmente, encontró en ese clínico ponderado un consuelo permanente. Caía una vez más, pues, bajo el encanto del indispensable amigo, capaz de ocupar, en su imaginario familiar, el lugar del hermano mayor.
Breuer mostraba una gran generosidad con sus amigos. Ayudó económicamente a Freud y le prodigó consejos ilustrados, alentándolo, por ejemplo, a inclinarse por la neurología en vez de la psiquiatría o a mantener las mejores relaciones con la burguesía vienesa. Por último, advertido de la intensa curiosidad de Freud por las experiencias innovadoras o transgresoras, lo impulsó a interesarse en el hipnotismo tan detestado por los partidarios del nihilismo, que consideraban esa técnica de adormecimiento de los pacientes con fines terapéuticos indigna de su ideal de cientificidad. Pero Breuer se obstinaba en mostrarse sensible a esa experiencia originada en el antiguo magnetismo. El propio Brentano, además, le había hablado maravillas de ella, tras visitar en Breslau al fisiólogo Rudolf Heidenhain, que estudiaba los estados modificados de la conciencia, de los cuales se pensaba que favorecían el develamiento de secretos patógenos enterrados en el subconsciente.
En 1880 Breuer empezó a tratar a Bertha Pappenheim, una joven vienesa de veintiún años perteneciente a una familia judía ortodoxa. La muchacha presentaba graves síntomas histéricos. Cuatro años después, Freud, que ya conocía la historia de Bertha, recibió a su primera paciente, afectada de idénticos trastornos.
Para todos los que en esos años aspiraban a tratar las enfermedades nerviosas, la escuela francesa parecía mucho más evolucionada que la escuela austríaca. París era pues, a los ojos de los jóvenes investigadores, la capital del saber más elaborado en la materia. Por eso Freud solicitó una beca para seguir la enseñanza de aquel a quien en todo el mundo occidental se consideraba como el más grande especialista en histeria: Jean-Martin Charcot, apodado el «César» del hospital de la Salpêtrière.
Autoritario y notablemente apuesto, en ocasiones propenso a adoptar la pose imperial con una mano dentro de su traje negro, este médico de origen modesto, a menudo tocado con un sombrero de copa, estaba por entonces en el apogeo de su carrera. Sombrío y silencioso, afectado por un leve estrabismo que contrastaba con la regularidad de los rasgos de su rostro lampiño, este personaje victorhuguiano temía el contacto con los seres humanos, pero apreciaba las mundanidades. Adoraba a los animales y vivía rodeado de perros y con una monita que testimoniaba su interés por el circo y los seres diferentes, víctimas de enfermedades neurológicas. Conocido por su defensa de las tesis de Pasteur y su combate contra la caza y la vivisección, este clínico de la mirada, erudito y esteta, parecía absolutamente ajeno a las batallas políticas que desgarraban a Francia en la segunda mitad del siglo XIX.
Heredero de la medicina experimental de Claude Bernard, símbolo del éxito republicano de la medicina hospitalaria, Charcot se había inclinado por la neurología y había descrito la terrible enfermedad que lleva su nombre: la esclerosis lateral amiotrófica. En 1870, mientras París sufría el asedio de las tropas prusianas, había decidido reformar la organización del psiquiátrico que tenía bajo su dirección, para lo cual separó a las alienadas de las epilépticas (no alienadas) y las histéricas. Y fue así como se metió de lleno en la cuestión de la histeria, una obsesión del discurso médico de la época.
Conocida desde siempre, esta extraña enfermedad, que ahora se denominaba neurosis, había sido vista durante siglos como la expresión de una locura sexual estrictamente femenina y de origen uterino. Las convulsiones y sofocos que hacían presa del alma y el cuerpo de las mujeres se atribuían a una posesión demoníaca. El diablo embustero, se decía, entraba en la matriz de las mujeres para desviarlas de su destino anatómico e impedirles ponerse al servicio de la perpetuación de la especie humana.
En realidad, fue Franz Anton Mesmer quien, en vísperas de la Revolución francesa, efectuó el tránsito de una concepción demoníaca a un enfoque científico de la histeria. Por medio de la falsa teoría del magnetismo animal, Mesmer sostenía que las enfermedades nerviosas tenían su origen en el desequilibrio en la difusión de un «fluido universal». Bastaba pues con que el médico provocara crisis convulsivas en los pacientes —en general, mujeres— para restablecer el equilibrio fluídico perdido. De esta concepción había salido la primera psiquiatría dinámica, que puso de relieve las «curas magnéticas». La histeria escapó entonces a la religión para pasar a ser considerada como una enfermedad de los nervios que afectaba a mujeres vistas como «simuladoras», es decir, poseídas por el demonio del sexo, brujas sin dios ni diablo y por consiguiente mucho más nocivas para la sociedad porque también se las acusaba de transmitir un temible mal: la sífilis. Al exhibir sus cuerpos sexuados, se decía, transgredían el orden procreativo y se negaban a ser madres y esposas.
Charcot reprobaba esas tesis y, durante sus famosas clases de los martes y los viernes, frecuentadas por médicos e intelectuales de todos los pelajes políticos, enseñaba su teoría de los diferentes aspectos del trance hipnótico: letargo, catalepsia, clownismo, sonambulismo. Pero en particular, al poner en escena a las locas de la Salpêtrière —esas mujeres del pueblo en estado de éxtasis y convulsión—, demostraba que sus parálisis o sus gesticulaciones obscenas no eran el resultado ni de una simulación diabólica ni de lesiones localizadas, sino que tenían un origen traumático. Y para probarlo hacía desaparecer y reaparecer los síntomas de la enfermedad. Blanche Wittmann, Augustine Gleizes, Rosalie Dubois, Justine Etchevery y muchas otras, maltratadas en la vida, violadas o víctimas de abusos en la infancia, fueron las heroínas de esas experiencias llevadas a cabo por un maestro cuya sombría mirada clínica lindaba con el genio. El destino de esas mujeres fue inmortalizado tanto por el cuadro de André Brouillet como por la _Iconographie photographique de la Salpêtrière_ realizada por Désiré-Magloire Bourneville y Paul Regnard: verdadero monumento levantado en honor de las representaciones visuales de la histeria de fin de siglo.
Para probar que no era un mal del siglo, Charcot hizo de la histeria una enfermedad funcional de origen hereditario y afirmó que sus estigmas estaban presentes en las obras de arte del pasado. Y para confundir a los inquisidores destacó que, en su época, estos habían hecho condenar por brujería a mujeres histéricas. Además, para liberar a la histeria de toda presunción uterina, demostró que también podía afectar a los hombres, sobre todo tras padecer traumas provocados por accidentes ferroviarios. De ese modo, asimilaba trastornos funcionales (histeria clásica) a trastornos postraumáticos (accidentes).
Charcot compartía con la escuela alemana la doctrina de las localizaciones y creía que la construcción de la medicina moderna iba a la par con la elaboración de una clasificación rigurosa. Sin adoptar el principio del nihilismo, apenas se ocupaba de tratar o curar las neurosis. Utilizaba la hipnosis, no con fines terapéuticos, sino para demostrar la precisión de su concepción de la histeria. Esta actitud le fue reprochada por su rival de la escuela de Nancy, Hippolyte Bernheim.
No hay ninguna duda de que Charcot proponía una nueva concepción de la histeria. Sin embargo, solo podía hacerlo porque esta se había convertido en toda Europa en la expresión de una rebelión impotente de las mujeres contra un poder patriarcal atormentado por el espectro de una posible feminización del cuerpo social. En Viena esa rebelión se mantenía confinada dentro del círculo de las familias burguesas. Pero en París —ciudad de los motines revolucionarios— asumía un cariz tanto más político cuanto que la medicina de Estado se pretendía popular y republicana.
Así, las mujeres exhibidas en la Salpêtrière eran, sin saberlo, las herederas de la figura de la bruja rehabilitada por Jules Michelet, y de la que Arthur Rimbaud se había erigido en heraldo al celebrar en 1872 «las manos de Jeanne-Marie», esa heroína de la Comuna tratada de «arpía histérica» y torturada por las tropas de Versalles.
Brücke intervino en favor de Freud. En junio de 1885 se autorizó a este a interrumpir durante seis meses sus funciones de médico residente. El 13 de octubre, siempre bajo la influencia de la cocaína, se instaló en el hotel de la Paix del callejón Royer-Collard, en pleno corazón del Barrio Latino, muy cerca de la Sorbona y el Panteón.
La idea de deambular por las calles de esa ciudad de las Luces, donde los judíos se habían emancipado por primera vez en Europa, le había proporcionado extrema felicidad. Una vez allí, fue al cementerio de Père-Lachaise para visitar las tumbas de Heine y Börne. Sin embargo, apegado a los ideales de las dinastías reales, le gustaba muy poco el espíritu republicano. Por eso consideraba la epopeya revolucionaria francesa como la expresión de una suerte de patología mental, a la manera de Hippolyte Taine y los reaccionarios de fines de siglo, obsesionados por el recuerdo de la Comuna, que señalaban como el equivalente de una crisis de histeria.
Al adoptar ese discurso de la contrarrevolución y la anti-Ilustración, que fue una de las fuentes del antisemitismo moderno, pronto encarnado por Édouard Drumont, Freud parecía olvidar su amor por Bonaparte, heredero del jacobinismo. Siempre excesivo, no tardó en juzgar con severidad al pueblo parisino, consideraba feas a las mujeres y apreciaba muy poco la gastronomía francesa: «Estoy bajo el pleno impacto de París», escribía a Minna,
y, hablando en tonos poéticos, podría compararlo con una esfinge de formas ampulosas y adornos estrafalarios que se zampara a todos los extranjeros incapaces de contestar correctamente a enigmas [...]. Básteme decir que la ciudad y sus habitantes me parecen irreales; es como si las personas pertenecieran a especies distintas de la nuestra, como si estuvieran poseídas por mil demonios. En lugar de oír sus _Monsieur_ y _Voilà l'Écho de Paris_ , les oigo gritar _À la lanterne_ y _À_ _bas_ tal o cual persona. Creo que desconocen el significado de la vergüenza o el temor. Mujeres y hombres, sin distinción, se apretujan frente a los desnudos, del mismo modo que lo hacen alrededor de los cadáveres en el depósito, o de los horrendos carteles que anuncian en las calles un nuevo folletín en tal o cual periódico, exhibiendo simultáneamente una muestra de su contenido. Son gente dada a las epidemias psíquicas y las convulsiones históricas de masas, y no han cambiado desde que Victor Hugo escribió _Notre-Dame_.
Y en una carta anterior a Martha: «En la Place de la République contemplé la estatua gigantesca que lleva representaciones pictóricas de los años 1789, 1792, 1830, 1848 y 1870. Esto da una idea de la existencia azarosa de esta pobre República».
Si la cultura republicana le resultaba desagradable y su puritanismo lo llevaba a veces a olvidar su propio espíritu de rebelión, no por ello Freud dejaba de ser sensible a las más diversas manifestaciones artísticas. En Viena siempre le habían gustado el teatro y la ópera, a la vez que miraba con malos ojos los cafés y los lugares que consideraba demasiado ruidosos. En París, tan pronto como pudo, fue a los grandes bulevares para admirar a su actriz preferida, Sarah Bernhardt, cuya voz y mirada hipnotizaban a las muchedumbres que él tanto aborrecía. Como Charcot, ella llevaba a las tablas los interrogantes de la época sobre la ambivalencia de la sexualidad humana, al representar ora papeles de hombres enfrentados a su femineidad, ora personajes de mujeres embargadas por una libido masculina. En el melodrama de Victorien Sardou, que Freud describía con entusiasmo a Martha, la Bernhardt encarnaba a Teodora, emperatriz maldita, vestida con suntuosos trajes bizantinos y enamorada de un amante patricio, que ignoraba su verdadera identidad.
Freud visitó con frecuencia los sitios culturales eminentes de la capital y fue en Notre-Dame de París donde tuvo la sensación de encontrarse por primera vez en una iglesia que no le recordaba en absoluto las que había recorrido en su infancia junto a su _nanny_. Se prometió releer la novela de Victor Hugo y no paró hasta conseguir subir a las torres para pasearse entre los monstruos y los diablos gesticulantes de la catedral, mientras soñaba con estrecharse en un ardoroso abrazo con su prometida.
Admiraba a tal extremo a su maestro Charcot que, al acudir a una velada que se celebraba en su palacete del bulevar Saint-Germain, su hija lo atrajo tanto que se vio en la necesidad de alejarse de ella y quedarse con «los ancianos caballeros». Tras señalar que, aunque fea, la joven era interesante a causa de un «parecido casi grotesco» con su padre, comenzó a imaginar, una vez más, lo que habría sido su vida si, en lugar de amar a Martha, hubiera sucumbido a los encantos de Jeanne Charcot: «Nada es tan peligroso como una joven que posee los rasgos del hombre a quien uno admira. En tal caso, todo el mundo haría befa de mí, me echarían de la casa y habría salido ganando la experiencia de una bella aventura. Después de todo, es mejor que no sea así». Esa noche había tomado una pequeña dosis de cocaína, se había hecho cortar la barba y el pelo y lucía con orgullo un atuendo nuevo: un traje negro, una camisa impecable, una corbata comprada en Hamburgo y guantes blancos. Se veía apuesto y tenía la mejor impresión de sí mismo.
El 28 de febrero de 1886 se marchó de París con destino a Wandsbek y de allí a Berlín, para asistir a los cursos de Adolf Aron Baginsky, un profesor de pediatría muy activo en la comunidad judía de la ciudad e iniciador de una política de prevención de las enfermedades infantiles, mentales y orgánicas. Freud tuvo entonces, sin duda, la oportunidad de descubrir en Berlín algunas torturas y mutilaciones infligidas a los niños para impedir que se masturbaran.
Si bien sentía muy poca simpatía por el imperio de los Hohenzollern, Freud amaba Berlín, la ciudad que encarnaba a sus ojos la quintaesencia de la cultura y la ciencia en el mundo germanoparlante. Ese encuentro debía permitirle prepararse para ejercer funciones importantes en el Departamento de Neurología de la Steindlgasse, primer instituto público vienés para el tratamiento de las enfermedades infantiles, dirigido por Max Kassowitz. En abril se instaló provisionalmente como médico privado en la Rathausstrasse y comenzó a recibir pacientes enviados por sus amigos. Mientras terminaba la traducción de la obra de Charcot, pensaba en Martha, con quien por fin iba a poder casarse a pesar de sus dificultades económicas y las prevenciones de su futura suegra.
A fuerza de cultivar la abstinencia y el _Sturm und Drang_ , tan pronto para complacerse en sufrimientos románticos como para mejor proyectarse en el porvenir, no dejaba de desear todo y nada. Por un lado se veía como un patriarca que vivía junto a una maravillosa esposa consagrada a las tareas de la casa y a su numerosa descendencia, y por otro temía que, una vez terminado el período de los esponsales, se levantara ante él el horrible obstáculo de «peligrosos rivales»: la pareja y el cuarto de los niños, el marido que se junta con sus amigos en el café, la esposa abandonada, etc.
La boda civil se celebró en Wandsbek el 13 de septiembre de 1886. Freud abrigaba la esperanza de que con eso bastara y no se viera obligado a ceder a los ritos religiosos, que lo horrorizaban. Pero, para su gran decepción, tuvo que hacer frente a la realidad: en Austria ese matrimonio jamás sería válido en ausencia de una ceremonia religiosa. Al día siguiente, en consecuencia, tuvo que aceptar a la fuerza esa ceremonia, celebrada en la sinagoga de Wandsbek por el rabino David Hanover. Por eso pidió a Elias Philipp, tío materno de Martha, que lo ayudara a repetir las oraciones hebreas y le enseñara cómo moverse cuando tuviera que pasar bajo el baldaquino que simboliza el Templo. El día de las nupcias, muy elegante y ya con la barba de los notables, se contentó con lucir una levita y un sombrero de copa, para evitar así usar el traje tradicional.
No bien instalados en su nuevo apartamento vienés de la Theresienstrasse, prohibió a Martha celebrar el sabbat y cocinar según las reglas del Kashrut. Ninguno de sus hijos sería circuncidado. El rechazo de los rituales fue para Freud la única manera de sentirse judío en el sentido de la judeidad sin tener que renegar de su identidad a través de una conversión cualquiera. Consciente, como Spinoza, de ser heredero de un pueblo que había cohesionado su unidad histórica, no tanto por la doctrina sagrada de la elección como por el odio que suscitaba en las otras naciones, hacía de tal modo de su orgullo de ser judío el fermento más poderoso de una resistencia a todos los conformismos.
Martha pasó del estado de novia febrilmente deseada al de esposa y madre colmada, respetada y deserotizada. Entre enero de 1887 y diciembre de 1895 trajo al mundo seis hijos: Mathilde, Martin, Oliver, Ernst, Sophie y Anna. Freud dio a los varones los nombres de pila de sus «héroes» favoritos —Charcot, Cromwell y Brücke— y a las niñas nombres tomados de un entorno familiar perfectamente delimitado: Mathilde, esposa de Josef Breuer; Sophie, esposa de Josef Paneth, y Anna, hija de Samuel Hammerschlag. Así como sus hijas quedaron «emparentadas» con las familias judías de la burguesía vienesa de las que su padre era amigo, sus hijos escaparon a ese tipo de designación al asociarse a una denominación más simbólica: por un lado la endogamia y la perpetuación del hogar, por otro la ciencia, la política y la salida del gueto.
En 1891 la familia se mudó a un apartamento bastante grande en Berggasse, 19. Sin embargo, el año siguiente Freud alquiló otro en la planta baja para instalar en él su consultorio. Cinco años después Minna se fue a vivir a ese mismo lugar para ayudar a su hermana en la crianza de los hijos y las tareas de la casa. Destino muy habitual en las familias extensas de esa época, cuando el lugar de la mujer soltera o viuda —hija, tía, prima, hermana— se definía según criterios rigurosos: segunda madre, jefa de la casa, compañía indispensable.
Ya en 1893, al notar a Martha agotada por sus sucesivos embarazos, Freud decidió recurrir una vez más a la abstinencia. Tras un primer fracaso que se tradujo en el nacimiento de Anna, su última hija, se negó a practicar el _coitus interruptus_ , al igual que los diversos medios contraceptivos utilizados en esos tiempos: preservativo, diafragma, esponja. Con apenas cuarenta años y víctima ocasional de impotencia, renunció a toda relación carnal para liberar a Martha del temor permanente de la maternidad. Ella se sintió menos angustiada y él más curioso al entregarse a una experiencia semejante, que excitaba su imaginación: Freud consideraba, en efecto, que la sublimación de las pulsiones sexuales era el arte de vivir reservado a una élite, la única capaz de acceder a un nivel elevado de civilización.
La vida carnal del más grande teórico moderno de la sexualidad habría de durar, por tanto, nueve años. Sin embargo, hasta los sesenta años, y a pesar de que no aprovechaba la libertad sexual que preconizaba en su doctrina, Freud tuvo numerosos sueños eróticos: se complacía particularmente en analizarlos y, por lo demás, no dejaba de buscar causas «sexuales» en todos los comportamientos humanos. Por eso se lo acusó en varias ocasiones de ser un burgués libidinoso, abortista clandestino, adepto a los burdeles y la masturbación, que no vacilaba en disimular las relaciones sexuales con su cuñada. Se publicaron decenas de libros, novelas y ensayos, para «demostrar» que Freud no había dejado, a lo largo de toda la vida, de ocultar su sexualidad, necesariamente salvaje y transgresora. En realidad, Freud intentó varias veces reanudar las relaciones carnales con Martha. Pero se sentía viejo y torpe y terminó por renunciar: «Cuando haya superado del todo mi libido (en el sentido corriente), me dedicaré a una "vida amorosa de los hombres"». Y también: «Lamentablemente, el rebrote de erotismo que nos ocupó durante el viaje se fundió en los afanes del tiempo de trabajo. Me adapto al hecho de ser viejo y ni siquiera pienso constantemente en el envejecer».
Todos los rumores sobre la vida sexual de Freud se apoyaban en una realidad mil veces reinterpretada: la endogamia, por una parte, y la teoría de los sustitutos, por otra. Fascinado desde la infancia por el deseo de incesto, los matrimonios consanguíneos, las relaciones intrafamiliares transgresoras, las genealogías defectuosas, Freud, en efecto, veía en cada hija la imagen negativa o positiva de la madre o el reflejo invertido de la hermana, e incluso en cada niñera el sustituto de una madre, una tía, una hermana o una abuela. Y consideraba asimismo a cada hijo o yerno como el heredero del padre o del abuelo y hasta como el cómplice del hermano. Y esa es la razón por la cual hizo de Minna su «segunda esposa», su hermana, su confidente de todos los momentos. Con la condición, empero, de que no ocupara jamás el lugar de Martha.
En septiembre de 1897, cuatro meses después de que el emperador Francisco José se resignara a convalidar la elección como alcalde de Viena de Karl Lueger, admirador de Drumont y cabecilla antisemita del Christlichsoziale Partei (Partido Socialcristiano), Freud se adhirió a la logia del B'nai B'rith, asociación judía humanitaria de fines benéficos y culturales, frente a la cual habría de pronunciar más adelante una veintena de conferencias. Ante «sus hermanos» en la alianza reivindicaba vínculos de naturaleza ética con el judaísmo, que no tenían nada que ver con «creencia» alguna. Freud seguía siendo un descreído y votaba al Partido Liberal, a la vez que frecuentaba a socialdemócratas.
El encuentro con Charcot había sido decisivo. No solo porque su concepción de la histeria le había abierto nuevas perspectivas sobre la vida psíquica y la realidad de la sexualidad humana, sino porque ese maestro pertenecía, mucho más que Brücke, a una estirpe de científicos cuya irradiación superaba ampliamente el ámbito cerrado de las facultades. Mundialmente conocido, Charcot era en primer lugar y ante todo un «vidente» dotado de un poder imaginativo que coincidía a la perfección con los sueños más extravagantes de Freud. ¿No había llegado él, al mismo tiempo que alejaba a la histeria de toda referencia a un sustrato anatómico, a susurrar al oído del joven vienés enamorado, convencido de su talento, que las verdaderas causas de ese mal convulsivo eran genitales? ¿No había dicho un día, delante de sus alumnos estupefactos, que la teoría, aun la más pertinente, era impotente frente a una realidad que la contradecía? «La teoría es buena, pero eso no impide que las cosas sean como son»: Freud siempre recordaría este imperativo categórico.
El estudio de la sexualidad se había convertido para todos los científicos de la época, tanto de Europa como del otro lado del Atlántico, en la gran cuestión del siglo próximo, y la histeria parecía ser su pieza maestra, mucho más allá de los debates médicos entre especialistas. Y no hay duda de que Charcot no era solo un maestro para Freud. Era la persona gracias a la cual se había conquistado un nuevo continente: el de la sexualidad.
Es cierto, el honesto Breuer había encauzado a Freud por el camino de la dilucidación de los fenómenos neuróticos al señalarle la importancia del determinismo psíquico en la etiología de la histeria. Pero, como profesional riguroso, deseoso de verificación experimental, dudaba de todo, formulaba sin cesar reservas sobre sus propias hipótesis y aconsejaba a Freud la mayor de las prudencias. Breuer quería a Freud y Freud quería a Breuer. Pero, bajo el influjo del amor que sentía por Charcot, Freud no sabía ser prudente.
Por eso, el 15 de octubre de 1886, invitado a dictar una conferencia en la prestigiosa Sociedad Imperial de Médicos de Viena, cometió el error de no elaborar un trabajo original como pretendía la tradición y, en cambio, se erigió en el vocero de las tesis de Charcot sobre la histeria masculina y el hipnotismo. Convencido de que las eminencias presentes en la sala ignoraban la doctrina del maestro francés, Freud les impartió una lección en toda regla. Atribuyó pues a Charcot haber descubierto, el primero, que la histeria no era ni una simulación ni una enfermedad del útero, olvidando que el hecho ya era bien conocido en Viena. Omitió señalar, por añadidura, que la disputa entre Viena y París se refería a la distinción entre histeria funcional e histeria traumática, que Charcot rechazaba.
En síntesis, Freud recibió severas críticas de Heinrich von Bamberger, de Emil Rosenthal y sobre todo de Theodor Meynert, muy hostil al hipnotismo. Esos juicios lo sumieron en una fuerte amargura y lo indujeron a concebir, como más adelante lo harían sus hagiógrafos, la idea de que lo detestaban debido a sus geniales innovaciones de sabio solitario. Sin embargo, no era así.
Breuer y Freud conversaban a menudo de sus pacientes e intercambiaban sus experiencias. Uno y otro utilizaban los tratamientos en vigencia en la época: electroterapia, balneoterapia, hidroterapia. Breuer se inclinaba por el método catártico, reactualizado por Jacob Bernays. Ese método permitía a los pacientes eliminar los efectos patógenos y luego, mediante una «abreacción», revivir los acontecimientos traumáticos a los cuales aquellos estaban ligados. Freud también recurriría a él. Pero en el otoño de 1887 decidió apoyarse más en la sugestión hipnótica, motivo de una verdadera disputa no solo entre los médicos vieneses sino entre la escuela de París y la de Nancy. Al pretenderse «hipnotizador», Freud buscaba, por la relación dinámica, una salida al nihilismo terapéutico. Frente a las eminencias médicas que lo habían criticado por usar cocaína y elogiar a Charcot, tenía toda la intención de desempeñar el papel de rebelde transgresor que tan oportuno le resultaba. Y al mismo tiempo se distanciaba de la enseñanza de la Salpêtrière.
Profesor de medicina interna en Nancy, Bernheim había adoptado el método hipnótico de Auguste Liébault y solo trataba a pacientes capaces de entrar en estado de hipnosis. Si el marqués Armand de Puységur había abierto, en vísperas de la revolución de 1789, el camino a la idea de que un maestro —noble, médico, sabio— podía ser limitado en el ejercicio de su poder por un sujeto capaz de oponerle una resistencia, Bernheim mostraba que, a fines del siglo XIX, la hipnosis ya no era más que un asunto de sugestión verbal. En esa época una clínica de la palabra sustituía a la clínica de la mirada, y Bernheim contribuía a eliminar los últimos vestigios del magnetismo al invertir la relación descrita por Puységur, a costa de disolver la hipnosis en la sugestión.
En consecuencia, el reproche fundamental que hacía a Charcot era el de fabricar artificialmente síntomas histéricos y manipular a los enfermos, mientras que la lógica de la fusión entre hipnosis y sugestión llevaba a Bernheim a sostener que los efectos obtenidos por el hipnotismo podían alcanzarse mediante una sugestión en estado de vigilia, lo que pronto se denominaría psicoterapia.
En el verano de 1889, acompañado por Anna von Lieben, una paciente perteneciente a la aristocracia judía de Viena a quien Charcot ya había tratado, Freud visitó a Bernheim antes de viajar una vez más a París para asistir a dos congresos internacionales. Fue testigo de sus experiencias de sugestión, tuvo discusiones estimulantes con él y se propuso traducir su libro. Sin renunciar a lo que había aprendido con Charcot, tomó de Bernheim el principio de una terapia que allanaba el camino a una cura por la palabra. No intervino, pues, en la disputa que oponía a las dos escuelas. Pero muy pronto se percató de que la sugestión solo funcionaba en determinadas circunstancias, y sobre todo en un medio hospitalario. Por eso prefirió valerse del método catártico, sin proscribir de todos modos el hipnotismo, lo cual lo condujo además a tener en cuenta el elemento erótico presente en la cura, es decir, la transferencia:
Me encontraba con una de mis pacientes más dóciles, en quien la hipnosis había posibilitado notabilísimos artilugios; acababa de liberarla de su padecer reconduciendo un ataque de dolor a su ocasionamiento, y hete aquí que al despertar me echó los brazos al cuello. [...] Me mantuve lo bastante sereno como para no atribuir este accidente a mi irresistible atractivo personal, y creí haber aprehendido la naturaleza del elemento místico que operaba tras la hipnosis. Para eliminarlo o, al menos, aislarlo, debía abandonar esta última.
A posteriori, Freud solo conservó de la hipnosis la posición acostada del paciente sobre un diván, detrás del cual se sentaba él para verlo sin ser visto. En cuanto a Anna von Lieben, gran ajedrecista, afectada de locura, obesa, consumidora ilimitada de caviar, champán y drogas y siempre insomne durante las noches, era en la época su principal paciente, su _prima donna_. Y en su familia llamaban a Freud _der Zauberer_ (el mago). Pero más adelante lo rechazaron, sin que lograra curar jamás a Anna de su adicción a la morfina, ni por la hipnosis ni por el método catártico.
Desde su boda y su establecimiento como especialista en enfermedades nerviosas Freud carecía de un interlocutor que estuviera lo bastante alejado de él para permitirle utilizar de nuevo sus incomparables talentos de epistológrafo. La espera duró un año, hasta el día del otoño de 1887 en que, aconsejado por Breuer, un tal Wilhelm Fliess, médico berlinés especializado en las patologías de la nariz y la garganta, acudió a él para asistir a sus clases, tras finalizar su formación en el Hospital General de Viena. De la misma generación de Freud y, como él, partidario del darwinismo y de la escuela positivista de Helmholtz, Fliess era hijo de un negociante de granos poco afortunado y depresivo cuya familia, judía sefaradí, estaba establecida en la marca de Brandemburgo desde el siglo XVII.
Es difícil saber qué es en verdad lo que sintió Fliess en esa relación de amistad volcánica que, otra vez, se apoderó de Freud. Contrariamente a la que había mantenido con Martha, la correspondencia intercambiada por los dos hombres nunca pudo reunirse por completo. Solo quedan las cartas de Freud. ¡Nuevo _Sturm und Drang_! Freud escribía a toda velocidad; multiplicaba las abreviaturas y las palabras latinas y hacía un menjunje con todo lo que se enteraba acerca de la vida sexual de sus pacientes y todo lo que sabía de la suya propia y la de las familias vienesas: padres, madres, hermanas, hijas, empleados domésticos. Clasificaba, ordenaba, multiplicaba los cuadros clínicos y manifestaba un entusiasmo frenético ante cada misiva recibida o enviada.
En resumen, desde el primer encuentro Freud cayó bajo el hechizo de ese médico que no se parecía a ninguno de sus amigos vieneses de la misma generación y ni siquiera a Breuer, quien, a pesar de su legendaria prudencia, sentía por su protegido la misma admiración que este por él.
Dotado de una sólida formación médica y científica, Fliess pertenecía no obstante a la prolongada estirpe de sabios prometeicos puestos en valor por la literatura romántica y cuya huella encontramos en la obra de Thomas Mann. Adepto a una teoría mística y organicista de la sexualidad, era en cierta forma un doble de Freud, su «demonio», su «álter», y suscitaba en él las más grandes excitaciones intelectuales. A fuerza de quererse, de oponerse, de tomarse recíprocamente por testigos de su cotidianeidad más íntima o de contarse historias de casos, a la vez que elucubraban las hipótesis más atrevidas, pero también a fuerza de encontrarse en diversas ciudades de Europa durante «congresos» de los que eran los únicos oyentes y los únicos participantes, llegaron a verse como hermanos mellizos y a hacerse fotografiar con la misma barba, la misma ropa, la misma mirada, y repartieron ese retrato entre sus amigos.
En 1892 Fliess se casó con Ida Bondy, una paciente de Breuer, cuya hermana, Melanie, se casaría cuatro años después con Oskar Rie, el médico de la familia Freud y compañero de Sigmund en el juego del tarot. De la unión de Fliess con Ida nacería Robert, que llegaría a ser psicoanalista, mientras que Oskar tendría dos hijas, Margarethe y Marianne. La primera sería la mujer de Herman Nunberg y la segunda, de Ernst Kris, ambos discípulos de Freud. ¡Una historia de familia, sin lugar a dudas!
Heredero de un enfoque científico en plena mutación, en el que se mezclaban las explicaciones más racionales, las más innovadoras y las más extravagantes acerca de las relaciones del alma y el cuerpo, Fliess, que padecía migrañas de origen desconocido, no dudaba jamás de sus hipótesis, que tomaba por certezas establecidas no bien las intuía. Apasionado por el arte, las matemáticas, la biología, la historia, la literatura y la antropología, había tomado la costumbre de poner en relación toda clase de manifestaciones patológicas de la vida humana que, sin embargo, no tenían nada que ver unas con otras. Su proceder era, pues, mucho más fascinante por tener como fundamento una concepción de la ciencia en que la duda no tenía lugar alguno, así como por basarse en especulaciones que llegado el caso eran delirantes.
Cuando conoció a Freud, Fliess estaba elaborando una doctrina articulada alrededor de tres ejes: una clínica de la neurosis, una teoría fisiológica de la periodicidad y una representación biomédica y cosmológica de la bisexualidad humana.
Tras haber descrito una entidad clínica denominada «neurosis nasal refleja», Fliess encontraba sus causas tan pronto en perturbaciones orgánicas ligadas a diversas enfermedades —entre ellas las migrañas— como en trastornos originados en los órganos genitales. Por eso relacionaba las mucosas nasales y las actividades genitales para colegir la existencia de un vínculo entre los cornetes de la nariz, las menstruaciones de la mujer, el embarazo y el parto. De ahí la idea de que los síntomas de esa «neurosis», al igual que las migrañas y otras secuelas de la menstruación, obedecían a un ritmo regular de veintiocho horas. Fliess agregaba a este otro ciclo de veintitrés días, del que hacía el equivalente masculino del ciclo menstrual femenino. Y como esos dos ciclos se manifestaban en cada uno de los dos sexos, deducía de ello la existencia de una bisexualidad fundamental del ser humano, que a su juicio se traducía en una bilateralidad fisiológica, por la que cada humano era a la vez hombre (a la derecha) y mujer (a la izquierda). Armado de este conocimiento de la periodicidad y la bisexualidad humana, creía poder determinar con certeza las fechas críticas de los ciclos que predeterminaban el nacimiento, la enfermedad y la muerte.
Convencido de que los diversos trastornos de su «pobre Konrad» podían, así, aliviarse o curarse mediante un tratamiento de las fosas nasales, Freud, que calificaba a Fliess de «Kepler de la biología», se hizo operar dos veces por él. Durante algún tiempo tuvo supuraciones. Fliess trató entonces en vano de hacerlo abandonar su adicción a la nicotina, que se intensificó cuando dejó de tomar cocaína. Y mientras llegaban a la edad madura, ambos hombres se entregaban a cálculos científicos para determinar, en virtud de la teoría fliessiana, las fechas de muerte y nacimiento.
En esa época, Freud temía morir antes de conocer Roma, su tierra prometida, o de consumar su obra: el paso de la neurología a la psicología. Sin embargo, rechazaba una y otra vez la oportunidad de hacer ese viaje, en razón de sus famosos cálculos. Cuando Ida se quedó embarazada casi al mismo tiempo que Martha, Fliess pronosticó el nacimiento de una hija y Freud el de un varón al que llamaría Wilhelm. Pero el destino decidió otra cosa: Fliess tuvo un varón (Robert) y Freud una niña (Anna).
Mientras Fliess avanzaba en la exploración cada vez más irracional de la bisexualidad humana, a la vez que propiciaba peligrosas operaciones de las fosas nasales, Freud elucubraba toda clase de hipótesis sobre el psiquismo humano. En un manuscrito de un centenar de páginas, _Proyecto de psicología_ , concebido como un tratado de psicología destinado a los neurólogos, expuso en honor de su amigo, en 1895, un plan general de su enfoque neurológico de la memoria, la percepción y la conciencia. En él describía los procesos patológicos a través de los cuales intentaba poner de manifiesto las características de los llamados fenómenos psicológicos «normales». Al contrario de Fliess, y siempre en duda con respecto a sí mismo, procuraba hacer de la psicología una ciencia natural muy alejada del proyecto de reducir los fenómenos psíquicos a trastornos orgánicos.
Planteaba además una serie de correlaciones entre las estructuras cerebrales y el aparato psíquico, en el propósito de representar los procesos psíquicos como otros tantos estados cuantitativamente determinados por partículas materiales o neuronas. Ordenaba estas en tres sistemas distintos: percepción (neuronas w), memoria (neuronas N) y conciencia (neuronas R). En cuanto a la energía transmitida (cantidad), la regían, en su opinión, dos principios —uno de inercia, otro de constancia— y provenía ora del mundo exterior, vehiculada en este caso por los órganos de los sentidos, ora del mundo interior, es decir, del cuerpo. La ambición de Freud era referir a ese modelo neurofisiológico el conjunto del funcionamiento psíquico, tanto normal como patológico: el deseo, los estados alucinatorios, las funciones del yo, el mecanismo del sueño, etc.
Esa necesidad de «neurologizar» el aparato psíquico equivalía además a fabricar una «mitología cerebral». Freud no tardó en advertirlo y renunció a ese proyecto para construir una teoría puramente psíquica del inconsciente. A partir de entonces calificó de delirio, balbuceo y galimatías lo que había elaborado.
En virtud de esa nueva perspectiva, que lo llevó a explorar los fenómenos inconscientes, consideraba que el origen de los síntomas neuróticos —y en especial los que caracterizaban a las histéricas— se encontraba en traumas sexuales sufridos en la infancia. Este postulado coincidía con lo que Freud había retenido de la enseñanza de Charcot. Y dio el nombre de «seducción» o «atentado» a los abusos sexuales padecidos en la infancia por las pacientes a quienes escuchaba y que, muy a menudo, los contaban con lujo de detalle en las curas y acusaban a un padre, un tío, un amigo de la familia.
Comoquiera que sea, entre 1892 y 1895 la joven y bella Emma Eckstein fue la principal víctima de los intercambios clínicos y las divagaciones teóricas de Fliess y Freud.
Perteneciente a la burguesía judía progresista y muy activa en el movimiento feminista austríaco, en su infancia Emma había sido víctima, al parecer, de una llamada ablación «terapéutica» destinada a impedirle masturbarse. Desde bastante tiempo atrás padecía molestias gástricas y menstruaciones dolorosas. Allegado a su familia, Freud decidió practicar con ella una cura catártica ad honórem en la propia casa de la muchacha. Se persuadió entonces de que sus dolores podían relacionarse con la mucosa de la nariz. Por eso pidió a Fliess que viajara desde Berlín para operarla. Fliess extirpó el tercio anterior del cornete medio izquierdo de la nariz de Emma.
Dos semanas después de la intervención la joven sintió espantosos dolores causados por secreciones infecciosas purulentas de las que se desprendía un olor fétido. Un fragmento de hueso se había partido y provocaba hemorragias. Preocupado, Freud llamó a su amigo Ignaz Rosanes; este, al limpiar la herida, advirtió que Fliess había olvidado en la cavidad nasal un pedazo de gasa impregnada de tintura de yodo. Al removerlo, salió un abundante chorro de sangre. A punto de desvanecerse, Freud se refugió en la habitación de al lado. Después de tomar una copa de coñac volvió junto a la paciente, que lo recibió con estas palabras: «He ahí al sexo fuerte». Emma padecería toda su vida secuelas de esa intervención quirúrgica: el hueso de la nariz se había necrosado de manera irreversible.
Realmente afectado por este asunto, Freud consideró que Fliess y él se habían mostrado irresponsables con Emma, quien, sin embargo, nunca les reprochó sus errores. Pero, para exonerar a su amigo, señaló que ella ya sufría desde la infancia violentas hemorragias nasales. Emma retomó el tratamiento con él. Al escucharla hablar de su temor a entrar en las tiendas, Freud dedujo que esa fobia se remontaba a una escena de seducción que se habría producido cuando ella tenía ocho años: un tendero habría intentado un toqueteo. La escena habría sido reprimida, pero era al parecer el origen del síntoma del que la joven se quejaba.
A continuación, tras haber propuesto la hipótesis de que la confesión hecha por las histéricas de las seducciones sufridas en la infancia se asemejaba a la del comercio sexual obtenida antaño bajo la tortura por los inquisidores, Freud se maravilló al ver que Emma confirmaba su tesis al contar una escena en que el diablo le clavaba agujas en los dedos y pasaba luego un caramelo por cada gota de sangre. Y de nuevo exoneraba a Fliess, quien por otra parte seguía negándose a reconocer su error.
Emma Eckstein fue la primera mujer psicoanalista de la historia del freudismo. Entre 1905 y 1910 escribió varios artículos e intercambió algunas cartas con Freud, que siguió ignorando las múltiples causas de las que dependían sus trastornos psíquicos y somáticos. Tras una desdichada aventura amorosa ella intentó suicidarse. Pero ni su sobrino, Albert Hirst, que dio a Kurt Eissler un testimonio conmovedor, ni médico alguno lograron curarla y ni siquiera comprenderla.
Consciente de la persistencia del misterio, pero no dispuesto a admitir que podía haberse extraviado mil veces, Freud pronosticó que Emma no se repondría jamás. ¡Increíble profecía! Paralizada por un mal inexplicable, ella pasó sus últimos años de vida tendida en una cama rodeada de sus libros.
En vista de este episodio podemos preguntarnos quién inventaba los presuntos abusos y otras maniobras perversas que, según se decía, se ocultaban en el seno de familias honorables. ¿El propio Freud o las pacientes que le hacían creer en la existencia de una empresa de seducción sistemática de los niños llevada adelante por los adultos? Al respecto, Breuer, que por entonces preparaba con su protegido un estudio sobre la histeria, se mostró siempre muy reservado en cuanto a la etiología traumática.
Durante años, pues, Freud se dejó hechizar por Fliess, y este lo encerró en una concepción de la ciencia en la que no había lugar ni para el error, ni para la experiencia, ni para la búsqueda de la verdad, dado que era la certeza, y solo ella, la que gobernaba el trabajo especulativo. Al paso de las cartas advertimos, sin embargo, que Freud evolucionaba en sentido contrario a Fliess. Si bien se negaba conscientemente a poner en duda las hipótesis de su amigo, se alejaba poco a poco de ellas a fuerza de renegación, ambivalencia y contorsiones, como si el trabajo que se operaba en él sin que lo supiera lo impulsara a dudar de lo que juzgaba como un verdadero proceder científico.
De hecho, el contacto con Fliess lo llevó a separarse de la neurología, a enemistarse definitivamente con Breuer, a inventar el tratamiento psicoanalítico, a renunciar a la teoría de la seducción, a invocar la tragedia griega en auxilio de su explicación del inconsciente y a preparar el gran libro que iba a hacer de él uno de los pensadores más importantes del siglo XX: _La interpretación de los sueños_. Como Emma Eckstein, Fliess fue la principal víctima de ese combate librado por Freud contra sí mismo. En tanto que en vida se encumbró a Fliess por su aporte a la biología médica, la posteridad lo juzgó severamente como un maniático de los números y un taumaturgo delirante, último testigo de una medicina romántica que agonizaba. Su obra cayó a tal punto en el olvido que solo tuvo existencia por el papel que los historiadores le atribuyeron en la dilucidación de los orígenes del psicoanálisis. Y el propio Freud rechazó siempre que lo asociaran a la tradición del romanticismo.
En los albores del siglo XX, después de tantos años de intercambiar locuras y de estar unidos por matrimonios cruzados entre amigos cercanos en el seno de una familia intelectual ampliada, y con el telón de fondo del doble auge de la modernidad vienesa y la modernidad berlinesa, los dos amigos se separaron para no volverse a ver nunca más. Freud fue el suntuoso beneficiario de esa amistad de unos quince años, cuyo saldo fue para Fliess un desastre y para el psicoanálisis un triunfo.
La ruptura fue de gran violencia. En julio de 1900 los dos hombres se reunieron a orillas del lago de Achen. Fliess acusó a Freud de dar muestras de animosidad contra él y Freud le reprochó no reconocer el valor de sus descubrimientos.
Muy poco tiempo después Freud expuso su teoría de la bisexualidad al jurista austríaco Hermann Swoboda, que se analizaba con él. Esa misma noche Swoboda habló del tema con su amigo Otto Weininger, célebre escritor judío vienés, quien, un año después, publicó su único libro, _Sexo y carácter_ , verdadero manifiesto de la bisexualidad y del odio a las mujeres y los judíos. Algún tiempo más tarde, Weininger puso en escena su suicidio: alquiló una habitación en la antigua casa de Beethoven y se disparó una bala en el corazón.
Fliess conoció la obra en 1904 y, al igual que Swoboda y Paul Julius Moebius, se sintió plagiado y acusó a Freud de haberle robado sus ideas durante los años de su amistad. Este asunto del «robo de ideas» fue la comidilla de la prensa y Freud reconoció su deuda con Fliess. Pero también sabía que, a diferencia del plagio, el «robo de ideas» no existe, y que la teoría de la bisexualidad impregnaba en esa época todos los trabajos de los científicos. Originada en el darwinismo y la embriología, reactualizaba en parte los mitos fundacionales de la antigua Grecia. Freud, es cierto, se sentía culpable de haber hablado con Swoboda, pero en ningún momento se adhirió a esa fantasía del «robo de ideas». En cuanto a la bisexualidad, ulteriormente hizo de ella un concepto central de la doctrina psicoanalítica que no tenía mucho que ver con la representación fliessiana de una bilateralidad.
Con todo, el episodio de esa amistad que, a través de una larga deriva, había hecho de él otro hombre, siguió asediando durante mucho tiempo a Freud. Sin atreverse a contarlo verdaderamente, este destruyó las cartas de Fliess y, cuando Marie Bonaparte compró las suyas a un comerciante, en 1936, se opuso con firmeza a su publicación.
A continuación, sobre la base de su propia concepción de la paranoia, Freud explicó a Sándor Ferenczi, en 1910, que la idea de ligar el conocimiento paranoico a una investidura homosexual y el conocimiento teórico a un rechazo de esta última se le había ocurrido a causa de una reactivación dolorosa de la ruptura con Fliess: «Desde el asunto de Fliess [...] una parte de la investidura homosexual se extinguió y me valí de ella para expandir mi propio yo. He triunfado donde el paranoico fracasa». Esta teoría era por lo menos discutible.
Sin embargo, Freud había creído sin asomo de duda que iba a poder deshacerse de esa parte de su historia. En agosto de 1897 pretendió que estaba haciendo un «autoanálisis». Una manera de poner en entredicho, sin decirlo, todo el sistema de pensamiento que había elaborado hasta entonces. Pero también este asunto se saldó con un fiasco. En un principio Freud había explicado a Fliess que su principal paciente era él mismo. Luego había analizado sus propios sueños para afirmar a continuación que no entendía nada de lo que le pasaba. Tras creer por un tiempo que el «autoanálisis» se había puesto efectivamente en marcha, terminó por admitir que era imposible:
Mi autoanálisis sigue interrumpido. He echado de ver por qué. Solo puedo analizarme a mí mismo con los conocimientos adquiridos objetivamente (como a un extraño), un autoanálisis genuino es imposible, de lo contrario no habría enfermedad. Como todavía tengo algunos enigmas en mis casos, esto no puede menos que estorbar en el autoanálisis.
Inventado para salir de un estancamiento, el concepto inhallable de autoanálisis tuvo una carrera afortunada en la comunidad freudiana, que acogió la idea de que solo Freud, como «padre fundador» de la disciplina, había llevado realmente a cabo una investigación de sí mismo que podría servir de modelo iniciático a toda la genealogía de las filiaciones venideras. Él se había «autoengendrado», se decía, y, en consecuencia, había que recusar toda historia contextual de los orígenes del psicoanálisis en beneficio de una mitología del «gran hombre».
Esa fue la posición de Jones en 1953. Desde ese punto de vista, este hizo de Fliess un falso científico iluminado y de Freud un héroe de la ciencia capaz, desde las alturas de su «espléndido aislamiento», de inventar todo sin deber nada a su época. Y de resultas, Jones se entregó a una interpretación psicoanalítica de la historia que la comunidad psicoanalítica, para su gran infortunio, repetiría durante varios decenios: una verdadera leyenda en lugar de la historia, según la cual Fliess habría ocupado en relación con su amigo la posición del seductor paranoico y del sustituto paterno del que Freud, a la larga, se habría liberado gracias a la fuerza de su genio.
Sabemos bien que leyendas semejantes no se sostienen frente a los estudios históricos. Aun cuando toda nueva disciplina deba sus enunciados a un «padre fundador», este instaura una discursividad que no puede pertenecerle porque, si dicha disciplina es racional, genera una posibilidad infinita de discursos susceptibles, a su vez, de reinterpretación.
Otra interpretación de ese episodio, mucho más interesante, fue la que propuso Freud al comienzo de su ruptura con Fliess. En una carta fechada el 7 de mayo de 1900, un día después de cumplir cuarenta y cuatro años, aquel reafirmó que, para pensar, necesitaba el contacto con un amigo capaz de revelarle lo que había de «femenino» en él. Y, tras destacar que ningún científico podía saber de antemano cuál sería el juicio de la posteridad, agregó:
Ningún crítico [...] puede ver con más acuidad que yo qué «desproporción» se abre entre problemas y soluciones, y como justo castigo me será dado el de que ninguna de las provincias todavía no descubiertas en la vida anímica, que yo soy entre los mortales el primero en hollar, lleve alguna vez mi nombre u obedezca a mis leyes. Cuando a mí en la contienda amenazaba acabárseme el aliento, rogué al ángel que soltara, y es lo que desde entonces él ha hecho. Pero yo no he sido el más fuerte, aunque desde entonces visiblemente cojeo. Sí, efectivamente ya tengo cuarenta y cuatro años, un viejo, tosco israelita.
Freud hace alusión aquí al célebre pasaje del Génesis que relata el combate nocturno de Jacob con el ángel. Solo en la noche, el hijo de Isaac y nieto de Abraham lucha hasta el alba con un misterioso adversario cuyo sexo ignora, y que es a la vez Dios y el enviado de Dios (Elohim y el ángel). Al comprender que no vencerá al hombre, el ángel lo hiere en la articulación del fémur y lo deja cojo. Y cuando quiere huir, Jacob le pide que lo bendiga. El ángel le anuncia entonces que en el futuro se lo llamará Israel. Vencedor del adversario pero herido de por vida, el tercer patriarca encarna la idea de que la más alta victoria del hombre es la que obtiene sobre sí mismo y sobre su arrogancia.
Y sin duda era mediante esa temática heredada del texto sagrado como Freud llevaba a cabo su ruptura con Fliess y se inventaba un destino: el de un hombre herido que se apresta al combate perpetuo contra los hombres y contra sí mismo. Tal era pues, en 1900, su estado de ánimo en el momento en que, como el tercer patriarca, creía haber hecho un descubrimiento cuyo devenir jamás controlaría, ya que se juzgaba demasiado viejo y «cojo» para ponerlo en práctica.
Esta aventura confirma, por si hubiera necesidad, que todo proceder científico está salpicado por el paso del error a la verdad. Jamás teoría alguna, aunque sea la más racional o más lógica, está inmune al irracionalismo al que pretende escapar. En otras palabras, Freud no se liberará nunca, en sus obras ulteriores, de los vestigios de una deriva —o de un perpetuo combate contra el ángel— cuyas huellas discernimos en su correspondencia con Fliess.
### 3
La invención del psicoanálisis
En 1895 la histeria de todas las mujeres observadas por tantos científicos conservaba su misterio. Y correspondió a los novelistas y a sus heroínas —de Flaubert a Tolstói, de Emma Bovary a Anna Karenina— el mérito de haber sabido darles un rostro humano: el de una rebelión impotente que conducía al suicidio o la locura. Por mucho que tanto en París como en Viena se afirmara la existencia de una histeria masculina, la «enfermedad» parecía afectar sobre todo a las mujeres.
El paradigma de «LA mujer histérica», progresivamente abandonado en el transcurso del siglo XX, siguió ligado a un estado de la sociedad en el cual, para expresar su aspiración a la libertad, las mujeres no tenían otro medio que la exhibición de un cuerpo sufriente. Si a fines del siglo XIX las mujeres locas o medio locas procedentes de los arrabales parisinos habían servido de motivo para la elaboración de una clínica de la mirada —la de Charcot—, las mujeres vienesas, recibidas en el secreto de un gabinete privado, fueron las actrices protagónicas de la construcción de una clínica de la escucha: una clínica de la interioridad y ya no de la exterioridad. Al contrario de las mujeres del pueblo, esas burguesas tuvieron derecho a una vida privada, un sentido íntimo. Su desamparo existencial permitió a los hombres de ciencia elaborar una nueva teoría de la subjetividad. Gracias a su presencia muda, y a través de los relatos clínicos que disfrazaban su vida real, esas mujeres estuvieron en el origen de la invención del psicoanálisis: origen indecible que el historiador tiene el deber de reconstruir.
No sorprenderá, por tanto, que los _Estudios sobre la histeria_ publicados en 1895 por Freud y Breuer hayan suscitado una impresión tan grande en los escritores debido a que la palabra se otorgaba tanto a las pacientes como a los médicos, aun cuando estos fueran los únicos autorizados a reconstruir la historia de aquellas. Al recorrer esos relatos de casos el lector de la época asistía a un abandono de la clínica de la mirada en provecho de una clínica de la relación transferencial: un renacimiento de la cura dinámica, procedente de los antiguos magnetizadores.
Pero la verdadera novedad radicaba en el hecho de que los dos autores optaban por el camino contrario a las descripciones frías y aderezadas de términos técnicos que tanto deleitaban a los médicos del alma, sus contemporáneos. Deseosos de cautivar la imaginación, aquellos privilegiaban, con talento, el relato novelesco en detrimento de la exposición del caso, y tenían la inquietud de penetrar de manera literaria en la geografía íntima de las ignominias familiares de su época para tornar vivos e insólitos los dramas cotidianos de una locura privada disimulada bajo las apariencias de la más grande de las normalidades: «[Ella] relata», escribe Freud, «que su propia madre pasó algún tiempo en el manicomio. Cierta vez tuvieron una criada cuya patrona anterior había estado en el manicomio un lapso prolongado, y solía contarle terroríficas historias». Y también:
Por ejemplo, hoy da en hablar sobre su familia, y a través de toda clase de rodeos llega hasta un primo; era un poco retrasado y los padres de él le hicieron sacar todos los dientes de una asentada. [...] Explica [...] cómo su hermano estaba muy enfermo por ingerir dosis excesivas de morfina, y tenía unos crudelísimos ataques, en que solía echarle mano de manera repentina [...]. Ha soñado cosas terroríficas, las patas y respaldos de las sillas eran, todos, serpientes; un monstruo con pico de buitre arremetió a picotazos contra ella y la devoraba por todo el cuerpo.
Es indudable que las mujeres cuyas angustias desplegaban Freud y Breuer jamás habrían imaginado que su historia —real o inventada— pudiese ser así expuesta al público, ya que su «enfermedad» parecía aún muy sospechosa a los representantes de la ciencia médica: parálisis, contracturas, tics, alucinaciones, gesticulaciones, terrores inscritos en el rostro, angustias, pavor y sobre todo obsesiones sexuales acompañadas de relatos de traumas y abusos vividos en la infancia.
Siempre preocupado por dar cuerpo a lo que descubría, Freud había empujado a Breuer, muy vacilante, a pasar a los hechos, sobre todo en lo concerniente a la asombrosa historia de Bertha Pappenheim, una joven vienesa de la buena burguesía judía, cuyo tratamiento se había desarrollado entre 1880 y 1882. Pero Breuer se resistía, muy poco satisfecho con los resultados obtenidos en esa paciente que, tras un maratón terapéutico a lo largo del cual había desplegado una serie impresionante de síntomas —alucinaciones, parálisis, ataques de tos, etc.—, había sido internada en el sanatorio Bellevue de Kreuzlingen, magnífica clínica dirigida por Robert Binswanger y situada a orillas del lago de Constanza. En ese lugar idílico ella había coincidido con la élite de enfermos mentales adinerados procedentes de los cuatro puntos cardinales de la vieja Europa. Morfinómana y siempre presa de las mismas angustias, a continuación había pasado por muchos otros establecimientos asistenciales antes de volver al seno de la familia.
En 1895 Breuer ya no utilizaba el método catártico y no quería interpretar como fenómenos transferenciales el hecho de que las pacientes pudiesen querer seducir a sus terapeutas. Freud creía, al contrario, que el tratamiento de Bertha aportaba no solo la prueba de la etiología sexual sino que, como era muy anterior a las experiencias llevadas a cabo por Pierre Janet con pacientes que presentaban los mismos síntomas, permitía demostrar que ese rival francés no era, como él creía, el inventor de este tipo de cura. Freud tuvo la última palabra y su fervor se impuso. Aunque estuviera perfectamente al tanto de la historia de Bertha, que había sido además amiga de Martha Bernays, no podía prescindir de la colaboración de Breuer, más conocido que él e iniciador del método.
En su presentación de la obra, los dos autores destacaban que su elección no había sido dictada por consideraciones de orden científico: «Nuestras experiencias», decían,
provinieron de la práctica particular en una clase de la sociedad que es culta y lectora, y su contenido muchas veces toca la vida y las peripecias más íntimas de nuestros enfermos. Sería un grave abuso de confianza publicar esas comunicaciones, a riesgo de que los enfermos fueran reconocidos y por su círculo de relaciones se difundieran unos hechos que solo al médico confiaron. Por eso hemos debido renunciar a las observaciones más instructivas y probatorias.
Había que privilegiar, en consecuencia, ciertos tramos de la vida y evitar al mismo tiempo sacar a la luz del día verdades capaces de perturbar un orden social común a los médicos y las pacientes. Las mujeres tratadas por Breuer y Freud formaban parte de una familia extensa: eran muchas veces amigas, hermanas o primas de sus esposas, y a los ojos de estas podían convertirse en rivales. Además, si presentaban síntomas semejantes, quería decir que esas mismas esposas podían ser portadoras, sin saberlo, de la gran plaga de la histeria. También era menester presentar todas esas curas como otros tantos éxitos terapéuticos y no como «experiencias» cuya validez pudiera impugnarse de inmediato. Si no, ¿de qué servía publicarlas?
Tal era pues el estado de ánimo de Freud y Breuer en vísperas de la aparición de su obra. Breuer dudaba de todo, privilegiaba la causalidad fisiológica y se negaba a encerrarse en la mera etiología sexual, temeroso, además, de los ataques virulentos de su colega Adolf Strümpell, que afirmaba, como Richard von Krafft-Ebing y muchos otros, que los enfermos, a través de sus síntomas, inducían a los médicos al error. Por su lado, Freud sostenía que la disociación mental constatada en el síntoma histérico era provocada por una defensa psíquica y reminiscencias ligadas a un trauma sexual de origen infantil. Confiado en su destino y convencido de la idoneidad de su teoría de la seducción, estaba muy decidido, contra el nihilismo, a probar el valor curativo de la psicoterapia:
Repetidas veces he tenido que escuchar de mis enfermos, tras prometerles yo curación o alivio mediante una cura catártica, esta objeción: «Usted mismo lo dice; es probable que mi sufrimiento se entrame con las condiciones y peripecias de mi vida; usted nada puede cambiar en ellas, y entonces, ¿de qué modo pretende socorrerme?». A ello he podido responder: «No dudo de que al destino le resultaría por fuerza más fácil que a mí librarlo de su padecer. Pero usted se convencerá de que es grande la ganancia si conseguimos mudar su miseria histérica en infortunio ordinario. Con una vida anímica restablecida usted podrá defenderse mejor de este último».
Los dos autores estaban en desacuerdo. Pero coincidían en la cuestión de las reminiscencias y la necesidad de afirmar que las ocho pacientes cuyos casos exponían se habían curado, si no de su enfermedad, sí al menos de sus síntomas: «señorita Anna O.», «señora Emmy von N.», «Miss Lucy», «Katharina», «señorita Elisabeth von R.», «señorita Mathilde H.», «señorita Rosalia H.», «señora Cäcilie M.». La verdadera identidad de cinco de estas mujeres fue revelada por los historiadores a partir de la década de 1960. Se llamaban Bertha Pappenheim, Fanny Moser, Aurelia Öhm, Anna von Lieben e Ilona Weiss. Ninguna de ellas se «curó», pero nada permite decir que la experiencia de la cura no transformó su existencia.
En este aspecto, los _Estudios sobre la histeria_ , considerados como el acta de nacimiento de la práctica psicoanalítica, no relataban más que curas hipnóticas y catárticas. A eso se agregaba un método de concentración (Ilona Weiss, «Miss Lucy») por presión en el cráneo o en un muslo, que Freud utilizaba para persuadir a sus pacientes de que le contaran todo lo que les venía a la mente.
En lo que se refiere al «caso fundacional» —«Anna O.»—, no fue otra cosa que una experiencia de cura que fascinaba a Freud, pero que había conducido Breuer. En cuanto a Bertha Pappenheim, nunca aceptó ser Anna O. Y las pacientes cuyos casos se daban a conocer a lo largo de los _Estudios sobre la histeria_ jamás se reconocieron en los retratos hechos de ellas por Freud sobre la base de sus notas. Así, Ilona Weiss, interrogada un día por su hija, respondió que se acordaba de que el famoso «médico barbudo de Viena», a quien la habían enviado, había intentado, contra su voluntad, convencerla de que estaba enamorada de su cuñado. Sin embargo, en esta historia no se puede sospechar mentira ni malversación en ninguno de los protagonistas. Expuestos por los científicos, los relatos de casos no tienen mucho que ver, en general, con la realidad vivida de los pacientes.
Digamos simplemente que en esa distancia se aprecia la oposición dialéctica entre dos regímenes de subjetividad —la del médico por un lado, la del enfermo por otro— y esos regímenes manifiestan una partición inherente a las relaciones entre la locura expresada y el discurso de la psicopatología. Partición entre una conciencia de sí y una conciencia crítica: por una parte la existencia anónima de un paciente sumido en el desamparo, por otra la racionalidad de una mirada clínica que se aleja de ella para aprehenderla mejor.
En este aspecto, se verifica que los estudios de casos siempre se construyen como ficciones, relatos o viñetas literarias destinadas a convalidar las hipótesis de los científicos. De ahí las necesarias revisiones que en general ponen de relieve hasta qué punto el enfermo rechaza la validez de un discurso reconstruido del que se siente víctima.
Esa fue la actitud de Bertha Pappenheim. Tras su cura con Breuer y su periplo terapéutico, rechazó todo lo que se relacionara con su tratamiento y exigió a su familia que no proporcionase jamás ninguna información sobre ese episodio de su vida. En varias oportunidades manifestó una gran hostilidad hacia el psicoanálisis y se negó a hacer comentario alguno sobre el destino legendario de Anna O., muy en especial después de la publicación de los _Estudios sobre la histeria_. ¿La curaron de algo? Sí, sin ninguna duda. ¿Su vida hubiera sido la misma de no haberse cruzado con Breuer? Nadie lo sabe.
En virtud de una suerte de sublimación, Bertha logró transformar sus síntomas patológicos en una actividad humanitaria, al extremo de convertirse, al cabo de algunos años, en una gran figura del feminismo judío alemán. En principio directora de un orfanato en Frankfurt, viajó luego a los Balcanes, Oriente Próximo y Rusia para realizar investigaciones sobre la trata de blancas. En 1904 fundó el Jüdischer Frauenbund, una organización destinada a promover la emancipación de las mujeres por el trabajo. Escribió un sinnúmero de artículos, cuentos y obras teatrales para niños antes de codearse con Martin Buber y Gershom Scholem. Hostil al sionismo, y tan piadosa y autoritaria como lo había sido su madre, se pronunció contra la emigración de los judíos de Alemania. Murió en 1936, tres años antes que Freud y después de escapar por poco a las persecuciones de los nazis.
Mientras Bertha proseguía con su existencia pública, Anna O., su aborrecido doble, conocía un destino muy distinto. Convencido de que Breuer se había espantado ante el carácter sexual de la transferencia amorosa de su paciente hacia él, Freud dio, entre 1915 y 1932 —sobre todo a Stefan Zweig—, varias versiones del final de esa cura, reconstruyendo a su manera la historia de la ruptura con su viejo amigo. Con el propósito de demostrar que el motivo de esa ruptura era una divergencia acerca de la etiología sexual de la neurosis histérica, afirmó que Anna, al parecer, había manifestado un día todos los signos de un embarazo nervioso. Temeroso por su reputación, Breuer habría desaparecido, en tanto que Mathilde, su mujer, habría estado tentada de suicidarse por celos.
Retomada por Jones, en 1953 la fábula de ese embarazo nervioso se transformó en una verdadera novela de los orígenes del psicoanálisis, en la que se enfrentaban el «miedoso» Breuer y el «valiente» Freud. Según esta versión, Breuer habría «huido» literalmente a Venecia con su esposa para vivir una nueva luna de miel, durante la cual, al parecer, concibieron a Dora, su hija. Y Jones elevaba la apuesta al contar que, diez años más adelante, Breuer habría llamado a Freud en consulta por un caso idéntico. Cuando Freud, dice Jones, le señaló que los síntomas de esa nueva enferma revelaban un embarazo psicológico, Breuer no pudo soportar la repetición de un hecho pasado: «Sin decir una sola palabra, tomó su bastón y su sombrero y se apresuró a marcharse de la casa».
Fuera como fuese, la ruptura entre Freud y Breuer era inevitable. No solo porque no tenían la misma concepción sobre el enfoque de las neurosis, sino porque Freud no toleraba que lo contradijera un hombre que había sido su benefactor. Deseoso de afirmarse en un momento en que se expandía su pasión por Fliess, e incapaz de dominar su orgullo, transformó una vez más al amigo íntimo en un enemigo.
En 1925, a la muerte de Breuer, lamentaría su actitud al enterarse de que su antiguo protector, a pesar de los años pasados desde la ruptura, no había dejado de interesarse en sus trabajos. A los setenta años y ya célebre, confesaría entonces al hijo de Breuer cuánto se había equivocado él mismo durante décadas: «Lo que usted dijo sobre la relación de su padre con mis trabajos más tardíos era una novedad para mí y actuó como un bálsamo sobre una herida dolorosa que nunca se había cerrado».
Fue pues en medio de un clima conflictivo que Freud atribuyó a Breuer, en marzo de 1896, la invención de un nuevo método de exploración del inconsciente: el _psicoanálisis_. Pero, en realidad, él mismo lo practicaba desde hacía ya seis años, al tender al paciente en una cama muy corta adornada con un tapiz oriental y cojines, que le había regalado una tal señora Benvenisti. Con el paso del tiempo, Freud había tomado la costumbre de sentarse detrás del diván para captar mejor el flujo de las palabras del paciente. Verdadero manifiesto contra los herederos franceses de Charcot, el texto donde aparecía por primera vez el término «psicoanálisis» contenía la primera gran clasificación freudiana de las neurosis.
El autor afirmaba en ese texto que la sacrosanta herencia —tan apreciada por los psiquiatras, los psicólogos y los partidarios del nihilismo terapéutico— no podía en ningún caso explicar el origen de las neurosis. A su entender, la verdadera causa estaba en un trauma real sobrevenido en la infancia. Con esa concepción de los trastornos psíquicos, Freud efectuaba una especie de revolución terapéutica. Sostenía, en efecto, que gracias al nuevo método de cura por la palabra inventado por Breuer y retomado por él, los trastornos psíquicos podían escucharse, tratarse y a veces curarse. Para ello bastaba con que el propio paciente, con la ayuda del terapeuta y conforme a la antigua técnica de la confesión, sacara a la luz el origen del mal. De ese modo, Freud, sin haberlo imaginado, se conectaba no solo con la herencia de Mesmer sino, en especial, y de manera mucho más remota, con el gran principio de la confesión heredado de la Contrarreforma y sobre todo del concilio de Trento, que había hecho de ella un sacramento, un ejercicio íntimo sin contacto visual o físico entre el confesor y el penitente. Quisiéralo o no, Freud también era, en mayor o menor medida, el heredero de ciertas tradiciones del catolicismo, religión en la que su querida niñera lo había iniciado, al mismo tiempo que era su «profesora de sexualidad».
Y para responder a las acusaciones de quienes sostenían que las confesiones de las histéricas no eran de fiar o que los propios médicos las inducían, Freud se erigía en vigoroso defensor de los pacientes sumidos en el sufrimiento, a la vez que se entregaba a un feroz despedazamiento del orden familiar de fin de siglo. Justificaba pues, a posteriori, la validez de los casos expuestos en los _Estudios sobre la histeria_.
Las más de las veces, decía, las niñas son víctimas de los abusos cometidos por sus hermanos mayores, que han sido iniciados en la sexualidad por una niñera o una criada. Pero, peor aún, Freud afirmaba la existencia, en el seno de todas las familias, de un «atentado precoz» siempre cometido por un adulto contra un niño que, en general, tenía entre dos y cinco años.
De ahí se desprendía su clasificación de las neurosis fundada en la diferencia de los sexos: la neurosis obsesiva por un lado, la neurosis histérica por otro. A su juicio, la primera era en el varón el resultado de una participación activa en la agresión sufrida, mientras que la segunda conducía a la niña a la aceptación pasiva del abuso:
La importancia del elemento activo de la vida sexual como causa de las obsesiones, y de la pasividad sexual para la patogénesis de la histeria, parece incluso revelar la razón del nexo más íntimo de la histeria con el sexo femenino y de la preferencia de los hombres por la neurosis de obsesiones. A veces uno encuentra parejas de enfermos neuróticos que han sido una pareja de pequeños amantes en su niñez temprana y de ellos el hombre sufre de obsesiones, y de histeria la mujer; si se trata de un hermano y su hermana, se podrá tomar equivocadamente por un efecto de la herencia nerviosa lo que en verdad deriva de experiencias sexuales precoces.
El 2 de mayo de 1896 Freud, siempre tan temerario, volvió a exponer su teoría de la seducción en la Sociedad de Psiquiatría y Neurología de Viena. La recepción fue glacial, sobre todo por parte de Krafft-Ebing, especialista en sexología y perversiones, que calificó su comunicación de «cuento de hadas científico», destacando una vez más que las «confesiones» de las histéricas podían haberse obtenido perfectamente bajo el efecto de una sugestión inducida por el médico. Freud se sintió otra vez perseguido por los mandarines del cuerpo médico. Sin embargo, quince meses después iba a tener que admitir que su teoría no se sostenía.
Entretanto, seguía con sus vagabundeos. Cuando murió Jacob, el 23 de octubre de 1896, sintió un sufrimiento real al recordar a ese padre claudicante que había tenido un papel tan importante en su vida, con ese modo de asociar la más profunda sabiduría a una manera de ser llena de fantasía: «Ya había gozado harto de la vida cuando murió, pero en lo interior, con esta ocasión, sin duda ha despertado todo lo más temprano».
Tres meses después Freud se convenció de que el desdichado Jacob se había comportado como todos los demás adultos, abusadores de niños: «Por desgracia, mi propio padre ha sido uno de los perversos y se ha hecho culpable de la histeria de mi hermano (cuyos malestares son, todos ellos, identificación) y de una hermana menor. La frecuencia de esta circunstancia me hace dudar a menudo». Sin embargo, dado que se sentía muy poco inclinado a considerarse él mismo como un padre que experimentara deseos culpables por su descendencia, comenzó a recelar de su teoría.
Adepto a la abstinencia, Freud se entregaba, como es sabido, a toda clase de pasiones sustitutivas, a las cuales se sumó la fiebre del viaje. A partir de 1895, embargado por un profundo deseo de explorar los grandes lugares de la cultura grecolatina y del arte del Renacimiento, había decido afrontar su temor a los accidentes ferroviarios y su obsesión con los pasos de fronteras para trasladarse todos los años a Italia. En septiembre de aquel año había descubierto las maravillas de Venecia. Un año después emprendió, en compañía de su hermano Alexander y de Felix Gattel, un prolongado periplo por Toscana, y el año siguiente volvió a Venecia para luego dirigirse a Siena, Orvieto, Perugia, Arezzo y Florencia. Más adelante, acompañado por Minna y luego por Alexander, Sándor Ferenczi o su hija Anna, no dejaría jamás de _tender_ hacia el sur: en primer lugar Roma y después Pompeya, Nápoles, Ravello, Sorrento, Capri, Palermo, Siracusa y Atenas. Fascinado por la egiptología, admirador de Champollion, muchas veces soñó, sin hacerlo jamás, con trasladarse a orillas del Nilo para conocer la antigua tierra de los faraones.
Lo cierto es que en septiembre de 1897, embriagado por su búsqueda de un mundo subterráneo semejante al descrito en un poema de Heinrich Heine, envió a Fliess una carta en la cual afirmaba buscar en Italia un «ponche de Leteo», una ebriedad del olvido, una nueva droga, fuente de creatividad: «Aquí y allí tomo un sorbo. Uno se regodea en una belleza extraña y en un esfuerzo de creación gigantesco, en ello tiene parte sin duda mi inclinación a lo disforme, a lo perverso-psíquico».
Esa primera inmersión en la embriaguez del viaje italiano fue el último acto de una prolongada reflexión que, a su retorno a Viena, lo llevó a renunciar a su teoría de la seducción: «No creo más en mi _neurótica_. [...] Es que podría sentirme muy insatisfecho. La expectativa de la fama eterna era demasiado bella, y la de la segura riqueza, la plena independencia, el viajar, el preservar a los hijos de los serios cuidados que me consumieron en mi juventud». ¡Demasiado tarde, no obstante, para hacer justicia a Jacob, injustamente señalado como sospechoso!
Al no haber aceptado nunca las críticas de sus contemporáneos, que veían en su teoría de la seducción una manera de convalidar una falsificación inducida por una sugestión, Freud tropezaba con una realidad compleja. Era impensable, por cierto, que todos los padres fuesen violadores. Pero, pese a ello, no podía considerarse a todas las histéricas simuladoras o mitómanas cuando afirmaban haber sido víctimas de abusos sexuales. Había que proponer además una hipótesis capaz de rendir cuenta de dos verdades contradictorias: ora que las histéricas inventaban escenas de seducción que no se habían producido, ora que dichas escenas, cuando habían existido, no explicaban por sí solas la eclosión de una neurosis.
Al abandonar su _neurótica_ , Freud se alejaba tanto de la neurología y la fisiología como de la sexología, disciplina ligada a la psiquiatría y la biología y cuyo objeto era estudiar el comportamiento sexual humano a fin de determinar normas y patologías.
Atentos al higienismo, la nosografía y la descripción de las «aberraciones», los grandes sexólogos de fines del siglo XIX —KrafftEbing, Albert Moll o Havelock Ellis— se preocupaban menos por la terapéutica que por las investigaciones eruditas sobre las diferentes formas de prácticas e identidades sexuales: homosexualidad, bisexualidad, travestismo, transexualismo, pedofilia, zoofilia, etc. En una palabra, se interesaban ante todo en la cuestión de las perversiones sexuales y su origen infantil. Si el paradigma de la mujer histérica había invadido todo el campo de estudio de las neurosis, las dos grandes figuras del «sexo no procreador» —el homosexual y el niño masturbador— eran el coto cerrado de los sexólogos, higienistas y pediatras. Y estos dejaban a los psiquiatras, herederos de los alienistas, la tarea de ocuparse de la locura, es decir, de las psicosis.
Al renunciar a la idea de que el orden familiar burgués pudiese fundarse en la alianza entre un progenitor perverso y un hijo víctima de abusos, Freud desplazaba la cuestión de la causalidad sexual de las neurosis a un terreno que ya no era el de la sexología, y tampoco el de la psiquiatría o la psicología. Dejaba el dominio de la descripción de los comportamientos para ir hacia el de la interpretación de los discursos, sobre la base de la consideración de que las famosas escenas sexuales descritas por los pacientes podían suponer una fantasía, es decir, una subjetividad o una representación imaginaria. Y agregaba que aun cuando una seducción hubiera tenido realmente lugar, no era por fuerza la fuente de una neurosis. Además aceptaba a la vez la existencia de la fantasía y la del trauma. Y destacaba que, gracias al método psicoanalítico —exploración del inconsciente y cura por la palabra—, el terapeuta debía ser en lo sucesivo capaz de discernir varios órdenes de realidad a menudo entrelazados: el abuso sexual real, la seducción psíquica, la fantasía, la transferencia.
Pero era menester además preguntarse cuál era el lugar del niño real en esas historias de seducciones confesadas o fantaseadas.
Hacía ya años que el cuerpo del niño se había convertido en un objeto de predilección para higienistas y médicos. Y centenares de libros se referían a los perjuicios de la masturbación infantil en la génesis de las neurosis y las perversiones. Freud se había interesado en esta cuestión en 1886, durante el período pasado en el servicio de pediatría de Adolf Baginsky, en Berlín. Y en cuanto él mismo había sido un niño criado en una familia extensa para ser luego un padre atento a sus numerosos hijos, no había dejado de pretender ser el observador advertido de las relaciones carnales reales o fantaseadas que sembraban la perturbación en el corazón de las relaciones de parentesco.
Todo el debate de esa segunda mitad del siglo XIX se refería a la cuestión de si un niño podía nacer, si no loco, sí al menos perverso, y si esa «locura» particular se manifestaba o no mediante una práctica sexual específica —la masturbación— cuyos perjuicios se hubieran desconocido hasta entonces. Como ahora se admitía que el niño era un sujeto sexuado —y no solo un objeto inerte disfrazado de adulto—, había que definir para él un marco jurídico, social y psíquico. Tras haber adquirido el derecho de existir, el niño debía ser protegido contra sí mismo y contra las tentativas de seducción que ponían en peligro su integridad.
En consecuencia, y siempre en la óptica del niño que debía llegar a ser un adulto «normal» bien integrado en el orden familiar, también había que convencerlo, en su fuero íntimo, de que el aprendizaje de la vida pasaba por un temible adiestramiento corporal y psíquico con objeto de hacer de él una persona mejor. Esos fueron los principios de una educación perversa, llevada a la práctica sobre todo en Alemania y consistente en hacer admitir a los niños que los maltratos corporales infligidos por los adultos los hacían mejores, les permitían combatir sus vicios a fin de acceder a un «soberano bien» y, más aún, desear acceder a él.
Entre los teóricos de esta «pedagogía negra», Gottlieb Moritz Schreber adquirió celebridad al redactar manuales por medio de los cuales pretendía remediar la decadencia de las sociedades a través de la creación de un hombre nuevo: una mente pura en un cuerpo sano. Sostenidas en un principio por los socialdemócratas, estas tesis serían retomadas a continuación por el nacionalsocialismo. Daniel Paul Schreber, jurista loco, sería una víctima de esta educación insensata, cuyas huellas encontramos en sus _Memorias_ , comentadas luego por Freud.
Si la pediatría tenía sus raíces en la filosofía de la Ilustración, la anexión del dominio de la infancia al discurso psiquiátrico se produjo a fines del siglo XIX, cuando se inició la gran ola de medicalización del conjunto de los comportamientos humanos a través de la sexología, la criminología y la psicología. Así, el saber psiquiátrico batió en retirada la noción de inocencia infantil, en beneficio de varias tesis contradictorias. En la perspectiva del darwinismo, se creía que el niño, nacido sin humanidad, portaba en sí, en su cuerpo y por lo tanto en sus órganos genitales, los vestigios de una animalidad todavía no superada. Pero también se estimaba que, si era perverso, esa manera de actuar emanaba de su alma y por lo tanto de un vicio propio de la humanidad misma.
Fue entonces cuando la masturbación comenzó a ser vista como la causa principal de ciertos delirios que se manifestaban no solo en los niños sino también, de manera más tardía, en todos los llamados sujetos «histéricos». Se catalogaba a unos y otros como «enfermos del sexo»: a los primeros, porque se entregaban sin límites a la práctica del sexo solitario, y a los segundos, porque habían vivido —o afirmaban haber vivido—, en su infancia, traumas de orden sexual idénticos a los inducidos por el onanismo (abuso, seducción, violación, etc.).
La idea de la peligrosidad de la masturbación había sido magistralmente enunciada por Jean-Jacques Rousseau, no solo en un pasaje célebre del _Emilio_ , de 1762 —«si llega a conocer ese peligroso suplemento»—, sino también en _Las confesiones_ , publicadas a título póstumo en 1780:
Yo había sentido el progreso de los años; mi temperamento inquieto por fin se había declarado y su primera erupción, muy involuntaria, me había suscitado alarmas sobre mi salud que pintan mejor que cualquier otra cosa la inocencia en que había vivido hasta entonces. Pronto tranquilizado, aprendí ese peligroso suplemento que engaña a la naturaleza y salva a los jóvenes de mi talante de muchos desórdenes a expensas de su salud, de su vigor y, a veces, de su vida.
Un siglo después, lejos de vérsela como un «peligroso suplemento», la masturbación llegó a considerarse, junto con la homosexualidad, como la más grande de las perversiones, una exposición peligrosa a la locura y la muerte; en síntesis, como una pérdida de sustancia que apuntaba a «suplir» a la naturaleza, a actuar en su lugar, a imponer un cultivo del sexo en ruptura con el orden natural del mundo viviente. En consecuencia, solo al hombre se juzgaba responsable de la seducción que efectuaba sobre sí mismo a causa de su manía autoerótica. Confiados en los progresos de un arte quirúrgico en plena expansión, los médicos de la infancia preconizaban un remedio preventivo para esa patología: ablación o cauterización del clítoris en las niñas, circuncisión en los varones. Se inventó también todo tipo de «terapéuticas» para acabar con la peste onanista: corsés antimasturbatorios, fundas para la erección, aparatos para separar las piernas de las chiquillas, conminaciones y amenazas de castración, esposas en las manos y, para terminar, procesos contra las nodrizas acusadas de «sevicias».
Pero, para aplicar tales «tratamientos» y proferir tales amenazas, hacía falta además probar la existencia de la excitación sexual. Se lanzó entonces, dentro de las familias, una búsqueda sistemática para detectar las huellas de la infame práctica. Se observaba con lupa cada inflamación de las partes genitales, cada hinchazón, cada edema, cada aparición de un herpes o un enrojecimiento. Pero la masturbación se conceptualizó no solo como el fruto de una práctica solitaria sino también como un placer «anónimo» que suponía a veces la presencia de una alteridad: roce, mano desconocida, vestimenta, sensación táctil u olfativa. Mucho después del triunfo de las tesis de Pasteur se creía aún en la fábula de que toda clase de enfermedades infecciosas o virales tenían por origen la práctica de la masturbación.
Pero ¿cuál era el origen de la pulsión masturbatoria?
En ese plano se enfrentaban dos hipótesis, y ambas establecían un nexo entre el autoerotismo y la seducción. Si la masturbación era un «peligroso suplemento», quería decir que la inducían la cultura y el entorno. Y si así sucedían las cosas, lo importante era entonces saber si el niño era el seductor de sí mismo, toda vez que se convertía en un ser social al pasar de la naturaleza a la cultura, o si la seducción era obra de un adulto corruptor que abusaba sexualmente de él. Todo el debate sobre la cuestión del trauma, por una parte, y las teorías sexuales infantiles, por otra, derivaba de esas dos hipótesis, que Freud terminó por abandonar, al mismo tiempo que renunciaba a cualquier concepción de la masturbación en términos de «peligroso suplemento».
Fue así como la gran _furia_ quirúrgica que se desató en Europa entre 1850 y 1890 se abatió tanto sobre el niño masturbador como sobre la mujer histérica. ¿No eran uno y otra —como por otra parte el invertido (el homosexual)— los actores más rutilantes de ese «peligroso suplemento»? En todo caso, tenían como punto en común, a juicio de la mirada médica, la preferencia por una sexualidad autoerótica en detrimento de una sexualidad procreadora.
Al abandonar su _neurótica_ y definir las condiciones originales de una terapéutica de la confesión, Freud exploraba una manera inédita de entender la sexualidad humana. Lejos de dedicarse a describir _ad nauseam_ violaciones, patologías sexuales, prácticas eróticas o comportamientos instintivos, y en vez de elaborar láminas anatómicas que se perdieran en mediciones, cálculos diversos o evaluaciones, e incluso de dictar normas o redactar el catálogo de todas las aberraciones sexuales, extendió la noción de sexualidad para hacer de ella una disposición psíquica universal y la erigió en la esencia misma de la actividad humana. Lo que adquirió un carácter primordial en su doctrina, por consiguiente, no fue tanto la sexualidad en sí misma como un conjunto conceptual que permitía representarla: la pulsión, fuente del funcionamiento psíquico inconsciente; la libido, término genérico que designaba la energía sexual; el apuntalamiento o proceso relacional; la bisexualidad, disposición propia de toda forma de sexualidad humana, y, para terminar, el deseo, tendencia, realización, búsqueda infinita, relación ambivalente con otro.
El científico positivista que era Freud, nutrido de fisiología y experimentación en el reino animal, se orientaba pues en 1897 hacia la construcción de una teoría del amor —o del eros—, como lo habían hecho antes que él los maestros de la filosofía occidental. Pero, como buen darwiniano, completamente imbuido de la leyenda de Fausto y su pacto con el diablo, afirmaba no solo que el principio cristiano de amar al prójimo como a uno mismo iba en contra de la naturaleza agresiva del ser humano, sino que la conquista de la libertad subjetiva pasaba por la aceptación de un determinismo inconsciente: «Yo es otro».
Ya sin deseos de ser filósofo, Freud tenía la convicción de que su doctrina debía ser ante todo una ciencia del psiquismo, capaz de subvertir el campo de la psicología, y cuyos fundamentos se inscribieran en la biología, las ciencias naturales. En realidad, ponía en práctica algo totalmente distinto: una revolución de lo íntimo originada en la Ilustración oscura y el romanticismo negro, una revolución a la vez racional y obsesionada por la conquista de los ríos subterráneos. Ulises en busca de una tierra prometida poblada de espectros, espejismos, tentaciones: tal era la promesa del viaje freudiano al corazón de un inconsciente definido como «otra escena», y que suponía una organización de las estructuras del parentesco capaz de explicar las modalidades de un nuevo orden familiar del que Freud aspiraba a ser el clínico, pero sin dejar de ser también su actor.
Marcado como toda su generación por los famosos «dramas de la fatalidad» que escenificaban terribles historias de reyes, príncipes y princesas contra un fondo de incestos y parricidios, Freud había querido ser el testigo privilegiado del mal de las familias que, en Viena, hacía estragos aun dentro de la propia dinastía imperial de los Habsburgo. En esos espectáculos, que lo horrorizaban, el «destino» intervenía bajo la forma de un _deus ex machina_ que permitía a un par de jóvenes aplastados por el poder paterno liberarse del peso de una genealogía engañosa.
Y fue al pensar en uno de ellos, y después de mencionar una vez más su infancia y su sentimiento amoroso por su madre judía y su niñera cristiana, que, en una carta a Fliess fechada el 15 de octubre de 1897, tuvo la idea genial de comparar el destino de las neurosis de fin de siglo con el de un héroe de la tragedia griega: «Cada uno de los oyentes fue una vez en germen y en la fantasía un Edipo así, y ante el cumplimiento de sueño traído aquí a la realidad retrocede espantado con toda la carga de la represión que separa su estado infantil de su estado actual».
Pero de inmediato Freud sumaba a su construcción teatral el personaje de Hamlet, príncipe melancólico que vacila en vengar a su padre y matar a su tío, ahora esposo de su madre. Y hacía de ese príncipe de Dinamarca un histérico feminizado a quien obsesiona el recuerdo de haber deseado a su madre: «¿[C]ómo explica su vacilación en vengar a su padre con la muerte de su tío [...]? No lo justificaría mejor que por la tortura que le depara el oscuro recuerdo de haber meditado la misma fechoría contra el padre por pasión hacia la madre».
Edipo, la figura más dolorosa concebida por Sófocles en su trilogía consagrada a la familia de los Labdácidas, pasó así a ser en la pluma de Freud el arquetipo del neurótico moderno, en lo que era una desvirtuación deliberada de la historia de ese tirano noble y generoso, afectado de desmesura y condenado por el oráculo a descubrirse otro y no lo que era. El Edipo de Sófocles era sin duda el asesino de su padre (Layo) y el esposo de su madre (Yocasta), pero no conocía la identidad de aquel así como no deseaba a esta, otorgada a él por la ciudad de Tebas después de que resolviera el enigma de la Esfinge, referido a las tres etapas de la evolución humana (infancia, madurez, vejez). Edipo, padre y hermano de los hijos que habría de tener de su madre, terminará su vida en el exilio, acompañado por Antígona, su hija maldita, obligada a no procrear jamás. Nada que ver con el Edipo reinventado por Freud, culpable de un doble deseo: matar al padre y poseer sexualmente el cuerpo de la madre.
A fines del siglo XIX, a raíz de las excavaciones que habían permitido localizar los emplazamientos de Troya y Micenas, el retorno a los trágicos griegos, las mitologías antiguas y la temática de la desmesura ( _hybris_ ) estaba a la orden del día. En el desarrollo de esas antiguas sagas que oponían a los dioses y los hombres, sin que estos últimos, sometidos al destino, fuesen nunca considerados culpables de sus actos, los pensadores de la modernidad creían ver desplegarse, como una catarsis colectiva, la historia presente de la agonía de un sistema patriarcal que ellos rechazaban, pero al cual estaban atados: el del poderío imperial europeo.
Las estructuras del parentesco propias de la familia de los Labdácidas, la privilegiada por Sófocles, fascinaban a los historiadores porque parecían confirmar, en la misma medida que obstaculizaban, la llegada del tan temido apocalipsis de una posible desaparición de la diferencia de los sexos. En la larga historia de los Labdácidas, las mujeres, los hombres y sus descendientes son condenados, en efecto, a no encontrar jamás su lugar como no sea bajo el signo de la locura, el asesinato y la mancha, hasta la extinción final de su _genos_.
Como contrapunto, en la historia de los Átridas cada crimen debe castigarse con otro crimen y cada generación, guiada por las Erinias, debe vengar y expiar los crímenes de la precedente. Así, Agamenón, rey de Micenas que ha sacrificado a su hija Ifigenia, es degollado por Clitemnestra, su esposa, con la complicidad de Egisto, su amante, hijo incestuoso de Tiestes. La madre venga a la hija, por lo cual Orestes está obligado a vengar a su padre y matar a su madre y a Egisto con la ayuda de su hermana Electra. Al final del ciclo, Apolo y Atenea acaban con la ley del crimen para instaurar el derecho y la justicia en la ciudad. Orestes, que se ha vuelto loco, es purificado; las Erinias, divinidades de la venganza, se convierten en las Euménides (las Benevolentes), y el orden de la civilización triunfa sobre el de la naturaleza, salvaje, incestuosa y destructiva.
Así como la historia de los Labdácidas pone en escena una autodestrucción implacable y ahistórica de la subjetividad de cada uno de los actores de cada generación, la de los Átridas señala que la civilización puede poner fin a la _hybris_ de los hombres y las divinidades. Por un lado la tragedia del inconsciente, la autodestrucción y la monstruosidad; por otro, la de la historia, la política y el advenimiento de la democracia. A la vista de esta diferencia se entiende por qué, en 1897, Freud escoge como modelo genealógico la familia de los Labdácidas, culpable de autodestruirse en torno de Tebas, ciudad casi «vienesa», endogámica, cerrada y replegada en sí misma: una locura interna al psiquismo.
Si el Edipo de Sófocles encarnaba para Freud el inconsciente conceptualizado por el psicoanálisis, el Hamlet de Shakespeare, príncipe cristiano de comienzos del siglo XVII, hacía posible una teorización de la «conciencia culpable». Sujeto copernicano, Hamlet no logra aún dudar de manera cartesiana de los fundamentos del pensamiento racional. Inquieto y débil, no puede seguir siendo un príncipe ni convertirse en rey, porque no tiene siquiera la certeza de «ser o no ser». En el sistema freudiano Hamlet es una suerte de Orestes cristianizado, culpable y neurótico.
Al inventar un sujeto moderno dividido entre Edipo y Hamlet, entre un inconsciente que lo determina sin que él lo sepa y una conciencia culpable que le pone trabas en su libertad, Freud concebía su doctrina como una antropología de la modernidad trágica, una «novela familiar»: la tragedia inconsciente del incesto y el crimen, decía, se repite en el drama de la conciencia culpable. Esta concepción del sujeto no tenía ya nada que ver con una psicología médica, fuera cual fuese. En cuanto al psicoanálisis, era un acto de transgresión, una manera de escuchar las palabras a espaldas de ellas mismas, y de recogerlas sin aparentar escucharlas o definirlas. Una disciplina extraña, una combinación frágil que unía el alma y el cuerpo, el afecto y la razón, la política y la animalidad: soy un _zoon politikon_ , decía Freud citando a Aristóteles.
En momentos en que por toda Europa se diseñaban vastos programas de investigación, fundados en el estudio de los hechos y las conductas, Freud se volvía, pues, hacia la literatura y las mitologías de los orígenes para dar a su teoría del psiquismo una consistencia que, a los ojos de sus contemporáneos, no podía en ningún caso invocarse como parte de la ciencia: ni de la psicología, que enumeraba comportamientos y aspiraba a la objetividad; ni de la antropología, que procuraba describir las sociedades humanas; ni de la sociología, que estudiaba realidades humanas; ni de la medicina que, desde Bichat, Claude Bernard y Pasteur, definía una norma y una patología fundadas en variaciones orgánicas y fisiológicas. Y pese a ello, Freud afirmaba ser el inventor de una verdadera ciencia de la psique.
Se entiende entonces por qué esa extraña revolución del sentido íntimo, contemporánea de la invención del arte cinematográfico —otra gran fábrica de sueños, mitos y héroes—, supo interesar a los escritores, los poetas y los historiadores y repeler a los adeptos de las ciencias positivas, los mismos a quienes Freud trataba de convencer. Fiel sin saberlo a la tradición del romanticismo negro, abrazaba la idea de los trágicos griegos de que el hombre es el actor inconsciente de su propia destrucción por el hecho mismo de su arraigo en una genealogía que no domina. Inversión de la razón en su contrario, rastreo de la parte oscura de uno mismo, búsqueda de la muerte que obra en la vida: esa era en verdad la naturaleza de la inmersión efectuada por el inventor del psicoanálisis en los albores del siglo XX, y a cuyo respecto Thomas Mann diría con tino, contra la opinión de Freud, que con ella estábamos frente a un «romanticismo hecho ciencia».
Desde su infancia Freud siempre había admirado a los héroes rebeldes: conquistadores, fundadores de dinastías, aventureros, capaces de abolir la ley del padre y, a la vez, de restablecer simbólicamente la soberanía de una paternidad vencida o humillada. Al ligar el destino de Hamlet con el de Edipo, atribuía al psicoanálisis un lugar imperial, es cierto, en el corazón de lo que más adelante recibiría el nombre de ciencias humanas, pero un lugar imposible de definir: entre saber racional y pensamiento salvaje, entre medicina del alma y técnica de la confesión, entre mitología y práctica terapéutica.
En el fondo, Freud llevaba a cabo una revolución simbólica: cambiaba la mirada que toda una época posaba sobre sí misma y sobre sus maneras de pensar. Inventaba un nuevo relato de los orígenes en que el sujeto moderno era el héroe, no de una mera patología, sino de una tragedia. Durante un siglo esta invención freudiana marcaría las mentes. Pero, a la vez que reactualizaba la tragedia de Edipo, Freud también corría el riesgo de encerrar su relato en un «complejo» y de generar así las condiciones de una reducción de su doctrina a una psicología familiarista. Necesitaría trece años para dar cuerpo a ese complejo edípico, sin dedicar jamás el más mínimo artículo a esta noción, presente por doquier en su obra pero, en definitiva, muy poco desarrollada. En efecto, fue en 1910, justo después de escribir su ensayo sobre Leonardo da Vinci, cuando utilizó por primera vez el término _Ödipuskomplex_.
Freud consideraba la historia del «caso Dora» como la primera cura psicoanalítica que había efectuado. Y sin embargo, si se examina con detenimiento ese caso, se advierte que la paciente a quien él había dado ese nombre, Ida Bauer, se parecía a las otras jóvenes vienesas de la burguesía judía acomodada cuyo destino mencionaba en los _Estudios sobre la histeria_. Una vez más, Freud se enfrentaba a una patología familiar, como médico y como especialista en enfermedades nerviosas. Y una vez más, escribió acerca de Ida, y con una pluma inmensamente talentosa, un relato que se dejaba leer como una novela breve de Stefan Zweig o Arthur Schnitzler. Víctima de un cuarteto de adultos cínicos, uno de los cuales había intentado abusar sexualmente de ella cuando tenía trece años, Ida Bauer fue obligada por su padre a iniciar un tratamiento con Freud.
Gran industrial, Philipp Bauer, tuerto y enfermo de sífilis, había contraído tuberculosis en 1888, por lo cual se había mudado a Merano, en el Tirol, con su mujer Katharina y toda su familia. En ese lugar había conocido a Hans Zellenka, un hombre de negocios con menos fortuna que él, casado con una bella italiana, Giuseppina o Peppina, que sufría trastornos histéricos y era asidua de los sanatorios. En un principio amante de Bauer, se había quedado a su lado cuando, en 1892, él sufrió un desprendimiento de retina.
En esa época, ya de regreso en Viena, Bauer vivía en la misma calle que Freud y lo consultó debido a un ataque de parálisis y confusión mental de origen sifilítico. Satisfecho con el tratamiento, le envió enseguida a su hermana, Malvine Friedmann, neurótica grave y hundida en el desastre de una vida conyugal atormentada, que murió poco después a raíz de una caquexia de rápida evolución.
Katharina, la madre de Ida, pertenecía como su marido a una familia judía originaria de Bohemia. Poco instruida y bastante tonta, padecía dolores abdominales permanentes, que su hija había heredado. Nunca se había interesado por sus hijos y, a partir de la enfermedad de su marido y la desunión resultante, presentaba todos los signos de una «psicosis de ama de casa»: sin entender en absoluto las aspiraciones de sus hijos, si damos crédito a Freud consagraba todos sus días a limpiar y mantener en condiciones la vivienda, los muebles y los utensilios domésticos, a tal punto que el uso y el disfrute de estos se habían tornado poco menos que imposibles. La hija no prestaba ninguna atención a la madre, la criticaba con dureza y se había sustraído por completo a su influencia. Una institutriz le servía de apoyo. Moderna y «liberada», esta mujer leía libros sobre la vida sexual e informaba sobre ellos a su alumna, en secreto. Y, en especial, le abrió los ojos sobre el amorío de su padre con Peppina. No obstante, después de haberla querido y escuchado, Ida se enemistó con ella.
En cuanto al hermano, Otto Bauer, soñaba sobre todo con huir de las disputas familiares. Cuando debía tomar partido, se alineaba con su madre. A los nueve años daba muestras de ser un niño prodigio, al extremo de escribir un drama sobre el fin del imperio de Napoleón. A continuación se rebeló contra las opiniones políticas de su padre, cuyo adulterio, por otra parte, aprobaba. Como él, tendría una doble vida, marcada por el secreto y la ambivalencia. Secretario del Partido Socialdemócrata de 1907 a 1914 y luego adjunto de Viktor Adler en el Ministerio de Asuntos Exteriores en 1918, sería una de las grandes figuras de la _intelligentsia_ austríaca de entreguerras.
En octubre de 1900, a los dieciocho años, Ida Bauer, presionada por su padre, visitó a Freud para emprender una cura que duraría exactamente once semanas. Afectada de diversos trastornos nerviosos —migrañas, tos convulsa, afonía, depresión, tendencias suicidas—, había sufrido una segunda afrenta. Consciente desde mucho tiempo atrás de la «falta» paterna y de la mentira sobre la que descansaba la vida familiar, había rechazado otra vez las proposiciones amorosas que le hacía Hans Zellenka a orillas del lago de Garda, tras lo cual lo había abofeteado. El drama estalló cuando Hans y su padre la acusaron de haber inventado del principio al fin la escena de seducción. Peor aún, fue desautorizada por Peppina Zellenka, que sospechaba que Ida leía libros pornográficos, en particular la _Fisiología del amor_ de Paolo Mantegazza, publicado en 1872 y traducido al alemán cinco años después. El autor era un sexólogo darwiniano muy citado por Richard von Krafft-Ebing y especializado en la descripción antropológica de las grandes prácticas sexuales humanas: lesbianismo, onanismo, masturbación, inversión, felación, etc.
Al enviar a su hija a ver a Freud, Philipp Bauer esperaba sin duda que este le diera la razón y se ocupara de poner fin a las presuntas fantasías sexuales de la muchacha. Lejos de suscribir la expectativa paterna, Freud se internó en una dirección muy distinta. En once semanas y a través de dos sueños —uno referido a un incendio en la casa familiar y otro a la muerte del padre—, reconstituyó la verdad inconsciente de ese drama. El primer sueño revelaba que Dora se había entregado a la masturbación y que estaba, en realidad, enamorada de Hans Zellenka. Pero esta evocación también despertaba un deseo incestuoso reprimido en relación con el padre. En cuanto al segundo, permitía ir aún más lejos en la investigación de la «geografía sexual» de Dora y poner de relieve, en particular, su perfecto conocimiento de la vida sexual de los adultos.
Freud se dio cuenta de que la paciente no soportaba la «revelación» de su deseo por el hombre a quien había abofeteado. Se lanzó entonces a hacer interpretaciones aventuradas y erróneas sobre una crisis de apendicitis como consecuencia de una fantasía de parto. La paciente se negó a asumir ese discurso. Por eso Freud dejó que se fuera cuando ella decidió interrumpir el tratamiento.
En un primer momento favorable a la cura, el padre no tardó en percatarse de que Freud no había aceptado la tesis de la fabulación. En consecuencia, se desinteresó del asunto. Por su lado, Ida no halló en Freud el consuelo que esperaba de él. Por entonces, en efecto, él todavía no sabía manejar la transferencia en la psicoterapia. Asimismo, como lo destacaría en una nota de 1923, era incapaz de comprender la naturaleza del lazo homosexual que unía a Ida y Peppina. «Si bien Freud utilizaba un lenguaje seco con Dora», escribe Patrick Mahony, «tampoco se expresaba con calma; se estremecía y dejaba traslucir su excitación en tonalidades de ironía, frustración, amargura, venganza y triunfalismo complaciente.»
En síntesis, Freud dudaba y se resistía a la tentación de aplicar su flamante teoría a la historia de esa desdichada joven histérica para hacer de ella un caso. Ida se le escapaba. Pero, sin importar lo que esta haya dicho más adelante, él, con todo, la había liberado en parte de las cadenas de una familia patógena.
Ida Bauer no sanó jamás de su rechazo por los hombres. Pero sus síntomas se mitigaron. Tras su breve análisis se vengó de la humillación sufrida haciendo confesar a Peppina su amorío y a Hans Zellenka su tentativa de seducción. A continuación contó la verdad a su padre y puso fin a toda relación con la pareja. En 1903 se casó con Ernst Adler, un compositor empleado en la fábrica paterna. Dos años después dio a luz un varón que más adelante hizo carrera como músico en Estados Unidos.
En 1923, afectada por nuevos trastornos —vértigos, zumbidos de oídos, insomnios, migrañas—, llamó en su auxilio a Felix Deutsch, discípulo de Freud. Le contó toda su historia, habló del egoísmo de los hombres, de sus frustraciones, de su frigidez. Al escuchar sus quejas, Deutsch reconoció el famoso caso «Dora». Afirmó que ella había olvidado su enfermedad pasada y que manifestaba un enorme orgullo por haber sido objeto de un escrito célebre en la literatura psiquiátrica. Ida discutió entonces las interpretaciones hechas por Freud de sus dos sueños. Cuando Deutsch volvió a verla, los ataques habían pasado.
El «caso Dora» será uno de los más comentados de toda la historia del psicoanálisis, más aún que el de Bertha Pappenheim, y dio lugar a decenas de artículos, ensayos, una pieza teatral y varias novelas. Reunía, en efecto, todos los ingredientes de esa sexualidad de fin de siglo que hacía las delicias de los escritores y los médicos del alma: irritación histérica, homosexualidad, obsesión por las enfermedades venéreas, explotación del cuerpo de las mujeres y los niños, placeres del adulterio.
Aun antes de abandonar su _neurótica_ , Freud dedicaba una buena parte de su tiempo al estudio de lo que más le atraía desde hacía años: el análisis de los sueños. Habituado al consumo de drogas, se entregaba con facilidad a intensas actividades oníricas. Llevaba además un diario de sus sueños. Soñaba con frecuencia y de manera desordenada: con viajes futuros, sus colegas, la vida cotidiana en Viena, hechos anodinos o, al contrario, acontecimientos importantes relacionados con la vida, la comida, el amor, la muerte, los lazos de parentesco.
A lo largo de sus peregrinaciones nocturnas repartía mandobles a sus rivales, se metía en situaciones de riesgo, revivía escenas de su infancia, soñaba que tenía un sueño y luego otro inmerso en el primero, para verse después en el corazón de una ciudad en ruinas, poblada de estatuas, columnas o casas sepultadas, y cuyas callejuelas recorría a la vez que se extraviaba en el laberinto arqueológico de sus deseos culpables. Soñaba en varias lenguas y varios estratos; soñaba con cosas sexuales, la actualidad política, los atentados anarquistas, la familia imperial, Aníbal, Roma, el antisemitismo, el ateísmo, madres, padres, tíos, nodrizas.
Soñaba: inventaba jeroglíficos y se proyectaba en personajes literarios, recorriendo ríos o entregándose a larguísimos paseos por museos europeos, para contemplar los cuadros de sus pintores favoritos. En sus ensoñaciones pasaba revista a todas las obras de la cultura occidental y mencionaba nombres de ciudades, lugares o científicos célebres o desconocidos. Y fue así como se lanzó a escribir la obra con la cual pretendía fundar su nueva teoría del psiquismo. En un principio esa obra adoptó la forma de una especie de enciclopedia varias veces retocada, antes de sosegarse en un recorrido iniciático salpicado por grandes momentos de exaltación, duda, angustia y melancolía.
A lo largo de ese nuevo _Sturm und Drang_ , durante el cual mantuvo entre 1895 y 1900 una conversación consigo mismo, sin dejar en ningún momento, empero, de dirigirse a Fliess como a un doble de Mefistófeles, Freud tomó la costumbre de referirse a la _Divina Comedia_ , al punto de mandar al infierno a enemigos y adversarios. Reunió así ciento sesenta sueños, entre ellos cincuenta de sí mismo y setenta contados por sus allegados, para componer un vasto poema en versos libres poblados de episodios oníricos de todo tipo: sueño de Bismarck, sueño del caballo gris, de Casimir Bonjour, de la monografía botánica, sueño de Fidelio, del hijo muerto que arde, del lince en el techo, de mi hijo el miope, de Julio César, de Napoleón, de Edipo disfrazado, sueño del padre muerto o de la sonata de Tartini. Ese libro, agregaría en 1908, tiene además «otro significado, subjetivo, que solo después de terminarlo pude comprender. Advertí que era parte de mi autoanálisis, que era mi reacción frente a la muerte de mi padre, vale decir, frente al acontecimiento más significativo y la pérdida más terrible en la vida de un hombre». Extraña observación que, en todo caso, confirma que a sus ojos el padre es mortal y la madre inmortal.
Al abandonarse a esa exploración de la psique, paralela tanto al viaje de Dante como al periplo de Ulises, Freud tuvo conciencia de que estaba creando, casi sin saberlo, una obra magistral que lo arrastraba a los bosques oscuros de su inconsciente en plena efervescencia. Esa «ciencia del sueño», salida de la tradición del romanticismo, movilizaba interrogantes sobre la sexualidad infantil y el origen de las neurosis, y se apoyaba a la vez en un retorno a los dioses y los héroes de la antigua Grecia. A través de ese viaje por las profundidades del alma, Freud quería ser el mensajero de una realidad rechazada, negada, reprimida: «Creo estar destinado», diría un día a Jones, «a no descubrir sino lo que es evidente: que los niños tienen una sexualidad —como lo sabe cualquier niñera— y que nuestros sueños nocturnos son, de la misma forma que nuestras ensoñaciones diurnas, realizaciones de deseo».
Consciente de abordar las riberas de un continente conocido desde la noche de los tiempos, y particularmente investigado durante la segunda mitad del siglo XIX, Freud decidió leer las obras más pertinentes sobre la cuestión, y de tal modo consagró las primeras ochenta páginas del primer capítulo de su gran libro a un análisis crítico de lo que habían escrito sus predecesores, desde Aristóteles y Artemidoro de Daldis hasta los contemporáneos más cercanos, los mismos que, escapando a la idea de que el sueño fuese una premonición, una «clave de los sueños» o la expresión de una actividad fisiológica inducida por estímulos sensoriales o somáticos, habían hecho de él un objeto de saber y de conocimiento de sí: Gotthilf Heinrich von Schubert, Eduard von Hartmann, Johannes Volkelt, Adolf Strümpell, Havelock Ellis, Albert Moll, Joseph Delbœuf, Yves Delage, Wilhelm Griesinger y muchos otros, y sobre todo Alfred Maury, Karl Albert Scherner y Hervey de Saint-Denys.
Todos estos autores, y más aún los tres últimos, habían inventado técnicas de investigación de esa parte de la vida humana protegida por el dormir. Habían percibido que los sueños eran otras tantas expresiones deformadas de pensamientos inconfesables, deseos reprimidos, recuerdos de infancia o fantasías sexuales relacionadas con prohibiciones fundamentales: incesto, masturbación, perversión, locura, transgresión. Varios de ellos ya habían planteado la hipótesis de que el desciframiento racional de las figuras retóricas propias de la estructura del sueño permitiría a los especialistas en enfermedades nerviosas tratar mejor a sus pacientes. Y así como algunos autores afirmaban que el sueño era de naturaleza similar a un síndrome psicótico, otros destacaban que la actividad onírica servía de remedio espontáneo para los trastornos de los sujetos perversos. En efecto, estos —se decía— podían muy bien escenificar, durante el dormir, sus aberraciones sexuales para mejor erradicarlas del estado de vigilia. En síntesis, al internarse en el camino del análisis de los sueños Freud se vio obligado a la vez a recibir una herencia y a diferenciarse de ella.
De tal modo, lejos de hacer referencia, como sus predecesores, a una «vida de los sueños» o una manera de dirigirlos, decidió efectuar una síntesis de todas las modalidades de enfoque posibles de la cuestión del sueño en general y de los sueños en particular, y presentar su _Traumbuch_ como el manifiesto de una nueva comprensión de la subjetividad humana. De ahí la elección de una fecha emblemática —1900 y no 1899— y de un título pasmoso: _Die Traumdeutung_. Mediante esa expresión genérica («la interpretación del sueño») Freud se vinculaba, más allá de las experiencias científicas, con la tradición de los adivinos. No «los sueños» sino «EL sueño», no dos palabras, _Deutung_ _des Traums_ , sino una sola denominación que connotaba la idea de entregar al público una suma definitiva, universal, semejante a una biblia que fuera al mismo tiempo un tratado de los oráculos y la expresión de una ciencia de la psique.
Para el epígrafe Freud escogió un verso tomado del canto VII de la _Eneida_ : « _Flectere si nequeo Superos, Acheronta movebo_ » («Si a los supernos no puedo doblegar, moveré el Aqueronte»), en el cual Juno defiende a Dido, reina cartaginesa, contra Eneas, troyano destituido y futuro fundador de Roma. Al no lograr convencer a Júpiter (los supernos) de que deje a Eneas desposar a Dido, Juno apela a una furia surgida del Aqueronte, Alecto, una suerte de Gorgona bisexual capaz de desencadenar las pasiones instintivas y los ejércitos en el campo de los aliados de Eneas. Abandonada por su amante, Dido se da muerte y, cuando Eneas se le une en los Infiernos, ella le niega todo perdón: él hablará con su espectro.
Con ese epígrafe Freud ponía en juego en una sola frase, no solo lo esencial de su doctrina de la sexualidad —las fuerzas pulsionales reactivadas por las potestades subterráneas del Infierno—, sino también algunos de los principales significantes de su propia historia. En él se encontraba en primer lugar la expresión de su rebelión contra la ciudad imperial tan deseada e imposible de alcanzar, esa ciudad que Aníbal, héroe freudiano por antonomasia, no había conseguido conquistar, incapaz con ello de vengar a Amílcar. Identificado con Aníbal, Freud, como se sabe, seguía sintiéndose culpable de no haber abandonado su teoría de la seducción antes de la muerte de su padre, injustamente señalado como sospechoso de haber abusado sexualmente de sus hijas.
Pero la imprecación de Juno, en la obra de Virgilio, remitía también a la actitud política ambivalente de Freud hacia la monarquía austríaca y sobre todo hacia su representante más temible, el conde Von Thun, con quien, según contaba, se había enfrentado. La escena se había producido en un andén de la estación del oeste de Viena, el 11 de agosto de 1898, cuando Freud se disponía a partir de vacaciones. Ese día se cruzó con el conde, que se trasladaba a la residencia estival del emperador, donde debían firmarse unos acuerdos económicos con Hungría. Aunque no tenía billete, Von Thun hizo a un lado al revisor y se instaló en un lujoso vagón. Freud comenzó entonces a silbar el aria del criado de _Las bodas de Fígaro_ de Mozart: «Si el señor conde quiere bailar, yo tocaré la guitarra». Fígaro, como es sabido, se burlaba así del conde Almaviva, que cortejaba a su prometida.
Al día siguiente Freud tuvo un «sueño revolucionario» en el que se identificaba con un estudiante que había contribuido al desencadenamiento de la revolución de 1848. Y veía aparecer a otro médico judío, Viktor Adler, ese ex condiscípulo al que antaño había desafiado con motivo de un duelo. En otra escena, después de dejar el episodio político, se veía en el andén de la estación. Pero, en vez de enfrentarse a Von Thun, acompañaba a un ciego al que tendía un orinal. Al analizar ese sueño, Freud interpretó que el anciano era la figuración de su padre moribundo, a quien otrora había desafiado orinando en su dormitorio. Había sustituido pues la imagen detestada de Von Thun por la de Jacob en su agonía.
¿Cómo no ver en ese sueño la ilustración del destino de Freud y de su concepción del poder, según la cual toda sociedad tiene por origen un conflicto entre un padre tiránico y un hijo rebelde obligado a darle muerte? Una concepción que más adelante Freud teorizaría en _Tótem y tabú_ y _Moisés y la religión monoteísta_.
Pero en 1900 también anunciaba, a través del epígrafe tomado de Virgilio, su firme intención de celebrar la primacía del psicoanálisis sobre la política y de hacer de su doctrina recién elaborada el instrumento de una revolución: cambiar al hombre mediante la exploración de la cara oculta de sus deseos.
En una carta de 1927 a Werner Achelis, Freud afirmaba haber conocido la frase virgiliana gracias a la lectura de un folleto publicado por Ferdinand Lassalle en 1859 contra la monarquía de los Habsburgo, juzgada oscurantista: «Usted traduce la expresión _Acheronta movebo_ por "hacer temblar las ciudadelas de la tierra"», decía a su interlocutor,
cuando, en realidad, significa «agitar el mundo subterráneo». Había tomado la cita de Lassalle, quien la empleó probablemente en sentido personal, refiriéndola a clasificaciones sociales y no psicológicas. Yo la adopté meramente para recalcar la parte más importante de la dinámica del sueño. El deseo rechazado por las instancias psíquicas superiores (el deseo reprimido del sueño) agita el mundo psíquico subterráneo (es decir, el inconsciente) para hacerse notar.
Como subraya Carl Schorske, había una gran similitud entre las elecciones políticas del joven Freud y las de Lassalle. Ambos rechazaban el catolicismo romano y la dinastía de los Habsburgo. Pero, en particular, Freud planteaba un paralelismo entre la revolución social ambicionada por Lassalle y la que él tenía como aspiración.
Sucedía que, al celebrar las pulsiones, las leyendas, los mitos, las tradiciones populares, su intención era atacar a los mandarines y representantes de la ciencia oficial. Y el recurso al sueño y a su interpretación equivalía a la proclamación de que la fuerza de lo imaginario, descifrada por un científico ambicioso, podía igualmente encarnarse en un vasto movimiento capaz de desafiar al poder político. Bajo la máscara de un Aníbal dotado del humor de un Fígaro, Freud fabricaba un mito, el del héroe solitario sumido en un «espléndido aislamiento» y enfrentado a un mundo hostil a su genio.
En virtud de esa construcción emblemática, comenzó a considerarse como el dueño y señor de una revolución de la sexualidad puesta bajo el signo de una nueva ciencia: el psicoanálisis. Pero pese a ello, Freud dudaba de sí mismo al punto de creerse objeto de toda clase de persecuciones:
Ese destino lo imaginé de la manera siguiente: probablemente, los éxitos terapéuticos del nuevo procedimiento me permitirían subsistir, pero la ciencia no repararía en mí mientras yo viviese. Algunos decenios después, otro, infaliblemente, tropezaría con esas mismas cosas para las cuales ahora no habían madurado los tiempos, haría que los demás las reconociesen y me honraría como a un precursor forzosamente malogrado. Entretanto, me dispuse a pasarlo lo mejor posible, como Robinson en su isla solitaria.
En esa época, sin embargo, Freud no estaba aislado ni era rechazado; antes bien, se lo veía como un médico brillante y con mucho futuro. Y si él mismo se consideraba un rebelde, los sexólogos lo juzgaban un conservador y los mandarines de la ciencia médica lo veían como un «literato».
De haber sido redactada como un suntuoso poema, la _Traumdeutung_ no habría permitido imponer un nuevo enfoque de la psique humana. Y por eso Freud, si bien adoptó para escribir esta obra un estilo apto para transmitir el aspecto novelesco de la vida soñada, también se consagró a hacer de ella un manifiesto teórico y clínico de una fuerza y una modernidad sin igual.
En dos partes fundamentales del libro expone su método interpretativo: este se funda en la asociación libre, es decir, en la escucha de lo que el que sueña expresa al dar libre curso a sus pensamientos sin discriminar entre ellos. Desde este punto de vista, el sueño dejó de ser un enunciado inmóvil para convertirse en narración, trabajo en movimiento, verdadera expresión deformada o censurada de un deseo reprimido cuya significación es preciso descifrar. Y para explicar sus modalidades Freud distingue un contenido manifiesto —relato del sueño una vez se está despierto— y un contenido latente, progresivamente sacado a la luz gracias al proceso asociativo.
A su entender, dos grandes operaciones estructuran la retórica del sueño: el desplazamiento, que transforma los elementos primordiales del contenido latente por medio de un deslizamiento, y la condensación, que realiza una fusión entre varias ideas de ese mismo contenido para culminar en la creación de una sola imagen en el contenido manifiesto.
A lo largo del famoso capítulo 7, muchas veces comentado, y que constituye un libro en sí mismo, inmerso, por decirlo de algún modo, en el vasto conjunto de la _Traumdeutung_ , Freud introduce su concepción del aparato psíquico —o primera tópica— sobre la base de los «manuscritos» enviados a Fliess, para cuya redacción se había inspirado en todas las teorías de la psique formuladas por los pensadores del siglo XIX. Distingue así el consciente, equivalente de la conciencia; el preconsciente, instancia accesible al consciente, y para terminar el inconsciente, «otra escena», lugar desconocido por la conciencia. Pero si se vale del tercero de estos términos, utilizado desde la noche de los tiempos y teorizado por primera vez en 1751, es para hacer de él el principal concepto de una doctrina que rompe de manera radical con las antiguas definiciones: ya no una supraconciencia, un subconsciente o un depósito de la sinrazón, sino un lugar instituido por la represión, es decir, por un proceso que apunta a mantener al margen de toda forma de conciencia, como un «defecto de traducción», todas las representaciones pulsionales capaces de convertirse en una fuente de displacer y, por lo tanto, de perturbar el equilibrio de la conciencia subjetiva. En el sistema freudiano de la primera tópica la represión es al Aqueronte lo que el inconsciente era a Edipo y el preconsciente a Hamlet.
Lo más asombroso en esta cuestión por la cual Freud explicaba que el análisis del sueño es la «vía regia del inconsciente» es que, aunque su _Traumbuch_ tenía una vocación universal, lo había construido sobre el modelo de lo que Viena había llegado a ser para los intelectuales de su generación: una ciudad dividida entre el odio y el amor, y cuya grandeza reprimida suscitaba en ellos una verdadera atracción, no solo por la atemporalidad y la deconstrucción del yo que se vivía en ella, sino también por la invención de una muy extraña modernidad centrada en el retorno a un pasado ancestral. Según las palabras de Hugo von Hofmannsthal, Viena era entonces, en el imaginario de esa generación, la «monstruosa residencia de un rey ya muerto y de un dios no nacido».
¿Cómo no ver en el famoso sueño de «la inyección de Irma», mil veces interpretado, la ilustración de la «novela familiar» que unía a Freud con Viena?
Durante el verano de 1895, una paciente apodada Irma había seguido una cura con Freud. Al comprobar que ella no sanaba, él le había propuesto interrumpir el tratamiento, pero la paciente se negó. Freud pasó entonces algunos días en familia en la residencia de Bellevue, en los altos de Viena, donde Oskar Rie se le unió tras una estancia con la familia de Irma. Su visitante le hizo algunos reproches acerca del tratamiento y Freud redactó su observación para presentársela a Breuer. En esos días Martha iba a festejar su cumpleaños y recibir a su amiga Irma.
En la noche del 24 de julio Freud soñó que se encontraba con Irma en una velada y le decía que, si aún tenía dolores, era por su exclusiva culpa. No obstante, al examinarla le descubría unas manchas grisáceas en la boca que se parecían a cornetes nasales o a los síntomas de una difteria. Llamaba enseguida en su auxilio al doctor M., que cojeaba y decía palabras de consuelo, y luego convocaba a otros dos amigos, Leopold y Otto. Este último ponía a Irma una inyección de trimetilamina para curar una infección que él mismo había provocado por usar una jeringa que no estaba bien limpia.
Freud creía que este sueño era de una importancia capital: el primero, decía, que había sometido a un análisis detallado a lo largo de unas quince páginas. A su juicio, se trataba del cumplimiento de un deseo que lo eximía de toda responsabilidad en la enfermedad de Irma.
Hay un vínculo entre la gran importancia que Freud atribuía a ese sueño y la operación de autoficción a la que se entregaba so capa de una impecable racionalidad. En la misma medida que la realización de un deseo o la afirmación de una interpretación llevada hasta el final, el sueño contenía en efecto una suerte de novela familiar de los orígenes vieneses del psicoanálisis. En él aparecían Oskar Rie (Otto), concuñado de Fliess; Ernst von Fleischl-Marxow (Leopold); Josef Breuer (el doctor M.) y, por último, una mezcla de Emma Eckstein y Anna Lichtheim (Irma), hija de Samuel Hammerschlag: la quintaesencia de la mujer judía vienesa de fin de siglo.
En el momento de presentarse como el inventor de una doctrina que debía revolucionar el mundo, Freud soñaba pues con el fracaso de la cura de Emma Eckstein. Atribuía la responsabilidad a Fliess —a través de Oskar Rie, encarnado por Otto— y a la propia Emma. Luego se vengaba de sus críticos transformando a sus amigos en adversarios. Al mismo tiempo justificaba sus decisiones frente a Breuer y recordaba que su hija Mathilde había estado a punto de morir de difteria. Se liberaba a continuación de su culpa con respecto a Fleischl-Marxow y afirmaba por último, frente a los mandarines de la ciencia médica, que el sueño no era reducible en modo alguno a la expresión de una actividad cerebral..
El 12 de junio de 1900 escribió a Fliess: «¿Crees tú por ventura que en la casa alguna vez se podrá leer sobre una placa de mármol: "Aquí se reveló el 24 de julio de 1895 al doctor Sigmund Freud el secreto del sueño"?». Y el 10 de julio, sintiéndose agotado e incapaz de acometer otros grandes problemas, tuvo la impresión de entrar en un infierno intelectual y distinguir, en el núcleo más oscuro de sus diferentes estratos, «la silueta de Lucifer Amor».
Hasta 1929 Freud nunca dejó de retocar ese libro inaugural, profundizar en su análisis y agregarle listas de obras de referencia, así como dos contribuciones de su amigo y discípulo Otto Rank.
Durante mucho tiempo prevaleció la idea de que el _Traumbuch_ había tenido una mala acogida. Acreditada por Freud en la misma medida que el mito del «autoanálisis» y del «espléndido aislamiento», esta presentación indignada de la recepción de una de las obras mayores del fundador del psicoanálisis fue retomada por Jones y por generaciones de profesionales. En su prefacio a la segunda edición, en 1908, el propio Freud mencionó «la condena del silencio» que había recaído sobre su obra y, un año después, se quejaba aún de que su trabajo no se tomara en cuenta. La realidad de las cosas invita, con todo, a matizar un poco el juicio, sobre todo cuando se sabe cómo era la vida intelectual y científica de esa época.
En rigor, Freud esperaba que esta obra tuviera un destino de best seller. Y, en especial, que los psicólogos y los médicos lo saludaran como un verdadero genio de la ciencia. La realidad fue muy diferente. El libro, es cierto, tuvo reseñas en la casi totalidad de las grandes revistas de medicina y psicología de Europa. Las ventas fueron de un promedio de setenta y cinco ejemplares anuales en un lapso de ocho años, pero el libro, no obstante, proporcionó a Freud un renombre internacional. Y además, los ataques e insultos que él tuvo que sufrir, así como las polémicas suscitadas por el libro, ¿no dan testimonio de una penetración de la doctrina freudiana en el campo de la psiquiatría y la psicopatología?
En cuanto a la recepción de la _Traumdeutung_ en los medios literarios, filosóficos y artísticos —y sobre todo en las vanguardias y el movimiento surrealista—, contribuyó a asegurar progresivamente a Freud el lugar eminente que le correspondía en la historia del pensamiento occidental.
Ya en 1897 Nothnagel y Krafft-Ebing habían propuesto su candidatura al cargo de profesor adjunto en la Universidad de Viena. Después de múltiples obstáculos administrativos, y visto que había sido docente no remunerado, ya que había optado por la carrera de médico de práctica privada, Freud obtuvo por fin, en febrero de 1902, la designación tan deseada a aquel cargo, lo que significaba sin duda que sus trabajos comenzaban a ser reconocidos. A partir de ahora sería _Herr Professor_.
A esas alturas ya había un antes y un después de Freud. Pero él, entregado por completo a su destino, a la vez lúcido, triunfador, amargo, seguro e inseguro de su genio, parecía no querer tomar aún conciencia del acontecimiento que lo había tenido por demiurgo.
## SEGUNDA PARTE
# FREUD, LA CONQUISTA
### 1
Una época tan bella
En una confidencia hecha a Marie Bonaparte, el 4 de enero de 1926, Freud contaba lo decepcionante que había sido para él la lectura de _Por el camino de Swann_ : «No creo que la obra de Proust vaya a ser duradera. ¡Y ese estilo! ¡Quiere ir siempre a las profundidades y nunca termina las frases!».
Si Freud menospreció de tal modo la obra proustiana, el autor de _En busca del tiempo perdido_ le pagó con la misma moneda y nunca hizo la más mínima alusión a sus trabajos, pese a que, entre 1910 y 1925, el medio literario parisino, de André Gide a André Breton, les brindó una fervorosa recepción. En 1924, intrigado por esa ignorancia mutua, Jacques Rivière, director de la _Nouvelle Revue Française_ , intentaría explicar, en las muy concurridas conferencias que dictaba en el teatro del Vieux-Colombier, hasta qué punto Freud y Proust habían explorado, de manera paralela y disímil, el sueño, el inconsciente, la memoria, la sexualidad.
Si Freud y Proust eran, cada uno a su manera, los narradores modernos de la exploración del yo, también tenían en común la idea de que la madre es el primer objeto de apego hacia el cual se vuelca el ser humano: la madre o su sustituto. Y de ahí se deducía, tanto para el escritor como para el científico, una concepción del amor conforme a la cual cada ser humano desea ser amado por otro como lo ha sido por su madre. O, en su defecto, como habría deseado serlo. Tratándose de la homosexualidad —que ambos denominaban «inversión»—, Freud y Proust la definían como la consecuencia de una bisexualidad necesaria para la civilización y la perpetuación del género humano. Sin ella, en efecto, los hombres, sometidos a una virilidad excesiva y poco inclinados a la sublimación, se habrían condenado a un perpetuo exterminio.
Más allá de esas analogías, tan innovadoras en los albores del siglo XX, Freud y Proust sentían una atracción real por las seducciones de una aristocracia declinante y aburguesada, que había renunciado al ejercicio del poder político para consagrarse a la búsqueda de sí, con el propósito, de tal modo, de acceder al tiempo recuperado: ilusión de una existencia condenada a su propio fin. Judíos y desjudaizados, ambos se sentían a la vez ajenos a la sociedad en la cual estaban inmersos y apegados a sus costumbres y tradiciones familiares. Sabían además, uno y otro, describir con lucidez las diferentes esferas de ese mundo que era profundamente suyo: los grandes burgueses, los nuevos ricos, los empleados domésticos, los marginales. Y habida cuenta de que _En busca del tiempo perdido_ terminaba inmediatamente después de la Primera Guerra Mundial, ¿cómo no advertir que ponía en escena la historia misma de una clase social cuyo ideal europeo estaba atravesado, desde el ascenso de los nacionalismos y el antisemitismo, por la convicción de que solo se sobreviviría a sí misma si transformaba cada destino singular en una obra de arte?
Los pacientes y los primeros discípulos de Freud se parecían, pues, a personajes proustianos, que cultivaban tanto la angustia de ser ellos mismos como la dicha de una libertad individual por fin conquistada dentro de una sociedad profundamente desigual donde los obreros, los campesinos y los pobres vivían en condiciones miserables.
Condenados a la búsqueda de sí y al culto del arte y los valores del liberalismo, los científicos de la Belle Époque depositaban además toda su esperanza en la ciencia. Por otro lado, en el corazón de ese continente europeo en plena mutación, los judíos vieneses eran, ellos también, los actores de un gran momento de efervescencia que al parecer habría de eternizarse. Alcanzado ya el ideal de la superación del gueto, hacían resplandecer con mil luces las facetas de su identidad múltiple. De ahí la búsqueda permanente de un futuro cuya realidad se proyectara en el pasado: racionalidad científica y restauración de los mitos en Sigmund Freud; sueño de un retorno a la tierra prometida en Nathan Birnbaum y Theodor Herzl; fantasma de una «Viena roja» en Viktor Adler y Otto Bauer; adopción de un ideal de destrucción y reconstrucción satírica de la lengua alemana en Karl Kraus; nostalgia de una fusión de la Ilustración francesa y la _Aufklärung_ alemana en Stefan Zweig; afirmación de una estética novelesca judía y austríaca en Arthur Schnitzler, y elaboración de un nuevo formalismo musical en Gustav Mahler y Arnold Schönberg. Todos estos judíos que ya no eran judíos buscaban expresar la cara oculta de una utopía capaz de suceder a la agonía de un mundo del que se sabían actores protagonistas.
A la vez que asumía la actitud de un judío espinosista, Freud mostró siempre los signos de una ambivalencia propia de la crisis de la identidad judía de fines de siglo. Hablaba sin ambages de «raza judía», «pertenencia racial» e incluso de «diferencias» entre los judíos y los «arios», como designaba, en efecto, a quienes no eran judíos. Cuando sus primeros discípulos lo exasperaban los trataba fácilmente de «judíos» incapaces de ganar amigos para la nueva doctrina. Sin embargo, el uso de tales expresiones no lo llevaba jamás a promover una psicología de la diferencia racial, como se explayó con Sándor Ferenczi en una carta del 8 de junio de 1913:
En cuanto al semitismo, hay sin duda grandes diferencias con el espíritu ario. Todos los días lo vemos confirmado. Por eso resultarán aquí y allá, a no dudar, concepciones del mundo diferentes y un arte diferente. Sin embargo, no debería haber una ciencia específica aria o judía. Los resultados tendrían que ser idénticos y solo la presentación podría variar [...]. Si esas diferencias intervinieran en la concepción científica de las relaciones objetivas, algo, entonces, no estaría en orden.
Dolido por no disfrutar del reconocimiento suficiente, Freud parecía ignorar que su «espléndido aislamiento» no era más que una fantasía y que, en la realidad, su obra dedicada al sueño generaba tantos elogios como críticas. Apenas tenía conciencia de ser el hombre de un tiempo en que los estados de ánimo se habían convertido en objeto de apasionamiento para una generación obsesionada por la introspección. Invadido por la duda, solo percibía de su época lo que le permitía alimentar su neurastenia y su condición de genio solitario. Ignoraba además que al reinventar a Hamlet y Edipo hacía del sujeto tendido en el diván el reflejo exacto de ese personaje dibujado por Alfred Kubin en 1902: un hombre decapitado y con el torso desnudo sumido en la contemplación de una inmensa cabeza melancólica que, desde el suelo y con la boca entreabierta, lo mira fijamente con sus ojos ciegos.
En esa época Freud llevaba una barba cuidadosamente cortada a diario por su peluquero. Levemente encorvado cuando caminaba a paso vivo con sus trajes un poco amplios pero sobrios y elegantes, siempre miraba a sus visitantes directamente a los ojos, como si quisiera mostrar que nunca se le escapaba nada. Hablaba el alemán con acento vienés y una voz clara y baja, y solía contar los hechos de la vida común y corriente sobre la base de ficciones. Cuando señalaba un olvido o un acto fallido y su interlocutor intentaba dar una explicación racional, se mostraba intransigente y la condena caía como una cuchilla. Trabajaba entre dieciséis y dieciocho horas al día, se desplazaba en calesa para visitar a sus pacientes cuando era necesario y exigía de los integrantes de su casa una estricta observancia de los horarios de las comidas. Martha, por su parte, se había convertido estrictamente en un ama de casa, atada a un ritual inmutable: la dirección adecuada del hogar.
De muy vasta erudición y una inteligencia excepcional, Freud leía y hablaba perfectamente en inglés, francés, italiano y español; usaba letras góticas para escribir en alemán, conocía el griego, el latín, el hebreo y el yiddish: «Mare nostrum», decía, calificándose de mediterráneo frente a los celtas, los germanos, los prusianos, los nórdicos, los americanos y los suizos. Era un producto puro de la cultura vienesa, verdadera Babel de las suntuosas sonoridades europeas. Ni goloso ni gourmet, no se negaba, sin embargo, algunos placeres de la mesa. Detestaba la carne de ave y la coliflor y no apreciaba los refinamientos de la gastronomía francesa, pero tenía una marcada afición por las pequeñas alcachofas italianas, la carne vacuna hervida y los asados encebollados. Intransigente con todas las formas de negligencia y dotado de un humor feroz, a pesar de carecer casi de encanto, no toleraba ni palabras malsonantes ni vestimenta inadecuada y manifestaba cierto desprecio por las personas demasiado corpulentas. No le gustaba ir a espectáculos ni comer en restaurantes, no bailaba el vals y no se sentía cómodo cuando debía frecuentar a la alta sociedad aristocrática.
Sin embargo, se movilizaba de buena gana para asistir a tal o cual representación de una ópera de Mozart, su compositor preferido. Galante y educado, regalaba flores a las señoras y tenía predilección por las orquídeas y más aún por las gardenias. A veces jugaba al ajedrez pero le gustaba en especial el tarot, tanto que le dedicaba la noche del sábado en compañía de Oskar Rie, Leopold Königstein y Ludwig Rosenberg, tres brillantes médicos. En 1895 hizo que instalaran en su casa el teléfono, instrumento detestable a sus ojos pero necesario, sin dejar pese a ello de escribir diariamente su famosa correspondencia.
Como todos los médicos vieneses de comienzos del siglo XX, tenía cuatro empleadas domésticas a su servicio: una cocinera, una encargada de la limpieza, una niñera y, por último, una criada que abría la puerta a sus pacientes. En general se tomaba un poco más de dos meses de vacaciones, entre mediados de julio y fines de septiembre. Durante ese lapso, y sobre todo en agosto, se ocupaba de sus hijos, y reservaba a sus viajes el mes siguiente. Le gustaba bañarse y nadar en el Adriático: «Tío Alexander», escribe Martin Freud,
nos acompañaba y tanto él como mi padre estaban raras veces fuera del agua y quedaban completamente tostados por el sol hasta donde lo permitían los decorosos trajes de baño del siglo pasado. Estos cubrían los hombros e incluso parte del brazo. Los de las mujeres eran aún peores: debían cubrirse las piernas con largas medias negras. No recuerdo haber visto jamás a mi madre o su hermana en traje de baño, ya fuera en la costa del Adriático o a orilla de los lagos donde fuimos más adelante. Es probable que ambas fuesen demasiado modestas o vanidosas para exhibirse aun en esos trajes de baño del siglo XIX; tal vez no sabían nadar.
Esa bella época fue la más feliz de la vida de Freud. En pocos años conquistó el mundo occidental, viajó con frenesí en busca de una cartografía del inconsciente con la que había soñado desde la infancia, fundó un movimiento internacional y se rodeó de un grupo de discípulos que, después de leer embargados por el entusiasmo _La interpretación de los sueños_ , contribuyeron a difundir y dar forma a su doctrina como ningún científico había sabido ni querido hacerlo entre sus contemporáneos, ni siquiera Pierre Janet y tampoco Théodore Flournoy. En la misma medida que el socialismo, el feminismo y las ideas de la vanguardia literaria y filosófica, el psicoanálisis se convirtió entonces en el símbolo de una asombrosa revolución del espíritu.
Encontramos huellas de esa dicha de vivir en _Psicopatología de la vida cotidiana_ , escrita como folletín y publicada en dos partes en una revista en 1901, para ser luego editada como libro, retocado sin cesar y aumentado a lo largo de los años. Así como el análisis del sueño sacaba a la luz el continente nocturno del pensamiento, esta nueva obra, más moderna en ciertos aspectos, mostraba que el inconsciente se manifiesta de manera permanente a través de los fenómenos normales de la vida psíquica de todos los hombres despiertos y de buena salud. Ese texto sería la alegría de los escritores, los poetas, los lingüistas, los estructuralistas, los autores de novelas policíacas, y de Jacques Lacan. Con un placer infinito, Freud se apoderaba de las palabras, la sintaxis, los discursos, los relatos: olvidos, lapsus, errores, actos fallidos, gestos intempestivos, recuerdos encubridores. Todo ese material lingüístico, decía, no hace sino delatar una verdad que escapa al sujeto para constituirse, sin que él lo sepa, en un saber organizado, una formación del inconsciente.
Antes de que Freud explorara esta cuestión, muchos autores ya habían reflexionado sobre el estatus de la «asociación libre» y destacado que permitía descifrar en el sujeto una parte desconocida por él mismo. Por ejemplo, Hans Gross, magistrado austríaco y padre fundador de la criminología, se había interesado en el lapsus y su valor de revelación en ciertos casos de falsos testimonios. En cuanto a sus alumnos, habían perfeccionado un método de investigación —una «prueba asociativa»— utilizable en la realización de las pesquisas y las instrucciones.
Pero Freud iba mucho más lejos: afirmaba que esos errores y otras equivocaciones eran la manifestación de un deseo reprimido, a menudo de carácter sexual, que venía a contradecir de manera radical una intención consciente. Y como siempre, recurría a numerosas anécdotas tomadas de su vida privada o la de su entorno. A través de la lengua alemana, y con el acento puesto en el prefijo _ver-_ , trazaba el cuadro lógico de todos los fallos del discurso: _versprechen_ (lapsus línguae), _verhören_ (lapsus auditivo), _verlesen_ (lapsus de lectura), _verschreiben_ (lapsus de escritura), _vergreifen_ (gesto fallido), _vergessen_ (olvido de palabras o nombres). A ello se sumaba un estudio de las creencias, las casualidades y las supersticiones.
¿Habrá de sorprendernos que ese libro, dedicado a la traición y las maneras de detectarla, haya puesto en escena la ruptura entre Freud y Fliess contra un fondo de actos fallidos y acusaciones recíprocas? Sea como fuere, en el momento de terminar la primera parte, con un epígrafe sacado de _Fausto_ y encontrado por el propio Fliess, Freud quiso una vez más convencerse de que la recepción que se le reservaba sería negativa: «[La obra] me produce un disgusto grandioso, cabe esperar que para otros sea todavía mayor. El trabajo carece de toda forma y hay en él una diversidad de cosas prohibidas». Y junto a estas palabras —o «cosas prohibidas»— ponía las tres cruces cristianas del conjuro, a las que se adjudicaba tradicionalmente el poder de curar una enfermedad o disipar un hechizo.
Freud se equivocaba una vez más: ese libro luminoso fue recibido con entusiasmo por un vasto público y contribuyó no solo a su celebridad sino a popularizar el concepto de inconsciente.
Y mientras volvía a dudar de sí mismo y se sentía más perseguido que nunca, Freud, al contemplar un objeto de su colección, soñó una vez más con alejarse de Viena: «Un trozo de muro de Pompeya con centauro y fauno me traslada a la Italia anhelada». Y añadía, pensando en su temporada en París: « _Fluctuat nec mergitur»_.
En una carta de septiembre de 1900 dirigida a Martha y escrita en Lavarone, una pequeña ciudad del Tirol del Sur, incluía una frase que resumía tanto su inclinación por el viaje como su deseo de llegar a Roma para, desde allí, escapar hacia el sur: «¿Por qué, entonces, dejamos ese lugar de belleza y calma ideales y abundante en setas? Simplemente porque apenas queda una semana y nuestro corazón, como lo hemos comprobado, tiende al sur, a los higos, las castañas, el laurel, los cipreses, las casas ornadas de balcones, los anticuarios, y así de seguido».
Un año después, el 2 de septiembre de 1901, acompañado por Alexander, tomó por fin posesión de Roma, la ciudad tantas veces deseada, eludida, rechazada:
Llegado a Roma después de las dos, me cambié a las tres después del baño y me convertí en romano. Es increíble que no hayamos venido años antes [...]. Mediodía frente al Panteón, y esto es pues lo que he temido durante años: hace un calor casi delicioso, y como consecuencia una maravillosa luz se difunde por doquier, aun en la Sixtina. Por lo demás, se vive divinamente si uno no está obligado a deslomarse para ahorrar. El agua, el café, la comida, el pan: excelentes [...]. Hoy introduje la mano en la _Bocca de la verità_ [ _sic_ ] jurando volver.
El viaje a Roma no era solo el cumplimiento de una revancha soñada. La ciudad era también el lugar de grandes promesas arqueológicas, de un reencuentro con la naturaleza inmemorial de la femineidad. Roma era para Freud un antídoto a Viena, un remedio, una droga. Tierra prometida, ciudad gloriosa, reino de los papas y del catolicismo, devolvía a Freud a su búsqueda de otra parte. Ciudad bisexuada, ciudad adulada tanto por su potencia masculina como por sus encantos femeninos: «A diferencia de su enfoque de Inglaterra o París», destacará Carl Schorske, «su concepción de Roma es judía; es la de un extranjero, pero también es doble. Por un lado, Roma es masculina, es la ciudadela del poder católico, y el sueño-deseo de Freud, en cuanto liberal y en cuanto judío, es conquistarla. Por otro, al mismo tiempo la sueña femenina, Santa Madre Iglesia, prometedora recompensa que se visita con amor».
En las entrañas y las ruinas de Roma, Freud se inició en las dulzuras y las violencias de un saber prohibido. En su topografía descubrió el secreto de placeres infinitos: placeres de la boca, placeres del ojo, placeres del oído, placeres del alma. Como antes Goethe, sentía que la Italia romana lo metamorfoseaba.
Tres años después, durante su estancia de cinco días en Atenas, y tras una larga travesía marítima que lo había llevado de Trieste a Corfú, visitó por fin la Acrópolis: «Me puse mi mejor camisa para la visita a la Acrópolis [...]. Esto supera todo lo que hayamos visto hasta el día de hoy y lo que hayamos podido imaginar».
Al llegar al pie del Partenón, pensó una vez más en su padre. Pero en el país de los Olímpicos se trataba menos de vengarlo, como en Roma, que de expresar otra vez hasta qué punto el acceso a la cultura griega le había permitido superarlo. Bajo la lluvia Freud murmuró entonces al oído de Alexander las palabras que Bonaparte había pronunciado el día de su coronación, dirigidas a su hermano Joseph: «¿Qué habría dicho nuestro padre?». Y en el preciso momento en que se identificaba con Bonaparte, se sintió atravesado, como en una narración proustiana, por una fuerte culpa. Al adherirse con fervor a esa cultura clásica, ¿no había renunciado a una parte de su identidad judía? Además, lo asaltó entonces la sensación de que todo lo que veía existía realmente, y no solo en los libros. «No soy digno de semejante felicidad», pensó, sin dejar de tener la impresión de algo ya visto o ya vivido: doble conciencia, escisión. Algo extraño, como una vida ya vivida, asomaba a su conciencia, como si lo que veía no fuera real.
Retomó esa temática en un libro que él mismo consideraba como una diversión, y que marcaba sin embargo la última etapa de la trilogía de la madurez consagrada al sueño, los lapsus y los actos fallidos: _El chiste y su relación con lo inconsciente_.
Una vez más, Freud se presentaba en él como un experto en asuntos familiares y sobre todo como un «casamentero judío» ( _Schaden_ ) que contaba historias de pedigüeños ( _Schnorrer_ ) por medio de las cuales se expresaban, a través de la risa, los grandes y los pequeños problemas de la comunidad judía de Europa central enfrentada al antisemitismo. Dotado de un humor corrosivo, Freud adoraba coleccionar anécdotas para burlarse de sí mismo o de su entorno y reírse de las realidades más lóbregas. Una manera como cualquier otra de enviar sus recuerdos al _Yiddishland_ , territorio de sus ancestros mercaderes de aceite y telas al que no regresaría jamás.
Tras la lectura de un famoso libro de Theodor Lipps, filósofo de la empatía, Freud decidió estudiar las relaciones entre el chiste y el inconsciente. Lo cual no le impidió inspirarse en Bergson e incluso en los aforismos de Lichtenberg, pero también en las historias cómicas contadas por Heinrich Heine o Cervantes.
En ese libro estudiaba en primer lugar la técnica del _Witz_ en cuanto permite representar social y psíquicamente el mecanismo del placer en presencia de al menos tres protagonistas: el autor de la broma, su destinatario y el espectador. Pero eso no basta —mostraba Freud— para alcanzar su objetivo último: el escepticismo. El chiste, como formación del inconsciente, debe acometer contra un cuarto participante, mucho más abstracto: la seguridad presunta del juicio. Por eso el chiste siempre es, según Freud, una especie de «sinsentido». Miente cuando dice la verdad y dice la verdad por la vía de la mentira, como lo testimonia esta famosa historia judía:
En una estación ferroviaria de Galitzia, dos judíos se encuentran en el vagón. «¿Adónde viajas?», pregunta uno. «A Cracovia», es la respuesta. «¡Pero mira qué mentiroso eres! —se encoleriza el otro—. Cuando dices que viajas a Cracovia me quieres hacer creer que viajas a Lemberg. Pero yo sé bien que realmente viajas a Cracovia. ¿Por qué mientes entonces?»
Si Freud veía el sueño como la expresión del cumplimiento de un deseo conducente a una regresión hacia el pensamiento en imágenes, hacía del chiste un productor de placer que autorizaba el ejercicio de una función lúdica del lenguaje. Su primer estadio, señalaba, es el juego infantil, y el segundo la broma: «La euforia que aspiramos a alcanzar por estos caminos no es otra cosa que el talante [...] de nuestra infancia, en la que no teníamos noticia de lo cómico, no éramos capaces de chiste y no nos hacía falta el humor para sentirnos dichosos en la vida».
Los niños y la infancia tenían un lugar esencial en la vida de Freud. Y como a su entender todos los problemas afectivos de los adultos encontraban allí su origen, se propuso escribir una pequeña obra en la cual pudiera exponer con claridad sus teorías sobre la sexualidad infantil y, más en general, sobre la sexualidad humana. El resultado fueron los _Tres ensayos de teoría sexual_.
Tras la suntuosa trilogía del cambio de siglo, tanto relato autobiográfico como exploración de las diversas formaciones del inconsciente, Freud pretendía ahora, por lo tanto, abordar un dominio que desde hacía años constituía el objeto de una multitud de estudios de pedagogos, médicos, juristas y sexólogos. Sin embargo, y al contrario de lo que sostiene una leyenda tenaz, no fue el héroe de una gran demolición del «verde paraíso de los amores infantiles». En 1905, cuando emprendió este nuevo trabajo, ese dominio, en efecto, ya había sido ampliamente explorado por los científicos de la época, que tenían la convicción —lo hemos sugerido— de que el niño era un ser perverso y polimorfo. No obstante, Freud contribuyó a deconstruir aún más el universo de la infancia al describir la sexualidad infantil como una «disposición perversa polimorfa». La utilización del término _Sexualtheorie_ marcaba deliberadamente la ruptura con los enfoques anteriores, porque Freud designaba con ello las hipótesis planteadas por los científicos y las «teorías» o representaciones fantasmáticas inventadas por los niños —y a veces por los adultos— para resolver el enigma de la copulación, la procreación, el engendramiento y la diferencia de los sexos.
En función de esa ambigüedad, Freud describía con humor y sin valerse de la más mínima jerga psiquiátrica, las actividades sexuales de los niños, y con ese fin ponía en juego todos los conocimientos que había acumulado sobre el tema, fuera en su infancia, fuera en contacto con sus propios hijos. Mencionaba sin embarazo ni obscenidad los chupeteos, tal o cual juego con los excrementos, la defecación, las diferentes maneras de orinar o decir palabrotas. En síntesis, hacía del niño de menos de cuatro años un ser de goce, cruel y bárbaro, y capaz de entregarse a toda clase de experiencias a las que, sin embargo, se vería obligado a renunciar en la edad adulta. De ahí la idea de los diferentes estadios —anal, oral, genital y más adelante fálico— tomada del evolucionismo, que servía para definir las etapas de la vida subjetiva conforme a los objetos escogidos: las heces, el pecho, los órganos genitales.
Freud añadía que la sexualidad infantil no conoce ni ley ni prohibición y que apunta a todos los fines y todos los objetos posibles. Y por eso las «teorías» fabricadas por los niños constituyen un verdadero pensamiento mágico: los bebés vienen al mundo por el recto, los seres humanos, sean hombres o mujeres, dan a luz por el ombligo, etc.
En un estilo diáfano y directo, Freud arrancaba con ello la antigua _libido sexualis_ al discurso médico para hacer de ella un determinante fundamental de la psique: la meta de la sexualidad humana, decía, no es la procreación sino el ejercicio de un placer que se basta a sí mismo y escapa al orden de la naturaleza. La sexualidad se apoya en una pulsión (un impulso), manifestada a través de un deseo de satisfacerse mediante la fijación en un objeto. Hay que controlarla, es cierto, pero indudablemente no erradicarla por medio de castigos corporales.
Al construir su doctrina sexual en torno de los términos de pulsión, libido, estadio, deseo o búsqueda del objeto, Freud liberaba al niño —y por ende al adulto— de todas las acusaciones que habían alimentado las prácticas médicas de fines del siglo XIX tendentes a reprimir las manifestaciones de su sexualidad, y sobre todo las procedentes de la «pedagogía negra». De acuerdo con esta óptica, además, se veía al niño masturbador ya no como un salvaje cuyos malos instintos había que domeñar, sino como el prototipo del ser humano en devenir. Freud normalizaba la «aberración sexual» al liberarla de todo enfoque en términos de patología o de disposición innata comparable a una «tara» o una «degeneración».
Fue muy natural entonces que llegara a analizar las perversiones sexuales presentes en los adultos, todas esas prácticas (pedofilia, fetichismo, zoofilia, sadomasoquismo, inversión, etc.) que los sexólogos de su época trataban de manera tan ostentosa. Pero, en vez de catalogarlas, Freud intentaba relacionarlas con una estructura ligada a determinado estadio de la evolución subjetiva. En ese marco en particular, hacía de la homosexualidad no solo la consecuencia de una bisexualidad presente en todos los seres humanos, sino un componente adquirido de la sexualidad humana: una inclinación inconsciente universal. De ahí esta célebre fórmula en la que ya había pensado en 1896: «La neurosis es, por así decir, el negativo de la perversión».
Con ese libro, que sufriría incesantes modificaciones, Freud abría el camino al desarrollo del psicoanálisis infantil y a una vasta reflexión sobre la educación sexual. Promovía la tolerancia de la sociedad hacia las diferentes formas de sexualidad —y en especial la homosexualidad— e insistía en que los adultos no mintieran a los niños acerca de su origen.
Comenzó así a imponerse una forma original de concebir el universal de la sexualidad. Con el paso de los años, ese pensamiento contribuyó a la extinción de la sexología —que había sido, empero, su matriz primera— y, en la segunda mitad del siglo XX, al auge de los trabajos de historiadores y filósofos sobre la historia de la sexualidad en Occidente, de Michel Foucault a Thomas Laqueur, pasando por John Boswell.
Una vez más, Freud se había convencido de que su nuevo libro estaba destinado a escandalizar desde el momento mismo de su publicación, y de que haría «universalmente impopular» a su autor. Con cada reedición se quejaba de la mala acogida que se le reservaba. En realidad, en 1905, y aunque no tuvo gran difusión, la obra suscitó una mayoría de artículos favorables. Sin embargo, algunos años después, y a medida que la doctrina psicoanalítica se difundía en las sociedades occidentales —a través de un movimiento organizado y nuevas publicaciones—, se la consideró retrospectivamente como una obra nociva, obscena, pornográfica, escandalosa, etc.
Fue pues en el momento en que el freudismo comenzaba a acceder al reconocimiento internacional cuando se levantaron frente a él las acusaciones de pansexualismo. La resistencia a esa nueva teoría de la sexualidad, expresada en los _Tres ensayos_ , se convirtió entonces en el síntoma de su progreso activo.
En 1909, en un violento ataque al psicoanálisis, el psiquiatra alemán Adolf Albrecht Friedländer afirmó que este debía su éxito a una presunta «mentalidad vienesa», que al parecer atribuía una importancia fundamental a la sexualidad. Retomaba con ello una tesis nacionalista, la del _genius loci_ , muy en boga desde el nacimiento del antisemitismo y la psicología de los pueblos, y según la cual cada nación podía no solo ser diferente a otra, sino superior a ella. Sobre esa base, la acusación de pansexualismo pudo servir de caballo de batalla a un antifreudismo primario en plena expansión. El término permitía afirmar, en efecto, que esa doctrina no era sino la expresión de una cultura que aspiraba a dominar a otra.
En Francia, país particularmente germanófobo, la teoría sexual de Freud se asimiló a una visión bárbara de la sexualidad, calificada de germánica, «teutona» o _boche_. A esa _Kultur_ alemana se oponía la presunta luminosidad cartesiana de la «civilización» francesa, mientras que en los países escandinavos y el norte de Alemania, al contrario, se acusaba al freudismo de privilegiar una concepción «latina» de la sexualidad, inadmisible para la «mentalidad» nórdica.
En esa época Freud recibió, en consultas breves, a personalidades del mundo artístico, curiosas por conocerlo, y que dejaron de él testimonios originales, retratos a través de los cuales se revelaba el entusiasmo de un hombre embargado por la creencia en su poder de descifrador de enigmas.
En 1905 el joven poeta suizo Bruno Goetz, que asistía en Viena a cursos sobre el hinduismo, sufrió violentas neuralgias faciales. Freud había leído algunos de sus poemas. Durante una hora Goetz le habló de su padre, capitán de altura, y de sus desgraciados amores con algunas muchachas y cierto marinero al que devoraba a besos. Freud lo obligó en principio a evocar un recuerdo de infancia ligado al dios Poseidón y le dijo que su caso no era apto para el análisis. Para terminar, con tono paternal, le recomendó que se alimentara bien y comiera carne y le entregó una receta y un sobre con doscientas coronas: «Pequeños honorarios por la alegría que me han procurado sus versos y la historia de su juventud».
Algún tiempo después, cuando volvió a verlo, lo previno contra la lectura del _Bhagavad-Gita_ , que podía llegar a sumirlo en un estado de anonadamiento. Las neuralgias cesaron:
Soy médico, dijo, y desearía ayudar en la medida de mis posibilidades a toda esa gente que interiormente vive hoy en un infierno. Y no es en un más allá, sea el que fuere, donde la mayoría vive en un infierno, sino aquí mismo, en la tierra. Eso es lo que Schopenhauer supo ver con mucha justeza. Mis conocimientos, mis teorías y mis métodos deben hacerles tomar conciencia de ese infierno, para que puedan liberarse de él. Solo cuando los hombres sepan respirar libremente volverán a aprender lo que puede ser el arte. Hoy hacen mal uso de él como un narcótico, para deshacerse, al menos por algunas horas, de sus tormentos. El arte es para ellos una suerte de aguardiente.
Un año más adelante, Bruno Walter, director de orquesta en la Ópera de la corte imperial, consultó a Freud por una neuralgia del brazo que le impedía tocar el piano y dirigir a sus músicos. En lugar de iniciar una cura con él, Freud le aconsejó viajar a Sicilia, lo que permitió al músico descubrir maravillado los templos griegos, sin curarse empero de sus calambres. A su regreso, Freud utilizó la sugestión para intentar asumir la «responsabilidad» del mal de Walter, y lo convenció de que no pensara más en él. Walter logró olvidar sus dolores. Más adelante recurrió a una autoterapia, inspirada por el libro del médico romántico Ernst von Feuchtersleben sobre la dietética del alma. Superó entonces su incapacidad, siguió admirando a Freud y aconsejó a su amigo Gustav Mahler, que por su parte se había hundido en la melancolía, que fuera a verlo.
Tras varias cancelaciones, los dos hombres se encontraron por fin en Leiden, el 26 de agosto de 1910, durante cuatro horas, la duración de una larga caminata por las calles de la ciudad. «Supongo», le dijo Freud a Mahler, «que su madre se llamaba Marie. Algunas de sus frases en esta conversación me llevan a pensarlo. ¿Cómo es que se casó con una mujer que tiene otro nombre, Alma, cuando es indudable que su madre tuvo en su vida un papel predominante?» Mahler respondió que había tomado la costumbre de llamar a su mujer Marie (y no Alma). En el transcurso de la conversación el músico logró comprender por qué la intrusión repetitiva de una melodía banal «echaba a perder» su música. En su infancia, a raíz de una disputa conyugal particularmente violenta entre su padre y su madre, se había lanzado a la calle, donde oyó una canción popular vienesa tocada en un organillo: la canción se le había fijado en la memoria y volvía bajo la forma de una melodía molesta.
Freud no advertía aún que en el corazón de esa época tan bella, que había soñado tanto con el gran florecimiento de la Europa de la Ilustración, en la huella del progreso, la industrialización y la democracia, se perfilaba, como un sombrío presagio, un odio recíproco de las naciones que iba a llevar al continente, a través de la Primera Guerra Mundial, a su propia aniquilación.
A fuerza de contemplarse en el espejo de su tedio, la burguesía más culta del mundo occidental había omitido tener en cuenta la gran miseria de los pueblos. Y el psicoanálisis, inventado por un judío de la Haskalá, ciencia teutona para unos y latina para otros, sufría ya las consecuencias: «No veíamos los signos de fuego escritos en el muro», escribiría Stefan Zweig acerca de ese «mundo de ayer»,
e, inconscientes como antaño el rey Baltasar, nos llenábamos con todos los platos deliciosos del arte, sin echar miradas ansiosas al porvenir. Y solo cuando, decenas de años después, techos y murallas se derrumbaron sobre nuestra cabeza, reconocimos que los cimientos estaban socavados desde hacía mucho y que con el nuevo siglo se había iniciado la ruina de la libertad individual en Europa.
### 2
Discípulos y disidentes
El psicoanálisis, esa extraña disciplina a medio camino de la arqueología, la medicina, el análisis literario, la antropología y la psicología más abisal —la de un más allá de lo íntimo—, nunca fue reducido por su inventor a un enfoque clínico de la psique. Freud quiso hacer de él, desde el inicio, un sistema de pensamiento hecho y derecho, capaz de expresarse a través de un movimiento del que su creador fuera, no el jefe, sino el maestro. Por eso inscribía su doctrina en la herencia de las grandes escuelas filosóficas de la antigua Grecia, a la que sumaba cierta tradición laicizada del mesianismo judeocristiano. En una época en que se desarrollaban el feminismo, el socialismo y el sionismo, Freud soñaba pues —él también— con conquistar una nueva tierra prometida y convertirse en el Sócrates de los tiempos modernos. Y para llevar a cabo su proyecto no podía conformarse con una enseñanza universitaria. Tenía que fundar un movimiento político.
A los cuarenta y cuatro años ya se había granjeado una notoriedad real dentro del vasto movimiento de renovación de la psicología y la psiquiatría dinámica que recorría Europa desde fines del siglo XIX, con el telón de fondo del poderoso ascenso de la incredulidad en materia de religión y una puesta en entredicho de las ilusiones alimentadas por esta. Por eso Freud comenzó a reunir a su alrededor, en un principio de manera informal, un círculo de discípulos que, en su mayoría, no estaban en el mismo nivel que los integrantes del mundo académico vienés. Médico de las curas termales, Rudolf Reitler, perteneciente a una familia de la burguesía católica, fue el primer profesional de ese cenáculo. En cuanto a Max Kahane, médico melancólico y francoparlante de origen rumano, amigo de juventud de Freud, apasionado por la hipnosis y diversas terapias, acompañó los comienzos del movimiento sin adherirse, empero, a la concepción freudiana de la sexualidad.
En el otoño de 1902 Reitler y Kahane participaron, junto con Alfred Adler y Wilhelm Stekel, en la fundación de la Sociedad Psicológica de los Miércoles (Psychologische Mittwochs-Gesellschaft, PMG), primer círculo de la historia del movimiento psicoanalítico. Pronto se les unió Paul Federn, que se comparaba gustoso con el apóstol Pablo o con un oficial subalterno del ejército psicoanalítico, y luego Hugo Heller, editor y librero; a continuación, Max Graf, musicólogo, y Eduard Hirschmann, psicobiógrafo obstinado, y por último Isidor Sadger y su sobrino Fritz Wittels, ambos fanáticamente freudianos y misóginos.
Inmersos en el espíritu vienés y casi todos judíos, esos hombres treintañeros —nacidos entre 1865 y 1880— tomaron la costumbre de reunirse los miércoles por la noche, después de cenar, en la casa de Freud. En cada sesión, sentados a una mesa oval, observaban el mismo ritual: ponían en una urna el nombre de los oradores del día y después escuchaban en silencio la comunicación de aquel cuyo nombre había salido sorteado. Durante una breve pausa tomaban café negro y comían deliciosos pasteles. Se lanzaban entonces a interminables discusiones mientras fumaban una profusión de cigarros y cigarrillos: estaba prohibido leer un documento redactado de antemano y ninguna mujer perturbaba ese banquete cuyo profeta secular era, contra su voluntad, el propio Freud. En esa época, y por breve tiempo, este tuvo siempre la última palabra y todos parecían venerarlo. Sin el diálogo que mantuvo entonces con esta primera generación de discípulos Freud jamás podría haber nutrido su obra, como lo hizo, con modificaciones incesantes a la luz de lo que cada uno le aportaba.
Esos hombres que todavía no practicaban la cura psicoanalítica solían compararse con paladines. Intelectuales y militantes, eran muy representativos de la cultura de la _Mitteleuropa_. Al crear ese cenáculo procuraban calmar sus angustias y dar cuerpo a sus sueños de un mundo mejor. Cuando hablaban de sus casos clínicos se referían las más de las veces a sí mismos, a su vida privada a menudo tumultuosa, a su complicada genealogía familiar, a sus neurosis, a su identidad judía, a sus perturbaciones psíquicas y sexuales, a su rebelión contra los padres y, con frecuencia, a su profunda melancolía.
En una palabra, constituían en cierta forma una familia extensa y se asemejaban a sus pacientes, quienes, por lo demás, pertenecían a su misma clase social. Freud trató por sus patologías a muchos de ellos, y varios tomaron la costumbre de atender a sus íntimos o derivarlos al consultorio del maestro o de sus colegas. Esposas, amantes y hermanas se convirtieron así en pacientes y más adelante en terapeutas. En cuanto a los hijos de esos hombres del primer círculo, fueron los primeros en experimentar la cura freudiana, que solo cobró vigencia entre ellos a partir de 1904.
Fue así como el musicólogo vienés Max Graf conoció a Freud por medio de Olga Hönig, que había sido paciente de este en 1897, en el momento del abandono de la teoría de la seducción. Sus dos hermanos se habían suicidado y ella misma había sufrido una tenaz neurosis. Cuando Max visitó a Freud, le preguntó si el estado mental de la joven le permitía casarse con él. Freud dio su bendición y, en 1902, Graf se incorporó al cenáculo de los miércoles. Seis años después, bajo el control del propio Freud, dirigió la cura de su hijo Herbert. Había comenzado a tomar notas sobre la manera en que el niño hablaba de la sexualidad haciendo preguntas directas y dedicándose a tocarse el «hace-pipí». Bajo el nombre de «pequeño Hans», Herbert Graf se convertiría en un caso célebre, que permitiría a Freud ilustrar sus teorías sobre la sexualidad infantil y dar un impulso decisivo al psicoanálisis de niños. Freud, por tanto, había tratado a la madre y después, cuando el padre se convirtió en su discípulo, aceptó que fuera, bajo su control, el analista de su propio hijo. En esos inicios, la historia del psicoanálisis no fue otra cosa que la de una familia recompuesta.
Médico y escritor prolífico, Stekel consideraba a Freud como un Cristo y se veía a sí mismo como su apóstol. Y adoptó las tesis sexuales de su maestro con un sectarismo que lo remitía a sus propios problemas neuróticos. Víctima de una compulsión patológica a la masturbación, el _Herr Professor_ lo trató a lo largo de ocho sesiones sin lograr liberarlo de sus síntomas. Freud admiraba su talento y su inventiva y tomó de él algunos temas que haría fructificar en su obra: en especial sobre el sueño, así como sobre la represión. Muy pronto, sin embargo, manifestó una fuerte exasperación hacia él, al extremo de considerarlo como un «completo cerdo» y querer apartarlo de su lado.
Si Alfred Adler fue el primer gran disidente de la historia del movimiento psicoanalítico, del que se separó en 1911, fue sin duda porque, al contrario de Stekel, nunca se adhirió a las tesis freudianas. Dentro de la comunidad de los miércoles ya elaboraba un sistema de pensamiento original centrado en la prevalencia del yo —la psicología individual—, que no debía nada a aquel de quien fue compañero y rival durante nueve años. Originario de una familia de comerciantes judíos de la comunidad germanoparlante del Burgerland, bastante más próspera que la de Galitzia oriental, Adler atribuía mucha más importancia a los lazos grupales y de fraternidad que a las relaciones intrapsíquicas y genealógicas. En tanto que Freud hacía de la familia la clave de bóveda de su teoría, al punto de querer aplicar su complejo edípico a todas las sociedades, Adler la consideraba como una comunidad cambiante cuyo estatus debían estudiar la sociología, la historia y la antropología. A su juicio, la neurosis era la consecuencia de una lucha entre lo femenino y lo masculino, y derivaba de un sentimiento de inferioridad reprimido ya en la primera relación del niño con la sexualidad. Adler se interesaba en el marxismo y frecuentó a León Trotski después de casarse con Raissa Epstein, que por su parte era una presencia asidua en las filas de la _intelligentsia_ rusa. Por añadidura, le era imposible ver a Freud, catorce años mayor que él, como un padre al que hubiera que someterse incondicionalmente.
Adler no solo no fue jamás freudiano ni pudo aceptar en ningún momento la mitología de los Labdácidas, sino que no tenía con su judeidad la misma relación que Freud. Aunque no lo animara, como sí sucedía con Karl Kraus u Otto Weininger, un sentimiento de «autoodio judío», en 1904 quiso escapar a su condición convirtiéndose al protestantismo, lo cual no le impidió llevar una vida de librepensador partidario de un socialismo reformista. Ya en esos momentos se dio cuenta de que no podría ser un discípulo como los demás integrantes del cenáculo. Y por ello comenzó a cuestionar la idea de que la causalidad sexual pudiese ser el eje central de una doctrina psicológica centrada, a su vez, en una concepción casi ontológica de la familia y de la fijación incestuosa del niño con el padre del sexo opuesto. La guerra y la ulterior ruptura entre ambos hombres eran inevitables. Uno, burgués elegante y cultivado, con títulos universitarios, seguro de su genio, quería construir un ejército de misioneros; otro, menos brillante y dolorido por la falta de reconocimiento académico, estaba en busca de un foro de discusión e intercambio: «Las teorías de Adler se apartaban en exceso del camino recto. Era hora de hacerles frente. Él olvida las palabras del apóstol Pablo que usted conoce mejor que yo: "si no tengo amor...". Ha creado para sí un sistema universal, sin amor, y yo estoy a punto de ejercer en su contra la venganza de la diosa Libido ofendida».
En mayo de 1906 algunos discípulos regalaron a Freud, que cumplía cincuenta años, una medalla de bronce grabada por Karl Maria Schwerdtner e inspirada en un soberbio dibujo _Jugendstil_ ( _Art Nouveau_ ) de Bertold Löffler, que servía de ex libris al _Herr Professor_. En el anverso aparecía su busto de perfil y en el reverso una representación estilizada de la escena de Edipo frente a la Esfinge. Desnudo y apoyado en un bastón, este Edipo vienés, pensativo y musculoso, no se asemejaba a ninguno de los retratos conocidos del personaje de Sófocles. Otro tanto ocurría con la Esfinge, representada con los rasgos de una mujer moderna un poco bruja, cuya parte animal era claramente menos importante que la parte humana. La inscripción grabada en griego había sido escogida por Federn y no remitía de manera alguna al «complejo de Edipo» sino a la verdadera significación de la _hybris_ sofocleana: «El que resolvió el famoso enigma y fue un hombre de muy grande poder».
Al leer esas palabras, Freud pareció olvidar por un instante su interpretación desviada de la tragedia de Sófocles para recordar con emoción que, durante sus estudios universitarios, había adquirido la costumbre de observar los bustos de los profesores célebres y se decía que, tal vez, el suyo se colocaría algún día junto a ellos, acompañado de la famosa cita.
Ese año el editor Hugo Heller envió a Freud y a varios otros intelectuales un cuestionario donde les pedía que nombraran diez libros que les gustara tener siempre junto a ellos. La respuesta de Freud, enviada el día de Todos los Santos, aclaraba al editor que su intención no había sido seleccionar obras maestras de la literatura mundial, sino «compañeros», «buenos amigos» a los «uno debe parte de su conocimiento de la vida y de su cosmovisión propia». Y a continuación daba, sin ningún orden, diez nombres y diez títulos: Multatuli (seudónimo de Eduard Douwes Dekker), _Cartas y obras_ ; Rudyard Kipling, _El libro de la jungla_ ; Anatole France, _Sobre la piedra blanca_ ; Émile Zola, _Fecundidad_ ; Dmitri Merezhkovski, _El romance de Leonardo_ ; Gottfried Keller, _La gente de Seldwyla_ ; Conrad Ferdinand Meyer, _Los últimos días de Hutten_ ; Thomas Babington Macaulay, _Estudios_ ; Theodor Gomperz, _Pensadores griegos_ , y Mark Twain, _Escritos con humor_. Esto es: dos escritores franceses, un holandés, dos suizos, dos ingleses, un ruso, un austríaco y un norteamericano, todos asociados a la tradición de la Ilustración. Una obra sobre la belleza de la jungla opuesta a los artificios de la vida moderna; otra contra el colonialismo; otra sobre la abolición de la esclavitud; una cuarta sobre la arqueología; otra más sobre el amor a Grecia; una acerca de la maternidad (cuyo autor era un gran dreyfusista); otra sobre la apología de un reformista prusiano; una más dedicada al goce dionisíaco; otra sobre la vida del mayor pintor del Renacimiento, y una última consagrada a historias macabras tratadas con humor por un escritor que defendía a los judíos. Freud había aceptado plegarse a una especie de prueba asociativa, que autorizó a sus lectores y futuros exégetas a entregarse a una multitud de interpretaciones sobre su vida y su obra. Como Edipo, los descifradores de enigmas se divirtieron de lo lindo.
En esa época Freud hizo entrar en su círculo de iniciados a un joven autodidacta, aprendiz de tornero, de veintiséis años: Otto Rank. Hijo de un artesano joyero alcohólico, originario como Adler del Burgenland, padecía un reumatismo articular y temía tanto esta enfermedad como su fealdad física. Por añadidura, había sido víctima de abusos sexuales en su infancia y sufría de una fobia por la cual no podía tocar nada sin guantes.
Freud lo quería profundamente y muy pronto lo consideró como su hijo adoptivo. Lo impulsó a ir a la universidad y obtener un doctorado de filosofía. Pero, en especial, lo nombró secretario de la Sociedad de los Miércoles y le encargó la transcripción de las actas de las reuniones. El cenáculo se convirtió entonces en un sitio privilegiado de la memoria y Rank fue su primer archivista. En las actas, cuidadosamente conservadas y luego legadas a la posteridad, él relata el nacimiento de un movimiento y se erige en el mensajero de un pensamiento dialéctico elaborado por el cenáculo.
En 1907, cuando la sociedad contaba aún con veintiún miembros activos, Freud decretó su disolución. Deseoso entonces de respetabilidad y con el propósito de marginar a algunos vieneses que en su opinión eran demasiado exaltados, demasiado fanáticos o demasiados disidentes, creó una verdadera asociación, la Wiener Psychoanalytische Vereinigung (WPV), la primera institución psicoanalítica de la historia del freudismo. Suprimió la regla que obligaba a todos los miembros a tomar la palabra en ciertas condiciones y sancionó una reglamentación que se fundaba, de facto, en la existencia de una jerarquía entre el maestro y sus alumnos e incluso entre _unos_ maestros y _unos_ alumnos. Y en particular propició la incorporación a esa nueva institución de discípulos «extranjeros», sobre todo Max Eitingon, Sándor Ferenczi, Karl Abraham, Carl Gustav Jung y Ernest Jones.
Fue así como se constituyó, entre 1907 y 1910, el primer núcleo de grandes discípulos de Freud —todos hombres— que, progresivamente, contribuyeron a la internacionalización del movimiento. Las más de las veces, se dedicaban a la práctica del psicoanálisis tras haber hecho una cura con alguno de sus pares o con el propio Freud, Federn o Ferenczi. El banquete socrático fue sucedido, de tal modo, por una especie de academia cruzada de disputas pero que tenía sobre todo la función de llevar a la práctica una política del psicoanálisis descentrada de Viena y orientada hacia Europa, y pronto hacia el continente americano. Y para asegurar la transmisión del saber psicoanalítico, Freud y sus discípulos fundaron tres revistas con la ayuda de Hugo Heller: el _Jahrbuch für Psychoanalytische und Psychopathologische Forschungen_ en 1909, el _Zentralblatt für Psychoanalyse. Medizinische Monatsschrift für Seelenkunde_ en 1910, y por último _Imago_ dos años después. El primero era una publicación generalista; el segundo, el órgano del movimiento internacional, y el tercero tenía una inspiración más estética.
El contacto con los miembros de este nuevo círculo llevó a Freud a reanudar la intensa actividad epistolar que echaba de menos desde la ruptura con Fliess. Cada día escribía una decena de misivas en caracteres góticos, en las cuales se ocupaba tanto de cuestiones teóricas, clínicas o políticas como de problemas cotidianos. En esa correspondencia, el tuteo, reservado a los amigos de juventud y los miembros de la familia, estaba excluido en el caso de los discípulos, hombres o mujeres: _Lieber Herr Kollege_ , _Herr Doktor_ , _Lieber Freund_ , _Dear Jones_ , _Liebe Marie_ , querida princesa, _Liebe Lou_ , _Verehter Freund und liebster alle Männer_.
_Herr Professor_ pedía a todos sus corresponsales noticias de sus esposas e hijos, se interesaba por su salud y no olvidaba nunca la fecha de sus cumpleaños. Cada discípulo ocupaba en esos intercambios un lugar singular, y con cada uno Freud hablaba de los otros, con objeto de establecer entre ellos un vínculo que pasara por él. A veces, en un mismo día, decía cosas contradictorias y a menudo cometía verdaderas indiscreciones so pretexto de transmitir a tal o cual confidencias sobre otro, y recíprocamente. De ese modo, cada uno tenía la impresión de ser el preferido del maestro. Esos hombres, que tenían ahora la misión de fundar a su alrededor escuelas y grupos a fin de divulgar la nueva doctrina, eran militantes consagrados a la causa de lo que era, a su juicio, la más grande revolución del siglo XX. Ninguno de ellos era servil y ninguno dudaba del genio de aquel a quien habían escogido por maestro. Freud formaba parte de su familia, de su vida íntima, de su historia.
Este progreso hacia una internacionalización del movimiento psicoanalítico estuvo en el origen, no solo de sus diferentes conflictos doctrinales o transferenciales, sino también de la construcción de una historia oficial fundada en la «leyenda del héroe». Con el paso de los años, los suyos consideraron a Freud como un pensador solitario injustamente atacado pero gloriosamente triunfante sobre sus enemigos, tanto de fuera como de dentro. En 1914 él mismo hizo su aporte a esa leyenda al publicar una contribución a la historia del movimiento psicoanalítico en la cual afirmaba que el psicoanálisis era su «asunto» ( _die Sache_ ): «En efecto, el psicoanálisis es creación mía, yo fui durante diez años el único que se ocupó de él, y todo el disgusto que el nuevo fenómeno provocó en los contemporáneos se descargó sobre mi cabeza en forma de crítica». Once años después, a petición de un editor, escribió, en la misma línea, una presentación de sí mismo ( _Selbstdartellung_ ) en la cual exponía su _Ego-Historie_ y la génesis subjetiva de sus descubrimientos.
Magníficamente escritas, esas dos obras unificaban la historia caótica de los orígenes del psicoanálisis en un relato mítico verosímil, estructurado por la dualidad freudiana del padre humillado y el hijo rebelde promovido a un destino heroico. En el ínterin, Freud añadió a esa construcción la idea de que el psicoanálisis, en cuanto disciplina, suponía un descentramiento del sujeto que pasaba por tres humillaciones narcisistas: no ocupar ya el centro del universo, no estar ya fuera del mundo animal, no ser ya dueño y señor en su propia morada. No conforme con asignar a su doctrina un destino edípico, Freud, que se había identificado con Aníbal y Bonaparte, ahora también se veía como el heredero de Copérnico. Nueva confirmación de una inquietud permanente: procurar que su movimiento pudiera referirse a una epopeya de los orígenes, una canción de gesta con sus fábulas, sus mitos, su historia piadosa, sus imágenes.
En 1908 se celebró en Salzburgo la primera gran reunión de los nuevos «psicólogos freudianos». Cuarenta y dos personas procedentes de seis países participaron en ella y se propusieron reencontrarse dos años después en Nuremberg. Firmemente decidido a sacar al psicoanálisis del «gueto judío vienés», Freud fundó entonces, en 1910, con Ferenczi, la Internationale Psychoanalytische Vereinigung (IPV), a la que apodó el «Verein» (asociación). Y puso su dirección en manos de Jung. En su alocución Ferenczi se entregó a un brillante ejercicio de historiador del clan, distinguiendo tres grandes etapas en el movimiento psicoanalítico: la llamada época «heroica» (1896-1907), durante la cual Freud había conformado un pequeño cenáculo; la llamada época «de Jung» (1907-1909), que le había permitido implantar el psicoanálisis en el terreno de la psiquiatría, y para terminar la llamada época «americana» (1909-1910), consecutiva a su viaje a la otra orilla del Atlántico.
Después de ese exaltado impulso, Ferenczi afirmaba la necesidad de que el movimiento se sometiera a una disciplina racional, a la vez que daba pruebas de una gran lucidez en lo concerniente al devenir de las organizaciones: «Conozco bien la patología de las asociaciones y sé hasta qué punto suelen reinar en las agrupaciones políticas, sociales y científicas la megalomanía pueril, la vanidad, el respeto de las fórmulas vacías, la obediencia ciega y el interés personal, en lugar de un trabajo concienzudo consagrado al bien común». Hasta 1918, después de Salzburgo y Nuremberg, el Verein celebraría sus congresos en el mundo germanoparlante, el de los imperios: Weimar (1911), Munich (1913) y Budapest (1918). A continuación, tras la Gran Guerra, de 1920 a 1936, la elección se ampliaría, con sus vaivenes, a distintos países: Holanda, Suiza, Gran Bretaña, y diversas ciudades: La Haya, Berlín, Salzburgo, Bad-Homburg, Innsbruck, Oxford, Wiesbaden, Lucerna, Marienbad.
Representante típico de la _intelligentsia_ de Budapest, Sándor Ferenczi era hijo de un librero judío de origen polaco que se había adherido a la causa del liberalismo y apoyado la primavera de los pueblos. Educado en el espíritu de la Ilustración por un padre al que adoraba, Ferenczi se había entregado con fervor a los estudios médicos, movido a la vez, como los intelectuales de su generación, por la convicción de que había que despojar a la antigua Hungría de sus sueños nostálgicos a fin de transformarla en un país moderno, semejante a las democracias occidentales.
Por eso se mostró desde el principio, a diferencia de Freud, abierto a los debates entablados por las revistas de vanguardia acerca del _Art Nouveau_ ( _Jugendstil_ ), la emancipación de las mujeres, la libertad sexual y la expansión de las nuevas ciencias del hombre. En 1905, cuando tenía treinta y dos años, y tras haber trabajado en el hospital Saint-Roch, puso un consultorio privado donde ejercía medicina general, neurología y psiquiatría, a la vez que trabajaba como perito judicial. Inmerso en el darwinismo, apasionado por la hipnosis, el espiritismo, la telepatía, el ocultismo y las mitologías, fascinado por el estudio de las drogas y los fenómenos psicosomáticos, tan conocedor de la filosofía como de la literatura, había asumido la defensa de los homosexuales —los «uranianos»— en un valeroso texto presentado ante la Asociación Médica de Budapest.
Sobre la base de los trabajos de Magnus Hirschfeld, Ferenczi refutaba todas las estigmatizaciones y se oponía a la teoría de la degeneración, haciendo valer la idea de la bisexualidad propia de la especie humana. Y salpicaba el texto con citas de Platón, Leonardo da Vinci, Miguel Ángel y Oscar Wilde:
Nadie castiga a los seres humanos que se aman con un amor heterosexual. De igual modo, la homosexualidad, en la medida en que no cause ningún daño a la sociedad, no debe ser sancionada. Los juristas tienen a veces el derecho de proteger los intereses de nuestra sociedad, pero no de castigar a alguien por un acto benigno. Cuando lo hacen, rechazan infaliblemente a seres de gran valor pero de desgraciados instintos que se convierten en víctimas de individuos turbios y miserables, lo cual no redunda en el interés de la sociedad.
Sensual, femenino y sensible al sufrimiento de sus pacientes, Ferenczi conoció a Freud en 1908 y se convirtió en su discípulo más cercano, no un delfín o un heredero, sino un hijo adoptivo amado por el maestro, a tal punto que este soñó con darle por esposa a su hija Mathilde. Ferenczi se autocalificaba de «paladín», «gran visir secreto» e incluso «astrólogo de corte» a quien le encantaba visitar a las videntes de Budapest. No vacilaba en embarcarse en controversias, y aunque rechazaba el autoritarismo de Freud jamás pensó en abandonarlo. Durante un cuarto de siglo los dos hombres intercambiaron mil doscientas cartas: un tesoro de invención clínica y teórica salpicado por confidencias y preciosos testimonios sobre las costumbres y la vida cotidiana de los freudianos de la Belle Époque. Mucho más terapeuta que Freud, Ferenczi inventó el concepto de contratransferencia y nunca dejó, a lo largo de su vida, de modificar los principios de la cura e introducir una empatía singular en la relación con sus pacientes y alumnos.
Como la mayoría de los discípulos del primer círculo, mezclaba las curas con la vida privada y los asuntos de familia. En 1908 emprendió el análisis de su amante, Gizella Pálos, todavía no divorciada de su primer marido, y cuya hija mayor, Magda, estaba casada con el propio hermano de Ferenczi, Lajos. Tres años después decidió analizar a Elma, la hija menor de Gizella, que sufría de depresión y de la que no tardó en enamorarse. Carta tras carta confió sus dificultades a Freud, que, una vez más, se entregó con deleite a sus actividades de «casamentero judío» y gran conocedor de los amores intrafamiliares. También él había pasado por situaciones idénticas, ya fuera al enamorarse de una joven cuya madre lo atraía, o al procurar arrancar a una novia de la influencia de una madre, a la vez que se convertía en cómplice de la otra hija de esta. Por añadidura, no dejaba de interrogarse sobre el deseo de incesto propio de la especie humana y sobre la cuestión de las relaciones entre amor y transferencia.
Confundido entre el deseo, el amor y la transferencia, Ferenczi decidió casarse con Elma, al mismo tiempo que forzaba a Freud a tomarla en análisis. Algún tiempo después dio marcha atrás y renunció a ese matrimonio, tras haber analizado su propia contratransferencia en el diván del maestro. En la creencia de que amaba a la hija, en realidad amaba a la madre y terminaría por casarse con ella al advertir que esta lo quería. En 1919, tras releer su intercambio epistolar donde se detallaba toda «la historia reciente de los desarrollos del psicoanálisis», Ferenczi testimonió un enorme agradecimiento a Freud por su solicitud:
En esta oportunidad comprendí como en una iluminación que, desde el momento en que usted me desaconsejara el casamiento con Elma, yo había dado pruebas de una resistencia contra su persona que ni siquiera el intento de cura psicoanalítica pudo superar, y que era responsable de todas mis susceptibilidades. Con rencor inconsciente en el corazón, seguí empero como «hijo» fiel todos sus consejos, dejé a Elma y me incliné otra vez por mi mujer actual [Gizella], con la que he perseverado, pese a innumerables y reiteradas tentaciones.
Así como se mostraba afectuoso con Ferenczi, Freud mantenía cierta distancia con Karl Abraham. Afable, atento, elocuente, culto, este último fue hasta su prematura muerte, en 1925, un ortodoxo inteligente de la doctrina psicoanalítica, un « _rocher de bronze»_ [«peñón de acero»], según las palabras de Freud, que consagró todos sus esfuerzos a la implantación de las ideas comunes en el medio psicoanalítico berlinés y a la organización de una sólida asociación de clínicos. El único discípulo que no buscó a Freud para pedirle su opinión sobre asuntos sentimentales o eventuales relaciones sexuales con sus pacientes, analizaría no obstante a su propia hija, Hilda Abraham, de seis años, futura psicoanalista, y describiría su «caso» en un artículo de 1913. En diciembre de 1907 se trasladó a Viena para conocer a Freud, que unos meses antes ya había recibido la visita de Max Eitingon, procedente de Zurich, y a quien analizaría durante unos «paseos vespertinos».
Segundo hijo de una familia de judíos ortodoxos originarios de Bielorrusia, Max Eitingon, sionista convencido, estaba acostumbrado desde la infancia a llevar una vida itinerante. Tenía doce años cuando su padre, rico comerciante peletero, se instaló en Leipzig; Max fue a la escuela en esa ciudad y luego comenzó estudios universitarios como oyente libre, primero en Marburgo y después en Heidelberg. En 1902, tras tomar la decisión de ser psiquiatra, hizo unas prácticas en la clínica del Burghölzli de Zurich bajo la dirección de Eugen Bleuler, y allí conoció a Carl Gustav Jung y Abraham, a quien volvería a ver en 1909 en Berlín, donde vivió hasta su partida definitiva a Palestina en 1934. En febrero de 1920, tras el derrumbe de los Imperios Centrales, llevaría a cabo, por amor al psicoanálisis, la gran obra de su vida: el Berliner Psychoanalytisches Institut (BPI), primer instituto de formación que iba a servir de modelo a todos los que se fundaron a continuación en el mundo entero. A lo largo de su existencia tumultuosa, Eitingon puso su fortuna al servicio del instituto, y también propuso, en el marco de una «policlínica», curas gratuitas para las personas desfavorecidas, pero de pago para los demás pacientes. En 1930 ya era por sí solo, según las palabras de Ernest Jones, «el corazón de todo el movimiento psicoanalítico internacional».
Situado en la colina arbolada del barrio de Riesbach, al sudeste de Zurich, el inmenso hospital del Burghölzli recibía desde su fundación en 1870 a pacientes con trastornos mentales. Los arquitectos habían tenido la precaución de levantar la estructura a espaldas del lago a fin de ahorrar la vista del agua a los internos que pudieran sentir la tentación de suicidarse. En un principio bajo la batuta de August Forel y luego de Eugen Bleuler, en los albores del siglo XX se había impuesto un nuevo enfoque de la locura en el corazón de esa prestigiosa fortaleza que, con el paso de los años, llegaría a ser un lugar de paso obligado para todos los especialistas en las afecciones del alma. En ese contexto, la apertura freudiana al mundo del sueño y el inconsciente suscitaba entusiasmo: los jóvenes terapeutas de la locura miraban la obra vienesa como una innovación capaz de hacer que el saber psiquiátrico se apartara del nihilismo terapéutico.
En 1898, cuando Bleuler asumió la dirección del establecimiento, la psiquiatría de lengua alemana —un faro en Europa y el mundo entero— estaba aún dominada por la nosografía de Emil Kraepelin. Contemporáneo de Freud, este había elaborado una clasificación rigurosa de las enfermedades mentales sin dejar de adherirse a una concepción represiva de la locura, que apenas buscaba mejorar la suerte de los alienados. Pese a su vigor, el sistema kraepeliniano ya estaba, empero, agrietándose bajo el efecto de los progresos realizados por un enfoque fundado en la escucha de los sujetos. Escuchar el sufrimiento de los pacientes, descifrar su lenguaje, comprender la significación de su delirio y establecer con ellos una relación transferencial: tal era el programa terapéutico promovido por el equipo hospitalario del Burghölzli.
Y por medio de un trabajo de largo aliento dedicado a la demencia precoz ( _Dementia praecox_ ), Bleuler sintetizó en 1911 ese enfoque y dio el nombre de esquizofrenia a una forma de locura caracterizada por una incoherencia del pensamiento y una actividad delirante. Sin renunciar a la etiología orgánica, situaba la enfermedad en el campo de las afecciones psicológicas y la caracterizaba por una disociación de la personalidad ( _Spaltung_ ) y un repliegue sobre sí mismo (autismo).
Aunque no compartía la concepción freudiana de la sexualidad, Bleuler proponía integrar el enfoque psicoanalítico en el tratamiento de las psicosis. De ahí la siguiente analogía: así como Freud había transformado la histeria en un paradigma moderno de la neurosis, Bleuler inventaba la esquizofrenia para hacer de ella el modelo estructural de la locura en el siglo XX.
En octubre de 1905, cuando Jung, por entonces asistente de Bleuler, se puso en contacto con Freud, este sabía ya que ese encuentro iba a ser decisivo para la historia de su movimiento. Hasta esa fecha, en efecto, la terapia psicoanalítica parecía exclusivamente destinada al tratamiento de las neurosis, pero he aquí que ahora se abría para ella, fuera de Viena y lejos de Berlín, el continente de la psicosis: una nueva «tierra prometida». Así como el psicoanálisis era un fenómeno urbano, que iba a la par con la transformación de la familia clásica y suponía la confrontación del sujeto consigo mismo, la psiquiatría, disciplina médica, seguía siendo tributaria de una concepción colectiva de los cuidados psíquicos. Además, desde mediados del siglo XIX los centros psiquiátricos se emplazaban fuera de las ciudades y en plena naturaleza. Suponía la creación de lugares de vida, transitorios o definitivos, en condiciones de suplir a familias débiles que no podían ocuparse de sus parientes. Así se habían desarrollado, sobre el modelo de los internados y los sanatorios, grandes espacios hospitalarios públicos o privados, dentro de los cuales cohabitaban médicos y pacientes, enfermeros y personal asistencial. Gracias a una organización federal y una situación geográfica privilegiada, asociada a una intensa tradición pedagógica de inspiración calvinista, Suiza —con sus numerosos lagos y sus regiones montañosas— había llegado a ser, al cabo de algunos decenios, uno de los países de Europa donde las clínicas eran más prósperas. Como Bleuler y todo el equipo del Burghölzli, Jung no bebía una gota de alcohol. Poseedor de un conocimiento íntimo de la locura, sentía verdadera atracción por los pacientes psicóticos. Jamás temía sus amenazas porque se sabía capaz de devolver los golpes, y organizaba con ellos veladas de baile y fiestas de disfraces.
Por primera vez Freud iba a enfrentarse con un joven discípulo de inteligencia excepcional, brillante alumno de Bleuler, que no le debía nada y que ya era conocido por sus propios trabajos sobre la asociación libre y la psicogénesis de las enfermedades mentales. Por eso quiso desde el principio transformar a ese hijo de un pastor, de enorme talento y a veces mitómano, en un delfín que habría de serle, creía él, mucho más útil por no ser ni judío ni vienés. Al otorgar un lugar semejante a este hombre de treinta años que soñaba como él en un glorioso destino, Freud creía sustraer al psicoanálisis de la tan temida calificación de «ciencia judía», que iba a la par con la acusación de «pansexualismo». En consecuencia, durante ese período se negó a ver que su querido príncipe heredero, a quien comparaba de buen grado con Josué, mantenía con la «cuestión judía» una relación por lo menos ambigua. Cosa que no había escapado a Karl Abraham: «Sea tolerante», le dirá Freud en 1908,
a usted le resulta más fácil que a Jung seguir mis pensamientos porque [...], debido a nuestro parentesco racial, está más próximo a mi constitución intelectual, mientras que él, como cristiano e hijo de un pastor, solo encuentra el camino que lleva a mí a costa de grandes resistencias interiores. Y por ello su adhesión tiene más valor. Casi diría que solo su entrada en escena ha sustraído al psicoanálisis al peligro de convertirse en un asunto nacional judío.
Así como Freud era el heredero de una concepción racionalista de la ciencia y de un universalismo que no toleraba forma alguna de relativismo, Jung procedía de una tradición muy distinta en la que se mezclaban esoterismo, antimaterialismo, espiritismo, ocultismo, impulso hacia la espiritualidad, atracción por lo inconsciente subliminal y los fenómenos de personalidades múltiples y, para terminar, adhesión a la psicología de los pueblos. Neurólogo y fisiólogo, Freud cultivaba la abstinencia a pesar de fundar su doctrina en la primacía de la pulsión sexual. Psiquiatra y lector de textos filosóficos —Kant, Nietzsche, Hegel—, Jung pretendía ser, por el contrario, adepto a una concepción ampliada de la libido entendida como «energía vital». Al mismo tiempo polígamo y calvinista, no vacilaría en multiplicar las aventuras amorosas con sus pacientes, a quienes haría sus discípulas.
En un primer momento la relación entre los dos hombres fue pasional, para ser luego conflictiva y al final bélica. Tras la ruptura de 1913 Freud acusaría a Jung de ceder al «lodo negro del ocultismo», mientras que Jung viviría como una liberación su separación de Freud, si bien fue presa a continuación de una crisis melancólica. Durante toda su vida tendría conciencia de la supremacía de la doctrina freudiana sobre la suya, si bien se sentía socialmente superior a Freud, que a su entender no era más que el hijo de un comerciante judío procedente de una clase popular y casado con una mujer pobre. En cuanto a Freud, convencido del valor de su sistema de pensamiento, habría de querer una vez más a un hombre a quien vio al comienzo como un hijo y un discípulo, para transformarlo luego en un enemigo.
Jung había vivido una infancia traumática, a tal punto que, una vez llegado a la edad adulta lo atormentaban reminiscencias terribles que le hacían odiar a los jesuitas y la Iglesia católica, y le recordaban cuán presente había estado, a lo largo de su escolaridad, la experiencia de un sentimiento de indignidad fantasmática. En efecto, se le había recordado sin cesar que era nieto de otro Carl Gustav —llamado «el Mayor»—, médico y rector de la Universidad de Basilea, al que una leyenda tenaz consideraba hijo natural de Goethe.
Colérico, insurrecto contra el orden patriarcal y víctima de numerosos desmayos, el joven Jung se refugió muy pronto en la contemplación y el estudio de los grandes textos de la civilización occidental, para volcarse luego en los estudios médicos. Se había forjado un conocimiento intuitivo de la locura dentro de su propia familia y sobre todo junto a su madre, Emilie Preiswerk, que se dedicaba en su presencia al espiritismo en compañía de su propio padre —un pastor iluminado—, su hermano y sus sobrinas. Cuando comenzó a intercambiar con Freud una correspondencia muy rica, Jung tuvo la sensación de haber dado con un mesías capaz de salvarlo de su «indignidad» ligada a una agresión sexual:
De hecho —debo confesárselo con renuencia—, tengo una admiración ilimitada por usted como hombre e investigador y, conscientemente, no lo envidio. No procede de ahí, pues, mi complejo de autoconservación, sino del hecho de que mi veneración por usted tiene el carácter de un entusiasmo apasionado y religioso que, aunque no me causa ningún desagrado, es para mí, no obstante, repugnante y ridículo debido a su irrefutable consonancia erótica. Ese sentimiento abominable es el resultado de haber sucumbido, de pequeño, a la agresión homosexual de un hombre a quien antaño había venerado.
Asistente de Bleuler desde 1895, Jung defendió su tesis sobre el caso de una joven médium afectada de sonambulismo, y de la que se revelaría más adelante que se trataba de su prima, Helene Preiswerk. En ese estudio, verdadera autobiografía enmascarada, Jung trazaba un cuadro aterrador del universo familiar de su paciente, a quien trataba de manera despreciativa, reduciéndola al carácter de un sujeto de observación y destacando que sus padres eran enfermos mentales. Bien recibido por Flournoy, ese texto suscitaría, no obstante, tempestuosas indignaciones.
Jung tuvo entonces la suerte de escapar de su familia al casarse con una mujer bella, inteligente, rica y distinguida, Emma Rauschenbach, cuya fortuna le permitió no solo escribir sin preocuparse por sus ingresos, sino también vivir en condiciones privilegiadas a la vez que frecuentaba los mejores círculos de la alta burguesía financiera de la Suiza alemánica. Pese a la esclavitud que implicaba su posición de madre y esposa, agotada por sus numerosos embarazos y herida por las infidelidades de su marido, Emma se convirtió en su discípula después de analizarse con él.
El domingo 3 de marzo de 1907, como de costumbre muy elegante, ella acompañó a su marido a Viena, donde se encontrarían por primera vez con Freud. Este la recibió en su hotel con un ramo de flores en la mano. Intimidado, Jung había pedido a Ludwig Binswanger que fuera con él a ese encuentro tan esperado. Sobrino de Otto Binswanger, jefe supremo de la célebre clínica de Kreuzlingen donde había pasado un tiempo Bertha Pappenheim, el joven Ludwig deseaba ardientemente conocer a ese maestro a quien tanto admiraba.
Impresionado por Emma, tan diferente a las mujeres de su entorno y sobre todo perteneciente a una clase social muy distinta de la suya, Freud hizo gala de una amabilidad exquisita. Invitados a compartir la comida de la familia al completo, los comensales captaron a las claras que los dos hombres sentían prisa por reunirse a solas e iniciar un diálogo que terminaría a altas horas de la noche. Jung habló sin parar durante tres horas, hasta que Freud optó por interrumpirlo para proponerle conversar de manera ordenada. El intercambio prosiguió entonces a lo largo de diez horas, y cada uno tuvo la sensación de compartir con el otro opiniones convergentes. Sin embargo, a Jung le llamaron la atención la falta «total de conciencia filosófica» de su interlocutor, su «positivismo» y la importancia extravagante que otorgaba a su teoría sexual.
Mientras departían, un fuerte ruido procedente de la biblioteca los hizo sobresaltar. Convencido de que se trataba de un fenómeno de «exteriorización cataléptica», Jung, siempre al acecho de las voces del más allá, anunció que no tardaría en hacerse oír un segundo ruido. Freud calificó de «puras tonterías» las supersticiones de su huésped, que creyó descubrir en su rostro un gesto de terror cuando se produjo un segundo crujido.
Persuadido de la profundidad del genio de Freud, Jung tuvo empero, desde el comienzo, la convicción de que su neurosis sería un obstáculo insuperable en las relaciones entre ambos. Por su lado, a despecho del temor de que Jung no estuviese a la altura de sus esperanzas, Freud le propuso unirse a su cenáculo sin sospechar que muy pronto, aquel, imbuido de su superioridad, los vería como un «amasijo de artistas, decadentes y mediocres». En realidad, ya desde ese primer encuentro Freud y Jung se vieron uno frente a otro en una situación insostenible. Freud creía haber hallado un heredero capaz de adherirse a su doctrina y Jung suponía haber conocido a un padre capaz de amarlo. Pero, en el momento mismo en que ambos procuraban convencerse del poder de su unión, el hijo se sublevaba ya contra el padre, en tanto que Freud temía que ese Josué imaginario se convirtiera en su principal rival.
Por añadidura, ninguno de los dos protagonistas quería ver, en esa época, que la invención freudiana estaba muy poco adaptada, stricto sensu, a la clínica psiquiátrica. Ahora bien, la mayoría de los alumnos de _Herr Professor_ —Jung el primero— eran psiquiatras que estimaban —con justa razón, además— que el método psicoanalítico, heredado del enfoque dinámico, iba a transformar de cabo a rabo la mirada que la sociedad occidental tenía de la locura. Y si Freud consideraba esta disciplina como una tierra prometida que había que conquistar, los psiquiatras veían el psicoanálisis como el arma que les permitiría realizar esa conquista.
Comoquiera que sea, la conceptualidad psicoanalítica procedía, en efecto, de un verdadero rechazo de las nociones vigentes en la psiquiatría y la psicología médica. Freud, aunque admiraba a Philippe Pinel, jamás se valía del vocabulario de los alienistas: estado mental, personalidad, carácter, desdoblamiento, psicología clínica, alienación, conducta, etc. No recetaba remedios, no pensaba en el acondicionamiento de los psiquiátricos y no se ocupaba de la gestión de la vida colectiva de los enfermos mentales. Solo tenía en cuenta la palabra, el lenguaje, la sexualidad, la neurosis, la vida, la muerte. A sus ojos, el destino humano se organizaba alrededor de instancias, principios energéticos, tópicas. En una palabra, Freud definía la psicosis como la reconstrucción inconsciente de una realidad delirante y la inscribía en una estructura tripartita en virtud de la cual aquella se diferenciaba de la neurosis y de la perversión.
Ni psiquiatra ni sexólogo, Freud rechazaba todas las formas de nomenclatura. Y, de resultas, no creía seriamente que se pudiese analizar a los locos, porque en ellos el inconsciente se mostraba al desnudo. Así, cuando se las veía frente a la locura individual, siempre intentaba «neurotizarla». Freud era ante todo un médico de la psique, un humanista de las palabras, el sueño y las mitologías, un clínico del sufrimiento solitario, un hombre de ciencia formado en la neurología y la fisiología. El mundo de la psiquiatría, con sus clasificaciones normativas, su universo de asilos, su observación de los cuerpos y los comportamientos, ese mundo políticamente organizado como un Estado dentro del Estado, ese mundo cerrado —el de Bleuler, de Jung, de Binswanger y de muchos otros—, no era el suyo.
Al día siguiente del memorable encuentro en la Berggasse, Freud se entregó a su ejercicio favorito y pidió a Jung y Binswanger que le contaran sus sueños: «Ya no recuerdo el sueño de Jung», dirá Binswanger,
pero me acuerdo de la interpretación que le dio Freud. Esa interpretación procuraba demostrar que Jung quería destronarlo para tomar su lugar. Por mi parte, había soñado con la entrada de la casa de Berggasse, 19, que estaba justamente en reconstrucción, y con la vieja araña cubierta a toda prisa, debido a la reparación. La interpretación de Freud, que no me pareció precisamente convincente [...], era que el sueño contenía el deseo de casarme con su hija (mayor), al mismo tiempo que el rechazo de ese deseo, porque sostenía [...]: «No me caso con nadie que sea de una casa donde cuelgan una araña tan lastimosa».
Freud y Jung continuaron durante mucho tiempo entregándose a su pasión de interpretar los sueños. Uno y otro, como todos los discípulos del primer cenáculo, tenían la certeza de que, gracias a su doctrina común, el inconsciente había hecho una entrada espectacular en la vida cotidiana de las sociedades europeas. Todo sucedía como si ya no pudiera contemplarse la posibilidad de sumergir el sueño en el dormir, disimularlo en lo recóndito de una vida nocturna, porque, por el milagro de la interpretación freudiana, el propio hombre se había convertido en la encarnación del sueño. Esa era la máxima de los nuevos tiempos, que el poeta Joë Bousquet resumiría en una fórmula sobrecogedora: «Pertenezco ahora a un tiempo en que ya no soñaremos, porque el hombre es el sueño».
Los freudianos de esta generación estaban convencidos de que la revolución simbólica representada por ellos debía extenderse a todos los dominios del pensamiento. Había que «aplicar» el psicoanálisis a la literatura, al estudio de los mitos y las religiones, a la ciencia histórica, a la antropología, al arte y a la totalidad de las producciones humanas. Dentro de la Sociedad de los Miércoles, y luego en la WPV, se entablaban intensas discusiones para distinguir el psicoanálisis aplicado de la «patografía» que se había desarrollado en consonancia con la pretensión del discurso médico de controlar la vida de los locos.
En ese contexto Jung recibió con vivo placer el ensayo de Freud dedicado a una novela de Wilhelm Jensen, _Gradiva: una fantasía pompeyana_. También el joven zuriqués adoraba contar sueños y comparar los textos literarios con los relatos clínicos. Y ya se interesaba por las grandes mitologías cósmicas y el orientalismo. Sabía, al respecto, que Freud se había sentido seducido por el famoso bajorrelieve de una muchacha griega en trance de caminar, con un atuendo que, levemente levantado, dejaba ver los pies calzados con sandalias, uno bien posado en tierra y otro tan alzado que solo las puntas de los dedos parecían rozar el suelo. Esa era Gradiva, mujer misteriosa, moldeada en la piedra, envuelta en una túnica de pliegues desordenados y encaminándose con paso guerrero hacia un destino desconocido: ¿iba al combate o quería dar vida?
Publicado en 1903, el relato de Jensen reunía todos los temas de la literatura amorosa de comienzos del siglo: confusión entre sueño y realidad, viaje entre pasado y presente y entre delirio y deseo, y omnipresencia de ruinas antiguas, mujeres muertas, duelos y pasiones evanescentes. Freud se sintió atraído a tal extremo por Gradiva que compró un molde del bajorrelieve y lo colgó de la pared de su consultorio.
En la novela breve de Jensen, Norbert Hanold, un joven arqueólogo, se enamora de la mujer del bajorrelieve que cautiva su mirada. En una pesadilla, la ve víctima de la erupción que sepultó Pompeya en el siglo I de la era cristiana. Al despertar, convencido de la veracidad de ese sueño, viaja a Pompeya después de haber atisbado en la calle una silueta similar a la de Gradiva. Y entonces, al visitar las ruinas, creer volver a verla al percibir a una muchacha bien real, Zoé Bertgang, cuyo nombre significa «la que brilla por su andar». Comprendiendo el estado mental en que se encuentra Hanold, la joven se propone curarlo y lo logra, ya que consigue hacerlo evocar recuerdos reprimidos. De hecho, ambos viven en la misma ciudad y, en la infancia, han sido buenos compañeros de juego.
Se entiende que _Herr Professor_ pudiera sentirse seducido por ese texto que también había llamado la atención de Jung. Esta ficción parecía poner en escena los mecanismos del inconsciente y el sueño y, al mismo tiempo, hacía encarnar a personajes novelescos los papeles respectivos del paciente y el terapeuta. Además, Freud podía confirmar su tesis de que los sueños inventados por los escritores pueden interpretarse como los de los pacientes. Mejor aún, el relato ilustraba a la perfección lo que le había dicho a Arthur Schnitzler: «A menudo me he preguntado con asombro cómo había llegado usted a tal o cual conocimiento íntimo y secreto que yo había adquirido solo después de una prolongada investigación sobre el tema, y, finalmente, llegué a envidiar al autor a quien antes admiraba».
Freud quiso ir más lejos, pero tropezó entonces con serias dificultades. En efecto, después de enviar a Jensen un ejemplar de su libro, recibió en respuesta una amable carta en la que se le confirmaba su comprensión del relato. Pero, por consejo de Jung, que le había señalado la existencia de otros dos textos del autor, imaginó que Jensen había experimentado un violento deseo incestuoso por su hermana menor, discapacitada a causa de un pie contrahecho. Se equivocaba una vez más, y lo mandaron a paseo. Irritado por sus peticiones, Jensen explicó para terminar que no tenía hermana pero que en su infancia había experimentado, en efecto, sentimientos amorosos por una amiga prematuramente desaparecida. De ese modo Gradiva conocería, gracias a Freud, una increíble posteridad, sobre todo entre los surrealistas. Según la concepción freudiana de la neurosis, Hanold tenía todos los rasgos del histérico. Pero para Jung esa novela era la expresión de un verdadero delirio, en el sentido psiquiátrico del término.
Freud se topaba sin cesar con la locura entre sus pacientes y sus discípulos, que encontraban en la tragedia edípica del alzamiento de los hijos contra los padres el eco de su propia rebelión.
Fue en ese contexto que Otto Gross se cruzó con la aventura freudiana. Hijo único, había sido criado como un príncipe por sus padres, que veían en él un prodigio de inteligencia. Su padre, Hans Gross, amigo de Krafft-Ebing y admirador de los primeros escritos de Freud, soñaba con asociar a este niño superdotado a sus propios trabajos. Por eso le brindó una educación privilegiada sin reproches ni coacciones, que contrastaba singularmente con las tesis que él defendía y ponía al servicio de la policía científica. Partidario de la lucha contra la presunta degeneración de las sociedades, este célebre penalista aspiraba en efecto a combatir la prostitución, la homosexualidad, las perversiones y la pornografía no solo mediante la represión policial sino también con la prohibición de las novelas juzgadas «inmorales», y hacía de las mujeres «virilizadas», los anarquistas, los vagabundos y los gitanos, «bribones y ladrones», el blanco de sus ataques.
Sometido durante años al amor de ese padre cuyas teorías delirantes parecían ser de un absoluto rigor y sobre todo conformes a la ideología racialista de fines del siglo XIX, Otto Gross llegó a ser un brillante psiquiatra. Pero no bien obtenido su doctorado se embarcó como médico de a bordo en los transatlánticos de la línea Hamburgo-América del Sur y se entregó al consumo de diversas drogas: cocaína, opio, morfina.
A su regreso, después de diferentes períodos en clínicas neurológicas de Munich y Graz, se sometió a una primera cura de desintoxicación en la clínica del Burghölzli. En 1903 se casó con Frieda Schloffer y por medio de esta conoció a Marianne Weber, la mujer del sociólogo Max Weber, y a las hermanas Von Richthofen, con las cuales tuvo un amorío. Designado _Privatdozent_ y catedrático de psicopatología, Gross comenzó a trabajar como asistente de Emil Kraepelin en Munich y se entusiasmó con la obra freudiana, a la vez que exigía que se lo considerara como un profeta. Tras conocer a Freud, a quien no le disgustaba tener como discípulo al hijo de una celebridad tan grande, se encauzó hacia la práctica del psicoanálisis y frecuentó los medios intelectuales del barrio muniqués de Schwabing, donde se mezclaban, a comienzos del siglo, los discípulos de Stefan George y de Ludwig Klages. Como pone de relieve Jacques Le Rider, el nietzscheanismo tomaba en ellos la forma de una metafísica del «eros cosmogónico», donde se manifestaba la nostalgia por un dionisismo arcaico inspirado en las investigaciones mitológicas de Bachofen sobre el «matriarcado».
Y a través de ese culto, y como impulsor del inmoralismo sexual y la práctica del éxtasis, Gross militó a favor del psicoanálisis para llevar la contraria a las tesis de su padre y dar valor a todo lo que este condenaba: la fragilidad de las personas, el hedonismo, el placer, el matriarcado, los anormales, el feminismo, la rebelión de las mujeres; «los degenerados son la sal de la tierra» y «el estado más sano para el neurótico debe ser el inmoralismo sexual», diría algún día. En síntesis, mezclaba freudismo y nietzscheanismo para elaborar un «programa» de liberación sexual que Wilhelm Reich y los freudomarxistas retomarían más adelante de otra manera.
En mayo de 1908, obligado por su padre, se internó otra vez en la clínica del Burghölzli para una segunda cura de desintoxicación, acompañado por su mujer, Frieda, sometida a sus caprichos. Freud, que había redactado un informe en su favor, pidió a Jung que lo desintoxicara de las drogas, con la esperanza de que luego pudiera tomarlo en análisis, cosa que no sucedería. Alabando sus méritos de teórico, Jung emitió dos diagnósticos sucesivos: neurosis obsesiva y demencia precoz. De ese modo Gross se convirtió en un paciente-discípulo atrapado entre un maestro y otro discípulo, él mismo futuro disidente. Gracias a él, en cierta forma, Jung pudo sostener frente a Freud la validez de la noción de demencia precoz, a la que este último se oponía. En un principio Jung se propuso considerar a Gross como un loco absoluto y luego se apegó a él hasta el punto de verlo como un hermano mellizo, sin lograr ayudarlo.
Gross solo comía verduras cocinadas a su manera, era desaliñado, jamás se lavaba ni se afeitaba y mezclaba con opio los productos destinados a desintoxicarlo. Se ponía mucha ropa cuando hacía calor y exigía que todas las lámparas estuviesen encendidas; deambulaba por los corredores de la clínica pintarrajeando con dibujos las paredes y el suelo, y dormía con una almohada ceñida sobre la cabeza.
El tratamiento resultó en un desastre. Tras una fase maníaca Gross se escapó de la clínica para hacerse tratar, sin más éxito, por Wilhelm Stekel. En el Burghölzli, Jung también tomó en tratamiento a Frieda, que le expuso los beneficios de su común emancipación erótica, mientras que a Ernest Jones le contó cuánto sufría por su situación y las extravagancias de su marido.
Muy pronto la mayoría de los discípulos comenzaron a ver a Gross como un peligroso extremista capaz de causar un perjuicio al movimiento. Licencioso, inmoral, anarquista, violentamente apegado a la temática de la revolución por el sexo, Freud lo abandonó sin miramientos tras darse cuenta de improviso de que desnaturalizaba la causa psicoanalítica. Esto no impidió que Gross siguiera practicando e invocando el freudismo. Tras suscitar un escándalo por tratar a una muchacha insurrecta contra la autoridad parental, vivió con una pintora anarquista que se mató en 1911. Acusado entonces de incitación al suicidio, luego internado varias veces y perseguido finalmente por la policía, que no dejaría de acosarlo por «actividades subversivas», terminaría su vida errante en 1920, tras la muerte de su padre y la caída de los Imperios, en una acera de Berlín, consumido por el frío y el hambre.
Es indudable que Freud no sabía qué hacer con esos discípulos locos, transgresores, inventivos y de gran talento que, en ciertos aspectos, tomaban su doctrina «al pie de la letra» leyendo en sus textos lo que estos no contenían, a fin de revolucionar a la persona y la sociedad en términos mucho más extremos que los preconizados por Freud. Pobre clínico de la locura, pero sobre todo deseoso de construir un movimiento capaz de servir de apoyo a sus tesis, _Herr Professor_ tenía el deber de presentar ante la opinión pública la prueba de que los soldados de su ejército eran honorables terapeutas. Por eso fue siempre muy injusto con aquellos que, por sus excesos, mostraban un rostro muy distinto de su doctrina. Ese rostro le recordaba los delirios de Fliess y sus propios extravíos.
En ese aspecto, Freud no disfrutaba del mismo margen de maniobra que los escritores y los poetas: se había propuesto construir un movimiento que la ciencia tuviera que aceptar. Misión imposible, claro está. Pero, en esas condiciones, ¿cómo ver que el culto de la ortodoxia termina siempre por alimentar la esterilidad del pensamiento, así como sus derivas y sus transgresiones?
Franz Kafka sería pues más perspicaz y daría de Gross un retrato que sobrecoge por su verdad: «Me hacía pensar en el desasosiego de los discípulos de Cristo a los pies del crucificado». En cambio, Max Weber, que había conocido el psicoanálisis a través de las extravagancias de Gross, se mostró muy severo con Freud y sus discípulos, considerando que esa disciplina no aportaba ninguna nueva exigencia ética a la humanidad y amenazaba con provocar la sustitución del científico por un «director de almas».
En 1908 Ernest Jones fue la persona indicada, el hombre que podía aportar a Freud lo que Jung no le ofrecía: los instrumentos políticos necesarios para la transmisión de su obra, la normalización de la práctica psicoanalítica y la ampliación mundial del Verein.
Nacido en Gales en una familia provinciana de la pequeña burguesía, y tras haber vivido una infancia difícil bajo la autoridad de un padre convencido de que los hijos no debían cometer ningún acto de insubordinación, se había orientado hacia la psiquiatría tras ser alumno del gran neurólogo John Hughlings Jackson. Cuando conoció los primeros escritos de Freud tuvo la convicción de que el psicoanálisis aportaba al mundo una nueva racionalidad y aprendió alemán para leer _La interpretación de los sueños_.
La educación que había recibido lo llevó, como a muchos otros, a rebelarse contra el orden establecido y las costumbres vigentes en una Inglaterra todavía muy victoriana. Muy pronto adquirió un agudo conocimiento de las prácticas sexuales y hablaba de ellas con una franqueza nada conveniente para su entorno; esa era su manera de impugnar la ley del padre. Y como por otra parte era un seductor de mujeres acostumbrado a tener numerosos amoríos, no podía ser indiferente a la nueva teoría freudiana de la sexualidad. Por eso comenzó en 1906 a ejercer espontáneamente el psicoanálisis. Un año después, en un congreso de neurología celebrado en Amsterdam, conoció a Jung y este lo invitó a trabajar con él en la clínica del Burghölzli, donde Jones se inició en la nueva psiquiatría a la vez que era testigo del extravío de Otto Gross y Frieda.
El 30 de abril de 1908, después del congreso de Salzburgo, visitó a Freud en compañía del psiquiatra Abraham Arden Brill, originario de Galitzia y emigrado a Estados Unidos hacia 1890 a raíz de unos violentos conflictos con su padre, oficial del ejército imperial. Jones deseaba conocer a Freud, en tanto que Brill quería ser su analizante y su propagandista norteamericano.
El resultado de esa visita fue desastroso para Jones pero beneficioso para Brill, a quien Freud encargó la traducción de sus obras sin darse cuenta de que ese discípulo antojadizo no dominaba el inglés y, sobre todo, de que soñaba con adaptar la doctrina vienesa a un presunto «espíritu americano».
En un primer momento Freud encontró desagradable a Jones. De ahí este intercambio con Jung: «Jones es sin duda alguien muy interesante y de gran valor, pero a su respecto diría casi que tengo la impresión de una raza extranjera. Es un fanático y come demasiado poco. [...] Me recuerda a Casio, el enjuto. Niega toda herencia. Para él yo soy ya un reaccionario». Y además: «Es muy interesante la mezcla de razas en nuestra hueste. Él es celta, y por eso para nosotros, el germano y el mediterráneo, no es del todo accesible».
Al principio, entonces, Freud no sintió ninguna simpatía por ese «celta» que venía de un mundo distinto del suyo. Jones no expresaba interés alguno por la _Mitteleuropa_ , no entendía ni las locuras barrocas de la Viena imperial ni los sueños de atemporalidad melancólica que asaltaban al primer círculo de discípulos del maestro. No era judío como ellos ni estaba fascinado por el espiritismo y las mesas giratorias como Jung, y si respetaba el genio clínico de Ferenczi, su futuro analista, no sentía ninguna inclinación por la telepatía y las videntes de Budapest. Conservador, pragmático, más neurólogo que psiquiatra y muy favorable a la emancipación de las mujeres en un país donde el feminismo estaba a la cabeza de todos los combates, rechazaba la idea de que el psicoanálisis fuera portador de una posible revolución social o filosófica. Por eso quería asociarlo a la medicina, a la vez que lo incitaba a abrir un debate con otras disciplinas, sobre todo la antropología, por entonces en plena expansión en el mundo angloparlante. En síntesis, llegado del otro extremo de Europa y como representante puro de los valores liberales de una de las más poderosas democracias occidentales, Jones era histórica, política y geográficamente el hombre del futuro del psicoanálisis.
Sin buscar jamás seducir a un maestro junto al cual habría podido encontrar un consuelo paternal, su única ambición era ser útil a una «causa» y defenderla, al precio, llegado el caso, de enfrentarse a su fundador y serle infiel. Desde el inicio se situó ante Freud como un heredero cuya fidelidad iba mucho más allá del apego a la persona. Y Freud se vio obligado a admitir que ese trabajador incansable, que no tenía ningún deseo de «superar al padre», le aportaba no solo la eficacia que necesitaba en la organización de su movimiento y la famosa salida del «gueto vienés», sino también la apertura al nuevo mundo con el cual soñaba: el reino de Shakespeare y de Cromwell y, del otro lado del océano, el de Nueva Inglaterra. Y como Jones no lograba descifrar su escritura gótica, Freud aceptó redactar en lo sucesivo sus misivas ya fuera en caracteres latinos, ya fuera en su «mal inglés».
En Londres, la situación de ese nuevo discípulo era poco envidiable. Después de haber sido públicamente denunciado por el hermano de una de sus pacientes deseosas de divorciarse, lo acusaron de haber hablado con crudeza de la sexualidad a dos niños a quienes había hecho un test. Es cierto, lo habían exculpado después de una noche en la cárcel, pero decidió marcharse de Gran Bretaña e instalarse con su compañera Loe Kann en Canadá, donde vivió cuatro años. Y desde Toronto empezó a escribir a Freud. Contra Brill, se impuso muy pronto como el mejor organizador de la implantación del freudismo de ese lado del Atlántico, sobre todo con la creación, en 1911, de la American Psychoanalytic Association (APsA).
Freud comprendió cuánta razón había tenido, a pesar de sus reticencias iniciales, al atar el destino de su movimiento a ese galés a quien no quería pero que iba a tener un papel considerable, para bien y para mal, en la historia del freudismo. Pensara lo que pensase de él, _Herr Professor_ había encontrado en Jones al amigo indispensable que no sería jamás su enemigo.
Desde su llegada a Toronto, Jones se enfrentó a una situación difícil. Por un lado, chocaba con movimientos religiosos que rechazaban todo enfoque racional del psiquismo y alababan los méritos de las curaciones milagrosas, y por otro, tenía que vérselas con los partidarios de toda una corriente de la psiquiatría dinámica, marcada por los trabajos de Pierre Janet y Morton Prince, gran especialista en las personalidades múltiples y pionero de la escuela bostoniana de psicoterapia, que libraban una guerra sin cuartel contra la teoría freudiana. En nombre de otro enfoque clínico considerado más «científico», veían a los freudianos como los defensores de una nueva religión. En cuanto a la burguesía de Toronto, a Jones le parecía detestable, mezquina y oscurantista.
No tardó en ser víctima de una campaña orquestada por una de esas ligas puritanas del Nuevo Mundo que asimilaban el freudismo a un demonio sexual y el psicoanálisis a una práctica de desenfreno y libertinaje. Convertido en un verdadero chivo expiatorio, lo acusaron de toda clase de crímenes imaginarios: incitaba a los jóvenes, se decía, a masturbarse; repartía en su entorno tarjetas postales obscenas o hacía que adolescentes de buena familia visitaran a prostitutas. Con sir Robert Alexander Falconer, ministro de la Iglesia presbiteriana, como principal enemigo, también lo llevó a la justicia la célebre Emma Leila Gordon, primera médica de Canadá y miembro de la muy puritana Women's Christian Temperance Union [Unión Cristiana Femenina de la Templanza]. Gordon lo acusaba de haber abusado sexualmente de una mujer histérica, delirante y morfinómana que Jones había tenido en tratamiento y a quien, además, le había dado tontamente dinero para que dejara de extorsionarlo. El caso tomó un viso trágico cuando la paciente quiso matarlo para después intentar suicidarse. Después de que una liga de la virtud la hiciera objeto de tales manipulaciones, la mujer fue expulsada de Ontario.
Impedido de proseguir su trabajo en ese clima de cacería de brujas, Jones pensó instalarse en Boston. En 1910, en efecto, el simpático James Jackson Putnam, convertido a la doctrina vienesa a pesar de su puritanismo, consideraba la posibilidad de darle un puesto en Harvard, si bien vacilaba en hacerlo debido a su muy fuerte tendencia a hablar de la sexualidad ante un público reticente. Finalmente, el intento quedó en nada y Jones se marchó de Canadá en el verano de 1912, para instalarse en Londres.
Un año después, aconsejado por Freud, pasó dos meses en Budapest para analizarse con Ferenczi, en el momento en que él mismo pedía al maestro que se encargara de tratar a Loe Kann, a quien la estancia en Toronto había dejado aterrada y que, además, tomaba morfina para calmar los dolores causados por una pielonefritis. Perteneciente a una rica familia de la burguesía judía holandesa, era bonita, espiritual y generosa y no le gustaba que le impusieran interpretaciones sobre sí misma que no le parecieran conformes a la verdad. Aceptó, no obstante, reunirse con Freud. A este le pareció deliciosa e intentó curarla de su frigidez y sus dolores abdominales, que tomó por síntomas histéricos. Se produjo entonces un enredo transferencial muy característico de las primeras curas psicoanalíticas.
Si bien Jones no se daba cuenta todavía de que Loe estaba a punto de dejarlo, temía con toda la razón las indiscreciones de Freud y Ferenczi a su respecto. Y de hecho, Freud mantenía informado a su discípulo del alma del desarrollo de la cura de la joven mujer, mientras que el húngaro lo tenía al tanto de las confidencias de Jones. En septiembre de 1912 Loe se instaló en Viena con Lina, su doncella, y Freud rogó a Jones —conforme a la famosa regla de la abstinencia que tanto le gustaba— que se alejara «sexualmente» de su paciente. Cuatro meses después Jones comenzó un amorío con Lina, mientras que Loe se enamoraba de Herbert «Davy» Jones (apodado Jones II), un millonario norteamericano cuya familia era propietaria de minas de zinc en Wisconsin. Por fidelidad al primer Jones, Loe lo acompañó a Londres para ayudarlo económicamente a rehacer su clientela.
En vísperas de la guerra Loe se casó con Herbert Davy en Budapest, en presencia de Rank y Ferenczi. Aunque escéptica con respecto al psicoanálisis, se hizo amiga de Anna Freud y conservó las buenas relaciones con _Herr Professor_. Nunca se curó ni de la adicción a la morfina ni de la frigidez. Pero la cura le permitió separarse de Jones.
Siempre inclinado a intervenir en las historias amorosas de sus discípulos, Freud se servía del psicoanálisis para interpretar la significación de los conflictos que surgían, no solo en la vida de aquellos, sino en cada etapa de la constitución de su movimiento. Por eso veía a sus partidarios más cercanos como otros tantos pacientes, y ellos mismos respondían a sus demandas. Todos compartían un mismo interés por la exploración de su propio inconsciente, sus sueños, su vida privada. Se analizaban sin cesar unos a otros y exponían sus casos clínicos en sus reuniones o sus intercambios epistolares. En síntesis, los discípulos del maestro desarrollaban en esa época una verdadera manía interpretativa, olvidando que la interpretación nunca debe caer en el delirio, ni servir de droga, ni alimentar el goce, so pena de perjuicio a la causa psicoanalítica.
Por añadidura, Freud se entregaba a interpretaciones sistemáticas en relación con conflictos políticos o doctrinales, valiéndose a diestra y siniestra del sacrosanto complejo de Edipo, transformado poco a poco por sus imitadores en una psicología familiarista. Así, aplicaba sus conceptos no solo a los textos literarios sino a situaciones conflictivas de gran banalidad. Y se negaba a ver que esa evolución amenazaba hacer del psicoanálisis una nueva teología que permitiera neutralizar toda forma de contradicción o compromiso.
Es indudable que ese rumbo daba en parte la razón a los antifreudianos que consideraban el psicoanálisis como un «método peligroso» y se regocijaban ante el espectáculo de sus disidencias. ¿Cómo no advertir que los grandes pioneros de esa magnífica doctrina se pasaban el tiempo comportándose, en su vida concreta, como personas incapaces de controlar sus pasiones? Jugaban con fuego.
En 1906 Jung acudió a Freud en relación con el caso de una muchacha rusa llamada Sabina Spielrein, que pertenecía a un medio de comerciantes judíos de Rostov. Había sido internada en el Burghölzli el 17 de agosto de 1904 a raíz de un episodio psicótico y después de haber pasado por varias clínicas y psiquiátricos sin que su estado mejorara. Su destino iba a ser emblemático de la saga de las primeras mujeres psicoanalistas.
Según el informe escrito por Jung en septiembre de 1905, Sabina había sido criada por padres neuróticos, cuyo matrimonio era producto de un arreglo entre sus propios progenitores. Aterrorizada frente a las «cosas sexuales», la madre dedicaba su tiempo a viajar, alojarse en suntuosos hoteles europeos y comprar joyas y ropa de lujo. En cuanto al padre, lunático y con tendencias suicidas, golpeaba a sus hijos, en particular a los varones, e insultaba a su hija. A los siete años esta ya hablaba varios idiomas y en la adolescencia comenzó a sentir excitación sexual a la vista de las manos de ese padre que, delante de ella, le había pegado a su hermano en las nalgas desnudas. Afectada por una compulsión a la masturbación acompañada de rituales ligados a un erotismo anal, había tomado la costumbre de doblar la pierna para presionar el pie contra el ano y retener los excrementos, a la vez que experimentaba un voluptuoso estremecimiento en cada intento de evacuar los intestinos. A su llegada al Burghölzli, a los diecinueve años, parecía gozar de sus rituales y su onanismo, sin dejar al mismo tiempo de gritar de manera convulsiva contra el mundo entero.
En 1906 Jung expuso su caso a Freud, señalando que había tratado a la joven como una «histérica psicótica». Pero Freud hizo una interpretación de su cosecha: a su entender, Sabina padecía un autoerotismo anal con fijación de la libido en el padre y perversión reprimida.
Hubo que esperar hasta 1908-1909 para que Jung le contara que Sabina se había enamorado de él, y tanto, que le había hecho un «feo escándalo». La realidad era muy diferente. En el transcurso de la cura, en efecto, Jung se había convertido en amante de su paciente; en medio de la relación, que duró varios años, ella comenzó a estudiar medicina. Celosa y desesperada, Emma divulgó el amorío e informó a los padres de la muchacha. Lleno de pánico, Jung terminó por confesar la verdad a Freud, que tomó partido por su querido delfín.
Curada de sus síntomas, Sabina se convirtió en otra mujer, tanto por la psicoterapia como por amor a su terapeuta: itinerario clásico, específico de las relaciones transferenciales y contratransferenciales. Por eso soñó de ahí en adelante con dedicarse a la defensa de la gran causa del psicoanálisis. Sin embargo, siempre enamorada de Jung, quien por su lado seguía profesándole un apego culpable, y deseosa de tener un hijo con él, se dirigió a Freud, que le aconsejó hacer el duelo de una relación sin futuro a fin de centrarse en otro objetivo.
En 1911 Sabina defendió su tesina sobre el caso de una mujer psicótica tratada en el Burghölzli. A continuación pronunció una conferencia en la WPV, en la cual expuso sus tesis sobre la pulsión de destrucción, destacando que esta atravesaba la pulsión sexual. Freud iba a inspirarse en esta hipótesis para presentarla, modificada, en su elaboración de una nueva concepción de la dualidad pulsional.
Ese mismo año, Sabina se casó con un médico judío y ruso, Pavel Naumovich Scheftel, para gran alegría de Freud, que en esa época ya no quería oír hablar de Jung, ni de su propia crítica de Herzl y el sionismo, ni del peligro de que el psicoanálisis fuera asimilado a una «ciencia judía»: «Por mi parte, como usted sabe», le escribió a Sabina, «estoy curado de toda secuela de predilección por los arios, y quiero suponer, si su hijo es un varón, que se convertirá en un inquebrantable sionista. Es preciso que sea moreno o, en todo caso, que llegue a serlo; basta de cabezas rubias [...]. Somos y seguiremos siendo judíos».
En el centro del enredo entre Freud y Jung, Sabina Spielrein tuvo pues un papel esencial en la evolución de las relaciones entre quien era su amante y aquel a cuya causa se adhería. Al procurar evitar la ruptura entre ambos, fue, para uno y para otro y en virtud de una terrible «astucia de la historia», el revelador de la degradación de una situación que marcó el final de cierta época del psicoanálisis, un momento de fervor en el que únicamente los hombres —discípulos o disidentes— estaban autorizados no solo a entregarse a justas intelectuales, sino también a creerse los exclusivos poseedores de un saber sobre el psiquismo, fundado en la decadencia de la autoridad patriarcal y la rebelión de los hijos. En lo sucesivo habría que vérselas con otra configuración en la que el lugar de las mujeres y el análisis de la sexualidad femenina —y ya no solo la clínica de la histeria, centrada en muchachas vienesas presas de reminiscencias— servirían al objetivo de un combate esencial en la historia del psicoanálisis.
A partir de 1910, por lo tanto, las mujeres hicieron su entrada en la historia del movimiento psicoanalítico: entre las primeras, Hermine von Hug-Hellmuth, Tatiana Rosenthal, Eugénie Sokolnicka, Margarethe Hilferding y la célebre Lou Andreas-Salomé.
En septiembre de 1911, en el congreso del Verein en Weimar, la ciudad de Goethe, rodeaban a Freud unos cincuenta discípulos procedentes de varios países. En la foto tomada delante de la escalinata de un gran hotel, lo vemos alto, subido a un escabel. De acuerdo con el fotógrafo, había preferido disimular su escasa altura a fin de aparecer como el señor del lugar, al lado de Jung, a su izquierda, y Ferenczi, a su derecha. Más lejos, Abraham, Jones, Brill, Eitingon, Sachs, en desorden. Estaban presentes todos los vieneses, así como Bleuler y muchos otros: Oskar Pfister, el suizo Alfons Maeder, Karl Landauer, el sueco Poul Bjerre, Ludwig Jekels. En una primera fila de sillas elegantemente dispuestas se habían situado ocho mujeres, una con sombrero y las demás con la cabeza descubierta, todas calzadas con botines y ceñidas por corsés: _Frau_ Emma, derecha y soberbia; _Fräulein_ Toni Wolff, inquietante en su extrañeza, y _Liebe_ Lou, radiante de belleza. Sabina no participaba de la reunión.
Durante ese momento de gran dicha, Jung era todavía el delfín preferido y Ferenczi, el hijo adorado. Frente a esta asamblea de hombres y mujeres que había aceptado posar ante la _camera oscura_ , Freud se entregó a un deslumbrante comentario de las _Memorias de un enfermo nervioso_ de Daniel Paul Schreber, jurista loco y ex presidente del Tribunal de Apelación de Sajonia. El autor de esa extraña autobiografía era hijo de un médico, Daniel Gottlieb Schreber, adepto de la «pedagogía negra» y célebre en Alemania por querer remediar la decadencia de las sociedades mediante la creación de un hombre nuevo modelado por ejercicios de gimnasia ortopédica: una mente pura en un cuerpo sano.
Gracias al relato de su vida, Daniel Paul, el hijo, tratado en principio en la clínica de enfermedades mentales de Leipzig por el profesor Paul Flechsig, y luego internado en Pirna, cerca de Dresde, había logrado salir del psiquiátrico al demostrar que su locura no podía aducirse como motivo de encierro. Schreber afirmaba que Dios, su perseguidor, le había encargado la misión salvadora de convertirse en mujer para engendrar una nueva raza de humanos. Freud hacía de él un paranoico rebelado contra la autoridad paterna, y al analizar su delirio situaba su origen en una homosexualidad reprimida y una tentativa de reconciliarse con la imagen de un padre muerto transformado en potestad divina.
Concluía su estudio con la mención del mito del águila y el sol, que tenía en Jung su fuente de inspiración. Sobre la base de lo que Schreber decía de su relación con los rayos solares y su incapacidad para procrear e integrar un orden genealógico, Freud ponía de relieve que, en los antiguos mitos, las águilas, al volar en las altas capas de la atmósfera, eran consideradas como los únicos animales que mantenían una relación íntima con el sol, símbolo de la potestad paterna. Y de resultas, imponían a sus crías la prueba de mirar al astro rey sin pestañear, bajo la amenaza, si no lo conseguían, de expulsarlas del nido. Freud traía ese mito al presente afirmando que el neurótico moderno ocultaba en sí los vestigios del hombre primitivo: cada hijo debe enfrentarse con su padre, a riesgo de morir, para hacer la prueba de su legitimidad.
Una vez más, rechazaba la historia de la rebelión de un hijo contra un padre; un hijo loco cuya locura había sido engendrada por la de un padre partidario de teorías educativas delirantes que, para la época, tenían la apariencia de la mayor normalidad: un «asesinato del alma». La historia de Daniel Paul Schreber exhibía muchos rasgos en común con la de Otto Gross, pero Freud no decía ni pío al respecto y sin duda no era consciente de ellos. Sin embargo, en 1905 Gross había comentado la obra en su presencia.
El caso Schreber se convertiría en un clásico comentado y revisado por decenas de psicoanalistas que, a diferencia de Freud, tuvieron en cuenta, en la génesis de la locura del jurista, las «teorías educativas» de su padre. En una perspectiva muy distinta, Elias Canetti estudió a su vez, en _Masa y poder_ , de 1960, el destino de Schreber, haciendo de su sistema de pensamiento uno de los paradigmas de la concepción conspirativa del poder, característica del siglo XX. Y proponía volver a sacar a la luz el delirio subterráneo de ese célebre paranoico para compararlo mejor con el empuje de las fuerzas oscuras que terminarían por triunfar sobre la democracia al transformar el orden de la soberanía legal en su contrario: repelente figura de un yo único, que suprime la alteridad, la razón y el pensamiento.
En 1909 Freud había aceptado tomar en análisis, a petición de sus padres, a un escritor vienés de veinticinco años, el barón Viktor von Dirsztay, conocido por sus extravagancias y delirios. Su padre, judío húngaro ennoblecido, había hecho fortuna en la banca y el comercio. Amigo de Karl Kraus y de Oskar Kokoschka, Viktor padecía una grave psicosis y una enfermedad de la piel cuya causa atribuía al desprecio que profesaba a su familia y la vergüenza que sentía por sus orígenes. Durante más de diez años, en tres períodos sucesivos, acudió a la Berggasse para contar su calvario.
Como Schreber, se sentía víctima de un «asesinato del alma». Cautivo de un enredo por el cual se oponía tan pronto a Kraus como a Freud, terminó por sentirse perseguido por el psicoanálisis y se internó en varios sanatorios para enfermos mentales, entre ellos el de Rudolf von Urbantschitsch, uno de los fundadores de la Sociedad de los Miércoles. Tras esas experiencias escribió una novela sobre su «caso», en la cual presentaba a un doble diabólico que lo arrastraba a la muerte. Con el paso de los años, el barón loco, que se creía embrujado, terminó por acusar a Freud y Reik de haberlo destruido. En 1935 puso fin a sus días junto con su mujer, también tratada por una grave psicosis en el hospital psiquiátrico Steinhof. Tal fue el destino de ese Schreber vienés, esteta y bohemio, de quien se decía que era discípulo de Freud y cuyo caso nunca se publicó; apenas se lo mencionó en alguna correspondencia y en la prensa.
En 1912, mientras Freud se debatía con ese nuevo «asesinato del alma» tras haber comentado las _Memorias_ de Schreber, Jung también se interesaba en la temática del astro solar, pero de manera muy diferente. En efecto, había tratado a un paciente psicótico, Emil Schwyzer, internado en el Burghölzli en 1901, quien, al mirar el sol, veía un _membrum erectum_ (miembro erecto). Schwyzer estaba convencido de que podía «influir en el clima» si movía el miembro eréctil al compás de los movimientos de la cabeza. Lejos de comparar el apéndice fálico con un sustituto de la potestad paterna, Jung relacionaba ese delirio con la liturgia de Mitra, divinidad indoeuropea. En tanto que Freud reinterpretaba los mitos a la luz del psicoanálisis, Jung veía en las mitologías la expresión de un inconsciente arcaico propio de cada pueblo y generador de tipos psicológicos. Las dos tesis eran incompatibles. Jung volvía al antiguo subconsciente de los espiritistas y los magos al creer que el hombre moderno era el heredero directo de sus ancestros, mientras que Freud tomaba en los mitos de origen los instrumentos aptos para metaforizar, por medio del lenguaje, la condición de ese mismo hombre.
Después de 1913, año de la ruptura entre el delfín y el maestro, y en vísperas de una guerra letal que iba a cambiar el destino del psicoanálisis tanto como el de Europa y el de las mujeres, Freud no experimentaría nunca más el mismo entusiasmo por un discípulo, y Jung jamás se sentiría atraído hacia un padre por el que quisiera tanto ser amado.
En cuanto a Sabina Spielrein, al pasar del estatus de enferma al de clínica, fue la primera mujer del movimiento psicoanalítico en realizar una verdadera carrera y, por lo tanto, en entrar en una historia de la que las mujeres estaban excluidas, salvo que se conformaran con el papel de pacientes o esposas. Su destino fue trágico. Tras participar en el auge del movimiento psicoanalítico ruso, los nazis la exterminarían junto a sus dos hijas en Rostov del Don, en julio de 1942.
### 3
El descubrimiento de América
Como en toda Europa, los científicos de la costa Este de Estados Unidos, marcados por el auge de la psiquiatría dinámica, procuraban resolver la cuestión de las enfermedades nerviosas. En ese país fundado por los descendientes de los puritanos tan admirados por Freud, la democracia se inspiraba en la Declaración de Independencia de 1776 y se basaba tanto en una concepción individualista de la libertad humana como en la creación de estados federados, cuyo proyecto era de inspiración religiosa. A través de sus «padres fundadores», el pueblo norteamericano se consideraba como el nuevo intérprete de la Biblia y el heredero de la antigua alianza divina con Israel. Durante toda la primera mitad del siglo XIX el florecimiento de la psiquiatría había coincidido con el desarrollo de los _state mental hospitals_ , sistema de seguros que se hacía cargo de los alienados indigentes, mientras que múltiples fundaciones y establecimientos privados se dedicaban al tratamiento de la locura.
Cuando Freud recibió la invitación a descubrir el Nuevo Mundo, dos grandes corrientes se enfrentaban en lo relacionado con el enfoque de las enfermedades del alma: por un lado los somaticistas, que atribuían el origen de los trastornos psíquicos a un sustrato neurológico y eran partidarios de un _educational treatment_ , y por otro los psicoterapeutas, quienes, si bien criticaban los excesos del somaticismo, buscaban una legitimidad negándose a que los asimilaran a sanadores. Todos los grandes especialistas norteamericanos de las enfermedades del alma —Morton Prince, Adolf Meyer, William James, James Jackson Putnam, Stanley Hall— eran refinados conocedores de las tesis europeas. Hablaban varios idiomas, habían viajado y seguían con interés las publicaciones de Janet, Flournoy, Bleuler, Jung y Freud.
Si la neurología, la psiquiatría y la psicología tenían un papel capital en el auge de los tratamientos psíquicos, la «moral civilizada» seguía siendo un componente esencial en la formulación de los diferentes enfoques terapéuticos. En ese país profundamente religioso, los ideólogos de la nueva sociedad industrial estaban convencidos, en efecto, de que el progreso de la civilización dependía de la estabilidad de la familia monogámica y del control ejercido sobre la sexualidad. En ese contexto, la construcción de una moral civilizada pasaba por una puesta en valor absoluta del matrimonio por amor en detrimento del matrimonio concertado y, en consecuencia, por la condena radical no solo de todas las prácticas de «fornicación» —masturbación, sodomía, felación, etc.— sino de todos los tipos de relaciones sexuales exteriores a la conyugalidad: tanto para los hombres como para las mujeres. Espantados por el poder de la energía sexual (o libido) —cuyos perjuicios se descubrían en los cuerpos convulsos de las histéricas—, los defensores de la ética protestante habían lanzado, en torno de 1900, una cruzada contra su posible «pérdida». Para ser útil a la familia industriosa, la libido debía canalizarse, desexualizarse, mesurarse e incluso orientarse hacia las llamadas actividades rentables, como la instrucción o la economía, y controlarse en el interior mismo de la conyugalidad burguesa. Así, frente a la prohibición del placer fuera del matrimonio, que, dictada por las ligas de la virtud, desembocaba en la abstinencia obligatoria, se afirmaba de manera simétrica la voluntad de luchar, dentro del matrimonio, contra la frigidez de las mujeres y la impotencia de los hombres. Una buena «unión civilizada» suponía pues la obligación de una sexualidad «normalizada», fundada tanto en el coito como en el orgasmo y la procreación. Pero como contrapartida, fuera de los lazos del matrimonio ninguna sexualidad «normal» tenía derecho de ciudadanía.
Esta posición era muy diferente de la de Freud, para quien, al contrario, la represión de la sexualidad era la causa de la neurosis, sin que la falta de control de la pulsión sexual brindara, empero, la solución a esta cuestión. En otras palabras, a sus ojos la idea de una «moral civilizada» descansaba, no sobre la preservación de la familia monogámica o la fidelidad conyugal, sino sobre la necesaria sublimación de las pulsiones en actividades creativas. Es cierto, Freud creía que la mente debía predominar sobre los sentidos, pero también sabía, por haberla practicado voluntariamente, que ninguna abstinencia sexual podía imponerse al sujeto en nombre de una moral higienista de inspiración religiosa.
En ese contexto, el simpático psicólogo Granville Stanley Hall lo invitó a pronunciar varias conferencias en la Clark University de Worcester con ocasión del vigésimo aniversario de su fundación. Reputado por sus «manías» —caminaba descalzo— y convencido de la validez de las teorías freudianas sobre la sexualidad, este gran especialista en la infancia y la adolescencia, adepto al higienismo, ignoraba hasta qué punto _Herr Professor_ , a despecho de sus tergiversaciones, soñaba con América, y tanto más cuanto que se sentía despreciado en Europa. Además, le encantaban los viajes, admiraba a Abraham Lincoln, quería ver puercoespines y aspiraba a conquistar una nueva tierra prometida.
Cuando se enteró de que Jung había sido invitado a la misma celebración como consecuencia de la defección de Ernst Meumann, especialista en la infancia, pidió a Ferenczi que lo acompañara; él correría con los gastos. Durante varias semanas se ocupó esencialmente de su ropa interior y de los trajes que tendría que usar en la travesía del Atlántico, en primera clase, a bordo del _George Washington_ , un soberbio paquebote de línea, la joya de la Norddeutscher Lloyd-Dampfer, dotado de camarotes elegantes, lugares para fumar, salones decorados, antenas Marconi, tumbonas con chales y mantas y varios pisos de puentes interconectados. ¿Habría bailes con trajes de etiqueta obligatorios? ¿Qué comidas servirían? ¿Qué trastornos digestivos serían de temer? ¿Cómo sería el barbero? ¿Y el baño? Provisto de su Baedeker y amontonando libros y ropa en un baúl, Ferenczi preparó minuciosamente su viaje sin omitir proponer a Freud la lectura de obras científicas sobre América. Freud no le hizo ningún caso.
Los tres hombres se reunieron en Bremen la víspera de la partida, el 20 de agosto de 1909, y almorzaron alegremente en un excelente restaurante. Acicateado por Freud y Ferenczi, Jung se decidió a romper su juramento de abstinencia y bebió vino por primera vez en nueve años. Freud interpretó ese acto como un juramento de obediencia en su favor y al punto las manías interpretativas reaparecieron con renovados bríos de uno y otro lado, delante de un Ferenczi que no tenía ningunas ganas de entrar en el gran juego del análisis silvestre.
Por la noche, Jung invitó a sus dos amigos a cenar en su hotel, y no bien sentados se puso a contar la leyenda de los cuerpos momificados de hombres prehistóricos encontrados en turberas alemanas —los _Moorleichen_ —, de quienes se ignoraba cómo habían muerto. Embargado de angustia, Freud tuvo un desmayo, y cuando recuperó el conocimiento explicó que ese relato traducía un anhelo del hijo de dar muerte al padre. Furioso, Jung recusó la interpretación, destacó todo lo que la «Causa» le debía y reprochó a Freud entregarse a un delirio proyectivo.
Durante la travesía del Atlántico, y mientras observaban los movimientos del océano, los dos hombres siguieron con su pretensión de analizarse mutuamente. Pensando en los ataúdes de cristal de la «cripta de plomo» de la catedral de Bremen, Jung contó un sueño en el que veía dos cráneos humanos en el suelo de una gruta. Freud se apresuró a reafirmar que su amigo deseaba inconscientemente su muerte.
En tanto que el maestro acusaba a su delfín de querer «matar al padre», Jung tomaba conciencia subrepticiamente de la evolución que se producía en él. En realidad, la fascinación que sentía por las grutas, las momias, los vestigios del pasado, respondía a su concepción del inconsciente. Jung nunca se había adherido a la teoría freudiana de un inconsciente pensado en términos de instancia, tejido de contenidos reprimidos y que se manifestaba a través de las palabras de la lengua común y corriente. Jamás había aceptado la idea de esa «otra escena» estructural cara a Freud, esa otra escena interna a la subjetividad y sin vínculo con absolutamente ninguna anterioridad. Jamás había tomado como fuente de inspiración el modelo de los trágicos griegos.
Jung pensaba ya en la posible existencia de un más allá del inconsciente, una forma de representación original que cada individuo lleva en sí mismo como patrimonio propio de toda la humanidad. La gruta, la caverna, lo arcaico, la genealogía de los ancestros, los espectros, las criptas o los secretos inconfesados constituían otros tantos temas que lo llevaban a esa convicción, es decir, a todo lo que Freud juzgaba irracional y muy poco científico. Lo que dividía a ambos hombres no era el deseo de Jung de «matar al padre», sino la imposibilidad en que uno y otro se veían de compartir una misma concepción de la clínica, de la psique y de la sexualidad: «Yo sospechaba», dirá Jung,
la existencia de un a priori colectivo de la psique personal, un a priori que consideraba en un principio como vestigios de modos funcionales anteriores [...]. No habría podido comunicar a Freud mis propias asociaciones para interpretar el sueño sin tropezar con su incomprensión y violentas resistencias. No me sentía a la altura necesaria para plantarle cara. Temía también perder su amistad si persistía en mi punto de vista.
Por el momento, Jung explicó que los dos cráneos eran los de su mujer y su cuñada. Freud no le creyó una palabra y, más adelante, lo invadió un franco enojo al advertir que Jung simpatizaba con William Stern, un psicólogo berlinés, adversario del psicoanálisis y partidario de la medición del «coeficiente intelectual». Freud trató a este hombre de «judío deplorable». No obstante, encantado con la travesía y la fuerte amistad que no dejaba de unirlo a su discípulo, dio pruebas de humor al comprobar que figuraba bajo el apellido de «Freund» en la lista de pasajeros. Y sintió verdadera alegría al cruzarse con un camarero que se deleitaba en la lectura de _Psicopatología de la vida cotidiana_.
Al llegar, a fines del verano, a las costas del Nuevo Mundo, y después de asistir la víspera al baile de despedida, Freud se sintió embargado por una intensa emoción. Había soñado con América, y ahora esta, gracias a una prestigiosa invitación, le prometía que el psicoanálisis saldría pronto, y de verdad, del «entorno vienés». Mientras el transatlántico se deslizaba en silencio sobre las aguas de la desembocadura del Hudson para echar anclas, el 29 de agosto por la noche, en el puerto de Hoboken (New Jersey), divisó la inmensa estatua de la Libertad con sus luces en lo alto. Se volvió entonces hacia Jung y pronunció estas palabras: «Si tan solo supieran lo que les traemos...». En enero había escrito a Ferenczi: «Muy pronto deberían incluirnos allá en el índex, no bien den con los basamentos sexuales de nuestra psicología».
Para hacer frente a lo que le esperaba, _Herr Professor_ había tomado la atinada decisión de no escribir de antemano ninguna conferencia e inclinarse, contra la opinión de Ferenczi, por hablar en alemán ante su auditorio, que conocía perfectamente el idioma, y sobre todo abordar sin rodeos la cuestión sexual.
Brill esperaba en el muelle a los tres hombres en compañía de Bronislaw Onuf, médico jefe de Ellis Island. Una vez cumplidas las formalidades, los llevó al hotel Manhattan, en la esquina de la avenida Madison y la calle Cuarenta y dos. Durante cinco días, haciendo caso omiso de los trastornos digestivos y el cansancio de los visitantes, les hizo descubrir Nueva York: el Metropolitan Museum y sus antigüedades griegas y egipcias, el Museo de Historia Natural, el Departamento de Psiquiatría de la Universidad de Columbia y los diferentes barrios —Chinatown, Harlem—, así como el parque de atracciones de Coney Island. Freud asistió por primera vez a una función cinematográfica, viajó en taxi y luego trató de visitar a un viejo compañero de estudios, Sigmund Lustgarten, y sobre todo a Eli Bernays y su mujer. Todos estaban ausentes debido a las vacaciones. Observó los carteles redactados en alemán, italiano o yiddish, y notó para su gran sorpresa que estos últimos tenían a veces caracteres hebreos. Para terminar, contó a Martha su peregrinaje por varios restaurantes y abundó, para su conocimiento, en el sabor del café, las frutas, el pan, las setas y la carne. En síntesis, se habituó a frecuentar un nuevo pueblo urbano, el del _melting pot_ norteamericano: negros, asiáticos, blancos, judíos, mestizos. Por momentos tenía la sensación de que esa mezcla no era sino la otra cara de la mezcla de la _Mitteleuropa_.
Durante horas discutió con Jung, en Central Park, las diferencias entre los pueblos y las «razas» y sobre todo entre los judíos y los «arios». La conversación se deslizó otra vez hacia los sueños. Freud tuvo un percance urinario que Jung interpretó, a la manera freudiana, como un deseo infantil de atraer la atención sobre él. Luego lo llevó a su hotel para someterlo a un «análisis en profundidad», más «junguiano».
Así como Freud veía en los sueños de Jung historias de asesinato del padre, Jung buscaba en el inconsciente de Freud misterios femeninos sepultados en una gruta arcaica. Y como solo se interesaba por las representaciones ligadas a su propia poligamia, estaba convencido de que, bajo el pretexto de la abstinencia, Freud escondía actividades culpables: «un material ardiente», es decir, relaciones carnales con su cuñada Minna. Por eso decidió, para aliviarlo, confesarle sus secretos patógenos. Con el argumento de su autoridad, Freud rechazó el ejercicio y Jung dedujo de esa actitud que aquel lo maltrataba, y se persuadió a la vez de que lo había curado provisionalmente de sus síntomas.
Tales eran pues las justas insensatas a las que se entregaban, en privado, los dos grandes representantes europeos del nuevo enfoque del psiquismo, invitados a dar a conocer sus trabajos clínicos y científicos frente a las más altas autoridades del mundo académico de Nueva Inglaterra. Cada uno a su manera, ambos ponían en juego los instrumentos propios de la exploración de la psique para infligirse un sufrimiento recíproco.
Jones se unió a Jung, Freud y Ferenczi la víspera de la partida hacia Worcester. Durante una cena en el Hammerstein's Roof Garden, volvió a aconsejar a Freud no avanzar demasiado en el terreno de la sexualidad. Tiempo perdido. El 5 de septiembre se instalaron todos en el Standish Hotel. Al día siguiente Jung y Freud tuvieron el privilegio de alojarse en la casa de Stanley Hall al mismo tiempo que William James, célebre psicólogo, que estimaba peligrosa la teoría freudiana —« _a dangerous method»_ — e incomprensible su interpretación del sueño. Se sentía más cerca de Jung por el interés que prestaba a la parapsicología, el espiritismo y la curación por la fe. Freud soñaba con convencerlo de la pertinencia de su doctrina y James quería conocer a toda costa a ese extravagante vienés que había trastornado el mundo de la psicología. Caminaron juntos por Worcester y Freud conservó de él el recuerdo emocionado de un hombre, ya muy enfermo, que afrontaba la muerte con serenidad.
Por primera vez en su vida, el 9 de septiembre, durante una cena en casa de sus anfitriones, Freud fue servido por criados negros que llevaban librea y guantes blancos. Por mucho que reivindicara las teorías sexuales de su invitado, Stanley Hall no dejaba de ser el heredero de una antigua familia de granjeros puritanos. Jung pareció halagado por la acogida, pero pese a ello escribió a Emma que apreciaba muy poco la «solemnidad virtuosa» de esa familia «rígida». Y para librarse de ella, se entregó a toda clase de bromas destinadas a suscitar la risa de los criados. Partidario de la jerarquía de las «razas», se sentía más cercano a sus «hermanos africanos» —enraizados, a su entender, en una genealogía primitiva— que a los hombres blancos civilizados de la costa Este. Freud, que veía en cada ser humano, más allá de cualquier diferencia, un sujeto universal —una singularidad—, no hizo por su parte ninguna observación sobre el servicio doméstico de sus anfitriones.
El 7 de septiembre, tras una extensa conversación con Ferenczi sobre lo que iba a decir, Freud inició su serie de cinco conferencias frente a una platea de ilustres científicos, entre ellos el antropólogo Franz Boas, los físicos Albert Michelson y Ernest Rutherford —ambos premios Nobel—, William James y muchos más. Adaptándose perfectamente al pragmatismo reclamado por su auditorio norteamericano, Freud se lanzó, sin recurrir a apuntes, a hacer una impresionante presentación de sus trabajos clínicos y teóricos. Y para no aparecer como el propietario de su doctrina, hizo un vibrante elogio de Breuer, el inventor de la palabra «psicoanálisis», y presentó con entusiasmo el caso «Anna O.» como la historia de una fantástica curación, sin saber, por lo demás, que Bertha Pappenheim había viajado desde la otra orilla del Atlántico al mismo tiempo que él para hablar allí de la prostitución. Luego expuso su método de interpretación de los sueños, su concepción de la represión, su técnica de la cura y su visión de la histeria. Para terminar, abordó de manera frontal la cuestión de la sexualidad infantil, con la mención del caso del «pequeño Hans» y estableciendo un paralelismo con la exposición de Jung sobre el «caso Ana».
En cada etapa de sus ponencias Freud daba ejemplos concretos. Así, para explicar la «moción de deseo», se refirió a la posible presencia de un «revoltoso» que quisiera perturbar el desarrollo de sus conferencias. Si sucedía eso, dijo, las personas presentes en la sala (las «resistencias») no tardarían en manifestarse para expulsar del anfiteatro al perturbador: se trataría en ese caso de una represión que permitiría el desarrollo apacible del curso. Pero una vez fuera, el revoltoso podría muy bien hacer aún más ruido y perturbar al conferenciante y sus oyentes de otra manera, no menos insoportable. Eso era, en efecto, lo que Freud llamaba síntoma: una manifestación desplazada de la moción inconsciente reprimida.
Comparó entonces al psicoanalista con un «mediador» capaz de entablar negociaciones con el revoltoso a fin de que este pudiera regresar al auditorio después de comprometerse a no molestar más a los oyentes. La tarea del psicoanalista era, pues, reconducir el síntoma al lugar de donde venía, es decir, hacia la idea reprimida.
Esas conferencias proponían una suerte de síntesis de la doctrina del primer Freud, un Freud optimista, un Freud de la Belle Époque convencido de haber aportado al mundo el impulso para una revolución de lo íntimo. En esos momentos no se trataba todavía de narcisismo, metapsicología, tópicas complicadas o pulsión de muerte. Freud hablaba de libido, de curación y de las manifestaciones del inconsciente en la vida cotidiana. Por añadidura, en relación con la sexualidad, tuvo la habilidad de citar los trabajos positivistas de Stanford Bell, investigador de la Clark University que había reunido una muestra de dos mil quinientos casos de niños: «Como diríamos en Europa, él trabajó al estilo norteamericano [...]. No me extrañaría que creyeran ustedes más en estas observaciones de su compatriota que en las mías».
Unánimemente apreciadas, las cinco conferencias de Worcester disfrutaron de una recepción triunfal en la prensa local y nacional. En un bello artículo, Stanley Hall calificó de nuevas y revolucionarias las concepciones freudianas, lo cual no le impediría más adelante, para gran furia de Freud, interesarse en las tesis de Adler. El 10 de septiembre, durante una solemne reunión, Freud recibió, al igual que Jung, el título de doctor en derecho, _honoris causa_ , de la Clark University. Sería esa su única distinción universitaria; para Jung, al contrario, la primera de una larga lista: estaba tan orgulloso de ella que a su regreso a Zurich encargó un nuevo papel de carta con el membrete de «Med. CG Jung, LL.D.» [ _Legum Doctor_ ].
Freud tuvo la impresión de que ese momento norteamericano marcaba el final de su aislamiento: «Por esa época yo solo tenía cincuenta y tres años», decía en 1925,
me sentía joven y sano, y la breve estancia en el Nuevo Mundo me resultó benéfica para mi sentimiento de mí mismo; si en Europa me sentía como despreciado, allá me vi aceptado por los mejores como uno de sus pares. Cuando en Worcester subí a la cátedra para dar mis cinco conferencias sobre psicoanálisis, me pareció la realización de un increíble sueño diurno. El psicoanálisis ya no era, pues, un producto delirante; se había convertido en un valioso fragmento de la realidad.
En la fotografía grupal tomada el día de la ceremonia se divisa, de pie en la primera fila, a Freud y Jung, vestidos con levita negra, al lado de Stanley Hall, Adolf Meyer, Franz Boas y William James. Detrás de ellos aparecen Jones, Brill, Ferenczi, Michelson y Rutherford. En medio de esos hombres de barba o bigote, algunos con bastón y sombrero en la mano, aparecía en la última fila, a la derecha, Solomon Carter Fuller, nacido en Liberia y nieto de esclavos norteamericanos que habían regresado a África. Primer psiquiatra negro del cuerpo de profesores de la Escuela de Medicina de la Universidad de Boston, conocía bien Europa y Alemania en particular por haber sido alumno de Alois Alzheimer en Munich, para convertirse luego en uno de los pioneros norteamericanos en el estudio de la terrible enfermedad. Practicante también de la psicoterapia, había asistido con interés a las conferencias de Freud.
No hay mujer alguna en esta fotografía, y sin embargo fue una mujer, la fogosa Emma Goldman, célebre anarquista, quien hizo el comentario más vívido de esa visita. También ella conocía Europa y hablaba alemán. En 1896, mientras cursaba estudios de comadrona en Viena, había tenido la oportunidad de seguir los cursos de Freud. En Worcester su intención era intervenir desde la sala, pero las «autoridades» habían sido terminantes en su negativa: era, se decía, «demasiado explosiva, demasiado peligrosa, demasiado histérica». En su autobiografía Goldman escribiría:
El suceso más importante de mi visita a Worcester fue la intervención de Freud [...]; me causaron una profunda impresión la lucidez de su mente y la simplicidad de sus palabras. Entre todos esos profesores, muy bien plantados, con aires de importancia y engalanados con sus togas, Freud, vestido con sencillez, modesto, casi apagado, se erguía como un gigante entre pigmeos.
«En apenas poco más de un año», escribe Linda Donn, «Freud había pasado de la modesta asamblea de Salzburgo a una posición de _primus inter pares_ en el campo de la psicología.» Tras la partida de Jones hacia Toronto, Jung, Freud y Ferenczi prosiguieron con su viaje. Visitaron las cataratas del Niágara y luego llegaron, a través del lago Placid, a Keene Valley, en las montañas Adirondack.
Como muchos otros representantes de la aristocracia de la costa Este, Putnam había comprado un lote de tierra en medio de los arces, los abetos y los pinos. Al llegar al lugar, Freud, que amaba los bosques y la naturaleza salvaje, se sintió estupefacto ante la suntuosidad de los paisajes y la manera de vivir de sus anfitriones en esa vieja granja transformada en residencia campestre, con salones, biblioteca, bañeras, chimeneas y cigarros por doquier. Para recibirlos, la familia Putnam había decorado la cabaña de los invitados, apodada «Chatterbox», en negro, rojo y oro, los colores de la Alemania imperial, olvidando que ninguno de ellos era alemán. Pero poco importaba. Jung entonó viejas canciones germánicas y Ferenczi ayudó a Freud a reponerse de una «apendicitis nerviosa» que no era otra cosa que la manifestación de sus habituales trastornos digestivos ( _Magenkatarrh_ ). _Herr Professor_ encontraba decididamente «espantosa» la comida norteamericana y se negaba a beber el agua helada que le servían, reclamando siempre, estuviera donde estuviese, vino del Rin.
Después de no pocos esfuerzos y largos paseos se cruzó por fin con su sueño: un puercoespín, pero desgraciadamente muerto. Para consolarlo, los Putnam le obsequiaron una estatuilla del animal, que Freud puso en su escritorio. Desde hacía mucho lo fascinaba la parábola de Schopenhauer, su filósofo preferido, sobre la sociabilidad:
Un helado día de invierno, los miembros de la sociedad de puercoespines se apretujaron para prestarse calor y no morir de frío. Pero pronto sintieron las púas de los otros, y debieron tomar distancias. Cuando la necesidad de calentarse los hizo volver a arrimarse, se repitió aquel segundo mal, y así se vieron llevados y traídos entre ambas desgracias, hasta que encontraron un distanciamiento moderado que les hizo tolerable la situación. Así, la necesidad de sociedad, nacida del vacío y la monotonía de su vida interior, empuja a los hombres los unos hacia los otros; pero sus muchas maneras de ser antipáticos y sus insoportables defectos vuelven a dispersarlos.
Schopenhauer llegaba a la conclusión de que la sociabilidad era inversamente proporcional al valor intelectual de un hombre y de que la sabiduría humana consistía en mantenerse al margen de la sociedad, dedicados al cultivo de un calor interior.
Si bien conquistó el Nuevo Mundo, Freud no dejaría de considerar que América era «una máquina loca»: «Mi éxito será breve», confiaría pronto a Barbara Low, «los norteamericanos me tratan como lo haría un niño que se entretiene con su nueva muñeca, para reemplazarla poco después por otro juguete».
Algunos años más adelante el psicoanálisis se convirtió en la «cura mental» más popular del continente americano. Barrió con las viejas doctrinas somáticas, sustituyó a la psiquiatría, hizo caer en el ridículo los grandes principios de la moral civilizada y provocó el entusiasmo de las clases medias. Se entiende entonces la furia que, a continuación, se desataría contra ese europeo pesimista, poco inclinado a adherirse al eje del bien y del mal en materia de sexualidad. En 1909, ¿no había sembrado la confusión en la conciencia perseguida de los puritanos? De hecho, los norteamericanos recibieron triunfalmente el psicoanálisis por lo que no era —una terapia de la felicidad— y lo rechazaron sesenta años después porque no había cumplido la promesa que no podía cumplir.
Como dos puercoespines, Jung y Freud eran peligrosos el uno para el otro, como lo era el psicoanálisis para Estados Unidos y Estados Unidos para el psicoanálisis. Freud lo sabía, pero ignoraba aún que su doctrina estaba destinada a «americanizarse» cada vez más a medida que Europa, tras una primera guerra letal y el exilio de sus principales discípulos, se convirtiera en presa del nazismo.
De desmayos a desacuerdos y de disputas a interpretaciones silvestres y enfermedades somáticas, la ruptura entre Freud y Jung se concretó en el verano de 1912, cuando el primero tuvo que ir precipitadamente a Kreuzlingen para ponerse a la cabecera de Binswanger, afectado por un tumor maligno. Había avisado a Jung de su visita y pensaba verlo junto a su común amigo. Por eso olvidó hacer un rodeo por Küsnacht, lugar de residencia que aquel acababa de acondicionar a orillas del lago de Zurich: un malentendido más. Vino a continuación el cuarto congreso del Verein en Munich; después, sombrías discusiones acerca de un artículo de Karl Abraham consagrado a Amenhotep IV, el hijo del faraón, y por último la publicación de _Transformaciones y símbolos de la libido_ , obra donde Jung proponía una completa desexualización del concepto de libido.
Durante todo ese tiempo Freud siguió extendiendo su doctrina a la dilucidación de los enigmas del arte y la literatura. Como un Sherlock Holmes, le encantaba abandonarse al desciframiento de la vida inconsciente de los «grandes hombres». Leonardo da Vinci formaba parte desde siempre de ese panteón de elegidos por quienes sentía una admiración sin límites.
En octubre de 1909, justo a su regreso de su periplo americano, decidió dedicar un ensayo a ese genio universal del _Cinquecento_ , zurdo, homosexual, vegetariano, atraído por las «cabezas extrañas y grotescas», conocido por haber dejado inacabadas sus obras, ingeniero, escultor, anatomista, caricaturista, arquitecto admirado en vida por todos sus contemporáneos, hijo ilegítimo de Piero da Vinci, un rico notable, y una humilde campesina, celebrado y protegido por príncipes y reyes, de Ludovico Sforza a Francisco I, pasando por Lorenzo de Médicis.
Freud anunció su proyecto a Jung como si emprendiera la conquista de un nuevo continente:
Debemos hacer igualmente nuestro el dominio de la biografía. Desde mi regreso no tengo más que una idea. De improviso, el enigma del carácter de Leonardo da Vinci se me ha tornado transparente. Ese sería pues un primer paso en la biografía. Pero el material sobre Leonardo es tan escaso que desespero de exponer a los otros de manera comprensible aquello de lo que a ciencia cierta estoy convencido.
Su convicción radicaba sobre todo en que la vida carnal del gran Leonardo era la ilustración perfecta de una de sus hipótesis acerca de las teorías sexuales infantiles, y deducía de ello que aquel había sido «sexualmente inactivo u homosexual» y que «había convertido su sexualidad en pulsión de saber», sin dejar de aferrarse a «la ejemplaridad del inacabamiento». Y añadía que poco tiempo atrás había visto en un neurótico (sin genio) una sintomatología idéntica. En otras palabras, planteaba una vez más una hipótesis que esperaba ver verificada a la luz de los hechos.
Para escribir su ensayo se apoyó en fuentes indiscutibles, casi todas traducidas al alemán: la biografía de Edmondo Solmi, el estudio de Smiraglia Scognamiglio dedicado a la infancia y la juventud de Leonardo, el estudio clásico de Giorgio Vasari, el del historiador del arte francés Eugène Müntz, el _Tratado de pintura_ del propio Leonardo y sus _Cuadernos_. Pero debía buena parte de sus hipótesis a la biografía novelada de Merezhkovski, su libro de cabecera. En esa novela histórica —muy bien documentada, por lo demás—, el escritor ruso, para elaborar el retrato de Leonardo, imaginaba que Giovanni Boltraffio, su alumno, llevaba un diario secreto sobre su maestro. Este recurso permitía a Merezhkovski hacer del pintor un personaje conforme a su concepción dualista del paganismo y el cristianismo: dos corrientes universales irreconciliables, decía, una vuelta hacia Dios y otra que se alejaba de él. Y pintaba entonces a Leonardo con los colores de una especie de Anticristo, hereje, impío y femenino, que no se acercaba jamás a las mujeres por el horror que le despertaba la mera idea de una posesión física. Esta interpretación de un Leonardo escindido e infiel, atraído tanto por la sonrisa de los ángeles andróginos como por los rostros monstruosos, y empeñado en destruir a través de su arte las Sagradas Escrituras, complacía a Freud, que conocía muy bien los otros libros del escritor ruso.
Como la cuasi totalidad de los biógrafos de Leonardo, Merezhkovski silenciaba la existencia de una homosexualidad activa en el pintor y se contentaba con mencionar sus relaciones ambiguas con su maestro Andrea del Verrocchio y dos de sus alumnos, Boltraffio y Francesco Melzi. A comienzos del siglo XX, atreverse a hablar crudamente de la vida sexual de Leonardo era todavía un acto de subversión que amenazaba provocar un inmenso escándalo. Sin embargo, aunque no se la nombrara, esa vida era conocida. Bastaba con consultar los archivos para saber que el pintor había estado a punto de morir en la hoguera a raíz de una denuncia, presentada el 9 de abril de 1476 ante los «oficiales de la noche» de la ciudad de Florencia, por «sodomía activa» en la persona de Jacopo Saltarelli, aprendiz de orfebre y chapero notorio. Leonardo fue liberado por falta de pruebas tras pasar dos meses en la cárcel, lo cual no le impidió seguir teniendo jóvenes amantes. En 1505 diría, además, que en su juventud lo habían condenado por actos que continuaba realizando en la vida adulta, y que eran entonces, sin duda, aún más reprobables.
Había recibido en su casa a Gian Giacomo Caprotti, apodado Salai (el diablo), un joven y agraciado ladrón de pelo rizado y sonrisa enigmática, que llegaría a ser su alumno y haría un retrato de Mona Lisa desnuda. En Leonardo, por lo tanto, no había «relaciones ambiguas» con los hombres, sino más bien amores disimulados a lo largo de toda su vida, para no incurrir en el riesgo de la pena de muerte. Y es poco probable que fuera, como creía Freud, un hombre «sexualmente inactivo» que, en virtud de una sublimación, había convertido su sexualidad en una pulsión de saber. Leonardo vivió hasta su muerte en compañía de Melzi, a quien haría su heredero.
Es indudable que Freud proyectaba en este genio sumamente admirado su culto de la abstinencia. En verdad era él, y no Leonardo, quien había convertido su pulsión sexual en una pulsión creadora. De todas maneras, faltaba explicar la génesis de esa homosexualidad. Y Freud sabía que en la vida del gran hombre aún quedaban por descifrar muchos enigmas, en particular un recuerdo de infancia detalladamente anotado en sus _Cuadernos_. En ellos Leonardo explicaba por qué le gustaban tanto las aves, al extremo de imaginar máquinas capaces de transformar a los hombres en ángeles voladores: «Parece que ya de antes me estaba destinado», escribía, «ocuparme tanto del buitre, pues me acude, como un tempranísimo recuerdo, que estando yo todavía en la cuna un buitre descendió sobre mí, me abrió la boca con su cola y golpeó muchas veces con esa cola suya contra mis labios». Freud citaba la versión alemana de ese texto, en el cual aparecía la palabra «buitre» ( _Geier_ ), pero en nota agregaba el original italiano, donde Leonardo hablaba de otra ave de presa llamada _nibbio_ (milano) que habría debido traducirse en alemán como _Hühnergeier_ o _Gabelweihe_. En ese original, citado por Scognamiglio y tomado del Códice Atlántico, Leonardo decía que la cola del ave había entrado «entre los labios» y no que los había «golpeado».
Fascinado con razón por ese increíble recuerdo infantil, que parecía salido directamente de _La interpretación de los sueños_ , Freud no se percató del error de traducción. Pero ¿olvidaba acaso que una palabra no es un mito? Al procurar resolver el enigma del vínculo entre la homosexualidad de Leonardo y su recuerdo de infancia, formuló pues la hipótesis de que el pintor se había inspirado en mitos de la civilización egipcia, en la cual la palabra «madre» se escribe por medio de un pictograma que remite a la imagen del buitre, animal cuya cabeza representaba una divinidad materna y cuyo nombre se pronunciaba _mut_. Y asociaba esa representación a la leyenda cristiana según la cual el buitre, ave hembra, abre la vagina para que el viento la fecunde, y encarna así a la virgen inmaculada.
Al cotejar esos dos mitos del recuerdo infantil de Leonardo, Freud deducía que la felación por la cola no era sino la repetición de una situación más antigua, la del lactante que recibe en la boca el pezón materno. La reminiscencia del buitre y la connotación pasiva asociada a ella debían pues ponerse en relación con la infancia del pintor, criado por su madre, Caterina, y objeto exclusivo de su amor, sin padre con el cual identificarse en el momento de surgimiento de su sexualidad. Esto equivale a decir que Freud establecía una relación de causalidad entre el vínculo infantil de Leonardo con su madre y la génesis de su homosexualidad. Luego interpretaba esta como un repliegue hacia una fase autoerótica que lo llevaba a amar exclusivamente a sustitutos de su propia persona. Es así, explicaba, como el homosexual masculino reprime el amor por la madre después de haber quedado fijado en ella, y encuentra a continuación sus objetos amorosos por el camino del narcisismo.
Hasta ese momento Freud se había conformado, en lo referido a la inversión masculina, con declaraciones contradictorias. A su entender, esa inversión derivaba no de una herencia sino de una bisexualidad e incluso de una predisposición o un autoerotismo. Pero, con referencia a Leonardo, hablaba por primera vez de una fijación en la madre y de una elección narcisista que excluía la identificación con el padre. Y procuraba, claro está, resolver el enigma de la famosa sonrisa de Mona Lisa del Giocondo, que desafiaba al espectador de ese cuadro a tal punto que, a lo largo de cuatro siglos, había hecho perder la cabeza a todos los especialistas que la contemplaban. Goethe había hecho de ella la encarnación más pura del eterno femenino, el equivalente de lo que el ideal griego había aportado a la estatuaria antigua. Para Freud, más simplemente, Leonardo había pintado la sonrisa de su madre, una madre transfigurada por la mirada de su hijo. Así, las bellas cabezas de ángeles y adolescentes apreciadas por el pintor eran otras tantas reproducciones de su propia persona infantil, y las mujeres sonrientes, réplicas de Caterina, que exhibía antaño la misma sonrisa ahora perdida por él.
Siempre lleno de audacia, Freud procedía a efectuar otra comparación entre _La Gioconda_ y _Santa Ana con la Virgen y el Niño_ ( _Anna Metterza_ ), afirmando que este segundo cuadro era una continuación del primero. En él, santa Ana sujetaba a su hija María; esta, a su vez, trataba con un gesto de hacer lo mismo con Jesús, que procuraba jugar con el cordero del sacrificio. Ana encarnaba a la Iglesia y María sabía que su hijo moriría. La primera sujetaba a la segunda que sujetaba al tercero, y cada actor de ese trío sabía, supuestamente, que la pasión y la redención de Jesús eran inevitables.
Olvidando que el tema de la _Anna Metterza_ era frecuente en la pintura del _Quattrocento_ y que Leonardo había hecho bosquejos de esa tela antes de su encuentro con Mona Lisa, Freud pretendía discernir en ella la presencia de dos madres: por un lado Caterina, la esposa legítima del padre, y Donna Albiera por otro. Ambas, decía Freud, tenían la misma edad y la misma sonrisa:
Cuando Leonardo fue acogido en casa de sus abuelos, no habiendo alcanzado todavía los cinco años de edad, sin duda que en su sentir la joven madrastra Albiera ocupó el lugar de su madre y él entró en esa relación de rivalidad con el padre que merece el nombre de normal. Como es notorio, la decisión en favor de la homosexualidad solo sobreviene en las cercanías de la pubertad. Cuando ella se hubo decretado para Leonardo, la identificación con el padre perdió toda significatividad para su vida sexual pero continuó en otros campos de quehacer no erótico.
Freud no solo atribuía dos madres a Leonardo: explicaba además que la identificación paterna había sido funesta para él porque, al sentirse el padre de sus obras, no se preocupó por ellas más de lo que su padre se había preocupado por él. Por eso el inacabamiento permanente. Para terminar, el amor por las aves y el sueño de levantar vuelo remitían, según Freud, a un deseo infantil de acceder a una intensa actividad sexual, que a posteriori se había convertido en una capacidad inaudita de crear objetos insólitos semejantes a juguetes de niño. Vasari contaba además que Leonardo fabricaba animales huecos y livianos a los que insuflaba aire para hacerlos volar, e incluso que había añadido alas al lomo de un gran lagarto, también provisto de ojos, cuernos y barba para asustar a sus amigos.
La invención freudiana de un Leonardo del nuevo siglo fue saludada con toda la razón como una verdadera hazaña. Por su estilo, la obra se parecía a una novela de iniciación —entre Balzac y Conan Doyle— que arrastraba al lector al corazón de un mundo oculto donde reinaba, cual una diosa enigmática, la extraña figura andrógina de la Gioconda de indescifrable sonrisa: «Lo único bello que he escrito», diría en 1919. Contra los psicólogos de su tiempo, Freud había asociado la historia del neurótico moderno al doble nombre de Hamlet y Edipo, y ahora, frente a los sexólogos, daba el nombre de Leonardo a cada representante de la antigua «raza maldita». A continuación no dejaría de cambiar de opinión con respecto al enfoque clínico de la homosexualidad masculina.
En notas agregadas en 1919 comentó los bosquejos, mostrando que en uno de ellos Leonardo había fundido los cuerpos de María y Ana como si se tratara de un proceso de condensación, a tal punto que ya no se podía distinguir uno de otro como no fuera por el rostro. También analizaba un célebre dibujo del pintor en el que se representa un coito, y deducía que Leonardo había tratado con cierto descuido el aparato genital femenino.
Durante años, discípulos y amigos se entretuvieron con el juego de «la imagen en clave inconsciente». En 1913 Oskar Pfister creyó así descubrir la silueta de un buitre en el drapeado que rodea a las dos mujeres de la _Anna Metterza_. Y de hecho, a través del juego de unas interpretaciones que eran, con todo, perfectamente racionales, Freud se inscribía sin saberlo en continuidad directa con una literatura simbológica y hierogámica que tomaba por tema los misterios de la vida y la obra de Leonardo da Vinci para hacer de este pintor universal el emblema de una visión sexualizada de las Sagradas Escrituras.
En este ensayo Freud también respondía a Jung, ávido de ese tipo de literatura. Ya no hablaba de asesinato del padre sino del vínculo precoz con la madre, como si quisiera mostrar que, en el plano simbólico, esta ocupaba un lugar tan determinante como el de aquel en la evolución del niño. En el texto la madre ya no supone una evidencia natural sino una posición estructural. De tal modo, por medio de este estudio Freud daba los últimos toques a su concepción de la familia occidental, sin dejar de correr, de todas formas, el riesgo de transformar un gran relato de los orígenes —el mismo inventado por él— en una vulgar psicología.
En efecto, no bien concluida la redacción de su brillante ensayo sobre Leonardo utilizó por primera vez el término _Ödipuskomplex_ o complejo de Edipo. Su pretensión era traducir clínicamente, contra el telón de fondo de una escena primitiva o un coito fantaseado, la historia del deseo por la madre y la rivalidad con el padre. Después de haber explicado todo el desprecio que el varón pequeño siente por las prostitutas cuando descubre que su madre, al acostarse con su padre, se les asemeja, señalaba:
Empieza a anhelar a su propia madre en el sentido recién adquirido y a odiar de nuevo al padre como un competidor que estorba ese deseo; en nuestra terminología: cae bajo el imperio del complejo de Edipo [ _Ödipuskomplex_ ]. No perdona a su madre, y lo considera una infidelidad, que no le haya regalado a él, sino al padre, el comercio sexual.
Fue con ocasión de una nueva incursión en un continente que se proponía explorar —el de la antropología— cuando Freud retomó su temática del asesinato del padre, con la publicación, entre 1911 y 1913, de cuatro pequeños ensayos reunidos a continuación bajo el título de _Tótem y tabú_ , uno de sus libros más bellos. Como la histeria, el totemismo, consistente en establecer una conexión entre una especie natural (un animal) y un clan exogámico a fin de explicar una hipotética unidad original de los diversos hechos etnográficos, atraía a los científicos de fines del siglo XIX.
El libro se presentaba como una fábula darwiniana sobre el origen de la humanidad, la omnipotencia del pensamiento y la relación de los hombres con los dioses. Por eso iba a contrapelo de la evolución de la antropología moderna, que en esa época ya había renunciado a la búsqueda de los mitos de origen para estudiar, por medio de expediciones y viajes, las costumbres, la lengua y la historia de los pueblos autóctonos. Y ahora resultaba que el sabio vienés, que solo había viajado por el mundo occidental, pretendía explorar, a través de un conocimiento puramente libresco, un terreno que no conocía. En síntesis, se proponía volver a poner en juego los mitos y las dinastías reales en el preciso momento en que el saber científico moderno —de Franz Boas a Bronislaw Malinowski— efectuaba una ruptura radical con todas las tesis antiguas relativas a la oposición entre el primitivo y el civilizado, el animal y el humano, y más aún con la temática colonial de la jerarquía de las razas.
Pero Freud no quería abandonar ese _Ödipuskomplex_ que acababa de teorizar y del que pretendía hacer, contra viento y marea, un complejo universal propio de todas las sociedades humanas y situado en el origen de todas las religiones. Esta es la trama de su relato tal como la expuso febrilmente a todos sus discípulos de la WPV: en un tiempo primitivo los hombres vivían dentro de pequeñas hordas, sometidas al poder despótico de un macho que se apropiaba de las hembras. Un día, los hijos de la tribu, rebelados contra el padre, pusieron fin al reino de la horda salvaje. En un acto de violencia colectiva, mataron al padre y se comieron su cadáver. Sin embargo, después del asesinato sintieron arrepentimiento, renegaron de su crimen e inventaron un nuevo orden social mediante la instauración simultánea de la exogamia (o renuncia a la posesión de las mujeres del clan del tótem) y el totemismo, fundado en la prohibición del asesinato del sustituto del padre (el tótem).
Totemismo, exogamia, prohibición del incesto: tal era el modelo común a todas las religiones, y en especial al monoteísmo. En esta perspectiva, el complejo de Edipo no era otra cosa, según Freud, que la expresión de los deseos reprimidos (deseo de incesto, deseo de matar al padre) contenidos en los dos tabúes característicos del totemismo: prohibición del incesto, prohibición de matar al padre-tótem. En consecuencia, era menester considerarlo como un paradigma universal, porque traducía las dos grandes prohibiciones fundacionales de todas las sociedades humanas.
Para construir esta fábula, Freud se apoyaba en la literatura evolucionista. En primer lugar, tomaba de Darwin la famosa historia de la horda salvaje, contada en _La descendencia del hombre_ , luego la teoría de la recapitulación, conforme a la cual el individuo repite las principales etapas de la evolución de las especies (la ontogénesis repite la filogénesis), y por último la tesis de la herencia de los caracteres adquiridos, popularizada por Jean-Baptiste Lamarck y adoptada por el propio Darwin y Haeckel. De James George Frazer —el autor de la célebre epopeya de _La rama dorada_ , la historia de ese rey asesino de la Antigüedad latina muerto por su sucesor, cuando él mismo debía su poder al asesinato de su predecesor—, Freud tomaba una concepción del totemismo como modo de pensamiento arcaico de las llamadas sociedades «primitivas». De William Robertson Smith adoptaba la tesis de la comida totémica y la sustitución de la horda por el clan. En James Jasper Atkinson encontraba la idea de que el sistema patriarcal llegaba a su fin en la rebelión de los hijos y la devoración del padre. Y para terminar, de la obra de Edward Westermarck extraía consideraciones sobre el horror al incesto y la nocividad de los matrimonios consanguíneos.
Si Freud hacía del salvaje un equivalente del niño y mantenía las etapas de la evolución, rechazaba en cambio todas las teorías de la «inferioridad» del estado primitivo. En consecuencia, no hacía del totemismo un modo de pensamiento mágico menos elaborado que el espiritualismo o el monoteísmo: lo veía, antes bien, como una supervivencia interna a todas las religiones. Y por esa misma razón, solo comparaba al salvaje con el niño para probar la adecuación entre la neurosis infantil y la condición humana en general, y erigir así el complejo de Edipo en modelo universal. Por último, con referencia a la prohibición del incesto y al origen de las sociedades, aportaba una nueva luz. Por un lado, renunciaba a la idea misma de origen, al afirmar que la famosa horda no existía en ninguna parte: el estado original era de hecho la forma interiorizada para cada sujeto (ontogénesis) de una historia colectiva (filogénesis) que se repetía con el paso de las generaciones; por otro, destacaba que la prohibición del incesto no había surgido, como creía Westermarck, de un sentimiento natural de repulsión de los hombres con respecto a esa práctica; había, al contrario, un deseo de incesto, y su corolario era la prohibición instaurada bajo la forma de una ley y un imperativo categórico. ¿Por qué, en efecto, habría de prohibirse un acto que horrorizaba a tal punto a la colectividad? En otras palabras, Freud aportaba a la antropología dos temas salidos en su doctrina: la ley moral, la culpa. En lugar del origen, un acto real: el asesinato necesario; en lugar del horror al incesto, un acto simbólico: la interiorización de la prohibición. Desde ese punto de vista, cada sociedad se fundaba en el regicidio, pero solo salía de la anarquía asesina a condición de que siguieran a ese regicidio una sanción y una reconciliación con la imagen del padre, la única que autorizaba la conciencia.
_Tótem y tabú_ era pues, en primer lugar, un libro político de inspiración kantiana, así como un manifiesto contra la psicología de los pueblos tan apreciada por Jung. Propondré además la hipótesis de que también era el fruto del viaje por Estados Unidos, durante el cual los dos hombres habían abordado con tanta frecuencia la cuestión de la mezcla de las «razas» y las «etnias», sobre todo en Nueva York. Freud y Jung no tenían ninguna opinión común al respecto, y _Tótem y tabú_ era la prueba de ello. Con el estudio sobre Leonardo, Freud había privilegiado la relación con la madre en respuesta a Jung, y he aquí que ahora volvía a la rebelión contra el padre para marcar una ruptura radical, tanto con el relativismo junguiano como con cualquier forma de colonialismo.
Su ensayo proponía en definitiva una teoría del poder democrático centrado en tres necesidades: necesidad de un acto fundador, necesidad de la ley, necesidad de la renuncia al despotismo. Sin embargo, la recepción brindada a _Tótem y tabú_ no lo destacó como un libro político sino como una contribución seria del psicoanálisis a la antropología. No suscitó la indignación prevista, pero sí cosechó severas críticas, a menudo justificadas, por otra parte. En efecto, Freud no solo se mantenía aferrado a los marcos del evolucionismo del que la etnología de principios de siglo estaba emancipándose, sino que, por añadidura, pretendía regentar un dominio del que no conocía nada, sin tener en cuenta los trabajos contemporáneos. Ese sería el sentido de la crítica elaborada en 1920 por el antropólogo norteamericano Alfred Kroeber, especialista en los indios de América del Norte, que muchos representantes de la disciplina harían suya.
Si _Tótem y tabú_ dio durante sesenta años pábulo a debates que aún perduran, fue en lo fundamental debido a las resistencias que despertó. Jones tuvo activa participación en ellos, sobre todo con Malinowski, y a continuación surgirían nuevas disputas y exámenes con Geza Roheim y Georges Devereux.
_Tótem y tabú_ fue la última gran obra del Freud de la Belle Époque, esa ensoñación roussoniana sobre el paso de la naturaleza a la cultura que no dejaba de evocar, en el plano clínico, la historia de Schreber. Tenía aún toda la frescura de los ideales mesiánicos de los que estaban imbuidos los primeros freudianos. Al leer ese libro tenemos verdaderamente la impresión de ver a Freud pasearse en medio de una naturaleza salvaje poblada de los relatos de aventuras que tanto había amado en su infancia. Recorría la geografía de los mitos y las creencias a través de los libros procedentes de una época pasada y con la misma vivacidad de sus primeras vacaciones en Italia, deslumbrado por Leonardo o rumbo al sur en busca de una inencontrable Gradiva.
Años después del periplo americano, ya consumada la ruptura, Jung fue asaltado por alucinaciones y temió extraviarse en abismos de ignorancia, al punto de olvidar que vivía en Küsnacht y tenía mujer e hijos. Había perdido un maestro, un amigo, un cómplice. De una y otra parte la ruptura había sido de extrema violencia a pesar de los esfuerzos de Emma, que intentó, como Sabina Spielrein, que ambos hombres no quemaran las naves. Mientras seguía ejerciendo como psiquiatra, Jung pasó por estados que conocía bien por haberlos descrito en sus pacientes. Después logró salir a la superficie y se rodeó de amantes y discípulos. Con Emma, que había estado a punto de divorciarse, constituyó una escuela de psicoterapia —la psicología analítica— y se embarcó en la exploración de las imagos y más adelante de los arquetipos. Jamás volvió a ver a Freud, pero, como él, no dejó de replantearse a lo largo de toda su vida lo que los había unido para luego separarlos.
Una vez más, en septiembre de 1913, invadido por la tristeza, Freud se trasladó a Roma, convencido de que la incomparable belleza de la ciudad le resultaba cada vez más necesaria. Hizo una parada en Bolonia para encontrarse con Minna, que lo acompañó en su periplo. Escribió estas palabras a sus hijos Sophie y Max: «Por supuesto, tendréis que venir aquí algún día. Pero en verdad no es una cuestión apremiante; con los años, la estancia es cada vez más sustancial y quizás vosotros seáis todavía demasiado jóvenes. Por el momento, vuestra casa debe apasionaros e interesaros mucho más que la más bella y eterna de las ciudades». Y a Anna: «Papá a su futura acompañante». Minna estaba agotada por los recorridos a paso vivo que le imponía su cuñado. Él, por su parte, soñaba ya con que su hija menor ocupara el lugar de su tía. Entretanto, un día, sentado a la mesa de un café, repartió chocolates entre los hijos de un viajero, no muy sorprendido al comprobar cómo se parecían ese hermano y esa hermana, Sigmund y Minna.
Todos los días, como ya había hecho el año anterior, visitaba la iglesia de San Pietro in Vincoli a fin de contemplar la imponente estatua esculpida por Miguel Ángel para engalanar la tumba de Julio II. Y fue allí donde se dio cuenta de que el profeta sostenía al revés las Tablas de la Ley y que, enfurecido contra su pueblo, estaba a punto de dejarlas caer antes de rehacerse: la calma sucedía a la tempestad. Como mantenía con ese trabajo de largo aliento «la relación que uno tiene con un hijo del amor», se identificó con Miguel Ángel, que había hecho de Moisés el ejemplo mismo de la capacidad humana de dominarse. Después de los trágicos griegos, América y los tormentos de la ruptura con Jung, había llegado para él, por la vía de su apego al Renacimiento italiano, la hora de interesarse en una nueva historia de asesinato del padre que lo devolvería a una reflexión sobre su judeidad. Por lo demás, la había iniciado en su soberbia ensoñación darwiniana sobre el origen de las sociedades. En marzo de 1914 publicó en _Imago_ este ensayo sobre el _Moisés_ de Miguel Ángel en forma anónima. Dudaba de sus hipótesis.
Mientras tanto, Jones había ocupado el lugar de Jung y creado el Ring (o Comité Secreto) para reagrupar a los discípulos más fieles: Karl Abraham, Hanns Sachs, Otto Rank y Sándor Ferenczi. Anton von Freund, industrial húngaro, quedó asociado a la empresa hasta su muerte en 1920 y Max Eitingon se unió al grupo en 1919. Para Freud, así rodeado por sus seis elegidos y por quien iba a financiar el Verlag —la editorial del movimiento—, la tarea consistía en construir un proyecto racional capaz de preservar la doctrina de cualquier tipo de desviación: rechazar las mitologías oscurantistas, el espiritismo y el pensamiento mágico; mantenerse firme en cuanto a la cuestión sexual; formar clínicos que ya no estuvieran afectados por trastornos patológicos; luchar contra los impostores, etc. Jones quería reunir en torno a Freud a combatientes capaces de responder a los enemigos externos, a fin de que él pudiese ocuparse exclusivamente de la elaboración de su obra y, de tal modo, quedar eximido de todas las molestias del liderazgo.
Inspirado en el modelo de las sociedades secretas del siglo XIX, el Ring se concibió, por lo tanto, como una asamblea de caballeros de la Tabla Redonda: igualdad entre los miembros, soberanía compartida con el maestro que no podía decidir nada sin ellos. Pero la iniciativa era también una manera de restablecer los principios de la medicina hipocrática: crear escuelas fundadas en la relación entre un maestro y un discípulo. Eje horizontal de un lado, eje vertical de otro: Freud retomaría esta teorización del poder en 1921, en _Psicología de las masas y análisis del yo_. Para sellar la alianza con sus nuevos paladines, les entregó una gema griega grabada en hueco de su colección, que ellos hicieron montar en un anillo de oro. Siempre embargado por el ideal olímpico, él llevó la que representaba a Zeus.
Una vez terminada la guerra, y cuando la unión sagrada contra Jung ya no era de actualidad, estallaron nuevos conflictos entre los propios paladines, que terminaron por poner fin a la hermosa aventura después de haber intercambiado una cantidad impresionante de circulares: las _Rundbriefe_.
En julio de 1914, de veraneo en Karlsbad, Freud no imaginaba ni por un momento que la guerra habría de ser larga, ni que provocaría millones de muertos, ni que la Europa que él conocía, la cuna del psicoanálisis, desaparecería para siempre. Revelaba entonces a su hermana Maria (Mitzi) lo viejo y cansado que se sentía: «Martha y yo tenemos problemas cardíacos. [...] Nos hemos convertido en una vieja generación». Y en una carta a Ferenczi mencionaba el sorprendente «asesinato de Sarajevo», sin pensar en las consecuencias que ese acontecimiento podría tener para su movimiento en plena expansión.
En Berlín, por su parte, Abraham no pensaba en otra cosa que en deshacerse de los partidarios de Jung, mientras se concentraba en la organización del quinto congreso del Verein que debía celebrarse en Dresde. En Londres, Jones, mucho más lúcido, preveía que Alemania y Austria serían los países vencidos en ese nuevo tipo de guerra. Y como Anna Freud residía en su casa, tuvo la impresión de que estaría más segura en Inglaterra que en Viena. De todas maneras, preparó su regreso. Ninguno de los miembros del comité soñó ni por un momento en verlo como un enemigo, y el propio Freud le envió sus cartas en inglés, a sabiendas de que serían abiertas.
El 9 de noviembre de 1914 Freud anunció a Ferenczi que la voz del psicoanálisis ya no podía oírse en el mundo desde que habían comenzado a tronar los cañones. Como en la novela de Tolstói, el tiempo de la guerra sucedía al de la paz, los cuerpos lacerados a la palabra, el odio al diálogo. Por doquier, los profesores universitarios devolvían sus diplomas _honoris causa_ a sus amigos, convertidos ahora en enemigos.
Con la publicación de un artículo sobre el narcisismo, Freud comenzaba en 1914 a modificar su doctrina y a generar una alternativa a la «libido desexualizada» de Jung, a la vez que se apoyaba en la aportación de Karl Abraham, clínico de las psicosis. Ya no se conformaba con hablar de la libido como una manifestación de la pulsión sexual: quería mostrar que podía referirse al yo. Y deducía de eso la existencia simultánea, en el psiquismo, de una oposición entre libido del yo y libido de objeto, y entre narcisismo primario, estado primero de la vida, y narcisismo secundario que evoluciona hacia un repliegue de las investiduras de objeto. Abría de tal modo el camino a una reflexión sobre los trastornos de la subjetividad que iba mucho más allá de la manera como había concebido hasta entonces la génesis del conflicto neurótico. Ahora, el sujeto ya no era simplemente Edipo reconvertido en Hamlet, sino Narciso culpable de contemplar su imagen hasta morir a causa de ello: una forma de señalar hasta qué punto el hombre del nuevo siglo estaba invadido por el deseo profundo y permanente de destruirse destruyendo al otro.
La guerra pareció dar la razón a Freud.
### 4
La guerra de las naciones
Si bien pretendía detestar Viena y la doble monarquía, tanto como detestaba, por otra parte, el espíritu prusiano, la guerra sorprendió a tal punto a Freud que comenzó a defender firmemente la Triple Alianza, a anhelar la victoria de Austria y a revolverse contra Francia, los serbios y Rusia. No creyó ni por un momento en la victoria de Francia e Inglaterra, ni en el apoyo de los norteamericanos, ni en la desaparición de los Imperios Centrales.
No había sabido ver el aliento nacionalista de los pueblos contra las últimas dinastías imperiales, ni el crecimiento del odio que, en unos sesenta años, había sustituido poco a poco a la primavera de los pueblos. Todavía no había tomado conciencia de la agonía de esa burguesía nobiliaria de la Belle Époque que, a fuerza de preocuparse por sí misma, había pasado por alto la miseria de los desheredados. Hasta ese día solo conocía la guerra por sus lecturas —Alejandro Magno, Julio César, Napoleón, Homero— y el recuerdo que le había dejado su período militar, durante el cual se las había dado de médico de los ejércitos con sus enfermeras para luchar contra su neurastenia. En lo inmediato, frente al desencadenamiento real de las armas, no quería en ningún caso arremeter contra Inglaterra, sin dejar de lamentar que esta no se alineara con los tres imperios: el prusiano, el austrohúngaro y el otomano.
Por eso entró en contradicción con la evolución del Verein, donde se codeaban médicos procedentes de todos o casi todos los países de Europa, así como de Estados Unidos, una nueva generación que aspiraba a un psicoanálisis independiente de Viena y, por lo tanto, del ideal freudiano de los paladines unidos en el Ring. Pero la guerra, sobre todo, clausuraba de antemano el progreso del movimiento y levantaba fronteras artificiales entre intelectuales, investigadores, médicos, escritores y psicólogos.
Esa primera guerra del siglo XX se desplegaba en el aire y el fondo de los océanos, en el mar, en tierra y en trincheras fangosas, arrasadas por gases tóxicos y cubiertas de cuerpos mutilados. Ya no tenía nada que ver con las guerras de los siglos anteriores, cuando se enfrentaban a plena luz del día ejércitos de colores variopintos, con cornetas, combates sangrientos con armas blancas y cantos de victoria y de muerte.
De improviso, esa guerra trasladó a otra escena los conflictos internos del psicoanálisis y, desde el inicio, forzó a los freudianos a renunciar a sus congresos, interrumpir sus actividades y suspender los intercambios epistolares y las producciones editoriales. En síntesis, los obligaba a interesarse en otra cosa y no en sus trabajos científicos y su lucha irrisoria contra «el brutal santurrón de Jung» o contra los «zuriqueses», que no participaban, además, en el furor de las otras naciones. Suiza, España, Holanda y los países escandinavos no integraban ninguna de las coaliciones.
Salvo Hanns Sachs, declarado inútil por su miopía, todos los miembros del comité fueron movilizados, uno tras otro. En 1915 Eitingon partió el primero como cirujano con uniforme austríaco, destinado a Praga y luego al norte de Hungría, mientras que Abraham fue enviado, también como cirujano, a un gran hospital de Prusia Oriental. Rank, incorporado a la artillería pesada, marchó a Cracovia, y Ferenczi fue llamado a filas para ejercer como comandante médico de los húsares húngaros; más adelante se lo envió, como psiquiatra, a un hospital militar de Budapest, lo que le permitió retomar sus actividades. En ningún momento abandonó su fe en el psicoanálisis y realizó una cura a caballo con un oficial de su regimiento, víctima de un trauma a raíz del estallido de un obús. Al mismo tiempo intentaba resolver sus problemas con Gizella.
Solo en Viena con Sachs, Martha, Anna y Minna, Freud afrontó esos tiempos de guerra con el temor constante de que sus tres hijos varones y su yerno —Martin, Oliver, Ernst y Max Halberstadt—, movilizados o alistados en la artillería, el cuerpo de ingenieros o en diversos frentes, fuesen víctimas de esa carnicería. Hermann Graf, su sobrino, hijo único de Rosa, muerto en el frente italiano en julio de 1917, fue el único de sus parientes que no volvió. Otro tanto ocurrió con Rudolf Halberstadt, hermano de Max.
En realidad, ya en los primeros meses del conflicto, y a pesar de su humor belicoso y su certeza sobre la victoria alemana, Freud comprendió que esa guerra sería larga y mortífera y cambiaría de arriba abajo el mundo en que vivía: «La humanidad, no lo dudo, se repondrá de esta guerra», escribía a Lou Andreas-Salomé en noviembre de 1914,
pero estoy seguro de que mis contemporáneos y yo ya no veremos el mundo bajo una luz dichosa. Todo es demasiado horrible. Lo más triste es que, conforme a las experiencias suscitadas por el psicoanálisis, es exactamente así como deberíamos habernos representado a los hombres y su comportamiento. A causa de esta postura con referencia a los hombres, jamás pude compartir su bienaventurado optimismo. El hecho de que viéramos tan atrozmente manchada de hipocresía la más alta cultura de nuestro tiempo me había llevado a la conclusión, en lo más recóndito de mi alma, de que no estamos orgánicamente hechos para ella.
Una vez más, Freud afirmaba que su doctrina era el revelador de los aspectos más oscuros de la humanidad, y buscaba en los acontecimientos —como, por otra parte, en los textos literarios, los mitos y las leyendas— la confirmación de la precisión de sus hipótesis. Y de resultas, no advertía que sus reflexiones, y en especial su estudio reciente sobre el narcisismo, no escapaban a la evolución mortífera de ese mundo por el que ya sentía nostalgia. Freud se veía a sí mismo como el creador de una doctrina sin imaginar que esta pudiera ser también el producto de una historia que él no controlaba. El psicoanálisis era su «cosa» ( _Sache_ ), y lo veía en acción por doquier.
La época bendita del viaje a América, de la pasión por Jung y de la convicción sobre los beneficios de la terapia analítica había terminado. Ahora, Freud pensaba en una organización muy distinta de todo lo concerniente al psicoanálisis. Y fue durante ese período de guerra, en efecto, cuando comenzó a efectuar una refundición de su sistema de pensamiento. Quisiéralo o no, la guerra lo afectaba en todos los aspectos: estaba irritable, multiplicaba los lapsus, contaba historias judías para luchar contra la angustia. Su libido, decía sin creerlo realmente, estaba movilizada con firmeza en favor de Austria-Hungría. En cuanto a su teoría, no existe la certeza de que por entonces hubiera podido resumirla.
Su actividad onírica y fantasmática adquirió muy pronto un nuevo cariz. Freud soñaba con la muerte de sus hijos y de sus discípulos, la dispersión de su movimiento, heridas atroces, campos de batalla sembrados de cadáveres anónimos. En una palabra, tanto de noche como de día lo invadía la idea de que el poder mortífero de las pulsiones inconscientes amenaza las formas más elevadas de la civilización humana.
Y al reflexionar sobre esta cuestión, en abril de 1915, escribió un ensayo sobre la guerra y la muerte en el cual contradecía de manera radical sus primeros arrebatos belicistas. En ese texto desesperado, que anunciaba todas las hipótesis venideras, comenzaba por entregarse a un vibrante elogio de la sociedad europea originada en la cultura grecolatina e impregnada de las luces de la ciencia, para mostrar hasta qué punto esa nueva guerra llevaba a la humanidad más ilustrada, no solo a una degradación de todo sentimiento moral y una peligrosa desilusión, sino también a un despertar de todas las formas posibles de crueldad, perfidia y traición, las mismas que se creían abolidas por el ejercicio de la democracia y el reino de la civilización. Y es así, decía, que el «ciudadano del mundo culto [...] puede quedar desorientado y perplejo en un mundo que se le ha hecho ajeno, despedazada su patria grande, devastado el patrimonio común, desavenidos y envilecidos sus ciudadanos».
En otras palabras, Freud tomaba nota del hecho de que esa guerra, provocada por el nacionalismo y el odio mutuo de los pueblos, traducía la quintaesencia de un deseo de muerte propio de la especie humana. Venía a recordar al sujeto moderno que no era otra cosa que el heredero de una genealogía de asesinos y que la guerra lo retrotraía a un arcaísmo pulsional cuyos perfiles el propio Freud había descrito en _Tótem y tabú_ , y lo autorizaba a transgredir la prohibición de dar muerte al otro. Peor aún, _Herr Professor_ constataba que, en ese conflicto, bajo el efecto de la abolición de la distinción entre combatientes y poblaciones civiles, ya nadie sabía reconocer las prerrogativas de los heridos y los médicos.
Con tono dramático, Freud ponía el acento en el hecho de que esta guerra perturbaba de manera inédita la relación del hombre con la muerte. Fenómeno «natural», decía, la muerte es la salida necesaria de toda vida y cada quien tiene el deber de prepararse para ella. Pero, como nuestro inconsciente es inaccesible a su representación, es preciso además, para aceptarla, negar su existencia, ponerla al margen y hasta teatralizarla en una identificación con un héroe idealizado. Ahora bien, la guerra moderna, con su poder de destrucción masiva, abolía en el ser humano el recurso a esas construcciones imaginarias capaces de preservarlo de la realidad de la muerte.
Al recordar la respuesta de Aquiles a Ulises, Freud hacía suya la idea de los antiguos de una oposición entre la «bella muerte», la heroica de los guerreros que eligen una vida breve, y la muerte natural ligada a una vida tranquila y prolongada. Y daba a entender que la guerra contemporánea borraba las fronteras entre las dos muertes, porque precipitaba al soldado —individuo anónimo— en lo cotidiano de su finitud inmediata aun antes de que tuviera tiempo de identificarse con nada. Además, esa guerra ponía al desnudo, decía, lo más ancestral en el hombre: el placer del asesinato generalizado más allá de la muerte heroizada y la muerte natural. En consecuencia, si la crueldad volvía para situarse de tal modo en el corazón de ese período turbulento, era porque la civilización nunca había podido erradicarla. Pese a su humanización y el acceso a la cultura, el hombre, por lo tanto, siempre sería otro y no el que creía ser. En los estratos profundos de su vida psíquica se disimulaba un bárbaro siempre presto a despertar.
Freud terminaba su ensayo con una profesión de fe inapelable: «Recordamos el viejo apotegma: _"Si vis pacem, para bellum"_. Si quieres conseguir la paz, ármate para la guerra. Sería tiempo de modificarlo: _"Si vis vitam, para mortem"_. Si quieres soportar la vida, prepárate para la muerte».
A los cincuenta y nueve años, Freud iba pues al encuentro del reino de los muertos. Pensaba tanto en su muerte y la de sus allegados como en la de los combatientes perdidos en la «noche polar» de una guerra a la que no le veía salida y que comparaba con una «artesanía repugnante». Minna y Martha ya lo llamaban «querido viejo». Cuatro meses antes de la declaración de las hostilidades, en la noche del 10 al 11 de marzo de 1914, había sido abuelo por primera vez con el nacimiento de Ernst (apodado «Ernstl») Halberstadt, hijo de Sophie y futuro «niño del carretel», cuyo juego describiría algunos años después: «¡Muy singular! ¡Un sentimiento de haber envejecido, de respeto frente a los milagros de la sexualidad!».
En el otoño de 1914 se enteró de la muerte, a los ochenta y un años, de Emanuel, su querido medio hermano que, decía Freud, no había soportado la guerra. Al cumplir sesenta años, en mayo de 1916, escribiría que él mismo franqueaba el umbral de la vejez, que ya no podía dejar nada para más adelante, que su corazón y sus arterias habían envejecido y que él no era lo que su padre había sido a su edad.
En varias ocasiones salió de Viena para visitar a su hija, luego a la esposa de Abraham y por último a Ferenczi, el amigo del alma. Su clientela escaseaba, los ahorros se esfumaban, faltaba la comida, las viviendas no tenían calefacción y la tuberculosis amenazaba a los más desfavorecidos o los más frágiles. El amargo «Konrad» desfallecía: dolores de garganta, hinchazón de la próstata, diversos trastornos somáticos. En 1917, a los sesenta y un años, Freud trató una vez más de dejar de fumar. Pero, contra toda lógica racional, logró convencerse de que el edema doloroso que sentía en el paladar era una consecuencia de la abstinencia de tabaco y volvió a encender cigarros aún con más ahínco para agudizar sus facultades intelectuales.
La constatación de las atrocidades bélicas y la presencia física de la muerte en su vida y su cuerpo llevaron a Freud a abandonarse a la soledad creadora que tanto le gustaba y que iba a la par con su adicción al tabaco, también con cierto masoquismo y con su culto de la abstinencia sexual. Solo el hombre que sufre puede llevar a cabo algo, pensaba, y a la vez afirmaba sin cesar que la pasión por los cigarros no era de la incumbencia del psicoanálisis. A pesar de los años de trabajo sobre sí mismo, seguía siendo el neurótico de siempre.
En 1896, en una carta a Fliess, ya había utilizado el término «metapsicología» para calificar la totalidad de su concepción de la psique, con el fin de distinguirla de la psicología clásica. Armado de ese término, pretendía realizar su viejo sueño de consagrarse a la filosofía o, mejor, de desafiarla. Luego, en la _Psicopatología de la vida cotidiana_ , había afirmado de manera aún más clara que el conocimiento de los factores psíquicos del inconsciente se reflejaba en la construcción de una realidad suprasensible que la ciencia transformaba en una psicología del inconsciente. Y, por lo tanto, se había asignado la tarea de descomponer los mitos relativos al mal y el bien, la inmortalidad y los orígenes de la humanidad, mediante la traducción de la metafísica en una metapsicología.
En otras palabras, si la metafísica era el estudio en filosofía de las causas primeras del ser y la existencia —y por ende de realidades separadas de la materia y lo vivido—, la metapsicología debía ser, en paralelo, el estudio de la realidad psíquica, es decir, de todo lo que escapa a la conciencia y la realidad material. Mediante ese rumbo especulativo, Freud aspiraba a fundar el psicoanálisis como una nueva disciplina desvinculada de la psicología. Hasta entonces, en efecto, siempre había enraizado su doctrina en la psicología sin teorizar jamás la idea de que pudiera subvertirla.
Rivalizando así con el saber filosófico, al que consideraba, sin embargo, como un sistema paranoico, Freud desafiaba a la psicología, disciplina gracias a la cual había salido antaño de la neurología. Empresa desmesurada, porque él pretendía hacer del psicoanálisis una «ciencia» en toda regla, entre psicología, filosofía y biología, al extremo de negarse a considerarla como una «ciencia humana» en el mismo concepto que la antropología o la sociología.
A partir de 1915 elaboró pues, bajo la denominación de «metapsicología», un conjunto de modelos definidos por la toma en consideración simultánea de los puntos de vista dinámico, tópico y económico. Por medio del enfoque dinámico relacionaba los procesos psíquicos con su origen inconsciente, y por tanto con las pulsiones. Según el eje tópico, definía lugares: el consciente, el preconsciente, el inconsciente. Y por último, en virtud de la perspectiva económica, distinguía los diferentes dominios de la energía psíquica.
Fue esa la perspectiva adoptada por Freud entre 1915 y 1917 para agrupar, precisamente bajo la denominación de «metapsicología», cinco ensayos austeros y complejos que contrastaban con sus escritos anteriores: «Pulsiones y destinos de pulsión», «La represión», «Lo inconsciente», «Complemento metapsicológico a la doctrina de los sueños» y «Duelo y melancolía». Freud proponía distinguir dos grupos de pulsiones, el de las pulsiones de autoconservación y el de las pulsiones sexuales. Ponía de relieve diferentes inversiones de pulsiones con objetos, metas, personas, pares opuestos: sadismo y masoquismo, voyeurismo y exhibición, pasividad y actividad. Y trazaba un cuadro sombrío de las múltiples facetas por las cuales el ser humano siente placer cuando seduce, se pavonea, se atormenta al atormentar a otro, odia al mismo tiempo que simula amar.
En lo referido a la represión, concepto fundamental, Freud inventaba una especie de cartografía de sus astucias, sus contornos, sus desfiguraciones, sus distanciamientos, sus persecuciones del sujeto, y distinguía a la vez la represión primordial, la fijación, la represión propiamente dicha y, por último, el retorno de lo reprimido, con sus representantes, sus representados, sus «montos de afecto», sus mecanismos de sustitución presentes en las principales neurosis: fobia, angustia, histeria, neurosis obsesiva.
En esa nueva perspectiva, el inconsciente, según Freud, ya no tenía mucho que ver con _La interpretación de los sueños_. Es cierto, seguía sin ser alcanzable salvo traspuesto o traducido en los sueños, los lapsus, los actos fallidos o las conversiones somáticas. Pero también era algo muy distinto: una hipótesis, un proceso «en sí», una forma derivada de la antigua animalidad del hombre revisada y corregida conforme a un principio originado en la filosofía de Kant. Y Freud indicaba que nunca había que poner la percepción de la conciencia en lugar del psiquismo inconsciente, aun cuando este fuera menos incognoscible que el mundo exterior. En ese aspecto, hacía del psicoanálisis una psicología de las profundidades articulada alrededor de la primacía del inconsciente —instancia hecha de contenidos reprimidos— sobre el consciente y el preconsciente, siempre en devenir.
En el momento de abordar el inmenso continente de la melancolía, tan magníficamente descrita en cada época de la historia de la humanidad por los poetas y los filósofos, y más adelante por los alienistas, Freud no trató de rivalizar con esos escritos, con mayor razón por el hecho de que él mismo ya había presentado a Hamlet, prototipo del príncipe melancólico de comienzos del siglo XVII, como un histérico. Se contentó con integrar la melancolía en su metapsicología y, por consiguiente, con arrancarla tanto a la nosografía psiquiátrica como a la tradición filosófica, con el objeto de redefinirla como una suerte de delirio narcisista. Los tiempos eran propicios para una reflexión semejante. Vestidas de negro, las mujeres reemplazaban a los hombres caídos en combate y tomaban las riendas de las actividades económicas de cada uno de sus países. Lejos de considerar la melancolía como uno de los grandes componentes de la condición humana, Freud la definía como la forma patológica del duelo: una enfermedad del autocastigo. Antes de la publicación envió su manuscrito a Abraham, que ya había comparado el duelo y la melancolía. Este le hizo numerosas observaciones y Freud se las agradeció y lo citó. Así incorporó los tormentos de la melancolía a un proceso de regresión de la libido y de abandono de la investidura inconsciente.
Freud destacaba que, en el trabajo del duelo, el sujeto llega gradualmente a separarse del objeto perdido, mientras que en la melancolía se siente culpable de la muerte acaecida, la desmiente o se cree poseído por el difunto o afectado por la enfermedad que lo llevó a la tumba. Enfrentado a esa pérdida irremediable, experimenta un sentimiento de indignidad y cree que su conciencia moral lo juzga y persigue. Más adelante, Freud dará a esta el nombre de «superyó».
_Herr Professor_ tenía el proyecto de escribir doce ensayos y agruparlos en un conjunto titulado «Elementos para una metapsicología». Pero dudaba de sí mismo y finalmente abandonó siete de los textos, de los cuales se encontró uno solo: _Sinopsis de las neurosis de transferencia_. Construida como un intercambio con Ferenczi, pero también como una «fantasía filogenética», esa sinopsis se había concebido como una continuación de _Tótem y tabú_. Era el resultado de una especulación «bioanalítica» en cuyo transcurso Freud se dedicaba a ampliar la teoría de las neurosis y del asesinato del padre al origen del hombre. En otras palabras, aspiraba a efectuar una recapitulación de la filogénesis por la ontogénesis. Por eso afirmaba la existencia de una analogía entre los estadios de la evolución de la especie humana y los de las neurosis. Si el orden cronológico muestra que, en el desarrollo individual, la histeria de angustia es la más precoz, seguida de la histeria de conversión y más adelante de la neurosis obsesiva, esto significa que esos tres tipos de neurosis tendrían su equivalente en una historia filogenética de la humanidad, situada entre los comienzos y el final de la era glacial. Encontraríamos así en cada ser humano la huella de una regresión neurótica correspondiente a un estadio ya presente en la filogénesis. En los albores de la era glacial la humanidad se habría vuelto ansiosa, para experimentar a continuación un conflicto entre autoconservación y deseo de reproducción, y de ahí la aparición de una histeria de angustia. En la fase siguiente se habría producido una sobrevaloración del pensamiento y el lenguaje correspondiente a una neurosis obsesiva, es decir, a una concepción religiosa del mundo. Seguía entonces, en la pluma de Freud, una nueva versión del relato de la «lucha por la existencia» reconvertido en fábula psicofilogenética: horda primitiva, asesinato del padre, hijos unidos por su homosexualidad, mujeres sumergidas en un continente desconocido — _dark continent_ —, retorno de la figura del padre en la paranoia, identificación con el padre muerto entre duelo y melancolía.
Una vez más, Freud reinventaba los componentes de su sistema de parentesco para hacer de él un modelo de comprensión del psiquismo. Se entiende que haya vacilado en hacer públicas sus especulaciones, con el resultado de destruir varios manuscritos. Su ambiciosa metapsicología era, por lo menos, oscura y frágil. En cuanto a la idea de dar al psicoanálisis un fundamento simétricamente idéntico al de la biología, equivalía a hacer de él una «metabiología», como deseaba Ferenczi. Y de hecho, Freud confesaba entonces querer poner la «tarjeta de visita» del psicoanálisis en el tarjetero de los biólogos.
Consciente de la fragilidad de su hipótesis, renunció a ella sin abandonar, empero, la idea de trasladar los mecanismos de la evolución al campo del psicoanálisis. Y para ello se puso a leer la _Filosofía zoológica_ de Lamarck, no con la intención de oponer el lamarckismo al darwinismo sino de mostrar que la idea lamarckiana de que «la necesidad crea el órgano» no significaba otra cosa que tomar en consideración el «poder de la representación inconsciente sobre el cuerpo propio», cuyos vestigios veía Freud en la histeria. En síntesis, decía, la «omnipotencia de los pensamientos». La adecuación por finalidad se explicaría entonces, añadía, «psicoanalíticamente, con lo cual se alcanzaría la consumación del psicoanálisis. Se desprenderían dos grandes principios del cambio (del progreso), el cambio por adaptación del cuerpo propio y el cambio ulterior por transformación del mundo exterior (autoplástico y heteroplástico), etc.».
Freud retomaría esa tesis en 1920, en escritos cada vez más especulativos, sin dar jamás un contenido más sólido a su metapsicología. Y por lo demás, esta no tendría nunca otra utilidad que la de servir de muralla contra algunas empresas de psicologización del psicoanálisis. Flaco consuelo.
Mientras se esbozaba ese cambio de perspectiva, Freud proseguía con su enseñanza en el Hospital General de Viena, donde se apretujaba para escucharlo un centenar de oyentes, estudiantes, médicos, padres, amigos o futuros discípulos: Max Schur, Edoardo Weiss, Anna Freud, etc. Surgía una nueva generación. Como de costumbre, Freud hablaba sin recurrir a anotaciones, y para su último año académico decidió exponer en veintiocho lecciones los principales logros de lo que todavía llamaba «una joven ciencia»: síntesis de _La interpretación de los sueños_ , de la _Psicopatología de la vida cotidiana_ , de los _Tres ensayos_.
A ello se sumaba una serie de ponencias sobre la técnica psicoanalítica, la transferencia, la definición de las neurosis. En ese nuevo ensayo de introducción al psicoanálisis, Freud reafirmaba con vigor que la primera elección de objeto del ser humano siempre es incestuosa, que en el hombre se dirige a la madre y la hermana y en la mujer a la madre y luego al padre y el hermano, y que solo una severa prohibición permite mantener a distancia esa tendencia pulsional, presente para siempre jamás en la sexualidad adulta.
No bien publicada, la obra conoció en todo el mundo un éxito fulminante. No obstante, contribuyó a alimentar los rumores acerca de la llamada organización «incestuosa» de la vida familiar de Berggasse 19. Más que nunca, el psicoanálisis fue recibido entonces por sus defensores entusiastas —escritores, filósofos o poetas— como una revolución de la libertad, capaz de cambiar el destino de los hombres, y por sus adversarios como una falsa ciencia que atentaba contra el orden familiar, las virtudes de la religión y los sentimientos patrióticos de los pueblos: un pensamiento lascivo salido de un cerebro degenerado y un imperio agonizante.
Por esos tiempos Freud soñaba con el premio Nobel. Su joven amigo y ex alumno Robert Barany, médico húngaro, galardonado en 1914 por sus trabajos fisiológicos sobre el aparato vestibular del oído, lo había designado como su candidato. Pero ¿en qué concepto y en nombre de qué disciplina? Pese a su notoriedad mundial, _Herr Professor_ no disfrutaba de reconocimiento ni como hombre de ciencia ni como escritor. En cuanto al psicoanálisis, no formaba parte de ningún campo del saber universitario. Freud jamás obtendría el tan anhelado premio.
Aunque no era partidario del marxismo, recibió con simpatía la Revolución de Octubre, que ponía fin a la participación de los rusos en la guerra. De igual manera, si bien no era en modo alguno favorable al sionismo, aprobó la declaración de lord Balfour, que abría el camino a la creación de un hogar nacional judío en Palestina. En noviembre de 1917 era tan pesimista que quería soñar con días mejores.
Mientras se acercaba el fin de las hostilidades, los miembros del comité entraron en guerra unos contra otros. Muy resuelto a tomar en sus manos los destinos del movimiento y llevarlo al campo de los vencedores, Jones la emprendió contra Abraham y defendió a Ferenczi. Contra el primero, que deseaba organizar el quinto congreso del Verein en Berlín, destacó que con ello se corría el riesgo de que el psicoanálisis pasara por ser una «ciencia _boche_ », y, con el acuerdo del segundo, eligió Budapest como lugar del encuentro. Freud aprobó esta opción. Todos los «paladines» sabían que Hungría no tardaría en separarse de Austria: Budapest, cuna de cierta idea ferencziana del psicoanálisis característica de la _Mitteleuropa_ , resplandecía con sus últimas luces.
El congreso se desarrolló el 28 y 29 de septiembre de 1918 en la Academia Húngara de Ciencias en presencia de representantes de los gobiernos húngaro, alemán y austríaco y con la participación de cuarenta y dos psicoanalistas, entre ellos Geza Roheim, futuro antropólogo norteamericano, y un número importante de mujeres, con sombreros discretos y ropa que ocultaba sus formas. A excepción de Freud, todos los hombres iban de uniforme. Melanie Klein, brillante alumna de Ferenczi, conoció entonces al maestro y asistió a su conferencia sobre los «Nuevos caminos de la técnica psicoanalítica».
En vez de improvisar como de costumbre, la intervención de Freud consistió en la lectura de un texto pasmoso, por no decir más. Contra sí mismo y contra su propia práctica —pero también contra Ferenczi—, anunciaba que el tratamiento psíquico debía efectuarse, en la medida de lo posible, «en un estado de privación, de abstinencia». No llegaba a decir que el paciente debía privarse de toda actividad sexual, pero propiciaba la idea de prohibirle aprovechar los beneficios de los primeros resultados de la terapia psicoanalítica. Sin ese rigor, decía, el paciente corría el riesgo de volver a caer en un fracaso irremediable.
No conforme con oponerse a la empatía terapéutica, y a la vez que desaprobaba la orientación puritana adoptada por su amigo Putnam, Freud anunciaba que el psicoanálisis iba a convertirse en una terapia de masas —como en Estados Unidos— y que había que crear por doquier instituciones capaces de llevar a buen puerto tratamientos gratuitos. Se podría así ayudar por fin a las poblaciones más pobres a salir de su condición. Al fomentar un programa semejante de higiene social, y llamar a los Estados democráticos a reconocer el valor profiláctico del psicoanálisis, Freud rompía con el mundo antiguo. Tras haber errado por su laberinto metapsicológico, quería creer que la cura ya no estaba reservada a grandes burgueses proustianos aferrados a cierta imagen de sí mismos ahora desvanecida con la guerra.
Convocaba además a las nuevas generaciones a proyectarse en el porvenir:
Haremos probablemente la experiencia de que el pobre está todavía menos dispuesto que el rico a renunciar a su neurosis; en efecto, no lo seduce la dura vida que le espera, y la condición de enfermo le significa otro título para la asistencia social. Es posible que en muchos casos solo consigamos resultados positivos si podemos aunar la terapia anímica con un apoyo material, al modo del emperador José. Y también es muy probable que en la aplicación de nuestra terapia a las masas nos veamos precisados a alear el oro puro del análisis con el cobre de la sugestión directa, y quizá el influjo hipnótico vuelva a hallar cabida, como ha ocurrido en el tratamiento de los neuróticos de guerra. Pero cualquiera que sea la forma futura de esta psicoterapia para el pueblo, y no importa qué elementos la constituyan finalmente, no cabe ninguna duda de que sus ingredientes más eficaces e importantes seguirán siendo los que ella tome del psicoanálisis riguroso, ajeno a todo partidismo.
La cuestión de las neurosis de guerra se discutió a lo largo de todo el congreso de Budapest, con ponencias de Abraham, Freud, Ferenczi, Ernst Simmel y Victor Tausk. Y el problema era fundamentalmente este: ¿cómo inscribir la intervención del psicoanálisis en el corazón de la vida de las sociedades, tanto en tiempos de guerra como en tiempos de paz? El interés de Freud y sus discípulos radicaba en mostrar la diferencia entre las neurosis traumáticas y las neurosis corrientes, por un lado, y, por otro, entre los sujetos neuróticos y los sujetos «sanos», atrapados unos y otros en la tormenta de la guerra.
Si bien los freudianos habían abandonado mucho tiempo atrás la causalidad traumática en la dilucidación de las neurosis, ahora se veían de nuevo enfrentados a ella, pero en una escala muy distinta. En esas circunstancias era imposible negar que los horrores de la guerra pudieran tener algún papel en la aparición de trastornos como los temblores compulsivos, las amnesias, los terrores, las pesadillas, el insomnio, etc. Enfrentados a las autoridades de sus respectivos países, los psicoanalistas, que habían sido movilizados como cualquier hijo de vecino, intentaron explicar que los soldados no reaccionaban de la misma manera ante el combate según hubieran sido o no neuróticos en la vida civil. Así, tal soldado podía exhibir signos graves de conmoción debidos a la dureza de los combates sin estar, pese a ello, deprimido o ansioso, mientras que tal otro, sin haber estado bajo fuego, podía perfectamente sumirse en un estado de shock ante la idea misma de encontrarse frente al enemigo. ¿Cómo había que tratar a los soldados afectados por esas neurosis? ¿La cura por la palabra era en todos los casos superior a la electroterapia, verdadera tortura impuesta a los pacientes, o a la hipnosis, juzgada muy eficaz?
Las intervenciones se publicaron en el marco del Internationaler Psychoanalytische Verlag, editorial financiada por Anton von Freund y que era la joya del movimiento. Freud publicaría en ella sus libros venideros.
Durante el congreso Herman Nunberg propuso por primera vez que, para ser psicoanalista, se impusiera como condición haber hecho un análisis. Rank y Ferenczi se opusieron a la votación de una moción en ese sentido. Tiempo perdido. La idea del análisis de los analistas —cura didáctica y análisis de supervisión— se impondría con el paso de los años a partir de la gran experiencia berlinesa. En la sesión de clausura todos fueron conscientes de que el movimiento psicoanalítico recuperaba su vigor. Freud creyó adecuado declarar que el centro neurálgico del psicoanálisis estaba en Hungría: se equivocaba.
Dos meses después, los representantes del Imperio austrohúngaro firmaban el armisticio de Villa Giusti, los plenipotenciarios alemanes se reunían con los aliados en el bosque de Compiègne, Guillermo II abdicaba, en Hungría se establecía la república. En nombre del derecho de los pueblos a disponer de sí mismos, y en virtud de los catorce puntos redactados por el presidente Thomas Woodrow Wilson, las diversas poblaciones de la antigua Europa central y los Balcanes fueron distribuidas dentro de nuevas fronteras, definidas algunos meses más tarde por los tratados de Versalles, de Saint-Germain-en-Laye y de Trianon. Austria ya no era entonces más que una «luz crepuscular, una sombra gris, incierta y sin vida de la antigua monarquía imperial».
Al fundarse la primera República húngara, Ferenczi, cercano a los medios progresistas y a la revista _Nyugat_ , fue sondeado para ocupar una cátedra de enseñanza del psicoanálisis en la universidad. A despecho de un primer informe negativo, el decreto correspondiente fue firmado por Georg Lukács, comisario del pueblo de Instrucción Pública y Cultura del nuevo gobierno de Béla Kun, que el 20 de marzo de 1920 había instaurado una república de consejos obreros según el modelo de la revolución bolchevique. El 10 de junio Ferenczi dio inicio a sus clases en un anfiteatro repleto de estudiantes entusiastas.
En esa ocasión Freud escribió un artículo que se publicó directamente en húngaro: «¿Debe enseñarse el psicoanálisis en la universidad?». En él hacía un inventario de todas las materias necesarias para el plan de estudios de la disciplina. No solo destacaba la necesidad de conocer bien la historia de las psicoterapias, para comprender las razones objetivas de la superioridad del método psicoanalítico, sino que proponía asimismo un programa referido a la literatura, la filosofía, el arte, la mitología, la historia de las religiones y las civilizaciones. Señalaba con énfasis que el psicoanálisis no debía en ningún caso limitar su campo de aplicación a las afecciones patológicas. Ese programa nunca se implementaría: ni en Budapest, ni en Viena, ni en ninguna universidad del mundo. Freud había errado el camino al pretender imponer el psicoanálisis como una disciplina con todas las de la ley. En realidad, este solo debía y debió su existencia a sus instituciones privadas. En las altas esferas de la enseñanza universitaria solo pudo implantarse como vector de otras disciplinas: psiquiatría y psicología por un lado, humanidades por otro. Por eso quedó escindido en dos ramas: una clínica, asociada al ideal médico de la atención, y otra cultural, vinculada a la filosofía, la historia, la literatura, la antropología.
La caída de la Comuna de Budapest y la sangrienta represión lanzada por las tropas del almirante Miklós Horthy, que se proclamó «regente», pusieron fin a la experiencia. Ferenczi perdió su cargo: «El aspecto más repugnante de los diez primeros años del régimen de Horthy», escribe William Johnston, «fue sin duda el terror blanco de 1920. Con espíritu de venganza [...], se aplicó la tortura a diestro y siniestro y se restableció la flagelación pública, mientras se echaba tierra a los asesinatos políticos y se expulsaba a los judíos refugiados a partir de 1914».
En otra actitud equivocada, Freud condenó tanto la Comuna como el terror blanco de Horthy. En cuanto a Jones, aprovechó la situación para tomar la dirección del IPV (Verein) y desplazar el centro neurálgico del movimiento hacia el oeste, es decir, hacia el mundo angloparlante.
En 1919 Freud ya no tenía más que algunos pacientes austríacos y húngaros. En Alemania sus hijos habían quedado arruinados por la guerra y, por el momento, él debía mantenerlos, así como ayudar a algunos amigos, en especial Lou Andreas-Salomé, a quien daría una pensión hasta su muerte. Con la esperanza de recibir nuevos discípulos, deseosos de formarse con él, perfeccionó aún más su dominio del inglés. Soñaba otra vez con irse de Viena para instalarse en Berlín o Londres: «Por aquí nos hemos convertido todos en mendigos hambrientos. Pero usted no ha de oír quejas. Todavía estoy de pie y no me considero en manera alguna responsable del absurdo del mundo». Y añadía: «Me encanta oír que el psicoanálisis florece en todas partes, y espero que también para usted la ciencia sea un consuelo». Cálidamente recibido en Viena en septiembre, Jones invitó a Freud y Ferenczi a almorzar: ambos estaban hambrientos.
Deprimido tras la caída de la Comuna, Ferenczi inició gestiones para emigrar a Estados Unidos. Freud se negó obstinadamente a dejarlo partir, a pesar de que, al mismo tiempo, lo hacía a un lado y se apoyaba cada vez más en Jones en lo tocante a la organización del movimiento internacional. Consciente de pertenecer al campo de los vencedores y deseoso de sacar de las manos de la Europa continental arruinada la administración de los asuntos, Jones comenzó a poner en práctica su política pragmática de normalización de la profesión. Contra Freud, defendió incluso la idea de que el ejercicio del psicoanálisis debía quedar exclusivamente reservado a los médicos, como sucedía en Estados Unidos.
En la misma perspectiva, impuso al comité una decisión catastrófica para el futuro, al inducirlo a adoptar una regla en virtud de la cual los homosexuales no podrían ser ni miembros de una asociación ni ejercer como psicoanalistas, porque, «en la mayoría de los casos, son anormales». Esta pasmosa disposición era contraria a la doctrina freudiana y escarnecía el nombre de Leonardo da Vinci. Los berlineses se opusieron y Rank previno a sus amigos al acusar a Jones de no tener en cuenta los diferentes tipos de homosexualidad.
Así, los homosexuales volvían a ser tratados como pervertidos por los mismos que se habían alejado de las tesis racistas de fines del siglo XIX. Está claro que esa disposición no les impidió en absoluto ser psicoanalistas, pero para ello tuvieron que disimular su orientación sexual. Una de las consecuencias de la medida fue favorecer hasta fines del siglo XX la difusión de una espantosa homofobia dentro de la comunidad psicoanalítica mundial. Esta posición del comité era mucho más absurda por el hecho de que Freud había apoyado la iniciativa de Magnus Hirschfeld para que se eliminara del Código Penal alemán el artículo 175, que condenaba con pena de cárcel y privación de derechos cívicos el comercio sexual entre personas del mismo sexo, sobre todo si eran hombres.
Las jerarquías militares de los países en guerra habían solicitado el concurso de los psiquiatras para contribuir a la detección de los «simuladores», considerados como desertores, malos patriotas o cobardes. En el núcleo de este debate reaparecía pues con fuerza la vieja pregunta sobre el estatus de la histeria: ¿verdadera enfermedad psíquica o disimulo?
En ese contexto se acusó de felonía a Julius Wagner-Jauregg, célebre psiquiatra vienés organicista y reformador de los psiquiátricos, por haber calificado de simuladores a soldados afectados por una neurosis traumática, a los que había sometido a tratamientos con electricidad. El caso se inició en 1920 a raíz de una denuncia hecha contra él y sus asistentes —en particular Michael Kozlowski— por el teniente Walter Kauders, un brillante patriota judío del ejército austríaco. Se convocó entonces a Freud como perito ante una comisión de instrucción presidida por Alexander Löffler e integrada, entre otros, por Julius Tandler. Freud escribió un informe y participó en los intercambios entre los miembros del jurado, el acusado y el demandante.
En 1915 Kauders había sufrido una fisura de cráneo como consecuencia de la explosión de un obús. Después de varias estancias en hospitales militares, quedó a medias alelado, debía usar bastón para caminar y padecía migrañas. Entre noviembre de 1917 y marzo de 1918, considerado como un enfermo mental, se lo había sometido a aislamiento en la clínica de Wagner-Jauregg, tras lo cual sufrió dos «faradizaciones» con pinzas metálicas realizadas por Kozlowski y reservadas a los simuladores: «Esas torturas se preparan especialmente desde un punto de vista psicológico. Se hace oír al paciente que se le va a aplicar un método conocido por su atrocidad [...]. Los dolores que provoca la faradización con pinza son indescriptibles. Es como si innumerables barrenas se hundieran hasta la médula de los huesos a una velocidad vertiginosa».
Con la aspiración, ante todo, de utilizar esa tribuna para defender su doctrina, atacada desde todos los flancos, Freud soslayó la cuestión de la responsabilidad de Wagner-Jauregg para hacer la apología del método psicoanalítico. Señalaba en un principio que los médicos debían ponerse al servicio del enfermo y no a las órdenes de la jerarquía militar y negaba la utilidad de la electroterapia. Con ello exoneraba a Wagner-Jauregg de toda responsabilidad en el caso, pero lamentaba que no fuera un ardiente partidario del psicoanálisis. Afirmaba en especial que no era un torturador y que no había cometido ninguna felonía al creer que un tratamiento como el aplicado podía ser un remedio a la simulación. A su juicio, la simulación no existía por la sencilla razón de que «todos los neuróticos son simuladores» y recíprocamente, habida cuenta de que «simulan sin saberlo y esa es su enfermedad». En otras palabras, Freud reducía otra vez a nada la noción de simulación: no simulamos lo que somos.
Wagner-Jauregg, por su parte, no podía aceptar ser defendido de tal modo por un hombre a quien estimaba, pero cuyo razonamiento rechazaba. No admitía la idea de que la simulación fuera una neurosis ni el principio de que el psiquiatra, en tiempos de guerra, debía ponerse exclusivamente al servicio del paciente. No obstante, fue absuelto.
Freud había cometido el error de emitir un diagnóstico de neurosis sin ocuparse de Kauders. Y sin embargo, este se asemejaba a buena parte de sus allegados. Había tenido un padre autoritario, un hermano mayor que se había suicidado y una media hermana afectada por problemas mentales, y su infancia había estado marcada por la humillación de ser judío. Era un neurótico, sin duda, pero había sufrido sobre todo un verdadero trauma de guerra, como destacaría Eissler en 1979:
Yo diría que el caso Kauders, pese a su aspecto trágico, encerraba en sí mismo una verdadera comedia austríaca. Tenemos aquí a un joven que parte con entusiasmo a la guerra. Es oficial, lo hieren y ya no puede seguir, sean cuales fueren las razones [...]. No sabemos si en la sala de audiencias alguien advirtió que en Wagner-Jauregg y Freud se enfrentaban los representantes de dos mundos diferentes: uno, el del punto de vista de la eficacia, otro, el de la humanidad que ve en el hombre el entrelazamiento del destino y el sufrimiento.
La cantidad de víctimas humanas de esa Primera Guerra Mundial se elevaba a cerca de cuarenta millones: un poco más de la mitad, muertos —civiles y militares—, y el resto, heridos de todo tipo. Los Aliados perdieron cinco millones de soldados, y los Imperios Centrales, cuatro millones, entre ellos Ernst Lanzer.
Este hombre había conocido a Freud a los veintinueve años, en octubre de 1907. Había tenido una infancia similar a la de muchos hijos de la burguesía judía vienesa, y se lo hubiera creído directamente salido de las novelas de Schnitzler o Zweig. El padre, Heinrich Lanzer, se había casado con su prima Rosa Herlinger, más rica que él, lo cual le había permitido entrar como empleado en la empresa de los Saborsky. Cuarto de siete hermanos, Ernst había visto a su madre agotarse en embarazos sucesivos y consideraba que su padre se había tornado violento a raíz de sinsabores financieros. En su infancia, ese padre lo había golpeado y tratado de «futuro criminal», porque se había atrevido a responder a sus insultos con los suyos propios.
A los cinco años se había refugiado debajo de las faldas de su aya y le había tocado los órganos genitales. De ahí una sexualidad precoz y sólidas erecciones, muchas veces alimentadas por las palabras de las sirvientas. Tras adoptar, como su hermano, «hábitos sexuales» y maneras de hablar poco elegantes, no vacilaba en pedir a su madre que «le frotara el culo». En 1897, cortejado por una costurera contratada al servicio de sus padres, se sintió culpable cuando ella se suicidó después de que él rechazara sus avances. A continuación se enamoró de Gisela Adler, una prima pobre, estéril y enclenque que disgustaba a su padre. Por eso pensó que solo la muerte de Heinrich eliminaría el obstáculo para un matrimonio anhelado.
Cuando esa muerte se produjo, Lanzer cayó una vez más presa de rituales sexuales, en el momento mismo en que se incorporaba al ejército austríaco con el grado de cabo primero. Obsesionado por el espectro de su padre que le perturbaba las noches, tomó la costumbre de contemplarse el pene erecto por medio de un espejo puesto entre las piernas. Asaltado sin cesar por ideas suicidas y por la voluntad de cortarse la garganta, a los veintiséis años, durante su primer coito, tuvo conciencia de estar afectado por una enfermedad psíquica. Viajó entonces a Munich para hacer un tratamiento de hidroterapia, y en esa ocasión entabló una relación sexual con una criada, mientras pensaba que, para obtener una satisfacción semejante, habría sido capaz de matar a su padre. Se masturbaba regularmente o se entregaba a rituales religiosos. Consultó a varios médicos, entre ellos WagnerJauregg, que no le aportó solución alguna.
En 1907, convertido en oficial de reserva, se trasladó a Galitzia para realizar ejercicios militares, y fue allí donde conoció a Nemeczek, un capitán particularmente cruel, partidario de los castigos corporales, que le habló de un suplicio oriental consistente en obligar a un prisionero a desvestirse y arrodillarse en el suelo, con la espalda doblada. En las nalgas del hombre se fijaba entonces, por medio de una correa, un gran recipiente perforado en el cual se movía intranquila una rata. Privado de alimento y excitado por una varilla calentada al fuego que se introducía por un agujero del recipiente, el animal intentaba escapar a la quemadura y penetraba en el recto del torturado, provocándole sangrientas heridas. Al cabo de una media hora la rata moría asfixiada, al mismo tiempo que el hombre. Ese día, en el transcurso de un ejercicio, Lanzer perdió sus lentes y telegrafió a su óptico vienés para pedirle que le enviara otro par por correo. A los dos días recuperó el objeto por medio del mismo capitán, quien le hizo saber que debía pagar los gastos postales al teniente David, encargado de la oficina postal.
Frente a esta contrariedad, Lanzer reaccionó con un comportamiento delirante y la historia del suplicio, mezclada con la de la deuda, hizo surgir el recuerdo de otro asunto de dinero: un día su padre había contraído una deuda de juego y fue un amigo quien, al prestarle la suma necesaria para saldarla, lo salvó del deshonor. Una vez terminado el servicio militar Heinrich había tratado de encontrar a ese amigo pero, al no lograrlo, nunca pudo reembolsar su deuda.
Así era el hombre que se presentó en la Berggasse el 1 de octubre de 1907. Comenzó de inmediato a mencionar sus recuerdos de infancia, y cada noche Freud escribía el diario de esa cura para reproducir con exactitud sus diálogos. Por una vez conocía a un paciente ideal, realmente afectado por los síntomas de una neurosis obsesiva tal como él la había descrito: una neurosis que tenía por origen un conflicto psíquico caracterizado por la fijación de la libido en un estadio anal. Odio al padre, ritos de conjuros, pensamientos obsesivos, dudas, escrúpulos, inhibiciones, matrimonios consanguíneos, ignominias familiares, presencia de los hermanos, las hermanas, los tíos, las tías: frente a una historia tan «freudiana», _Herr Professor_ no tendría necesidad de construir una ficción en la cual el paciente no se reconociera. Y como Lanzer estaba a la búsqueda de una autoridad paterna que le permitiera comprender el significado de su neurosis, entre ambos hombres se estableció una transferencia positiva, a tal punto, además, que Freud pudo forzarlo a contar la terrible escena del suplicio, mientras imaginaba que, con esta evocación, su paciente experimentaba «horror ante su placer, ignorado por él mismo».
Freud se dejó injuriar a fin de que, por la vía dolorosa de la transferencia, Lanzer confesara el odio inconsciente que sentía por su padre. Y el enigma se resuelve: fue el relato del castigo por medio de las ratas, dice en sustancia Freud, el que despertó el erotismo anal de Lanzer. Al erigirse en defensor de un castigo corporal por las ratas, el capitán había ocupado, a los ojos del paciente, el lugar del padre y atraído sobre sí una animosidad comparable a la que antaño respondía a la crueldad de Heinrich. Según Freud, la rata revestía aquí la significación del dinero y por lo tanto de la deuda, que se manifestaba en la cura a través de una asociación verbal: «florín/rata» o «cuotas ( _Raten_ )/ratas ( _Ratten_ )». Recordemos que, desde el inicio del tratamiento, el paciente había adoptado la costumbre de contar el importe de los honorarios de este modo: «Tantos florines, tantas ratas».
En 1908 Freud expuso durante cinco horas, en el primer congreso del Verein en Salzburgo, el caso de ese _Rattenmann_ frente a un público sorprendido por la construcción lógica del relato. Para la publicación modificó las palabras del paciente y le atribuyó interpretaciones que le eran propias, y omitió también contar varios sucesos. Por añadidura, presentó al padre como un hombre ejemplar y no dijo casi nada de la madre. Sin embargo, no se trataba de una pura «construcción especulativa» destinada a ilustrar su teoría, como han pretendido algunos. De un modo u otro, Ernst Lanzer juzgó que ese tratamiento de cuatro meses había sido beneficioso para él y que la interpretación freudiana lo había curado de su padecimiento y, sobre todo, de sus obsesiones. Autorizó, además, la publicación de su caso. Freud, por su parte, afirmó que se estaba en presencia de un restablecimiento total.
En 1910 Lanzer se casó con su querida Gisela y en 1913 obtuvo el título de abogado. Enrolado en el ejército imperial en agosto de 1914, los rusos lo tomaron prisionero en noviembre y luego lo ejecutaron. Su madre murió dos meses después. ¿Qué habría sido de él, de haber sobrevivido?
En el caso de Lanzer, Freud se había enfrentado otra vez a una tragedia familiar y matrimonios consanguíneos, pero ciertamente no a un complejo edípico. El oficial del ejército imperial había leído algunas de sus obras y lo había buscado como un descifrador de enigmas, un Edipo que ocupaba el lugar de la Esfinge, pero durante su cura nunca se trató de ningún deseo inconsciente dirigido a la madre. Lanzer había tenido en efecto anhelos culpables de matar a un padre claudicante y brutal, pero no de poseer a la madre, ni siquiera cuando recordaba haber buscado en ella una protección contra un padre temido. Su madre había seguido siendo para él un objeto de asco cuyos olores nauseabundos, debidos a sus trastornos intestinales, lo horrorizaban. Y solo la veía como una mujer rígida y frustrada que había intentado impedirle contraer matrimonio con la mujer de su vida para casarlo con una Saborsky.
En vez de añadir una interpretación que refute o complete todas las propuestas por los psicoanalistas desde la publicación del caso, es más útil, sin duda, señalar lo representativa que es la historia de Lanzer de lo que fueron las primeras curas freudianas, caracterizadas por la imbricación entre cierto estado de la familia occidental —marcado por la demolición de la autoridad patriarcal— y la primacía atribuida a una palabra individual capaz de recoger su confesión. El propio Freud era el actor de esa historia y se alimentaba de ella para afinar su doctrina, enfrentado al riesgo permanente de extraviarse en el laberinto de las interpretaciones más extravagantes o intentar discernir con el mayor rigor la significación de un destino.
A la conminación de un matrimonio concertado que habría sido la repetición del de sus padres, Lanzer había opuesto las virtudes del matrimonio por amor, sin cuestionar la consanguinidad entre primos. Jamás había intentado, como otros judíos vieneses, superar al padre, y la incorporación a la vida militar no le había permitido resolver el conflicto que lo enfrentaba a su familia. El encuentro con Freud hizo de él el actor de su existencia, cuando los otros tratamientos corporales que le habían infligido eran una muestra del nihilismo terapéutico. Como muchos de los jóvenes de esa época, no tuvo tiempo de conocer la continuación de su historia, porque su destino fue la muerte en combate: «El paciente, a quien el análisis le había devuelto su salud psíquica, murió en la Gran Guerra como tantos otros jóvenes valiosos y prometedores».
El 28 de junio de 1914, Sergius (o Serguéi) Konstantínovich Pankejeff paseaba por el Prater pensando en su análisis con Freud cuando se enteró de la noticia, pasmosa para él, del asesinato del archiduque Francisco Fernando, cometido por un nacionalista bosnio. Su cura se había iniciado en enero de 1910, dos años después del final de la de Lanzer, y ahora, sin saberlo, se encontraba en un campo opuesto al de ese oficial del ejército austríaco que, como él, había frecuentado el consultorio de Berggasse 19. Miembro de una rica familia de la aristocracia rusa, Pankejeff había sido criado en Odesa junto con su hermana Anna por tres empleadas domésticas (Grusha, Nania y miss Owen) y varios preceptores. En esa residencia palaciega, su padre, Konstantin, depresivo y alcohólico, llevaba la vida activa de un político liberal y culto y organizaba a la vez cacerías de lobos que encantaban a Serguéi. Por la noche, tras las batidas, su madre, permanentemente afectada por diversos trastornos somáticos, solía bailar con sus dos hijos delante de un montón de animales transformados en trofeos.
De los dos lados de la genealogía, los integrantes de esta familia patológica hacen pensar en los personajes de _Los hermanos Karamazov_. El abuelo paterno había muerto alcohólico y su mujer se había hundido en la depresión. El tío Pierre, primer hermano del padre, sufría paranoia y se había tratado con el psiquiatra Serguéi Korsakov. Reacio a los contactos humanos, vivió como un salvaje en medio de los animales y terminó su vida en un psiquiátrico. El tío Nicolas, segundo hermano del padre, había querido raptar a la prometida de uno de sus hijos y casarse con ella a la fuerza. Un primo, hijo de la hermana de la madre, había sido internado en un psiquiátrico de Praga, afectado, también él, por una forma de delirio persecutorio. En cuanto a Konstantin, lo había tratado Moshe Wulff, uno de los primeros discípulos rusos de Freud, que también tenía en tratamiento a dos primos maternos afectados de esquizofrenia. Cuando Konstantin viajó a Munich para consultar a Kraepelin, este le diagnosticó una psicosis maníaco depresiva, sin brindarle empero el más mínimo apoyo.
Desde muy pronto Serguéi se vio frente a lobos y extraños rabos. Un día, miss Owen, a quien detestaba, blandió ante él unos largos caramelos y los comparó con pedazos de serpiente. Otro día se abrió el vestido por detrás y, meneándose, exclamó: «¡Pero miren mi rabito!». En cuanto a Anna, la hermana querida, masculina y temeraria, imitaba a miss Owen para burlarse de su hermano. Un día, con el propósito de despertar su curiosidad, le mostró la bella imagen de una muchacha. Pero detrás de la hoja había escondido el retrato de un horrible lobo erguido sobre sus patas traseras y a punto de devorar a Caperucita Roja. Enamorado de esa hermana que era la preferida de Konstantin, Serguéi dibujaba con ella árboles, caballos, lobos, borrachos y avaros. Y cuando lo embargaba el miedo, se refugiaba en los brazos de su Nania, nodriza adorada, muy piadosa, que le contaba historias de santos, mártires y persecuciones.
En 1896, a los diez años, Serguéi presentó signos de fobia a los animales. En 1905 su hermana Anna se suicidó y, dos años después, quien se dio muerte fue el padre. En esa época Serguéi iba a la escuela secundaria. Conoció a una mujer del pueblo, Matrona, con la cual contrajo una enfermedad venérea. Cayó entonces en frecuentes crisis depresivas que pronto lo llevaron —de sanatorio en psiquiátrico y de casa de reposo en establecimiento termal— a ser, como todos los miembros de su familia, un enfermo ideal a los ojos de los partidarios del saber psiquiátrico de fin de siglo: un melancólico crónico víctima de accesos de exaltación y depresión y siempre en busca de hallar su identidad. Contaba a cada médico una versión diferente de su «caso», tanto para hacerse querer por él como para atribuirse cierta consistencia.
Atendido en un primer momento por Vladímir Bejtérev, que utilizó la hipnosis; luego por Theodor Ziehen en Berlín, y finalmente por Friedländer en Frankfurt, se trasladó a Munich para ver a Emil Kraepelin, quien, recordando la herencia paterna, emitió de nuevo un diagnóstico de psicosis maníaco depresiva. En el sanatorio de Neuwittelsbach, donde siguió tratamientos tan diversos como inútiles —masajes, baños, etc.—, Serguéi, siempre muy atraído por las nodrizas y las mujeres del pueblo, se enamoró de una enfermera, Teresa Keller, algo mayor que él y madre de una niña (Else). Se estableció entonces una relación pasional que generó la oposición no solo de su familia sino también de su psiquiatra, convencido de que ese tipo de contacto con una mujer «inferior» tendría como consecuencia un agravamiento de su locura.
De retorno en Odesa, Pankejeff comenzó a tratarse con un joven médico, Leonid Drosnes, quien decidió llevarlo a Viena para una consulta en la Berggasse. Con una frase mordaz, Freud estigmatizó el nihilismo terapéutico de sus colegas psiquiatras: «Hasta ahora», le dijo a Pankejeff, «usted ha buscado la causa de su enfermedad en un orinal».
La interpretación tenía una doble significación. Freud apuntaba tanto a la inutilidad de los tratamientos anteriores como a la patología propia de Serguéi, que sufría trastornos intestinales permanentes y sobre todo un estreñimiento crónico. Erróneamente, _Herr Professor_ estaba convencido de que ese trastorno era de origen psíquico. Por eso ordenó a su paciente que interrumpiera las lavativas que le aplicaba un estudiante, a causa de su «carácter homosexual».
Por consejo de Freud, Pankejeff se instaló en Viena. Mientras Drosnes asistía a los seminarios de la WPV y se iniciaba en el psicoanálisis, Serguéi daba clases de esgrima y se dedicaba a sus estudios de derecho. Por la noche iba al teatro o jugaba a las cartas. Le encantaban Viena, el Prater, los cafés, la vida urbana que le hacía olvidar su infancia rural poblada de lobos y ancestros pavorosos.
En vez de prohibirle ver a Teresa, Freud le pidió simplemente que esperara hasta el final de la cura para volver con ella. No se opuso al matrimonio: «Teresa», dijo, «es el impulso hacia la mujer». En una carta a Sándor Ferenczi, de febrero de 1910, señaló la violencia de las manifestaciones transferenciales de su paciente:
El joven ruso rico que he tomado como paciente a causa de una pasión amorosa compulsiva me ha confesado, después de la primera sesión, las siguientes transferencias: como soy un judío estafador, le gustaría dármela por detrás y cagarme en la cabeza. A los seis años, el primer síntoma manifiesto consistía en injurias blasfemas contra Dios: cochino, perro, etc. Cuando veía tres montones de bosta en la calle, se sentía incómodo a causa de la Santísima Trinidad y buscaba ansiosamente un cuarto montón para destruir la evocación.
Pankejeff tuvo por primera vez la impresión de ser escuchado y ya no tratado como un enfermo. El tratamiento contribuyó a darle una identidad y sacarlo de la nada existencial en la cual lo habían mantenido los distintos médicos con quienes se había cruzado durante sus vagabundeos por los hospitales. Y en particular, mantuvo con Freud relaciones amistosas y terminó por venerarlo. Al final del tratamiento, Freud, por su lado, manifestó una fuerte empatía hacia él. Conocería finalmente a Teresa y aprobaría el matrimonio, que se celebró en Odesa en 1914. Pankejeff se sintió entonces curado y afirmó que el análisis le había permitido casarse con la mujer que amaba.
Con este paciente Freud se había enfrentado una vez más a una historia que ilustraba a la perfección su concepción de las neurosis familiares: sexualidad precoz, relaciones ambiguas entre hermanos y hermanas, papel de las institutrices y las malas nodrizas, escenas de seducción, patología de los padres, tíos y primos, sojuzgamiento de las mujeres, etc. Olvidó pues que su paciente padecía una melancolía crónica incurable e hizo de él un caso de histeria de angustia con fobia a los animales, transformada a continuación en neurosis obsesiva o neurosis infantil.
Inmerso en ese estado de ánimo, y en medio de la tormenta de la guerra, escribió en dos meses, de octubre a noviembre de 1914, la historia de ese ruso depresivo y ambivalente, sin recurrir a la denominación «Hombre de los Lobos». A petición del propio Serguéi, el relato se publicó en 1918 con el título de «Extracto de la historia de una neurosis infantil». En él Freud no hacía ninguna referencia a lo que acababa de escribir sobre la melancolía. Sin embargo, en varias ocasiones habría de agregar notas al texto original.
Contrariamente al caso del Hombre de las Ratas, donde la lógica de la terapia psicoanalítica se exponía de manera implacable, Freud, para escribir la historia de Pankejeff, se lanzó a un verdadero trabajo de reconstrucción biográfica, al extremo de «inventar», a fuerza de interpretaciones, acontecimientos que sin duda jamás se habían producido, en un relato centrado en su totalidad en la infancia del paciente y su sexualidad.
El cuadro familiar freudiano estaba compuesto por la madre, el padre, la hermana y tres empleadas: la niñera (Nania), la institutriz inglesa (miss Owen) y la criada (Grusha). Según Freud, que se basaba en los recuerdos evocados por Serguéi en su cura, este habría sido objeto de un intento de seducción a los tres años y medio por su hermana Anna, que le habría mostrado la «cola», en tanto que él, a continuación, se exhibió presuntamente delante de Nania y se ganó el reto de esta. Freud contaba que hacia los diez años el paciente ruso había querido, a su turno, seducir a su hermana, que lo había rechazado. En consecuencia, prefirió en lo sucesivo escoger mujeres de condición inferior a la suya. Sobre la base de la interpretación de un sueño que Serguéi tuvo a los cuatro años, luego contado y dibujado por él durante las sesiones, Freud reconstruye el origen de la neurosis infantil: «He soñado que es de noche», dice el paciente,
y estoy en mi cama [...] Sé que es de noche [...]. De repente, la ventana se abre sola y veo con gran terror que sobre el nogal grande frente a la ventana están sentados unos cuantos lobos blancos. Eran seis o siete. Los lobos eran totalmente blancos y parecían más bien como unos zorros o perros ovejeros, pues tenían grandes rabos como zorros y sus orejas tiesas como de perros al acecho. Presa de gran angustia, evidentemente de ser devorado por los lobos, rompo a gritar y despierto.
Relacionando ese sueño de los lobos blancos con varios recuerdos del paciente acerca de su sexualidad infantil, Freud inventó, con detalles de una precisión inaudita, una extraordinaria «escena primordial» ( _Urszene_ ), que será célebre en los anales del psicoanálisis y constituirá el objeto de muchos comentarios:
[Serguéi, por entonces de dieciocho meses,] dormía, pues, en su camita en la habitación de sus padres cuando despertó, tal vez a consecuencia de un aumento de la fiebre, pasado el mediodía, quizá hacia las cinco de la tarde, la hora señalada luego para la depresión. Armoniza con la hipótesis de un caluroso día de verano que los padres desvestidos a medias se hubieran retirado para dormir la siesta. Al despertar fue testigo de un _coitus a tergo_ repetido tres veces, pudo ver los genitales de la madre así como el miembro del padre y comprendió el hecho así como su significado. [...] El niño interrumpió al fin el estar juntos de sus padres mediante una evacuación que le dio motivo para berrear.
Según Freud, el sueño de los lobos era, por tanto, la representación invertida de una antigua escena de amor. Serguéi Pankejeff jamás admitió la existencia de esa escena, pero no dejó de considerarla fascinante y de señalar que había dado un sentido a su vida. Tan pronto afirmaba que Freud había acertado al reconstruir de tal modo su vida psíquica inconsciente como dudaba de la pertinencia de esa interpretación.
Otros dos episodios de la vida de Serguéi suscitaron una serie de interpretaciones. Uno incumbía a Grusha, cuyas nalgas, comparadas con alas de mariposa y luego con el número romano V, remitían a los cinco lobos del sueño y la hora en la que habría tenido lugar el famoso coito; el segundo tenía que ver con una alucinación visual. En su infancia Serguéi había visto su dedo meñique seccionado por una navaja, para advertir enseguida que no había ninguna herida. Freud dedujo de ello que, en este asunto, su paciente había manifestado una actitud de rechazo ( _Verwerfung_ ) consistente en ver la sexualidad únicamente desde la óptica de una teoría infantil: el contacto por el ano.
Después de esta gran inmersión en la infancia de Serguéi, Freud tuvo la certeza de haberlo curado. Hasta la primavera de 1918 Pankejeff vivió en Odesa entre su madre y Teresa, que no se llevaban bien. Retomó a continuación sus estudios y no tardó en obtener el título de jurista. En cuanto a Teresa, se vio obligada a salir de Rusia para reunirse con su hija, que murió en Viena. Serguéi se le unió allí. La Revolución de Octubre lo había arruinado y el antiguo aristócrata acaudalado se convirtió en otro hombre, un emigrado pobre y sin recursos, forzado a aceptar un empleo en una compañía de seguros donde trabajaría hasta jubilarse.
Los cambios acaecidos en su vida lo sumieron en una nueva depresión, que lo incitó a acudir otra vez a Freud. Este lo recibió de buena gana, le obsequió sin demora el relato de su caso, que acababa de publicar, y después volvió a tomarlo en análisis, de noviembre de 1919 a febrero de 1920. Si le damos crédito, esta «posterapia» permitió liquidar un resto de transferencia no analizada y curar por fin al paciente.
En realidad, Serguéi siguió presentando los mismos síntomas, agravados bajo el efecto de una mala situación económica. Para ayudarlo, Freud recolectó dinero en el círculo de sus discípulos vieneses. Fue entonces cuando Pankejeff comenzó a identificarse con la historia de su caso y a verse verdaderamente como el Hombre de los Lobos, a tal punto que se atribuyó el nombre de _Wolfsmann_.
En 1926, siempre afectado por los mismos síntomas, volvió a consultar a Freud, quien se negó a tratarlo por tercera vez y lo derivó a Ruth Mack-Brunswick, morfinómana y casi tan enferma como él. Serguéi se vio entonces atrapado en un increíble enredo transferencial. Freud no solo analizaba al mismo tiempo a Ruth, a su marido y al hermano de este, sino que, por añadidura, ese mismo año derivó al diván de aquella a una norteamericana, Muriel Gardiner, que iba a convertirse en amiga y confidente de Pankejeff a medida que se desarrollaban sus respectivos análisis.
Partidaria de las teorías de Melanie Klein, Ruth Mack-Brunswick identificó en el paciente, tras un tratamiento de seis meses, no una neurosis sino una paranoia. En 1928 publicó una segunda versión del caso. Por primera vez, atribuyó al paciente el nombre que este quería llevar y que de allí en adelante lo identificaría: «el Hombre de los Lobos». Lo describió como un hombre perseguido, antipático, avaro, sórdido, hipocondríaco, obsesionado por su imagen y, en particular, por una pústula que le carcomía la nariz. Con ese nuevo diagnóstico, el movimiento psicoanalítico se dividió en dos campos: los partidarios de la psicosis por un lado, los de la neurosis por otro. Pankejeff juzgó que su segunda terapeuta estaba loca y que había mostrado una dureza increíble con Teresa, pero que lo había ayudado.
Siempre en 1926, en el momento del estallido de la terrible desavenencia entre Freud y Rank, este criticó la interpretación freudiana del sueño de los lobos. A su entender, era imposible que un niño de cuatro años hubiera podido soñarlo; Rank afirmaba por eso que se estaba en realidad frente a un deseo transferencial del paciente. La cama del niño, decía en sustancia, representa el diván; los árboles son los que se ven desde el consultorio, y los lobos no son más que la representación de los miembros del comité cuya fotografía adorna el escritorio de Freud, e incluso los hijos de este. Y Rank añadía que ese sueño probaba la existencia de sus propias teorías sobre la transferencia materna y el trauma del nacimiento. A sus ojos, el paciente había soñado con un «árbol genealógico», lo cual había despertado sus celos infantiles, en los que Freud ocupaba para él el lugar de una madre con un pene adosado.
Furioso, Freud redujo a nada las hipótesis de su querido discípulo al demostrar, con la aportación de pruebas, que en el momento del relato del sueño el paciente no había podido ver los retratos de los miembros del comité, dado que en la pared, encima de la _Lección clínica del profesor Charcot en la Salpêtrière_ , solo colgaban dos o tres retratos. Y para confirmar esa aserción, pidió a Pankejeff que le enviara un testimonio escrito: «No tengo ninguna razón para dudar de la exactitud de ese recuerdo [...]. Además, que yo sepa, el recuerdo de ese sueño infantil nunca sufrió cambios [...]. Siempre me pareció que el sueño de los lobos estaba en el centro de mis sueños infantiles [...]. Le conté el sueño de los lobos al comienzo de la cura». A raíz de este episodio, Freud encargó a Ferenczi que atacara las tesis de Rank. Triste combate, cuyo saldo para aquel fue la pérdida de dos de sus mejores discípulos.
Para generaciones de psicoanalistas, historiadores y filósofos, el nombre de Pankejeff permaneció ignorado en los anales del psicoanálisis. Solo subsistió, durante decenios, la historia del _Wolfsmann_ tal como había sido contada por Freud y reinterpretada hasta el infinito, en virtud de teorías a cual más extravagante, por prestigiosos comentaristas.
Hasta que por fin se reveló, en dos obras contradictorias y con diez años de intervalo, la verdadera vida de Serguéi Pankejeff, era imposible discernir con claridad porque este seguía haciéndose llamar «el Hombre de los Lobos». Con el paso de los años el antiguo paciente se había metamorfoseado en una suerte de archivo, un personaje novelesco surgido de otro siglo, arruinado por dos guerras, refugiado en Viena, que dibujaba una y otra vez su árbol con lobos y multiplicaba las dedicatorias destinadas a psicoanalistas del mundo entero deseosos de ostentar en sus consultorios el recuerdo de una época finiquitada. Tomado a su cargo por la comunidad psicoanalítica vienesa, a la vez como paciente y como leyenda, Pankejeff no dejó hasta su muerte, en 1979, de contar a cada uno de sus interlocutores varias versiones diferentes de su historia.
Tras haber adquirido gran competencia en lo concerniente a la realidad de su melancolía, había aprendido a rivalizar con todos los comentaristas de su «caso». ¿No había tenido el privilegio, decía, de ser un fragmento inalterable de la obra freudiana y el «amigo» de un «pensador genial»? Los antifreudianos afirmaron entonces que el desdichado ruso era la víctima de una empresa criminal, y Freud un estafador que manipulaba a sus pacientes para hacer creer que el psicoanálisis los curaba.
Dos años antes de la Gran Guerra, durante la cual moriría Lanzer pero a la que Pankejeff sobreviviría, Freud se había valido de la idea de que el crimen, bajo la forma del asesinato del padre, estaba en el origen de todas las sociedades. Pero el único tipo de crimen que verdaderamente le interesaba era el ligado al incesto, y de él hacía el paradigma de todos los actos mortíferos. Armado de tal hipótesis, daba a entender que toda sociedad, en función de su evolución, repetía ese acto, presente como un «resto» o un «vestigio», tanto en las colectividades humanas como en la vida individual. Y no había que negar ese resto, sino reinterpretarlo en cuanto suponía una prohibición. Por eso Freud se oponía a la pena de muerte, no como simple ciudadano sino, diría, porque es incompatible con la enseñanza del psicoanálisis:
Si la humanidad sigue negando a la pena de muerte su carácter de asesinato sancionado por la ley, es porque siempre se negó hasta aquí a mirar a la realidad a la cara, a reconocer la existencia de la vida afectiva inconsciente. Mi posición con respecto a la pena capital no procede, por lo tanto, de razones humanitarias, sino del reconocimiento de la necesidad psicológica de la prohibición universal: no matarás [...]. Afirmo ser un resuelto adversario del asesinato, ya se presente bajo la forma de un crimen individual o de represalias ejercidas por el Estado.
Freud concebía su teoría como una ciencia cuyo objetivo era traducir en la lengua de los mitos la epopeya psíquica de la especie humana y de su origen. Por eso estaba convencido de que, en su mundo, todo sucedía como en los mitos que él había construido. En su práctica clínica, en su vida cotidiana —con Lanzer, Pankejeff y muchos otros—, intentaba encontrar sus construcciones científicas. La guerra, es cierto, había puesto fin a sus viejos arrebatos de optimismo, y en 1920 él veía a su alrededor la muerte en acción. Pero en ese mismo momento su doctrina era recibida triunfalmente por doquier como una higiene de vida, una nueva moral civilizada, no solo por los partidarios de una nueva psiquiatría dinámica, sino también y sobre todo por los escritores que veían en ella una suntuosa manera de explorar las profundidades del inconsciente.
La Belle Époque y los años mortíferos fueron sucedidos durante un decenio, al menos para las clases dominantes de la sociedad, por la era de los felices años veinte, marcada por la recuperación económica y la aspiración a todas las formas de revolución: literaria, artística, política, sexual, musical. Llegado de Hollywood, el arte cinematográfico procuraba aportar a las masas una representación inédita de la realidad. Alentados por el socialismo, el feminismo y el psicoanálisis, todos querían creer que la jerarquía entre las clases sociales y los sexos estaba condenada a una próxima desaparición. La familia se transformaba, los divorcios eran más frecuentes y el índice de natalidad disminuía. En los medios urbanos —París, Berlín, Londres, Nueva York— se expandían el culto de la bisexualidad y las experiencias transgresoras. En cuanto a las mujeres, se liberaban del corsé de la familia, llevaban ropa de corte fluido que dejaba traslucir sus formas y reclamaban el derecho a participar en la vida política. En una palabra, se negaban a ser reducidas, como antaño, al estatus de novia tonta, madre agotada por una sucesión de embarazos no deseados, esposa condenada a las tareas domésticas.
En Francia, país de todos los contrastes, el psicoanálisis suscitaba mucho más entusiasmo en los escritores debido al rechazo que sufría, como «ciencia _boche_ » u «obscenidad científica», en una buena parte de las instituciones médicas. Y cuando los surrealistas dieron un lugar de privilegio a la «revolución freudiana», Freud se negó a escuchar sus voces y no entendió demasiado la admiración que le profesaban André Breton y sus amigos. Él seguía admirando a Anatole France y se obstinaba en desconocer la importancia de las vanguardias literarias, a la vez que mantenía correspondencia con Romain Rolland, escritor prolífico, amigo íntimo de Stefan Zweig, hostil a todos los nacionalismos y galardonado con el premio Nobel de Literatura en 1915. En pocas palabras, Freud seguía aferrado al «mundo de ayer» y más aún a la manera como había concebido ese mundo al aportarle una revolución cuyo alcance, es indudable, no apreciaba. Extraña contradicción, soberbiamente freudiana.
En el momento mismo en que la guerra terminaba y aparecían nuevos modos de vida, una pandemia de gripe mortal se abatió sobre el mundo. Procedente de China, el virus llegó a Estados Unidos y, después de pasar por España y sufrir una mutación, se propagó por Europa. En pocos meses provocó una hecatombe aún más considerable que la de los combates.
En enero de 1920 Freud no daba señales de gran simpatía por las aspiraciones de las jóvenes generaciones. Poco sensible a los entusiasmos de la modernidad, pensaba en su propia muerte y la de sus allegados, en el envejecimiento de los cuerpos y los rostros y en sus viejas enfermedades: trastornos de la vejiga y los intestinos, supuración de la nariz. Temía morir antes que su madre y, más aún, en el caso de suceder así, que fuera menester ocultarle a esta la verdad. Cuando Jones le anunció la muerte de su propio padre, lo consoló, considerando como una suerte que ese anciano no hubiera tenido que soportar demasiado tiempo los sufrimientos de un cáncer que lo habría carcomido a fuego lento.
No fue el caso de Anton von Freund, su amigo y benefactor. Freud creía erróneamente haberlo preservado de una recaída al tratar su neurosis, y tuvo que desengañarse. El amigo Toni murió el 20 de enero a los cuarenta años: «Toni Freund murió ayer, apaciblemente liberado de su mal incurable. Una pesada pérdida para nuestra causa, un vivo dolor para mí, pero para el cual pude prepararme en el transcurso de los últimos meses. Soportó su falta de esperanza con una lucidez heroica y no avergonzó al psicoanálisis».
Cinco días después, Sophie Halberstadt, debilitada bajo los efectos de un embarazo no deseado, sucumbió a una neumonía gripal. Debido al cierre de las redes ferroviarias, ningún vienés pudo viajar a Hamburgo para el entierro:
La brutalidad sin velo de la época nos agobia. Mañana incineran a nuestra pobre niña favorecida por los dioses [...]. Sophie deja dos hijos de seis años y trece meses y un marido inconsolable que ahora va a pagar caro la felicidad vivida a lo largo de siete años. Felicidad que solo existía entre ellos, no exteriormente. Guerra, ocupación, herida, desaparición de su fortuna; pero supieron mantener su coraje y su alegría.
Y también:
¿Con qué fin escribo, entonces? Solo creo que no estamos juntos y que en esta miserable época de encierro no podemos ir uno a casa de otro [...]. Un acto absurdo y brutal del destino nos ha arrebatado a nuestra Sophie: algo frente a lo cual no se puede ni acusar ni cavilar, sino bajar la cabeza ante el golpe, como pobres seres humanos sin recursos con quienes juegan las potestades superiores.
Así como la muerte lo afectaba, el suicidio, muy frecuente en las filas de los intelectuales y psicoanalistas de Viena, lo dejaba frío. Aferrado a una concepción heroica de la muerte y profundamente marcado por la cultura grecolatina y el romanticismo negro, Freud rechazaba la psiquiatrización de ese acto, que veía con toda la razón como un derecho. Pero solo le interesaba ya fuera para relacionarlo con su concepción de la diferencia de los sexos, ya fuera para mostrar que el deseo de matarse suponía una inversión del deseo de matar. A su entender, las mujeres no se suicidaban de la misma manera que los hombres. Estos, decía, prefieren las armas, es decir, un sustituto del pene, y las mujeres eligen más bien ahogarse, arrojarse por una ventana, envenenarse: tres maneras, a su juicio, de dar nacimiento, alumbrar o desear un embarazo.
Esto equivale a decir que Freud, obsesionado por el asesinato primordial, la guerra, la bella muerte y la idea de la finitud biológica de la vida, no entendía gran cosa de la esencia de la muerte voluntaria: crimen multifacético contra sí mismo, presente en el núcleo de todas las sociedades humanas, desafío constante a todas las formas de autoridad. Se divertía cuando anunciaban su propio suicidio y le gustaba citar el telegrama de Mark Twain. Es cierto, veía con claridad que no se trataba de un acto de locura y establecía un vínculo entre el suicidio y la melancolía, llegando a veces a hablar de una «liberación» que seguía a un exceso de sufrimiento psíquico, pero no discernía hasta qué punto la muerte voluntaria podía ser también la expresión de la más alta de las libertades. En una palabra, tenía tendencia a «psicologizar» el suicidio.
Por esa razón se mostró tan duro con Victor Tausk, uno de sus discípulos más brillantes de la primera generación, a quien habían criado en Croacia un padre tiránico y una madre perseguida. Como Lou Andreas-Salomé, su amante, que lo llamaba «tú, hermano animal», había sentido en sí mismo la presencia de una fuerza primitiva. Poseído por el odio al padre, Tausk había adoptado con Freud una actitud ambivalente, hecha de rebelión, adoración y sometimiento. A la hora de los combates había estado en el frente serbio para luego regresar a Viena, abatido por el derrumbe del Imperio, y Freud no encontró nada mejor que incorporarlo a una triangulación transferencial cuyos secretos dominaba. Lo envió, en efecto, a analizarse con Helene Deutsch, que por entonces frecuentaba su propio diván, y a través de ella pensaba controlar el desarrollo de su cura. Ahora bien, en julio de 1919 Tausk puso fin a sus días estrangulándose con el cordón de una cortina y disparándose una bala de revólver en la sien.
Freud compuso sobre él una necrológica elogiosa. Pero, en una carta privada enviada a Lou Andreas-Salomé, escribió estas palabras:
El pobre Tausk, a quien usted distinguió durante un tiempo con su amistad, se ha suicidado de la manera más radical. Había vuelto desgastado, minado por los horrores de la guerra, y se había visto en la obligación de intentar restablecerse en Viena en las circunstancias más desfavorables de una existencia arruinada por la entrada de las tropas; procuró incorporar una nueva mujer a su vida y debía casarse ocho días después...., pero decidió otra cosa. Las cartas de despedida a su prometida, a su primera mujer y a mí son igualmente tiernas, dan testimonio de su perfecta lucidez, no acusan a nadie sino a su propia insuficiencia y su vida fracasada y, por lo tanto, no arrojan luz alguna sobre su acto supremo.
Y añadía: «Confieso que no lo echo verdaderamente de menos. Hacía tiempo que lo consideraba inútil e incluso como una amenaza para el futuro».
Una vez restablecida la paz, los miembros del comité se entregaron a feroces batallas internas. Las sociedades psicoanalíticas de Londres y Berlín habían cobrado mayor importancia que la WPV, y la New York Psychoanalytic Society (NYPS) ganaba una amplitud considerable. Ferenczi y Rank se interesaban cada vez más, como antaño Jung, en el origen «femenino» y «materno» de las neurosis y las psicosis, y ya no solo en la cuestión del asesinato del padre. Freud siempre había afirmado que la madre era el primer objeto de amor del ser humano, pero, al psicologizar la tragedia de Edipo, había transformado esta en un «complejo» que no podía explicar todos los aspectos de la psique. Y los psicoanalistas de la nueva generación procuraban despegarse de la figura tutelar del padre erigido en tótem. Por eso dejaban de lado el crimen primordial para preguntarse sobre el apego precoz a la madre. De resultas, Ferenczi proponía, mediante la aplicación de la «técnica activa», una transformación radical de la práctica de la terapia psicoanalítica. En el congreso de Budapest ya se había opuesto a Freud en la cuestión de los «nuevos caminos». Y ahora iba a ir aún más allá.
Lejos de limitarse a plantear interpretaciones apuntadas a extirpar del inconsciente los relatos de escenas primordiales, el analista moderno debía, en opinión de Ferenczi, intervenir en la sesión por medio de conminaciones y prohibiciones. A la figura de la Esfinge poseedora de secretos y enigmas oponía la imagen del terapeuta benévolo, empático, femenino, sensual y maternal, deseoso de aliviar el sufrimiento del paciente. A la luz de semejante revolución, Freud aparecía como un monarca honrado que imperaba sobre un reino arcaico.
Al apoyar a Abraham, Jones buscaba por su parte profesionalizar el oficio y combatía a Rank y Ferenczi para lograr encauzar la dirección del movimiento hacia el mundo angloparlante. La victoria de los Aliados parecía darle la razón. En este caso contra Abraham, y pese a las dificultades económicas de los vencidos, impuso la elección de La Haya para la celebración del sexto congreso del IPV. En lo sucesivo sería su presidente hasta 1925. Freud lo apoyó.
En septiembre de 1920, delante de sesenta y dos participantes, entre los cuales había muchas mujeres, Abraham pronunció su discurso inaugural en latín para no herir las susceptibilidades de los vencedores de la guerra. De todos modos, la lengua alemana dominó los debates. Y Berlín, gracias a la creación de su prestigioso instituto, seguiría siendo, durante unos diez años más, el centro neurálgico de una expansión del psicoanálisis hacia el mundo occidental y oriental. Freud, en lo que significaba para él la oportunidad de modificar una vez más su _Traumbuch_ , volvió a dictar una conferencia sobre el sueño, mientras que Ferenczi se explayó sobre la técnica activa; Binswanger se ocupó de la clínica psiquiátrica y Geza Roheim, en inglés, habló del totemismo en Australia. Los holandeses se mezclaban de buena gana con los ingleses y los polacos para intercambiar impresiones de viaje e ideas en el transcurso de largos paseos en automóvil, en barco o a caballo. Al término de esas jornadas de alegría y reencuentros, un distendido banquete, ofrecido por los vencedores, permitió a los vencidos de los fenecidos Imperios Centrales dejar de verse como los parias de la nueva Europa.
Ahora célebre en el planeta entero, Freud asistía así al triunfo mundial de su movimiento. Pero sobre todo se aburría y añoraba el tiempo en que él mismo se había considerado como un descubridor solitario. Puesto que, de hecho, no aceptaba la manera en que sus numerosos discípulos y admiradores interpretaban su doctrina y la hacían vivir al ritmo vibrante de los felices años veinte, y sentía que entre «él y los otros» se había abierto una brecha irreparable: «En su última circular», escribiría a Ferenczi,
me parece excelente el pasaje donde usted dice que las cosas van mal para todos nosotros, pero muy bien para nuestra causa. Es efectivamente así: la causa nos devora y, en cierta forma, nos disolvemos en ella. Y quizá esté bien que suceda de ese modo; yo habría deseado simplemente que la segunda generación analítica, la más joven, pudiera resistir la disolución todavía un tiempo.
En La Haya, no obstante, Freud sintió una verdadera felicidad al ver llegar desde Baden-Baden, a orillas del Rin, y acompañado de su amante, a un médico poco común: Georg Groddeck. En medio de esta culta asamblea que intentaba hacer el duelo de los años de guerra y normalizar la formación de los profesionales, Groddeck afirmaba, en efecto, con un tono bastante exaltado y una voz atronadora, que era un «analista silvestre» y pretendía curar las enfermedades orgánicas mediante un tratamiento psíquico adaptado. En 1900, por lo demás, había fundado un sanatorio en Baden-Baden para aplicar en él sus teorías: una medicina del «sujeto» con hidroterapia, masajes, régimen alimentario y conversaciones entre pacientes y personal de atención. Ferenczi lo adoraba y Freud ya le había expresado su entusiasmo: «Es usted un analista de primera fila [...]. El hombre que ha reconocido que la transferencia y la resistencia constituyen los puntos clave del tratamiento pertenece irrevocablemente a la "jauría" [...]. [M]e inclino a acoger su colaboración con los brazos abiertos». Y añadía: «¿Por qué se arroja usted [...] de cabeza al misticismo, por qué [...] se liga usted a inútiles teorías filosóficas [...]? Sus experiencias, después de todo, no suponen sino la comprensión de que los factores psicológicos representan un elemento inesperadamente importante también en el origen de las enfermedades orgánicas».
A la inversa de buen número de discípulos y pacientes de Freud, Groddeck no había padecido ninguna tiranía paterna sino la frialdad de una madre que, a sus ojos, había eclipsado la figura adorada del padre. Criada ella misma en el culto de un padre autoritario, aquella no había sabido transmitir a sus hijos el afecto necesario para su desarrollo. Afectados por diversas enfermedades orgánicas, cuatro de ellos habían muerto prematuramente, y Georg era el único superviviente. Médico reputado, Carl Theodor, su padre, dirigía un establecimiento de baños y se lo conocía por sus posiciones ultraconservadoras. Terminada la primavera de los pueblos, había publicado una obra en la que equiparaba la democracia a una plaga, una epidemia capaz de «contaminar» Europa y provocar en los individuos la desaparición de toda forma de autoconciencia. Esa tesis, que está presente en los sociólogos de las multitudes, y sobre todo en Gustave Le Bon, hacía de Carl Theodor Groddeck un partidario del canciller Bismarck.
Acicateado por su padre, Georg se inició en la carrera médica como asistente de Ernst Schweninger, un médico marginal que había conquistado fama al tratar con éxito las diferentes «enfermedades» del canciller Bismarck —tabaquismo, toxicomanía, obesidad— por medio de un régimen draconiano. Ultraconservador también él, había trasladado a la medicina los principios del autoritarismo prusiano e instaurado con sus pacientes una relación de sugestión y de sumisión absoluta de la que hacía depender el tratamiento y la naturaleza misma de la curación. Su divisa — _Natura sanat, medicus curat_ — fue utilizada por Groddeck en 1913, al publicar su primera obra.
Como su maestro y su padre, Groddeck reivindicaba la idea de una «pureza de la raza» y proponía despojar de sus derechos cívicos a todo ciudadano alemán casado con una persona extranjera. En 1929, en sus _Lebenserinnerungen_ , lamentaría su actitud de entonces y la corregiría, sin renunciar jamás a la utopía higienista que le servía de fundamento y que además compartían muchos médicos y sexólogos alemanes apegados a la idea de la «mejora de la especie humana». En ese mismo libro atacaba enérgicamente el psicoanálisis, poniendo en guardia al lector contra los peligros de una técnica a menudo mal dominada por profesionales incompetentes.
Muy poco después Groddeck había dado un giro. Y Freud estaba fascinado por ese médico que le recordaba a Fliess y los deliciosos delirios de antaño. En contacto con él podía desafiar de nuevo a la medicina de su tiempo, soñar con conquistar el territorio del cuerpo, imaginar una amistad con un doble femenino de Jung, plantear un reto al tedioso pragmatismo de Jones y complacerse en especulaciones sobre la naturaleza bisexual de la humanidad. En una palabra, reencontraba en Groddeck el entusiasmo de sus años de juventud, y poco importaba que algunas de sus tesis fueran en contra de la ciencia médica, porque tenían en cuenta el sufrimiento subjetivo, abandonado por la ciencia.
En el sanatorio de Baden-Baden Groddeck recibía pacientes afectados por toda clase de enfermedades orgánicas frente a las cuales la medicina de la época se revelaba impotente. En 1916, para hacerlos participar en su propio tratamiento, se le ocurrió la idea de dictar conferencias dirigidas a ellos y crear, luego, una revista, _Sanatorium_ , donde pudieran expresarse en un nivel de igualdad con el terapeuta. Groddeck se ocupaba de cánceres, úlceras, reumatismos, diabetes, y pretendía encontrar en el trazado de la enfermedad la expresión de un deseo orgánico. Así, veía en el bocio un deseo infantil y en la diabetes el deseo del organismo de endulzarse. En la misma perspectiva, sexualizaba los órganos del cuerpo: el nervio óptico estaba del lado de la masculinidad y las cavidades cardíacas, del lado de la femineidad.
Ese deseo orgánico derivaba de lo que Groddeck llamaba el ello ( _Es_ ). Con ese pronombre neutro tomado de Nietzsche designaba una sustancia arcaica, anterior al lenguaje, una especie de naturaleza salvaje e irredentista que sumergía las instancias subjetivas: algo así como las «grutas» de Jung. La curación consistía en dejar actuar en el sujeto el manar del ello, fuente de verdad.
Un año después de su encuentro con Freud, Groddeck publicó una «novela psicoanalítica», _El escrutador de almas_ , en la cual contaba la epopeya de un hombre transfigurado por la revelación de su inconsciente que sale a la caza, a través del mundo, de chinches e «imágenes de almas». Freud admiró el estilo picaresco del autor, que le recordaba a Rabelais y el _Quijote_ de Cervantes. En 1923 Groddeck publicó el famoso _Libro del ello_ , donde ponía en escena su relación epistolar con Freud por medio de un conjunto de cartas ficticias enviadas por el narrador, Patrick Troll, a una amiga. Quería popularizar de tal modo los conceptos del psicoanálisis y su propia doctrina. Freud se apoderó del ello y modificó radicalmente su definición. Y fue entonces cuando comenzó a desilusionarse e irritarse con ese médico extravagante a quien tanto había querido, y al que ahora acusaba de sembrar la discordia en la jauría de sus discípulos:
Lamento que trate de alzar un muro entre usted y los demás leones que aloja la jaula del Congreso. Es difícil practicar el psicoanálisis en medio del aislamiento, pues se trata de una empresa exquisitamente social. Sería mucho más agradable que todos rugiéramos o aulláramos a coro y con el mismo ritmo, en lugar de limitarnos a gruñir en solitario sin movernos de nuestro rincón.
Freud se negó a desplazarse a Baden-Baden, a pesar de que Ferenczi iba a esa ciudad a someterse a un tratamiento y de que Jones y Abraham ponían el grito en el cielo. En definitiva, Freud afirmó que las ideas de Groddeck eran buenas, pero no servían para la investigación científica.
Correspondió a Thomas Mann el mérito de hacer el más bello retrato de Groddeck. En _La montaña mágica_ se lo presenta, bajo el nombre de doctor Edhin Krokovski, director médico del Berghof, como un hipnotizador a la antigua, obsesionado por la sexualidad, pero que al parecer no ha accedido todavía a las luces de la razón: «Por allí pasa, conocedor de todos los secretos de nuestras señoras. Se ruega observar el refinado simbolismo de su atuendo. Viste de negro para indicar que el ámbito específico de sus estudios es la noche». Krokovski manifiesta un pesimismo radical con respecto a la salud humana, a tal punto que solo ve en el hombre un sujeto invadido por la enfermedad. Desplazándose entre materialismo y ocultismo, se entrega a experiencias de telepatía que lo sumergen en el universo fáustico de un subconsciente desordenado. Tal era el magnífico sanador del que Freud se había prendado sin mostrar nunca una verdadera adhesión a sus extravagancias.
En tanto que Karl Kraus y Otto Weininger equiparaban la judeidad a una esencia femenina responsable de la decadencia de la cultura patriarcal, Groddeck proponía, por el contrario, la necesidad de encontrar en cada ser humano una bisexualidad original reprimida en la religión judía por la práctica de la circuncisión. A sus ojos, esa práctica habría favorecido la afirmación de una unisexualidad del hombre y el rechazo de su esencia femenina frente a un Dios bisexual y omnipotente. Por esta hostilidad a la religión del padre y en nombre de una búsqueda mesiánica de la femineidad, la única capaz de salvar a la humanidad, Groddeck rechazaba pues el judaísmo por razones opuestas a las de Weininger. Sin embargo, compartían la misma problemática: por un lado, el judío era equiparado a una mujer cuando todo el mal de la civilización provenía de la femineidad, y por otro, encarnaba el mal al reprimir los beneficios de lo femenino.
En 1920 Freud pensaba mucho más en el valor de sus descubrimientos que en sus amistades. Muy decidido a consagrar a su obra el tiempo que le quedara de vida, aceptó que las actividades del movimiento psicoanalítico se desplazaran hacia el mundo angloparlante. Por eso dejó cada vez más en manos de Jones la gestión de los asuntos. Por su parte, iba a orientarse ahora hacia tres tipos de investigación: un estudio especulativo sobre la vida y la muerte, que iba a la par con una reformulación de su primera tópica; un análisis de los mecanismos colectivos del poder social y una interpretación del fenómeno de la telepatía: una manera de sumergirse de nuevo en ese mundo de lo irracional que no dejaba de asediarlo cuando más se definía como un pensador de la Ilustración y la razón.
## TERCERA PARTE
# FREUD EN SU PROPIA CASA
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La Ilustración oscura
Pensador de la Ilustración, Freud era el heredero de Kant y de la idea de que el hombre debía escapar a toda alienación para entrar en el mundo de la razón y el entendimiento. Veía con buenos ojos la famosa máxima del coraje y la necesidad del saber —«atrévete a pensar»— y creía en el posible sometimiento de los instintos al dominio de sí mismo. Por eso estaba convencido de que las élites debían guiar a las multitudes y no conformarse con el papel de representantes del pueblo. Y en ese aspecto seguía aferrado a una figura de la autoridad patriarcal, aunque esta estuviera menoscabada. Pero al mismo tiempo quería ser el dinamitero de los ideales del progreso, porque no dejaba de reivindicar el _Sturm und Drang_ , a Goethe, a Fausto y el pacto con Mefistófeles, así como la peligrosa supremacía de la pasión sobre la razón. Pertenecía además a la tradición de la «Ilustración oscura» por su capacidad de dejarse hechizar por lo demoníaco, lo oculto, el _pharmakon_ o la «inquietante extrañeza» ( _Unheimliche_ ), para distanciarse al punto de ello mediante la invocación del ideal de la ciencia. Y es en ese juego dialéctico entre la oscuridad y la luz donde se puede situar a Freud como heredero de Nietzsche, toda vez que su proyecto supone una voluntad de transformar el romanticismo en una ciencia.
Al tiempo que reivindicaba una filiación con Diderot, Freud se había erigido en el inventor de una visión de la sexualidad que, si bien se pretendía racional, no dejaba de estar inmersa en el recuerdo de las grandes locuras de Sade. Como él mismo decía, aspiraba a ser «un _advocatus diaboli_ que no por eso ha entregado su alma al diablo». Y pese a ello, rechazaba cualquier herencia de la filosofía. Quería incluso ahorrarse toda deuda a su respecto, al punto de considerarla como un «ancestro indigno». En 1925 diría:
He leído a Schopenhauer tarde en mi vida. En cuanto a Nietzsche, el otro filósofo cuyas intuiciones e intelecciones coinciden a menudo de la manera más asombrosa con los resultados que el psicoanálisis logró con trabajo, lo he rehuido durante mucho tiempo por eso mismo; me importa mucho menos la prioridad que conservar mi posición imparcial.
Fascinado por la muerte y el amor, por el sexo y el deseo, pero preocupado por explicar de manera inteligible los aspectos más crueles y ambivalentes del alma humana, Freud ponía al sujeto moderno frente a su destino: el de un inconsciente que, sin privarlo de su libertad, lo determina a sus espaldas. Y quería a toda costa que el psicoanálisis fuera una revolución simbólica con la vocación primordial de cambiar al hombre mostrando que «el yo no es el amo en su propia casa». Mediante ese gesto —ya lo he señalado— se había diferenciado de los psicólogos y los sexólogos de su tiempo, al hacer legible, por los mitos y los sueños, la vida nocturna de la humanidad, lejos de todas las presuntas ciencias del comportamiento. Así daba un contenido existencial a ese ámbito en vez de pretender describirlo por medio de los instrumentos propios de la ciencia positiva. Lo que tomaba de Darwin no era, además, nada distinto de lo que tomaba de Sófocles: la novela trágica de un hombre que, después de verse como un dios, advierte que es otra cosa y no lo que creía: un asesino e incluso el descendiente de la especie animal.
Por añadidura, Freud admitía, no el carácter judío del psicoanálisis, sino la idea de que los judíos, después de que Moisés los condujera a través del desierto, no renunciaban jamás a nada y se inventaban sin cesar un sustituto para hacer frente a lo que habían perdido: sustituto de un territorio, de una madre, de un padre, de un ancestro, de un dios, de un objeto. En otras palabras, se apoyaba en esa tradición para reflexionar sobre la cuestión universal de la herencia, la genealogía, la transmisión, la fidelidad, el exilio. Sostenía que cada pérdida permite al hombre superarse a sí mismo y por lo tanto acceder a una suerte de inmortalidad —la de las pulsiones de vida—, aun cuando en el fondo persistía en él una atracción por la nada, la muerte y la autodestrucción. A su entender, el destino humano se confundía con la búsqueda de un «más allá» de sí, un más allá de la muerte y el amor. Y con ello, la causalidad estrictamente sexual que había invocado hasta entonces contra Jung y contra todos los disidentes ya no bastaba para explicar las patologías y otras neurosis, fueran o no traumáticas.
Desde ese punto de vista, podría atribuírsele la definición del hombre dada por La Fontaine, el libertino ateo, aferrado a un orden natural del mundo: «En relación con nosotros, los hombres, yo haría nuestra suerte infinitamente más fuerte. Tendríamos un doble tesoro: uno, esa alma igual en todos en cuanto somos, sabios, locos, niños, idiotas, huéspedes del universo bajo el nombre de animales; otro, una segunda alma, entre nosotros y los ángeles».
Así, Freud había inventado una «disciplina» imposible de integrar, no solo en el campo de la ciencia, sino en el de las ciencias humanas por entonces en plena expansión desde fines del siglo XIX. Para los científicos el psicoanálisis era literatura; para los antropólogos y los sociólogos daba testimonio de un resurgimiento de las antiguas mitologías; a los ojos de los filósofos se asemejaba a una extraña psicología procedente a la vez del romanticismo y el darwinismo, y en opinión de los psicólogos ponía en peligro el principio mismo de toda psicología. De tal modo, todas las disciplinas académicas rechazaban el psicoanálisis, a tal punto que este aparecía como la propiedad de un maestro cuyo proyecto era restablecer el banquete socrático más que favorecer el auge del saber moderno. Y, después de todo, el Ring, con sus anillos sagrados, sus protocolos ( _Rundbriefe_ ) y sus juramentos, parecía legitimar esa visión de las cosas. En cuanto al objetivo terapéutico del psicoanálisis, no entraba ni en el campo de la medicina ni en el de la psicología, aun cuando, como medicina del alma, algunos lo consideraran capaz de «influir» en la psiquiatría, sin dejar de estar en la órbita del magnetismo. En realidad, la clínica freudiana consistía en un arte de la interpretación capaz de obtener del paciente la confirmación de una construcción puesta de relieve por la transferencia y el trabajo de la cura. En ese sentido, reducía a la nada el nihilismo terapéutico, que consistía en clasificar las enfermedades psíquicas sin escuchar nunca al enfermo.
Renovador de una crítica de las genealogías familiares, Freud era tanto un pensador de lo irracional como el teórico de una democracia elitista. Así, afirmaba que solo la civilización —es decir, la coacción de una ley impuesta a la omnipotencia de las pulsiones mortíferas— permite a la sociedad escapar de la barbarie tan deseada por la propia humanidad. Y si bien nunca había sido un gran lector de Sade, compartía con él, no obstante, la idea de que la existencia humana se caracteriza menos por la aspiración al bien y la virtud que por la búsqueda de un permanente goce del mal: pulsión de muerte, deseo de crueldad, amor al odio, aspiración a la desdicha y el sufrimiento. Por esta razón, recuperaba la hermosa idea de que la perversión es necesaria para la civilización en su carácter de parte maldita de las sociedades. Pero, en lugar de anclar el mal en el orden natural del mundo, y en vez de hacer de la animalidad del hombre el signo de una inferioridad racial, prefería sostener que solo las artes y la cultura son capaces de arrancar a la humanidad de su propia voluntad de anonadamiento.
En una obra apasionante, Gilles-Gaston Granger pone en evidencia tres grandes modalidades de lo irracional propias de la historia de las ciencias. La primera aparece cuando un científico debe enfrentarse al obstáculo constituido por un conjunto de doctrinas que rigen el pensamiento de una época y que se han tornado dogmáticas, restrictivas o estériles. Para el científico la cuestión pasa entonces por innovar y poner en entredicho un modelo dominante mediante la apelación a objetos insólitos o colocando bajo la mirada de la ciencia objetos sobre los que se arroje otra luz. Por ejemplo, el inconsciente, la locura, la sinrazón, lo femenino, lo sagrado. En síntesis, todo lo que Georges Bataille llama lo heterogéneo. El recurso a lo irracional permite entonces resucitar una figura de la razón y volver a partir a la conquista de _otra_ racionalidad.
La segunda modalidad de lo irracional aparece cuando un pensamiento está anquilosándose en un dogma o un racionalismo demasiado restrictivo. Para obtener resultados convincentes e insuflarle un nuevo vigor, el científico debe ponerlo entonces en contradicción consigo mismo a fin de prolongar el acto creador que le ha dado origen.
La tercera modalidad se refiere a la adopción, por parte de científicos o creadores, de un modo de pensamiento íntegramente irracional fundado en el abandono de la razón y la adhesión a falsas ciencias o a actitudes de rechazo sistemático del saber dominante. De ahí una valorización de la magia y lo religioso, asociada a una creencia en el más allá o en el poder de un ego no controlado. Esta tercera modalidad se acompaña en general de rechazo violento del sistema anteriormente adoptado. Es fácil incluir en esta categoría las derivas revisionistas llevadas al extremo, cuando proclaman un odio por el objeto antaño adulado.
Estas tres modalidades de lo irracional son perfectamente identificables —ya lo he dicho en varias ocasiones— en la historia del psicoanálisis. Sin embargo, Freud siempre se mantuvo en los límites de las dos primeras, que son inherentes al proceso mismo de la innovación teórica. En una primera etapa, a través de su relación con Fliess, se enfrentó con lo irracional biológico, lo que a continuación le permitió, en virtud de una inversión dialéctica, elaborar hasta 1915 los principios de una nueva racionalidad. Vinieron después los años de guerra, momento de la gestación de una nueva revolución simbólica.
En una segunda etapa de 1920 a 1935, una vez construida su doctrina, Freud introdujo la duda en el corazón de la racionalidad del psicoanálisis. Pretendía así, al volcarse hacia lo irracional especulativo, combatir el positivismo que lo amenazaba desde dentro. Planteó entonces la hipótesis de una pulsión de muerte, que aplicó al análisis de las «multitudes», y luego inició un extenso debate sobre la cuestión de la telepatía, mientras se lanzaba a un combate contra la religión y en favor del psicoanálisis lego.
«La muerte es la compañera del amor. Juntos, dirigen el mundo. Eso es lo que dije en mi libro _Más allá del principio de placer_.» Tal era, en 1926, el juicio emitido por el propio Freud sobre esa obra inaudita, esbozada entre marzo y mayo de 1919, atravesada por la experiencia de lo _Unheimliche_ (la inquietante extrañeza), y que parecía renegar de los principios mismos de la doctrina psicoanalítica anterior a 1915. En realidad, Freud se enfrentaba cada vez más a la eventualidad de su propia muerte. Pero también intentaba dar cuerpo a su metapsicología, inventando un nuevo dualismo pulsional. Y para ello convocaba a algunos grandes nombres de la ciencia, la literatura y la filosofía —Fechner, August Weismann, el Tasso (Torquato Tasso), Schopenhauer, Goethe, Gomperz, Platón—, y también los de sus allegados: Sabina Spielrein, Sándor Ferenczi y Ernstl Wolfgang Halberstadt, su nieto. A lo cual se sumaban referencias a los _Upanishads_ y el nirvana.
Desde 1911 afirmaba que dos principios rigen la vida psíquica. Uno tiene por meta procurar el placer, y otro, modificar el primero imponiéndole las restricciones necesarias para la adaptación a los constreñimientos de la realidad. Pero he aquí que ahora, como si diera continuidad a su concepción del narcisismo, pretendía sustituir esos dos principios por un nuevo dualismo: la vida y la muerte. Más allá del aspecto especulativo de su reflexión, Freud se apoyaba en una realidad clínica. Después de tantos años de práctica terapéutica y de sesiones que no habían desembocado en los resultados previstos, se había dado cuenta de que su teoría de las neurosis no permitía explicar un fenómeno conocido por todos los especialistas en las enfermedades del alma: algunos pacientes se mantienen inaccesibles al tratamiento, cualquiera que este sea. Y peor aún, cuando recurren a él, sufren una regresión y su estado se agrava cada vez más. Todo sucede pues como si, inconscientemente, y sea cual fuere el talento del terapeuta, se las ingeniaran para obedecer a una compulsión de repetición capaz de arrastrarlos a su propia destrucción. Algunas personas, destacaba Freud, dan en efecto
la impresión de un destino que las persiguiera, de un sesgo demoníaco en su vida [...]. La compulsión que así se exterioriza no es diferente de la compulsión de repetición de los neuróticos [...]. Se conocen individuos en quienes toda relación humana lleva a idéntico desenlace: benefactores cuyos protegidos (por disímiles que sean en lo demás) se muestran ingratos pasado cierto tiempo, y entonces parecen destinados a apurar entera la amargura de la ingratitud; hombres en quienes toda amistad termina con la traición del amigo; otros que en su vida repiten incontables veces el acto de elevar a una persona a la condición de eminente autoridad para sí mismos o aun para el público, y tras el lapso señalado la destronan para sustituirla por una nueva.
En unas pocas frases, Freud trazaba un cuadro sin concesiones de todas las actitudes inconscientes mediante las cuales un sujeto busca autodestruirse, una circunstancia en la que el masoquismo es mucho más poderoso que el sadismo. Y designaba como «eterno retorno de lo igual» esa repetición mortífera.
Lejos de conformarse con esa constatación, deducía de ella que la meta de toda vida es la muerte y que, en ese combate, las pulsiones de vida no hacen sino prolongar la trayectoria que conduce a la muerte. En consecuencia, había sin duda, en su opinión, fuerzas psíquicas que actúan «más allá del principio de placer». Y tomaba como ejemplo del dominio de ese «más allá» una práctica lúdica —el _fort da_ — cuyo desenvolvimiento había observado en su nieto, Ernstl Halberstadt, que por entonces tenía dieciocho meses.
Cuando su madre se ausentaba, Ernstl se entretenía lanzando pequeños objetos lejos de su cama y acompañaba ese gesto con una expresión de satisfacción que adoptaba la forma vocal de una «o-o-o-o» prolongada, en la cual podía reconocerse la palabra alemana _fort_ , es decir, «se fue». Un día, el niño se entregó al mismo juego, pero esta vez con un carretel de madera atado a un cordel: lanzaba el carretel, gritaba «o-o-o-o» y después, tirando del cordel, lo hacía volver y lo saludaba con un alegre _da_ («aquí está»).
De ese modo, Ernstl transformaba un estado de pasividad o displacer ligado a la partida de su madre en una situación controlada. Por medio de ese juego encontraba pues, según Freud, la manera de expresar sentimientos hostiles, inconfesables en presencia de su madre, y vengarse de su partida. En otras palabras, soportaba un desagrado por la repetición de una separación que le procuraba una ganancia de placer. Esa era la «compulsión de repetición» que se observaba asimismo en las curas, y que no tenía demasiado que ver con la realidad de una verdadera pérdida.
Sin pretender generalizar a partir de ese caso, Freud se aferraba, con todo, a otro ejemplo. Deseoso de retrotraer la condición del hombre moderno a mitos ancestrales o epopeyas literarias, comparaba el destino de los neuróticos compulsivos con el del héroe de Tasso en _La Jerusalén libertada_. En la gran tradición de Homero y Virgilio, este poema épico en veinte cantos cuenta la primera cruzada y la conquista de Jerusalén. Prototipo del caballero valeroso, Tancredo, un hombre tan melancólico como Tasso, se enfrenta a los infieles y ama con un amor atormentado y no correspondido a una guerrera sarracena de rubia cabellera, una tal Clorinda, acerca de la cual nos enteraremos en el transcurso del relato que ha nacido cristiana. Ignorante de su identidad, Tancredo la desafía creyendo combatir a un caballero enemigo. Serán, dice él, «el combate y la muerte», y ella replica: «Los tendrás, porque los buscas». Durante una noche entera se baten a duelo, sin desfallecer y en una especie de cuerpo a cuerpo sangriento en el que cada uno intenta reducir al otro a la nada. Al alba, cuando llega a su fin esta larga lucha a muerte, Clorinda cae, con heridas en todo el cuerpo. Si bien se niega a decirle su nombre, pide a Tancredo que la bautice y le tiende la mano en señal de perdón: «En medio de los tormentos y los remordimientos», dice él, «viviré errante y exaltado. El espanto me perseguirá en las tinieblas [...]. Y tendré en horror y execración el rostro de ese sol que me ha revelado mi crimen. Tendré miedo de mí mismo, de mí siempre querré escapar y a mí, siempre, he de volver».
Tras los funerales de su amada, Tancredo penetra en el oscuro bosque tan temido por los cruzados. Un «ominoso bosque encantado», poblado de espíritus y aparecidos; « _in dem unheimlichen Zauberwald_ ». Allí, parte en dos un ciprés. Y entonces escucha la voz de Clorinda, cuya alma se ha refugiado en ese árbol. Ella se queja del mal que él le ha infligido. A continuación, los cristianos llevarán a la Jerusalén libertada a Tancredo, después de que Herminia, otra sarracena loca de amor por él, lo haya salvado.
Freud tomaba de ese poema la temática del héroe condenado por el destino a ser sin cesar el causante de su propia infelicidad. Aceptaba además la idea de que la pulsión de muerte estaba anclada a tal punto en el inconsciente que condenaba al sujeto a no liberarse jamás de ella. Pero, curiosamente, no tenía en cuenta el episodio del combate nocturno entre Tancredo y Clorinda, que, sin embargo, habría debido recordarle el de Jacob y el ángel. Y no decía una palabra de la evidente melancolía del héroe. En realidad, en ese ensayo luchaba contra sí mismo. Afirmaba una cosa y la contraria: la pulsión de muerte domina la vida humana, decía por un lado, pero, sostenía por otro, es impensable que la vida no sea más que una mera preparación para la muerte. Y sacaba de ello la conclusión de que las pulsiones de muerte, por poderosas que sean, se topan con su límite en el hecho mismo de que la vida se reproduce, más allá de la muerte. El psiquismo es pues un campo de batalla, una escena nocturna en la que se enfrentan dos fuerzas elementales —Eros y Tánatos—, condenadas a amarse y odiarse por toda la eternidad.
Se comprende entonces que Freud haya podido encontrar una confirmación de sus especulaciones en los últimos trabajos del biólogo alemán August Weismann, cuando, por otra parte, este rechazaba las tesis neolamarckianas sobre la herencia de los caracteres adquiridos, a la vez que proponía un modelo genético. Weismann establecía una distinción en la sustancia viviente entre una parte mortal (el «soma») y otra inmortal, el «plasma germinal» destinado a la conservación y la propagación de la especie. Esta analogía inesperada entre las teorías de Weismann y sus propias tesis permitía a Freud fundar sus especulaciones en la ciencia, y ya no en el mero corpus mitológico o literario.
Pero, mediante una nueva inversión, se proponía apoyarse en esa analogía para convertir el modelo genético en una suerte de modelo metapsicológico. Así, afirmaba que las células germinales dan prueba de un «narcisismo absoluto», al punto de ser portadoras, también ellas, de una pulsión de muerte. Y llegaba a decir que las células de los tumores malignos, tan destructivas para el organismo, podrían ser «narcisistas en este mismo sentido». De ese modo transformaba las pulsiones en entidades mitológicas e incluso en diosas o semidiosas.
Es indudable que Freud se servía del modelo genético tomado de Weismann para reformular su concepción de conjunto del psiquismo. Sustituía el antiguo dualismo pulsional por uno nuevo, y a las viejas instancias de la primera tópica —consciente, preconsciente, inconsciente— añadía las de una segunda: el yo, el superyó, el ello. Freud, es cierto, no había descubierto los mecanismos del funcionamiento psíquico, pero con esta refundición permitía abordarlo de otra manera. Concebido como un depósito caótico, el ello se convertía en el lugar por excelencia de las pulsiones de muerte, una entidad «amoral», un dios de las tinieblas, en tanto que el yo, más «moral», estaba incorporado en parte, pero solo en parte, a él, cual un héroe melancólico, una especie de Tancredo, heredero de Edipo. En lo concerniente al concepto de superyó, Freud lo erigía en el censor implacable y cruel de los desbordamientos del alma y por lo tanto del ello y del yo. Diría más adelante que «donde Ello era, Yo debo devenir» ( _wo Es war, soll Ich werden_ ) y haría de esta conminación una nueva tarea para la cultura, tan importante como el desecamiento del Zuiderzee.
Después de haber rechazado toda herencia filosófica, Freud se las ingeniaba ahora para introducir en su refundición de la psique dos de los más grandes nombres de la filosofía alemana: Kant y Nietzsche. Del primero tomaba el imperativo categórico transformado en superyó, y del segundo, «lo impersonal sometido a las necesidades del ser», retomado por Groddeck bajo la forma del ello.
Lejos de dejar la última palabra al modelo biológico genético, Freud terminaba _Más allá del principio de placer_ con la evocación de un episodio del _Banquete_ de Platón durante el cual Aristófanes cuenta el mito de los humanos dobles o enteros. En el origen, dice en sustancia Aristófanes, tres especies conformaban la humanidad: el hombre, la mujer y el andrógino. Cada ser se asemejaba a una esfera compuesta de cuatro manos, cuatro piernas y dos rostros en una cabeza única con cuatro orejas y dos sexos. Esos humanos originales se desplazaban hacia delante o hacia atrás. El varón procedía del Sol, la mujer, de la Tierra, y el andrógino, de la Luna. Un día ascendieron al cielo para ocupar el lugar de los dioses. Fue entonces cuando Zeus, deseoso de castigarlos pero no de eliminarlos, decidió partirlos en dos. Sin embargo, cada pedazo, añorante de su mitad, trataba de unirse a ella al precio de morir de hambre y de inacción. Para poner fin a esa autodestrucción, Zeus trasladó los órganos sexuales a la parte delantera del cuerpo y de ese modo hizo posible el acoplamiento entre las mujeres y los hombres y la perpetuación de la raza humana. Los hombres que amaban a los hombres, en vez de alumbrar la vida, alumbrarían el espíritu. Los seres más consumados serían pues, según Aristófanes, puramente masculinos. En virtud de ese mito, el amor (Eros) procedería de un desgarramiento. Por eso es a la vez el mal y el remedio al mal para los humanos, que no dejan de soñar con un estado original de fusión sin dejar, a la vez, de separarse de él.
Freud se apoyaba apenas en una parte ínfima del discurso de Aristófanes y afirmaba querer retraducir la historia de las relaciones entre Eros y Tánatos en términos fisiológicos y químicos. En consecuencia, otra vez daba un giro y pasaba de la mitología a la biología. Pero en el capítulo final de _Más allá del principio de placer_ otorgaba la última palabra a la poesía contra la arrogancia de una ciencia que aspirara a ser un «catecismo». Contra el cientificismo, pero también contra sí mismo, contra su propia _hybris_ de científico, reivindicaba el derecho a la duda, a la especulación y a la incertidumbre y citaba para ello a Friedrich Rückert, orientalista alemán y traductor de una _maqâma_ de al-Hariri, gramático árabe del siglo XI: «Lo que no puede tomarse volando / hay que alcanzarlo cojeando. / [...] La Escritura dice: cojear no es pecado».
Al escribir la última línea de ese ensayo barroco, construido a la manera de un _work in progress_ , Freud se encontraba como Edipo: príncipe cojo, interrogado por una Esfinge andrógina que encarnaba a la vez el saber absoluto y la puesta en entredicho de todos los saberes. Ese texto puede interpretarse, sin duda, como la profecía de un hombre que sentía verdadera nostalgia por el mundo de otrora —el de los mitos y los sueños y su juventud vienesa— y que, pese a ello, se negaba a lamentar la grandeza perdida de los viejos tiempos o a adoptar un discurso decadente sobre presuntas catástrofes venideras. La huida en la especulación le permitía dudar de todo y abrir un nuevo camino al conocimiento del alma humana, tan tendida hacia la vida como hacia su propia destrucción. En otras palabras, aun si esta obra tenía la huella evidente de la época bélica durante la cual había sido concebida, no dejaba de ser también la consecuencia de una evolución generada por un trabajo del pensamiento.
Como Freud hacía de la pulsión de muerte una fuerza muda que atenazaba tanto la psique como el soma, solo podía descubrir su existencia si recurría a interpretaciones extraídas de la literatura, de la realidad social o de los comportamientos individuales. Así definida, la pulsión de muerte era una entidad inhallable desde el punto de vista de la biología: una quimera. Para los críticos resultó fácil entonces afirmar que las causas de la especulación freudiana no suponían un proceder intelectual sino exclusivamente un determinismo externo.
Durante varios años la obra fue mal recibida en el mundo angloparlante. William McDougall la caracterizaría en 1936 como «el ejemplar más grotesco de toda la galería de monstruos de Freud». Pero fue sobre todo en el seno del comité, y entre los demás discípulos, donde la oposición fue más intensa. Eitingon y Ferenczi aceptaron la hipótesis pero Jones tomó distancia señalando que Freud siempre había estado angustiado por la muerte —tanto la propia como la de sus allegados—, que se entregaba al respecto a cálculos permanentes y que temía envejecer y se estremecía ante la idea de la degradación corporal. En cuanto a Wittels, no vaciló en psicologizar aún más la invención freudiana, con la pretensión de demostrar que la teorización de la pulsión de muerte era una secuela del dolor experimentado ante la muerte de Sophie.
Aun antes de afrontar esas críticas, Freud había tomado la precaución de escribir a Eitingon: «Por fin he concluido el _Más allá_. Usted podrá confirmar que estaba terminado a medias cuando Sophie vivía y estaba llena de salud».
¡«Terminado a medias»! Semejante frase autorizaba todas las interpretaciones, incluida la de achacar a Freud haberse entregado a una pura negación. En 1980 Jacques Derrida afirmó que Freud había deseado la muerte de Julius, su hermano menor, y que, cuando esta se produjo, experimentó un sentimiento de culpa que nunca lo abandonaría. De lo cual deducía que aquel trataba su ensayo como un _fort-da_ «para enviarse a sí mismo el mensaje de su propia muerte».
Las discusiones sobre _Más allá del principio del placer_ jamás terminaron. Los partidarios de la escuela americana no podían aceptar su lado especulativo que, en su opinión, hacía de Freud un «psicólogo del ello» más que un terapeuta del yo. Melanie Klein y los suyos se apoderaron del segundo dualismo pulsional, de manera estrictamente clínica, y destacaron que la pulsión de muerte contribuía a instalar al sujeto en una posición depresiva hecha de angustia y destrucción. Y fue en Francia donde ese texto, producto puro de la _Aufklärung_ oscura, tuvo los mejores comentarios, en su vertiente clínica y como momento decisivo de la historia del pensamiento filosófico.
El 6 de mayo de 1921, al cumplir sesenta y cinco años, Freud recibió como regalo el original del busto realizado por David Paul Königsberger:
Un doble de bronce fantasmal y amenazante [...]. He dado de manera muy repentina un paso hacia el verdadero envejecimiento. Desde entonces, la idea de la muerte ya no me abandona y a veces tengo la impresión de que siete órganos se disputan aún el honor de poder poner fin a mi vida [...]. Pero no he sucumbido a esta hipocondría, la considero con soberana frialdad, un poco como las especulaciones del _Más allá_.
Dividido entre lo que era y lo que hacía, estaba claro pues que Freud, a través de _Más allá del principio de placer_ , se había enviado un mensaje cuyo destino ulterior no pretendía controlar. Una vez más, suscitó a su respecto polémicas de todo tipo.
Hacía ya tiempo que deseaba prolongar su análisis de las sociedades humanas, no como lo había hecho en _Tótem y tabú_ , sino con el propósito más político de describir el camino que lleva de la colectividad al individuo. Frente a los defensores de la psicología social en pleno auge, quería construir una metapsicología de las relaciones entre el yo y las multitudes. Su aspiración, una vez más, era responder a Jung —o, mejor, a su espectro— y situarse a la vez en la misma perspectiva que Hugo von Hofmannsthal y Arthur Schnitzler, que habían tenido idéntico proyecto. Y para hacerlo, no vacilaba en referirse a la concepción aristotélica del hombre como animal político. Pero fue de Gustave Le Bon, médico polígrafo, de quien tomó, en 1921, lo esencial de su investigación, mucho menos especulativa que _Más allá del principio de placer_.
Ideólogo de la contrarrevolución, obsesionado por el recuerdo de la Comuna de París y rechazado por los medios académicos, Le Bon ambicionaba ser el fundador de una sociología del pueblo para uso de los tiranos deseosos de liberarse del miedo que provocaba la existencia misma de ese pueblo. A su juicio, la multitud era un conjunto bárbaro e histérico, una especie de sustrato orgánico femenino donde el individuo quedaba abolido para fundirse en la masa de un cuerpo amenazante. La multitud se mueve como una «medusa», decía Le Bon, la atraviesan instintos irreflexivos y está sujeta a todos los «contagios». Por eso es capaz de obedecer a tiranos sanguinarios, toda vez que encarna las fuerzas más oscuras del alma humana: la enfermedad mental, la sinrazón, la muerte, la decadencia. Después de describir el alma de las multitudes, Le Bon convocaba a la constitución de una ciencia que permitiera ayudar al hombre político a ser un psicólogo capaz de dominarlas por medio de la sugestión.
Esa era pues la obra que Freud admiraba y que, en ciertos aspectos, confirmaba su aversión a los ideales de la Revolución francesa: el pueblo es peligroso tan pronto como se le otorga un poder demasiado grande y se transforma en una «masa». Y cuando se basaba en los escritos de William McDougall, el mismo que calificaría de «monstruo» _Más allá del principio de placer_ , no decía otra cosa: Freud tendía, sin duda, a confundir al pueblo con una masa...
Psicólogo de origen escocés emigrado a Estados Unidos, adepto de la eugenesia y de las tesis neolamarckianas sobre la herencia de los caracteres adquiridos, McDougall sostenía, contra el conductismo, el principio de que el hombre estaba embargado por un «instinto» gregario peligroso que lo impulsaba a «pegarse» a sus semejantes. En 1920, analizado por Jung y apasionado por la telepatía y la parapsicología, McDougall acababa de publicar _The Group Mind_ , libro donde desplegaba ideas, clásicas en la época, sobre la desigualdad de las «razas»:
La pequeña cantidad de negros de América a quienes puede calificarse de eminentes —como Douglass, Booker Washington, Du Bois— fueron en todos los casos, creo, mulatos o tenían cierta proporción de sangre blanca. Podemos más bien atribuir la incapacidad de la raza negra para formar una nación a la falta de hombres dotados de las cualidades de los grandes líderes, aun cuando estén por encima del nivel más bajo en el promedio de las aptitudes.
Freud compartía con los ideólogos del miedo a las multitudes la idea de que la aparición de la sociedad de masas ligada al auge de la industrialización ponía en peligro la relación de las élites con el pueblo, a riesgo de favorecer la tiranía. Pero, contrariamente a ellos, sostenía que esa peligrosa actitud colectiva de las multitudes constituía la parte arcaica de la subjetividad individual, y que al pasar de una a otra —de lo arcaico a un estrato superior— el psiquismo humano avanzaba hacia el progreso. Se apoyaba así en Le Bon y McDougall sin poner en entredicho sus concepciones de la multitud o de la inferioridad de los negros con respecto a los blancos. De ese modo soslayaba la cuestión que se planteaban por entonces los fundadores de las ciencias sociales, unos modernistas y orientados hacia una explicación coherente de los fenómenos de masas, otros partidarios de una concepción instintiva o racial del alma de los pueblos.
Trazaba Freud una distinción entre las masas con conductor y las masas sin conductor. Tomaba por modelo dos masas organizadas y estables en el tiempo —la Iglesia y el ejército—, que a su entender se estructuraban en torno de dos ejes: uno vertical, concerniente a la relación entre la masa y el jefe; otro horizontal, que corresponde a las relaciones entre los individuos de una misma masa. En el primer caso los sujetos se identifican con un objeto puesto en el lugar de su ideal del yo (el jefe); en el segundo, se identifican unos con otros. Freud había pensado, claro está, en la posibilidad de que el lugar del conductor fuera ocupado, no por un hombre real, sino por una idea o una abstracción: Dios, por ejemplo. Y se refería a la experiencia comunista para mostrar que el «lazo socialista», al sustituir al lazo religioso, amenazaba desatar contra «los de fuera» la misma intolerancia que en la época de las guerras de religión.
En virtud de su teoría de la identificación, Freud asignaba al eje vertical una función primordial, de la que dependía el eje horizontal. Además, la identificación con el padre, el jefe o una idea era, a su entender, primaria con respecto a la relación entre los miembros de un mismo grupo. Y por esa vía se distanciaba de las tesis de la psicología de las masas, que seguían fundadas en la idea de que la sugestión o la hipnosis —y no la identificación— eran fuentes de la relación de fascinación existente entre las multitudes y los jefes.
Durante años esta nueva tesis freudiana serviría para interpretar el modo de funcionamiento político del fascismo. En realidad, cuando publicó su ensayo, Freud pensaba en la experiencia comunista, a la que había sido profundamente hostil en 1917, a pesar de que en un primer momento le había reservado una acogida favorable como el signo de que la guerra iba a llegar a su fin: «Freud proponía un marco conceptual», destaca Michel Plon, «que permitía comenzar a pensar cuestiones que la sociología, la historia y la filosofía política de ese siglo, olvidadizas tanto de Maquiavelo como de La Boétie, estaban aún lejos de poder empezar a formular».
De ese modo, Freud se diferenciaba claramente de cualquier pensamiento fundado en el odio de los pueblos, el rechazo de la democracia y la revalorización de una ideología del caciquismo. Sin embargo, su desconocimiento de la experiencia revolucionaria del siglo XX le haría cometer numerosos errores, sobre todo en relación con el movimiento psicoanalítico ruso y con sus discípulos freudomarxistas: Wilhelm Reich y Otto Fenichel. En este aspecto puede decirse que una parte de su proceder —la más inconsciente y reprimida— seguía enraizada en lo que él pretendía denunciar. Su elección de Le Bon y McDougall como modelos no era inocente. A través de ellos, recordaba, para exorcizarla mejor, la gran historia junguiana de las grutas, las cavernas o las criptas. El mundo subterráneo del caos y los Titanes.
Freud no esperaba, sin duda, la utilización inaudita que su sobrino norteamericano, Edward Bernays, iba a hacer no solo de su psicología de las masas, sino también de su consumo de tabaco. Inventor de un nuevo arte en la gestión de la opinión masiva, en la década de 1920 Bernays se apoyó, en efecto, en la conceptualidad freudiana para desplegar una formidable campaña publicitaria en favor de la industria del tabaco y en particular de los cigarrillos Lucky Strike, destinada a las mujeres. En continuidad directa con la política de emancipación de los movimientos feministas, rodó filmes publicitarios con la intención de probar que las mujeres debían tener derecho a fumar en un pie de igualdad con los hombres, y que para ellas el cigarrillo consumido en público era el equivalente, como una «antorcha de la libertad», de un jubiloso pene que podían exhibir sin la más mínima prohibición a fin de liberarse de la dominación masculina.
Mientras trataba de explicar racionalmente los fenómenos irracionales, Freud comenzó a entregarse con deleite a una inmersión en las profundidades de las fábulas danubianas. En 1921, en una carta dirigida a Hereward Carrington, un especialista norteamericano en el espiritismo que le había preguntado su opinión acerca de los fenómenos ocultos, respondió con estas palabras: «Si estuviera comenzando y no acabando mi carrera científica, quizá hasta hubiera llegado a elegir ese terreno de investigación». Luego pedía a su interlocutor que no mencionara su nombre, porque no creía en la «supervivencia de la personalidad después de la muerte» y sobre todo porque le interesaba establecer una línea de demarcación muy clara entre el psicoanálisis como ciencia y «esa aún inexplorada esfera», para no generar el menor malentendido al respecto.
Se recordará que este asunto de las «cosas ocultas» había comenzado en Viena durante la primera visita de Jung a la Berggasse. A continuación, había resurgido en 1910, cuando Ferenczi pretendía salir a cazar videntes y adivinas en los suburbios de Budapest para demostrarle a su adorado maestro la existencia de la transmisión de pensamientos. Freud había luego interrumpido el debate con una condena inmisericorde, en nombre de la ciencia, de las experiencias telepáticas de un tal profesor Roth a quien Ferenczi había llevado a la WPV.
Pero a partir de 1920 y hasta 1933 la cuestión de lo oculto volvió al primer plano a medida que se establecían —entre Londres, Berlín y Nueva York— las grandes reglas convencionales del análisis didáctico que harían del Verein un movimiento organizado conforme a los principios del racionalismo positivista. En ese contexto, donde el ideal de una posible cientificidad del psicoanálisis iba a la par con la institucionalización progresiva de los principios de la cura, Freud asumió de nuevo la defensa de la telepatía. En compañía de su hija Anna y de Ferenczi, «hizo girar las mesas» y se entregó a experiencias de transmisión de pensamientos durante las cuales se fingía médium y analizaba sus asociaciones verbales.
Jones y Eitingon intentaron frenar entonces su entusiasmo con el argumento de que la conversión del psicoanálisis a la telepatía aumentaría las resistencias del mundo anglosajón a la doctrina freudiana y la presentaría como la obra de un impostor. Para lograr que el psicoanálisis se incorporara a la era de la ciencia y marcar el final definitivo de su arraigo en el viejo mundo austrohúngaro, poblado de gitanos y magos, Jones proponía erradicar de los congresos internacionales las investigaciones sobre el ocultismo. Freud aceptó.
Sin embargo, en 1921 escribió un artículo (sin título) sobre esas cuestiones, que se proponía presentar en el congreso de Berlín del año siguiente. Eitingon y Jones lo disuadieron de hacerlo. Retiró el texto, que finalmente se publicaría en 1941 a título póstumo. Tras ese rechazo, volvió a la carga, el mismo año, con otro artículo, «Sueño y telepatía», que hizo publicar en _Imago_. Diez años después dictaría una conferencia sobre el tema del sueño y el ocultismo, a la cual sumaría el material de 1921 y en especial el caso de David Forsyth, que debía figurar en «Psicoanálisis y telepatía».
Según su opinión, la llamada ciencia «oficial» había dado un tratamiento desdeñoso tanto al ocultismo como al psicoanálisis. Y sin embargo, el progreso de las ciencias podía tener por doble efecto hacer concebible lo que antaño se rechazaba por ocultista. Es cierto, cuando uno se proponía reactivar ese tipo de interrogación —agregaba Freud— existía el riesgo de suscitar nuevas fuerzas oscurantistas. De ahí el peligro que _Herr Professor_ acababa de señalar en relación con su psicología de las masas; personas irresponsables podrían plantearse manipular ciertas técnicas del ocultismo para aprovechar en su beneficio la credulidad de los hombres.
Freud disfrutaba mucho con su pasión renovada por las cifras, los enigmas y los cálculos. Así, se refería con deleite a la historia del joven que, al consultar a una adivina, le había dado la fecha de nacimiento de su cuñado. La mujer había afirmado al punto que el cuñado en cuestión moriría envenenado tras comer ostras y cangrejos. Estupefacto, el joven comprobó que lo anunciado ya se había producido: gran aficionado a los frutos de mar, el cuñado, en efecto, había estado a punto de morir el año anterior por envenenamiento con ostras. Freud llegaba a la conclusión de que en el origen de la predicción había un fenómeno de telepatía entre el joven y la vidente: ese saber se había transmitido a esta por vías desconocidas, al margen de los modos de comunicación que conocemos, y Freud planteaba la existencia de una «transferencia de pensamiento». En consecuencia, abandonaba el terreno de lo oculto y de la telepatía para optar por el de la interpretación psicoanalítica. Una vez más, jugaba con el diablo a la vez que se erigía en abogado del diablo.
Para Jones todas esas historias de videncia eran puras elucubraciones que ponían en peligro la política del Verein: «Usted podría ser bolchevique», le decía a Freud en 1926, «pero si lo anunciara no favorecería la aceptación del psicoanálisis». A lo cual Freud respondía:
Es verdaderamente difícil no herir las susceptibilidades inglesas. No se me abre en Inglaterra ninguna perspectiva de pacificar a la opinión pública, pero me gustaría al menos explicarle mi aparente inconsecuencia en lo que toca a la telepatía [...]. Cuando aleguen ante usted que he caído en el pecado, responda calmosamente que mi conversión a la telepatía es un asunto de mi sola incumbencia, como el hecho de ser judío, de fumar con pasión y de tantas otras cosas, y que el tema de la telepatía es por esencia ajeno al psicoanálisis.
El juego al que Freud se entregó durante esos años confirma que para él se trataba de afirmar, contra una primacía demasiado racional de la ciencia, un saber mágico que escapaba a las constricciones del orden establecido. El hecho de que se interesara por adoptar un papel de adivino del viejo Imperio austrohúngaro y se entretuviera en simular creer en la telepatía, cuando en realidad la reducía a una manifestación del inconsciente y la transferencia, indica a las claras cuál puede ser el estatus específico del psicoanálisis en su relación ambigua con la ciencia, así como la recurrencia de su interrogación sobre sus orígenes. Como señalaría Jacques Derrida en 1981: «El psicoanálisis, entonces [...], se asemeja a una aventura de la racionalidad moderna para tragar y rechazar a la vez el cuerpo extraño llamado telepatía, asimilarlo y vomitarlo sin poder resolverse a hacer ni lo uno ni lo otro [...]. La "conversión" no es una resolución ni una solución, es aún la cicatriz parlante del cuerpo extraño».
### 2
Familias, perros, objetos
La familia, decía Freud, es una gran felicidad pero también el comienzo de preocupaciones sin fin. En verdad, _Herr Professor_ manifestaba un gran apego al espíritu familiar, a las familias en general y a las ignominias familiares. Y por eso había insertado su doctrina en la idea misma de que el crisol familiar servía de soporte ontológico a la concepción psicoanalítica. Su mundo social y su universo psíquico estaban poblados de padres, madres, hermanas, hermanos, sobrinos y primos, que estaban afectados por patologías y se sustituían unos a otros. Todos habrían podido recurrir a una terapia psicoanalítica, pues la cuestión del sexo y de lo íntimo había llegado a ser dominante en el mundo occidental de fines del siglo XIX y comienzos del siglo XX. A los ojos de Freud, la comunidad familiar era el modelo por antonomasia de toda forma de organización social. En ella residía el poder de la vida y de la transmisión.
A la vez liberal y conservador, Freud había construido su pensamiento y su movimiento sobre la base de un modelo comunitario que no debía nada al Estado ni a sus instituciones. De ahí una gran contradicción: cuanto más se internacionalizaba el movimiento freudiano, sin patria ni fronteras, más caía en desuso el modelo comunitario en el que se apoyaba. Jones era consciente de ello y Freud lo sufría. Por eso, dolorido, se refugiaba en los valores de la «solidaridad familiar» que había puesto en práctica en su doctrina, sin vacilar en subvertirlos en la teoría mientras los preservaba en su intimidad. Se rodeaba así de todo lo que le permitía protegerse mejor de las perturbaciones del tiempo presente: la casa y sus habitantes, los animales, los objetos de colección, la exploración arqueológica del alma humana por medio de la experiencia del diván.
Si sus padres se habían unido conforme a los principios de los matrimonios concertados y Amalia había traído al mundo ocho hijos en diez años, Sigmund, al contrario, se había casado por amor con la mujer de su elección. Y Martha le había dado seis hijos en ocho años. Tras ello los esposos habían dejado voluntariamente de procrear. De las cinco hermanas de Freud, cuatro tuvieron hijos. Cinco en el caso de Anna Bernays —Judith, Lucia, Edward, Hella y Martha—, tres de ellos nacidos en Viena y dos en Nueva York; dos, Rosa Graf —Hermann y Cäcilie—, nacidos en Viena; cinco, Maria Freud —Margarethe, Lilly, Martha, Theodor y Georg—, uno nacido en Roznau, dos en Viena y dos en Berlín, y una tuvo Paula Winternitz —Rosa Béatrice—, nacida en Nueva York y casada con el poeta Ernst Waldinger. En cuanto a Alexander, casado tardíamente con Sophie Schreiber, tuvo un solo hijo, Harry, nacido en Viena.
Había por lo tanto pocas diferencias manifiestas entre la situación de los padres de Freud —Amalia y Jacob— y la de sus hijos. Con una generación de intervalo, la cantidad de mujeres solteras o viudas era la misma y ninguna había recurrido a la contracepción o el aborto. Ninguna de ellas había podido estudiar y solo una —Anna Bernays— había logrado establecerse en el extranjero al casarse con Eli Bernays, el hermano de Martha. Entre los sobrinos de Sigmund Freud, uno solo —Hermann Graf— perdió la vida en la Gran Guerra; otros dos se suicidaron —Cäcilie Graf y Tom (Martha) Seidmann-Freud—, y un cuarto —Theodor Freud— murió ahogado de manera accidental. Todos los integrantes de esta vasta comunidad vienesa se casaron con judíos o judías a pesar de no adherirse a un judaísmo de obediencia ortodoxa, si bien en algunos casos tenían la inquietud de respetar los ritos.
A diferencia de Martha, Freud era favorable a los matrimonios mixtos. Pero la sociedad en la que vivía se prestaba muy poco a ello. Y al comprobar que todos sus hijos elegían espontáneamente cónyuges judíos, cuando no estaban en modo alguno obligados a hacerlo, Freud llegó a la conclusión de que entre los judíos la vida familiar era más íntima, más cálida, y más fuertes las solidaridades. Él mismo se había criado en el seno de una comunidad que proscribía los matrimonios mixtos.
Entre sus seis hijos, que atravesaron dos guerras devastadoras, solo cuatro tuvieron descendencia, una permaneció soltera (Anna) y otra murió de enfermedad (Sophie). A diferencia de sus abuelos, pero como sus padres, los hijos de Freud escogieron libremente a sus cónyuges: todos judíos. Pero gracias a la contracepción tuvieron claramente menos hijos y en su mayor parte adquirieron la ciudadanía inglesa después de huir del nazismo. Martin tuvo dos hijos, Anton Walter y Sophie; Oliver, una sola, Eva; Ernst tuvo tres, Stefan, Lucian y Clemens, y Sophie Halberstadt, dos, Ernstl y Heinz. Al contrario de su madre y sus tías, las tres hijas de Freud cursaron algunos estudios, a pesar de que en Viena no había instrucción pública obligatoria para las niñas y tampoco existían verdaderas perspectivas profesionales. Freud tuvo la inquietud de casarlas bien e inculcarles la idea de que habían nacido para ser madres y ocuparse de las tareas domésticas. De todos modos, no obedecía el precepto judío de los matrimonios concertados, según el cual un padre solo tiene la custodia de su hija para entregarla a otro hombre. Muy cercano a sus hijas, comprendió que nunca serían parecidas a su madre y su abuela, pero quiso evitar, con la excepción de Anna, que se emanciparan, a imagen de sus discípulas. Por lo demás, ellas no deseaban otro destino que el que les tocó.
Freud amaba profundamente no solo a su mujer, su hermano y su cuñada, sino también a sus hijos y nietos. Con los hijos se mostró siempre muy generoso; y cuando fue posible, otro tanto hizo con los sobrinos. Todos los miembros de su familia le profesaban una admiración sin límites y eran conscientes de su genio.
Los hijos de Freud vivieron dos guerras mundiales y se mantuvieron unidos en la adversidad, a pesar de conflictos incesantes. Todos tuvieron un conocimiento real de la doctrina de su padre, al igual que el hermano de este, Alexander. Sus tres hijos varones desempeñaron además un papel en el movimiento psicoanalítico y su última hija se convirtió en su discípula.
En la vivienda de dos plantas de la Berggasse que alquilaba, Freud vivía como un patriarca a la antigua. Había querido «modelar» a Martha para conseguir que se ajustara por completo a la imagen de esposa con que él soñaba. En vano. Ella se le resistía sin apartarse jamás de una actitud conciliadora. Y cuando él le buscaba las cosquillas, Martha se replegaba en sí misma. Por eso Freud le reprochaba que reprimiera su agresividad, sin dejar de profesarle una especie de adoración.
Martha criaba a los niños y reinaba sobre los habitantes de la casa, incluidas dos y a veces tres empleadas domésticas, pero no se mezclaba en los asuntos intelectuales de su esposo, aunque este reunía a sus discípulos en su domicilio. Así, cuando uno de los residentes de la Berggasse pretendía cambiar de habitación o modificar lo que fuera en la organización de los cuartos, debía dirigirse a ella.
Freud se ocupaba de la educación de sus hijos y sufría al estar separado de ellos, muy en especial cuando dejaban la casa para casarse. Ya desde muy pronto había exigido que se informasen de la realidad de la vida sexual por lecturas, y no por él mismo.
Minna, a quien se llamaba su «segunda esposa» —aun antes de que Jung hiciese correr el rumor de que había una relación carnal entre ellos—, ocupaba un dormitorio contiguo al de su hermana y su cuñado, y acompañaba de buena gana a su querido «Sigi» en sus viajes de septiembre. En agosto de 1898, particularmente, había pasado unos días con él en Maloja, en la Engadina, y Freud se había sentido varias veces «molesto» por ser visto junto a una mujer que no era la suya. En 1900, durante otro viaje, Freud había vendido numerosos libros antiguos de su colección para que Minna pudiese trasladarse a Merano a fin de hacerse tratar por una afección de los bronquios. No hizo falta más para que algunos imaginasen una oscura historia de aborto clandestino. Y como a continuación Minna había sufrido dolores en el bajo vientre, cualquiera pudo pensar, en efecto, que los problemas pulmonares daban para todo. Así, el rumor se extendió, sobre todo tras la publicación de los _Tres ensayos_. Cuarenta años después de la muerte de Freud, el gran rumor se convirtió en un objeto de investigación para historiadores y comentaristas.
Como Martha, su cómplice en todo, Minna había engordado y, con el paso de los años, renunciado a ocuparse de su femineidad. Cuando contestaba el teléfono decía con toda naturalidad «Frau Professor Freud», a la vez que se burlaba mordazmente de los cotilleos. Lejos de ser una verdadera «segunda esposa», se comportaba más bien como una suerte de compañera de los hijos de su hermana y su cuñado: una actitud tanto más comprensible cuanto que tenía muy pocas ganas de ocupar un lugar de madre o de esposa de nadie.
Al término de la Gran Guerra, Freud, convertido en una celebridad, fue al mismo tiempo objeto de odios en todo el mundo en nombre de las diferentes concepciones de la noción de «pansexualismo». En Viena se lo acusaba de toda clase de infamias: lascivo, incestuoso, destructor de la moral familiar. En Francia se lo trataba de «científico _boche_ », es decir, de personaje lascivo devorado por un presunto instinto teutón. En la pluma de un Charles Blondel, su doctrina se calificaba incluso de «obscenidad promovida a la jerarquía de ciencia».
La imagen que a través de esos ataques se mostraba de él estaba en contradicción radical con sus costumbres y opiniones. Se olvidaba que _Herr Professor_ era, en lo personal, un partidario de la abstinencia sexual, un neurótico de la sublimación. Y como no se le conocía ninguna relación extraconyugal, era imperioso inventarle una «verdadera» vida sexual, preferentemente transgresora, a fin de justificar el carácter repugnante de su concepción de la sexualidad.
En este aspecto, el modo de vida endogámico que había adoptado y el uso abusivo que hacía de su famoso complejo de Edipo, popularizado en multitud de publicaciones, autorizaban todas las caricaturas. Y Karl Kraus se divertía de lo lindo al afirmar en voz bien alta que el psicoanálisis era una enfermedad del espíritu que se consideraba el remedio de sí misma. El brillante polemista había sido víctima, es cierto, del fanatismo del primer círculo freudiano que, en la persona de Wittels, lo había declarado afectado por una frustración edípica.
En su espléndida autobiografía, Elias Canetti cuenta que durante los años veinte, en Viena, el culto del edipismo se había vuelto tan nocivo que desacreditaba los aspectos más innovadores de la doctrina freudiana. Así como defendía la idea de interpretar los juegos de palabras y los actos fallidos, Canetti rechazaba la reducción de la tragedia de Sófocles a lo que él consideraba como una psicología de la «palabrería universal». En 1980 escribía:
Todos (incluso los hijos póstumos) sacaban a relucir su Edipo de algún modo, y al final el grupo entero quedaba homogéneamente culpabilizado: amantes de su madre y parricidas en potencia, envueltos en la bruma de aquel nombre mítico, reyes secretos de Tebas. [...] Sabía quién era Edipo, había leído a Sófocles y no aceptaba que me escamotearan el horror de aquel destino. Cuando llegué a Viena aquello se había convertido en una letanía universal de la que nadie quedaba exceptuado; ni el esnob más recalcitrante temía hablar de su Edipo, aunque la palabra estuviera en boca de todo el mundo, incluido el más necio.
En esa época Freud mantenía una familia ampliada: Amalia, Anna, Minna; sus hijos con sus cónyuges, a menudo necesitados de dinero; cuatro hermanas, de tanto en tanto; la servidumbre, y algunos de sus discípulos que apenas tenían pacientes. En varias ocasiones tuvo la fantasía de casar a tal o cual de sus hijas con uno de sus discípulos. En realidad, quería mantenerlas en el seno de la familia. Por eso veía a sus yernos y nueras como sus propios hijos.
Frágil de salud, Mathilde, la mayor de la fratría, había rozado varias veces la muerte, y las secuelas de una operación de apendicitis realizada por el cirujano que había intervenido a Emma Eckstein le impidieron ser madre. Freud había pensado casarla con Ferenczi, pero en 1909 ella había contraído matrimonio en la sinagoga con Robert Hollitscher, un comerciante textil poco dotado para los negocios y siempre pesimista, a quien Freud calificaba de «tierno y valeroso». La pareja vivía en un apartamento cerca de la Berggasse, lo que permitía a Mathilde visitar a diario a sus padres. Siempre muy elegante y con cierta apariencia de frialdad, estaba dedicada a los suyos y compartía con su madre y su tía el amor por las labores de punto. Gracias a su talento en esa materia pudo ganar algo de dinero, lo cual le posibilitó no depender por completo de su familia.
Sophie, la más bella de las hijas, que por eso despertaba los celos de Anna, se interesaba mucho menos que sus hermanas por los asuntos del intelecto. Aficionada a la danza, las veladas en la Ópera, la vida mundana y la gente joven, no se sentía cómoda en esa familia demasiado rígida. Enamorada de Hans Lampl, compañero de escuela de sus hermanos y futuro discípulo de su padre, debió no obstante renunciar a él (que también la amaba) a causa de la oposición de sus padres, que lo encontraban demasiado joven y lamentaban que no tuviera una buena posición. En Hamburgo, lejos de casa, conoció a Max Halberstadt, un fotógrafo perteneciente a la parentela ampliada de los Bernays, y se casó con él en una sinagoga de Viena. Max era creyente. Freud lo adoptó como un hijo, a tal punto que le concedió el monopolio comercial de sus retratos oficiales. A diferencia de su hermano Rudolf, Max sobrevivió a la Gran Guerra, discapacitado, sin embargo, a raíz de una neurosis traumática con cefaleas y depresión. Mucho después de su desmovilización fue víctima de la crisis financiera y, a pesar de contar con un verdadero talento, se vio en la situación de ser mantenido por su suegro, que lo mimaba y le suplicaba que tuviera confianza en el futuro.
Sophie rechazó el destino de su madre y su abuela. Temerosa de quedar embarazada por tercera vez, después del nacimiento de sus dos hijos pidió consejo a Freud, que le recomendó recurrir a la contracepción y hacerse poner un «pesario». Si bien en su caso no había querido utilizar el preservativo, ahora Freud era favorable, si no al aborto, sí al menos al control de la natalidad reclamado en la época por los movimientos feministas, en el momento mismo en que las naciones europeas sancionaban leyes rigurosas contra la interrupción de los embarazos. Cuando Sophie, de manera accidental, volvió a quedar encinta, Freud la alentó a aceptar la situación. Creía, erróneamente, que su rechazo de la maternidad se debía a las dificultades económicas de Max.
En 1920, debilitada por su estado, Sophie contrajo gripe y murió al cabo de pocos días, pese a los esfuerzos de Arthur Lippmann, médico internista del Hospital General de Hamburgo, que no logró salvarla. En una carta, Freud, abrumado por el dolor y la culpa, le confesó no haber advertido hasta qué punto ese embarazo no deseado había modificado el estado psíquico y físico de su hija:
Me parece que el destino desgraciado de mi hija comporta una advertencia que nuestra corporación no suele tomar con la seriedad necesaria. Frente a una ley inhumana y carente de empatía, que impone incluso a la madre que no lo quiere la prosecución del embarazo, es manifiesto que el médico tendría que asumir como un deber la enseñanza de los caminos apropiados e inofensivos capaces de impedir los embarazos no deseados, en el marco del matrimonio.
Para aliviar a Max, Mathilde se hizo cargo de Heinz (Heinerle) y Anna se ocupó de Ernstl, que se convirtió en su primer hijo «adoptado» y más adelante en su analizante. Una y otra fueron así las segundas madres de los hijos de su hermana. Cuando Heinz murió, el 19 de junio de 1923, a raíz de una tuberculosis miliar, Mathilde quedó privada otra vez de lo que más deseaba. A continuación no dejó de ocuparse de sus sobrinas y sobrinos. En cuanto a Freud, desesperado por esa pérdida, sobrevenida tres meses después del descubrimiento de su cáncer, siguió queriendo a Max y ayudándolo económicamente, incluso cuando este volvió a casarse: «Quien haya sido alguna vez feliz en el matrimonio, vuelve a serlo con facilidad».
Freud siempre había tenido la convicción de que la felicidad familiar estaba hecha a imagen del gran ciclo de la vida y la muerte y de la sustitución de un objeto deseado por otro, con la condición, empero, de que la compulsión de repetición no fuese de naturaleza mórbida. Creía además que si un ser perdido era reemplazado por otro, este último solo sería amado por ocupar el lugar de quien lo había sido antes que él. Tal era la filosofía freudiana de la felicidad.
Ninguno de los tres hijos varones de Freud se le parecía, y tampoco se parecían entre ellos. Pero todos participaron del impulso del movimiento psicoanalítico y de la vida de los discípulos de su padre. Martin tenía una elevada opinión de sí mismo. Practicaba esgrima, se batía en duelo, escribía poemas, no era buen alumno y multiplicaba sus relaciones con las mujeres. Alistado como voluntario en 1914, después de estudiar derecho, la guerra había sido para él el período más dichoso de su vida. En el combate había dado pruebas de insolencia y humor y sabido afrontar el peligro: no tiene ni superyó ni inconsciente, se decía en la familia. Cuando se casó con la bella y elegante Ernestine (Esti) Drucker, procedente de un medio adinerado, a Freud la muchacha le pareció «demasiado bonita» para formar parte de su hogar. En realidad, la juzgaba «maliciosamente chiflada» y poco apta para soportar las calaveradas de su hijo. Conforme a la regla que había establecido para sí mismo, la obligó a poner a su primer hijo el nombre de pila de Anton, en recuerdo de Von Freund, y a su hija el de Sophie. Esti trabajaba y se negaba a quedarse embarazada una y otra vez, al mismo tiempo que padecía su condición de mujer mantenida y engañada. Pese al apoyo de su padre y su suegro, Martin no tardó en experimentar problemas económicos. Además, se peleaba con su mujer, de la que terminaría por separarse. Durante varios años, hasta el exilio de 1938, se ocupó de la administración del Verlag.
Hijo preferido de su madre, Oliver jamás pudo ejercer un verdadero oficio en épocas en que la crisis económica había sucedido a la guerra. Cuando se instaló en Berlín, después de una ruptura y un divorcio, pidió a Eitingon que lo tomara en análisis. Por sentirse demasiado cercano a la familia, Eitingon se negó, y fue Franz Alexander, húngaro de origen y futuro ciudadano norteamericano, quien aceptó la pesada tarea. Freud insistió en pagar las sesiones. Oliver se casó con Henny Fuchs, pintora con la que tuvo una hija, Eva. Freud amaba a ese hijo neurótico, frágil y extraño que sufría a causa de una terrible rivalidad con su hermano menor, Ernst, más inteligente que él.
Después de obtener su título de arquitecto en Munich, este último se enamoró de Lucie Brasch, una mujer fascinante y melancólica, rubia y de ojos azules, perteneciente a una rica familia de banqueros. La boda se celebró en Berlín el 18 de mayo de 1920 en presencia de Abraham y Eitingon, quienes, como Ernst, proclamaban su simpatía por el movimiento sionista. Lucie supo encandilar a Freud y ambos obligaron a Ernst a internarse tres meses en el sanatorio de Arosa para tratarse de la tuberculosis que había contraído durante la guerra.
Ernst profesaba una adoración tan grande a su esposa que se hizo llamar Ernst L. Freud, con la inicial «L» (por Lucie) agregada a su nombre para indicar hasta qué punto tenía una existencia «simbiótica» con ella. «Mi corazón en llamas no conoce el reposo», escribía Lucie, y también: «No puedo vivir por amor a mí misma». Entre 1921 y 1924 trajo al mundo tres hijos —Stefan Gabriel, Lucian Michael y Clemens Raphael—, apodados «los arcángeles», y luego se consagró a la causa de la familia, mientras que Ernst disfrutó de una carrera excepcional gracias al movimiento psicoanalítico. En efecto, trabajó como arquitecto para Eitingon, Abraham, Karen Horney, René Spitz, Sándor Rado, Hans Lampl y, más adelante, para Melanie Klein. Se ocupó además del acondicionamiento de la célebre «policlínica» y después del sanatorio de Tegel, fundado por Ernst Simmel. Su inclinación por el modernismo significaba una ruptura con la asfixiante estética de los interiores vieneses tan apreciados por su padre: tapices amontonados, pesadas colgaduras, vitrinas desbordantes, paredes llenas de cuadros, muebles invadidos de objetos. Freud apenas se interesaba en este aspecto del talento de su hijo, quien, tras el exilio londinense, decoró por otra parte la última morada paterna en el más puro estilo de la Viena de antaño, por el que, sin embargo, no sintió jamás la más mínima nostalgia. Más alemán que austríaco y más inglés que alemán, Ernst estuvo a punto de emigrar a Palestina a petición de Chaim Weizmann, que quería encargarle la construcción de su casa.
Freud siempre decía que su última hija había nacido al mismo tiempo que el psicoanálisis. Y como había asociado su invención a una novela familiar poblada de príncipes melancólicos y princesas ociosas, no habrá de sorprender que aquella le contara en 1915 un sueño que lo remitía a la historia común de ambos: «Hace poco soñé», le decía ella, «que tú eras un rey y yo una princesa, y que por intrigas políticas querían que nos enfrentáramos».
Fue por amor a Anna que Freud incorporó a la familia un nuevo círculo, el de los perros: «Nuestros dos perros», diría un día, «el fiel Wolf y la dulce china Lun Yu, representan el aumento más reciente de la familia». En 1914 había enviado a su hija, desde Brioni, una tarjeta postal donde se veía a un chimpancé vestido y peinándose frente a un espejo: «Miss, un mono muy inteligente que se asea». En tanto que a Anna le gustaban los machos, Freud apreciaba en particular la compañía de las hembras chow-chows, criaturas de largo pelaje parecidas a leones en miniatura. Y a partir de 1920 comenzó a manifestar un gran apego por ellas, como lo testimonian sus intercambios con dos mujeres que las adoraban tanto como él: Hilda Doolittle y más aún Marie Bonaparte. Prefería las pelirrojas a las negras y las consideraba como seres excepcionales sobre los cuales la civilización ( _Kultur_ ) no tenía ningún ascendiente. En consecuencia, decía, se los podía querer plenamente, porque encarnaban «una existencia perfecta en sí», desprovista de ambivalencia, una vida no humana, por tanto, pero que venía a recordar al hombre algo de un estado anterior a él mismo. ¿No estaban los perros dispuestos en todo momento a hacer fiestas a sus amos y morder a sus enemigos? Freud no dejaba de asociar el amor que le inspiraba la raza canina a un aria del _Don Giovanni_ de Mozart.
Con todo, en ningún momento cuestionaba la atribución exclusiva de la función simbólica a la humanidad. Muy por el contrario, como era darwiniano y había definido su descubrimiento como la tercera herida narcisista infligida al hombre, sabía que entre la humanidad y la animalidad existía una brecha: la del lenguaje y la cultura. Y por eso destacaba que la civilización no tenía ascendiente alguno sobre la animalidad, sobre esa «vida no humana», deliciosa, despojada de odio. Podría agregarse que, por la misma razón, la perversión y el goce del mal no existen en el reino animal.
A decir verdad, cuando se refería a los de su casa, Freud ponía en el mismo plano a los «ocupantes humanos» y el «Estado de los perros», donde las hembras, a quien él apodaba «las damas», eran mayoritarias: «Como de costumbre», dirá Hilda Doolittle,
Yofi está sentada en el suelo, heráldica, emblemática... El profesor le presta más atención que a mi historia... Freud me ha dicho que Yofi tuvo un bebé negro, muerto al nacer, tan negro como el diablo, porque ella había tenido un marido negro... Ahora, si tiene dos cachorros de otro color, los dueños del padre recibirán uno, pero si no hay más que uno, seguirá siendo «un Freud».
Cuando Yofi murió, Arnold Zweig, que conocía la pasión de Freud por los perros, le escribió estas palabras: «Yofi era una hija que venía de lejos, que le era devota como un verdadero hijo, con un corazón más sabio que el común de nuestros hijos».
Freud, que en su juventud había adorado el «Coloquio de los perros» de Cervantes, amaba la naturaleza y a los animales, y sobre todo a aquellos con los que se cruzaba en el parque de la Villa Borghese en medio de las estatuas antiguas y las columnas: pavos reales, gacelas, faisanes. La animalidad nunca dejaba de estar presente en la relación que hacía de sus casos clínicos, en sus sueños, en los de sus pacientes, en su evocación de las sociedades primigenias, en su ensayo sobre Leonardo y en _Tótem y tabú_ : ratas, lobos, pájaros, caballos, buitres, quimeras, demonios, dioses de Egipto. Su atracción por los perros —sobre todo, ya se dijo, por las hembras— lo llevaba a rechazar a los gatos, demasiado femeninos en su opinión, demasiado narcisistas, demasiado ajenos a la alteridad. Y un día, con infinita malicia, la tomó injustamente con Mirra Eitingon, la mujer de su devoto discípulo: «No la aprecio. Tiene la naturaleza de un gato, y a ellos tampoco los aprecio. Ha compartido ampliamente el encanto y la gracia de un gato, pero ya no es un joven gatito adorable».
Sin embargo, en 1913 Freud se había sentido seducido por una «gata narcisista» que había entrado en su despacho por la ventana entreabierta. Sin inquietarse siquiera por su presencia, se había instalado en el diván y de inmediato se complació en mezclarse con los objetos de colección. Freud se vio obligado a reconocer que esa gata no causaba ningún daño a las cosas amontonadas en su despacho y comenzó a observarla, a quererla, a alimentarla. Observaba con gusto sus ojos verdes, almendrados y helados y consideraba que su ronroneo era la expresión de un verdadero narcisismo. Debía insistir, en efecto, para que la gata le prestara atención. Sus relaciones duraron algún tiempo, hasta el día en que Freud la encontró tendida en su diván y ardiendo de fiebre. Sucumbió a una neumonía, dejando tras de sí el recuerdo de ese «encanto egoísta y femenino» propio de los felinos, que él describiría tan bien en su artículo dedicado al narcisismo.
Anna no había sido deseada ni por su madre ni por su padre y había dedicado la juventud a la lucha por existir y luego a la rivalidad con su tía Minna para acceder al conocimiento de la obra paterna. En enero de 1913 había dado rienda suelta a los celos que sentía hacia su hermana: «Ya no bordo la manta de Sophie, pero la actitud no deja de parecerme desagradable cuando me digo que, de un modo u otro, me habría gustado terminarla. Pienso a menudo en su casamiento, desde luego. Pero Max, en realidad, me resulta indiferente».
Por entonces se arraigó en Freud una incomprensión de las verdaderas inclinaciones sexuales de su hija, que en una carta había aludido a sus «malos hábitos» (la masturbación): «No quiero que me vuelva a pasar», escribía ella el 7 de enero. Convencido de que Anna, a quien llamaba «mi hija única», había convertido su antigua rivalidad con Sophie en celos hacia el marido de esta, la exhortó a no tener miedo de ser deseada por los hombres. Freud no sospechaba aún que estaba celosa de su hermana y no de Max. Se sentía atraída por las mujeres.
En julio de 1914, cuando ella fue a visitar a Jones, a Freud se le metió en la cabeza que corría un riesgo: «Sé de fuentes muy fiables que el doctor Jones tiene serias intenciones de hacerte la corte. [...] Me doy cuenta de que no es el hombre más conveniente para una criatura femenina de naturaleza refinada». Y explicaba a Jones que Anna no pedía que la trataran como una mujer, ya que todavía estaba muy «alejada de los deseos sexuales y rechaza más bien al hombre».
Cuando prohibía a su hija dejarse cortejar por su discípulo, Freud no advertía que a ella le atraía mucho más Loe, con quien a decir verdad soñaba, que Jones. Pero este último había tomado conciencia de ello: «Tiene un bello carácter», escribiría a Freud, «y más adelante será a no dudar una mujer notable, a condición de que su represión sexual no le haga daño. Está terriblemente apegada a usted, por supuesto, y este es uno de los raros casos en que el padre real corresponde a la imagen del padre».
El apego era recíproco y Freud no vacilaba jamás en despedir a sus discípulos vieneses cautivados por Anna: August Aichhorn, Siegfried Bernfeld, Hans Lampl. Por su lado, ella no dejó de acercarse a él, sobre todo durante todo el transcurso de la guerra, cuando se propuso seguir con sus estudios para ser maestra.
Inquieto ante la idea de que Anna se quedara soltera, Freud se percató de que, a fuerza de prohibiciones y represiones, su hija rechazaba a los hombres, pero a la vez deseaba ser madre. Y para «despertar su libido» le propuso, en octubre de 1918, encargarse de analizarla.
La psicoterapia se desarrolló en dos tiempos: entre 1918 y 1920, y entre 1922 y 1924. A medida que se afirmaba su apego mutuo, reforzado por el análisis, y cuyo principal testigo, a través de una correspondencia cruzada, llegaría a ser Lou Andreas-Salomé, Freud se vio obligado a admitir que, si la libido de Anna se había «despertado», su «elección de objeto» no la llevaba en modo alguno hacia los hombres.
En esa época Freud empezó a tratar a una joven, Margarethe Csonka, cuyos padres pertenecían a la muy alta burguesía austríaca judía convertida al catolicismo. Despreocupada y mundana, amante del lujo y la libertad que le brindaban su fortuna y su elegancia, Margarethe siempre se había sentido atraída por las mujeres, sin desear, empero, tener relaciones carnales con ellas. Por eso había rechazado los avances de su amiga Christl Kmunke, partidaria de un lesbianismo declarado. En 1917 experimentó una pasión delirante por la llamativa baronesa Leonie von Puttkamer, mujer galante perteneciente a la nobleza prusiana, que era mantenida por los hombres y se exhibía abiertamente con mujeres. Vestida de manera lujosa y tocada con fabulosos sombreros, Leonie se paseaba gustosa por las más bellas avenidas vienesas acompañada de un inmenso perro lobo sujeto con una correa. La complacía deambular por los cafés y recorrer los mercados en busca de frutas con las que se deleitaba sin preocuparse en lo más mínimo por la penuria que padecían los vieneses, en el momento mismo en que brillaban las últimas luces de un imperio ya en plena descomposición.
La divertía ver a Margarethe seguirla a todas partes, adularla, servirla y jactarse de ser una suerte de trovador salido directamente de la literatura cortesana. Un día, sorprendida por su padre del brazo de la baronesa, Margarethe huyó para no tener que soportar su mirada. Leonie decidió interrumpir las relaciones y la joven, entonces, trató de suicidarse. Su padre, Arpad Csonka, la obligó a visitar a Freud para poner fin al escándalo de esa homosexualidad juzgada intolerable. Su intención era casarla lo más rápidamente posible.
Sin deseo alguno de hacer un tratamiento, Margarethe decidió de todos modos obedecer el mandato paterno. Freud aceptó, aun sabiendo a ciencia cierta que jamás lograría cambiar la orientación sexual de esa paciente. Nunca, en todo caso, la vio como una «enferma». Sin embargo, le pidió respetar el principio de abstinencia y dejar de frecuentar a la baronesa durante la cura.
Margarethe llevó entonces una doble vida. En cada sesión inventaba sueños e historias de familia ajustados a la doctrina freudiana, mientras que con la baronesa se quejaba de las interpretaciones de su terapeuta:
Sabes que desde hace un tiempo me interroga sobre mis padres y mis hermanos y que quiere saberlo todo acerca de ellos. La última vez se empeñó sobre todo con el menor. Imagina lo que me dijo hoy: que me habría gustado tener un hijo de mi padre, y como fue mi madre, claro, quien lo tuvo, la odio por eso y también a mi padre, y por esa razón me aparto por completo de los hombres. Es indignante.
Freud advirtió el doble juego de Margarethe y puso fin a la cura. Así, el padre quedaba satisfecho al saber que su hija había seguido un tratamiento y ella estaba fascinada por poder seguir viviendo como pretendía. A modo de despedida, Freud le dijo estas palabras: «Sus ojos son tan astutos que si yo fuera su enemigo no me gustaría encontrármela en la calle».
En realidad, aprovechó esa experiencia para modificar una vez más su definición de la homosexualidad. Si bien confirmaba que esta era la consecuencia de la bisexualidad, se decía convencido de que, cuando se trataba de una elección excluyente, dependía de una fijación infantil en la madre. En los varones esa elección excluía a la mujer, decía Freud, y en las niñas provoca una decepción con el padre. En el caso de Margarethe ese rechazo radical del padre se había traducido, en su vida, en la elección de un sustituto de la madre, y en la cura, en una transferencia negativa con el analista. Y Freud agregaba:
No es misión del psicoanálisis solucionar el problema de la homosexualidad. Tiene que conformarse con revelar los mecanismos psíquicos que han llevado a decidir la elección de objeto, y rastrear desde ahí los caminos que llevan hasta las disposiciones pulsionales. En ese punto cesa su tarea y abandona el resto a la investigación biológica, que precisamente hoy, en los experimentos de Steinach, ha producido esclarecimientos tan importantes sobre la influencia de la primera de las series mencionadas sobre la segunda y la tercera. El psicoanálisis se sitúa en un terreno común con la biología en la medida en que adopta como premisa una originaria bisexualidad del individuo humano (así como del animal).
De ese modo, Freud remitía la explicación final de la homosexualidad a una causa biológica, cuando antes había afirmado su origen psíquico. Nueva y audaz interpretación, que parecía contradecir sus posiciones anteriores. Por añadidura, distinguía ahora la homosexualidad innata de la homosexualidad adquirida.
Sin lugar a dudas, si Margarethe padecía de algo no era de su homosexualidad. Lo cierto es que retomó su vida de lesbiana y se enamoró sin cesar de mujeres con las cuales no encontraba ninguna satisfacción carnal. Tuvo varios intentos de suicidio antes de casarse (sin amor) con el barón Eduard von Trautenegg, más interesado en la fortuna de la familia Csonka que en su esposa. Ambos tuvieron que convertirse al protestantismo para poder casarse, porque Eduard se había divorciado de una primera mujer y, de permanecer en el catolicismo, no podía volver a contraer matrimonio.
Cuando después del _Anschluss_ Von Trautenegg se acercó a los nacionalsocialistas, aprovechó para pedir la anulación de ese matrimonio con una mujer de origen judío y apoderarse así de su fortuna. Margarethe se vio despojada de todo, y sin ser ya ni católica ni protestante. Volvía a ser judía, cuando no lo había sido nunca y a pesar de sentir muy poco afecto por los judíos. Sin marido, corría además el riesgo de que la vieran como una notoria homosexual. En consecuencia, se marchó de Austria. Tras un largo periplo que la llevó a viajar sin cesar alrededor del mundo en busca de sí misma, decididamente amante de las mujeres y fiel a su perro, siempre forzada a no establecerse en ninguna parte, regresó a Viena y murió casi centenaria después de contar varias versiones de su cura a distintos psicoanalistas o investigadores, deslumbrados por esa aventura característica de una época desaparecida para siempre.
La manera en que Freud concibió la homosexualidad femenina a partir de su encuentro con Margarethe no podía ayudarlo a escuchar lo que sucedía en la terapia psicoanalítica de Anna. ¿Cómo imaginar, en ese caso, una fijación infantil inconsciente en la madre y el rechazo de un padre que la hubiera decepcionado? El propio Freud había prohibido a su hija dejarse seducir por los hombres, y en especial por sus alumnos. Por su parte, ella soñaba con ser la discípula de un padre adorado y rechazaba el destino de su madre. En otras palabras, Freud se enfrentaba a una realidad que contradecía su teoría.
Si esa cura —que no lo era— terminó en un fiasco, la de Anna Guggenbühl, joven psiquiatra suiza formada en el Burghölzli, tuvo bastante éxito, según el testimonio de la paciente. Esta acudió al diván de Freud cuando tenía veintisiete años, por voluntad propia y con una transferencia positiva, en un momento en que Anna Freud había interrumpido su análisis. Comprometida desde hacía varios años con un compañero de estudios, y con numerosas aventuras amorosas en su haber, Anna G. dudaba de sus ganas de casarse. Su deseo se atenuaba, a pesar de que su familia ya había planeado la boda. Decidida a comprender las razones inconscientes de su vacilación, dejó a sus padres y su trabajo con toda la libertad que le daba su deseo de conocer a quien consideraba como el mejor oído de su época. Como virtuoso de la interpretación contundente, Freud, después de escucharla, le explicó que en el «nivel superior» de su vida se desplegaba el conflicto con su prometido. Para comprender su significado, añadió, había que explorar el «nivel intermedio», que la remitía a su relación neurótica con su hermano, y luego el «nivel inferior» —totalmente inconsciente—, que era el de su relación con los padres.
En otras palabras, Freud afirmaba que Anna G. estaba enamorada de su padre, que deseaba la muerte de su madre y que el apego por su hermano, sustituto del padre, explicaba sus titubeos permanentes: «Sus amantes son sustitutos de sus hermanos, y por eso tienen todos la misma edad, aunque son menos maduros que ellos». La cura terminó cuando Freud le dijo a Anna Guggenbühl que se encontraba bajo el influjo de un desafío lanzado a sus padres. Y puede suponerse que fue la liberación del deseo reprimido de estar bajo el influjo de su propio desafío lo que la llevó a romper su compromiso, desobedecer al padre y escoger por sí sola su destino.
En 1922, mientras preparaba su primera ponencia para la WPV, Anna Freud, de nuevo en análisis con su padre, sintió cuánto la atraían las mujeres y confió su perturbación a Lou:
Por primera vez tuve un sueño diurno en el que aparecía una protagonista femenina. Era incluso una historia de amor en la cual no he dejado de pensar. Quería aprovecharla y escribirla de inmediato, pero papá consideró más adecuado que la dejara de lado y pensara en mi ponencia. La historia me abandonó, por lo tanto, pero si en julio todavía la recuerdo, la pondré de todos modos por escrito. Desdichadamente, solo aparecen en ella personas conocidas.
La ponencia de Anna no era ajena a ese asunto. Su tema, en efecto, eran las fantasías de flagelación en los niños pequeños, y seguía a un célebre artículo de su padre, «Pegan a un niño», donde Freud describía el caso de una niña cuyas fantasías infantiles se parecían mucho a las que le había contado su propia hija. Y esta, a su vez, las analizó como si no fueran suyas, explicando que la niña había logrado sustituir el recuerdo de esas escenas por «bellas historias».
En 1923 Anna Freud decidió oficialmente renunciar al matrimonio. Su padre no tardó en apodarla «Antígona» y luego le regaló un pastor alemán, Wolf (o Wolfi), que pasó a ser de inmediato un miembro más de la casa. Freud reveló su desasosiego a Lou. Temía que la «genitalidad» de Anna le jugara una mala pasada y confesó que no lograba liberarla de sí mismo ni separarse de ella.
Si la cura con su padre permitió a Anna afirmarse como líder de una escuela, rodeada por los mejores discípulos de aquel dentro del _Kinderseminar_ , su consecuencia nefasta consistiría en hacerle odiar su propia homosexualidad. A lo largo de toda su existencia Anna se mostraría hostil a la idea de que los homosexuales pueden ejercer el psicoanálisis. Contra la opinión de su padre, mantendría la convicción —como Jones, por otra parte— de que la homosexualidad es una enfermedad.
Algún tiempo después del final del segundo período en el diván de su padre, Anna conoció a la mujer que iba a ser su compañera de toda la vida: Dorothy Tiffany Burlingham. Nacida en Nueva York y nieta del fundador de las joyerías Tiffany & Co., esta se había casado con un cirujano, Robert Burlingham, afectado por una psicosis maníaco depresiva. Para escapar a sus raptos de locura ella se había trasladado a Viena, plenamente decidida a tratar su fobia y confiar a la familia Freud el destino de sus cuatro hijos: Bob, Mary («Mabbie»), Katrina («Tinky») y Michael («Mikey»). Después de una entrevista preliminar, Anna empezó un análisis con los dos primeros y propuso a Dorothy psicoanalizarse con Theodor Reik.
Muy pronto, las dos mujeres comenzaron a tratarse como si fueran mellizas y a dedicar su tiempo libre a pasear por los alrededores de Viena en el Ford T de Dorothy. A Freud le encantaba acompañarlas. Ambas adoptaron la costumbre de usar idéntica ropa, a la vez que entablaban relaciones de intimidad muy semejantes a las que podían tener dos lesbianas. Pero Anna negó categóricamente la existencia de una relación carnal con su nueva amiga, como una manera de seguir fiel al único hombre que amó en su vida: su padre.
Una vez terminada la cura con su padre, Anna escogió a Max Eitingon como confidente y luego hizo otra amiga, Eva Rosenfeld, una judía berlinesa perteneciente a un medio acomodado y sobrina de Yvette Guilbert, una cantante francesa admirada por Freud. Anna la ayudó a superar la muerte de dos de sus hijos, debida a la disentería. Con ella y Dorothy, fundó en 1927 una escuela privada destinada a recibir a los niños en terapia psicoanalítica con ella o con otros discípulos del entorno familiar, y cuyos padres también se analizaban en Viena. Entre esos niños estaba Peter Heller, quien más adelante se casaría con Tinky, la hija de Dorothy: «La escuela Burlingham-Rosenfeld», escribirá, «fue para mí una experiencia privilegiada, muy prometedora. La inspiraba y animaba un ideal de humanismo más puro, más sincero que los otros establecimientos a los que asistí. En ella se difundía un auténtico sentido de la comunidad en un ambiente luminoso, soleado y cálido».
También en 1927, Anna impulsó a Dorothy a analizarse con Freud, lo que permitió a este aprehender mejor la naturaleza de sus relaciones, al mismo tiempo que recibía a un nuevo visitante: una hembra chow-chow llamada Lun Yu, que se entendía a las mil maravillas con Wolf.
Felices y libres, Anna y Dorothy no tardaron en comprar una pequeña granja con un huerto y animales: las dos familias pasaban en ella sus vacaciones. En el otoño de 1929, mientras se cernía sobre el mundo la amenaza de la crisis bursátil norteamericana, Dorothy se instaló con sus cuatro hijos en un apartamento de Berggasse 19. A partir de entonces no tuvo más que bajar un piso para tenderse en el diván de Freud, a quien consideraba como Dios Padre. Gracias a la instalación de una línea telefónica directa podía hablar con Anna, por la noche, sin perturbar a los habitantes de la casa: asombrosa puesta en práctica de la utopía telepática que, en esa época turbulenta, asediaba el imaginario de Freud y Ferenczi.
De ese modo cumplió Anna su anhelo de ser madre, al convertirse, por medio del psicoanálisis, en «coprogenitora» y terapeuta de los hijos de Dorothy, al mismo tiempo que era ya la madre adoptiva y la analista de su sobrino Ernstl. En cuanto a Freud, se consideró más que nunca como el patriarca dichoso de una familia recompuesta, sometida a la erosión de la antigua autoridad patriarcal, cuyo fruto era el psicoanálisis: «Nuestros vínculos simbióticos con una familia norteamericana (sin marido)», escribiría en 1929, «cuyos hijos son analíticamente seguidos por mi hija con mano firme, se tornan cada vez más sólidos, de manera que adoptamos resoluciones comunes para el verano. Nuestros dos perros, el fiel Wolf y la dulce china Lun Yu, representan el aumento más reciente de la familia».
Desde comienzos de siglo Freud se había prendado con pasión de las antigüedades, tan indispensables para su cotidianeidad como los cigarros o los personajes de los trágicos griegos, y tan necesarios para su horizonte como Roma, Atenas o Egipto. Mucho más lector de obras de arqueología que de psicología, había transformado su casa de la Berggasse en un verdadero museo: «Solo puede comprenderse la revolución freudiana en toda su dimensión», escribe Peter Gay, «si se recuerda cuáles eran las ideas y los supuestos científicos de fines del siglo XIX. Ahora bien, esa revolución nació en un lugar que es su antítesis, donde sus banderas y consignas son invisibles».
Toda una serie de figuras inanimadas —griegas, chinas, egipcias, precolombinas— poblaban las diferentes habitaciones de la morada freudiana. Como en una película muda, los objetos procedentes de las civilizaciones antiguas hacían que sus luces y sus sombras se cernieran sobre la vida de perros y humanos. Cada año más numerosos, se desplegaban en medio de un decorado atestado donde se amontonaban tapices y colgaduras de colores, unos en el suelo, los sillones y los sofás, y otras en las paredes. Una veintena de estatuillas, entre las más conmovedoras y las más dispares, se erguían sobre el escritorio de _Herr Professor_ , frente a sus manuscritos. A cada una se atribuía una personalidad propia, y todas contribuían a mantener el espíritu creativo del dueño del lugar. No bien entraba a ese cuarto donde recibía a sus pacientes en presencia de su chow-chow, Freud saludaba a su sabio chino instalado al borde del escritorio, flanqueado por una estatuilla de Imhotep —dios del saber y la medicina— a la izquierda y otra de una divinidad egipcia menor a la derecha. Así, los custodios del cuerpo y la mente velaban por el buen desarrollo de las sesiones o los ejercicios de escritura.
Por doquier, vitrinas, muebles, bibliotecas y porcelanas orientales colmaban el espacio de esa casa en forma de laberinto donde no se toleraba ningún lugar vacío, como si cada cosa —pintura al pastel del templo de Abu Simbel, Jano de piedra, Horus, Anubis, Neftis, Isis y Osiris, molde de la _Gradiva_ , bajorrelieve de _La muerte de Patroclo_ , camello de la dinastía Tang, budas diversos— encarnara a la vez las tres regiones de la vida psíquica y el surgimiento de una pulsión ancestral de inmediato reprimida. En medio de esa profusión de imágenes, jeroglíficos, símbolos funerarios, estatuillas sagradas —hombres y animales mezclados—, aparecían en la penumbra las huellas de una memoria judía: un aguafuerte de Rembrandt — _Los judíos en la sinagoga_ —, un grabado de Kruger que mostraba a Moisés levantando las Tablas de la Ley, un candelabro (menorá) de Januká y, para terminar, dos copas para el Kidush dispuestas frente a unas estatuillas egipcias.
Freud también coleccionaba fotos y cuadros: reproducción de la famosa _Lección clínica en la Salpêtrière_ , de Brouillet; _Edipo y la Esfinge_ , de Ingres; _La pesadilla_ de Füssli; _El beso de Judas_ de Durero, etc. A ellos se añadían decenas de fotografías: medallones de madres, hermanas e hijos, retratos de discípulos o mujeres admiradas: Lou AndreasSalomé, Marie Bonaparte, Yvette Guilbert.
En agosto de 1922 Cäcilie Freud, la hija de Rosa Graf, se suicidó con una fuerte dosis de veronal. Embarazada al margen del matrimonio, disculpaba a su amante. Fuera como fuese, en una carta a su madre, que quedaba así sin descendencia, explicaba que morir era muy simple y que la idea incluso le daba cierta alegría. Profundamente conmovido por ese acto, Freud no vaciló en mencionar el turbulento porvenir de Austria. Era perfectamente consciente de los conflictos políticos que agitaban a la nueva república, cuya capital, ahora bautizada «Viena la roja», era gobernada por una coalición de socialdemócratas y demócratas cristianos influidos por los principios del austromarxismo. Freud percibía el crecimiento espectacular de los populistas antisemitas y pangermanistas, que denunciaban los ambiciosos programas de la izquierda social. Sabía además que esos grupos buscaban nuevos chivos expiatorios con su denuncia de los extranjeros y más aún de los judíos llegados de Polonia, Rumanía y Ucrania.
Pero por el momento Freud seguía lanzando mandobles contra el presidente Thomas Woodrow Wilson, a quien, decididamente, no perdonaba sus «catorce puntos». No creía ni por un instante en la concepción wilsoniana del derecho de los pueblos de los desaparecidos imperios a disponer de sí mismos y solo veía en ese proyecto un intento de balcanización de la _Mitteleuropa_. En síntesis, tenía a ese presidente iluminado por el responsable de la desventura de aquellos a quienes pretendía liberar del yugo de sus amos. Lejos de respetar a los vencidos, decía, los había tratado de manera despreciativa. Por lo demás, acababa de ver confirmada su opinión a través de la lectura de un libro del periodista norteamericano William Bayard Hale, que denunciaba el estilo ampuloso de Wilson y se refería al método psicoanalítico. Freud había intercambiado algunas cartas con el autor, lo cual alimentaba en él, pese a los consejos de Jones, el cultivo de cierto antiamericanismo. Ni él ni nadie de su entorno pensaban en esa fecha en el papel que iba a desempeñar Adolf Hitler en la historia del psicoanálisis.
Freud siempre se había preocupado por su salud. En varias ocasiones había constatado la existencia de una lesión sospechosa en la parte derecha del paladar y había resuelto no inquietarse demasiado por ella. Pero en vez de renunciar al tabaco, prefería creerse afectado por una simple leucoplasia. No obstante, el 20 de abril de 1923 hizo que le quitaran un tumor calificado de «benigno» que él mismo caracterizó como un epitelioma. Luego se decidió a consultar a su viejo amigo Max Steiner, cofundador de la Sociedad de los Miércoles, que le aconsejó otra vez dejar de fumar, a la vez que le ocultaba el carácter cancerígeno del tumor.
Fue entonces cuando Felix Deutsch, su discípulo y médico personal, que el 7 de abril había comprobado la presencia de esa lesión, se negó a decir la verdad a su venerado maestro por temor a espantarlo, y le aconsejó una nueva operación. Conocido de los más grandes profesores de medicina de Viena, Freud habría podido elegir desde el principio a uno de los mejores. Acudió, en cambio, a Marcus Hajek, otorrinolaringólogo que —estaba seguro— lo tranquilizaría por completo. No se equivocaba. Ese doble de Fliess procedió a una nueva ablación del tumor que terminó en un desastre y una terrible hemorragia. A continuación Freud tuvo que someterse a una inútil radioterapia cuyo único efecto consistió en agravar sus dolores. En esa época, plenamente absorbido por la muerte del pequeño Heinz (Heinerle), su «niño querido», seguía sin querer conocer la verdad. A fines de junio viajó a Gastein con Minna; luego se trasladó al Tirol y finalmente a Lavarone, donde la familia se reunió con él.
A fines de agosto de 1923 los miembros del comité se encontraron en San Cristoforo, al pie de la montaña donde se alojaba Freud. En esa época había entre ellos una violenta disputa alrededor de la «técnica activa». Además, Rank y Ferenczi se sentían marginados por los berlineses —Abraham y Eitingon—, mientras que Jones seguía tratando de desarrollar el psicoanálisis fuera del mundo germanoparlante. No deseoso de tomar partido, Freud permaneció en su hotel y solo Felix Deutsch y Anna se unieron al grupo para compartir una cena en San Cristoforo. Esa noche los principales discípulos tomaron conciencia de la gravedad del cáncer de Freud. Y como era necesaria una nueva operación, se embarcaron en una discusión tumultuosa sin decidirse, empero, a decirle la verdad.52 Lo dejaron partir para hacer un último viaje al sur. En 1913 Freud se había prometido iniciar a Anna en su amor por Roma y nada ni nadie podía impedir la realización de ese proyecto. Juntos, padre e hija caminaron por la ciudad durante varias horas. Conforme a un itinerario rigurosamente establecido, visitaron el Capitolio, el Panteón, Tívoli, la Capilla Sixtina: «Son nuestros últimos días», escribió Freud a sus otros hijos. «Para facilitar la partida, el siroco se puso a soplar y las reacciones de mi mandíbula me hacen sufrir más que nunca. Anna está como unas castañuelas. Hoy incluso intentó con una opereta.»
A continuación Freud riñó con Deutsch, a quien trató de «cobarde miserable». Luego se reconcilió con él. Pero en 1927 eligió a otro médico para que lo tratara: Max Schur, que había asistido a sus conferencias en 1916 y que habría de atenderlo hasta su muerte. Perteneciente a una familia de emigrados judíos de Polonia, Schur se ocupó de su prestigioso paciente tras analizarse con Ruth Mack-Brunswick. Más joven que los discípulos del primer círculo, admiraba a Freud, pero no por eso lo veneraba al extremo de mentirle.
Mucho antes de ese encuentro, al retorno de su último viaje a Roma, Freud ya había decidido acudir a Hans Pichler, un estomatólogo austríaco considerado por entonces como uno de los más grandes especialistas europeos en cirugía maxilofacial. Formado en la Northwestern University de Chicago, Pichler había adquirido durante la guerra una destreza excepcional en la reconstrucción del rostro de heridos graves.
El médico recibió a Freud el 26 de septiembre de 1923 y el 4 de octubre lo sometió a una dura prueba al practicar la ablación de una buena parte de su mandíbula superior y de su paladar derecho. El 13 de noviembre, una nueva intervención. A partir de ese día, Pichler operó a su paciente veinticinco veces y en 1931 solicitó la ayuda de su colega norteamericano Varaztad Kazanjian, ex médico honorario del ejército británico, célebre por sus innovaciones en el perfeccionamiento de las mejores prótesis dentarias destinadas a las «caras rotas». De ese modo, Freud pudo beneficiarse con los progresos de la cirugía facial debidos a la guerra de las naciones. Sin embargo, iba a sufrir un martirio durante los dieciséis años que le restaban de vida.
La «prótesis» hizo su entrada en el conjunto que conformaban los objetos de colección, los libros, los cigarros, los perros, los pacientes y el universo cotidiano de _Herr Professor_ y su entorno. Maldita prótesis, horrible monstruo, instrumento de tortura, objeto mal ajustado: así calificaba Freud esa cosa innombrable que perturbaba su cuerpo enfermo. Describiría el intruso a cada uno de sus corresponsales, sin renunciar jamás al tabaco: « _Lieber Max_ , el estado de tensión que genera la prótesis me absorbe por completo. Comer, beber y hablar son momentos que temo». Y a Lou Andreas-Salomé:
_Liebe Lou_ , no hay nada más irritante que un sustituto corporal alzado en rebelión, a pesar de no ser otra cosa que un artificio, como un par de gafas, una dentadura postiza o una peluca [...]. Pequeños acuerdos con este objeto intruso y salvador alimentan una ilusión, es decir, la esperanza de lograr conversar sin pensar en mi boca. [...] Todas las recientes intervenciones, presentadas como inevitables, han sido empero inútiles.
En 1931, acerca de Kazanjian: «Tiene la sonrisa de Charles Chaplin [...]. Este mago ha dado instrucciones para construir una prótesis provisoria de la mitad de tamaño y la mitad de peso de la actual. Con ella puedo masticar, hablar, fumar al menos tan bien como antes».
Freud tuvo que pasar por varios tipos de operaciones: unas con anestesia local complementada con sedantes, otras con anestesia total. Después de cada intervención le costaba hablar y, con el paso de los años, tuvo cada vez más dificultades para alimentarse, a la vez que sufría de manera permanente una sordera del oído derecho que lo obligaba a mover el diván para oír bien a sus pacientes. La prótesis debía limpiarse, reajustarse y reemplazarse constantemente, al precio de interminables dolores. Cuando Freud no lograba ponérsela, reclamaba la ayuda de Anna, que a veces luchaba durante una hora con el «monstruo»: «Lejos de inspirar impaciencia o asco», escribe Peter Gay, «esa proximidad no hizo sino estrechar los lazos entre el padre y la hija. Él llegó a ser tan irreemplazable para ella como ella se había tornado indispensable para él».
### 3
El arte del diván
Varias decenas de artículos o libros se dedicaron a los pacientes de Freud y su suerte después de que este se estableciera como especialista en enfermedades nerviosas, más adelante como psicoanalista y por último como formador de analistas. La consulta de los archivos depositados en la Biblioteca del Congreso (LoC), así como de diversos testimonios o relatos de casos reconstruidos o publicados, permite establecer que Freud, a lo largo de su vida profesional, trató a alrededor de ciento sesenta personas muy diferentes unas de otras, pero en su mayoría pertenecientes a la alta burguesía o la clase media acomodada. Es probable, además, que en el futuro se descubran otros relatos de terapias psicoanalíticas, lo cual no debería cambiar en gran medida las consideraciones que los historiadores pueden hacer sobre la práctica clínica compleja de Freud.
Entre 1895 y 1914 los pacientes procedían de los Imperios Centrales y del oeste, el norte y el sur de Europa, mientras que después de 1920 empezaron a llegar del continente norteamericano, de Francia o del Reino Unido, es decir, de los países «vencedores». En esta etapa de su existencia Freud se convirtió esencialmente en analista de analistas, sin dejar de considerar la cura como un asunto de familia. No solo analizó a su hija sino también a los amigos de sus otros pacientes, así como a varios de sus discípulos, sus cónyuges o sus allegados. Se sabe que no respetaba ninguna de las reglas técnicas establecidas por las sociedades psicoanalíticas. Es preciso saber además que dichas «reglas» se instauraron poco a poco a partir de 1918 y que para el movimiento psicoanalítico era impensable obligar a Freud a respetarlas. ¿Cómo forzarlo a someterse a una cura y luego a una supervisión para poder ser psicoanalista? ¿Cómo prohibirle analizar a sus parientes o a los cónyuges de estos cuando, hasta 1920, los miembros de su primer círculo todavía no habían elaborado esas reglas que, por lo demás, solo se aplicaron verdaderamente en el IPV (Verein) a medida que el oficio de psicoanalista se profesionalizaba? En realidad, el primer círculo las elaboró para las generaciones venideras.
Desde 1920 se produjo un cambio esencial en la historia del conocimiento de los «casos». En vez de ser reconstruidas por Freud como otros tantos relatos clínicos, la narración de las psicoterapias del período de entreguerras quedó a cargo de los propios analizantes bajo la forma de testimonios, autoficciones o notas transmitidas a la posteridad y publicadas por historiadores o los herederos. En otras palabras, con referencia a este período, el trabajo clínico de Freud puede evaluarse y comprenderse de manera retrospectiva a través de la mirada de un analizante que cuenta su cura, y ya no sobre la base de los relatos publicados por él. La diferencia no es menor.
Sabemos además que los pacientes recibidos por Freud a título de «enfermos» —antes y después de 1914— eran más o menos obligados por su entorno a hacerse tratar: así sucedió con todas las mujeres de los _Estudios sobre la histeria_ , con Ida Bauer, con Margarethe Csonka y con muchas otras. En esas condiciones, las curas tenían pocas posibilidades de vivirse como «éxitos», sobre todo cuando se trataba de mujeres jóvenes en rebelión contra sus familias, y a juicio de las cuales Freud aparecía como un médico lascivo o cómplice de los padres. Al contrario, los pacientes que acudían por su propia voluntad a analizarse en la Berggasse se sentían en general satisfechos. De ahí la siguiente paradoja: las curas fueron más «exitosas» en la medida en que eran el resultado de una decisión libremente consentida del sujeto. Y Freud postularía, en efecto, que ninguna experiencia psicoanalítica es posible sin la cooperación total del paciente. Es menester aclarar además que en la época, cuanto más aspiraba un analizante a ser analista, más probable era que la cura fuera terapéutica antes de convertirse en didáctica, porque el paciente se comprometía con una causa. En consecuencia —y salvo excepciones—, las terapias psicoanalíticas más consumadas, es decir, las más satisfactorias desde el punto de vista de los sujetos, fueron las que eran el resultado, por un lado, de una voluntad consciente, y por otro, de un compromiso militante.
En su gran mayoría los pacientes de Freud eran judíos y padecían neurosis, en el sentido muy amplio dado a este término durante la primera mitad del siglo: neurosis a veces leves pero con mucha frecuencia muy graves, y que más adelante se calificarían de estados _borderline_ e incluso de psicosis. Muchos de ellos eran intelectuales, a menudo célebres —músicos, escritores, creadores, médicos, etc.—, deseosos no solo de tratarse sino también de experimentar la cura por la palabra con el padre fundador. De manera general, acudían a la Berggasse tras un periplo que los había llevado a hacerse examinar por todas las eminencias del mundo médico europeo: psiquiatras o especialistas en toda clase de enfermedades nerviosas. Y, dígase lo que se diga, sobre todo antes de 1914, se habían enfrentado a ese famoso «nihilismo terapéutico» tan característico del estado de la medicina psiquiátrica de la época.
En este aspecto, el inmenso éxito vivido por el psicoanálisis era la consecuencia de la invención freudiana de un sistema de interpretación de las afecciones del alma fundado en grandes epopeyas narrativas que tenían que ver más con los desciframientos de enigmas que con la nosografía psiquiátrica. En el diván de ese científico tan original, él mismo víctima de un cuerpo sufriente, rodeado de sus suntuosas colecciones de objetos y esos perros de una belleza sorprendente, cualquiera podía verse como el héroe de una escena teatral sabiamente compuesta de príncipes, princesas, profetas, reyes caídos y reinas en desamparo. Freud contaba cuentos, resumía novelas, leía poemas, evocaba mitos. Historias judías, _Witz_ , relatos de deseos sexuales enterrados en las profundidades del alma: a sus ojos, todo servía para dotar al sujeto moderno de una mitología que lo devolviera al esplendor de los orígenes de la humanidad. En el plano técnico, para justificar esa posición, Freud afirmaba que un análisis correctamente encaminado —es decir, exitoso— tenía el objetivo de convencer al paciente de aceptar la verdad de una construcción científica por el simple hecho de que esta producía un beneficio superior al de la mera reconquista de un recuerdo recuperado. En otras palabras, una cura exitosa era una cura que permitía al sujeto comprender la causa profunda de sus tormentos y sus fracasos, y superarlos para realizar mejor sus deseos.
Freud recibía ocho pacientes al día en sesiones de cincuenta minutos a razón de seis veces por semana, durante varias semanas y en ocasiones algunos meses. Podía haber curas que resultaran interminables, jalonadas de retornos y recaídas. Además, Freud también recibía a otros pacientes con fines de mera consulta, de atención médica o para realizar algunas sesiones de psicoterapia. En general no tomaba notas durante las sesiones y todo su arte del diván consistía en una iniciación al viaje: Virgilio guiado por Dante en la _Divina Comedia_. Si recomendaba la abstinencia, nunca obedecía a ningún principio de «neutralidad» y prefería la «atención flotante» que facilitaba el desenvolvimiento de la actividad inconsciente. Hablaba, intervenía, explicaba, interpretaba, se equivocaba y fumaba cigarros sin ofrecerlos a los pacientes, lo cual suscitaba en ellos diversas reacciones. Para terminar, mencionaba llegado el caso algunos detalles de su propia vida y se refería a sus gustos, sus elecciones políticas, sus convicciones. En una palabra, se implicaba en la psicoterapia convencido de que acabaría con las resistencias más tenaces. Y cuando no lo lograba, intentaba comprender por qué, hasta el momento en que abandonaba toda esperanza de éxito. Por otra parte, a veces cometía indiscreciones e informaba a sus corresponsales del contenido de las sesiones que realizaba, e incluso leía a algunos pacientes cartas que había recibido en relación con ellos, sin respetar la confidencialidad que habría debido protegerlas.
Freud llevaba sus cuentas día tras día en una agenda especial ( _Kassa-Protokoll_ ) y en sus cartas hablaba sin cesar de dinero. Entre 1900 y 1914 había conquistado un estatus social equivalente al de los grandes profesores de medicina, que también atendían pacientes en privado. Era, pues, tan rico como los profesionales más afamados de su generación, y su tren de vida era similar.
Durante la guerra sus ingresos se derrumbaron al unísono con la economía austríaca. Pero a partir de 1920 comenzó a reconstruir su fortuna al recibir, ya no solo a pacientes de los desaparecidos Imperios Centrales, arruinados por la crisis económica y las depreciaciones de la moneda, sino a psiquiatras o intelectuales extranjeros adinerados procedentes de Estados Unidos o deseosos de formarse en el psicoanálisis. Freud se convirtió así, poco a poco, en el analista de los analistas.
Cuando era posible, hacía que le pagaran las terapias psicoanalíticas en divisas. Con el paso de los años logró colocar activos en el extranjero, que se sumaban a sus derechos de autor, bastante considerables. Y si ganaba menos que un psicoanalista instalado en Nueva York o Londres, tenía una posición claramente más acomodada que sus discípulos alemanes, húngaros y austríacos, a quienes les costaba sobrevivir en un contexto económico desastroso. En octubre de 1921, con deseos de que Lou Andreas-Salomé viajara a Viena, como ella había dicho que quería hacer, le escribió lo siguiente:
Si el hecho de estar cortadas las relaciones con su país natal afectara su libertad de movimiento, permítame disponer que desde Hamburgo le remitan el dinero para su viaje. Mi yerno maneja desde allí mis tenencias en marcos, y gracias a mis ganancias en monedas extranjeras sólidas (norteamericanas, inglesas, suizas) soy relativamente rico. Pero querría en verdad sacar algún placer de esas nuevas riquezas.
A título de comparación, señalemos que en 1896 Freud cobraba diez florines la hora; en 1910, entre diez y veinte coronas por sesión; en 1919, doscientas coronas, o cinco dólares en el caso de un paciente norteamericano (el equivalente de setecientas cincuenta coronas), o una guinea, es decir, un poco más de una libra esterlina (seiscientas coronas), si se trataba de un paciente inglés sin fortuna. Para terminar, en 1921 pensó en pedir quinientas o mil coronas y luego fijó el precio de una hora en veinticinco dólares, lo cual no le impedía aceptar sumas menores de algunos pacientes.
Por momentos no podía reprimir un antiamericanismo injusto y virulento que lo llevaba a afirmar, por ejemplo, que sus discípulos del otro lado del Atlántico solo servían para aportarle dólares. Un día sostuvo ante un interlocutor atónito que la estatua de la Libertad podía reemplazarse «por la de un mono blandiendo una Biblia». En otra ocasión, delante de uno de sus alumnos en análisis, afirmó que los norteamericanos eran tan estúpidos que su modo de pensamiento podía reducirse a un silogismo ridículo: «Ustedes, los norteamericanos, son más o menos así: el ajo es sabroso, el chocolate es sabroso, ¡pongamos pues un poco de ajo en un chocolate y comámoslos!».
Freud sentía como una humillación profunda la derrota de los Imperios Centrales y la preponderancia cada vez más grande que adquirían los psicoanalistas norteamericanos en el movimiento internacional. La necesidad de hacer pagar a todos sus pacientes lo perturbaba, y se mostraba favorable a la idea de que algún día hubiese instituciones capaces de ofrecer curas gratuitas a los más desposeídos. En líneas generales, le horrorizaba la concepción norteamericana de la democracia, la libertad individual y los derechos de los pueblos a disponer de sí mismos: «Los norteamericanos», diría un día a Sándor Rado, «trasladan el principio democrático del dominio político al de la ciencia. Todo el mundo debe ser presidente por turno. Por eso son incapaces de llevar a cabo nada».
Siempre había considerado que la terapia psicoanalítica no era conveniente para las personas estúpidas, incultas, de mucha edad, melancólicas, maníacas, anoréxicas o afectadas por un estado episódico de confusión histérica. Excluía asimismo de la experiencia psicoanalítica a los psicóticos y los perversos «que no anhelen reconciliarse consigo mismos». A partir de 1915 agregó a la categoría de los no analizables a las personas que padecían neurosis narcisistas graves, invadidas por pulsiones de muerte y destrucción crónicas e imposibles de sublimar. Y más adelante, cuando Ferenczi le propuso analizarlo, respondió con humor que, tratándose de un septuagenario afectado de tabaquismo y de una lesión cancerosa, ninguna indicación de cura era posible. Afirmaba en cambio que la cura era indicada para tratar la histeria, la neurosis obsesiva, las fobias, las angustias, las inhibiciones y los trastornos de la sexualidad. Y añadía que solo podía tener éxito en el caso de personas inteligentes, dotadas de sentido moral y capaces de desear implicarse en ella.
En 1928 reconoció de manera muy clara ante su discípulo húngaro István Hollos, artífice de la reforma de los psiquiátricos, que los psicóticos no le gustaban:
Finalmente tuve que confesarme que esos enfermos no me gustaban y que les reprochaba que fueran tan diferentes a mí y a todo lo humano. Es una curiosa clase de intolerancia que, desde luego, me hace inepto para la psiquiatría. [...] ¿Me comporto en este caso como los médicos que nos precedieron lo hacían con las histéricas? ¿Es un resultado de la opción por el intelecto afirmada cada vez con mayor claridad, la expresión de una hostilidad hacia el ello?
Si estas declaraciones se toman al pie de la letra y se da crédito al fundador del psicoanálisis, cabría pensar que este solo conviene a sujetos cultos, capaces de soñar o fantasear, conscientes de su estado, deseosos de mejorar su bienestar, de una moralidad por encima de toda sospecha y susceptibles de ser curados en unas cuantas semanas o meses, en virtud de una transferencia o una contratransferencia positivas. Ahora bien, sabemos sin lugar a dudas que la mayoría de los pacientes que acudían a la Berggasse distaban bastante de ajustarse a ese perfil.
En otras palabras, desde comienzo de siglo había una gran contradicción entre las indicaciones de psicoterapia recomendadas por Freud en sus escritos y la realidad de su práctica con los pacientes. Y él era tanto más consciente de ello por el hecho de haber modificado su doctrina al describir, en «Introducción del narcisismo» y _Más allá del principio de placer_ , casos en los que dudaba de toda forma de éxito terapéutico. Y sin embargo, en oposición al nihilismo —pero bajo la presión de las necesidades económicas, y siempre interesado en aceptar desafíos—, tomaba en análisis a personas calificadas de «inanalizables», con la esperanza de lograr, si no curarlas, sí al menos aliviar sus sufrimientos o modificar su condición existencial.
Ya se ha dicho que esos pacientes, maníacos, psicóticos, melancólicos, suicidas, perversos, masoquistas, sádicos, autodestructivos, narcisistas, consultaban a otros especialistas que no obtenían mejores resultados que él. Pero solo Freud fue acusado de todas las ignominias, en vida y más aún después de su muerte: impostor, estafador, codicioso, etc.
Por eso es tan importante estudiar en detalle ciertas terapias psicoanalíticas, algunas de las más desastrosas y algunas de las más satisfactorias. Destaquemos en primer lugar que, de ciento veinte pacientes tratados por Freud —sin distinción de tendencias—, una veintena no sacó beneficio alguno de la cura y alrededor de diez la rechazaron al extremo de odiar al terapeuta. En su mayoría, estos pacientes recurrieron a otras terapias, en idénticas condiciones económicas, y no lograron mejores resultados. Hasta el día de hoy ningún investigador ha sido capaz de decir cuál habría sido el destino de esos pacientes si nunca hubieran hecho nada para tratar sus padecimientos.
A comienzos del siglo fue en Trieste, ciudad portuaria y barroca por entonces bajo la dominación austríaca, y vía de paso entre la _Mitteleuropa_ y la península italiana, donde echó raíces una de las aventuras clínicas más singulares a las que Freud habría de enfrentarse. En octubre de 1908 vio llegar a la Berggasse a un joven estudiante de medicina, Edoardo Weiss, que le profesaba una gran admiración desde su lectura de _La interpretación de los sueños_. Weiss era hijo de un industrial judío originario de Bohemia que había hecho fortuna con el comercio de aceites alimentarios: «Cuando me preparaba para irme», diría a Kurt Eissler,
Freud me preguntó por qué estaba tan apurado. Supuse entonces que estaba contento de conocer a alguien que venía de Trieste. En el pasado él mismo, como se sabe, había estado en la ciudad juliana. Amaba Italia y lo regocijaba la idea de que una persona procedente de Trieste se interesara en sus trabajos. Yo tenía entonces diecinueve años. Una vez terminada la visita, le pregunté cuánto le debía por la consulta, y él, de manera encantadora, me contestó que no aceptaba nada de un colega.
Freud no quería llevar a cabo el análisis de quien iba a ser el introductor de su doctrina en Italia y uno de sus mejores discípulos. Por eso lo derivó para que se formara en el diván de Paul Federn, que llegaría a ser maestro y amigo de Weiss hasta en el exilio americano.
Muy semejantes a los vieneses de la Belle Époque, los intelectuales triestinos se pretendían «irredentistas». Manifestaban no solo una compleja reivindicación de su identidad italiana, sino también un profundo apego a esa cultura europea que los hacía sensibles a todos los grandes movimientos de la vanguardia literaria y artística. En cuanto a los intelectuales judíos desjudaizados y pertenecientes a la burguesía comercial —rica o sin dinero—, aspiraban a una emancipación idéntica a la de los vieneses, y planteaban a la vez una crítica feroz y melancólica de la monarquía de los Habsburgo. En síntesis, se sentían más italianos que austríacos, más judíos que italianos y lo bastante atormentados por sus neurosis familiares para sentirse atraídos por la idea de explorar su subjetividad.
En el mismo momento en que Weiss se comprometía con la causa del psicoanálisis, Italo Svevo —seudónimo de Ettore Schmitz— también se interesaba por la obra freudiana, que en esa época era comentada con pasión por la _intelligentsia_ triestina: un verdadero «ciclón», según Giorgio Voghera. Svevo, también procedente de una familia de comerciantes judíos, se había casado con su prima Livia Veneziani, cuyos acaudalados padres se habían convertido al catolicismo y cuyo hermano, Bruno Veneziani, homosexual, fumador y toxicómano, era un amigo de juventud de Weiss. Mientras entablaba amistad con Umberto Saba, poeta triestino, pronto analizado por Weiss, y con James Joyce, que enseñaba inglés en la Berlitz School de Trieste, Svevo, tan adicto al tabaco como Freud, publicó dos novelas sin conocer el éxito. Y cuando en 1911 conoció a Isidor Sadger, de veraneo en Bad Ischl, lo hizo partícipe de su dependencia de la nicotina.
Bajo la apariencia de la normalidad más grande en su vida profesional de hombre de negocios que dirigía la empresa de sus suegros, en privado Svevo no dejaba de sufrir la invasión de fantasías sexuales y homicidas. Soñaba con devorar a su mujer a pedazos empezando por los botines, se mostraba celoso y excéntrico y pensaba sin cesar en morderle la cara. Así, se parecía a tal punto a un personaje de novela que Joyce se inspiró en él para esbozar su retrato de Leopold Bloom en _Ulises_. También se acordaría de Livia y de su «larga cabellera rubia» en el momento de acometer _Finnegans Wake_.
En cuanto a Olga Veneziani, madre de Livia y de Bruno, parecía directamente salida de un relato de los grandes casos freudianos. Extremadamente nerviosa, odiaba a su yerno, sufría las calaveradas de un marido que la engañaba y «llenaba el mundo de calderas»; estaba tan prendada de su único hijo varón que quería hacer de él un genio: músico glorioso y gran empresario. Por eso Bruno sufrió, desde su infancia, graves convulsiones, por las que lo trataba sin el menor resultado Augusto Murri, una de las eminencias de la medicina positivista de la época. Frente al influjo de esa madre riquísima y afectada por la desmesura, aquel experimentaba un sentimiento de horror y llevaba una vida escandalosa en la que exhibía abiertamente su homosexualidad.
Por consejo de Weiss y su madre, Bruno Veneziani consultó a varios psicoanalistas: Wilhelm Stekel, Isidor Sadger, Rudolf Reitler, Karl Abraham. Luego, entre 1912 y 1914, visitó de tanto en tanto el diván de Freud, que tardó mucho en darse cuenta de que ningún tratamiento acabaría con esas patologías, tan intensamente deseadas por el paciente. El 31 de octubre de 1914, exasperado, afirmó que no había nada que hacer con ese «mal tipo», y Abraham le señaló que el narcisismo de este terrible paciente se sustraía a toda forma de interpretación. Impresionado por el fracaso radical del tratamiento de su cuñado y por las sumas invertidas en su curación, una viva amargura embargó a Svevo, que se forjó la convicción de que la terapia psicoanalítica era peligrosa: es inútil, diría, querer explicar qué es un hombre. Solo la novela vivida como un autoanálisis permitiría, a su juicio, no «tratar la vida», sabiendo que esta es en sí misma una enfermedad mortal.
Veneziani regresó a Trieste mientras Svevo se proponía, en plena guerra, traducir textos de Freud, al mismo tiempo que pensaba en la génesis de una nueva novela que tendría por objeto la historia de una falsa curación psicoanalítica y por tema el tabaquismo de un hombre afectado por el síndrome «del último cigarrillo». ¿Cómo poner fin a una adicción así, como no fuera no tomando jamás la más mínima decisión de deshacerse de ella? Pregunta freudiana por excelencia.
En 1919 Bruno Veneziani, adicto también a la morfina, volvió a emprender a petición de su madre su interminable periplo curativo, en el momento mismo en que Svevo comenzaba a escribir la historia de su doble —Zeno Cosini—, que era también la de Ettore Schmitz y Edoardo Weiss. Y fue entonces cuando este último propuso a Bruno regresar al diván de _Herr Professor_ y participar en las reuniones de la WPV. Pero Freud dio una respuesta negativa a ese proyecto:
Creo que no representa un caso favorable. Le faltan dos cosas: por un lado, un conflicto entre su yo y sus exigencias pulsionales, lo cual hace que esté satisfecho consigo mismo y padezca el antagonismo de circunstancias externas; por otro, le falta un yo más o menos normal y capaz de cooperar con el analista. Sin ello, intenta siempre engañarlo y deshacerse de él mediante el fingimiento. De ahí la existencia en él de un yo narcisista en extremo, refractario a toda influencia y servido, desgraciadamente, por un talento y unos dones personales.
Freud destacaba que Olga no quería soltar a su hijo, y recomendaba enviar al paciente al sanatorio de Baden-Baden. Bruno Veneziani se trasladó de inmediato al lugar, donde, bajo la atención de Groddeck y en tres estancias sucesivas, conoció a un nuevo amante sin renunciar jamás a su toxicomanía. Emigró a continuación a la clínica Bellevue, dirigida por Binswanger, y en ella tuvo la oportunidad de verse frente a los sufrimientos melancólicos de una buena parte de la élite de la _intelligentsia_ europea. Por último, más desdichado que nunca, regresó a Trieste. Internado de manera intermitente en el hospital psiquiátrico, adoptó el papel de un personaje de novela, inepto y decadente, similar al héroe descrito en 1923 por su cuñado en _La conciencia de Zeno_. Desde el fondo de su infelicidad se convirtió entonces en espectador de las grandes catástrofes de Europa, siempre en busca de una imposible alteridad.
Tras la muerte de Olga, que le legó en 1936 la mayor parte de la herencia familiar, el ex paciente de Freud se instaló en Roma para embarcarse en una ilusoria carrera de concertista barroco. Dos años después, justo antes de emigrar, Weiss lo derivó a un colega junguiano, que se hizo cargo de él y le propuso traducir obras del maestro de Zurich. Finalmente, Veneziani encontró la paz con un amante que lo ayudó a escapar de las persecuciones fascistas. Murió en 1952, con «el hígado corroído por los dolores y los venenos», tras haber cedido la mitad de las acciones de la fábrica de la familia para comprar un clavecín.
Apoyado en la historia de esta vida extraviada, que le evitó la experiencia del diván, a pesar de que había soñado con analizarse con Freud, Svevo creó uno de los personajes más fascinantes de la literatura del siglo XX: un antihéroe moderno, Zeno, atormentado por su inconsistencia, su melancolía, su tabaquismo y los absurdos de una vida condenada al fracaso. En síntesis, Svevo fue el primer escritor de su generación en crear de principio a fin un paciente freudiano del primer cuarto del siglo XX, enfermo crónico, enfrentado a un psicoanalista impotente y vengativo —el doctor S.—, obsesionado con la muerte del padre y el poder de las mujeres, que rivaliza con un álter ego suicida y sueña por fin con una grandiosa catástrofe que haga estallar el planeta: «Y otro hombre», escribe, «hecho también como todos los demás, pero un poco más enfermo que ellos, robará ese explosivo y se situará en el centro de la Tierra para colocarlo en el punto donde su efecto pueda ser más fuerte. Habrá una explosión enorme que nadie oirá y la Tierra, tras recuperar la forma de nebulosa, errará en los cielos libre de parásitos y enfermedades».
Como se mantenía deliberadamente al margen de la modernidad literaria, sobre todo cuando esta se inspiraba en su obra, Freud no se interesó nunca en _La conciencia de Zeno_. En cuanto a Weiss, se negó a hacer una reseña de la novela, pese a la petición del autor. Peor aún, treinta años después de la muerte de este seguía afirmando que la novela no reflejaba en absoluto el método psicoanalítico y que él mismo no se parecía al doctor S. Una vez más, como la mayor parte de los psicoanalistas, buscaba en las obras literarias el reflejo de la doctrina freudiana, sin atribuir la menor importancia a la contribución que dicha doctrina había hecho a la renovación de la literatura.
Años después de su muerte Edoardo Weiss fue a su vez la víctima expiatoria de su propio método, cuando algunos comentaristas, armados con la doctrina freudiana, explicaron que su rechazo de la novela se debía a una contratransferencia negativa con Svevo, quien habría cometido el sacrilegio de no respetar su «autoridad paterna».
El destino de Veneziani se asemeja en definitiva a los de Otto Gross, el barón Von Dirsztay, Victor Tausk, Horace Frink y muchos otros, como Carl Liebman. Estos son en cierta forma los antihéroes de la historia de la saga freudiana. Olvidados, rechazados o maltratados por la historiografía oficial, luego revalorizados por los antifreudianos, constituyen una suerte de comunidad maldita que ya ningún historiador puede ignorar, so pena de no comprender en absoluto la complejidad de la aventura freudiana.
Después de 1920 Freud podría haber experimentado una gran felicidad al contemplar el inmenso éxito que el psicoanálisis experimentaba de un extremo a otro del planeta. En esa época era absolutamente evidente que su causa progresaba, y sin embargo la situación apenas lo satisfacía. Todo sucedía como si temiera que, después de haber sufrido el rechazo de sus ideas, ahora solo se las aceptara para deformarlas. ¿Qué hará la «chusma» cuando yo ya no esté vivo?, se decía, pensando en todas las «desviaciones» que los contemporáneos infligían a su doctrina. Como muchos fundadores, Freud pretendía ser el custodio feroz de sus conceptos e invenciones, y corría de tal modo el riesgo de legitimar a los idólatras o los cándidos.
Con ese estado de ánimo recibió en la Berggasse a todos los pacientes procedentes de los países vencedores —y en especial a los norteamericanos—, que le aportaban divisas al acudir a formarse en la profesión de psicoanalista, a la vez que deseaban conocerse a sí mismos. Por más que refunfuñara, Freud estaba sin duda obligado a admitir que esas sesiones francamente realizadas en inglés con discípulos dispuestos a cooperar le planteaban un futuro posible para el psicoanálisis, con el que ni siquiera había soñado. Fue así que se vio forzado a moderar su antiamericanismo y admitir que otras tierras prometidas se abrían a su doctrina: Francia, el Reino Unido, Estados Unidos, América Latina, Japón, etc.
Nacido en Nueva York y perteneciente a una familia de sastres judíos originarios de Ucrania, Abram Kardiner, joven médico de treinta años, viajó a Viena en octubre de 1921 para emprender una cura con Freud, como lo harían en la época varios de sus compatriotas: Adolph Stern, Monroe Meyer, Clarence Oberndorf, Albert Polon, Leonard Blumgart. Apasionado por la antropología y contrario a los dogmas, ya practicaba el análisis tras una primera cura que consideraba insuficiente, en el diván de Horace Frink.
Durante seis meses contó a Freud la historia de sus padres, emigrantes pobres que huían de las persecuciones antisemitas: la llegada a la isla Ellis, la búsqueda de un empleo, la muerte de su madre enferma de tuberculosis cuando él tenía tres años, las oraciones pronunciadas en una lengua que él no conocía, el miedo al paro, el hambre y, después, la entrada en escena de una nueva mamá, llegada de Rumanía y que había suscitado en él un intenso deseo sexual. Kardiner habló de su afición a la música, del descubrimiento de su judeidad, de la lengua yiddish y del antisemitismo, de su deseo de ser un gran «doctor» y de su interés por las comunidades minoritarias —indios, irlandeses, italianos—, ese famoso _melting pot_ que no dejaba de tener semejanza con el de la _Mitteleuropa_.
Kardiner evocó también sus recuerdos de adolescente. Su madrastra padecía una malformación del útero que le impedía tener más hijos, cosa que a él le alegraba. En cuanto a su padre, recordó que antaño había insultado y golpeado a su madre, con quien se había casado sin amarla. Por eso Abram había guardado en la memoria el recuerdo de esa mujer desdichada que lo había traído al mundo sin disfrutar de tiempo para criarlo. Bajo la influencia de su segunda madre adorada, el padre del paciente había podido llegar a ser un verdadero esposo dedicado a su familia. Tras amores difíciles con una muchacha, seguidos de un estado depresivo, Kardiner se había sumergido en los estudios de medicina, pasando así del estatus de hijo de un sastre judío naturalizado norteamericano al de brillante intelectual seducido por el psicoanálisis y el culturalismo. Sufría no obstante una fuerte angustia, que lo hacía frágil en todos los acontecimientos de su vida.
Contó a Freud dos sueños. En el primero veía a tres italianos que, con el pene erecto, le orinaban encima, y en el segundo se acostaba con su madrastra. Kardiner era sin lugar a dudas un «paciente freudiano» ideal, inteligente, capaz de soñar, afectado por una neurosis fóbica y una fijación amorosa con una madrastra sustituta de una madre víctima de un padre perseguido, que antes de emigrar había hecho un matrimonio concertado. Pero él deseaba simplemente esa experiencia con el maestro vienés, sin manifestar por él la más mínima idolatría. Si bien lo admiraba, discutía con franqueza sus interpretaciones.
No fue ese el caso de Clarence Oberndorf, en tratamiento al mismo tiempo que Kardiner, y fundador con Brill de la New York Psychoanalytic Society (NYPS). Freud lo despreciaba y lo consideraba estúpido y arrogante. Sin embargo, Oberndorf le era mucho más fiel que Kardiner, aunque tuviera muchas reservas —con toda la razón— con respecto a la manía de los psicoanalistas de buscar «escenas primordiales» por todas partes. Y ya estimaba que las curas a la antigua habían dejado de servir en los tiempos modernos.
El primer día de su análisis contó un sueño en el cual lo llevaban a un destino desconocido en una calesa tirada por dos caballos, uno negro y otro blanco. Freud sabía que su paciente, nacido en Atlanta y perteneciente a una familia sudista, había tenido en su infancia una nodriza negra por la cual sentía mucho afecto. Por eso dio de entrada a ese sueño una interpretación inapelable: Oberndorf no conseguiría casarse porque era incapaz de decidirse entre una mujer blanca y una mujer negra. Fuera de sí, el paciente discutió durante varios meses ese sueño con Freud y Kardiner. Se sentía aún más humillado por el hecho de ser ya un analista curtido, formado en el diván de Federn y avezado, él mismo, en la interpretación de los sueños. Según Kardiner, permaneció soltero y Freud no dejó de despreciarlo.
Freud tenía motivos para sentirse mucho más feliz con Kardiner que con Oberndorf. Como una profetisa danubiana, le explicó que se había identificado con la desdicha de su madre —lo cual testimoniaba una «homosexualidad inconsciente»—, que los tres italianos de su sueño representaban a su padre, por quien se sentía humillado, y que la ruptura con su prometida repetía un abandono primordial que nunca más se produciría porque él se había recuperado por sí solo. En relación con otro sueño, Freud interpretó que Kardiner deseaba seguir sometido a su padre para no «despertar al dragón dormido». Se equivocaba en dos aspectos —la homosexualidad inconsciente y la sumisión al padre—, y el paciente se dio cuenta.
Al cabo de seis meses Freud consideró que Kardiner estaba muy bien analizado y le pronosticó una magnífica carrera, un éxito económico excepcional y un dichoso destino en su vida amorosa: había visto bien. En 1976, apartado del dogmatismo psicoanalítico y en disidencia tanto con el edipismo generalizado como con las interpretaciones canónicas sobre la homosexualidad reprimida o la ley del padre, Kardiner recordó con deleite el tiempo pasado en la Berggasse:
Hoy, que tengo una perspectiva de conjunto, diría que Freud llevó a cabo un brillante trabajo con mi análisis. Si era un gran analista, es porque jamás utilizaba expresiones teóricas —al menos en esa época— y formulaba sus interpretaciones en un lenguaje corriente. Con la excepción de su referencia al complejo de Edipo y al concepto de homosexualidad inconsciente, trataba el material sin separarlo de la vida cotidiana. En cuanto a su interpretación de los sueños, era excepcionalmente penetrante e intuitiva.
Y añadía, con respecto al error de Freud acerca del «dragón dormido»: «El hombre que había inventado el concepto de transferencia no sabía reconocerlo cuando se presentaba. Se le había escapado una sola cosa. Sí, por supuesto, yo le tenía miedo a mi padre cuando era pequeño, pero en 1921 el hombre al que temía era Freud en persona, que podía darme la vida o destruirla, cosa que ya no sucedía con mi padre».
Lo que realza el interés de este testimonio es el hecho de que Kardiner había viajado a Viena porque juzgaba insuficiente su análisis con Frink. Ignoraba, de todos modos, que el tratamiento de este con Freud había sido muy difícil. Había notado la agresividad de Frink, sí, pero no había discernido en él signos de psicosis. Más dogmáticamente freudiano que el propio Freud, Frink había interpretado como un deseo de muerte edípica la relación de Kardiner con su padre: «Usted estaba celoso de él y celoso de que poseyera a su madrastra», le había dicho. Y esta interpretación errónea había inducido en Kardiner un recrudecimiento de la angustia y el anhelo legítimo de poner fin a la terapia psicoanalítica. Sin tratar de perjudicar a Frink, Freud la invalidó. Pero al final del análisis confió sus temores a Kardiner. Los problemas terapéuticos ya no le interesaban, dijo: «Actualmente me impaciento demasiado. Padezco una serie de discapacidades que me impiden ser un gran analista. Entre otras, soy excesivamente padre. Y me ocupo en demasía de la teoría».
En abril de 1922, cuando Kardiner afirmó delante de él que el psicoanálisis no podía perjudicar a nadie, Freud le mostró dos fotografías de Frink, una tomada antes de su análisis (octubre de 1920) y otra, un año después. En la primera, Frink se parecía al hombre que Kardiner había conocido, mientras que en la otra tenía un aspecto azorado y demacrado. ¿Era realmente la experiencia del diván la que había provocado esa metamorfosis? Kardiner dudaba de ello mucho más que Freud, que nunca logró liberarse de la pesadilla de esa cura trágica en la que se entremezclaban relaciones conyugales, adulterio, endogamia psicoanalítica y error de diagnóstico.
Nacido en 1883, Horace Westlake Frink no era ni judío, ni hijo de inmigrantes europeos, ni rico, ni neurótico. Dotado de una inteligencia excepcional, había comenzado muy tempranamente a estudiar psiquiatría para ser psicoanalista. Víctima desde su juventud de una psicosis maníaco depresiva, había estado en análisis con Brill y luego se incorporó a la NYPS, antes de publicar, algunos años más tarde, un verdadero best seller que contribuyó a incrementar aún más la popularidad del freudismo del otro lado del Atlántico. En 1918 era ya uno de los psicoanalistas más reputados de la costa Este, sin que dejara de sufrir, empero, crisis maníacas y melancólicas con delirios y obsesiones suicidas. Repartía su vida entre su esposa legítima, Doris Best, con quien había tenido dos hijos, y su amante, Angelika Bijur, su ex paciente, una riquísima heredera casada con Abraham Bijur, un ilustre jurista norteamericano analizado por él y luego por Thaddeus Ames.
Presionado por su amante que lo instaba al divorcio, Frink se trasladó a Viena para emprender una psicoterapia con Freud a fin de decidir cuál sería la mujer de su vida. A su vez, Angelika (Angie) consultó al mismo Freud, que le aconsejó divorciarse y casarse con Frink; de lo contrario, este corría el riesgo de hacerse homosexual de una manera más o menos disimulada. Y, del mismo modo, diagnosticó en su paciente una homosexualidad reprimida. En realidad, estaba encandilado por ese hombre brillante a quien calificaba de «muy amable muchacho, cuyo estado se estabilizaría con un cambio de vida». Y lo alentó a reemplazar a Brill.
Para Frink era imposible aceptar semejante diagnóstico. Sin embargo, cegado por el influjo que ejercía sobre _Herr Professor_ , tomó la decisión de abandonar a Doris y casarse con Angie. Escandalizado por ese comportamiento, que juzgaba contrario a toda ética, Abraham Bijur redactó un borrador de carta abierta para el _New York Times_ , en el cual trataba a Freud de «gran doctor impostor». Entregó una copia a Thaddeus Ames y este la envió a Freud junto con un comentario sobre la peligrosa situación en que se vería la NYPS si la prensa la publicaba. En una carta a Jones, que intentaba apagar el incendio, Freud afirmó que Angie había entendido mal sus palabras. Señaló no obstante —y ese era su pensamiento profundo— que la sociedad toleraba mejor el adulterio que el divorcio entre dos personas desdichadas en pareja pero deseosas de volver a casarse. Una manera de confesar que, en efecto, había empujado a Horace y Angie al divorcio, toda vez que, en su opinión, ya no se entendían con sus respectivos cónyuges.
En otras circunstancias Freud tomaba decisiones diferentes, sobre todo cuando tenía la convicción de que un adulterio no era más que el síntoma de un problema no resuelto con un cónyuge al que todavía se amaba. En síntesis, así como condenaba el adulterio, también favorecía las «buenas separaciones», con la condición de que resultaran en un nuevo matrimonio. En lo tocante a este asunto, se equivocaba gravemente con Frink. Y perseveró en el error al enviarle una carta insensata:
He exigido a Angie que no repita a extraños el consejo que le he dado: casarse con usted porque usted corría el riesgo de sufrir una descompensación nerviosa. [...] ¿Puedo sugerirle que su idea de que ella ha perdido una parte de su belleza podría transformarse en la idea de la adquisición de una parte de su fortuna? Usted se queja de no comprender su homosexualidad, lo cual implica que no es consciente de su fantasía de hacer de mí un hombre rico. Si todo resulta bien, convirtamos ese obsequio imaginario en una contribución real al fondo psicoanalítico.
Como todos sus discípulos, Freud contribuía a la financiación del movimiento psicoanalítico. Y en este aspecto no es de sorprender que haya sido capaz de plantear la idea de que Frink también podía participar en ese financiamiento mediante una donación, a fin de sanar de sus fantasías. En cuanto a la interpretación de que una mujer que a ojos de su amante ha perdido su belleza pueda ser deseada por su fortuna, suponía una concepción tradicional de la familia burguesa. Freud, en consecuencia, se comportaba con su paciente como una suerte de casamentero paternal a la antigua, y confundía así diván y asesoramiento conyugal. Prueba de que no había comprendido nada de la locura de Frink, a quien tomaba por un neurótico inteligente que reprimía su homosexualidad enfocada en el padre. Una vez en libertad de casarse con su amante, aquel experimentó un pavoroso sentimiento de culpa y volvió una vez más a Viena en noviembre de 1922. En el transcurso de un episodio delirante se imaginó metido en una tumba, y durante las sesiones no hacía más que dar vueltas frenéticas en círculo, a tal punto que Freud tuvo que contratar a un médico, Joe Asch, para que lo cuidara y lo vigilara en su hotel. La situación empeoró cuando Doris murió a raíz de una neumonía tras la boda de su ex marido con Angie. Frink afirmó entonces que amaba a su primera mujer y comenzó a violentar a la segunda.
En mayo de 1924 Freud se vio obligado a desautorizar a su paciente y declararlo enfermo mental e inepto para dirigir la NYPS:
Yo había depositado todas mis esperanzas en su persona, a pesar de la naturaleza psicótica de sus reacciones en el transcurso del análisis [...]. Cuando vio que no estaba autorizado a satisfacer libremente sus deseos infantiles, se derrumbó. Sucedió lo mismo en la relación con su nueva esposa. Con el pretexto de que era imposible tratar con ella en las cuestiones de dinero, él no recibió todos los signos de afecto que no dejaba de reclamarle.
Internado a petición propia en la clínica psiquiátrica del hospital Johns Hopkins de Baltimore, y puesto bajo los cuidados de Adolf Meyer, Frink se enteró de que Angie quería separarse de él. Tras una vida hecha de alternancias entre la exaltación y la melancolía, murió olvidado en 1936.
Cuarenta años después, su hija, Helen Kraft, encontró en los papeles de Adolf Meyer la correspondencia de su padre con Freud, así como varios documentos cuyo contenido hizo público, a la vez que acusaba de impostor al maestro de Viena. Los partidarios del antifreudismo aprovecharon entonces para sostener que Freud había manipulado a todos sus pacientes, quienes, según ellos, habían sido víctimas de las perfidias de su doctrina. En cuanto a los psicoanalistas, siguieron ignorando tranquilamente los errores clínicos del maestro idolatrado.
Tras este episodio el aborrecimiento que Freud sentía por Estados Unidos y los estadounidenses se intensificó, lo que le valió una áspera y lúcida respuesta de Jones:
Me acuerdo de estas palabras de Pitt: no se incoa un proceso a una nación. Son seres humanos, con las mismas potencialidades que otros. [...] Dentro de cincuenta años serán los árbitros del mundo, de modo que es imposible ignorarlos. Sea como fuere, perseveraré en mis esfuerzos por consolidar allí la implantación aún discreta del psicoanálisis.
Durante esos años, en el barrio londinense de Bloomsbury, se reunía la élite inconformista de la literatura, las ciencias, la economía y las artes alrededor de Virginia Woolf, Lytton y James Strachey, Dora Carrington, John Maynard Keynes y Roger Fry. Animados de una voluntad feroz de desterrar el espíritu victoriano y poner fin a las guerras imperiales, los miembros de esa élite habían rechazado por objeción de conciencia toda participación en la gran carnicería de las trincheras y proclamaban su deseo de transformar las costumbres de la sociedad británica, instaurar la igualdad entre hombres y mujeres, combatir el imperialismo y moderar los ardores mercantiles del capitalismo.
Por eso defendían, tanto a través de sus prácticas sexuales como en sus escritos, una nueva concepción del amor capaz de provocar la expansión, sin reprimirlas, de todas las llamadas tendencias «naturales» de la persona, y en particular la homosexualidad y la bisexualidad. Pertenecientes a la burguesía intelectual inglesa y formados en las mejores universidades del reino —el Trinity College en Cambridge—, los _Bloomsburies_ admiraban la obra freudiana, consideraban el puritanismo como una amenaza para la civilización y pretendían oponerse a él por medio de un ideal ético y estético fundado tanto en el liberalismo como en el socialismo. En el corazón de esa bella modernidad crítica surgió, con el apoyo de Jones, la escuela inglesa de psicoanálisis, contemporánea del nacimiento del posimpresionismo.
En 1917 Leonard y Virginia Woolf habían fundado la que sería una prestigiosa editorial, la Hogarth Press, destinada a dar a conocer a los autores que ellos estimaban. Un año después Lytton Strachey publicaba en esa editorial su biografía de cuatro victorianos eminentes, considerados como héroes en cada uno de sus ámbitos: Florence Nightingale, Thomas Arnold, Charles Gordon y Edward Manning. Pero los describía bajo una luz sombría para poder criticar, a través de su acción, los aspectos negativos de la política victoriana: evangelismo corto de miras, colonialismo, sistema educativo represivo, humanitarismo egoísta. Strachey reivindicaba, por otra parte, el derecho del escritor a interpretar libremente los hechos e introducir en el relato una escritura del yo. En ese sentido, renovaba el arte biográfico en una perspectiva intimista que no estaba lejos de la del psicoanálisis.
Además, Lytton Strachey se interesaba tanto en Freud como en la vida atormentada de los héroes de la monarquía inglesa. Y por eso, después de escribir una sátira de los victorianos eminentes, consagró dos obras a la vida amorosa de dos grandes reinas: Isabel I y Victoria. Ambas tenían como punto en común el hecho de haberse dejado dominar, al final de su vida, por amantes cuya existencia misma implicaba una contradicción con el ideal que había marcado su reinado.
Es sabido que durante más de diez años, de 1587 a 1601, Isabel sintió una pasión arrolladora por su muy joven primo, Robert Devereux, conde de Essex, que no cesó de imponerle la idea de que los más altos cargos del Estado le correspondían a él. Para tener mayor ascendiente sobre esa reina que envejecía y era víctima de oscuros tormentos sexuales, Devereux la provocaba, la amenazaba, se retiraba abruptamente en su castillo y expresaba rencor y amargura, para obtener su perdón y volver con los mismos hechizos. Para terminar de una vez con tantas locuras, que amenazaban hundir el reino en la anarquía, Isabel, carcomida por la pena y los sufrimientos, lo hizo asesinar sin aceptar jamás una relación carnal con él. En su libro, Strachey trazaba un cuadro de los misterios de la era barroca y de la implacable voluntad isabelina de encarnar una imagen perfecta, conforme a su leyenda, en vez de rebajarse a ser una mujer común y corriente.
De igual modo, se dedicaba a describir la pasión experimentada por Victoria, tras la muerte del príncipe Alberto, por el antiguo escudero de este, James Brown. Transgrediendo sus propios códigos, la reina había hecho de este favorito brutal y vulgar el instrumento de su revancha contra un reinado que, según su voluntad, debía mantener las apariencias de la mayor perfección.
En cuanto a Keynes, que llegaría a ser uno de los más grandes economistas del siglo XX, tenía en común con Freud, no la memoria invertida de las dinastías heroicas, sino un franco aborrecimiento por el Tratado de Versalles. Miembro de la delegación inglesa en el momento de las negociaciones de París, se había rebelado contra la política francesa consistente en humillar a Alemania. En 1919 escribió un panfleto para denunciar esa «paz cartaginesa» y profetizar que sus consecuencias serían desastrosas para Europa, y sostener que el tratado provocaría un resentimiento popular incontrolable en el mundo germanoparlante y en el corazón de los imperios desintegrados. No se equivocaba.
James Strachey, el hermano de Lytton, deseaba desde hacía tiempo viajar a Viena para formarse en el diván de _Herr Professor_ a fin de ser psicoanalista. Pero, poco adinerado, no podía abonar por su cura los mismos honorarios que los psiquiatras norteamericanos. Por eso pidió a Jones que intercediera en su favor, cosa que este último hizo de inmediato. Deseoso de desplegar una política de conquista en la otra orilla del Atlántico, Jones tenía conciencia, por un lado, de que Freud nunca se entendería con sus discípulos norteamericanos, y por otro, de que el movimiento inglés era capaz de erigirse en un útil contrapeso a la futura potencia estadounidense.
En su opinión, Strachey era pues la persona indicada. Inteligente, culto, refinado, cáustico, tolerante, alejado de todo espíritu mercantil, despojado de pragmatismo y ya comprometido en una causa intelectual de la que el psicoanálisis formaba parte, no estaba a la búsqueda, a los treinta años, de un padre de reemplazo con el cual pudiera rivalizar, ni de un hermano que lo dominara, ni de una madre que se pareciera a su hermana, ni del sustituto de una nodriza posesiva. Tampoco era presa de una homosexualidad reprimida. Para terminar, no era ni judío ni inmigrante y no lo movía una voluntad de revancha social o psíquica. En síntesis, no tenía otro deseo que poner el talento de su pluma al servicio de una aventura espiritual que juzgaba excepcional. Bisexual declarado, enamoradizo de muchachos que parecían mujeres y de mujeres con apariencia de varón, no padecía ninguna patología en especial y había recibido una notable educación dentro de una sorprendente familia atípica en la que se cultivaba el amor por los libros y las libertades. A lo sumo, mostraba un síntoma permanente de indecisión y una elocución difícil ligada a «cierto» cansancio de existir.
En 1920 se casó con Alix Sargant-Florence, que terminó por ser su compañera de toda la vida. También ella provenía de una familia inconformista. Su madre, feminista comprometida y viuda al nacer Alix, la había alentado a estudiar, y fue en el Newnham College de Cambridge donde ella descubriría la obra freudiana. Desde la infancia se negaba a usar ropa femenina y a los veinte años, después de atravesar un período de anorexia mental, experimentó su primera crisis melancólica.
Cuando conoció a James se enamoró locamente; él, por su parte, la consideró deliciosa: «un verdadero varón», escribía. De viva inteligencia, Alix intentaba siempre disimular su estado detrás de un velo de risas, detalle que no escapó a Virginia Woolf, a quien le gustaba compararla con una «desesperación sepulcral». Como James, ella sufría de cierta incapacidad para escoger la actividad de su gusto, pero también padecía estados depresivos y crisis de palpitaciones. Quería participar en la causa psicoanalítica.
En agosto de 1920 James y Alix se instalaron en Viena, y en octubre James comenzó su análisis con Freud:
Todos los días, salvo el domingo, paso una hora en el diván de Freud [...], un hombre muy afable y un artista asombroso. Cada sesión se construye prácticamente como un todo orgánico y estético. A veces los efectos dramáticos son desconcertantes y hasta estrepitosos [...]. Sentimos que en nuestro interior suceden cosas terribles y no logramos saber de qué se trata; Freud, entonces, da una pequeñísima indicación y algo se aclara, captamos otra cosita y al final toda una serie de fenómenos se tornan más claros; nos hace una pregunta más, le damos una última respuesta, y mientras toda la verdad se nos devela de tal modo, él se levanta, atraviesa la habitación hasta el timbre y nos acompaña a la puerta [...]. Hay otros momentos en que uno permanece tendido durante toda la sesión con un peso enorme en el estómago.
Es evidente que Freud no se comportaba de la misma manera con Strachey que con sus pacientes norteamericanos. Abram Kardiner se percató de ello cuando habló de su terapia psicoanalítica con él y con John Rickman, que también se analizaba con el profesor. Freud hablaba mucho con los norteamericanos y muy poco con los ingleses. Y Kardiner, con humor, dedujo que esa actitud había dado origen a la escuela inglesa de psicoanálisis: «El analista no abre la boca salvo para decir "buenos días" y "hasta la vista". Y así durante cuatro, cinco o seis años». Rickman, por su parte, tuvo la impresión de que el silencio de Freud y sus «ausencias» se debían a su enfermedad. Versado en arqueología, señaló además que había comprado algunas estatuillas falsas y que no distinguía bien los objetos griegos de los egipcios.
El testimonio de Kardiner sobre las sesiones silenciosas e interminables, típicas de la década de 1950, no corresponde a la experiencia vienesa de los años veinte. Y hay que pensar más bien que Freud no necesitaba asestar tal o cual interpretación a Strachey y que Rickman le resultaba sencillamente antipático.
_Herr Professor_ no tuvo la curiosidad de interesarse en la obra de Virginia Woolf, pero admiraba la de Lytton Strachey y estaba impresionado con James. En cuanto a Alix, si bien no tenía la intención de analizarse, con motivo de una de sus «crisis» pidió a James que organizara una cura de a tres, cosa contraria a la ética misma del psicoanálisis. No obstante, interesado en las reacciones y contrarreacciones generadas por esa experiencia, Freud decidió analizar simultáneamente a Alix y James. En el invierno de 1922 los declaró aptos para la práctica, pero aconsejó vivamente a Alix que consultara a Abraham. Sabia decisión: Abraham era por entonces uno de los mejores clínicos de la melancolía.
Algunas semanas después de ese análisis, que iba a extenderse, con interrupciones, hasta el invierno de 1922, Freud propuso a Strachey la traducción de varias de sus obras: «En los Strachey», escribe Meisel,
encontró la encarnación perfecta de lo que Inglaterra, su país preferido, significaba para él. Veía en ellos la sensibilidad adecuada para traducir su obra a la única lengua, además del alemán, con la cual se sentía en armonía. Era la lengua de su poeta favorito, Milton, una lengua embellecida por la urbanidad chirriante del esteticismo contemporáneo.
Ayudado por Alix, James encontró por fin su camino para realizar la gran obra de su vida: la traducción completa de la obra de Freud al inglés, la futura _Standard Edition_. Tal fue pues el éxito de ese análisis fundado en una transferencia a la lengua de Freud más que a su persona. El objetivo de Strachey, su cultura, su formación, su adhesión al espíritu de los _Bloomsburies_ , coincidían además con el ideal de Freud, que había querido ser a la vez escritor y hombre de ciencia.
Las primeras traducciones realizadas por Brill eran mediocres; por otra parte, antes de conocer a Strachey, Freud solo se había preocupado de difundir sus ideas en el extranjero, sin prestar demasiada atención a la manera como un traductor pudiera encarnar su estilo, trasladar sus conceptos o establecer un verdadero aparato crítico con notas, bibliografía científica, fuentes y remisiones. James comenzó por publicar en la Hogarth Press tres volúmenes de _Collected Papers_ , y fue Jones quien, a continuación, tuvo la idea de llevar a cabo la edición completa y hacer que las sociedades psicoanalíticas norteamericanas financiaran el trabajo, sin dejar de poner la empresa bajo la égida de Gran Bretaña.
Consciente de que el movimiento psicoanalítico norteamericano estaba destinado a ganar amplitud, Jones —ya lo hemos dicho— tenía la inquietud de fortalecer el poderío inglés. En 1919 había fundado la British Psychoanalytical Society (BPS) para sustituir a la antigua London Psychoanalytic Society (LPS) creada en 1913, y a posteriori reunió a su alrededor a muchos adeptos, entre ellos Barbara Low, John Rickman, Sylvia Payne, Joan Riviere, Ella Sharpe y Susan Isaacs. En 1920 publicó el primer número del _International Journal of Psychoanalysis_ ( _IJP_ ), primera revista de psicoanálisis en inglés, que se convertiría en el órgano oficial del Verein y, después, de la International Psychoanalytical Association (IPA).
Con el propósito de honrar la obra de Freud, Strachey jamás fue servil. Su trabajo reflejaba sus propias orientaciones. Así, tendió a hacer caso omiso de todo lo que asociaba el texto freudiano al romanticismo alemán y la _Naturphilosophie_ , para privilegiar su aspecto médico, científico y técnico. Esa decisión se expresó en la elección de algunas palabras latinas y griegas, por un lado, y en cierta «anglización», por otro. De tal modo, para traducir el ello ( _Es_ ), el yo ( _Ich_ ) y el superyó ( _Überich_ ), utilizó los pronombres latinos _id_ , _ego_ y _superego_ , mientras que para investidura ( _Besetzung_ ) y acto fallido ( _Fehlleistung_ ) recurrió a términos griegos: _cathexis_ , _parapraxis_. Para terminar, cometió el error de traducir pulsión ( _Trieb_ ) como _instinct_ , con el pretexto de que el término _drive_ (trayecto, conducción) —adoptado a continuación— no era conveniente.
Strachey contribuyó de tal manera a acentuar el irreversible proceso de anglofonización de la doctrina freudiana. Su traducción nunca dejó de ser objeto de críticas —injustas, además—, que tuvieron su ejemplo más virulento en Bruno Bettelheim, también él convertido en angloparlante a raíz de su emigración a Estados Unidos. En 1982, en una obra que gozó de gran repercusión, _Freud y el alma humana_ , Bettelheim reprochó a Strachey haber privado al texto freudiano de su «alma alemana» y su «espíritu vienés».
En tanto que James volvía a Londres para emprender otro tratamiento con James Glover y empezar a trabajar como psicoanalista, Alix, que acababa de curarse de una neumonía contraída en Viena, se instalaba en Berlín. Durante un año tuvo todo el tiempo libre para descubrir, maravillada, otra manera de practicar el psicoanálisis. La sociedad fundada por Abraham estaba entonces en «el apogeo de su espléndida decadencia» y la ciudad imperial brillaba aún con todas sus luces antes de la catástrofe de 1933. En ella Alix conoció a la élite del movimiento psicoanalítico germanoparlante, cuyos miembros iban a emigrar pronto a Estados Unidos u otros lugares: Hanns Sachs, Sándor Rado, Franz Alexander, Otto Fenichel, Felix y Helene Deutsch, Hans Lampl, Karen Horney, Ernst Freud. Y aprendió a reconocer las ambivalencias de esa ciudad donde se codeaban las ideas más nuevas y las intolerancias más bárbaras, entre levedad, erupción fratricida y ciénaga relumbrante. En los cafés y los cabarets uno se cruzaba entonces con Bertolt Brecht, George Grosz y toda clase de artistas audaces en busca de nuevas maneras de vivir y pensar.
Alix aprendió a hablar alemán perfectamente, descubrió lo numerosos que eran los judíos en el medio psicoanalítico y saboreó los placeres de las fiestas y el teatro. Un día conoció al célebre doctor Fliess, encantador y anticuado, con su aspecto de enano y su abultado vientre. Había cambiado muy poco, y le preguntó si algún miembro de su familia había muerto en esa época del año, único modo de explicar, a su entender, por qué ella tenía fiebre e inflamación de las amígdalas.
Pero fue al conocer a Melanie Klein, radicada en Berlín desde 1921 y en análisis con Abraham, después de haber pasado por el diván de Ferenczi, cuando Alix tuvo la revelación de lo que podía ser la profundidad clínica del psicoanálisis. Ella, que no quería tener hijos, comprendió muy rápidamente que las conferencias y ponencias de Klein sobre el análisis de niños pequeños, la relación arcaica con la madre o la precocidad del complejo edípico trastocaban la perspectiva freudiana clásica al permitir una comprensión más temprana de la génesis de las neurosis y las psicosis. En tanto que Freud afirmaba que un varón de tres años no tenía conciencia alguna de la existencia de la vagina, Melanie Klein sostenía, al contrario, sobre la base de sus observaciones, que todo niño varón deseaba introducir su pene en la vagina de su madre. En otras palabras, si para Freud el niño era un ser narcisista y salvaje, que recorría «estadios» y a quien era preciso educar, para Klein estaba más cerca del caníbal sádico que busca copular con su madre y está sumido en un mundo interior tejido de fantasías, odio, locura y angustia.
En el octavo congreso del IPV, celebrado en Salzburgo en abril de 1924, Melanie Klein presentó una ponencia sobre el análisis de los niños pequeños en la que afirmaba que la preferencia marcada por el padre del otro sexo aparecía en el segundo año, y que la madre era percibida a partir de entonces como terrorífica y castradora. Había hecho esos «descubrimientos» al analizar a sus propios hijos. Separada de su marido, muy pronto enroló a su hija Melitta en su pasión por la causa psicoanalítica. Por entonces, la muchacha estudiaba medicina con el objeto de ser psicoanalista. En Berlín frecuentaba el diván de las voces cantantes del movimiento —Hanns Sachs, Max Eitingon, Karen Horney— y, a la vez, se sentía odiada por su madre, quien, en efecto, la veía ya como una rival. Fue en esa ciudad donde conoció a Walter Schmideberg, psicoanalista vienés culto, alcohólico y homosexual, formado en las filas de la WPV, con quien luego se casaría. Las relaciones ulteriores de Melanie y su hija son una de las páginas más dolorosas de la historia del psicoanálisis.
Por el momento, Alix admiraba el encanto de Melanie, su erotismo, su potencia verbal, esa determinación que, sin embargo, disimulaba un fuerte sufrimiento melancólico. A través de ella, y sin conocer bien su historia, Alix descubrió que las mujeres podían tener un lugar igual a los hombres en la elaboración de las teorías psicoanalíticas. Desde Berlín tomó por tanto distancia con Viena y soñó con ayudar a Melanie a ser inglesa, así como James, en la época, se obstinaba en hacer de Freud un científico británico. Después de facilitar su incorporación a la BPS, Alix sería la traductora de Klein.
Entretanto, en Berlín, daba cursos de inglés. El 31 de enero de 1925, Melanie, disfrazada de Cleopatra, la arrastró a un baile de máscaras organizado por los socialistas. Las dos mujeres bailaron toda la noche. Quince días después la «policlínica» celebraba su quinto aniversario bajo la batuta de Max Eitingon, y todos tuvieron entonces la impresión de que el movimiento psicoanalítico estaba firmemente arraigado, y lo estaría mucho tiempo, en el corazón de la ciudad berlinesa. Sin embargo, el 25 de diciembre murió Abraham, a los cuarenta y ocho años, a raíz de una septicemia desencadenada por un absceso sin duda causado por un cáncer. Melanie ya había partido con Alix hacia Inglaterra. Abatido, Freud perdía a uno de sus más fervientes discípulos. Para esa fecha John Rickman ya había organizado en Londres un instituto de psicoanálisis conforme al modelo de su par de Berlín. Así, el movimiento psicoanalítico inglés estaba cobrando una considerable amplitud en el momento mismo en que los berlineses todavía se veían, frente a los vieneses, como la vanguardia del freudismo europeo.
Así como Freud no comprendía nada de la modernidad literaria que se inspiraba en su descubrimiento, también ignoraba el nuevo arte del siglo, el cinematógrafo, que había nacido al mismo tiempo que el psicoanálisis. Y sin embargo, había una gran proximidad entre los modos de enfocar el inconsciente que uno y otro ponían en práctica. Convencido de que su doctrina no debía en ningún caso popularizarse por ese medio, Freud creía que solo la palabra podía dar acceso al inconsciente. Nueva contradicción: ¿no había afirmado él mismo que el sueño era un viaje a un más allá de la razón? Un viaje visual tramado de hablas y palabras. En realidad, desconocía tanto el arte cinematográfico como el gran movimiento expresionista, que afirmaba su voluntad de expresar, mediante colores violentos o líneas de fractura, una visión de la subjetividad atormentada, pulsional, violenta, caótica, atravesada por un imaginario fantástico.
Es cierto, puede entenderse que Freud se haya negado a prestar su apoyo, por la suma de cien mil dólares, al proyecto de Samuel Goldwyn de realizar una película sobre amores célebres. Pero cuando Hans Neumann, a mediados de los años veinte, invitó a Hanns Sachs a participar en la escritura del guión de _Misterios de un alma_ [ _Geheimnisse einer Seele_ ], que debía filmar Wilhelm Pabst, cineasta de origen austríaco, Freud adoptó la misma actitud, a pesar de que se trataba de un proyecto muy distinto. Sostuvo que las abstracciones de su pensamiento no podían representarse de manera plástica. No advertía hasta qué punto el cine mudo en blanco y negro había invadido ya el dominio del sueño con sus sobreimpresiones, su técnica del fundido encadenado, sus subtítulos, sus movimientos de cámara capaces de abolir el pasado y el presente, de deslizarse de un decorado a otro, de un rostro a otro, e incluso de representar escenas primordiales, reminiscencias, objetos extraños, y ligar a la vez la alucinación a una realidad sabiamente reconstruida.
Obra maestra del cine expresionista, _Misterios de un alma_ se realizó pues sin la aprobación de Freud y sin despertar siquiera en él el más mínimo interés. Werner Krauss, actor ya de renombre, interpretaba el papel del profesor Matthias, un hombre obsesionado por sus deseos de asesinar con sables y cuchillos, y curado por el psicoanálisis. Se trataba del primer filme inspirado en las tesis freudianas. Hanns Sachs había redactado un opúsculo, «El enigma del inconsciente», que funcionó como instrucciones de uso para la película, y su nombre figuraba en los créditos junto al de Karl Abraham. Los dos habían hecho caso omiso de la desaprobación de Freud, que se quedó con las manos vacías, reducido a confesar a Ferenczi su hostilidad al mundo moderno: no le gustaban, le dijo entonces, ni el cine ni las mujeres peinadas _à la garçonne_.
El 25 de marzo de 1925, fecha del estreno en la gran sala del cine Gloria Palast de Berlín, la prensa recibió el filme con entusiasmo:
Imagen tras imagen descubrimos el pensamiento de Freud. Cada rodeo de la acción podría ser una de las proposiciones del hoy tan célebre análisis de los sueños. [...] Los alumnos de Freud pueden regocijarse. Nada en el mundo sería capaz de hacerles publicidad con tanto tacto. Pero también puede estar orgullosa la gente del cine alemán.
Cuando Jones asistió a una proyección de la película en Berlín, la consideró nociva para el psicoanálisis, sin pronunciar siquiera el menor juicio sobre su calidad estética. Lamentaba que en Nueva York pudieran imaginar que Freud había dado su consentimiento a la empresa, origen de una nueva controversia entre vieneses y berlineses. En su biografía de Freud, Jones ni siquiera menciona el nombre de Pabst. En lo sucesivo, las relaciones entre los herederos de Freud y los cineastas siempre serían pésimas.
Si bien Freud no se interesaba en la modernidad artística, nunca dejó de examinar ciertos enigmas que rodeaban a los autores de su predilección. Así, desde hacía algunos años, y en franco desafío a sus discípulos de los años veinte, se adhería a una teoría conspirativa en lo relacionado con la identidad de Shakespeare. Todos los freudianos del primer círculo compartían entonces su idolatría por el gran dramaturgo inglés y todos se entregaban, al igual que en el caso de Leonardo da Vinci, a especulaciones infinitas sobre cada uno de los personajes de su teatro y en especial sobre Hamlet, prototipo del primer neurótico moderno.
A mediados del siglo XIX, con el auge de la ciencia histórica y del arte novelesco ligado a ella, había germinado la idea de que la paternidad de las obras de Shakespeare debía atribuirse a otra persona y no a este. Los partidarios de esta tesis pretendían oponerse a la llamada historia «oficial», y afirmaban entonces que Shakespeare no había nacido en Stratford y que no era más que el testaferro del filósofo empirista sir Francis Bacon. Los «antistratfordianos» imaginaban pues la existencia, a fines del siglo XVII, de una conspiración destinada a proteger al verdadero autor de la obra que, a sus ojos, no podía en ningún caso ser el hijo de un guantero, comerciante de pieles y lana y descendiente de campesinos. Pero ¿por qué la elección de Bacon? Porque Delia Salter Bacon, dramaturga norteamericana iluminada, autora en 1857 de un éxito de ventas sobre la cuestión y adepta de esa tesis, había ido a la tumba de Shakespeare y pretendía haberle arrancado sus secretos. Tras sus pasos, una multitud de descifradores de enigmas habían imaginado que Bacon, viejo amigo del conde de Essex, no podía correr el riesgo de pasar por un saltimbanqui. Los antistratfordianos exhibían «un fanatismo absoluto y se adherían a teorías conspirativas que rozaban la paranoia», escribe Peter Gay, y prosigue: «Hacia fines de la década de 1880 el eminente político Ignatius Donnelly, un populista que mostraba cierta inclinación por las causas extravagantes, lanzó así la moda de leer las obras de Shakespeare como un gigantesco pictograma».
La polémica se reactivó en 1920 por iniciativa de un maestro de escuela, Thomas Looney, un partidario del positivismo de Auguste Comte que, con los mismos argumentos, esta vez atribuía la paternidad de las obras de Shakespeare no a Bacon sino a Edward de Vere, conde de Oxford. A diferencia de los otros antistratfordianos, Looney aducía basarse en tesis científicas y daba muestras de tamaña erudición que sus argumentos parecían la antítesis de un delirio monomaníaco. Todo indicaba que estábamos ante un gran sabio solitario que hacía al mundo el regalo de su genial descubrimiento. Por eso Looney logró convencer a varios autores y críticos, entre ellos Mark Twain, de la validez de su gran revisión de las verdades oficiales.
Nada podía seducir más a Freud, que en la misma época manifestaba gran interés por los fenómenos ocultos, las novelas policíacas y los relatos fantásticos. También él se veía a sí mismo como un descifrador de enigmas, solitario y grandioso, inventor de una doctrina rechazada por la ciencia oficial. ¿No había sido admirador de las tesis de Fliess? ¿No había descifrado la vida enigmática de Leonardo da Vinci al admitir la idea de la presencia de un buitre en un cuadro célebre? Pese a las advertencias de Strachey y Jones, que intentaron en vano disuadirlo de tomar en serio la nueva teoría «oxoniense», comenzó a creer en las extrapolaciones de Looney.
Convencido, después de un «examen» minucioso de los hechos, de que el autor de las obras de Shakespeare no podía ser sino un hombre de letras apasionado por el teatro, gran viajero y de rango social elevado, Looney había indagado durante varios años a quién podía corresponder ese perfil social y psicológico. Y fue así que descubrió en De Vere todos los indicios capaces de apuntalar su tesis. El destino del conde de Oxford coincidía con su hipótesis y Looney añadía a esa certeza la idea de que Hamlet era un «doble» del autor, que hacía un culto de su padre y detestaba a su madre. En otras palabras, sin saberlo, hacía de Hamlet, sustituto de De Vere, un personaje freudiano asediado por su complejo de Edipo.
Freud no renunció jamás a ese revisionismo, del que él mismo no tardaría en ser víctima. Sucede que adoraba los rumores. En diciembre de 1928, en una larga carta a Lytton Strachey, en respuesta al envío de la biografía de Isabel y Essex, le pedía su opinión sobre una de sus hipótesis: creía que en el personaje de lady Macbeth se ocultaba un retrato de la reina Isabel, puesto que ambas mujeres estaban igualmente atormentadas por un asesinato. Y añadía que Macbeth y su esposa no eran, de hecho, más que un solo personaje escindido, y encarnaban ambos el destino de esa reina virgen, homicida, depresiva e histérica. Pero, en especial, reafirmaba su creencia en la tesis de Looney, aunque tenía la precaución de decir que se «sentía ignorante» y no tenía plena certeza acerca de la hipótesis oxoniana. Agregaba sin embargo que De Vere tenía un gran parecido con Essex, para sumirse luego en una inverosímil espiral interpretativa:
De nacimiento tan noble como Essex y tan orgulloso como este en ese aspecto, [De Vere] encarnaba asimismo el tipo del noble tiránico. Además, aparece sin duda en _Hamlet_ como el primer neurótico moderno. De igual modo, en su juventud, la reina había flirteado con él, y si su suegra no hubiera hecho una campaña tan feroz por su hija, habría estado aún más cerca del destino de Essex. Era a buen seguro un amigo muy íntimo de Southampton. El destino de Essex no puede haberlo dejado indiferente. Pero ya es suficiente. Como sea, tengo la sensación de que debo presentarle mis humildes excusas por la muy mala caligrafía de la segunda mitad de mi carta.
Lytton Strachey nunca respondió a esta carta de Freud. Sin embargo, en esa fecha habría podido aconsejarle con provecho que desconfiara de la hipótesis oxoniana. Un año después Freud ya no tenía dudas. Por eso recomendó la lectura del libro de Looney a Smiley Blanton, gran especialista en la cuestión shakespeariana. Atónito, este, pensando que _Herr Professor_ , hombre de ciencia y de razón, se había extraviado en absurdas tonterías, estuvo a punto de interrumpir la cura.
Para explicar este extravío, Jones imaginó que Freud se identificaba con la tesis de Looney porque él mismo se había proyectado inconscientemente en una novela familiar según la cual habría podido ser hijo de su medio hermano Emanuel, más próspero en los negocios que Jacob, con lo cual su fantasía oxoniense no era más que la traducción de un deseo de cambiar una parte de su propia realidad familiar.
En vez de añadir una interpretación edípica a una divagación freudiana sobre las identidades múltiples de Shakespeare y sus personajes, se puede formular la hipótesis de que Freud siempre fue en parte heredero de cierto modelo de pensamiento que había surgido a fines del siglo XIX y que remitía a la idea de que la sociedad humana está dividida entre búsqueda racional y atracción por lo oculto y entre espíritu lógico y delirio paranoico. Desde ese punto de vista, se parecía tanto a Giovanni Morelli, inventor de un método capaz de distinguir las obras de arte de las imitaciones, como a Sherlock Holmes, célebre detective y personaje de novela, maestro en el arte de resolver un enigma mediante la mera observación de algunas huellas: cenizas, pelos, hilos de tejido, jirones de piel. Desde luego, todos esos métodos de desciframiento podían, como el psicoanálisis, transformarse en su contrario y servir para fabricar falsos enigmas, cuya existencia supuesta debía aportar la prueba de la validez del enfoque destinado a interpretarlos. Por eso el cuestionamiento de la historicidad de un acontecimiento o de un personaje conducía a sustituir los hechos por fábulas, luego presentadas con un rigor indiscutible como otros tantos enigmas por descifrar a fin de demostrar que ocultaban una conspiración: Napoleón no murió en Santa Elena, Jesús se casó y tuvo hijos, tal rey no es en realidad más que su hermano mellizo, etc.
Si Freud, pese a la persistencia de sus dudas, se llenaba a tal punto de ardor cuando se trataba de poner de relieve falsos enigmas, era también porque desde la infancia lo obsesionaba la idea de que las personas que observaba a su alrededor —padre, madre, tías, hermanas, hermanos, fratrías múltiples— no eran nunca lo que parecían ser sino los sustitutos de una permanente alteridad: un padre generado por un ancestro, una madre en el lugar de una nodriza y recíprocamente, un hermano que podría ser el padre, santa Ana mezclada con María, etc. Y detrás del padre supuesto o renegado, y más allá de la madre de sustitución, se perfilaba una «novela familiar» en virtud de la cual el sujeto siempre era otro y no el que creía ser: hijo de un rey o un héroe, asesino de un padre tirano, plebeyo, niño expósito que se acostaba con su madre, impostor, etc. De esa tesis derivaba la necesidad clínica de descifrar en el inconsciente elementos insignificantes capaces de remitirse a una huella mítica.
Nunca se insistirá lo suficiente en que Freud, hombre de la Ilustración y descifrador de los verdaderos enigmas de la psique humana, no dejó, como contrapunto a su apego a la ciencia, de desafiar simultáneamente a las fuerzas oscuras propias de la humanidad para iluminar su poderío subterráneo, a riesgo de extraviarse en ellas.
Tal fue para él el objetivo de esa pasión desplegada para descifrar, como si se tratara de un verdadero enigma, un rumor que, sin embargo, era una invención de principio a fin. Ese rumor parecía ajustarse a su teoría de las sustituciones infinitas, y fue así que, hasta el final de sus días, lo obsesionó este interrogante: ¿quién, entonces, se oculta siempre bajo el nombre de un «gran hombre»?
### 4
Entre las mujeres
A partir de los años veinte las mujeres estuvieron cada vez más presentes en el movimiento psicoanalítico, dentro del cual se desarrollaban además varios debates que las incumbían en su existencia y su práctica: la femineidad, la maternidad, el análisis de niños, la sexualidad femenina. Así como reclamaban el derecho a existir como ciudadanas con todas las de la ley, comenzaban también a ocupar el lugar que les correspondía en las filas de los psicoanalistas, y no solo a título de esposas. Y de resultas, propusieron una nueva mirada sobre la manera de enfocar la cuestión de las terapias psicoanalíticas. Por añadidura, en un principio les tocó a ellas el papel de analizar a los niños. Esta llamada función «educativa» no las obligaba a estudiar medicina, carrera todavía reservada a los hombres. Desde ese punto de vista, puede decirse que el análisis infantil favoreció la emancipación femenina. Si las mujeres psicoanalistas eran a menudo analizadas por sus esposos o los colegas de estos, analizaron a su vez a sus hijos o dejaron esta tarea en manos de otras.
En 1924 Rank y Ferenczi, que ya habían propuesto innovaciones técnicas en la conducción de las sesiones, procuraron transformar la visión freudiana de la familia para hacerla más adecuada a la modernidad de la posguerra. A principios de ese año Rank abrió las hostilidades con la publicación de un libro iconoclasta, _El trauma del nacimiento_ , que llevó a Jones y Abraham a hacer sonar los tambores de guerra. Con su crítica de la concepción —que consideraba demasiado rígida— de la organización edípica del psiquismo, fundada en el lugar preponderante atribuido a la autoridad paterna, Rank sostenía la idea de que al nacer todo ser humano sufre un trauma real. Esta primera separación de la madre se convertía así, según él, en el prototipo de una angustia más determinante para la subjetividad humana que la triangulación edípica. Con ese planteamiento, Rank relanzaba el viejo debate sobre el origen traumático de las neurosis.
En vez de refutar esa tesis que desaprobaba, Freud exigió «pruebas». Parecía olvidar que él mismo había condenado, en sus adversarios, el recurso abusivo al famoso modelo experimental: «En primer lugar, y antes de cualquier aplicación extendida», dijo a Ferenczi, «habría que exigir la prueba estadística de que los primogénitos o los niños nacidos con dificultades, en estado de asfixia, manifiestan en su infancia, en promedio, una mayor disposición a la neurosis o al menos a la producción de angustia». Y agregaba que también habría que estudiar el caso de los niños nacidos por cesárea. Incapaz de proporcionar esas «pruebas», Rank fue entonces acusado por Jones y Abraham de no ser ni médico ni analizado, justamente cuando iban a entrar en vigor, en el congreso de Bad-Homburg de la IPV, las nuevas reglas que hacían obligatorio el análisis didáctico. Y de inmediato la manía interpretativa volvió por sus fueros: Rank, dijeron, no había resuelto su conflicto con el padre. Razón por la cual se lo obligó a entrar en análisis, durante algunas sesiones, con su maestro venerado. ¡Trabajo inútil!
En realidad, Rank ya no quería seguir dependiendo de Freud. Tentado por nuevos progresos técnicos y deseoso de marcharse de Viena con su mujer, viajó a Estados Unidos, actitud que para Freud constituía una verdadera traición. En ese país dictó conferencias y seminarios, disfrutó de una excelente acogida y afirmó que, sin traicionar la doctrina del maestro, ahora era preciso tener en cuenta a la madre y desarrollar el principio de las terapias breves. Cuando volvió a Viena Freud se mostró conciliador, resueltamente decidido a no romper con ese discípulo al que tanto quería. Pero Rank, enardecido por su triunfo norteamericano, no pensaba sino en volver a irse. En diciembre de 1925 se marchó otra vez de Viena pero luego desanduvo el camino. En un gran arranque de masoquismo, hizo su autocrítica, se humilló y admitió estar afectado por un complejo de rebelión contra el padre.
Por su lado, Ferenczi sostenía entonces en _Thalassa_ que todo ser humano sentía nostalgia por el útero materno y que, para no despegarse de él, buscaba regresar sin cesar a las profundidades marítimas de un estado fetal. Este enfoque del psicoanálisis a través de la metáfora de la cripta se acompañaba de innovaciones técnicas. Si la sesión analítica, decía Ferenczi, repite una secuencia de la historia individual y, por otra parte, la ontogénesis recapitula la filogénesis, hay que preguntarse, en la propia sesión, cuál es el estado traumático simbólicamente repetido por la ontogénesis.
En un primer momento y a pesar de su discrepancia con la teoría del trauma del nacimiento, Ferenczi defendió la posición de Rank porque compartía con este la idea de que el vínculo con la madre debía explorarse mucho más allá de la concepción freudiana del complejo de Edipo. Esta actitud no sirvió de nada. En abril de 1926 Rank se alejó definitivamente de Freud para realizar su propio destino. Como obsequio de ruptura le dio las obras completas de Nietzsche: veintitrés volúmenes encuadernados en cuero blanco. Freud nunca había querido leer la obra de ese filósofo a quien tanto debía, como le había dicho varias veces a su querido discípulo. Abrumado de dolor pero siempre cruel en la manera de rechazar a sus mejores amigos, escribió estas palabras a Ferenczi: «Le hemos dado mucho pero a cambio él ha hecho mucho por nosotros. ¡Estamos pues en paz! Durante su última visita no tuve la oportunidad de expresarle el afecto especial que le profeso. Fui sincero y duro. Por eso podemos hacerle la cruz. Abraham tenía razón». Seguía reprochándole a Rank su interpretación del sueño de Pankejeff sobre los lobos.
Tuvo de todos modos la precaución de responder en un libro apresuradamente escrito: _Inhibición, síntoma y angustia_. Si bien tenía en cuenta la posición de Rank, Freud evitaba el escollo de atribuir al parto en sí mismo una realidad traumática. Admitía así la idea de que se asociara un valor paradigmático e incluso fantasmático a la separación respecto de la madre, pero soslayaba la cuestión de los disgustos que podría causar, sobre todo en Estados Unidos, la idea de que todo parto —normal o con fórceps— pudiera ser la causa de una angustia existencial o una neurosis.
Sin romper con Freud, Ferenczi se alejó de él no solo por sus innovaciones técnicas sino también por su reactivación de la cuestión del trauma y los abusos sexuales reprimidos y activos como una «impronta» psíquica, una herida imposible de cicatrizar y capaz de dañar el yo. Jones se valió de eso para combatirlo sin descanso, tanto más cuanto que no soportaba su inclinación por la telepatía ni la amistad inquebrantable que Freud le profesaba. En esa querella de los antiguos y los modernos, Freud no tenía más razón que Rank. En efecto, si la tesis del trauma del nacimiento era errónea desde el punto de vista experimental, preparaba empero el camino a una nueva concepción de la angustia de separación. Freud lo admitía, y a continuación tendría la honestidad de revisar su posición y reconocer los méritos de su querido Rank. Demasiado tarde.
Entretanto, Jones estaba ganando su batalla por la supremacía del mundo angloparlante sobre la Europa continental: para él, una manera de ser infiel a Freud y mantener su fidelidad a lo que a su juicio iba a ser el futuro del psicoanálisis. Había comprendido desde el comienzo, como Alix Strachey, que la única manera seria de poner en entredicho la doctrina vienesa original —centrada en la primacía de la ley del padre— pasaba por una renovación de la doble cuestión del psicoanálisis de niños y la sexualidad femenina.
Si hasta entonces Freud había concebido su complejo de Edipo conforme al modelo de la familia nuclear —padre, madre, hijo—, también había asignado a cada uno un lugar que solo permitía esclarecer la génesis de las neurosis y los conflictos originados en la infancia. Freud elaboraba una concepción crítica de la familia burguesa, que exploraba sobre la base de su famosa estructura edípica, sin advertir los peligros de esa psicologización de la vida psíquica, que terminaría además por caer en el ridículo después de haber representado una verdadera innovación.
Creía así que el niño era siempre y necesariamente el hijo de un hombre o de su sustituto, que encarnaba la autoridad paterna, y de una mujer o su sustituto, que había desplazado su investidura libidinal hacia la maternidad. En consecuencia, el niño, en el sentido freudiano, repetía inconscientemente la historia de sus padres y por lo tanto de sus ancestros. Desde ese punto de vista, el análisis no podía abordarlo en ningún caso como un ser completamente separado del par parental. En el sentido freudiano, el niño era considerado, por cierto, como un sujeto hecho y derecho, pero si era preciso tratarlo a causa de alguna patología, había que proceder «en familia» y nunca antes de que tuviera cuatro o cinco años. Por lo demás, Freud había llevado a cabo el análisis de Herbert Graf a través del discurso de su padre y con su madre en el diván. Y cuando comprendió que su hija quería ser madre sin tener necesariamente que dar a luz, aceptó la idea de que pudiese formar una familia con una mujer que había abandonado a su esposo, a condición, de todas formas, de que una y otra fueran, gracias a los beneficios del psicoanálisis, tanto padres como educadoras. Para Freud, la dicha de existir se apoyaba en un tríptico: ideal educativo, maternidad feliz, paternidad consumada. Impregnada de ese modelo, la escuela vienesa había disfrutado en un principio de los favores de Ferenczi. Así, en 1913 este había descrito el caso de un niño de cinco años, Arpad, que, obsesionado por las aves de corral, cacareaba como un gallo.
Por su lado, rodeada por August Aichhorn y Siegfried Bernfeld, que se ocupaban de niños delincuentes, discapacitados, traumatizados o pobres, Anna Freud proseguía su carrera consagrándose a la educación infantil a través del psicoanálisis. Y Freud solo la apoyaba en la medida en que estaba convencido, como sus discípulos vieneses del primer círculo, de que el tratamiento psíquico de los niños debía hacerse por la mediación de la autoridad parental: «Planteamos como elemento previo», escribiría a Joan Riviere en octubre de 1927,
que el niño es un ser pulsional, con un yo frágil y un superyó apenas en vías de formación. En el adulto trabajamos con la ayuda de un yo fortalecido. Por lo tanto, no seremos infieles al análisis si en nuestra técnica tomamos en cuenta la especificidad del niño, cuyo yo es preciso sostener en el análisis contra un ello pulsional omnipresente. Ferenczi ha observado con mucho ingenio que si la señora Klein tiene razón, en verdad ya no hay niños. Naturalmente, será la experiencia la que tenga la última palabra. Hasta hoy mi única constatación es que un análisis sin objetivo educativo no hace sino agravar el estado de los niños y tiene efectos particularmente perniciosos en los abandonados y asociales.
Los argumentos de Freud eran perfectamente admisibles. Pero además hacía falta que los padres aceptaran dejar a su progenie en manos de psicoanalistas, en una época en la cual eran los psiquiatras o los pediatras quienes se ocupaban de las patologías infantiles. En ausencia de pacientes exteriores al círculo psicoanalítico, la experiencia de la cura se realizaba con hijos o allegados de los analistas, hecho que no debía darse por descontado y que podía incluso dar origen a estafas.
En 1919 Hermine von Hug-Hellmuth, miembro de la WPV y en análisis con Sadger, el más misógino de todos los discípulos de Freud, fabricó de principio a fin, sobre la base de sus recuerdos de infancia, una obra presentada como el auténtico diario de una verdadera adolescente llamada Grete Lainer. En el prefacio Freud afirmaba que ese diario era «una joya que testimonia la sinceridad de la que es capaz el alma infantil en el estado actual de la cultura». Todos admiraban a esa pionera del psicoanálisis de niños, dotada de un auténtico talento literario, pero nadie se dio cuenta de que no solo era una falsaria sino también una fanática de la interpretación silvestre. Durante varios años había alojado en su casa a su sobrino Rolf Hug para someterlo a su religión edípica. Ni uno solo de los comportamientos de ese pobre muchacho escapaba a la vigilancia interpretativa de su tía: su sadismo infantil, su deseo reprimido por la madre, su sexualidad pulsional, su fijación por objetos o sustitutos parentales. En septiembre de 1924, en un acceso de ira, él la estranguló.
La comunidad psicoanalítica vienesa se sintió muy salpicada por ese escándalo debido a que Rolf Hug, condenado a doce años de cárcel, afirmaba haber sido víctima del psicoanálisis. En 1930 solicitó una reparación a Federn, por entonces presidente de la WPV. Entretanto, claro está, el diario, que había tenido un considerable éxito, fue retirado de la venta. Freud se había dejado engañar por una superchería directamente emanada de su doctrina.
Melanie Klein no compartía las concepciones freudianas de la familia. Y lo que había aprendido de la suya la alejaba de toda idea de mezclar pedagogía y psicoanálisis. Hija de un padre galitziano y una madre de origen eslovaco —ambos aferrados a un judaísmo ortodoxo—, había tenido una infancia desdichada. Su madre, una mujer bella y culta, despreciaba a su marido, que por su parte prefería a la hija mayor, fea y poco inteligente. Por eso Melanie encontró refugio en su hermano. Criada sin principios ni ética, a la vez que presenciaba las disputas incesantes a las que se entregaban sus padres, se casó sin pasión con Arthur Klein, un primo de la rama materna, con quien tendría tres hijos no deseados. Y se embarcó en la aventura psicoanalítica con un fervor cercano a la conversión mística: revancha contra la infelicidad, deseo de conjurar una existencia melancólica.
Aunque dotada de talento, Melanie no atribuía ninguna importancia a la vida real de los niños ni a su educación. Solo le interesaban los procesos inconscientes que podía descubrir en los muy pequeños. Lugar eminente de todos los odios y todas las ignominias, la familia en el sentido kleiniano era a Freud lo que las telas de Picasso eran a la pintura clásica. La nariz, la boca, los rostros eran sin duda los mismos, pero desfasados, desplazados, situados en lugares inesperados. En cuanto a las visiones que Melanie tenía de la infancia, podría hablarse de un cuadro de Max Ernst: pesadillas, naturaleza mineralizada, reconstrucción nocturna donde se mezclaban animalidad, humanidad, elementos líquidos.
Melanie Klein reivindicaba la psicología edípica pero acentuaba peligrosamente sus rasgos para sumergirse mejor en el llamado universo «preedípico» del niño: cripta maternal, apropiación por el niño del interior del cuerpo de la madre, avidez voraz, tumulto, terror al castigo, angustia, psicosis. En este aspecto era más «moderna» que los freudianos clásicos: estaba más cerca de un modelo literario del siglo XX que del siglo XIX. Y era eso lo que tanto fascinaba a Alix Strachey. En muy poco tiempo Melanie conquistó a la mayoría de los psicoanalistas británicos y sobre todo a Jones, que le encargó el análisis de sus hijos.
A sus ojos, había que eliminar todas las barreras que impedían al terapeuta acceder al inconsciente del niño. En consecuencia, oponía a la «protección» según Freud una doctrina del _infans_ —el niño de dos a tres años—, es decir, del niño que aún no habla pero que ya no es un lactante porque ha reprimido a este en sí mismo.
Si Freud había sido el primero en descubrir en el adulto al niño reprimido, Melanie Klein fue la primera en identificar en el niño lo que ya está reprimido, es decir, el lactante. De resultas, proponía no solo una doctrina sino también un marco necesario para el ejercicio de terapias psicoanalíticas específicamente infantiles: un decorado apropiado, una habitación especialmente adaptada, muebles simples y robustos, una mesita y una silla, un pequeño diván. Cada niño debía tener su caja de juegos reservada para el tratamiento y compuesta de casitas, pequeños personajes, animales de granja y animales salvajes, cubos, pelotas, canicas y todo un pequeño equipamiento: tijeras, cordel, lápices, papel, plastilina.
Esta concepción del enfoque clínico de los niños iba a la par, en Melanie Klein y sus partidarios, con una refundición de la doctrina de la sexualidad femenina. Con modelos tomados de la biología darwiniana, Freud sostenía la tesis de un monismo sexual y una esencia «masculina» de la libido humana. Esa tesis derivaba de la observación clínica hecha por él de las teorías sexuales infantiles y no tenía por objetivo ni describir la diferencia de los sexos a partir de la anatomía ni resolver la cuestión de la condición femenina en la sociedad moderna.
En la perspectiva de la libido única, Freud afirmaba que en el estadio infantil la niña ignoraba la existencia de la vagina y hacía cumplir al clítoris el papel de un homólogo del pene. A su entender tenía entonces, además, la impresión de que le habían endosado un órgano castrado. En función de esa disimetría, que se movía en torno de un polo único de representaciones, el complejo de castración, decía, no se organiza de igual manera para los dos sexos. El destino de cada uno de ellos es diferente, no solo por la anatomía sino bajo el efecto de las distintas representaciones ligadas a la existencia de esta. En la pubertad la vagina se manifiesta para ambos sexos: el varón ve en la penetración una meta para su sexualidad, mientras que la niña reprime su sexualidad clitoridiana. Pero antes, cuando advierte que la niña no se le asemeja, el varón interpreta la falta de pene en ella como una amenaza de castración para sí mismo. En el momento del complejo de Edipo se aparta de la madre y escoge un objeto del mismo sexo.
La sexualidad de la niña, siempre según Freud, se organiza en torno del falo: ella quiere ser un varón. En el momento del Edipo desea un hijo del padre y este nuevo objeto se inviste con un valor fálico. Contrariamente al varón, la niña debe apartarse de un objeto del mismo sexo, la madre, en favor de otro de sexo diferente. El apego a la madre es el elemento primordial para ambos sexos.
Este llamado análisis de «la envidia del pene» se basaba en una observación empírica hecha por Freud en cierta época, y sobre la cual se apoyaba para construir su teoría de la sexualidad infantil. En esa óptica —que se ajustaba a lo que enunciaban los propios niños—, Freud constataba que las niñas se identificaban con varones. De ahí el dogma psicoanalítico que reencontraremos, por ejemplo, en Karl Abraham: las mujeres desean inconscientemente ser hombres porque, en su infancia, envidiaron el pene y anhelaron tener un hijo de su padre. Que esta tesis sea empíricamente exacta no significa que sea universalizable, toda vez que, aun cuando esté en armonía con la subjetividad infantil, puede modificarse en función de las transformaciones de la sociedad.
Si bien partidario de un monismo sexual, Freud consideraba errónea cualquier argumentación que afirmara la naturaleza instintiva de la sexualidad. A sus ojos, no existían ni «instinto maternal» ni «raza» femenina, como no fuera en las fantasías y los mitos construidos por los hombres y las mujeres. En cuanto a la diferencia sexual, Freud, inspirado en los mitos griegos, la reducía a una oposición entre un logos separador —principio masculino simbolizado— y una arcaicidad copiosa, estado de desorden materno anterior a la razón. De ahí su célebre fórmula: «La anatomía es el destino». En contra de lo que haya podido decirse, Freud nunca sostuvo que la anatomía era el único destino posible para la condición humana. Y tomaba esta fórmula de Napoleón, quien había querido inscribir la historia de los pueblos venideros en la política más que en la referencia a los antiguos mitos.
En otras palabras, mediante esa fórmula, si bien ponía en un lugar muy eminente las tragedias antiguas, Freud no dejaba de plantearse, bajo los rasgos de una dramaturgia moderna y casi política, el gran asunto de la diferencia sexual. La escena que describía se inspiraba así en la escena del mundo y la guerra de los pueblos concebida por el emperador.
En resumen, diremos que si para Freud la anatomía forma parte del destino humano, este no puede representar en ningún caso, para cada ser humano, un horizonte insuperable. Esa es sin duda la teoría de la libertad que surge del psicoanálisis y le es propia: reconocer la existencia de un destino para emanciparse mejor de él. Por lo demás, Freud terminaría por decir que la anatomía nunca basta para determinar lo que es femenino o masculino.
En el plano clínico, la existencia de la libido única no excluía la de la bisexualidad. Al contrario, la explicaba: en la perspectiva freudiana ningún sujeto podía ser poseedor de una pura especificidad masculina o femenina. En otras palabras, si el monismo sexual es una hipótesis fundada, significa que, en las representaciones inconscientes del sujeto —sea hombre o mujer—, la diferencia de los sexos, en el sentido biológico, no existe. La bisexualidad, que es el corolario de esa organización monista, afecta por tanto a ambos sexos. La atracción de un sexo por otro no solo no es muestra de una complementariedad, sino que la bisexualidad disuelve la idea misma de una organización así. De ahí los dos modos distintos de la homosexualidad: femenina cuando la niña queda «unida» a su madre al punto de elegir una pareja del mismo sexo, masculina cuando el varón efectúa una elección similar al punto de negar la castración materna.
La tesis freudiana de la llamada escuela «vienesa» fue sostenida por algunas mujeres, en especial Marie Bonaparte, Helene Deutsch y Jeanne Lampl-De Groot. Pero desde 1920 la rechazaron otras mujeres de la llamada escuela «inglesa»: Melanie Klein, Josine Müller y muchas más. Así como estas ponían en entredicho la primacía otorgada a la ley del padre, al «falocentrismo» freudiano y al ideal educativo en el enfoque psicoanalítico de los niños, también criticaban, con toda la razón, la extravagante hipótesis freudiana de la ausencia, en la niña, de la sensación de la vagina, y oponían un dualismo a la noción de libido única. Además, en la psicoterapia con los niños no percibían esa presunta ausencia de la sensación de la vagina, y tampoco el lugar atribuido al clítoris como sustituto del pene. En esas condiciones, la escuela inglesa prolongaba la idea de una «naturaleza femenina», es decir, de una diferencia fundada en la anatomía, cuando Freud la había relativizado al poner la no diferenciación inconsciente de los dos sexos bajo la categoría de un solo principio masculino y de una organización edípica en términos de disimetría. En otras palabras, los partidarios de la escuela inglesa eran más «naturalistas» que Freud: consideraban que se nace mujer de una vez y para siempre, en tanto que él decía, antes bien, que la femineidad se construye por medio de representaciones. De ahí la idea de que la mujer se ve a sí misma como un «hombre fallido».
En el congreso de Innsbruck, en septiembre de 1927, bajo la presidencia de Max Eitingon, estalló una guerra sin cuartel entre Anna y Melanie. Esta llegó, luminosa y magistral, rodeada por primera vez por sus partidarios, boquiabiertos frente a sus planteamientos sobre los «estadios precoces del conflicto edípico», que ya no eran estadios sino «fases» o «posiciones intrapsíquicas». Cada vez más afectado por el cáncer, Freud había decidido en esa fecha retirarse del movimiento. Jones, que defendía las tesis de la escuela inglesa, tanto en el caso del análisis de niños como en la cuestión de la sexualidad femenina, no hizo nada por apagar el incendio. Había logrado aislar a Ferenczi y generar una tensión cada vez mayor entre Freud y su discípulo húngaro, juzgado «paranoico», cuando en realidad tenía buenas razones para sentirse perseguido. Jones quería disolver el comité y soñaba ya con celebrar el congreso del Verein en Inglaterra. Una vez más, su política era coherente.
El debate sobre las mujeres y los niños cobró una amplitud histórica considerable. A través de esta nueva querella de los antiguos y los modernos se ponía en marcha un cambio de paradigma ligado a las transformaciones de la sociedad occidental. Y desde ese punto de vista, la sociedad inglesa, fundada en el liberalismo, el empirismo, el individualismo —pero también en el culturalismo—, era más apta que la Europa continental para dar cabida a las tesis kleinianas, consideradas más «feministas», más democráticas y más igualitaristas que las de Freud, en las que se expresaba una adhesión todavía muy fuerte a un modelo patriarcal. Hay que señalar además que ese debate era contemporáneo del despliegue internacional del movimiento feminista, que por la vía del sufragismo condujo a la emancipación política y jurídica de las mujeres. Encontramos sus huellas en un hermoso ensayo de Virginia Woolf, _Tres guineas_ , publicado en 1938. En él la autora alentaba a las mujeres a reconocer su diferencia. Por eso comparaba el sexismo masculino con los fascismos triunfantes de Alemania e Italia, ya que en la época le parecía que el instinto guerrero era patrimonio de los hombres. Sin embargo, no excluía que ese fenómeno pudiese ser de orden cultural y no sexual.
Freud se quejó ante Jones de la campaña orquestada por los kleinianos contra Anna. Lo perturbaba en particular ver que la bella Joan Riviere, miembro de la aristocracia inglesa y ligada al grupo de Bloomsbury, se hubiera dejado seducir por las teorías kleinianas. Melancólica e insomne, había sido perfectamente analizada por él, que la estimaba mucho y le tenía un profundo afecto, pese a que Anna la detestaba. Joan Riviere sabría mantener distancia sin ceder jamás a ningún tipo de idolatría kleiniana.
En septiembre Jones escribió a Freud para confirmar su desacuerdo con las posiciones de Anna, pero adjudicaba las resistencias de esta a las insuficiencias del análisis con su padre: nueva oportunidad de psicologizar conflictos científicos, cuyos motivos eran, empero, indiscutiblemente históricos y políticos. Freud había actuado así contra Jung, después Jung lo había hecho contra Freud, Jones contra Rank, etc. Una vez más, un debate de envergadura entre dos enfoques diferentes de una misma realidad era interpretado por los protagonistas mismos no como un cambio de paradigma, sino como un asunto edípico.
Jones reafirmaba, de todos modos, su fidelidad inquebrantable al maestro y a su hija. Freud no quiso meterse en ese combate, aunque siguió pensando que el camino kleiniano era erróneo, sin dejar de admitir que la experiencia tendría la última palabra. Pero lo ofuscaba que las posiciones de la escuela inglesa ya fuesen un hecho consumado aun antes de la entrada en escena de Anna en el debate: «En el comportamiento de los ingleses respecto de Anna», señalaba,
hay dos aspectos imperdonables: por un lado, el reproche poco habitual entre nosotros, y contrario a todas las buenas costumbres, de que ella no se habría analizado lo suficiente, un reproche público que usted mismo repite en público. Y la observación de Mrs. Klein, que creía que Anna evitaba por principio el Edipo. Ese malentendido habría podido evitarse fácilmente con un poco de buena voluntad. Más que esas tormentas en un vaso de agua, me abruman las declaraciones teóricas de Riviere, precisamente porque siempre tuve en muy alta estima su inteligencia. En este aspecto, debo reprocharle a usted que haya llevado demasiado lejos la tolerancia. Cuando un miembro de nuestros grupos expresa opiniones esenciales tan erróneas y engañosas, se le presenta al jefe del grupo una buena oportunidad de aleccionarlo en particular, pero no es un acontecimiento al que se busque asegurar la más amplia publicidad sin condimentarlo con observaciones críticas.
Contra Freud, la experiencia dio la razón a las teorías kleinianas que se afianzaron en todo el mundo entre los profesionales de la primera infancia, a medida que Londres imponía su liderazgo en la organización internacional del psicoanálisis. Pero fueron corregidas y modificadas por doquier de una manera «annafreudiana», es decir, en el sentido de la integración de un modelo educativo al desenvolvimiento de las curas de niños.
Armado de su psicología edípica, de su creencia en un clítoris como sustituto del pene y de su convicción de que las niñas tendrían conciencia de la inferioridad de «su pequeño pene», Freud había permanecido anclado en una concepción de las mujeres, la femineidad y la vida amorosa deudora del romanticismo alemán y la _Naturphilosophie_. A pesar de que su doctrina del monismo sexual se alejaba del naturalismo, él no dejaba de invocarlo en la mirada que posaba sobre las mujeres y la «naturaleza» de la femineidad. Una vez más, sus posiciones eran de extrema complejidad y Freud se contradecía y estaba todo el tiempo en guerra consigo mismo.
En su opinión, las mujeres eran más pasivas que los hombres, también más bisexuales y, por consiguiente, la homosexualidad femenina era diferente de la homosexualidad masculina; la necesidad de las mujeres de ser amadas era mayor que la de los hombres y, de resultas, en el plano patológico, eran más masoquistas que sádicas, porque en ellas esa necesidad se convertía con facilidad en el goce de sufrir un maltrato. Al mismo tiempo, Freud afirmaba que las mujeres solo se complacían en las perversiones sexuales bajo la directriz de los hombres. Insistía en el hecho de que, en la infancia, las niñas se ven a sí mismas como «disminuidas» y dejadas de lado y reprochan a sus madres haberlas hecho nacer mujeres y no hombres: tienen «envidia del pene». Concebía las relaciones entre el hombre y la mujer como una complementariedad, postura que chocaba con su doctrina del monismo sexual. La mujer debe ser la dulce compañera del hombre, decía, y no gana nada con dedicarse a una actividad profesional o estudiar, porque su condición natural es mantener con el hombre tres relaciones «inevitables»: ser su progenitora, su compañera y su destructora, tres formas por las cuales pasaba para él la imagen de la madre en el transcurso de la vida: la madre misma, la amante que él elige a imagen de la primera y, para terminar, la madre tierra que vuelve a acogerlo en su seno.
Como buen darwiniano, partidario de la teoría de los «estadios» de la evolución, y como gran descifrador, al igual que Edipo frente a la Esfinge, del enigma del destino humano —es decir, de las tres edades de la vida—, siempre afirmó que la mujer encarnaba para el hombre tres formas de femineidad: la muchacha deseable, la esposa amada, la madre que tiene por el lactante un amor más intenso que por el niño convertido en adolescente. En otras palabras, la mujer concebida por Freud encerraba en sí misma no solo tres tipos de femineidad que remitían a la tierra nutricia y por lo tanto al nacimiento y la muerte, sino también, como las tres Moiras de la mitología griega (las Parcas romanas), tres modalidades del destino. En cada mujer, pensaba él, el hombre encuentra tres diosas procedentes del Olimpo: la «hiladora», que maneja el huso sobre el cual se desenvuelve la existencia; la «fatídica», que tiene el reloj de arena, es decir, la medida del tiempo, y la «inflexible», que corta el hilo de la vida. De ahí el hecho de que, para él, la mayor aportación de las mujeres a la cultura hubiera sido la invención del tejido y el trenzado.
Para apuntalar el principio de esta representación de la mujer, Freud se apoyaba en uno de sus personajes favoritos: el rey Lear. En la obra de Shakespeare el monarca loco se empecina en saber cuál de sus tres hijas lo prefiere, y condena al destierro a la mejor de ellas, Cordelia, con lo cual ocasiona la destrucción de su reino y su genealogía. Y es así que, al final de la tragedia, reconociendo demasiado tarde su error, sostiene entre sus brazos el cuerpo inerte de Cordelia: «El hombre viejo en vano se afana por el amor de la mujer, como lo recibiera primero de la madre; solo la tercera de las mujeres del destino, la callada diosa de la muerte, lo acogerá en sus brazos».
Padre de tres hijas y rodeado en la Berggasse por tres mujeres —Martha, Minna y Anna—, Freud encontraba en la mitología griega y los dramas de Shakespeare el eco de su concepción de las tres funciones de femineidad —la mujer-madre, la amante-esposa, la diosa Tierra— que se presentan al hombre a lo largo de su vida. Identificaba especialmente su temática en el juicio de Paris, en un cuento de Perrault («La Cenicienta») y en otro de Apuleyo («Eros y Psique»), pero también en una escena célebre de _El mercader de Venecia_ de Shakespeare, vertiente cómica de la tragedia del rey Lear. En esa obra, la joven Porcia se ve obligada, por voluntad de su padre, a tomar por esposo a aquel de sus pretendientes que, de los tres cofres que se le den a elegir, sepa optar por el adecuado. Uno de los cofres es de oro, otro de plata y el tercero de plomo, y el «adecuado» es el que contiene el retrato de la muchacha. Dos de los competidores ya se han retirado derrotados al escoger el oro y la plata. Bassanio, el tercero, se decide por el plomo y obtiene a la novia que, ya antes de la prueba, se inclinaba por él.
Según Freud, cada cofre representa un tipo de femineidad, y Porcia, asimilada al plomo (metal «mudo»), es la más simple de las tres mujeres, la menos alborotadora: ama y se calla. En este aspecto se parece a la fiel Cordelia, la «muerta».
A Freud le gustaban las mujeres fieles e inteligentes, no demasiado bellas pero instruidas en las cosas de la vida, consagradas a su familia, y estaba de acuerdo en que disfrutaran de derechos cívicos. El adulterio lo horrorizaba y le disgustaban las cortesanas y los burdeles. Censuraba la misoginia de algunos de sus discípulos vieneses y de los médicos de su medio, que consideraban a la mujer como un ser fisiológicamente inferior al hombre. Esta desigualdad, decía, no existe en el inconsciente: es una construcción fantasmática. Además, veía en el odio a las mujeres y en su degradación una de las raíces inconscientes del antisemitismo.
Y así como había descrito la sexualidad infantil sobre la base de las teorías inventadas por los niños, para construir su doctrina de la sexualidad tenía en cuenta tanto las representaciones masculinas de la femineidad como las representaciones femeninas de la masculinidad. Por eso su teoría de la femineidad siguió siendo en parte deudora del estado de la sociedad donde él vivía. Y esa es una de las razones por las cuales Freud no dejó de contradecirse tanto a lo largo de los años.
Si la mujer, a su entender, se siente privada de un pene, el hombre necesita, para acceder a una mujer que no sea su madre, superar el respeto que esta le impone. Y, agregaba Freud, debe integrar la idea del incesto con la madre o la hermana. Según su explicación, ese paso de la madre a _la otra mujer_ se expresaba en la necesidad experimentada por el hombre de mantener relaciones sexuales con mujeres de una clase social inferior a la suya: «La inclinación, tan a menudo observada, de los hombres de las clases sociales elevadas a elegir una mujer de inferior extracción como amante duradera, o aun como esposa».
Freud prefería un buen divorcio a un mal matrimonio y creía que el uso de «preservativos» impedía el orgasmo en las mujeres del mismo modo que lo hacía el _coitus interruptus_. Sin embargo, a partir de los años veinte consideró que la contracepción femenina era preferible, con mucho, a los otros métodos utilizados para controlar la procreación. Puritano encantador, le gustaba a rabiar seducir a las mujeres por la palabra. Su arte epistolar, que lindaba con el genio, era tan rico como limitados eran sus deseos carnales, y su imaginación erótica tan lujuriosa como pobre su práctica sexual. En el fondo de sí mismo se interrogaba sobre una de las escisiones más evidentes y conocidas de la vida amorosa: ¿cómo mantener unidos en el hombre el amor y el deseo? «Cuando aman no anhelan, y cuando anhelan no pueden amar.» Aunque parezca extraño, no quería ver que las mujeres estaban sometidas en la misma medida que los hombres a esa escisión y que también ellas podían, sin duda, escoger por amante o esposo a un hombre de condición inferior.
Había motivos para que esas distintas representaciones de la mujer resultaran chocantes, no solo para generaciones de feministas sino también para las mujeres que en esa época participaban en el movimiento psicoanalítico. Por otra parte, a estas últimas se les planteaba una vez más una contradicción no solo con la doctrina freudiana de la sexualidad femenina, sino con la actitud que Freud adoptaba en relación con las mujeres en general. En efecto, en vez de incitarlas a tejer o hacer punto, las impulsaba a tener una actividad profesional y ganarse la independencia social. Sabía que la organización familiar a la que se adhería en la vida privada no duraría y que las mujeres y los hombres de las generaciones futuras serían muy diferentes de los que él había conocido: veía las huellas de esa evolución en la manera de vivir de sus hijos, aun cuando, para defenderse de ella, imaginaba a estos a su imagen. Convencido con razón de que su doctrina, aunque muy alejada de las luchas feministas, tenía amplia influencia en la emancipación de las mujeres, se veía como un hombre del pasado que no había aprovechado la revolución sexual que él mismo había traído a la sociedad occidental. En cierta forma, el siglo XX era más freudiano que el propio Freud.
Sin mencionar a Amalia, Freud no vacilaba en afirmar que solo la relación con el hijo varón brindaba a una madre una satisfacción ilimitada. Y agregaba: «La madre puede transferir sobre el varón la ambición que debió sofocar en ella misma, esperar de él la satisfacción de todo aquello que le quedó de su complejo de masculinidad. El matrimonio mismo no está asegurado hasta que la mujer haya conseguido hacer de su marido también su hijo, y actuar [como] madre respecto de él». En otras palabras, para Freud toda mujer es para el hombre, ante todo, una madre potencial que él necesita degradar para convertirla en un objeto sexual. En consecuencia, decía, el punto de partida de toda vida sexual depende de la oralidad: chupar el pecho o su sustituto. Cada persona repite en su vida esa elección inicial: recuperar a la madre bajo formas múltiples, de la pasión al odio y de la felicidad a la desesperación.
A la vez que construía una teoría racional de la sexualidad, opuesta a las visiones de los ideólogos obsesionados por el terror a lo femenino, Freud hacía suya la idea ancestral de que la mujer es para el hombre el enigma más grande de toda la historia de la cultura. Los hombres, decía, siempre temieron el poder secreto y aterrador poseído por las mujeres, y no están listos para emanciparse de él. Acordémonos aquí de Tiresias. Hombre y mujer a la vez, conocía el misterio sobre el cual se interrogaban los dioses y los mortales: ¿quién se beneficia más con el acto sexual, el hombre o la mujer? Consultado por Zeus y Hera, se había atrevido a afirmar que la mujer obtenía del coito nueve veces más placer que el hombre. Por revelar el secreto de un goce tan salvajemente guardado, Hera lo castigó con la ceguera, pero Zeus lo recompensó con el don de la profecía y el poder de vivir durante siete generaciones.
Era sin duda esa mitología la que Freud prolongaba en términos procedentes a la vez del romanticismo negro —«¿Qué quiere la mujer?»— y de la literatura colonial: «La vida sexual de la mujer adulta», decía en 1926, «sigue siendo un _dark continent_ para la psicología». En esos momentos hacía alusión al best seller del periodista británico Henry Morton Stanley, que había explorado el Congo a fines del siglo XIX y elaborado, como consecuencia de esa expedición, una visión ingenua y paternocéntrica de África, considerada oscura y hechizadora, femenina y salvaje, aún inexplorada por la civilización. Y Freud comparaba la vida sexual de la mujer con ese «continente negro» hacia el cual se proyectaba la misión civilizadora de Occidente. Por medio de ese sintagma destinado al éxito expresaba tanto el temor del hombre blanco frente a un continente reinventado por el discurso colonial como la angustia experimentada por el _Hombre_ (en sentido genérico) frente a los desmanes de la sexualidad femenina: naturaleza indómita, parte oscura, enigma todavía no dilucidado por la ciencia, etc. No cabe duda que en un momento muy temprano de su vida Freud había sentido ese mismo pavor. ¿No expresaba cierto temor frente a los chow-chows negros? ¿Él mismo no había nacido «negro»?
Lo cierto es que esa doctrina freudiana era en buena medida el fruto de una representación masculina de la mujer y de la femineidad heredada de finales del siglo XIX. Freud lo sabía, y afirmaba que solo las mujeres más modernas, formadas en el psicoanálisis, serían capaces en el futuro de comprender la llamada sexualidad femenina «preedípica». La posteridad dio la razón a los dos enfoques —el kleiniano y el freudiano— y a muchos otros más eficaces.
A partir de 1920 las principales discípulas o pacientes de Freud se diferenciaron nítidamente de las mujeres de su familia. Inglesas, norteamericanas, alemanas, austríacas, casi todas provenían de las clases más altas de la sociedad y todas habían adoptado una independencia y un modo de vida que contrastaban, no solo con los de las pioneras de la primera generación de la WPV, sino también con la situación de las mujeres de la Berggasse y de las hermanas, la madre o las hijas de Freud.
Hasta la década de 1920 —con unas pocas excepciones— las mujeres psicoanalistas que participaban en el movimiento se habían mantenido a la sombra de los hombres. Ahora más visibles, y liberadas del corsé y las amplias enaguas, hicieron pues su segunda entrada en la historia para convertirse en protagonistas hechas y derechas del movimiento psicoanalítico. Si en su mayoría estaban afectadas por la melancolía, el tedio o diversas neurosis, debidas a menudo a un contexto familiar o conyugal perturbado, encontraron en el psicoanálisis la manera de acceder a una profesión, comprometerse con una causa, transformar su existencia o más simplemente participar en una aventura intelectual. Así sucedió, en particular, con Helene Deutsch, Hilda Doolittle, Edith Jacobson, Ruth Mack-Brunswick, Dorothy Burlingham, Joan Riviere, Marianne Kris, Margaret Stonborough-Wittgenstein.
Dos mujeres muy diferentes, Lou Andreas-Salomé y Marie Bonaparte, ninguna de las dos judía —una alemana y otra francesa—, tuvieron un papel estelar en la segunda parte de la vida de Freud, integradas tanto en el círculo de sus discípulos como en su intimidad familiar. Ambas recibieron el anillo de los iniciados del Ring.
Nacida en San Petersburgo cinco años después de Freud, Lou pertenecía a una familia de la aristocracia alemana. Desde su juventud había decidido consagrarse a la vida intelectual y no someterse jamás a las normas del matrimonio burgués. Figura emblemática de esa femineidad narcisista que ella llevaba a su incandescencia, consideraba que las mujeres eran más libres que los hombres. Estos, decía, están obligados, por su cultura, a una dominación que no puede sino hacerlos sentirse culpables. En cambio, añadía, las mujeres, capaces de darse por entero en el acto sexual, no sienten ni vergüenza ni molestia. En esa perspectiva, concebía el amor sexual como una pasión física que se agota una vez saciado el deseo. En consecuencia, solo el amor intelectual, fundado en una absoluta fidelidad, es capaz de resistir al tiempo. En un opúsculo sobre el erotismo aparecido en 1910 Lou comentaba uno de los grandes temas de la literatura —de Emma Bovary a Anna Karenina—, según el cual la división entre la locura amorosa y la quietud conyugal, por lo común imposible de superar, debía vivirse plenamente. Sabía que sus argumentos en favor de un matrimonio que autorizara a cada cónyuge una libertad regeneradora eran bastante extravagantes, no solo porque iban en contra de los preceptos morales de las religiones sino porque eran incompatibles con el poderoso instinto de posesión arraigado en el hombre.
Pese a ello, no dejó a lo largo de su vida de llevar a la práctica esa división y de burlarse de las invectivas, los rumores y los escándalos. Después de Nietzsche, tocó a Freud quedar deslumbrado por esta mujer que trastocó su existencia: el mismo orgullo, la misma desmesura, la misma energía, el mismo coraje, la misma manera de amar y poseer febrilmente los objetos elegidos. Uno había escogido la abstinencia sexual con la misma fuerza y la misma voluntad que empujaban a la otra a satisfacer sus deseos. Compartían la intransigencia y la certeza de que la amistad nunca debía ocultar las divergencias ni hacer mella en la libertad de cada cual.
En junio de 1887 Lou se había casado con el orientalista alemán Friedrich-Carl Andreas, docente en la Universidad de Gotinga. El matrimonio no se consumó y su primer amante fue uno de los fundadores del Partido Socialdemócrata alemán, Georg Ledebour, sucedido algún tiempo después por Friedrich Pineles, un médico vienés. Esta segunda relación terminó con un aborto y una trágica renuncia a la maternidad. Lou se instaló entonces en Munich, donde conoció al joven poeta Rainer Maria Rilke: «Fui tu mujer durante años», escribiría ella en _Mirada retrospectiva_ , «porque tú fuiste la primera realidad, en la que el hombre y el cuerpo son indiscernibles uno de otro, hecho indiscutible de la vida misma. [...] Éramos hermano y hermana, pero como en ese pasado lejano, antes de que el matrimonio entre hermano y hermana se convirtiera en sacrilegio».
Esa adhesión a la concepción nietzscheana del narcisismo, y más en general al culto del ego, característico de la _Lebensphilosophie_ de fines de siglo, preparó el encuentro de Lou con el psicoanálisis. Como destaca Jacques Le Rider, en todos sus textos ella buscaba, en efecto, recuperar un eros cosmogónico capaz de colmar la pérdida irreparable del sentimiento de Dios. Se encontró con Freud por primera vez en 1911, en Weimar. Era entonces amante de Poul Bjerre, un joven psicoanalista sueco quince años menor que ella: «El tiempo había suavizado sus rasgos», escribe Heinz Frederick Peters, su mejor biógrafo, «y ella les agregaba alguna femineidad al llevar suaves pieles, boas, esclavinas sobre los hombros. [...] Su belleza física era igualada, si no superada, por la vivacidad de su mente, su alegría de vivir, su inteligencia y su cálida humanidad».
Freud, que huía de la belleza femenina, desconfió en un primer momento de la atracción que sentía hacia esa mujer excepcional. Muy pronto, sin embargo, amó en ella la inteligencia del alma, la pasión por la vida, el optimismo inquebrantable. Ella encarnaba todas las facetas de esa femineidad que le era tan cercana y tan extraña a la vez. En efecto, Lou parecía contradecir su teoría de los tres estados de la vida femenina, porque había seguido siendo una muchacha deseable sin convertirse en madre, y una mujer madura que, al negarse a adoptar el papel de esposa en el hogar, no renunció jamás a la actividad sexual. En vez de considerarla como un enigma, Freud le ofreció la más alta forma de amor de que era capaz: una amistad hecha de elegancia, seducción y cortesía, y un intercambio intelectual como nunca lo había tenido con ninguno de sus discípulos o sus interlocutores. Por primera vez, no transformaría al amigo indispensable en un indispensable enemigo.
Desde el primer encuentro Freud se dio cuenta de que Lou aspiraba a ser admirada e incluso liberada de su personalidad demasiado fuerte, y de que había vivido una tragedia al renunciar a la maternidad. Comprendió desde ese momento que ella quería verdaderamente consagrarse al psicoanálisis y que nada se lo impediría. Por eso la admitió de inmediato entre los miembros de la WPV. Su presencia muda era a los ojos de todos el testimonio de una continuidad entre Nietzsche y Freud, entre Viena y la cultura alemana, entre la literatura y el psicoanálisis. Freud estaba enamorado de ella, no cabía duda alguna, y por eso se esforzaría en destacar, como para defenderse de lo que sentía, que ese apego era ajeno a toda atracción carnal.
Instalada en Viena en 1912, Lou asistía tanto a las reuniones del círculo freudiano como a las que organizaba Alfred Adler. Celoso, Freud la dejó hacer sin privarse de tratar a su rival de «personaje repugnante». Una noche, el sufrimiento causado por su ausencia lo llevó a escribirle estas palabras:
La eché de menos ayer por la noche en la sesión, y me alegra enterarme de que su visita al campo de la protesta masculina es ajena a su ausencia. He tomado la mala costumbre de dirigir siempre mi conferencia a cierta persona de mi círculo de oyentes, y ayer no dejé de mirar como con fascinación el lugar vacío que se había reservado para usted.
Ella no tardó en abrazar con exclusividad la causa del freudismo, y fue entonces cuando se enamoró de Victor Tausk, el hombre más atractivo y melancólico del círculo freudiano, que tenía casi veinte años menos que ella. Junto a él, Lou se inició en la práctica analítica, visitó hospitales, observó casos que le interesaban, conoció a intelectuales vieneses. Después de cada reunión de los miércoles Freud la llevaba a su hotel y, después de cada cena, la cubría de flores. Un día, un discípulo particularmente fanático se aventuró a hacerla objeto de uno de los deportes favoritos del grupo: la manía de la interpretación. Mientras ella tejía, como lo hacían muchas mujeres en la época, la señaló con el dedo y le hizo notar que parecía gozar entregada a un coito continuo, simbolizado por el movimiento de las agujas. Ella no respondió.
Lou Andreas-Salomé pertenecía al mismo mundo que Freud y compartía con él los mismos valores y la misma representación elitista de la Europa de la Belle Époque, cuya profunda miseria desconocía. Por eso la sorprendió el estallido de la Gran Guerra. Si Freud ponía de relieve que ese conflicto se asemejaba a una erupción pulsional sepultada en el inconsciente de los pueblos, ella veía en la guerra en general una especie de vampiro que chupa la sangre para apaciguar la necesidad del hombre de autodestruirse:
Siempre seremos nuestros propios asesinos. Quizá sea inevitable, pero, a causa de ello, nuestra culpa es universal y nuestro único modo de redención es aceptarla tal como es. [...] Cuando comprendí esto, me di cuenta, con asombro, de que por esa razón yo también habría combatido si hubiera sido un hombre, y de haber tenido hijos los hubiera mandado a la guerra.
Freud se encontraba claramente en el campo de los vencidos, pero para Lou la guerra representaba un hundimiento aún más grande. ¿En qué campo habría combatido? ¿Con los rusos o con los alemanes? No compartía los sentimientos nacionalistas de sus compatriotas del mundo germanoparlante pero tampoco podía adherirse, sin embargo, al combate antialemán de sus hermanos rusos. Por eso consideraba ese desencadenamiento de odio como una lucha fratricida interna a su propia subjetividad. Y en el momento de la Revolución de Octubre se mostró resueltamente hostil al bolchevismo. Antaño había admirado a los revolucionarios rusos y su ideal utópico, pero ahora, como el conde Pierre Bezujov cuando las tropas napoleónicas avanzan hacia Moscú, ya no veía más que la tragedia que se abatía sobre su país. Y Freud le respondió en el mismo tono: «Creo que no se puede tener simpatía por las revoluciones hasta que no han terminado. Por eso deberían ser breves. La bestia humana tiene, de un modo u otro, necesidad de ser domeñada. En síntesis, uno se vuelve reaccionario como ya lo había hecho el rebelde de Schiller frente a la Revolución francesa». Ni Freud ni Lou habían comprendido la gran miseria de los pueblos.
Después de la guerra Lou dedicó seis meses a ocuparse de los traumas nerviosos en un campo de trabajo de Königsberg. Mientras Freud se mostraba cada vez más pesimista con respecto a las tendencias homicidas de la humanidad, ella recuperaba su alegría de vivir a medida que, en su ciudad de Gotinga, se dedicaba a la práctica del psicoanálisis. Así, durante varios años estuvo presente en el movimiento psicoanalítico de la misma manera que Freud: siempre alejada y siempre próxima a ese círculo familiar que la había acogido pero que, ya, dejaba su lugar a la nueva generación de profesionales jóvenes y angloparlantes, menos aferrada al recuerdo del mundo de ayer.
Con Lou, Freud encontró por fin una interlocutora a quien podía tratar como una igual, como una extraña y como una mujer de su familia. Por eso la alentó a ser la protectora de su hija, con la cual él tenía tantas dificultades. Y al tomar conocimiento de los secretos que Anna le revelaba sobre su análisis, sobre su sexualidad, sobre sus conflictos, Lou se convirtió en su segunda terapeuta: supervisaba la cura llevada a cabo por Freud con la «hija-Anna» y a la vez gustaba con tacto y fruición los sabores que le ofrecía esa relación. Lou evocaba con Anna los chales, las pellizas, las pieles y los largos vestidos que le recordaban su juventud rusa impregnada de las novelas de Tolstói. Entre confidencia y confidencia, Anna le hablaba del olor de los bollos y del amor compartido por la vida canina y la recolección de setas.
Con el paso de los años Freud y Lou se vieron envejecer mientras presenciaban la descomposición de la Alemania de Goethe y Nietzsche de la que eran herederos. En 1931, cuando su querido profesor cumplió setenta y cinco años, ella le dedicó un libro en el cual expresaba su gratitud y sus desacuerdos, en especial con respecto a los errores cometidos por el movimiento en el caso de la creación artística y de la fe reducida por Freud a una alienación: un alegato contra el dogmatismo ya muy consolidado. Freud le respondió que ella ponía un orden femenino en el desorden ambivalente de su propio pensamiento. No podría decirse mejor.
Lou Andreas-Salomé casi no tuvo oportunidad de conocer a Marie Bonaparte, veinte años menor que ella. Opuestas una a la otra, tanto por su origen como por su cultura, su modo de vida o su adhesión al freudismo, estas dos mujeres tuvieron en común, no obstante, el amor vibrante que profesaban a Freud. Lou provenía de un mundo en agonía, Marie era una conquistadora que enarbolaba muy alta la enseña viril de su tío bisabuelo, cuyo nombre reivindicaba mucho más que su pompa imperial: «Si alguna vez alguien escribe mi vida, que la titule "La última Bonaparte", porque lo soy. Mis primos de la rama imperial solo son Napoleón». Si Lou fue para Freud la encarnación de la inteligencia, la belleza y la libertad —algo así como _la mujer_ —, Marie se convirtió más bien en la hija, la alumna, la paciente, la discípula, la excepcional traductora, la embajadora devota, la enamorada de los chow-chows y la organizadora del movimiento psicoanalítico francés, sobre el cual reinaría de manera a veces desastrosa durante décadas.
Ella reconcilió a Freud con la Francia que él amaba: la de Voltaire, Anatole France, Balzac, Sarah Bernhardt, Philippe Pinel, Charcot y Zola. Pero, igual que él, no se interesaba en los verdaderos representantes de la modernidad literaria —en especial los surrealistas—, que tenían empero un papel central en la introducción del psicoanálisis en Francia. Freud la llamaba _Prinzessin_ (su princesa), y cuando ella pretendió rivalizar con _la otra mujer_ , exclamó: «Lou AndreasSalomé es un espejo, no tiene ni su virilidad, ni su sinceridad, ni su estilo».
Hija de Roland Bonaparte, por su parte nieto de Lucien, Marie había perdido a su madre al nacer y la habían criado un padre que solo se ocupaba de sus trabajos antropológicos y una abuela paterna, verdadera tirana doméstica, ávida de éxito y notoriedad. Por eso Marie acarreaba consigo una angustia suicida que se constataba con frecuencia en los herederos de las dinastías europeas de principios del siglo XX, condenados a vagabundear en el simulacro de su grandeza perdida. Heredera por el lado de su madre de una inmensa fortuna con la que no sabía qué hacer, se asemejaba a un personaje del gran teatro freudiano de los comienzos: una verdadera princesa víctima de una neurosis aristocrática y en busca de un maestro que fuera a la vez su padre, su madre, su rey, su ancestro.
No obstante, sin olvidar jamás sus orígenes corsos y su pertenencia a la genealogía de los Bonaparte, que había hecho de ella una republicana racional y apegada a los ideales de la ciencia más evolucionada de su tiempo, no manifestaba la más mínima nostalgia por el mundo antiguo, a pesar de que su matrimonio concertado con el príncipe Jorge de Grecia, homosexual y amante de su tío Valdemar, príncipe de Dinamarca, la había elevado al rango de alteza real, de alta nobleza monárquica y colmada de honores. En realidad, al mismo tiempo que se mantenía aferrada a los códigos y rituales de su casta, Marie se burlaba de todos los convencionalismos, multiplicaba las aventuras amorosas y sufría de una indomable frigidez que la llevaba a encandilarse por todas las teorías sexológicas de su época. Habida cuenta de tal condición de princesa, atormentada por su femineidad deficiente, y cuyo nombre y lazos de parentesco remitían tanto al reino de Hamlet como a la tragedia de Edipo o el puente de Arcole, ¿habría podido escapar a un destino freudiano?
Cuando, por consejo de René Laforgue, conoció a Freud en Viena el 30 de septiembre de 1925, estaba al borde del suicidio. Se instaló con su doncella en una suite del hotel Bristol, donde la recibieron con todos los honores debidos a su título de alteza real, princesa de Grecia y de Dinamarca. El lugar le pareció lúgubre.
Con el seudónimo de A. E. Narjani, acababa de publicar en Bélgica un artículo en el que ensalzaba los méritos de una intervención quirúrgica, de moda en la época, consistente en acercar el clítoris a la vagina para transferir a esta el orgasmo clitoridiano. Marie creía así remediar la frigidez femenina y experimentó la operación en sí misma, en Viena, sin obtener jamás el menor resultado.
En un principio Freud desconfió de esta mujer célebre y mundana que gastaba fortunas en ropa y en el mantenimiento de su tren de vida. En respuesta a Laforgue, que elogiaba los méritos intelectuales de la princesa y su deseo de emprender un análisis didáctico y terapéutico, exigió que supiera hablar alemán o inglés, olvidando que ella era tan europea como él y tan políglota como la mayoría de sus discípulos. En lo fundamental, tenía muy pocas ganas de ocuparse de una persona a quien juzgaba frívola. Pero, pese a ello, llevó a cabo con ella, de 1925 a 1928 y en períodos sucesivos, una de las terapias psicoanalíticas más exitosas de toda la historia de su práctica: le evitó el suicidio y numerosas transgresiones destructivas. Marie consignó el desarrollo de ese análisis en su «Sommaire», con el agregado de notas, reflexiones y confidencias sobre Freud, de un interés considerable para todos los historiadores.
Desde el comienzo de la cura Marie tuvo derecho a una considerable interpretación. A raíz del relato de un sueño, en el que ella se veía en su cuna y asistía a escenas de coito, Freud afirmó con tono perentorio que no solo había oído esas escenas, como la mayoría de los niños que duermen en el cuarto de sus padres, sino que las había visto a plena luz del día. Atónita y siempre deseosa de contar con pruebas materiales, ella rechazó esa afirmación y protestó que no había tenido madre. Freud no desistió y contraatacó con la presencia de una nodriza. Finalmente, Marie decidió preguntar al medio hermano de su padre, que se ocupaba de los caballos en la casa de su infancia. A fuerza de mencionarle con insistencia el elevado alcance científico del psicoanálisis, consiguió que aquel le confesara su viejo amorío con la nodriza. Un poco avergonzado, el anciano contó que había hecho el amor a plena luz delante de la cuna de Marie. Era cierto entonces que esta había visto escenas de coito, felación y cunnilingus.
Hay que comparar esta interpretación con la dada a Serguéi Pankejeff. En el primer caso Freud había inventado una escena primordial que jamás había tenido lugar, pero que permitió al paciente dar un sentido a su sueño de los lobos. En el segundo, la paciente se negaba a creer en la existencia de esa escena que, empero, como pudo verificarlo, se había producido realmente. Tanto en un caso como en otro, la noción de «escena primordial» asumía el valor de un mito, que remitía a una genealogía inconsciente.
Con esa mujer que lo colmaba de regalos Freud dio, pues, pruebas de su genio clínico. En el transcurso del análisis le evitó una relación incestuosa con su hijo y le explicó por qué los pacientes no debían desnudarse durante la sesión. Además, se negó a responder a las preguntas que ella le hacía sobre su vida sexual y le hizo entender que no debía exhibirse frente a él. Por último, impuso ciertos límites a sus experiencias quirúrgicas sin lograr, con todo, impedirle pasar a los hechos. Como él mismo sufría dolorosas intervenciones, casi no tenía manera, en semejante situación transferencial, de interpretar el goce experimentado por Marie al manejar el bisturí.
Integrada en el movimiento psicoanalítico, ella participó en el debate sobre la sexualidad femenina de una manera muy personal. En efecto, transformó la doctrina freudiana en una tipología psicológica de los instintos biológicos, que se apartaba a la vez de la escuela vienesa y de la escuela inglesa. Distinguía en sustancia tres categorías de mujeres: las reivindicativas, que procuran apropiarse del pene del hombre; las obedientes, que se adaptan a la realidad de sus funciones biológicas o su rol social, y las esquivas, que se alejan de la sexualidad.
No hay duda de que Freud estaba fascinado por esas historias de clítoris cortados y de que encontraba en la obstinación quirúrgica de Marie el eco «biologizado» de sus propias tesis. Y esa fue la razón por la cual le regaló _Neger-Eros_ , la célebre obra del antropólogo vienés Felix Bryk dedicada a la práctica de la ablación entre los nandis. En ella el autor mostraba que los hombres de esta tribu buscaban así, mediante la supresión del último vestigio del órgano peniano, feminizar a ultranza el cuerpo de sus compañeras. Y Freud hacía notar a su paciente que la operación no anulaba la capacidad orgásmica de las mujeres, porque de haberlo hecho los hombres de la tribu no la habrían admitido.
Una vez más, Freud manejaba la ambivalencia. Por un lado le decía a Marie que ninguna cirugía podía resolver el problema de la frigidez femenina, y por otro la alentaba a efectuar investigaciones en ese ámbito. Ella no pedía tanto. Al punto, se apresuró a realizar investigaciones de campo sobre su tema fetiche. Y repetiría ese gesto durante toda su vida.
Tal fue el límite interpretativo con que Freud se topó en esa psicoterapia: nunca logró impedir que su querida princesa prosiguiera con su búsqueda descabellada de una inhallable femineidad. ¿Habrá que ver en este fracaso el signo de la imposibilidad en la que Freud se encontraba de escapar a la espiral infernal del «clítoris cortado», verdadero _dark continent_ de su propio pensamiento de lo femenino?
## CUARTA PARTE
# FREUD, LOS ÚLTIMOS TIEMPOS
### 1
Entre medicina, fetichismo y religión
A medida que la medicina se tornaba cada vez más científica, los Estados sentían una necesidad creciente de reglamentar las actividades terapéuticas. Parte integrante de la medicina, la psiquiatría aspiraba a ser más racional en sus clasificaciones por el hecho de que no se basaba en los mismos criterios clínicos que la disciplina médica. No obstante, al transformar al loco en un «caso», es decir, en un «enfermo», se había acercado a esta última al extremo de considerar ya al sujeto únicamente como un objeto apto para ser incluido en un marco nosográfico. Y en ese terreno, Freud, procedente de la neurología y la fisiología, había construido su disciplina como una rama de la psicología, a la vez que era un heredero de la tradición dinámica de Franz Anton Mesmer: magnetismo, hipnotismo, sugestión, catarsis y, para terminar, transferencia. El psicoanálisis devolvía la palabra al sujeto y reactivaba la idea antigua de que el paciente tiene, más que el médico, el poder de acabar por sí mismo con sus sufrimientos psíquicos.
Sin embargo, al crear en toda Europa y del otro lado del Atlántico instituciones destinadas a formar profesionales, _Herr Professor_ y sus discípulos ya no podían escapar, tras la Primera Guerra Mundial, a las reglamentaciones progresivamente sancionadas por los Estados con el fin de proteger a los pacientes de los falsarios, los impostores, los que vendían drogas y otros psicoanalistas salvajes a quienes por entonces se llamaba «impostores».
Toda sociedad, como es sabido, otorga un lugar a la figura del impostor, por el hecho mismo de que solo puede reproducirse si define con claridad lo que rechaza y lo que incluye en virtud de las normas que fija para sí. Así, el impostor, sea cual fuere el nombre que se le dé, es siempre una figura de lo heterogéneo. Definido como la parte maldita, es lo que escapa a la razón o el logos: el diablo, lo excluido, lo sagrado, la mancha, la pulsión, lo inconfesable. Pero es al mismo tiempo la droga ( _pharmakon_ ), el proveedor de drogas ( _pharmakos_ ), el drogado, el chivo expiatorio o el mártir a quien hay que castigar para que la ciudad se regenere. El impostor es pues un ser doble. Carga con la sanción pero es la condición misma de toda sanción. Envenenador o reparador, tirano o miserable, el impostor es el _otro_ de la ciencia y la razón, el _otro_ de nosotros mismos. En relación con ese tema, Freud, hombre de la Ilustración oscura, que había sido adicto a la cocaína, estaba en terreno conocido, entre nostalgia y ejercicio de un humor mordaz. Cada día sufría más por el intruso de dos cabezas que ponía trabas a su palabra: la prótesis que llamaba su «bozal» y el cáncer que se extendía irremediablemente.
Así, los representantes de la autoridad médica veían el psicoanálisis como una extrañeza: una intrusión, un impostor. Después de todo, la doctrina freudiana reivindicaba a Edipo, sabio entre los sabios pero también monstruo y mancha, cuando, al mismo tiempo, su movimiento estaba compuesto por una élite burguesa: médicos, letrados, juristas, cada uno de ellos con su título universitario. La acusación de impostura se explica en parte por el hecho de que Freud consideraba el psicoanálisis como una disciplina en toda regla que solo los «iniciados», debidamente analizados, estaban autorizados a ejercer. De ahí su hostilidad a la creación de una enseñanza del psicoanálisis en la universidad, a pesar de que él mismo lo enseñaba en un marco universitario. En otras palabras, tachaba de antemano de «impostora» a cualquier persona que se autorizara a enseñar su doctrina sin haber sido analizada.
Por otra parte, como Jones, ¿no se mostraba deseoso de excluir de su movimiento a quienes juzgaba «peligrosos», psicóticos, desviados, suicidas, transgresores, e incluso a los «analistas legos», etc.? Rank y Ferenczi terminarían por pagar las consecuencias. Y sin embargo —hay que admitirlo—, él mismo se había extraviado al garantizar la promoción de psicóticos y falsarios —Horace Frink o Hermine von Hug-Hellmuth— e interesarse peligrosamente en toda clase de fenómenos ocultos. Y como los partidarios de la medicina científica se dedicaban entonces a cazar impostores, los psicoanalistas serían las mejores piezas de esa cacería.
Los problemas comenzaron en Austria en 1924, cuando Freud derivó a Theodor Reik a un médico norteamericano, Newton Murphy, que quería seguir una cura psicoanalítica. No advirtió que ese paciente, aparentemente neurótico, presentaba signos de psicosis. Descontento con el tratamiento, Murphy se enemistó con su analista y lo denunció por ejercicio ilegal de la medicina. Antes de que se produjera ese incidente, el fisiólogo Arnold Durig, miembro del Consejo Superior de Salud de la ciudad de Viena, ya había pedido a Freud una evaluación sobre la cuestión del análisis practicado por no médicos: _Laienanalyse_ , el llamado análisis «lego». Su opinión no había sido convincente y el caso cobró una amplitud considerable cuando, en febrero de 1925, se prohibió a Reik el ejercicio del psicoanálisis: situación mucho más dramática para él, dado que no contaba con ninguna otra fuente de ingresos. Durante más de un año la cuestión de la definición de la impostura enardeció los ánimos, tanto en el mundo germanoparlante como en la prensa norteamericana. Una prohibición de esas características amenazaba perjudicar ante todo a las mujeres psicoanalistas, con muchos menos títulos que los hombres, pero también a quienes afirmaban, con toda la razón, que la disciplina inventada por Freud superaba largamente el marco de una medicina del alma. La riqueza del movimiento psicoanalítico se debía a la diversidad de quienes se habían unido a él. Originarios de los cuatro puntos cardinales de Europa y casi todos políglotas, los freudianos habían adquirido una gran cultura en el ámbito de las ciencias, las letras, la sociología, la filosofía y la antropología. Pocos de ellos eran autodidactas. La voluntad de encerrarlos en un molde único contribuía a una reducción real de su poder de intervención social e ideológica.
Siempre dispuesto a combatir a la WPV, Wilhelm Stekel, presidente de la Asociación de Analistas Médicos Independientes, se lanzó a la batalla contra el psicoanálisis lego, con contundentes denuncias relacionadas con el escándalo del caso Hug-Hellmuth y los excesos cometidos por los discípulos de Freud. Sin recordar que él mismo caía en sombríos estados patológicos, reafirmó la tesis de que un análisis demasiado prolongado conducía forzosamente al suicidio. Pero no aclaraba en qué aspecto los médicos podían ser mejores clínicos del alma que los no médicos. En cuanto al terrible Karl Kraus, se desfogó una vez más en _Die Fackel_ , donde sostuvo que la moda del freudismo perturbaba el turismo vienés: el mundo entero, decía, se apiñaba en los palacios de la antigua capital de los Habsburgo para tener el honor de frecuentar el diván de la Berggasse. Por su lado, Julius Wagner-Jauregg, a pesar de haber sido víctima de una acusación de mala praxis, no vaciló en escribir un informe donde estipulaba que solo los médicos debían tener el privilegio de practicar la cura freudiana.
Acusados de «sabotear» las curas, los psicoanalistas no médicos se convertían de tal modo en chivos expiatorios. No hay duda de que se trataba de un nuevo ataque al propio psicoanálisis. Los acusadores sabían muy bien, en efecto, que en el dominio de los tratamientos psíquicos la condición de médico no impedía ni los errores de diagnóstico ni los extravíos de los pacientes víctimas de la locura o la melancolía, que en muchos casos eran médicos. Ya hacía mucho que, de tanto en tanto, sus colegas acusaban de impostores a los psiquiatras, aunque estos eran médicos como ellos. E incluso de estar tan locos como sus pacientes: cosa que a veces, en efecto, era cierta. En realidad, como ya he dicho, en ese debate de los años veinte y treinta la preocupación por la seguridad se imponía claramente a la consideración de las cualidades clínicas de los médicos o los no médicos.
Sin embargo, se planteaba otra cuestión: ¿cómo habría de ser capaz un analista no médico de diferenciar entre un síntoma histérico y una enfermedad orgánica? Por más que se dijera que un analista con formación médica podía equivocarse aún más que un analista lego deseoso de dar prueba de su valía en materia de diagnósticos, siempre se terminaba por concluir en la necesidad de que el profesional tuviera un título de medicina y no de filosofía o psicología. Solo escapaba al dilema el psicoanálisis de niños, que se asociaba a una pedagogía.
Procedente de una familia de la mediana burguesía judía, Reik había conocido a Freud en 1911, y lo consideró desde el primer momento como un padre. Freud lo quería tanto como a Rank y le aconsejó renunciar a los estudios de medicina, que él contemplaba emprender, para consagrarse mejor a las investigaciones históricas y antropológicas. Envidiado por Jones y varios otros discípulos, Reik era objeto de burlas por su arrogancia y la manera de someterse al maestro y de justificar siempre las críticas que este le hacía.
En Viena se lo llamaba el niño terrible del psicoanálisis, el «bufón del rey» e incluso «Símil Freud». Reik se complacía en imitar a _Herr Professor_ con una especie de pasión que no hacía sino traducir ese ímpetu de la transferencia y la contratransferencia de las que él mismo era un brillante teórico. Se parecía a Freud, llevaba la barba de Freud, fumaba los cigarros de Freud, hablaba como Freud, pero nunca se atrevió a calificarse de amigo de Freud: «No, no soy su amigo», confesó un día, «porque no se puede ser amigo de un genio». Esta identificación con la figura del «gran hombre» no le impidió ser un autor original, y por esa razón Freud mostró a su respecto una fidelidad ejemplar, como sabía hacerlo cuando reconocía entre sus allegados un verdadero talento. Lo ayudó económicamente, le derivó pacientes y le encargó tareas intelectuales y militantes, sin omitir jamás criticarlo cuando lo estimaba necesario.
En Reik el amor por Goethe había precedido al amor por Freud. Pero, incapaz de llegar a ser un gran escritor, se había impuesto la tarea de leer la totalidad de la obra del poeta. Más adelante había descubierto en Freud la imagen sublimada de un Goethe transfigurado por el psicoanálisis. Y de resultas, el texto goethiano se había convertido para él en la fuente inagotable de todas las formas posibles de expresión autobiográfica, una manera de contarse sin que pareciera que cedía al ritual del diario íntimo. Como Freud, pensaba que los escritores y los poetas accedían al inconsciente —en especial al propio— más profundamente que los especialistas del alma. Por eso las obras literarias debían servir de modelos, no solo para la escritura de los casos clínicos, sino para el mismo método psicoanalítico en cuanto exploración científica de la subjetividad.
El texto goethiano ocupaba pues un lugar privilegiado en el centro de ese dispositivo. Enmascarado como un modelo de introspección freudiana, permitía a Reik proyectar su propia historia en la del narrador de _Poesía y verdad_ , es decir, en una autobiografía reinterpretada, por su parte, a la luz del psicoanálisis y los escritos de Freud. Goethe, como es sabido, cultivaba con deleite el autodisimulo y declaraba de buen grado que ningún hombre puede conocerse jamás. Lo cual no le impidió confesarse y hablar en abundancia de sí mismo. Por esa razón ya era en esa época uno de los autores más estudiados por la comunidad psicoanalítica de lengua alemana. Su _Fausto_ era objeto de una gran cantidad de interpretaciones, en la misma medida que _Hamlet_ o _Edipo_.
Cuando fue víctima de la acusación de impostura, pese a ser doctor en psicología y filosofía, Reik sufrió una desestabilización agravada por el hecho de que sus colegas vieneses no le prestaron ninguna ayuda. En cuanto a Freud, como no podía permanecer indiferente a la suerte de ese discípulo, su reacción consistió en enviar el 8 de marzo de 1925 una carta a Julius Tandler, a quien conocía bien desde la cuestión de las neurosis de guerra. Consejero municipal a cargo de la beneficencia y la salud, un año antes Tandler había contribuido a la designación de Freud como «ciudadano de honor de la ciudad de Viena». Si bien socialdemócrata y eminente personalidad de «Viena la roja», se lo conocía por sus posturas conservadoras. Hostil a la incorporación de las mujeres a la universidad y a la liberalización del aborto, defendía no obstante los intereses del psicoanálisis en conexión con Karl Friedjung, socialdemócrata como él, pediatra sionista, miembro de la WPV y puro representante de la cultura vienesa de fin de siglo, por la que seguía sintiendo nostalgia.
En su carta, Freud señalaba que el psicoanálisis no era ni una ciencia ni una técnica de obediencia médica, y que como tal no se enseñaba en la facultad de Medicina:
La requisitoria municipal me parece una injerencia injustificada en favor de la profesión médica y en detrimento de los pacientes y la ciencia.
El interés terapéutico queda protegido en tanto que la decisión sobre si un caso determinado ha de adoptar el tratamiento psicoanalítico continúe en manos de un médico. En todos los casos del señor Reik, yo mismo he tomado estas decisiones. Después de todo, también me creo en el derecho de enviar a un paciente que se queje de dolores en los pies y dificultades para andar a un zapatero ortopédico (si puedo diagnosticar que tiene pies planos) en lugar de prescribirle un tratamiento antineurálgico y eléctrico.
Si las autoridades oficiales, que hasta ahora han dado al psicoanálisis tan pocos motivos de agradecimiento, desean hoy reconocerlo como tratamiento eficaz y aun peligroso en determinadas circunstancias, deben crear garantías para que tal tratamiento no sea llevado a cabo temerariamente por los legos, médicos o no.
Y Freud proponía que la WPV participara en una comisión de control adecuada.
Esta intervención y la visita de Reik a Tandler no tuvieron el efecto previsto, y por esa razón Freud volvió a la carga, en septiembre de 1926, con un libro de asombrosa singularidad: ¿ _Pueden los legos ejercer el análisis_?, subtitulado «Diálogos con un juez imparcial». Entendía por «imparcial» a un personaje que se parecía tanto a Julius Tandler como a Arnold Durig. En cuanto al protagonista principal, que supuestamente le respondía, le atribuía el papel del analista lego, poseedor de la interpretación verdadera y la escucha más sutil. Por su forma, esta obra se inspiraba en una tradición literaria picaresca que Freud conocía bien: la de Cervantes. Pero tomaba más bien de una herencia platónica la idea de hacer dialogar a dos protagonistas tan opuestos uno a otro como respetuosos de sus opiniones mutuas. Con ese diálogo, Freud ponía claramente en escena dos facetas de sí mismo y dejaba ver, una vez más, cuán identificado estaba con el interminable combate singular del ángel y Jacob, Fausto y Mefistófeles, Hamlet y el espectro, Leonardo y su buitre, el uno siempre como sustituto del otro.
Las controversias sobre el _Laienanalyse_ provocaron en el movimiento psicoanalítico internacional un sismo mucho más perdurable que las relacionadas con la sexualidad femenina y el psicoanálisis de niños. En ellas se enfrentaron tres posiciones: los opositores a toda forma de análisis lego; los adeptos al análisis lego hostiles a toda forma de restricción, y los partidarios de un análisis lego enmarcado por reglas estrictas, con preferencia por la formación médica y sobre todo psiquiátrica.
Los primeros contaban con el apoyo de la casi totalidad de las sociedades norteamericanas, deseosas de librar un combate sin cuartel contra los sanadores, las sectas, los chamanes y los iluminados, numerosos en Estados Unidos. Los segundos se alineaban con Freud, Ferenczi y la Europa germanoparlante, con Rank, Ernst Kris, Anna Freud, Sachs, Bernfeld, etc. Apoyados por Jones y la escuela inglesa, los terceros se mostraban liberales y pragmáticos y contaban en sus filas con muchos analistas legos de primera línea: Joan Riviere, Melanie Klein, James y Alix Strachey.
En el desarrollo de las controversias se invocó toda clase de argumentos: en especial el tratamiento de las psicosis y la relación que el psicoanálisis debía mantener con los progresos futuros de la química y la biología. Pero como los norteamericanos, empezando por Brill, hacían obligatorio en sus institutos el título de medicina, tuvieron que hacer frente a la furia de Freud, cada vez más inclinado a pensar que en Estados Unidos el psicoanálisis se había convertido en la criada para todo al servicio de la psiquiatría. En realidad, su expansión en ese país había sido tan grande que, en el ámbito médico, ocupaba el lugar correspondiente en Europa a la tradición psiquiátrica, mientras que, del lado de los legos, se lo asimilaba a una «autoterapia» de la felicidad: «La palabra "psicoanálisis" es tan conocida aquí como en el Este profundo», escribiría Bernfeld en 1937, y añadiría: «El nombre de Freud es menos habitual y se pronuncia "Frud" [...]. Hasta las personas muy poco cultivadas saben que el psicoanálisis cura inquietudes, malestares conyugales, la falta de éxito y otros sinsabores, aun cuando busquen una _therapy_ más segura en el Liquor Bar».
Olvidando que junto con Jung había soñado con sitiar la tierra prometida del saber psiquiátrico, Freud consideraba ahora que la formación médica amenazaba incluso ser nociva para la práctica del psicoanálisis por quienes no eran médicos.
Finalmente, en mayo de 1927 Reik se benefició con un sobreseimiento, ya que se había descalificado al denunciante debido a sus contradicciones. La prensa de Estados Unidos anunció que la demanda de un norteamericano «contra Freud» se había desestimado. El análisis lego parecía a salvo por algún tiempo más, pero para Reik el mal ya estaba hecho. Perseguido por sus allegados, ridiculizado por Stekel y Kraus, jamás logró recuperar la paz en Viena. Por eso decidió instalarse en Berlín. Integrado en el BPI, formó alumnos y participó durante cinco años del auge espectacular del psicoanálisis en Alemania, que llegó a su fin con el ascenso del nazismo.
Freud perdió pues la batalla del análisis lego, que en el fondo no tenía otro objetivo que la afirmación de la irreductibilidad del psicoanálisis a cualquier saber constituido. Como tal, esta disciplina nunca se impondría en el campo universitario, y quienes habían combatido por el _Laienanalyse_ se vieron obligados, poco a poco, a obtener títulos universitarios y sobre todo a someterse a las reglamentaciones impuestas por los Estados. Durante la segunda mitad del siglo XX se convirtieron mayoritariamente en psicólogos.
Después de haber combatido en defensa del psicoanálisis lego contra los médicos, Freud decidió lanzar sus ataques contra la religión. Deseaba poner el análisis al abrigo de los sacerdotes que se pretendían confesores o pastores del alma, según fueran católicos o protestantes. Y temía que también ellos, como los médicos, quisieran incorporar la doctrina creada por él a su práctica. Soñaba, una vez más, con atribuir a ella un estatus que todavía no existía y que, además, nunca existiría. En su carácter de no creyente, Freud siempre se había declarado el peor enemigo de la religión, que consideraba una ilusión, lo cual no le impedía interesarse en ella de múltiples maneras.
Como Charcot y tantos otros científicos de su época, especialistas en las enfermedades del alma, Freud había estudiado los fenómenos de posesión con el propósito de arrebatar su significación a los representantes de la Iglesia y los exorcistas. En 1897 se había deleitado con la lectura del _Malleus Maleficarum_ , ese terrible manual publicado en latín a fines del siglo XV y utilizado por la Inquisición para enviar a presuntas brujas a la hoguera. Diez años después había publicado una comunicación sobre los actos obsesivos y los ejercicios religiosos en la cual comparaba la neurosis obsesiva con una «religión privada». Para terminar, en 1923, a petición del consejero áulico Payer-Thurn, estudió el caso de Christoph Haizmann, un pintor bávaro que en 1677, ocho años después de haber firmado un pacto con el diablo, sufrió convulsiones de las que se curó más adelante gracias a un exorcismo. Freud se propuso hacer del diablo un sustituto del padre y mostró que en realidad el pintor, convertido en hermano Crisóstomo, jamás se había curado. En su monasterio de Mariazell seguía recibiendo la visita del Maligno cada vez que bebía más de la cuenta. Freud oponía finalmente los beneficios del psicoanálisis a los fracasos del exorcismo y criticaba las prácticas religiosas de los tiempos antiguos, juzgadas poco compatibles con la _Aufklärung_.
La histérica asociada a una bruja, el diablo sustituto del padre lascivo, la religión como versión de una neurosis obsesiva procedente de la infancia o de la noche de los tiempos: esos eran los tres temas mediante los cuales Freud pretendía abordar la cuestión. Una vez más, el razonamiento estaba afectado por un importante defecto, consistente en interpretar retroactivamente fenómenos de posesión como otros tantos casos patológicos que solo la ciencia psicoanalítica podría esclarecer. Bajo el efecto de su manía interpretativa, Freud daba así pábulo, como sus discípulos, a una crítica que no beneficiaba en nada los intereses de su doctrina. Y sin embargo, al fabricar ficciones como esas, también contribuía a introducir en el trabajo del historiador un modelo de inteligibilidad subjetiva que la ciencia positiva excluía: daba un sentido a ese delirio antiguo que parecía reencarnarse en el sujeto moderno. Aquí, como en otros lugares, debido a su amor por el diablo, observaba desde una óptica inédita un campo narrativo, si bien intentaba apropiárselo de manera errónea. Contado por él, el drama de Haizmann tenía algún parecido con _La letra escarlata_ de Nathaniel Hawthorne, en especial cuando se trata de las diferentes apariciones del Maligno dotado de un pene estirado en forma de serpiente y coronado por dos grandes pechos, verdadera proyección de un emblema sexual materno sobre el órgano eréctil que sustituye al padre. E incluso cuando Freud se lanza a la descripción de la «neurosis ulterior» del malhadado pintor, aterrado por visiones femeninas y enfrentado a la voz de Jesucristo y luego a la imposibilidad de distinguir a las potestades divinas del Espíritu del mal. En la última frase de su escrito Freud zanjaba las cosas en favor del demonio, siempre presente pese a todas las confesiones de curación. Mefistófeles, el amigo de siempre, el indispensable enemigo, volvía así en la pluma de un narrador ambivalente presa de sus propios tormentos: ¿Freud o Haizmann?
Con _El porvenir de una ilusión_ Freud arremetía contra la institución misma, la religión como sistema de dominio. De ese modo respondía a Romain Rolland, que le había enviado un ejemplar de _Lilulí_ , su pieza teatral, con esta dedicatoria: «Al destructor de la ilusión». En esta farsa «aristofanesca», el escritor hacía una sátira de la ilusión personificada por una muchacha cándida que sembraba la discordia entre sus interlocutores. En cuanto a Freud, después de decir una vez más que la idea de cultura radicaba en la instauración de una muralla que obligara a los hombres a la renuncia pulsional, destacaba que las ideas religiosas que permitían precisamente mantener a la humanidad en la compulsión se desmoronaban a medida que la ciencia y la racionalidad las desmentían. Pero la religión, sin embargo, en su carácter de ilusión necesaria, no tenía que someterse al criterio de verdad ni enfrentarse a la prueba de la realidad. En cuanto neurosis infantil, decía Freud, en un mundo copernicano y darwiniano que ya ha derribado la idea de la omnipotencia divina, está destinada a ser superada. Viniendo de un hombre que no dejaba de visitar las ciudades italianas y que estaba profundamente imbuido de los valores de la civilización occidental —herencia tanto de la época medieval como del Renacimiento—, el argumento parecía un poco débil, si se tenían en cuenta las evidentes relaciones de la técnica psicoanalítica de la manifestación del inconsciente con la confesión.
Pero, en el fondo, si _Herr Professor_ reducía la religión a una ilusión, preveía que estaba en vías de imponerse como una cultura. En esa época la Iglesia católica combatía el freudismo tanto como Freud combatía la religión. Pero pretendía hacerlo de manera racional, exaltando las investigaciones científicas contra el oscurantismo, como lo testimoniaba en Italia el padre Agostino Gemelli, monje franciscano, médico y ex alumno de Kraepelin, que procuraba integrar los trabajos de la psicología experimental en la neoescolástica. Gemelli había fundado en Milán una Escuela de Psicología dentro de la Universidad Católica del Sagrado Corazón y se apoyaba en las teorías de Janet, para dar así una respuesta a la doctrina demasiado «sexual» de los freudianos.
Freud creía, sin ninguna duda, que el psicoanálisis podía curar al sujeto moderno de la pérdida de la ilusión religiosa: a riesgo de ocupar su lugar y fracasar, a semejanza del socialismo que no había conseguido erradicarla.
En el aborrecimiento que sentía por el socialismo revolucionario, sustituto a sus ojos de una nueva religión, Freud apuntaba no solo a la Revolución de Octubre de 1917 sino también a un enemigo de siempre, Alfred Adler, a quien reprochaba, en el colmo de la ironía, su manía interpretativa: «Tengo frente a mí», escribía a Ferenczi,
las palabras que ha escupido sobre Mussolini. Tal vez usted no las haya leído y no sabe aún cómo puede explicarse el fascismo. Voy a decírselo: por el sentimiento de inferioridad infantil de Mussolini. Él habría dado la misma explicación si M. hubiera establecido en Italia un orden social homosexual donde el coito normal fuera castigado con la prisión, o un régimen de trapenses donde estuviera prohibido hablar por ser una actitud antipatriótica. El único fenómeno al cual no ha aplicado su teoría es el socialismo, porque forma parte de él.
En la última parte de _El porvenir de una ilusión_ Freud la emprendía con su discípulo y amigo Oskar Pfister, pastor en Zurich. Este había ido a visitarlo a Viena en 1909 y se había mantenido de su parte durante el gran conflicto con Jung. Freud apreciaba su generosidad, su optimismo, y sabía bien que este «querido hombre de Dios», como lo llamaba, se pretendía heredero de las curas del alma ( _Seelsorge_ ) y jamás renunciaría a su fe. Se había embarcado en la causa freudiana porque, en su juventud, lo habían conmocionado el espectáculo de la degradación moral ligada a la industrialización y la incapacidad de la vieja teología abstracta para responder a las angustias del hombre moderno. Su aspiración era ser pedagogo. En 1919 había fundado la Sociedad Suiza de Psicoanálisis (SSP) y había tenido que enfrentarse a los opositores al psicoanálisis lego, en especial a Raymond de Saussure, que le reprochaba sus psicoterapias de corta duración.
Inconformista e incapaz de la más mínima idolatría, Pfister no vacilaba en criticar a Freud. Y si pensaba que el psicoanálisis era el heredero de la tradición del «pastorado de almas testamentario», mucho más que de la tradición de la confesión católica, tenía la convicción de que esas dos formas de terapia apuntaban a liberar al sujeto por medio de un acceso a la verdad del alma y la restauración del amor. Por eso replicó a _El porvenir de una ilusión_ con un brillante ensayo publicado en la revista _Imago_ : «La ilusión de un porvenir». En él afirmaba con toda la razón que la verdadera fe era una protección contra la neurosis y que la posición misma de Freud era una ilusión. Desconocía —decía Pfister— la significación de las experiencias místicas, que no tenían nada que ver con la religión. Freud ignoraba además que ese modo de conocimiento de los misterios de Dios y la fe, expresado en flamígeras narraciones literarias, siempre había sido rechazado por las Iglesias: «¡Cuán remotos son para mí los mundos en que desarrolla usted su existencia! El misticismo constituye en mi caso un libro tan cerrado como la música», diría Freud a Romain Rolland. Pero también confesaba, en relación con la muerte, que todo individuo inteligente conoce «un límite más allá del cual puede convertirse en místico e ingresar en su ser más personal». El amigo Pfister había puesto el dedo en algo que Freud no había pensado, presente en los intersticios de la obra del maestro. _El porvenir de una ilusión_ era un mal libro y Freud lo sabía.
Más allá del intercambio luminoso con Pfister, otro diálogo se desplegaba en la sombra entre Freud y Carl Liebman, un joven norteamericano afectado de fetichismo y cuya silueta, apenas sugerida, se dejaba adivinar en varias ocasiones en la correspondencia de _Herr Professor_ , sin irrumpir jamás con claridad. Entre un científico célebre, cuya existencia estaba a la vista de todos, y un paciente anónimo sumido en el sufrimiento de una vida minúscula, se había entablado desde 1925 una relación importante para la evolución de la conceptualidad psicoanalítica. De nuevo se oponían, en las entrelíneas de una confrontación con Pfister, dos órdenes de realidad: conciencia crítica del médico por un lado, conciencia trágica del enfermo por otro, división entre razón y sinrazón y entre pensamiento clínico y locura.
Por su bisabuelo, Samuel Liebman, creador de la célebre cerveza Rheingold, el joven Carl Liebman, nacido en 1900 e hijo de Julius Liebman, descendía de una familia de comerciantes judíos alemanes naturalizados norteamericanos a mediados del siglo XIX. Llevaba el nombre de pila de su abuelo y había pasado la infancia en la soberbia Julius Liebman Mansion que su padre había hecho construir en Brooklyn. Como un personaje de la literatura novelesca de los primeros veinticinco años del siglo, también él se asemejaba a muchos otros pacientes de Freud afectados de patologías múltiples y casi incurables. Carl siempre se había sentido diferente a los otros adolescentes. A los cinco años, mientras su niñera lo bañaba junto a su hermana, había experimentado un terrible miedo. La mujer lo había amenazado con «cortarle el pene» como «había hecho con su hermana» si seguía quejándose porque ella lo secaba demasiado vigorosamente con una toalla. A posteriori manifestó muchas veces una excitación sexual extrema al observar a jóvenes que llevaban _slips_ de atletas o «suspensorios» ( _athletic supporter_ ), intensificada por su apartamiento de las actividades deportivas y su negativa a trepar a los árboles. El joven Carl, un muchachote erudito, demacrado y políglota, evitaba todo contacto con las chicas. Lo obsesionaba la supervivencia de sus espermatozoides, a los que llamaba «espermanimálculos», y cuando eyaculaba se sentía un asesino de masas. Un día creyó incluso que había matado a un bebé. En la Universidad de Yale, donde cursaba estudios destinados a hacer de él el brillante heredero de una de las dinastías más adineradas de Estados Unidos, se lo trataba de «maricón». Pronto adquirió el hábito de masturbarse de manera compulsiva y usar permanentemente un suspensorio debajo de la ropa: un fetiche.
Después de obtener su título el joven buscó ayuda con un psicoanalista norteamericano. Al no encontrar ningún consuelo, viajó solo a Europa para ser «artista». En Zurich, en 1924, consultó a Pfister, que tomó conciencia de la extrema gravedad de su estado y le recomendó que visitara a Bleuler. Tras una entrevista de cuarenta y cinco minutos, este emitió un diagnóstico oscilante entre la neurosis obsesiva y la esquizofrenia. Se inclinó en definitiva por una «esquizofrenia leve» y agregó que Carl le había mencionado su compulsión de lavarse las manos y su convicción de ser observado sin cesar por la gente en la calle. Durante la conversión había manoseado todos los objetos del escritorio del psiquiatra, incluido un cenicero, sin preocuparse por la suciedad. Bleuler recomendaba una cura analítica y la elección de una profesión capaz de liberarlo de sus síntomas.
El 21 de diciembre de 1924 Freud respondió favorablemente a la solicitud de Pfister y, el 22 de febrero del año siguiente, aceptó ocuparse de la terapia analítica del joven por veinte dólares. En mayo, sin siquiera haberlo visto, se reunió con sus padres, Julius y Marie, a quienes consideró demasiado dispuestos a «sacrificarse» por su hijo. Después de algunas vacilaciones y de hacer notar a Pfister que sin duda era preferible dejar que Carl «marchara a su ruina» bajo el efecto de su insociabilidad, lo recibió por fin en septiembre. Pero muy pronto, consciente del estado de deterioro en que se encontraba el joven, escribió a sus padres para comunicarles la posibilidad de que la cura nunca resultara en una mejoría. No obstante, con el paso de los encuentros comenzó a sentir un verdadero apego por Carl, sin dejar de estar convencido de que era psicótico (demencia paranoide) e impermeable a cualquier evolución y, sobre todo, de que no vacilaría en suicidarse tan pronto como se le presentara la oportunidad. Así, Freud volvía a tomar en análisis a un paciente para quien ningún tratamiento parecía posible. Pero si él, el gran especialista en las enfermedades del alma, renunciaba a tratar a ese tipo de enfermos ¿quién lo haría en su lugar? Decidió, pues, pelear por él.
En la época, con el impulso de su refundición teórica y clínica y en el marco de los grandes debates acerca de la sexualidad femenina, Freud reflexionaba sobre la mejor manera de explicar en términos estructurales la diferencia entre neurosis, psicosis y perversión. Distinguía además las principales figuras de la negatividad capaces de marcar dicha diferencia y servir de puntos de apoyo a una caracterización de los mecanismos de defensa en acción dentro de esa trilogía.
En 1923 definía lo que llamaba desestimación o desmentida ( _Verleugnung_ ) para caracterizar un mecanismo de defensa mediante el cual el sujeto se niega a reconocer la realidad de una percepción negativa y en especial la falta de pene en la mujer. La idea de la alucinación negativa, inventada por Bernheim, se había aceptado mucho tiempo atrás en la psiquiatría y era moneda corriente en la literatura: reconocer la realidad de algo que no existe para negarla mejor. Dos años después, con motivo de un intercambio epistolar con René Laforgue sobre la cuestión de la escotomización, Freud reafirmaba con vigor su elección del término «desmentida» para referirse a ese mecanismo de defensa y, al mismo tiempo, proponía otro término, la denegación ( _Verneinung_ ), para caracterizar otro mecanismo de defensa por medio del cual el sujeto expresa de manera negativa un deseo o un pensamiento cuya existencia reprime. Por ejemplo, en una frase como «no es mi madre» pronunciada por un paciente en relación con un sueño, lo reprimido se identifica de manera negativa sin aceptarse. Freud asociaba la desmentida con el proceso de la psicosis —negación de una realidad exterior con reconstrucción de una realidad alucinatoria— y hacía de la denegación lo característico de un proceso neurótico. Pero, en ese contexto, ¿cómo caracterizar el mecanismo de defensa propio de la perversión? Para responder a esta pregunta Freud utilizaba la noción de escisión ( _Spaltung_ ), también utilizada en la literatura psiquiátrica y sobre todo en Bleuler, para designar fenómenos de disociación de la conciencia o de discordancia que ocasionan una alienación mental o un trastorno grave de la identidad: la esquizia, por ejemplo, presente en la esquizofrenia.
Si en la clínica freudiana la desmentida, en el sentido de rechazo de la realidad, caracteriza la psicosis, y la denegación es específica de la neurosis, la desmentida propia de la perversión está «entre las dos», toda vez que es también la expresión de una escisión de la que deriva la coexistencia, dentro del yo, de dos actitudes contradictorias, una consistente en negar la realidad y otra, en aceptarla. En esta perspectiva, Freud llevaba la discordancia al corazón del yo ( _Ichspaltung_ ), en tanto que la psiquiatría dinámica la situaba entre dos instancias y la caracterizaba como un estado de incoherencia y no como un fenómeno estructural. De ese modo, Freud incorporaba la perversión a un continuo entre neurosis y psicosis. En la neurosis hay represión de las exigencias de ello; en la psicosis, rechazo de la realidad, y en la perversión, escisión entre el saber y la creencia: «Sé que tal cosa existe pero no quiero saber nada de ella», y una variante: «Sé que tal cosa no existe pero no quiero saber nada de esa inexistencia». Para Freud, siempre dispuesto a remitir todo conflicto a una causalidad sexual, esa desmentida de la inexistencia significa que el sujeto no quiere saber nada de la falta del pene en la mujer y, por lo tanto, que la sustituye por otra cosa, conforme a su creencia.
Sin dedicarse jamás a elaborar, como los sexólogos, un gran catálogo de las perversiones sexuales, Freud no podía no abordar la cuestión, por el hecho mismo de que trataba en análisis a pacientes acerca de quienes era difícil decir si padecían una psicosis o una perversión. Y en particular los fetichistas, esos casos tan apasionantes para los especialistas en las enfermedades del alma. Según el autor de _Tótem y tabú_ , que adoraba a los animales y las divinidades, y que veía al salvaje como un niño y la infancia como un estadio anterior a la edad adulta, el fetichismo era ante todo una forma de religión.
Esta se caracteriza por la transformación de animales y objetos inanimados en divinidades a las que se atribuye un poder mágico. Pero como perversión sexual, esta religión individualizada vira hacia la patología cuando el sujeto solo puede apegarse a objetos inanimados y siempre venerados como otras tantas partes del cuerpo femenino. En ese sentido, Freud consideraba que el fetiche —zapatos, ropa e incluso una parte del cuerpo, pie o nariz brillante, etc.— era el sustituto de un pene. Y de esa consideración deducía la conclusión de que no había fetichismo femenino porque, decía, en las mujeres está fetichizado el conjunto del cuerpo, y no tal o cual objeto o zona corporal. A su entender, entonces, el presunto fetichismo femenino no era más que una manifestación del narcisismo en el cuerpo. Freud parecía desconocer con ello la existencia —poco común, es cierto— de mujeres verdaderamente fetichistas.
Sus reflexiones estaban en ese punto cuando recibió a Carl Liebman. Consciente de estar frente a un caso difícil, y sobre todo ante un joven desdichado cuyos padre querían a toda costa verlo conforme a las altísimas aspiraciones sociales que habían concebido para él, trató por todos los medios de atribuir una significación a sus angustias, sus delirios, su práctica compulsiva de la masturbación y su fetichismo. Durante las sesiones, en vez de colocarse detrás del diván, caminaba de un lado a otro rodeando a su perro o meneando su cigarro, ansioso él mismo por no lograr ningún asidero en la patología de ese paciente, que se forjó entonces la convicción de que _Herr Professor_ se negaba a considerarlo como un verdadero hombre, viril, dado que no le ofrecía cigarros.
En cierto momento de la cura, de acuerdo con sus hipótesis sobre la desmentida perversa de la falta del pene en la mujer, Freud le explicó que su fetiche era el sustituto del pene (o del falo) de su madre. Por eso el joven usaba un suspensorio. Y agregó que esa prenda le servía para ocultar por completo sus órganos genitales y, por ende, para negar la existencia de la diferencia de los sexos. En razón de ello, ese fetiche expresaba la idea de que la mujer puede estar tanto castrada como no castrada, y de que es el hombre quien lo está. En otras palabras, si seguimos a Freud, el fetiche de Carl servía para disimular todas las formas posibles de falta del pene y por lo tanto para negar la existencia de la diferencia de los sexos. Freud añadió que Liebman, en su infancia, debía de haber sentido una conmoción al descubrir que su madre no tenía pene. ¿Pensaba asimismo en el recuerdo de la amenaza de amputación del pene?
De toda esta historia también deducía que Carl debía de haber visto, de niño, una estatua antigua con el sexo oculto bajo una hoja de parra, y que esa escena había constituido para él el primer momento de un esbozo de su fetiche actual. Después de comunicarle esa interpretación sobre una hipotética «escena primordial», Freud exigió a Carl dejar de masturbarse, la única manera, en su opinión, de llegar a comprender algo de sus síntomas: «Me empeño en este momento», dijo a Pfister,
en exigirle que se resista expresamente a la masturbación fetichista a fin de confirmar, por aquello que le es personal, todo lo que adiviné acerca de la naturaleza del fetiche. Pero él no quiere creer que esa abstinencia ha de llevarnos a ese punto y que es indispensable para el progreso de la cura. Por otra parte, ligado a él por una gran simpatía, no puedo decidirme a despedirlo y correr así el riesgo de una salida funesta. Sigo adelante, pues, y es probable que se me escape cuando yo abandone definitivamente mi obra.
Sobre la base de la historia de Liebman, Freud se apresuró entonces a escribir un artículo sobre el fetichismo en el cual universalizaba la idea, ya esbozada en el libro dedicado a Leonardo da Vinci, de que el objetivo y el sentido del fetiche son los mismos en todos los casos:
el fetiche es un sustituto del pene [...]. [M]e apresuro a agregar que no es el sustituto de uno cualquiera, sino de un pene determinado, muy particular, que ha tenido gran significatividad en la primera infancia, pero se perdió más tarde. [...] Para decirlo con mayor claridad: el fetiche es el sustituto del falo de la mujer (de la madre) en que el varoncito ha creído y al que no quiere renunciar; sabemos por qué.
Freud ya había formulado una hipótesis similar en una carta a Jung acerca del «pie hinchado de Edipo», al destacar que se trataba sin duda del pene erecto de la madre. En su artículo de 1927 designaba el fetiche de Carl como unas «bragas íntimas [ _Schamgürtel_ ], como las que pueden usarse a modo de traje de baño».
Armado con esa interpretación, Freud creía poder aliviar al paciente. Este, sin embargo, siguió masturbándose compulsivamente. Durante algún tiempo se encerró en su habitación de hotel para apartarse del mundo. Es indudable que Freud tenía razón al pensar que el suspensorio era el sustituto de un órgano genital, pero se obstinaba, para designarlo, en utilizar la vieja palabra alemana _Schamgürtel_ , cuyo significado literal es «cinturón de vergüenza». En la época, dicha palabra remitía también a una prenda derivada del _subligaculum_ latino, paños plegados o enrollados que cubren el sexo y las nalgas de los hombres. Cuando se sabe que el análisis se desarrollaba en parte en inglés, cabe preguntarse por qué Freud no se limitó a traducir _athletic support_ como _suspensorium_. En efecto, lejos de llevar un cinturón de vergüenza —una manera de disimular la diferencia de los sexos—, Carl exhibía al contrario, gracias a su fetiche, un símbolo de la arrogancia fálica que tanto admiraba en los jóvenes atletas de su universidad. Bajo la ropa disimulaba, en realidad, lo que más le faltaba: un miembro recubierto por un estuche y realzado por una «concavidad». ¿Se trataba del pene faltante de la madre? Freud se obstinaba en decirlo, pero nada lo prueba.
Es de imaginar en todo caso la conmoción que sintió el joven cuando Freud le contó que su fetiche lo remitía a una escena primordial en cuyo transcurso él habría descubierto la falta de pene de la madre. Es cierto, esta interpretación daba un significado a su terror antiguo por el pene cortado. Pero no hacía eco en absoluto a lo que para él era ese suspensorio fetichizado, bien conocido en los campus universitarios. Carl, no obstante, recibió la palabra freudiana a la vez que la negaba. Y Freud interpretó ese rechazo como una manifestación de resistencia. Notó, de todos modos, una leve mejoría en su paciente.
Podemos preguntarnos cómo habría reaccionado Liebman si la interpretación hubiese sido diferente y, en lugar de designar el fetiche como un cinturón de vergüenza, Freud lo hubiera erigido en el símbolo de una arrogancia fálica, sin perjuicio de considerarlo como el sustituto del pene faltante de la madre. En ese caso, ¿habría rechazado el joven la interpretación con tanta violencia? Nadie puede decirlo. Parece indudable, en todo caso, que ningún consejo, ninguna ayuda, ninguna terapia, ninguna interpretación parecían en condiciones de influir sobre el estado de ese joven, tan distanciado de sí mismo y tan replegado en la contemplación mística de su propia destrucción.
Interesado en no mentir, Freud se dirigió a Marie Liebman. Le reveló que su hijo sufría una esquizofrenia paranoide pero que, no obstante, él, Freud, abrigaba no solo temores sino también esperanzas para el futuro. El análisis se prolongó durante otros tres años. Una vez más, a despecho de su pesimismo sobre el resultado de la cura y el temor que sentía ante la idea de un posible suicidio de Carl, Freud la prolongó sin que, pese al trabajo hecho, la psicosis dejara de agravarse. Liebman se apegó cada vez más a su ilustre analista al mismo tiempo que se hundía sin límites en la locura y las obsesiones. Cuando Freud comprendió que, a pesar de toda la atención que prestaba a ese paciente, no lograría aliviarlo, lo derivó a Ruth Mack-Brunswick, convencido de que una mujer sería más apta para hacerse oír. Los resultados obtenidos por ella no fueron mejores.
En 1931 Carl visitó una última vez a Freud antes de regresar a Estados Unidos. En París tuvo algunas sesiones con Rank, que diagnosticó un trauma de nacimiento. Sus padres lo pusieron bajo vigilancia, pero él no tardó en descubrir la maniobra. Tras vagabundear y caer en la miseria material y psíquica, en el momento mismo en que la crisis económica se intensificaba, retornó al seno de su familia, donde su padre lo contrató como chófer.
Algún tiempo después intentó suicidarse clavándose un cuchillo de caza en la caja torácica, razón por la cual Abraham Brill tomó la decisión de internarlo en la lujosa clínica McLean de Harvard, donde se admitía, como en el sanatorio Bellevue, a pacientes adinerados. Pero Carl Liebman quería seguir una cura analítica con discípulos norteamericanos de Freud, por quien sentía la veneración de siempre. Su madre se opuso. Él contó entonces a quien quisiera escucharlo que Freud le había hecho descubrir el origen de su enfermedad: la vista del pene faltante de la madre. Sufrió mucho la estupidez de esa vida carcelaria y se quejó a menudo del vacío de su existencia, salpicada de ejercicios con plastilina y de la obligación de jugar al billar o hacer cerámica. Prefería a ese calvario la turbulencia de sus años vieneses, durante los cuales había escuchado toda clase de relatos sobre penes ausentes, vergonzosos o cortados.
Con el paso de los años, después de haber intentado evadirse, se convirtió en un caso célebre y fue sometido a todos los tratamientos posibles ligados a los «progresos» de la psiquiatría en centros hospitalarios: electrochoques, convulsoterapia, topectomía. A posteriori nunca olvidaría su fetiche adorado, y cuando se lo visitaba para escuchar la legendaria historia de su cura con _Herr Professor_ , en medio de los chow-chows y los cigarros, repetía lo que les decía cada día a sus médicos y enfermeros: «Soy el pene de mi padre».
Tal fue el destino de ese inolvidable paciente freudiano, poseído por la locura y condenado a no curarse nunca y cuya psicoterapia, si bien nunca fue objeto de un relato por ninguno de sus protagonistas, sigue presente para siempre en las entrelíneas de una obra, de una correspondencia y de un archivo, como la huella arqueológica de una progresión de la muerte en las existencias paralelas de Freud y Liebman, una gloriosa, otra oscura.
A partir de 1929 el cansancio comenzó a afectar a Freud en el ejercicio de su práctica. Cada vez más dolorido por el cáncer y los tratamientos que se le aplicaban, bajaba de peso y toleraba cada vez menos las curas difíciles, aun cuando le aportaran la comodidad material que necesitaba para mantener a su familia, sus allegados y el movimiento psicoanalítico. Con el propósito de entretenerse, se abonó a una biblioteca atendida por Emy Moebius y su amiga Gerty Kvergic, la Fremdsprachige Leihbibliothek, frecuentada por diplomáticos y especializada en el préstamo de libros en lenguas extranjeras. Minna acudía a ella en su nombre y le llevaba novelas policíacas de Dorothy Sayers y Agatha Christie, que le encantaban. Emy se convirtió entonces en amiga de la familia y siguió siéndolo hasta su emigración a Estados Unidos.
El futuro era sombrío: crisis económica en Estados Unidos, instauración de un régimen fascista en Italia, ascenso del nazismo en el mundo germanoparlante. Europa parecía otra vez presa de esa pulsión de destrucción que Freud había descrito con tanta claridad. Él señalaba con desprecio lo que llamaba la «chusma»: los imbéciles, las masas enfurecidas, la necedad del tiempo presente. En julio de 1930 soñó una vez más con el Nobel cuando la ciudad de Frankfurt le concedió el premio Goethe no solo porque «su psicología había enriquecido la ciencia médica» sino porque su obra había contribuido a la literatura y las artes. Muy honrado, Freud declaró que Goethe se habría apasionado, sin duda alguna, por los descubrimientos del psicoanálisis.
La muerte lo obsesionaba cada vez más, y cuando Amalia, a los noventa y cinco años, falleció a raíz de una terrible gangrena en la pierna, se sintió aliviado: a tal punto había temido que un día le anunciaran que su hijo la había precedido en la tumba. Opuesto a los ritos religiosos y agotado por sus propios sufrimientos, no participó de las exequias: sin duelo no hay dolor. Tuvo con todo la convicción de que en los estratos profundos de su inconsciente esa muerte iba a trastocar su vida. No sería así.
Freud había perdido a su padre antes de elaborar su obra y perdía a su madre nueve años antes de su propia muerte: ella había tenido tiempo para contemplar la gloria de su «Sigi» adorado. La enterraron junto a Jacob conforme al rito judío. Algunos días después Adolfine se refugió en la Berggasse. Había sido el principal sostén de su madre y también la víctima de todos sus ataques. Ahora su familia quedaba reducida a su hermano, sus hermanas, sus sobrinos. Freud la acogió con calidez, a pesar de que, en líneas generales, casi no prestaba atención a sus cuatro hermanas cuando acudían los domingos a visitar a Martha y Minna.
En esa época había comenzado a escribir su «Kürzeste Chronik», «La más breve crónica», una especie de diario íntimo e informal en el que anotaba día tras día, y de manera lacónica, los acontecimientos que le parecían importantes: lo sucedido a sus perros y a los objetos de su colección, las inclemencias, los asuntos familiares, los fallecimientos, las visitas, las menudencias de la vida cotidiana, la actualidad política. Inauguraba de ese modo un nuevo estilo narrativo, entre la escritura periodística —las noticias breves— y el catálogo de nombres y cosas, las listas. Una literatura minimalista, una descripción despojada de la realidad que no aspiraba a ninguna interpretación.
A pesar de la enfermedad, Freud conservaba todas sus facultades intelectuales. Quería cada día más a sus hijos, sus nietos y sus mujeres: Lou, Anna, Minna, Martha, Dorothy, Marie. A sus dos empleadas domésticas, Anna y Maria, sumó una tercera, de veintisiete años, una antigua aya de los hijos de Dorothy: Paula Fichtl. A Martha le caía bien. Hija de un molinero alcohólico de Salzburgo, había trabajado desde niña como criada y nunca quiso fundar un hogar. Huía de los hombres como de la peste después de cada nueva aventura. Entre los ya avejentados Freud encontró una verdadera familia sustituta. _Herr Professor_ vivía pues en la Berggasse rodeado de seis mujeres, cada una de las cuales se encargaba de una tarea perfectamente definida.
Por otra parte, Freud seguía con atención los asuntos amorosos y conyugales de los otros miembros de su familia: en especial los de sus sobrinos y sobrinas. Repartía con generosidad dinero para pequeños gastos entre sus nietos. Dos nuevos interlocutores, ambos judíos, cobraron entonces gran importancia en sus intercambios epistolares: Stefan Zweig, escritor vienés, liberal y conservador, profundamente europeo, ya célebre en el mundo entero, y Arnold Zweig, escritor berlinés, sionista, socialista y comunista, radicado en Palestina desde 1933. Ni uno ni otro eran sus discípulos y ninguno de ellos pasó del estatus de amigo al de enemigo.
Stefan Zweig le enviaba a Freud todas sus obras dedicadas y le recordaba sin cesar cuánto le debían los escritores contemporáneos: Proust, Joyce y otros. Pero Freud no respondía nada, ¡y con razón! Seguía sin conocer las obras de esos escritores, lo cual lo llevaba muchas veces a mostrarse severo con Zweig, en especial cuando este escribió un ensayo, _La curación por el espíritu_ , en el que trazaba un paralelismo entre tres vidas: las de Mesmer, el propio Freud y Mary Baker Eddy, fundadora norteamericana de una secta, la Christian Science, que pretendía curar las enfermedades por el éxtasis y la fe.
Si bien Freud admitía la idea de que Mesmer había sido en efecto el iniciador, más allá del magnetismo, del procedimiento de la sugestión, no se consideraba su heredero. Demasiado aferrado a una concepción mitológica y genealógica de la ciencia histórica, le resultaba difícil admitir el concepto de larga duración, ya apreciado por los historiadores. Pero lo peor para él, en el momento en que arreciaba la batalla en favor del _Laienanalyse_ , era que lo pusieran junto a Mary Baker Eddy, que encarnaba todo aquello de lo que el movimiento psicoanalítico quería, con toda la razón, mantenerse a distancia, a veces contra el propio Freud. Y este respondió al escritor que Eddy era ante todo una enferma mental: «Sabemos que el loco furioso desarrolla en su crisis fuerzas de las que no dispone en los tiempos normales. Lo que hay de insensato y criminal en todo lo que sucedió con Mary B. E. no se destaca en la presentación que usted hace de ella, y tampoco la indecible desolación del telón de fondo norteamericano».
En cuanto al retrato que Zweig presentaba de él, Freud no se reconocía. A su entender, el escritor veía en él a un pequeñoburgués, y le reprochó haber olvidado decir que prefería la arqueología a la psicología. En rigor, ese retrato «caracterológico» era una suerte de construcción literaria, a medio camino entre la ficción y la realidad. Zweig transformaba a Freud en un ser luminoso, valiente y sano, trabajador infatigable y solitario que arrostraba a dioses y hombres y estaba animado de un coraje sin tacha. De todas formas, describía la evolución de su cuerpo y su rostro de una manera extrañamente familiar, en la que oponía los años de juventud a los de la vejez, como si hubiera proyectado en él su propio rechazo del futuro: «Desde que sale a la luz la parte inferior de la cara, huesuda pero plástica», decía de Freud, «se descubre algo duro, algo indiscutiblemente ofensivo: la voluntad inflexible, obstinada y casi sañuda de su naturaleza. Desde el fondo, la mirada, antes solo contemplativa, se abre paso ahora más sombría, más aguda y penetrante».
Zweig recurría a menudo a la técnica freudiana del desciframiento de los sueños, sobre todo al utilizar el procedimiento narrativo de la integración del relato principal en otro. Y una vez terminada su famosa novela breve _Veinticuatro horas en la vida de una mujer_ , inspirada en una novela epistolar de Constance de Salm, princesa del siglo XIX que animaba un salón y que a su vez se había inspirado en _La princesa de Clèves_ , la envió a Freud.
El motivo de esa novela breve era la pasión amorosa de una anciana inglesa (la señora C.), que revelaba al narrador un recuerdo de juventud, mientras este trataba de comprender la huida de otra mujer que residía en un hotel de la Riviera. Freud apreció el relato, que hacía pensar, además, en una exposición de caso en la que el narrador hubiera ocupado el lugar del terapeuta que libera a una paciente del peso anónimo de su pasado. La dama inglesa contaba que, veinticinco años atrás, había intentado en vano salvar a un joven pianista de su pasión por el juego. Pero este, rechazando el amor que ella le profesaba, había huido, y la señora C. sufrió a continuación, durante años, por la relación culpable que había tenido con él y que había transformado su existencia. Diez años más adelante se enteraría de que el pianista se había suicidado.
Según Freud, el motivo del relato era el de una madre que inicia a su hijo en las relaciones sexuales para salvarlo de los peligros del onanismo. Pero ella ignora que está afectada por una fijación libidinal por su hijo, y por eso el destino la sorprenderá. Freud agregaba: «Lo que digo es analítico y no intenta de manera alguna hacer justicia a la belleza literaria». Cuando aceptaba no adosar su doctrina a los escritos que tenía a la vista, era capaz de las mejores interpretaciones. Pero la significación del relato le interesaba mucho más que su forma, aunque esta estuviese inspirada en sus propios escritos.
Por otro lado, Freud comenzó a mantener una cálida relación con Thomas Mann, un hombre a quien respetaba profundamente y consideraba como un gran novelista, sin tener empero un conocimiento real de su obra. En 1929 Mann publicó uno de los más bellos textos jamás escritos sobre la obra y la persona de _Herr Professor_ : «El puesto de Freud en la historia del espíritu moderno». Freud no se reconoció en ese deslumbrante retrato que hacía de él un desilusionador, heredero de Nietzsche y Schopenhauer, capaz de explorar todas las formas de lo irracional y de transformar el romanticismo en una ciencia. Por eso prefirió pensar que Mann hablaba más de sí mismo que del psicoanálisis y de su inventor: «El artículo de Thomas Mann es muy halagador. Al leerlo me dio la impresión de que tenía listo un ensayo sobre el romanticismo cuando le llegó el encargo de un ensayo dedicado a mí. [...] No importa, cuando Mann dice algo, lo que dice se tiene en pie».
Freud no había renunciado nunca a hacer del psicoanálisis una ciencia «pura», comparable al «cálculo infinitesimal». Por eso se equivocaba gravemente con respecto a la cuestión del romanticismo alemán, cuya herencia rechazaba. En marzo de 1932 Thomas Mann lo visitó por primera vez en la Berggasse, donde fue calurosamente recibido por Martha y Minna, dos de sus fervientes lectoras, que lo consideraban un compatriota, nacido, como ellas, en el norte de Alemania.
En la misma época un nuevo «enemigo» irrumpió en el entorno vienés de Freud: Wilhelm Reich, perteneciente a una familia judía de Galitzia, tan marxista como freudiano y más sexólogo que psicoanalista. Durante diez años Reich ocupó el lugar antaño correspondiente a ese linaje de médicos locos —Fliess u Otto Gross— cuya presencia parece ir a la par con la eclosión del movimiento psicoanalítico. Entre ellos, Reich fue con mucho el más interesante y el más fecundo: «Tenemos aquí a un doctor Reich», escribía Freud a Lou en 1927, «un bravo pero impetuoso jinete de caballos de batalla que ahora venera en el orgasmo genital el antídoto de cualquier neurosis».
Es a este Freud, el de los años treinta, un Freud crepuscular, a quien Julius Tandler, gran anatomista, partidario del higienismo médico, de la eutanasia y de la eliminación de las «vidas indignas de vivirse», consagró un retrato cruel, poco conocido pero de brillante agudeza. Originario de Moravia, había participado, como hemos visto, en el auge del psicoanálisis en Viena, y consideraba a su amigo Freud como la parte oscura de sí mismo, en cierto modo su doble enigmático, tan vienés como él. En un cuaderno íntimo que llevaba en secreto lo describía como un anciano salvaje capaz de destruir todas las ilusiones de la humanidad, un «masacrador de valores», un autócrata virtuoso poseedor de un dominio inaudito de la lengua alemana. Un jefe, un verdadero hombre duro, que de no ser judío habría podido ser Bismarck. Un hombre excepcional, en todo caso, que se complacía, como un detective, en tender trampas a sus interlocutores por medio de razonamientos geniales; un pensador dotado de una intensa vida pulsional reprimida sin cesar, y con intención de formar «cazadores de sexo» ( _sexus_ ), obstinado, terco, discutidor, que disecaba con crueldad la crueldad humana y observaba en soledad, como a través de una mirilla, un mundo aborrecible.
El Freud descrito por Tandler parecía directamente salido de una novela de Thomas Mann o de Tolstói, un alma atormentada, una naturaleza viva y desmesurada, impregnada de una energía vital sin límites y una espiritualidad desbordante:
Raza poderosa, gran tenacidad interior, fortísima vitalidad que da a este anciano la penetración de la juventud. Este hombre de edad, verdaderamente de edad, siempre tiene impulsos apasionados, pero padece de una inhibición de su voluntad. [...] Cuando levanta un sistema, encontramos en este una lógica natural. Y cuando este hombre construye algo, tenemos la sensación de que queda resuelto un enigma vital. Y siempre, esa construcción procede de un intelecto de una agudeza incomparable.
Freud jamás tuvo conocimiento de lo que su amigo había escrito sobre él. Pero en su «más breve crónica», el 7 de noviembre de 1929, anota: «Incidentes antisemitas». Por la mañana varios estudiantes nazis la habían emprendido con Tandler frente al Instituto de Anatomía, al grito de «¡Mueran los judíos!». En octubre de 1931 Freud le brindó su apoyo financiero cuando su amigo organizó el «Socorro de Invierno», destinado a auxiliar a las víctimas de la crisis económica.
Tandler murió en Moscú en 1936, cuando encabezaba allí una misión humanitaria. Contrariamente a Freud, los beneficios aportados por sus iniciativas le otorgaron el derecho a un homenaje. Las autoridades vienesas dieron su nombre a una de las plazas más célebres de la antigua capital imperial: la Julius Tandler Platz. ¿Qué viajero del siglo XXI recuerda el papel que tuvo este hombre tan típicamente vienés en la vida de Freud?
### 2
Frente a Hitler
En 2007, en una bella obra dedicada a los últimos años de la vida de Freud, el universitario norteamericano Mark Edmundson retomó una idea muy apreciada por los historiadores —pero también por Thomas Mann— al trazar un paralelismo entre dos vidas vienesas de la Belle Époque: una infame, la del joven Adolf Hitler, de veinte años en 1909, y otra brillante, la de un Sigmund Freud en plena ascensión a la gloria. El primero iba a convertirse en el mayor asesino de todos los tiempos, destructor de Alemania, genocida de los judíos y de la humanidad en su esencia, y el segundo, en el pensador más renombrado y controvertido del siglo XX: «Casi en todos los aspectos eran», decía Edmundson, «lo que el poeta William Blake habría llamado "enemigos espirituales"».
Nacido en un medio de campesinos desclasados, maltratado por un padre estúpido y violento que se había casado con su joven y desdichada prima, en su juventud Hitler odiaba al mundo entero y más aún a Austria, a la que deseaba ver algún día bajo la dominación de la Alemania guillermina. En Linz, donde cursaba una escolaridad marcada por el fracaso permanente, en el mismo centro al que asistía un joven judío que llegaría a ser un filósofo célebre, Ludwig Wittgenstein, y a quien Hitler ya detestaba, este se había dejado seducir muy tempranamente por los símbolos y los encantamientos del nacionalismo pangermánico, del que un poco más adelante haría la punta de lanza de su combate contra los judíos. Así, se oponía al nacionalismo de su padre, muy afecto a la grandeza del imperio de los Habsburgo.
Tras la muerte de sus padres Hitler se trasladó a Viena con la esperanza de hacer fortuna como pintor y arquitecto, pero fracasó dos veces en su intento de ingresar en la Academia de Bellas Artes, lo cual exacerbó su odio por el mundo de la cultura, las artes y el espíritu. Convencido de su genio, iba con frecuencia a la Ópera disfrazado de dandi, para escuchar con fervor la música de Wagner. Sin embargo, despreciaba esa ciudad «inmóvil», embargada por el sentimiento de la inminencia de su muerte, y se mantenía apartado de sus presuntos «miasmas»: prostitución, sexualidad licenciosa, histeria, literatura inmoral, homosexualidad, pintura y arquitectura decadentes.
En síntesis, Hitler rechazaba todos los aspectos más innovadores producidos por esa ciudad, de los que estaba excluido. Perezoso, desprovisto de talento y con una preferencia por abandonarse a los afectos y no al pensamiento, adoraba a los animales para odiar mejor a los humanos. Jamás comía carne, no bebía vino ni ninguna otra bebida alcohólica y tenía la convicción de que el tabaco era la plaga más perjudicial para la salud de los pueblos. Desde el fondo de su miseria se consideraba como un notable humanista y un excelente poeta, y soñaba con rediseñar Viena y transformarla en un paraíso digno de una humanidad regenerada. También él se adhería a la medicina higienista alemana que terminaría por ser un medio de segregación racial.
Para decirlo brevemente, Hitler acumulaba pues todas las patologías que habrían podido hacer de él un paciente vienés ideal, un caso directamente salido de la nomenclatura de Krafft-Ebing, revisada y corregida a la luz de _Más allá del principio de placer_ : «Si Hitler y Freud se hubiesen cruzado en la calle una tarde del frío otoño de 1909», imagina Edmundson,
¿qué habrían percibido? En Hitler, Freud habría visto a un don nadie, una rata de albañal (no era populista). Pero se habría sentido asimismo desolado, sin duda, por ese desventurado. Por su lado, Hitler habría visto en Freud a un burgués vienés (despreciaba a la clase media alta) y habría advertido, a no dudar, que era judío. Avergonzado por llevar un abrigo raído y zapatos agujereados, habría tenido el impulso de echarse atrás. Si su situación hubiera sido particularmente mala, habría podido tender la mano para mendigar. El hecho de que Freud le hubiese dado o no algo —tal vez le hubiera dado, porque tenía buen corazón— no habría cambiado mucho las cosas: ese encuentro habría despertado una gran furia en el joven Adolf Hitler.
En 1925, con la publicación de _Mi lucha_ , Hitler dejó establecidos los objetivos de su odio: los judíos, los marxistas, el Tratado de Versalles, las llamadas razas inferiores. Y afirmó sus pretensiones: llegar a ser el jefe de un nuevo Reich depurado de todos los miasmas de una presunta degeneración, un jefe capaz de tomar revancha sobre los vencedores de la Gran Guerra que habían humillado a Alemania. En esa fecha respondía a la perfección a la figura del jefe tal como Freud la había descrito en _Psicología de las masas y análisis del yo_ : aquel que no necesita amar a nadie, versión última de la locura narcisista, la desmentida de la alteridad y el repliegue sobre sí mismo. Había bastado con que la situación política, social y económica de Europa se degradara a tal punto —más aún la del mundo germanoparlante— para que fuese posible la aparición de una personalidad semejante. Freud la había concebido de manera abstracta, sin imaginar ni por un instante que pudiese existir bajo los rasgos de un hombre que iba a tomar el poder en Alemania doce años después.
En 1939, sesenta y ocho años antes del brillante comentario de Mark Edmundson, Thomas Mann, exiliado en la costa Oeste de Estados Unidos, ya había reflexionado sobre esta cuestión de las dos vidas paralelas, la del monstruo y la del sabio, al publicar un extraño ensayo de inspiración freudiana que suscitó muchas polémicas: «Bruder Hitler» («Hermano Hitler»). Mann sabía que Freud estaba entonces instalado en Londres, rodeado por su familia, y que solo le quedaban algunos meses de vida.
A diferencia de Bertolt Brecht y los otros exiliados alemanes, Mann se negaba a oponer de manera radical la Alemania de la _Aufklärung_ y la de la barbarie hitleriana. Es cierto, sabía perfectamente que la Alemania de Goethe era muy diferente a la de los nazis, pero sentía por el «monstruo» una verdadera curiosidad clínica y se preguntaba cómo había podido producirse tamaña inversión de valores en uno de los países más civilizados de Europa. ¿Cómo era posible que hubiese llegado al poder —y en todas las instancias de la República de Weimar y el antiguo imperio bismarckiano— lo contrario de lo que la tradición cultural alemana veneraba en el más alto grado: el saber, la competencia, la ciencia, la filosofía, el progreso? Hitler era un fracasado, un «mendigo de asilo», una «adulteración» ( _Verhunzung_ ), un «patito feo» que se creía un cisne, un «impostor», un «Lohengrin de trascocina», escribía Mann. En resumen, era todo lo contrario de lo que la ética protestante había modelado durante decenios, todo lo contrario de las creaciones más civilizadas de la _Aufklärung_. Pero resultaba que había logrado conquistar a un pueblo allí donde la socialdemocracia había fracasado: «Expulsad a Hitler», ya había escrito el mismo Mann en 1933, «ese miserable, ese impostor histérico, ese no alemán de vil origen, ese estafador del poder cuyo arte consiste únicamente en buscar con un repugnante talento de médium la cuerda sensible del pueblo y hacerla vibrar en el trance obsceno al que lo arroja un don de orador increíblemente bajo». Y se negaba, con toda la razón, a trazar comparación alguna entre Napoleón y Hitler:
Hay que prohibir, porque es un absurdo, que se los nombre en un mismo aliento; el gran hombre de guerra y el gran cobarde, el maestro cantor del pacifismo, cuyo papel llegaría a su fin el primer día de una guerra verdadera, y el ser a quien Hegel llamó «el alma del mundo» a caballo, el cerebro gigantesco que dominaba todo, la más formidable capacidad de trabajo, la encarnación de la Revolución, el tiránico portador de la libertad, cuya figura está grabada para siempre en la memoria humana como la estatua de bronce del clasicismo mediterráneo, y ese triste holgazán, ese fracasado, ese soñador de quinta categoría, ese cretino que odia la revolución social, ese sádico solapado, ese rencoroso sin honor.
Para explicar esa inversión que había transformado a un monstruo llegado de la nada en el dictador de un nuevo orden germánico, Thomas Mann destacaba que había que considerarlo como «un hermano» invertido, es decir, como la parte inconsciente de la cultura alemana, su parte tenebrosa, tan irracional como podía serlo lo que Freud había descrito con el término de «pulsión»: una impresionante proyección del inconsciente en la realidad. Y en vez de cerrar los ojos ante ese hermano inmundo, Mann convocaba a sus contemporáneos a mirar el mal de frente para oponerle mejor una racionalidad sin ilusiones. Y agregaba:
¡Un hombre como ese debe odiar el psicoanálisis! Mi secreta sospecha es que la furia con la que marchó contra cierta capital se dirigía en el fondo contra el viejo analista allí radicado, su enemigo verdadero y esencial, el filósofo que desenmascaró la neurosis, el gran desilusionador, aquel que sabía a qué atenerse y conocía muy bien lo que era el genio.
Hitler: ese era el hombre, tan bien descrito por Mann en términos freudianos, que iba a convertirse en el peor enemigo del gran desilusionador y de la ciudad de Viena, cuna inicial del psicoanálisis.
Una vez más, y contrariamente a Thomas Mann, Freud tardó algún tiempo en comprender que se estaba frente a un nuevo tipo de guerra, no una guerra entre las naciones sino algo así como la expresión misma de un principio de destrucción que, a través del exterminio de una presunta «raza» (los «semitas»), apuntaba a la aniquilación de la especie humana y su reemplazo por otra «raza» (los «arios»), la única autorizada a existir en el planeta. ¿No había afirmado Freud en 1915 que la Gran Guerra, engendrada por el nacionalismo y el progreso de las técnicas de destrucción masiva, traducía la quintaesencia de un deseo de muerte arraigado en la especie humana? Hoy, enfrentado al ascenso del nazismo en Alemania, no percibía aún la naturaleza de la máquina de muerte puesta en marcha por el nacionalsocialismo. No era el único.
Lo cierto es que en julio de 1929, cuando puso punto final a una nueva obra que era la continuación de _El porvenir de una ilusión_ , no sospechaba que acababa de escribir el que sería, entre sus libros, el más leído y el más traducido, el más negro, sin duda, pero también el más luminoso, el más lírico, el más político: _El malestar en la cultura_. Se había dedicado a él mientras estaba de veraneo en Berchtesgaden, en los Alpes bávaros, lugar de residencia preferido de la princesa María Isabel de Sajonia-Meiningen, que no había sobrevivido a la caída de las monarquías alemanas. Muy cerca de allí, encaramada en lo alto del Obersalzberg, se encontraba la casa donde, desde 1927, Hitler recibía a los dirigentes del Partido Nacionalsocialista (NSDAP).
En un primer momento Freud pensó dar a ese ensayo el título de «La felicidad y la cultura» («Das Glück und die Kultur»), y luego «La infelicidad en la cultura» («Das Unglück in der Kultur»), para reemplazar finalmente _Unglück_ por _Unbehagen_ : descontento, malestar. Sea como fuere, más allá de la inquietud que le generaba el tiempo presente, para él se trataba en verdad de lanzar un manifiesto en favor de la felicidad de los pueblos: himno al amor, al progreso, a la ciencia y a la república platónica.
Después de recordar que la religión no brindaba ningún remedio a la frustración, Freud afirmaba que las fuentes principales de la infelicidad del sujeto moderno radicaban en una ausencia de ideal, que lo reducía a tres determinantes: el cuerpo biológico, el mundo exterior y las relaciones con los otros. Enfrentado a esa finitud y convertido en una suerte de «dios-prótesis» ( _Art Prothesengott_ ), el ser humano, para escapar a su sufrimiento, no tenía otra opción que inventarse nuevas ilusiones sobre la base de tres elecciones inconscientes: la neurosis (angustia, conflicto), la intoxicación (las drogas, la bebida) y la psicosis (la locura, el narcisismo, la desmesura).
Pero había un camino muy distinto que era igualmente posible, explicaba Freud: el acceso a la civilización (a la cultura), la única capaz de permitir, mediante la sublimación, la dominación de las pulsiones de destrucción, es decir, del estado de naturaleza, ese estado salvaje y bárbaro que es un componente de la psique humana desde la antigua «horda primitiva». Freud destacaba que los hombres que habían renunciado a la ilusión religiosa no tenían nada que esperar de ningún retorno a una presunta «naturaleza». A su entender, el único camino de acceso a la sabiduría, esto es, a la más alta de las libertades, consistía pues en una investidura de la libido en las formas más elevadas de la creatividad: el amor (Eros), el arte, la ciencia, el saber, la capacidad de vivir en sociedad y de comprometerse, en nombre de un ideal común, en la búsqueda del bienestar de todos. De ahí esa apología de la felicidad —o de la «vida buena»— en el progreso, que no habría disgustado a Saint-Just. Y Freud se lanzaba a plantear una defensa incondicional de las realizaciones técnicas y científicas del siglo XX: el teléfono, el transporte marítimo y aéreo, el microscopio, las gafas, la fotografía, el fonógrafo, la higiene doméstica, la limpieza, etc.
Decía además que, como «el hombre es un lobo para el hombre», para romper con su pulsión de autodestrucción primaria no hay otro recurso que vivir con sus semejantes. De tal manera, fundaba toda relación social en la existencia de la familia (célula germinal de la sociedad), por un lado, y el lenguaje, por otro: «El primero que en vez de arrojar una flecha al enemigo le lanzó un insulto fue el fundador de la civilización». Y agregaba que el primero que había renunciado al placer de orinar sobre las llamas también era el héroe de una gran conquista de la civilización —el dominio del fuego—, porque así daba a la mujer (su indispensable álter ego) la manera de mantener un fogón. Freud parodiaba aquí sin decirlo, y con razón, la célebre frase de Jean-Jacques Rousseau sobre el origen de la desigualdad:
El primero que, tras cercar un terreno, tuvo la ocurrencia de decir «esto es mío», y halló gente lo bastante simple para creerle, fue el verdadero fundador de la sociedad civil. Cuántos crímenes, guerras, asesinatos, cuántas miserias y horrores habría ahorrado al género humano aquel que, arrancando las estacas o cegando el foso, hubiera gritado a sus semejantes: «¡Guardaos de escuchar a este impostor!».
Contrariamente a Rousseau y a los herederos de los filósofos de la Ilustración francesa, Freud no creía en la posible abolición de las desigualdades. Convencido de que las fuerzas pulsionales son siempre más poderosas que los intereses racionales, sostenía que ninguna sociedad puede construirse en la renuncia a la agresividad, el conflicto y la autoafirmación. Pero no por eso dejaba de sostener que el lenguaje, la palabra y la ley eran las únicas tres maneras de pasar del estado de naturaleza al estado de cultura. Ya había formulado esta tesis en _Tótem y tabú_. Pero ahora la transformaba en un verdadero programa político articulado en torno de una filosofía psicoanalítica, una ideología, una representación del mundo ( _Weltanschauung_ ).
En síntesis, Freud afirmaba a la vez que la cultura era para el hombre una fuente de decepciones, porque lo forzaba a renunciar a sus pulsiones, pero también una necesidad racional, siempre que no indujera un exceso de represión de la sexualidad y la agresividad necesarias a toda forma de existencia. De ahí el malestar. La cultura solo es un remedio a la infelicidad, explicaba, en la medida en que también crea una infelicidad: la pérdida de las ilusiones, la compulsión. La pulsión de vida (Eros) solo es concebible porque se opone a la pulsión de muerte y se articula con la compulsión, el destino, la necesidad de vivir juntos (Ananké).
Armado de ese manifiesto, Freud rechazaba a la vez, por tanto, el _American way of life_ que, al favorecer un exceso de individualismo, conducía a desastres económicos; el catolicismo que, al fundarse en el amor al prójimo, desconocía la fascinación humana por su propia destrucción, y la revolución comunista que, al creer a pie juntillas en la ilusión de la igualdad entre los hombres, pretendía abolir uno de los grandes resortes de la actividad pulsional humana: el deseo de poseer riquezas. En otras palabras, Freud se posicionaba en contra de todas las creencias modernas en el advenimiento de un «hombre nuevo» presuntamente «liberado» de todo influjo del pasado. Así, criticaba además tanto la utopía del «nuevo judío» como el sueño americano de desligarse del pasado y el proyecto comunista de abolición de las clases. Para terminar, rechazaba, como es obvio, toda forma de dictadura. Al final de su ensayo, en una última frase, con referencia una vez más a la dialéctica de Fausto y Mefistófeles, destacaba hasta qué punto el advenimiento del progreso siempre podía convertirse en su contrario:
Hoy los seres humanos han llevado tan adelante su dominio sobre las fuerzas de la naturaleza que con su auxilio les resultará fácil exterminarse unos a otros, hasta el último hombre. Ellos lo saben; de ahí buena parte de la inquietud contemporánea, de su infelicidad, de su talante angustiado. Y ahora cabe esperar que el otro de los dos «poderes celestiales», el Eros eterno, haga un esfuerzo para afianzarse en la lucha contra su enemigo igualmente inmortal.
En realidad, este manifiesto oponía a esas tres concepciones de la sociedad —la religiosa, la individualista y la comunista— una representación del hombre fundada en el psicoanálisis. Freud desconfiaba tanto de la democracia, que amenazaba otorgar demasiado poder a las masas no educadas, como de las dictaduras, que no hacían sino parodiar peligrosamente la noble figura de la autoridad. Prefería a ello una república de elegidos procedente de la tradición platónica y de la monarquía constitucional: un pueblo ilustrado por un soberano preocupado por el bien común. Por esa razón, además, sostenía, como Thomas Mann, Einstein y Ortega y Gasset, el proyecto de su compatriota austríaco Nikolaus von Coudenhove-Kalergi, que apuntaba a restablecer la unidad europea sobre el fundamento de una referencia común a la cultura grecolatina y cristiana.
Freud volvía a hacer de la ciudad de Roma el principal significante de su doctrina de la cultura. Sabía que nunca más iría a Italia y que de ahora en adelante la ciudad imperial, lugar de todos sus deseos, le estaba prohibida. Sabía que en ella resonaba el ruido de las botas y que entre el Coliseo y el Panteón se desplegaban los siniestros emblemas de los camisas negras. Y en vez de creer en el hombre nuevo, fuera cual fuese su proyecto, señalaba que la cultura no era otra cosa que la expresión de una constante reconciliación entre pasado y presente, entre tiempo arqueológico —el del inconsciente— y tiempo de la conciencia proyectada en el porvenir:
Desde que hemos superado el error de creer que el olvido, habitual en nosotros, implica una destrucción de la huella mnémica, vale decir su aniquilamiento, nos inclinamos a suponer lo opuesto, a saber, que en la vida anímica no puede sepultarse nada de lo que una vez se formó, que todo se conserva de algún modo y puede ser traído a la luz de nuevo en circunstancias apropiadas, por ejemplo en virtud de una regresión de suficiente alcance.
Imaginemos, seguía diciendo, que Roma no es «morada de seres humanos, sino un ser psíquico cuyo pasado fuera igualmente extenso y rico, un ser en que no se hubiera sepultado nada de lo que una vez se produjo, en que junto a la última fase evolutiva pervivieran todas las anteriores».
En otras palabras, la _Kultur_ , según Freud, no era sino la construcción que él había propuesto de ella desde su _Traumbuch_ , al unir todas las etapas del tiempo humano y hacer así del «yo es otro» la única «tierra prometida» dedicada al sujeto moderno. Un ello pulsional, sepultado en los escombros de una genealogía ancestral, un superyó prohibitivo, símbolo de una felicidad accesible, y un yo repartido entre memoria e historia. Ese era en efecto, en «el año 1930 d.C.», el fundamento de la esperanza en una vida mejor que Freud prometía a sus contemporáneos. En ese sistema Roma se confundía con Viena y Viena con la Berggasse, lugar poblado de todos los adornos de las culturas antiguas, último refugio de una _Mitteleuropa_ en agonía donde afluían visitantes del mundo entero. Hasta esa fecha, el nombre de Hitler no figuraba aún en ninguno de los escritos del maestro.
_El malestar en la cultura_ fue un éxito de ventas y, con motivo de su reedición en 1931, Freud agregó algunas palabras lacónicas a la frase final: «¿Pero quién puede prever el desenlace?». Pensaba entonces en la victoria electoral conseguida por los nazis el 14 de septiembre de 1930. En ese momento el NSDAP se convirtió en el segundo partido de Alemania, detrás del SPD (socialdemócrata) y delante del KPD (comunista). Hermann Göring, Joseph Goebbels y Heinrich Himmler hicieron su entrada en el Reichstag. Aniquilado por la crisis económica, el país tenía más de cuatro millones de parados.
En 1932 el Comité Permanente de Letras y Artes de la Sociedad de Naciones (SDN) sondeó a Albert Einstein a fin de interesarlo en la reunión de testimonios de intelectuales en favor de la paz y el desarme. Por eso Einstein se dirigió a Freud, a quien ya conocía: «El hombre tiene dentro de sí un apetito de odio y destrucción. En épocas normales esta pasión existe en estado latente, y únicamente emerge en circunstancias inusuales; pero es relativamente sencillo ponerla en juego y exaltarla hasta el poder de una psicosis colectiva». Y pedía al «experto en el conocimiento de las pulsiones humanas» que resolviera el enigma.
Freud se apresuró a responder con un manifiesto político, «¿Por qué la guerra?», que prolongaba _El malestar en la cultura_. Contra los amos que querían convertirse en dictadores y contra los oprimidos que quisieran derrocarlos, Freud defendía un gran retorno al banquete platónico y por ello proponía a la SDN la creación de una república internacional de sabios, comunidad de elegidos «que hubieran sometido su vida pulsional a la dictadura de la razón» y capaces, por su autoridad, de imponer a las masas un verdadero Estado de derecho fundado en la renuncia al asesinato. Todo lo que promueve la cultura, decía, contribuye al debilitamiento del instinto bélico. Una vez más, proponía a los grandes de este mundo el arte de una gobernanza de las naciones conforme a la doctrina psicoanalítica.
Si bien su doctrina siempre había sido el vector de una representación del mundo, una ideología, un proyecto político y un pensamiento antropológico fundados en la renuncia al asesinato y en la instauración de un Estado de derecho, Freud no había dejado de contradecirse al afirmar que el psicoanálisis no era una _Weltanschauung_. Designaba con este término «un concepto específicamente alemán cuya traducción a lenguas extranjeras acaso depare dificultades». En filosofía la palabra remitía a la idea de una metafísica del mundo, una concepción global de la condición humana en el mundo. Pero para Freud, deseoso de hacer del psicoanálisis una ciencia de la naturaleza —cosa que este nunca fue—, la expresión no era conveniente. A su juicio, formaba parte del discurso filosófico, la religión y el compromiso político, es decir, de toda clase de ilusiones y otras construcciones de la mente que la razón científica —y por lo tanto el psicoanálisis— tenía el deber de deconstruir. Por lo demás, en 1932 Freud volvía a burlarse abiertamente de la filosofía, que consideraba como una especie de pequeña religión de uso restringido:
La filosofía no es opuesta a la ciencia, ella misma se comporta como una ciencia; en parte trabaja con iguales métodos, pero se distancia de ella en cuanto se aferra a la ilusión de poder brindar una imagen del universo coherente y sin lagunas, imagen que, no obstante, por fuerza se resquebraja con cada nuevo progreso de nuestro saber. [...] Pero la filosofía no tiene influjo directo sobre la multitud, y aun dentro de la delgada capa superior de los intelectuales interesa a un pequeño número, siendo apenas asible para los demás. En cambio, la religión es un poder inmenso que dispone de las emociones más potentes de los seres humanos.
Y citaba la célebre «burla» de uno de sus poetas preferidos, Heinrich Heine: «Con sus gorros de dormir y jirones de su bata [el filósofo] tapona los agujeros del edificio universal».
Del mismo modo, como en _El malestar en la cultura_ , se entregaba a un vibrante elogio de los progresos de la ciencia como una manera de fustigar mejor, y sin distinción, el bolchevismo, el marxismo y la oscura dialéctica hegeliana, a la vez que, en relación con esta última, afirmaba que no la entendía muy bien, dado que él atribuía la formación de las clases sociales a las luchas ancestrales entre hordas humanas —o «razas»— poco diferentes unas de otras.
En consecuencia, Freud seguía interpretando las luchas de los pueblos por su emancipación conforme al modelo de _Tótem y tabú_. Y, al mismo tiempo, admitía que el despotismo ruso ya estaba condenado antes de que la guerra fuera una causa perdida, «pues ningún cruzamiento de las familias dominantes en Europa habría podido engendrar una casta de zares capaz de resistir el poder deflagratorio de la dinamita». En otras palabras, atribuía la derrota del Imperio ruso tanto al progreso de las técnicas científicas como a la incapacidad de las dinastías reales de renovarse, debido a los cruzamientos consanguíneos. Como los Labdácidas, esas dinastías estaban condenadas a la autodestrucción. Freud parecía olvidar que eso no bastaba para explicar el hundimiento de los viejos imperios.
Al procurar de ese modo diferenciarse de la filosofía y de la teoría de la historia, para hacer del psicoanálisis una ciencia sin dejar de mantener su análisis mitográfico de las dinastías imperiales y su concepción de una república de los elegidos, Freud cometía un error. En efecto, en nombre de ese rechazo de toda _Weltanschauung_ se planteó, con su acuerdo, la idea de que, como el psicoanálisis era una ciencia, debía mostrarse «neutral» frente a todos los cambios de la sociedad, y por lo tanto «apolítico». En otras palabras, a pesar de que había criticado el cientificismo y el positivismo; a pesar de que con su interés en el ocultismo pretendía desafiar la racionalidad científica, y a pesar de que había inventado una concepción original de la historia «arcaica» de la humanidad, he aquí que se negaba a ver que su doctrina era portadora de una política, una filosofía, una ideología, una antropología y un movimiento de emancipación.
Nada era más contrario al espíritu del psicoanálisis que enmascararlo como una presunta ciencia positiva y mantenerlo apartado de todo compromiso político. Después de haber criticado tanto a la religión, Freud, en nombre de una presunta «neutralidad», corría así el riesgo de ver su doctrina transformada en catecismo. Esta actitud fue un desastre para el movimiento psicoanalítico del período de entreguerras, enfrentado a la mayor barbarie que Europa hubiera conocido. Y el más vigilante en la aplicación de esta línea «neutralista», convalidada por Freud, fue Ernest Jones.
Convertido fuera de la Europa continental en el principal organizador del movimiento psicoanalítico, Jones, como buen discípulo pragmático, militante de una concepción médica de la práctica de la terapia psicoanalítica, fue así el destructor del freudismo original —el del romanticismo y la _Mitteleuropa_ — y, a la vez, el salvador de una comunidad que, frente al ascenso del nazismo, no tenía otra alternativa que exiliarse en el mundo angloparlante.
En nombre de esa neutralidad y ese apoliticismo, Jones no brindó ningún apoyo a los freudianos de izquierda —sobre todo a los freudomarxistas— que en Alemania y Rusia aspiraban a vincular las dos revoluciones del siglo: la primera apuntada a transformar al sujeto mediante la exploración del inconsciente, la segunda con voluntad de transformar la sociedad a través de la lucha colectiva.
En 1921, con la ayuda del movimiento psicoanalítico ruso, Vera Schmidt había creado en Moscú una casa pedagógica: el Hogar Experimental de Niños, donde había recibido a una treintena de hijos de dirigentes y funcionarios del Partido Comunista a fin de educarlos con métodos que combinaban los principios del marxismo y del psicoanálisis. Se abolía así el sistema educativo tradicional basado en las vejaciones y los castigos corporales. Pero la empresa se fundaba en la utopía de una posible abolición de la familia patriarcal en beneficio de métodos educativos que privilegiaran lo colectivo y los intercambios igualitarios. El programa también preveía que los educadores se analizaran y no coartaran los juegos sexuales de los niños. En otras palabras, el ideal pedagógico de Vera Schmidt era un testimonio del nuevo espíritu de los años veinte, a través del cual se expresaba, inmediatamente después de la Revolución de Octubre, el sueño de una fusión posible entre la libertad individual y la igualdad social.
En ese contexto, Vera, acompañada por su marido, el matemático Otto Schmidt, había viajado a Berlín y Viena para recabar el apoyo de Freud y Abraham en favor del hogar. La discusión se refirió en esencia a la manera de tratar el complejo de Edipo en el marco de una educación colectiva. Es indudable que esa experiencia no era compatible con los principios de la psicología edípica. Y, por las mismas razones, era objeto de severas críticas de los funcionarios del Ministerio de Salud soviético.
Freud habría querido ayudar a los Schmidt, pero Jones prefirió sostener, contra el de Moscú, al grupo psicoanalítico de Kazán, que promovía una política favorable a los médicos, mucho más neutral con respecto al marxismo. Al cabo de un prolongado trámite, y a pesar del apoyo provisional de Nadezhda Krupskaia, la mujer de Lenin, se puso fin a la experiencia. Criticada tanto por los freudianos como por el régimen soviético, cada vez más imbuido por el espíritu estalinista, Vera Schmidt también lo fue por su amigo Wilhelm Reich, que la visitó en 1929. Ya célebre en Alemania, Reich consideraba que la experiencia no era suficientemente revolucionaria.
Si tenemos en cuenta el debate sobre la sexualidad tal como se desarrollaba desde fines del siglo XIX, esta posición de Reich era en realidad simétrica de la de Jung. En efecto, si este último desexualizaba el sexo en beneficio de una suerte de impulso vital, Reich procedía a una desexualización de la libido en beneficio de una genitalidad biológica fundada en la expansión de una felicidad orgásmica de la que estaba excluida la pulsión de muerte. Después de haber sido miembro del Partido Socialdemócrata Austríaco, Reich se afilió al KPD y militaba con ardor sin dejar de construir una mitología obrerista según la cual la genitalidad del proletariado estaría exenta del «microbio» burgués. Así, no vacilaba en afirmar que las neurosis eran más infrecuentes en la clase obrera que en las capas superiores de la sociedad. Nuevo argumento contra la pulsión de muerte.
Reich no tardó en crear una Sociedad Socialista de Información e Investigaciones Sexuales, así como clínicas de higiene sexual destinadas a la información de los asalariados (Sexpol). Sentía una admiración sin límites por Freud, en tanto que este mostraba una animadversión desmesurada hacia él. Temía su locura, su celebridad y su compromiso político. En cuanto a sus discípulos, hicieron todo lo posible por deshacerse de un hombre que hacía vacilar su conformismo, perturbaba sus convicciones y restablecía lazos con los orígenes fliessianos de la doctrina freudiana, cuya importancia ellos procuraban relativizar. Esta actitud los llevó en 1934 a cometer numerosos errores políticos.
Como ya he señalado, Freud no había dejado de reivindicar su identidad judía, al tiempo que se negaba a someterse a los ritos del judaísmo. Y, de igual modo, solo se sentía judío porque se oponía al proyecto sionista de una reconquista de la tierra prometida. En una palabra, Freud era un judío de la diáspora que no creía que, para los judíos, la respuesta al antisemitismo pudiese traducirse en el retorno a ningún territorio. Y si bien solía apoyar la instalación de colonias judías en Palestina, exhibía gran prudencia frente al proyecto de fundar un «Estado de los judíos». Lo testimonia la respuesta que dio a Chaim Koffler, miembro vienés del Keren Hayesod, cuando este le pidió, como a otros intelectuales de la diáspora, su apoyo a la causa sionista en Palestina y el principio del acceso de los judíos al Muro de las Lamentaciones. Señalemos que desde 1925, gracias a la intervención de Chaim Weizmann, que quería establecer la enseñanza oficial del psicoanálisis en Palestina, Freud era miembro del consejo de administración de la Universidad de Jerusalén, al igual, por otra parte, que su discípulo inglés David Eder.
Esto no le impidió declinar la propuesta de Koffler:
No puedo hacer lo que usted desea. Mi reticencia a interesar al público en mi personalidad es insuperable y me parece que las circunstancias críticas actuales no incitan en absoluto a hacerlo. Quien quiere ejercer su influencia sobre las mayorías debe tener algo resonante y entusiasta para decirles, y eso no lo permite mi juicio reservado sobre el sionismo. Tengo sin duda los mejores sentimientos de simpatía por los esfuerzos libremente consentidos, estoy orgulloso de nuestra Universidad de Jerusalén y la prosperidad de los establecimientos de nuestros colonos me llena de júbilo. Pero, por otro lado, no creo que Palestina pueda jamás llegar a ser un Estado judío ni que el mundo cristiano, como el mundo islámico, puedan estar algún día dispuestos a confiar sus Santos Lugares a la custodia de los judíos. Me habría parecido más atinado fundar una patria judía sobre un suelo que no tuviera esa carga histórica; es cierto, sé que un designio tan racional nunca hubiera podido suscitar la exaltación de las masas ni la cooperación de los ricos. También admito, con pesar, que el fanatismo poco realista de nuestros compatriotas tiene su parte de responsabilidad en el despertar de la desconfianza de los árabes. No puedo sentir la menor simpatía por una piedad mal interpretada que hace de un pedazo de muro de Herodes una reliquia nacional y, a causa de ella, desafía los sentimientos de los habitantes del país. Juzgue usted mismo si, con un punto de vista tan crítico, soy la persona adecuada para llevar consuelo a un pueblo agitado por una esperanza injustificada.
Ese mismo día —26 de febrero de 1930— Freud envió a Albert Einstein otra carta, que retomaba punto por punto esta argumentación: aborrecimiento de la religión, escepticismo con respecto a la creación de un Estado judío en Palestina, solidaridad con sus «hermanos» sionistas —a quienes a veces llamaba sus «hermanos de raza»— y, para terminar, empatía con el sionismo, cuyo ideal, empero, no compartía en razón de sus «extravagancias sagradas». Freud se declaraba de nuevo orgulloso de «nuestra» universidad y «nuestros» kibutz, pero reiteraba que no creía en la fundación de un Estado judío porque, decía, los musulmanes y los cristianos nunca aceptarían dejar sus santuarios en manos de los judíos. Por eso deploraba el «fanatismo poco realista de sus hermanos judíos» que contribuía a «despertar la desconfianza de los árabes».
Así, Freud tuvo indudablemente la intuición de que la cuestión de la soberanía sobre los Santos Lugares estaría algún día en el centro de una disputa casi insoluble, no solo entre los tres monoteísmos sino entre los dos pueblos hermanos residentes en Palestina. Temía con toda la razón que una colonización abusiva terminara por oponer, en torno de un fragmento de muro idolatrado, a árabes antisemitas y judíos racistas.
Así como se mostraba lúcido en la cuestión de su judaísmo y con respecto al futuro de los judíos en Palestina, Freud dio pruebas, en cambio, de una verdadera ceguera en cuanto a la naturaleza misma del antisemitismo nazi y la respuesta política que convenía dar a la cuestión de la supervivencia del psicoanálisis en Alemania, Austria e Italia durante el período de los años negros. Una vez más, la referencia a la _Weltanschauung_ sirvió de pretexto para la adopción de un peligroso neutralismo.
Desde su llegada al poder Hitler llevó a la práctica la doctrina nacionalsocialista, cuya tesis central apuntaba al exterminio de todos los judíos de Europa, habida cuenta de que se los asimilaba a una «raza inferior». Ese programa debía aplicarse a todos los hombres considerados como «viciados» o perturbadores del cuerpo social. Así, la homosexualidad y la enfermedad mental se trataron como equivalentes de lo judío. En ese contexto, los artífices de la nueva medicina del Reich incluyeron en su programa la destrucción del psicoanálisis, de su vocabulario, de sus conceptos, de sus obras, de su movimiento, de sus instituciones, de sus profesionales. Entre todas las escuelas de psiquiatría dinámica y psicoterapia fue la única en recibir el calificativo de «ciencia judía», tan temido por Freud. En cuanto al programa de limpieza, fue orquestado por el siniestro Matthias Heinrich Göring, primo del mariscal.
Luterano y pietista, este psiquiatra había sido asistente de Emil Kraepelin; se interesó luego en la hipnosis y adoptó más adelante las tesis de la psicología individual de Adler. A continuación tomó por modelo la psicología junguiana, que pensaba erigir en el prototipo de una nueva psicoterapia hitleriana centrada en la superioridad del alma alemana. Pragmático y dogmático, conservador y mezquino, nazi convencido y temible bajo su apariencia de abuelito de poblada barba, vilipendiaba el poder de la teoría freudiana, que era a su entender el fruto de lo que más odiaba en el mundo: el universalismo «judío» ligado a la _Aufklärung_. Pronto se lo llamaría el Führer de la psicoterapia.
En marzo de 1933, como muchos otros austríacos, Freud no percibía el peligro que el nazismo significaba para su país. Se creía protegido por las leyes de la República y, pese a los consejos de sus amigos extranjeros, rechazaba cualquier perspectiva de marcharse de Viena:
No existe la certeza de que el régimen hitleriano también se apodere de Austria. Es posible, desde luego, pero todo el mundo cree que la cosa no llegará aquí al mismo nivel de brutalidad que en Alemania. Personalmente no corro, sin duda, ningún peligro, y si usted supone que la vida bajo la opresión será bastante incómoda para nosotros, los judíos, no olvide, en ese aspecto, el escaso atractivo que promete a los refugiados la vida en el extranjero, sea en Suiza o en Inglaterra. Me parece que la huida solo se justificaría de existir un peligro vital directo y, después de todo, si nos muelen a palos, será una manera de morir como cualquier otra.
Negándose a ver que el nazismo iba a extenderse por toda Europa, Freud pensaba que el canciller Engelbert Dollfuss, conservador y nacionalista, aliado de Mussolini, estaba en la mejor situación para oponer resistencia al Partido Nazi austríaco, que procuraba concretar lo más rápidamente posible la anexión de Austria por Alemania ( _Anschluss_ ). Es cierto, Freud no sentía ninguna simpatía por ese dictador fascista, católico y reaccionario, pero pensaba que la instauración de un régimen autoritario sería un mal menor para los judíos. Aceptó pues las medidas de Dollfuss que cancelaban las libertades fundamentales: supresión del derecho de huelga, censura de la prensa, persecución de los socialistas y marxistas. Y el 12 de febrero de 1934, cuando el canciller reprimió a sangre y fuego la huelga general declarada por los militantes socialistas, se mantuvo «neutral»:
Hemos pasado por una semana de guerra civil [...]. No hay duda de que los rebeldes representaban a la mejor parte de la población, pero su éxito habría sido de corta duración y hubiera causado la invasión militar del país. Por añadidura, eran bolcheviques, y yo no espero que la salvación provenga del comunismo. Así, no podíamos atorgar nuestras simpatías a ninguno de los bandos combatientes.
Freud no confundía el comunismo y el nazismo. Reconocía en la revolución bolchevique un ideal revolucionario, en tanto que consideraba la barbarie hitleriana como una regresión fundamental hacia los instintos más homicidas de la humanidad. Pero, enfrentado a la realidad del fascismo y del nazismo, tardó en comprender que no era posible ninguna negociación. No miraba a Hitler a la cara, no pronunciaba su nombre y no había leído _Mein Kampf_. Todo lo contrario de Thomas Mann.
En ese contexto, Edoardo Weiss, radicado en Roma desde hacía dos años, visitó a Freud el 25 de abril de 1933. Había contemplado varias veces la posibilidad de huir del fascismo, pero el maestro le había aconsejado insistentemente que se quedara en su país, convencido de que no se le abría ninguna otra perspectiva, a pesar de los ataques incesantes de la Iglesia católica y sobre todo del padre Wilhelm Schmidt, director del Museo Misionero Etnológico del Vaticano en el palacio del Letrán, que denunciaba el freudismo como una teoría «nefasta» responsable, en la misma medida que el marxismo, de la «destrucción de la familia cristiana». Freud se obstinaba en rechazar cualquier posibilidad de emigración al continente americano. A sus ojos, el combate en favor de la perduración y el salvamento del psicoanálisis debía librarse en Europa.
Lo cierto es que en esa ocasión Weiss fue a Viena en compañía de Giovacchino Forzano y de Concetta, la hija de este, a quien él trataba por una agorafobia y una grave histeria. Como no lograba encauzar correctamente esa difícil cura, pidió la intervención de Freud en carácter de supervisor y con la presencia de la muchacha. La experiencia fue un éxito y Weiss pudo a continuación seguir adelante con el análisis de Concetta, sin dejar de pedir consejos a Freud por la vía epistolar.
Dramaturgo marcado por la obra de D'Annunzio, Forzano había llegado a ser un amigo muy estrecho de Mussolini, con quien había escrito una pieza en tres actos sobre los Cien Días de Napoleón. Los autores se apropiaban de manera grotesca de la imagen del emperador para hacer de él la prefiguración del Duce. Para seducir a Freud, en cuyas manos ponía el destino de su hija, Forzano llevó a la Berggasse la edición alemana de la obra. En el frontispicio había escrito una dedicatoria en nombre de los dos autores: «A S. F., que hará el mundo mejor, con admiración y agradecimiento». Y por esa razón pidió a _Herr Professor_ que, a cambio, le diera una fotografía y un libro suyos, acompañados de una mención autógrafa para Mussolini. Deseoso de proteger a Weiss, que organizaba el movimiento psicoanalítico y acababa de publicar el primer número de la _Rivista italiana di psicoanalisi_ , Freud tomó de su biblioteca un ejemplar de _¿Por qué la guerra?_ y redactó un texto destinado a suscitar violentas polémicas: «Para Benito Mussolini, con los humildes saludos de un anciano que reconoce en el hombre de poder un adalid de la cultura».
Si bien admiraba a los conquistadores, a Freud lo horrorizaban los dictadores, como lo probaban todos sus escritos y más aún la elección de ese libro. Pero no podía en ningún caso eludir la propuesta de Forzano. Salió del apuro, pues, con humor, al rendir homenaje a un «hombre de poder» que, a la vez que se tomaba por una mezcla de Napoleón y César, había puesto en marcha excavaciones arqueológicas que enloquecían de placer al humilde sabio de Viena.
Freud estaba erróneamente convencido de que Weiss tenía buenas relaciones con Mussolini, como le diría más adelante a Arnold Zweig en una carta. La realidad reveló ser mucho más compleja. Protector del psicoanálisis, Forzano, ligado a Weiss, no obtuvo de hecho ningún apoyo de Mussolini, que no tenía la más mínima intención de oponerse a la Iglesia católica. Además, el 30 de junio de 1933 el dictador denunció el psicoanálisis como un «fraude orquestado por un _pontifex maximus_ », a tal punto que, pese a una gestión ante Galeazzo Ciano, Weiss no pudo impedir que los servicios de propaganda suspendieran la aparición de la _Rivista_. Peor aún, la diplomacia fascista ordenó una ridícula investigación sobre las actividades de la WPV, destinada a probar que Sigismond ( _sic_ ) Freud mantenía relaciones sospechosas con el pensador anarquista Camillo Berneri y que sus discípulos se dedicaban a hacer operaciones mercantiles apoyadas por los socialistas y los comunistas. En consecuencia, ningún psicoanalista italiano pudo inscribirse en la WPV.
Tres meses después de que Hitler tomara el poder, los nazis devastaron la sede del Instituto de Sexología y dispersaron archivos, documentos, libros, objetos y toda la iconografía reunida por Magnus Hirschfeld sobre las diferentes formas minoritarias de sexualidad. Arruinaron así decenios de trabajo e investigaciones, en el momento preciso en que acababa de incorporarse al gobierno Ernst Röhm, jefe de las tropas de asalto del partido y notorio homosexual, que moriría asesinado un año después por decisión de Hitler.
Fuera de Berlín ese día, Hirschfeld, que por entonces seguía un tratamiento en Suiza, decidió exiliarse en París y luego en Niza, donde murió, desesperado por haber visto el hundimiento de la obra de toda una vida. En muy poco tiempo, los cafés, cabarets, lugares de encuentro y otras instituciones que habían hecho de Berlín la ciudad del este de Europa más floreciente de los años veinte, y la más abierta a los homosexuales, quedaron reducidos a nada a raíz de las ocupaciones, las clausuras, los saqueos y las destrucciones.
El 11 de mayo de 1933 Goebbels ordenó la quema de veinte mil libros «judíos». Puesto en escena a lo largo de toda una noche en la Opernplatz, el espectáculo reunió a profesores, estudiantes y tropas de las SS y las SA. Todos desfilaron alegremente con antorchas y entonando himnos patrióticos y fórmulas encantatorias: «Contra la lucha de clases y el materialismo, entrego a las llamas los libros de Marx y Kautsky; contra la exaltación de los instintos y por el ennoblecimiento del alma humana, entrego a las llamas los escritos de Sigmund Freud». Este último replicó desde Viena: «¡Cuántos progresos hemos hecho! En la Edad Media me habrían quemado a mí; ahora se conforman con quemar mis libros».
¡Qué frase! Freud habría estado más inspirado de haber dicho que la quema de los libros «judíos» llevaría a quemar, no solo a sus autores, sino a los propios judíos y a otros representantes de las llamadas «razas inferiores». Aún pensaba que el nazismo solo era la expresión de un antisemitismo recurrente. ¿Cómo podía imaginar en esa fecha que lo que había escrito en 1930 sobre las capacidades de autodestrucción del hombre pudiera realizarse con tamaña rapidez? Había pensado entonces en el _American way of life_ , jamás en Europa.
En un artículo de septiembre de 1933, acompañado de inmundas caricaturas, un periodista nazi afirmó que «el judío Sigmund Freud» había inventado un método «asiático» destinado a destruir la raza alemana al obligar al ser humano a obedecer a sus pulsiones destructivas y por lo tanto a «gozar por temor a morir». Acusaba al maestro de Viena de querer propagar en la juventud toda clase de prácticas sexuales transgresoras: masturbación, perversiones, adulterio. Por eso era menester, en opinión del periodista, deshacerse de esa plaga. Tal era pues el programa de destrucción de esta «doctrina judía» al que obedecía Göring.
Después de proclamar que _Mein Kampf_ le serviría de guía en el momento de implementar su política en materia de salud mental, el mismo Göring dedicó entonces una atención especial a granjearse los favores de los freudianos interesados en colaborar con el régimen: Felix Boehm y Carl Müller-Braunschweig fueron los primeros en adherirse, y Harald Schultz-Hencke y Werner Kemper les pisaron los talones. Miembros de la Deutsche Psychoanalytische Gesellschaft (DPG) y del Berliner Psychoanalytisches Institut (BPI), estos cuatro hombres eran unos personajes mediocres, celosos de sus colegas judíos. El advenimiento del nacionalsocialismo fue para ellos una oportunidad de oro que les permitió hacer carrera. Con un sentimiento de inferioridad con respecto a quienes consideraban como señores, se convirtieron en servidores de los verdugos.
En 1930 la DPG tenía noventa miembros, en su mayoría judíos. A partir de 1933 estos emprendieron el camino del exilio. A esas alturas los intercambios epistolares entre Max Eitingon y Sigmund Freud se tornaron más tensos debido a la necesidad de utilizar un lenguaje codificado, habida cuenta de que sus cartas estaban sometidas a la censura. Aislado dentro del BPI, Eitingon no tardó en verse obligado a renunciar, en tanto que Jones, hostil a la izquierda freudiana alemana —Otto Fenichel, Ernst Simmel, etc.— e interesado en fortalecer el poderío angloamericano, se apoyaba en Boehm para favorecer la política de colaboración con el nuevo régimen. Esa política consistía en mantener, bajo el nazismo, una llamada práctica «neutra» del psicoanálisis, a fin de preservar a este de toda contaminación con las otras escuelas de psicoterapia, introducidas por su parte en el seno del nuevo BPI «arianizado».
Hostil a esta línea, Max Eitingon exigió, antes de tomar una decisión, que Freud le expusiera por escrito sus propias orientaciones. En una carta del 21 de marzo de 1933 este último cumplió lo solicitado y destacó que su discípulo tenía que elegir entre tres soluciones: 1) trabajar por el cese de las actividades del BPI; 2) colaborar en su perduración bajo la batuta de Boehm «para sobrevivir a tiempos desfavorables», y 3) abandonar la nave, a riesgo de dejar que los junguianos y los adlerianos se apoderaran de la joya, lo cual obligaría al IPV a desautorizarla. En esta fecha, por lo tanto, Freud había optado por la segunda solución, la «neutralista» propiciada por Jones, que dos años después desembocaría en la nazificación completa del BPI en manos de Göring. Sin embargo, no deseaba imponerla a Eitingon, convencido por otra parte —equivocadamente— de que Hitler no era una amenaza para Austria, a la que creía protegida por el austrofascismo.
El 17 de abril se congratuló de que Boehm lo hubiera liberado de Reich, a quien odiaba —y que a continuación sería excluido del IPV y emigraría a Noruega y luego a la otra orilla del Atlántico—, y de Harald Schultz-Hencke, adleriano nazi, que no tardaría en reintegrarse en la BPI. Frente a tal ceguera, consistente en creer que el psicoanálisis podía sobrevivir bajo el nazismo, Eitingon decidió empero mantener su fidelidad tanto al freudismo como al sionismo. Sin hacer el menor reproche a Freud, abandonó Alemania para instalarse en Jerusalén en abril de 1934. Allí se reencontró con Arnold Zweig y fundó una sociedad psicoanalítica y un instituto según el modelo de la entidad berlinesa, sentando así las bases de un futuro movimiento psicoanalítico israelí.
Cuando Ferenczi murió, el 22 de mayo de 1933, como consecuencia de una anemia perniciosa, y en un momento en que el antiguo reino del psicoanálisis estaba reducido a cenizas, Freud experimentó la necesidad, como siempre le sucedía en circunstancias similares, de reaccionar en caliente. Cuando era cuestión de los «traidores» a la causa, de los enemigos o de quienes a sus ojos se habían vuelto «inútiles», sabía captar de un plumazo lo esencial de un momento de vida susceptible de ser incorporado a los anales de su movimiento. Tenía el sentido de la memoria más que de la historia. En lo concerniente a Ferenczi, el compañero de siempre, con quien nunca había querido romper, Freud se propuso disimular su tristeza detrás del esbozo de un balance clínico. Por eso dio a Jones una interpretación psicoanalítica por lo menos discutible de los conflictos que habían acompañado su agonía:
Se desarrolló simultáneamente con una lógica aterradora una degeneración psíquica que adoptó la forma de una paranoia. Esta se centraba en la convicción de que yo no lo amaba lo suficiente, no quería reconocer sus trabajos y, además, lo habría analizado mal. Sus innovaciones técnicas [...] eran regresiones hacia los complejos de su infancia, cuya mayor herida era el hecho de que él, un hijo del medio de once a trece años, no había sido amado por su madre con el ardor, con la exclusividad suficientes. Así se convirtió él mismo en una mejor madre y encontró también los hijos que necesitaba, entre ellos una americana. Cuando esta se marchó, él creyó que lo influenciaba por medio de ondas que se desplazaban por encima del océano [...]. Prestaba fe a sus más extraños traumas infantiles, que a continuación defendía frente a nosotros. En esas aberraciones se extinguió su inteligencia. Pero queremos que la tristeza de su final quede entre nosotros como un secreto.
Nada permite asegurar que Ferenczi se hubiera vuelto paranoico. Lo testimonia, de ser necesario, su _Diario clínico_ , en el cual reprochaba a Freud su desinterés gradual por el aspecto terapéutico del psicoanálisis, su hostilidad para con los pacientes psicóticos, su falta de empatía en la cura y su antiamericanismo. Es cierto, sabemos que esos reproches se justificaban en parte. Pero es forzoso constatar que ambos, Freud y Ferenczi, tenían razón, el primero en su crítica de la vuelta a la explicación exclusivamente traumática de los trastornos psíquicos, el segundo en su comprobación del rumbo errático de una técnica de la terapia psicoanalítica demasiado centrada en la frustración y la búsqueda de la explicación unívoca. Lo cierto es que Ferenczi fue realmente perseguido por Jones e injustamente criticado por los freudianos ortodoxos. Había decidido mantenerse fiel a Freud, quien nunca le comunicó lo que pensaba secretamente acerca de su estado mental. En sus últimas cartas Ferenczi dio muestras de una gran lucidez con respecto a sí mismo y a la evolución de la catástrofe europea. El 9 de abril de 1933 envió a Freud un mensaje con estas palabras: «Aquí, en Budapest, todo está en calma: ¿quién habría pensado, hace diez o catorce años, que mi patria sería un lugar relativamente tranquilo del continente europeo?».
Una vez más, como después de la muerte de Karl Abraham, Freud redactó el obituario de Ferenczi. En él recordaba los años felices del viaje a Worcester y de la fundación del IPV, y luego añadía que algún día, acaso, surgiría el «bioanálisis» con que el maravilloso clínico de Budapest había soñado. También mencionaba las divergencias entre ellos, pero afirmaba que Ferenczi había tenido un papel excepcional en la historia de la ciencia analítica. Tras escribir ese adiós al amigo de siempre, experimentó una sensación de vacío y un profundo malestar.
Si Freud perdía a su mejor discípulo, Jones perdía a su analista y su adversario, y estaba destinado a ocupar en lo sucesivo un lugar fundamental en el entorno del maestro. Pronto sería el actor central del movimiento psicoanalítico, antes de erigirse en el primer biógrafo de aquel cuya política había de conducir. Así, en el corazón de la tormenta, tendría a su cargo proseguir, desde Londres, con la implementación del presunto «salvamento» del psicoanálisis.
En el decimotercer congreso del IPV, que se celebró en Lucerna en agosto de 1934, precisamente cuando los psicoanalistas judíos se marchaban de la Alemania nazi, Reich fue desterrado de la comunidad freudiana en razón de su «bolchevismo», considerado peligroso para el psicoanálisis. Sin embargo, él se oponía, contra Jones y con fundadas razones, a toda forma de colaboración con el nazismo y reclamaba la disolución de la DPG. Expulsado del movimiento comunista alemán por izquierdismo, acababa de publicar su obra central, _Psicología de masas del fascismo_ , que respondía directamente al libro de Freud sobre la psicología de las masas. Lejos de considerar el fascismo como el producto único de una política o de una situación económica, veía en él la expresión de una estructura inconsciente y ampliaba esta definición a la colectividad para destacar que se explicaba por una insatisfacción sexual de las masas.
El error de apreciación de Freud, al que Eitingon se opuso, se confirma al leer el informe escrito por Boehm en agosto de 1934, después de una visita a aquel: «Antes de despedirnos», dice, «Freud formuló dos anhelos: primero, jamás había que elegir a Schultz-Hencke para integrar el comité de dirección de nuestra Sociedad. Le di mi palabra de no reunirme nunca con él. Segundo: "Libéreme de Reich"».
Obligado a exiliarse en Noruega y tratado de psicótico por los freudianos, Reich comenzó a sentirse aún más perseguido y su paranoia se intensificó. Desde 1936 se apartó definitivamente del psicoanálisis al fundar en Oslo un Instituto de Investigaciones Biológicas de Economía Sexual que agrupaba a médicos, psicólogos, educadores, sociólogos y animadores de jardines de infancia. Paralelamente inventó un nuevo método, la vegetoterapia, futura orgonterapia. El objetivo era disociar cura por la palabra e intervención sobre el cuerpo. En esa perspectiva, Reich presentaba la neurosis como la obra de una rigidez o una constricción del organismo, que había que sanar mediante ejercicios de relajamiento muscular para liberar el «reflejo orgásmico». A continuación, atraído por la teoría de los biones (partículas de energía vital), dio libre curso a su fascinación por las teorías fisicobiológicas, intentando conciliar los temas cosmogónicos tan apreciados por el romanticismo con la tecnología cuantitativa propia de la sexología.
Jones se había equivocado de enemigo al combatir a los freudomarxistas, y ahora aceptaba colaborar con los nazis, a la vez que ayudaba a los judíos a abandonar Alemania y emigrar al mundo angloparlante. En 1935 presidió oficialmente la sesión de la DPG durante la cual los nueve miembros judíos fueron forzados a dimitir. Un solo no judío se opuso a esta mascarada: se llamaba Bernhard Kamm, y se marchó de la sociedad en solidaridad con los excluidos. Tomó de inmediato el camino del exilio y se instaló en Topeka, Kansas, para trabajar en la famosa clínica de Karl Menninger, verdadero punto nodal de todos los psicoterapeutas exiliados de Europa. Freud calificó de «triste debate» todo este asunto. De allí en adelante, los freudianos partidarios de Göring terminarían sus cartas con el consabido « _Heil Hitler_ ».
Mientras los nazis destruían el psicoanálisis en Berlín, Freud seguía recibiendo pacientes en Viena. Entre ellos, la poetisa norteamericana Hilda Doolittle, amante de Ezra Pound y de Annie Winifred Ellerman (llamada Bryher), ya analizada en Londres por una kleiniana a raíz de una depresión crónica. Contaría su cura en dos momentos y con once años de intervalo (1945 y 1956): por un lado un informe textual, y por otro una reinterpretación en forma de relato. En esos dos textos Doolittle relataba de manera luminosa las intervenciones de Freud centradas en sus sueños, pero también daba testimonio de la vida cotidiana en la Berggasse y de sus encuentros con los demás pacientes, en su mayoría psicoanalistas. Después de esta experiencia no dejaría de proseguir el trabajo analítico con otros terapeutas. En el mundo angloparlante, la obra, la vida y el diario del análisis de Hilda Doolittle (H. D.) fueron el origen de numerosos textos dedicados al lesbianismo y los estudios de género.
Psiquiatra norteamericano originario de un medio de intelectuales judíos y socialistas, Joseph Wortis también viajó a Viena en 1934 para conocer a Freud, alentado por Adolf Meyer y provisto de una carta de recomendación de Havelock Ellis. Wortis llevaba a cabo investigaciones sobre la homosexualidad. Rebelde a toda forma de sometimiento transferencial, se negaba a emprender una psicoterapia, pero Freud lo obligó a hacerlo, al menos durante cuatro meses, pues consideraba que para efectuar esas investigaciones era preciso haber pasado por la experiencia clínica del psicoanálisis. De resultas, Wortis se comportó como un verdadero detective, para gran regocijo de Ellis, con quien mantenía una copiosa correspondencia.
El análisis, en definitiva, no se produjo, pero los dos hombres se entregaron a un violento cuerpo a cuerpo intelectual que tuvo como consecuencia la transformación de Wortis en un antifreudiano radical, obsesionado durante toda su vida por el espectro del maestro de Viena. Sin embargo, logró la proeza de recoger confidencias de Freud sobre su propia vida, sus discípulos, sus amigos y su concepción del mundo, y de elaborar así un documento de gran interés para los historiadores. Pese a la enfermedad y la dificultad que tenía para expresarse, Freud sabía en esa época mostrar una intensa animadversión hacia sus enemigos, como si, sabedor de que su fin se acercaba, no vacilara, aun frente a un adversario, en dar libre curso a juicios que en otro tiempo habría preferido enmascarar.
Desde Zurich, Jung, como los freudianos, colaboraba con Göring desde la dirección de la Allgemeine Ärztliche Gesellschaft für Psychotherapie (AÄGP), en la que había sucedido a Ernst Kretschmer. Fundada en 1926, esta asociación tenía el objetivo de unificar las diferentes escuelas europeas de psicoterapia bajo la égida del saber médico. Una revista, el _Zentralblatt für Psychotherapie_ , fundada en 1930, servía de órgano de difusión a la entidad.
Psiquiatra de renombre internacional, Ernst Kretschmer, gran patrono de la neuropsiquiatría de Marburgo, siempre se había asignado la misión de hacer cohabitar dentro de la AÄGP todas las tendencias de la psiquiatría y la psicoterapia, incluido el psicoanálisis, a condición de que todos los profesionales interesados fueran médicos. En el congreso de Dresde de 1932 había rendido homenaje a los trabajos de Freud. Ahora bien, con la llegada de Hitler al poder ya no podía aspirar a realizar ese objetivo. Por eso prefirió renunciar a la presidencia de la AÄGP. En ese mismo momento se imponía a la rama alemana de la sociedad y al _Zentralblatt_ , editado en Leipzig, la obligación de ponerse al servicio de los nazis. Fue entonces cuando los psicoterapeutas alemanes, interesados a la vez en complacer al régimen y mantener sus actividades nacionales y europeas, pidieron a Jung que asumiera la dirección de la AÄGP, de la que ya era vicepresidente. Muy prestigioso en Alemania, los nazis no molestaron a Kretschmer durante el transcurso de la guerra.
Deseoso de garantizar el predominio de la psicología analítica sobre el conjunto de las escuelas de psicoterapia, Jung aceptó la presidencia de la AÄGP y, por ende, la colaboración con Göring. De ese modo pretendía proteger al mismo tiempo a los terapeutas no médicos, marginados antaño por Kretschmer, y a los colegas judíos que ya no tenían derecho a ejercer en Alemania. En realidad, los profesionales alemanes lo habían elegido debido a la confianza que inspiraba a los promotores de la psicoterapia «aria», radicalmente opuestos al pensamiento freudiano.
Impulsado por Walter Cimbal y Gustav Richard Heyer, Jung se embarcó así en una aventura de la que podría haberse librado con facilidad. Como lo demuestra una carta del 23 de noviembre de 1933 remitida a su discípulo Rudolf Allers, que debía emigrar a Estados Unidos, aceptó todas las condiciones dictadas por Göring en relación con el _Zentralblatt_ :
Es absolutamente necesario contar con un jefe de redacción «normalizado» que sea mejor que todos los demás y esté mucho más capacitado que yo para prever, sin riesgo de error, lo que puede y lo que no puede decirse. En todo caso, habrá que andar con pies de plomo [...]. La psicoterapia debe procurar mantenerse dentro del Reich alemán en vez de instalarse fuera de él, sean cuales fueren las dificultades que encuentre para existir.
Y añadía: «Göring es un hombre muy amable y razonable, por lo cual nuestra colaboración se inicia bajo los mejores auspicios».
Jung comenzó entonces a publicar textos favorables a la Alemania nazi. El primero apareció en 1933. Con el título de _Geleitwort_ («Editorial»), mostraba una concepción clásica de la diferencia entre las razas y las mentalidades, cada una de ellas dotada, a su juicio, de una «psicología» específica:
La tarea más noble del _Zentralblatt_ será pues, sin dejar de respetar de manera imparcial todas las colaboraciones que se presenten, la de crear una concepción de conjunto que haga a los hechos fundamentales del alma humana más justicia que la recibida hasta ahora. Ya no deben borrarse las diferencias que sin duda existen —y que además son reconocidas desde hace mucho por personas clarividentes— entre la psicología germánica y la psicología judía, ya no deben borrarse, y de ese modo la ciencia saldrá beneficiada. En psicología, más que en cualquier otra ciencia, hay una «ecuación personal», y su desconocimiento desvirtúa los resultados de la práctica y la teoría. No se trata con ello, desde luego —y me gustaría que esto se entienda formalmente—, de una desvalorización cualquiera de la psicología semita, así como no se desvaloriza la psicología china cuando se habla de la psicología propia de los habitantes del Lejano Oriente.
El 26 de junio de 1933, de paso por Berlín debido a un seminario, Jung concedió una entrevista radiofónica a su discípulo Adolf von Weizsäcker, neurólogo y psiquiatra partidario del nazismo. En esa ocasión, este último presentó al maestro de Zurich como un eminente protestante de Basilea y como el «investigador más grande de la psicología moderna». Hábilmente, afirmó que su teoría del psiquismo era más creativa y más cercana al «espíritu alemán» que las de Freud y Adler. Después indujo a Jung a hacer un retrato apologético de Hitler y de la bella juventud alemana y a condenar a las democracias europeas «inmersas en el parlamentarismo». A modo de conclusión de la entrevista, Jung propuso a las naciones «enriquecerse» mediante la ejecución de un programa de renovación del alma fundado en el culto del jefe: «Como Hitler decía hace poco», declaró, «el jefe debe ser capaz de estar solo y de tener el valor de seguir su propio camino. [...] El jefe es el portavoz y la encarnación del alma nacional. Es la punta de lanza de la falange de todo el pueblo en marcha. La necesidad de las masas siempre exige un jefe, sea cual fuere la forma del Estado».
Negándose a comprender que la ideología nazi apuntaba a la expulsión de todos los judíos de la profesión de psicoterapeuta, para luego exterminarlos, Jung tampoco admitía que una buena cantidad de junguianos alemanes, con quienes colaboraba en el _Zentralblatt_ , hubiesen adoptado las tesis del nacionalsocialismo. En este aspecto, su conducta no fue más honorable que la de los mediocres freudianos de Berlín. También ellos suponían que protegían la integridad del psicoanálisis frente a las desviaciones; también ellos consideraban al abuelito Führer de poblada barba como un hombre amable y razonable. Sin embargo, si Jung pudo aceptar sin pestañear esa colaboración, también fue porque su concepción del inconsciente coincidía en gran parte con la defendida por los artífices de la psicoterapia «arianizada». En la huella de una teoría de la diferencia de las razas, Jung consideraba el psiquismo individual como el reflejo del alma colectiva de los pueblos. En otras palabras, lejos de ser un ideólogo de la desigualdad de las razas, a la manera de Vacher de Lapouche o Gobineau, se afirmaba como un teósofo en busca de una ontología diferencial de la psique. Por eso quería elaborar una «psicología de las naciones» capaz de explicar a la vez el destino del individuo y de su alma colectiva. Dividía el arquetipo en tres instancias: el _animus_ (imagen de lo masculino), el _anima_ (imagen de lo femenino) y el _Selbst_ (el sí mismo), verdadero centro de la personalidad. Si le damos crédito, los arquetipos constituían la base de la psique, una suerte de patrimonio mítico propio de una humanidad organizada en torno del paradigma de la diferencia. Armado de su psicología de los arquetipos, Jung incluía a los judíos en la categoría de los pueblos desarraigados, condenados al vagabundeo y tanto más peligrosos cuanto que, para escapar a su desnacionalización psicológica, no vacilaban en invadir el universo mental, social y cultural de los no judíos.
En ese contexto, evolucionó hacia una concepción desigualitaria del psiquismo arquetipal. Hasta entonces se había contentado con un enfoque en términos clásicamente diferencialistas. Pero en abril de 1934 publicó en el _Zentralblatt_ un extenso artículo titulado «Zur gegenwärtigen Lage der Psychotherapie», en el cual hacía la apología del nacionalsocialismo y afirmaba a la vez la superioridad del inconsciente ario sobre el inconsciente judío. Ese texto llegaría a ser tristemente célebre y tendría un peso enorme en el destino ulterior de Jung y el movimiento junguiano.
Estaban reunidos todos los ingredientes para transformar la teoría freudiana en un pansexualismo obsceno ligado a la «mentalidad» judía. Jung parecía olvidar que veinticinco años antes había defendido el psicoanálisis contra argumentos del mismo tipo que lo comparaban con una epidemia originada en la decadencia de la Viena imperial. Aquí algunos extractos de ese artículo:
Los judíos tienen en común con las mujeres la siguiente particularidad: como son físicamente más débiles, deben buscar los defectos en la armadura de sus adversarios y, gracias a esta técnica que se les impuso a lo largo de los siglos, están mejor protegidos en los puntos donde otros son más vulnerables. [...] El judío, que como el chino cultivado pertenece a una raza y una cultura tres veces milenarias, es psicológicamente más consciente de sí mismo que nosotros. Por eso en general no teme desvalorizar su inconsciente. En cambio, el inconsciente ario está cargado de fuerzas explosivas y de la simiente de un futuro aún por nacer. No puede, por tanto, desvalorizarlo o tacharlo de romanticismo infantil, so pena de poner su alma en peligro. Todavía jóvenes, los pueblos germánicos pueden producir nuevas formas de cultura y ese porvenir duerme aún en el inconsciente oscuro de cada ser, donde descansan gérmenes colmados de energía y prontos a abrasarse. El judío, que tiene algo de nómada, jamás ha producido y, sin duda, jamás producirá una cultura original, pues sus instintos y sus dones exigen, para expandirse, un pueblo anfitrión más o menos civilizado. Por eso, según mi experiencia, la raza judía tiene un inconsciente que solo puede compararse bajo ciertas condiciones con el inconsciente ario. A excepción de algunos individuos creativos, el judío común y corriente ya es demasiado consciente y demasiado diferenciado para llevar en su seno las tensiones de un futuro venidero. El inconsciente ario tiene un potencial superior al inconsciente judío: [esas son] la ventaja y el inconveniente de una juventud todavía próxima a la barbarie. El gran error de la psicología médica consistió en aplicar sin distinción categorías judías —que ni siquiera son válidas para todos los judíos— a eslavos y alemanes cristianos. En consecuencia, solo vio en los tesoros más íntimos de los pueblos germánicos —su alma creadora e intuitiva— ciénagas infantiles y banales, mientras que sobre mis advertencias recaía la sospecha de antisemitismo. Esa sospecha emanaba de Freud, que no comprendía la psique germánica, como, por otra parte, tampoco la comprendían sus discípulos alemanes. El grandioso fenómeno del nacionalsocialismo, que el mundo entero contempla con asombro, ¿no los ha ilustrado?
En su correspondencia de 1934 Jung se quejó varias veces porque ya resultaba imposible hablar de los judíos sin ser tachado de antisemitismo. Cuando los ataques se redoblaron, los atribuyó a una polémica anticristiana: «El mero hecho de que hable de diferencia entre psicología judía y psicología cristiana», escribía a James Kirsch,
basta para que todo el mundo proclame la idea preconcebida de que soy antisemita [...]. Esa actitud es simplemente la muestra de una susceptibilidad enfermiza que hace casi imposible cualquier discusión. Como usted sabe, Freud ya me acusó de antisemitismo porque yo me sentía incapaz de aprobar su materialismo sin alma. Con esa propensión a olfatear antisemitismo por todas partes, los judíos terminan por provocarlo realmente.
A la vez que reprochaba a los judíos generar las condiciones de su persecución, Jung pretendía ayudarlos a ser mejores judíos. En una carta remitida a su alumno Gerhard Adler y fechada el 9 de junio de 1934, aprobó la idea propuesta por este, según la cual Freud era en cierta manera culpable de haberse apartado de su arquetipo judío, de sus «raíces» judías. Esto era tanto como decir que, conforme a su teoría, Jung rechazaba el modelo freudiano del judío sin religión, el judío de la Ilustración. Condenaba la figura moderna del judío desjudaizado, culpable, según él, de haber renegado de su «naturaleza» judía: «Cuando critico el aspecto judío de Freud no critico a _los judíos_ , sino su condenable capacidad de renegar de su propia naturaleza, que se manifiesta en Freud». Interesado en llevar a los judíos al terreno de una psicología de la diferencia, Jung se consagró a seguir con atención la evolución de sus discípulos judíos exiliados en Palestina. Por fin arraigados en la nueva Tierra Prometida, estos podrían llegar a ser verdaderos junguianos. El 22 de diciembre de 1935 envió a Erich Neumann, instalado en Tel Aviv, una carta en la que fustigaba a los intelectuales judíos europeos «siempre a la búsqueda de lo no judío». Él, en contraste, valoraba a los judíos palestinos que por fin habían encontrado su «suelo arquetípico»:
Su convicción muy positiva de que la tierra palestina es indispensable para la individuación judía es preciosa para mí. ¿Cómo conciliar esa idea con el hecho de que los judíos en general han vivido mucho más tiempo en otros países que en Palestina [...]? ¿Será que los judíos están tan acostumbrados a no ser judíos que necesitan concretamente que el suelo palestino les recuerde su judeidad?
En otras palabras, Jung era sionista por antisemitismo, mientras que Freud rechazaba el sionismo porque no creía ni por un momento en la idea de que los judíos hallarían una solución al antisemitismo en la conquista de la Tierra Prometida. Sería hasta el final un judío de la diáspora, un judío universal, en tanto que su viejo discípulo se aferraba a la idea de que los judíos solo podían sobrevivir si se aseguraban un anclaje en un verdadero territorio: oposición entre la Tierra Prometida del inconsciente, interna a la subjetividad, y el territorio de los arquetipos.
Si observamos las cosas con más detenimiento, nos damos cuenta de que Jung utilizaba a veces, en sus textos, la famosa lengua del Tercer Reich — _Lingua Tertii Imperii_ ( _LTI_ )— tan bien descrita por el filólogo Victor Klemperer, una especie de jerga hitleriana que ponía en valor los términos alemanes más simplistas para facilitar la propaganda. Empresa de destrucción de la riqueza de la lengua alemana, la _LTI_ terminaría por contaminar todos los discursos y escritos de quienes colaboraban con el régimen. A menudo, los textos escritos en esa «neolingua» multiplicaban las referencias a las presuntas especificidades del judío, siempre designado como una «cosa» inerte o nómada, despreciable, nihilista, al margen de la humanidad, en oposición al «ario» grandioso y sublime, quintaesencia de todas las formas de superioridad «racial».
En este aspecto, puede ser útil comparar las posiciones respectivas de Carl Gustav Jung y Martin Heidegger, feroz enemigo del psicoanálisis. Considerando que los judíos «no tenían mundo» y que el psicoanálisis se emparentaba con un nihilismo, el filósofo anotó, en su cuaderno XIV de 1940-1941, que no había que «indignarse demasiado ruidosamente contra el psicoanálisis» del «judío Freud», como lo hacían los partidarios del biologismo racial, pero añadía al punto que aquel era un modo de pensamiento que no toleraba el ser y que reducía todo a los instintos y a un marchitamiento de lo instintivo. También él utilizaba la jerga del Tercer Reich ( _LTI_ ).
Así como Jung excluía al judío de la diáspora de todo acceso a la «individuación judía», Heidegger excluía al judío de la humanidad pensante para reducirlo a las ciénagas del instinto. Tanto de un lado como de otro, ese antisemitismo que no quería confesar su nombre pretendía suprimir el espíritu judío de la escena del mundo, en cuanto habría dado origen a una doctrina específicamente judía. Para Jung el psicoanálisis carecía de «suelo arquetípico», y para Heidegger era un nihilismo que llevaba el nombre del judío Freud. Ambos tenían en común la adhesión a una suerte de teología antijudeocristiana y politeísta.
En 1936 Göring pudo por fin realizar su sueño. Creó su Deutsches Institut für Psychologische Forschung und Psychotherapie (Instituto Alemán de Investigación Psicológica y Psicoterapia), pronto llamado Göring Institut o Instituto Göring. Para marcar con claridad el triunfo del nazismo sobre el psicoanálisis, la nueva entidad se instaló en la sede de la prestigiosa BPI, símbolo del poderío freudiano que Göring había tenido tantos deseos de aniquilar. El instituto reunía a «freudianos», «junguianos», «independientes» y «adlerianos», que se detestaban unos a otros.
A lo largo de toda la guerra una veintena de freudianos prosiguieron así con sus actividades terapéuticas y sus disputas ideológicas en defensa de un «buen psicoanálisis» bajo la batuta del Instituto Göring y bajo la bota nazi. En nombre de un presunto salvamento, esos hombres se deshonraron al colaborar en una destrucción que se habría producido de todos modos y que hubiera sido preferible que se llevase a cabo sin ellos. Se sumaron a la lengua del Tercer Reich, aceptaron la erradicación sistemática de todo el vocabulario freudiano y, afirmaran lo que afirmasen para su defensa ulterior, se negaron a analizar a pacientes judíos, que por otra parte estaban excluidos de todo tratamiento y eran enviados a los campos.
En mayo de 1936 la celebración del cumpleaños de Freud cobró dimensiones considerables. Abrumado por los honores, el ilustre sabio, ahora confinado en Viena, recibió regalos y cartas, como si todos los que le rendían homenaje —H. G. Wells, Romain Rolland, Albert Schweitzer y muchos otros— tuvieran conciencia de que su situación era desesperada: «Hasta hace poco», destacaba Albert Einstein,
yo no podía sino advertir el poder especulativo de su pensamiento, así como su enorme influencia sobre la _Weltanschauung_ de nuestra época, sin estar pese a ello en condiciones de hacerme una opinión definitiva acerca de la verdad que contenía. No hace mucho, sin embargo, tuve la oportunidad de oír hablar de algunos casos, no muy importantes en sí mismos pero que, a mi juicio, excluían toda interpretación que no fuese la proporcionada por la teoría de la represión.
Ese día, su sobrina, Lilly Freud-Marlé, le envió tres ensayos que había escrito con destino a él y que le llegaron al corazón, por la conciencia que tenía de la ineluctable dispersión de los miembros de su familia ya exiliados.
Al día siguiente Freud recibió la visita de Binswanger y Thomas Mann, que volvió a visitarlo el 14 de mayo en su villa de Grinzing, donde aquel se instalaba con frecuencia, para leerle el discurso sobre la «vida ya vivida» que había pronunciado en su honor en el Akademische Verein für Medizinische Psychologie. Esta vez Freud se sintió verdaderamente impresionado, al extremo de aceptar que el escritor incluyera su obra en la herencia de la filosofía y lo calificara a él mismo de hijo de Nietzsche y Schopenhauer, además de «pionero de un humanismo del futuro»: «La ciencia», decía Thomas Mann, «jamás hizo el más mínimo descubrimiento que la filosofía no hubiera autorizado y orientado». Y terminaba su elogio con una vibrante llamada a la libertad de los pueblos, al mismo tiempo que destacaba la gran semejanza de Freud con Fausto. Los dos hombres entablaron luego una larga conversación sobre el nombre de José, héroe bíblico, hijo de Jacob y nieto de Isaac, pero también personaje histórico, hermano de Napoleón Bonaparte, siempre muy presente en los escritos freudianos. En enero, además, Freud había escrito un texto sobre ese tema para un libro de homenaje a Romain Rolland.
Mann y Freud sentían pasión por la egiptología y el primero había comenzado a escribir una voluminosa novela bíblica dedicada a José, el último de los patriarcas. En el último libro del Génesis, José, hijo preferido de Jacob, se complace en despertar los celos de sus once hermanos, a quienes cuenta dos sueños proféticos: en el primero, once gavillas del campo se inclinan ante la suya, mientras que en el segundo once estrellas se prosternan. Por haber desafiado a sus hermanos, estos lo arrojan a un pozo y luego lo venden por veinte piezas de plata a los ismaelitas, que lo llevan a Egipto; allí lo compra Putifar, comandante de la guardia del faraón. José se convierte en su mayordomo y tiene que resistir la pasión culpable que la mujer de aquel siente por él. Dios vela por su destino y José, gracias a sus talentos de descifrador de sueños, llegará a ser virrey de Egipto. Al cabo de una vida de exilio, ya poderoso, perdonará a sus hermanos y se reencontrará con su padre, que bendecirá a los hijos que José ha tenido con Asnat, hija de Putifar, y lo designará como heredero privilegiado de la Alianza divina con el linaje de Abraham. En su agonía, José profetizará el Éxodo. A continuación, al conducir a los hebreos hacia la Tierra Prometida, Moisés tomará la precaución de llevar consigo la osamenta del hijo de Jacob.
Para decirlo con otras palabras, en el mismo momento en que Freud, después de haberse sentido subyudado durante toda su vida por el combate de Jacob y el ángel, se interesaba en Moisés, Thomas Mann escribía una novela en cuatro partes donde hacía de José un héroe moderno, una especie de Narciso colmado de privilegios por un padre sometido a lo largo de toda la vida a un combate perpetuo. Convencido de que su belleza y su superioridad intelectual le acarrearían el poder y la gloria, José se envolvía en el velo nupcial de su madre, Raquel, suscitando los celos de sus hermanos. Y entonces su destino lo hacía caer en la servidumbre. Tras ser esclavo, desplegaba todos sus talentos de organizador ante el faraón Amenhotep IV. De ese modo favorecía la transformación de las antiguas mitologías en una religión monoteísta y se convertía en la encarnación de un humanista progresista.
Judío y egipcio, pragmático y administrador, el José de Thomas Mann era el héroe de una espiritualidad que solo podía consumarse en el exilio y la afirmación de una subjetividad inédita frente a un padre todavía aferrado a un universo arcaico. Mediante esta saga el escritor pretendía poner de relieve, frente al nazismo, la tesis de la predestinación de los patriarcas de Israel revisada y corregida por el humanismo que lo inspiraba.
Freud había leído los tres primeros volúmenes de esa tetralogía, aparecidos entre 1933 y 1936, y se inspiró en ellos para comunicar a Mann una asombrosa interpretación del lugar ocupado por José en el destino de Napoleón Bonaparte. A los ojos del emperador, aquel habría tenido el papel de un modelo, alternativamente sublime y demoníaco. Freud partía de la idea de que el joven Bonaparte había sentido en su infancia una intensa hostilidad hacia su hermano mayor José y, para ocupar su lugar, había convertido en amor su odio primitivo, sin perder empero algo de la antigua agresividad, fijada a continuación en otros objetos. Adulado por su madre, Napoleón se habría convertido luego en un sustituto paterno para sus hermanos y habría profesado una pasión desmesurada por Josefina, encarnación femenina de José. Su amor por esta joven viuda, que sin embargo lo trataba mal y lo engañaba, solo habría sido pues, según Freud, el producto de una identificación con José. Pero, para asumir plenamente su papel de sustituto de su hermano mayor, Napoleón habría echado el ojo a Egipto, estableciendo así un lazo con la vida del hijo de Jacob. De tal modo, la campaña egipcia había marcado un momento sublime en la epopeya napoleónica porque permitió a Europa, y por ende al propio Freud, descubrir los vestigios de una fabulosa civilización y abrir un nuevo campo de estudios a la arqueología. Al repudiar luego a Josefina, Napoleón se habría tornado infiel a su mito y habría orquestado él mismo su caída al transformarse en un tirano diabólico. Incorregible soñador, habría tenido en Egipto el mismo papel que José, hijo de Jacob, para contribuir a continuación a su propia destrucción y la de Europa.
Como la mayoría de los novelistas del siglo XIX —de Balzac a Tolstói pasando por Hugo—, Freud siempre se había interesado en el destino heroico de ese conquistador moderno, admirador de las ciencias, hostil al oscurantismo religioso, que había transformado el mundo europeo y otorgado a los judíos derechos cívicos que favorecieron su asimilación. Por otra parte, Freud le había rendido homenaje al recordar que Isaac Bernays, el abuelo de Martha, había aprovechado el Código Civil sancionado por el ocupante francés para ir a la universidad y llegar a ser más adelante gran rabino de Hamburgo. Por otra parte, el duque de Reichstadt pertenecía por su madre a la casa de los Habsburgo. Todas esas genealogías estaban presentes en la memoria de Freud. Pero, a diferencia de Thomas Mann, él también consideraba al emperador como un bribón y un «magnífico canalla», que había «recorrido el mundo como un sonámbulo para hundirse mejor en el delirio de grandeza». Freud parecía olvidar entonces que en su infancia había admirado a Masséna, masón y mariscal del imperio, nacido el 6 de mayo como él y a quien tomaba por judío.
Como buen anglófilo, consideraba al emperador como un producto puro del jacobinismo francés, sin dejar de proclamar que su historia familiar interesaba en el más alto grado a la doctrina psicoanalítica y que el hombre tenía genio y una «clase magnífica». Además, el destino romántico de ese hombre, que había conocido a Goethe y encarnado la voluntad de toda una época de romper con las mitologías de los orígenes para garantizar el progreso de una nueva conciencia histórica, había suscitado enorme interés en la comunidad freudiana. Jones había sido el primero en hablar a Freud de la historia de José y del complejo oriental de Bonaparte, tras lo cual Ludwig Jekels y Edmund Bergler dedicaron, cada uno por su lado, un ensayo a la vida de Napoleón y a su complejo fraterno o paterno.
Lo cierto es que, en su intercambio de ideas con Thomas Mann, Freud se había acordado de su visita a la Acrópolis y de la perturbación que había experimentado al comprobar que su destino era tan diferente al de su padre.
El interés del intercambio de ideas con Mann radicaba en la similitud entre los dos modos de proceder. Como el escritor, Freud apelaba a la egiptología para traducir la historia bíblica del judaísmo en una novela de la judeidad moderna, a través de la cual un héroe forzado al exilio había sido el fruto de dos identidades: una judía, otra egipcia. Mann había escogido a José y Freud a Moisés, como si cada uno de ellos quisiera, a su manera, ilustrar la grandeza de esa judeidad de la diáspora condenada al genocidio. Mann terminaría su libro en la costa Oeste de Estados Unidos, en compañía de Brecht, Adorno y Fritz Lang, y Freud el suyo en su casa de Londres, rodeado por su familia. Así supieron, uno y otro, preservar desde el fondo de su exilio la belleza de la lengua alemana, ese único bien del que Hitler nunca pudo despojarlos.
En agosto de 1936 Jones presidió en Marienbad el decimocuarto congreso del IPV. Allí propuso abandonar la sigla alemana para adoptar el nombre de International Psychoanalytical Association (IPA). Esa decisión se justificaba porque, ahora, el inglés era mayoritario en los intercambios internacionales y los exiliados de la antigua _Mitteleuropa_ lo hablaban a la perfección. Mientras volvían a enfrentarse los partidarios de Melanie Klein y los de Anna Freud, y Melita Schmideberg, apoyada por Edward Glover, libraba una batalla contra su madre, Jacques Lacan, psiquiatra francés ya conocido en su país, hacía su entrada en el movimiento psicoanalítico internacional con una ponencia sobre el «estadio del espejo». Al cabo de diez minutos, Jones le quitó la palabra. Lacan viajó entonces a Berlín a ver las manifestaciones de la undécima Olimpíada, de siniestra memoria. También él quería ver de frente a Hitler. Ante ese espectáculo, que lo horrorizó, y tras la humillación infligida por Jones, sintió que había llegado la hora de llevar a cabo una segunda «revolución freudiana». Por eso redactó un manifiesto, «Más allá del principio de realidad», que aspiraba a ser el corolario de _Más allá del principio de placer_. Por el momento, en el ámbito de la IPA nadie sospechaba todavía el impacto que en el futuro tendría la refundición lacaniana de la obra de Freud.
En noviembre, durante una reunión de la WPV, Boehm comprobó, como Anna Freud, que muchos estudiantes seguían cursos de psicoanálisis en el marco del Instituto Göring. A esas alturas Freud comenzaba a darse cuenta de que la política de «salvamento» del psicoanálisis no era, sin duda, la mejor opción. Pidió a Boehm que le expusiera la situación, justo antes de retomar sus ataques contra Adler y recomendar no hacer concesión alguna a los partidarios de la «psicología de la protesta masculina».
Boehm había logrado hacerse pasar por un defensor del freudismo, sin dejar de admitir que lo que sucedía por entonces en Alemania jamás habría sido tolerado por el movimiento un año antes. Lo inaceptable se había banalizado. Propuso de todos modos invitar a un miembro de la WPV a Berlín: «¿A quién invitará?», preguntó Freud. Y Boehm mencionó a Richard Sterba, el único no judío de esa entidad, hostil, además, a cualquier forma de colaboración con el nazismo: «Aceptaré de buen grado la invitación», respondió Sterba, «después de que inviten a uno de mis colegas judíos de Viena a hablar en el Instituto de Berlín». Quería creer que Freud desaprobaba por completo la política de Jones, cosa que todavía no sucedía. Siniestra reunión.
En el Instituto Göring cada cual se dedicaba a sus investigaciones y experiencias. En las filas de la fenecida DPG, John Rittmeister, August Watermann, Karl Landauer y Salomea Kempner fueron —exterminados o asesinados— las principales víctimas de esa política, como, por otra parte, varios otros terapeutas húngaros o austríacos que nunca consiguieron exiliarse.
Algunos partidarios alemanes de Alfred Adler también participaron en esa política de colaboración. Sin embargo, los nazis jamás consideraron las tesis adlerianas como una «ciencia judía», aunque el padre fundador de la psicología individual era tan judío como Freud. Pero, a diferencia del psicoanálisis, la psicología adleriana oponía un particularismo extraño al universalismo freudiano. En síntesis, solo el psicoanálisis fue considerado como una «ciencia judía», debido a su pretensión de aplicarse a la subjetividad humana como tal. En ese concepto, caía bajo el peso de una condena mucho más radical. No solo había que exterminar a sus partidarios sino también destruir su lengua y sus conceptos.
Empeñados en combatirse unos a otros, freudianos, adlerianos y junguianos, reunidos en el Instituto Göring, colaboraron pues en su propia erradicación. Hasta su muerte Adler trató a Freud de farsante y conspirador, mientras que este último no dejaba de decir cosas del mismo tipo contra su antiguo rival: «paranoico, Fliess en pequeño», etc. Cuando Adler murió en Escocia en mayo de 1937, durante una gira de conferencias, Freud pronunció estas palabras vengativas: «Para un muchacho judío salido de los arrabales de Viena, morir en Aberdeen es un final inesperado y la prueba del camino que ha recorrido. Ha recibido una recompensa realmente buena por haberse encargado de aportar la contradicción al psicoanálisis».
Desde el verano de 1934 Freud trabajaba en su obra sobre Moisés, inspirada por la de Thomas Mann y la reacción común de ambos a las persecuciones antisemitas. Había hablado de ese proyecto por primera vez con Arnold Zweig, y después con Lou Andreas-Salomé: «Moisés no era judío», decía, «sino un egipcio distinguido [...], ardiente partidario de la creencia monoteísta de la que Amenhotep IV había hecho en 1350 a.C. una religión de Estado».
Lou Andreas-Salomé había recibido con alegría el anuncio de ese nuevo ensayo. Pero un año después se refirió a su decaimiento físico, que coincidía en Gotinga con la profundización cada vez más criminal del furor nazi. Perseguida por el odio de Elisabeth Förster, que hasta su muerte en 1935 contribuyó a la adaptación de la obra de Nietzsche a los principios del nazismo, se había visto obligada a adherirse a la Asociación de Escritores del Reich y a llenar formularios para dar fe de su pertenencia a la «raza aria». Día tras día comprobaba que sus vecinos, enardecidos por el hitlerismo, enarbolaban en sus postigos ostentosas cruces gamadas: la llamaban la «bruja». En un momento de angustia escribió un texto que pensaba entregar a un editor, dedicado a su «adhesión a la Alemania de nuestros días». Pero cuando se dio cuenta de que iban a poder utilizarlo como una prueba de su apoyo al régimen, lo rompió. Su fiel amigo Ernst Pfeiffer recogió los pedazos rotos y los conservó en sus archivos. Bajo ese título ambiguo Lou se refería al alma alemana y no a una adhesión a lo que Alemania había llegado a ser. Y se valía de un estilo que siempre la había caracterizado: culto de la naturaleza, vitalismo, aspiración a una espiritualidad.
Cuando Freud se enteró de su muerte, escribió de inmediato su obituario, en el que saludaba la memoria de esa mujer excepcional a la que había amado tanto: «Quien se le acercaba recibía la más intensa impresión de la autenticidad y la armonía de su ser, y también podía comprobar, para su asombro, que todas las debilidades femeninas y quizá la mayoría de las debilidades humanas le eran ajenas, o las había vencido en el curso de su vida».
Algunos días más tarde un funcionario de la Gestapo irrumpió en la casa de Lou para confiscar su biblioteca, que terminaría en los sótanos del ayuntamiento. Para justificar esa requisa se adujo que había sido psicoanalista, que practicaba una «ciencia judía», que había sido amiga de Freud y que los anaqueles de su biblioteca contenían libros de autores judíos.
Cada vez más aferrado al pasado y a sus viejas amistades, Freud quiso, en ese año muy sombrío, volver al debate que lo había opuesto a sus dos discípulos preferidos: Ferenczi y Rank. Y por eso publicó en 1937 dos grandes artículos sobre la técnica psicoanalítica: «Análisis terminable e interminable» y «Construcciones en el análisis».
En el primero señalaba que Rank, mediante la hipótesis de un trauma del nacimiento, procuraba eliminar la causalidad psíquica de la neurosis. Y también acometía contra la tentativa de acortar la duración de la cura, haciendo notar que estaba ligada a una coyuntura histórica: «El intento de Rank era hijo de su época», decía, «fue concebido bajo el influjo de la oposición entre la miseria europea de posguerra y la _prosperity_ norteamericana, y estaba destinado a acompasar el tempo __ de la terapia analítica a la prisa de la vida norteamericana».
En cuanto a Ferenczi, Freud criticaba en este «maestro del análisis» el peligro que representaba la búsqueda permanente de un retorno a la hipnosis como sustituto del análisis de la transferencia. Y agregaba que la práctica del psicoanálisis era el ejercicio de una «profesión imposible» y que, de antemano, nunca se podía estar seguro de su resultado. El esfuerzo terapéutico, decía, oscila entre un fragmento de análisis del ello y un fragmento de análisis del yo: en un caso se quiere llevar a la conciencia algo del ello, y en otro, corregir el yo. Sin esa oscilación, añadía, no puede haber éxito terapéutico. En consecuencia, seguía diciendo, el analista no es más normal que su paciente y, como copartícipe «activo», está sometido más que este último a los peligros del análisis. Por eso, «todo analista debería hacerse de nuevo objeto de análisis periódicamente, quizá cada cinco años, sin avergonzarse por dar ese paso. Ello significaría, entonces, que el análisis propio también, y no solo el análisis terapéutico de enfermos, se convertiría de una tarea terminable en una interminable».
Este artículo mostraba que, en 1937, Freud se oponía aún al método ferencziano en relación con el dominio de la contratransferencia y la idea de sostén activo al paciente. Si la formación del terapeuta supone una tarea infinita es porque, decía en sustancia, el análisis de los analistas nunca se termina, así como la curación nunca es un hecho consumado. La noción de análisis interminable obedece pues al proverbio «lo que pronto se gana, más rápido se pierde». Como Ferenczi, Freud afirmaba así la irreductibilidad de la psicoterapia a la institucionalización y ponía al futuro didáctico en una posición idéntica a la del paciente. Una vez más, dudaba de la eficacia de la psicoterapia pero afirmaba que los fracasos experimentados obedecen también a múltiples factores: tipos de patología, resistencia de los pacientes, actitudes de los analistas. En síntesis, más allá de la crítica que hacía a Rank y Ferenczi, Freud tomaba nota de las dificultades con que él mismo se había topado en muchas terapias psicoanalíticas.
Ese texto abría el camino a numerosas interpretaciones y sobre todo a la idea de que algún día los analistas, como los pacientes, podrían recurrir durante toda su vida a nuevos «períodos» de análisis para explorar indefinidamente las causas de sus patologías.
En el segundo artículo, aún más interesante, Freud volvía a la historia de Serguéi Pankejeff para distinguir la noción de interpretación de la de construcción. Y admitía que las construcciones puestas en práctica en la cura podían perfectamente ser de la misma naturaleza que los delirios de los pacientes.
Por medio de esas dos intervenciones Freud quería tomar posición, por última vez, con respecto a una cuestión que, mucho tiempo después de su muerte, se revelaría esencial en la historia del movimiento psicoanalítico.
Por esos días Rank seguía haciendo una carrera fulgurante en Estados Unidos. Rechazado por la IPA, practicaba curas breves, cara a cara, y no dejaba de analizar lapsus, actos fallidos y sueños. Un día un paciente le pidió que lo recibiera, a pesar de que ya lo habían analizado cuatro terapeutas: dos freudianos, un junguiano y un adleriano. El hombre afirmaba no padecer de ningún problema sexual, pero necesitaba ayuda. Rank comprendió al punto que ese paciente buscaba la manera de hacer fracasar la cura misma. Por eso aceptó ayudarlo, con la única condición de abordar con él la cuestión sexual. De ese modo daba a entender que nadie podía ejercer un control sobre el devenir del análisis: ni el paciente ni el terapeuta.
Muy a menudo Rank mencionaba con nostalgia el recuerdo de Freud y de su juventud vienesa. En cuanto a Freud, despechado, consideraba que su antiguo discípulo estaba afectado desde hacía tiempo por una psicosis maníaco depresiva que se había agravado después de su mudanza definitiva al continente americano.
En Berlín, Hitler había consolidado su alianza con Mussolini. Brindaba su apoyo a los nacionalistas españoles y contemplaba seriamente la posibilidad de anexionar Austria al gran Reich. En esas circunstancias, Weiss ya no tenía nada que esperar de Forzano y Freud comenzaba a comprender que Viena estaba tan amenazada como el psicoanálisis: «Es indudable», escribía a Jones en marzo de 1937,
que la irrupción de los nazis ya no podrá impedirse; las consecuencias, incluso para el análisis, serán funestas [...]. Si nuestra ciudad cae, los bárbaros prusianos inundarán Europa. Por desdicha, el poder que nos ha protegido hasta hoy —Mussolini— parece ahora dejar las manos libres a Alemania. Querría vivir en Inglaterra como Ernst e ir a Roma como usted.
A pesar de esa comprobación, Freud aún quería creer que Kurt von Schuschnigg, el sucesor de Dollfuss en la cancillería, un hombre perteneciente a la vieja nobleza imperial, conseguiría salvaguardar la independencia del país. Se equivocaba. Se negaba a admitir la realidad aun cuando la tenía frente a sus ojos, actitud idéntica a la que había adoptado durante su visita a la Acrópolis. En noviembre de 1937 Stefan Zweig lo visitó y le sugirió la necesidad de escribir un libro sobre la tragedia de los judíos: «Cuando pienso en Viena y el ánimo se me ensombrece, lo evoco a usted. De año en año su negra severidad me resulta cada vez más ejemplar. Y me siento ligado a usted con una gratitud siempre creciente».
La política del pretendido «salvamento», orquestada por Jones y defendida por Freud, fue un completo fracaso que se traduciría, tanto en Alemania como en toda Europa, en una colaboración lisa y llana con el nazismo, pero sobre todo en la disolución de todas las instituciones freudianas y la emigración hacia el mundo angloparlante de la casi totalidad de sus representantes. De no habérsela implementado, el destino del freudismo en Alemania no habría cambiado en nada, pero se hubiera preservado el honor de la IPA. Y sobre todo, esa desastrosa actitud de neutralidad, de no compromiso, de apoliticismo, no se hubiera repetido a posteriori bajo otras dictaduras, como en Brasil, Argentina y muchos otros lugares del mundo.
Corroído por el cáncer, Freud iba a asistir durante los dos últimos años de su vida al derrumbe y la ruina de todo lo que había construido: editoriales destruidas, libros quemados, discípulos perseguidos, asesinados u obligados a exiliarse, institutos desmantelados, objetos saqueados, vidas humanas reducidas a la nada.
### 3
La muerte en acción
En los últimos años de su vida Freud entabló una hermosa relación de amistad con William Bullitt, diplomático y periodista dandi, perteneciente a una riquísima familia de abogados de Filadelfia y asesor del presidente Woodrow Wilson. Enviado en misión a Rusia y gran admirador de la Revolución de Octubre, se había reunido con Lenin con la firme intención de reanudar las relaciones entre los dos países. Pero, fracasadas las negociaciones, participó en la Conferencia de Paz y luego criticó severamente el Tratado de Versalles, que juzgaba inaceptable para los vencidos. A causa de ello se forjó una vigorosa hostilidad hacia Wilson. En 1924 se casó con Louise Bryant, una bella militante anarquista, antigua amante de Eugene O'Neill y viuda del célebre periodista John Reed, autor de _Diez días que estremecieron al mundo_ , con quien había tenido una hija. Afectada hacia 1928 por la terrible enfermedad de Dercum, que la hacía sufrir y la tornaba monstruosa, Louise se hundió en el alcoholismo y la locura, lo cual la llevó, por consejo de su marido, a consultar a Freud. Egocéntrico, colérico, emotivo e incapaz de soportar esa situación, Bullitt no dejaba de abrumar a Louise con sus reproches, y se separó de ella cuando advirtió que tenía un amorío con una escultora, Gwen Le Gallienne. Peor aún, aprovechó esa circunstancia para obtener la custodia de su hija, con la deliberada intención de apartar a su madre de la vida de esta.
Fue en mayo de 1930, en el momento de su divorcio, cuando Bullitt conoció a Freud en el sanatorio de Tegel, Berlín. Tratado entonces por una neumonía, deprimido y con la muerte como único pensamiento, Freud escuchó con interés las palabras de Bullitt, que le transmitió su intención de escribir una biografía de Wilson sobre la base de los muchos archivos que tenía a su disposición. Se recordará que Freud había conocido la vida del vigésimo octavo presidente norteamericano al leer la obra de Hale, _The Story of a Style_. Por eso propuso su ayuda a Bullitt. Soñaba desde siempre con escribir una verdadera psicobiografía que, por su estilo, fuera muy diferente del ensayo literario que había dedicado a Leonardo da Vinci. Esta vez, gracias a ese seductor diplomático, podría sin duda disponer de toda la documentación necesaria. Pero en esos mismos días el periodista Ray Stannard Baker estaba escribiendo una monumental biografía oficial de Wilson, y Bullitt sabía que tendría que obrar con astucia para resistir el choque que significaba semejante competidor. De ahí el interés de arrastrar a la aventura al maestro vienés, a quien también pidió que lo tomara en análisis. Paralelamente, puso a su amigo Edward Mandell House al tanto de su proyecto que, recomendaba, no debía divulgarse de ninguna manera.
En octubre Freud, al poco tiempo de haber sufrido una nueva operación, se sintió muy feliz de volver a ver a Bullitt para compartir algunas sesiones de trabajo y de análisis. Juntos, consultaron más de un millar de páginas dactilografiadas y discutieron punto por punto cada momento importante de la vida y la actividad de Wilson. Freud escribió entonces un primer borrador de algunas partes del futuro manuscrito mientras Bullitt se encargaba de otras, y tomaron la decisión de publicar la obra en Estados Unidos, bajo la responsabilidad del diplomático. En enero de 1932 este remitió a su coautor la suma de dos mil quinientos dólares en carácter de anticipo de la edición norteamericana, pero en la primavera estalló una disputa cuya clave nadie conocería jamás y que no pareció afectar en exceso a Freud. El año siguiente este declaró que Bullitt era el único norteamericano que comprendía a Europa y deseaba hacer algo por su futuro. Finalmente, tras ser nombrado embajador en Moscú por Roosevelt, Bullitt decidió, de acuerdo con Freud, dejar madurar la obra y que cada uno firmara los capítulos de cuya redacción se había encargado.
La obra se publicaría en inglés en 1967 tras la muerte de Edith Bolling Galt, segunda mujer de Wilson, y en vísperas de la de Bullitt. La portada lleva el nombre de los dos autores. En esa fecha el libro no despertó la atención ni de los historiadores, ni de los políticos, ni de los psicoanalistas.
Además, los herederos de Freud solo creyeron reconocer la pluma del maestro en el prefacio. Es cierto, el estilo de la obra era muy diferente al de los otros libros de Freud. Se trataba de una verdadera psicobiografía cuyo método se ajustaba por entero a la teoría freudiana de las sustituciones. En otras palabras, Bullitt había logrado escribir un libro tan fiel a la doctrina freudiana que parecía ser demasiado servilmente freudiano para haber salido de la pluma de Freud. Le faltaban la duda, la ambivalencia, las hipótesis osadas, todas esas cosas tan características del proceder de _Herr Professor_.
De un antiamericanismo virulento, la obra proponía un análisis de la locura de un hombre de Estado, en apariencia normal, en el ejercicio de sus funciones. Identificado desde su más tierna infancia con la figura de su padre, pastor presbiteriano y gran autor de sermones, Wilson se había tomado en un principio, según Bullitt, por el hijo de Dios, para convertirse luego a una religión de su propia cosecha en la que se atribuía el lugar de Dios, y había decidido abrazar la carrera política para realizar sus sueños mesiánicos. Cuando llegó a la presidencia todavía no había cruzado las fronteras de Estados Unidos, que consideraba, en el mismo concepto que la Inglaterra de Gladstone, como el país más hermoso del mundo. Por lo demás, era por completo ignorante de la geografía de Europa y no sabía que en ese continente se hablaban varias lenguas. Así, con motivo de las negociaciones del Tratado de Versalles pareció «olvidar» la existencia del paso del Brennero y cedió a Italia el Tirol del Sur y sus austríacos, sin saber que hablaban en alemán. De igual manera, dio pleno crédito a un allegado que le dijo que la comunidad judía estaba constituida por cien millones de individuos repartidos en los cuatro puntos cardinales del mundo. Odiaba Alemania y pensaba que sus habitantes vivían como animales salvajes.
No contento con estas acusaciones, Bullitt afirmaba que, para llevar a buen puerto su política internacional, el presidente norteamericano se había apoyado en silogismos delirantes. Así, como Dios es bueno y la enfermedad es mala, Wilson deducía que si Dios existe, la enfermedad no existe. Este tipo de razonamientos le permitía negar la realidad en beneficio de una creencia en la omnipotencia de sus discursos, lo cual lo llevó, según los autores, al desastre diplomático. De tal modo, había creado la Sociedad de Naciones antes de que se iniciara la discusión sobre las condiciones de paz, y a raíz de ello los vencedores, seguros de la protección norteamericana, pudieron despedazar tranquilamente Europa y condenar a Alemania con toda impunidad.
Wilson creyó entonces, según Bullitt, tener en los «catorce puntos» la clave de la fraternidad universal. Pero en vez de tratar con sus socios y discutir cuestiones económicas y financieras, les soltó un sermón de la montaña y se marchó de Europa, convencido de haber instaurado la paz eterna sobre la Tierra.
Tratándose de la «libido» de Wilson, Bullitt afirmaba que era particularmente débil. Casado una primera vez con una amiga de su prima, Ellen Axson, apenas unos meses después de la muerte de esta contrajo matrimonio con Edith Bolling Galt. Ambas mujeres eran sustitutas de su madre, añadía el diplomático, y bastaban para satisfacer sus tibios deseos. Y Bullitt llegaba entonces a la conclusión de que, conforme muestra la experiencia, los hombres que han sido felices en pareja suelen volver a casarse muy rápidamente. Se reconocía en ello la tesis freudiana de las sustituciones: una mujer sustituye a la madre y una segunda a la primera.
Cualquiera que haya sido el motivo de la disputa entre Freud y Bullitt, esa obra, rechazada por los historiadores, tachada de apócrifa por la comunidad freudiana y ridiculizada por los antifreudianos, era fiel en no pocos puntos a la concepción freudiana de la historia. En efecto, describía el encuentro entre un destino individual, donde interviene una determinación inconsciente, y una situación histórica precisa sobre la cual actúa esa determinación. Pero también hacía pensar en una ensoñación sobre un héroe caído. Sea como fuere, con su prefacio que apoyaba el proceder de Bullitt, Freud daba una consistencia aún más fuerte a su antiamericanismo, a su aborrecimiento de la democracia igualitaria y a su convicción de que la vieja Europa había sido destruida por un don Quijote oscurantista.
La personalidad de Wilson se prestaba a un análisis semejante y Freud tenía buenas razones para detestar a este idealista fanático que pretendía otorgar a los pueblos de Europa el derecho a disponer de sí mismos, como si hubiesen sido ignorantes en materia de derecho y democracia. Pero ese retrato psicológico tenía el defecto de hacer de la neurosis de Wilson, y de su postura de profeta iluminado que había reprimido su odio al padre, las únicas causas de lo que Freud y Bullitt veían como fracasos de su política. Olvidaban el importante papel desempeñado por Clemenceau. Además, la hipótesis de la «libido débil» distaba de confirmarse: se sabe, en efecto, que durante su primer matrimonio Wilson había tenido una relación oculta con otra mujer. En el fondo, lo criticable era el principio mismo de la aplicación del método interpretativo al trabajo histórico. Y sabemos hasta qué punto es nociva en ese ámbito la pretensión de esclarecer un destino a la luz de un presunto complejo edípico.
El gran tema de esos últimos años fue para Freud la escritura de una «novela histórica» dedicada a la cuestión de la identidad judía: _Moisés y la religión monoteísta_. La génesis de esta obra fundamental, única en su género y una de las más comentadas del mundo, merece relatarse, en virtud de la gran conexión de su historia con la del avance del nazismo en Europa.
Desde hacía mucho, e incluso antes de hablar sobre el tema con Lou Andreas-Salomé, Zweig o Mann, Freud estaba obsesionado con la figura del primer profeta del judaísmo que prefiguraba a Jesucristo para los cristianos y precedía a Mahoma para los musulmanes. Admiraba en primerísimo lugar a aquel a quien Miguel Ángel había representado tan magníficamente, un Moisés capaz de dominar sus pulsiones, un Moisés del Renacimiento italiano, un Moisés de la Ilustración mucho más resplandeciente que el del texto sagrado, un Moisés que había sacado a su pueblo del letargo imponiéndole leyes, indicándole el camino de la Tierra Prometida e inventando una nueva intelectualidad ( _Geistigkeit_ ). Una vez más, frente al resurgimiento de un antisemitismo cuyo alcance genocida él no alcanzaba a discernir, Freud se preguntaba por qué el judío se había granjeado tanto odio. Pero, sobre todo, se hacía la pregunta sobre la identidad judía: ¿cómo llega uno a ser judío?
Como en _Tótem y tabú_ , pretendía meterse de lleno en la cuestión del origen. Por lo demás, la semejanza entre las dos obras es sorprendente: varios relatos literarios yuxtapuestos, la misma interrogación a contrapelo de la evolución de las ciencias humanas de la época, la misma inquietud por privilegiar mitos de origen a fin de inventar otros mitos necesarios para la exploración del psiquismo inconsciente, la misma fascinación por la exégesis y la arqueología, la misma voluntad de asociar el psicoanálisis tanto a las ciencias de la naturaleza como al poder fundacional de los mitos.
En 1934 Freud comenzó a escribir un primer ensayo, «Moisés, un egipcio», en el cual toma como fuentes de inspiración a Mann, Goethe y Schiller, pero también muchos trabajos de historiadores egiptófilos interesados en dar una denominada interpretación «racional» de la historia bíblica. En ese texto retomaba la tesis, muy en boga desde fines del siglo XVIII, según la cual Moisés habría sido un alto dignatario egipcio, partidario del monoteísmo y asesinado por su pueblo. Y para explicar esa «egipcianidad» recurría a la noción de «novela familiar» aplicable, como decía Rank, a numerosos relatos, leyendas y mitos, entre ellos el de Edipo. Un niño «expósito» debido a un destino supuestamente trágico es recogido por una familia que lo cría. En la edad adulta, el personaje descubre que no es quien cree ser y cumple su destino. En la mayoría de los casos la primera familia, la de nacimiento del niño, es de alto rango, y la segunda, donde este crece, es de humilde condición. En la historia de Edipo las dos familias son de alto rango, mientras que en la de Moisés, tal como la presenta la Biblia, la primera es humilde (los hebreos) y la segunda, de sangre real (el faraón).
Con intención de demostrar que Moisés era egipcio, Freud proponía invertir los términos de la leyenda. La verdadera familia, de sangre real, decía, era la que abandona al niño en el agua dentro de una cesta, y la otra, humilde, la familia inventada (los hebreos). Así, el héroe habría descendido de sus alturas para ir hacia el pueblo de Israel a fin de salvarlo.
En un segundo ensayo, «Si Moisés era egipcio...», Freud exploró la historia del nacimiento del monoteísmo a partir del reino de Amenhotep IV (Akenatón), en el siglo XIV a.C. Se deleitaba con esta nueva inmersión en una historia arcaica en la que se encadenaban los unos a los otros los nombres más prestigiosos de la antigüedad egipcia, y llegaba a la conclusión de que Moisés, personaje pintoresco de novela, había transmitido la religión de sus padres al pueblo de Israel. Luego había impuesto a este el rito egipcio de la circuncisión a fin de probar que Dios lo había elegido mediante esa alianza.
Para contar la continuación de esa historia, Freud se remitía a los trabajos de un exégeta berlinés, Ernst Sellin, que en 1922, sobre la base de una lectura del relato del profeta Oseas, había propuesto la idea de que Moisés habría sido víctima de un asesinato colectivo cometido por su pueblo, que prefería entregarse al culto de los ídolos. Convertida en una tradición esotérica, la doctrina mosaica, según Sellin, habría sido transmitida a posteriori por un círculo de iniciados. Y sobre ese sustrato habría nacido la fe en Jesús, también un profeta asesinado, y fundador del cristianismo. De esta interpretación cristiana que hacía Sellin del relato bíblico, Freud deducía la idea de que los hebreos, una vez liberados de su cautiverio, no habrían tolerado la nueva religión. En consecuencia, habrían matado al hombre que se pretendía profeta y luego borrado de su memoria el recuerdo de ese asesinato.
Conforme a la hipótesis de Eduard Meyer, orientalista y egiptólogo, a continuación Freud asociaba a este acontecimiento otra historia bíblica, más tardía, concerniente a la alianza forjada por los israelitas con las tribus beduinas instaladas en el país de Madián, cuyo dios, Yahvé, era una divinidad brutal y pulsional. Dentro de esas tribus, otro Moisés, un levita recogido por Jetró, había desposado a la hija de este y se había convertido en sacerdote tras escapar de las persecuciones del faraón. De esos dos relatos nació la leyenda bíblica de un Moisés único, fundador de una religión que unía el antiguo culto de Yahvé y el nuevo monoteísmo importado de Egipto. Y Freud añadía que la religión arcaica de Yahvé había excluido y luego reprimido el monoteísmo mosaico, mucho más intelectual. Sin embargo, al cabo de varios siglos, este había resurgido. Y Yahvé había sido dotado entonces de los atributos intelectuales del monoteísmo, mientras que la figura escindida de Moisés se reunificaba bajo los rasgos de un solo profeta que imponía la ley de un Dios único: un Dios del verbo y la elección, portador de un mensaje altamente intelectual.
Una vez más, Freud aplicaba a ese relato reinventado su doctrina de las sustituciones valiéndose de su talento de descifrador de enigmas: un Moisés disimula otro, este toma los atributos del primero y recíprocamente, en tanto que el recuerdo del asesinato sigue reprimido. Pero, más aún, recuperaba una figura apreciada por él: la oposición entre un Moisés oscurantista, primitivo y destructor, y un Moisés legislador y racional.
En 1937, entre enero y agosto, Freud publicó esos dos ensayos, mientras continuaba trabajando en un tercero. De todos modos, antes de terminarlo redactó dos «advertencias preliminares», una en Viena en marzo de 1938, otra en Londres en junio del mismo año. En la primera hacía un balance de la situación política de Europa y tomaba nota del hecho de que la Rusia soviética no había logrado extirpar «el opio del pueblo» (la religión) de la nueva sociedad comunista, a pesar de haber otorgado a los individuos cierta dosis de libertad sexual. Constataba luego que el pueblo italiano vivía ahora bajo el yugo de un régimen autoritario, mientras que Alemania retrocedía hacia la más oscura de las barbaries. Y sacaba como conclusión que las democracias conservadoras se habían convertido, en el mismo concepto que la Iglesia católica, en las guardianas del progreso cultural. Por eso afirmaba no querer escandalizar a sus compatriotas austríacos con la publicación de la última parte de su estudio sobre Moisés, que contribuía una vez más a desacralizar la religión monoteísta —y por lo tanto el judeocristianismo— al transformarla en una novela histórica, poblada de mitos y héroes neuróticos. Y se decía convencido de que el psicoanálisis no tenía «un hogar más preciado que la ciudad donde ha nacido y crecido». Por entonces Freud todavía creía que su movimiento contaba con la protección de la Iglesia católica y el gobierno austríaco que, a su entender, sabría resistir al nazismo. Y sin embargo, también tenía conciencia, desde marzo de 1937, de que ya nada detendría a Hitler. En síntesis, en vísperas del _Anschluss_ sabía sin querer saber y todavía esperaba.
En la segunda advertencia preliminar, escrita en junio de 1938, ya exiliado en Londres, Freud daba un giro:
De pronto sobrevino la invasión alemana; el catolicismo reveló ser, para decirlo con palabras bíblicas, una «caña flexible». En la certidumbre de que ahora no me perseguirían solo por mi modo de pensar, sino también por mi «raza», abandoné con muchos amigos la ciudad que había sido mi patria desde mi temprana infancia y durante setenta y ocho años.
Hallé la más amistosa acogida en la bella, libre y generosa Inglaterra. Aquí vivo ahora, como huésped bien visto, y he recobrado el aliento, pues aquella opresión ha desaparecido y ahora vuelvo a tener permitido hablar y escribir —casi estuve por decir: pensar— como quiero o debo. Oso, pues, mostrar la última parte de mi trabajo.
Hubieron de ser necesarios cinco años, por tanto, entre la toma del poder por los nazis en 1933 y el _Anschluss_ , para que Freud comprendiese. Pero no habría de ser el único que no mirara a Hitler a la cara. Ese desconocimiento de la situación de Austria y de la naturaleza del nazismo confirma en todo caso hasta qué punto Freud, por lo común tan lúcido, estaba más apegado a Viena y a su judeidad vienesa de lo que él mismo creía, y hasta qué punto su obra era, mucho más de lo que suponía, el producto de una historia inmediata que él no controlaba, lo cual la hace, además, tan interesante. Cuanto más exploraba los mitos de origen, más interpretaba los textos sagrados para tornarlos compatibles con sus construcciones y más hablaba del tiempo presente, es decir, de las mutaciones del antisemitismo y su impacto sobre la redefinición de la identidad judía.
En el tercer ensayo, «Moisés, su pueblo y la religión monoteísta», Freud retomaba la tesis de los dos Moisés, el madianita y el egipcio, para ligar el destino del judaísmo al del cristianismo. El pueblo que el profeta había elegido, decía, habría matado al padre fundador pero reprimido el recuerdo del asesinato, que habría retornado con el cristianismo. Freud se inspiraba aquí en el antiguo antijudaísmo cristiano para interpretarlo a contrapelo de su enfoque clásico, el del pueblo deicida. Y de resultas vinculaba el judaísmo al cristianismo al hacer del primero la religión del padre, del segundo la religión del hijo, y de los cristianos los legatarios de un asesinato reprimido por los judíos: «El viejo dios-padre se oscureció detrás de Cristo, y Cristo, el hijo, advino a su lugar, en un todo como lo había ansiado cada hijo varón en aquel tiempo primordial».
Siempre según Freud, Pablo de Tarso, continuador del judaísmo, también habría sido su destructor: con la introducción de la idea de redención habría logrado conjurar el espectro de la culpa humana, pero al precio de contradecir la idea de que los judíos eran el pueblo elegido. En consecuencia, al renunciar al signo manifiesto de esa elección —la circuncisión—, habría transformado el cristianismo en una doctrina universal capaz de dirigirse a todos los hombres.
Pero Freud afirmaba también que el odio hacia los judíos era alimentado por su creencia en la superioridad del pueblo elegido y la angustia de castración que suscitaba la circuncisión como signo de la elección. A su entender, ese rito apuntaba a ennoblecer a los judíos y llevarlos a despreciar a los otros, los incircuncisos. Desde el mismo punto de vista, tomaba al pie de la letra, para desplazar su significación, la queja principal del antijudaísmo, es decir, la negativa de los judíos a admitir que habían dado muerte a Dios. El pueblo judío, decía, se obstina en negar el asesinato del padre y los cristianos no dejan de acusar a los judíos de deicidas, porque se han liberado de la culpa original desde que Cristo, sustituto de Moisés, sacrificó su vida para redimirlos. En otras palabras, si el cristianismo es una religión del hijo que confiesa el asesinato y lo redime, el judaísmo sigue siendo una religión del padre que se niega a reconocer el asesinato de Dios. Y no por ello los judíos dejan de ser perseguidos por el asesinato del hijo, del que son inocentes. Freud llegaba a la conclusión de que esa negativa exponía a los judíos al resentimiento de los otros pueblos.
Después de admitir que la historia de los judíos no puede separarse de la del antijudaísmo de los cristianos, Freud explicaba que el antisemitismo moderno da fe de un desplazamiento hacia los judíos del odio al cristianismo:
Todos estos pueblos que hoy se precian de odiar a los judíos solo se hicieron cristianos tardíamente en la historia, a menudo forzados a ello por una sangrienta compulsión. Uno podría decir que todos son «falsos conversos», y bajo un delgado barniz de cristianismo han seguido siendo lo que sus antepasados eran, esos antepasados suyos que rendían tributo a un politeísmo bárbaro. No han superado su inquina contra la religión nueva que les fue impuesta, pero la desplazaron a la fuente desde la cual el cristianismo llegó a ellos. [...] Su odio a los judíos es, en el fondo, odio a los cristianos; no cabe asombrarse, pues, si en la revolución nacionalsocialista alemana este íntimo vínculo entre las dos religiones monoteístas halla tan nítida expresión en el hostil trato dispensado a ambas.
En otras palabras, si el judaísmo, religión «fósil», es superior al cristianismo por su fuerza intelectual, pero inepto para la universalidad, hay que asociarlos históricamente —en su diferencia misma— para fecundar una cultura judeocristiana capaz de oponerse al antisemitismo moderno.
En el fondo, este proceder consistía en sacar a la luz las raíces inconscientes del antisemitismo a partir del propio judaísmo, y ya no en considerarlo como un fenómeno exterior a este. Una manera de recuperar la problemática de _Tótem y tabú_ , cuya continuación era de hecho _Moisés y la religión monoteísta_. Si la sociedad había nacido, en efecto, debido a un crimen cometido contra el padre, que ponía fin al reino despótico de la horda salvaje, y luego debido a la instauración de una ley donde se revalorizaba la figura simbólica del padre, eso significaba que el judaísmo debía obedecer al mismo patrón. Y, efectivamente, el asesinato de Moisés había engendrado el cristianismo, fundado en el reconocimiento de la culpa: el monoteísmo participaba así de la historia interminable de la instauración de la ley del padre sobre la cual Freud había levantado toda su doctrina.
De ese modo, Freud obedecía a la conminación de volver a la autoridad eminente de la Biblia y a la religión de sus padres. Pero, lejos de adoptar la solución de la conversión como respuesta al antisemitismo, o la del sionismo, se redefinía una vez más como un judío sin Dios —judío de reflexión y de saber—, a la vez que rechazaba el autoodio judío. Yo diría de buen grado que se proponía separar el judaísmo del sentimiento de la judeidad propio de los judíos incrédulos, soslayando así tanto la alianza como la elección, considerada como una suerte de delirio. Sin embargo, en el momento mismo en que desjudaizaba a Moisés para hacer de él un egipcio, Freud asignaba a la judeidad, comprendida a la vez como esencia y como pertenencia, una posición de eternidad. Ese sentimiento, en virtud del cual un judío sigue siéndolo en su subjetividad aun cuando adopte una posición de exterioridad con respecto al judaísmo, Freud lo experimentaba en sí mismo y no vacilaba en asimilarlo a una herencia filogenética. En algunos aspectos se mantenía fiel al judaísmo de Moisés por la vía de su reivindicación permanente de una identidad judía y asignaba como misión al psicoanálisis la asunción de la herencia de ese judaísmo, un judaísmo convertido en una judeidad de la diáspora.
Al escribir el _Moisés_ , Freud tuvo absoluta conciencia de redactar una especie de testamento que atestiguaba tanto su negativa a marcharse de Viena, ciudad donde se había realizado una fusión inédita entre una judeidad de la diáspora y una nueva manera de concebir la universalidad del inconsciente, como su deseo de exilarse y vivir por fin en un lugar donde pudiera producirse el renacimiento de su doctrina. De ahí su sueño de vivir en Inglaterra, país por antonomasia de la alianza entre un sistema monárquico y la democracia liberal. Sin duda esa era para él una suerte de respuesta al hundimiento de la vieja Europa de la Ilustración, una respuesta fundada en la alianza del espíritu de disidencia espinosista y de las tres grandes figuras míticas de la cultura occidental que siempre habían estado presentes en la elaboración de su doctrina: Edipo, tirano del mundo griego; Hamlet, príncipe cristiano, y Moisés, profeta judío reinventado por Miguel Ángel, el italiano, y luego egipcianizado por los eruditos alemanes del siglo XIX. En 1938, ese Moisés, resplandeciente con las luces de un gran deseo de Inglaterra, era a los ojos de Freud todo lo contrario de Wilson, el norteamericano de la triste figura.
De hecho, Freud temía a esa democracia norteamericana que desacreditaba la idea misma de una república de elegidos, en beneficio del predominio de las masas. Y maldecía el nazismo que daba libre curso a la destrucción del hombre por las pulsiones salvajes. Tanto de un lado como de otro, esas dos modalidades de gobernanza ponían en entredicho la noción misma de autoridad tal como él la entendía. Y estaba convencido, en especial desde la crisis económica de 1929 y la publicación de _El malestar en la cultura_ , de que la búsqueda inmoderada de riquezas era tan peligrosa como el sometimiento a la tiranía. Por eso creía que Estados Unidos sería un día devorado por sus tres demonios: la locura puritana, la búsqueda individual de la proeza sexual y la especulación ilimitada. Razón por la cual solo la vieja Europa imperial de los Habsburgo había contado con su favor durante tanto tiempo, porque protegía a las minorías y alentaba el control de las pulsiones. Pero la Primera Guerra Mundial la había devorado. Se imponía entonces el deseo de Inglaterra.
En 1938 solo ese país podía ser para Freud una tierra de acogida. Reinaba sobre un imperio, era el heredero de un pasado glorioso, cultivaba la libertad individual y el respeto por las dinastías reales. Para terminar, siempre había sabido resistir las tentaciones dictatoriales, al precio de un regicidio y de la restauración de la dignidad monárquica. Freud amaba a Cromwell, gran protector de los judíos, pero admiraba también el hecho de que las familias reales británicas no hubiesen sido apartadas del poder —aunque fuera simbólico— por una república jacobina cualquiera: «Freud era un patriarca», escribe Mark Edmundson, «que obró con un talento incomparable para deconstruir el patriarcado. Escribió y vivió para poner fin a la forma de autoridad que él mismo encarnaba y aprovechaba».
El _Moisés_ , testamento de una judeidad freudiana en el exilio, dio lugar a numerosas interpretaciones contradictorias. Los enfoques críticos que se perfilaron son tres. El primero, debido a David Bakan, inscribiría la obra freudiana en la tradición de la mística judía. El segundo —de Carl Schorske a Peter Gay, pasando por Yirmiyahu Yovel— mostraría por el contrario un Freud ateo, descentrado de su judeidad y presa de la doble problemática de la disidencia espinosista y la integración en la cultura alemana. El tercero y último, el de Yosef Yerushalmi, intentaría poner de manifiesto las ambivalencias judaicas de Freud frente a su judeidad. Por mi parte, me inclino por las dos últimas opciones.
Por el lado de los intelectuales israelíes especialistas en la historia judía, la obra freudiana disfrutaría de muy poco aprecio y se la criticaría injustamente. Martin Buber reprochó a Freud su escasa seriedad científica y Gershom Scholem prefirió a Jung —al menos por algún tiempo—, que se había convertido en un sionista cada vez más ferviente a medida que se afinaban su antisemitismo y su apoyo a la Alemania nazi.
A comienzos de 1938 el cáncer de Freud se extendió hasta la base de la órbita. Las lesiones de la cavidad bucal se agravaban semana tras semana y los tejidos necrosados, que le causaban dolor, requerían una limpieza cotidiana. Las intervenciones quirúrgicas y las electrocoagulaciones retrasaban el avance del mal. Deseoso todavía de trabajar y conservar intacta su lucidez, Freud, que adelgazaba a ojos vista, se negaba a tomar analgésicos. Pese a los estragos que la enfermedad le producía en el rostro y al aumento de la sordera causada por las infecciones posoperatorias, su interés era mantener una apariencia digna. Por eso exigió a Pichler la ablación de un ateroma de la mandíbula que había crecido de tamaño al extremo de impedirle acicalarse la barba: «Tal vez haya usted notado que he embellecido. ¿No me desfiguraba acaso un quiste sebáceo, un ateroma que usted jamás mencionó, sin duda por tacto? Me han quitado ese adorno».
Contrariamente a Freud, Hitler sentía horror por la monarquía de los Habsburgo y, desde que Austria se había convertido en una pequeña república y Viena en una ciudad dañada pero siempre orgullosa de su pasado imperial, no soñaba en otra cosa que en reducirla a la nada: «La Austria germana debe volver a la gran patria alemana», había afirmado en _Mein Kampf_ , «pero no debido a alguna razón económica. No, no, aun cuando esta fusión, económicamente hablando, sea indiferente e incluso perjudicial, debe producirse como sea: una sola sangre exige un solo Reich».
A comienzos de 1938, en consecuencia, Hitler esperaba con impaciencia el momento propicio para una intervención en Austria a fin de realizar su proyecto de fusión, el mismo con el que había soñado desde su juventud. Se sentía sencillamente investido de la misión «grandiosa» de conquistar Viena, presentarse en ella a pleno día, como un espectro en medio de una tormenta primaveral. Por eso convocó a Kurt von Schuschnigg al Berghof para obligarlo a ceder dos ministerios a simpatizantes nazis, en especial el del Interior a Arthur Seyss-Inquart, bajo la amenaza de una invasión militar. Schuschnigg aceptó y luego intentó en vano organizar un plebiscito para salvaguardar la independencia de Austria, actitud que desató una furia «histérica» en Hitler, convencido —con razón, además— de que Italia, Francia e Inglaterra no reaccionarían: «La suerte está echada, escribió Goebbels, nos encaminamos a todo tren directamente a Viena y el Führer mismo se traslada a Austria».
Desesperado, Schuschnigg solicitó la ayuda de los británicos, lo que le valió un cínico telegrama de lord Halifax: «El gobierno de Su Majestad no está en condiciones de garantizar vuestra protección». El 11 de marzo aquel renunció a su cargo y por la noche pronunció por radio un vibrante discurso, mientras que en todas las ciudades austríacas las multitudes ya se lanzaban a las calles a atacar a los judíos al grito de «muerte a Judas», glorificaban el nombre de Hitler y ocupaban los edificios públicos.
En la Berggasse Freud escuchó el discurso de Schuschnigg, que terminaba con estas palabras: «Dios salve a Austria». El 12 de marzo escribió en su agenda: «Finis Austriae». Por segunda vez, plenamente decidido a mantener hasta el final su rango de patriarca del psicoanálisis, asistía a la agonía de un mundo que había sido el suyo. Y sin embargo, se sabía amenazado: había recibido la visita de John Wiley, amigo de William Bullitt y cónsul general de Estados Unidos en Viena, que tenía ahora la misión de ocuparse de su exilio y el de su familia. Wiley no tardaría en alertar a Cordell Hull, secretario de Estado del presidente Roosevelt, acerca del peligro que corría Freud pese a su edad y su mala salud. En París, Bullitt se presentó en la embajada alemana para advertir al conde Von Wilczek a fin de que _Herr Professor_ no sufriese ningún daño. Por último, Dorothy Burlingham quedó a cargo de alertar por teléfono a la embajada norteamericana en Viena en caso de que se produjera el más mínimo incidente.
El 13 de marzo, en el momento de la proclamación oficial del _Anschluss_ , el Comité Directivo de la WPV se reunió en la Berggasse en presencia de Freud y bajo la presidencia de Anna. Jones había hecho saber que deseaba implementar en Viena la misma política de presunto «salvamento» que en Berlín. Único no judío del comité, Richard Sterba se negó a desempeñar el papel de Felix Boehm y declaró que tenía la intención de marcharse de Austria con su familia en el más breve plazo con destino a Suiza y luego a Estados Unidos. En consecuencia, se tomó la decisión de disolver la WPV y establecer su sede en el lugar donde Freud decidiera vivir. Se cumplía así el primer acto político de un descentramiento que iba a hacer del psicoanálisis el equivalente de una judeidad de la diáspora. Si Viena dejaba de ocupar un lugar central en el movimiento —aunque ese lugar ya estuviera en tela de juicio—, significaba que Freud podía a su vez abandonarla para hacer en el exilio, y antes de morir, una refundación de otro orden: conmemorativa, esta vez. Frente a la destrucción organizada, había que transmitir a toda costa a las generaciones venideras la huella de lo que había sido la historia de su vida, de su doctrina, de su enseñanza y del primer cenáculo de sus discípulos: libros, archivos, manuscritos, cartas, colecciones, notas de trabajo, declaraciones textuales, recuerdos colectivos, etc. Todo eso pertenecía ahora al futuro mucho más que al pasado. Salvar las huellas, salvar la historia, salvar la memoria, salvar el recuerdo de Viena. Esas tareas eran tan indispensables como la de salvar vidas, y no podían estar más alejadas de cualquier ánimo de colaboración con el nazismo.
Freud recibió con claridad el mensaje que le dirigían los miembros del comité y, esta vez, renunció a toda pretensión de «salvamento» con estas palabras:
Después de que Tito destruyera el Templo de Jerusalén, el rabino Johanan ben Zakkai solicitó autorización para abrir en Jamnia una escuela consagrada al estudio de la Torá. Nosotros vamos a hacer lo mismo. Después de todo, estamos acostumbrados a ser perseguidos en nuestra historia y nuestras tradiciones, y algunos de nosotros por experiencia, con una excepción.
Cada vez más excitadas por el anuncio de la llegada de Hitler, las masas intensificaron aún más sus ataques contra los judíos, los comunistas y los socialdemócratas. Freud había creído que los austríacos eran menos brutales que los alemanes. Estaba equivocado: la ferocidad de los primeros fue superior a la de los maestros del nazismo, a tal punto que despertó el asombro de estos. Arrancados a la fuerza de sus oficinas, los judíos fueron despojados en el acto de todos sus bienes y luego transformados en «cuadrillas de limpieza» bajo la vigilancia de bandas de saqueadores que los golpeaban e insultaban al grito de « _Heil Hitler!_ »: «El Hades había abierto sus puertas y liberado a los espíritus más viles, más despreciables e impuros, señaló el dramaturgo Carl Zuckmayer. Viena se había convertido en una pesadilla de Hieronymus Bosch».
Hitler había preparado bien su entrada en Austria. Se detuvo en primer lugar en Braunau am Inn, su ciudad natal, donde lo esperaba una multitud alborozada. Se trasladó luego a Linz, donde, profundamente emocionado por la recepción que le brindaban los habitantes, lloró al pronunciar un discurso en el que se presentaba como un héroe designado por la Providencia para llevar a cabo la sagrada misión de aniquilar la identidad austríaca. Por último, el 15 de marzo, tomó la palabra en Viena frente a una muchedumbre delirante de alegría, para ser luego triunfalmente recibido por los altos dignatarios de la Iglesia católica, que brindaron sin demora su apoyo al _Anschluss_ , el nacionalsocialismo, las leyes antisemitas y toda forma de cruzada contra el bolchevismo. El cardenal Innitzer, primado de Austria, puso su firma en la declaración de anexión y agregó, de su puño y letra, « _Heil Hitler_ ».
En muy poco tiempo se concretó la expoliación de las empresas judías y se invistió de inmediato a un _Nazi Kommissar_ de todos los poderes de confiscación, liquidación, detención y estímulo a la delación. Vino a continuación, y muy rápidamente, la deportación a los campos de concentración, que no eran todavía lugares de exterminio. Sin darle demasiado crédito, Freud se había enterado de su existencia gracias a la lectura del diario _Das Neue Tagebuch_ , editado en Francia por Leopold Schwarzchild, un periodista alemán exiliado, el mismo que más adelante publicaría en Estados Unidos la primera versión del «Bruder Hitler» de Thomas Mann.
Freud había supuesto que el catolicismo austríaco protegería a los judíos. Se equivocaba una vez más, y gravemente. En cuanto a Forzano, el amigo de Weiss, envió un mensaje inútil a Mussolini: «Recomiendo a Su Excelencia a un glorioso anciano de ochenta y dos años que lo admira mucho: Freud, un judío».
Esta vez resultaba urgente organizar con la mayor rapidez posible la partida de Freud a Inglaterra. El 16 de marzo de 1938 Jones llegó a Viena, seguido al día siguiente por Marie Bonaparte. A semejanza del capitán del _Titanic_ que se había negado a dejar su nave, Freud afirmó que nunca abandonaría su puesto. Pero Jones tuvo entonces la idea de replicarle con otra historia: la del oficial del mismo transatlántico al que la explosión de una caldera había arrojado al mar. Durante la investigación se le preguntó en qué momento había dejado el barco y respondió: «No lo dejé, fue él el que me abandonó». Freud reconoció que su caso era idéntico. Y como Viena lo había abandonado a los nazis, aceptó emigrar a Inglaterra.
Pero, conforme a las decisiones tomadas por el comité de la WPV, quería llevar con él a sus últimos discípulos vieneses. Ahora bien, Jones sabía que los kleinianos nunca aceptarían que estos se incorporaran masivamente en la BPI. Además, para la recepción de refugiados judíos el gobierno británico imponía cupos muy restringidos. En síntesis, para negociar esa partida fue menester movilizar todas las fuerzas disponibles: Marie Bonaparte, dispuesta a poner en juego su fortuna y sus relaciones; Bullitt, Wiley y Cordell Hull, que hacían valer su posición en Estados Unidos, y Jones, que apeló a todas sus relaciones en Londres: su cuñado Wilfred Trotter, que integraba el consejo de la Royal Society; sir William Bragg, médico eminente y premio Nobel, y sir Samuel Hoare, ministro del Interior y miembro del Partido Conservador.
Llegó la hora. La víspera, 15 de marzo, integrantes de las SA habían allanado el local de la Verlag, en el número 7 de la Berggasse. Martin Freud, director editorial, fue amenazado por un joven corpulento que le apoyó en la sien el cañón de su pistola. Aquel no había tenido tiempo de destruir todos los documentos que probaban que Freud tenía activos en bancos extranjeros. Ese mismo día otra cohorte nazi organizó un registro en el domicilio familiar. Martha mostró mucha sangre fría al tratar a los saqueadores como visitantes comunes y corrientes e invitarlos a dejar sus armas en el paragüero de la entrada. La pandilla confiscó varios pasaportes y se llevó seis mil chelines a cambio de un recibo oficial.
En Estados Unidos ya circulaba el rumor de que Freud había sido ejecutado por los nazis. Enviado por un diario, un reportero se trasladó entonces a Viena y fue a la Berggasse en compañía de Emy Moebius. Martha los recibió y les dijo que en ese momento Freud estaba descansando.
Por su lado, a partir del 17 de marzo Marie Bonaparte comenzó, con la ayuda de Anna, Martha y Paula, a seleccionar, ordenar y embalar los tesoros que Freud había acumulado durante toda una vida. Siempre deseosa de salvar las huellas, Marie rescató documentos importantes que _Herr Professor_ , por su parte, habría querido tirar o quemar. Como compartía la vida cotidiana de la familia, podía sustraer objetos para trasladarlos clandestinamente al extranjero por medio de la legación griega, donde se alojaba. Recuperó así varias monedas de oro que Freud había dejado de lado. Un día escondió bajo sus faldas una estatuilla de bronce que representaba a la diosa Atenea con una copa para libaciones en la mano derecha, una lanza en la izquierda, un casco corintio en la cabeza y un peto ornado con un rostro de Medusa sobre el pecho. Sabedora de que Freud estaba apegado a ese icono guerrero, que aliaba las virtudes del combate a las de la inteligencia, se había propuesto salvarla para dársela cuando él se alojara en su casa parisina. Freud había obtenido la autorización para llevarse sus colecciones y una parte de sus libros. Pero, obligado a dejar en Viena unos ochocientos volúmenes de un valor incalculable, convocó al gran librero Heinrich Hinterberger, que seleccionó una buena cantidad de libros de arte.
El 20 de marzo, bajo la batuta de Jones —siempre aferrado a la idea de la colaboración con los nazis—, los miembros del Comité Directivo de la WPV aceptaron firmar un protocolo de acuerdo que ponía a la organización bajo la tutela de la DPG. Por orden de Matthias Göring, Müller-Braunschweig participó en esa reunión, donde se estableció una especie de _Anschluss_ por el que los psicoanalistas berlineses «arianizados» se anexionaban a los vieneses, los mismos que, empero, habían rechazado toda forma de «salvamento». En su carácter de director comercial del Verlag, Martin Freud estampó su firma junto a las de su tía Anna, Marie Bonaparte, Eduard Hitschmann, Heinz Hartmann, Ernst Kris y Robert Walder. Los miembros judíos de ese comité firmaban al mismo tiempo su dimisión, dado que la tutela los excluía de facto de toda función dentro de la WPV. Furioso por la ausencia de Sterba, Jones señaló que el _Shabbes Goy_ se había sustraído a sus deberes.
Un mes después, confortablemente instalado en el número 7 de la Berggasse, ahora _judenfrei_ , Müller-Braunschweig informó a Sterba de su intención de transformar el local del Verlag en instituto «arianizado», a fin de asegurar la presunta «supervivencia» del psicoanálisis en Austria. Y le pidió que, en su condición de único «ario» de la WPV, se prestara a esa siniestra operación. La respuesta de Sterba consistió en desestimar la petición. Antes de marchar al exilio, este último tuvo la oportunidad de comprobar que en la entrada de la casa de Freud colgaba una imponente cruz gamada. Cuando se reencontró con Jones en Londres, tomó conciencia de que había contribuido al fracaso de una política que desaprobaba. No obstante, no consiguió un visado para radicarse en Inglaterra; procuró entonces emigrar a Sudáfrica para reunirse con Wulf Sachs y se exilió luego a Estados Unidos. Freud y su hija, por su parte, habían aprobado la decisión de Jones de poner la WPV bajo tutela, después de haber rechazado el 13 de marzo su política de «salvamento».
En la reunión del 20 de marzo también había participado Anton Sauerwald, ex alumno de Josef Herzig, eminente profesor de química de la Universidad de Viena. En su carácter de _Nazi-Kommissar_ , Sauerwald tenía la misión de despojar a los judíos de su fortuna para «desjudaizar la economía austríaca». Por eso debía ocuparse de los bienes de la familia Freud, así como de todas las operaciones relativas a la WPV y el Verlag. Violentamente antisemita, comenzó por insultar a todos los no judíos que habían osado mezclarse con « _Jüdische Schweinereien_ ». Pero como tenía frente a sí a un ilustre sabio, cuya dignidad le infundía respeto, se puso a leer varias obras de psicoanálisis y sobre todo a diferenciarse de los otros funcionarios nazis. Cuando se dio cuenta de que Freud tenía una fortuna y había colocado dinero en el extranjero, decidió no «denunciarlo» y, al contrario, ayudarlo a obtener las autorizaciones necesarias para su exilio. Pensaba recuperar algún día, en su propio beneficio, el dinero así salvado del embargo y con ese fin se asoció con un abogado, Alfred Indra, otro personaje dudoso que, en esos tiempos turbulentos, hacía fortuna asesorando a ricas familias judías vienesas obligadas a pagar rescates exorbitantes. Allegado a la familia Wittgenstein, relacionado con Marie Bonaparte, el letrado Indra, ex oficial del ejército imperial, coleccionista de objetos de arte, lector asiduo de Karl Kraus, aficionado a la montería y los chistes, pasaba por ser un notable jurista cuando daba a entender a sus clientes que las autoridades nazis eran estúpidas y fáciles de embaucar. Se convirtió en el abogado de Freud y colaboró con todos los miembros de su entorno.
El 22 de marzo Anna Freud fue llevada al hotel Metropole, cuartel general de la Gestapo, para someterla a un interrogatorio en regla sobre sus «actividades subversivas». Marie Bonaparte exigió que la llevaran con ella, pero los SS, impresionados por su condición de alteza real, no quisieron saber nada. Con habilidad, Anna logró convencer a sus carceleros de su apoliticismo. De vuelta a la Berggasse, encontró a Freud en un estado de agitación extrema. Él nunca supo que Anna había llevado consigo veronal, por si la torturaban.
Para evitar en el futuro intrusiones semejantes, la princesa decidió montar guardia en la escalera: «Visón negro azulado ceñido sobre los hombros, en las manos guantes claros y en la cabeza un gran sombrero de frágil apariencia. A su lado, un bolso de cocodrilo marrón. Envuelta en una nube de _Stephanotis_ , su perfume preferido, se mantenía en cuclillas». Sin que _Herr Professor_ lo supiera, Paula le llevaba té o chocolate.
A esas alturas ya habían sido detenidas y torturadas más de siete mil quinientas personas y millares de judíos encarcelados ignoraban todavía a qué lugar se los deportaría. A principios de abril, un primer tren de los llamados presos «políticos» partió con rumbo a Dachau. Ayudados o no por Jones o por sus amigos extranjeros, los psicoanalistas huían abandonando sus bienes, su casa, sus muebles, su clientela, su pasado y a veces a varios de sus parientes que no podían seguirlos por carecer de visados o de «certificados de no objeción» ( _Unbedenklichkeitserklärung_ ) demostrativos de que habían pagado el famoso impuesto de salida ( _Reichsfluchtsteuer_ ) necesario para toda partida oficial.
Ernst Freud, Lucie y sus tres hijos, Stefan, Lucian y Clemens, se habían marchado de Alemania y vivían en Londres; Oliver, Henny y su hija Eva estaban instalados en el sur de Francia, y Max Halberstadt se había radicado en Sudáfrica con su segunda mujer, Bertha, y Eva, la hija de ambos. En cuanto al joven Ernstl Halberstadt, el «niño del carretel», planeaba desde Londres unirse a su padre en Johannesburgo, tras un periplo por Palestina junto a Eitingon y un retorno a Viena. Tras el _Anschluss_ , había saltado de un tren para escapar a París: «Me había tocado una suerte insolente, no me habían reprimido y no me había pasado nada enojoso. Además, tuve la dicha de poder esperar a mi familia en Inglaterra».
Convertido en un abogado célebre que libraba un valeroso combate contra la pena de muerte, Albert Hirst tuvo el tiempo justo para volver a Viena y ayudar a los suyos a emigrar a Estados Unidos. Después de tantos años durante los cuales había estado mal dispuesto contra Freud, se dio cuenta de que, en definitiva, había superado su neurosis y sus problemas sexuales. En 1972 consideró que había tenido una «buena vida» gracias a Dios, Estados Unidos y Freud.
El 19 de abril Freud festejó en familia el cumpleaños de su hermano Alexander y le legó, cuando este se aprestaba a partir a Suiza, su colección de cigarros. No había renunciado a fumar, pero por el momento el tabaco no le gustaba. Esforzándose por superar su anglofobia, Alexander, acompañado por su esposa Sophie Schreiber, planeaba llegar a Londres y luego emigrar a Canadá. Su hijo Harry estaba por entonces en Davos, donde recibía tratamiento médico. Después de la guerra, incorporado al ejército norteamericano, volvería a Viena.
Mientras seguían adelante con múltiples gestiones, los miembros de la familia Freud se preguntaban cómo resolver el problema de las cuatro tías, ancianas nonagenarias que desde hacía tiempo no tenían ninguna actividad. Mantenidas por sus dos hermanos, Sigmund y Alexander, y por su hermana, Anna Bernays-Freud, habían tenido una vida marcada por la tragedia. Adolfine Freud (Dolfi) vivía sola desde la muerte de Amalia, rodeada por Regine Debora (Rosa) Graf, Maria (Mitzi) Freud y Pauline Regine (Paula) Winternitz, viudas las tres, con tres hijas como descendencia, radicadas en el extranjero. Margarethe Freud-Magnus, hija de Maria, vivía en Dinamarca, y su hermana Lilly Marlé-Freud seguía en Londres con su carrera de actriz junto a su marido, Arnold Marlé, aprovechando, llegado el caso, el apoyo económico que le brindaba su tío. En cuanto a Rose Winternitz, hija de Paula, afectada de trastornos mentales, se había casado con el poeta Ernst Waldinger y acababa de marcharse de Austria rumbo a Estados Unidos, donde Paul Federn se haría cargo de ella.
Es cierto, Freud percibía el peligro que corrían sus hermanas, pero no podía imaginar que los nazis iban a tratar de exterminar a personas ancianas sin recursos ni actividades. Pensaba, como todos sus allegados, que las persecuciones antisemitas se focalizaban ante todo en los judíos activos que tenían fortuna o ejercían profesiones. En síntesis, estaba convencido de que sus hermanas podrían emigrar un poco más adelante, después de los discípulos y los demás miembros de la familia. Por añadidura, los impuestos exigidos para permitirles salir eran tan exorbitantes que él no tenía manera de financiar su partida, con el agravante de que las autoridades británicas exigían que los exiliados pudiesen costearse sus necesidades una vez instalados en Gran Bretaña.
Freud había reclamado que lo acompañaran quince personas sobre quienes recaía una amenaza inmediata: Martha, Minna, Anna, Paula, Martin, su mujer Esti y sus dos hijos —Anton Walter y Sophie—, Ernstl Halberstadt, Mathilde y Robert Hollitscher y Max Schur, su mujer y sus dos hijos, Peter y Eva. Bullitt estaba convencido de que Freud jamás lograría reunir la suma necesaria para organizar ese operativo, ni siquiera con la ayuda de Marie Bonaparte. Y ofreció la entrega de diez mil dólares para contribuir a la partida de esa «comitiva».
Fue entonces cuando Freud y Alexander decidieron dar a sus cuatro hermanas ciento sesenta mil chelines austríacos, y pidieron a Alfred Indra y Anton Sauerwald que administraran esa fortuna en espera de días mejores. Cuando salió de Viena, después de pagar todos los impuestos reclamados, Alexander ya no tenía un centavo y en el exilio tuvo que recurrir a la ayuda de sus amigos o sus parientes. Su fortuna había sido embargada y su abogado nazi, Erich Führer, había aprovechado la situación para enriquecerse.
Tras varias semanas de negociaciones, Jones obtuvo los visados de entrada en Inglaterra y los permisos de trabajo necesarios para Freud y las personas que lo acompañaban. Pero aún había que conseguir la autorización para salir de Austria. Comisionado para tasar las colecciones de Freud, Hans von Demel, el conservador del Kunsthistorisches Museum, estimó una cantidad de treinta mil marcos del Reich [Reichsmarks, RM], suma inferior a la realidad. A ello se agregaba el cálculo de los activos imponibles —125.318 RM—, sobre los cuales Freud debía pagar aún un impuesto de 31.329 RM. Pero como los bienes del Verlag y su cuenta bancaria habían sido embargados, él no podía saldar esa «deuda» obligatoria. Y fue Marie Bonaparte quien pagó el rescate.
Acompañada por Dorothy Burlingham, Minna partió el 5 de mayo, seguida diez días después por Mathilde y Robert. Ya separada de Martin, que tenía numerosos amoríos, Esti tomó el tren con Sophie y Anton Walter. Siempre había detestado a Freud, que no la quería y la consideraba «clínicamente loca», a la vez que procuraba darle excelentes consejos que ella nunca seguía. Al marcharse a París, Esti dejaba atrás a una parte de su familia. Su madre, Ida Drucker, sería asesinada en Auschwitz.
Martin salió de Viena el 14 de mayo para reunirse con Esti y sus hijos en París, pero al día siguiente volvió a marcharse, sin ella, y acompañado por su hijo varón, rumbo a Londres. Sophie vivió con su madre en París y Anton Walter con el padre en la capital inglesa. En junio de 1940 Esti y Sophie partieron hacia el sur de Francia, de allí pasaron a Casablanca y luego emigraron a Estados Unidos, donde la familia Bernays les prestó ayuda. Muchos de sus amigos vieneses perecieron exterminados en las cámaras de gas.
No pocos años después, cuando Sophie, ya ciudadana norteamericana, sintió la necesidad de criticar severamente las teorías de su abuelo, recordó que le debía la vida: «Debo pues a mi abuelo el hecho de haberme contado entre los pocos que tuvieron la fortuna de poder marcharse de Viena antes del comienzo de la mortal persecución de los judíos. Cuando mi hermano se enteró de mis críticas a las teorías del abuelo, me dijo: "Sin el abuelo, los nazis habrían hecho pantallas con tu piel"».
Deseoso también él de conservar huellas del esplendor de los comienzos, August Aichhorn pidió a Edmund Engelmann, fotógrafo vienés perteneciente a una familia judía de Galitzia, que tomara una serie de fotografías de los lugares todavía intactos e hiciera retratos de Freud. Para burlar la vigilancia de los nazis, Engelmann tuvo que evitar los flashes y los proyectores. Llevó consigo una Rolleiflex y una Leica, dos objetivos y la cantidad de películas que cabían en su maletín. Durante varios días fotografió minuciosamente, en blanco y negro, objetos, muebles y habitaciones desde diferentes ángulos, y mostró así, entre penumbras y claroscuros, cuánto más cerca estaba ese lugar, a imagen misma de una travesía del sueño, de un grabado de Max Ernst que de un cuadro renacentista. Amenazado por la Gestapo, Engelmann debió irse muy rápidamente de Viena. Por prudencia, dejó los negativos en manos de Aichhorn. Pero volvió justo después de la partida de Freud: «Unos obreros habían empezado a reacondicionar las habitaciones. Habían lijado y encerado el parqué: la sombra del diván ya no estaba».
El 4 de junio Freud tomó el Orient Express con Anna, Martha, Paula y su perra Lun. Josefine Stross, pediatra, había ocupado el lugar de Max Schur, obligado a operarse de urgencia a raíz de una crisis de apendicitis aguda flemonosa. El 10 de junio Schur tuvo que huir del hospital en una silla de ruedas, vendado y con un drenaje en el estómago, para escapar con su familia de la Gestapo. Gracias al visado obtenido por Freud y Jones pasó a París, luego a Londres y por fin a Nueva York, donde emprendió todos los trámites necesarios para su radicación definitiva en el continente americano.
El día de su partida Freud firmó una declaración obligatoria redactada por Alfred Indra, en la cual reconocía haber sido bien tratado: «Declaración. Confirmo de buen grado que hasta el día de hoy, 4 de junio de 1938, ni mi persona ni los integrantes de mi casa hemos sido importunados. Las autoridades y los funcionarios del Partido se han comportado en todo momento de manera correcta y deferente conmigo y con los integrantes de mi casa. Viena, 4 de junio de 1938. Prof. Dr. Sigm. Freud». Durante decenios, historiadores, testigos y comentaristas estuvieron convencidos de que Freud había incluido por sí mismo, al final de esta declaración, la siguiente frase: «Puedo recomendar cordialmente la Gestapo a todos». Otra leyenda más verdadera que la realidad. Rumor absurdo. Era imposible, en efecto, ridiculizar de ese modo un documento oficial. Lo cierto es que Martin afirmó que su padre la había colado en la parte inferior de la declaración.
Freud y las cuatro mujeres que viajaban con él atravesaron algunas ciudades antes de llegar a la frontera francesa. En varias ocasiones Freud estuvo a punto de caer víctima de un paro cardíaco, y Josefine Stross le administró estricnina y otros estimulantes. Por fin, el 5 de junio, hacia las tres y media, el convoy franqueó el Rin por el puente de Kehl. Freud exclamó: «Ahora somos libres».
Al llegar el tren a la estación del Este, Paula se impresionó mucho por la recepción brindada a Freud, pero señaló lo perdido que estaba este en medio de los fotógrafos y periodistas. Flanqueado por Bullitt, particularmente elegante con su sombrero de fieltro de borde ondulado y su pañuelo de encaje, pero también por Marie Bonaparte, que lucía un vestido de alta costura y una estola de marta cebellina, parecía llegado de otro mundo. Lo seguía Martha, envarada en un impermeable arrugado y con el bolso aferrado por las dos manos, mientras que Anna sonreía, con la cara oculta a medias por un pobre bonete de lana que le cruzaba la frente. Dos lujosos automóviles con chófer llevaron a los exiliados a la propiedad de la princesa en Saint-Cloud. Pasaron allí el día, para viajar después a Calais y atravesar el canal de la Mancha. En las fotos se ve a Freud tocado con una gorra que le cae sobre las gafas, el cuerpo tendido en un sillón de mimbre, las piernas disimuladas bajo unas mantas, el rostro inerte, la mejilla derecha ennegrecida y hundida, la barba blanca. Lun está prudentemente acostada a su izquierda.
Al día siguiente los viajeros llegaron a la estación Victoria, donde los esperaban Jones, su mujer y Ernst. Dejaron a Lun en manos de un veterinario ya que debía cumplir una cuarentena obligatoria de seis meses y luego se alojaron provisionalmente en Elsworthy Road.
A su llegada, Freud se reencontró con su sobrino Sam, a quien no había vuelto a ver desde su estancia en Manchester, y se enteró de los numerosos artículos periodísticos que anunciaban su llegada, al mismo tiempo que recibía una avalancha de telegramas, cartas, flores y obsequios. Anna le regaló un pequinés al que él, por antífrasis, bautizó como Jumbo. El 17 de julio, al escribirle a su hermano Alexander sobre el exilio, señaló que Jones tropezaba con muchas dificultades ante las autoridades británicas para conseguir la entrada de los emigrados, porque existía el riesgo de que estos no encontraran trabajo: «Jones ha conseguido una multitud de cosas, pero solo para analistas». En su carta explicaba que había ayudado a Harry con unas palabras de recomendación y agregaba que Martin no sabía todavía qué iba a hacer, que Robert había encontrado un empleo y que Minna estaba enferma. El 27 de septiembre se instaló con su familia en una bella casa en el 20 de Maresfield Gardens, Hampstead. Ernst Freud la había acondicionado según el modelo de la Berggasse: sería la última residencia de Freud.
El 11 de octubre recibió la visita de Anton Sauerwald, que llegaba sin duda a reclamarle dinero. Cuando Alexander le preguntó al visitante qué hacía en Londres, Sauerwald explicó que la policía vienesa lo había contratado como experto en explosivos, pero que en realidad los fabricaba él mismo por cuenta de organizaciones secretas nazis. ¡Extraña historia! Según Max Schur, Sauerwald adujo que Hitler se sentía en «estado de sitio» debido a que los judíos eran demasiado individualistas para asimilarse a una población. En consecuencia, había que eliminarlos, decía, pero eso no impedía que a título personal un individuo —aunque fuese nazi— pudiera ayudar a otro, como él mismo había hecho en el caso de la familia Freud.
Durante los dieciocho meses que le quedaban de vida, Freud tuvo la gran dicha de ser honrado, visitado, reconocido, admirado, celebrado como nunca antes. También se sentía libre y pudo terminar su libro sobre Moisés y escribir un opúsculo, el _Esquema del psicoanálisis_ , donde efectuaba una síntesis de su obra y profetizaba el próximo descubrimiento de poderosas sustancias químicas capaces de actuar directamente sobre el cerebro. Reafirmaba que Shakespeare se llamaba Edward de Vere y hacía la apología de su _Ödipuskomplex_.
Mientras los tumores cancerosos proliferaban en los huesos de su mandíbula, Freud asistía a la destrucción de la Europa continental. Pero al mismo tiempo cobraba conciencia de la fuerza de su doctrina en el mundo angloparlante. El 25 de junio recibió a una delegación de la Royal Society que lo invitó a firmar su libro oficial, el mismo donde figuraba el nombre de Charles Darwin. Lo visitaron también muchos escritores e intelectuales. Llevado por Stefan Zweig, Salvador Dalí hizo varios croquis de su devastado rostro, conforme al principio surrealista de «la voluta y el caracol». Freud parecía indiferente y ese día explicó al pintor que solo se interesaba en la pintura clásica para discernir en ella la expresión del inconsciente, mientras que en el arte surrealista prefería observar la expresión de la conciencia.
Cuando Arthur Koestler fue a verlo, en el otoño, se quedó estupefacto al oír a Freud murmurar, con referencia a los nazis: «Vea, no hicieron otra cosa que desencadenar la fuerza de agresión reprimida en nuestra civilización. Tarde o temprano un fenómeno de ese tipo debía producirse. No sé si, desde ese punto de vista, puedo culparlos». Una vez más, Freud afirmaba que el mundo en el cual vivía estaba hecho a imagen de lo que él había descrito en su obra. Judío húngaro nacido en Budapest, sionista de derechas, allegado a Vladimir Jabotinsky y fino conocedor del psicoanálisis, aunque prefería la parapsicología, Koestler no ignoraba que su madre, Adele Jeiteles, había conocido a Freud con ocasión de una consulta, en 1890, y que lo vilipendiaba. Víctima de una melancolía crónica, detestaba en la misma medida a su hijo (a quien trataba de perverso), que, como lo testimonia su autobiografía, le pagaba con la misma moneda. En el momento de su encuentro, los dos hombres no evocaron su juventud vienesa.
Cuando recibió la visita de su viejo amigo vienés Walter Schmideberg, Freud fue más lejos aún, ya que lo saludó con un « _Heil Hitler!_ », como si consintiera por fin en pronunciar, a través de ese chiste lúgubre, el nombre infame del destructor de su obra.
Los miembros de la BPI vivieron como una verdadera intrusión la llegada de la familia Freud. Sucedía que, desde hacía años, los kleinianos dominaban la sociedad británica y habían elaborado sus propias tesis, que no tenían demasiado que ver con el freudismo original. Por añadidura, habían marginado a los viejos freudianos y consideraban al propio Freud como un patriarca de otra época, directamente salido del siglo XIX. Les parecían rígidas las costumbres de sus mujeres —Martha, Minna, Anna, Paula— y ridículas sus maneras de hablar y vestirse. Apenas entendían sus rituales, esa cortesía estudiada, ese humor glacial, esos gustos alimentarios. En una palabra, los veían como seres extraños aferrados a viejas mitologías y poco abiertos al nuevo enfoque del inconsciente centrado en las posiciones, las relaciones objetales, el núcleo psicótico, las pulsiones destructivas discernidas en los niños pequeños. Los kleinianos y los freudianos no hablaban el mismo lenguaje. En ese contexto, Jones, que siempre había apoyado a Melanie Klein, tuvo un papel esencial en la incorporación de Anna Freud a la BPI.
El 29 de julio de 1938 Anna participó en el decimoquinto congreso de la IPA, celebrado en París bajo la presidencia de Jones. Leyó en él el capítulo del _Moisés_ dedicado al progreso del espíritu humano y la grandeza del Imperio británico. Freud había transmitido a sus partidarios un mensaje de un antiamericanismo virulento, en el cual los exhortaba a la vigilancia contra todo intento de transformar el psicoanálisis en «criada para todo» de la psiquiatría. En su discurso de clausura del congreso, Jones elogió su política de «salvamento» del psicoanálisis en Berlín sin decir una palabra del exilio de los judíos ni del éxodo de la flor y nata de la _intelligentsia_ freudiana. Y se atrevió a congratularse por la puesta bajo tutela de la WPV. Después de esas siniestras palabras, los participantes acudieron a una recepción en Saint-Cloud, en los jardines de la suntuosa residencia de la princesa, donde Freud había pasado algunas horas a su llegada a Francia.
Max Eitingon había viajado a París para participar en el congreso. Se trasladó a continuación a Londres para hacer una última visita a Freud. Se lo acusaba entonces de ser un agente del NKVD, implicado en el secuestro del general Yevgeny Miller, que había sido organizado por Nikolái Skoblin, agente doble germano-soviético y esposo de la cantante Nadezhda Plevitskaia, a quien Eitingon conocía bien. No hacía falta tanto para que a continuación, a raíz de sus vínculos con Plevitskaia, el rumor se extendiera. ¿No habría sido también hermano de Leonid Eitingon, otro espía soviético y organizador en 1940 del asesinato de Trotski a manos de Ramón Mercader? Aunque no existía la más mínima relación de parentesco entre Leonid y Max, la leyenda de un Eitingon freudiano y estalinista, agente doble y triple, mercader de pieles e instigador de crímenes, no dejaría de reaparecer, y perdura aún en nuestros días en la pluma de autores obstinados en demostrar la presunta confluencia de destino entre dos internacionales, la comunista y la psicoanalítica.
En ruta hacia América, los exiliados vieneses reunidos en París pensaron una última vez, antes del apocalipsis, en esa Europa de sueño cuyos fulgores jamás volverían a ver. La gran Yvette Guilbert, tan admirada por Freud, cantó «Dites-moi que je suis belle» frente a una multitud subyugada por su potencia vocal y sus ochenta años. En Italia, en cumplimiento de las primeras leyes antisemitas, Mussolini entregaba entonces a los judíos a la deportación. En enero de 1939 Edoardo Weiss también se vería obligado a exiliarse a Estados Unidos, dejando atrás a su hermana, su cuñado y la familia de su mujer, exterminados en su totalidad por los nazis. Nunca más querría acordarse de las esperanzas que había depositado en Mussolini a través de su amistad con Forzano.
El día mismo de su mudanza a Maresfield Gardens, Freud, que acababa de sufrir una nueva y espantosa operación en la London Clinic, tomó conocimiento de los acuerdos de Munich en virtud de los cuales Francia y el Reino Unido entregaban Checoslovaquia a Hitler. En esta ocasión, Neville Chamberlain, recibido en Londres como el salvador de la paz, pronunció un discurso sobre la inutilidad de librar batalla por un país lejano que los ingleses no conocían. Sin creer demasiado en ella, Freud aprobó no obstante esa política, que permitiría a los nazis anexionarse de inmediato la región de los Sudetes: «Naturalmente, nosotros también agradecemos esta tregua, que, sin embargo, no puede proporcionarnos auténtica alegría».
Tres semanas después escribió para el diario de Koestler, _Die Zukunft_ , una breve nota en la cual, con palabras de Mark Twain y Nikolaus von Coudenhove-Kalergi, ponía de relieve hasta qué punto el combate contra el antisemitismo debía ser librado ante todo por no judíos. Mientras tanto, los alemanes seguían adelante con las persecuciones exhibiendo a mujeres alemanas o austríacas a quienes habían rapado porque les reprochaban haber tenido relaciones amorosas con judíos. Durante la Noche de los Cristales Rotos destruyeron edificios, comercios y sinagogas y deportaron a treinta mil personas a los campos de Dachau y Buchenwald. En Viena, al detener al profesor Arthur Freud, nacido en Moravia y sionista militante, un oficial nazi lanzó un grito de victoria, convencido de haber capturado finalmente a su célebre homónimo.
El espectro de Freud iba a asediar durante largos años la conciencia de los hitlerianos. Pero Freud se preocupaba por sus hermanas:
Los últimos pavorosos acontecimientos registrados en Alemania agravan el problema de lo que podremos hacer por las cuatro ancianas, cuyas edades oscilan entre los setenta y cinco y los ochenta años. No tenemos medios suficientes para mantenerlas en Inglaterra, y el dinero que les dejamos a nuestra marcha, que ascendía a unos sesenta mil chelines austríacos, quizá haya sido confiscado ya. [...] Hemos estado dando vueltas a la idea de buscarles casa en la Riviera francesa, en Niza o en algún lugar cercano. Pero ¿sería esto posible?
Para responder a esas preocupaciones, Marie Bonaparte intentó conseguir visados de las autoridades francesas o, en su defecto, de la legación griega. En vano. Era demasiado tarde. Con perfecta lucidez respecto de las persecuciones que afectaban a los judíos, la princesa desplegó gran energía para salvar vidas, e incluso propuso a Roosevelt, en una carta del 12 de diciembre, crear un Estado judío en el sur de California para acoger en el más breve plazo a millares de refugiados. Tampoco aceptaría jamás en Francia el menor intento de «salvamento» y marcharía al exilio en febrero de 1941.
El 7 de diciembre Freud recibió en su domicilio a técnicos de la BBC para grabar un discurso que había redactado. Lo leyó en inglés, con una voz ahogada por su prótesis, y al final del mensaje añadió una frase en alemán: «A los ochenta y dos años, dejé mi casa en Viena como consecuencia de la invasión alemana y vine a Inglaterra, donde espero terminar mi vida en libertad». Es el único documento existente de la voz de Freud.
Durante el último año de su vida se rodaron en Maresfield Gardens varios filmes mudos, algunos de ellos en color. En cada imagen vemos a un Freud cada vez más encorvado caminar por su jardín del brazo de Anna y siempre con la compañía de Lun y Jumbo; la mandíbula, trabada por su «bozal», y los labios en movimiento como si masticara algo. En su rostro se lee un inmenso sufrimiento.
Freud seguía recibiendo numerosas visitas de sus amigos londinenses y de todos los que acudían a darle un último adiós antes de su partida hacia otros continentes. Sufría cada vez más y se tendía en la mecedora del jardín o en su diván, a menudo bajo un mosquitero. Prefería comer solo al abrigo de las miradas y, por lo demás, ya no tenía apetito. Un olor fétido comenzaba a desprenderse de su boca, pero en sus ojos centelleantes seguía brillando la llama del dios Eros. Freud siempre había dicho que prefería, en la hora de la agonía, asistir con plena conciencia al naufragio de su Konrad, y no estar senil o derrumbarse a causa de un ataque cerebral: morir con las botas puestas, como el rey Macbeth. Sabía que Max Schur se ocuparía de él hasta el final antes de emigrar definitivamente a Estados Unidos.
De acuerdo con las indicaciones de Hans Pichler, George Exner, especialista en cirugía facial, seguía la fase terminal de la enfermedad con Wilfred Trotter, cuñado de Jones, miembro de la Royal Society y especialista en tratamientos contra el cáncer. En febrero Marie Bonaparte hizo ir a Londres al profesor Antoine Lacassagne, autoridad suprema del Instituto Curie de París, que se vio obligado a admitir que no era posible ninguna operación más. Para no decepcionar a Anna y Minna, que querían mantener las esperanzas, sugirió un tratamiento intensivo con rayos X y no con radio, lo cual dio pábulo a este comentario de Freud: «Ya no hay duda de que se trata de un nuevo ataque de mi viejo y querido carcinoma, con el que comparto mi existencia desde hace ya dieciséis años. ¿Quién sería el más fuerte en ese momento? Como es natural, no podíamos decirlo de antemano». Y confesó entonces a su querida princesa que quería terminar de una vez.
A comienzos de marzo, algunos meses antes de la aparición de la edición alemana del _Moisés_ en Amsterdam, Jones organizó en el hotel Savoy una cena de gala con motivo del vigésimo quinto aniversario de la fundación de la BPI, a la que acudieron Anna, Martin, Ernst, Virginia Woolf, H. G. Wells y muchos otros. Demasiado débil para moverse, Freud envió un mensaje de apoyo: «Los acontecimientos de estos últimos años han querido que Londres se convirtiera en la capital y el centro del movimiento psicoanalítico. Pueda la sociedad cumplir con mucha brillantez las funciones que así le corresponden». Durante el verano Wells intentó en vano obtener la nacionalidad británica para el moribundo, a fin de responder a un anhelo de juventud que era querido para este desde la partida de su hermano a Manchester: «No se necesitaba nada más que una pequeña moción de un simple diputado [...]. Me apena que no haya podido ser así». A principios de agosto Freud dejó de recibir a sus cuatro últimos pacientes, pero Dorothy Burlingham y Smiley Blanton prosiguieron hasta fin de mes una cura de objetivos didácticos.
El 3 de septiembre de 1939, día de la declaración de guerra de Francia e Inglaterra a Alemania, Jones se despidió de su viejo maestro. En ese momento crítico, señaló que por fin se encontraban en el mismo campo, unidos contra la misma barbarie:
La última vez que Inglaterra combatió contra Alemania, hace ya veinticinco años de esto, estábamos a uno y otro lado del frente, pero hallamos la manera de comunicarnos nuestra amistad. Aquí estamos hoy, muy cerca uno de otro y unidos en nuestras simpatías militares. Nadie puede decir si veremos el final de esta guerra, pero, de todos modos, ha sido una vida muy interesante y ambos hemos hecho nuestra aportación a la existencia humana, aunque en medidas muy diferentes.
Descendiente de una familia aristocrática de Auvernia, Raphaël de Valentin, el héroe de _La piel de zapa_ , creado por Balzac, soñaba con la gloria. Empujado por Rastignac, abandona la creación artística para probar suerte en el mundo, hasta arruinarse y pensar en el suicidio. En ese momento descubre en el local de un anticuario un talismán —una piel de zapa— dotado del poder mágico de cumplir todos los deseos de su poseedor. Como Fausto, Valentin no quiere renunciar a nada y firma, para su desgracia, un pacto con el Diablo. Cada vez que se embriaga con sus placeres, la piel se encoge. Matar los sentimientos para vivir hasta viejo o morir joven aceptando el martirio de las pasiones: tal es la temática de esa novela, que expone el enigma de la condición humana.
Al decidir leer ese libro en vísperas de su muerte, Freud se enfrentaba, es cierto, a la imagen de su cuerpo descompuesto y su agonía por inanición, pero, antes que nada, la novela desplegaba ante su vista la historia de una vida mala que habría podido ser la suya si él no hubiera sobrevivido a su combate contra sí mismo. Freud era el hombre que había querido enseñar a los hombres hasta qué punto los embarga el deseo de su propia destrucción y les había dicho que solo el acceso a la cultura es capaz de contener esa pulsión. Creía que lo que les pasaba estaba ya inscrito en su inconsciente aun antes de que se les revelara, y tenía la convicción de que el complejo de Edipo era el nombre de esa inscripción. Sin embargo, en ese instante no se enfrentaba al complejo sino a la piel de zapa —Edipo o Macbeth—, es decir, al límite de su libertad. Libraba un último combate contra el suplicio de la muerte, en paz consigo mismo cuando el mundo entraba en guerra; cuando el ello triunfaba del yo; cuando la enfermedad corroía el interior de su boca al punto de asomar a la superficie en la mejilla, y cuando, finalmente, por encima de su casa aullaban las sirenas que anunciaban las primeras alertas aéreas. El 25 de agosto había puesto punto final a su agenda y a su vida con estas palabras: «Pánico de guerra» ( _Kriegspanik_ ).
El 21 de septiembre Freud recordó a Schur la promesa que este le había hecho de ayudarlo a poner fin cuando llegara el momento, y le pidió que hablara de ello con Anna: «Si ella cree que es justo, acabemos de una vez, entonces». A sus ojos, vivir en esas condiciones ya no tenía ningún sentido. Schur, que había vuelto a Londres el 8 de agosto, le estrechó la mano y prometió darle el calmante adecuado. Administró una primera vez una dosis de tres centígramos de morfina y luego la repitió dos veces, con varias horas de intervalo. Sabía que la dosis calificada de «calmante» no podía superar los dos centígramos. En consecuencia, había escogido la muerte mediante una sedación profunda y continua.
Freud murió el sábado 23 de septiembre de 1939, a las tres de la mañana. Era la festividad de Yom Kipur, la más sagrada del año judío, día de expiación de los pecados del becerro de oro. Durante la jornada los judíos londinenses practicantes se congregaron en la sinagoga para implorar el gran perdón de ese Dios a quien Freud tanto había maltratado. Por doquier se apilaban bolsas de arena destinadas a proteger los edificios contra las incursiones enemigas; algunas estatuas habían sido trasladadas de su emplazamiento y se habían cavado trincheras.
Ese mismo día, en el otro extremo de una Europa abandonada desde hacía tiempo por los freudianos, Adam Czerniakow, un viejo ingeniero químico, aceptó su designación, por el alcalde de Varsovia, como presidente del Judenrat, mientras que en Sokolow Podlaski, un distrito cercano, los nazis incendiaban la sinagoga. Czerniakow escondió en su cajón un frasco con veinticuatro pastillas de cianuro. También él sabría morir en el momento deseado.
El cuerpo de Freud fue incinerado en el crematorio de Golders Green sin ningún ritual, y sus cenizas se depositaron en una crátera de la antigua Grecia adornada con escenas de ofrenda. Frente a un centenar de personas, Jones tomó la palabra en inglés para hacer el elogio de su maestro, a la vez que recordaba los nombres de todos los miembros del comité, muertos o dispersos: «Si hay un hombre de quien pueda decirse que domeñó la muerte misma y le sobrevivió a pesar del rey de las Tinieblas, que no le inspiraba temor alguno, ese hombre lleva el nombre de Freud».
Tras él, Stefan Zweig pronunció en alemán una espléndida oración fúnebre: «Gracias por los mundos que nos has abierto y que ahora recorremos solos, sin guía, fieles para siempre y venerando tu memoria, Sigmund Freud, el amigo más precioso, el maestro adorado».
Zweig se suicidaría en Petrópolis, Brasil, en febrero de 1942.
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Epílogo
Desde Nueva York, a donde había conseguido emigrar, Harry Freud, el hijo de Alexander, anunció a las cuatro hermanas que habían quedado en Viena la muerte de su hermano Sigmund: «Está ahora en el otro mundo, que esperamos mejor [...]. Pasó sus últimos días en su despacho, donde le habían instalado la cama. Desde allí podía ver el jardín y, en los mejores momentos, alegrarse con la vista de la naturaleza. Deseo que recibáis esta noticia con sosiego. Las otras noticias de la familia son buenas».
En lo que respecta al sosiego, las cuatro ancianas pronto iban a verse obligadas a vivir, como otras mujeres perseguidas, en el antiguo apartamento de Alexander. En nombre del impuesto punitivo —la JUVA— se las despojó de sus posesiones, de las que disponía Erich Führer, el administrador nazi de los bienes de Alexander. Harry alertó a Alfred Indra, que intentó ponerse en contacto con Anton Sauerwald. Pero este había sido movilizado y estaba en el frente ruso. El 20 de junio de 1940 Indra reclamó el auxilio urgente de Harry. Pero las gestiones emprendidas no sirvieron de nada. El 15 de enero de 1941 las cuatro mujeres remitieron una carta desesperada al abogado: «Estamos confinadas en una sola habitación que debe hacer las veces de dormitorio y sala de estar. Como usted sabe, somos personas de edad, a menudo enfermas y con la necesidad de guardar cama, y una ventilación normal y la limpieza son imposibles sin afectar a la salud».
Para entonces, como tenían más de sesenta y cinco años, no se las había tenido en cuenta a la hora de decidir quiénes irían en los primeros convoyes hacia los campos de trabajo. Pero después de la conferencia de Wannsee de enero de 1942 fueron deportadas al gueto de Theresienstadt (Terezin), donde Adolfine murió de desnutrición el 29 de septiembre de ese mismo año. En cuanto a las otras tres hermanas, se las trasladó a campos de exterminio, de los que nunca volverían: Maria y Paula a Maly Trostinec el 23 de septiembre de 1942 y Rosa Graf a Treblinka el 29 de septiembre de 1942 o el 1 de marzo de 1943.
El 27 de julio de 1946, Samuel Rajzman, originario de Varsovia, prestó este testimonio ante el tribunal de Nuremberg acerca del _Obersturmbannführer_ Kurt Franz, comandante delegado del campo:
El tren venía de Viena. Yo estaba en el andén cuando sacaron a la gente de los vagones. Una mujer de cierta edad se acercó a Kurt Franz, presentó un _Ausweis_ [documento de identidad] y dijo ser la hermana de Sigmund Freud. Pidió que la destinaran a un trabajo de oficina sencillo. Franz examinó con cuidado el documento y dijo que probablemente se trataba de un error. La llevó al tablero de horarios ferroviarios y dijo que un tren regresaba a Viena dos horas después. Ella podía dejar sus objetos de valor y sus documentos aquí, ir a las duchas y, después del baño, los documentos y el billete para Viena estarían a su disposición. Como es evidente, la mujer entró en las duchas y jamás salió de ellas.
Tras la muerte de su padre y abuelo, los hijos y nietos de Freud tuvieron que adaptarse, como sus discípulos, a un mundo muy diferente al que habían conocido. Debieron afrontar el tiempo de la guerra sin haber tenido la oportunidad de saborear una nueva paz. Pero esta vez, en virtud de su exilio, se encontraban en el campo de los vencedores, quienes los veían como intrusos que lo habían perdido todo. Nunca olvidaron que eran judíos, pero a medida que descubrían la magnitud de la destrucción que se había abatido sobre su mundo de antaño y sobre quienes no habían podido escapar, quisieron romper con los horrores del pasado. Como muchas víctimas que habían conseguido sobrevivir, se enfrentaron entonces a la cuestión del exterminio de los judíos. Y varios de ellos participaron en la cacería de los nazis.
Muy dotada para la costura, Mathilde estableció en Londres, junto con otros austríacos exiliados, una tienda de moda. Martin siguió viviendo como antes, solitario, seductor y sin dinero, considerándose un «viejo judío enfermo». Terminó por trabajar como encargado de un quiosco de tabaco y diarios cerca del Museo Británico. Radicado en Filadelfia, Estados Unidos, Oliver procuró en vano adoptar un niño superviviente del genocidio y luego ocupó un puesto de investigador en una empresa de transporte, donde se hacía llamar «profesor Freud». Niño mimado por la fortuna, Ernst, el más elegante, prosiguió con su carrera de arquitecto inglés. Dos de sus hijos tuvieron un destino excepcional: Lucian Freud, uno de los pintores figurativos más innovadores de la segunda mitad del siglo XX, y Clemens, convertido en sir Clement, político, periodista, humorista, dueño de restaurantes, propietario de un club nocturno, que siguió como observador el desarrollo de los procesos de Nuremberg y publicó su autobiografía, _Freud Ego_.
Lucian tuvo catorce hijos de varias mujeres diferentes; Clement, cinco, uno de ellos adoptado, y Stefan (Stephen), el hermano mayor, el olvidado, el ferretero, el marginal, pasó la vida en medio de disputas con sus hermanos, que por otra parte se detestaban entre sí. Hija de Lucian, Esther Freud contó en varias de sus novelas las distintas facetas de su difícil existencia entre un padre ausente, a quien solo conoció de adolescente, y una madre atormentada. Muchas veces evocó el silencio de ese padre sobre los acontecimientos de los años treinta. En cuanto al propio Lucian, glacial, pernicioso, mágico, de una increíble belleza, cultor del secreto y la provocación y entusiasta de Velázquez, su pintor preferido, adoraba a su abuelo, del que se acordaba muy bien, y le horrorizaban todas las formas de expresión antisemita.
Hacia los diez años, ya muy original en su manera de observar el mundo que lo rodeaba, había querido «ver a Hitler», el enemigo absoluto. Durante una manifestación nazi en Berlín había llegado incluso a fotografiarlo, y nunca olvidó sus rasgos y sus gestos. Asfixiado por una madre (Lucie) que mantenía con él una relación fusional, solo se desprendió de ese influjo gracias a su genio creativo. A la inversa de su abuelo, a quien tanto se parecía, Lucian se interesaba no en la palabra sino en el cuerpo en su desnudez misma, no en la represión del deseo sino en la libido en toda su violencia pulsional. Para pintar se quitaba la ropa y exigía que sus modelos también se desnudaran, incluso cuando hacía el retrato de sus parientes, en particular de sus hijas. Todo sucedía como si Lucian actualizara en su obra pictórica la parte oscura de la de Sigmund, de quien se pretendía el heredero demoníaco. Así como rechazaba el complejo edípico, consideraba a _Herr Professor_ como un fabuloso zoólogo, fascinado —él, el primer científico en determinar el sexo de las anguilas— por el mundo animal. Lucian tenía un vínculo casi animalista con el cuerpo fantaseado de su abuelo.
Sabía que le debía en parte su libertad y rememoraba con intensa emoción la escena en que Marie Bonaparte había recurrido al duque de Kent para que Ernst y su familia pudiesen obtener la nacionalidad británica. En razón de esa deuda contraída con la familia real, cincuenta y cinco años después obsequió a la reina Isabel II el retrato que había hecho de ella. La obra generó tanto escándalo como las teorías freudianas: la prensa afirmó que el pintor había «travestido» el rostro de la soberana al darle un cuello de jugador de rugby y un mentón azul que parecía cubierto por una barba incipiente. En razón de ese sacrilegio, sugirió un periodista, había que encerrar a Lucian en la Torre de Londres.
Enrolado en el ejército, Anton Walter, el hijo de Martin, mucho más politizado que su padre, tuvo a su cargo, en abril de 1945, la liberación del aeropuerto de Zeltweg, en Estiria. Lanzado en paracaídas en medio de la noche, reivindicó su nombre y, para su gran sorpresa, los oficiales austríacos, deseosos de terminar de una vez con la guerra, no le brindaron una recepción demasiado inamistosa. A continuación, ascendido al grado de capitán, se especializó en la búsqueda de viejos criminales nazis y contribuyó, con sus investigaciones, a entregar a la justicia a Bruno Tesch, cuya empresa fabricaba el Zyklon B para el campo de Auschwitz. Juzgado culpable por el tribunal militar de Hamburgo, Tesch fue condenado a muerte y ahorcado en marzo de 1946. Gracias a su tenacidad, Anton también contribuyó a la condena de Alfred Trzebinski, médico de las SS, torturador y especializado en las experiencias de inyección de bacterias en niños. Más adelante Anton Walter trabajó, hasta jubilarse, como ingeniero químico en diversas empresas inglesas.
En cuanto a su primo Harry Freud, incorporado al ejército norteamericano, también volvió a Austria para rastrear a Anton Sauerwald, a quien acusaba de haber saqueado los bienes de su familia. Detenido y juzgado por las autoridades norteamericanas, el antiguo comisario-gerente se declaró «no culpable». Su mujer pidió a Anna Freud que prestara testimonio. Esta aceptó de buen grado y en un escrito afirmó que Sauerwald había brindado ayuda a la familia. El hombre fue liberado.
Tras la muerte de su padre, Anna decidió permanecer en Londres y vivir en la casa familiar del número 20 de Maresfield Gardens, en Hampstead. Después de que murieran Martha y Minna la acompañó allí Dorothy, que había vuelto de Nueva York en 1940 y estaba convencida de no poder prescindir más de su amiga. Juntas, ambas prosiguieron con sus actividades en favor de la infancia y fundaron las Hampstead Nurseries y la Hampstead Child Therapy Clinic, un centro de investigación y clínica donde aplicaron sus teorías en estrecha colaboración con los padres de los niños que se trataban en él.
En 1946 Anna se enteró por su gran amiga Kata Levy, hermana de Anton von Freund, de la suerte que habían corrido sus cuatro tías, sin saber aún en qué campo habían encontrado la muerte. De inmediato transmitió la información a sus tres primas, Margarethe Magnus, Lilly Freud-Marlé y Rose Waldinger. Martha se apresuró a acompañarlas en su duelo y Anna se sintió culpable de no haber sido lo bastante vigilante. Durante años puso a los austríacos en la picota y no quiso oír hablar más de la Berggasse. No obstante, ayudó desde Londres a su viejo amigo Aichhorn a reconstruir la WPV.
Se enfrentó a la cuestión del exterminio al hacerse cargo, entre 1945 y 1947, de seis pequeños huérfanos judíos alemanes, nacidos entre 1941 y 1942 y cuyos padres habían sido enviados a la cámara de gas. Internados en el campo de Theresienstadt (Terezin), en la sección de niños sin madre, habían sobrevivido pegados unos a otros y privados de juguetes y comida. Cuando los albergaron en Bulldogs Bank y luego, al ser confiados a Anna —que restableció entonces su relación con la lengua alemana—, hablaban entre sí en un lenguaje grosero, rechazaban los regalos, rompían los muebles, mordían, pegaban, aullaban, se masturbaban, insultaban a los adultos. En una palabra, para sobrevivir no habían tenido otra opción que constituir una entidad única que les servía de fortaleza. Al cabo de un año de tratamiento recuperaron una vida normal. Hijos del genocidio y del abandono absoluto, fueron los primeros en experimentar un nuevo enfoque psicoanalítico, que mostraría a las generaciones futuras que nunca hay nada que esté determinado de antemano y que, aun en las situaciones más extremas, siempre es posible una nueva vida. En ese dominio Anna reveló sus verdaderos dones de clínica.
Sus amigos vieneses que se habían radicado en Estados Unidos la amaban por su devoción, su rectitud y su sentido de la fidelidad. Con ellos, Anna podía evocar, con nostalgia, la grandeza pasada del freudismo original. Ella seguía siendo la memoria viva de una época devorada por dos guerras mundiales.
Heredera legal, con su hermano Ernst, de los archivos y la obra de su padre, Anna se inclinó por Jones —y no por su amigo Siegfried Bernfeld— para que escribiera la primera biografía autorizada de Freud, que se publicaría en tres volúmenes entre 1953 y 1957: una obra magistral basada en archivos y fuentes indiscutibles. Por medio de ella, la diáspora freudiana pudo representarse sus orígenes bajo la forma de una historia, oficial, es cierto, pero no hagiográfica o piadosa. Jones privilegiaba la idea de que Freud, sabio solitario y universal, había logrado por la sola fuerza de su genio apartarse de las «falsas ciencias» de su época para develar al mundo la existencia del inconsciente. Tenía poco interés en situar la obra de Freud y su persona en la larga duración de la historia, y omitía por completo su propia política de presunto «salvamento» del psicoanálisis, que no lamentaba en modo alguno. Disimulaba los suicidios, los rumbos erráticos y los relatos de terapias psicoanalíticas, y trataba muy mal a Breuer, Fliess, Jung, Reich, Rank y muchos otros.
Pero, sobre todo, transformaba a Freud en un científico más inglés que vienés, más positivista que romántico, mucho menos atormentado por sus decisiones de lo que había sucedido en los hechos. En síntesis, construía para uso de sus contemporáneos un monumento conmemorativo en honor del príncipe y el sabio al que había servido. Esta monumental biografía suscitó un enorme debate historiográfico que, a lo largo de cuarenta años, sería tan intenso como las querellas entre psicoanalistas.
Ningún historiador podría, en el futuro, escapar a una confrontación con esa primera biografía escrita por un contemporáneo de Freud, que también había sido su discípulo y el organizador de su movimiento. Es cierto, Jones había cedido a la ilusión introspectiva al presentar a un héroe en marcha hacia su destino, pero en definitiva había sido el primero en tener acceso a los archivos, recurrir a una metodología coherente y atenerse a ella.
Jones incorporó a su trabajo las investigaciones de Siegfried Bernfeld, mientras que Anna supervisaba estrechamente, en el mismo momento, la publicación de las correspondencias, en especial la mantenida con Fliess, en la que se censuraba todo lo que a su juicio amenazaba deslucir la imagen ideal que ella se había forjado de su padre: un héroe sin miedo y sin tacha, un Freud «históricamente correcto» para un psicoanálisis pragmático, reglamentado y pronto esclerosado.
En 1972 Max Schur corrigió la versión de Jones y dio de Freud la imagen más vienesa de un científico ambivalente, adepto a la cocaína, angustiado por la muerte y vacilante entre el error y la verdad. Reveló además, por primera vez, la existencia de Emma Eckstein, y abrió así el camino para que otros investigaran la historia de los pacientes de Freud.
Anna y Dorothy vivieron una vida dichosa pero complicada. Jamás aceptaron que se las considerara lesbianas a pesar de que formaban una verdadera pareja, y Anna nunca estuvo dispuesta en vida a confesar públicamente o permitir revelar que su padre la había analizado.
Los niños que ambas mujeres habían amado y criado juntas, y que estaban muy perturbados, volvían regularmente a Londres. Bob frecuentó el diván de Anna durante cuarenta y cinco años y fue, como su hermana Mabbie, uno de los diez casos relatados en la primera parte de _The Psycho-Analytical Treatment of Children_. Asmático y depresivo, murió en 1969, a los cincuenta y cuatro años. Cinco años después, siempre en análisis en Londres y de manera episódica en Nueva York con Marianne Kris, Mabbie se mató en el número 20 de Maresfield Gardens con barbitúricos. Si bien era la preferida de Dorothy, nunca había soportado el conflicto que oponía a su padre psicótico, rechazado por la familia Freud, y su madre, que encarnaba a sus ojos el mundo de la salud y de los sanadores del alma.
Hijo del psicoanálisis, como Anna y los hijos de Dorothy, Ernstl Halberstadt se interesó durante toda su vida en los niños, las relaciones precoces de los bebés con su madre, los prematuros, la infancia de todos los países: en Jerusalén, Moscú, Johannesburgo. En busca de una identidad que pudiera vincularlo a su abuelo, se hizo llamar W. Ernst Freud para que no lo confundieran con su tío. A la muerte de Anna viajó a Alemania para ejercer el psicoanálisis y restableció así, para practicarla, el lazo con la lengua de su infancia. Fue de tal modo el único psicoanalista entre los descendientes varones de la familia Freud.
Con frecuencia evocaba su llegada a Londres y las rarezas muy freudianas de su primo, el joven Lucian, que había roto con los suyos, detestaba a su madre y soñaba con un gran destino de pintor. Un día, en un tren, a los dieciséis años, Lucian se había levantado de improviso para tomar una maleta en la que ocultaba un secreto: «Un cráneo de caballo. Lo contempló largamente y después lo guardó. Lo había encontrado en Dartmoor y se había apegado a él».
La reconstrucción de la vida del «gran hombre» y las diferentes publicaciones controladas no bastaron para unir por completo una comunidad psicoanalítica dispersa por los cuatro puntos cardinales del mundo ni para dar al movimiento freudiano el rostro civilizado y honorable que este quería mostrar de sí mismo a la opinión pública.
Además hacía falta, para completar la empresa editorial e historiográfica, reconstruir una memoria verdadera a fin de que nadie olvidara lo que había sido el esplendor de la _Mitteleuropa_ destruida por el nazismo. Esa sería la obra de Kurt Eissler.
Nacido en Viena en 1908 y analizado por Aichhorn, Eissler había emigrado a Chicago en 1938, dejando atrás a un hermano al que deportarían. Se instaló a continuación en Nueva York, tras su incorporación al servicio médico del ejército norteamericano para dirigir, con el grado de capitán, una consulta en un campo de entrenamiento. Íntegramente volcado en el pasado, manifestaba una intensa hostilidad hacia la escuela norteamericana, a la que reprochaba el abandono del freudismo original. Por eso decidió consagrar su vida a la constitución de un corpus de archivos que permitiera a las nuevas generaciones conocer la vida y la obra de Freud hasta en sus más mínimos detalles: una vida vienesa, una vida europea. Bernfeld había pensado en ello antes que él, pero Eissler lo dejó a un lado para apoyarse en Anna, como había hecho Jones en el caso de su iniciativa biográfica. Se puso en contacto con Luther Evans, el director de la prestigiosa Biblioteca del Congreso (LoC) de Washington, que aceptó recibir en ella los futuros archivos Freud.
En febrero de 1951 Eissler fundó los Sigmund Freud Archives (SFA), de los que fue conservador, rodeado por un consejo de administración exclusivamente compuesto de psicoanalistas miembros de la IPA: Bertram Lewin, Ernest Jones, Willi Hoffer, Hermann Nunberg y Siegfried Bernfeld. A ellos se añadían algunos miembros honorarios: Albert Einstein, Thomas Mann, Anna Freud.
Durante treinta años Eissler reunió un fabuloso tesoro: cartas, documentos oficiales, fotografías, textos, conversaciones con todas las personas que habían conocido a Freud, incluyendo a los pacientes, los vecinos o los visitantes más anodinos. Todos los psicoanalistas que habían conocido a _Herr Professor_ y la mayoría de los miembros de su familia le entregaron sus documentos y testimonios. De conformidad con Anna Freud, Eissler puso en práctica una política tan notable en el plano archivístico como desastrosa para la investigación. En efecto, preocupado por clasificar, ordenar, dominar y controlar toda la memoria de un mundo del que solo había conocido los últimos instantes, negó a los historiadores profesionales el acceso a los archivos y reservó su consulta a los psicoanalistas debidamente formados en el círculo restringido de la IPA. Ahora bien, desde la década de 1960 esos psicoanalistas se dedicaban a trabajos cada vez más clínicos y, de todos modos, estaban muy poco preparados para emprender investigaciones historiográficas o simplemente históricas.
Desde 1970 el idioma inglés dominó claramente los trabajos historiográficos. El trabajo jonesiano fue sucedido, de un lado, por una mirada disidente, y de otro, por un enfoque científico. Inaugurada por Ola Andersson en 1962, la historiografía científica se expandió a continuación gracias al innovador trabajo de Henri F. Ellenberger. Su _Historia del descubrimiento del inconsciente_ , que yo tomé como punto de partida para emprender mis propias investigaciones sobre la historia del psicoanálisis en Francia, fue en efecto la primera en introducir la larga duración en la aventura freudiana y situar el psicoanálisis en la historia de la psiquiatría dinámica. Freud salía desacralizado de ella y se dejaba ver bajo los rasgos de un científico dividido entre la duda y la certeza.
Ellenberger dio origen, sin haberlo querido, a una historiografía revisionista, crítica en un primer momento, sobre todo con la publicación de una obra de Frank J. Sulloway dedicada a los orígenes biológicos del pensamiento freudiano, y después más radicalmente antifreudiana, a través de varios ensayos —de quienes optan por el _Freud bashing_ — que hacían de Freud un estafador, violador e incestuoso, y oponían así una leyenda negra a una leyenda dorada.
Paralelamente, los trabajos de los historiadores norteamericanos o ingleses sobre la Viena de fin de siglo —Carl Schorske, William Johnston—, seguidos en Francia por los de Jacques Le Rider, transformaron la mirada posada sobre las circunstancias sociales y políticas que habían rodeado el descubrimiento freudiano. El Freud de Jones fue sucedido a continuación por un hombre inmerso en el movimiento de ideas que había estremecido el Imperio austrohúngaro de la década de 1880. Ese Freud encarnaba, de algún modo, todas las aspiraciones de una generación de intelectuales vieneses obsesionados con la judeidad, la sexualidad, el declive del patriarcado, la feminización de la sociedad y, por último, una voluntad común de explorar las fuentes profundas de la psique humana. En cuanto a la historiografía disidente, cobró cuerpo hacia 1975, tras la publicación de _Freud y sus discípulos_ , de Paul Roazen.
A partir de los años 1975-1980, por lo tanto, ya se daban las condiciones para que se impusiera una verdadera escuela histórica del freudismo. En ese contexto, frente a la aparición de los trabajos científicos y los enfoques críticos, los representantes de la legitimidad psicoanalítica (IPA) perdieron terreno y ya no lograron impedir que los historiadores produjeran obras que escapaban a la imagen oficial. En lo sucesivo conservarían un solo monopolio: el de la administración y el control de los famosos archivos depositados en la Biblioteca del Congreso.
Frente a esa realidad, Kurt Eissler y Anna Freud tomaron una decisión catastrófica al poner la fijación de la correspondencia con Fliess en manos de Jeffrey Moussaieff Masson, brillante políglota, ex profesor de sánscrito y discípulo de Paul Brunton, místico judío convertido a su vez a la espiritualidad hinduista por el gurú Ramana Maharshi. Debidamente sometido a análisis por la camarilla, Masson, seductor e inteligente, exhibía en apariencia todas las cualidades requeridas para emprender ese trabajo. Sin embargo, en medio de sus investigaciones el afortunado elegido se transformó en un contestatario radical. Como si fuera el profeta de un freudismo revisado, comenzó a creer que América había sido pervertida por una mentira freudiana original. Afirmó así que las cartas de Freud encerraban un «secreto»: Freud, decía, habría abandonado la teoría de la seducción por cobardía, para no revelar al mundo las atrocidades cometidas por los adultos en niños inocentes. Por eso habría inventado la teoría de la fantasía: sería en consecuencia un falsario.
En 1984 Masson publicó un ensayo sobre ese tema que fue uno de los más grandes éxitos de venta en la historia de la literatura psicoanalítica norteamericana. En él cuestionaba violentamente la doctrina freudiana y reactivaba a la vez el viejo debate entre Freud y Ferenczi sobre el trauma y los abusos sexuales. Y ahora el autor se apoyaba en la idea, muy en boga en los años ochenta, de que una inmensa mentira freudiana habría pervertido a América desde el triunfo de Freud en 1909, una mentira que sería solidaria de un poder fundado en la opresión: la colonización de las mujeres por los hombres, de los niños por los adultos, del afecto y la emoción por el dogma y los conceptos.
Eissler no se repuso nunca del terremoto que él mismo había desencadenado. Quería profundamente a Masson y había contemplado la posibilidad de que fuera su sucesor en la dirección de los SFA, y en lugar de ello se vio obligado a quitarle su cargo. Trabajador incansable, Eissler jamás había dejado de responder con erudición a todas las críticas y ataques lanzados contra Freud. Y habría querido, desde luego, que la persona a quien él había formado siguiera ese mismo camino. Para colmo, había impuesto la designación de Masson a Anna, que desconfiaba de él, y pensado incluso en encargarle la transformación del número 20 de Maresfield Garden en museo.
A raíz de este asunto, la corriente revisionista norteamericana —en especial Peter Swales, Adolf Grünbaum y muchos otros— se lanzó durante diez años a despedazar la doctrina freudiana y al propio Freud, reconvertido en un científico diabólico culpable de entregarse a relaciones carnales dentro de su familia. Ya en 1981, Peter Swales, autor iconoclasta, experto en el freudismo y fino conocedor de los archivos, afirmaba sin pruebas que Freud había tenido relaciones sexuales con su cuñada, quien, embarazada, habría sido obligada por él a abortar. Eissler sentía cierta simpatía por Swales, en tanto que Anna, superada por los acontecimientos, ya no sabía cómo afrontar las locuras revisionistas.
En 1986, cuatro años después de su muerte, el Freud Museum abrió sus puertas. Con el paso de los años se afirmó como un importante centro de investigaciones, exposiciones y conferencias. En él podían verse las colecciones de Freud, su despacho y su biblioteca, y consultar veinticinco mil documentos. En Viena, tras no pocas peripecias, se había creado en 1971 un primer Freud Museum, sin objetos, sin muebles, sin biblioteca: un museo del recuerdo de lo que había desaparecido en 1938; en síntesis, un museo anterior al segundo museo.
Como consecuencia del caso Masson se impuso en los medios la imagen de un Freud maltratador, violador, mentiroso e infame debido a la publicación de novelas y ensayos dedicados a su inexistente vida sexual, mientras que el interés por el psicoanálisis decaía en las sociedades occidentales —sobre todo en Francia— y, por el lado de los historiadores más clásicos, se ponía en marcha un retorno a la tradición historiográfica, con la publicación en 1988 de la obra de Peter Gay, historiador especializado en la época victoriana.
La crisis de los archivos llegó a su punto culminante en el momento en que se organizaba en la Biblioteca del Congreso una exposición sobre Freud, programada desde bastante tiempo atrás. Cuarenta y dos investigadores independientes, en su mayoría norteamericanos, firmaron entonces un escrito conjunto y lo enviaron a James Billington, director de la biblioteca, a Michael Roth, comisario de la exposición, y a James Hutson, responsable de la División de Manuscritos. Entre los firmantes se contaban autores excelentes —Phyllis Grosskurth, Elke Mühlleitner, Nathan Hale, Patrick Mahony— que criticaban con razón el carácter demasiado institucional del futuro catálogo y reclamaban que se incluyeran en él sus propios trabajos. Pero, para apoyar esta iniciativa colectiva, Peter Swales y Adolf Grünbaum desataron una violenta campaña de prensa contra Freud, en la que reiteraban las acusaciones habituales. Espantados frente a esa cacería de brujas, los organizadores de la exposición prefirieron postergarla, a pesar de que muchos periodistas e intelectuales norteamericanos manifestaban en la prensa su hostilidad a esas posturas extremistas.
En ese contexto, y por iniciativa de Philippe Garnier, psiquiatra y psicoanalista francés, y de mí misma, se hizo desde Francia otra recogida de firmas que criticaba tanto a los contestatarios como a los organizadores de la exposición de la Biblioteca del Congreso, incapaces de imponer su autoridad y demasiado aferrados a una antigua ortodoxia. Firmado por ciento ochenta intelectuales y profesionales de todos los países, de todas las tendencias y de todas las nacionalidades, esta segunda campaña conoció un éxito importante. El principal efecto de la ofensiva antifreudiana de Adolf Grünbaum y Peter Swales consistió en marginar a los otros firmantes y favorecer el academicismo. Inaugurada en octubre de 1998, la exposición de la Biblioteca del Congreso presentaba, en efecto, a un Freud cuyas teorías ya no tenían importancia alguna en relación con la ciencia y la verdad: «No me importa que las ideas de Freud sean verdaderas o falsas», decía Michael Roth. «Lo importante es que han impregnado toda nuestra cultura y nuestra manera de comprender el mundo a través del cine, el arte, los cómics o la tele.»
Pese al éxito en Francia de dos best sellers, _El libro negro del psicoanálisis_ , obra colectiva que reúne las colaboraciones de unos cuarenta autores, y _El crepúsculo de un ídolo_ , un panfleto de Michel Onfray, las tesis de los adeptos del _Freud bashing_ no echaron raíces en el medio universitario francés, ni siquiera con el auge de las terapias cognitivas. Más aún, fueron rechazadas después de haber hecho las delicias de cierta prensa escrita y audiovisual ávida de sensaciones freudianas.
No obstante, dichas tesis contribuyeron a instalar en la opinión una imagen turbia de la vida y la obra de Freud, una imagen fundada, llegado el caso, en los rumores más delirantes que, sin embargo, se exponían como verdades establecidas. De ahí mi decisión de emprender este trabajo biográfico e histórico, en un momento en que por fin los SFA se abrían a los investigadores, en tanto que, por la vía de internet, se multiplicaban publicaciones y debates de suma riqueza.
En abril de 2014, algunos días antes de mi partida a Washington, fui al crematorio de Golders Green, Londres, lugar de inhumación laico situado frente al cementerio judío del mismo nombre, y que recibe a creyentes, no creyentes, escritores, comunistas, actores, librepensadores. Me demoré frente a los mausoleos, las estatuas y las criptas de estilo gótico, llenas de placas, inscripciones, urnas y objetos diversos. Sabía que unos meses antes, durante la noche de Año Nuevo, unos vándalos habían roto el cristal detrás del cual estaba la crátera griega con las cenizas de Sigmund Freud y Martha Bernays. Con la intención, sin duda, de sustraer objetos de valor, los ladrones habían hecho caer la urna de su gran pie de mármol, dejando así al visitante el triste espectáculo de un monumento decapitado. Presas del pánico, habían huido sin llevarse nada.
Al observar ese lugar maltratado, cubierto de ofrendas y recuerdos, donde descansan en pequeñas cajas las cenizas de los miembros de la familia Freud y algunos amigos cercanos, y escuchar a Eric Willis, el responsable del crematorio, contarme la larga historia de ese sabio que había ido a morir a Londres, no pude dejar de pensar que esta profanación —o, mejor, esta «decapitación»— señalaba en verdad que Freud, setenta y cinco años después de su muerte, seguía perturbando la conciencia occidental con sus mitos, sus dinastías principescas, su travesía de los sueños, sus historias de hordas salvajes, de Gradiva en marcha, de un buitre encontrado en Leonardo, de un asesinato del padre y de un Moisés que pierde las Tablas de la Ley.
Lo imaginaba blandiendo su bastón contra los antisemitas, poniéndose su mejor camisa para visitar la Acrópolis, descubriendo Roma como un amante loco de felicidad, fustigando a los imbéciles, hablando sin notas frente a un público de norteamericanos atónitos, reinando en su morada inmemorial en medio de sus objetos, sus chow-chows pelirrojos, sus discípulos, sus mujeres, sus pacientes locos, y esperando a Hitler a pie firme sin conseguir pronunciar su nombre, y me dije que aún seguiría siendo, durante mucho tiempo, el más grande pensador de su tiempo y del nuestro.
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Agradecimientos
Doy las gracias a Anthony Ballenato, que ha realizado en internet numerosas investigaciones en inglés y me ha acompañado a Londres y la Biblioteca del Congreso de Washington.
A Olivier Mannoni, traductor de las obras de Freud, que me ilustró en muchas ocasiones. A Isabelle Mons, germanista y biógrafa de Lou Andreas-Salomé, por la ayuda prestada. Y también a Christian Sommer, que me ayudó a analizar un escrito de Martin Heidegger sobre Freud y el psicoanálisis.
A Lisa Appignanesi, Dany Nobus y todo el equipo del Freud Museum de Londres, que me brindaron un cálido recibimiento. A John Forrester, profesor de historia y filosofía de las ciencias de la Universidad de Cambridge, fino conocedor de la obra freudiana y de las relaciones entre Freud y Minna Bernays. A Julia Borossa, directora de programa en psicoanálisis de la Universidad de Middlesex. A Eric Willis, que me recibió en el crematorio de Golders Green, Londres.
A Inge Scholz-Strasser y Daniela Finzi por su acogida en el Freud Museum de Viena.
A Margaret McAleer, conservadora en jefe de la División de Manuscritos de la Biblioteca del Congreso, que me ayudó en mis investigaciones. Y a Anton O. Kris, director de los Sigmund Freud Archives (SFA), que me habló de sus recuerdos. También a François Delattre, embajador de Francia en Estados Unidos, que me recibió cálidamente. Estoy en deuda con Catherine Albertini, agregada cultural de la embajada de Francia en Estados Unidos, por su apoyo y su entusiasmo. No olvido la ayuda que me prestó Jean-Louis Desmeure.
A Maurizio Serra, diplomático y biógrafo de Italo Svevo, que me ayudó, a lo largo de un apasionante intercambio epistolar, a comprender con claridad las relaciones entre Edoardo Weiss, Giovacchino Forzano y Bruno Veneziani. A Albrecht Hirschmüller por sus valiosas indicaciones sobre la vida de Freud.
Doy las gracias asimismo a Carlo Bonomi por su conocimiento de las relaciones de Freud con la pediatría y por todo lo que me aportó en relación con la cuestión de los traumas infantiles. Guido Liebermann, historiador del psicoanálisis en Palestina, me dio testimonios decisivos sobre la vida de Max Eitingon. Debo mucho a Patrick Mahony y a los intercambios que mantenemos desde hace veinte años. Doy las gracias a Henri Rey-Flaud, que estuvo presente a lo largo de toda la redacción de este libro. No olvido mi deuda con Carl Schorske y Jacques Le Rider.
A Gilles Pecout, que dio cabida a mi seminario sobre la historia del psicoanálisis en el Departamento de Historia de la Escuela Normal Superior. Y a todos los fieles oyentes que han seguido ese seminario desde hace más de veinte años. A Thomas Piketty por su tasación de la fortuna de Freud. A Luc Fachetti por su paciencia y a Jean-Claude Baillieul por la minuciosidad de sus correcciones. No olvido el apoyo que me brinda desde hace tantos años André Gueslin en el Departamento de Historia de la Universidad de París VIIDiderot.
Para terminar, muchísimas gracias a Olivier Bétourné, que editó y corrigió este libro con talento y entusiasmo.
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Bibliografía
Para escribir este libro consulté numerosos archivos, cuya lista presento aquí. Recurrí a las diferentes ediciones de las obras completas de Freud en alemán e inglés, pero también a varias obras y manuales de referencia, indispensables para el conocimiento de la obra y la vida de Freud. La más vasta cronología de la vida de este establecida hasta el día de hoy está disponible en alemán; también la he consultado. Señalemos que las obras prepsicoanalíticas de Freud están en proceso de fijación.
Tratándose de Francia, me he inclinado por mencionar diferentes traducciones según el caso.
1. Algunas de las primeras traducciones realizadas para Gallimard, las Presses Universitaires de France y Payot por Samuel Jankélévitch, Yves Le Lay, Ignace Meyerson, Blanche Reverchon-Jouve, Marie Bonaparte y Anne Berman.
2. Las traducciones realizadas a continuación por Fernand Cambon, Cornélius Heim, Philippe Koeppel, Patrick Lacoste, Denis Messier, Marielène Weber y Rose-Marie Zeitlin bajo la dirección de Jean-Bertrand Pontalis (1924-2013) en Gallimard.
3. Las _Œuvres complètes de Freud. Psychanalyse_ ( _OC._ _P_ ), edición iniciada en 1988 y todavía no terminada, por un equipo compuesto por Jean Laplanche (1924-2012), Pierre Cotet, André Bourguignon (1920-1996), François Robert y una veintena de autores, en las Presses Universitaires de France. Los artífices de esta empresa, muy controvertida, pretenden volver a una «germanidad natural» del texto freudiano. Por eso se atribuyen la condición de «freudólogos», convencidos de que la lengua de Freud no es el alemán sino el «freudiano», es decir, un «lenguaje del alemán que no es el alemán sino una lengua inventada por Freud». Así traducida, la obra de Freud comporta numerosos neologismos, entre los cuales _souhait_ anhelo] o _désirance_ [deseancia, añoranza] en lugar de _désir_ [deseo, _animique_ [anímico] en lugar de _âme_ [alma] ( _Seele_ ) o de psique, _fantaisie_ [fantasía] en lugar de _fantasme_ [fantasma] ( _Fantasie_ ).
4. Las traducciones realizadas bajo la dirección de Jean-Pierre Lefebvre en las Éditions du Seuil, col. «Points Essais».
5. Las traducciones de Olivier Mannoni en Payot, col. «Petite Bibliothèque Payot».
6. Algunas otras traducciones.*
En esta bibliografía se hallarán asimismo las referencias de los volúmenes de correspondencia de Freud traducidos al francés.
1. FUENTES MANUSCRITAS
1. The Library of Congress (LoC), Washington D. C., Manuscript Division, Sigmund Freud Collection, The Papers of Sigmund Freud: proyectos, correspondencia ológrafa y dactilografiada de los escritos de Freud, papeles de familia, historiales de pacientes, documentos jurídicos y de sucesión, legajos militares y escolares, certificados, cuadernos, datos genealógicos, entrevistas realizadas por Kurt Eissler, testimonios, fotografías y dibujos, recortes periodísticos y otros impresos. Material para alimentar las numerosas facetas de la vida de Freud y el estudio de sus escritos: relaciones con la familia, los amigos, los colegas.
2. Archivos, obras y documentos del Freud Museum de Londres y el Freud Museum de Viena.
3. Archivos de Marie Bonaparte (fuente: Célia Bertin).
4. Archivos de Elisabeth Roudinesco (cartas, documentos, notas, seminarios).
5. Archivos de Henri F. Ellenberger, Sociedad Internacional de Historia de la Psiquiatría y el Psicoanálisis (SIHPP), biblioteca Henri-Ey, hospital Sainte-Anne.
2. FUENTES IMPRESAS
_Obras completas de Freud en alemán e inglés_
_Gesammelte Schriften_ ( _GS_ ), 12 volúmenes: Viena, 1924-1934.
_Gesammelte Werke_ ( _GW_ ), 18 volúmenes y uno complementario no numerado. Vols. 1-17: Londres, 1940-1952. Vol. 18: Frankfurt, 1968. Volumen complementario: Frankfurt, 1987. Toda la edición, desde 1960: Frankfurt, S. Fischer Verlag.
_Studienausgabe_ , 10 volúmenes y uno complementario no numerado: Frankfurt, S. Fischer Verlag, 1969-1975.
_The Standard Edition of the Complete Psychological Works of Sigmund Freud_ ( _SE_ ), 24 volúmenes: textos editados por James Strachey en colaboración con Anna Freud, Alix Strachey y Alan Tyson, Londres, The Hogarth Press and the Institute of Psycho-Analysis, 1953-1974.
_Obras completas de Freud en francés_
_Œuvres complètes de Freud. Psychanalyse_ ( _OC._ _P_ ), 1886-1939, 21 volúmenes (edición incompleta, faltan los vols. 1 y 21), París, Presses Universitaires de France, 1988-2014, con un glosario, un índice y un volumen de presentación: _Traduire Freud_ , de André Bourguignon, Pierre Cotet, Jean Laplanche y François Robert. El vol. 1, de próxima aparición, contiene artículos y conferencias sobre la histeria, las fobias, las neuropsicosis de defensa, J.-M. Charcot, H. Bernheim, la hipnosis, la sugestión y otros problemas clínicos. La mayoría de esos textos han aparecido traducidos en diversas revistas. El vol. 21, de próxima aparición, contiene un índice y un glosario.
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_Cronología de las principales obras y artículos_
1884-1887. _De la cocaïne_ , cinco artículos sobre la cocaína, edición de Robert Byck, traducción de E. Sznycer, Bruselas, Complexe, 1976; otra versión: _Un peu de cocaïne pour me délier la langue_ , traducción de M. Roffi, París, Max Milo, 2005. [Hay trad. cast.: _Escritos sobre la cocaína_ , traducción de E. Hegewicz, Barcelona, Anagrama, 1980.]
1891. _Contribution à la conception des aphasies: une étude critique_ , traducción de C. van Reeth, París, Presses Universitaires de France, 1983; otra versión: _Pour concevoir les aphasies: une étude critique_ , traducción de F. Cambon, París, EPEL, 2010. [Hay trad. cast.: _La afasia_ , traducción de R. Alcalde, Buenos Aires, Nueva Visión, 1973.]
1893. «Charcot», traducción de J. Altounian, A. Bourguignon y A. Rauzy, en _Résultats, idées, problèmes_ , vol. 1, París, Presses Universitaires de France, 1984. [Hay trad. cast.: «Charcot», en _Obras completas_ [en lo sucesivo _OC_ ], 24 vols., traducción de J. L. Etcheverry, Buenos Aires, Amorrortu, 1979-1985, vol. 3, 1981.]
1895. _Études sur l'hystérie_ , traducción de A. Berman, prefacio de M. Bonaparte, París, Presses Universitaires de France, 1967; otra versión con el mismo título, traducción de J. Altounian, P. Cotet, P. Haller, C. Jouanlanne, F. Kahn, R. Lainé, M.-T. Schmidt, A. Rauzy y F. Robert, en _OC.P_ , vol. 2, 2009. [Hay trad. cast.: _Estudios sobre la histeria_ , en _OC_ , vol. 2, 1978.]
«Deux comptes rendus contemporains sur la conférence "De l'hystérie"», traducción de F. Kahn y F. Robert, en _OC.P_ , vol. 2, 2009. [Hay trad. cast.: «Sobre la histeria», traducción de F. G. Rodríguez y M. S. Vallejo, _Affectio Societatis_ (Antioquía, Colombia), 11(20), enero-junio de 2014.]
«Obsessions et phobies» (publicado en francés), en _OC.P_ , vol. 3, 1989. [Hay trad. cast.: «Obsesiones y fobias. Su mecanismo psíquico y su etiología», en _OC_ , vol. 3, 1981.]
1896. «L'hérédité et l'étiologie des névroses» (publicado en francés), en _OC.P_ , vol. 3, 1989. [Hay trad. cast.: «La herencia y la etiología de las neurosis», en _OC_ , vol. 3, 1981.]
«L'étiologie de l'hystérie», traducción de J. Bissery y J. Laplanche, en _Névrose, psychose et perversion_ , París, Presses Universitaires de France, 1973; otra versión: «Sur l'étiologie de l'hystérie», traducción de J. Altounian y A. Bourguignon, en _OC.P_ , vol. 3, 1989. [Hay trad. cast.: «La etiología de la histeria», en _OC_ , vol. 3, 1981.]
1899. «Sur les souvenirs-écrans», traducción de D. Berger, P. Bruno, D. Guérineau y F. Oppenot, en _Névrose, psychose et perversion_ , París, Presses Universitaires de France, 1973; otra versión: «Des souvenirs-couverture», traducción de J. Doron, en _OC.P_ , vol. 3, 1989; y una tercera: «Sur les souvenirs-écrans», traducción de D. Messier, en _Huit études sur la mémoire et ses troubles_ , París, Gallimard, 2010. [Hay trad. cast.: «Sobre los recuerdos encubridores», en _OC_ , vol. 3, 1981.]
1900. _L'Interprétation des rêves_ , traducción de I. Meyerson, París, Presses Universitaires de France, 1926; otra versión: _L'Interprétation du rêve_ , traducción de J. Altounian, P. Cotet, R. Lainé, A. Rauzy y F. Robert, en _OC.P_ , vol. 4, 2003; y una tercera con el mismo título, traducción de J.-P. Lefebvre, París, Seuil, 2010. [Hay trad. cast.: _La interpretación de los sueños_ , en _OC_ , vols. 4 y 5, 1979.]
1901. _Psychopathologie de la vie quotidienne_ , traducción de S. Jankélévitch, París, Payot, 1969; otra versión: _La Psychopathologie de la vie quotidienne_ , traducción de D. Messier, París, Gallimard, 1997; y una tercera, _Sur la psychopathologie de la vie quotidienne_ , traducción de J. Altounian y P. Cotet, en _OC.P_ , vol. 5, 2012. [Hay trad. cast.: _Psicopatología de la vida cotidiana (Sobre el olvido, los deslices en el habla, el trastrocar las cosas confundido, la superstición y el error_ , en _OC_ , vol. 6, 1979.]
_Le Rêve et son interprétation_ , traducción de H. Legros, París, Gallimard, 1925; otra versión: _Sur le rêve_ , traducción de C. Heim, París, Gallimard, 1988; una tercera con el mismo título, traducción de J.-P. Lefebvre, París, Seuil, 2011; y una cuarta: _Du rêve_ , traducción de P. Cotet y A. Rauzy, en _OC.P_ , vol. 5, 2012. [Hay trad. cast.: _Sobre el sueño_ , en _OC_ , vol. 5, 1979.]
1903. «La méthode psychanalytique de Freud», traducción de A. Berman, en _La Technique psychanalytique_ , París, Presses Universitaires de France, 1953; otra versión con el mismo título, traducción de J. Altounian, P. Cotet, J. Laplanche y F. Robert, en _OC.P_ , vol. 6, 2006. [Hay trad. cast.: «El método psicoanalítico de Freud», en _OC_ , vol. 7, 1978.]
1904. «De la psychothérapie», traducción de A. Berman, en _La Technique psychanalytique_ , París, Presses Universitaires de France, 1953; otra versión con el mismo título, traducción de P. Cotet y F. Lainé, en _OC.P_ , vol. 6, 2006. [Hay trad. cast.: «Sobre psicoterapia», en _OC_ , vol. 7, 1978.]
1905. «Fragment d'une analyse d'hystérie» (Dora), traducción de M. Bonaparte y R. M. Loewenstein, en _Cinq psychanalyses_ , París, Presses Universitaires de France, 1966; otra versión con el mismo título, traducción de F. Kahn y F. Robert, en _OC.P_ , vol. 6, 2006. [Hay trad. cast.: _Fragmento de análisis de un caso de histeria_ , en _OC_ , vol. 7, 1978.]
_Le Mot d'esprit et ses rapports avec l'inconscient_ , traducción de M. Bonaparte y el doctor M. Nathan, París, Gallimard, 1930; otra versión: _Le Mot d'esprit et sa relation à l'inconscient_ , traducción de D. Messier, París, Gallimard, 1988; y una tercera: _Le Trait d'esprit et sa relation à l'inconscient_ , traducción de J. Altounian, P. Haller, D. Hartmann, C. Jouanlanne, F. Kahn, R. Lainé, A. Rauzy y F. Robert, en _OC.P_ , vol. 7, 2014. [Hay trad. cast.: _El chiste y su relación con lo inconciente_ , en _OC_ , vol. 8, 1979.]
_Trois essais sur la théorie de la sexualité_ , traducción de B. Reverchon-Jouve, París, Gallimard, 1923; otra versión: _Trois essais sur la théorie sexuelle_ , traducción de P. Koeppel, París, Gallimard, 1987; una tercera con el mismo título, traducción de P. Cotet y F. Rexand-Galais, en _OC.P_ , vol. 6, 2006; una cuarta con el mismo título, traducción de M. Géraud, París, Seuil, 2012; y una quinta con el mismo título, traducción de C. Cohen-Skalli, O. Mannoni y A. Weill, París, Payot, 2014. [Hay trad. cast.: _Tres ensayos de teoría sexual_ , en _OC_ , vol. 7, 1978.]
1906. «L'établissement des faits par voie diagnostique et la psychanalyse», traducción de A. Rauzy, en _L'Inquiétante étrangeté et autres essais_ , París, Gallimard, 1985; otra versión: «Diagnostic de l'état des faits et psychanalyse», traducción de A. Rauzy, en _OC.P_ , vol. 8, 2007; y una tercera con el mismo título, traducción de O. Mannoni, en _L'Inquiétant familier_ , París, Payot, 2011. [Hay trad. cast.: «La indagatoria forense y el psicoanálisis», en _OC_ , vol. 9, 1979.]
1907. _Délire et rêves dans un ouvrage littéraire: la «Gradiva» de Jensen_ , traducción de M. Bonaparte, París, Gallimard, 1931; otra versión: _Le Délire et les rêves dans la «Gradiva» de W. Jensen_ , traducción de P. Arhex y R.-M. Zeitlin, París, Gallimard, 1991; una tercera con el mismo título, traducción de J. Altounian, P. Haller, D. Hartmann y C. Jouanlanne, en _OC.P_ , vol. 8, 2007; y una cuarta con el mismo título, traducción de D. Tassel, prefacio de H. Rey-Flaud, París, Seuil, 2013. [Hay trad. cast.: _El delirio y los sueños en la «Gradiva» de W. Jensen_ , en _OC_ , vol. 9, 1979.]
«Les explications sexuelles données aux enfants: lettre ouverte au Dr. M. Fürst», traducción de D. Berger, en _La Vie sexuelle_ , París, Presses Universitaires de France, 1969; otra versión: «Sur les éclaircissements sexuels apportés aux enfants: lettre ouverte au Dr. M. Fürst», traducción de P. Cotet y F. Rexand-Galais, en _OC.P_ , vol. 8, 2007. [Hay trad. cast.: «El esclarecimiento sexual del niño (Carta abierta al doctor M. Fürst)», en _OC_ , vol. 9, 1979.]
«Actes obsédants et exercices religieux», traducción de M. Bonaparte, en _L'Avenir d'une illusion_ , París, Presses Universitaires de France, 1971; otra versión: «Actions de contrainte et exercices religieux», traducción de F. Kahn y F. Robert, en _OC.P_ , vol. 8, 2007; y una tercera: «Actes compulsionnels et exercices religieux», traducción de D. Messier, en _Religion_ , París, Gallimard, 2012. [Hay trad. cast.: «Acciones obsesivas y prácticas religiosas», en _OC_ , vol. 9, 1979.]
1908. «Le créateur littéraire et la fantaisie», traducción de B. Féron, en _L'Inquiétante étrangeté et autres essais_ , París, Gallimard, 1985; otra versión: «Le poète et l'activité de fantaisie», traducción de P. Cotet, R. Lainé y M.-T. Schmidt, en _OC.P_ , vol. 8. 2007; y una tercera con el mismo título, traducción de O. Mannoni, en _L'Inquiétant familier_ , París, Payot, 2011. [Hay trad. cast.: «El creador literario y el fantaseo», en _OC_ , vol. 9, 1979.]
«La morale sexuelle "civilisée" et la maladie nerveuse des temps modernes», traducción de D. Berger, en _La Vie sexuelle_ , París, Presses Universitaires de France, 1969; otra versión: «La morale sexuelle "culturelle"», traducción de P. Cotet y R. Lainé, en _OC.P_ , vol. 8, 2007. [Hay trad. cast.: «La moral sexual "cultural" y la nerviosidad moderna», en _OC_ , vol. 9, 1979.]
«Les theóries sexuelles infantiles», traducción de J.-B. Pontalis, en _La Vie sexuelle_ , París, Presses Universitaires de France, 1969; otra versión con el mismo título, traducción de R. Lainé y A. Rauzy, en _OC.P_ , vol. 8. 2007. [Hay trad. cast.: «Sobre las teorías sexuales infantiles», en _OC_ , vol. 9, 1979.]
«Le roman familial des névrosés», traducción de J. Laplanche, en _Névrose, psychose et perversion_ , París, Presses Universitaires de France, 1973; la misma versión en _OC.P_ , vol. 8, 2007. [Hay trad. cast.: «La novela familiar de los neuróticos», en _OC_ , vol. 9, 1979.]
1909. «Analyse d'une phobie chez un petit garçon de cinq ans» (el pequeño Hans), traducción de M. Bonaparte y R. M. Loewenstein, en _Cinq psychanalyses_ , París, Denoël et Steele, 1935; otra versión con el mismo título, traducción de R. Lainé y J. Stute-Cadiot, en _OC.P_ , vol. 9, 1998. [Hay trad. cast.: _Análisis de la fobia de un niño de cinco años_ , en _OC_ , vol. 10, 1980.]
«Remarques sur un cas de névrose obsessionnelle» (el Hombre de las Ratas), traducción de M. Bonaparte y R. M. Loewenstein, en _Cinq psychanalyses_ , París, Denoël et Steele, 1935; otra versión: «Remarques sur un cas de névrose de contrainte», traducción de P. Cotet y F. Robert, en _OC.P_ , vol. 9, 1998. [Hay trad. cast.: _A propósito de un caso de neurosis obsesiva_ , en _OC_ , vol. 10, 1980.]
1910. _Cinq leçons sur la psychanalyse_ , traducción de Y. Lelay, reeditado con el título de _La Psychanalyse_ , París, Payot, 1923; otra versión: _Sur la psychanalyse: cinq conférences_ , traducción de C. Heim, París, Gallimard, 1991; una tercera: _De la psychanalyse_ , traducción de R. Lainé y J. Stute-Cadiot, en _OC.P_ , vol. 10, 1993; y una cuarta: _Cinq conférences sur la psychanalyse_ , traducción de B. Lortholary, París, Seuil, 2012. [Hay trad. cast.: _Cinco conferencias sobre psicoanálisis_ , en _OC_ , vol. 11, 1979.]
«Les perspectives d'avenir de la thérapeutique analytique», traducción de A. Berman, en _La Technique psychanalytique_ , París, Presses Universitaires de France, 1953; otra versión con el mismo título, traducción de F. Cambon, París, Gallimard, 1985; y una tercera: «Les chances d'avenir de la thérapie psychanalytique», traducción de R. Lainé y J. Stute-Cadiot, en _OC.P_ , vol. 10, 1993. [Hay trad. cast.: «Las perspectivas futuras de la terapia psicoanalítica», en _OC_ , vol. 11, 1979.]
«À propos de la psychanalyse dite "sauvage"», traducción de A. Berman, en _La Technique psychanalytique_ , París, Presses Universitaires de France, 1953; otra versión: «De la psychanalyse "sauvage"», traducción de J. Altounian, A. Balseinte y E. Wolff, en _OC.P_ , vol. 10, 1993. [Hay trad. cast.: «Sobre el psicoanálisis "silvestre"», en _OC_ , vol. 11, 1979.]
«Des sens opposés dans les mots primitifs», traducción de M. Bonaparte y E. Marty, en _L'Inquiétante étrangeté et autres essais_ , París, Gallimard, 1933; otra versión con el mismo título, traducción de F. Cambon, París, Gallimard, 1985; y una tercera: «Du sens opposé des mots originaires», traducción de J. Altounian, A. Bourguignon y P. Cotet, en _OC.P_ , vol. 10, 1993. [Hay trad. cast.: «Sobre el sentido antitético de las palabras primitivas», en _OC_ , vol. 11, 1979.]
_Un souvenir d'enfance de Léonard de Vinci_ , traducción de M. Bonaparte, París, Gallimard, 1927; otra versión con el mismo título, traducción de J. Altounian, A. Bourguignon, P. Cotet y R. Lainé, prefacio de J.-B. Pontalis, París, Gallimard, 1987; una tercera con el mismo título, traducción de los anteriores y A. Rauzy, en _OC.P_ , vol. 10, 1993; y una cuarta con el mismo título, traducción de D. Tassel, París, Seuil, 2011. [Hay trad. cast.: _Un recuerdo infantil de Leonardo da Vinci_ , en _OC_ , vol. 11, 1979.]
1911. «Le maniement de l'interprétation du rêve en psychanalyse», traducción de A. Berman, en _La Technique psychanalytique_ , París, Presses Universitaires de France, 1953; otra versión con el mismo título, traducción de P. Cotet, R. Lainé, A. Rauzy, F. Robert y J. Stute-Cadiot, en _OC.P_ , vol. 11, 1998. [Hay trad. cast.: «El uso de la interpretación de los sueños en el psicoanálisis», en _OC_ , vol. 12, 1980.]
«Remarques psychanalytiques sur l'autobiographie d'un cas de paranoïa» (el presidente Schreber), traducción de M. Bonaparte y R. M. Loewenstein, en _Cinq psychanalyses_ , París, Denoël et Steele, 1935; otra versión: «Remarques psychanalytiques sur un caso de paranoïa ( _Dementia paranoides_ ) décrit sous forme autobiographique», traducción de P. Cotet y R. Lainé, en _OC.P_ , vol. 10, 1993; y una tercera: _Le Président Schreber: un cas de paranoïa_ , traducción de O. Mannoni, París, Payot, 2011. [Hay trad. cast.: _Puntualizaciones psicoanalíticas sobre un caso de paranoia (_ Dementia paranoides _) descrito autobiográficamente_ , en _OC_ , vol. 12, 1980.]
«Grande est la Diane des Éphésiens», traducción de J. Altounian, A. Bourguignon, P. Cotet y A. Rauzy, en _Résultats, idées, problèmes_ , vol. 1, París, Presses Universitaires de France, 1984; otra versión con el mismo título y los mismos traductores, en _OC.P_ , vol. 11, 1998; y una tercera con el mismo título, traducción de D. Messier, en _Religion_ , París, Gallimard, 2012. [Hay trad. cast.: «¡Grande es Diana Efesia!», en _OC_ , vol. 12, 1980.]
1912. «Conseils au médecin dans le traitement psychanalytique», traducción de A. Berman, en _La Technique psychanalytique_ , París, Presses Universitaires de France, 1953; otra versión con el mismo título, traducción de J. Altounian, F. Baillet, A. Bourguignon, E. Carstanjen, P. Cotet, R. Lainé, C. von Petersdorff, A. Rauzy, F. Robert y J. Stute-Cadiot, en _OC.P_ , vol. 11, 1998. [Hay trad. cast.: «Consejos al médico sobre el tratamiento psicoanalítico», en _OC_ , vol. 12, 1980.]
«La dynamique du transfert», traducción de A. Berman, en _La_ ___Technique psychanalytique_ , París, Presses Universitaires de France, 1953; otra versión: «Sur la dynamique du transfert», traducción de A. Rauzy, en _OC.P_ , vol. 11, 1998. [Hay trad. cast.: «Sobre la dinámica de la transferencia», en _OC_ , vol. 12, 1980.]
«Contributions à la psychologie de la vie amoureuse», tres textos (1910-1918): 1) «Un type particulier de choix d'objet chez l'homme»; 2) «Sur le plus général des rabaissements de la vie amoureuse», y 3) «Le tabou de la virginité», traducción de J. Laplanche, en _La Vie sexuelle_ , París, Presses Universitaires de France, 1969; otra versión: «D'un type particulier de choix d'objet chez l'homme», «Du rabaissement généralisé de la vie amoureuse» y «Le tabou de la virginité», traducción de J. Altounian, F. Baillet, A. Bourguignon, P. Cotet y A. Rauzy, en _OC.P_ , vols. 10, 11 y 15, 1993, 1998 y 1996, respectivamente. [Hay trad. cast.: «Sobre un tipo particular de elección de objeto en el hombre (Contribuciones a la psicología del amor, I)», «Sobre la más generalizada degradación de la vida amorosa (Contribuciones a la psicología del amor, II)» y «El tabú de la virginidad (Contribuciones a la psicología del amor, III)», en _OC_ , vol. 11, 1979.]
_Totem et tabou_ , traducción de S. Jankélévitch, París, Payot, 1923; otra versión con el mismo título, traducción de M. Weber, París, Gallimard, 1993; una tercera con el mismo título, traducción de J. Altounian, F. Baillet, A. Bourguignon, E. Carstanjen, P. Cotet y A. Rauzy, en _OC.P_ , vol. 11, 1998; una cuarta con el mismo título, traducción de M. Crépon y M. de Launay, en _Anthropologie de la guerre_ , París, Fayard, 2010; y una quinta con el mismo título, traducción de D. Tassel, París, Seuil, 2011. [Hay trad. cast.: _Tótem y tabú: algunas concordancias en la vida anímica de los salvajes y de los neuróticos_ , en _OC_ , vol. 13, 1980.]
1913. «Le thème des trois coffrets», traducción de E. Marty y M. Bonaparte, en _Essais de psychanalyse appliquée_ , París, Gallimard, 1952; otra versión: «Le motif du choix des coffrets», traducción de B. Féron, en _L'Inquiétante étrangeté et autres essais_ , París, Gallimard, 1985; y una tercera con el mismo título, traducción de P. Cotet y R. Lainé, en _OC.P_ , vol. 12, 2005. [Hay trad. cast.: «El motivo de la elección del cofre», en _OC_ , vol. 12, 1980.]
«Le début du traitement», traducción de A. Berman, en _La Technique psychanalytique_ , París, Presses Universitaires de France, 1981; otra versión: «Sur l'engagement du traitement», traducción de J. Altounian, P. Haller y D. Hartmann, en _OC.P_ , vol. 12, 2005. [Hay trad. cast.: «Sobre la iniciación del tratamiento (Nuevos consejos sobre la técnica del psicoanálisis, I)», en _OC_ , vol. 12, 1980.]
1914. «Le _Moïse_ de Michel Ange», traducción de P. Cotet y R. Lainé, en _L'Inquiétante étrangeté et autres essais_ , París, Gallimard, 1985; otra versión con el mismo título, traducción de J. Altounian, A. Bourguignon, P. Cotet, P. Haller, D. Hartmann, R. Lainé, J. Laplanche, A. Rauzy y F. Robert, en _OC.P_ , vol. 12, 2005; y una tercera con el mismo título, traducción de O. Mannoni, en _L'Inquiétant familier_ , París, Payot, 2011. [Hay trad. cast.: «El _Moisés_ de Miguel Ángel», en _OC_ , vol. 13, 1980.]
«Remémoration, répétition et perlaboration», traducción de A. Berman, en _De la technique psychanalytique_ , París, Presses Universitaires de France, 1981; otra versión con el mismo título, traducción de J. Altounian, A. Bourguignon, P. Cotet, P. Haller, D. Hartmann, R. Lainé, J. Laplanche, A. Rauzy y F. Robert, en _OC.P_ , vol. 12, 2005. [Hay trad. cast.: «Recordar, repetir y reelaborar (Nuevos consejos sobre la técnica del psicoanálisis, II)», en _OC_ , vol. 12, 1980.]
«Observation sur l'amour de transfert», traducción de A. Berman, en _La Technique psychanalytique_ , París, Presses Universitaires de France, 1953; otra versión: «Remarques sur l'amour de transfert», traducción de J. Altounian, A. Bourguignon, P. Cotet, P. Haller, D. Hartmann, R. Lainé, J. Laplanche, A. Rauzy y F. Robert, en _OC.P_ , vol. 12, 2005. [Hay trad. cast.: «Puntualizaciones sobre el amor de transferencia (Nuevos consejos sobre la técnica del psicoanálisis, III)», en _OC_ , vol. 12, 1980.]
«Pour introduire le narcissisme», traducción de J. Laplanche, en _La Vie sexuelle_ , París, Presses Universitaires de France, 1969; otra versión con el mismo título y el mismo traductor, en _OC.P_ , vol. 12, 2005; y una tercera con el mismo título, traducción de O. Mannoni, París, Payot, 2012. [Hay trad. cast.: «Introducción del narcisismo», en _OC_ , vol. 14, 1979.]
_Sur l'histoire du mouvement psychanalytique_ , traducción de C. Heim, París, Gallimard, 1991; otra versión: _Contribution à l'histoire du mouvement psychanalytique_ , traducción de P. Cotet y R. Lainé, en _OC.P_ , vol. 12, 2005. [Hay trad. cast.: _Contribución a la historia del movimiento psicoanalítico_ , en _OC_ , vol. 14, 1979.]
«De la fausse reconnaissance ("déjà raconté") au cours du traitement psychanalytique», traducción de A. Berman, en _La Technique psychanalytique_ , París, Presses Universitaires de France, 1981; otra versión: «De la fausse reconnaissance ("déjà raconté") pendant le travail psychanalytique», traducción de P. Cotet y R. Lainé, en _OC.P_ , vol. 12, 2005. [Hay trad. cast.: «Acerca del _fausse reconnaissance_ ( _"déjà raconté"_ ) en el curso del trabajo psicoanalítico», en _OC_ , vol. 13, 1980.]
«Extrait de l'histoire d'une névrose infantile» (el Hombre de los Lobos), escrito en 1914 y publicado en 1918, traducción de M. Bonaparte y R. M. Loewenstein, en _Cinq psychanalyses_ , París, Presses Universitaires de France, 1954; otra versión: «À partir d'une névrose infantile», traducción de J. Altounian y P. Cotet, en _OC.P_ , vol. 13, 1988. [Hay trad. cast.: _De la historia de una neurosis infantil_ , en _OC_ , vol. 17, 1979.]
1915. «Considérations actuelles sur la guerre et sur la mort», traducción de S. Jankélévitch, en _Essais de psychanalyse_ , París, Payot, 1927; otra versión con el mismo título, traducción de A. Bourguignon, A. Cherki y P. Cotet, París, Payot, 1981; una tercera: «Actuelles sur la guerre et la mort», traducción de J. Altounian, A. Balseinte, A. Bourguignon, A. Cherki, P. Cotet, J.-G. Delarbre, D. Hartmann, J.-R. Ladmiral, J. Laplanche, J.-L. Martin, A. Rauzy y P. Soulez, en _OC.P_ , vol. 13, 1988; y una cuarta: «Considération actuelle sur la guerre et la mort», traducción de M. Crépon y M. de Launay, en _Anthropologie de la guerre_ , París, Fayard, 2012. [Hay trad. cast.: «De guerra y muerte. Temas de actualidad», en _OC_ , vol. 14, 1979.]
«Un cas de paranoïa en contradiction avec la théorie psychanalytique», traducción de D. Guérineau, en _Névrose, psychose et perversion_ , París, Presses Universitaires de France, 1973; otra versión: «Communication d'un cas de paranoïa contredisant la théorie psychanalytique», traducción de J. Altounian, A. Bourguignon, P. Cotet, J.-G. Delarbre y D. Hartmann, en _OC.P_ , vol. 13, 1988. [Hay trad. cast.: «Un caso de paranoia que contradice la teoría psicoanalítica», en _OC_ , vol. 14, 1979.]
1915-1917. Conjunto de textos sobre la metapsicología: «Pulsions et destin des pulsions», «Le refoulement», «L'inconscient», «Complément métapsychologique à la doctrine du rêve» y «Deuil et mélancolie», traducción de A. Berman y M. Bonaparte, en _Métapsychologie_ , París, Gallimard, 1952; otra versión con los mismos títulos, traducción de J. Laplanche, J.-B. Pontalis, J.-P. Briand, J.-P. Grossein y M. Tort, en _Métapsychologie_ , París, Gallimard, 1968; y una tercera con los mismos títulos salvo el primero, «Pulsions et destins de pulsions», traducción de J. Altounian, A. Balseinte, A. Bourguignon, A. Cherki, P. Cotet, J.-G. Delarbre, D. Hartmann, J.-R. Ladmiral, J. Laplanche, J.-L. Martin, A. Rauzy y P. Soulez, en _OC.P_ , vol. 13, 1988. [Hay trad. cast.: «Pulsiones y destinos de pulsión», «La represión», «Lo inconsciente», «Complemento metapsicológico a la doctrina de los sueños» y «Duelo y melancolía», en _OC_ , vol. 14, 1979.]
«Pulsion et destins des pulsions», traducción de O. Mannoni, París, Payot, 2012.
_Vue d'ensemble des névroses de transfert: un essai métapsychologique_ , traducción de P. Lacoste, París, Gallimard, 1986; otra versión con el mismo título, traducción de J. Laplanche, en _OC.P_ , vol. 13, 1988. [Hay trad. cast.: _Sinopsis de las neurosis de transferencia: ensayo de metapsicología_ , traducción de A. Ackermann Pilári y A. Vicens, Barcelona, Ariel, 1989.]
1916-1917. «Fugitivité», traducción de M. Bonaparte, _Revue française de psychanalyse_ , 20(3), 1956; otra versión: «Passagèreté», traducción de J. Altounian, A. Bourguignon, P. Cotet y A. Rauzay, en _OC.P_ , vol. 13, 1988; y una tercera: «Éphémère destinée», traducción de D. Messier, en _Huit études sur la mémoire et ses troubles_ , París, Gallimard, 2010. [Hay trad. cast.: «La transitoriedad», en _OC_ , vol. 14, 1979.]
_Introduction à la psychanalyse_ , traducción de S. Jankélévitch, París, Payot, 1922; otra versión: _Conférences d'introduction à la psychanalyse_ , traducción de F. Cambon, París, Gallimard, 1999; y una tercera: _Leçons d'introduction à la psychanalyse_ , traducción de A. Bourguignon, J.-G. Delarbre, D. Hartmann y F. Robert, en _OC.P_ , vol. 14, 2000 (veintiocho conferencias). [Hay trad. cast.: _Conferencias de introducción al psicoanálisis_ , en _OC_ , vols. 15 y 16, 1978.]
«Parallèle mythologique à une représentation obsessionnelle plastique», traducción de B. Ferron, en _L'Inquiétante étrangeté et autres essais_ , París, Gallimard, 1985; otra versión: «Parallèle mythologique avec une représentation de contrainte d'ordre plastique», traducción de J. Altounian, A. Bourguignon, P. Cotet, J.-G. Delarbre, J. Doron, R. Doron, J. Dupont, D. Hartmann, R. Lainé, J. Laplanche, C. von Petersdorff, A. Rauzy, F. Robert, J. Stute-Cadiot, C. Vincent y A. Zäh-Gratiaux, en _OC.P_ , vol. 15, 2002. [Hay trad. cast.: «Paralelo mitológico de una representación obsesiva plástica», en _OC_ , vol. 14, 1979.]
1917. «Une difficulté de la psychanalyse», traducción de M. Bonaparte y E. Marty, en _Essais de psychanalyse appliquée_ , París, Gallimard, 1933; otra versión con el mismo título, traducción de B. Féron, en _L'Inquiétante étrangeté et autres essais_ , París, Gallimard, 1985; y una tercera con el mismo título, traducción de J. Altounian, A. Bourguignon, P. Cotet y A. Rauzy, en _OC.P_ , vol. 15, 1996. [Hay trad. cast.: «Una dificultad del psicoanálisis», en _OC_ , vol. 17, 1979.]
«Sur les transpositions des pulsions, plus particulierèment dans l'érotisme anal», traducción de J. Laplanche, en _La Vie sexuelle_ , París, Presses Universitaires de France, 1969; otra versión: «Des transpositions pulsionnelles, en particulier celles de l'érotisme anal», traducción de J. Altounian, A. Bourguignon, P. Cotet y J. Stute-Cadiot, en _OC.P_ , vol. 15, 1996. [Hay trad. cast.: «Sobre las trasposiciones de la pulsión, en particular del erotismo anal», en _OC_ , vol. 17, 1979.]
«Un souvenir d'enfance en _Fiction et vérité_ de Goethe», traducción de M. Bonaparte y E. Marty, en _Essais de psychanalyse appliquée_ , París, Gallimard, 1933; otra versión: «Un souvenir d'enfance de _Poésie et vérité_ de Goethe», traducción de B. Féron, en _L'Inquiétante étrangeté et autres essais_ , París, Gallimard, 1985; y una tercera con el mismo título, traducción de J. Altounian, A. Bourguignon, P. Cotet y R. Lainé, en _OC.P_ , vol. 15, 1996. [Hay trad. cast.: «Un recuerdo de infancia en _Poesía y verdad_ », en _OC_ , vol. 17, 1979.]
1919. «Les voies nouvelles de la thérapeutique psychanalytique», traducción de A. Berman, en _La Technique psychanalytique_ , París, Presses Universitaires de France, 1981; otra versión: «Les voies de la thérapeutique psychanalytique», traducción de J. Altounian y P. Cotet, en _OP.C_ , vol. 15, 1996. [Hay trad. cast.: «Nuevos caminos de la terapia psicoanalítica», en _OC_ , vol. 17, 1979.]
«Doit-on enseigner la psychanalyse à l'Université?», traducción de J. Dor, en _Résultats, idées, problèmes_ , vol. 1, París, Presses Universitaires de France, 1984; otra versión: «Faut-il enseigner la psychanalyse à l'Université?», traducción de J. Dupont, en _OC.P_ , vol. 15, 1996. [Hay trad. cast.: «¿Debe enseñarse el psicoanálisis en la universidad?», en _OC_ , vol. 17, 1979.]
«On bat un enfant. Contribution à l'étude de la genèse des perversions sexuelles», traducción de H. Hoesli, _Revue française de psychanalyse_ , 6(3-4), 1933; otra versión: «Un enfant est battu. Contribution à la connaissance de la genèse des perversions sexuelles», traducción de D. Guérineau, en _Névrose, psychose et perversion_ , París, Presses Universitaires de France, 1973; y una tercera con el mismo título, traducción de J. Altounian y P. Cotet, en _OC.P_ , vol. 15, 1996. [Hay trad. cast.: «"Pegan a niño." Contribución al conocimiento de la génesis de las perversiones sexuales», en _OC_ , vol. 17, 1979.]
«L'inquiétante étrangeté», traducción de M. Bonaparte y E. Marty, en _Essais de psychanalyse appliquée_ , París, Gallimard, 1952; otra versión con el mismo título, traducción de B. Ferron, en _L'Inquiétante étrangeté et autres essais_ , París, Gallimard, 1985; una tercera: «L'inquiétant», traducción de J. Altounian, A. Bourguignon, P. Cotet y J. Laplanche, en _OC.P_ , vol. 15, 1996; y una cuarta, _L'Inquiétant familier_ , traducción de O. Mannoni, París, Payot, 2011. [Hay trad. cast.: «Lo ominoso», en _OC_ , vol. 17, 1979.]
«Introduction à _La Psychanalyse des névroses de guerre_ », traducción de J. Altounian, en _Résultats, idées, problèmes_ , vol. 1, París, Presses Universitaires de France, 1984; otra versión: «Introduction a _Sur la psychanalyse des névroses de guerre_ », traducción de A. Bourguignon y C. von Petersdorff, en _OC.P_ , vol. 15, 1996; y una tercera: «De la psychanalyse des névroses de guerre», traducción de O. Mannoni, en _Sur les névroses de guerre_ , París, Payot, 2010. [Hay trad. cast.: «Introducción a _Zur Psychoanalyse der Kriegsneurosen_ », en _OC_ , vol. 17, 1979.]
1920. «Sur la psychogenèse d'un cas d'homosexualité féminine», traducción de D. Guérineau, en _Névrose, psychose et perversion_ , París, Presses Universitaires de France, 1973; otra versión: «De la psychogenèse d'un cas d'homosexualité féminine», traducción de J. Altounian, P. Cotet, C. Vincent y A. Zäh-Gratiaux, en _OC.P_ , vol. 15, 1996. [Hay trad. cast.: «Sobre la psicogénesis de un caso de homosexualidad femenina», en _OC_ , vol. 18, 1979.]
_Au-delà du principe de plaisir_ , traducción de J. Laplanche y J.-B. Pontalis, en _Essais de psychanalyse_ , París, Payot, 1981; otra versión con el mismo título, traducción de J. Altounian, A. Bourguignon, P. Cotet y A. Rauzy, en _OC.P_ , vol. 15, 1996; y una tercera con el mismo título, traducción de J.-P. Lefebvre, París, Seuil, 2014. [Hay trad. cast.: _Más allá del principio de placer_ , en _OC_ , vol. 18, 1979.]
1921. «Psychanalyse et télépathie», traducción de B. Chabot, en _Résultats, idées, problèmes_ , vol. 2, París, Presses Universitaires de France, 1995; otra versión con el mismo título y traducción de J. Altounian, A. Bourguignon, J. Laplanche, A. Rauzy, B. Chabot y J. Stute-Cadiot, en _OC.P_ , vol. 16, 1991. [Hay trad. cast.: «Psicoanálisis y telepatía», en _OC_ , vol. 18, 1979.]
_Psychologie collective et analyse du moi_ , traducción de S. Jankélévitch, París, Payot, 1924; otra versión: _Psychologie des foules et analyse du moi_ , traducción de J. Laplanche y J.-B. Pontalis, en _Essais de psychanalyse_ , París, Payot, 1972; una tercera con el mismo título, traducción de J. Altounian, A. y O. Bourguignon y A. Rauzy, París, Payot, 1981; una cuarta: _Psychologie des masses et analyse du moi_ , traducción de J. Altounian, A. Bourguignon, P. Cotet y A. Rauzy, en _OC.P_ , vol. 16, 1991; y una quinta: _Psychologie de masse et analyse du moi_ , traducción de D. Tassel, París, Seuil, 2014. [Hay trad. cast.: _Psicología de las masas y análisis del yo_ , en _OC_ , vol. 18, 1979.]
1922. «De quelques mécanismes névrotiques dans la jalousie, la paranoïa et l'homosexualité», traducción de J. Lacan, _Revue française de psychanalyse_ , 5(3), 1932; otra versión: « Sur quelques mécanismes névrotiques dans la jalousie, la paranoïa et l'homosexualité», traducción de D. Guérineau, en _Névrose, psychose et perversion_ , París, Presses Universitaires de France, 1973; y una tercera: «De quelques mécanismes névrotiques dans la jalousie, la paranoïa et l'homosexualité», traducción de J. Altounian y F. M. Gathelier, en _OC.P_ , 16, 1991. [Hay trad. cast.: «Sobre algunos mecanismos neuróticos en los celos, la paranoia y la homosexualidad», en _OC_ , vol. 18, 1979.]
«Rêve et télépathie», traducción de J. Altounian, A. y O. Bourguignon, G. Goran, J. Laplanche y A. Rauzy, en _Résultats, idées, problèmes_ , vol. 2, París, Presses Universitaires de France, 1995; otra versión con el mismo título, traducción de los mismos más B. Chabot, F.-M. Gathelier y J. Stute-Cadiot, en _OC.P_ , vol. 16, 1991. [Hay trad. cast.: «Sueño y telepatía», en _OC_ , vol. 18, 1979.]
«Une névrose démoniaque au XVIIe siècle», traducción de M. Bonaparte y E. Marty, en _Essais de psychanalyse appliquée_ , París, Gallimard, 1952; otra versión: «Une névrose diabolique au XVIIe siècle», traducción de B. Féron, en _L'Inquiétante étrangeté et autres essais_ , París, Gallimard, 1985; una tercera con el mismo título, traducción de P. Cotet y R. Lainé, en _OC.P_ , vol. 16, 1991; y una cuarta con el mismo título, traducción de O. Mannoni, en Honoré de Balzac, _La Peau de chagrin, suivi de Une névrose diabolique au_ XVIIe _siècle_ , París, Payot & Rivages, 2014. [Hay trad. cast.: «Una neurosis demoníaca en el siglo XVII», en _OC_ , vol. 19, 1979.]
1923. _Le Moi et le ça_ , traducción de J. Laplanche, en _Essais de psychanalyse_ , París, Payot, 1981; otra versión con el mismo título, traducción de C. Baliteau, A. Bloch, J.-M. Rondeau y J. Stute-Cadiot, en _OC.P_ , vol. 16, 1991. [Hay trad. cast.: _El yo y el ello_ , en _OC_ , vol. 19, 1979.]
«L'organisation génitale de la vie sexuelle infantile», traducción de J. Laplanche, en _La Vie sexuelle_ , París, Presses Universitaires de France, 1969; otra versión: «L'organisation génitale infantile», traducción de J. Doron y R. Doron, en _OC.P_ , vol. 16, 1991. [Hay trad. cast.: «La organización genital infantil (Una interpolación en la teoría de la sexualidad)», en _OC_ , vol. 19, 1979.]
1924. «Le déclin du complexe d'Œdipe», traducción de D. Berger, en _La Vie sexuelle_ , París, Presses Universitaires de France, 1969; otra versión: «La disparition du complex d'Œdipe», traducción de P. Cotet, H. Hildebrand y A. Lindenberg, en _OC.P_ , vol. 17, 1992. [Hay trad. cast.: «El sepultamiento del complejo de Edipo», en _OC_ , vol. 19, 1979.]
1925. _Ma vie et la psychanalyse_ , traducción de M. Bonaparte, París, Gallimard, 1925; otra versión: _Sigmund Freud présenté par lui-même_ , traducción de F. Cambon, París, Gallimard, 1984; una tercera, _Autoprésentation_ , traducción de J. Altounian, C. Avignon, A. Balseinte, A. Bourguignon, M. Candelier, C. Chiland, P. Cotet, J.-G. Delarbre, J. Doron, R. Doron, M. Hanus, D. Hartmann, H. Hildebrand, R. Lainé, J. Laplanche, A. Lindenberg, C. von Petersdorff, M. Pollack-Cornillot, A. Rauzy y M. Strauss, en _OC.P_ , vol. 17, 1992. [Hay trad. cast.: _Presentación autobiográfica_ , en _OC_ , vol. 20, 1979.]
«Résistances à la psychanalyse», artículo escrito en francés, _La Revue juive_ , 1, 1925, reeditado en _Résultats, idées, problèmes_ , vol. 2, París, Presses Universitaires de France, 1985; traducido de la versión alemana con el título de «Les résistances contre la psychanalyse», traducción de J. Altounian y P. Cotet, en _OC.P_ , vol. 17, 1992. [Hay trad. cast.: «Las resistencias contra el psicoanálisis», en _OC_ , vol. 19, 1979.]
«Note sur le "Bloc-notes magique"», traducción de J. Laplanche y J.-B. Pontalis, en _Résultats, idées, problèmes_ , vol. 2, París, Presses Universitaires de France, 1985; otra versión: «Note sur le "Bloc magique"», traducción de J. Altounian y P. Cotet, en _OC.P_ , vol. 17, 1992; y una tercera: «Note sur le "Bloc-notes magique"», traducción de D. Messier, en _Huit études sur la mémoire et ses troubles_ , París, Gallimard, 2010. [Hay trad. cast.: «Nota sobre la "pizarra mágica"», en _OC_ , vol. 19, 1979.]
«La négation», traducción de J. Laplanche, en _Résultats, idées, problèmes_ , vol. 2, París, Presses Universitaires de France, 1985; reeditado sin modificaciones en _OC.P_ , vol. 17, 1992; otra versión: «La dénégation», traducción de O. Mannoni, en _Trois mécanismes de défense_ , París, Payot, 2012. Este artículo fue objeto de una decena de traducciones, y fue Jean Hyppolite quien, en 1956, propuso el término «denegación» en vez de «negación». [Hay trad. cast.: «La negación», en _OC_ , vol. 19, 1979.]
«Quelques conséquences psychologiques de la différence anatomique entre les sexes», traducción de D. Berger, en _La Vie sexuelle_ , París, Presses Universitaires de France, 1969; otra versión: «Quelques conséquences psychiques de la différence des sexes au niveau anatomique», traducción de M. Candelier, C. Chiland y M. Pollack-Cornillot, en _OC.P_ , vol. 17, 1992. [Hay trad. cast.: «Algunas consecuencias psíquicas de la diferencia anatómica entre los sexos», en _OC_ , vol. 19, 1979.]
1926. _Inhibition, symptôme et angoisse_ , traducción de M. Tort, París, Presses Universitaires de France, 1965; otra versión con el mismo título, traducción de J. Doron y R. Doron, en _OC.P_ , vol. 17, 1992; y una tercera con el mismo título, traducción de O. Mannoni, París, Payot, 2014. [Hay trad. cast.: _Inhibición, síntoma y angustia_ , en _OC_ , vol. 20, 1979.]
_Psychanalyse et médecine_ , traducción de M. Bonaparte, París, Gallimard, 1928; otra versión: _La Question de l'analyse profane_ , traducción de J. Altounian, A. y O. Bourguignon, P. Cotet y A. Rauzy, París, Gallimard, 1985; y una tercera con el mismo título y los mismos traductores, en _OC.P_ , vol. 18, 1994. [Hay trad. cast.: _¿Pueden los legos ejercer el análisis? Diálogos con un juez imparcial_ , en _OC_ , vol. 20, 1979.]
1927. «Le fétichisme», traducción de D. Berger, en _La Vie sexuelle_ , París, Presses Universitaires de France, 1969; otra versión: «Fétichisme», traducción de R. Lainé, en _OC.P_ , vol. 18, 1994; y una tercera: «Le fétichisme», traducción de O. Mannoni, en _Trois mécanismes de défense_ , París, Payot, 2012. [Hay trad. cast.: «Fetichismo», en _OC_ , vol. 21, 1979.]
_L'Avenir d'une illusion_ , traducción de M. Bonaparte, París, Presses Universitaires de France, 1971; otra versión con el mismo título, traducción de J. Altounian, A. Balseinte, A. Bourguignon, P. Cotet, J.-G. Delarbre y D. Hartmann, en _OC.P_ , vol. 18, 1994; una tercera con el mismo título, traducción de B. Lortholary, París, Seuil, 2011; una cuarta con el mismo título, traducción de D. Messier, en _Religion_ , París, Gallimard, 2012; y una quinta con el mismo título, traducción de C. Gillie, prefacio de P.-L. Assoun, París, Cerf, 2012. [Hay trad. cast.: _El porvenir de una ilusión_ , en _OC_ , vol. 21, 1979.]
1928. «Un événement de la vie religieuse», traducción de M. Bonaparte, en _L'Avenir d'une illusion_ , París, Presses Universitaires de France, 1971; otra versión: «Une expérience vécue religieuse», traducción de A. Balseinte y E. Wolff, en _OC.P_ , vol. 18, 1994; y una tercera: «Une expérience vécue à caractère religieux», traducción de D. Messier, en _Religion_ , París, Gallimard, 2012. [Hay trad. cast.: «Una vivencia religiosa», en _OC_ , vol. 21, 1979.]
«Dostoïevski et le parricide», traducción de J.-B. Pontalis y C. Heim, en _Résultats, idées, problèmes_ , vol. 2, París, Presses Universitaires de France, 1985; otra versión: «Dostoïevski et la mise à mort du père», traducción de J. Altounian, A. Bourguignon, E. Carstanjen y P. Cotet, en _OC.P_ , vol. 18, 1994. [Hay trad. cast.: «Dostoievski y el parricidio», en _OC_ , vol. 21, 1979.]
1930. _Malaise dans la civilisation_ , traducción de C. Odier (1934), París, Presses Universitaires de France, 1971; otra versión: _Le Malaise dans la culture_ , traducción de P. Cotet, R. Lainé, J. Stute-Cadiot y J. André, París, Presses Universitaires de France, 1995; una tercera con el mismo título, traducción de P. Cotet, R. Lainé y J. Stute-Cadiot, en _OC.P_ , vol. 18, 1994; una cuarta: _Malaise dans la civilisation_ , traducción de B. Lortholary, París, Seuil, 2010; y una quinta con el mismo título, traducción de M. Crépon y M. de Launay, en _Anthropologie de la guerre_ , París, Fayard, 2010. [Hay trad. cast.: _El malestar en la cultura_ , en _OC_ , vol. 21, 1979.]
1931. «Des types libidinaux», traducción de D. Berger, en _La Vie sexuelle_ , París, Presses Universitaires de France, 1969; otra versión con el mismo título, traducción de M. Candelier, C. Chiland y M. Pollack-Cornillot, en _OC.P_ , vol. 19, 1995. [Hay trad. cast.: «Tipos libidinales», en _OC_ , vol. 21, 1979.]
«Sur la sexualité féminine», traducción de D. Berger, en _La Vie sexuelle_ , París, Presses Universitaires de France, 1969; otra versión: «De la sexualité féminine», traducción de M. Candelier, C. Chiland y M. Pollack-Cornillot, en _OC.P_ , vol. 19, 1995. [Hay trad. cast.: «Sobre la sexualidad femenina», en _OC_ , vol. 21, 1979.]
1933. _Nouvelles conférences d'introduction à la psychanalyse_ , traducción de A. Berman, París, Gallimard, 1936; otra versión: _Nouvelle suite des leçons d'introduction à la psychanalyse_ , traducción de M. R. Zeitlin, París, Gallimard, 1984; y una tercera con el mismo título, traducción de J. Altounian, A. Bourguignon, P. Cotet, A. Rauzy y M. R. Zeitlin, en _OC.P_ , vol. 19, 1995. [Hay trad. cast.: _Nuevas conferencias de introducción al psicoanálisis_ , en _OC_ , 22, 1979 (siete conferencias: «Revisión de la doctrina de los sueños», «Sueño y ocultismo», «La descomposición de la personalidad psíquica», «Angustia y vida pulsional», «La feminidad», «Esclarecimientos, aplicaciones, orientaciones» y «En torno de una cosmovisión»).]
_Pourquoi la guerre?_ , traducción de M. Blaise Briod, París, Institut International de Coopération Intellectuelle, Société des Nations, 1933; otra versión con el mismo título, traducción de J. Altounian, A. Bouguignon, P. Cotet y A. Rauzy, en _OC.P_ , vol. 19, 1995; y una tercera: «Pourquoi la guerre? Lettre à Albert Einstein», traducción de M. Crépon y M. de Launay, en _Anthropologie de la guerre_ , París, Fayard, 2010. [Hay trad. cast.: «¿Por qué la guerra? (Einstein y Freud)», en _OC_ , vol. 22, 1979.]
1936. «Un trouble de mémoire sur l'Acropole», traducción de M. Robert, en _Résultats, idées, problèmes_ , vol. 2, París, Presses Universitaires de France, 1985; otra versión: «Un trouble du souvenir sur l'Acropole: lettre à Romain Rolland», traducción de P. Cotet y R. Lainé, en _OC.P_ , vol. 19, 1995; y una tercera: «Un trouble de mémoire sur l'Acropole», traducción de D. Messier, en _Huit études sur la mémoire et ses troubles_ , París, Gallimard, 2010. [Hay trad. cast.: «Carta a Romain Rolland (Una perturbación del recuerdo en la Acrópolis)», en _OC_ , vol. 22, 1979.]
1937. «Analyse terminée et analyse interminable», traducción de A. Berman, _Revue française de psychanalyse_ , 11(1), 1939; otra versión: «L'analyse avec fin et l'analyse sans fin», traducción de J. Altounian, A. Bourguignon, P. Cotet, J. Laplanche y F. Robert, en _Résultats, idées, problèmes_ , vol. 2, París, Presses Universitaires de France, 1985; y una tercera: «L'analyse finie et l'analyse infinie», traducción de J. Altounian, A. Bourguignon, P. Cotet, J. Laplanche y F. Robert, en _OC.P_ , vol. 20, 2010. [Hay trad. cast.: «Análisis terminable e interminable», en _OC_ , vol. 23, 1980.]
«Constructions dans l'analyse», traducción de E. R. Hawelka, U. Huber y J. Laplanche, en _Résultats, idées, problèmes_ , vol. 2, París, Presses Universitaires de France, 1985; otra versión con el mismo título, traducción de J. Altounian, P. Cotet, J. Laplanche y F. Robert, en _OC.P_ , vol. 20, 2010. [Hay trad. cast.: «Construcciones en el análisis», en _OC_ ,vol. 23, 1980.]
1938. «Un mot sur l'antisémitisme», traducción de P. Cotet y R. Lainé, en _OC.P_ , vol. 20, 2010. [Hay trad. cast.: «Comentario sobre el antisemitismo», en _OC_ , vol. 23, 1980.]
1939. _Moïse et le monothéisme_ , traducción de A. Berman, París, Presses Universitaires de France, 1948; otra versión: _L'Homme Moïse et la religion monothéiste_ , traducción de C. Heim, París, Gallimard, 1986; una tercera con el mismo título, traducción de J. Altounian, P. Cotet, P. Haller, C. Jouanlanne, R. Lainé y A. Rauzy, en _OC.P_ , vol. 20, 2010; una cuarta con el mismo título, traducción de J.-P. Lefebvre, París, Seuil, 2012; y una quinta con el mismo título, traducción de O. Mannoni, París, Payot, 2014. [Hay trad. cast.: _Moisés y la religión monoteísta_ , en _OC_ , vol. 23, 1980.]
1940. _Abrégé de psychanalyse_ , traducción de A. Berman, París, Presses Universitaires de France, 1951; otra versión con el mismo título, traducción de A. Berman revisada por J. Laplanche, París, Presses Universitaires de France, 1985; y una tercera con el mismo título, traducción de F. Kahn y F. Robert, en _OC.P_ , vol. 20, 2010. [Hay trad. cast.: _Esquema del psicoanálisis_ , en _OC_ , vol. 23, 1980.]
_Compilaciones de cartas de Freud en francés_
_La Naissance de la pyschanalyse: lettres à Wilhelm Fliess_ , edición incompleta establecida por M. Bonaparte, A. Freud y E. Kris, traducción de A. Berman, París, Presses Universitaires de France, 1956. Incluye «Esquisse d'une psychologie scientifique» (1895). [Hay trad. cast.: _Fragmentos de la correspondencia con Fliess_ , en _OC_ , vol. 1, 1982 (incluye el «Proyecto de psicología»).]
_Lettres à Wilhelm Fliess, 1887-1904_ , edición completa establecida por J. M. Masson, revisada y aumentada por M. Schröter, transcripción de G. Fichtner, traducción de F. Kahn y F. Robert, París, Presses Universitaires de France, 2006. Incluye «Esquisse d'une psychologie scientifique» (1895). La presentación de Masson no figura en la edición francesa. [Hay trad. cast.: _Cartas a Wilhelm Fließ (1887-1904)_ , traducción de J. L. Etcheverry, Buenos Aires, Amorrortu, 1994, que incluye el prólogo y la introducción de J. M. Masson.]
_Correspondance, 1873-1939_ , traducción de A. Berman y J.-P. Grossein, París, Gallimard, 1960. [Hay trad. cast.: _Epistolario, 1873-1939_ , traducción de la edición inglesa de J. Merino Pérez, Madrid, Biblioteca Nueva, 1963.]
_«Notre cœur tend vers le sud.» Correspondance de voyage, 1895-1923_ , traducción de J.-C. Capèle, edición y presentación de C. Tögel con la colaboración de M. Molnar, prefacio de É. Roudinesco, París, Fayard, 2005. [Hay trad. cast.: _Cartas de viaje, 1895-1923_ , traducción de C. Martín, Madrid, Siglo XXI, 2006.]
_Lettres à ses enfants_ , edición establecida por M. Schröter con la colaboración de I. Meyer-Palmedo y E. Falzeder, traducción de F. Cambon, París, Aubier, 2012. [Hay trad. cast.: _Cartas a sus hijos_ , traducción de F. Martín y A. Obermeier, Buenos Aires, Paidós, 2012.]
_Correspondencia de Freud en francés_
Karl Abraham: _Correspondance complète, 1907-1926_ , traducción del alemán, presentación y notas de F. Cambon, París, Gallimard, 2006. [Hay trad. cast.: _Correspondencia completa, 1907-1926_ , traducción de T. Schilling, Madrid, Síntesis, 2005.]
Lou Andreas-Salomé: _Correspondance, 1912-1936_ , seguido de _Journal d'une année, 1912-1913_ , traducción del alemán de L. Jumel, prefacio y notas de E. Pfeiffer, París, Gallimard, 1970. [Hay trad. cast.: _Sigmund Freud, Lou Andreas-Salomé: correspondencia_ , traducción de J. Muñoz, México, Siglo XXI, 1977.]
Ludwig Binswanger: _Correspondance, 1908-1938_ , edición e introducción de G. Fichtner, traducción del alemán de R. Menahem y M. Strauss, prefacio de J. Gillibert, París, Calmann-Lévy, 1995. [Hay trad. cast.: _Correspondencia de Sigmund Freud_ (edición crítica en orden cronológico), vols. 2-5, traducción de N. Caparrós, Madrid, Biblioteca Nueva, 1995-2002.]
Hilda Doolittle: _Visage de Freud_ , traducción del inglés de F. de Gruson, París, Denoël, 1977; otra versión: _Pour l'amour de Freud_ , traducción de N. Casanova y E. Ochs, prefacio de É. Roudinesco, París, Éditions Des Femmes/Antoinette Fouque, 2010. [Hay trad. cast.: _Tributo a Freud_ , traducción de A. Palomas, Barcelona, El Cobre, 2004.]
Max Eitingon: _Correspondance, 1906-1939_ , edición de M. Schröter, traducción del alemán de O. Mannoni, París, Hachette Littératures, 2009.
Sándor Ferenczi: _Correspondance, 1906-1939_ , 3 vols., edición dirigida por A. Haynal, traducción del alemán del grupo de traducción del _Coq-Héron_ , París, Calmann-Lévy, 1992-2000. [Hay trad. cast. parcial: _Correspondencia completa, 1908-1919_ , traducción de T. Schilling, 4 vols., Madrid, Síntesis, 2001.]
Anna Freud: _Correspondance, 1904-1938_ , edición de I. Meyer-Palmedo, traducción del alemán de O. Mannoni, prefacio de É. Roudinesco, París, Fayard, 2012. [Hay trad. cast.: _Correspondencia 1904-1938_ , traducción de M. Fernández Polcuch y S. Villegas, Buenos Aires, Paidós, 2014.]
Familia Freud: _Lettres de famille de Sigmund Freud et des Freud de Manchester, 1911-1938_ , presentación y traducción del inglés de C. Vincent, París, Presses Universitaires de France, 1996. [Hay trad. cast.: _Viena y Manchester: correspondencia entre Sigmund Freud y su sobrino Sam Freud (1911-1938)_ , traducción de P. Navarro Serrano, Madrid, Síntesis, 2000.]
Ernest Jones: _Correspondance complète, 1908-1939_ , edición de R. Andrews Paskauskas, traducción del inglés y el alemán de P.-E. Dauzat con la colaboración de M. Weber y J.-P. Lefebvre, introducción de R. Steiner, París, Presses Universitaires de France, 1998. [Hay trad. cast.: _Correspondencia completa, 1908-1939_ , traducción de E. Sánchez-Pardo González, Madrid, Síntesis, 2001.]
Carl Gustav Jung: _Correspondance, 1906-1914_ , 2 vols., edición de W. McGuire, traducción del alemán y el inglés de R. Fivaz-Silbermann, París, Gallimard, 1975. [Hay trad. cast.: _Correspondencia_ , traducción de A. Guéra Miralles, Madrid, Trotta, 2012.]
Oskar Pfister: _Correspondance, 1909-1939_ , edición de E. L. Freud y H. Meng, traducción del alemán de L. Jumel, prefacio de D. Widlöcher, París, Gallimard, 1991. Versión incompleta. [Hay trad. cast.: _Correspondencia, 1909-1939_ , traducción de M. Rodríguez Cabo, México, Fondo de Cultura Económica, 1966.]
Romain Rolland: _Correspondance, 1923-1936_ , edición y traducción de H. Vermorel y M. Vermorel, prefacio de A. Bourguignon, París, Presses Universitaires de France, 1993.
Eduard Silberstein: _Lettres de jeunesse, 1882-1939_ , traducción del alemán de C. Heim, París, Gallimard, 1990. [Hay trad. cast.: _Cartas de juventud: con correspondencia en español inédita_ , traducción de A. Ackermann Pilári, Barcelona, Gedisa, 1992.]
Sabrina Spielrein: _Sabina Spelrein entre Freud et Jung_ , legajo descubierto por Aldo Carotenuto y Carlo Trombetta, edición francesa de M. Guibal y J. Nobécourt, traducción del italiano de M. Armand y del alemán de M. de Launay y P. Rusch, París, Aubier-Montaigne, 1981. [Hay trad. cast.: _Una secreta simetría: Sabina Spielrein entre Freud y Jung_ , traducción de R. Alcalde, Barcelona, Gedisa, 1984.]
Edoardo Weiss: _Lettres sur la pratique psychanalytique_ , precedido de _Souvenirs d'un pionnier de la psychanalyse_ , traducción de J. Etoré, introducción de J. Chazaud y M. Grotjahn, Toulouse, Privat, 1975. [Hay trad. cast.: _Problemas de la práctica psicoanalítica: correspondencia Freud-Weiss_ , traducción de J. Bodmer, Barcelona, Gedisa, 1979.]
Arnold Zweig: _Correspondance, 1927-1939_ , edición de E. y L. Freud, traducción del alemán de L. Weibel con la colaboración de J.-C. Gehrig, prefacio de M. Robert, París, Gallimard, 1973. [Hay trad. cast.: _Correspondencia 1927-1939_ , traducción de M. Miller, Barcelona, Gedisa, 2000.]
Stefan Zweig: _Correspondance, 1908-1939_ , traducción del alemán de G. Hauer y D. Plassard, texto y notas de H.-U. Lindken, prefacio de R. Jaccard, París, Payot & Rivages, 1995. [Hay trad. cast.: _Correspondencia: con Sigmund Freud, Rainer Maria Rilke y Arthur Schnitzler_ , traducción de R. S. Carbó, Barcelona, Paidós, 2004.]
_Compilación de textos en francés e inglés_
Herman Nunberg y Ernst Federn, eds., _Les Premiers psychanalystes: minutes de la Société psychoanalytique de Vienne, 1906-1918_ , 4 vols., traducción de N. Schwab-Bakman, París, Gallimard, 1976-1983. [Hay trad. cast. parcial: _Las reuniones de los miércoles: actas de la Sociedad Psicoanalítica de Viena_ , 2 vols. ( _1906-1908_ y _1908-1909_ ), traducción de I. Pardal, Buenos Aires, Nueva Visión, 1979.]
_Revue internationale d'histoire de la psychanalyse_ ( _RIHP_ ), seis números, 1988-1993, bajo la dirección de Alain de Mijolla, París, Presses Universitaires de France.
J. Keith Davies y Gerhard Fichtner, _Freud's Library: A Comprehensive Catalogue — Freuds Bibliothek: völlstandiger Katalog_ , Londres y Tubinga, The Freud Museum/Diskord, 2006. Acompaña esta obra un disco compacto que contiene los títulos de los volúmenes de la biblioteca de Freud.
En preparación, bajo la dirección de Mark Solms, la publicación de doscientos artículos, textos e intervenciones de Freud de 1877 a 1900. Cf. Filip Geerardyn y Gertrudis van de Vijver, eds., _Aux sources de la psychanalyse: une analyse des premiers écrits de Freud (1877-1900)_ , París y Montreal, L'Harmattan, 2006.
Laurence Joseph y Céline Masson, eds., _Résumé des œuvres complètes de Freud_ , 4 vols., París, Hermann, 2009.
3. OBRAS DE REFERENCIA
Jean Laplanche y Jean-Bertrand Pontalis, _Vocabulaire de la psychanalyse_ , París, Presses Universitaires de France, 1967. [Hay trad. cast.: _Diccionario de psicoan_ á _lisis_ , traducción de F. Cervantes Gimeno, Barcelona, Paidós, 1996.]
Elisabeth Roudinesco y Michel Plon, _Dictionnaire de la psychanalyse_ (1997), cuarta edición, París, Librairie Générale Française, 2011, col. «La Pochothèque». [Hay trad. cast.: _Diccionario de psicoanálisis_ , segunda edición revisada y actualizada, traducción de J. Piatigorsky y G. Villalba, Buenos Aires, Paidós, 2008.]
Paul-Laurent Assoun, _Dictionnaire thématique, historique et critique des œuvres psychanalytiques_ , París, Presses Universitaires de France, 2009.
4. CRONOLOGÍA COMPLETA DE LA VIDA Y LA OBRA DE FREUD
Véase Christfried Tögel, _Freud-Diarium_ , 470 páginas en alemán: <http://www.freud-biographik.de>.
###
Los pacientes de Freud
Altman, Rosa: 1898
Ames, Thaddeus H.: 1921
Banfield Jackson, Edith: 1930-1936
Bauer, Ida (caso «Dora»): 1900
Beddow, David: 1933-1934
Bernfeld Suzanne Paret (de soltera Cassirer): 1932-1934
Bieber (dentista): 1919
Blanton, Smiley: 1929, 1930; y de manera intermitente: 1935, 1937, 1938
Blum, Ernst: 1922
Blumgart, Leonard: 1921
Bonaparte, Eugénie: algunas sesiones después de 1925
Bonaparte, Marie: 1925-1938
Boss, Medard: algunas sesiones alrededor de 1925
Brunswick, David: 1927-1931
Brunswick, Mark: 1924-1928
Brunswick, Ruth Mack: 1922
Bryant, Louise: 1930
Bullitt, William C.: 1930
Burlingham, Dorothy: 1927-1939
Burrow, Trigant: 1924
Cherniakova, Sascha: 1905
Choisy, Maryse: 1924, tres sesiones
Csonka, Margarethe: 1920
David, Jakob Julius: ?
Deutsch, Helene: 1918-1919
Dirsztay, Viktor von: 1909, 1917-1920
Doolittle, Hilda: 1933-1934
Dorsey, John: 1935-1936
Dubovitz, Margit: 1920
Eckstein, Emma: 1895-1904
Eder, David: 1913
Eim, Gustav: 1893
Eitingon, Max: 1909
Fellner, Oscar: 1895-1900
Ferenczi, Sándor: 1914-1916
Ferstel, baronesa Marie von (de soltera Thorsch): 1899-1903
Fischer-Colbrie, Arthur: 1915-1916
Flournoy, Henri: 1922
Forsyth, David: 1920
Forzano, Concetta: 1933, una consulta
Freud, Anna: 1918-1921, 1924-1929
Freund, Anton von: 1918-1919
Freund, Rózsi von (de soltera Brody): 1915-1916
Frink, Horace W.: 1920-1921
Gattel, Felix: 1897-1898
Goetz, Bruno: 1905
Gomperz, Elise (de soltera Von Sichorsky): 1886-1892
Graf, Herbert, por medio de Max Graf: 1908
Grinker, Roy: 1935-1936
Guggenbühl, Anna: 1921
Haller, Maggie: 1901-1912
Hartmann, Dora (de soltera Karplus): 1920
Hartmann, Heinz: 1925
Hering, Julius: 1919
Hinkle-Moses, Beatrice: 1909
Hirschfeld, Elfriede: 1908
Hirst, Ada (Hirsch de nacimiento): 1908
Hirst, Albert (Hirsch de nacimiento): 1909
Hitschmann, Eduard: 1907
Hoesch-Ernst, Lucy: 1913-1914
Hönig, Olga: 1897
Jekels, Ludwig: 1905
Jeteles, Adele: 1890
Jokl, Robert Hans: 1919
Kann, Loe: 1912-1914
Kardiner, Abram: 1921
Karpas, Morris J.: 1909, algunas sesiones
Kosawa, Heisaku: 1932
Kremzir, Margit (de soltera Weiss de Szurda): 1900, catorce sesiones
Kriser, Rudolf: 1916, 1917-1919
Lampl-De Groot, Jeanne (de soltera De Groot): 1922-1925, 1931
Landauer, Karl: 1912
Lanzer, Ernst (caso del «Hombre de las Ratas»): 1907-1908
Lehrman, Phillip: 1928-1929
Levy, Kata (de soltera Toszegh): 1918
Lieben, baronesa Anna von: 1887
Liebman, Carl: 1925-1930
Mahler, Gustav: 1908, cuatro horas
Mayreder, Karl: 1915, diez semanas
McCord, Clinton: 1929
Meyer, Monroe: 1921
Money-Kyrle, Roger: 1922-1924
Moser, Fanny (de soltera Sulzer-Wart) (caso «Emmy von N.»): 1889-1890
Nacht, Tamara: 1911
Nunberg, Margarethe (de soltera Rie): 1918-1919
Oberhozer, Emil: 1913
Oberndorf, Clarence: 1921
Öhm, Aurelia (de soltera Kronich) (caso «Katharina»): 1893
Palmstierna, Vera (de soltera Duke): 1934
Pálos, Elma: 1912
Pankejeff, Serguéi (o Sergius) Konstantínovich (caso del «Hombre de los Lobos»): 1910-1914
Polon, Albert: 1921
Powers, Lillian Delger: 1924-1926
Putnam, James J.: 1911, seis horas
Rank, Otto: 1924
Reik, Theodor: 1930
Revesz-Rado, Erszébet: 1918
Rickman, John: 1920-1922
Riviere, Joan: 1922-1926
Rosanes, Flora: 1896
Rosenfeld, Eva: 1929-1932
Sarasin, Philippe: 1923, dos horas
Saussure, Raymond de: 1920
Schmideberg, Walter: 1935-1937
Schwarcz, Aranka: 1916, 1917, 1918
Silberstein, Pauline: 1891, una consulta
Sokolnicka, Eugenie: 1913
Spitz, René A.: 1910-1911
Stekel, Wilhelm: 1900, algunas semanas
Stern, Adolph: 1919
Strachey, Alix: 1920
Strachey, James: 1920
Swoboda, Hermann: 1900
Tansley, Arthur: 1922, 1923, 1924
Thayer, Scofield: 1921
Van der Leeuw, Jan: 1934
Van Emden, Jan: 1912
Veneziani, Bruno: 1912-1914
Vest, Anna von: 1903 y 1925
Vezeg, Kurt Redlich Edler von: 1905
Wallentin-Metternich, condesa Claire: 1911, dos meses
Walter, Bruno: 1906, una consulta
Walter, Margarethe: 1936, una consulta
Weiss, Amalia (hermana de Edoardo Weiss): 1921-1922
Weiss, Ilona (caso «Elisabeth von R.»): 1892
Wittgenstein, Margaret: una consulta
Wortis, Joseph: 1934-1935
Young, George M.: 1920-1921
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Árboles genealógicos
Para optimizar la lectura de estas páginas, amplíe el tamaño de las imágenes en su dispositivo.
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Notas
INTRODUCCIÓN
. Especialista en las ediciones de las obras de Freud, Gerhard Fichtner (1932-2012) dedicó la vida a buscar sus inéditos y reunir sus cartas. Cf. Gerhard Fichtner, «Les lettres de Freud en tant que source historique» y «Bibliographie des lettres de Freud», _Revue internationale d'histoire de la psychanalyse_ , 2, 1989, pp. 51-80 y 81-108, respectivamente. Cf. asimismo Ernst Falzeder, «Existe-t-il encore un Freud unconnu?», _Psychothérapies_ , 27(3), 2007, pp. 175-195.
. En el epílogo y la bibliografía se refieren todas las fuentes utilizadas en esta obra. Al final del volumen el lector también encontrará indicaciones genealógicas y cronológicas que permiten comprender las disputas suscitadas en torno de los archivos de Freud. La mayoría de las biografías existentes se mencionan en las diferentes notas.
PRIMERA PARTE
#### 1. LOS COMIENZOS
. Karl Marx y Friedrich Engels, _Manifeste du parti communiste_ (1848), París, Éditions Sociales, 1966, p. 25 [hay trad. cast.: _Manifiesto del Partido Comunista_ , Moscú, Progreso, 1964, entre otras ediciones].
. Cf. Vincenzo Ferrone y Daniel Roche, eds., _Le Monde des Lumières_ (1997), París, Fayard, 1999 [hay trad. cast.: _Diccionario histórico de la Ilustración_ , Madrid, Alianza, 1998].
. William Michael Johnston, _L'Esprit viennois: une histoire intellectuelle et sociale, 1848-1938_ (1972), París, Presses Universitaires de France, 1985, p. 27. Cf. asimismo Jean Clair, ed., _Vienne, 1880-1938: l'apocalypse joyeuse_ , catálogo de la exposición, París, Centre Georges Pompidou, 1986.
. En Elisabeth Roudinesco, _Retour sur la question juive_ , París, Albin Michel, 2009 [hay trad. cast.: _A vueltas con la cuestión judía_ , Barcelona, Anagrama, 2011], he abordado esta problemática.
. Todos los documentos relativos al estado civil de la familia Freud fueron publicados por Marianne Krüll, _Sigmund, fils de Jakob: un lien non dénoué_ (1979), París, Gallimard, 1983. Cf. asimismo Renée Gicklhorn, «La famille Freud à Freiberg» (1969), _Études freudiennes_ , 11-12, enero de 1976, pp. 231-238; Ernest Jones, _La Vie et l'œuvre de Sigmund Freud_ , vol. 1, _La Jeunesse, 1856-1900_ (1953), París, Presses Universitaires de France, 1958 [hay trad. cast.: _Vida y obra de Sigmund Freud_ , vol. 1, _Infancia y juventud, 1856-1900_ , Buenos Aires, Hormé, 1989]; Henri F. Ellenberger, _Histoire de la découverte de l'inconscient_ (1970), París, Fayard, 1994, pp. 439-446 [hay trad. cast.: _Historia del descubrimiento del inconsciente: historia y evolución de la psiquiatría dinámica_ , Madrid, Gredos, 1976], y Peter Gay, _Freud, une vie_ (1988), París, Hachette, 1991 [hay trad. cast.: _Freud: una vida de nuestro tiempo_ , Barcelona, Paidós, 1990]. Cf. también Emmanuel Rice, _Freud and Moses: The Long Journey Home_ , Nueva York, State University of New York Press, 1990. Kallamon (Salomón) a veces se escribe Kalman, Kallmann o Kelemen. Tysmenitz puede transcribirse como Tysmienica o Tismenitz. Freiberg es a veces Freyberg o, en checo, Príbor o Prbor. Para Jacob se constata también Jakob, y para Peppi, Pepi. Cf. asimismo la carta de Freud al burgomaestre de la ciudad de Príbor, 25 de octubre de 1931, LoC, caja 38, carpeta 42 [hay trad. cast.: «Carta al burgomaestre de la ciudad de Príbor», en _Obras completas_ (en lo sucesivo _OC_ ), 24 vols., traducción de José Luis Etcheverry, Buenos Aires, Amorrortu, 1978-1985, vol. 21, 1979, pp. 257-258].
. Carta de Freud a Martha Bernays, 10 de febrero de 1886, en _Correspondance, 1873-1939_ (1960), París, Gallimard, 1967, pp. 223-224 [hay trad. cast.: «A Martha Bernays», en _Epistolario, 1873-1939_ , Madrid, Biblioteca Nueva, 1963, p. 233]. La tesis errónea de la «neurosis judía» estaba muy en boga en la época, sobre todo en virtud de la enseñanza de Charcot. Cf. Elisabeth Roudinesco, _Histoire de la psychanalyse en France_ (1982-1986) y _Jacques Lacan: esquisse d'une vie, histoire d'un système de pensée_ (1993), en un solo volumen (en lo sucesivo _HPF-JL_ ), París, Librairie Générale Française, 2009, col. «La Pochothèque» [hay trad. cast.: _La batalla de cien años: historia del psicoanálisis en Francia_ , 3 vols., Madrid, Fundamentos, 1988-1993, y _Lacan: esbozo de una vida, historia de un sistema de pensamiento_ , Buenos Aires, Fondo de Cultura Económica, 1994].
. Varios comentaristas han imaginado, erróneamente, que Jacob había mantenido un fuerte apego a los ritos ortodoxos.
. Dejo testimonio de mi agradecimiento a Michel Rotfus, que me dio a conocer varias fuentes sobre la evolución de los judíos de las cuatro provincias del imperio de los Habsburgo.
. Sigmund Freud, _Lettres de famille de Sigmund Freud et des Freud de Manchester, 1911-1938_ , París, Presses Universitaires de France, 1996 [hay trad. cast.: _Viena y Manchester: correspondencia entre Sigmund Freud y su sobrino Sam Freud (1911-1938)_ , edición de Thomas Roberts, Madrid, Síntesis, 2000].
. En 1979, con el propósito de cristianizar el destino de Freud, Marie Balmary descubrió una presunta «falta oculta» en la vida de Jacob y adujo, sin fundamentos, que Rebekka se habría suicidado saltando de un tren. Cf. Marie Balmary, _L'Homme aux statues: Freud et la faute cachée du père_ , París, Grasset, 1979.
. El acta de nacimiento lo designa con su nombre de pila judío, Schlomo (Shelomoh), nacido en Freiberg el martes Rosch Hodesch Iyar de 5616 del calendario judío, es decir, el 6 de mayo de 1856. La casa natal estaba en la calle de los Cerrajeros, 117. Marie Balmary pretende que Amalia habría quedado embarazada antes de casarse y que Freud habría nacido el 6 de marzo y no el 6 de mayo de 1856. Estas afirmaciones carecen de todo fundamento. El documento original está ahora disponible en internet y la fecha del 6 de mayo no suscita duda alguna.
. Traducido del hebreo por Yosef Hayim Yerushalmi, _Le «Moïse» de Freud: judaïsme terminable et interminable_ (1991), París, Gallimard, 1993, pp. 139-140 [hay trad. cast.: _El Moisés de Freud: judaísmo terminable e interminable_ , Buenos Aires, Nueva Visión, 1996]. Yerushalmi plantea la hipótesis de que Freud, en contra de lo que siempre afirmó, sabía hebreo. Es indiscutible que sabía más de lo que decía. En 1930 escribiría estas palabras a Abraham Roback, que le había enviado un ejemplar dedicado de su libro: «Mi educación fue tan poco judía, que hoy me siento incapaz de leer incluso su dedicatoria, que evidentemente está escrita en hebreo. En mi vida ulterior he tenido ocasión de lamentar muchas veces estos fallos de mi educación». Cf. carta de Freud a Roback, 20 de febrero de 1930, en S. Freud, _Correspondance, 1873-1939_ , _op. cit._ , p. 430 [hay trad. cast.: «A A. A. Roback», en _Epistolario, 1873-1939_ , _op. cit._ , pp. 440-441].
. Sigmund Freud, _L'Interprétation des rêves_ (1900), París, Presses Universitaires de France, 1967, p. 171 [hay trad. cast.: _La interpretación de los sueños_ , en _OC_ , vol. 4, 1979, p. 207]. He elegido la traducción de Ignace Meyerson, revisada por Denise Berger. Traducida por primera vez con el título de _La Science des rêves_ , la obra se reeditó en francés como _L'Interprétation des rêves_. En realidad, _Die Traumdeutung_ debe traducirse como «La interpretación del sueño». Ese es el título escogido en la edición de las obras completas: _L'Interprétation du rêve_ , en _Œuvres complètes: psychanalyse_ (en lo sucesivo _OC.P_ ), vol. 4, París, Presses Universitaires de France, 2003, así como el elegido por Jean-Pierre Lefebvre para la edición aparecida en Seuil en 2010.
. Sigmund Freud, «En mémoire du professeur S. Hammerschlag» (1904), en _OC.P_ , vol. 6, 2006, p. 41 [hay trad. cast.: «En memoria del profesor S. Hammerschlag», en _OC_ , vol. 7, 1978, p. 230]. Cf. Théo Pfrimmer, _Freud, lecteur de la Bible_ , París, Presses Universitaires de France, 1982. Cf. asimismo Ernst Hammerschlag (nieto de Samuel), LoC, caja 113, carpeta 20, s.d.
. El nombre dado a esta niñera es fuente de incertidumbres. Resi Wittek es el registrado en un documento oficial del 5 de junio de 1857. El de Monika Zajic figura en otro documento como pariente del cerrajero Zajic, en cuya casa vivía la familia Freud en Freiberg. No hay duda de que ambos nombres corresponden a una misma persona. Cf. M. Krüll, _Sigmund, fils de Jacob..._ , _op. cit._ , p. 335.
. Carta 141 de Freud a Fliess, 3 de octubre de 1897, en Sigmund Freud, _Lettres à Wilhelm Fliess, 1887-1904_ , edición completa, París, Presses Universitaires de France, 2006, p. 341 [hay trad. cast.: _Cartas a Wilhelm Fließ (1887-1904)_ , traducción de J. L. Etcheverry, Buenos Aires, Amorrortu, 1994, p. 290]. Véase asimismo Sigmund Freud, _La Naissance de la psychanalyse_ (1950), edición incompleta, edición de Marie Bonaparte, Anna Freud y Ernst Kris, París, Presses Universitaires de France, 1956 [hay trad. cast.: _Fragmentos de la correspondencia con Fliess_ , en _OC_ , vol. 1, 1982].
. Sigmund Freud, _Trois essais sur la théorie sexuelle_ (1905), París, Gallimard, 1987 [hay trad. cast.: _Tres ensayos de teoría sexual_ , en _OC_ , vol. 7, _op. cit._ ].
. Marianne Krüll planteó esta hipótesis, y muchos la siguieron...
. Sigmund Freud, «Les souvenirs-écrans» (1899), en _Névrose, psychose et perversion_ , París, Presses Universitaires de France, 1973, pp. 121-126 [hay trad. cast.: «Sobre los recuerdos encubridores», en _OC_ , vol. 3, 1981, pp. 305-311]. Cf. asimismo Siegfried Bernfeld, «An unknown autobiographical fragment by Freud», _American Imago_ , 4(1), agosto de 1946, pp. 3-19, y Siegfried Bernfeld y Suzanne Cassirer-Bernfeld, «Freud's early childhood», _Bulletin of the Menninger Clinic_ , 8, 1944, pp. 107-115. Como ya he señalado, he evitado cuidadosamente reconstruir la vida de Freud sobre la base de una reinterpretación de sus sueños.
. Carta 141 de Freud a Fliess, 3 de octubre de 1897, en S. Freud, _Lettres à Wilhelm Fliess..._ , _op. cit._ , p. 340 [ _Cartas a Wilhelm Fließ..._ , _op. cit._ , p. 289].
. S. Freud, _L'Interprétation du rêve_ , _op. cit._ , p. 412 [ _La interpretación de los sueños_ , _op. cit._ , _OC_ , vol. 5, 1979, p. 479].
. Citado en Fritz Wittels, _Freud, l'homme, la doctrine, l'école_ , París, F. Alcan, 1925, pp. 46-47 [hay trad. cast.: _Freud: el hombre, la doctrina, la escuela_ , Santiago de Chile, Pax, 1936]. Reeditado en Edward Timms, ed., _Freud et la femme-enfant: les mémoires de Fritz Wittels_ , París, Presses Universitaires de France, 1999 [hay trad. cast.: _Freud y la mujer niña: memorias de Fritz Wittels_ , Barcelona, Seix Barral, 1997].
. Otros galitzianos tendrán un destino prestigioso: Isidor Isaac Rabi, cuyos padres emigraron a Estados Unidos en 1899, obtendría el premio Nobel de Física en 1944; de igual manera, Roald Hoffmann, nacido en 1937 y exiliado en Estados Unidos, sería premio Nobel de Química, y Georges Charpak, emigrado a Francia, premio Nobel de Física. Freud soñaba con ese galardón, que nunca obtuvo.
. S. Freud, _L'Interprétation du rêve_ , _op. cit._ , p. 175 [ _La interpretación de los sueños_ , _op. cit._ , vol. 4, p. 211].
. Sigmund Freud, «Sur la préhistoire de la technique analytique» (1920), en _OC.P_ , vol. 15, 2002, p. 268 [hay trad. cast.: «Para la prehistoria de la técnica analítica», en _OC_ , vol. 18, 1979, p. 259]. Akibah Ernst Simon, «Freud und Moses», en _Entscheidung zum Judentum: Essays und Vorträge_ , Frankfurt, Suhrkamp, 1980, pp. 196-211. Jones señala que ese regalo se le entregó al cumplir catorce años.
. S. Freud, _L'Interprétation du rêve_ , _op. cit._ , p. 127 [ _La interpretación de los sueños_ , _op. cit._ , vol. 4, p. 157].
. Alain de Mijolla, «Mein Onkel Josef à la une», _Études freudiennes_ , 15-16, abril de 1979, pp. 183-192, y Nicholas Rand y Maria Torok, _Questions à Freud_ , París, Les Belles Lettres, 1995.
. Sigmund Freud, _Lettres de jeunesse_ (1989), París, Gallimard, 1990 [hay trad. cast.: _Cartas de juventud: con correspondencia en español inédita_ , Barcelona, Gedisa, 1992]. Freud recibirá en consulta a la esposa de Eduard, Pauline Silberstein (1871-1891), afectada por una psicosis melancólica. La joven se suicidará lanzándose desde el último piso de su edificio. Cf. James W. Hamilton, «Freud and the suicide of Pauline Silberstein», _The Psychoanalytic Review_ , 89(6), 2002, pp. 889-909.
. Carta de Freud a E. Silberstein, 27 de febrero de 1875, en S. Freud, _Lettres de jeunesse_ , _op. cit._ , pp. 133-134.
. S. Freud, _L'Interprétation du rêve_ , _op. cit._ , p. 191 [ _La interpretación de los sueños_ , _op. cit._ , vol. 4, p. 230].
. La _Neue Freie Presse_ sucedió a _Die Presse_ , fundado durante la primavera de marzo de 1848.
. S. Freud, _Lettres de jeunesse_ , _op. cit._ , p. 46; reproducido en S. Freud, «Les souvenirs-écrans», _op. cit._
. Carta de Freud a Emil Fluss, septiembre de 1872, en _ibid._ , p. 228. Meseritsch (o Gross-Meseritsch) es una ciudad de Moravia situada entre Freiberg y Viena. Algunos periodistas creyeron discernir un rasgo antisemita en esta descripción.
. _Ibid._ , p. 230.
. Anna Freud-Bernays, _Eine Wienerin in New York: die Erinnerungen der Schwester Sigmund Freuds_ , edición de Christfried Tögel, Berlín, Aufbau-Verlag, 2004.
. Judith Heller-Bernays (1885-1977), Lucy Leah-Bernays (1886-1980), Hella Bernays (1893-1994) y Martha (1894-1979). Sobre el destino excepcional de Edward Bernays (1891-1995), teórico moderno de la propaganda, véase _infra_. Martha Bernays, hermana de Eli, se casaría con Sigmund Freud.
. Hermann Graf (1897-1917) y Cäcilie Graf (1899-1922).
. Margarethe Freud-Magnus, llamada Gretel (1887-1984), Lilly Freud-Marlé (1888-1970), Martha Gertrud, llamada Tom Seidmann-Freud (1892-1930), Theodor Freud (1904-1927) y Georg Freud (mellizo mortinato, 1904). Cf. Christfried Tögel, «Freuds Berliner Schwester Maria (Mitzi) und ihre Familie», _Luzifer-Amor_ , 33, 2004, pp. 33-50, y Lilly Freud-Marlé, _Mein Onkel Sigmund Freud_ , Berlín, Aufbau-Verlag, 2006.
. Rose Winternitz-Waldinger (1896-1969). Sobre el destino y los testimonios de los sobrinos y sobrinas de Freud, recogidos por Kurt Eissler para la Biblioteca del Congreso, véase _infra_.
. Comprobada por todos los demógrafos, este descenso no puede atribuirse simplemente a la contracepción que comenzaba a difundirse en las clases acomodadas, con el uso del preservativo o la práctica del _coitus interruptus_. En Elisabeth Roudinesco, _La Famille en désordre_ , París, Fayard, 2002 [hay trad. cast.: _La familia en desorden_ , Buenos Aires, Fondo de Cultura Económica, 2003], he abordado este problema.
. Marie Bonaparte, diario inédito.
. Jacques Le Rider, _Modernité viennoise et crise de l'identité_ , París, Presses Universitaires de France, 1994, y P. Gay, _Freud, une vie_ , _op. cit._ , pp. 22-27. En un texto polémico, Jacques Bénesteau ha afirmado que en Viena no había antisemitismo alguno a raíz de la presencia masiva de los judíos en las profesiones liberales e intelectuales, y que Freud inventó las persecuciones antisemitas en su contra; véase Jacques Bénesteau, _Mensonges freudiens_ , Sprimont (Bélgica), Mardaga, 2002, pp. 190-191. Al contrario, esa presencia contribuyó a un fuerte aumento del antisemitismo en Viena.
. Sobre el nacimiento de la pareja infernal del semita y el ario, cf. Maurice Olender, _Les Langues du paradis. Aryens et sémites: un couple providentiel_ , París, Gallimard/Seuil, 1989, col. «Hautes Études» [hay trad. cast.: _Las lenguas del Paraíso. Arios y semitas: una pareja providencial_ , Buenos Aires, Fondo de Cultura Económica, 2005].
. André Bolzinger, _Portrait de Sigmund Freud: trésors d'une correspondance_ , París, Campagne Première, 2012, p. 132.
. Sigmund Freud, _Sigmund Freud présenté par lui-même_ (1925), París, Gallimard, 1984, p. 16 [hay trad. cast.: _Presentación autobiográfica_ , en _OC_ , vol. 20, 1979, p. 8].
. En la huella de Luise von Karpinska, psicóloga polaca, se debe a Maria Dorer el primer estudio científico, en 1932, sobre el lugar de las tesis de Herbart en la génesis de la teoría freudiana del inconsciente: cf. Maria Dorer, _Les Bases historiques de la psychanalyse_ , París, L'Harmattan, 2012. El historiador y psicoanalista sueco Ola Andersson retomaría esta cuestión en 1962 en _Freud avant Freud: la préhistoire de la psychanalyse, 1886-1896_ , Le Plessis-Robinson, Synthélabo, 1997, col. «Les Empêcheurs de penser en rond», con prefacio de Per Magnus Johansson y Elisabeth Roudinesco y, en un apéndice, un intercambio epistolar entre Andersson y Ellenberger.
. Josef Paneth también daría un respaldo económico a Freud. Cf. el testimonio de Marie Paneth (nuera de Josef) del 7 de marzo de 1950, recogido por Kurt Eissler.
. E. Jones, _La Vie et l'œuvre..._ , vol. 1, _op. cit._ , p. 32. Sin embargo, como veremos más adelante, Freud no se apartaría tanto como creía de la especulación filosófica.
. Para el estudio del método anatomoclínico (Xavier Bichat), cf. Michel Foucault, _Naissance de la clinique: une archéologie du regard médical_ , París, Presses Universitaires de France, 1963 [hay trad. cast.: _El nacimiento de la clínica: una arqueología de la mirada médica_ , Buenos Aires, Siglo XXI, 1966]. Sobre la fisiología y el método experimental, cf. Georges Canguilhem, «Claude Bernard», en _Études d'histoire et de philosophie des sciences_ , París, Vrin, 1968 [hay trad. cast.: «Claude Bernard», en _Estudios de historia y de filosofía de las ciencias_ , Buenos Aires, Amorrortu, 2009, pp. 135-182].
. Carta de Freud a Silberstein, en S. Freud, _Lettres de jeunesse_ , _op. cit._ , p. 171.
. Se encontrará una bella descripción de la vida de ese medio en la obra de Albrecht Hirschmüller, _Josef Breuer_ (1978), París, Presses Universitaires de France, 1991, pp. 52-72.
. El lector hallará un buen análisis de este período de la vida de Freud en Frank J. Sulloway, _Freud, biologiste de l'esprit_ (1979), prefacio de Michel Plon, París, Fayard, 1998. En este libro Sulloway propone la hipótesis (discutible) de que Freud habría seguido siendo a lo largo de toda su vida un biólogo oculto (un criptobiólogo), a pesar de su orientación hacia la psicología. Cf. asimismo Filip Geerardyn y Gertrudis van de Vijver, eds., _Aux sources de la psychanalyse: une analyse des premiers écrits de Freud (1877-1900)_ , París y Montreal, L'Harmattan, 2006.
. Jacques Le Rider, _Les Juifs viennois à la Belle Époque_ , París, Albin Michel, 2012, p. 142.
. Elise Gomperz (1848-1929), la mujer de Theodor Gomperz, sufría de trastornos nerviosos. Consultó a Charcot, que en 1892 la derivó a Freud a fin de que este la sometiera a un tratamiento catártico. Freud utilizó la electroterapia y la hipnosis. Nada permite decir que este tratamiento fue un fracaso, como lo sugiere Mikkel Borch-Jacobsen, _Les Patients de Freud: destins_ , Auxerre, Éditions Sciences Humaines, 2011. Elise siguió siendo durante toda su vida lo que era, una mujer «nerviosa» y melancólica, pero sus relaciones con Freud fueron excelentes hasta el final.
. Fleischl murió de manera prematura en 1891, y el sucesor de Brücke fue Exner.
. S. Freud, _Sigmund Freud présenté..._ , _op. cit._ , p. 17 [ _Presentación autobiográfica_ , _op. cit._ , p. 9].
#### 2. AMORES, TEMPESTADES Y AMBICIONES
. S. Freud, _L'Interprétation du rêve_ , _op. cit._ , p. 414 [ _La interpretación de los sueños_ , _op. cit._ , vol. 5, p. 479]. Esta cita corresponde al _Fausto_ de Goethe.
. Sigmund Freud, «Grande est la Diane des Éphésiens» (1911), en _OC.P_ , vol. 11, 2009, pp. 51-53, según un poema de Goethe [hay trad. cast.: «¡Grande es Diana Efesia!», en _OC_ , vol. 12, 1980, pp. 366-368].
. Es decir, con abundante pelo oscuro al nacer.
. Monique Schneider, «Freud, lecteur et interprète de Goethe», _Revue germanique internationale_ , «Goethe cosmopolite», 12, 1999, pp. 243-256.
. Novela epistolar de Goethe aparecida en 1774.
. Se encontrará una descripción bastante exhaustiva de las «enfermedades» de Freud en la obra de Max Schur, _La Mort dans la vie de Freud_ (1972), París, Gallimard, 1975 [hay trad. cast.: _Sigmund Freud: enfermedad y muerte en su vida y en su obra_ , 2 vols., Barcelona, Paidós, 1980]. Por otra parte, en su correspondencia Freud se presta gustoso a contar sus «enfermedades» en términos técnicos, como suelen hacerlo los médicos.
. Cf. _ibid._ , p. 86. Freud menciona a veces en sus cartas, de manera indirecta, su práctica de la masturbación.
. Cf. Jean Bollack, _Jacob Bernays: un homme entre deux mondes_ , Villeneuve-d'Ascq, Presses Universitaires du Septentrion, 1998. Freud se inspiró en la teoría de la catarsis de Jacob Bernays y recomendó a Arnold Zweig la lectura de sus cartas. Sigmund Freud y Arnold Zweig, _Correspondance, 1927-1939_ (1968), París, Gallimard, 1973, p. 84 [hay trad. cast.: _Correspondencia 1927-1939_ , Barcelona, Gedisa, 2000].
. La publicación de la correspondencia del noviazgo entre Sigmund Freud y Martha Bernays (mil quinientas cartas de 1882 a 1886) está en proceso de realización bajo la dirección de Ilse Grubrich-Simitis y Albrecht Hirschmüller. Han aparecido los dos primeros volúmenes, que abarcan el período 1882-1883. Otros tres deberán aparecer próximamente. Cf. Sigmund Freud y Martha Bernays, _Sein mein, wie ich mir's denke_ , vol. 1, _Die Brautbriefe_ , Frankfurt, S. Fischer Verlag, 2011, y vol. 2, _Unser Roman in Fortsetzungen_ , Frankfurt, S. Fischer Verlag, 2013. Yo utilicé además S. Freud, _Correspondance, 1873-1939_ , _op. cit._ , que contiene noventa y tres cartas de Freud a Martha. Ernest Jones y Peter Gay analizaron intensamente esa correspondencia, que se conserva en la Biblioteca del Congreso y a la que tuvieron acceso. Cf. asimismo Katja Behling, _Martha Freud_ (2003), prólogo de Anton W. Freud y prefacio de Judith Dupont, París, Albin Michel, 2006, e Ilse Grubrich-Simitis, «L'affectif et la théorie. Sigmund et Martha: prélude freudien. Germes de concepts psychanalytiques fondamentaux», _Revue française de psychanalyse_ , 76(3), 2012, pp. 779-795. Esa correspondencia, todavía inédita en parte, es una fuente importante para comprender la evolución de Freud. Además de las misivas amorosas que yo menciono, contiene numerosas observaciones sobre su trabajo, sus encuentros, sus gustos, su vida cotidiana, sus angustias, sus investigaciones y algunos retratos inolvidables de sus maestros y contemporáneos. Cf. también la obra de A. Bolzinger, _Portrait de Sigmund Freud..._ , _op. cit._ Las investigaciones de Hanns Lange sobre la familia figuran en el catálogo del Freud Museum de Londres. Algunos extractos se citan en la obra de E. Rice, _Freud and Moses..._ , _op. cit._
. Carta de Freud a Martha Bernays, 30 de junio de 1884, en S. Freud, _Correspondance, 1873-1939_ , _op. cit._ , pp. 130-131 [ _Epistolario, 1873-1939_ , _op. cit._ , p. 134].
. Hermana de Freud. Eli devolvió la totalidad de la suma.
. Carta inédita de Freud a Martha Bernays, 27 de diciembre de 1883, citada por E. Jones, _La Vie et l'œuvre..._ , vol. 1, _op. cit._ , p. 130.
. La correspondencia entre Freud y Minna Bernays está en curso de traducción al francés y será publicada por Éditions du Seuil. Agradezco a Olivier Mannoni haberme permitido acceder a ella. Cf. Sigmund Freud y Minna Bernays, _Briefwechsel, 1882-1938_ , texto fijado por Albrecht Hirschmüller, Tubinga, Diskord, 2005. [La versión francesa de la correspondencia entre Sigmund Freud y Minna Bernays, con el título de _Correspondance (1882-1938)_ , se publicó en marzo de 2015, con posterioridad a la aparición de este libro de Elisabeth Roudinesco. _(N. del T.)_ ]
. Sobre la génesis de este extraordinario rumor siempre de actualidad, véase _infra_.
. Sobre este punto la mejor referencia es Sigmund Freud, _De la cocaïne_ , edición de Robert Byck, Bruselas, Complexe, 1976 [hay trad. cast.: _Escritos sobre la cocaína_ , Barcelona, Anagrama, 1980]. Esta obra reúne los cinco textos de Freud sobre el tema: «Über coca» (1884), «Contribución al conocimiento de los efectos de la cocaína» (1885), «Sobre el efecto general de la cocaína» (1885), «Addenda a "Über coca"» (1885) y «Anhelo y temor de la cocaína» (1887), y contiene además comentarios de varios investigadores. Cf. asimismo Jacques Michel, «La cocaïne et Freud», en Jean-Claude Beaune, ed., _La Philosophie du remède_ , Seyssel, Champ Vallon, 1993, pp. 1-14; Françoise Coblence, «Freud et la cocaïne», _Revue française de psychanalyse_ , 66(2), 2002, pp. 371-383, y F. J. Sulloway, _Freud, biologiste de l'esprit_ , _op. cit._ , pp. 21-22.
. Carta de Freud a Martha Bernays, 2 de junio de 1884, en S. Freud, _De la cocaïne_ , _op. cit._
. Se acusó a Freud, sobre todo, de haber asesinado con premeditación a su amigo Fleischl para eliminar a un rival; de haber contribuido al auge del tercer flagelo de la humanidad (tras el alcohol y la morfina), y, por último, de haber escrito el conjunto de su obra bajo la influencia de la cocaína. En realidad, dejó de consumirla de manera regular en 1887 y de manera definitiva en 1892, y desde entonces aumentó aún más su consumo de tabaco. Sobre las acusaciones sin fundamento, cf. E. M. Thornton, _Freud and Cocaine: The Freudian Fallacy_ , Londres, Blond & Briggs, 1983. Por su parte, los historiadores oficiales minimizaron durante muchos años la importancia del episodio de la cocaína.
. _Allotrion_ : término griego que significa lo que es distinto o ajeno a uno mismo.
. Carta de Freud a Martha Bernays, 5 de octubre de 1882, en S. Freud y M. Bernays, _Sein mein..._ , vol. 1, _op. cit._ , p. 367.
. Cf. W. M. Johnston, _L'Esprit viennois..._ , _op. cit._ , pp. 267-283.
. H. F. Ellenberger, _Histoire de la découverte..._ , _op. cit._ , p. 455, según el retrato de Bernard Sachs, alumno norteamericano de Theodor Meynert. Cf. también A. Hirschmüller, _Josef Breuer_ , _op. cit._ , p. 122.
. Sigmund Freud, «Esquisse d'une psychologie scientifique», en _La Naissance de la psychanalyse_ , _op. cit._ [hay trad. cast.: _Proyecto de psicología_ , en _OC_ , vol. 1, _op. cit._ , pp. 323-389]. Cf. asimismo Christine Lévy-Friesacher, _Meynert-Freud, «l'amentia_ », París, Presses Universitaires de France, 1983.
. Los pacientes afectados de neurosis eran tratados igualmente en servicios de psiquiatría o por psiquiatras particulares. Además, se apelaba con frecuencia al término «neuropsicosis» para designar esas patologías, cuyos perfiles varían según las épocas.
. La mejor obra sobre Josef Breuer es la que le dedicó Albrecht Hirschmüller, que cito en abundancia. Señalemos que Ernest Jones, por su parte, da una imagen detestable, injusta y errónea de Breuer, a quien presenta como un terapeuta temeroso, incapaz de comprensión alguna en lo referido a la sexualidad.
. A. Hirschmüller, _Josef Breuer_ , _op. cit._ , p. 59.
. _Ibid._ , p. 129.
. Término propuesto en 1769 por el médico escocés William Cullen (1710-1790) para definir las enfermedades nerviosas que ocasionaban trastornos de la personalidad. Cf. Elisabeth Roudinesco y Michel Plon, _Dictionnaire de la psychanalyse_ (1997), París, Librairie Générale Française, 2011, col. «La Pochothèque» [hay trad. cast.: _Diccionario de psicoanálisis_ , Buenos Aires, Paidós, 1998].
. Conforme a la expresión utilizada por Henri Ellenberger, que sigue siendo el mejor historiador de la psiquiatría dinámica y en especial de la historia de la evolución del magnetismo y del paso de las curas magnéticas a la psicoterapia. Cf. asimismo Jean Clair, ed., _L'Âme au corps: arts et sciences, 1793-1993_ , catálogo de la exposición, París, Réunion des Musées Nationaux/Gallimard/Electa, 1993.
. Me referí extensamente a la trayectoria de Charcot y la cuestión de la histeria y su desmantelamiento por Joseph Babinski, así como a las críticas que le dirigió Léon Daudet (su ex alumno). Cf. _HPF-JL_ , _op. cit._ Aquí, veo la cuestión bajo una luz diferente. Cf. asimismo Jean-Martin Charcot, _Leçons du mardi à la Salpêtrière, professeur Charcot: policlinique 1887-1888_ , 2 vols., París, Lecrosnier & Babé, 1892 [hay trad. cast.: _Lecciones sobre las enfermedades del sistema nervioso: dadas en la Salpêtrière_ , 3 vols., Madrid, Librería de Hernando y Compañía, 1898]; Jean-Martin Charcot y Paul Richer, _Les Démoniaques dans l'art_ (1887), París, Macula, 1984 [hay trad. cast.: _Los endemoniados en el arte_ , Jaén, Del Lunar, 2000], y Georges Didi-Huberman, _L'Invention de l'hystérie: Charcot et l'iconographie photographique de la Salpêtrière_ , París, Macula, 1982 [hay trad. cast.: _La invención de la histeria: Charcot y la iconografía fotográfica de la Salpêtrière_ , Madrid, Cátedra, 2007]. Véase también Marcel Gauchet y Gladys Swain, _Le Vrai Charcot: les chemins imprévus de l'inconscient_ , París, Calmann-Lévy, 1997 [hay trad. cast.: _El verdadero Charcot: los caminos imprevistos del inconsciente_ , Buenos Aires, Nueva Visión, 1997].
30. La estancia de Freud en París fue de cuatro meses y medio.
. Hippolyte Taine, _Les Origines de la France contemporaine_ , París, Laffont, 1986, col. «Bouquins». La obra comenzó a publicarse en 1875. La tesis de las muchedumbres patológicas y el miedo que inspiran reaparece en Gustave Le Bon, _Psychologie des foules_ (1895), París, Presses Universitaires de France, 1963 [hay trad. cast.: _Psicología de las masas_ , Madrid, Morata, 1983]. Es sabido que Freud se apoyaría en esta obra para elaborar su psicología colectiva, sin hacer suyo, no obstante, el tema del desigualitarismo y el inconsciente hereditario «a la francesa».
. Su libro _La France juive_ [ _La Francia judía_ ] se publicó en 1886.
. Cartas de Freud a Minna Bernays, 3 de diciembre de 1885, y a Martha Bernays, 19 de octubre de 1885, en S. Freud, _Correspondance, 1873-1939_ , _op. cit._ , pp. 200 y 186, respectivamente [ _Epistolario, 1873-1939_ , _op. cit._ , pp. 208 y 193, respectivamente].
. Carta de Freud a Martha Bernays, 20 de enero de 1886, en _ibid._ , p. 209 [ _ibid._ , p. 218]. Él mismo traduciría al alemán las _Lecciones del martes_ y, a la muerte de Charcot, en 1893, escribió un hermoso obituario donde mostraba la importancia que había tenido para él la enseñanza del maestro de la Salpêtrière. Cf. Sigmund Freud, «Charcot», en _Résultats, idées, problèmes_ , vol. 1, _1890-1920_ , París, Presses Universitaires de France, 1984, pp. 61-73 [hay trad. cast.: «Charcot», en _OC_ , vol. 3, _op. cit._ , pp. 7-24].
. Véase _infra_. Cf. Carlo Bonomi, «Pourquoi avons-nous ignoré Freud le "pédiatre"? Le rapport entre la formation pédiatrique de Freud et les origines de la psychanalyse», en André Haynal, ed., _La Psychanalyse: cent ans déjà... Contributions à l'histoire intellectuelle du_ XX _e siècle_ , Ginebra, Georg, 1996, pp. 87-153.
. Este hecho fue verificado por Albrecht Hirschmüller, quien consultó en Viena el registro de la comunidad judía en relación con el nacimiento de los tres hijos varones de Freud. En él no se menciona la circuncisión. Cf. Emanuel Rice, «The Jewish heritage of Sigmund Freud», _Psychoanalytic Review_ , 81(2), verano de 1994, pp. 236-258. Carlo Bonomi consultó el mismo registro. Sobre la resistencia al conformismo, cf. Sigmund Freud, _Lettres à ses enfants_ (2010), París, Aubier, 2012, p. 96 [hay trad. cast.: _Cartas a sus hijos_ , Buenos Aires, Paidós, 2012].
. En el capítulo 3 del _Tratado teológico político_ , publicado en 1670, Spinoza atribuye la supervivencia del pueblo judío al odio de las naciones.
. S. Freud, _Lettres à ses enfants_ , _op. cit._ La cuestión del círculo de familia se tratará en la tercera parte de este libro.
. Cartas de Freud a Jung del 19 de septiembre de 1907 y el 2 de febrero de 1910 (tras el viaje a Estados Unidos), en Sigmund Freud y Carl Gustav Jung, _Correspondance_ , vol. 1, _1906-1909_ , y vol. 2, _1910-1914_ , París, Gallimard, 1975, pp. 142 (vol. 1), y 22 (vol. 2) [hay trad. cast.: _Correspondencia_ , Madrid, Trotta, 2012]. Agradezco a John Forrester que me haya informado sobre su artículo dactilografiado que se ocupa del tema: «The Minna affair: Freud's other women?». Freud tuvo ya en época muy temprana la impresión de ser viejo, justamente a causa de la desaparición de su «libido». Volveré a esta cuestión.
. Por eso escogerá como modelo de parentesco la tragedia de Edipo.
. S. Freud, «Charcot», _op. cit._ , p. 62 [«Charcot», _op. cit._ , p. 15; la frase está en francés en el texto de Freud: «La théorie, c'est bon, mais ça n'empêche pas d'exister». _(N. del T.)_ ].
. Moriz Benedikt había sostenido en 1864 que la histeria era una enfermedad sin causas uterinas. También afirmaba la existencia de la histeria masculina. Sobre el destino de este extraño pionero, cf. Henri F. Ellenberger, _Médecines de l'âme: essais d'histoire de la folie et des guérisons psychiques_ , París, Fayard, 1995.
. Sigmund Freud, «Über männliche Hysterie» (1886). Esta conferencia está inédita, al igual que la segunda, pronunciada el 26 de noviembre. Su contenido se conoce por las reseñas: _Anzeiger der k. k. Gesellschaft der Ärtze_ (Viena), 25, 1886, pp. 149-152; _Münchener medizinische Wochenschrift_ , 33, 1886, p. 768, y _Wiener medizinische Wochenschrift_ , 36(43), 1886, pp. 1445-1447. Ellenberger fue el primero en contar cuál era el contenido de los debates que enfrentaban a Freud con sus colegas vieneses. Cf. Henri F. Ellenberger, «La conférence de Freud sur l'hystérie masculine. Vienne le 15 octobre 1886» (1968), en _Médecines de l'âme..._ , _op. cit._ , pp. 207-225. Cf. asimismo F. J. Sulloway, _Freud, biologiste de l'esprit_ , _op. cit._ , p. 31. Las conferencias se publicarán próximamente en _OC.P_ , vol. 1.
. En su autobiografía Freud se refiere a la mediocre recepción que se brindó a su conferencia e insiste en el hecho de que uno de los oyentes negaba la existencia de la histeria masculina. Cf. S. Freud, _Sigmund Freud présenté..._ , _op. cit_. Por otra parte, afirmó que en vísperas de su muerte Meynert le habría confesado que él mismo era un caso de histeria masculina. La confidencia parece demasiado buena para ser cierta.
. Hippolyte Bernheim, _Hypnotisme, suggestion, psychothérapie: avec considérations nouvelles sur l'hystérie_ (1891), París, Fayard, 1995, col. «Corpus des œuvres de philosophie en langue française». Cf. asimismo É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. La transferencia se convertiría en un concepto fundamental de la teoría freudiana.
. S. Freud, _Sigmund Freud présenté..._ , _op. cit._ , p. 47 [ _Presentación autobiográfica_ , _op. cit._ , pp. 26-27].
. Josef Breuer y Sigmund Freud, _Études sur l'hystérie_ (1895), París, Presses Universitaires de France, 1967 [hay trad. cast.: _Estudios sobre la histeria_ , en _OC_ , vol. 2, 1978]. Anna von Lieben aparece bajo el nombre de señora Cäcilie M.
. Entrevista de Kurt Eissler a Henriette Motesiczky von Kesseleökeö (1882-1978), hija de Anna von Lieben, LoC, caja 116, 1973. Cf. además Peter Swales, «Freud, his teacher, and the birth of psychoanalysis», en Paul E. Stepansky, ed., _Freud: Appraisals and Reappraisals_ , Hillsdale (New Jersey), The Analytic Press, 1986, pp. 3-82.
. Es decir, otorrinolaringólogo.
. Freud envió a Fliess 287 cartas. Los intercambios epistolares entre ambos se extendieron de 1887 a 1904. S. Freud, _Lettres à Wilhelm Fliess..._ , edición completa, _op. cit._ , y _La Naissance de la psychanalyse_ , edición expurgada, _op. cit._
. W. A. Hack (1851-1887), un otorrinolaringólogo de Friburgo de Brisgovia, ya se había empeñado antes que él en describir la neurosis nasal refleja.
. Wilhelm Fliess, _Les Relations entre le nez et les organes génitaux féminins, présentées selon leurs significations biologiques_ (1897), París, Seuil, 1977, col. «Le Champ freudien» (dirigida por Jacques Lacan). En un artículo de 1895 dedicado a una monografía de Paul Julius Moebius (1853-1907) sobre la migraña, Freud elogiaba a Fliess, notable investigador berlinés. Cf. Sigmund Freud, «La migraine de Moebius» (1895), en _OC.P_ , vol. 3, 2005, pp. 97-103.
. S. Freud, _Esquisse d'une psychologie..._ , _op. cit_. Nueva traducción con el título de _Projet d'une psychologie_ , en S. Freud, _Lettres à Wilhelm Fliess..._ , _op. cit._ , pp. 593-693.
. Max Schur fue el primero en revelar, en 1966, el calvario de Emma, cuya identidad fue ocultada durante mucho tiempo por los psicoanalistas. Su historia, descrita con amplitud en las cartas de Freud a Fliess, fue a posteriori objeto de numerosos comentarios. Cf. M. Borch-Jacobsen, _Les Patients de Freud..._ , pp. 66-73. Carlo Bonomi plantea la hipótesis de que Emma vivió su operación como una repetición de la ablación que había sufrido en su niñez y que Freud menciona en su correspondencia con Fliess. Cf. Carlo Bonomi, «Withstanding trauma: the significance of Emma Eckstein's circumcision to Freud's Irma dream», _The Psychoanalytic Quarterly_ , 83(3), julio de 2013, pp. 689-740.
. Carta 56 de Freud a Fliess, 8 de marzo de 1895, en S. Freud, _Lettres à Wilhelm Fliess..._ , _op. cit._ , p. 153 [ _Cartas a Wilhem Fließ..._ , _op. cit._ , p. 119].
. S. Freud, _Projet d'une psychologie_ , _op. cit._ , p. 657 [ _Proyecto de psicología_ , _op. cit._ , pp. 401-403].
. Carta 118 de Freud a Fliess, 17 de enero de 1897, en S. Freud, _Lettres à Wilhelm Fliess..._ , _op. cit._ , p. 286 [ _Cartas a Wilhelm Fließ..._ , _op. cit._ , p. 239].
. Albert Hirst (1887-1974), LoC, caja 115, carpeta 12. Su verdadero nombre era Albert Hirsch, pero se cambió el apellido al emigrar a Estados Unidos. Se analizó con Freud, que le dijo desde el comienzo que su costumbre de masturbarse no era nociva. En vez de hacerlo tenderse en el diván, una vez hizo que se sentara en una silla y le pidió que adoptara la posición utilizada para masturbarse. Hirst también padecía problemas de eyaculación. David J. Lynn, «Sigmund Freud's psychoanalysis of Albert Hirst», _Bulletin of History of Medicine_ , 71(1), primavera de 1997, pp. 69-93.
. Las transcripciones de las conversaciones de 1952 con Eissler se encuentran en la Biblioteca del Congreso.
. Cf. F. J. Sulloway, _Freud, biologiste de l'esprit_ , _op. cit._ , p. 132 y ss.
. El mejor historial sobre las relaciones entre Freud y Fliess es el reunido por Érik Porge, ed., _Vol d'idées? Wilhelm Fliess, son plagiat et Freud_ , seguido de _Pour ma propre cause_ , de Wilhelm Fliess, París, Denoël, 1994 [hay trad. cast.: _¿Robo de ideas? Wilhelm Fliess, su plagio y Freud_ , seguido de _Por mi propia causa_ , de Wilhelm Fliess, Buenos Aires, Kliné, 1998]. Véanse también M. Schur, _La Mort dans la vie..._ , _op. cit._ , y, desde luego, F. J. Sulloway, _Freud, biologiste de l'esprit_ , _op. cit._
. Otto Weininger, _Sexe et caractère_ (1903), Lausana, L'Âge d'Homme, 1975 [hay trad. cast.: _Sexo y carácter_ , Barcelona, Península, 1985]. Traducido a diez lenguas, ese libro fue en su época un verdadero best seller y tuvo veintiocho reediciones hasta 1947, para caer luego en el olvido. Cf. Jacques Le Rider, _Le Cas Otto Weininger: racines de l'antiféminisme et de l'antisémitisme_ , París, Presses Universitaires de France, 1982.
. Paul Julius Moebius (1853-1907): neurólogo alemán, autor de varias patografías, convencido de la existencia de una inferioridad mental de las mujeres con respecto a los hombres. Sostenía la idea de que las manifestaciones histéricas se producen en el plano corporal por obra de representaciones psicológicas.
. En la obra de Érik Porge, ed., _Vol d'idées?..._ , _op. cit._ , se encontrarán todos los documentos relacionados con el caso. Peter Swales imaginó, sin aportar la más mínima prueba en apoyo de su conjetura, que durante el encuentro en el lago de Achen Freud habría intentado asesinar a Fliess: cf. Peter Swales, «Freud, Fliess and fratricide: the role of Fliess in Freud's conception of paranoia», en Laurence Spurling, ed., _Sigmund Freud: Critical Assessments_ , vol. 1, _Freud and the Origins of Psychoanalysis_ , Londres y Nueva York, Routledge, 1982, pp. 302-329.
. Sigmund Freud, «Lettre à Fritz Wittels», 15 de agosto de 1924, _Revue internationale d'histoire de la psychanalyse_ , 8, 1993, p. 98 [hay trad. cast.: carta 209, «A Fritz Wittels», en _Epistolario, 1873-1939_ , _op. cit._ , pp. 395-397].
. Ernest Jones, Max Schur, Peter Gay y, por supuesto, la propia Marie Bonaparte se cuentan entre quienes informaron de este episodio.
. Carta de Freud a Ferenczi, 6 de octubre de 1910, en Sigmund Freud y Sándor Ferenczi, _Correspondance_ , vol. 1, _1908-1914_ , París, Calmann-Lévy, 1992, p. 231 [hay trad. cast.: _Correspondencia completa, 1908-1919_ , tomo I, vol. 1, Madrid, Síntesis, 2001]. Véase también Chawki Azouri, « _J'ai réussi là où le paranoïaque échoue»: la théorie a-t-elle un père?_ , París, Denoël, 1990 [hay trad. cast.: « _He triunfado donde el paranoico fracasa»: ¿tiene un padre la teoría?,_ Buenos Aires, Ediciones de la Flor, 1995].
. Carta 146 de Freud a Fliess, 14 de noviembre de 1897, en S. Freud, _Lettres à Wilhelm Fliess..._ , _op. cit_., p. 331, 339, 351 y 357 [ _Cartas a Wilhelm Fließ..._ , _op. cit._ , p. 305]. Freud terminará por reducir su presunto autoanálisis a un fragmento; véase _ibid._ , p. 430.
. Hubo que esperar los trabajos de la historiografía científica para que se pusiera en entredicho la leyenda dorada de un Freud autoengendrado, propia del movimiento psicoanalítico. Señalemos que Octave Mannoni reemplazó en 1967 el término «autoanálisis» por «análisis original», como una manera de mostrar que el lugar ocupado por las teorías fliessianas en la doctrina de Freud era la expresión de una división compleja entre saber y delirio. Cf. Octave Mannoni, _Clefs pour l'imaginaire ou L'Autre scène_ , París, Seuil, 1969, pp. 115-131 [hay trad. cast.: _La otra escena: claves de lo imaginario_ , Buenos Aires, Amorrortu, 1990].
. Carta 244 de Freud a Fliess, 7 de mayo de 1900, en S. Freud, _Lettres à Wilhelm Fliess..._ , _op. cit._ , p. 521 [ _Cartas a Wilhelm Fließ..._ , _op. cit._ , p. 452].
. Génesis 32, 22-29, _La Bible: Ancien Testament_ , París, Gallimard, 1992, col. «Bibliothèque de la Pléiade», pp. 109-110.
. Señalemos al respecto que Freud sentía gran admiración por el escritor vienés Richard Beer-Hofmann y que le gustaba en especial una de sus piezas teatrales más conocidas, _Jaákobs Traum_ [«El sueño de Jacob»], publicada en 1918. El combate con el ángel estuvo presente a lo largo de toda su vida. Y él lo utilizó para referirse al tirano interior que lo acechaba, y sobre todo a su cáncer. Israel es también el nombre que se daría en 1948 al Estado judío soñado por Theodor Herzl. Un Estado condenado al combate perpetuo contra los hombres y contra sí mismo, temática retomada por Freud en 1930 y luego en _Moisés y la religión monoteísta_.
#### 3. LA INVENCIÓN DEL PSICOANÁLISIS
. Para ser reemplazado por el de «sujeto depresivo», cansado de sí mismo. En Elisabeth Roudinesco, _Pourquoi la psychanalyse?_ , París, Fayard, 1999 [hay trad. cast.: _¿Por qué el psicoanálisis?_ , Barcelona, Paidós, 2000], me refiero a esta problemática. Cuanto más se emancipen las mujeres a lo largo del siglo XX, menos histéricas se las considerará. En consecuencia, la histeria masculina será cada vez más estudiada.
. El historiador Mark Micale imagina que Freud (en los _Estudios sobre la histeria_ ) omitió exponer casos de histeria masculina en razón de su proximidad demasiado grande con esta neurosis. Y propone la hipótesis, sin apoyarla en la más mínima prueba, de que la neurastenia de Freud era una histeria enmascarada y que este la habría «teorizado» simulando su propio caso detrás de su descripción de los casos de mujeres histéricas. Cf. Mark Micale, _Hysterical Men: The Hidden History of Male Nervous Illness_ , Cambridge (Massachusetts), Harvard University Press, 2008.
. J. Breuer y S. Freud, _Études sur l'hystérie_ , _op. cit._ , pp. 41-47 [ _Estudios sobre la histeria_ , _op. cit._ , pp. 77-84].
. Breuer atribuyó a Anna O. (Bertha Pappenheim), que hablaba inglés, la invención de dos expresiones: _talking cure_ (cura por la palabra) y _chimney sweeping_ (deshollinamiento de chimenea que permitía una rememoración).
. Debemos a Albrecht Hirschmüller la mejor reconstrucción biográfica de la historia de Bertha Pappenheim.
. Como ya he señalado, no me ocupo —o me ocupo muy poco— de la cuestión de la implantación del psicoanálisis en Francia, que ya he estudiado extensamente. Sobre las relaciones de Freud y Janet, el lector puede remitirse a _HPF-JL_ , _op. cit._
. J. Breuer y S. Freud, _Études sur l'hystérie_ , _op. cit._ , «Avant-propos à la première édition» [ _Estudios sobre la histeria_ , _op. cit._ , «Prólogo a la primera edición», p. 23].
. J. Breuer y S. Freud, _Études sur l'hystérie_ , _op. cit._ , p. 247 [ _Estudios sobre la histeria_ , _op. cit._ , p. 309].
. Sobre todo por Ernest Jones, Ola Andersson, Henri F. Ellenberger, Peter Swales, Albrecht Hirschmüller y Mikkel Borch-Jacobsen.
. La mayoría de estas pacientes figuran bajo su verdadero nombre y con su verdadera trayectoria en É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Cf. Dora Edinger, _Bertha Pappenheim: Leben und Schriften_ , Frankfurt, Ner-Tamid-Verlag, 1963.
. Liga de Mujeres Judías.
. Sigmund Freud y Stefan Zweig, _Correspondance_ (1987), París, Payot & Rivages, 1995, pp. 88-89 [hay trad. cast.: _Correspondencia: con Sigmund Freud, Rainer Maria Rilke y Arthur Schnitzler_ , Barcelona, Paidós, 2004].
. E. Jones, _La Vie et l'œuvre..._ , vol. 1, _op. cit._ , p. 249. Sobre la revisión de esta leyenda puede consultarse, además de los textos de Henri F. Ellenberger y Albrecht Hirschmüller, el de John Forrester, «The true story of Anna O.», _Social Research_ , 53(2), «Sexuality and madness», verano de 1986, pp. 327-347 [hay trad. cast.: «La verdadera historia de Anna O.», en _Seducciones del psicoanálisis: Freud, Lacan y Derrida_ , México, Fondo de Cultura Económica, 1995, pp. 29-32]. Por mi parte, di a conocer a Mikkel Borch-Jacobsen el pasaje muy esclarecedor de un manuscrito inédito de Marie Bonaparte sobre las confidencias de Freud. Cf. Mikkel Borch-Jacobsen, _Souvenirs d'Anna O.: une mystification centenaire_ , París, Aubier, 1995. A pesar de todos estos trabajos, los psicoanalistas siguen prefiriendo la leyenda de Anna O. a la historia de Bertha Pappenheim. Cf. É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._ , p. 1127.
. Sigmund Freud, carta a Robert Breuer, 26 de junio de 1925, citada en A. Hirschmüller, _Josef Breuer_ , _op. cit._ , p. 268.
. Sigmund Freud, «L'hérédité et l'étiologie des névroses» (1896), en _OC.P_ , vol. 3, _op. cit._ , pp. 105-120 [hay trad. cast.: «La herencia y la etiología de las neurosis», en _OC_ , vol. 3, _op. cit._ , pp. 139-156; el término aparece en la p. 151. _(N. del T.)_ ]. Publicado en francés el 30 de marzo de 1896.
. Según el testimonio de Marie Bonaparte, que debía la información al propio Freud.
. La Iglesia medieval privilegiaba la devoción y las peregrinaciones, en tanto que la Iglesia salida del concilio de Trento (1542) instauró la confesión en respuesta a la ofensiva de los protestantes. Jacques Le Goff mantuvo siempre la convicción, como Michel Foucault y Michel de Certeau, de que la invención freudiana tiene elementos en común con esa práctica.
. S. Freud, «L'hérédité et l'étiologie...», _op. cit._ , p. 120 [«La herencia y la etiología...», _op. cit._ , p. 154].
. Sigmund Freud, «Sur l'étiologie de l'hystérie» (1896), en _OC.P_ , vol. 3, _op. cit._ , pp. 147-180 [hay trad. cast.: «La etiología de la histeria», en _OC_ , vol. 3, _op. cit._ , pp. 185-218].
. Carta 109 de Freud a Fliess, 2 de noviembre de 1896, en S. Freud, _Lettres à Wilhelm Fliess..._ , _op. cit._ , p. 258 [ _Cartas a Wilhelm Fließ..._ , _op. cit._ , pp. 213-214].
. Carta 120 de Freud a Fliess, 8 de febrero de 1897, en _ibid._ , p. 294 [ _ibid._ , p. 246].
. Freud era un gran lector de las obras de Jacob Burckhardt. Estas figuran en un lugar privilegiado de su biblioteca y tienen algunas anotaciones en los márgenes.
. Sigmund Freud, _«Notre cœur tend vers le sud»: correspondance de voyage, 1895-1923_ , París, Fayard, 2005 [hay trad. cast.: _Cartas de viaje, 1895-1923_ , Madrid, Siglo XXI, 2006].
. Carta 138 de Freud a Fliess, 6 de septiembre de 1897, en S. Freud, _Lettres à Wilhelm Fliess..._ , _op. cit._ , p. 333 [ _Cartas a Wilhelm Fließ..._ , _op. cit._ , p. 283].
. Carta 139 (llamada «del equinoccio») de Freud a Fliess, 21 de septiembre de 1897, en _ibid._ , pp. 334-336 [ _ibid._ , pp. 284-286], también en _La Naissance de la psychanalyse_ , _op. cit._ , p. 192 [ _Fragmentos de la correspondencia..._ , _op. cit._ , p. 301].
. Sobre esta cuestión, cf. Carlo Bonomi, _Sulla soglia della psicoanalisi: Freud e la follia infantile_ , Turín, Bollati Boringhieri, 2007.
. En 1977 la historiadora Katharina Rutschky dio el nombre de «pedagogía negra» a esos métodos educativos. La psicoanalista suiza Alice Miller hizo suya la expresión, y Michael Haneke ilustró los perjuicios de esa pedagogía en su filme _La cinta blanca_ [ _Das weiße Band_ ], de 2009.
. Daniel Paul Schreber, _Mémoires d'un névropathe_ (1903), París, Seuil, 1975 [hay trad. cast.: _Memorias de un enfermo de nervios_ , Madrid, Sexto Piso, 2003, entre otras ediciones]. Cf. Sigmund Freud, «Remarques psychanalytiques sur l'autobiographie d'un cas de paranoïa» (1911), en _Cinq psychanalyses_ , París, Presses Universitaires de France, 1954, pp. 263-321, y, con el título de «Remarques psychanalytiques sur un caso de paranoïa ( _Dementia paranoides_ ) décrit sous forme autobiographique», en _OC.P_ , vol. 10, 2009, pp. 225-305 [hay trad. cast.: _Puntualizaciones psicoanalíticas sobre un caso de paranoia (Dementia paranoides) descrito autobiográficamente_ , en _OC_ , vol. 12, _op. cit._ , pp. 1-76].
. Jean-Jacques Rousseau, _Les Confessions_ (1780), en _Œuvres complètes_ , vol. 1, París, Gallimard, 1959, col. «Bibliothèque de la Pléiade», pp. 108-109 [hay trad. cast.: _Las confesiones_ , Madrid, Alianza, 2007, entre otras ediciones].
. Cf. Jacques Derrida, «Ce dangereux supplément», en _De la grammatologie_ , París, Éditions de Minuit, 1967 [hay trad. cast.: «Ese peligroso suplemento», en _De la gramatología_ , México, Siglo XXI, 1978, pp. 181-208]. Cf. asimismo Thomas Laqueur, _La Fabrique du sexe: essai sur le genre et le corps en Occident_ (1990), París, Gallimard, 1992 [hay trad. cast.: _La construcción del sexo: cuerpo y género desde los griegos hasta Freud_ , Madrid, Cátedra, 1994].
. Carta 142 de Freud a Fliess, 15 de octubre de 1897, en S. Freud, _La Naissance de la psychanalyse_ , _op. cit._ , p. 198 [ _Fragmentos de la correspondencia..._ , _op. cit._ , p. 307], y _Lettres à Wilhelm Fliess..._ , _op. cit._ , p. 344 [ _Cartas a Wilhelm Fließ..._ , _op. cit._ , p. 293].
. _Ibid._ , pp. 198-199 y 344-345, respectivamente [ _ibid._ , p. 308 y p. 294, respectivamente].
. Del que existen varias versiones.
. «Novela familiar» es una expresión creada por Freud y Rank en 1909 para designar la manera en que un sujeto modifica sus lazos genealógicos inventándose otra familia distinta de la suya. Cf. Otto Rank, _Le Mythe de la naissance du héros – (suivi de) La Légende de Lohengrin_ , París, Payot, 1983 [hay trad. cast.: _El mito del nacimiento del héroe_ , Barcelona, Paidós, 1992].
. La expresión aparece por primera vez en Sigmund Freud, «D'un type particulier de choix d'objet chez l'homme» (1910), en _OC.P_ , vol. 10, _op. cit._ , p. 197 [hay trad. cast.: «Sobre un tipo particular de elección de objeto en el hombre (Contribuciones a la psicología del amor, I)», en _OC_ , vol. 11, 1979, p. 164]. Señalemos que Freud se equivoca al referirse a la primera aparición del famoso «complejo» en su obra, que sitúa en _L'Interprétation du rêve_ , _op. cit._ , p. 229, n. 1 [ _La interpretación de los sueños_ , _op. cit._ , vol. 4, p. 272, n. 25].
. Sigmund Freud, «Fragment d'une analyse d'hystérie (Dora)» (1905), en _Cinq psychanalyses_ , _op. cit._ , pp. 1-91, y _OC.P_ , vol. 6, _op. cit._ , pp. 183-291 [hay trad. cast.: _Fragmento de análisis de un caso de histeria_ , en _OC_ , vol. 7, _op. cit._ , pp. 1-107]. La mejor reconstrucción de la historia de Dora es la propuesta por Patrick Mahony, _Dora s'en va: violence dans la psychanalyse_ (1996), París, Les Empêcheurs de Penser en Rond, 2001. Cf. asimismo Arnold Rogow, «A further footnote to Freud's "Fragment of an analysis of a case of hysteria"», _Journal of the American Psychoanalytical Association_ , 26(2), abril de 1978, pp. 331-356; Hélène Cixous, _Portrait de Dora, suivi de La Prise de l'école de Madhubaî_ , París, Éditions Des Femmes, 1986, y Hannah S. Decker, _Freud, Dora and Vienna, 1900_ , Nueva York, The Free Press, 1991, libro en que se encontrará una bella descripción de los judíos de Bohemia de fin de siglo [hay trad. cast.: _Freud, Dora y la Viena de 1900_ , Madrid, Biblioteca Nueva/Asociación Psicoanalítica de Madrid, 1999].
. P. Mahony, _Dora s'en va..._ , _op. cit._ , p. 201.
. La enfermedad de Ménière.
. Al igual que Felix Deutsch, Ida emigró a Estados Unidos y escapó a las persecuciones nazis. Murió de cáncer en 1945. Deutsch se enteró de su muerte diez años después y afirmó, según un informante, que había sido una de «las histéricas más repelentes que yo haya conocido». Kurt Eissler señaló su oposición a ese testimonio en una carta a Anna Freud del 10 de agosto de 1952. Por lo demás, parece ser que, en contra de las palabras que Deutsch le había atribuido en 1923, Ida nunca habló del orgullo de ser un caso célebre.
. S. Freud, «Préface à la deuxième édition», en _L'Interprétation du rêve_ , _op. cit._ , p. 4 [«Prólogo a la segunda edición», en _La interpretación de los sueños_ , _op. cit._ , vol. 4, p. 20].
. E. Jones, _La vie et l'œuvre..._ , vol. 1, _op. cit._ , p. 384.
. Karl Albert Scherner, _La Vie du rêve_ (1861), Nimes, Théétète Éditions, 2003; Alfred Maury, _Le Sommeil et les rêves: études psychologiques sur ces phénomènes et les divers états qui s'y rattachent_ , París, Didier, 1861; Léon d'Hervey de Saint-Denys, _Les Rêves et les moyens de les diriger: observations pratiques_ (1867), Île Saint-Denis, Oniros, 1995, y Joseph Delbœuf, _Le Sommeil et les rêves – Le Magnétisme animal – Quelques considérations sur la psychologie de l'hypnotisme_ (1885), París, Fayard, 1993 [hay trad. cast.: _El dormir y el soñar_ , Madrid, Daniel Jorro, 1904]. Se encontrará un estudio de conjunto en Jacqueline Carroy, _Nuits savantes: une histoire des rêves (1800-1945)_ , París, École des Hautes Études en Sciences Sociales, 2012. Freud había reunido en su biblioteca una impresionante cantidad de obras sobre el sueño.
. Cf. F. J. Sulloway, _Freud, biologiste de l'esprit_ , _op. cit._ , p. 309. Henri F. Ellenberger dedicó páginas muy hermosas a las obras sobre el sueño en general y a la de Freud en particular. Cf. asimismo É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Franz von Thun und Hohenstein (1847-1916), aristócrata, propietario terrateniente y burócrata característico de la monarquía imperial. Fue en dos ocasiones gobernador de Bohemia y luego ocupó brevemente, de marzo de 1898 a octubre de 1899, el cargo de ministro presidente de Austria.
. Carl E. Schorske, _Vienne, fin de siècle: politique et culture_ (1961), París, Seuil, 1981, en especial el capítulo 4, «Politique et parricide dans _L'Interprétation du rêve_ de Freud» [hay trad. cast.: _La Viena de fin de siglo: política y cultura_ , Buenos Aires, Siglo XXI, 2011, en especial «Sigmund Freud: política y parricidio en _La interpretación de los sueños_ »]. Cf. asimismo Jacques Le Rider, «Je mettrai en branle l'Achéron: fortune et signification d'une citation de Virgile», _Europe_ , 86(954), octubre de 2008, pp. 113-122.
. Carta de Freud a Werner Achelis, 30 de enero de 1927, en S. Freud, _Correspondance, 1873-1939_ , _op. cit._ , p. 408 [ _Correspondance, 1873-1939_ , _op. cit._ , p. 419; traducción modificada]. Freud había anunciado su elección a Fliess; cf. carta 206, 17 de julio de 1899, en S. Freud, _Lettres à Wilhelm Fliess..._ , _op. cit._ , p. 458 [ _Cartas a Wilhelm Fließ..._ , _op. cit._ , p. 396]. Cf. Ferdinand Lassalle, _Der italienische Krieg und die Aufgabe Preussens_ , Berlín, F. Duncker, 1859.
. La expresión _splendid isolation_ se utilizaba habitualmente para definir la política exterior británica de fines del siglo XIX. Freud la hacía suya conminado por Fliess, que intentaba consolarlo.
. Sigmund Freud, _Sur l'histoire du mouvement psychanalytique_ (1914), París, Gallimard, 1991, p. 39 [hay trad. cast.: _Contribución a la historia del movimiento psicoanalítico_ , en _OC_ , vol. 14, 1979, p. 21].
. Freud vivió toda su vida en Viena, y el hecho de que detestara la ciudad no hacía sino apegarlo más a ella.
. Didier Anzieu, _L'Auto-analyse de Freud et la découverte de la psychanalyse_ (1959), París, Presses Universitaires de France, 1988 [hay trad. cast.: _El autoanálisis de Freud y el descubrimiento del psicoanálisis_ , 2 vols., México, Siglo XXI, 1978-1979]; M. Schur, _La Mort dans la vie..._ , _op. cit._ , y Jacques Lacan, _Le Séminaire, Livre II, Le Moi dans la théorie de Freud et dans la technique de la psychanalyse (1954-1955)_ , edición de Jacques-Alain Miller, París, Seuil, 1978, pp. 177-207 [hay trad. cast.: _El Seminario de Jacques Lacan. Libro 2. El yo en la teoría de Freud y en la técnica psicoanalítica. 1954-1955_ , Buenos Aires, Paidós, 1983].
. Alison Rose, _Jewish Women in Fin de Siècle Vienna_ , Austin, University of Texas Press, 2008.
. Carta 248 de Freud a Fliess, 12 de junio de 1900, en S. Freud, _Lettres à Wilhelm Fliess..._ , _op. cit._ , p. 527 [ _Cartas a Wilhelm Fließ..._ , _op. cit._ , p. 457]. Hubo que esperar hasta el 6 de mayo de 1977 para que ese deseo de Freud se cumpliera gracias a la instalación de una placa sobre la pared de la casa de Bellevue. Cf. asimismo _ibid._ , p. 532 [ _ibid._ , p. 460].
. En 1988 Gerd Kimmerle y Ludger M. Hermanns dieron el nombre de _Luzifer-Amor_ a una revista de historia del psicoanálisis, dirigida desde 2004 por Michael Schröter. Cf. Renata Sachse, « _Luzifer-Amor_ numéro 51: _Zeitschrift zur Geschichte der Psychoanalyse_ », _Essaim_ , 32, enero de 2014, pp. 103-111.
. Norman Kiell, ed., _Freud without Hindsight: Reviews of His Work, 1893-1939_ , Madison, International Universities Press, 1988, y H. F. Ellenberger, _Histoire de la découverte..._ , _op. cit._
. Sobre las relaciones de Freud con los surrealistas franceses, que no abordo en este libro, cf. _HPF-JL_ , _op. cit._
. La carta, del 5 de marzo de 1902, llevaba la firma del emperador Francisco José. Cf. H. F. Ellenberger, _Histoire de la découverte..._ , _op. cit._ , pp. 476-478.
SEGUNDA PARTE
#### 1. UNA ÉPOCA TAN BELLA
. Conversación inédita, archivos de Marie Bonaparte.
. Cf. Jean-Yves Tadié, _Le Lac inconnu: entre Proust et Freud_ , París, Gallimard, 2012 [hay trad. cast.: _El lago desconocido: entre Proust y Freud_ , Barcelona, Ediciones del Subsuelo, 2013]. Y, sobre las relaciones de Freud con los escritores franceses —André Gide, Romain Rolland, André Breton, etc.—, véase _HPF-JL_ , _op. cit._
. Cf. J. Le Rider, _Les Juifs viennois à la Belle Époque_ , _op. cit._
. Carta de Freud a Ferenczi, 8 de junio de 1913, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 1, _op. cit._ , pp. 519-520.
. Alfred Kubin, _Reflexión_ , 1902. Peter Gay ha advertido con mucha claridad este detalle...
. Testimonio de Judith Heller-Bernays, marzo de 1953, LoC, caja 120, carpeta 36.
. Martin Freud, _Freud, mon père_ (1958), París, Denoël, 1975, pp. 54-55 [hay trad. cast.: _Sigmund Freud, mi padre_ , Buenos Aires, Hormé, 1966].
. Sigmund Freud, _La Psychopathologie de la vie quotidienne_ (1905), París, Gallimard, 1997, con un excelente prefacio de Laurence Kahn [hay trad. cast.: _Psicopatología de la vida cotidiana_ , en _OC_ , vol. 6, 1979].
. En mi caso, por consejo de mi madre, fue el primer libro de Freud que leí, antes de abordar la obra clásica consagrada a Leonardo da Vinci.
. Sobre Otto Gross, hijo de Hans, véase _infra_.
. «De esa lobreguez está tan lleno el aire / que nadie sabe cómo podría evitarla.»
. Carta 267 de Freud a Fliess, 8 de mayo de 1901, en S. Freud, _La Naissance de la psychanalyse_ , _op. cit._ , pp. 293-294, y _Lettres à Wilhelm Fliess..._ , _op. cit._ , p. 556 [ _Cartas a Wilhelm Fließ..._ , _op. cit._ , p. 484].
. _Ibid._ ( _Lettres..._ ) [ _ibid._ ]. Divisa inscrita en el escudo de armas de París: «Las olas lo azotan, pero no se hunde».
. Carta de Freud a Martha Freud, 1 de septiembre de 1900, en S. Freud, « _Notre cœur tend vers le sud_ »..., _op. cit._ , p. 132.
. Tarjetas postales de Freud a Martha Freud, 2 y 3 de septiembre de 1901, en _ibid._ , p. 15.
. Carl E. Schorske, _De Vienne et d'ailleurs: figures culturelles de la modernité_ (1998), París, Fayard, 2000, p. 264 [hay trad. cast.: _Pensar con la historia: ensayos sobre la transición a la modernidad_ , Madrid, Taurus, 2001].
. Tarjeta postal de Freud a Martha Freud, 4 de septiembre de 1904, en S. Freud, « _Notre cœur tend vers le sud_ »..., _op. cit._
. En una carta de 1936 Freud le contará a Romain Rolland la perturbación que había experimentado ese día en la Acrópolis. Cf. Sigmund Freud, «Un trouble de mémoire sur l'Acropole» (1936), en _Huit études sur la mémoire et ses troubles_ , París, Gallimard, 2010, pp. 41-61 [hay trad. cast.: «Carta a Romain Rolland (Una perturbación del recuerdo en la Acrópolis)», en _OC_ , vol. 22, 1979, pp. 209-221]. Este texto ha sido objeto de decenas de comentarios. Henri Rey-Flaud interpreta ese fenómeno de extrañeza como un punto «psicótico» en el universo psíquico de Freud. Cf. Henri Rey-Flaud, _Je ne comprends pas de quoi vous me parlez: pourquoi refusons-nous de reconnaître la réalité?_ , París, Aubier, 2014. Yo diría, por mi parte, que también hay que leerlo como una reflexión sobre «José», personaje bíblico pero hermano de Bonaparte, sobre el estatus del judaísmo y sobre la cuestión de la vida ya vivida, como dirá Thomas Mann.
. Sigmund Freud, _Le Mot d'esprit dans sa relation avec l'inconscient_ (1905), París, Gallimard, 1988 [hay trad. cast.: _El chiste y su relación con lo inconciente_ , en _OC_ , vol. 8, 1979]. Freud introdujo muy pocas modificaciones en este libro, al contrario de lo que había hecho con los otros dos de la misma línea.
. Theodor Lipps, _Komik und Humor: eine psychologisch-ästhetische Untersuchung_ (1898), Bremen, Dogma, 2013.
. S. Freud, _Le Mot d'esprit..._ , _op. cit._ , p. 411 [ _El chiste..._ , _op. cit._ , p. 223]. Jacques Lacan conceptualizó la noción de _Witz_ y calificó la obra de «texto canónico». La utilizó además como una poderosa fuente de inspiración para definir su concepción del significante, al extremo de proponer traducir el término como _trait d'esprit_ [agudeza]. En inglés, James Strachey se inclinó por la palabra _joke_.
. Utilizado aquí por primera vez.
. Me he ocupado de esta cuestión en _HPF-JL_ , _op. cit_. Cf. asimismo É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Adolf Albrecht Friedländer, «Hysterie und moderne Psychoanalyse», _Psychiatrie_ , actas del XVI Congreso Internacional de Medicina, Budapest, 1909, sección 12, pp. 146-172.
. La tesis del _genius loci_ fue retomada por Pierre Janet en el famoso congreso de Londres que lo enfrentó a Jones y Jung. Cf. Pierre Janet, «La psycho-analyse», informe al XVII Congreso de Medicina de Londres, 1913, _Journal de psychologie normale et pathologique_ , 11, marzo-abril de 1914, pp. 1-36 y 97-130. Véase también _HPF-JL_ , _op. cit._
. Bruno Goetz, «Souvenirs sur Sigmund Freud», en Roland Jaccard (presentación), _Freud: jugements et témoignages_ , París, Presses Universitaires de France, 1976, pp. 221-222 [hay trad. cast.: «Recuerdos sobre Sigmund Freud», en Graciela Musachi, _El oriente de Freud_ , Buenos Aires, Editores Contemporáneos, 2001].
. Bruno Walter, _Thème et variations: souvenirs et réflexions de Bruno Walter_ , Lausana, M. et P. Foetisch, 1952, y André Haynal, «Freud psychothérapeute. Essai historique», _Psychothérapies_ , 27(4), 2007, pp. 239-242. La «cura» de Gustav Mahler se contó muchas veces.
. A. Haynal, «Freud psychothérapeute...», _op. cit._ , y É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Stefan Zweig, _Le Monde d'hier: souvenirs d'un européen_ (1944), París, Belfond, 1993, p. 91 [hay trad. cast.: _El mundo de ayer: memorias de un europeo_ , Barcelona, Acantilado, 2001].
#### 2. DISCÍPULOS Y DISIDENTES
. En 1923, arruinado por la derrota de los Imperios Centrales, se suicidó cortándose la arteria radial.
. La PMG se reuniría entre octubre de 1902 y septiembre de 1907. No se cuenta ni con fotografías ni con transcripciones de los debates sostenidos en ella entre 1902 y 1906. Para el período siguiente pueden consultarse: Herman Nunberg y Ernst Federn, eds., _Les Premiers psychanalystes: minutes de la Société psychanalytique de Vienne_ , vol. 1, _1906-1908_ (1962), París, Gallimard, 1976, con introducción de Herman Nunberg [hay trad. cast.: _Las reuniones de los miércoles: actas de la Sociedad Psicoanalítica de Viena, 1906-1908_ , Buenos Aires, Nueva Visión, 1979]; _ibid._ , vol. 2, _1908-1910_ (1967), París, Gallimard, 1978 [hay trad. cast. parcial: _Las reuniones de los miércoles: actas de la Sociedad Psicoanalítica de Viena, 1908-1909_ , Buenos Aires, Nueva Visión, 1979]; _ibid._ , vol. 3, _1910-1911_ (1967), París, Gallimard, 1978, e _ibid._ , vol. 4, _1912-1918_ (1975), París, Gallimard, 1983. En esos volúmenes se incluye la transcripción de doscientas cincuenta reuniones. Cf. asimismo Elke Mühlleitner, _Biographisches Lexikon der Psychoanalyse: die Mitglieder der Psychologischen Mittwoch-Gesellschaft und der Wiener Psychoanalytischen Vereinigung, 1902-1938_ , Tubinga, Diskord, 1992, al igual que Ernst Falzeder y Bernhard Handlbauer, «Freud, Adler et d'autres psychanalystes: des débuts de la psychanalyse organisée à la fondation de l'Association psychanalytique internationale», _Psychothérapies_ , 12(4), 1992, pp. 219-232. En este capítulo me apoyo en el seminario inédito que dicté sobre el tema en la Universidad de París VII-Diderot en 1998.
. Entre 1902 y 1907 la Sociedad Psicológica de los Miércoles contó con veintitrés miembros de varias nacionalidades, entre ellos, además de Freud, nueve vieneses de pura cepa, seis austríacos, tres rumanos (de Bucovina), un polaco (de Galitzia), un checo (de Praga) y dos húngaros. De los diecisiete miembros judíos, cinco sería exterminados por los nazis (Alfred Bass, Adolf Deutsch, Alfred Meisl, Isidor Isaak Sadger y Guido Brecher). Los otros, todavía vivos en 1938 (once), emigraron a Gran Bretaña o Estados Unidos. En ese primer círculo eran mayoría los médicos (diecisiete), y el índice de suicidio un poco más alto que en otros sectores de la población: dos de veintitrés. Las mujeres estarán representadas a partir de 1910, cuando la PMG se convierta en la Wiener Psychoanalytische Vereinigung [Asociación Psicoanalítica de Viena] (WPV). Margarethe Hilferding, vienesa, morirá a manos de los nazis, al igual que su marido, Rudolf Hilferding.
. Olga Hönig (1877-1961) había sido víctima de abuso sexual por parte de sus hermanos. Se negó a dar un testimonio a Kurt Eissler.
. Sigmund Freud, «Analyse d'une phobie chez un petit garçon de cinq ans (le petit Hans)» (1909), en _Cinq psychanalyses_ , _op. cit._ , pp. 93-198, y _OC.P_ , vol. 9, 1998, pp. 1-131 [hay trad. cast.: _Análisis de la fobia de un niño de cinco años_ , en _OC_ , vol. 10, 1980, pp. 1-118]. Cf. asimismo Max Graf, «Réminiscences sur le professeur Freud» (1942), _Tel Quel_ , 88, verano de 1981, pp. 52-101 [hay trad. cast.: «Reminiscencias del profesor Freud», _Fort-da. Revista de psicoanálisis con niños_ , 8, septiembre de 2005], y «Entretien avec Kurt Eissler» (1952), _Bloc-notes de la psychanalyse_ , 14, 1995, pp. 123-159 [hay trad. cast.: «Reportaje a Max Graf», _Fort-da. Revista de psicoanálisis con niños_ , 10, noviembre de 2008]. Kurt Eissler también mantuvo una conversación con Herbert Graf, depositada en la Biblioteca del Congreso.
. Wilhelm Stekel, _Autobiography: The Life Story of a Pioneer Psychoanalyst_ , edición de Emil A. Gutheil, Nueva York, Liveright, 1950; Vincent Brome, _Les Premiers disciples de Freud: les luttes de la psychanalyse_ (1967), París, Presses Universitaires de France, 1978, y Paul Roazen, _La Saga freudienne_ (1976), París, Presses Universitaires de France, 1986 [hay trad. cast.: _Freud y sus discípulos_ , Madrid, Alianza, 1978]. Steckel se suicidó en Londres, donde estaba exiliado, el 25 de junio de 1940.
. El escritor Manès Sperber le consagró una admirable biografía: _Alfred Adler et la psychologie individuelle: l'homme et sa doctrine_ (1970), París, Gallimard, 1972. Véase también Paul E. Stepansky, _Adler dans l'ombre de Freud_ (1983), París, Presses Universitaires de France, 1992. La editorial Payot publica las obras de Adler traducidas al francés. La ruptura entre él y Freud fue, por ambas partes, de una extrema violencia. Con toda la razón, Henri F. Ellenberger atribuye a Adler y su enseñanza un lugar importante en la historia de la psiquiatría dinámica y las psicoterapias. Sus intervenciones en la Sociedad Psicológica de los Miércoles fueron diez.
. Sigmund Freud, _Sigmund Freud: correspondance avec le pasteur Pfister, 1909-1939_ (1963), París, Gallimard, 1966, p. 86 [hay trad. cast.: _Correspondencia, 1909-1939_ , México, Fondo de Cultura Económica, 1966].
. J. Keith Davies y Gerhard Fichtner, _Freud's Library: A Comprehensive Catalogue – Freuds Bibliothek: völlstandiger Katalog_ , Londres y Tubinga, The Freud Museum/Diskord, 2006, p. 20. Acompaña esta obra un disco compacto que contiene la totalidad de los títulos de la biblioteca de Freud.
. Carta de Freud a Jung, 19 de septiembre de 1907, en S. Freud y C. G. Jung, _Correspondance_ , vol. 1, _op. cit._ , pp. 141-142.
. Cf. Alexander Grinstein, _Freud à la croisée des chemins_ (1990), París, Presses Universitaires de France, 1998. En este libro se encontrará un extenso análisis de la significación posible de los libros escogidos por Freud. Cf. asimismo Sérgio Paulo Rouanet, _Oz dez amigos de Freud_ , Río de Janeiro, Companhia das Letras, 2003.
. Su verdadero nombre era Otto Rosenfeld. Cf. E. James Lieberman, _La Volonté en acte: la vie et l'œuvre d'Otto Rank_ (1985), París, Presses Universitaires de France, 1991.
. Es decir, exteriores al cenáculo de origen. El vienés Hanns Sachs tampoco formaba parte del primerísimo círculo. Se incorporó a la WPV en 1909 y en 1920 se radicó en Berlín para participar de la expansión del Berliner Psychoanalytisches Institut (BPI). Theodor Reik, otro vienés, se asoció en 1911. Amigo de Jung, el pastor Oskar Pfister visitó a Freud en 1909 y trabó amistad con él. Ambos intercambiaron una importante correspondencia: _Sigmund Freud: correspondance avec le pasteur Pfister..._ , _op. cit_. Cf. É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Los tres títulos terminaron por fusionarse para dar origen al _Internationale Zeitschrift für Psychoanalyse und Imago_ ( _IZP-Imago_ ), que dejaría de aparecer en 1941 para ser reemplazado por el _International Journal of Psychoanalysis_ ( _IJP_ ), fundado por Jones en 1920. Cf. É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Amigo muy honrado, el mejor de los hombres. Cf. A. Bolzinger, _Portrait de Sigmund Freud..._ , _op. cit._
. Cf. Alain de Mijolla, «Images de Freud, au travers de sa correspondance», _Revue internationale d'histoire de la psychanalyse_ , 2, 1989, pp. 9-50, y G. Fichtner, «Les lettres de Freud...» y «Bibliographie des lettres de Freud», _op. cit._ Elisabeth Roudinesco, seminario inédito sobre la correspondencia de Freud, 1999.
. S. Freud, _Sur l'histoire du mouvement..._ , _op. cit._ , p. 13 [ _Contribución a la historia..._ , _op. cit._ , p. 7].
. S. Freud, _Sigmund Freud présenté..._ , _op. cit._
. Sigmund Freud, «Une difficulté de la psychanalyse» (1917), en _OC.P_ , vol. 15, _op. cit._ , pp. 41-51 [hay trad. cast.: «Una dificultad del psicoanálisis», en _OC_ , vol. 17, 1979, pp. 125-135].
. Que en 1936 se convertiría en la International Psychoanalytical Association (IPA). A partir de 1910, todos los grupos constituidos, incluida la WPV, se reunieron en esta organización centralizada.
. Sándor Ferenczi, «De l'histoire du mouvement psychanalytique» (1911), en _Œuvres complètes: psychanalyse_ , vol. 1, _1908-1912_ , París, Payot, 1968, p. 166 [hay trad. cast.: «Sobre la historia del movimiento psicoanalítico», en _Obras completas_ , vol. 1, _1908-1912: psicoanálisis I_ , Madrid, Espasa-Calpe, 1981, pp. 177-187].
. Magnus Hirschfeld (1868-1935): psiquiatra alemán, militó por una mejor comprensión de los «estados sexuales intermedios» (homosexualidad, travestismo, hermafroditismo, transexualismo) y entre 1908 y 1911 participó en la fundación de la Asociación Psicoanalítica de Berlín. En 1897 había creado la primera organización en favor de la igualdad de derechos: el Comité Científico Humanitario (Wissenschaftlich-humanitäres Komitee), que se convertiría luego en el Instituto Hirschfeld. Cf. Laure Murat, _La Loi du genre: une histoire culturelle du troisième sexe_ , París, Fayard, 2006.
. Sándor Ferenczi, «États sexuels intermédiaires», en _Les Écrits de Budapest_ , París, EPEL/École Lacanienne de Psychanalyse, 1994, p. 255 [hay trad. cast.: «Estados sexuales intermedios», en _Obras completas_ , vol. 1, _op. cit._ Cf. asimismo Sándor Ferenczi, _Œuvres complètes_..., vol. 1, _op. cit._ ; _Œuvres complètes: psychanalyse_ , vol. 2, _1913-1919_ , París, Payot, 1970 [hay trad. cast.: _Obras completas_ , vol. 2, _1913-1919: psicoanálisis I_ , Madrid, Espasa-Calpe, 1981]; _Œuvres complètes: psychanalyse_ , vol. 3, _1919-1926_ , París, Payot, 1974 [hay trad. cast.: _Obras completas_ , vol. 3, _1919-1926: psicoanálisis III_ , Madrid, Espasa-Calpe, 1981]; _Œuvres complètes: psychanalyse_ , vol. 4, _1927-1933_ , París, Payot, 1982 [hay trad. cast.: _Obras completas_ , vol. 4, _19127-1933: psicoanálisis IV_ , Madrid, Espasa-Calpe, 1984], y _Journal clinique, janvier-octobre 1932_ , París, Payot, 1985 [hay trad. cast.: _Sin simpatía no hay curación: el diario clínico de 1932_ , Buenos Aires, Amorrortu, 1997]. Véanse también Sándor Ferenczi y Otto Rank, _Perspectives de la psychanalyse: sur l'indépendance de la théorie et de la pratique_ (1924), París, Payot, 1994 [hay trad. cast.: _Metas para el desarrollo del psicoanálisis: de la correlación entre teoría y práctica_ , México, Epeele, 2005]; Sándor Ferenczi y Georg Groddeck, _Correspondance, 1921-1933_ , París, Payot, 1982 [hay trad. cast.: _Correspondencia, 1921-1933_ , Jaén, Del Lunar, 2003], y Sigmund Freud y Sándor Ferenczi, _Correspondance_ , vol. 1, _op. cit._ ; _Correspondance_ , vol. 2, _1914-1919_ , París, Calmann-Lévy, 1996 [hay trad. cast.: _Correspondencia completa, 1908-1919_ , t. I, vol. 1, _1914-1916_ , y t. I, vol. 2, _1917-1919_ , Madrid, Síntesis, 2001], y _Correspondance_ , vol. 3, _1920-1933_ , París, Calmann-Lévy, 2000.
. Encontramos este tema en Sigmund Freud, _Totem et tabou: quelques concordances entre la vie psychique des sauvages et celle des névrosés_ (1912), París, Gallimard, 1993, y _OC.P_ , vol. 11, _op. cit._ , pp. 189-385 [hay trad. cast.: _Tótem y tabú: algunas concordancias en la vida anímica de los salvajes y de los neuróticos_ , en _OC_ , vol. 13, 1980, pp. 1-164].
. Carta de Ferenczi a Freud, 23 de mayo de 1919, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 2, _op. cit._ , pp. 393-394.
. Karl Abraham, _Œuvres complètes_ (1965), 2 vols., París, Payot, 1989 [hay trad. cast.: _Obras completas_ , Barcelona, RBA, 2004], y Sigmund Freud y Karl Abraham, _Correspondance complète, 1907-1925_ (1965), París, Gallimard, 2006 [hay trad. cast.: _Correspondencia completa, 1907-1926_ , Madrid, Síntesis, 2005].
. Freud y Eitingon intercambiaron 821 cartas: Sigmund Freud y Max Eitingon, _Correspondance, 1906-1939_ (2004), París, Hachette Littératures, 2009. Véase también Guido Liebermann, _La Psychanalyse en Palestine, 1918-1948: aux origines du mouvement analytique israélien_ , París, Campagne Première, 2012.
. Sobre el desarrollo del psicoanálisis en Berlín véase _infra_.
. «Policlínica» [ _policlinique_ ]: clínica en la ciudad ( _polis_ ). No confundir con el término «policlínica» [ _polyclinique_ ], lugar de tratamiento de las diversas patologías.
. Se encontrará una muy bella descripción de las actividades de la clínica en la obra de H. F. Ellenberger, _Histoire de la découverte..._ , _op. cit_. Véase también É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Eugen Bleuler, _Dementia praecox ou groupe des schizophrénies_ (1911), París, EPEL-GREC, 1993 [hay trad. cast.: _Demencia precoz: el grupo de las esquizofrenias_ , Buenos Aires, Hormé, 1960].
. No hay en francés una edición estándar de las obras de Jung. La editorial Albin Michel publicó algunas traducciones de estas. Cf. en especial Carl Gustav Jung, _Psychogenèse des maladies mentales_ , París, Albin Michel, 2001 [hay trad. cast.: _Psicogénesis de las enfermedades mentales_ , vol. 1, _Psicología de la demencia precoz_ , Barcelona, Paidós, 1987, y vol. 2, _El contenido de las psicosis_ , Barcelona, Paidós, 1990]. Entre 1906 y 1914 Freud y Jung intercambiaron 359 cartas publicadas en dos volúmenes por Gallimard en 1975. La mejor fuente para la historia de la vida privada de Jung es la biografía de Deirdre Bair, _Jung: une biographie_ , París, Flammarion, 2007. La autora tuvo acceso, en particular, a los «Protocolos», transcripción de conversaciones que sirvieron de esbozo a la autobiografía de Jung. Los diferentes biógrafos dieron varias versiones de las relaciones de este con Freud. El lector encontrará un excelente análisis del destino de Jung en H. F. Ellenberger, _Histoire de la découverte..._ , _op. cit._ Cf. asimismo Carl Gustav Jung, _Ma vie: souvenirs, rêves et pensées_ , recogidos por Aniéla Jaffé (1962), París, Gallimard, 1966 [hay trad. cast.: _Recuerdos, sueños, pensamientos_ , Barcelona, Seix Barral, 1971]. La obra completa de Jung está disponible en inglés y alemán [y en curso de publicación en castellano, por la editorial Trotta de Madrid _(N. del T.)_ ]. El 29 de agosto de 1953 Jung mantuvo una conversación con Kurt Eissler; cf. LoC, caja 114, carpeta 4.
. Carta de Freud a Abraham, 3 de mayo de 1908, en S. Freud y K. Abraham, _Correspondance complète..._ , _op. cit._ , p. 71.
. «Usted será quien, como Josué, si yo soy Moisés, tomará posesión de la tierra prometida de la psiquiatría, que yo solo puedo columbrar a la distancia.» Carta de Freud a Jung, 17 de enero de 1909, en S. Freud y C. G. Jung, _Correspondance_ , vol. 1, _op. cit._ , p. 271.
. Cf. Elisabeth Roudinesco, «Carl Gustav Jung: de l'archétype au nazisme. Dérives d'une psychologie de la différence», _L'Infini_ , 63, otoño de 1998, pp. 73-94.
. Carta de Freud a Abraham, 3 de mayo de 1908, en S. Freud y K. Abraham, _Correspondance complète..._ , _op. cit._ , p. 71. Como todos sus contemporáneos, y según ya he señalado, Freud utilizaba la palabra «raza», así como los términos «semita» y «ario», inventados por los filólogos del siglo XIX. Cf. É. Roudinesco, _Retour sur la question juive_ , _op. cit._
. La lectura de la obra de Théodore Flournoy, _Des Indes à la planète Mars_ (1900), París, Seuil, 1983, había influido mucho a Jung. Cf. _HPF-JL_ , _op. cit._
. Lo que Ellenberger llama una «neurosis creativa».
. Jung llegará a ser el iniciador de una escuela de psicología analítica que no evitará los escollos del sectarismo. Su antisemitismo será cada vez más notorio a partir de la década de 1930. Numerosos trabajos se consagraron a su ruptura con Freud. Al respecto, Deirdre Bair y Peter Gay propusieron versiones sensiblemente diferentes, pero más objetivas, no obstante, que la de Jones. El relato más interesante es el de Linda Donn, _Freud et Jung: de l'amitié à la rupture_ (1988), París, Presses Universitaires de France, 1995 [hay trad. cast.: _Freud y Jung: los años de amistad, los años perdidos_ , Buenos Aires, Javier Vergara, 1990].
. D. Bair, _Jung..._ , _op. cit._ , p. 257.
. Carta de Jung a Freud, 28 de octubre de 1907, en S. Freud y C. G. Jung, _Correspondance_ , vol. 1, _op. cit._ , p. 149. Freud fue el primero en formular la hipótesis de ese «complejo de autoconservación». El autor del atentado era un sacerdote católico, amigo del padre de Jung. Cf. D. Bair, _Jung..._ , _op. cit._ , p. 115.
. El caso fue revelado en 1975 por Stephanie Zumstein-Preiswerk, sobrina de Helene, y estudiado por H. F. Ellenberger, _Médecines de l'âme..._ , _op. cit._
. Psiquiatra inspirado por la corriente fenomenológica de Edmund Husserl y Martin Heidegger, Ludwig Binswanger (1881-1966) también fue durante toda su vida un admirador de Freud y su doctrina. Cf. Sigmund Freud y Ludwig Binswanger, _Correspondance, 1908-1938_ (1992), París, Calmann-Lévy, 1995 [hay trad. cast.: _Correspondencia de Sigmund Freud_ (edición crítica en orden cronológico), vols. 2-5, Madrid, Biblioteca Nueva, 1995-2002].
. Hay varias versiones de este encuentro del que Freud no habla ni en la _Contribución a la historia del movimiento psicoanalítico_ ni en la _Presentación autobiográfica_. He cotejado, por lo tanto, las diferentes fuentes. Cf. C. G. Jung, _Ma vie..._ , _op. cit._ , y «Entretien dactylographié de Carl Gustav Jung avec Kurt Eissler» (1953), LoC. D. Bair hace un relato muy creíble en _Jung..._ , _op. cit._ , pp. 182-189. Cf. asimismo Ludwig Binswanger (que cuenta en parte el acontecimiento), _Discours, parcours et Freud: analyse existentielle, psychiatrie clinique et psychanalyse_ , París, Gallimard, 1970, pp. 267-277 [hay trad. cast.: _Mis recuerdos de Sigmund Freud_ , Buenos Aires, Almagesto, 1992], y M. Freud, _Freud, mon père_ , _op. cit_. Véase también L. Donn, _Freud et Jung..._ , _op. cit._
. Los partidarios del espiritismo creían que un fluido emanado de un sujeto cataléptico podía ser la causa de los crujidos de muebles, los movimientos de veladores y los desplazamientos de objetos.
. Ernest Jones, _La Vie et l'œuvre de Sigmund Freud_ , vol. 2, _Les Années de maturité, 1901-1919_ , París, Presses Universitaires de France, 1958, p. 36 [hay trad. cast.: _Vida y obra de Sigmund Freud_ , vol. 2, _Los años de madurez: 1901-1919_ , Buenos Aires, Hormé, 1989]. El propio Freud, como es sabido, no apreciaba demasiado a sus primeros discípulos de la Sociedad de los Miércoles, como le confiaría más adelante a Binswanger: «Entonces, ¿se da cuenta ahora de lo que es esa banda?», en L. Binswanger, _Discours, parcours..._ , _op. cit._ , p. 271. De ahí su voluntad de rodearse de un nuevo cenáculo.
. L. Binswanger, _Discours, parcours..._ , _op. cit._ , pp. 268-269.
. Sigmund Freud, _Le Délire et les rêves dans la «Gradiva» de W. Jensen_ (1907), París, Gallimard, 1986, y, con el mismo título, París, Seuil, 2013, col. «Points Essais», con un hermoso prefacio de Henri Rey-Flaud [hay trad. cast.: _El delirio y los sueños en la «Gradiva» de W. Jensen_ , en _OC_ , vol. 9, 1979, pp. 1-79].
. Carta de Freud a Schnitzler, 8 de mayo de 1906, en _Correspondance, 1873-1939_ , _op. cit._ , p. 270 [ _Epistolario, 1873-1939_ , _op. cit._ , p. 282].
. Otto Gross, _Psychanalyse et révolution: essais_ , París, Éditions du Sandre, 2011, con una extensa y notable presentación de Jacques Le Rider. D. Bair, _Jung..._ , _op. cit._ , pp. 209-223, hace un relato interesante de las relaciones entre Jung y Otto Gross.
. Hay que vincular las tesis de Hans Gross con las de la «pedagogía negra».
. Sobre este aspecto de la vida de Gross puede consultarse la obra de Martin Burgess Green, _Les Sœurs Von Richthofen: deux ancêtres du féminisme dans l'Allemagne de Bismarck, face à Otto Gross, Max Weber et D. H. Lawrence_ (1974), París, Seuil, 1979.
. Ernest Jones trabajaba por entonces en la clínica. Cf. carta de Jones a Freud, 13 de mayo de 1908, en Sigmund Freud y Ernest Jones, _Correspondance complète, 1908-1939_ (1993), París, Presses Universitaires de France, 1998, p. 47 [hay trad. cast.: _Correspondencia completa, 1908-1939_ , Madrid, Síntesis, 2001].
. Hubo muchos otros, entre ellos Victor Tausk, Georg Groddeck y Wilhelm Reich, los tres más célebres e inventivos.
. Citado en O. Gross, _Psychanalyse et révolution..._ , _op. cit._ , p. 78.
. Ernest Jones, _Free Associations: Memories of a Psycho-analyst_ , Nueva York, Basic Books, 1959. Además de la biografía de Freud, Jones escribió numerosos artículos incluidos en varias compilaciones: _Hamlet et Œdipe_ (1949), París, Gallimard, 1967 [hay trad. cast.: _Hamlet y Edipo_ , Barcelona, Mandrágora, 1975], y _Essais de psychanalyse appliquée_ , vol. 1, _Essais divers_ , y vol. 2, _Psychanalyse, folklore, religion_ (1923-1964), París, Payot, 1973 [hay trad. cast.: _Ensayos de psicoanálisis aplicado_ , en _Obras escogidas_ , Barcelona, RBA, 2006]. Entre 1908 y 1939 Freud y Jones intercambiaron 671 cartas.
. Cartas de Freud a Jung, 3 de mayo y 18 de julio de 1908, respectivamente, en S. Freud y C. G. Jung, _Correspondance_ , vol. 1, _op. cit._ , pp. 210 y 233.
. Su verdadero nombre era Louise Dorothea Kann.
. Entre las dos guerras, la APsA se convertiría en la mayor potencia psicoanalítica de la IPA, ya que logró reunir en su seno a todas las sociedades psicoanalíticas americanas compuestas, a continuación, por casi todos los emigrados de lengua alemana escapados de Europa tras el ascenso del nazismo al poder en 1933. Desde Londres, Jones mantendría un poder real sobre esa asociación.
. James Jackson Putnam se carteó con Freud. Cf. Nathan G. Hale, ed., _L'Introduction de la psychanalyse aux États-Unis: autour de James Jackson Putnam_ (1958), París, Gallimard, 1978.
. Sobre la historia de la implantación del psicoanálisis en Canadá, cf. É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Lisa Appignanesi y John Forrester, _Freud's Women_ , Nueva York, Basic Books, 1992 [hay trad. cast.: _Las mujeres de Freud_ , Buenos Aires, Planeta, 1996].
. En 1910, consciente de los efectos nefastos de esa manía, Freud dio el nombre de «psicoanálisis silvestre» a un error técnico cometido por el analista, consistente en introducir en la mente del paciente, ya en la primera sesión, secretos que cree haber adivinado. Cf. Sigmund Freud, «De la psychanalyse sauvage» (1910), en _OC.P_ , vol. 10, _op. cit._ , pp. 118-125 [hay trad. cast.: «Sobre el psicoanálisis "silvestre"», en _OC_ , vol. 11, _op. cit._ , pp. 217-227].
. La historia de Sabina Spielrein fue motivo de unas cuantas novelas y películas, en especial la muy lograda de David Cronenberg, _Un método peligroso_ [ _A Dangerous Method_ ], de 2011, y se la contó varias veces. Hay además varios relatos sobre ella. Cf. Aldo Carotenuto y Carlo Trombetta, eds., _Sabina Spielrein entre Freud et Jung: dossier découvert par Aldo Carotenuto et Carlo Trombetta_ (1980), edición francesa establecida por Michel Guibal y Jacques Nobécourt, París, Aubier-Montaigne, 1981 [hay trad. cast.: _Una secreta simetría: Sabina Spielrein entre Freud y Jung_ , Barcelona, Gedisa, 1984]. En ese libro se reúnen los principales artículos de Sabina Spielrein. Véase asimismo «Sabina Spielrein, un classique méconnu de la psychanalyse» (documento colectivo), _Le Coq-Héron_ , 197, agosto de 2009. Y también É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit_. Deirdre Bair relata en detalle, con la aportación de nuevos elementos, el tratamiento de Sabina y sus relaciones con Jung y Bleuler.
. Informe de Carl Gustav Jung, citado por D. Bair, _Jung..._ , _op. cit._ , p. 139, que lo consultó en los archivos del Burghölzli.
. Carta de Freud a Jung, 27 de octubre de 1906, en S. Freud y C. G. Jung, _Correspondance_ , vol. 1, _op. cit._ , p. 47.
. Sabina Spielrein, «Über den psychologischen Inhalt eines Fallen von Schizophrenie ( _Dementia praecox_ )», _Jahrbuch für psychoanalytische und psychopathologische Forschungen_ , 3, agosto de 1911, pp. 329-400 [hay trad. cast.: «Sobre el contenido psicológico de un caso de esquizofrenia ( _Dementia praecox_ )», _Clínica y Pensamiento_ , núm. extra 1, 2005, pp. 29-106]. El texto fue reproducido y comentado en Carl Gustav Jung, _Métamorphoses et symboles de la libido_ (1912), París, Buchet-Castel, 1953, reeditado con el título de _Métamorphoses de l'âme et ses symboles: analyse des prodromes d'une schizophrénie_ , Ginebra, Georg, 1973 [hay trad. cast.: _Símbolos de transformación: análisis del preludio a una esquizofrenia_ , Madrid, Trotta, 2012].
. Sabina Spielrein, «La destruction comme cause du devenir» (1912), en A. Carotenuto y C. Trombetta, eds., _Sabina Spielrein entre Jung..._ , _op. cit._ , pp. 212-262.
. Carta de Freud a Sabina Spielrein, en _ibid._ , p. 273. A posteriori, Freud no dejaría nunca de reprocharle a Sabina su apego constante a Jung; llegó al extremo de hacerle interpretaciones salvajes sobre su presunto deseo de tener un hijo de él, idealizado como «caballero germánico», como una manera de expresar mejor su rebelión contra un padre de quien, en realidad, ella habría anhelado un hijo.
. Elisabeth Roudinesco, «Les premières femmes psychanalystes», _Mil neuf cent: revue d'histoire intellectuelle_ , 16, 1998, pp. 27-41; reeditado en _Topique_ , 71, 2000, pp. 45-56; véase también seminario inédito, 1998. Cf. asimismo É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._ Entre las cuarenta y dos mujeres integrantes de la WPV en 1938, la tasa de suicidio, locura y muerte violenta era un poco más alta que entre los hombres. É. Roudinesco, seminario inédito, y É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Antonia Anna Wolff (1888-1953): paciente y luego amante y discípula de C. G. Jung.
. D. P. Schreber, _Mémoires d'un névropathe_ , _op. cit._ , y S. Freud, «Remarques psychanalytiques...», _op. cit_.
. Tesis retomada en _Tótem y tabú_.
. Martin Stingelin, «Les stratégies d'autolégitimation dans l'autobiographie de Schreber», en Daniel Devreese, Zvi Lothane y Jacques Schotte, eds., _Schreber revisité: colloque de Cerisy_ , Lovaina, Presses Universitaires de Louvain, 1998, pp. 115-127.
. Luiz Eduardo Prado de Oliveira, ed., _Le Cas Schreber: contributions psychanalytiques de langue anglaise_ , París, Presses Universitaires de France, 1979, y C. Azouri, « _J'ai réussi où..._ », _op. cit._
. Elias Canetti, _Masse et puissance_ (1960), París, Gallimard, 1966 [hay trad. cast.: _Masa y poder_ , Barcelona, Muchnik, 1994].
. Rudolf von Urbantschitsch (1879-1964): psiquiatra y psicoanalista, emigraría a California en 1936.
. La reconstrucción de esta trágica historia se debe a Ulrike May. Cf. Renate Sachse, «À propos de la recherche d'Ulrike May: sur dix-neuf patients en analyse chez Freud (1910-1920)», _Essaim_ , 2, 2008, pp. 187-194, y Ulrike May, «Freuds Patientenkalender: Siebzehn Analytiker in Analyse bei Freud (1910-1920)», _Luzifer-Amor_ , 19(37), 2006, pp. 43-97. Cf. asimismo M. Borch-Jacobsen, _Les Patients de Freud..._ , _op. cit._
. C. G. Jung menciona el caso del «hombre del sol fálico» en _Métamorphoses et symboles de la libido_ , _op. cit_. Jung había puesto el tratamiento de este paciente en manos de su alumno Johann Honneger, afectado por trastornos maníacos, que puso fin a sus días en marzo de 1911 con una dosis masiva de morfina.
#### 3. EL DESCUBRIMIENTO DE AMÉRICA
. La mejor obra sobre la introducción del psicoanálisis en Estados Unidos es Nathan Hale, _Freud et les Américains: l'implantation de la psychanalyse aux États-Unis_ (1971, 1995), París, Les Empêcheurs de Penser en Rond, 2001. Cf. asimismo Eli Zaretsky, _Le Siècle de Freud: une histoire sociale et culturelle de la psychanalyse_ (2004), París, Albin Michel, 2008 [hay trad. cast.: _Secretos del alma: una historia social y cultural del psicoanálisis_ , Madrid, Siglo XXI, 2012].
. N. Hale, _Freud et les Américains..._ , _op. cit._ , p. 43.
. Sigmund Freud, «La morale sexuelle "civilisée" et la maladie nerveuse des temps modernes» (1908), en _La Vie sexuelle_ , París, Presses Universitaires de France, 1973, pp. 28-46, y con el título de «La morale sexuelle "culturelle"», _OC.P_ , vol. 8, 2007, pp. 196-219 [hay trad. cast.: «La moral sexual "cultural" y la nerviosidad moderna», en _OC_ , vol. 9, _op. cit._ , pp. 159-181].
. Hay numerosas versiones del viaje de los tres hombres a Estados Unidos. Pueden leerse las de Ernest Jones, Peter Gay, Linda Donn, Deirdre Bair, Nathan Hale y, por último, Vincent Brome, _Les Premiers disciples..._ , _op. cit._ , y _Jung: Man and Myth_ , Nueva York, Atheneum, 1981. A ello se agregan los testimonios mismos de los protagonistas: Jung menciona el periplo en _Ma vie..._ , _op. cit._ , así como en su conversación con Kurt Eissler conservada en la Biblioteca del Congreso. Freud habla del viaje en _«Notre cœur tend vers le sud»_..., _op. cit._ También hay que leer las diferentes correspondencias entre Ferenczi, Jung, Freud, Putnam y Stanley Hall. Consulté asimismo, sobre este punto, la obra de Saul Rosenzweig, _Freud, Jung, and Hall the King-Maker: The Historic Expedition to America, with G. Stanley Hall as Host and William James as Guest_ , Saint Louis y Seattle, Rana House/Hogrefe & Huber, 1992, y Anthony Ballenato, «Freud et la modernité américaine: l'introduction de la psychanalyse à New York (1909-1917)», máster II, Universidad de París VII, 2007-2008, bajo la dirección de Elisabeth Roudinesco. Anthony Ballenato utilizó archivos inéditos.
. Freud omitió referirse a este incidente en su diario de viaje, y se contentó con señalar que había sido víctima de un ataque de debilidad a causa del cansancio.
. C. G. Jung, _Ma vie..._ , _op. cit._ , pp. 187-189. El tema de lo arcaico es recurrente en la historia del psicoanálisis y reaparecerá bajo otras formas en los debates ulteriores entre Freud y Rank; más tarde entre los freudianos y los kleinianos, y por último con los lacanianos. Lo abordé en _HPF-JL_ , _op. cit._ Cf. asimismo las posiciones de Nicolas Abraham y Maria Torok sobre la cuestión de la cripta, y H. Rey-Flaud, _Je ne sais pas de quoi..._ , _op. cit._
. Cosa que permite una vez más a los antifreudianos afirmar que Freud era antisemita, y a los junguianos, que Jung no lo era porque simpatizaba con un judío y un buen número de sus discípulos también lo eran. William Stern (1871-1938) había sido invitado a Worcester en la misma calidad que muchos otros psicólogos.
. Esos son los términos exactos pronunciados por Freud y comunicados por Jung en su conversación de la Biblioteca del Congreso con Kurt Eissler. Cf. asimismo V. Brome, _Jung: Man and Myth_ , _op. cit._ , p. 117. Sobre la génesis de la frase inventada por Lacan en 1955 y atribuida a Freud, tras su propio encuentro con Jung, cf. Elisabeth Roudinesco, _HPF-JL_ , _op. cit._ , y «Lacan, the plague», _Psychoanalysis and History_ , 10(2), julio de 2008, pp. 225-236. Lacan pretende que Freud habría dicho: «No saben que les traemos la peste». Hoy se sabe, pues, que Freud jamás pronunció esa frase. Pero la leyenda es tenaz.
. Carta de Freud a Ferenczi, 10 de enero de 1909, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 1, _op. cit._ , p. 40.
. Propagado a continuación por Jung, el rumor de un Freud incestuoso se convirtió con el paso de los años en una de las grandes temáticas de la historiografía psicoanalítica en el mundo angloparlante, sobre todo a partir de la publicación, en 1947, de la obra de Helen Walker Puner, _Freud: His Life and Mind_ , Nueva York, Howell, Soskin; reedición, New Brunswick (New Jersey), Transaction Publishers, 1992, con presentación de Paul Roazen y prefacio de Erich Fromm [hay trad. cast.: _Freud, su vida y su mente_ , Barcelona, Luis Miracle, 1951]. Ningún historiador serio pudo jamás presentar la más mínima prueba de la existencia de esa «relación», que dio lugar a un sinnúmero de artículos y varios libros. Cf. Elisabeth Roudinesco, _Mais pourquoi tant de haine?_ , París, Seuil, 2010 [hay trad. cast.: _¿Por qué tanto odio?_ , Buenos Aires, Libros del Zorzal, 2011].
. Hay varias versiones de esta historia. Cf. la conversación de Carl Gustav Jung con Kurt Eissler, 29 de agosto de 1953, LoC, caja 114, carpeta 4, reproducida por Deirdre Bair, y C. G. Jung, _Ma vie..._ , _op. cit._ , p. 185. Esta es la traducción de las palabras de Jung: «La hermana menor tenía una gran transferencia con Freud y él no era insensible a eso». Y: «Oh, ¿un amorío? No sé hasta qué punto, pero, Dios mío, uno sabe bien cómo son esas cosas, ¿no?». Más adelante presento la versión original, en alemán, de esta declaración (véase la nota 7 en la tercera parte, capítulo 2).
. Cf. D. Bair, _Jung..._ , _op. cit._ , p. 254.
. El mejor relato de este episodio está en William A. Koelsch, «"Incredible daydream": Freud and Jung at Clark, 1909», The Fifth Annual S. Clarkson Lecture, 1909, Worcester, Friends of the Goddard Library, Clark University, 1984 (celebración del septuagésimo quinto aniversario de la visita de Freud). Versión francesa: «"Une incroyable rêverie": Freud et Jung à Clark, 1909», puede consultarse en «D'un divan l'autre», http://www.dundivanlautre.fr/sur-freud/w-koelsch-freud-et-jung-a-la-clark-university. Koelsch investigó los archivos de la universidad y proporcionó numerosos detalles sobre los conferenciantes invitados en 1909 y presentes en las conferencias dictadas por Freud entre el 6 y el 10 de septiembre. Es preciso completar esta fuente con los comentarios de Deirdre Bair, que brinda detalles sobre las reacciones de Jung. Señalemos que Freud estaba convencido de que algún día los negros serían mayoritarios en Estados Unidos.
. En una de sus conferencias Jung expuso el caso de una niña: se trataba de su propia hija.
. A continuación, Freud puso por escrito esas cinco conferencias, muy pronto traducidas a varios idiomas. Cf. Sigmund Freud, _Sur la psychanalyse: cinq conférences_ (1910), París, Gallimard, 1991; cita sobre Bell en pp. 92-93 [hay trad. cast.: «Cinco conferencias sobre psicoanálisis», en _OC_ , vol. 11, _op. cit._ , pp. 1-51; cita en pp. 37-38].
. S. Freud, _Sigmund Freud présenté..._ , _op. cit._ , p. 88 [ _Presentación autobiográfica_ , _op. cit._ , pp. 48-49].
. Emma Goldman, _Living my Life_ , vol. 1, Nueva York, A. A. Knopf, 1931, p. 173 [hay trad. cast.: _Viviendo mi vida_ , Madrid, Fundación de Estudios Libertarios Anselmo Lorenzo/Nossa y Jara, 1995], y A. Ballenato, «Freud et la modernité américaine...», _op. cit._ , p. 30.
. L. Donn, _Freud et Jung..._ , _op. cit._ , p. 138.
. Testimonio de Judith Bernays Heller, LoC, citado, y Marion Ross, «Carnets, miscellaneous, 1914-1975», LoC, caja 121, carpeta 7.
. Freud retomaría esta idea en _Psychologie des masses et analyse du moi_ (1921), en _OC.P_ , vol. 16, 2010, pp. 1-85 [hay trad. cast.: _Psicología de las masas y análisis del yo_ , en _OC_ , vol. 18, _op. cit._ , pp. 63-136; mención de la parábola de Schopenhauer en p. 96].
. Testimonio de Barbara Low (1877-1955), s.d., LoC, caja 121, carpeta 5.
. Del que terminaría curándose.
. Carta de Freud a Jung, 17 de octubre de 1909, en _Correspondance_ , vol. 1, _op. cit._ , p. 336. Sigmund Freud, _Un souvenir d'enfance de Léonard de Vinci_ (1910), París, Gallimard, 1987, con un excelente prefacio de Jean-Bertrand Pontalis y una buena bibliografía de las fuentes en las que se basó Freud. Con el mismo título, también en _OC.P_ , vol. 10, _op. cit._ , pp. 79-164 [hay trad. cast.: _Un recuerdo infantil de Leonardo da Vinci_ , en _OC_ , vol. 11, _op. cit._ , pp. 53-127]. Escrito entre enero y marzo de 1910, el ensayo se publicó en mayo de ese mismo año.
. Pueden consultarse en la biblioteca de Freud, con las anotaciones de puño y letra. En su obra cita a veces la versión original de los textos italianos, aunque en su biblioteca tenía la traducción alemana. En francés: Eugène Müntz, _Léonard de Vinci, l'artiste, le penseur, le savant_ , París, Hachette, 1899 [hay trad. cast.: _Leonardo de Vinci: el artista, el pensador, el sabio_ , Buenos Aires, El Ateneo, 1956]; Giorgio Vasari, _La Vie des meilleurs peintres, sculpteurs et architectes_ (1550), 2 vols., edición dirigida por André Chastel, París, Berger-Levrault, 1983 [hay trad. cast.: _Las vidas de los más excelentes arquitectos, pintores y escultores italianos desde Cimabue a nuestros días_ , Madrid, Cátedra, 2007]; Dmitri S. Merezhkovski, _Le Roman de Léonard de Vinci: la résurrection des dieux_ (1902), París, Gallimard, 1934 (se trata de la parte central de una trilogía titulada _Cristo y Anticristo_ ) [hay trad. cast.: _El romance de Leonardo, el genio del Renacimiento_ , Barcelona, Edhasa, 2004], y Nino Smiraglia Scognamiglio, _Ricerche e documenti sulla giovinezza di Leonardo da Vinci, 1452-1482_ , Nápoles, Riccardo Margheri Di Gius, 1900.
. Marie Bonaparte se enfrentaría a toda una intriga al publicarse su traducción francesa del libro de Freud.
. S. Freud, _Un souvenir d'enfance..._ , _op. cit._ , p. 89 [ _Un recuerdo infantil..._ , _op. cit._ , p. 77].
. Códice Atlántico: recopilación de dibujos y notas de Leonardo da Vinci conservado en la Biblioteca Ambrosiana de Milán. Cf. Sigmund Freud, _Eine Kindheitserinnerung des Leonardo da Vinci_ , en _Studienausgabe_ , vol. 10, Frankfurt, S. Fischer Verlag, 1982, p. 109, n. 1.
. Freud utilizaba aquí por primera vez este término.
. Leonardo pintó el primero de esos cuadros entre 1503 y 1506, y el segundo entre 1508 y 1516.
. En 1956 Meyer Schapiro reprocharía a Freud no solo su confusión entre el buitre y el milano, sino también, y sobre todo, su desconocimiento de la historia del arte. Así como el primer error me parece mínimo, es preciso tener en cuenta el segundo, que es un testimonio de los peligros propios de la interpretación, aun cuando sepamos que Freud tenía conocimiento de los bosquejos, que comenta en notas añadidas en 1919 y 1923. Cf. Meyer Schapiro, «Léonard et Freud», en _Style, artiste et société: essais_ , París, Gallimard, 1982 [hay trad. cast.: «Freud y Leonardo: un estudio histórico del arte», en _Estilo, artista y sociedad: teoría y filosofía del arte_ , Madrid, Tecnos, 1999]. Kurt Eissler respondió a Schapiro en _Léonard de Vinci: étude psychanalytique_ (1961), París, Gallimard, 1982. Véase también Jacques Lacan, _Le Séminaire, Livre IV, La Relation d'objet (1956-1957)_ , texto establecido por Jacques-Alain Miller, París, Seuil, 1994, pp. 411-435 [hay trad. cast.: _El Seminario de Jacques Lacan. Libro 4. La relación de objeto. 1956-1957_ , Buenos Aires, Paidós, 1998]. Los antifreudianos trataron a Freud de estafador y falsario. Cf. Han Israëls, «L'homme au vautour: Freud et Léonard de Vinci», en Catherine Meyer, ed., _Le Livre noir de la psychanalyse: vivre, penser et aller mieux sans Freud_ , París, Les Arènes, 2005 [hay trad. cast.: «El hombre del buitre: Freud y Leonardo da Vinci», en _El libro negro del psicoanálisis: vivir, pensar y estar mejor sin Freud_ , Buenos Aires, Sudamericana, 2007].
. S. Freud, _Un souvenir d'enfance..._ , _op. cit._ , p. 152 [ _Un recuerdo infantil..._ , pp. 112-113].
. Sobre todo, como hemos visto, al hacer de la paranoia una manifestación de defensa contra la homosexualidad.
. Dan Brown aprovechará ampliamente este juego del desciframiento infinito para escribir _El código Da Vinci_. Por otra parte, un caricaturista anónimo, al dibujar el rostro de Freud, pondrá en lugar de su nariz y su frente el cuerpo en éxtasis de una mujer desnuda, acompañado por esta frase: _What's on a man's mind_. Vendida en millares de ejemplares, la caricatura se reprodujo a continuación casi tanto como _La Gioconda_ en prendas de vestir y diversos artículos de consumo.
. La expresión aparece por primera vez en 1910 en S. Freud, «D'un type particulier de choix...», _op. cit._ , p. 197 [«Sobre un tipo particular de elección...», _op. cit._ , p. 164]. Reiteremos que Freud se equivoca al referirse a la aparición del complejo en su obra, que remonta a _La interpretación de los sueños_.
. _Ibid._
. S. Freud, _Totem et tabou..._ , _op. cit._
. Dediqué mi seminario de 1995 al estudio de las relaciones entre el psicoanálisis y la antropología. Retomo aquí varios elementos de ese curso. Cf. asimismo Elisabeth Roudinesco, prefacio a Georges Devereux, _Psychothérapie d'un indien des plaines: réalité et rêve_ , reedición, París, Fayard, 1998, y É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit_. Véase también Claude Lévi-Strauss, _Le Totémisme aujourd'hui_ , París, Presses Universitaires de France, 1962 [hay trad. cast.: _El totemismo en la actualidad_ , México, Fondo de Cultura Económica, 1965]. Freud citaba en abundancia la obra del historiador francés Salomon Reinach, _Cultes, mythes et religions_ , 5 vols., París, Ernest Leroux, 1905-1923.
. Edward Burnett Tylor, _La Civilisation primitive_ (1871), 2 vols., París, Reinwald, 1876-1878 [hay trad. cast.: _Cultura primitiva_ , 2 vols., Madrid, Ayuso, 1976-1981]; William Robertson Smith, _Lectures on the Religion of the Semites: The Fundamental Institutions_ (1889), Nueva York, Macmillan, 1927; Edward Westermarck, _Histoire du mariage_ (1891), 4 vols., París, Mercure de France, 1934-1938 [hay trad. cast.: _Historia del matrimonio en la especie humana_ , Madrid, La España Moderna, 1900]; James Jasper Atkinson, «Primal law», en Andrew Lang, ed., _Social Origins_ , Londres, Nueva York y Bombay, Longmans, Green, and Co., 1903, y James George Frazer, _Le Rameau d'or_ (1911-1915), 4 vols., París, Laffont, 1981-1984, col. «Bouquins» [hay trad. cast.: _La rama dorada: magia y religión_ , México, Fondo de Cultura Económica, 2011 (traducción de la edición inglesa resumida de 1922)]. En la biblioteca de Freud está la edición inglesa de la obra de Frazer.
. Remito aquí a las entradas de É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._ , y a Alfred L. Kroeber, « _Totem and Taboo_ : an ethnological psychoanalysis» (1920), _American Anthropologist_ , 22, 1920, pp. 48-55 [hay trad. cast.: « Tótem y tabú: un psicoanálisis etnológico», _Artefacto_ (México), 6, «El parricidio», 1998]; Bronislaw Malinowski, _Les Argonautes du Pacifique occidental_ (1922), París, Gallimard, 1963 [hay trad. cast.: _Los argonautas del Pacífico occidental: un estudio sobre comercio y aventura entre los indígenas de los archipiélagos de la Nueva Guinea melanésica_ , Barcelona, Planeta-Agostini, 1986], y _La Sexualité et sa répression dans les sociétés primitives_ (1927), París, Payot, 1932 [hay trad. cast.: _Sexo y represión en la sociedad primitiva_ , Buenos Aires, Nueva Visión, 1974]; E. Jones, _Essais de psychanalyse appliquée_ , vol. 2, _op. cit._ , y Eugène Enriquez, _De la horde à l'État: essai de psychanalyse du lien social_ , París, Gallimard, 1983.
. S. Freud, « _Notre cœur tend vers le sud_ »..., _op. cit._ , p. 331.
. Testimonio de Jerome Alexander, 21 de octubre de 1951, LoC, caja 120, carpeta 2.
. Sigmund Freud, «Le _Moïse_ de Michel-Ange» (1914), en _L'Inquiétante étrangeté et autres textes_ , París, Gallimard, 1985, pp. 83-125 [hay trad. cast.: «El Moisés de Miguel Ángel», en _OC_ , vol. 13, _op. cit._ , pp. 213-242].
. Cf. E. Jones, _La vie et l'œuvre..._ , vol. 2, _op. cit._ , pp. 386-390, e Ilse Grubrich-Simitis, _Freud, retour aux manuscrits: faire parler des documents muets_ (1993), París, Presses Universitaires de France, 1997, pp. 217-218 [hay trad. cast.: _Volver a los textos de Freud: dando voz a documentos mudos_ , Madrid, Biblioteca Nueva/Asociación Psicoanalítica de Madrid, 2003].
. Phyllis Grosskurth, _Freud: l'anneau secret_ (1991), París, Presses Universitaires de France, 1995.
. Gerhard Wittenberger y Christfried Tögel, eds., _Die Rundbriefe des «Geheimen Komitees»_ , 4 vols., Tubinga, Diskord, 1995-2006 [hay trad. cast. parcial: _Las circulares del «Comité Secreto»_ , 2 vols., Madrid, Síntesis, 2002 (vol. 1, _1913-1920_ , vol. 2, _1921_ )].
. Carta de Freud a Mitzi Freud, 13 de julio de 1914, papeles de familia, LoC.
. Cf. P. Gay, _Freud, une vie_ , _op. cit._ , p. 401. Phyllis Grosskurth hace una buena descripción de las actividades del comité durante la guerra, y luego entre 1920 y 1927. Para comprender bien el período previo al conflicto es menester, desde luego, hacer un examen cruzado de la correspondencia entre Freud y sus discípulos.
. Sigmund Freud, «Pour introduire le narcissisme» (1914), en _La Vie sexuelle_ , _op. cit._ , pp. 81-105, y _OC.P_ , vol. 12, 2005, pp. 213-247 [hay trad. cast.: «Introducción del narcisismo», en _OC_ , vol. 14, _op. cit._ , pp. 65-98].
#### 4. LA GUERRA DE LAS NACIONES
. Carta de Freud a Abraham, 26 de julio de 1914, en S. Freud y K. Abraham, _Correspondance complète..._ , _op. cit._ , p. 234.
. Mathilde, la mayor de las hijas de Freud, casada con Robert Hollitscher, y Sophie, esposa de Max Halberstadt, vivían en Hamburgo.
. Carta de Freud a Andreas-Salomé, 25 de noviembre de 1914, en Lou Andreas-Salomé, _Correspondance avec Sigmund Freud, 1912-1936, suivi du Journal d'une année, 1912-1913_ (1966), París, Gallimard, 1970, p. 29 [hay trad. cast.: _Sigmund Freud, Lou Andreas-Salomé: correspondencia_ , México, Siglo XXI, 1977].
. Carta de Freud a Ferenczi, 23 de agosto de 1914, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 1, _op. cit._
. Peter Gay dedica hermosas páginas a este momento freudiano de la guerra. Cf. P. Gay, _Freud, une vie_ , _op. cit._ , pp. 395-411. Cf. asimismo P. Grosskurth, _Freud: l'anneau secret_ , _op. cit._ , pp. 56-86.
. Sigmund Freud, «Actuelles sur la guerre et la mort» (1915), en _OC.P_ , vol. 13, 2005, pp. 125-157 [hay trad. cast.: «De guerra y muerte. Temas de actualidad», en _OC_ , vol. 14, _op. cit._ , p. 282]. He escogido la excelente traducción de Marc Crépon y Marc B. de Launay: Sigmund Freud, «Considération actuelle sur la guerre et la mort», en _Anthropologie de la guerre_ , edición bilingüe, París, Fayard, 2010, p. 267, con epílogo de Alain Badiou («Le malaise des fils dans la "civilisation" contemporaine»).
. Homero, _L'Odysée_ , traducción de Victor Bérard, París, Les Belles Lettres, 1925, vol. 2, pp. 178-179 [hay trad. cast.: _Odisea_ , Madrid, Gredos, 1982, entre otras ediciones].
. S. Freud, «Considération actuelle...», _op. cit._ , p. 313 [«De guerra y muerte...», _op. cit._ , p. 301].
. Carta de Freud a Ferenczi, 11 de marzo de 1914, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 1, _op. cit._ , p. 583.
. A. Bolzinger, _Portrait de Sigmund Freud..._ , _op. cit._ , p. 80.
. Carta de Freud a Ferenczi, 6 de noviembre de 1917, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 2, _op. cit._
. Y a partir de 1920: el yo, el ello y el superyó.
. Sigmund Freud, «Pulsions et destin des pulsions», «Le refoulement», «L'inconscient», «Complément métapsychologique à la doctrine du rêve» y «Deuil et mélancolie», en _OC.P_ , vol. 13, _op. cit._ [hay trad. cast.: «Pulsiones y destino de pulsión», «La represión», «Lo inconsciente», «Complemento metapsicológico a la doctrina de los sueños» y «Duelo y melancolía», en _OC_ , vol. 14, _op. cit._ ]. Cf. asimismo Sigmund Freud, _Métapsychologie_ , París, Gallimard, 1986, y Sándor Ferenczi, «La métapsychologie de Freud», en _Œuvres complètes_..., vol. 4, _op. cit._ , pp. 253-265 [hay trad. cast.: «La metapsicología de Freud», en _Obras completas_ , vol. 4, _op. cit._ ]. Los textos metapsicológicos de Freud se cuentan entre los más comentados por la comunidad psicoanalítica internacional, pero son pocos los comentarios que suscitan entre los investigadores. Cf. É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. El 30 de diciembre de 1914 Victor Tausk había hecho una comunicación al respecto a la WPV. A continuación Freud escribió un primer esbozo de su texto.
. S. Freud y K. Abraham, _Correspondance complète..._ , _op. cit._ , pp. 376-383.
. Sigmund Freud, _Vue d'ensemble des névroses de transfert: un essai métapsychologique_ (1985), París, Gallimard, 1986 [hay trad. cast.: _Sinopsis de las neurosis de transferencia: ensayo de metapsicología_ , Barcelona, Ariel, 1989]. Texto hallado en 1983 en los archivos de Ferenczi y comentado por Ilse Grubrich-Simitis.
. Sándor Ferenczi, «Le développement du sens de réalité et ses stades» (1913), en _Œuvres complètes_..., vol. 2, _op. cit._ , pp. 51-65 [hay trad. cast.: «El desarrollo del sentido de realidad y sus estadios», en _Obras completas_ , vol. 2, _op. cit._ , pp. 63-79].
. La teoría de la recapitulación afirma que el desarrollo individual de un organismo reproduce las etapas de la evolución de sus ancestros.
. Cf. Lucille B. Ritvo, _L'Ascendant de Darwin sur Freud_ (1990), París, Gallimard, 1992. En esta obra se encontrará el mejor análisis de la teoría freudiana de la recapitulación, tomada tanto de Darwin como de Jean-Baptiste Lamarck. Ese análisis contradice, con toda la razón, la tesis de Frank J. Sulloway, para quien Freud es un criptobiólogo. Sería más bien un biólogo del alma, un heredero del romanticismo y un continuador de las filosofías del sujeto.
. S. Freud, _Vue d'ensemble des névroses..._ , _op. cit._ , p. 132, y carta de Ferenczi a Freud, 26 de octubre de 1915, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 2, _op. cit._ , p. 97.
. Jean-Baptiste Lamarck, _Philosophie zoologique_ (1809), París, Éditions Culture et Civilisation, 1969 [hay trad. cast.: _Filosofía zoológica_ , Barcelona, Alta Fulla, 1986].
. Contrariamente a una extendida idea, se sabe que ambas concepciones de la evolución de la humanidad no se oponían. Como Lamarck, Darwin tenía en cuenta la idea de la herencia de los caracteres adquiridos. Esta tesis, sostenida por Freud y Ferenczi contra Jones, había sido invalidada por August Weismann.
. Carta de Freud a Abraham, 11 de noviembre de 1917, en S. Freud y K. Abraham, _Correspondance complète..._ , _op. cit._ , p. 449.
. Sigmund Freud, _Conférences d'introduction à la psychanalyse_ (1916-1917), París, Gallimard, 1999, y, con el título de _Leçons d'introduction à la psychanalyse_ , _OC.P_ , vol. 14, 2000 [hay trad. cast.: _Conferencias de introducción al psicoanálisis_ , en _OC_ , vols. 15 y 16, 1978].
. Cf. _HPF-JL_ , _op. cit._
. S. Freud y K. Abraham, _Correspondance complète..._ , _op. cit._ , pp. 452-453.
. Phyllis Grosskurth, _Melanie Klein: son monde et son œuvre_ (1986), París, Presses Universitaires de France, 1990, p. 101 [hay trad. cast.: _Melanie Klein: su mundo y su obra_ , Barcelona, Paidós, 1990], y Sigmund Freud, «Les voies nouvelles de la thérapeutique psychanalytique» (1918), en _La Technique psychanalytique_ , París, Presses Universitaires de France, 1975, pp. 131-141, y, con el título de «Les voies de la thérapie psychanalytique», _OC.P_ , vol. 15, _op. cit._ , pp. 97-109 [hay trad. cast.: «Nuevos caminos de la técnica psicoanalítica», en _OC_ , vol. 17, _op. cit._ , pp. 151-163].
. S. Freud, «Les voies nouvelles...», _op. cit._ , p. 141 [«Nuevos caminos...», _op. cit._ , p. 163]. Como es sabido, este programa comenzaría a hacerse realidad con la fundación en Berlín del primer Instituto de Psicoanálisis, modelo que se repetiría en el mundo entero.
. Sigmund Freud, Sándor Ferenczi y Karl Abraham, _Sur les névroses de guerre_ , París, Payot & Rivages, 2010, con un bello prefacio de Guillaume Piketti. Ernst Simmel (1882-1947): psiquiatra y psicoanalista alemán, fundador del sanatorio Schloss Tegel en 1925, sobre el modelo de las grandes clínicas Bellevue y del Burghölzli. Detenido por la Gestapo en 1933, logró emigrar a Estados Unidos gracias a Ruth Mack-Brunswick, que pagó un rescate a los nazis. Se instaló en Los Ángeles y mantuvo durante toda su vida la nostalgia por el viejo mundo europeo. Sobre la trayectoria de V. Tausk, véase _infra_.
. Fundado en enero de 1919.
. S. Zweig, _Le Monde d'hier..._ , _op. cit._
. Sigmund Freud, «Faut-il enseigner la psychanalyse à l'Université?» (1920), en _OC.P_ , vol. 15, _op. cit._ , pp. 109-115 [hay trad. cast.: «¿Debe enseñarse el psicoanálisis en la universidad?», en _OC_ , vol. 17, _op. cit._ , pp. 165-171].
. W. Johnston, _L'Esprit viennois..._ , _op. cit._ , p. 398.
. Carta de Freud a Jones, 18 de abril de 1919, en S. Freud y E. Jones, _Correspondance complète..._ , _op. cit._ , p. 409.
. P. Grosskurth, _Freud: l'anneau secret_ , _op. cit._ , p. 101, y G. Wittenberger y C. Tögel, eds., _Die Rundbriefe..._ , _op. cit._ , reuniones del 1 y el 11 de diciembre de 1921 y el 11 de enero de 1922. Jones se había negado a incorporar a la IPV a cierto psicoanalista holandés preso a raíz de su homosexualidad, y se valía de este caso como pretexto para justificar su postura.
. Sobre esta cuestión se publicó una gran cantidad de obras, y yo misma me referí a ella en varias ocasiones. Cf. Elisabeth Roudinesco, «Psychanalyse et homosexualité: réflexions sur le désir pervers, l'injure et la fonction paternelle», conversación con François Pommier, _Cliniques méditerranéennes_ , 65(1), primavera de 2002, pp. 7-34 [hay trad. cast.: «Psicoanálisis y homosexualidad: reflexiones sobre el deseo perverso, la injuria y la función paterna», _El Rapto de Europa: crítica de la cultura_ , 3, 2003, pp. 85-102].
. La petición lanzada por Magnus Hirschfeld había reunido, con el paso de los años, seis mil firmas, entre ellas las de Albert Einstein y Stefan Zweig. El artículo en cuestión establecía: «La fornicación contra natura, practicada entre personas de sexo masculino o entre personas y animales, es castigada con pena de prisión».
. Sobre esa tarea de detección en Francia y el papel de Joseph Babinski, discípulo de Charcot, cf. _HPF-JL_ , _op. cit._
. En 1927 obtendría el premio Nobel por haber perfeccionado la malarioterapia. Admirador del nacionalismo alemán, expresó al final de su vida simpatías por el nazismo. Cf. Clare Chapman, «Austrians stunned by Nobel Prize-winner's Nazi ideology», _Scotland on Sunday_ , 25 de enero de 2004.
. Esos tratamientos de shock recibían el nombre de «electroterapia» o «faradización».
. El expediente de este caso, que incluye documentos, testimonios y la instrucción, fue exhumado y publicado por Kurt Eissler, ed., _Freud und Wagner-Jauregg vor der Kommission zur Erhebung militärischer Pflichtverletzungen_ , Viena, Löcker, 1979; versión francesa, _Freud sur le front des névroses de guerre_ , París, Presses Universitaires de France, 1992, con un excelente prefacio de Érik Porge. En él pueden consultarse sobre todo «L'expertise sur le traitement électrique des névroses de guerre», las declaraciones de los testigos y la de Sigmund Freud, «Rapport d'expertise sur le traitement électrique des névrosés de guerre», en _OC.P_ , vol. 15, _op. cit._ , pp. 217-225 [hay trad. cast.: «Informe sobre la electroterapia de los neuróticos de guerra», en _OC_ , vol. 17, _op. cit._ , pp. 209-213], así como numerosos documentos. Cf. asimismo el relato que al respecto hace H. F. Ellenberger, _Histoire de la découverte..._ , _op. cit._ , pp. 860-862. Como no tuvo acceso a la totalidad de los archivos, Ellenberger da una versión diferente de la de Eissler, que tiene no obstante el mérito de rectificar los errores de Jones. Los documentos utilizados por Eissler se encuentran en la Biblioteca del Congreso.
. K. Eissler, ed., _Freud sur le front..._ , _op. cit._ , p. 29.
. Testimonio recogido por K. Eissler, _ibid._ , p. 143.
. _Ibid._ , p. 169.
. Rica familia industrial que había adoptado a Rosa.
. La identidad de Ernst Lanzer fue revelada por primera vez en 1986 por Patrick Mahony en un libro notable, _Freud et l'Homme aux rats_ , París, Presses Universitaires de France, 1991. Además de hacer una rigurosa investigación histórica, Mahony compara la versión dada por Freud en el llamado caso del «Hombre de las Ratas» con las notas preliminares escritas por él mismo y no incorporadas al relato del caso. Se incluirán más adelante, en Sigmund Freud, _L'Homme aux rats: journal d'une analyse_ (notas de Freud transcritas por Elsa Ribeiro Hawelka), París, Presses Universitaires de France, 1974. Cf. Sigmund Freud, «Remarques sur un cas de névrose obsessionnelle: "l'Homme aux rats"» (1909), en _Cinq psychanalyses_ , _op. cit._ , pp. 199-261, y, con el título de «Remarques sur un cas de névrose de contrainte», _OC.P_ , vol. 9, _op. cit._ , pp. 131-215 [hay trad. cast.: _A propósito de un caso de neurosis obsesiva_ , en _OC_ , vol. 10, _op. cit._ , pp. 119-194, y «Anexo. Apuntes originales sobre el caso de neurosis obsesiva», en _ibid._ , pp. 195-249].
. En 1965, Leonard Shengold fue el primero en señalar que el relato provenía de la famosa obra de Octave Mirbeau, _Le Jardin des supplices_ (1899), París, Gallimard, 1988 [hay trad. cast.: _El jardín de los suplicios_ , __ Madrid, Impedimenta, 2010].
. En este aspecto, no comparto la opinión de M. Borch-Jacobsen, _Les Patients de Freud..._ , _op. cit._ , p. 111. Las distorsiones que existen entre las notas y el relato del caso, puestas en evidencia por Patrick Mahony, muestran al contrario que Freud encontró en Lanzer un paciente ejemplar por quien sintió una verdadera empatía.
. Publicado bajo la forma de «extracto».
. Patrick Mahony estima, al contrario, que estamos aquí frente a un drama edípico en el cual Lanzer desempeñaría el papel de una «Esfinge vienesa». Y propone una interpretación kleiniana del caso: Lanzer se habría identificado con su madre para introyectar el pene de su padre. Se han escrito decenas de comentarios sobre esta historia, a tal punto que el «caso» del «Hombre de las Ratas» eclipsó la historia del paciente.
. Aun cuando a veces lo dude, como informa S. Freud, _L'Homme aux rats: journal..._ , _op. cit._ , pp. 77 y 85.
. S. Freud, «Remarques sur un cas de névrose obsessionnelle...», _op. cit._ , p. 261 [ _A propósito de un caso de neurosis obsesiva_ , _op. cit._ , p. 194].
. En la Biblioteca del Congreso hay varias fotografías donde se ve a Pankejeff, su hermana y su madre delante de una pila de animales. Los distintos comentaristas no las han tenido en cuenta, a pesar de que Pankejeff se refiere a ellas en el relato que hace de su vida. La verdadera identidad de este paciente, apodado «Hombre de los Lobos», se reveló en 1973. Para reconstruir su historia hay que cruzar varias fuentes contradictorias; véanse Muriel Gardiner, ed., _L'Homme aux loups par ses psychanalystes et par lui-même_ (1971), París, Gallimard, 1981 [hay trad. cast.: _El hombre de los lobos por el hombre de los lobos_ , Buenos Aires, Nueva Visión, 1976], y Karin Obholzer, _Entretiens avec l'Homme aux loups: une psychanalyse et ses suites_ (1980), París, Gallimard, 1981 [hay trad. cast.: _Conversaciones con el Hombre de los Lobos: un psicoanálisis y sus consecuencias_ , Buenos Aires, Nueva Visión, 1996]. En estas dos obras, escritas al final de su vida, Pankejeff se equivoca con frecuencia y da versiones opuestas de su análisis con Freud: una, destinada a los psicoanalistas, se confió a Muriel Gardiner, y otra, dirigida al «gran público», a Karin Obholzer, una periodista austríaca. Cf. además Patrick Mahony, _Les Hurlements de l'Homme aux loups_ (1984), París, Presses Universitaires de France, 1995, una reconstrucción muy fiable. Cf. asimismo M. BorchJacobsen, _Les Patients de Freud..._ , _op. cit._ , y Mikkel Borch-Jacobsen y Sonu Shamdasani, _Le Dossier Freud: enquête sur l'histoire de la psychanalyse_ , París, Les Empêcheurs de Penser en Rond, 2006. Estos dos textos cargan demasiado contra Freud, aunque los documentos citados son indiscutibles. A ellos deben añadirse las entrevistas realizadas por Kurt Eissler y depositadas en la Biblioteca del Congreso, cinco carpetas, 1954-1955, caja 116.
. Carta de Freud a Ferenczi, 13 de febrero de 1910, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 1, _op. cit._ , p. 149. Pankejeff no menciona esta escena.
. Sigmund Freud, «Extrait de l'histoire d'une névrose infantile» (1918), en M. Gardiner, ed., _L'Homme aux loups..._ , _op. cit._ , pp. 172-268; con el título de «À partir de l'histoire d'une névrose infantile», en _OC.P_ , vol.13, _op. cit._ , pp. 1-119, y con el título de «Extrait de l'histoire d'une névrose infantile: l'Homme aux loups», en _Cinq psychanalyses_ , _op. cit._ , pp. 371-477 [hay trad. cast.: _De la historia de una neurosis infantil_ , en _OC_ , vol. 17, _op. cit._ , pp. 1-111].
. De ahí las diferencias entre los testimonios de Pankejeff y las confidencias recibidas o reconstruidas por Freud en el relato de la terapia.
. S. Freud, «Extrait de l'histoire...», _op. cit._ , p. 190 [ _De la historia de una neurosis..._ , _op. cit._ , p. 29].
. Había utilizado esta expresión en una carta a Fliess del 2 de mayo de 1897, con referencia a los actos de seducción.
. S. Freud, «Extrait de l'histoire...», _op. cit._ , p. 197 [ _De la historia de una neurosis..._ , _op. cit._ , pp. 36-37 y 74].
. Ruth Mack-Brunswick, «Supplément a l'Extrait d'une névrose infantile», en M. Gardiner, ed., _L'Homme aux loups..._ , _op. cit._ , pp. 268-317 [hay trad. cast.: «Suplemento a la "Historia de una neurosis infantil" de Freud», en M. Gardiner, ed., _El Hombre de los Lobos..._ , _op. cit._ ].
. Otto Rank, _Le Traumatisme de la naissance: influence de la vie prénatale sur l'évolution de la vie psychique individuelle et collective. Étude psychanalytique_ (1924), París, Payot, 1928 [hay trad. cast.: _El trauma del nacimiento_ , Barcelona, Paidós, 1985], y _Technik der Psychoanalyse_ , vol. 1, Leipzig y Viena, Deutike, 1926. Cf. asimismo P. Grosskurth, _Freud: l'anneau secret_ , _op. cit._ , pp. 173-174.
. S. Freud y S. Ferenczi, _Correspondance_ , vol. 3, _op. cit._ , pp. 289-293.
. Cf. la tercera parte de este volumen.
. Sobre los comentarios de Jacques Lacan, Serge Leclaire, Nicolas Abraham, Maria Torok, Jacques Derrida y Gilles Deleuze, cf. _HPF-JL_ , _op. cit._ Carlo Ginzburg señala que el sueño puede haber sido inspirado por leyendas relativas a los hombres lobos: en vez de convertirse en uno de ellos, como habría sido su destino tres siglos antes, Pankejeff se habría convertido en un neurótico al borde de la psicosis. Cf. Carlo Ginzburg, «Freud, l'Homme aux loups, et les loups-garous», en _Mythes, emblèmes, traces: morphologie et histoire_ , París, Flammarion, 1989 [hay trad. cast.: «Freud, el Hombre de los Lobos y los hombres-lobo», en _Mitos, emblemas e indicios: morfología e historia_ , Buenos Aires, Prometeo Libros, 2013].
. M. Gardiner, ed., _L'Homme aux loups..._ , _op. cit._ , y K. Obholzer, _Entretiens avec l'Homme aux loups..._ , _op. cit._
. Es lo que afirman, en especial, Mikkel Borch-Jacobsen y muchos más.
. Testimonio recogido en 1926 por Theodor Reik, _Le Besoin d'avouer: psychanalyse du crime et du châtiment_ , París, Payot, 1973, pp. 400-401.
. No abordo aquí la historia del psicoanálisis en Francia.
. Carta de Freud a Eitingon, 21 de enero de 1920, en S. Freud y M. Eitingon, _Correspondance..._ , _op. cit._ , p. 208.
. Carta de Freud a Pfister, 27 de enero de 1920, en S. Freud, _Sigmund Freud: correspondance avec le pasteur Pfister..._ , _op. cit_., p. 119. Sobre las circunstancias de esta muerte, véase la nota 16 en la tercera parte, capítulo 2.
. S. Freud, _Lettres à ses enfants_ , _op. cit._ , p. 492.
. Sigmund Freud, «Contribution à la discussion sur le suicide» (1910), en _OC.P_ , vol. 10, _op. cit._ , pp. 75-79 [hay trad. cast.: «Contribuciones para un debate sobre el suicidio», en _OC_ , vol. 11, _op. cit._ , pp. 231-232].
. S. Freud y S. Ferenczi, _Correspondance_ , vol. 3, _op. cit._ , p. 22. Mark Twain envió el siguiente telegrama al diario que había anunciado su muerte: «Noticia de mi fallecimiento un tanto exagerada».
. Sigmund Freud, «Victor Tausk», en _OC.P_ , vol. 15, _op. cit._ , pp. 203-209 [hay trad. cast.: «Victor Tausk», en _OC_ , vol. 17, _op. cit._ , pp. 266-268], y L. Andreas-Salomé, _Correspondance avec Sigmund Freud..._ , _op. cit._ Este asunto suscitó un considerable debate historiográfico. Cf. Victor Tausk, _Œuvres psychanalytiques_ , París, Payot, 1975 [hay trad. cast.: _Trabajos psicoanalíticos_ , Barcelona, Granica, 1977]; Paul Roazen, _Animal, mon frère, toi: l'histoire de Tausk et Freud_ (1969), París, Payot, 1971 [hay trad. cast.: _Hermano animal: la historia de Freud y Tausk_ , Madrid, Alianza, 1973], y Kurt Eissler, _Le Suicide de Victor Tausk: avec les commentaires du Pr_ _Marius Tausk_ (1983), París, Presses Universitaires de France, 1988.
. Sándor Ferenczi, «La technique psychanalytique» (1919), en _Œuvres complètes_..., vol. 2, _op. cit._ , pp. 327-338 [hay trad. cast.: «La técnica psicoanalítica», en _Obras completas_ , vol. 2, _op. cit._ , pp. 425-437].
. Jones cuenta su versión de las disensiones internas del comité en el último volumen de su biografía: Ernest Jones, _La Vie et l'œuvre de Sigmund Freud_ , vol. 3, _Les Dernières années, 1919-1939_ (1957), París, Presses Universitaires de France, 1969, pp. 48-87 [hay trad. cast.: _Vida y obra de Sigmund Freud_ , vol. 3, _La etapa final, 1919-1939_ , Buenos Aires, Hormé, 1989]. Es preciso cotejarla con las de los otros miembros del comité, por medio de la lectura de los _Rundbriefe_. Cf. asimismo P. Grosskurth, _Freud: l'anneau secret_ , _op. cit._
. Carta de Freud a Ferenczi, 25 de diciembre de 1920, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 3, _op. cit._ , p. 44.
. Carta de Freud a Groddeck, 5 de junio de 1917, citada y traducida en A. Bolzinger, _Portrait de Sigmund Freud..._ , _op. cit._ , pp. 202-203 [hay trad. cast.: «A Georg Groddeck», en _Epistolario, 1873-1939_ , _op. cit._ , pp. 357-358]. Cf. asimismo Georg Groddek, _Ça et moi: lettres à Freud, Ferenczi et quelques autres_ , París, Gallimard, 1977. La obra de Groddeck se conoce en Francia gracias al trabajo de Roger Lewinter, y también gracias a Catherine Clément, «La sauvagerie de l'amour même», _L'Arc_ , 78, «Georg Groddeck», 1980, pp. 1-4.
. Jacquy Chemouni, «Psychopathologie de la démocratie», _Frénésie (histoire, psychiatrie, psychanalyse)_ , 10, primavera de 1992, pp. 265-282.
. «La naturaleza sana, el médico cura.»
. Georg Groddeck, _«Nasamecu»: la nature guérit_ , prefacio de Catherine Clément, París, Aubier-Montaigne, 1992.
. Georg Groddeck, _Lebenserinnerungen_ (1929), en _Der Mensch und sein Es: Briefe, Aufsätze, Biografisches_ , Wiesbaden, Limes Verlag, 1970.
. Recordemos que en 1911 Freud había firmado, con Ellis, Hirschfeld y Eduard Bernstein, una petición a los hombres y las mujeres de todos los países civilizados para promover una política higienista encaminada a mejorar la salud física y psíquica de la «raza» humana. Cf. Paul Weindling, _L'Hygiène de la race_ , vol. 1, _Hygiène raciale et eugénisme médical en Allemagne, 1870-1933_ (1989), París, La Découverte, 1998, p. 53. Sobre la evolución de la idea eugénica, cf. _HPF-JL_ , _op. cit._
. Georg Groddeck, _Conférences psychanalytiques à l'usage des malades prononcés au sanatorium de Baden-Baden_ , 3 vols., edición de Roger Lewinter, París, Champ Libre, 1982 [hay trad. cast. parcial: _Las primeras 32 conferencias psicoanalíticas para enfermos_ , Buenos Aires, Paidós, 1983].
. Georg Groddeck, _Le Chercheur d'âme: un roman psychanalytique_ (1921), París, Gallimard, 1982 [hay trad. cast.: _El escrutador de almas: novela psicoanalítica_ , México, Era, 1986].
. Georg Groddeck, _Le Livre du ça_ (1923), París, Gallimard, 1973 [hay trad. cast.: _El libro del ello: cartas psicoanalíticas a una amiga_ , Buenos Aires, Sudamericana, 1968].
. Carta de Freud a Groddeck, 21 de diciembre de 1924, citada y traducida en A. Bolzinger, _Portrait de Sigmund Freud..._ , _op. cit._ , p. 203 [hay trad. cast.: «A Georg Groddeck», en _Epistolario, 1873-1939_ , _op. cit._ , p. 400]. Cf. asimismo G. Groddeck, _Ça et moi_..., _op. cit._
. Cf. É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Georg Groddeck, _Un problème de femme_ (1903), París, Mazarine, 1979, y «Le double sexe de l'être humain» (1931), _Nouvelle Revue de Psychanalyse_ , 7, primavera de 1973, pp. 193-199 [hay trad. cast.: «La bisexualidad del ser humano», _Revista de la Asociación Española de Neuropsiquiatría_ , 21(79), 2001, pp. 83-87]. Cf. asimismo J. Le Rider, _Modernité viennoise..._ , _op. cit._
. En 1965 dos biógrafos de Groddeck imaginaron que este había mantenido correspondencia con Hitler. Roger Lewinter invalidó el rumor en un artículo de _Le Monde_ del 7 de septiembre de 1980.
TERCERA PARTE
#### 1. LA ILUSTRACIÓN OSCURA
. Expresión utilizada por Theodor Adorno.
. Freud designa con el término _Unheimliche_ («lo extraño familiar») una impresión pavorosa que emana de cosas conocidas desde hace mucho y familiares desde siempre: el miedo a la castración, la figura del doble y el autómata. Cf. Sigmund Freud, «L'inquiétante étrangeté» (1919), en _L'Inquiétante étrangeté et autres essais_ , París, Gallimard, 1985, pp. 209-263 [hay trad. cast.: «Lo ominoso», en _OC_ , vol. 17, _op. cit._ , pp. 215-251]. Cf. asimismo Jean Clair, _Malinconia: motifs saturniens dans l'art de l'entre-deux-guerres_ , París, Gallimard, 1996, en particular el capítulo «De la métaphysique à l'"inquiétante étrangeté"», pp. 59-85 [hay trad. cast.: _Malinconia: motivos saturninos en el arte de entreguerras_ , Madrid, Visor, 1999, capítulo «De la melancolía a la "inquietante extrañeza"», pp. 53-75].
. Sigmund Freud, _Au-delà du principe de plaisir_ (1920), en _Essais de psychanalyse_ , París, Payot, 1981, col. «Petite Bibliothèque Payot», pp. 117-205, y en _OC.P_ , vol. 15, _op. cit._ , pp. 273-339 [hay trad. cast.: _Más allá del principio de placer_ , en _OC_ , vol. 18, _op. cit._ , pp. 1-62]. Sobre la génesis del texto y sus variantes, cf. I. Grubrich-Simitis, _Freud: retour aux manuscrits..._ , _op. cit._ , pp. 228-239. Una polémica importante se suscitó entre Ilse Grubrich-Simitis, por un lado, y Michael Schröter y Ulrike May, por otro, acerca de la génesis de _Más allá del principio de placer_. Encontramos su eco en la revista _Luzifer-Amor_ , 51, 2013, íntegramente dedicada a esa obra, y en _Psyche_ , 67(7), julio de 2013, pp. 679-688, y 67(8), agosto de 2013, pp. 794-798.
. Según la observación de Jacques Derrida, que escribió uno de los comentarios más deslumbrantes sobre _Más allá del principio de placer_ ; véase Jacques Derrida, _La Carte postale: de Socrate à Freud et au-delà_ , París, Aubier-Flammarion, 1980 [hay trad. cast.: _La tarjeta postal: de Sócrates a Freud y más allá_ , México, Siglo XXI, 2001].
. S. Freud, _Sigmund Freud présenté..._ , _op. cit._ , p. 100 [ _Presentación autobiográfica_ , _op. cit._ , p. 56].
. Carta de Freud a Ernst Freud, 17 de enero de 1938, en S. Freud, _Lettres à ses enfants_ , _op. cit._ , p. 389.
. Jean de La Fontaine, «Les deux rats, le renard et l'œuf», en _Fables_.
. Cf. J. K. Davies y G. Fichtner, eds., _Freud's Library..._ , _op. cit._ Freud se interesaba en la vida de Sade pero no en sus obras. Cf. Elisabeth Roudinesco, _La Part obscure de nous-mêmes: une histoire des pervers_ , París, Albin Michel, 2007 [hay trad. cast.: _Nuestro lado oscuro: una historia de los perversos_ , Barcelona, Anagrama, 2009].
. Gilles-Gaston Granger, _L'Irrationnel_ , París, Odile Jacob, 1998. Ya me apoyé en esta obra en É. Roudinesco, _Pourquoi la psychanalyse?_ , _op. cit._
. George Sylvester Viereck, «Entretien avec Sigmund Freud» (1926), traducción y presentación de Claude-Noëlle Pickman, _Revue de l'Association Analyse freudienne_ , 13, nueva serie, «Nouvelles formes de la parentalité», otoño de 1996, pp. 115-127 [hay trad. cast.: «Sigmund Freud, entrevistado por George Sylvester Viereck», en Christopher Silvester, ed., _Las grandes entrevistas de la historia, 1859-1992_ , Buenos Aires, Aguilar, 1997]. Cf. asimismo Emilio Rodrigué, _Freud: le siècle de la psychanalyse_ , 2 vols., París, Payot, 2000 [edición original: _Sigmund Freud: el siglo del psicoanálisis_ , 2 vols., Buenos Aires, Sudamericana, 1996].
. En un texto fechado el 31 de enero de 1919 expresa el anhelo de que al morir su cuerpo sea incinerado. Conversación con Eric Willis, responsable del crematorio de Golders Green, el 24 de abril de 2014. Cf. asimismo Helen P. Fry, _Freuds' War_ , Stroud, History Press, 2009.
. S. Freud, _Au-delà du principe..._ , _op. cit._ , p. 26 [ _Más allá del principio..._ , _op. cit._ , pp. 21-22].
. S. Freud, «Pulsions et destin des pulsions», _op. cit_. Sobre la génesis de la noción de sadomasoquismo, cf. É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. En una nota ulterior, Freud agregaría: «Teniendo el niño cinco años y nueve meses, murió la madre. Ahora que realmente "se fue" (o-o-o-o), el muchachito no mostró duelo alguno por ella. Es verdad que entretanto había nacido un segundo niño, que despertó sus más fuertes celos». S. Freud, _Au-delà du principe..._ , _op. cit._ , p. 18 [ _Más allá del principio..._ , _op. cit._ , p. 16]. Se trata de Heinz (Heinerle) Halberstadt (1918-1923), segundo hijo de Sophie, que murió a los cuatro años.
. Freud cita la versión italiana antigua: Torquato Tasso, _La Gerusalemme liberata_ , Ferrara, Vittorio Baldini, 1581, canto XIII. En francés he utilizado la siguiente versión: _La Jérusalem délivrée_ , París, Charpentier, 1845, traducida por Auguste Desplaces y precedida por una noticia sobre la vida y las obras del autor; canto XIII, p. 292 [hay trad. cast.: _La Jerusalén libertada_ , Madrid, Aguilar, 1957].
. El eunuco Arsete se lo informa en el canto XII, temeroso de que al cambiar de armadura tomen a Clorinda por el guerrero que mató a Arimón, compañero de Tancredo.
. T. Tasso, _La Jérusalem délivrée_ , _op. cit._ , canto XII, pp. 198-199.
. Los términos que utiliza Freud.
. S. Freud, _Au-delà du principe..._ , _op. cit._ , p. 27 [ _Más allá del principio..._ , _op. cit._ , p. 22].
. La temática no era nueva, sobre todo en los románticos. Cf. H. F. Ellenberger, _Histoire de la découverte..._ , _op. cit._ , pp. 549-552.
. August Weismann, _Essais sur l'hérédité et la sélection naturelle_ , París, C. Reinwald, 1892. Freud cita esencialmente tres artículos de este volumen. Cf. Charles Lenay, «Les limites naturelles de la durée de vie et la question de l'hérédité de l'acquis», _Études sur la mort_ , 124, «Mort biologique, mort cosmique», diciembre de 2003, pp. 43-58.
. S. Freud, _Au-delà du principe..._ , _op. cit._ , p. 64 [ _Más allá del principio..._ , _op. cit._ , p. 49]. F. J. Sulloway, _Freud, biologiste de l'esprit_ , _op. cit._ , p. 390, califica de «fábula biogenética» la concepción freudiana de la pulsión de muerte.
. Freud teorizaría esta tópica dos años después. Cf. Sigmund Freud, _Le Moi et le ça_ (1923), en _OC.P_ , vol. 16, _op. cit._ , pp. 255-303 [hay trad. cast.: _El yo y el ello_ , en _OC_ , vol. 19, 1979, pp. 1-59].
. Sigmund Freud, «La décomposition de la personnalité psychique», en _Nouvelles conférences d'introduction à la psychanalyse_ (1933), París, Gallimard, 1984, p. 110, y, bajo el título de _Nouvelle suite des leçons d'introduction à la psychanalyse_ , _OC.P_ , vol. 19, 1995 [hay trad. cast.: «La descomposición de la personalidad psíquica», en _Nuevas conferencias de introducción al psicoanálisis_ , en _OC_ , vol. 22, p. 74]. Sobre las diferentes traducciones de este sintagma, y en especial sobre la de Lacan, cf. Jacques Lacan, «La chose freudienne ou sens du retour à Freud en psychanalyse», en _Écrits_ , París, Seuil, 1966, pp. 401-436 [hay trad. cast.: «La cosa freudiana o sentido del retorno a Freud en psicoanálisis», en _Escritos_ , vol. 1, tercera edición revisada y corregida, México, Siglo XXI, 2009, pp. 379-410].
. François Requet, «Nietzsche et Freud: le rapport entre cruauté, culpabilité et civilisation», máster de la Universidad del Franco Condado, sección de filosofía, 2005-2006.
. Señalaba además que debía a Heinrich Gomperz, el hijo de Theodor y de Elise (su antigua paciente), indicaciones de las que se valía. Y remitía las palabras de Aristófanes a un mito idéntico incluido en las _Upanishads_. La traducción alemana del _Banquete_ que figura en la biblioteca de Freud data de 1932.
. S. Freud, _Au-delà du principe..._ , _op. cit._ , p. 81 [ _Más allá del principio..._ , _op. cit._ , p. 62].
. William McDougall, _Psycho-analysis and Social Psychology_ , Londres, Methuen, 1936, p. 96.
. E. Jones, _La Vie et l'œuvre..._ , vol. 3, _op. cit._ , pp. 304-326. Cf. asimismo F. J. Sulloway, _Freud, biologiste de l'esprit_ , _op. cit._ , p. 377.
. Carta de Freud a Wittels, 18 de diciembre de 1923, citada en E. Jones, _La Vie et l'œuvre..._ , vol. 3, _op. cit._ , p. 45.
. Carta de Freud a Eitingon, 18 de julio de 1920, en S. Freud y M. Eitingon, _Correspondance..._ , _op. cit._ , p. 230.
. J. Derrida, _La Carte postale..._ , _op. cit._ , p. 378.
. Cf. Yirmiyahu Yovel, _Spinoza et autres hérétiques_ (1989), París, Seuil, 1991, col. «Libre examen» [hay trad. cast.: _Spinoza, el marrano de la razón_ , Madrid, Anaya & Mario Muchnik, 1995].
. Sobre todo en Jacques Lacan, _Le Séminaire, Livre XI, Les Quatre concepts fondamentaux de la psychanalyse (1964)_ , París, Seuil, 1973 [hay trad. cast.: _El Seminario de Jacques Lacan. Libro 11. Los cuatro conceptos fundamentales del psicoanálisis. 1964_ , Buenos Aires, Paidós, 1986]. Cf. asimismo Jean Laplanche, _Vie et mort en psychanalyse_ , París, Flammarion, 1970 [hay trad. cast.: _Vida y muerte en psicoanálisis_ , Buenos Aires, Amorrortu, 1973], y É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._ La noción de pulsión de muerte se aceptó muy pronto en Japón con la creación, en 1928, del primer instituto de psicoanálisis de Tokio. El psicólogo Yaekichi Yabe, de paso por Viena en 1930, contó a Freud que para los japoneses la idea de que la vida tendía a la muerte formaba parte de la enseñanza del budismo clásico. Cf. É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Carta de Freud a Ferenczi, 8 de mayo de 1921, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 3, _op. cit._ , p. 61.
. Sigmund Freud, _Psychologie des foules et analyse du moi_ (1921), en _Essais de psychanalyse_ , _op. cit._ , pp. 117-205 [hay trad. cast.: _Psicología de las masas y análisis del yo_ , en _OC_ , vol. 18, _op. cit._ , pp. 63-136]. He escogido aquí, como en el caso de _Más allá del principio de placer_ , la traducción de Jean Laplanche y Jean-Bertrand Pontalis, pero también hay que remitirse a otra traducción, _Psychologie des masses et analyse du moi_ , en _OC.P_ , vol. 16, _op. cit._ , pp. 1-85. Freud comenta el texto de Le Bon en la traducción alemana de Rudolf Eisler, donde _foule_ se vierte como _Masse_. En la versión de las _OC.P_ los traductores citan en nota los pasajes franceses del texto original de Le Bon y traducen del alemán al francés el utilizado por Freud. La obra de Gustave Le Bon, _Psychologie des foules_ (1895), París, F. Alcan, 1905, fue durante decenios, y hasta mucho después de la muerte de su autor, en 1931, uno de los más grandes éxitos de venta de todos los tiempos, admirada tanto por los adversarios de la Ilustración, hostiles a la Revolución de 1789, como por los dictadores: Mussolini y Hitler.
. Sobre el papel de Gustave Le Bon en la historia del psicoanálisis en Francia, cf. _HPF-JL_ , _op. cit._ , pp. 277-278. Marie Bonaparte le profesaba una gran admiración, al extremo de compararlo con Freud.
. William McDougall, _The Group Mind_ (1920), Londres, Ayer Co. Pub., 1973. Freud cita la edición original en inglés. _Group mind_ significa «mentalidad de grupo».
. McDougall hace referencia aquí a tres escritores norteamericanos, militantes de los derechos de los negros: Frederick Douglass (1818-1895), Booker T. Washington (1856-1915) y W. E. B. Du Bois (1868-1963).
. En Francia, sobre todo, Georges Bataille la utilizó en abundancia al fundar, con René Allendy, Adrien Borel, Paul Schiff y otros, una sociedad de psicología colectiva. Cf. _HPF-JL_ , _op. cit._ , pp. 615-647 y 1653-1677. Sobre la refundición llevada a cabo por Lacan, cf. _ibid._ , pp. 1718-1719. Señalemos que Elias Canetti, que también había estudiado la cuestión de la irrupción de lo irracional en los fenómenos de masas, no cita jamás la obra de Freud, de la que tenía, no obstante, perfecto conocimiento. Cf. E. Canetti, _Masse et puissance_ , _op. cit._
. Michel Plon, «"Au-delà" et "en deçà" de la suggestion», _Frénésie (histoire, psychiatrie, psychanalyse)_ , 8, 1989, p. 96.
. Véase _infra_.
. En internet pueden encontrarse fragmentos de esos filmes, así como una entrevista a Edward Bernays sobre el tema poco antes de su muerte en 1995. Entre 1922 y 1931 Freud escribiría varias veces a ese sobrino que se ocupaba de la gestión de sus derechos de autor en Estados Unidos, LoC, caja 1, carpeta 1-5.
. Sobre la historia del espiritismo en el origen del psicoanálisis, cf. H. F. Ellenberger, _Histoire de la découverte..._ , _op. cit._ , pero también el muy asombroso libro de Arthur Conan Doyle, _Histoire du spiritisme_ (1927), París, Dunod, 2013 [hay trad. cast.: _Historia del espiritismo: sus hechos y sus doctrinas_ , Madrid, Eyras, 1983], y É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Carta de Freud a Carrington, 24 de julio de 1921, en S. Freud, _Correspondance, 1873-1939_ , _op. cit._ , p. 364 [hay trad. cast.: «A Hereward Carrington», en _Epistolario, 1873-1939_ , _op. cit._ , p. 377].
. Wladimir Granoff y Jean-Michel Rey, _L'Occulte, objet de la pensée freudienne_ , París, Presses Universitaires de France, 1983.
. Sigmund Freud, «Psychanalyse et télépathie» (1921), en _OC.P_ , vol. 16, _op. cit._ , pp. 99-119 [hay trad. cast.: «Psicoanálisis y telepatía», en _OC_ , vol. 18, _op. cit._ , pp. 165-184]; «Rêve et télépathie» (1922), en _OC.P_ , vol. 16, _op. cit._ , pp. 119-145 [hay trad. cast.: «Sueño y telepatía», en _OC_ , vol. 18, _op. cit._ , pp. 185-211], y «Rêve et occultisme», en _Nouvelles conférences..._ , _op. cit._ , pp. 45-79, y en _OC.P_ , vol. 19, _op. cit._ , pp. 112-139 [hay trad. cast.: «Sueño y ocultismo», en _Nuevas conferencias..._ , _op. cit._ , pp. 29-52].
. E. Jones, _La Vie et l'œuvre..._ , vol. 3, _op. cit._ , p. 447.
. En _HPF-JL_ , _op. cit._ , mostré que se trata también de un síntoma recurrente en la historia del psicoanálisis.
. Jacques Derrida, «Télépathie» (1981), en _Psyché: inventions de l'autre_ , París, Galilée, 1987, pp. 237-271.
#### 2. FAMILIAS, PERROS, OBJETOS
. En un texto de cuarenta páginas dirigido a Kurt Eissler el 28 de octubre de 1952, Ernst Waldinger evoca la vida cotidiana de los Freud en Viena en el período de entreguerras: LoC, caja 121, carpeta 33.
. Sobre el destino de los diferentes sobrinos de Freud, véase _infra_ , y el árbol genealógico al final del volumen.
. Al igual que Rudolf Halberstadt, el hermano de Max.
. Cf. Joseph Wortis, _Psychanalyse à Vienne, 1934: notes sur mon analyse avec Freud_ (1954), París, Denoël, 1974, p. 159 [hay trad. cast.: _Mi análisis con Freud_ , Buenos Aires, Editorial Universitaria, 1965].
. Ernstl Halberstadt, el niño del carretel, fue, entre los hijos de las hijas de Freud, el único que volvió a vivir en Alemania y también el único que fue psicoanalista. Anna y Mathilde no tuvieron hijos. Eva Freud (1924-1944) murió sin descendencia. Sobrevivieron seis nietos de Freud: cinco varones —Anton Walter, Stefan, Lucian, Clemens y Ernstl— y una mujer, Sophie. Sobre el destino de los nietos y sobrinos de Freud, véase _infra_.
. Sobre la vida de los hijos de Freud, cf. S. Freud, _Lettres à ses enfants_ , _op. cit._ ; Elisabeth Young-Bruehl, _Anna Freud_ (1988), París, Payot, 1991 [hay trad. cast.: _Anna Freud_ , Buenos Aires, Emecé, 1991], y Günter Gödde, _Mathilde Freud: die älteste Tochter Sigmund Freuds in Briefen und Selbstzeugnissen_ , Giessen, Psychosozial-Verlag, 2003. Cf. asimismo, a pesar de sus interpretaciones discutibles, la obra bien documentada de Eva Weissweiler, _Les Freud: une famille viennoise_ (2006), París, Plon, 2006. Véanse también Paul Ferris, _Dr. Freud: A Life_ , Washington, Counterpoint, 1998, y Hans Lampl, conversación con Kurt Eissler, 1953, LoC, caja 114, carpeta 13.
. Estas son las palabras exactas de Jung en una entrevista en alemán con Kurt Eissler, realizada en 29 de agosto de 1953: « _Die jüngere Schwester hatte eine grosse Übertragung, und Freud, und Freud was not insensible_ ». Y, ante otra pregunta de Eissler sobre la «relación», responde: « _Och, Bindung? Ich weiss nicht wieviel!? Ja! Aber, Gott, man weiss ja, wie die Sachen sind, nicht war!?_ ». Traducción: «La hermana menor tenía una gran transferencia con Freud, y él _was not insensible_ [no era insensible]». Eissler le pide entonces que aclare si había o no una relación carnal, y Jung responde: «Ah, ¿una relación? No sé hasta qué punto, pero, Dios mío, uno sabe bien cómo son esas cosas, ¿no?», LoC, caja 114, carpeta 4. Al parecer, en 1957 dio otro testimonio del mismo tipo a su amigo John Billinsky, quien lo haría público en 1969, tras la muerte de Jung. Pero Deirdre Bair afirma que Billinsky atribuyó a Jung palabras que este no pronunció; cf. D. Bair, _Jung..._ , _op. cit._ , p. 1057. Se recordará que Jung había intentado hacer hablar a Freud de su sexualidad durante el periplo americano.
. Christfried Tögel, «Freud Diarium», http://www.freud-biographik.de/freud-diarium/.
9. Decenas de novelas, artículos y ensayos se dedicaron a esa «relación» que sin duda jamás existió y que, en todo caso, se convirtió en uno de los tópicos del antifreudismo de fines del siglo XX, especialmente en la pluma de Peter Swales, Franz Maciejewski y Michel Onfray. Este último llega a afirmar que Freud obligó a Minna a abortar un hijo suyo en 1923, olvidando que en esa fecha ella tenía... cincuenta y ocho años. Cf. Michel Onfray, _Le Crépuscule d'une idole: l'affabulation freudienne_ , París, Grasset, 2010 [hay trad. cast.: _El crepúsculo de un ídolo: la fabulación freudiana_ , Buenos Aires, Taurus, 2011]. Sobre la vida privada de Freud, cf. Ronald W. Clark, _Freud, the Man and the Cause: A Biography_ , Nueva York, Random House, 1980 [hay trad. cast.: _Freud: el hombre y su causa_ , Barcelona, Planeta, 1985]. Sobre sus viajes, cf. S. Freud, « _Notre cœur tend vers le sud_ »..., _op. cit._ En mi prefacio a este último libro enumeré todas las fuentes concernientes al rumor. Véase también E. Weissweiler, _Les Freud..._ , _op. cit._ , pp. 124-125. En esa obra la autora retoma la hipótesis de la «relación» y el «aborto» y destaca que se trata en verdad de una interpretación y no de un hecho establecido. Tras los pasos de Peter Gay y John Forrester, he dedicado por mi parte un extenso estudio a ese extraordinario rumor: É. Roudinesco, _Mais pourquoi tant de haine?_ , _op. cit._
. Todo ese griterío tendría eco en numerosos ensayos, novelas o biografías imaginarias tras la muerte de Freud, pero sobre todo después de la publicación de la biografía de Jones y los trabajos de la historiografía científica o crítica (de Ellenberger a Sulloway).
. Esta campaña germanófoba seguía a la que se había lanzado contra Einstein. Cf. _HPF-JL_ , _op. cit._ , y Charles Blondel, _La Psychanalyse_ , París, Félix Alcan, 1924. En 1910, el psiquiatra alemán Alfred Hoche (1865-1943), de obediencia eugénica, había calificado de «epidemia» el psicoanálisis y caracterizado a sus miembros como una «secta»; véase Alfred Hoche, «Eine psychische Epidemie unter Ärzten», _Medizinische Klinik_ , 6(26), 1910.
. «Karl Kraus», edición de Éliane Kaufholz, _Cahiers de l'Herne_ , 28, 1975; Karl Kraus, _Aphorismes: dires et contre-dires_ , París, Payot, 2011 [hay trad. cast.: _Dichos y contradichos_ , Barcelona, Minúscula, 2003], y Fritz Wittels, «La névrose de _Fackel_ », en H. Nunberg y P. Federn, eds., _Les Premiers psychanalystes..._ , vol. 2, _op. cit._ , pp. 373-378. Durante esa sesión de enero de 1910 Freud había considerado errada la posición de Wittels.
. Elias Canetti, _Le Flambeau dans l'oreille: histoire d'une vie, 1921-1931_ (1980), París, Albin Michel, 1982, p. 134 [hay trad. cast.: _La antorcha al oído: historia de una vida, 1921-1931_ , Madrid, Alianza/Muchnik, 1984, p. 126].
. Anillo contraceptivo o «diafragma».
. El aborto se consideraba, desde fines del siglo XIX, como un crimen contra el individuo, la raza y la nación. Jean-Yves Le Naour y Catherine Valenti, _Histoire de l'avortement,_ XIX _e-_ XX _e siècle_ , París, Seuil, 2003.
. Carta de Freud a Lippmann, 15 de febrero de 1920, en S. Freud, _Lettres à ses enfants_ , _op. cit._ , p. 569. Freud no decía nada de la contracepción fuera del matrimonio, y tampoco del aborto. Señalemos que el uso del pesario ya se recomendaba a comienzos del siglo XX en los libros de higiene sexual; lo hacía en particular la célebre Anna Fischer-Dückelmann (1856-1917), vienesa emigrada a Suiza y autora de un best seller sobre el tema. El propio Freud, en una carta del 26 de enero de 1920, anunció a su madre la muerte de Sophie; cf. LoC, caja 3, carpeta 1.
. A fines de febrero de 1923 Freud detectó por primera vez, en el lado derecho de su mandíbula, lo que llamaba una «leucoplasia» y que era en realidad un epitelioma, como se confirmaría el 7 de abril de ese mismo año. Cf. M. Schur, _La Mort dans la vie..._ , _op. cit._ , pp. 415-436.
. El 20 de noviembre de 1923 Max se casó con Bertha Katzenstein (1897-1982), con quien tuvo una hija: Eva Spangenthal, medio hermana de Ernstl. Cf. S. Freud, _Lettres à ses enfants_ , _op. cit._ , pp. 533-534.
. Anton Walter Freud (1921-2004) y Sophie Freud-Lowenstein (nacida en 1924). Cf. Sophie Freud, _À l'ombre de la famille Freud: comment ma mère a vécu le_ XX _e_ _siècle_ (2006), París, Éditions Des Femmes/Antoinette Fouque, 2008.
. Archivos de la British Architectural Library (RIBA). El catálogo puede consultarse en internet, http://riba.sirsidynix.net.uk/uhtbin/webcat. El proyecto no se concretó.
. Carta de Freud a Binswanger, 11 de enero de 1929, en S. Freud y L. Binswanger, _Correspondance..._ , _op. cit._ , pp. 278-279.
. Tarjeta postal de Freud a Anna Freud, abril de 1914, en Sigmund Freud y Anna Freud, _Correspondance 1904-1938_ (2006), París, Fayard, 2012, p. 111 [hay trad. cast.: _Correspondencia 1904-1938_ , Barcelona, Paidós, 2014].
. Un psicoanalista, Jean-Pierre Kamieniak, imaginó que los perros eran para Freud sustitutos que le servían para hacer el duelo por su hija y su nieto. No es así, aun cuando Freud señalara que la presencia canina lo consolaba de esa pérdida o que la muerte de un perro le recordaba la de los seres humanos. En realidad, asociaba esa presencia indispensable de la raza canina a su alrededor a la de las mujeres, pero jamás vio a los perros como sustitutos de nada. Cf. Jean-Pierre Kamieniak, «Citizen Canis: Freud et les chiens», _Le Coq-Héron_ , 215, abril de 2013, pp. 96-108. Las posiciones de Freud a ese respecto aparecen en los intercambios inéditos con Marie Bonaparte.
. Marie Bonaparte, archivos inéditos.
. Es lo que mostré en É. Roudinesco, _La Part obscure..._ , _op. cit._ No comparto la opinión de Élisabeth de Fontenay, quien, sin haber podido tener acceso a los archivos inéditos de Marie Bonaparte, se equivoca al imaginar que Freud habría atribuido a los animales una capacidad simbólica casi similar a la de los humanos. Y le adjudica la paternidad original de una presunta «cuarta herida narcisista» inexistente en sus dichos. Cf. Élisabeth de Fontenay, «L'homme et les autres animaux. Préface», _Le Coq-Héron_ , 215, abril de 2013, p. 12.
. Hilda Doolittle, _Pour l'amour de Freud_ (1956), París, Éditions Des Femmes/Antoinette Fouque, 2010, p. 113 [hay trad. cast.: _Tributo a Freud_ , Barcelona, El Cobre, 2004].
. Carta de Zweig a Freud, en S. Freud y A. Zweig, _Correspondance..._ , _op. cit._ , p. 176.
. Carta de Freud a Arnold Zweig, 10 de febrero de 1937, en S. Freud y M. Eitingon, _Correspondance..._ , _op. cit._ , p. 909.
. Lou Andreas-Salomé, «Journal d'une année», en _Correspondance avec Sigmund Freud..._ , _op. cit._ , p. 324 [hay trad. cast.: _Aprendiendo con Freud: diario de un año, 1912-1913_ , Barcelona, Laertes, 2001].
. Carta de A. Freud a S. Freud, enero de 1913, en S. Freud y A. Freud, _Correspondance..._ , _op. cit._ , p. 89.
. Carta de S. Freud a A. Freud, 16 de julio de 1914, en _ibid._ , p. 114.
. Sigmund Freud, «Sur la psychogenèse d'un cas d'homosexualité féminine» (1920), en _Névrose, psychose et perversion_ , _op. cit._ , pp. 245-270, y, con el título de «De la psychogenèse d'un cas d'homosexualité féminine», en _OC.P_ , vol. 15, _op. cit._ , pp. 233-263 [hay trad. cast.: «Sobre la psicogénesis de un caso de homosexualidad femenina», en _OC_ , vol. 18, _op. cit._ , pp. 137-164]. La vida de Margarethe Csonka (1900-1999) generó una importante literatura, en la que cabe destacar el relato de Ines Rieder y Diana Voigt, dos historiadoras del lesbianismo que la conocieron poco antes de su muerte. Cf. Ines Rieder y Diana Voigt, _Heimliches Begehren: die Geschichte der Sidonie C._ , Viena, Deuticke, 2000, traducido al francés con el muy discutible título de _Sidonie Csillag, homosexuelle chez Freud, lesbienne dans le siècle_ , París, EPEL, 2003 [hay trad. cast.: _Sidonie Csillag: la «joven homosexual» de Freud_ , Buenos Aires, El Cuenco de Plata, 2004]. En esta obra, que es una recopilación de testimonios, Margarethe aparece bajo el seudónimo de Sidonie Csillag. En la traducción francesa su «caso» es reinterpretado de manera «lacaniana» por Jean Allouch. Mikkel Borch-Jacobsen hace una interpretación menos fantasiosa de esta historia, si bien afirma que Freud se dejó engañar por Margarethe. Cf. M. Borch-Jacobsen, _Les Patients de Freud..._ , _op. cit._ , pp. 180-186. Señalemos que Kurt Eissler recogió el testimonio de Margarethe Csonka von Trautenegg, que confirma que esta no apreciaba mucho a Freud y no tenía gran cosa que decirle, LoC, caja 2.
. Citado en I. Rieder y D. Voigt, _Sidonie Csillag..._ , _op. cit._ , p. 66.
. _Ibid._ , p. 77.
. Se trata de tres series de caracteres: 1) sexuales somáticos; 2) sexuales psíquicos, y 3) modo de elección del objeto.
. S. Freud, «Sur la psychogenèse...», _op. cit._ , p. 270 [«Sobre la psicogénesis...», _op. cit._ , pp. 163-164]. Eugen Steinach (1861-1944): médico austríaco, pionero de la endocrinología y de los principios de la diferenciación sexual. Ganó celebridad por haber inventado una vasoligadura de los canales que a su juicio podría regenerar las células hormonales y, por lo tanto, favorecer el rejuvenecimiento. Freud se sometió a esa operación en 1923. Como el cáncer es una enfermedad de la vejez, se consideraba que al estimular las células hormonales se podía retrasar la aparición de una recaída.
. El análisis de Anna G. transcurrió entre el 1 de abril y el 14 de julio de 1921, a razón de una hora al día.
. Anna G., _Mon analyse avec le professeur Freud_ , edición dirigida por Anna Koellreuter, París, Aubier, 2010. La edición alemana es mucho más fiable: _Wie benimmt sich der Prof. Freud eigentlich?_ , Giessen, Psychosozial-Verlag, 2009.
. Carta de A. Freud a L. Andreas-Salomé, en Lou Andreas-Salomé y Anna Freud, _Correspondance, 1919-1937_ , París, Hachette Littérature, 2006, p. 43.
. Sigmund Freud, «Un enfant est battu. Contribution à la connaissance de la genèse des perversions sexuelles» (1919), en _Névrose, psychose et perversion_ , _op. cit._ , pp. 219-243 [hay trad. cast.: «"Pegan a un niño". Contribución al conocimiento de la génesis de las perversiones sexuales», en _OC_ , vol. 17, _op. cit._ , pp. 173-200], y Anna Freud, «Fantasme d'"être battu" et "rêverie"» (1922), en Marie-Christine Hamon, ed., _Féminité mascarade: études psychanalytiques_ , París, Seuil, 2004, pp. 57-75 [hay trad. cast.: «Relación entre fantasías de flagelación y sueño diurno», _Revista de Psicoanálisis_ (Buenos Aires), 4(2), 1946, pp. 258-271].
. Carta de Freud a L. Andreas-Salomé, en L. Andreas-Salomé, _Correspondance avec Sigmund Freud..._ , _op. cit._ Esta correspondencia está expurgada y en ella no se encuentra ninguna alusión a ese análisis.
. Peter Heller, _Une analyse d'enfant avec Anna Freud_ (1983), París, Presses Universitaires de France, 1996, p. 31.
. Carta de Freud a Binswanger, 11 de enero de 1929, en S. Freud y L. Binswanger, _Correspondance..._ , _op. cit._ , pp. 278-279. La correspondencia entre Anna Freud y Dorothy Burlingham se conserva en el Freud Museum de Londres. Todavía no es accesible a los investigadores.
. Alrededor de tres mil objetos, dos mil de los cuales se trasladarían a Inglaterra. Cf. Richard H. Armstrong, _A Compulsion for Antiquity: Freud and the Ancient World_ , Ithaca, Cornell University Press, 2005.
. Peter Gay, «Notice biographique», en Edmund Engelmann, _La Maison de Freud, Berggasse 19, Vienne_ (fotografías) (1976), París, Seuil, 1979, p. 124.
. Januká: fiesta judía. Kidush: ceremonia del comienzo del sabbat. Sobre estos objetos y las discusiones relacionadas con ellos, cf. Y. H. Yerushalmi, _Le «Moïse» de Freud..._ , _op. cit._ , pp. 201-203, y Erica Davies, «Eine Welt wie im Traum: Freuds Antikesammlung», catálogo de la exposición «Meine alten und dreckigen Götter»: aus Sigmund Freuds Sammlung, edición de Lydia Marinelli, Frankfurt, Stroemfeld, 1998. Sobre los objetos mexicanos de Freud cf. Rubén Gallo, _Freud au Mexique_ (2010), París, Campagne Première, 2013 [hay trad. cast.: _Freud en México: historia de un delirio_ , México, Fondo de Cultura Económica, 2013].
. Varias decenas de libros ilustrados dan testimonio de la fantástica organización que gobernaba la vida cotidiana de la Berggasse. Véanse Ernst Freud, Lucie Freud e Ilse Grubrich-Simitis, eds., _Sigmund Freud: lieux, visages, objets_ (1976), con una parte biográfica escrita por Kurt Eissler, Bruselas, Complexe, 1979, y Sigmund Freud, _Chronique la plus brève: carnets intimes, 1929-1939_ (1992), anotados y presentados por Michael Molnar, París, Albin Michel, 1992.
. William Bayard Hale, _The Story of a Style_ , Nueva York, B. W. Huebsch, Inc., 1920.
. Afección de las mucosas caracterizada por la presencia de placas de color blanco.
. Varias obras se dedicaron al cáncer de Freud. Cf. en especial M. Schur, _La Mort dans la vie..._ , _op. cit._ Ernest Jones y Peter Gay dieron versiones perfectamente ajustadas a la realidad.
. Se trataba de un carcinoma verrugoso, que el médico norteamericano Lauren V. Ackerman (1905-1993) describiría por primera vez en 1948. En 1923 se hablaba de «cáncer del maxilar superior de evolución lenta». Cf. M. Schur, _La Mort dans la vie..._ , _op. cit._
. Algunos años después, en Londres, Jones informó de esta discusión a Freud. Furioso, este dio rienda suelta a su ira: ¿con qué derecho ( _mit welchem Recht_ ) habían decidido ocultarle la verdad? Freud no soportaba el «tutelaje» ( _Bevormundung_ ). Cf. P. Grosskurth, _Freud: l'anneau secret_ , _op. cit._ , p. 124. Ernest Jones y Peter Gay dan la misma versión.
. S. Freud, « _Notre cœur tend vers le sud»..._ , _op. cit._ , p. 338.
. Sharon Romm y Edward Luce, «Hans Pichler: oral surgeon to Sigmund Freud», _Oral Surgery, Oral Medicine and Oral Pathology_ , 57(1), enero de 1984, pp. 31-32, y Xavier Riaud, _Pionniers de la chirurgie maxillo-faciale (1914-1918)_ , París, L'Harmattan, 2010. Algunos comentaristas han afirmado que el cáncer maxilofacial de Freud —descrito por varios historiadores de la medicina y certificado por los archivos— carecía de gravedad o era imaginario; que la causa principal de su agravamiento radicaba en la operación fallida de Hajek, la radioterapia y los malos tratamientos de Schur, y que la cocaína era responsable de la aparición de una primera lesión. Cf. J. Bénesteau, _Mensonges freudiens_ , _op. cit._ , pp. 162-163. En esta obra, íntegramente compuesta de rumores, los nombres de Pichler y Kazanjian no figuran en ninguna parte. Por añadidura, el autor confunde «papilomatosis» y «carcinoma» y da a entender que el cáncer de Freud fue inventado por sus idólatras a fin de presentarlo como un mártir. La presunta «inexistencia del cáncer de Freud» es, como la hipotética relación incestuosa con Minna, uno de los grandes temas predilectos de la escuela revisionista.
. A. Bolzinger, _Portrait de Sigmund Freud..._ , _op. cit._ , pp. 71-72. Todas estas citas están tomadas de la correspondencia de Freud y fueron traducidas por el autor.
. P. Gay, _Freud, une vie_ , _op. cit._ , p. 508.
#### 3. EL ARTE DEL DIVÁN
. Al final del volumen se encontrará una lista no exhaustiva de los pacientes de Freud establecida por Richard G. Klein y Ernst Falzeder, a la que yo agregué algunos nombres. Cf. asimismo Ulrike May, «Neunzehn Patienten in Analyse bei Freud (1910-1910), Teil I: Zur Dauer von Freuds Analysen», y «Teil II: Zur Frequenz von Freuds Analysen», _Psyche: Zeitschrift für Psychoanalyse und ihre Anwendungen_ , 61(6), junio de 2007, pp. 590-625, y 61(7), julio de 2007, pp. 686-709. David J. Lynn y George E. Vaillant, «Anonymity, neutrality and confidentiality in the actual methods of Sigmund Freud: a review of 43 cases, 1907-1939», _American Journal of Psychiatry_ , 155(2), febrero de 1998, pp. 163-171, analizaron y evaluaron cuarenta y tres casos de Freud. Mikkel Borch-Jacobsen ha presentado un retrato muy interesante, pero demasiado contrario a Freud, de treinta y un pacientes; cf. M. Borch-Jacobsen, _Les Patients de Freud..._ , _op. cit._ Cf. también la obra ya antigua de P. Roazen, _La Saga freudienne_ , _op. cit._ ; Manfred Pohlen, _En analyse avec Freud_ (2006), París, Tallandier, 2010, y É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._ Algunos de los archivos depositados en la Biblioteca del Congreso y dedicados a los pacientes todavía no se han desclasificado, aunque se puede tener acceso a ellos. He identificado algo más de ciento veinte pacientes, cuya lista presento al final del libro.
. He abordado esta cuestión en _HPF-JL_ , _op. cit._ Cf. asimismo É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._ , donde se encontrará la bibliografía concerniente a este tema.
. Si los psicoanalistas no pudieron realizar jamás una verdadera evaluación de la práctica de Freud fue sin duda porque no quisieron enfrentarse a esas curas no contadas por él. Fueran de la tendencia que fuesen —kleinianos, lacanianos, poslacanianos, ferenczianos, etc.—, se conformaron con comentar, como si se tratara de un cuerpo canonizado, la historia de Anna O. y los «casos» relatados en los _Estudios sobre la histeria_ , así como los famosos «cinco psicoanálisis», de los cuales solo tres pueden calificarse de curas. Por eso dejaron el campo libre a los antifreudianos, que lo aprovecharon para transformar a Freud en un impostor incapaz de curar a ningún paciente. La realidad, como hemos visto, es indudablemente mucho más compleja.
. Ernst Blum, Marie Bonaparte, Maryse Choisy, Jakob Julius David, Viktor von Dirsztay, Hilda Doolittle, Henri Flournoy, Horace W. Frink, Bruno Goetz, Abram Kardiner, Carl Liebman, Gustav Mahler, Raymond de Saussure, James y Alix Strachey, Bruno Walter, Margaret Wittgenstein, Joseph Wortis, etc.
. Puede consultarse en la Biblioteca del Congreso.
. A petición mía, el matemático Henri Roudier evaluó la fortuna de Freud en las diferentes etapas de su vida. En florines y coronas antes de la Primera Guerra Mundial y luego, desde 1924, en chelines y dólares. Señalemos que ninguno de los «métodos» que se propusieron para evaluar los honorarios de las sesiones de Freud y convertirlos a euros o dólares del siglo XXI tiene fundamento científico, y además los autores se contradicen entre sí: cuatrocientos cincuenta euros para unos, mil para otros y mil trescientos para un tercer grupo. No se puede en ningún caso tomar en serio esas conversiones, que pretenden sin duda dar a entender que Freud era un estafador o un codicioso, y su fortuna solo puede evaluarse si se la compara con la de sus contemporáneos que ejercían la misma profesión que él y pertenecían a la misma clase social. Está claro que se había hecho rico en comparación con la relativa pobreza en que vivía su padre a la misma edad que él. Cf. Henri Roudier, «Freud et l'argent», inédito. Cf. asimismo Christfried Tögel, «Sigmund Freud's practice: visits and consultation, psychoanalyses, remuneration», _The Psychoanalytic Quarterly_ , 78(4), octubre de 2009, pp. 1033-1058. Véase la evaluación de Thomas Piketty, nota 8 de este capítulo.
. Carta de Freud a Andreas-Salomé, octubre de 1921, en L. Andreas-Salomé, _Correspondance avec Sigmund Freud..._ , _op. cit._ , p. 138. Freud alude a la pérdida parcial de la fortuna de la familia de Lou como consecuencia de la revolución bolchevique.
. En la misma fecha, los honorarios de una sesión en Nueva York ascendían a cincuenta dólares. Thomas Piketty calculó a petición mía los ingresos de Freud: «Freud era un médico acomodado, lo cual no tenía nada de escandaloso dado el muy alto nivel de desigualdad que caracterizaba la época. El ingreso medio era por entonces de mil doscientos a mil trescientos francos oro por año y por habitante. Hoy, en 2013-2014, el ingreso medio (antes de impuestos) es del orden de los veinticinco mil euros por año y por habitante adulto. Para comparar las cantidades lo mejor es, por lo tanto, multiplicarlas, expresadas en francos oro de 1900-1910, por un coeficiente del orden de 20. Christfried Tögel atribuye a Freud un ingreso de unos veinticinco mil florines, lo que correspondería actualmente a quinientos mil euros anuales. Son unos ingresos muy elevados, por supuesto, pero bastante representativos del más alto nivel de la época. A desigualdad constante, correspondería más bien a alrededor de doscientos cincuenta mil euros de ingreso anual en nuestros días».
. Carta de Freud a Ferenczi, 27 de agosto de 1925, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 3, _op. cit._ , p. 252, y Smiley Blanton, _Journal de mon analyse avec Freud_ , París, Presses Universitaires de France, 1973, p. 72 [hay trad. cast.: _Diario de mi análisis con Freud_ , Buenos Aires, Corregidor, 1974]. No comparto la opinión de Patrick Mahony, que interpretó con talante kleiniano el antiamericanismo de Freud mediante la hipótesis de que este protegía así de manera defensiva la imagen idealizada de su madre, en tanto que América representaba para él una «madre arcaica» cuyo poder demoníaco habría reprimido. Cf. Louise Grenier e Isabelle Lasvergnas, eds., _Penser Freud avec Patrick Mahony_ , Montreal, Liber, 2004, p. 39.
. Carta de Freud a Rado, 30 de septiembre de 1925, LoC.
. Carta de Freud a Hollos, 4 de octubre de 1928, en István Hollos, «Mes adieux à la Maison jaune», _Le Coq-Héron_ , 100, 1986.
. A título de ejemplo señalaremos que el arquitecto vienés Karl Mayreder (1856-1935), tratado por Freud durante diez semanas de 1915 a causa de su melancolía crónica, batió todas las marcas al consultar a cincuenta y nueve médicos, cuyas recetas y otras terapias fueron totalmente ineficaces. Pero a continuación solo se acusó a Freud de no haberlo curado. Esta tesis de la responsabilidad exclusiva de Freud se retoma en M. Borch-Jacobsen, _Les Patients de Freud..._ , _op. cit._ ; Frank Cioffi, _Freud and the Question of Pseudoscience_ , Chicago, Open Court, 1999, y J. Bénesteau, _Mensonges freudiens_ , _op. cit._
. Conversación de Edoardo Weiss con Kurt Eissler, 13 de diciembre de 1953, LoC, caja 121, carpeta 34, con diversos comentarios y recuerdos. Cf. asimismo Anna Maria Accerboni, «Sigmund Freud dans les souvenirs d'Edoardo Weiss, pionnier de la psychanalyse italienne», _Revue internationale d'histoire de la psychanalyse_ , 5, 1992, pp. 619-633.
. Giorgio Voghera, _Gli anni della psicoanalisi_ , Pordenone, Edizioni Studio Tesi, 1980.
. Cf. Maurizio Serra, _Italo Svevo ou l'Antivie_ , París, Grasset, 2013, pp. 258-259, e Italo Svevo, _Romans_ , edición establecida y presentada por Mario Fusco, París, Gallimard, 2010, col. «Quarto» (contiene _Ecrits intimes_ , _Une vie_ , _Senilità_ y _La Conscience de Zeno_ ) [hay trad. cast.: _La conciencia de Zeno_ , Barcelona, Círculo de Lectores, 2001; _Senectud_ , Barcelona, Acantilado, 2001, y _Una vida_ , Madrid, Joseph K, 2003].
. Una empresa de pintura de cascos de barcos.
. Son los términos utilizados por Svevo.
. M. Serra, _Italo Svevo..._ , _op. cit._ , p. 261.
. S. Freud y K. Abraham, _Correspondance..._ , _op. cit._ , pp. 352-354.
. Anna Maria Accerboni Pavanello, «La sfida di Svevo alla psicoanalisi», en Riccardo Cepach, ed., _Guarire dalla cura: Italo Svevo e i medici_ , Trieste, Comune di Trieste, 2008, pp. 110-112. Cf. asimismo M. Serra, _Italo Svevo..._ , _op. cit._ , p. 249.
. M. Serra, _Italo Svevo..._ , _op. cit._ , p. 264.
. Italo Svevo, _La Conscience de Zeno_ , en _Romans_ , _op. cit._ , p. 908.
. Mario Lavagetto, _L'impiegato Schmitz e altri saggi su Svevo_ , Turín, Einaudi, 1975. También reproducido en M. Serra, _Italo Svevo..._ , _op. cit._
. A. M. Accerboni Pavanello, «La sfida di Svevo...», _op. cit._
. Véanse _infra_ las relaciones entre Freud y Oskar Pfister.
. Entre los pacientes de Freud hay una veintena de norteamericanos, casi todos de Nueva York. Thaddeus Ames (1885-1963) lo había conocido en Viena entre 1911 y 1912. Monroe Meyer (1892-1939), psiquiatra melancólico, se suicidaría a los cuarenta y siete años con un picahielos. Los antifreudianos acusarán a Freud de haber causado esa muerte voluntaria, producida dieciocho años después de la estancia de Meyer en Viena. Leonard Blumgart (1881-1959) se mantuvo fiel a la ortodoxia freudiana.
. Así le dijo a Jones. Cf. P. Gay, _Freud, une vie_ , _op. cit._ , p. 651.
. Testimonio de Clarence Oberndorf del 12 de diciembre de 1952, LoC.
. Clarence Oberndorf (1882-1954) era un ortodoxo del freudismo, hostil al psicoanálisis lego. Fue autor de la primera obra oficial sobre la historia del psicoanálisis en Estados Unidos [ _A History of Psychoanalysis in America_ , Nueva York, Grune & Stratton, 1953. _(N. del T.)_ ].
. Abram Kardiner, _Mon analyse avec Freud_ (1977), París, Belfond, 1978, pp. 141 y 89 [hay trad. cast.: _Mi análisis con Freud: reminiscencias_ , México, Joaquín Mortiz, 1979].
. _Ibid._ , pp. 103-104.
. Freud las había recibido en octubre de 1921, cuando Kardiner comenzaba su análisis.
. A. Kardiner, _Mon analyse avec Freud_ , _op. cit._ , p. 101.
. Horace W. Frink, _Morbid Fears and Compulsions: Their Psychology and Psychoanalytic Treatment_ , Nueva York, Moffat, Yard & Co., 1918.
. La primera cura de Frink duró cinco meses, de marzo a julio de 1921. La segunda se extendió de abril a julio de 1922, y la tercera transcurrió entre noviembre y diciembre de ese mismo año. Cf. P. Roazen, _La Saga freudienne_ , _op. cit._ , y Lavinia Edmunds, «Freud's American tragedy», _Johns Hopkins Magazine_ , 30, 1988, pp. 40-49. Véanse también L. Grenier e I. Lasvergnas, eds., _Penser Freud..._ , _op. cit._ , pp. 40-45, y M. Borch-Jacobsen, _Les Patients de Freud..._ , _op. cit._ , pp. 198-202. La comunidad psicoanalítica y varios biógrafos de Freud callan sobre el análisis de Frink; la excepción es P. Gay, _Freud, une vie_ , _op. cit._ , p. 652, que lo cuenta correctamente y destaca el antiamericanismo de aquel. Por otra parte, el asunto se menciona en S. Freud y E. Jones, _Correspondance complète..._ , _op. cit._ Cf. igualmente É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Carta de Freud a Jones, 6 de noviembre de 1921. Abraham Bijur murió en mayo de 1922 sin haber publicado su carta abierta.
. Carta de Freud a Frink, 17 de noviembre de 1921, LoC. Citada en parte en L. Grenier e I. Lasvergnas, eds., _Penser Freud..._ , _op. cit._ , p. 43.
. Carta de Freud a Jones, 25 de septiembre de 1924, en S. Freud y E. Jones, _Correspondance complète..._ , _op. cit._ , p. 639.
. Medical Archives of Johns Hopkins Medical Institutions, The Frink Family Collection, y Michael Specter, «Sigmund Freud urged his disciple to divorce: wanted him to marry another woman, daughter finds», _Los Angeles Times_ , 12 de noviembre de 1987.
. Carta de Jones a Freud, 20 de septiembre de 1924, en S. Freud y E. Jones, _Correspondance complète..._ , _op. cit._ , p. 641.
. Jeannine Hayat, «Lytton Strachey: l'historien intime de deux reines», _LISA e-journal_ , enero de 2007, y Lytton Strachey, _Victoriens éminents_ (1918), París, Gallimard, 1933 [hay trad. cast.: _Victorianos eminentes_ , Madrid, Aguilar, 1989], _La Reine Victoria_ (1921), París, Payot, 1923 [hay trad. cast.: _Reina Victoria: símbolo de una era_ , Buenos Aires, El Ateneo, 2004], y _Élisabeth et le comte d'Essex, histoire tragique_ (1928), París, Gallimard, 1929 [hay trad. cast.: _Isabel y Essex_ , Barcelona, Lumen, 1984]. Cf. Floriane Reviron, «De Lytton Strachey à Virginia Woolf», en Frédéric Regard, ed., _La Biographie littéraire en Angleterre,_ XVIII-XIX _e: configuration, reconfiguration du soi artistique_ , Saint-Étienne, Publications de l'Université de Saint-Étienne, 1999, pp. 117-139.
. John Maynard Keynes, _Les Conséquences économiques de la paix_ (1919), seguido de Jacques Bainville, _Les Conséquences politiques de la paix_ , París, Gallimard, 2002, col. «Tel» [hay trad. cast. del primero: _Las consecuencias económicas de la paz_ , Barcelona, RBA, 2012]. Bainville fue uno de los críticos más virulentos de Keynes. Cf. Gilles Dostaler y Bernard Maris, _Capitalisme et pulsion de mort_ , París, Albin Michel, 2008. Estos dos autores comparan la crítica hecha por Keynes de la capacidad de autodestrucción del capitalismo con la teorización freudiana de la pulsión de muerte.
. Cf. la excelente obra de Perry Meisel y Walter Kendrick, eds., _Bloomsbury/Freud: James et Alix Strachey, correspondance 1924-1925_ (1985), París, Presses Universitaires de France, 1990.
. _Ibid._ , p. 43.
. A. Kardiner, _Mon analyse avec Freud_ , _op. cit._ , p. 117.
. Testimonio de Lionel S. Penrose del 28 de julio de 1953, LoC, caja 117. Sobre la trayectoria de John Rickman, analizado a continuación por Sándor Ferenczi y Melanie Klein, cf. É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. P. Meisel y W. Kendrick, eds., _Bloomsbury/Freud..._ , _op. cit._ , p. 8.
. James Strachey, «Bibliography: list of English translations of Freud's works», _International Journal of Psycho-Analysis_ , 26(1-2), 1945, pp. 67-76; «Editor's note», en Sigmund Freud, _The Standard Edition of the Complete Psychological Works of Sigmund Freud_ , 24 vols., Londres, The Hogarth Press, 1953-1974, vol. 3, 1962, pp. 71-73 [hay trad. cast.: «Nota introductoria», en S. Freud, _OC_ , vol. 3, _op. cit._ , pp. 71-73], y «General preface», en _ibid._ , vol. 1, 1966, pp. XIII-XXII [hay trad. cast.: «Prólogo general», en _OC_ , vol. 1, _op. cit._ , pp. xv-xxv], y James Strachey y Allan Tyson, «A chronological hand-list of Freud's works», _International Journal of Psycho-Analysis_ , 37(1), 1956, pp. 19-33. Cf. asimismo Bruno Bettelheim, _Freud et l'âme humaine_ (1982), París, Laffont, 1984 [hay trad. cast.: _Freud y el alma humana_ , Barcelona, Crítica, 1983].
. Según las palabras de P. Meisel y W. Kendrick, eds., _Bloomsbury/Freud..._ , _op. cit._ , p. 13.
. Melanie Klein, _La Psychanalyse des enfants_ (1932), París, Presses Universitaires de France, 1969 [hay trad. cast.: _El psicoanálisis de niños_ , en _Obras completas_ , vol. 2, Buenos Aires, Paidós, 1987]. Melanie tuvo tres hijos: Hans Klein, Erich Klein (futuro Eric Clyne) y Melitta, que terminaría por ser su peor enemiga.
. Sobre la trayectoria de Melanie Klein, de la que nos ocuparemos en el próximo capítulo, cf. P. Grosskurth, _Melanie Klein..._ , _op. cit._
. Melanie Klein se instaló definitivamente en Londres en septiembre de 1926.
. Cf. R. W. Clark, _Freud, the Man..._ , _op. cit._
. Patrick Lacoste, _L'Étrange cas du professeur Freud: psychanalyse à l'écran_ , París, Gallimard, 1990, pp. 93-94.
. E. Jones, _La Vie et l'œuvre..._ , vol. 3, _op. cit._ , p. 132.
. Sobre todo cuando John Huston quiso filmar una película sobre la vida de Freud a partir de un guión de Jean-Paul Sartre. Cf. Elisabeth Roudinesco, _Philosophes dans la tourmente_ , París, Fayard, 2005 [hay trad. cast.: _Filósofos en la tormenta_ , Buenos Aires, Fondo de Cultura Económica, 2007].
. Francis Bacon (1561-1626): filósofo, hombre de ciencia y lord canciller.
. Peter Gay, «Freud et l'homme de Stratford», en _En lisant Freud: explorations et divertissements_ (1990), París, Presses Universitaires de France, 1995, p. 17 [hay trad. cast.: «Freud y el hombre de Stratford», en _Freud, otra vez: exploraciones y divertimentos_ , Buenos Aires, Ada Korn, 1995].
. J. Thomas Looney, « _Shakespeare» Identified in Edward de Vere, the Seventeenth Earl of Oxford_ , Londres, Cecil Palmer, 1920. En 2012 Roland Emmerich retomó la tesis de Looney en su filme _Anónimo_ [ _Anonymous_ ].
. Entre los ochenta y dos candidatos alternativos a la paternidad de la obra de Shakespeare figuraban, entre otros, Christopher Marlowe, Cervantes, John Donne, Robert Devereux (Essex) y Daniel Defoe. Dos discípulos de Looney también imaginaron que la reina Isabel había tenido un hijo con De Vere.
. Edward de Vere (1550-1604), decimoséptimo conde de Oxford, lord gran chambelán, poeta, par y cortesano del período isabelino, había contraído matrimonio con Anne Cecil, condesa de Oxford (1558-1588), hija de William Cecil (1520-1598), consejero de Estado de la reina Isabel (1558-1603), y de Mildred Cooke (1526-1589). Cayó en desgracia y se lo envió a la Torre de Londres por haber seducido a Anne Vavasour (1560-1650), dama de honor de Isabel. Henry Wriothesley (1573-1624), tercer conde de Southampton, amigo del segundo conde de Essex (1565-1601), presunto destinatario de los _Sonetos_ de Shakespeare y supuesto amante de este. Muchos autores intentaron probar que Shakespeare era homosexual. Sobre el absurdo de la atribución de la paternidad de las obras de Shakespeare a De Vere, cf. Alan H. Nelson, _Monstrous Adversary: The Life of Edward de Vere, 17th Earl of Oxford_ , Liverpool, Liverpool University Press, 2003.
. Carta de Freud a Lytton Strachey, 25 de diciembre de 1928, en P. Meisel y W. Kendrick, _Bloomsbury/Freud..._ , _op. cit._ , pp. 373-375.
. Numerosos libros se dedicaron a la semejanza entre Freud y el detective inventado por Arthur Conan Doyle, también él apasionado por el espiritismo.
. El historiador Carlo Ginzburg ha designado este fenómeno como el surgimiento, en el enfoque racional de los signos, de una cosa turbia y perturbadora que escapa siempre a la ciencia.
#### 4. ENTRE LAS MUJERES
. Freud a Ferenczi, carta del 26 de marzo de 1924, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 3, _op. cit._ , p. 155.
. Noveno congreso de la IPV, 2 a 5 de septiembre de 1925.
. Beata Rank (1896-1967), apodada Tola, también sería psicoanalista.
. O. Rank, _Le Traumatisme de la naissance..._ , _op. cit._ , y Sándor Ferenczi, _Thalassa: essai sur la théorie de la génitalité_ , en _Œuvres complètes_ , vol. 3, _op. cit._ , pp. 250-323 [hay trad. cast.: _Thalassa: ensayo sobre la teoría de la genitalidad_ , en _Obras completas_ , vol. 3, _op. cit._ , pp. 303-383].
. Carta de Freud a Ferenczi, 23 de abril de 1926, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 3, _op. cit._ , p. 285, y Sigmund Freud y Otto Rank, _The Letters of Sigmund Freud and Otto Rank: Inside Psychoanalysis_ , edición de James Lieberman y Robert Kramer, Baltimore, The Johns Hopkins University Press, 2012, carta del 4 de agosto de 1922; versión francesa: _Correspondance 1907-1926_ , París, Campagne Première, 2015.
. Sigmund Freud, _Inhibition, symptôme et angoisse_ (1926), en _OC.P_ , vol. 17, 1992, pp. 203-287 [hay trad. cast.: _Inhibición, síntoma y angustia_ , en _OC_ , vol. 20, _op. cit._ , pp. 71-161].
. Sándor Ferenczi, «Confusion des langues entre les adultes et l'enfant: le langage de la tendresse et de la passion» (1932), en _Œuvres complètes_ , vol. 4, _op. cit._ , pp. 125-138 [hay trad. cast.: «Confusión de lengua entre los adultos y el niño: el lenguaje de la ternura y la pasión», en _Obras completas_ , vol. 4, _op. cit._ , pp. 139-149].
. Sobre la estancia de Rank en París y sus relaciones con Anaïs Nin, cf. _HPF-JL_ , _op. cit._ , p. 451 y ss., y J. Lieberman, _La Volonté en acte..._ , _op. cit._ A continuación Rank se radicaría definitivamente en Estados Unidos.
. Sándor Ferenczi, «Un petit homme coq», en _Œuvres complètes_ , vol. 2, _op. cit._ , pp. 72-79 [hay trad. cast.: «Un pequeño hombre gallo», en _Obras completas_ , vol. 2, _op. cit._ , pp. 89-96].
. Anna Freud, _Le Traitement psychanalytique des enfants_ (1927), París, Presses Universitaires de France, 1951.
. Carta de Freud a J. Riviere, 9 de octubre de 1927, en «Lettres de Sigmund Freud à Joan Riviere (1921-1939)», _Revue internationale d'histoire de la psychanalyse_ , 6, 1993, p. 470.
. Hermine von Hug-Hellmuth, _Journal d'une petite fille_ , París, Denoël, 1998, con carta prefacio de Sigmund Freud; el texto, presentado como una obra auténtica, se editó por primera vez en francés en 1928. Cf. asimismo Hermine von Hug-Hellmuth, _Essais psychanalytiques: destin et écrits d'une pionnière de la psychanalyse des enfants_ , textos reunidos, presentados y traducidos por Dominique Soubrenie, prefacio de Jacques Le Rider, epílogo de Yvette Tourne, París, Payot, 1991. Cuando escribí para _Libération_ , en 1991, la reseña de esta obra que revelaba la superchería, recibí cartas de psicoanalistas que me acusaban de «conspirar» contra Freud. Todavía creían que el asesinato y la falsificación eran calumnias inventadas por los antifreudianos.
. Como muchas mujeres psicoanalistas de esta generación, con la excepción de Karen Horney. Cf. É. Roudinesco, «Les premières femmes psychanalystes», _op. cit._
. Phyllis Grosskurth describe muy bien la infancia de Melanie Klein y las relaciones con sus padres, su marido y sus hijos, sobre la base de su «autobiografía» inédita y los archivos conservados en el Melanie Klein Trust. Tuve la oportunidad de conversar con Grosskurth durante una de sus visitas a París.
. Cf. Sigmund Freud, «Sur le plus général des rabaissements de la vie amoureuse» (1912), en _La Vie sexuelle_ , _op. cit._ , p. 65 [hay trad. cast.: «Sobre la más generalizada degradación de la vida amorosa (Contribuciones a la psicología del amor, II)», en _OC_ , vol. 11, _op. cit._ , p. 181], y «La féminité», en _Nouvelles conférences..._ , _op. cit._ [hay trad. cast.: «La feminidad», en _Nuevas conferencias..._ , _op. cit._ ].
. Durante un encuentro con Goethe en Erfurt, el 2 de octubre de 1808, el emperador mencionó las tragedias del destino que él desaprobaba y que, a su entender, suponían una época más oscura que la suya: «Qué nos importa hoy el destino», dijo, «la política es el destino». He comentado esta frase en _La Famille en désordre_ , _op. cit._ , capítulo «Les femmes ont un sexe».
. S. Freud, «La féminité», _op. cit._ , p. 153 [«La feminidad», _op. cit._ , p. 106].
. Los textos del debate histórico entre Viena y Londres se tradujeron al francés en M.-C. Hamon, ed., _Féminité mascarade..._ , _op. cit._ Cf. asimismo Sigmund Freud, «Quelques conséquences psychologiques de la différence anatomique entre les sexes» (1925), en _La Vie sexuelle_ , _op. cit._ , pp. 123-132 [hay trad. cast.: «Algunas consecuencias psíquicas de la diferencia anatómica entre los sexos», en _OC_ , vol. 19, _op. cit._ , pp. 259-276], y Helene Deutsch, _Psychanalyse des fonctions sexuelles de la femme_ , París, Presses Universitaires de France, 1994. El título de _Féminité mascarade_ proviene de un texto célebre de Joan Riviere, «La féminité en tant que mascarade» [«La femineidad como máscara»], en el cual la autora muestra que las mujeres intelectuales que han alcanzado un éxito completo en su integración social y su vida conyugal son condenadas a exhibir su femineidad como una máscara para disimular mejor su angustia.
. Virginia Woolf, _Trois guinées_ (1938), precedido de «L'autre corps», prefacio de Viviane Forrester, París, Éditions Des Femmes, 1978 [hay trad. cast.: _Tres guineas_ , Barcelona, Lumen, 1999].
. Carta de Freud a Jones, 9 de octubre de 1927, en S. Freud y E. Jones, _Correspondance complète..._ , _op. cit._ , p. 727.
. Numerosas obras se dedicaron a la historia del psicoanálisis infantil a partir de 1945, y en especial a la escuela inglesa representada por D. W. Winnicott y John Bowlby. Cf. É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._ , y para Francia, _HPF-JL_ , _op. cit._
. S. Freud, «La féminité», _op. cit._ , p. 177 [«La feminidad», _op. cit._ , p. 122].
. Sigmund Freud, «Le thème des trois coffrets» (1913), en _L'Inquiétante étrangeté..._ , _op. cit._ , p. 81 [hay trad. cast.: «El motivo de la elección del cofre», en _OC_ , vol. 12, _op. cit._ , p. 317].
. S. Freud, «Sur le plus général des rabaissements...», _op. cit._ , p. 61 [«Sobre la más generalizada degradación...», _op. cit._ , p. 179].
. _Ibid._ , p. 59 [ _ibid._ , p. 176].
. S. Freud, «La féminité», _op. cit._ , p. 179 [«La feminidad», _op. cit._ , p. 124; traducción ligeramente modificada].
. Nicole Loraux, _Les Expériences de Tirésias: le féminin et l'homme grec_ , París, Gallimard, 1989 [hay trad. cast.: _Las experiencias de Tiresias: lo femenino y el hombre griego_ , Buenos Aires, Biblos, 2003].
. Sigmund Freud, _La Question de l'analyse profane_ (1926), París, Gallimard, 1985, p. 75 [hay trad. cast.: _¿Pueden los legos ejercer el análisis? Diálogos con un juez imparcial_ , en _OC_ , vol. 20, _op. cit._ , p. 199].
. Henry Morton Stanley, _Through the Dark Continent, or, The Sources of the Nile around the Great Lakes of Equatorial Africa, and down the Livingstone River to the Atlantic Ocean_ (1878), 2 vols., Mineola (Nueva York), Dover Publications, 1988 [hay trad. cast.: _El continente misterioso: las fuentes del Nilo, los grandes lagos del África ecuatorial, del río Livingstone al océano Atlántico_ , Barcelona, Manuel Salvat, 1890]. Véase también Michèle Lurdos, «Au cœur du continent noir: Henry Morton Stanley», en Jean Sévry, ed., _Regards sur les littératures coloniales_ , vol. 3, _Afrique anglophone et lusophone_ , París, L'Harmattan, 1999, pp. 97-108.
. Cf. Georges Duby y Michelle Perrot, eds., _Histoire des femmes en Occident_ , vol. 4, _Le_ XIX _e siècle_ , edición de Geneviève Fraisse y Michelle Perrot, París, Plon, 1991 [hay trad. cast.: _Historia de las mujeres en Occidente_ , vol. 4, _El siglo_ XIX, Madrid, Taurus, 2000].
. Sobre los debates posteriores en relación con la sexualidad femenina, y en especial sobre las posiciones respectivas de Simone de Beauvoir, Jacques Lacan y sus sucesores, cf. _HPF-JL_ , _op. cit._ , así como É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._ , y Elisabeth Roudinesco, «Soudain, _Le Deuxième sexe..._ », _Les Temps modernes_ , 647-648, enero-marzo de 2008, pp. 192-213. Es considerable la literatura dedicada a la cuestión y sobre todo a la distinción del sexo y el género ( _gender_ ), tanto dentro como fuera del movimiento psicoanalítico. Cf. también L. Appignanesi y J. Forrester, _Freud's Women_ , _op. cit._
. Cf. Célia Bertin, _La Femme à Vienne au temps de Freud_ , París, Stock/Laurence Pernoud, 1989, y Ursula Prokop, _Margaret Stonborough-Wittgenstein: intellectuelle, mécène et bâtisseuse_ (2005), Lausana, Éd. Noir sur Blanc, 2010. Cercano a Margaret, Freud no tuvo contacto ni con el Círculo de Viena, fundado por Moritz Schlick, ni con Ludwig Wittgenstein, hermano de aquella y amigo de Karl Kraus, que criticó su teoría del sueño. Cf. Ludwig Wittgenstein, «Entretiens sur Freud» (1943-1946), en R. Jaccard, presentación, _Freud: jugements et témoignages_ , _op. cit._ , pp. 251-266 [hay trad. cast.: «Conversaciones sobre Freud», en _Lecciones y conversaciones sobre estética, psicología y creencia religiosa_ , Barcelona, Paidós/Universidad Autónoma de Barcelona, 1992, pp. 115-128].
. Cf. É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Lou Andreas-Salomé, _Ma vie_ (1901), París, Presses Universitaires de France, 2009 [hay trad. cast.: _Mirada retrospectiva: compendio de algunos recuerdos de la vida_ , Madrid, Alianza, 2005].
. J. Le Rider, _Modernité viennoise..._ , _op. cit._ , y Lou Andreas-Salomé, _L'Amour du narcissisme: textes psychanalytiques_ (1977), París, Gallimard, 1980 [hay trad. cast.: _El narcisismo como doble dirección: obras psicoanalíticas_ , Barcelona, Tusquets, 1982].
. Heinz Frederick Peters, _Ma sœur, mon épouse: biographie de Lou Andreas-Salomé_ (1962), París, Gallimard, 1967, col. «Tel», p. 257 [hay trad. cast.: _Lou Andreas-Salomé, mi hermana, mi esposa: biografía_ , Barcelona, Paidós, 1995]. La vida y la obra de Lou Andreas-Salomé fueron objeto de muchos trabajos. Entre los mejores, Angela Livingstone, _Lou Andreas-Salomé, sa vie de confidente de Freud, de Nietzsche et de Rilke et ses écrits sur la psychanalyse, la religion et la sexualité_ (1984), París, Presses Universitaires de France, 1990, e Isabelle Mons, _Lou Andreas-Salomé: en toute liberté_ , París, Perrin, 2012.
. Carta de Freud a Andreas-Salomé, 10 de noviembre de 1912, en L. Andreas-Salomé, _Correspondance avec Freud..._ , _op. cit._ , p. 17.
. Lou Andreas-Salomé, citada en H. F. Peters, _Ma sœur, mon épouse..._ , _op. cit._ , p. 283.
. Personaje central de _Guerra y paz_ , novela de Tolstói.
. Carta de Freud a Andreas-Salomé, 17 de febrero de 1918, en L. Andreas-Salomé, _Correspondance avec Sigmund Freud..._ , _op. cit._ , p. 98.
. Lou Andreas-Salomé, _Lettre ouverte à Freud_ (1931), París, Seuil, 1994, col. «Points».
. Marie Bonaparte, «Chronologie biographique en huit cahiers», octubre de 1951, inédito, y Célia Bertin, _Marie Bonaparte_ , París, Plon, 1999 [hay trad. cast.: _Marie Bonaparte: biografía_ , Barcelona, Tusquets, 2013]. La primera edición de este libro, de 1982, se titulaba _La Dernière Bonaparte_ [«La última Bonaparte»]. Sobre la trayectoria de Marie Bonaparte y su papel en la historia del psicoanálisis en Francia, cf. _HPF-JL_ , _op. cit._ , y É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Marie Bonaparte, «Sommaire de mon analyse et de ma correspondance avec Freud, avec Agenda (Cahiers noirs)», 14 de diciembre de 1925. Los archivos de Marie Bonaparte, conservados en la Biblioteca del Congreso, están cerrados a la consulta hasta 2020. Tengo una copia gracias a Célia Bertin. Además del «Sommaire», en esos archivos hay ciento veintiséis cartas (1926-1938) —de las cuales Ernest Jones y Max Schur publicaron quince— y una larga conversación sobre temas varios. Cf. asimismo Marie Bonaparte, _Cinq cahiers écrits par une petite fille entre sept ans et demi et dix ans et leurs commentaires_ , 4 vols., París y Londres, impresos por el autor/Imago Publishing, 1939-1951, y «Extraits du Cahier 1», _L'Infini_ , 2, primavera de 1984, pp. 76-89. Véase, en _ibid._ , Elisabeth Roudinesco, «Entretien avec Philippe Sollers sur l'histoire de la psychanalyse en France», pp. 62-75. En la Biblioteca Nacional de Francia se conserva y puede consultarse una correspondencia de Marie Bonaparte con Anne Berman, que tiene por tema esencial la situación del psicoanálisis francés.
. René Laforgue (1894-1962), psiquiatra y psicoanalista, fundador del movimiento psicoanalítico francés y de la Sociedad Psicoanalítica de París (SPP, 1926) junto con Édouard Pichon, Eugénie Sokolnicka, Marie Bonaparte, Rudolph Loewenstein y Raymond de Saussure. Cf. _HPF-JL_ , sobre todo el capítulo «Histoire des douze».
. A. E. Narjani, «Considérations sur les causes anatomiques de la frigidité chez la femme», _Bruxelles médical_ , 27(4), 1924.
. En especial con el profesor Halban. Esta amputación, que no es otra cosa que una ablación, se denomina «operación Halban-Narjani».
. Marie Bonaparte, _Sexualité de la femme_ (1951), París, Presses Universitaires de France, 1957 [hay trad. cast.: _La sexualidad de la mujer_ , Barcelona, Península, 1972].
CUARTA PARTE
#### 1. ENTRE MEDICINA, FETICHISMO Y RELIGIÓN
. Cf. H. F. Ellenberger, _Histoire de la découverte..._ , _op. cit._ , en especial las muy bellas páginas dedicadas a la historia de la psiquiatría dinámica, de Mesmer a Freud.
. Cf. Georges Bataille, _La Part maudite_ , en _Œuvres complètes_ , vol. 7, París, Gallimard, 1976 [hay trad. cast.: _La parte maldita, precedida de La noción de gasto_ , Barcelona, Icaria, 1987]. He abordado esta cuestión en Elisabeth Roudinesco, _Le Patient, le thérapeute et l'État_ , París, Fayard, 2004 [hay trad. cast.: _El paciente, el terapeuta y el Estado_ , Buenos Aires, Siglo XXI, 2005].
. Recordemos que, en la tragedia de Sófocles, Edipo, tras su crimen, pasa del estatus de sabio y tirano al de mancha y chivo expiatorio.
. En francés, _Laienanalyse_ debe traducirse como _analyse profane_ [«análisis profano»]. En alemán _laien_ significa a la vez lego, aficionado y profano, en oposición a lo que es sagrado. La palabra francesa _laïc_ [lego, laico] remite al ideal republicano de la laicidad, que no conviene cuando se trata de las batallas libradas en esa época a favor del psicoanálisis practicado por quienes no eran médicos.
. Recordemos que Wilhelm Stekel se suicidaría en Londres en 1940.
. Peter Gay da una buena versión de este asunto. Cf. asimismo Harald Leupold-Löwenthal, «Le procès de Theodor Reik», y Susann HeenenWolff, «La discussion sur l'"analyse profane" dans l' _Internationale Zeitschrift für Psychoanalyse_ de l'année 1927», _Revue internationale d'histoire de la psychanalyse_ , 3, 1990, pp. 57-69 y 71-88, respectivamente. Véase también _International Journal of Psycho-Analysis_ , 8, 1927. Para el debate francés, cf. _HPF-JL_ , _op. cit._
. Cf. Richard Sterba, _Réminiscences d'un psychanalyste viennois_ (1982), Toulouse, Privat, 1986, pp. 66-67, y Theodor Reik, _Le Psychologue surpris: deviner et comprendre les processus inconscients_ (1935), París, Denoël, 2001. Retomo aquí algunos elementos de mi prefacio a la reedición de ese libro.
. Cf. Pascal Hachet, _Les Psychanalystes et Goethe_ , París, L'Harmattan, 1995. Fue Kurt Eissler quien hizo el estudio más magistral sobre Goethe, al dedicar dos mil páginas a la dilucidación de un período de diez años de la vida del poeta, reconocido como la inauguración de una nueva etapa de creatividad; cf. Kurt Eissler, _Goethe: A Psychoanalytic Study, 1775-1786_ , 2 vols., Detroit, Wayne State University Press, 1963.
. Emigraría en 1938 a Palestina, donde se reunió con Max Eitingon.
. Carta de Freud a Tandler, 8 de marzo de 1925, en S. Freud, _Correspondance, 1873-1939_ , _op. cit._ , pp. 389-390 [hay trad. cast.: «A Julius Tandler», en _Epistolario, 1873-1939_ , _op. cit._ , pp. 401-402; traducción levemente modificada].
. S. Freud, _La Question de l'analyse profane_ , _op. cit._ , con un excelente prefacio de Jean-Bertrand Pontalis y un apéndice de Michel Schneider sobre las controversias.
. Ludger M. Hermanns, «Document inédit: lettre de Siegfried Bernfeld à Anna Freud sur la pratique de la psychanalyse à San Francisco, le 23 novembre 1937», _Revue internationale d'histoire de la psychanalyse_ , 3, 1990, pp. 331-341, cita en p. 335.
3. Sobre las grandes controversias francesas, cf. _HPF-JL_ , _op. cit._
. Debe señalarse que el tercer monoteísmo, el islam, está casi ausente de la obra de Freud, que solo hace contadas referencias a él. Cf. Fethi Benslama, _La Psychanalyse à l'épreuve de l'islam_ , París, Aubier, 2002.
. Heinrich Institoris y Jakob Sprenger, _Le Marteau des sorcières: Malleus Maleficarum_ (1486), París, Jérôme Millon, 2005 [hay trad. cast.: _El martillo de las brujas para golpear a las brujas y sus herejías con poderosa maza: Malleus Maleficarum_ , Valladolid, Maxtor, 2004]. Freud consultó este libro en latín, pero tenía una traducción alemana.
. Sigmund Freud, «Actes obsédants et exercices religieux» (1907), en _Religion_ , París, Gallimard, 2012, pp. 91-118 [hay trad. cast.: «Acciones obsesivas y prácticas religiosas», en _OC_ , vol. 9, _op. cit._ , pp. 97-109], y «Une névrose diabolique au XVIIe siècle» (1923), en _L'Inquiétante étrangeté..._ , _op. cit._ , pp. 265-320 [hay trad. cast.: «Una neurosis demoníaca en el siglo XVII», en _OC_ , vol. 19, _op. cit._ , pp. 67-106].
. El mejor comentario de este enfoque es el de Michel de Certeau, _L'Écriture de l'histoire_ , París, Gallimard, 1975, pp. 291-312 [hay trad. cast.: _La escritura de la historia_ , México, Universidad Iberoamericana, 1993].
. Sigmund Freud, _L'Avenir d'une illusion_ (1927), en _Religion_ , _op. cit._ , pp. 134-235 [hay trad. cast.: _El porvenir de una ilusión_ , en _OC_ , vol. 21, _op. cit._ , pp. 1-55].
. Carta de Freud a Ferenczi, 26 de enero de 1927, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 3, _op. cit._ , p. 330.
. La correspondencia de Freud y Pfister, publicada en francés por Gallimard en 1966, es incompleta y poco fiable, además de carecer de índice. Está en preparación una nueva edición.
. Danielle Milhaud-Cappe, _Freud et le mouvement de pédagogie psychanalytique, 1908-1937: A. Aichhorn, H. Zulliger, O. Pfister_ , París, Vrin, 2007.
. Cf. É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. Oskar Pfister, «L'illusion d'un avenir» (1928), _Revue française de psychanalyse_ , 41(3), 1977, pp. 503-546.
. Carta de Freud a R. Rolland, 20 de julio de 1929, acerca del sentimiento oceánico; cf. _HPF-JL_ [hay trad. cast.: «A Romain Rolland», en _Epistolario, 1873-1939_ , _op. cit._ , p. 434]. Freud, sin embargo, amaba a Mozart.
. Cf. Michel de Certeau, _La Fable mystique,_ XVI _e-_ XVII _e siècle_ , vol. 2, París, Gallimard, 2013, p. 36.
. _Slip_ abierto o cerrado en las nalgas, acompañado de una concavidad destinada a proteger o sostener los órganos genitales del hombre durante las competencias deportivas. Podía utilizárselo como traje de baño y simbolizaba la arrogancia masculina. En el argot norteamericano de los campus se daba a esa prenda el nombre de _jockstrap_.
. He reconstruido la historia de Carl Liebman sobre la base de los relatos que él mismo entregó a sus psiquiatras, después de 1935, durante su ingreso en la clínica psiquiátrica McLean de Harvard, y que están incorporados a su historia clínica. A ellos se agregan algunos intercambios epistolares de Julius y Marie Liebman con Freud y las indicaciones de Leopold Stieglitz, el médico de la familia. He consultado las cartas de Freud a Pfister y Ferenczi; este último da su propia versión del caso. Cf. David J. Lynn, «L'analyse par Freud d'un homme psychotique, A. B., entre 1925 et 1930» (1993), traducción de L. E. Prado de Oliveira, _Filigrane: écoutes psychothérapeutiques_ , 16(1), 2007, pp. 109-122, y Alex Beam, _Gracefully Insane: The Rise and Fall of America's Premier Mental Hospital_ , Nueva York, Public Affairs, 2001, capítulo 6, pp. 93-117. Cf. asimismo la conversación de Julius Liebman con Kurt Eissler, 6 de febrero de 1954, LoC, caja 114, carpeta 16. Con frecuencia se designa a Carl (o Karl) Liebman con las iniciales «A. B., el joven psicótico». Señalemos que Mikkel Borch-Jacobsen da una versión que minimiza demasiado la lucidez de Freud sobre la tragedia de esta psicoterapia. Cf. M. Borch-Jacobsen, _Les Patients de Freud..._ , _op. cit._
. Sigmund Freud, «L'organisation génitale de la vie sexuelle infantile» (1923), en _La Vie sexuelle_ , _op. cit._ , pp. 113-116 [hay trad. cast.: «La organización genital infantil (Una interpolación en la teoría de la sexualidad)», en _OC_ , vol. 19, _op. cit._ , pp. 141-149]. El término se había utilizado por primera vez en 1914 en «Introducción del narcisismo».
. Sigmund Freud, «La négation» (1925), en _OC.P_ , vol. 17, _op. cit._ , pp. 165-171 [hay trad. cast.: «La negación», en _OC_ , vol. 19, _op. cit._ , pp. 249-257]. He optado por la traducción de Jean Hyppolite de 1956, retomada por Olivier Mannoni: «denegación». Sobre este muy prolongado debate que desembocará en la creación del concepto de forclusión por Lacan, cf. _HPF-JL_ , _op. cit._
. La primera descripción del fetichismo fue obra del magistrado francés Charles de Brosses (1709-1777), y la conceptualización del término se debe a Alfred Binet (1857-1911).
. En especial Erzsébet Bathory (1560-1614), célebre condesa húngara convencida de que, si se bañaba en la sangre de otras mujeres, conservaría la juventud. Cf. É. Roudinesco, _La Part obscure..._ , _op. cit._ Algunas mujeres toman por fetiche el cuerpo o parte del cuerpo de su hijo.
. Freud no distingue ambos términos y utiliza de manera indistinta «pene» o «falo».
. Carta de Freud a Pfister, 11 de abril de 1927, en S. Freud, _Sigmund Freud: correspondance avec le pasteur Pfister..._ , _op. cit._ , p. 160.
. Sigmund Freud, «Le fétichisme» (1927), en _La Vie sexuelle_ , _op. cit._ , pp. 134 y 137; en _OC.P_ , vol. 18, 2002, pp. 123-133, y en _Trois mécanismes de défense_ , traducción de Olivier Mannoni, París, Payot, 2012, col. «Petite Bibliothèque Payot», pp. 69-81 [hay trad. cast.: «Fetichismo», en _OC_ , vol. 21, _op. cit._ , pp. 141-152, cita en pp. 147-148].
. Carta de Freud a Jung, 15 de octubre de 1909, en S. Freud y C. G. Jung, _Correspondance_ , vol. 1, _op. cit._ , p. 346.
. En francés, _Schamgürtel_ se tradujo como _gaine pubienne_ [«faja pubiana»] o _cache-sexe_ [«taparrabos»]. Solo Olivier Mannoni señaló que esa palabra remitía al _subligaculum_ utilizado por los romanos, mientras que en nuestros días designa una prenda sadomasoquista compuesta de correas y abierta en las partes sexuales. En la _Standard Edition_ , la palabra escogida por James Strachey y Joan Riviere para traducir _Schamgürtel_ es perfectamente equivalente al suspensorio: _support-belt_ y _suspensory-belt_ , términos que no tienen nada que ver con un cinturón de vergüenza o una faja pubiana.
. Carta de Emy I. Moebius a Kurt Eissler, 11 de septiembre de 1952, LoC, caja 21, carpeta 8.
. S. Freud, _Chronique la plus brève..._ , _op. cit._ ,
. Detlef Berthelsen, _La Famille Freud au jour le jour: souvenirs de Paula Fichtl_ (1987), París, Presses Universitaires de France, 1991 [hay trad. cast.: _La vida cotidiana de Sigmund Freud y su familia: recuerdos de Paula Fichtl_ , Barcelona, Ediciones 62, 1995]. Antes de la Primera Guerra Mundial, cuando sus hijos menores vivían con él, Freud tenía cuatro personas a su servicio.
. Su primer encuentro data de 1908. Cf. Stefan Zweig, _Appels aux Européens_ (1932-1934), traducción y prefacio de Jacques Le Rider, París, Bartillat, 2014, col. «Omnia Poche».
. Carta de Freud a S. Zweig, 17 de febrero de 1931, en S. Freud y S. Zweig, _Correspondance_ , _op. cit._ , p. 74, y Stefan Zweig, _Sigmund Freud: la guérison par l'esprit_ (1931), París, Librairie Générale Française, 2010, col. «Livre de poche» [hay trad. cast.: _La curación por el espíritu (Mesmer, Mary Baker-Eddy, Freud)_ , Barcelona, Acantilado, 2006].
. S. Zweig, _Sigmund Freud: la guérison..._ , _op. cit._ , p. 52.
. Las obras de Stefan Zweig están reunidas en _Romans, nouvelles et récits_ , 2 vols., edición de Jean-Pierre Lefebvre, París, Gallimard, 2013, col. «Bibliothèque de la Pléiade» [hay trad. cast.: _Veinticuatro horas en la vida de una mujer_ , Barcelona, Acantilado, 2001].
. Carta de Freud a S. Zweig, 4 de septiembre de 1926, en S. Freud y S. Zweig, _Correspondance_ , _op. cit._ , p. 48. Freud haría otros comentarios sobre varias novelas breves de Zweig.
. Thomas Mann, «Freud dans l'histoire de la pensée moderne» (1929), en _Sur le mariage – Lessing – Freud et la pensée moderne – Mon temps_ , edición bilingüe, París, Aubier-Flammarion, 1970, pp. 107-149 [hay trad. cast.: «El puesto de Freud en la historia del espíritu moderno», en _Schopenhauer, Nietzsche, Freud_ , Madrid, Alianza, 2000, pp. 136-168].
. Carta de Freud a Andreas-Salomé, 28 de julio de 1929, en L. Andreas-Salomé, _Correspondance avec Sigmund Freud..._ , _op. cit._ , p. 225.
. Carta de Freud a Andreas-Salomé, 9 de mayo de 1928, en _ibid._ , p. 216.
. Estas notas serían exhumadas en 1985 por Karl Sablik, «Freud et Julius Tandler: une mystérieuse relation», _Revue internationale d'histoire de la psychanalyse_ , 3, 1990, p. 96.
#### 2. FRENTE A HITLER
. Mark Edmundson, _La Mort de Sigmund Freud: l'héritage de ses derniers jours_ (2007), París, Payot & Rivages, 2009, p. 9. Sobre la vida de Hitler, la mejor fuente es Ian Kershaw, _Hitler (1889-1945)_ (1998-2000), 2 vols., París, Flammarion, 2009 [hay trad. cast.: _Hitler, 1889-1936_ , Barcelona, Península, 1999, y _Hitler, 1936-1945_ , Barcelona, Península, 2000]. También Vincent Brome había hecho ese paralelismo histórico en _Les Premiers disciples..._ , _op. cit_. Y asimismo C. Schorske, _Vienne, fin de siècle..._ , _op. cit._ Debe señalarse, por otra parte, que muchos psicoanalistas dedicaron a Hitler una literatura «psicobiográfica» muy débil, cuyas tesis fueron luego invalidadas por Kershaw.
. M. Edmundson, _La Mort de Sigmund Freud..._ , _op. cit._ , pp. 13-14.
. Texto escrito en 1938, después del _Anschluss_ : Thomas Mann, _Bruder Hitler_ (1939), Berlín, Heyne Verlag, 1991 [hay trad. cast.: «Hermano Hitler», en _Hermano Hitler y otros textos sobre la cuestión judía_ , Barcelona, Global Rhythm, 2007]. La primera versión en inglés se remonta a marzo de 1939 y su título era «That man is my brother», _Esquire_ , 11(3), marzo de 1939. Traducción francesa: «Frère Hitler», en _Les Exigences du jour_ , París, Grasset, 1976. Cf. asimismo Jean Finck, _Thomas Mann et la psychanalyse_ , París, Les Belles Lettres, 1982.
. Thomas Mann, «Allemagne ma souffrance», en _Les Exigences du jour_ , _op. cit._ , p. 186.
. T. Mann, «Frère Hitler», _op. cit._ , p. 309.
. Mann retomaría esta temática de la doble Alemania en _Doctor Faustus_. Y otro tanto hace Ian Kershaw cuando afirma, al final de su biografía de Hitler: «La Alemania que había engendrado a Adolf Hitler, que había reconocido su futuro en su visión y lo había servido de tan buena gana; en síntesis, la Alemania que había tomado parte en su _hybris_ , tuvo que compartir también su némesis».
. T. Mann, «Frère Hitler», _op. cit._ , p. 308.
. Residencia de descanso apodada «el Berghof», comprada por Hitler en 1933 gracias a los derechos de autor de _Mi lucha_. Sería destruida en 1945.
. En francés hay varias traducciones de _El malestar en la cultura_. En alemán Freud utiliza la palabra _Kultur_ para designar a la vez la civilización ( _Zivilisation_ ) y el espíritu de la Ilustración, en el sentido francés y alemán ( _Aufklärung_ ). Se niega pues a distinguir la cultura que abarca un conjunto de tradiciones, modos de pensamiento, representaciones y creencias, de la civilización, término más amplio que supone la idea de una razón universal propia de la humanidad, que opone el «salvaje», el «bárbaro» o el «ineducado» al sujeto civilizado. En consecuencia, se puede traducir _Kultur_ , en el sentido freudiano, tanto por «cultura» como por «civilización». En Francia, debates intensos enfrentaron a los partidarios de la palabra «cultura» con los adeptos al término «civilización». He estudiado esa historia en _HPF-JL_ , _op. cit._ , sobre todo con referencia a la valorización que hacía Édouard Pichon de la «civilización francesa» en detrimento de la _Kultur_ alemana. Cf. asimismo Jacques Le Rider, Michel Plon, Gérard Raulet y Henri Rey-Flaud, _Autour du «Malaise dans la culture» de Freud_ , París, Presses Universitaires de France, 1998, y Pierre Pellegrin, presentación, dossier y notas, en Sigmund Freud, _Malaise dans la culture_ , París, Garnier-Flammarion, 2010, pp. 7-88 y 177-214. Las dos mejores traducciones francesas del libro son las de Bernard Lortholary, París, Seuil, 2010, y Marc Crépon y Marc B. de Launay, en S. Freud, _Anthropologie de la guerre_ , _op. cit._ , edición bilingüe. Estos tres traductores optaron por _Le Malaise dans la civilisation_. Cf. asimismo Sigmund Freud, _Malaise dans la culture_ , en _OC.P_ , vol. 18, _op. cit._ , pp. 245-333 [hay trad. cast.: _El malestar en la cultura_ , en _OC_ , vol. 21, _op. cit._ , pp. 57-140].
. Desplazamiento de la pulsión hacia una meta no sexual.
. Jean-Jacques Rousseau, _Discours sur l'origine et les fondements de l'inégalité_ (1755), París, Gallimard, 1965, col. «Idées», p. 87 [hay trad. cast.: _Discurso sobre el origen de la desigualdad entre los hombres_ , Madrid, Aguilar, 1981].
. Sobre este término, véase _infra_.
. S. Freud, _Le Malaise dans la civilisation_ , _op. cit._ (traducción de Bernard Lortholary), p. 173 [ _El malestar en la cultura_ , _op. cit._ , p. 140].
. Richard Nikolaus von Coudenhove-Kalergi (1894-1972): diplomático austríaco que fue el primero en adoptar el _Himno a la alegría_ de Beethoven como himno europeo. Tras el _Anschluss_ se exilió en Francia y luego en Suiza y Estados Unidos. Se haría gaullista después de adoptar la ciudadanía francesa. Su padre, Heinrich Johann Maria von Coudenhove-Kalergi, es autor de un libro sobre el antisemitismo, que Freud conocía bien: _Das Wesen des Antisemitismus_ , Berlín, S. Calvary, 1901.
. Desde su último viaje con su hija Anna, en 1923.
. S. Freud, _Le Malaise dans la civilisation_ , _op. cit._ (traducción de Bernard Lortholary), pp. 50-52 [ _El malestar en la cultura_ , _op. cit._ , pp. 69-71].
. Son las palabras de Freud.
. Carta de Albert Einstein a Freud, en S. Freud, _OC.P_ , vol. 19, _op. cit._ , p. 67 [hay trad. cast.: «Carta de Einstein», en S. Freud, _OC_ , vol. 22, _op. cit._ , p. 185].
. Sigmund Freud, «Pourquoi la guerre?» (1932), en _OC.P_ , vol. 19, _op. cit._ , pp. 69-81 [hay trad. cast.: «¿Por qué la guerra?», en _OC_ , vol. 22, _op. cit._ , pp. 187-198, cita en p. 196].
. Los traductores franceses se inclinaron ora por conservar este término en alemán, ora por traducirlo como «visión del mundo». En la _Standard Edition_ no se traduce. Remito a Sigmund Freud, «Sur une _Weltanschauung_ », en _Nouvelles conférences..._ , _op. cit._ , pp. 211-243, y, con el título «D'une vision du monde», en _Nouvelle suite des leçons..._ , _op. cit._ ( _OC.P_ ), pp. 242-269 [hay trad. cast.: «En torno de una cosmovisión», en _Nuevas conferencias..._ , _op. cit._ , pp. 146-168]. Literalmente, el término está compuesto de _Welt_ , mundo, y _Anschauung_ , contemplación, visión, experiencia, y tiene varios significados: ideología, concepción política del mundo, visión del mundo e incluso discurso filosófico.
. S. Freud, «Sur une _Weltanschauung_ », _op. cit._ , p. 215 [«En torno de una cosmovisión», _op. cit._ , pp. 148-149; traducción ligeramente modificada].
. _Ibid._ , p. 237 [ _ibid._ , p. 164].
. Conviene leer, al respecto, el bello artículo de Bernd Nitzschke, «La psychanalyse considérée comme une science "a"-politique», _Revue internationale d'histoire de la psychanalyse_ , 5, 1992, pp. 170-182.
. Todavía no se ha escrito la historia del psicoanálisis en Rusia. En este aspecto, la obra de Alexandre Etkind, _Histoire de la psychanalyse en Russie_ , París, Presses Universitaires de France, 1993, es insuficiente. Cf. Jean Marti, «La psychanalyse en Russie (1909-1930)», _Critique_ , 346, «La psychanalyse vue du dehors», marzo de 1976, pp. 199-237, y Alberto Angelini, _La psicoanalisi in Russia: dai precursori agli anni trenta_ , Nápoles, Liguori, 1988. Yo misma investigué parte de esa historia en _HPF-JL_ , _op. cit._ , para el período 1930-1950. El movimiento psicoanalítico ruso fue progresivamente erradicado a partir de 1930. La calificación de «ciencia burguesa» solo aparecería en 1949, en el marco de la cruzada estalinista contra las ciencias y las artes, orquestada por Trofim Lysenko y Andréi Zhdánov.
. Kommunistische Partei Deutschlands, Partido Comunista Alemán.
. Keren Hayesod: organismo fundado en 1920 con vistas a la radicación de inmigrantes en Palestina.
. Sobre el tema, véase G. Liebermann, _La Psychanalyse en Palestine..._ , _op. cit._ David Montague Eder (1866-1936): psiquiatra y psicoanalista, fundador con Ernest Jones del movimiento psicoanalítico inglés y primo de Israel Zangwill (1864-1926), militante sionista y socialista.
. Carta de Freud a Koffler, 26 de febrero de 1930, traducción francesa de Jacques Le Rider. El manuscrito original y la copia dactilografiada por un desconocido se conservan en la colección Abraham Schwadron de la Universidad Hebrea de Jerusalén. Ya he publicado esta carta y comentado su contenido en Elisabeth Roudinesco, «À propos d'une lettre inédite de Freud sur le sionisme et la question des lieux saints», _Cliniques méditerranéennes_ , 70, 2004, pp. 5-17. Cf. asimismo É. Roudinesco, _Retour sur la question juive_ , _op. cit._
. Carta de Freud a Einstein, 26 de febrero de 1930, citada en P. Gay, _Freud, une vie_ , _op. cit._ , p. 688.
. Sobre la imposible resolución de la cuestión de los Santos Lugares, cf. Charles Enderlin, _Le Rêve brisé: histoire de l'échec du processus de paix au Proche-Orient, 1995-2002_ , París, Fayard, 2002, y _Au nom du Temple: Israël et l'irrésistible ascension du messianisme juif (1967-2013)_ , París, Seuil, 2013.
. Entre las mejores fuentes para el estudio de la colaboración de los psicoanalistas con el nazismo, cf. Jean-Luc Évard, presentación y traducción, _Les Années brunes: la psychanalyse sous le IIIe Reich_ , París, Confrontation, 1984; Hans-Martin Lohmann, ed., _Psychoanalyse und Nationalsozialismus: Beiträge zur Bearbeitung eines unbewältigten Traumas_ , Frankfurt, Fischer, 1984; Geoffrey Cocks, _La Psychothérapie sous le IIIe Reich: l'Institut Göring_ (1985), París, Les Belles Lettres, 1987; Regine Lockot, _Erinnern und Durcharbeiten: zur Geschichte der Psychoanalyse und Psychotherapie im Nationalsozialismus_ , Frankfurt, Fischer, 1985, y Jennyfer Curio, «Ce qui est arrivé à la psychanalyse en Allemagne», memoria para el DEA [diploma de estudios avanzados] de psicopatología y psicoanálisis, bajo la dirección de Émile Jalley, Université de Paris-Nord, 1997. Ernest Jones y Peter Gay omiten mencionar este episodio.
. Carta de Freud a Ferenczi, 2 de abril de 1933, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 3, _op. cit._ , pp. 512-513.
. Los historiadores dan el nombre de austrofascismo a este episodio de la historia de Austria, que se extendió de marzo de 1933 a julio de 1934, fecha en que los nazis austríacos asesinaron a Dollfuss.
. Carta de Freud a H. Doolittle, 5 de marzo de 1934, en H. Doolittle, _Pour l'amour de Freud_ , _op. cit._ , p. 256.
. Que utilizaba el término _Hitlerei_ (hitlería) para designar la política hitleriana. El sufijo _ei_ marca habitualmente el lugar de ejercicio de una profesión.
. Carta de Maurizio Serra a Elisabeth Roudinesco, 5 de marzo de 2014. Cf. Roberto Zapperi, _Freud e Mussolini: la psicoanalisi in Italia durante il regime fascista_ , Milán, Franco Angeli, 2013.
. Sobre la que haría en 1934 una película conforme a los cánones de la estética fascista. Cf. Giovacchino Forzano, « _Les Cent Jours_ (Campo di Maggio), trois actes et treize tableaux, tirés d'un scénario de M. Benito Mussolini, par Giovacchino Forzano, adaptation française d'André Mauprey», _Les Cahiers de Bravo_ (París), 23, suplemento al número de enero de 1932.
. El ejemplar alemán del libro de Forzano figura, en efecto, en el catálogo de la biblioteca de Freud (2583) con la dedicatoria en italiano.
. Dedicatoria manuscrita en alemán fechada el 26 de abril de 1933. Cf. Anna Maria Accerboni, «Psychanalyse et fascisme: deux approches incompatibles. Le rôle difficile d'Edoardo Weiss», _Revue internationale d'histoire de la psychanalyse_ , 1, 1988, pp. 225-245; Paul Roazen, «Questions d'éthique psychanalytique: Edoardo Weiss, Freud et Mussolini», _Revue internationale d'histoire de la psychanalyse_ , 5, 1992, pp. 151-167, y Glauco Carloni, «Freud and Mussolini: a minor drama in two acts, one interlude and five characters», en Arnaldo Novelletto, ed., _L'Italia nella psicoanalisi_ , catálogo de exposición, Roma, Istituto della Enciclopedia Italiana, 1989, pp. 51-60. Los comentarios de Weiss enviados a Kurt Eissler se conservan en la Biblioteca del Congreso, caja 121.
. Hay que ser muy ignorante de la historia para pensar que Freud habría sido «fascista», como no deja de afirmarlo Michel Onfray en su controvertido _Le Crépuscule d'une idole..._ , _op. cit._ , pp. 524-533 y 590-591. Este autor no consultó ni los archivos de la Biblioteca del Congreso ni la correspondencia de Freud y Weiss sobre el tema. No tiene en cuenta las fuentes adecuadas, tergiversa las citas de la obra de Cocks y critica a Paul-Laurent Assoun, autor de un _Dictionnaire thématique, historique et critique des œuvres psychanalytiques_ , París, Presses Universitaires de France, 2009, para afirmar que la comunidad psicoanalítica ha mantenido silencio sobre la historia de esta dedicatoria, olvidando que la mayoría de los historiadores del freudismo y los biógrafos de Freud la comentaron en diversas oportunidades.
. Como le diría a Paul Roazen, Edoardo Weiss siempre negó la existencia de ese encuentro. Accerboni afirma, por el contrario, que lo hubo. Es posible que el contacto entre Weiss y Ciano se haya producido de manera indirecta.
. En 1935 Camillo Berneri envió a Freud su obra _Le Juif antisémite_ , París, Vita, 1935, con la siguiente dedicatoria: «En respetuoso homenaje». También había escrito un artículo sobre el libro dedicado a Leonardo da Vinci. Biblioteca Freud, núm. 217, Freud Museum de Londres.
. Giancarlo Gramaglia, «Enquête sur Sigmund Freud et sur la Wiener Psychoanalytische Vereinigung effectuée par la diplomatie fasciste italienne en 1935», _Revue internationale d'histoire de la psychanalyse_ , 5, 1992, pp. 143-150.
. Elena Mancini, _Magnus Hirschfeld and the Quest for Sexual Freedom: A History of the First International Sexual Freedom Movement_ , Nueva York, PalgraveMacmillan, 2010.
. E. Jones, _La Vie et l'œuvre..._ , vol. 3, _op. cit._ , p. 209.
. Karen Brecht, Volker Friedrich, Ludger M. Hermanns, Isidor J. Kaminer _et al._ , _«Ici la vie continue d'une manière fort surprenante»: contribution à l'histoire de la psychanalyse en Allemag_ ne (1985), edición francesa establecida por Alain de Mijolla y Vera Renz, París, Association Internationale d'Histoire de la Psychanalyse (AIHP)/Goethe Institut, 1987, pp. 237-238. El artículo se publicó en la _Deutsche Volksgesundheit aus Blut and Boden_.
. Carta de Freud a Eitingon, 21 de marzo de 1933, en S. Freud y M. Eitingon, _Correspondance..._ , _op. cit._ , p. 785. En su controvertido texto Onfray afirma que Eitingon compartía la opinión de Jones sobre el «salvamento» del psicoanálisis; cf. M. Onfray, _Le Crépuscule d'une idole..._ , _op. cit._ , p. 549.
. Carta de Freud a Jones, 29 de mayo de 1933, en S. Freud y E. Jones, _Correspondance complète..._ , _op. cit._ , p. 824. La «americana», Elizabeth Severn, participaba de la experiencia del análisis mutuo. Ferenczi la menciona en su diario clínico bajo las iniciales R. N.
. S. Ferenczi, _Journal clinique..._ , _op. cit._ Este diario se publicó mucho después de la muerte de Ferenczi, y Freud no lo conoció.
. Carta de Ferenczi a Freud, 9 de abril de 1933, en S. Freud y S. Ferenczi, _Correspondance_ , vol. 3, _op. cit._ , p. 514.
. Sigmund Freud, «Ferenczi», en _OC.P_ , vol. 19, _op. cit._ , pp. 309-315 [hay trad. cast.: «Sándor Ferenczi», en _OC_ , vol. 22, _op. cit._ , pp. 226-228], y _Chronique la plus brève..._ , _op. cit._ , p. 153.
. Wilhelm Reich, _La Psychologie de masse du fascisme_ (1933), París, Payot, 1978 [hay trad. cast.: _Psicología de masas del fascismo_ , Barcelona, Bruguera, 1980], y _Reich parle de Freud: Wilhelm Reich discute de son œuvre et de ses relations avec Sigmund Freud_ (1967), conversación con Kurt Eissler, París, Payot, 1970 [hay trad. cast.: _Reich habla de Freud: Wilhelm Reich comenta su obra y su relación con Sigmund Freud_ , Barcelona, Anagrama, 1970]. Sobre el destino de la izquierda freudiana, cf. Russell Jacoby, _Otto Fenichel: destins de la gauche freudienne_ (1983), París, Presses Universitaires de France, 1986.
. K. Brecht _et al._ , « _Ici la vie continue d'une manière fort surprenante_ »..., _op. cit._ , p. 247. El relato de Boehm es perfectamente compatible con la posición de Freud, como lo testimonia la carta de este a Eitingon fechada el 17 de abril de 1933, en S. Freud y M. Eitingon, _Correspondance..._ , _op. cit._ , p. 789.
. Acusado de estafa por haber comercializado acumuladores de orgones, Reich terminó su vida, en 1957, en la penitenciaría de Lewisburg, Pensilvania. Una parte de sus archivos, y en especial los concernientes a sus relaciones con Freud, se conservan en la Biblioteca del Congreso.
. Cf. H. Doolittle, _Pour l'amour de Freud_ , _op. cit._ Escribí un prefacio para la reedición francesa de este libro.
. J. Wortis, _Psychanalyse à Vienne..._ , _op. cit._ Joseph Wortis (1906-1995) introdujo en Estados Unidos la insulinoterapia en el tratamiento de la esquizofrenia. Brindó su ayuda a los republicanos durante la Guerra Civil española, participó a continuación en la campaña antifreudiana orquestada por los partidos comunistas, denunció el psicoanálisis como una «ciencia burguesa» y escribió en 1950 el primer estudio serio sobre la llamada psiquiatría «soviética».
. Sociedad Médica General de Psicoterapia.
. Ernst Kretschmer, _Archiv für Psychiatrie und Krankheiten_ , 96, 1932, p. 219.
. Carta de Jung a Allers, 23 de noviembre de 1933, en Carl Gustav Jung, _Correspondance_ , vol. 1, _1906-1940_ (1972), París, Albin Michel, 1992, pp. 181-182.
. Carl Gustav Jung, «Geleitwort», _Zentralblatt für Psychotherapie_ , 6(1), 1933, pp. 10-11, reeditado en Carl Gustav Jung, _Gesammelte Werke_ , vol. 10, Olten y Friburgo de Brisgovia, Walter Verlag, 1974, pp. 581-583. Traducido y publicado en francés con el título de «Éditorial», _Cahiers jungiens de psychanalyse_ , 82, primavera de 1995, pp. 9-10.
. Carl Gustav Jung, «Une interview à Radio-Berlin», 26 de junio de 1933, en _C. G. Jung parle: rencontres et interviews_ , edición de William McGuire y Richard F. C. Hull, París, Buchet-Castel, 1985, pp. 55-61 [hay trad. cast.: «Una entrevista en Radio Berlín», en _Encuentros con Jung_ , Madrid, Trotta, 2000, pp. 77-83]. La versión original de este texto se conoció en 1987 y fue objeto de un análisis de Matthias von der Tann, «A Jungian perspective on the Berlin Institute for Psychotherapy: a basis for mourning», _The San Francisco Jung Institute Library Journal_ , 8(4), 1989, pp. 43-73.
. Explica esta política en dos cartas del 22 de enero de 1934, una a Poul Bjerre, otra a Alfons Maeder, en C. G. Jung, _Correspondance_ , vol. 1, _op. cit._ , pp. 184-188.
. Carl Gustav Jung, «Zur gegenwärtigen Lage der Psychotherapie», _Zentralblatt für Psychotherapie_ , 7, 1934, pp. 1-16, reproducido sin modificaciones en C. G. Jung, _Gesammelte Werke_ , vol. 10, _op. cit._ , pp. 181-201 [hay trad. cast.: «Acerca de la situación actual de la psicoterapia», en _Civilización en transición_ , vol. 10 de la _Obra completa_ , Madrid, Trotta, 2001]. Versión inglesa: «The state of psychotherapy today», en _Collected Works_ , vol. 10, Princeton, Princeton University Press, 1970, pp. 157-176. Versión francesa: «La situation actuelle de la psychothérapie», _Cahiers jungiens de psychanalyse_ , 96, otoño de 1999, pp. 43-63. Cf. asimismo la versión del texto traducida en Y. H. Yerushalmi, _Le «Moïse» de Freud..._ , _op. cit._ , pp. 103-104, y É. Roudinesco, _Retour sur la question juive_ , _op. cit._ , p. 153, donde cito el texto según la traducción de Jacques Le Rider. No comparto ni la opinión de Deirdre Bair, que exime a Jung de todo antisemitismo y considera que su colaboración con Göring se debía a la influencia de Cimbal (cf. D. Bair, _Jung..._ , _op. cit._ , p. 665), ni la de Richard Noll, _Jung, le «Christ aryen»: les secrets d'une vie_ (1997), París, Plon, 1999 [hay trad. cast.: _Jung, el Cristo ario_ , Barcelona, Ediciones B, 2002], que reduce el conjunto de su obra a una doctrina nazi. Sobre el antisemitismo de Jung, cf. asimismo Andrew Samuels, «Psychologie nationale, national-socialisme et psychologie analytique: réflexions sur Jung et l'antisémitisme», _Revue internationale d'histoire de la psychanalyse_ , 5, 1992, pp. 183-219. Organicé sobre el tema el XVI coloquio de la Société Internationale d'Histoire de la Psychiatrie et de la Psychanalyse (SIHPP), «Carl Gustav Jung, l'œuvre, la clinique, la politique», celebrado el 24 de noviembre de 2001 con la participación de Deirdre Bair, Mireille Cifali, Christian Jambet, Michel Plon y Andrew Samuels.
. Carta de Jung a Kirsch, 26 de mayo de 1934, en C. G. Jung, _Correspondance_ , vol. 1, _op. cit._ , p. 216.
. Carta de Jung a Adler, 9 de junio de 1934, en _ibid._ , p. 219.
. Carta de Jung a Neumann, 22 de diciembre de 1935, en _ibid._ , pp. 268-269.
. Victor Klemperer, _LTI, la langue du IIIe Reich: cahiers d'un philologue_ (1975), París, Albin Michel, 1996 [hay trad. cast.: _LTI: la lengua del Tercer Reich. Apuntes de un filólogo_ , Barcelona, Minúscula, 2002].
. « _Mann sollte sich nicht allzulaut über die Psychoanalyse des Juden "Freud" empören, wenn man und solange man überhaupt nicht anders über Alles und Jedes "denken" kann als so, daß Alles als "Ausdruck" "des Lebens" einmal und auf "Instinkte" und "Instinktschwund zurückführt". Diese "Denk"-weise, die überhaupt im voraus kein "Sein" zuläßt, ist der reine Nihilismus._ » Extracto del «Überlegungen XIV» (1940-1941), texto establecido por Peter Trawny, en Martin Heidegger, _Gesamtausgabe_ , vol. 96, Frankfurt, Klostermann, 2014, p. 218. Cf. asimismo Peter Trawny, _Heidegger et l'antisémitisme: sur les «Cahiers noirs»_ (2014), París, Seuil, 2014.
. Sobre las relaciones que Heidegger mantendría con el psiquiatra suizo alemán Medard Boss (1903-1990), formado en el Burghölzli, cf. Martin Heidegger, _Séminaires de Zurich_ (1987), París, Gallimard, 2010. Sobre las relaciones de Lacan y Heidegger, cf. _HPF-JL_ , _op. cit._ , pp. 1773-1791.
. Carta de Einstein a Freud, 21 de abril de 1936, en S. Freud, _Chronique la plus brève..._ , _op. cit._ , p. 200.
. Lilly Freud-Marlé, _Mein Onkel Sigmund Freud: Erinnerungen an eine grosse Familie_ , cartas reunidas por Christfried Tögel, Berlín, Aufbau, 2006.
. Famoso lugar de veraneo, situado al nordeste de Viena, con restaurantes y residencias de descanso. Desde 1934 Freud alquilaba en Grinzing una hermosa casa con jardín, donde se instalaba con su familia en primavera o verano.
. Thomas Mann, «Freud et l'avenir», en R. Jaccard, presentación, _Freud: jugements et témoignages_ , _op. cit._ , pp. 15-43 [hay trad. cast.: «Freud y el futuro», en Thomas Mann, _Freud, Goethe, Wagner, Tolstoi_ , Buenos Aires, Poseidón, 1944].
. S. Freud, «Un trouble de mémoire...», _op. cit._
. Los tres volúmenes figuran en su biblioteca (núm. 2345): _Las historias de Jacob_ (1933), _El joven José_ y _José en Egipto_. El último volumen, _José el proveedor_ , se publicaría en 1943. La versión francesa es _Joseph et ses frères_ , 4 vols., París, Gallimard, 1980, col. «L'Imaginaire» [hay trad. cast.: _José y sus hermanos_ , 4 vols., Madrid, Guadarrama, 1977]. Carta de Freud a Mann, 29 de noviembre de 1936, en S. Freud, _Correspondance, 1873-1939_ , _op. cit._ , pp. 471-473 [hay trad. cast.: «A Thomas Mann», en _Epistolario, 1873-1939_ , _op. cit._ , pp. 480-482].
. Napoleón Francisco Carlos José Bonaparte (1811-1832), llamado «el Aguilucho», rey de Roma y duque de Reichstadt, hijo de Napoleón y María Luisa de Austria.
. Carta de Freud a Arnold Zweig, 15 de julio de 1934, en S. Freud y A. Zweig, _Correspondance..._ , _op. cit._ , pp. 123-124. Zweig acababa de escribir una pieza teatral sobre la toma de Jaffa —acaecida el 7 de marzo de 1799— y la visita de Napoleón a los apestados.
. Freud conocía la vida de Bonaparte por Bergler y por la obra de Albert Vandal, _L'Avènement de Bonaparte_ , París, Plon-Nourrit et Cie., 1910, que tenía en su biblioteca (núm. 3497). E. Jones, _La Vie et l'œuvre..._ , vol. 3, _op. cit._ , pp. 218-219. También había leído los volúmenes de Adolphe Thiers sobre el Consulado y el Imperio.
. Jacques Lacan, «Au-delà du principe de réalité» (1936), en _Écrits_ , _op. cit._ , pp. 73-92 [hay trad. cast.: «Más allá del principio de realidad», en _Escritos_ , vol. 1, _op. cit._ , pp. 81-98].
. R. Sterba, _Réminiscences d'un psychanalyste..._ , _op. cit._ , p. 142.
. Abraham H. Maslow, «Was Adler a disciple of Freud? A note», _Journal of Individual Psychology_ , 18, 1962, p. 125.
. Carta de Freud a Arnold Zweig, 22 de junio de 1937, citada por primera vez por Ernest Jones, no incluida en la correspondencia entre Freud y Zweig; también la cita P. E. Stepansky, _Adler dans l'ombre..._ , _op. cit._ , p. 262.
. Carta de Freud a Andreas-Salomé, 6 de enero de 1935, en L. Andreas-Salomé, _Correspondance avec Sigmund Freud..._ , _op. cit._ , p. 252.
. Lou Andreas-Salomé, «Mein Bekenntnis zum heutigen Deutschland» (1934), inédito, archivos de Lou Andreas-Salomé en Gotinga. En 2008 Dorian Astor pretendió que ese texto, al que los investigadores no tienen acceso, era de inspiración nazi y contenía pasajes antisemitas. Cf. Dorian Astor, _Lou Andreas-Salomé_ , París, Gallimard, 2008, pp. 348-353. Isabelle Mons invalidó esta tesis con sólidos argumentos. Cf. I. Mons, _Lou Andreas-Salomé..._ , _op. cit._ , pp. 300-308. No he consultado ese archivo, pero Isabelle Mons me dio a conocer las notas que tomó tras examinarlo.
. Sigmund Freud, «Lou Andreas Salomé», en _OC.P_ , vol. 20, 2010, p. 11 [hay trad. cast.: «Lou Andreas-Salomé», en _OC_ , vol. 23, 1980, pp. 299-300].
. El primer artículo se publicó en francés con diversos títulos: «Analyse terminée et analyse interminable», «L'analyse avec fin et l'analyse sans fin». Cf. Sigmund Freud, «L'analyse avec fin et l'analyse sans fin» y «Constructions dans l'analyse», en _Résultats, idées, problèmes_ , vol. 2, _1921-1938_ , París, Presses Universitaires de France, 1985, pp. 231-268 y 269-281, respectivamente, y en _OC.P_ , vol. 20, _op. cit._ (el primero traducido como «L'analyse finie et l'analyse infinie»), pp. 13-55 y 57-75, respectivamente [hay trad. cast.: «Análisis terminable e interminable» y «Construcciones en el análisis», en _OC_ , vol. 23, _op. cit._ , pp. 211-254 y 255-270, respectivamente]. Cf. asimismo S. Freud, _Nouvelles conférences..._ , _op. cit._
. De ese modo, incluía el análisis en la categoría de las profesiones imposibles, como las de gobernar o educar.
. S. Freud, «L'analyse avec fin...», _op. cit._ , p. 265 [«Análisis terminable...», _op. cit._ , p. 251].
. E. J. Lieberman, _La Volonté en acte..._ , _op. cit._ , p. 441, y J. Wortis, _Psychanalyse à Vienne..._ , _op. cit._ , p. 135. Jones haría suya la tesis de la «locura» de Rank, como la de Ferenczi.
. Carta de Freud a Jones, 2 de marzo de 1937, en S. Freud y E. Jones, _Correspondance complète..._ , _op. cit._ , p. 863.
. Carta de S. Zweig a Freud, 15 de noviembre de 1937, en S. Freud y S. Zweig, _Correspondance_ , _op. cit._ , p. 113.
#### 3. LA MUERTE EN ACCIÓN
. Cf. Mary V. Dearborn, _Queen of Bohemia: The Life of Louise Bryant_ , Boston, Houghton Mifflin, 1996. La enfermedad de Dercum es una adiposis dolorosa acompañada de trastornos mentales. Louise Bryant murió en Francia en 1936.
. Edward Mandell House (1858-1938): diplomático y político, asesor de Wilson en la redacción de los «catorce puntos». En 1919 se lo hizo a un lado.
. Sigmund Freud y William Bullitt, _Le Président Thomas Woodrow Wilson: portrait psychologique_ (1967), París, Payot, 1990 [hay trad. cast.: _El Presidente Thomas Woodrow Wilson: un estudio psicológico_ , Buenos Aires, Letra Viva, 1973]. Solo la introducción, traducida del alemán, se reproduce en las _OC.P_ : Sigmund Freud, «Introduction à _Thomas Woodrow Wilson_ de S. Freud y W. C. Bullitt», en _OC.P_ , vol. 18, _op. cit._ , pp. 363-372, con una noticia explicativa sobre las condiciones en que Bullitt publicó el texto. Para la interpretación de este, cf. asimismo É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit_. El dinero remitido por Bullitt sirvió para sacar a flote el Verlag. También puede leerse la argumentación planteada por P. Gay, _Freud, une vie_ , _op. cit._ , pp. 869-870.
. De ahí la severidad de Erik Erikson, quien destacó que el texto parecía haber sido escrito por un estudiante poco dotado que no entendía ni la lengua ni el pensamiento de su maestro.
. Redactado por Wilson sin concertarlo con sus pares europeos, el discurso pretendía reformular las fronteras de los antiguos Imperios Centrales y manejar las relaciones internacionales mediante la creación de una Sociedad de Naciones (SDN).
. Véase al respecto Catherine Clément, _Pour Sigmund Freud_ , París, Mengès, 2005, pp. 127-143.
. La palabra alemana _Geistigkeit_ significa «espiritualidad» o «intelectualidad», e incluso «vida del espíritu». El término «espiritualismo» no es conveniente para la hipótesis freudiana. Hay varias traducciones francesas de la obra. He elegido la de Cornélius Heim, _L'Homme Moïse et la religion monothéiste_ (1939), París, Gallimard, 1986 [hay trad. cast.: _Moisés y la religión monoteísta_ , en _OC_ , vol. 23, _op. cit._ , pp. 1-132]. Cf. asimismo la traducción de Jean-Pierre Lefebvre, París, Seuil, 2012, col. «Points Essais», con una excelente presentación, y _OC.P_ , vol. 20, _op. cit._ , pp. 132-219. Entre los mejores comentaristas, además de Y. H. Yerushalmi, cuyo _Le «Moïse» de Freud..._ , _op. cit._ , fue un verdadero acontecimiento, deben retenerse los nombres de Jacques Le Rider, _Freud, de l'Acropole au Sinaï: le retour à l'Antique des Modernes viennois_ , París, Presses Universitaires de France, 2002; Edward Said, _Freud et le monde extra-européen_ (2003), París, Le Serpent à Plumes, 2004 [hay trad. cast.: _Freud y los no europeos_ , Barcelona, Global Rhythm, 2006], y Henri Rey-Flaud, _«Et Moïse créa les Juifs...»: le testament de Freud_ , París, Aubier, 2006. He comentado la mayor parte de estas obras, así como la de Freud, en _Retour à la question juive_ , _op. cit._ Cf. asimismo Ilse Grubrich-Simitis, «Un rêve éveillé: le _Moïse_ de Freud», _Revue française de psychanalyse_ , 56(4), 1992, pp. 1241-1243. Por otra parte, en 1994 organicé junto con René Major el coloquio de Londres de la SIHPP, durante el cual Jacques Derrida respondió a Yerushalmi con _Mal d'archive: une impression freudienne_ , París, Galilée, 1995 [hay trad. cast.: _Mal de archivo: una impresión freudiana_ , Madrid, Trotta, 1996]. Este acontecimiento fue objeto de un comentario malévolo y trufado de errores durante un coloquio de homenaje a Yerushalmi, organizado en París por Sylvie-Anne Goldberg, en el Museo de Arte e Historia del Judaísmo, el 11 de abril de 2011. Cf. Sylvie-Anne Goldberg, ed., _L'Histoire et la mémoire de l'histoire: hommage à Y. H_. Y _erushalmi_ , París, Albin Michel, 2012. Publiqué una respuesta sobre el tema a Sylvie-Anne Goldberg y Michael Molnar en el _Bulletin de la SIHPP_ , 30 de agosto de 2012.
. El nombre y las obras de Spinoza no figuran en el catálogo de la biblioteca de Freud, quien nunca hizo referencia al célebre pasaje sobre la supervivencia de los judíos, en Baruch Spinoza, _Traité théologique-politique_ , París, Presses Universitaires de France, 1999, capítulo 3 [hay trad. cast.: _Tratado teológico-político_ , Buenos Aires, Lautaro, 1946].
. La mejor obra sobre la génesis del mito de la nacionalidad egipcia de Moisés desde fines del siglo XVII es Jan Assmann, _Moïse l'Égyptien: un essai d'histoire de la mémoire_ , París, Aubier, 2001; reedición, París, Flammarion, 2010, col. «Champs» [hay trad. cast.: _Moisés el egipcio_ , Madrid, Anaya, 2003]. Cf. asimismo Jacques Le Rider, «Moïse égyptien», _Revue germanique internationale_ , 14, 2000, pp. 127-150. En la biblioteca de Freud hay una cantidad impresionante de obras de egiptólogos y de exégetas de la Biblia. En ese ámbito, él exhibía una inmensa erudición.
. O. Rank, _Le Mythe de la naissance..._ , _op. cit._
. En el relato bíblico la hija del faraón encuentra al niño en la canastilla, lo adopta y hace que su madre lo alimente.
. En 1912 Karl Abraham había publicado un artículo sobre el tema: «Amenhotep IV: contribution psychanalytique à l'étude de sa personnalité et du culte monothéiste d'Aton», en _Œuvres complètes_ , vol. 1, _op. cit._ , pp. 232-257 [hay trad. cast.: «Amenhotep IV: una contribución psicoanalítica para la comprensión de su personalidad y del culto monoteísta de Atón», en _Obras completas_ , _op. cit._ , pp. 635-662].
. Ernst Sellin, _Mose und seine Bedeutung für die Israelitisch-jüdische Religionsgeschichte_ , Leipzig y Erlangen, A. Deichertsche Verlagsbuchhandlung, 1922. La tesis de Sellin sobre el asesinato de Moisés ya había sido refutada en esa época por Abraham Shalom Yahuda (1877-1951). Freud la había conocido a través de Arnold Zweig.
. En la versión bíblica Moisés destruye las Tablas de la Ley al ver a los hebreos adorar al becerro de oro. Vuelve a subir al Sinaí para que Yahvé le entregue nuevas tablas y muere a los ciento veinte años sin haber alcanzado la Tierra Prometida. Su sucesor es Josué. Los hebreos deambulan durante cuarenta años por el desierto.
. Eduard Meyer, _Die Israeliten und ihre Nachbarstämme: Alttestamentliche Untersuchungen_ , Halle, Max Niemeyer, 1906.
. Hijo de Abraham, cuyos descendientes son los madianitas. Freud menciona a otros historiadores y exégetas. Sus obras, así como las de Meyer, forman parte del catálogo de su biblioteca. La de Sellin, de 1922, no figura en él.
. En el relato bíblico las dos historias están ligadas. En la edad adulta, Moisés mata a un egipcio y huye al país de Madián, donde descubre su vocación: desde el interior de una zarza, Yahvé lo convoca a volver a Egipto y liberar a los hebreos sometidos a la esclavitud.
. Jacques Lacan identificó perfectamente ese dualismo freudiano en _Le Séminaire, Livre VII, L'Éthique de la psychanalyse (1959-1960)_ , texto establecido por Jacques-Alain Miller, París, Seuil, 1986, p. 203 ss. [hay trad. cast.: _El Seminario de Jacques Lacan. Libro 7. La ética del psicoanálisis. 1959-1960_ , Buenos Aires, Paidós, 1988].
. S. Freud, _L'Homme Moïse..._ , _op. cit._ (traducción de Heim), p. 133 [ _Moisés y la religión monoteísta_ , _op. cit._ , p. 53].
. _Ibid._ , pp. 135-136 [ _ibid._ , p. 55].
. _Ibid._ , p. 180 [ _ibid._ , p. 84].
. _Ibid._ , p. 185 [ _ibid._ , p. 88].
. Cosa que destaca muy bien Peter Gay, _Un Juif sans Dieu: Freud, l'athéisme et la naissance de la psychanalyse_ (1987), París, Presses Universitaires de France, 1989 [hay trad. cast.: _Un judío sin Dios: Freud, el ateísmo y la construcción del psicoanálisis_ , Buenos Aires, Ada Korn, 1994]. He desarrollado esta tesis en _Retour sur la question juive_ , _op. cit._
. Lo que lleva a Yerushalmi a decir que Freud hizo del psicoanálisis una prolongación del judaísmo sin Dios: un judaísmo interminable. Yo hablaría más bien de una judeidad interminable. He desarrollado esta tesis en _Retour sur la question juive_ , _op. cit._
. En 1655, a petición del rabino Menasseh ben Israel, Cromwell había puesto fin a la proscripción de los judíos y autorizado la libertad de cultos.
. M. Edmundson, _La Mort de Sigmund Freud..._ , _op. cit._ , p. 116.
. David Bakan, _Freud et la tradition de la mystique juive_ (1958), París, Payot, 1977.
. Martin Buber, _Moïse_ , París, Presses Universitaires de France, 1986 [hay trad. cast.: _Moisés_ , Buenos Aires, Imán, 1949]; C. E. Schorske, _Vienne, fin de siècle..._ , _op. cit._ ; Y. Yovel, _Spinoza et autres hérétiques_ , _op. cit._ , y P. Gay, _Un Juif sans Dieu..._ , _op. cit._
. Carta de Freud a Marie Bonaparte, 27 de enero de 1938, archivos inéditos. Citada por Max Schur.
. Citado en I. Kershaw, _Hitler..._ , vol. 2, _op. cit._ , p. 129.
. _Ibid._ , p. 144.
. En ese sentido, el 15 de marzo Wiley envió al secretario de Estado un telegrama, cuya reproducción facsimilar figura en S. Freud, _Chronique la plus brève..._ , _op. cit._ , p. 229.
. La unificación de Austria y Alemania.
. R. Sterba, _Réminiscences d'un psychanalyste..._ , _op. cit._ , pp. 145-146. La «excepción» era Sterba.
. I. Kershaw, _Hitler..._ , vol. 2, _op. cit._ , p. 149. Peter Gay hace una excelente descripción del furor que se desató en Austria en marzo de 1938.
. El 2 de abril de 1938 Francia, Gran Bretaña y Estados Unidos reconocieron la legalidad del _Anschluss_.
. Carta de Giovacchino Forzano a Mussolini, 14 de marzo de 1938, citada en P. Roazen, «Questions d'éthique psychanalytique...», _op. cit._ , p. 162. A pesar de las afirmaciones de Concetta Giovacchino al respecto, Mussolini parece no haber dado curso a esta petición de su padre. Pedí a Maurizio Serra que investigara la cuestión, pero en los archivos no se encontró nada. En su testimonio conservado en la Biblioteca del Congreso, Edoardo Weiss dice que jamás tuvo la más mínima prueba de las intenciones favorables de Mussolini con referencia a Freud, en las que, sin embargo, Forzano creía.
. Sobre la emigración de Freud, además de los archivos de la Biblioteca del Congreso y los de Marie Bonaparte, pueden consultarse las obras ya citadas de Ernest Jones, Max Schur, Martin Freud, Eva Weissweiler, Richard Sterba, Mark Edmundson, Detlef Berthelsen (sobre Paula Fichtl) y Elisabeth Young-Bruehl. También hay que cotejar los epistolarios de Freud con Ernest Jones, Max Eitingon, Arnold Zweig, Minna Bernays, Anna Freud y los otros hijos. Cf. asimismo S. Freud, _Chronique la plus brève..._ , _op. cit._ ; K. Brecht _et al._ , « _Ici la vie continue d'une manière fort surprenante_ »..., _op. cit._ , y Sophie Freud, _À l'ombre de la famille Freud_..., _op. cit._ La consulta de todas estas fuentes permite conocer en detalle y día a día la totalidad de las gestiones financieras, jurídicas y administrativas que desembocaron en la emigración de Freud y de los miembros de su familia, así como en el traslado a Inglaterra de sus archivos y colecciones. Un rumor propagado por Barbara Hannah pretende que Franz Riklin Jr. habría sido enviado a Viena por Jung para entregar a Freud una suma importante de dinero a fin de ayudarlo a exiliarse. D. Bair, _Jung..._ , _op. cit._ , p. 692, invalidó este rumor. Cf. asimismo el testimonio de Robert McCully recogido por Kurt Eissler, LoC, s.d., caja 121, carpeta 17.
. Testimonio de Emy Moebius, que emigraría a Florida, LoC, documento citado.
. Un año después los adquirió Jacob Schatsky, bibliotecario del Instituto Psiquiátrico de Nueva York.
. «Le protocole d'accord signé à Vienne le 20 mars 1938», _Revue internationale d'histoire de la psychanalyse_ , 5, 1992, pp. 32-35.
. Se llama así al no judío encargado de ayudar a los judíos practicantes a llevar a cabo ciertas tareas corrientes el día del sabbat.
. Carta de Müller-Braunschweig a Sterba, 5 de mayo de 1938, que, según la fórmula ritual, terminaba con el « _Heil Hitler_ », en R. Sterba, _Réminiscences d'un psychanalyste..._ , _op. cit._ , p. 151.
. «Puercos judíos.»
. Sobre el papel de Alfred Indra, cf. Alexander Waugh, _Les Wittgenstein: une famille en guerre_ (2008), París, Perrin, 2011 [hay trad. cast.: _La familia Wittgenstein_ , Barcelona, Lumen, 2009]. Sobre el detalle de las leyes antijudías aplicadas a la familia Freud y a las hermanas de Sigmund, cf. Harald Leupold-Löwenthal, «L'émigration de la famille Freud en 1938», _Revue internationale d'histoire de la psychanalyse_ , 2, 1989, pp. 442-461, y Alfred Gottwaldt, «Les sœurs de Sigmund Freud et la mort: remarques concernant leur destin de déportation et de meurtre de masse», _Revue française de psychanalyse_ , 68(4), 2004, pp. 1307-1316.
. En el sitio de este suntuoso hotel, destruido en 1945, Simon Wiesenthal instalaría su Centro de Documentación de la Resistencia Austríaca. En 1985 se levantó un monumento en recuerdo de las víctimas.
. D. Berthelsen, _La Famille Freud..._ , _op. cit._ , p. 81.
. Eva Freud (1924-1944) murió en Marsella a raíz de una septicemia provocada por un aborto. Cf. É. Roudinesco y M. Plon, _Dictionnaire de la psychanalyse_ , _op. cit._
. W. Ernst Freud, «Souvenirs personnels à propos de l'Anschluss de 1938», _Revue internationale d'histoire de la psychanalyse_ , 3, 1990, pp. 409-417.
. D. J. Lynn, «Sigmund Freud's psychoanalysis of Albert Hirst», _op. cit._ , y «Obituary», _Insurance Advocate_ , 85, 1974, p. 89. El testimonio de Hirst está depositado en la Biblioteca del Congreso, documento citado.
. Lilly adoptó a Angela, su sobrina huérfana, hija de Tom Seidmann-Freud, que se había suicidado en 1930, al igual que su marido, que se había matado poco tiempo antes que ella. En una carta a su hermana Mitzi, del 28 de diciembre de 1930, Freud explica que no puede tomar a su cargo a Angela en Viena, LoC, caja 3, carpeta 11.
. Había nacido en Estados Unidos, donde su madre había emigrado, para después retornar a Viena. Cf. Ernst Waldinger, «My uncle Sigmund Freud», _Books Abroad_ , 15, enero de 1941. Un extenso testimonio de Waldinger se conserva en la Biblioteca del Congreso, documento citado.
. Freud insistió, en vano, para que se incluyera en la comitiva a Maximilian Steiner, miembro de la WPV desde 1908.
. Sophie Freud, _À l'ombre de la famille Freud_..., _op. cit._ , p. 206. Nacida en 1924, Sophie Freud se casó en Estados Unidos con Paul Lowenstein, inmigrante alemán que se había evadido de un campo de tránsito en Francia. Psicosocióloga, se especializó en la protección de la infancia.
. August Aichhorn (1878-1949) permaneció en Viena, debido a la detención de su hijo por los nazis y su deportación a Dachau como preso político. Tras la guerra y la liberación del hijo, participó en la reconstrucción de la WPV. Ernst Federn (1914-2007), hijo de Paul Federn, fue deportado a Buchenwald, de donde se escapó, como también lo haría Bruno Bettelheim (1903-1990). Federn volvió a instalarse en Viena en 1972, después de un periplo americano. Bettelheim vivió en Chicago.
. E. Engelmann, _La Maison de Freud..._ , _op. cit._ , p. 27. Las fotografías se vendieron en el mundo entero: eran el testimonio vivo de cuarenta y siete años de vida consagrados a la ciencia, el arte y la cultura.
. « _Erklärung. Ich bestätige gerne, dass bis heute den 4. Juni 1938, keinerlei Behelligung meiner Person oder meiner Hausgenossen vorgekommen ist. Behörden und Funktionäre der Partei sind mir und meinen Hausgenossen ständig korrekt und rücksichtsvoll entgegen getreten. Wien, den 4. Juni 1938. Prof. Dr. Sigm. Freud_.» Este documento, con la firma manuscrita de Freud, figura en el catálogo Nebehay del 11 de mayo de 1989. Fue adquirido por la Biblioteca Nacional de Austria (Österreichische Nationalbibliothek), donde puede consultarse.
. Ernest Jones, Peter Gay, Mark Edmundson y muchos otros han comentado profusamente la frase. En Francia, Alain de Mijolla fue uno de los primeros en poner en tela de juicio la veracidad de esta declaración. Cf. Alain de Mijolla, dir., _Dictionnaire international de la psychanalyse: concepts, notions, biographies, œuvres, événements, institutions_ , París, Calmann-Lévy, 2002, vol. 1, p. 683 [hay trad. cast.: _Diccionario Akal internacional de psicoanálisis: conceptos, nociones, biografías, obras, acontecimientos, instituciones_ , 2 vols., Madrid, Akal, 2008].
. El mejor testimonio sobre este viaje es el de Paula Fichtl recogido por Detlef Berthelsen. Ella describe en detalle las reacciones de los viajeros, la ropa que llevaban, lo que comían.
. Carta de S. Freud a Alexander Freud, 17 de julio de 1938, LoC, papeles de familia.
. M. Schur, _La Mort dans la vie..._ , _op. cit._ , p. 588, y S. Freud, _Chronique la plus brève..._ , _op. cit._ , p. 449. Hay varias versiones sobre la actitud de Sauerwald. Cf. asimismo el testimonio de Ernst Waldinger, documento citado.
. Sigmund Freud, _Abrégé de psychanalyse_ (1940), París, Presses Universitaires de France, 1967, y _OC.P_ , vol. 20, _op. cit._ [hay trad. cast.: _Esquema del psicoanálisis_ , en _OC_ , vol. 23, _op. cit._ , pp. 133-209].
. Arthur Koestler, _Hiéroglyphes_ , París, Calmann-Lévy, 1955, p. 493 [hay trad. cast.: _Autobiografía_ , vol. 2, _La escritura invisible_ , __ Barcelona, Debate, 2000]. Ernest Jones destaca que Koestler publicó dos versiones diferentes sobre su visita a Freud, ambas con errores. Véase E. Jones, _La Vie et l'œuvre..._ , vol. 3, _op. cit._ , p. 269.
. Adele Jeiteles (1871-1970), que murió casi centenaria, provenía de una gran familia judía del Imperio austrohúngaro. Su tío, afectado por una psicosis melancólica, también había consultado a Freud en 1900, antes de suicidarse.
. Kurt Eissler realizó en 1953 una entrevista con Arthur Koestler y otra con su madre; esta sería utilizada por el biógrafo del escritor, que presenta un terrible retrato de Koestler. Véase Michael Scammell, _Koestler: The Literary and Political Odyssey of a Twentieth-Century Skeptic_ , Nueva York, Random House, 2009, y Arthur Koestler, _Œuvres autobiographiques_ , París, Laffont, 1993, col. «Bouquins».
. Melitta Schmideberg, «Contribution à l'histoire du mouvement psychanalytique en Angleterre» (1971), _Confrontation_ , 3, primavera de 1980, pp. 11-22.
. Ernest Jones, citado en Edward Glover, «Fifteenth International Psycho-Analytical Congress», _Bulletin of IPA_ , 20, 1939, pp. 116-127. Cf. asimismo _HPF-JL_ , _op. cit._ , pp. 1606-1607.
. Alexandre Etkind retomó esta tesis en su _Histoire de la psychanalyse en Russie_ , _op. cit._ , y tras él muchos otros hicieron lo mismo. Sin embargo, G. Liebermann, _La Psychanalyse en Palestine..._ , _op. cit._ , invalidó la tesis sobre la base de una consulta en los archivos.
. Carta de Freud a Marie Bonaparte, 4 de octubre de 1938, en S. Freud, _Correspondance, 1873-1939_ , _op. cit._ , p. 493 [hay trad. cast.: «A Marie Bonaparte», en _Epistolario, 1873-1939_ , _op. cit._ , p. 501]. En el _Times_ del 7 de noviembre de 1938, Winston Churchill dirá: «Debían elegir entre el deshonor y la guerra. Eligieron el deshonor, y tendrán la guerra».
. Sigmund Freud, «Un mot sur l'antisémitisme» (1938), en _OC.P_ , vol. 20, _op. cit._ , pp. 326-329 [hay trad. cast.: «Comentario sobre el antisemitismo», en _OC_ , vol. 23, _op. cit._ , pp. 289-295]. Finalmente liberado, Arthur Freud dejó un testimonio escrito citado por Martin Gilbert, _Kristallnacht: Prelude to Destruction_ , Nueva York, HarperCollins, 2006, pp. 54-55 [hay trad. cast.: _La noche de los cristales rotos: el preludio de la destrucción_ , Madrid, Siglo XXI, 2008].
. M. Edmundson, _La Mort de Sigmund Freud..._ , _op. cit._ , p. 163.
. Carta de Freud a Marie Bonaparte, 12 de noviembre de 1938, en S. Freud, _Correspondance, 1873-1939_ , _op. cit._ , p. 497 [hay trad. cast.: «A Marie Bonaparte», en _Epistolario, 1873-1939_ , _op. cit._ , p. 504]. Freud se equivocaba: se trataba de ciento sesenta mil chelines. [La edición castellana citada dice correctamente «ciento sesenta mil». _(N. del T.)_ ]
. C. Bertin, _Marie Bonaparte_ , _op. cit._ , p. 327.
. Cf. _HPF-JL_ , _op. cit._
. El texto se reproduce en facsímil en Ruth Sheppard, _Sigmund Freud: à la découverte de l'inconscient_ (2012), París, Larousse, 2012. [La grabación puede escucharse en www.youtube.com/watch?v=_sm5YFnEPBE. _(N. del T.)_ ]
. Cf. _Sigmund Freud: l'invention de la psychanalyse_ , documental de 1997 dirigido por Élisabeth Kapnist, con guión de esta y Elisabeth Roudinesco y producción de Françoise Castro. [Puede verse en https://www.youtube.com/watch?v=I0jw6tYp0yI (primera parte) y https://www.youtube.com/watch?v=BuR8Jpvd7nA (segunda parte). _(N. del T.)_ ]
. Carta de Freud a A. Zweig, 5 de marzo de 1939, en S. Freud y A. Zweig, _Correspondance..._ , _op. cit._ , p. 221. Véanse asimismo los archivos inéditos de Marie Bonaparte. Cf. igualmente Denis Toutenu, «Freud, une photo inédite: la consultation du Pr Lacassagne à Londres le 26 février 1939», _Revue française de psychanalyse_ , 66(4), 2002, pp. 1319-1323. El informe médico se encuentra en LoC, caja 120, carpeta 53.
. Carta de Freud a Jones, 7 de marzo de 1939, en S. Freud y E. Jones, _Correspondance complète..._ , _op. cit._ , p. 877.
. S. Freud, _Chronique la plus brève..._ , _op. cit._ , p. 306.
. Carta de Jones a Freud, 3 de septiembre de 1939, en S. Freud y E. Jones, _Correspondance complète..._ , _op. cit._ , p. 878. El día anterior los nazis habían invadido Polonia.
. Según las palabras de Jean-Paul Sartre, citadas como epígrafe de este libro.
. Las notas de Max Schur se conservan en la Biblioteca del Congreso. Su contenido es diferente a la versión que él mismo da en su libro _La Mort dans la vie..._ , _op. cit._ Peter Gay las tuvo ampliamente en cuenta en su _Freud, une vie_ , _op. cit._ , pp. 830-832, y señala que, sin duda, a Freud se le aplicaron tres inyecciones y no dos. Cf. asimismo M. Edmundson, _La Mort de Sigmund Freud..._ , _op. cit._ , pp. 195-197. En su testimonio, Paula Fichtl afirma que Schur no estaba presente en el momento de la muerte de Freud y que fue Josefine Stross quien administró la dosis letal. Si bien es cierto que Schur debía volver a Estados Unidos lo más pronto posible, nada prueba que no estuviera presente a la cabecera de Freud. Paula se equivoca además con respecto a la dosis, el día y la cantidad de inyecciones. Su versión fue retomada por Roy B. Lacoursière, «Freud's death: historical truth and biographical fictions», _American Imago_ , 65(1), primavera de 2008, pp. 107-128. En este artículo, Lacoursière afirma que Stross habría dejado archivos sobre la cuestión, pero no dice cuál es su contenido y tampoco los consultó. Freud leyó la novela de Balzac en francés, en una edición de 1920 perteneciente a Anna. Referencia LDFRD 5680. Para saber más habrá que esperar a la apertura, en el Freud Museum, de la correspondencia de Josefine Stross.
. Y no a las 23.45, como dice Marie Bonaparte en su diario.
. Raul Hilberg, _La Destruction des Juifs d'Europe_ (1961), París, Fayard, 1988, p. 190 [hay trad. cast.: _La destrucción de los judíos europeos_ , Madrid, Akal, 2005].
. E. Jones, _La Vie et l'œuvre..._ , vol. 3, _op. cit._ , p. 282.
. Stefan Zweig, «Sur le cercueil de Sigmund Freud» (1939), en _Sigmund Freud: la guérison..._ , _op. cit._ , p. 149 [hay trad. cast.: «Palabras pronunciadas junto al ataúd de Sigmund Freud, el 26 de septiembre de 1939 en el crematorio de Londres», en _Tiempo y mundo: impresiones y ensayos, 1904-1940_ , Barcelona, Juventud, 1959, pp. 35-38].
#### EPÍLOGO
. Carta de Harry Freud a Dolfi, Paula, Rosa y Mitzi, 25 de septiembre de 1939, LoC, caja 3, carpeta 7 y siguientes.
. H. Leupold-Löwenthal, «L'émigration de la famille Freud...», _op. cit._ , p. 459.
. Cuarenta y siete mil judíos vieneses fueron deportados y asesinados. El nombre de Adolfine no figura en las listas de muertos de Theresienstadt de esa fecha. Debido a una confusión de nombres, muchas veces se da el 5 de febrero de 1943 como fecha de su deceso. En una novela descabellada, el escritor macedonio Goce Smilevski acusa a Freud de ser responsable de la deportación de sus hermanas, cuyos nombres se habría negado a incluir en su «lista» de candidatos a la emigración. Con un razonamiento semejante, podría hacerse responsables del exterminio de sus parientes a todos los judíos vieneses que lograron exiliarse en 1938. Cf. Goce Smilevski, _La Liste de Freud_ (2010), París, Belfond, 2013 [hay trad. cast.: _La hermana de Freud_ , Madrid, Alfaguara, 2013]. Cf. asimismo Michel Rotfus, blog «Médiapart», entrada del 11 de octubre de 2013, «Goce Smilevski, _La Liste de Freud_ : "Poétiser à Auschwitz", dit-il».
. _Procès des grands criminels de guerre devant le Tribunal Militaire International, Nuremberg, 14 novembre 1945-1er octobre 1946_ , vol. 8, Nuremberg, 1947, nota de las actas del 20 de febrero al 7 de marzo de 1946, pp. 359-360, citado por Harald Leupold-Löwenthal y Alfred Gottwaldt. Pudo establecerse que el testimonio de Samuel Rajzman se refería a Rosa Graf. Christfried Tögel cree que Rosa fue transportada el 1 de marzo de 1943: cf. Christfried Tögel, «Bahnstation Treblinka: zum Schicksal von Sigmund Freuds Schwester Rosa Graf», _Psyche: Zeitschrift für Psychoanalyse und ihre Anwendungen_ , 44(11), 1990, pp. 1019-1024. En cuanto a Alfred Gottwaldt, destaca la posibilidad de que también las otras dos hermanas fueran asesinadas en Treblinka, y señala que Rosa había llegado el 29 de septiembre de 1942, en el transporte Bs 800. Han circulado varios rumores sobre la deportación de las hermanas de Freud. Michel Onfray llega a decir que Rosa, Mitzi y Paula se habrían cruzado con Rudolf Höss en Auschwitz e imagina que este habría sido, para ellas, un sustituto de su hermano, porque Freud, también verdugo y fascista partidario de Mussolini, habría sido incapaz de ver la diferencia entre un verdugo y una víctima. Cf. M. Onfray, _Le Crépuscule d'une idole..._ , _op. cit._ , p. 566.
. En Inglaterra, al comienzo de la guerra, considerados como «extranjeros enemigos» ( _enemy aliens_ ), vivieron en campos de internamiento.
. Clement Freud, _Freud Ego_ , Londres, BBC Worldwide Publishing, 2001.
. Esther Freud, _Marrakech Express_ (1993), París, Le Livre de Poche, 1999 [hay trad. cast.: _Una infancia en Marraquech_ , Barcelona, Círculo de Lectores/Galaxia Gutenberg, 1998], y _Nuits d'été en Toscane: roman_ (2007), París, Albin Michel, 2009.
. Cf. Geordie Greig, _Rendez-vous avec Lucian Freud_ (2013), París, Christian Bourgois, 2014, p. 59.
. _Ibid_.
. S. Freud, _Chronique la plus brève..._ , _op. cit._ , p. 304. David Cohen dedicó a este asunto un libro que generó numerosas interpretaciones: David Cohen, _Escape of Sigmund Freud_ , Londres, Overlook Press, 2012.
. En un primer momento Dorothy se instaló en otra casa de Maresfield Gardens.
. Kata Levy (1883-1969): psicoanalista húngara analizada por Freud. En 1956 emigró a Londres con su marido. La Cruz Roja le había informado del exterminio de las hermanas de Freud.
. Anna Freud y Sophie Dann, «Survie et développement d'un groupe d'enfants: une expérience bien particulière», en Anna Freud, _L'Enfant dans la psychanalyse_ , París, Gallimard, 1976, pp. 110-160 [hay trad. cast.: «La crianza en grupo: un experimento», en _El psicoanálisis y la crianza del niño_ , Barcelona, Paidós, 1980, pp. 79-128]. Jenny Aubry se inspiró en esa tesis para llevar a cabo su propia experiencia con niños abandonados. Cf. Jenny Aubry, _Psychanalyse des enfants séparés: études cliniques, 1952-1986_ , París, Denoël, 2003. Cf. asimismo la ponencia inédita de Maria Landau en el marco de la tercera jornada de la Asociación Jenny Aubry, dedicada a la separación, 18 de abril de 2013. Reseña en Michel Rotfus, blog «Médiapart», entrada del 26 de abril de 2013, «Les enfants et la psychanalyse, 3ème journée de l'Association Jenny Aubry: les maladies de la séparation».
. Cuya versión expurgada apareció en 1950 con el título de _Aus des Anfängen der Psychoanalyse_ [«Los orígenes del psicoanálisis»].
. Sobre la génesis de la obra y las dificultades con que tropezó Jones, cf. M. Borch-Jacobsen y S. Shamdasani, _Le Dossier Freud..._ , _op. cit._ , pp. 365-418.
. A. Freud, _Le Traitement psychanalytique..._ , _op. cit._
. Después del intento de suicidio de Lucie, en respuesta a la muerte de Ernst, Lucian realizará, a partir de 1972, una quincena de retratos de ella.
. E. Weissweiler, _Les Freud..._ , _op. cit._ , p. 374. En el parque nacional de Dartmoor se desarrolla _El sabueso de los Baskerville_ , la novela de Arthur Conan Doyle.
. No comparto la opinión de Mikkel Borch-Jacobsen, para quien Kurt Eissler engañó —e incluso estafó— al pueblo norteamericano al valerse de la Biblioteca del Congreso como una caja fuerte destinada a confiscar los archivos en su beneficio y ocultarlos a los investigadores. Cf. M. Borch-Jacobsen y S. Shamdasani, _Le Dossier Freud..._ , _op. cit._ , p. 424.
. Reeditada en Fayard por iniciativa de Olivier Bétourné, conforme a la elección del propio Ellenberger, que a continuación dejó en manos de la SIHPP la administración de sus archivos, de los que hoy me ocupo yo misma con la ayuda de su hijo, Michel Ellenberger.
. «Destrucción o denigración de Freud.»
. Todas estas obras se citan en las notas.
. Jeffrey Moussaieff Masson, _Le Réel escamoté: le renoncement de Freud à la théorie de la séduction_ (1984), París, Aubier-Montaigne, 1984 [hay trad. cast.: _El asalto a la verdad: la renuncia de Freud a la teoría de la seducción_ , Barcelona, Seix Barral, 1985].
. Janet Malcolm, _Tempête aux Archives Freud_ (1984), París, Presses Universitaires de France, 1988 [hay trad. cast.: _En los archivos de Freud_ , Barcelona, Alba, 2004].
. Tuve la oportunidad de conocer a J. M. Masson cuando se publicó la traducción francesa de su libro. Estaba realmente convencido de que todos los niños eran víctimas de abusos sexuales cometidos por adultos. Nacido en 1941, autor de numerosas obras, hoy es vegetariano y militante del derecho de los animales y vive en Auckland con su familia y sus muchos perros. Tuve con Eissler un breve intercambio de cartas entre diciembre de 1994 y enero de 1995 acerca de Henri F. Ellenberger, mientras me ocupaba de la edición de _Médecines de l'âme..._ , _op. cit._
. Cf. E. Young-Bruehl, _Anna Freud_ , _op. cit._ , pp. 412-413.
. Adolf Grünbaum, _Les Fondements de la psychanalyse: une critique philosophique_ (1984), París, Presses Universitaires de France, 1996. En esta obra, Grünbaum arremete con furia contra tres filósofos —Karl Popper, Jürgen Habermas y Paul Ricœur— y les reprocha no haber criticado suficientemente el psicoanálisis. En É. Roudinesco, _Pourquoi la psychanalyse?_ , _op. cit._ , he analizado ese libro.
. Como ya señalé, yo misma organicé allí, en 1994, con René Major y en el marco de la Sociedad Internacional de Historia de la Psiquiatría y el Psicoanálisis (SIHPP), un coloquio sobre los archivos.
29. Documento dactilografiado del 31 de julio de 1995. Tuve algunos intercambios epistolares sobre el tema con Carl Schorske, Peter Gay, Yosef Yerushalmi, Patrick Mahony, Ilse Grubrich-Simitis, John Forrester y varios otros. En una carta que me remitió en esos momentos, Schorske indicaba que veía en esa ofensiva el retorno de cierto macartismo.
. Entrevista de Nicolas Weill y Raphaëlle Rérolle con Elisabeth Roudinesco y de Nicolas Weill con Mikkel Borch-Jacobsen, _Le Monde_ , 14 de junio de 1996.
. Entrevista con Patrick Sabatier, _Libération_ , 26 de octubre de 1998. Cf. Michael S. Roth, ed., _Freud: Conflict and Culture. Essays on His Life, Work and Legacy_ , Nueva York, Knopf, 1998.
. Coordiné dos libros colectivos en respuesta a esos best sellers, con Sylvain Courage, Pierre Delion, Christian Godin, Roland Gori, Franck Lelièvre, Guillaume Mazeau, Jack Ralite y Jean-Pierre Sueur: _Pourquoi tant de haine? Anatomie du «Livre noir de la psychanalyse»_ , París, Navarin, 2005, y _Mais pourquoi tant de haine?_ , _op. cit._
. En compañía de Anthony Ballenato.
. La irrupción se produjo la noche del 31 de diciembre de 2013 al 1 de enero de 2014.
* En lo que se refiere a la traducción castellana de las _Obras completas_ , la primera fue la de Luis López Ballesteros, publicada en Madrid por la editorial Biblioteca Nueva en diecisiete volúmenes entre 1922 y 1934 (por tanto, en vida de Freud). En 1948 se la refundió en dos volúmenes y en 1967-1968 se agregó un tercero, con traducción de Ramón Rey Ardid; por último, entre 1972 y 1975 se publicó la edición en rústica en nueve volúmenes. Una segunda edición es la realizada por la Editorial Americana de Buenos Aires entre 1943 y 1944 con traducción de Ludovico Rosenthal. El proyecto preveía veintidós volúmenes, pero solo se publicaron diecinueve. Ya completa, la misma traducción fue reeditada por el sello Santiago Rueda, también de Buenos Aires, entre 1952 y 1956. Para terminar, la editorial Amorrortu de Buenos Aires, con traducción de J. L. Etcheverry, publicó entre 1978 y 1985 la obra completa en veinticuatro volúmenes, según el formato adoptado por la _Standard_ _Edition_ inglesa. Como ya se ha señalado, es esa última traducción de J. L. Etcheverry la que hemos utilizado en este volumen. _(N. del T.)_
**Elisabeth Roudinesco**. Historiadora y directora de investigación en la Universidad de París-VII, Elisabeth Roudinesco es la autora de numerosas obras, entre las que destacan _Jacques Lacan. Esbozo de una vida, historia de un sistema de pensamiento_ (1995), _¿Por qué el psicoanálisis?_ (2000) y _Nuestro lado oscuro, una historia de los perversos_ (2009).
Título original: _Sigmund Freud. En son temps et dans le nôtre_
Edición en formato digital: septiembre de 2015
© 2014, Éditions du Seuil
© 2015, Penguin Random House Grupo Editorial, S. A. U.
Travessera de Gràcia, 47-49. 08021 Barcelona
© 2015, Horacio Pons, por la traducción
Diseño de portada: Penguin Random House Grupo Editorial / Nora Grosse
Fotografía de portada: © Getty Images
Penguin Random House Grupo Editorial apoya la protección del _copyright._ El _copyright_ estimula la creatividad, defiende la diversidad en el ámbito de las ideas y el conocimiento, promueve la libre expresión y favorece una cultura viva. Gracias por comprar una edición autorizada de este libro y por respetar las leyes del _copyright_ al no reproducir ni distribuir ninguna parte de esta obra por ningún medio sin permiso. Al hacerlo está respaldando a los autores y permitiendo que PRHGE continúe publicando libros para todos los lectores. Diríjase a CEDRO (Centro Español de Derechos Reprográficos, <http://www.cedro.org>) si necesita reproducir algún fragmento de esta obra.
ISBN: 978-84-9992-582-0
Composición digital: M.I. maqueta, S.C.P.
www.megustaleer.com
Índice
Freud en su tiempo y en el nuestro
Introducción
Primera parte. Vida de Freud
1. Los comienzos
2. Amores, tempestades y ambiciones
3. La invención del psicoanálisis
Segunda parte. Freud, la conquista
1. Una época tan bella
2. Discípulos y disidentes
3. El descubrimiento de América
4. La guerra de las naciones
Tercera parte. Freud en su propia casa
1. La Ilustración oscura
2. Familias, perros, objetos
3. El arte del diván
4. Entre las mujeres
Cuarta parte. Freud, los últimos tiempos
1. Entre medicina, fetichismo y religión
2. Frente a Hitler
3. La muerte en acción
Epílogo
Agradecimientos
Bibliografía
Los pacientes de Freud
Árboles genealógicos
Notas
Biografía
Créditos
| {
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\section{IF07 Executive Summary}
In pursuit of its physics goals, the high energy physics community
develops increasingly complex detectors, with each subsequent
generation pushing to ever finer granularity. For example, the
emergence and growing dominance
of particle-flow reconstruction methods has stressed
the increasing importance of very fine detector granularity, not
only for tracking detectors but also for calorimetry, and has also
initiated the push to "4D" detectors that combine precision measurements
of both spatial and time coordinates to their measurements of
energy and momentum. While these developments have led to enormous
growth in detector channel counts, the analog performance requirements
for energy and momentum measurements, as well as spatial and timing precision,
are being maintained or (more typically) even tightened.
These challenging detector requirements drive the corresponding development of
readout electronics. A variety of factors, including the growing
specialization of the functionality required, and the explosive
growth in channel counts and typically modest (if any) increases in the
material budget and the power and cooling budgets,
lead to the increasing reliance on custom-developed Application
Specific Integrated Circuits (ASICs). This trend is further
exacerbated by challenges in the various experimental environments,
including radiation hardness requirements, cryogenic
and deep-cryogenic operations, and
space-based detector systems.
The development of custom ASICs in advanced technology nodes allows HEP detector
subsystems to achieve higher channel density, enhanced
performance, lower power consumption, lower mass, much greater radiation
tolerance, and improved cryogenic temperature performance than is possible
with commercial integrated circuits (ICs) or discrete components.
The higher level of integration also leads to fewer components and
fewer connections, leading to higher reliability, as required by
experiments that can run for decades and that provide access to
the on-detector electronics at most annually, and sometimes never.
This writeup summarizes the work of ``IF07'', namely
Topical Working Group 7 of the
Instrumentation Frontier group of the Snowmass 2021 process. Group IF07
dealt with issues pertaining to ASICs and Readout Electronics. The
community efforts as part of IF07 were organized across 7 white papers
submitted to the Snowmass process. The first~\cite{whitepaper1}
discusses issues related to the need to maintain the talented
workforce required to successfully develop future HEP electronics
systems, and to provide the appropriate training and recruitment.
The remaining papers focused on electronics for particular detector
subsystems or technologies, including calorimetry~\cite{whitepaper2},detectors for fast timing~\cite{whitepaper4}, optical links~\cite{whitepaper5}, smart sensors using AI~\cite{whitepaper6},cryogenic readout~\cite{whitepaper7},
and RF readout systems~\cite{whitepaper8}.
In the following section, a brief overview is provided of each
of the white papers in turn.
A white paper on silicon and photo-detectors was originally considered. This content is now captured by other frontiers with contributions form ASICs and readout electronics.
There are some overarching goals for advancing the field of readout and ASICs. Efforts with broad impact include:
There are some overarching goals for advancing the field of readout and ASICs. Efforts with broad impact include:
\begin{itemize}
\item[{\bf IF07-1}]: Provide baseline support and specialized {\bf training opportunities} for the instrumentation work force to keep the US electronics instrumentation and ASIC workforce current.
\item[{\bf IF07-2}]: Improve mechanisms for {\bf shared access to advanced technology} providing broader access by the community to foster real exchange of information and accelerate development.
\item[{\bf IF07-3}]: Continue to develop methodologies to {\bf adapt the technology for operation in extreme environments}. Deep cryogenics, ultra-radio pure materials, radiation-harsh environments with limited power budget and long lifetime for all cases.
\item[{\bf IF07-4}]: Develop novel techniques to manage very high {\bf data rates}. Data reduction and optimization needs to be as close as possible to the generation point with acceptable power consumption.
\item[{\bf IF07-5}]: Create framework and platform for {\bf easy access to design tools}. Develop specialized online resources for the HEP community (e.g. system simulations and design repository). Provide the basis for true co-design R\&{}D efforts: from simulation to verification and implementation.
\end{itemize}
\section{Overview of IF07 White Papers}
A brief overview and high-level summary of each
of the 7 IF07 white papers is provided below. For a more detailed
discussion of each of the various topics, the interested reader
is referred to
the white papers themselves, and to the references therein.
\subsection{Workforce and Training Needs}
Two decades ago as we embarked on the design of the LHC detector systems \emph{on detector} readout was focused on the integration of custom sensors and multiple types of Application Specific Integrated Circuits with communications rates at or below 100 Mbps. Significant effort went into the design of printed circuits on boards or flexible substrates. A new generation of ASICs were coming into use that could survive radiation tolerance levels consistent with the needs of LHC provided specialized layout techniques were employed. Designers were faced with learning new tools and rules for commercial ASICs that were attainable in a few months and system interfaces were being designed that allowed multiple institutions to design parts of a readout system nearly independently.
As LHC systems were being placed into service commercial ASICs and communications systems were leap frogging forward and significant change was moving the state of the art forward faster than our communities and budgets could maintain pace. Today's HL-LHC designs have been able to take advantage of advances that are still several technology generations behind the commercial state of the art to move what previously was multi-chip functionality onto a single silicon substrate to make systems on a chip that operate at much higher clock rates and can hold and selectively readout more data and contain most or all of the readout blocks for modules of thousands of small size sensors. The price for successful submission of these far more complex, low power integrated circuits has been the requirement for a workforce with knowledge of a broad set of new tools for design and verification as well as formalized design management and integration tools that don't allow new versions or blocks to compromise the overall performance or design progress of these now highly complex systems on a chip. We also recognize the revolution in capabilities offered by new, complex FPGA's that comprise a large part of the off detector readout of detector systems designed over the past decade. Here too the required knowledge base has expanded sufficiently far that coding is no longer an easy to skill to learn for this or next generation designers. We foresee the need for continuing workforce training past the qualifying academic degrees to update commercial design skills. Many designs require HEP specialized knowledge to enable successful first time designs for extreme temperature and radiation environments. Our community exploit the internet to provide an archive with searchable access to design examples from previous generations of detectors to replace the institutional knowledge passed down from previous teams. This is especially important given that the time between large detector system developments may exceed career lifetimes. In these extended interim's it is recognized that core HEP instrumentation specialists need to update their skills with practical projects to ensure their familiarity with the evolving state of the art in ASIC designs. This can be encouraged by DOE provided annual FOA's to support the design of service blocks that will be necessary in yet to be defined front end ASICs for next generation sensor arrays: High speed communication links, data storage blocks, PLL's, power converters and regulators etc. Having silicon tested designs for next generation ASICs will both speed up design cycles and help maintain workforce skill levels consistent with current (at the time of need) ASIC design tool familiarity to minimize the number of design submissions required to assure reliable ASIC performance. It would also be helpful for DOE to encourage a hybrid Instrumentation Based qualification for PHD degrees as part of a basic High Energy Physics degree.
In addition it will be beneficial to have instrumentation conferences with training available to introduce new design approaches or technologies.
We see the recent support from DOE for Instrumentation based traineeship to be an important step towards having a better trained, better informed workforce not only for designing systems but also for the benefit of future peer reviewed systems.
\subsection{Calorimeter Readout Electronics}
Calorimeters will continue to serve as key detector subsystems
at future colliders, as well as in many other applications.
The traditional challenges of calorimeter readout electronics systems,
including providing high precision energy measurements over a very
wide dynamic range, are increasingly compounded by the demands of much
finer granularity and correspondingly higher readout rates, as well
as the demand of providing precision time measurements in
the move toward ``4D calorimetry''. The on-detector location of
the frontend electronics, necessitated by signal-to-noise and
other requirements, imposes additional challenges, including
tolerance to radiation and/or magnetic fields, reliability over periods
of a year or more without maintenance, and power and cooling budgets.
Some of the key innovations in calorimetry that are driving ongoing and future readout electronics developments include
particle flow algorithms, in which measurements of energies from
calorimeters are combined with the momentum
measurements from charged-particle tracking detectors.
and dual-readout detectors, which provide a more flexible combination
of the electromagnetic and hadronic components of a shower. Both
of these methods aim to significantly improve the energy
resolution, and both can be implemented
either with or without timing information as an added component.
Particle flow algorithms are pushing calorimeter designs to
ever finer granularities, and therefore greatly increasing
channel counts. As an example, the High Granularity Endcap
Calorimeter (HGCAL)
being developed currently for the CMS HL-LHC upgrade
includes over 6 million
readout channels, a dramatic increase over the $\approx 200k$
channels of the ATLAS liquid argon (LAr) calorimeters that
set the scale for "finely segmented" among the original LHC detectors.
Meeting the challenges for frontend calorimeter readouts
has relied on custom ASICs for over 30 years, and ASICs will only
become increasingly important. Fortunately, the higher level of
integration available today has permitted some consolidation;
for example, while the current ATLAS liquid argon (LAr) frontend
required development of 11 different custom ASICs, spread over
a variety of technologies, the HL-LHC development underway requires
only three. The higher level of integration is most clearly seen
in the digital realm, where for example the lpGBT chip in 65~nm CMOS
fulfills a number of functions, including clock and control
distribution, slow control monitoring, and data serialization
and formatting, that were spread over a number of different ASICs for
the original LHC developments. However, even in the analog realm some
consolidation has been achieved, such as the 130~nm ASIC developed for
LAr that combines the functions of both the preamplifiers and the shapers
from the original construction.
Of key importance to maintaining the
ability to develop ASICs to meet the challenges of future calorimeters
will be to maintain affordable access to the specialized ASIC
processes in industry, and to qualify these processes concerning
their radiation tolerance and, in some applications, also their
performance in cryogenic environments. A fortunate development has
been the typically increasing radiation tolerance of new ASIC
processes with smaller feature sizes; while the original LHC readout
ASICs exploited a number of specialized processes, or used
standard cells
and design rules that had to be explicitly developed to improve the
radiation tolerance, the HL-LHC developments can focus on
commercial
130~nm and 65~nm CMOS processes and use commercial standard cell
libraries. The move to ever smaller feature-size ASIC processes
also greatly helps reduce the power consumption. However, the
corresponding evolution to lower power rails presents a significant
challenge for the very frontend analog circuits that must
handle input signals over a very wide, often around 16-bit,
dynamic range.
Other challenges for the development of future calorimeter readouts
include powering systems, ranging from power supplies, to DC-DC
convertors and low dropout regulators (LDO) or on-chip
regulation, that can provide
the needed power in a practical and radiation-tolerant manner,
and high-speed optical links that can move off-detector the
huge data volumes generated by the calorimeter frontends. Optical
links will be discussed further in Section~\ref{sec:links}. Powering
has long proved a thorny issue at the LHC, and carefully evaluating
over many years
the radiation tolerance of commercial devices has clearly
demonstrated that the great majority would not survive the LHC
conditions. As a result, industrial
partnerships were launched for both the original LHC and for the
HL-LHC to develop radiation-tolerant LDOs.
\subsection{Electronics for Fast Timing}
Picosecond-level timing will be an important component of the next generation of particle physics detectors. The ability to add a 4$^{th}$ dimension to our measurements will help address the increasing complexity of events at hadron colliders and provide new tools for precise tracking and calorimetry for all experiments. Time is crucial for background rejection in dark matter searches and neutrino detectors. As resolution continues to increase, time will likely become an equal partner to position measurement in particle tracking and particle flow event fitting. All this has been enabled both by the rapid and continuous advance of fast electronics and the ability to generate fast signals with good signal/noise from a variety of solid state sensors, photodetectors, and micropattern gas-based detectors.
Fast silicon sensors with gain, (e.g. Low-gain Avalanche Detectors LGAD) and sensors without gain (e.g. 3D sensors), micro-pattern gaseous detectors, Cerenkov light and fast scintillators such as LYSO, microchannel plate (e.g. LAPPD), semiconductor-based photodetectors such as SPADs and SIPMs, and other sensors provide all very fast signals.
There are several R\&D efforts aimed at the development of fast ASIC electronics for future HEP applications with focus on using specific and advanced technology (e.g. SiGe, 28 and 22 nm CMOS) and implementing suitable concepts for the needed time resolution (e.g. full waveform digitation, TDC, monolithic solutions).
The design and optimization of the front-end amplifier is particularly important for fast electronics. The front end typically defines the signal/noise and thus the time jitter of the system. It can also consume significant power. Each design must be optimized for its environment, considering signal source, input capacitance required resolution, and subsequent processing and developed as element of a larger system design effort.
Fast timing applications put special emphasis on noise and rise time, which often requires higher front-end power. Increased pixel density to cope with required resolution and occupancy although somewhat balanced by lower load capacitance, also strains the power budget. Improved per hit time resolution may require more complex processing of the input waveform with corrections for delta rays, nonuniform ionization and varying weighting fields. This will require more complex, power hungry on-chip calculations or increased waveform information sent to downstream processing.
For ultimate time resolution non-homogenous sensor responses must be compensated, either on-detector or as part of the processing chain. This is an opportunity to employ emerging technologies such as machine learning to front or back end systems to take advantage of all possible information.
Most of the sub-75 ps systems demonstrated to date have either been in small, well constrained systems, or in beam tests. Distribution and maintenance of the clock system will be a challenge for large systems. In large systems timing must be monitored and temperature and aging effects compensated. Optical transceivers can have several ps/degree delay variation. This has been considered in detail for Xilinx Ultrascale transceivers and techniques have been developed to provide 1 ps phase resolution.
Using a combination of these instrumentation techniques and developments, including Constant Fraction Discrimination (CFD), waveform sampling combined with precise clock distribution and newly developed sensors we expect that it will be reasonable for future fast timing detector sub-systems to set a 10pS timing resolution goal that will allow for unprecedented accuracy and significantly improve the physics reach of next generation high rate, collider detectors. We anticipate that the grand challenge of measuring particles with a
resolution of about 1 ps may be possible and would provide revolutionary physics opportunities.
\subsection{Optical Links}
The dramatic increase in channel count that has resulted
from detectors with ever finer granularity, plus the need to
deliver in real time either all or at least more of the full-granularity,
full-precision detector readout data, has placed increasing
demands on the optical links used to transmit the data from
the on-detector frontend electronics to the off-detector
digital processing and TDAQ systems. The radiation-tolerance
specifications for the detector mounted links has led to reliance on custom
developments, for the most part, though the original LHC detectors
did use some commercial link components which were tested to be
sufficiently radiation hard.
The radiation requirements plus the reliance on custom solutions have
resulted in link speeds per fiber which are significantly lower than
used in commercial systems. The original LHC detectors employed
on-detector optical links from several 100~Mbps up to 1.6~Gbps per fiber.
The per-fiber bandwidth increased
to 5~Gbps for the recently completed Phase I upgrade of the LHC experiments,
and currently to 10~Gbps for the ongoing HL-LHC developments. This substantial increase in
per-fiber bandwidth has, however, not kept pace with the growth in
data volume. For example, the original ATLAS LAr readout used a
single 1.6~Gbps link per 128 channels, while the corresponding HL-LHC readout
will need 22 fibers at 10~Gbps each for 128 channels. The
relatively low (up to 10~Gbps) per-fiber bandwidth, compared to industry rates of
up to 56~Gbps, results
in large fiber plants and an inefficient use of the SerDes resources
of the fast (and expensive) FPGAs that are typically used to
receive and process the on-detector digital data once it arrives off-detector and
away from radiation.
Realization of a functional optical link requires several building
blocks, including a data fan-in and serializer, combined with a
electrical-to-optical conversion coupled to an optical module that
couples to the fibers.
For serializers, the custom-designed 5~Gbps GBT was developed by CERN in 128~nm
CMOS, predominantly for use in the Phase I upgrades of the LHC detectors.
Following this successful mode, the 10~Gbps lpGBT was
then developed in 65~nm CMOS, and will be used in most HL-LHC on-detector electronic
readout applications.
R\&D is underway that aims to increase the bandwidth by a factor of two
in the short term, still within 65~nm CMOS, and then to move
to 56~Gbps utilizing 28~nm CMOS.
The critical components for the optical modules themselves
have been mostly
satisfied by commercially available VCSELs and pin diodes, which
must be painstakingly selected for radiation tolerance. However, a custom
optical module that integrates these functions plus the optical
connections is still required, due mostly to the tight spatial and mechanical
constraints, as well as material budget, imposed, in particular,
by the inner detectors at the LHC and HL-LHC.
It is apparent that future detector readouts will continue to deliver increasingly
large data volumes. Meeting the corresponding readout bandwidth requirements,
and in particular for on-detector environments with a significant
radiation-tolerance requirement, poses a number of
very significant challenges. Meeting
these needs will require ongoing R\&D, to facilitate the continued evolution
to higher bandwidths, and in particular per-fiber bandwidths.
\subsection{Smart Sensors Using Artificial Intelligence}
Modern particle physics experiments and accelerators, exploring nature at increasingly finer spatial and temporal scales in extreme environments, create massive amounts of data which require real-time data reduction as close to the data source and sensors as possible. The demand for increasingly higher sensitivity in experiments, along with advances in the design of state-of-the-art sensing systems, has resulted in rapidly growing big data pipelines such that transmission of acquired data for offline processing via conventional methods is no longer feasible. Data transmission is commonly much less efficient than data processing. Therefore, placing data compression, extracting waveform features and processing as close as possible to data creation while maintaining physics performance is a crucial task in modern physics experiments. The implementation of Artificial intelligence (AI) and machine learning (ML) in near-detector electronics is a natural path to add capability for detector readout. It will enable more powerful data compression and filtering which better preserves the physics content of experiments, reduces downstream system complexity, and provides fast feedback and control loops. While the application of AI/ML is growing rapidly in science and industry, the needs of particle physics for speed, throughput, fidelity, interpretability, and reliability in extreme environments require advancing state-of-the-art technology in use-cases that go far beyond industrial and commercial applications.
AI, and more specifically ML, has recently been demonstrated to be a powerful tool for data compression, waveform processing, and analysis in physics and many other domains. While progress has been made towards generic real-time processing through inference including boosted decision trees and neural networks (NNs) using FPGAs (Field Programmable Gate Arrays) in off-detector electronics, ML methods are not commonly used to address the significant bottleneck in the transport of data from front-end ASICs to back-end FPGAs.
Embedding ML as close as possible to the data source has a number of potential benefits
\begin{itemize}
\item ML algorithms can enable powerful and efficient non-linear data reduction or feature extraction techniques, beyond simple summing and thresholding, which better preserves the physics content that would otherwise be lost;
\item This could in turn reduce the complexity of down stream processing systems which would then have to aggregate less overall information all the way to offline computing;
\item This enables real-time data filtering and triggering like at the LHC and the EIC which would otherwise not be possible or be much less efficient; or in the case of cryogenic systems, creates less data bandwidth from cold to warm electronics and thus reduce the system complexity;
\item Furthermore, intelligent processing as close as possible to the source will enable faster feedback loops. For example, in continuous learning applications, if the data is part of a control or operations loop where feedback is needed such as in quantum information systems or particle accelerators.
\end{itemize}
With rapidly growing machine learning applications comes the acute need for their efficient hardware implementations. Most of the efforts are focused on digital CMOS technology, such as implementations based on general-purpose TPUs/GPUs, FPGAs, and more specialized ML hardware accelerators. The steady improvements in such hardware platforms' performance and energy efficiency over the past decade are attributed to the use of very advanced, sub-10-nm CMOS processes and holistic optimization of circuits, architectures, and algorithms.
The opportunities for building more efficient hardware may come from biological neural networks. Indeed, it is believed that the human brain, with its $>$1000$\times$ more synapses than the weights in the largest transformer network, is extremely energy efficient, which serves as a general motivation for developing neuromorphic hardware. There is a long history of CMOS neuromorphic circuits. However, unleashing the full potential of neuromorphic computing might require novel, beyond-CMOS device and circuit technologies that allow for more efficient implementations of various functionalities of biological neural systems.
There are several ongoing R\&D efforts in our community focused on on-detector AI/ML and the key elements of both the design and implementation, and the design tools themselves. Though early in the exploration of these applications, the existing work highlights the needs for configurable and adaptable designs and open-source and accessible design tools to implement efficient hardware AI. Novel ML techniques are particularly important for resource-constrained real-time AI; advancing design, implementation, and verification tools which accelerate the development process; and emerging microelectronics technologies which could provide large gains in efficiency and speed. Different classes of future applications require dedicated investments to advance our capabilities in this field.
Many emerging devices and circuit technologies are currently being explored for neuromorphic hardware implementations.
Neuromorphic inference accelerators utilizing analog in-memory computing based on floating gate memories are perhaps the closest to widespread adoption, given the maturity of such technology, the practicality of its applications, and competitive performance with almost 1000x improvement in power as compared to conventional (digital CMOS) circuit implementations. The radiation hardness of these techniques and their applicability for robust performance in extreme environments is yet to be evaluated.
\subsection{Cryogenics Readout}
Many applications, including direct Dark Matter detection
and neutrino experiments, require electronics
designed to perform within cryogenic environments.
Some operate at deep cryogenic levels going from liquid helium temperatures at a few Kelvin down
to milli-Kelvin.
Time projection chambers (TPCs) used in neutrino detection and dark matter searches use noble liquids as a target material. Most current generation TPC's keep the active electronics in the warm, outside the cryostat.
The sheer scale of the DUNE LArm TPC being designed today makes it impracticalto
bring all the raw analog detector signals into the warm, and instead embeds the active front end
electronics in the cold. For the DUNE wire-based LAr TPC readout, the required cold functionality is achieved by a set of 3 custom ASICs, one that amplifies and provides analog filtering,
one that digitizes at 2~MSPS, and one that collects and serializes the data for transmission over copper cables to the warm electronics outside the cryostat.
The DUNE near detector will use a low power pixel readout utilizing the self-triggering LarPix 64-channel pixel ASIC submerged in LAr. Four programmable readout paths on the chip allow a board-level fault tolerant readout path. Track reconstruction results from prototype boards populated with 100 ASICs each have shown very promising physics results.
A second very low power readout is being investigated by the Qpix Collaboration that utilizes a novel approach to record the times of arrival of a fixed unit of charge, enabling offline reconstruction of the ionization current sensed at the pixel with a sub-femto Coulomb unit charge sensitivity.
Deep-cryogenic CMOS circuits and systems have seen rapid development in recent years, with quantum computing being the primary technological and economic driver. Early work focused on studying and modeling the properties of devices, including MOSFETs, resistors, and capacitors, in various CMOS technologies at cryogenic temperatures. The results suggested that devices in modern nm-scale fabrication technologies (including bulk CMOS, silicon-on-insulator, and FinFET) function successfully at temperatures as low as 50 mK. The main deleterious effects of cryogenic operation on nanoscale MOSFETs include a moderate increase in threshold voltage and degradation in 1/f noise and matching properties, both of which can be overcome using well-known precision circuit design techniques. A potentially more serious problem is the self-heating of such devices due to internal power dissipation. For example, a recent study shows that the channel temperature of 40~nm bulk CMOS transistors can increase by over 40~K compared to a LHe ambient of 4.2 K when dissipating only 2 mW. Thus, integrated electrothermal modeling is an important requirement for successfully designing deep-cryogenic CMOS systems.
Given the availability of reliable cryogenic CMOS device models, research has focused on using these models to develop and test functional blocks necessary for qubit control and readout, including cryogenic frequency synthesizers, low-noise amplifiers, and circulators. Cryogenic operation of embedded memory, including standard SRAM cells, has also been demonstrated. The availability of these building blocks has motivated the recent development of complete cryogenic CMOS qubit control and readout interface and monolithic quantum processors that integrate on-chip silicon charge qubits with CMOS readout electronics.
Precision sensing is another major driver for cryogenic CMOS circuits and systems where ultra-low-noise analog front ends is a major application area.
\subsection{RF Electronics}
RF electronics utilizes the RF domain to sense or control EM radiation well below ionization energies to make highly sensitive measurements of natural phenomena. The sophistication and sensitivity of RF related detection systems has improved dramatically with advances in wireless communications. HEP now has the opportunity to probe electromagnetic field signals measuring amplitude, phase, frequency, and polarization with unprecedented signal-to-noise and orders-of-magnitude improvement in signal processing throughput per unit of power consumption.
Combining RF A/D, D/A high precision and bandwidth performance and High speed FPGA's to readout arrayed superconducting sensors such as: Transition Edge Sensors TES, Kinetic Induction Detectors KID and superconducting bolometer systems with reduced the sensor size and will give us a better view of the universe.
Measurements of the extreme red shifted 21\,cm (1420 MHz) hyperfine transition of neutral atomic hydrogen are helping researchers to explore the early Universe searching in the red shifted range of 10-500 MHz inferring times before the creation of stars where a homogenous mix of materials allow robust theoretical predictions to be tested. The IF7 RF white paper describes the sophisticated very low noise techniques that are required to achieve the necessary electronics noise levels. To achieve reasonable levels of detection, undistorted signal backgrounds can only be found locally on the far side of the moon. Multiple proposals are being developed with the objective of installing sensitive antennae and electronics there with lunar orbiting satellite relay stations. The results of these explorations will benefit the ongoing development of cosmological models and may be an indicator of new physics.
\newpage
\bibliographystyle{JHEP}
\input{bibliography}
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
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We want to produce Oscar-worthy shows: Ali Hussein, Eros Now
Counterpoint Technology's latest report on the OTT market in India, has brought much cheer to the Eros Now camp. As per the report, the on-demand South Asian entertainment video service from Eros International had the most engaged users, with 68 per cent of its users indicating that they watch content on the platform daily. The platform continues to thrive through partnerships. In India, it partnered with Xiaomi for pre-installation on smart TVs. Eros Now has the highest percentage of its users consuming content on Smart TVs. A total of 27 per cent of Eros Now users watch content on Smart TVs. Eros Now also remains the only major Indian OTT platform to partner with Apple for its' new Apple TV+ service which will launch across the globe later this year. Further, the survey reveals that 9 per cent of Eros Now's users see content on the platform for more than 21 hours a week. This is the highest among all other OTT platforms in India.
The study also revealed that Eros Now has the largest share (59 per cent) of users in the 25-39 age bracket in Tier 2/3 cities, the highest among all major OTT platforms.
Content from comfort of home: 96% of Eros Now customers prefer watching content at home
Smart TV – the new choice: Eros Now has the highest percentage of its users watching content on Smart TV with a total of 27% – the highest among all other leading OTT platforms
Demographic trends: Eros Now has the highest share of business owners as users – over 14%
Importance of Xiaomi: More than half (53%) of Eros Now's users in Tier 2/3 cities own a Xiaomi smartphone.
Ali Hussein, COO, Eros Now, speaks to Adgully on Eros Now's strategy to tap the Tier 2 and 3 markets, leveraging social media and more. Reacting to Netflix's series, 'Roma', being nominated at the Oscars this year, Hussein informed that Eros Now had also been nominated at a global platform for the packaging of content for its show, 'SSW'. "One of our endeavours will be to produce shows worthy of being nominated for the Oscars," he affirmed.
What has led to the strong connection of Eros Now with users in Tier 2 and 3 cities?
The Originals are a great kind of perspective of the brand, the culture, and the story you want to believe. There is a lot more development of recreational kind of content today. That, coupled with movies that leave a mark on the audiences, infuse the on-demand behaviour pattern. We still get viewership on the platform for cult movies like 'Tanu Weds Manu', 'Bajirao Mastaani', etc., irrespective of what time or date of the year it is.
How you are leveraging your digital platform beyond Eros Now to remain on top of mind of consumers?
Social media plays a big role in ensuring visibility for our programming and since we are not India specific, it has also helped us in engaging with fans all around the world. We have 17-18 million subscribers on the YouTube channel and over 10 million Facebook followers. Chats, emails and push notifications also form part of our social media strategy.
With growing calls for regulating content in the digital space, do you think self-regulation is the way to go for OTT platforms?
I think in general self-regulation is a good space because it puts the responsibility in the hands of the creator. I feel there is no better judge than the customer themselves; and by that I don't mean customer in an individual capacity, but the customer on scale. Viewer feedback and their experience can form a strong basis for creators to be responsible about their content. Thus, it puts the responsibility in the hands of the creator and at the same time gives flexibility to the viewers and the platform.
With the rapidly growing OTT space – 30 platforms and counting, as per PwC – do you see the players co-existing or there will there be consolidation in the market some time in the future?
I think the platforms will co-exist right now. OTT is seeing the growth stage that any business goes through, in which you have the traditional players, innovators, the disrupters and all the various forms of organisations getting in. It is difficult to predict what will happen down the line, but right now they will co-exist in their own way.
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66% of Hotstar viewership came from audience beyond big metros
Behrouz Biryani's OOH campaign offers visual culinary treat to onlookers | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,535 |
{"url":"http:\/\/www.azimuthproject.org\/azimuth\/show\/Analytical%20hydrodynamics","text":"# Contents\n\n## Idea\n\nAnalytical hydrodynamics, as it is understood here, means the investigation of fluid flows using tools from topology and differential geometry. These tools enable us to describe properties and conservation laws of fluid flows that may be important for computational fluid dynamics, especially for climate models. Climate models need to solve the Navier-Stokes equations for the atmosphere and the oceans, they need to use discrete approximation schemes for this task. Such schemes can cause artefacts like the violation of conservation laws of the partial differential equations that they approximate. This phenomenon poses a huge problem for long running models like climate models.\n\nA climate model that violates the conservation of energy, for example, cannot be used to predict an average temperature (or, quite possible, to predict anything about the climate at all). Some currently used climate model suffer from these insufficiencies. Necessary corrections have to be added manually and heuristically and are commonly called \u201cflow corrections\u201d. It is a part of ongoing research to remove these kinds of corrections from climate models.\n\n## Details\n\n### Ideal Fluids\n\nThe flow of an ideal fluid, that is an incompressible, inviscid and homogenuous fluid, filling a certain domain, is from the mathematical viewpoint described by a geodesic on the group of diffeomorphisms of that domain that preserve volume elements. The geodesics are the geodesics of the Riemannian metric given by the kinetic energy.\n\nWe\u2019ll make all of this precise in the following:\n\nAs domain we take a compact Riemannian manifold $M$. The diffeomorphisms of $M$ form an infinite dimensional group $D\\left(M\\right)$. $D\\left(M\\right)$ is a Fr\u00e9chet manifold, so that some concepts from finite dimensional differential geometry may be defined on it.\n\nFor ideal fluids we\u2019ll actually look at the subgroup of diffeomorphisms that conserve a given volume form $\\omega$ on $M$:\n\n$\\mathrm{SDiff}\\left(M\\right):=\\left\\{f\\in D\\left(M\\right):{f}^{*}\\omega =\\omega \\right\\}$SDiff(M) := \\{ f \\in D(M): f^* \\omega = \\omega \\}\n\n$\\mathrm{SDiff}$ is clearly a subgroup, it is also a closed subgroup and therefore a Lie group.\n\nThe (infinite dimensional) Lie algebra of $\\mathrm{SDiff}\\left(M\\right)$ is the vector space of all vector fields on $M$ with zero divergence.\n\n### Quick Reminder of Differential Geometry\n\n#### Divergence, Pullback\n\nLet M be a smooth orientable Riemannian manifold of dimension n. A volume form $\\omega$ is a n-form that vanishes nowhere. In ${\u211d}^{3}$ with cartesian coordinates $x,y,z$ the canonical example would be\n\n$\\omega =dx\\wedge dy\\wedge dz$\\omega = d x \\wedge d y \\wedge d z\n\nThe dual basis of $dx$ etc. is denoted by ${\\partial }_{x}$ etc. in our example.\n\nThe divergence of a vector field $X$ with respect to a volume form $\\omega$ is the unique scalar function $\\mathrm{div}\\left(X\\right)$ such that:\n\n$\\mathrm{div}\\left(X\\right)\\omega =d\\left({\\iota }_{X}\\omega \\right)$div(X) \\omega = d(\\iota_X \\omega)\n\nWhen we use our example we\u2019d write of course\n\n$X={f}_{1}{\\partial }_{x}+{f}_{2}{\\partial }_{y}+{f}_{3}{\\partial }_{z}$X = f_1 \\partial_x + f_2 \\partial_y + f_3 \\partial_z\n\nand the divergence of X would be\n\n$\\mathrm{div}\\left(X\\right)={\\partial }_{x}{f}_{1}+{\\partial }_{y}{f}_{2}+{\\partial }_{z}{f}_{3}$div(X) = \\partial_x f_1 + \\partial_y f_2 + \\partial_z f_3\n\nwhich we get if we plug in the expression for $X$ into the formula $d\\left({\\iota }_{X}\\omega \\right)$.\n\nGiven two manifolds $M,N$ and a differentiable map $f:M\\to N$, we can pull back a differential form $\\omega$ on $N$ to one on $M$ via\n\n${f}^{*}{\\omega }_{p}\\left({v}_{1},...,{v}_{n}\\right):={\\omega }_{f\\left(p\\right)}\\left(df\\left({v}_{1}\\right),...,df\\left({v}_{n}\\right)\\right)$f^{*} \\omega_p (v_1, ..., v_n) := \\omega_{f(p)} (d f(v_1), ..., d f(v_n))\n\n#### Levi-Civita Connection and Geodesics\n\nOn a Riemannian manifold $M$ with tangential bundle $\\mathrm{TM}$ there is a unique connection, the Levi-Civita connection, with the following properties for vector fields $X,Y,Z\\in \\mathrm{TM}$:\n\n$Z\u27e8X,Y\u27e9=\u27e8{\\nabla }_{Z}X,Y\u27e9+\u27e8X,{\\nabla }_{Z}Y\u27e9\\phantom{\\rule{thickmathspace}{0ex}}\\text{(compatibility with the metric)}$Z \\langle X, Y \\rangle = \\langle \\nabla_Z X, Y \\rangle + \\langle X, \\nabla_Z Y \\rangle \\; \\text{(compatibility with the metric)}\n${\\nabla }_{X}Y-{\\nabla }_{Y}X=\\left[X,Y\\right]\\phantom{\\rule{thickmathspace}{0ex}}\\text{(torsion freeness)}$\\nabla_X Y - \\nabla_Y X = [X, Y] \\; \\text{(torsion freeness)}\n\nIf we combine both formulas we get\n\n$2\u27e8{\\nabla }_{X}Y,Z\u27e9=X\u27e8Y,Z\u27e9+Y\u27e8Z,X\u27e9-Z\u27e8X,Y\u27e9+\u27e8\\left[X,Y\\right],Z\u27e9-\u27e8\\left[Y,Z\\right],X\u27e9+\u27e8\\left[Z,X\\right],Y\u27e9$2 \\langle \\nabla_X Y, Z \\rangle = X \\langle Y, Z \\rangle + Y \\langle Z, X \\rangle - Z \\langle X, Y \\rangle + \\langle [X, Y], Z \\rangle - \\langle [Y, Z], X \\rangle + \\langle [Z, X], Y \\rangle\n\nIf the scalar products are constant along every flow, i.e. the metric is invariant, then the first three terms on the right hand side vanish, so that we get\n\n$2\u27e8{\\nabla }_{X}Y,Z\u27e9=\u27e8\\left[X,Y\\right],Z\u27e9-\u27e8\\left[Y,Z\\right],X\u27e9+\u27e8\\left[Z,X\\right],Y\u27e9$2 \\langle \\nabla_X Y, Z \\rangle = \\langle [X, Y], Z \\rangle - \\langle [Y, Z], X \\rangle + \\langle [Z, X], Y \\rangle\n\nThis latter formula can be written in a more succinct way if we introduce the coadjoint operator. Remeber the adjoint operator defined to be\n\n${\\mathrm{ad}}_{X}Z=\\left[X,Z\\right]$ad_X Z = [X, Z]\n\nWith the help of the scalar product we may define\n\n$\u27e8{\\mathrm{ad}}_{X}^{*}Y,Z\u27e9:=\u27e8Y,{\\mathrm{ad}}_{X}Z\u27e9=\u27e8Y,\\left[X,Z\\right]\u27e9$\\langle ad^*_X Y, Z \\rangle := \\langle Y, ad_X Z \\rangle = \\langle Y, [X, Z] \\rangle\n\nThen the formula above for the covariant derivative can be written as\n\n$2\u27e8{\\nabla }_{X}Y,Z\u27e9=\u27e8{\\mathrm{ad}}_{X}Y,Z\u27e9-\u27e8{\\mathrm{ad}}_{Y}^{*}X,Z\u27e9-\u27e8{\\mathrm{ad}}_{X}^{*}Y,Z\u27e9$2 \\langle \\nabla_X Y, Z \\rangle = \\langle ad_X Y, Z \\rangle - \\langle ad^*_Y X, Z \\rangle - \\langle ad^*_X Y, Z \\rangle\n\nSince the inner product is nondegenerate, eliminating $Z$ leads to\n\n$2{\\nabla }_{X}Y={\\mathrm{ad}}_{X}Y-{\\mathrm{ad}}_{X}^{*}Y-{\\mathrm{ad}}_{Y}^{*}X$2 \\nabla_X Y = ad_X Y - ad^*_X Y - ad^*_Y X\n\nA geodesic curve is one whose tangent vector $X$ is transported parallel to itself, that is we have\n\n${\\nabla }_{X}X=0$\\nabla_X X = 0\n\nUsing the formula for the covariant derivative for an invariant metric above we get\n\n${\\nabla }_{X}X=-{\\mathrm{ad}}_{X}^{*}X=0$\\nabla_X X = - ad^*_X X = 0\n\nas a reformulation of the geodesic equation. For time dependent dynamical systems, we have the time axis as an additional dimension and every vector field has ${\\partial }_{t}$ as an additional summand. So, in this case we get as geodesic equation (again: for an invariant metric)\n\n${\\nabla }_{X}X={\\partial }_{t}X-{\\mathrm{ad}}_{X}^{*}X=0$\\nabla_X X = \\partial_t X - ad^*_X X = 0\n\n### Ideal Fluids Continued\n\nThe Euler viewpoint of fluids is that there are fluid packages or \u201cparticles\u201d. The fluid flow is described by specifying where each package or particle is at a given time t. When we start with a time ${t}_{0}=0$ on a given manifold $M$, the flow of every fluid package is decribed by a path on $M$ parameterized by time, and for every time $t>{t}_{0}$ there is a diffeomorphism ${g}_{t}$ of $M$ defined by the requirement that it maps the initial position of every fluid package to the position at time $t$.\n\nTo be continued\u2026\n\n## Examples\n\n### Burgers\u2019 Equation as Geodesic Equation\n\nIt is possible to derive Burgers equation as the geodesic equation of the diffeomorphism group ${\\mathrm{DS}}^{1}$ of the circle ${S}^{1}$. See this blog post.\n\n### Hamiltonian Formulation\n\nWe can turn the linear space of divergence free vector fields into a Lie algebra $\ud835\udd24$ by giving it the negative Jacobi-Lie bracket:\n\n$\\left[v,w\\right]=\\sum _{j=1}^{n}\\left({w}_{j}{\\partial }_{j}v-{v}_{j}{\\partial }_{j}w\\right)$[v, w] = \\sum_{j = 1}^n \\left( w_j \\partial_j v - v_j \\partial_j w \\right)\n\nTODO: explain why it is the negative of the usual definition (left Lie algebra bracket).\n\nWe also have a scalar product on $\ud835\udd24$:\n\n$\u27e8v,w\u27e9\u2254{\\int }_{M}v\\cdot wd\\mu$\\langle v, w \\rangle \\coloneqq \\int_M v \\cdot w d \\mu\n\nRemember from last time that one can define the directional derivative on Fr\u00e9chet spaces just like in finite dimensions:\n\nLet $F$ and $G$ be Fr\u00e9chet spaces, $U\\subseteq F$ open and $P:U\\to G$ a continuous map. The derivative of $P$ at the point $f\\in U$ in the direction $h\\in F$ is the map\n\n$DP:U\u00d7F\\to G$D P: U \\times F \\to G\n$DP\\left(f\\right)h\u2254\\underset{t\\to 0}{\\mathrm{lim}}\\frac{1}{t}\\left(P\\left(f+th\\right)-P\\left(f\\right)\\right)$D P(f) h \\coloneqq \\lim_{t \\to 0} \\frac{1}{t} ( P(f + t h) - P(f))\n\nFor a real valued function $T$ of $\ud835\udd24$, the derivative $DT$ eats two vector fields and spits out a real number. If you have a derivative $DT$ and a fixed vector field $\\delta v$, you can determine for every vector field $u$ another vector field $\\frac{\\delta T}{\\delta v}\\left(u\\right)$ by requiring that\n\n$DT\\left(u,\\delta v\\right)=\u27e8u,\\frac{\\delta T}{\\delta v}\\left(u\\right)\u27e9$D T (u, \\delta v) = \\langle u, \\frac{\\delta T}{\\delta v} (u) \\rangle\n\nholds. I used the funny $\\delta$\u2019s to match the notation of\n\n\u2022 Jerrold E. Marsden, Tudor S. Ratiu: \u201cIntroduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems\u201d, 2nd edition, Springer, New York, 1999\n\nWe can now define the ideal fluid bracket which plays the role of the Lie-Poisson bracket for real valued functions $T,S$ of $\ud835\udd24$:\n\n$\\left\\{T,S\\right\\}\\left(u\\right)\u2254{\\int }_{M}u\\cdot \\left[\\frac{\\delta T}{\\delta u},\\frac{\\delta S}{\\delta u}\\right]d\\mu$\\{ T, S \\} (u) \\coloneqq \\int_M u \\cdot \\left[ \\frac{\\delta T}{\\delta u}, \\frac{\\delta S}{\\delta u} \\right] d \\mu\n\nWe choose as energy function, the Hamiltonian $H$, simply the kinetic energy:\n\n$H\\left(v\\right)\u2254\\frac{1}{2}{\\int }_{M}\\parallel u{\\parallel }^{2}d\\mu$H(v) \\coloneqq \\frac{1}{2} \\int_M \\| u \\|^2 d \\mu\n\nThen we can show that\n\n$\\stackrel{\u02d9}{F}=\\left\\{F,H\\right\\}$\\dot{F} = \\{F, H \\}\n\nfor all functions $F$ is equivalent to Euler\u2019s equation.\n\n## References\n\n\u2022 V.I. Arnold, ; B.A. Khesin: Topological methods in hydrodynamics. (Springer 1998, ZMATH)\n\n\u2022 Boris Khesin, Robert Wendt: The geometry of infinite-dimensional groups. (Springer 2009, ZMATH)\n\n\u2022 Tsutomu Kambe: Geometrical theory of dynamical systems and fluid flows. Revised ed. (ZMATH)\n\nA paper dedicated to the Burgers equation:\n\n\u2022 Boris Khesin, Gerard Misiolek: Shock waves for the Burgers equation and curvatures of diffeomorphism groups (arXiv)","date":"2014-04-18 18:10:10","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 85, \"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\": 0.9536681771278381, \"perplexity\": 597.654096750251}, \"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-2014-15\/segments\/1397609535095.7\/warc\/CC-MAIN-20140416005215-00532-ip-10-147-4-33.ec2.internal.warc.gz\"}"} | null | null |
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Stay warm in the woods with this softshell hunting jacket. Its a smooth quilted shell filled with midweight insulation. Built to handle light showers on the stand, it has a water-repellent coating plus safety harness exit.
Rain Defender®, Durable water repellent—water beads up and rolls off.
Rain Defender® durable water repellent garments are just as functional and comfortable while fishing, hunting, working, or standing on the sidelines at a football game in a sudden November rain. Water will bead up and roll off your sweatshirt, jacket, overalls, pants, and more, so a little rain won't stop you from finishing the job without changing your gear.
The sweatshirt is very warm , and very durable. It is great if it's just a little cold out to wear.
Love this jacket, perfect for hunting. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,889 |
SuperUser Account
André joined the higher education sector for the first time on a full-time professional basis in October 2008 when he became the Director of the Transdisciplinary Programme at the University of Fort Hare. Between 1996 and 2008, he worked in and with independent public institutions responsible for navigating the crucial transitional phase in South Africa's contemporary history whilst also teaching part-time and on a visiting basis at universities across the world. Most of his post-1994 work and teaching focussed on processes aimed at deepening democracy, social justice and the promotion and protection of human rights. Joining the South African Human Rights Commission in 1996, André later on became its Deputy Chief Executive Officer.
On a unanimous recommendation from parliament, the president appointed André as a part-time Commissioner to the Commission for Gender Equality in 2008. He is a frequently invited speaker at South African and other universities abroad, as well as at academic conferences. André is presently based as the Director of the Institute for Reconciliation and Social Justice and advisor to the Rectorate. He was also appointed to serve as the Acting Vice-Rector (student affairs and external relations) until the end of December 2017. His research and postgraduate supervision focus on four areas: critical studies in higher education transformation; social justice, social cohesion and reconciliation; human rights, democracy and citizenship education; and public participation, critical citizenship and democracy development.
Total: 0 Comment(s) | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,087 |
Fate of Afghan women still tied to arranged matches
November 29, 2012 :: RSS :: Print :: Email
The Washington Post: Just before she leapt from her roof into the streets of Kabul, Farima thought of the wedding that would never happen and the man she would never marry. Her fiance would be pleased to see her die, she later recalled thinking. It would offer relief to them both. Farima, 17, had resisted her engagement to Zabiullah since it was ordained by her grandfather when she was 9. Full news...
Political Meddling Hampers Inquiry Into Kabul Bank Debacle
The New York Times: Persistent political interference has hampered efforts to unravel the colossal fraud at Kabul Bank, with President Hamid Karzai and a small panel of his top aides actually dictating to prosecutors who should be charged and who should not, according to Afghan and Western officials and the results of a public inquiry into the scandal. Full news...
Complaints about Schools Grow in Afghanistan
RFE/RL: Sheila, a 15-year-old Afghan girl, has spent years attending a refugee-camp school on the north side of Kabul. But she still does not know how to write her own name. "I am supposed to study the Koran, Dari, mathematics, Pashto, the English language -- altogether I am enrolled in 11 subjects," she says. "But there are no lessons at my school because the teachers come for just a few minutes. Then they leave. So we sit there doing nothing." Full news...
Human Rights Watch against Afghan government's amnesty for Taliban crimes
ANI: The Afghan government should not grant Taliban representatives amnesty from prosecution for serious crimes as part of talks with the insurgent group, Human Rights Watch has said. "Future government talks with the Taliban should not hinge upon denying justice to victims of war crimes and other abuses. Afghanistan's civilians should not be forced to choose between justice and peace," The News quoted Brad Adams, HRW Asia director, as saying. Full news...
Bomb Attack Hits Market In Khost, injures 19, kills 2 civilians
By RFE/RL's Radio Mashaal: At least 19 people have been injured in a bomb attack in the eastern Afghan city of Khost. Local officials say the bomb was planted on a bicycle and detonated early on November 26 in a market. Full news...
State land grabbers flee abroad
PAN: Three warlords accused of grabbing and selling state-owned land by using fake documents in the Paghman district of Kabul have fled the country to evade arrests, an official said on Monday. More than 50 acres of land, allocated for the Qargha Park, was occupied before being sold, Deputy Attorney General Noor Habib Jalal told a news conference in Kabul. Full news...
Sharp rise in crimes against women
Killid Group: On Oct 12, three people were arrested in the murder of a woman, Mah Gul, at her home in Shalbafan Village, Injil district, Herat. The woman's head had been cut off. The police arrested her husband, mother- and father-in-law and a person who assisted in the crime. The dead woman's brother,who took her body to the office of the Women's Affairs Department in Herat City, says she was killed by her husband and his family. Full news...
Drugs in prison
Killid Group: Polecharkhi prisoners suffer from sexually transmitted diseases and drug abuse. Killid interviewed prisoners and a doctor in the Kabul prison to find that opium addiction and diseases like HIV-Aids are rampant among the 7,000 inmates. While 70 prisoners have been diagnosed with syphilis, 150 of the 700 prisoners on drugs were injecting the drug, according to Dr Hemat who leads a medical group in Polecharkhi. Full news...
Burns unit brides tell story of Afghan abuse
Scotland on Sunday: Waheeda cannot now explain how she reached the final, terrible decision to set herself alight. She does remember the months of beatings and her brothers-in-laws' abuse. But the moments before she poured oil over her legs outside the room where her in-laws were and ignited her clothes with a match are now clouded by 40 days of pain. Full news...
Afghan universities shut after sectarian clash
AFP: Afghanistan has closed down three major public universities in the capital Kabul for more than a week after sectarian clashes left one student dead and nearly 30 others wounded, an official said Sunday. The clashes erupted on Saturday after a ritual marking the Shiite Muslim festival of Ashura was interrupted by Sunni students. Full news...
2 killed, 60 wounded in suicide bombing attack in eastern Afghanistan
The Associated Press: A suicide attacker detonated a car laden with explosives Friday in eastern Afghanistan, killing two civilians and wounding about 60 others, officials said. Taliban spokesman Zabiullah Mujahid claimed responsibility for the bombing, saying in a statement that the attack was in response to the recent execution of four Taliban detainees at the Afghan government's main detention center in Kabul. Full news...
"I am a victim of revolution"
Killid Group: "I don't know what happiness is," says Qalam Gul who lost both legs and one hand in the civil war. From the remote area of Rod Khana in Nangarhar, Gul remembers the exact moment shrapnel changed his life forever. "It was 8 O'clock in the morning. I was having breakfast along with my sisters and brothers. There was bombing day and night. A rocket slammed into our house... Full news...
Afghanistan marks Universal Children's Day with sad tales
Xinhua: It is ironic that when the world marked the Universal Children's Day Tuesday to celebrate the joy of childhood, hundreds of Afghan children were seen scavenging in Kabul's dumps trying to eke out a living by selling whatever usable items to support their families. "I will be happy if I find some plastic packets, cardboard box or Pepsi cans to sell and earn some money," the nine-year-old Jawad told Xinhua in a brief interview. Full news...
Rise in Afghan poppy farming fuelled by high opium prices
The Guardian: The amount of Afghan farmland planted with opium poppies has increased by nearly 20% this year, after high prices in 2011 tempted more farmers into growing the drug. Blight and bad weather meant the harvest of opium in the world's biggest producer of "black gold" fell by a third, according to the United Nations annual opium survey. But in the longer run that shortage could help keep prices near record highs, fueling further expansion of poppy farming. Full news...
Afghans protest execution of 13 teenagers in Iran
Khaama Press: According to reports Iran has executed at least 13 Afghan nationals around two months ago. A number of the close relatives of the victims who gathered near provincial government compound urged the government officials to transfer the dead bodies of the victims from Iran to Afghanistan. Full news...
Police accused of robbing Afghan bank
Los Angeles Times: The bank robbers were men who were often seen around town in uniform – police uniforms. They were, in fact, police. Three Afghan National Police officers fled a bank in Afghanistan's Nuristan province after breaking in after hours and stealing more than 29 million Afghanis (about USD 550,000) late Friday night, according to Gen. Ghulamullah Nuristani, the provincial police chief. Full news...
Relentless Afghan conflict leaves traumatized generation
Reuters: On a low bed in a quiet, all-female hospital ward, a depressed Afghan teenager huddles silently under blankets, her mother close by. In a nearby room are men suffering from schizophrenia, delusions of persecution and power, anxiety and panic disorders. Among them are some of the unseen victims of the war in Afghanistan: a generation of people mentally damaged by their exposure to incessant conflict. Full news...
Afghan Sikhs protest over cremation
PAN: Members of the minority Sikh community rallied against residents of the Qalacha neighbourhood of Kabul for opposing the cremation of their relatives' bodies. Dozens of protestors in Pashtunistan Ward also accused the Afghan police and army of preventing them from burning their dead in line with their religious tradition. Full news...
Roadside Bomb Kills 17 wedding guests in Afghanistan
VOA: A roadside bomb has ripped through a vehicle in western Afghanistan, killing 17 civilians who were part of a wedding celebration. Afghan officials say Friday's blast occurred on a road in relatively peaceful Farah province. Most of the victims were women and children. At least 10 people were wounded in the attack. Full news...
Afghanistan: Unchecked Opium Production in Uruzgan
IWPR: Uruzgan province in central Afghanistan is fast becoming a major source of opium, and local informal powerbrokers are making millions of dollars from the trade. The authorities appear powerless to act against major figures in the trade, who have occupied large swathes of land that in theory belongs to the state and are reaping huge rewards from the poppy trade, backed by small private armies. Full news...
Kabul in bid to thwart airport cash smuggling worth 4.5bn USD
The National: Passengers flying out of Kabul carried with them more than USD 4.5 billion (Dh16.52bn) in cash last year, leading to new rules restricting the amount of foreign currency that travellers can take out of the country to 20,000 USD at a time. "I am very concerned about cash leaving Kabul Airport in dollars," said the central bank governor Noorullah Delawari. Full news...
Protestors want district officials involved in abductions, land grab and torture, fired
PAN: Nearly 200 people staged a rally in the Baghlan-i-Markazi district of northern Baghlan province on Tuesday against local officials of involvement in abductions, land grab and torture. The protestors gathered in Jar Khoshk area, burning tyres and blocking the busy Baghlan-Kunduz highway for three hours. They called for the immediate sacking of senior district officials. Full news...
Afghanistan halts Helmand police fuel supplies after major theft
The Guardian: Senior Afghan officials are said to have discovered large-scale theft of fuel in Helmand and halted all deliveries to police in the province, compromising the ability of the force to operate in one of the Taliban's major strongholds. The cost of stolen or "misallocated" fuel in the province is thought to run into hundreds of millions of dollars. One official estimated its worth at 600m USD (380m GBP)... Full news...
Women in Afghanistan: A Human Rights Tragedy a Decade after September 11
The Global Research in International Affairs (GLORIA) Center: Over a decade after the September 11, 2001, attacks in the United States and the military campaign in Afghanistan, there is some good news, but still much bad news pertaining to women in Afghanistan. The patterns of politics, military operations, religious fanaticism, patriarchal structures and practices, and insurgent violence continue to threaten girls and women in the most insidious ways. Full news...
ISAF airstrike injures children in Kunar
PAN: Three children were injured during an airstrike by the International Security Assistance Force (ISAF) in the Watapur district of eastern Kunar province, an official said on Sunday. The air raid targeting a rebel hideout was conducted in Qaro area, the governor's spokesman, Wasifullah Wasifi, told Pajhwok Afghan News. But he had no information about militants' casualties. Full news...
Bomb kills Afghan family including hours-old baby
Reuters: A roadside bomb killed a family of six, including a baby born just hours before, in eastern Afghanistan on Sunday, local officials said. The family was leaving a maternity hospital in Khost province in a pick-up truck when the bomb exploded, said a statement from the office of the provincial governor. Full news...
Jihadi Council Distributing Weapons to "Units": Herat Spox
November 9, 2012 :: RSS :: Print :: Email
TOLOnews.com: The Jihadi Council led by Afghanistan's Energy and Water Minister Mohammad Ismail Khan has started distributing weapons to its members in western Herat province, the provincial spokesman Mahiuddin Noori said Wednesday. Noori warned that armed groups apart from the Afghan security forces are against the law and the distribution of weapons is a criminal offence. Full news...
Afghan corruption, and how the U.S. facilitates it
The Washington Post: When it comes to corruption in Afghanistan, the time may be now for the United States to look in the mirror and see what lessons can be learned from contracting out parts of that war. On Sept. 30, Afghan President Hamid Karzai told CBS's "60 Minutes" that the corruption wracking his government and its people has been at a level "not ever before seen in Afghanistan." Full news...
Afghanistan bomb attacks 'kill 20'
BBC News: At least 20 people, including 12 civilians, have been killed in four separate militant attacks in Afghanistan, officials say. Women and children were among 10 killed when a minibus hit a roadside bomb in southern Helmand province. Other bombings killed five Afghan soldiers in Laghman in the east, three police in Kandahar and two boys in Zabul province. Full news...
Brother of Kunduz MP Arrested for Hanging Wife
TOLOnews.com: The brother of a Kunduz lawmaker was arrested in the northern province for allegedly hanging his wife on Monday, officials told TOLOnews. Zarghona, who was married to the brother of MP Shukria Paikan, was killed in her home last night by hanging. Kunduz police said Zarghona's husband used a rope to hang his wife and was being detained until investigations were complete. Full news...
< Previous 1 2 3 ... 13 14 15 Next > | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,089 |
#ifndef http_parser_h
#define http_parser_h
#define HTTP_PARSER_VERSION_MAJOR 1
#define HTTP_PARSER_VERSION_MINOR 0
#include <sys/types.h>
#if defined(_WIN32) && !defined(__MINGW32__) && \
(!defined(_MSC_VER) || _MSC_VER<1600) && !defined(__WINE__)
#include <BaseTsd.h>
#include <stddef.h>
typedef __int8 int8_t;
typedef unsigned __int8 uint8_t;
typedef __int16 int16_t;
typedef unsigned __int16 uint16_t;
typedef __int32 int32_t;
typedef unsigned __int32 uint32_t;
typedef __int64 int64_t;
typedef unsigned __int64 uint64_t;
#else
#include <stdint.h>
#endif
#if __cplusplus
namespace proxygen {
#endif /* __cplusplus */
/* Compile with -DHTTP_PARSER_STRICT=1 to parse URLs and hostnames
* strictly according to the RFCs
*/
#ifndef HTTP_PARSER_STRICT
# define HTTP_PARSER_STRICT 0
#endif
/* Compile with -DHTTP_PARSER_DEBUG=1 to add extra debugging information to
* the error reporting facility.
*/
#ifndef HTTP_PARSER_DEBUG
# define HTTP_PARSER_DEBUG 0
#endif
/* Maximium header size allowed */
#define HTTP_MAX_HEADER_SIZE (80*1024)
typedef struct http_parser http_parser;
typedef struct http_parser_settings http_parser_settings;
typedef struct http_parser_result http_parser_result;
/* Callbacks should return non-zero to indicate an error. The parser will
* then halt execution.
*
* The one exception is on_headers_complete. In a HTTP_RESPONSE parser
* returning '1' from on_headers_complete will tell the parser that it
* should not expect a body. This is used when receiving a response to a
* HEAD request which may contain 'Content-Length' or 'Transfer-Encoding:
* chunked' headers that indicate the presence of a body.
*
* http_data_cb does not return data chunks. It will be call arbitrarally
* many times for each string. E.G. you might get 10 callbacks for "on_path"
* each providing just a few characters more data.
*/
typedef int (*http_data_cb) (http_parser*, const char *at, size_t length);
typedef int (*http_cb) (http_parser*);
/* Request Methods */
enum http_method
{ HTTP_DELETE = 0
, HTTP_GET
, HTTP_HEAD
, HTTP_POST
, HTTP_PUT
/* pathological */
, HTTP_CONNECT
, HTTP_OPTIONS
, HTTP_TRACE
/* webdav */
, HTTP_COPY
, HTTP_LOCK
, HTTP_MKCOL
, HTTP_MOVE
, HTTP_PROPFIND
, HTTP_PROPPATCH
, HTTP_UNLOCK
/* subversion */
, HTTP_REPORT
, HTTP_MKACTIVITY
, HTTP_CHECKOUT
, HTTP_MERGE
/* upnp */
, HTTP_MSEARCH
, HTTP_NOTIFY
, HTTP_SUBSCRIBE
, HTTP_UNSUBSCRIBE
/* RFC-5789 */
, HTTP_PATCH
};
enum http_parser_type { HTTP_REQUEST, HTTP_RESPONSE, HTTP_BOTH };
/* Flag values for http_parser.flags field */
enum flags
{ F_CHUNKED = 1 << 0
, F_TRAILING = 1 << 3
, F_UPGRADE = 1 << 4
, F_SKIPBODY = 1 << 5
};
/* Map for errno-related constants
*
* The provided argument should be a macro that takes 2 arguments.
*/
#define HTTP_ERRNO_MAP(XX) \
/* No error */ \
XX(OK, "success") \
\
/* Callback-related errors */ \
XX(CB_message_begin, "the on_message_begin callback failed") \
XX(CB_path, "the on_path callback failed") \
XX(CB_query_string, "the on_query_string callback failed") \
XX(CB_url, "the on_url callback failed") \
XX(CB_fragment, "the on_fragment callback failed") \
XX(CB_header_field, "the on_header_field callback failed") \
XX(CB_header_value, "the on_header_value callback failed") \
XX(CB_headers_complete, "the on_headers_complete callback failed") \
XX(CB_body, "the on_body callback failed") \
XX(CB_message_complete, "the on_message_complete callback failed") \
XX(CB_reason, "the on_reason callback failed") \
XX(CB_chunk_header, "the on_chunk_header callback failed") \
XX(CB_chunk_complete, "the on_chunk_complete callback failed") \
\
/* Parsing-related errors */ \
XX(INVALID_EOF_STATE, "stream ended at an unexpected time") \
XX(HEADER_OVERFLOW, \
"too many header bytes seen; overflow detected") \
XX(CLOSED_CONNECTION, \
"data received after completed connection: close message") \
XX(INVALID_VERSION, "invalid HTTP version") \
XX(INVALID_STATUS, "invalid HTTP status code") \
XX(INVALID_METHOD, "invalid HTTP method") \
XX(INVALID_URL, "invalid URL") \
XX(INVALID_HOST, "invalid host") \
XX(INVALID_PORT, "invalid port") \
XX(INVALID_PATH, "invalid path") \
XX(INVALID_QUERY_STRING, "invalid query string") \
XX(INVALID_FRAGMENT, "invalid fragment") \
XX(LF_EXPECTED, "LF character expected") \
XX(INVALID_HEADER_TOKEN, "invalid character in header") \
XX(INVALID_CONTENT_LENGTH, \
"invalid character in content-length header") \
XX(HUGE_CONTENT_LENGTH, \
"content-length header too large") \
XX(INVALID_CHUNK_SIZE, \
"invalid character in chunk size header") \
XX(HUGE_CHUNK_SIZE, \
"chunk header size too large") \
XX(INVALID_CONSTANT, "invalid constant string") \
XX(INVALID_INTERNAL_STATE, "encountered unexpected internal state")\
XX(STRICT, "strict mode assertion failed") \
XX(PAUSED, "parser is paused") \
XX(UNKNOWN, "an unknown error occurred")
/* Define HPE_* values for each errno value above */
#define HTTP_ERRNO_GEN(n, s) HPE_##n,
enum http_errno {
HTTP_ERRNO_MAP(HTTP_ERRNO_GEN)
};
#undef HTTP_ERRNO_GEN
/* Get an http_errno value from an http_parser */
#define HTTP_PARSER_ERRNO(p) ((enum http_errno) (p)->http_errno)
/* Get the line number that generated the current error */
#if HTTP_PARSER_DEBUG
#define HTTP_PARSER_ERRNO_LINE(p) ((p)->error_lineno)
#else
#define HTTP_PARSER_ERRNO_LINE(p) 0
#endif
struct http_parser {
/** PRIVATE **/
unsigned char type : 2; /* enum http_parser_type */
unsigned char flags : 6; /* F_* values from 'flags' enum; semi-public */
unsigned char state; /* enum state from http_parser.c */
unsigned char header_state; /* enum header_state from http_parser.c */
unsigned char index; /* index into current matcher */
uint32_t nread; /* # bytes read in various scenarios */
int64_t content_length; /* # bytes in body (0 if no Content-Length header) */
/** READ-ONLY **/
unsigned short http_major;
unsigned short http_minor;
unsigned short status_code; /* responses only */
unsigned char method; /* requests only */
unsigned char http_errno : 7;
/* 1 = Upgrade header was present and the parser has exited because of that.
* 0 = No upgrade header present.
* Should be checked when http_parser_execute() returns in addition to
* error checking.
*/
char upgrade : 1;
#if HTTP_PARSER_DEBUG
uint32_t error_lineno;
#endif
/** PUBLIC **/
void *data; /* A pointer to get hook to the "connection" or "socket" object */
};
struct http_parser_settings {
http_cb on_message_begin;
http_data_cb on_url;
http_data_cb on_header_field;
http_data_cb on_header_value;
http_data_cb on_headers_complete;
http_data_cb on_body;
http_cb on_message_complete;
http_data_cb on_reason;
/* When on_chunk_header is called, the current chunk length is stored
* in parser->content_length.
*/
http_cb on_chunk_header;
http_cb on_chunk_complete;
};
enum http_parser_url_fields
{ UF_SCHEMA = 0
, UF_HOST = 1
, UF_PORT = 2
, UF_PATH = 3
, UF_QUERY = 4
, UF_FRAGMENT = 5
, UF_USERINFO = 6
, UF_MAX = 7
};
/* Result structure for http_parser_parse_url().
*
* Callers should index into field_data[] with UF_* values iff field_set
* has the relevant (1 << UF_*) bit set. As a courtesy to clients (and
* because we probably have padding left over), we convert any port to
* a uint16_t.
*/
struct http_parser_url {
uint16_t field_set; /* Bitmask of (1 << UF_*) values */
uint16_t port; /* Converted UF_PORT string */
struct {
uint16_t off; /* Offset into buffer in which field starts */
uint16_t len; /* Length of run in buffer */
} field_data[UF_MAX];
};
void http_parser_init(http_parser *parser, enum http_parser_type type);
size_t http_parser_execute(http_parser *parser,
const http_parser_settings *settings,
const char *data,
size_t len);
/* Returns a string version of the HTTP method. */
const char *http_method_str(enum http_method m);
/* Return a string name of the given error */
const char *http_errno_name(enum http_errno err);
/* Return a string description of the given error */
const char *http_errno_description(enum http_errno err);
/* Parse a URL; return nonzero on failure */
int http_parser_parse_url(const char *buf, size_t buflen,
int is_connect,
struct http_parser_url *u);
/* Pause or un-pause the parser; a nonzero value pauses */
void http_parser_pause(http_parser *parser, int paused);
#if __cplusplus
}
#endif /* __cplusplus */
#endif
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,215 |
{"url":"https:\/\/www.elastic.co\/blog\/what-are-you-breathing-analyzing-air-quality-data-with-elasticsearch-on-elastic-cloud-part-1","text":"Engineering\n\n# What Are You Breathing: Analyzing Air Quality Data with Elasticsearch on Elastic Cloud (Part 1)\n\nThe Elastic Stack has proven to be more than up to the task of collecting, indexing, and providing insightful information from data. Integrated information management is not only possible, but as we\u2019ll see over this series of posts, it can be a pleasant mission. We\u2019ll walk the whole path from raw and meaningless data to conclusions any modern city dweller can use to improve their daily life.\n\nThe increasing population in main cities across the world poses many challenges. Among these, air pollution is probably one of those with more impact on their inhabitants\u2019 health. In an effort to alert citizens and take emergency measures, some public institutions have deployed sensor fields that harvest information about the concentration of different pollutants across the city.\n\nSince these measurements are a responsibility of public institutions, it is not unusual that they get published for anyone to make use of them. That is the case of samples taken at the third-largest european city (by population, with over three million inhabitants): Madrid.\n\nLet\u2019s see how easy it is to use Elasticsearch to make these, otherwise opaque chemical measurements talk about the customs of Madrid inhabitants.\n\n## From CSV Files to Elasticsearch Documents\n\nFirst, we\u2019ll need to take a look at the data source. Madrid\u2019s City Hall maintains an Open Data Portal where it is possible to locate the hourly-air-quality-measurements data set (in Spanish).\n\nThere we can find an HTTP endpoint serving a CSV file which gets updated on an hourly basis and contains the measurements for the current day up to the last hour.\n\nEach row of the file corresponds to a (Location, Chemical) key pair and contains the hour-by-hour measurements for a whole day. Each hour value is captured in a column.\n\n ... STATION CHEMICAL ... MONTH DAY 0 AMMeasure 0 AMIs valid? ... 11 PMMeasure 11 PMIs valid? Number (Code) Code (Code) Number Number Number 'V' or 'F' (True\/False) Number 'V' or 'F' (True\/False)\n\nFields such as STATION and CHEMICAL are given as numeric values associated with geographical positions and compound formulation respectively. That association is provided via tables present at the data source site.\n\nOn the other hand, hourly measurements (i-th AM\/PM Measurement) and flags indicating if they are valid (i-th AM\/PM Is Valid?) are given as raw values. Units are provided by another table of the source specification while the validation flag can take V or F values representing the words \u201cVerdadero\u201d and \u201cFalso\u201d (\u201cTrue\u201d and \u201cFalse\u201d in Spanish).\n\nChemical sampling results are represented as measurements in space and time. Does that ring a bell? You got it right: time series of spatial events! That means rows are not events. On the contrary, up to 24 events are collected in each row \u2014 all of them sharing the same location and chemical compound.\n\nIf we encoded each event as JSON documents, they would look like the following example:\n\n{\n\"timestamp\": 1532815200000,\n\"location\": {\n\"lat\": 40.4230897,\n\"lon\": -3.7160478\n},\n\"measurement\": {\n\"value\": 7,\n\"chemical\": \"SO2\",\n\"unit\": \"\u03bcg\/m^3\"\n}\n}\n\n\nOptionally we could effortlessly enrich it with the World Health Organization (WHO) limits by just adding an additional field within the measurement sub-document. Breaking each CSV row into separate JSON documents makes them easier to understand, and even easier to ingest into Elasticsearch.\n\n{\n\"timestamp\": 1532815200000,\n\"location\": {\n\"lat\": 40.4230897,\n\"lon\": -3.7160478\n},\n\"measurement\": {\n\"value\": 7,\n\"chemical\": \"SO2\",\n\"unit\": \"\u03bcg\/m^3\",\n\"who_limit\": 20\n}\n}\n\n\nThe set of all documents matching this structure can be described using another JSON document. This is a mapping in Elasticsearch and we will use it to describe how documents are stored in a given index.\n\n{\n\"air_measurements\": {\n\"properties\": {\n\"timestamp\": {\n\"type\": \"date\"\n},\n\"location\": {\n\"type\": \"geo_point\"\n},\n\"measurement\": {\n\"properties\": {\n\"value\": {\n\"type\": \"double\"\n},\n\"who_limit\": {\n\"type\": \"double\"\n},\n\"chemical\": {\n\"type\": \"keyword\"\n},\n\"unit\": {\n\"type\": \"keyword\"\n}\n}\n}\n}\n}\n}\n\n\n## Deploy a Cluster in Seconds on Elastic Cloud\n\nAt this point, you could either set up an Elasticsearch cluster locally or start a 14-day free trial of the Elasticsearch Service on Elastic Cloud. Learn how to spin up a new cluster with just a few clicks. For this demonstration, I\u2019ll be using Elastic Cloud.\n\nOnce you\u2019re logged into Elastic Cloud, you\u2019ll need to deploy a new cluster. To size the cluster for this use case we should consider that a month\u2019s worth of JSON measurement events file takes around 34 MB of disk space (before indexing), so we can use the smallest cluster offered (1 GB RAM\/24 GB disk space). This small cluster should be enough to initially host our data. Elastic Cloud makes scaling easy, so if needed, we can always increase this size later, as well as change the number of availability zones or perform other changes in our cluster.\n\nIn less time than it takes to cook a microwave meal, we\u2019ll have our Elasticsearch cluster ready to receive and index our collection of measure events.\n\nGoing from the original CSV file to a collection of JSON documents coding measurements isn\u2019t a task anyone would like to manually perform (that sounds more like a sisyphean punishment). That\u2019s a task to be automated.\n\nFor this, let\u2019s start drafting an automation script to flatten the CSV table into JSON documents. Let\u2019s use Scala to do that:\n\n\u2022 As a language which allows centering on the data flow rather than on the program flow, it offers operations to easily transform collections of documents.\n\u2022 It comes with lots of JSON manipulation libraries.\n\u2022 Thanks to Ammonite, it is possible to write data manipulation scripts in the blink of an eye.\n\nThe following snippet of the extractor.sc script condenses the transformation logic:\n\n \/\/ Fetch the file from Madrid's city hall open data portal\nlazy val sourceLines = scala.io.Source.fromURL(uri).getLines().toList\n\/* The CSV first line contains the columns labels, it is not difficult\nto compute a map from label to position thus making the rest of the code\n\/\/ For each line, we'll produce several events, that's easilt via flatMap\nlazy val entries = sourceLines.tail flatMap { rawEntry =>\nval positionalEntry = rawEntry.split(\";\").toVector\nval entry = label2pos.mapValues(positionalEntry)\n\/* The first 8 positions are used to extract the information common to the\n24 hourly measurements. *\/\nval stationId = entry(\"ESTACION\").toInt\nval ChemicalEntry(chemical, unit, limit) = chemsTable(entry(\"MAGNITUD\").toInt)\n\/\/ Measurement values are contained in the 24 last columns\npositionalEntry.drop(8).toList.grouped(2).zipWithIndex collect {\ncase (List(value, \"V\"), hour) =>\nval timestamp = new DateTime(\nentry(\"ANO\").toInt,\nentry(\"MES\").toInt,\nentry(\"DIA\").toInt,\nhour, 0, 0\n)\n\/\/ And there it go: The generated event as a case class!\nEntry(\ntimestamp,\nlocation = locations(stationId),\nmeasurement = Measurement(value.toDouble, chemical, unit, limit)\n)\n}\n}\n\n1. Fetch the last published hourly report \u2014 containing the measurements taken up to an hour ago.\n2. For each row:\n1. Extract the fields common to all the events generated from the row \u2014 station id and measured chemical.\n2. Extract the measurements corresponding to the ones taken so far during the day (up to 24). Filter out those not labeled as valid measurements.\n3. For each of these, generate the measurement timestamp as the composition of the row date and the measurement column number. Combine the row common fields, the timestamp, and the registered value into a single event object (Entry).\n\nThe script continues serializing Entry objects as JSON documents and printing them as a succession of independent JSONs.\n\nExtractor.sc can receive arguments to instruct it to fetch the data to transform from other sources, such as local files, or to add actions required by Elasticsearch\u2019s Bulk API when uploading whole day files a time.\n\nextractor\n--bulkIndex\n--bulkType\n\n\nSo we\u2019ve just got a script which does the translation from CSV files to lists of documents. How can we index them? Easy, we have just to make a couple of calls to our cluster.\n\n## Index Creation\n\nFirst things first: We need to create the index. We already came up with a JSON for our document mappings and we can nest it within our index definition: .\/payloads\/index_creation.json\n\n{\n\"settings\" : {\n\"number_of_shards\" : 1\n},\n\"mappings\" : {\n\"air_measurements\" : {\n\"properties\" : {\n\"timestamp\": { \"type\": \"date\" },\n\"location\" : { \"type\" : \"geo_point\" },\n\"measurement\": {\n\"properties\": {\n\"value\": { \"type\": \"double\" },\n\"who_limit\": { \"type\": \"double\" },\n\"chemical\": { \"type\": \"keyword\" },\n\"unit\": { \"type\": \"keyword\" }\n}\n}\n}\n}\n}\n}\n\n\nThen ship it to our cluster\u2019s index creation endpoint:\n\ncurl -u \"$ESUSER:$ESPASS\" -X PUT -H 'Content-type: application\/json' \\\n\"$ESHOST\/airquality\" \\ -d \"@.\/payloads\/index_creation.json\" After which we\u2019ll end up with the airquality index. ## Bulk Upload The fastest way to load all that data into Elasticsearch is with the Bulk API. The idea is to establish a connection, upload a package of documents, and finish the operation. If we did the upload one document at a time, we would have to establish a TCP connection, send the document, receive confirmation, and close the connection for every measurement in every row of the CSV! That\u2019s too inefficient for me. As the Bulk API documentation establishes, you are required to upload a NDJSON file with two lines per document: \u2022 One with the action to perform at Elasticsearch \u2022 A second with the document affected by that action. The action we\u2019re interested in is index. Thus extractor.sc comes with two additional options to control of the index action and its appearance right before each document: \u2022 bulkIndex INDEX \u2014 If passed, it makes the extraction script to precede each document by an index into INDEX action. \u2022 bulkType TYPE \u2014 If passed after bulkIndex, completes the index action with the type the document should match. \/* The collection of events is then serialized and printed in the standard ouput. That way, we can use them as a ndjson file. *\/ val asJsonStrings = entries flatMap { (entry: Entry) => Some(bulkIndex).filter(_.nonEmpty).toList.map { index => val entryId = { import entry._ val id = s\"${timestamp}_${location}_${measurement.chemical}\"\njava.util.Base64.getEncoder.encodeToString(id.getBytes)\n}\n\/* Optionally, we can also serialize bulk actions to improve data transfer\nperformance. *\/\nBulkIndexAction(\nBulkIndexActionInfo(\n_index = index,\n_id = entryId,\n_type = Some(bulkType).filter(_.nonEmpty)\n)\n).asJson.noSpaces\n} :+ entry.asJson.noSpaces\n}\nasJsonStrings.foreach(println)\n\n\nThis way we can generate our giant NDJSON file with all the entries for the day:\n\ntime .\/extractor.sc --bulkIndex airquality --bulkType air_measurements > today_bulk.ndjson\n\n\nTaking 1.46 seconds, it has generated the file we can send to the Bulk API as follows:\n\ntime curl -u $ESUSER:$ESPASS -X POST -H 'Content-type: application\/x-ndjson' \\\n$ESHOST\/_bulk \\ --data-binary \"@today_bulk.ndjson\" | jq '.' The upload request took 0.98 seconds to complete. The total time for this method took 2.44 seconds (1.46 seconds from data fetching and transformation plus 0.98 seconds from the bulk upload request), which is 182 times faster than if we uploaded one document at a time. That\u2019s right, 2.44 seconds vs. 7 minutes and 26 seconds! An important takeaway here is: Use bulk uploads for processes indexing larger quantities of documents! ## From Data to Insight Congratulations! We\u2019ve reached the point where we have our city\u2019s air measurements indexed in Elasticsearch. That means, for example, we can easily search and fetch the data much more easily than having to download, extract, and manually search the information we are looking for. Take this case as an example \u2014 If after enjoying the contemplation of Las Meninas, we had to choose whether to: \u2022 Spend some time enjoying Madrid\u2019s sunny outdoors \u2022 Keep having a great time at El Prado museum We could ask Elasticsearch which option would be better for our health by requesting it to tell us what was the latest NO2 measurement taken at the closest weather-station within 1 km: .\/es\/payloads\/search_geo_query.json { \"size\": \"1\", \"sort\": [ { \"timestamp\": { \"order\": \"desc\" } }, { \"_geo_distance\": { \"location\": { \"lat\": 40.4142923, \"lon\": -3.6912903 }, \"order\": \"asc\", \"unit\": \"km\", \"distance_type\": \"plane\" } } ], \"query\": { \"bool\": { \"must\": { \"match\": { \"measurement.chemical\": \"NO2\" } }, \"filter\": { \"geo_distance\": { \"distance\": \"1km\", \"location\": { \"lat\": 40.4142923, \"lon\": -3.6912903 } } } } } } curl -H \"Content-type: application\/json\" -X GET -u$ESUSER:$ESPASS$ESHOST\/airquality\/_search -d \"@.\/es\/payloads\/search_geo_query.json\"\n\n\n{\n\"took\": 4,\n\"timed_out\": false,\n\"_shards\": {\n\"total\": 1,\n\"successful\": 1,\n\"skipped\": 0,\n\"failed\": 0\n},\n\"hits\": {\n\"total\": 4248,\n\"max_score\": null,\n\"hits\": [\n{\n\"_index\": \"airquality\",\n\"_type\": \"air_measurements\",\n\"_id\": \"okzC5mQBiAHT98-ka_Yh\",\n\"_score\": null,\n\"_source\": {\n\"timestamp\": 1532872800000,\n\"location\": {\n\"lat\": 40.4148374,\n\"lon\": -3.6867532\n},\n\"measurement\": {\n\"value\": 5,\n\"chemical\": \"NO2\",\n\"unit\": \"\u03bcg\/m^3\",\n\"who_limit\": 200\n}\n},\n\"sort\": [\n1532872800000,\n0.3888672868035024\n]\n}\n]\n}\n}\n\n\nTelling us that the weather station at El Retiro reports 5 \u03bcg\/m^3 of NO2. Not a bad result taking into account that the WHO limit is 200 \u03bcg\/m^3, so let\u2019s go have some tapas!\n\nTo be honest, I\u2019ve never found anyone pulling a laptop out and start writing cURL commands within the museum. However, these requests are so easy to code in almost any programming language that it\u2019s possible to provide frontend applications in a few days. That is, we already have a full-fledged analytics back end with our information index.\n\n## Visualizing the Invisible with Kibana\n\nWhat if we didn\u2019t need to write the application at all? What if, with the current cluster, we could start exploring the data by clicking our way into insightful information? Thanks to Kibana, that\u2019s definitely possible. We can go to our cluster management at cloud.elastic.co, and click on the link giving us access to our Kibana deployment:\n\nWith Kibana, we can create comprehensive visualizations and dashboards fed with the documents indexed in Elasticsearch.\n\nIndex patterns are the way we have to register indices into Kibana so they can be used by visualizations to pull data. Therefore, the first step before creating charts for our airquality index is to register it.\n\nOnce created, we can add our first visualization. Let\u2019s start with something simple: Plotting the evolution over time of the average concentration levels across the city for a chemical. Let\u2019s do it for NO2:\n\nFirst, we need to create a Line Chart where Y-Axis is an Average aggregation for the field measurement.value over hourly buckets represented on the X-Axis. To select the target chemical we can use Kibana\u2019s query bar which makes it easy to filter NO2 measurements and, by enabling autocomplete, we can get suggestions guiding us through the query definition process.\n\nFinally, with Time Range we choose the timespan of the visualized data.\n\nFew clicks, immediate results:\n\nOne of the more insightful charts we can use for this dataset are Coordinate Maps. As each measurement comes with the coordinates of the station which captured it, we can represent pollution hotspots. That is, shifting from averaging spatial entries in time buckets to averaging time entries in spatial locations. So the buckets are now Geohash aggregations over location, the field containing the point of measurement.\n\nIf we select the last hour time range, we can get an idea of what are the cleaner areas to visit at this time. Yearly time ranges tell us what are the cleaner areas on average and can help us, for example, to take a decision on where to buy a house to live a healthier life.\n\n## Scripted Fields\n\nSince our documents piggy back the WHO recommended levels for some chemicals, it is possible to visualize how unhealthy is the air. One way to do this is by using gauge visualization over the proportion of a measured level and the WHO limit. But that division wasn\u2019t performed when we loaded the data. That\u2019s not a problem as it is still possible to generate new fields from the indexed ones using the\u00a0Painless\u00a0scripting\u00a0language,\u00a0which is easy to understand and write by anyone who has ever used Java (since Kibana 6.4, it is also possible to get a preview of the results yielded by the Painless script).\n\nThen use them in our visualizations as if they were regular indexed fields:\n\nIt is worth noting how simple rules yield rich visualizations in Kibana. In the example above we:\n\n\u2022 Filtered documents \u2014 selecting only those for which there are WHO limits.\n\u2022 Used Split Groups and Term Aggregation over measurement.chemical.\n\nThus generating a gauge graph for each chemical for which there known WHO limits.\n\nKibana visualizations can be leveraged to build dashboards that aggregate visualizations, which is key to interpret and understand the state of a system in real time. In this case, the system is the atmosphere composition and its interactions with human activities.\n\nIn the dashboard above, a user can pick any chemical, a time period and get a pretty good idea of where and in what quantity that compound is polluting the atmosphere. Take a look yourself! (user: test, password: madrid_air).\n\nIt is also possible to get a general idea (same user and password) of Madrid\u2019s air quality.\n\nHow do these dashboards help? Let\u2019s take a look at any random week in March (From March 12 to March 18):\n\nDo these NOx (a compound produced by combustion in diesel engines) peaks tell us something about Madrid citizens habits? Indeed, they do. They occur twice per day\u2026\n\nOne around 8 am CEST and the second around 9 pm CEST. What we see here is the increasing use of diesel cars to move across the city when workers head to their workplaces. Almost no one uses them during working hours, and there is a surge of smoke when they finish their work at the office and go back home.\n\nIt is also interesting to see how O3 concentration increases as NOx reduces. O3 is a by-product of the reactions between NOx and organic compounds in the presence of sunlight so a correlation of NOx and O3 is expected.\n\nWe can also find that the general situation improves on weekends:\n\nSee how El Retiro park (a huge green area within the heart of the city) is surrounded by NO2 emissions hotspots while being a lower emissions area itself due to thick vegetation and lack of traffic:\n\nDetect pollution peaks on the days people usually take their cars to their summer vacation destinations:\n\nOr add an additional scripted field (hour_of_day) to bucket out entries in hours to present the average measurements, by chemical, in a heatmap. It seems 6 am is the best time to schedule a running session:\n\nAt the end of the day we got convinced that there is more in the air than just Nitrogen, Oxygen, Carbon Dioxide, Argon, and water. So no! It is not just air what we are breathing when we walk down Gran Via in Madrid. And probably not when you are exploring Manhattan, feeling like checking by yourself? You now know the path, an open data source is what it takes to start.\n\n## Conclusion\n\nIf we were data engineers asked to set up tools for our company\u2019s data scientists to analyze pollution levels in Madrid, we would have finished our job when we registered the airquality index pattern in Kibana, wrapped the access link in an email, and let them play with it. The Elastic Stack offers a full analytics stack from where it is possible to get answers in minutes and in a very intuitive way where the only code to write is that one of the scripted fields (when needed).\n\nThanks to Elastic Cloud, our job as data engineers has been simplified to just a few clicks and writing the Extract Transform Load (ETL) service. But, would we actually need to write an ETL to fetch and get our data into Elasticsearch? Next post will show that the Elastic Stack can also take care of that.","date":"2021-09-23 19:58:00","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.299839049577713, \"perplexity\": 3175.8368338827545}, \"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-2021-39\/segments\/1631780057447.52\/warc\/CC-MAIN-20210923195546-20210923225546-00507.warc.gz\"}"} | null | null |
package eu.seaclouds.monitor.monitoringdamgeneratorservice;
public class ApplicationRules {
private String rules;
public ApplicationRules(String toSet) {
this.rules = toSet;
}
public String getRules() {
return rules;
}
public void setRules(String rules) {
this.rules = rules;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 92 |
\section{Introduction}
Both the Belle~\cite{belle} and Babar~\cite{babar} experiments
have measured the branching fractions for \btaunu\ and \dsmunu\
decays~\cite{charge-conjugates}. These decays proceed via the
annihilation diagram of Fig.~\ref{fig:diagram}. Within the
Standard Model (SM), the predicted rates are
\begin{eqnarray}
{\cal B}(B^+\!\rightarrow\!\tau^+\nu) & = &
\tau^{}_{B^+}\,\frac{G^2_F}{8\pi}|V^{}_{ub}|^2 f^2_{B^+}\,m^2_{\tau}\,
m^{}_{B^+}\biggl( 1-\frac{m^2_{\tau}}{m^2_{B^+}}\biggr)^2
\label{eqn:fb} \\
{\cal B}(D^+_s\!\rightarrow\!\ell^+\nu) & = &
\tau^{}_{D^{}_s}\,\frac{G^2_F}{8\pi}|V^{}_{cs}|^2 f^2_{D^{}_s}\,m^2_{\ell}\,
m^{}_{D^{}_s}\biggl( 1-\frac{m^2_{\ell}}{m^2_{D^{}_s}}\biggr)^2 \,.
\label{eqn:fds}
\end{eqnarray}
For the $D^+_s$, all parameters on the right-hand-side
except for $f^{}_{D^{}_s}$\ are well-known. The Cabibbo-Kobayashi-Maskawa (CKM)
matrix element $|V^{}_{cs}|$ is well-constrained by a global fit to
several experimental observables and unitarity of the CKM matrix.
Thus a measurement of ${\cal B}(D^+_s\!\rightarrow\!\mu^+\nu)$
allows one to determine the decay constant~$f^{}_{D^{}_s}$.
This can be compared to QCD lattice calculations, which have
become relatively precise. For the $B^+$, the CKM matrix
element $|V^{}_{ub}|$ is known to only 9\%; this is
nonetheless more precise than measurements of
${\cal B}(B^+\!\rightarrow\!\ell^+\nu)$ and allows one to extract~$f^{}_B$.
\begin{figure}
\includegraphics[height=.15\textheight]{annihilation.eps}
\caption{Annihilation diagram for a heavy meson decaying to a lepton
and neutrino.}
\label{fig:diagram}
\end{figure}
\section{Measurement of \textbf{\btaunu}}
Belle has done two \btaunu\ analyses~\cite{btaunu_belle_old,btaunu_belle};
the most recent one used 605~fb$^{-1}$ of data and obtained
evidence for a signal. This analysis employed a semileptonic tag:
one $B$ in an event is fully reconstructed as
$B^-\!\rightarrow\! D^{(*)0}\ell^-\bar{\nu}$, where $D^{*0}\!\rightarrow\! D^0\pi^0\!,\,D^0\gamma$
and $D^0\!\rightarrow\! K^-\pi^+(\pi^0),\,K^-\pi^+\pi^-\pi^+$.
The signal decays $\tau^+\!\rightarrow\!\mu^+\nu_\mu\bar{\nu}^{}_\tau,\,
e^+\nu^{}_e\bar{\nu}^{}_\tau$
and $\tau^+\!\rightarrow\!\pi^+\bar{\nu}^{}_\tau$ are then searched for by
reconstructing a single track not associated with the tag side.
The signal yield is obtained by fitting the distribution
of $E^{}_{\rm ECL}$, which is the energy sum of calorimeter
clusters not associated with a charged track.
A peak near $E^{}_{\rm ECL}\!=\!0$ indicates a
$\tau^+\!\rightarrow\!\ell^+\nu^{}_\ell\bar{\nu}^{}_\tau$ or
$\tau^+\!\rightarrow\!\pi^+\bar{\nu}^{}_\tau$
decay. The main backgrounds are $b\!\rightarrow\! c$ processes and
$e^+e^-\!\rightarrow\! q\bar{q}$ continuum events. The fit is unbinned
and uses a likelihood function
\begin{eqnarray}
{\cal L} & = &
\frac{e^{-\sum_j n^{}_j}}{N!}\,
\prod_i \sum_j n^{}_j\,f^{}_j(E^{}_i)\,,
\end{eqnarray}
where $i$ runs over all events ($N$), $j$ runs over all signal
and background categories, $n^{}_j$ is the yield
of category $j$, and $f^{}_j$ is the probability density
function (PDF) for category $j$.
The branching fraction is calculated as
${\cal B}= n^{}_s/(2\cdot\varepsilon\cdot N^{}_{B^+B^-})$,
where $\varepsilon$ is the reconstruction efficiency as
calculated from Monte Carlo (MC) simulation.
The fit results are listed in Table~\ref{tab:btaunu_belle},
and the fit projections are shown in Fig.~\ref{fig:btaunu_belle}.
The systematic errors are dominated by uncertainty in the
background PDF and the tag reconstruction efficiency. The
overall result is
\begin{eqnarray}
{\cal B}(B^+\!\rightarrow\!\tau^+\nu)\Bigr|^{}_{\rm Belle} & = &
\Bigl(1.65\,^{+0.38}_{-0.37}\,^{+0.35}_{-0.37}\Bigr)\times 10^{-4}\,,
\label{eqn:btaunu_belle}
\end{eqnarray}
where the first error is statistical and the second is systematic.
\begin{table}
\renewcommand{\baselinestretch}{1.3}
\begin{tabular}{|l|ccc|}
\hline
Decay Mode &
Signal Yield &
$\varepsilon$ (\%) &
${\cal B}\times 10^4$ \\
\hline
$\tau^-\!\rightarrow\! e^-\bar{\nu}\nu^{}_\tau$ & $78\,^{+23}_{-22}$ & 0.059
& $2.02\,^{+0.59}_{-0.56}$ \\
$\tau^-\!\rightarrow\! \mu^-\bar{\nu}\nu^{}_\tau$ & $15\,^{+18}_{-17}$ & 0.037
& $0.62\,^{+0.76}_{-0.71}$ \\
$\tau^-\!\rightarrow\!\pi^-\nu^{}_\tau$ & $58\,^{+21}_{-20}$ & 0.047
& $1.88\,^{+0.70}_{-0.66}$ \\
\hline
Combined &
$154\,^{+36}_{-35}$ & 0.143 & $1.65\,^{+0.38}_{-0.37}$ \\
\hline
\end{tabular}
\caption{Fit results for \btaunu, from Belle~\cite{btaunu_belle}.
The data sample corresponds to 605~fb$^{-1}$.}
\label{tab:btaunu_belle}
\end{table}
\begin{figure}
\includegraphics[height=.50\textheight]{btaunu_belle.eps}
\caption{
$E^{}_{ECL}$ distribution of data events (points) and
fit projections for \btaunu, from Belle~\cite{btaunu_belle}.
{\it (a)}\ all $\tau$ decay modes combined;
{\it (b)}\ $\tau^-\!\rightarrow\! e^-\bar{\nu}^{}_e\,\nu^{}_\tau$;
{\it (c)}\ $\tau^-\!\rightarrow\!\mu^-\bar{\nu}^{}_\mu\,\nu^{}_\tau$;
{\it (d)}\ $\tau^-\!\rightarrow\!\pi^-\nu^{}_\tau$.
The open and hatched histograms correspond to signal and
background, respectively.}
\label{fig:btaunu_belle}
\end{figure}
Babar has published two analyses of \btaunu\ decays: one using a
semileptonic tag~\cite{btaunu_babar_semi} and the other using
a hadronic tag~\cite{btaunu_babar_hadr}. Both analyses use
data samples consisting of $383\times 10^6$ $B\overline{B}$ pairs.
The former is similar to that used in the Belle analysis: the
tag side is reconstructed
as $B^-\!\rightarrow\! D^{(*)0}\ell^-\bar{\nu}^{}_\ell$, where
$D^{*0}\!\rightarrow\! D^0\pi^0,\,D^0\gamma$ and
$D^0\!\rightarrow\! K^-\pi^+(\pi^0),\,K^-\pi^+\pi^-\pi^+\!,\,K^{}_S\,\pi^+\pi^-$.
Babar searches for
$\tau^+\!\rightarrow\!\ell^+\nu^{}_\ell\bar{\nu}^{}_\tau$,
$\tau^+\!\rightarrow\!\pi^+\bar{\nu}^{}_\tau$, and also
$\tau^+\!\rightarrow\!\pi^+\pi^0\bar{\nu}^{}_\tau$, where for the last mode
the $\pi^+\pi^0$ mass is required to be near that of the $\rho^+$.
The signal is identified by plotting $E^{}_{\rm extra}$,
the energy sum of calorimeter clusters not associated with
a charged track; a peak near zero indicates $\tau^+$ decay.
The signal yield is obtained by
counting events in a signal region, e.g., $E^{}_{\rm extra}<0.50$,
and subtracting off background as estimated from $E^{}_{\rm extra}$
sidebands. The number of events in the final sample is 245, the
background estimate is $222\pm 13$, and the resulting
branching fraction is
$(0.9\,\pm 0.6{\rm\ (stat.)}\,\pm 0.1{\rm\ (syst.)})\times 10^{-4}$.
The Babar hadronic-tag analysis is more complicated.
The tagging side is reconstructed as $B^-\!\rightarrow\! D^{(*)0}X^-$, where
$X^-$ denotes a hadronic system of total charge $-1$ composed of
$n^{}_1(\pi^\pm)$,
$n^{}_2(K^\pm)$,
$n^{}_3(K^0_S)$, and
$n^{}_4(\pi^0)$, where
$n^{}_1+n^{}_2\leq 5$, $n^{}_3\leq 2$, and $n^{}_4\leq 2$.
The $D^{(*)0}$ is reconstructed in the same channels as those
used for the semileptonic analysis, as is the $\tau^+$ on the
signal side. A background subtraction is done on the tag side.
The signal yield is obtained by counting events
in an $E^{}_{\rm extra}$ signal region and subtracting
off background as estimated from an $E^{}_{\rm extra}$ sideband.
There are 24 signal candidates and $14.3\pm3.0$ estimated
background events; the resulting branching fraction is
$(1.8\,^{+0.9}_{-0.8}\,\pm 0.4\,\pm 0.2)\times 10^{-4}$,
where the first error is statistical, the second is due to
the background uncertainty, and the third is due to other
systematic sources. The data
is shown in Fig.~\ref{fig:btaunu_babar} along with
projections of the fit. This result is consistent with the
semileptonic-tagged result; combining the two gives
\begin{eqnarray}
{\cal B}(B^+\!\rightarrow\!\tau^+\nu)\Bigr|^{}_{\rm Babar} & = &
\Bigl(1.2\,\pm 0.4{\rm\ (stat.)}\,\pm 0.3{\rm\ (bkg.)}\,\pm 0.2{\rm\ (syst.)}\Bigr)
\times 10^{-4}\,.
\end{eqnarray}
This is consistent with the Belle result, Eq.~(\ref{eqn:btaunu_belle}).
\begin{figure}
\includegraphics[height=.38\textheight]{btaunu_babar.eps}
\caption{
$E^{}_{\rm extra}$ distribution of data events (points) and
fit projections for \btaunu, from Babar using a hadronic
tag~\cite{btaunu_babar_hadr}.
{\it (a)}\ $\tau^-\!\rightarrow\! e^-\bar{\nu}^{}_e\,\nu^{}_\tau$;
{\it (b)}\ $\tau^-\!\rightarrow\!\mu^-\bar{\nu}^{}_\mu\,\nu^{}_\tau$;
{\it (c)}\ $\tau^-\!\rightarrow\!\pi^-\nu^{}_\tau$;
{\it (d)}\ $\tau^-\!\rightarrow\!\pi^-\pi^0\nu^{}_\tau$.
The hatched histogram shows the combinatorial background
component, and, for comparison, the open histogram shows
\btaunu\ signal for a branching fraction of 0.3\%.}
\label{fig:btaunu_babar}
\end{figure}
\section{Measurement of \dsmunu}
The Belle analysis of \dsmunu\ decays~\cite{dsmunu_belle}
uses 548~fb$^{-1}$ of data and searches for
$e^+e^-\!\rightarrow\! DKD^*_s\,n(\pi,\gamma)$, where the primary
$D$ and $K$ can be charged or neutral;
the $D^*_s$ is ``reconstructed'' (see below) via $D^+_s\gamma$;
$n(\pi,\gamma)\equiv X$ signifies any number of additional pions
and up to one photon (from fragmentation);
the $D$ is reconstructed via $D\!\rightarrow\! K\,n(\pi)$, where $n\!=\!1,2,3$;
and neutral kaons are reconstructed via $K^0_S\!\rightarrow\!\pi^+\pi^-$.
If the primary $K$ is charged, both it and the $D$ must
have flavors opposite to that of the $D^+_s$;
these constitute a ``right-sign'' (RS) sample. If the
flavors are not both opposite, the event is categorized
as ``wrong-sign'' (WS) and used to parameterize the
background. The same classification applies to primary
neutral $K$ events, except for these only the $D$ flavor
must be opposite to that of the $D^+_s$ for the event to
be classified as RS.
The decay sequence is
identified via a recoil mass technique. First, the
recoil mass of the $D$, $K$, and $X$ particles is
calculated and required to be within 150~MeV/$c^2$\ of
$M^{}_{D^*_s}$; then the $\gamma$ is included and
the recoil mass is required to be within 150~MeV/$c^2$\ of
$M^{}_{D^+_s}$; and finally, the $\mu^+$ is included
and the recoil mass required to be within
0.55~GeV/$c^2$\ of zero. The final $DK\,X\gamma\mu^+$
recoil mass distribution is shown in Fig.~\ref{fig:widhalm1};
a sharp peak is observed near zero, indicating \dsmunu\ decay.
\begin{figure}
\includegraphics[height=.40\textheight]{widhalm1.eps}
\caption{Recoil mass distribution for $e^+e^-\!\rightarrow\! DK\,X\gamma\mu^+$,
from Belle~\cite{dsmunu_belle}.}
\label{fig:widhalm1}
\end{figure}
The analysis is complicated by the fact that the recoil
mass technique is very sensitive to the number of tracks
in an event and the track reconstruction efficiency, as
all tracks must be reconstructed for the recoil mass to
be accurate. As it is difficult to simulate track
multiplicity accurately due to uncertainties in quark
fragmentation, the data is divided
into bins of $n^{R}_x$, the number of ``primary particles''
reconstructed in an event. Here, a primary particle is one
that is not a daughter of any particle reconstructed in the
event. The minimum value for $n^{R}_x$ is three, corresponding
to $e^+e^-\!\rightarrow\! D K D^*_s$ without any additional particles from
fragmentation. The data is then fit in two dimensions,
$DK\,X\gamma$ recoil mass vs. $n^{R}_x$
(see Fig.~\ref{fig:widhalm2}).
The signal PDF is obtained from MC and modeled
separately for different values of $n^{T}_x$, the
{\it true\/} number of primary particles in an event
($n^{T}_x$ can differ from $n^{R}_x$ due to particles being
lost or incorrectly assigned).
The branching fraction is obtained from two fits:
the first fit uses the $DK\,X\gamma$ recoil mass spectrum
and yields the number of $D^+_s$ candidates; the result is
$N^{}_{D^{}_s} = 32100\,\pm 870{\rm\ (stat)}\,\pm 1210{\rm\ (syst)}$.
For this fit the background shape is taken from the WS sample and
the background levels floated in the fit.
The second fit uses the $DK\,X\gamma\mu^+$ recoil mass
spectrum and yields the number of \dsmunu\ candidates; the result
is $N^{}_{\mu\nu} = 169\,\pm 16{\rm\ (stat)}\,\pm 8{\rm\ (syst)}$.
For this fit the background shape is
taken from a RS ``$D^+_s\!\rightarrow\! e^+\nu$'' sample, i.e., all
selection criteria are the same except that an electron
candidate is required instead of a muon candidate. As
true $D^+_s\!\rightarrow\! e^+\nu$ decays are suppressed by $\sim\!10^{-5}$,
this sample provides a good model of the \dsmunu\ background.
The systematic errors listed are dominated by uncertainties in
the signal and background PDFs and are obtained by varying
the shapes of these PDFs.
The branching fraction is the ratio
$N^{}_{\mu\nu}/N^{}_{D^{}_s}$, corrected for the ratio of
reconstruction efficiencies. The result is
\begin{eqnarray}
{\cal B}(D^+_s\!\rightarrow\!\mu^+\nu)\Bigl|^{}_{\rm Belle}
& = & \Bigl(6.44\,\pm 0.76{\rm\ (stat.)}\,\pm 0.57{\rm\ (syst.)}\Bigr)\times 10^{-3}\,.
\end{eqnarray}
\begin{figure}
\vbox{
\vskip0.30in
\begin{center}
\includegraphics[height=.38\textheight]{widhalm_lego.eps}
\end{center}
}
\caption{Two-dimensional $DK\,X\gamma$ recoil mass
vs. $n^{R}_x$ distribution (see text), from Belle~\cite{dsmunu_belle}.}
\label{fig:widhalm2}
\end{figure}
The Babar experiment searches for \dsmunu~\cite{dsmunu_babar}
using 230~fb$^{-1}$ of data by fully reconstructing a flavor-specific
$D^{(*)-},\,\overline{D}{}^0$, or $D^-_s$ decay on the tagging side. Tag
candidates are reconstructed in the following modes:
$\overline{D}{}^0\!\rightarrow\! K^+\pi^-(\pi^0),\,K^+\pi^-\pi^+\pi^-$;
$D^-\!\rightarrow\! K^+\pi^-\pi^-(\pi^0),\,K^0_S\,\pi^-(\pi^0),\,K^0_S\,\pi^-\pi^-\pi^+,\,
\,K^+K^-\pi^-,\,K^0_S\,K^-$;
$D^-_s\!\rightarrow\! K^0_S K^-,\,\phi\rho^-$; and
$D^{*-}\!\rightarrow\!\overline{D}{}^0\pi^-$ with
$\overline{D}{}^0\!\rightarrow\! K^0_S\,\pi^+\pi^-(\pi^0),\,K^0_S\,K^+K^-,\,K^0_S\,\pi^0$.
An isolated $\mu^+$ track is required. The neutrino
momentum is taken to be the missing momentum in the event:
$\vec{p}^{}_\nu\equiv\vec{p}^{}_{e^+e^-}\!-\vec{p}^{}_{\rm rest}$.
A photon is required and paired with the $D^+_s$ candidate to make
a $D^{*+}_s$, and the mass difference
$\Delta M\equiv M(\mu^+\nu\gamma) -M(\mu^+\nu)$ is calculated.
The data is subsequently divided into four subsamples:
a tag-side mass sideband and a tag-side signal
region for $\mu^+$ and $e^+$ candidates. For both
lepton samples, the tag-side-sideband $\Delta M$
spectrum is subtracted from the tag-side-signal
$\Delta M$ spectrum (Fig.~\ref{fig:dsmunu_babar1}),
and then the sideband-subtracted
$e^+$ spectrum is subtracted from the
sideband-subtracted $\mu^+$ spectrum.
The final $\Delta M$ distribution
(Fig.~\ref{fig:dsmunu_babar2}a) is
fit with signal and background PDFs; the signal
yield obtained is $N^{}_{\mu^+\nu} = 489\,\pm 55$ events.
To determine the branching fraction, the signal yield
is normalized to $D^+_s\ra\phi\pi^+$\ decays. Like
the signal mode, the $D^+_s$ candidate is required to
originate from $D^{*+}_s\!\rightarrow\! D^+_s\gamma$.
The tag-side-sideband $\Delta M$ spectrum is subtracted
from the tag-side-signal $\Delta M$ spectrum, and the
resulting spectrum is fit with signal and background PDFs
(Fig.~\ref{fig:dsmunu_babar2}b). The signal yield obtained
is $N^{}_{\phi\pi^+} = 2093\,\pm 99$ events.
Dividing $N^{}_{\mu^+\nu}$ by $N^{}_{\phi\pi^+}$
and correcting for the ratio of reconstruction
efficiencies gives
\begin{eqnarray}
\frac{\Gamma(D^+_s\!\rightarrow\!\mu^+\nu)}{\Gamma(D^+_s\!\rightarrow\!\phi\pi^+)}\Bigl|^{}_{\rm Babar}
& = & 0.143\,\pm 0.018{\rm\ (stat.)}\,\pm 0.006{\rm\ (syst.)}\,.
\label{eqn:dsratio_babar}
\end{eqnarray}
For this analysis, the $\phi$ is
reconstructed via $\phi\!\rightarrow\! K^+K^-$ with
$|M^{}_{K^+K^-}-M^{}_\phi |\equiv\Delta M^{}_{KK}<5.5$~MeV~\cite{joncoleman}.
Conveniently, CLEO has measured the branching fraction
${\cal B}(D^+_s\!\rightarrow\! K^+K^-\pi^+)$ for $\Delta M^{}_{KK}=5{\rm\ MeV}$;
the result is $(1.69\,\pm 0.08\,\pm 0.06)\%$~\cite{cleo_dskkp}.
To multiply the two results together to obtain
${\cal B}(D^+_s\!\rightarrow\!\mu^+\nu)$ requires dividing
Eq.~(\ref{eqn:dsratio_babar}) by ${\cal B}(\phi\!\rightarrow\! K^+K^-) = 0.491$
and subtracting (in quadrature) the 1.2\% uncertainty in
${\cal B}(\phi\!\rightarrow\! K^+K^-)$ from the systematic error. In
addition, Babar has subtracted off a small amount of
$D^+_s\!\rightarrow\! f^{}_0(980)(K^+K^-)\pi^+$ background (48 events);
as this process is included in the CLEO measurement, these
events must be added back in to Babar's $\phi\pi^+$ yield.
Thus the Babar result becomes
\begin{eqnarray}
\frac{\Gamma(D^+_s\!\rightarrow\!\mu^+\nu)}{\Gamma(D^+_s\!\rightarrow\! K^+K^-\pi^+)}
\biggr|^{}_{\Delta M^{}_{KK}=5.5{\rm\ MeV}} & = &
0.285\,\pm 0.035{\rm\ (stat.)}\,\pm 0.011{\rm\ (syst.)}\,.
\label{eqn:ratio_adjusted}
\end{eqnarray}
Multiplying this by CLEO's measurement
gives
\begin{eqnarray}
{\cal B}(D^+_s\!\rightarrow\!\mu^+\nu)\Bigl|^{}_{\rm Babar} & = &
\Bigl(4.81\,\pm 0.63{\rm\ (stat.)}\,\pm 0.25{\rm\ (syst.)}\Bigr)\times 10^{-3}\,.
\end{eqnarray}
\begin{figure}
\includegraphics[height=.30\textheight]{dsmunu_babar1.eps}
\caption{$\Delta M$ spectra for the tag-side sideband region (dashed)
and tag-side signal region (solid) for $\mu^+$ (top) and $e^+$ (bottom)
samples, from Babar~\cite{dsmunu_babar}.}
\label{fig:dsmunu_babar1}
\end{figure}
\begin{figure}
\hbox{
\includegraphics[height=.18\textheight]{dsmunu_babar2a.eps}
\hskip0.02in
\includegraphics[height=.18\textheight]{dsmunu_babar2b.eps}
}
\caption{Background-subtracted $\Delta M$ spectra (see text) and
projections of the fit result, from Babar~\cite{dsmunu_babar}.
The left-most (right-most) distribution corresponds to
\dsmunu\ ($D^+_s\ra\phi\pi^+$) candidates.
The dashed line is the background component, and the solid
line is the signal plus background components combined.}
\label{fig:dsmunu_babar2}
\end{figure}
\section{Extraction of Decay Constants}
The Belle and Babar collaborations have used their
measurements of ${\cal B}(B^+\!\rightarrow\!\tau^+\nu)$ and
Eq.~(\ref{eqn:fb}) to calculate the product of the $B$ decay constant
$f^{}_B$ and the CKM matrix element $|V^{}_{ub}|$. The results are
\begin{eqnarray*}
f^{}_B\times |V^{}_{ub}| \times 10^4 & = &
\left\{
\begin{array}{l}
9.7\,\pm 1.1{\rm\ (stat.)}\,^{+1.0}_{-1.1}{\rm\ (syst.)}{\rm\ GeV\ \
(Belle)} \\ \\
7.2\,^{+2.0}_{-2.8}{\rm\ (stat.)}\,\pm 0.2{\rm\ (syst.)}{\rm\ GeV\ \
(Babar\ semileptonic)} \\ \\
10.1\,^{+2.3}_{-2.5}{\rm\ (stat.)}\,^{+1.2}_{-1.5}{\rm\ (syst.)}
{\rm\ GeV\ \ (Babar\ hadronic)}.
\end{array}\right.
\end{eqnarray*}
Taking a weighted average gives
\begin{eqnarray}
f^{}_B\times |V^{}_{ub}|\,^{}_{\rm (Belle+Babar\ avg.)} & = &
(9.2\pm 1.2)\times 10^{-4}{\rm\ \ GeV}\,,
\end{eqnarray}
and dividing by the Particle Data Group value
$|V^{}_{ub}| = (0.393\,\pm0.036)\%$~\cite{pdg_vub} gives
\begin{eqnarray}
f^{}_B\bigr|^{}_{\rm (Belle+Babar\ avg.)} & = & 233\pm 37~{\rm MeV}\,.
\end{eqnarray}
This value is $1\sigma$ higher than the most recent
lattice QCD results, that of the HPQCD collaboration
($190\,\pm 13$~MeV~\cite{hpqcd_b}) and that of the
Fermilab/MILC collaboration ($195\,\pm 11$~MeV~\cite{milc}).
\vskip0.20in
The Heavy Flavor Averaging Group (HFAG) has calculated
a world average (WA) value for ${\cal B}(D^+_s\!\rightarrow\!\mu^+\nu)$
and used this to determine a WA value for the $D^+_s$ decay
constant $f^{}_{D^{}_s}$~\cite{hfag_ds}. This value can be compared to
recent lattice QCD calculations; a significant difference
could indicate new physics.
The WA value for $f^{}_{D^{}_s}$\ is obtained by inverting Eq.~(\ref{eqn:fds}):
\begin{eqnarray}
f^{}_{D^{}_s} & = & \frac{1}
{G^{}_F |V^{}_{cs}| m^{}_{\ell}
\biggl( 1-\frac{\displaystyle m^2_{\ell}}{\displaystyle m^2_{D^{}_s}}\biggr)}
\sqrt{\frac{8\pi\,{\cal B}(D^+_s\!\rightarrow\!\ell^+\nu)}{m^{}_{D^{}_s} \tau^{}_{D^{}_s}}}\,,
\label{eqn:fds_inverted}
\end{eqnarray}
where, for ${\cal B}(D^+_s\!\rightarrow\!\ell^+\nu)$, the WA value is inserted.
The error on $f^{}_{D^{}_s}$\ is calculated as follows:
values for variables on the right-hand-side of Eq.~(\ref{eqn:fds_inverted})
are sampled from Gaussian distributions having
means equal to the central values and standard deviations
equal to their respective errors. The resulting values of
$f^{}_{D^{}_s}$\ are plotted, and the distribution is fit to a
bifurcated Gaussian to obtain the $\pm 1\sigma$ errors.
The results of this procedure are shown in Fig.~\ref{fig:hfag_fds}.
Also included are measurements of
${\cal B}(D^+_s\!\rightarrow\!\mu^+\nu)$~\cite{cleo_dsmunu} and
${\cal B}(D^+_s\!\rightarrow\!\tau^+\nu)$~\cite{cleo_dstaunu}
from CLEO. Thus there are three types of measurements:
$f^{}_{D^{}_s}$\ from the absolute \dsmunu\ branching fraction,
$f^{}_{D^{}_s}$\ from the absolute \dstaunu\ branching fraction, and
$f^{}_{D^{}_s}$\ from the $\Gamma(D^+_s\!\rightarrow\!\mu^+\nu)/\Gamma(D^+_s\!\rightarrow\! K^+K^-\pi^+)$
ratio. The overall WA value is obtained by averaging
the three results, carefully accounting for
correlations such as the input values for $|V^{}_{cs}|$ and
$\tau^{}_{D^{}_s}$. The result is $256.9\,\pm 6.8$~MeV.
This value is higher than the two most precise lattice
QCD results, that of the HPQCD ($241\,\pm 3$~MeV~\cite{hpqcd_ds})
and Fermilab/MILC ($249\,\pm 11$~MeV~\cite{milc}) collaborations.
The weighted average of the theory results is $241.5\,\pm 2.9$~MeV,
which differs from the HFAG result by~$2.1\sigma$.
\begin{figure}
\includegraphics[height=.53\textheight]{f_ds_8sept09.eps}
\caption{Heavy Flavor Averaging Group (HFAG) WA value
for $f^{}_{D^{}_s}$, from Ref.~\cite{hfag_ds}.
For each measurement, the first error listed is the total
uncorrelated error, and the second error is the total
correlated error (mostly from $\tau^{}_{D^{}_s}$).}
\label{fig:hfag_fds}
\end{figure}
\section{Summary}
In summary, Belle has observed \btaunu\ with $3.8\sigma$ significance.
From the measured branching fraction they determine the product
$f^{}_B\times |V^{}_{ub}|$. Babar has observed \btaunu\ with $2.6\sigma$
significance and has also measured the branching fraction to determine
$f^{}_B\times |V^{}_{ub}|$. The results from the two experiments are
consistent; the weighted average has 13\% precision and is
consistent with lattice QCD calculations.
For \dsmunu\ decays, Belle has observed this mode using a
recoil mass technique and has measured the branching fraction with
15\% precision. Babar has also observed this mode and has measured
the branching fraction relative to that for $D^+_s\ra\phi\pi^+$\ with
13\% precision. Dividing this by the branching fraction for
$\phi\!\rightarrow\! K^+K^-$ and including $D^+_s\!\rightarrow\! f^{}_0(980)(K^+K^-)\pi^+$
decays allows one to multiply by CLEO's measurement of
${\cal B}(D^+_s\!\rightarrow\! K^+K^-\pi^+)$ to obtain
${\cal B}(D^+_s\!\rightarrow\!\mu^+\nu)$.
The Heavy Flavor Averaging Group has used the Belle and Babar
measurements and also measurements from CLEO to calculate a
world average value for $f^{}_{D^{}_s}$; the result is $256.9\,\pm 6.8$~MeV.
This value is $2.1\sigma$ higher than the average of two recent
lattice QCD calculations; the difference could indicate
new physics.
\begin{theacknowledgments}
We thank the organizers of CIPANP 2009 for
a stimulating scientific program and excellent hospitality.
We thank Laurenz Widhalm, Yoshihide Sakai, and Andreas Kronfeld
for reviewing this manuscript and suggesting many improvements.
\end{theacknowledgments}
\bibliographystyle{aipproc}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 952 |
«Залишити слід» () — радянський художній фільм 1982 року, знятий на кіностудії «Мосфільм».
Сюжет
Студентка Ніна Денисова разом з концертною бригадою приїжджає на будівництво залізниці. Тут вона зустрічає свого колишнього однокласника, в якого таємно закохана і вирішує залишитися на будівництві. Ніна не відразу зрозуміє, що через Толіка не варто кидати інститут і змінювати своє життя, але про своє рішення не пошкодує.
У ролях
Світлана Колишева — Ніна
Сергій Проханов — Толік
Іван Рижов — Захарушкін
Лев Пригунов — Воробйов
— Борис
Тетяна Догілева — Томка
Наталія Потапова — Зіна
Микола Пеньков — Ємельянов
Ігор Ясулович — Менеес
Любов Соколова — Поліна Петрівна
Леонід Трутнєв — епізод
Знімальна група
Режисер: Герман Лавров
Сценарій: Олександр Розін
Оператор: Михайло Біц
Композитор: Ісаак Шварц
Текст пісень Булат Окуджава
Посилання
Фільми СРСР 1982 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,618 |
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} | 7,807 |
\section{Introduction}
The recent COVID-19 pandemic~\cite{bick2020work} has driven the rise in adoption of the online virtual environment as a viable alternative for a growing range of shared human experiences. For example, UC Berkeley held its graduation ceremony in Minecraft\footnote{https://news.berkeley.edu/2020/05/16/watch-blockeley-uc-berkeleys-online-minecraft-commencement/}, that was originally created to be a gaming platform. Together with the advancement of other enabling technologies ranging from the advent of $5$G to blockchain to Virtual Reality (VR)/Augmented Reality (AR), the conditions towards the development of the \textit{metaverse}, also known as the next-generation internet, have been gradually fulfilled.
As described by venture capitalist Matthew Ball \cite{ball}, the metaverse is an embodied version of the Internet. Similar to sci-fi films such as \textit{Ready Player One}~\cite{readyplayer}, users can leverage VR/AR technologies to navigate freely within a virtual environment with their customized avatars. Beyond gaming functions, the metaverse can support novel ecosystems of service provisions that will blur the lines between the physical and virtual worlds. For example, the American rapper Lil Nas X held his concert online on the Roblox platform\footnote{https://techcrunch.com/2020/11/10/roblox-to-host-its-first-virtual-concert-featuring-lil-nas-x/}, whereas the Facebook Infinite Office enables users to collaborate with their colleagues in an immersive online environment.
\subsection{Overview of Metaverse and Virtual Education Case Study}
The metaverse can be considered to follow a three-layer architecture~\cite{duan2021metaverse}. Firstly, the \textit{physical} layer consists of all the hardware to support the operational functions of the metaverse, i.e., computation, communication, and storage. A robust physical layer is of utmost importance to ensure the scalable and ubiquitous access to the metaverse. Secondly, the \textit{virtual} layer provides a parallel living world in which the users' avatars can interact with each other or with other objects. For immersivity, the virtual layer should also capture and reflect the real-time data and analytics of the real world using technologies such as edge intellgience empowered digital twins~\cite{el2018digital}. Finally, the \textit{interaction} layer serves as a bridge to connect the users in the physical world to the virtual world. The users can upload their inputs in the physical world that is eventually translated into specific actions in the virtual world. To enhance service delivery, the wealth of data collected from the users can be leveraged to train the Artificial Intelligence (AI) system to deliver highly personalized services to users.
Similar to the mobile internet, the Quality of Service (QoS) provided by the metaverse is a critical factor that will determine its successful adoption. Users will expect the metaverse to be scalable, seamless, and synchronous. In addition, the AI system in the metaverse can be trained in the edge using the shared user data. However, the challenge of maintaining a high QoS is further exacerbated by the fact that the metaverse is characterized by such diverse types of resources amid a highly dynamic demand environment. For example, with the uncertainty in the amount of data users shares, it is difficult for the virtual service provider to subscribe to the correct number of edge servers. Therefore, there exists a crucial need to establish new paradigms of resource allocation that serve not only to meet metaverse users' interests but also to minimize the costs of virtual service providers.
\begin{figure*}[t]
\centering
\includegraphics[width=14cm, height=4cm,trim={0cm 23.5cm 1cm 0},clip]{timeline.pdf}
\caption{Resource allocation timeline in virtual education case study. $\mathcal{X}=\{x:Grammarly\}$, $\mathcal{Y}=\{y:Classroom\}$, $\mathcal{Z}=\{z:Edge\; server\; 1\}$, and $\mathcal{Y}=\{y:Teacher\; 1\}$.}
\label{fig:timeline}
\vspace*{-5mm}
\end{figure*}
In this paper, we propose the case study of virtual education in the metaverse. The pandemic has necessitated an evolution of the education industry as schools and private enrichment centres face disruption to physical classes \cite{roe2021impact} and more students resort to online resources. The education providers can put up the services that they provide in the metaverse, e.g., personalized lessons in the virtual world delivered by the AI tutors (cyber resources) \cite{ndukwe2019machine}, lessons taught by the teachers (people resources), as well as conducive classrooms that users may book to study and edge servers (physical resources) to store and process the students' relevant information, e.g., to train the AI system for teaching content personalization. With the help of edge servers, the AI tutors can be deployed at the edge. For example, by offloading/caching some parts of data and services to reduce latency and to maintain the privacy of user's data as the data is kept at the edge server locally, e.g., servers in a community or the neighborhood area network.
\subsection{Contributions of This Work}
Similar to models in the sharing economy \cite{puschmann2016sharing}, the cyber, physical, and people resources are not always owned by the virtual education providers. Instead, separate entities may own the resources, and the virtual education providers have to subscribe to these resources before offering them to the users. In general, there are two subscription plans i.e., reservation (i.e., long-term) and on-demand plan (i.e., ad-hoc). For example, full-time teachers can be hired for a long term (i.e., considered to be ``reservation'') while part-time teachers may be hired for a few weeks (i.e., considered to be ``on-demand"). Generally, the reservation plan is cheaper than the on-demand plan~\cite{5394134}. Figure~\ref{fig:timeline} shows the subscription timeline of the virtual service providers. The users can access the metaverse using the smartphone interface. Then, the virtual service provider can subscribe to these resources to offer services to the users based on users' demands. However, the virtual service provider will need to decide on the resources to be allocated via reservation plan before an actual student demand is known. Therefore, a resource over-provisioning problem can occur if the virtual service provider subscribes too many resources, i.e., the resources subscribed in the reservation plan are more than the users' demands. In contrast, a resource under-provisioning problem can happen if the virtual service provider subscribes too little resources, i.e., the resources subscribed in the reservation plan are less than the users' demands. Then, the virtual service provider has to meet the demands of the users with the more expensive plan, which is the on-demand plan. Therefore, with the demand uncertainty of the users, we propose a two-stage stochastic integer programming (SIP) for the virtual service providers in metaverse to minimize its operation cost by allocating the resources most strategically.
The contributions of this paper are summarized as follows.
\begin{itemize}
\item We first provide a brief overview of the metaverse, including the architecture and the metaverse applications. Then, we illustrate with an example of how metaverse is applied to the education sector.
\item We propose a unified decision-making framework by incorporating the stochastic optimal resource allocation scheme (SORAS) to minimize the cost of the virtual service provider. SORAS uses a two-stage SIP to obtain the optimal decisions of the virtual education provider by minimizing the overall network cost. The formulation incorporates the uncertainty modeling for users' demands.
\item The performance evaluation substantiates the importance of optimal resource allocation. For example, the performance evaluation shows that intuitively adopting average demand leads to a sub-optimal solution, and it is significantly inferior to the solution from our scheme.
\end{itemize}
The remainder of the paper is organized as follows: In Section~\ref{system}, we present the system model. In Section~\ref{problem} we formulate the problem. We discuss and analyze the simulation result in Section~\ref{simulation}. Section~\ref{conclusion} concludes the paper.
\section{System Model}\label{system}
We consider the system model from the perspective of one virtual service provider participating in metaverse. As depicted in Fig.~\ref{fig:timeline}, we classified the resources in the metaverse into three major types, i.e., cyber, physical, and people. For simplicity, we did not consider the network resources. These resources can be, for example, used for communications from users to cyber, physical, and people resources.
\begin{itemize}
\item \textbf{Cyber}: Let $\mathcal{V}~=\{1,\ldots,v,\ldots,V\}$ denote the set of cyber resource and $\mathcal{W}~=\{1,\ldots,w,\ldots,W\}$ denote the set of users in the network. The user $w$ has a demand, i.e., the number of hours to use the cyber resources. Since the cyber resources are implemented on the metaverse platform, the cyber resources can be acquired and deployed in a much shorter time scale than those of physical and people resources.
\item \textbf{Physical}: Let $\mathcal{X}~=\{1,\ldots,x,\ldots,X\}$ denote the set of physical resources. Edge servers are also part of the physical resources, and it is denoted by a different set notation $\mathcal{Z}~=\{1,\ldots,z,\ldots,Z\}$. Under our consideration, each edge server $z$ can store and process $I_z$ amount of data by the virtual service providers.
\item \textbf{People}: Let $\mathcal{Y}~=\{1,\ldots,y,\ldots,Y\}$ denote the set of people resources. Virtual service providers hire people resources to provide services to the users. To maximize the service outcome, each people resource can support $E_y$ hours for the users to use. For example, in the virtual education service, teachers are the people resource hired by the virtual education provider to provide consultation to the students (users). People resources are more unreliable (unavailable randomly) than cyber and physical resources. For example, a people resource $y$ can be on medical leave even if $y$ is hired by the virtual service provider.
\end{itemize}
\subsection{Provisioning Plans and costs}
When subscribing the resources, the virtual service provider can consider the reservation plan or on-demand plan. The virtual service provider can obtain the optimal plan if the provider knows the demand of each user. However, the demand of each user is not always the same. For example, some students may need more hours of consultation with teachers. With the two subscription plans mentioned above, there are two corresponding subscription costs for each of the resources used, i.e., reservation and on-demand costs. The cost function is defined in dollars per resource unit per unit time. $c^r_v$, $c^r_x$, $c^r_z$ and $c^r_y$ are the reservation costs for cyber resource $v$, physical resource $x$, edge server $z$, and people resource $y$ respectively. $c^o_v$, $c^o_x$, $c^o_z$, and $c^o_y$ are the on-demand costs for cyber resource $v$, physical resource $x$, edge server $z$, and people resource $y$ respectively. $c^r_v$ and $c^o_v$ are used to pay for the cyber resources. $c^r_y$ and $c^o_y$ are used to pay for the physical resources. $c^r_y$ and $c^o_y$ are used to pay for the people resources.
\subsection{Uncertainty in Demands}
Under uncertainty of demands, the number of resources required by the user is not exactly known when the reservation of the resources is made. Let $\lambda_i$ denote the $i$ demand scenario of all the users. The set of scenarios is denoted by $\Omega$, i.e., $\lambda_i\in\Omega$. Let $P(\lambda_i)$ denote the probability that scenario $\lambda_i\in\Omega$ is realized, where $P(\lambda_i)$ can be obtained from the historical records~\cite{5394134}. The uncertainty of demands is expressed as follows:
\begin{center}
{\footnotesize
$\lambda_i =\begin{bmatrix}
\arraycolsep=3pt
\medmuskip=1mu
(F_{1,v},F_{1,x},F_{1,y},\bar{F}_{1,y},F_{1}) & \ldots & (F_{w,v},F_{w,x},F_{w,y},\bar{F}_{w,y},F_{w})
\end{bmatrix}$,}
\end{center}
\noindent where $F_{w,v}$, $F_{w,x}$, and $F_{w,y}$ represent the amounts of time required for cyber resource $v$, physical resource $x$, and people resource $y$ required by user $w$, respectively. $\bar{F}_{w,y}$ is a binary parameter that represents the availability of people resource $y$ when it is requested by the user $w$. $F_{w}$ is a positive parameter that indicates the amount of data in Gb that the user $w$ is willing to share.
If user $w$ has a demand, the user is allocated with a resource duration in each component. For example, $\lambda_i=~\{(F_{w,v}~:~0.3,~F_{w,x}~:~0.3,~F_{w,y}~:~0.4~,~\bar{F}_{w,y}~:1~,~F_{w}~:0.5~)\}$ means that user $w$ requires 0.3hr to the cyber resource $v$, 0.3hr to use physical resource $x$, 0.4hr to use people resource $y$ and people resource $y$ is available as $\bar{F}_{w,y}=1$. User $w$ is also willing to share 0.5Gb of his own data with the virtual service provider. Therefore, $F_{w,v} =0$ $\forall v\in\mathcal{V}\setminus\{v\}$, $F_{w,x}=0$ $\forall x\in\mathcal{X}\setminus\{x\}$, and $F_{w,y}=0$ $\forall y\in\mathcal{Y}\setminus\{y\}$.
\section{Problem Formulation}\label{problem}
This section introduces the Deterministic Integer Programming (DIP) and Stochastic Integer Programming (SIP) to optimize the resources used by minimizing the virtual service provider total cost.
\subsection{Deterministic Integer Programming}\label{dip}
All the resources can be subscribed to in the reservation plan if users' actual demand is precisely known. Therefore, the on-demand plan is not required. In total, there are four decision variables.
\begin{itemize}
\item $m_{w,v}^{(\mathrm{c},\mathrm{r})}$ indicates the duration that is reserved for user $w$ to use cyber resource $v$. For example, $m_{w,v}^{(\mathrm{c},\mathrm{r})}=1.2$ means that the virtual education provider reserves 1.2 hours for user $w$ to use cyber resource $v$.
\item $m_{w,x}^{(\mathrm{p},\mathrm{r})}$ indicates the duration that is reserved for user $w$ to use physical resource $x$.
\item $m_{w,z}^{(\mathrm{p},\mathrm{r})}$ indicates whether edge server $z$ is reserved to store and process the data from user $w$.
\item $m_{w,y}^{(\mathrm{h},\mathrm{r})}$ indicates the duration that is reserved for user $w$ to use people resource $y$.
\end{itemize}
A DIP can be formulated to minimize the total cost of the virtual education provider as follows:
\noindent $\displaystyle\min_{m_{w,v}^{(\mathrm{c},\mathrm{r})},m_{w,x}^{(\mathrm{p},\mathrm{r})},m_{w,z}^{(\mathrm{p},\mathrm{r})},m_{w,y}^{(\mathrm{h},\mathrm{r})}}$:
\begin{align}\label{dip1}
\sum_{w\in \mathcal{W}}\biggl(\sum_{v\in\mathcal{V}}(m_{w,v}^{(\mathrm{c},\mathrm{r})}c^r_v)+ \sum_{x\in\mathcal{X}}(m_{w,x}^{(\mathrm{p},\mathrm{r})}c^r_x)+\nonumber\\\sum_{z\in\mathcal{Z}}m_{w,z}^{(\mathrm{p},\mathrm{r})}c^r_z+\sum_{y\in\mathcal{Y}}m_{w,y}^{(\mathrm{h},\mathrm{r})}c^r_y\biggl),
\end{align}
subject to:
\begin{align}
&m_{w,v}^{(\mathrm{c},\mathrm{r})} = D_{w,v}, &\forall w\in \mathcal{W}, \forall v\in\mathcal{V},\label{dip_cons1}\\
&m_{w,x}^{(\mathrm{p},\mathrm{r})} = D_{w,x}, &\forall w\in \mathcal{W}, \forall x\in\mathcal{X},\label{dip_cons2}\\
&\bar{D}_{w,y}m_{w,y}^{(\mathrm{h},\mathrm{r})} = D_{w,y}, &\forall y\in\mathcal{Y}, \forall w\in \mathcal{W},\label{dip_cons3}\\
&\sum_{w\in \mathcal{W}}m_{w,y}^{(\mathrm{h},\mathrm{r})}\leq E_y, &\forall y\in\mathcal{Y},\label{dip_cons4}\\
&\sum_{z\in\mathcal{Z}}m_{w,z}^{(\mathrm{p},\mathrm{r})}I_z\geq D_w, &\forall w\in\mathcal{W},\label{dip_cons5}\\
&\sum_{w\in\mathcal{W}}m_{w,z}^{(\mathrm{p},\mathrm{r})} \leq 1, &\forall z\in\mathcal{Z},\label{dip_cons6}\\
&m_{w,z}^{(\mathrm{p},\mathrm{r})} \in\{0,1\}, &\forall z\in\mathcal{Z},\label{dip_cons7}\\
&m_{w,y}^{(\mathrm{h},\mathrm{r})} \in\{0,\ldots,E_y\},&\forall w\in \mathcal{W},\forall y\in\mathcal{Y},\label{dip_cons8}\\
&m_{w,v}^{(\mathrm{c},\mathrm{r})}, m_{w,x}^{(\mathrm{p},\mathrm{r})}, \in\mathbb{Z}^+, &\forall w\in \mathcal{W}, \forall v\in\mathcal{V},\forall x\in\mathcal{X}.\label{dip_cons9}
\end{align}
The objective function in~(\ref{dip1}) is to minimize the total cost due to resource reservation. $D_{w,v}$, $D_{w,x}$, and $D_{w,y}$ are the actual time demands for user $w$ to use cyber resource $v$, physical resource $x$, and people resource $y$. $\bar{D}_{w,y}$ is the actual availability of people resource $y$ when it is requested by user $w$. $D_w$ is the actual amount of data that user $w$ shared. The constraints in (\ref{dip_cons1})~-~(\ref{dip_cons3}) ensure that the demand is met. In~(\ref{dip_cons3}), if people resource $y$ is not available, user $w$ should request the service from another available people resource. (\ref{dip_cons4}) ensures that the number of hours allocated to people resource $y$ does not exceed $E_y$. (\ref{dip_cons5}) ensures that the number of edge servers should be large enough to support the amount of data user $w$ shared. (\ref{dip_cons6}) ensures that each edge server can only be used once in the whole network. (\ref{dip_cons7}) indicates that $m_{w,z}^{(\mathrm{p},\mathrm{r})}$ is a binary variable. (\ref{dip_cons8}) and~(\ref{dip_cons9}) indicate that $m_{w,v}^{(\mathrm{c},\mathrm{r})}$, $m_{w,x}^{(\mathrm{p},\mathrm{r})}$, and $m_{w,y}^{(\mathrm{h},\mathrm{r})}$ are positive decision variables.
\subsection{Stochastic Integer Programming}\label{sip_pro}
If the demands for the resources are not known, the DIP formulated in~(\ref{dip1})~-~(\ref{dip_cons4}) is no longer applicable. Therefore, SIP with a two-stage recourse is developed. This section introduces the SIP to minimize the total cost of the network by optimizing the number of hours allocated to each user for different types of resources. The first stage consists of all decisions that must be selected before the demands are realized and observed. The virtual service provider has to subscribe to the duration for the resources to be used in advance before observing the demands. In the second stage, decisions are allowed to adapt to the demand observed. After the demand is observed, the virtual service provider has to pay for the additional hours needed if the reserved duration is shorter than the demand.
Other than the four decision variables listed in Section~\ref{dip}, there are four more decision variables in the SIP formulation.
\begin{itemize}
\item $m_{w,v}^{(\mathrm{c},\mathrm{o})}(\lambda_i)$ indicates the duration that is used as on-demand for user $w$ to use cyber resource $v$ in scenario $\lambda_i$.
\item $m_{w,x}^{(\mathrm{p},\mathrm{o})}(\lambda_i)$ indicates the duration that is used as on-demand for user $w$ to use physical resource $x$ in scenario $\lambda_i$.
\item $m_{w,z}^{(\mathrm{p},\mathrm{o})}(\lambda_i)$ indicates if edge server $z$ is used as on-demand to store and process the data shared by user $w$ in scenario $\lambda_i$.
\item $m_{w}^{(\mathrm{h},\mathrm{o})}(\lambda_i)$ indicates the duration that the virtual education provider has to outsource for user $w$ for people resource in scenario $\lambda_i$.
\end{itemize}
The objective function given in~(\ref{sip1}) and~(\ref{sip2}) is to minimize the cost of the resource allocation. The expressions in~(\ref{sip1}) and~(\ref{sip2}) represent the first- and second-stage SIP, respectively. The SIP formulation can be expressed as follows:
\noindent $\displaystyle\min_{m_{w,v}^{(\mathrm{c},\mathrm{r})},\ldots,m^{(\mathrm{h},\mathrm{o})}_{w,y}(\lambda_i)}$:
\begin{align}\label{sip1}
\sum_{w\in \mathcal{W}}\biggl(\sum_{v\in\mathcal{V}}(m_{w,v}^{(\mathrm{c},\mathrm{r})}c^r_v)+ \sum_{x\in\mathcal{X}}(m^{(\mathrm{p},\mathrm{r})}_{w,x}c^r_x)+\sum_{z\in\mathcal{Z}}m_{w,z}^{(\mathrm{p},\mathrm{r})}c^r_z+\nonumber\\\sum_{y\in\mathcal{Y}}m^{(\mathrm{h},\mathrm{r})}_{w,y}c^r_y\biggl)+\mathbb{E}\biggl[\mathcal{Q}(m_{w,v}^{(\mathrm{c},\mathrm{r})},m^{(\mathrm{p},\mathrm{r})}_{w,x},m_{w,z}^{(\mathrm{p},\mathrm{r})},m^{(\mathrm{h},\mathrm{r})}_{w,y},\lambda_i)\biggr],
\end{align}
where
\begin{align}\label{sip2}
\mathcal{Q}(m_{w,v}^{(\mathrm{c},\mathrm{r})},m^{(\mathrm{p},\mathrm{r})}_{w,x},m_{w,z}^{(\mathrm{p},\mathrm{r})},m^{(\mathrm{h},\mathrm{r})}_{w,y},\lambda_i) =\sum_{\lambda_i\in\Omega}P(\lambda_i)\sum_{w\in \mathcal{W}}\nonumber\\\biggl(\sum_{v\in\mathcal{V}}
(m_{w,v}^{(\mathrm{c},\mathrm{o})}(\lambda_i)c^o_v)+ \sum_{x\in\mathcal{X}}(m^{(\mathrm{p},\mathrm{o})}_{w,x}(\lambda_i)c^o_x)+\nonumber\\\sum_{z\in\mathcal{Z}}m_{w,z}^{(\mathrm{p},\mathrm{o})}(\lambda_i)c^o_z+
\sum_{y\in\mathcal{Y}}m^{(\mathrm{h},\mathrm{o})}_{w,y}(\lambda_i)c^o_y\biggl),
\end{align}
subject to:
\begin{align}
m^{(\mathrm{c},\mathrm{r})}_{w,v} + m^{(\mathrm{c},\mathrm{o})}_{w,v}(\lambda_i) \geq F_{w,v}(\lambda_i),\hspace*{+25mm}\nonumber\\ \forall w\in \mathcal{W}, \forall v\in\mathcal{V}, \forall \lambda_i\in\Omega,\label{sip_cons1}
\end{align}
\begin{align}
m^{(\mathrm{p},\mathrm{r})}_{w,x} + m^{(\mathrm{p},\mathrm{o})}_{w,x}(\lambda_i) \geq F_{w,x}(\lambda_i),\hspace*{+25mm}\nonumber\\ \forall w\in \mathcal{W}, \forall x\in\mathcal{X},\forall \lambda_i\in\Omega,\label{sip_cons2}
\end{align}
\begin{align}
\bar{F}_{w,y}(\lambda_i)m^{(\mathrm{h},\mathrm{r})}_{w,y} + m^{(\mathrm{h},\mathrm{o})}_{w}(\lambda_i) \geq F_{w,y}(\lambda_i),\hspace*{+11mm}\nonumber\\ \forall y\in\mathcal{Y}, \forall w\in \mathcal{W},\forall \lambda_i\in\Omega,\hspace*{-1mm}\label{sip_cons3}
\end{align}
\begin{align}
&\sum_{w\in \mathcal{W}}m^{(\mathrm{h},\mathrm{r})}_{w,y}\leq E_y,\hspace*{+18mm} &\forall y\in\mathcal{Y},\label{sip_cons4}\\
&\sum_{w\in\mathcal{W}}m_{w,z}^{(\mathrm{p},\mathrm{r})} \leq 1, &\forall z\in\mathcal{Z},\label{sip_cons6}\\
&\sum_{w\in\mathcal{W}}m_{w,z}^{(\mathrm{p},\mathrm{r})}(\lambda_i) \leq 1, &\forall z\in\mathcal{Z},\forall \lambda_i\in\Omega,\label{sip_cons7}
\end{align}
\begin{align}
\sum_{z\in\mathcal{Z}}m_{w,z}^{(\mathrm{p},\mathrm{r})}I_z +\sum_{z\in\mathcal{Z}}m_{w,z}^{(\mathrm{p},\mathrm{o})}(\lambda_i)I_z \geq F_w(\lambda_i),\hspace*{+8mm} \nonumber\\ \forall w\in \mathcal{W},\forall \lambda_i\in\Omega,\hspace*{-0mm}\label{sip_cons8}
\end{align}
\begin{align}
&m_{w,z}^{(\mathrm{p},\mathrm{r})}+ m_{w,z}^{(\mathrm{p},\mathrm{r})}(\lambda_i) =1, &\forall w\in \mathcal{W},\forall z\in\mathcal{Z},\forall \lambda_i\in\Omega,\label{sip_cons9}\\
&m_{w,z}^{(\mathrm{p},\mathrm{r})},m_{w,z}^{(\mathrm{p},\mathrm{r})}(\lambda_i) \in\{0,1\}, &\forall w\in \mathcal{W},\forall z\in\mathcal{Z},\forall \lambda_i\in\Omega,\label{sip_cons10}
\end{align}
\begin{align}
m^{(\mathrm{h},\mathrm{r})}_{w,y},m^{(\mathrm{h},\mathrm{o})}_{w,y}(\lambda_i)\in\{0,\ldots,E_y\},\hspace*{+28mm}\nonumber\\\forall w\in \mathcal{W},\forall y\in\mathcal{Y},\forall \lambda_i\in\Omega,\label{sip_cons11}
\end{align}
\begin{align}
m^{(\mathrm{c},\mathrm{r})}_{w,v}, m^{(\mathrm{p},\mathrm{r})}_{w,x}, m^{(\mathrm{c},\mathrm{o})}_{w,v}(\lambda_i),m^{(\mathrm{p},\mathrm{o})}_{w,x}(\lambda_i) \in\mathbb{Z}^+,\hspace*{+8mm} \nonumber\\\forall w\in \mathcal{W}, \forall v\in\mathcal{V},\forall x\in\mathcal{X},\forall \lambda_i\in\Omega.\label{sip_cons12}
\end{align}
(\ref{sip_cons1})~-~(\ref{sip_cons3}) ensure that each user's demand has to be met by using the reservation and on-demand plan. In~(\ref{sip_cons3}), if the people resource $y$ is not available, user $w$ should request the on-demand service from another available people resource. (\ref{sip_cons4}) ensures that the number of hours allocated to people resource $y$ in the reservation plan does not exceed $E_y$. (\ref{sip_cons6}) and~(\ref{sip_cons7}) ensure that each edge server can only be used once in the whole network. (\ref{sip_cons8}) ensures that there should be enough edge servers for the virtual service provider to store and process the shared data. (\ref{sip_cons9}) ensures that each edge server can subscribe only one time in each of the plans. (\ref{sip_cons10}) indicates that $m^{(\mathrm{h},\mathrm{r})}_{w,y}$ and $m^{(\mathrm{h},\mathrm{o})}_{w,y}(\lambda_i)$ are binary variables. (\ref{sip_cons11}) and~(\ref{sip_cons12}) indicate that $m^{(\mathrm{c},\mathrm{r})}_{w,v}$, $m^{(\mathrm{p},\mathrm{r})}_{w,x}$, $m^{(\mathrm{h},\mathrm{r})}_{w,y}$, $m^{(\mathrm{c},\mathrm{o})}_{w,v}(\lambda_i)$, $m^{(\mathrm{p},\mathrm{o})}_{w,x}(\lambda_i)$, and $m^{(\mathrm{h},\mathrm{o})}_{w,y}(\lambda_i)$ are positive decision variables.
\begin{figure}[t]
\includegraphics[width=8cm, height=4cm,trim={0cm 9cm 0cm 0},clip]{metaverse.png}
\caption{3D English Education Metaverse prototype through metaverse viewer.}
\label{fig:prototype}
\end{figure}
\begin{figure*}[t]
\centering
\begin{multicols}{4}
\includegraphics[width=0.95\columnwidth]{optimal_cost_cyber.pdf}
\caption{The cost structure in a simple SIP network for using cyber resource $\bar{w}$.}
\label{fig:optimal cost cyber}
\includegraphics[width=0.95\columnwidth]{optimal_cost_physical.pdf}\par
\caption{The cost structure in a simple SIP network for using physical resource $\bar{c}$.}
\label{fig:optimal cost physical}
\includegraphics[width=0.85\columnwidth]{optimal_cost_edge.pdf}\par
\caption{The cost structure in a simple SIP network for using edge servers.}
\label{fig:optimal cost edge}
\includegraphics[width=0.95\columnwidth]{optimal_cost_human.pdf}\par
\caption{The cost structure in a simple SIP network for using people resource $\bar{y}_1$.}
\label{fig:optimal cost human}
\end{multicols}
\vspace*{-5mm}
\end{figure*}
\section{Performance Evaluation}\label{simulation}
\subsection{English Education Metaverse Prototype}
We develop the 3D English Education metaverse (EEM) on Unity~\cite{unity}, a cross-platform development engine. As shown in Fig.~\ref{fig:prototype}, we illustrate the interface of the proposed 3D English Education Metaverse prototype through the implemented metaverse viewer. The metaverse viewer is built for the users to interact with the metaverse. By using the smartphone as the platform, the users can access the metaverse any time and any place with Internet access.
In this EEM, the resource owners first charge the virtual education provider with the on-demand (hourly) or the reservation cost (per semester). Then, after the resources are purchased, the virtual education provider offers the users services according to the users' demands. Then, the users can navigate about in the virtual world using their avatars to choose the service they want. All the users can communicate with the NPCs if any of them has any issues. Each user has different demands, and the virtual education provider needs to allocate the optimal resource to serve the users. The two-stage SIP from Section~\ref{sip_pro} is used to optimize resource allocation by minimizing each user's reservation and on-demand cost. The first stage (\ref{sip1}) is to minimize the reservation cost, and the second stage (\ref{sip2}) is to minimize the on-demand cost.
\begin{figure*}[t]
\centering
\begin{multicols}{4}
\includegraphics[width=0.95\columnwidth]{smallscale.pdf}\par
\caption{The cost of edge servers and cyber resources.}
\label{fig:smallscale}
\includegraphics[width=0.95\columnwidth]{largescale.pdf}
\caption{The cost of physical and people resources.}
\label{fig:largescale}
\includegraphics[width=0.85\columnwidth]{probability_threshold.pdf}\par
\caption{The probability threshold of edge servers.}
\label{fig:threshold}
\includegraphics[width=0.95\columnwidth]{EVF.pdf}\par
\caption{SIP comparing with EVF and randoms cheme.}
\label{fig:evf}
\end{multicols}
\vspace*{-5mm}
\end{figure*}
\subsection{Parameter Setting}
We consider the English language school to be is the virtual service provider that offers services to ten users, and there are 20 edge servers available $|\mathcal{Z}|=20$. Teachers are the people resources $\mathcal{Y}~=~\{\bar{y}_1,\bar{y}_2,\bar{y}_3,\bar{y}_4\}$. $\mathcal{V}~=~\{\bar{w},\bar{s},\bar{l}\}$, where $\bar{w}$ represents the writing practice such as Grammarly~\cite{grammarly}, $\bar{s}$ represents the speaking practice such as ELSA~\cite{ELSA}, and $\bar{l}$ represents gamified learning such as Brainscape~\cite{brainscape}. $\mathcal{X}=\{\bar{c}\}$, where $\bar{c}$ represents a physical classroom.
All the resource owners offer a short-term plan and a long-term plan. We consider the long-term plan as the reservation plan, and the short-term plan is the on-demand plan. Therefore, $c^r_{v:\bar{w}}=\$0.017$/hr, $c^o_{v:\bar{w}}=\$0.035$/hr, $c^r_{v:\bar{s}}=\$0.005$/hr, $c^o_{v:\bar{s}}=\$0.009$/hr, $c^r_{v:\bar{l}}=\$0.010$/hr, $c^o_{v:\bar{l}}=\$0.014$/hr, $c^r_{x:\bar{c}}=\$3.5$/hr, and $c^o_{x:\bar{c}}=\$4$/hr~\cite{grammarly,ELSA,brainscape,classroom}. We assume that the virtual education provider update its data every hour by store and process the data that the users are willing to share. Thus, the costs are $c^r_z=\$0.07625$/use and $c^o_z= \$0.13875$/use~\cite{smartphone}.
We use the full-time teacher's salary as the reservation plan and the part-time teacher's salary as the on-demand plan. Then, $c^o_{y}=\$19.6$/hr and $c^r_{y}=\$25$/hr~\cite{teacher}.
To solve SIP, we assume that the probability distribution of all scenarios in set $\Omega$ are known~\cite{dyer2006computational}, then, the complexity of the problem depends on the total number of scenarios in stage two~\cite{dyer2006computational}. For example in Section~\ref{sip_pro}, the complexity for the formulated two-stage SIP is $|\Omega|$. For the presented experiments, we implement the SIP model using GAMS script~\cite{chattopadhyay1999application}.
\subsection{Simulations}
\subsubsection{Cost structure} We first study the cost structure of the network. As an illustration, a simple network is considered with only one component in each resource set, e.g., $|\mathcal{V}|=1$, one user, and two demand scenarios $|\Omega|=2$. The first demand scenario is $\lambda_1$, the user has a demand to use all the resources and is willing to share some data. The second demand scenario is $\lambda_2$, and the user has another demand to use all the resources and is willing to share a different amount of data. We consider a stochastic system with $P(\lambda_1)= 0.6$ and $P(\lambda_1)= 0.4$. We observe the cost structure of the network by varying the number of hours reserved for all the resources except for edge servers, where we vary the number of edge servers reserved. The cost structures are shown in Figs.~\ref{fig:optimal cost cyber}~-~\ref{fig:optimal cost human}. In Fig.~\ref{fig:optimal cost cyber}, the costs in the first and second stages, as well as the overall cost under different number of hours reserved for cyber resource $\bar{w}$ is presented. We can observe that the first stage cost (reservation cost), increases as the number of hours of resource reserved increases. With more hours reserved in the first stage, stage 2 cost is reduced as the need for on-demand reduces. It can be identified that even in this simple network, the optimal solution is not trivial to obtain due to the uncertainty of demands. For example, the optimal cost is not the point where the cost in the first and second stages intersect. Therefore, SIP formulation is required to guarantee the minimum cost to the network.
\subsubsection{Individual resources}\label{setup2} There are two demand scenarios $|\Omega|=2$, including i) all the users have demands and all the teachers are not available, e.g., medical leave, denoted by $\lambda_1$ and ii) all the users have no demand denoted by $\lambda_2$. We analyze individually each resource by varying both the demand probabilities $P(\lambda_1)$ and $P(\lambda_2)$. The cost of resources are shown in Figs.~\ref{fig:smallscale} and~\ref{fig:largescale}. For better visualization, the cost of the resources is split into two parts. When the probability of the demand $P(\lambda_1)$ is low, it is cheaper for the virtual education provider to subscribe to the resources using the on-demand plan. From the results, the decision on choosing the subscription plans is also affected by the magnitude of differences between the reservation cost and on-demand cost. If the reservation cost is close to the on-demand cost, the virtual education provider will only subscribe to that resource when $P(\lambda_1)$ is very high. For example, the virtual education provider only books the classroom using the reservation plan when $P(\lambda_1)=1$. However, if the reservation cost is much lower than the on-demand cost, e.g., $c^o_{v:1}$ is more than two times $c^r_{v:1}$, it is cheaper for the virtual education provider to subscribe to that resource in the reservation plan when $P(\lambda_1)$ is not high.
\subsubsection{Probability threshold of demand scenario} We consider the settings similar to Section \ref{setup2}. From Fig.~\ref{fig:smallscale}, the virtual education provider changes its decisions for edge servers when $P(\lambda_1)$ increases from 0.5 to 0.75. In this simulation, we will increase $P(\lambda_1)$ with a small step of 0.01 to determine the probability threshold that causes the virtual education provider to change subscription decisions. The result is illustrated in Fig.~\ref{fig:threshold}. When the probability of scenario 1 is greater or equal to 0.55, we can observe the probability threshold for the virtual education provider to consider the reservation plan as the cheaper plan than that of the on-demand plan.
\subsubsection{Comparing between EVF, SIP and random scheme}
We compare the SIP with expected-value formulation (EVF)~\cite{5394134} as well as the random scheme. For EVF, the number of hours in the first stage is fixed by the average value of demand, an approximation scheme. In the random scheme, the values of the decision variables are randomly generated. We vary the on-demand cost to compare the difference between EVF, SIP, and random schemes. Fig.~\ref{fig:evf} depicts the comparison result. As shown in the result, EVF and random scheme cannot adapt to the change in cost. On the other hand, SIP can always achieve the best solution among the three to reduce the on-demand cost.
\section{Conclusion}\label{conclusion}
In this paper, we have presented a unified resource allocation framework SORAS for the edge-based metaverse in a case study of education sector. To achieve the optimal allocation, SORAS minimizes the total cost of the network. The performance evaluation of SORAS has been performed by numerical studies and simulations. Compared to the benchmark, SORAS based on SIP can achieve the best solution as it can better adapt to changes in the probability of users' demands.
\bibliographystyle{IEEEtran}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,670 |
Dr. Nina Lum
Never be oppressed by restrictions
"I'm Christian and I believe that God places us in different phases of our lives for different reasons, and the biggest dream I have is to be able to meet my calling or my purpose." – Dr. Nina Lum
At a very young age, Dr. Nina Lum was exposed to how life changing a career in medicine could be. Her mother is a paediatrician in her native Cameroon. Growing up Nina was familiar with the late-night knocks on their door from frantic parents with a sick child. She'd watch as her mother tended to the child, and then marvel when a few days later that child was fully back to health.
Inspired by her mother's example, Nina decided to pursue medicine as a career. But with only one medical school in the whole country, Nina soon came face to face with crushing disappointment – she was not accepted into the Cameroonian medical school.
"You will meet and encounter difficulties. You will be restricted, and to a certain degree succumb to it, but never be oppressed by it." – Dr. Nina Lum
Undeterred, she pursued a Plan B, and then a Plan C, and was contemplating a Plan D when she was finally accepted into medical school in the Caribbean.
Nina talks about the many challenges, but also triumphs, of her journey to becoming 'Dr Nina'. She also shares the big dreams she has for the future, and her plans to give back to her home country.
"Coming out of residency, I made a conscious decision that I was going to prioritize my health and wellness as much as my clinical practice, because I've had to learn the hard way that if I didn't take care of myself, I was never going to be able to take care of other people." – Dr. Nina Lum
Dr. Nina also hosts a podcast called The IMG Roadmap. Her podcast is dedicated to guiding International Medical Graduates (IMGs) with success blueprints for this unique pathway, offering practical tools equipping IMGs with applicable strategies to achieve their "US doctor goals".
How seeing her mother's work ethic inspired her to follow her dreams
What inspired Nina to want to pursue a career in medicine
How she had to go through Plan A, Plan B, Plan C and was thinking of going to a Plan D to pursue her dream of medical school
What it was like being an immigrant going through medical school
How Nina keeps balance in her life
Why she felt it was important to participate in the writing of the book 'The Chronicles of Women in White Coats'
The greatest lesson she learned from her mother
The best advice she has ever been given
How Nina hopes to impact the world
Nina on Instagram
Nina on Twitter
Nina's Website
Dr Nina's Book 'The Chronicles of Women in White Coats' website
The IMG Roadmap Podcast | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,574 |
North Carolina legislators reconvened on Monday to kick off a full week of committee presentations and floor votes. House lawmakers held several floor votes this week, including an unanimous vote on HB 283: Conner's Law, which increases penalties for assaulting law enforcement officers and emergency personnel with the use of a gun or deadly weapon. The list of approved House bills also includes one that would make an arts education credit a graduation requirement, regulate "mini-trucks", and set the process for state board of community colleges appointments, to name a few.
Both the House and the Senate will reconvene on Monday, March 25th for no vote sessions, the House at 7:00pm and the Senate at 2:00pm.
Broadband Legislation
The latest in a series of bills aimed at improving access to high-speed internet was filed by House lawmakers Thursday. HB 431: FIBER NC Act would allow cities, towns, and counties to build broadband internet infrastructure and lease it to private internet providers. The N.C. League of Municipalities and the Association of County Commissioners back the bill, arguing that it would give more people access to high-speed internet through public-private partnerships. Kevin Austin, president of the county commissioners' association, feels this bill would allow counties, especially those in rural parts of the state, the ability to connect.
A similar bill passed the House in 2017 but was not heard in the Senate, as then Senate Majority Leader Harry Brown (R-Onslow) felt partnerships with local governments would not solve the problem because many municipalities already have broadband. Instead, Sen. Brown has supported grants to internet providers in hopes of making it economically feasible to offer high-speed internet to less populated areas of the state. Through what is known as the GREAT program, an initial $10 million in grants will soon be awarded to parts of the state, with several additional proposals in the legislature to add more funds.
Opponents argue that the measure would be a poor use of taxpayer dollars, particularly given the serious need across the state for more funding for schools and infrastructure. Most municipalities already have multiple options when it comes to choosing a broadband provider, leading some to see a government-run broadband option as redundant. Under North Carolina law, municipalities already have the authority to provide broadband services to the few remaining areas of the state without broadband access.
Rep. Dean Arp (R-Union) proposed $150 million for the "GREAT" program over the next decade through HB 398: Growing GREAT-Rural Broadband Funding. The bill would allocate $15 million to the program each year for 10 years and would adjust the formula used to evaluate grant applicants. Rep. Arp has also sponsored HB 381: School Construction & Broadband Investm't Act., a bill that would add $15 million each year to the GREAT program from the State Capital and Infrastructure Fund. Governor Roy Cooper's budget proposal, released earlier this month, includes $30 million for the GREAT grant program.
Charter Moratorium
Senate Democrats are looking to place an indefinite moratorium on new charter school applications while a proposed study committee looks into the effectiveness of the growing school alternative. SB 247: Charter School Study/Moratorium on Growth calls for a joint legislative study committee on the impact of charter schools on local school administrative units to make recommendations on topics such as the potential benefits and harms of charter school expansion on public school districts.
Members of the Wake County and Durham County school boards joined Senate Minority Leader Dan Blue (D-Wake) at a news conference Wednesday to express support for the bill. It is not clear how long the proposed moratorium on new charter school applications would last, as the bill would leave it in place until legislation is enacted using the report and recommendations of the study committee. The bill would give the study committee a deadline of March 1, 2021. SB 247 would also prevent current charter schools from expanding their allotted enrollments or adding additional grades. 39 counties in North Carolina do not yet have a charter school and a moratorium may delay those counties the ability to get that option.
UNC Board of Governors Election
Both House and Senate legislators elected members to the UNC Board of Governors this week. Wednesday, House members were asked to vote up or down a slate of six candidates put together by chamber leadership. Democratic members urged their Republican colleagues to consider the importance of racial and ideological diversity among members of the board, which oversees the state's public university system. Republican House members defended their candidates and the election process, resulting in the passage of the slate in a 63-52 vote.
The approved House appointees are:
Pearl Burris-Floyd
C. Phillip Byers
James Holmes Jr.
Hilton Terry Hutchens
J. Alex Mitchell
David Powers
During session on Thursday, it was the Senate's turn. Members were tasked with electing six members of the board. While 11 people were nominated for the positions earlier this month, four had removed themselves from consideration, leaving the chamber with 7 candidates to choose from. Senate Democrats voiced their concerns on the rules of the election, which required each senator to vote for six candidates or their votes would be thrown out. Senate Republicans replied by pointing to the unanimous resolution establishing the process for this year's election earlier in this year's session.
The approved Senate appointees are:
Darrell Allison
Thomas Goolsby
Martin Holton
Anna Spangler Nelson
Temple Sloan
Michael Williford
Hemp Crop
North Carolina Lawmakers are looking to hemp production as the cash crop of the future. The annual Farm Act, rolled out on Wednesday, used 10 of its 16-page proposal to outline the necessary infrastructure the state would need to make the most of the federal government's loosening of hemp production restrictions. Following a two-year government-sponsored pilot project, the state's hemp production has boomed to 634 licensed farmers on about 8,000 acres of land and 3.4 million square feet of greenhouse space. The Farm Act calls for establishing a nine-member state commission to license growers who would have to agree to allow state and local law enforcement on their property to conduct spot inspections, ensuring farmers are not trying to grow marijuana instead of hemp.
The Farm Act also includes branding North Carolina-grown sweet potatoes for both domestic and international markets, allows hunting, fishing, and shooting to be added to agritourism use, and would allow farmers the ability to post promotional signs on their property.
This week, the Senate Judiciary committee moved SB 168: Expand Allowed Medical Uses/Cannabis Extract along to the Rules and Operations committee. This bill would allow CBD oil treatments for all individuals who experience autism, multiple sclerosis, Crohn's disease, and mitochondrial disease. This same bill was filed during the 2017 session but did not receive action by the Senate Health Committee.
Upcoming Legislative Meetings
Monday, March 25th
2:00PM Senate: Session Convenes
3:00PM House: Rules, Calendar, and Operations of the House
3:00PM Senate: Select Committee on Prison Safety
7:00PM House: Session Convenes
Tuesday, March 26th
8:30AM Senate: Joint Appropriations on Justice and Public Safety
8:30AM House: Appropriations, Education (Joint)
8:30AM Senate: Joint Appropriations on Education/Higher Education
9:00AM House: Appropriations, Agriculture and Natural and Economic Resources (Joint)
9:00AM Senate: Joint Appropriations on Agriculture, Natural, and Economic Resources
9:00AM House: Appropriations, Health and Human Services (Joint)
9:00AM Senate: Joint Appropriations on Health and Human Services
10:00AM House: Transportation
10:00AM House: Health
11:00AM House: Education – Community Colleges
1:00PM House: Education – K-12
2:00PM Senate: State and Local Government
2:00PM House: Aging
8:15AM House: Finance, Subcommittee on Annexation/Deannexation
8:30AM House: Finance
8:30AM House: Appropriations, Health and Human Services
10:00AM Senate: Agriculture/Environment/Natural Resources
10:00AM House: Commerce
11:00AM Senate: Education/Higher Education
12:00PM Senate: Transportation
Thursday, March 28th
8:30AM House: Appropriations, Transportation (Joint)
11:00AM House: Regulatory Reform
Harrison Kaplan
Jeffrey Barnhart
Franklin Freeman
D. Heath
Johnny Tillett
Kerri Burke
Sarah Wolfe
Tommy Sevier
Tyler Ford | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,683 |
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