M(eta)

Melancholia

2011-10-11T11:38:00.000+01:00

Si on définit la mélancolie comme une inaptitude au bonheur, on peut imaginer reconstruire grossièrement le processus qu'a suivi Lars von Trier pour écrire le scénario de son dernier film Melancholia. Il lui fallait d'abord poser comme cadre un événement qui se prête pleinement au bonheur -- un mariage fastueux, un avenir professionnel radieux, etc. -- pour mieux faire ressortir le caractère (apparemment) abbérant des sentiments d'abatement de la mariée Justine (Kirsten Dunst, prix d'interprétation féminine à Cannes, même si c'est plutôt Charlotte Gainsbourg qu'on regarde.. mais bon elle l'avait déjà pécho en 2009 pour sa prestation dans Antichrist). Sa froideur et son détachement incompréhensibles finissent par faire capoter le mariage et partir le marié.

La deuxième partie du film décrit les quelques jours précédant la collision d'une planète nommée Melancholia qui se cachait jusque-là derrière le Soleil. J'y vois une variation sur le même thème d'un bonheur à portée de main (une jolie famille dans une belle propriété, un événement astronomique unique et excitant à observer, etc.) qui périclite malgré tout. La destruction de la vie sur Terre (et donc partout selon Justine) qui s'ensuit est l'image amplifiée de la séparation des mariés qui les prive de leur chance de progéniture. C'est donc la même histoire qui est racontée de deux manières différentes: la première fois à un niveau personnel, famillial, et la seconde à un niveau cosmologique. Une telle projection de motifs psychologiques sur des éléments naturels me fait penser à la manière dont les alchimistes projetaient leurs conflits internes sur les métaux. Jung disait que l'alchimie constituait le revers de la médaille du christianisme en ce sens qu'alors que les chrétiens se considéraient comme pécheurs originels et cherchaient à se sauver par la foi, les alchimistes considéraient que c'était la matière physique qui était corrompue et voulaient la purifier en transformant par exemple le plomb en or (philosophique).

Peut-être Lars a-t-il été influencé par la lecture de Saturne et la Mélancolie de Panofsky et Saxl?

WoW for science

2011-09-17T18:27:00.004+01:00

I found this talk by Jane McGonigal on the benefits of gaming quite inspiring (see also a more recent one). She makes a convincing point that after having spent about 10,000 hours playing online games during their youth (almost as much as they spend in school) gamers have acquired mad skillz and it would be nice to see this potential realize itself in the real world. She refers to the game "World of Warcraft" (WoW) as the "ideal collaborative problem-solving environment" (4:30) and I immediately thought this kind of platform should be used for scientific research. This would basically turn research into video game. Note that this isn't a very long stretch since the feeling of research can be as exciting as that of video game.
I have to say though that I don't know the first thing about WoW, except that you have to "pwn the noobs" and become a "leet king" (1337). Apparently, you are being assigned a mission matching the abilities of your avatar (orcs, trolls, dwarfs, paladin, etc.), and you collaborate with hundreds of other players to achieve an "epic win". You get frequent feedback on your performance and your level increases.

Now imagine that instead of having to kill a dragon or whatever, the players are given actual unsolved scientific problems. Pretty cool, hu?

In fact, similar platforms already exists, most notably Tim Gowers' Polymath project, and it's also interesting to recall that in their early days the internet and the world wide web were inextricably linked to scientific research. The arXiv is a brilliant example. This all comes together in Michael Nielsen's promotion of open science. [Btw, all those TeD talks are so insufferably optimistic and well-intentioned!]
Maybe another site worth mentioning would be the Open Problem Garden.

That's more like a collection of hyperlinks than a proper reflection, but I'll leave it at that for now.

Uncle Boonmee Who Can Recall His Past Lives

2011-01-17T23:23:00.011Z

The 2010 Palme d'Or finally arrived in Oxford. It was at the Ultimate Picture Palace, I was sitting on the very first row, and I had the time of my life. It's a sublime jewel of supernatural enchantments, simple and sophisticated altogether, traditional and avant-garde. Well done Apichatpong Weerasethakul!

I just want to talk about one single shot, not because it is the most representative of the movie, but because it struck my imagination. It's a static shot of a room, facing a wall against which there is a bench on which two persons are sitting. They are watching a tv on a table against the left wall of the room. So they are not facing the tv but rather have a very oblique perspective on it. So much so that I wondered if they were actually able to see the screen. It seems completely unrealistic. A more conventional way to edit such a scene would have been to show the people frontally and then cut on a shot of the tv that they're watching (btw the last scene of the movie is of that type:(. Then I realized that it did not matter after all, since the scene makes perfect narrative sense as it is. It's clear that they're watching the tv, even though both their faces and the tv are visible simultaneously. This stylistic effect is somehow reminiscent of certain cubist paintings which show a face both in profile and frontally. But it goes even further: whereas the cubist portrait presents different perspectives on one object, Apichatpong's shot encompasses both the observers and what they observe at once. Some sort of primordial unity regained!

Googoo Gaga

2011-01-14T22:55:00.020Z

I've been willing to write about Lady Gaga for a little while, but it was incompatible with postdoc application time so I postponed. Also, I wasn't too sure, to be honest, what I could possibly write about her that would not be too obviously dumb. My attention was brought to her by this video (not exactly the official vid -- careful). Check out this video rather, viewed more than 300m times (I remember a time where a million views was amazing..) [I'm not saying there's nothing lame about the video btw]. I liked the fact that some of the lyrics are in French, or at least in some sort of French. Quite glam I thought, for an American pop song. Also there's a purer rave sound than you'd expect, stuff that was underground in the 90s but that still does the job OK. Then I realized that Lady Gaga is closer to a performance artist than a pop star, and a rather interesting one moreover. My first suspicion of her significance was confirmed when I learned that the young US officer that smuggled the 240,000 diplomatic cables published by Wikileaks did so by burning them on a Lady Gaga CD! This mixture of art and political revelations might appear coincidental but I like to imagine, a bit in the spirit of Wreck & Salvage, that there is some deeper connections, whose roots dive into the current American Zeitgeist. Whatever.

Gaga's first words in Bad Romance are something like

Rha rha a ah aha
Roma rromama a
Gaga oh lala a
Want your bad romance

[Just to mention, there are already two French elements in there: the rolled "r" and the "oh lala".]

And this is the kind of thing that will play in your head while you're cooking for instance. So at some point I asked myself but what is she saying for fuck's sake? There are words that I can recognize, specially the last bit, that's rather clear, and "Gaga" also makes an apparition, and there are bits that are clearly just sounds, like the "ohooho" of the introduction; but what I find puzzling is that there is also something that is between the two.

First, the "rha rha" are purely bestial (think MGM lion) and they degenerate, just like every line, to some simply musical sounds. Then comes the intriguing part: "Roma". This also appears as just a meaningless sound but it's far too close [sic] to the "romance" in the title of the song not to be related to it. Certainly it has to be some embryonic version of it. Something is taking shape here, from the bestiality of a prelinguistic realm towards some more advanced form of communication, namely language. Notice also that when the "roma" degenerates, one could hear "mama" [compare to "papa paparazzi"]. Just like what happens in the development of a child, the first thing that comes out of the undefined darkness is the figure of the mother. Then comes "Gaga", the ego. This also frequently a child's first sounds. And finally something resembling a sentence expressing a desire towards the other can be formulated.

So my verdict would be that this chorus illustrates the genetics of the artistic process, through which a raw emotion is sublimed into some creation that resort to a higher level language.

Now one could wonder if this emergence process was successfully performed in this case. After all, it all comes to wanting "your bad romance". Sounds more like a destructive drive to me. In addition, the ego/other or subject/object couple is not adequately articulated. Not only is the "I" still missing, but also it would seem more natural to want "our romance" instead of "yours". Similarly, later in the song one hears "And I want your revenge": what is that suppose to mean? Well, maybe this is intended as "I want my revenge on you". That would make more sense. Unless... Could the artist be skillfully using this me/you confusion to underline the fact that such a vicious spiral of projections and counter-projections often characterizes a "bad romance"? Stefani Germanotta: brava!

Early thoughts

2010-09-05T15:11:00.029+01:00

I have a rather clear memory of what might have been the first time I realised that I was capable of thinking. We were having a lunch with my family in the annex of our house, where we used to roast meat on Sundays. The conversation came to the subject of the existence of God, and whether it was possible to prove it or not. I said that I considered that such a proof was not even desirable since since according to Saint Paul's Apocalypse God would come back on Earth at the end of time if we managed by earthly considerations to prove that He's here, then that would be the end of time. My parents' and sister's reaction was that of surprise that such ideas could circulate in my head. This made me aware that a thought had been created within me that had not been introduced there from the outside.

Some years (?) later I came across Saint Anselme of Canterbury's "ontological argument" for the existence of God. Roughly, it resorted to the reductio ad absurdum and said that given that the Perfect Being must have all positive qualities, if He didn't exist, He would lack one of those qualities, namely the quality of existing. I imagined a refutation of it, which went as follows. If the existence of God could be proven, then we humans would have no choice but to believe in Him -- in which case He would also lack a quality, the generosity of letting His creatures decide freely if they want to believe in Him or not.

Beyond the naive scholasticism of those early thoughts, something in their spirit is still very much akin to what turns me on nowadays.

Had I pushed my reflections a bit further, I would have realised that I was dealing with an absurd absurdity. By the same type of reasoning it has to be true that God does exist but it must also be impossible for us to prove it. How can this be? And then of course it's Godel's incompleteness theorem that comes to mind. (Godel who btw wrote down an ontological proof of his own using modal logic, which he kept secret until he thought his last days had arrived...)

PS: Those memories came back to me today while I was playing with the following thought:

"The meaning of life is to search for the meaning of life."

I like it because of its circularity and because it's contradictory in the sense that it implies that were we to actually find the meaning of life it would be gone. In fact it's also contradictory in the sense that it undermines its own content: it gives you the meaning so why search for it? The entire substance of the sentence is sucked in by the word "search", which then operates just like a minus sign in an equation. One could for example symbolise it abstractly as

\[ \infty - \infty = 0.\]

I fancy writing it in repetitive style as well:

" The meaning of life

is to search for the meaning of life

is to search for the meaning of life."

Just like that.

PPS: the etymology of the word "search" is agreeable since, along with chercher in French and cercare in Italian, it comes from the Latin word circus, the circle. :) Should we push the perversity yet another step further and replace it by the word "research"?

Laughing and research

2010-07-05T18:37:00.006+01:00

What is it that makes us laugh in a joke, after all?
It seems to me that a joke always requires from the audience a certain amount of mental effort to see the meaning of the joke. There is a gap in the plot and it has to be filled for the joke to be funny.
For instance:

A guy comes into a bar, completely drunk, and asks for a drink. The barman tells him that he never serves drunk people. The guy goes away but comes back five minutes later. The barman refuses again. The guy goes away but comes back ten minutes later, and so on.
Finally the drunk guy asks the barman: "Is there a single bar in this city where you don't work?"

To laugh at this joke you need to understand that the guy thinks he is visiting different bars, but he is so drunk he always ends up in the same bar.

The misanthropically inclined mind will think that then the laughter is only a demonstration of pride to have been able to crack the mystery.

But another interpretation would be that cracking the mystery is a pleasure in itself, and the real cause of the laughter.

We researchers are devoting our time to crack mysteries, although of different proportions. We are laughing the great laughter.

The geometry of 3-manifolds

2010-03-21T18:39:00.011Z

If you want to get an idea of the famous Poincaré conjecture for which Grigoriy Perelman was recently awarded a Millenium prize, I highly recommend watching this very entertaining lecture by Curtis McMullen at Harvard in 2006.

I had never realised that tori of genus greater than one are hyperbolic! It makes sense, if you think that a sphere (genus 0) has positive curvature, a torus (genus 1) is flat, that tori of genus 2 and more have negative curvature. These higher tori can be constructed by gluing together the edges of polygons.

I wonder whether anti-de Sitter space can also be viewed as a high genus space. Are the many black holes in the universe implying that it has a high "genus"? But the notion of genus isn't clear in higher dimensions...

So I started (very naively) to think about black holes on a latex surface, like the ones shown in the lecture. Consider a sphere and put a stone at the north pole. The sphere will bend, just like spacetime bends around the sun. Now imagine that you had a way to increase the mass of the stone, it would create a well at the north pole which would eventually touch the south pole from the inside. What happens then? The well could continue to become deeper and deeper but now it would create a spike out of the south pole. This is certainly misleading. More likely, once the stone approaches the south pole from the inside, its mass sucks it in, creating a well (as well).

Ultimately, what you'll end up with is a torus. The Planckian mass is at the centre of this torus, where there is really no spacetime: that's the black hole!

I had an unexpected confirmation of this picture in my kitchen. There was a frying pan full of a layer of greasy water and I noticed that it tended to leave discs where there was no water. By slowly pouring more water into the pan, the discs would shrink until there reach zero size, at which point a circular wave was emitted. I had just witnessed a topology change;) I could also reverse the process by taking some water out of the pan and stirring up the water. When the water had stabilised enough, discs were suddenly appearing and expanding quickly. That's my version of frying pan black holes: try it at home!

PS: the key is the circular wave.

"Holographic Superconductos in M-theory"

2010-02-15T20:15:00.009Z

Last Monday we had Jerome Gauntlett telling us about exciting applications of the AdS/CFT correspondence to Condensed Matter systems.

Some quantum critical points (second order phase transitions) are at strong coupling, and hence intractable with standard CM technics, but the AdS/CFT comes to the rescue. This happens for example for "heavy fermions" (quasi-particles condensing to give Cooper pairs) or for high $T_c$ cuprates that have a superconducting phase. Holographic descriptions of such systems have been put forth by Gubser and by Hartnoll, Herzog, and Horowitz. The strongly coupled CFT in 3d has a holographic AdS dual, which has a $U(1)$ gauge symmetry that can be spontaneously broken by a charged field $\chi$. A finite temperature the description is in terms of a black hole in AdS, and it acquires charged hair at low temperature that breaks the $U(1)$.

Almost all the work on this topic has been taking a "bottom up" approach, but Jerome took the "top down" approach: constructing holographic superconductors from M-theory using consistent Kaluza-Klein truncation with Sasaki-Einstein spaces. Here consistent truncation means that you can keep only a finite set of the light KK fields (you cut the infinite KK towers) but then any solution of the low dimensional theory involving those remaining fields has to uplift to an exact solution of the original higher dimensional theory. So consider a stack of M2-branes at the tip of a Calabi-Yau cone on a Sasaki-Einstein seven-manifold for which the near-horizon limit is $AdS_4 \times SE_7$ with metric \[ d s^2 = \frac{1}{4} d s^2 (AdS_4) + d s^2 (SE_7) \] with \[ d s^2 (SE_7) = d s^2 (KE_6) + \eta \otimes \eta~,\] where $\eta$is the contact form. There is an associated Killing vector, which (although it does not always have to close) generates the required $U(1)$ symmetry. The four-form field strength is $G_4 = \frac{3}{8} \text{Vol}(AdS_4)$. This geometry is dual to $\mathcal{N} =3$ SCFTs in $d=3$ (or $\mathcal{N} = 8$ if $SE_7$ is replaced by a seven-sphere).
Now, had the membranes been replaced by anti-membranes, $G_4$ would have the opposite sign but more importantly the dual SCFTs would have $\mathcal{N}=0$. The corresponding geometry is called skew-whiffed $AdS_4 \times SE_7$. It is this geometry that can reproduce and generalize the HHH models. The consistent truncation found by Jerome has an extra neutral scalar field $h$ which corresponds to a deformation of the skew-whiffed CFT by an operator $\mathcal{O}_h$. At low temperature this system exhibits a superconducting phase.
Jerome concluded by suggesting that if superconductivity had not already been discovered, such a study would have pointed it out to us. M-theory might thus lead to a similarly radical discovery of qualitatively new phenomena...

David Blaine

2010-01-24T23:17:00.006Z

I watched this TeD video where the magician David Blaine explains how he broke the Guiness record of apnea by staying a little more than 17 minutes under water.

To me, this guy is more than a magician, and more than an athlete, he's a pure artist. His determination to push the human body beyond its clinical limits is of course very spectacular and impressive, but it also says something about what it means to live. How much can one deprave the body from resources (food, oxygen) and still survive? There is also a sense of askesis very similar to what one can find in several religious traditions (fast, meditation, etc.)...

However, what struck me particularly was the fact that after a failed attempt he finally broke the record (live on TV) when he was convinced that he had no chance to succeed since his heartbeat was unusually high during the immersion. I think there might be some universal truth in this: great things are often achieved just at the moment when a long chain of intense efforts oriented to a precise goal ultimately gives way to the disappearance of all hope.

Nirmali

2009-11-26T00:21:00.001Z

II. The twofold task in working out the question of Being. Method and design of our investigation

2009-11-05T00:08:00.005Z

This is a summary of Heidegger's second introduction to Being and Time.

5. The ontological analytic of Dasein as laying bare of the horizon for an interpretation of the meaning of Being in general.

Dasein is a tricky thing to analyse in that it is in some respect obvious to us and in some other obscure. MH writes that "Dasein is ontically 'closest' to itself and ontologically farthest; but pre-ontologically it is surely not a stranger." As regard to its existence, we understand it immediately since "we are it". But "in spite of this, or rather for just this reason", it is the most difficult thing to really understand in its essence, because we are naturally inclined to consider it as obvious, self-evident. However, intuitively we have some sort of embryonic understanding of its essence since "Dasein is in such a way as to be something which understands something like Being". To perform an analytic of Dasein we must "choose such a way of access and such a kind of interpretation that this entity can show itself in itself and from itself".

MH announces that "we shall point to temporality as the meaning of the Being of that entity which we call "Dasein"," and that "we shall show that whenever Dasein tacitly understands and interprets something like Being, it does so with time as its standpoint". And in consequence, "time needs to be explicated primordially as the horizon for the understanding of Being, and in terms of temporality as the Being of Dasein, which understands Being." But the conception of time required will have to depart from the ordinary understanding of time (in particular time as a "criterion for naively discriminating various realms of entities", such as temporal, non-temporal, 'supra-temporal' eternal entities...).

"The central problematic of all ontology is rooted in the phenomenon of time, if rightly seen and rightly explained".

6. The task of destroying the history of ontology

Dasein's own past "is not something which follows along after Dasein, but something which already goes ahead of it" (Dasein "is its past"). This has the perverse effect that Dasein "falls prey to the tradition of which it has more or less explicitly taken hold. This tradition keeps him from providing its own guidance, whether inquiring or in choosing". And this also holds true for ontological understanding. Tradition "becomes master" and conceals itself. "It blocks our access to those primordial 'sources' from which the categories and concepts handed down to us have been in part quire genuinely drawn". The Greek ontology has thus "deteriorated to a tradition in which it gets reduced to something self-evident". Then "in the Middle Ages this uprooted Greek ontology became a fixed body of doctrine". Subsequent concepts such as "the ego cogito of Descartes, the subject, the "I", reason, spirit, person" (...) "all remain uninterrogated as to their Being". Just like in certain oriental philosophies, the primordial clarity of mind has deteriorated throughout history into rigidified clichés.

Our task is clear: "we are to destroy the traditional content of ancient ontology". AC/DC man! But nihilist enthusiasm is inappropriate: this destruction is "far from having the negative sense of shaking off the ontological tradition" (or "bury the past in nullity"). "We must, on the contrary, stake out the positive possibilities of that tradition, and this always means keeping it within its limits".

The point of departure for the task of destroying the problematic of Temporality will be the Kantian doctrine of time. After all, Kant is "the first and only person who has gone any stretch of the way towards investigating the dimension of Temporality". Still he didn't go very far because he "took over Descartes' position quite dogmatically". And Descartes, with his radical discovery of the 'cogito sum', left undetermined the meaning of the Being of the 'sum'. He "is 'dependent' upon medieval scholasticism". Furthermore, "Kant's basic ontological orientation remains that of the Greeks", and more precisely that of Aristotle.

In summary, the strategy is clear: in order to concretely address the question of Being with time as a horizon we must first destroy the associated tradition "until we arrive at those primordial experiences in which we achieved our first ways of determining the nature of Being".

7. The phenomenological method of investigation

"AdS/CFT from F-theory?"

2009-10-28T15:57:00.014Z

At the lunch group meeting James told us about a fairly recent paper by Polchinski and Silverstein, entitled Dual Purpose Landscaping Tools: Small Extra Dimensions in AdS/CFT. Their goal is to construct vacua of string or M-theory with minimal supersymmetry of the form $AdS_d \times \text{small}$, where small means that the internal space is small compared to the AdS radius. The problem is that in the case of the standard Freund-Rubin backgrounds (whose dual CFTs are rather well understood in terms of the near-horizon limit of D3- or M2-branes at the tip of a Calabi-Yau cone), the radius of the internal space is of the same size as the AdS radius.

The new idea is to add some D7-branes. These contribute to the potential energy with an opposite sign to the curvature of the internal manifold, and so could be chosen such that the resulting cosmological constant is small.

This is where F-theory comes into play. The construction there is to glue IIB solutions using the $SL(2,\mathbb{Z})$ duality symmetry, and to allow for D7-branes. A D7-brane, which is codimension two and thus can be surrounded by a circle, is a unit magnetic source for the axion $C_0$ (a periodic RR scalar field): \[\int_{S^1} d C_0 =1~.\] The axion combines with the dilaton $\phi$in a complex field in the upper half-plane \[\tau = C_0 + i e^{-\phi} = C_0 +\frac{i}{g_s}~.\] $C_0$ has monodromy one around the D7-brane, meaning that going around the circle transforms it as $C_0 \to C_0 +1$.

Now splitting the 10d metric as a 4d Minkowski space-time times a 6d manifold $B$ and requiring $\mathcal{N}=1$ susy in 4d implies that $B$ is a Kaehler manifold and that $\tau$ is (anti-)holomorphic: $\bar\partial \tau =0$.

Mathematically, specifying the modular parameter $\tau$ in the fundamental region is equivalent to specifying an elliptic curve, and so this whole construction can be seen as an elliptic fibration $\pi: X\to B$, with $X$ a four complex dimensional manifold. The fibre over a point $p\in B$ on the base is an elliptic curve $E_{\tau}$ that is "biholomorphically" equivalent to a torus determined by a lattice $(1,\tau)$:
\[\pi^{-1} (p) \cong E_{\tau} \cong \mathbb{C}/(1,\tau)~.\]
What is very nice is that the D7-branes are located where the elliptic fibration degenerates, i.e. where the torus gets pinched off and becomes singular.
James made the point that this is not just a mathematical construction since one can T-dualise to IIA and the lift to M-theory, where the resulting solution is the product of a 3d Minkowski space-time and a CY four-fold. Polchinski and Silverstein's idea is to get $AdS_5 \times \text{small}$ solutions by looking at CY four-fold cones that are elliptically fibered...

Etymology of yo

2009-10-26T21:24:00.003Z

Today, I think I made an etymological breakthrough: the interjection "yo", at least in some of its acceptations, is none other than the contraction of "you know". Word up!

"Gauge/gravity in three dimensions"

2009-10-23T15:33:00.009+01:00

Today's Theoretical Particle Physics seminar was given by Diego Rodriguez-Gomez (Queen Mary, U. of London), based mainly on 0809.3237 and 0903.3231.

Given the broad audience, he started by a small review of the AdS/CFT correspondence as a specially clean incarnation of 't Hooft's and Susskind's holographic principle. Whereas the 4d case has been relatively well understood for some time, the 3d case began to reveal itself only recently. In fact, until roughly two years ago, it was thought that the IR fixed point at the end of the RG flow of the maximally supersymmetric $\mathcal{N}=8$ SYM in 3d had no Lagrangian description. The reason for this belief was that the dual description has a non-constant dilaton blowing up at small radius: $e^{\phi} =(R/r)^{5/4}$. The BLG theory (anticipated by Schwarz) was an $\mathcal{N}=8$ Chern-Simons-like theory but it had an $SU(2)$ gauge group instead of the large $N$ needed in the AdS/CFT context. The resolution came from relaxing the requirement of maximal susy down to $\mathcal{N}=6$, which allowed arbitrary $N$ [ABJM].

Diego was interested in reducing the supersymmetry to $\mathcal{N}=2$ by putting the M2-branes at the tip of a Calabi-Yau four-fold. He focused on a specific example: the cone over $Q^{1,1,1}$, which is similar to the conifold in 6d and has the advantage to have been extensively studied (the metric is explicitly known). The simplest proposal (inspired by crystal models) is that the dual field theory is a quiver with four gauge groups, six fields, and a sextic superpotential $W$ with two terms. As in the ABJM case, all the global symmetries are not manifest, but appear by studying how scalar fields get identified. This results in a mesonic moduli space that is an $\mathcal{N}=2$ orbifold $Q^{1,1,1}/\mathbb{Z}_2$. Here are the toric diagram and the associated quiver:
Diego and his collaborators were able to show that the chiral operator spectrum is matching the supergravity harmonics, at least at large CS level $k$. This is a non-trivial check of the non-Abelian superpotential $W= C_1 A_1 B_1 C_2 A_2B_2 - C_1 A_1 B_2 C_2 A_2B_1$.

Remaining mysteries include the question of whether theories with $\mathcal{N}<3$ susy are conformal, which would require to have an equivalent in 3d of a-maximization; the inverse algorithm (from the CY4 to the quiver) and the connection to type IIA string theory; the small $k$ limit and monopoles operators, which is the genuinely M-theoretic limit, since at large $k$ the theory reduces to IIA.

I. The necessity, structure, and priority of the question of Being

2009-10-22T22:02:00.009+01:00

This is a summary of the first section of the Introduction of Martin Heidegger's major work, Being and Time (1926), where he is aiming at reawakening an understanding of the meaning of the question of Being.

I. THE NECESSITY, STRUCTURE, AND PRIORITY OF THE QUESTION OF BEING

1. The Necessity for Explicitly Restating the Question of Being

Since Plato and Aristotle the question of Being has been trivialized, and hence considered as superfluous. MH lists three prejudices, according to which this question is unnecessary. First, the assertion that 'Being' is the most universal concept does not imply that it is also the clearest: "It is rather the darkest of all." Secondly, even though 'Being' cannot be defined -- since a definition is typically of the form "something is this and that", it presupposes an understanding of the word "is" -- this does not eliminate the question of its meaning. Thirdly, the "self-evident" character of the concept of 'Being' remains, a priori, an enigma. So not only does the question of Being lack a clear answer, but "the question itself is obscure and without direction".

2. The Formal Structure of the Question of Being

The structure of any question splits into: that which is asked about [sein Gefragtes], the starting point of the curiosity; that which is interrogated [sein Befragtes], the things one turns to in order to find an answer; and that which is to be found out by asking [das Erfragte], the answer itself.

In the case of the question of Being, the Gefragtes is... Being [damn! I knew it], or more explicitly "that which determines entities as entities". But "the Being of entities 'is' not itself an entity", in the sense explained above that Being cannot be defined. Rather, Being "must be exhibited in a way of its own" (quite intriguing ain't it?). [I'll hereinafter push the acronym perversity so far as to reduce Being to B.]

The Befragtes are the entities themselves, that is "everything we talk about, everything we have in view, everything towards which we comport ourselves in any way" (a rather broad concept, mind you). [As an aside, I find such periphrases very revealing of the superiority of the German language to forge concepts.] But in sight of the unlimited possible choice, can one single out a specific entity that will be particularly useful to discern the meaning of B? Well we can, and it is ourselves, the inquirers. MH calls this special entity the "Dasein": "This entity which each of us is himself and which includes inquiring as one of the possibilities of its Being". What singles us out, among the infinities of entities, is the very fact that we are able to grow an interest in that which determines us as entities, i.e. our B.

There is an apparent danger of 'circular reasoning': are we supposed to come to grip with the meaning of B by inquiring into entities that are inquiring into their own B by inquiring into entities that are inquiring into their own B by inquiring--you got it--? MH discards this "always sterile" argument, since (if I understand correctly) it is fine to 'presuppose' B "provisionally". No circular reasoning then, but "a remarkable 'relatedness backward and forward' " between the Gefragtes (B) and the Befragtes (us, Dasein). [This is somewhat reminiscent of self-consistent systems in condensed matter theory.]

3. Ontological Priority of the Question of Being

The message of this subsection is basically that "Basically, all ontology, no matter how rich and firmly compacted a system of categories it has at its disposal, remains blind and perverted from its ownmost aim, it if has not firstly clarified the meaning of B, and conceived this clarification as its fundamental task". What MH means (supposedly) is that among all the scientific investigations, the question of B is the most primordial. But I suspect that he doesn't mean "priority" in the sense that it has to come first. Indeed, in any of the fields of scientific research (or "areas of subject-matter"), the "basic concepts" are (provisionally, "beforehand") "worked out after a fashion in our pre-scientific ways of experiencing...". So the subject-matter of interest is primitively understood, may I say, intuitively, and it is over this original intuition that a science, that is a "system of categories", develops. But:

"The 'real' movement of the sciences takes place when their basic concepts undergo a more or less radical revision which is transparent to itself. The level which a science has reached is determined by how far it is capable of a crisis in its basic concepts." (p.9)

[Remark: I have a similar approach to evaluate the richness of a personality.] And MH to enumerate a few instances in science of what he perceives as "freshly awakened tendencies to put research on new foundations": the foundational crisis in mathematics, in spite of it being "seemingly the most rigorous and most firmly constructed of the sciences" (a clear presentiment of Goedel's incompleteness theorem of 1931); the "problem of matter" in the context of the relativity theory of physics (I don't understand his point at all, even at the seventeenth reading...); the "new kind of B" defined in biology; and the realisation of the "inadequate" foundation of theology (he's probably being polite).

Ontological (concerned primarily with B) inquiries, such as Kant's Critique of the Pure Reason, are "more primordial" than the ontical (concerned primarily with entities) inquiry of the positive sciences. But they still lack an understanding of 'what we really mean by this expression "Being" '.

4. The Ontical Priority of the Question of Being

I find this last section more difficult to understand, perhaps because MH "anticipate[s] later analyses". Here we see listed and swiftly defined a series of key Heideggerian mottos and concepts. For instance, about Dasein, he is writing that "Being is an issue for it" and that

"Understanding of Being is itself a definite characteristic of Dasein's Being. Dasein is ontically distinctive in that it is ontological."

The distinction between "existentiell" and "existential" is also briefly described. As far as I can tell, the former means what you would naively expect, namely it characterises an understanding of existence, and more precisely Dasein's own existence.

"Dasein always understands itself in terms of its existence--in terms of a possibility of itself: to be itself or not itself."

(Here one can foresee the concept of authenticity.) MH underlines that Dasein is responsible for its existence, either actively or passively (for example, I suppose, if it lets external circumstances like childhood trauma dictate its conduct).

"Only the particular Dasein decides its existence, whether it does so by taking hold or by neglecting."

"Existential" on the other side characterises an understanding of the context of the "structure of existence".

"By "existentiality" we understand the state of Being that is constitutive for those entities that exist."

Coming back to the ideas of the previous section, MH writes that "Sciences are ways of Being in which Dasein comports itself towards entities which it needs not be itself", but his message is that Dasein "must first be interrogated ontologically." And just like the basic concepts of sciences are first worked out in a pre-scientific way, the question of B has to be worked out in a pre-ontological way:

"the question of Being is nothing other that the radicalization of an essential tendency-of-Being which belongs to Dasein itself--the pre-ontological understanding of Being."

This is the end of the first introduction of Being and Time.

I mean come on! How amazing is that? The guy is slowly cracking the very kernel of the most fundamental question you can imagine, the question of Being. Heidegger was saying in an interview that an entirely new form of thought is now called for, in our modern time. It is simpler than the old way of thinking, more natural, but it is also more difficult, in that it requires a much greater care with the use of language. This perspective should be motivation enough to overcome the disgust inspired by the bestiary of Heideggerian concepts. So let's keep calm and carry on!

"Topology and Relativity"

2009-10-16T15:27:00.018+01:00

OK, so for this Friday's Theoretical Physics Seminar we had Maulik Parikh from IUCAA in India talking about two of his current projects paired for the occasion under the title "Topology and Relativity".

Topology and special relativity

This is a collaboration with Brian Greene and Jana Levin, to appear.

The starting point is the twin paradox on a cylinder. For memory, the twin paradox in flat space-time concerns the age difference of two twins, one of which has been sent to the outer space and back. There is in fact no paradox, since the Principle of Relativity states that all inertial observers are equivalent, whereas the space twin accelerated and decelerated on his Odyssey.

In the case where space is a circle and time a line, and so on a space-time cylinder, both twins, gracefully christened A and B, could be inertial and still go their different ways and meet again. Who, then, asketh Maulik, is younger?
Well, the catch is that the periodic identification of the space coordinate picks a globally preferred frame (the one with winding number zero I suppose). So the first lesson is that

A nontrivial topology breaks global Lorentz symmetry.

The preferred frame could be determined by experiments by sending photons in different directions. In particular, Einstein clock synchronization would only be possible for preferred observers. There is also a discontinuity in the time coordinate, as the inhabitants of Kiribati, lying (not anymore since 1995) on the International Date Line, know very well (after all, as far as time zones are concerned, the Earth's worldvolume is essentially a cylinder).

Suppose there is a compact extra dimension (of mm size according to the ADD scenario). Can we tell the velocity of our (3+1)-brane around it? Obama says "Yes we can!", for which Maulik thinks he should get the Physics Nobel Prize as well...

If the LHC fires gravitons in the extra dimensions, then measuring their return time could make it possible to determine the motion of the brane. This is in fact not realistic, since graviton interactions are suppressed by the Planck mass.

Another effect of an compact extra dimension would be a modification of Newton's law. Since a source placed at a point along the extra coordinate would be repeated infinitely at interval $L$, the standard potential
\[
V(r) = -\frac{GM}{\pi r^2}
\]would be replaced by
\[
V(r) = -\frac{GM}{\pi } \sum_{n=-\infty}^{\infty} \frac{1}{r^2 +(nL)^2}\\
\simeq -\frac{GM}{r} (1+ 2e^{-2\pi r/L})~.
\]For a moving brane, one would have to replace $L$ by $\gamma L$ where $\gamma$ is the relativistic factor. This opens the amusing possiblity of a magnified extra dimension, if our brane were to move ultra-relativistically.

Topology and the Fate of the Universe

The second part of Maulik's talk was on a disconnected topic, base on his paper Enhanced Instability of de Sitter Space in Einstein-Gauss-Bonnet Gravity. The geometry of the early universe is well-described by de Sitter space, which is perturbatively stable. However, Bousso and Hawking showed that dS space can be destabilized by non-perturbative effects (such as instantons, black hole tunneling, etc.). The probability of a gravitational instanton is
\[
\Gamma \sim \frac{\exp(-I_E[\text{instanton}])}{\exp(-I_E[\text{background}])}~.
\]where $I_E$ is the Euclidean action. Now instead of taking the usual Hilbert-Einstein action, Maulik considered the Einstein-Gauss Bonnet action (which appears for instance in the low energy effective action of heterotic string theory). The novelty is the in our dimension the Gauss-Bonnet action is a topological invariant
\[
I_{GB} = -\frac{\Lambda V_4}{8\pi G} - \frac{2\pi \alpha}{G} \chi~,
\]where $\Lambda$ is the cosmological constant, $V_4$ is the volume, $\alpha$ the coupling constant, and last but not least $\chi$ is the Euler number.

The Gauss-Bonnet topological term can enhance the instability of primordial de Sitter space.

In the case of the extremal Nariai black hole with topology $S^2\times S^2$, using the Hilbert-Einstein action as Bousso and Hawking did leads to an instanton probability $\Gamma = \exp[(-\pi L^2/3G)$, which means this is only relevant for a length scale $L$ close to the Planck scale. Disappointing.

In contrast, with its additional topological term, the EGB action leads to an enhanced production of Nariai black holes (with $\chi =2+2=4$) by a factor of $\exp(4\pi\alpha/G)$.

Maulik also mentioned a bound on the maximal curvature of empty dS space.

Other applications include the effect of the topological term on the probabilities of Calabi-Yau manifolds in the string landscape. For example, the quintic has $\chi=-200$, which means it could be suppressed by roughly $\exp(-2000)$.

"Mirror symmetry, Langlands duality, and the Hitchin system"

2009-10-12T16:02:00.032+01:00

Today, at the Geometry and Analysis Seminar organized by Nigel Hitchin, Tamas Hausel talked about his paper with Michael Thaddeus Mirror symmetry, Langlands duality, and the Hitchin system. The room was packed. He started by giving some background informations about the three concepts in his title.

Mirror symmetry

The basic idea is that the symplectic geometry of a d-dimensional Calabi-Yau manifold $X$ can be related to the complex geometry of another CY manifold $Y$. There is a topological test of this relation, referred to as topological mirror symmetry, which equates (mirror pairs of) Hodge numbers of the two CYs:
\[ h^{p,q} (X) = h^{d-p,q}(Y)~. \]

Note that any hyperkaehler manifold satisfies $h^{p,q} (X) = h^{d-p,q}(X)$, so in a certain sense TMS is already built-in. Tamas mentioned two important developments in the history of mirror symmetry: homological mirror symmetry proposed by Kontsevich in 1994, which reads
\[
\mathcal{D}^b (\text{Fuk}(X,\omega)) \cong \mathcal{D}^b (\text{Coh}(Y,I))~,
\] where $\omega$ is the symplectic form and $I$ the complex structure. Another breakthrough was the geometric construction of $Y$ from $X$ elaborated by Strominger, Yau and Zaslow in 1996.

Langlands duality

The aim of the Langlands program is to describe $\text{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$ via representation theory.
To each reductive group $G$ is associated a Langlands dual $^LG$. The Langlands conjecture leads for instance to class field theory, in the case $G=GL_1$; in the case $G=GL_2$, it leads to the Taniyama-Shimura conjecture (which is famous because it implies Fermat's last theorem). An important progress towards the proof of the conjecture was made by Ngo in 2008 with his proof of the fundamental lemma for the function field $\mathbb{F}_q(X)$.
There is a geometric version of the conjecture, obtained by replacing $\mathbb{F}_q(X)$ by $\mathbb{C}(X)$ for $X/\mathbb{C}$ (Laumon 1987, Beilinson & Drinfeld 1995):
\[
\{ G\text{-local systems on $X$} \}
\]\[
\leftrightarrow \{ \text{Hecke eigensheaves on Bun$_{^LG}(X)$}\}~.\]
Hitchin systems

Recall that a Hamiltonian system $(X^{2d}, \omega)$ has an energy functional $H: X\to \mathbb{R}$ and an Hamiltonian vector field $X_H$ such that $\text{d}H=\omega(X_H,\cdot)$. A function $f:X\to \mathbb{R}$ is a first integral if $X_H f = \omega(X_H, X_f) =0$ (involution). The system is completely integrable if there is $d$ first integrals. The generic fibre is then a torus (examples: Euler and Kovalevskaya tops, spherical pendulum).
An algebraic version is obtaiend by replacinf $\mathbb{R}$ by $\mathbb{C}$, and many examples can be formulated as Hitchin systems (1987).

Now I cannot say I completely followed the rest of the talk in all its glory, but I'll try to restate what I understood. Tamas was considering different moduli spaces, which are all smooth non-compact varieties: $\mathcal{M}_{\text{Dol}}^d (G)$ is the moduli space of rank $n$ and degree $d$ Higgs bundles $(E,\phi)$, $\mathcal{M}_{\text{DR}}^d (G)$ is the moduli space of flat $G$-connections on a genus $g$ curve, $\mathcal{M}_{\text{B}}^d (G)$ is yet another thing -- but they're all equivalent by a non-Abelian Hodge theorem. The Hitchin map $\chi(\phi)$ is completely integrable and its fibre $\chi^{-1}(a)$ is a torsor.

Inspired by the SYZ conjecture, Hausel and Thaddeus noticed in 2003 that $\chi^{-1}_{SL_n}(a)$ and $\chi^{-1}_{PGL_n}(a)$ are torsors for dual Abelian varieties. (I think this means they are related by T-duality on the toroidal Hitchin fibres, but he said "fibrewise Fourier-Mukai tranform" instead :)

A confirmation that their conjecture are more or less sane came from the 2006 work of Kapustin and Witten on S-duality (electric-magnetic duality) in $\mathcal{N}=4$ super-Yang-Mills in four dimensions, which Tamas qualified as "a major work" with many fertile ideas. (In fact T-duality in the Hitchin moduli space corresponds to S-duality in the gauge theory, see Witten's Strings on the Beach! talk in 2005.)

Using stringy Hodge numbers (also known as "orbifold cohomology") Tamas made a conjecture with a TMS test, but he also made another one using mixed Hodge numbers.
His final questions were: "Why two conjectures? Why same Hodge numbers instead of mirrored ones? Why Geometric Langlands and not classical Langlands?

He ended up by mentioning a curious hard Lefschetz conjecture for weight and perverse filtrations that left the crowd speechless.

"Adding Flavor to AdS4/CFT3"

2009-10-08T17:20:00.028+01:00

I thought I would try to write short summaries of interesting talks I attend here in Oxford. The first one of Hilary term is

Adding Flavor to AdS4/CFT3 by Andy O'Bannon from the Max Planck Institut in Munich, based on 0909.3845.

The motivation is that the AdS/CFT correspondence only really becomes useful for applications (quark-gluon plasma at RHIC, condensed matter systems, often 3-dimensional) when it involves not only fields in the adjoint representation of the gauge group---strings starting and ending on the same brane---but also fields in the fundamental representation. For this one needs to add new branes so that strings can stretch between different branes.

Such procedure is well-understood in the AdS5/CFT4 context: the supergravity action acquires a new term describing the new Dp-branes (be it D5 or D7), $\large S_{10d} = S_{IIB} + S_{Dp}$, and this is dual to super-Yang-Mills with flavors in 4d, $S_{4d} = S_{\mathcal{N}=4} + S_{\text{flavor}}$. The story in M-theory is less understood. The "membrane minirevolution" (as Lubos calls it) led to a duality between $N_c$ M2-branes with a $AdS_4 \times S^7/\mathbb{Z}_k$ horizon, and a (2+1)dimensional Chern-Simons theory with N=6 supersymmetries with fields in the bifundamental of $U(N_c)_k \times U(N_c)_{-k}$. This is the famous ABJM theory (see Klebanov & Torri for a recent review). The goal of the talk is to understand what happens on the field theory side when on add M5-branes. What is the $S_{\text{flavor}}$ dual to $S_{M5}$?

Since the whole heuristic argument is based on being able to use the intuition of a string stretched between different branes being in the fundamental, and since there is no string in M-theory, the strategy is to start with type IIB supergravity with $N_c$ D3-branes, add Dp-branes and NS5-branes to get some flavor, and then T-dualise to IIA and lift to eleven-dimensional supergravity, the low-energy limit of M-theory. Here is roughly how it goes.

The D3-branes are first considered as hanging along one direction between two NS5-branes, as so (thanks to Cyril for allowing me to use his drawing device:):
Now perform a dimensional reduction on this compact interval and you get a (2+1)d SYM with N=4 and gauge group $U(N_c)$. If you replace one NS5 by a (1,k)5 = NS5 + k D5, then you get (after considering bounday terms...) a Chern-Simons theory with level k. Pretty close already!

Now consider two stacks of D3-branes stretched between the (1,k)5 and the NS5
(the (1,k)5 has to be tilted to preserve N=3 superymmetries, with and angle $\large \tan\theta = k$):
What you get now is a CS theory with N=3 and fields in the bifundamental of $U(N_c)_k \times U(N_c)_{-k}$, which is starting to realy look like the ABJM theory. The superymmetry can be enhanced because of Kaluza-Klein monopoles (which correspond on the field theory side to take the low energy limit by integrating out masses greater than $g_{YM}^2 k$) but Andy passed over this important subtlety, and so do I.

All that is left to do is to T-dualise this whole brane construction and lift to eleven dimensions to produce M2-branes and Kaluza-Klein monopoles (which are described purely geometrically...):
\[D3 \to D2 \to M2 \]

\[NS5 \to KK \to KK \]

\[(1,k)5 \to KK + D6 \to KK'\]

The KK monopoles interesect at a $\mathbb{C}^4/\mathbb{Z}_k$ orbifold singularity, and placing $N_c \to \infty$ M2-branes at this singularity produces a near-horizon geometry $AdS_4 \times S^7/\mathbb{Z}_k$, which is dual to the ABJM theory.

So now to understand flavors in AdS4/CFT3 you can add some Dp-branes in the IIB background and repeat this translation procedure to M-theory. Andy went through two examples, one with D5-branes, the other with D-branes, and showed that they in fact both lead to the same CS theory with flavor and $SU(4) \times U(1)$ isometry.

He finished by mentioning an application: fractional quantum Hall effect.

Merleau-Ponty: L'Œil et l'Esprit

2009-10-04T17:12:00.020+01:00

L'Œil et l'Esprit, écrit en 1960, est le dernier texte de Maurice Merleau-Ponty (1908-1961). J'en ai souligné quelques passages et je tente maintenant d'en restituer l'argument. [Désolé pour l'état squelettique de cette note..]

Section I

MMP (c'était aussi le surnom d'un charismatique professeur à la barbe blanche de Quantentheorie à la Humboldt Universität:) prend le problème du désenchantement de la science moderne comme point de départ.

"La science manipules les choses et renonce à les habiter." (p.9, première phrase du folio)

"Il faut que la pensée de science -- pensée de survol, pensée de l'objet en général -- se replace dans un « il y a » préalable, dans le site, sur le sol du monde sensible et du monde ouvré tels qu'ils sont dans notre vie, pour notre corps, non pas ce corps possible"…

"Dans cette historicité primordiale, la pensée allègre et improvisatrice de la science apprendra à s'appesantir sur les chose mêmes et sur soi-même, redeviendra philosophie…" (p.12-13)

La solution doit venir de la peinture, le vrai sujet qui intéresse MMP.

"Or l'art et notamment la peinture puisent à cette nappe de sens brut dont l'activisme ne veut rien savoir." (p.13)

Note comme la ponctuation, son absence en fait, indique bien comme MMP ne compte pas s'appesantir sur les autres arts que la peinture, qu'il discrédite tous en deux phrases expédiées. Lui, c'est la peinture son truc.

"Le peintre est seul à avoir droit de regard sur toutes choses sans aucun devoir d'appréciation." … "Quelle est donc cette science secrète qu'il a ou qu'il cherche?"

Le décor est planté.

Section II

MMP essaie de cerner "cet extraordinaire empiétement" du monde tel que nous le voyons et du monde dans lequel nous nous déplaçons (je ne suis pas certain de bien le suivre ici; oppose-t-il la perception visuelle à la perception tactile?).

"C'est en prêtant son corps au monde que le peintre change le monde en peinture." …

"Le monde visible et celui de mes projets moteurs sont des parties totales du même Être." (p.16-17)

"L'énigme tient en ceci que mon corps est à la fois voyant et visible." (p.18)

"… l'indivision de sentant et du senti." (p.20)

C'est intéressant, et j'aimerais y acquiescer (et faire le lien avec la théorie quantique, éventuellement…), mais je peine à trouver la substance de sa réflexion. Ses formules sonnent creux:

"le dessin et le tableau"… "sont le dedans du dehors et le dehors du dedans"… (p.23)

See what I mean?

Ce qui a le plus excité mon crayon sont des citations:

"« la nature est à l'intérieur », dit Cézanne." (p.22)

"Max Ernst"… "« … le rôle du peintre et de cerner et de projeter ce qui se voit en lui. »" (p.30)

Même si je ne suis pas emballé par l'argumentation de MMP, je trouve ces citations très inspirantes. Après tout, ce n'est pas réellement les sortir de leur contexte, MMP s'en est déjà chargé.

(Il m'arrive d'ailleurs souvent d'aimer une citation au fi de son utilisation particulière. Par exemple, bien que je ne me soie pas à vrai dire délecté de La Porte Etroite (1909) d'André Gide (1869-1951), j'ai été profondément touché par une citation paradoxale du Christ, elle-même tirée de Pascal: "Qui veut sauver sa vie la perdra.")

Ce que j'aime dans la citation de Cézanne, c'est sa force et sa beauté brute. Elle est faite de mots simples, tirés du langage quotidien, et pourtant elle frappe l'entendement et fait résonner les hautes sphères spirituelles. La nature, c'est ce qu'il y a devant moi, là, ce que je vois par-delà ma fenêtre. Et en moi sont mes sentiments et mes idées, immatérielles et intimes. Et bien les deux ne s'opposent pas, on ne peut pas poser l'une comme fondamentale (tels les cartésiens l'esprit, ou les positivistes la réalité physique) et y prendre appui pour explorer l'autre, non. Les deux sont une seule et même chose, et il ne fait sens de les considérer qu'en conjonction.

"Les parfums, les couleurs et les sons se répondent." Certes, certes, bravo Charles, voilà qui devrait faire mollir les âmes tendres, mais ce n'est pas tout! La nature est à l'intérieur. Comprends bien ça.

Quand Cézanne peint la montagne Sainte-Victoire (plagié-je?), il se fout pas mal du paysage, tout comme il se fout pas mal du panier de pommes qu'il peint. Ce qui l'intéresse c'est l'intérieur, ou plutôt le fait hallucinant que la montagne, toute géologique qu'elle puisse être, elle est à l'intérieur. A l'intérieur de lui, quand il la voit.

Et c'est là que MMP nous dit à point

"la peinture ne célèbre jamais d'autre énigme que celle de la visibilité." (p.26)

Section III

"Comme tout serait plus limpide dans notre philosophie si l'on pouvait exorcise ces spectres, en faire des illusions ou des perception sans objet, en marge d'un monde sans équivoque! La Dioptrique de Descartes est cette tentative. C'est le bréviaire d'une pensée qui ne veut plus hanter le visible et décide de la reconstruire selon le modèle qu'elle s'en donne." (p.36)

On croirait presque entendre le sarcasme des physiciens quantiques à l'égard de ceux qui (comme Einstein) ne veulent pas abandonner leur rêves déterministes...

Le mot clé ici est "hanter". Si nous étions immortels nous pourrions nous en passer. A défaut, nous hantons, et c'est tant mieux.

Après avoir discrédité "la chose même" et "l'espace en soi", "l'en soi par excellence" cartésiens, MMP concède

"Descartes avait raison de délivrer l'espace. Son tort était de l'ériger en un être tout positif, au-delà de tout point de vue, de toute latence, de toute profondeur, sans aucune épaisseur vraie." (p.48)

J'aime bien cette idée qu'il est nécessaire de passer par une étape de pensée rigide, positiviste, réaliste, avant de pouvoir dans un deuxième temps s'en affranchir et accepter l'incertitude. MMP nous dit par exemple que

"l'espace n'a pas trois dimensions"

en quoi, de nouveau, je serais friand de pouvoir le suivre mais je ne vois pas bien comment.

"les dimensions sont prélevées par les diverses métriques sur une dimensionnalité, un Être polymorphe, qui les justifie toutes sans être complètement exprimé par aucune."

Mais, ai-je presque envie de dire, cet "Être polymorphe" est-il Calabi-Yau?

Si je comprends bien, la dimensionnalité serait une propriété du mode de perception plus qu'une propriété intrinsèque des choses. Une qualité secondaire, et non une qualité primaire. Hm. Intéressant.

"Quelque chose dans l'espace échappe à nos tentatives de survol." (p.50)

"En vérité il est absurde de soumettre à l'entendement pur le mélange de l'entendement et du corps." (p.55)

La science moderne, nous dit MMP, est tellement dégénérée, plus cartésienne que Descartes etc, qu'il nous en faudrait une autre, entièrement nouvelle, pour pouvoir envisager une cohabitation amicale avec la philosophie.

"si nous retrouvons un équilibre entre la science et la philosophie, entre nos modèles et l'obscurité du « il y a », il faudra que ce soit un nouvel équilibre. Notre science a rejeté aussi bien les justifications que les restrictions de champ que lui imposait Descartes."

"La pensée opérationnelle"... "est fondamentalement hostile à la philosophie comme pensée au contact"... (p.57)

"Notre science et notre philosophie sont deux suites fidèles et infidèles du cartésianisme, deux monstres nés de son démembrement."

Et voici la voie à suivre selon MMP:

"Nous sommes le composé d'âme et de corps"... (p.58)

"L'espace n'est pas celui dont parle la Dioptrique, réseau de relations entre objets, tel que le verrait un tiers témoin de ma vision, ou un géomètre qui la reconstruit et la survole, c'est un espace compté à partir de moi comme point ou degré zéro de la spatialité. Je ne le vois pas selon son enveloppe extérieure, je le vis du dedans, j'y suis englobé."... "La lumière est retrouvée comme action à distance, et non plus réduite à l'action de contact"... (p.58-59)

"Toutes les recherches que l'on croyait closes se rouvrent. Qu'est-ce que la profondeur, qu'est-ce que la lumière"... " non pas pour l'esprit qui se retranche du corps, mais pour celui dont Descartes a dit qu'il y était répandu"...

Section IV

MMP nous dit qu'il a le sentiment

"d'une discordance profonde, d'une mutation dans les rapports de l'homme et de l'Être, quand il confronte massivement un univers de pensée classique avec les recherches de la peinture moderne." (p.63)

"Quatre siècles après les « solutions » de la Renaissance et trois siècles après Descartes, la profondeur est toujours neuve"... (p.64)

"De la profondeur ainsi comprise, on ne peut plus dire qu'elle est « troisièmes dimension »." (p.65)

Et de nouveau une très belle contribution de Cézanne au débat:

"Quand Cézanne cherche la profondeur, c'est cette déflagration de l'Être qu'il cherche, et elle est dans tous les modes de l'espace, dans la forme aussi bien. Cézanne sait déjà ce que le cubisme redira : que la forme externe, l'enveloppe, est seconde, dérivée, qu'elle n'est pas ce qui fait qu'une chose prend forme, qu'il faut la briser cette couille d'espace, rompre le compotier --- et peindre, à la place, quoi?"

[Le lecteur attentif aura remarqué une coquille dans le mot "coquille" -- justement...]

"C'est donc ensemble qu'il faut chercher l'espace et le contenu."

La couleur est "« l'endroit où notre cerveau et l'univers se rejoignent »"

(comme la théorie des cordes;)

"C'est cette animation interne, ce rayonnement du visible que le peintre cherche sous les noms de profondeur, d'espace, de couleur."

"L'effort de la peinture moderne n'a pas tant consisté à choisir entre la ligne et la couleur, ou même entre la figuration des choses et la création de signes, qu'à multiplier les systèmes d'équivalences,"...

Ce qui me fait penser aux dualités de la physique théorique...

Il y a aussi un passage sur le cinéma et la photo.

"Rodin a ici un mot profond : « C'est l'artiste qui est véridique et c'est la photo qui est menteuse, car, en réalité, le temps ne s'arrête pas. »" (p.80)

"La peinture ne cherche pas le dehors du mouvement, mais ses chiffres secrets."

La vision est "le moyen qui m'est donné d'être absent de moi-même, d'assister de dedans à la fission de l'Être, au terme de laquelle seulement je me ferme sur moi."

..."par elle nous touchons le soleil, les étoiles, nous sommes en même temps partout"...

"la «simultanéité » ''' mystère que les psychologues manient comme un enfant des explosifs."

Parle-t-il de la synchronicité de Jung?

... "le propre du visible est d'avoir une doublure d'invisible"...

Section V

... "profondeur, couleur, forme, ligne, mouvement, contour, physionomie sont des rameaux de l'Être"...

A propos du "vrai peintre":

"Même quand elle a l'air partielle, sa recherche est toujours totale."

A rapprocher de la façon dont Tim Gowers explique dans sa conférence The Importance of Mathematics au Clay Mathematics Institute en 2000 qu'il serait faux de discréditer les domaines de recherches mathématiques qui paraissent les moins applicables parce que les mathématiques forment un réseau intriqués de connexions, et qu'on ne peut en couper une partie sans par la même occasion en affaiblir la totalité organique..

... "la trouvaille est ce qui appelle d'autre recherches. L'idée d'une peinture universelle, d'une totalisation de la peinture, d'une peinture toute réalisée est dépourvue de sens." (p.90)

(tout comme l'idée d'une Theory of Everything...)

"Le plus haut point de la raison est-il de constater ce glissement du sol sous nos pas, de nommer pompeusement interrogation un état de stupeur continuée, recherche un cheminement en cercle, Être ce qui n'est jamais tout à fait?

Mais cette déception est celle du faux imaginaire, qui réclame une positivité qui comble exactement son vide. C'est le regret de n'être pas tout."

... "chaque création change, altère, éclaire, approfondit, confirme, exalte, recrée ou crée d'avance toutes les autres."

Zen Zoe

2009-07-19T23:41:00.008+01:00

If you wander around in one of Oxford's many parks, you might meet an old lady peacefully drawing on a huge sheet of paper. Well, it's Zoe Peterssen. The rest of the story has been told many times, for instance here---needless to say that I was quite disappointed to see that many people had experienced just the same intimacy with Zoe, and that I wasn't "special" at all, she opened up to pretty much everybody. Fuck you for that Zoe bitch!

Under such circumstances, I'll just restrain to a couple of remarks.

Firstly, about her technique. She's drawing on huge sheets of paper, I told that already. What's surprising then, is that the next step is to photocopy those sheets repeatedly, reducing the size by half every time, until the tree is small enough to hold on a little card that she gracefully gives to wanderers that she likes (who are welcomed to then also give her something, a few pounds will do). So from say 2 meters to 3 centimetres, she must photocopy a drawing six times. What a labour! This shrinking process is actually akin to bonsai growing.

This comparison came to me because when I said that I was doing particle physics she mentioned a book she'd read about it, The Tao of Physics by Fritjof Capa (1975). I'd like to re-read this book.

She also mentioned bows and told the story of a man who wanted to learn archery and spent many years at it until finally he shot an arrow without feeling any shot, to which his Zen master said that he now knew how to shoot an arrow. I'd like to know how to shot an arrow.

Masterclass with Mitsuko Uchida

2009-06-24T21:28:00.013+01:00

Yesterday I went to a master class given by Mitsuko Uchida to four performance students of the Music Faculty. The students presented pieces by Schubert, Schumann, Bach, and Beethoven. It was fascinating to see how much emotion and contrast she was able to percieve in those pieces and how well she could communicate it. She used a variety of ways to do it: obviously by playing herself on the piano, and by singing and screaming, but also with her body, directing with her hands and dancing, jumping around really, but also through more indirect ways. She used metaphors, she talked about a "dry sunny day, when it hasn't rained yet and you can smell the warm sand" and so on. She also resorted to musical analysis, for instance she explained how Bach was moving between the tonic, the dominant, and the sub-dominant---in fact, she apologized for having to sound so technical but it was just a way for her to express how she felt the piece should be played, what was at stake, what psychological tensions and what resolutions.

The precious moments when Mitsuko was playing for more than two seconds revealed the depth of her concentration and total involvement into the music. It was amazing---also certainly completely unavoidable to any great performer---how she was never playing lightly, but always mobilizing her full life's experience, all her pains, all her joys, all her emotions and sensations, her entire mind and body focused on the musicality.

She had something of a yoga teacher trying to encourage her students to stretch their bodies. She has probed the extremities of the various human emotions. One advice that struck me particularly and that she repeated to almost every performer of the day (at least the girls) was not to play "too beautifully". She encouraged them not to iron the peculiarities, the oddities of the compositions, but on the contrary to make the strangeness emerge, accentuate the dissonance, show how bizarre reality is. (It is something I think about a lot these days, bringing out the surreal...)

So you had for example this nice little American blonde playing as beautifully as she could, and hirsute Mitsuko shouting to her to play it uglier. At some point she told her "Play with your biggest pain!"

She also got mad when one of the students told her that the reason she was playing in a certain way was because of the influence of some famous pianist (although I think she misunderstood what the student meant). She said that every interpret makes mistake and so it is pointless to copy them, one should create her/his own mistakes :)

Mitsuko has recently become a 'Dame' and

today she was receiving and honorary doctorate at Oxford's Encaenia Ceremony (the word apparently meaning "festival of renewal"). Since she lives in London I was looking forward to her next concert, but according to her agenda, she will have sooner toured the planet several times than perform again in the UK. Farewell Mitsuko!

La religion comme mise en abîme de soi-même

2009-06-07T10:34:00.022+01:00

Je suis tombé sur la reproduction d'un tableau très étonnant:

Ce qui a d'abord attiré mon attention est que je n'avais jamais vu un autoportrait de femme aussi ancien. Sofonisba Anguissola [Cremona, c. 1532-Palermo, 1625] l'a peint en 1556 -- seulement huit ans après le probable premier autoportrait féminin par Caterina von Hemessen, lequel est également le premier autoportrait (tous sexes confondus!) à représenter l'artiste devant son trépied.

J'ai d'abord hésité quant au sexe de Sofonisba, étant donné que ce prénom est en soi déjà tellement étrange qu'il pourrait tout aussi bien être celui d'un homme, que son corset rigide ne laisse pas entrevoir sa morphologie, et que son visage pourrait être celui d'un jeune apprenti aux traits efféminés. Mon réflexe en cas de telles incertitudes est de lire quelques phrase du texte accompagnateur jusqu'au premier pronom "il/elle". Ca m'a pris un peu plus de temps que d'habitude: l'image issue du catalogue de l'exposition El retrato del Renacimiento au Musée du Prado était accompagnée d'un texte en espagnol, langue moins portée sur les pronoms sexués que le Français (mais heureusement plus encline que lui à spécifier le sexe d'une profession: "la artista", "la pintora", etc.). Bref, Sofonisba est bel et bien une femme.

Je me suis mis ensuite à admirer sa simple féminité sans artifices. Bien qu'elle ait embrassé une carrière habituellement réservée aux hommes, elle a su conserver une sensibilité de femme, enfantine et délicate. La grâce de ses mains et de son visage émerge de l'habit sévère qui cache ses formes.

Je note en passant (franchement, excusations pour toutes ces digressions!) qu'il était inacceptable à l'époque pour les artistes femmes de s'exercer au dessin anatomique, qu'il était pourtant nécessaire de maîtriser pour pouvoir prétendre composer des oeuvres de larges envergures impliquant de nombreux personnages. Ca explique en partie qu'elles se soient rabattues sur les portraits, et en particulier les autoportraits.

(Une tache vive de couleur magenta sur sa palette m'a fait sourire, parce que j'ai une théorie selon laquelle les adolescentes d'Oxford portent des vêtements de cette couleur le soir pour indiquer leur disponibilité sexuelle...)

Mais mon enthousiasme a vraiment pété le plafond lorsque je me suis posé la question "mais que peint-elle?" Naïvement, le tableau nous montre Sofonisba peignant une scène religieuse , sans doute à usage dévotionel, représentant la Vierge et le Christ (ou, peut-être, à cause de l'attitude sensuelle des personnages, Aphrodite et Cupidon?). Mais à la réflexion, ce n'était pas une scène religieuse qu'était en train de peindre Sofonisba lorsqu'elle peignait son autoportrait (et pour cause), mais sa propre image: je crie à la supercherie!

Si Sofonisba avait voulu peindre fidèlement ce qu'elle voyait, c'est-à-dire sa propre réflexion dans le miroir, ce qu'elle aurait peint sur son canevas aurait été une seconde reproduction d'elle-même en train d'en peindre une troisième et ainsi de suite jusqu'à l'infini. Ce procédé d'incrustation répétée ad libitum dans une image d'une réplique d'elle-même au format réduit est une mise en abîme. Mais Sofonisba a choisi de remplacer ce puits sans fond s'ouvrant sur elle-même par une image pieuse. J'y vois un enseignement sur la religion:

La religion se substitue à la limite infinie

de l'auto-représentation.

Je trouve ça très intéressant. (On pourrait presque pousser jusqu'à y voir une manifestation du principe holographique...)

Une interprétation alternative serait que Sofonisba, par le remplacement de sa propre reproduction par l'image religieuse, essaie d'exprimer qu'elle s'identifie à la Vierge -- un peu à la manière dont un bon chrétien est censé s'identifier au Christ et tâcher d'imiter sa vie. La croix que forment son pinceau et son bâton d'appui (comment appelle-t-on cet outil?) confirment cette lecture. Mais il faut admettre que c'est forcément plus compliqué, puisque le tableau que peint Sofonisba ne représente pas seulement la Vierge, mais aussi son enfant (voire même Aphrodite et Cupidon). S'il y a identification, ce n'est donc pas avec un seul, mais deux personnages bibliques (mythologiques). Elle s'identifierait avec quelque chose de plus abstrait, du genre de l'amour maternel (ou de la sensualité amoureuse).

Alien mathematics

2009-04-06T23:58:00.009+01:00

Unlike what you might be expecting from the title, this post is not about Großendieck's fundamental reploughing of algebraic geometry, but about the following hypothetical question:

Imagine we discover another civilisation living in some corner of some galaxy, where we know that the physics is essentially the same than on earth. Would they have the same mathematics than us? And if yes, would they have the same mathematics history than us?

David Gross was proposing this thought exercise at the end of a public talk by Robbert Dijkgraaf at KITP, and I figured the best way to attack it was by taking a hot bath. In fact, the bath was so hot that I could feel my spirits evaporate and I felt that were I to think about this question in such circumstances, I would develop biased conceptions that would definitely screw all my chances to reach any interesting conclusions... Nevertheless I did it, and it's a mess.

(Note that Dijkgraaf wasn't too inspired by the question -- I guess this is the difference between a Nobelised and a non-Nobelised physicist: the former becomes philosophically oriented (remember Josephson))

Probably it is sensible to start by the second part of the question, assuming the answer to the first is positive. Then it is obvious that it would be quite challenging to defend the opinion that their math history is exactly the same as ours. They would have needed to have e.g. an Evariste Galois killed at 20 in an obscure duel, etc. But might they have had the same structure in the development of their mathematics?

What would Kant say about this question? I believe that it would be something along the line of "Their mathematics would resemble ours inasmuch as we are able to perceive them, and them us. (After all they could be made of "dark matter", in which case it would be strange if they had the same concepts as ours...)

Mehr Licht/Mehr Nicht

2009-03-29T20:54:00.014+01:00

"Mehr Licht!" Tels sont les derniers mots traditionnellement attribués à Goethe sur son lit de mort. Mais les mauvaises langues ont prétendu qu'il fallait en réalité entendre "Mehr nicht!" -- je n'en puis plus. Cette anecdote m'est revenue en tête hier, et j'ai pensé qu'on pouvait y voir plus qu'une moquerie: et si les deux interprétations n'étaient pas inconciliables? Ma thèse est celle de la coincidence, dans l'esprit du créateur, de l'instant de l'illumination et de celui de l'épuisement. Après tout, comment pourrait-il en être autrement, étant donne que pour percer la coque opaque de l'inconnu par un éclair de lucidité, il faut avoir atteint la frontière lugubre du périmètre de sécurité de l'esprit? Prenons l'example de l'athlète qui établit un nouveau record: le mehr Licht autant que le mehr nicht l'habitent, et se confondent en lui.

Dans The Crucible d'Arthur Miller, il y a un vieil homme honnête qui est exécuté par l'Inquisition par écrasement: on lui pose des pierres de plus en plus lourdes sur la poitrine jusqu'à ce que mort s'en suive... Ses dernières paroles furent : "More weight!"

Ici aussi on peut le comprendre de plusieurs manières: la manière comique (qui n'est pas ma favorite, va sans dire) selon laquelle il se moquait de ses bourreaux, mais aussi la manière, disons, existentielle qui appelle à plus de poids dans les décisions et les attitudes de vie de ces concitoyens. Une vie plus lourde de sens.

Fun with the G-string

2009-02-23T22:30:00.005Z

If you like parodies of academic articles (and I know you do), check out how the early fathers of string theory used to have fun: The Super G-String. I don't know who is behind it (it is hosted on Warren Siegel's webpage) but the fake authors are V. Gates ("wie geht's?", a reference to Jim Gates), Empty Kangaroo, M. Roachcock (cockroach), and W.C. Gall (let me know if you crack this one---my attempt is the French word calvitie...).

I came across this paper because it is mentioned in the introduction of Aspinwall's lectures on D-Branes on Calabi-Yau Manifolds, where he writes in a footnote about D-branes that "The first reference to such objects that the author is aware of is, oddly enough, section 4 of [1]."

And indeed, on section 4 of the parody, there is an allusion to what we would call nowadays braneworld model-building, with the open string ending on a four-dimensional submanifold. So humour can be serious sometimes! After all the researcher's work isn't that different in its essence from a ludic fantasy...

Failblog

2009-01-03T21:48:00.009Z

There is a YouTube channel called failblog which is dedicated to the biggest possible failures. At first I laughed my ass off by watching some of those videos, but then I started to think that there might also be something very interesting there. After all this is a precious collection of what is know as "actes manqués" in psychology (parapraxis), which are the equivalent in action of what a Freudian slip is in conversation. Where it becomes interesting is that such failures are, according to standard psychanlaytic theory, expressions of subconscious pulsions, and as such it is possible to make sense out of them.

Let us watch a few examples and you'll see what I mean.

First a very awkward frisk by a policeman who is probably repressing his homosexual tendencies. It's called "Frisk Fail" :

What is very striking is that the gesture of the policeman does not look at all like an inadvertent slip but rather like an intentional pass. The policeman is overwhelmed by a subconscious desire and loses touch with admissible behaviour. When he realises what he did and his conscious self takes control again, he certainly cannot believe it and apologizes repeatedly.

This interpretation is corroborated by the discussion that they are having, which resembles some kind of seduction game :

Cop -- Spread your legs for me please... I see you're shaking, I make you nervous/That makes me nervous.

Guy -- It's cold outside.

Cop (laughing, at ease) -- Yeah? It's cold? ...

The policeman is trying to relieve the tension in this delicate situation, full of sexual implications, but when the guy acknowledges his sensitivity to the cold like a shy girl adorably shaking in her first evening dress he's getting so loose that repressed emotions take over and push him to make the fatal move.

Now let's look at this other failure, also of sexual origin I'm afraid (most of them probably are---but not all !---which misled Freud to think that sexual repression alone could account for the entirety of human behaviour).

The failure here is unbelievable : how could she fail to see the pole just in front of her ? There is apparently something big going on here ! But there is not far to look for to find it (some YouTubers also suggested it in the comments of this video in fact). She is obsessed by her sexual frustration in her little village in Alaska. When she's faced to a symbol of her object of desire (a phallus), she fails to recognise it. (Notice the similarity with the cop video...)

Now the "Best Man Fail" :

The obvious thing to say here is that the best man is probably secretly in love with the bride, to the point that he does not even admit it to himself. His subconscious then forces him to do what he should have had the guts to do in full possession of his senses : throw himself at her feet to tell her his love and interrupt the wedding...

But what I find more interesting here is that there is a controversy in the comments of this video (like for many other videos on failblog) about its authenticity [I always find that very disappointing, not being able to trust something as a piece of reality, but I have to live with it you know; after all everything is fiction, etc.]. Someone is writing that the best man is acting like a bad actor in a Bollywood movie when he shouts "Nooooo!", and another that everyone is behaving totally unnaturally. And it is indeed quite weird how they all repeat "Oh my god!" one after the other... However, I do not think that this video is a fake, but that it is an illustration of how we Americans are preconditioned to behave in a stereotypical manner in our everyday life.

Here comes a video that amazed me deeply, "Proposal Fail" (you might enjoy it more without the sound first) :

This girl, unless her great emotion and the pressure of the crowd, is still able to swim against the tide, and to do it with the grace of an angel. I was moved to the soul by her lovely body language : the sparkle in her eyes and the little lateral movement of her mouth just before she starts speaking, her hand gently laid on her unfortunate lover's raised arm while she speaks, the other protecting her genitalia, her quiet precipitation and awe once she's spoken...

Alas, alas ! This girl was not for real : the proposal was a prank, as guessed by the reporters, and confirmed by a commentator who remembers reading it in the paper the next day.

(See here for a genuine reaction -- note the larsen effect at the crucial moment...)

I thougt I'd also show an example that is not related to any kind of Freudian bullshit :

Actually I failed. Notice his reaction : "Oh ffffffff.. Shit. Oh my god." This guy manages to repress his impulse to say "fuck", but only to replace it by another similarly vulgar word, namely "shit". The "oh my god" comes only after, once the first emotion has passed. No doubt Freud would have concluded that his sexuality is repressed, and expresses itself in a scatological way...

Sorry for this tasteless post.

Compactification and singularity

2008-12-30T14:53:00.023Z

On the train from Lausanne to Geneva Airport I recalled the way Polchinski introduces his chapter on toroidal compactification :

"In general relativity, the geometry of spacetime is dynamical. The three spatial dimensions we see are expanding and were once highly curved. It is a logical possibility that there are additional dimensions that remain small."

J. Polchinski, String Theory, volume I, CUP 1998 (p. 231)

My personal version of this argument is to say that in GR space can be curved and hence it is a "logical possibility" that there are dimensions so curved that they actually close on themselves. I find that it is a very seducing way to introduce the notion of extra dimensions that are hidden because of their compactness, since it follows from the well-established curvature of space-time.

Polchinski then goes on to explain Kaluza-Klein theory with a periodic dimension without further explanations. This leaves the following question open :

What kind of massive object curves some dimensions so as to make them compact while leaving other dimensions non-compact ?

I've been drawing a lot since then and realized a few things that amazed me for five seconds before revealing their complete triviality... Nevertheless, here are some of my reflections.

At first the idea that an object curves only some dimensions and not all of them seems bizarre. Imagine a toy universe that has only two dimensions so that one can envision curvature as the bending of an elastic membrane with a ball on it. This video which is part of a documentary about Hawking has a nice illustration of this after 3:00.

Now if some dimensions are to be so strongly curved that they become compact, this must be the effect of a very massive object. So let us give the ball a tremendous mass; the way I picture what happens is that the weight of the ball stretches the membrane in the form of an extremely long tube. So neglecting the extremities, the membrane has now the topology of a cylinder, which is the direct product of a non-compact manifold, a real line, with a compact one, a circle. What seems a bit weird is that the radial direction, which is curved by the ball, remains non-compact, whereas the angular direction, which is not curved, is compact ! But there is a fallacy here : to have an angular coordinate (with a finite range) does not mean there is a compact dimension. The plane is not any compacter in polar coordinates than in Cartesian coordinates...

I'd like to understand spaces that have a non-compact part and a compact part. For simplicity I'll take direct products of real lines and spheres. The simplest case is R x S^1. This is pretty clearly a cylinder if you think of it as an S^1 fibration over R, but you could also think of it as a R fibration over S^1, in which case one can see that is is also a cylinder by taking into account that the fibers must not intersect. In fact, only the topology matters here and the cylinder can be continuously deformed at will. The formal definition of this direct product is R x S^1 = {(x, theta) | x \in (-\infty, \infty), theta \in [0, 2\pi]}. So you just need to specify a couple of coordinates, one for the real line (x), and one for the circle (theta).

An interesting deformation of the cylinder is achieved through a conformal mapping, where one defines a coordinate z = exp(x + i theta). This can be thought of as a radial coordinate r = exp(x), and an angular coordinate theta. The radial coordinate ranges from 0 to infinity but at r=0 the circle degenerates, which does not correspond to the cylinder bounded by circles at both its extremities at infinity. In consequence, the origin has to be removed. So one ends up with the manifold R^2 (in fact the complex plane...) with the origin removed : R x S^1 ~ R^2\{0}. R^2 is non-compact but by removing a point you make it isomorphic to a space that is the direct product of a compact space with a non-compact space. There is thus an equivalence between manifolds with a singularity and partially compact manifolds !

Coming back to our latex membrane, we understand now that in order to obtain a compact dimension the ball must be so heavy that it produces a black hole singularity.

Now consider R x S^2. It is hard to understand as a fibration : is it some kind of solid cylinder ? I guess that a particle can move arbitrarily inside the cylinder but as it approaches the surface it is forced to move tangentially to it (?) It is much easier to think about it after a conformal mapping, which leads to R^3\{0}. Again, the origin is removed for the angular coordinates to be well-defined everywhere. (Notice that the manifold is not complex anymore, given that it is odd-dimensional...)

Another simple case is R^2 x S^1, which can be reduced to the first case by rewriting it as R x R x S^1 ~ R x R^2\{0}. We get a manifold R^3 with a line singularity along the third axis. This is nice because it means we can get more than just one non-compact dimension (the radial direction), namely the dimensions of the singularity itself.

We are ready to generalize : after conformal mapping, the direct product R^n x S^d gives a (n-1)-dimensional singularity at the origin of a (d+1)-dimensional space.

String theory requiring 10 dimensions for its consistency while we only observe 4 non-compact dimensions, we might try the direct product R^4 x S^6. However, according to our reasoning, this is isomorphic to R^3 x R^7\{0}, so that the fourth non-compact dimension differs from the others in that its boundaries at infinity are six-spheres... (how bad is that ?)

If this has to be avoided, one must rather consider R^5 x S^5 ~ R^4 x R^6\{0}. This is pretty close to what appears in the context of the AdS/CFT correspondence ! There, the singularity would be black 3-branes and there would be a warping between R^4 and the radial coordinate to get AdS_5.

Remark :

The bending latex representation is misleading since it implies that the membrane is curved towards a third dimension. I don't think this is the proper way to view it, because otherwise the curvature of four-dimensional space-time would by itself imply the existence of extra dimensions... Rather, one should maybe picture a curved space by a density plot. The darker the color, the larger the curvature. The surface of the black hole would be a very dark circle.

From the density plot the surface of the black hole is at a fixed radius, but from the curved membrane representation it forms a very long tube. It is folly to suppose the coordinate along the tube is the coordinate U = r/alpha' with r->0 defined by Maldacena.

Party String Theory

2008-11-10T23:01:00.023Z

And of course you go to a party and of course someone asks you what you do and of course you say string theory and of course what is it ? and of course you don't know where to start. // Classic.

So it gets you thinking about how to present string theory and so you find one way and so you feel warm inside and so you post a post. // Classic.

A good way to introduce string theory is as a conceptual framework that unifies the two current pillars of theoretical physics : general relativity and quantum mechanics. To give a feel of what string theory is about, it suffices to focus the explanations on just one specific (but pretty central) aspect of each theory : black holes for GR, the uncertainty principle for QM.

1. The central result of Einstein's general relativity is that a very massive object -- or equivalently a very energetic object, remember E=mc^2 -- has the effect of curving the neighbouring space-time (which in fact implies gravity...). But there is a bound to this phenomenon, since if an object is too massive, it will curve space-time so much that it will end up tearing it apart and creating a black hole. (As an illustration, imagine space-time had only two dimensions, and think about it as a stretched piece of cloth ; putting heavy objects on it will curve it, and if an object is heavy enough it will make a hole in it.)

2. At the heart of quantum physics lies Heisenberg's uncertainty principle, according to which a particle cannot have both a precise position and a precise momentum (mass times speed). There is a tension between the precisions of those two properties : if the position of a particle is determined with great accuracy, unavoidably its momentum becomes very uncertain -- we know precisely where it is but not where it is going nor at which speed it is moving. And inversely, if the momentum is precise, it is the position which becomes uncertain, as if the particle were dissolved into some sort of a fuzzy cloud...

Now if you ask the philosophical question of knowing what is the ultimate building block of reality, and that you undertake to break objects down into little pieces, then in littler pieces, and then yet littler and so on, there will be a point where the piece you consider is so small that by the uncertainty principle its momentum (and so its energy) is so fuzzy that it can produce a black hole. From this point, the division process cannot be carried any further.

String theory aims at describing what is happening at this ultimate scale, where tiny black holes appear and disappear randomly by quantum fluctuations, and where the very notions of space and time lose their pertinence...

[Poetic suspension]

What we call "reality" is nothing but the surface of a chaos of black holes...

[Poetic suspension again]

And hence holography, AdS/CFT, and the like. Good.

*********************************************************

On a related note, people are usually amazed when I tell them that I switched from philosophy and art to physics. The most coherent explanation in my bag of tricks has to do with my interest in perception and the essence of reality, but I think I just found a new twist on it, as I was staring at the moon (beautifully speckled tonight). It goes something like this :

At some point in my early life it occurred to me that creation was the purest source of joy (this expression is in fact taken from my application letter to Oxford -- how naive I was...). So that might explain why I was interested in arts and why I even wanted to become a painter. But I was aware (I think) that the product of an artist's creation is not a work of art (although it is, don't get me wrong !), but rather a new perspective on existence.

[Which example could I find to illustrate that ??? I reckon that if you don't already know it, it will be quite impossible to convince you... For example when the Gothic cathedrals started to be built with thinner walls and with more light, it was not (even though maybe ingenuously it was) to make a "pretty" building, but to be in phase with the evolution of the societies from a feudal to a seigniorial organisation. (About this fascinating topic I recommend the brilliant book L'Art féodal et son enjeu social by André Scobeltzine.) But it is not a real good example, because the notion of artist was ill-defined at the time... Anyways !]

OK so the point is that what I am doing currently, namely theoretical physics, is also a creative venture. And what the theoretical physicist creates [notice my emphasis on the "theoretical" bit ? ; )] is not an article, not even a physical theory (although it is, don't get me wrong !), but -- reality itself !

Just like the philosopher in fact... And like the artist as well in fact... I'm afraid I would have utterly lost my party interlocutors by this time in fact... Perhaps that explanation ought to be substantiated more substantially in fact...

Addendum : Well my basic intuition arises roughly from the following type of considerations. Before Galileo the earth was the centre of the universe. It's not just that everybody wrongly thought it was. Go back to Timbuktu : if nobody sees the Dalmatian in the picture then there is no Dalmatian in the picture. Peace.

Time thickening

2008-10-17T23:47:00.010+01:00

On Sunday I went to a Coffee Concert by John Myewrscough (cello) and Lara Dodds-Eden (piano). They played various compositions among which the mind-blowing Cello Sonata n° 1 by Alfred Schnittke (1934-1998). Here I just want to talk about a thought that came to me during the concert.

The enjoyment of music increases with the ability to "grasp" with the mind a piece of melody as a whole -- at once. I mean as a unique entity rather than as a succession of individual notes (Husserl tried to explain the possibility of such a thing in his Vorlesungen zur Phänomenologie des inneren Zeitbewusstseins). The broader the perception of a fragment of music, the deeper the pleasure (think about Mozart who was able to restitute an entire concerto after hearing it only once...). So listening to music encourages the development of the ability to grasp longer periods of time instantaneously, i.e. to have them "present" interiorly as sensations.

This is how music enriches our existences : by teaching us how to thicken our present time.

(The cellist's name contains the name "Myers", so I'll call that the timelike Myers effect ; )

Schubert : Winterreise

2008-10-14T21:40:00.013+01:00

I finally overcame my aversion for classical singing : ) I think the key factor was the realisation of the importance of the lyrics, without which the songs often sound like empty gargles to me.

I went to the Oxford Lieder Festival to hear Florian Boesch (bass baritone) and Andrew West (piano) play Schubert's Die Winterreise ("The Winter Journey"), composed in 1827, one year before his death at age 31. It is based on a cycle of 24 poems written by the (also short-lived) poet Wilhelm Müller (1794-1827).

The organizers had the presence of mind to distribute the full text of the poems, and I followed them closely during the entire concert. I only looked at the stage occasionally to see Boesch's raging face, which would have scared the most pitiless murderers. The story of Winterreise is about a man that has to leave the house of his fiancée -- for an unknown reason (the pre-concert speaker mentioned something about her getting married to a rich man...) -- and shouts out his anger and sadness as he wanders across wintry landscapes. He's going through a succession of phases from deep despair to vain attempts at cheering up, from a sparkle of hope to impatience for death. His journey finally leads him to a graveyard, but he's pissed off not to find an unoccupied grave and keeps on walking against the snow storm in an outburst of nihilist courage :

Lustig in die Welt hinein
Gegen Wind und Wetter !
Will kein Gott auf Erden sein,
Sind wir selber Götter !

The two last songs then appear as mysterious epilogues :

xxiii. Die Nebensonnen

Drei Sonnen sah ich am Himmel stehn,
Hab' lang' und fest sie angesehn ;
Und sie auch standen da so stier,
Als wollten sie nicht weg von mir.
Ach, meine Sonnen seid ihr nicht !
Schaut Andren doch in's Angesicht !
Ja, neulich hatt' ich auch wohl drei ;
Nun sind hinab die besten zwei.
Ging' nur die dritt' erst hinterdrein !
Im Dunkeln wird mir wohler sein.

xxiv. Der Leiermann

Drüben hinter'm Dorfe
Steht ein Leiermann
Und mit starren Fingern
Dreht er, was er kann.

Barfuss auf dem Eise
Wankt er hin und her ;
Und sein kleiner Teller
Bleibt ihm immer leer.

Keiner mag ihn hören,
Keiner sieht ihn an,
Und die Hunde knurren
Um den alten Mann.

Und er lässt es gehen
Alles, wie es will,
Dreht und seine Leier
Steht ihm nimmer still.

Wunderlicher Alter,
Soll ich mit dir gehn ?
Willst zu meinen Liedern
Deine Leier drehn ?

The picture shows a "Leier" ("vielle à roue" in French ; I remember my grandfather use to have one of those instruments that always fascinated me). In this last song, I understand it as a symbol of an implacable periodic cycle that transcends men's miserable finiteness. The organ-player looks weak and insane, an outcast, but it is the disguise of ultimate wisdom, whose concern is stretching beyond death.

The lover's misfortune should not be taken too literally but rather as an illustration of a more universal departure from a state of being where meaning was god-given (some sort of Garden of Eden) towards an absurd world depraved of unquestionable foundations (the speaker had presented Schubert as a predecessor of Nietzsche...). After having gone through all stages of despair, touching the bottom in the graveyard, he finds an unexpected solution : although life has lost the a priori meaning it use to have in more rudimentary periods, it is still possible (and necessary) to make sense of it by its representation in the arts [and sciences], and in particular music. The Leiermann is a symbol of the lover's creative drive.

The 24 songs properly form a cycle in the sense that they themselves are the response to the last question : "Willst zu meinen Liedern / Deine Leier drehn ?" By listening to them the empathic audience has participated in their transfiguration by acknowledging and validating their representational power.

Les deux clochers de Martinville

2008-10-06T23:14:00.002+01:00

"
[...] Une fois pourtant,—où notre promenade s’étant prolongée fort au delà de sa durée habituelle, nous avions été bien heureux de rencontrer à mi-chemin du retour, comme l’après-midi finissait, le docteur Percepied qui passait en voiture à bride abattue, nous avait reconnus et fait monter avec lui,—j’eus une impression de ce genre et ne l’abandonnai pas sans un peu l’approfondir. On m’avait fait monter près du cocher, nous allions comme le vent parce que le docteur avait encore avant de rentrer à Combray à s’arrêter à Martinville-le-Sec chez un malade à la porte duquel il avait été convenu que nous l’attendrions. Au tournant d’un chemin j’éprouvai tout à coup ce plaisir spécial qui ne ressemblait à aucun autre, à apercevoir les deux clochers de Martinville, sur lesquels donnait le soleil couchant et que le mouvement de notre voiture et les lacets du chemin avaient l’air de faire changer de place, puis celui de Vieuxvicq qui, séparé d’eux par une colline et une vallée, et situé sur un plateau plus élevé dans le lointain, semblait pourtant tout voisin d’eux.

En constatant, en notant la forme de leur flèche, le déplacement de leurs lignes, l’ensoleillement de leur surface, je sentais que je n’allais pas au bout de mon impression, que quelque chose était derrière ce mouvement, derrière cette clarté, quelque chose qu’ils semblaient contenir et dérober à la fois.

Les clochers paraissaient si éloignés et nous avions l’air de si peu nous rapprocher d’eux, que je fus étonné quand, quelques instants après, nous nous arrêtâmes devant l’église de Martinville. Je ne savais pas la raison du plaisir que j’avais eu à les apercevoir à l’horizon et l’obligation de chercher à découvrir cette raison me semblait bien pénible; j’avais envie de garder en réserve dans ma tête ces lignes remuantes au soleil et de n’y plus penser maintenant. Et il est probable que si je l’avais fait, les deux clochers seraient allés à jamais rejoindre tant d’arbres, de toits, de parfums, de sons, que j’avais distingués des autres à cause de ce plaisir obscur qu’ils m’avaient procuré et que je n’ai jamais approfondi. Je descendis causer avec mes parents en attendant le docteur. Puis nous repartîmes, je repris ma place sur le siège, je tournai la tête pour voir encore les clochers qu’un peu plus tard, j’aperçus une dernière fois au tournant d’un chemin. Le cocher, qui ne semblait pas disposé à causer, ayant à peine répondu à mes propos, force me fut, faute d’autre compagnie, de me rabattre sur celle de moi-même et d’essayer de me rappeler mes clochers. Bientôt leurs lignes et leurs surfaces ensoleillées, comme si elles avaient été une sorte d’écorce, se déchirèrent, un peu de ce qui m’était caché en elles m’apparut, j’eus une pensée qui n’existait pas pour moi l’instant avant, qui se formula en mots dans ma tête, et le plaisir que m’avait fait tout à l’heure éprouver leur vue s’en trouva tellement accru que, pris d’une sorte d’ivresse, je ne pus plus penser à autre chose. A ce moment et comme nous étions déjà loin de Martinville en tournant la tête je les aperçus de nouveau, tout noirs cette fois, car le soleil était déjà couché. Par moments les tournants du chemin me les dérobaient, puis ils se montrèrent une dernière fois et enfin je ne les vis plus.

Sans me dire que ce qui était caché derrière les clochers de Martinville devait être quelque chose d’analogue à une jolie phrase, puisque c’était sous la forme de mots qui me faisaient plaisir, que cela m’était apparu, demandant un crayon et du papier au docteur, je composai malgré les cahots de la voiture, pour soulager ma conscience et obéir à mon enthousiasme, le petit morceau suivant que j’ai retrouvé depuis et auquel je n’ai eu à faire subir que peu de changements:

«Seuls, s’élevant du niveau de la plaine et comme perdus en rase campagne, montaient vers le ciel les deux clochers de Martinville. Bientôt nous en vîmes trois: venant se placer en face d’eux par une volte hardie, un clocher retardataire, celui de Vieuxvicq, les avait rejoints. Les minutes passaient, nous allions vite et pourtant les trois clochers étaient toujours au loin devant nous, comme trois oiseaux posés sur la plaine, immobiles et qu’on distingue au soleil. Puis le clocher de Vieuxvicq s’écarta, prit ses distances, et les clochers de Martinville restèrent seuls, éclairés par la lumière du couchant que même à cette distance, sur leurs pentes, je voyais jouer et sourire. Nous avions été si longs à nous rapprocher d’eux, que je pensais au temps qu’il faudrait encore pour les atteindre quand, tout d’un coup, la voiture ayant tourné, elle nous déposa à leurs pieds; et ils s’étaient jetés si rudement au-devant d’elle, qu’on n’eut que le temps d’arrêter pour ne pas se heurter au porche. Nous poursuivîmes notre route; nous avions déjà quitté Martinville depuis un peu de temps et le village après nous avoir accompagnés quelques secondes avait disparu, que restés seuls à l’horizon à nous regarder fuir, ses clochers et celui de Vieuxvicq agitaient encore en signe d’adieu leurs cimes ensoleillées. Parfois l’un s’effaçait pour que les deux autres pussent nous apercevoir un instant encore; mais la route changea de direction, ils virèrent dans la lumière comme trois pivots d’or et disparurent à mes yeux. Mais, un peu plus tard, comme nous étions déjà près de Combray, le soleil étant maintenant couché, je les aperçus une dernière fois de très loin qui n’étaient plus que comme trois fleurs peintes sur le ciel au-dessus de la ligne basse des champs. Ils me faisaient penser aussi aux trois jeunes filles d’une légende, abandonnées dans une solitude où tombait déjà l’obscurité; et tandis que nous nous éloignions au galop, je les vis timidement chercher leur chemin et après quelques gauches trébuchements de leurs nobles silhouettes, se serrer les uns contre les autres, glisser l’un derrière l’autre, ne plus faire sur le ciel encore rose qu’une seule forme noire, charmante et résignée, et s’effacer dans la nuit.» Je ne repensai jamais à cette page, mais à ce moment-là, quand, au coin du siège où le cocher du docteur plaçait habituellement dans un panier les volailles qu’il avait achetées au marché de Martinville, j’eus fini de l’écrire, je me trouvai si heureux, je sentais qu’elle m’avait si parfaitement débarrassé de ces clochers et de ce qu’ils cachaient derrière eux, que, comme si j’avais été moi-même une poule et si je venais de pondre un oeuf, je me mis à chanter à tue-tête.

Les délices de Proust

2008-10-05T13:29:00.011+01:00

Dans une note précédente, je rapprochais inopinément le passage de la petite cuillerée de Proust d'un extrait des Paradis Artificiels de Baudelaire.
Que ce soit une allusion délibérée de Proust, c'est dur à dire, mais ce qui est sûr c'est qu'il tenait Baudelaire en grande estime, comme l'atteste son fameux questionnaire de 1889-90 :

"Mes poètes préférés. - Baudelaire et Alfred de Vigny."

De plus, un peu plus loin dans Combray Baudelaire est explicitement nommé :

"[...] cette sorte de tendresse, de sérieuse douceur dans la pompe et dans la joie qui caractérisent certaines pages de Lohengrin, certaines peintures de Carpaccio, et qui font comprendre que Baudelaire ait pu appliquer au son de la trompette l’épithète de délicieux."

On peut donc penser que dans le cerveau de Proust le mot "délicieux" est relié par un certain nombre de synapses à l'image de Baudelaire. Grâce à Wikisource c'est très facile de rechercher toutes les occurrences de ce mot dans Combray. Il apparaît notamment dans ce passage important où le petit Marcel, mortellement angoissé d'avoir été envoyé au lit sans que sa mère, retenue par des invités, ne vinsse l'embrasser, lui a envoyé un billet par l'intermédiaire de la domestique Françoise :

"[...] puisque cette salle à manger interdite, hostile, où, il y avait un instant encore, la glace elle-même — le « granité » — et les rince-bouche me semblaient receler des plaisirs malfaisants et mortellement tristes parce que maman les goûtait loin de moi, s’ouvrait à moi et, comme un fruit devenu doux qui brise son enveloppe, allait faire jaillir, projeter jusqu’à mon cœur enivré l’attention de maman tandis qu’elle lirait mes lignes. Maintenant je n’étais plus séparé d’elle ; les barrières étaient tombées, un fil délicieux nous réunissait. Et puis, ce n’était pas tout : maman allait sans doute venir !"

(C'est moi qui souligne [sic].) Sa ruse échoue mais il joue le tout pour le tout et descend surprendre sa mère une fois les invités partis. Elle veut le gronder mais son père est suffisamment clairvoyant pour s'apercevoir de sa détresse profonde et les invite, exceptionnellement, à passer la nuit ensemble [il y aurait beaucoup à dire sur les résonances œdipiennes de cet épisode...]. Voici comment Marcel relate la suite :

"Maman s’assit à côté de mon lit ; elle avait pris François le Champi à qui sa couverture rougeâtre et son titre incompréhensible donnaient pour moi une personnalité distincte et un attrait mystérieux. Je n’avais jamais lu encore de vrais romans. J’avais entendu dire que George Sand était le type du romancier. Cela me disposait déjà à imaginer dans François le Champi quelque chose d’indéfinissable et de délicieux. Les procédés de narration destinés à exciter la curiosité ou l’attendrissement, certaines façons de dire qui éveillent l’inquiétude et la mélancolie, et qu’un lecteur un peu instruit reconnaît pour communs à beaucoup de romans, me paraissaient simples — à moi qui considérais un livre nouveau non comme une chose ayant beaucoup de semblables, mais comme une personne unique, n’ayant de raison d’exister qu’en soi — une émanation troublante de l’essence particulière à François le Champi. Sous ces événements si journaliers, ces choses si communes, ces mots si courants, je sentais comme une intonation, une accentuation étrange."

Ce que je trouve intéressant dans ces passages c'est que l'épithète "délicieux" semble lié, chez Proust, d'une part à la figure de la mère, mais aussi, et surtout (en tout cas pour mon propos présent), à l'écriture et à la lecture : ce "fil délicieux" que sa mère "lirait" c'est le billet qu'il lui a écrit, peut-être une des premières choses qu'il ait écrites de sa propre impulsion, sans y être invité par un professeur, lui faisant soudain sentir l'importance vitale que peut avoir l'écriture. Mais la soirée est encore plus riche en révélations, car le petit Marcel va entendre de la bouche de sa mère adulée la lecture de son premier "vrai roman". Et ce qu'il trouve "délicieux", ce n'est pas, comme pour la plupart des enfants, le pouvoir captivant de l'histoire, le suspens, mais ce qui se cache derrière eux, de nature intrinsèquement littéraire, à savoir les "procédés de narration". Pas la surface du roman, mais bien sa structure interne, comme seul la verrait un écrivain. Et de fait c'est bien ce qu'il est devenu ce soir-là, notre petit Marcel, un écrivain, car il a fait lui-même l'expérience de la puissance de l'écrit comme vecteur de nos émotions les plus intenses.

La dernière phrase du second extrait, avec cette opposition "commun/étrange", fait écho à l'épisode de la petite madeleine, où une banale cuillerée provoque quelque chose "d'extraordinaire" en Marcel. Je vous le donne en mille :

"Un plaisir délicieux m'avait envahi, isolé, sans la notion de sa cause".

Cette cause qui échappe aux tentatives enfantines pour la découvrir, l'épithète "délicieux" nous la révèle cependant : c'est le plaisir littéraire ! Mais un plaisir littéraire ici à l'état bruto-brut. Je m'explique. La petite madeleine, gorgée de thé, est aussi gorgée de sens pour Marcel [oui je fais dans la métaphore facile -- un problème ? ; )]. Elle contient le souvenir du temps (et de l'espace !) où la tante de Marcel lui donnait des morceaux de madeleine trempés dans le tilleul, le dimanche matin, à Combray (c'est un roman ; c'est CE roman). Cette essence précieuse dont la madeleine remplit Proust ("ou plutôt cette essence n'était pas en moi, elle était moi.") n'est rien d'autre que la narration littéraire.

À l'appui de cette thèse, cette phrase de Baudelaire, toujours dans les Paradis Artificiels :

"le délire poétique ressemble à celui que m’a procuré une petite cuillerée de confiture [...]"

Et je ne résiste pas à citer encore un passage d'une beauté ahurissante, qui clôt la première partie de Combray :

"Mais, quand d’un passé ancien rien ne subsiste, après la mort des êtres, après la destruction des choses, seules, plus frêles mais plus vivaces, plus immatérielles, plus persistantes, plus fidèles, l’odeur et la saveur restent encore longtemps, comme des âmes, à se rappeler, à attendre, à espérer, sur la ruine de tout le reste, à porter sans fléchir, sur leur gouttelette presque impalpable, l’édifice immense du souvenir.

Et dès que j’eus reconnu le goût du morceau de madeleine trempé dans le tilleul que me donnait ma tante (quoique je ne susse pas encore et dusse remettre à bien plus tard de découvrir pourquoi ce souvenir me rendait si heureux), aussitôt la vieille maison grise sur la rue, où était sa chambre, [ 69 ]vint comme un décor de théâtre s’appliquer au petit pavillon donnant sur le jardin, qu’on avait construit pour mes parents sur ses derrières (ce pan tronqué que seul j’avais revu jusque-là) ; et avec la maison, la ville, la Place où on m’envoyait avant déjeuner, les rues où j’allais faire des courses depuis le matin jusqu’au soir et par tous les temps, les chemins qu’on prenait si le temps était beau. Et comme dans ce jeu où les Japonais s’amusent à tremper dans un bol de porcelaine rempli d’eau de petits morceaux de papier jusque-là indistincts qui, à peine y sont-ils plongés s’étirent, se contournent, se colorent, se différencient, deviennent des fleurs, des maisons, des personnages consistants et reconnaissables, de même maintenant toutes les fleurs de notre jardin et celles du parc de M. Swann, et les nymphéas de la Vivonne, et les bonnes gens du village et leurs petits logis et l’église et tout Combray et ses environs, tout cela qui prend forme et solidité, est sorti, ville et jardins, de ma tasse de thé."

Timbuktu

2008-10-04T11:35:00.023+01:00

Take a tower in a town.
Face it.
Compare the apparent widths of its base and of its top.
Notice the latter is smaller.
Conclude the tower is apparently trapezoidal.

In case you think it's a classical perspective effect (i.e. all lines seem to converge to a fixed point), repeat the experience, but now with a very broad building (a palace if you can ; or if you liked it when it was vertical, imagine yourself at the top of a tower adjacent to the 8:46 Twin Tower...), and compare the apparent height of its centre to those of its lateral extremities.
Notice the latter are smaller.
Conclude the palace is apparently an almond.

I remember reading in an art theory book (possibly by Gombrich) that this effect is merely an illusion because you actually have to turn your head to compare the different part of the building, so that in the end you're comparing quantities that shouldn't be... I was never able to make sense of this argument : even with my eyes fixed on the centre, my peripheral vision still allows me to perceive this almond effect.

Now most of the people would agree that the edges of the "real" tower -- not the apparent one -- are of course parallel (they would prove it by taking a ruler and measuring the width of the tower at different places). So this tells us something about the meaning of the word "real" : what is considered "real" is not what we perceive but rather an artificially reconstructed idealisation of the perceived objects, that is abstracted from an infinite series of representations acquired from different points of view.

In other words, to "see" a physical object, it is necessary to look at it from all possible sides, travelling across an entire virtual globe around it -- or rotating it in all possible ways in our hand. But in fact we quickly get so good at it during our formation years that just a few glimpses at an object (provided it is not too extraordinary) and we are able to construct a very efficient mental image of its "real" shape.

What about its colour ? Perhaps you would say its colour is what you see when it is lit with pure white light, but you have to take into account the particularities of your visual organs (imagine you're daltonian). The "true" colour of an object is naturally taken to be the colour that most of us would agree upon, i.e. it is defined intersubjectively. [Aristotelian philosophers referred to the colour as an example of "secondary quality" and opposed it to "primary qualities" such as the shape. Throughout history the number of primary qualities kept on decreasing, until it reached absolute zero with Hume (not quite in fact maybe...). My belief is that this distinction is not pertinent, that every quality is secondary.]

Go further : what does the concept of "liberty" "really" mean ? [yes, I know, I am not fully happy with my use of inverted commas myself...] It is also clear that the definition of any concept will require some sort of concertation between the individuals of the group within which the concept is in use. So let me formalize that in the following

Lemma 1.1 The "reality" of an object (either physical or conceptual) is determined by intersubjective agreement.

Keep that in mind, switch it off, and tell me what you see in the picture below. Nothing ? Sure ?

Still not ? What about now ?

Yes, no ? HA ! NOW you see the Dalmatian don't ya ? [Shit I start talking like Palin now ; )]
I saw this picture in an online lecture about cognitive psychology and the lecturer asked the lady that said "HA" the loudest what happened on the screen at that moment. She replied "On the screen nothing, in my brain something happened," which the lecturer, very pleased, repeated : "On the screen nothing, but in the brain -- I couldn't have said any better." At the time I found it rather obvious (selbstverständlich as the German say), but this morning when I woke up I realized it wasn't so. (I should have been alarmed by the fact that the expert's analysis coincided with the old lady's plain common sense, whereas one would expect that profound science would reach the extreme boundaries of common sense and beyond...)

It is NOT obvious that the "real" picture on the screen did not change before and after the realisation of its representational content. Just use Lemma 1.1 : once the entire audience has identified the representation of the Dalmatian in the picture (and you too, and me), it CANNOT be denied its share of "reality".

(Without elaborating any further, I suspect that this kind of considerations should reach their full flavour in the context of the foundations of quantum mechanics...)

(Rigid philosophers like Bertrand Russell would use arguments such as "The table I write on, I can touch it, so it exists, and it exists even if I close my eyes" etc. My impression is that he is under the same spell than the old lady, were she asked to "un-see" the Dalmatian once she's seen it. Very difficult to do, I'll have you know ! The only way I can get myself to do it is by focusing on a small fraction of the picture. That again seems to indicate that "de-realisation" effects are to be expected in the microscopic realm.)

La petite madeleine Reloaded

2008-09-30T21:17:00.024+01:00

"
Et bientôt, machinalement, accablé par la morne journée et la perspective d'un triste lendemain, je portai à mes lèvres une cuillerée de thé où j'avais laissé s'amollir un morceau de madeleine. Mais à l'instant même où la gorgée mêlée des miettes du gâteau toucha mon palais, je tressaillis, attentif à ce qui se passait d'extraordinaire en moi. Un plaisir délicieux m'avait envahi, isolé, sans la notion de sa cause. Il m'avait aussitôt rendu les vicissitudes de la vie indifférentes, ses désastres inoffensifs, sa brièveté illusoire, de la même façon qu'opère l'amour, en me remplissant d'une essence précieuse : ou plutôt cette essence n'était pas en moi, elle était moi. J'avais cessé de me sentir médiocre, contingent, mortel. D'où avait pu me venir cette puissante joie ? Je sentais qu'elle était liée au goût du thé et du gâteau, mais qu'elle le dépassait infiniment, ne devait pas être de même nature. D'où venait-elle ? Que signifiait-elle ? Où l'appréhender ? Je bois une seconde gorgée où je ne trouve rien de plus que dans la première, une troisième qui m'apporte un peu moins que la seconde. Il est temps que je m'arrête, la vertu du breuvage semble diminuer. Il est clair que la vérité que je cherche n'est pas en lui, mais en moi. Il l'y a éveillée, mais ne la connaît pas, et ne peut que répéter indéfiniment, avec de moins en moins de force, ce même témoignage que je ne sais pas interpréter et que je veux au moins pouvoir lui redemander et retrouver intact, à ma disposition, tout à l'heure, pour un éclaircissement décisif. Je pose la tasse et me tourne vers mon esprit. C'est à lui de trouver la vérité. Mais comment ? Grave incertitude, toutes les fois que l'esprit se sent dépassé par lui-même ; quand lui, le chercheur, est tout ensemble le pays obscur où il doit chercher et où tout son bagage ne lui sera de rien. Chercher ? pas seulement : créer. Il est en face de quelque chose qui n'est pas encore et que seul il peut réaliser, puis faire entrer dans sa lumière.
"

C'est là, tel quel, le passage cultissime de la petite madeleine Proustienne, situé à la fin de la première section de la première partie : Combray du premier roman : Du Côté de chez Swann (1913) de la volumineuse somme : À la Recherche du Temps Perdu de Marcel Proust (1871-1922) -- qui n'était pas le dernier des imbéciles.

Dans mon cas en revanche, je ne serais pas aussi assertif, étant donné que la première lecture que j'ai faite de ce passage était manifestement complètement à côté de la plaque... XP [Ceci n'est pas un smiley.]
Néanmoins ! cette interprétation erronée ayant suscité en moi un émoi de grande magnitude et fait se bousculer toutes sortes d'idées creuses et galipétantes dans mon cervelet, c'est d'elle que je vais parler ici.
Caveat (donc) : ci-dessous gît l'oeuvre du malin, car, comme qui dirait, ErrareHvmanvmEstPerseverareDiabolicvm !

Bon. Bien sûr ce sera ultimement pour des raisons psychologiques, à savoir que cette madeleine lui rappelle celles que sa tante lui donnaient lorsqu'il était plus jeune etc., et c'est très bien -- rien à redire -- même si la cause de son émotion ne lui reviendra que beaucoup plus tard, nous dit le narrateur (et à l'heure de la publication j'ignore encore de quoi il sera question...), mais moi ce que j'y ai d'abord lu, dans ce passage, est d'une nature plus abstraite. Je l'ai lu comme ça, à ma guise, parce que ça s'accordait avec des expériences qu'il m'arrive parfois de vivre. Des expériences qui, dans la morosité du quotidien, me ravissent l'âme sans grande cause apparente. La plupart du temps c'est à l'occasion d'une perception visuelle que je ressens cela : une quelconque perception visuelle ! J'entends par là que ce n'est pas l'objet de ma perception qui, par sa prodigieuse beauté, par ses qualités esthétiques extraordinaires, produirait cet effet sur moi (même si ça peut aider), mais bien l'acte perceptif lui-même. Le phénomène de la vision lui-même.

[Minute linguistique : après tout, ne dit-on pas d'une performance qu'elle est "phénoménale" ; ne lâche-t-on pas, sitôt le bout-en-train reparti, "Quel phénomène celui-là !" ? alors qu'en fait un phénomène c'est ce qu'il y a de plus banal, tout est phénomène... (si l'on veut bien)]

Ce qui m'éblouit dans ces moments-là, c'est la possibilité de la perception, de l'interaction entre l'esprit et la matière... Et aussi la "rondeur", la plénitude de la perception.

Il y a une scène du film eXistenZ (1999) de David Cronenberg qui illustre bien ce que j'essaie de dire. Le scénario tourne autour d'un jeu vidéo futuriste tellement perfectionné que les joueurs finissent par ne plus savoir s'il sont dans le jeu ou dans le monde réel (avec une technologie semi-organique, un "pod" aux allures de crapauds qu'on s'enfile dans la moelle épinière, faut pas chercher). Au milieu du film, l'héroïne, qui a conscience d'être dans le jeu, profite d'un moment de désoeuvrement dans une station essence pour admirer les qualités de réalisme du jeu. Elle ramasse un caillou et le jette sur la pompe à essence. Au moment où le caillou percute la pompe se produit un son, "kling". Elle sourit.

Pourquoi sourit-elle ? Ce dont elle jouit ce n'est pas le petit bruit produit par le petit caillou sur la pompe à essence (ce qui, somme toute, serait assez niais), mais la cohérence perceptive (visuelle, sonore, etc.) de l'univers artificiel dans lequel elle est immergée. Ce dont elle s'émerveille pourrait être exprimé (en parodiant Lacan) en une phrase condensée :

"Ça" fait sens.

Les geeks et les Neo-théologiens s'empresseront de dire que si Ça veut bien faire sens, c'est uniquement parce que les programmateurs du jeu l'ont voulu ainsi, et que donc, une fois la métaphore rapportée au monde "réel", c'est à l'infinie bonté du Créateur que l'on doit la présence de sens. A quoi je répondrais a). get a life ! et b). "[...] tout ce que dit la théologie chrétienne est absolument vrai à condition d'être appliqué non pas à un Dieu transcendant et imaginaire, mais à l'Homme réel vivant dans le Monde. Le théologien fait de l'anthropologie sans s'en rendre compte. " (Alexandre Kojève, 1947)
Après les avoir bien bien cassés de la sorte, je retourne pépère à mon propos.

A vrai dire, pas vraiment. Le fil de mes idées s'est rompu. Je repars avec autre chose :

La "cuillerée de thé où j'avais laissé s'amollir un morceau de madeleine" m'a soudain rappelé un passage des Paradis Artificiels (1860) de Baudelaire :

"
Voici la drogue sous vos yeux : un peu de confiture verte, gros comme une noix, singulièrement odorante [...] -- Voilà donc le bonheur ! il remplit la capacité d’une petite cuiller ! le bonheur avec toutes ses ivresses, toutes ses folies, tous ses enfantillages !
"

N'est-ce pas déroutant ?

[Note for self : L'an de grâce 1927 vit la parution de trois ouvrages d'une importance capitale :

1. Sein und Zeit de Heidegger (New College, 2007),
2. Les Vorlesungen zur Phänomenologie des inneren Zeitbewußtseins de Husserl publiées sous la direction de Heidegger, (Akademie der Künste, Berlin, 2005),
3. Le Temps Retrouvé de Proust (bien qu'il ne l'ait guère modifié depuis sa mort en 1922).

Moralité : 1927 = gros dossier "temps" !]

Spider-scientist

2008-09-21T22:18:00.008+01:00

I was absorbed in abyssal thoughts about my research when a little black spider landed on my left shoulder from totally nowhere!

I have been quite amazed with spiders recently: how do they manage to build their webs hanging between two unrelated objects? That don't make no sense to me! (Also, the other day when I went running - in fact it was this morning - I was thinking about the fact that spiders always seem to know where they can build their webs and where they don't, for example in a place with a high circulation; but then I thought it certainly is absurd to think about it that way...)

And so, plötzlich, it struck me that a researcher has something to learn from a spider, in fact. Just like the spider, he is flying through the air from one idea to the other, blown by the wind of his imagination, and like the spider, his ultimate goal is the construction of a large web of concepts (able to catch some juicy preys... for the SOUL nigga!).

[As an aside, I would put forth the comment that when Witten was saying string theory is a piece of the XXIst century mathematics (did he venture to say IIIrd millenium?) fallen by chance into the XXth century, that would translate in my metaphor into a spider web with positive slope, built with the help of a favourable wind.]

But that only works if the researcher keeps track of his own thought process. If the line breaks, it won't be possible to relate the distant concepts, and everything is lost. Which, as you may imagine, is just what happened to me that day when the little spider paid me an unexpected visit... She was clearly philosophical enough to know that sometimes when you want to get a message through you have to violate its spirit.

Orphée

2008-09-16T22:45:00.006+01:00

Je me suis envoyé Orphée de Jean Cocteau (1950): pas transcendant. C'est plus proche du Testament d'Orphée (1960) que du Sang d'un Poète (1930) - remarque j'aurais pu m'en douter si j'avais un peu plus de jugeote... Plus proche donc d'un rafistolage de plaisanteries (méta-)poétiques d'un vieux Monsieur très convenable que des tâtonnements inspirés d'un amateur d'opium.

Une scène néanmoins a attiré mon attention, par la ressemblance qu'elle recèle avec mon travail de recherche. La Princesse de la Mort exhorte son chauffeur Heurtebise à faire usage de pouvoirs surnaturels pour renvoyer Orphée dans le monde des vivants, auprès de sa femme Eurydice. ("La Mort d'un poète," souligne Cocteau au passage, "doit se sacrifier pour le rendre immortel.") Heurtebise saisit la tête d'Orphée et ferme les yeux, concentré, tandis que la Mort l'encourage:

"
La Mort -- Travaillez, travaillez! Heurtebise je vous aide. Je travaille avec vous.
Ne faiblissez pas!
Comptez! Calculez! Acharnez-vous comme je m'acharne!
Allez: murez-le, il le faut!
Sans la volonté nous sommes des infirmes!
Allez, allez! Allez, allez!
Heurtebise -- Je ne peux pas.
M -- Il faut vouloir Heurtebise! Il le faut!
H -- Je ne peux pas.
M -- Vous travaillez mal. Ne me parlez plus. Enfoncez-vous en vous-mêmes.
Et quittez-vous! Courez! Courez! Volez! Renversez les obstacles!
Vous approchez... Vous arrivez! Je le vois.
H -- J'arrive.
M -- Un dernier effort Heurtebise. Faites-le. Faites-le! Y êtes-vous? Répondez-moi: y êtes-vous?
H -- J'y suis.
M -- Alors en route...
Remontez le temps! Il faut que ce qui a été ne soit plus!
(...)
H -- Je suis très fatigué..
M -- Je m'en moque! Travaillez! Travaillez je vous l'ordonne.
"
Ce genre d'encouragements serait tout à fait ce dont j'ai parfois besoin lorsque je me retrouve face à mon bureau recouvert de trois couches d'articles de physique théorique des hautes énergies...

First Live Citation

2008-08-21T21:42:00.005+01:00

On Monday appeared my paper written with He and Lukas, entitled "An Abundance of Heterotic Vacua" [I tried to put forth something more irreverent like "Get Your Fill of Heterotic Vacua," playing on the full/empty contradiction, or "Heterotic Bundles All Over the Place," to convey the image of some kind of orgy, but some of my collaborators were not so hot about it...]. Given that Ron Donagi was giving a talk on Tuesday at Strings 08 about "Heterotic Standard Models," the eventuality that he would mention our paper was non-negligible. Indeed, his last slide contained a reference that slightly differed from the other by its typography, indicating its late addition. It was just cryptically reading: "[GHL]." Ron undertook to enumerate the authors: "He, Lukas, and... [I was getting excited]... errmmm... I can't remember, never mind."

Great! Thanks Ron! Two thumbs up! :-P
So close to my first live citation, and yet so far...

However I got my revenge today, during Hermann Verlinde's talk on "Holographic Gauge Mediation." I arrived late to that talk because I had already heard it at Eurostrings, so I wasn't following with great attention. I suddenly woke up when I saw my name on the screen: "cf. Gabella, Gherghetta, Giedt." My first paper from my Master project in Minneapolis!

That was a pleasant feeling to have the impression to participate to a collective research effort. (My joy was soon to be a bit tempered by the fact that he then kept referring to us as "some phenomenologists" (in which he wasn't completely wrong, I have to confess...)).

Linde's speech at Strings 08 banquet

2008-08-21T00:07:00.011+01:00

The task of entertaining the audience at the end of the Strings 08 banquet at UniMail was accomplished with spirit by Andrei Linde. He started by saying that he was going to make a discourse in the Georgian-Russian fashion, but maybe it was not appropriate... He said that after our visit at the United Nations on Monday, he was seeing two goals of utmost importance: 1). world peace, and 2). experimental evidence for string theory.

Given that we live in an expanding universe, in a few billion years the galaxies will be beyond each other's horizon, and so there will be no intergalactic war any more. First problem solved.

He addressed the second problem with a succession of anecdotes from various famous physicists. One of them was about a Russian scientist (something in Z... I forgot) that once told physicists which were discouraged by the absence of experimental evidences in favour of baryon asymmetry that the fact that parallel lines do not intersect was actually an evidence (he quickly explained what he meant but I couldn't get it). "That is another type of evidence," Andrei said.

Then he talked about Murray Gell-Mann who asked one of his students to measure the height of a tower with a barometer. One week later the student came back and said that he had found three ways of doing it: The first option was to go to the top of the tower, attach a rope to the barometer, slide it down, and then measure the length of the rope. "Myeaaah. What is the second way?" Murray asked. The second option was to go to the top of the tower, throw the barometer down, and count the time it takes to reach the ground. "That is not really what I expected..." The student's third way was to go to the superintendent and tell him: "This barometer is worth about 30 €. It is yours if you tell me the height of the tower."

Andrei's point was that in order to get evidence for string theory, we need to use the barometer in a clever way (measuring the pressure difference at the top and bottom of the tower). There
is no straightforward way to do it (like the first two solutions of the naive student), and all the superintendents left the universe about 13.7 billion years ago (that is, at its creation).

And this clever way is to think about dolphins (not fishes: dolphins!). Dolphins live in water because it is the place where they can live, just as we live on the ground because we can live here. The tiny value of the cosmological constant can be explained in this way, but only at the condition that there exist a huge number of possible universes with different values of it. (Huge as in 10^500, which journalists, as they cannot typeset exponents, write as 10,500... "Anyway: big number.") Yes: anthropic reasoning. [I thought about David Gross at that point, who certainly won't miss on Friday to repeat his warning of last year's conference in Madrid: "Do not give up!"]

Andrei ended his discourse by saying that he could have proposed a toast for the LHC, the biggest machine ever built -- but that would have been too banal. Then for string theory -- not surprising enough. He had to be surprising (Georgian-Russian style!). He finally drank a toast to "You, the people that are making string theory, because we enjoy working together and learning." I found this apparition of a human, relational factor indeed quite surprising in such a context (although it would have been completely trivial in many other contexts).

In summary, Andrei's discourse operated two shifts:

A shift from the dream of a unique and unambiguous explanation of everything to the acknowledgement of the relevance of environmental determination.

A shift from a machine or a theory to mutual enjoyment.

Baroque Bach

2008-08-17T22:12:00.028+01:00

Only once in his lifetime did Johann Sebastian Bach (1685-1750) pose for a painter but it is known that, being a busy man, he actually left the workshop before the end of the session! So even though Haussmann's painting (1748, right) is the best we have, it remains very unreliable. This could have been the end of Bach's iconography, but it is not. In 1895 Bach's body was exhumed, and a sculpture made from his skull (below; recently, a Scottish anthropologist made a computer-modeled reproduction of Bach's bust, shown on the right below).

Imagine that: you come out of your mother's womb, you do your thing, you die. So far so good. But 145 years after your burial, someone removes your body from your grave in Leipzig to look at the shape of your skull and try to figure out what you might have looked like during your time! You'd agree that would be surprising.

But in fact, in the case of Bach, there was a catch: when I said he did his thing, that would be an euphemism to say that was an euphemism. After his death, even though he never thought his music would survive him, but rather that other composers will simply replace it by their own compositions, he came to be considered as the greatest composer that ever lived by such people as Mozart, Chopin, Liszt, Wagner, Debussy, etc.

Bach's musical involvement was absolutely permanent. Jack Gibbons (the pianist-lecturer of that evening) used the -- somewhat dubious -- image that if you were to copy every note he's ever written, you wouldn't achieve it in your lifetime ("Think about it for a minute," he added with humour). Bach must have been mostly writing in one throw, without any correction. Add to this his numerous administrative duties (he even had to teach Latin during his last position in Leipzig, where he was taken only as a third choice!), his immense family of twenty or so children, and you have the picture of an extremely productive composer sleeping barely a couple of hours every night.

Bach's family was so musical that they had it in their blood: a usual Sunday afternoon leisure was to improvise fugues on popular themes, an very technical exercise! (The last of the Goldberg Variations is an illustration of these "games.") The word "Bach" was practically a synonym for "Musiker" (By the way, the equivalence in England was the Gibbons family -- and Jack Gibbons to add that it is not known if there are any living descendants nowadays... (I can think of Beth Gibbons at least.))

I've admired the effects of such a pure dedication to music in a documentary about Ravi Shankar. I had been struck by the fact that most (if not all?) of his children decided to become musicians (his daughter Anoushka Shankar who plays the sitar too, and also of course Norah Jones). The intensity of his passion was powerful enough to diffuse to his children. The documentary had a magical scene where he gives a concert with Anoushka and during his solo you can see her face illuminating by delight and surprise.

[There I saw the beauty of the (rather old-fashioned) tradition of a family business: the son of the baker become a baker and so on. It is sad if this continuation is due to some kind of inertia, but it can also be due to a sincere love of work, a proudness and joy of creation, which acts as a positive force (rather than a negative constraint) on successive generations... The example of Ravi Shankar is less ambiguous here, as his own parents were not musicians, so that the choice of becoming musician was less automatic than in Bach's family.]

Bach's first wife died as he was on a trip, and he found her buried when he came back. He was however to find love again in Anna Magdalena, which was 17 years younger than him. They had a very joyful marriage, as JG illustrated by playing one of the French Suites, if I remember correctly. He said Anna was also an accomplished musician (which is a bit in contradiction with the technical ease of the Notebüchlein für Anna Magdalena Bach...). Their passion for music was so fusional that Anna ended up having the same handwriting than her husband, for the greatest confusion of modern musicologists.

The second part of the lecture-concert was devoted to the famous Goldberg Variations (1741). Bach composed them by the request of a Russian Ambassador, Count Kaiserling, who wanted to be distracted during his long nights of insomnia. Goldberg was the name of the Count's personal musician (his Hi-Fi set in some sense), who must have damned Bach every time he had to get up in the middle of the night to play those amazingly hard variations. It is fascinating to imagine the sleepless Count meditating on the infinite depths of the Variations in the darkness of his luxurious room...

Bach died of the sequels of disastrous eye surgery operations. As his blindness was keeping him away from his work, he decided to precipitate a second operation very shortly after the failure of the first. Several months later, he suddenly recovered his full vision for a few hours and then died.

Chat-brole, True/Faux, God::Art !

2008-08-13T00:23:00.000+01:00

A note about the French Nouvelle Vague.

In Paris of the late 50's, a group of film critics from the famous Cahiers du Cinéma decided that it was about time to revolutionize the way of making movies. The most prominent ones among them were Jean-Luc Godard, François Truffaut, and Claude Chabrol. They were the kind of guys that could watch ten movies and read ten books every week (specially JLG in fact); that could love american movies and pop culture religiously but stand up in the middle of an academic movie to say "C'est de la merde!" (again, JLG). And so they went on shooting four or five movies every year (yes, mostly JLG).

My point tonight is that I've been watching a few movies by Truffaut (Jules et Jim (1962)) and Chabrol (La Rupture (1970), Poulet au Vinaigre (1985), Les Noces Rouges (1973)), and I really cannot put them on the same level than the Godard's masterpieces such as A Bout de Souffle (1960) and Pierrot le Fou (1965). I find them unquestionably inferior.

Take Jules and Jim: it seems to me that it is nothing else but the work of someone who is very much willing to overcome old-fashioned ways of conceiving existence, but that is unfortunately unable to come up with something fresh and interesting to replace them, and ends up reproducing them in a transvestite way. (A bit like a rebellious kid who cannot go beyond his anger at his parents is doomed to recreate what he hates in them so much...)
Also, I could find a lot of cinematographic ideas that have been properly stolen from A Bout de Souffle. For example, Jeanne Moreau is saying at one point "Avant de vous connaître je ne riais jamais. J'étais comme ça..." and she makes faces that are frozen on the screen for a few seconds each time. It is of course directly inspired by the sequence of ABdS in which Jean-Paul Belmondo is looking at his face in the mirror and takes various exaggerated expressions...

Also, the supposedly "tragically beautiful" ending, is just stupid, pointless, and nihilist in comparison to ABdS's ending. At least, when Godard goes into tragic, he does it with the pinch of ironic ambiguity necessary to make it more than the banal expression of an existential mal-être: Lying on the street mortally wounded by the police, Michel Poiccard (Jean-Paul Belmondo) mumbles something like "chvraiment dégueulasse" ('mreally disgusting), and dies. But Patricia the American did not get it, and a man interprets (freely) what Michel said: "Il a dit: vous êtes vraiment une dégueulasse!" She looks inside the camera and says: "Qu'est-ce que c'est, dégueulasse?" FIN.
Alive, Michel and Patricia couldn't understand each other ("Je te parlais de moi, et toi tu me parlais de toi; alors que j'aurais dû parler de toi, et toi de moi..."), and death comes not as a resolution to this tension (like some kind of electric earthing), but on the contrary it comes to exacerbate the misunderstanding: his mea culpa degenerating into an accusation, and the very meaning of the words vanishing into interrogation dots... FIN.

In my sense, Truffaut takes himself way too seriously. He seems to believe that there is something edifying in the portrayal of a pathetic surrender to fatality. Godard knows that just the contrary is true: "La morrt ne peut jamais zêtrre une solution!" (Fritz Lang in Le Mépris (1963)). The passionate suicide at the end of Pierrot le Fou transcends the personal misery of Ferdinand by resorting to ancestral quasi-tribal (shamanic!) rituals: he paints his face in blue, and wraps it with a first layer of yellow dynamites and then a second of red dynamites. He climbs to the highest mountain, lights the wick, but suddenly realizes: "Après tout, chuis con! Merde, merde..." Too late: Boum! By going through the immemorial ceremonials that symbolize the travel to the other world, this individual comes to a more global perception of his life, and understand how it can still be preserved in this wider context. (Or is it just me being silly?)

[Here you might think: But hey, you were fustigating Truffaut for reproducing old values, and now you make the apology of Godard for going back to ancestral paganism?! And you would be right; in some sense. But I'd say that although I find it pretty sad to bluntly copy what the previous generation was used to do, recreating the magical actions that must have been going on inside prehistoric tribes where the collective unconscious has its roots is damn fine with me!]

I have also been rather disappointed by Chabrol, which I nevertheless learned to love through movies like Le Boucher (1970), another one in which Isabelle Huppert savagely murders an entire bourgeois family (La Cérémonie (1995)), and also some of his latest movies like Merci pour le Chocolat (2000) (even though I left the first time I saw it at an open-air cinema. I remember being deeply moved when, after the final rape/murder scene, the old auntie who killed both her parents with impunity in her youth says to her niece: "Le temps n'existe pas ma chérie. C'est un présent perpétuel"...).
La Rupture is kind of interesting, but again there is a very simplistic portrayal of the society, with the bad rich guys that want to crush the weaker ones, the nymphomaniac, the old ladies, etc. The only fascinating scene is the LSD deus ex machina at the end (but it comes a bit too late to be visionary, 1968 is already behind...). Les Noces Rouges is quite nicer, and almost brings Chabrol's redemption, as it could be seen as a satire of the fake adventurousness of bourgeois lovers, which can bring themselves to kill the weak wife and the strong (decidedly too modern) husband, but not to conceive that they could have just left their beloved little town altogether instead... The last image is a close-up of their handkerchiefs as we hear the voice of the commissioner who just arrested them ask them: "But I don't understand: Why didn't you simply leave?" - "Leave?? ... No, we never thought about leaving." All they could think about was to change this or that disturbing detail in their usual picture, but to start afresh with an entirely new canvas was just inconceivable...

Unbelievable Franz Liszt

2008-08-11T23:11:00.000+01:00

So I went to one of the conferences-concerts given by the pianist Jack Gibbons the other day, and that one was about Franz Liszt (1811-1886). He started by saying that if someone was ever to make a movie about Liszt's life, and keep to the facts with the highest strictness, then he would indefectibly be accused of exaggeration. Nice image - though not so original of course (unlike the 1841 daguerreotype above).

But first a word on the pianist-lecturer. Born in 1962, Gibbons apparently started to play piano at 10 but already at the age of 15 he was giving his first professional performance. And in fact it was in that very same Holywell Music Room ("the first purpose-built concert hall in the world" (1748)), with that very same Sonata in B minor by Liszt, on which he ended that night! It was very touching to see this (I wouldn't say old, let's say mature) pianist come back to the exact same circumstances in which everything began for him (even more so by taking into account that in 2001 he almost died in a car accident). He recorded many CDs and is a world-authority on Gershwin.

So that night he played about ten pieces by Liszt and told stories about his life between them. Here is what I recall:

Liszt, just like Mozart before him, was a child prodigy, and him tour the entire world with his father, amassing a huge fortune that was to ensure his wealth until the end of his life. He had such a magnetic personality that people treated him as a rock star, collecting his cigar stubs and glasses he'd drunk in. Beethoven himself was so impressed by his playing that he came on stage to kiss him - although by the time he was already profoundly deaf... Liszt was the first pianist to give concerts alone, without any other musicians, and the word piano "recitals" was coined after his kind of performances. His concerts were actually quite free, as he often stopped his playing to start chatting with members of the audience for a while. He also had a number of tricks that he loved to play on the audience: for instance he would engage in an impossibly fast Tarantella, which, at the precise instant where he couldn't possibly finish what he had started, he would suddenly interrupt to rescue a lady in the first row (his accomplice) that had fainted (the day the lady forgot to faint at his signal, he had no other option than to faint himself...).

During his youth (and after) he was perpetually falling in love with ladies and religions, that he feverishly worshiped one after the other. He was both deeply romantic and religious.
He was to find his soul mate at 36 in the person of the immensely rich Princess Carolyne von Sayn-Wittgenstein (any connection to Ludwig?). She persuaded him to dedicate himself to composition, and he entered the second phase of his life, much darker and tempered by doubts. In spite of all their efforts, Rome would not allow Carolyne's divorce, which would eventually lead her into madness: she locked herself into a cell, smoked obsessively, and produced a 24-volumes critics of the catholic church...

Liszt's compositions did not receive a warm welcome; he was eclipsed by the genius of his son-in-law Richard Wagner. He considered it a duty to teach everything he learned about piano, and never charged any of his numerous students. He was so generous that he gave money to his friends until he consumed his entire fortune. He died ruined, alone and insecure.

Among the most admirable pieces played by Gibbons that night were Funérailles, written a few days after Chopin's death in 1849, which begins by an astonishing repetitive sound of funeral bell; Nuages Gris, a premonition of Debussy's impressionism; and of course the most famous Sonata in B minor, basically constructed around four small musical ideas.
Liszt is also well-known for having transposed a lot of other composers pieces, and for his first bis Gibbons chose a transcription of Schumann (the second bis was his own composition, apparently to make sure that it would be the last...).

I was hoping that he would also play the transcription of Bach's Prelude BWV 543, that Yvonne Lefèbure played so gorgeously well, but that didn't happen. Maybe at Gibbons' next conference-concert on Bach this Wednesday!

Le Père Goriot

2008-08-03T20:56:00.001+01:00

Le Père Goriot, publié en 1835, est souvent considéré comme la première concrétisation des intentions de Balzac de composer sa Comédie Humaine (appelée d'abord plus crument Etudes Sociales), un ensemble de récits décrivant la société de son temps à travers une panoplie de personnages récurrents.
L'origine de l'intrigue trouve sa source dans une brève note télégraphique dans son album:

"Un brave homme - pension bourgeoise - 600 F de rentes - s'étant dépouillé pour ses fille qui, toutes deux, ont 50 000 F de rentes - mourant comme un chien."

A ce stade, il était encore loin du chef d'oeuvre achevé, mais bref l'essence est là. (Je trouve très émouvant de voir l'idée littéraire de Père Goriot dans un état de telle concision, comme d'admirer la petitesse de la graine qui a donné naissance à un immense arbre...)

Les dernières pages du livre, qui décrivent la lente mort du Père Goriot et les désistements de ses filles, m'ont profondément touché; la dernière phrase m'a cependant laissé songeur.

"(...) Le jour tombait, un humide crépuscule agaçait les nerfs, il regarda la tombe et y ensevelit sa dernière larme de jeune homme, cette larme arrachée par les saintes émotions d'un coeur pur, une de ces larmes qui, de la terre où elles tombent, rejaillissent jusque dans les cieux. Il se croisa les bras, contempla les nuages, et, le voyant ainsi, Christophe le quitta.

Rastignac, resté seul, fit quelques pas vers le haut du cimetière et vit Paris tortueusement couché le long des deux rives de la Seine où commençaient à briller les lumières. Ses yeux s'attachèrent presque avidement entre la colonne de la place Vendôme et le dôme des Invalides, là où vivait ce beau monde dans lequel il avait voulu pénétrer. Il lança sur cette ruche bourdonnante un regard qui semblait par avance en pomper le miel, et dit ces mots grandioses: "A nous deux maintenant!"

Et pour premier acte du défi qu'il portait à la Société, Rastignac alla dîner chez madame de Nucingen. "

J'ai d'abord été déstabilisé par cette pirouette finale, de laquelle je ne parvenais à tirer aucun sens: comment Eugène irait-il tranquillement dîner chez une des filles de Goriot (de laquelle il était amoureux) après une pareille tragédie? Soit il lui en veut terriblement de ne pas s'être montrée à l'enterrement et il y va pour lui faire des reproches, soit il s'avère qu'elle était dans l'impossibilité absolue de s'y rendre et il y va pour partager sa tristesse déchirante. Mais en aucune façon ne paraît-il pouvoir s'agir d'un "dîner" ce soir-là!

J'ai lu dans la préface notamment que cette dernière phrase témoigne de l'arrivisme d'Eugène. Ses sentiments provoqués par la mort de Goriot seraient bien vite évacués en faveur de sa volonté de pouvoir social. Je rejette cette interprétation, je crois ses émotions sincères, et l'emploi du plus que parfait ("avait voulu") indique bien que ses ambitions sociales ne le tourmentent plus.

Ce à quoi j'aboutis est qu'Eugène entreprend désormais de détruire la "Société" de l'intérieur, faisant siens les principes du forçat Vautrin. Il se lance dans une guerre vengeresse contre elle non pas de but en blanc, ce qui serait désespéré, mais en s'y infiltrant comme un virus pour la pourrir.

Cette méthode me paraît d'une efficacité douteuse... Je découvre un Balzac bien plus radical et belliqueux que je ne l'avais imaginé. Une telle hargne destructrice me fait venir à l'esprit (sans nuances) quelques autres défricheurs sans merci comme le Marquis de Sade, Stirner, Schopenhauer, et consorts. J'estime ces auteurs, j'apprécie la nécessité de leur oeuvres dévastatrices, mais enfin après tout, je ne peux pas en rester là. Je me pose la question: Une fois la mauvaise herbe ratiboisée, que comptez-vous planter Messieurs? Quelles nouvelles valeurs inventez-vous pour remplacer les déchéances?

Ce n'est pas que je veuille sous-entendre "Vous n'avez rien de mieux à proposer, donc ne touchez à rien!", ce n'est pas ça. Au contraire, comme je l'ai dit, j'applaudis tous les dégâts qu'ils ont pu faire. Seulement, s'arrêter là, au creux de la phase destructrice, et ne pas envisager comment recréer du relief à nouveau, ça me paraît un peu court.
A première vue.

A mieux y regarder, je me demande si je ne suis pas un peu trop positiviste sur ce coup-là. N'est-ce pas naïf d'imaginer qu'on puisse, comme ça, débarquer avec des nouvelles valeurs fraîchement moulues, et en faire offrande à la communauté pour la plus grande félicité? Ca ressemble suspicieusement à un des buts les plus niais des doctrines religieuses...

Question: Balzac ne propose-t-il vraiment rien comme alternative à l'hypocrisie de la haute société parisienne?

Autre question: A supposer que c'était le cas, en se contentant de peindre ce qu'elle a d'inacceptable, n'induirait-il pas tout de même chez le lecteur la volonté de se détacher de ses façons odieuses, et donc d'en embrasser de nouvelles?

A la première question je répondrais qu'il est possible que Balzac veuille promouvoir des attitudes courageuses et solidaires, comme celles d'Eugène et de l'étudiant en médecine Bianchon au chevet de Goriot agonisant (ou celle de Mme de Beauséant). Sans doute oppose-t-il la sincérité à la superficialité vénale, mais tout le monde est d'accord là-dessus, non, si?

La seconde question me plaît bien. J'aime l'idée qu'il suffise de décrire quelque chose, de la mettre sous les feux de la conscience, pour fournir à la fois le pouvoir de la faire changer. Je reviendrai sans doute sur cette idée et ses nombreux avatars.

Je termine cette note confuse sur une réplique de Rastignac qui m'a particulièrement surpris:

"(...) Les deux étudiants, frappés de ce terrible éclat d'une force de sentiment qui survivait à la pensée, laissèrent tomber chacun des larmes chaudes sur le moribond qui jeta un cri de plaisir aigu.
- Nasie ! Fifine ! dit-il.
- Il vit encore, dit Bianchon.
- A quoi ça lui sert-il ? dit Sylvie.
- A souffrir, répondit Rastignac."

Souffrance et joie ne s'opposent pas, et enrichissent. Mais ça, les servantes qui aspirent au bonheur monolithique ne peuvent pas le concevoir.

Shakespeare's As You Like It

2008-07-22T21:11:00.002+01:00

I went to see a play by Shakespeare the other day, entitled As You Like It. 'twas in the beautiful garden of Trinity College! Taking into account that Shakespeare's language could be quite awkward, especially for a non-native speaker, and that I was sitting completely on the side behind a big guy with a broken neck that was hiding most of the scenes to me (I ended up quite liking him nevertheless, as he and his wife were among the most strongly laughing people in the audience), it isn't hard to imagine that some small subtleties (say 60 per cent of the play) escaped my understanding.

From what I gathered, the play is about the son of a banished duke, Orlando, who gains the love of her cousin (?) Rosalind by beating up in a formal fight the wrestler hired by his brother to kill him. He falls in love too, but unfortunately is forced to flee. Her love is also banished, and decides to take the disguise of a man (for some reason, which the guy in front of me must have understood thoroughly). They meet again in the forest, but she stays under cover (did he break his neck in a car accident?). So naturally the rest of the play for Rosalind consists of testing the loyalty of his love to her and finding the way to reveal her true identity to him---and to the foolish girl who fell in love with her. The play ends in a happy quadruple wedding, celebrated in an uninhibited orgiastic dance. Not the deepest of Shakespeare's plays, nor the most brilliant actors either, but rather fun in any case.

What really interested me was the short epilogue written for the actor playing Rosalind (I emphasize):

It is not the fashion to see the lady the epilogue;
but it is no more unhandsome than to see the lord
the prologue. If it be true that good wine needs
no bush, 'tis true that a good play needs no
epilogue; yet to good wine they do use good bushes,
and good plays prove the better by the help of good
epilogues. What a case am I in then, that am
neither a good epilogue nor cannot insinuate with
you in the behalf of a good play! I am not
furnished like a beggar, therefore to beg will not
become me: my way is to conjure you; and I'll begin
with the women. I charge you, O women, for the love
you bear to men, to like as much of this play as
please you: and I charge you, O men, for the love
you bear to women--as I perceive by your simpering,
none of you hates them--that between you and the
women the play may please. If I were a woman I
would kiss as many of you as had beards that pleased
me, complexions that liked me and breaths that I
defied not: and, I am sure, as many as have good
beards or good faces or sweet breaths will, for my
kind offer, when I make curtsy, bid me farewell.

Exeunt

So we have sweet Rosalind, who spent more than half of the play pretending to be a man which we spectators knew was really a woman, speaking to us not as a character, but as the comedian playing her---a man in Shakespeare's time! (although it was a proper girl that day in the gardens.) Funny Will is just messing up with our gender preconceptions here:

During the play did you, if you're a man, fall in love with the beautiful Rosalind, or did you, if you're a woman, fall in love with the spiritual man she's been faking?

In either case what do you say now that Rosalind shows you what's really under her dress?

This kind of Brechtian distanciation effect was quite visionary.
(The last I saw was in Cassavetes' Opening Night (1977), specially at the moment where the perturbed actress asks for a light from the stage to the backstage to light her cigarette.)

A. Diverses manières d'interroger en direction de la chose

2008-05-11T14:48:00.001+01:00

J'ai commencé l'étude du texte Qu'est-ce qu'une chose ? de Heidegger (Die Frage nach dem Ding). C'est un texte basé sur un cours donné à l'Université de Fribourg-en-Brisgau en 1935-36. Si j'ai bien compris la biographie d'Heidegger par la BBC, à cette période il avait été placé à la direction de l'Université par le régime nazi et en avait profité, non pas à faciliter les recherches de son ancien mentor Edmund Husserl, mais à interdire l'accès à "ce juif" - donc pas forcément la période où il a brillé par son humanité. {Je note en passant qu'on pourrait légitimement douter de la santé profonde de la doctrine d'un homme qui a cru avec une ferveur intense au renouveau hitlérien. Mais pour l'instant, à l'instar de Hanna Arendt, je prends le parti de lui pardonner, quitte à réexaminer ma position au terme de mon étude. [J'ai souvent soutenu l'opinion, d'ailleurs, qu'un artiste ne doit pas être jugé pour sa position (ou absence de position) politique, par exemple Leni Riefenstahl.]}. Gageons (sans grand risque) que ce cours est basé sur son chef-d'oeuvre antérieur Sein und Zeit, écrit en 1926, à une époque où ses propres amis ne le considéraient pas encore comme verrückt.

J'attaque donc aujourd'hui par l'étude de l'introduction de Qu'est-ce qu'une chose ?, intitulée "A. Diverses manières d'interroger en direction de la chose" (je lis la traduction française de la jolie collection Tel Gallimard, 1971).

I. INTERROGATION PHILOSOPHIQUE ET INTERROGATION SCIENTIFIQUE

Heidegger commence la partie introductrice A. Diverses manières d'interroger en direction de la chose par une comparaison entre l'interrogation scientifique et l'interrogation philosophique. Selon lui, "en philosphie, à la différence des sciences, un accès immédiat aux questions n'est jamais possible. En philosophie, il est toujours et nécessairement besoin d'une introduction". J'annonce dès ici qu'en tant que (méta-) théoricien des cordes du XXIème siècle, mon acceptation des termes "science" et "philosophie" diffère passablement de celle de Heidegger, qui devait sans doute tendre à considérer comme sciences avant tout les sciences disons classiques (en opposition à la relativité générale, la mécanique quantique, etc). En particulier, je classe les théories scientifiques de gravité quantique parmi la "philosophie", tant à cause de l'inaccessibilité expérimentale de leurs observables qu'à cause des difficultés inhérentes d'identification de ces mêmes observables --- que décrire une fois que les concepts d'espace et de temps ont perdu leur pertinence?

Heidegger donne une définition de la philosophie amusante (le texte contient de nombreuses plaisanteries, qui rappellent son origine orale):

"La philosophie est cette pensée avec laquelle on ne peut essentiellement rien entreprendre et à propos de laquelle les servantes ne peuvent s'empêcher de rire."

(De nouveau, c'est dur de ne pas penser "String Theory!")
Il fait même mine qu'on y perdrait rien à négliger complètement la métaphysique:

"Lorsqu'on fait la sourde oreille à la question de la chose, lorsqu'on interprète un poème de manière insatisfaisante, tout se passe comme s'il ne se produisait rien."

(J'aime beaucoup cette comparaison entre la philosophie et la poésie; pour moi la vraie philosophie (et la vraie science) est poétique...)
Mais il enchaîne par une petite menace, d'autant plus inquiétante que furtive (et que, si Heidegger n'était pas Heidegger, on pourrait interpréter comme une mise en garde contre la montée du fascisme, du nationalisme, de l'extrémisme):

"Un beau jour toutefois [beau?], après cinquante ou cent ans peut-être [moins que ça!], il arrive quelque chose."

"Quelque chose": ça me glace la sang! Ce quelque chose si désinvolte c'est l'obscurité, c'est le néant, le retour de la bête, le règne de l'horreur.
"Quelque chose": voilà à quoi ça mène de mal lire un poème. Prenez garde, malheureux écoliers, le sort du monde dépend de votre inspiration poétique!

J'éprouve une grande sympathie pour cette idée qu'un défaut de poésie puisse ruiner la réalité.

Heidegger, Qu'est-ce qu'une chose ?

2008-05-11T14:23:00.000+01:00

Il y a quelques temps, un article est paru sur arXiv dont l'abstract contenait quelque chose que je n'aurais jamais imaginé possible dans ce contexte : une citation d'un philosophe, et qui plus est, de Martin Heidegger! Il s'agit de l'article d'Andreas Döring et Chris Isham `What is a Thing?': Topos Theory in the Foundations of Physics, dont le but avoué n'est rien de moins que de mettre sur pied "a fundamentally new way of constructing theories of physics." Comme j'ai pris au premier trimestre un cours sur Heidegger par Stephen Mulhall, et que la théorie des catégories fait partie des matières que je convoite (qu'elle transforme la façon de concevoir la physique théorique, ou qu'elle serve d'autres fonctions, peut-être plus modestes, comme la description des D-branes...), j'ai décidé de me lancer dans l'étude attentive premièrement de Heidegger, et en particulier du livre Qu'est-ce qu'une chose ? recommandé par ces gentlemen pour sa compréhensibilité, deuxièmement des catégories, et finalement de leur article même.

C'est plutôt optimiste: ma recherche pourrait me contraindre à revoir mes ambitions à la baisse...
Pour l'instant, je trouve facilement le temps de lire quelques sections de Heidegger en fin de soirée.