Early thoughts

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

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"?

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

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

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

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!

Merleau-Ponty: L'Œil et l'Esprit

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."

Alien mathematics

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...)

Time thickening

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 ; )

Timbuktu

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.)