Sunday, February 10, 2019

the only three types of ingenuity when the parameter is infinity: the limited, the false & the genuine




Bernhard Bolzano, picture taken from the Internet;
Duchamp in Maya Deren's Witch's Cradle (1943);
The Great Abyss Inframince (A/Z 2018, for more see here);

"E pois, te digo, as estrelas,
no céu imenso espalhadas,
são a metade e outro tanto
das mesmas por Deus criadas;
e, se imaginas que minto
na quantidade que dei,
te desafio a contá-las...
para ver que não errei!"
Cancioneiro Guasca

"... la majorité est travaillé par une minorité proliférante et non dénombrable qui risque de détruire la majorité dans son concept même, c'est-à-dire en tant qu'axiome... le étrange concept de non-blanc ne constitue pas un ensemble dénombrable... Le propre de la minorité, c'est de faire valoir la puissance du non-dénombrable, même quand elle est composée d'un seul membre. C'est la formule des multiplicités. Femme, nous avons tous à le devenir, que nous soyons masculins ou féminins. Non-blanc, nous avons tous à le devenir, que nous soyons blancs, jaunes ou noirs."
Deleuze & Guattari (Mille plateaux)
"Ce qui caractérise le chaos, en effet, c'est moins l'absence de déterminations que la vitesse infinie à laquelle elles s'ébauchent et s'évanouissent: ce n'est pas un mouvement de l'une à l'autre, mais au contraire l'impossibilité d'un rapport entre deux déterminations, puisque l'une n'apparaît pas sans que l'autre ait déjà disparu, et que l'une apparaît comme évanouissante quand l' autre disparaît comme ébauche."
Deleuze  & Guattari (Qu'est-ce que la philosophie)
"Et je reçus de lui de merveilleuses explications et des éclaircissements extrêmement précis sur la façon dont le Peyotl ressuscite dans le trajet entier du moi nerveux, la mémoire de telles vérités souveraines, par lesquelles la conscience humaine, me fut-il dit, ne perd plus, mais au contraire, retrouve la perception de l'Infini."
"Et d'après des vieux Chinois le foie est le filtre de l'inconscient mais la rate est le répondant physique de l'infini."
A. Artaud (Le Rite du Peyotl chez les Tarahumaras)
"This relative freedom of a hero does not violate the strict specificity of the construction, just as the specificity of a mathematical formula is not violated by the presence of irrational or transfinite quantities."
Mikhail Bakhtin (Problems of Dostoevsky's Poetics, Caryl Emerson translation)

"... the world burst into a brilliant but complex series of geometric patterns so elaborate that no mere mortal could even BEGIN to comprehend their true significance. Only  God and I understood..."
James St. James
"The vistas echoed endlessly, paralleling the way that drum hits, guitar chords, and horn licks were turned into reverb trails by dub producers like King Tubby..."
Simon Reynolds
"Note the parallels between ordinary awareness, classical physics, and the natural and counting integers..."
Dean Radin (Real Magic)
"... interrompidas não porque terminassem, mas porque ninguém podia levá-las a um fim."
Clarice Lispector
"So Art is limited to infinite, and beginning there cannot progress."
Whistler

"Of course, not everyone in postpunk attended art school, or even college. Self-educated in a scattered, omnivorous fashion, figures like John Lydon or Mark E. Smith of the Fall fit the syndrome of the anti-intellectual intellectual, ravenously well read but scornful of academia and suspicious of art in its institutionalized forms."
Simon Reynolds
"I had been occluded from space-time like an eel's ass occludes when he stops eating on the way to Sargasso... Locked out... Never again would I have a Key, a Point of Intersection... The Heat was off me from here on out... relegated with Hauser and O'Brien to a landlocked junk past where heroin is always twenty-eight dollars an ounce and you can score for yen pox in the Chink laundry of Sioux Falls... Your plan was unworkable then and useless now... Like da Vinci's flying machine plans..."
William S. Burroughs

"Denken wir uns nun einen äußersten Fall: daß ein Buch von lauter Erlebnissen redet, die gänzlich außerhalb der Möglichkeit einer häufigen oder auch nur seltneren Erfahrung liegen, — daß es die erste Sprache für eine neue Reihe von Erfahrungen ist. In diesem Falle wird einfach Nichts gehört, mit der akustischen Täuschung, daß, wo Nichts gehört wird, auch Nichts da ist... Dies ist zuletzt meine durchschnittliche Erfahrung und, wenn man will, die Originalität meiner Erfahrung."
"Ich komme aus Höhen, die kein Vogel je erflog, ich kenne Abgründe, in die noch kein Fuß sich verirrt hat..."
"Man büßt es teuer, unsterblich zu sein..."
Nietzsche

"Car toutes ces femmes étaient des actrices du monde, et il est vrai que même considérée à ce point de vue, la comtesse Molé n'était pas égale à l'extraordinaire réputation d'intelligence qu'on lui faisait, et qui donnait à penser à ces acteurs ou à ces romanciers médiocres qui à certaines époques ont une situation de génie, soit à cause de la médiocrité de leurs confrères, parmi lesquels aucun artiste supérieur n'est capable de montrer ce qu'est le vrai talent, ou de la médiocrité du public, qui, existât-il une individualité extraordinaire, serait incapable de la comprendre."
Marcel Proust (le narrateur, La Prisonnière)

"... one of the two professors assigned to assess his thesis, doubtless bewildered by the extent of its expertise and scholarship, declared it incomprehensible and threatened not to approve it."
Malcolm Hayes (Anton von Webern)
"N'ayant jamais consenti à vivre dans notre univers salarié, le célèbre linguiste n'avait pas cotisé à la M.G.E.N. Résultat: impossible de le faire soigner dans une clinique sérieuse. N'était-ce pas inadmissible?"
Olga (Les Samouraïs)
"On n'élimine pas, on neutralize en marginalisant..."
Edward (Les Samouraïs)
"Au-delà de l'erreur, au-delà de la bêtise elle-même: une certaine bassesse de l'âme..."
Deleuze/Nietzsche
"Dans le pain et le vin destinés à sa bouche
Ils mêlent de la cendre avec d'impurs crachats..."
Charles Baudelaire
"One will know well if ignorance is removed. Those who know well always desire to act."
Myoe (Mark Unno, Shingon Refractions)
********************************************************************

In his The Mystery of the Aleph, Amir D. Aczel writes: "Infinity is an intimidating concept—one where our everyday intuition no longer servers to guide us."
We start by finding our three types by identifying two more general types: the ones who stick to everyday intuition, the ones who dare to face infinity's paradoxes. 
I argue that, in any case, the paradoxes related to infinity are real
Then to stick to everyday intuition is limited or false ingenuity. To face infinity, genuine ingenuity.
The most clear and distinct example of limited ingenuity is to be found in Descartes. He preferred to stick to everyday intuition, but acknowledged that infinity is (and has to be) real.
False ingenuity, which should rather be called bêtise or deliberate ingenuousness is the case of a person who not only sticks to everyday intuition but denies that the paradoxes of infinity can be real and really hates them. There are so many examples of this lamentable case (trifling in nature, tedious in telling), we fortunately won't need even to give any names (I'm positive). It might just as well be the rule. And since alle Schweiger sind dyspeptisch, choose your own favourite member of whatever academic Kroneckian priesthood you happen to be acquainted with, reverenced scientists (several might do the job), inveterate analytic philosophers, hard-nosed economists, bureaucrats &/or famous CEOs. Choose and say it out & aloud.
Very ordinary people don't count because they are all geniuses in a very Warholian peculiar way: by never raising such questions on their own. Thanks gosh, they definitely don't belong to any of our three categories.

Examples of genuine ingenuity are the following (under construction now made public list) [it was hard to agree on a truly certified census beyond all possibility of doubt, so we left a few ghostly holes in the form of question (& others totally hidden) marks]:
- Nicolas of Cusa;
- Giordano Bruno;
- Galileo Galilei (?);
- G. W. Leibniz (?);
- Salomon Maimon;
- Bernhard Bolzano;
- Bernhard Riemann (?);
- Kingdon Clifford (?);
- Karl Weierstrass;
- Nietzsche (?);
- Sonja Kowalewski (?);
- Gösta Mittag-Leffler (?);
- Richard Dedekind;
- Georg Cantor;
- Baudelaire! ("Tout cerveau bien conformé porte en lui deux infinis, le ciel et l'enfer...");
- Raymond Roussel (?);
- Henri Bergson (?);
- Der Herr Warum
- Melanie Klein (?);
- Claude Lévi-Strauss (?);
- Jacques Lacan (?);
- Georges Bataille (?);
- Maurice Blanchot (?);
- Pierre Klossowski (?);
- Gilles Deleuze;
- Jacques Derrida ["... l'axiome fondamental de tout ce qu'il dit partout, c'est la divisibilité du point. Tout ce qu'il écrit, tout ce qu'il pense est une protestation contre le point comme indivisible..." Hélène Cixous];
- Julia Kristeva (?);
- Sylvia Leclercq ["Jamais comblée, une différence demeure (cf. Hekhalot, Demeures Célestes, Moradas) toujours entre l'Être et l'ensemble ouvert des 'sujets', des 'singularités', des 'nombres' susceptibles de l'exprimer, et dans lesquels je me dissémine en écrivant et en agissant. J'appartiens à une géométrie qui n'est plus algébrique, mais analytique. Je suis un site du signifiant illimité..."];
- me;

Amir Aczel provides us also with a parable about the fate of genuine ingenuity by giving an account of a set of pitiful misadventures and cross accidents sustained by Bernhard Bolzano throughout his life:
"In 1805, Bolzano was ordained a priest and nominated to the chair of the department of the philosophy of religion at the University of Prague. Bolzano had wanted the position for several years but had been passed over for promotion by lesser-qualified but better-connected individuals... A mere decade and a half after his installment as chair, Bolzano was summarily fired and stripped of his priestly rank... One B. Frint had written a textbook which he had hoped would be used by Bolzano in his courses. But Bolzano, in his new position, resisted the pressure and did not adopt the book. Frint successfully turned people against the new chair of the philosophy of religion department. The slow but systematic case against Bolzano was built in a series of state papers documenting what officials considered objectionable elements in Bolzano's sermons. The most offensive infraction was Bolzano's preaching peace to the students... When the first attacks on him occurred, Bolzano had the support of the Archbishop of Prague, and this helped him evade any serious consequences" The Mystery of the Aleph (WSP, 2000).
To this it may be interesting to juxtapose the following passage from Nietzsche: "Il y a des vies où les difficultés touchent au prodige; ce sont les vied des penseurs. Et il faut prêter l'oreille à ce qui nous est raconté à leur sujet, car on y découvre des possibilités de vie, dont le seul récit nous donne de la joie et de la force, et verse une lumière sur la vie de leurs successeurs. Il y a là autant d'invention, de réflexion, de hardiesse, de désespoir et d'espérance que dans les voyages des grands navigateurs; et, à vrai dire, ce sont aussi des voyages d'exploration dans les domaines les plus reculés et les plus périlleux de la vie..." (as quoted by Deleuze in Nietzsche et la philosophie).
Also, from Ecce Homo: "Wenn trotzdem an mir manche kleine und große Missethat verübt worden ist, so war nicht der 'Wille', am wenigsten der böse Wille Grund davon: eher schon hätte ich mich —ich deutete es eben an — über den guten Willen zu beklagen, der keinen kleinen Unfug in meinem Leben angerichtet hat."

Poincaré & Wittgenstein:


On Wittgenstein and finitism &/or on the difference between the infinite and the huge (see also here): "Wittgenstein’s famous matching of finitism and behaviourism, united by their denial of the existence of something (infinite sets and inner states, respectively), in the correct but badly executed attempt to avoid confusion (that between the infinite and a very large quantity, and that between an inner state and a private entity), shows, on this point, the agreement and, at the same time, the distance between the Austrian philosopher’s position and finitism. The denial of the existence of infinite sets is a mistaken way to draw a grammatical distinction which, though it may be opportune, should be done differently: by showing that the grammar of the word “infinite” cannot in the slightest be clarified by taking into account only the picture of something huge, a picture which usually accompanies the use of the word. As Wittgenstien affirms in one of his lectures in 1939: “If one were to justify a finitist position in mathematics, one should say just that in mathematics ‘infinite’ does not mean anything huge. To say ‘There’s nothing infinite’ is in a sense nonsensical and ridiculous. But it does make sense to say we are not talking of anything huge here”... Wittgenstein moves some criticisms against the platonistic interpretation of the true import of Cantor’s proof; nevertheless they do not originate in any way from a presupposed identification of legitimate mathematics with finitist mathematics and, even less so, from the violation, by Cantor’s proof, of the requirements imposed by strict finitism. Once the appropriate clarifications have been made about what, in his opinion, it really demonstrates, Cantor’s proof is more than good enough for Wittgenstein, in spite of the certainly non-finite nature of the “objects” it deals with... proofs which are finitistically (not only strict finitistically) unacceptable are actually accepted by Wittgenstein or are not questioned on the basis of the restriction of admissible mathematical procedures to the finitary ones," Pasquale Frascolla, Wittgenstein's Philosophy of Mathematics (Routledge 1994).

***Russel & Quine with irony: "[they] were born to be nominalists even if the hard knocks of mathematical and philosophical experience shattered childhood complacency. (Russell actually began as an idealist in the Hegelian manner of late Victorian England, but that was his infancy, not his childhood)," Ian Hacking, Why is there Philosophy of Mathematics at all (Cambridge 2014).

See also:
And also:

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