Monday, February 11, 2019

the odd transformation of Der Herr Warum (run over with this turn & application)














L'Année Dernière à Marienbad (Alain Resnais/Grillet 1961);
Duchamp in Maya Deren's Witch's Cradle (1943);
The Dimension of Dali (Joan Úbeda & Susi Marquès, 2004); 
John Cage performing Water Walk on TV (1960);
Les théorèmes d'incompletude de Gödel (Lê Nguyên Hoang/ Science4All 2016);
Imaginary Numbers Are Real: Riemann Surfaces (Welch Labs/Youtube); 
Secret Kinks of Elementary Functions (Imaginary Angle/Youtube 2024); 
Intro to the Fundamental Group: Algebraic Topology (Trefor Bazett & Tom Crawford/ Youtube); 
The Subtle Reason Taylor Series Work (Morphocular/Youtube 2024); 
Nancarrow's Study for Player Piano n. 41a (Youtube); 
Understanding Exponentiation and Multiplication with Negative Numbers (A/Z 2022);
The Great Abyss Inframince (A/Z 2018, for more see here);

vestibule (with commentary, scholium, illustration & key to the adventitious parts):


"De ce terrible paysage,
Tel que jamais mortel n'en vit,
Ce matin encore l'image,
Vague et lointane me ravit..."
Baudelaire
"... o Diabo na rua no meio do redemoinho. É com ele que Riobaldo tem o encontro-desafio, na encruzilhada, à noite, o encontro com o Nada, com o Não Ser, ou seja, em termos mallarmaicos, o desafio ao Acaso..."
Augusto de Campos
"[Sounds that are not noted] appear in the written music as silences, opening the doors of the music to the sounds that happen to be in the environment... The glass houses of Mies van der Rohe... There is no such thing as an empty space or an empty time."
John Cage (Experimental Music)

"Only by bending can you be whole; 
Only by twisting can you be straight.
Only by hollowing out can you be full; 
Only by being used up can you be new."
Daodejing/22 (Edmund Ryden's translation)

"Il n'a pas de nombre, entier ni fractionnaire, pour compter les choses qui en présentent les propriétés, mais un chiffre qui en condense, en accumule les composantes parcourues et survolées. Le concept est une forme ou une force, jamais une fonction en aucun sens possible."
Deleuze & Guattari (Qu'est-ce que la philosophie)
"Le concept d'archi-trace doit faire droit et à cette nécessité et à cette rature. Il est en effet contradictoire et irrecevable dans la logique de l'identité. La trace n'est pas seulement la disparition de l'origine, elle veut dire ici — dans le discours que nous tenons et selon le parcours que nous suivons — que l'origine n'a même pas disparu, qu'elle n'a jamais été constituée qu'en retour par une non-origine, la trace, qui devient ainsi l'origine de l'origine."
Jacques Derrida (Grammatologie) 
"Existem segundos — apenas uns cinco ou seis simultâneos — em que você sente de chofre a presença de uma harmonia eterna plenamente atingida. Isso não é da terra; não estou dizendo que seja do céu, mas que o homem não consegue suportá-lo em sua forma terrestre." 
Kiríllov (from Dostoevsky's Demons, as translated by Paulo Bezerra)
"But what if there is no dying 'in the true sense,' what if dying is always and by definition 'improper,' arriving at the wrong time and place? This point of impossibility is one feature of the Lacanian objet a: it designates that which is subtracted from reality (as impossible) and thus gives it consist­ency—if it gets included in reality, it causes a catastrophe."
Slavoj Zizek (Haunted by A/Z, Feyerabend with vengeance & the New Wave)

"... la nature nous présente une série infinie de lignes courbes, fuyantes, brisées,  suivant une loi de génération impeccable, où le parallélisme est toujours indécis et sinueux, où les concavités et les convexités se correspondent et se poursuivent..."
Baudelaire (Exposition universelle)   
"... the blindness of humanity to all the beauty and wonder of the Universe is due to this illusion of straightness. It is significant that Riemann, Bolyai and Lobatchewsky seem to have been the mathematical prophets of the New Revelation..."
Aleister Crowley, The Book of Thoth
"L'espace pour le peintre d'Asie, n'est ni extérieur, ni intérieur, il est jeu d'énergies — surgissement pur. Il est l'insituable... un camp magnétique où se rencontrent et s'enchevêtrent des forces —un lieu où s'ébattent sillages et trajectoires. Et renoncer au foyer unique... Ces considerations sur l'émancipation spatiale, et l'expression des forces élémentaires ne se limitaient pas à la peinture à l'encre ou à l'eau, elles s'étendaient à la pratique de l'huile, dans le sens de la fluidité et de l'emportement. Ainsi, le Turner de la dernière période y trouverait sa place."
André Masson (Une peiture de l'essentiel/Écrits, anthologie établie par Françoise Levaillant)
"And though we may string ever so many clauses into a single compound sentence, motion leaks everywhere, like electricity from an exposed wire."
Ezra Pound (Chinese Character as a Medium for Poetry)

"... when you work with people who misunderstand you, instead of getting transmissions you get transmutations, and that's much more interesting in the long run..."
Andy Warhol, The Philosophy of Andy Warhol
"... listening one takes as a springboard the first sound that comes along; the first something springs us into nothing and out of that nothing arises something; etc. like an alternating current..."
John Cage (45' for a Speaker)
"There's a lot of unfolding. Everything just slides away, like many curtains opening at once."
"The universe is decoding itself to you, and even though nothing makes sense, it all comes together."
James St. James
"... no fundo do poço sem fundo do inconsciente..."
Caio Fernando Abreu (carta a José Márcio Penido/Zézim) 
"... irei até onde o vácuo faz uma curva..."
Clarice Lispector
"... physics can only (correctly) assert that photomultiplier #n firing is perfectly correlated with my knowing that photomultiplier #n fired for either value of n. The question that physics does not answer is how it can be that I know that it is #1 and is not #2. This is indeed a problem. It is part of the problem of consciousness."

"C'est alors que la vraie division commence, de vingt-deux par sept par exemple, et que les cahiers s'emplissent des vrais chiffres enfin."
Molloy
"Vous dite en somme que l'ironie de Platon est romanesque, et que le roman est ironique, indécidable."
Bréhal (Les Samouraïs)
"L'indécidable n'est pas une coupure est un bondir rapide entre deux possibilités opposées mais qui se touchent. Son mouvement intérieur, c'est d'être toujours lá où on ne l'attend pas."
Hélène Cixous (Portrait de Jacques Derrida)
"Tout vrai sentiment est en réalité intraduisible. L'exprimer c'est le trahir. Mais le traduire c'est le dissimuler. L'expression vraie cache ce qu'elle manifeste."
A. Artaud (Théâtre oriental et théâtre occidental)
"Zur Aufgabe einer Umwerthung der Werthe waren vielleicht mehr Vermögen nöthig, als je in einem Einzelnen bei einander gewohnt haben, vor Allem auch Gegensätze von Vermögen, ohne daß diese sich stören, zerstören dürften."
Nietzsche
"Weber singulariza o seu tratamento da série radicalizando o princípio do espelho: ele procura configurações intervalares de doze sons que já sejam, elas mesmas, a condensação de um espaço simétrico, ao mesmo tempo que labiríntico e sem centro (uma série que já contenha, em avesso do avesso, os seus próprios espelhos)."
José Miguel Wisnik

"Causal thinking never yields accurate description of metabolic processes (limitations of existing language)."
"This ass talk had a sort of gut frequency. It hit you right down there like you gotta go."
"Fear seals the turd message with a cuneiform account."
William S. Burroughs
"Ce n'est pas moi qui choisis les turbulences. Nous y sommes. Et si tu essaies de ne pas y penser, elles vont t'emporter d'une façon que j'ignore"
Olga (Les Samouraïs)
"Man muß die Größe seines Magens kennen... Das Tempo des Stoffwechsels steht in einem genauen Verhältniß zur Beweglichkeit oder Lahmheit der Füße des Geistes; der 'Geist' selbst ist ja nur eine Art dieses Stoffwechsels."
Nietzsche
"Pero la exploración interior, Tito, es un dédalo con más vueltas que un intestino y el Minotauro agazapado en la esquina de cada meandro, y fija que está en el colon."
(El Bataraz, narrator)

"Or comme celui que je venais subitement de redevenir n'avait pas existé depuis ce soir lointain où ma grand-mère m'avait déshabillé à mon arrivée à Balbec, ce fut tout naturellement, non pas après la journée actuelle que ce moi ignorait, mais — comme s'il y avait dans le temps des séries différentes et parallèles — sans solution de continuité, tout de suite après le premier soir d'autrefois, que j'adhérai à la minute où ma grand-mère s'était penchée vers moi. Le moi que j'étais alors et qui avait disparu si longtemps, était de nouveau si près de moi qu'il me semblait encore entendre les paroles qui avaient immédiatement précédé et qui n'étaient pourtant plus qu'un songe,  comme un homme mal éveillé croit percevoir tout près de lui les bruits de son rêve qui s'enfuit. Je n'étais plus que cet être qui cherchait à se réfugier dans les bras de sa grand-mère, à effacer les traces de ses peines en lui donnant des baisers, cet être que j'aurais eu à me figurer, quand j'étais tel ou tel de ceux qui s'étaient succédé en moi depuis quelque temps, autant de difficulté que maintenant il m'eût fallu d'efforts, stériles d'ailleurs, pour ressentir les désirs et les joies de l'un de ceux que, pour un temps du moins, je n'était plus." 
Marcel Proust (le narrateur, Sodome et Gomorrhe)

"Un Coup de Dés fez de Mallarmé o inventor de um processo de composição poética cuja significação se nos afigura comparável ao valor da 'série', introduzida por Schöenberg, purificada por Webern e, através da filtração deste, legada aos jovens músicos eletrônicos, a presidir os universos sonoros de um Boulez ou um Stockhausen. A esse processo definiríamos, de início, com a palavra estrutura, tendo em vista uma entidade onde o todo é mais que a soma das partes ou algo qualitativamente diverso de cada componente. Eisenstein na fundação da sua teoria da montagem, Pierre Boulez e Michel Fano, com relação ao princípio serial, testemunharam — como artistas — o interesse da aplicação dos conceitos gestaltianos ao campo das artes. E é em estritos termos de Gestalt que entendemos o título de um dos livros de poesia de E. E. Cummings: Is 5. Para a poesia, e em especial para a poesia de estrutura de Mallarmé ou Cummings, dois mais dois pode ser rigorosamente igual a cinco."
Augusto de Campos (pontos-periferia-poesia concreta/Teoria da Poesia Concreta)

"El Universo es una esfera cuyo centro está en todas partes y la periferia en ninguna [Nicolas de Cusa]: ¿podría extenderse al tiempo está concepción tradicional del infinito? ¡Qué mejor símbolo del fin de la confusión entre irreversibilidad y degradación! Reencontraríamos aqui la flecha del tiempo asociada a la inestabilidad y a la probabilidad, y ella no significaría ya evolución hacia la muerte térmica, hacia el fin de toda historia, sino posibilidad de un eterno volver a comenzar. El Universo sería creación continua, sucesión infinita de Universos que nacen por doquier y van hacia el infinito."
Spanish translation (by Javier García Sanz) from the end of chapter 7 of Prigogine & Stengers' Entre le temps et l'eternité [it is an ill-fated instance of the malignancy of this world that it happens I don't have the French original of this book, & shall therefore by my ashes stand forever indebted (compound interest) to the heroine soul (chaste star!) who peradventure send me, with all her fraternity, the French original of just this choicest morsel so I could definitely pen it down here as a seasonable kindness to our whole parish!]

"We know the difference that separates the Hilbertian conception of mathematics from that of Russell and Whitehead’s Principia Mathematica (1910). Hilbert has replaced the method of genetic definitions with that of axiomatic definitions, and far from claiming to reconstruct the whole of mathematics from logic, introduced on the contrary, by passing from logic to arithmetic and from arithmetic to analysis, new variables and new axioms which extend each time the domain of consequences. Here is, for example, according to Bernays, who in the complete works of Hilbert published a study of all his work on the foundations of mathematics, all that is necessary to be given to formalize arithmetic: the propositional calculus, the axioms of equality, the arithmetic axioms of the ‘successor’ function (a + 1), the recurrence equations for addition and multiplication, and finally some form of the axiom of choice. To formalize analysis, it is necessary to be able to apply the axiom of choice, not only to numeric variables, but to a higher category of variables, those in which the variables are functions of numbers. Mathematics thus presents itself as successive syntheses in which each step is irreducible to the previous step. Moreover, and this is crucial, a theory thus formalized is itself incapable of providing the proof of its internal coherence. It must be overlaid with a metamathematics that takes the formalized mathematics as an object and studies it from the dual point of view of consistency and completion. The duality of planes that Hilbert thus established between the formalized mathematics and the metamathematical study of this formalism has as a consequence that the notions of consistency and completion govern a formalism from the interior of which they are not figured as notions defined in this formalism."
"... it is impossible to consider a mathematical ‘whole’ as resulting from the juxtaposition of elements defined independently of any overall consideration relative to the structure of the whole in which these elements are integrated. There thus exists a descent from the whole towards the part, as a ascent from the part to the whole, and this dual movement, illuminated by the idea of completion, allows the observation of the first aspect of the internal organization of mathematical entities. If one claims to admit that the study of such structural connections is an essential task for mathematical philosophy, one cannot fail to notice the differences that separate mathematical philosophy thus conceived from the entire current of logicist thought that developed after Russell had discovered the paradoxes of set theory. The logicians have since always claimed to prohibit non-predicative definitions, that is, those in which the properties of an element are supportive of the set to which that element belongs. Mathematicians have never been willing to admit the legitimacy of this interdiction, rightly showing the necessity, to define certain elements of a set, to sometimes call upon the global properties of this set... We thus hope to make evident this idea that the true logic is not a priori in relation to mathematics but that for logic to exist a mathematics is necessary."
Albert Lautman (Essay on the Notions of Structure and Existence in Mathematics, Simon B. Duffy's translation [it is ALSO an ill-fated instance of the malignancy of this world that it happens I don't have the French original of Lautman's essays, & shall therefore by my ashes stand forever indebted to the heroine soul (chaste star!) who peradventure send me, with all her fraternity, the French original of just at least these choicest morsels so I could definitely pen them down here as a seasonable kindness to our whole parish!])

"In contrast to the possibility of eliminating infinity as just described stand a number of results that show that some finitary statements can only be proved through infinitary considerations. These results originally emerge with Gödel’s incompleteness theorems (1931) but have been recently refined by displaying statements of mathematical interest... establishing the truth of the Gödel sentence and of the new incompleteness results requires appeal to some “infinitary” principles (when the truth of the Gödel sentence G is established through appeal to the statement expressing the consistency of Peano Arithmetic, it is establishing the latter that requires some portion of infinitary reasoning, such as induction up to an infinite ordinal called ε0)."
"More surprising still is the fact that dimensionality is not the arbiter of the power of a set. The power of the set of points in a unit line segment is just the same as that of the points in a unit area or in a unit volume—or, for that matter, all the three-dimensional space. (Dimensionality, however, retains some measure of authority in that any one-to-one mapping of points in a space of unlike dimensionality is necessarily a discontinuous mapping.) So paradoxical were some results in point-set theory that Cantor himself on one occasion in 1877 wrote to Dedekind, 'I see it, but I don't believe it'; and he asked his friend to check the proof."
Carl B. Boyer (A History of Mathematics)
"... the objects of transfinite set theory... clearly do not belong to the physical world and even their indirect connection with physical experience is very loose (owing primarily to the fact that set-theoretical concepts play only a minor role in the physical theories of today)... The set-theoretical paradoxes are hardly any more troublesome for mathematics than deceptions of the senses are for physics... The mere psychological fact of the existence of an intuition which is sufficiently clear to produce the axioms of set theory and an open series of extensions of them suffices to give meaning to the question of the truth or falsity of propositions like Cantor's continuum hypothesis. What, however, perhaps more than anything else, justifies the acceptance of this criterion of truth in set theory is the fact that continued appeals to mathematical intuition are necessary not only for obtaining unambiguous answers to the questions of transfinite set theory, but also for the solution of the problems of finitary number theory (of the type of Goldbach's conjecture), where the meaningfulness and unambiguity of the concepts entering into them can hardly be doubted. This follows from the fact that for every axiomatic system there are infinitely many undecidable propositions of this type."
Der Herr Warum (What is Cantor's Continuum Problem?/Supplement to the Second Edition)
"The Divine Spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and not-being, which we call the imaginary root of negative unity."
Leibniz on imaginary numbers as quoted by Morris Kline (who has no understanding whatsoever of Leibniz's nature)

"Conlon Nancarrow (1912–1997) made amazingly precise music using mechanically driven instruments. Operating a custom-built hole-punching machine, he produced piano rolls that drove two synchronized player pianos. Nancarrow was obsessed with the simultaneous layering of multiple tempo strands, where the tempi were related by a mathematical ratio. For example, in his Study for Player Piano 41a (1965), the tempi are related by an irrational factor, and cascades of notes sweep up and down the keyboard at superhuman speed."
"Complex contrapulsations can lead to chaotic cloud textures whose internal rhythm can only be perceived statistically. A classic example is Ligeti’s Poème Symphonique (1962) for 100 metronomes, where each metronome is set to a different tempo."
Curtis Roads, Composing Electronic Music
************************************************************** 

thereof main hall to hit upon:


"Marienbad: the name conjures up images of expensively dressed men and women walking leisurely on wide white paths through expansive manicured gardens, large fountains spewing the mineral-rich waters high into the air... The Gödel family is likely to have stayed at the elegant Baroque-style hotel at the springs, where many famous people have enjoyed their holidays, among them King Friedrich Wilhelm IV of Prussia, King Otto I of Greece, the Persian Shah Nasredding, Edward VII of Britain, as well as Goethe, Mark Twain, and Sigmund Freud, to name but a few."
"As Kurt described the experience many years later, at Marienbad he underwent a transformation. Until the Gödel expected to pursue his interests in the humanities, social studies, and languages, as an educated man of the period. But walking the long corridors of the elegant hotel, strolling through the lavish parks, and soaking in the steaming mineral waters, he was suddenly changed..."
- Amir D. Aczel, The Mystery of the Aleph (WSP 2000).

More  (to led us a vagary some zillions of zillions into the very heart of ANY planetary system):
"... [as revealed by Stefan Zweig in The World of Yesterday] before World War I, 'A ballet dancer ... was available for any man at any hour in Vienna for two hundred crowns.' [But] to marry someone with such associations could destroy even a well–established career [which happened indeed in many a family which were of an original character throughout & in which nothing ever wrought after the ordinary way]" John W. Dawson, Logical Dilemmas (A. K. Peters, 1997).
"[Morgenstern] was astonished... to learn that Gödel took an interest in ghosts, and he was very dismayed by Gödel’s choice of wife, whom he described as 'a Viennese washerwoman type: garrulous uncultured, [and] strong-willed,'" John Dawson, Logical Dilemmas (cf. Dejection & Affliction, which I forgot which but was unanimously  agreed  and lamented).
Dawson tells also that Gödel didn't care much for classical music and preferred dismally popular songs. But according to him Gödel was otherwise interested in Modern art, television and Kafka, and (in compliancy with this humours of his) believed in afterlife.
In The Mystery of Aleph (a book actually written to the literal edification of this scurvy and disasterous world of ours & in spight of all gentlemen reviewers in the Continent), Amir D. Aczel characterizes Gödel's incompleteness theorem as follows: "there will always be propositions that cannot be proven within the system. Even if a theorem is true, it may be mathematically impossible to prove." This is fair enough (that is, sans condition, anglicé, to the very end of the world), but what Aczel says next is (if I mistake not, which I don't) completely wrong: "The human mind, existing within a limited universe, cannot perceive an immense entity that extends beyond the confines of the system." This is completely wrong because what is beyond the system is not bigger but smaller. The outside is inside, and the biggest is the smallest, something I own (even as you and I are in a manner perfect strangers to each other) is impossible for you to guess, and I really think it is so. 

Consistency (from head to tail):
"Vladmir Voevodsky worried in a lecture at the Princeton Institute for Advanced Study that mathematics as we know it, and as analysed in present-day Foundations of Mathematics, might be inconsistent... that would, perhaps, be liberating... Most philosophers and logicians have jeered at Wittgenstein's asking, what's so great about consistency? Could we not do perfectly good mathematics from an inconsistent basis?" Ian Hacking, Why is there Philosophy of Mathematics at all? (Cambridge, 2014).

Totality (as crawling forth):
"Alain Connes is a Platonist. He thinks there is a totality of arithmetical truths, simply given with the number series itself. Thanks to Gödel we know that totality cannot be characterized by any recursive axiom system adequate to express its own syntax. This is not an argument for Platonism. It is an enrichment of Platonism with a new depth of understanding. As an attitude to reality and to incompleteness, this seems to me to be impeccable. But to avoid misunderstanding... as an argument for the existence of an archaic arithmetical reality, with all its truths intact, it begs the question" Hacking, Why is there Philosophy of Mathematics (actually no mere pudding-headed Argumentum Fistulatorium as sworn).

Consistency & Totality  (to be fretted and fumed inwardly):
"Nothing capable of proof ought to be accepted in science without proof," Richard Dedekind, as quoted in Hacking, Why is there Philosophy of Mathematics.

Rêve et perception extracorporelle (not anglicé):
"Même s'il est souvent déclenché involontairement par une sensation physique, le souvenir permet de se dématérialiser, d'échapper en partie aux déterminations temporelles et spatiales... Quant au rêve, il nous offre un témoignage plus vigoureux encore du dédoublement puisque la vivacité des images que l'on en rapporte semble mal s'accorder ave l'état d'inertie corporelle qui en est la condition. Moins courantes, enfin, sont ces situations de dissociation extrême induites par les hallucinations, les insensibilités temporaires comme l'extase ou la catalepsie, voir ces expériences de perception extracorporelle associées à la prise de psychotropes ou aux cas de quasi-mort..."
Philippe Descola, Par-delà nature et culture

See also:
- actual infinite falling (against Carlo Rovelli's pseudo-problem);
- the dogma of semantic uniformity & Python Gored Naturalism;
the only three types of ingenuity;

And also (with the whole of it):

*****extremely useful site for reviewing almost all mathematical concepts and skills in a systematic and organized way (Sal Khan's Academy): https://www.khanacademy.org/math

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