bridge-tarp...: Wittgenstein

Showing posts with label Wittgenstein. Show all posts

Friday, February 15, 2019

two sentences, the dogma of semantic uniformity & alchemy (or how not to use the method of shouting to close a window)

Der fürchterliche Pauli as a young student (picture taken from the Internet/CERN);
Duchamp in Maya Deren's Witch's Cradle (1943);
The Dimension of Dali (Joan Úbeda & Susi Marquès, 2004);

Monster Group (John Conway) (Numberphile/Youtube);

What is the number "e" and where does it come from? (Eddie Woo/Youtube);

500 Years of NOT Teaching the Cubic Formula (Burkard Polster, Mathologer/Youtube);

The Subtle Reason Taylor Series Work (Morphocular/Youtube 2024);

Imaginary Numbers Are Real: Riemann Surfaces (Welch Labs/Youtube);

Secret Kinks of Elementary Functions (Imaginary Angle/Youtube 2024);

Testing Crazy Recipes from a 1933 Chemical Formulary Book (Styropyro/Youtube);

The Origins of Mass (Don Lincoln, Fermilab/Youtube);

The Devil & Father Amorth (William Friedkin, 2018);

12 Aves do Brasil com Canto Estranhos (Planeta Aves/Youtube);

Wrote upon strong vellum and now in perfect preservation:

"People sometimes say that the way things happen in the movies is unreal, but actually it's the way things happen to you in life that's unreal."

The Philosophy of Andy Warhol

"It is not the Copenhagen interpretation of quantum mechanics that is strange, but the world itself."

N David Mermin (Quantum mysteries for anyone)

"Para ela a realidade era demais para ser acreditada."

Clarice Lispector (A Hora da Estrela)

"And the Gods stand by and marvel..."

Whistler

"Dieu est un scandale, — un scandale qui rapporte."

Baudelaire (Fusées)

"Too many shadows whispering voices

Faces on posters too many choices..."

Pet Shop Boys

"Chance, to be precise, is a leap, provides a leap out of reach of one's own grasp of oneself."

John Cage (45' for a Speaker)

"Pode o céu produzir flores,

A terra estrelas criar..."

Cancioneiro Guasca

"Nem mesmo sabemos onde habita agora o que é vivo, o que ele é, como se chama."

Memórias do Subsolo (tradução Boris Schnaiderman)

"... olho para ela e é como se no escuro ela também olhasse para mim, não se mexe."

Dária Oníssimovna (tradução Paulo Bezerra)

"... across the great brown river where whole trees float with green snakes in the branches and sad-eyed lemurs watch the shore out over a vast plain..."

W. S. Burroughs (Naked Lunch)

"Joe the Dead belongs to a select breed of outlaws known as the NOs, natural outlaws dedicated to breaking the so-called natural laws of the universe foisted upon us by physicists, chemists, mathematicians, biologists and, above all, the monumental fraud of cause and effect, to be replaced by the more pregnant concept of synchronicity."

W. S. Burroughs (The Western Lands)

"And maybe wisdom and madness do look very similar, at some point."
Monica Gagliano (Do Plants Have Something to Say? NYTimes)

"Le monde n'est ni vrai, ni réel, mais vivant."
Gilles Deleuze (Nietzsche et la philosophie)

"L'imagination se lassera plutôt de concevoir que la nature de fournir."

Pascal (as cited by Benoît Mandelbrot in The Fractal Geometry of Nature)

"Rien n’est plus fécond, tous les mathématiciens le savent, que ces obscures analogies, ces troubles reflets d’une théorie à une autre, ces furtives caresses, ces brouilleries inexplicables..."

"... les analogies entre le calcul des différences finies et le calcul différentiel servir de guide à Leibniz, à Taylor, à Euler, au cours de la période héroïque durant laquelle Berkeley pouvait dire, avec autant d’humour que d’à-propos, que les 'croyants' du calcul infinitésimal étaient peu qualifiés pour critiquer l’obscurité des mystères de la religion chrétienne, celui-là étant pour le moins aussi plein de mystères que celle-ci. Un peu plus tard, d’Alembert, ennemi de toute métaphysique en mathématique comme ailleurs, soutint dans ses articles de l’Encyclopédie que la vraie métaphysique du calcul infinitésimal n’était pas autre chose que la notion de limite. S’il ne tira pas lui-même de cette idée tout le parti dont elle était susceptible, les développements du siècle suivant devaient lui donner raison; et rien ne saurait être plus clair aujourd’hui, ni, il faut bien le dire, plus ennuyeux, qu’un exposé correct des éléments du calcul différentiel et intégral."

"Heureusement pour les chercheurs, à mesure que les brouillards se dissipent sur un point, c’est pour se reformer sur un autre."

André Weil (De la métaphysique aux mathématiques)

"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)

"... 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)

"Es treten in uns fortwährend neue Vorstellungs-massen auf, welche sehr rasch aus unserm Bewusstsein wieder verschwinden. Wir beobachten eine stetige Thätigkeit unserer Seele. Jedem Act derselben liegt etwas Bleibendes zu Grunde, welches sich bei besonderen Anlässen (durch die Erinnerung) als solches kundgiebt, ohne einen dauernden Einfluss auf die Erscheinungen auszuüben. Es tritt also fortwährend (mit jedem Denkact) etwas Bleibendes in unsere Seele ein, welches aber auf die Erscheinungswelt keinen dauernden Einfluss ausübt. Jedem Act unserer Seele liegt also etwas Bleibendes zu Grunde, welches mit diesem Act in unsere Seele eintritt, aber in demselben Augenblick aus der Erscheinungswelt völlig verschwindet. Von dieser Thatsache geleitet, mache ich die Hypothese, dass der Weltraum mit einem Stoff erfüllt ist, welcher fortwährend in die ponderablen Atome strömt und dort aus der Erscheinungswelt (Körperwelt) verschwindet..."

Bernhard Riemann (Neue mathematische Prinzipien der Naturphilosophie)

"... un nombre imaginaire est symbolique parce qu’il se réduit à un couple de nombre associés suivant certaines conventions. De même, une équation imaginaire est symbolique, parce qu’elle représente en réalité deux équations entre quantités réelles associées suivant des conventions définies. Or il semblerait a priori que des symboles, ainsi définis, ne pussent être rendus intuitifs par des images appropriées, et que l'intuition dût se limiter à illustrer des réalités intellectuelles correspondant aux quantités réelles. Mais l'idée du plan d'Argand-Caucy et, d'une façon plus systématique, les recouvrements des surfaces de Riemann démontrent qu'en fait on a su pour ces concepts symboliques créer une intuition satisfaisante."

Jules Vuillemin (La philosophie de l'algèbre)

"... fractal geometry is a new branch born belatedly of the crisis of mathematics that started when DuBois Reymond 1875 first reported on a continuous nondifferentiable function constructed by Weierstrass. The crisis lasted approximately to 1925, major actors being Cantor, Peano, Lebesgue, and Hausdorff. These names, and those of Besicovitch, Bolzano, Cesaro, Koch, Osgood, Sierpinski, and Urysohn, are not ordinarily encountered in the empirical study of Nature, but I claim that the impact of the work of these giants far transcends its intended scope."

Benoît Mandelbrot (Fractal Written Account of Chimeric Notions)

"Der phantasiestarke Mathematiker wird den Gebilden seines Denkens auch die Lebendigkeit der Anschauung einzuhauchen wissen, während Geister von schwächerer Flugkraft oder mehr abstrakter Richtung ihm in sein Reich konkreter Schöpfung und Belebung nicht zu folgen vermögen."

Felix Hausdorff (Das Raumproblem/Annalen der Naturphilosophie 1904)

"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

"... qué habrían dicho los defensores de la racionalidad y del rigor mecanicista si hubieran conocido la extraña fuerza newtoniana? Ya que, detrás de las prudentes declaraciones de Newton (no habrá ninguena hipótesis en lo que se refiere a la naturaleza de las fuerzas), se disimulará la pasión de un alquimista?... Lo que inspiro la fuerza newtoniana que anima a la materia inerte y que constitue en su sentido más fuerte la actividad de la naturaleza, parecen ser fuerzas que el químico Newton observó entre los cuerpos, fuerzas de atracción, de repulsión que regula la 'vida social' de la materia, fuerzan a todo cuerpo a formar pares estables con otros, a provocar por repulsión la disolución de los compuestos, a servir de mediadores que permiten el acercamiento y el acoplamiento de otros cuerpos..."

Spanish translation (by Manuel García Velarde and María Cristina Martín Sanz) of Prigogine & Stengers's La nouvelle alliance

[it is an ill-fated instance of the malignancy of this world that it happens I don't have the French originals of these two books by Prigogine & Stengers, & 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 originals of just this choicest morsel so I could definitely pen it down here as a seasonable kindness to our whole parish!]

"Since Einstein introduced discontinuity into the study of light, and de Broglie the continuity of waves into the study of matter, it is impossible to maintain the old idea of domains of physical facts that are separate from one another. The physics of the continuous represents a mode of treatment by differential equations of physical facts. The physics of discontinuity represents a mode of treatment of the same facts by other methods: group theory, calculation of matrices, quantum statistics, etc. There thus exists a certain analogy between contemporary physics and contemporary mathematics, in that they offer each other the spectacle of facts amenable to being studied at the same time by the calculus of the continuous and by the calculus of the discontinuous."

Albert Lautman (Essay on the Unity of Mathematical Sciences, Simon B. Duffy's translation)

"Mathematics is constituted like physics: the facts to be explained were throughout history the paradoxes that the progress of reflection rendered intelligible by a constant renewal of the meaning of essential notions. Irrational numbers, the infinitely small, continuous functions without derivatives, the transcendence of e and of r, the transfinite had all been accepted by an incomprehensible necessity of fact before there was a deductive theory of them. They had the fate of these physical constants like c or h which were essential in an incomprehensible way in the most different domains, up until the genius of Maxwell, Planck and Einstein knew to see in the constancy of their value the connection of electricity and light, of light and energy."

"Facts are... organized under the unity of the notion that generalizes them. The real ceases to be the pure discovery of the new and unforeseeable fact, in order to depend on the global intuition of a supra-sensible entity. [Pierre] Boutroux [L'Ideal scientifique des mathématiciens, 1920] takes as an example the reality of the ellipse. The ellipse is for him neither the locus of points such that the sum of their distances to the foci is constant, nor a curve defined by its algebraic equation, nor a curve to the projective properties of conics. It is all that and much more. It is, he says, 'a whole that does not include parts... a sort of Leibnizian monad. This monad is pregnant with the properties of the ellipse; I mean that these properties, even though they have not been explicitly formulated (and they cannot be since they are infinite in number) are contained in the notion of ellipse.'"

Albert Lautman (Essay on the Notions of Structure and Existence in Mathematics, Simon B. Duffy's translation)

"... it is for reasons that depend on the very nature of their conception of the problem of the foundation of mathematics that most theorists of contemporary mathematical logic judge this ‘purification’ of arithmetic of any analytic elements as extremely desirable. Whether it is an undertaking to reconstruct all of mathematics from the single notion of the whole number, or the requirement to at least reduce the consistency of analysis to that of arithmetic, it seems that it will always rely on the idea that arithmetic is metaphysically anterior to analysis, and that calling upon analysis to prove arithmetic results is consequently contrary to the natural order of things. In any case, whatever the effort dispensed on this route, it does not currently appear that it will ever be possible, for example in the theory of prime numbers, to eliminate analysis from arithmetic. If this negative result is then compared with the proof by Gödel of the impossibility of formalizing a supposedly consistent proof of the consistency of arithmetic without appeal to means that exceed arithmetic, it can lead to thinking that it is incorrect to consider arithmetic as fundamentally simpler than analysis."

Albert Lautman (New Research on the Dialectical Structure of 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!])

"Ce n’est qu’après le temps de Planck de 10−43 sec que les lois de la physique commencèrent à se créer. Les quatre forces fondamentales (éléctromagnetisme, force faible, force forte, gravitation) se 'condensèrent' après 10−12 sec. Un milliard d’années après surgirent les galaxies, et ensuite les éléments chimiques lourds tel que le fer. Notre terre naquit il y a seulement 4,6 milliards d’années, suivie par les protistes 800 millions d’années plus tard. Malgré le succès dû à sa puissance explicatrice et prédicative des phénomènes de la nature inanimée, la physique ne concerne qu’un segment limité de la réalité. L’ontologie de la physique ne pourrait se libérer de celle des mathématiques, c’est-à-dire d’une ontologie de nature parfaitement spirituelle. Ce fait prend une portée dramatique en particulier au moment planckien de la naissance des lois de la physique: c’est un processus qui ne peut exister qu’au sein de la réalité des mathématiques, non humaines, mais bien 'divines', si l’on y tient. Le lieu de naissance des lois de la physique touche à une réalité non physique. Ce type de recours inevitable à la base mathématique est d’ailleurs une des obstructions les plus dures à la réduction de l’activité intelligente de l’esprit humain aux purs processus neuronaux de la substance cérébrale dont les neuro-scientifiques voudraient nous persuader. En particulier, ce plaidoyer est une mise en relief des autres strates de la réalité: de la biologie et de la culture, de la logique du vivant et surtout de la dynamique mentale qui nous élèvent au-dessus de la matière animée ou non. Le succès de la physique s’avère être le succès de son immersion fondamentale au sein de la réalité spirituelle des mathématiques."

"Le Big Bang biologique créa des lois de l’évolution biologique dont la logique est loin d’être comprise. Elles semblent se situer loin au-delà des lois de la physique, qui elle ne sait rien de la vie, de sa dynamique selective, des jeux chaotiques et catastrophiques dont la téléologie de la survie échappe à la causalité, même brisée par les lois de la mécanique quantique, et dont l’organisation circulaire requiert des mathématiques fort différentes de celles de la physique, par exemple les fractales, les réseaux neuronaux, la théorie du chaos, des catastrophes, des automates cellulaires, ou alors des ensembles non bien fondés. Mais encore, comme en physique, la réalité biologique ne pourrait fonctionner comme base réductrice pour la réalité spirituelle, car toute description précise de ses phénomènes recourt aux mathématiques et aucune mathématique ne pourrait être expliquée en termes purement biologiques. C’est ici un point bien délicat qui semble échapper à quelques représentants des sciences cognitives: l’analyse cognitive reste totalement impuissante si l’on en exclut la contribution des mathématiques dont elle fait usage."

"On sait que pour le musicien, la compréhension du temps en tant qu’axe muni d’une seule dimension réelle est inacceptable. La réalité musicale du temps est vécue dans une variété fort complexe comprenant la stratification en rythmes locaux et globaux, en hiérarchies de courbes des tempi, et en dimensions temporelles engendrées par l’action et l’interaction de l’instrumentiste dans la genèse corporelle des vibrations sonores. Cette apparente confrontation des conceptions de temporalités ne se réduit pas à la simple négation de l’axe temporel et au contraire met en évidence le fait que cette mince ligne temporelle est une projection d’ontologies complexes dont les lois de la temporalité ne peuvent se concevoir en une seule dimension. Tout se passe dans un espace complexe temporel, dont la ligne du temps 'mesuré' ne présente qu’une image illusoire."

Guerino Mazzola (La vérité du beau dans la musique)

"But those infinities are perhaps not inevitable... I regard Peirce's hypostatization as name magic, Wittgenstein's alchemy."

"Pythagoreanism is the deeper naturalism."

Ian Hacking (Why is There Philosophy of Mathematics At All?)

"... 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."

David Mermin (What is quantum mechanics trying to tell us?)

"'Delusion' is such a word; its very vagueness helps by preventing us from seeing to the bottom of it. The two conceptions of reality and of deception are mingled in it, and perhaps the mingling has more justification than we know, and is less strange in nature than it is to our downright processes of thought."

Thomas Mann (An Experience in the Occult/H. T. Lowe-Porter translation)

"En faisant de la volonté l'essence des choses ou le monde vu du dedans, on refuse en principe la distinction de deux mondes: c'est le même monde qui est sensible et suprasensible."

Gilles Deleuze (Nietzsche et la philosophie)

"Mais tout cela est suffisant pour faire toucher du doigt une différence bien plus grande encore, celle qui sépare l'Occident moderne de tous ces peuples du présent et du passé qui n'ont pas jugé nécessaire de procéder à une naturalisation du monde."

Philippe Descola

"... car loin de croire le surnaturel, le divin inventé par l'homme je pense que c'est l'intervention millénaire de l'homme qui a fini par nous corrompre le divin."

"Le vieux totémisme des bêtes, des pierres, des objets chargés de foudre, des costumes bestialement imprégnés, tout ce qui sert en un mot à capter, à diriger, et à dériver des forces..."

"... les idées claires sont, au théâtre comme partout ailleurs, des idées mortes et terminées."

Antonin Artaud

"Commodum limen evaserant, et fores ad pristinum statum integrae resurgunt: cardines ad foramina residunt, postes ad repagula redeunt, ad claustra pessuli recurrunt..."

"At ille, odore alioquin spurcissimi humoris percussus quo me Lamiae illae infecerant, vehementer aspernatur..."

"Verum tamen et ipse per somnium iugulari visus sum mihi, nam et iugulum istum dolui et cor ipsum mihi avelli putavi, et nunc etiam spiritu deficior et genua quatior et gradu titubo et aliquid cibatus refovendo spirito desidero."

Apuleius

"Às duas da manhã o preso, que até então se mantivera surpreendentemente calmo e até adormecera, súbito começou a gritar, passou a esmurrar freneticamente a porta, com uma força antinatural arrancou da janelinha da porta a grade de ferro, quebrou o vidro e cortou as mãos..."

"Liámchin começou a gritar com uma voz que não era de gente, mas de algum animal."

Dostoiévski (Os Demônios, tradução de Paulo Bezerra)

"Y un día, cuando harto de caminar por las tierras que están a la orilla de la nuestra, entré por un sendero bordeado de lustros y descubrí mi casa y salí a la calle, la gente descubrió que jo estaba desnudo porque posiblemente no veía mi traje de capitán acusándome, además, de homicidio y pederasta."

Roberto Arlt (El traje del fantasma)

"Le phénomène 'Rachel' qui n'opère dans aucun espace-temps n'est pas compréhensible, pas plus que ne le sont les plus petits éléments en physique."

Anselm Kiefer (L'Art survivra à ses ruines)

"... si tout à l'heure je trouvais que Bergotte avait dit faux en parlant des joies de la vie spirituelle, c'était parce que j'appelais 'vie spirituelle', à ce moment-là, des raisonnements logiques qui étaient sans rapport avec elle..."

"... il y avait peut-être sous ces signes quelque chose de tout autre que je devais tâcher de découvrir, une pensée qu'ils traduisaient à la façon de ces caractères hiéroglyphique que on croirait représenter seulement des objets matériels... un grimoire compliqué et fleuri..."

"... sans laisser de côté ces mystères qui n'ont probablement leur explication que dans d'autres mondes et dont le pressentiment est ce qui nous émeut le plus dans la vie et dans l'art."

Marcel Proust (le narrateur)

"... ich bin, um es in Räthselform auszudrücken, als mein Vater bereits gestorben, als meine Mutter lebe ich noch und werde alt."

"Ich schätze den Werth von Menschen, von Rassen darnach ab, wie nothwendig sie den Gott nicht abgetrennt vom Satyr zu verstehen wissen..."

"Theologisch geredet — man höre zu, denn ich rede selten als Theologe — war es Gott selber, der sich als Schlange am Ende seines Tagewerks unter den Baum der Erkenntniss legte: er erholte sich so davon, Gott zu sein…"

Nietzsche (Ecce Homo)

"Ein solcher Gott muss nützen un schaden können, muss Freund und Feind sein können—man bewundert ihn im Guten wie in Schlimmen. Die widernatürliche Kastration eines Gottes zu einem Gotte bloss des Guten läge hier ausserhalb aller Wünschbarkeit."

"Das ist es nicht, was uns abscheidet, dass wir keinen Gott wiederfinden, weder in der Geschichte, noch in der Natur, noch hinter der Natur—sondern dass wir, was als Gott verehrt wurde, nicht als 'göttlich', sondern als erbarmungswürdig, als absurd, als schädlich empfinden, nicht nur als Irrtum, sondern als Verbrechen am Leben... Wir leugnen Gott als Gott..."

Nietzsche (Der Antichrist)

"Et que de dieux sont encore possibles! Je ne douterais point de l'existence de toutes sortes de dieux..."

Nietzsche (traduit par Klossowski)

"... veja bem, um Deus não é o mesmo que Deus, please!"

Hélio Oiticica

"Sans doute la version nietzschéenne du polythéisme est-elle bien nécessairement aussi éloignée de la dévotion antique que sa propre notion du divin instinct générateur de plusieurs dieux l'est nécessairement de la notion chrétienne de la divinité. Mais ce dont cette 'version' témoigne c'est le refus de s'installer dans une morale athée qui, pour Nietzsche, n'était pas moins irrespirable que la morale monothéiste, et il ne pouvait pas ne pas voir dans la morale athée et humanitaire autre chose que la continuation de ce qu'il éprouvait comme la tyrannie d'une vérité unique... l'incroyance à l'égard d'un Dieu unique et normateur, d'un Dieu qui est la Vérité, ne s'affirme pas moins comme une impiété d'inspiration proprement divine et s'interdit tout repliement de la raison dans les limites strictement humaines... non que cette impiété aspire au pur et simple déchaînement des forces aveugles comme on est généralement convenu de le dire au sujet de Nietzsche, alor qu'il n'a rien de commun avec un vitalisme faisant table rase de toutes les formes élaborées de la culture; Nietzsche est aux antipodes de tout naturisme... c'est pourquoi on retrouverait dans l'incantation de Zarathoustra comme un appel à une insurrection des images, de ces images que, dans ses phantasmes, l'âme humaine, au contact des forces obscures en elle, est capable de former; phantasmes qui témoignent pour l'âme comme d'une aptitude à la métamorphose toujours inépuisée, d'un besoin d'investissement universel inassouvi où les diverses formes extra-humaines de l'existence se proposent à l'âme comme autant de possibilités d'être..."

"... la doctrine de l'éternel retour se conçoit encore une fois comme un simulacre de doctrine dont le caractère parodique même rend compte de l'hilarité comme attribut de l'existence se suffisant à elle-même lorsque le rire éclate au fond de l'entière vérité, soit que la vérité explose dans le rire des dieux, soit que les dieux eux-mêmes meurent de fou rire..."

"... car si les dieux meurent de ce rire, c'est aussi de ce rire qui éclate du fond de l'entière vérité que les dieux renaissent."

''Zarathoutra, dès lors qu'il a voulu l'éternel retour de toutes choses, a d'avance choisi de voir tourner en dérision sa propre doctrine... Quel autre sens, si ce n'est celui-là, attribuerait-on à l'extraordinaire parodie de la Cène où le meurtrier de Dieu est aussi celui qui offre le calice à l'âne — figure sacrilège du Dieu chrétien du temps de la réaction païenne, mais plus spécifiquement animal sacré des mystères antiques, l'âne d'or de l'initiation isiaque, animal digne par son infatigable Ia (ita est!) — son infatigable oui donné au retour de toutes choses — digne de représenter la longanimité divine, digne donc aussi d'incarner une antique divinité, Dionysos, le dieu de la vigne, ressuscité dans l'ivresse générale. Et en effet, comme Voyageur le déclare à Zarathoustra: la mort, chez les dieux, n'est jamais qu'un préjugé."

Pierre Klossowski (Un si funeste désir)

"In a famous article, Pierre Cartier, one of Grothendieck’s main disciples, had conjectured that ‘there are many reasons for believing in a 'cosmic Galois group' acting on the fundamental constants of physical theories. This group should be closely related to the Grothendieck-Teichmüller group’... ‘Cartier’s dream’, as his conjecture was known for some years, had therefore ‘come true’, thanks to the results of Connes and his team, and it thus represents a sort of intensified, infinitely refined Pythagoreanism, harking back to the first, rough and original hypotheses regarding the existence of harmonic correspondences between mathematika (the study of quantity) and kosmos (order). In Connes’s work, this arithmetico-geometrico-physical refinement extends to deeper analogies between physical divergences in field theory and arithmetical mixtures in Tate motifs, thus approaching what Connes calls the very ‘heart’ of mathematics: ‘modular forms, L-functions, arithmetic, prime numbers, all sorts of things linked to that.'"

Fernando Zalamea (Synthetic Philosophy of Mathematics)

"As Messiaen observed, when combining multiple simultaneous rhythms, one confronts 'neutralizing forces' that prevent clear perception of their superimposition. In general, these forces pertain to any kind of similarity between the various rhythmic voices, be it timbral, registral, harmonic, durational, or similarity of intensity and attack time. Messiaen was especially insistent on how isochronous pulsations destroy the polyrhythmic 'scaffolding' (échafaudage). Messiaen suggested that polyrhythms be articulated by polytonality and polymodality."

"The early electronic music of Stockhausen is a classic example of the integration of pitched and non-pitched elements. Gesang der Jünglinge (1956) juxtaposed sung serial melodies and chords against such elements as 'sine complex showers,' 'impulse complex showers,' filtered and broadband noise, and 'chords' of narrow noise bands. His Kontakte (1960) takes the contrasts even further. At any given instant, Stockhausen pits noise against pitch, fixed against moving, close against far, short against long, high against low register, soft against loud—always in sharp relief. This unrelenting counterpoint of contrasts marks Kontakte as an especially inventive composition, as Stockhausen discovered oppositions that were never before articulated."

Curtis Roads, Composing Electronic Music

"When talking about miracles, we should of course bear in mind Lacan's qualification that the only 'irrationality' he admits is that of irrational numbers in mathematics—in a homologous way, the only 'miracles' a radical materialist allows for are mathematical ones."

"... it is the subjective act of transcendental synthesis which transforms the chaotic array of sensual impressions into 'objective reality.' Shamelessly ignoring the objection that we are confounding ontological and empirical levels, here we must invoke quantum physics: it is the collapse of the quantum waves in the act of perception which fixes quantum oscillations into a single objective reality. And, furthermore, this point must be universalized: every figure of reality is rooted in a determinate standpoint. Even at a level closer to us, we know how different 'reality' appears to a hog or a bird, starting with the different tapestry of colors: each living being perceives (and interacts with) its own 'reality.' And one should push this insight to the extreme of Cartesian doubt: the very notion of greatness should be relativized. How do we know that our Milky Way is not just a speck of dust in another universe? Why, when we think about aliens, do we always accept that, though they may be smaller or larger than us, they nonetheless live in a world which is proportionally of the same order of greatness as ours? Perhaps aliens are already here, but just so large or so small that we do not even notice each other."

Slavoj Zizek (Haunted by A/Z, Feyerabend with vengeance & the New Wave)

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

a 2025 discovery:

"Si el lado tiene un número, no lo tiene la diagonal, y viceversa. Entre el uno y la otra se abre un abismo infranqueable para el número. La longitud de la diagonal se transcendente (utilizo este término en

su sentido general, no como terminus technicus matemático) en relación con la longitud de los lados. Este hecho fue descubierto por primera vez por Pitágoras: como se sabe, el geómetra se asustó por la profundidad del hecho que es presentaba ante él y por las consecuencias que de él se derivaban. Porque sólo con este hecho, y de una vez por todas, se ha asestado un golpe que ha abierto brechas irreparables en cualquier racionalismo.[...] estas substancías no pueden ya ser expresadas mediante símbolos finitos, sino que nos más bien postuladas por estos últimos, se basan en ellos y les otorgan un nuevo sentido, superior. Sin embargo, basta con que queramos pensar estas substancias aritméticas nuevas utilizando los términos viejos, basta con que queramos verter el vino nuevo en odres viejos para que es produzca la descomposición del símbolo de la nueva substancia en aquellos elementos que la componen, elementos incompatibles unos con otros en el antiguos conceptos, y la substancia misma es evapore.

De la noción de la igualdad de dos irracionales, se establece que la parte finita de los símbolos a' puede ser eliminada de a; que del grupo (a', a'', a''')... podemos elegir y separar un grupo infinito; que podemos, finalmente, efectuar una permutación por parejas — una «transposición» — de una multitud infinita de elementos a' (con la condición de que no se modifique la estructura de la serie, con la condición de que los elementos no se disloquen de tal modo que no estén ya en condiciones de retornar al orden inicial por permutaciones determinadas en pares) y así y todo a no se modificará.

[...] No quedaba más que una alternativa: o bien renunciar al problema mismo, o bien situarnos por encima de aquel plano del pensamiento que opera con símbolos «finitos», introducir una nueva idea, la idea de una infinitud actual (esto es, sintetizada), y con su ayuda, construir, por medio de un acto creativo especial del espíritu, una substancia del pensamiento completamente nueva: el número irracional. ¿Se ha dado aquí una consecuencia lógica en las deducciones? ¡Seguro que no! Hemos llevado a cabo un salto, una ruptura en el desarrollo; hemos introducido algo que es completamente nuevo. Podíamos también no haber lo introducido, contentándonos con aquellas substancias que ya están das das, es decir, con las substancias «finitas», procediendo a la esterilización positivista de la razón y descansando tranquilos en la imposibilidad de salir más allá de los límites de los símbolos dados.

[...] E necesario sobrepasar la autosuficiencia del entendimiento, transgredir le circulo mágico de sus conceptos finitos..."

Pavel Florenski, "Los irracionales en matemática y en el dogma" (La Columna y el Fundamento de la Verdad, traducción e edición de Francisco José López Sáez);

Another:

"Non seulement la volonté du souverain Etre peut créer la matière, mais nous ne savons pas à priori si la matière ne peut pas être créée par la volonté de tout autre être, ou de toute autre cause que l'imagination la plus fantasque puisse concevoir."

David Hume, cité par Christian Cherfils (Un essai de religion scientifique: introduction à Wronski, philosophe et réformateur);

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

Two sentences:

"There are at least three perfect numbers greater than 17."

"There are at least three large cities older than New York."

- from Ian Hacking's (person of no small note and consequence) Why is there Philosophy of Mathematics at all (Cambridge, 2014, p. 216-17);

From the dogma of semantic uniformity:

Both sentences are to be analysed in the same way [also from Hacking's Why is there Philosophy of Mathematics, p. 217, but Hacking doesn't subscribe to the dogma, he derides it as an abominable thing].

What is semantic uniformity, standard semantics, denotational semantics? Something that is at odds with a minimal insightful understanding of mathematics. Something that is at odds with a minimal insightful understanding of "natural languages" (and moreover, who said that languages such as English not to speak Portuguese or Polish and even Hungarian are supposed to be natural?!):

"Nobody who takes Wittgenstein seriously is likely to agree to denotational [or referential] semantics applied to mathematics," Hacking's Why is there Philosophy of Mathematics, p. 218 [and even more important: "As his philosophy evolved, Wittgenstein absolutely rebelled against the uniformity-of-semantics premise"] [aside on Sir Peter Frederick Strawson (a man of erudition): "expressions have meanings, while we use some expressions to refer," "Strawson's lesson, that words do not refer, but that speakers use words to refer, seems to have been largely forgotten," Hacking, p. 219];

Brewing the alchemy [but that against semantic uniformity & in favour of Python Gored Naturalism—to heroine it into so violent and hazardous an extream]:

- what is 17?

- what is New York?

- what is a perfect number?

- what is a large city?

- what are numbers?

- what are cities?

- what is an object?

- what is an entity?

...

→ there are things, real things (although not all things are like that) which we are acquainted with and with which we don't have causal relations [for example, some mathematical stuff &/or phenomena related to non-locality, which was impossible for you to guess];

"... it is very much a philosopher's view that the only objects there are are physical or material objects, or regions of space-time, or whatever it is that philosophers tell us... to maintain that there aren't any numbers at all because numbers are abstract and not physical objects seems like a demented way to show respect for physics, which of course everyone admires," George Boolos (person of no small note and consequence), as quoted by Hacking, Why is there Philosophy of Mathematics at all.

"We are of divine species," Dedekind (person of no small note and consequence) as quoted by Hacking, Why is there Philosophy of Mathematics at all.

***More on the dogma of semantic uniformity, or an expatiation on how to accommodate Python Gored Naturalism with Styles of Scientific Reasoning & Pedestrian Reality: "... when facing this possibility of using the notion of styles of thinking to address so diversified kinds of human undertakings, a special point must be considered. Hacking is not saying that in order to point to truth or falsehood every proposition depends on some kind of style of thinking. He “rejects any uniform all-purpose semantics,” and the “idea that a uniform theory of truth or of meaning should apply across the board to an entire language”... In contrast to sentences that would depend on styles of thinking in order to point to truth or falsehood, Hacking refers to “the boring utterances that crop up in almost any language, and which make radical translation relatively easy.” He refers to “propositions that have a sense for almost all human beings,” and to the “boring domains of ‘observations’ that we share with all people as people.” As an example of such an observation, Hacking suggests the proposition “my skin is warm”... It is possible to sustain that even the most apparently obvious propositions are in any case theory-laden. But the conflation of Hacking’s distinction between more and less sophisticated kinds of propositions would imply a very implausible oversimplification of the way real people use language. Under normal viewing conditions, no one would even think much less utter a proposition such as this table is brown, so obvious people take to be its meaning... Someone could perfectly say, however, this chair is made of Brazilian rosewood, and this would make sense exactly for denoting some kind of expertise. We can understand the first sentence as not depending on any specific style whatsoever, and capable of being understood straightforwardly by most people just by the use of the most elementary discursive and perceptual abilities. The second sentence demands the use of other skills, which do not have to be styles of thinking, but only a slightly more elaborated and technical use of elementary discursive and perceptual abilities. Finally, another sentence could be added in order to extend the comparison: the heat which has the refrangibility of the red rays is occasioned by the light of those rays... This latter sentence demands the use of styles of thinking, because it mentions concepts and types of objects (refrangibility, rays) which would not even exist for people unless they are engaged in certain specific and complex practices by which these concepts and objects are made possible... Ultimately, the problem with saying that everything is theory-laden [this is the core of Hacking's criticism of theory-laden armchair infatuation] is that this position undermines elementary distinctions that constitute human discursive practices—elementary distinctions such as between on the one hand saying, telling, giving an account of something, and on the other hand doing something. A person might just say to another that he or she feels cold and wants the window to be closed, but unless one goes over there and effectively interacts with the window the cold will not merely disappear just by saying close the window no matter how loudly you shout. Perhaps the cold goes away if you are Brian de Palma’s Carrie (1976), but what makes Carrie a Carrie either in movies or in real life (supposing there might be such a thing) is that her thought and talk are imbued with a special sui generis power that is faraway more effective than ordinary people’s thought and talk (and even limbs). You would still need distinctions between thinking, saying, and doing in order to make any sense of Carrie. Differences between things such as mental states, sentences, and external objects are all constitutive and germane to what is here called styles of thinking. Without such elementary distinctions, there is not much to be done with a sentence such as the heat which has the refrangibility of the red rays is occasioned by the light of those rays," Alessandro Zir (person of no small note and consequence besides being meself), Luso-Brazilian Encounters of the Sixteenth-Century (Fairleigh Dickinson University Press, 2011, p. 6-7).

Getting Wolfgang Pauli & the naive Portuguese, as a plus (for the edification of the world, but literally):

"Generally speaking scientists are no Carries, though there might have been a few registered but far less noxious cases such as Wolfgang Pauli and the Pauli effect," Alessandro Zir, The Sixteenth-Century Corpus of the Portuguese Colonizers of Brazil (Dalhousie, PhD thesis) [the paragraph of this sentence (which refers also to Ludwik Fleck) wasn't (if I mistake not) incorporated in the book Luso-Brazilian Encounters published in 2011 by FDU Press—an incident not necessarily ranking as a fatal blow to die Geissel Gottes' scholarship (I'm positive)].

"Sérgio Buarque de Holanda remarks that the Portuguese were naive realist people. Their realism would come exactly from their credulity, which would be, as he defines it, “a radical gentleness and passivity in face of reality” that “does not deny Nature infinite possibilities” and the supernatural... If this is correct, the Portuguese would be people capable of recognizing the most strange things in nature, without having to deny all the humdrum propositions that make sense to most people, including people having no sensibility whatsoever to apparitions of monsters and the devil. Besides seeing devils and monsters, the Portuguese would not have any difficulty and do not invoke anything spiritual in order to answer a simple question such as are you cold? They also never use the method of shouting in order to close windows," Alessandro Zir, Luso-Brazilian Encounters of the Sixteenth-Century (Fairleigh Dickinson University Press, 2011, p. 6-7).

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);
Georg Cantor et les infinis, par Patrick Dehornoy (SMF/Youtube 2009);

The Subtle Reason Taylor Series Work (Morphocular/Youtube 2024);

Problems with Zero (Numberphile/Youtube);

Indeterminate: the hidden power of zero divided by zero (Mathologer/Youtube);

Secret Kinks of Elementary Functions (Imaginary Angle/Youtube 2024);

L'étonnant puzzle fractal de von Koch (Mickaël Launey/Youtube);

El Problema indemostrable (Mates Mike/Youtube);

History of the Natural Logarithm: Was it Discovered? (Tarek Said/Youtube);

Euler's Identity (Mark Newman/Youtube);

The Great Abyss Inframince (A/Z 2018) [I took this video out of Youtube, because I wanted to change it];

Foundation out of the common track:

"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

"... but I'm prejudiced. I have loved Cantor's hierarchy of cardinals ever since I was exposed to it at a tender age."

Ian Hacking (Why Is There Philosophy of Mathematics At All?)

Der Herr Warum (What is Cantor's Continuum Problem?/Supplement to the Second Edition)

Bernhard Riemann (Neue mathematische Prinzipien der Naturphilosophie)

"Considerer une infinité dénombrable d'objets à travers leur représentation finie idéale pouvait déjà paraître dépasser les possibilités humaines, mais Pythagore découvrit l'insuffisance de cette donnée, selon laquelle tout segment aurait dû être commensurable avec tout autre. Dès lors surgissaient sur la droite idéale, elle-même substitut d'une infinité dénombrable de droites, une infinité de points non rationnels, dont on apprit, avec Cantor, que l'ensemble cessait d'être dénombrable. En ce qui concerne les radicaux carrés et les expressions rationnelles d'un nombre fini de radicaux carrés, la doctrine des idées permit de résoudre entièrement le problème, dans la mesure où elle admit les constructions par la règle et le compass. Mais, résolu sur ce point, le scandale devait renaître avec les autres nombres algébriques, puis avec les nombres transcendants."

"[Dans la projection téréographique sur la sphère de Riemann] P peut être choisi comme représentant du nombre complexe x + iy... quand P se dirige vers N, Q tend à s'éloigner de l'origine et Ne peut être regardé comme le représentant unique de tous les point à l'infini du plan imaginaire, points qui deviennent uniques et perdent ainsi, dans la représentation intuitive de Riemann, le privilège qu'ils conservaient dans celle d'Argand-Cauchy. La conformité de la représentation est conservée quand on passe du plan à la sphère complexe."

Jules Vuillemin (La philosophie de l'algèbre)

"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 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!])

"The supermultitudinous character of Peirce’s continuum shows, according to Peirce, that the Cantorian real line is just 'the first embryo of continuity', 'an incipient cohesiveness, a germinal of continuity.' Nevertheless, the cardinal indetermination of Cantor’s continuum inside ZF—a profound discovery of 20th century mathematical logic that Peirce could not imagine—shows that the Cantorian model can also be considered as a valid generic candidate to capture the supermultitudeness of the continuum... The indetermination of 2ˆAleph0 is not well appreciated by the specialists, who consider that the incompleteness of ZF must be repaired. In any of the 'normative' responses given to the cardinal size of the continuum, it ceases immediately to be supermultitudinous since the additional axioms force it to adjust within a determinate level of a hierarchy."

"... while Cantor and, systematically, most of his followers, try to bound (and bind) the continuum, Peirce tries to unbound it: to approach a supermultitudinous continuum, not restricted in size, truly generic in the transfinite, never totally determined. It comes then, as a most remarkable fact, that many indications of the indeterminacy of the continuum found at the core of contemporary Cantorian set theory (free analysis of the set theoretic universe through disparate filters, using forcing techniques, with many phenomena possibly coexistent) seem to assure in retrospect the appropriateness of Peirce’s vision. The generality of Peirce’s continuum implies, as we shall now see, that it cannot be reconstructed from the 'particular' or the 'existent', and that it must be thought in the true general realm of possibilia."

Fernando Zalamea (Peirce's Logic of Continuity)

"What if, however, we treat this set of elements forever 'open' to addition as a closed totality and posit the infinite as an element of its own, as the external frame of the endless set of elements it contains? The transfinite is thus a number or an element with the paradoxical property of being insensitive to addition or subtraction: whether we add a unit to it or subtract one from it, it remains the same..."

"... the subject as such is hysterical... [it] is capable of relating to a term that remains outside the limits of the game; indeed, this relationship to a term 'out-of-play' is constitutive of the subject itself..."

"When cognitivists from Dennett onwards try to explain consciousness, they enumerate a whole series of specifically human capacities which 'cannot really function without consciousness'—what if, however, instead of focusing on 'what we can (only) do with consciousness,' we should shift the terrain and ask: what is the specific point of impossibility of consciousness? What is it that we cannot do with consciousness? How is consciousness related to what we a priori cannot become conscious of?"

"... the unfinished (ontologically incomplete) character of reality which compels us to include the virtuality of teleiosis in the definition of an object is thus not its limitation, but a positive condition of its actual existence..."

Slavoj Zizek (Haunted by A/Z, Feyerabend with vengeance & the New Wave)

"Nous connaissons qu'il y a un infini, et ignorons sa nature..."

Pascal (Pensées, 233)

"Ainsi il y a des propriétés communes à toutes choses, dont la connaissance ouvre l'esprit aux plus grandes merveilles de la nature. La principale comprend les deux infinites qui se rencontrent dans toutes: l'une de grandeur, l'autre de petitesse... De même, quelque grande que soit un nombre... Et au contraire, quelque petit que soit un nombre..."

"Voilà l'admirable rapport que la nature a mis entre ces choses, et les deux merveilleuses infinites qu'elle a proposées aux hommes, non pas à concevoir, mais à admirer..."

Pascal (Fragments de l'esprit géométrique)

"... la conception d’une quantité finie porte toujours sur l'objet du savoir, sur l’être qui est opposé au savoir et qui constitue l’objet de la connaissance; tandis que l’idée de l’infini... ne peut porter que sur les fonctions mêmes du savoir, où elle introduit la plus haute unité intellectuelle ou la plus haute signification dans la production même de la connaissance de la quantité."

Höené Wronski (Philosophie de l'Infini)

"Quis neget, naturam instinctu solo, sine etiam ratiocinatione, docere geometriam?"

Johannes Kepler (Stereometria Dolii Austriaci in Specie, Theorema V)

"... 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)

"We do not confine ourselves any more to using infinity as a figure of speech, or as shorthand for the statement that no matter how great a number there is one greater: the act of becoming invokes the infinite as the generating principle for any number; any number is now regarded as the ultra-ultimate step of an infinite process; the concept of infinity has been woven into the very fabric of our generalized number concept."

"... while Galileo dodged the issue by declaring that the attributes of equal, greater, and less are not applicable to infinite, but only to finite quantities, Cantor takes the issue as a point of departure for his theory of aggregates. And Dedekind goes even further: to him it is characteristic of all infinite collections that they possess parts which may be matched with the whole... The reader will remember Liouville's discovery of transcendentals..."

Tobias Dantzig, Number: the language of science

"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)."

Kenny Easwaran et al. (Infinity, Stanford Encyclopedia of Philosophy)

"I should advise that by number... there be understood not the class (the system of all mutually similar finite systems), but rather something new (corresponding to this class) which the mind creates. We are of divine species and without doubt possess creative power not merely in material things (railroads, telegraphs), but quite specially in intellectual things... you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut..."

Richard Dedekind (to Heinrich Weber, as quoted in Ian Hacking's Why Is There Philosophy of Mathematics At All?)

"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."

"Dedekind and Cantor were among the most capable mathematicians, and certainly the most original, of their day; yet neither man secured a top-ranking professional position. Dedekind spent almost a lifetime teaching on the secondary level..."

Carl B. Boyer (A History of Mathematics)

"Expressions like 1/0, 3/0, 0/0 etc. [that is, divisions by zero] will be for us meaningless symbols. For if division by zero were permitted, we could deduce from the true equation 0.1 = 0.2 the absurd consequence 1 = 2. It is however sometimes useful to denote such expressions by the symbol ∞ (read 'infinity'), provided that one does not attempt to operate with the symbol ∞ as though it were subject to the ordinary rules of calculation with numbers."

"We cannot include the symbol ∞ in the real number system and at the same time preserve the fundamental rules of arithmetic. Nevertheless the concept of the infinite pervades all mathematics..."

Richard Courant & Herbert Robbins (What is Mathematics)

"Ces constructions montrent de manière exemplaire la dynamique des mathématiques qui engendre la conceptualisation des intervalles. Il s’agit là d’un débat passionnant de longue durée qui nous incite à nous poser la question de la signification de tels outils pour la musique : est-il légitime de faire intervenir des structures mathématiques dans la théorie de la musique sans en connaître la signification ou la portée? Nous voudrions plutôt nous restreindre aux objets ayant uniquement une « carte de séjour des musiciens », et éviter de faire jouer des objets 'étrangers'. Je mets en évidence ce type de réflexe instinctif qui est totalement absent chez les physiciens. Pour ces derniers, les concepts et les théorèmes mathématiques sont non seulement le langage de la nature — depuis Galilée, le 'livre' de la Nature s’écrit avec le 'langage' des mathématiques. Si l’on suit les réflexions de Roger Penrose, les mathématiques sont même une base ontologique — qui diffère peu de l’approche pythagoricienne au final, bien qu’étant infiniment plus complexe. Ce réflexe 'xénophobe' est d’autant plus irritant que les compositeurs, eux, ne montrent pas ces réserves, qu’il s’agisse de Xenakis, Boulez, Stockhausen, Ligeti, ou même Mozart ou Beethoven. J’insiste sur ce point car le débat sur la justification des mathématiques dans la musique doit pénétrer plus profondément au cœur des deux cultures pour créer un enrichissement mutuel. Nous pouvons citer ici de nouveau Novalis : 'Aller Genuss ist musikalisch, mithin mathematisch.'"

Guerino Mazzola (La vérité du beau dans la musique)

"Walter Benjamin hat 'das Vermögen der Phantasie' als 'die Gabe, im unendlich Kleinen zu interpolieren' definiert. Das beleuchtet blitzhaft die wahre Interpretation. (...) Im dicht gewobenen Zusammenhang des Notentextes sind die minimalen Hohlräume zu entdecken, in denen sinnverleihende Interpretation ihre Zuflucht findet"

Theodor Adorno, as quoted by Guerino Mazzola

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a 2025 discovery:

"La irracionalidad es absolutamente transcendente, absolutamente inalcanzable para el ámbito racional. Y de una vez por todas, de modo definitivo e irreversible, es necesario que renunciemos a la intención de representar la irracionalidad en la forma de una combinación finita de racionalidades... podemos, con la ayuda de unas determinaciones constructivas completamente nuevas, introducir en el agregado de los números racionales, que no está cualificado como una totalidad integral, una nueva substancia que estructure aquel agregado. Entonces en esta «materia» vendrá impreso y encarnado el número irracional. Cada número racional en particular, cada elemento, cada átomo de este agregado, tomado por sí mismo, en su sentido primario, no tiene nada en común con el todo integral (tselym) que en el se encarna, del mismo modo en que la idea estética de una estatua no tiene nada en común con los cristales de mármol que componen su materia, o el sentido de un poema con los sonidos de las palabras particulares. Pero el coniunto infinito — más exactamente, suprafinito — de aquellos elementos refleja totalmente este todo integral, esta idea.

[...] Pero el conjunto de los números a, vinculados entre sí por la propiedad de la convergencia y por la determinación de su «actuación» sobre a como sobre un objeto único, expresa con exactitud esta substancia transcendente a. En lo sucesivo, cuando a esté ya plenamente estudiada, se verá que es

posible transponer todo a', en la forma propia de a, aunque no será posible la operación inversa, es

decir, transponer a en la forma de a'; entonces se establece le concepto de «semejanza» entre a' y a, si bien esta semejanza-convergencia es sólo una semejanza de indicio y alusión, y no de tautegoría. Esto significa que, si bien a es transcendente respecto a cualquier a', si bien es «inconcebible» e inalcanzable desde el punto de vista de a', todo a', sin embargo, le es inmanente a a, es transparente hasta el fondo para su mirada.

[...] además de este caso, existen aún numerosos ejemplos semejantes en los que viene aplicado el

concepto básico de la superación de la finitud. Asi, una función analítica transcendente no puede ser expresada por ningún número finito de elementos, mientras que esto mismo resulta siempre posible en relación con la función algebraica, como descubrió Weierstrass. Pero entonces sale a la luz el

principio de la superación de la finitud, y resulta, de acuerdo con el teorema de Poincaré, que «toda función analítica puede ser definida con la ayuda de una multitud numérica de elementos...

[...]

A este mismo dominio de la superación de la finitud pertenecen las investigaciones, extremamente interesantes desde el punto de vista de la teoría del conocimiento y de la ontología, que versan sobre los signos de convergencia y divergencia de las series infinitas, en relación con el problema del crecimiento y de la disminución de las funciones y con la teoría de las integrales determinadas. Aquí las «funciones ideales» de P. du Bois-Reymond pueden, en un cierto sentido, ser asimiladas de nuevo a las irracionalidades, pero no ya entre números y funciones, sino entre integrales. Los estudios de N. Abel, N. .V Bugaev, P. du Bois-Reymond, .E Borel, J. Hadamard, H. Poincaré, etc. a pesar del carácter particular de los problemas planteados y de los métodos empleados, tienen gran importancia para la fi-

losofia, y no podemos menos de admirarnos por el hecho de que no hayan incontrado hasta ahora ninguna aplicación filosófica..."

Pavel Florenski, "Los irracionales en matemática y en el dogma" (La Columna y el Fundamento de la Verdad, traducción e edición de Francisco José López Sáez);

Another:

"Il faudrait plutôt, dit Wronski au sujet des nombres irrationnels, les nommer nombres rationnels, comme étant produits par l'influence de la raison, suivant la déduction que nous venons d'en donner; et cela malgré le mot raison, pris dans sa signification de rapport. Ce qui n'est pas possible en réalité, dans le domaine sensible de l'entendement, l'est au moins en idée, dans le domaine intellectuel de la raison", et cette dernière faculté ne se désiste point, autant qu'il est en elle, de ramener toutes les fonctions algorithmiques à la loi de continuité indéfinie ou, en général, à la loi de l'absolu. Telle est la déduction métaphysique de ces nombres vraiment extraordinaires, qui forment un des phénomènes intellectuels les plus remarquables, et qui donnent une preuve non équivoque de l'influence qu'exerce, dans le savoir de l'homme, la faculté législatrice de la raison, dont ces nombres sont un produit, en quelque sorte malgré l'entendement."

Joseph Hoëné-Wronski (Introdution à la philosophie des mathématiques e technique de l'algorithmie), cité par Christian Cherfils (Un essai de religion scientifique: introduction à Wronski, philosophe et réformateur);

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Memoire presenté à Messieurs les Docteurs de Sorbonne (if to be detected):

In his The Mystery of the Aleph (a book written to the literal edification of this scurvy and disasterous world of ours & in spight of all gentlemen reviewers in England & the Continent), Amir D. Aczel, person (if I mistake not) of no small note and consequence, writes: "Infinity is an intimidating concept—one where our everyday intuition no longer servers to guide us."

As you (known by the name of "reader") and I are in a manner perfect strangers to each other, before finding our three types, we shall start 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 (your worship) 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 (wether she was deceiving or deceived in this manner) really hates them. There are so many examples of this dismally 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 (though in no way becomes me to decide). 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 (whose number has been lately worn down to a thread), hard-nosed economists, bureaucrats &/or famous CEOs (who presently are legion). Choose and vituperate it out & aloud—with abhorrence.

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. Blessed be the Lord, they definitely don't belong to any of our three categories, remaining (with great candor & modesty) baffled & overthrown.

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]:

- Anaximander;

- Melissos;

- Zeno;

- Democritus;

- Plato (?);

- Epicuros (?);

- Archimedes (?);

- Lucretius (?);

- Hasdai Crescas (?);

- Nicolas of Cusa;

- Girolamo Cardano (?);
- Giordano Bruno;

- Johannes Kepler (?);
- Galileo Galilei (?);

- Blaise Pascal;

- Torricelli (?);

- Girard Desargues (?);

- John Wallis (?);
- G. W. Leibniz (?);

- Newton (?);

- Euler (?);
- Salomon Maimon;

- Jean Baptiste Bordas-Demoulin;

- Höené Wronski;
- Bernhard Bolzano;
- Bernhard Riemann (?);
- Kingdon Clifford (?);
- Karl Weierstrass (?);

- Baudelaire! ("Tout cerveau bien conformé porte en lui deux infinis, le ciel et l'enfer...");
- Nietzsche (?);

- Charles Sanders Peirce (?);
- Sonja Kowalewski (?);
- Gösta Mittag-Leffler (?);

- Richard Dedekind;
- Georg Cantor;

- Pavel Florensky;

- David Hilbert (?);

- Henri Bergson (?);

- Raymond Roussel (?);

- Melanie Klein (?);

- Jacques Lacan (?);
- Georges Bataille (?);
- Maurice Blanchot (?);
- Pierre Klossowski (?);

- Der Herr Warum;

- Andre Weil (?);

- Albert Lautman;

- Jules Vuillemin (?);

- Claude Lévi-Strauss (?);

- 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..."];

- Alexander Grothendieck (?);

- Paul Cohen (?);

- Hugh Woodin (?);

- Alain Connes (?);

- Fernando Zalamea (?);

- me (which I own);

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 francisé passage from Nietzsche (no muddle-headed): "Il y a des vies où les difficultés touchent au prodige; ce sont les vies 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:

Did Poincaré say set theory is a disease? According to Jeremy Gray, it seems he didn't.

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).

About

Distinctively & as immemorially concocted in the Anti-Shandean pasquils of the likes of G. Richter & F. Wedmore (against which they till nowadays survive), the posts here assembled have a merit of their own many do not wish to understand (and have little to recommend save the eccentricity of their titles). They do not feel much, though a few find genious in insanity and amateur prodigy (popularity is the only insult that has not yet been offered me, since years ago I became a person of high promise; scandal—oh mystère effroyable, paradoxe, aporie: trop d'exemples, un à chaque pas, aaaaai, larvale simulacrum, tô com fome! however, is an insidious form of fame). Quis ille? Paucis accipe: of a breed holding by ancient roots to the heights of Rotzo (& later marooned in the bogs of the land of the Southern lapwing), Alessandro Zir is PhD in Interdisciplinary Studies by Dalhousie University (Halifax, Canada), where Ian Hacking was the external (& eternal) examiner of his thesis. He (the poor Wight of a Dedicator, homem sem profissão, sob as ordens de mamãe) has publications in Brazil, Canada, Chile, England, Germany, Poland, Portugal and USA, including a book (Luso-Brazilian Encounters of the Sixteenth Century, Lanham), and otherwise just "small" works such as chapters of books, literary and movie "criticism", papers, translations, and fragmentary fictional texts. As any good old & new kerosineshchik, he also plays the piano and has experimented with video and other arts. Among his translations (not even mentioned for the Jabuti you never heard about) are books from Agatha Christie, Conan Doyle, Georges Simenon, Charles Baudelaire and Petronius (CV in English and Portuguese). Living in a bye corner of the kingdom.

Clarification

About the many quotations you find in these posts: they appear within quotation marks and an author is always identified. In the case of fiction, I might occasionally attribute them directly to the characters. More rarely, I may even use a nickname for the author. In any case I don't bother to give full details for most quotations (page, year, publishing house, even title!), because the purpose of this site is to stimulate people to think, and do their own research. Almost all of the content of these quotations were transcribed by hand from printed books while I was reading them, with the exception of quotes from news articles in my clippings. Everything is curated through my careful reading, selection and editing. On the one hand, I work here like an "arranger," in the same way James Joyce's narrator was characterized by people like David Hayman. On the other hand, I leave traces for future developments, for my own work and the work of others.

Financial Support

Since 2018 I stopped being dependent on universities, whose system (with its royalties and signories, rights and jurisdictions, privileges & hereditaments) I believe is in degeneracy and utterly corrupt. In the twilight of so-called "liberal" societies, both private corporations and public bureaucracies fight among themselves for the trophies of the final consummation of human stupidity and evil. They are allies. Actually, for cultivated and creative individuals, everywhere became like the Neue Musik cubbbyhole: "Man muß schon taubstumme Eltern haben oder mit einer namhaften feministischen Schriftstellerin zusammen arbeiten, um als Komponist die Aufmerksamkeit der Öffentlichkeit auf sich zu ziehen... comissioni, borse di studio, forme di sostegno e promozione vengono quasi interamente erogate per ricompensare il carrierismo, l'opportunismo e ogni mancanza di vigore" (Claus-Steffen Mahnkopf). To support my intellectual independence, you can buy my art works at Fine Art America, and Urban Arts, or my books at Amazon. Besides, you can also donate: PIX 88182207053, Banco do Brasil (Agência 2817-7, Conta Corrente 7245-1). Any value (of good and lawful money) is helpful.