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);
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)
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)
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."
"'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)
"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)
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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).
More on Pauli:
"Pauli was never what our expert in didactics would call a good lecturer. Nevertheless he was an inspiring and intoxicating teacher. In particular when he was not too well prepared (this happened not infrequently), one could experience the spirit in statu nascendi, and this was awesome. With his ruthless demand for precision and lucidity Pauli never intended to hurt his students or colleagues. His sharp tongue notwithstanding, his criticism was always honest and reflected not only his dislike of half-truths but also his demonic depths... In despite of his critical stance, he was certainly not one of these petty reasoning minds which cannot endure any paradoxes," Harald Atmanspacher's & Hans Primas's "The Hidden Side of Wolfgang Pauli," Journal of Consciousness Studies, 3, 2, 1996, pp. 112-26.
"Impossible de dire quelques mots sur la place de Pauli dans les écrits de Bachelard sans rappeler qu’il était l’homme des boutades et du Witz, c’est-à-dire quelqu’un de profondément 'spirituel'. Lors d’un séminaire, John von Neumann démontrait un théorème au tableau; Pauli l’apostrophe: 'Si faire de la physique, c’était démontrer des théorèmes, tu serais un grand physicien.' C’est ainsi qu’il terrorisait un peu tous les autres physiciens de par le monde, y compris Louis de Broglie ou Werner Heisenberg qui fuyaient littéralement les colloques où il était présent," Charles Alunni, L'École de l'ETH dans l'oeuvre de Gaston Bachelard, Revue de synthèse: 5 Série, année 2005/2.
More on fairies & witches:
"I'm hitting art from both sides of the brain. I used to be really into math and science in school, I was a bit of a nerd. I was into quantum physics and all the strange magic that exists there. All of the ideas that an intuitive mind might come up with can be proven on a microscopic scientific level. I saw my fairy godmother the other day. We were talking about the future and I was stressed out, and she was like, "Just remember you're a witch." It was so cool to hear her say that in a chill way, just a casual thing to say. Ever since I was little I believed in stuff beyond what I could see. You could also just call that having an imagination, but I believed so much in it and how to manifest all of my dreams," India Salvor Menuez (Vice interview);
***To raise the dead— &/or evidence for the villainous affair, the tale of family disonour, Romish church's pact with the devil (considered the greatest outrage against sense and decency, to be plagued and pestered, though solemnly ratified, à Dieu rien n'est impossible, menteur avéré, nom d'un chien):
"Although Greek names were sometimes applied to the church modes and the principle of diatonic octave scales is found in both systems, certain significant discrepancies seem to belie any direct historical connection. Most conspicuous is the different meaning attributed to the names of the Greek octave species and of the church modes. Comparing the two systems provides a plausible explanation: medieval theorists apparently assumed wrongly that the Greek octave species were named in ascending rather than descending order. The Greek octave species Dorian (E–E), Phrygian (D–D), Lydian (C–C), and Mixolydian (B–B) thus appeared in the church modes as Dorian (D–D), Phrygian (E–E), Lydian (F–F), and Mixolydian (G–G)," (from "Mode," entry in Brittanica, by Mieczyslaw Kolinski);
- actual infinite falling (against Carlo Rovelli's pseudo-problem);
- the odd transformation of Der Herr Warum (Gödel with Resnais);
- the only three types of ingenuity;
- why self-help books are not to be dismissed;
- the most auspicious tetrahedron;
- what is REAL space? what is REAL number?
- Timothy Leary in the 1990s;
- 5G?! Get real...
- list of charming scientists/engineers;
- pick a soul (ass you wish);
- view from Berthe Trépat's apartment;
- list des déclencheurs musicaux;
- Dark Consciousness;
- The Doors of Perception;
- Structuralism, Poststructuralism;
- List des figures du chaos primordial (Deleuze);
- Brazilian Perspectivism (Viveiros de Castro vs. Haroldo de Campos);
- Piano Playing (Kochevitsky);
- L'Affirmation de l'âne (review of Smolin/Unger's The Singular Universe);
And also (with the whole of it):
- Spooky Blue;
*****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;
