Musée d'Orsay/January 2018 (for more A/Z photography see portfolio here);

Clara Colosimo in Fellini's Prova d'orchestra;

Arquipélago dos Pombos Correios (o soverdouro);

The great abyss inframince (by A/Z, for more see here);

"... the term quantum mechanics is very much a misnomer. It should, perhaps, be called quantum nonmechanics..."

David Bohm

"Ich komme aus Höhen, die kein Vogel je erflog, ich kenne Abgründe, in die noch kein Fuß sich verirrt hat..."

"Vor mir giebt es diese Umsetzung des dionysischen in ein philosophisches Pathos nicht."

"... ein vollkommnes Ausser-sich-sein mit dem distinktesten Bewusstsein einer Unzahl feiner Schauder und Überrieselungen bis in die Fusszehen; eine Glückstiefe, in der das Schmerzlichste und Düsterste nicht als Gegensatz wirkt, sondern als bedingt, als herausgefordert, sondern als eine nothwendige Farbe innerhalb eines solchen Lichtüberflusses; ein Instinkt rhythmischer Verhältnisse, der weite Räume von Formen überspannt..."

Nietzsche

"But he wants The Cold like he wants His Junk—NOT OUTSIDE where it does him no good but INSIDE so he can sit around with a spine like a frozen hydraulic jack..."

"Because Fats' nerves were raw and peeled to feel the death spasms of a million cold kicks... Fats learned The Algebra of Need and survived..."

"Cure is always:

"Because Fats' nerves were raw and peeled to feel the death spasms of a million cold kicks... Fats learned The Algebra of Need and survived..."

"Cure is always:

*Let Go! Jump!*"
William S. Burroughs

"Ihr verehrt mich: aber wie, wenn eure Verehrung eines Tages umfällt?""Ich komme aus Höhen, die kein Vogel je erflog, ich kenne Abgründe, in die noch kein Fuß sich verirrt hat..."

"Vor mir giebt es diese Umsetzung des dionysischen in ein philosophisches Pathos nicht."

"... ein vollkommnes Ausser-sich-sein mit dem distinktesten Bewusstsein einer Unzahl feiner Schauder und Überrieselungen bis in die Fusszehen; eine Glückstiefe, in der das Schmerzlichste und Düsterste nicht als Gegensatz wirkt, sondern als bedingt, als herausgefordert, sondern als eine nothwendige Farbe innerhalb eines solchen Lichtüberflusses; ein Instinkt rhythmischer Verhältnisse, der weite Räume von Formen überspannt..."

Nietzsche

"... 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. Non-blanc, nous avons tous à le devenir, que nous soyons blancs, jaunes ou noirs."

Deleuze & Guattari

"Eighteenth-century masters achieved most pleasing effects with forgrounds of warm brown and fading distances of cool, silvery blues... Constable wanted to try out the effect of respecting the local color of grass somewhat more, in his

Ernst H. Gombrich (Art and Illusion)

"Oboukhoff acumule alors en un étroit espace les demi-tons; la sensation est déchirante, horripilante... Avec le glissando, c'est tout l'infini du monde sonore qui fait irruption dans la musique tempérée..."

Boris de Schloezer (1925)

"Eighteenth-century masters achieved most pleasing effects with forgrounds of warm brown and fading distances of cool, silvery blues... Constable wanted to try out the effect of respecting the local color of grass somewhat more, in his

*Wivenhoe Park*he is seen pushing the range more in the direction of bright greens. Only in the direction of, it is a transposition, not a copy."Ernst H. Gombrich (Art and Illusion)

"Oboukhoff acumule alors en un étroit espace les demi-tons; la sensation est déchirante, horripilante... Avec le glissando, c'est tout l'infini du monde sonore qui fait irruption dans la musique tempérée..."

Boris de Schloezer (1925)

"Note the parallels between ordinary awareness, classical physics, and the natural and counting integers..."

Dean Radin (Real Magic)

"É a luz que dá o salto e cria toda mágica do espetáculo."

Ney Matogrosso

"É a luz que dá o salto e cria toda mágica do espetáculo."

Ney Matogrosso

###
*Vestibule*:

This is AGAINST Carlo Rovelli's

*dictum*or pseudo-problem: "

*visto que tudo se atrai, a única maneira de um Universo finito não desmoronar sobre si mesmo é que se expanda*" [since all things attract one another, the only way a finite Universe can avoid collapse is to expand] (

*A realidade não é o que parece*, p. 105)—but why should one use the term "finite" (or even "infinite") to describe a universe with no definite borders (like a 3-sphere, or something even more complex)? The infinite is not equivalent to the

*huge*. The infinite is simply (according to Dedekind) what can be matched up to its own parts (the only reason to deny this is hysteria, paradox-freakishness). The universe (the

*chaosmos*) both expands & collapse! As a whole and at the length of its space-time infinitesimals (or epsilon-delta limits, whatever), the macro/micro contractions, the revolving ruminations (what Rovelli confusedly calls "granulations," as if they were incompatible with any notion of continuity) of an autophagic real-virtual Einsteinian mollusk. If you have three fundamental constants (as Rovelli suggests,

*A realidade não é o que parece*, p. 229), velocity [of light], information and Planck's length (

*c*,

*ħ*,

*ℓp*), what matters is the relation among them (which might be revealed in established, finite proportions) not each one of their supposedly fixed (absolute) values (and even the relation might vary, fluctuate). Otherwise you behave like a very stupid painter arguing over the positive value of (what we call) green or brown in the transposition of tonal gradations to canvas.

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

###
*Main Hall*:

Time out of joints or the excessive solution (academically and sophistically called 'the measurement problem'):

"If quantum state evolution proceeds via the Schrödinger equation or some other linear equation, then, as we have seen in the previous section, typical experiments will lead to quantum states that are superpositions of terms corresponding to distinct experimental outcomes. It is sometimes said that this conflicts with our experience, according to which experimental outcome variables, such as pointer readings, always have definite values. This is a misleading way of putting the issue, as it is not immediately clear how to interpret states of this sort as physical states of a system that includes experimental apparatus, and, if we can’t say what it would be like to observe the apparatus to be in such a state, it makes no sense to say that we never observe it to be in a state like that," Wayne Myrvold's "Philosophical Issues in Quantum Mechanics,"

*Stanford Encyclopedia of Philosophy*.
"... von Neumann makes the logical structure of quantum theory very clear by identifying two very different processes, which he calls process 1 and process 2... Process 2 is the analogue in quantum theory of the process in classic physics that takes the state of a system at one time to its state at a later time. This process 2, like its classic analogue, is local and deterministic. However, process 2 by itself is not the whole story: it generates a host of ‘physical worlds’, most of which do not agree with our human experience. For example, if process 2 were, from the time of the big bang, the only process in nature, then the quantum state (centre point) of the moon would represent a structure smeared out over a large part of the sky, and each human body–brain would likewise be represented by a structure smeared out continuously over a huge region. Process 2 generates a cloud of possible worlds, instead of the one world we actually experience...," Jeffrey M. Schwartz's, Henry P. Stapp's and Mario Beauregard's "Quantum physics in neuroscience and psychology: a neurophysical model of mind–brain interaction,"

*Philosophical Transactions of the Royal Society*(2005).
"... a seminal discovery by Heisenberg... in order to get a satisfactory quantum generalization of a classic theory one must replace various numbers in the classic theory by actions (operators). A key difference between numbers and actions is that if A and B are two actions then AB represents the action obtained by performing the action A upon the action B. If A and B are two different actions then generally AB is different from BA: the order in which actions are performed matters. But for numbers the order does not matter: AB=BA. The difference between quantum physics and its classic approximation resides in the fact that in the quantum case certain differences AB–BA are proportional to a number measured by Max Planck in 1900, and called Planck’s constant. Setting those differences to zero gives the classic approximation," Jeffrey M. Schwartz's, Henry P. Stapp's and Mario Beauregard's "Quantum physics in neuroscience and psychology: a neurophysical model of mind–brain interaction,"

"When we say that we wish to make sense of something we meant o put it into spacetime terms, the terms of Euclidean geometry, clock time, etc. The Fourier transform domain is potential to this sensory domain. The waveforms which compose the order present in the electromagnetic sea which fills the universe make up an interpenetrating organization similar to that which characterizes the waveforms "broadly cast" by our radio and television stations. Capturing a momentary cut across these airwaves would constitute their hologram. The broadcasts are distributed and at any location they are enfolded among one another. In order to make sense of this cacophany of sights and sounds, one must tune in on one and tune out the others. Radios and television sets provide such tuners. Sense organs provide the mechanisms by which organisms tune into the cacophany which constitutes the quantum potential organization of the elecromagnetic energy which fills the universe," Karl Pribram's "The Implicate Brain";

"... the cloud chamber photograph does not reveal a “solid” particle leaving a track. Rather it reveals the continual unfolding of process with droplets forming at the points where the process manifests itself. Since in this view the particle is no longer a point-like entity, the reason for quantum particle interference becomes easier to understand. When a particle encounters a pair of slits, the motion of the particle is conditioned by the slits even though they are separated by a distance that is greater than any size that could be given to the particle. The slits act as an obstruction to the unfolding process, thus generating a set of motions that gives rise to the interference pattern," Basil J. Hiley's "Mind and matter: aspects of the implicate order described through algebra" (in K. H. Pribram's and J. King's

"Let us... ask what the algebraic structure tells you about the underlying phase space. Because the algebra is non-commutative there is no single underlying manifold. That is a mathematical result. Thus if we take the algebra as primary then there is no underlying manifold we can call the phase space. But we already know this. At present we say this arises because of the 'uncertainty principle,' but nothing is 'uncertain,'" Basil Hiley's "From the Heisenberg Picture to Bohm: a New Perspective on Active Information and its relation to Shannon Information" (in A. Khrennikov, Proc. Conf.

"What Gelfand showed was that you could either start with an a priori given manifold and construct a commutative algebra of functions upon it or one could start with a given commutative algebra and deduce the properties of a unique underlying manifold. If the algebra is non-commutative it is no longer possible to find a unique underlying manifold. The physicist’s equivalent of this is the uncertainty principle when the eigenvalues of operators are regarded as the only relevant physical variables. What the mathematics of non-commutative geometry tells us is that in the case of a non-commutative algebra all we can do is to find a collection of shadow manifolds... The appearance of shadow manifolds is a necessary consequence of the non-commutative structure of the quantum formalism," Basil Hiley's "Phase Space Descriptions of Quantum Phenomena" (in A. Khrennikov,

*Philosophical Transactions of the Royal Society*(2005).
"At their narrowest points, calcium ion channels are less than a nanometre in diameter... The narrowness of the channel restricts the lateral spatial dimension. Consequently, the lateral velocity is forced by the quantum uncertainty principle to become large. This causes the quantum cloud of possibilities associated with the calcium ion to fan out over an increasing area as it moves away from the tiny channel to the target region... This spreading of this ion wave packet means that the ion may or may not be absorbed on the small triggering site. Accordingly, the contents of the vesicle may or may not be released... the quantum state of the brain splits into a vast host of classically conceived possibilities, one for each possible combination of the release-or-no-release options at each of the nerve terminals... a huge smear of classically conceived possibilities," Jeffrey M. Schwartz's, Henry P. Stapp's and Mario Beauregard's "Quantum physics in neuroscience and psychology: a neurophysical model of mind–brain interaction,"

"... waves make diffraction patterns precisely because multiple waves can be at the same place at the same time, and a given wave can be at multiple places at the same time... by definition particles are localized entities that take up space, they can be here or there, but not in two places at once. However it turns out that particles can produce diffraction patterns under specific circumstances... a given particle can be in a state of superposition... to be in a state of superposition between two positions, for exemple, is not to be here or there or even here and there, but rather it is to be indeterminately here-there. That is, it is not simply that the position is unknown, but rather there is no fact of the matter to whether it is here or there... it is a matter of ontological indeterminacy and not merely epistemological uncertainty... patterns of difference... are arguably at the core or what matter is and are at the heart of how quantum physics understands the world... the quantum probabilities are calculated by taken account of all the possible paths connecting the points. In other words, a given particle that starts out here and winds up there is understood as is understood to be in a superposition of all possible paths between two points. Or in its four dimensional quantum field theory elaboration, all possible space-time histories... the very meaning of superposition is that all possible histories are happening together, they all coexist and mutually contribute to this overall pattern or else there wouldn't be a diffraction pattern..." Karen Barad's "Troubling Time's & Ecologies of Nothingness,"

"Quantum physics opens up another possibility beyond the relatively familiar phenomena of spatial diffraction, namely, temporal diffraction. The existence of temporal diffraction is due to a less well-known indeterminacy principle than the usual position/momentum indeterminacy principle... something call the energy/time indeterminacy principle. This indeterminacy principle plays a key role in quantum field theory... temporalities are not merely multiple, but rather temporalities are specifically entangled and threaded through one another such that there is no determinate answer to the question

"During the waning decades of the 20th century, the most murdering century by some accounts in history, the notion that the past might be open to revision through a quantum erasure came to the fore. The quantum erasure experiment is a variation of the two slit diffraction experiment, an experiment which Feynman said contains all the mysteries of quantum physics. Against this fantastic claim of the possibility of erasure, I will claim that in paying close attention to the material labours entailed the claim of erasure possibility fades, at least full erasure, while at the same time bringing to the forth a relational ontology sensibility to questions of time, memory and history... the nature of time and being, or rather time-being itself is in question and can't be assumed. What this experiment tells us is not simply that a given particle would have done something different in the past, but that the very nature of its being, its ontology, in the past remains open to future reworkings... In particular I argue that this experiment offers empirical evidence for a relational ontology or perhaps more accurately a hauntology as against a metaphysics of presence... Remarkably this experiment makes evident that entanglement survives the measurement process and further more that material traces of attempts at erasure can be found in tracing the entanglements... While the past is never finished, and the future is not what would unfold, the world holds or rather is the memories of its iterated reconfigurings" Karen Barad's "Troubling Time's & Ecologies of Nothingness,"

"If classical physics insists that the void has no matter and no energy, the quantum principle of ontological indeterminacy, and particularly the indeterminacy relation between energy and time, pose into question the existence of such a zero energy, zero matter state... the indeterminacy principle allows for fluctuations of the vacuum... the vacuum is far from empty, it is fill with all possible indeterminate yearnings of space-time mattering... we can understand vacuum fluctuation in terms of virtual particles. Virtual particles are the quanta of the vacuum fluctuations... the void is a spectral ground, not even nothing can be free of ghosts... there is infinite number of possibilities, but not everything is possible. The vacuum isn't empty but neither is anything in it... particles together with their antiparticles and pairs can be created out of the vacuum by putting the right amount of energy into the vacuum... So, similarly, particles together with their antiparticles and pairs can go back into the vacuum, emitting the excess energy" Karen Barad's "Troubling Time's & Ecologies of Nothingness,"

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

###

"This was on Friday afternoon. Saturday morning I awoke early and read the two papers. Bohm, in simple clear language, declared that indeed there were conceptual problems in both macro- and microphysics, and that they were not to be swept under the carpet... And, further, Bohm suggested that the root of those problems was the fact that conceptualizations in physics had for centuries been based on the use of lenses which objectify (indeed the lenses of telescopes and microscopes are called objectives). Lenses make objects, particles," Karl Pribram's "The Implicate Brain";

"An equally important step in understanding came at a meeting at the University of California in Berkley, in which Henry Stapp and Geoffrey Chew of the Department of Physics pointed out that most of quantum physics, including their bootstrap formulations based on Heisenberg's scatter matrices, were described in a domain which is the Fourier transform of the spacetime domain. This was of great interest to me because Russell and Karen DeValois of the same university had shown that the spatial frequency encoding displayed by cells of the visual cortex was best described as a Fourier transform of the input pattern. ***The Fourier theorem states that any pattern, no matter how complex, can be analyzed into regular waveform components of different frequencies, amplitudes, and (phase) relations among frequencies. Further, given such components, the original pattern can be reconstructed. This theorem was the basis for Gabor's invention of holography," Karl Pribram's "The Implicate Brain";

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

[***when different wave patterns meet, they add up to form new patterns; you can analyse complex wave patterns as if they were a superposition of more simple waves, which have, for instance a definite, uniforme wavelength; the illustration at left is taken from the site of professor John D. Norton (Pittsburg University): "Einstein for Everyone"; it is important to note that real wave patterns studied in physics are much more complex than this two dimensional representation, and that they are ultimately formed by something that is neither strictly speaking a wave nor a particle as these are classically understood; I shall also say that not all John D. Norton's explanations given in the referred site seem very enlightening to me]

(see picture above)

From Maxwell's equations, we should expect an infinite number of frequencies of electromagnetic waves (or radiation, which includes visible light, and waves whose frequencies are bellow the one which produces the red colour, such as radio waves, and also waves whose frequencies are above the one which produces the violet colour, such gama rays). All these electromagnetic waves travel at what is called the speed of light (the frequencies can vary because the wavelength also varies proportionally) and constitute the

*Philosophical Transactions of the Royal Society*(2005)."... waves make diffraction patterns precisely because multiple waves can be at the same place at the same time, and a given wave can be at multiple places at the same time... by definition particles are localized entities that take up space, they can be here or there, but not in two places at once. However it turns out that particles can produce diffraction patterns under specific circumstances... a given particle can be in a state of superposition... to be in a state of superposition between two positions, for exemple, is not to be here or there or even here and there, but rather it is to be indeterminately here-there. That is, it is not simply that the position is unknown, but rather there is no fact of the matter to whether it is here or there... it is a matter of ontological indeterminacy and not merely epistemological uncertainty... patterns of difference... are arguably at the core or what matter is and are at the heart of how quantum physics understands the world... the quantum probabilities are calculated by taken account of all the possible paths connecting the points. In other words, a given particle that starts out here and winds up there is understood as is understood to be in a superposition of all possible paths between two points. Or in its four dimensional quantum field theory elaboration, all possible space-time histories... the very meaning of superposition is that all possible histories are happening together, they all coexist and mutually contribute to this overall pattern or else there wouldn't be a diffraction pattern..." Karen Barad's "Troubling Time's & Ecologies of Nothingness,"

*European Graduate School Video Lectures*(YouTube), my transcription."Quantum physics opens up another possibility beyond the relatively familiar phenomena of spatial diffraction, namely, temporal diffraction. The existence of temporal diffraction is due to a less well-known indeterminacy principle than the usual position/momentum indeterminacy principle... something call the energy/time indeterminacy principle. This indeterminacy principle plays a key role in quantum field theory... temporalities are not merely multiple, but rather temporalities are specifically entangled and threaded through one another such that there is no determinate answer to the question

*what time is it?*Karen Barad's "Troubling Time's & Ecologies of Nothingness,"*European Graduate School Video Lectures*(YouTube), my transcription."During the waning decades of the 20th century, the most murdering century by some accounts in history, the notion that the past might be open to revision through a quantum erasure came to the fore. The quantum erasure experiment is a variation of the two slit diffraction experiment, an experiment which Feynman said contains all the mysteries of quantum physics. Against this fantastic claim of the possibility of erasure, I will claim that in paying close attention to the material labours entailed the claim of erasure possibility fades, at least full erasure, while at the same time bringing to the forth a relational ontology sensibility to questions of time, memory and history... the nature of time and being, or rather time-being itself is in question and can't be assumed. What this experiment tells us is not simply that a given particle would have done something different in the past, but that the very nature of its being, its ontology, in the past remains open to future reworkings... In particular I argue that this experiment offers empirical evidence for a relational ontology or perhaps more accurately a hauntology as against a metaphysics of presence... Remarkably this experiment makes evident that entanglement survives the measurement process and further more that material traces of attempts at erasure can be found in tracing the entanglements... While the past is never finished, and the future is not what would unfold, the world holds or rather is the memories of its iterated reconfigurings" Karen Barad's "Troubling Time's & Ecologies of Nothingness,"

*European Graduate School Video Lectures*(YouTube), my transcription."If classical physics insists that the void has no matter and no energy, the quantum principle of ontological indeterminacy, and particularly the indeterminacy relation between energy and time, pose into question the existence of such a zero energy, zero matter state... the indeterminacy principle allows for fluctuations of the vacuum... the vacuum is far from empty, it is fill with all possible indeterminate yearnings of space-time mattering... we can understand vacuum fluctuation in terms of virtual particles. Virtual particles are the quanta of the vacuum fluctuations... the void is a spectral ground, not even nothing can be free of ghosts... there is infinite number of possibilities, but not everything is possible. The vacuum isn't empty but neither is anything in it... particles together with their antiparticles and pairs can be created out of the vacuum by putting the right amount of energy into the vacuum... So, similarly, particles together with their antiparticles and pairs can go back into the vacuum, emitting the excess energy" Karen Barad's "Troubling Time's & Ecologies of Nothingness,"

*European Graduate School Video Lectures*(YouTube), my transcription.**************************************************************

###
*Labyrinthine corridors, rooms*:* *

"An equally important step in understanding came at a meeting at the University of California in Berkley, in which Henry Stapp and Geoffrey Chew of the Department of Physics pointed out that most of quantum physics, including their bootstrap formulations based on Heisenberg's scatter matrices, were described in a domain which is the Fourier transform of the spacetime domain. This was of great interest to me because Russell and Karen DeValois of the same university had shown that the spatial frequency encoding displayed by cells of the visual cortex was best described as a Fourier transform of the input pattern. ***The Fourier theorem states that any pattern, no matter how complex, can be analyzed into regular waveform components of different frequencies, amplitudes, and (phase) relations among frequencies. Further, given such components, the original pattern can be reconstructed. This theorem was the basis for Gabor's invention of holography," Karl Pribram's "The Implicate Brain";

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

[***when different wave patterns meet, they add up to form new patterns; you can analyse complex wave patterns as if they were a superposition of more simple waves, which have, for instance a definite, uniforme wavelength; the illustration at left is taken from the site of professor John D. Norton (Pittsburg University): "Einstein for Everyone"; it is important to note that real wave patterns studied in physics are much more complex than this two dimensional representation, and that they are ultimately formed by something that is neither strictly speaking a wave nor a particle as these are classically understood; I shall also say that not all John D. Norton's explanations given in the referred site seem very enlightening to me]

(see picture above)

From Maxwell's equations, we should expect an infinite number of frequencies of electromagnetic waves (or radiation, which includes visible light, and waves whose frequencies are bellow the one which produces the red colour, such as radio waves, and also waves whose frequencies are above the one which produces the violet colour, such gama rays). All these electromagnetic waves travel at what is called the speed of light (the frequencies can vary because the wavelength also varies proportionally) and constitute the

*electromagnetic spectrum*. High frequency means also high photon energy. The photon energy is related to how single atoms of different material objects can absorb and emit electromagnetic waves, which happens always in quantum discrete amounts. As concrete musical instruments, atoms can produce oscillations only in certain restricted ways, and they do so very energetically. The physical production of what we perceive as forms and colours has to do, however, more directly with the way electromagnetic waves travel much more freely and continuously in space, through, for instance, air or water, interfering (constructively or destructively) with one another, interacting with molecules—and we are talking about electromagnetic waves of lower energy and frequencies, which are visible. What we see, although, isn't everything.
Does the continuum (infinitely divisible) preclude plurality? Does the discrete precludes unity? Of course no! Except for the lack of imagination of the purist & prudish. But thanks gosh, in philosophy we also have Leibniz's "

*Natura non facit saltus,"*and Peirce's synechism (everything is connected), the immemorial and unending, irreducible battles between the*one*and the*many**.*Why should people be so afraid of a conundrum of straight lines, curves, and points (which besides going for these one- and two-dimensions, can be extrapolated to n-)? Infinitesimals, differentials, and limits, what is the*real difference*? Epsilon-delta definition (Cauchy, Bolzano, Weierstrass) and nonstandard analysis (Abraham Robinson) are all in the end perfectly compatible. Add to that*synthetic differential geometry*or*the smooth infinitesimal*(F. W. Lawvere), whatever! The actual infinite—everything else starts from it!*Just don't be afraid of lingo*—the science wars are an affair of securing university bonus in times of economic havoc. And don't forget that continuity doesn't have to be only local, that is, the chaosmos is full of nonlocal connections, the innermost separations! What matters is attitude, not content or specific formulations.
["Whenever a point x is within δ units of c, f(x) is within ε units of L," graphic and definition from the

["Infinitesimals (ε) and infinites (ω) on the hyperreal number line (1/ε = ω/1)," graphic and definition from

(see picture above)

"Cusanus... took the circle to be an infinilateral regular polygon, that is, a regular polygon with an infinite number of (infinitesimally short) sides... The idea of considering a curve as an infinilateral polygon was employed by a number of later thinkers, for instance, Kepler, Galileo and Leibniz... Traditionally, geometry is the branch of mathematics concerned with the continuous and arithmetic (or algebra) with the discrete. The infinitesimal calculus that took form in the 16th and 17th centuries, which had as its primary subject matter

"... science needs calculus; calculus needs the continuum; the continuum needs a very careful definition; and the best definition requires there to be actual infinities (not merely potential infinities) in the micro-structure and the overall macro-structure of the continuum... Informally expressed [for Dedekind], any infinite set can be matched up to a part of itself; so the whole is equivalent to a part. This is a surprising definition because, before this definition was adopted, the idea that actually infinite wholes are equinumerous with some of their parts was taken as clear evidence that the concept of actual infinity is inherently paradoxical... [Cantor's] new idea [similar to Dedekind's] is that the potentially infinite set presupposes an actually infinite one. If this is correct, then Aristotle’s two notions of the potential infinite and actual infinite have been redefined and clarified," Bradley Dowden's "The Infinite" (

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

###

*Wikipedia*'s epsilon-delta entry ]["Infinitesimals (ε) and infinites (ω) on the hyperreal number line (1/ε = ω/1)," graphic and definition from

*Wikipedia*'s hyperreal number entry](see picture above)

"Cusanus... took the circle to be an infinilateral regular polygon, that is, a regular polygon with an infinite number of (infinitesimally short) sides... The idea of considering a curve as an infinilateral polygon was employed by a number of later thinkers, for instance, Kepler, Galileo and Leibniz... Traditionally, geometry is the branch of mathematics concerned with the continuous and arithmetic (or algebra) with the discrete. The infinitesimal calculus that took form in the 16th and 17th centuries, which had as its primary subject matter

*continuous variation*, may be seen as a kind of synthesis of the continuous and the discrete, with infinitesimals bridging the gap between the two. The widespread use of indivisibles and infinitesimals in the analysis of continuous variation by the mathematicians of the time testifies to the affirmation of a kind of mathematical atomism which, while logically questionable, made possible the spectacular mathematical advances with which the calculus is associated. It was thus to be the infinitesimal, rather than the infinite, that served as the mathematical stepping stone between the continuous and the discrete," John L. Bell's "Continuity and Infinitesimals" (*Stanford Encyclopedia of Philosophy*) [I like this passage very much, and this is a very useful article, but I'm not subscribing in detail to all ideas Bell developed there];"... science needs calculus; calculus needs the continuum; the continuum needs a very careful definition; and the best definition requires there to be actual infinities (not merely potential infinities) in the micro-structure and the overall macro-structure of the continuum... Informally expressed [for Dedekind], any infinite set can be matched up to a part of itself; so the whole is equivalent to a part. This is a surprising definition because, before this definition was adopted, the idea that actually infinite wholes are equinumerous with some of their parts was taken as clear evidence that the concept of actual infinity is inherently paradoxical... [Cantor's] new idea [similar to Dedekind's] is that the potentially infinite set presupposes an actually infinite one. If this is correct, then Aristotle’s two notions of the potential infinite and actual infinite have been redefined and clarified," Bradley Dowden's "The Infinite" (

*Internet Encyclopedia of Philosophy*) [I like this passage very much, and this is a very useful article, but I'm not subscribing in detail to all ideas Dowden developed there];**************************************************************

"... in Quantum Electrodynamics... processes of much greater complexity [than a simple electron-electron scattering] could intervene in the scattering process. For example, the exchanged photon could convert to an electron-positron pair which would subsequently recombine... or one of the incoming electrons might emit a photon and reabsorb it on the way out... in general, the exchange of arbitrarily large numbers of photons, electrons and positrons can contribute to electromagnetic interactions... very complicated multiparticle exchanges have to be taken into account in the analysis of physical systems. Indeed, no exact solutions to the Quantum Electrodynamics are known, nor have such solutions ever been shown rigorously to exist [but precise approximations are possible]," Andrew Pickering's

"... in quantum field theory all forces are mediated by particle exchange... It is equally important to stress that the exchanged particles... are not observable... To explain why this is so, it is necessary to make a distinction between 'real' and 'virtual' particles... particles with unphysical values of energy and momentum are said to be 'virtual' or 'off mass-shell' particles. In classical physics they could not exist at all... In quantum physics, in consequence of the Uncertainty Principle, virtual particles can exist, but only for an infinitesimal and experimentally undetectable length of time. In fact, the lifetime of a virtual particle is inversely dependent upon how far its mass diverges from its physical value," Andrew Pickering's

"In quantum mechanics the particles themselves can be represented as fields. An electron, for example, can be considered a packet of waves with some finite extension in space. Conversely, it is often convenient to represent a quantum mechanical field as if it were a particle. The interaction of two particles through their interpenetrating fields can then be summed up by saying the two particles exchange a third particle, which is called the quantum of the field. For example, when two electrons, each surrounded by an electromagnetic field, approach each other and bounce apart, they are said to exchange a photon, the quantum of the electromagnetic field. The exchanged quantum has only an ephemeral existence... The larger their energy, the briefer their existence. The range of an interaction is related to the mass of the exchanged quantum. If the field quantum has a large mass, more energy must be borrowed in order to support its existence, and the debt must be repaid sooner lest the discrepancy be discovered. The distance the particle can travel before it must be reabsorbed is thereby reduced and so the corresponding force has a short range. In the special case where the exchanged quantum is massless [such as a photon] the range is infinite," Gerard 't Hooft's "Gauge Theories of the Forces between Elementary Particles" (

*Constructing Quarks*(p. 63);"... in quantum field theory all forces are mediated by particle exchange... It is equally important to stress that the exchanged particles... are not observable... To explain why this is so, it is necessary to make a distinction between 'real' and 'virtual' particles... particles with unphysical values of energy and momentum are said to be 'virtual' or 'off mass-shell' particles. In classical physics they could not exist at all... In quantum physics, in consequence of the Uncertainty Principle, virtual particles can exist, but only for an infinitesimal and experimentally undetectable length of time. In fact, the lifetime of a virtual particle is inversely dependent upon how far its mass diverges from its physical value," Andrew Pickering's

*Constructing Quarks*(p. 64-65);"In quantum mechanics the particles themselves can be represented as fields. An electron, for example, can be considered a packet of waves with some finite extension in space. Conversely, it is often convenient to represent a quantum mechanical field as if it were a particle. The interaction of two particles through their interpenetrating fields can then be summed up by saying the two particles exchange a third particle, which is called the quantum of the field. For example, when two electrons, each surrounded by an electromagnetic field, approach each other and bounce apart, they are said to exchange a photon, the quantum of the electromagnetic field. The exchanged quantum has only an ephemeral existence... The larger their energy, the briefer their existence. The range of an interaction is related to the mass of the exchanged quantum. If the field quantum has a large mass, more energy must be borrowed in order to support its existence, and the debt must be repaid sooner lest the discrepancy be discovered. The distance the particle can travel before it must be reabsorbed is thereby reduced and so the corresponding force has a short range. In the special case where the exchanged quantum is massless [such as a photon] the range is infinite," Gerard 't Hooft's "Gauge Theories of the Forces between Elementary Particles" (

*Scientific American*, vol. 242, n. 6, 1980, pp. 104-141);
"It was not immediately apparent that quantum electrodynamics could qualify as a physically acceptable theory. One problem arose repeatedly in any attempt to calculate the result of even the simplest electromagnetic interactions, such as the interaction between two electrons. The likeliest sequence of events in such an encounter is that one electron emits a single virtual photon and the other electron absorbs it. Many more complicated exchanges are also possible, however; indeed, their number is infinite. For example, the electrons could interact by exchanging two photons, or three, and so on. The total probability of the interaction is determined by the sum of the contributions of all the possible events... Perhaps the best defense of the theory is simply that it works very well. It has yielded results that are in agreement with experiments to a n accuracy of about one part in a billion, which makes quantum electrodynamics the most accurate physical theory ever de vised," Gerard 't Hooft's "Gauge Theories of the Forces between Elementary Particles" (

"If an electron enters a medium composed of molecules that have positively and negatively charged ends, for example, it will polarize the molecules. The electron will repel their negative ends and attract their positive ends, in effect

"A nuvem de probabilidades que acompanha os elétrons entre uma interação e outra é um pouco parecida com um campo. Mas os campos de Faraday e Maxwell, por sua vez, são feitos de grãos: os fótons. Não apenas as partículas estão em certo sentido difusas no espaço como campos, mas também os campos interagem como partículas. As noções de campo e de partícula, separadas por Faraday e Maxwell, acabam convergindo na mecânica quântica. A forma como isso acontece na teoria é elegante: as equações de Dirac determinam quais valores cada variável pode assumir. Aplicadas à energia das linhas de Faraday, dizem-nos que essa energia pode assumir apenas certos valores e não outros... As ondas eletromagnéticas são de fato vibrações das linhas de Faraday, mas também, em pequena escala, enxames de fótons... Por outro lado, também os elétrons e todas as partículas de que é feito o mundo são 'quanta' de um campo... semelhante ao de Faraday e Maxwell," Carlo Rovelli's

"A 'nuvem' que representa os pontos do espaço onde é provável encontrar o elétron é descrita por um objeto matemático chamado 'função de onda.'O físico austríaco Erwin Schrödinger escreveu uma equação que mostra como essa função de onda evolui no tempo. Schrödinger esperava que a 'onda' explicasse as estranhezas da mecânica quântica... Ainda hoje alguns tentam entender a mecânica quântica pensando que a realidade é a onda de Schrödinger. Mas Heisenberg e Dirac logo compreenderam que esse caminho é equivocado. A função [de onda] não está no espaço físico, está em um espaço abstrato formado por todas as possíveis [virtuais!] configurações do sistema... A realidade do elétron não é uma onda [?]: é esse aparecer intermitente nas colisões," Carlo Rovelli's

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

*Scientific American*, vol. 242, n. 6, 1980, pp. 104-141);"If an electron enters a medium composed of molecules that have positively and negatively charged ends, for example, it will polarize the molecules. The electron will repel their negative ends and attract their positive ends, in effect

*screening itself*in positive charge. The result of the polarization is to reduce the electron's effective charge by an amount that in creases with distance... The uncertainty principle of Werner Heisenberg suggests... that the vacuum is not empty. According to the principle, uncertainty about the energy of a system increases as it is examined on progressively shorter time scales. Particles may violate the law of the conservation of energy for unobservably brief instants; in effect, they may materialize from nothingness. In QED [Quantum Electrodynamics] the vacuum is seen as a complicated and seething medium in which pairs of charged "virtual" particles, particularly electrons and positrons, have a fleeting existence. These ephemeral vacuum fluctuations are polarizable just as are the molecules of a gas or a liquid. Accordingly QED predicts that in a vacuum too electric charge will be screened and effectively reduced at large distances," Chris Quigg's Elementary Particles and Forces (*Scientific American*, vol. 252, n. 4, 1985, pp. 84-95);"A nuvem de probabilidades que acompanha os elétrons entre uma interação e outra é um pouco parecida com um campo. Mas os campos de Faraday e Maxwell, por sua vez, são feitos de grãos: os fótons. Não apenas as partículas estão em certo sentido difusas no espaço como campos, mas também os campos interagem como partículas. As noções de campo e de partícula, separadas por Faraday e Maxwell, acabam convergindo na mecânica quântica. A forma como isso acontece na teoria é elegante: as equações de Dirac determinam quais valores cada variável pode assumir. Aplicadas à energia das linhas de Faraday, dizem-nos que essa energia pode assumir apenas certos valores e não outros... As ondas eletromagnéticas são de fato vibrações das linhas de Faraday, mas também, em pequena escala, enxames de fótons... Por outro lado, também os elétrons e todas as partículas de que é feito o mundo são 'quanta' de um campo... semelhante ao de Faraday e Maxwell," Carlo Rovelli's

*A realidade não é o que parece*(Objetiva, 2014, p. 125);"A 'nuvem' que representa os pontos do espaço onde é provável encontrar o elétron é descrita por um objeto matemático chamado 'função de onda.'O físico austríaco Erwin Schrödinger escreveu uma equação que mostra como essa função de onda evolui no tempo. Schrödinger esperava que a 'onda' explicasse as estranhezas da mecânica quântica... Ainda hoje alguns tentam entender a mecânica quântica pensando que a realidade é a onda de Schrödinger. Mas Heisenberg e Dirac logo compreenderam que esse caminho é equivocado. A função [de onda] não está no espaço físico, está em um espaço abstrato formado por todas as possíveis [virtuais!] configurações do sistema... A realidade do elétron não é uma onda [?]: é esse aparecer intermitente nas colisões," Carlo Rovelli's

*A realidade não é o que parece*(Objetiva, 2014, p. 271);**************************************************************

###
*Backdoors*:

"When we say that we wish to make sense of something we meant o put it into spacetime terms, the terms of Euclidean geometry, clock time, etc. The Fourier transform domain is potential to this sensory domain. The waveforms which compose the order present in the electromagnetic sea which fills the universe make up an interpenetrating organization similar to that which characterizes the waveforms "broadly cast" by our radio and television stations. Capturing a momentary cut across these airwaves would constitute their hologram. The broadcasts are distributed and at any location they are enfolded among one another. In order to make sense of this cacophany of sights and sounds, one must tune in on one and tune out the others. Radios and television sets provide such tuners. Sense organs provide the mechanisms by which organisms tune into the cacophany which constitutes the quantum potential organization of the elecromagnetic energy which fills the universe," Karl Pribram's "The Implicate Brain";

"... the cloud chamber photograph does not reveal a “solid” particle leaving a track. Rather it reveals the continual unfolding of process with droplets forming at the points where the process manifests itself. Since in this view the particle is no longer a point-like entity, the reason for quantum particle interference becomes easier to understand. When a particle encounters a pair of slits, the motion of the particle is conditioned by the slits even though they are separated by a distance that is greater than any size that could be given to the particle. The slits act as an obstruction to the unfolding process, thus generating a set of motions that gives rise to the interference pattern," Basil J. Hiley's "Mind and matter: aspects of the implicate order described through algebra" (in K. H. Pribram's and J. King's

*Learning as Self-Organisation*, New Jersey, Lawrence Erlbaum Associates, 1996, pp. 569-86);

"Let us... ask what the algebraic structure tells you about the underlying phase space. Because the algebra is non-commutative there is no single underlying manifold. That is a mathematical result. Thus if we take the algebra as primary then there is no underlying manifold we can call the phase space. But we already know this. At present we say this arises because of the 'uncertainty principle,' but nothing is 'uncertain,'" Basil Hiley's "From the Heisenberg Picture to Bohm: a New Perspective on Active Information and its relation to Shannon Information" (in A. Khrennikov, Proc. Conf.

*Quantum Theory: reconsideration of foundations*, Sweden, Växjö University Press, pp. 141-162, 2002).

"What Gelfand showed was that you could either start with an a priori given manifold and construct a commutative algebra of functions upon it or one could start with a given commutative algebra and deduce the properties of a unique underlying manifold. If the algebra is non-commutative it is no longer possible to find a unique underlying manifold. The physicist’s equivalent of this is the uncertainty principle when the eigenvalues of operators are regarded as the only relevant physical variables. What the mathematics of non-commutative geometry tells us is that in the case of a non-commutative algebra all we can do is to find a collection of shadow manifolds... The appearance of shadow manifolds is a necessary consequence of the non-commutative structure of the quantum formalism," Basil Hiley's "Phase Space Descriptions of Quantum Phenomena" (in A. Khrennikov,

*Quantum theory: Reconsiderations of Foundations*, Vaxjo University Press, 2003).

- 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);

- en profane: Orsay & Centre Pompidou;

- 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;

- Piano Playing (Kochevitsky);

- L'Affirmation de l'âne (review of Smolin/Unger's

*The Singular Universe*);

And also:

- Spooky Blue;