caco ergo sum


CHAPTER 2

THE UNIVERSE

Are you dreaming me and everything else,
and am I dreaming you and everything else,
so cleverly that our dreams match?”
Erwin Schrödinger

In order to have a universal grasp of the three paradigms of universe, consciousness and self within the environment, developed in the last chapter; let us try to understand them in the light of prevailing scientific theories, experiments and discoveries.  Let us begin by “exploring” the universe.[1]

At the annual meeting of the American Association for the Advancement of Science in San Francisco in February 2001, a panel at the NASA booth prominently read: 

TANGLED BEGINNINGS

About 10-35 second after the Big Bang, objects called semilocal strings may have condensed out of interacting quantum fields. Some strings linked with others into space-spanning filaments. Still others rolled up head to tail and shrank away to nothing.  Semilocal string theory may help explain how the universe developed 'lumpy' structures such as stars and galaxies, despite its perfectly homogeneous beginnings.[2]

Even though a few years have passed since I incorporated this quote, and even though recently loop quantum gravity and quantum information theories are challenging string theory’s dominant position, the quotation above does, in a nutshell, present the prevailing Standard Model assumptions about the beginning of the universe.[3]

The “Big Bang,” then, is where, according to our current scientific concepts, it all began. A word of caution may be appropriate here about scientific terminology and imagery.  Terms like Big Bang, semilocal strings or filaments can evoke images which could limit the conception of an idea. We will come back to this topic later.

The quotation from NASA above tries to patch up a major scientific hurdle which has to be addressed.  It suggests that the "semilocal string theory" may solve the problem of the discrepancy between the smooth universe of general theory of relativity and the turbulent quantum flux.  But  for the purposes of this essay 10-35th of a second after the Big Bang is relatively too late!

 The Big Bang suggests that time and space, the two major causes of man's claim to existence – the other causes being his senses and consciousness that we will be attending to later – began around 10-35th of a second after the Big Bang.  The idea of the Big Bang is relatively recent.  Although man has philosophically conceived of infinity ever since he gazed into the starry night, scientifically he did not perceive the universe beyond the Milky Way, his own run-of-the-mill constellation, until 1925 when Hubble observed the multitude of constellations racing through the space.[4]

 In 1948 George Gamov, basing himself on his Russian professor Alexandr Friedmann’s theory of a dynamic  -- expanding and retracting – universe, and  by reversing Hubble’s observation of the expansive universe, advanced the idea of an explosive birth of the universe; from an infinitesimally small, extremely hot and dense initial state some fifteen billion years ago into what we experience now.[5]

 

 

 

 

In the blank space above you can see an infinitesimally small speck – in fact, because it is so infinitesimally small, you cannot see it!  It is an idea, and you can imagine it anywhere you like.  As you look for it, however, what you see is the blank.  Which begs the often asked philosophical question: what did the small, hot, dense initial state blow into?  The question assumes differentiation between pre-Big Bang and post Big Bang, unless we assume that the initial idea was all that was: the blank whole.  The assumption being that if there were only the blank whole and no speck, or only the speck but no blank, there would have been no Big Bang and no universe.   That, however, as we shall see in a moment, is not quantum impossibility.

We are not supposed to know what happened before that “time”.  But there was no time!   In fact, there is presently a threshold of scientific insight – the Planck epoch – from the "beginning" to 10-43rd of a second which defies the existence of space-time curvature.[6] At that “point” space-time calculation breaks down.

That 10-43 fraction of a second evokes a good number of religious explanations of creation from the Bible to the Rig Veda. It is amazing to note that those who pondered the enigma of being all ended up with a fraction of a second or so discrepancy just as the Planck epoch does scientifically.[7]  But, above all, don’t take my amazement as a statement of faith.  Remember, Copernicus removed man from the center of the universe, Darwin destitute him as the image of God, Freud made him a creature of libido and I have just reduced him, in the last chapter, to a shit-making machine.  Please keep this in mind; as in the discourse that follows there are instances that, if irrationally stretched, can lend them to cult development.

Scientifically, Planck epoch in quantum physics could imply that before 10-43 fraction of the second, before calculable curvatures, at 0, there “is” naught: Either dimensionless speck or all blank, which ever pleases you!   It is naught.  Before 10-43rd of a second we can conceive 10-50, 10-100 … 10-= 0.  That naught, as science detects 10-43rd of a second later, contains the universe.  Universe is thus the unity of the whole with its opposite.  It contains the whole, and the whole, if indeed be the whole, contains its own negation – nothing.  As Giordano Bruno put it: “It contains all, yet it is not contained.”[8] Those who gave universe its name had already figured it out.  Universe says it all: "Uni": one whole, and "versum": its opposite. Their symmetry is naught.[9]  Hence the idea of symmetry and the potentiality of asymmetry.  It is essential to emphasize “idea” in this proposition.[10]  As soon as we attempt measuring we are beyond idea and in the realm of quantum physics with the dilemma of uncertainty principle, i.e., we have assumed the existence of curvature, waves and particles.

In quantum terms we could conceive of the initial expansion as a symmetry/asymmetry pulsation. The idea of symmetry/asymmetry pulsation precedes the Big Bang. 

In short!:  Universe is the "idea" of the pulse – the potentiality of symmetry/asymmetry polarization.

At point zero there are no dimensions, no movement, no friction and consequently no temperature. Temperature, just like symmetry and asymmetry, is idea.[11]

In terms of naught, symmetry/asymmetry polarization couples with depolarization in the same pulse, hence the initial state – of nothingness.  If that is the case, then what of “reality” and “existence?” 

It is that man is caught in the pulse – between the “uni ” and the “versum” of the universe – and perceives space-time and the ensuing existence.  Remember, the universal pulse contains all, including the potential of pulse sequences that could be conceived, as we shall discuss later, as continuum of waves with different frequencies, spins, curvatures and twists.  According to human perception, in the eventual symmetry/asymmetry polarization, a parity interference occurs, creating energy twisting into matter. Andrei Sakharov noted in 1967 that without a break in symmetry there would have been no matter in the universe at all. The “CP” theory (C stands for “charge conjugation” and P stands for “parity”) proposed by Susumo Okubo in 1958, holds that a violation of the charge conjugation parity between particles and antiparticles at the Big Bang caused the survival of some particles and the generation of matter. [12] 

Note my emphasis on  perception, because without human perception there would be nothing. To “illustrate” the point let us evoke the standard scientific depictions of the Big Bang.  They are in general in the shape of a funnel, beginning with a point at the Big Bang and expanding into the “present” large space-time universe at the other end.[13]  Here below is NASA's depiction: 

 

Universe Big Bang-2 Waves_crop [14]

 

Probing the blue canopy of the firmament for the afterglow of the Big Bang – the cosmic background radiation – NASA produced the following:

 

Universe Fate-1 Accelerating Universe[15]

 

According to NASA, it is the "baby picture of the universe only 400,000 years after it was born." Beyond the above picture, at “year” zero there is nothing, hard to visualize.

But what "was" – time – "there" – space – before – time?  NOTHING :  For us humans, at best, the idea of nothingness; and at worst, some kind of a creator god

In describing time and space, visualizing the universe in forms, showing the Big Bang as a moment beyond “singularity” and drawing the two axes of time and space spreading out as a funnel makes it hard to conceive the fact that reaching the confines of the universe we are not at 12, 13.7, 15  or whatever light years away from the moment of the Big Bang, but “in” it – at no time and no space. 

Of course, for that, we will have to travel faster than light and the "expansion" of the universe.  There exists one potential for that:  Mind.  In your “mind,” you can travel faster than light and time.  If, in your mind, you were presently at the confine of the Big Bang universe, what would you “encounter?”  “There,” you would “encounter” not the perceived immensity of the space-time, but the infinity of nothingness.  That cannot be  “illustrated.”  It cannot be visualized, but conceived.  “Encounter,” and “there” have been put in quotes because if indeed, in your mind, you commune with the infinite nothingness, you are naught.

*      *      *

Before we go any further, I need to tell you where I am coming from.  I mentioned in the last chapter my “rational” childhood upbringing.  It did not only de-program the superstitions that I was exposed to, but also encouraged me to examine them in order to understand why they existed. I was driven by that searching spirit in school when in the calculus class I came across the hyperbola graph: X=1/Y

The teacher added X≠0 on the blackboard. I asked why?  He said: “Because X and Y axes of hyperbola are asymptotes.  At  X = 0,  Y would be .  It does not make sense.” 

Make sense?! I thought.[16]  But we have only five senses.  And we know that even other species have more senses.[17] Not to speak of the fact that beyond all the senses of all species, there are potentials we haven’t the foggiest idea about.  So  X = 0, Y = , and  Y = 0, X = would be the two axes themselves!  I drew the two axes across the paper and conceived it rolled around into a sphere.  On the sphere, at opposite 0, all , whether of X or Y axes, whether positive or negative, meet and become 0.  And, for , 0 is .  The proposition is true as you move the axes anywhere on or within the sphere.  Every point on and within the sphere – and beyond my piece of paper turned into the sphere – could be 0∪∞.  So, as far as I could conceive, the ultimate “formula” is: 0 ∪∞∪ 0.  A concept that mathematics, physics and generally all exact sciences attempt to approach, yet avoid. [18]

In a 360 global radius, I sublimed the infinite as zero “out there.”  The infinite was here at zero, zero was out there, and I was one with both!  I had no problem!  I was at the cocky age when we think we know it all. I was probably influenced by the rudimentary knowledge I was acquiring in my philosophy class at the time, and attempting to solve Kant’s dilemma in observing the firmament and sublimating the awe of the infinite universe beyond sensual understanding and turning it into the impenetrable noumenon.[19]  I was liberating Kant’s infinite from God’s grip!

To make the point in calculus terms would be to conceive curvatures gradually moving the derivatives of x and y to the integer of x = y stretching from 0 to which, in every direction would reach x = 1/y  at ∞∪0.

The calculus formula of the sphere: x2+y2+z2 = r2 would represent the pre-Big Bang at  r = 0.  Symmetry is the coincidence of zero and infinity. There is symmetry at zero and infinity. Symmetry engendering asymmetry within, at 0 – before the Big Bang – and at the confine of the Big Bang – beyond virtual infinite (see our later presentation of it) – at infinite.  But to conceive the sphere expanding to infinite at  r = as both and 0  “does not make sense” mathematically and can only be realized conceptually.

In mathematics,  Euler Formula: e iΠ+ 1= 0 , where e, the natural logarithm constant (2.718281828459….) power the multiplication of i, the complex imaginary number  and Π, plus 1 equals  0,  comes closest to my concept of x = 1/y.  Euler Formulates the same concept but avoids the asymptotic central 0 = .  Euler formula also has the merit of engendering the three universal constants independent of human terms of reference.  I say “Universal constants” as distinct from “man made constants.”  To illustrate, Planck time[20] is based on "constants” conceived by man, whether Newtonian gravity or the speed of light in vacuum.[21]

*         *         *

The problem for human “mind” to travel “straight” to the confines of the universe and conceive 0 ∪∞∪ 0 is that thought ends up taking the curvature of the Relativity Theory, and as Einstein has it, hits the back of our head!  What is proposed here is thought freed from Einstein’s Talmudic hang-up.  In his letter of 19 June 1935 to Schrödinger, Einstein writes: “The real problem is that physics is a kind of metaphysics; physics describes ‘reality.’  But we do not know what ‘reality’ is.  We know it only through physical description …  But the Talmudic philosopher sniffs at ‘reality’, as at a frightening creature of the naïve mind.[22]  Imbued with religious dimension, whether Talmudic, Hindu, Soufi, Christian or Buddhist, we will have god as the universal curvature hitting back into our head.  And it could come quite close to the universal!  Teilhard de Chardin reaching his Omega Point comes to mind: “Only one reality seems to survive and be capable of succeeding and spanning the infinitesimal and the immense: energy – that floating, universal entity from which all emerges and into which all falls back as into an ocean; energy, the new spirit; the new god.  So, at the world’s Omega, as at its Alpha, lies the Impersonal.” [23]

To possibly succeed, thought has to go before the Planck Epoch; before curvature.

Schrödinger, pondering "reality," expresses his astonishment that the external world is there at all.  He goes on to wonder:Are you dreaming me and everything else, and am I dreaming you and everything else, so cleverly that our dreams match?” – that indeed all reality is illusion?   It is true that, in order not to be taken for a mystic and ridiculed by his physicist community as a crackpot, he immediately adds “But this is mere foolish playing with words,[24]

It does take more than sitting in a lotus position to commune with universal consciousness, and that applies to this author too!   Hic Rhodus, hic saltus.[25] 

To continue our quest to relate the universal to human consciousness, however, we need to jump into “reality” and delve into the scheme of the universe to find man's place in it.


*      *     *

©2006 Anoush Khoshkish
All rights reserved


[1] The purpose here is not to present an exhaustive review of contemporary cosmological theories but to inject a philosophical perspective into them in order to go where we need to go to contemplate human species within its universe. 

As for the review of contemporary cosmological theories, recently there has been an abundance of literature with different levels of scientific difficulty.  It is noteworthy that popular books on contemporary theories of cosmology surged in the 1990’s after Stephen Hawking’s A Brief History of Time: From the Big Bang to Black Holes became a best seller. The herd instinct of Publishers’ made them chase eager scientists for manuscripts on the subject.  A short  list of the literature includes: Alain Boutot, L’Invention des Formes, Paris: Editions Odile Jacob, 1993; David Darling, Equations of Eternity, New York: Hyperion, 1993;  Paul Davies, The Cosmic Blueprint, &  –  About Time, New York: Simon & Schuster, 1995;  Armand Delsemme, Les Origines Cosmiques de la Vie, Paris: Flammarion, 1994;  Frank Drake and Dava Sobel, Is Anyone out There? New York: Dell, 1994;  Alan Dressler, Voyage to the Great Attractor, New York: Vintage, 1994;  Timothy Ferris, The Whole Shebang, New York: Simon & Schuster, 1997 (A well-rounded coverage of the subject);  Murray Gell-Mann, The Quark and the Jaguar, New York: W. H. Freeman & Co., 1994;  James Gleick, Chaos, New York: Penguin, 1987;  Brian Greene, The Elegant Universe, New York: W. W. Norton & Co., 1999;  – The Fabric of the Cosmos: Space, Time, and the Texture of Reality, New York, Alfred A. Knopf, 2004;  Stephen W. Hawking, A Brief History of Time, New York: Bantam, 1988;  – Black Holes and Baby Universes, New York, Bantam, 1993;  – and Roger Penrose, The Nature of Space and Time, Princeton, NJ: Princeton University Press, 1995;  Michio Kaku, Hyperspace, New York: Oxford University Press, 1994;  Leon Lederman, The God Particle, New York: Dell, 1993;  Michael D. Lemonick, The Light at the Edge of the Universe, New York: Villar – Random House, 1993;  Andrei Linde, Inflation and Quantum Cosmology, New York: Academic Press, 1990; Ian Marshall and Danah Zohar, Who’s Afraid of Schrödinger’s Cat?, New York: William Morrow & Co., 1997;  Heinz R. Pagels, The Cosmic Code, New York: Simon & Schuster, 1982;  Roger Penrose,  The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics, Oxford, Oxford University Press, 1989;  –  Shadows of the Mind: An Approach to the Missing Science of Consciousness, Oxford, Oxford University Press, 1994; – The Road to Reality: A Complete Guide to the Laws of the Universe, London, Jonathan Cape, 2004; Simon Singh, Big Bang: The Origin of the Universe, New York, HarperCollins, 2004;  Kip S. Thorne, Black Holes & Time Warps, New York: W. W. Norton, 1994;  Danah Zohar and Ian Marshall, The Quantum Society,  New York: William Morrow & Co., 1994. [And, of course, on the internet such sites as those of CERN, NASA, Physics etc. For a more extended list see http://www.ericweisstein.com/encyclopedias/books/Cosmology.html ]

[2] Signed:  Julian Borril, NERSC/LBNL & Center for Particle Astronomic, UC Berkeley.

[3] http://particleadventure.org/   See also “Constructing Space-time – no Strings Attached” in Science, 8 November 2002, Vol. 298 p. 1166, and Lee Smolin, “Atoms of Space and Time” in Scientific American, January 2004, Vol. 290 No 1, pp. 66-75.

[4]  See “The Scale of the Universe: Great Debate in 1996”, Debate Proceedings, notably, Sidney van den Bergh, “The Extragalactic Distance Scale” in Publications of the Astronomical Society of the Pacific, 108, pp. 1091-1096, December 1996.  For an inventory of recent observations and pending problems see Yvline Lebreton, “Stellar Structure and Evolution: Deductions from Hipparcos, in the AnnualReview of Astronomy and Astrophysics, Vol. 38, pp. 35 – 77, September 2000. 

[5]Alexandr Friedmann ‘s (1888-1925) mathematical model of a dynamic universe was further elaborated by Belgian Abbé Georges Lemaître (1894-1966), American Howard Robertson and British Arthur Walker, and became known as Friedmann-Le Maître-Robertson-Walker Model of the homogeneous expanding  universe. It inspired George Gamow who, in collaboration with his colleague Ralph Alpher, advanced the idea that the universe originally existed in a primordial state called the "Ylem." A Big Bang started the expansion of the universe. Helium and perhaps other elements were formed from the Ylem shortly after. Gamow’s friend Hans Bethe joined in the authorship of the paper published in 1948 as the Alpher -Bethe -Gamow Theory (or alpha-beta-gamma theory standing for the three first letters of the Greek alphabet:). For an extended story see Simon Singh, Big Bang: The Origin of the Universe, New York, Harper Collins (Fourth Estate), 2004.

[6] That is a very short time. It is not one tenth of a second: 0.1, or one thousandth of a second: 0.001; it is 0.0000000000000000000000000000000000000000001th of a second.  A very short time indeed.

[7]"The earth was without form and void, and darkness was upon the face of the deep; and the Spirit of God moved upon the face of waters.  And God said ‘Let there be light’; and there was light. And God saw that light was good" in the Genesis.  It is interesting to note that God realized that light was good after seeing it.  It reflects the quantum idea of symmetry and asymmetry. Or, "Then was not non-existent nor existent, there was no realm of air, no sky beyond it" in Rig Veda X:129, in R. T. H. Griffith, The Hymns from the Rig Veda, Benares, E. J. Lazarus, 1920, vol. II, pp. 575-6.

[8] See On the Infinite Universe and Worlds – Dialogues. Notably, in First Dialogue.  Philotheo: “the primal container is by naught contained,”) 

[9] Symmetry (from Greek sun, syn, sum = same, equal; and metron, metros = measure) implies parity and balance.  When there is parity, things cancel each other out.  Hence there remains “nothing.”  So, in universal symmetry, potentially matter and antimatter cancel each other out.  But humanity “perceives” “reality” and “existence” and, as we shall see later, concludes that in the scheme of the universe some “violation”

[10] The antecedents to our idea, among others, are those of Plato – see notably his Parmenides and Sophist Dialogues –, Hegel – see notably the preface to his Phänomenologie des Geistes (Phenomenology of Spirit)  – and Encyklopädie der Philosophischen Wissenschaften im Grundrisse (Encyclopedia of Philosophal Sciences in Outline); and Jean-Paul Sartre, notably, his L'être et le néant (Being and Nothingness).

[11] The idea precedes the Third Law of Thermodynamics – see my later discussion of asymptotes. It encompasses heat as well as no heat – encompassing absolute “zero” (-275.16c), Bose-Einstein Condensate and all other temperature variations.

[12] See, for example, Robert K. Adair, “A Flaw in a Universal Mirror” in Scientific American, February 1988, pp. 50-56. In my conception, however, I am not really talking about “particles” before 10-43rd of a second but rather the “idea” of symmetry and “potentiality” of asymmetry.

[13] The string theory would produce a so-called Calabi Yau fuzball shape on the computer. See Scientific American, November 2003, p.73. See also Brian Greene, The Elegant Universe, New York, W.W. Norton, 1999, p. 207 et seq.

[14]  http://map.gsfc.nasa.gov/media/020622/index.html

http://map.gsfc.nasa.gov/media/060915/index.html

For other interesting funnel depictions of the universe see, for example, Jonathan J. Halliwell, “Quantum Cosmology and the Creation of the Universe”, Scientific American. December 1991, p. 84; Richard B. Larson, “The First Stars in the Universe”, Scientific American, December 2001, p. 67, and, for an original discussion of the subject, see Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe, New York, Alfred A. Knopf, 2006, §27.11 Cosmology pp. 717 et seq.

[15]  http://science.nasa.gov/astrophysics/focus-areas/what-powered-the-big-bang/

[16] I was not yet familiar with Euler Formula: ei+ 1= 0. It would have helped me along in my concept of 0.  See our later discussion.

[17] Dogs hear what we cannot hear, fishes and birds sense the magnetic field of the earth that guides them over thousands of kilometers. More on that when we discuss consciousness in later chapters. See, for example, Micheal M. Walker et al., “Structure and Function of the Vertebrate Magnetic Sense” in Nature, 27 November 1997, Vol. 390, pp. 371-376; Thorsten Ritz et al., “A Model for Photoreceptor-Based Magnetoreception in Birds” in Biophysical Journal, February 2000, Vol. 78, No. 2, pp. 707-718, and William W. Cochran et al., “Migrating Songbirds Recalibrate Their Magnetic Compass Daily from Twilight Cues” in Science, 16 April 2004,

[18] Those who come up with formulae to get around infinities in different contexts get Nobel prize. Just to point to a few recent ones, the Nobel Prize in Physics in 1965 was given to Sin-Itiro Tomonaga, Julian Schwinger, and Richard P. Feynman for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles; the 1999 Prize went to Gerardus 't Hooft and Martinus J.G. Veltman for elucidating the quantum structure of electroweak interactions in physics and in 2004 David Gross, H. David Politzer and Frank Wilczek received the Nobel prize in physics for their discovery of asymptotic freedom in the theory of the strong interaction.

In praise of the Noble prize given to David Gross, H. David Politzer and Frank Wilczek for having formulated “asymptotic freedom” – the property of the strong force that “glues” quarks – Charles Seife wrote in Science:  “Particle physics is swimming with infinities: places where the equations that describe the behavior of a particle seem to blow up into a meaningless jumble of singularities. One reason is that every region of space, even the deepest vacuum, is seething with "virtual" particles that pop in and out of existence--and these particles make even the simplest concepts very difficult.” (Science 15 October 2004: Vol. 306. no. 5695, p. 400)

Attempts to circumvent infinities that render formulae meaningless reminds us of the well known story of the man who was looking for his lost key under the lamp post.  For those not familiar with the story, it is that of a passerby who at night sees a man looking for something on the ground under the street light and having been told by the man that he is looking for his house key, joins in the search. After a moment, to make his help more effective, the passerby asks the man whereabouts he thinks he might have lost his key.  The man, pointing to some distance away, says “there, in front of my house.”  Astonished, the passerby asks: Why are you looking for it here?”  “Because it is too dark there,” the man replies.

[19] See Emmanuel Kant, Critique of Judgement (Kritik der Urteilkraft), para. 26 et seq. 1790 and his treatment of noumenon in his other writings.

[20] Planck Time approximates the following formula:

Planck Time

Where G  is Newton's gravitation constant (6.67 X 10-8 dyne-centimeter2gram2), h is Planck constant: 6.6262 X 10-27 erg second (not to be confused with  Planck h which is the “PlanckConstantReduced” and equals Planck Constant Reduced), and c is the speed of light in vacuum (2.998X1010 meter second).  Planck Time is the time light travels a distance of 1 Planck Length.

[21] See “Values of Fundamental Constants Adjusted,” in Science, Vol. 235, pp.633-4, 6 February 1987, on CODATA – Committee on Data for Science and Technology of the International Council of Scientific Unions: http://www.codata.org/.  See also Werner Heisenberg, Across the Frontiers, New York, Harper & Row, 1974, p. 12 referring to the “so-called ‘constants’”.

[22] Quoted by Arthur Fine in “The Natural Ontological Attitude,” in The Philosophy of Science, Richard Boyd, Philip Gasper, and J. D. Trout (Eds), Cambridge, Mass, The MIT Press, 1991, p. 268.

[23] Pierre Teilhard de Chardin,  Le Phénomene Humain, (Written in Peking 1938-40 – published in 1955) translated as The Phenomenon of Man by Bernard Wall, New York, Harper & Row, 1959, p. 258. He approaches the infinite through his Point Oméga (Omega Point) – see Book IV: Survival, Chapter II: Beyond the Collective: the Hyper-Personal, 1. The Convergence of the Person and the Omega Point: A. The Personal Universe, B. The Personalizing Universe.

“Because it contains and engenders consciousness, space-time is necessarily of a convergent nature. Accordingly its enormous layers, followed in the right direction, must somewhere ahead become involuted to a point which we might call Omega, which fuses and consumes them integrally in itself.” (p. 259)

[24] Erwin Schrödinger, My View of the World (1961), Woodbridge, CT, Ox Bow Press, 1983, p.105.

[25] Which literally means “Here is Rhodes; here, jump!” attributed to Aesop, sixth century B.C. Greek philosopher’s fable about a man who boasted of his extraordinary jump in Rhodes and was challenged to replicate it on the spot elsewhere.  The proverb was rendered into Latin by Erasmus in his Adagia, III.iii, 28, Paris 1500.