Hanna Newcombe How Things Come Together ======================== Volume 3 on one page ==================== Volume 3 articles are listed by category below. Most categories overlap with those used in Volume 1 and Volume 2, although in some cases names might be changed or categories combined. Time and Space ============== FROM HERE TO ETERNITY (by Tim Folger: excerpts) APPROACHING A BLACK HOLE Matter and Energy ================= TOWARD A THEORY OF EVERYTHING SUPERORDINATE ESSENCES ASYMMETRY AND SUPERSYMMETRY SIX OR NINE NUMBERS OF THE UNIVERSE. QUANTUM THEORY IMPLICATIONS. SIZE SPECTRUM OF CELESTIAL BODIES QUANTUM PROPERTIES THE QUINTESSENTIAL UNIVERSE. IT'S TURTLES ALL THE WAY DOWN? Information, Meaning, Knowledge =============================== NINE AXIOMS Mind ==== A UNIVERSE OF CONSCIOUSNESS. CHALMERS-CRICK SYNTHESIS. LONG-TERM POTENTIATION. EXPANDING BEYOND OUR SENSE-DERIVED EXPERIENCE. EVOLUTION OF SEX DIFFERENCES (by Doreen Kimura) A NEW DEFINITION OF LUCID DREAMING? HOW WE KNOW THE WORLD. ANIMAL MINDS. LEFT AND RIGHT MISUNDERSTOOD. DREAMING THE WORLD INTO EXISTENCE. NOT BY GENES ALONE. DENNETT'S LADDER. Spirit ====== ARGUMENTS FOR THE EXISTENCE OF GOD. MEDITATION ON CAETANI'S TREE OF GOD. GNOSTICISM. SECOND THOUGHTS ON GNOSTICISM. INTER-FAITH CORRELATIONS. GOD OF THE UNIVERSES. INTER-SECTS. THE RED SNAKE. WHO WAS JESUS? FROM "VARIETIES OF RELIGIOUS EXPERIENCE" (William James) SPARKS OF DIVINE ESSENCE. SEE THE WORLD FROM BOTH SIDES NOW. MULTIPLE PATHS TO TRUTH. OM-GAIA MEDITATION. HEAVEN AND HELL. TRUTH AND BEAUTY. THE MODE SWITCH. Life ==== DEFINITIONS OF LIFE. PREBIOTIC EVOLUTION. YUCK AND YUM. NANO-CHEMISTRY IS CELL BIOLOGY FROM ERRORS TO STABILITY: IS THAT PROGRESS? GENE SWAPPING AND KINSHIP STRUCTURES THE STORY OF THE GENES. IS LIFE IMMORTAL? UPROOTING THE TREE OF LIFE. ARE WE ALONE? CONTRASTS. GAIA'S RITE OF EXTINCTION. Society and Politics ==================== ETHNOS TO ETHOS. CRITERIA FOR HUMANITARIAN INTERVENTION. EVOLUTION OF THE WAR SYSTEM BIOTECHNOLOGY: PROS AND CONS. GENOCIDES. DEFINITIONS OF PEACE. MILITARY SPENDING AND POVERTY. REVIEW OF "THE NEXT STEP" BY PROF. JAMES A. YUNKER. NONVIOLENT REVOLUTION. Passages ======== COSMIC EVOLUTION. UNIFICATIONS AND GENERALIZATIONS. FROM OUSIS TO MATTER. THE BIFURCATION TEST. NECESSITY IS THE MOTHER OF INVENTION. THE SAME OR IDENTICAL? Conclusions =========== IS THE WORLD STRUCTURE DISCRETE OR CONTINUOUS? 3 or 4? 6 or 7? 10 or 26? SELF-ORGANIZATION OF HUMAN SOCIETY. =========================================================================== FROM HERE TO ETERNITY (by Tim Folger: excerpts) =============================================== In Barbour’s universe, every moment of every individual’s life— birth, death, and everything in between— exists forever. “Each instant we live,” Barbour says, “is, in essence, eternal.” That means each and every one of us is immortal. Like the perpetually unmoving lovers in Keats’s “Ode on a Grecian Urn,” we are “for ever panting, and for ever young.” We are also for ever aged and decrepit, on our deathbeds, in the dentist’s chair, at Thanksgivings with our in-laws, and reading these words. Barbour’s central argument is that a mistaken belief in the reality of time prevents physicists from achieving their ultimate goal: the unification of the submicroscopic atomic world of quantum mechanics with the vast cosmic one of general relativity. The problem arises because each theory provides a radically different conception of time, and physicists simply don’t know how to reconcile the two views. Until they do, they will never have one seamless theory of the universe comprising the very smallest objects to the very largest. And certain middling-sized objects— human beings— will never understand the true nature of time and existence. What makes the two versions of time so different? Time in the quantum realm has no remarkable properties at all. In theories of quantum mechanics, time is essentially taken for granted; it simply regularly ticks away in the background, just as it does in our own lives. Like a clock at a sporting event, it provides an invisible framework in which events unfold. That’s not the case in Einstein’s general theory of relativity. To describe the universe on the largest scale, Einstein had to weave time and space together into the very fabric of the universe. As a result, in general relativity, there is no invisible framework, no clock ticking outside the universe against which to measure events. How could there be? Time and space joined together have weird consequences: Space and time curve around stars and other massive bodies and make light bend away from straight-line paths. Near black holes, time seems to slow down or even come to a full stop. Barbour is not alone in recognizing that the pictures of time in general relativity and quantum mechanics are fundamentally incompatible. Theoretical physicists around the world, spurred by Nobel dreams, sweat over the problem. But Barbour has taken perhaps the most unorthodox approach by proposing that the way to solve the conundrum is to leave time out of the equations that describe the universe entirely. He has been obsessed with this solution for more than 10 years, since he learned of a vexing mathematical tour de force by a young American physicist named Bryce DeWitt. DeWitt, with the help of the eminent American physicist John Wheeler, developed an equation in 1967 that apparently melded quantum mechanics with general relativity. He did this by taking the principles from quantum mechanics that describe the interactions of atoms and molecules and applying them to the entire universe, a mind-bending feat not unlike trying to make a jockey’s suit fit Michael Jordan. Specifically, DeWitt hijacked the SchrÖdinger equation, named for the great Austrian physicist who created it. In its original form, the equation reveals how the arrangement of electrons determines the geometrical shapes of atoms and molecules. As modified by DeWitt, the equation describes different possible shapes for the entire universe and the position of everything in it. The key difference between SchrÖdinger’s quantum and DeWitt’s cosmic version of the equation— besides the scale of the things involved— is that atoms, over time, can interact with other atoms and change their energies. But the universe has nothing to interact with except itself and has only a fixed total energy. Because the energy of the universe doesn’t change with time, the easiest of the many ways to solve what has become known as the Wheeler-DeWitt equation is to eliminate time. Every Now is a complete, self-contained, timeless, unchanging universe. We mistakenly perceive the Nows as fleeting, when in fact each one persists forever. Because the word universe seems too small to encompass all possible Nows, Barbour coined a new word for it: Platonia. The name honors the ancient Greek philosopher who argued that reality is composed of eternal and changeless forms, even though the physical world we perceive through our senses appears to be in constant flux. =========================================================================== APPROACHING A BLACK HOLE ======================== Time slows down for observers moving at great speeds, according to the theory of special relativity. When we, as observers in our frame of reference with respect to motion, see something or someone falling into a black hole, we perceive that they are accelerating, until at the black hole’s horizon they reach the speed of light. However, someone who is falling in feels it quite differently. When they reach the horizon, they perceive themselves as sitting still forever at the horizon. Time has, for them, virtually disappeared. How do we know that we are not in that state already? We feel quite comfortable in our frame of reference, while “actually” (whatever that means), we are already in the grip of an unavoidable catastrophe. =========================================================================== TOWARD A THEORY OF EVERYTHING ============================= Three of the fundamental forces were theoretically unified in a theory called GUT (Grand Unification Theory). In nature, this unification would happen only at a very high temperature; only the electromagnetic-weak unification has so far been experimentally observed, in collisions with an energy of about 100 to 1,000 GeV (giga-electron-volts). A further unification of the electro-weak force with the strong force has been supported theoretically; but a final unification with gravity is an unsolved problem even theoretically. Even Einstein could not solve it, although he worked on it for many years. According to an article in Scientific American, August 2000 (by Nima Arkadi-Hamed et aI, pp. 62-69), gravity and GUT cannot be reconciled by present methods, because gravity operates in a 4th spatial dimension in addition to our usual 3. The writers speculate that our 3-dimensional universe may be “plastered” on the wall of a 1 mm diameter curled-up cylinder of the 4th dimension. This 1 mm cylinder diameter is called “large”, since curled-up extra dimensions usually have a diameter of the order of 10 to the minus 35 millimeters, which is the Planck dimension. What we observe in our universe is similar to what was suggested people would see on the walls of Plato’s cave — not a faithful representation of the real world; only a projection to a lower dimension. Large-scale paradoxes, such as extra dimensions of space, combine with the small-scale paradoxes of string theory of sub-atomic particles; the latter also assumes many dimensions, sometimes 26, sometimes 10 or 11. String theory and cosmology combine to give us these alien and almost incomprehensible views of the universe at extreme size scales. Our brain evolved for survivability, to which extra space dimensions are of no value. Quantum theory has several other examples of such “meta-evolutionary” concepts: non-locality, entanglement, complementarity, superposition, collapse of the wave packet. While our senses and imaginations cannot picture these realities, our symbolic capability can reason about them mathematically. We have some reach toward ultimate reality, even though it escapes our experiential grasp. Another speculation in the article is that gravity, which of course normally increases when distances get smaller (since it varies inversely with the square of the distance between massive objects) actually increases much faster at distances such as prevail in atomic nuclei and between quarks. Conventional theory would have gravity increase to infinity at Planck distances (10 to minus 35 mm), where it would meet the absolute impenetrability of all fermions (the Pauli exclusion principle). An infinite force would meet an immovable obstacle. However, it is postulated here that gravity increases much faster at small enough dimensions, so that it actually reaches a maximum at only 10 to minus 19 mm, where it is counteracted by the strong nuclear force between protons, neutrons and quarks. What does this mean for negative gravity (“quintessence” or the cosmological constant), postulated elsewhere, in an article on the accelerated expansion of space? I see three possibilities: 1. The “strong plus” of gravity at ultra-small dimensions may flip to a “strong minus” at infinity (change of attraction to repulsion), like paramagnetic temperature does. 2. Real particles (or only fermions) have positive gravity (attraction), while virtual particles (those that flicker in and out of existence because they have only borrowed energy from the vacuum field) have negative gravity (repulsion). 3. It is “fermion pressure” (generated’by the Pauli exclusion principle) that creates the repulsion, which is even stronger at ultra-small distances (above I called it “absolute”) than strong gravity. I prefer the third alternative. Fermion pressure would be even greater than strong gravity or the strong nuclear force at ultra-small distances. As virtual particles are continually created (and destroyed) in inter-galactic space, their fermionic repulsion would constitute the quintessence that makes space expand exponentially with time, as intergalactic space itself expands. Incidentally: if virtual particles continually arise in open space, would they include whole protons? Could extra matter be constantly created in space, in the form of hydrogen, as Fred Hoyle once proposed? (It would mean the conversion of virtual to real protons.) The Big Bang theory replaced Hoyle’s continuous creation theory, but maybe they will eventually be found complementary. Note that “repelling” means “creating space”. Early “inflation”, soon after the Big Bang, was probably caused by the quintessence force — the fermionic pressure that caused the Big Bang in the first place, after the supersymmetric transformation, which I have postulated in the essay “Eons of the Universe”. In that sense, “attraction” leads to the Big Crunch. Love = Crush? Maybe… Is the Universe “infinite in all directions”? (Title of book by Freeman Dyson.) Only in 4 dimensions, 3 of space and 1 of time. The other dimensions, tightly (more or less) rolled up into cylinders, are infinite in another sense: you could keep going around and around forever, like going around the Earth either East or West, withou ever coming to the end (Finis Terrae). Now in the film “The Truman Show”, Truman, who lived in a virtual world to provide entertainment for the television audience (without knowing it), finally touched the canvas at the limit of his Finis Terrae, his constructed world, after barely surviving an (artificial) storm at sea. Then he stepped into the real world from the virtual, and decided to stay real. But just how real is our real world? Is some TV audience (in the 4th dimension?), watching us struggle, for the thrills? =========================================================================== SUPERORDINATE ESSENCES ====================== A recent article in CANADIAN GEOGRAPHIC describes the Aurora Borealis as an intrusion of cosmic plasma into the terrestrIal essences which are largely limited to solid, liquid, and gas (rock, water, and air), with the occasional occurrence of fire. Yet 90% of the visible matter in the cosmos is composed of plasma. Our Earth is an island of exception. We are not only “three-dimensional”, but also largely tri-phasic. Yet the Fourth Phase (or Element) pervades the material universe. We are either a backwater or a miracle. However, the Universe in its appearance is also an exception, or at least an illusion to our senses. For its far overwhelming (70%) Dark Energy, Quintessence, dominates all the rest. The universe as a whole is penta-phasic. =========================================================================== ASYMMETRY AND SUPERSYMMETRY =========================== Two books expound these seemingly opposed aspects of our universe: “Lucifer’s Legacy” by Frank Close, and “Supersymmetry” by Gordon Kane. But they are not really contradicting each other. In fact, “Lucifer’s Legacy”, which is mainly about asymmetry, has a closing chapter on supersymmetry. Close explains the consequences of parity non-conservation at the sub-atomic level in its linkage to the matter/antimatter asymmetry and the chirality (handedness) of many biological molecules. Mirror images are strangely interrelated, while we usually think of them as separate. It, is circularly polarized sunlight which selectively destroys one of the enantiomers, e.g. d-amino acids and 1-sugars. And the light is polarized in one circular dimension because parity (charge and mirror-inversion) is not conserved in the operation of the weak force which produces neutrinos in the Sun. The universe began in symmetric fashion, but very early (tiny fractions of a second) the symmetry broke. This led to the other asymmetries mentioned above, and also, eventually, to differences between left and right brain in human, and the position of some internal organs (heart and stomach on the left, liver and appendix on the right). The lengths of our limbs are not equal, and even the two sides of our faces differ. Kane’s book explains that each sub-atomic particle of the so-called “standard model” may have a supersymmetric partner; i.e. each fermion has a boson partner, and each boson has a fermion partner. The superpartners of the standard-model particles have not been observed, and we do not even know their masses. But the search is on, in the big collider machines, for the “LSP”, the lightest superpartner, whichever it turns out to be. The search also concerns the Higgs boson, the boson of the field that imparts mass to the particles. So really, asymmetry and supersymmetry have very little in common, except that both concepts are at the leading edge of modern particle/physics, and explain many of the mysteries of the early and present universe. See also “The Secrets of Stardust” by J. Mayo Greenberg in Scientific American, December 2000, pp. 70-75. Dust particles in intragalactic space in the Milky Way spin in one preferred direction, because of magnetic fields in the dust cloud. The dust particles contain organic compounds adhering to the silicate cores of the particles, or are dissolved in the ice covering. The organic compounds include amino acids and polycyclic aromatic hydrocarbons. The preferred spin direction of the dust particles polarized starlight in a preferred circular direction. This in turn polarized the amino acids. The particles may have seeded life on Earth. =========================================================================== SIX OR NINE NUMBERS OF THE UNIVERSE. ==================================== It is interesting to compare two books: Martin Rees’ “Just Six Numbers” and Michael Rowan Robinson’s “Nine Numbers of the Universe”. I will do this in tabular form. Nine Numbers Six Numbers Anisotropy of microwave background Ripples in microwave Background (Q) Hubble Constant H - Age of the Universe - Temperature of Microwave Background - Density of Cold Dark Matter Total Matter in Universe Density of Hot Dark Matter Cosmological Constant Cosmological Constant Rate of Star Formation - - Ratio of gravity to electro-magnetic force - Mass deficit H to He - Dimensionality (3) Comments: There is some overlap in the numbers which each author considers important. This is because of the different aim: Robinson aims at a complete description of the universe; hence he picks numbers which are not derived from each other — the independent constants. Reese emphasizes only numbers which are “finely tuned” to make life possible. But his six are also mutually independent. =========================================================================== QUANTUM THEORY IMPLICATIONS. ============================ The Copenhagen model elaborated by Nils Bohr postulates the principle of complementarity between the particle and wave aspects of electrons, photons etc. It recommends pursuing the mathematical features of the quantum theory, which works very well in experiments, and not debating questions of the underlying reality, which seemed so paradoxical and counter-intuitive. Heisenberg joined in with his principle of indeterminacy, according to which it was impossible in principle to measure accurately both the position and the momentum (or velocity) of a wave-particle object. The wave packet, according to this view, represents only probabilities, not certainties. Thus the theory is fundamentally nondetermi~istic. This was unsatisfactory to Einstein, among others, who engaged in a long debate with Bohr, declaring that “God does not play dice with the Universe”. At first, I considered the following alternatives: -Betchov’s soliton, a non-linear component of the wave function, essentially a standing wave. * De Broglie’s “guiding wave”, which tells the electron or photon where the slits are in the two-slit experiment, or if there is one or two slits. * Bohm’s elaboration of the quantum potential. Then I realized that these alternatives were essentially the same. The quantum potential, which is the phase of the wave, indicates where the particle “really” is. The quantum potential is the same as the soliton, a high peak moving very rapidly across the wave packet, back and forth (like the resonance of chemical bonds in a benzene ring, only still faster). Since the probability of finding the particle is equal to the wave amplitude squared, the particle is very probably where the soliton is. In a measurement, the wave packet collapses because there is no more probability, we have found the particle. We could not predict where it would be, but it had to be SOMEWHERE along the wave packet, as the soliton vibrated rapidly across it. That probability was greatest at the middle of the wave packet, where the amplitude is greatest. This restores determinism to the theory, although it does not affect the ‘experimental findings or the mathematics. It is simply an alternative interpretation. However, it does not eliminate the “weirdness” of quantum theory, it only displaces it to other aspects. The Bohr and Bohm alternatives, as I briefly call them, are interpretations of the results of the two-slit experiment, which led to the wave-particle duality, the principle of indeterminacy, and the collapse of the wave packet when a measurement is made. We now have to pay attention to another quantum paradox, the EPR (Einstein-Podolsky-Rosen) experiment and the Bell theorem, according to which two particles flying apart from their point of creation remain non-locally entangled: they maintain the same spin (or other properties) even when only one of them is switched and they are too far apart to communicate at speeds less than the speed of light. Here again I see some alternative explanations: * Non-locality * Time travel: the particles return backward in time to their point of joint origin. * Connection by origin, like identical twins sometimes unknowingly doing the same thing at the same time, though far apart and not in contact. * Superliminal speeds are possible, perhaps through tunnelling or a wormhole. Again, I consider the first three alternatives as different versions of the same mechanism, violating in various ways our intuitive notions of space or time. The fourth alternative would be inconsistent with the special theory of relativity. Yet tunnelling is a real phenomenon on which some technical devices are based, and wormholes may be possible at subatomic size levels, with which we are dealing here. The book “The Non-Local Universe” by Robert Nadeau and Menas Kafatos (Oxford university Press, 1999) also considers philosophical implications of the new physics, both for epistemology and for metaphysics. The book is co-authored by a physicist and a philosopher, but I must admit that I understand the philosopher even less than the physicist, in spite of the inherent difficulty of quantum theory concepts. What I glean from the philosopher is again only my own interpretation. It is as follows: Phenomenology reflects the real world, although it is not identical with it; it translates sense data into perceived objects, but there is still a one-to-one correspondence, like the shadows on Plato’s cave. However, once we get to a more abstract sYmbolic level, e.g. expressing what we sense into linguistic form, we get more distant from reality. We can move entirely within the symbolic sphere (as described e.g. by Terence Deacon in “The Symbolic Species”) and IMAGINE (falsely) that we are getting a one-to-one correspo~dence between our theories and physical reality. But then (and this is my addition), if we then test our theories experimentally, as in science, we can get back to one-to-one correspondence to reality, if the experiments confirm the theories. Science is actually a reality check, to keep us from wandering too far in our imagination. Anything not tested is mere imagination, though it may by chance be true, especially if the theory is “elegant” or “beautiful”; but that may prove to be a false clue. Some post-modernist philosophers claim that we live in “a prison house of language”, in which language can only validate itself — it is self-referential. To me this sounds too extreme. The authors conclude that metaphysically the universe is a seamless whole, more than the sum of its parts, because it is non-local. Everything is connected by quantum entanglement because of past multiple interactions. However, I have concluded from other readings that quantum entanglements can be broken and often are, just as chemical bonds are broken. Therefore I don’t see that the leap from the EPR experiment to the assumption that “the universe is more like an organism than like a machine” is warranted. However, it MAY be true, because it is elegant and beautiful to think so. =========================================================================== SIZE SPECTRUM OF CELESTIAL BODIES ================================= Scientific American, April 2000, had an article on “Brown Dwarfs”, also known as “failed stars”. These accumulations of matter from dust and gas clouds are not massive enough or hot enough to sustain nuclear fusion (hydrogen to helium) in their cores, and so do not shine brightly like stars, but emit only weak light from the energy liberated by their gravitational contraction, as well as some from deuterium fusion. . Yet they are bigger than the solar planet Jupiter, our biggest, which also generates some internal heat. A minimum-size brown dwarf has a mass of about 13 Jupiters, while a minimum-size star would have a mass of about 75 Jupiters. Our Sun is 1000 times bigger than Jupiter. There now seems to be a continuous series of sizes in celestial objects, from an asteroid (which may have an irregular shape like a big rock, not even be spherical), to a satellite like our Moon, to a small stony planet like Earth or Mars, to a big gaseous planet like Jupiter, to a small brown dwarf like Gliese 229B, to a larger brown dwarf like Teide 1, to a red dwarf star like Gliese 229A, to a yellow star like the Sun, to a big blue star which lasts only a few million years, because of its fast production of energy. As the picture accompanying the article shows, these objects differ in mass, radius, surface temperature, age, the presence or absence of nuclear reactions, presence or absence of lithium (only brown dwarfs have it, not stars), and whether they mix from surface to centre by convection or have a layered structure like Jupiter and smaller planets. “Planets versus Brown Dwarfs”: ============================== Is there a fundamental difference between the largest planets and the smallest brown dwarfs? The classical view is that planets form in a different way than brown dwarfs or stars do. Gas-giant planets are thought to build up from planetesimals — small rocky or icy bodies-amid a disk of gas and dust surrounding a star. Within a few million years these solid cores attract huge envelopes of gas.This model is based on our own solar system and predicts that all planets should be found in circular orbits around stars and that gas giant planets should travel in relatively distant orbits. These expectations have been shattered by the discovery of the first extrasolar giant planets. Most of these bodies have been found in close orbits, and most travel in eccentric ovals rather than in circles. Some theorists have even predicted the existence of lone planets, thrown out of their stellar systems by orbital interactions with sibling planets. This makes it very hard for observers to distinguish planets from brown dwarfs on the basis of how or where they formed or what their current location and motion is. We can find brown dwarfs by themselves or as orbital companions to stars or even other brown dwarfs. The same may be true for giant planets. An alternative view is gaining adherents: to distinguish between planets and brown dwarfs based on whether the object has ever managed to produce any nuclear fusion reactions. In this view, the dividing line is set at about 13 Jupiter-masses. Above that mass, deuterium fusion occurs in the object. The fact that brown dwarfs seem to be less common than planets-at least as companions to more massive stars-suggests that the two types of objects may form by different mechanisms. A mass-based distinction, however, is much easier to observe. -G.B. =========================================================================== QUANTUM PROPERTIES ================== The four properties we are considering are: entanglement, decoherence, superposition, and the uncertainty principle. Entanglement occurs when two newly created particles must always have the same spin (and all other quantum numbers), and when the spin of one is changed, the other also changes, although they are too far apart to communicate by signals even at the speed of light. It is as if the two particles were connected by an eternal string. (No pun intended. ) Decoherence is the opposite of entanglement. The connection (“string”) between two entangled particles is broken by interaction with the environment. This is why ordinarily entanglement is not observed in the everyday world, where other dense interconnections exist. Superposition is the existence of two different quantum states for the same particle. It occurs by the addition of the two wave equations, as if by Fourier synthesis. Thus, while entanglement is a single state for two particles, superposition means two states for a single particle. The Heisenberg uncertainty principle says that we cannot know the position and the momentum of a wave-particle at the same time, in the same experiment. Perhaps it is evident that a wave does not have position and a particle does not have frequency (by analogy with “the dolphin click”, an essay in this collection). Scientific American (April 2000) has an article on teleportation, in this case of a photon, in which the concepts of these properties is used. It shows that the teleportation (transfer in space) is theoretically possible for a photon (and other elementary particles perhaps), though it has not yet been done in the laboratory. But it also argues that it is not even theoretically possible for a large complex physical object, such as a person. (Star Trek’s “Beam me down, scottie” will remain science fiction.) It seems to me that this is because elementary particles are “fungible” (indinguishable from one another) *, while large objects and persons are not. It is fundamentally impossible to preserve all the complex interrelationships in these larger bodies during spatial transfer. The information content exceeds all practical limits. * See my essay From Fungibility to Personality in this collection. =========================================================================== THE QUINTESSENTIAL UNIVERSE. ============================ This is a summary of my (imperfect) understanding of the essay of the same title by Jeremiah P. Ostriker and Paul J. Steinhardt in Scientific American, January 2001, pp. 4755. Dark Energy, which accounts for 70% of the total mass in the Universe, and which causes the recently observed acceleration in the expansion of the Universe, comes in two varieties (both assumptions): 1. Vacuum energy (Einstein’s cosmological constant), which is static and constant, just so much per unit of space, but of course a growing total as space expands. 2. Quintessence, which varies slowly, up or down, and is a dynamic quantum field. A further elaboration specifies the “tracker field”, which for a stretch of cosmic history tracks the decreasing energy density in the Universe. Both types originate from the quick generation and annihilation of virtual particles in “empty” space. There are 3 numbers (not either 6 or 9 as in two recent books) that characterize the Universe, illustrated in a “cosmic triangle”: relative density of dark energy, relative density of dark matter, and the curvature of space-time. It appears that the curvature is = 1, i.e. space is flat, not either hyperbolic or spherical. H2. Recipe for the Universe. Dark energy 70% Exotic dark matter 26% Ordinary dark matter 3.5% Visible matter 0.5% Radiation 0.005% ——- 100.005% Exotic dark matter, according to other authors, is called “hot dark matter” (mainly neutrinos) or WIMPS (weakly interacting (nearly) massless particles). Ordinary dark matter is also called “cold dark matter”, mainly brown dwarfs or Jupiter-sized planets, or MACHOS (massive astra-like cold halo objects, found in the halos of galaxies. ‘ Visible matter consists of stars, galaxies, quasars, planets, and luminous interstellar clouds. “Visible” means not only by visible light, but also by ultraviolet, X-rays, infrared, or microwave; in fact the whole electromagnetic spectrum. As I said before, quantum fields in “empty” space generate pairs of virtual particles. These fluctuations contribute positive (repulsive) energy (explosion) if the virtual particles are fermions (since fermions obey the Pauli exclusion principle and so cannot occupy the same (quantum) space at the same time, by Fermi-Dirac statistics), but contribute negative (attractive) energy (implosion) (ordinary gravity) if the virtual particles are bosons. Fermions (e.g. electrons and quarks) have halfintegral spins, while bosons (e.g. photons and gluons) have whole-integer spins. Fermions are particles of matter while bosons carry the forces between fermions. There is not an exact cancellation of the positive and negative energy, i.e. antigravity (dark energy) and gravity. However, super symmetry (a theory that postulates that each particle has a superpartner of the different type of spin) would very nearly balance them, to 120 decimal places; but supersymmetry comes into play only at very high temperatures, which may have been present at the Big Bang origin of the Universe. This near-balancing seems like another example of fine tuning, which made galaxies, stars, planets, and life possible in our Universe. This could be justified by the anthropic principle (if it were not so, we would not be here to wonder about it, and perhaps in other universes we are not there), but another scenario is possible, as explained below. An early event due to the overbalancing of antigravity over gravity could be the stipulated early “inflation” (super-rapid expansion or explosion) of the Universe, which occurred at 10 to the minus 35 seconds after the Big Bang. When inflation ended, quintessence (now the preferred version of the dark energy) achieved balance with gravity and expansion of the Universe slowed down considerably. After that, the decrease in the dark energy density tracked the decrease in the density of (ordinary) energy, until the Universe was about 30,000 or 300,000 years old, when matter and energy decoupled and the Universe became transparent to radiation. This tracking (hence “tracker field”) actually continued until almost the present age, when the Universe was 5 billion years old. (It is now 15 billion years old, which is not much later than 5 billion on a logarithmic scale.) So since 5 billion years ago, when the density of total matter began to exceed the density of energy, the tracking by quintescence density of energy density stopped and changed sign again, to initiate the present trends of accelerated expansion of the Universe, which may continue at an exponential rate forever, unless quintessence changes its sign again. If accelerated expansion continues forever at an exponential rate, galaxies and stars will move beyond the distance where communication (even at the speed of light) is possible, and there may be only isolated islands of life that don’ t (can’f} know about each other (so what’s new?), or: no life at all if everything gets too cold. If quintessence changes sign again, the Universe may contract back to its present size (or beyond?), and the age of galaxies, stars and life may reappear; but they will never know that a preexisting age of stars and life was ever here. Or are we already that second (or even nth) generation? This is a pulsating model of the Universe, not necessarily through a previously postulated alternation of Big Bang and Big Crunch, and not necessarily my previous model in “Ages of the Universe” involving a “supersYmmetry transformation” from a supercold Bose-Einstein condensate to a super-hot Big Bang unstable fermion ball. Either version of the pulsating Universe would not predict a dead end of life and humanity; but the version proposed here would do so only if quintessence is the correct model of the dark energy. If dark energy is a static invariable “vacuum energy”, the pulsation could not occur, and the dead end would be final. A pulsating Universe was long ago postulated, without benefit of modern cosmology or quantum physics, by ancient Vedic philosophy. =========================================================================== IT'S TURTLES ALL THE WAY DOWN? ============================== A woman of the native religion explained that the world rests on the back of a giant turtle. A doubter asked “And what does the turtle rest on?” “On a bigger turtle”, said the woman. “And what does the bigger turtle sit on?” was the persistent question. The woman, seeing the infinite regress, replied defiantly “It’s turtles all the way down”. That is exactly what it is NOT. Under ordinary substances are molecules, under molecules are atoms, under atoms are nuclei, under nuclei are protons and neutrons, under these are quarks, under them are strings. The underlying entities differ radically from the ones above. The laws change from ordinary mechanics to quantum mechanics to whatever obtains at Planck dimensions. Beyond common organisms is the planet Earth with its rocks, seas and air, beyond that is the solar system, beyond that the Milky Way galaxy, then the local supercluster, finally the whole universe, and maybe beyond. Again, the entities and laws change, from Newton to Einstein to Hawking. Similarly, we encounter phase transitions when we go to high temperatures (solids to liquids to gases to nucleielectron plasma to proton-neutron plasma to quark-gluon plasma) or to extremely low temperatures (to solids with various transitions or superfluids and finally to BoseEinstein condensate). Even numbers go beyond infinity to many different kinds of infinity. Black holes out-do neutron stars which out-do white dwarfs which follow stars on the main sequence which are bigger than brown dwarfs which are bigger than giant gas planets like Jupiter which are bigger and different than rocky planets which differ from asteroids which differ from comets which differ from meteorites. It’s definitely NOT turtles all the way down. It’s a many-splendoured thing, like Love. =========================================================================== THE MAP IS NOT THE TERRITORY. ============================= No living creature could survive in its environment without some kind of a map. We use mainly a visual map, dogs a scent map, bats an auditory map. We also use our other senses to give us partial maps. And the brain coordinates the various sense maps and makes rational decisions on how to navigate and make a living. We all get a sense of beauty from our sensual maps, and derive our joy of living from them. We say we love “Nature”. Yet all we know are Nature’s maps. Like Plato’s sage, we see (hear, smell, touch, taste) only the two-dimensional shadow on the cave wall. A shadow of what7 Of the Real Thing that casts the shadow, the thingin-itself in multiple dimensions of which we receive our navigational maps. Only when we dig very deep in the physical sciences do we get an inkling of what lies beyond our cave. When we zoom in on the very small, do we get an inkling of the quantum world, and beyond that the micro-string world. No wonder that we find it very weird — we can have no experience of it through any of our sense maps. Only mathematical maps (models) can help us to navigate. Only when we zoom out to the very large (in space and time), do we get an inkling of cosmology, of beginnings and distant futures of the universe. This too is weird, in different ways. We don’t even know how to put together the very small and the very large, though there are hints that they are quite intimately connected. Is cosmology and the quantum world the Thing-in Itself? Probably not, only the first layer in the boundary between our maps and the territory. Bohm spoke about the quantum world being enfolded in the deeper reality, and unfolded back out of it. Mystics perceive a reality which they cannot even describe in words. As in Cantor’s mathematics of infinite sets, there are always infinities beyond infinities ad infinitum. There are dimensions beyond dimensions (maybe only up to 26). There is Beauty beyond beauty, Truth beyond truth. THAT, my friend, is the Territory. Meanwhile, let us enjoy our maps, and a little bit beyond. What is lacking to make this a religion, is love. We are immersed in divine love, but like fish in the ocean, we discuss the existence of the Ocean. =========================================================================== LAKOFF VERSUS PENROSE. ====================== Two mega-theories can be distinguished. In his two books (“Philosophy in the Flesh” and “Where Mathematics Comes From”), George Lakoff claims that both mathematics and language are cognitive products of the mind, and hence of the brain and the body. These abstract concepts (numbers, words, structures for combining and extending them) are formed by metaphors based on experiences from daily life, related ultimately to survival, and hence the evolution of body and mind. There are innate (genetic) propensities for forming such metaphors (and hence concepts) based on and brought out by experience. Roger Penrose, on the other hand, believes that mathematics and abstract thought exist independently in the external world, in what he calls “the Platonic sphere”. (Both Lakoff and Keith Devlin [in “The Math Gene”] call this “the romantic view” of mathematics, which we can choose to believe or not to believe, just as the belief in God.) Penrose presents his Platonic sphere in a diagram of two spheres on pages 3-4 in his book “The Large, the Small and the Human mind”, in which he pictures the physical influencing the Platonic, and the Platonic, in turn, influencing the physical. In other words, abstract ideas do come from the brain via the physical body, but the ideas in the brain reflect, or represent in some way, the structures of the external world. (How else could we survive in the external world unless we knew “the truth”?) In Penrose’s three-sphere scheme (presented on page 96), the mental sphere has links both to the physical sphere and the Platonic sphere, while the physical and the Platonic are also linked, in that mathematics has large applications in the physical world. If this is a “romantic view” of where mathematics and language structure come from, I am ready to believe it, without a proof necessarily, except for the inference bracketed in the preceding paragraph. It is a question of faith, like belief in God, which I also share. To that extent, Lakoff and Devlin are also right. I also have another question. cognitive science, as used by Lakoff, is based on scientific (i.e. objective) observations of the very mind which the experimenter and the theorist uses in his/her studies. Is there not a circular argument in this somehow? =========================================================================== COLOUR VISION AND THE FOUR-COLOUR MAP PROBLEM. ============================================== From article by Dale Purves, Beau Lotto, and Thomas Polger, Journal of Cognitive Neuro-science, Vol. 12, No.2, March 2000, pp. 233-237. The authors argue that the fact that the human eye can detect four primary colours, red. green, blue, and yellow, is somehow related to the fact that at least four colours are required to colour a map so that no two colours are adjacent to each other. [But I thought that the eye has 3 cone colour receptors in the retina.] In any case, their diagram shows 3 colour wheels, above one another. The uppermost one is all white, the lowest one is all black, and the middle one shows hues (colours) of increasing saturation toward the circumference, while the middle is gray. Brilliance increases in the upward direction. The uppermost wheel could represent Heaven or Nirvana; not only a White Hole, but a White Whole — all of the Divine Essence. The lowest wheel is a Black Hole or a Black Whole of bottomless despair. We are in the middle wheel, the coloured one. Even at the centre, we see only gray; this is why the Godhead is incomprehensible to us. We lack the brilliance to see the White Hole, unless we are lifted up to Eternity, or achieve Enlightenment. However, we DO have the rainbow, which Eternity lacks. =========================================================================== NON-COMMUTATIVE DICE MOVES. =========================== Addition and multiplication are commutative operations, since A+B=B+A and A.B=B.A. Subtraction and division are not commutative, neither is raising to a power. Another interesting case of non-commutative operations is turning a die left (L), right ®, down towards you (D), or up away from you (U). A few experiments with a die convinced me of the following. There are 16 moves if we permute the 4 simple operations in pairs: LL, RR, DD, 00, LR, RL, DU, UD, LD, DL, RD, DR, LU, UL, RU, and UR. The first 4 of these give you the opposite face of the die. The next 4 give you the starting face. The last 8, which combine the 2 dimensions, are the interesting ones. They are not commutative, i.e. the result depends on the order in which you perform the operations. We obtain: RD=D, but DR=R LD=D, but DL=L RU=U, but UR=R LU=U, but UL=L. The rule seems to be that the result conforms to the last (second) letter, i.e. is equivalent to that single move. In practice, this gets much more interesting if instead of a die we have an airplane that can yaw up and down, turn left and right, and rollover either way. In some combinations, it will be pointing straight down to the ground — not a healthy condition. I am waiting to get hold of a model airplane to try it. I don’t have enough spatial imagination to do it in the abstract. =========================================================================== SENSUAL MAPS. ============= The world we SEE with our EYES is only a MAP of reality. It is barely 3-dimensional; for me without binocular vision only 2-dimensional. Bats and dolphins form acoustic maps with their different echo-location senses; not optical maps which we enjoy. Dogs live by olfactory maps. Which sense maps are closer to reality? None of them, probably. They only provide us with means to survive in an unknown and unknowable world. Taste maps help us savour and enjoy the flavours and texture of the food that nourishes us. Touch maps? They enable us to savour and enjoy the map of the body of our beloved. =========================================================================== VERY LARGE GRAPHS. ================== According to Brian Hayes’ article (“Graph Theory in Practice, Part II”, American Scientist, March-April 2000), very large graphs (networks of points/vertices and links/edges) come in three varieties: very ordered ones like rings (in which every vertex is linked to 2 neighbours and 2 next-to-neighbours), semi-ordered ones (in which some of the links in rings are opened up to join randomly across the ring), and disordered ones (with very dense random links across the ring, but not quite completely connected). The second type, the randomly but sparsely connected ones across the ring, are good models for “small-world graphs”, such as the graph of world acquaintainceships (Milgram’s “small world”), the World Wide Web (now 800 million pages, and still adding daily), the Hollywood graph (225,000 actors, and when do 2 of them appear in the same movie), the electric power grid, and telephone connections. These small world graphs (the Watts-Strogatz model) have some properties in common: (1) they tend to be sparse (only about n edges, where n is the number of vertices, not n(n-1)/2, as would be the case in a “clique”, a completely connected graph); (2) they tend to be clustered; (3) they tend to have a small diameter (shortest edge between the most distant vertices, about log n. Erdos and Renyi worked on these graphs. They predict real-world small world graphs fairly well. So small world graphs are not quite regular (ordered) and not quite random. There is a parameter, b, such that if b>3.4785, almost every graph is disconnected; if 1