Scientific Enlightenment, Div. One Book 2: Human Enlightenment of the First Axial 2.B.1. A genealogy of the philosophic enlightenment in classical Greece Chapter 17: Plato's Allegory of the Cave in the Republic and its modern scientific parallel ACADEMY | previous section | Table of Content | next section | GALLERY

If the end of Plato's divided line is what in his functional perspective (without any time dimension) corresponds to (to the best of our knowledge as yet) the standard model of elementary particles (which has a time dimension) in the structural perspective, then his famed allegory of the cave serves also as a parable for the spontaneous symmetry breaking 10^-36 second after the creation of the universe which gives rise to the structure of reality captured by the standard model. We will then here explore the second symmetry-breaking, i.e. on the level of the Grand Unified Theory (or rather, grand unified theories) and its analogy with the disillusionment that is the prelude to salvation in the second mode, specifically illustrated by Plato's allegory of the cave.

The second symmetry-breaking is responsible, on the side of forces, for the breaking-up of Grand Unification, and, on the side of matter, for the distinctions among the various subatomic particles of the Standard Model and then for the CPT symmetry-breaking that results in the predominance of particles over anti-particles. The breaking-up of Grand Unification involves the settling of the Higgs fields from zero to non-zero values. Certainly we have to explain this modern scenario before we can show how Plato's parable may apply here. But interestingly, in giving one such popular exposition of it, Alan Guth (The Inflationary Universe) makes use of precisely a modern version of Plato's allegory of the cave.

1. The spontaneous symmetry breaking on the level of Grand Unified Theory and the diversity of existence.

The "energy scale of unification [of electromagnetic, weak, and strong nuclear forces] is determined by the measurements of the strength of the three interactions at energies of about 100 GeV. The unification energy is high because the measured values of the three interaction strengths [at the current temperature level of the Universe, that is] are very different from each other." (Guth, p. 135.)

Spontaneous symmetry breaking "is intimately related to the Higgs particle of the standard model" (which is "yet to be found"). (p. 136) A "spontaneously broken symmetry is a symmetry which is present in the underlying theory describing a system, but which is hidden when the system is in its equilibrium state." (Ibid.) Present but hidden is the truth about reality discovered when the illusion we live in -- the equilibrium or stable state of the system after its phase-transition -- is overcome. Guth makes use of an analogous occurrence of spontaneously broken symmetry in the more familiar situation of the formation of a crystal to clarify the one involved in the breaking of the originally symmetric grand unified force (i.e. of one interaction strength) into the three different forces (of three interaction strengths).

"To make the analogy between spontaneous symmetry breaking in crystals and in grand unified theories as clear as possible, we will consider a particularly simple type of crystal, called orthorhombic, an example of which is the mineral topaz. These crystals have a rectangular structure, as illustrated in Figure [below], so all the angles are right angles. Unlike a cubic crystal, the three principal lengths of an orthorhombic crystal are all different, a feature that will make the analogy with grand unified theories a little closer." (Ibid.)

The structure of an orthorhombic crystal (Guth, ibid., p. 137)

"An outline of the crystal/GUT analogy is shown as Table [below], which can be used as a checklist to help keep track of the following discussion. Starting at the top of the table, the first row indicates the symmetry that is involved. For the case of the crystal, the relevant symmetry is rotational invariance. The physical laws that describe the system are rotationally invariant, which means that they make no distinction between one direction of space and another. In the case of the grand unified theory... the symmetry is what is sometimes called an internal symmetry, one that relates the behavior of one type of particle to the behavior of another. In this case, the underlying symmetry of the grand unified theory has two manifestations. First, the symmetry implies that [on this bosonic side] the three interactions of the standard model -- SU(3) [strong], SU(2) [weak], and U(1) [electromagnetic] -- are really one interaction, and hence indistinguishable. Second, the GUT symmetry implies that [on the fermionic side] the underlying laws of physics make no distinction between an electron, a neutrino [i.e. between these two kinds of leptons], or a quark. Both manifestations of the GUT symmetry are analogous to the indistinguishability of the different directions of space for the crystal." (p. 136 - 7)

"The second row of [our Table] describes the mechanism of spontaneous symmetry breaking -- what is it that breaks the symmetry?" In the salvational terms in which we will pursue the matter: how is the illusion we live in -- the diversified, pluralistic material world around -- generated? "In the case of the crystal, the atoms arrange themselves along crystal axes which are picked out randomly by the first few atoms as the crystal starts to grow. Thus the three directions of the principal axes become distinguishable from each other and from all other directions. In the construction of GUTs, theorists include a set of fields specifically for the purpose of spontaneously breaking the symmetry. These fields are known as Higgs fields... and the spontaneous symmetry breaking mechanism is called the Higgs mechanism." (p. 137 - 8) Recall that in the Standard Model every particle (boson and fermion) is associated with a field, and is represented as a regional concentration of that field, so that for example the energy of the electromagnetic field is seen concentrated in bundles called "photons", and the energy of the electron field in bundles interpreted as "electrons". "The energy of the Higgs field is concentrated into particles that are... called Higgs particles. The Higgs particles associated with the breaking of the grand unified symmetry are expected to have masses corresponding to energy in the vicinity of 10¹⁶ GeV... too massive to be produced experimentally... The Higgs particle of the standard model [i.e. associated with electroweak unification], on the other hand, is expected to have a mass in the vicinity of 10³ GeV." (p. 139) The difference between the bosonic and fermionic fields on the one hand and the Higgs fields on the other is that whereas the former fields have their lowest possible energy density value in zero, i.e. when they vanish, the latter have it when they have non-zero values (in addition to the fact that the ordinary bosons are vector fields -- having a particular direction at each point -- whereas the Higgs bosons have spin 0 and so are scalar fields -- since having spin 0 means that they behave like a scalar under Lorentz transformations -- so that their interaction with other particles does not depend on direction). "The Higgs field in empty space [i.e. when it does not occur] -- often called vacuum -- will therefore have nonzero values, since they will settle into the state of lowest possible energy density." (Ibid.)¹

The energy density of the Higgs field in a region of space-time depends on the interactions between the individual fields, such as the two in the illustration below furnished by Guth, rather than on the sum of them. (In actuality the simplest grand unified theory requires 24 fields.) "The three-dimensional diagram shows the energy density of the Higgs fields, for any specified pair of values for the two Higgs fields. For example, suppose that Higgs field A has the value 3 and Higgs field B has the value 2. To find the energy density of the Higgs field from the diagram, first find the point in the base plane corresponding to this pair of values, as shown. Then determine the energy density from the height of the surface above the point in the base plane." (Ibid.)

"Energy density of the Higgs fields. The graph shows the energy density for an illustrative theory that includes two Higgs fields. The motion of a ball rolling on this surface, as shown, is very similar to the evolution of the Higgs fields. The energy density has a large value if both of the Higgs fields are zero, but the energy density vanishes when the Higgs fields correspond to any point on the 'vacuum circle'. A random point on the vacuum circle is determined by random processes in the early history of the universe, spontaneously breaking the symmetry of the underlying theory." (Guth, p. 140)

In the figure the rolling ball represents the sliding value of the energy density of the Higgs fields and so their behaviour. "Since energy is needed to lift the imaginary ball, the gravitational energy of the ball increases with its height. The gravitational energy of the ball is therefore proportional to the energy density of the Higgs fields, which on the diagram is shown by the height of the surface. Although gravitational energy may not seem familiar, the effects of gravity are easy to visualize. The ball will be pulled downward by gravity, toward the curve labelled 'vacuum circle'. The evolution of the Higgs fields is in fact very similar to the motion of this ball." (p. 140) That is, if energy is high enough (such as to lift the ball up) the Higgs fields will vanish, in contradistinction to the "ordinary" fields associated with bosons and fermions. But they (or the system) will then try to release the potential energy they thus have in order to settle on the lowest possible energy level, resulting in the appearance of their value. This is the phase transition -- a change of state (usually in matter) when the temperature of the system changes -- during which the Higgs fields "appear" from nowhere. (More ordinary examples of phase transition are (Daney: ibid.): a magnetized piece of iron retains its magnetism up to a temperature of about 768° C but loses it above that point. Upon cooling below that point, the magnetic field reappears; a number of materials have the property of superconductivity at very low temperatures, but lose this property at a few tens of degrees above absolute zero; water has a small number of distinct symmetry axes at low temperature, e.g. in the form of an ice crystal or snowflake, but loses these axes, and becomes more symmetrical, when the temperature is high enough. Systems tend to exhibit a higher amount of symmetry at higher temperatures but lose it below a certain critical point, thus during precipitation, condensation, crystallization, etc.) "The state of lowest possible energy density is not unique: any of the points on the 'vacuum circle' correspond to zero energy density. The imaginary rolling ball could eventually come to rest at any point on this circle. The values of the Higgs fields in the vacuum are therefore not determined by energy considerations. Just as the atoms in the crystal can align equally well along any of an infinite number of possible orientations, the set of Higgs fields in the vacuum can settle equally well at any point on the vacuum circle. Some particular point on the vacuum circle would be chosen randomly in the early history of the universe, just as the directions of the crystalline axes are chosen randomly as a crystal begins to form. This random choice of non-zero Higgs field values breaks the grand unified symmetry, just as the orientation of the crystal breaks the rotational symmetry. In both cases the underlying laws of physics remain exactly symmetric -- the symmetry is broken 'spontaneously', in the sense that it is only an accident of history that chooses the orientation of the crystal or the point on the vacuum circle for the Higgs field. The other particles in the theory interact with the Higgs fields, so they are affected by the random choice of Higgs field values. Since different particles interact with different Higgs fields, distinctions arise between particles that would otherwise be indistinguishable. For example, suppose the fields in the vacuum settle at the point for which Higgs Field A has the value 10 and Higgs Field B has the value 0. Then, as one might guess, the particles that interact with Higgs Field A will behave very differently from those particles that interact with Higgs Field B." (p. 141) This is the process of differentiation of the same substratum into a variety of differences. "In particular, the mass of a particle is determined by its interaction with the Higgs fields, so the masses of the particles that interact with Higgs Field A will become different from the masses of the particles that interact with Higgs Field B. In a full grand unified theory with a large number of Higgs fields, some of the [fermionic] particles are caused to act like electrons, some like neutrinos, and others like quarks. Similarly some of the force-carrying [bosonic] particles will be caused to act like the gluons that carry the strong interactions; others will be caused to act like the W⁺, W^-, and Z⁰ of the weak interactions, and one will be caused to act like the photon of the electromagnetic interactions." (p. 141 - 2) That is, when particles move through the Higgs field they are respectively associated with, their interaction (coupling) with this Higgs field would result in their appearing as having "mass". Photons and gluons which do not couple with any Higgs field then do not have mass. The W particle weighs 85 times as much as a proton, and Z 97 times, because of the strength of their coupling with their respective Higgs fields.² The spontaneous symmetry breaking associated with the acquisition of Higgs field values first breaks up the gluon and the electroweak (at 10^-35 second after creation, at a temperature of 10²⁸K and energies of 10¹⁵GeV), then photons and W and Z particles within the electroweak (at 10^-12 second, 10¹⁶K and 10³GeV). Since the range of a force is inversely proportional to the mass of the boson carrying it, this Higgs field coupling explains why electromagnetism has long range and weak force short range after the asymmetry leaves all the mass to one side and none to the other. Furthermore even charge parity (CP) violation -- a fundamental asymmetry between matter and antimatter responsible for matter dominance and the existence of material, physical "things" -- is generated by this Higgs-coupling.

CPT symmetry breaking is currently the answer as to why the universe is dominated by matter. If CPT symmetry were always conserved for every type of interaction then there should have been equal amounts of matter and anti matter in the early universe. They would then annihilate each other in the production of radiation-energy -- returning to the energy pool from which they came, in the Presocratic manner -- and no matter would be left in the present universe. For the purpose of the creation of our material world (galaxies, stars, organisms), therefore, it is not enough for asymmetry to appear between the various types of fermions, but also between (the numbers of) the particles and the anti-particles of each fermionic type. CPT -- charge conjugation, parity conservation, and time reversal -- symmetry is expected to be conserved according to the principle of conservation: if we make particle interactions into their mirror image (left becoming right and right left: P), swap particles for anti-particles (all positive charge becoming negative and negative positive: C), and run their interactions in time backward (T), all at the same time, the result should be the same as before. "The laws of physics are unaffected by a complete CPT transformation, which is why [and this is the problem] it had seemed natural to assume that each component of CPT itself was 'symmetric' [i.e. conserved] in the appropriate sense." (Gribbin, p. 338)

But while the strong force usually obeys the individual conservation of C, P, and T, this turns out not to be true of the weak force. We thus see that the misapplication of conservation continues to the 20th century. We have seen that primitive animism applies it to the breath-soul, resulting in the worship of the dead; that pre-classical peoples apply it to pain-pleasure, resulting in karmic thinking; that early scientists apply it to matter only -- until Einstein's E = mc² shows that it is the underlying matter-energy that is conserved, not the individual matter or energy. The gradual precision in the application of the conservational principle (and of entropy as well) governs the history of human consciousness or its various shifts in paradigms of "worldviews": one of the principal themes of this work. By 1960s physicists finally realize that it is the totality of CPT together that is conserved, not the individual C, P, and T. What the case of the weak force reveals is that the nonconservation or breaking of C symmetry can be cancelled by P-breaking during the same interaction to ensure conservation, or that CP breaking together can be cancelled out by T-breaking.

An example of this can be seen with K (0/L), a neutral kaon which, just like photon, is its own antiparticle. It can decay (through the weak force) either into (1) p^- (hadron), positron (lepton) and an neutrino (lepton) or (2) p⁺, electron, and an antineutrino (the exact opposite of (1)). The two types of decay are supposed to balance, i.e. cancel, each other out to ensure conservation of C, P, or T; but (as it is discovered in 1963 in the experiment by J. Christenson, J. Cronin, V. Fitch, and R. Turlay) the first pathway of decay turns out to be more frequent than the second, thereby increasing the proportion of positrons to electrons in the universe by a small amount. This indicates the universe's preference for a certain "left-handedness", "as far as electrons are concerned." (Gribbin, ibid., p. 340)³ This means: "This violation of CP conservation in the weak decay of the kaon means that time reversal invariance must also be violated in order that CPT be conserved. Hence on the microscopic scale there exist subatomic systems for which time has a unique direction of flow!" (Cal State LA nuclear physics lecture)⁴

It is the famed Russian physicist Sakharov (1967) who first formulates the scenario wherein this kind of CP violation can explain why there is more matter than anti-matter in the early universe. Here we come to the baryons and the strong interaction. "To come out of the Big Bang with an excess of matter over anti-matter, Sakharov said, 3 conditions must be satisfied. First, there must be processes that produce baryons out of non-baryons. Second, these baryon interactions -- or, at least, the ones that matter -- must violate both C and CP conservation. Otherwise, even if baryons are made by some process [out of non-baryons: the first condition], there will be an equal number of antibaryons made in the equivalent antiprocesses, and eventually the particles [baryons] and antiparticles [antibaryons] will meet and annihilate. And third, the universe must evolve from a state of thermal equilibrium into a state of disequilibrium -- there must be a definite flow of time so that CP processes together can be nonconserved, even though CPT remains conserved." (Gribbin, p. 341) Note that this is another instance showing that "existence" as we know it is possible only in time, i.e. in an irreversible time dimension: the excess of matter over anti-matter requires the arrow of time (thermal disequilibrium), which furthermore makes possible the arrangement of the excess of matter into orders such as open dissipative structures (nonlinear entropy), and consciousness not only requires this ordering for its physical constitution but also for its psychological constitution (i.e. memory or the storage of information).

This thermal disequilibrium requires the fall of temperature and the expansion of the universe, which, we have seen, is also what allows the Higgs fields to appear (phase transition). "It is only if the temperature of the universe falls that the balance of equations is tilted in one direction, in favor of the lower energy-state [i.e. in favor of the surplus of particles over antiparticles and their non-conversion back to radiation] -- and the fact that the universe is evolving from a hot state to a less hot state provides a direction of time." (p. 342) According to the current thinking the surplus of matter is produced at the end of the GUT era (slightly after 10^-35 second after creation) by the decay of a very heavy gauge boson (the X boson) that violates CP. It is first of all interactions involving the X boson which can make baryons out of non-baryons and vice versa, so that quarks and leptons are interchangeable when there is enough energy available for X bosons to exist: "An up-quark can change into an anti-up quark by emitting a X boson that decays into an anti-down quark and a positron. The GUTs specify a prescription for turning quarks into leptons and also for creating quarks and leptons out of X bosons [the first of Sakharov's conditions]." (p. 343; this fact means that protons have a finite lifetime, currently estimated in between 10¹⁷ and 10³⁰ years.) During the GUT era, high energy ensured the reversal of all processes, hence X and anti-X bosons were produced and annihilated at the same rate. But by 10^-35 second after t = 0 "the number of new pairs being created no longer matched the rate at which existing X and anti-X particles were being used up, because the universe was cooling below 10¹⁵ GeV. If the using-up process had consisted only of pair annihilation events, that would have been the end of the story. The universe would have settled out as an expanding region of space-time containing nothing but cooling electromagnetic radiation. But... the X particles can also decay into quarks and leptons, and many did so before they were annihilated." Specifically X also decays into (1) 2 quarks or (2) an anti-quark and a lepton; anti-X into (1) 2 anti-quarks or (2) a quark and an anti-lepton. "But because the decay processes violate the C and CP symmetries, they do not work at the same rate for anti-X as they do for X [the second of Sakharov's conditions]." (p. 344) For every number of anti-X decays into 1 billion anti-quarks, the equivalent number of Xs decay into 1 billion and 1 quarks -- the source of all the matter in the universe. Sakharov's third condition is manifest here in that within the expanding and cooling universe having an arrow of time, "1 quark in a billion (10⁹) failed to find an anti-quark partner after the GUT era and so never annihilated, but instead stayed around to form the protons and neutrons that make up the bulk of the matter in the univers today. We owe our existence to a very tiny imbalance in the laws of physics, a preference for matter over anti-matter in the decay of the X bosons that amounts to no more than 1 extra quark for every billion antiquarks -- an imbalance equivalent to one ten millionth of one percent of all the matter that existed in the form of X and anti-X pairs in the GUT era." (p. 344; note that 10⁹ happens to be the ratio of photons to baryons in the universe today.)

An up quark changing into an anti-down quark
and positron via X boson

2. This diversity of existence due to symmetry breaking and the creation of illusion that is our experience of the world.

Symmetry breaking is the result of fallen temperature which prescribes a behavior of low energy physics in the two analogous systems as described by the third row of our Table, and our observation of this behavior explains why we are said to be "living in illusion." "Here the analogy can be made more illustrative by whimsically imagining a world of intelligent creatures living inside an orthorhombic crystal -- we will call them Orthorhombons. Let us assume that the Orthorhombons can somehow move about and carry on task of scientific investigation, but that they cannot muster enough energy to melt or even significantly perturb the crystal in which they live. Since the crystal would be immutable, the Orthorhombons would not recognize it as an object. Instead, the crystalline structure would be taken as a fixed property of space. An Orthorhombon physics book [before their awakening to the Grand Unified Theory of the crystalline] would make no mention of rotational symmetry, but would instead contain a chapter discussing the properties of space and its three primary axes. The orthorhombic structure would affect the propagation of light through the crystal, so an Orthorhombon table of physical constants would list three speeds of light, one for each primary direction. If grand unification is correct, then our universe is similar to this crystal world. The Orthorhombons live inside a crystal, the effects of which they mistakenly view as fixed attributes of space. We live in a region permeated by Higgs fields, the effects of which we mistakenly view as fixed attributes of the laws of physics. Our tabulation of the different properties of the strong, weak, and electromagnetic interactions is analogous to the Orthorhombon tabulation of the three different speeds of light. Similarly, the distinct properties that we observe for electrons, neutrinos, and quarks are not fundamental -- they represent the different ways that particles can interact with the fixed Higgs fields that exist throughout the visible universe." (Guth, p. 142 - 3; emphasis added.)

We have said that the essence of the second mode of salvation everywhere consists in this that salvation -- or at least the salvational state of mind, i.e. enlightenment, awakening to Truth -- is achieved when the illusion about the nature of the world around us (and our existence itself) is overcome. Although the first mode, e.g. Christianity, wrestles with something similar, the "truth" therewith associated is a drama -- the historico-salvational function of Christ's sacrifice and his status as the son of God -- whose acceptance could, of course, as the Gospel of John emphasizes, be just as difficult a task as the overcoming of illusion about how the world works. In the first mode, that is, the salvational state is the belief in the (diachronic) world-historical drama, whereas in the second mode the truth associated with the salvational state concerns the synchronic structure of reality. And disillusionment in the second mode consists precisely in no longer mistaking the effects of an underlying reality for the reality itself.

We have said that the Platonic mode of overcoming illusion (or "uneducatedness" in Plato's words: apaideusiaV; ignorance in Buddha's words: avidya) -- through the study of eidos -- reproduces precisely in the functional perspective the scientific project in the structural perspective. Indeed, compared with the Upanishadic mode (overcoming the illusion of the separateness of the ego in the formula Atman = Brahman, or of the distinction among all things ultimately), the Buddhist mode (overcoming the illusion of the very existence of any ego, even an universal one, and of the existence of the whole cosmos ultimately), and the Daoist mode (transcending the limitation of a provincial perspective, adopting the universal perspective of the Dao), the Platonic postulation of firstly an eidetic underlying reality and secondly the empirical reality as its effect -- and the most forceful expression of this postulation in the allegory of the cave matches almost exactly the Orthorhombon parable here -- corresponds more closely with the progress of science as the advancement of a structural perspective that no longer mistakes the effects of an underlying reality for the reality itself. In effect Guth is advancing here an equivalent in the structural perspective to Plato's story of the cave in the functional perspective. When Socrates says (The Republic, Book VII) "make an image [i.e. a parable] of our nature in its education [paideias] and want of education [apaideusias]", it might as well describe the Orthorhombons' -- and our physicists' -- educational process before understanding symmetry-breaking and after.

In the same way, the Orthorhombons, unable to see the crystal itself in which they dwell, unable to see their situation, name as real (to on auto: Being itself) the three speeds of light which are in fact only the distortions or shadows produced by the rotational a-symmetry of the crystalline medium. In the same way, our pre-enlightened physicists name as real the four different forces of nature and the variety of fermions (quarks and leptons), which are in fact distortions or shadows produced by the broken symmetry of spacetime. They are still "bound up" in the "cave", just as the primitives were when these believed in the independent reality of consciousness-and-metabolism and objectified it as the breath-soul. Even though our scientists have advanced away from illusion, they have yet to achieve total liberation by discovering completely the reality of which what we experience as matter and force are just the "shadows" or "effects". But at least ever since the beginning of the structural perspective of science, some of humanity have been gradually coming to the realization that what they have hitherto taken as the "real" things (whether the "elements" or the "breath-soul-life force" or the geocentric cosmos) seem only to be the shadows or effects of some as yet undisclosed reality. As we will see, "effect" or "shadow" being illusion means that what we have hitherto taken as the "real" reality is either a particular limited case of the whole reality the ignorance of which outside the limited case renders our knowledge of the limited case shallow and incorrect, or only the surface of some deeper reality the ignorance of which, again, renders the conclusion about reality drawn from that surface incorrect. Although what Plato means by "shadow" (or illusion: doxa) and "real" (to on) are empirical things and the forms of these things rather than the structural reality or the broken and restored symmetry of reality, his illustration of the process of overcoming the naturally given state of illusion -- taking the shadows or the effects of something else as that something else -- still holds and demonstrates that our natural state of existence is unquestionably a dwelling in illusions: we necessarily live in illusion because our existence as the orders that we are -- macroscopic dissipative structures -- is not only conditioned upon the broken symmetry of reality but dictates that this asymmetry and other effects of the true reality be our immediate experience, just as the shadows are for the prisoners, the diversity of light-speeds for the Orthorhombons, the diversity of matter and force for the pre-enlightened physicists, the belief in the singular ego and the multivarious material things for the commoners past and present -- this dictation of illusion further reinforced by the natural desires for consumption (in Buddha's word: tanha) inherent in an open dissipative structure (c.f. the Phaedo).

"Now consider," Socrates continues, "what their release and healing from bonds and folly would be like if something of this sort were by nature to happen to these people." (515 c4; Skopei dh... autwn lusin te kai iasin twn te desmwn kai thV afrosunhV, oia tiV an eih, ei fusei toiade sumbainoi autoiV.) The high temperature behaviour of the two systems described in the last row of the Table illustrates what happens when the illusion is broken up. "If a crystal is heated sufficiently, it will melt and become a liquid. The melting of a crystal is an example of what is called phase transition -- a sudden change in the behavior of a material as the temperature is varied. The distribution of molecules in the liquid phase is rotationally symmetric, looking the same no matter how the liquid is turned. At high temperatures, therefore, the rotational symmetry is restored." (p. 143) At such time the Orthorhombons will have overcome their illusion and noticed that there are never three speeds of light, but only one. Now to visualize this same phase transition in our case, "recall that at zero temperature the two Higgs fields in our sample theory assume a pair of values on the vacuum circle of [the] Figure... [The ball representing their values] at zero temperature lies motionless at some point on the vacuum circle. As the temperature is raised, the Higgs fields acquire thermal energy and begin to oscillate... [as if] vibrations [were] caus[ing] the rolling ball to jiggle along the surface. When the temperature is low, the ball will undergo only small oscillations, which will continue to be centered on some point on the vacuum circle. Since the average values of the Higgs fields described by the oscillating ball are nonzero, the symmetry remains spontaneously broken. Once the temperature exceeds a certain value, however, the ball begins to thrash about wildly, sometimes crossing the central peak. Its average position becomes the center of the Mexican hat, and all evidence of the initial zero-temperature values of the Higgs fields is lost." Higgs fields now disappear again during this phase transition. "Each Higgs field then has an average value of zero, so the grand unified symmetry is restored. The SU(3), SU(2), and U(1) interactions all merge into a single interaction, and there is no distinction whatever between electrons, neutrinos, and quarks." Note here the equivalent in modern physics to the perennial philosophical enlightenment "Being is One" stirred up by the anamnesis of conservation: like the moment when we realize that Brahman is One and all the different things in the world are just illusory aspects of the one Brahman, or that all are run through by the one, same Dao. This grand unification (symmetry-restoration) is hinted at less adequately during the First Axial by the immanentist insights, such as the Presocratic Anaximenes' (or afterwards the Neoconfucians') pure air before its rarefaction and condensation, which matches more with the homogeneous radiation aspect of this era (when particles can never fully materialize but immediately annihilate with their antiparticles back into radiation). "For a typical GUT, this transition occurs at a temperature in the vicinity of 10²⁹K (...10¹⁶GeV). If we lived at such extraordinary temperatures, our observations would directly exhibit the full grand unified symmetry." (P. 143 - 4, emphasis added.) But of course, we -- or any macroscopic open dissipative structures with consciousness -- cannot possibly exist at such temperatures. Not only is existence only possible as an illusion (as virtual and as diversified) but consciousness is only possible as consciousness of illusion. Consider now the grand unification diagram. "The unification scale, where the three lines meet, is identified with the typical energies associated with the Higgs fields. More precisely, the important issue is the effect of the Higgs fields on the force-carrying particles. For interactions of particles at energies higher than the unification scale, the nonzero values of the Higgs fields are irrelevant. Such high energy particles are unaffected by the Higgs fields, just as high speed bullet passes undeflected through a sheet of paper. Since the Higgs fields are unimportant at these energies, the force-carrying particles all behave the same way and the observed interactions reflect the full GUT symmetry. In particular, at these energies all of the force-carrying particles interact with the same strength. For the interaction of particles at energies below the unification scale, however, the effect of the Higgs fields is substantial. Some of the force-carrying particles behave like SU(3) force carriers, while others carry the SU(2) or SU(1) forces, and thus the standard model of particle physics is reproduced. The strengths of the three interactions are all related, however, because they must all meld into the single strand unified interaction at the unification scale." (P. 144, emphasis added.) Here the physicists' (or humans') illusion about there being a variety of forces and particles is overcome. The possible effect of such disillusionment on an ordinary person or an ordinary Orthorhombon used to building his or her life on the supposition of the "real existence" of the diversity in the material world can be sensed from Plato's allegory of the cave:

At first denial; at first he would want to flee away from the Truth that's less familiar and less comprehensible; and if only by force were he dragged out of the cave and saw the real things, the real human beings, and the real celestial entities, and finally the sun by itself -- "and after that he would already conclude about it that this is the producer [provider] of the seasons and years and the guardian of all that is in the visible place, and is in a certain way the cause [aitios: reason] of all those things he and his companions had been seeing." (516 c; Kai meta taut'an hdh sullogizoito peri autou oti outoV o taV te wraV parecwn kai eniautouV kai panta epitropeuwn ta en twi orwmenwi topwi, kai ekeinwn wn sfeiV ewrwn tropon tina pantwn aitioV.) Recall that in the functional perspective of Plato the ultimate cause or reason (aitia) of which the sun serves as the analogy (in the visible realm) is the idea of the Good, the Agathon, and that Agathon corresponds in the structural perspective to the "theory of everything", the truly fundamental theory of physics, perhaps the superstring theory, which would explain the origin of the physical laws themselves and also why the universe should come to be at all -- i.e. not just the second symmetry-breaking but even the first (creation and inflation). In the Orthorhombon example: the Orthorhombons would know, once they get to the cause of the creation of their illusion -- the breaking of the rotational symmetry of the crystalline that makes three out of one constant of the speed of light -- also where the crystalline itself came from in the first place. The current example from modern physics therefore falls a bit short of the allegory of the cave, only analogous up to the moment just before the eye of the liberated prisoner is set upon the sun itself.

Because the professionalization of cosmology has comfortably restricted those engaged in it to the confines of university offices and classrooms, laboratories in supercolliders, and observatories, they have neither to suffer the fate of the "seer" come enlightened in Plato's allegory of the cave nor to consider the salvational implication of such overcoming of illusion (enlightenment) -- except perhaps experience the sense of wonder (thaumasthai) at the true nature of reality and also at their fortune that "they actually get paid for doing this." They do, sometimes, when returning to the illusory everyday world of the manipulation of objects and maneuvering among human relations (the world of conventional or relative truth, sammuti- or vohara-sacca in Buddha's words), seem "clumsy", a "geek" or a "nerd", just as Socrates describes the liberated prisoner who returns to the darkness of the cave: "And if he once more had to compete with those perpetual prisoners in forming judgments about those shadows while his vision was still dim, before his eyes had recovered, and if the time needed for getting accustomed were not at all short, wouldn't he be the source of laughter, and wouldn't it be said of him that he went up and came back with his eyes corrupted, and that it's not even worth trying to go up?" (517a) This is indeed how the "common people of society" frequently treat not just the scientists today but all the past enlightened ones, whether Socrates, Buddhist monks, or even Jesus. "And if they were somehow able to get their hands on and kill the man who attempts to release and lead up, wouldn't they kill him?" (517a) The cosmologist or scientists in general do not yet have such problem because they do not yet associate spiritual and salvational implications with their work and certainly do not try hard to conduct social justice according to their discoveries. (But think about what they would have to endure in a society ruled by religious fundamentalists.) But our purpose is precisely to drag a second mode of salvation out of the illusion-overcoming process involved in modern science -- this is why we are here taking the trouble of re-reading Plato and finding out how much Plato would have loved to do modern sciences if he could be born in the structural instead of the functional perspective -- in order to propound a salvational system out of sciences such as is done in Phaedo and an political philosophy in accordance with this system such as is done in The Republic. (For now, however, it must be mentioned that we don't think it's enough, in order to produce an ultimate spirituality and salvation, simply studying modern sciences in Plato's spirit alone, but only if also in the spirit of Buddha and the Daoists.) Actually, for reason to be seen, we are not quite interested in producing a political theory out of science. But for Plato, the liberated prisoner in this allegory is obligated to go back to the cave and educate his fellow perpetual prisoners and rule them, since the man who has seen the idea of the Good will have achieved not only eternal (major) salvation but, having his soul ordered by the vision, also the most proper minor salvation, and become the only one truly comprehending politea (justice, order) with which he can best order society as well -- and if he attempts to do so he will evidently be killed by the society. Plato's thinking is like saying that our "spiritually minded physicist", having comprehended the "theory of everything" and (somehow) become the most ordered in mind, person, and spirit, must now go into politics and rule his nation. Good luck with that. We, heeding Marcel Conche's advice (in Tao-Te King), will afterwards only be concerned with our own salvation and not with society's order nor with anyone else's salvation, consequently avoiding being killed. "Do you suppose it is anything surprising if a man, come from acts of divine contemplation [qeiwn qewriwn] to the human affairs [ta anthropeia], is graceless and looks quite ridiculous when -- with his sight still dim and before he has gotten sufficiently accustomed to the surrounding darkness -- he is compelled in courts or elsewhere to contest about the shadows of the just or the representations of which they are the shadows, and to dispute about the way these things are understood by men who have never seen justice itself?" (517 d3) This explains why Socrates and Jesus are executed by their fellow countrymen. (More on this later, with Conche.)⁵

Both the cosmologists and we who will pursue salvation with their work will enjoy the new state of disillusionment and have pity over those common people of society: "When he recalled his first home [the cave] and the wisdom there, and his fellow prisoners in that time, don't you suppose he would be happy [eudaimonizein] for the change and pity the others?... And if in that time there were among them any honors, praises, and prizes for the man who is sharpest at making out the things that go by, and most remembers which of them are accustomed to pass before, which after, and which at the same time as others, and who is thereby most able to divine what is going to come, in your opinion would he be desirous of them and envy those who are honored and hold power among these men? Or, rather, would he be affected as Homer says and want very much 'to be on the soil, a serf to another man, to a portionless man,' and to undergo anything whatsoever rather than to opine those things and live that way?" (516 d) This must speak to the heart of any of our spiritually minded scientists who observe the illusionists that are the demagogues ruling the society being honoured by the ordinary stupid people for being "smart" and "important human beings". The human economic and political cosmos is just a worthless and illusory game played by those sleeping in their dream, and taking this illusion in full seriousness without ever awakening they exhaust themselves and even get themselves killed while trying to win the game -- as we shall later understand much better. We would delight in our new condition, and be "in the human cosmos but not of it".

As said, this illusion-overcoming process Plato calls "education" (paideias), quite different than the Buddhist, Hinduist, and Daoist way of addressing the manner: Plato's manner is more in tuned with "learning", hence with modern science. Of education he says:

Consequently Plato defines "education" as "the art of turning around" (tecnh thV periagwghV), "concerned with the way in which this power can most easily and efficiently be turned around, not an art of producing sight in it. Rather, this art takes it that the soul already has sight, but is not rightly turned or looking at what it ought to look at, and [this art] accomplishes this." (518 d: tina tropon wV rasta te kai anusimwtata metastrafhsetai, ou tou empoihsai autwi to oran, all'wV econti men auto, ouk orqwV de tetrammenwi oude bleponti oi edei, touto diamhcanhsasqai). We have shown that in the modern context the "turning" is the acquisition of the general scientific stance in every subject of study: in linguistic the "soul" must turn away from the diachronic manifestations of language (speech, parole, which is corrupted, containing grammatical mistakes all the time) and toward the language itself (the grammar, langue); and, in the observation of the motion (e.g. falling) of objects or natural phenomena, away from the concrete instances right then and there ("falling of this and that" or the magnetism of an iron rod) and toward the ideals governing these (d = 1/2 at² or Maxwell's equations), and eventually toward the foundation for these derivative ideals, the "theory of everything" which is yet to be found. (In the other direction it must turn away from this and that thing and toward the equipmental and referential whole [Zeugganzheit or Verweisungsganzheit] and finally toward temporality itself all of which underlie the intelligibility of individual things.) Given the complexity of modern scientific knowledge, it would seem that this educational process ("awakening") is more than just simple turning (as here) or remembrance (as in Phaedo) but gets to be actually like the process of putting knowledge into one's head. (Only in the Heideggerian direction does the "turning" itself seem enough.) This is because reality is much more complicated than Plato has thought. But the turning itself remains essential, and, just like learning language, must be done early or else might be impossible in later life. When a person is "turned" since early childhood s/he will surely become immune to the sucking power of the blackhole of illusion, e.g. to the "rapture" of Evangelism. But even when scientific discoveries (whether in physics, chemistry, or biology) are taught to an adult Evangelical s/he can no longer learn the essence behind them because his or her soul has not been "turned" during early years and can probably never be turned now. This is why we can find today occasionally engineers, chemists, and doctors among the Evangelists who are still waiting for the "rapture", i.e. live in a worldview based on the reality of solid things, interpersonal relationships, shallow moral values (e.g. the ten commandments), and drama -- these shadows of the "real things." Simply putting ready-made knowledge in one's head is not enough.

We can see easily that the basic principle we have described earlier (1.1. Ch. 1) for the evolution of consciousness -- that, as consciousness grows, it gradually becomes aware of its limitation, of the localness and relativeness of the "world" of which it is conscious, sheds its provincial (functional) perspective, and acquires knowledge of that which is hidden behind, the hidden Truth -- is just Plato's allegory of the cave, so that the allegory is, on the phylogenic level, simply the story of the journey of human consciousness in its upward (spiritual) dimension. And we have here explored how Plato's theory of form is (in one direction) "pre-science science", a "metaphor of modern physics" (and in the other direction, pre-phenomenological Dasein-analytic). What this means is that, just like Comte's "laws of the three stages", the journey of consciousness is completed only in modern science (albeit in a new way). The fact that this "pre-science" of Plato is no longer self-sufficient in the modern structural perspective means just that the allegory of the cave illustrating Plato's journey in philosophy is not yet complete. So, we learn that when the prisoner leaves the cave, he has merely come upon another cave, albeit one that encompasses the previous. He now has to leave this larger cave too (philosophy) in order to finally really come to the open, the nature with the sun in the sky (science: hopefully this is not yet another cave!). Reality is just so much more complicated than we have so far imagined. But, once the equivalence is established between Plato's eidetic study and modern science (especially physics), and the principle (for the spiritual growth of consciousness) is set in the allegory of the cave, later we will re-interpret the history of science in terms of the liberation of the prisoner from the cave through the modern version of the eidetic study.

Footnotes:

1. As Charles Daney explains: "Think of the graph of energy vs. field strength has having the shape of a 'W'. There is an energy peak when the strength is 0, while the actual minimum energy (the y-coordinate) occurs at some nonzero point on the x-axis. The value of the field at which the minimum occurs is said to be its 'vacuum' value, because the physical vacuum is defined as the state of lowest energy." "The simplest mathematical curve with such a shape is a fourth degree polynomial of the form E = x⁴ + Bx², where E is energy and x is field strength. (E is plotted on the y-axis.) If B is negative, then for values of x close to 0 (but not exactly 0), E will be negative. Hence for such values, you actually get a lower energy with a non-zero field... [I]t turns out that in theories with supersymmetry, it is actually possible to compute how the coefficient B in this equation behaves as a function of temperature. It is found that at high temperatures (say, corresponding to an energy of 1000 GeV), B is positive. The polynomial expression for E in that case has just a single minimum value (of 0) when the field strength is 0. On the other hand, at lower temperatures (such as what we have in the universe at present), B is negative. In that case, there are two minima of the polynomial for E, at nonzero value of the field strength, which is just what we need." This explains how a nonzero Higgs field could appear "from nowhere" at relatively low temperatures, i.e. during a phase transition. "That is, the field doesn't exist at high temperatures, because minimizing energy requires it to not exist. Yet at lower temperatures it does exist, because in the changed circumstances, that is what yields a minimum energy."

2. If we speak in terms of the isospin, the Higgs fields provide individual identities to the particles by providing "a frame of reference, a direction against which the arrow that defines proton or neutron can be measured. A proton can be distinguished from a neutron by comparing the direction of its isospin arrow with the direction defined by the Higgs field. But when the isospin arrow rotates during a gauge transformation, the Higgs arrow rotates as well, so that the angle stays the same. The angle that used to correspond to a proton now corresponds to a neutron, and vice versa. Without the Higgs mechanism, there would be no way to tell the difference between proton and neutron at all, because there would be nothing to measure their isospin against... And the Higgs field does this even though the field itself is a scalar..." (John Gribbin, In Search of the Big Bang, p. 305)

3. C.f. Roger A. Hegstrom and Dilip K. Kondepudi, "The Handedness of the Universe", Scientific American, Jan. 1990, in which the authors have noted that the emission of beta rays (energetic electrons-positrons and neutrinos-antineutrinos) from radioactive nuclei through the weak force always involves left-handed electrons (moving along their spin axes) and right-handed antineutrinos (moving against their spin axes), and right-handed positrons and left-handed neutrinos: "Right-handed neutrinos and left-handed antineutrinos seem not to exist in the universe." (p. 110) Here what is symmetric is called achiral and asymmetric chiral. "At rest, an elementary particle such as an electron or positron is spherically symmetric and hence achiral. But if a spinning particle is moving in either direction along its spin axis, it becomes chiral." (p. 111) This is the effect of parity nonconservation. The electroweak force distinguishes between left and right through "weak charged currents" and "weak neutral currents" (carried by the W and Z bosons respectively) whose strength between 2 particles depends on the distance between them and their charges. Since the weak W charge is nonzero for a left-handed but zero for a right-handed electron (which thus does not "feel" the W force), the beta decay, governed by the W force, produces mostly left-handed electrons. "As for the Z force, left- and right-handed electrons have Z charges of opposite signs and approximately equal magnitudes. The difference in sign causes [during high energies with traveling speed near that of light] right-handed electrons to be attracted to the nucleus by the Z force and left-handed ones to be repelled." (Ibid.) The opposite, mirror image, of this Z process is not observed in the real world, hence the weak force is chirally asymmetric and parity is not conserved. This Z force asymmetry causes all atoms to also be chiral, which could then cause chiral asymmetry in biological molecules, with the prevalence of L-amino acids and D-sugars over their mirror images (the observed condition of life), when the solution system is not closed to the inflow of energy. The phenomenon of chiral asymmetry (or "spontaneous symmetry breaking") therefore extends from the pre-geospheric world of elementary particles (standard model) through the geospheric chemical world of atomic elements (periodic table) to the bio-spheric world of biological molecules. Chiral asymmetry in biological molecules should have arisen in the primordial soup of life, since "it is difficult to understand how a protein or nucleic acid consisting of both L- and D-monomers could function. Experiments show that strings of amino acids containing both L- and D-acids do not correctly form the alpha helix shape that is crucial for the catalytic functions of proteins" and that "L-proteins interact more efficiently with D-nucleic acids." (p. 115) How exactly the first cells became chirally asymmetric is not clear.

4. Kaon is meson. The neutral kaon is made up of a down quark (- 1/3) and an anti strange quark (+ 1/3) or, in the case of the anti-neutral kaon, an anti down quark (+ 1/3) and a strange quark (- 1/3). In the quark picture of the first type of kaon decay an anti strange quark, emits a W⁺ which decays into a positron and a neutrino. In the quark picture of the second kaon decay (decay of anti-neutral kaon) a strange quark, s, emits a W^- which decays into an electron and an anti neutrino.