Meditation on the Beginning
Διαλογισμὸς περὶ τὴς Ἀρχής

Postquam homines sibi persuaserunt, omnia quae fiunt propter ipsos fieri; id in unaquaque re praecipuum iudicare debuerunt quod ipsis utilissimum, et illa omnia praestantissima aestimare, a quibus optime afficiebantur. Unde has formare debuerunt notiones, quibus rerum naturas explicarent scilicet bonum, malum, ordinem, confusionem, calidum, frigidum, pulchritudinem et deformitatem etc.; et quia se liberos existimant, inde hae notiones ortae sunt, scilicent laus et vituperium, peccatum et meritum.

After men persuaded themselves, that everything which is created is created for their sake, they were bound to consider as the chief quality in everything that which is most useful to themselves, and to account those things the best of all which have the most beneficial effect on mankind. Further, they were bound to form abstract notions for the explanation of the nature of things, such as goodness, badness, order, confusion, warmth, cold, beauty, deformity, and so on; and from the belief that they are free agents arose the further notions praise and blame, sin and merit.

Baruch Spinoza, The Ethics, Part I: "Concerning God," Appendix, translated by R.H.M. Elwes (1883), color added



Ἐν ἀρχῇ ἐποίησεν ὁ Θεὸς τὸν οὐρανὸν καὶ τὴν γῆν.
In principio creavit Deus caelum et terram.
In the beginning, God created the heaven and the earth.

Genesis 1:1


Thus many quantum-gravity theorists believe there is a deeper level of reality, where space does not exist...

These days, many of us working on quantum gravity believe that causality itself is fundamental -- and is thus meaningful even at a level where the notion of space has disappeared.

Lee Smolin, The Trouble with Physics, The Rise of String Theory, the Fall of a Science, and What Comes Next [Houghton Mifflin Company, 2006, pp.240, 241].


Καὶ ὁ ἄγγελος... ὤμοσεν... ὅτι χρόνος οὐκέτι ἔσται.
Et angelum... iuravit... quia tempus amplius non erit.
And the angel... swore... that time will be no more.

Revelation 10:5-6


ὅτε ἤμην νήπιος, ἐλάλουν ὡς νήπιος, ἐφρόνουν ὡς νήπιος, ἐλογιζόμην ὡς νήπιος· ὅτε γέγονα ἀνήρ, κατήργηκα τὰ τοῦ νηπίου.

Cum essem parvulus, loquebar ut parvulus, sapiebam ut parvulus, cogitabam ut parvalus; quando factus sum vir, evacuavi quae erant parvuli.

When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things.

1 Corinthians 13:11

In modern cosmology, it is generally accepted that the universe began with the "Big Bang," a point in time a bit over 13 billion years ago when all the mass and energy of the universe emerged from what may have been a single geometrical point, a "singularity." Many things about this make astronomers, physicists, and philosophers nervous.

For one thing, this is a unique object. We know about "Black Holes," where anything that falls in is overcome by gravity and is reduced to a singularity because no forces of nature can resist gravity to maintain any volume of space. Yet it is common to say that the laws of nature break down inside a Black Hole. It is more like only one law survives, gravity, which shuts out everything else.

The Big Bang looks like the opposite of this. All the matter and energy of the universe are not falling in, but coming out. The opposite of gravity. This would be called a "White Hole," for which there is speculation but so little positive physics that we don't hear much about it. As it happens, there has now popped into physics a force that does seem to be the opposite of gravity, namely the "dark energy" that is accelerating the expansion of the universe. No one knows what this is, but if we want a force that would dominate a White Hole, this looks lined up to fill the bill.

Another uneasy feature of the Big Bang involves space. For decades, much of the excitement about Einstein's General Relativity was the idea that space had a non-Euclidean geometry which allowed for a "finite but unbounded" volume, i.e. space was finite in volume, but whatever direction you went off in, you never got to an edge or boundary but instead came back around to where you started. This is said to be a space with "positive curvature."

While Einstein originally favored a static universe, once the existence of the Big Bang came to be accepted, it was realized that we got a kind of cosmological jackpot. This meant that not only matter and energy began at the Big Bang but all of space and time did also. So the Big Bang was "everywhere" because "everywhere" was already packed into the original singularity. As the universe subsequently expands, gravity could slow it enough that the expansion could be stopped; and the universe would eventually collapse back onto itself, dragging all of space with it. This was very tidy.

But such a happy picture was subsequently ruined. For gravity to slow and stop the expansion of the universe, a sufficient density of matter would be needed. And it's not there. Indeed, there is so little visible matter in the universe, and the density is so low, that most of the mass of the universe is now thought to be "dark matter," whose character is nearly as much a matter of speculation as that of "dark energy" -- Sky & Telescope reports that the composition of the universe is currently thought to be 4.9% baryons, 26.4% cold dark matter, and 68.7% dark energy [March 2022, p.16].

Even the dark matter only brings the density of matter up to the point where the universe now appears to have a "flat" Euclidean geometry ("zero curvature") -- this after decades of philosophers essentially pouring scorn on Euclidean geometry and derision on mathematicians or philosophers who might have thought that Euclidean geometry perhaps made more sense than non-Euclidean -- see my analysis of Kant's theory of geometry.

Euclidean space is infinite, as would have been the non-Euclidean low-density Lobachevsian geometry ("negative curvature"). But in those terms, the Big Bang cannot have taken place "everywhere." The White Hole singularity is going to have a specific location in the Void. This violates the ancient metaphysical principle of Sufficient Reason, since there is no reason why the Big Bang should be at one location rather than another -- except for the arbitrary will of a Creator God.

Luckily, nervous astronomers have a way out. We do not, after all, look off into infinity. We are looking back in time, and at 13+ billion light years out, we get to the edge of the "Observable" universe. It's finite. The curious and conscientious wonder what is beyond that. If the universe had expanded at a rate slower that the velocity of light, then the Observable edge would be the actual edge -- except for the opaque gasses filling the space between the Observable edge and the Big Bang singularity itself. However, the popular theory of "Inflation" postulates that the early universe expanded faster than light for some brief period. This puts some unknown volume of the universe outside the Observable edge, even if the Observable universe were transparent all the way down to the Big Bang singularity.

How much of the universe exists outside the Observable limit then depends. If space is Euclidean and infinite, then there is an infinite universe out there. Nobody much seems to like that. Instead, contradicting the observed density of matter in the universe, it is popular to sneak the finite but unbounded universe back in, meaning that only a finite volume of universe exists outside the Observable limit. This is often accomplished, as we see with Frank Wilczek, by a kind of slight of hand, i.e. an absence of direct discussion about space, non-Euclidean geometry, etc. This is not, of course, entirely honest.

But it is common. There seems to be universal complacency about speaking of the universe in the old finite but unbounded terms, regardless of the physics of it. Thus, if the universe is large enough, and the Observable universe small enough, our little fragment of space can look Euclidean even with a positive curvature of the whole. Indeed, Inflation is recruited into this, since the sudden expansion "smooths" out our local space, which otherwise might have displayed some curvature.

So there is universal amnesia about the meaning of the density of matter. And if the universe is indeed large enough, then whether it is finite or infinite will never be betrayed by our local curvature, or lack of it. The limits of the Observable universe happily conceal the whole metaphysics problem, and the traditional exultation over the solution to Kant's First Antinomy can be swept under the rug with all other awkward questions.

But these difficulties are not my principal concern here. Instead, I want to follow the discussion of Roger Penrose about the entropy, ἐντροπία, of the Big Bang.

Penrose asserts that the Big Bang was a very low entropy, i.e. highly Ordered, event. If not, then the Big Bang would have resulted in the creation of a large number of small Black Holes, which would carry away any high entropy of the event -- Black Holes themselves are very high entropy, i.e. chaotic. Since the Black Holes would be small, many would be evaporating, according to the formula of Stephen Hawking, and would announce their presence with small, characteristic bursts of energy. But such small cosmological Black Holes, or any such bursts of energy, have not been observed.

An alternative theory is that large Black Holes, "primordial" ones, survive from the Big Bang and perhaps constitute the dark matter of the universe. This suffers from the difficulty that so many such objects would collide regularly, releasing tremendous energy and Gravitational Waves. Such waves have now have been observed, but their rarity conflicts with the needed numbers of "primordial" Black Holes. Thus, the energy signature of either small Black Holes or large ones doesn't exist.

We must then consider that the total mass and energy of the universe are a constant, as long as mass-energy is conserved, and thus that the primordial ratio of energy to temperature (which will have been very high at the Big Bang) is going to be very low. As we see in Boltzmann's Law, the units of entropy are Joules/Kelvin, or units of energy per units of absolute temperature.

As the universe expands, it cools, down now to about 3oK. This means that each degree Kelvin is in relation to a good third of the total mass-energy of the universe. Very high entropy indeed. But that is what we expect. Entropy increases over time. The universe becomes less orderly.

These simple considerations seem to escape some science writers. Indeed, Frank Wilczek ignores entropy and order altogether, despite its fundamental place in physics. If I were the suspicious sort, I might wonder if there is something about it he doesn't like and so seeks to misdirect us. Since Wilczek, and so many others, are reductionistic materialists, it would not surprise me if the whole issue of order did not induce uneasiness and even bad faith. After all, they often celebrate Baruch Spinoza, not understanding that he wasn't a materialist, but understanding quite well that he rejected order and purpose as merely subjective matters that we impose on the world [note].

Roger Penrose is not like that. Instead, he directly tackles the whole question of how complex life can arise in a universe that has become increasingly less ordered. Creationists like to pounce on this sort of thing. Conventional science often answers the challenge with little better than huffing and puffing.

Instead, Penrose looks at the geometry of the energy budget of the Earth. Sunlight streams in, half the day, from a point source in the sky, in the highly ordered Black Body radiation of the sun. The Earth heats up. In turn, the heat is radiated back into space, from all over the planet, in many random wavelengths. In other words, as heat is the highest entropy form of energy, the Earth receives order and vents disorder.

So, why is there life on Earth? It is because the Earth has absorbed order and expelled disorder. This may not make a big difference right away, but over time it adds up. Occasionally something may happen to reverse things, as when the Earth is hit by an asteroid, but then the process takes over again.

Others have noticed this, although not always in the same terms. Thus, J. Scott Turner says:

Although the form of orderliness might differ, the important point is that there is orderliness in the first place. Let us reflect on why. We spoke in the preface of the spontaneous orderliness of open thermodynamic systems, the Fourth Law of Thermodynamics. Orderliness in open thermodynamic systems is a form of work: it takes energy to sustain it. At the same time, orderly systems spontaneously decay to disorder, unusually wrought by the disruptive power of diffusion. That is the Second Law of Thermodynamics. Orderliness in a open thermodynamic system therefore persists only when sufficient order-generating energy flows through to overcome diffusion's disruptive power. [Purpose & Desire, What Makes Someting "Alive" and Why Modern Darwinism Has Failed to Explain It, HarperCollins, 2017, p.250, boldface added]

Penrose seems to explain this more simply. And just from his diagram, we see where we get the "order-generating energy flows," from the Sun. There seems to be disagreement on just what to call the "Fourth Law" of Thermodynamics, but from the jargon used on the internet, it is hard to tell what the alternatives are or what their significance is. Turner's description here is more to the point. The "thermodynamic system" of the Earth generates and sustains low entropy, i.e. "orderliness."

This all raises many questions. Where do the forms of order that we see, like the laws of nature, the panoply of life, or even the geometry of the pyramids, come from? Conventionally speaking, we cannot say. All the possibilities must somehow have been packed into everything right at the Big Bang; but then the laws of physics do not allow for that.

That is because quantum mechanics rules out "hidden variables." This was tested through Bell's Theorem. It means that physics only sees the quantum numbers of mass, charge, etc. that are attributed to particles -- the wet dream of the reductionistic materialist. Thus, if the possibilities of "Life, the Universe, and Everything" are contained at the moment of the Big Bang, it is not in a way that can be recognized by physics. If we want to know how all possibilities are present in the Big Bang, physics is going to be no help. At the same time, the quantum mechanical wave function is the sum of all possibilities, just only the physical ones. Nevertheless, we can then say that the Big Bang itself is the sum of all possibilities, both physical and otherwise.

So if the possibilities for life, writing, music, and Shakespeare are contained in the Big Bang, it will not be in a way visible to physics. And there is not a lot about this in the history of philosophy. Aristotle's theory of "matter," ὕλη, holds all power and possibility, perhaps the only such metaphysic in philosophy, but it holds no structure within it. The forms, εἴδη, of things simply come-to-be out of it. Where those forms might come from, Aristotle could not say, except that they are derived from previous forms, by causal processes. But if the new forms are novel, the previous causes alone cannot account for them. Instead, Aristotle perhaps can cover it with his teleology:  The "final causes" of things are implicit in the causes, the "entelechy," ἐντελέχεια; but we have no clue that the entelechy contains things that perhaps have never been seen before. Aristotle certainly believed that there is nothing new under the sun; and that the forms of life simply repeat themselves.

However, Plato already had a theory. His whole World of Being, containing the forms of everything, although existing to him in a separate reality, can be reconceived as itself a theory of possibility. Wedding Aristotle's chaotic matter and entelechy to Plato's World of Forms would seem an unlikely marriage. But, metaphysically, it does the job we require. The Big Bang is pregnant (often the result of marriage) with the possibilities of everything. The "emergent order" that we see in the course of the history of life does not just pop, unpredictably, out of nothing. It still is, indeed, unpredictable, but it is slightly less mysterious. Novelties can have already been there among the Forms.

Another precedent in the history of philosophy might be Leibniz. The peculiar metaphysics of the "Monads" posits dimensionless objects that exist independently of each other and do not communicate in any way. Each contains the script, created by God, of its own entire existence, with a representation of the existence of all other things. Since there is no connection with other things, the God of Leibniz assures us that the representation of all things will correspond in a "preestablished harmony." Our existence as such does not even tell us that anything else exists, except on the reliability of God.

This peculiar theory nevertheless now looks like a theory of possibility. Yet there is no real possibility in the theory. The actuality of the future is already lined up in the Monads, merely waiting to unfold. This sounds like many modern theories of possibility, as in quantum mechanics, where "possibility" means the actual creation of all the infinite possibilities into actual worlds. Leibniz is not so profligate. But all such theories do not seem to Save the Phenomena -- if we believe the real possibility also means real variety, while real possibility also means that many possibilities fail to be realized. We certainly would not want all of them to be realized.

A theory of possibility that generates novelty is something we might discern in Hegel. The "Dialectic" is both a method and a process, in both logic and reality, that is supposed to generate both new concepts and new objective phenomena. However, the Dialectic does not draw on a reserve of positive novelty, like Plato's Forms or even Aristotle's entelechy. It is supposed to generate novelty from its own logical resources. But that means nothing more than negation. The Dialectic piles negation on negation, creating a complexity that Hegel says is the equivalent of new positive and substantial conceptual content.

No actual logician takes this seriously, or usually even bothers to notice it; and Hegel begins to look like some kind of magician, who sweeps away the sheet and announces, out of nowhere, that now we have "heat," "gravity," "religion," or any of the other real things that Hegel wants to write about. I would rather the reveal were just the magician's comely and appealingly dressed female assistant. But philosophers rarely have available such assistants -- if the philosophers are not college professors with graduate students.

We can assign some of the blame for this to Kant, who thought that he could derive the "categories" of "understanding," like causality or substance, from the forms of logic alone. Also, Kant argued that the whole content of morality could be derived from simple logical characteristics, like universality, consistency, and rule making. The absurdity of this seems to be rarely noted, especially when Kant was so inconsistent as to introduce concepts, like personhood and purposiveness, that he complacently used to develop a reasonable system of morality. The slight of hand involved is not unlike the dramatic magician's reveals of Hegel. The proper question, where the new concepts actually come from, usually is not asked.

Apart from that issue, what Plato, Leibniz, and Hegel all require is contingency as well as necessity -- even Hegel's Dialectic, like Spinoza's Natura Naturans, operates (albeit absurdly) as a necessary process. I have written separately about the "perfect fallacy," where Western metaphysics always posits what is finished and unchangeable, rather than what has the potential for something new. Plato's World of Forms sounds like a kind of furniture warehouse, where you simply unpack finished items. Instead, it can only hold abstract templates, whose realization can take many forms, with the details filled in either randomly or purposefully. It is more factory than warehouse, with various unique items assembled as needed.

We see versions of the perfect fallacy in both Einstein and "many worlds" quantum mechanics. Each relies on actuality to either explain or to replace possibility. Einstein really believed that time was simply another dimension of space, where past and future already exist just as much as the present. Thus, the future is fixed and future events are already determined. This is a kind of Fatalism that even goes beyond the determinism of Spinoza, for whom Einstein otherwise expressed a preference. At the same time, "many worlds" quantum mechanics posits alternative universes for all possibilities. This not only grossly violates Ockham's Razor but it also violates the conservation of mass and energy.

The best I can make of such an idea is that theorists rely on the Uncertainty Principle to borrow energy from nothing to create those universes. But the principle is that the more energy you borrow, the less time you can keep it. Enough energy for a universe wouldn't even allow it to exist for a nanosecond. I think some confusion about scale may be involved. But this is not a theory, of course, that allows for the real phenomena of possibility, especially for possibilities that are never realized. I would rather not allow that there is a universe, or many universes, where the Germans won World War II.

As we see in the diagram for the "modes of necessity" of Friesian metaphysics, each form of necessity corresponds to a form of contingency, by which the expressions of necessity vary. This is much like what we see in the growth of a tree. The form of the trunks, limbs, and leaves of a tree is set by its genetics, but each tree grows in a unique way, with its own particular growth of trunk and limbs. Each tree becomes a unique individual.

The combination of necessity and contingency is something that reductionistic thought does not want to entertain. Thus, Stephen Jay Gould (1941-2002), while a bit of a rebel in Evolutionary circles, nevertheless acted terrified at the thought that Evolution might result in "higher," i.e. better or more perfect, forms. All that counted, apparently, was the random and the contingent, so that we could not say that humans, for instance, were superior life forms to toads. There was nothing of the rebellious about that idea.

L'Etoile Perdue, "The Lost Pleiad," 1884, by William-Adolphe Bouguereau (18251905)
Orthodox science despises any sort of "anthropocentric" view of the world. The universe doesn't revolve around the Earth; and it certainly doesn't revolve around us.

At the opposite end of the spectrum was the old idea of "orthogenesis," that Evolution advances in pretty straight lines to Platonic perfection. Eohippus, the ancestral horse, was meant to lead to the proper horse, Equus, the perfection of the type. Onward and upward, Australopithecines lead to forms, straighter, taller, and less hirsute, that flower into modern Homo sapiens, the "paragon of animals." And since the female of the species is the least hirsute and the most gracile, she is obviously the most evolved.

Orthogenesis is generally rejected in biology, but Gould's fear of manifest progress can only remain popular as long as lower entropy is not understood as having a physical meaning of greater order. It is still too easy to reject "order" itself as subjective. But almost everything that grows, grows in a combination of order and contingency, even the crystals that grow in cooling igneous magmas. And beyond individual trees, with the randomization of characteristic types, we see the rules vary in the same way between different species, whose "radiation" from ancestral forms has already often been compared to the limbs of a tree. The Tree of Life.

Perhaps even better than trees are clouds. We don't have or need DNA there. Just physics. Clouds are phenomena of some simple physical variables:  temperature, humidity, wind, and atmospheric pressure. The result, however, is infinitely variable. To be sure, we get some basic types -- stratus, cumulus, and cirrus. Then there are varieties of these, like "altocumulus." These are forms of the basic emerging order from what is given.

With some of those types there isn't much variety. June in Santa Monica witnesses the featureless gray of the "marine layer" stratus, which layers chill and gloom over the beach and can reach up as fog in the passes over the Santa Monica Mountains. The idea of a June wedding is nice, and of a wedding on the beach, but in Southern California those don't always go together well. The wedding guests are just lucky that this doesn't often produce rain.

On the other hand, the cumulonimbus of thunderstorms, something you don't see often in the Los Angeles Basin, but that are common in the California desert, in New Mexico, or in Texas, are where we get all the variety of towering and boiling cumulus clouds, reaching into thunderheads, different every time. And there is a variety of different clouds at different times, all the time, some of them strange and mysterious, even magical.

Thus, while clouds as such develop into what may be a small number of types, limiting the kinds of novelty that we can expect -- although unsual types can stand out as remarkable -- these are able to display an almost infinite variety of certain forms. People watch clouds with fascination as they begin to suggest faces and other shapes. All as ephemeral as anything in life. But the farmer may also watch with hope and fear, if he needs rain but experiences drought.

Gould can have his random element, which is not always adaptive or even useful; but this usually adds to a particular feature of life, aesthetic variation, that gives us, not deer and antelope grazing in Australia, but kangaroos. I wouldn't want it any other way.

For this all to happen, two things are needed. We need the rules which allow for the inception and development of life in the first place; and we need the lowering of entropy which, after a fashion, draws out the new forms and expressions of order, such as have not been seen before. That gives us novelty, even as Gould's randomness gives us variety. Novelty is also a kind of variety, but it is then the foundation for whole ranges of new kinds of variation.

As life develops, we eventually get to a point that is significantly transformative of its terms. Rational beings do not just wait around for low entropy to engender novelty. They draw novel ideas from themselves. This may start slowly, but it builds up, just as it did, over time, with life itself. Suddenly, creative beings are virtual volcanoes of innovation, and variety.

Just consider language. It is a whole world of novelty in its own right, which then blooms into hundreds of human languages; and within each language is its own separate universe of prose and poetry, with unique features that give each language, with its own intonations, rhythms, and meanings, a particular appeal, whether in ordinary speech or in its literature.

If we would like a kind of patron saint of creative innovation, we might do no better than the Egyptian Imhotep, , who was the "overseer of works" for King Djoser of the III Dynasty. He designed and built the first free standing stone building, the Step Pyramid, Djoser's tomb. Imhotep was remembered as a god, not just of architecture, but also as a version of Aesculapius, Ἀσκληπιός (Asclepius), the Greek god of healing.

The transformative point, of course, goes with the inception of consciousness. This turns the world inside out. The blind causes that previously alone drove events are now matched with the freedom and purposes of conscious beings. This is not "anthropocentric," but it does acknowledge the profound difference that distinguishes rational beings from other beings, the sentient and the merely animate. Rational beings not only have language, not only have intentions and purposes, but they have moral duties as well as natural rights.

None of this is discernable among the natural possibilities of the Big Bang. Yet it is perhaps the most radical development in the whole history of life. It poses dilemmas for the materialists. Like Spinoza, they have decided that there are no real purposes in the universe. What we might think of as purposes are illusions and confabulations by which we are deceived about the sources of our own behavior. Why we would evolve with such a system of illusions in our consciousness is a question that may not get addressed.

And it is also not that simple. Consciousness is the physical difference between wave and particle in orthodox quantum mechanics. Thus, the materialist did not live happily through the long era when there was no consciousness. No one like that was around. Instead, the dawn of knowledge and science is already wielding the consciousness that then, alarmingly, turns up to make a physical difference in matter. Waves behave differently from particles. And while Niels Bohr's principle of Complementarity gives equal status to each, the history of physics features one effort after another to deny the proper reality of one or the other. I have discussed a couple of cases of bias against the reality of the wave function [note].

One of the most striking results in quantum mechanics is that the collapse of the wave function propagates instantaneously. It is as though space doesn't exist, and the limitation of the velocity of light in Special Relativity simply does not apply. What Einstein hoped would be a reductio ad absurdum of quantum mechanics instead piled new paradoxes on top of the old ones.

This throws a conspicuous feature of cosmology into a stark perspective. Space is vast beyond our comprehension. We can barely imagine the prospect of traveling to a nearby star, with the technology we have, while the rest of the galaxy, nearby galaxies, and the Expanse of the Universe vault off into untouchable distances. We might wonder: Why so much space? And it is nearly all empty. The only advantage we derive from this is its visibility. We can see the universe in a way that we could not were it dense with matter. Were this the design of some Being, we might think we were being taunted and teased. The empty boast of Ozymandias, "Look on my Works, ye Mighty, and despair!" overwhelms the truth of the infinitesimal speck we make in the universe.

For some reason, materialists enjoy rubbing this in. We are the equivalent of nothing. Perhaps this is their substitute for the infinitude of God; but then God is supposed to care about us, and the cold Void of the universe certainly doesn't. Any minute, a gamma-ray burst could wipe out life on Earth. So there.

Even scientists who wax eloquent about beauty cannot tell us why beauty should mean anything. It is just a twitch in the human body, like a burp or a hiccup. If you expect more, if the beauty of physics or mathematics is really going to mean something, you would need to be a Platonist. But most materialists may not even understand the question. Others, who begin to understand what they are saying, may begin to feel despair.

But if space does not extend down to the fundaments of existence, as Kant had thought, things look a bit different. In terms of possibilities, we are adjacent to everything, including the Big Bang itself. The present is still the instantaneous effect of the collapse of the wave function of possibility in the Big Bang.

"I want to know, for example, why beauty exists," she [Gabrielle] said, "why nature continues to contrive it, and what is the link between the life of a tree and its beauty, and what connects the mere existence of the sea or a lightning storm with the feelings these things inspire in us? If God does not exist, if these things are not unified into one metaphorical system, then why do they retain for us such symbolic power?..."

Anne Rice (1941-2021), The Vampire Lestat [1985]


The scarlet macaws' flaming bodies, for instance, offer a magnificent mystery: Why do we perceive as beautiful the colors and plumes that birds themselves also [?] see as beautiful? Long before humans, Life developed for itself [?] an ability not just to perceive but to create -- and to desire -- what we call beauty. Why does the perception of beauty exist on Earth?

Carl Safina, Becoming Wild, How Animal Cultures Raise Families, Create Beauty, and Achieve Peace [Henry Holt and Company, 2020, p.xii]; Safina takes some liberties with what scarlet macaws see and what "Life" was developing "for itself."

Stars, 1926, Maxfield Parrish (1870-1966)
Which brings me to the ultimate curiosity of our condition. The orderliness of the Big Bang, dispersed as entropy increases in the history of the universe, has been restored, in us. As the Earth radiates disorder, in the description of Roger Penrose, and life evolves, the whole process approaches a return to the low entropy of the Source. We don't need to wonder what the condition was of the Big Bang, separated from us by so much apparent time and space, because that is what we are becoming, in everything we are, from consciousness to Twinkies, let alone art and literature and philosophy and science.

Others have marvelled how human life seems to be the moment where the universe perceives its own nature. Matter alone does not do that; and even the rich life of animals, which is so fascinating to us, does not include looking at the sky and wondering what is going on. Cats tolerantly observe our antics, but then they file no reports or analyses about it -- as far as we know.

Of course, we are not at the end yet. If there is some sort of "Omega Point," as imagined by Teilhard de Chardin (1881-1955), its nature will be as unpredictable as has been every other stage in the emergent order of life, although I would say with some confidence that it would at least embody aesthetic variety, including even erotic value, i.e. "lust" (, ; Cantonese yu̿k; Japanese yoku; Korean , yok; Vietnamese dục).

But what it sounds like now is that the Omega, Ὦ μέγα, and the Ἄλφα, the Beginning, the Ἀρχή, become, in some sense, the same. This has been said:

Γέγοναν. ἐγὼ τὸ Ἄλφα καὶ τὸ Ὦ, ἡ ἀρχὴ καὶ τὸ τέλος.
Factum est: ego sum alpha et omega, initium et finis.
It is done. I am Alpha and Omega, the beginning and the end.

Revelation 21:6

What we can say is that as we go along we should be understanding things better, both physically and morally. Thus, much work remains to be done. The Marxists who want to enslave and murder people, all in the name of some kind of justice that they don't even believe in, are as much a threat to humanity as they were in the last century. Hopefully they won't kill or starve as many as they did before, but they are working on it. And in this they are insensibly aided by the nihilists, whose Existentialist world has no meaning, which sets them adrift in life without principles or goals, leaving them vulnerable to any nonsense
Good
Will
z
+6ℏ
Justice+5ℏ
Right+4ℏ
Good+3ℏ
Beauty+2ℏ
Sublime+ℏ
Holy0
-- often supplied by their Marxist and anti-American college professors. A gamma-ray burst might be more merciful.

The greatest metaphysical puzzle has always been with matters of value. Understanding gravity is one thing, understanding the right and the good, something else. The easy way out for materialists and nihilists is that they don't need to worry about it. They can pretend it doesn't matter to them, or that it is not necessary, probably when they are screaming "racist" at everyone who disagrees with them. But it is a real challenge.

When Plato put the Form of the Good in the World of Being this was a kind of warning shot. Aristotle could only retreat into what we now call "Positivism," that what is actual is paradigmatic of what is right and good. Justice might as well be no more than the will of the sovereign in that case, without the Shakespearean caution about the "insolence of office." But it is clear that justice and righteousness stand independent of all authority, whose obligation is to conform to them, not the other way around. And then we hear the echo of Plato's shot, which rejects the paradigm of all that is actual.

That is as far as I will go here. My argument on this page is how the progress of our understanding, in science and morals, returns us to our origin in the very mystery of the Big Bang. Since, among so much else, we would like to understand the nature of that origin, we find several paths leading to the same goal. The Big Bang, then, is not just the sum of physical possibilities, it is not unlike Plato's own Form of the Good, not in a different world, but holding all possibilities of the good and the beautiful. So much of the beauty is still with us, as we see the stars in the heavens, but the good has become something rather different, and a thing of understanding and will, and not just perception. This calls for effort and action, not just contemplation.

Zwei Dinge erfüllen das Gemüt mit immer neuer and zunehmenden Bewunderung und Ehrfurcht, je öfter und anhaltender sich das Nachdenken damit beschäftigt:  Der bestirnte Himmel über mir, und das moralische Gesetz in mir.

Two things fill the mind with ever new and increasing admiration and awe, the oftener and more steadily we reflect on them:  the starry heavens above me and the moral law within me.

Immanuel Kant, Critique of Practical Reason [Lewis White Beck translation, A Liberal Arts Press Book, Bobbs-Merrill, 1956, p.166]; Kritik der praktischen Vernunft, A 289 [Kritik der praktischen Vernunft, Grundlegung zur Metaphysik der Sitten, Herausgaben von Wilhelm Weischedel, Suhrkamp Taschenbuch Wissenschaft, Erste Auflage, 1974, 1956, p.300], boldface added.

The title of this essay, "Meditation on the Beginning," Διαλογισμὸς περὶ τὴς Ἀρχής, stands in need of a couple of points of explanation.

"Beginning," ἀρχή, echoes the earliest days of Greek philosophy, where each philosopher posited a certain archḗ, an "original stuff," which led to the theory of the four elements. Plato and Aristotle began to see the archḗ in abstract terms, leading to the theory of "first principles." Here, in turn, I take ἀρχή in its most literal meaning, as the temporal beginning of the universe with the Big Bang, as we see expressed by Genesis 1:1.

"Meditation" does not seem to be a concept that occurs in Classical Greek. While the diary of Marcus Aurelius is called the Meditations, the title in Greek is actually "To Himself," Τὰ εἰς ἑαυτόν. There are several possible Modern Greek translations of "meditation," and I have chosen διαλογισμός, in part because this is a word that occurs in Classical Greek, where it means "balancing of accounts," "calculation, consideration," "debate, argument, discussion," and even "judicial inquiry" [the Unabridged Liddell & Scott Greek Lexicon, Oxford, 1843, 1940, 1996, p.402].

This is, of course, related to the modern word "dialogue," whose meaning has become confused by a false etymology. Since "dialogue" has come to mean a discussion between various participants, it is commonly said that the prefix "di" means "two," to indicate this plurality. However, the prefix is actually "dia," which is a preposition meaning "through," and signifies that one has gone "through" the material under consideration, whether one's financial accounts, a legal case, or philosophical questions.

If the "Omega Point" is a culmination that unites with the beginning of the universe, this probably would not arrive very soon. On the other hand, death will arrive quite soon enough for all of us. Death, Light, and Black Holes considers Black Holes in relation to our personal fate. Similarly, if death threatens us with nothingness, The Metaphysics of Nothing is probably going to be relevant to the issue. More generally, order appears to increase as part of the problem of purpose; and the place of purpose in the world is considered in Cause and Purpose, The World Turned Inside Out.

The Emperor's New Mind, Roger Penrose, Oxford University Press, 1990

Childhood's End, the Mystery of Order

A Summary of Modern Cosmology

A Lecture on the Good

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Philosophy of Religion

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Meditation on the Beginning, Note 1

Whose Blunder?

Materialists may feel an instinctive aversion to entropy. I cannot tell where he is really coming from, and if it is for that reason, but Arieh Ben-Naim, a retired Chemistry professor from Hebrew University, launches a furious assault against everything that makes entropy of general interest to others. This is in his book Entropy: The Greatest Blunder in the History of Science [eBookPro Publishing, 2020].

The title of the book itself may be a Freudian slip, since Ben-Naim doesn't really think that entropy itself is a "blunder"; but the "blunder" is only the interpretations of entropy and the Second Law of Thermodynamics that have anything to do with the direction of time or the issue of order and disorder, especially as this might be applied to the nature of life or to cosmology.

But the paradox of the title of the book might make us wonder if Ben-Naim is going to be able to explain matters in a cogent way. And often he doesn't. Instead, his rhetoric can be abusive and insulting. Thus, "One thing I can say with certainty; the topic on which the most stupid things were ever said is undoubtedly the relationship between Entropy and Time!" [p.11]. Then, after calling many of the greatest names in science the equivalent of idiots, and their ideas קִישְׁקוּשִׁים [Hebrew kīshkūshīm, "nonsense, scribblings"], he says, "I sincerely hope that the authors whose works I have criticized will not take it personally" [p.17]. Of course, Ludwig Boltzmann committed suicide years ago over something of the sort, but many others in the book, like Irwin Schrödinger, are also dead. So it doesn't much matter whether they take it personally.

Indeed, Schrödinger comes in for special notice, because of his book What Is Life? [1944]. Among much else, we get the following passage:

Chapter 6 titled "Order, disorder, and entropy." He starts with the common and erroneous statement of the Second Law in terms of the "order" and "disorder."

"It has been explained in Chapter 1 that the laws of physics, as we know them, are statistical laws. They have a lot to do with the natural tendency of things to go over into disorder."

There is of course, no such "natural tendency," except in the minds of those who have a distorted view of the Second law. [p.213]

"Of course," if we ask where in physics issues like the directionality of time or of order and disorder are treated, only Thermodynamics offers any clue. Yet here Ben-Naim, as all through his book, reminds us that, as he sees it, the traditional interpretation of entropy that, all else being equal, disorder increases, is "wrong." Irwin Schrödinger, like so many others, has a "distorted view." And our interest, as Schrödinger had himself, how the orderly functions of life can maintain themselves against decay, at least for a while, is irrelevant to the physics here.

So, while the Buddha said, "Decay is inherent in all composite things," Arieh Ben-Naim seems to lack any of the natural curiosity that is obvious in other people, including great mathematicians and physicists, who have written about thermodynamics. If his claim is that entropy is irrelevant to such concerns, we might wonder what he thinks is. But we get no indication from Ben-Naim that the larger questions concern him at all. Fair enough. But Ben-Naim is thus himself irrelevant to the general concerns of philosophy and humanism.

My thoughts in this essay, deriving from the treatment by Roger Penrose, wouldn't survive for a minute under Ben-Naim's onslaught. Ben-Naim, however, seems to be a little careful with Penrose:

Finally, I want also to comment on Penrose's approach to entropy and the Second Law... I admire Penrose's writings. Here, I chose Penrose's writings to demonstrate a more general "mechanism of going astray." Penrose starts with a perfectly correct approach (the description of a micro-state in Phase space) which he claims to be essential to be understanding entropy an the Second Law (but which I believe is superfluous, and potentially misleading), and then he is carried away into conclusions which seems "natural," based on his approach, but in fact are unwarranted conclusions. I hope that Penrose will agree with my criticism of some of his statements. [pp.18-19]

Ben-Naim's hope here to gain Penrose's agreement is less abusive than we get with others. Perhaps Ben-Naim senses that Penrose, as a mathematician and thinker, could evicerate his "criticism." In any case, Ben-Naim rejects Penrose's reflections or order, life, etc.

Ben-Naim does begin his book by describing the basics of entropy as laid out in the history of science. We get the basic equation of Rudolf Clausius (1882-1888), , which relates entropy, "S," to energy, "Q" (as heat), and temperature, "T" [p.33]. He has some discussion of the operator "d," which indicates the infinitesimal amount in a derivative, but he doesn't mention that a derivative is involved. In fact, we could write this equation as , making temperature a derivative of energy with respect to entropy.

Indeed, what we are certainly not going to get is the equation of Clausius written as a function of time, namely . The overdot on "Q" is a notation indicating a derivative of time, which could be written in full as . Time has been expelled from entropy by Ben-Naim. We get an early explanation of this:

After introducing the definitons of entropy it will be clear that entropy is a state function. Almost everyone who writes about entropy knows that "entropy is a state function." Unfortunately, many also forget or do not understand what a "state function" means. This single fact is enough to convince anyone why entropy is not a function of time, why there is no indication that the entropy of the system always increases, or that entropy "tends to increase" without reference to a specific system. It will also be clear why entropy cannot be applied to the life phenomenon and to the entire universe. [p.15]

Thus, if entropy is a "state function," it describes a "state," which means something that doesn't change. So the very principle of the Second Law of Thermodynamics that, all things being equal, entropy will increase, is purged from the physics.

Ben-Naim's principle, as I understand it, is that entropy only describes a system in equilibrium, which means it no longer changes. This, however, seems like a very arbitrary principle; and the relation of energy to temperature will obviously, I think, exist for many systems that are not in equilibrium. All you need for the equation is energy and temperature. If so, that system will have an entropy value, which then will change, with time, as the system moves towards equilibrium. That will describe both life and the universe, which Ben-Naim drops from his consideration, perhaps for his own idiosyncratic reasons.

From Clausius, Ben-Naim moves on to Boltzmann, where the equation associated with him, although he did not write it, is S = k ln W. Ben-Naim writes this as S = kB log W. The "W" is a statistical number, "the number of accessible micro-states of the system" [p.38]. So this definition doesn't refer to energy or temperature.

One noteworthy thing about how Ben-Naim writes this equation is that he uses the expression "log" to indicate the logarithm of "W." But from the version of the equation I have given indicates that this sould be the "natural logarithm," ln. Ben-Naim explains that when he writes "log," sometimes he actually means a natural logarithm, sometimes the logarithm to the base 2, and sometimes the expected logarithm of the base 10. He can leave us guessing. This is rather careless, but it is consistent with Ben-Naim's habit to often leave things, especially factors in equations, unexplained or ambiguous. This is not conscientious, especially if he is writing, in part, for a lay audience.

Ludwig Boltzmann, of course, had a more expansive conception of entropy than Ben-Naim.

In Boltzmann's words:

"...a system... when left to itself, it rapidly proceeds to disordered, most probable state."
[p.38]

So we must add Boltzmann to the list of great scientists who have not understood entropy as well as Arieh Ben-Naim. Fair enough. I don't think Hegel understood much of anything, but many think he was one of the greatest philosophers. So Ben-Naim can have his say.

Ben-Naim wants to make his case on the basis of his own definition of entropy, which goes back to an equation about "information" by Claude Shannon (1916-2001), which is . Ben-Naim doesn't explain much about this equation. I don't remember what kind of logarithm the "log" here is supposed to be. Wikipedia says "The choice of base for log, the logarithm, varies for different applications."

There is a basic question what "H" itself is supposed to be. John von Neumann (19031957) himself, told Shannon to call it "entropy," because "No one knows what entropy really is" [1949]. Ben-Naim, of course, says that he knows what entropy is, and then "H," while it is not entropy itself, gives us a beginning to derive Ben-Naim's own definition of entropy.

Another basic question is what "information" is supposed to be. Ben-Naim explains that this is not the ordinary meaning of information that contains actual meaning. So it can be gibberish as well as language. Even numbers, as in the results of an experiment (Ben-Naim's own examples), would have meaning. But we get no further explanation.

After a lengthy introduction of the SMI ["Shannon's measure of information," 1948] we are ready to define the concept of entropy as a special case of SMI. This definition leads naturally to a simple, intuitive and irrefutable interpretation of entropy. [p.56]

A "simple, intuitive and irrefutable" definition of entropy would certainly be nice. Unfortunately, what Ben-Naim ends up giving us is:

This is actually an equation for an "ideal gas," where, I think, "E" is energy, "V" is volume, and "N" is the number of particles. Nothing simple or intuitive about this. But Ben-Naim admits that it isn't yet his definition of entropy:

The next step in the definition of entropy is to add to the entropy of an ideal gas, the mutual information due to intermolecular interactions. [p.65]

Then we get a page or so about "intermolecular interactions," and we expect Ben-Naim to then give us a corrected equation or a conceptual definition -- the "ABN," "Arieh Ben-Naim," definition. I don't see either. Maybe I have missed it or misunderstood, but I can't tell where Ben-Naim in fact gives us his definition. The first I notice is him talking about the definiton:

The most important conclusion of this definition is that entropy, being a state function, is not a function of time. Entropy does not change with time, and entropy does not have a tendency of increase. It is very common so say that entropy increases towards its maximum at equilibrium. This is wrong. The correct statement is: The entropy is the maximum! As such it is not a function of time. [p.68]

As an application of his own definition, whatever that is, Ben-Naim cannot be faulted. It is just that his definition, whatever it is, is a very narrow, special case:

From this definition it is clear that entropy is defined for a well-defined thermodynamic system at equilibrium. It is also clear that entropy is not defined for any living system, and not for the entire universe. [p.69]

Indeed, his entropy is "not defined for any living system, and not for the entire universe." But this is what is called, in philosophy, "reductionistic." It is always a neat trick. As I said above, a "well-defined thermodynamic system at equilibrium" is not the only system to which the equations of Clauius and Boltzmann apply. So much in the universe is in disequilibrium, but energy, temperature, and entropy apply to such systems also. And it would have helped if Ben-Naim could have offered a defintion as "simple, intuitive and irrefutable" as he promised.

One more point:

The idea of absolute irreversibility of these processes, was used to identify the direction of these process with the so-called Arrow of Time. This idea is not only not true; it is also erroneously associated with the very definition of entropy. [p.75]

I may agree with Ben-Naim on one thing. I suspect that time is irreversible because of the metaphysics of time, not because of entropy. So if entropy is irreversible, such that the broken glass does not spontaneously reassemble itself, this depends first of all on the nature of time, not the other way around. Where Ben-Naim says that many have gotten the causality backwards, he may be right, if we are talking about the same thing.

However, the irreversibility of entropy is at the very least a clue that the equations of Newton and Einstein, where time can as easily go backwards as forwards, means that they have left something out and missed a fundamental feature of reality. I'm not sure that Ben-Naim notices or cares about anything of the sort.

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Meditation on the Beginning, Note 2

In a book co-authored with Stephen Hawking, Roger Penrose makes an intriguing statement comparing Einstein and Bohr:

For Einstein argued that there should exist something like a real world, not necessarily represented by a wave function, whereas Bohr stressed that the wave function doesn't describe a "real" microworld but only "knowledge" that is useful for making predictions. [Stephen Hawking and Roger Penrose, The Nature of Space and Time, Princeton University Press, 1996, pp.134-135]

The curious thing here is that, according to Penrose, neither Einstein nor Bohr had a Realistic view of the wave function. Yet in Maxwell's physics, the waves, as of electromagnetic radiation, were the only reality. Einstein can be said to have replaced the waves with particles in the Photoelectric Effect (that is the way Feynman states it -- "the wave theory collapsed"), but we can say that Complementarity added waves back in. How that works remains up in the air.

Bohr's anti-Realism or Positivism is clear enough, as this is endorsed by Hawking in the same book. But for Einstein, the "not necessarily" means that he was uncertain about the very meaning of the wave function. The problem there may be what the wave function had come to be.

Schrödinger's Cat was a challenge to the interpretation of the wave function as the sum of possibilities. Thus, while we can understand how a wave, an extended object, can be in two places at once, while a discrete particle could not be, it is much harder to understand how Schrödinger's Cat would be both dead and alive. However, if we need a boundary between macroscopic effects, where a cat cannot be both dead and alive, and microscopic ones, where a wave is a physical reality that can go through both slots in Thomas Young's experiment, this boundary has never been clearly drawn. Indeed, there seems to be a disinclination to even tackle the issue.

Clearly what gave Einstein (and Schrödinger) pause was the development of the wave function as part of a theory of possibility. For a Realistic metaphysics, which Einstein wanted, this is not going to seem quite right. However, when a "Many Worlds" quantum mechanics deals with possibility by postulating an infinite number of new universes at every moment (full of mass and energy from nowhere!), the wave function as possibility begins to look modest indeed.

Indeed, we are faced, not so much with a dilemma, as with an opportunity. A metaphysics of possibility is needed, without turning it into an Ockham's Razor-busting extension of actuality, and without simply ignoring it all. This is what I am exploring. Schrödinger's Cat cannot be both dead and alive, but this is to substitute actual states, again, for only possible ones -- while we must ask why the consciousness of the cat could not itself collapse the wave function. Yet we also must allow for actual microscopic waves, or we cannot explain the interference effects of Young's (with light), or de Broglie's (with electrons), experiments.

That is an area where philosophers might have as much to contribute as physicists, if, that is, academic philosophers were not wasting their time on Heidegger, Nietzsche, and Wittgenstein, while screaming "racist" at everyone.

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