Thoughts on Timaeus, Part I

              Timaeus is definitely the most difficult and rewarding of the dialogues that I have read so far. It took me far more time, effort, and research to understand this one and I’m sure future readings will reward me with even more knowledge I missed on this go-around. This will be reflected in the fact that I will have to divide this into two blog posts – it would just be too long otherwise. This was the first dialogue that forced me to read secondary literature in order to understand it. I’ve been attempting to avoid that insofar as possible so I can make my own interpretation of it, unclouded by the thoughts of others, though they know more than me. This classic dialogue is definitely one of the pinnacles of all of Plato’s writings. It is esoteric, weird, bewildering, highly technical in terms of mathematics, and covers a fairly large array of topics that Plato nevertheless manages to consummately reign into an intelligible whole just as his demiurge does to the cosmos envisioned in the work. In the main, Timaeus is largely a creation myth which uses the fictional device of the demiurge in order to explore eternal truths about the world. At least that’s how I read most of the Neoplatonists read it in contradistinction to Aristotle who had a penchant for literal-mindedness and was almost incapable of seeing the value in mythology and allegory. That being so, ontology is the name of the game for most of the dialogue – Plato discusses his two ultimate principles – The One and the Indefinite Dyad – though the latter is done in a “abductive” manner—meaning Plato expects you to figure it out yourself and not be spoon-fed the answer. Being and becoming, how they are different, how order could come out of chaos, why there is anything at all, etc. – all these big fundamental questions we still ask today are on display here. The role of mathematics in all this approaches divine status. Plato defends his stance as an antimaterialist and antinominalist here and also spends a short amount of time at the end defending the intellectualist view of freedom he is famous for.

              The discussion starts in media res with Socrates finishing up speaking to Timaeus about things spoken of elsewhere. I would guess the Republic, but I haven’t read it and I’ve seen it briefly that many scholars disagree, and I don’t know enough to disagree with them, so I’ll shelve that for now. Anyways, he says women should be allowed to be just as morally developed as men although he does ultimately seem to defend some sort of eugenics where good people should be allowed to breed only with other good ones and the bad with other bad people. He quickly moves on though and wants to hear a story about a perfect republic like the one he has been envisioning with Timaeus. Another person present, Critias, says his grandfather told him just such a story and it is corroborated by Solon, wisest of the 7 sages. Apparently, Solon once went to Egypt where he was told by a priest that all the civilizations of the earth were as children compared to them. The reason why is because the topography of Egypt, and especially the Nile river have acted as safeguards against the catastrophes that wipe out civilizations periodically like deluges, fires, earthquakes, etc. As such, the priest has records that indicate the Greeks used to be the most technologically advanced and noble race of men on the face of the earth until they were wiped out. In fact, Athens is the most ancient city on Earth, being founded by Athena (who is identical to the Egyptian goddess Neith) 11k years ago, a full 1k years before the Egyptian city Sais!

              Part of what made Athens so great was its wonderful climate which the priest says is conducive to the development of wisdom and virtue. I’ve often wondered about this, and I think in the final analysis I have to disagree. I think a good climate would encourage laxity, complacency, and overindulgence in pleasure. I know a bad climate can also provoke anger, envy, and restlessness in us, but I think those are less dangerous than the laziness that always threatens those who are too comfortable. I think I must tend to agree with Helmholtz Watson from Brave New World and the desert fathers that isolation, solitude, and bad climate can be more conducive to virtue and good art. When being told he must be exiled to an island for reading a “heretical” poem to his students he is asked whether he would like to go to Samoa where the temperature is 85°F year-round or to the Falkland Islands where the highest temperature of the year is~55°F. He chooses the Falkland Islands: “I should like a thoroughly bad climate. I believe one would write better if the climate were bad. If there were a lot of wind and storms, for example… (p. 174)”

              Continuing on with the myth – we get to the exciting part that got really overblown by people who took things far too literally in the 19^th century. The island of Atlantis, which was bigger than both Libya and Asia (at that time) combined, attacked and was winning against all of Asia and Europe. As powerful as it was, it was defeated by the godlike might of the ancient Athenians. But alas, no good deed goes unpunished and so the ancient Athenians and the Atlanteans were all wiped out soon after in a single night and day of floods and earthquakes so powerful that they made the island of Atlantis forever disappear into the sea, never to be seen again. This elaborate myth, though it serves many other purposes, (of note to me is it showed ancients understood myths as allegories far better than us literal minded moderns do) was mainly created as backstory to advance the aims of the dialogue. This story spurned Socrates to ask Timaeus of Locri, Italy to speak about how the world came to be. Timaeus is uniquely qualified to speak on this since he is a polymath of sorts – an expert astronomer, politician, and philosopher. He begins his examination of the cosmos with a prayer, “All men, Socrates, who have any degree of right feeling, at the beginning of every enterprise, whether small or great, always call upon God” (27c). Good advice.

              He begins right away with ontology. An eternal thing is something which always is and never changes or becomes. These kinds of things are apprehended by the intellect alone. Of their very nature they are also incorporeal and invisible to the sense. A temporal thing is something which never is but is always becoming and perishing – always in change and flux. These kinds of things are beheld by opinion, without reason but with the aid of sensation – our senses and experience often deceive us. It is part of its very nature that it must be tangible, concrete, and “visible” to the senses – it has a body. Knowing this, he declares the universe must have had a beginning in time since it is sensible and tangible and therefore can’t be eternal (without beginning) (28a). I find this amazing that Plato proved something philosophically so easily so long ago. Even a great philosopher like Aquinas thought proving that the universe began in time was immune to philosophical proof and had to be accepted as an article of faith. Unfortunately, he didn’t have access to Plato, only Aristotle. It is not the strongest proof I’ve seen but it seems to be reasonable to me, although I am not near as smart as any of these other guys. I also found some other doctrines I hold dear in seed form in this dialogue. Timaeus declares that “the father and maker of all this universe is past finding out, and even if we found him, to tell of him to all men would be impossible” (28e) which upholds the apophatic over the cataphatic, which I think is the correct view. He also defends the analogia entis at 29b – there must be an analogy between the original and the copy or else there is no meaning possible – everything would be equivocal. “As being is to becoming so is truth to belief” (29c). The truth is absolute, is objective, and does really exist. Our intuition that there is some one real truth behind things is correct though we must balance this against the fact that we are mere mortals and the best we can hope for is to accept “the most likely story” and inquire no further.

              Next, we move onto the creation myth, beginning with the creation of the cosmos as a whole. The Demiurge (Greek for craftsman) is good and so desires all things to be good like himself, as far as this is attainable (30a). Since the demiurge isn’t The Good as such (God) it may not be possible for him to do so. The Christian view has a higher claim: God is good and so all WILL be well, full stop. In the beginning there was chaos, disorder, irregularity, and irrationality omnipresent throughout the “visible sphere” and that being so, the demiurge wanted to create order out of this. In order to do so, the demiurge looked to the eternal patterns known as the forms and made sensible things in their image since they are perfect, and nothing can be beautiful which is imperfect (30c). Every animal in this visible sphere is an image of an archetypal intelligible reality. If you add up all those you get all of intelligible reality as a whole and the universe is an image of that and so it is THE living animal complete with soul, body, and intellect. I find this absolutely fascinating that Plato and the ancients more generally had this intuition that all of reality was alive, the universe itself was a living animal with a soul and intellect. This does seem to hint at some sort of panpsychism in terms of consciousness and the unity of the spiritual and material realms – although I am far too ignorant to be able to parse that out completely. I’m eagerly expecting David Bentley Hart’s forthcoming book on consciousness which is supposed to be very Platonic and also supposed to have a panpsychical bent to it. I also really enjoy seeing this perspective in stories like At the Back of the North Wind and Lord of the Rings, so it really rings true for me. The best cinema that supports this view are the renowned Studio Ghibli movies, so I recommend checking them out.

              Since, according to Timaeus, the physical universe is the image of all of intelligible reality as a whole there must only be one cosmos and not many, especially not infinitely many since there would be no other archetypes from which to pattern more reality – they are all included in the universe already. The most common view of the origin of the universe in the ancient Mediterranean world was that everything could be reduced to one fundamental principle of matter—monism and atomism. Thales believed it was water, Xenophanes thought it was earth, Heraclitus leaned towards fire, and Anaximenes was a proponent of air. Parmenides was a bit different, being a dualist in this respect, fire and earth being the two fundamental principles. Empedocles is the one we most remember – that all 4 elements were fundamental. Plato innovated on this even more—none were fundamental.  Now we are going to see just how Pythagorean Plato was – he believed the Divine manifested itself throughout the world by way of mathematics, specifically Numbers (often interchangeable with Forms).

 In Plato’s mind the 4 elements were all Platonic solids which could transmute into one another (except for Earth) because they were made of yet more fundamental building blocks – planes. Planes can be broken down to triangles. Of these there are 2 primary elements – the 30°, 60°, 90° half-equilateral scalene right triangle with hypotenuse √3, and the 45°,45°,90° isosceles right triangle with hypotenuse of √2.  The half-equilateral was used to make fire, air, and water which are the elements that can be destroyed, and it is because this one isn’t as stable as the isosceles. Fire is the simplest and “most cutting” of the elements and is in the shape of trigonal pyramid made up of 24 scalene triangles. Air is an octahedron made up of 48 scalene triangles. Water is an icosahedron made up of 120 scalene triangles. The isosceles triangle is the most stable and because of that, Earth can never be destroyed nor transmuted though it can be broken down. That’s why Earth is the strongest shape – a cube made up of 24 isosceles right triangles.

Plato may have been wrong about things ultimately being made up of triangles but it’s unclear if he meant that to be taken literally. His intuition, no matter what his exact thoughts were (if he had any on the matter) were definitely correct. Even today we know that what once were considered indivisible things (atoms) can be reduced even further. In fact, it seems Plato was furtively showing us something in a non-straightforward manner. Elements can be broken down to planes. Planes can be broken down to triangles. Triangles can be further reduced to lines and lines are ultimately reducible to numbers – so numbers aka math is the most fundamental reality. I think that is probably true.

 

               Even though Plato didn’t regard the 4 elements as the most fundamental principles – he did agree with Parmenides that fire was necessary to make things visible and earth was necessary to make them tangible. These 2 principles are extreme and contrary to one another so they would need a third thing to be a bond of union between them (31c). In fact, there would need to be two means in between the 2 extremes since we are dealing with solids which are cubic. Between a³ and b³ there is not only a²b but also ab². The two means between earth and fire are water and air, which joined make the third thing. There are 3 different types of Pythagorean means: arithmetic, geometric, and harmonic. The arithmetic mean is the simplest and the one we are most familiar with: when you add up the items of interest and divide by the number of them present; it is normally used to calculate average test scores. The geometric mean is obtained by multiplying (rather than adding) the values and then taking the square root of them; it is typically used to calculate average compound interest earned. The harmonic is the rarest and is obtained by putting the number of entities in the numerator and dividing by the sum of the reciprocals of the values obtained; it is typically used for changing rates like average speed. There is an ordinal relationship between them: arithmetic > geometric > harmonic. The geometric mean is always in the middle – something the Greeks and the Buddhists love, the middle and moderate way. The continuous geometric mean that is the most beautiful and most fitting to provide unity among hostile objects is the golden section.

              Johannes Kepler once said: “Geometry has two great treasures: one is the theorem of Pythagoras; the other the division of a line into extreme and mean ratio (golden ratio).” The golden section is the ratio you get when a total line segment AB is bisected by point C such that AB/AC = AC/CB and the ratio we get is Φ = 1.618. It is a fascinating number that shows up again and again in art and nature and there are countless books on it, so I won’t belabor the point here, but it was extremely important in the ancient world, even accounted a quasi-divine status and it is still dear to us today. This golden ratio can also be found by the Fibonacci sequence, which I also found is also called Pingala’s Matrameru because it was found by an Indian thinker from the 400s BC who found it some 2000 years before Fibonacci. At any rate the Matrameru is found starting with 1 then adding the succession of numbers like this: 1, 2, 3, 5, 8, 13,21,34, etc. The golden ratio, Φ, is approximated by taking one number in the sequence and dividing it by the one immediately prior to it. 21/13 = 1.615; 34/21 = 1.619, etc. So, to recap the reason the golden ratio is so important is that it makes it so that 3 things can be joined in the closest way. Look at the line segment—the total length divided by the big segment AC is the exact same ratio as the big segment divided by the small segment. The number obtained is the same and so the three are now basically one. As Plato says they are joined by a “spirit of friendship” since they are all in due proportion.

              For Plato, math is divine since it is embedded in the fabric of the world, in fact it probably just is the nature of the intelligible world shining out in a mirror darkly into ours. Mathematics shows that the world is simultaneously good, beautiful, and intelligently organized. You probably don’t know enough math if you are not in total shock and awe at how these functions and equations can so beautifully and fittingly be mapped onto the world. As Stephen Hawking even says, it seems like there is something that “breathes fire” into the equations. It not only explains things but actually brings the fabric of reality together. Proportion for Plato was not just a description of the relationships between things, but a unitive force that joined things concretely. In fact, one might even say there is a moral dimension to math. This is another function that the geometric mean has for Plato. Most of us would normally think of dividing a line right in half so the two are equal, but for him that was not just. As he says elsewhere in Laws – equal treatment of the unequal is unjust. The Pareto principle, discovered in 1896, only confirms this. It is a power law distribution that shows that most things are not equally distributed – that is for the simple minded. The top 20% of earners pay 80% of taxes. 20% of most people’s workload takes 80% of their time. 80% of the world’s problems are caused by 20% of the people. 20% of the patients in hospitals use 80% of the resources. I could go on and on, but this unequal but fixed ratio, just like the golden mean seems to be a fixture of nature and I think Plato would have supported his belief in a meritocracy with the Pareto principle, if he’d known about it. This also goes to show you that in the modern world we have lost the sense of the unity of knowledge that was commonplace in ancient times. For Plato, math could be simultaneously a discipline in its own right while also being a means of gaining moral wisdom and even divinization of the soul through theosis. How much more beautiful and fascinating is that compared to us moderns who typically say, “When am I gonna use fractions at the grocery store?” Oh, how the mighty have fallen.

              A good question is why is proportion necessary to unite things in the first place? The overarching reason is, for Plato, because the world started out bad – in a state of chaos and irrationality and the demiurge is not God in the most proper sense. He is just a very powerful being among other beings – he didn’t create everything, he just came upon this seething mass of chaos and wanted to make it more orderly and intelligible. He immediately finds himself under 2 constraints. The first is that he can’t change anything that is uniform. By definition change involves a mover and something moved – and to be able to be distinguished as such, there must be a difference. The definition of uniformity precludes such a difference. This is why the demiurge was needed to do anything at all. Many would ask, if the sensible world was patterned off of the eternal Forms, why we need a demiurge to be a middleman. The reason is because the Forms are perfectly uniform, so they never change nor perish and as such can never effect change in anything else by themselves either. The second constraint is that non-uniform things are resistant to mixing and even have a tendency to destroy one another when left to themselves. Rest is instrinic to uniformity and motion is intrinsic to difference. That’s also why Plato says that uniform and like things are better than unlike and different things since they don’t destroy one another (33b).

              Proportion (and specifically the golden section, the proportion par excellence) is how he overcomes the 2 constraints, through 3 steps. First, he uses division, as we see in the creation of the World-Soul. He first mixes together Being, Sameness, and Difference into a mixture that is perfectly uniform and then needs to divide it so it is no longer uniform and could therefore effect change in something else. The second step is to unite opposing things into one and this is seen in the creation in the body of the universe. As we saw earlier fire and earth are hostile elements and need a 3^rd term to bind them. Proportion is the relationship of relationships that creates sameness in difference. This is why the division cannot be random, if it were then there would be no linkage between the disparate elements. Proportion also doesn’t just link them to some 3^rd thing, like a peg holding together two chains – the chains are still separate and if the peg falls out, they will become undone. Proportion is like joining the two chains into one chain – a much stronger bond like a covalent rather than an ionic chemical bond. The 3^rd step is to unite similar things that are separate. This is seen in the building up of the elements by triangles into Platonic solids. This shows that proportion always increases or keeps the level of complexity the same – it can never make something simpler and more fundamental. It is how we go from the one to the many and how Plato thought the divine, intelligible world was linked to the sensible, mortal realm. The golden section is what provokes unity between being and becoming.

I also find it interesting that we see basically the doctrine of the Trinity in a seed form here. Plato says that 2 things must be united by a 3^rd so there won’t be strife. That is very crude and far from the glorious idea of the perichoresis inherent in the Holy Trinity, but it is a start. Aristotle too noticed that “the triad is divine.” Lao-tzu in the Tao Te Ching 42 wrote, “The Tao gave birth to One. The One gave birth to Two. The Two gave birth to Three. The Three gave birth to all of creation.” There are probably many more such examples, though I can’t think of any off the top of my head. This is all very fascinating to me and perhaps I’m reading too much into it, but I can’t see it as a coincidence. There is a question we must ask ourselves here and interpretation is all-important. An atheist reading this might be thinking, “The reason all these people from wildly different times, cultures, backgrounds, and languages all thought similar things is because reality is 3 dimensional and that’s what is significant about the number three.” I used to think I was deep thinking such thoughts… until I realized there were deeper thinkers who would respond to that in the following way: “Yes, that is probably why they all saw the significance of the number three since we see it reflected in intelligible reality. But couldn’t it be that the reason there are 3 dimensions and that 3 seems like such a special number is because it is but a partial reflection of the more glorious nature of the Source of all things, the Infinite, the Holy Trinity- the Reality of Realities? Rather than that we invented some fictious being to map our erroneous imposition of meaning onto meaningless things?” I know what Plato and all the people I’ve read who I think basically got it right would say. Stay tuned for part two and remember the immortal words of Bill Murray: “For relaxing times, make it Suntory time.”

Cheers my friends! Merry Christmas! Christ is Born!