Spirituality, Philosophy and Psychedelics

Thomas, long time no hear. I was curious to get your take on something that I'm not sure what to make of, intellectually and emotionally: the increasingly popular idea that Western spirituality, but more concretely, Greek spirituality is rooted in psychedelic experience. It seems that the Eleusinian mysteries in particular are now being identified as quasi-mushroom cults, while Shamanic transformation is also more and more considered a product of substance use. Again, not sure what to make of it. I mean, would there be no Plato, Empedocles or Pythagoras without mushrooms? Is that the idea? Strange. Anyways, hope all is well. Johannes

...........,

Sorry for the delay in replying. I don't think that Greek spirituality is rooted in psychedelic experience, though you are right that scholars are trying to identify the opposite to be the case. They've been doing this for years, and particularly since the sixties. That's anthropology for you: just imagine how it must have been, rather than read the texts carefully. 

It is true that the ancient Greeks and Romans used drugs as part of religious ritual in some cases (there is a contributed chapter by Robert Graves in William Sargant's 'Battle for the Mind', which is worth a read) But that does not mean that religion or spirituality emerges from the use of psychedelics. The point of using drugs enables those who run the rituals to show that what you think you understand and what you think you see might be quite different. That was the significance of drug use all the way up to the romantic poets and beyond. Trying to understand Plato, Empedocles and Pythagoras  as the product of the use of psychedelic mushrooms however is a complete joke.

Hope this is useful.

Best, Thomas 

Plato and the Transcendental Infinite

 

[This post is an extract from:'Evading the Infinite',   one of twenty-one essays in the book Man and the Divine, published in August 2018.  Information about Man and the Divine can be found here] Part of a critical commentary on Adrian Moore’s A History of the Infinite, broadcast in ten episodes by the BBC (on Radio 4) across two weeks in late September/early October 2016. The first episode was broadcast on the 19^th September. The book is available in ePub format from leading retailers of eBooks, such as Barnes & Noble, Blio, Kobo, Itunes, Inktera, Smashwords, etc.

***

I have spent many years studying Greek philosophy, and as a result I found both Moore’s arguments and his narrative concerning the idea of the infinite to be oddly structured. There is a gaping hole at the start, since Plato is scarcely mentioned, and none of his arguments appear in the narrative (sometimes voiced in the dialogues by his master Socrates).  He does discuss the ideas of Pythagoras, but in such a way that it is hard to recognise him, and the many parallels which exist in Plato’s writing. As a result, this history of the infinite is not a complete history, tracing the discussion of the idea from the earliest period possible, but a history with a strong point of view, which begins at a point which is convenient for the arguments which follow (Moore’s book on the infinite has a much broader compass).

Part of my purpose here is to outline Plato’s engagement with the idea of the infinite, and to place it before Moore’s chosen point of departure. Understanding what Plato said concerning the unlimited and unbounded necessarily changes the interpretation of Aristotle’s views and arguments, with which Moore begins. Simply writing Plato out of the narrative not only creates something of a fictitious narrative, but also creates difficulties that otherwise would not exist.

Oddly for an account of man’s engagement with the infinite, the first of the series of programmes is titled ‘Horror of the Infinite’. Moore quotes the mathematician David Hilbert:

The infinite has always stirred the emotions of mankind more deeply than any other question; the infinite has stimulated and fertilized reason as few other ideas have; but also the infinite, more than other notion, is in need of clarification. 

Moore accepts Hilbert’s characterisation of the idea of the infinite. He begins by saying that

ever since people have been able to reflect, they’ve been captivated and puzzled by the infinite, in its many varied guises; by the endlessness of space and time; by the thought that between any two points in space, however close, there is always another; by the fact that numbers go on forever; and by the idea of an all-knowing, all powerful god. People have been by turns attracted, fascinated, perplexed, and disturbed, by these various different forms of infinity. 

Indeed yes. But Moore’s account appears to start at ‘disturbed’, rather than ‘attracted’.

Is God the Infinite, and Reality itself? Moore does not much concern himself with this question in this sequence of programmes, at least not in the terms in which the Greeks understood the question. The following is an extract from The Sacred History of Being (2015):

 The Greeks did not contemplate the idea that the ‘existence’ of God, or the supremely perfect Being, was subject to proof. This would have been anathema to them, for the reason that they understood the very concept of the divine is inevitably beyond the capacity of the human mind to understand, or to frame. It is also beyond space and time. It is possible to say something about the divine, but that is all. Saying that the supreme perfect Being has a property ‘perfection’ is fine, but the meaning of this perfection is strictly limited in its human understandability. To attribute the property of secular ‘existence’ to this Being would have been regarded as absurd.

Yet it would be granted that one could argue that, without the property of existence, the perfection, or the completeness of God, was compromised. But for it to be in the world of change and corruption would also be understood as compromising the perfection of the supreme Being. At least in terms of public discussion. Thus the Greek view of reality and the Divine was that there was a paradox at the root of reality and the gods, and that it was not possible to define the nature of the Divine without exposing that definition to contradiction. The enlightened enquirer into the nature of the divine therefore is spared further pointless argument about the nature and the very existence of God. Both are conceivably true. But the true nature of the Divine, being a paradox, rises beyond our capacity to argue about that nature. It remains a matter of conjecture.

Our human experience tells us we live in a world in which change is possible, and inevitable. The definition of the Divine on the other hand, tells us, the divine reality beyond this world of appearances is a place of eternal invariance. It suggests that at the apex of reality, it is not possible for the divine to act in any way, or to participate in the world of change. Again there is a difficulty if we hold that the greatest and most perfect Being can do nothing without contravening its essential nature. A whole range of properties would clearly be missing from the divine nature.

It would seem that the Greek solution to this problem was to argue, as Plato and the neoplatonists did, that the world of reality was in fact invariable, as the theory requires. And it did not at any time change. But a copy was made. As a copy it was less than perfect, and this imperfection created the possibility of change, action, and corruption. This copy is eternally partnered by the original, which stands behind it, unchanging and unchanged by anything which happens in the copy of the original divine model. As a copy it is the same, but as a copy it is different.

This however, is a solution which Plato labelled as a likelihood. Which is code for: ‘this is not the answer to the problem’. 

One of the properties of the supremely perfect Being would be that he was one and not two. In the creation of a copy, the invariability of the divine has been breached, and the divine is now two, not one. Two, not one, would seem to be a fatal objection. Firstly the copy is a representation of the original, and not the original itself. Secondly, the copy is imperfect, and through the act of representation, it has become different. The original continues complete in its original nature, with its original properties and characteristics.  Plato hints at territory beyond this contradiction, but does not venture into it overtly.

This is the key mystery of ancient thought. To understand the full significance of this problem, and its implications for ancient models of reality, we need to look closely, as they would, at what a copy of Being actually means. There can be no copy, at least not in an objective sense. And if there is no objective copy, then the world which moves and which has existence, must be a subjective view of Being.

Apart from anything else, if the world is a wholly subjective experience, occurring (if we dare to use that word) within Being itself, then the change and motion which is apparent to us, and which contradistinguishes the world of existence from Being, which is itself and only itself, must be illusory. The illusion may be convincing, but ultimately it remains as an illusion, however persuasive it is to us, that there is an objective reality which is subject to change and movement.

This is the correct answer to the problem. Our experience in the world is of finite things, which are finite representations of things which are infinite. But this world is also infinite, and at the same time. It is therefore a matter of apprehension, understanding, and will, if man is to engage with infinity, and reality itself.

Hence Plato’s discussion of the ascent to The Good via the Forms, to that infinite place where all knowledge is to be had, and to descend again with divine knowledge, again entirely via the Forms, to the world of sensibles. What he is actually talking about is a formal process and discipline by which the finite human mind can engage with infinity.

Pythagoras was much closer to Plato in terms of doctrine than scholars normally allow. I can demonstrate this by quoting the Neoplatonist Porphyry who wrote about Pythagoras many centuries after his lifetime. Porphyry’s account tells us that:

He cultivated philosophy, the scope of which is to free the mind implanted within us from the impediments and fetters within which it is confined; without whose freedom none can learn anything sound or true, or perceive the unsoundedness in the operation of sense. Pythagoras thought that mind alone sees and hears, while all the rest are blind and deaf. The purified mind should be applied to the discovery of beneficial things, which can be effected by, certain artificial ways, which by degrees induce it to the contemplation of eternal and incorporeal things, which never vary. This orderliness of perception should begin from consideration of the most minute things, lest by any change the mind should be jarred and withdraw itself, through the failure of continuousness in its subject-matter.

That is exactly the doctrine of the ascent and descent via the Forms which is described by Plato. The definition of transcendent reality in Plato (articulated by Socrates) is that it is a place beyond shape, form, size, etc., and occupies no place on earth. It is however the place where knowledge has its reality (the ‘eternal and incorporeal things’ mentioned by Pythagoras). Connection with transcendent reality is possible by the likenesses to the transcendent which have existence on earth, such as things which are complete and whole, which therefore participate in the completeness and wholeness of the transcendent reality. Completeness and wholeness require (in the world of the mundane) delineation and limits, and so the limits and the extremes of things are also things which participate in transcendent reality.

The principle of ascent to the ‘eternal and incorporeal things’ is entirely a mental process, which does not involve any of the senses. It proceeds via chains of similitudes, both up and down, as a sequence of orderly perceptions. The goal is a form of communion with that which never varies, and which is always one and unchanging, as Plato tells us in the Sophist. The return from the communion with the Good delivers beneficial things, because the Good is the source of all knowledge.

What is transmitted to us via the writings of the Platonists, is something of the basis of both their understanding of what the Divine actually is (the Infinite, the Limitless, and Reality itself), and how man may have commerce with the Divine, through sacred rather than profane practices, in a world which has a double nature, and in which man has a choice.

Looked at in this way, rather than being a history of infinity, Moore’s argument is about the idea of the infinite from the point of view of finitude. This is the way Aristotle chose to deal with the infinite, by dividing the concept into the actual infinite, and a potential infinite, and dealing with the latter. Moore has said elsewhere that the way he treats the infinite is generally in terms of an Aristotelian Finitism.

We might pause here and consider what the implications might be of the identification of the Infinite and the Divine, which seems to be implicit in the views of a number of ancient philosophers. If they did so identify these concepts, then much of Greek religious thought and practice was based on a philosophical understanding of the infinite. In which case, Moore’s history is a history of what happens when the actual importance of the infinite in the life of man is forgotten, misunderstood, and eventually no longer noticed for what it is. Much of Moore’s argument is shaped by his Aristotelian Finitism.

In the first programme, Moore argues that the Pythagoreans thought finite things were good, and that infinite things were bad (this information comes to us via Aristotle), and that they thought they had evidence that the finite had some kind of control over what was infinite. And that the usefulness of rational numbers showed that this was the case. This is clearly a garbling of Pythagorean thought from a distant age, if Pythagoras thought that ascent to eternal and incorporeal things was important, as I’ve suggested. There is also discussion of musical ratios, and the Pythagorean discovery that different string lengths with simple ratios are more consonant to the ears than those which involve large values. Their ‘discovery’ of irrational numbers, which can be found using the theorem of Pythagoras, is said to have filled the Pythagoreans with horror, and the story of one of their number being drowned at sea after revealing their existence, is referenced. Rather than revealing their horror of irrational numbers, this is a story which points to their interest in whole numbers. The idea that they once had no idea about the existence of irrational numbers is absurd.  

The programme moves on to consider whether other ancient Greeks had the same resistance to the infinite. The views of Anaxagoras on infinite divisibility are discussed. Anaxagoras was relatively comfortable about these ideas. Zeno’s paradoxes in connection with infinite divisibility are also discussed, including his paradox of travelling by an infinite number of half distances, which seems to imply that movement is impossible. The similar paradox of Achilles and the Tortoise is also referenced. Observation and reflection thus seem to contradict each other. Zeno distrusted observation to the point that he believed that movement was impossible. Parmenides was Zeno’s teacher, and taught the universe to be a simple unity. So, only the appearance of motion is possible. Otherwise the universe would have to have infinite complexity. Moore winds up the episode by suggesting that because of these paradoxes, and the existence of irrational numbers, that there is some truth in the suggestion that the Greeks had a horror of the infinite.  

Looking at the content of this episode in the light of the added preamble about ideas of the infinite held by Plato and Pythagoras, we can see that something old and valuable is contained in the writings of some earlier philosophers, transformed into more or less secularised accounts of the arguments the Greeks used to illustrate the paradoxical nature of the infinite aspects of the world, as they manifest in the world of the finite. 

We  get many clues about the Greek understanding of the infinite and the unlimited from a number of Plato’s dialogues, including The Timaeus, The Sophist, The Republic, The Theaetetus, The Laws, and The Parmenides. In skipping Plato, the first reference to Parmenides and his notion of the universe as simply one and one alone, is as an introduction in the first episode to his pupil Zeno of Elea, and his response to paradox. There is no discussion of Plato’s demolition of Parmenides arguments, no discussion of the Platonic forms, no discussion of the relationship of the forms to the form of the Good, which is another way of talking about what is infinite, and no discussion of what amounts to a different logical modality in the pages of Plato (where he discusses things passing into one another by means of their similitude), which is a way of understanding the relationship of finite things to the infinite.  

Essentially Aristotle’s rapprochement, which Moore characterises as an attempt to make the concept of the infinite more palatable to the Greeks, involved dividing the idea of the infinite into two. As already mentioned, one of these was the potential infinite, and the second was the actual infinite. As outlined in the first episode, Zeno’s paradoxes depended on the idea of an infinite divisibility, which seemed to make the idea of any kind of movement impossible, since that would require a universe of infinite complexity. Zeno therefore regarded all forms of movement as illusion. Since in order to travel a certain distance, you would have to travel half the distance to your destination, and then half of the distance remaining, and then half of that, and half of what still remained, and so on. Which would result in an infinite number of steps. Which would be impossible. 

Aristotle’s response was that though the various stages of the journey could be understood in such a way, the stages were not marked, and did not have to be considered in making a journey. The idea of limit is however a crucial point. What Aristotle was saying is that there are two ways of looking at the idea of what a limit is.  Essentially there is limitation which is defined by what a thing is, and there is limitation which is not. In the first case the limit of a thing cannot be transcended without the nature of that thing turning into something else.

The essence of this argument is that there are forms of limit which can be ignored. One of which is the actual infinite: instead we should deal with the potential infinite. The actual infinite, by its nature, is always there. But we cannot deal with it. The potential infinite we can work with, since it is not always there, and spread infinitely through reality. So we can count numbers without ever arriving at infinity, or ever being in danger of arriving there. Moore mentioned that this conception of infinity more or less became an orthodoxy after Aristotle, though not everyone accepted that his argument against actual infinity was solid. Which is something of an understatement. Aristotle’s distinction between the potential infinite and the actual infinite is between what is, in practical terms, something we can treat as finite, and what is actually infinite. 

It might seem surprising that Moore’s first port of call in part three is the philosopher Plotinus, who was writing in the third century C.E., some five centuries after Aristotle. The reason that he has jumped to Plotinus is because he argues that Plotinus claimed not only that the divine was infinite, but that the divine was the infinite. Thus conflating the ideas of divinity and infinity in a way that – he says – no one had done before. Or, to be more precise, he declared the identity of the divine and the infinite in a way no-one had done before.  

Well no. As I’ve argued at the beginning of this essay, Plato’s principal interest was in a transcendent reality, which it would be hard to distinguish from the infinite, except in hair-splitting terms. He refers to the necessity of ‘looking to the one thing’, and that the ‘one thing’ is something which is found nowhere on earth. In one of his dialogues, he has Socrates describe that transcendent realm as something which possesses ‘no form, shape or colour.’ It is clearly without definition and limitation, with no finite properties and attributes, which means it is unlimited, and infinite. It is also the ultimate source of all knowledge. So it also seems to possess the properties and attributes which are associated with the divine. Plotinus’ supposed innovation is therefore no such thing. Anaximander’s understanding of the ‘apeiron’ (the unlimited) as the cause of all things is just such an equation of the divine with the infinite, which means the idea was around in the sixth century B.C.E. 

Revolt in Athens in the late Seventh Century BCE (A letter to SemprePhi)

At 19:12 29/11/2020, Thomas Yaeger wrote:

[.......]

Hi. I didn't mean to do any work on the DoP [Death of Pan] today, but it was a quiet Sunday, and I decided in the morning to explore expanding the content headings into sections. This is a much more abstract discussion than in the earlier books, but that is how imagined it would be. So I need a lot of references to existing articles and chapters, enabling readers to have access to real detail. The article 'An Appetite for Knowledge' will be the basis of this, but much expanded.

So far I've argued that a great deal of intellectual and philosophical input to Greek civilization comes from Mesopotamia and Egypt, which is the case. But I've been arguing in terms of a sixth century BCE input, via Pythagoras, just to open the door to an acceptance of the possibility of an east-west transmission. Plato's determination to get hold of the three volumes concerning Pythagorean doctrine offered for sale by Philolaus, tells us that he understood that they contained information useful for the understanding of cult doctrine in Greece.Something had been lost along the way.

Martin Bernal argued, on the basis of comparisons of Egyptian and Greek words, that the Greek vocabulary was heavily indebted to Egyptian, and that the borrowings probably dated back to the mid-2nd millennium, when there were major population movements from Egypt and North Africa. Some of those ended up in the Peloponnese and in Anatolia. I think that he is right about that line of transmission.

But there is a third route of transmission. After the second millennium, but before Pythagoras. I mentioned it in a chapter which didn't make it into SHB for one reason and another, but which has since been published. There is an obscure quote preserved in Eusebius, which says that the Assyrian king Sennacherib captured Athens. This would have been around 701-700 BCE. Any classicist reading that will find it deeply shocking. Generally I try not to mention it.

[……………] This story is [likely to be] true because it explains a peculiarity in Sennacherib's campaign records - half of them are missing from the archives in Assyria. The quotation goes on to mention that Sennacherib built a temple in Athens, which he filled with brazen statues, and that his exploits were recorded in cuneiform on the statues. Now we know why they were missing.

It takes a while to build a temple, and to fill it with brazen statues, so Sennacherib and his troops were there for a while.

I sent the completed chapter to Simo Parpola, and asked if he had anything else to add to the pot. He replied *the same day* with an article he'd contributed to a volume of conference proceedings in 2004, in which he was able to trace the westward expansion of the Assyrians across Anatolia, from their records, all the way to Ionia, which of course was part of greater Greece at this time. They were always aiming for Greece. He didn't know they made the mainland. But they did.

How long were the Assyrians in Athens, and in Attica? I guessed five years or so. But I started to look for some kind of end point to  the Assyrian occupation. I could find nothing.  Parpola had pointed out in his article that a number of features of Greek political and social organisation looked like borrowings from Assyrian organisation, such as naming eponyms for each year, and the institution of Archons. So I looked further, and found an interesting account of a tyrants revolt in 632 BCE (revolt of Cilon). The Greeks recorded tyrants often with very little detail. They were tyrants if they opposed the established authorities. The detail we have is that conspirators were hunted down by the Archons and killed (their grave site has been excavated, and it isn't pretty - the skeletons are in manacles and their mouths have been stopped up with stones).

The date is significant. The last important king of Assyria was Ashurbanipal, who disappears entirely from the record in 632-1 BCE (the empire staggered on till about 609). Possibly as the result of a palace revolt. We don't know. But this would be the right time to rise up  against a hated occupying force.

If the revolt and the collapse of the Assyrian empire are connected, this would mean that the Assyrians were in Athens  for  nearly *seventy  years.*

[..........................................................] 

I'll deal with the Assyrian occupation in a couple of papers further down the line.
 
Best, Thomas

Transcendental Reality in the Ancient World (Writing to Marie aux Bois)

Date: Thu, 19 Mar 2020 16:24:58 
To: Marie aux Bois
From Thomas Yaeger

Marie,

Re: the paper on the mathematics of the megalithic yard - there's been a lot of movement since I wrote it in the middle of February, and I will write several other articles on the back of it. One of the objections to the argument will be that arriving at Euler's number would have been impossibly complicated for them to do (quite apart from the general case I'm making as to the sense it made for them to want do this). But it isn't true that this is complicated to do, particularly if you work it out geometrically, and use the right kind of exponentiating series (i.e., ones which arrive at the limit of the series in the shortest number of steps). I've already drafted this one.

The argument of the article is fine I think, but at various points it trades on what I know, and what I've written about elsewhere. So I'm going to write another article which brings the relevant information together.

I can make a list of the most significant things in the article:

1. It brings together concepts which were present in Greek civilization and philosophy, as well as in Mesopotamia. So the same ideas are going on in their heads, even if on the face of things the cultures are quite different. For the neolithic case, they are writing in terms of number and geometry.

2 If this argument is sound, it pushes the development of sophisticated mathematical and geometric thought back to the middle to late 4th millennium (3500 -3200 BCE).

3. The argument shows that, on the basis of the mathematics and geometry in the stone circles, that the builders had the same general concept of the existence of a transcendent level of reality which we know for certain the Greeks had. Indeed, historians of ideas pick the Greeks as the originators of the idea of a transcendent level of reality, and behave as if all the other religions in the world did not, before this time.

4 This transcendent level of reality was in fact infinity itself. They came to this conclusion in the Neolithic on the same basis as the Greeks did much later. Which is that the version of reality we inhabit isn't reality at all, but a poor copy of it (I echo Plato's words here). This was established on purely logical grounds, and on the basis of puzzling things about the physical universe (why is there something rather than nothing? If reality itself is necessarily one, otherwise it breaches its nature, how is it possible that there is multiplicity?)

5. And how is it that there are irrational numbers? Again, historians of ideas argue that before the Greeks, and the Pythagoreans in particular, people had no knowledge or understanding of irrational numbers, and when the Pythagoreans discovered their existence, they tried to keep this secret. In fact *the entire basis of Pythagorean thought, both in Greece, and the protoPythagorean megalithic culture was based on the existence and significance of irrational numbers.* I've talked around this issue both in SHB, and in "Understanding Ancient Thought", firstly by discussion of how ancient people conceived that commerce between the Gods and Man was possible, and by discussion of the logical modality that Plato discusses in the "Timaeus", which is based on irrationals.

6. The esoteric core of ancient religion was often kept secret. We know this for sure about the Pythagoreans, the Spartans, the Athenians, and also the ancient Romans. Plus the Assyrians and Babylonians. Modern historians assume that a transcendentalism isn't involved, but rather a doctrine which serves societal and political functions. But what if the esoteric core is too difficult and too dangerous to  convey outside a tight circle of those who understand?

7. Plato discusses how the disagreements about the nature of reality in antiquity might be resolved, in more than one place in "The Sophist". The position  which must be accepted (he says) is that *Reality is both One and Many at the same time*. In other words, the esoteric core of religion, based on the consideration of natural puzzles and the reality of irrational numbers, is that transcendent reality is necessarily paradoxical in nature.

8. Hence the common representation of the transcendent reality as *the inversion of ours* (look up 'Seahenge'). It is the same as this one, but it has different properties. In that transcendent reality, all things are commensurate.

9. Finally, this argument offers the possibility of proving that  transcendental thought did exist at the close of the 4th millennium around a number of cultures. If transcendental thought about the nature of reality was expressed mathematically and geometrically, and  necessarily involved irrational numbers, we should be able to find such references to transcendentalism in many of the architectural and engineering achievements of the ancient world. These have been noticed already in a number of structures, long before I started pursuing this question, but (for example) the golden section, clearly present in a number of Egyptian structures, is written off as a coincidence, or as consequence of the way the structure was laid out in practical terms, and that the builders had no knowledge of  its presence, and did not think the proportion had any significance in itself.

We know the measures the Egyptians used. Scope I think for a nifty little computer programme to number crunch all of these, to look for the presence of Euler's number, and other irrationals.

Best, Thomas

The paper 'The Mathematical Origins of the Meglalithic Yard' is at: https://shrineinthesea.blogspot.com/2020/02/the-mathematical-origins-of-megalithic.html

Meaning and Function in the British Neolithic (Writing to Paul Devereux)

Date: Fri, 14 Feb 2020 20:23
To: PAUL DEVEREUX 
From: Thomas Yaeger 
Subject: The Mathematical Origins of the Megalithic Yard

Dear Paul,

Hi. You might be interested in the following blogpost, which looks at why the supposed 'megalithic yard' has the dimensions it has. It takes an entirely different approach to both Thom's surveys and Ruggles later efforts (not statistical analysis, which doesn't do much except expose the general parameters of something which might exist), and which avoids (to a large extent at least), the risk of selection bias. These seem to be the main complaints.

What I've done is to take an entirely new approach, which looks at the megalithic yard as something which serves a function in the context of megalithic structures, and which has a strict mathematical relation to what we already know about these structures (the focus on whole numbers, the use of pythagorean triangles in their construction, and the fact that they are often deformed in various ways, in order to achieve commensuration between the sides of the triangles and the circumference of the circles).

There is a view of reality buried in pythagoreanism, which emerges from the mathematics. This is true both for the later Pythagoreanism of the sixth century BCE, and for the earlier proto-pythagoreanism, since the mathematics are the same, and the interests in the mathematics are essentially the same. That's where the megalithic yard comes from, and I describe this in the post.

I'm afraid the text is as dense as in the paper I submitted to 'Time and Mind' a couple of years ago (it is a tricky subject), but I've kept the necessary mathematics to the bare minimum. It is just under 5k words, so you will need about an hour to digest it.

....

The post is 'The Mathematical Origins of the Megalithic Yard', and is at: https://t.co/BiLRKVq5O1

Hope you are well!

Best regards, Thomas Yaeger

Answers to Questions (Writing to Euan MacKie)

(Photo by Simon Ledingham, May 2005)

Date: Wed, 11 Mar 2020 20:35

To: Euan.MacKie
From: Thomas Yaeger
Subject: The Mathematical Origins of the Megalithic Yard

Euan,

Hi. You might be interested in looking at this article, 'The Mathematical Origins of the Megalithic Yard'  http://shrineinthesea.blogspot.com/2020/02/the-mathematical-origins-of-megalithic.html  

Which I think may be the definitive answer to a number of questions about the construction and purpose of megalithic circles. Obviously this article is subject to criticism, which is fine, and I would be grateful for any comments you may care to make. 

I got to this point over seven years of rumination, and several articles on the Neolithic and patterns of thought in the Neolithic, in so far as they might be inferred from both the archaeological remains, and what ancient writers said about Britain before the Romans arrived.

I was given a classical education at school in Edinburgh (minus Greek literature), and a wider education at UCL later, where I studied Rome, Greece, and the Greek language. As well as Mesopotamia, Egypt and other cultures. My particular interest has always been Greek philosophy. Eventually I found my way back to an interest in British prehistory. I was struck by some of the things which Alexander Thom found through a phenomenological analysis, about the mindset of the Neolithic architects, because they echoed ideas which are commonplace in later Greek philosophy (the importance of the idea that reality itself is necessarily unchanging, meaning the idea of the 'One'; and of Totality, and the importance of commensurate values, and the significance of the fact that commensurate values are sometimes lacking in the physical world, etc.). I've written extensively about the Pythagoreanism of the 1st millennium BCE. Much of which came from the ANE, during Pythagoras's travels. Mainly, but not exclusively from Egypt. It is a technical substrate of Egyptian religion, which Pythagoras imported into his view of the world, after (reputedly, according to the neoplatonists) twenty years of study in Egypt. Meaning that the pythagorean perspective is older than Pythagoras himself, and possibly of immense age.

What we have in the stone circles of the British Isles, is just such a technical substrate of ancient religion, written in mathematics and geometry. Personally, I think most religions got started this way, though we are a long way off from being able to say this for sure. It is not however an argument that is considered at all at the moment in archaeological circles. I think it should be considered, even if only to finally eliminate it for rational consideration.

[Other materials relevant to this article can be found by using the search box on my blog ["neolithic" will pick most of them up].

Best wishes, Thomas  

The Mathematical Origins of the Megalithic Yard

Did Alexander Thom discover interesting stuff about the British Neolithic, or was he deluded in what he thought he saw? The modern consensus among the archaeological community is that he discovered nothing of importance which was actually present in the evidence. This was supposedly shown by a large scale resurvey of the stone circles conducted by Clive Ruggles in the eighties. This resurvey was conducted with a great sensitiveness to the possibility of selection bias. This sensitivity was taken to such extremes however, that it would have been impossible to verify much of Thom’s surveying and interpretation as the archaeologist Euan Mackie has indicated.

That of course, was the point. We already had some nice models of antiquity which didn’t involve much in the way of interpretative mathematics, there was little interest in the precision which seemed to be present in an ancient preoccupation with the sky, and in the observation of rising and setting points, equinoxes and solstices, and in the nineteen year metonic cycle of the moon’s movements. The foresights which seemed to be used to indicate something of importance to the ancient astronomers and priests were largely ignored in the Ruggles resurvey. We liked the models we had before, and didn’t like or understand what might be implied in a British antiquity which was populated by mathematicians, engineers and astronomers who thought the sky was a key object of interest, and who threw vast resources at the construction of monuments whose purpose was hard to fathom.

After the resurvey of the monuments the archaeological community turned away from the questions which Thom’s original surveys and measurements had thrown up. Enough doubt had been sown to make the territory he had explored a matter of disinterest to the community, and entirely lacking in anything that archaeologists needed to consider. Whatever we could find out about the megalith builders would not be found out by following Thom’s lead. There is still interest out there in Thom’s work of course, but no-one is pursuing similar research within an academic context.

We know from Classical writers that the study of aporia was a matter of some interest to those interested in philosophy, mathematics and physics, discussed in Plato’s Sophist and the Timaeus, and also in Bk 3 of Aristotle’s Metaphysics. Pythagorean triangles are one kind of puzzle which could be explored, and it was evidently a matter of great interest in the Neolithic, since they used a number of the Pythagorean triangles, and not just the basic 3.4.5. instance. The 16 basic triangles can be enumerated as follows:

(3, 4, 5)  (5, 12, 13)  (8, 15, 17)  (7, 24, 25)

(20, 21, 29)  (12, 35, 37)  (9, 40, 41)  (28, 45, 53)

(11, 60, 61)  (16, 63, 65)  (33, 56, 65)  (48, 55, 73)

(13, 84, 85)  (36, 77, 85) (39, 80, 89) (65, 72, 97)

To us, these are just geometrical figures, and we don’t ask many questions about why these exist. But that was not the case in antiquity. For those engaging with these figures, they were puzzles. Why did these triangles with sides which were whole numbers meet and agree once two of the sides were squared and the hypotenuse was squared? Their sides don’t meet and agree when considered as triangles, yet they do when multiplied into their square values.

We also know from classical writers that there was a great deal of interest in the idea that things should ‘meet and agree’. Once of the most famous stories from antiquity concerns a conversation between Solon and Croesus, involving some bizarre mathematics to bring together the mathematics of the cosmos and the days of the life of a man. (Herodotus).

So looking at these stone circles as forms of puzzle, with some relation to the universe in which we live, and as objects which were intended in some way to meet and agree with that cosmos, may provide some answers.

I’ve written about some aspects of this before, in ‘Pythagorean Triples and the Generation of Space’. I quote some passages from it here:

In antiquity, it was obvious to anyone interested in number, mathematics and geometry, that there were several aspects of the physical world that involved irrationality, long before it was possible to provide logical proof of such irrationality. One of these irrationalities was the relationship between the diameter and the circumference of the circle. We know that irrationality (understood as an absence of commensuration) was a major concern in antiquity, since the existence of it seemed to undermine the idea that the world was rational, and constructed by the divine on rational principles. In other words, the existence of irrational things served to undermine the idea that the world made sense, and that it was good.

What we understand as Pythagoreanism is actually a way of approaching the world and reality on the basis of number, mathematics and geometry. We have lost a grasp of this, particularly since the close of the ancient world. Pythagorean ideas are not the creation of Pythagoras in the sixth century B.C.E., but a range of ideas about the world, focussing particularly on numbers and geometry, and the puzzles which the study of these throws up … As such, these ideas and puzzles belong to any culture which chooses to address the divine in terms of how the universe is constructed. As already suggested, the Babylonians had a sense of this, though they were also interested in the practical applications. It is also the case that the inhabitants of Britain in the late Neolithic and the early Bronze Age had such a sense.

…. Alexander Thom surveyed many of the megalithic circles across Britain from the 1930s into the 1970s, and established that the circles were constructed on the basis of a number of different Pythagorean triangles, and that these circles were not in fact circular. The circumferences of these circles were modified in order to make their lengths commensurate with the length of the sides of the underlying triangles.These modifications testify to the contemporary idea in ancient times that the incommensurate nature of diameter and circumference shouldn’t be the case.

I’ve written elsewhere that Pythagoreanism, whether in the sixth century or long before, was a transcendentalist view of the world. Meaning that the world of physics and appearance in which we live, is not reality itself, but simply a presentation of it. And the presentation of it is, in a number of ways, crooked. So some aspects of physical reality are not rational. 

This does not mean that the ancient Pythagoreans were pitching themselves against the workings of the divine, but rather that they were trying to understand why what they saw, experienced and understood, was not rational. The answer was that their place of refuge was not reality itself, but a false representation of it.

In the physical world, they could therefore not expect rationality to be woven all through it. Thom identified the obsessive concern of the ancient Britons with whole numbers, and as a consequence (though this was not understood at the time he was studying the megaliths), we know that they were looking to a world beyond the puzzles and paradoxes, in which the relationships of one thing to another were rational in nature.

The theorem of Pythagoras, however it was articulated in the late Neolithic and the early Bronze Age, provided the answer to this. The relationship between the sides of a 3, 4, 5 triangle is irrational in nature, but by squaring the sides, the result is rational and commensurate. This would have been understood to point to a world which transcended space, in that it indicated a one-dimensional reality.

 In that world, some things which are incommensurate here,were commensurate. Which they might have taken to indicate that, beyond that limited  form of reality, there was another reality with no dimensions at all, in which all irrational values existed as commensurate with one another.

Plato echoed a range of Pythagorean ideas in his work, including that reality itself exists in no particular place, has no form or shape or colour. He also suggested that forms existed beyond geometrical figures existing in space, and that these were to be accessed in the mind alone.

The Pythagoreans may have understood physical reality to have been generated as the square root of mathematical values in a higher reality. The resulting incommensuration would necessarily generate space. We could not possibly live in a reality which embraced only one dimension, or even none at all. In which case physical reality might have been understood by the ancient Pythagoreans as a compromise of sorts, which made it possible for mankind to live.

Alexander Thom didn’t know any of this of course. He was an engineer and mathematician. Intellectually he was enormously bright, curious, and industrious, but he was lacking basic information about the ancient past, just as many archaeologists were in the 60s and 70s. He gave us a phenomenological and statistical description of what he was seeing. He noted the obsession with whole numbers, the construction of the stone circles using various instances of Pythagorean triangles, and the fact that many of the circles were not in fact circles, but were modified ellipses and egg shapes, designed to make the circumferences commensurate with the values of the triangles used in their construction.

We can see now that what the megalith builders were up to is reflected in written texts from the 1^st millennium B.C.E if we read them carefully. The three things noted by Thom are all discussed – the importance of whole numbers, the interest in the strange nature of Pythagorean triangles, and the importance of making the incommensurate commensurate with itself.

This actually means that the world of the megalith builders is (in theory at least) intellectually accessible to us, though the last circles were built in the 14th century BCE, or thereabouts, and the builders left no written records about anything, never mind the construction of their circles. Those three things we know for sure, are huge clues to what they understood about what they were doing.

In ‘Patterns of Thought in Neolithic and Early Bronze Age Britain’ I wrote that:

…. the syncretism of Pythagoras draws on mathematical and geometrical ideas, as well as religious ideas. We normally choose to keep these separate. We imagine that they are separate. However, it is …. clear that they perceived the necessary impact of the various puzzles and paradoxes which investigation of mathematics and geometry had on their view of reality. These were not parlour games.

Pythagoras was putting together a new religion, rather than a secular philosophy. It is unlikely to have occurred to him that a secular philosophy was possible, or for him to imagine what that would mean. We think of Pythagoras as a philosopher, because of how we understand what came after Pythagoras and his school. It is possible for us to so distinguish religion and philosophy, because we have lost sight of some very important aspects of how the gods were understood in antiquity. Pythagoras was well aware of the importance of the mathematical and geometrical aspects of religion, which is why he included them with the materials that we more naturally understand as religious ideas.

….

 Much of what we think we understand of ancient religion is the product of a more or less modern view, which sees a continuity between the religion of the common era and antiquity. So, since ’rational belief’ concerning the divine, rather than actual knowledge of the divine was (and is) of great importance in the major religions of the common era, it is assumed that ancient religions drew their strength from the same source, and are qualitatively similar phenomena. Modern scholarship is able to hold this view because, since the Enlightenment, we see the phenomenon of religion as irrational. The behaviour which supported ancient cultic life (sacrifice, divination by entrails, the worship of statues, etc.) is clearly more irrational than medieval religious practice, so there is little about it which demands the application of modern critical thought.

If belief is what is important in ancient religion, then we have missed nothing. If however there is a technical substrate to ancient religious thought, a substructure which depends on a combination of logical analysis, number theory, mathematics and geometry, then we have missed almost everything. Such a substructure does exist, and Pythagoras was aware of it, which is why religious precepts, number theory, mathematics and geometry were all present in the three books of Pythagoras.

It is possible to make a list of things which are part of this technical substructure in the religions of the ancient world.  These are:

Extremity, the Mean, Totality, Perfection, Completion, Invariance, Integral (whole) numbers, the Incorruptible, the Commensurate, Greatness, Rising, Setting, Beginning, Ending, Duration, Periodicity, Points of transformation. And so on.

This list illustrates some of the things have exemplars on both the earth, and in the sky. These characteristics would, within this conceptual model of Pythagoras, have been understood to provide points of contact, and a bridge to the divine.

Why would Pythagoras want to create a synthesis of key components of ancient religions? There are many possible reasons, but the most important may be the intention to restore the technical level of religious thought and practice, then experiencing a long slow decline, so that number, mathematics and geometry might serve again, to make sense of the transcendental understanding of reality.

Can we apply the content of this discussion to the Late Neolithic and the early Bronze age in Britain? If, for the purposes of argument, we make the assumption that just as Pythagorean number, mathematics, geometry, and the transcendentalist outlook were, in the mind of Pythagoras, necessarily connected with each other, these four things would also be present in megalithic culture in Britain and Gaul, for the reason that the missing piece in the record, the philosophical transcendentalism, is the necessary logical consequence of an understanding of number, mathematics, and geometry.

As we know from the studies made by Alexander Thom, the stone circles were built on the basis of various sizes of pythagorean right-angled triangles, and laid out with ropes of precise length. There has been some critical discussion of the ubiquity of the measure he described as the megalithic yard, which measured 2.72 feet, which he established by statistical analysis. However, if Thom identified different standard pythagorean triangles in the construction of different megalithic circles, all of which were based on the measure, then the presence and use of the measure is confirmed. It need not however, have been the only standard measure.

The construction process was designed and executed in such a way that the circumference of the circles, whether elliptical, egg-shaped, or flattened, would always be an integral number of the units used. This interest in integral numbers appears to have been universal among the builders of the circles. The connectivity the integral numbers opened to transcendent Being is the reason why this was important.

This transcendent reality, understood to lie behind the physical world of appearances and its paradoxes (such as the essential identity of commensurate and incommensurate values), would be the principle focus of the megalith builders interest, and the design of the megalithic structures would have been understood to serve the function of strengthening the connections between the two worlds. The transcendent world contains what is perfect, and the world of phenomena contains only approximations to such perfections. As Robin Heath pointed out in his account of Thom’s work, Cracking the Stone Age Code, the phenomenal world would have seemed to the megalith builders to be something of a crooked universe.

Looked at from this point of view, we can discern a significant motive in the geometrical construction of the major circles which Thom surveyed and analysed in detail. We can also begin to understand why there were different approaches to the construction of the circles, rather than a single standard design. In a crooked universe, there could be no universal answer to the problems they were trying to resolve. This universe is full of irrationality, simply because it is not the transcendent reality, but an imperfect representation of it. The irrationality could however be overcome in the physical world in specific instances of geometrical construction. In one case, by creating a design utilising an ellipse which measured precisely a specific multiple of the units employed in the pythagorean triangle used as the basis of the structure. In another, by making the structure egg-shaped, again with the same intention. The circle might also be flattened, in order to make the circumference commensurate with the units of the underlying triangle. 

But there is also the astronomical function of megalithic circles. As Thom identified, some are connected with the sun and its movements throughout the year. Others are keyed to the complex movements of the moon. For the later Pythagoreans, and for Plato, the heavens represented a moving image of eternity. For these earlier pythagoreans, the heavens would be understood in the same way, and for the same reason. A megalithic circle might therefore be conceived as a representation, in an abstracted form, of some the properties and attributes of Eternity. Eternity is something which is whole and complete, and returns into itself.

It therefore made sense to mark the extreme points of the movement of the heavenly bodies (which have their existence in the moving image of eternity), as a further embodiment of the connection between the worlds. These were constructed using only integral values, derived where possible, proportionately, from the movement of the heavens in relation to the earth. Heavenly cycles would be explored and represented in the structure where possible, together with indications of their periods. The motive for building the circles was performative, meaning that the structures served a set of religious functions on account of their existence and nature.

One of the objections made by the archaeologist Jaquetta Hawkes in the Chronicle documentary on Alexander Thom, made by the BBC in 1970, was that since the megalith builders did not have writing, there was no way of handing information on to succeeding generations. She also suggested that the inhabitants of the island during the period of megalithic culture were ‘simple farming communities... nomadic even’. But we know that the later Pythagoreans cultivated memory. We are also told in Caesar’s account that becoming a priest in the late 1^st millennium involved many years of study (around twenty), during which time a vast amount of information was committed to memory. So Hawkes suggestion that there was an absence of a means of handing on information is likely to be false. The cultivation of memory is built into the pythagorean view of reality, since what exists in the mind was understood to be more real than what could be understood by the senses.

Alexander Thom reported that the standard measure used in the construction  of the megalithic circles was 2.72 feet. This was established on the basis of a statistical analysis of the data from his surveys. What is perhaps peculiar to us now about this value is that it is expressed in terms of English feet. But Thom had been doing his surveys for forty years or so, beginning long before the UK chose to use the metric system, so that is how he had been analysing data since he began. It was based on the traditional measures used in the UK as far back as anyone knew. We don’t know the origin of the English foot.

Land measures have been associated with kings since time immemorial, but the reasons for this have long been lost. Archaeologists do two things when discussing this question: they acknowledge the association with kings, but then reify, and argue that the value of the measure is literally the length of a king’s foot. This is ridiculous of course, since all kings are human beings, and of different proportions. But it enables them to argue that there is no universally agreed measure on lengths, and consequently no understanding of standard measures. The whole history of metrology argues against this, but it is convenient to dispose of such arguments by reference to the length of a particular king’s foot.

Archaeologists like the model of progress, which implies (actually requires) that the further back you go, the less rational and intelligent people were, and that they were on a long hike to where we are now. This might be true. But they assume that it is true, which is why Thom’s work was more or less anathema to the profession.

Part of the problem is that we have a different model of what rational thought is, from what was understood to be rational thought in antiquity. There is a large grey zone between the two which is mostly unknown to both archaeologists and the historians of ideas, and issues relating to that zone are very rarely discussed. Archaeologists also like to go looking for what they expect to find, rather than what they ‘know’ isn’t there. So things which don’t fit, don’t get a lot of attention. But you don’t know what doesn’t exist by not being open to evidence which might not support your argument. Impossibilities need to be considered, even if only to decisively rule them out. Alexander Thom provided one of those impossibilities, and it is still on the table, even if most of the archaeological profession is ignoring it.

Did Alexander Thom discover the megalithic yard in his surveys of the megalithic circles? Certainly the measure was there, looked at from a phenomenological and statistical point of view. But he didn’t have any inside understanding of how the megalith builders thought about their constructions. He reported what he saw. But what you see is not necessarily what is there.

As a mathematician, he knew logarithms, and knew about Euler’s number. That number, rounded up very slightly, in terms of the convention, is 2.72. Exactly the number which Thom identified as the basis of the megalithic yard, expressed in terms of English feet. There is, as far as I know, no evidence that the knowledge of this ‘coincidence’ gave him a moment’s pause. But it gave me pause.

I think that what Thom actually discovered in the British Neolithic, was the early presence of the English foot. And that that measure was disguised by its multiplication by Euler’s number. The reason for that disguise of the basic unit of measure will be explained in the course of what follows.

First, we need to explore how ancient priests in Britain might have known about Euler’s number.

Let’s look at that number, and its significance. I’ve borrowed from two Wikipedia articles – the first on Euler’s number a), and the second b) on logarithms:

a) The number e is a mathematical constant that is the base of the natural logarithm: the unique number whose natural logarithm is equal to one. It is approximately equal to 2.71828, and is the limit of (1 + 1/n)ⁿ as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series.^.

The constant can be characterized in many different ways. For example, it can be defined as the unique positive number a such that the graph of the function y = a^x has unit slope at x = 0. The function f(x) = e^x is called the (natural) exponential function, and is the unique exponential function equal to its own derivative. The natural logarithm, or logarithm to base e, is the inverse function to the natural exponential function. The natural logarithm of a number k > 1 can be defined directly as the area under the curve y = 1/x between x = 1 and x = k, in which case e is the value of k for which this area equals one. ….

e is sometimes called Euler's number after the Swiss mathematician Leonhard Euler …. Euler's choice of the symbol e is said to have been retained in his honour. The constant was discovered by the Swiss mathematician Jacob Bernoulli while studying compound interest.

The number e has eminent importance in mathematics, alongside 0, 1, π, and i. All five of these numbers play important and recurring roles across mathematics, and these five constants appear in one formulation of Euler's identity. Like the constant π, e is also irrational, (i.e. it cannot be represented as ratio of integers) and transcendental, (i.e. it is not a root of any non-zero polynomial with rational coefficients). The numerical value of e truncated to 50 decimal places is

2.71828182845904523536028747135266249775724709369995... 

So Euler’s number is intimately related to the idea of ‘one’, and is in a sense another representation of it. But instead of the representation being a rational whole number, this constant number is irrational in nature, and cannot be expressed in terms of a ratio of rational numbers. It is also a limit to which an infinite series tends, and it reaches that limit at infinity.

The history of our knowledge of logarithmic functions is relatively modern:

b) Logarithms were introduced by John Napier in 1614 as a means to simplify calculations. They were rapidly adopted by navigators, scientists, engineers, surveyors and others to perform high-accuracy computations more easily. Using logarithm tables, tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition. This is possible because of the fact—important in its own right—that the logarithm of a product is the sum of the logarithms of the factors.

I am not claiming that logarithms were known or used in the British Neolithic. I am suggesting however that those responsible for the stone circles were interested in the idea of infinite series, and knew, as consequence of that interest, the fact that such series tend towards a limit. That limit can be rounded up to 2.72. And that is what we now call Euler’s number.

So, if this hypothesis is correct (and to some extent I’m attempting to enter the souls of the priests here), why would they multiply these two numbers together, to arrive at what Thom called ‘the megalithic yard’? As already mentioned, making things ‘meet and agree’ is an interest arising out of the consideration of natural puzzles, where not everything is commensurable. The ancient priests and their scholars had a notion, arising out of the nature of some natural puzzles,that the natural world is full of irrational numbers, which by definition are not commensurate with each other. They also had the notion that these numbers are somehow commensurate with each other in some other place. Not necessarily somewhere conceived of as a physical space. The pythagorean triangles are an instance of this, in that, when subjected to a standard operation such as the squaring of their sides, they meet and agree. They can be represented meeting and agreeing in physical space also, but without representing one of the principal characteristics of triangles, which is that they enclose space.

The ‘some other place’ where incommensurate things are commensurate with one another cannot be seen, because it is not actually a place. Plato was careful to define the Heavens not as Eternity itself, but as a moving image of Eternity. I think it likely that the same notion was entertained in the British Neolithic. The heavens, however, as some kind of representation of Eternity, could be studied for clues about the nature of reality, hence the ancient interest in the Heavens.

But if Eternity is in no physical space, then it must be present all through the physical world. Not easily detectable, but often aspects of it could be manifest in physical instances. Some of which could be understood to meet and agree, even if represented in what is essentially a crooked representation of Eternity .I listed these things – abstract concepts – earlier in this essay. Hence the importance of wholes and totalities, and what is complete.

It follows that if Eternity itself is all through the world, then the nature of reality is necessarily two fold. Eternity is infinite, and physical reality is finite. But in fact the two are essentially the same thing, just viewed from different perspectives. We cannot see the infinite, but we can know that it is there, and that it is something which stands behind all sense experience. In which case, religious observance, expressed through the building of the monuments, and through ritual action, was about both honouring the underlying identity between the worlds, and healing the rift which exists between them. The major preoccupation of the priests was to bring more of eternal reality into the physical world.  

Eternity is one, whole, the totality of what is possible, and is complete in itself. On earth we can identify wholes as things which also belong to Eternity. In Eternity it is possible for all things which on earth are incommensurate, to be commensurate. On earth, wholes can be understood as things which are not irrational (such as whole numbers). But we can also represent a whole with an irrational number, which is the number which we know as Euler’s number. In Eternity both these numbers are commensurate with each other.

In multiplying these two numbers together, one rational, and the other entirely irrational, into the measure we know as the ‘megalithic yard’, they were attempting to represent in their monuments a state which properly exists in Eternity alone. A  state in which all things meet and agree.

Thomas Yaeger, February 13-14, 2020.

An Appetite for Knowledge

I have argued elsewhere that ideas of Being, of the nature of reality, and the divine, were once approached  in terms of conjectures about the reality (or otherwise) of the one and the many. These conjectures follow on from the initial question, which is: why is there something rather than nothing? Plato’s argument, following on from propositions made by Parmenides, who declared that we should look only to the one, and that only the one truly is real, is the most sophisticated of all discussions in antiquity concerning why there should be something rather than nothing.

Plato argues that we should always look to the ‘one true thing’. This is different from saying only the one exists, or only the one is truly real.

The anthropologist and classicist J.G. Frazer was very dismissive of Greek questions concerning the one and the many, saying that they constituted ‘popular questions of the day’. The argument of Parmenides about the nature of Being  remained entirely undiscussed by Frazer.  But then he argued that questions concerning Being were entirely barren, since nothing could be predicated of Being.*1

This of course is a spectacular instance of intellectual blindness, by which the richness of the intellectual matrix of ancient Greek thought was spirited into nothingness. We like to see Plato’s articulate discussion of Being as the surfacing of a human capacity to grapple with abstract ideas, and the marker of our emancipation from irrational ideas about the world and the gods. For Frazer, Plato was as guilty of intellectual error as any of his contemporaries, as well as his predecessors.

In late Hellenistic times, there seems to have been a very poor grasp of the context of the development of philosophy around the Mediterranean. Nods were made toward the notion that the discipline of philosophy might not have been first developed in Greece, including (tellingly) at the beginning of Diogenes Laertius’ Lives of the Philosophers.  Plato after all argued against the idea that this was so in the Protagoras, saying that the practice of philosophy was of a great age – perhaps contemporary with the arrival of peoples from Egypt, who settled in the Peloponnese, and also in Crete. He also presented Solon in discussion with Egyptian priests in the pages of the Timaeus, who found the Greeks to be very young, and not conversant with knowledge ‘hoary with age’.  

Aristotle presented the common sense view that philosophy was first developed in a place where there was a leisured class, with the time and resources to think about philosophical questions. He may have had Egypt in mind, since Egypt had professionalised priesthoods. Later philosophers such as Porphyry suggested that key parts of Pythagorean doctrine came west to Greece from Babylon, in the late sixth century B.C.E.*2  Plato references details of this doctrine, without connecting it explicitly to Pythagoras.*3 Aspects of that doctrine can be found elsewhere in the pages of Herodotus (concerning Solon),*4  and also in Homer’s Iliad (Book 18), where a number of key details associated with the doctrine are run together in close order, without being explained. *5

The former Priest of Bel at Babylon, Berossus, moved to Athens, and wrote about Babylonian history and philosophy, describing their system of knowledge as based on the idea of an initial plenum (which is a philosophical concept) using the image of a sage emerging daily from beneath the sea (symbolising primal fulness and abundance), granting knowledge to man about the sciences, agriculture, and the practical arts. *6 He also gave information about the Babylonian New Year festival (Enuma Elish), the liturgy for which contained accounts of two creations: the first irrational, and the second one, rational, and which was given its rational character by the chief of the Babylonian gods.*7  Berossus' book was the Babyloniaka, unfortunately now lost. But the christian writer Eusebius had access to it as late as the early fourth century C.E, and quoted a number of passages from it which survive in his writings. Recovered Mesopotamian texts, including tablets containing the Enuma Elish liturgy, generally confirm the accuracy of Berossus. 

Not much of this was of use to the Enlightenment agenda, which preferred to look at the development of philosophy in Greece as the first beginnings of a rational understanding of the world. And so the information was deprecated and ignored. The phrase ‘I doubt that’ is a dangerous one in the classics community. It is a way of saying ‘this is not the consensus view of scholars and the profession’. Usually no discussion follows, since the opinion is usually an opinion of the worth (or otherwise) of evidence. Scholars weigh evidence, and they do so (they are convinced) with better tools than were available to ancient scholars. The judgement is fitted to modern requirements. So, as a result, it is clear that it is unlikely that Solon visited Egypt, and that Pythagoras visited Babylon. Tread carefully, or your credibility as a scholar may be in doubt.

Thus, the scholarly consensus is that philosophy is an autochthonous development. The culture of the modern west rests on this idea.Why in Greece? The idea of the ‘Greek genius’ won’t cut the mustard any more, at least by itself, but I have heard the phrase uttered by people who should know better. But during the high days of the enlightenment, and the beginnings of what became the fully-fledged discipline of Classics, that is what the scholars wanted. Something pure and out of the orbit of other cultures, which, by definition, had no philosophy or anything which would measure up to something like rational thought.

Sometimes history is built backwards. It isn’t just a matter of looking to the historical record and starting from that. History always has been in part about critical scrutiny of sources and judgements, even among the Greeks *8 But as Bernal pointed out in the first volume of his Black Athena, the critical revision begun in the enlightenment was wholesale, and created an alternative representation of the origins of European civilisation.

That was the agenda. To reinterpret the past, and in terms of a rational and enlightened understanding of the world. Hence, the philosophe Denis Diderot wrote not just about ideas and philosophy in his Encyclopédie, but also about the arts and crafts. The latter may have been wrapped up with myth, folklore, and superstition, but they were still essential to the rational life of man, so these were also added to the Encyclopédie. Everything from the past which served some purpose, or which could be made to serve some purpose within the rational enlightenment model of reality, was critically examined, and reworked to fit what was intended to become a new understanding of man and his place in a new world of reason. A new understanding of how man might live.

I wrote in the article ‘Logical Modality in Classical Athens’ that there are in fact two logical modalities present in the writings of Plato and Aristotle. Aristotle is mostly (though not always) concerned with the modality which has come down to us as the basis of formal logic. Plato is clearly aware of this modality, but, though no modern academic has dared to identify the other modality as logical, it is. It is simply that to us, it does not describe relationships which should be described as logical. Plato  talks about this other logical modality several times, in the Republic and in the Timaeus. It is connected with the doctrine of wholes and totalities, and is the basis of explaining how things may participate in other things, which is not a pattern of ideas which fits with Aristotle’s general understanding of logic.*9

Why is this important? Simply put, it matters because it is the basis of the Greek understanding of how transcendent reality relates to secular and physical existence, which was a matter of great significance up to the middle of the first millennium B.C.E, and beyond.  The doctrine underpins the understanding of the divine as something which can be both transcendent, and immanent, and thus be present in existence. *10 *11 It also points to a rather strange conclusion about the nature of the reality in which we live and think.*12

It might be imagined therefore that this doctrine would be the subject of a great deal of scholarship. In fact there is very little on the subject. The dialogues in which the doctrine appears have been written about endlessly over the last two centuries, but, though Plato’s discussion is noted, the fact that his discussion is based on an alternate logical modality is not acknowledged, and the conclusions which might follow from treating it as such, do not follow, and are therefore not discussed. It is treated as it is often presented by Plato – as mathematical and geometrical metaphors for how things might possess some form of congruence with each other.

I've argued elsewhere that there is, in general, very little appetite for attempting to understand Plato in his own terms.*13  When he talks about transcendent reality, this is treated as some sort of literary fiction, which has no necessary properties of its own. When Plato talks about the Forms, this also is treated as a species of literary fiction, which Plato records as being demolished in his Parmenides and in the Sophist. When Plato discusses the soul (in the Timaeus), it turns out that it is something which has the property of being connected with the Form of the Good, and so he argues that knowledge is acquired by the activation of that connection. We have forgotten what we knew (apparently) through the shock of physical birth, but it is possible for us to reacquire this knowledge by looking to the one true thing.*14 

Deriving all knowledge from the Form of the Good is also seen as a bafflingly impenetrable notion to the modern mind, since Plato talks about ascending purely in the mind from Form to Form, and then descending back to the world of physical reality, Form by Form, and says this is the only way to acquire genuine knowledge. How can real knowledge be acquired in this way? Why should Plato argue like this?  How can any of this make sense to us?

It makes very little sense to us, because we have lost the original doctrinal context of his discussions, and we are not that interested in attempting to recover what we can of that context, even for the purposes of a better scholarly understanding of what he is talking about. So the study of Plato languishes lifeless in the seminar room, taught and discussed from generation to generation by people who have no clear idea of what Plato meant. Books and papers are published, which clear up a minor detail here, discuss another one there, but do not leave us much the wiser.

We can understand the range of existing discussion about Plato in terms of what scholars do not or cannot understand about Plato, and their attempts to fit what they think they understand about his work into some kind of modern frame. It is their minds, and the categories of their own understanding which create the problem, not the obscurity of Plato’s ideas.

One of the principal reasons we cannot easily understand Plato is down to the loss of an understanding of that alternative logical modality. That understanding needs to be restored, along with a basic comprehension of why it is important. Not just for our understanding of Plato himself, but also for our understanding of his cultural context; the context in which philosophy was understood to be of inestimable value; and also for an understanding of some very strange things about the ancient world, which are all the stranger because (it seems) they made sense in antiquity (sacrifice, divination, idolatry, prophecy, omens, oracles, etc.).

One of the most valued books in my library is Religion and Magic: Approaches and Theories, which is a survey of modern anthropological thought. *15 The author is Graham Cunningham, a specialist in the ancient Near East and the relevant languages. Anthropology is a relatively young discipline, though crowded with many points of view. *16 Cunningham’s book covers the whole range of these, at least in terms of summarising the views of those who first suggested those theoretical approaches. He divides the approaches into several sections, which are:

1 German pioneers, 2 Early Intellectualist approaches, 3 Emotionalist approaches, 4 Phenomenological Approaches, 5 Structural Functional Approaches, 6 Symbolic Approaches, 7 Recent Intellectualist Approaches, 8 Structural approaches, 9 Cognitive Approaches, 10  Feminist Approaches.

All of these approaches were developed and used without any meaningful distinction being made between ancient cultural phenomena and cultural phenomena of modern times. I write carefully here, since there are unpleasant presumptions in the discipline of anthropology, which have not yet been rooted out. Anthropology as a formal subject was founded in the early nineteenth century, and the presumptions of the time are necessarily locked into the work of the pioneers. Many of these can be called into the light of day if you scratch the modern anthropologist in the course of discussion. The fact is that a dangerous equation was early made between the cultures of antiquity and the world of  'the primitive and the savage' in the modern world (which the Classicist D’Arcy Wentworth Thompson referred to as ‘running folklore to the death’).*17

So Cunningham’s book covers two centuries of thought about culture, civilization, religion, magic and ritual. All premised on the assumptions, understanding and categories of knowledge of those living and working in those two centuries. Nothing about those matters is covered from earlier centuries. It is as if the study of human culture, human thought, and the nature of man himself, began only in Hegel’s study, and nothing of worth came before Hegel. *18 

I could digress here, and lay out what came before in detail, but that is for another time. I will allow myself to say that Plato had something else to bring to the party, which is not covered in Cunningham’s survey; the Neoplatonists (who thought of themselves as Platonists, but we will not let them be what they are) would have brought the same thing to the party, as would some of the early Gnostic writers. The Platonists of the Italian and English Renaissances also understood what Plato was writing about, at least for the most part, and would be shocked that, not only do we not understand Plato, but that we have chosen to explain much of human culture in terms of a fundamental conceptual error about the way reality works, and with a complete disregard for the way the human mind was once understood to engage with that reality.

It is assumed by the moderns (in the west, at least) that philosophy is a cultural phenomenon which, in historical terms, follows on from religious thought, and does not precede it. We are sure of this because we are sure we know what religion is, and what philosophy is. We think that religion enshrines a form of knowledge about the world and the universe which is less than rational, and that the devotees of religion are often credulous. Religious thought is often transfixed by the numinous and the invisible, and its responses to these things are unfathomable to the rational mind. We also think religion, to a great extent, developed in response to the ideological needs of social groups, sometimes in conflict with other social groups, which can give very distinctive structures to the myths and rituals which become part of the bedrock of the public show of these religions.We believe this (admittedly oversimplified) picture to be a correct interpretation of what religion is. Modern religion differs from ancient religion only in details.

Whereas philosophy is about a critical and rational understanding of the world and how it presents itself to us. Religion is cast as an un-philosophical and irrational understanding of that reality. The development of philosophy represents progress.

These notions are subject to nuance of course, but this is the core of the enlightenment idea of what these things are.

We assume that religion, as it presents itself to us in the form of the relatively young Abrahamic religions, is not fundamentally different in nature to other religions, either elsewhere now, or in the distant past. We make such an assumption, because there is nothing in our understanding of other religions which suggests to us, at least not with any clarity, that any other process is active in the creation and operation of religion. The dynamics are the same, and the functions are the same.

Graham Cunningham’s postscript makes it clear that religion is generally understood by anthropologists to be a relic of an earlier time where rational thought was absent. Certainly in terms of what we would recognise. Somehow religion is still with us, because large parts of the human race believe in the importance and efficacy of belief in the divine: that belief in the reality of the divine is something which is essential to the religious life, and the religious understanding of reality. *19

Yet this is not what ancient writers tell us. They tell a different story, as I’ve suggested, and one which is not represented by any current anthropological approach. That different story is that religion in the ancient world was not about belief, but concerned both knowledge and conjecture about the nature of the divine; and about the nature of reality itself.*20

I prefer to write about ancient religion in terms of divine cult. I distinguish the two for clarity - religion is often understood in the modern world in terms of sociological and ideological functions. And indeed religion has these functions: it often provides social cohesion, ideology, and useful rules of social behaviour. But to attempt to explain the core of divine cult in such terms is presumptive. If the core of a divine cult involves rational conjecture about the nature of reality itself, we will not easily find this out, even if the evidence is screaming this at us. In antiquity the ritual practice of divine cult was often a private affair, rather than a public one, which implies an important division between the performative function of ritual, and the outward show. Ritual and observance were the important things. The public show might echo the thought behind the cult in some respects, and offer clues to its significance and nature, but it is not the cult itself. *21

The association of knowledge with the core divine cult (and, consequently, a confirmation of the  connection of the cult with the divine itself), gave the rituals of ancient religion (both private and public) their efficacy, and patterned their meaning. But this did not involve belief.  Belief is something which is not supported by credible argument, or is a step beyond the limits of an rational argument.  That is not what was involved in ancient discussion of questions concerning the divine. Can you have knowledge without rational modes of thought? And what did the ancient writers mean by knowledge of the divine, and by equating knowledge with the divine? Clearly, it is not possible to have actual knowledge of something without rational modes of thought. But what rational thought is, is another one of those things which we are quite clear about in modern times, even if the evidence points to a different conclusion, and exists in teeming quantities.

___

 1. Frazer wrote this in his prize essay of 1879 on the 'Growth and Development of Plato's Ideal Theory'. Published finally in 1930. I'd found this essay after noticing that there were odd features in the structure of The Golden Bough. I wrote about this in J. G. Frazer and the Platonic Theory of Being (2016), and also in the more compact essay 'Frazer and the Association of Ideas', published in Understanding Ancient Thought (2017).
2. In his 'Life of Pythagoras' Porphyry tells us that Pythagoras travelled extensively around the Near East and Egypt in the service of Cyrus. Discussed in 'Pythagoreanism, the Divine, and the Nature of Eternity'.
 3. In the Timaeus. Discussed in 'The Platonic Theory of Being' (full text with notes). Originally published in The Sacred History of Being (2015).
4. Discussed in 'Solon in the Court of Croesus' (extract). The full text is a chapter in The Sacred History of Being (2015).
5. Discussed in 'Working Wonders: Hephaestus and the Armour of Achilles'. A retitled chapter from The Sacred History of Being (2015), originally titled  'Being in Homer'.
 6. Discussed in 'Oannes and the Instruction of Mankind', which is one of the appendices to The Sacred History of Being (2015).
7 Discussed in 'The Babylonian Creation': an extract from the chapter 'Creation' in The Sacred History of Being (2015).
 8. Modern scholars are well aware of this. Ancient historians arranged information, but also questioned it. The Assyrians seemed to have a similar attitude to their materials - the chronicles associated with Ashurbanipal's reign exist in more than one version, with events recorded in a different order.
 9. Discussed in 'Logical Modality in Classical Athens' which is a chapter in Understanding Ancient Thought (2017).
10. Consequently this ought to be a matter of interest to Christian theologians, owing to the importance of the idea of the incarnation of the divine in the Gospels. For centuries the incarnation has been presented as a mystery (to both believers and theologians), without any kind of theoretical basis. But the theoretical basis is present in ancient literature, in various places. It even surfaces in a text in the Nag Hammadi documents.
 11. The logical basis of the incarnation is discussed in 'The Keys of the Kingdom: Binding and Loosing in Heaven and Earth', a chapter from Echoes of Eternity (2020).
12. Discussed in 'The Transcendental understanding of Reality', and in 'The Greek Ontological Model in the 1st Millennium B.C.E.'  from Echoes of Eternity (2020).
13.  'The Sweet Song of Swans'. The full text of this chapter, which concerns (among other things) the modern creation of the Greeks as the originators of philosophy, was published in the The Sacred History of Being (2015).
 14. In the chapter 'Plato's Theory of Vision', from The Sacred History of Being (2015). This extract concerns the discussion of the cosmos as “a perceptible God made in the image of the Intelligible.”
 15. Cunningham, Graham, Religion & Magic: Approaches & Theories, Edinburgh University Press, 1999.
 16. That there are so many conflicting views might suggest that perhaps few, or even none of the approaches are correct, but are simply the product of the failure to grasp the sophistication of ancient thought.

17. Discussed in 'Running Folklore to the Death', an extract from section 13 of J.G. Frazer and the Platonic Theory of Being (2016).
18. I've discussed Eriksen and Nielsens' A History of Anthropology (2001) in the chapter 'Before Anthropology', which book illustrates that modern anthropology is sometimes about how things ought to be, rather than a profound engagement with the evidence. They do however give a useful account of what came before Hegel. Published in Man and the Divine (2018).
 19  We tend to inject our presumptions about the past onto the evidence, as if common sense is a servicable tool in understanding it. It takes more than that. Discussed in 'Beyond the Religious Impulse'. Published as a chapter in Understanding Ancient Thought (2017). See also 'Distinguishing Belief and Faith', in Man and the Divine (2018).
20 A close look at Assyrian divination reports makes it clear that there was nothing mystical or vague about Assyrian queries about the future. The queries to the Sungod (Shamash) were expected to provide accurate information in response. This is because the diviners and scholars formulating the questions understood the universe to be rooted in a plenum. In which case,  all things which might be, already exist in the plenum. The diviners were therefore asking the Sungod for information which was available to the god. Twenty divinatory queries are available on the page 'Who will Appear before the City?' The concept of the plenum and its connection with the Mesopotamian story of the creation is discussed in the chapter: 'The Idea of the Plenum in Babylon'; further discussion of  the concept can be found in  'Pleroma, Cosmos, and Physical Existence', both from Understanding Ancient Thought (2017).

21. Discussed in 'Shar Kishati and the Cult of Eternity', published in Understanding Ancient Thought (2017).

Draft version, October 29, 2019. Final version, All Hallows Eve, 2019. Updated 11 January 2020. TY.