The Wider Scope of Ancient Mathematics (letter to an American Scholar)

 

Avebury Circle, photographed in 2001

Dear....., 

Hi. I became aware of your short book [.......................]  relatively recently. I wish I’d known it earlier.

I have a strong interest in the idea and function of the concept of limit in antiquity. My main object of study at UCL was ancient  Assyria (mostly the text corpus). Like the Greeks, they had a strong interest in the idea of limit, which is illustrated on the walls of their buildings, and is also represented in their images of the sacred tree. Limit also serves an important function in setting up their gods in heaven (I’ve written about both Assyrian and Babylonian rituals for this).

This tells us something of the actual basis of Mesopotamian religion, which has an origin which is quite different from what we imagine. 

Essentially ancient religions are transcendentalist in nature. In other words, they have their origins in a focus on abstract conceptions (limit, infinity, infinite series,completion, totality, etc). Which makes a nonsense of the idea that the Greeks were the first to grapple with sophisticated abstract thought. Clement of Alexandria created a list of civilizations which practised philosophy, and added the Greeks as the* last* to adopt the practice of philosophy.

Since you might be interested in the wider scope of ancient mathematics, I am writing to you to point you at a couple of articles which illustrate that these concerns were a feature of building projects in Neolithic Britain also. The Horus numbers are there, as the basis of establishing Euler’s number via a geometric construction. Euler’s number being the final result of a convergent infinite series.

Did they get their mathematics from Egypt, or did they develop them themselves? I have no idea. Why Euler’s number? It’s a mathematical stand-in for the extreme limit, which is infinity.


‘At Reality’s Edge’

https://shrineinthesea.blogspot.com/2020/12/at-realitys-edge.html?spref=tw%20%20# (Short article)

‘The Mathematical Origins of the Megalithic Yard’

http://shrineinthesea.blogspot.com/2020/02/the-mathematical-origins-of-megalithic.html (Long  article)

Best regards,

 

Thomas Yaeger

Abstraction and the Instantiation of Divine things in Mesopotamia

My work The Sacred History of Being is cited in an article by the writer Ben Thomas - "The God Enki and the Ocean of Everywhen" - on his website 'The Strange Continent'' (published August 3, 2017). This is a fascinating article which is well worth checking out - the link to the full article is at the foot of this post. We've been corresponding occasionally over the past few years, mostly about Mesopotamia and Mesopotamian modes of thought. The argument of The Sacred History of Being is complex and sometimes abstruse, and it is always a joy to find it has been understood.

I've quoted the passages most relevant to The Sacred History of Being. Ben wrote:

...The upwelling of cool, sweet, fresh water seems to have spoken of something deeper to these people: a limitless potentiality; a permission to play with the world and reinterpret it; to import new realities from the world of Mind. 

Because it’s clear – as the philosopher Thomas Yaeger’s book The Sacred History of Being explains in depth – that certain ancient Mesopotamians understood the concepts of Being, Becoming, Matter and Mind every bit as clearly as the Greek philosophers did. 

But where the Greeks defined and explored these concepts explicitly, in writing and debate, the Mesopotamians explored them experientially, through symbol and ritual: The Ceremony of the Tree. The Opening of the Mouth of a God. (When Mesopotamian texts say, “This is how to make a god,” Yaeger argues, they mean it literally!) The intercessory deities who hold cups overflowing with endless streams of fresh water. 

The Sumerians consciously recognized that they stood on a great threshold – and across thousands of years, they perfected the techniques of stepping back and forth across it; carrying material facts one way, and new inventions the other. 

And what lived on the other side of that doorway? The god Enki – lord of intelligence and knowledge, keeper of the arts and crafts; also called Nudimmud, “the Shaper,” who “opens the doors of understanding” (emphasis mine) and teaches humans how to construct canals, plan temples, write letters and compose music. 

From his hidden “House in the Waters,” Enki monitors the flow of all information in the world, and guards new ideas until they’re ready to be born. He’s not exactly a trickster, but he’s definitely playful, and he inspires playfulness.  

Still more crucially, Enki is the custodian of the mé – an untranslatable (plural) Sumerian word, which the great Sumerologist Samuel Noah Kramer explained as the “fundamental, unalterable, comprehensive assortment of powers and duties, norms and standards, rules and regulations, relating to… civilized life.” 

The Sumerians have left us lists of more than 100 mé, including “kingship,” “truth,” “law,” “sexual intercourse,” “weapons,” “scribeship,” “sacred prostitution,” “leatherwork,” “judgment,” and “the troubled heart.” 

As Kriwaczek says, the mé “show how self-consciously aware the ancient Mesopotamians were of the difference between civilization and other ways of living… that they expressed it with an entirely new cognitive concept, for which we have no equivalent.  

As Yaeger explains in his Sacred History, the mé are far more than just abstract concepts. In the poem known as Inanna and Enki, the goddess Inanna gets Enki drunk, steals the mé, and loads them onto her “boat of heaven.” Braving seven attacks by sea monsters, Inanna manages to transport the mé to the cities of Eridu and Uruk, where the people unload them amidst great jubilation and feasting. 

This would be a very strange way to talk about the mé if they were simply abstractions. But a clue is offered by the fact that the Sumerians treated many seemingly abstract concepts in similar ways. 

Ceremonies for “opening the mouth of a god” refer to “putting on the melammu,” the divine splendor, as if it were a sort of cloak. Kingship, too, is often described as something that “descended from Heaven,” and can be “carried” from one city to another. 

In light of all this, it seems very likely that – just as the term mé is untranslatable into our frame of reality – our discrete categories of “symbol,” “referent,” “abstract” and “concrete” would have been equally baffling to a Sumerian.  

This framing is so different from ours that it can be difficult to comprehend: a scepter does not symbolize kingship; it is kingship. The statue does not symbolize Enki; once its “mouth is opened,” the statue is Enki – even as the god Enki is not limited by this one statue, and dwells in the eternal ocean.

To ask whether the Sumerians thought of the mé as abstractions or physical objects is to pose a wrong question. The mé sat at the border between reality and Mind – and once the Sumerians had stumbled on that doorway, they took great pains to keep it open, and to facilitate passage across it. 

I knew none of this, of course, as I sat in my apartment paging through images of Mesopotamian archaeology. I only knew that I’d stumbled on some primordial wellspring of originality; a mystery I wanted not so much to solve as to experience for myself. 

.....

The great historian Thorkild Jacobsen describes the god Enki as “the numinous inner will-to-form in the Deep.” This is not the dead god of a vanished civilization – this is the Ocean where “2+2=4” and “the steam engine” and “scribeship” and “the troubled heart” have always lived, along with all things unimagined and yet to be.

To bring new things across the doorway, we must re-learn the trick of standing on its threshold.

Bravo Ben!

"The God Enki and the Ocean of Everywhen" is at:

https://thestrangecontinent.com/2017/08/03/the-god-enki-and-the-ocean-of-everywhen/

Is the History of Human Thought Upside Down? Writing to an Egyptologist.

I wrote to this particular Egyptologist because I found that Daniel Richard McBride, the author of 'The Egyptian Foundations of Gnosis', had been a postgraduate student of his. McBride's work is truly extraordinary, and approaches the nature of Neoplatonic philosophy in a way no-one ever has before. Or at least since the Neoplatonists themselves, who, in late antiquity, understood ancient religion in both Egypt and Assyria as the product of philosophical thought. Iamblichus, author of the
The Mysteries of the Egyptians, Chaldeans, and Assyrians, was the most explicit exponent of this idea. 

Is this a viable understanding of the evidence? It is. And McBride's work associates ideas in Neoplatonic thought with the various Egyptian priestly colleges and their views on the divine. It is an extraordinary achievement, which (so far), has not been taken on board or even discussed, by any tenured scholars of the ancient world in the West (to my knowledge at least).

Daniel McBride used to have a website, from which it was possible to download his thesis. That disappeared a long time ago. It is still possible to find his thesis online (there is a link to the PDF file on my site), but he himself seems to have disappeared. I continue to wish to make contact with him to discuss his work and its implications. 

The Egyptologist did not reply. 

TY, June 26, 2019.

To:******@*****.edu

November 3, 2016 

Subject: Is the history of human thought upside down?

Dear ****,

Weve not met, but we may have trod something of the same path, or similar paths over the past twenty plus years.

I published a book a year ago about the idea that our intellectual history, for one reason and another, is actually upside down (The Sacred History of Being). And that the earliest history of the human race can only be understood if we understand that there was a very sophisticated level of abstract thought at the beginnings of civilisation.

My background is a heavy engagement with philosophy, both ancient and modern, from age fifteen onwards (I am now sixty years old). I was also interested in art, religion, history, and some other subjects. Eventually, in the early eighties, I noticed that there were concepts present in texts from the second millennium B.C.E. (principally in Akhenaten's 'Hymn to the Sun') which were embedded also in the philosophical writings of the Greeks from nearly a thousand years later. I understood that they shouldn't be there, if there was no sophisticated philosophical thought present in the second millennium. Iconography was also particularly revealing.

I decided in the end to major in ancient history at university (as a mature student of thirty or so), rather than philosophy, though I did some of that too. I wanted to know if I was barking up the wrong tree (I didn't think I was).

So I spent three years studying Greece, Egypt, Mesopotamia, and also Assyria, in great detail at UCL and SOAS in London (1989-92). Finding abundant evidence for the heretical idea that the human race had a profound capacity for abstract thought from the earliest times. And I became increasingly perplexed at the fact that scholars could not see what was before their eyes, or understand what the evidence actually meant.

Sometime before moving to London (I lived in Edinburgh in the eighties) I had read On the Mysteries by Iamblichus. So I was aware that the Neoplatonists had the idea that there was a common intellectual system underpinning both Assyrian and Egyptian theology. Which, by itself, suggested that there was an immense level of abstraction involved, stretching back thousands of years. And that I might, just possibly, be on the right track.

I found myself focusing on ancient Assyria while I was in London. I had already noticed the continuities between Greek and Egyptian ideas, but if Iamblichus was right, I should find the same intellectual system underpinning their theology, and the structure of their divine pantheon. I thought of that as a check on the idea that a high level of abstraction was present in both cultures.

I was not at all disappointed. And there were also direct connections between Greek and Mesopotamian thought. None of which made any sense to the historians.

[.......]

And then, in 1997 (I think), I discovered the thesis of Daniel Richard McBride, on The Egyptian Foundations of Gnosis. That had a huge impact on me.

So, if philosophy could draw on Egyptian theology, then Egyptian theology necessarily was essentially based on a series of philosophical arguments. Otherwise none of it would have made sense to the Neoplatonists.

I could go in several directions from here, but some of them might be conversations for the future. So I will confine myself to the suggestion that the Egyptians were philosophical, and concerned with abstractions, and everything around these abstractions, and that, given the antiquity of Egyptian religion, these ideas are of immense antiquity.

I have tried to contact Daniel McBride. He had a website at one point, now gone. He is referenced often, but he seems to be impossible to contact. As the supervisor of his thesis, it occurred to me that what he was writing about was something which interested you.

I know how tight Egyptology is, not least in avoiding any conflict with the classicist view that the Greeks invented philosophy. You are a working and eminent Egyptologist - I have no intention of making problems for you [....]. But I would be interested to know if we are sharing the same heresy.

My website is at: http://shrineinthesea.blogspot.co.uk/



Best regards,

Thomas Yaeger