Showing posts with label Neolithic. Show all posts
Showing posts with label Neolithic. Show all posts

Tuesday, 2 March 2021

The 'Hill of Many Stanes'




[An extract from a conversation with a correspondent in the US, from May and June, 2020, shortly after 'The Mathematics of the Megalithic Yard' was completed.] 

On Monday, June 1, 2020, 09:31:47 AM PDT, Thomas Yaeger [....] wrote:

[....], hi. Thanks for your mail. I'm going to respond to it in separate mails, since there is a lot to say. Interleaved, as usual (bad academic habit!)

At 06:03 29/05/2020, [....]  wrote:


Hi Thomas,
Sorry I haven't responded sooner. I've been working on a response to your article (& other emails) about the Megalithic Yard and didn' t want to write again until I had made some progress. I'm probably making it into too much of a project lol. [....} So, I'll send what I have for now (including other stuff I've been putting in a draft) and get it off to you. Sorry if it doesn't do justice to your arguments. 
[....] 
Your argument is very compelling and interesting. It seems like a real breakthrough although, naturally, I'm not enough of an expert to judge!

I think it is a real breakthrough, but it took a while to make it (as I said, the article was written in about a day and a half, after thinking it through for around two years). Developments are happening very fast now, which is interfering with my writing programme.


. I understand that math as such isn't the point of your argument, it's more about what Euler's number signified, right?

Yes. It's Euler's number, what it represents, and how they calculated it in the 2nd and 1st millennia BCE. I think I've changed my mind about how much Alexander Thom actually knew. I think he knew that it was a pointer towards the idea of the infinite. But he did not know that in those ancient days the ideas of the divine, the infinite, and reality itself were regarded as coterminous, and were just different ways of speaking about the same thing (which is an understanding which still survives in Hindu thought and religion). So for Thom, he could see the mathematics, but didn't understand the idea of reality itself as a primal fulness, or a plenum, and why that would engage ancient interest.

There is in Scotland a site near John O'Groats which is known as 'the hill of many stanes', which has remained uncleared since the neolithic. In the documentary he says he is impressed by what the builders of the circles were able to do without pen and paper, and logarithms. But that without such constructions (as the 'hill of many stanes') 'you can't really do it'.

What was he talking about in this short insert into the documentary? He doesn't explain what the small stones were for, or how they were used. I think I understand now that the field of stones was used to calculate Euler's number, in the context of an engineering construction. That site needs extensive re-evaluation.

Thom's book publications are very plain and not dogged with interpretation. I think he realised that what he could do, and get away with, was to draw attention to the fact that something very interesting and mathematically disciplined was happening in the Neolithic and Early Bronze Age, but the whole thing was just too big a pill to swallow for the academic community. He held back.


One thing that interests me is people's motivations, in particular, which of their psychological needs are being served by engaging in different courses of thought and action. I assume that people have always been curious about life and the world (some more than others, of course!), but what struck me about what you wrote is people's need for or a sense of order and structure in order to feel a degree of safety in a world that is challenging to fathom.

 It depends on where you are in society. Sometimes, as now people are told convenient lies (there is no money!), or circumspect evasions. Ancient priesthoods, because of their picture of the world, understood themselves to be dealing with the nature of reality itself. Neophytes would be chosen from all levels of society, since it was necessary to put a premium on intelligence, in order to join the worlds and make the incommensurate commensurate. Reality itself was the home of all knowledge, and all possibility. You can't deal with that without intelligence. The rest of society would have to make do with what Plato described as likelihoods, because they were too far from an understanding of reality.

Thom was not a classicist or a historian, so he did not know (as most modern scholars still don't) that ancient religion was about *knowledge* (scientia). The ancient priesthoods understood themselves to be dealing with knowledge, and that their activity was a science. That's all changed, but we continue to project modern religious intellectual weaknesses into the ancient past.

Thanks for the photographs.

More later,

Best,Thomas

Wednesday, 23 December 2020

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

Friday, 6 March 2020

Before the Ontological Argument (Writing to Alvin Plantinga)





Date: Thu, 05 Mar 2020 23:44:33 +0000
To: Alvin Plantinga 
From: Thomas Yaeger 
Subject: Before the Ontological Argument



Dear Professor Plantinga,

Things have moved along a great deal since I last wrote to you. You might like to read the following article, which argues that the idea of the One, and its transcendent nature, was known in the Neolithic and the Early Bronze Age in Britain. Which, if this argument is correct, means we are talking about more than five thousand years ago, and long before Anselm and Aquinas attempted to make rational sense of religion.

There are many parallels in the mathematics which are evident in the Neolithic monuments with ideas which we can identify in later times - in particular in the case of ancient Greece. Such as the ideas of totality, the important role of integral numbers in connecting us with what is Divine, and the centrality of mathematical and geometric commensurability.  Greek conceptions about these is a development of the earlier ideas, as close study shows.

The underlying perception in the British Neolithic was that the physical reality in which we live is not Reality itself, which is demonstrated by the various puzzles (the aporia) which physical reality contains. This view also emerges from Plato, since he argues (through Socrates) that Reality itself exists in no time or space. Time and space are representations of a transcendent reality, and not truly real in themselves.

I'm arguing that a rational basis for belief in the Divine is a contradiction in terms. I know how important this is to you, so my apologies. The ancient arguments however make the modern idea of belief irrelevant to any conjecture about the Divine. If there is a transcendent reality which we might term as the Divine, it is necessarily real, since it is what lies behind all human experience, despite having its reality nowhere in time and space.

As I suggested before, the ancient conception was that Reality and the Divine were coterminous - or otherwise, two ways of speaking about the same thing.

One of the implications of the idea that reality itself is One, and cannot change, but stands behind physical reality, is that Reality and physical reality are essentially the same (I've argued this in detail in my books). Though they are represented differently to the human understanding. Physical reality contains a number of incommensurable values, whereas Reality contains values which are commensurable, and often related to what is incommensurable in physical reality. If they are in fact one and the same reality, but with a double nature, reconciling the differences between these worlds might have been a matter of some importance to religious establishments in the ancient world. Which is what I argue (in this article) the priests responsible for the design and building of megalithic structures were doing. The mathematics bear this out.

This offers important clues to the actual origin and significance of human religion, despite some of the nonsense which has been written on this subject.

The article is at:

'The Mathematical Origins of the Megalithic Yard'.

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

....

 Best wishes,

Thomas Yaeger

Sunday, 5 May 2019

Echoes of Eternity






 Much of the cultural production of the ancient world, east and west, was based on the idea of reflecting aspects of the divine in human life and thought. Many social structures and institutions were based on this approach. The model for these things was was astronomy and the heavens, and the heavens were conceived of as a moving image of eternity, and eternity was understood to be coterminous with the Divine. Since it moved, it contained life and thought, and repaid the attention of man. We still live, work and think inside what is a scarcely changed neolithic temple, which is the sky.

 The final word count is around 56 thousand words. Two of the chapters - 'The Greek Ontological Model in the 1st Millennium B.C.E', and 'Patterns of thought in Late Neolithic and Early Bronze Age Britain', are quite large pieces of work (6k and 10k words respectively). The introduction and a chapter each from the three parts of the book are available via the list below.


The chapter list:

Introduction: The Interpretation of Ancient History

Part One. 6

Camera Obscura: Marx, Aristotle & Ptolemy. 7
Synoikismos and the Origins of the Polis. 12
Proskynesis, and the Deification of Alexander. 25


Part Two. 34

The Greek Ontological Model in the 1st Millennium B.C.E. 35
Greece and the cultural Impact of the Assyrian Empire. 57
The Threshold in Ancient Assyria. 68
Symmetry and Asymmetry in the Iconography of the Ancient Near East. 75

Part Three. 80

Being and Eternity in the Neolithic. 87
Patterns of thought in Late Neolithic and Early Bronze Age Britain. 93
The Mathematical Origins of the Megalithic Yard
What We Have Lost, and How the Ancient Concept of the Cosmos Died
Marx and Historicism.. 129

Publication date, June 30, 2020.

TY, May 5, 2019. Details updated May 27,  July 5, and September 6 and 17, October 1,  November 26,   December 12, 2019, May 5 2020, and June 14 2020.. Updated October 10.

Saturday, 6 October 2018

Bringing the Divine to Earth. Writing to the Poet Leona Esther Medlin




I wrote to Leona Esther Medlin on the 26th of January 2018, and headed the letter, 'After the Bronze Age Wreck'. The letter is an update on where I was with my research. The original (rather squibish) article 'The Bronze Age Wreck' was shared only with one archaeologist in May 2013, since it depended very much on an understanding of the arguments in 'The Sacred History of Being'. That book was not published for another two and a half years. 

***

The focus of The Sacred History of Being is the presence of the idea of Being in cultures around the Mediterranean from the eighteenth century BCE onwards. Particularly in Mesopotamia. The date was chosen because it marks the earliest appearance in the archaeology of a standard symbol for divine Being in Mesopotamia.

It was obvious from Egyptian iconography (and from elsewhere) that the idea of Being is much older. I chose not to go back before this date however, for the purposes of argument. Or to go anywhere near Egyptian stuff, for obvious reasons.

I found in 2013 that it might be possible to identify the (functional) presence of the idea of Being in the Neolithic and early Bronze Age in Britain. How? There is no writing. Just lots of big stones in lines and circles. But as Alexander Thom’s surveys from the 1930s onwards showed, the circles betray a profound interest in various Pythagorean triangles, and in whole numbers (the circles are not strictly circular, and the circumferences are expressed in whole numbers). This is a form of writing, just writing in terms of number and geometry.

There are several ways of talking about Being, and one of the terms often used in antiquity to reference Being was ‘totality’. I wrote about this way of thinking extensively in The Sacred History of Being (hereinafter SHB). It was a major part of Pythagorean doctrine, and also in Mesopotamian thought. Plato discusses the idea, and in fact his whole argument about ascending to the Good and returning depends on the significance it was supposed to have.

I also wrote extensively in SHB about the installation of divine statues in Mesopotamia, and the connection between the idea of totality and divine Being. The installation process lasted three days, during which time the statues were pointed at the heavens, which was regarded as an image of eternity or totality. The rite was a rite d’aggregation. The statue did not embody the divine without the performance of this ritual: the statue need to participate in totality to be divine.

After seeing the documentary ‘Cracking the Stone Age Code’ in early 2013, it occurred to me that the mathematical and geometrical aspects of stone circles may have served the same sort of function as divine statues in Mesopotamia and elsewhere. The hypothesis was that in their construction the circles embodied aspects of divine Being on earth, and they therefore established a bridge between earth and eternity. 

In just a few days in May 2013 I wrote an extensive essay arguing this case. It had the title ‘The Bronze Age Wreck’. I called it that because the body of ideas which lay behind the building of the megalithic circles was lost to us, apart from a few clues. It seems also to have been lost to those living in the British Bronze Age itself, since the building of the circles more or less ceased around 1400 BCE (I’ve not written about that, but I think I know what happened. For another time).

The essay depended very much on a reading of SHB, so it wasn’t much use to circulate it. What I’m writing now is based on that essay, but readers are not required to have read SHB first.

In November 2016 I wrote another essay, called: ‘Stone Circles, Phenomenology, and the Neolithic Mind’. It discussed the archaeological evidence, Plato’s arguments about the heavens as an image of divine Being, and Mesopotamian ritual for the installation of gods, both in heaven and on earth. The essay was published on my website, and it received significant attention. It resulted in a commission in November 2017 to write about these ideas for the journal Time and Mind.

This article of 10.5 thousand words was written and delivered in four weeks, and it has the title ‘Patterns of thought in Late Neolithic and Early Bronze Age Britain.’ It was quite different from the first, largely as the result of a conversation with the philosopher Adrian Moore across the year, which moved from ideas of Being in antiquity to Greek discussion and understanding of irrational numbers. This discussion prompted a general review of Pythagorean mathematics, and the sources. In the end, the new article suggested that there was a connection between mathematical and geometrical puzzles and paradoxes, and the idea of a transcendent reality (divine Being) standing behind appearance. The article also argued that Pythagoras travelled widely, borrowing much of what later became known as Pythagoreanism from priestly establishments in Babylonia, Egypt, Phoenicia, and other places. What he was doing involved looking for a universal substructure of number, mathematics and geometry which pointed to the nature of Being.

Shortly after this paper was completed in December 2017, I wrote a post for my website which discussed the two papers on stone circles and Pythagoreanism from 2016 and 2017. It is titled: ‘Thought in Late Neolithic and Early Bronze Age Britain’. It contains the abstract for the paper intended for the journal, and thirteen section headings, but no actual quotations from the body of the text.

Earlier in 2017 I was asked for a copy of a paper – ‘The Esoteric Conception of Divinity in the Ancient World’, published in the Bibliotheca Philosophica Hermetica Newsletter in December 2015. The inquirer was Nico Bader, who runs the Pythagoras Foundation in Amsterdam. I wrote to him sometime after forwarding the paper, suggesting that he might be interested in looking at the two posts on the web concerning stone circles and their significance. He found this line of research to be interesting. Yesterday he offered to summarise the argument in these posts for the Pythagoras Foundation’s Newsletter (number 23), which will be published in March. The newsletter (it is a bit more than that) is read by everyone who is seriously interested in Pythagoras and Pythagoreanism. If Time and Mind publishes ‘Patterns of Thought in Late Neolithic and Early Bronze Age Britain’ in their upcoming issue, both will items will appear in March.

January 26, 2018.

***
Stone Circles, Phenomenology, and the Neolithic Mind: http://shrineinthesea.blogspot.co.uk/2016/11/stone-circles-phenomenology-and.html
Thought in Late Neolithic and Early Bronze Age Britain (now retitled 'Being and Eternity in the Neolithic'): http://shrineinthesea.blogspot.co.uk/2017/12/patterns-of-thought-in-late-neolithic.html
‘Cracking the Stone Age Code’ (the original BBC Chronicle documentary, broadcast in October 1970, which I didn’t see until early 2013. Worth 50 minutes of your time on a wet Sunday: http://www.bbc.co.uk/archive/chronicle/8604.shtml

[The article 'Patterns of Thought in Late Neolithic and Early Bronze Age Britain' was rejected  by the editorial board of the journal 'Time and Mind'. It is available here. All about what a pre-pythagorean pythagoreanism might have meant in the context of the British Neolithic. Nico Bader, on the other hand, did follow through with publishing his summaries of my posts. At: https://www.academia.edu/36071620/PYTHAGORAS_FOUNDATION_NEWSLETTER_23_2018.pdf]

[Updated May 13, 2020]

Sunday, 19 August 2018

The Time Bomb Under Archaeology





Text from the Spectator archive, November 14, 1970. The programme was broadcast on October 31, 1970 (the Spectator came out once a fortnight). An edited excerpt from their review of TV programming. It is coming up for fifty years since the programme was broadcast, and the 'time-bomb under archaeology' may be about to explode. There is new information.

Magnus Magnusson wrote and narrated an excellent programme about even older good old days, four thousand years ago, when some of the natives of these islands were 'prehistoric Einsteins.' Chronicle: Cracking The Stone Age Code' (BBC 2) was about Professor Alexander Thom's study of megalithic mathematics and astronomy. Now seventy-six, Professor Thom, a retired engineer, has spent the past thirty years studying ancient stone circles. His measurements have demonstrated to his satisfaction that Stone Age man was no barbaric simpleton but erected stones in patterns founded on Pythagorean geometry two thousand years before Pythagoras.
Professor Thom discovered that stone circles all over Britain used a standard megalithic unit of measurement, precisely 2.72 feet in length. Using the crudest instruments, the Stone Age astronomer-priests were able to predict accurately various astronomical events, such as lunar eclipses.

Mr Magnusson suggested that Professor Thom's findings have put 'a time- bomb under archaeology.' Archaeological sceptics were given opportunities to voice their disagreement on the programme, but Thom appeared to be entirely undisturbed by expressions of dissent. Chronicle enterprisingly sent him to Carnac, a megalithic site in Brittany. His findings there fitted his British observations and demonstrated, as Mr Magnusson said, that 'there was an intellectual common market four thousand years ago.' Perhaps Malcolm Muggeridge is right,... when he says that our civilisation is in decline.

The original programme is available from the BBC Archive, and is an extraordinary time capsule from the time in which it was made. There was no consensus about the implications of Thom's work, or even that his suggestions about the basis on which the monuments were laid out were reliably rooted in Thom's phenomenological and statistical analysis.

Since then a resurvey of 300 of the monuments by Clive Ruggles, using a highly unorthodox and inconsistent methodology, has removed the need for archaeologists to engage with the implications of Thom's original study of the monuments. *1 This is because many of the things which Thom drew attention to are now understood by the archaeological community to be the product of a 'selection bias'. As the archaeologist Euan MacKie (who appears in the programme) has pointed out however, Ruggles resurvey was conducted in such a way that it could not possibly verify some of Thom's findings, such as the deliberate orientation of the monuments on foresights in the landscape, even if those findings were correct.

Thom was an engineer, mathematician, and an excellent surveyor. He detected some key components to the construction of the monuments, such as a near obsessive interest in whole numbers, and what appeared to be the use of pythagorean triangles in the laying out of the structures. Those aspects of the circles and ellipses he did not over-interpret, because he had nothing to go on. He reported on what he could see, and how the structures might have been laid out given those clear interests of the original designers of the monuments.

Being an engineer, and a mathematician, there were other things he must have noticed during his surveys, but for which he could offer no sensible explanation. And at the time this documentary was made, nobody else could have either. The phenomenological and statistical analysis of the monuments remains however as a remarkable body of work. There is more information in those surveys than meets the eye.

The interpretative frame has moved forward in the meantime. We know much more about the nature and origins of Pythagorean thought than we did - it is possible, for example, to understand Pythagoreanism as a way of thinking which is rooted in the consideration of natural puzzles. Such an interest necessarily has a bearing on the human response to such puzzles, which can be a religious response (and was, in the case of the later Pythagoreans). Many constants in nature are mathematically irrational, such as pi and phi, etc, which makes them a phenomenon of interest to those disposed to philosophical inquiry. These are staples of Greek philosophy. Such an interest also offers an explanation of how a Pythagorean way of thinking could have arisen so long before the advent of the Pythagorean sect we know from much more recent times.

***


1. Ruggles describes his resurveying work in a chapter in Records in Stone. His 'methodology', might have seemed to him to make sense at the time, but now it looks like what it is: an attempt to unsee a large body of unpalatable evidence for which the discipline of archaeology was entirely unprepared. It was about protecting an academic and cultural narrative, which then, as now, was firmly entrenched. [Records in Stone: Papers in Memory of Alexander Thom, edited by C.L.N. Ruggles, CUP, 1988]

[Readers of this article might be interested in reading Patterns of Thought in Late Neolithic and Early Bronze Age Britain, which explores the pre-Pythagorean Pythagoreanism which Thom said was suggested by the evidence. Much of Pythagorean thought was evidently derived from Pythagoras's travels around the ancient Near East, which are documented, and elements of Pythagoreanism might have been a staple ingredient of religious thought from the Neolithic onwards].



Sunday, 10 December 2017

Being and Eternity in the Neolithic




For the past three weeks or so I've been writing a paper on aspects of mind during the late Neolithic and the early Bronze Age in Britain, during the period when most of the megalithic circles were built. I wrote a paper in 2016 (Stone Circles, Phenomenology, and the Neolithic Mind) which explored the possibility that we might have enough information from the structures to infer thought and motive of their builders. 

In that article I wrote: 



The main objection of the archaeological community to the acceptance of this view of the circles as sophisticated tools for the observation of the heavens and its movements is two-fold. The first is that there is nothing (beyond what these objects seem to show) which suggests to us that the megalith builders and their contemporary culture was concerned at all with precision. The second is that, even if the circles can be shown to mark certain astronomically precise points, we have no clue at all about why the megalith builders would want to do this. We have no understanding of the function and purpose of such observations, and so we can say virtually nothing about either the purpose of the monuments, or about the culture which gave rise to them. In other words we are no further forward in our understanding.

This two-fold objection is sound, at least from the archaeologists point of view. We have no contemporary description of anything at all from the time and culture of the megalith builders. We have no understanding of their intentions, and no understanding of the function of the circles, and it is unlikely that archaeological interpretation by itself will reveal these things to us. It seems to be gone altogether, and all we are left with is insupportable speculation. Perhaps it would be best to draw a veil over this apparently anomalous aspect of the past, since we can have no understanding of it.

The upshot of the article was not as negative. I argued that:

[in] both Greece and Assyria, the heavens, and what the heavens represented, were of particular importance for cult practice. Plato is clear that the heavens represent an image of divine Being, also spoken of as the ‘Living Animal’, created out of the materials of other gods, by the demiourgos (the ‘Living Animal’ is created by the Demiourgos rather than by God directly, so that there should be not too much of the divine present in the world). He is also quite explicit that the body of the ‘Living Animal’ was created with precision.

In which case astronomy is important for the understanding of divine Being. An infamously unintelligible passage in Plato’s Timaeus talks about the perception of images being possible only because the soul already contains exemplars of these. If the heavens represent an image of divine Being, then all other images are poor imitations, and we should direct our attention principally to the heavens. The soul represents the heavens most closely, and in antiquity was notionally the part of us which is most connected to the divine. It is the soul which recognizes divine knowledge when it is presented to it.

We already know the importance of the soul in Britain in the late 1st millennium BCE, from several sources, including Julius Caesar.  It may be that these ideas were similarly tied together in Britain, and perhaps at a much earlier period. I explored a Mesopotamian parallel:

In ancient Assyria, part of the ritual for creating an image of a god (thereby conferring divinity on the object) involves the image being exposed to the sight of the heavens. As a god, it needs to have perception of Being, of which it is an aspect. We have this ritual from the reign of Esarhaddon (7th century BCE), who was the predecessor of Ashurbanipal, one of the last Assyrian kings, and the owner of the famous palace library, much of which is now located in the British Museum.
So the point is the establishment of contact - even an identity with - what is divine. It is possible to see this concern with connecting Heaven and Earth as a parallel to what Plato describes more abstractly in his Republic. I wrote:

...Plato argues that the philosopher should ascend to the idea of the Good, which is another way of referencing the idea of transcendent Being, by a series of connected images, without specifying what those images might be. These images, as imperfect representations of Being, are subject to change. Matters are complicated by the fact that the things which are imaged are also subject to change. Thus both subjective impression and objective reality are subject to change and uncertainty.
So the process is problematic, and complex. To some extent it is a matter of conjecture, as well as knowledge.
A key characteristic of ancient religion was that it entertained conjecture regarding knowledge of the gods. Plato refers to this in his discussion of the divided line in The Republic. We cannot know Being itself directly. We cannot know the lesser gods directly either, but we can understand some of the characteristics of these gods, though full knowledge is necessarily beyond our understanding. We can approach some limited understanding of Being via the images and descriptions of the lesser gods however, which is one reason why they were deemed to have some kind of reality.
In which case knowledge of divine things is a journey through the problematic and sometimes paradoxical aspects of reality as it presents itself to us. You need a priesthood for dealing with that. They were dealing with ontological questions, and did the best they could within the limitations of human knowledge.
This limited set of characteristics and properties emerges from thorough and precise discussion of the nature of ontology (Being), as the focus of human conjecture. This is quite clear in both Plato and also in what we know of the teachings of Pythagoras. The paradox of knowledge is the consequence of the idea that all knowledge is present in the divine, and that we only have knowledge because we have a soul. In other words, we can have knowledge as the result of the divine having a presence in us already.

I suggested that Plato, rather than exploring a pattern of ideas created in the Academy in Athens, was in fact transmitting and refurbishing some

...key aspects of a Bronze Age philosophy, which has its roots in the Neolithic in both Europe and the near East. The transcendental doctrine which is enshrined in his work is actually in plain sight to anyone who can follow his reasoning that all the merely likely stories are just that: no more than likely. The single argument which is not a mere likelihood, is counterintuitive, paradoxical, and beyond common sense. And it remains a matter of conjecture. This argument about the nature of the world used to be the apex of learning and knowledge. Reality is transcendental, and neither subjective or objective. Nothing lay beyond this fundamental understanding of the world.
If this argument is correct, then we can know what Neolithic man was up to, and in some detail. In short, for the intellectually sophisticated in the Neolithic period, the heavens represented, as for Plato much later, a moving image of eternity. To measure the parameters of this moving image of the divine was to know God, and to have knowledge of divine things.


This represents a radical departure in our understanding of the development and the history of human thought. We know that the heavens were important in the neolithic and the early Bronze Age in Britain, and if that importance stemmed from an understanding that the heavens represented a moving image of eternity, then the people who built the megalithic circles had a concept of Being, and of a reality which transcended most human experience. Such an idea is the most abstract of all. It transcends all images of what is real. It implies a culture built on responses to questions about the nature of reality, and many conjectures about what can be known.

The Pythagoreanism which the surveyor of many of the megalithic sites in Britain, Alexander Thom, detected in his findings, was very basic in nature, and based on statistical analysis of his data, and the geometrical construction which could be found in the monuments. Which means the observance of the importance of the Pythagorean right angled triangle, and the concern with whole numbers.  Both of these were of importance to the later Pythagoreans, as we know. A further clue was the statements by a number of ancient authors to the effect that the religious belief of the Britons in the late 1st millennium BCE was akin to Pythagoreanism.

But there is very little detail about what Pythagoreanism in Britain might have entailed, if the identification is correct. This is rather surprising, since we have a great deal of information about Pythagoras and Pythagorean doctrine available to us from sources other than Julius Caesar, and the authors whose opinions have survived as a result of being quoted by Eusebius (though often inconsistent, and sometimes quite obscure in meaning). We have a biography of Pythagoras from both the neoplatonist Iamblichus, and also from Porphyry. We also have an extensive and rather good account from the author of the Lives of the Philosophers, Diogenes Laertius. Plus we have the works of Plato, who is constantly referencing the doctrines of the Pythagoreans.

So this new paper looks at the material we have concerning Pythagoras, in order to know a fuller range of what Pythagoreanism implied in the late sixth century BCE, both in Italy and in Greece. As it turns out, certain key ideas in Pythagoreanism arise as the logical consequence of the kind of discussions which they entertained, mainly concerning number, mathematics and geometry. And these key ideas shape their ideas about religion, divinity, the nature of reality, of Being, and of Eternity.

The paper concludes with the suggestion that, if  key religious ideas emerge in the Pythagoreanism of the 1st millennium BCE, in the course of logical argument concerning number, mathematics and geometry, then we should entertain the notion that parallel discussions may have taken place in the late Neolithic and the early British Bronze Age, on account of their own evident concern with number, mathematics and geometry.

***

The title of the paper is: 

Patterns of thought in Late Neolithic and Early Bronze Age Britain

Abstract: Pythagorean elements detected in megalith circles in ancient Britain have no easy explanation, and precede 1st millennium Pythagoreanism by an extraordinary period of time. This paper explores the idea that there is a connection between some core Pythagorean mathematical and geometrical concerns, and ideas of divinity and eternity.  On the basis of a close examination of Pythagorean ideas in the 1st millennium, for which we have extensive documentation, it is suggested that this connection is based on a series of logical inferences. It is therefore possible that similar conclusions were arrived at in the Late Neolithic.

Key words: Megalith, Pythagoras, Philosophy, Religion, Mathematics


Paper sections are:

1 The Longevity of Ideas
2 Pythagoreanism in 1st Millennium Britain
3.The Principal Sources for Pythagoreanism
4 The Core of Pythagorean Doctrine 
5 Diogenes Laertius on Pythagoreanism
6 Pythagorean Thought in Italy
7 The Existence of Irrational Numbers
8 Religious Aspects of Pythagoreanism
9 The Pattern of Eternity
10  Pythagorean Syncretism
11. Transcendentalism in Late Neolithic and early Bronze Age Britain
12 Walking back the Insight into Ancient Mind
13 Pythagoreanism and the Deep
TY, December 10, 2017.

The paper was reviewed a short time ago, and rejected for publication in Time and Mind (for reasons I understand, but disagree with). Thanks to Paul Devereux, who thought it was worth the shot. Rather than waste a lot of time looking at the very few options available for publishing this kind of article in a scholarly journal, I've opted to make it available here, at: Patterns of Thought in Late Neolithic and Early Bronze Age Britain.

TY, March 8, 2018.

I changed the name of this post to 'Thought in Late Neolithic and Early Bronze Age Britain' on January 26 2018, in order to avoid confusion with the actual paper intended for journal publication. The title was changed again, to 'Being and Eternity in the Neolithic', on May 6 2019, while the foregoing text was being edited for inclusion in Mirrors of the Divine, along with 'Patterns of Thought in Late Neolithic and Early Bronze Age Britain',

TY May 6, 2019.


Wednesday, 15 November 2017

Philosophical Thought in the Neolithic (and why we cannot see it)



While responding to a mail from the managing editor of a scholarly magazine,  who I'd pointed in the direction of a couple of articles on my blog, I found myself condensing my project into the compass of just four paragraphs. This covers both what I am doing, and why. I reproduce them here:

Years ago I read Adolf Erman's collection of Egyptian Literature in English translation. One text in particular made me sit up, since it involved the use of concepts I associated with classical Greece. The text was Akhenaten's 'Hymn to the Aten'. Akhenaten lived some nine hundred years before Plato and Aristotle, yet he seemed to be comfortable with concepts which are supposed to have been first discussed among the Greeks. I looked for other 'anticipations', and found them.


That propelled me to study in London (in 1989). By that time I'd started to look at antiquity quite differently from the way I'd been taught by classicists. Instead of seeing classical Greece (and the work of the later philosophers all the way up to the closure of the philosophical schools in 529 CE) as the beginnings of sophisticated thought about abstract concepts, I began to treat major components of classical thought as the possible end point of a way of thinking, which might conceivably stretch back into the neolithic. The notion of excellence is one of those components, which as we now know was a concern for the megalith builders.


That's the basic hypothesis. The idea of Greece as the birthplace of philosophy is a modern construct. Plato himself said it was a very old discipline, but classicists don't bother to discuss what he had to say about that when they are writing about the history of philosophy. The evidence from around the eastern Mediterranean however, bears out what Plato said.


My focus so far has been mainly on Mesopotamia, and back to the 14th century BCE, because it is the area where I have the most expertise. It is now pretty clear however that the hypothesis that the presence of abstract ideas stretches back into the Neolithic is sound, and that this insight can deliver great riches. If only we can escape our enlightenment presumptions about the intellectual poverty of our distant ancestors.



Best regards,


Thomas Yaeger


The two articles the managing editor was pointed at were: Stone Circles, Phenomenology, and the Neolithic Mind, and: Frazer and the Association of Ideas, 

I introduced the first article as looking at the context and function of Stone Circles, particularly when looked at as structures which may have served a similar function to divine statues in both Greece and Mesopotamia. In Mesopotamia, during the installation of divine statues, the three day ritual necessarily involved pointing them at defined areas of the sky, because the heavens were understood to represent an image of the Divine - of Being and Reality itself. 

The second article I described as a review of J. G. Frazer's approach to the meaning of evidence from the ancient world. He was trained in Classics, and knew the works of Plato virtually backwards and his concern with the idea of Being, but chose to write his account of ancient thought entirely without reference to the idea of Being in antiquity. He suggested that since nothing could be predicated of Being, it was an entirely barren concept. So Frazer's voluminous output is really a species of fiction, replacing sophisticated thought about the nature of reality with the argument that ancient human thought was, more or less entirely, built on intellectual error.

Saturday, 26 November 2016

Stone Circles, Phenomenology, and the Neolithic Mind



Some notes on the cultural context of Stone Circles, and the function of observations made with them.



[This is one of twenty-one essays in the book Man and the Divine, published in August 2018. The book is available in ePub format from leading retailers of eBooks, such as Barnes & Noble, Blio, Kobo, Itunes, Inktera, Smashwords, etc. Information about Man and the Divine can be found here]


How could we ever understand the function of these objects, in the absence of any contemporary account? Archaeology and scholarship have been applied to the problem of these mysterious objects, but we are apparently still none the wiser. When it was first noticed that these objects were in some way astronomically aligned, that was a step forward, but in fact the observation did not advance us much in understanding the function of the monuments. They mark rising and setting points, and other extreme positions, and so there is the possibility of a calendrical function.

It is hard however to imagine that keeping tabs on the seasons was a principal function of these objects. You don’t need to observe the heavens in any detail in order to know it is time to sow, and time to harvest. If you want to know the length of the year, this can be established with simple observation. After that you could tell that you were in midwinter or at midsummer, at least until the precession of the equinoxes and the imperfection of the quarter day at the end of the year gradually moved things out of kilter. And so leap years would be invented to keep the seasons roughly where they should be, and intercalary days and months would be introduced where necessary over longer periods of time. All this has been done elsewhere, and through time, in the context of relatively basic observations.

The work of Alexander Thom, who surveyed the megalithic monuments in Britain over a period of more than 40 years, from the 1930s onwards, confirmed to those of us with eyes to see, that indeed the circles have a serious astronomical function. He also confirmed that the circles, with their observational platforms and their distant farsights, often on hills and mountains many miles away, have in many cases, a fearful precision about them, whether these farsights mark the rising and declination of the principal stars, the rising and setting of the sun at different points in the year, the solstices and the equinoxes, and the peculiar movements of the moon at various points during the 19 year metonic cycle.

The main objection of the archaeological community to the acceptance of this view of the circles as sophisticated tools for the observation of the heavens and its movements is two-fold. The first is that there is nothing (beyond what these objects seem to show) which suggests to us that the megalith builders and their contemporary culture was concerned at all with precision. The second is that, even if the circles can be shown to mark certain astronomically precise points, we have no clue at all about why the megalith builders would want to do this. We have no understanding of the function and purpose of such observations, and so we can say virtually nothing about either the purpose of the monuments, or about the culture which gave rise to them. In other words we are no further forward in our understanding.

This two-fold objection is sound, at least from the archaeologists point of view. We have no contemporary description of anything at all from the time and culture of the megalith builders. We have no understanding of their intentions, and no understanding of the function of the circles, and it is unlikely that archaeological interpretation by itself will reveal these things to us. It seems to be gone altogether, and all we are left with is insupportable speculation. Perhaps it would be best to draw a veil over this apparently anomalous aspect of the past, since we can have no understanding of it.

Yet we do know that other cultures had a concern with precision, and with precise measure. Egypt is well known to have had such a concern, at least during some parts of its history, as the orientation of its temples show. Precision is a feature of Mesopotamian civilization, as exemplified in Babylonian mathematics; and Hebrew literature also contains precise descriptions of objects. Ancient Greece likewise understood precision (akribeia), exemplified in the design of the Parthenon.

What does this concern with precision mean? We can start from what we know, and throw off what we only think we know about the Neolithic mind. One of these presumptions is that intelligence and intellectual sophistication is relatively new, and that consequently these things are not to be found in the Neolithic period. If we presume instead that it is present, and in fact it is not, we will know our mistake soon enough. If we presume that intellectual sophistication is not present, and in fact it is, we will be left with the intractable puzzle we are attempting to solve.

I have argued elsewhere that, for both Greece and Assyria, the heavens, and what the heavens represented, were of particular importance for cult practice. Plato is clear that the heavens represent an image of divine Being, also spoken of as the ‘Living Animal’, created out of the materials of other gods, by the demiourgos (the ‘Living Animal’ is created by the Demiourgos rather than by God directly, so that there should be not too much of the divine present in the world). He is also quite explicit that the body of the ‘Living Animal’ was created with precision.

In which case astronomy is important for the understanding of divine Being. An infamously unintelligible passage in Plato’s Timaeus talks about the perception of images being possible only because the soul already contains exemplars of these. If the heavens represent an image of divine Being, then all other images are poor imitations, and we should direct our attention principally to the heavens. The soul represents the heavens most closely, and in antiquity was notionally the part of us which is most connected to the divine. It is the soul which recognizes divine knowledge when it is presented to it.

In ancient Assyria, part of the ritual for creating an image of a god (thereby conferring divinity on the object) involves the image being exposed to the sight of the heavens. As a god, it needs to have perception of Being, of which it is an aspect. We have this ritual from the reign of Esarhaddon (7th century BCE), who was the predecessor of Ashurbanipal, one of the last Assyrian kings, and the owner of the famous palace library, much of which is now located in the British Museum.

In the Republic, Plato argues that the philosopher should ascend to the idea of the Good, which is another way of referencing the idea of transcendent Being, by a series of connected images, without specifying what those images might be. These images, as imperfect representations of Being, are subject to change. Matters are complicated by the fact that the things which are imaged are also subject to change. Thus both subjective impression and objective reality are subject to change and uncertainty.

In his dialogues, Plato shows that most arguments about the nature of the ultimate reality fail – particularly in his dialogue most concerned with Being, the Sophist. Here the participants in the dialogue agree to accept that a communion between man and the divine must be granted to exist, even if it cannot be argued certainly to be the case. The necessity of this communion is vital to religion, otherwise it is not possible for man to connect with the divine, and therefore he would be powerless in the world in which he finds himself.

A key characteristic of ancient religion was that it entertained conjecture regarding knowledge of the gods. Plato refers to this in his discussion of the divided line in The Republic. We cannot know Being itself directly. We cannot know the lesser gods directly either, but we can understand some of the characteristics of these gods, though full knowledge is necessarily beyond our understanding. We can approach some limited understanding of Being via the images and descriptions of the lesser gods however, which is one reason why they were deemed to have some kind of reality.

This limited set of characteristics and properties emerges from thorough and precise discussion of the nature of ontology (Being), as the focus of human conjecture. This is quite clear in both Plato and also in what we know of the teachings of Pythagoras. The paradox of knowledge is the consequence of the idea that all knowledge is present in the divine, and that we only have knowledge because we have a soul. In other words, we can have knowledge as the result of the divine having a presence in us already.

Since the divine is transcendent, there must be only a limited set of properties of the divine which can have exemplars in the world of appearance (the mundane earthly world). These properties cannot be things which have no meaning or permanent reality in the divine world. Thus one would not expect arbitrary sizes and colours, for example, or things which are changeable and impermanent. Since the reality of Being is at the extreme of our understanding, and is in itself necessarily an extreme, those who would look for things on earth which are exemplars of the divine would look for things which were in some way extreme, and which exist in conjunction with other things which participate in the divine extremity.

In both Greece and Assyria (I suggest), during the inauguration of divine statues, the statues, which are treated as markers of divinity on earth, representing and, in some instances, creating divinity through the will of the inaugurators, were pointed at the sky at a key point in the ritual. This is so that the statues could see (and know) Being, as represented by the heavenly bodies. In the ritual from Nineveh, the gaze of the statue is pointed at different parts of the sky and different parts of the horizon, in a precise sequence.

So we have an understanding of what was understood to be taking place in such a ritual, once we have a clear understanding of the model of reality in which the ritual served its function. There is evidence from Mesopotamia that this conceptual model was in existence at least as far back as the eighteenth century B.C.E.

It is possible that this model of reality, essentially established through logical argument, was very widely spread, and was not confined to the near East, and was in fact something like a standard view for those who had the time and the liberty to think about such matters.

The evidence from the megaliths makes the importance of the sky very clear. The hypothetical argument to be tested here, is that also in Britain and around the megalithic world, the sky was seen as a representation of divinity, of Being. As an image of the divine, it was an image of totality itself.

The megalithic observatory, or temple, according to this hypothesis, was a device to embody aspects of divinity, of Being, actually in its structure, in the same way in which the gods in Mesopotamia might be invited to occupy their representations on earth.

What about this representation of divinity might qualify as capable of representation on earth? Not the motion of the planets in themselves, since they appeared to be subject to a degree of arbitrariness (with the exception of Venus). The most obvious candidates for the establishment of extreme rising and setting points were the Sun and the Moon – the most prominent aspect of the heavenly representation. The equinoxes would also be of interest, since these represent the points at which the Sun and Moon pass along the path of the ecliptic and cross the celestial equator.

The doctrine of totality is common to both Pythagoras and Plato, and also surfaces, much earlier, in Assyria, as far back as Shamshi Adad I, who reigned in the eighteenth century B.C.E. One of his titles was: ‘King of Totality’ (Shar Kishati). This doctrine makes it clear that many aspects of the world have something of a double nature: Plato argued for example that ‘greatness’ implied participation in ‘the great’. Likewise the divine reality is total, and participation in the divine reality implies the presence of a form of totality in whoever was regarding the heavenly representation of the divine. The sacred is, in some respects, always present in the secular. Both Pythagoras and Plato held that things only come to be by wholes through wholes.

We can now make a preliminary list of things which, if we assume an intellectual sophistication, born of a culture familiar with logical argument, would perhaps have been of particular interest to observers who were part of megalithic culture:

Extremity, Totality, Perfection, Completion, Invariance, Integral (whole) numbers, The incorruptible, Greatness, Rising, Setting, Beginning, Ending, Duration, Periodicity,  Points of transformation.

This list illustrates the sort of abstracted interest I propose the megalithic builders had in aspects of the world, which interest follows from the conceptual model of reality which I have described. All of these have exemplars on both the earth, and in the sky. These characteristics would, within this conceptual model, have been understood to provide points of contact, and a bridge to the divine.

A megalithic circle might therefore be conceived as a representation, in an abstracted form, of the perfection of the heavens, and of Being itself. It would demonstrate its perfection to those who had the understanding to see this for themselves, and would mark the extreme points of the movement of the heavenly bodies. It would be constructed only using integral values, derived where possible, proportionately, from the movement of the heavens in relation to the earth. It would be built out of the most incorruptible materials (most often stone), and where possible, the stone would remain unworked, as something which, in its natural state, already possessed commonality with divine Being. The stones would be large, since their largeness by itself represents unworldliness, and another commonality with Being. The arrangement of the stones would be the way in which this commonality would be reduplicated and intensified. Heavenly cycles would be embodied in the structure where possible, together with indications (in some cases) of their duration.

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

We are told by Julius Caesar (in his Gallic Wars), that the Druids, at the time of his arrival in Northern Europe, taught astronomy and mathematics, and held to a doctrine akin to Pythagoreanism. In fact this section of the text seems to belong to the Roman equivalent of the CIA factbook, so it is probably a fairly accurate assessment by those in Rome whose job it was to collect useful information about cultures around the known world, into which Rome was expanding.

There are strong parallels between the ideas of Plato and Pythagoras as has already been noted, and Plato is reputed to have made significant efforts to obtain texts from the Pythagoreans. Both regarded the world as the product of mind: both the transcendental realm of Being, and the world of appearance. So there is, at a conjectural level, a series of connections between the divine world and the world of appearance, which can be discovered. All other stories about the world are mere likelihood. Modern scholarship on Greek philosophy stops short of this understanding of Greek thought. Plato’s highest level of reality is never explored, and even the approach to it is left shrouded in mystery.

The presence of an articulate idea of Being explains aspects of Mesopotamian theology and ideas about creation, as well as illuminating aspects of Homer’s Iliad, which of course precedes both Plato and Pythagoras by several centuries. There are strong parallels between Greek and Mesopotamian ideas of Being, which I have explored elsewhere. Both cultures practice theurgy (though the term does not make an appearance until much later), and the theoretical basis for this is similar, in that the twofold aspect of creation makes it possible for workmen (under the direction of the king, who in himself embodies several aspects of divinity in his official position) to have their sacred aspect initialized, so that they can set up gods in heaven. They can do this because they have had divinity put upon them by the king who is directing operations, in conjunction with instructions from his diviners. This is possible because they already possess divinity and connection to the divine, though ‘they are blind and deaf’ to this understanding throughout their lives, as Esarhaddon tells us.

Thus, they, like everyone else, and the world, are representations and images of Being, and the divine reality.

What I suggest Plato is doing, during a period of intense cultural crisis in Greece, is transmitting in writing, in a scrambled and elliptical fashion, key aspects of a Bronze Age philosophy, which has its roots in the Neolithic in both Europe and the near East. The transcendental doctrine which is enshrined in his work is actually in plain sight to anyone who can follow his reasoning that all the merely likely stories are just that: no more than likely. The single argument which is not a mere likelihood, is counterintuitive, paradoxical, and beyond common sense. And it remains a matter of conjecture. This argument about the nature of the world used to be the apex of learning and knowledge. Reality is transcendental, and neither subjective or objective. Nothing lay beyond this fundamental understanding of the world.

If this argument is correct, then we can know what Neolithic man was up to, and in some detail. In short, for the intellectually sophisticated in the Neolithic period, the heavens represented, as for Plato much later, a moving image of eternity. To measure the parameters of this moving image of the divine was to know God, and to have knowledge of divine things.

What was once a complete and deafening silence is now filled with many voices. We can never know the words they used, but we can know what they talked about, since anyone who talks about Being, and the connections between Being and the world of appearance will talk about the same things, and come to the same sort of conclusions. Some of these arguments have a practical upshot in the creation of sacred sites. They would look for extreme points in the heavens, since the heavens comprise a representation of the divine. The extreme points of the motions of the heavenly bodies represent a connection between the extreme of Being, and the secular world.

The principal concern was the nature and reality of Being, and the nature of reality itself. All  philosophical instruction would have been designed to lead the neophyte, by dint of the repeated failure of argument to establish any solid and reliable conclusion within the confines of common sense, to the conclusion that the reality that we perceive is essentially transcendental in nature. And that the nature of the divine is a conjecture which must be held as just that, a conjecture. Anything less and it becomes an opinion, which isn’t real knowledge.

Many practices in the ancient world emanate from this perspective on reality. Sacrifice is one. The origin of the idea is that something which has been completed is connected with the divine, which is also complete. Even if the termination of life is artificial and precipitate. The idea is also reflected in the conversation between Solon and Croesus in Herodotus, where Solon, in response to Croesus, says ‘call no man happy until his end’. Divination by entrails also is based on the same idea, that by inspection of the entrails of an animal whose life has been ‘completed’ (even now we may say ‘totalled,’ to mean something utterly ended), something of the divine can be understood.

***

[The BBC Chronicle documentary from 1970 - 'Cracking the Stone Age Code', on the work of Alexander Thom, is available to watch (complete) by clicking on the image at the head of this article.] 

Thomas Yaeger, November 26, 2016

This article eventually gave rise to another article which focussed particularly on the pythagorean aspects of the Neolithic and the Early Bronze Age. This new article uploaded on March 5, 2018,  'Patterns of Thought in Late Neolithic and Early Bronze Age in Britain' is perhaps the place you want to go next.


Thomas Yaeger, March 6, 2018