Showing posts with label Reality. Show all posts
Showing posts with label Reality. 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

Thursday, 4 February 2021

The Paradoxical Nature of Reality

 


 



[This is the postscript to The Sacred History of Being, first published in November 2015. It makes the case that we live in a reality which has two states, and that moving between these states has been a major preoccupation of ancient civilizations. The statue is of Amenhotep III, who was the father of Amenhotep IV,  who later changed his name to Akhenaten. Amenhotep III is shown wearing the Khepresh Crown, also known as the Blue Crown. "During the New Kingdom, pharaohs were shown with this crown in military circumstances. However, some scholars think that the crown was also meant to evoke the divine power of the pharaoh, and was thereby worn to religiously situate kings as manifestations of gods on earth."] 

 

The argument of this book is complex and necessarily discursive, since its purpose is to uncover an ancient implex of ideas which was almost always discursively expressed, whether in the course of argument, in the formation of myth, liturgy, or ritual, and was, for the most part, conjured in terms of images. The argument however has a clear focus, which is the consistent reference point of these images - that which does not change - and secondarily the body of ideas which grew up around this notion of a reality which is beyond all merely human understanding.

 

We know that this idea was pursued in Greece, in particular by Plato, who was 'always looking to the one thing.' This 'one thing' has been very difficult for students of Plato to disinter, since it seemed to be hedged about with logical difficulties which, not least, cast considerable doubt on the possibility of there ever being something which could be referred to as the 'one thing.'

 

This difficulty isn't simply the result of the coy and often allusive way in which Plato discusses the relationship between the world of change and the world of unchanging reality. It also has something to do with us, and the weight of cultural baggage which we bring to bear on certain questions. We read Plato with many assumptions.

 

It is also the case that we do not read Plato (or any Greek philosophical writer for that matter) in cultural context. The Platonic canon is about philosophy, and philosophy is currently treated, almost universally, as a subject which can be abstracted from its original context without any significant damage to its meaning or worth. What that original cultural context is, is difficult to determine.

I have attempted to turn this assumption on its head. The Platonic canon belongs very precisely in its cultural context, and we do damage to our capacity to understand both Plato, and the culture to which the canon belongs, by breaking these connections without any grasp of what is lost.

 

The culture of Greece in the 5th and 4th centuries B.C.E is generally interpreted by classicists in terms of something which happened in isolation from other cultures around the Mediterranean, because it is assumed that the culture of Greece is, in essence, an autocthonous development. The loss this creates for our understanding of all of the cultures of the first millennium B.C.E - including Greece itself - is colossal. Greek intellectual life is relatively well documented when compared with other cultures around the Mediterranean; but rather than using one to illuminate the other, the classicist and philosophical communities assume that they are so far apart, no meaningful comparisons can be made. 

 

 I have attempted to stand this assumption on its head too, by comparison with aspects of the culture of the Neo-Assyrian empire. Some key details of Greek thought and religious life, which are entirely missing from the record, are documented in Assyria (and in Babylonia) in the mid-1st millennium B.C.E. In writing about the Forms, Plato is, as a key passage indicates to us, also writing about divine statuary and their cultic function. The Forms, as discussed in the canon, reflect a hierarchy which leads to the contemplation of the 'one thing.' This one thing Plato referred to as 'The Good'. This is the ground of Being, or reality itself. All of the Forms participate in some way in Being, and represent aspects of it. Being is conceived by Plato to be the home of real knowledge, and this knowledge can be accessed via the hierarchy of Forms, contemplated in the mind. The Forms represent perfect or ideal approximations to the perfection of Being itself, and provide the access route.

 

Assyria too possessed the ultimate abstract idea of Being also, some considerable time before Plato wrote about the idea. We know this because of the close relationship which has been established between the structure of the Kabbalah and the Assyrian sacred tree, which is represented many times in royal palaces and on seals. The Assyrians regarded the pursuit of knowledge as an essential component of kingship, which we know about from several sources, including a personal account of the scribal training of Ashurbanipal. The wider training of the king involved the pursuit of excellence in various skills. The king was understood to represent divine Being on earth.

 

'Looking to one thing' was also essential to the Assyrians, since they too conceived that knowledge resided in transcendent Being, which, they called by many different names. One of the principle images of Being is the undersea Abzu, the home of Ea, the god of wisdom. This is the place where generation is made possible, and where the destinies are determined. Assyrian rituals for inaugurating divine statues invoke the beginning of creation in the Abzu, and feature a long series of images which repeatedly point toward this idea of Being. And in order for a statue to become a living being in heaven, it must be (and is) granted the wide knowledge of Ea himself.

 

Plato's account of the creation involves the use of an image of Being as a pattern for the generation of the world. This image of Being was used by the Demiourgos to pattern the heavens, with its constellations and moving planets. It is therefore striking that the making of a divine statue in Assyria involves a ritual which exposes the statue to the heavens in order that it may have knowledge of the divine. The parallel Babylonian ritual goes into more detail about the aspects of the heavens which impart divine knowledge to the new god.

 

In both Assyria and Greece generation is associated with the sea. In both cases the sea is understood as an image of the limit of reality - Okeanos, the encircling ocean in the case of Greece, and the upper and lower sea, in the case of Assyria. It is the limit which is significant, and which gives rise to the image of it. Plato has much to say about the transcendent realm of The Good, in which Forms can have no location, size, shape or colour. The limit appears as the site of generation in Assyrian ritual in the form of the riverbank, which was regarded as the gateway to the Abzu and its threshold. Similarly therefore, in Assyria, generation is understood to emerge from a place which has no location, size, shape or colour. The pure reeds of the riverbank are stated to have their roots in the Abzu.

 

The precise nature of the cultural relationship between the cult of knowledge in Greece and in Assyria, is currently unclear, apart from the obvious parallels. It will take time and effort to clarify this. But we do know that another important philosophical idea was held in common both in Greece and in Mesopotamia, and we know the nature of the doctrine which emerges from it.  This is the doctrine of wholes or totalities, which we are told was acquired by Pythagoras while he was in Babylon. This doctrine concerns how ideas and forms can participate in one another. It seems like a small thing, outside its proper context. But the doctrine has huge importance in understanding ancient philosophical theology, and indeed in knowing that it existed at all. Anything which is whole, or total in some respect, was understood to participate in wholeness or totality itself. Being was understood in both cultures as a form of totality. In fact in both cultures, it was understood as the entirely transcendent form of totality.

 

Plato employs this doctrine in his account of the creation, and it is the means by which it is possible for one thing to pass into another, as he tells us. So the creation of wholes and totalities is of key importance. The Forms are wholes, and point to the totality at the root of reality.

 

It is possible to understand the consequence of the presence of this idea in Mesopotamia, because it is possible, with some teasing out, to understand the consequence of its presence in Greece. Which is that if the ground of Being is transcendent totality, then all other things which possess totality are in some way connected with it, and can be understood as representations of it. This is part of the logical basis for the creation of divine statues. But only part.

 

The transcendent totality is a plenitude, but it is ungenerated, and so it has no size. It contains the potential for all creation. It is one alone, because otherwise it would be other than it is. And yet Plato speaks of God creating a copy of Being, after which the world was patterned. If a copy of Being was created, then Being would be divided, not whole, and not what it is. It would have been subject to change, which is contrary to its very definition. And yet if it does not exist in the world of change, then it can do nothing. Movement and thought would be impossible. This would be a disastrous state of affairs for any cult which placed knowledge at the heart of Being.

 

Plato's argumentation about Being is unlike any other from Anselm onwards, in that he identifies Being with the nature of reality itself. Anselm and Descartes speak of supposed properties and attributes of the divine, but since they are attempting proof of the reality of God (framed in terms of some kind of existence), rather than proof of the realness of reality, there is an implicit and unaddressed separation between the divine and the nature of reality in their arguments. There is no sense in either case that the divine is absolutely dependent on the nature of reality.

 

Plato does not tell us how the paradox of one Being, who is necessarily two for the generation of the world of movement and change, and therefore not real Being, is resolved, nor does he resolve for us the question of whether or not the unchanging divine can be present in the world of movement and change.  What he does do is to proceed with the discussions, on the basis that it is necessarily so, that, somehow, the generated world is patterned after a representation of Being;  and that it must be the case that the divine can, somehow,  be present in the world of movement and change.

 

If we turn over in our minds the idea that the world is patterned after Being, without its essential nature being compromised, which is totality, alone and undivided, there is only one possible rational logical solution: that the world of movement and change is not, in reality, separated out from the nature of Being. What we see are aspects of Being itself, represented to us in various ways which are available to our capacity to perceive.

 

Language here does not serve us well, but essentially the logical conclusion must be that, if the essential nature of Being is to retain its integral nature, the world of movement and change is illusory. It has no reality apart from Being. Indeed, there is no such thing as existence 'apart' from Being: Being and the generated world are in some way coterminous.  The world we see and live in is a perception, no more and no less, contained entirely within unchanging Being, and composed of elements and aspects of Being. It is a perceptible world, rather than real; an immensely complex illusion generated within a reality which has no location, extension, shape or colour.

 

The consequence of this - and this is the crux of the matter - is that though Being retains its essential unchanging nature, and remains always purely is what it is, the generated world must have a double nature. That is, the world of generation is finite, and contains finite things, but it also necessarily contains things which are infinite. These things which relate to the infinite are the completions and perfections, and the other things which participate in the ground of Being. As finitudes, as conceivable images, they belong in the generated world as representations of the divine reality. Considered as representations of Being, they represent what we can understand of the divine, but they must necessarily also be Being itself, and be able to pass in and out of Being. Though we necessarily perceive these images as representations, unless we have profound knowledge of the divine.

 

It turns out therefore that we can add Plato to the list of ancient philosophers who were addressing reality as a paradoxical phenomenon. That changes quite a lot. It changes our understanding of the Greek mind, and our understanding of Greek culture.

 

We get some idea of the logic of divine images, their creation and worship, from this perception of reality and the world we live in as a paradoxical matrix. Things necessarily exist in two potential states. Secular and divine. Finite and infinite. Changeable and unchangeable. Sacred and Profane. These two states exist at the same time. It is a matter of understanding, which allows us to know that what belongs to the secular world, is also divine; that what is finite is also infinite; that what is subject to change also belongs to the realm of the unchanging; and that we can find elements of the sacred in the profane.  And, since the world of change is an illusion, so too are living and generated beings.

 

Formerly I've contrasted reality itself with the world of existence, which is, according to this way of looking at things, not truly real. It is sometimes useful to look at this contrast the other way round, in which the transcendently real world is the only one which has existence. This makes it possible to characterise the world of space and time as one which does not have real existence, only the appearance of existence to us.

 

However real things and people seem to be in space and time, they come to be and pass away, and do not abide. We think it has real existence of a kind because it has a form of consistency about it, in that physical laws exist and operate in it, and mathematics and geometry apply. This makes it possible to understand it in terms of a form of reality which has the property of objective existence, which is not dependent on mind. Mind observes it, according to this view, but it has existence apart from mind. 

 

Which brings us to the concept of necessity (anangke), which is key to the understanding of the natural world and the cosmos in Greece. Things which come to be and pass away are subject to it, as well as the objects which move in the heavens. Necessity refers to that force which determines how things behave which are not subject to the operation of the human will. So plants come forth and bloom, human beings are subject to divinely determined fate and destiny, and the planets move inexorably along their paths in the sky. The world of generation is characterised by the presence of necessity: it is a mark of things which have been generated, as opposed to those things which are aspects of unchanging Being.  But this property of the finite is necessarily determined by the infinite, as things which are finite are generated by it. They are patterned accordingly.

 

Greece shares with Assyria the notion that fate is all powerful, and that the destinies of both men and gods have been decreed at the moment of creation. In both cases however, fate and destiny are decreed by the transcendent divine, for the reason that the world of movement and change is an illusion contained within unchanging Being itself. It necessarily contains within it the start and the finish of all things which may take place in the secular view of reality. And Being determines these, according to its nature.

 

Maintaining this view of the division between the real world and the world of illusion, it follows that only the properties and attributes of Being are truly real, and truly existent. So, Being itself is real and existent, and its representations are also real, owing to their possession of its properties and attributes (by virtue of the fact that they are wholes and totalities, etc.). According to this view, things which have come to be are patterned after Being itself, and the Forms, which have divine properties as representations of Being.

 

In assembling lists of things which are pure, which have a common property, or a genealogy of the gods with their properties laid out as epithets which define their perfections and responsibilities, ancient scholars were also listing those things which they understood to be real and to have real existence, and which pointed to the place of creation. By contrast the world of generation contains mainly approximations to those truly real and existent things. These approximations to what is real however can be made perfect by skill, application and the pursuit of divine knowledge, and perfection and divine status can also be accorded to things and individuals by those who already have this knowledge.

 

By a short extension of this idea, it follows that those beings who live in the generated world have their true existence somewhere else. They are born into existence according to their destiny, and leave at the appointed time. Looked at from this point of view, death can be understood as a return to the place where the essential nature of the individual has its reality.

 

None of the foregoing implies belief of any sort. All of it may be teased out of the argument Plato makes about the nature of reality. This outlook is best understood as a doctrinal view, based on logical and philosophical discussion. It would have been subject to questions from neophytes and other philosophers; and would have been occasionally refreshed by interaction with those who understood similar doctrines from other places and cultures.

 

The normative view of religion in Israel for the first half of the first millennium B.C.E is that there was present a form of monotheistic culture and belief, engaged in a struggle with polytheistic ideas within Israel, and with Israel's neighbours in Mesopotamia. In fact we know almost nothing of religion in Israel in that period: there is no solid evidence which can give us reliable information. According to the redacted documents in the Old Testament, dating from the middle years of the  first millennium, it is clear that there was a protracted political struggle taking place for hearts and minds at some point, but most of the objections to polytheism seem to relate to experience of Mesopotamian religious cult and their ideas concerning the gods. Much of this valuable information may therefore post-date the Babylonian exile. 'Thou shall have no other gods before me' might be understood as a purely Israelite sentiment. However, 'I am that which is,' and 'I do not change,' (Malachi) references a philosophical notion of the divine, which we can now see is present in the context of the Mesopotamian divine pantheon.

 

Parts two and three of this work were written first, with the umbrella title of 'Being and Representation in Greece and Assyria.' I came to realise in the course of writing that it was important to make it clear that later discussions of the divine in the early modern period were addressing a much more limited set of concepts of the nature of the divine (which I have referred to as 'properties and attributes' more or less throughout), though these also represented an important subset of discussion of the nature of Being in Greece and Assyria. This early modern discussion represents a significant obstacle in understanding ideas about the divine in the ancient world.

 

Thomas Yaeger, 9th April 2015.

 

Wednesday, 23 December 2020

At Reality's Edge

 

[Some notes I made while I was writing up The Mathematical Origins of the Megalithic Yard in early 2020. The notes conclude with some observations of the importance of the idea of limit in Mesopotamia, and its connection with the Assyrian Sacred Tree, and their notion of kingship.  I could have finished up with a short discussion of Egyptian interest in the idea of limit, particularly since we know (from the Rhind Papyrus) that they used the same method of calculation of Euler's number as in ancient Britain. That discussion with follow later.]


***


It has been twenty two days since I started to write up the article ‘The Mathematical Origins of the Megalithic Yard’ (mid February 2020). In this article, I suggested that those who designed the. circles came to the idea of the megalithic yard of 2.72 feet as the consequence of an interest in infinite series, and particularly those which approach a limit. The most important of these limits is the one which is known as Euler’s number, which, when rounded up from 2.7218… is 2.72.

This limit was first noticed in relatively modern times in the context of the calculation of compound interest, but the number, and the process by which it is arrived at, can be found in many other contexts.

Effectively, the number (when worked out to thousands of places), is the number as it would be found at infinity. So it can stand as an indicator of ultimate limit and of infinity. It is associated with the idea of ‘one’, as I’ve discussed in the article, and also as an irrational equivalent of one, which is a rational whole number.

An irrational counterpart to ‘one’, in a proto-pythagorean community, would have been easy to understand as belonging to a world beyond this one – i.e., a transcendent reality which is more perfect than this world, which is full of irrationality and measures which are incommensurable. The number may have been understood as being irrational to us because it is being represented in our finite world, and not irrational.

It also stood for the edge of our reality, and therefore would have signified the possibility of a joining between the transcendent reality, and our world of physical reality. Finding ways in which the worlds could be joined, and the incommensurate made commensurate, seems to have been a major preoccupation in the Neolithic, as it was also to philosophers and mathematicians in Greece during the second half of the first millennium BCE.

After I finished the article, I wondered how difficult it is to construct a series which will arrive at Euler’s number, how it might have been done, and how long it would take to come to the result.

A little research showed that there were many ways to construct suitable series of numbers, and a geometric calculation could produce a reasonable approximation reasonably quickly, without enormous calculations.  

 We don’t know for certain what base was used for calculations in the British Neolithic, but they were certainly aware of base 10, since they used powers of ten in their construction (ie, instead of a 3,4,5 triangle, they would sometimes use 30,40, 50 as their measures, knowing that the sides would be similarly commensurate after squaring). If they were using the English foot as their basic measure, it is likely they were counting to base 12 (ie, in duodecimal). But the construction of a series only requires whole numbers, arranged as fractions.

1 + 1/100000)^100000 = 2.7182682371923

100,000 is a lot of iterations, so it is unlikely that the determination was done in this way. The process will result in Euler’s number with any consistently generated series.

It can be done geometrically, which is much more practical, and is probably the technique which was used in the Neolithic. Using a sequence such as:

1/2  +  1/4  +  1//8  +  1/16  + ... = 1



Those who generated such a geometrical figure did so knowing that the series converged on a limit from observing the initial results. What they wanted was to find out a reasonably accurate value for the limit itself. The square could therefore be of any size (read as the value ‘one’), and might well have been created in a large field, with the fractions indicated by small stones.

I’ve written elsewhere about the importance given to limits and boundaries in ancient Assyria and Babylonia, particularly in connection with sites connected with the gods, and the rituals for the installation of the gods in Heaven. Sometimes aspects of the design of the Assyrian Sacred Tree were unwrapped, and represented on pavings as lotuses, alternately open and closed. Which is a way of indicating at these edge points that both possibilities are open, and even perhaps that opposing states are commensurate with each other in infinity.

It has already been identified that the Sacred Tree represents a form of limit, and consequently of the nature of divinity which has its true existence in a world beyond the constraints of finitude.  The design of the alternating lotuses also was used to separate the registers of images adjoining the collosal Lamassu statues which guarded the entrances of royal palaces. There was an image of the sacred tree, with two winged genies behind Assurbanipal’s throne, which seems to indicate that the king was understood to embody the transcendent reality which lies behind the world of the here and now.[the identification of the king with the divine reality appears in various royal letters] He is the perfect man, and the very image of God

[March 8, 2020]

 

[ Minor text corrections, Jan 1, 2021]