Registered: Oct 2003
Posts: 3

Last week I've attended a conference about Hebrew mysticism where Mr. Moshe Idel was invited [Moshe Idel is professor at Hebrew University from Jerusalem and the specialist No.1 in the field]. He talked about enormous influence of hebrew matematical techniques used in Kabbalah [K. is a religious practice which works in a combinatoric way using the numerical correspondence from hebrew alphabet] upon Western european culture. He gives solid "proofs" of this neo-kabbalism found in european writings. Philosophers like G.W. Leibniz, Paul Ricoeur, Umberto Eco or Jacques Derrida, to name only some of them, have a thinking entirely based on numerical systems, thinks Mr. Moshe Idel. In few words, Mr. Idel said that the most interesting ideas in Western culture[even they are artistic or philosophical] were provoked by the influence of a thinking based on numbers(Kabbalah) but I suspect this is a half true because Kabbalah has a lot of CA features. It has generative rules and is working out infinitely. It has only begining but no end and is... computational irreducible.

To see human thinking as a product determined by a dynamical number system is one of the newest views in the history of ideas and therefore I think it requires a very serious investigation. When a researcher like Professor Idel states that the engine of Western culture is a thinking based on numbers we have to take it seriously. Personally, I think that Western culture is the fascinating result of another kind of mathematical mecanism [guess which one ?] and I also strongly believe that NKS could mark a dramatical turn in the interpretation of any cultural fact. I think you'll find this interesting.

Remark: at this address: http://www.hyperorg.com/blogger/mtarchive/001708.html I've found this statement by Jason Cawley:
""Q: When you think about philosophers, which one strikes you as being Wolframian?
A: Hmm. Plato, because of his focus on forms. But Plato thought the forms had to be less detailed and specific than their instances, whereas Wolfram is all about seeing the complexity of forms. [I think he's more like Hegel in the Logic, deriving everything from the simplest of starting points.""

I think we cannot name Wolfram platonist. Plato's world of Ideas is a pure transcendentalist viewpoint. To name a man who's rebuilding the Universe grace to one of the most rationalist principles is a mistake. I think that Wolfram could be named platonist in the same measure in which cellular automaton is a transcendental principle which supports "our" reality. He's more nearer by Hegel but Plato....? The wolframian becoming of the world is quite different from the platonic becoming. Wolfram assumes a formal reality, a reality based on informational impulses. Plato's concrete world is not more than a well done illusion. A very untrustful one. Plato's archetypes are not Wolfram's cellular automata. The platonic archetype is a very static ideal object, the certainty and objectivity of our world is measured and guaranteed by these Forms. An cellular automaton is an dynamical system, always changing itself. Plato's Ideas "live" in eternity in a world beyond us, Wolfram's CA's are all around us. They are not beyond our world, they are our world. Besides, where is the complexity in Plato's archetypes ?

Thank you !

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Registered: Aug 2003
Posts: 712

First just to be clear about who is speaking, where - in the previous, the qualified comparison to Plato is something I said at NKS 2003 in response to a question. The bracketed reference to Hegel is not me speaking, but somebody else reacting to my comment.

If one looks only for single points of similarity, one can find numerous previous thinkers that agree with this or that NKS point. Each also will have differences. Which are viewed as important is a matter of judgment. Obviously the whole NKS point of view is not found in any one predecessor, or they would have said, way back when, what in fact has only been said recently.

That said, here is something of a "reading list" of previous philosophy points that one might relate to NKS.

Whitehead and "process philosophy"
Pierce relating logic to form and ontology
Hegel for dynamic formal structure
Leibniz on interrelated information, complexity from simple laws
Spinoza-esque determinism
Descartes on thinkables (math-like reals), also "vortices" as analogs of network "tangles"
Scholastic realism on math-like formal entities
Augustine on apparent free will with (absolute) foreknowledge, but not for us
Lucretius on complexity from underlying simples, analogy to language
Plato on reality of formal patterns, generating both reals and thoughts
Pythagoreans on underlying math-like primitives
Any number of idealisms that relate things to thoughts

There are also less systematic prior references or analogies. Historically there have been many more or less confused ideas one can relate to universality, or to imagined significance of this or that formal system, linguistic or numerical based. Thus various neo-Platonic, neo-Pythagorean, Kabalist or Hermetic "thought". Which are less independent than some might suppose, but instead have influenced each other, as syncretic literary aftereffects of limited prior philosophical points. Is any one of these the same as NKS, or its basic thought? No, not really.

With some of the more solid philosophy subjects above one will get no more than a loose analogy, or one or two sensible points that are also found in NKS. The more sensible among them, to varying degrees, point away from themselves toward mathematics.

One can just as easily run through a list like that and pick out specific differences, that mark each of the above as different from the views presented in the NKS book.

For example, Whitehead's process philosophy wants to find an intermediary between realized things and abstract thoughts, in the area of dynamics. But "privileges" time in doing so, in a way NKS patterns can, but need not (compare abstract graphs vs. time evolution of CAs). Experiences in Whitehead's sense are also more thoroughly phenomenal (appearences). Otherwise put, NKS patterns are more nearly just structures, posited as "out there".

Or in the case of Pierce, the hot new formal development in his era was continuum infinities as developed by Cantor, while universality was as yet undiscovered. So he winds up tracing many things to continuity, where NKS emphasizes discreteness.

Or with Hegel, the sort of dynamic formal structures he is thinking about are vastly simpler and more uniform than arbitrary NKS formal systems. Although he is associated with it, he didn't come up with the developing formal system idea anyway. Most of it is already there in Fichte, and there are some predecessors clear back to the middle Platonists (as Hegel himself is aware, e.g. in his Logic or his history of philosophy).

Leibniz had monads and also invented binary numbers, but every monad is unique and he wants real infinities of them, point-like rather than enumerably discrete as we think of it today. Augustine wants not just wills apparently free to us but in some sense really free yet foreknowable, which is a "stronger" sense of it but perhaps a more contradictory one. Idealisms may be compatible with NKS thinking about formal patterns, but NKS does not entail idealism since it is also compatible with "realist" formalism, generating thoughts from real formal patterns rather than the other way around.

As a matter of history, each of these is an interesting case, where the question is just what and how much previous thinkers made from points they saw already, when other bits were missing or wrong or have a different position on this or that question.

But is one going to learn NKS from the study of a single one of them? No. To learn NKS one must study NKS, especially the characteristics of the formal systems themselves. By all means look at these things too, for ideas or to understand the history of thought. When you know how to think, they are things worth thinking about. But to train the mind to see things, start with the formal systems themselves.

Suitably generalizing from the math of his era to include simple programs in ours, I'll give Pierce the last word -

The highest kind of observation is the observation of systems, forms, and ideas. No other exercise I know of is half so good for strengthening this faculty as the study of pure mathematical theories, and practice in making ourselves such theories. I would not advise any man to go without reading Hegel's 'Phenomenology of Spirit', but in my opinion as a discipline for the mind it is almost immeasurably inferior to the study of mathematics. - CS Pierce

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Registered: Aug 2003
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As for the point of similarity with Plato, I suppose that may not be obvious. What is rule 30? It is an abstract system, obviously. It is not its instantiation in the hunks of silicon on my desk. It is a pattern in those certainly, also in any other instance. It supervenes over its instances. We say it is abstract, or mathlike, or software, or formal. These are all various ways of pointing to the same thing about it.

But if there is a real natural system governed by some rule, it is not just an abstraction for our thinking. It is a real pattern in things, that yes we manage to read out of things by modeling, but that is also really there and makes the natural system what it is, behaving how it behaves, etc. In the view put forward in the NKS book, moreover, there isn't at bottom anything else real. (Ontologically, all the fundamental physics rule will use is some network form, a pre-space abstract kind that generates even space as an emergent pattern we discern in a network where our sense of space is not yet present). A formal system accounts for everything we experience. All the patterns we see are subsidiary possible patterns within it. Some limited subset of possible patterns is instantiated, we call that "actuality".

So, abstract patterns in things are real, are the discernables. Our modeling proceeds in terms of abstractions for the best possible reason - that is what there is. Now, I immediately allowed a point of difference. Plato wanted to account for stable essences in particulars this way, by real formal patterns that repeat from particular instance to particular instance. He allowed the particulars to be "imperfect" with respect to those patterns. But he thought that this way he could reduce the multiplicity of particulars to a smaller set of generating universals, that would be simpler than all the instances.

In NKS thinking, on the other hand, the universe is some one instance of a formal system. (The universe is the particular). In principle, the space of possible formal systems of the NKS type is much vaster. (There is possible universe rule n, and n+1, and n+2, etc). Actuality is a tiny selection out of a larger formal possibility space. Particularity is not more numerous than abstraction, it is a special case subset. Clearly, that is a different role for the reality of formal abstractions than in Plato. But it is reality for formal abstraction; that much they have in common. That was the thought behind my Plato comment at NKS 2003, that the blogger reports (without much context).

I hope this helps.

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Registered: Oct 2003
Posts: 69

Vasile Gheorghiu writes:

To see human thinking as a product determined by a dynamical number system is one of the newest views in the history of ideas and therefore I think it requires a very serious investigation. When a researcher like Professor Idel states that the engine of Western culture is a thinking based on numbers we have to take it seriously.

Comment:

Moshe Idel's views accord perfectly with the research findings of the late (d. 1996) Icelandic scholar Einar Pálsson as set forth in an eleven-volume set on 'The Roots of Icelandic Culture', based on a half-century of research.

Salient aspects of Pálsson's findings are detailed in three English-language books:

1. The Sacred Triangle of Pagan Iceland, Reykjavik, Iceland, 1993. ISBN 9979-60-046-2.

2. Evil and the Earth - The Symbolic Background of Mörðr Valgarðsson in Njáls Saga - A Study in Medieval Allegory, Reykjavik, 1994. ISBN 9979-9117-0-0.

3. Allegory in Njáls Saga and its Basis in Pythagorean Thought, Reykjavik, 1998. ISBN 9979-9117-2-7.

Anyone interested can order copies of these books from the University of Iceland Student Bookstore - their email address is boksala@boksala.is.

Gunnar

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