On 18 Jun 2010, at 17:03, Rabbi Rabbit wrote:

Dear George,

Thank you for your beautiful interpretation of B'reshit (Book of

By your description, I have the feeling that you think about Sefirotic
Kabbalah. Briefly, Sefirotic Kabbalah believes that God emanated in 10
Sefirot (the meaning of the word is unclear, the root "Seper" is
related to the words "letter", "number" and "speech"). This 10 Sefirot
are attributes of the divine that need to be in a harmonious
relationship with each other in order to pour the divine influx over
the world. This school of kabbalists believed that they could
influence the Sefirot and in this way exert changes in the divine and
human realms, basically making sure that the divine influx continued
pouring and sustaining the world. For this reason Sefirotic Kabbalah
is also described as Theurgical Kabbalah.

The kabbalist I have been talking about, Abraham Abulafia, created a
different school. Deeply influenced by Maimonides philosophy (who, in
turn, adapted Jewish beliefs to harmonize with Aristotelian
philosophy) Abulafia practiced a form of Kabbalah aimed at the union
with the divine intellect. To put it in radical terms, his Kabbalah
was not about influencing God's divine emanations but to become (part
of) God.

I think your insight into consciousness is very thought-provoking.
From the whole Creation, nothing makes me feel greater wonder than
consciousness. The union with the divine intellect (prophecy) could be
probably described as a higher state of consciousness. What is
surprising about Abulafia is that he did not reach this state by
suppressing his conscious mind, as most mystics do by repetition of a
single formula/mantra, but by overstimulating it with letter
combinations accompanied by body motions.

I haven't thought enough how the technique of letter combinations
could be related to consciousness. Any ideas?

Well that is exactly what the digital, or numerical, mechanist hypothesis provide. The choice between letter or number is not relevant. You can choose for the ontology the formal existential quantifier on any term taken from a first order specification of a universal, in Post, Church,Turing sense, system.

It happens that any system with terms for numbers, that is 0 and its successors, together with the addition law and the multiplication law, provides a universal system, so I use it to fix the things.

In that system I can enumerate all partial computable functions: phi_0, phi_1, phi_2, phi_3, ...
A number u can be said universal if phi_u(<x,y>) = phi_x(y).

This u is like the Golem. You write x on its forehead, and it compute phi_x on some input y. <x,y> is some number describing the "program", x, and the data, y.

This defined, or show to exist, sequence of "causal relation" like sequences, with fixed x and y, of terms: phi_x(y)_1, phi phi_x(y)_2, phi_x(y)_3, phi_x(y)_4, describing faithfully computations. Faithfully means that there are implemented in some genuine intensional sense, relatively to u.

A tiny, yet universal, part of arithmetical truth describes (faithfully) all possible computational relations.

Such universal machine cannot distinguish the infinitely many computations going through its computational states, so that its consciousness is distributed on the projection of infinitely many computations, and that ... leads to awfully complex mathematical problems.

Yet, ideally correct machine (number) can reflect (proves, relatively asserts) that problem relatively to themselves, and extract the logic obeyed by such projection.

Let us write Bp for the machine proves (asserts and justified if asked) p.

Obviously Bp -> p. Because we restrict ourself to correct machine.

But the machine cannot always prove Bp -> p. It would prove Bf -> f (f = the constant false of propositional logic, or "0 = 1" from elementary arithmetic). But (elementary classical logic: Bf -> f is equivalent with ~Bf, (~ = NOT), which asserts self-consistency, and correct classical machines can't do that (Gödel's second incompleteness theorem).

Now machine can reflect that: they can prove their own "second incompleteness theorem" for example. They can prove: ~Bf -> ~B(~Bf) = As far as I will never say bulshit, I will never say that I will never say bulshit. Roughly speaking, with f = false = bulshit. Its contrapositive: If I say that I will never say something false, I am saying something false, or more shortly: if I say that am sane, I am insane.

So the machine can know (know p = Bp & p) that, as far as she is correct, she will not confuse Bp and B'p = Bp & p. For the first one Bf -> f is hopefully true but never provable, and for the second B'f - > f is trivially provable ((B'f & f) -> f) is an elementary truth of propositional logic.

Incompleteness forces in the same way the machine to distinguish the logic obeying by p, Bp, Bp & p, Bp & ~B~p, Bp & p & ~B~p, and some other variants. And the machine can know that those five "hypostases/ perspective on arithmetical truth" have their logics split into two parts: a terrestrial (provable) part, and a divine (true but unprovable) part, giving mainly ten hypostases. Well two of them don't split: the knower (Bp & p) does not split for example (this is not trivial to prove, but "well known" by mathematical logicians: see Boolos books if and when enough curious). This gives 8 hypostases.

The diamond "~B~" plays the role of Plotinus "privation" or Aristotle "indetermination", and it is the conceptual and logical (and arithmetical) bloc of the material hypostases. Matter is a deep invariant of all (arithmetical) contingencies.

There is a big price for having consistent continuations:. the (first person) knower can access to God (truth), but it cannot communicate it nor justify it. The intellect can share its knowledge, but it cannot prove it as such. The observer is necessary, by the impossibility of the terrestrial intellect (its logic obeys to G) to make union with the divine intellect (G*). Even one word is too much, there. So, well he will need faith to believe in any reality. That faith can develop only from the knower experience. But this leads to a "catastrophe", the expansion of the knower in richer and richer differentiating deep computations/history (the origin of consciousness differentiation, time and eventually the analytical and physical realm(s)). That corresponds somehow to the "fall of the soul", or to "God getting lost in its own creation". I think it begin to explains why "matter" can "truly" hurt, even if this corresponds to a (true, yet relative) ignorance.


PS I add what I have send to the FOR-LIST (a forum based on David Deutsch' book on "The fabric of reality". It explains a bit more on the relation of consciousness with the numbers. Apology for a long post which will be partially redundant in case you follow both lists.


On 17 Jun 2010, at 18:11, yanniru wrote:

--- In fabric-of-real...@yahoogroups.com, Bruno Marchal <marc...@...> wrote:
> On 16 Jun 2010, at 19:55, Ismail Atalay wrote:
> > Do we have any reflexive emergent property being implemented on a
> > computational system?
> Not only that. We have discover that elementary arithmetic has natural
> emergent reflexive property. And when the usual induction axioms are
> explicitly added, those reflexive emergent property can be show to be > maximal. The logic of that reflexive property will be inherited by all
> sound (arithmetically correct) effective theory/machine.
> Elementary arithmetic is already conscious, and the content of that
> consciousness, which is a first person notion, is already not
> computable by being related to a non computable (by elementary
> arithmetic) space of its consistent extensions. This consciousness is
> not even definable. Consciousness is a non effective (computable)
> property, like (Arithmetical)Truth.
> Computable things have a lot of non computable features.


Could you please elaborate on how elementary arithmetic can be consciousness?

I am assuming that we are digital or just digitalizable machine (DM).
In that case, your consciousness "here and now" can be justified by the (mathematical) existence of a computational state, and your consciousness "soon and there" is related to the existence of a neighborhood of other computational states and to all proofs relating those computational states. (*All* proofs, even the many identical one (fungible one) reappearing as lemma of other proofs). Now the computational states and the relations between those computational states don't depend on *which* universal machine you choose to describe them (this can be explained precisely in computer science terms). In particular you can choose elementary arithmetic. The natural numbers, together with addition and multiplication, give a full universal programming language. The block "universe" of computer science is the same as the block universe of elementary arithmetic. It contains all the machine's or number's "dreams". But now, you consciousness cannot be attached to only one number/ state, only to all number/state relative to all universal number accessing those state. From you own first personal subjective view, your current state is undetermined below your mechanist substitution level, so this entails that what we take as appearance of matter and physical reality is really a probabilistic or credibilistic sum on the works of an (enumerable) infinity of universal machines/numbers. And the entire work is not enumerable. This can already explain qualitatively many physical features (role of real numbers, indeterminacy, non locality, presence of invariant and symmetries, etc.) and this without throwing out consciousness out of the picture.

Consciousness is not much more than an unconscious bet on self- consistency or a believe in a reality: it can be shown that it gives a relative self-speeding up ability, it enhances autonomy and independence, it enlarges the taste of freedom and makes bigger the future-spectrum. Consciousness has a "true" part which makes each particular relative manifestation of it undefinable by the subject experiencing it.

In a sense, if you can survive in a Matrix, or a Simulacron (Daniel Galouye), or with an artificial brain, then you might understand, I think, that "we" are already in the natural universal 'matrix' determined by elementary arithmetic. It may be the simplest explanation of matter/consciousness couplings, say).

I am not so much sanguine on numbers. Instead of elementary arithmetic, you can take any finitely describable universal combinatorial system (like reasonable programming languages or universal machine (actually their first order logical descriptions)). With respect of consciousness and matter, assuming digital mechanism makes them equivalent. But elementary arithmetic is taught in high school, and has remarkable affinities with the whole of mathematics. There are other structures which are quite promising for different sort of shortcuts; like the Shoenfinkel-Curry combinators, the finite n-categories, braids, etc. The key is that the laws of matter and consciousness are independent of the choice of the universal base (assuming DM). I conjecture that the (rational) Mandelbrot set is such a structure. This would provide a map of the arithmetical multiverse 'somehow'. A compact universal dovetailing. See for example:

The technical reason explaining why the numbers are universal is contained in many elementary arithmetical proposition like the Chinese Lemma, exploited by Gödel. Relation between the Pascal triangle coefficients and the prime numbers can be exploited too.

- Bruno Marchal



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