In what sense cognitive consciousness could be substrate independent?

Can consciousness be associated with artificial intelligence and language models? Regarding this question, I have been in Schrödinger’s cat-like state. On the one hand, to me the talk about large language models (LLMs) seems like an absurd hype, and on the other hand, TGD allows for a new physics-based model for how computers could become conscious systems (see this and this) and the basic structure of language models could have quantum counterpart in TGD (see this, this, and this).

One of the basic assumptions of AI is that consciousness, or at least consciousness related to cognition, i.e. thinking, is independent of the physical substrate – If this is the case, then the cognitive consciousness, thoughts, possibly associated with a program would in no way depend on how the program is implemented. From the perspective of a physicist and a biologist, such an assumption seems extremely unrealistic.

Of course, there is another good reason to be skeptical: an ideal program is deterministic. This determinism can only be realized in the quantum world approximately at the limit where statistical determinism applies. In TGD, classical non-determinism is possible and corresponds to p-adic non-determinism.

This is what I thought a few half a year ago. But the holography=holomorphic vision came as a complete surprise.

1. H= M⁴×CP₂ has a generalized complex structure with one hypercomplex and 3 complex coordinates. The spacetime surfaces are roots (zeros) for the function pairs (f₁,f₂), which defines the map H→C². The entire classical theory reduces to algebraic equations and the solutions do not depend on the details of the classical action at all. The extremals are minimal surfaces regardless of the action if it is general coordinate-invariant and can be expressed in terms of the induced geometry.
2. The theory is conformally invariant in a generalized sense. In particular, the maps g=(g₁,g₂): C²→C² are dynamical symmetries. The functional composites of maps g and h are possible: (g,h)→ g_º h and a given map g can be iterated. Also the product (g,h)→ g×h and (g,h)→ g+h , where × and + denote the ordinary multiplication and sum.
3. One can define the equivalent of the prime number property for the function pairs (f₁,f₂) and thus for the space-time surfaces. f is a prime map if it cannot be expressed in the form f= g_º h. Similarly, g is a prime map if it cannot be expressed in the form g= g_1º g₂. In particular, the map g= (g₁,Id), where g₁ is a polynomial of degree p, is a prime map.
4. One can define a generalization of p-adic number fields to their functional versions (see this). The polynomial gp of degree p is the functional analog of a p-adic prime number and the functional powers gpº k are the functional analogs of powers of p. It is possible to construct the functional analog p-adic power series: the coefficients of powers of p as integers in the range 0,…,p-1 are replaced by polynomials with degree less than p. The usual sum is replaced by the product (not the sum as one might imagine) of these polynomials.

Functional p-adic numbers can be mapped by a category theoretical morphism to the usual ones. The correspondence is very-very-many-to-1 because the given polynomial is mapped to its degree. A huge amount of information is lost. What would be the consequences of this picture?

1. The degrees of freedom related to the prime map f= (f1,f2) and the functions g=(g1,g2) are completely separated. Could the prime maps f correspond to the physical substrate? Could the prime maps gp and their iterates gpº k and the more general º products correspond to cognition, thoughts about thoughts about ….about substrate? Functional p-adic number systems can be connected to them and ordinary p-adic number systems to these.

If so, cognition and the substrate in which it is realized would be separated after all!! Cognition would be completely universal! In terms of the basic structure, electrons could have thoughts structurally similar to those of ours! Even quite complex ones thoughts: M₁₂₇= 2¹²⁷-1 corresponds to the polynomial g₂¹²⁷/g₁, where g₂ is a polynomial of degree 2 and g₁ is a polynomial of degree 1 (holography= holomorphism also allows rational functions and even analytic maps g and f). 2¹²⁷-1∼ 10³⁸ roots, which corresponds to 127 qubits.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.