p-adic mind

TGD stands for Topological GeometroDynamics, a theory of everything due to the Finnish physicist Matti Pitkänen. It is a theory of branes in a specific higher-dimensional space, first published in 1983 (thus preceding even the supermembrane research of the 1980s, let alone the D-brane revolution in string theory of the 1990s). Fundamental particles are actually different topological structures in the branes. These structures can also occur at different discrete scales apart from the one that produces the standard model; these other scales give rise to dark matter. 

Along with providing an explanation for fundamental physical phenomena, more controversially, Pitkänen also wants to use the physics of TGD's other scales to explain paranormal and anomalous phenomena that have been reported by various scientific dissidents. For example, spiritualists often talk about a "subtle body", and Pitkänen proposes that this arises from the "dark matter" excitations associated with the normal visible body. 

He is also interested (as are the most avantgarde string theorists) in grounding TGD mathematically in concepts like Langlands number theory; and also in the ontological identifications that will allow consciousness to be explained. It is these two which provide the occasion for this post. 

In his latest blog post, he asks whether the p-adic algebra of "Witt vectors" can describe both fundamental space-time structures, and play a role in "mathematical cognition". I haven't had time to look at the details at all, but it's very much the kind of proposal that interests me. (Shanna Dobson provides another example, e.g. see her coauthored paper on using "perfectoid diamonds" to model higher-order thought.) 

Anyonic language of thought

Two years ago I mentioned Sati and Schreiber's work on obtaining anyons from M-theory. In the context of the quantum mind, my interest is whether this can provide a model of anyons in the microtubule. 

But another branch of their project is the development of a programming language for anyonic quantum computing, using category-theoretic tools like "HoTT". The way I think about these things, a topos combines some universe of objects (e.g. a set theory) and a logic for reasoning about them, and it's as if they have a K-theory topos in which the objects are the M-theory anyons, and the logic is a theory of quantum data types that you can build from them. 

I'm a little skeptical about the connection - the distinction between physical qubits and logical qubits is a basic one in quantum computing, and I don't see why the M-theoretic details of how they implement anyons, would be particularly relevant for understanding the combinatorial possibilities of anyonic computation. That's software, M-theory is hardware, and you can program without knowing about the hardware of your computer. So I wonder if they were seduced into this digression by the prospect of quantum venture capital; apparently Quantum now rates alongside AI and Crypto, as a buzzword that can pull in some of the billions of dollars constantly seeking profit from technology. 

Nonetheless: if there is something there, maybe it would also be relevant for the nature of cognition implemented by the (hypothetical) natural anyonic computation of the microtubule! You could call it an "anyonic language of thought", after the theory in cognitive science that thought itself, and not just the spoken or written word, has the structure of a language. 

JT gravity

Shortly after Hameroff and Penrose combined their ideas to produce the Orch OR theory, three particle physicists (Ellis, Mavromatos, Nanopoulos) came out with a string-theoretic alternative, in which the microtubule is modelled as a 1+1 dimensional quantum gravitational system.

Thanks to an ideonomy from T.L., I realised that it might be time for another look at their model, as there has been a revolution in 2D quantum gravity since those days, associated with extending holographic duality to "JT gravity". 

My main misgiving is that the microtubule is not actually just a 1+1 dimensional line, it's a 2+1 dimensional cylinder. But perhaps there's an uplift to M theory that adds the extra dimension... 

Comment on Orch OR, I

It's almost ten years since I promised to comment here, on Stuart Hameroff and Roger Penrose's theory of consciousness. But first let me state some of my general views on quantum theories of mind:

1) Subjectively we know that consciousness is a complex unity. For the details, see phenomenological studies of qualia, intentionality, etc. 

2) Given what physics offers us, if we are going to identify that complex unity with something from the physical world, it's apriori likely that entanglement is involved. 

3) The microtubule is a good candidate for the basic locus of biological entanglement, since the entanglement can be wrapped around the cylinder and thereby stabilized against the thermal fluctuations of living matter. 

4) Ultimately one wants a detailed correspondence between the mereology (the structure and composition) of consciousness, and the mereology of the physical quantum mind. (One would want this for a physical theory of mind that is not quantum, too.) 

So, what does their theory of Orchestrated Objective Reduction say? 

a) The neural correlate of consciousness is a quantum state "in layer 5 pyramidal neuron soma and dendrite microtubules. So anywhere in cortex, moving around depending on the task and mode". 

b) The individual tubulins (from which these microtubules are made) get into objective quantum superpositions thanks to molecular dynamics, and then these superpositions are collapsed by an unknown supra-quantum dynamics. 

c) Inter-neuronal quantum dynamics is mediated by dendritic-dendritic gap junctions, which allow direct interactions between the cytoplasm of neighboring cells. 

d) Everything to do with consciousness involves the structure and dynamics of this mobile, multi-neuronal, microtubular quantum state. All the other information processing of the brain is unconscious. 

To be continued... 

Nonabelions I

 As may be seen, the quantum mind idea that I have spent the most time on, is the idea that topological quantum states in microtubules exist and are robust. The mainstream idea of computing by braiding nonabelian anyons was an inspiration; also the idea of a Temperley-Lieb algebra hidden in a triangular lattice of qubits... I think a talk by Michael Freedman was important, but can't seem to find it. 

Anyway, this month there was a bit of hype about "simulated" nonabelions being created in an ordinary quantum computer. Originally I dismissed it as a distraction, but probably I should give it a closer look. So this is the reminder to myself. 

Mathematical advances

Sati and Schreiber have released a paper on cohomology for topological quantum states, and promise another paper on quantum computing in this medium. 

Hyperbole

It would be great if hyperbolic band theory (twitter explications #1 #2) could be applied to the microtubule, whose cylindrical shell is, after all, a kind of crystal, with a repeating fundamental domain (one per tubulin subunit). Unfortunately, a cylinder is geometrically flat, not curved (in the sense of Riemannian geometry)...