Wednesday, December 18, 2024

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. 

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