Thoughts about this Bayesian Mechanics paper?

[Fra]

TL;DR Summary

self-organising system that looks as if it is modelling its embedding environment

Looking for something else I just stumbled over this paper the declare as introducing a field they call "bayesian mechanics".

I thought I would create a new thread for a change and just highlight this paper. It's the first time I've seen this from the authors so I don't have their full perspective yet, but I share many of hte overall ideas but see one issue of jumping right into continuum models, which i fear will cause problems later. Parts of the paper also made me think of Demystifiers solipsist HV.

On Bayesian Mechanics: A Physics of and by Beliefs

"The aim of this paper is to introduce a field of study that has emerged over the last decade called Bayesian mechanics. Bayesian mechanics is a probabilistic mechanics, comprising tools that enable us to model systems endowed with a particular partition (i.e., into particles), where the internal states (or the trajectories of internal states) of a particular system encode the parameters of beliefs about external states (or their trajectories). These tools allow us to write down mechanical theories for systems that look as if they are estimating posterior probability distributions over the causes of their sensory states. This provides a formal language for modelling the constraints, forces, potentials, and other quantities determining the dynamics of such systems, especially as they entail dynamics on a space of beliefs (i.e., on a statistical manifold)
...
Bayesian mechanics is premised on the conjugation of the dynamics of the beliefs of a system (i.e., their time evolution in a space of beliefs) and the physical dynamics of the system encoding those beliefs (i.e., their time evolution in a space of possible states of trajectories) [6, 2]; the resulting mathematical structure is known as a \conjugate information geometry" in [1], where one should note that \conjugate" is a synonym for \adjoint" or \dual"). Using the tools of Bayesian mechanics, we can form mechanical theories for a self-organising system that looks as if it is modelling its embedding environment. Thus, Bayesian mechanics describes the image of a physical system as a flow in a conjugate space of probabilistic beliefs held by the system, and describes the systematic relationships between both perspectives."

-- https://arxiv.org/abs/2205.11543, there are several authors of the paper

/Fredrik

 

[Fra]

Apparently this path isn't very appealing for most here. Not sure if it's because of the early conceptual state with not not so much mature mathematics, or if the conceptual points come accross as strange.

I think it might be instructive to compare some of the key conceptual ideas in the above paper with say Bohrs conceptual ideas, I'm not sure if this helps see the promises of this research path.

Here is a train of tought...

1. Bohrs view was that the quantum description is essentially defined using a "classical context". You simply can not encode a quantum state, without the classical context. So without classical world, there is no quantum theory.
   (An objection here might be that, as quantum mechanics replaces classical mechanics, so there is no "classical world", so why should be need concepts of the "outdated world" to describe the new picture, this seems silly? A solution there would be to replace the word "classical context" with "macroscopic context" and a decoherence view, rooted essentially an asymptotic classical context. But I think that is an ugly solution, as it explains nothing, it just moves the problem around (or away to asymptotics, which later begs again for explanations. I think we can do better).
2. I see a good motivation for Bohrs stance from the perspective of inference. I see Bohrs idea having nothing todo with thinking that "classical physics" is fundamental, I see it more that in order to make a precise statistical inference about something that is seemingly random, you need a reliable way to
   stora empirical data, otherwise one will not be able to arrive at a stable statistical prediction. This means a irreversible and stable memory, that different physicists can also "read" without changing things. This is the purpose the "classical context" is. A sort of, to all observers, a shared stable, memory storing observations of the quantum system.
3. The idealisation implicit in (2) is clearly acceptable FAPP, when it comes to macrocopic experimental laboratories studying molecular, atomic or subatomic scale phenomena. The experimental data are indeed stored FAPP irreversible in classical pointer states, that can be communicated, copied around between observers with classical communication.
4. The problems start when the idealizations(3) no longer holds. This happens when,
   a) the "observer" - which as per Bohr must be part of a shared classical memory, becomes part of a "quantum description". Then there is a conceptual conflict. Because we need to describe the "action of an observer", how do we construct this hamiltonian?
   b) the "observer" is smaller than the quantum system itself, in terms of complexity and information capacity, this is the case for cosmology. Instead of a dominant lab probing atomic scale things, with 100% control of the environment. The observer is "living" inside the system of study! This clearly breaks the assumptions.
5. I think the insight of the paper, is that in the general case - ie an observer not obeying the idealisations(3) - that we need to replace the "classical context" that was so critical with Bohr with something else - what? The idea here is - we replace it with th observers/agents own internal state, what the paper refers to as "the internal states (or the trajectories of internal states) of a particular system encode the parameters of beliefs about external states". This means that the NEW theory we seek (improvement to QM), that Bohr insistent must be formulated in terms of classical information/cotext, here must be formulated and constructed using the only thing that is at hand - the observers own internal state!
6. Which comes to the next thing, what is the origin of the exact stracuture of classical reality in the first place? say 4D spactime? why 4D? This can help there too, the paper above says "self-organising system that looks as if it is modelling its embedding environment." and conceptually this means, by implication, that "effective classical reality" can perhaps be explained, from a low level, by considering interacting self-organising systems (agents, which is of course just matter). So my conclusion is that the benefit of this is this. But generalisting the notion of "observer" beyond the "classical observer", we can perhaps gain new explanatory power to explain the actual structure of the "classical observer" itself as some sort of steady state.
7. The question is then howto realized this with explicit mathematics and algorithms. But noone will bother sort this out until the potential benefits are conceptually comprehensible, right? This is the step we are at right now.

/Fredrik

 

[mattt]

I think something along these lines will be the next step in the far future: to show that the dynamics of part of our scientific description of the interior of our brains/nervous system, is "isomorfic" to our Experiential/Phenomenological Space, and a smaller subset of it, "isomorfic" to our mathematical descriptions of Physics, (which is part of our phenomenological/experiential space).

I think this will be achieved in the far future and possibly nothing fundamentally new (Physics-wise) will be required to accomplish it. (That will also "evaporate" the Hard Problem of Consciousness, by the way).

I also think that the fundamental reason why we have not yet achieved something like this today, is that the appropriate mathematical description of our fenomenological states just doesn't admit a sufficiently coarse-grained description (and our conscious states are ill-prepared to manage/ represent extremely complex (in the information theory sense) mathematical descriptions of states).

 

[Fra]

I can follow what you mean, and I largely agree, but talking about brains in this context tend to create confusion, especially for anyone that doesn't already conceptually see the ~"isomorphisms" and jump into the conclusions just like all those that mix up the abstraction of an observer with a "human", so I prefer to keep it at the relevant abstractions.

I think something along these lines will be the next step in the far future: to show that the dynamics of part of our scientific description of the interior of our brains/nervous system, is "isomorfic" to our Experiential/Phenomenological Space, and a smaller subset of it, "isomorfic" to our mathematical descriptions of Physics, (which is part of our phenomenological/experiential space).

Yes, I see that physical interactions and inference as two perspectives of the same thing. The inside view is inference as a self-preserving survival gaming strategy which is almost tautological, as only self-preserving systems would be ambigous in nature, although nothing needs to be "banned" by constraints. The external view is physical interactions, which is more descriptive. Both views overlap however, as in practice the descriptive view is the result of an inference(abduction) as well, except from a dominant perspective, or limiting case. So the descriptive physics becomes and increasingly stable "expectation" of the interactions of a part of the environment. But the limit itself is a fiction, thus we should not achor the explanatory power in this limit. This is what causes problems, finetuning, renormalizations require fine tuning etc etc.

I think this will be achieved in the far future and possibly nothing fundamentally new (Physics-wise) will be required to accomplish it. (That will also "evaporate" the Hard Problem of Consciousness, by the way).

I agree there is indeed a striking similarity here

"why and how humans have qualia or phenomenal experiences"
vs
"why and how does an inside observer encode and experience information about the environment"

A "soft" answer to the latter is I think effectively that we can explain via decoherence that a small system (measurement device) can respond to the environment in a way that mimics a collapse and information update, but that explanation uses information in the bigger context, that in the extrem becomes too large that leads to fine tuning. The understanding from the inside, still lacks. Analogous to the hard problem vs soft problem.

I also think that the fundamental reason why we have not yet achieved something like this today, is that the appropriate mathematical description of our fenomenological states just doesn't admit a sufficiently coarse-grained description (and our conscious states are ill-prepared to manage/ represent extremely complex (in the information theory sense) mathematical descriptions of states).

I think a new paradigm is required. The modern paradigm of descripting physical theory invariably leads to "effective theories". This is nothing bad per see, but the difference is like the difference between the result of an inference, and the process of the inference itself. The former is descriptive, the latter is more algorithmic in nature I think.

/Fredrik