Donald Hoffman's search for a mathematical theory of consciousness

[Pantalaimon]

In a previous installment of the "Beyond Us" interview series, Donald Hoffman talks about his wish to find / develop a mathematical theory of consciousness (the segment starts at 20:41).



Could it be that he's following a red herring, that such an exact mathematical theory of consciousness cannot be found in principle, since mathematics is part of consciousness and as such cannot be used to either encompassingly or correctly describe itself (by following Goedel's incompleteness theorem)? Or would it be feasible to model the behaviour of consciousness by formulating an approximate theory without falling prey to the incompleteness theorem?

I'm eager to hear your thoughts about this. Have a good day!

[Ben Iscatus]

I share your intuition, Pantalaimon. To my way of thinking, you can't describe consciousness in terms of something that derives from it. It would be like describing an ocean in terms of the number and variety of fish it contains (and he does strike me as a bit of a cold fish). I baulk when he continually makes statements like, "without the maths, it's all handwaving". Yet he's not even a mathematician. Odd.

[SanteriSatama]

Could it be that he's following a red herring, that such an exact mathematical theory of consciousness cannot be found in principle, since mathematics is part of consciousness and as such cannot be used to either encompassingly or correctly describe itself (by following Goedel's incompleteness theorem)? Or would it be feasible to model the behaviour of consciousness by formulating an approximate theory without falling prey to the incompleteness theorem?

I'm eager to hear your thoughts about this. Have a good day!

To be precise, Hoffman is not calling for mathematical theory that consciousness could be reduced to, but such that could generate or at least supervene the appearance of physical world in consciousness. So, in essence, what he's asking for is a programming language of Matrix/Universe creation.

And that's kind of what mathematical physics has been doing all along, the basic twist is just the replace the philosophical presupposition of describing to creating. Thus measurement problem of quantum physics becomes ethical choice of finding better theories of math to measure/decohere (those terms are synonyms in this context) superposition of all possible worlds (such that life like us can inhabit and experience) into better worlds to experience.

An important notion here is implicate order, as the far out complex implications of the standard theories, as well as alternatives and heretics and evolution of math play same part in how we cocreate this world, both the consensual and parallel realities which Relational Quantum Mechanics already accepts to some degree.

Obviously, the situation is very fuzzy for various reasons, the implicate complexity is too complex for even a strong mind melt deep work to fully comprehend in full detail, and possibility of evolution requires that the process is not reducible to very limiting axioms of deterministic mechanics, but stays fundamentally incomplete and open - Gödel's incompleteness theorem makes this explicit.

So, my main criticism to what was said in the discussion, is that "mathematical exactness" is not a well defined concept at least in this context. In my own approach to foundations of mathematics, I've made a distinction between definite and indefinite areas of mathematics. They are in complementary relation, definite area (such as rational domain with exact numerical values), roughly corresponding to static states and the notion of discrete, and indefinite (e.g. undecidability of Halting problem and relational operators as such) corresponding to processes and the notion of continuity. Despite the complementary character, there's also dependence hierarchy. As Zeno showed, continuity can't be reduced to discrete. On the other hand I've found out that discrete structures can be constructed from continua fairly easily, when starting construction of math with only relational operators < and > in the tool box.

The current state of set theoretical ontology, as observed and theorized by Badiou, is highly unsatisfactory in many regards. The problems of set theory can't be solved on the same level as they have been created, radically more coherent and honest foundational approach is necessary.

PS: if anyone thinks it would be worth the effort and knows how to contact and communicate with Donald Hoffman, it would be OK by me to share my thoughts with him in the spirit of constructive dialogue. Writing in longer and more formal form of "official" publications is a very big challenge for me nowadays for variety of reasons.

[Simon Adams]

This is where I part from some interpretations of idealism, as I have a more Platonic view of where maths comes from. This is distinct from the abstraction of maths which is secondary to consciousness. To me the whole endeavour of maths is to create an abstract reflection of the mathematical forms. The intuitionist take is better than the coherentist version, but even physicists with their crazy multiverse and many worlds theories assume a more transcendent foundation of maths...

[SanteriSatama]

This is where I part from some interpretations of idealism, as I have a more Platonic view of where maths comes from. This is distinct from the abstraction of maths which is secondary to consciousness. To me the whole endeavour of maths is to create an abstract reflection of the mathematical forms. The intuitionist take is better than the coherentist version, but even physicists with their crazy multiverse and many worlds theories assume a more transcendent foundation of maths...

What is 'coherentist version', and how does it differ from intuitionist philosophy of mathematics, which consciously and openly subscribes to some version of idealism?

At least historically, Platonism emphasizes eternalism and immutability of mathematical ontology, intuitionism has more evolutionary view tending IMO more and more towards process philosophy. Undecidability of Halting problem together with Curry-Howard correspondence and some other factors suggests that constructive proof events don't spread to whole eternity of past and future, only to indefinite durations (of past and future, and what else?). . .
A speculation that comes now to mind is that constructive evolutionary structures and how those figure between interplay of MAL level math gods and alters could cease in singularities, where only the creative potential of zero-energy ontology remains based on polarity of basic number-antinumber scheme.

[Cleric K]

PS: if anyone thinks it would be worth the effort and knows how to contact and communicate with Donald Hoffman, it would be OK by me to share my thoughts with him in the spirit of constructive dialogue. Writing in longer and more formal form of "official" publications is a very big challenge for me nowadays for variety of reasons.

Some years ago I exchanged a couple of emails with Don (you can see his email on his website http://www.cogsci.uci.edu/~ddhoff/ )

At that time I was musing on the ideas that I outlined in the metaphor. I wanted to ask him few things but I got the feeling he's not inclined to spend time on general speculations.

Actually I was led to this (the previous) forum in a similar way. Since I don't have any philosophical background, neither I have philosopher friends, I tried to contact few people. Michael Bitbol never responded. Bernardo responded and invited to the forum but apparently he didn't have the time to look in my questions. And I don't blame any of them. I can only imagine how many such emails they have to go through on daily basis.

What I was asking was to be pointed at some current/past philosophical developments that take time in the sense of the metaphor. My thinking was that we don't experience the time flow in certain direction because of some external law (like increasing entropy, etc.) but because this is the only way stream of consciousness can be experienced. For example, in physics we have phase space of all possible states of the universe. Then we have a law that describes the transition from state to state. We as humans, experience the transitions and ask what that law governing the transitions is. We ask this question because we implicitly assume that the universe will make these transitions even if there's no one to observe them - thus there should be a law for the direction and our consciousness only observes the workings of that law. My point was that there's no need for such a law. If we imagine a phase space of states of being, then the only way we can ever experience a stream of existence is if the states progress in integrative way, such that every next state embeds the echo of the previous ones as memory. Even if we hypothesize that the transition to all other states is possible, if they don't correspond to a gradual increment over the former state and don't containing the echo of the chain that led to them, we'll simply have no conscious experience that we can talk about. So it's something like the anthropic principle applied to time/consciousness. It allows us to think of all possible states of being existing simultaneously and experienced in an integrative flow.

I was interested where I can see other's works in the same lines because it's certain that many others have come to these ideas long before me. Unfortunately I still don't know the answer.

~~~

Other than that, as others already pointed out, I'm also on the opinion that strict mathematical theory of consciousness can never be. Donald said that "mathematics are everywhere we look". I see two aspects of this. The first is the more trivial - we see mathematics everywhere because we look at everything through mathematical glasses. A shoemaker might view the whole reality as different metamorphoses of the Archetypal Shoe. A painter can see everything as canvases and paint strokes. We see in reality whatever concepts and ideas we project over the perceptions. This is the more superficial aspect.

The deeper aspect is that mathematics is the closest we can get to clean experience of the spiritual realm through intellectual thinking. In pure thinking (mathematics included) we are already living in the spiritual world. In mathematics we find thinking that supports itself, it's the object of itself, independent of sensory and other perceptions. The mathematical thoughts are determined through their inner relations. This is a prelude to what the ego secretly yearns for but has not yet the courage to approach - the wider spiritual world, of which mathematical thinking is only a rigidified instance. In our ordinary consciousness perceptions and concepts are somewhat orthogonal - we connect them together but we can't say that they are organically connected (except for the perceptions of our own thinking). That's the intuitive reason to assume our concepts are only representations of reality (the 'real' thing causing the perceptions). And this is natural, the concepts seem like inert mineral-like entities. It is only through our own thinking that they are set in motion and connected to perceptions. We have no reason to assume concepts/ideas as having some creative role.

In the Imaginative realm we find concepts in their more fundamental essence, as creative processes/beings and we directly perceive how ideas shape the perceptual world. The difference is marked. In our ordinary state our concepts are only like frozen extracts of the higher realm that are completely dead and motionless if it was not that we move them through our thinking. The living idea processes have life of their own, they are moving themselves, without any action on our part. And it's for this reason that we can perceive how they are also transforming the perceptual elements. They are no longer orthogonal inert elements that can be related only through our activity but the perceptual elements reflect the life of the living ideas.

For example, if in ordinary consciousness I experience hunger, I attach the abstract concept of 'hunger' to this feeling. To me it seems only as a representational label for some 'real' process for which I have perception (the feeling of hunger). In the Imaginative world I find the actual being of hunger, which in my ordinary state precipitates only as a concept, an idea. In the higher world hunger is an active, living idea/being, interacting with other processes/beings, for example activating salivation, attracting the images of my favorite food etc.

[Simon Adams]

What is 'coherentist version', and how does it differ from intuitionist philosophy of mathematics, which consciously and openly subscribes to some version of idealism?

I may well be using the term coherentism incorrectly , but I’m referring to people who think that nature is not mathematical, and that maths is just a tool we have invented to describe the patterns of nature. It’s the far opposite view from the platonic one, with intuitionism being a kind of half way view to my thinking.

At least historically, Platonism emphasizes eternalism and immutability of mathematical ontology, intuitionism has more evolutionary view tending IMO more and more towards process philosophy. Undecidability of Halting problem together with Curry-Howard correspondence and some other factors suggests that constructive proof events don't spread to whole eternity of past and future, only to indefinite durations (of past and future, and what else?). . .

So this is my distinction between the activity/process we do we call maths, and what I mean by platonic maths as the real foundation, the reason why our abstract shadow of it works. I don’t expect our constructed proofs to be transcendent, but the mathematical forms are, and allow us to create the proofs. Does that make sense?

A speculation that comes now to mind is that constructive evolutionary structures and how those figure between interplay of MAL level math gods and alters could cease in singularities, where only the creative potential of zero-energy ontology remains based on polarity of basic number-antinumber scheme.

This is where our different forms of idealism come to a head, because I don’t see MAL as god. I see maths as entwined in the language of creation, and I see MAL as created.

[SanteriSatama]

I may well be using the term coherentism incorrectly , but I’m referring to people who think that nature is not mathematical, and that maths is just a tool we have invented to describe the patterns of nature. It’s the far opposite view from the platonic one, with intuitionism being a kind of half way view to my thinking.

It's a new term for me, so I can't tell. I'm familiar with the materialist narrative you are referring to, good to have a word for that and keep learning. Coherentism in that sense is closely associatied with Hilbert's formalism and materialism/physicalism.

So this is my distinction between the activity/process we do we call maths, and what I mean by platonic maths as the real foundation, the reason why our abstract shadow of it works. I don’t expect our constructed proofs to be transcendent, but the mathematical forms are, and allow us to create the proofs. Does that make sense?

Some sense, yes. My experience with the intuitions suggests that in good case constructed proofs and objects are - and should be result of two-way intuitive communication between subjective/constructive and transcendental. Dynamic, evolutionary holography with both top down and bottom up communication, and of course peer-to-peer. Also the transcendental level evolves in this view, at least to large extent, through participation of heuristic subroutines of "alters" or whatever the term. My thoughts on what elements are keepers and what evolving and deconstructable have not gone very far in details.

This is where our different forms of idealism come to a head, because I don’t see MAL as god. I see maths as entwined in the language of creation, and I see MAL as created.

I use the term 'god' in a very loose sense. I'm not religious, just animist, so no basic problem with created gods/MAL/higher selves etc. fancy words. Creating a tulpa doesn't make it less real, though.

[SanteriSatama]

Some years ago I exchanged a couple of emails with Don (you can see his email on his website http://www.cogsci.uci.edu/~ddhoff/ )

Thanks!

I've become more and more wary of trying to push my thoughts in the social sphere. There's still need to try to express and share them, to keep them at least evolving, and casual chitty-chatty way on supportive forum like this is very good. for that purpose. For a degree of more serious/pro level dialogue, there could be also a time and place for that, and I wanted to test if there's any pull towards such possibility now.

I'll respond to the rest of your post later if I find anything worth to say.

[AshvinP]

PS: if anyone thinks it would be worth the effort and knows how to contact and communicate with Donald Hoffman, it would be OK by me to share my thoughts with him in the spirit of constructive dialogue. Writing in longer and more formal form of "official" publications is a very big challenge for me nowadays for variety of reasons.

Some years ago I exchanged a couple of emails with Don (you can see his email on his website http://www.cogsci.uci.edu/~ddhoff/ )

At that time I was musing on the ideas that I outlined in the metaphor. I wanted to ask him few things but I got the feeling he's not inclined to spend time on general speculations.

So he never responded? I really want to get him in a discussion with JP, who is very interested in challenging the idea of 'world as objects' and promoting the idea of 'world as function-value-meaning', and of course metaphysical idealism which Hoffman could revitalize through his rigorous scientific approach.