Donald Hoffman's search for a mathematical theory of consciousness

[SanteriSatama]

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.

Ok, fascinating. Another way to formulate similar question, familiar to physicists, is how unidirectional time experience emerges from palindromic geometric time of QM. I agree with those physicists who say that thermodynamics in current form is poorly formulated woo, and hence by implication, also thermodynamic arrow of time.

My attempt at a more full answer starts from foundational principle of Divinely Integrated Differentiation, which is an ethical axiom that can be stated also this way: All unique has inherent value, and only unique has inherent value. Creating more of the same is not creation, it's mechanical repetition.

Only differences are experienced. And qualities of differences can and do differentiate without end. Smooth and gradual changes, more abrupt polarities, etc. The différance of difference, as Derrida said, of eron erå, as we swedify the the Finnish translation of Derrida's post-structuralist word play exemplification of the qualitative evolutionary principle. Divinely Integrated, because there is the palindromic polarity-symmetry at the bottom of the process. The simplest, most economic way to write the palindromic symmetry is "<>2, both more and less (cf. the notion of interval), and I call that form 'Self'. Self-referentiality is not formalizable in terms of classical logic, as Gödel showed, because it contains relations <, > and =. Notion of equivalence is derived from modal negation neither more nor less, which can be formally written ><, and consequently >=< and >[]<, as we develop static elements of the foundationally dynamic theory. In natural language: If A is neither more nor less than B, then A and B are equivalent (in a given context).

A very natural interpretation of <> is Bergson duration, an open ended process that is neither unity nor multiplicity, but sharing same indefinite quality as undecidability of Halting problem. That is why I call further development of this approach also Mereology of durations and/or Bergson lattice.

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.

There's a critical issue to "mathematics are everywhere we look". If we limit mathematics foundationally or otherwise to quantification, the claim is pure myopia of "to a hammer, everything looks like a nail". If we start and expand math from the more-less relation, we do see that in it's various qualitative differentiation pretty much everywhere, it's wholly natural. Same can't be said of quantification, which is purely metaphysical if postulated as foundational axiom.

[Cleric K]

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.

He did respond to my first email, attached some of his papers. Then I wanted to ask something else, to which I never got response. But that's OK, I'm under no illusion that these professionals have the time to address every random thing that they get. He was polite enough to respond to my first mail.

Don is obviously interested in true mathematical model of reality. My own thinking was more using math as language for pictorial expression. For me these things lie on a scale. The more specific the mathematical structure becomes, the more spiritual activity becomes rigidified in that structure. It's like the spirit creates a complicated irrigation system and then forces itself to flow only through its channels. It could be the case that the channels are so arranged that they reflect fundamental aspects of experience but in the final run the 'truth' of existence can't lie in a mathematical model. It doesn't make sense for everyone to rigidify their spiritual activity in the same irrigation system and call that 'the truth'.

This is one side of the scale. On the other we are moving more towards spiritual perception. It's not about choosing abstract mathematical patterns and mapping them to perceptual experiences but it's more that mathematical thinking itself becomes the reality to be explored. Then mathematics becomes something living, we are moving into the area of sacred geometry and the mystery of number. For example, if we experience a triangle meditatively, we not only have an abstract floating concept but we are able to became aware of certain spiritual forces that flow through us and become concentrated in the object of our concentration. There's something archetypal in the experience of three-foldness. This links with the number three. If we go really deep we can find that the being of 'three' has something to do with the three-foldness of our soul life - thinking, feeling, willing. This also has to do with the three-foldness of space. Just as thinking, feeling and willing are not simply three same things orthogonal to each other, but are gradations, iterations of something more fundamental, so are the three dimensions of space. Only in our superficial age have the dimensions become something purely abstract. In earlier ages the dimensions were still livingly experienced and it'll be our task to find our way again to these living experiences. For example, as the primordial consciousness was diversifying, the first 'dimension' to appear - which was not dimension of space, but dimension of inner experience - was the up/down dimension. Of course up/down doesn't make any sense without the other two dimensions. We should imagine only the qualitive aspect of up/down. The corresponding qualitative experiences of the other two dimensions left/right, front/back still don't exist (or it can be said that they only exist as not yet realized/decohered potential). And unfortunately today this qualitative aspect has been completely lost and not only that but, as it's seen from other threads, there's fierce opposition even to allow ourselves to experience this aspect. In these ancient states of existence, of purely spiritual nature, consciousness attained so to speak a degree of freedom. Metaphorically speaking that's an 'axis'. When the precursor being of man 'looked up' it was experiencing integration of consciousness, bliss and the deeds of higher beings. When it 'looked down' it experienced the abyss and darkness of fragmentation and ultimately unconsciousness. At that stage there are not yet desires, no inner personal life, there's no physical body, no Earth. The conscious life belongs to Cosmic spiritual space. It can be said that 'up' corresponded to something akin to a spiritual Sun and 'down' was away from it, towards the Cosmic abyss. But this has nothing to do with spatial space yet. It's 'space' of inner experience. Man at that stage had life similar to a plant, through his activity he was striving towards the Sun, through integration and harmonization of the living spiritual processes on which his consciousness was carried. In our Earthly stage, the ancients still experienced this up/down in the most real sense. We still have have remnants of it but only as historical figures of speech, in general the deep experience is not there. Man of old still felt deeply that everything that was worthy to be revered, that was noble, virtuous, stood higher than him. Not in a geometrical sense but as inner soul experience. He felt that that being possesses something that he doesn't and he could feel something streaming into his soul from 'above' from that being. It's quite impossible to explain this today unless one recovers these experiences within himself. And this is one of the pathologies of our age. There's a great one-sidedness in science and philosophy which addresses only what is 'lower' than us - such as our thoughts and perceptions. The idea that the soul gaze could look 'up' and open towards what's higher than us causes the most disturbing feelings.

I say the above to hint how mathematics can be experienced on the scale from purely abstract juggling with concepts towards mathematics becoming spiritualized. We do that when we are able to experience the archetypal living forces that precipitate as abstract number and geometry in the intellect. I'm pretty sure JP grasps this. I don't know about DH. Certainly his professional work is focused on the abstract end of the scale. This doesn't mean that he doesn't have his own deeper experiences. In any case, although I can say that it's my prime interest to seek for gradient between abstract and spiritual cognition, it turns out it's not only about explaining things. We can explain things very well but finally it is up to the listener to find the missing elements within themselves that will make the dry explanations a living reality. And this is not something that people have the desire to do. The up/down, higher/lower axis of inner experience is good example. If one is not willing to find these soul experiences within their inner life, no amount of explanations can give it externally.

[Cleric K]

Only differences are experienced. And qualities of differences can and do differentiate without end. Smooth and gradual changes, more abrupt polarities, etc. The différance of difference, as Derrida said, of eron erå, as we swedify the the Finnish translation of Derrida's post-structuralist word play exemplification of the qualitative evolutionary principle. Divinely Integrated, because there is the palindromic polarity-symmetry at the bottom of the process. The simplest, most economic way to write the palindromic symmetry is "<>2, both more and less (cf. the notion of interval), and I call that form 'Self'. Self-referentiality is not formalizable in terms of classical logic, as Gödel showed, because it contains relations <, > and =. Notion of equivalence is derived from modal negation neither more nor less, which can be formally written ><, and consequently >=< and >[]<, as we develop static elements of the foundationally dynamic theory. In natural language: If A is neither more nor less than B, then A and B are equivalent (in a given context).

A very natural interpretation of <> is Bergson duration, an open ended process that is neither unity nor multiplicity, but sharing same indefinite quality as undecidability of Halting problem. That is why I call further development of this approach also Mereology of durations and/or Bergson lattice.

I can't say I can grasp deeply enough your pinpointers, it's more that I try to find the hyperspace coordinates of the condition you're describing. So far I can describe it pictorially as a stable center with expanding kaleidoscopic, mandala-like inner space, going symmetrically in and out, past and future, etc. forming all elements within the opposites.

[SanteriSatama]

I can't say I can grasp deeply enough your pinpointers, it's more that I try to find the hyperspace coordinates of the condition you're describing. So far I can describe it pictorially as a stable center with expanding kaleidoscopic, mandala-like inner space, going symmetrically in and out, past and future, etc. forming all elements within the opposites.

Cool. The formal language is of course mainly for the formal purposes of constructive mathematical work, which requires communicable language open to further development.

Your vision sounds like very nice and rich symbolism of Self.

The foundational process-orientation instead of the object-orientation, which has been dominant in static math so far, has in its relatively late stage involved also a vision of all dissolving flux. That can be associated for example with the Nature metaphor of larval stage dissolving into goo in the chrysalis, as it is transforming into butterfly. Which can be thought as a mandala in motion.

Our animistic conceptualization of Anima Mundi - as well as its subprocesses - is tripartite, consisting of Self, Nature and Spirit/Breathing.

[AshvinP]

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.

He did respond to my first email, attached some of his papers. Then I wanted to ask something else, to which I never got response. But that's OK, I'm under no illusion that these professionals have the time to address every random thing that they get. He was polite enough to respond to my first mail.

Don is obviously interested in true mathematical model of reality. My own thinking was more using math as language for pictorial expression. For me these things lie on a scale. The more specific the mathematical structure becomes, the more spiritual activity becomes rigidified in that structure. It's like the spirit creates a complicated irrigation system and then forces itself to flow only through its channels. It could be the case that the channels are so arranged that they reflect fundamental aspects of experience but in the final run the 'truth' of existence can't lie in a mathematical model. It doesn't make sense for everyone to rigidify their spiritual activity in the same irrigation system and call that 'the truth'.

This is one side of the scale. On the other we are moving more towards spiritual perception. It's not about choosing abstract mathematical patterns and mapping them to perceptual experiences but it's more that mathematical thinking itself becomes the reality to be explored. Then mathematics becomes something living, we are moving into the area of sacred geometry and the mystery of number. For example, if we experience a triangle meditatively, we not only have an abstract floating concept but we are able to became aware of certain spiritual forces that flow through us and become concentrated in the object of our concentration. There's something archetypal in the experience of three-foldness. This links with the number three. If we go really deep we can find that the being of 'three' has something to do with the three-foldness of our soul life - thinking, feeling, willing. This also has to do with the three-foldness of space. Just as thinking, feeling and willing are not simply three same things orthogonal to each other, but are gradations, iterations of something more fundamental, so are the three dimensions of space. Only in our superficial age have the dimensions become something purely abstract. In earlier ages the dimensions were still livingly experienced and it'll be our task to find our way again to these living experiences. For example, as the primordial consciousness was diversifying, the first 'dimension' to appear - which was not dimension of space, but dimension of inner experience - was the up/down dimension. Of course up/down doesn't make any sense without the other two dimensions. We should imagine only the qualitive aspect of up/down. The corresponding qualitative experiences of the other two dimensions left/right, front/back still don't exist (or it can be said that they only exist as not yet realized/decohered potential). And unfortunately today this qualitative aspect has been completely lost and not only that but, as it's seen from other threads, there's fierce opposition even to allow ourselves to experience this aspect. In these ancient states of existence, of purely spiritual nature, consciousness attained so to speak a degree of freedom. Metaphorically speaking that's an 'axis'. When the precursor being of man 'looked up' it was experiencing integration of consciousness, bliss and the deeds of higher beings. When it 'looked down' it experienced the abyss and darkness of fragmentation and ultimately unconsciousness. At that stage there are not yet desires, no inner personal life, there's no physical body, no Earth. The conscious life belongs to Cosmic spiritual space. It can be said that 'up' corresponded to something akin to a spiritual Sun and 'down' was away from it, towards the Cosmic abyss. But this has nothing to do with spatial space yet. It's 'space' of inner experience. Man at that stage had life similar to a plant, through his activity he was striving towards the Sun, through integration and harmonization of the living spiritual processes on which his consciousness was carried. In our Earthly stage, the ancients still experienced this up/down in the most real sense. We still have have remnants of it but only as historical figures of speech, in general the deep experience is not there. Man of old still felt deeply that everything that was worthy to be revered, that was noble, virtuous, stood higher than him. Not in a geometrical sense but as inner soul experience. He felt that that being possesses something that he doesn't and he could feel something streaming into his soul from 'above' from that being. It's quite impossible to explain this today unless one recovers these experiences within himself. And this is one of the pathologies of our age. There's a great one-sidedness in science and philosophy which addresses only what is 'lower' than us - such as our thoughts and perceptions. The idea that the soul gaze could look 'up' and open towards what's higher than us causes the most disturbing feelings.

Thanks! The above corresponds well with Gebser's The Ever-Present Origin, which I presume is only considering the five "epochs" of the current age rather than the much longer "ages". He does a good job of communicating and reminding of the qualitative nature of what is being discussed; that only examining the past with our modern 'rational' mode of consciousness will not be sufficient, especially for the 'archaic-magical' epochs.

I say the above to hint how mathematics can be experienced on the scale from purely abstract juggling with concepts towards mathematics becoming spiritualized. We do that when we are able to experience the archetypal living forces that precipitate as abstract number and geometry in the intellect. I'm pretty sure JP grasps this. I don't know about DH. Certainly his professional work is focused on the abstract end of the scale. This doesn't mean that he doesn't have his own deeper experiences. In any case, although I can say that it's my prime interest to seek for gradient between abstract and spiritual cognition, it turns out it's not only about explaining things. We can explain things very well but finally it is up to the listener to find the missing elements within themselves that will make the dry explanations a living reality. And this is not something that people have the desire to do. The up/down, higher/lower axis of inner experience is good example. If one is not willing to find these soul experiences within their inner life, no amount of explanations can give it externally.

Right, at most the explanations will simply be helpful nudges in certain directions. I say JP-Hoffman simply because I think they will truly listen to each other, given various factors. They both embrace a 'Darwinian' (contrasted from 'Newtonian') approach to understanding why we experience the world the way we do now, they are both no doubt well-read in cognitive and evolutionary psychological studies/literature, and they both maintain a rigorous empirical approach despite having some deeper spiritual beliefs informing them. They seem like kindred souls in that regard.

[Cleric K]

Thanks! The above corresponds well with Gebser's The Ever-Present Origin, which I presume is only considering the five "epochs" of the current age rather than the much longer "ages". He does a good job of communicating and reminding of the qualitative nature of what is being discussed; that only examining the past with our modern 'rational' mode of consciousness will not be sufficient, especially for the 'archaic-magical' epochs.

Thank you! I'll take a look at Gebser.

They seem like kindred souls in that regard.

They most certainly are! And kinda gives goosebumps if one is able to read the signs of the times and see how they are fulfilling. At the same time awe but also a feeling of responsibility because it is us that must fulfill the times. It is actually possible that humanity misses the intersection.

[AshvinP]

I say the above to hint how mathematics can be experienced on the scale from purely abstract juggling with concepts towards mathematics becoming spiritualized. We do that when we are able to experience the archetypal living forces that precipitate as abstract number and geometry in the intellect. I'm pretty sure JP grasps this. I don't know about DH. Certainly his professional work is focused on the abstract end of the scale. This doesn't mean that he doesn't have his own deeper experiences. In any case, although I can say that it's my prime interest to seek for gradient between abstract and spiritual cognition, it turns out it's not only about explaining things. We can explain things very well but finally it is up to the listener to find the missing elements within themselves that will make the dry explanations a living reality. And this is not something that people have the desire to do. The up/down, higher/lower axis of inner experience is good example. If one is not willing to find these soul experiences within their inner life, no amount of explanations can give it externally.

Hey Cleric,

These two finally met for an interview - better late than never, I suppose!





Here are some of my comments on it for anyone who doesn't want to watch the video, or watches it and is unsure of the issues at stake.

Hoffman presents the usual IPT and explains that there is no homomorphism between the structure of perceptions and the structure of reality that gives rise to the perceptions, using the computer and VR metaphors. JP, on the other hand, is trying to point attention to the fact that the qualitative structure of meaning is preserved (or what he calls 'functional patterns' across configuration spaces), but DH doesn't really grasp that's what he is speaking of. Instead, DH feels JP is saying some quantitative perceptual structure is preserved, and so he continues to challenge that, but that's not really the issue JP is pointing to. 

JP presents a great metaphor of how our conceptual-perceptual activity allows us to 'get a grip' on the functional landscape like our hands can be articulated to get a grip on objects that will help us fulfill our intentions. He even points out a connection between the left hemisphere's linguistic capacity and the capacity for articulation of the hands. That is something we also find in esoteric scientific research. And when our thinking becomes more sensitive through higher development, it indeed becomes more like an organ of touch that can navigate its 'feelers' through the ideal landscape of meaning which is structuring our normal conceptual-perceptual space. 

When DH gets into his mathematical modeling of the probability spaces of conscious agents, it's interesting that he gives examples of perceiving green, hearing a trumpet, tasting mint, etc., i.e. any possible conscious experiences we can have, but he doesn't mention thoughts, feelings, and desires. Obviously, the latter also are part of our conscious experiences, our intuitive context at any given time. The only reason to leave these out of account is because they make the mathematical functions too complex, or rather impossible. It sets a clear limit on how much progress can be made towards genuine insight into the conscious agentic structure via mathematical modeling (intellectual activity). 

The whole disconnect between JP and DH, as usual, is the ignoring of real-time thinking activity. At one point, JP asks - "is it the case that you are seeing the damn probability space when you perceive an object??" He is once again trying to show how the perceptual landscape embeds the meaningful potential that has been narrowed down or stepped down through various convolutions of thinking. DH responds that, "I don't think you are seeing the actual probability space". He expects to find this probability space as some visual object side by side with other perceptions, and since the probability space is simply a symbol for our ideational activity which is obviously not just another external perception, he concluded it is only an artifact of our spacetime interface. DH conceives the 'noumenal' reality that projects into our spacetime interface as some completely orthogonal domain of conscious agents, some 'pure consciousness' that projects itself into various lower perspectives to explore the candy shop of conscious experiences, and that's why he keeps emphasizing there is no homology between the perceptual landscape and the conscious architecture, preserving the disconnect. The experience of human agents working through the perceptual landscape to fulfill intentions has almost no relevance to 'reality in itself' for DH.

JP makes his best effort to question the justifications for that mystically reducing disconnect - i.e. to question why the evolutionary process and the arrow of time is just an "artifact" and nothing more in DH's view. But the case would be self-evident if they could speak in terms of the phenomenology of cognition, the real-time experience of cognitive activity, which always maintains the meaningful link between the sphere of potentiality and the sphere of actualized inner and outer perceptions. They mention how every theory needs to start with a 'miracle', an axiomatic presupposition. The experience of one's own thinking could rightly be called a miracle, but it is no theoretical assumption or axiom. It is the only experience we can have absolute epistemic confidence in.

JP mentions towards the end of the video, the story of Abraham in relation to the evolution of conscience and sacrifice as a means of fulfilling 'fitness' goals across generations of time, which is fantastic. He uses it to illustrate how 'reproduction' cannot be limited to only biological sex or genes trying to propagate themselves. Essentially, the question becomes whether evolution has brought the One Spirit to the point where it can set Cosmic ideals for itself and actually attain them through the metamorphic process, which is what we call a thinking "human being" on Earth. When we think about these things more fluidly and imaginatively, we don't need to abandon the principles of evolutionary theory but only reintegrate them with their qualitative significance for agents pursuing the whole spectrum of intentions from Earthly needs to Cosmic ideals. Overall, JP questions the whole notion of a 'transcendent' reality that is completely beyond the conscious agentic interfaces, which is a nagging assumption we absolutely need to sacrifice before any genuine insight into the agentic architecture can be gained.

[AshvinP]

I had stopped short of the end before the last post, but the final statement on the ethical dimension is why all this really matters. JP asks whether there is any responsibility for us to be the best possible 'avatars' we can be, and DH responds that morals are rules we play by in the headset but he suspects that when we take the headset off, we will just laugh about our silly moral compass on Earth...

[Cleric K]

I had stopped short of the end before the last post, but the final statement on the ethical dimension is why all this really matters. JP asks whether there is any responsibility for us to be the best possible 'avatars' we can be, and DH responds that morals are rules we play by in the headset but he suspects that when we take the headset off, we will just laugh about our silly moral compass on Earth...

Thank you for the summary, Ashvin!

Yes, DH as many other thinkers in that area have grown comfortable with their senso-intellectual desktop, and even though they all feel the transcendental aspect of existence, the conclusion is that as long as we're within this headset, that's the best we can do. Really, the most these outlooks can provide is some modern-day trust in the afterlife. And even this doesn't come from concrete inner knowledge but rather because it seems to be more and more widely accepted and talked about. If one has to be honest, none of these borderline mystical experiences give a true inner certainty that the "I" can have continuity of consciousness without the headset.

And in the end, all that refusal to seek lucidly conscious experience beyond the surface of the headset, stems from the fact that this depth may have something (in fact everything) to reveal about our Earthly existence. Thus true spiritual knowledge is feared (on the surface of consciousness simply disliked or ridiculed) because in its light it might turn out that we need to make real course corrections - both individually and collectively. That's why one prefers to imagine that after death they will laugh at the Earthly theater stage. It's so much more convenient to imagine that this stage has nothing to do with the expected transcendental existence. This is a basic symptom of our age, where souls stand with one foot firmly in materialism and the other barely dipping its toe in the spiritual. It's an inner conflict because the soul yearns for the spiritual but at the same time it has fallen in love with what materialism has so diligently developed - the sense of being restricted only by completely external forces, while having our private inner life untouched by anything (let alone something spiritual).

On the other side, I wish JP could cultivate some more gentleness His words feel like hammers. I think it's a great example of the choleric temperament. The "I" strives to affirm itself in every gesture.

[lorenzop]

DH is thinking the headset is for evolutionary advantage - which ultimately is measured as a capacity for spawning. IOW, there is no evolutionary advantage to knowing and understanding any underlying patterns except as it gets us an advantage to breed.
JP needed to suggest the underlying patterns have an intrinsic\persistent\universal value (if this is what JP means) - perhaps then DH could have responded to this point.
I doubt DH could respond positively to the assertion there are intrinsic\persistent\universal patterns, as they've never been measured or found, nor believed except by a handful of people.