Donald Hoffman's search for a mathematical theory of consciousness

[Cleric K]

Regardless of what DH claims his CA theory to be or to do, IMHO it has its important place. If successful, it would fill a missing link in the philosophy of consciousness and address the main challenge from the materialistic camp, namely - if everything is consciousness and the whole reality is nothing more than qualitative conscious first-person experiences, how is it that on the level of perceptions the experience is highly mathematically structured (e.g. always strictly following Schrodinger equation?) Obviously, notwithstanding the undeniable experiential fact that all we know about ourselves and reality is only conscious experiences, it is also undeniable fact that sensory experiences are highly ordered and structured mathematically, and this fact needs to be explained. This is precisely what DH theory is trying to address. Obviously, structured perceptional experiences constitute only a limited set of the totality of our conscious experiences (which includes all kinds of non-sensory experiences that are not mathematically structured), and so, CA theory would have only a limited applicability and cannot be claimed to be the exhaustive theory of consciousness. I'm very confident that consciousness cannot be reduced to mathematics. So, let's appreciate the CA theory for what it can do while understanding and accepting its limits.

I don't see anything wrong to assume that the universe of Consciousness contains not only the hierarchy of cognizant free-willing CAs, but also a multiplicity of elementary level non-cognizant CAs which make a "computational machinery" put in place by the Divine-level consciousness in order to produce structured sensory experiences. We also can appreciate that these mathematical machinery is firmly algorithmically structured while at the same time allowing wide "openings" to allow for the flowing of possibilities and meanings through its cracks. This is due to the quantum-probabilistic nature of these structures. Even though the distribution of probabilities is totally deterministic and mathematically structured, the actual events-experiences are not deterministic and not mathematically structured at all and allow for the execution of Willing and Thinking according to higher-order meanings to freely flow through the sensory screen. I can intuit here a breathtaking Wisdom of such creation scheme.

Years ago when I first found DH's work I was very enthusiastic about it because it really was the first of that kind that I had seen. However, even though it stimulates the imagination, I think that it still formulates things in such a way that it is greatly susceptible to 'spiritual atomism' (where the atoms are the conscious agents). This quickly leads to flat-MAL-like conception, where it is very difficult to make proper sense of the depth-contextuality of existence. In particular, any ideas of hierarchy necessarily appear as a corporate pyramid of equal peers, where some happen to be on top and exploit the lower.

Today I think we have more fruitful frameworks. They are of course still abstract intellectual models, but they have more potential to awaken intuition for the true nature of depth-contextuality. Probably the best at this time is the work of Michael Levin (which we have dealt with here). Another of great value is that of Justin Riddle which you introduced here.

In both cases, even though abstractly, we are led to ideas that are much more in tune with the inner contextual depth of our being, where all the mystery lies. Interacting CAs too easily leads to the Toruk Makto fallacy since every agent considers themselves a fully complete and self-sufficient atom of existence (which can theoretically be extracted from its environment, placed elsewhere, and one would still feel innerly intact).

It's not so much the concrete tokens of the theory in question but the way of thinking that is important. Presently the break from spiritual atomism is greatly urgent. There are (at least) two important ideas that must be deeply grasped if we are to find our upright stature within reality and overcome the centuries-old Newtonian way of thinking, which when it creeps into spiritual life, leads to something like spiritual atomism - spatially-like enclosed CAs that exist in the spiritual vacuum and interact through spiritual 'photons'. This simply translates our physical sense of existence into a fantasized state, and thus we make a caricature of the spiritual realm.

The first is that we need to grasp something like Levin's nested fields of autonomous spiritual activity. A short prelude to the essays currently in the writing has been posted here, which treats these nested fields as Symphony of Minds.

The second is that we need to find the proper attitude toward the higher-order curvatures within which our states of being metamorphose. Here we need to overcome the tendency of the intellect to act like it can encompass the higher order reality within its thought-fragments. A very simple analogy can be drawn.

The atmospheric pressure gradually changes throughout the day. Now we can imagine that it begins to change faster and faster. When the changes of pressure become quicker than twenty cycles per second, this begins to be perceived as sound. The critical thing to note here is how in the first instance the scale of our now-span is embedded within more encompassing wavelengths of change. When we think intellectually about these wavelengths we live in their intuitive nature but the thoughts that we produce are like compressed symbols (tones) which fit in our now-span.

The most desperately missing skill in our materialistic age is the proper inner attitude toward the higher order mind-fields - who are autonomous beings within which our existence is embedded. This is why we keep stressing about the importance of prayer, as the means of letting go (surrender) and feeling the willed intuitive curvatures within which our existential movie meanders. We can symbolize the intuition of these fields through Imagination and concepts but we should remember that these are indeed only symbols - elemental wave packets that fit within the now-span of our consciousness. We can find the reality of the higher-order minds only by consciously trying to become concentric to their life. Then our thinking life becomes a compressed artistic expression of our intuition of the higher-order mind fields. The thought wave-packets are not the reality of the higher order patterns of intuitive intents but they are resonantly attuned to them and thus become symbols. The critical thing is to develop this inverted cognitive attitude toward that which can't fit in our thought wave packets, yet can be intuitively known (by becoming concentrically resonant with it) and expressed through such packets.

[Stranger]

Years ago when I first found DH's work I was very enthusiastic about it because it really was the first of that kind that I had seen. However, even though it stimulates the imagination, I think that it still formulates things in such a way that it is greatly susceptible to 'spiritual atomism' (where the atoms are the conscious agents). This quickly leads to flat-MAL-like conception, where it is very difficult to make proper sense of the depth-contextuality of existence. In particular, any ideas of hierarchy necessarily appear as a corporate pyramid of equal peers, where some happen to be on top and exploit the lower.

Today I think we have more fruitful frameworks. They are of course still abstract intellectual models, but they have more potential to awaken intuition for the true nature of depth-contextuality. Probably the best at this time is the work of Michael Levin (which we have dealt with here). Another of great value is that of Justin Riddle which you introduced here.

In both cases, even though abstractly, we are led to ideas that are much more in tune with the inner contextual depth of our being, where all the mystery lies. Interacting CAs too easily leads to the Toruk Makto fallacy since every agent considers themselves a fully complete and self-sufficient atom of existence (which can theoretically be extracted from its environment, placed elsewhere, and one would still feel innerly intact).

It's not so much the concrete tokens of the theory in question but the way of thinking that is important. Presently the break from spiritual atomism is greatly urgent. There are (at least) two important ideas that must be deeply grasped if we are to find our upright stature within reality and overcome the centuries-old Newtonian way of thinking, which when it creeps into spiritual life, leads to something like spiritual atomism - spatially-like enclosed CAs that exist in the spiritual vacuum and interact through spiritual 'photons'. This simply translates our physical sense of existence into a fantasized state, and thus we make a caricature of the spiritual realm.

The first is that we need to grasp something like Levin's nested fields of autonomous spiritual activity. A short prelude to the essays currently in the writing has been posted here, which treats these nested fields as Symphony of Minds.

Right, and if you actually read the latest DH paper or listen his lates interviews, he was able to break through this atomism and show mathematically how the interference of lower-level CAs leads to their fusion into higher-level CAs, or as he calls it, "nested hierarchy of conscious agents"

an interview with Donald Hoffman

The second is that we need to find the proper attitude toward the higher-order curvatures within which our states of being metamorphose. Here we need to overcome the tendency of the intellect to act like it can encompass the higher order reality within its thought-fragments. A very simple analogy can be drawn.

The atmospheric pressure gradually changes throughout the day. Now we can imagine that it begins to change faster and faster. When the changes of pressure become quicker than twenty cycles per second, this begins to be perceived as sound. The critical thing to note here is how in the first instance the scale of our now-span is embedded within more encompassing wavelengths of change. When we think intellectually about these wavelengths we live in their intuitive nature but the thoughts that we produce are like compressed symbols (tones) which fit in our now-span.

The most desperately missing skill in our materialistic age is the proper inner attitude toward the higher order mind-fields - who are autonomous beings within which our existence is embedded. This is why we keep stressing about the importance of prayer, as the means of letting go (surrender) and feeling the willed intuitive curvatures within which our existential movie meanders. We can symbolize the intuition of these fields through Imagination and concepts but we should remember that these are indeed only symbols - elemental wave packets that fit within the now-span of our consciousness. We can find the reality of the higher-order minds only by consciously trying to become concentric to their life. Then our thinking life becomes a compressed artistic expression of our intuition of the higher-order mind fields. The thought wave-packets are not the reality of the higher order patterns of intuitive intents but they are resonantly attuned to them and thus become symbols. The critical thing is to develop this inverted cognitive attitude toward that which can't fit in our thought wave packets, yet can be intuitively known (by becoming concentrically resonant with it) and expressed through such packets.

I would actually argue that most of the scientific breakthroughs were achieved by scientists intuiting into the higher-order mind fields. However, in most cases they were not consciously aware of it, even though still many were. As Bach said in his last words on his death bed: "Do not cry for me as I go where the music is born"

[AshvinP]

I would actually argue that most of the scientific breakthroughs were achieved by scientists intuiting into the higher-order mind fields. However, in most cases they were not consciously aware of it, even though still many were. As Bach said in his last words on his death bed: "Do not cry for me as I go where the music is born"

I will briefly quote a section from my Part I essay in connection with the above:

The natural-spiritual evolutionary process is such that the contracting space of natural potential (left) should transition into the expanding space of spiritual potential (right). The archetype of the ‘old wise man’ speaks to this process that was more akin to a natural law in ancient times. At a certain stage of life, the mature adults simply began growing in spiritual wisdom such that other members of the community could have complete confidence in their guidance. In more technical language, we could say that, after the spirit instinctively impresses its qualities into the outer forms of the physical, psychic, and mental landscapes, the latter draws on those forms to recover their inner significance, beginning with mental forms. It is as if we are undressing layers of clothing from our spirit – we can’t take off our shirt before we take off our coat.
...
In the last few thousand years, this process has been exemplified not so much in the growth of tribal spiritual wisdom, but in the learning of new artistic or innovative skills or the exploration of existential questions through philosophy, theology, and science. In modern times, however, the average adult life has increasingly reached a stage where the pushing process exhausts its potential and then very little seems to happen, no popping process seems to follow. In the late Middle Ages, for example, it seemed art, philosophy, and science could only become more innovative, reaching groundbreaking insights. One can hardly downplay the significance of such thinkers as Newton, Galileo, Bacon, Rosseau, Leibniz, Kant, and Hegel, among many others. Yet now we understandably expect very little of existential relevance to come from these fields.

That is because humanity has now been thrown back on its own resources in the mental space to the greatest possible extent, and it has been tasked with doing for itself what was once done for it as a part of natural development. It was only in this way that it could reach the grounds of inner freedom. The inspirations that previously flowed into consciousness as a matter of course must now be actively sought after, in accordance with each individual’s freely chosen ideals, but the motivation to do so is waning in our indolent times.

Although nature still carries forward our physical and psychic development to some extent without our participation, it does so very little in our intellectual development. The modern scientific breakthroughs were running on the momentum of natural contributions to mental development. Of course, 'nature' here is simply the mirror image of the higher-order intuitive mind fields. It is how we perceive the latter in our aliased intellectual perception. We could never become free spiritual beings if the Celestial Music continued to inspire the imaginative activity of the Bachs of its own accord. That is why the inverted activity such as concentration/prayer has become necessary - it allows us to continue receiving that higher inspiration while also remaining free. Practically, that also means if we don't actively surrender (I know, a paradox for the intellect) for our higher mental development on Earth, the Music will grow dimmer and dimmer after death as well.

[Stranger]

We could never become free spiritual beings if the Celestial Music continued to inspire the imaginative activity of the Bachs of its own accord. That is why the inverted activity such as concentration/prayer has become necessary - it allows us to continue receiving that higher inspiration while also remaining free.

Fully agree, and by the way, Bach was deeply religious person and always considered his musical creative work as part of his spiritual path.

[AshvinP]

Right, and if you actually read the latest DH paper or listen his lates interviews, he was able to break through this atomism and show mathematically how the interference of lower-level CAs leads to their fusion into higher-level CAs, or as he calls it, "nested hierarchy of conscious agents"

an interview with Donald Hoffman

From what I have heard so far, I don't see how this is any less atomistic. In a certain sense, we only overcome the spiritual atomism when we refrain from conceiving the 'nested hierarchy'. That doesn't mean we stop thinking about it, but we resist forming any rigid models and rather prayerfully feel our way into its concentric layers, as Cleric suggested. The very fact that DH continues to pursue a mathematical model of the CA hierarchy means he is forced to conceive them atomistically, because the 'rules' of mathematical thinking are conditioned by the same atomistic intuition that derives from aliased intellectual-sensory perception. The intellect can refine the atomistic structure more and more so that it projects back some basic experiential dynamics, but nevertheless it remains atomistic and therefore fundamentally limited and ultimately misleading for any genuine spiritual understanding of our be-ing, which is actually (temporally) 'spread across' the contextual depth axis and modulated in unique and complicated ways through each contextual layer (according to corresponding spiritual intents).

[Stranger]

Right, and if you actually read the latest DH paper or listen his lates interviews, he was able to break through this atomism and show mathematically how the interference of lower-level CAs leads to their fusion into higher-level CAs, or as he calls it, "nested hierarchy of conscious agents"

an interview with Donald Hoffman

From what I have heard so far, I don't see how this is any less atomistic. In a certain sense, we only overcome the spiritual atomism when we refrain from conceiving the 'nested hierarchy'. That doesn't mean we stop thinking about it, but we resist forming any rigid models and rather prayerfully feel our way into its concentric layers, as Cleric suggested. The very fact that DH continues to pursue a mathematical model of the CA hierarchy means he is forced to conceive them atomistically, because the 'rules' of mathematical thinking are conditioned by the same atomistic intuition that derives from aliased intellectual-sensory perception. The intellect can refine the atomistic structure more and more so that it projects back some basic experiential dynamics, but nevertheless it remains atomistic and therefore fundamentally limited and ultimately misleading for any genuine spiritual understanding of our be-ing, which is actually (temporally) 'spread across' the contextual depth axis and modulated in unique and complicated ways through each contextual layer (according to corresponding spiritual intents).

I agree that it's still atomistic. However, the model has to be mathematically structured, and I have no idea how to formulate mathematically the "be-ing, which is actually (temporally) 'spread across' the contextual depth axis and modulated in unique and complicated ways through each contextual layer (according to corresponding spiritual intents)". Perhaps some topological formulation would better reflect this.

But my feel is that this in-depth level of spiritual reality is simply not mathematically tractable, and it does not need to be. What DH is doing is only to address the "computational machinery" layer of spiritual reality where the sensory experiences are being algorithmically generated and mathematically structured, and that layer may very well be atomistic by its structure, which would perfectly co-exist with non-atomistic structures on deeper spiritual levels. As an analogy, the biological organisms are atomistic in their cellular structure, which does not prevent them from being integrated into the hierarchy of non-atomistic levels of reality.

[AshvinP]

Right, and if you actually read the latest DH paper or listen his lates interviews, he was able to break through this atomism and show mathematically how the interference of lower-level CAs leads to their fusion into higher-level CAs, or as he calls it, "nested hierarchy of conscious agents"

an interview with Donald Hoffman

From what I have heard so far, I don't see how this is any less atomistic. In a certain sense, we only overcome the spiritual atomism when we refrain from conceiving the 'nested hierarchy'. That doesn't mean we stop thinking about it, but we resist forming any rigid models and rather prayerfully feel our way into its concentric layers, as Cleric suggested. The very fact that DH continues to pursue a mathematical model of the CA hierarchy means he is forced to conceive them atomistically, because the 'rules' of mathematical thinking are conditioned by the same atomistic intuition that derives from aliased intellectual-sensory perception. The intellect can refine the atomistic structure more and more so that it projects back some basic experiential dynamics, but nevertheless it remains atomistic and therefore fundamentally limited and ultimately misleading for any genuine spiritual understanding of our be-ing, which is actually (temporally) 'spread across' the contextual depth axis and modulated in unique and complicated ways through each contextual layer (according to corresponding spiritual intents).

I agree that it's still atomistic. However, the model has to be mathematically structured, and I have no idea how to formulate mathematically the "be-ing, which is actually (temporally) 'spread across' the contextual depth axis and modulated in unique and complicated ways through each contextual layer (according to corresponding spiritual intents)". Perhaps some topological formulation would better reflect this.

But my feel is that this in-depth level of spiritual reality is simply not mathematically tractable, and it does not need to be. What DH is doing is only to address the "computational machinery" layer of spiritual reality where the sensory experiences are being algorithmically generated and mathematically structured, and that layer may very well be atomistic by its structure, which would perfectly co-exist with non-atomistic structures on deeper spiritual levels. As an analogy, the biological organisms are atomistic in their cellular structure, which does not prevent them from being integrated into the hierarchy of non-atomistic levels or reality.

That layer is our own conceptual thinking. DH is modeling our own aliased way of conceptually encoding imaginative experiences into sensory-like atomistic structures. There are no atomistic structures at the elemental level, it's simply how we conceive-perceive the complex interference of holistic higher-order topologies of intents. It could be somewhat helpful if DH and others understood the models as imaginative symbols for realities that can only be further explored through our prayerful inverse efforts, which always involve the full human being (thinking, feeling, and will). Here is a great quote to contemplate on that:

Spiritual science should be an aid to this, but this will be impossible as long as man believes that the ascent of the physical into the etheric has nothing to do with his inner being. It is of no matter in the laboratory whether a man has a strong or weak moral character. This is not the case, however, when one is concerned with etheric forces. Then one's moral constitution affects one's results. For this reason, it is impossible for modern man to develop this ability if he remains as he is. The laboratory table must first become an altar, just as it was for Goethe who, as a child, kindled his small altar to nature with the rays of the rising sun.

This will happen before long. Those who are able to say, “Not I, but Christ in me,” will be able to work with the plant forces in the same way that mineral forces are now understood. Man's inner being and his outer surroundings work into one another reciprocally; what is outside transforms itself for us, depending on whether our vision is clear or clouded. (GA 118)

This is why Cleric says DH's approach is so susceptible to the TM fallacy. In the video, it is said that DH understands the fabric of space-time as 'derivative from the perspective of the CA hierarchy interactions' (around 38 min). What this means is that the space-time fabric is felt to be derivative of his own conceptual perspective. Because the modeling activity itself is constrained by that perspective and cannot envision how its own movements are modulated by the true imperceptible soul-spiritual hierarchy. That all changes when "our thinking life becomes a compressed artistic expression of our intuition of the higher-order mind fields", as Cleric put it. Then we don't invest too much in the modeling efforts but use it as one limited tool in our toolkit for orienting our higher intuition. It is that lucidly explored intuition that will gradually elucidate the sensory dynamics in a living way, as we resonate more and more with the spiritual intents along which the former unfold.

[Stranger]

This is why Cleric says DH's approach is so susceptible to the TM fallacy. In the video, it is said that DH understands the fabric of space-time as 'derivative from the perspective of the CA hierarchy interactions' (around 38 min). What this means is that the space-time fabric is felt to be derivative of his own conceptual perspective. Because the modeling activity itself is constrained by that perspective and cannot envision how its own movements are modulated by the true imperceptible soul-spiritual hierarchy. That all changes when "our thinking life becomes a compressed artistic expression of our intuition of the higher-order mind fields", as Cleric put it. Then we don't invest too much in the modeling efforts but use it as one limited tool in our toolkit for orienting our higher intuition. It is that lucidly explored intuition that will gradually elucidate the sensory dynamics in a living way, as we resonate more and more with the spiritual intents along which the former unfold.

That is correct, but the challenge is to "elucidate the sensory dynamics in a living way, as we resonate more and more with the spiritual intents along which the former unfold" while simultaneously provide a mathematically clean explanation of how it happens that all sensory experiences always exactly mathematically obey the Schrodinger equation while simultaneously being a flow of the expression of "the spiritual intents along which the former unfold". (I actually asked Cleric many times about such explanation before). There must be a certain mathematical or algorithmic structure in place at a certain level of reality that is responsible for shaping the sensory experiences in a mathematically structured way.

As I said in my first post, there is no contradiction between the mathematical structure and the "the spiritual intents along which the former unfold", because the probabilistic nature of the structure allows the spiritual intents to flow freely through the windows of probabilistic possibilities of this structure. So, the universe of spiritual intents can perfectly co-exist with the mathematical structure of the fabric of sensory experiences. As an analogy, it's like a metal mesh strainer that has a very rigid structure, but at the same being transparent for light and easily penetrable by fluids through its multiplicity of holes.

[AshvinP]

This is why Cleric says DH's approach is so susceptible to the TM fallacy. In the video, it is said that DH understands the fabric of space-time as 'derivative from the perspective of the CA hierarchy interactions' (around 38 min). What this means is that the space-time fabric is felt to be derivative of his own conceptual perspective. Because the modeling activity itself is constrained by that perspective and cannot envision how its own movements are modulated by the true imperceptible soul-spiritual hierarchy. That all changes when "our thinking life becomes a compressed artistic expression of our intuition of the higher-order mind fields", as Cleric put it. Then we don't invest too much in the modeling efforts but use it as one limited tool in our toolkit for orienting our higher intuition. It is that lucidly explored intuition that will gradually elucidate the sensory dynamics in a living way, as we resonate more and more with the spiritual intents along which the former unfold.

That is correct, but the challenge is to "elucidate the sensory dynamics in a living way, as we resonate more and more with the spiritual intents along which the former unfold" while simultaneously provide a mathematically clean explanation of how it happens that all sensory experiences always exactly mathematically obey the Schrodinger equation while simultaneously being a flow of the expression of "the spiritual intents along which the former unfold". (I actually asked Cleric many times about such explanation before). There must be a certain mathematical or algorithmic structure in place at a certain level of reality that is responsible for shaping the sensory experiences in a mathematically structured way.

As I said in my first post, there is no contradiction between the mathematical structure and the "the spiritual intents along which the former unfold", because the probabilistic nature of the structure allows the spiritual intents to flow freely through the windows of probabilistic possibilities of this structure. So, the universe of spiritual intents can perfectly co-exist with the mathematical structure of the fabric of sensory experiences. As an analogy, it's like a metal mesh strainer that has a very rigid structure, but at the same being transparent for light and easily penetrable by fluids through its multiplicity of holes.

I'm sure Cleric can respond with more helpful elaborations, but I will only say that we are externalizing thinking (CA) as long we keep looking for some other 'mathematical or algorithmic structure' that should be responsible for shaping sensory experience, besides our own CA. We have to experience how our own thoughts unfold along the curvatures of spiritual intents, including the very thoughts we are thinking now, and then we will naturally understand how sensory experience is formatted through that intimate thought-structure. Of course, this is heavily resisted for many reasons we have discussed at length in previous discussions.

Again I will quote the essay on this point:

For this inverse movement, our verbal concepts should be understood as testimonies to more mysterious ‘curvatures’ that constrain them and along which they stream. When we see a stranger who is walking down the street, we know that the quantitative properties of the arm and leg movements, the walking direction, the speed, and so on, do not exhaust the meaning of the activity – we know the person is also driven by some invisible feelings and desires; walking for some imperceptible purpose. The outer perceptions testify to this invisible inner life. Likewise, our conceptual explorations here can also testify to the shared inner life that animates their movements so long as we keep this nexus in view and approach the descriptions vividly and from the most varied angles.
...
Most people would not be thrilled to discover that their ‘informed’ and impassioned thinking about politics, economics, world events, and so on, is simply an unconscious commentary on the pictures which have filled their soul space throughout the course of life. We could say it is a space of thought-potential from which linear sequences of verbal thoughts collapse, according to how images interfere with one another based on unexamined sympathies and antipathies, likes and dislikes, feelings of pleasure and pain... We don’t know exactly why they lead us to think in one way and not others, to pay attention to certain ideas and not others, to hold certain opinions and not others, etc. As uncomfortable as it may be to confront this aspect of our conceptual life, becoming more conscious of these relations is the path to spiritual freedom.

[Stranger]

I'm sure Cleric can respond with more helpful elaborations, but I will only say that we are externalizing thinking (CA) as long we keep looking for some other 'mathematical or algorithmic structure' that should be responsible for shaping sensory experience, besides our own CA. We have to experience how our own thoughts unfold along the curvatures of spiritual intents, including the very thoughts we are thinking now, and then we will naturally understand how sensory experience is formatted through that intimate thought-structure. Of course, this is heavily resisted for many reasons we have discussed at length in previous discussions.

Again I will quote the essay on this point:

For this inverse movement, our verbal concepts should be understood as testimonies to more mysterious ‘curvatures’ that constrain them and along which they stream. When we see a stranger who is walking down the street, we know that the quantitative properties of the arm and leg movements, the walking direction, the speed, and so on, do not exhaust the meaning of the activity – we know the person is also driven by some invisible feelings and desires; walking for some imperceptible purpose. The outer perceptions testify to this invisible inner life. Likewise, our conceptual explorations here can also testify to the shared inner life that animates their movements so long as we keep this nexus in view and approach the descriptions vividly and from the most varied angles.
...
Most people would not be thrilled to discover that their ‘informed’ and impassioned thinking about politics, economics, world events, and so on, is simply an unconscious commentary on the pictures which have filled their soul space throughout the course of life. We could say it is a space of thought-potential from which linear sequences of verbal thoughts collapse, according to how images interfere with one another based on unexamined sympathies and antipathies, likes and dislikes, feelings of pleasure and pain... We don’t know exactly why they lead us to think in one way and not others, to pay attention to certain ideas and not others, to hold certain opinions and not others, etc. As uncomfortable as it may be to confront this aspect of our conceptual life, becoming more conscious of these relations is the path to spiritual freedom.

Oh, I agree with that, being a meditator myself. I have no misconception that DH's CAs theory is only a model, a mental representation of the actual process that happens in the living thinking, and as a mental representation, it is doomed to be inaccurate and abstracted. This is exactly per Cleric's comments in this thread related to the "real hard problem of consciousness". But with such disclaimer, there is still a place for mathematical and other abstracted models of reality. If natural science would not develop such models, we would not have technology and would not be communicating on this forum. We need to appreciate the fact that all modern technology is the product of abstracted scientific models, even though they, by their very nature, are always inherently inaccurate representations of the living spiritual reality.

The problem is that mathematics is by nature a mental abstraction. Yet, from the direct experience we know that the sensory experiences are always structured with precise mathematical regularities, and if we want to approach and understand/explain this fact, we need to use mathematics. There is a paradox here, may be Cleric can elaborate on this.