Our mathematical universe and the hard problem of consciousness

In the beautiful words of David Chalmers, “Consciousness poses the most baffling problem in science. There is nothing that we know more intimately than conscious experience, but there is nothing that is harder to explain. All sorts of phenomena have yielded to scientific investigation in recent years, but consciousness has stubbornly resisted. Many have tried to explain it, but the explanations always seem to fall short of the target. Some have been led to suppose that the problem is intractable, and that no good explanation can be given.”

What follows here is what we believe to be a good explanation of the solution to ‘the hard problem of Consciousness’. It is a solution that, in its most essential aspects, has been hinted upon by an elite group of scientists of the Nobel level caliber for a relatively long period of time (click here for some examples).

This paper starts with describing the problem of conscious experience. Then, it abandons attempts of explaining it in the materialistic terms and instead, it explores the implications of the paradigmatic shift in which consciousness exists as a fundamental and irreducible entity which experiences an experience. The problem of interaction is resolved as a next step. Finally, a comprehensible picture of the reality is presented that completely subsumes physical sciences into itself as an integral subsystem, as well as sheds light on a few severe problems that now easily lend themselves to a resolution in the terms of the new worldview.

The Hard Problem of Consciousness

Let’s start with reviewing the experience of color. Thermonuclear reactions in the sun produce photons – carrier particles of electromagnetic energy. The photons propagate towards earth and eventually hit optic nerve in our eyes. The optic nerve, in response, generates electrical signals that travel further along the neural pathways of the brain. The neural cells get excited and start firing even more electrical impulses. This entire cascade of electrochemical activity is a purely physical phenomena, and, despite being undoubtedly difficult to trace and decode in details in a lab, represents absolutely no fundamental conceptual problem. But suddenly, if as by magic, in the midst of this purely physical phenomena, arises an experience of redness – e.g., the perception, awareness, and experience of a color.

What do we make out of this? The big 3 questions immediately come to mind: 1) where is this experience to be found? 2) what is experiencing this? and 3) why and how purely physical phenomena is accompanied by any subjective experience at all?

1) Where is this experience of redness to be found? It’s thought that it resides somewhere in the volume of space occupied by the brain. But imagine we could magnify the brain to such an extend that we could simply walk into it. What would we see around us when inside? We would see a cellular structure. We would see the neural cells themselves here and there. We would see some flashes of electromagnetic energy between the synapses of the cells. We would see lots and lots of space. We would see some molecules moving in all directions. But would we see redness there? Would we see enjoyment of redness there? Pain? Falling in love with it? Fear of it? No, we would not. So where is the experience to be found?

2) What in the brain is experiencing redness? The neural cells of the brain? The chemical and electrical activity? Information processing and integration done by the cells? The space between the cells? Molecules that make up the cells? Chemical bonds between the molecules? Quarks and electrons that make up the molecules? Some quantum effects? Name any physical concept you want and ask yourself if it is capable of experiencing redness. The answer will stay the same: not that, not that. So what is experiencing an experience?

3) Why and how purely physical phenomena is accompanied by any subjective experience at all? Gary Gutting – a philosopher, powerfully demonstrated the predicament initially proposed by Frank Jackson: consider Mary, a leading neuroscientist who specializes in color perception. Mary lives at a time in the future when the neuroscience of color is essentially complete, and so she knows all the physical facts about colors and their perception. Mary, however, has been totally color-blind from birth. Fortunately, due to research Mary herself has done, there is an surgical operation that gives her normal vision. When the bandages are removed, Mary looks around the room and sees a bouquet of red roses sent by her husband. At that moment, Mary for the first time experiences the color red and now knows what red looks like. Her experience, it seems clear, has taught her a fact about color that she did not know before. Before this she knew all the physical facts about color and its underlying mechanism, but not the experience of redness. Therefore, there is a fact about color that is not physical and physical science cannot express all the facts about color and other subjective experiences that accompany purely physical phenomena.

No one has a slightest idea how answer these big 3 questions – because simply, they are utterly incomprehensible to everyone who deeply thinks about them. In the several millennia of attempting to find an answer, it’s not even been conceived in a very rough and the most general outline. Literally all attempts from the materialistic perspective to approach these questions have been shown to be completely unsatisfactory.

The main reason for that is the unbridgeable conceptual chasm between categories of matter/energy and subjective experience. The experience seems to be immaterial. It seems to be of fundamentally different type and expressing it in terms of matter/energy has even warranted its own term: category mistake.

Some insist that consciousness/experience is a mere information processing and integration, but somehow they fail to realize that even though consciousness does have characteristics of information processing/integration and of intelligence and these characteristics can be simulated in a computer (aka artificial intelligence), these characteristics only abstract certain aspects of consciousness while forgetting about the experience itself, which is really the key characteristic. As Christof Koch beautifully put it: “You can simulate weather in a computer, but it will never be ‘wet’.”

Some philosophers like Willard Quine and Daniel Dennett got so desperate that they started insisting on the most incomprehensible solution – that subjective experience is just an illusion and really does not exist at all. It just shows the level of desperation!

Nevertheless, it’s been strongly assumed that this problem must be resolved in physical terms – meaning that it’s assumed that Matter is at the very bottom of the ontological hierarchy – that Matter is the substratum of everything that exists and that literally everything is made up of Matter and can be explained in the terms of Matter, its measurable parameters and its behavior – in other words in terms of energy, mass, charge, spin, speed, motion, etc. There is essentially nothing else in the conceptual apparatus of fundamental physics that could be invoked to account for the phenomena of subjective experience.

So how do we find a way out of this cognitive conundrum? ‘If the materialistic paradigm is so helpless indeed, what is the alternative?’ you ask? Let’s get down to the core of what I am trying to say here.

It’s plainly obvious that neither the neural cells of the brain nor the electrochemical reactions/interactions between them nor any other physical phenomena one cares to name experiences anything in themselves. But out of necessity, we can assume that they are only communicating information about what to experience to some other entity ― an independent entity that is capable of experiencing in a fundamental and irreducible way. In other words, an entity that is, in itself, actually capable of a subjective experience. One such entity — in fact, the only entity that is fundamentally capable of subjective experience is called consciousness. The question then becomes ‘How can we explain how physical neural cells of the brain can even interact with this independent and immaterial consciousness?’. In the materialistic paradigm, interaction between everything is accomplished by an exchange of physical energy (through carrie particles of the 4 fundamental forces). But immaterial consciousness, if indeed, being so different from anything physical as argued here, would seem to be incapable of interacting with a physical entity. This is called the problem of interaction and it’s resolved below.

In order for us to see the light in the end of the tunnel, we need to start with re-stating that physical matter/energy and immaterial consciousness/subjective experience are fundamentally of different type – of different categories. In order for us to make sense of how one interacts with another, we must admit that both must be of the same type – of the same category – otherwise we are stuck in irreconcilable conceptual chasm.

We have two alternatives here: either both are of material/physical type or both are of intangible/immaterial type since consciousness/experience seem to be immaterial. At this point, we don’t know which alternative is true, but we do know that materialistic alternative of reducing consciousness to physical terms leads us to incomprehensible conceptual difficulties and even forces some to completely deny the existence of the subjective experience altogether treating it as a mere illusion. So, let’s see to where the other alternative leads us, and let’s judge the tree by its fruits.

We know that consciousness/subjective experience seem to be immaterial. But how can physical matter/energy be immaterial as well? Isn’t it just another incomprehensible idea? At first glance, it seems to be. After all, we believe we look into outside world and feel its solidity. But the image of the outside world and the feeling of solidity as well as all other sensations of it are just that – immaterial sensations inside our consciousness, sense data. Even the materialists agree that we don’t see the outside world itself – we only see our sense data (we don’t see photons striking the optic nerve of our eyes – we only see colors correlated to the above process). The presence of this sense data in our consciousness does not prove at all that it is produced by the physical universe – it only proves it is produced by something. And here comes a very elegant solution which has become possible to conceive only recently thanks to some new developments in physics and computer science – modern physics is highly mathematical. In fact, on the level of subatomic particles – which is literally all that’s currently believed to exist, it’s pure math. Can it be that what we call ‘the physical universe’ is really nothing more than an immaterial mathematical structure? Can it be that our sense data is produced by this mathematical structure?

It’s not merely my idea that the universe is mathematical and informational; there are some Nobel level theoretical physicists saying exactly that: “it from bit” in the words of John Wheeler.

Please realize that the existence of the universe is not denied. What is meant here is that it’s not physical/material, but mathematical and this mathematical structure representing the universe is an elaborate system of abstract equations and algorithms according to which our sense data is produced. In other words, the universe is a mathematical simulation/matrix.

But the question is, ‘where does this mathematical structure exist?’ If we cannot imagine where it can possibly exist, it means that we are stuck in another incomprehensible pit. After all, it’s very hard to imagine that this mathematical structure exists by itself in some kind of void. Moreover, there must be something that computes it because we do know that the universe is dynamic and not static. Fortunately, the answer is easy.

From our own subjective experience, we know that all abstract concepts, including mathematical ones, exist in our individual consciousness. If we re-interpret the entire physical universe as The Grand Mathematical Structure, than this structure must as well exist in some kind of consciousness – not in our individual consciousness, but in a Consciousness external to ours – Cosmic Consciousness?

This Cosmic Consciousness literally thinks (more precisely – computes) The Grand Mathematical Structure into the existence at this very moment. The results of this computation/simulation are input into our individual consciousness as colors of 3-d image, sounds, smells, flavors, sensations of solidity, temperature, pleasure/pain, and all other sense data. You can also think of the totality of sense data as a virtual ‘holographic’ matrix (yes, just like in The Matrix movie) – a matrix that we naively mistake for the external ‘material’ world around us – only instead of machines, as in the movie, there is Cosmic Consciousness there. In the plainest language – external ‘material’ universe is simply the thoughts of Cosmic Consciousness projected into our individual consciousness as sense data. As Plato famously stated in his Allegory of The Cave – we only observe the shadows of reality; we only observe sense data (shadows) projected into our individual consciousness according to The Grand Mathematical Structure (abstract platonic forms).

Instead of the physical universe, there is Cosmic Consciousness out there; thus it’s no wonder that our individual consciousness exists. And obviously, since it’s consciousness here and there – inside and outside – both have no trouble of interacting with each other.

In this new ontological paradigm, Cosmic Consciousness is the only ‘thing’ that fundamentally exists. Everything else that exists – exists inside it either as an individual consciousness or as information/experience/sense data – absolutely without any physicality. What we call ‘the external universe’ is just a virtual ‘holographic’ matrix/simulation/sense data projected into our individual consciousness. The matrix itself is computed by Cosmic Consciousness according to the algorithms and equations of the Grand Mathematical Structure.

Cartesian dualism is completely resolved in a worldview in which both on the inside and on the outside, there is nothing but immaterial consciousness. Both are of the same immaterial type/category and thus both have no trouble interacting with each other – both interact by exchanging information (which is immaterial as well) and not by exchanging bundles of energy as in the materialistic view. The information is translated into sense data/subjective experiences, and specifies how our individual consciousness is changed to produce experience.

This, no doubt, sounds fantastical (though not to philosophers of the eastern mindset and not to the elite group of Nobel level thinkers), but to say the least, it fits very nicely and is completely comprehensible – infinitely more so as compared to trying to do the impossible and explain how consciousness/subjective experience arises in a swirl of elementary particles doing their mindless thing. We are literally forced by reason to accept this idealistic worldview. Here. we should apply Sherlock Holmes’s dictum: “When you have excluded the impossible, whatever remains, however improbable, must be the truth”.


The most obvious implications of this new ontology, which is literally forced upon us by the necessity to explain existence of consciousness/subjective experience:

  1. It provides ontological framework for the resolution of quantum mechanics duality of particles/waves. There are no particles or waves in the mind of Cosmic Consciousness; there are only the equations of The Grand Mathematical Structure. According to the current formulations – these are the equations of the wave function. At the point of observation, the equations are computed and the results are translated into our sense data. We are freed from all the misleading linguistic baggage that comes from trying interpreting the equations of the quantum mechanics. None of that is real, but the equations are.
  2. It resolves quantum entanglement mystery – “spooky action at a distance”. When two photons become entangled, regardless of how far they travel away from each other, they still keep informational link to each other; e.g., measuring spin of one photon, instantly results in the opposite spin for another – despite the fact that many light years might be separating them – obviously violating the speed of light limit. That’s a great mystery in current physics. In the new paradigm, all that exists inside The Grand Mathematical Structure is an equation that describes this system of entangled photons. There is no need to communicate anything across light years as the information about spins is simply embedded as variables in the equation itself. When spin of one photon is measured by us, the equation is computed by Cosmic Consciousness – the result includes spins for both photons – they are determined at exactly the same time.
  3. It explains the nature of space. There is no ‘space’ inside Cosmic Consciousness. There is only The Grand Mathematical Structure computed by it. This mathematical structure includes primitive numeric variables like mass, charge, spin, distance, time interval, speed, etc – all integrated into abstract geometry. Space itself is an abstraction in that abstract geometry.
  4. It explains what space is expanding into. Astronomical observations show that the universe is expanding – more precisely, the space itself is expanding. The question of course is what is it expanding into. Is there more space beyond? That would mean that space is infinite – something that physics absolutely cannot accept as it insists at any costs that the universe is a finite system. It’s a great mystery. In the new paradigm, space itself is simply the abstract geometry of The Grand Mathematical Structure. There is nothing that is expanding into anything – only variables in the equations of The Grand Mathematical Structure change their values.
  5. It explains what space curves into. The general relativity showed that space is curved around mass, but what exactly does space curve into? Space needs another dimension to do this. If space is simply abstract geometry of  The Grand Mathematical Structure, this problem resolves itself.
  6. It explains why multi-dimensional formulations like those in the string theory do not present a fundamental problem. Even though, our sense data seems to be 3-dimensional, we are not forced to insist that The Grand Mathematical Structure itself is formulated in and is limited to 3 dimensional geometry. For example, a wave-system of electrons does not exist in 3-dimensional or 10-dimensional space – it exists as a formula/equation in the mind of Cosmic Consciousness. The equation is computed and the result of the computation is translated into our 3-d sense data. This also means that holographic principle can work for our universe, as it shows that the three dimensions of reality we observe may in fact be a two-dimensional information structure “painted” on some sort of cosmological surface. It’s all hard to imagine, but if the reality is The Grand Mathematical Structure, than it’s easy to see how mathematical formalism of the holographic principle can literally describe our universe.
  7. It explains the nature of the substance of elementary particles. There is no physicality/material substance in the mind of Cosmic Consciousness – there are no electrons, quarks, atoms, etc – there are only numeric variables like mass, charge, spin, speed, distance, etc. These are variables in the equations of the Grand Mathematical Structure. In other words, if we wish to speak in terms of Objects/Properties, there are indeed properties, but no objects. Thus, the notion of the substance out of which objects are made is not even required.
  8. It explains why math is so good at describing our universe and why physical laws that we discover are mathematical. Cosmic Consciousness is the the best mathematician in existence; It designed The Grand Mathematical Structure. When physicists discover mathematical equations that describe the universe, they literally discover equations that correspond to those in the mind of Cosmic Consciousness. We are not there completely yet; all the equations we have discovered so far are approximations at this point. But we will get there some day and we will know exactly what The Grand Mathematical Structure is.
  9. It explains complete discretization of the universe. Imagine a thought experiment where we use a hypothetical microscope capable of magnifying matter without any (uncertainty) constrains. With every jump of magnification, The Grand Mathematical Structure needs to be computed to produce new sense data. If matter were continuous, there would be infinite number of magnification jumps possible – a situation akin to Zeno’s paradoxes, so the computation process that Cosmic Consciousness would have to do, would be infinite. For the computation to be finite, it must be done in discrete blocks. Moreover, the precision of the computation must always be the same. The level of discreteness and precision is probably specified by Planck’s constant, Planck’s length, Planck’s time, etc. There is a minimal mass and a minimal amount of energy. The geometry of space time is discrete/pixilated; i.e., there is a minimal length, area, and volume. This is in complete agreement with Quantum physics. Quantum means discreet. Discretization of The Grand Mathematical Structure is the mechanism to deal with computational infinities.
  10. It resolves Cartesian dualism and the problem of interaction
  11. It resolves the hard problem of consciousness. It turns out that consciousness, if assumed to be fundamental and not tried to be reduced to something else, is not hard at all. In the words of Donald Hoffman: “If you want to solve the mind-body problem you can take the physical as given and explain the genesis of conscious experience, or take conscious experience as given and explain the genesis of the physical. Explaining the genesis of conscious experience from the physical has proved, so far, intractable. Explaining the genesis of the physical from conscious experience has proved quite feasible”. As described in this writing, the key to the latter is realizing that matter/energy and consciousness/subjective experience MUST be of the same type/category – either both are material/physical (which proved intractable and incomprehensible) or both are immaterial (proved extremely productive) – otherwise, there is no conceptual bridge to link them and conceive even in principle how one can interact with another.
  12. It explains where consciousness comes from. Our individual consciousness exists only because Cosmic Consciousness itself is what the ultimate reality is. We are just ripples in the infinite ocean of Cosmic Consciousness. Metaphorically, the best way to visualize the relationship between Cosmic Consciousness and our individual consciousness is by imagining an ocean. The ocean itself is Cosmic Consciousness, but each individual wave in the ocean is our individual consciousness. Both are inseparable – just as each wave is a part of the entire ocean, though, it is at the same time a distinctly identified entity within the ocean.
  13. It resolves the fine tuned universe problem. By recent calculations, the probability of ending up with a universe such as ours is practically nil. There have been multiple parameters identified that must be exactly what they are – to an extremely high level of precision – for the universe to allow existence of stars, stable atoms, and life. Isn’t it highly ironic that we live in a universe that we observe? – despite that a statistical improbability of the multitude of “cosmic coincidences” is just unimaginably high! But, if there is an entity that is conscious and which computes The Grand Mathematical Structure into our sense data, then this entity must have designed it. If that is so, then the fine-tuned universe problem simply falls away.
  14. It resolves the problem of free will and purpose in universe. In the traditional materialistic universe, there is no purpose in the impersonal ‘ocean’ of elementary particles doing their mindless thing. But if the universe is designed – it’s designed for a purpose. The purpose of human life must obviously be aligned with the purpose of its Creator. But it’s a question for free will to decide on that. Free will in itself is an inherent and irreducible capacity of intellect, which is itself an inherent and irreducible capacity of human consciousness. These capacities in animal consciousness appear to be negligible or completely zero.
  15. It explains the nature and function of brain. The human brain is simply an algorithm (in The Grand Mathematical Structure) that processes and communicates information to our individual consciousness about what and how to experience. By finding the right triggers, it’s possible to instruct our consciousness to experience (or not to experience) all kinds of things – e.g. psychedelic substances, anesthesia, etc. Another function of this algorithm is to filter out information. Clearly, there is so much more happening in The Grand Mathematical Structure that what our consciousness is instructed to experience. It should be possible in principle to find a way to tweak a brain to filter out less information.
  16. It explains why there will never be a Turing machine (aka a binary/quantum computer) capable of consciousness/subjective experience.  Even a human brain cannot produce consciousness and experience in itself; it only processes and communicates information to an entity that is fundamentally capable of subjective experience. Such independent entity is called consciousness. Intelligence is not consciousness; it’s only one aspect that characterizes it – experience being the main one. A computer can only simulate intelligence  – thanks to some smart algorithms, but fundamentally – all there is is just a flow of electrons and voltage states (computed according to Boolean logic in the case of a binary computer and the logic of superpositions in the case of a quantum computer). In other words, there are just ones and zeros in a logical pattern. What is possible, however, is to integrate computers into a brain and influence consciousness through it.
  17. It explains the nature of mystical experience. Cosmic Consciousness can literally flow into an individual consciousness and become its subjective experience. Needless to say, all boundaries are dissolved in that state and there is simply an awareness of cosmic oneness and the most perfect state of consciousness
  18. It explains near death experience. It’s not fiction, fraud, psychosis, hallucination, but occasionally observed phenomena under the strict clinical conditions when a brain is pronounced to be clinically dead with flat EEG for a significant period of time over which a surgery takes place, but the owner of the brain later gives precise description of what he observed from aside while his brain was clinically dead and at the same time insisting that he was literally out of his body. In the brain is consciousness/experience worldview, this is not possible. But if consciousness exists independently, it’s obvious how this conundrum is resolved

Experimental proof

It must be said, however, that, while all of this is completely consistent with the existing scientific evidence, none of it is testable and provable in the strict (experimental) sense, as this entire subject is what’s called a meta subject – as in metaphysics. But it’s obvious that the materialistic paradigm is exactly of the same nature as well; it too is completely untestable and unprovable, and in addition, it is completely incomprehensible.

Materialism, or physicalism, is a philosophical opinion that is closely associated with science. It grew up alongside of science, and many people have a hard time distinguishing it from science. But it is not science. It is merely a philosophical opinion – such that leads to incomprehensible conceptual difficulties in the understanding of the universe – specifically the hard problem of consciousness and the phenomena of subjective experience.

Truly, all we know is our own sense-data on top of which we layer an elaborate system of abstractions (language). What lies behind the sense-data – physical universe or The Grand Mathematical Structure computed by Cosmic Consciousness is strictly speaking not accessible to scientific inquiry in its strict (experimental) sense. Physics operates solely inside the realm of the sense-data in a sense that constructions and conclusions of our intellect are compared against experimental data – which is nothing more but sense-data. But if we want to go further, we have no means to compare constructions and conclusions of our intellect against what lies behind the sense-data. Only pure reason not backed by experimental data (or mystical experience) can take us there.

it would seem that as long as pure reason actually solves problems in a manner that is both self consistent within itself and consistent with the conclusions of experimental physics, we are completely justified to accept it as our belief system. The alternative is a forever unresolved tangle of incomprehensible conceptual difficulties. Here, it’s really not a question of rebuttal – both paradigms are equally irrefutable in a strict sense, and by standards generally accepted and practiced in the physical sciences. Here, it’s a question of which paradigm has a better explanatory power and the one with a greater power should be chosen.

So if the idealistic paradigm is not testable and provable in the strict sense, do we need to bother? The answer and the choice are strictly yours. However, if you do decide it’s not worth anything and assuming you want to be intellectually honest with yourself, you must also admit that habitually sticking to the materialistic paradigm, from the perspective of formal (experimental) proof, is not only equally unjustified for the same reasons as above, but is actually counter productive and, at this point – after several millennia of intellectually struggling to think in terms of the materialistic paradigm – even dumb, as it only leads to incomprehensible conceptual chasm with no hope of resolution, as the history has shown.

So the choice is yours: either stay agnostic, waiting for a resolution which will literally never come if you insist on strict formal experimental proof or you simply pick a side. By picking the idealistic side, many of the immense conceptual difficulties are resolved – while at the same time incorporating and even elevating math and mathematical physics into the tools by means of which we truly discover the content of the mind of God. For me, the choice is easy. The age of materialism is overdue to be overthrown once and for all. Enjoy!

 

P.S.

I am not theistic at all in the traditional sense, but needless to say, Cosmic Consciousness is of course instantly identified with God (God The Father in Christian terms). Cosmic Consciousness is fundamentally the only ‘thing’ that exists – thus omnipresent – because everything else exists inside It. For this very reason, It’s omniscient; its thoughts constitute The Grand Mathematical Structure. It’s omnipotent – because by changing Its thoughts, It changes the universe. The act of designing and thinking The Grand Mathematical Structure into existence is an act of love. Cosmic Consciousness is infinite, but It divided a finite part of Itself into distinct entities – us. Thus we are created in the ‘image’ of God.

Ironically, I’m reminded of a great quote from Robert Jastrow’s “God and the Astronomers”: “For the scientist who has lived by his faith in the power of reason, the story ends like a bad dream. He has scaled the mountains of ignorance; he is about to conquer the highest peak; and as he pulls himself over the final rock, he is greeted by a band of mystics who have been sitting there for centuries”.

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