Introduction

This post will present a popular introduction to the ideas developed in On the Psycho-Physical Parallelism.

To put matters succinctly (if bluntly), it will introduce a physics-oriented reformulation of the Hard Problem of Consciousness, and follow a path outlined by key conceptual constraints onto a novel, experimentally-falsifiable physical model offering a resolution to the Hard Problem while maintaining consistency with known physics (and illuminating other well-known oddities in physics).

As is usually the case with inquiries into fundamental physics, despite the daunting objective of “better describing the universe”, the core ideas underlying the proposed model are ultimately simple.

The path we will follow

For millennia, the puzzle of consciousness has captured the attention and imagination of countless deep thinkers [and a fair share of quacks], giving rise to ever-more-refined philosophical (and increasingly, scientific) ideation.

Yet despite the increasingly refined exposition of the puzzle of consciousness, the study of consciousness has infamously and discouragingly failed to yield much (if any) convincing understanding. In many ways, a satisfying theory of consciousness seems as elusive today as ever.

Concerns that consciousness may forever defy elucidation have (somewhat amusingly) managed to creep so deeply into our belief system that they have manifested in our vocabulary -- with consciousness studies’ defining question having been dubbed the Hard Problem. Not the Interesting Problem, or the Key Problem, or even the Odd Problem, but the Hard Problem.

To make meaningful progress we will have to try something different. Rather than follow and untangle the threads of reasoning underlying the well-known philosophical debates, we’re going to cut through the Gordian knot and bootstrap a consciousness-compatible model of the universe from first principles.

I believe that a primary reason for the (legitimate yet) endlessly repetitive philosophical back and forth concerning consciousness is the lack of any available resolution of the puzzle that seems reasonably convincing. And so rather than delve into the same old discussions, we will press through the philosophical minutia as quickly as possible on the way to the proposed model. A reasonable model in our hands will cast some fresh light on the well known debates, which you may then return to at your leisure.

It will of course be up to you to decide if the arguments we will cover succeed in their aim of meaningfully illuminating consciousness.

Philosophical underpinnings

Science fiction author Robert Heinlein once wrote that “writing is not necessarily something to be ashamed of, but do it in private and wash your hands afterwards”. A foundational physicist must adopt a similar attitude towards philosophy.

Philosophy tends to have a bad reputation in physics circles, and in some ways this reputation is well-earned. But the truth of the matter is that advancements in fundamental physics usually build upon threads of reasoning which are more philosophical than physical or even mathematical. This has largely been the case since the dawn of physics, and will likely largely remain the case for some time to come. At any rate it is the case for us here.

I will keep the philosophical arguments as direct and as limited as possible, and furthermore, aim to construct a theoretical model which will bring them, too, into the realm of the empirical when we are through.

A working definition for “consciousness”

The term “consciousness” has come to refer to an almost ineffable quality of the mind, one with related yet orthogonal dimensions which would be best understood in terms of fields as varied as physics (mind-matter correspondence), psychology (the “self”), computer science (intelligence, self-modeling computation/self-awareness), and even spirituality (the “soul”).

We will explore only the physical aspect of the term.

Judging by the fact that you are reading this article, you likely have a certain notion of that which is referred to by the term "consciousness" (in the context of the mind-body problem). Furthermore, this notion is likely similar to others’ notion of the term. And yet we don’t have a true definition for “consciousness” at our disposal. Why is that?

A key reason is that we simply lack a model of the universe able to fully accommodate our implicit notion of the term — and are hence left without a language to describe it.

A light parallel

We can draw a parallel between our predicament and pre-Maxwellian attempts to define light.

Wikipedia defines light as follows: light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. This definition is useful because it reduces an observed phenomenon (light) to a specific manifestation of a primitive of our physical theory (the electromagnetic field). But for such a definition to be feasible, we must have a model of the universe broad enough to accommodate relevant aspects of the observed phenomenon. How would one go about defining the word "light" without possessing a model of the universe which accommodates Maxwell's equations (and by extension, the notion of "electromagnetic radiation")?

The answer is of course obvious to anyone who has successfully learned to associate the word "light" with a certain concept prior to studying the physics of Maxwell's equations. A working definition for light is simply: that which is sensed by our eyes. Though this definition is patently lacking from a modern standpoint, it’s good enough to frame the initial inquiry into the underlying structure of the observed phenomenon.

A working definition isn’t (and doesn’t aim to be) precise or complete. Instead, it aims to make it possible to vaguely refer to some object or structure without first precisely grounding it in some coherent knowledge system.

Before we go back to discussing consciousness, note that even this crude working definition for ‘light’ draws on certain primitives; for instance, it is only intelligible for someone who has a rough notion of the universe as a 3-dimensional arena of sorts. Modern physics has utterly redefined every aspect of these crude primitives, and has in a sense retroactively invalidated this working definition; but physics is a bootstrapper’s pursuit, where every rung in the ladder of conjectured physical primitives always holds-out long enough for us to climb closer to the truth.

The consciousness instance

Our primary object of study in this post is somewhat different from the structure typically considered in discussions of consciousness (primarily in its “temporal extent”, as we shall soon see). We’ll therefore diverge a bit from the standard nomenclature, and dub it the consciousness instance.

The working definition we will use for the consciousness instance is that which each of us is completely certain of.

[Please indulge a bit of over-the-top philosophizing as I attempt to draw attention to the particular substructure of the universe pointed to by this working definition. Things will get a bit hairy but rest assured that we will quickly return to a more eye-level discussion.]

As French philosopher René Descartes famously recognized (along with the writers of The Matrix), the only thing one can be absolutely sure about is one’s experience. You can never be absolutely certain that you are not in fact living in a Matrix-style simulation, and further, that advanced neurological surgery wasn’t used to implant all of your memories.

Suppose you were presented with convincing evidence that the universe was in fact created last Tuesday at 4:07pm [pacific time], that all of your memories prior to that have been implanted, that you are plugged into a simulation, and that the “real” universe has laws of physics so different from those of your perceived universe as to be rendered nearly nonsensical. Perhaps you even find out that the closest thing to a physical body you have in this real universe is a structure somehow reminiscent of a giant 8-dimensional lizard.

To say that such a revelation would turn your world upside down would be an understatement [and besides, which way is up in an 8-dimensional universe?]; your current belief system would be rendered nearly entirely and absolutely mistaken.

And yet, one element of your knowledge system would survive such a revelation unscathed: your knowledge of the ”experience” which “accompanies” your existence.

Recall that the point of this brief discussion is not to cast cheap existential doubt on aspects of life, but rather to help draw your attention to that substructure of the universe pointed to by our working definition for the consciousness instance (“that which each of us is completely certain of”).

As a highly simple demonstration, take a look at this picture of a blue rectangle:

While you gaze at the picture, you can be certain that the so-called “mental image” of a blue rectangle is a structure which exists in the universe — even if those structures we call "molecules", "pixels”, “screens", "eyes", “neurons”, "brains", even "space-time" — are not.

This “mental image” — an instance of experience itself — is what we dub the consciousness instance.

The consciousness instance vs. a “consciousness continuation”

Each consciousness instance, in a sense, corresponds to a single time slice of one's experiences (one is only completely sure of one's experience here and now). However the continuation of all consciousness instances associated with a single individual over time also forms a structure of interest; it is that which we typically associate with the dynamic yet persistent "I" at the core of our being.

Consciousness-instance continuations are what people typically refer to when they use the term “consciousness” (e.g when saying things like “when you look at the red rose, a picture of a red rose comes into your consciousness”). For clarity, we will refer to such structures as consciousness continuations.

Since a consciousness continuation is composed of a series of many (“locally” similar) consciousness instances, we are going to tentatively consider it an emergent phenomenon to be explained in terms of the more fundamental consciousness instance.

The consciousness continuation vs. an effective consciousness continuation

Let’s take a moment to cover a source of [seemingly endless!] confusion and miscommunication that all-to-often hinders discussions and deliberations on the nature of consciousness.

The “consciousness instance” — that substructure of the universe which is revealed to us via a kind of introspective analysis — appears to also reveal itself in an entirely different manner: via imprints upon the so-called “real world out there”, i.e. the world of particles, and fields, and tables, and chairs.

You can open your mouth and report (i.e. imprint upon the world of particles) not only your belief that your body is associated with a consciousness instance, but also a detailed account of the contents of your current consciousness instance. Moreover, as we all know, people have a strong intuition that “the consciousness continuation inside of them” is responsible for much of their actions; or put another way: consciousness continuations are reported by brains to play a key role in their observable behavior as cognitive agents.

Such reports bring into the universe an “outside view” of sorts of the consciousness continuation — one that captures a computational role that the consciousness continuation appears to play in the brain’s cognition.

This “outside view” is crucially important: it is where much of our conjectures about the nature of consciousness come from, including our belief in the existence of consciousness instances other than the one we are each currently associated with. In fact, before we are through we will put this “outside view” of the consciousness instance to work as a major constraint guiding the construction of a consciousness-compatible model of the universe.

Nevertheless it is crucial to remember that this “outside view” of the consciousness continuation captures structure distinct from the consciousness continuation itself; it ultimately captures complex patterns encoded in (and revealed through) the arrangements of particles, and hence simply does not intersect with the substructure of the universe captured by our working definition for the consciousness instance — which is given without reference to the arrangement of particles (think back to “the mental image of a blue rectangle”).

A critical feature of this “outside view” of the consciousness continuation is that it captures complex, high-level hallmarks of cognition — not some particular mechanism or structure. An “apparently conscious” system isn’t a system which produces some special pitch of sound, or some particular twitch of a muscle — but a system which exhibits high-level behavior we associate with emotion and (a particular kind of) intelligence. As such we will dub this “outside view” an effective consciousness continuation, as it is revealed only via the effective behavior of complex systems (i.e. brains), with the underlying mechanisms abstracted out.

To put this idea into a more familiar context, imagine a black box which outputs a video feed of a billiard-ball bouncing inside the box. Among other options, the box might contain a camera live-streaming an actual billiard ball bouncing inside of it — or an accelerometer-equipped computer simulating the behavior of a bouncing billiard ball. Given the high-level information outputted by the box, both scenarios are indistinguishable despite the fact that they are implemented as entirely distinct physical processes (whose structures carry a certain non-trivial correspondence). In the spirit of our previous discussion, the box could be said to contain an effective bouncing billiard ball.

Again

The confusion between the consciousness-continuation and the effective-consciousness-continuation is so pervasive that this point bears repeating.

In a sense, each of us has only a single data point concerning the consciousness continuation: we have (more or less) direct evidence of the consciousness continuation associated with our own body. In the context of this single data-point, we identify a strong correspondence between the contents of our consciousness continuations and a subset of our body’s behaviors (e.g. cognitively complex speech, expression of emotion, etc.) — and hence declare said subset of behavior as characteristic of an effective consciousness continuation.

Through the course of our lives, we interact with a certain class of physical structures which we dub “other people”. Since “other people” exhibit those same consciousness-characteristic behaviors [though bureaucrats do sometimes make you wonder…], and since they also share many meaningful similarities with our own body (e.g. concerning their underlying mechanisms of operation, manner of origin, etc.), we conjecture that these “other people” are likely also associated with consciousness continuations.

This is all well and good but it’s crucial to remember that in principle, there is no a-priori reason to believe with certainty that a consciousness instance is always accompanied by behavior characteristic of an effective consciousness continuation — or vice-versa. For our purposes, the important take-away is that the consciousness instance/continuation are structures related to yet completely distinct from the effective consciousness continuation.

It’s an it, not an I

We are used to thinking of the consciousness instance (the “mental image of a blue rectangle”) as a manifestation of a “self”, of an “I” which observes the universe and is somehow external to it. While it may well make sense to think of consciousness in such terms under certain circumstances, in this physics-oriented exposition, we must think of the consciousness instance as a thing, a structure, an “it” which simply exists in the universe — not so differently from, say, a particle or a photon (or a table).

In other words, the “mental image of a blue rectangle” is to be thought of not as an “observation” of the universe but as itself a structure which exists in the universe, and which must somehow be accounted for by any description of the universe which purports to be complete.

If you are used to thinking of the universe as a 3-dimensional arena full of rigid bodies, this kind of view must seem jarring; the “mental image of a blue rectangle”, at face value, is neither a 3-dimensional rigid body nor a pattern encoded in the behavior of 3-dimensional rigid bodies (unlike e.g. a tennis ball, a storm, sound, and manifestations of effective consciousness continuations). But the universe is not merely some 3-dimensional arena — that much is made clear by modern physics [we can’t tell the universe what to be!]. And by definition, any structure in existence is part of the universe. The consciousness instance is no exception; it exists and it is therefore (trivially) a structure which can and does exist in the universe.

Look-back

So far all we have done is come up with a few working definitions:

• The consciousness instance refers to that which each of us is completely certain of (during any given moment); think back to the “mental image of a blue rectangle”. We regard it as an “it” — as a structure which exists in the universe and which must be accounted for by descriptions of the universe.
• The consciousness continuation refers to the stream-like collection of (“locally”-similar) consciousness instances associated with a single individual over time; the dynamic-yet-persistent “I”. We tentatively regard it as an emergent structure to be described in terms of a series of consciousness instances.
• The effective consciousness continuation refers to a cognitive agent which gives rise to high-level behaviors (manifesting in the effectively-classical world) indicative of intelligence and of emotion. We intuitively associate such behaviors with the consciousness instance because when said behaviors are acted-out by our own bodies (e.g. through speech, facial expressions, etc.), they strongly correlate with the contents of our own consciousness continuations.

These working definitions aim simply to ground our discussion in some shared context -- and to help us avoid the same old mis-communications which are so prevalent in discussions concerning consciousness.

What kind of questions are we allowed to ask? [or: what’s the point of physics, anyway?]

The physics-oriented reformulation of the Hard Problem we will seek to answer is: what is a good theoretical description of a consciousness instance, and what is the minimal regularity relating consciousness instances to “matter”?

To see that this really is the key question we must seek to answer, let’s take a step back.

The dividing line between confusion and understanding

What is it about our conception of consciousness that renders it so uniquely ill-understood? A good way to answer this question is to contrast consciousness with better-understood natural phenomena.

Consider gravity. Under present-day physics we consider gravitation to be the manifestation of patterns of space-time curvature permeating the universe in the manner described by general relativity. In the future, our theory of gravity will likely refine, and perhaps even utterly redefine this picture of gravity in terms of a richer structure — of which the general-relativistic account is but an effective description.

But the sense in which we consider gravity (unlike consciousness) to be understood doesn’t truly depend on any general-relativistic subtleties, and in fact, goes all the way back to Newton’s account of gravity in terms of his namesake law of universal gravitation.

What is it exactly that Newton did for gravity, and which hasn’t yet been done for the consciousness instance?

Newton didn’t explain why gravity manifests in the universe, or “what gravity really is”. Instead, what Newton did was the following:

1. He defined (theoretical) structures constituting the primitives of a physical model, and which are conjectured to correspond to elements of physical reality -- to that which is: (Galilean) space-time, and 3-dimensional solid objects with “mass”, as well as a (relative) position and a (relative) velocity in the space-time (“particles”).
2. He formulated regularities relating said theoretical primitives to one another: Newton’s laws of motion, and his law of universal gravitation.
3. He compared the model's structure against the structure of observable physical reality, and found agreement.

This prescription is followed by every fundamental theory of physics, from classical Newtonian mechanics, to classical electrodynamics, to special & general relativistic dynamics, to quantum mechanics.

A fundamental physical model simply defines a set of theoretical primitives which are conjectured to correspond to elements of physical reality, along with a set of regularities conjectured to describe the relations between said elements of reality. If the model’s emergent structure matches our observations, we say that the model is a good model of reality.

The right questions to ask about the consciousness instance

That the consciousness instance is a structure manifesting in our universe is simply a fact, more subtle but ultimately even less refutable than the conjecture that the ‘particle’ is a structure manifesting in our universe.

Physics cannot explain “why” a certain fundamental structure exists, or “what it is, really” — except perhaps in conjecturing that the structure isn’t fundamental after all, and is given in terms of different fundamental structures, of which, in turn, such questions are not asked.

All we can ask of physics is to maximally describe the universe, and to do so using the most minimal description sufficient for the job.

How do these principles apply to the study of the consciousness instance?

Whatever else may be true of the consciousness instance, it obviously carries internal structure, and this internal structure obviously relates to other kinds of objects which are captured by our existing models of the universe. For instance, it is clear that a consciousness instance encoding the picture of a rectangle is different from one encoding the picture of a triangle, one encoding the taste of a sandwich, or the altogether absence of a consciousness instance. Furthermore, we strongly expect a consciousness instance encoding the picture of a rectangle to manifest in the universe while one gazes at a picture of a rectangle, i.e. while photons encoding the picture of a rectangle interact with one’s retina so as to bring about a certain cascade of neural activity.

All we can ask for, then, is for our physical theory to maximally describe the consciousness instance, and to tell us how it relates to all other objects described by our physical theory.

Ok, but why bring fundamental physics into this discussion?

Our existing physical models (as given by the quantum-mechanical standard model, and by general relativity) capture a whole lot of nature’s structure.

They can model practically every aspect of nature we have explicitly probed thus far, from macroscopic mechanics, to chemical interactions, to energetic particle collisions, to astrophysical phenomena.

In particular, no property of the brain we have thus far probed (in the laboratory, or by the water-cooler) has given us any reason to doubt our existing theories’ capacity to model the brain as well (including the peculiar phenomena whereby human brains utilize muscle tissue coupled to them via a network of nerves to vocalize claims of being associated with consciousness instances).

In some sense it might seem natural to conclude that our existing physical theories indeed model the consciousness instance as well — and that our physics-oriented variant of the Hard Problem will be answered by identifying the way in which the physical primitives of our existing models interact to bring about a complex conglomerate identifiable as a consciousness instance.

That we find this prospect unlikely is evident by the fact that we think of the Hard Problem as so… well, hard. Nevertheless a precise articulation as to why we find this prospect unlikely is difficult to come by. Can we provide such a precise articulation?

Look-back

Having provided working definitions for the consciousness instance, the consciousness continuation, and the effective consciousness continuation, we set our sights on the consciousness instance as our fundamental object of study. We then identified a physics-oriented variant of the Hard Problem in the question: what is a good theoretical description of a consciousness instance, and what is the minimal regularity relating consciousness instances to all structures captured by our existing physical theories? Finally, we hinted that this variant of the Hard Problem must be answered at the level of fundamental physics rather than at the level of emergent effectively-classical dynamics.

We are now ready to explicitly delineate those characteristics of the consciousness instance which are incompatible with any dynamical classical account -- and which for so long have been implicitly taken to render any resolution of the Hard Problem beyond reach.

The classically-incompatible qualities of the consciousness instance

Interaction with brains may have yet to directly suggest any conflict between nature and our existing picture of the universe. But we of course know about the consciousness instance less through interaction with other brains, and more through an (imperfect) capacity to analyze the consciousness instance associated with our own brain (which incidentally, is an aspect of the consciousness instance which also begs an explanation in a final model). This “introspective” capacity is what our working definition for the consciousness instance relies on.

It is sometimes claimed that we should dismiss knowledge acquired via “introspection” of the consciousness instance and restrict our attention to knowledge acquired via more objective means, such as measurements conducted by lab instrumentation. Though this claim is not entirely ludicrous, a part of me is itching to ask how one could distrust even basic observations of the consciousness instance and yet maintain trust in lab instrumentation results, seeing as how observation of the consciousness instance forms the (Des)Cartesian ground floor of all conscious thinking (conscious thinking in the psychological aspect of the term); has anyone ever read a lab instrument’s result in a way that does not involve “reading” his or her consciousness instance?

But reminding myself of my commitment to circumvent the philosophical rabbit holes and push through to a description of a physical model as quickly as possible, let’s abandon this line of thinking and simply take this “introspective” knowledge for granted for the time being. Once we have a model in our possession, we can return to this discussion with fresh perspective and a clearer vocabulary.

“Introspective” analysis of the consciousness instance suggests it possesses 2 key qualities which render it incompatible with any classical model — regardless of the particulars involved (the meaning of “classical” will soon become clear enough, but for now you can think of the world of Newtonian billiard balls and Leibniz’s mills).

How could we make such a wide claim without regard to specifics? Well, the 2 qualities we will discuss simply do not manifest in any classical model — and so it seems all but impossible to identify the consciousness instance with any structure which does manifest in some given classical model.

Non-correspondence to classical information

“Is my blue the same as your blue?”

When introducing the concept of consciousness, philosophers are fond of presenting questions along the lines of ‘is your blue the same as my blue?’. Such questions try to get at the fact that any consciousness instance which encodes “seeing the color blue” has an aspect to it which is not captured by the label “blue” (and which therefore may differ from person to person). [In the context of our discussion, we would further say that this aspect is classically-indescribable and therefore not captured by any label you might come up with; but more on that, in a moment.]

To appreciate this, let’s think through what the label “blue” does capture.

Color-Blind Billy

Suppose Billy is an adult who’s been fully color-blind from birth, and who is given a special set of glasses designed to fill the color gap by superimposing a color-encoding shape on top of each object in the glasses’ field of vision.

For instance, say that the glasses superimpose little triangles on top of all red objects, little circles on top of all yellow objects, etc.

Even if you told Billy nothing about the glasses, he would soon pick up on the fact that the glasses sort all objects into a few largely consistent categories: a triangle category, a circle category, etc. Not much later, Billy would realize that the glasses’ shape categories correspond to the commonly used color categories. If Billy was looking for the apartment “with the yellow door”, he would know to look for the door with little circles superimposed on top of it.

This illustrates the universal significance of color labels captured by our language: they sort the visual world into categories which are largely common across all people and which are largely consistent over time (and which are of course ultimately rooted in the sensitivity of our eyes to different wavelengths of light). When there are inconsistencies, they have satisfying explanations (e.g. the white fence was painted blue).

What would it mean for your blue to be different from my blue?

Suppose that Billy has a friend, Sheila, who is likewise colorblind from birth.

And suppose further that Sheila also got a pair of color-shaping glasses, but ones made by a different brand, which uses a different color-to-shape mapping: red objects are superimposed with stars, yellow objects with pentagons, etc. [talk about vendor lock-in].

Bob and Sheila could have an entire functional conversation peppered with “pass me the green book”, “the keys are in the gray drawer”, “watch out for this flying blue box”, etc. — even though each experiences the color categories in completely different ways.

The indescribability of the “experience” of color

This little thought experiment is getting at the fact that color-seeing people could likewise each “experience” wildly different sensations in association with the same color labels. And furthermore, unlike Billy and Sheila, who could ultimately discover the discrepancy by jotting down the shapes they each associate with color labels, color-seeing people have nothing to jot down or say about the “experience” of color that isn’t tied back to experience of color. [If you disagree, describe the color “red” to a congenitally blind man, I’m sure he would appreciate it!]

The classical incompatibility

A characteristic common to all of our existing models of the universe is the correspondence between the possible states of each model and sequences of classical bits. In other words, all possible states of the model are fully expressible, in some manner, using “classical information” — i.e. some expression which could be written down.

This information can come in many forms: a Newtonian model might describe a certain distribution of massive 3-dimensional objects; a Maxwellian model might add that ‘the electric and magnetic fields over this region take on such and such values’; a quantum-mechanical model might say that ‘the wave-function corresponding to the position of the electron is given by such and such function’. In all cases, reality is presumed to be fully described by some expression that can be written down.

To an extent, the expression of phenomena as transformations over classical information is the very essence of our idea of a model. And yet a defining property of the consciousness instance is that it has aspects to it which can’t be described or written down; what expression could possibly describe “the experience of blue”? If no expression could fully describe it, how could any model possibly accommodate it?

It is likely this quality of the consciousness instance which is most often taken to spell doom for our entire endeavor, rendering the consciousness instance forever beyond the grasp of reason. But we will soon see that even this characteristic of the consciousness instance can be absorbed into a scientific theory.

Objective integration of complex information

Each consciousness instance harbors complex internal organization which (partially) corresponds to complex classical information -- i.e. to classical information given by many bits.

For instance, when you gaze at a picture of a rectangle, a part of your current consciousness instance encodes the structure of the (informationally complex) shape of a rectangle; likewise, when you gaze at a printout of the binary string “101001”, a part of your current consciousness instance encodes the structure of that (informationally complex) binary string.

This informational complexity of the consciousness instance is one of its most fundamental attributes. Each consciousness instance can be thought of as a conglomerate of sorts; as a collection of many simple elements which add up to a single complex whole.

The classical incompatibility

As we shall see, there is a sense in which the tactics we use to identify “units” of complex information under classical models are fundamentally arbitrary and subjective, while the “unit” of complex information defined by the consciousness instance must be objectively determined.

Complex conglomerates under classical models

Classical models can support complex conglomerates of many kinds; from mills, to computers, to birds, to the stock market. However they are all identified in the same manner: by looking for structures which efficiently capture some of the complex patterns which manifest in the underlying particulate substrate.

There are instances in which a collection of primitives of a classical model (e.g. atoms) may be efficiently abstracted as a single entity (e.g. a tennis ball, or a bird), governed by some set of emergent higher-level regularities. But such emergent abstractions provide merely an effective description of the behavior dictated by the fundamental lower-level regularities.

Since the regularities which define classical models operate on individual primitive elements (and are unaffected by any efficiencies of description), complex classical conglomerates ultimately make for convenient yet redundant, incomplete, and arbitrarily-defined abstractions over the fundamental particulate reality.

For example, a sufficiently advanced classical model of the brain would depict not some unified structure, but rather a whole bunch of organic molecules interspersed with water and other molecules, interacting chemically, electrically, and physically amongst themselves. While the activity of molecules which make up one part of this brain could influence the activity of molecules which make up other parts of the brain more “easily” than it could influence activity in a nearby rock, such influence would be mediated by chains of local interactions which once again, operate only on individual molecules — and are thus blind to the “brain” conglomerate.

In the context of such a classical model, the complex structure we call “a brain” is an extremely useful (for us, as thinking agents) abstraction efficiently capturing much of the emergent behavior of relevant primitive elements of the model. It allows us to make reasonably good predictions about the high-level behavior of a world containing brains without painstakingly working out the roughly 10^24 [that’s a 1 followed by 24 0’s] particle interactions taking place within each brain during any given moment. Nevertheless the fact remains that the brain — as an integrated conglomerate — is ultimately nothing but a subjectively-defined description of the (objective) particulate structure with which the model operates. On a fundamental level, it adds nothing which is not already there in the particulate description, and hence it is not indicated by the model itself.

The point isn’t that complex structures such as a tennis ball, or a brain, or the stock market are “real” / “not real” under classical models. The fact of the matter is that they depict real high-level patterns in the underlying particulate structure; we can leave it up to philosophers to decide whether or not this qualifies for use of the word “real”. The point is that the manner in which we identify “units” of complex information in classical models is not determined by any law-like fundamental principle indicated by nature and revealed through experiment, and is thus subject to subjectivity and to freedom of choice. This freedom isn’t merely a freedom of fuzzy edges — identifying any integrated conglomerate whatsoever in a classical world is not a procedure indicated by the fundamental model.

The informational complexity of the consciousness instance

First, let’s note what we don’t do when we recognize the complex information manifesting in the contents of a single consciousness instance: we don’t look at some intricate particulate description of reality and identify parts which are conveniently abstracted as integrated wholes. This can be exemplified in the context of the Matrix-style simulation argument we covered earlier: even if the true nature of the universe is radically different from the picture you currently hold on to, the complex information you would consider to constitute the parts of a single complex unit (as the contents of a single consciousness instance) would remain unchanged. The integration of the complex information manifesting in the consciousness instance precedes and transcends any notion of a model in which it could prove conceptually useful.

(This is a good time to remind ourselves that we are discussing the consciousness instance, not the effective consciousness continuation. An effective consciousness continuation, unlike the consciousness instance, is defined precisely by looking for high-level patterns of behavior which can and do manifest in the “medium” of effectively classical structures.)

If we think of the consciousness instance as a structure which objectively exists in the universe and which carries some objective information content [and it’s hard to think of any structure more objective], then we must have some objective rule to tell us what (complex) information each consciousness instance contains. And yet as we’ve seen, complex units of information are simply never objectively-defined under classical models.

Look-back

What have we got so far?

Having provided a working definition for the consciousness instance, we set out to answer the physics-oriented variant of the Hard Problem: what is a good theoretical description of a consciousness instance, and what is the minimal regularity relating consciousness instances to all structures captured by our existing physical theories?

We proceeded to identify 2 qualities of the consciousness instance which render it incompatible with any possible classical model:

1. The consciousness instance is not fully expressible using classical information; it has aspects which simply cannot be written down (“is your blue the same as my blue?”). In contrast, under classical models, all possible structures are fully expressible using classical information.
2. The consciousness instance harbors complex internal structure which (partially) corresponds to complex classical information -- and which we require to be objectively given by our model. However we’ve seen that under classical models, complex conglomerates are arbitrarily-defined -- as they are identified by looking for structures which merely efficiently capture complex patterns which manifest in the underlying particulate substrate.

These classically-incompatible qualities of the consciousness instance make it impossible to identify the consciousness instance with any structure which manifests in an effectively-classical model. Hence we must evidently turn to fundamental physics in our search for a resolution of the Hard Problem.

A way forward

So the consciousness instance can’t be captured by any classical model. So what?

Putting aside for a moment the “small problem” that classical models seem to do a decent job of describing our universe (and in particular, our brains), the way forward is clear: we need to find a theory which is capable of modeling the consciousness instance.

What would such a theory look like? For starters, it would have to capture the 2 classically-incompatible qualities of the consciousness instance we just described.

Objective integration of complex information: potential solutions

One way to get objective information integration out of a given model without too much fuss is to conjecture some ad-hoc regularity which simply serves to identify units of complex information in the states of the (otherwise-classical) model. For instance, we could decree that the information making up a single consciousness instance is encoded in the relative positions of particles lying within some magical “consciousness volume” in relation to one another. Or perhaps that all particles which behave in a way that gives rise to an effective consciousness continuation bring into existence corresponding consciousness instances — regardless of the particular mechanisms involved [presumably as an act of heavenly grace].

A more elegant and reasonable-sounding example is given by the ‘Integrated Information Theory’ of consciousness (IIT), which finds information integration in the long-term causal relations between the primitive elements of a classical model.

But no matter how aesthetically pleasing the conjectured regularity, at its core it is arbitrary, as the supposed "integrity" of the complex information it identifies doesn’t affect the model's measurable behavior in any way whatsoever. It is therefore undetectable and unverifiable; there is no way to distinguish a world with such information integration from one without it.

Assuming that the universe isn’t out to get us [admittedly, perhaps the least likely proposition in this entire exposition], objective identification of information integration must be inexorably and uniquely pointed to by the model itself, rather than by some arbitrary analysis of the model’s emergent high-level structure. A plausible criterion which would satisfy this condition is that for information to be regarded as objectively integrated with respect to a given model, it should be impossible to state the regularities of the model in terms of subsets of the information.

Candidate models

This consideration significantly constrains the form of any theoretical framework which could possibly model the consciousness instance. But it also constrains the pool of candidate models we could reasonably draw from, since there is only a single model choice which would not itself be arbitrary: the model given by the fundamental laws of nature.

This doesn’t mean that the only theoretical framework which could possibly effectively model the consciousness instance is some final Theory of Everything. But it does mean that the fundamental information integration we identify in a candidate theory must extend all the way down to the fundamental fabric of reality, through every intermediary effective theory. A candidate consciousness-modeling theory which ascribes objective integration to some unit of information would be ruled out from consideration were it found to arise out of a more fundamental model which does not.

Non-correspondence to classical information: potential solutions

[This section will quickly escalate. Now would be a good time to be paying close attention].

Where we get stuck

Consider once again the (“classically-indescribable”) manifestation of color within a consciousness instance — or as philosophers would call it, color-associated qualia (singular: quale).

When we imagine to ourselves a model of the universe which “maximally accounts” for consciousness, we imagine a model which would not only describe the complex classical information manifesting in each consciousness instance, but also assign identities — “qualia RGB values” of sorts — to each possible color-associated quale (akin to the RGB values which can be assigned to the light waves sensed as color).

Such a model would be far from useless, and would at first glance appear to go a very long way towards resolving the variant of the Hard Problem we have been contending with. It would allow us to say things such as “the model predicts that there are 4 consciousness instances associated with the effectively-classical structures in this room; here is the classical information manifesting in each, and here are the qualia manifesting in each”. Within the context of such a model, the proverbial “is Alice’s blue the same as Bob’s blue?” could finally be answered (if only in principle).

Yet when we imagine such a model, we quickly realize that it would leave a central quality of reality’s consciousness instance unaccounted for; you could always ask: why does quale #424.491.f9 feel like this and not like that? We would maintain that such a model must be accompanied by an unobservable “qualia dictionary” mapping each quale-representing object captured by the model to the actual quale manifesting in reality which corresponds to it — to some missing piece not captured by the label.

Even more disturbingly, if such a model was indeed experimentally found to correctly capture all observable behavior in our universe — including the cognitive mechanisms underlying our intuition that there is a certain classically indescribable aspect to the consciousness instance — we would be forced to conclude that there isn’t any classically-indescribable aspect to the consciousness instance after all, and that the “qualia dictionary” can be discarded (if this point is not clear, it would be worth revisiting it after reading the following section).

And yet (thinking back to the Matrix-style simulation argument) we are more sure of the classical-indescribability of the consciousness instance than we could be of the authenticity of experimental evidence pointing to the contrary... Leaving us in an endless and hopeless loop of confusion and mystery.

A way forward

This loop of confusion would be avoided under a model satisfying a simple yet drastic conceptual leap: admittance of structures which are partially yet fundamentally classically-indescribable.

What in the world could that possibly mean? We can imagine a model containing structures which are fundamentally not fully isomorphic to any sequence of classical bits, and hence could not be fully described by any expression that could be written down (not even in principle).

Objects in such a model (i.e. the structures intended to correspond to elements of reality) could be thought of as consisting of 2 components: a “standard” component capturing the classically-describable substructure of the relevant slice of reality, and a “novel” component formalizing an uncertainty about the particular classically-indescribable substructure also appearing in the makeup of that slice of reality.

To be meaningfully supported by the model, the classically-indescribable substructure of an object must observably participate in the regularities described by the model (e.g. the laws of dynamical evolution).

Though this idea is rather vague as stated, you might already sense that it can be made mathematically precise, and that characteristics of such a model could be worked out theoretically — regardless of whether such a model has anything to do with reality.

How such a model would capture the consciousness instance

To make matters concrete in the context of consciousness, imagine 2 consciousness instances corresponding to 2 people looking at the same picture — whose color-associated qualia are entirely distinct.

In this (simplified) case, the classically-describable substructure of both consciousness instances would be identical, and in fact would be given by the structure of the picture itself (since both consciousness instances are partially isomorphic to the information conveyed by the picture). The classically-indescribable substructure of each consciousness instance, however, would be distinct.

Since (by definition) a description of the classically-indescribable substructure could not be written down, both consciousness instances would be described by the same object under the model — where the modeling object would capture the classically-describable substructure of each consciousness instance, as well as formalize an uncertainty about the particular qualia making up each consciousness instance.

Hold your horses! I can label a consciousness instance! [Or: the price we pay for the conceptual leap]

Conjecturing that consciousness instances are fundamentally (partially) classically-indescribable comes with a cost. In fact the conjecture conflicts with a key quality we intuitively ascribe to the consciousness instance — but a quality which, as we shall presently see, we were never justified in ascribing to the consciousness instance in the first place.

In asking the proverbial “is Alice’s experience of blue the same as Bob’s experience of blue?” we tacitly assume that it is meaningful to ask questions about some particular qualia which can be referred to as “Alice’s experience of blue” and “Bob’s experience of blue”. But such references make for classically-describable labels we can attach to qualia instances — and are thus incompatible with a world in which qualia are meaningfully classically-indescribable.

If every one of reality’s qualia could be assigned a label such as “Alice’s blue” or “Bob’s red” (if only in principle), then fundamentally, the universe could be described with a model akin to the one we recounted earlier. The model could state “there is a consciousness instance associated with the objects in this room; it is composed of “Alice’s blue” and “Bob’s red” making up the inside and outside of a star shape”. But once again, the model would have to be implicitly supplemented by an unobservable “metaphysical qualia dictionary” mapping each quale-describing entity captured by the model (e.g. “Alice’s blue”) to the real quale it in fact corresponds to.

And once again, given such a model, we would be justified in slicing the unobservable “qualia dictionary” out of our theory altogether — abandoning our notion that there is a (classically-indescribable) aspect of the consciousness instance not captured by some label, and leaving us once again in a loop of confusion and mystery…

We seem stuck... but are we?

Is YOUR blue the same as your blue?

The idea that it’s sensible to ascribe a label such as “Alice’s blue” to a particular quale is based on the notion that there is a certain constancy to the qualia which manifest across a consciousness continuation. You intuitively deem the quale you associate with the label “blue” today to be no different from the one you associated with the label “blue” yesterday.

But how do you know that the quale you label “blue” today is identical to the quale you labeled “blue” yesterday? You are probably thinking, ‘that’s silly, I remember what yesterday’s “blue” quale was, and it’s exactly identical to what it is today’.

This kind of an answer should make you pause, because that is an extraordinary statement! It is claiming that the oh-so-ineffable color sensation, which you can’t describe, jot down, or make absolute in any way, is in fact something your brain can memorize!

But before we get too excited about such a prospect, let’s take a step back.

There is no doubt that the comparability of color qualia within a single consciousness instance is part of our most basic notion of the consciousness instance. For instance in the picture below, you can tell that the “indescribable color experience” you associate with the triangle is identical to the one you associate with the circle, and different from the one you associate with the square.

Hence any satisfying model of the consciousness instance would have to account for the fact that qualia, though classically-indescribable, may be compared against one another. But when you are recalling yesterday’s blue sensation, you are not directly accessing the quale manifesting in yesterday’s consciousness instance. Instead, color information which was present in yesterday’s consciousness instance becomes encoded in your current consciousness instance. When you supposedly compare “yesterday’s experience of blue” with “today’s experience of blue” you are in fact comparing sensations associated with the labels “yesterday’s experience of blue” and “today’s experience of blue” — which both manifest within your current consciousness instance.

Of course, we could entertain the notion that color-associated qualia really are constant across an entire consciousness continuation; but the point is that contrary to our naive intuition, we have no evidence whatsoever to support this proposition. And thus if a coherent model of the universe requires us to abandon this idea, we can do so without reservation.

We generally accept that it is only the classically-describable substructure of the consciousness instance which meaningfully “leaks out” into “the real world out there” (via our speech, writings, actions, etc.); you can tell your friend that you saw a blue flower, but you can't tell your friend which color-associated quale manifested this experience. Supposing that it is otherwise when it comes to our memories is a hypothesis that buys us nothing. If your color-associated qualia were only consistent for 8 days at a time (or for 8 seconds at a time), you would be none the wiser. Furthermore, no modification to anything else you think about the universe would be necessary to accommodate such a picture of reality.

And so this is the conclusion that we are forced into: if the ideas we have been outlining are correct, then qualia are not constant across a consciousness continuation, and the quale you called ‘blue’ yesterday (or 2 minutes ago) is not identical to the quale you would call ‘blue’ right now.

[This conclusion conflicts with my own naive intuition as much as it conflicts with yours… But what must have crossed the minds of ancient scholars when they first realized their ideas implied the rotation of the Earth?]

One last philosophical leap: can the consciousness instance be measured?

Before we can finally cross from the philosophical over to the scientific, we have to undertake one last philosophical endeavor. It concerns a point which is as trivial as it is profound, and to which we have already alluded in passing many times throughout this article. Nevertheless it is important enough (and as far as I can tell — disregarded enough) to warrant addressing explicitly.

If we are ever to resolve the physics-oriented variant of the Hard Problem, we must be able to experimentally detect the consciousness instance in the laboratory. Since measurement results are ultimately encoded in arrangements of matter (‘matter’ in the sense of everyday physics) — e.g. in the position of a lab instrument’s dial — a scientific theory of consciousness could ultimately be achieved only if the consciousness instance is able to influence this arrangement of matter. Should we expect this to be possible?

False start: the appearance of ‘free will’

One might naively draw some encouragement from the persistent appearance of what some call ‘free will’: we generally feel as though the ‘consciousness continuation inside of us’ controls much of our bodies’ high-level function — which would seem to suggest that indeed, consciousness instances can influence matter.

However in principle, it is entirely conceivable that the consciousness-continuation representation of ‘having the will to do X’ is brought about by the same mechanism which causes X to be physically acted out — but doesn’t itself participate in the causal chain which leads to X being acted out; in other words, that our observation that ‘the consciousness continuation inside of us controls our bodies’ actions’ is in fact nothing but a psychological illusion. As such, this observation doesn’t fundamentally teach us anything about the ability of the consciousness instance to influence the arrangement of matter.

Extracting insight from our knowledge of the consciousness instance

A profound quality of the consciousness instance comes into full view upon asking the simple question: how has consciousness come to be discussed in the ‘real world out there’, e.g. in papers presented in philosophical journals?

For discussions of consciousness to appear on paper, ink molecules (for the sake of argument) must be arranged on paper to define words and sentences. Let’s imagine tracing the causal chain leading to the placement of one such molecule in its final position.

Immediately prior to appearing on paper, the ink molecule was ejected from a printing head due to a pressure differential, caused by the expansion of superheated ink. The superheating resulted from the conduction of electric current through a material offering significant electric resistance, resulting in the heating of the material, and the subsequent conduction of the heat to nearby ink molecules…

We may continue tracing the causal chain in this fashion, to arbitrary precision, essentially solving our physical model’s equations of motion for the entire system. In due course, this causal chain would lead us back to the muscle contractions of the paper-author’s fingers typing away at the keyboard, then to the electric signals carried along the author’s nerves (triggering the muscle contractions), and eventually, to the author’s brain. When we continue tracing the causal chain within the author’s brain, we will find 1 of 2 things to be true:

1. All of the brain’s relevant computational operations are well-modeled by classical abstractions.
2. The relevant computational operations taking place in the brain cannot be fully understood without taking the consciousness instance (as an objectively integrated, partially classically-indescribable structure) into account.

Option (1)

By and large, the physics and neuroscience communities appear to have accepted the 1st possibility as the only viable option, and have all but forsaken any serious examination into an alternative. Even some philosophers have wondered if the consciousness instance (or aspects of it, e.g. its “classical-indescribability”) may in some sense constitute a causally-inert structure which runs “in parallel” to causally-significant behavior manifesting in the brain [you might call this the “movie theater” theory of consciousness; you can watch, but you can’t particpate].

But taking a step back, it becomes clear that this position is tantamount to the claim that the consciousness instance played no role whatsoever in the causal chain concluding with the writing of the paper which claims to discuss the characteristics of the consciousness instance. It would further imply that the consciousness instance has had no influence on any thought ever had in reference to the nature of consciousness.

Proponents of this 1st option would then be forced to conclude that the consciousness instance simply does not exist. Why should anyone believe in the existence of a structure whose existence arguments bear no relation to its actual existence? If the arguments in favor of the existence of consciousness manifest in the universe regardless of whether the consciousness instance actually exists, the arguments are vacant.

Option (2)

Some philosophers have reached similar realizations, and have gone on to conclude that the consciousness instance indeed does not exist; that it is simply a psychological fiction.

Despite the intuitive and instinctive recoil many have to this idea, we must give credit where credit is due: the conclusion that the consciousness instance is a psychological fiction is in some sense the closest thing to a coherent proposal which has heretofore been suggested.

And yet in its (premature) strive for coherence, the argument fails catastrophically and completely. There is of course the matter that the existence of the consciousness instance is all but beyond doubt; through our working definition (“that which each of us is completely certain of”), we have utilized this aspect of the consciousness instance to uniquely identify it among all of reality’s structure.

But the argument is also simply internally inconsistent in a more mundane manner. We of course don’t yet understand the brain in nearly sufficient detail to be able to claim that its computational operations are well-modeled by classical abstractions (and so the argument is experimentally premature if nothing else). But even supposing we did possess such understanding, the argument would effectively conclude that the consciousness instance does not exist — on grounds of information gleaned from the consciousness instance. The ideas of a (3+1) dimensional universe, of the existence of particles, of physical structures abstracted as "brains" – are all revealed to us through the structure and relations within the consciousness instance. They thus cannot be used to justify the claim that the consciousness instance does not exist [at least not coherently].

Our hand is thus forced; if we are to ever possess a coherent picture of reality we must accept the 2nd option as the only viable way forward.

Implications

The implications of this simple argument are profound:

1. A complete and internally-consistent model of the universe must describe structures identifiable with consciousness instances, which further, must participate in the time evolution of structures we identify as "particles". In other words, the consciousness instance is measurable – and therefore amenable to scientific examination.
2. A-priori, one could expect the effects of the consciousness instance to be buried arbitrarily deep down the array of physical abstractions (e.g. in yet-to-be-discovered sub-sub-quantum physics). But the above argument ties the "consciousness-matter" interaction to a common, specific, phenomenon: the vocalization (or the writing-out, or the hand-signing, etc.) of the thought "my body is associated with a consciousness continuation”. Thus if a certain abstraction proves sufficiently powerful to model the brain’s cognitive operations underlying this vocalization, it must somehow effectively capture an explicit "consciousness-matter" interaction.

There is a certain expectation in the physics community that the Hard Problem can forever be swept under the rug; that physics can describe the entirety of the universe without revealing any insight into the regularities governing the consciousness instance. This attitude has likely evolved, at least in part, due to the great difficulty of as much as envisioning a resolution for the Hard Problem.

Nevertheless it has taken on a life of its own, leading to widespread implicit and even explicit denials of the Hard Problem – and thus to a near complete lack of research towards its resolution. Yet here we have a simple argument requiring a consistent model of the universe not only to incorporate consciousness instances – but also to specify a measurable interaction between consciousness instances and so-called “physical matter". If the attainment of a fundamental model of reality is truly our aim, we evidently have no choice but to confront the matter of the consciousness instance head-on.

Summary so far

To recap, all we are after is a resolution to the physics-oriented variant of the Hard Problem posed thus: what is a good theoretical description of a consciousness instance, and what is the minimal regularity relating consciousness instances to all other objects described by our physical theory (e.g. “particles”)?

The primary obstacle standing in our way is the 2 classically-incompatible qualities which we (typically implicitly) ascribe to the consciousness instance: its (partial) classical-indescribability, and its objective integration of complex information. We have seen that in principle, both qualities could manifest in a coherent (if somewhat peculiar) model of reality — as long the as the model satisfies the appropriate constraints:

1. The theory must support structures which are fundamentally not fully isomorphic to any sequence of classical bits — and which may be represented by objects formalizing an uncertainty about their particular classically-indescribable makeup.
2. The integration of the complex information manifesting in a consciousness instance must be inexorably and uniquely pointed to by the model itself, rather than by some arbitrary analysis of the model’s emergent high-level structure. A plausible criterion satisfying this condition is that it should be impossible to state the regularities of the model in terms of subsets of said information.

From observations of everyday phenomena, we can tally 2 additional constraints which must be satisfied by any consciousness-compatible model of reality:

1. (Trivially,) consciousness instances must be affected by the arrangement of “matter” (“matter” in the sense of everyday-physics); after all, this is how we come to know about said matter.
2. (Less trivially,) consciousness instances must affect the arrangement of “matter”.

If we found a model satisfying the above constraints, and verified that it indeed corresponds to our reality, the Hard Problem as posed would all but disappear.

And so our path is laid out before us.

Making contact with the details of known physics

Up to this point our discussion has been sufficiently abstract to get by on little more than a careful analysis of everyday experience. This approach has carried us far (surprisingly far) and has allowed us to sketch-out a deep (if rough) skeleton of a model of the universe which could resolve the Hard Problem as posed.

But we aren’t looking for a skeleton of a model. We are looking for a concrete model which would specifically describe our own universe — and which could be verified by experiment.

Our apparently desperate position

We know a fair bit about the structure of the universe — and what is known is packed together rather tightly. The prospect of finding a consciousness-shaped gap in our current understanding therefore seems rather hopeless. Our position seems even more desperate when we take into account our earlier conclusion: a coherent account of consciousness requires that the consciousness instance (as an objectively integrated, partially-classically-indescribable object) explicitly manifest in the operations of the brain relevant to everyday cognition. How could we possibly find a consciousness-shaped gap in our understanding of physical processes as seemingly mundane as those involved in cognition? Unknown-unknowns could of-course always catch us by surprise and turn the tables on any inquiry... Nevertheless the prospect of discovering fundamentally novel physical effects in the brain does not seem promising.

And it gets worse: it can be shown that any physical theory compatible with the consciousness constraints we identified earlier would necessarily conflict with 2 foundational physical principles which were once thought so fundamental as to transcend the mere details of any given theory: the principles of locality, and of predictability (a concept adjacent to yet distinct from determinism).

A consciousness-shaped gap

This article isn’t aimed solely at a physics-literate audience, but mention of locality and predictability may ring Bells of quantum mechanics in your mind [I hope someone appreciated this pun]. In 1964 John Bell was the first to peer into the heart of quantum mechanics as he formulated what has come to be known as Bell’s Theorem. Bell’s Theorem identifies the empirically-verifiable classically-incompatible essence of quantum mechanics; a certain quality of our universe which is in sharp conflict with any classical account of reality, and yet which must transcend any possible reinterpretation or extension of the existing theory. This essence has everything to do with locality and predictability, and with their intricate interplay under quantum theory through the phenomenon of quantum entanglement.

The philosophical ideas we just covered may have told an interesting story [certainly a long story] — but they only told half of the story. The second half is no less crucial or rich, and in fact extends beyond the conundrum that is the Hard Problem into seemingly unrelated conundrums of modern physics — most immediately of quantum mechanics.

A cop-out

When I first set out to write this post, I intended for it to be much shorter than it actually turned out to be. But as I started writing out what you just read, I found that I couldn’t do justice to the important ideas with a shorter post. And the section you just read was supposed to be the easy part, what with it requiring virtually no prior knowledge nor mathematical reasoning.

I do think it is possible to describe the relevant aspects of quantum mechanics to a dedicated lay audience. But if I tried to do that in this post, it would quickly turn into a book (and not a very good one at that). I may eventually try to introduce these ideas in a separate series of posts — but I won’t do that now. If you want to get the second half of the story — the part which concerns quantum mechanics — I invite you to read the paper linked in the introduction to this post.

10,000 foot overview

Here is the gist: the math of quantum entanglement captures what we would expect the interaction between an effectively-classical world and an objectively integrated, partially classically-indescribable structure to look like; in other words, the interaction between an effectively-classical world and a consciousness instance. And so the consciousness-shaped gap in our knowledge is filled not by some novel physical effect, but by a fresh understanding of established physical phenomena.

As previously alluded to, the proposed consciousness-instance--quantum-mechanics correspondence is partially motivated by the surprising fact that quantum mechanics manifests the “no-predictability” and “no-(information)-locality” properties which can be derived to characterize any consciousness-compatible theory (without referencing quantum effects in any way). This is noteworthy because it is not at all easy to come up with any model which manifests these consciousness-compatible properties without outright contradicting known facts about our universe (in particular, facts concerning relativistic phenomena); in fact, that this is at all possible was at one point in time quite surprising to the broad physics community. And yet quantum mechanics manages not only to achieve this theoretical marvel, but to do so while actually describing our own universe, and in particular, effects which could conceivably manifest in the brain.

But it is not only the ‘consciousness’ side of the equation which is illuminated by this emerging correspondence. Quantum mechanics, as a mathematical construct, has many aspects to it which seem to contradict one another, and yet which manage to subtly avoid outright conflict. Under existing theoretical accounts of quantum phenomena, this kind of contradiction-avoidance seems to almost miraculously follow from mundane calculations -- leaving us wondering if there are in fact simpler and more fundamental principles at play. The idea that quantum effects arise out of the dynamics of objectively integrated, partially classically-indescribable structures appears to provide just such a principle.

Without delving too deeply into the details of quantum mechanics, I will say that thinking of quantum entanglement as the manifestation of the dynamics of objectively-integrated, partially classically-indescribable structures offers natural accounts for the paradoxical-seeming simultaneous truths of several apparently (but not quite) contradictory quantum theorems: the no-communication theorem (and hence relativistic compatibility) and Bell’s theorem; the no-cloning theorem and quantum teleportation; and Holovo’s theorem and superdense coding.

Now, having touted the virtues of this emerging account of quantum phenomena, I also want to point out that it is very much an emerging account, and that furthermore -- like all existing accounts of quantum phenomena -- it does not fully settle all open questions of the field. In particular, the emerging theory does not yet offer a derivation of the Born rule -- though it does suggest a (qualitatively) particular origin for it. Nevertheless it makes for an extremely suggestive direction for further investigation, which incidentally, quickly intersects with many other ongoing investigative efforts such as the search for quantum(-compatible) gravity, research into black hole dynamics, and many areas of quantum information science.

It is a marvelous property of physics that it subtly yet firmly resists premature efforts for unification and completion.

Experimental verification

The study of consciousness is often thought of as experimentally intractable, but we’ve already shown that this position is not logically coherent: you can’t simultaneously believe that the consciousness instance exists and that the behavior of effectively-classical matter can be accounted for without explicitly accounting for consciousness instances.

In fact, there is no need to reach for abstract arguments to motivate the viability of the experimental investigation of consciousness. Even crude and intuitive notions of consciousness dynamics (e.g. your expectation that a consciousness instance encoding the picture of a rectangle would manifest in the universe while your eyes gaze at a picture of a rectangle) are ultimately rooted in falsifiable conjectures which are (implicitly) thought by all of us to have withstood experimental scrutiny. And so just as the ideas we’ve covered aim to render notions of consciousness dynamics more precise and more general, so do they render the associated falsifiable assertions more precise and more general.

The falsifiable conjectures underlying intuitive notions of consciousness

Let’s begin by explicitly reviewing those falsifiable conjectures underlying intuitive notions of consciousness dynamics.

During any given moment, much of the information manifesting in each of our consciousness continuations encodes the rich structure of a “real world out there” as it is captured by our senses: a roughly Euclidean 3-dimensional arena in which roughly-solid objects linearly evolve in time. Early on in our lives, we (instinctively) come to realize that within this vast 3-dimensional arena lies a specific structure which is somehow unique: the structure we come to think of as “our body”. This 3-dimensional structure is deemed unique due to the strong correspondence between its state and the information manifesting in our consciousness continuations: when light reaches the eyes of this 3-dimensional structure, corresponding information manifests in our consciousness continuations as “vision”; when air vibrations reach the ears of this 3-dimensional structure, corresponding information manifests in our consciousness continuations as “sound”; and when this 3-dimensional structure stubs its toes on a piece of furniture, corresponding information manifests in our consciousness continuations as “pain”. And so we come to recognize this 3-dimensional body as “me”.

The conjecture that one’s consciousness continuation corresponds to the state of a 3-dimensional structure thought of as “one’s body” can be considered the 1st layer of the “mirror test”. We are so used to this conjecture confirming itself over and over again during every waking moment of our lives that we don’t typically recognize it for the falsifiable supposition that it is.

Through much experimentation through the ages, we’ve slowly come to refine this crude understanding: we’ve realized that it is really a specific substructure of our 3-dimensional body which in fact directly corresponds to the information manifesting in our consciousness continuations: the brain. It is today understood that the state of the body corresponds to our consciousness continuations only insofar as it serves as a good proxy for the state of the brain. If the nerves coupling the state of your brain to the state of your body were to malfunction (e.g. due to the application of a local anesthetic), the information manifesting in your consciousness-continuation would cease to correspond to the state of your body. That this is the case is not at all intuitively obvious, but anyone who has as much as opted for a numbing agent during a minor dental operation has implicitly relied on this crude understanding of consciousness instance dynamics.

We can think of the idea that the information in our consciousness continuations corresponds to the states of our brains as the 2nd layer of the mirror test. Modern neuroscience has of course carried this crude depiction much farther, and today we can point to substructures of the brain whose state corresponds to subsets of the information manifesting in one’s consciousness continuation. For instance, we know that vision information manifesting in one’s consciousness continuation corresponds to the state of a particular region of one’s brain known as the visual cortex. And furthermore, we know it is particularly the electro-chemical activity of neurons within this visual cortex which directly corresponds to the information in one’s consciousness continuation. Other aspects of the brain’s state (e.g. blood flow within the visual cortex, or nerve activity elsewhere in the brain) may correspond to visual information manifesting in the consciousness instance -- but only insofar as they serve as good proxies to the neural activity in the visual cortex.

To summarize: even intuitive everyday notions about consciousness dynamics are ultimately rooted in (crude yet) falsifiable conjectures. We can think of the conjecture that the information in your consciousness continuation corresponds to the state of your body as the 1st layer of the mirror test, and of the conjecture that said information corresponds in particular to the state of your brain as the 2nd layer of the mirror test. In principle, any moment could bring with it a refutation of either conjecture [the information in your consciousness continuation might start corresponding to the weather in Chile, or to the state of a nearby fish] -- but we do not find the prospect likely [to say the least].

The (refined) falsifiable predictions underlying our (refined) proposal

The ideas covered in this post can be thought of as predicting a 3rd and final layer to the mirror test.

The basic prediction put forth is that we will find the information manifesting in our consciousness continuations to correspond to the state of objectively-integrated, partially classically-indescribable structures which will be found to manifest in brains. In particular -- that we will find all information contained in consciousness continuations to manifest as (quantum) entanglement relations (which, to reiterate, is what we suggest objectively-integrated, partially classically-indescribable structures look like “from the outside”). Correspondingly, it is predicted that the states of other sub-structures of the brain (e.g. effectively-classical electro-chemical neural activity) will be understood to correspond to the information manifesting in consciousness continuations only insofar as they serve as good proxies for the state of entanglement relations manifesting in the brain.

Philosophical nitpicking aside, this prediction is not fundamentally different from the predictions underlying the 1st and 2nd layers of the mirror test -- and so we can examine it with the same ease.

Taking a step back, the larger picture we are lead to posit could be described as follows:

1. The brain will be understood as a complex conglomerate consisting of many effectively-classical structures as well as objectively-integrated, partially-classically-indescribable structures (i.e. consciousness instances).
2. Said structures interact in a manner that facilitates various information flows and computations.
3. The resultant configuration coherently accounts both for the “intuitive” ontological conjectures underlying notions of consciousness (e.g. the notion that the universe contains an informationally-complex, partially-classically-indescribable structure) -- and for the mechanisms underlying complex thought (including thought about consciousness itself).

A satisfying resolution of the Hard Problem could be attained only through a model which coherently accounts for both aspects of the phenomenon.

Concrete mechanisms underlying entanglement in the brain

Complex entanglement is a very general quantum phenomenon which may manifest under wildly distinct concrete instantiations (which incidentally, accounts for the plethora of distinct approaches to the development of quantum computing hardware). It is also a very fragile phenomenon which is difficult to sustain and control (which incidentally, accounts for the relatively modest successes of current-day quantum computing hardware in proportion to the sizable investments made in the field).

I do not presume to understand the brain or quantum dynamics in sufficient detail to be able to propose some particular mechanism which could support complex entanglement in the brain. But such proposals have famously been made before (often in conjunction with suggestions that such effects may play some role related to consciousness -- though for reasons very different from those described in this post). Perhaps the most well-known example of such a proposal is Penrose and Hamerhoff’s conjecture that quantum effects could be found in microtubules in the brain. Personally, I find Matthew Fisher’s proposal that the Posner molecule could support complex entangled states in the brain particularly promising.

And yet concrete evidence supporting any such proposal has yet to be found -- which is of course at least a little discouraging. But we must weigh such discouragement against the question: supposing there is in fact complex quantum entanglement to be found in the brain -- how difficult should we expect its detection to be?

I am writing this post in the midst of the coronavirus pandemic, which has highlighted the difficulty of answering questions as simple as ‘how effective are masks at curbing the spread of a given novel virus in a population?‘ -- even given tremendous incentives and resources. Turning our gaze back to consciousness, then: how difficult should we expect the detectability of complex entanglement in the brain to be? Pretty darn difficult.

Putting it all together

We set out in search of a resolution to the physics-oriented variant of the Hard Problem, as given by a straightforward question: what is a good theoretical description of a consciousness instance, and what is the minimal regularity relating consciousness instances to all other objects described by our physical theories? We further identified this question as the defining concern of any physical model.

Having set our sights on the search for a physical model, we proceeded to identify 2 qualities of the consciousness instance which render it incompatible with any classical model of reality: its (partial) classical-indescribability, and its objective integration of complex information. We also identified 2 high-level traits which must manifest under a final theory of consciousness-instance dynamics: consciousness instances must affect, and be affected by the arrangement of effectively-classical “matter” (“matter” in the sense of everyday-physics). Having explicitly characterized these constraints, we pressed onwards in search of a physically-plausible model which would satisfy them.

We then briefly explored a possible correspondence between quantum mechanics and consciousness dynamics -- rooted in the notion that the mathematical structure of quantum entanglement describes what we would expect the interaction between an effectively-classical world and (partially) classical-indescribable, objectively integrated structures to look like; in other words, the interaction between an effectively-classical world and consciousness instances. We also briefly alluded to the clarity that such a correspondence could bring to the field of quantum mechanics itself, as it would point to a simple principle underlying and guiding the miraculous-seeming contradiction-avoidance which is repeatedly exhibited by quantum phenomena.

There is a lot more that can be said about this topic -- and I have said some of it in the aforementioned paper this post is summarizing. But at the risk of ending on too abrupt a note -- you’ve got to stop somewhere.