Binding Problem

The Binding Problem (also referred to as the Boundary- or Combination Problem) is the problem of explaining the apparent unity of consciousness. QRI has proposed a unique solution published in the Frontiers in Human Neuroscience journal, based on topological segmentation of the electromagnetic field.

While this is currently the longest article in this wiki, it need not be read chronologically. The following will provide a brief overview of the different sections.

• Section 1 provides a simplified treatment of the topic. It covers the same ground as the remaining article but with much less depth.
• Sections 2 and 3 discuss the importance and difficulty of the problem, respectively. They are included due to the discrepancy in how different people view the problem: QRI considers it to be the most consequential subproblem of consciousness, whereas many other people find it intuitively unimportant, especially upon first impression. Note that both sections assume realism about consciousness; this assumption is made to avoid lengthy disclaimers throughout.
• Section 4 explains QRI's original proposal.
• Section 5 discusses the significance of binding under an illusionist lens.

Finally (as with every article), links to other relevant articles and videos are provided in the Resources section.

Layman Explanation

The binding problem is the problem of explaining how and why we perceive several things at once. For example, you might currently see your desk, hear background noises, and experience the sensations of sitting. While many people find the binding problem to be intuitively innocuous (our brains process lots of information, so why wouldn't we perceive several things at once?), there are reasons why it may be more profound than it appears:

• The brain is said to "compute with neurons", which are like tiny biological processors. Presumably, we perceive many things at once because neurons integrate different types of information by communicating with each other. But if communication is the relevant process, why is there precisely one unified mind per human? Different humans also communicate with each other; why doesn't this lead to unified minds at the level of families, companies, countries, planets, etc.? Conversely, communication is stronger within certain brain areas than the whole brain, so why do we have just one unified mind per brain, rather than a few?

• Physics tells us that there is no instant communication over a distance: every effect or signal has to travel across a continuous path. This principle makes it difficult to explain how simultaneous awareness of several things is physically possible, given that every piece of information must be physically encoded at a different spatial point in a brain.

More generally, people tend not to question things they have always perceived a certain way. Since we are used to our particular kind of unified consciousness, it's natural to accept its properties without question. However, it is possible to imagine alternative ways our consciousness could work that seem equally plausible given our knowledge of the brain. E.g., imagine that, rather than having a single consciousness, there is one conscious entity in your brain for each type of sensation (hearing, seeing, thinking, feeling, etc.). Each entity receives relevant information from others (corresponding to the fact that the brain integrates different types of information), but it does so in an intangible way – e.g., the entity doing the thinking would experience a subtle intuition about the presence of visual information, rather than perceiving them as vivid images.

The more alternatives one can imagine, the more it becomes prudent to explain why consciousness works the way it does. Consequently, we ought to demand a high level of precision from any theory of binding: it should provide a precise criterion that explains why binding occurs at the specific spatial scale of one mind per human.

In practice, this standard is rarely met; researchers who study consciousness often don't talk about binding at all, and when they do, it's usually in the form of a general appeal to a certain criterion. One such criterion is the degree of integration, implying that sufficient information exchange leads to a unified consciousness. In addition to the lack of precision discussed above, another problem with this type of approach is that binding is a discrete property (any two qualia can only be experienced together or separately, with no middle ground), whereas integration is a continuous property (different neurons may exchange no information, a lot of information, or anything in between). Because of this discrepancy, trying to explain binding with information integration is a little like trying to push a round toy into a square hole. This point is especially problematic if one shares the belief that there is a close coupling between physical effects and conscious effects, meaning that for any conscious story (e.g., "I felt an itch and decided to scratch it") there must be a corresponding equivalent physical story (e.g., "nerve fibers in my arm sent a signal to my brain, which issued motor commands to my other arm"). Such a coupling seems impossible with a discrete property on one side (i.e., whether several percepts appear in one experience) and a continuous property on the other (i.e., the extent to which different physical parts communicate). This problem of explaining a discrete property with a continuous property also exists for most alternative criteria.

Some of the problems raised above may depend on one's philosophical views on consciousness. Specifically, if one views consciousness as an ordinary computational process, one may simply deny many motivating properties such as the existence of several bits of information at a time. This perspective is discussed further in section 5.

If one does take these problems seriously, it suggests looking for a physical mechanism with inherently sharp boundaries, i.e., a physical mechanism with the property that different points either affect each other a lot or not at all, but nothing in between. If one also views consciousness as a fundamental feature of the universe, this further suggests looking at basic physical models to find such a mechanism. In fact, the current gold standard theory of physics models all of reality as a collection of fields, which are like invisible expanses that fill all of space. Among these fields, the only one that could plausibly support such a mechanism is the electromagnetic (=EM) field because:

1. the EM field is known to have the ability to encode complex information; and
2. the brain is known to communicate via electrical activity, so the mechanisms to shape the field are in place.

Once one associates consciousness with the EM field, the question becomes how the brain imposes a boundary in the field to carve out a region corresponding to a single, unified consciousness. This is why the problem is often referred to as the boundary problem within the QRI memeplex.

An illustration of the electric field exhibited by two point charges. The black lines are called field lines, which denote the flow of energy within the field (specifically, the force that a positively charged particle at that point would experience). Conversely, each yellow line denotes a set of points in which the magnitude of this force is constant.

If you have ever taken a class on electricity in physics, you may have seen pictures like the one to the right, which illustrate the flow of energy within the electric field in a particular case. The crucial point is that there are also cases in which the field lines form closed loops, such that energy is trapped within a part of the field, capable of traveling within the part but not of leaving it. Such a "segmented" part is also called a pocket of the field, and the underlying claim is that the particular size and structure of this pocket shapes our consciousness. Note that this pocket is likely spatially small, contained entirely within each person's physical head, which is why different people can't merge their fields together.

Thus, the solution suggests that the brain is a hybrid computer, with a segmented pocket of the EM field at the center and an unconscious shell around it. This means that the unconscious component of the brain operates roughly within the conventional paradigm (which states that neurons are the principled computational units of the brain), whereas the conscious component works in a more alien way that defies description in conventional computational terms. That said, the brain still obeys the laws of physics (specifically Maxwell's equations), so the view doesn't entail any magical or non-physical ingredients; it simply implies that the conscious part of the brain is alien relative to how we usually think about computation. Understanding the conscious component and its properties better is a core part of QRI's research agenda.

Motivation

Intuitive Arguments

At the most basic level, the binding problem can be motivated by the observation that a moment of consciousness seems to contain several units of information. E.g., the Stanford Encyclopedia of Philosophy writes:

Human consciousness usually displays a striking unity. When one experiences a noise and, say, a pain, one is not conscious of the noise and then, separately, of the pain. One is conscious of the noise and pain together, as aspects of a single conscious experience. Since at least the time of Immanuel Kant (1781/7), this phenomenon has been called the unity of consciousness. More generally, it is consciousness not of A and, separately, of B and, separately, of C, but of A-and-B-and-C together, as the contents of a single conscious state.

In contrast to this apparent unity, biological neurons are a priori separate physical entities that are only "connected" by their exchange of information. Philosopher David Pearce (who is most well-known for the abolitionist project) draws a parallel between neurons in a brain and people in a country, arguing that the type of interaction is similar in both cases. Thus, if one would consider it incredible if the United States itself were to exhibit a unitary consciousness, one should consider it equally incredible that a human brain does so.

While neurons in a brain don't interact in precisely the same way as people in a country, they appear to be qualitatively similar, making it difficult to explain why unity seems only to exist at the level of humans. Specifically, if it were a matter of degree, one might expect the USA to be at least minimally conscious, and similarly with many other functionally integrated groups of people. This general problem of matching a quantitative property (degree of interaction) to an arguably binary property (whether a system exhibits consciousness) also presents a first technical challenge.

Technical Difficulties

A graphical illustration of how the binding criterion of Integrated Information Theory (formally called the "Exclusion Postulate") leads to a causal discontinuity between the physical and conscious aspects of a system. As more edges are added between two identical subsystems, a particular quantity grows for the entire system but remains constant for each subsystem. Once this quantity for the entire system exceeds that of each subsystem, the Exclusion Postulate dictates that both subsystems (red boxes) cease to exist as conscious entities and the entire system (purple box) appears as a new conscious entity.

Note that even if both subsystems were vastly larger (e.g., with billions of nodes and edges), one could still construct the example such that the shift is triggered at the precise step where a single additional edge is added.

Binding seems to be a discrete or binary property: any two units of information seem to either be bound or not bound together, but cannot be somewhat or partially bound. Differently put, the boundaries between different qualia appear to be hard and well-defined, rather than soft and fuzzy. If one accepts this premise and also has a view of consciousness that demands a continuous relationship between a system's physical description and exhibited qualia, then one requires a physical mechanism with equally hard boundaries to explain the phenomenon. (A "continuous relationship" means that small changes to the physical aspect of a system come with proportionately small changes to its qualia (and vice-versa); such a relationship is required by many physicalist views of consciousness, including Dual-Aspect Monism.)

An example of a formal proposal for binding that does not utilize such a mechanism is given by Integrated Information Theory (IIT). Roughly, IIT measures the degree of causal integration between subsystems (an inherently quantitative property) and constructs a hard/binary criterion for binding by declaring that only the subsystem with the highest integration among overlapping subsystems is conscious. Thus, the solution is based on defining a threshold: a certain quantity of integration such that binding is decided based on whether or not the integration of a different system exceeds the quantity. As a result of this rule, one can construct examples that exhibit a causal discontinuity (see animation to the right) in which an arbitrarily small physical change – that pushes the degree of causal interaction above the relevant threshold – causes an arbitrarily large change to the system's qualia.

Given the discontinuous jump in the conscious aspect of the example system, the task of defining a continuous relationship to its physical aspect may be compared to the task of defining a continuous function from a disconnected to a connected space (e.g., from $[0,1]\cup [3,4]$ to $[1,3]$), which is known to be impossible. Consequently, one may expect that any proposal for a solution that doesn't utilize a physical mechanism with hard boundaries (such as any proposal based on thresholds) will exhibit a similar discontinuity. Unfortunately, most proposals aren't sufficiently formalized to conduct such an analysis, which is why IIT is the go-to example throughout this wiki.

Physical Considerations

If one takes apparent simultaneous awareness of different qualia seriously, this poses a separate challenge for any physicalist theory due to the principle of locality of physics, which states that any spatial point can only influence its immediate neighbors. For example, if one pushes against a pen from one end, the pen does not move instantaneously. Instead, a signal propagates throughout the material, causing the other end of the pen to move after a small temporal delay. Specifically, the particles in one's finger exchange force particles with the particles on one side of the pen (primarily electrons exchanging photons), thus kick-starting a domino-like signal that propagates throughout the pen at about the speed of sound. Consequently, a unified conscious moment with several bits of information presents an apparent physical paradox since it implies that several spatially separate objects exert causal power simultaneously.

A way to dissolve this paradox is by asserting that a "slice" or "moment" of consciousness corresponds to a physical substrate across a span of time rather than at a single point in time. Under such a view, "simultaneous" awareness of several bits of information corresponds to a physical integration of information across a (small) span of time, which no longer violates locality. However, note that such an approach requires the respective theory to also define a boundary in time, in addition to the boundary in space.

Metaphysical Considerations

As a final consideration, note that if one has an ontology of consciousness in which it does not emerge from a priori unconscious matter but is instead a basic feature of the universe, then one may be forced to believe that everything is at least minimally conscious, even if the amount of consciousness is usually so small that it effectively rounds to zero. Given such a view, there is a sense in which the problem of consciousness is primarily the problem of specifying conditions under which such minimally conscious building blocks combine into larger entities – or in other words, the problem of consciousness is primarily about binding.

Implications

If one accepts the difficulty of the binding problem, then consciousness may be best viewed as a constraint satisfaction problem, which can only be solved if all its relevant properties are considered simultaneously. Thus, one may wish to have a solution to the binding problem in mind from the start, rather than attempting to add such a solution to an existing theory. Given the rarity of sharp boundaries within physics, the constraint imposed by the binding problem may be particularly significant – and perhaps sufficient to rule out all but a small part of the explanatory space.

Solution Desiderata

Due to its difficulty, one may wish to approach the binding problem in terms of smaller problems. The following provides a list of necessary criteria, i.e., requirements that any solution to the binding problem should satisfy.

• D1: Frame-Invariance. A solution must be frame-invariant, i.e., it must define a boundary that exists as a fact of the universe, independent of who examines it.
• D2: Explain the Spatial Scale. A solution must explain why binding happens at the particular scale of humans, rather than at any smaller scale (particles, neurons, brain regions, etc.) or larger scale (families, companies, countries, etc.).
• D3: Exhibit Weak Emergence. An object or phenomenon is weakly emergent (terminology due to David Chalmers) if its behavior is surprising, or intuitively unified, relative to the underlying system. (Examples include a car, an ant colony, or a glider gun in Conway's Game of Life.) Since humans and other animals exhibit such unity, the corresponding physical mechanisms ought to be such that a phenomenon with a surprising unity is exhibited at this particular spatial scale.
• D4: Avoid Strong Emergence. An object or phenomenon is strongly emergent (terminology also due to Chalmers, same source) if its existence or behavior is not logically entailed by the underlying laws that govern its parts. (Real examples may not exist in our universe but are common in video games, e.g., the line clear in Tetris is strongly emergent.) Thus, if one assumes physicalism, consciousness must not be strongly emergent.
• D5: Address Physical Locality. A solution should address how it is compatible with the principle of locality (see section 2.4).

It's worth noting that this list does not provide a proper decomposition of the problem since the items listed here are neither disjoint nor sufficient (i.e., satisfying all five doesn't guarantee that a solution is correct). Indeed, the crucial challenge remains to find a physical mechanism with hard boundaries, and many of the items above can be viewed as different articulations of what goes wrong absent such a mechanism.

In practice, the list is most useful as a vetting tool: since the items are designed to be necessary properties, any solution that fails to satisfy one or more of them can be identified as insufficient (modulo disagreement with the validity of the respective item). Indeed, QRI is currently not aware of any proposal other than its own that satisfies all five of the above. The following will provide three applications of the list to different approaches.

Application: Integrated Information Theory

IIT performs its analysis based on a graph of discrete elements and a transition probability matrix that proceeds in time steps. If there are several possible ways to construct such a graph, the analysis is to be performed in all possible ways, where the one leading to the highest amount of consciousness is the one that counts. Thus, IIT solves the frame-invariance problem by selecting a specific frame out of all possible frames, thereby satisfying D1 and D2. Furthermore, since the discrete time steps of IIT may span a variable amount of time, IIT at least has the potential to satisfy D5 as well.

However (as demonstrated earlier in the text), the physical substrate of a conscious system is only quantitatively (and in extreme cases, infinitesimally) more unified than that of an unconscious system, which means that consciousness does not, in general, exhibit weak emergence under IIT. For the same reason, the sudden appearance of conscious entities is strongly emergent. Thus, IIT fails both D3 and D4.

Application: Temporal Synchrony

Temporal synchronization of different neurons in the brain is frequently mentioned in the context of the binding problem, often citing the work of Peter Milner on visual recognition. If taken literally as a proposal, such an approach fails D1 since the simultaneity of events is a frame-dependent property due to special relativity, and it also fails D5 since it provides no mechanism to draw temporal boundaries.

However, it's worth noting that the theory was (at least originally) intended to be a neuroscientific explanation for computational properties of visual shape recognition, not a solution to the philosophical problem of binding. Due to the (usually unacknowledged) difference between realist and illusionist views on consciousness, it is not uncommon for theories to be discussed in the context of questions they weren't designed to answer. Note also that the existence of neural synchronization is fully compatible with QRI's views on consciousness, and in fact, QRI suspects that synchrony is related to local binding.

Application: Informal Approaches

For any one formalized solution to the binding problem, there are a great many informal suggestions. Most of these make reference to concepts like functional integration or the instantiation of particular computational objects (e.g., self-references). While a precise analysis is not possible, these approaches tend to fail D2 (since functional integration exists on many different scales, yet unified conscious entities seem to exist on only a single scale) as well as D1 (since computation, in general, is frame-dependent).

QRI's Proposal

This section will introduce QRI's proposed solution to the binding problem based on topological segmentation of the electromagnetic (henceforth EM) field. We will begin with a brief introduction of topological properties before explaining the solution itself.

Topological Properties

Roughly put, "topological properties" are properties of objects that are preserved under continuous deformations. Such deformations include stretching, twisting, and bending, but do not include tearing or gluing. These properties are the study of the branch of mathematics called "topology".

For example, the surface surface of a sphere can be changed by stretching the sphere, so it's not a topological property. Conversely, the absence of boundaries on a sphere cannot be affected by any continuous transformation, so it is a topological property. For this reason, a sphere is considered "topologically distinct" from a closed rectangle: even though the rectangle could be continuously deformed to approximately resemble the sphere, there would always remain a boundary around a hole at the top.

With respect to the Boundary Problem, the notion of being a topological property becomes important because of Special Relativity, which shows that many apparently objective properties are actually frame-dependent, including the size of an object and the simultaneity of events. In particular, a Lorentz Transformation describes how the coordinates of an event change when observed from two different frames of reference (that are moving at a constant velocity relative to each other). Any property that can change under a Lorentz transformation is frame-dependent, so any frame-invariant property must be invariant under Lorentz transformations (i.e., it must be the same before and after a transformation is applied). Topological properties fulfill this requirement.

Segmentation in the EM Field

A visualization of electric field lines creating a topologically closed structure. Notice that no field line is traveling from the inside to the outside. The geometrical object associated with these field lines is the volume enclosed by the outermost layer of looping field lines.

Recall that field lines as such are only a modeling tool to denote the flow of energy, so they "exist" at every point in space. Thus, one could also draw field lines outside this structure, which would presumably no longer form loops.

Corresponding to our requirement of a physical mechanism with sharp boundaries, the state of the field that makes the most promising candidate for a solution would be one where energy is trapped, i.e., it moves around within a part of the field but doesn't enter or exit. Indeed, such cases are known to arise in other contexts, and they can be formalized by the notion of field lines, which are a modeling tool to describe the flow of energy within the field. Whenever the field lines form closed loops (see graphic to the right), their insides become causally disconnected (hence "segmented") from the remaining field. Topologically speaking, this occurs whenever the volume enclosed by the outer layer of looping field lines forms a closed manifold. The size, shape, and internal structure of this manifold are then proposed to correspond to properties of the person's consciousness.

Thus, the proposal claims that human brains repeatedly segment a small part of the EM field in this way, thereby creating topological pockets corresponding to our consciousness. This process is utilized (and was evolutionarily recruited) as a form of nonstandard computation.

Applying the framework of section 3 to this proposal, we can see that none of the five desiderata are violated:

1. As a topological property, segmentation is frame-invariant.
2. The field lines determine a precise geometric structure, and hence, select a spatial scale.
3. Since field lines describe the flow of energy, a closed pocket intrinsically behaves like a unit, thus exhibiting weak emergence.
4. This functional unity of the EM field is proposed to correspond precisely to the unity of consciousness. Thus, since the functional unity is entirely upstream of Marxwell's equations, consciousness is not strongly emergent.
5. Pockets in the EM field can be naturally viewed as existing in 4-dimensional space-time. Consequently, the solution proposes that a slice of consciousness spans a small but not infinitesimal amount of time, thus making it possible for a slice of consciousness to integrate several units of information without causing a violation of the proximity principle.

The Scope of the Hypothesis

The promise of topological segmentation as a solution to the binding problem is the primary reason QRI subscribes to the EM hypothesis, which states that non-local properties of the EM field play a crucial role for consciousness. This section will clarify the scope of the hypothesis, which can be misunderstood as either making a weaker or stronger claim than it really does. Specifically:

• The EM hypothesis makes a stronger claim than electromagnetism being the dominant force in the human brain. The gold-standard theory of physics for the relevant scales is called the Standard Model of Particle Physics. It contains only three proper forces called the strong-, weak-, and electromagnetic force, as well as gravity (which is not considered a proper force for technical reasons but behaves similarly). Among these, the first two forces are negligible in all but a few contexts, leaving only electromagnetism and gravity as relevant players. Thus, whenever interactions are not due to gravity – as is the case in the human brain – all relevant interactions are necessarily due to electromagnetism. Because of this, there is a (very abstract) sense in which all physicalist theories of consciousness can be viewed as electromagnetic theories, even including functionalist proposals. This is why the EM hypothesis states that non-local properties of the EM field play a role for consciousness: non-locality is the crucial property that differentiates the EM hypothesis from neuron-centric views, which only care about electromagnetism as a force to submit discrete signals in highly localized areas.

• The EM hypothesis makes a weaker claim than the EM field being the sole substrate of consciousness. Electromagnetic theories of consciousness in the literature (such as cemi theory or Susan Pockett's hypothesis) often go as far as to claim that consciousness is identical to either the EM field or to certain patterns within the field. Due to the relative dominance of the EM force within the brain, there is substantial overlap in the predictions made by such a claim vs. the (strictly weaker) EM hypothesis, especially when compared to functionalist or illusionist proposals. However, the theories are nonetheless distinct, and the EM hypothesis is agnostic about the role of other forces or effects. This difference could matter both for additional physical mechanisms within the brain, as well as for an application to non-human systems (in which the EM force may not be dominant). Note also that the standard model of particle physics is not a complete description of the universe, and it is unclear to what extent the four forces are fundamentally separate.

On Binding vs. Boundaries

The term "binding problem" suggests that one begins with inherently disconnected elements (such as neurons), and the problem is to find a mechanism that binds such elements together. Conversely, QRI's approach begins with an inherently unified physical substrate (namely the entire EM field), and the mechanism of topological segmentation imposes boundaries into the substrate. Consequently, the problem is often referred to as the boundary problem within the QRI memeplex. Thus, both terms refer to the same problem, but phrasing it in terms of boundaries suggests a different conceptual approach.

Implications for the Brain

An illustration of different regions of the human brain. Note that the thalamus does not intersect the surface of the brain, and thus, is only visible because the graphic shows a cross-section.

A reproduction of Figure 1.1 from Grossberg's book. See the quoted text for details.

The claim that segmentation in the EM field can solve the binding problem has significant implications for the computational and biological structure of the human brain (as well as the brains of other animals that are presumed to be conscious). Specifically, it implies that all consciously perceived elements (i.e., all qualia) are represented within this field, implying that the brain operates outside the conventional paradigm to a significant extent, specifically in a way that utilizes nonstandard computation.

Throughout this wiki, the brain is often described as a hybrid computer, wherein the unconscious component operates largely or entirely within the aforementioned paradigm (thus utilizing standard computation), and the conscious component performs "field computations" as determined by the holistic structure of the segmented pocket. QRI suspects (though the remaining model does not rely on this assumption) that the relevant pocket of the EM field is located mostly or entirely within the thalamus, whereas the entire outer layer of the brain constitutes the unconscious component.

The details of how such a pocket is utilized for computation is a topic of ongoing research, but see Consciousness as a Resonance Hierarchy for an introduction.

Note that this model makes significant empirical predictions. For one, a significantly precise measurement of the brain's endogenous EM field (which may become possible in the future) could prove or falsify the model outright. Even absent such technology, however, the model has significant implications for the types of processing in the brain. Consider:

• The conventional view of the brain models consciousness as a type of interface, where the selection of consciously accessible information is due to a design decision by evolution and could presumably be different. E.g., it would be possible to have similar brains with less conscious access to visual details but more access to language generation.
• Conversely, the EM-centered view implies a crisp line between conscious and unconscious processing; in fact, conscious processing follows a different computational paradigm.

Thus, the theory is amendable to scientific inquiry by studying the computational properties of conscious vs. unconscious processing, with the overarching prediction that both follow systematically different computational principles. While all percepts we can report on are necessarily consciously perceived (which means that introspection alone cannot definitively determine how a conscious element was computed), the degree of conscious access is likely a good proxy for the involvement of the brain's EM pocket. For example, sentences in natural language tend only to be consciously perceived as or immediately before we speak them, which indicates that language generation is primarily unconscious process. On the other hand, thought in general likely has significant contributions from both components, given that we have significant but not complete insight into and control over the flow of thought.

A particularly significant category is vision, whose conscious component is both consistently present and contains a large amount of information compared to other sensory modalities. (Vision is also the modality with by far the largest amount of brain mass devoted to it.) In general, QRI's views suggest that the EM field computes the more vivid (or "visible") visual elements, whereas the more intangible (or "invisible") elements are computed by the unconscious brain, with merely the result broadcast into consciousness (similar to language generation). This view aligns well with the work of acclaimed neuroscientist Stephen Grossberg, who has studied these two types of visual processing extensively, as detailed in his book Conscious Mind, Resonant Brain:

While looking at [the image in Figure 1.1 (right column)], we can all recognize that there is a vertical line, or boundary, of some sort that is interpolated between the ends of the horizontal blue lines. But we do not see this line, because it does not have a different brightness or color from its background. It is invisible. Nor does it separate the image into regions of different brightness or color. [...] In Figure 1.1 (left column), in contrast, the circle around the bright disk is visible because the disk that it encloses is brighter than the surrounding background brightness.

Throughout the book, he proposes many computational models for various aspects of seeing, which often have unusual properties for digital computers. An example is his work on perceptual filling-in, which uses differential equations to model the propagation of color across the field (thus treating vision as an inherently spatial phenomenon), which also has been empirically validated.

The Illusionist Perspective

Many apparent properties of consciousness, including the simultaneous presence of several bits of information, can simply be denied under an illusionist lens. However, while QRI's proposal is substantially motivated by such properties, its implications (such as those discussed in the preceding section) do not depend on one's metaphysical views. In general, the apparent unity of consciousness has significant functional consequences, which can be coherently discussed even under a strict illusionist lens.

Throughout this section, we will refer to a restricted version of the binding problem as the functional binding problem, which subsumes only those parts that are coherent under an illusionist perspective. Importantly, note that since binding is a ubiquitous feature of human consciousness, there is no difference between explaining the functional properties of binding vs. explaining the functional properties of consciousness as a whole.. Thus, the functional binding problem can be defined as the problem of explaining the set of tasks people can accomplish and the introspective reports they make, including detailed descriptions of their phenomenology. Any biological or computational description of the brain that precisely accounts for both of these should be considered a satisfactory solution to the functional binding problem (or, equivalently, to the problem of consciousness under an illusionist lens), regardless of what metaphysical status it ascribes to consciousness.

In the philosophical literature, the functional binding problem is rarely treated as a profound obstacle. On the one hand, realist authors tend to focus on the philosophical aspects of binding, which are precisely the components not included in the functional problem. On the other hand, illusionist authors tend to emphasize establishing a proof of concept on how the problem might be approached rather than dealing with any part of the problem in depth. For example, in Consciousness Explained (which is the most frequently cited book about consciousness), Daniel Dennett spends a full chapter arguing for a concept called "heterophenomenology", which performs a reduction of the problem of consciousness analogous to that of the preceding paragraph. Once this goal has been established, most of the succeeding discussion is very abstract, usually gesturing at how a set of properties can be explained or appealing to future neuroscientific progress rather than going into details himself.

One may reasonably argue that the task of philosophers is precisely to provide such a qualitative analysis, and thus, that one should look to the neuroscience literature for a technical treatment of phenomenological details. However, while neuroscience (specifically computational neuroscience) has produced a vast amount of work on reverse-engineering functions of the brain, the focus tends to be on capabilities of people (such as the ability to keep seven items in short-term memory at a time, or the ability to locate particular shapes among a set of similar items), rather than on analyzing details of phenomenological reports (such as the fact that people report seeing images at all). Throughout all of academia, the field whose mission statement may come closest to "solve the functional binding problem" may be the niche field of neurophenomenology, which was founded in 1996 to "marry modern cognitive science and a disciplined approach to human experience". However, even the research published under this line of work does not address the problem's concrete components.

Despite the lack of academic interest in the functional binding problem, QRI's views suggest that it is highly nontrivial. In particular, dual-aspect monism combined with our high amount of introspective access suggests that our phenomenology restricts our brain's computational architecture significantly, regardless of the metaphysical status of consciousness. In fact, it is entirely possible that phenomenology itself is sufficient, or almost sufficient, to determine the physical substrate of human consciousness, in which case finding a proper solution to the functional binding problem is (almost) as hard as finding a proper solution to the problem of consciousness as a whole. The remaining difference would then be a practical one: if one takes the illusionist point of view, an inadequate solution is much harder to identify as such since one has to rely on phenomenological details, rather than on an analysis like the one conducted in section 3.

One example of an elaborate theory based primarily on phenomenology is Steven Lehar's "Harmonic Gestalt" model of visual perception. Based on analyzing aspects of our visual system, such as the geometry of our perceived visual world, the construction of three-dimensional percepts based on two-dimensional inputs, and the role of visual illusions, Lehar has concluded that the brain must utilize complex physical mechanisms (such as wave propagation and resonance) rather than relying solely on neuron-based computations. His conclusions are highly compatible with the views of QRI, and because of this, he has his own QRI research lineage. It's worth noting that, despite his work having significant overlap with that of Stephen Grossberg, it has been largely rejected within academia.

Resources

• Electromagnetic Field Topology as a Solution to the Boundary Problem of Consciousness – the YouTube video explaining the solution presented in the academic paper, by Andrés.
• Don’t forget the boundary problem! How EM field topology can address the overlooked cousin to the binding problem for consciousness – the academic paper itself, by Andrés and Chris Percy.
• Solving the Phenomenal Binding Problem: Topological Segmentation as the Correct Explanation Space – an earlier video that goes into more detail on the shortcomings of alternative approaches.
• Harmonic Gestalt – a two-hour presentation of his model for visual perception, by Steven Lehar.
• An Introduction to Steven Lehar, part I: Bubble worlds and force fields – the first in a three-part series of posts on Steven Lehar by QRI collaborator CubeFlipper.
• Digital Computers Will Remain Unconscious Until They Recruit Physical Fields for Holistic Computing Using Well-Defined Topological Boundaries – a QualiaComputing blog post on the binding problem and its relation to digital computers.
• A Paradigm for AI Consciousness – an alternative perspective on binding (and consequently, AI consciousness) by QRI co-founder Michael Edward Johnson. Note that, while the views articulated in this article would be considered very similar to those of QRI relative to the broader discourse, they are likely about as different as is possible given the similar set of philosophical assumptions.