A Very Preliminary Theory of Time and Consciousness, Part III

3,600 words

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Review: Three models of phenomenal time

This section covers content that I discussed in Part 2 of this series. Feel free to skip ahead to the next section (“The nature of retentions”) if you’ve already read Part 2.

An essential feature of our consciousness of time, also known as phenomenal time, is the experience of succession, as opposed to a succession of experiences. Simple introspection reveals that our experience of time does not consist of discrete “snapshots” of the world that are disconnected from one another. Even though there may be discontinuities in our subjective experience when our gaze moves from one object to another, there is nevertheless a single awareness that observes the progression of moments, rather than a new and distinct awareness at each moment. Indeed, it is precisely because we have this experience of succession that we feel as though time flows, rather than, say, jumping or skipping from one moment to the next.

In the philosophical literature on phenomenal time, three models are generally proposed to explain the experience of succession: (1) cinematic antirealism, (2) extensionalism, and (3) retentionalism. Cinematic antirealism claims that each moment of experience is actually a still, static snapshot of reality, and the impression that these snapshots flow into one another is an illusion produced by the mechanisms in the brain that govern perception. However, it seems like flow is an intrinsic feature of our experience, rather than an artifact of perceptual processes taking place in the brain. Indeed, if it is true that the brain “samples” reality at a rate of 10-13 perceptual frames per second, and dynamic, flowing motion actually occurs in the external world, then our snapshots of the world must contain a flow of events. Given that objects in the world often change their position in space more than 10-13 times per second, our perception would not accurately represent motion if each moment of experience were completely still.

Extensionalism assumes that moments of experience are not discrete but rather continuous. That is, our consciousness is spread out over a period of, say, two seconds. Therefore, within any time interval of two seconds, our conscious experience does not change (or if it does change, then the change is not substantial enough to give rise to a new experience). However, we can easily apply transitivity to demonstrate that our conscious experience would never change under this framework [1]. The theory implies that our experience at moment t = 0 (call this E0) is identical to our experience not only at moment t = 2 (call this E2), but also at every moment in between. Therefore, E1 = E0 = E2. However, E1 is also equal to E3, so E0 = E3. Extending this conclusion, we would find that each moment of conscious experience would be identical to every other one.

Retentionalism, on the other hand, supposes that moments of experience are discrete; it states that, at any given moment, we are conscious of exactly one physical “time-slice” that has either an infinitesimal or very short duration. Unlike cinematic antirealism, however, the model claims that the experience of succession arises from representations (or “retentions”) of the immediate past that are embedded within the present. Under the assumption that moments of experience are not extended across time and that flow actually does feature into our immediate, direct perception of reality, retentionalism must be true.


The nature of retentions

I initially thought that the most straightforward version of retentionalism would hold that retentions are after-images of the immediate past. When an object moves rapidly through our visual field, we don’t see the object at just a single point in space; rather, we also observe traces of the object at its previous positions as well. According to the neuroscientist Steve Lehar, we actually perceive these after-images whenever motion is taking place in our environment, but when the rate of motion is sufficiently slow, the after-images are so faint that they are virtually imperceptible. However, I realized that the “after-images account” of retentionalism faces two problems. Firstly, we can be conscious of the passage of time even if nothing at all is moving around us. Secondly, after-images only occur in our visual perception, not in other sensory modalities, but we still experience the flow of time even if our eyes are closed. While one might respond to this objection by noting that we can experience “after-tastes,” it seems like we would still maintain an experience of succession even if we were to lose all of our sensory perception. People who are placed in sensory deprivation chambers do not seem to report that their experience of time came to a stop, for instance.

Although I was originally skeptical of it because it seemed poorly defined, I now agree with the view that retentions are “primary memories.” These kinds of memories are to be distinguished from secondary memories, which are recollections of the past. A recollection brings the experience of an event back to the fore of our consciousness, after the event has already faded from our immediate awareness of the present. However, according to William James, “an object of primary memory is not thus brought back; it never was lost; its date was never cut off in consciousness from that of the immediately present moment. In fact it comes to us as belonging to the rearward portion of the present space of time, and not to the genuine past.” Primary memories, therefore, are phenomena from the immediate past that are still present in the current moment of experience. While James thought that primary memories are essentially like after-images, the philosopher Edmund Husserl believed that the two are entirely different from one another (Husserl, in fact, never used the phrase “primary memories” in his writing, referring to them instead as “retentional consciousness.”) Husserl never really clarified what exactly a primary memory is, nor did he explain how an experience of the immediate past gets preserved in the present.

My objective for the remainder of this blogpost is to offer an account of how primary memory gets “bound” to a present moment of experience, thereby giving rise to an experience of succession. I’ll discuss recent empirical findings in neuroscience that appear to shed light on this issue [2], and then I will show that they are inadequate because they presuppose a philosophically misguided view of the mechanisms of phenomenal binding, i.e. the binding of multiple experiential objects into a single consciousness. In particular, they imply that a moment of experience is functionally unitary, rather than ontologically unitary. I will then propose a novel theory of a potential mechanism for ontologically unitary binding between primary memory and present experience.


Synchrony of neural oscillations

First, some necessary neuroscience background: The fundamental information-processing unit in the brain is a neuron. Neurons relay information to one another by transmitting action potentials, which are essentially electrical pulses. Neurons can be either excitatory or inhibitory; that is, they either stimulate the flow of information, or they impede it, respectively. When networks of neurons coordinate their behavior, such that excitatory and inhibitory activity alternate in cycles, they generate oscillations. A prevailing hypothesis in neuroscience claims that the brain integrates information across large scales by synchronizing the oscillations of different neuronal networks. (There are many different types of functionally relevant synchronization in the brain; due to the limited scope of this blogpost, I will ignore those differences here, though suffice it to say that oscillations don’t have to be perfectly overlap with one another in order to be considered “synchronized.”)

If the hypothesis is true, then it seems that the brain must synchronize the neural signals corresponding to primary memory and the signals correlated with present experience in order to bind the two together into a single, unitary moment of awareness. Indeed, there is evidence that theta-frequency (3-9 Hz) neural oscillations in the prefrontal cortex, which is associated with short-term memory, become more synchronized with oscillations in V4, a region of the brain that is responsible for processing visual data, when monkeys perform a task that requires visual short-term memory. Furthermore, the spiking activity of neurons in V4, i.e. the discharge of action potentials, becomes strongly locked to the phase of oscillations in the prefrontal cortex, and vice versa. Additionally, the degree of synchrony between the oscillations predicts the monkeys’ performance on the behavioral task, suggesting that the strength of synchrony correlates with improvements in memory. Other studies have also found synchrony between oscillations in the visual cortex and regions of the brain that are involved in regulating short-term memory. Furthermore, the module that consolidates memories in the default mode network (DMN), which is active even when the brain isn’t receiving any sensory input, is persistently synchronized with the DMN module that is associated with self-consciousness. This finding aligns with my previous observation that we would still experience ourselves as unitary subjects that persist through time even if we were entirely disconnected from our sense perceptions.

All of this experimental data seems to lend support to the “binding by synchrony” (BBS) hypothesis, which claims that the synchrony of neural oscillations binds the various contents of our experience. However, BBS cannot explain what is arguably the most essential feature of phenomenal binding: namely, the unity that it produces between different segments or aspects of our experience. Indeed, at any moment in time, we have one, globally unitary experience of our entire environment, even though the various objects within it can clearly be distinguished from one another. All that BBS accounts for is the simultaneity between distinct experiential objects. However, the fact that multiple subjective phenomena are simultaneous with one another does not imply that they form one whole experience. For instance, it is possible to imagine an animal that has a separate consciousness of each object in its visual field, even though it sees all of the objects at the same time. Similarly, since the oscillations that encode our primary memory and our direct perception of the present are two discrete, separate entities, the synchrony between them does not necessarily yield one, unified moment of experience. In general, two populations of neurons that do the same thing may not necessarily be the same thing; as the Qualia Research Institute has noted, the functional unity of neural oscillations does not seem to give rise to the ontological unity of experience. Furthermore, as the philosopher David Pearce has said, “Mere synchronous neuronal firings cannot bind any more than, say, synchronous activation … could phenomenally bind a community of skull-bound … minds.” Indeed, two human brains can actually display synchrony between their respective oscillations, but obviously the brains do not form a single pan-experiential subject.

To be clear, I am not claiming that synchrony is totally irrelevant for phenomenal binding; in fact, it is likely a necessary, though insufficient, condition for binding. Given that moments of experience are discrete and (nearly) instantaneous, as I established earlier, everything that we perceive in a moment must be synchronized. In the next section, I will hope to show that synchrony is an artifact of a deeper phenomenon known as symmetry, which does produce ontological unity between the physical objects that it relates.

Before moving on, I want to address Pearce’s philosophically compelling proposal that quantum coherence may be responsible for ontologically unitary binding between neurons, since two systems that exhibit such coherence can be treated as one unified, “entangled” entity. Unfortunately, quantum events take place at the subatomic level in the vast majority of physical systems; hence, as skeptical neuroscientists have argued, they likely do not exert a significant influence on any macro-level processes in the brain, such as the synchronization of neural oscillations. Pearce himself acknowledges that quantum coherence decays in less than 10-13 seconds, whereas basic information-processing activity in the brain takes place on the scale of milliseconds. It seems unlikely, therefore, that coherence is biologically relevant, even though it does pose a metaphysically satisfying answer to the Binding Problem.


Symmetry and the “coupled cell systems” formalism

In the broadest sense, the concept of symmetry in physics refers to any kind of invariance under transformation. In particle physics, symmetries describe, among other things, the properties of a particle that are preserved when it undergoes a change in its identity. For instance, as I once wrote,

“In the 1930s, Werner Heisenberg noticed that, aside from their differences in electric charge, protons and neutrons are virtually indistinguishable; they have, for instance, very similar masses. As such, he posited that a deeper symmetry underlies the proton and neutron. In particular, he discovered that the symmetry in the interactions between protons and neutrons, also known as the strong force, [is] invariant under the action of one of the aforementioned algebraic groups. Protons and neutrons, as such, are nothing more than up and down states of a single entity that displays an internal symmetry known as the isospin, which, critically, doesn’t get altered when particles change into new ones … Though the identities of the individual particles appear to be conditional on the observer’s frame of reference, the symmetry [of the particles] remains constant, no matter the various transformations that may be applied to them.”

Therefore, it seems as though the ontological unity of the proton and neutron – their persistence as a single entity across time – is attributable to the symmetries that they participate in. While philosophers have rarely ever discussed symmetry in the context of ontological unity, the notion that there may be a relationship between the two concepts can be traced back to 1937, when the physicist Eugene Wigner was able to predict the properties of fundamental particles from a particular kind of representation of a symmetry “group.” (A group, in this case, is an abstract algebraic structure that contains all the transformations under which the particle would be invariant. It is also worth noting that “representation” has a special mathematical meaning in this context as well, but a detailed discussion of its definition would be outside the limited scope of this essay.) Since then, physicists have discovered new types of fundamental particles, such as quarks and bosons, by identifying them with states in the representation of the relevant symmetry group. In fact, some physicists have gone so far as to say that a particle is a certain representation of symmetry groups in nature. In “basement reality,” the unity of a particle is a mapping between abstract, algebraic spaces that preserves some kind of mathematical structure. (Obviously, a great deal of specificity is lost at this level of abstraction.)

What relevance does symmetry have for binding between neurons? More specifically, how does synchrony emerge from ontologically unitary symmetry? (Recall that I essentially set forth this latter question in the previous section.) In order to answer this question, I will introduce the “coupled cell systems” formalism, which attempts to import the concept of symmetry into the study of biological networks. According to the formalism, patterns of synchrony arise naturally when such a network exhibits symmetry. The explanation is quite technical, so feel free to skip ahead to the next section if you’re not concerned with the details. Also, it’s worth noting that I’m not sure whether my explanation is correct, primarily due to my lack of background in advanced math. [4]

——– beginning of technical section ——–

As defined in the formalism, the symmetry group of a network is the group of all the permutations of the constituent cells that preserves the number of pairwise connections in the network. Additionally, an orbit is defined as the set of permutations g of a cell c such that g is a member of the symmetry group. Finally, if S is a subgroup of the symmetry group, then the fixed-point subspace of S, Fix(S), consists of all the points x that are invariant when they are transformed by a member of S (a point x also corresponds to a particular configuration of the network). The formalism yields the (mathematically proven) theorem that a configuration of the network that lies in Fix(S) has the pattern of synchrony determined by the orbits of S on cells.

Through this theorem, we can predict the patterns of synchrony in a network of neurons based on its symmetry groups. Consider a simple system of three coupled neurons whose membrane voltage evolves over time in accordance with the FitzHugh-Nagumo model, which is used to describe neurons that behave as relaxation oscillators [3]:

Screen Shot 2019-07-31 at 3.28.59 PM

Eq. 1

where v is membrane potential; w is a variable representing the recovery of the neuron’s ion channels after they have been stimulated; a, b, g are parameters with 0 < a < 1, b > 0, g > 0; and c is a constant reflecting the strength of coupling between the neurons. If two neurons are coupled, they are capable of influencing each other’s activity by, for instance, transmitting electrical pulses between their respective synapses. Most of these variables aren’t important for the discussion that lies ahead; the only one that’s worth paying attention to is c, the coupling constant.

In this example, we have three neurons labeled by the indices {1, 2, 3}. As indicated at the end of each voltage equation, neuron 1 is coupled to neuron 2; neuron 2 is coupled to neuron 3; and neuron 3 is coupled to neuron 1. We can view each coupling as a permutation g, such that g(1) = 2, g(2) = 3, and g(3) = 1. (Therefore, the set {1, 2, 3} permutes to {2, 3, 1}.) The permutation is depicted graphically in the figure below:

Screen Shot 2019-07-31 at 3.32.37 PM

Fig 1. Coupling (permutations) between the three neurons modeled in Eq. 1.

We know that the network possesses a symmetry group because the number of arrows between neuron c and d is the same as that between g(c) and g(d); neurons 1 and 2 are connected by one arrow, as are neurons g(1) and g(2) (which correspond to neurons 2 and 3, respectively). In particular, the symmetry group for this network is known as the cyclic group Z3. If we choose our subgroup S to be identical to the symmetry group [5], then the orbits of S will form the set {2, 3, 1}, since this corresponds to the permutations of the neurons {1, 2, 3}. The orbits, then, contain all of the neurons, so all three neurons will be synchronized with one another.

——– end of technical section ——–


Next steps in my research

My goal, as I described earlier in the blogpost, is to explain how our primary memory is bound to our direct experience of the present. I also established (1) that phenomenal binding must be ontologically unitary and (2) that binding must take place between synchronous neuronal outputs that correspond to the content we perceive in a moment of experience. (Recall that (2) is a necessary, but insufficient, condition for binding.) So far, I have discussed a mathematical theory that demonstrates how synchrony emerges from symmetry, which is ontologically unitary. I have also presented evidence that the neuronal oscillations that encode very short-term memory are synchronized with those that encode our immediate, sensory perception of the present. I have not yet shown that the interactions between these oscillations constitute a symmetry group; hopefully, my research in the coming weeks will fill this gap, though I am not confident that I have a sufficient mathematical background to explore this issue in depth.

The coupled cell systems formalism faces some rather severe limitations. In particular, there are some big-picture, philosophical concerns: if neuronal oscillations are actually ontologically unitary, and not functionally unitary, then they must truly be one and the same in “basement reality.” They cannot merely form a unit in an idealized mathematical model that over-fits a real phenomenon. As Andrés Gomez Emilsson of the Qualia Research Institute has said to me, we have to find the ground-truth mathematical structure that comprises the ontological unity of neuronal oscillations. Right now, there is little reason to think that the coupled cell systems formalism is the ground truth. Furthermore, it is unclear whether the symmetries between neurons actually yield ontological unity. The unity produced by the symmetries between fundamental particles may not “scale up” to the level of neurons, which are many orders of magnitude larger and are governed by completely different forces and dynamics.

There are technical objections as well. Firstly, cyclic groups are undoubtedly a far too simplistic model for the actual coupling that takes place between neurons. Due to the vast number of interconnections between neurons, it’s very unlikely that the coupling interactions between neurons form a neat, closed loop, as they do in Figure 1. Secondly, neuronal oscillations are often generated by tens of thousands of neurons that are activated in tandem, and it must become exceedingly difficult to identify the relevant symmetry group when so many neurons are involved. Thirdly, the system of differential equations in (1) describes only one kind of neuronal activity, and the large-scale networks that govern memory and sensory perception probably include neurons that exhibit very different dynamics.


[1] This argument should be credited to Andrés Gomez Emilsson, founder of the Qualia Research Institute, where I interned this summer.

[2] It is worth noting that most neuroscientists do not really address the experience of succession in their research. While many seek to find the neural correlates of memory, they do not explicitly aim to explain how our memory of the immediate past is contained within our present moment of experience.

[3] A relaxation oscillator is a neuron that undergoes a trajectory in the phase space defined by its voltage and the recovery action of its ion channels, before subsequently relaxing back to its rest values.

[4] I’ve asked Ian Stewart, the author of the formalism, to check for any errors, and I’m waiting to hear back from him.

[5] Note that the subgroup does not have to be a “strict subset” of the symmetry group, so the two can be equal to each other.


One thought on “A Very Preliminary Theory of Time and Consciousness, Part III

  1. Great stuff Kenneth!!
    May I just make a couple of comments?
    1) Temporal experience, the Hard Problem and the binding problem are closely linked. Solving one will probably involve solving all three. In recent years, the intrinsic nature argument has gained a modest academic currency (cf. Tommy Aahlberg’s nice 2019 review: https://digitalrepository.trincoll.edu/cgi/viewcontent.cgi?article=1078&context=trinitypapers). According to the intrinsic nature argument for constitutive panpsychism / non-materialist physicalism, our subjective experience discloses the essence of the physical. The mathematical formalism of physics describes fields of sentience rather than insentience. The biggest technical challenge for constitutive panpsychism / non-materialist physicalism is often reckoned the binding problem. Until his recent conversion, Phil Goff used to argue the binding problem was fatal (“Why Panpsychism doesn’t Help Us Explain Consciousness” – https://www.jstor.org/stable/24706312?seq=1#page_scan_tab_contents).

    I won’t argue (here) whether constitutive panpsychism / non-materialist physicalism is credible. Instead, just consider what the conjecture entails. Intuitively, yes, the fleeting neuronal macro-superpositions mandated by unitary-only QM are irrelevant to the phenomenally-bound world-simulations run by minds. But as far as I can tell, this dismissal is _not_ an option if experience discloses the intrinsic nature of the physical. If the intrinsic nature argument is sound, then all fundamental physical states, regardless how large, small or short-lived – micro or macro – are experiential. If any individual physical state is _non_ experiential, then the intrinsic nature argument fails. Superpositions are individual states, not classical aggregates – that’s what makes “cat states” so weird. Thus the quantum-theoretic version of intrinsic nature argument isn’t about – or refuted by calculation of – “dynamical timescales”. Whether we invoke effective decoherence times in the CNS of picoseconds, femtoseconds or attoseconds, the non-classical interference signature should disclose – or fail to disclose! – a perfect structural match. Zurek’s “quantum Darwinism” (cf. https://www.quantamagazine.org/quantum-darwinism-an-idea-to-explain-objective-reality-passes-first-tests-20190722/) must be applied not just outside but inside the skull:

    2) True or false, a “Schrödinger’s neurons” conjecture is not metaphysical. Most likely, I guess, is it’s demonstrably false! The conjecture that what crude neuroscanning suggests is binding by synchrony (how?) is really binding by superposition should be empirically refutable by interferometry. Moreover, phenomenal binding not something subtle and obscure like e.g. the Lucas-Penrose argument regarding Gödel’s theorem. Phenomenal binding – both local and global – is about as fundamental to our experience as it gets. So the conjecture should really be easy to falsify empirically. I just haven’t been smart enough to think how an “easy” experimental refutation would work. The only protocol I can think of is fiendishly hard to implement.

    Anyhow, sorry to sound like an advocate – or worse, a crank with an axe to grind. But otherwise, most researchers who stumble across the idea won’t turn their heads to devising a clean, elegant, practical experimental falsification. Instead, they’ll just balk at the timescales involved – and move on.


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