Context is key to separability
While you are reading these words, you can see each of them as a separate object. How does this work? At a low level of processing, your visual system can identify the edges of the shapes on the page by detecting the areas of maximum contrast – here, between the black letters and the white background. Then, your visual system can track the shapes defined by these edges and recognize them as letters. Finally, the strings of letters separated by spaces on each side are identified as individual words.
Your brain also generates top-down predictions at each of these steps and compares incoming sensory data with these predictions. However, let’s focus on the bottom-up part of visual processing, such as identifying individual shapes on the page.
Consider the contrast between the black color of any letter and the white background. This contrast can be seen as a boundary, and our visual system is optimized to detect such boundaries. The background plays a critical role here – only with a light background can we identify the letters. Change the background to black, and the letters disappear.
Each word is also demarcated by boundaries, most often blank spaces and sometimes by a comma or a period. Boundaries also demarcate each sentence and each paragraph.
Any time we have an identifiable boundary, we can talk about having a rudimentary context, where a system within the boundary is embedded in and separated from a larger environment. The very persistence of this system depends on separability from its environment.
Let’s take this a step further. Imagine zooming in on this text so that one line of any letter occupies most of your screen. Will you see any letters? Next, imagine moving away from the screen by ten feet, such that you could only see a block of text in a paragraph. By zooming in or out, you can see that the words are only recognizable when you are located within a certain distance from the screen – your optimal “reading distance.”
Now imagine that you can look at the screen for a microsecond, which is much shorter than you need to visually perceive anything – you won’t see any words then. The appropriate temporal range is as important for perception as the optimal distance.
Therefore, if you replace the white background with black, zoom in or out too much, or change the temporal scale, all words disappear. This is context dependence.
The simple example above can be extended to nonverbal stimuli, other sensory domains, the meaning of words, and other areas. In all these cases, our ability to perceive individual objects is context-dependent. Not only that, but you and I are context-dependent systems overall, including our brains and minds.
Chris Fields and James Glazebrook show this principle to be fundamental and applicable to a wide range of systems, from electrons to black holes. They claim that separability of scales is context-dependent. More simply, “separability requires contextuality.”
Fields and Glazebrook have proven this principle within the framework they’ve built by combining quantum information theory and the Free Energy Principle (FEP). The FEP part implies that they describe systems that persist in time.
You may ask why quantum mechanics (QM) would have anything to do with you and me? You may have heard that QM only applies to micro systems, such as electrons, and you would not be alone in that. However, the majority view in contemporary physics suggests that QM does apply to macroscopic systems, and we do not observe quantum effects in larger objects because of quantum decoherence.
In fact, QM has been applied to systems much larger than us, such as black holes (e.g.,Hawking Radiation). You can go even larger than that – the entire universe is a closed system in physics, because it encompasses everything, therefore it has no “environment” to interact with and no boundaries. QM has certainly been applied to the universe: in fact, there is a wave function of the universe.
According to Chris Fields, any physical system is a quantum system. Chris also suggests that, at its core, quantum theory is about communication. He says that QM is about “agents that set up experiments, make measurements, and communicate results to other agents” - agents like you and me.
In Fields and Glazebrook’s framework, they define separability as the absence of quantum entanglement. When things lose separability, they become entangled with one another.
The term “scale” they use is specific. In physics, scales refer to distinct processes occurring across widely separated ranges of energy, time, or distance, which create a hierarchical organization of physical phenomena.
An example would be a separation of the atomic and nuclear scales. Atomic binding energies are approximately five to six orders of magnitude smaller than nuclear binding energies. Consequently, the motion of electrons can be treated separately from nuclear structures.
To be clear, Fields and Glazebrook do not claim that scales are impossible to separate. They state that there is a prerequisite for such separation: contextuality.
Context is also formally defined in their theory. Here, I will illustrate just one aspect of it – the commutation of measurements. In standard arithmetic, we assume the commutation of addition and multiplication, such that 2 + 3 and 3 + 2 are equal, as are 6 x 7 and 7 x 6. This is a decontextualized system.
In contrast, in Fields and Glazebrook’s theory, when contextuality is present, the quantum reference frames (QRFs) do not commute, so measuring M followed by N does not necessarily yield the same outcome as measuring N followed by M. This is hardly intuitive, so let’s spend more time on that.
Chris states: “The Kochen–Specker theorem basically tells us that the context in which we make a measurement always matters, and by altering the context one can alter the measurement outcome.”
Earlier, I illustrated this point by showing that our perception of the words on this page depends on our distance from the screen, the background color, and having enough time. Another example of context is a sequence of repeated measurements. Imagine perceiving two apples and then 3 oranges, vs. 3 oranges followed by 2 apples. Contextuality implies that these two sequences are not equal.
You may find this to be counterintuitive, as classical mathematics is deeply entrenched in our culture. However, systems with commutation are just one possible scenario. In non-Abelian mathematics, commutation is not assumed.
If we move from the abstract, universal, time-invariant mathematical concepts to living systems, then I would predict that a rat’s reaction to two portions of peanut butter followed by three pieces of bread would be noticeably different from her reaction to bread followed by peanut butter. The rat would be more motivated by the first scenario than the second.
We don’t even have to go far to see context-dependent calculations in life. Daniel Kahneman and Amos Tversky have shown that humans do not respond equally to a possibility of losing 100 dollars and to gaining 100 dollars – we are more averse to the former than motivated by the latter. Therefore, (-100 +100) does not equal zero for us. Why? Because our emotional systems provide context in which we make these calculations.
Let us look at contextuality from yet another angle, the FEP. We can see a roughly analogous process to what Chis calls a “measurement” in a FEP system interacting with its environment through an action-perception cycle. The FEP system compares its weighted top-down predictions with the weighted bottom-up sensory input. As a result of this comparison, the system may update its predictions or modify the environment via action. Then, after such an interaction, the FEP system, the environment, or both are no longer the same. It follows that the second measurement would likely be influenced by the first, because each measurement changes the properties of the system, its environment, or both.
To be even more specific, the stream of predictions made by the FEP system can be seen as creating the context in which the system evaluates the incoming data. Conversely, sensory data coming in, as some indication of the environment, contextualizes the system’s internal beliefs/predictions. In this process, the FEP system adapts to its environment. When the environment changes, we have a continuous dynamic adaptation to the new contexts. We have arrived at contextuality by another route – the FEP.
Therefore, we can state that Fields and Glazebrook’s point, “separability requires contextuality,” applies to the classical FEP systems. Here is a citation from Andy Clark’s book “The Experiencing Machine,” to illustrate this point further, now with respect to phenomenology.
“All this suggests is that we can never simply experience the way things really are or the true signal from the world. Indeed, if predictive processing is a good account of perception, it’s not even clear what this could mean. To perceive is to bring weighted predictions to bear on the incoming sensory signal. An experience arises as these twin elements meet.
That does not mean that we can never get things wrong, but it does mean that there is no single way of getting things right. To return to a metaphor used in Chapter 1, perception is more like painting than some kind of point and shoot photography. It’s an act of creation that draws upon our own needs and history. In this act of creation there can be no such thing as a perfect rendition of the raw, incoming signal. Instead, we bring ourselves, our past experience and our current projects to bear on incoming sensory signals.
Predictions, anticipating the future and permeated with the past, shape human experience in all its forms.”
This a nice account of contextuality in FEP.
So why am I spending so much time on separability and contextuality?
I have seen numerous theories and models built on the premise of scale separability, which is assumed to be rather obvious. To be fair, I helped create some of them, so I am not better than anyone else in this regard. An assumption of separability is justified when we deal with contextual systems. The point Fields and Glazebrook make: “separability requires contextuality” seems to be a fundamental principle, which should be considered in theory building and applied to a wide range of disciplines, including biology, neuroscience, and clinical psychology.
Moreover, I think we can consider extending the separation of scales to separability in general, for example, by separating a system N from its environment or separating various components of a system from one another. I think that we can apply Fields and Glazebrook’s principle to nearly any scenario where we draw a boundary.
Let me give you some examples. Anil Seth challenges a somewhat straight and narrow assumption that you can clearly separate the “wetware” of the brain (e.g., neurons, glia, etc.) from the “software” (e.g., mental phenomena). He claims that these two are tightly intertwined, and it is far from obvious that they can be clearly separated, as we routinely separate hardware and software in computers. The data he presents in support of his argument are compelling.
Wetware and software are not scales in the strict sense of physics, but the separability between them is widely assumed. Furthermore, Seth challenges theories of consciousness, mind, or intelligence based on “substrate independence”. The term “sub-strate” implies the separability of strata, which is an assumption. More importantly, the claim of independence of substrates suggests separability, for example, the circumstances where the same algorithm can run on different kinds of computers. A full substrate independence seems to be a rather strong claim for biological systems. It is useful to ask: what are the prerequisites for substrate independence?
Luiz Pessoa makes a point in his book “Entangled Brain” that our traditional models in neuroscience are based on an idea of the brain’s modularity. For example, modularity implies that there are clearly defined things called the “insula” and the “PFC,” and that these two things can interact to produce something together.
Well, where exactly is the boundary of the insula? When someone claims “your insula is doing XYZ” – what exactly does that mean? As Pessoa suggests, the processes mediated by the neuronal networks in the insula may participate in a function N only when the thalamus, PFC, and amygdala are operating in specific regimes, while the same network in the insula may be participating in a different function M when the thalamus and the PFC are in different regimes.
We encounter context-dependence again, which, along with transience and emergence, is a standard feature of nonlinear dynamical systems. The modular brain idea is based on linear systems that can be decomposed into parts without losing functionality.
In psychiatry, when we hear that “the effect size of SSRIs for depression is 0.3,” we hear a decontextualized statement. We can challenge this statement in many ways, for example, we can investigate the psychiatrist effect, where doctor Smith, who prescribes medication XYZ for depressed patients, is consistently reaching higher levels of symptom reduction than doctor Kline, who prescribes the same medication in the same dose for depressed patients.
Why? Because psychiatry is a human interaction with a component of placebo, which depends on the quality of the relationship between the doctor and the patient. Can you then clearly separate the effect of a pill itself from the doctor who prescribed it or from the patient who took it?
These are only a few examples in which separability was assumed too quickly, and the entire frameworks were built on this assumption.
Finally, we can ask a reasonable question: what about mathematics? Classical math is mostly decontextualized from the very foundation of Aristotle’s logic and all the way to topology. Consider, for example, the key concepts “true” and “false” used in math. They are universal and context independent, as are the constructs built on their foundation, such as “falsifiability.”
Knowing that math is mostly decontextualized, we should be careful about extrapolating mathematical methods to other fields, because their foundations differ significantly from the formal systems of standard mathematics. For example, considering branches of mathematics where contextuality is a standard feature, such as nonlinear dynamical systems, seems warranted when modeling nonlinear phenomena in psychology or biology.
To illustrate this point, Edward Frenkel suggests that the Pythagorean theorem works universally, for anyone, anywhere, at any time, within the framework of Euclid’s geometry, which assumes a perfectly flat plane. He suggests further that such a perfectly flat plane only exists as an abstraction – there are no perfectly flat planes in the physical world. A Euclidean formulation of the Pythagorean theorem he described is universal – decontextualized.
Now, take Euclid’s fifth axiom – that the parallel lines do not intersect. Is this statement true or false? On a perfect plane, it is true. On a sphere, it is not. We have a different geometry on a sphere – a Lobachevsky/Riemann geometry. So parallel lines intersect in one context and not in another.
Imagine now a very large spherical object like Earth. If you look at a standard sheet of paper, then parallel lines will certainly seem as if they would never intersect. However, if you extend them by four thousand miles up and down along the surface of the Earth, you will see that they do.
Incidentally, the Pythagorean theorem looks differently on the sphere; it is not identical to the one on the plane. We return to contextuality even with rather abstract concepts.
To be fair, it is premature to generalize Fields and Glazebrook’s theory (built on a specific set of axioms and definitions and applicable to a certain class of systems) onto an entirely different class of systems, such as abstract concepts in math. It is also a leap to go from separability of scales to separability in general.
With these caveats in mind, is it entirely accurate to say that something is purely “abstract” and “not physical” - is there any information in the world that is encoded, stored, and retrieved, that is “not physical” and does not require energy expenditure?
If we form a belief that there is such a thing as a perfectly flat plane, this belief does not occur in a vacuum; it occurs in a system capable of forming counterfactuals. Examples of such systems can be you, me, and a broader human collective intelligence mediated by language and culture. The belief is embedded in these systems. These systems use energy. Can a belief be separable from the system that it is embedded in? I don’t think so; it would lose all meaning. The extraction of meaning from a belief is an active process that occurs within the system that holds it.
Are the words written on paper or a computer screen non-physical? Is it not an underlying assumption that purely abstract/non-physical systems exist and are clearly detached from the physical systems?
While I cannot formally prove it, I propose that if we delve deeper into the separability of abstract constructs created by our brain-minds, we would likely find contextuality to be necessary there as well.
To summarize, no system can be separable from its environment without a context. On a practical note, it is useful to remember that you and I are contextual systems.
Acknowlegement: I appreciate Chris Field’s help in reviewing the draft of this text.