The Optical Limits of Theoretical Constructs


A camera has three essential components: the aperture at the front, a lens in the middle, and a film at the back. When you take a photograph, the aperture opens briefly letting light rays pass through the lens and onto the film inscribing an image. One can modulate the focus by adjusting the distance between the three components. The apparatus imposes limits on how far and how close one can focus. Beyond these limits the image gets severely distorted.

Something very similar is going on with theoretical constructs. Facts live in the wild in the extant world. One cannot directly commune with reality. Our knowledge of the world out there depends critically on our interpretation of sensory and empirical data. This intermediate step cannot be superseded. One can pretend otherwise, but implicit premises and theoretical constructs are absolutely necessary in order to make sense of external reality. To believe otherwise is to fall for the fallacy of pure empiricism.

To take the optical analogy further, our conceptual apparatus serves as the lens. Different lenses – conceptual frameworks – allow us to focus on different aspects of reality. Moreover, each lens blots out large parts of external reality which become out of focus and inaccessible. To comprehend different aspects of reality – which are, so to speak, superimposed on each other – we must be willing to use different lenses.

It is incumbent upon the careful thinker to examine each lens to judge its suitability and usefulness to comprehend extant phenomena. If one does this often enough and carefully enough across a broad spectrum of phenomena, a stark fact emerges. Namely, every theoretical or conceptual construct, no matter how carefully or precisely defined, disappears when examined under a fine enough resolution. This is a stunning observation. Ex ante, there is no reason for us to suspect this to be the case. It is quite insidious that all conceptual notions are inherently fuzzy.

Take the notion of a particle in physics. We have come a long way from the atomic theory of matter in which everything is composed of atoms with the familiar imagery of billiard balls. These atoms turned out to be fairly complex internally, themselves composed of subatomic particles, with substantial internal degrees of freedom. Subsequent examination of subatomic particles yielded more constituent parts raising the spectre of turtles all the way down. Fortunately, the Heisenberg Uncertainty Principle places firm limits on our resolution. Nature limits this resolution at the Planck length. At this finest resolution, however, the notion of a particle disintegrates completely. There is no difference between energy and matter at this resolution.

As one moves up the hierarchy the fragility of theoretical constructs becomes ever more manifest. Consider the notion of a species. Biologists love their elegant classification system but the notion of the species is inherently fuzzy at the boundary. It is unclear when to regard a mutation as heralding the arrival of a new species. Species which are genetically close, may or may not be able to procreate.

Even everyday notions like the difference between a baby and a pregnancy is incorrigibly fuzzy. We can agree at an egg that has just been fertilized with a sperm is most certainly not a baby, and a minute before childbirth, it is certainly a baby (a human being if you will). However, there is no specific point in time (say 8 months, 3 days, 4 hours, 17 min, and ten seconds after conception) where we can say it is now a baby.

This generalized uncertainty principle extends way beyond. Think of the notion of a state. What we regard as a unity turns out upon closer examination to be a collection of competing institutions. Take the Pakistani state. Suppose the elected government has a certain policy regarding the Taliban, and the ISI has a different, contradictory, policy in play. What is the policy of the Pakistani state vis-à-vis the Taliban?

Nations, nation-states, national economies, world-economies, capital, labor, wages, profits, everything is inherently and necessarily fuzzy at the margins. Hell, if I keep chopping off an inch of wood from this table that I am writing on, how long can we keep calling it a table?

The most devastating application of this generalized uncertainty principle is the realization that there is no such absolute unity as the self. Suppose we start replacing the organs of your body one by one. You can hold the position that it is still you even if the only original thing that is left is your brain. Fine, what if we start altering your brain? At what point after we replace your personality, your memories, your acquired skills, your language does it stop being you?

At this point you may withdraw into your stream of consciousness and say hey, as long as I possess this continuous stream, it is still me. Well, after we have removed every other thought, memory, and bit of information from your brain you are left with a mental construct with no physical counterpart whatsoever. Moreover, one which is defined with respect to a time dimension: it is the continuous stream of awareness that you identify as yourself. But there is nothing to stop us from erasing the memory of this stream of consciousness as well now, is there? 

Thus reborn into a darkness with no sensory data, no memory, and no continuous stream of consciousness in what sense is this empty figment of a mental state you? Identity is, in fact, constructed from external reality. The strong sense in which you know who you are is due to the thickness of accumulated data, perceptions, and memories that you have gathered trapped in your mind and body all these years since you came online. A newborn has no notion of a self.

Thinking about all this led me to rethink an old problem. There is a great debate among philosophers over determinism and free will. The non-compatabilists believe that a deterministic universe is inconsistent with free will and that our feeling that we have free will is an illusion. The compatabilist position is that determinism and free will are compatible. The question boils down to this: if we specify the position and momenta of all the particles of the universe then the laws of physics guarantee the (perhaps probabilistic) evolution of the universe till eternity. In what sense then can we speak of agents in such a universe as having free will?

I have been thinking about this for a very long time, speculating time and time again that emergent phenomena cannot be accounted for by lower-level dynamics. For instance, evolution, market equilibria, and so on and so forth, cannot be accounted for by physical laws and initial conditions. This holds, a fortiori, for higher order emergent phenomena like consciousness and free will. But there was always the fear that determinism at the physical level left no degrees of freedom for independent higher order dynamics.

The foregoing seem to suggest that these degrees of freedom cannot be eliminated, even theoretically. Namely, just like current physical theories, we will never find a physical theory that provides a complete description of extant physical reality. Like Gödel’s impossibility theorem which shows that formal axiomatic systems are necessarily incomplete, it seems likely that physical theory cannot – even in principle – capture all aspects of physical reality. This then leaves sufficient room for higher-order dynamics. If I am indeed right about this, then it is good news in an otherwise dismal world.

In the concluding chapter of The History of Western Philosophy, Bertrand Russell made a case for humility. Essentially saying that logical reasoning cannot actually accomplish all that much. Only some questions can be answered with any precision, if at all. The moral of this essay is in some sense the converse of Russell’s point. Namely, since we are necessarily peddling in conceptually uncertain notions, we should judge lenses by their usefulness and self-consistency, juggle multiple frames of analysis, and be agnostic when it comes to theorizing about the extant world.  

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