Maps and the territory

I used to struggle, especially in youth, with several scientific concepts that were presented as eerily problematic. Is the axiom of choice the right assumption? What happens when we observe a Schrödinger's cat? Is the spooky action at distance really there? It felt natural to question the theories when they lead to so much confusion.

With age, however, I came to realization that I was barking up the wrong tree. It is not that the theories are problematic, they are all working extremely well, as the advancements of technology and science demonstrate time after time. We have very successful models of reality. The problem is that we often talk about them as if they actually were the reality and we end up saying so preposterous things that inexperienced people end up thinking it all is more confusing than it needs to be.

Yes, we all know that a map is not the territory, that each map tells its own story. And yet...

For all we know, infinities may or may not exist. Any observation we can make, any check we can perform, is necessarily limited, and is always going to be finite. If anything is truly endless, we would not be able to tell, and therefore it is unfalsifiable, and thus, I dare to say, not really scientific. I am all for acting as if there is no infinity in nature. But even if real numbers are in such sense not real, they are a powerful tool that allows to talk about patterns occurring at different scales. It does not mean that all the scales from infinitesimal to infinitely large do exist, but mathematical abstraction allows us to talk about the ones that do, all at once.

A map that we already have may become applicable to new areas, if they exhibit similar patterns. A real number can represent a distance, but also a translation by such distance. If we consider mixing translations with rotations of a plane, it naturally leads to treating them as complex numbers. This does not mean that we suddenly need to consider existence of imaginary distances, that would be a misuse of a map intended for a different place (a "category error" as some like to call it). If complex numbers turn out to describe an existing phenomenon, like a phase of a wave, it does not entail that we suddenly have to count an imaginary number of ducks. Accepting complex numbers as not less real than real numbers should not be mind-bending. And yet...

The words are abstractions, and we are mostly aware of their limitations. "Is the stain on the seat a part of the chair or not?" is not really a useful question in general and we mostly know better than to dwell on such issues. Yet we still expect a quantum particle to be a well-defined object at all times!? The collapse of wavefunction in quantum mechanics is problematic, because it appears as a radical, instantaneous change at the time of observation. But if we remember that things like particles are just models, a map of reality, then a rapid change in this map becomes much less baffling. John S. Bell writing about effects faster than light pointed out that "when the Queen dies in London (...) the Prince of Wales, lecturing on modern architecture in Australia, becomes instantaneously King". His example has been criticized as misleading when applied to quantum entanglement, since it demonstrates an update of description but not causal influence. But the more I learn, the more I become convinced that such criticism is yet another instance of mistaking a map for the territory. Once we know the result of observation, we can tell the story of what happened in terms of particles. But whatever was really there, it could be described by different stories, and we've chosen one that fits the known outcome, and the outcome itself is yet another such story, and it is all a simplification of emergent phenomena in the underlying fields (or whatever it is down there). We may have been forced to choose a specific description (by requiring one in the first place), but it does not affect the underlying reality, there is no causality in such "collapse".

Have you ever wondered why quantum entanglement seems to imply faster-than-light influence, but at the same time it does not allow to send any information that way? It may seem like a mysterious conspiracy if you treat the model as reality, because the model truly changes instantaneously everywhere, just like in Bell's example. But I argue that the reality does not change, and whatever is down there, giving emergence to the structures that we can observe, cannot propagate faster than the known limit.

It is common knowledge that descriptions are imperfect, that we can tell wildly different accounts of the same event, that every one of us has their own model of the world, and no one has all the truth. And yet we still propagate myths that rely on assuming the opposite to portray the reality as whimsical. I consider it harmful, especially nowadays, when we produce more stories than ever. I want to stress that there is one common underlying reality, which is very strict and consistent. Reliable, even if harsh. Solipsism does not benefit anyone. After all, we may describe the same actions in very different ways, but we are all going to share their consequences.