Hypnagogic insight: the uncertainty principle is natures way of dealing with infinity. Without it there would be, at any given time, either an infinite number of particles, or some particular finite number of them.

It seems absurd to think that there is a particular number of particles — that number would of course be very large — eg 10^80 — but it would be a function of a number that would be a fundamental constant of the universe.

Another view: observers are what map mathematical constructs onto the real world. Mathematical constructs don’t have uncertainty (I don’t think [1]) — a set either has cardinality 3, or it doesn’t — but an observation always has uncertainty, because memory always has uncertainty.

Memory always has uncertainty. Perhaps it would be better to say that "human memory always has uncertainty". I think we can take that as true. But if we defined some abstract model of memory as a process, it might be the case that uncertainty would be an unavoidable characteristic. It’s at least a fundamental characteristic of any memory that is not complete, because there are multiple real events that could lead to the same memory.

Define memory as follows: An "experience" is an observer observing an event occuring in real time. A "trace" is an enduring feature of the real world. A "memory" is a set of traces from which a representation of some past experience can be constructed by an observer. The traces exist quiescent unless the reconstruction process is active. The nature of the reconstruction is also an experience. A perfect memory would be a where the experience that is reconstructed memory is identical to the original experience. That is, all the information in the original experience would be recorded in the traces. This might indeed be true, for example, in the case of computer memories.

And, while it might be true in some particular human memories (exercise: what kind of memories would these be?), in general experience tells us that it isn’t.

[1] Mathematical models with uncertainty. At some level they clearly exist — the uncertainty principle itself is part of a mathematical model — but what I mean is that the mathematics itself used to create that model doesn’t have its own uncertainty principle. Alas, I fear that these are just words thrown together in a superficially meaningful way…​