question about uncertainty

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I was reading about Heisenberg, Gödel and Poincare's discoveries regarding uncertainty. Everyone says they are very complicated (hence no previous mathematician discovered them). While the formal proofs and examples are no doubt complicated, I can't help thinking that the concepts are very simple and easy to understand. As I see it:

Heisenberg = variables.
As Pythagoras pointed out, the universe is made of math. A lot of it is variables. These are fundamentally unknown until some other variable (such as us looking in the box) limits the possible answers down to just one.

Poincare = complexity.
Some problems are so complicated that solving them would either take unfeasibly long or require unfeasible quantities of initial data, or usually both.

Gödel = axioms
Any mathematical system is based on axioms that are, of course, unproven. Hence the system itself will contain statements that,. while true, cannot be proven.

Have I got these completely wrong?

Sounds roughly right to me. The significant thing that these guys did, of course, was to prove their theorems, That takes more than saying "It's obvious".

Details, details

Seriously though, yes, it is amazingly hard to prove even the simplest "intuitive fact" so hats off to them. It is only by these geniuses defining exactly what we mean and showing the subtleties that help us avoid easy errors that they enable mankind to take the next intellectual steps.

Thanks for the reply.

Somewhat. The cosmos is made of matter and energy, not mathematical theorems. Theorems only exist in our heads. Not Out There.

ruveyn

Perhaps. But I find the computational universe argument to be compelling.

I am not sure what Heisenberg specifically proved, but I know that the Heisenberg Uncertainty Principle is this:

Take an electron. Try to measure its momentum and position with photons.
Higher frequency photons make more uncertainty in the momentum of the electron.
Lower frequency photons make more uncertainty in the position of the electron.
So, the certainty of one quality must be sacrificed in order to gain certainty in another.
This is true of all measurements involving reflections of particles off of a larger particle. In cases where the size of the small particle is much, much less than the larger particle, the uncertainty produced in one area by increasing the certainty in another becomes insignificant.

Since most of human experiences involve the situation where the uncertainty produced is insignificant (basically, anything above atomic scales), I'd say that the HUPrinciple is completely NON-intuitive. Most people confuse it with the Observer Effect, or think it has something to do with misinterpretation/mis-measurement of variables. In fact, it's more to do with correctly measuring variables with (relatively) imprecise techniques that only get precise when they start to fck up another dimension of measurement.

You also mentioned something about the determination of variables (unknowns) via the use of knowns, and a cat. I think you were referencing Schrodinger's Cat, which is a really cool thought experiment that brilliantly illustrates the tenets of Quantum Mechanics.

Also, technically, the cat isn't REALLY in a quantum superposition of alive and dead states. The fact that the atom that is supposed to decay, and thus kill the cat, is in a superposition... does not mean the cat is in that same superposition until humans observe it. When they cat dies, it will go through physical, mechanical processes that interact with the box around it. This means that the dead cat will be observed by the surrounding box/reality, which means that it is not in any kind of macroscopic superposition (though its constituent subatomic particles might be). The thought experiment just illustrates that the tenets of quantum mechanics, especially when extended to directly affect macroscopic situations, are WEIRD and counter-intuitive.

As a slightly off-topic side note:
Photosynthesis abuses the heck out of some of the weirder quantum properties of electrons. When plants transport energy, they don't judge where to send electrons/don't send them randomly/don't have mechanisms that limit the travel of the electrons/don't have anything that attracts them or repels them well enough to produce the efficiency observed. This confused the scientific community for decades. Then some team at UC Berkeley figured out a really neat thing was going on at quantum mechanical scales in the process of photosynthesis. The process exhibits long-term, wavelike quantum electrical coherence. This means that the electrons can "feel out" every possible way in which they can get from point A to point B, and then decide which path is most efficient... INSTANTLY. They're everywhere they could possibly be in transit from point A (existing as the wavefunction). When they get to point B, the energetic value of the transmission shows that the electrons took the most efficient path. Before the wavelike coherence was discovered, the efficiency looked like black magic. I cannot wait for someone to figure out how to mimic this behavior!

Fascinating stuff. Thanks.

Uncertainty simply states that making a measurement is an additional variable that may affect the behavior you are measuring.

Ie you can know precisely where something is or presicisely how fast it is moving. But not both at once