Recent content by Marcaias

Ahh, thank you.

Whoa, a theorem in what? Gödel showed it is not a theorem in ZF, and neither is its negation (assuming ZF is consistent, of course.)

From Wikipedia:

First of all, a Hilbert space by definition must have an inner product defined on it. (A Hilbert space is a vector space over the real or complex numbers with a complete inner product.) Secondly, in a finite-dimensional space, if you fix any positive-definite matrix M, then the expression...

"Q=2 3 4 1 5" means that this mapping happens: \begin{tabular}{ | c | c | c | c | c | } \hline 1 & 2 & 3 & 4 & 5 \\ \Downarrow & \Downarrow & \Downarrow & \Downarrow & \Downarrow \\ 2 & 3 & 4 & 1 & 5 \\ \hline \end{tabular} In other words: 1 gets mapped to 2, 2...

It's not that there's an axiom in ZF explicitly preventing Russell's Paradox, but rather ZF *doesn't* include the axiom of comprehension, which is the cause of all the trouble. Instead, it only allows for sets to be "built from" other sets, by union, by image under a function, by power set, and...

If you intend your interpretation to be predictive in the slightest, you still need to apply the usual probabilistic Rules of Quantum Mechanics at some point or you end up simply engaging in philosophical onanism. And the fact will remain that what you call Nature probabilistically choosing a...

If any of the people who told you "the tree doesn't even exist if we aren't around to observe it" are physicists, please smack them for me. :) To expand on what I meant... In quantum computing, it's called the "principle of deferred measurement." I believe it to be the fundamental paradox in...

Of course not! However, the behaviour of the system is exactly the same as if all the "observations" made by the tree, the grass, the wildlife, and so on were instead made by you when you stumbled into the forest a year later.

You're not my dad. Nonetheless, done.

So, I dug up some literature. Some good: Rats love it: So do strippers: And computer programmers: And it does seem to relieve some types of chronic pain: Surprise, though, it's not a cure-all: Dogs also seemed unimpressed: So, the websites selling this stuff...

You have a Master's of Art degree in Physics.

Wouldn't this correspond (roughly) to the Heisenberg picture of QM: fixed states with evolving positions and momenta?

A group's operation is associative by definition. If you take out the associativity axiom, you get what's (apparently) called a loop. If you also remove the need for an identity, you get a quasigroup. This page on Wikipedia has a nice little table of what you call groups minus this or that...

By the way, you don't even need the hermitian property. The same argument works for any diagonalizable matrix A.